LMFDB - Embedded newform 69.7.f.a.37.6

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			37.6
Character	$\chi$	$=$	69.37
Dual form			69.7.f.a.28.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.78187 + 2.28496i) q^{2} +(10.2083 + 11.7810i) q^{3} +(1.49619 - 0.961540i) q^{4} +(-172.710 + 24.8319i) q^{5} +(-106.358 - 68.3524i) q^{6} +(-306.304 - 139.884i) q^{7} +(330.469 - 381.382i) q^{8} +(-34.5825 + 240.527i) q^{9} +O(q^{10})$	\(q+(-7.78187 + 2.28496i) q^{2} +(10.2083 + 11.7810i) q^{3} +(1.49619 - 0.961540i) q^{4} +(-172.710 + 24.8319i) q^{5} +(-106.358 - 68.3524i) q^{6} +(-306.304 - 139.884i) q^{7} +(330.469 - 381.382i) q^{8} +(-34.5825 + 240.527i) q^{9} +(1287.26 - 587.874i) q^{10} +(-121.275 + 413.023i) q^{11} +(26.6013 + 7.81086i) q^{12} +(-640.014 - 1401.43i) q^{13} +(2703.24 + 388.668i) q^{14} +(-2055.61 - 1781.20i) q^{15} +(-1747.51 + 3826.51i) q^{16} +(-2186.75 + 3402.66i) q^{17} +(-280.478 - 1950.77i) q^{18} +(-1504.77 - 2341.46i) q^{19} +(-234.529 + 203.221i) q^{20} +(-1478.86 - 5036.53i) q^{21} -3491.20i q^{22} +(9586.02 + 7492.94i) q^{23} +7866.57 q^{24} +(14219.9 - 4175.35i) q^{25} +(8182.73 + 9443.37i) q^{26} +(-3186.66 + 2047.94i) q^{27} +(-592.792 + 85.2306i) q^{28} +(32098.4 + 20628.4i) q^{29} +(20066.5 + 9164.05i) q^{30} +(18941.1 - 21859.1i) q^{31} +(259.110 - 1802.15i) q^{32} +(-6103.81 + 2787.52i) q^{33} +(9242.09 - 31475.7i) q^{34} +(56375.2 + 16553.3i) q^{35} +(179.534 + 393.125i) q^{36} +(31212.2 + 4487.64i) q^{37} +(17060.0 + 14782.6i) q^{38} +(9976.83 - 21846.2i) q^{39} +(-47604.8 + 74074.6i) q^{40} +(-11418.0 - 79413.7i) q^{41} +(23016.6 + 35814.5i) q^{42} +(34028.7 - 29486.0i) q^{43} +(215.689 + 734.570i) q^{44} -42400.0i q^{45} +(-91718.2 - 36405.3i) q^{46} -132494. q^{47} +(-62919.1 + 18474.7i) q^{48} +(-2789.37 - 3219.10i) q^{49} +(-101117. + 64984.1i) q^{50} +(-62409.6 + 8973.14i) q^{51} +(-2305.12 - 1481.41i) q^{52} +(213629. + 97561.2i) q^{53} +(20118.7 - 23218.2i) q^{54} +(10689.1 - 74344.6i) q^{55} +(-154573. + 70591.3i) q^{56} +(12223.6 - 41629.9i) q^{57} +(-296920. - 87183.6i) q^{58} +(70155.4 + 153619. i) q^{59} +(-4788.27 - 688.449i) q^{60} +(-297267. - 257583. i) q^{61} +(-97449.4 + 213385. i) q^{62} +(44238.6 - 68836.6i) q^{63} +(-36213.4 - 251870. i) q^{64} +(145337. + 226149. i) q^{65} +(41129.7 - 35639.1i) q^{66} +(-51135.9 - 174153. i) q^{67} +7193.66i q^{68} +(9582.62 + 189423. i) q^{69} -476528. q^{70} +(332256. - 97559.1i) q^{71} +(80304.1 + 92675.8i) q^{72} +(56283.9 - 36171.5i) q^{73} +(-253144. + 36396.6i) q^{74} +(194351. + 124902. i) q^{75} +(-4502.82 - 2056.37i) q^{76} +(94922.2 - 109546. i) q^{77} +(-27720.6 + 192801. i) q^{78} +(-58948.5 + 26920.9i) q^{79} +(206792. - 704270. i) q^{80} +(-56657.1 - 16636.0i) q^{81} +(270311. + 591898. i) q^{82} +(-554734. - 79758.8i) q^{83} +(-7055.47 - 6113.60i) q^{84} +(293179. - 641973. i) q^{85} +(-197432. + 307211. i) q^{86} +(84646.5 + 588730. i) q^{87} +(117442. + 182743. i) q^{88} +(782815. - 678313. i) q^{89} +(96882.5 + 329951. i) q^{90} +518792. i q^{91} +(21547.2 + 1993.48i) q^{92} +450877. q^{93} +(1.03105e6 - 302744. i) q^{94} +(318031. + 367027. i) q^{95} +(23876.1 - 15344.3i) q^{96} +(-594426. + 85465.6i) q^{97} +(29062.0 + 18677.0i) q^{98} +(-95149.1 - 43453.1i) 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 $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{21}{22}\right)$	$1$

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 $

$2$	−7.78187	+	2.28496i	−0.972733	+	0.285620i	−0.729222	−	0.684278i	$-0.760118\pi$
$2$	−7.78187	+	2.28496i	−0.972733	+	0.285620i	−0.243512	+	0.969898i	$0.578299\pi$
$3$	10.2083	+	11.7810i	0.378084	+	0.436332i
$3$	10.2083	+	11.7810i	0.378084	+	0.436332i
$4$	1.49619	−	0.961540i	0.0233779	−	0.0150241i
$5$	−172.710	+	24.8319i	−1.38168	+	0.198655i	−0.792758	−	0.609536i	$-0.791356\pi$
$5$	−172.710	+	24.8319i	−1.38168	+	0.198655i	−0.588920	+	0.808192i	$0.700447\pi$
$6$	−106.358	−	68.3524i	−0.492400	−	0.316446i
$7$	−306.304	−	139.884i	−0.893014	−	0.407826i	−0.0845825	−	0.996416i	$-0.526956\pi$
$7$	−306.304	−	139.884i	−0.893014	−	0.407826i	−0.808431	+	0.588591i	$0.799683\pi$
$8$	330.469	−	381.382i	0.645448	−	0.744887i
$9$	−34.5825	+	240.527i	−0.0474383	+	0.329940i
$10$	1287.26	−	587.874i	1.28726	−	0.587874i
$11$	−121.275	+	413.023i	−0.0911153	+	0.310310i	−0.992423	−	0.122870i	$-0.960790\pi$
$11$	−121.275	+	413.023i	−0.0911153	+	0.310310i	0.901308	+	0.433180i	$0.142609\pi$
$12$	26.6013	+	7.81086i	0.0153943	+	0.00452017i
$13$	−640.014	−	1401.43i	−0.291313	−	0.637886i	0.706227	−	0.707985i	$-0.250396\pi$
$13$	−640.014	−	1401.43i	−0.291313	−	0.637886i	−0.997540	+	0.0700994i	$0.977668\pi$
$14$	2703.24	+	388.668i	0.985147	+	0.141643i
$15$	−2055.61	−	1781.20i	−0.609070	−	0.527762i
$16$	−1747.51	+	3826.51i	−0.426638	+	0.934208i
$17$	−2186.75	+	3402.66i	−0.445096	+	0.692582i	−0.989222	−	0.146421i	$-0.953225\pi$
$17$	−2186.75	+	3402.66i	−0.445096	+	0.692582i	0.544127	+	0.839003i	$0.316861\pi$
$18$	−280.478	−	1950.77i	−0.0480929	−	0.334493i
$19$	−1504.77	−	2341.46i	−0.219386	−	0.341371i	0.714063	−	0.700081i	$-0.246853\pi$
$19$	−1504.77	−	2341.46i	−0.219386	−	0.341371i	−0.933449	+	0.358710i	$0.883217\pi$
$20$	−234.529	+	203.221i	−0.0293161	+	0.0254026i
$21$	−1478.86	−	5036.53i	−0.159687	−	0.543843i
$22$		−	3491.20i		−	0.327874i
$23$	9586.02	+	7492.94i	0.787871	+	0.615841i
$23$	9586.02	+	7492.94i	0.787871	+	0.615841i
$24$	7866.57			0.569052
$25$	14219.9	−	4175.35i	0.910076	−	0.267223i
$26$	8182.73	+	9443.37i	0.465563	+	0.537288i
$27$	−3186.66	+	2047.94i	−0.161899	+	0.104046i
$28$	−592.792	+	85.2306i	−0.0270040	+	0.00388259i
$29$	32098.4	+	20628.4i	1.31610	+	0.845806i	0.994867	−	0.101194i	$-0.0322664\pi$
$29$	32098.4	+	20628.4i	1.31610	+	0.845806i	0.321233	+	0.947000i	$0.395903\pi$
$30$	20066.5	+	9164.05i	0.743202	+	0.339409i
$31$	18941.1	−	21859.1i	0.635798	−	0.733750i	−0.342828	−	0.939398i	$-0.611385\pi$
$31$	18941.1	−	21859.1i	0.635798	−	0.733750i	0.978626	+	0.205648i	$0.0659303\pi$
$32$	259.110	−	1802.15i	0.00790741	−	0.0549973i
$33$	−6103.81	+	2787.52i	−0.169848	+	0.0775668i
$34$	9242.09	−	31475.7i	0.235144	−	0.800826i
$35$	56375.2	+	16553.3i	1.31487	+	0.386082i
$36$	179.534	+	393.125i	0.00384804	+	0.00842603i
$37$	31212.2	+	4487.64i	0.616197	+	0.0885958i	0.443344	−	0.896352i	$-0.353792\pi$
$37$	31212.2	+	4487.64i	0.616197	+	0.0885958i	0.172854	+	0.984948i	$0.444701\pi$
$38$	17060.0	+	14782.6i	0.310906	+	0.269402i
$39$	9976.83	−	21846.2i	0.168189	−	0.368283i
$40$	−47604.8	+	74074.6i	−0.743826	+	1.15742i
$41$	−11418.0	−	79413.7i	−0.165668	−	1.15224i	−0.887713	−	0.460397i	$-0.847707\pi$
$41$	−11418.0	−	79413.7i	−0.165668	−	1.15224i	0.722045	−	0.691846i	$-0.243202\pi$
$42$	23016.6	+	35814.5i	0.310665	+	0.483404i
$43$	34028.7	−	29486.0i	0.427996	−	0.370861i	−0.414061	−	0.910249i	$-0.635890\pi$
$43$	34028.7	−	29486.0i	0.427996	−	0.370861i	0.842057	+	0.539388i	$0.181345\pi$
$44$	215.689	+	734.570i	0.00253204	+	0.00862333i
$45$		−	42400.0i		−	0.465295i
$46$	−91718.2	−	36405.3i	−0.942285	−	0.374017i
$47$	−132494.			−1.27616			−0.638078	−	0.769972i	$-0.720270\pi$
$47$	−132494.			−1.27616			−0.638078	+	0.769972i	$0.720270\pi$
$48$	−62919.1	+	18474.7i	−0.568930	+	0.167053i
$49$	−2789.37	−	3219.10i	−0.0237093	−	0.0273619i
$50$	−101117.	+	64984.1i	−0.808938	+	0.519873i
$51$	−62409.6	+	8973.14i	−0.470479	+	0.0676447i
$52$	−2305.12	−	1481.41i	−0.0163939	−	0.0105357i
$53$	213629.	+	97561.2i	1.43494	+	0.655314i	0.972832	−	0.231511i	$-0.0743668\pi$
$53$	213629.	+	97561.2i	1.43494	+	0.655314i	0.462106	+	0.886825i	$0.347094\pi$
$54$	20118.7	−	23218.2i	0.127767	−	0.147451i
$55$	10689.1	−	74344.6i	0.0642472	−	0.446849i
$56$	−154573.	+	70591.3i	−0.880178	+	0.401964i
$57$	12223.6	−	41629.9i	0.0660048	−	0.224792i
$58$	−296920.	−	87183.6i	−1.52179	−	0.446839i
$59$	70155.4	+	153619.i	0.341590	+	0.747978i	0.999989	−	0.00469133i	$-0.00149330\pi$
$59$	70155.4	+	153619.i	0.341590	+	0.747978i	−0.658399	+	0.752669i	$0.728766\pi$
$60$	−4788.27	−	688.449i	−0.0221679	−	0.00318727i
$61$	−297267.	−	257583.i	−1.30966	−	1.13482i	−0.981763	−	0.190108i	$-0.939116\pi$
$61$	−297267.	−	257583.i	−1.30966	−	1.13482i	−0.327893	−	0.944715i	$-0.606338\pi$
$62$	−97449.4	+	213385.i	−0.408888	+	0.895340i
$63$	44238.6	−	68836.6i	0.176921	−	0.275295i
$64$	−36213.4	−	251870.i	−0.138143	−	0.960807i
$65$	145337.	+	226149.i	0.529220	+	0.823482i
$66$	41129.7	−	35639.1i	0.143062	−	0.123964i
$67$	−51135.9	−	174153.i	−0.170021	−	0.579037i	−0.999781	−	0.0209177i	$-0.993341\pi$
$67$	−51135.9	−	174153.i	−0.170021	−	0.579037i	0.829761	−	0.558120i	$-0.188477\pi$
$68$			7193.66i			0.0228783i
$69$	9582.62	+	189423.i	0.0291701	+	0.576613i
$70$	−476528.			−1.38929
$71$	332256.	−	97559.1i	0.928319	−	0.272579i	0.217586	−	0.976041i	$-0.430182\pi$
$71$	332256.	−	97559.1i	0.928319	−	0.272579i	0.710733	+	0.703462i	$0.248363\pi$
$72$	80304.1	+	92675.8i	0.215149	+	0.248296i
$73$	56283.9	−	36171.5i	0.144682	−	0.0929817i	−0.466297	−	0.884628i	$-0.654412\pi$
$73$	56283.9	−	36171.5i	0.144682	−	0.0929817i	0.610979	+	0.791647i	$0.290776\pi$
$74$	−253144.	+	36396.6i	−0.624700	+	0.0898184i
$75$	194351.	+	124902.i	0.460683	+	0.296063i
$76$	−4502.82	−	2056.37i	−0.0102576	−	0.00468447i
$77$	94922.2	−	109546.i	0.207920	−	0.239952i
$78$	−27720.6	+	192801.i	−0.0584142	+	0.406280i
$79$	−58948.5	+	26920.9i	−0.119562	+	0.0546019i	−0.474298	−	0.880365i	$-0.657298\pi$
$79$	−58948.5	+	26920.9i	−0.119562	+	0.0546019i	0.354736	+	0.934966i	$0.384571\pi$
$80$	206792.	−	704270.i	0.403891	−	1.37553i
$81$	−56657.1	−	16636.0i	−0.106610	−	0.0313036i
$82$	270311.	+	591898.i	0.490254	+	1.07351i
$83$	−554734.	−	79758.8i	−0.970177	−	0.139490i	−0.361035	−	0.932552i	$-0.617577\pi$
$83$	−554734.	−	79758.8i	−0.970177	−	0.139490i	−0.609141	+	0.793062i	$0.708486\pi$
$84$	−7055.47	−	6113.60i	−0.0119039	−	0.0103148i
$85$	293179.	−	641973.i	0.477393	−	1.04535i
$86$	−197432.	+	307211.i	−0.310401	+	0.482993i
$87$	84646.5	+	588730.i	0.128544	+	0.894042i
$88$	117442.	+	182743.i	0.172336	+	0.268160i
$89$	782815.	−	678313.i	1.11043	−	0.962189i	0.110926	−	0.993829i	$-0.464618\pi$
$89$	782815.	−	678313.i	1.11043	−	0.962189i	0.999499	+	0.0316397i	$0.0100729\pi$
$90$	96882.5	+	329951.i	0.132898	+	0.452608i
$91$			518792.i			0.688445i
$92$	21547.2	+	1993.48i	0.0276712	+	0.00256005i
$93$	450877.			0.560544
$94$	1.03105e6	−	302744.i	1.24136	−	0.364496i
$95$	318031.	+	367027.i	0.370935	+	0.428082i
$96$	23876.1	−	15344.3i	0.0269867	−	0.0173433i
$97$	−594426.	+	85465.6i	−0.651303	+	0.0936432i	−0.460043	−	0.887896i	$-0.652166\pi$
$97$	−594426.	+	85465.6i	−0.651303	+	0.0936432i	−0.191259	+	0.981540i	$0.561257\pi$
$98$	29062.0	+	18677.0i	0.0308779	+	0.0198440i
$99$	−95149.1	−	43453.1i	−0.0980616	−	0.0447832i
$100$	17260.9	−	19920.2i	0.0172609	−	0.0199202i
$101$	−5841.85	+	40631.0i	−0.00567005	+	0.0394360i	−0.992460	−	0.122569i	$-0.960887\pi$
$101$	−5841.85	+	40631.0i	−0.00567005	+	0.0394360i	0.986790	+	0.162005i	$0.0517959\pi$
$102$	465160.	−	212431.i	0.438330	−	0.200179i
$103$	−125030.	+	425811.i	−0.114420	+	0.389678i	−0.996712	−	0.0810239i	$-0.974181\pi$
$103$	−125030.	+	425811.i	−0.114420	+	0.389678i	0.882292	+	0.470702i	$0.155999\pi$
$104$	−745987.	−	219042.i	−0.663180	−	0.194727i
$105$	380480.	+	833135.i	0.328673	+	0.719693i
$106$	−1.88536e6	−	271074.i	−1.58298	−	0.227599i
$107$	−745366.	−	645864.i	−0.608441	−	0.527217i	0.295240	−	0.955423i	$-0.404600\pi$
$107$	−745366.	−	645864.i	−0.608441	−	0.527217i	−0.903681	+	0.428206i	$0.859146\pi$
$108$	−2798.66	+	6128.21i	−0.00222167	+	0.00486477i
$109$	651287.	−	1.01342e6i	0.502913	−	0.782548i	−0.493267	−	0.869878i	$-0.664197\pi$
$109$	651287.	−	1.01342e6i	0.502913	−	0.782548i	0.996179	+	0.0873306i	$0.0278337\pi$
$110$	86693.1	+	602964.i	0.0651338	+	0.453016i
$111$	265754.	+	413522.i	0.194317	+	0.302363i
$112$	1.07054e6	−	927626.i	0.761988	−	0.660266i
$113$	−244052.	−	831163.i	−0.169140	−	0.576038i	−0.999814	−	0.0192789i	$-0.993863\pi$
$113$	−244052.	−	831163.i	−0.169140	−	0.576038i	0.830674	−	0.556759i	$-0.187955\pi$
$114$			351889.i			0.237515i
$115$	−1.84166e6	−	1.05606e6i	−1.21092	−	0.694379i
$116$	67860.1			0.0434751
$117$	359216.	−	105475.i	0.224284	−	0.0658556i
$118$	−896954.	−	1.03514e6i	−0.545914	−	0.630018i
$119$	1.14579e6	−	736354.i	0.679929	−	0.436964i
$120$	−1.35863e6	+	195342.i	−0.786246	+	0.113045i
$121$	1.33445e6	+	857600.i	0.753263	+	0.484093i
$122$	2.90186e6	+	1.32524e6i	1.59807	+	0.729816i
$123$	819013.	−	945192.i	0.440125	−	0.507931i
$124$	7320.89	−	50917.9i	0.00383971	−	0.0267058i
$125$	127725.	−	58330.0i	0.0653952	−	0.0298650i
$126$	−186970.	+	636761.i	−0.0934674	+	0.318321i
$127$	3.09775e6	+	909581.i	1.51229	+	0.444048i	0.929576	−	0.368630i	$-0.120173\pi$
$127$	3.09775e6	+	909581.i	1.51229	+	0.444048i	0.582713	+	0.812678i	$0.301991\pi$
$128$	905727.	+	1.98327e6i	0.431884	+	0.945695i
$129$	694748.	+	99889.7i	0.323637	+	0.0465320i
$130$	−1.64773e6	−	1.42777e6i	−0.749993	−	0.649872i
$131$	−1.12335e6	+	2.45980e6i	−0.499693	+	1.09417i	0.476877	+	0.878970i	$0.341769\pi$
$131$	−1.12335e6	+	2.45980e6i	−0.499693	+	1.09417i	−0.976569	+	0.215204i	$0.930958\pi$
$132$	−6452.13	+	10039.7i	−0.00280531	+	0.00436515i
$133$	133382.	+	927691.i	0.0566946	+	0.394320i
$134$	795866.	+	1.23839e6i	0.330770	+	0.514688i
$135$	499514.	−	432831.i	0.203023	−	0.175921i
$136$	575057.	+	1.95846e6i	0.228609	+	0.778572i
$137$		−	4.98779e6i		−	1.93975i	−0.243599	−	0.969876i	$-0.578328\pi$
$137$		−	4.98779e6i		−	1.93975i	0.243599	−	0.969876i	$-0.421672\pi$
$138$	−507394.	−	1.45217e6i	−0.193067	−	0.552559i
$139$	2.58865e6			0.963894			0.481947	−	0.876200i	$-0.339930\pi$
$139$	2.58865e6			0.963894			0.481947	+	0.876200i	$0.339930\pi$
$140$	100264.	−	29440.3i	0.0365395	−	0.0107290i
$141$	−1.35254e6	−	1.56091e6i	−0.482494	−	0.556828i
$142$	−2.36265e6	+	1.51838e6i	−0.825153	+	0.530294i
$143$	656442.	−	94382.1i	0.224486	−	0.0322761i
$144$	−859945.	−	552653.i	−0.287994	−	0.185082i
$145$	−6.05594e6	−	2.76565e6i	−1.98645	−	0.907181i
$146$	−355343.	+	410088.i	−0.114180	+	0.131771i
$147$	9449.54	−	65723.0i	0.00297480	−	0.0206902i
$148$	51014.4	−	23297.5i	0.0157365	−	0.00718661i
$149$	−1.00500e6	+	3.42271e6i	−0.303813	+	1.03469i	0.656166	+	0.754617i	$0.272177\pi$
$149$	−1.00500e6	+	3.42271e6i	−0.303813	+	1.03469i	−0.959978	+	0.280074i	$0.909641\pi$
$150$	−1.79781e6	−	527884.i	−0.532684	−	0.156410i
$151$	668794.	+	1.46445e6i	0.194250	+	0.425349i	0.981546	−	0.191227i	$-0.0612467\pi$
$151$	668794.	+	1.46445e6i	0.194250	+	0.425349i	−0.787296	+	0.616576i	$0.788519\pi$
$152$	−1.39027e6	−	199891.i	−0.395885	−	0.0569196i
$153$	−742806.	−	643645.i	−0.207396	−	0.179710i
$154$	−488363.	+	1.06937e6i	−0.133715	+	0.292796i
$155$	−2.72850e6	+	4.24563e6i	−0.732704	+	1.14011i
$156$	−6078.82	−	42279.1i	−0.00160120	−	0.0111366i
$157$	167170.	+	260122.i	0.0431976	+	0.0672168i	0.862181	−	0.506601i	$-0.169098\pi$
$157$	167170.	+	260122.i	0.0431976	+	0.0672168i	−0.818983	+	0.573818i	$0.805462\pi$
$158$	397216.	−	344190.i	0.100706	−	0.0872623i
$159$	1.03142e6	+	3.51269e6i	0.256592	+	0.873874i
$160$			317683.i			0.0775593i
$161$	−1.88809e6	−	3.63605e6i	−0.452423	−	0.871268i
$162$	478911.			0.112644
$163$	3.72098e6	−	1.09258e6i	0.859200	−	0.252284i	0.177684	−	0.984088i	$-0.443139\pi$
$163$	3.72098e6	−	1.09258e6i	0.859200	−	0.252284i	0.681515	+	0.731804i	$0.261321\pi$
$164$	−93442.9	−	107839.i	−0.0211843	−	0.0244480i
$165$	984969.	−	633001.i	0.219266	−	0.140913i
$166$	4.49912e6	−	646875.i	0.983565	−	0.141415i
$167$	−4.57824e6	−	2.94226e6i	−0.982990	−	0.631729i	−0.0527217	−	0.998609i	$-0.516790\pi$
$167$	−4.57824e6	−	2.94226e6i	−0.982990	−	0.631729i	−0.930268	+	0.366880i	$0.880426\pi$
$168$	−2.40956e6	−	1.10041e6i	−0.508171	−	0.232074i
$169$	1.60649e6	−	1.85398e6i	0.332826	−	0.384101i
$170$	−814598.	+	5.66565e6i	−0.165805	+	1.15320i
$171$	615223.	−	280963.i	0.123039	−	0.0561902i
$172$	22561.2	−	76836.6i	0.00443382	−	0.0151002i
$173$	880993.	+	258683.i	0.170151	+	0.0499608i	0.365698	−	0.930733i	$-0.380830\pi$
$173$	880993.	+	258683.i	0.170151	+	0.0499608i	−0.195547	+	0.980694i	$0.562648\pi$
$174$	−2.00393e6	−	4.38800e6i	−0.380396	−	0.832950i
$175$	−4.93969e6	−	710220.i	−0.921691	−	0.132519i
$176$	−1.36851e6	−	1.18582e6i	−0.251021	−	0.217511i
$177$	−1.09361e6	+	2.39468e6i	−0.197217	+	0.431845i
$178$	−4.54185e6	+	7.06725e6i	−0.805327	+	1.25311i
$179$	−719934.	−	5.00725e6i	−0.125526	−	0.873053i	−0.951127	−	0.308799i	$-0.900073\pi$
$179$	−719934.	−	5.00725e6i	−0.125526	−	0.873053i	0.825601	−	0.564254i	$-0.190836\pi$
$180$	−40769.3	−	63438.3i	−0.00699063	−	0.0108776i
$181$	−578313.	+	501111.i	−0.0975275	+	0.0845081i	−0.702260	−	0.711921i	$-0.747826\pi$
$181$	−578313.	+	501111.i	−0.0975275	+	0.0845081i	0.604732	+	0.796429i	$0.293280\pi$
$182$	−1.18542e6	−	4.03717e6i	−0.196634	−	0.669674i
$183$		−	6.13157e6i		−	1.00050i
$184$	6.02556e6	−	1.17975e6i	0.967261	−	0.189381i
$185$	−5.50209e6			−0.868986
$186$	−3.50867e6	+	1.03024e6i	−0.545260	+	0.160103i
$187$	−1.14018e6	−	1.31584e6i	−0.174360	−	0.201223i
$188$	−198236.	+	127399.i	−0.0298338	+	0.0191730i
$189$	1.26256e6	−	181529.i	0.187011	−	0.0268881i
$190$	−3.31352e6	−	2.12947e6i	−0.483090	−	0.310463i
$191$	8.29009e6	+	3.78596e6i	1.18976	+	0.543345i	0.909147	−	0.416476i	$-0.136735\pi$
$191$	8.29009e6	+	3.78596e6i	1.18976	+	0.543345i	0.280613	+	0.959821i	$0.409462\pi$
$192$	2.59760e6	−	2.99778e6i	0.367001	−	0.423542i
$193$	−966714.	+	6.72365e6i	−0.134470	+	0.935261i	0.805157	+	0.593062i	$0.202081\pi$
$193$	−966714.	+	6.72365e6i	−0.134470	+	0.935261i	−0.939627	+	0.342200i	$0.888828\pi$
$194$	4.43046e6	−	2.02332e6i	0.606797	−	0.277115i
$195$	−1.18061e6	+	4.02080e6i	−0.159222	+	0.542261i
$196$	−7268.72	−	2134.29i	−0.000965360	−	0.000283455i
$197$	2.81663e6	+	6.16756e6i	0.368410	+	0.806705i	0.999519	+	0.0310109i	$0.00987265\pi$
$197$	2.81663e6	+	6.16756e6i	0.368410	+	0.806705i	−0.631109	+	0.775694i	$0.717400\pi$
$198$	839726.	+	120734.i	0.108179	+	0.0155538i
$199$	4.99236e6	+	4.32590e6i	0.633500	+	0.548931i	0.911318	−	0.411703i	$-0.135066\pi$
$199$	4.99236e6	+	4.32590e6i	0.633500	+	0.548931i	−0.277818	+	0.960634i	$0.589611\pi$
$200$	3.10685e6	−	6.80306e6i	0.388357	−	0.850382i
$201$	1.52968e6	−	2.38023e6i	0.188371	−	0.293110i
$202$	−47379.7	−	329533.i	−0.00574829	−	0.0399802i
$203$	−6.94626e6	−	1.08086e7i	−0.830353	−	1.29206i
$204$	−84748.3	+	73434.8i	−0.00998253	+	0.00864991i
$205$	3.94399e6	+	1.34320e7i	0.457798	+	1.55912i
$206$		−	3.59930e6i		−	0.411733i
$207$	−2.13376e6	+	2.04657e6i	−0.240566	+	0.230736i
$208$	6.48104e6			0.720203
$209$	1.14957e6	−	337543.i	0.125920	−	0.0369735i
$210$	−4.86453e6	−	5.61396e6i	−0.525270	−	0.606194i
$211$	4.88771e6	−	3.14114e6i	0.520305	−	0.334380i	−0.253988	−	0.967207i	$-0.581742\pi$
$211$	4.88771e6	−	3.14114e6i	0.520305	−	0.334380i	0.774293	+	0.632828i	$0.218106\pi$
$212$	413438.	−	59443.4i	0.0433913	−	0.00623873i
$213$	4.54110e6	+	2.91839e6i	0.469918	+	0.301998i
$214$	7.27612e6	+	3.32289e6i	0.742435	+	0.339059i
$215$	−5.14489e6	+	5.93752e6i	−0.517679	+	0.597434i
$216$	−272046.	+	1.89212e6i	−0.0269948	+	0.187753i
$217$	−8.85946e6	+	4.04598e6i	−0.867018	+	0.395954i
$218$	−2.75260e6	+	9.37448e6i	−0.265689	+	0.904852i
$219$	1.00070e6	+	293831.i	0.0952730	+	0.0279747i
$220$	−55492.4	−	121511.i	−0.00521153	−	0.0114117i
$221$	6.16815e6	+	886847.i	0.571450	+	0.0821621i
$222$	−3.01294e6	−	2.61073e6i	−0.275380	−	0.238618i
$223$	8.38233e6	−	1.83547e7i	0.755875	−	1.65514i	0.000363783	−	1.00000i	$-0.499884\pi$
$223$	8.38233e6	−	1.83547e7i	0.755875	−	1.65514i	0.755511	−	0.655136i	$-0.227389\pi$
$224$	−331459.	+	515760.i	−0.0294907	+	0.0458884i
$225$	512522.	+	3.56467e6i	0.0449951	+	0.312948i
$226$	3.79835e6	+	5.91035e6i	0.329056	+	0.512021i
$227$	8.32208e6	−	7.21112e6i	0.711466	−	0.616489i	−0.222046	−	0.975036i	$-0.571273\pi$
$227$	8.32208e6	−	7.21112e6i	0.711466	−	0.616489i	0.933511	+	0.358548i	$0.116728\pi$
$228$	−21740.0	−	74039.6i	−0.00183423	−	0.00624683i
$229$			3.34744e6i			0.278745i	0.990240	+	0.139372i	$0.0445085\pi$
$229$			3.34744e6i			0.278745i	−0.990240	+	0.139372i	$0.955492\pi$
$230$	1.67446e7	+	4.01002e6i	1.37623	+	0.329581i
$231$	2.25955e6			0.183310
$232$	1.84748e7	−	5.42469e6i	1.47950	−	0.434421i
$233$	5.94709e6	+	6.86330e6i	0.470150	+	0.542582i	0.940453	−	0.339923i	$-0.110401\pi$
$233$	5.94709e6	+	6.86330e6i	0.470150	+	0.542582i	−0.470303	+	0.882505i	$0.655855\pi$
$234$	−2.55436e6	+	1.64159e6i	−0.199359	+	0.128120i
$235$	2.28830e7	−	3.29009e6i	1.76324	−	0.253515i
$236$	252676.	+	162385.i	0.0192233	+	0.0123541i
$237$	−918916.	−	419655.i	−0.0690289	−	0.0315244i
$238$	−7.23384e6	+	8.34829e6i	−0.536584	+	0.619251i
$239$	309771.	−	2.15451e6i	0.0226907	−	0.157817i	−0.975326	−	0.220770i	$-0.929143\pi$
$239$	309771.	−	2.15451e6i	0.0226907	−	0.157817i	0.998016	+	0.0629534i	$0.0200519\pi$
$240$	1.04080e7	−	4.75316e6i	0.752892	−	0.343834i
$241$	−5.41781e6	+	1.84514e7i	−0.387055	+	1.31819i	0.503768	+	0.863839i	$0.331947\pi$
$241$	−5.41781e6	+	1.84514e7i	−0.387055	+	1.31819i	−0.890823	+	0.454350i	$0.849872\pi$
$242$	−1.23441e7	−	3.62456e6i	−0.870991	−	0.255746i
$243$	−382382.	−	837301.i	−0.0266489	−	0.0583529i
$244$	−692444.	−	99558.4i	−0.0476667	−	0.00685343i
$245$	561688.	+	486705.i	0.0381941	+	0.0330954i
$246$	−4.21373e6	+	9.22677e6i	−0.283049	+	0.619790i
$247$	−2.31834e6	+	3.60740e6i	−0.153846	+	0.239389i
$248$	−2.07724e6	−	1.44476e7i	−0.136186	−	0.947195i
$249$	−4.72324e6	−	7.34951e6i	−0.305944	−	0.476058i
$250$	−860657.	+	745764.i	−0.0550820	+	0.0477289i
$251$	−3.78702e6	−	1.28974e7i	−0.239484	−	0.815608i	−0.988260	−	0.152784i	$-0.951176\pi$
$251$	−3.78702e6	−	1.28974e7i	−0.239484	−	0.815608i	0.748775	−	0.662824i	$-0.230642\pi$
$252$		−	145530.i		−	0.00909389i
$253$	−4.25729e6	+	3.05055e6i	−0.262889	+	0.188372i
$254$	−2.61846e7			−1.59788
$255$	1.05559e7	−	3.09950e6i	0.636613	−	0.186926i
$256$	−915243.	−	1.05625e6i	−0.0545527	−	0.0629572i
$257$	1.93941e7	−	1.24638e7i	1.14254	−	0.734264i	0.174398	−	0.984675i	$-0.444202\pi$
$257$	1.93941e7	−	1.24638e7i	1.14254	−	0.734264i	0.968140	+	0.250411i	$0.0805657\pi$
$258$	−5.63468e6	+	810145.i	−0.328103	+	0.0471741i
$259$	−8.93267e6	−	5.74068e6i	−0.514141	−	0.330418i
$260$	434902.	+	198613.i	0.0247441	+	0.0113002i
$261$	−6.07171e6	+	7.00713e6i	−0.341499	+	0.394111i
$262$	3.12124e6	−	2.17087e7i	0.173549	−	1.20706i
$263$	−3.16912e7	+	1.44729e7i	−1.74209	+	0.795587i	−0.751337	+	0.659919i	$0.770591\pi$
$263$	−3.16912e7	+	1.44729e7i	−1.74209	+	0.795587i	−0.990754	+	0.135668i	$0.956682\pi$
$264$	−954015.	+	3.24908e6i	−0.0518493	+	0.176583i
$265$	−3.93185e7	−	1.15449e7i	−2.11280	−	0.620375i
$266$	−3.15770e6	−	6.91440e6i	−0.167775	−	0.367375i
$267$	1.59824e7	+	2.29792e6i	0.839668	+	0.120726i
$268$	−243964.	−	211396.i	−0.0126742	−	0.0109823i
$269$	1.22728e7	−	2.68737e7i	0.630504	−	1.38061i	−0.277123	−	0.960834i	$-0.589381\pi$
$269$	1.22728e7	−	2.68737e7i	0.630504	−	1.38061i	0.907627	−	0.419777i	$-0.137892\pi$
$270$	−2.89815e6	+	4.50960e6i	−0.147241	+	0.229112i
$271$	1.30486e6	+	9.07553e6i	0.0655628	+	0.455999i	0.995986	+	0.0895117i	$0.0285306\pi$
$271$	1.30486e6	+	9.07553e6i	0.0655628	+	0.455999i	−0.930423	+	0.366487i	$0.880560\pi$
$272$	−9.19894e6	−	1.43138e7i	−0.457121	−	0.711294i
$273$	−6.11188e6	+	5.29597e6i	−0.300391	+	0.260290i
$274$	1.13969e7	+	3.88143e7i	0.554033	+	1.88686i
$275$			6.37953e6i			0.306754i
$276$	196475.	+	274197.i	0.00934501	+	0.0130418i
$277$	−3.63645e7			−1.71096			−0.855478	−	0.517839i	$-0.826736\pi$
$277$	−3.63645e7			−1.71096			−0.855478	+	0.517839i	$0.826736\pi$
$278$	−2.01445e7	+	5.91497e6i	−0.937612	+	0.275308i
$279$	4.60268e6	+	5.31177e6i	0.211933	+	0.244583i
$280$	2.49434e7	−	1.60301e7i	1.13627	−	0.730236i
$281$	−2.89922e7	+	4.16845e6i	−1.30666	+	0.187869i	−0.760239	−	0.649643i	$-0.774918\pi$
$281$	−2.89922e7	+	4.16845e6i	−1.30666	+	0.187869i	−0.546419	+	0.837512i	$0.684009\pi$
$282$	1.40919e7	+	9.05631e6i	0.628379	+	0.403835i
$283$	−3.70848e7	−	1.69361e7i	−1.63620	−	0.747228i	−0.636492	−	0.771284i	$-0.719615\pi$
$283$	−3.70848e7	−	1.69361e7i	−1.63620	−	0.747228i	−0.999711	+	0.0240552i	$0.992342\pi$
$284$	403309.	−	465444.i	0.0176069	−	0.0203195i
$285$	−1.07739e6	+	7.49342e6i	−0.0465413	+	0.323702i
$286$	−4.89269e6	+	2.23442e6i	−0.209146	+	0.0955137i
$287$	−7.61136e6	+	2.59219e7i	−0.321971	+	1.09653i
$288$	424504.	+	124646.i	0.0177707	+	0.00521795i
$289$	3.23093e6	+	7.07476e6i	0.133855	+	0.293102i
$290$	5.34459e7	+	7.68436e6i	2.19139	+	0.315075i
$291$	−7.07493e6	−	6.13046e6i	−0.287107	−	0.248779i
$292$	49430.9	−	108239.i	0.00198541	−	0.00434744i
$293$	−2.01417e7	+	3.13411e7i	−0.800742	+	1.24598i	0.164953	+	0.986301i	$0.447253\pi$
$293$	−2.01417e7	+	3.13411e7i	−0.800742	+	1.24598i	−0.965695	+	0.259678i	$0.916384\pi$
$294$	76639.5	+	533039.i	0.00301586	+	0.0209757i
$295$	−1.59312e7	−	2.47894e7i	−0.620557	−	0.965606i
$296$	1.20262e7	−	1.04208e7i	0.463717	−	0.401813i
$297$	−459387.	−	1.56453e6i	−0.0175352	−	0.0597192i
$298$		−	2.89314e7i		−	1.09325i
$299$	4.36568e6	−	1.82298e7i	0.163319	−	0.681974i
$300$	410883.			0.0152179
$301$	−1.45477e7	+	4.27160e6i	−0.533453	+	0.156636i
$302$	−8.55069e6	−	9.86802e6i	−0.310442	−	0.358269i
$303$	−538308.	+	345949.i	−0.0193510	+	0.0124361i
$304$	1.15892e7	−	1.66628e6i	0.412510	−	0.0593099i
$305$	5.77372e7	+	3.71054e7i	2.03496	+	1.30779i
$306$	7.25112e6	+	3.31148e6i	0.253070	+	0.115573i
$307$	−1.90673e6	+	2.20048e6i	−0.0658982	+	0.0760506i	−0.787741	−	0.616006i	$-0.788750\pi$
$307$	−1.90673e6	+	2.20048e6i	−0.0658982	+	0.0760506i	0.721843	+	0.692057i	$0.243295\pi$
$308$	36688.3	−	255173.i	0.00125567	−	0.00873338i
$309$	−6.29281e6	+	2.87383e6i	−0.213289	+	0.0974059i
$310$	1.15317e7	−	3.92734e7i	0.387087	−	1.31830i
$311$	−2.18522e7	−	6.41638e6i	−0.726463	−	0.213309i	−0.102467	−	0.994736i	$-0.532674\pi$
$311$	−2.18522e7	−	6.41638e6i	−0.726463	−	0.213309i	−0.623996	+	0.781427i	$0.714492\pi$
$312$	−5.03471e6	−	1.10245e7i	−0.165772	−	0.362990i
$313$	−1.89623e7	−	2.72637e6i	−0.618385	−	0.0889103i	−0.173999	−	0.984746i	$-0.555669\pi$
$313$	−1.89623e7	−	2.72637e6i	−0.618385	−	0.0889103i	−0.444386	+	0.895836i	$0.646578\pi$
$314$	−1.89527e6	−	1.64226e6i	−0.0612183	−	0.0530459i
$315$	−5.93109e6	+	1.29873e7i	−0.189759	+	0.415515i
$316$	−62312.4	+	96960.0i	−0.00197476	+	0.00307278i
$317$	5.09573e6	+	3.54416e7i	0.159966	+	1.11259i	0.898691	+	0.438583i	$0.144520\pi$
$317$	5.09573e6	+	3.54416e7i	0.159966	+	1.11259i	−0.738724	+	0.674008i	$0.764571\pi$
$318$	−1.60527e7	−	2.49785e7i	−0.499192	−	0.776758i
$319$	−1.24127e7	+	1.07557e7i	−0.382379	+	0.331333i
$320$	1.25088e7	+	4.26011e7i	0.381739	+	1.30008i
$321$		−	1.53743e7i		−	0.464815i
$322$	2.30011e7	+	2.39810e7i	0.688939	+	0.718290i
$323$	1.12577e7			0.334075
$324$	−100766.	+	29587.5i	−0.00296263	+	0.000869908i
$325$	−1.49524e7	−	1.72560e7i	−0.435574	−	0.502679i
$326$	−2.64597e7	+	1.70046e7i	−0.763715	+	0.490810i
$327$	1.85876e7	−	2.67249e6i	0.531594	−	0.0764317i
$328$	−3.40603e7	−	2.18892e7i	−0.965221	−	0.620310i
$329$	4.05835e7	+	1.85339e7i	1.13962	+	0.520449i
$330$	−6.21851e6	+	7.17655e6i	−0.173039	+	0.199698i
$331$	9.53106e6	−	6.62899e7i	0.262819	−	1.82795i	−0.248589	−	0.968609i	$-0.579967\pi$
$331$	9.53106e6	−	6.62899e7i	0.262819	−	1.82795i	0.511408	−	0.859338i	$-0.329124\pi$
$332$	−906677.	+	414066.i	−0.0247764	+	0.0113150i
$333$	−2.15880e6	+	7.35218e6i	−0.0584627	+	0.199106i
$334$	4.23502e7	+	1.24351e7i	1.13662	+	0.333742i
$335$	1.31562e7	+	2.88081e7i	0.349943	+	0.766267i
$336$	2.18567e7	+	3.14252e6i	0.576191	+	0.0828437i
$337$	−1.34697e7	−	1.16715e7i	−0.351939	−	0.304957i	0.460893	−	0.887456i	$-0.347529\pi$
$337$	−1.34697e7	−	1.16715e7i	−0.351939	−	0.304957i	−0.812831	+	0.582499i	$0.802075\pi$
$338$	−8.26518e6	+	1.80982e7i	−0.214044	+	0.468690i
$339$	7.30056e6	−	1.13599e7i	0.187395	−	0.291592i
$340$	−178632.	−	1.24241e6i	−0.00454489	−	0.0316104i
$341$	6.73126e6	+	1.04740e7i	0.169759	+	0.264150i
$342$	−4.14559e6	+	3.59218e6i	−0.103635	+	0.0898006i
$343$	1.15653e7	+	3.93878e7i	0.286599	+	0.976067i
$344$		−	2.27222e7i		−	0.558180i
$345$	−6.35874e6	−	3.24772e7i	−0.154851	−	0.790898i
$346$	−7.44685e6			−0.179781
$347$	4.82024e7	−	1.41535e7i	1.15367	−	0.338747i	0.351698	−	0.936113i	$-0.385604\pi$
$347$	4.82024e7	−	1.41535e7i	1.15367	−	0.338747i	0.801969	+	0.597366i	$0.203786\pi$
$348$	692734.	+	799458.i	0.0164372	+	0.0189696i
$349$	5.86749e7	−	3.77081e7i	1.38031	−	0.887070i	0.381012	−	0.924570i	$-0.375576\pi$
$349$	5.86749e7	−	3.77081e7i	1.38031	−	0.887070i	0.999297	+	0.0374996i	$0.0119393\pi$
$350$	4.00628e7	−	5.76016e6i	0.934410	−	0.134348i
$351$	4.90957e6	+	3.15519e6i	0.113533	+	0.0729632i
$352$	712906.	+	325573.i	0.0163457	+	0.00746484i
$353$	−4.30574e6	+	4.96909e6i	−0.0978867	+	0.112967i	−0.802579	−	0.596546i	$-0.796539\pi$
$353$	−4.30574e6	+	4.96909e6i	−0.0978867	+	0.112967i	0.704693	+	0.709513i	$0.251085\pi$
$354$	3.03861e6	−	2.11340e7i	0.0684959	−	0.476399i
$355$	−5.49612e7	+	2.50999e7i	−1.22849	+	0.561032i
$356$	519012.	−	1.76759e6i	0.0115034	−	0.0391771i
$357$	2.03715e7	+	5.98161e6i	0.447732	+	0.131466i
$358$	1.70438e7	+	3.73208e7i	0.371465	+	0.813395i
$359$	5.93674e7	+	8.53574e6i	1.28311	+	0.184484i	0.749930	−	0.661517i	$-0.230087\pi$
$359$	5.93674e7	+	8.53574e6i	1.28311	+	0.184484i	0.533182	+	0.846001i	$0.320996\pi$
$360$	−1.61706e7	−	1.40119e7i	−0.346592	−	0.300324i
$361$	1.63254e7	−	3.57477e7i	0.347011	−	0.759848i
$362$	3.35533e6	−	5.22100e6i	0.0707311	−	0.110060i
$363$	3.51908e6	+	2.44757e7i	0.0735715	+	0.511701i
$364$	498840.	+	776210.i	0.0103433	+	0.0160944i
$365$	−8.82257e6	+	7.64480e6i	−0.181433	+	0.157213i
$366$	1.40104e7	+	4.77151e7i	0.285764	+	0.973223i
$367$		−	8.95680e6i		−	0.181199i	−0.995887	−	0.0905993i	$-0.971122\pi$
$367$		−	8.95680e6i		−	0.181199i	0.995887	−	0.0905993i	$-0.0288782\pi$
$368$	−4.54235e7	+	2.35871e7i	−0.911459	+	0.473293i
$369$	1.94960e7			0.388031
$370$	4.28166e7	−	1.25721e7i	0.845292	−	0.248200i
$371$	−5.17882e7	−	5.97667e7i	−1.01417	−	1.17041i
$372$	674596.	−	433537.i	0.0131043	−	0.00842165i
$373$	1.91625e7	−	2.75515e6i	0.369254	−	0.0530907i	0.0448098	−	0.998996i	$-0.485732\pi$
$373$	1.91625e7	−	2.75515e6i	0.369254	−	0.0530907i	0.324444	+	0.945905i	$0.394823\pi$
$374$	1.18793e7	+	7.63439e6i	0.227079	+	0.145935i
$375$	1.99104e6	+	909275.i	0.0377559	+	0.0172426i
$376$	−4.37853e7	+	5.05309e7i	−0.823692	+	0.950591i
$377$	8.36591e6	−	5.81862e7i	0.156131	−	1.08591i
$378$	−9.41030e6	+	4.29754e6i	−0.174232	+	0.0795691i
$379$	1.95609e7	−	6.66184e7i	0.359312	−	1.22370i	−0.559441	−	0.828870i	$-0.688984\pi$
$379$	1.95609e7	−	6.66184e7i	0.359312	−	1.22370i	0.918753	−	0.394834i	$-0.129198\pi$
$380$	828745.	+	243341.i	0.0151032	+	0.00443471i
$381$	2.09069e7	+	4.57797e7i	0.378020	+	0.827748i
$382$	−7.31632e7	−	1.05193e7i	−1.31251	−	0.188710i
$383$	−2.62165e7	−	2.27167e7i	−0.466636	−	0.404342i	0.389554	−	0.921004i	$-0.372629\pi$
$383$	−2.62165e7	−	2.27167e7i	−0.466636	−	0.404342i	−0.856190	+	0.516661i	$0.827175\pi$
$384$	−1.41189e7	+	3.09160e7i	−0.249349	+	0.545997i
$385$	−1.36738e7	+	2.12768e7i	−0.239610	+	0.372841i
$386$	−7.84044e6	−	5.45314e7i	−0.136326	−	0.948167i
$387$	5.91538e6	+	9.20451e6i	0.102059	+	0.158806i
$388$	−807194.	+	699437.i	−0.0138192	+	0.0119744i
$389$	2.33298e7	+	7.94540e7i	0.396335	+	1.34979i	0.880180	+	0.474639i	$0.157421\pi$
$389$	2.33298e7	+	7.94540e7i	0.396335	+	1.34979i	−0.483846	+	0.875153i	$0.660760\pi$
$390$		−	3.39870e7i		−	0.572952i
$391$	−4.64582e7	+	1.62327e7i	−0.777198	+	0.271557i
$392$	−2.14951e6			−0.0356846
$393$	−4.04464e7	+	1.18761e7i	−0.666349	+	0.195658i
$394$	−3.60113e7	−	4.15592e7i	−0.588776	−	0.679483i
$395$	9.51248e6	−	6.11330e6i	0.154349	−	0.0991938i
$396$	−184143.	+	26475.7i	−0.00296530	+	0.000426346i
$397$	−2.66591e7	−	1.71328e7i	−0.426063	−	0.273814i	0.309987	−	0.950741i	$-0.399675\pi$
$397$	−2.66591e7	−	1.71328e7i	−0.426063	−	0.273814i	−0.736051	+	0.676926i	$0.763312\pi$
$398$	−4.87344e7	−	2.22563e7i	−0.773012	−	0.353023i
$399$	−9.56751e6	+	1.10415e7i	−0.150619	+	0.173824i
$400$	−8.87246e6	+	6.17093e7i	−0.138632	+	0.964208i
$401$	−3.09234e7	+	1.41223e7i	−0.479573	+	0.219014i	−0.640508	−	0.767951i	$-0.721276\pi$
$401$	−3.09234e7	+	1.41223e7i	−0.479573	+	0.219014i	0.160935	+	0.986965i	$0.448549\pi$
$402$	−6.46504e6	+	2.20179e7i	−0.0995161	+	0.338921i
$403$	−4.27567e7	−	1.25545e7i	−0.653264	−	0.191816i
$404$	30327.8	+	66408.7i	0.000459936	+	0.00100712i
$405$	1.01983e7	+	1.46630e6i	0.153520	+	0.0220728i
$406$	7.87521e7	+	6.82391e7i	1.17675	+	1.01966i
$407$	−5.63875e6	+	1.23471e7i	−0.0836372	+	0.183140i
$408$	−1.72023e7	+	2.67672e7i	−0.253282	+	0.394115i
$409$	5.09680e6	+	3.54490e7i	0.0744951	+	0.518125i	0.992566	+	0.121708i	$0.0388373\pi$
$409$	5.09680e6	+	3.54490e7i	0.0744951	+	0.518125i	−0.918071	+	0.396416i	$0.870254\pi$
$410$	−6.13832e7	−	9.55141e7i	−0.890631	−	1.38585i
$411$	5.87610e7	−	5.09167e7i	0.846376	−	0.733389i
$412$	222367.	+	757314.i	0.00317965	+	0.0108289i
$413$		−	5.68677e7i		−	0.807263i
$414$	1.19283e7	−	2.08017e7i	0.168104	−	0.293155i
$415$	9.77886e7			1.36818
$416$	−2.69143e6	+	790275.i	−0.0373855	+	0.0109774i
$417$	2.64257e7	+	3.04968e7i	0.364433	+	0.420578i
$418$	−8.17451e6	+	5.25344e6i	−0.111926	+	0.0719308i
$419$	3.86344e7	−	5.55479e6i	0.525209	−	0.0755136i	0.125390	−	0.992108i	$-0.459982\pi$
$419$	3.86344e7	−	5.55479e6i	0.525209	−	0.0755136i	0.399819	+	0.916594i	$0.369073\pi$
$420$	1.37036e6	+	880678.i	0.0184964	+	0.0118869i
$421$	6.87631e7	+	3.14030e7i	0.921529	+	0.420848i	0.818942	−	0.573876i	$-0.194561\pi$
$421$	6.87631e7	+	3.14030e7i	0.921529	+	0.420848i	0.102587	+	0.994724i	$0.467288\pi$
$422$	−3.08581e7	+	3.56122e7i	−0.410612	+	0.473872i
$423$	4.58198e6	−	3.18684e7i	0.0605386	−	0.421055i
$424$	1.07806e8	−	4.92334e7i	1.41431	−	0.645895i
$425$	−1.68882e7	+	5.75161e7i	−0.219997	+	0.749242i
$426$	−4.20066e7	−	1.23343e7i	−0.543362	−	0.159545i
$427$	5.50221e7	+	1.20482e8i	0.706730	+	1.54752i
$428$	−1.73623e6	−	249632.i	−0.0221450	−	0.00318397i
$429$	7.81305e6	+	6.77005e6i	0.0989575	+	0.0857472i
$430$	2.64699e7	−	5.79609e7i	0.332925	−	0.729004i
$431$	4.76784e7	−	7.41890e7i	0.595511	−	0.926633i	−0.404417	−	0.914575i	$-0.632525\pi$
$431$	4.76784e7	−	7.41890e7i	0.595511	−	0.926633i	0.999927	−	0.0120579i	$-0.00383825\pi$
$432$	−2.26776e6	−	1.57726e7i	−0.0281285	−	0.195638i
$433$	−3.80292e6	−	5.91746e6i	−0.0468439	−	0.0728906i	0.817042	−	0.576579i	$-0.195613\pi$
$433$	−3.80292e6	−	5.91746e6i	−0.0468439	−	0.0728906i	−0.863886	+	0.503688i	$0.831976\pi$
$434$	5.96982e7	−	5.17288e7i	0.730285	−	0.632796i
$435$	−2.92386e7	−	9.95774e7i	−0.355212	−	1.20974i
$436$		−	2.14251e6i		−	0.0258501i
$437$	3.11970e6	−	3.37204e7i	0.0373826	−	0.404063i
$438$	−8.45868e6			−0.100665
$439$	1.00171e8	−	2.94128e7i	1.18399	−	0.347651i	0.370279	−	0.928920i	$-0.379262\pi$
$439$	1.00171e8	−	2.94128e7i	1.18399	−	0.347651i	0.813711	+	0.581269i	$0.197444\pi$
$440$	−2.48213e7	−	2.86453e7i	−0.291384	−	0.336275i
$441$	870744.	−	559593.i	0.0101525	−	0.00652464i
$442$	−5.00262e7	+	7.19268e6i	−0.579336	+	0.0832959i
$443$	−6.04412e6	−	3.88432e6i	−0.0695219	−	0.0446790i	0.505418	−	0.862875i	$-0.331338\pi$
$443$	−6.04412e6	−	3.88432e6i	−0.0695219	−	0.0446790i	−0.574940	+	0.818196i	$0.694975\pi$
$444$	795235.	+	363172.i	0.00908546	+	0.00414919i
$445$	−1.18356e8	+	1.36590e8i	−1.34311	+	1.55003i
$446$	−2.32903e7	+	1.61987e8i	−0.262525	+	1.82590i
$447$	−5.05821e7	+	2.31001e7i	−0.566336	+	0.258637i
$448$	−2.41403e7	+	8.22144e7i	−0.268478	+	0.914352i
$449$	−1.45446e8	−	4.27069e7i	−1.60681	−	0.471802i	−0.649378	−	0.760466i	$-0.724971\pi$
$449$	−1.45446e8	−	4.27069e7i	−1.60681	−	0.471802i	−0.957430	+	0.288664i	$0.906789\pi$
$450$	−1.21335e7	−	2.65687e7i	−0.133152	−	0.291563i
$451$	3.41844e7	+	4.91498e6i	0.372648	+	0.0535787i
$452$	−1.16434e6	−	1.00891e6i	−0.0126086	−	0.0109254i
$453$	−1.04255e7	+	2.28286e7i	−0.112150	+	0.245575i
$454$	−4.82842e7	+	7.51316e7i	−0.515985	+	0.802888i
$455$	−1.28826e7	−	8.96005e7i	−0.136763	−	0.951210i
$456$	−1.18374e7	−	1.84193e7i	−0.124842	−	0.194258i
$457$	1.68764e7	−	1.46234e7i	0.176819	−	0.153215i	−0.561955	−	0.827168i	$-0.689950\pi$
$457$	1.68764e7	−	1.46234e7i	0.176819	−	0.153215i	0.738774	+	0.673953i	$0.235405\pi$
$458$	−7.64878e6	−	2.60493e7i	−0.0796151	−	0.271144i
$459$		−	1.53215e7i		−	0.158439i
$460$	−3.77092e6	+	190766.i	−0.0387413	+	0.00195987i
$461$	1.53551e8			1.56729			0.783645	−	0.621209i	$-0.213358\pi$
$461$	1.53551e8			1.56729			0.783645	+	0.621209i	$0.213358\pi$
$462$	−1.75835e7	+	5.16299e6i	−0.178312	+	0.0523571i
$463$	−1.12961e8	−	1.30364e8i	−1.13811	−	1.31345i	−0.943046	−	0.332661i	$-0.892053\pi$
$463$	−1.12961e8	−	1.30364e8i	−1.13811	−	1.31345i	−0.195066	−	0.980790i	$-0.562492\pi$
$464$	−1.35027e8	+	8.67765e7i	−1.35166	+	0.868657i
$465$	−7.78709e7	+	1.11961e7i	−0.774491	+	0.111355i
$466$	−6.19618e7	−	3.98204e7i	−0.612303	−	0.393503i
$467$	6.54788e7	+	2.99032e7i	0.642910	+	0.293607i	0.710066	−	0.704135i	$-0.248665\pi$
$467$	6.54788e7	+	2.99032e7i	0.642910	+	0.293607i	−0.0671560	+	0.997742i	$0.521393\pi$
$468$	436035.	−	503211.i	0.00425386	−	0.00490922i
$469$	−8.69813e6	+	6.04968e7i	−0.0843155	+	0.586427i
$470$	−1.70555e8	+	7.78899e7i	−1.64275	+	0.750218i
$471$	−1.35797e6	+	4.62482e6i	−0.0129965	+	0.0442621i
$472$	8.17717e7	+	2.40103e7i	0.777637	+	0.228335i
$473$	8.05160e6	+	1.76305e7i	0.0760849	+	0.166603i
$474$	8.10978e6	+	1.16601e6i	0.0761507	+	0.0109488i
$475$	−3.11741e7	−	2.70125e7i	−0.290880	−	0.252049i
$476$	1.00628e6	−	2.20344e6i	0.00933034	−	0.0204306i
$477$	−3.08539e7	+	4.80096e7i	−0.284286	+	0.442357i
$478$	2.51237e6	+	1.74739e7i	0.0230038	+	0.159995i
$479$	5.17824e7	+	8.05750e7i	0.471168	+	0.733151i	0.992769	−	0.120038i	$-0.0383016\pi$
$479$	5.17824e7	+	8.05750e7i	0.471168	+	0.733151i	−0.521601	+	0.853189i	$0.674665\pi$
$480$	−3.74261e6	+	3.24299e6i	−0.0338416	+	0.0293239i
$481$	−1.36871e7	−	4.66141e7i	−0.122992	−	0.418872i
$482$		−	1.55966e8i		−	1.39280i
$483$	2.35620e7	−	5.93613e7i	0.209108	−	0.526819i
$484$	2.82120e6			0.0248828
$485$	1.00541e8	−	2.95215e7i	0.881288	−	0.258769i
$486$	4.88885e6	+	5.64203e6i	0.0425890	+	0.0491504i
$487$	3.78882e7	−	2.43493e7i	0.328033	−	0.210814i	−0.366249	−	0.930517i	$-0.619358\pi$
$487$	3.78882e7	−	2.43493e7i	0.328033	−	0.210814i	0.694282	+	0.719703i	$0.255722\pi$
$488$	−1.96475e8	+	2.82489e7i	−1.69063	+	0.243076i
$489$	5.08564e7	+	3.26834e7i	0.434929	+	0.279512i
$490$	−5.48308e6	−	2.50404e6i	−0.0466054	−	0.0212840i
$491$	9.62615e7	−	1.11092e8i	0.813220	−	0.938506i	−0.185808	−	0.982586i	$-0.559490\pi$
$491$	9.62615e7	−	1.11092e8i	0.813220	−	0.938506i	0.999028	+	0.0440800i	$0.0140357\pi$
$492$	316556.	−	2.20170e6i	0.00265800	−	0.0184868i
$493$	−1.40382e8	+	6.41105e7i	−1.17158	+	0.535043i
$494$	9.79820e6	−	3.33696e7i	0.0812766	−	0.276803i
$495$	1.75122e7	+	5.14204e6i	0.144386	+	0.0423955i
$496$	5.05446e7	+	1.10677e8i	0.414219	+	0.907013i
$497$	−1.15418e8	−	1.65946e7i	−0.940167	−	0.135176i
$498$	5.35490e7	+	4.64005e7i	0.433574	+	0.375694i
$499$	6.80570e7	−	1.49024e8i	0.547736	−	1.19937i	−0.410096	−	0.912043i	$-0.634505\pi$
$499$	6.80570e7	−	1.49024e8i	0.547736	−	1.19937i	0.957831	−	0.287331i	$-0.0927681\pi$
$500$	135014.	−	210085.i	0.00108011	−	0.00168068i
$501$	−1.20733e7	−	8.39714e7i	−0.0960090	−	0.667757i
$502$	5.89402e7	+	9.17128e7i	0.465908	+	0.724968i
$503$	7.30067e6	−	6.32607e6i	0.0573666	−	0.0497084i	−0.625706	−	0.780059i	$-0.715189\pi$
$503$	7.30067e6	−	6.32607e6i	0.0573666	−	0.0497084i	0.683072	+	0.730351i	$0.260643\pi$
$504$	−1.16335e7	−	3.96202e7i	−0.0908700	−	0.309475i
$505$		−	7.16243e6i		−	0.0556143i
$506$	2.61593e7	−	3.34667e7i	0.201918	−	0.258322i
$507$	3.82412e7			0.293432
$508$	5.50941e6	−	1.61771e6i	0.0420256	−	0.0123398i
$509$	2.01062e7	+	2.32038e7i	0.152467	+	0.175957i	0.826845	−	0.562430i	$-0.190133\pi$
$509$	2.01062e7	+	2.32038e7i	0.152467	+	0.175957i	−0.674378	+	0.738387i	$0.735588\pi$
$510$	−7.50625e7	+	4.82398e7i	−0.565865	+	0.363659i
$511$	−2.22998e7	+	3.20622e6i	−0.167124	+	0.0240288i
$512$	−1.07852e8	−	6.93121e7i	−0.803558	−	0.516415i
$513$	9.59037e6	+	4.37978e6i	0.0710368	+	0.0324414i
$514$	−1.22443e8	+	1.41307e8i	−0.901664	+	1.04058i
$515$	1.10201e7	−	7.66465e7i	0.0806796	−	0.561139i
$516$	1.13552e6	−	518575.i	0.00826506	−	0.00377452i
$517$	1.60682e7	−	5.47232e7i	0.116277	−	0.396004i
$518$	8.26301e7	+	2.42624e7i	0.594496	+	0.174560i
$519$	5.94588e6	+	1.30197e7i	0.0425318	+	0.0931317i
$520$	1.34278e8	+	1.93063e7i	0.954984	+	0.137306i
$521$	6.30665e7	+	5.46475e7i	0.445950	+	0.386418i	0.848685	−	0.528899i	$-0.177395\pi$
$521$	6.30665e7	+	5.46475e7i	0.445950	+	0.386418i	−0.402735	+	0.915317i	$0.631940\pi$
$522$	3.12382e7	−	6.84022e7i	0.219621	−	0.480904i
$523$	2.34593e7	−	3.65035e7i	0.163988	−	0.255170i	−0.749529	−	0.661972i	$-0.769720\pi$
$523$	2.34593e7	−	3.65035e7i	0.163988	−	0.255170i	0.913516	+	0.406802i	$0.133356\pi$
$524$	684453.	+	4.76047e6i	0.00475718	+	0.0330869i
$525$	−4.20586e7	−	6.54444e7i	−0.290654	−	0.452267i
$526$	2.13546e8	−	1.85039e8i	1.46736	−	1.27147i
$527$	3.29597e7	+	1.12250e8i	0.225191	+	0.766931i
$528$		−	2.82276e7i		−	0.191766i
$529$	3.57477e7	+	1.43655e8i	0.241480	+	0.970406i
$530$	3.32351e8			2.23239
$531$	−3.93756e7	+	1.15617e7i	−0.262993	+	0.0772216i
$532$	1.09158e6	+	1.25975e6i	0.00724969	+	0.00836659i
$533$	−1.03986e8	+	6.68274e7i	−0.686738	+	0.441340i
$534$	−1.29623e8	+	1.86370e7i	−0.851255	+	0.122392i
$535$	1.44770e8	+	9.30381e7i	0.945404	+	0.607574i
$536$	−8.33177e7	−	3.80499e7i	−0.541057	−	0.247092i
$537$	5.16410e7	−	5.95969e7i	0.333482	−	0.384858i
$538$	−3.41000e7	+	2.37171e8i	−0.218982	+	1.52305i
$539$	1.66784e6	−	761679.i	0.0106510	−	0.00486413i
$540$	331181.	−	1.12790e6i	0.00210322	−	0.00716289i
$541$	2.16741e7	+	6.36409e6i	0.136883	+	0.0401925i	0.349456	−	0.936953i	$-0.386366\pi$
$541$	2.16741e7	+	6.36409e6i	0.136883	+	0.0401925i	−0.212573	+	0.977145i	$0.568184\pi$
$542$	−3.08915e7	−	6.76430e7i	−0.194018	−	0.424840i
$543$	−1.18071e7	−	1.69761e6i	−0.0737472	−	0.0106032i
$544$	5.56549e6	+	4.82252e6i	0.0345706	+	0.0299556i
$545$	−8.73183e7	+	1.91200e8i	−0.539406	+	1.18113i
$546$	3.54607e7	−	5.51780e7i	0.217856	−	0.338991i
$547$	−2.33415e7	−	1.62343e8i	−0.142615	−	0.991911i	−0.927914	−	0.372794i	$-0.878400\pi$
$547$	−2.33415e7	−	1.62343e8i	−0.142615	−	0.991911i	0.785299	−	0.619117i	$-0.212509\pi$
$548$	−4.79596e6	−	7.46266e6i	−0.0291430	−	0.0453473i
$549$	7.22359e7	−	6.25928e7i	0.436552	−	0.378274i
$550$	−1.45770e7	−	4.96446e7i	−0.0876152	−	0.298390i
$551$		−	1.06198e8i		−	0.634836i
$552$	7.54091e7	+	5.89437e7i	0.448339	+	0.350445i
$553$	2.18219e7			0.129038
$554$	2.82984e8	−	8.30916e7i	1.66430	−	0.488684i
$555$	−5.61669e7	−	6.48200e7i	−0.328550	−	0.379167i
$556$	3.87311e6	−	2.48909e6i	0.0225338	−	0.0144816i
$557$	−2.00178e8	+	2.87813e7i	−1.15838	+	0.166550i	−0.694598	−	0.719398i	$-0.744418\pi$
$557$	−2.00178e8	+	2.87813e7i	−1.15838	+	0.166550i	−0.463784	+	0.885948i	$0.653509\pi$
$558$	−4.79546e7	−	3.08186e7i	−0.276012	−	0.177382i
$559$	−6.31016e7	−	2.88175e7i	−0.361247	−	0.164976i
$560$	−1.61858e8	+	1.86794e8i	−0.921656	+	1.06365i
$561$	3.86258e6	−	2.68648e7i	0.0218770	−	0.152158i
$562$	2.16089e8	−	9.86843e7i	1.21737	−	0.555955i
$563$	3.94079e7	−	1.34211e8i	0.220830	−	0.752078i	−0.772320	−	0.635233i	$-0.780904\pi$
$563$	3.94079e7	−	1.34211e8i	0.220830	−	0.752078i	0.993150	−	0.116845i	$-0.0372779\pi$
$564$	−3.52453e6	−	1.03489e6i	−0.0196455	−	0.00576844i
$565$	6.27894e7	+	1.37490e8i	0.348130	+	0.762298i
$566$	3.27288e8	+	4.70568e7i	1.80501	+	0.259522i
$567$	1.50272e7	+	1.30211e7i	0.0824381	+	0.0714330i
$568$	7.25931e7	−	1.58957e8i	0.396141	−	0.867429i
$569$	−1.84865e8	+	2.87655e8i	−1.00350	+	1.56148i	−0.188455	+	0.982082i	$0.560348\pi$
$569$	−1.84865e8	+	2.87655e8i	−1.00350	+	1.56148i	−0.815046	+	0.579396i	$0.803289\pi$
$570$	−8.73807e6	−	6.07746e7i	−0.0471836	−	0.328169i
$571$	−7.19636e7	−	1.11978e8i	−0.386549	−	0.601482i	0.592386	−	0.805654i	$-0.298186\pi$
$571$	−7.19636e7	−	1.11978e8i	−0.386549	−	0.601482i	−0.978935	+	0.204172i	$0.934550\pi$
$572$	891407.	−	772409.i	0.00476308	−	0.00412724i
$573$	4.00252e7	+	1.36313e8i	0.212750	+	0.724560i
$574$		−	2.19113e8i		−	1.15859i
$575$	1.67598e8	+	6.65241e7i	0.881589	+	0.349926i
$576$	6.18338e7			0.323563
$577$	4.88417e7	−	1.43412e7i	0.254251	−	0.0746550i	−0.152123	−	0.988362i	$-0.548611\pi$
$577$	4.88417e7	−	1.43412e7i	0.254251	−	0.0746550i	0.406375	+	0.913707i	$0.366793\pi$
$578$	−4.13083e7	−	4.76723e7i	−0.213921	−	0.246878i
$579$	−8.90795e7	+	5.72479e7i	−0.458926	+	0.294934i
$580$	−1.17201e7	+	1.68510e6i	−0.0600686	+	0.00863656i
$581$	1.58760e8	+	1.02029e8i	0.809493	+	0.520230i
$582$	6.90640e7	+	3.15405e7i	0.350335	+	0.159992i
$583$	−6.62028e7	+	7.64021e7i	−0.334096	+	0.385567i
$584$	4.80496e6	−	3.34192e7i	0.0241241	−	0.167787i
$585$	−5.94209e7	+	2.71366e7i	−0.296805	+	0.135546i
$586$	8.51267e7	−	2.89915e8i	0.423032	−	1.44071i
$587$	2.66303e8	+	7.81936e7i	1.31662	+	0.386596i	0.863273	−	0.504737i	$-0.168410\pi$
$587$	2.66303e8	+	7.81936e7i	1.31662	+	0.386596i	0.453350	+	0.891332i	$0.350229\pi$
$588$	−49057.0	−	107420.i	−0.000241307	−	0.000528388i
$589$	−7.96842e7	−	1.14569e7i	−0.389966	−	0.0560686i
$590$	1.80617e8	+	1.56506e8i	0.879433	+	0.762033i
$591$	−4.39069e7	+	9.61427e7i	−0.212701	+	0.465751i
$592$	−7.17158e7	+	1.11592e8i	−0.345660	+	0.537858i
$593$	5.11760e6	+	3.55937e7i	0.0245416	+	0.170690i	0.998406	−	0.0564397i	$-0.0179749\pi$
$593$	5.11760e6	+	3.55937e7i	0.0245416	+	0.170690i	−0.973864	+	0.227130i	$0.927066\pi$
$594$	7.14978e6	+	1.11253e7i	0.0341141	+	0.0530825i
$595$	−1.79604e8	+	1.55628e8i	−0.852638	+	0.738815i
$596$	1.78741e6	+	6.08735e6i	0.00844277	+	0.0287534i
$597$			1.02975e8i			0.483958i
$598$	7.68123e6	+	1.51837e8i	0.0359192	+	0.710026i
$599$	1.11904e8			0.520675			0.260337	−	0.965518i	$-0.416166\pi$
$599$	1.11904e8			0.520675			0.260337	+	0.965518i	$0.416166\pi$
$600$	1.11862e8	−	3.28457e7i	0.517881	−	0.152063i
$601$	5.43050e7	+	6.26713e7i	0.250159	+	0.288699i	0.866916	−	0.498455i	$-0.166099\pi$
$601$	5.43050e7	+	6.26713e7i	0.250159	+	0.288699i	−0.616756	+	0.787154i	$0.711554\pi$
$602$	1.03448e8	−	6.64821e7i	0.474169	−	0.304730i
$603$	4.36568e7	−	6.27691e6i	0.199113	−	0.0286282i
$604$	2.40877e6	+	1.54802e6i	0.0109316	+	0.00702533i
$605$	−2.51769e8	−	1.14979e8i	−1.13693	−	0.519221i
$606$	3.39856e6	−	3.92214e6i	0.0152713	−	0.0176241i
$607$	−2.14344e7	+	1.49079e8i	−0.0958396	+	0.666579i	0.884102	+	0.467294i	$0.154771\pi$
$607$	−2.14344e7	+	1.49079e8i	−0.0958396	+	0.666579i	−0.979942	+	0.199285i	$0.936138\pi$
$608$	−4.60957e6	+	2.10512e6i	−0.0205092	+	0.00936625i
$609$	5.64264e7	−	1.92171e8i	0.249822	−	0.850815i
$610$	−5.34088e8	−	1.56822e8i	−2.35301	−	0.690905i
$611$	8.47982e7	+	1.85682e8i	0.371760	+	0.814041i
$612$	−1.73027e6	−	248775.i	−0.00754847	−	0.00108531i
$613$	−2.29711e8	−	1.99046e8i	−0.997241	−	0.864114i	−0.00651323	−	0.999979i	$-0.502073\pi$
$613$	−2.29711e8	−	1.99046e8i	−0.997241	−	0.864114i	−0.990727	+	0.135865i	$0.956619\pi$
$614$	9.80989e6	−	2.14807e7i	0.0423798	−	0.0927988i
$615$	−1.17981e8	+	1.83581e8i	−0.507207	+	0.789230i
$616$	−1.04100e7	−	7.24033e7i	−0.0445358	−	0.309753i
$617$	−1.86940e8	−	2.90885e8i	−0.795880	−	1.23841i	−0.967405	−	0.253234i	$-0.918506\pi$
$617$	−1.86940e8	−	2.90885e8i	−0.795880	−	1.23841i	0.171525	−	0.985180i	$-0.445131\pi$
$618$	4.24032e7	−	3.67426e7i	0.179652	−	0.155670i
$619$	−1.40714e7	−	4.79228e7i	−0.0593288	−	0.202055i	0.924495	−	0.381194i	$-0.124487\pi$
$619$	−1.40714e7	−	4.79228e7i	−0.0593288	−	0.202055i	−0.983824	+	0.179139i	$0.942669\pi$
$620$			8.97581e6i			0.0376616i
$621$	−4.58925e7	−	4.24583e6i	−0.191632	−	0.0177291i
$622$	1.84712e8			0.767581
$623$	−3.34665e8	+	9.82664e7i	−1.38403	+	0.406388i
$624$	6.61602e7	+	7.63530e7i	0.272297	+	0.314248i
$625$	−2.15417e8	+	1.38440e8i	−0.882349	+	0.567051i
$626$	1.53792e8	−	2.21120e7i	0.626918	−	0.0901372i
$627$	1.57117e7	+	1.00973e7i	0.0637412	+	0.0409640i
$628$	500236.	+	228450.i	0.00201974	+	0.000922385i
$629$	−8.35234e7	+	9.63912e7i	−0.335627	+	0.387334i
$630$	1.64795e7	−	1.14618e8i	0.0659057	−	0.458384i
$631$	−5.52016e7	+	2.52097e7i	−0.219717	+	0.100341i	−0.522233	−	0.852803i	$-0.674901\pi$
$631$	−5.52016e7	+	2.52097e7i	−0.219717	+	0.100341i	0.302516	+	0.953144i	$0.402174\pi$
$632$	−9.21354e6	+	3.13784e7i	−0.0364985	+	0.124303i
$633$	8.69007e7	+	2.55164e7i	0.342620	+	0.100602i
$634$	−1.20637e8	−	2.64158e8i	−0.473383	−	1.03656i
$635$	−5.57598e8	−	8.01705e7i	−2.17771	−	0.313107i
$636$	4.92079e6	+	4.26389e6i	0.0191277	+	0.0165743i
$637$	−2.72613e6	+	5.96939e6i	−0.0105470	+	0.0230947i
$638$	7.20177e7	−	1.12062e8i	0.277317	−	0.431514i
$639$	1.19753e7	+	8.32902e7i	0.0458970	+	0.319221i
$640$	−2.05676e8	−	3.20038e8i	−0.784592	−	1.22085i
$641$	−2.69707e8	+	2.33703e8i	−1.02404	+	0.887338i	−0.993686	−	0.112201i	$-0.964210\pi$
$641$	−2.69707e8	+	2.33703e8i	−1.02404	+	0.887338i	−0.0303576	+	0.999539i	$0.509665\pi$
$642$	3.51297e7	+	1.19641e8i	0.132761	+	0.452141i
$643$			1.25619e8i			0.472524i	0.971689	+	0.236262i	$0.0759224\pi$
$643$			1.25619e8i			0.472524i	−0.971689	+	0.236262i	$0.924078\pi$
$644$	−6.32114e6	−	3.62473e6i	−0.0236667	−	0.0135712i
$645$	−1.22470e8			−0.456406
$646$	−8.76063e7	+	2.57235e7i	−0.324966	+	0.0954186i
$647$	−2.44432e8	−	2.82089e8i	−0.902494	−	1.04153i	−0.998932	−	0.0461949i	$-0.985290\pi$
$647$	−2.44432e8	−	2.82089e8i	−0.902494	−	1.04153i	0.0964382	−	0.995339i	$-0.469255\pi$
$648$	−2.50681e7	+	1.61103e7i	−0.0921291	+	0.0592078i
$649$	−7.19562e7	+	1.03457e7i	−0.263229	+	0.0378467i
$650$	1.55787e8	+	1.00118e8i	0.567273	+	0.364564i
$651$	−1.38105e8	−	6.30706e7i	−0.500573	−	0.228604i
$652$	4.51672e6	−	5.21257e6i	0.0162960	−	0.0188065i
$653$	6.61121e7	−	4.59820e8i	0.237433	−	1.65138i	−0.427158	−	0.904177i	$-0.640485\pi$
$653$	6.61121e7	−	4.59820e8i	0.237433	−	1.65138i	0.664591	−	0.747207i	$-0.268606\pi$
$654$	−1.38540e8	+	6.32690e7i	−0.495269	+	0.226182i
$655$	1.32933e8	−	4.52727e8i	0.473051	−	1.61106i
$656$	3.23831e8	+	9.50853e7i	1.14711	+	0.336823i
$657$	6.75376e6	+	1.47887e7i	0.0238150	+	0.0521475i
$658$	−3.58164e8	−	5.14963e7i	−1.25720	−	0.180758i
$659$	−1.52105e8	−	1.31800e8i	−0.531480	−	0.460530i	0.347302	−	0.937753i	$-0.387098\pi$
$659$	−1.52105e8	−	1.31800e8i	−0.531480	−	0.460530i	−0.878782	+	0.477223i	$0.841643\pi$
$660$	865040.	−	1.89417e6i	0.00300888	−	0.00658852i
$661$	2.65442e8	−	4.13036e8i	0.919105	−	1.43015i	0.0164136	−	0.999865i	$-0.494775\pi$
$661$	2.65442e8	−	4.13036e8i	0.919105	−	1.43015i	0.902691	−	0.430289i	$-0.141588\pi$
$662$	7.73006e7	+	5.37638e8i	0.266446	+	1.85317i
$663$	5.25183e7	+	8.17200e7i	0.180206	+	0.280406i
$664$	−2.13741e8	+	1.85208e8i	−0.730103	+	0.632638i
$665$	−4.60727e7	−	1.56909e8i	−0.156667	−	0.533560i
$666$		−	6.21465e7i		−	0.210375i
$667$	1.53129e8	+	4.38255e8i	0.516034	+	1.47689i
$668$	−9.67900e6			−0.0324714
$669$	3.01806e8	−	8.86181e7i	1.00797	−	0.295968i
$670$	−1.68205e8	−	1.94119e8i	−0.559262	−	0.645423i
$671$	1.42439e8	−	9.15398e7i	0.471477	−	0.303000i
$672$	−9.45977e6	+	1.36011e6i	−0.0311726	+	0.00448194i
$673$	−3.63122e7	−	2.33364e7i	−0.119126	−	0.0765577i	0.479721	−	0.877421i	$-0.340738\pi$
$673$	−3.63122e7	−	2.33364e7i	−0.119126	−	0.0765577i	−0.598847	+	0.800863i	$0.704374\pi$
$674$	1.31488e8	+	6.00486e7i	0.429444	+	0.196121i
$675$	−3.67633e7	+	4.24271e7i	−0.119537	+	0.137953i
$676$	620922.	−	4.31861e6i	0.00201000	−	0.0139799i
$677$	−1.52365e8	+	6.95828e7i	−0.491043	+	0.224252i	−0.645518	−	0.763745i	$-0.723359\pi$
$677$	−1.52365e8	+	6.95828e7i	−0.491043	+	0.224252i	0.154475	+	0.987997i	$0.450631\pi$
$678$	−3.08551e7	+	1.05083e8i	−0.0990005	+	0.337165i
$679$	1.94030e8	+	5.69724e7i	0.619812	+	0.181993i
$680$	−1.47950e8	−	3.23966e8i	−0.470532	−	1.03032i
$681$	1.69908e8	+	2.44291e7i	0.537988	+	0.0773510i
$682$	−7.63146e7	−	6.61270e7i	−0.240577	−	0.208461i
$683$	−7.43384e7	+	1.62778e8i	−0.233320	+	0.510899i	−0.989687	−	0.143249i	$-0.954245\pi$
$683$	−7.43384e7	+	1.62778e8i	−0.233320	+	0.510899i	0.756367	+	0.654147i	$0.226972\pi$
$684$	650330.	−	1.01193e6i	0.00203220	−	0.00316216i
$685$	1.23856e8	+	8.61439e8i	0.385342	+	2.68011i
$686$	−1.79999e8	−	2.80085e8i	−0.557569	−	0.867595i
$687$	−3.94361e7	+	3.41716e7i	−0.121625	+	0.105389i
$688$	5.33632e7	+	1.81738e8i	0.163861	+	0.558061i
$689$		−	3.61828e8i		−	1.10623i
$690$	1.23692e8	+	2.38203e8i	0.376525	+	0.725105i
$691$	6.44861e8			1.95448			0.977241	−	0.212131i	$-0.0680405\pi$
$691$	6.44861e8			1.95448			0.977241	+	0.212131i	$0.0680405\pi$
$692$	1.56686e6	−	460073.i	0.00472839	−	0.00138838i
$693$	2.30661e7	+	2.66197e7i	0.0693066	+	0.0799841i
$694$	−3.42765e8	+	2.20281e8i	−1.02546	+	0.659021i
$695$	−4.47085e8	+	6.42812e7i	−1.33179	+	0.191483i
$696$	2.52504e8	+	1.62274e8i	0.748929	+	0.481307i
$697$	2.95186e8	+	1.34807e8i	0.871761	+	0.398120i
$698$	−3.70439e8	+	4.27509e8i	−1.08931	+	1.25713i
$699$	−2.01469e7	+	1.40125e8i	−0.0589898	+	0.410283i
$700$	−8.07360e6	+	3.68709e6i	−0.0235382	+	0.0107495i
$701$	1.56415e8	−	5.32699e8i	0.454070	−	1.54642i	−0.341095	−	0.940029i	$-0.610798\pi$
$701$	1.56415e8	−	5.32699e8i	0.454070	−	1.54642i	0.795165	−	0.606393i	$-0.207384\pi$
$702$	−4.54151e7	−	1.33351e7i	−0.131277	−	0.0385464i
$703$	−3.64595e7	−	7.98351e7i	−0.104941	−	0.229788i
$704$	1.08420e8	+	1.55884e7i	0.310735	+	0.0446770i
$705$	2.72357e8	+	2.35998e8i	0.777268	+	0.673506i
$706$	2.21525e7	−	4.85072e7i	0.0629519	−	0.137845i
$707$	7.47301e6	−	1.16282e7i	0.0211465	−	0.0329045i
$708$	666333.	+	4.63444e6i	0.00187755	+	0.0130586i
$709$	−2.90636e8	−	4.52238e8i	−0.815475	−	1.26890i	−0.960167	−	0.279427i	$-0.909855\pi$
$709$	−2.90636e8	−	4.52238e8i	−0.815475	−	1.26890i	0.144692	−	0.989477i	$-0.453781\pi$
$710$	3.70348e8	−	3.20909e8i	1.03475	−	0.896616i
$711$	−4.43660e6	−	1.51097e7i	−0.0123436	−	0.0420384i
$712$		−	5.22714e8i		−	1.44818i
$713$	3.45358e8	−	6.76181e7i	0.952799	−	0.186550i
$714$	−1.72196e8			−0.473073
$715$	−1.11030e8	+	3.26014e7i	−0.303755	+	0.0891905i
$716$	−5.89183e6	−	6.79954e6i	−0.0160513	−	0.0185242i
$717$	2.85444e7	−	1.83444e7i	0.0774397	−	0.0497674i
$718$	−4.81493e8	+	6.92282e7i	−1.30082	+	0.187029i
$719$	8.27825e7	+	5.32011e7i	0.222716	+	0.143131i	0.647241	−	0.762285i	$-0.275923\pi$
$719$	8.27825e7	+	5.32011e7i	0.222716	+	0.143131i	−0.424525	+	0.905416i	$0.639559\pi$
$720$	1.62244e8	+	7.40945e7i	0.434682	+	0.198513i
$721$	9.78613e7	−	1.12938e8i	0.261099	−	0.301324i
$722$	−4.53602e7	+	3.15487e8i	−0.120521	+	0.838243i
$723$	−2.72682e8	+	1.24529e8i	−0.721508	+	0.329501i
$724$	−383425.	+	1.30583e6i	−0.00101033	+	0.00344088i
$725$	5.42567e8	+	1.59312e8i	1.42377	+	0.418056i
$726$	−8.33112e7	−	1.82426e8i	−0.217718	−	0.476735i
$727$	4.44744e8	+	6.39445e7i	1.15746	+	0.166418i	0.694185	−	0.719796i	$-0.255765\pi$
$727$	4.44744e8	+	6.39445e7i	1.15746	+	0.166418i	0.463276	+	0.886214i	$0.346674\pi$
$728$	1.97858e8	+	1.71445e8i	0.512814	+	0.444356i
$729$	5.96075e6	−	1.30522e7i	0.0153857	−	0.0336901i
$730$	5.11880e7	−	7.96501e7i	0.131583	−	0.204747i
$731$	2.59184e7	+	1.80267e8i	0.0663524	+	0.461491i
$732$	−5.89576e6	−	9.17398e6i	−0.0150316	−	0.0233897i
$733$	−5.78345e7	+	5.01138e7i	−0.146850	+	0.127246i	−0.725188	−	0.688551i	$-0.758247\pi$
$733$	−5.78345e7	+	5.01138e7i	−0.146850	+	0.127246i	0.578338	+	0.815798i	$0.303702\pi$
$734$	2.04660e7	+	6.97006e7i	0.0517540	+	0.176258i
$735$			1.15856e7i			0.0291782i
$736$	1.59872e7	−	1.53340e7i	0.0400996	−	0.0384610i
$737$	7.81307e7			0.195173
$738$	−1.51715e8	+	4.45476e7i	−0.377450	+	0.110829i
$739$	3.09192e8	+	3.56827e8i	0.766117	+	0.884147i	0.996026	−	0.0890657i	$-0.0283881\pi$
$739$	3.09192e8	+	3.56827e8i	0.766117	+	0.884147i	−0.229908	+	0.973212i	$0.573843\pi$
$740$	−8.23216e6	+	5.29049e6i	−0.0203151	+	0.0130557i
$741$	−6.61649e7	+	9.51307e6i	−0.162620	+	0.0233812i
$742$	5.39573e8	+	3.46763e8i	1.32081	+	0.848830i
$743$	4.49840e8	+	2.05435e8i	1.09671	+	0.500850i	0.879801	−	0.475342i	$-0.157676\pi$
$743$	4.49840e8	+	2.05435e8i	1.09671	+	0.500850i	0.216908	+	0.976192i	$0.430403\pi$
$744$	1.49001e8	−	1.71956e8i	0.361802	−	0.417542i
$745$	8.85804e7	−	6.16091e8i	0.214224	−	1.48996i
$746$	−1.42825e8	+	6.52258e7i	−0.344022	+	0.157110i
$747$	3.83682e7	−	1.30670e8i	0.0920470	−	0.313483i
$748$	−2.97115e6	−	872408.i	−0.00709936	−	0.00208456i
$749$	1.37962e8	+	3.02095e8i	0.328333	+	0.718950i
$750$	−1.75716e7	−	2.52642e6i	−0.0416513	−	0.00598855i
$751$	−5.48973e7	−	4.75688e7i	−0.129608	−	0.112306i	0.587645	−	0.809119i	$-0.300055\pi$
$751$	−5.48973e7	−	4.75688e7i	−0.129608	−	0.112306i	−0.717253	+	0.696813i	$0.754601\pi$
$752$	2.31535e8	−	5.06991e8i	0.544457	−	1.19219i
$753$	1.13285e8	−	1.76275e8i	0.265331	−	0.412863i
$754$	6.78508e7	+	4.71913e8i	0.158286	+	1.10090i
$755$	−1.51872e8	−	2.36318e8i	−0.352889	−	0.549106i
$756$	1.71448e6	−	1.48561e6i	0.00396796	−	0.00343826i
$757$	−1.16136e8	−	3.95521e8i	−0.267718	−	0.911764i	−0.978133	−	0.207981i	$-0.933311\pi$
$757$	−1.16136e8	−	3.95521e8i	−0.267718	−	0.911764i	0.710415	−	0.703783i	$-0.248507\pi$
$758$			5.63111e8i			1.29296i
$759$	−7.93980e7	−	1.90143e7i	−0.181587	−	0.0434865i
$760$	2.45077e8			0.558292
$761$	−3.73072e8	+	1.09544e8i	−0.846523	+	0.248562i	−0.676101	−	0.736809i	$-0.736332\pi$
$761$	−3.73072e8	+	1.09544e8i	−0.846523	+	0.248562i	−0.170423	+	0.985371i	$0.554513\pi$
$762$	−2.67300e8	−	3.08480e8i	−0.604134	−	0.697208i
$763$	−3.41253e8	+	2.19310e8i	−0.768251	+	0.493725i
$764$	1.60439e7	−	2.30676e6i	0.0359773	−	0.00517276i
$765$	1.44273e8	+	9.27185e7i	0.322255	+	0.207101i
$766$	2.55920e8	+	1.16875e8i	0.569401	+	0.260037i
$767$	1.70386e8	−	1.96636e8i	0.377615	−	0.435791i
$768$	3.10056e6	−	2.15649e7i	0.00684474	−	0.0476062i
$769$	−2.20620e8	+	1.00754e8i	−0.485138	+	0.221555i	−0.642941	−	0.765916i	$-0.722286\pi$
$769$	−2.20620e8	+	1.00754e8i	−0.485138	+	0.221555i	0.157803	+	0.987471i	$0.449559\pi$
$770$	5.77907e7	−	1.96817e8i	0.126586	−	0.431112i
$771$	3.44816e8	+	1.01247e8i	0.752359	+	0.220912i
$772$	5.01867e6	+	1.09894e7i	0.0109078	+	0.0238847i
$773$	−4.09480e6	−	588743.i	−0.00886531	−	0.00127464i	0.137881	−	0.990449i	$-0.455971\pi$
$773$	−4.09480e6	−	588743.i	−0.00886531	−	0.00127464i	−0.146746	+	0.989174i	$0.546880\pi$
$774$	−6.70646e7	−	5.81118e7i	−0.144634	−	0.125326i
$775$	1.78071e8	−	3.89921e8i	0.382550	−	0.837668i
$776$	−1.63845e8	+	2.54947e8i	−0.350628	+	0.545589i
$777$	−2.35563e7	−	1.63838e8i	−0.0502163	−	0.349262i
$778$	−3.63099e8	−	5.64993e8i	−0.771056	−	1.19979i
$779$	−1.68763e8	+	1.46234e8i	−0.356997	+	0.309340i
$780$	2.09974e6	+	7.15107e6i	0.00442468	+	0.0150691i
$781$			1.49061e8i			0.312903i
$782$	3.24440e8	−	2.32476e8i	0.678444	−	0.486136i
$783$	−1.44532e8			−0.301079
$784$	1.71924e7	−	5.04815e6i	0.0356770	−	0.0104757i
$785$	−3.53313e7	−	4.07744e7i	−0.0730382	−	0.0842906i
$786$	2.87612e8	−	1.84837e8i	0.592296	−	0.380646i
$787$	−1.80369e8	+	2.59331e7i	−0.370030	+	0.0532023i	−0.324822	−	0.945775i	$-0.605304\pi$
$787$	−1.80369e8	+	2.59331e7i	−0.370030	+	0.0532023i	−0.0452083	+	0.998978i	$0.514395\pi$
$788$	1.01446e7	+	6.51951e6i	0.0207326	+	0.0133241i
$789$	−4.94016e8	−	2.25610e8i	−1.00580	−	0.459332i
$790$	−6.00562e7	+	6.93086e7i	−0.121808	+	0.140574i
$791$	−4.15127e7	+	2.88727e8i	−0.0838787	+	0.583389i
$792$	−4.80161e7	+	2.19282e7i	−0.0966521	+	0.0441395i
$793$	−1.70731e8	+	5.81457e8i	−0.342368	+	1.16600i
$794$	2.46605e8	+	7.24099e7i	0.492653	+	0.144656i
$795$	−2.65363e8	−	5.81064e8i	−0.528128	−	1.15644i
$796$	1.16290e7	+	1.67200e6i	0.0230571	+	0.00331511i
$797$	5.07507e8	+	4.39757e8i	1.00246	+	0.868637i	0.991342	−	0.131302i	$-0.0419156\pi$
$797$	5.07507e8	+	4.39757e8i	1.00246	+	0.868637i	0.0111176	+	0.999938i	$0.496461\pi$
$798$	4.92237e7	−	1.07785e8i	0.0968647	−	0.212104i
$799$	2.89732e8	−	4.50832e8i	0.568011	−	0.883842i
$800$	−3.84008e6	−	2.67083e7i	−0.00750016	−	0.0521647i
$801$	1.36081e8	+	2.11746e8i	0.264788	+	0.412019i
$802$	2.08373e8	−	1.80556e8i	0.403942	−	0.350018i
$803$	8.11385e6	+	2.76332e7i	0.0156704	+	0.0533685i
$804$		−	5.03212e6i		−	0.00968240i
$805$	4.16381e8	+	5.81096e8i	0.798185	+	1.11394i
$806$	3.61413e8			0.690239
$807$	4.41883e8	−	1.29749e8i	0.840789	−	0.246878i
$808$	1.35654e7	+	1.56553e7i	0.0257157	+	0.0296775i
$809$	−2.20055e7	+	1.41420e7i	−0.0415609	+	0.0267096i	−0.561256	−	0.827642i	$-0.689682\pi$
$809$	−2.20055e7	+	1.41420e7i	−0.0415609	+	0.0267096i	0.519695	+	0.854352i	$0.326045\pi$
$810$	−8.27125e7	+	1.18923e7i	−0.155638	+	0.0223774i
$811$	−2.05276e8	−	1.31923e8i	−0.384835	−	0.247319i	0.333891	−	0.942612i	$-0.391638\pi$
$811$	−2.05276e8	−	1.31923e8i	−0.384835	−	0.247319i	−0.718726	+	0.695293i	$0.755275\pi$
$812$	−2.07858e7	−	9.49256e6i	−0.0388239	−	0.0177303i
$813$	−9.35981e7	+	1.08018e8i	−0.174179	+	0.201013i
$814$	1.56673e7	−	1.08968e8i	0.0290482	−	0.202035i
$815$	−6.15518e8	+	2.81098e8i	−1.13702	+	0.519260i
$816$	7.47255e7	−	2.54492e8i	0.137530	−	0.468385i
$817$	−1.20246e8	−	3.53073e7i	−0.220497	−	0.0647438i
$818$	−1.20662e8	−	2.64214e8i	−0.220451	−	0.482720i
$819$	−1.24783e8	−	1.79411e7i	−0.227146	−	0.0326587i
$820$	1.88163e7	+	1.63045e7i	0.0341267	+	0.0295709i
$821$	1.72394e8	−	3.77490e8i	0.311525	−	0.682145i	−0.687505	−	0.726180i	$-0.741294\pi$
$821$	1.72394e8	−	3.77490e8i	0.311525	−	0.682145i	0.999030	+	0.0440350i	$0.0140213\pi$
$822$	−3.40927e8	+	5.30493e8i	−0.613828	+	0.955135i
$823$	−1.32484e8	−	9.21443e8i	−0.237663	−	1.65299i	−0.663493	−	0.748182i	$-0.730927\pi$
$823$	−1.32484e8	−	9.21443e8i	−0.237663	−	1.65299i	0.425830	−	0.904803i	$-0.359982\pi$
$824$	1.21078e8	+	1.88402e8i	0.216414	+	0.336747i
$825$	−7.51570e7	+	6.51239e7i	−0.133847	+	0.115979i
$826$	1.29940e8	+	4.42537e8i	0.230571	+	0.785252i
$827$		−	2.68523e8i		−	0.474751i	−0.971418	−	0.237375i	$-0.923713\pi$
$827$		−	2.68523e8i		−	0.474751i	0.971418	−	0.237375i	$-0.0762871\pi$
$828$	−1.22464e6	+	5.11374e6i	−0.00215734	+	0.00900841i
$829$	−4.70716e8			−0.826220			−0.413110	−	0.910681i	$-0.635558\pi$
$829$	−4.70716e8			−0.826220			−0.413110	+	0.910681i	$0.635558\pi$
$830$	−7.60978e8	+	2.23443e8i	−1.33088	+	0.390781i
$831$	−3.71219e8	−	4.28410e8i	−0.646885	−	0.746545i
$832$	−3.29802e8	+	2.11951e8i	−0.572642	+	0.368015i
$833$	1.70532e7	−	2.45188e6i	0.0295033	−	0.00424193i
$834$	−2.75325e8	−	1.76941e8i	−0.474622	−	0.305021i
$835$	8.63768e8	+	3.94470e8i	1.48367	+	0.677570i
$836$	1.39541e6	−	1.61038e6i	0.00238826	−	0.00275620i
$837$	−1.55925e7	+	1.08448e8i	−0.0265912	+	0.184946i
$838$	−2.87955e8	+	1.31505e8i	−0.489320	+	0.223465i
$839$	9.10375e6	−	3.10045e7i	0.0154147	−	0.0524976i	−0.951427	−	0.307876i	$-0.900382\pi$
$839$	9.10375e6	−	3.10045e7i	0.0154147	−	0.0524976i	0.966841	+	0.255378i	$0.0822000\pi$
$840$	4.43480e8	+	1.30217e8i	0.748231	+	0.219701i
$841$	3.57676e8	+	7.83202e8i	0.601316	+	1.31670i
$842$	−6.06860e8	−	8.72533e7i	−1.01661	−	0.146166i
$843$	−3.45068e8	−	2.99003e8i	−0.576000	−	0.499107i
$844$	4.29259e6	−	9.39946e6i	0.00713990	−	0.0156342i
$845$	−2.31418e8	+	3.60093e8i	−0.383554	+	0.596822i
$846$	3.71617e7	+	2.58465e8i	0.0613740	+	0.426866i
$847$	−2.88783e8	−	4.49355e8i	−0.475249	−	0.739501i
$848$	−7.46639e8	+	6.46966e8i	−1.22440	+	1.06095i
$849$	−1.79049e8	−	6.09783e8i	−0.292582	−	0.996443i
$850$		−	4.86171e8i		−	0.791649i
$851$	2.65576e8	+	2.76890e8i	0.430923	+	0.449281i
$852$	9.60047e6			0.0155229
$853$	9.06856e8	−	2.66277e8i	1.46114	−	0.429029i	0.547930	−	0.836524i	$-0.315416\pi$
$853$	9.06856e8	−	2.66277e8i	1.46114	−	0.429029i	0.913207	+	0.407495i	$0.133598\pi$
$854$	−7.03471e8	−	8.11849e8i	−1.12946	−	1.30347i
$855$	−9.92781e7	+	6.38021e7i	−0.158838	+	0.102079i
$856$	−4.92642e8	+	7.08312e7i	−0.785434	+	0.112928i
$857$	−8.49794e8	−	5.46129e8i	−1.35012	−	0.867667i	−0.352442	−	0.935834i	$-0.614649\pi$
$857$	−8.49794e8	−	5.46129e8i	−1.35012	−	0.867667i	−0.997674	+	0.0681669i	$0.978285\pi$
$858$	−7.62694e7	−	3.48311e7i	−0.120750	−	0.0551449i
$859$	8.59430e7	−	9.91835e7i	0.135591	−	0.156480i	−0.683893	−	0.729582i	$-0.739715\pi$
$859$	8.59430e7	−	9.91835e7i	0.135591	−	0.156480i	0.819484	+	0.573102i	$0.194260\pi$
$860$	−1.98855e6	+	1.38307e7i	−0.00312637	+	0.0217444i
$861$	−3.83084e8	+	1.74949e8i	−0.600184	+	0.274095i
$862$	−2.01508e8	+	6.86272e8i	−0.314608	+	1.07146i
$863$	5.69635e8	+	1.67260e8i	0.886266	+	0.260231i	0.693019	−	0.720919i	$-0.256280\pi$
$863$	5.69635e8	+	1.67260e8i	0.886266	+	0.260231i	0.193247	+	0.981150i	$0.438098\pi$
$864$	2.86501e6	+	6.27349e6i	0.00444206	+	0.00972675i
$865$	−1.58580e8	−	2.28003e7i	−0.245019	−	0.0352284i
$866$	4.31150e7	+	3.73594e7i	0.0663857	+	0.0575235i
$867$	−5.03653e7	+	1.10285e8i	−0.0772812	+	0.169222i
$868$	−9.36503e6	+	1.45723e7i	−0.0143202	+	0.0222827i
$869$	−3.96999e6	−	2.76119e7i	−0.00604965	−	0.0420762i
$870$	4.55061e8	+	7.08089e8i	0.691054	+	1.07530i
$871$	−2.11336e8	+	1.83124e8i	−0.319830	+	0.277135i
$872$	−1.71271e8	−	5.83294e8i	−0.258305	−	0.879707i
$873$		−	1.45931e8i		−	0.219333i
$874$	5.27728e7	+	2.69536e8i	0.0790452	+	0.403722i
$875$	−4.72821e7			−0.0705785
$876$	1.77976e6	−	522584.i	0.00264758	−	0.000777399i
$877$	6.96713e8	+	8.04049e8i	1.03289	+	1.19202i	0.981128	+	0.193362i	$0.0619391\pi$
$877$	6.96713e8	+	8.04049e8i	1.03289	+	1.19202i	0.0517647	+	0.998659i	$0.483515\pi$
$878$	−7.12310e8	+	4.57774e8i	−1.05241	+	0.676344i
$879$	−5.74840e8	+	8.26495e7i	−0.846409	+	0.121695i
$880$	2.65801e8	+	1.70820e8i	0.390040	+	0.250663i
$881$	8.17038e8	+	3.73129e8i	1.19485	+	0.545671i	0.910684	−	0.413103i	$-0.135555\pi$
$881$	8.17038e8	+	3.73129e8i	1.19485	+	0.545671i	0.284169	+	0.958774i	$0.408282\pi$
$882$	−5.49736e6	+	6.34430e6i	−0.00801214	+	0.00924651i
$883$	−1.48123e8	+	1.03022e9i	−0.215150	+	1.49640i	0.540456	+	0.841372i	$0.318252\pi$
$883$	−1.48123e8	+	1.03022e9i	−0.215150	+	1.49640i	−0.755606	+	0.655027i	$0.772657\pi$
$884$	1.00814e7	−	4.60404e6i	0.0145937	−	0.00666473i
$885$	1.29413e8	−	4.40741e8i	0.186702	−	0.635849i
$886$	5.59101e7	+	1.64167e7i	0.0803876	+	0.0236039i
$887$	−4.45912e8	−	9.76411e8i	−0.638967	−	1.39914i	−0.900887	−	0.434053i	$-0.857083\pi$
$887$	−4.45912e8	−	9.76411e8i	−0.638967	−	1.39914i	0.261921	−	0.965089i	$-0.415644\pi$
$888$	2.45533e8	+	3.53024e7i	0.350648	+	0.0504156i
$889$	−8.21616e8	−	7.11934e8i	−1.16940	−	1.01329i
$890$	6.08928e8	−	1.33337e9i	0.863765	−	1.89138i
$891$	1.37421e7	−	2.13832e7i	0.0194277	−	0.0302300i
$892$	−5.10730e6	−	3.55221e7i	−0.00719609	−	0.0500499i
$893$	1.99373e8	+	3.10230e8i	0.279970	+	0.435642i
$894$	3.40840e8	−	2.95340e8i	0.477022	−	0.413342i
$895$	2.48679e8	+	8.46924e8i	0.346873	+	1.18134i
$896$		−	7.34178e8i		−	1.02065i
$897$	2.59330e8	−	1.34662e8i	0.359315	−	0.186582i
$898$	1.22943e9			1.69775
$899$	1.05889e9	−	3.10920e8i	1.45738	−	0.427926i
$900$	4.19440e6	+	4.84060e6i	0.00575364	+	0.00664005i
$901$	−7.99122e8	+	5.13565e8i	−1.09254	+	0.702135i
$902$	−2.77249e8	+	3.98624e7i	−0.377790	+	0.0543180i
$903$	−1.98831e8	−	1.27781e8i	−0.270035	−	0.173541i
$904$	−3.97642e8	−	1.81597e8i	−0.538254	−	0.245812i
$905$	8.74367e7	−	1.00907e8i	0.117964	−	0.136137i
$906$	2.89671e7	−	2.01471e8i	0.0389512	−	0.270912i
$907$	1.12849e9	−	5.15363e8i	1.51243	−	0.690703i	0.525342	−	0.850891i	$-0.323937\pi$
$907$	1.12849e9	−	5.15363e8i	1.51243	−	0.690703i	0.987086	+	0.160188i	$0.0512102\pi$
$908$	5.51759e6	−	1.87912e7i	0.00737042	−	0.0251013i
$909$	−9.57081e6	−	2.81024e6i	−0.0127426	−	0.00374156i
$910$	3.04984e8	+	6.67823e8i	0.404719	+	0.886211i
$911$	−4.91410e8	−	7.06541e7i	−0.649963	−	0.0934506i	−0.190556	−	0.981676i	$-0.561029\pi$
$911$	−4.91410e8	−	7.06541e7i	−0.649963	−	0.0934506i	−0.459407	+	0.888226i	$0.651938\pi$
$912$	1.37936e8	+	1.19523e8i	0.181842	+	0.157567i
$913$	1.00217e8	−	2.19445e8i	0.131683	−	0.288346i
$914$	−9.79155e7	+	1.52360e8i	−0.128237	+	0.199540i
$915$	1.52259e8	+	1.05898e9i	0.198755	+	1.38237i
$916$	3.21870e6	+	5.00840e6i	0.00418788	+	0.00651647i
$917$	6.88175e8	−	5.96307e8i	0.892465	−	0.773325i
$918$	3.50090e7	+	1.19230e8i	0.0452534	+	0.154119i
$919$			6.89409e8i			0.888240i	0.895967	+	0.444120i	$0.146484\pi$
$919$			6.89409e8i			0.888240i	−0.895967	+	0.444120i	$0.853516\pi$
$920$	−1.01138e9	+	3.53380e8i	−1.29882	+	0.453815i
$921$	−4.53882e7			−0.0580984
$922$	−1.19491e9	+	3.50858e8i	−1.52455	+	0.447650i
$923$	−3.49371e8	−	4.03196e8i	−0.444306	−	0.512756i
$924$	3.38071e6	−	2.17265e6i	0.00428540	−	0.00275406i
$925$	4.62574e8	−	6.65081e7i	0.584461	−	0.0840329i
$926$	1.17692e9	+	7.56362e8i	1.48223	+	0.952570i
$927$	−9.80951e7	−	4.47986e7i	−0.123143	−	0.0562373i
$928$	4.54924e7	−	5.25010e7i	0.0569239	−	0.0656937i
$929$	−1.02919e8	+	7.15818e8i	−0.128366	+	0.892803i	0.819261	+	0.573422i	$0.194384\pi$
$929$	−1.02919e8	+	7.15818e8i	−0.128366	+	0.892803i	−0.947626	+	0.319382i	$0.896525\pi$
$930$	5.80398e8	−	2.65059e8i	0.721568	−	0.329529i
$931$	−3.34006e6	+	1.13752e7i	−0.00413909	+	0.0140965i
$932$	1.54973e7	+	4.55042e6i	0.0191429	+	0.00562087i
$933$	−1.47482e8	−	3.22940e8i	−0.181591	−	0.397628i
$934$	−5.77875e8	−	8.30859e7i	−0.709240	−	0.101973i
$935$	2.29594e8	+	1.98945e8i	0.280884	+	0.243387i
$936$	7.84834e7	−	1.71855e8i	0.0957085	−	0.209572i
$937$	5.47733e8	−	8.52289e8i	0.665809	−	1.03602i	−0.329948	−	0.943999i	$-0.607031\pi$
$937$	5.47733e8	−	8.52289e8i	0.665809	−	1.03602i	0.995757	−	0.0920203i	$-0.0293325\pi$
$938$	−7.05453e7	−	4.90653e8i	−0.0854790	−	0.594519i
$939$	−1.61453e8	−	2.51226e8i	−0.195007	−	0.303437i
$940$	3.10738e7	−	2.69256e7i	0.0374119	−	0.0324176i
$941$	−2.41827e7	−	8.23588e7i	−0.0290226	−	0.0988419i	0.943708	−	0.330780i	$-0.107312\pi$
$941$	−2.41827e7	−	8.23588e7i	−0.0290226	−	0.0988419i	−0.972731	+	0.231938i	$0.925493\pi$
$942$		−	3.90927e7i		−	0.0467673i
$943$	4.85589e8	−	8.46816e8i	0.579074	−	1.00984i
$944$	−7.10422e8			−0.844502
$945$	−2.13549e8	+	6.27036e7i	−0.253048	+	0.0743015i
$946$	−1.02942e8	−	1.18801e8i	−0.121595	−	0.140329i
$947$	−4.07142e8	+	2.61654e8i	−0.479397	+	0.308090i	−0.757929	−	0.652337i	$-0.773789\pi$
$947$	−4.07142e8	+	2.61654e8i	−0.479397	+	0.308090i	0.278532	+	0.960427i	$0.410152\pi$
$948$	−1.77838e6	+	255693.i	−0.00208738	+	0.000300119i
$949$	−8.67144e7	−	5.57280e7i	−0.101460	−	0.0652041i
$950$	3.04316e8	+	1.38976e8i	0.354939	+	0.162095i
$951$	−3.65518e8	+	4.21830e8i	−0.424979	+	0.490451i
$952$	9.78161e7	−	6.80326e8i	0.113370	−	0.788508i
$953$	−1.84405e8	+	8.42149e7i	−0.213056	+	0.0972995i	−0.519085	−	0.854723i	$-0.673727\pi$
$953$	−1.84405e8	+	8.42149e7i	−0.213056	+	0.0972995i	0.306028	+	0.952022i	$0.401000\pi$
$954$	1.30401e8	−	4.44105e8i	0.150188	−	0.511493i
$955$	−1.52579e9	−	4.48013e8i	−1.75180	−	0.514376i
$956$	−1.60817e6	−	3.52140e6i	−0.00184059	−	0.00403034i
$957$	−2.53424e8	−	3.64369e7i	−0.289143	−	0.0415725i
$958$	−5.87075e8	−	5.08703e8i	−0.667724	−	0.578586i
$959$	−6.97713e8	+	1.52778e9i	−0.791081	+	1.73222i
$960$	−3.74189e8	+	5.82250e8i	−0.422939	+	0.658106i
$961$	7.24644e6	+	5.04001e7i	0.00816496	+	0.0567886i
$962$	2.13023e8	+	3.31470e8i	0.239277	+	0.372322i
$963$	1.81124e8	−	1.56945e8i	0.202814	−	0.175739i
$964$	9.63569e6	+	3.28161e7i	0.0107560	+	0.0366316i
$965$		−	1.18524e9i		−	1.31894i
$966$	−4.77183e7	+	5.15780e8i	−0.0529363	+	0.572180i
$967$	1.06805e9			1.18117			0.590587	−	0.806974i	$-0.298896\pi$
$967$	1.06805e9			1.18117			0.590587	+	0.806974i	$0.298896\pi$
$968$	7.68069e8	−	2.25525e8i	0.846787	−	0.248639i
$969$	1.14922e8	+	1.32627e8i	0.126308	+	0.145768i
$970$	−7.14941e8	+	4.59464e8i	−0.783348	+	0.503427i
$971$	7.10864e7	−	1.02207e7i	0.0776478	−	0.0111641i	−0.103381	−	0.994642i	$-0.532966\pi$
$971$	7.10864e7	−	1.02207e7i	0.0776478	−	0.0111641i	0.181029	+	0.983478i	$0.442057\pi$
$972$	−1.37721e6	−	885081.i	−0.00149969	−	0.000963795i
$973$	−7.92914e8	−	3.62112e8i	−0.860770	−	0.393101i
$974$	−2.39204e8	+	2.76056e8i	−0.258876	+	0.298759i
$975$	5.06543e7	−	3.52309e8i	0.0546516	−	0.380110i
$976$	1.50512e9	−	6.87367e8i	1.61891	−	0.739331i
$977$	2.23335e6	−	7.60611e6i	0.00239483	−	0.00815603i	−0.958287	−	0.285808i	$-0.907738\pi$
$977$	2.23335e6	−	7.60611e6i	0.00239483	−	0.00815603i	0.960682	+	0.277652i	$0.0895562\pi$
$978$	−4.70438e8	−	1.38133e8i	−0.502905	−	0.147666i
$979$	1.85224e8	+	4.05583e8i	0.197400	+	0.432247i
$980$	1.30838e6	+	188116.i	0.00139013	+	0.000199870i
$981$	2.21232e8	+	1.91698e8i	0.234337	+	0.203054i
$982$	−4.95254e8	+	1.08445e9i	−0.522990	+	1.14519i
$983$	−4.89561e8	+	7.61771e8i	−0.515402	+	0.801981i	−0.997237	−	0.0742808i	$-0.976334\pi$
$983$	−4.89561e8	+	7.61771e8i	−0.515402	+	0.801981i	0.481836	+	0.876262i	$0.339970\pi$
$984$	−8.98203e7	−	6.24714e8i	−0.0942734	−	0.655686i
$985$	−6.39612e8	−	9.95255e8i	−0.669280	−	1.04142i
$986$	9.45947e8	−	8.19668e8i	0.986816	−	0.855081i
$987$	1.95940e8	+	6.67311e8i	0.203785	+	0.694028i
$988$			7.62651e6i			0.00790779i
$989$	5.47137e8	−	2.76789e7i	0.565597	−	0.0286128i
$990$	−1.48027e8			−0.152558
$991$	1.19062e9	−	3.49597e8i	1.22335	−	0.359208i	0.394614	−	0.918847i	$-0.370878\pi$
$991$	1.19062e9	−	3.49597e8i	1.22335	−	0.359208i	0.828737	+	0.559639i	$0.189060\pi$
$992$	−3.44856e7	−	3.97985e7i	−0.0353267	−	0.0407692i
$993$	8.78255e8	−	5.64420e8i	0.896960	−	0.576441i
$994$	9.36087e8	−	1.34589e8i	0.953140	−	0.137041i
$995$	−9.69649e8	−	6.23156e8i	−0.984341	−	0.632597i
$996$	−1.41337e7	−	6.45464e6i	−0.0143047	−	0.00653272i
$997$	−1.04097e9	+	1.20135e9i	−1.05040	+	1.21222i	−0.0737728	+	0.997275i	$0.523504\pi$
$997$	−1.04097e9	+	1.20135e9i	−1.05040	+	1.21222i	−0.976625	+	0.214949i	$0.931041\pi$
$998$	−1.89096e8	+	1.31519e9i	−0.190235	+	1.32312i
$999$	−1.08653e8	+	4.96203e7i	−0.108980	+	0.0497695i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.f.a.37.6	yes	240
23.5	odd	22	inner	69.7.f.a.28.6	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.f.a.28.6	✓	240	23.5	odd	22	inner
69.7.f.a.37.6	yes	240	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-7.78187 + 2.28496i) q^{2} +(10.2083 + 11.7810i) q^{3} +(1.49619 - 0.961540i) q^{4} +(-172.710 + 24.8319i) q^{5} +(-106.358 - 68.3524i) q^{6} +(-306.304 - 139.884i) q^{7} +(330.469 - 381.382i) q^{8} +(-34.5825 + 240.527i) q^{9} +O(q^{10})\)	\(q+(-7.78187 + 2.28496i) q^{2} +(10.2083 + 11.7810i) q^{3} +(1.49619 - 0.961540i) q^{4} +(-172.710 + 24.8319i) q^{5} +(-106.358 - 68.3524i) q^{6} +(-306.304 - 139.884i) q^{7} +(330.469 - 381.382i) q^{8} +(-34.5825 + 240.527i) q^{9} +(1287.26 - 587.874i) q^{10} +(-121.275 + 413.023i) q^{11} +(26.6013 + 7.81086i) q^{12} +(-640.014 - 1401.43i) q^{13} +(2703.24 + 388.668i) q^{14} +(-2055.61 - 1781.20i) q^{15} +(-1747.51 + 3826.51i) q^{16} +(-2186.75 + 3402.66i) q^{17} +(-280.478 - 1950.77i) q^{18} +(-1504.77 - 2341.46i) q^{19} +(-234.529 + 203.221i) q^{20} +(-1478.86 - 5036.53i) q^{21} -3491.20i q^{22} +(9586.02 + 7492.94i) q^{23} +7866.57 q^{24} +(14219.9 - 4175.35i) q^{25} +(8182.73 + 9443.37i) q^{26} +(-3186.66 + 2047.94i) q^{27} +(-592.792 + 85.2306i) q^{28} +(32098.4 + 20628.4i) q^{29} +(20066.5 + 9164.05i) q^{30} +(18941.1 - 21859.1i) q^{31} +(259.110 - 1802.15i) q^{32} +(-6103.81 + 2787.52i) q^{33} +(9242.09 - 31475.7i) q^{34} +(56375.2 + 16553.3i) q^{35} +(179.534 + 393.125i) q^{36} +(31212.2 + 4487.64i) q^{37} +(17060.0 + 14782.6i) q^{38} +(9976.83 - 21846.2i) q^{39} +(-47604.8 + 74074.6i) q^{40} +(-11418.0 - 79413.7i) q^{41} +(23016.6 + 35814.5i) q^{42} +(34028.7 - 29486.0i) q^{43} +(215.689 + 734.570i) q^{44} -42400.0i q^{45} +(-91718.2 - 36405.3i) q^{46} -132494. q^{47} +(-62919.1 + 18474.7i) q^{48} +(-2789.37 - 3219.10i) q^{49} +(-101117. + 64984.1i) q^{50} +(-62409.6 + 8973.14i) q^{51} +(-2305.12 - 1481.41i) q^{52} +(213629. + 97561.2i) q^{53} +(20118.7 - 23218.2i) q^{54} +(10689.1 - 74344.6i) q^{55} +(-154573. + 70591.3i) q^{56} +(12223.6 - 41629.9i) q^{57} +(-296920. - 87183.6i) q^{58} +(70155.4 + 153619. i) q^{59} +(-4788.27 - 688.449i) q^{60} +(-297267. - 257583. i) q^{61} +(-97449.4 + 213385. i) q^{62} +(44238.6 - 68836.6i) q^{63} +(-36213.4 - 251870. i) q^{64} +(145337. + 226149. i) q^{65} +(41129.7 - 35639.1i) q^{66} +(-51135.9 - 174153. i) q^{67} +7193.66i q^{68} +(9582.62 + 189423. i) q^{69} -476528. q^{70} +(332256. - 97559.1i) q^{71} +(80304.1 + 92675.8i) q^{72} +(56283.9 - 36171.5i) q^{73} +(-253144. + 36396.6i) q^{74} +(194351. + 124902. i) q^{75} +(-4502.82 - 2056.37i) q^{76} +(94922.2 - 109546. i) q^{77} +(-27720.6 + 192801. i) q^{78} +(-58948.5 + 26920.9i) q^{79} +(206792. - 704270. i) q^{80} +(-56657.1 - 16636.0i) q^{81} +(270311. + 591898. i) q^{82} +(-554734. - 79758.8i) q^{83} +(-7055.47 - 6113.60i) q^{84} +(293179. - 641973. i) q^{85} +(-197432. + 307211. i) q^{86} +(84646.5 + 588730. i) q^{87} +(117442. + 182743. i) q^{88} +(782815. - 678313. i) q^{89} +(96882.5 + 329951. i) q^{90} +518792. i q^{91} +(21547.2 + 1993.48i) q^{92} +450877. q^{93} +(1.03105e6 - 302744. i) q^{94} +(318031. + 367027. i) q^{95} +(23876.1 - 15344.3i) q^{96} +(-594426. + 85465.6i) q^{97} +(29062.0 + 18677.0i) q^{98} +(-95149.1 - 43453.1i) 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

Related objects

Downloads

Learn more