LMFDB - Embedded newform 69.7.f.a.7.19

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			7.19
Character	$\chi$	$=$	69.7
Dual form			69.7.f.a.10.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(6.08888 - 7.02694i) q^{2} +(-13.1138 + 8.42776i) q^{3} +(-3.19530 - 22.2238i) q^{4} +(-77.8070 + 35.5333i) q^{5} +(-20.6273 + 143.466i) q^{6} +(-42.4272 - 144.494i) q^{7} +(324.984 + 208.854i) q^{8} +(100.946 - 221.041i) q^{9} +O(q^{10})$	\(q+(6.08888 - 7.02694i) q^{2} +(-13.1138 + 8.42776i) q^{3} +(-3.19530 - 22.2238i) q^{4} +(-77.8070 + 35.5333i) q^{5} +(-20.6273 + 143.466i) q^{6} +(-42.4272 - 144.494i) q^{7} +(324.984 + 208.854i) q^{8} +(100.946 - 221.041i) q^{9} +(-224.067 + 763.103i) q^{10} +(1462.85 - 1267.56i) q^{11} +(229.200 + 264.510i) q^{12} +(2669.61 + 783.867i) q^{13} +(-1273.68 - 581.672i) q^{14} +(720.884 - 1121.72i) q^{15} +(4825.14 - 1416.79i) q^{16} +(481.163 + 69.1808i) q^{17} +(-938.592 - 2055.23i) q^{18} +(5243.53 - 753.906i) q^{19} +(1038.30 + 1615.63i) q^{20} +(1774.14 + 1537.30i) q^{21} -17997.4i q^{22} +(8123.32 + 9058.01i) q^{23} -6021.96 q^{24} +(-5440.88 + 6279.11i) q^{25} +(21763.1 - 13986.3i) q^{26} +(539.088 + 3749.44i) q^{27} +(-3075.64 + 1404.60i) q^{28} +(3330.89 - 23166.8i) q^{29} +(-3492.86 - 11895.6i) q^{30} +(450.660 + 289.621i) q^{31} +(9153.37 - 20043.1i) q^{32} +(-8500.83 + 28951.2i) q^{33} +(3415.87 - 2959.87i) q^{34} +(8435.48 + 9735.06i) q^{35} +(-5234.92 - 1537.11i) q^{36} +(-70634.7 - 32257.8i) q^{37} +(26629.6 - 41436.4i) q^{38} +(-41615.0 + 12219.3i) q^{39} +(-32707.3 - 4702.60i) q^{40} +(-5198.93 - 11384.1i) q^{41} +(21605.1 - 3106.34i) q^{42} +(14154.6 + 22025.0i) q^{43} +(-32844.4 - 28459.8i) q^{44} +20785.5i q^{45} +(113112. - 1928.99i) q^{46} +124060. q^{47} +(-51335.8 + 59244.6i) q^{48} +(79894.2 - 51344.9i) q^{49} +(10994.1 + 76465.4i) q^{50} +(-6892.94 + 3147.90i) q^{51} +(8890.32 - 61833.5i) q^{52} +(54702.2 + 186299. i) q^{53} +(29629.5 + 19041.7i) q^{54} +(-68779.1 + 150605. i) q^{55} +(16390.0 - 55819.3i) q^{56} +(-62409.1 + 54077.8i) q^{57} +(-142511. - 164466. i) q^{58} +(217347. + 63818.9i) q^{59} +(-27232.3 - 12436.6i) q^{60} +(12222.6 - 19018.7i) q^{61} +(4779.17 - 1403.29i) q^{62} +(-36221.9 - 5207.92i) q^{63} +(48591.8 + 106401. i) q^{64} +(-235567. + 33869.5i) q^{65} +(151678. + 236015. i) q^{66} +(-387062. - 335391. i) q^{67} -10914.3i q^{68} +(-182867. - 50323.9i) q^{69} +119770. q^{70} +(-373104. + 430585. i) q^{71} +(78971.1 - 50751.6i) q^{72} +(24071.5 + 167421. i) q^{73} +(-656760. + 299932. i) q^{74} +(18432.0 - 128198. i) q^{75} +(-33509.3 - 114122. i) q^{76} +(-245220. - 157593. i) q^{77} +(-167525. + 366828. i) q^{78} +(185517. - 631812. i) q^{79} +(-325087. + 281689. i) q^{80} +(-38668.9 - 44626.3i) q^{81} +(-111651. - 32783.7i) q^{82} +(-198281. - 90551.9i) q^{83} +(28495.8 - 44340.4i) q^{84} +(-39896.1 + 11714.6i) q^{85} +(240954. + 34643.9i) q^{86} +(151564. + 331878. i) q^{87} +(740138. - 106416. i) q^{88} +(191338. + 297728. i) q^{89} +(146058. + 126560. i) q^{90} -418999. i q^{91} +(175347. - 209474. i) q^{92} -8350.74 q^{93} +(755384. - 871759. i) q^{94} +(-381195. + 244979. i) q^{95} +(48882.3 + 339984. i) q^{96} +(85156.8 - 38889.8i) q^{97} +(125669. - 874045. i) q^{98} +(-132515. - 451304. i) 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 $

$2$	6.08888	−	7.02694i	0.761110	−	0.878368i	−0.234486	−	0.972120i	$-0.575341\pi$
$2$	6.08888	−	7.02694i	0.761110	−	0.878368i	0.995596	+	0.0937519i	$0.0298861\pi$
$3$	−13.1138	+	8.42776i	−0.485698	+	0.312139i
$3$	−13.1138	+	8.42776i	−0.485698	+	0.312139i
$4$	−3.19530	−	22.2238i	−0.0499266	−	0.347247i
$5$	−77.8070	+	35.5333i	−0.622456	+	0.284266i	−0.701571	−	0.712599i	$-0.747518\pi$
$5$	−77.8070	+	35.5333i	−0.622456	+	0.284266i	0.0791150	+	0.996865i	$0.474791\pi$
$6$	−20.6273	+	143.466i	−0.0954966	+	0.664194i
$7$	−42.4272	−	144.494i	−0.123695	−	0.421265i	0.874241	−	0.485493i	$-0.161360\pi$
$7$	−42.4272	−	144.494i	−0.123695	−	0.421265i	−0.997935	+	0.0642278i	$0.979542\pi$
$8$	324.984	+	208.854i	0.634734	+	0.407919i
$9$	100.946	−	221.041i	0.138472	−	0.303211i
$10$	−224.067	+	763.103i	−0.224067	+	0.763103i
$11$	1462.85	−	1267.56i	1.09906	−	0.952340i	0.0999688	−	0.994991i	$-0.468126\pi$
$11$	1462.85	−	1267.56i	1.09906	−	0.952340i	0.999090	+	0.0426507i	$0.0135803\pi$
$12$	229.200	+	264.510i	0.132639	+	0.153073i
$13$	2669.61	+	783.867i	1.21511	+	0.356790i	0.825613	−	0.564236i	$-0.190829\pi$
$13$	2669.61	+	783.867i	1.21511	+	0.356790i	0.389501	+	0.921026i	$0.372648\pi$
$14$	−1273.68	−	581.672i	−0.464171	−	0.211980i
$15$	720.884	−	1121.72i	0.213595	−	0.332361i
$16$	4825.14	−	1416.79i	1.17801	−	0.345896i
$17$	481.163	+	69.1808i	0.0979368	+	0.0140812i	0.191109	−	0.981569i	$-0.438792\pi$
$17$	481.163	+	69.1808i	0.0979368	+	0.0140812i	−0.0931722	+	0.995650i	$0.529701\pi$
$18$	−938.592	−	2055.23i	−0.160938	−	0.352406i
$19$	5243.53	−	753.906i	0.764475	−	0.109915i	0.250962	−	0.967997i	$-0.419253\pi$
$19$	5243.53	−	753.906i	0.764475	−	0.109915i	0.513513	+	0.858082i	$0.328344\pi$
$20$	1038.30	+	1615.63i	0.129788	+	0.201954i
$21$	1774.14	+	1537.30i	0.191571	+	0.165998i
$22$		−	17997.4i		−	1.69021i
$23$	8123.32	+	9058.01i	0.667652	+	0.744473i
$23$	8123.32	+	9058.01i	0.667652	+	0.744473i
$24$	−6021.96			−0.435616
$25$	−5440.88	+	6279.11i	−0.348216	+	0.401863i
$26$	21763.1	−	13986.3i	1.23823	−	0.795761i
$27$	539.088	+	3749.44i	0.0273885	+	0.190491i
$28$	−3075.64	+	1404.60i	−0.140107	+	0.0639849i
$29$	3330.89	−	23166.8i	0.136573	−	0.949889i	−0.800145	−	0.599806i	$-0.795244\pi$
$29$	3330.89	−	23166.8i	0.136573	−	0.949889i	0.936719	−	0.350083i	$-0.113847\pi$
$30$	−3492.86	−	11895.6i	−0.129365	−	0.440578i
$31$	450.660	+	289.621i	0.0151274	+	0.00972178i	0.548183	−	0.836359i	$-0.315320\pi$
$31$	450.660	+	289.621i	0.0151274	+	0.00972178i	−0.533055	+	0.846080i	$0.678956\pi$
$32$	9153.37	−	20043.1i	0.279339	−	0.611666i
$33$	−8500.83	+	28951.2i	−0.236548	+	0.805609i
$34$	3415.87	−	2959.87i	0.0869091	−	0.0753072i
$35$	8435.48	+	9735.06i	0.196746	+	0.227057i
$36$	−5234.92	−	1537.11i	−0.112202	−	0.0329456i
$37$	−70634.7	−	32257.8i	−1.39448	−	0.636839i	−0.430448	−	0.902615i	$-0.641644\pi$
$37$	−70634.7	−	32257.8i	−1.39448	−	0.636839i	−0.964035	+	0.265777i	$0.914372\pi$
$38$	26629.6	−	41436.4i	0.485304	−	0.755147i
$39$	−41615.0	+	12219.3i	−0.701546	+	0.205993i
$40$	−32707.3	−	4702.60i	−0.511052	−	0.0734782i
$41$	−5198.93	−	11384.1i	−0.0754332	−	0.165176i	0.868158	−	0.496287i	$-0.165304\pi$
$41$	−5198.93	−	11384.1i	−0.0754332	−	0.165176i	−0.943592	+	0.331111i	$0.892576\pi$
$42$	21605.1	−	3106.34i	0.291614	−	0.0419277i
$43$	14154.6	+	22025.0i	0.178029	+	0.277019i	0.918787	−	0.394753i	$-0.129170\pi$
$43$	14154.6	+	22025.0i	0.178029	+	0.277019i	−0.740758	+	0.671772i	$0.765533\pi$
$44$	−32844.4	−	28459.8i	−0.385570	−	0.334098i
$45$			20785.5i			0.228098i
$46$	113112.	−	1928.99i	1.16208	−	0.0198179i
$47$	124060.			1.19491			0.597457	−	0.801901i	$-0.296178\pi$
$47$	124060.			1.19491			0.597457	+	0.801901i	$0.296178\pi$
$48$	−51335.8	+	59244.6i	−0.464191	+	0.535705i
$49$	79894.2	−	51344.9i	0.679090	−	0.436424i
$50$	10994.1	+	76465.4i	0.0879526	+	0.611724i
$51$	−6892.94	+	3147.90i	−0.0519630	+	0.0237307i
$52$	8890.32	−	61833.5i	0.0632277	−	0.439758i
$53$	54702.2	+	186299.i	0.367432	+	1.25136i	0.911144	+	0.412088i	$0.135200\pi$
$53$	54702.2	+	186299.i	0.367432	+	1.25136i	−0.543712	+	0.839272i	$0.682982\pi$
$54$	29629.5	+	19041.7i	0.188167	+	0.120928i
$55$	−68779.1	+	150605.i	−0.413398	+	0.905215i
$56$	16390.0	−	55819.3i	0.0933288	−	0.317849i
$57$	−62409.1	+	54077.8i	−0.336995	+	0.292008i
$58$	−142511.	−	164466.i	−0.730404	−	0.842931i
$59$	217347.	+	63818.9i	1.05827	+	0.310737i	0.764156	−	0.645032i	$-0.223156\pi$
$59$	217347.	+	63818.9i	1.05827	+	0.310737i	0.294118	+	0.955769i	$0.404974\pi$
$60$	−27232.3	−	12436.6i	−0.126075	−	0.0575767i
$61$	12222.6	−	19018.7i	0.0538485	−	0.0837898i	−0.813285	−	0.581865i	$-0.802323\pi$
$61$	12222.6	−	19018.7i	0.0538485	−	0.0837898i	0.867134	+	0.498075i	$0.165960\pi$
$62$	4779.17	−	1403.29i	0.0200529	−	0.00588806i
$63$	−36221.9	−	5207.92i	−0.144860	−	0.0208278i
$64$	48591.8	+	106401.i	0.185363	+	0.405889i
$65$	−235567.	+	33869.5i	−0.857779	+	0.123330i
$66$	151678.	+	236015.i	0.527582	+	0.820933i
$67$	−387062.	−	335391.i	−1.28693	−	1.11513i	−0.986922	−	0.161198i	$-0.948464\pi$
$67$	−387062.	−	335391.i	−1.28693	−	1.11513i	−0.300011	−	0.953936i	$-0.596990\pi$
$68$		−	10914.3i		−	0.0347113i
$69$	−182867.	−	50323.9i	−0.556657	−	0.153189i
$70$	119770.			0.349185
$71$	−373104.	+	430585.i	−1.04245	+	1.20305i	−0.0637044	+	0.997969i	$0.520291\pi$
$71$	−373104.	+	430585.i	−1.04245	+	1.20305i	−0.978745	+	0.205082i	$0.934254\pi$
$72$	78971.1	−	50751.6i	0.211578	−	0.135973i
$73$	24071.5	+	167421.i	0.0618778	+	0.430370i	0.997087	+	0.0762738i	$0.0243023\pi$
$73$	24071.5	+	167421.i	0.0618778	+	0.430370i	−0.935209	+	0.354096i	$0.884789\pi$
$74$	−656760.	+	299932.i	−1.62073	+	0.740164i
$75$	18432.0	−	128198.i	0.0436908	−	0.303876i
$76$	−33509.3	−	114122.i	−0.0763353	−	0.259974i
$77$	−245220.	−	157593.i	−0.537135	−	0.345196i
$78$	−167525.	+	366828.i	−0.353017	+	0.772999i
$79$	185517.	−	631812.i	0.376272	−	1.28147i	−0.526069	−	0.850442i	$-0.676335\pi$
$79$	185517.	−	631812.i	0.376272	−	1.28147i	0.902341	−	0.431023i	$-0.141847\pi$
$80$	−325087.	+	281689.i	−0.634935	+	0.550174i
$81$	−38668.9	−	44626.3i	−0.0727623	−	0.0839722i
$82$	−111651.	−	32783.7i	−0.202498	−	0.0594588i
$83$	−198281.	−	90551.9i	−0.346774	−	0.158366i	0.234411	−	0.972137i	$-0.424684\pi$
$83$	−198281.	−	90551.9i	−0.346774	−	0.158366i	−0.581186	+	0.813771i	$0.697411\pi$
$84$	28495.8	−	44340.4i	0.0480777	−	0.0748103i
$85$	−39896.1	+	11714.6i	−0.0649642	+	0.0190752i
$86$	240954.	+	34643.9i	0.378824	+	0.0544667i
$87$	151564.	+	331878.i	0.230164	+	0.503989i
$88$	740138.	−	106416.i	1.08609	−	0.156156i
$89$	191338.	+	297728.i	0.271414	+	0.422328i	0.950027	−	0.312168i	$-0.101055\pi$
$89$	191338.	+	297728.i	0.271414	+	0.422328i	−0.678613	+	0.734496i	$0.737419\pi$
$90$	146058.	+	126560.i	0.200354	+	0.173608i
$91$		−	418999.i		−	0.556018i
$92$	175347.	−	209474.i	0.225183	−	0.269009i
$93$	−8350.74			−0.0103819
$94$	755384.	−	871759.i	0.909461	−	1.04957i
$95$	−381195.	+	244979.i	−0.444607	+	0.285732i
$96$	48882.3	+	339984.i	0.0552508	+	0.384278i
$97$	85156.8	−	38889.8i	0.0933049	−	0.0426109i	−0.368216	−	0.929740i	$-0.620031\pi$
$97$	85156.8	−	38889.8i	0.0933049	−	0.0426109i	0.461521	+	0.887129i	$0.347304\pi$
$98$	125669.	−	874045.i	0.133521	−	0.928657i
$99$	−132515.	−	451304.i	−0.136571	−	0.465118i
$100$	156931.	+	100853.i	0.156931	+	0.100853i
$101$	606019.	−	1.32700e6i	0.588196	−	1.28797i	−0.348330	−	0.937372i	$-0.613251\pi$
$101$	606019.	−	1.32700e6i	0.588196	−	1.28797i	0.936526	−	0.350597i	$-0.114021\pi$
$102$	−19850.2	+	67603.5i	−0.0187053	+	0.0637043i
$103$	1.00310e6	−	869190.i	0.917978	−	0.795432i	−0.0612654	−	0.998122i	$-0.519514\pi$
$103$	1.00310e6	−	869190.i	0.917978	−	0.795432i	0.979243	+	0.202689i	$0.0649681\pi$
$104$	703865.	+	812303.i	0.625733	+	0.722134i
$105$	−192666.	−	56571.9i	−0.166432	−	0.0488690i
$106$	1.64218e6	+	749961.i	1.37881	+	0.629681i
$107$	−715751.	+	1.11373e6i	−0.584266	+	0.909136i	−1.00000		0.000350571i	$-0.999888\pi$
$107$	−715751.	+	1.11373e6i	−0.584266	+	0.909136i	0.415734	+	0.909486i	$0.363525\pi$
$108$	81604.3	−	23961.2i	0.0647801	−	0.0190212i
$109$	−1.06890e6	−	153684.i	−0.825383	−	0.118672i	−0.283337	−	0.959021i	$-0.591441\pi$
$109$	−1.06890e6	−	153684.i	−0.825383	−	0.118672i	−0.542047	+	0.840348i	$0.682350\pi$
$110$	639506.	+	1.40032e6i	0.480471	+	1.05208i
$111$	1.19815e6	−	172268.i	0.876080	−	0.125961i
$112$	−409435.	−	637093.i	−0.291427	−	0.453470i
$113$	494084.	+	428127.i	0.342425	+	0.296713i	0.809047	−	0.587744i	$-0.199984\pi$
$113$	494084.	+	428127.i	0.342425	+	0.296713i	−0.466622	+	0.884457i	$0.654529\pi$
$114$			767819.i			0.518256i
$115$	−953913.	−	416129.i	−0.627213	−	0.273611i
$116$	−525499.			−0.336665
$117$	442752.	−	510963.i	0.276441	−	0.319030i
$118$	1.77185e6	−	1.13870e6i	1.07840	−	0.693048i
$119$	−10418.2	−	72460.3i	−0.00618234	−	0.0429991i
$120$	468551.	−	213980.i	0.271152	−	0.123831i
$121$	281083.	−	1.95498e6i	0.158664	−	1.10353i
$122$	−59221.5	−	201690.i	−0.0326137	−	0.111072i
$123$	164120.	+	105474.i	0.0881956	+	0.0566799i
$124$	4996.50	−	10940.8i	0.00262060	−	0.00573831i
$125$	576761.	−	1.96427e6i	0.295301	−	1.00570i
$126$	−257146.	+	222819.i	−0.128549	+	0.111388i
$127$	−1.05629e6	−	1.21903e6i	−0.515671	−	0.595116i	0.436871	−	0.899524i	$-0.356087\pi$
$127$	−1.05629e6	−	1.21903e6i	−0.515671	−	0.595116i	−0.952542	+	0.304408i	$0.901541\pi$
$128$	2.39662e6	+	703710.i	1.14280	+	0.335555i
$129$	−371242.	−	169540.i	−0.172937	−	0.0789777i
$130$	−1.19634e6	+	1.86155e6i	−0.544535	+	0.847313i
$131$	−4.15845e6	+	1.22103e6i	−1.84977	+	0.543142i	−0.849902	+	0.526941i	$0.823339\pi$
$131$	−4.15845e6	+	1.22103e6i	−1.84977	+	0.543142i	−0.999869	+	0.0162004i	$0.994843\pi$
$132$	670568.	+	96413.1i	0.291555	+	0.0419193i
$133$	−331403.	−	725672.i	−0.140865	−	0.308451i
$134$	−4.71355e6	+	677706.i	−1.95900	+	0.281661i
$135$	−175175.	−	272577.i	−0.0711984	−	0.110787i
$136$	141922.	+	122976.i	0.0564198	+	0.0488880i
$137$		−	735166.i		−	0.285906i	−0.989729	−	0.142953i	$-0.954340\pi$
$137$		−	735166.i		−	0.285906i	0.989729	−	0.142953i	$-0.0456598\pi$
$138$	−1.46708e6	+	978577.i	−0.558233	+	0.372355i
$139$	1.12144e6			0.417572			0.208786	−	0.977961i	$-0.433049\pi$
$139$	1.12144e6			0.417572			0.208786	+	0.977961i	$0.433049\pi$
$140$	189396.	−	218575.i	0.0690220	−	0.0796556i
$141$	−1.62690e6	+	1.04554e6i	−0.580367	+	0.372979i
$142$	753910.	+	5.24356e6i	0.263302	+	1.83131i
$143$	4.89883e6	−	2.23722e6i	1.67527	−	0.765069i
$144$	173910.	−	1.20957e6i	0.0582421	−	0.405083i
$145$	564027.	+	1.92090e6i	0.185010	+	0.630088i
$146$	1.32303e6	+	850258.i	0.425119	+	0.273207i
$147$	−614998.	+	1.34666e6i	−0.193607	+	0.423941i
$148$	−491192.	+	1.67285e6i	−0.151519	+	0.516025i
$149$	29425.9	−	25497.7i	0.00889552	−	0.00770801i	−0.650402	−	0.759590i	$-0.725399\pi$
$149$	29425.9	−	25497.7i	0.00889552	−	0.00770801i	0.659297	+	0.751882i	$0.270854\pi$
$150$	−788607.	−	910101.i	−0.233661	−	0.269659i
$151$	−5.55411e6	−	1.63083e6i	−1.61318	−	0.473674i	−0.654009	−	0.756487i	$-0.726914\pi$
$151$	−5.55411e6	−	1.63083e6i	−1.61318	−	0.473674i	−0.959175	+	0.282813i	$0.908732\pi$
$152$	1.86152e6	+	850128.i	0.530075	+	0.242077i
$153$	63863.2	−	99373.1i	0.0178310	−	0.0277456i
$154$	−2.60051e6	+	763579.i	−0.712028	+	0.209070i
$155$	−45355.7	−	6521.17i	−0.0121797	−	0.00175118i
$156$	404532.	+	885801.i	0.106556	+	0.233325i
$157$	−3.86920e6	+	556307.i	−0.999821	+	0.143753i	−0.622741	−	0.782428i	$-0.713981\pi$
$157$	−3.86920e6	+	556307.i	−0.999821	+	0.143753i	−0.377080	+	0.926181i	$0.623072\pi$
$158$	−3.31012e6	−	5.15064e6i	−0.839213	−	1.30584i
$159$	−2.28744e6	−	1.98207e6i	−0.569059	−	0.493093i
$160$			1.88474e6i			0.460142i
$161$	964177.	−	1.55808e6i	0.231036	−	0.373346i
$162$	−549036.			−0.129139
$163$	−1.76157e6	+	2.03296e6i	−0.406759	+	0.469425i	−0.921758	−	0.387766i	$-0.873247\pi$
$163$	−1.76157e6	+	2.03296e6i	−0.406759	+	0.469425i	0.514999	+	0.857191i	$0.327792\pi$
$164$	−236385.	+	151916.i	−0.0535907	+	0.0344406i
$165$	−367306.	−	2.55467e6i	−0.0817666	−	0.568699i
$166$	−1.84361e6	+	841949.i	−0.403037	+	0.184061i
$167$	−596777.	+	4.15067e6i	−0.128133	+	0.891187i	0.819784	+	0.572672i	$0.194093\pi$
$167$	−596777.	+	4.15067e6i	−0.128133	+	0.891187i	−0.947918	+	0.318515i	$0.896816\pi$
$168$	255495.	+	870137.i	0.0538834	+	0.183510i
$169$	2.45178e6	+	1.57566e6i	0.507950	+	0.326439i
$170$	−160605.	+	351676.i	−0.0326898	+	0.0715807i
$171$	362669.	−	1.23514e6i	0.0725307	−	0.247017i
$172$	444250.	−	384945.i	0.0873057	−	0.0756508i
$173$	1.86679e6	+	2.15439e6i	0.360542	+	0.416088i	0.906821	−	0.421515i	$-0.138502\pi$
$173$	1.86679e6	+	2.15439e6i	0.360542	+	0.416088i	−0.546279	+	0.837603i	$0.683956\pi$
$174$	3.25494e6	+	955737.i	0.617868	+	0.181422i
$175$	1.13813e6	+	519768.i	0.212363	+	0.0969830i
$176$	5.26257e6	−	8.18872e6i	0.965295	−	1.50203i
$177$	−3.38811e6	+	994838.i	−0.610995	+	0.179404i
$178$	3.25716e6	+	468308.i	0.577535	+	0.0830370i
$179$	3.26430e6	+	7.14783e6i	0.569156	+	1.24628i	0.947246	+	0.320509i	$0.103854\pi$
$179$	3.26430e6	+	7.14783e6i	0.569156	+	1.24628i	−0.378089	+	0.925769i	$0.623419\pi$
$180$	461932.	−	66415.8i	0.0792065	−	0.0113882i
$181$	1.60223e6	+	2.49312e6i	0.270203	+	0.420444i	0.949665	−	0.313267i	$-0.101423\pi$
$181$	1.60223e6	+	2.49312e6i	0.270203	+	0.420444i	−0.679463	+	0.733710i	$0.737787\pi$
$182$	−2.94428e6	−	2.55123e6i	−0.488388	−	0.423191i
$183$			352417.i			0.0575048i
$184$	748143.	+	4.64030e6i	0.120097	+	0.744891i
$185$	6.64210e6			1.04904
$186$	−50846.7	+	58680.2i	−0.00790175	+	0.00911911i
$187$	791560.	−	508704.i	0.121048	−	0.0777930i
$188$	−396408.	−	2.75708e6i	−0.0596580	−	0.414931i
$189$	518899.	−	236973.i	0.0768595	−	0.0351005i
$190$	−599596.	+	4.17028e6i	−0.0874174	+	0.608002i
$191$	−467193.	−	1.59111e6i	−0.0670496	−	0.228350i	0.919151	−	0.393906i	$-0.128876\pi$
$191$	−467193.	−	1.59111e6i	−0.0670496	−	0.228350i	−0.986200	+	0.165556i	$0.947058\pi$
$192$	−1.53395e6	−	985810.i	−0.216724	−	0.139280i
$193$	−1.39240e6	+	3.04892e6i	−0.193683	+	0.424106i	−0.981411	−	0.191917i	$-0.938530\pi$
$193$	−1.39240e6	+	3.04892e6i	−0.193683	+	0.424106i	0.787729	+	0.616023i	$0.211257\pi$
$194$	245233.	−	835187.i	0.0335872	−	0.114388i
$195$	2.80375e6	−	2.42946e6i	0.378125	−	0.327647i
$196$	−1.39637e6	−	1.61149e6i	−0.185452	−	0.214023i
$197$	969873.	+	284780.i	0.126857	+	0.0372487i	0.344545	−	0.938770i	$-0.388033\pi$
$197$	969873.	+	284780.i	0.126857	+	0.0372487i	−0.217688	+	0.976019i	$0.569851\pi$
$198$	−3.97815e6	−	1.81676e6i	−0.512491	−	0.234047i
$199$	−5.10852e6	+	7.94901e6i	−0.648240	+	1.00868i	0.349191	+	0.937052i	$0.386456\pi$
$199$	−5.10852e6	+	7.94901e6i	−0.648240	+	1.00868i	−0.997431	+	0.0716299i	$0.977180\pi$
$200$	−3.07962e6	+	904257.i	−0.384952	+	0.113032i
$201$	7.90246e6	+	1.13620e6i	0.973138	+	0.139916i
$202$	−5.63475e6	−	1.23384e7i	−0.683629	−	1.49694i
$203$	−3.48879e6	+	501612.i	−0.417048	+	0.0599625i
$204$	91983.4	+	143129.i	0.0108347	+	0.0168592i
$205$	809027.	+	701026.i	0.0939078	+	0.0813716i
$206$		−	1.23411e7i		−	1.41173i
$207$	2.82220e6	−	881216.i	0.318183	−	0.0993507i
$208$	1.39918e7			1.55483
$209$	6.71486e6	−	7.74936e6i	0.735526	−	0.848843i
$210$	−1.57065e6	+	1.00940e6i	−0.169598	+	0.108994i
$211$	−843073.	−	5.86370e6i	−0.0897466	−	0.624201i	−0.984203	−	0.177045i	$-0.943346\pi$
$211$	−843073.	−	5.86370e6i	−0.0897466	−	0.624201i	0.894456	−	0.447156i	$-0.147563\pi$
$212$	3.96548e6	−	1.81097e6i	0.416186	−	0.190066i
$213$	1.26396e6	−	8.79105e6i	0.130796	−	0.909708i
$214$	3.46800e6	+	1.18109e7i	0.353865	+	1.20515i
$215$	−1.88394e6	−	1.21074e6i	−0.189563	−	0.121825i
$216$	−607892.	+	1.33110e6i	−0.0603205	+	0.132084i
$217$	22728.3	−	77405.4i	0.00222427	−	0.00757517i
$218$	−7.58830e6	+	6.57530e6i	−0.732445	+	0.634667i
$219$	−1.72665e6	−	1.99267e6i	−0.164389	−	0.189715i
$220$	3.56679e6	+	1.04730e6i	0.334973	+	0.0983569i
$221$	1.23029e6	+	561854.i	0.113980	+	0.0520531i
$222$	6.08489e6	−	9.46828e6i	0.556153	−	0.865390i
$223$	−1.47490e7	+	4.33070e6i	−1.32999	+	0.390520i	−0.868088	−	0.496411i	$-0.834651\pi$
$223$	−1.47490e7	+	4.33070e6i	−1.32999	+	0.390520i	−0.461902	+	0.886931i	$0.652833\pi$
$224$	−3.28445e6	−	472233.i	−0.292226	−	0.0420158i
$225$	838703.	+	1.83650e6i	0.0736310	+	0.161229i
$226$	6.01684e6	−	865091.i	0.521247	−	0.0749440i
$227$	1.97712e6	+	3.07646e6i	0.169027	+	0.263011i	0.915425	−	0.402489i	$-0.131855\pi$
$227$	1.97712e6	+	3.07646e6i	0.169027	+	0.263011i	−0.746398	+	0.665500i	$0.768218\pi$
$228$	1.40123e6	+	1.21417e6i	0.118224	+	0.102442i
$229$		−	1.77261e7i		−	1.47607i	−0.674763	−	0.738035i	$-0.735754\pi$
$229$		−	1.77261e7i		−	1.47607i	0.674763	−	0.738035i	$-0.264246\pi$
$230$	−8.73237e6	+	4.16933e6i	−0.717709	+	0.342675i
$231$	4.54393e6			0.368634
$232$	5.92098e6	−	6.83318e6i	0.474165	−	0.547216i
$233$	−413989.	+	266054.i	−0.0327281	+	0.0210331i	−0.556903	−	0.830578i	$-0.688010\pi$
$233$	−413989.	+	266054.i	−0.0327281	+	0.0210331i	0.524174	+	0.851611i	$0.324374\pi$
$234$	−894644.	−	6.22238e6i	−0.0698237	−	0.485634i
$235$	−9.65271e6	+	4.40824e6i	−0.743782	+	0.339674i
$236$	723809.	−	5.03420e6i	0.0550666	−	0.382997i
$237$	2.89192e6	+	9.84898e6i	0.217241	+	0.739854i
$238$	−572610.	−	367994.i	−0.0424744	−	0.0272967i
$239$	−9.16181e6	+	2.00616e7i	−0.671100	+	1.46950i	0.200705	+	0.979652i	$0.435677\pi$
$239$	−9.16181e6	+	2.00616e7i	−0.671100	+	1.46950i	−0.871805	+	0.489853i	$0.837050\pi$
$240$	1.88913e6	−	6.43378e6i	0.136656	−	0.465406i
$241$	4.00769e6	−	3.47268e6i	0.286314	−	0.248093i	−0.499848	−	0.866113i	$-0.666611\pi$
$241$	4.00769e6	−	3.47268e6i	0.286314	−	0.248093i	0.786162	+	0.618021i	$0.212065\pi$
$242$	−1.20260e7	−	1.38788e7i	−0.848547	−	0.979276i
$243$	883197.	+	259330.i	0.0615515	+	0.0180732i
$244$	−461723.	−	210862.i	−0.0317843	−	0.0145154i
$245$	−4.39188e6	+	6.83390e6i	−0.298643	+	0.464697i
$246$	1.74047e6	−	511047.i	0.116912	−	0.0343285i
$247$	1.45891e7	+	2.09760e6i	0.968141	+	0.139198i
$248$	85968.4	+	188245.i	0.00563617	+	0.0123415i
$249$	3.36338e6	−	483580.i	0.217860	−	0.0313235i
$250$	−1.02910e7	−	1.60130e7i	−0.658621	−	1.02483i
$251$	1.72868e7	+	1.49791e7i	1.09319	+	0.947251i	0.998833	−	0.0482880i	$-0.0153765\pi$
$251$	1.72868e7	+	1.49791e7i	1.09319	+	0.947251i	0.0943523	+	0.995539i	$0.469922\pi$
$252$			821629.i			0.0513422i
$253$	2.33648e7	+	2.95365e6i	1.44278	+	0.182388i
$254$	−1.49977e7			−0.915213
$255$	424464.	−	489858.i	0.0255988	−	0.0295426i
$256$	1.32398e7	−	8.50873e6i	0.789156	−	0.507160i
$257$	335040.	+	2.33026e6i	0.0197377	+	0.137279i	0.997308	−	0.0733327i	$-0.0233635\pi$
$257$	335040.	+	2.33026e6i	0.0197377	+	0.137279i	−0.977570	+	0.210612i	$0.932454\pi$
$258$	−3.45180e6	+	1.57638e6i	−0.200995	+	0.0917915i
$259$	−1.66422e6	+	1.15749e7i	−0.0957880	+	0.666220i
$260$	1.50542e6	+	5.12699e6i	0.0856520	+	0.291704i
$261$	−4.78457e6	−	3.07486e6i	−0.269105	−	0.172943i
$262$	−1.67402e7	+	3.66559e7i	−0.930801	+	2.03817i
$263$	8.23984e6	−	2.80623e7i	0.452951	−	1.54261i	−0.344239	−	0.938882i	$-0.611863\pi$
$263$	8.23984e6	−	2.80623e7i	0.452951	−	1.54261i	0.797190	−	0.603728i	$-0.206319\pi$
$264$	−8.80921e6	+	7.63322e6i	−0.478768	+	0.414855i
$265$	−1.08760e7	−	1.25516e7i	−0.584430	−	0.674468i
$266$	−7.11713e6	−	2.08978e6i	−0.378146	−	0.111034i
$267$	−5.01836e6	−	2.29181e6i	−0.263650	−	0.120405i
$268$	−6.21689e6	+	9.67367e6i	−0.322975	+	0.502559i
$269$	−1.56413e7	+	4.59269e6i	−0.803553	+	0.235945i	−0.657620	−	0.753350i	$-0.728437\pi$
$269$	−1.56413e7	+	4.59269e6i	−0.803553	+	0.235945i	−0.145933	+	0.989294i	$0.546619\pi$
$270$	−2.98200e6	−	428747.i	−0.151501	−	0.0217826i
$271$	9.34505e6	+	2.04628e7i	0.469541	+	1.02815i	0.985208	+	0.171363i	$0.0548170\pi$
$271$	9.34505e6	+	2.04628e7i	0.469541	+	1.02815i	−0.515667	+	0.856789i	$0.672456\pi$
$272$	2.41969e6	−	347900.i	0.120241	−	0.0172881i
$273$	3.53122e6	+	5.49469e6i	0.173555	+	0.270057i
$274$	−5.16597e6	−	4.47634e6i	−0.251131	−	0.217606i
$275$			1.60820e7i			0.773291i
$276$	−534076.	+	4.22480e6i	−0.0254024	+	0.200946i
$277$	6.72028e6			0.316190			0.158095	−	0.987424i	$-0.449465\pi$
$277$	6.72028e6			0.316190			0.158095	+	0.987424i	$0.449465\pi$
$278$	6.82831e6	−	7.88029e6i	0.317818	−	0.366782i
$279$	109510.	−	70378.0i	0.00504246	−	0.00324059i
$280$	708184.	+	4.92553e6i	0.0322606	+	0.224377i
$281$	1.42666e7	−	6.51536e6i	0.642988	−	0.293643i	−0.0671102	−	0.997746i	$-0.521378\pi$
$281$	1.42666e7	−	6.51536e6i	0.642988	−	0.293643i	0.710098	+	0.704103i	$0.248651\pi$
$282$	−2.55901e6	+	1.77983e7i	−0.114110	+	0.793654i
$283$	−735603.	−	2.50523e6i	−0.0324552	−	0.110532i	0.941672	−	0.336531i	$-0.109254\pi$
$283$	−735603.	−	2.50523e6i	−0.0324552	−	0.110532i	−0.974128	+	0.225999i	$0.927435\pi$
$284$	1.07614e7	+	6.91595e6i	0.469802	+	0.301923i
$285$	2.93431e6	−	6.42524e6i	0.126757	−	0.277559i
$286$	1.41076e7	−	4.80459e7i	0.603051	−	2.05380i
$287$	−1.42435e6	+	1.23421e6i	−0.0602521	+	0.0522087i
$288$	−3.50634e6	−	4.04653e6i	−0.146783	−	0.169397i
$289$	−2.29331e7	−	6.73376e6i	−0.950100	−	0.278974i
$290$	1.69324e7	+	7.73275e6i	0.694262	+	0.317059i
$291$	−788979.	+	1.22768e6i	−0.0320174	+	0.0498201i
$292$	3.64382e6	−	1.06992e6i	0.146355	−	0.0429738i
$293$	2.92589e7	+	4.20680e6i	1.16320	+	0.167243i	0.696758	−	0.717307i	$-0.254625\pi$
$293$	2.92589e7	+	4.20680e6i	1.16320	+	0.167243i	0.466445	+	0.884550i	$0.345534\pi$
$294$	5.71824e6	+	1.25212e7i	0.225020	+	0.492724i
$295$	−1.91788e7	+	2.75750e6i	−0.747061	+	0.107411i
$296$	−1.62180e7	−	2.52356e7i	−0.625347	−	0.973059i
$297$	5.54126e6	+	4.80153e6i	0.211514	+	0.183278i
$298$		−	362027.i		−	0.0136802i
$299$	1.45858e7	+	3.05489e7i	0.545653	+	1.14283i
$300$	−2.90794e6			−0.107701
$301$	2.58193e6	−	2.97971e6i	0.0946771	−	0.109263i
$302$	−4.52781e7	+	2.90985e7i	−1.64387	+	1.05645i
$303$	3.23636e6	+	2.25094e7i	0.116340	+	0.809163i
$304$	2.42326e7	−	1.10667e7i	0.862542	−	0.393910i
$305$	−275206.	+	1.91410e6i	−0.00969969	+	0.0674628i
$306$	−309433.	−	1.05383e6i	−0.0107995	−	0.0367797i
$307$	2.99895e7	+	1.92731e7i	1.03646	+	0.666094i	0.944110	−	0.329632i	$-0.106925\pi$
$307$	2.99895e7	+	1.92731e7i	1.03646	+	0.666094i	0.0923535	+	0.995726i	$0.470561\pi$
$308$	−2.71877e6	+	5.95328e6i	−0.0930509	+	0.203753i
$309$	−5.82916e6	+	1.98523e7i	−0.197574	+	0.672877i
$310$	−321989.	+	279005.i	−0.0108083	+	0.00936542i
$311$	−3.30316e7	−	3.81205e7i	−1.09812	−	1.26729i	−0.960943	−	0.276746i	$-0.910744\pi$
$311$	−3.30316e7	−	3.81205e7i	−1.09812	−	1.26729i	−0.137173	−	0.990547i	$-0.543802\pi$
$312$	−1.60763e7	−	4.72042e6i	−0.529324	−	0.155423i
$313$	−4.26191e7	−	1.94635e7i	−1.38986	−	0.634728i	−0.426881	−	0.904308i	$-0.640388\pi$
$313$	−4.26191e7	−	1.94635e7i	−1.38986	−	0.634728i	−0.962978	+	0.269580i	$0.913115\pi$
$314$	−1.96500e7	+	3.05759e7i	−0.634706	+	0.987622i
$315$	3.00337e6	−	881869.i	0.0960898	−	0.0282145i
$316$	−1.46341e7	−	2.10406e6i	−0.463771	−	0.0666802i
$317$	1.27997e6	+	2.80274e6i	0.0401811	+	0.0879843i	0.928658	−	0.370937i	$-0.120963\pi$
$317$	1.27997e6	+	2.80274e6i	0.0401811	+	0.0879843i	−0.888477	+	0.458921i	$0.848236\pi$
$318$	−2.78558e7	+	4.00507e6i	−0.866233	+	0.124546i
$319$	−2.44929e7	−	3.81117e7i	−0.754515	−	1.17405i
$320$	−7.56157e6	−	6.55214e6i	−0.230761	−	0.199955i
$321$		−	2.06375e7i		−	0.623938i
$322$	−5.07776e6	−	1.62622e7i	−0.152091	−	0.487091i
$323$	2.57515e6			0.0764179
$324$	−868207.	+	1.00196e6i	−0.0255263	+	0.0294589i
$325$	−1.94470e7	+	1.24978e7i	−0.566503	+	0.364069i
$326$	3.55951e6	+	2.47569e7i	0.102739	+	0.714569i
$327$	1.53125e7	−	6.99300e6i	0.437929	−	0.199996i
$328$	688045.	−	4.78546e6i	0.0194982	−	0.135613i
$329$	−5.26350e6	−	1.79259e7i	−0.147804	−	0.503375i
$330$	−2.01880e7	−	1.29740e7i	−0.561760	−	0.361021i
$331$	1.18894e6	−	2.60342e6i	0.0327851	−	0.0717893i	−0.892531	−	0.450986i	$-0.851072\pi$
$331$	1.18894e6	−	2.60342e6i	0.0327851	−	0.0717893i	0.925316	+	0.379197i	$0.123800\pi$
$332$	−1.37884e6	+	4.69590e6i	−0.0376790	+	0.128323i
$333$	−1.42606e7	+	1.23568e7i	−0.386193	+	0.334638i
$334$	2.55328e7	+	2.94665e7i	0.685267	+	0.790840i
$335$	4.20337e7	+	1.23422e7i	1.11805	+	0.328290i
$336$	1.07385e7	+	4.90412e6i	0.283091	+	0.129284i
$337$	−9.89000e6	+	1.53891e7i	−0.258408	+	0.402091i	−0.946081	−	0.323929i	$-0.894996\pi$
$337$	−9.89000e6	+	1.53891e7i	−0.258408	+	0.402091i	0.687673	+	0.726021i	$0.258632\pi$
$338$	2.60006e7	−	7.63448e6i	0.673339	−	0.197710i
$339$	−1.00875e7	−	1.45036e6i	−0.258931	−	0.0372287i
$340$	387822.	+	849212.i	0.00986725	+	0.0216063i
$341$	1.02636e6	−	147568.i	0.0258843	−	0.00372160i
$342$	−6.47099e6	−	1.00691e7i	−0.161768	−	0.251716i
$343$	−2.41985e7	−	2.09681e7i	−0.599662	−	0.519610i
$344$			1.01140e7i			0.248455i
$345$	1.60165e7	−	2.58230e6i	0.390041	−	0.0628853i
$346$	2.65054e7			0.639890
$347$	4.18110e7	−	4.82525e7i	1.00070	−	1.15486i	0.0127728	−	0.999918i	$-0.495934\pi$
$347$	4.18110e7	−	4.82525e7i	1.00070	−	1.15486i	0.987923	−	0.154946i	$-0.0495204\pi$
$348$	6.89131e6	−	4.42878e6i	0.163517	−	0.105086i
$349$	−2.13464e6	−	1.48467e7i	−0.0502167	−	0.349265i	−0.999403	−	0.0345501i	$-0.989000\pi$
$349$	−2.13464e6	−	1.48467e7i	−0.0502167	−	0.349265i	0.949186	−	0.314715i	$-0.101909\pi$
$350$	1.05823e7	−	4.83279e6i	0.246818	−	0.112718i
$351$	−1.49991e6	+	1.04321e7i	−0.0346851	+	0.241240i
$352$	−1.20159e7	−	4.09225e7i	−0.275505	−	0.938283i
$353$	3.27658e6	+	2.10573e6i	0.0744898	+	0.0478717i	0.577356	−	0.816493i	$-0.304085\pi$
$353$	3.27658e6	+	2.10573e6i	0.0744898	+	0.0478717i	−0.502866	+	0.864364i	$0.667721\pi$
$354$	−1.36391e7	+	2.98655e7i	−0.307451	+	0.673224i
$355$	1.37300e7	−	4.67602e7i	0.306892	−	1.04518i
$356$	6.00527e6	−	5.20360e6i	0.133101	−	0.115333i
$357$	747301.	+	862431.i	0.0164244	+	0.0189548i
$358$	7.01033e7	+	2.05842e7i	1.52788	+	0.448626i
$359$	−2.84371e7	−	1.29868e7i	−0.614613	−	0.280684i	0.0836842	−	0.996492i	$-0.473331\pi$
$359$	−2.84371e7	−	1.29868e7i	−0.614613	−	0.280684i	−0.698297	+	0.715808i	$0.746059\pi$
$360$	−4.34113e6	+	6.75494e6i	−0.0930456	+	0.144782i
$361$	−1.82139e7	+	5.34809e6i	−0.387153	+	0.113678i
$362$	2.72748e7	+	3.92153e6i	0.574958	+	0.0826665i
$363$	1.27900e7	+	2.80062e7i	0.267393	+	0.585509i
$364$	−9.31176e6	+	1.33883e6i	−0.193076	+	0.0277601i
$365$	−7.82196e6	−	1.21712e7i	−0.160856	−	0.250297i
$366$	2.47642e6	+	2.14583e6i	0.0505103	+	0.0437674i
$367$		−	4.43674e7i		−	0.897565i	−0.893641	−	0.448782i	$-0.851858\pi$
$367$		−	4.43674e7i		−	0.897565i	0.893641	−	0.448782i	$-0.148142\pi$
$368$	5.20294e7	+	3.21971e7i	1.04401	+	0.646061i
$369$	−3.04115e6			−0.0605284
$370$	4.04430e7	−	4.66737e7i	0.798432	−	0.921440i
$371$	2.45982e7	−	1.58083e7i	0.481705	−	0.309573i
$372$	26683.1	+	185585.i	0.000518332	+	0.00360508i
$373$	6.19543e7	−	2.82936e7i	1.19384	−	0.545207i	0.283459	−	0.958984i	$-0.408518\pi$
$373$	6.19543e7	−	2.82936e7i	1.19384	−	0.545207i	0.910378	+	0.413777i	$0.135791\pi$
$374$	1.24507e6	−	8.65968e6i	0.0238002	−	0.165534i
$375$	8.99081e6	+	3.06199e7i	0.170492	+	0.580644i
$376$	4.03174e7	+	2.59104e7i	0.758453	+	0.487428i
$377$	2.70519e7	−	5.92354e7i	0.504863	−	1.10550i
$378$	1.49432e6	−	5.08917e6i	0.0276673	−	0.0942262i
$379$	−4.49509e7	+	3.89502e7i	−0.825697	+	0.715470i	−0.961363	−	0.275284i	$-0.911228\pi$
$379$	−4.49509e7	+	3.89502e7i	−0.825697	+	0.715470i	0.135666	+	0.990755i	$0.456683\pi$
$380$	6.66240e6	+	7.68883e6i	0.121417	+	0.140123i
$381$	2.41257e7	+	7.08395e6i	0.436219	+	0.128086i
$382$	−1.40253e7	−	6.40515e6i	−0.251607	−	0.114905i
$383$	−6.63694e6	+	1.03273e7i	−0.118133	+	0.183819i	−0.895284	−	0.445495i	$-0.853028\pi$
$383$	−6.63694e6	+	1.03273e7i	−0.118133	+	0.183819i	0.777151	+	0.629314i	$0.216664\pi$
$384$	−3.73595e7	+	1.09698e7i	−0.659793	+	0.193733i
$385$	2.46796e7	+	3.54840e6i	0.432471	+	0.0621799i
$386$	1.29465e7	+	2.83488e7i	0.225107	+	0.492916i
$387$	6.29725e6	−	905408.i	0.108647	−	0.0156211i
$388$	−1.13638e6	−	1.76824e6i	−0.0194549	−	0.0302724i
$389$	−6.88084e7	−	5.96228e7i	−1.16894	−	1.01289i	−0.999626	−	0.0273313i	$-0.991299\pi$
$389$	−6.88084e7	−	5.96228e7i	−1.16894	−	1.01289i	−0.169315	−	0.985562i	$-0.554155\pi$
$390$		−	3.44945e7i		−	0.581509i
$391$	3.28200e6	+	4.92036e6i	0.0549046	+	0.0823126i
$392$	3.66879e7			0.609067
$393$	4.42427e7	−	5.10588e7i	0.728894	−	0.841189i
$394$	7.90657e6	−	5.08125e6i	0.129271	−	0.0830771i
$395$	8.01585e6	+	5.57515e7i	0.130064	+	0.904618i
$396$	−9.60627e6	+	4.38704e6i	−0.154693	+	0.0706457i
$397$	−6.76734e6	+	4.70679e7i	−0.108155	+	0.752234i	0.861500	+	0.507757i	$0.169525\pi$
$397$	−6.76734e6	+	4.70679e7i	−0.108155	+	0.752234i	−0.969655	+	0.244477i	$0.921384\pi$
$398$	2.47521e7	+	8.42979e7i	0.392611	+	1.33711i
$399$	1.04618e7	+	6.72337e6i	0.164697	+	0.105844i
$400$	−1.73568e7	+	3.80061e7i	−0.271200	+	0.593846i
$401$	1.86041e7	−	6.33599e7i	0.288520	−	0.982610i	−0.679904	−	0.733301i	$-0.737978\pi$
$401$	1.86041e7	−	6.33599e7i	0.288520	−	0.982610i	0.968424	−	0.249309i	$-0.0802034\pi$
$402$	5.61012e7	−	4.86119e7i	0.863563	−	0.748281i
$403$	976059.	+	1.12643e6i	0.0149129	+	0.0172104i
$404$	−3.14273e7	−	9.22790e6i	−0.476610	−	0.139945i
$405$	4.59443e6	+	2.09821e6i	0.0691618	+	0.0315851i
$406$	−1.77180e7	+	2.75698e7i	−0.264750	+	0.411960i
$407$	−1.44217e8	+	4.23458e7i	−2.13911	+	0.628098i
$408$	−2.89755e6	−	416604.i	−0.0426629	−	0.00613399i
$409$	1.99377e7	+	4.36575e7i	0.291410	+	0.638100i	0.997549	−	0.0699740i	$-0.0222916\pi$
$409$	1.99377e7	+	4.36575e7i	0.291410	+	0.638100i	−0.706138	+	0.708074i	$0.749564\pi$
$410$	9.85214e6	−	1.41652e6i	0.142948	−	0.0205529i
$411$	6.19580e6	+	9.64085e6i	0.0892425	+	0.138864i
$412$	−2.25219e7	−	1.95154e7i	−0.322043	−	0.279052i
$413$		−	3.41130e7i		−	0.484250i
$414$	1.09918e7	−	2.51971e7i	0.154906	−	0.355099i
$415$	1.86453e7			0.260870
$416$	4.01470e7	−	4.63321e7i	0.557665	−	0.643579i
$417$	−1.47064e7	+	9.45122e6i	−0.202814	+	0.130341i
$418$	−1.35683e7	−	9.43699e7i	−0.185780	−	1.29213i
$419$	−1.05912e8	+	4.83684e7i	−1.43980	+	0.657536i	−0.973833	−	0.227265i	$-0.927022\pi$
$419$	−1.05912e8	+	4.83684e7i	−1.43980	+	0.657536i	−0.465970	+	0.884801i	$0.654294\pi$
$420$	−641617.	+	4.46255e6i	−0.00866020	+	0.0602330i
$421$	1.41836e7	+	4.83049e7i	0.190081	+	0.647358i	0.998290	+	0.0584612i	$0.0186194\pi$
$421$	1.41836e7	+	4.83049e7i	0.190081	+	0.647358i	−0.808208	+	0.588897i	$0.799562\pi$
$422$	−4.63373e7	−	2.97792e7i	−0.616585	−	0.396255i
$423$	1.25233e7	−	2.74222e7i	0.165462	−	0.362311i
$424$	−2.11320e7	+	7.19689e7i	−0.277231	+	0.944163i
$425$	−3.05234e6	+	2.64487e6i	−0.0397619	+	0.0344538i
$426$	−5.40781e7	−	6.24095e7i	−0.699508	−	0.807275i
$427$	−3.26666e6	−	959177.i	−0.0419585	−	0.0123201i
$428$	2.70384e7	+	1.23480e7i	0.344865	+	0.157495i
$429$	−4.53877e7	+	7.06247e7i	−0.574866	+	0.894509i
$430$	−1.99789e7	+	5.86633e6i	−0.251285	+	0.0737838i
$431$	−9.10217e7	−	1.30869e7i	−1.13688	−	0.163458i	−0.451931	−	0.892053i	$-0.649265\pi$
$431$	−9.10217e7	−	1.30869e7i	−1.13688	−	0.163458i	−0.684945	+	0.728595i	$0.740174\pi$
$432$	7.91334e6	+	1.73278e7i	0.0981541	+	0.214927i
$433$	5.06716e7	−	7.28548e6i	0.624168	−	0.0897418i	0.177028	−	0.984206i	$-0.443352\pi$
$433$	5.06716e7	−	7.28548e6i	0.624168	−	0.0897418i	0.447140	+	0.894464i	$0.352443\pi$
$434$	−405534.	−	631022.i	−0.00496087	−	0.00771926i
$435$	−2.35855e7	−	2.04369e7i	−0.286534	−	0.248283i
$436$			2.42460e7i			0.292537i
$437$	4.94238e7	+	4.13717e7i	0.592232	+	0.495746i
$438$	−2.45157e7			−0.291758
$439$	−8.80157e7	+	1.01575e8i	−1.04032	+	1.20059i	−0.0610271	+	0.998136i	$0.519438\pi$
$439$	−8.80157e7	+	1.01575e8i	−1.04032	+	1.20059i	−0.979291	+	0.202456i	$0.935108\pi$
$440$	−5.38067e7	+	3.45794e7i	−0.631652	+	0.405938i
$441$	−3.28432e6	−	2.28429e7i	−0.0382939	−	0.266340i
$442$	1.14392e7	−	5.22410e6i	0.132473	−	0.0604985i
$443$	−1.54606e7	+	1.07531e8i	−0.177835	+	1.23687i	0.683926	+	0.729551i	$0.260271\pi$
$443$	−1.54606e7	+	1.07531e8i	−0.177835	+	1.23687i	−0.861761	+	0.507315i	$0.830638\pi$
$444$	−7.65693e6	−	2.60771e7i	−0.0874794	−	0.297927i
$445$	−2.54667e7	−	1.63665e7i	−0.288997	−	0.185727i
$446$	−5.93733e7	+	1.30009e8i	−0.669248	+	1.46545i
$447$	−170998.	+	582367.i	−0.00191456	+	0.00652040i
$448$	1.33127e7	−	1.15355e7i	0.148058	−	0.128293i
$449$	−7.50293e7	−	8.65885e7i	−0.828881	−	0.956579i	0.170706	−	0.985322i	$-0.445395\pi$
$449$	−7.50293e7	−	8.65885e7i	−0.828881	−	0.956579i	−0.999587	+	0.0287425i	$0.990850\pi$
$450$	1.80118e7	+	5.28873e6i	0.197660	+	0.0580382i
$451$	−2.20353e7	−	1.00632e7i	−0.240209	−	0.109700i
$452$	7.93586e6	−	1.23484e7i	0.0859367	−	0.133720i
$453$	8.65801e7	−	2.54222e7i	0.931372	−	0.273476i
$454$	3.36565e7	+	4.83908e6i	0.359668	+	0.0517124i
$455$	1.48884e7	+	3.26011e7i	0.158057	+	0.346097i
$456$	−3.15764e7	+	4.53999e6i	−0.333018	+	0.0478807i
$457$	−9.24178e7	−	1.43805e8i	−0.968294	−	1.50669i	−0.858547	−	0.512735i	$-0.828632\pi$
$457$	−9.24178e7	−	1.43805e8i	−0.968294	−	1.50669i	−0.109747	−	0.993960i	$-0.535004\pi$
$458$	−1.24560e8	−	1.07932e8i	−1.29653	−	1.12345i
$459$			1.84139e6i			0.0190418i
$460$	−6.19992e6	+	2.25292e7i	−0.0636961	+	0.231458i
$461$	9.74400e6			0.0994568			0.0497284	−	0.998763i	$-0.484164\pi$
$461$	9.74400e6			0.0994568			0.0497284	+	0.998763i	$0.484164\pi$
$462$	2.76675e7	−	3.19299e7i	0.280571	−	0.323797i
$463$	−8.43840e7	+	5.42303e7i	−0.850192	+	0.546385i	−0.891635	−	0.452755i	$-0.850441\pi$
$463$	−8.43840e7	+	5.42303e7i	−0.850192	+	0.546385i	0.0414424	+	0.999141i	$0.486805\pi$
$464$	−1.67505e7	−	1.16502e8i	−0.167677	−	1.16622i
$465$	649746.	−	296729.i	0.00646227	−	0.00295122i
$466$	−651179.	+	4.52905e6i	−0.00643491	+	0.0447558i
$467$	4.06618e6	+	1.38481e7i	0.0399242	+	0.135969i	0.977044	−	0.213040i	$-0.0683364\pi$
$467$	4.06618e6	+	1.38481e7i	0.0399242	+	0.135969i	−0.937119	+	0.349009i	$0.886518\pi$
$468$	−1.27703e7	−	8.20696e6i	−0.124584	−	0.0800654i
$469$	−3.20400e7	+	7.01578e7i	−0.310580	+	0.680076i
$470$	−2.77977e7	+	9.46703e7i	−0.267741	+	0.911843i
$471$	4.60517e7	−	3.99040e7i	0.440740	−	0.381904i
$472$	5.73055e7	+	6.61340e7i	0.544967	+	0.628925i
$473$	4.86240e7	+	1.42773e7i	0.459481	+	0.134916i
$474$	8.68167e7	+	3.96479e7i	0.815208	+	0.372293i
$475$	−2.37956e7	+	3.70266e7i	−0.222032	+	0.345488i
$476$	−1.57706e6	+	463065.i	−0.0146226	+	0.00429360i
$477$	4.67015e7	+	6.71467e6i	0.430305	+	0.0618684i
$478$	8.51863e7	+	1.86532e8i	0.779984	+	1.70793i
$479$	1.16185e8	−	1.67048e7i	1.05716	−	0.151997i	0.408259	−	0.912866i	$-0.366136\pi$
$479$	1.16185e8	−	1.67048e7i	1.05716	−	0.151997i	0.648905	+	0.760869i	$0.275227\pi$
$480$	−1.58841e7	−	2.47162e7i	−0.143628	−	0.223490i
$481$	−1.63281e8	−	1.41484e8i	−1.46724	−	1.27137i
$482$		−	4.93066e7i		−	0.440315i
$483$	487026.	+	2.85582e7i	0.00432226	+	0.253449i
$484$	−4.43452e7			−0.391120
$485$	−5.24392e6	+	6.05180e6i	−0.0459654	+	0.0530469i
$486$	7.19997e6	−	4.62714e6i	0.0627223	−	0.0403092i
$487$	2.29840e7	+	1.59857e8i	0.198993	+	1.38403i	0.807213	+	0.590260i	$0.200975\pi$
$487$	2.29840e7	+	1.59857e8i	0.198993	+	1.38403i	−0.608220	+	0.793768i	$0.708116\pi$
$488$	7.94428e6	−	3.62803e6i	0.0683589	−	0.0312185i
$489$	5.96767e6	−	4.15061e7i	0.0510362	−	0.354964i
$490$	2.12798e7	+	7.24723e7i	0.180875	+	0.616004i
$491$	−2.92809e6	−	1.88177e6i	−0.0247366	−	0.0158973i	0.528214	−	0.849111i	$-0.322862\pi$
$491$	−2.92809e6	−	1.88177e6i	−0.0247366	−	0.0158973i	−0.552951	+	0.833214i	$0.686498\pi$
$492$	1.81961e6	−	3.98440e6i	0.0152786	−	0.0334555i
$493$	3.20540e6	−	1.09166e7i	0.0267511	−	0.0911059i
$494$	1.03571e8	−	8.97449e7i	0.859128	−	0.744439i
$495$	2.63469e7	+	3.04059e7i	0.217227	+	0.250693i
$496$	2.58483e6	+	758974.i	0.0211830	+	0.00621988i
$497$	7.80467e7	+	3.56427e7i	0.635748	+	0.290337i
$498$	1.70811e7	−	2.65787e7i	0.138302	−	0.215202i
$499$	8.07381e7	−	2.37069e7i	0.649796	−	0.190797i	0.0598088	−	0.998210i	$-0.480951\pi$
$499$	8.07381e7	−	2.37069e7i	0.649796	−	0.190797i	0.589987	+	0.807413i	$0.299133\pi$
$500$	−4.54964e7	−	6.54140e6i	−0.363971	−	0.0523312i
$501$	−2.71548e7	−	5.94608e7i	−0.215940	−	0.472843i
$502$	2.10515e8	−	3.02674e7i	1.66407	−	0.239257i
$503$	2.79533e7	+	4.34962e7i	0.219649	+	0.341780i	0.933538	−	0.358478i	$-0.116704\pi$
$503$	2.79533e7	+	4.34962e7i	0.219649	+	0.341780i	−0.713889	+	0.700259i	$0.753068\pi$
$504$	−1.06838e7	−	9.25759e6i	−0.0834517	−	0.0723113i
$505$			1.24783e8i			0.968909i
$506$	1.63020e8	−	1.46199e8i	1.25832	−	1.12847i
$507$	−4.54315e7			−0.348605
$508$	−2.37162e7	+	2.73700e7i	−0.180907	+	0.208777i
$509$	1.93618e8	−	1.24430e8i	1.46822	−	0.943569i	0.470080	−	0.882624i	$-0.344225\pi$
$509$	1.93618e8	−	1.24430e8i	1.46822	−	0.943569i	0.998141	−	0.0609450i	$-0.0194114\pi$
$510$	−857690.	−	5.96537e6i	−0.00646577	−	0.0449704i
$511$	2.31700e7	−	1.05814e7i	0.173646	−	0.0793013i
$512$	−1.92482e6	+	1.33874e7i	−0.0143410	+	0.0997441i
$513$	5.65345e6	+	1.92539e7i	0.0418756	+	0.142615i
$514$	1.84146e7	+	1.18343e7i	0.135604	+	0.0871474i
$515$	−4.71630e7	+	1.03273e8i	−0.345286	+	0.756072i
$516$	−2.58161e6	+	8.79214e6i	−0.0187906	+	0.0639949i
$517$	1.81480e8	−	1.57254e8i	1.31328	−	1.13796i
$518$	7.12029e7	+	8.21725e7i	0.512281	+	0.591204i
$519$	−4.26374e7	−	1.25195e7i	−0.304992	−	0.0895537i
$520$	−8.36294e7	−	3.81923e7i	−0.594770	−	0.271622i
$521$	9.21528e7	−	1.43393e8i	0.651621	−	1.01394i	−0.345522	−	0.938411i	$-0.612298\pi$
$521$	9.21528e7	−	1.43393e8i	0.651621	−	1.01394i	0.997143	−	0.0755319i	$-0.0240655\pi$
$522$	−5.07395e7	+	1.48985e7i	−0.356726	+	0.104744i
$523$	−1.12375e8	−	1.61571e7i	−0.785532	−	0.112942i	−0.262135	−	0.965031i	$-0.584426\pi$
$523$	−1.12375e8	−	1.61571e7i	−0.785532	−	0.112942i	−0.523397	+	0.852089i	$0.675336\pi$
$524$	4.04235e7	+	8.85151e7i	0.280957	+	0.615210i
$525$	−1.93058e7	+	2.77575e6i	−0.133417	+	0.0191824i
$526$	−1.47021e8	−	2.28769e8i	−1.01023	−	1.57195i
$527$	196805.	+	170532.i	0.00134463	+	0.00116513i
$528$			1.51737e8i			1.03084i
$529$	−1.60591e7	+	1.47162e8i	−0.108481	+	0.994098i
$530$	−1.54422e8			−1.03725
$531$	3.60469e7	−	4.16003e7i	0.240760	−	0.277852i
$532$	−1.50683e7	+	9.68379e6i	−0.100076	+	0.0643147i
$533$	−4.95550e6	−	3.44663e7i	−0.0327270	−	0.227621i
$534$	−4.66606e7	+	2.13092e7i	−0.306427	+	0.139940i
$535$	1.61160e7	−	1.12089e8i	0.105243	−	0.731984i
$536$	−5.57410e7	−	1.89836e8i	−0.361976	−	1.23278i
$537$	−1.03048e8	−	6.62247e7i	−0.665450	−	0.427659i
$538$	−6.29652e7	+	1.37874e8i	−0.404346	+	0.885395i
$539$	5.17901e7	−	1.76381e8i	0.330735	−	1.12638i
$540$	−5.49797e6	+	4.76402e6i	−0.0349157	+	0.0302546i
$541$	3.56111e7	+	4.10974e7i	0.224902	+	0.259551i	0.856975	−	0.515358i	$-0.172341\pi$
$541$	3.56111e7	+	4.10974e7i	0.224902	+	0.259551i	−0.632073	+	0.774909i	$0.717796\pi$
$542$	2.00692e8	+	5.89284e7i	1.26047	+	0.370107i
$543$	−4.20228e7	−	1.91912e7i	−0.262474	−	0.119868i
$544$	5.79086e6	−	9.01076e6i	0.0359705	−	0.0559712i
$545$	8.86285e7	−	2.60237e7i	0.547500	−	0.160760i
$546$	6.01120e7	+	8.64280e6i	0.369303	+	0.0530978i
$547$	−9.98843e6	−	2.18716e7i	−0.0610289	−	0.133635i	0.876660	−	0.481110i	$-0.159766\pi$
$547$	−9.98843e6	−	2.18716e7i	−0.0610289	−	0.133635i	−0.937689	+	0.347475i	$0.887039\pi$
$548$	−1.63382e7	+	2.34908e6i	−0.0992801	+	0.0142743i
$549$	−2.97009e6	−	4.62154e6i	−0.0179495	−	0.0279299i
$550$	1.13008e8	+	9.79216e7i	0.679234	+	0.588559i
$551$		−	1.23987e8i		−	0.741178i
$552$	−4.89183e7	−	5.45470e7i	−0.290840	−	0.324305i
$553$	−9.91640e7			−0.586379
$554$	4.09190e7	−	4.72230e7i	0.240655	−	0.277731i
$555$	−8.71035e7	+	5.59780e7i	−0.509515	+	0.327445i
$556$	−3.58334e6	−	2.49227e7i	−0.0208479	−	0.145001i
$557$	−2.51822e7	+	1.15003e7i	−0.145723	+	0.0665495i	−0.486942	−	0.873434i	$-0.661888\pi$
$557$	−2.51822e7	+	1.15003e7i	−0.145723	+	0.0665495i	0.341219	+	0.939984i	$0.389160\pi$
$558$	172253.	−	1.19805e6i	0.000991435	−	0.00689558i
$559$	2.05225e7	+	6.98932e7i	0.117488	+	0.400129i
$560$	5.44949e7	+	3.50217e7i	0.310307	+	0.199422i
$561$	−6.09315e6	+	1.33421e7i	−0.0345107	+	0.0755678i
$562$	4.10848e7	−	1.39922e8i	0.231458	−	0.788274i
$563$	3.48573e7	−	3.02040e7i	0.195330	−	0.169254i	−0.551705	−	0.834039i	$-0.686022\pi$
$563$	3.48573e7	−	3.02040e7i	0.195330	−	0.169254i	0.747034	+	0.664785i	$0.231477\pi$
$564$	2.84344e7	+	3.28151e7i	0.158492	+	0.182909i
$565$	−5.36560e7	−	1.57548e7i	−0.297490	−	0.0873511i
$566$	−2.20831e7	−	1.00850e7i	−0.121790	−	0.0556196i
$567$	−4.80761e6	+	7.48078e6i	−0.0263742	+	0.0410391i
$568$	−2.11182e8	+	6.20087e7i	−1.15242	+	0.338383i
$569$	1.70280e7	+	2.44825e6i	0.0924328	+	0.0132898i	0.188376	−	0.982097i	$-0.439678\pi$
$569$	1.70280e7	+	2.44825e6i	0.0924328	+	0.0132898i	−0.0959432	+	0.995387i	$0.530587\pi$
$570$	−2.72831e7	−	5.97417e7i	−0.147323	−	0.322592i
$571$	−2.55071e8	+	3.66737e7i	−1.37010	+	0.196991i	−0.787775	−	0.615963i	$-0.788767\pi$
$571$	−2.55071e8	+	3.66737e7i	−1.37010	+	0.196991i	−0.582328	+	0.812954i	$0.697858\pi$
$572$	−6.53728e7	−	1.01722e8i	−0.349308	−	0.543534i
$573$	1.95362e7	+	1.69282e7i	0.103843	+	0.0899802i
$574$			1.75238e7i			0.0926600i
$575$	−1.01074e8	+	1.72370e6i	−0.531663	+	0.00906688i
$576$	2.84241e7			0.148737
$577$	1.87282e8	−	2.16135e8i	0.974920	−	1.12512i	−0.0172034	−	0.999852i	$-0.505476\pi$
$577$	1.87282e8	−	2.16135e8i	0.974920	−	1.12512i	0.992123	−	0.125265i	$-0.0399782\pi$
$578$	−1.86955e8	+	1.20148e8i	−0.968172	+	0.622207i
$579$	−7.43591e6	−	5.17179e7i	−0.0383088	−	0.266443i
$580$	4.08875e7	−	1.86727e7i	0.209559	−	0.0957025i
$581$	−4.67168e6	+	3.24923e7i	−0.0238202	+	0.165673i
$582$	3.82281e6	+	1.30193e7i	0.0193916	+	0.0660417i
$583$	3.16167e8	+	2.03188e8i	1.59555	+	1.02540i
$584$	−2.71438e7	+	5.94366e7i	−0.136280	+	0.298411i
$585$	−1.62930e7	+	5.54890e7i	−0.0813831	+	0.277165i
$586$	2.07715e8	−	1.79986e8i	1.03223	−	0.894429i
$587$	1.43075e8	+	1.65118e8i	0.707376	+	0.816355i	0.989729	−	0.142955i	$-0.0456605\pi$
$587$	1.43075e8	+	1.65118e8i	0.707376	+	0.816355i	−0.282353	+	0.959310i	$0.591115\pi$
$588$	3.18930e7	+	9.36463e6i	0.156878	+	0.0460637i
$589$	2.58140e6	+	1.17888e6i	0.0126331	+	0.00576933i
$590$	−9.74008e7	+	1.51559e8i	−0.474249	+	0.737946i
$591$	−1.51188e7	+	4.43929e6i	−0.0732412	+	0.0215056i
$592$	−3.86525e8	−	5.55739e7i	−1.86300	−	0.267859i
$593$	660951.	+	1.44728e6i	0.00316961	+	0.00694047i	0.911210	−	0.411942i	$-0.135149\pi$
$593$	660951.	+	1.44728e6i	0.00316961	+	0.00694047i	−0.908041	+	0.418882i	$0.862422\pi$
$594$	6.74801e7	−	9.70217e6i	0.321971	−	0.0462924i
$595$	3.38536e6	+	5.26773e6i	0.0160714	+	0.0250076i
$596$	−660681.	−	572483.i	−0.00312071	−	0.00270411i
$597$		−	1.47296e8i		−	0.692256i
$598$	3.03477e8	+	8.35151e7i	1.41913	+	0.390536i
$599$	−2.93930e8			−1.36761			−0.683807	−	0.729663i	$-0.739677\pi$
$599$	−2.93930e8			−1.36761			−0.683807	+	0.729663i	$0.739677\pi$
$600$	3.27648e7	−	3.78125e7i	0.151689	−	0.175058i
$601$	9.96078e7	−	6.40140e7i	0.458849	−	0.294884i	−0.290723	−	0.956807i	$-0.593896\pi$
$601$	9.96078e7	−	6.40140e7i	0.458849	−	0.294884i	0.749572	+	0.661923i	$0.230259\pi$
$602$	−5.21716e6	−	3.62862e7i	−0.0239136	−	0.166323i
$603$	−1.13207e8	+	5.17001e7i	−0.516324	+	0.235797i
$604$	−1.84963e7	+	1.28645e8i	−0.0839410	+	0.583822i
$605$	4.75965e7	+	1.62099e8i	0.214936	+	0.732004i
$606$	1.77878e8	+	1.14315e8i	0.799290	+	0.513673i
$607$	5.91359e7	−	1.29490e8i	0.264415	−	0.578987i	−0.730129	−	0.683309i	$-0.760540\pi$
$607$	5.91359e7	−	1.29490e8i	0.264415	−	0.578987i	0.994544	+	0.104322i	$0.0332673\pi$
$608$	3.28854e7	−	1.11997e8i	0.146316	−	0.498307i
$609$	4.15239e7	−	3.59807e7i	0.183843	−	0.159301i
$610$	1.17746e7	+	1.35886e7i	0.0518746	+	0.0598665i
$611$	3.31190e8	+	9.72462e7i	1.45196	+	0.426333i
$612$	−2.41251e6	−	1.10176e6i	−0.0105248	−	0.00480653i
$613$	2.14201e8	−	3.33304e8i	0.929910	−	1.44697i	0.0356782	−	0.999363i	$-0.488641\pi$
$613$	2.14201e8	−	3.33304e8i	0.929910	−	1.44697i	0.894232	−	0.447605i	$-0.147723\pi$
$614$	3.18033e8	−	9.33829e7i	1.37394	−	0.403425i
$615$	−1.65175e7	−	2.37486e6i	−0.0710101	−	0.0102097i
$616$	−4.67784e7	−	1.02431e8i	−0.200126	−	0.438215i
$617$	−3.37576e8	+	4.85361e7i	−1.43720	+	0.206638i	−0.816469	−	0.577389i	$-0.804072\pi$
$617$	−3.37576e8	+	4.85361e7i	−1.43720	+	0.206638i	−0.620727	+	0.784027i	$0.713162\pi$
$618$	1.04008e8	+	1.61839e8i	0.440657	+	0.685676i
$619$	−3.01830e8	−	2.61537e8i	−1.27259	−	1.10271i	−0.989639	−	0.143576i	$-0.954140\pi$
$619$	−3.01830e8	−	2.61537e8i	−1.27259	−	1.10271i	−0.282955	−	0.959133i	$-0.591315\pi$
$620$			1.02881e6i			0.00431680i
$621$	−2.95833e7	+	3.53410e7i	−0.123530	+	0.147572i
$622$	−4.68996e8			−1.94894
$623$	3.49020e7	−	4.02790e7i	0.144340	−	0.166577i
$624$	−1.83486e8	+	1.17919e8i	−0.755178	+	0.485324i
$625$	6.44555e6	+	4.48298e7i	0.0264010	+	0.183623i
$626$	−3.96271e8	+	1.80971e8i	−1.61536	+	0.737710i
$627$	−2.27479e7	+	1.58215e8i	−0.0922867	+	0.641868i
$628$	2.47265e7	+	8.42109e7i	0.0998354	+	0.340008i
$629$	−3.17552e7	−	2.04078e7i	−0.127604	−	0.0820059i
$630$	1.20903e7	−	2.64741e7i	0.0483522	−	0.105877i
$631$	−4.48910e7	+	1.52885e8i	−0.178678	+	0.608522i	0.820635	+	0.571453i	$0.193620\pi$
$631$	−4.48910e7	+	1.52885e8i	−0.178678	+	0.608522i	−0.999313	+	0.0370686i	$0.988198\pi$
$632$	1.92247e8	−	1.66583e8i	0.761566	−	0.659901i
$633$	6.04738e7	+	6.97905e7i	0.238427	+	0.275160i
$634$	2.74883e7	+	8.07129e6i	0.107865	+	0.0316720i
$635$	1.25503e8	+	5.73153e7i	0.490154	+	0.223846i
$636$	−3.67402e7	+	5.71689e7i	−0.142814	+	0.222223i
$637$	2.53534e8	−	7.44442e7i	0.980883	−	0.288013i
$638$	−4.16943e8	−	5.99473e7i	−1.60551	−	0.230838i
$639$	5.75135e7	+	1.25937e8i	0.220428	+	0.482670i
$640$	−2.11479e8	+	3.04061e7i	−0.806727	+	0.115990i
$641$	2.15636e8	+	3.35536e8i	0.818743	+	1.27399i	0.958867	+	0.283854i	$0.0916133\pi$
$641$	2.15636e8	+	3.35536e8i	0.818743	+	1.27399i	−0.140125	+	0.990134i	$0.544750\pi$
$642$	−1.45018e8	−	1.25659e8i	−0.548047	−	0.474885i
$643$			4.08529e8i			1.53670i	0.640027	+	0.768352i	$0.278923\pi$
$643$			4.08529e8i			1.53670i	−0.640027	+	0.768352i	$0.721077\pi$
$644$	−3.77072e7	−	1.64492e7i	−0.141178	−	0.0615866i
$645$	3.49096e7			0.130096
$646$	1.56798e7	−	1.80954e7i	0.0581624	−	0.0671230i
$647$	−4.34642e8	+	2.79328e8i	−1.60479	+	1.03134i	−0.639984	+	0.768389i	$0.721059\pi$
$647$	−4.34642e8	+	2.79328e8i	−1.60479	+	1.03134i	−0.964810	+	0.262949i	$0.915305\pi$
$648$	−3.24637e6	−	2.25790e7i	−0.0119309	−	0.0829811i
$649$	3.98840e8	−	1.82144e8i	1.45903	−	0.666318i
$650$	−3.05889e7	+	2.12750e8i	−0.111384	+	0.774694i
$651$	354299.	+	1.20663e6i	0.00128418	+	0.00437352i
$652$	5.08089e7	+	3.26529e7i	0.183315	+	0.117809i
$653$	−6.95130e7	+	1.52212e8i	−0.249647	+	0.546651i	−0.992420	−	0.122893i	$-0.960783\pi$
$653$	−6.95130e7	+	1.52212e8i	−0.249647	+	0.546651i	0.742773	+	0.669543i	$0.233510\pi$
$654$	4.40968e7	−	1.50180e8i	0.157643	−	0.536881i
$655$	2.80170e8	−	2.42768e8i	0.997005	−	0.863909i
$656$	−4.12144e7	−	4.75640e7i	−0.145995	−	0.168487i
$657$	3.94368e7	+	1.15797e7i	0.139061	+	0.0408320i
$658$	−1.58013e8	−	7.21620e7i	−0.554644	−	0.253297i
$659$	−3.26410e7	+	5.07903e7i	−0.114053	+	0.177470i	−0.893587	−	0.448890i	$-0.851820\pi$
$659$	−3.26410e7	+	5.07903e7i	−0.114053	+	0.177470i	0.779534	+	0.626360i	$0.215456\pi$
$660$	−5.56008e7	+	1.63259e7i	−0.193397	+	0.0567864i
$661$	−4.80756e8	−	6.91223e7i	−1.66464	−	0.239339i	−0.755296	−	0.655384i	$-0.772507\pi$
$661$	−4.80756e8	−	6.91223e7i	−1.66464	−	0.239339i	−0.909344	+	0.416045i	$0.863416\pi$
$662$	−1.10547e7	−	2.42065e7i	−0.0381044	−	0.0834369i
$663$	−2.08690e7	+	3.00050e6i	−0.0716078	+	0.0102956i
$664$	−4.55259e7	−	7.08398e7i	−0.155509	−	0.241976i
$665$	5.15710e7	+	4.46866e7i	0.175364	+	0.151954i
$666$			1.75448e8i			0.593915i
$667$	2.36903e8	−	1.58020e8i	0.798351	−	0.532520i
$668$	9.41507e7			0.315860
$669$	1.56918e8	−	1.81093e8i	0.524076	−	0.604816i
$670$	3.42666e8	−	2.20218e8i	1.13932	−	0.732198i
$671$	−6.22767e6	−	4.33144e7i	−0.0206138	−	0.143372i
$672$	4.70517e7	−	2.14878e7i	0.155048	−	0.0708083i
$673$	−5.27005e7	+	3.66540e8i	−0.172890	+	1.20248i	0.699850	+	0.714290i	$0.253250\pi$
$673$	−5.27005e7	+	3.66540e8i	−0.172890	+	1.20248i	−0.872740	+	0.488186i	$0.837659\pi$
$674$	4.79196e7	+	1.63199e8i	0.156507	+	0.533013i
$675$	−2.64762e7	−	1.70152e7i	−0.0860885	−	0.0553257i
$676$	2.71830e7	−	5.95225e7i	0.0879950	−	0.192682i
$677$	3.12479e7	−	1.06420e8i	0.100706	−	0.342972i	−0.893691	−	0.448682i	$-0.851893\pi$
$677$	3.12479e7	−	1.06420e8i	0.100706	−	0.342972i	0.994397	+	0.105710i	$0.0337116\pi$
$678$	−7.16131e7	+	6.20531e7i	−0.229775	+	0.199102i
$679$	−9.23231e6	−	1.06547e7i	−0.0294918	−	0.0340353i
$680$	−1.54122e7	−	4.52544e6i	−0.0490161	−	0.0143924i
$681$	−5.18553e7	−	2.36815e7i	−0.164192	−	0.0749839i
$682$	5.21243e6	−	8.11070e6i	0.0164319	−	0.0255685i
$683$	3.48246e7	−	1.02254e7i	0.109301	−	0.0320937i	−0.226625	−	0.973982i	$-0.572769\pi$
$683$	3.48246e7	−	1.02254e7i	0.109301	−	0.0320937i	0.335926	+	0.941888i	$0.390951\pi$
$684$	−2.86083e7	−	4.11325e6i	−0.0893972	−	0.0128534i
$685$	2.61229e7	+	5.72011e7i	0.0812735	+	0.177964i
$686$	−2.94684e8	+	4.23691e7i	−0.912817	+	0.131243i
$687$	1.49391e8	+	2.32457e8i	0.460739	+	0.716924i
$688$	9.95025e7	+	8.62194e7i	0.305540	+	0.264752i
$689$			5.40223e8i			1.65164i
$690$	7.93768e7	−	1.28270e8i	0.241628	−	0.390462i
$691$	2.58843e7			0.0784517			0.0392258	−	0.999230i	$-0.487511\pi$
$691$	2.58843e7			0.0784517			0.0392258	+	0.999230i	$0.487511\pi$
$692$	4.19137e7	−	4.83710e7i	0.126485	−	0.145971i
$693$	−5.95884e7	+	3.82952e7i	−0.179045	+	0.115065i
$694$	−8.44851e7	−	5.87607e8i	−0.252756	−	1.75796i
$695$	−8.72559e7	+	3.98484e7i	−0.259920	+	0.118702i
$696$	−2.00585e7	+	1.39510e8i	−0.0594936	+	0.413787i
$697$	−1.71398e6	−	5.83727e6i	−0.00506182	−	0.0172390i
$698$	−1.17325e8	−	7.54001e7i	−0.345003	−	0.221720i
$699$	3.18674e6	−	6.97799e6i	0.00933073	−	0.0204314i
$700$	7.91455e6	−	2.69545e7i	0.0230745	−	0.0785845i
$701$	−5.79408e7	+	5.02060e7i	−0.168202	+	0.145748i	−0.734894	−	0.678182i	$-0.762768\pi$
$701$	−5.79408e7	+	5.02060e7i	−0.168202	+	0.145748i	0.566693	+	0.823929i	$0.308223\pi$
$702$	6.41730e7	+	7.40595e7i	0.185499	+	0.214077i
$703$	−3.94695e8	−	1.15893e8i	−1.13604	−	0.333573i
$704$	2.05953e8	+	9.40555e7i	0.590269	+	0.269567i
$705$	8.94325e7	−	1.39160e8i	0.255228	−	0.397142i
$706$	3.47475e7	−	1.02028e7i	0.0987438	−	0.0289938i
$707$	−2.17455e8	−	3.12652e7i	−0.615333	−	0.0884715i
$708$	3.29351e7	+	7.21179e7i	0.0928025	+	0.203209i
$709$	6.32756e8	−	9.09765e7i	1.77540	−	0.255265i	0.824746	−	0.565503i	$-0.191318\pi$
$709$	6.32756e8	−	9.09765e7i	1.77540	−	0.255265i	0.950659	+	0.310239i	$0.100409\pi$
$710$	−2.44980e8	−	3.81197e8i	−0.684473	−	1.06506i
$711$	−1.20929e8	−	1.04786e8i	−0.336451	−	0.291536i
$712$			1.36719e8i			0.378781i
$713$	1.03746e6	+	6.43477e6i	0.00286222	+	0.0177527i
$714$	1.06105e7			0.0291501
$715$	−3.01667e8	+	3.48143e8i	−0.825297	+	0.952444i
$716$	1.48422e8	−	9.53847e7i	0.404350	−	0.259860i
$717$	−4.89274e7	−	3.40298e8i	−0.132738	−	0.923212i
$718$	−2.64407e8	+	1.20751e8i	−0.714332	+	0.326225i
$719$	7.42196e7	−	5.16209e8i	0.199679	−	1.38880i	−0.605538	−	0.795816i	$-0.707042\pi$
$719$	7.42196e7	−	5.16209e8i	0.199679	−	1.38880i	0.805217	−	0.592980i	$-0.202049\pi$
$720$	2.94486e7	+	1.00293e8i	0.0788982	+	0.268703i
$721$	−1.68151e8	−	1.08064e8i	−0.448637	−	0.288321i
$722$	−7.33217e7	+	1.60552e8i	−0.194814	+	0.426584i
$723$	−2.32893e7	+	7.93161e7i	−0.0616228	+	0.209868i
$724$	5.02871e7	−	4.35740e7i	0.132508	−	0.114818i
$725$	1.27344e8	+	1.46963e8i	0.334168	+	0.385650i
$726$	2.74674e8	+	8.06517e7i	0.717808	+	0.210767i
$727$	−1.71580e8	−	7.83581e7i	−0.446544	−	0.203930i	0.179435	−	0.983770i	$-0.442573\pi$
$727$	−1.71580e8	−	7.83581e7i	−0.446544	−	0.203930i	−0.625979	+	0.779840i	$0.715300\pi$
$728$	8.75098e7	−	1.36168e8i	0.226810	−	0.352924i
$729$	−1.37677e7	+	4.04255e6i	−0.0355368	+	0.0104345i
$730$	−1.33153e8	−	1.91446e7i	−0.342281	−	0.0492126i
$731$	5.28696e6	+	1.15768e7i	0.0135349	+	0.0296372i
$732$	7.83206e6	−	1.12608e6i	0.0199684	−	0.00287102i
$733$	3.02388e8	+	4.70525e8i	0.767808	+	1.19473i	0.976239	+	0.216696i	$0.0695281\pi$
$733$	3.02388e8	+	4.70525e8i	0.767808	+	1.19473i	−0.208431	+	0.978037i	$0.566836\pi$
$734$	−3.11767e8	−	2.70148e8i	−0.788392	−	0.683145i
$735$		−	1.26632e8i		−	0.318921i
$736$	2.55906e8	−	7.99051e7i	0.641870	−	0.200420i
$737$	−9.91342e8			−2.47640
$738$	−1.85172e7	+	2.13700e7i	−0.0460688	+	0.0531662i
$739$	6.16228e8	−	3.96026e8i	1.52689	−	0.981273i	0.536359	−	0.843990i	$-0.319799\pi$
$739$	6.16228e8	−	3.96026e8i	1.52689	−	0.981273i	0.990532	−	0.137284i	$-0.0438372\pi$
$740$	−2.12235e7	−	1.47613e8i	−0.0523748	−	0.364275i
$741$	−2.08998e8	+	9.54460e7i	−0.513673	+	0.234587i
$742$	3.86914e7	−	2.69104e8i	0.0947114	−	0.658733i
$743$	1.75540e8	+	5.97835e8i	0.427967	+	1.45752i	0.838110	+	0.545501i	$0.183661\pi$
$743$	1.75540e8	+	5.97835e8i	0.427967	+	1.45752i	−0.410143	+	0.912021i	$0.634521\pi$
$744$	−2.71386e6	−	1.74409e6i	−0.00658974	−	0.00423497i
$745$	−1.38353e6	+	3.02950e6i	−0.00334594	+	0.00732659i
$746$	1.78415e8	−	6.07625e8i	0.429749	−	1.46359i
$747$	−4.00313e7	+	3.46873e7i	−0.0960368	+	0.0832164i
$748$	−1.38346e7	−	1.59660e7i	−0.0330569	−	0.0381497i
$749$	1.91295e8	+	5.61691e7i	0.455258	+	0.133676i
$750$	2.69908e8	+	1.23263e8i	0.639782	+	0.292179i
$751$	2.16770e8	−	3.37301e8i	0.511776	−	0.796338i	−0.485171	−	0.874419i	$-0.661243\pi$
$751$	2.16770e8	−	3.37301e8i	0.511776	−	0.796338i	0.996947	+	0.0780806i	$0.0248791\pi$
$752$	5.98605e8	−	1.75766e8i	1.40762	−	0.413316i
$753$	−3.52937e8	−	5.07447e7i	−0.826632	−	0.118852i
$754$	−2.51528e8	−	5.50769e8i	−0.586775	−	1.28486i
$755$	4.90098e8	−	7.04655e7i	1.13879	−	0.163733i
$756$	−6.92449e6	−	1.07747e7i	−0.0160259	−	0.0249368i
$757$	−1.41402e8	−	1.22526e8i	−0.325963	−	0.282449i	0.476470	−	0.879191i	$-0.341916\pi$
$757$	−1.41402e8	−	1.22526e8i	−0.325963	−	0.282449i	−0.802433	+	0.596742i	$0.796462\pi$
$758$			5.53030e8i			1.26982i
$759$	−3.31295e8	+	1.58179e8i	−0.757686	+	0.361763i
$760$	−1.75047e8			−0.398763
$761$	5.48241e8	−	6.32703e8i	1.24399	−	1.43564i	0.385584	−	0.922673i	$-0.374000\pi$
$761$	5.48241e8	−	6.32703e8i	1.24399	−	1.43564i	0.858407	−	0.512969i	$-0.171455\pi$
$762$	1.96677e8	−	1.26397e8i	0.444517	−	0.285674i
$763$	2.31439e7	+	1.60969e8i	0.0521030	+	0.362384i
$764$	−3.38678e7	+	1.54669e7i	−0.0759463	+	0.0346835i
$765$	−1.43795e6	+	1.00012e7i	−0.00321189	+	0.0223392i
$766$	3.21577e7	+	1.09519e8i	0.0715481	+	0.243670i
$767$	5.30206e8	+	3.40743e8i	1.17506	+	0.755162i
$768$	−1.01916e8	+	2.23164e8i	−0.224987	+	0.492653i
$769$	−1.85615e8	+	6.32148e8i	−0.408164	+	1.39008i	0.457390	+	0.889266i	$0.348784\pi$
$769$	−1.85615e8	+	6.32148e8i	−0.408164	+	1.39008i	−0.865555	+	0.500814i	$0.833034\pi$
$770$	1.75206e8	−	1.51817e8i	0.383774	−	0.332542i
$771$	−2.40325e7	−	2.77350e7i	−0.0524367	−	0.0605152i
$772$	7.22078e7	+	2.12021e7i	0.156940	+	0.0460816i
$773$	−7.78474e8	−	3.55517e8i	−1.68541	−	0.769701i	−0.999101	−	0.0423903i	$-0.986503\pi$
$773$	−7.78474e8	−	3.55517e8i	−1.68541	−	0.769701i	−0.686309	−	0.727311i	$-0.740770\pi$
$774$	3.19810e7	−	4.97634e7i	0.0689713	−	0.107321i
$775$	−4.27055e6	+	1.25395e6i	−0.00917442	+	0.00269385i
$776$	3.57969e7	+	5.14682e6i	0.0766056	+	0.0110142i
$777$	−7.57261e7	−	1.65817e8i	−0.161429	−	0.353481i
$778$	−8.37932e8	+	1.20476e8i	−1.77939	+	0.255837i
$779$	−3.58433e7	−	5.57733e7i	−0.0758221	−	0.117981i
$780$	−6.29508e7	−	5.45472e7i	−0.132653	−	0.114945i
$781$			1.10281e9i			2.31499i
$782$	5.45588e7	+	6.89702e6i	0.114089	+	0.0144225i
$783$	8.86583e7			0.184686
$784$	3.12756e8	−	3.60940e8i	0.649019	−	0.749008i
$785$	2.81284e8	−	1.80770e8i	0.581481	−	0.373695i
$786$	−8.93988e7	−	6.21782e8i	−0.184104	−	1.28047i
$787$	5.47336e8	−	2.49960e8i	1.12287	−	0.512798i	0.234588	−	0.972095i	$-0.424626\pi$
$787$	5.47336e8	−	2.49960e8i	1.12287	−	0.512798i	0.888283	+	0.459297i	$0.151899\pi$
$788$	3.22987e6	−	2.24642e7i	0.00660095	−	0.0459106i
$789$	1.28446e8	+	4.37448e8i	0.261512	+	0.890627i
$790$	4.40570e8	+	2.83137e8i	0.893580	+	0.574269i
$791$	4.08990e7	−	8.95564e7i	0.0826387	−	0.180954i
$792$	5.11917e7	−	1.74343e8i	0.103044	−	0.350936i
$793$	4.75376e7	−	4.11916e7i	0.0953274	−	0.0826016i
$794$	2.89538e8	+	3.34144e8i	0.578421	+	0.667533i
$795$	2.48408e8	+	7.29392e7i	0.494384	+	0.145164i
$796$	1.92981e8	+	8.81313e7i	0.382626	+	0.174740i
$797$	−2.14671e8	+	3.34035e8i	−0.424032	+	0.659807i	−0.985884	−	0.167431i	$-0.946453\pi$
$797$	−2.14671e8	+	3.34035e8i	−0.424032	+	0.659807i	0.561852	+	0.827238i	$0.310089\pi$
$798$	1.10945e8	−	3.25764e7i	0.218323	−	0.0641054i
$799$	5.96929e7	+	8.58255e6i	0.117026	+	0.0168258i
$800$	7.60503e7	+	1.66527e8i	0.148536	+	0.325248i
$801$	8.51248e7	−	1.22391e7i	0.165638	−	0.0238151i
$802$	−3.31948e8	−	5.16521e8i	−0.643497	−	1.00130i
$803$	2.47430e8	+	2.14399e8i	0.477866	+	0.414073i
$804$		−	1.79253e8i		−	0.344905i
$805$	−1.96562e7	+	1.55490e8i	−0.0376800	+	0.298067i
$806$	1.38585e7			0.0264673
$807$	1.66411e8	−	1.92048e8i	0.316637	−	0.365418i
$808$	4.74095e8	−	3.04683e8i	0.898735	−	0.577582i
$809$	−1.30213e8	−	9.05650e8i	−0.245928	−	1.71047i	−0.621284	−	0.783586i	$-0.713389\pi$
$809$	−1.30213e8	−	9.05650e8i	−0.245928	−	1.71047i	0.375356	−	0.926881i	$-0.377521\pi$
$810$	4.27189e7	−	1.95091e7i	0.0803831	−	0.0367097i
$811$	1.32951e8	−	9.24695e8i	0.249247	−	1.73355i	−0.353341	−	0.935495i	$-0.614954\pi$
$811$	1.32951e8	−	9.24695e8i	0.249247	−	1.73355i	0.602587	−	0.798053i	$-0.294136\pi$
$812$	2.22955e7	+	7.59314e7i	0.0416436	+	0.141825i
$813$	−2.95005e8	−	1.89588e8i	−0.548982	−	0.352809i
$814$	−5.80556e8	+	1.27124e9i	−1.07639	+	2.35697i
$815$	6.48249e7	−	2.20773e8i	0.119748	−	0.407825i
$816$	−2.87995e7	+	2.49549e7i	−0.0530047	+	0.0459288i
$817$	9.08247e7	+	1.04817e8i	0.166547	+	0.192206i
$818$	4.28177e8	+	1.25724e8i	0.782282	+	0.229699i
$819$	−9.26158e7	−	4.22962e7i	−0.168591	−	0.0769927i
$820$	1.29944e7	−	2.02197e7i	0.0235675	−	0.0366718i
$821$	−3.84392e8	+	1.12868e8i	−0.694617	+	0.203958i	−0.609937	−	0.792450i	$-0.708805\pi$
$821$	−3.84392e8	+	1.12868e8i	−0.694617	+	0.203958i	−0.0846803	+	0.996408i	$0.526987\pi$
$822$	1.05471e8	+	1.51645e7i	0.189897	+	0.0273031i
$823$	3.50631e8	+	7.67775e8i	0.629000	+	1.37732i	0.908789	+	0.417256i	$0.137008\pi$
$823$	3.50631e8	+	7.67775e8i	0.629000	+	1.37732i	−0.279789	+	0.960062i	$0.590264\pi$
$824$	5.07525e8	−	7.29711e7i	0.907144	−	0.130428i
$825$	−1.35535e8	−	2.10897e8i	−0.241374	−	0.375586i
$826$	−2.39710e8	−	2.07710e8i	−0.425350	−	0.368568i
$827$			3.70995e8i			0.655921i	0.944691	+	0.327961i	$0.106361\pi$
$827$			3.70995e8i			0.655921i	−0.944691	+	0.327961i	$0.893639\pi$
$828$	−2.86018e7	−	5.99044e7i	−0.0503851	−	0.105528i
$829$	−5.10425e8			−0.895917			−0.447959	−	0.894054i	$-0.647849\pi$
$829$	−5.10425e8			−0.895917			−0.447959	+	0.894054i	$0.647849\pi$
$830$	1.13529e8	−	1.31019e8i	0.198551	−	0.229140i
$831$	−8.81287e7	+	5.66369e7i	−0.153573	+	0.0986953i
$832$	4.63166e7	+	3.22139e8i	0.0804205	+	0.559337i
$833$	4.19943e7	−	1.91781e7i	0.0726532	−	0.0331796i
$834$	−2.31322e7	+	1.60888e8i	−0.0398767	+	0.277349i
$835$	−1.01054e8	−	3.44157e8i	−0.173577	−	0.591149i
$836$	−1.93676e8	−	1.24468e8i	−0.331481	−	0.213030i
$837$	−842973.	+	1.84585e6i	−0.00143760	+	0.00314790i
$838$	−3.05003e8	+	1.03875e9i	−0.518290	+	1.76513i
$839$	7.06055e8	−	6.11800e8i	1.19551	−	1.03591i	0.197051	−	0.980393i	$-0.436864\pi$
$839$	7.06055e8	−	6.11800e8i	1.19551	−	1.03591i	0.998458	−	0.0555205i	$-0.0176818\pi$
$840$	−5.07981e7	−	5.86242e7i	−0.0857057	−	0.0989097i
$841$	4.51211e7	+	1.32488e7i	0.0758564	+	0.0222734i
$842$	4.25798e8	+	1.94455e8i	0.713291	+	0.325749i
$843$	−1.32181e8	+	2.05677e8i	−0.220640	+	0.343323i
$844$	−1.27620e8	+	3.74726e7i	−0.212271	+	0.0623285i
$845$	−2.46754e8	−	3.54778e7i	−0.408972	−	0.0588013i
$846$	−1.16441e8	−	2.54971e8i	−0.192307	−	0.421095i
$847$	−2.94408e8	+	4.23295e7i	−0.484506	+	0.0696614i
$848$	5.27892e8	+	8.21415e8i	0.865680	+	1.34702i
$849$	3.07601e7	+	2.66538e7i	0.0502648	+	0.0435547i
$850$			3.75529e7i			0.0611487i
$851$	−2.81597e8	−	9.01850e8i	−0.456920	−	1.46334i
$852$	−1.99410e8			−0.322424
$853$	−5.78996e8	+	6.68196e8i	−0.932885	+	1.07661i	0.0640166	+	0.997949i	$0.479609\pi$
$853$	−5.78996e8	+	6.68196e8i	−0.932885	+	1.07661i	−0.996902	+	0.0786579i	$0.974937\pi$
$854$	−2.66304e7	+	1.71143e7i	−0.0427566	+	0.0274780i
$855$	1.56703e7	+	1.08989e8i	0.0250714	+	0.174375i
$856$	−4.65215e8	+	2.12457e8i	−0.741707	+	0.338726i
$857$	−8.09535e7	+	5.63044e8i	−0.128615	+	0.894540i	0.818696	+	0.574227i	$0.194697\pi$
$857$	−8.09535e7	+	5.63044e8i	−0.128615	+	0.894540i	−0.947312	+	0.320313i	$0.896212\pi$
$858$	2.19915e8	+	7.48962e8i	0.348171	+	1.18576i
$859$	1.50488e8	+	9.67129e7i	0.237423	+	0.152583i	0.653943	−	0.756544i	$-0.273114\pi$
$859$	1.50488e8	+	9.67129e7i	0.237423	+	0.152583i	−0.416519	+	0.909127i	$0.636750\pi$
$860$	−2.08874e7	+	4.57371e7i	−0.0328390	+	0.0719074i
$861$	8.27713e6	−	2.81893e7i	0.0129679	−	0.0441647i
$862$	−6.46181e8	+	5.59919e8i	−1.00886	+	0.874185i
$863$	−5.84768e8	−	6.74858e8i	−0.909811	−	1.04998i	−0.998545	−	0.0539224i	$-0.982828\pi$
$863$	−5.84768e8	−	6.74858e8i	−0.909811	−	1.04998i	0.0887342	−	0.996055i	$-0.471718\pi$
$864$	8.00848e7	+	2.35150e7i	0.124168	+	0.0364589i
$865$	−2.21801e8	−	1.01293e8i	−0.342702	−	0.156507i
$866$	2.57339e8	−	4.00427e8i	0.396234	−	0.616552i
$867$	3.57492e8	−	1.04969e8i	0.548540	−	0.161066i
$868$	−1.79287e6	−	257775.i	−0.00274150	−	0.000394169i
$869$	−5.29480e8	−	1.15940e9i	−0.806845	−	1.76674i
$870$	−2.87218e8	+	4.12957e7i	−0.436168	+	0.0627115i
$871$	−7.70401e8	−	1.19877e9i	−1.16590	−	1.81418i
$872$	−3.15276e8	−	2.73188e8i	−0.475490	−	0.412015i
$873$		−	2.27489e7i		−	0.0341914i
$874$	5.91652e8	−	9.53906e7i	0.886201	−	0.142880i
$875$	−3.08295e8			−0.460195
$876$	−3.87675e7	+	4.47400e7i	−0.0576707	+	0.0665555i
$877$	−9.82623e6	+	6.31493e6i	−0.0145676	+	0.00936203i	−0.547904	−	0.836541i	$-0.684574\pi$
$877$	−9.82623e6	+	6.31493e6i	−0.0145676	+	0.00936203i	0.533337	+	0.845903i	$0.320938\pi$
$878$	1.77848e8	+	1.23696e9i	0.262764	+	1.82756i
$879$	−4.19151e8	+	1.91420e8i	−0.617168	+	0.281851i
$880$	−1.18493e8	+	8.24137e8i	−0.173878	+	1.20935i
$881$	6.57064e7	+	2.23775e8i	0.0960903	+	0.327254i	0.993483	−	0.113979i	$-0.0363596\pi$
$881$	6.57064e7	+	2.23775e8i	0.0960903	+	0.327254i	−0.897393	+	0.441232i	$0.854541\pi$
$882$	−1.80514e8	−	1.16009e8i	−0.263090	−	0.169078i
$883$	−4.31884e7	+	9.45693e7i	−0.0627313	+	0.137362i	−0.938401	−	0.345548i	$-0.887693\pi$
$883$	−4.31884e7	+	9.45693e7i	−0.0627313	+	0.137362i	0.875670	+	0.482910i	$0.160420\pi$
$884$	8.55539e6	−	2.91370e7i	0.0123846	−	0.0421782i
$885$	2.28269e8	−	1.97796e8i	0.329319	−	0.285356i
$886$	6.61477e8	+	7.63385e8i	0.951072	+	1.09760i
$887$	−1.94636e8	−	5.71502e7i	−0.278902	−	0.0818930i	0.139290	−	0.990252i	$-0.455518\pi$
$887$	−1.94636e8	−	5.71502e7i	−0.278902	−	0.0818930i	−0.418192	+	0.908359i	$0.637336\pi$
$888$	4.25360e8	+	1.94255e8i	0.607460	+	0.277417i
$889$	−1.31326e8	+	2.04348e8i	−0.186916	+	0.290847i
$890$	−2.70070e8	+	7.92997e7i	−0.383095	+	0.112487i
$891$	−1.13133e8	−	1.62661e7i	−0.159940	−	0.0229959i
$892$	1.43372e8	+	3.13941e8i	0.202009	+	0.442338i
$893$	6.50510e8	−	9.35293e7i	0.913482	−	0.131339i
$894$	3.05107e6	+	4.74756e6i	0.00427012	+	0.00664443i
$895$	−5.07972e8	−	4.40160e8i	−0.708550	−	0.613962i
$896$		−	3.76153e8i		−	0.522926i
$897$	−4.48735e8	−	2.77688e8i	−0.621745	−	0.384751i
$898$	−1.06530e9			−1.47110
$899$	8.21071e6	−	9.47567e6i	0.0113006	−	0.0130416i
$900$	3.81342e7	−	2.45074e7i	0.0523103	−	0.0336178i
$901$	1.34324e7	+	9.34244e7i	0.0183645	+	0.127728i
$902$	−2.04884e8	+	9.35672e7i	−0.279182	+	0.127498i
$903$	−8.74680e6	+	6.08353e7i	−0.0118792	+	0.0826214i
$904$	7.11533e7	+	2.42326e8i	0.0963141	+	0.328016i
$905$	−2.13254e8	−	1.37050e8i	−0.287707	−	0.184898i
$906$	3.48535e8	−	7.63186e8i	0.468665	−	1.02623i
$907$	2.38860e8	−	8.13481e8i	0.320126	−	1.09025i	−0.629536	−	0.776971i	$-0.716755\pi$
$907$	2.38860e8	−	8.13481e8i	0.320126	−	1.09025i	0.949662	−	0.313277i	$-0.101427\pi$
$908$	6.20531e7	−	5.37693e7i	0.0828908	−	0.0718252i
$909$	−2.32145e8	−	2.67909e8i	−0.309078	−	0.356695i
$910$	3.19740e8	+	9.38840e7i	0.424299	+	0.124585i
$911$	−4.28936e8	−	1.95888e8i	−0.567332	−	0.259092i	0.111033	−	0.993817i	$-0.464584\pi$
$911$	−4.28936e8	−	1.95888e8i	−0.567332	−	0.259092i	−0.678365	+	0.734725i	$0.737311\pi$
$912$	−2.24516e8	+	3.49354e8i	−0.295980	+	0.460554i
$913$	−4.04835e8	+	1.18870e8i	−0.531944	+	0.156193i
$914$	−1.57323e9	−	2.26196e8i	−2.06041	−	0.296242i
$915$	−1.25225e7	−	2.74205e7i	−0.0163467	−	0.0357942i
$916$	−3.93942e8	+	5.66403e7i	−0.512561	+	0.0736951i
$917$	3.52863e8	+	5.49066e8i	0.457613	+	0.712060i
$918$	1.29393e7	+	1.12120e7i	0.0167257	+	0.0144929i
$919$			1.22587e9i			1.57942i	0.613480	+	0.789710i	$0.289769\pi$
$919$			1.22587e9i			1.57942i	−0.613480	+	0.789710i	$0.710231\pi$
$920$	−2.23096e8	−	3.34464e8i	−0.286502	−	0.429522i
$921$	−5.55706e8			−0.711322
$922$	5.93301e7	−	6.84705e7i	0.0756976	−	0.0873597i
$923$	−1.33356e9	+	8.57028e8i	−1.69593	+	1.08991i
$924$	−1.45192e7	−	1.00984e8i	−0.0184047	−	0.128007i
$925$	5.86865e8	−	2.68012e8i	0.741503	−	0.338633i
$926$	−1.32731e8	+	9.23163e8i	−0.167163	+	1.16264i
$927$	−9.08676e7	−	3.09467e8i	−0.114070	−	0.388485i
$928$	−4.33846e8	−	2.78816e8i	−0.542865	−	0.348878i
$929$	4.08283e8	−	8.94015e8i	0.509230	−	1.11506i	−0.464128	−	0.885768i	$-0.653632\pi$
$929$	4.08283e8	−	8.94015e8i	0.509230	−	1.11506i	0.973358	−	0.229291i	$-0.0736406\pi$
$930$	1.87113e6	−	6.37248e6i	0.00232624	−	0.00792245i
$931$	3.80219e8	−	3.29461e8i	0.471177	−	0.408278i
$932$	7.23557e6	+	8.35029e6i	0.00893768	+	0.0103146i
$933$	7.54441e8	+	2.21524e8i	0.928925	+	0.272757i
$934$	1.22069e8	+	5.57468e7i	0.149818	+	0.0684195i
$935$	−4.35130e7	+	6.77075e7i	−0.0532334	+	0.0828327i
$936$	2.50604e8	−	7.35840e7i	0.305605	−	0.0897338i
$937$	9.38054e8	+	1.34872e8i	1.14027	+	0.163947i	0.686472	−	0.727156i	$-0.259158\pi$
$937$	9.38054e8	+	1.34872e8i	1.14027	+	0.163947i	0.453801	+	0.891103i	$0.350068\pi$
$938$	2.97907e8	+	6.52325e8i	0.360971	+	0.790416i
$939$	7.22933e8	−	1.03942e8i	0.873175	−	0.125544i
$940$	1.28811e8	+	2.00434e8i	0.155085	+	0.241317i
$941$	−6.61548e6	−	5.73234e6i	−0.00793949	−	0.00687960i	0.650882	−	0.759179i	$-0.274399\pi$
$941$	−6.61548e6	−	5.73234e6i	−0.00793949	−	0.00687960i	−0.658821	+	0.752299i	$0.728945\pi$
$942$		−	5.66573e8i		−	0.677803i
$943$	6.08844e7	−	1.39569e8i	0.0726058	−	0.166438i
$944$	1.13915e9			1.35414
$945$	−3.19536e7	+	3.68764e7i	−0.0378638	+	0.0436971i
$946$	3.96392e8	−	2.54745e8i	0.468221	−	0.300907i
$947$	9.78683e7	+	6.80689e8i	0.115237	+	0.801491i	0.962687	+	0.270616i	$0.0872275\pi$
$947$	9.78683e7	+	6.80689e8i	0.115237	+	0.801491i	−0.847450	+	0.530875i	$0.821863\pi$
$948$	2.09641e8	−	9.57400e7i	0.246066	−	0.112375i
$949$	−6.69744e7	+	4.65817e8i	−0.0783629	+	0.545026i
$950$	1.15296e8	+	3.92661e8i	0.134475	+	0.457980i
$951$	−4.04061e7	−	2.59675e7i	−0.0469792	−	0.0301917i
$952$	1.17479e7	−	2.57243e7i	0.0136160	−	0.0298149i
$953$	8.38835e7	−	2.85681e8i	0.0969165	−	0.330067i	−0.896735	−	0.442567i	$-0.854068\pi$
$953$	8.38835e7	−	2.85681e8i	0.0969165	−	0.330067i	0.993652	+	0.112500i	$0.0358859\pi$
$954$	3.31543e8	−	2.87284e8i	0.381852	−	0.330877i
$955$	9.28883e7	+	1.07199e8i	0.106648	+	0.123078i
$956$	4.75119e8	+	1.39508e8i	0.543787	+	0.159670i
$957$	6.42392e8	+	2.93370e8i	0.732933	+	0.334719i
$958$	5.90051e8	−	9.18137e8i	0.671109	−	1.04427i
$959$	−1.06227e8	+	3.11911e7i	−0.120442	+	0.0353650i
$960$	1.54381e8	+	2.21967e7i	0.174494	+	0.0250885i
$961$	−3.68563e8	−	8.07041e8i	−0.415281	−	0.909338i
$962$	−1.98840e9	+	2.85888e8i	−2.23346	+	0.321123i
$963$	1.73928e8	+	2.70636e8i	0.194755	+	0.303045i
$964$	−8.99821e7	−	7.79699e7i	−0.100444	−	0.0870354i
$965$		−	2.86704e8i		−	0.319045i
$966$	2.03642e8	+	1.70465e8i	0.225911	+	0.189106i
$967$	1.40527e8			0.155410			0.0777050	−	0.996976i	$-0.475241\pi$
$967$	1.40527e8			0.155410			0.0777050	+	0.996976i	$0.475241\pi$
$968$	4.99653e8	−	5.76631e8i	0.550862	−	0.635728i
$969$	−3.37701e7	+	2.17027e7i	−0.0371160	+	0.0238530i
$970$	1.05961e7	+	7.36974e7i	0.0116099	+	0.0807490i
$971$	−7.13956e8	+	3.26053e8i	−0.779855	+	0.356148i	−0.765240	−	0.643745i	$-0.777380\pi$
$971$	−7.13956e8	+	3.26053e8i	−0.779855	+	0.356148i	−0.0146154	+	0.999893i	$0.504652\pi$
$972$	2.94122e6	−	2.04566e7i	0.00320279	−	0.0222759i
$973$	−4.75796e7	−	1.62041e8i	−0.0516514	−	0.175908i
$974$	1.26325e9	+	8.11843e8i	1.36714	+	0.878608i
$975$	1.49696e8	−	3.27789e8i	0.161509	−	0.353655i
$976$	3.20302e7	−	1.09085e8i	0.0344516	−	0.117331i
$977$	−2.74895e8	+	2.38198e8i	−0.294770	+	0.255420i	−0.789672	−	0.613529i	$-0.789749\pi$
$977$	−2.74895e8	+	2.38198e8i	−0.294770	+	0.255420i	0.494902	+	0.868949i	$0.335204\pi$
$978$	−2.55324e8	−	2.94660e8i	−0.272945	−	0.314995i
$979$	6.57289e8	+	1.92997e8i	0.700500	+	0.205685i
$980$	1.65909e8	+	7.57680e7i	0.176275	+	0.0805021i
$981$	−1.41871e8	+	2.20755e8i	−0.150275	+	0.233832i
$982$	−3.10519e7	+	9.11765e6i	−0.0327909	+	0.00962828i
$983$	−4.02912e8	−	5.79299e7i	−0.424179	−	0.0609877i	−0.0730800	−	0.997326i	$-0.523283\pi$
$983$	−4.02912e8	−	5.79299e7i	−0.424179	−	0.0609877i	−0.351099	+	0.936338i	$0.614192\pi$
$984$	3.13078e7	+	6.85545e7i	0.0328600	+	0.0719533i
$985$	−8.55821e7	+	1.23049e7i	−0.0895518	+	0.0128756i
$986$	−5.71930e7	−	8.89940e7i	−0.0596640	−	0.0928389i
$987$	2.20099e8	+	1.90717e8i	0.228911	+	0.198353i
$988$		−	3.30929e8i		−	0.343134i
$989$	−8.45200e7	+	3.07128e8i	−0.0873717	+	0.317490i
$990$	3.74084e8			0.385535
$991$	8.20929e8	−	9.47403e8i	0.843500	−	0.973450i	−0.156399	−	0.987694i	$-0.549989\pi$
$991$	8.20929e8	−	9.47403e8i	0.843500	−	0.973450i	0.999899	+	0.0142436i	$0.00453404\pi$
$992$	9.92996e6	−	6.38160e6i	0.0101721	−	0.00653724i
$993$	6.34938e6	+	4.41609e7i	0.00648461	+	0.0451014i
$994$	7.25676e8	−	3.31405e8i	0.738897	−	0.337443i
$995$	1.15024e8	−	8.00012e8i	0.116767	−	0.812133i
$996$	−2.14940e7	−	7.32018e7i	−0.0217540	−	0.0740873i
$997$	1.57265e9	+	1.01068e9i	1.58689	+	1.01983i	0.973107	+	0.230355i	$0.0739886\pi$
$997$	1.57265e9	+	1.01068e9i	1.58689	+	1.01983i	0.613781	+	0.789476i	$0.289648\pi$
$998$	3.25018e8	−	7.11690e8i	0.326976	−	0.715978i
$999$	8.28703e7	−	2.82230e8i	0.0831194	−	0.283079i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.f.a.7.19	✓	240
23.10	odd	22	inner	69.7.f.a.10.19	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.f.a.7.19	✓	240	1.1	even	1	trivial
69.7.f.a.10.19	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)

\(f(q)\)	\(=\)	\(q+(6.08888 - 7.02694i) q^{2} +(-13.1138 + 8.42776i) q^{3} +(-3.19530 - 22.2238i) q^{4} +(-77.8070 + 35.5333i) q^{5} +(-20.6273 + 143.466i) q^{6} +(-42.4272 - 144.494i) q^{7} +(324.984 + 208.854i) q^{8} +(100.946 - 221.041i) q^{9} +O(q^{10})\)	\(q+(6.08888 - 7.02694i) q^{2} +(-13.1138 + 8.42776i) q^{3} +(-3.19530 - 22.2238i) q^{4} +(-77.8070 + 35.5333i) q^{5} +(-20.6273 + 143.466i) q^{6} +(-42.4272 - 144.494i) q^{7} +(324.984 + 208.854i) q^{8} +(100.946 - 221.041i) q^{9} +(-224.067 + 763.103i) q^{10} +(1462.85 - 1267.56i) q^{11} +(229.200 + 264.510i) q^{12} +(2669.61 + 783.867i) q^{13} +(-1273.68 - 581.672i) q^{14} +(720.884 - 1121.72i) q^{15} +(4825.14 - 1416.79i) q^{16} +(481.163 + 69.1808i) q^{17} +(-938.592 - 2055.23i) q^{18} +(5243.53 - 753.906i) q^{19} +(1038.30 + 1615.63i) q^{20} +(1774.14 + 1537.30i) q^{21} -17997.4i q^{22} +(8123.32 + 9058.01i) q^{23} -6021.96 q^{24} +(-5440.88 + 6279.11i) q^{25} +(21763.1 - 13986.3i) q^{26} +(539.088 + 3749.44i) q^{27} +(-3075.64 + 1404.60i) q^{28} +(3330.89 - 23166.8i) q^{29} +(-3492.86 - 11895.6i) q^{30} +(450.660 + 289.621i) q^{31} +(9153.37 - 20043.1i) q^{32} +(-8500.83 + 28951.2i) q^{33} +(3415.87 - 2959.87i) q^{34} +(8435.48 + 9735.06i) q^{35} +(-5234.92 - 1537.11i) q^{36} +(-70634.7 - 32257.8i) q^{37} +(26629.6 - 41436.4i) q^{38} +(-41615.0 + 12219.3i) q^{39} +(-32707.3 - 4702.60i) q^{40} +(-5198.93 - 11384.1i) q^{41} +(21605.1 - 3106.34i) q^{42} +(14154.6 + 22025.0i) q^{43} +(-32844.4 - 28459.8i) q^{44} +20785.5i q^{45} +(113112. - 1928.99i) q^{46} +124060. q^{47} +(-51335.8 + 59244.6i) q^{48} +(79894.2 - 51344.9i) q^{49} +(10994.1 + 76465.4i) q^{50} +(-6892.94 + 3147.90i) q^{51} +(8890.32 - 61833.5i) q^{52} +(54702.2 + 186299. i) q^{53} +(29629.5 + 19041.7i) q^{54} +(-68779.1 + 150605. i) q^{55} +(16390.0 - 55819.3i) q^{56} +(-62409.1 + 54077.8i) q^{57} +(-142511. - 164466. i) q^{58} +(217347. + 63818.9i) q^{59} +(-27232.3 - 12436.6i) q^{60} +(12222.6 - 19018.7i) q^{61} +(4779.17 - 1403.29i) q^{62} +(-36221.9 - 5207.92i) q^{63} +(48591.8 + 106401. i) q^{64} +(-235567. + 33869.5i) q^{65} +(151678. + 236015. i) q^{66} +(-387062. - 335391. i) q^{67} -10914.3i q^{68} +(-182867. - 50323.9i) q^{69} +119770. q^{70} +(-373104. + 430585. i) q^{71} +(78971.1 - 50751.6i) q^{72} +(24071.5 + 167421. i) q^{73} +(-656760. + 299932. i) q^{74} +(18432.0 - 128198. i) q^{75} +(-33509.3 - 114122. i) q^{76} +(-245220. - 157593. i) q^{77} +(-167525. + 366828. i) q^{78} +(185517. - 631812. i) q^{79} +(-325087. + 281689. i) q^{80} +(-38668.9 - 44626.3i) q^{81} +(-111651. - 32783.7i) q^{82} +(-198281. - 90551.9i) q^{83} +(28495.8 - 44340.4i) q^{84} +(-39896.1 + 11714.6i) q^{85} +(240954. + 34643.9i) q^{86} +(151564. + 331878. i) q^{87} +(740138. - 106416. i) q^{88} +(191338. + 297728. i) q^{89} +(146058. + 126560. i) q^{90} -418999. i q^{91} +(175347. - 209474. i) q^{92} -8350.74 q^{93} +(755384. - 871759. i) q^{94} +(-381195. + 244979. i) q^{95} +(48882.3 + 339984. i) q^{96} +(85156.8 - 38889.8i) q^{97} +(125669. - 874045. i) q^{98} +(-132515. - 451304. i) 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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