LMFDB - Embedded newform 69.7.f.a.7.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,7,Mod(7,69)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 19]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("69.7");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	69.f (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.8737317698$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			7.11
Character	$\chi$	$=$	69.7
Dual form			69.7.f.a.10.11

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.826670 + 0.954028i) q^{2} +(-13.1138 + 8.42776i) q^{3} +(8.88136 + 61.7712i) q^{4} +(46.0457 - 21.0284i) q^{5} +(2.80051 - 19.4779i) q^{6} +(134.637 + 458.531i) q^{7} +(-134.239 - 86.2703i) q^{8} +(100.946 - 221.041i) q^{9} +O(q^{10})$	\(q+(-0.826670 + 0.954028i) q^{2} +(-13.1138 + 8.42776i) q^{3} +(8.88136 + 61.7712i) q^{4} +(46.0457 - 21.0284i) q^{5} +(2.80051 - 19.4779i) q^{6} +(134.637 + 458.531i) q^{7} +(-134.239 - 86.2703i) q^{8} +(100.946 - 221.041i) q^{9} +(-18.0029 + 61.3124i) q^{10} +(-54.3885 + 47.1279i) q^{11} +(-637.062 - 735.208i) q^{12} +(3575.30 + 1049.80i) q^{13} +(-548.752 - 250.607i) q^{14} +(-426.614 + 663.824i) q^{15} +(-3638.95 + 1068.49i) q^{16} +(-6295.59 - 905.170i) q^{17} +(127.430 + 279.033i) q^{18} +(-1068.24 + 153.590i) q^{19} +(1707.90 + 2657.54i) q^{20} +(-5630.00 - 4878.42i) q^{21} -90.8474i q^{22} +(-10817.5 - 5569.38i) q^{23} +2487.46 q^{24} +(-8554.19 + 9872.06i) q^{25} +(-3957.13 + 2543.09i) q^{26} +(539.088 + 3749.44i) q^{27} +(-27128.3 + 12389.1i) q^{28} +(-3941.76 + 27415.6i) q^{29} +(-280.638 - 955.765i) q^{30} +(7044.95 + 4527.51i) q^{31} +(6231.27 - 13644.6i) q^{32} +(316.060 - 1076.40i) q^{33} +(6067.94 - 5257.90i) q^{34} +(15841.6 + 18282.2i) q^{35} +(14550.5 + 4272.41i) q^{36} +(-48971.7 - 22364.6i) q^{37} +(736.552 - 1146.10i) q^{38} +(-55733.4 + 16364.8i) q^{39} +(-7995.26 - 1149.54i) q^{40} +(-44988.4 - 98510.8i) q^{41} +(9308.30 - 1338.33i) q^{42} +(12442.6 + 19361.0i) q^{43} +(-3394.19 - 2941.09i) q^{44} -12300.7i q^{45} +(14255.8 - 5716.14i) q^{46} +111990. q^{47} +(38715.6 - 44680.2i) q^{48} +(-93151.4 + 59864.8i) q^{49} +(-2346.73 - 16321.9i) q^{50} +(90188.0 - 41187.5i) q^{51} +(-33094.1 + 230174. i) q^{52} +(37808.5 + 128764. i) q^{53} +(-4022.72 - 2585.24i) q^{54} +(-1513.33 + 3313.74i) q^{55} +(21484.1 - 73168.1i) q^{56} +(12714.3 - 11017.0i) q^{57} +(-22896.7 - 26424.2i) q^{58} +(150250. + 44117.5i) q^{59} +(-44794.2 - 20456.8i) q^{60} +(162180. - 252357. i) q^{61} +(-10143.2 + 2978.32i) q^{62} +(114945. + 16526.6i) q^{63} +(-92965.5 - 203566. i) q^{64} +(186703. - 26843.8i) q^{65} +(765.640 + 1191.36i) q^{66} +(134923. + 116911. i) q^{67} -396926. i q^{68} +(188796. - 18131.1i) q^{69} -30537.5 q^{70} +(64647.6 - 74607.3i) q^{71} +(-32620.1 + 20963.7i) q^{72} +(39282.1 + 273213. i) q^{73} +(61819.9 - 28232.2i) q^{74} +(28979.0 - 201553. i) q^{75} +(-18974.8 - 64622.4i) q^{76} +(-28932.3 - 18593.7i) q^{77} +(30460.6 - 66699.5i) q^{78} +(-227848. + 775981. i) q^{79} +(-145089. + 125721. i) q^{80} +(-38668.9 - 44626.3i) q^{81} +(131173. + 38515.7i) q^{82} +(488235. + 222969. i) q^{83} +(251344. - 391099. i) q^{84} +(-308919. + 90706.9i) q^{85} +(-28756.8 - 4134.61i) q^{86} +(-179360. - 392744. i) q^{87} +(11366.8 - 1634.30i) q^{88} +(-669175. - 1.04126e6i) q^{89} +(11735.2 + 10168.6i) q^{90} +1.78073e6i q^{91} +(247954. - 717673. i) q^{92} -130543. q^{93} +(-92578.8 + 106842. i) q^{94} +(-45958.1 + 29535.5i) q^{95} +(33277.3 + 231448. i) q^{96} +(-263340. + 120263. i) q^{97} +(19892.8 - 138357. i) q^{98} +(4926.89 + 16779.4i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9}+O(q^{10}) $ 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9} - 384 q^{13} + 33816 q^{16} + 22880 q^{17} + 4860 q^{18} - 31680 q^{19} - 157696 q^{20} + 36488 q^{23} + 39204 q^{24} + 200664 q^{25} + 99032 q^{26} - 202752 q^{28} - 181712 q^{29} - 128496 q^{31} + 439300 q^{32} - 400026 q^{34} + 368744 q^{35} + 42282 q^{36} + 446688 q^{37} + 550550 q^{38} - 52488 q^{39} - 156750 q^{40} - 606080 q^{41} - 1274130 q^{42} - 429000 q^{43} - 867482 q^{44} + 309288 q^{46} + 1111152 q^{47} + 837864 q^{48} + 722136 q^{49} + 1786926 q^{50} + 463320 q^{51} - 812550 q^{52} - 367840 q^{53} - 354294 q^{54} - 398088 q^{55} - 3696550 q^{56} - 1240272 q^{57} + 1903134 q^{58} + 545800 q^{59} + 2450250 q^{60} - 495264 q^{61} + 488776 q^{62} - 2699808 q^{64} - 290400 q^{67} + 23328 q^{69} - 392616 q^{70} + 255392 q^{71} + 228420 q^{72} + 1346880 q^{73} - 5387470 q^{74} + 365472 q^{75} + 2123022 q^{76} + 6134240 q^{77} + 171072 q^{78} + 4025472 q^{79} + 10626462 q^{80} - 1417176 q^{81} + 2025492 q^{82} - 2474560 q^{83} - 8866152 q^{85} - 15634300 q^{86} - 611712 q^{87} - 10636560 q^{88} - 5901720 q^{89} + 6566394 q^{92} - 2484432 q^{93} + 13931490 q^{94} + 8183072 q^{95} - 4682124 q^{96} + 12319560 q^{97} + 14139580 q^{98} + 2993760 q^{99}+O(q^{100}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9 - 384 * q^13 + 33816 * q^16 + 22880 * q^17 + 4860 * q^18 - 31680 * q^19 - 157696 * q^20 + 36488 * q^23 + 39204 * q^24 + 200664 * q^25 + 99032 * q^26 - 202752 * q^28 - 181712 * q^29 - 128496 * q^31 + 439300 * q^32 - 400026 * q^34 + 368744 * q^35 + 42282 * q^36 + 446688 * q^37 + 550550 * q^38 - 52488 * q^39 - 156750 * q^40 - 606080 * q^41 - 1274130 * q^42 - 429000 * q^43 - 867482 * q^44 + 309288 * q^46 + 1111152 * q^47 + 837864 * q^48 + 722136 * q^49 + 1786926 * q^50 + 463320 * q^51 - 812550 * q^52 - 367840 * q^53 - 354294 * q^54 - 398088 * q^55 - 3696550 * q^56 - 1240272 * q^57 + 1903134 * q^58 + 545800 * q^59 + 2450250 * q^60 - 495264 * q^61 + 488776 * q^62 - 2699808 * q^64 - 290400 * q^67 + 23328 * q^69 - 392616 * q^70 + 255392 * q^71 + 228420 * q^72 + 1346880 * q^73 - 5387470 * q^74 + 365472 * q^75 + 2123022 * q^76 + 6134240 * q^77 + 171072 * q^78 + 4025472 * q^79 + 10626462 * q^80 - 1417176 * q^81 + 2025492 * q^82 - 2474560 * q^83 - 8866152 * q^85 - 15634300 * q^86 - 611712 * q^87 - 10636560 * q^88 - 5901720 * q^89 + 6566394 * q^92 - 2484432 * q^93 + 13931490 * q^94 + 8183072 * q^95 - 4682124 * q^96 + 12319560 * q^97 + 14139580 * q^98 + 2993760 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{19}{22}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.826670	+	0.954028i	−0.103334	+	0.119253i	−0.805061	−	0.593193i	$-0.797867\pi$
$2$	−0.826670	+	0.954028i	−0.103334	+	0.119253i	0.701727	+	0.712446i	$0.252413\pi$
$3$	−13.1138	+	8.42776i	−0.485698	+	0.312139i
$3$	−13.1138	+	8.42776i	−0.485698	+	0.312139i
$4$	8.88136	+	61.7712i	0.138771	+	0.965176i
$5$	46.0457	−	21.0284i	0.368365	−	0.168227i	−0.222627	−	0.974904i	$-0.571463\pi$
$5$	46.0457	−	21.0284i	0.368365	−	0.168227i	0.590993	+	0.806677i	$0.298736\pi$
$6$	2.80051	−	19.4779i	0.0129653	−	0.0901757i
$7$	134.637	+	458.531i	0.392528	+	1.33683i	0.884632	+	0.466290i	$0.154410\pi$
$7$	134.637	+	458.531i	0.392528	+	1.33683i	−0.492104	+	0.870536i	$0.663772\pi$
$8$	−134.239	−	86.2703i	−0.262186	−	0.168497i
$9$	100.946	−	221.041i	0.138472	−	0.303211i
$10$	−18.0029	+	61.3124i	−0.0180029	+	0.0613124i
$11$	−54.3885	+	47.1279i	−0.0408629	+	0.0354079i	−0.675053	−	0.737769i	$-0.735879\pi$
$11$	−54.3885	+	47.1279i	−0.0408629	+	0.0354079i	0.634190	+	0.773177i	$0.281334\pi$
$12$	−637.062	−	735.208i	−0.368670	−	0.425468i
$13$	3575.30	+	1049.80i	1.62735	+	0.477835i	0.962982	−	0.269567i	$-0.0868804\pi$
$13$	3575.30	+	1049.80i	1.62735	+	0.477835i	0.664373	+	0.747401i	$0.268699\pi$
$14$	−548.752	−	250.607i	−0.199983	−	0.0913290i
$15$	−426.614	+	663.824i	−0.126404	+	0.196689i
$16$	−3638.95	+	1068.49i	−0.888416	+	0.260862i
$17$	−6295.59	−	905.170i	−1.28142	−	0.184240i	−0.532230	−	0.846600i	$-0.678646\pi$
$17$	−6295.59	−	905.170i	−1.28142	−	0.184240i	−0.749186	+	0.662360i	$0.769555\pi$
$18$	127.430	+	279.033i	0.0218501	+	0.0478451i
$19$	−1068.24	+	153.590i	−0.155743	+	0.0223924i	−0.219745	−	0.975557i	$-0.570523\pi$
$19$	−1068.24	+	153.590i	−0.155743	+	0.0223924i	0.0640024	+	0.997950i	$0.479613\pi$
$20$	1707.90	+	2657.54i	0.213487	+	0.332192i
$21$	−5630.00	−	4878.42i	−0.607926	−	0.526771i
$22$		−	90.8474i		−	0.00853187i
$23$	−10817.5	−	5569.38i	−0.889084	−	0.457745i
$23$	−10817.5	−	5569.38i	−0.889084	−	0.457745i
$24$	2487.46			0.179938
$25$	−8554.19	+	9872.06i	−0.547468	+	0.631812i
$26$	−3957.13	+	2543.09i	−0.225144	+	0.144691i
$27$	539.088	+	3749.44i	0.0273885	+	0.190491i
$28$	−27128.3	+	12389.1i	−1.23580	+	0.564371i
$29$	−3941.76	+	27415.6i	−0.161621	+	1.12410i	0.733959	+	0.679194i	$0.237671\pi$
$29$	−3941.76	+	27415.6i	−0.161621	+	1.12410i	−0.895579	+	0.444902i	$0.853239\pi$
$30$	−280.638	−	955.765i	−0.0103940	−	0.0353987i
$31$	7044.95	+	4527.51i	0.236479	+	0.151976i	0.653514	−	0.756915i	$-0.273294\pi$
$31$	7044.95	+	4527.51i	0.236479	+	0.151976i	−0.417034	+	0.908891i	$0.636931\pi$
$32$	6231.27	−	13644.6i	0.190163	−	0.416399i
$33$	316.060	−	1076.40i	0.00879483	−	0.0299524i
$34$	6067.94	−	5257.90i	0.154385	−	0.133775i
$35$	15841.6	+	18282.2i	0.369484	+	0.426407i
$36$	14550.5	+	4272.41i	0.311867	+	0.0915725i
$37$	−48971.7	−	22364.6i	−0.966807	−	0.441526i	−0.131504	−	0.991316i	$-0.541981\pi$
$37$	−48971.7	−	22364.6i	−0.966807	−	0.441526i	−0.835303	+	0.549790i	$0.814708\pi$
$38$	736.552	−	1146.10i	0.0134231	−	0.0208868i
$39$	−55733.4	+	16364.8i	−0.939554	+	0.275878i
$40$	−7995.26	−	1149.54i	−0.124926	−	0.0179616i
$41$	−44988.4	−	98510.8i	−0.652752	−	1.42933i	−0.889124	−	0.457666i	$-0.848686\pi$
$41$	−44988.4	−	98510.8i	−0.652752	−	1.42933i	0.236372	−	0.971663i	$-0.424042\pi$
$42$	9308.30	−	1338.33i	0.125638	−	0.0180641i
$43$	12442.6	+	19361.0i	0.156496	+	0.243513i	0.910644	−	0.413192i	$-0.135586\pi$
$43$	12442.6	+	19361.0i	0.156496	+	0.243513i	−0.754148	+	0.656705i	$0.771950\pi$
$44$	−3394.19	−	2941.09i	−0.0398454	−	0.0345263i
$45$		−	12300.7i		−	0.134987i
$46$	14255.8	−	5716.14i	0.146460	−	0.0587258i
$47$	111990.			1.07866			0.539331	−	0.842094i	$-0.318677\pi$
$47$	111990.			1.07866			0.539331	+	0.842094i	$0.318677\pi$
$48$	38715.6	−	44680.2i	0.350076	−	0.404010i
$49$	−93151.4	+	59864.8i	−0.791774	+	0.508842i
$50$	−2346.73	−	16321.9i	−0.0187738	−	0.130575i
$51$	90188.0	−	41187.5i	0.679889	−	0.310495i
$52$	−33094.1	+	230174.i	−0.235364	+	1.63699i
$53$	37808.5	+	128764.i	0.253958	+	0.864901i	0.983491	+	0.180956i	$0.0579191\pi$
$53$	37808.5	+	128764.i	0.253958	+	0.864901i	−0.729533	+	0.683945i	$0.760263\pi$
$54$	−4022.72	−	2585.24i	−0.0255469	−	0.0164180i
$55$	−1513.33	+	3313.74i	−0.00909592	+	0.0199173i
$56$	21484.1	−	73168.1i	0.122336	−	0.416637i
$57$	12714.3	−	11017.0i	0.0686544	−	0.0594893i
$58$	−22896.7	−	26424.2i	−0.117351	−	0.135431i
$59$	150250.	+	44117.5i	0.731576	+	0.214810i	0.626244	−	0.779627i	$-0.284591\pi$
$59$	150250.	+	44117.5i	0.731576	+	0.214810i	0.105332	+	0.994437i	$0.466410\pi$
$60$	−44794.2	−	20456.8i	−0.207380	−	0.0947075i
$61$	162180.	−	252357.i	0.714508	−	1.11180i	−0.274161	−	0.961684i	$-0.588400\pi$
$61$	162180.	−	252357.i	0.714508	−	1.11180i	0.988669	−	0.150113i	$-0.0479636\pi$
$62$	−10143.2	+	2978.32i	−0.0425599	+	0.0124967i
$63$	114945.	+	16526.6i	0.459694	+	0.0660940i
$64$	−92965.5	−	203566.i	−0.354635	−	0.776543i
$65$	186703.	−	26843.8i	0.679846	−	0.0977471i
$66$	765.640	+	1191.36i	0.00266313	+	0.00414391i
$67$	134923.	+	116911.i	0.448601	+	0.388715i	0.849655	−	0.527340i	$-0.176810\pi$
$67$	134923.	+	116911.i	0.448601	+	0.388715i	−0.401054	+	0.916055i	$0.631356\pi$
$68$		−	396926.i		−	1.26236i
$69$	188796.	−	18131.1i	0.574706	−	0.0551921i
$70$	−30537.5			−0.0890307
$71$	64647.6	−	74607.3i	0.180625	−	0.208452i	−0.658216	−	0.752829i	$-0.728689\pi$
$71$	64647.6	−	74607.3i	0.180625	−	0.208452i	0.838841	+	0.544377i	$0.183234\pi$
$72$	−32620.1	+	20963.7i	−0.0873953	+	0.0561655i
$73$	39282.1	+	273213.i	0.100978	+	0.702316i	0.975926	+	0.218100i	$0.0699859\pi$
$73$	39282.1	+	273213.i	0.100978	+	0.702316i	−0.874949	+	0.484216i	$0.839105\pi$
$74$	61819.9	−	28232.2i	0.152557	−	0.0696706i
$75$	28979.0	−	201553.i	0.0686909	−	0.477756i
$76$	−18974.8	−	64622.4i	−0.0432252	−	0.147212i
$77$	−28932.3	−	18593.7i	−0.0633740	−	0.0407280i
$78$	30460.6	−	66699.5i	0.0641882	−	0.140553i
$79$	−227848.	+	775981.i	−0.462131	+	1.57387i	0.317895	+	0.948126i	$0.397024\pi$
$79$	−227848.	+	775981.i	−0.462131	+	1.57387i	−0.780026	+	0.625747i	$0.784794\pi$
$80$	−145089.	+	125721.i	−0.283378	+	0.245548i
$81$	−38668.9	−	44626.3i	−0.0727623	−	0.0839722i
$82$	131173.	+	38515.7i	0.237904	+	0.0698548i
$83$	488235.	+	222969.i	0.853875	+	0.389952i	0.793754	−	0.608240i	$-0.208124\pi$
$83$	488235.	+	222969.i	0.853875	+	0.389952i	0.0601213	+	0.998191i	$0.480851\pi$
$84$	251344.	−	391099.i	0.424064	−	0.659856i
$85$	−308919.	+	90706.9i	−0.503023	+	0.147701i
$86$	−28756.8	−	4134.61i	−0.0452112	−	0.00650039i
$87$	−179360.	−	392744.i	−0.272375	−	0.596419i
$88$	11366.8	−	1634.30i	0.0166798	−	0.00239819i
$89$	−669175.	−	1.04126e6i	−0.949226	−	1.47702i	−0.877487	−	0.479600i	$-0.840782\pi$
$89$	−669175.	−	1.04126e6i	−0.949226	−	1.47702i	−0.0717385	−	0.997423i	$-0.522855\pi$
$90$	11735.2	+	10168.6i	0.0160977	+	0.0139487i
$91$			1.78073e6i			2.36305i
$92$	247954.	−	717673.i	0.318425	−	0.921644i
$93$	−130543.			−0.162295
$94$	−92578.8	+	106842.i	−0.111462	+	0.128634i
$95$	−45958.1	+	29535.5i	−0.0536032	+	0.0344487i
$96$	33277.3	+	231448.i	0.0376126	+	0.261602i
$97$	−263340.	+	120263.i	−0.288537	+	0.131771i	−0.554426	−	0.832233i	$-0.687062\pi$
$97$	−263340.	+	120263.i	−0.288537	+	0.131771i	0.265888	+	0.964004i	$0.414335\pi$
$98$	19892.8	−	138357.i	0.0211357	−	0.147002i
$99$	4926.89	+	16779.4i	0.00507770	+	0.0172931i
$100$	−685782.	−	440725.i	−0.685782	−	0.440725i
$101$	−622493.	+	1.36307e6i	−0.604186	+	1.32298i	0.322295	+	0.946639i	$0.395546\pi$
$101$	−622493.	+	1.36307e6i	−0.604186	+	1.32298i	−0.926480	+	0.376343i	$0.877181\pi$
$102$	−35261.7	+	120090.i	−0.0332279	+	0.113164i
$103$	−373114.	+	323305.i	−0.341452	+	0.295870i	−0.808658	−	0.588278i	$-0.799806\pi$
$103$	−373114.	+	323305.i	−0.341452	+	0.295870i	0.467207	+	0.884148i	$0.345260\pi$
$104$	−389378.	−	449367.i	−0.346156	−	0.399485i
$105$	−361822.	−	106241.i	−0.312556	−	0.0917747i
$106$	−154099.	−	70374.8i	−0.129385	−	0.0590881i
$107$	−331077.	+	515165.i	−0.270257	+	0.420528i	−0.949682	−	0.313217i	$-0.898593\pi$
$107$	−331077.	+	515165.i	−0.270257	+	0.420528i	0.679424	+	0.733746i	$0.262230\pi$
$108$	−226820.	+	66600.3i	−0.180057	+	0.0528694i
$109$	−193314.	−	27794.4i	−0.149274	−	0.0214624i	0.0672726	−	0.997735i	$-0.478570\pi$
$109$	−193314.	−	27794.4i	−0.149274	−	0.0214624i	−0.216547	+	0.976272i	$0.569479\pi$
$110$	−1910.37	−	4183.13i	−0.00143529	−	0.00314285i
$111$	830690.	−	119435.i	0.607394	−	0.0873300i
$112$	−979875.	−	1.52472e6i	−0.697456	−	1.08526i
$113$	2.09039e6	+	1.81134e6i	1.44875	+	1.25535i	0.911105	+	0.412175i	$0.135231\pi$
$113$	2.09039e6	+	1.81134e6i	1.44875	+	1.25535i	0.537643	+	0.843172i	$0.319315\pi$
$114$			21237.2i			0.0143345i
$115$	−615213.	−	28972.1i	−0.404513	−	0.0190496i
$116$	−1.72850e6			−1.10738
$117$	592960.	−	684313.i	0.370227	−	0.427265i
$118$	−166297.	+	106872.i	−0.101213	+	0.0650458i
$119$	−432571.	−	3.00860e6i	−0.256694	−	1.78535i
$120$	114537.	−	52307.1i	0.0662828	−	0.0302703i
$121$	−251382.	+	1.74840e6i	−0.141899	+	0.986928i
$122$	106686.	+	363340.i	0.0587528	+	0.200094i
$123$	1.42019e6	+	912704.i	0.763190	+	0.490472i
$124$	−217101.	+	475386.i	−0.113867	+	0.249334i
$125$	−409124.	+	1.39335e6i	−0.209471	+	0.713394i
$126$	−110789.	+	95998.8i	−0.0553838	+	0.0479904i
$127$	−1.59482e6	−	1.84052e6i	−0.778576	−	0.898525i	0.218429	−	0.975853i	$-0.429907\pi$
$127$	−1.59482e6	−	1.84052e6i	−0.778576	−	0.898525i	−0.997006	+	0.0773278i	$0.975361\pi$
$128$	1.19218e6	+	350055.i	0.568475	+	0.166919i
$129$	−326340.	−	149034.i	−0.152020	−	0.0694252i
$130$	−128732.	+	200311.i	−0.0585943	+	0.0911746i
$131$	2.93511e6	−	861827.i	1.30560	−	0.383359i	0.446326	−	0.894871i	$-0.352732\pi$
$131$	2.93511e6	−	861827.i	1.30560	−	0.383359i	0.859277	+	0.511511i	$0.170914\pi$
$132$	69297.7	+	9963.50i	0.0301298	+	0.00433202i
$133$	−214250.	−	469142.i	−0.0910681	−	0.199411i
$134$	−223073.	+	32073.0i	−0.0927113	+	0.0133299i
$135$	103667.	+	161309.i	0.0421347	+	0.0655629i
$136$	767026.	+	664632.i	0.304925	+	0.264219i
$137$		−	951049.i		−	0.369863i	−0.982751	−	0.184932i	$-0.940794\pi$
$137$		−	951049.i		−	0.369863i	0.982751	−	0.184932i	$-0.0592064\pi$
$138$	−138775.	+	195105.i	−0.0528047	+	0.0742389i
$139$	3.31488e6			1.23431			0.617154	−	0.786842i	$-0.288286\pi$
$139$	3.31488e6			1.23431			0.617154	+	0.786842i	$0.288286\pi$
$140$	−988619.	+	1.14093e6i	−0.360284	+	0.415790i
$141$	−1.46862e6	+	943824.i	−0.523904	+	0.336693i
$142$	17735.2	+	123351.i	0.00619401	+	0.0430803i
$143$	−243930.	+	111399.i	−0.0834175	+	0.0380955i
$144$	−131157.	+	912216.i	−0.0439242	+	0.305499i
$145$	395003.	+	1.34526e6i	0.129568	+	0.441267i
$146$	−293126.	−	188381.i	−0.0941880	−	0.0605309i
$147$	717047.	−	1.57011e6i	0.225733	−	0.494287i
$148$	946555.	−	3.22367e6i	0.291985	−	0.994410i
$149$	−3.32813e6	+	2.88384e6i	−1.00610	+	0.871791i	−0.991760	−	0.128106i	$-0.959110\pi$
$149$	−3.32813e6	+	2.88384e6i	−1.00610	+	0.871791i	−0.0143400	+	0.999897i	$0.504565\pi$
$150$	168331.	+	194265.i	0.0498760	+	0.0575599i
$151$	1.56083e6	+	458300.i	0.453340	+	0.133113i	0.500428	−	0.865778i	$-0.333176\pi$
$151$	1.56083e6	+	458300.i	0.453340	+	0.133113i	−0.0470881	+	0.998891i	$0.514994\pi$
$152$	156650.	+	71539.6i	0.0446066	+	0.0203711i
$153$	−835593.	+	1.30021e6i	−0.233303	+	0.363027i
$154$	41656.4	−	12231.4i	0.0114056	−	0.00334900i
$155$	419596.	+	60328.8i	0.112677	+	0.0162005i
$156$	−1.50586e6	−	3.29738e6i	−0.396654	−	0.868550i
$157$	1.38876e6	−	199673.i	0.358862	−	0.0515966i	0.0394741	−	0.999221i	$-0.487432\pi$
$157$	1.38876e6	−	199673.i	0.358862	−	0.0515966i	0.319388	+	0.947624i	$0.396523\pi$
$158$	−551952.	−	858854.i	−0.139936	−	0.217745i
$159$	−1.58100e6	−	1.36995e6i	−0.393316	−	0.340810i
$160$		−	759307.i		−	0.185378i
$161$	1.09730e6	−	5.71000e6i	0.262935	−	1.36823i
$162$	74541.1			0.0175328
$163$	5.08610e6	−	5.86967e6i	1.17442	−	1.35535i	0.252671	−	0.967552i	$-0.418691\pi$
$163$	5.08610e6	−	5.86967e6i	1.17442	−	1.35535i	0.921745	−	0.387796i	$-0.126764\pi$
$164$	5.68557e6	−	3.65390e6i	1.28897	−	0.828371i
$165$	−8081.76	−	56209.8i	−0.00179909	−	0.0125130i
$166$	−616328.	+	281467.i	−0.134737	+	0.0615324i
$167$	−1787.31	+	12431.0i	−0.000383752	+	0.00266905i	−0.990012	−	0.140980i	$-0.954975\pi$
$167$	−1787.31	+	12431.0i	−0.000383752	+	0.00266905i	0.989629	+	0.143649i	$0.0458837\pi$
$168$	334904.	+	1.14058e6i	0.0706305	+	0.240545i
$169$	7.62011e6	+	4.89714e6i	1.57870	+	1.01457i
$170$	168837.	−	369702.i	0.0343654	−	0.0752498i
$171$	−73884.8	+	251628.i	−0.0147763	+	0.0503236i
$172$	−1.08545e6	+	940545.i	−0.213316	+	0.184839i
$173$	−296313.	−	341963.i	−0.0572285	−	0.0660452i	0.726414	−	0.687258i	$-0.241186\pi$
$173$	−296313.	−	341963.i	−0.0572285	−	0.0660452i	−0.783642	+	0.621213i	$0.786640\pi$
$174$	522960.	+	153555.i	0.0992706	+	0.0291485i
$175$	−5.67836e6	−	2.59322e6i	−1.05952	−	0.483866i
$176$	147561.	−	229610.i	0.0270666	−	0.0421165i
$177$	−2.34217e6	+	687723.i	−0.422375	+	0.124021i
$178$	1.54657e6	+	222364.i	0.274227	+	0.0394279i
$179$	3.19697e6	+	7.00039e6i	0.557416	+	1.22057i	0.953232	+	0.302241i	$0.0977347\pi$
$179$	3.19697e6	+	7.00039e6i	0.557416	+	1.22057i	−0.395816	+	0.918330i	$0.629538\pi$
$180$	759829.	−	109247.i	0.130286	−	0.0187323i
$181$	2.05269e6	+	3.19405e6i	0.346169	+	0.538649i	0.970061	−	0.242861i	$-0.0780860\pi$
$181$	2.05269e6	+	3.19405e6i	0.346169	+	0.538649i	−0.623892	+	0.781510i	$0.714450\pi$
$182$	−1.69887e6	−	1.47208e6i	−0.281802	−	0.244183i
$183$			4.67618e6i			0.763023i
$184$	971658.	+	1.68086e6i	0.155977	+	0.269822i
$185$	−2.72523e6			−0.430415
$186$	107916.	−	124542.i	0.0167706	−	0.0193543i
$187$	385067.	−	247467.i	0.0588859	−	0.0378437i
$188$	994624.	+	6.91776e6i	0.149687	+	1.04110i
$189$	−1.64665e6	+	752002.i	−0.243903	+	0.111387i
$190$	9814.50	−	68261.3i	0.00143089	−	0.00995208i
$191$	2.76751e6	+	9.42526e6i	0.397181	+	1.35267i	0.879175	+	0.476499i	$0.158095\pi$
$191$	2.76751e6	+	9.42526e6i	0.397181	+	1.35267i	−0.481994	+	0.876175i	$0.660087\pi$
$192$	2.93474e6	+	1.88604e6i	0.414635	+	0.266470i
$193$	5.26382e6	−	1.15262e7i	0.732199	−	1.60329i	−0.0637780	−	0.997964i	$-0.520315\pi$
$193$	5.26382e6	−	1.15262e7i	0.732199	−	1.60329i	0.795977	−	0.605327i	$-0.206958\pi$
$194$	102961.	−	350652.i	0.0141015	−	0.0480254i
$195$	−2.22216e6	+	1.92551e6i	−0.299689	+	0.259682i
$196$	−4.52523e6	−	5.22240e6i	−0.600997	−	0.693588i
$197$	−2.16751e6	−	636439.i	−0.283507	−	0.0832451i	0.136888	−	0.990587i	$-0.456290\pi$
$197$	−2.16751e6	−	636439.i	−0.283507	−	0.0832451i	−0.420394	+	0.907342i	$0.638108\pi$
$198$	−20081.0	−	9170.67i	−0.00258695	−	0.00118142i
$199$	4.78051e6	−	7.43862e6i	0.606618	−	0.943915i	−0.393084	−	0.919502i	$-0.628592\pi$
$199$	4.78051e6	−	7.43862e6i	0.606618	−	0.943915i	0.999702	−	0.0244129i	$-0.00777165\pi$
$200$	1.99997e6	−	587245.i	0.249997	−	0.0734056i
$201$	−2.75465e6	−	396059.i	−0.339218	−	0.0487722i
$202$	−785811.	−	1.72069e6i	−0.0953375	−	0.208760i
$203$	−1.31016e7	+	1.88373e6i	−1.56616	+	0.225180i
$204$	3.34519e6	+	5.20522e6i	0.394031	+	0.613125i
$205$	−4.14304e6	−	3.58996e6i	−0.480903	−	0.416705i
$206$		−	623227.i		−	0.0712927i
$207$	−2.32304e6	+	1.82890e6i	−0.261906	+	0.206195i
$208$	−1.41320e7			−1.57042
$209$	50861.6	−	58697.4i	0.00557123	−	0.00642954i
$210$	400464.	−	257363.i	0.0432420	−	0.0277900i
$211$	−494224.	−	3.43741e6i	−0.0526110	−	0.365918i	−0.999071	−	0.0430963i	$-0.986278\pi$
$211$	−494224.	−	3.43741e6i	−0.0526110	−	0.365918i	0.946460	−	0.322821i	$-0.104631\pi$
$212$	−7.61811e6	+	3.47907e6i	−0.799539	+	0.365137i
$213$	−219006.	+	1.52322e6i	−0.0226630	+	0.157625i
$214$	−217791.	−	741728.i	−0.0222228	−	0.0756839i
$215$	980057.	+	629844.i	0.0986134	+	0.0633750i
$216$	251098.	−	549829.i	0.0249163	−	0.0545590i
$217$	−1.12750e6	+	3.83990e6i	−0.110341	+	0.375786i
$218$	186324.	−	161450.i	0.0179845	−	0.0155837i
$219$	−2.81771e6	−	3.25181e6i	−0.268265	−	0.309594i
$220$	−218134.	−	64050.0i	−0.0204859	−	0.00601521i
$221$	−2.15584e7	−	9.84538e6i	−1.99728	−	0.912128i
$222$	−572762.	+	891235.i	−0.0523498	+	0.0814579i
$223$	222358.	−	65290.2i	0.0200511	−	0.00588754i	−0.271692	−	0.962384i	$-0.587583\pi$
$223$	222358.	−	65290.2i	0.0200511	−	0.00588754i	0.291743	+	0.956497i	$0.405765\pi$
$224$	7.09543e6	+	1.02017e6i	0.631298	+	0.0907670i
$225$	1.31862e6	+	2.88737e6i	0.115763	+	0.253486i
$226$	−3.45613e6	+	496917.i	−0.299409	+	0.0430485i
$227$	−649319.	−	1.01036e6i	−0.0555112	−	0.0863770i	0.812389	−	0.583116i	$-0.198167\pi$
$227$	−649319.	−	1.01036e6i	−0.0555112	−	0.0863770i	−0.867900	+	0.496739i	$0.834530\pi$
$228$	793455.	+	687532.i	0.0669449	+	0.0580081i
$229$			1.26714e7i			1.05516i	0.849506	+	0.527578i	$0.176900\pi$
$229$			1.26714e7i			1.05516i	−0.849506	+	0.527578i	$0.823100\pi$
$230$	536218.	−	562980.i	0.0440715	−	0.0462711i
$231$	536117.			0.0434934
$232$	2.89429e6	−	3.34019e6i	0.231781	−	0.267490i
$233$	1.08479e7	−	6.97150e6i	0.857584	−	0.551136i	−0.0363476	−	0.999339i	$-0.511572\pi$
$233$	1.08479e7	−	6.97150e6i	0.857584	−	0.551136i	0.893932	+	0.448203i	$0.147936\pi$
$234$	162671.	+	1.13140e6i	0.0126959	+	0.0883017i
$235$	5.15666e6	−	2.35497e6i	0.397342	−	0.181460i
$236$	−1.39076e6	+	9.67297e6i	−0.105808	+	0.735908i
$237$	−3.55181e6	−	1.20963e7i	−0.266811	−	0.908676i
$238$	3.22788e6	+	2.07443e6i	0.239434	+	0.153875i
$239$	−7.08596e6	+	1.55161e7i	−0.519045	+	1.13655i	0.450755	+	0.892648i	$0.351155\pi$
$239$	−7.08596e6	+	1.55161e7i	−0.519045	+	1.13655i	−0.969800	+	0.243902i	$0.921572\pi$
$240$	843136.	−	2.87146e6i	0.0609908	−	0.207715i
$241$	−8.41087e6	+	7.28806e6i	−0.600883	+	0.520668i	−0.901331	−	0.433130i	$-0.857409\pi$
$241$	−8.41087e6	+	7.28806e6i	−0.600883	+	0.520668i	0.300449	+	0.953798i	$0.402864\pi$
$242$	−1.46021e6	−	1.68518e6i	−0.103032	−	0.118905i
$243$	883197.	+	259330.i	0.0615515	+	0.0180732i
$244$	1.70288e7	+	7.77677e6i	1.17223	+	0.535340i
$245$	−3.03036e6	+	4.71533e6i	−0.206061	+	0.320637i
$246$	−2.04478e6	+	600401.i	−0.137354	+	0.0403307i
$247$	−3.98051e6	−	572311.i	−0.264149	−	0.0379788i
$248$	−555118.	−	1.21554e6i	−0.0363941	−	0.0796919i
$249$	−8.28176e6	+	1.19074e6i	−0.536444	+	0.0771291i
$250$	−991082.	−	1.54215e6i	−0.0634292	−	0.0986978i
$251$	−686129.	−	594534.i	−0.0433895	−	0.0375972i	0.632896	−	0.774237i	$-0.281866\pi$
$251$	−686129.	−	594534.i	−0.0433895	−	0.0375972i	−0.676286	+	0.736640i	$0.736411\pi$
$252$			7.24708e6i			0.452857i
$253$	850820.	−	206895.i	0.0525383	−	0.0127758i
$254$	3.07430e6			0.187605
$255$	3.28666e6	−	3.79301e6i	0.198214	−	0.228751i
$256$	1.07294e7	−	6.89535e6i	0.639520	−	0.410995i
$257$	−633050.	−	4.40296e6i	−0.0372940	−	0.259385i	0.962641	−	0.270781i	$-0.0872818\pi$
$257$	−633050.	−	4.40296e6i	−0.0372940	−	0.259385i	−0.999935	+	0.0113953i	$0.996373\pi$
$258$	411958.	−	188135.i	0.0239880	−	0.0109550i
$259$	3.66148e6	−	2.54662e7i	0.210745	−	1.46576i
$260$	3.31635e6	+	1.12944e7i	0.188686	+	0.642606i
$261$	5.66205e6	+	3.63878e6i	0.318458	+	0.204661i
$262$	−1.60416e6	+	3.51263e6i	−0.0891958	+	0.195312i
$263$	7.87033e6	−	2.68039e7i	0.432639	−	1.47343i	−0.398396	−	0.917213i	$-0.630433\pi$
$263$	7.87033e6	−	2.68039e7i	0.432639	−	1.47343i	0.831035	−	0.556220i	$-0.187749\pi$
$264$	−135289.	+	117229.i	−0.00735277	+	0.00637121i
$265$	4.44861e6	+	5.13397e6i	0.239049	+	0.275877i
$266$	624689.	+	183425.i	0.0331909	+	0.00974573i
$267$	1.75509e7	+	8.01523e6i	0.922074	+	0.421097i
$268$	−6.02345e6	+	9.37267e6i	−0.312925	+	0.486921i
$269$	803601.	−	235958.i	0.0412842	−	0.0121221i	−0.261025	−	0.965332i	$-0.584061\pi$
$269$	803601.	−	235958.i	0.0412842	−	0.0121221i	0.302309	+	0.953210i	$0.402242\pi$
$270$	−239592.	−	34448.2i	−0.0121725	−	0.00175015i
$271$	6.93184e6	+	1.51786e7i	0.348290	+	0.762649i	0.999991	+	0.00417288i	$0.00132827\pi$
$271$	6.93184e6	+	1.51786e7i	0.348290	+	0.762649i	−0.651701	+	0.758476i	$0.725944\pi$
$272$	2.38765e7	−	3.43293e6i	1.18649	−	0.170592i
$273$	−1.50076e7	−	2.33522e7i	−0.737602	−	1.14773i
$274$	907327.	+	786203.i	0.0441075	+	0.0382193i
$275$		−	940067.i		−	0.0452023i
$276$	2.79675e6	+	1.15011e7i	0.133023	+	0.547033i
$277$	−2.01140e7			−0.946366			−0.473183	−	0.880964i	$-0.656895\pi$
$277$	−2.01140e7			−0.946366			−0.473183	+	0.880964i	$0.656895\pi$
$278$	−2.74031e6	+	3.16249e6i	−0.127546	+	0.147196i
$279$	1.71192e6	−	1.10019e6i	0.0788264	−	0.0506586i
$280$	−549355.	−	3.82085e6i	−0.0250253	−	0.174055i
$281$	−6.18499e6	+	2.82459e6i	−0.278753	+	0.127302i	−0.549886	−	0.835240i	$-0.685329\pi$
$281$	−6.18499e6	+	2.82459e6i	−0.278753	+	0.127302i	0.271133	+	0.962542i	$0.412602\pi$
$282$	313629.	−	2.18134e6i	0.0139852	−	0.0972691i
$283$	2.46362e6	+	8.39031e6i	0.108696	+	0.370185i	0.995819	−	0.0913484i	$-0.0291177\pi$
$283$	2.46362e6	+	8.39031e6i	0.108696	+	0.370185i	−0.887123	+	0.461533i	$0.847300\pi$
$284$	5.18275e6	+	3.33075e6i	0.226258	+	0.145407i
$285$	353769.	−	774647.i	0.0152822	−	0.0334633i
$286$	95371.8	−	324807.i	0.00407682	−	0.0138844i
$287$	3.91132e7	−	3.38918e7i	1.65454	−	1.43367i
$288$	−2.38698e6	−	2.75473e6i	−0.0999245	−	0.115319i
$289$	1.56553e7	+	4.59683e6i	0.648588	+	0.190443i
$290$	−1.60995e6	−	735240.i	−0.0660113	−	0.0301464i
$291$	2.43985e6	−	3.79648e6i	0.0990112	−	0.154064i
$292$	−1.65278e7	+	4.85300e6i	−0.663845	+	0.194922i
$293$	9.56729e6	+	1.37557e6i	0.380352	+	0.0546864i	0.329839	−	0.944037i	$-0.393005\pi$
$293$	9.56729e6	+	1.37557e6i	0.380352	+	0.0546864i	0.0505127	+	0.998723i	$0.483914\pi$
$294$	905171.	+	1.98205e6i	0.0356196	+	0.0779960i
$295$	7.84609e6	−	1.12810e6i	0.305624	−	0.0439421i
$296$	4.64452e6	+	7.22701e6i	0.179088	+	0.278666i
$297$	−206023.	−	178520.i	−0.00786407	−	0.00681425i
$298$		−	5.55911e6i		−	0.210066i
$299$	−3.28290e7	−	3.12684e7i	−1.22813	−	1.16975i
$300$	1.27076e7			0.470651
$301$	−7.20240e6	+	8.31202e6i	−0.264106	+	0.304794i
$302$	−1.72752e6	+	1.11021e6i	−0.0627195	+	0.0403073i
$303$	−3.32434e6	−	2.31213e7i	−0.119503	−	0.831160i
$304$	3.72316e6	−	1.70031e6i	0.132523	−	0.0605212i
$305$	2.16103e6	−	1.50303e7i	0.0761661	−	0.529747i
$306$	−549675.	−	1.87202e6i	−0.0191841	−	0.0653351i
$307$	−4.17796e6	−	2.68501e6i	−0.144394	−	0.0927964i	0.466449	−	0.884548i	$-0.345533\pi$
$307$	−4.17796e6	−	2.68501e6i	−0.144394	−	0.0927964i	−0.610843	+	0.791752i	$0.709169\pi$
$308$	891596.	−	1.95232e6i	0.0305152	−	0.0668189i
$309$	2.16822e6	−	7.38428e6i	0.0734900	−	0.250284i
$310$	−404422.	+	350434.i	−0.0135753	+	0.0117631i
$311$	1.60198e7	+	1.84878e7i	0.532568	+	0.614617i	0.956733	−	0.290969i	$-0.0939775\pi$
$311$	1.60198e7	+	1.84878e7i	0.532568	+	0.614617i	−0.424164	+	0.905585i	$0.639432\pi$
$312$	8.89340e6	+	2.61134e6i	0.292822	+	0.0859804i
$313$	4.97346e7	+	2.27130e7i	1.62191	+	0.740699i	0.999130	−	0.0417016i	$-0.0132779\pi$
$313$	4.97346e7	+	2.27130e7i	1.62191	+	0.740699i	0.622775	+	0.782401i	$0.286005\pi$
$314$	−957551.	+	1.48998e6i	−0.0309295	+	0.0481272i
$315$	5.64025e6	−	1.65613e6i	0.180454	−	0.0529861i
$316$	−4.99569e7	−	7.18272e6i	−1.58319	−	0.227629i
$317$	−7.38766e6	−	1.61767e7i	−0.231915	−	0.507823i	0.757518	−	0.652814i	$-0.226412\pi$
$317$	−7.38766e6	−	1.61767e7i	−0.231915	−	0.507823i	−0.989433	+	0.144991i	$0.953685\pi$
$318$	2.61394e6	−	375828.i	0.0812857	−	0.0116871i
$319$	−1.07765e6	−	1.67686e6i	−0.0331976	−	0.0516564i
$320$	−8.56132e6	−	7.41842e6i	−0.261271	−	0.226392i
$321$		−	9.54603e6i		−	0.288608i
$322$	4.54039e6	+	5.76714e6i	0.135996	+	0.172740i
$323$	6.86423e6			0.203697
$324$	2.41319e6	−	2.78497e6i	0.0709506	−	0.0818813i
$325$	−4.09475e7	+	2.63153e7i	−1.19283	+	0.766583i
$326$	1.39531e6	+	9.70456e6i	0.0402732	+	0.280106i
$327$	2.76934e6	−	1.26471e6i	0.0792013	−	0.0361700i
$328$	−2.45935e6	+	1.71052e7i	−0.0696946	+	0.484736i
$329$	1.50780e7	+	5.13509e7i	0.423405	+	1.44198i
$330$	60306.7	+	38756.8i	0.00167812	+	0.00107846i
$331$	−2.38029e7	+	5.21210e7i	−0.656365	+	1.43724i	0.229506	+	0.973307i	$0.426289\pi$
$331$	−2.38029e7	+	5.21210e7i	−0.656365	+	1.43724i	−0.885871	+	0.463932i	$0.846438\pi$
$332$	−9.43690e6	+	3.21391e7i	−0.257878	+	0.878253i
$333$	−9.88697e6	+	8.56711e6i	−0.267751	+	0.232007i
$334$	−10382.0	−	11981.5i	−0.000278639	−	0.000321567i
$335$	8.67105e6	+	2.54605e6i	0.230641	+	0.0677224i
$336$	2.56999e7	+	1.17367e7i	0.677506	+	0.309406i
$337$	2.07175e7	−	3.22370e7i	0.541312	−	0.842298i	−0.457589	−	0.889164i	$-0.651287\pi$
$337$	2.07175e7	−	3.22370e7i	0.541312	−	0.842298i	0.998901	+	0.0468660i	$0.0149234\pi$
$338$	−1.09713e7	+	3.22147e6i	−0.284125	+	0.0834265i
$339$	−4.26786e7	−	6.13626e6i	−1.09550	−	0.157509i
$340$	−8.34670e6	−	1.82767e7i	−0.212363	−	0.465009i
$341$	−596537.	+	85769.0i	−0.0150444	+	0.00216305i
$342$	−178982.	−	278502.i	−0.00447437	−	0.00696225i
$343$	2.49917e6	+	2.16554e6i	0.0619317	+	0.0536641i
$344$		−	3.67243e6i		−	0.0902149i
$345$	8.31198e6	−	4.80493e6i	0.202417	−	0.117012i
$346$	571195.			0.0137897
$347$	2.53685e7	−	2.92768e7i	0.607165	−	0.700705i	−0.366052	−	0.930594i	$-0.619291\pi$
$347$	2.53685e7	−	2.92768e7i	0.607165	−	0.700705i	0.973217	+	0.229889i	$0.0738363\pi$
$348$	2.26673e7	−	1.45674e7i	0.537851	−	0.345656i
$349$	−2.80445e6	−	1.95054e7i	−0.0659738	−	0.458858i	−0.995852	−	0.0909899i	$-0.970997\pi$
$349$	−2.80445e6	−	1.95054e7i	−0.0659738	−	0.458858i	0.929878	−	0.367868i	$-0.119912\pi$
$350$	7.16813e6	−	3.27358e6i	0.167187	−	0.0763516i
$351$	−2.00877e6	+	1.39713e7i	−0.0464525	+	0.323084i
$352$	304131.	+	1.03577e6i	0.00697321	+	0.0237486i
$353$	−4.04816e7	−	2.60159e7i	−0.920309	−	0.591447i	−0.00756161	−	0.999971i	$-0.502407\pi$
$353$	−4.04816e7	−	2.60159e7i	−0.920309	−	0.591447i	−0.912747	+	0.408525i	$0.866043\pi$
$354$	1.28009e6	−	2.80302e6i	0.0288557	−	0.0631852i
$355$	1.40787e6	−	4.79478e6i	0.0314687	−	0.107173i
$356$	5.83765e7	−	5.05835e7i	1.29386	−	1.12114i
$357$	3.10284e7	+	3.58087e7i	0.681953	+	0.787016i
$358$	−9.32140e6	−	2.73701e6i	−0.203157	−	0.0596523i
$359$	−6.85098e7	−	3.12874e7i	−1.48071	−	0.676217i	−0.498998	−	0.866603i	$-0.666299\pi$
$359$	−6.85098e7	−	3.12874e7i	−1.48071	−	0.676217i	−0.981709	+	0.190386i	$0.939026\pi$
$360$	−1.06118e6	+	1.65123e6i	−0.0227449	+	0.0353917i
$361$	−4.40226e7	+	1.29262e7i	−0.935739	+	0.274758i
$362$	−4.74411e6	−	682100.i	−0.100007	−	0.0143788i
$363$	−1.14385e7	−	2.50469e7i	−0.239139	−	0.523641i
$364$	−1.09998e8	+	1.58153e7i	−2.28076	+	0.327924i
$365$	7.55398e6	+	1.17542e7i	0.155345	+	0.241722i
$366$	−4.46120e6	−	3.86566e6i	−0.0909932	−	0.0788460i
$367$			3.24962e7i			0.657408i	0.944433	+	0.328704i	$0.106612\pi$
$367$			3.24962e7i			0.657408i	−0.944433	+	0.328704i	$0.893388\pi$
$368$	4.53151e7	+	8.70831e6i	0.909284	+	0.174739i
$369$	−2.63163e7			−0.523775
$370$	2.25286e6	−	2.59994e6i	0.0444764	−	0.0513285i
$371$	−5.39519e7	+	3.46728e7i	−1.05654	+	0.678995i
$372$	−1.15940e6	−	8.06381e6i	−0.0225219	−	0.156643i
$373$	−1.88976e7	+	8.63024e6i	−0.364150	+	0.166302i	−0.589083	−	0.808073i	$-0.700511\pi$
$373$	−1.88976e7	+	8.63024e6i	−0.364150	+	0.166302i	0.224933	+	0.974374i	$0.427784\pi$
$374$	−82232.3	+	571938.i	−0.00157191	+	0.0109329i
$375$	−6.37761e6	−	2.17201e7i	−0.120938	−	0.411878i
$376$	−1.50334e7	−	9.66141e6i	−0.282810	−	0.181751i
$377$	−4.28739e7	+	9.38808e7i	−0.800146	+	1.75207i
$378$	643809.	−	2.19261e6i	0.0119201	−	0.0405963i
$379$	3.92530e7	−	3.40129e7i	0.721033	−	0.624779i	−0.215031	−	0.976607i	$-0.568985\pi$
$379$	3.92530e7	−	3.40129e7i	0.721033	−	0.624779i	0.936065	+	0.351828i	$0.114440\pi$
$380$	−2.23261e6	−	2.57657e6i	−0.0406876	−	0.0469560i
$381$	3.64257e7	+	1.06956e7i	0.658618	+	0.193388i
$382$	−1.12798e7	−	5.15130e6i	−0.202353	−	0.0924116i
$383$	3.90715e7	−	6.07964e7i	0.695446	−	1.08214i	−0.296445	−	0.955050i	$-0.595801\pi$
$383$	3.90715e7	−	6.07964e7i	0.695446	−	1.08214i	0.991892	−	0.127086i	$-0.0405624\pi$
$384$	−1.85842e7	+	5.45682e6i	−0.328209	+	0.0963710i
$385$	−1.72320e6	−	247759.i	−0.0301964	−	0.00434158i
$386$	6.64483e6	+	1.45502e7i	0.115537	+	0.252991i
$387$	5.53559e6	−	795898.i	0.0955061	−	0.0137317i
$388$	−9.76764e6	−	1.51987e7i	−0.167222	−	0.260203i
$389$	−3.62568e7	−	3.14167e7i	−0.615944	−	0.533718i	0.290049	−	0.957012i	$-0.406328\pi$
$389$	−3.62568e7	−	3.14167e7i	−0.615944	−	0.533718i	−0.905993	+	0.423293i	$0.860874\pi$
$390$		−	3.71176e6i		−	0.0625729i
$391$	6.30612e7	+	4.48542e7i	1.05495	+	0.750366i
$392$	1.76691e7			0.293330
$393$	−3.12273e7	+	3.60383e7i	−0.514467	+	0.593726i
$394$	2.39900e6	−	1.54174e6i	0.0392231	−	0.0252071i
$395$	5.82616e6	+	4.05218e7i	0.0945347	+	0.657503i
$396$	−992729.	+	453364.i	−0.0159862	+	0.00730065i
$397$	−8.96716e6	+	6.23680e7i	−0.143312	+	0.996759i	0.783542	+	0.621339i	$0.213411\pi$
$397$	−8.96716e6	+	6.23680e7i	−0.143312	+	0.996759i	−0.926855	+	0.375421i	$0.877498\pi$
$398$	3.14475e6	+	1.07100e7i	0.0498811	+	0.169880i
$399$	6.76346e6	+	4.34661e6i	0.106476	+	0.0684278i
$400$	2.05800e7	−	4.50640e7i	0.321563	−	0.704125i
$401$	−3.66907e6	+	1.24957e7i	−0.0569014	+	0.193788i	−0.983039	−	0.183398i	$-0.941290\pi$
$401$	−3.66907e6	+	1.24957e7i	−0.0569014	+	0.193788i	0.926137	+	0.377187i	$0.123108\pi$
$402$	2.65504e6	−	2.30061e6i	0.0408689	−	0.0354131i
$403$	2.04348e7	+	2.35830e7i	0.312216	+	0.360317i
$404$	−8.97271e7	−	2.63463e7i	−1.36075	−	0.399553i
$405$	−2.71895e6	−	1.24170e6i	−0.0409295	−	0.0186919i
$406$	9.03358e6	−	1.40565e7i	0.134984	−	0.210039i
$407$	3.71749e6	−	1.09155e6i	0.0551400	−	0.0161906i
$408$	−1.56600e7	−	2.25157e6i	−0.230575	−	0.0331516i
$409$	2.27856e7	+	4.98935e7i	0.333036	+	0.729246i	0.999873	−	0.0159573i	$-0.00507959\pi$
$409$	2.27856e7	+	4.98935e7i	0.333036	+	0.729246i	−0.666837	+	0.745204i	$0.732352\pi$
$410$	6.84985e6	−	984860.i	0.0993870	−	0.0142897i
$411$	8.01521e6	+	1.24719e7i	0.115449	+	0.179642i
$412$	−2.32847e7	−	2.01763e7i	−0.332950	−	0.288503i
$413$			7.48343e7i			1.06231i
$414$	175568.	−	3.72814e6i	0.00247426	−	0.0525401i
$415$	2.71698e7			0.380138
$416$	3.66028e7	−	4.22418e7i	0.508433	−	0.586763i
$417$	−4.34708e7	+	2.79370e7i	−0.599501	+	0.385276i
$418$	13953.2	+	97046.7i	0.000191049	+	0.00132878i
$419$	6.66472e7	−	3.04368e7i	0.906024	−	0.413767i	0.0927778	−	0.995687i	$-0.470425\pi$
$419$	6.66472e7	−	3.04368e7i	0.906024	−	0.413767i	0.813246	+	0.581919i	$0.197698\pi$
$420$	3.34914e6	−	2.32938e7i	0.0452049	−	0.314407i
$421$	−1.54999e7	−	5.27877e7i	−0.207722	−	0.707436i	−0.995775	−	0.0918282i	$-0.970729\pi$
$421$	−1.54999e7	−	5.27877e7i	−0.207722	−	0.707436i	0.788053	−	0.615607i	$-0.211089\pi$
$422$	3.68794e6	+	2.37010e6i	0.0490735	+	0.0315376i
$423$	1.13049e7	−	2.47543e7i	0.149364	−	0.327062i
$424$	6.03311e6	−	2.05469e7i	0.0791487	−	0.269556i
$425$	6.27896e7	−	5.44075e7i	0.817939	−	0.708748i
$426$	−1.27215e6	−	1.46814e6i	−0.0164555	−	0.0189906i
$427$	1.37549e8	+	4.03880e7i	1.76674	+	0.518763i
$428$	−3.47628e7	−	1.58756e7i	−0.443388	−	0.202488i
$429$	2.26002e6	−	3.51666e6i	0.0286246	−	0.0445408i
$430$	−1.41107e6	+	414328.i	−0.0177478	+	0.00521122i
$431$	−6.53538e7	−	9.39645e6i	−0.816280	−	0.117363i	−0.278486	−	0.960440i	$-0.589833\pi$
$431$	−6.53538e7	−	9.39645e6i	−0.816280	−	0.117363i	−0.537793	+	0.843077i	$0.680742\pi$
$432$	−5.96796e6	−	1.30680e7i	−0.0740244	−	0.162091i
$433$	1.17225e8	−	1.68544e7i	1.44397	−	0.207611i	0.624629	−	0.780922i	$-0.285250\pi$
$433$	1.17225e8	−	1.68544e7i	1.44397	−	0.207611i	0.819338	+	0.573311i	$0.194341\pi$
$434$	−2.73131e6	−	4.25000e6i	−0.0334119	−	0.0519899i
$435$	−1.65175e7	−	1.43125e7i	−0.200667	−	0.173879i
$436$		−	1.21881e7i		−	0.147054i
$437$	1.24111e7	+	4.28798e6i	0.148718	+	0.0513817i
$438$	5.43163e6			0.0646410
$439$	5.02771e7	−	5.80229e7i	0.594260	−	0.685813i	−0.376348	−	0.926478i	$-0.622820\pi$
$439$	5.02771e7	−	5.80229e7i	0.594260	−	0.685813i	0.970608	+	0.240666i	$0.0773657\pi$
$440$	489026.	−	314278.i	0.00574082	−	0.00368940i
$441$	3.82930e6	+	2.66333e7i	0.0446481	+	0.310534i
$442$	2.72144e7	−	1.24284e7i	0.315161	−	0.143929i
$443$	1.52290e7	−	1.05920e8i	0.175171	−	1.21834i	−0.692581	−	0.721340i	$-0.743526\pi$
$443$	1.52290e7	−	1.05920e8i	0.175171	−	1.21834i	0.867752	−	0.496998i	$-0.165564\pi$
$444$	1.47553e7	+	5.02520e7i	0.168578	+	0.574123i
$445$	−5.27085e7	−	3.38737e7i	−0.598137	−	0.384399i
$446$	−121528.	+	266109.i	−0.00136985	+	0.00299955i
$447$	1.93403e7	−	6.58669e7i	0.216541	−	0.737470i
$448$	8.08248e7	−	7.00351e7i	0.898899	−	0.778900i
$449$	4.85984e7	+	5.60855e7i	0.536887	+	0.619601i	0.957777	−	0.287511i	$-0.0928277\pi$
$449$	4.85984e7	+	5.60855e7i	0.536887	+	0.619601i	−0.420890	+	0.907112i	$0.638282\pi$
$450$	−3.84469e6	−	1.12890e6i	−0.0421914	−	0.0123885i
$451$	7.08946e6	+	3.23765e6i	0.0772829	+	0.0352939i
$452$	−9.33230e7	+	1.45213e8i	−1.01059	+	1.57250i
$453$	−2.43309e7	+	7.14419e6i	−0.261736	+	0.0768526i
$454$	1.50068e6	+	215766.i	0.0160369	+	0.00230576i
$455$	3.74458e7	+	8.19949e7i	0.397529	+	0.870468i
$456$	−2.65720e6	+	382047.i	−0.0280240	+	0.00402924i
$457$	−1.51504e6	−	2.35744e6i	−0.0158736	−	0.0246998i	0.833226	−	0.552932i	$-0.186491\pi$
$457$	−1.51504e6	−	2.35744e6i	−0.0158736	−	0.0246998i	−0.849100	+	0.528233i	$0.822855\pi$
$458$	−1.20888e7	−	1.04750e7i	−0.125831	−	0.109033i
$459$		−	2.40929e7i		−	0.249144i
$460$	−3.67429e6	−	3.82598e7i	−0.0377485	−	0.393069i
$461$	−8.71507e7			−0.889545			−0.444773	−	0.895644i	$-0.646715\pi$
$461$	−8.71507e7			−0.889545			−0.444773	+	0.895644i	$0.646715\pi$
$462$	−443192.	+	511471.i	−0.00449434	+	0.00518674i
$463$	5.73667e7	−	3.68674e7i	0.577986	−	0.371449i	−0.218746	−	0.975782i	$-0.570197\pi$
$463$	5.73667e7	−	3.68674e7i	0.577986	−	0.371449i	0.796732	+	0.604333i	$0.206560\pi$
$464$	−1.49494e7	−	1.03976e8i	−0.149648	−	1.04083i
$465$	−6.01095e6	+	2.74511e6i	−0.0597839	+	0.0273024i
$466$	−2.31660e6	+	1.61123e7i	−0.0228925	+	0.159221i
$467$	2.12383e7	+	7.23310e7i	0.208530	+	0.710189i	0.995632	+	0.0933657i	$0.0297626\pi$
$467$	2.12383e7	+	7.23310e7i	0.208530	+	0.710189i	−0.787102	+	0.616823i	$0.788419\pi$
$468$	4.75372e7	+	3.05503e7i	0.463762	+	0.298042i
$469$	−3.54418e7	+	7.76068e7i	−0.343556	+	0.752283i
$470$	−2.01615e6	+	6.86637e6i	−0.0194191	+	0.0661354i
$471$	−1.65292e7	+	1.43226e7i	−0.158193	+	0.137075i
$472$	−1.63634e7	−	1.88844e7i	−0.155614	−	0.179588i
$473$	−1.58918e6	−	466624.i	−0.0150172	−	0.00440945i
$474$	1.44764e7	+	6.61116e6i	0.135933	+	0.0620787i
$475$	7.62167e6	−	1.18596e7i	0.0711163	−	0.110659i
$476$	1.82003e8	−	5.34409e7i	1.68755	−	0.495511i
$477$	3.22786e7	+	4.64097e6i	0.297413	+	0.0427615i
$478$	−8.94503e6	−	1.95869e7i	−0.0819027	−	0.179342i
$479$	−7.74425e7	+	1.11346e7i	−0.704649	+	0.101313i	−0.485319	−	0.874337i	$-0.661296\pi$
$479$	−7.74425e7	+	1.11346e7i	−0.704649	+	0.101313i	−0.219331	+	0.975651i	$0.570387\pi$
$480$	6.39926e6	+	9.95744e6i	0.0578636	+	0.0900376i
$481$	−1.51610e8	−	1.31371e8i	−1.36236	−	1.18049i
$482$		−	1.40490e7i		−	0.125460i
$483$	3.37326e7	+	8.41279e7i	0.299370	+	0.746618i
$484$	−1.10234e8			−0.972250
$485$	−9.59674e6	+	1.10752e7i	−0.0841198	+	0.0970794i
$486$	−977520.	+	628214.i	−0.00851563	+	0.00547267i
$487$	−6.05789e6	−	4.21336e7i	−0.0524487	−	0.364789i	−0.999096	−	0.0425165i	$-0.986462\pi$
$487$	−6.05789e6	−	4.21336e7i	−0.0524487	−	0.364789i	0.946647	−	0.322272i	$-0.104447\pi$
$488$	−4.35418e7	+	1.98849e7i	−0.374668	+	0.171105i
$489$	−1.72302e7	+	1.19838e8i	−0.147354	+	1.02487i
$490$	−1.99345e6	−	6.78907e6i	−0.0169441	−	0.0577062i
$491$	1.97451e8	+	1.26894e8i	1.66807	+	1.07200i	0.904705	+	0.426039i	$0.140091\pi$
$491$	1.97451e8	+	1.26894e8i	1.66807	+	1.07200i	0.763366	+	0.645966i	$0.223545\pi$
$492$	−4.37656e7	+	9.58333e7i	−0.367483	+	0.804676i
$493$	4.96315e7	−	1.69029e8i	0.414206	−	1.41066i
$494$	3.83657e6	−	3.32441e6i	0.0318246	−	0.0275761i
$495$	579706.	+	669016.i	0.00477961	+	0.00551596i
$496$	−3.04738e7	−	8.94793e6i	−0.249737	−	0.0733293i
$497$	4.29138e7	+	1.95981e7i	0.349565	+	0.159641i
$498$	5.71029e6	−	8.88538e6i	0.0462349	−	0.0719429i
$499$	2.19388e8	−	6.44181e7i	1.76567	−	0.518449i	0.772493	−	0.635023i	$-0.219010\pi$
$499$	2.19388e8	−	6.44181e7i	1.76567	−	0.518449i	0.993182	+	0.116575i	$0.0371914\pi$
$500$	−8.97023e7	−	1.28972e7i	−0.717619	−	0.103178i
$501$	−81327.0	−	178081.i	−0.000646728	−	0.00141614i
$502$	1.13440e6	−	163103.i	0.00896720	−	0.00128929i
$503$	−6.54593e7	−	1.01857e8i	−0.514360	−	0.800360i	0.482795	−	0.875733i	$-0.339621\pi$
$503$	−6.54593e7	−	1.01857e8i	−0.514360	−	0.800360i	−0.997155	+	0.0753734i	$0.975985\pi$
$504$	−1.40044e7	−	1.21349e7i	−0.109389	−	0.0947858i
$505$			7.58535e7i			0.588981i
$506$	−505964.	+	982740.i	−0.00390542	+	0.00758555i
$507$	−1.41201e8			−1.08346
$508$	9.95272e7	−	1.14861e8i	0.759190	−	0.876152i
$509$	−5.35170e7	+	3.43933e7i	−0.405825	+	0.260808i	−0.727591	−	0.686012i	$-0.759360\pi$
$509$	−5.35170e7	+	3.43933e7i	−0.405825	+	0.260808i	0.321766	+	0.946819i	$0.395724\pi$
$510$	901653.	+	6.27114e6i	0.00679718	+	0.0472755i
$511$	−1.19988e8	+	5.47966e7i	−0.899237	+	0.410668i
$512$	−1.36083e7	+	9.46475e7i	−0.101389	+	0.705179i
$513$	−1.15175e6	−	3.92250e6i	−0.00853112	−	0.0290543i
$514$	4.72387e6	+	3.03585e6i	0.0347863	+	0.0223558i
$515$	−1.03817e7	+	2.27328e7i	−0.0760059	+	0.166430i
$516$	6.30770e6	−	2.14820e7i	0.0459115	−	0.156360i
$517$	−6.09097e6	+	5.27785e6i	−0.0440773	+	0.0381932i
$518$	2.12686e7	+	2.45453e7i	0.153020	+	0.176595i
$519$	6.76778e6	+	1.98720e6i	0.0484110	+	0.0142148i
$520$	−2.73786e7	−	1.25034e7i	−0.194716	−	0.0889239i
$521$	−1.26251e8	+	1.96451e8i	−0.892734	+	1.38912i	0.0282833	+	0.999600i	$0.490996\pi$
$521$	−1.26251e8	+	1.96451e8i	−0.892734	+	1.38912i	−0.921017	+	0.389521i	$0.872640\pi$
$522$	−8.15214e6	+	2.39368e6i	−0.0573139	+	0.0168289i
$523$	−1.05524e8	−	1.51720e7i	−0.737641	−	0.106057i	−0.236754	−	0.971570i	$-0.576084\pi$
$523$	−1.05524e8	−	1.51720e7i	−0.737641	−	0.106057i	−0.500887	+	0.865513i	$0.666993\pi$
$524$	7.93039e7	+	1.73651e8i	0.551189	+	1.20694i
$525$	9.63201e7	−	1.38487e7i	0.665640	−	0.0957045i
$526$	1.90655e7	+	2.96665e7i	0.131006	+	0.203849i
$527$	−4.02540e7	−	3.48803e7i	−0.275028	−	0.238313i
$528$			4.25468e6i			0.0289045i
$529$	8.59999e7	+	1.20493e8i	0.580939	+	0.813947i
$530$	−8.57548e6			−0.0576011
$531$	2.49189e7	−	2.87579e7i	0.166435	−	0.192076i
$532$	2.70767e7	−	1.74011e7i	0.179829	−	0.115569i
$533$	−5.74300e7	−	3.99434e8i	−0.379277	−	2.63793i
$534$	−2.21556e7	+	1.01181e7i	−0.145499	+	0.0664470i
$535$	−4.41157e6	+	3.06831e7i	−0.0288092	+	0.200373i
$536$	−8.02595e6	−	2.73339e7i	−0.0521197	−	0.177503i
$537$	−1.00922e8	−	6.48587e7i	−0.651724	−	0.418837i
$538$	−439201.	+	961717.i	−0.00282044	+	0.00617590i
$539$	2.24506e6	−	7.64598e6i	0.0143371	−	0.0488278i
$540$	−9.04357e6	+	7.83630e6i	−0.0574326	+	0.0497657i
$541$	2.65133e7	+	3.05979e7i	0.167445	+	0.193242i	0.833270	−	0.552866i	$-0.186466\pi$
$541$	2.65133e7	+	3.05979e7i	0.167445	+	0.193242i	−0.665825	+	0.746108i	$0.731920\pi$
$542$	−2.02112e7	−	5.93454e6i	−0.126939	−	0.0372725i
$543$	−5.38373e7	−	2.45867e7i	−0.336267	−	0.153568i
$544$	−5.15802e7	+	8.02604e7i	−0.320395	+	0.498545i
$545$	−9.48576e6	+	2.78527e6i	−0.0585980	+	0.0172059i
$546$	3.46849e7	+	4.98694e6i	0.213090	+	0.0306377i
$547$	1.78693e7	+	3.91282e7i	0.109180	+	0.239072i	0.956334	−	0.292277i	$-0.0944128\pi$
$547$	1.78693e7	+	3.91282e7i	0.109180	+	0.239072i	−0.847153	+	0.531348i	$0.821686\pi$
$548$	5.87475e7	−	8.44661e6i	0.356983	−	0.0513264i
$549$	−3.94097e7	−	6.13227e7i	−0.238169	−	0.370599i
$550$	896850.	+	777125.i	0.00539054	+	0.00467093i
$551$		−	2.98918e7i		−	0.178689i
$552$	−2.69080e7	−	1.38536e7i	−0.159980	−	0.0823655i
$553$	−3.86488e8			−2.28539
$554$	1.66276e7	−	1.91893e7i	0.0977915	−	0.112857i
$555$	3.57382e7	−	2.29675e7i	0.209052	−	0.134349i
$556$	2.94407e7	+	2.04764e8i	0.171287	+	1.19132i
$557$	8.66938e7	−	3.95917e7i	0.501675	−	0.229107i	−0.148471	−	0.988917i	$-0.547435\pi$
$557$	8.66938e7	−	3.95917e7i	0.501675	−	0.229107i	0.650146	+	0.759810i	$0.274708\pi$
$558$	−365587.	+	2.54271e6i	−0.00210420	+	0.0146351i
$559$	2.41607e7	+	8.22836e7i	0.138316	+	0.471062i
$560$	−7.71813e7	−	4.96014e7i	−0.439489	−	0.282442i
$561$	−2.96411e6	+	6.49050e6i	−0.0167883	+	0.0367612i
$562$	2.41821e6	−	8.23565e6i	0.0136234	−	0.0463969i
$563$	−7.24545e7	+	6.27822e7i	−0.406013	+	0.351813i	−0.833800	−	0.552067i	$-0.813839\pi$
$563$	−7.24545e7	+	6.27822e7i	−0.406013	+	0.351813i	0.427786	+	0.903880i	$0.359294\pi$
$564$	−7.13445e7	−	8.23360e7i	−0.397671	−	0.458936i
$565$	1.34343e8	+	3.94467e7i	0.744852	+	0.218708i
$566$	−1.00412e7	−	4.58566e6i	−0.0553778	−	0.0252902i
$567$	1.52563e7	−	2.37392e7i	0.0836950	−	0.130232i
$568$	−1.51146e7	+	4.43806e6i	−0.0824808	+	0.0242185i
$569$	−2.62584e8	−	3.77538e7i	−1.42538	−	0.204939i	−0.613930	−	0.789360i	$-0.710412\pi$
$569$	−2.62584e8	−	3.77538e7i	−1.42538	−	0.204939i	−0.811450	+	0.584421i	$0.801322\pi$
$570$	446584.	+	977883.i	0.00241145	+	0.00528035i
$571$	4.42932e7	−	6.36840e6i	0.237919	−	0.0342076i	−0.0223239	−	0.999751i	$-0.507106\pi$
$571$	4.42932e7	−	6.36840e6i	0.237919	−	0.0342076i	0.260243	+	0.965543i	$0.416197\pi$
$572$	−9.04770e6	−	1.40785e7i	−0.0483448	−	0.0752260i
$573$	−1.15726e8	−	1.00278e8i	−0.615132	−	0.533015i
$574$			6.53324e7i			0.345456i
$575$	1.47516e8	−	5.91493e7i	0.775953	−	0.311133i
$576$	−5.43808e7			−0.284563
$577$	8.90166e7	−	1.02731e8i	0.463386	−	0.534776i	−0.475174	−	0.879892i	$-0.657615\pi$
$577$	8.90166e7	−	1.02731e8i	0.463386	−	0.534776i	0.938560	+	0.345115i	$0.112160\pi$
$578$	−1.73273e7	+	1.11356e7i	−0.0897320	+	0.0576673i
$579$	2.81107e7	+	1.95514e8i	0.144823	+	1.00726i
$580$	−7.95901e7	+	3.63476e7i	−0.407920	+	0.186291i
$581$	−3.65040e7	+	2.53891e8i	−0.186128	+	1.29455i
$582$	1.60500e6	+	5.46612e6i	0.00814153	+	0.0277275i
$583$	−8.12472e6	−	5.22144e6i	−0.0410018	−	0.0263502i
$584$	1.82969e7	−	4.00647e7i	0.0918629	−	0.201152i
$585$	1.29133e7	−	4.39786e7i	0.0645014	−	0.219672i
$586$	−9.22132e6	+	7.99032e6i	−0.0458248	+	0.0397074i
$587$	−2.02082e8	−	2.33215e8i	−0.999110	−	1.15303i	−0.988212	−	0.153093i	$-0.951077\pi$
$587$	−2.02082e8	−	2.33215e8i	−0.999110	−	1.15303i	−0.0108978	−	0.999941i	$-0.503469\pi$
$588$	1.03356e8	+	3.03481e7i	0.508399	+	0.149279i
$589$	−8.22107e6	−	3.75444e6i	−0.0402330	−	0.0183738i
$590$	−5.40989e6	+	8.41796e6i	−0.0263410	+	0.0409874i
$591$	3.37882e7	−	9.92111e6i	0.163683	−	0.0480616i
$592$	2.02102e8	+	2.90579e7i	0.974104	+	0.140055i
$593$	1.47194e8	+	3.22310e8i	0.705873	+	1.54565i	0.832701	+	0.553722i	$0.186793\pi$
$593$	1.47194e8	+	3.22310e8i	0.705873	+	1.54565i	−0.126828	+	0.991925i	$0.540480\pi$
$594$	340627.	−	48974.7i	0.00162525	−	0.000233675i
$595$	−8.31839e7	−	1.29437e8i	−0.394901	−	0.614478i
$596$	−2.07697e8	−	1.79970e8i	−0.981049	−	0.850084i
$597$			1.37838e8i			0.647807i
$598$	5.69697e7	−	5.47110e6i	0.266404	−	0.0255841i
$599$	2.21270e8			1.02954			0.514769	−	0.857329i	$-0.327878\pi$
$599$	2.21270e8			1.02954			0.514769	+	0.857329i	$0.327878\pi$
$600$	−2.12782e7	+	2.45563e7i	−0.0985100	+	0.113687i
$601$	−5.55180e7	+	3.56792e7i	−0.255747	+	0.164359i	−0.662232	−	0.749299i	$-0.730391\pi$
$601$	−5.55180e7	+	3.56792e7i	−0.255747	+	0.164359i	0.406485	+	0.913657i	$0.366754\pi$
$602$	−1.97589e6	−	1.37426e7i	−0.00905675	−	0.0629911i
$603$	3.94620e7	−	1.80217e7i	0.179981	−	0.0821946i
$604$	−1.44475e7	+	1.00485e8i	−0.0655665	+	0.456025i
$605$	2.51910e7	+	8.57926e7i	0.113757	+	0.387421i
$606$	2.48065e7	+	1.59422e7i	0.111467	+	0.0716357i
$607$	−6.22470e7	+	1.36302e8i	−0.278325	+	0.609447i	−0.996235	−	0.0866884i	$-0.972372\pi$
$607$	−6.22470e7	+	1.36302e8i	−0.278325	+	0.609447i	0.717910	+	0.696136i	$0.245099\pi$
$608$	−4.56082e6	+	1.55327e7i	−0.0202923	+	0.0691094i
$609$	1.55937e8	−	1.35120e8i	0.690394	−	0.598230i
$610$	1.25529e7	+	1.44868e7i	0.0553036	+	0.0638238i
$611$	4.00398e8	+	1.17567e8i	1.75537	+	0.515422i
$612$	−8.77367e7	−	4.00680e7i	−0.382760	−	0.174801i
$613$	9.49702e7	−	1.47776e8i	0.412293	−	0.641540i	−0.571552	−	0.820566i	$-0.693658\pi$
$613$	9.49702e7	−	1.47776e8i	0.412293	−	0.641540i	0.983844	+	0.179026i	$0.0572946\pi$
$614$	6.01537e6	−	1.76627e6i	0.0259871	−	0.00763049i
$615$	8.45865e7	+	1.21617e7i	0.363643	+	0.0522840i
$616$	2.27977e6	+	4.99200e6i	0.00975324	+	0.0213566i
$617$	−4.05037e8	+	5.82356e7i	−1.72441	+	0.247932i	−0.932102	−	0.362195i	$-0.882027\pi$
$617$	−4.05037e8	+	5.82356e7i	−1.72441	+	0.247932i	−0.792303	+	0.610128i	$0.791118\pi$
$618$	5.25241e6	+	8.17291e6i	0.0222532	+	0.0346267i
$619$	−2.59363e8	−	2.24739e8i	−1.09354	−	0.947559i	−0.0946917	−	0.995507i	$-0.530187\pi$
$619$	−2.59363e8	−	2.24739e8i	−1.09354	−	0.947559i	−0.998850	+	0.0479475i	$0.984732\pi$
$620$			2.64547e7i			0.111001i
$621$	1.50505e7	−	4.35619e7i	0.0628457	−	0.181900i
$622$	−3.08810e7			−0.128327
$623$	3.87353e8	−	4.47029e8i	1.60193	−	1.84872i
$624$	1.85325e8	−	1.19101e8i	0.762748	−	0.490189i
$625$	−1.85855e7	−	1.29265e8i	−0.0761261	−	0.529469i
$626$	−6.27829e7	+	2.86720e7i	−0.255929	+	0.116879i
$627$	−172304.	+	1.19840e6i	−0.000699023	+	0.00486181i
$628$	2.46681e7	+	8.40119e7i	0.0995995	+	0.339205i
$629$	2.88062e8	+	1.85126e8i	1.15753	+	0.743902i
$630$	−3.08264e6	+	6.75003e6i	−0.0123282	+	0.0269950i
$631$	−7.78811e7	+	2.65239e8i	−0.309987	+	1.05572i	0.646250	+	0.763126i	$0.276337\pi$
$631$	−7.78811e7	+	2.65239e8i	−0.309987	+	1.05572i	−0.956237	+	0.292594i	$0.905482\pi$
$632$	9.75303e7	−	8.45105e7i	0.386356	−	0.334780i
$633$	3.54508e7	+	4.09124e7i	0.139770	+	0.161304i
$634$	2.15402e7	+	6.32477e6i	0.0845243	+	0.0248186i
$635$	−1.12138e8	−	5.12116e7i	−0.437957	−	0.200008i
$636$	7.05819e7	−	1.09828e8i	0.274361	−	0.426914i
$637$	−3.95890e8	+	1.16244e8i	−1.53164	+	0.449730i
$638$	2.49063e6	+	358099.i	0.00959064	+	0.00137893i
$639$	−9.96534e6	−	2.18210e7i	−0.0381935	−	0.0836321i
$640$	6.22558e7	−	8.95103e6i	0.237487	−	0.0341455i
$641$	−2.17293e8	−	3.38115e8i	−0.825034	−	1.28378i	−0.956287	−	0.292429i	$-0.905537\pi$
$641$	−2.17293e8	−	3.38115e8i	−0.825034	−	1.28378i	0.131254	−	0.991349i	$-0.458100\pi$
$642$	9.10718e6	+	7.89142e6i	0.0344175	+	0.0298229i
$643$		−	2.54237e8i		−	0.956326i	−0.878271	−	0.478163i	$-0.841303\pi$
$643$		−	2.54237e8i		−	0.956326i	0.878271	−	0.478163i	$-0.158697\pi$
$644$	3.62459e8	+	1.70692e7i	1.35707	+	0.0639081i
$645$	−1.81605e7			−0.0676781
$646$	−5.67445e6	+	6.54866e6i	−0.0210487	+	0.0242915i
$647$	−6.59751e7	+	4.23996e7i	−0.243594	+	0.156549i	−0.656742	−	0.754116i	$-0.728066\pi$
$647$	−6.59751e7	+	4.23996e7i	−0.243594	+	0.156549i	0.413147	+	0.910664i	$0.364429\pi$
$648$	1.34096e6	+	9.32657e6i	0.00492822	+	0.0342765i
$649$	−1.02510e7	+	4.68150e6i	−0.0375003	+	0.0171258i
$650$	8.74447e6	−	6.08191e7i	0.0318415	−	0.221463i
$651$	−1.75759e7	−	5.98582e7i	−0.0637053	−	0.216960i
$652$	4.07748e8	+	2.62044e8i	1.47112	+	0.945434i
$653$	1.41784e8	−	3.10463e8i	0.509198	−	1.11499i	−0.464171	−	0.885746i	$-0.653648\pi$
$653$	1.41784e8	−	3.10463e8i	0.509198	−	1.11499i	0.973369	−	0.229243i	$-0.0736251\pi$
$654$	−1.08276e6	+	3.68753e6i	−0.00387077	+	0.0131826i
$655$	1.17026e8	−	1.01404e8i	0.416447	−	0.360854i
$656$	2.68968e8	+	3.10406e8i	0.952774	+	1.09956i
$657$	6.43564e7	+	1.88968e7i	0.226932	+	0.0666333i
$658$	−6.14548e7	−	2.80654e7i	−0.215714	−	0.0985132i
$659$	1.86010e8	−	2.89437e8i	0.649949	−	1.01134i	−0.347339	−	0.937740i	$-0.612915\pi$
$659$	1.86010e8	−	2.89437e8i	0.649949	−	1.01134i	0.997288	−	0.0736008i	$-0.0234491\pi$
$660$	3.40037e6	−	998440.i	0.0118276	−	0.00347288i
$661$	1.59803e7	+	2.29763e6i	0.0553327	+	0.00795564i	0.169926	−	0.985457i	$-0.445647\pi$
$661$	1.59803e7	+	2.29763e6i	0.0553327	+	0.00795564i	−0.114593	+	0.993413i	$0.536556\pi$
$662$	−3.00478e7	−	6.57955e7i	−0.103571	−	0.226789i
$663$	3.65688e8	−	5.25780e7i	1.25479	−	0.180411i
$664$	−4.63046e7	−	7.20513e7i	−0.158168	−	0.246115i
$665$	−1.97306e7	−	1.70967e7i	−0.0670927	−	0.0581361i
$666$		−	1.65146e7i		−	0.0559044i
$667$	1.95328e8	−	2.74614e8i	0.658243	−	0.925434i
$668$	−783753.			−0.00262936
$669$	−2.36572e6	+	2.73019e6i	−0.00790105	+	0.00911830i
$670$	−9.59710e6	+	6.16768e6i	−0.0319092	+	0.0205068i
$671$	3.07233e6	+	2.13685e7i	0.0101695	+	0.0707304i
$672$	−1.01646e8	+	4.64202e7i	−0.334952	+	0.152967i
$673$	−5.28129e7	+	3.67322e8i	−0.173259	+	1.20504i	0.698683	+	0.715431i	$0.253770\pi$
$673$	−5.28129e7	+	3.67322e8i	−0.173259	+	1.20504i	−0.871942	+	0.489609i	$0.837139\pi$
$674$	1.36285e7	+	4.64145e7i	0.0445112	+	0.151591i
$675$	−4.16261e7	−	2.67515e7i	−0.135349	−	0.0869835i
$676$	−2.34826e8	+	5.14197e8i	−0.760161	+	1.66452i
$677$	−7.49297e7	+	2.55187e8i	−0.241484	+	0.822418i	0.746169	+	0.665757i	$0.231891\pi$
$677$	−7.49297e7	+	2.55187e8i	−0.241484	+	0.822418i	−0.987652	+	0.156661i	$0.949927\pi$
$678$	4.11353e7	−	3.56439e7i	0.131985	−	0.114366i
$679$	−9.05999e7	−	1.04558e8i	−0.289413	−	0.334001i
$680$	4.92944e7	+	1.44741e7i	0.156773	+	0.0460326i
$681$	1.70301e7	+	7.77740e6i	0.0539233	+	0.0246259i
$682$	411313.	−	640015.i	0.00129664	−	0.00201761i
$683$	−6.24178e7	+	1.83275e7i	−0.195905	+	0.0575230i	−0.378213	−	0.925718i	$-0.623461\pi$
$683$	−6.24178e7	+	1.83275e7i	−0.195905	+	0.0575230i	0.182308	+	0.983241i	$0.441643\pi$
$684$	−1.61996e7	−	2.32915e6i	−0.0506216	−	0.00727829i
$685$	−1.99990e7	−	4.37917e7i	−0.0622209	−	0.136245i
$686$	−4.13197e6	+	594088.i	−0.0127993	+	0.00184026i
$687$	−1.06791e8	−	1.66170e8i	−0.329356	−	0.512487i
$688$	−6.59650e7	−	5.71590e7i	−0.202557	−	0.175517i
$689$			5.00061e8i			1.52885i
$690$	−2.28723e6	+	1.19020e7i	−0.00696244	+	0.0362302i
$691$	−1.96062e8			−0.594236			−0.297118	−	0.954841i	$-0.596026\pi$
$691$	−1.96062e8			−0.594236			−0.297118	+	0.954841i	$0.596026\pi$
$692$	1.84918e7	−	2.13407e7i	0.0558035	−	0.0644007i
$693$	−7.03056e6	+	4.51827e6i	−0.0211247	+	0.0135760i
$694$	6.95952e6	+	4.84045e7i	0.0208210	+	0.144813i
$695$	1.52636e8	−	6.97065e7i	0.454676	−	0.207644i
$696$	−9.80497e6	+	6.81950e7i	−0.0290816	+	0.202267i
$697$	1.94059e8	+	6.60906e8i	0.573108	+	1.95183i
$698$	2.09270e7	+	1.34490e7i	0.0615377	+	0.0395479i
$699$	−8.35032e7	+	1.82846e8i	−0.244496	+	0.535371i
$700$	1.09755e8	−	3.73791e8i	0.319985	−	1.08977i
$701$	2.89550e8	−	2.50897e8i	0.840563	−	0.728352i	−0.123978	−	0.992285i	$-0.539565\pi$
$701$	2.89550e8	−	2.50897e8i	0.840563	−	0.728352i	0.964541	+	0.263933i	$0.0850199\pi$
$702$	−1.16684e7	−	1.34661e7i	−0.0337288	−	0.0389251i
$703$	5.57484e7	+	1.63692e7i	0.160460	+	0.0471153i
$704$	1.46499e7	+	6.69038e6i	0.0419872	+	0.0191749i
$705$	−4.77765e7	+	7.43417e7i	−0.136347	+	0.212161i
$706$	5.82849e7	−	1.71140e7i	0.165631	−	0.0486337i
$707$	−7.08821e8	−	1.01913e8i	−2.00576	−	0.288384i
$708$	−6.32832e7	−	1.38571e8i	−0.178315	−	0.390456i
$709$	2.95149e8	−	4.24360e7i	0.828138	−	0.119068i	0.284805	−	0.958586i	$-0.408071\pi$
$709$	2.95149e8	−	4.24360e7i	0.828138	−	0.119068i	0.543333	+	0.839517i	$0.317162\pi$
$710$	3.41051e6	+	5.30685e6i	0.00952892	+	0.0148273i
$711$	1.48523e8	+	1.28696e8i	0.413223	+	0.358060i
$712$			1.97507e8i			0.547196i
$713$	−5.09932e7	−	8.82123e7i	−0.140684	−	0.243366i
$714$	−5.98127e7			−0.164323
$715$	−8.88939e6	+	1.02589e7i	−0.0243195	+	0.0280661i
$716$	−4.04029e8	+	2.59654e8i	−1.10071	+	0.707385i
$717$	−3.78416e7	−	2.63194e8i	−0.102663	−	0.714034i
$718$	8.64840e7	−	3.94959e7i	0.233648	−	0.106704i
$719$	1.76967e7	−	1.23084e8i	0.0476109	−	0.331141i	−0.952070	−	0.305880i	$-0.901049\pi$
$719$	1.76967e7	−	1.23084e8i	0.0476109	−	0.331141i	0.999681	−	0.0252610i	$-0.00804168\pi$
$720$	1.31432e7	+	4.47616e7i	0.0352130	+	0.119925i
$721$	−1.98480e8	−	1.27556e8i	−0.529556	−	0.340325i
$722$	2.40602e7	−	5.26845e7i	0.0639276	−	0.139982i
$723$	4.88768e7	−	1.66459e8i	0.129327	−	0.440446i
$724$	−1.79070e8	+	1.55165e8i	−0.471853	+	0.408863i
$725$	−2.36930e8	−	2.73431e8i	−0.621735	−	0.717520i
$726$	3.33513e7	+	9.79282e6i	0.0871571	+	0.0255916i
$727$	−1.90180e7	−	8.68524e6i	−0.0494951	−	0.0226037i	0.390514	−	0.920597i	$-0.372297\pi$
$727$	−1.90180e7	−	8.68524e6i	−0.0494951	−	0.0226037i	−0.440009	+	0.897993i	$0.645025\pi$
$728$	1.53624e8	−	2.39044e8i	0.398167	−	0.619560i
$729$	−1.37677e7	+	4.04255e6i	−0.0355368	+	0.0104345i
$730$	−1.74585e7	−	2.51016e6i	−0.0448785	−	0.00645256i
$731$	−6.08083e7	−	1.33152e8i	−0.155672	−	0.340875i
$732$	−2.88853e8	+	4.15308e7i	−0.736451	+	0.105886i
$733$	−3.74886e8	−	5.83334e8i	−0.951891	−	1.48117i	−0.874995	−	0.484131i	$-0.839136\pi$
$733$	−3.74886e8	−	5.83334e8i	−0.951891	−	1.48117i	−0.0768952	−	0.997039i	$-0.524501\pi$
$734$	−3.10023e7	−	2.68637e7i	−0.0783982	−	0.0679324i
$735$		−	8.73753e7i		−	0.220053i
$736$	−1.43398e8	+	1.12896e8i	−0.359676	+	0.283168i
$737$	−1.28480e7			−0.0320947
$738$	2.17549e7	−	2.51064e7i	0.0541237	−	0.0624620i
$739$	−3.95273e8	+	2.54027e8i	−0.979408	+	0.629428i	−0.929304	−	0.369316i	$-0.879592\pi$
$739$	−3.95273e8	+	2.54027e8i	−0.979408	+	0.629428i	−0.0501046	+	0.998744i	$0.515955\pi$
$740$	−2.42037e7	−	1.68341e8i	−0.0597292	−	0.415426i
$741$	5.70231e7	−	2.60416e7i	0.140151	−	0.0640048i
$742$	1.15216e7	−	8.01345e7i	0.0282034	−	0.196159i
$743$	1.19850e8	+	4.08173e8i	0.292195	+	0.995126i	0.966499	+	0.256671i	$0.0826258\pi$
$743$	1.19850e8	+	4.08173e8i	0.292195	+	0.995126i	−0.674303	+	0.738454i	$0.735556\pi$
$744$	1.75240e7	+	1.12620e7i	0.0425515	+	0.0273462i
$745$	−9.26035e7	+	2.02773e8i	−0.223954	+	0.490391i
$746$	7.38858e6	−	2.51632e7i	0.0177969	−	0.0606107i
$747$	9.85705e7	−	8.54118e7i	0.236475	−	0.204907i
$748$	1.87063e7	+	2.15882e7i	0.0446974	+	0.0515836i
$749$	−2.80795e8	−	8.24488e7i	−0.668257	−	0.196218i
$750$	2.59938e7	+	1.18710e7i	0.0616149	+	0.0281386i
$751$	−4.39778e8	+	6.84307e8i	−1.03828	+	1.61559i	−0.284248	+	0.958751i	$0.591744\pi$
$751$	−4.39778e8	+	6.84307e8i	−1.03828	+	1.61559i	−0.754030	+	0.656840i	$0.771893\pi$
$752$	−4.07526e8	+	1.19660e8i	−0.958301	+	0.281383i
$753$	1.40084e7	+	2.01410e6i	0.0328097	+	0.00471733i
$754$	−5.41223e7	−	1.18511e8i	−0.126259	−	0.276469i
$755$	8.15067e7	−	1.17189e7i	0.189388	−	0.0272299i
$756$	−6.10766e7	−	9.50371e7i	−0.141355	−	0.219952i
$757$	−8.47138e7	−	7.34049e7i	−0.195284	−	0.169214i	0.551730	−	0.834023i	$-0.313968\pi$
$757$	−8.47138e7	−	7.34049e7i	−0.195284	−	0.169214i	−0.747014	+	0.664808i	$0.768513\pi$
$758$			6.55659e7i			0.150546i
$759$	−9.41386e6	+	9.88369e6i	−0.0215299	+	0.0226044i
$760$	8.71741e6			0.0198585
$761$	3.92499e8	−	4.52968e8i	0.890603	−	1.02781i	−0.108827	−	0.994061i	$-0.534710\pi$
$761$	3.92499e8	−	4.52968e8i	0.890603	−	1.02781i	0.999430	−	0.0337500i	$-0.0107450\pi$
$762$	−4.03159e7	+	2.59095e7i	−0.0911196	+	0.0585590i
$763$	−1.32826e7	−	9.23828e7i	−0.0299027	−	0.207978i
$764$	−5.57631e8	+	2.54661e8i	−1.25045	+	0.571062i
$765$	−1.11342e7	+	7.74402e7i	−0.0248700	+	0.172974i
$766$	2.57023e7	+	8.75339e7i	0.0571854	+	0.194756i
$767$	4.90875e8	+	3.15466e8i	1.08789	+	0.699144i
$768$	−8.25910e7	+	1.80849e8i	−0.182326	+	0.399239i
$769$	1.23774e8	−	4.21535e8i	0.272176	−	0.926946i	−0.704043	−	0.710158i	$-0.748624\pi$
$769$	1.23774e8	−	4.21535e8i	0.272176	−	0.926946i	0.976219	−	0.216789i	$-0.0695582\pi$
$770$	1.66089e6	−	1.43917e6i	0.00363805	−	0.00315239i
$771$	4.54088e7	+	5.24045e7i	0.0990779	+	0.114342i
$772$	7.58735e8	+	2.22785e8i	1.64907	+	0.484209i
$773$	4.80904e7	+	2.19621e7i	0.104116	+	0.0475484i	0.466792	−	0.884367i	$-0.345410\pi$
$773$	4.80904e7	+	2.19621e7i	0.104116	+	0.0475484i	−0.362676	+	0.931915i	$0.618137\pi$
$774$	−3.81680e6	+	5.93906e6i	−0.00823145	+	0.0128084i
$775$	−1.04960e8	+	3.08189e7i	−0.225485	+	0.0662083i
$776$	4.57257e7	+	6.57437e6i	0.0978533	+	0.0140692i
$777$	1.66606e8	+	3.64817e8i	0.355164	+	0.777700i
$778$	5.99449e7	−	8.61877e6i	0.127296	−	0.0183023i
$779$	6.31885e7	+	9.83233e7i	0.133668	+	0.207991i
$780$	−1.38677e8	−	1.20164e8i	−0.292227	−	0.253216i
$781$			7.10449e6i			0.0149135i
$782$	−9.49230e7	+	2.30825e7i	−0.198496	+	0.0482685i
$783$	−1.04918e8			−0.218557
$784$	2.75008e8	−	3.17376e8i	0.570686	−	0.658607i
$785$	5.97475e7	−	3.83974e7i	0.123512	−	0.0793767i
$786$	−8.56682e6	−	5.95835e7i	−0.0176422	−	0.122704i
$787$	−2.21049e8	+	1.00950e8i	−0.453487	+	0.207100i	−0.629045	−	0.777368i	$-0.716554\pi$
$787$	−2.21049e8	+	1.00950e8i	−0.453487	+	0.207100i	0.175559	+	0.984469i	$0.443827\pi$
$788$	2.00632e7	−	1.39542e8i	0.0410035	−	0.285186i
$789$	1.22686e8	+	4.17831e8i	0.249784	+	0.850687i
$790$	−4.34753e7	−	2.79399e7i	−0.0881782	−	0.0566687i
$791$	−5.49111e8	+	1.20238e9i	−1.10951	+	2.42948i
$792$	786185.	−	2.67750e6i	0.00158252	−	0.00538957i
$793$	8.44766e8	−	7.31994e8i	1.69401	−	1.46787i
$794$	−5.20879e7	−	6.01127e7i	−0.104058	−	0.120089i
$795$	−1.01606e8	−	2.98343e7i	−0.202218	−	0.0593764i
$796$	5.01950e8	+	2.29233e8i	0.995225	+	0.454504i
$797$	−2.20212e8	+	3.42657e8i	−0.434977	+	0.676837i	−0.987670	−	0.156547i	$-0.949964\pi$
$797$	−2.20212e8	+	3.42657e8i	−0.434977	+	0.676837i	0.552694	+	0.833385i	$0.313600\pi$
$798$	−9.73794e6	+	2.85932e6i	−0.0191628	+	0.00562670i
$799$	−7.05044e8	−	1.01370e8i	−1.38222	−	0.198733i
$800$	8.13966e7	+	1.78234e8i	0.158978	+	0.348113i
$801$	−2.97710e8	+	4.28043e7i	−0.579290	+	0.0832894i
$802$	−8.88814e6	−	1.38302e7i	−0.0172301	−	0.0268106i
$803$	−1.50124e7	−	1.30083e7i	−0.0289938	−	0.0251232i
$804$		−	1.73676e8i		−	0.334173i
$805$	−6.95458e7	−	2.85995e8i	−0.133316	−	0.548241i
$806$	−3.93917e7			−0.0752315
$807$	−8.54969e6	+	9.86687e6i	−0.0162678	+	0.0187741i
$808$	2.01155e8	−	1.29275e8i	0.381327	−	0.245064i
$809$	1.07592e8	+	7.48316e8i	0.203204	+	1.41332i	0.794697	+	0.607006i	$0.207630\pi$
$809$	1.07592e8	+	7.48316e8i	0.203204	+	1.41332i	−0.591493	+	0.806310i	$0.701461\pi$
$810$	3.43230e6	−	1.56748e6i	0.00645847	−	0.00294948i
$811$	2.26655e7	−	1.57642e8i	0.0424916	−	0.295536i	−0.957484	−	0.288488i	$-0.906848\pi$
$811$	2.26655e7	−	1.57642e8i	0.0424916	−	0.295536i	0.999975	−	0.00704780i	$-0.00224340\pi$
$812$	−2.32720e8	−	7.92573e8i	−0.434677	−	1.48037i
$813$	−2.18825e8	−	1.40630e8i	−0.407216	−	0.261702i
$814$	−2.03177e6	+	4.44895e6i	−0.00376704	+	0.00824867i
$815$	1.10763e8	−	3.77225e8i	0.204608	−	0.696832i
$816$	−2.84181e8	+	2.46244e8i	−0.523028	+	0.453206i
$817$	−1.62653e7	−	1.87711e7i	−0.0298260	−	0.0344211i
$818$	−6.64360e7	−	1.95074e7i	−0.121379	−	0.0356401i
$819$	3.93613e8	+	1.79757e8i	0.716503	+	0.327216i
$820$	1.84961e8	−	2.87804e8i	0.335458	−	0.521982i
$821$	−1.86856e8	+	5.48658e7i	−0.337658	+	0.0991453i	−0.446166	−	0.894950i	$-0.647211\pi$
$821$	−1.86856e8	+	5.48658e7i	−0.337658	+	0.0991453i	0.108508	+	0.994096i	$0.465393\pi$
$822$	−1.85245e7	−	2.66342e6i	−0.0333527	−	0.00479539i
$823$	4.08394e8	+	8.94257e8i	0.732621	+	1.60422i	0.795324	+	0.606184i	$0.207301\pi$
$823$	4.08394e8	+	8.94257e8i	0.732621	+	1.60422i	−0.0627030	+	0.998032i	$0.519972\pi$
$824$	7.79781e7	−	1.12116e7i	0.139377	−	0.0200394i
$825$	7.92266e6	+	1.23279e7i	0.0141094	+	0.0219547i
$826$	−7.13940e7	−	6.18633e7i	−0.126684	−	0.109772i
$827$			1.25087e8i			0.221154i	0.993868	+	0.110577i	$0.0352698\pi$
$827$			1.25087e8i			0.221154i	−0.993868	+	0.110577i	$0.964730\pi$
$828$	−1.33605e8	−	1.27254e8i	−0.235359	−	0.224171i
$829$	3.53007e8			0.619612			0.309806	−	0.950800i	$-0.399736\pi$
$829$	3.53007e8			0.619612			0.309806	+	0.950800i	$0.399736\pi$
$830$	−2.24604e7	+	2.59207e7i	−0.0392811	+	0.0453328i
$831$	2.63772e8	−	1.69516e8i	0.459648	−	0.295398i
$832$	−1.18675e8	−	8.25405e8i	−0.206058	−	1.43317i
$833$	6.40631e8	−	2.92566e8i	1.10834	−	0.506162i
$834$	9.28334e6	−	6.45671e7i	0.0160032	−	0.111305i
$835$	179106.	+	609979.i	0.000307645	+	0.00104774i
$836$	4.07753e6	+	2.62047e6i	0.00697876	+	0.00448498i
$837$	−1.31778e7	+	2.88553e7i	−0.0224733	+	0.0492096i
$838$	−2.60577e7	+	8.87444e7i	−0.0442797	+	0.150803i
$839$	3.18357e8	−	2.75858e8i	0.539049	−	0.467088i	−0.342276	−	0.939599i	$-0.611198\pi$
$839$	3.18357e8	−	2.75858e8i	0.539049	−	0.467088i	0.881325	+	0.472511i	$0.156652\pi$
$840$	3.94053e7	+	4.54762e7i	0.0664840	+	0.0767266i
$841$	−1.65347e8	−	4.85503e7i	−0.277977	−	0.0816215i
$842$	6.31743e7	+	2.88507e7i	0.105829	+	0.0483304i
$843$	5.73040e7	−	8.91668e7i	0.0956538	−	0.148840i
$844$	2.07943e8	−	6.10577e7i	0.345874	−	0.101558i
$845$	4.53852e8	+	6.52540e7i	0.752218	+	0.108153i
$846$	1.42709e7	+	3.12489e7i	0.0235689	+	0.0516087i
$847$	−8.35543e8	+	1.20133e8i	−1.37505	+	0.197702i
$848$	−2.75166e8	−	4.28167e8i	−0.451240	−	0.702144i
$849$	−1.03019e8	−	8.92664e7i	−0.168343	−	0.145870i
$850$			1.04880e8i			0.170780i
$851$	4.05193e8	+	5.14671e8i	0.657466	+	0.835104i
$852$	−9.60365e7			−0.155281
$853$	3.87443e7	−	4.47133e7i	0.0624252	−	0.0720426i	−0.723678	−	0.690138i	$-0.757550\pi$
$853$	3.87443e7	−	4.47133e7i	0.0624252	−	0.0720426i	0.786103	+	0.618095i	$0.212095\pi$
$854$	−1.52239e8	+	9.78379e7i	−0.244428	+	0.157085i
$855$	1.88926e6	+	1.31401e7i	0.00302269	+	0.0210232i
$856$	8.88869e7	−	4.05933e7i	0.141715	−	0.0647192i
$857$	8.54589e7	−	5.94380e8i	0.135773	−	0.944325i	−0.802061	−	0.597242i	$-0.796263\pi$
$857$	8.54589e7	−	5.94380e8i	0.135773	−	0.944325i	0.937835	−	0.347083i	$-0.112828\pi$
$858$	1.48670e6	+	5.06323e6i	0.00235375	+	0.00801615i
$859$	−1.82798e8	−	1.17477e8i	−0.288398	−	0.185342i	0.388440	−	0.921474i	$-0.373014\pi$
$859$	−1.82798e8	−	1.17477e8i	−0.288398	−	0.185342i	−0.676838	+	0.736132i	$0.736650\pi$
$860$	−3.02020e7	+	6.61332e7i	−0.0474833	+	0.103974i
$861$	−2.27293e8	+	7.74088e8i	−0.356103	+	1.21278i
$862$	6.29905e7	−	5.45816e7i	0.0983452	−	0.0852166i
$863$	−2.82253e8	−	3.25737e8i	−0.439143	−	0.506798i	0.492430	−	0.870352i	$-0.336109\pi$
$863$	−2.82253e8	−	3.25737e8i	−0.439143	−	0.506798i	−0.931573	+	0.363554i	$0.881563\pi$
$864$	5.45187e7	+	1.60081e7i	0.0845287	+	0.0248199i
$865$	−2.08349e7	−	9.51496e6i	−0.0321916	−	0.0147014i
$866$	−8.08269e7	+	1.25769e8i	−0.124452	+	0.193651i
$867$	−2.44043e8	+	7.16574e7i	−0.374463	+	0.109952i
$868$	−2.47209e8	−	3.55433e7i	−0.378012	−	0.0543499i
$869$	−2.41780e7	−	5.29425e7i	−0.0368435	−	0.0806761i
$870$	2.73091e7	−	3.92645e6i	0.0414714	−	0.00596269i
$871$	3.59655e8	+	5.59634e8i	0.544292	+	0.846934i
$872$	2.35525e7	+	2.04084e7i	0.0355212	+	0.0307793i
$873$			7.03490e7i			0.105734i
$874$	−1.43507e7	+	8.29575e6i	−0.0214951	+	0.0124257i
$875$	−6.93977e8			−1.03591
$876$	1.75843e8	−	2.02934e8i	0.261585	−	0.301885i
$877$	1.07037e9	−	6.87882e8i	1.58684	−	1.01980i	0.613714	−	0.789529i	$-0.289675\pi$
$877$	1.07037e9	−	6.87882e8i	1.58684	−	1.01980i	0.973126	−	0.230272i	$-0.0739615\pi$
$878$	1.37929e7	+	9.59315e7i	0.0203784	+	0.141735i
$879$	−1.37057e8	+	6.25918e7i	−0.201806	+	0.0921617i
$880$	1.96624e6	−	1.36755e7i	0.00288529	−	0.0200676i
$881$	2.27782e8	+	7.75753e8i	0.333113	+	1.13448i	0.940421	+	0.340011i	$0.110431\pi$
$881$	2.27782e8	+	7.75753e8i	0.333113	+	1.13448i	−0.607309	+	0.794466i	$0.707751\pi$
$882$	−2.85745e7	−	1.83637e7i	−0.0416460	−	0.0267642i
$883$	2.24936e8	−	4.92540e8i	0.326720	−	0.715418i	−0.672986	−	0.739655i	$-0.734989\pi$
$883$	2.24936e8	−	4.92540e8i	0.326720	−	0.715418i	0.999706	+	0.0242375i	$0.00771579\pi$
$884$	4.16694e8	−	1.41913e9i	0.603198	−	2.05430i
$885$	−9.33851e7	+	8.09187e7i	−0.134725	+	0.116740i
$886$	8.84615e7	+	1.02090e8i	0.127190	+	0.146785i
$887$	7.35097e8	+	2.15844e8i	1.05335	+	0.309292i	0.762171	−	0.647376i	$-0.224133\pi$
$887$	7.35097e8	+	2.15844e8i	1.05335	+	0.309292i	0.291181	+	0.956668i	$0.405952\pi$
$888$	−1.21815e8	−	5.56310e7i	−0.173965	−	0.0794471i
$889$	6.29216e8	−	9.79079e8i	0.895559	−	1.39352i
$890$	7.58890e7	−	2.22830e7i	0.107649	−	0.0316085i
$891$	4.20628e6	+	604772.i	0.00594656	+	0.000854986i
$892$	6.00790e6	+	1.31555e7i	0.00846503	+	0.0185358i
$893$	−1.19632e8	+	1.72005e7i	−0.167994	+	0.0241539i
$894$	4.68508e7	+	7.29013e7i	0.0655699	+	0.102029i
$895$	2.94413e8	+	2.55111e8i	0.410666	+	0.355844i
$896$			5.93782e8i			0.825473i
$897$	6.94037e8	+	1.33375e8i	0.961624	+	0.184797i
$898$	−9.36820e7			−0.129368
$899$	−1.51894e8	+	1.75295e8i	−0.209055	+	0.241263i
$900$	−1.66645e8	+	1.07096e8i	−0.228594	+	0.146908i
$901$	−1.21474e8	−	8.44868e8i	−0.166076	−	1.15509i
$902$	−8.94944e6	+	4.08707e6i	−0.0121948	+	0.00556920i
$903$	2.43995e7	−	1.69703e8i	0.0331374	−	0.230476i
$904$	−1.24348e8	−	4.23491e8i	−0.168320	−	0.573244i
$905$	1.61683e8	+	1.03907e8i	0.218132	+	0.140185i
$906$	1.32979e7	−	2.91182e7i	0.0178812	−	0.0391544i
$907$	2.96544e8	−	1.00994e9i	0.397436	−	1.35354i	−0.481435	−	0.876482i	$-0.659884\pi$
$907$	2.96544e8	−	1.00994e9i	0.397436	−	1.35354i	0.878871	−	0.477060i	$-0.158298\pi$
$908$	5.66443e7	−	4.90826e7i	0.0756657	−	0.0655647i
$909$	2.38456e8	+	2.75193e8i	0.317480	+	0.366391i
$910$	−1.09181e8	−	3.20584e7i	−0.144884	−	0.0425419i
$911$	−6.12081e8	−	2.79528e8i	−0.809569	−	0.369718i	−0.0327675	−	0.999463i	$-0.510432\pi$
$911$	−6.12081e8	−	2.79528e8i	−0.809569	−	0.369718i	−0.776802	+	0.629745i	$0.783159\pi$
$912$	−3.44952e7	+	5.36755e7i	−0.0454751	+	0.0707606i
$913$	−3.70624e7	+	1.08825e7i	−0.0486992	+	0.0142994i
$914$	3.50150e6	+	503440.i	0.00458581	+	0.000659339i
$915$	9.83323e7	+	2.15318e8i	0.128361	+	0.281071i
$916$	−7.82726e8	+	1.12539e8i	−1.01841	+	0.146425i
$917$	7.90350e8	+	1.22981e9i	1.02497	+	1.59488i
$918$	2.29853e7	+	1.99169e7i	0.0297113	+	0.0257450i
$919$		−	1.47625e8i		−	0.190201i	−0.995468	−	0.0951003i	$-0.969683\pi$
$919$		−	1.47625e8i		−	0.190201i	0.995468	−	0.0951003i	$-0.0303172\pi$
$920$	8.00863e7	+	5.69638e7i	0.102848	+	0.0731536i
$921$	7.74178e7			0.0990973
$922$	7.20448e7	−	8.31442e7i	0.0919200	−	0.106081i
$923$	3.09457e8	−	1.98876e8i	0.393546	−	0.252917i
$924$	4.76145e6	+	3.31166e7i	0.00603564	+	0.0419788i
$925$	6.39697e8	−	2.92140e8i	0.808257	−	0.369119i
$926$	−1.22509e7	+	8.52066e7i	−0.0154289	+	0.107310i
$927$	3.37992e7	+	1.15110e8i	0.0424295	+	0.144501i
$928$	3.49512e8	+	2.24617e8i	0.437339	+	0.281060i
$929$	−2.66195e8	+	5.82885e8i	−0.332011	+	0.727002i	−0.999850	−	0.0173033i	$-0.994492\pi$
$929$	−2.66195e8	+	5.82885e8i	−0.332011	+	0.727002i	0.667840	+	0.744305i	$0.267219\pi$
$930$	2.35016e6	−	8.00391e6i	0.00292179	−	0.00995070i
$931$	9.03133e7	−	7.82570e7i	0.111919	−	0.0969782i
$932$	5.26982e8	+	6.08170e8i	0.650951	+	0.751237i
$933$	−3.65892e8	−	1.07435e8i	−0.450513	−	0.132283i
$934$	−8.65629e7	−	3.95320e7i	−0.106241	−	0.0485185i
$935$	1.25268e7	−	1.94921e7i	0.0153252	−	0.0238465i
$936$	−1.38634e8	+	4.07067e7i	−0.169061	+	0.0496408i
$937$	2.87803e8	+	4.13798e7i	0.349846	+	0.0503002i	0.314998	−	0.949092i	$-0.397996\pi$
$937$	2.87803e8	+	4.13798e7i	0.349846	+	0.0503002i	0.0348478	+	0.999393i	$0.488905\pi$
$938$	−4.47404e7	−	9.79677e7i	−0.0542115	−	0.118707i
$939$	−8.43631e8	+	1.21296e8i	−1.01896	+	0.146504i
$940$	1.91267e8	+	2.97618e8i	0.230280	+	0.358323i
$941$	−7.22368e8	−	6.25935e8i	−0.866941	−	0.751209i	0.102966	−	0.994685i	$-0.467167\pi$
$941$	−7.22368e8	−	6.25935e8i	−0.866941	−	0.751209i	−0.969907	+	0.243476i	$0.921712\pi$
$942$		−	2.76093e7i		−	0.0330296i
$943$	−6.19833e7	+	1.31620e9i	−0.0739162	+	1.56959i
$944$	−5.93892e8			−0.705979
$945$	−6.00080e7	+	6.92529e7i	−0.0711072	+	0.0820621i
$946$	1.75890e6	−	1.13037e6i	0.00207762	−	0.00133521i
$947$	1.36652e8	+	9.50437e8i	0.160904	+	1.11911i	0.896935	+	0.442163i	$0.145789\pi$
$947$	1.36652e8	+	9.50437e8i	0.160904	+	1.11911i	−0.736031	+	0.676948i	$0.763302\pi$
$948$	7.15661e8	−	3.26831e8i	0.840006	−	0.383618i
$949$	−1.46374e8	+	1.01806e9i	−0.171264	+	1.19117i
$950$	5.01374e6	+	1.70752e7i	0.00584778	+	0.0199157i
$951$	2.33214e8	+	1.49878e8i	0.271152	+	0.174259i
$952$	−2.01485e8	+	4.41190e8i	−0.233524	+	0.511346i
$953$	3.15062e8	−	1.07300e9i	0.364013	−	1.23972i	−0.550389	−	0.834909i	$-0.685520\pi$
$953$	3.15062e8	−	1.07300e9i	0.364013	−	1.23972i	0.914402	−	0.404807i	$-0.132661\pi$
$954$	−3.11114e7	+	2.69582e7i	−0.0358323	+	0.0310488i
$955$	3.25629e8	+	3.75796e8i	0.373864	+	0.431462i
$956$	−1.02138e9	−	2.99905e8i	−1.16900	−	0.343249i
$957$	2.82643e7	+	1.29079e7i	0.0322480	+	0.0147272i
$958$	5.33967e7	−	8.30869e7i	0.0607321	−	0.0945010i
$959$	4.36086e8	−	1.28046e8i	0.494443	−	0.145182i
$960$	1.74792e8	+	2.51314e7i	0.197565	+	0.0284055i
$961$	−3.39549e8	−	7.43510e8i	−0.382589	−	0.837754i
$962$	2.50663e8	−	3.60399e7i	0.281556	−	0.0404816i
$963$	8.04516e7	+	1.25185e8i	0.0900857	+	0.140176i
$964$	−5.24892e8	−	4.54822e8i	−0.585921	−	0.507704i
$965$		−	6.41419e8i		−	0.713773i
$966$	−1.08146e8	−	3.73641e7i	−0.119972	−	0.0414499i
$967$	−2.00594e8			−0.221839			−0.110920	−	0.993829i	$-0.535380\pi$
$967$	−2.00594e8			−0.221839			−0.110920	+	0.993829i	$0.535380\pi$
$968$	1.84581e8	−	2.13017e8i	0.203498	−	0.234849i
$969$	−9.00164e7	+	5.78500e7i	−0.0989351	+	0.0635817i
$970$	−2.63274e6	−	1.83111e7i	−0.00288465	−	0.0200632i
$971$	−1.03329e9	+	4.71888e8i	−1.12867	+	0.515444i	−0.890138	−	0.455691i	$-0.849392\pi$
$971$	−1.03329e9	+	4.71888e8i	−1.12867	+	0.515444i	−0.238528	+	0.971136i	$0.576665\pi$
$972$	−8.17514e6	+	5.68594e7i	−0.00890218	+	0.0619160i
$973$	4.46306e8	+	1.51998e9i	0.484500	+	1.65006i
$974$	4.52045e7	+	2.90511e7i	0.0489220	+	0.0314403i
$975$	3.15200e8	−	6.90191e8i	0.340073	−	0.744655i
$976$	−3.20523e8	+	1.09160e9i	−0.344754	+	1.17413i
$977$	−3.72946e8	+	3.23159e8i	−0.399910	+	0.346524i	−0.831479	−	0.555556i	$-0.812505\pi$
$977$	−3.72946e8	+	3.23159e8i	−0.399910	+	0.346524i	0.431569	+	0.902080i	$0.357960\pi$
$978$	−1.00085e8	−	1.15505e8i	−0.106993	−	0.123476i
$979$	8.54676e7	+	2.50956e7i	0.0910864	+	0.0267454i
$980$	−3.18186e8	−	1.45311e8i	−0.338067	−	0.154390i
$981$	−2.56580e7	+	3.99246e7i	−0.0271778	+	0.0422896i
$982$	−2.84287e8	+	8.34742e7i	−0.300208	+	0.0881491i
$983$	−1.77684e9	−	2.55470e8i	−1.87062	−	0.268955i	−0.888737	−	0.458418i	$-0.848416\pi$
$983$	−1.77684e9	−	2.55470e8i	−1.87062	−	0.268955i	−0.981888	+	0.189463i	$0.939325\pi$
$984$	−1.11907e8	−	2.45041e8i	−0.117455	−	0.257190i
$985$	−1.13188e8	+	1.62740e7i	−0.118438	+	0.0170288i
$986$	1.20230e8	+	1.87081e8i	0.125424	+	0.195164i
$987$	−6.30504e8	−	5.46335e8i	−0.655747	−	0.568208i
$988$		−	2.50964e8i		−	0.260220i
$989$	−2.67684e7	−	2.78735e8i	−0.0276715	−	0.288139i
$990$	−1.11749e6			−0.00115169
$991$	9.29433e7	−	1.07262e8i	0.0954987	−	0.110211i	−0.705989	−	0.708223i	$-0.749497\pi$
$991$	9.29433e7	−	1.07262e8i	0.0954987	−	0.110211i	0.801487	+	0.598012i	$0.204042\pi$
$992$	1.05675e8	−	6.79132e7i	0.108252	−	0.0695695i
$993$	−1.27116e8	−	8.84112e8i	−0.129823	−	0.902941i
$994$	−5.41726e7	+	2.47398e7i	−0.0551595	+	0.0251905i
$995$	6.36999e7	−	4.43043e8i	0.0646650	−	0.449755i
$996$	−1.47107e8	−	5.00999e8i	−0.148886	−	0.507060i
$997$	−2.02846e8	−	1.30361e8i	−0.204683	−	0.131542i	0.434284	−	0.900776i	$-0.357001\pi$
$997$	−2.02846e8	−	1.30361e8i	−0.204683	−	0.131542i	−0.638967	+	0.769234i	$0.720638\pi$
$998$	−1.19905e8	+	2.62554e8i	−0.120627	+	0.264136i
$999$	5.74547e7	−	1.95673e8i	0.0576274	−	0.196261i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.f.a.7.11	✓	240
23.10	odd	22	inner	69.7.f.a.10.11	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.f.a.7.11	✓	240	1.1	even	1	trivial
69.7.f.a.10.11	yes	240	23.10	odd	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	69.f (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.826670 + 0.954028i) q^{2} +(-13.1138 + 8.42776i) q^{3} +(8.88136 + 61.7712i) q^{4} +(46.0457 - 21.0284i) q^{5} +(2.80051 - 19.4779i) q^{6} +(134.637 + 458.531i) q^{7} +(-134.239 - 86.2703i) q^{8} +(100.946 - 221.041i) q^{9} +O(q^{10})\)	\(q+(-0.826670 + 0.954028i) q^{2} +(-13.1138 + 8.42776i) q^{3} +(8.88136 + 61.7712i) q^{4} +(46.0457 - 21.0284i) q^{5} +(2.80051 - 19.4779i) q^{6} +(134.637 + 458.531i) q^{7} +(-134.239 - 86.2703i) q^{8} +(100.946 - 221.041i) q^{9} +(-18.0029 + 61.3124i) q^{10} +(-54.3885 + 47.1279i) q^{11} +(-637.062 - 735.208i) q^{12} +(3575.30 + 1049.80i) q^{13} +(-548.752 - 250.607i) q^{14} +(-426.614 + 663.824i) q^{15} +(-3638.95 + 1068.49i) q^{16} +(-6295.59 - 905.170i) q^{17} +(127.430 + 279.033i) q^{18} +(-1068.24 + 153.590i) q^{19} +(1707.90 + 2657.54i) q^{20} +(-5630.00 - 4878.42i) q^{21} -90.8474i q^{22} +(-10817.5 - 5569.38i) q^{23} +2487.46 q^{24} +(-8554.19 + 9872.06i) q^{25} +(-3957.13 + 2543.09i) q^{26} +(539.088 + 3749.44i) q^{27} +(-27128.3 + 12389.1i) q^{28} +(-3941.76 + 27415.6i) q^{29} +(-280.638 - 955.765i) q^{30} +(7044.95 + 4527.51i) q^{31} +(6231.27 - 13644.6i) q^{32} +(316.060 - 1076.40i) q^{33} +(6067.94 - 5257.90i) q^{34} +(15841.6 + 18282.2i) q^{35} +(14550.5 + 4272.41i) q^{36} +(-48971.7 - 22364.6i) q^{37} +(736.552 - 1146.10i) q^{38} +(-55733.4 + 16364.8i) q^{39} +(-7995.26 - 1149.54i) q^{40} +(-44988.4 - 98510.8i) q^{41} +(9308.30 - 1338.33i) q^{42} +(12442.6 + 19361.0i) q^{43} +(-3394.19 - 2941.09i) q^{44} -12300.7i q^{45} +(14255.8 - 5716.14i) q^{46} +111990. q^{47} +(38715.6 - 44680.2i) q^{48} +(-93151.4 + 59864.8i) q^{49} +(-2346.73 - 16321.9i) q^{50} +(90188.0 - 41187.5i) q^{51} +(-33094.1 + 230174. i) q^{52} +(37808.5 + 128764. i) q^{53} +(-4022.72 - 2585.24i) q^{54} +(-1513.33 + 3313.74i) q^{55} +(21484.1 - 73168.1i) q^{56} +(12714.3 - 11017.0i) q^{57} +(-22896.7 - 26424.2i) q^{58} +(150250. + 44117.5i) q^{59} +(-44794.2 - 20456.8i) q^{60} +(162180. - 252357. i) q^{61} +(-10143.2 + 2978.32i) q^{62} +(114945. + 16526.6i) q^{63} +(-92965.5 - 203566. i) q^{64} +(186703. - 26843.8i) q^{65} +(765.640 + 1191.36i) q^{66} +(134923. + 116911. i) q^{67} -396926. i q^{68} +(188796. - 18131.1i) q^{69} -30537.5 q^{70} +(64647.6 - 74607.3i) q^{71} +(-32620.1 + 20963.7i) q^{72} +(39282.1 + 273213. i) q^{73} +(61819.9 - 28232.2i) q^{74} +(28979.0 - 201553. i) q^{75} +(-18974.8 - 64622.4i) q^{76} +(-28932.3 - 18593.7i) q^{77} +(30460.6 - 66699.5i) q^{78} +(-227848. + 775981. i) q^{79} +(-145089. + 125721. i) q^{80} +(-38668.9 - 44626.3i) q^{81} +(131173. + 38515.7i) q^{82} +(488235. + 222969. i) q^{83} +(251344. - 391099. i) q^{84} +(-308919. + 90706.9i) q^{85} +(-28756.8 - 4134.61i) q^{86} +(-179360. - 392744. i) q^{87} +(11366.8 - 1634.30i) q^{88} +(-669175. - 1.04126e6i) q^{89} +(11735.2 + 10168.6i) q^{90} +1.78073e6i q^{91} +(247954. - 717673. i) q^{92} -130543. q^{93} +(-92578.8 + 106842. i) q^{94} +(-45958.1 + 29535.5i) q^{95} +(33277.3 + 231448. i) q^{96} +(-263340. + 120263. i) q^{97} +(19892.8 - 138357. i) q^{98} +(4926.89 + 16779.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9}+O(q^{10}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9	\( 240 q + 20 q^{2} - 816 q^{4} + 324 q^{6} + 940 q^{8} - 5832 q^{9} - 384 q^{13} + 33816 q^{16} + 22880 q^{17} + 4860 q^{18} - 31680 q^{19} - 157696 q^{20} + 36488 q^{23} + 39204 q^{24} + 200664 q^{25} + 99032 q^{26} - 202752 q^{28} - 181712 q^{29} - 128496 q^{31} + 439300 q^{32} - 400026 q^{34} + 368744 q^{35} + 42282 q^{36} + 446688 q^{37} + 550550 q^{38} - 52488 q^{39} - 156750 q^{40} - 606080 q^{41} - 1274130 q^{42} - 429000 q^{43} - 867482 q^{44} + 309288 q^{46} + 1111152 q^{47} + 837864 q^{48} + 722136 q^{49} + 1786926 q^{50} + 463320 q^{51} - 812550 q^{52} - 367840 q^{53} - 354294 q^{54} - 398088 q^{55} - 3696550 q^{56} - 1240272 q^{57} + 1903134 q^{58} + 545800 q^{59} + 2450250 q^{60} - 495264 q^{61} + 488776 q^{62} - 2699808 q^{64} - 290400 q^{67} + 23328 q^{69} - 392616 q^{70} + 255392 q^{71} + 228420 q^{72} + 1346880 q^{73} - 5387470 q^{74} + 365472 q^{75} + 2123022 q^{76} + 6134240 q^{77} + 171072 q^{78} + 4025472 q^{79} + 10626462 q^{80} - 1417176 q^{81} + 2025492 q^{82} - 2474560 q^{83} - 8866152 q^{85} - 15634300 q^{86} - 611712 q^{87} - 10636560 q^{88} - 5901720 q^{89} + 6566394 q^{92} - 2484432 q^{93} + 13931490 q^{94} + 8183072 q^{95} - 4682124 q^{96} + 12319560 q^{97} + 14139580 q^{98} + 2993760 q^{99}+O(q^{100}) \) 240 * q + 20 * q^2 - 816 * q^4 + 324 * q^6 + 940 * q^8 - 5832 * q^9 - 384 * q^13 + 33816 * q^16 + 22880 * q^17 + 4860 * q^18 - 31680 * q^19 - 157696 * q^20 + 36488 * q^23 + 39204 * q^24 + 200664 * q^25 + 99032 * q^26 - 202752 * q^28 - 181712 * q^29 - 128496 * q^31 + 439300 * q^32 - 400026 * q^34 + 368744 * q^35 + 42282 * q^36 + 446688 * q^37 + 550550 * q^38 - 52488 * q^39 - 156750 * q^40 - 606080 * q^41 - 1274130 * q^42 - 429000 * q^43 - 867482 * q^44 + 309288 * q^46 + 1111152 * q^47 + 837864 * q^48 + 722136 * q^49 + 1786926 * q^50 + 463320 * q^51 - 812550 * q^52 - 367840 * q^53 - 354294 * q^54 - 398088 * q^55 - 3696550 * q^56 - 1240272 * q^57 + 1903134 * q^58 + 545800 * q^59 + 2450250 * q^60 - 495264 * q^61 + 488776 * q^62 - 2699808 * q^64 - 290400 * q^67 + 23328 * q^69 - 392616 * q^70 + 255392 * q^71 + 228420 * q^72 + 1346880 * q^73 - 5387470 * q^74 + 365472 * q^75 + 2123022 * q^76 + 6134240 * q^77 + 171072 * q^78 + 4025472 * q^79 + 10626462 * q^80 - 1417176 * q^81 + 2025492 * q^82 - 2474560 * q^83 - 8866152 * q^85 - 15634300 * q^86 - 611712 * q^87 - 10636560 * q^88 - 5901720 * q^89 + 6566394 * q^92 - 2484432 * q^93 + 13931490 * q^94 + 8183072 * q^95 - 4682124 * q^96 + 12319560 * q^97 + 14139580 * q^98 + 2993760 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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