LMFDB - Embedded newform 37.8.e.a.11.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,8,Mod(11,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("37.11");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	37.e (of order $6$, degree $2$, 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:	$11.5582459429$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.11
Character	$\chi$	$=$	37.11
Dual form			37.8.e.a.27.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.05422 - 1.18601i) q^{2} +(3.39795 - 5.88542i) q^{3} +(-61.1868 + 105.979i) q^{4} +(-176.269 - 101.769i) q^{5} -16.1199i q^{6} +(721.166 - 1249.10i) q^{7} +593.889i q^{8} +(1070.41 + 1854.00i) q^{9} +O(q^{10})$	\(q+(2.05422 - 1.18601i) q^{2} +(3.39795 - 5.88542i) q^{3} +(-61.1868 + 105.979i) q^{4} +(-176.269 - 101.769i) q^{5} -16.1199i q^{6} +(721.166 - 1249.10i) q^{7} +593.889i q^{8} +(1070.41 + 1854.00i) q^{9} -482.794 q^{10} +8107.21 q^{11} +(415.819 + 720.220i) q^{12} +(-3447.63 - 1990.49i) q^{13} -3421.23i q^{14} +(-1197.91 + 691.612i) q^{15} +(-7127.55 - 12345.3i) q^{16} +(18375.5 - 10609.1i) q^{17} +(4397.71 + 2539.02i) q^{18} +(36462.1 + 21051.4i) q^{19} +(21570.7 - 12453.8i) q^{20} +(-4900.97 - 8488.73i) q^{21} +(16654.0 - 9615.19i) q^{22} +5486.72i q^{23} +(3495.28 + 2018.00i) q^{24} +(-18348.6 - 31780.8i) q^{25} -9442.93 q^{26} +29411.4 q^{27} +(88251.7 + 152856. i) q^{28} -131958. i q^{29} +(-1640.51 + 2841.45i) q^{30} +81579.0i q^{31} +(-95116.4 - 54915.5i) q^{32} +(27547.9 - 47714.3i) q^{33} +(25164.9 - 43586.9i) q^{34} +(-254239. + 146785. i) q^{35} -261979. q^{36} +(31019.3 - 306545. i) q^{37} +99868.2 q^{38} +(-23429.8 + 13527.2i) q^{39} +(60439.5 - 104684. i) q^{40} +(-215571. + 373381. i) q^{41} +(-20135.4 - 11625.2i) q^{42} +720613. i q^{43} +(-496054. + 859190. i) q^{44} -435738. i q^{45} +(6507.28 + 11270.9i) q^{46} +267472. q^{47} -96876.2 q^{48} +(-628390. - 1.08840e6i) q^{49} +(-75384.3 - 43523.1i) q^{50} -144197. i q^{51} +(421899. - 243584. i) q^{52} +(94569.2 + 163799. i) q^{53} +(60417.5 - 34882.0i) q^{54} +(-1.42905e6 - 825063. i) q^{55} +(741824. + 428293. i) q^{56} +(247792. - 143063. i) q^{57} +(-156503. - 271072. i) q^{58} +(-1.06567e6 + 615265. i) q^{59} -169270. i q^{60} +(1.75917e6 + 1.01566e6i) q^{61} +(96753.1 + 167581. i) q^{62} +3.08777e6 q^{63} +1.56413e6 q^{64} +(405141. + 701725. i) q^{65} -130688. i q^{66} +(1.89933e6 - 3.28974e6i) q^{67} +2.59655e6i q^{68} +(32291.7 + 18643.6i) q^{69} +(-348175. + 603057. i) q^{70} +(1.68520e6 - 2.91885e6i) q^{71} +(-1.10107e6 + 635703. i) q^{72} -2.71154e6 q^{73} +(-299843. - 666500. i) q^{74} -249391. q^{75} +(-4.46199e6 + 2.57613e6i) q^{76} +(5.84664e6 - 1.01267e7i) q^{77} +(-32086.6 + 55575.6i) q^{78} +(6.51411e6 + 3.76092e6i) q^{79} +2.90146e6i q^{80} +(-2.24104e6 + 3.88160e6i) q^{81} +1.02267e6i q^{82} +(-4.14160e6 - 7.17347e6i) q^{83} +1.19950e6 q^{84} -4.31871e6 q^{85} +(854651. + 1.48030e6i) q^{86} +(-776630. - 448388. i) q^{87} +4.81478e6i q^{88} +(-6.98320e6 + 4.03175e6i) q^{89} +(-516787. - 895101. i) q^{90} +(-4.97264e6 + 2.87095e6i) q^{91} +(-581475. - 335715. i) q^{92} +(480126. + 277201. i) q^{93} +(549447. - 317223. i) q^{94} +(-4.28476e6 - 7.42142e6i) q^{95} +(-646401. + 373200. i) q^{96} -2.83859e6i q^{97} +(-2.58171e6 - 1.49055e6i) q^{98} +(8.67802e6 + 1.50308e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 18 q^{2} - 42 q^{3} + 1114 q^{4} - 672 q^{5} + 156 q^{7} - 9128 q^{9}+O(q^{10}) $ 40 * q + 18 * q^2 - 42 * q^3 + 1114 * q^4 - 672 * q^5 + 156 * q^7 - 9128 * q^9	\( 40 q + 18 q^{2} - 42 q^{3} + 1114 q^{4} - 672 q^{5} + 156 q^{7} - 9128 q^{9} - 5124 q^{10} + 12468 q^{11} + 6926 q^{12} + 10512 q^{13} + 36402 q^{15} - 31094 q^{16} - 22440 q^{17} - 153504 q^{18} + 49086 q^{19} + 28662 q^{20} + 7736 q^{21} + 132018 q^{22} + 2754 q^{24} + 72328 q^{25} - 680244 q^{26} + 42984 q^{27} + 105488 q^{28} + 382084 q^{30} + 523656 q^{32} + 9228 q^{33} + 276914 q^{34} - 904452 q^{35} - 204828 q^{36} + 1333776 q^{37} + 50208 q^{38} + 122040 q^{39} - 1205236 q^{40} - 871440 q^{41} + 1436094 q^{42} - 994326 q^{44} - 987942 q^{46} - 586932 q^{47} + 3984388 q^{48} - 1766072 q^{49} + 1818708 q^{50} - 2745228 q^{52} + 1661988 q^{53} + 1102554 q^{54} - 2733258 q^{55} - 5943924 q^{56} + 3920592 q^{57} + 5021672 q^{58} + 5296632 q^{59} - 4588524 q^{61} - 8143398 q^{62} - 2503648 q^{63} + 10662964 q^{64} - 1652736 q^{65} + 1940622 q^{67} - 10266552 q^{69} - 5038546 q^{70} + 6420528 q^{71} - 6576036 q^{72} - 3313032 q^{73} + 16192386 q^{74} - 5168536 q^{75} + 10328022 q^{76} - 8599404 q^{77} + 18210222 q^{78} - 15094374 q^{79} + 1733956 q^{81} - 191670 q^{83} + 1175224 q^{84} - 18053592 q^{85} + 18575940 q^{86} - 3762762 q^{87} - 14873004 q^{89} + 37293212 q^{90} - 76496700 q^{91} + 27846618 q^{92} + 26687652 q^{93} + 35421402 q^{94} + 14310774 q^{95} - 30894534 q^{96} - 13793868 q^{98} - 37141758 q^{99}+O(q^{100}) \) 40 * q + 18 * q^2 - 42 * q^3 + 1114 * q^4 - 672 * q^5 + 156 * q^7 - 9128 * q^9 - 5124 * q^10 + 12468 * q^11 + 6926 * q^12 + 10512 * q^13 + 36402 * q^15 - 31094 * q^16 - 22440 * q^17 - 153504 * q^18 + 49086 * q^19 + 28662 * q^20 + 7736 * q^21 + 132018 * q^22 + 2754 * q^24 + 72328 * q^25 - 680244 * q^26 + 42984 * q^27 + 105488 * q^28 + 382084 * q^30 + 523656 * q^32 + 9228 * q^33 + 276914 * q^34 - 904452 * q^35 - 204828 * q^36 + 1333776 * q^37 + 50208 * q^38 + 122040 * q^39 - 1205236 * q^40 - 871440 * q^41 + 1436094 * q^42 - 994326 * q^44 - 987942 * q^46 - 586932 * q^47 + 3984388 * q^48 - 1766072 * q^49 + 1818708 * q^50 - 2745228 * q^52 + 1661988 * q^53 + 1102554 * q^54 - 2733258 * q^55 - 5943924 * q^56 + 3920592 * q^57 + 5021672 * q^58 + 5296632 * q^59 - 4588524 * q^61 - 8143398 * q^62 - 2503648 * q^63 + 10662964 * q^64 - 1652736 * q^65 + 1940622 * q^67 - 10266552 * q^69 - 5038546 * q^70 + 6420528 * q^71 - 6576036 * q^72 - 3313032 * q^73 + 16192386 * q^74 - 5168536 * q^75 + 10328022 * q^76 - 8599404 * q^77 + 18210222 * q^78 - 15094374 * q^79 + 1733956 * q^81 - 191670 * q^83 + 1175224 * q^84 - 18053592 * q^85 + 18575940 * q^86 - 3762762 * q^87 - 14873004 * q^89 + 37293212 * q^90 - 76496700 * q^91 + 27846618 * q^92 + 26687652 * q^93 + 35421402 * q^94 + 14310774 * q^95 - 30894534 * q^96 - 13793868 * q^98 - 37141758 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	2.05422	−	1.18601i	0.181569	−	0.104829i	−0.406461	−	0.913668i	$-0.633237\pi$
$2$	2.05422	−	1.18601i	0.181569	−	0.104829i	0.588030	+	0.808839i	$0.299904\pi$
$3$	3.39795	−	5.88542i	0.0726595	−	0.125850i	−0.827407	−	0.561603i	$-0.810185\pi$
$3$	3.39795	−	5.88542i	0.0726595	−	0.125850i	0.900066	+	0.435753i	$0.143518\pi$
$4$	−61.1868	+	105.979i	−0.478022	+	0.827958i
$5$	−176.269	−	101.769i	−0.630640	−	0.364100i	0.150360	−	0.988631i	$-0.451957\pi$
$5$	−176.269	−	101.769i	−0.630640	−	0.364100i	−0.781000	+	0.624531i	$0.785290\pi$
$6$		−	16.1199i		−	0.0304673i
$7$	721.166	−	1249.10i	0.794680	−	1.37643i	−0.128362	−	0.991727i	$-0.540972\pi$
$7$	721.166	−	1249.10i	0.794680	−	1.37643i	0.923042	−	0.384699i	$-0.125695\pi$
$8$			593.889i			0.410100i
$9$	1070.41	+	1854.00i	0.489441	+	0.847737i
$10$	−482.794			−0.152673
$11$	8107.21			1.83652			0.918262	−	0.395973i	$-0.129592\pi$
$11$	8107.21			1.83652			0.918262	+	0.395973i	$0.129592\pi$
$12$	415.819	+	720.220i	0.0694656	+	0.120318i
$13$	−3447.63	−	1990.49i	−0.435231	−	0.251280i	0.266342	−	0.963879i	$-0.414185\pi$
$13$	−3447.63	−	1990.49i	−0.435231	−	0.251280i	−0.701572	+	0.712598i	$0.747518\pi$
$14$		−	3421.23i		−	0.333222i
$15$	−1197.91	+	691.612i	−0.0916439	+	0.0529106i
$16$	−7127.55	−	12345.3i	−0.435031	−	0.753496i
$17$	18375.5	−	10609.1i	0.907127	−	0.523730i	0.0276211	−	0.999618i	$-0.491207\pi$
$17$	18375.5	−	10609.1i	0.907127	−	0.523730i	0.879506	+	0.475889i	$0.157873\pi$
$18$	4397.71	+	2539.02i	0.177735	+	0.102615i
$19$	36462.1	+	21051.4i	1.21956	+	0.704114i	0.964824	−	0.262896i	$-0.0846776\pi$
$19$	36462.1	+	21051.4i	1.21956	+	0.704114i	0.254737	+	0.967010i	$0.418011\pi$
$20$	21570.7	−	12453.8i	0.602919	−	0.348095i
$21$	−4900.97	−	8488.73i	−0.115482	−	0.200021i
$22$	16654.0	−	9615.19i	0.333456	−	0.192521i
$23$			5486.72i			0.0940298i	0.998894	+	0.0470149i	$0.0149708\pi$
$23$			5486.72i			0.0940298i	−0.998894	+	0.0470149i	$0.985029\pi$
$24$	3495.28	+	2018.00i	0.0516111	+	0.0297977i
$25$	−18348.6	−	31780.8i	−0.234862	−	0.406794i
$26$	−9442.93			−0.105366
$27$	29411.4			0.287569
$28$	88251.7	+	152856.i	0.759749	+	1.31592i
$29$		−	131958.i		−	1.00472i	−0.864659	−	0.502359i	$-0.832466\pi$
$29$		−	131958.i		−	1.00472i	0.864659	−	0.502359i	$-0.167534\pi$
$30$	−1640.51	+	2841.45i	−0.0110931	+	0.0192139i
$31$			81579.0i			0.491827i	0.969292	+	0.245913i	$0.0790879\pi$
$31$			81579.0i			0.491827i	−0.969292	+	0.245913i	$0.920912\pi$
$32$	−95116.4	−	54915.5i	−0.513134	−	0.296258i
$33$	27547.9	−	47714.3i	0.133441	−	0.231126i
$34$	25164.9	−	43586.9i	0.109804	−	0.190186i
$35$	−254239.	+	146785.i	−1.00231	+	0.578686i
$36$	−261979.			−0.935854
$37$	31019.3	−	306545.i	0.100676	−	0.994919i
$37$	31019.3	−	306545.i	0.100676	−	0.994919i
$38$	99868.2			0.295246
$39$	−23429.8	+	13527.2i	−0.0632473	+	0.0365158i
$40$	60439.5	−	104684.i	0.149318	−	0.258625i
$41$	−215571.	+	373381.i	−0.488481	+	0.846074i	−0.999912	−	0.0132505i	$-0.995782\pi$
$41$	−215571.	+	373381.i	−0.488481	+	0.846074i	0.511431	+	0.859324i	$0.329115\pi$
$42$	−20135.4	−	11625.2i	−0.0419360	−	0.0242118i
$43$			720613.i			1.38217i	0.722772	+	0.691087i	$0.242868\pi$
$43$			720613.i			1.38217i	−0.722772	+	0.691087i	$0.757132\pi$
$44$	−496054.	+	859190.i	−0.877899	+	1.52057i
$45$		−	435738.i		−	0.712822i
$46$	6507.28	+	11270.9i	0.00985706	+	0.0170729i
$47$	267472.			0.375782			0.187891	−	0.982190i	$-0.439835\pi$
$47$	267472.			0.375782			0.187891	+	0.982190i	$0.439835\pi$
$48$	−96876.2			−0.126437
$49$	−628390.	−	1.08840e6i	−0.763033	−	1.32161i
$50$	−75384.3	−	43523.1i	−0.0852876	−	0.0492408i
$51$		−	144197.i		−	0.152216i
$52$	421899.	−	243584.i	0.416099	−	0.240235i
$53$	94569.2	+	163799.i	0.0872538	+	0.151128i	0.906349	−	0.422529i	$-0.138858\pi$
$53$	94569.2	+	163799.i	0.0872538	+	0.151128i	−0.819096	+	0.573657i	$0.805524\pi$
$54$	60417.5	−	34882.0i	0.0522137	−	0.0301456i
$55$	−1.42905e6	−	825063.i	−1.15819	−	0.668679i
$56$	741824.	+	428293.i	0.564473	+	0.325899i
$57$	247792.	−	143063.i	0.177225	−	0.102321i
$58$	−156503.	−	271072.i	−0.105324	−	0.182426i
$59$	−1.06567e6	+	615265.i	−0.675524	+	0.390014i	−0.798166	−	0.602437i	$-0.794196\pi$
$59$	−1.06567e6	+	615265.i	−0.675524	+	0.390014i	0.122642	+	0.992451i	$0.460863\pi$
$60$		−	169270.i		−	0.101170i
$61$	1.75917e6	+	1.01566e6i	0.992322	+	0.572917i	0.905967	−	0.423347i	$-0.139145\pi$
$61$	1.75917e6	+	1.01566e6i	0.992322	+	0.572917i	0.0863541	+	0.996265i	$0.472478\pi$
$62$	96753.1	+	167581.i	0.0515577	+	0.0893006i
$63$	3.08777e6			1.55580
$64$	1.56413e6			0.745837
$65$	405141.	+	701725.i	0.182982	+	0.316935i
$66$		−	130688.i		−	0.0559539i
$67$	1.89933e6	−	3.28974e6i	0.771505	−	1.33629i	−0.165233	−	0.986255i	$-0.552838\pi$
$67$	1.89933e6	−	3.28974e6i	0.771505	−	1.33629i	0.936738	−	0.350031i	$-0.113829\pi$
$68$			2.59655e6i			1.00142i
$69$	32291.7	+	18643.6i	0.0118336	+	0.00683216i
$70$	−348175.	+	603057.i	−0.121326	+	0.210143i
$71$	1.68520e6	−	2.91885e6i	0.558788	−	0.967850i	−0.438810	−	0.898580i	$-0.644600\pi$
$71$	1.68520e6	−	2.91885e6i	0.558788	−	0.967850i	0.997598	−	0.0692696i	$-0.0220669\pi$
$72$	−1.10107e6	+	635703.i	−0.347657	+	0.200720i
$73$	−2.71154e6			−0.815804			−0.407902	−	0.913026i	$-0.633739\pi$
$73$	−2.71154e6			−0.815804			−0.407902	+	0.913026i	$0.633739\pi$
$74$	−299843.	−	666500.i	−0.0860168	−	0.191200i
$75$	−249391.			−0.0682599
$76$	−4.46199e6	+	2.57613e6i	−1.16595	+	0.673164i
$77$	5.84664e6	−	1.01267e7i	1.45945	−	2.52784i
$78$	−32086.6	+	55575.6i	−0.00765584	+	0.0132603i
$79$	6.51411e6	+	3.76092e6i	1.48648	+	0.858222i	0.999881	−	0.0154021i	$-0.00490283\pi$
$79$	6.51411e6	+	3.76092e6i	1.48648	+	0.858222i	0.486602	+	0.873624i	$0.338236\pi$
$80$			2.90146e6i			0.633580i
$81$	−2.24104e6	+	3.88160e6i	−0.468547	+	0.811546i
$82$			1.02267e6i			0.204828i
$83$	−4.14160e6	−	7.17347e6i	−0.795051	−	1.37707i	−0.922807	−	0.385263i	$-0.874111\pi$
$83$	−4.14160e6	−	7.17347e6i	−0.795051	−	1.37707i	0.127755	−	0.991806i	$-0.459223\pi$
$84$	1.19950e6			0.220812
$85$	−4.31871e6			−0.762760
$86$	854651.	+	1.48030e6i	0.144892	+	0.250960i
$87$	−776630.	−	448388.i	−0.126444	−	0.0730022i
$88$			4.81478e6i			0.753159i
$89$	−6.98320e6	+	4.03175e6i	−1.05000	+	0.606218i	−0.922649	−	0.385640i	$-0.873981\pi$
$89$	−6.98320e6	+	4.03175e6i	−1.05000	+	0.606218i	−0.127351	+	0.991858i	$0.540647\pi$
$90$	−516787.	−	895101.i	−0.0747244	−	0.129427i
$91$	−4.97264e6	+	2.87095e6i	−0.691738	+	0.399375i
$92$	−581475.	−	335715.i	−0.0778528	−	0.0449483i
$93$	480126.	+	277201.i	0.0618964	+	0.0357359i
$94$	549447.	−	317223.i	0.0682304	−	0.0393928i
$95$	−4.28476e6	−	7.42142e6i	−0.512736	−	0.888085i
$96$	−646401.	+	373200.i	−0.0745681	+	0.0430519i
$97$		−	2.83859e6i		−	0.315792i	−0.987456	−	0.157896i	$-0.949529\pi$
$97$		−	2.83859e6i		−	0.315792i	0.987456	−	0.157896i	$-0.0504711\pi$
$98$	−2.58171e6	−	1.49055e6i	−0.277087	−	0.159976i
$99$	8.67802e6	+	1.50308e7i	0.898871	+	1.55689i
$100$	4.49077e6			0.449077
$101$	−4.51928e6			−0.436460			−0.218230	−	0.975897i	$-0.570028\pi$
$101$	−4.51928e6			−0.436460			−0.218230	+	0.975897i	$0.570028\pi$
$102$	−171018.	−	296212.i	−0.0159566	−	0.0276377i
$103$		−	6.50201e6i		−	0.586296i	−0.956067	−	0.293148i	$-0.905297\pi$
$103$		−	6.50201e6i		−	0.586296i	0.956067	−	0.293148i	$-0.0947029\pi$
$104$	1.18213e6	−	2.04751e6i	0.103050	−	0.178488i
$105$			1.99507e6i			0.168188i
$106$	388532.	+	224319.i	0.0316852	+	0.0182935i
$107$	−1.91573e6	+	3.31814e6i	−0.151179	+	0.261849i	−0.931661	−	0.363329i	$-0.881640\pi$
$107$	−1.91573e6	+	3.31814e6i	−0.151179	+	0.261849i	0.780482	+	0.625178i	$0.214974\pi$
$108$	−1.79959e6	+	3.11698e6i	−0.137464	+	0.238095i
$109$	1.63704e6	−	945146.i	0.121078	−	0.0699046i	−0.438238	−	0.898859i	$-0.644397\pi$
$109$	1.63704e6	−	945146.i	0.121078	−	0.0699046i	0.559316	+	0.828955i	$0.311064\pi$
$110$	−3.91411e6			−0.280388
$111$	−1.69874e6	−	1.22418e6i	−0.117895	−	0.0849604i
$112$	−2.05606e7			−1.38284
$113$	−8.95802e6	+	5.17191e6i	−0.584033	+	0.337192i	−0.762735	−	0.646712i	$-0.776144\pi$
$113$	−8.95802e6	+	5.17191e6i	−0.584033	+	0.337192i	0.178702	+	0.983903i	$0.442810\pi$
$114$	339347.	−	587766.i	0.0214525	−	0.0371567i
$115$	558379.	−	967140.i	0.0342363	−	0.0592989i
$116$	1.39848e7	+	8.07411e6i	0.831864	+	0.480277i
$117$		−	8.52255e6i		−	0.491948i
$118$	−1.45941e6	+	2.52778e6i	−0.0817696	+	0.141629i
$119$		−	3.06037e7i		−	1.66479i
$120$	−410740.	−	711423.i	−0.0216987	−	0.0375832i
$121$	4.62396e7			2.37282
$122$	4.81829e6			0.240233
$123$	1.46500e6	+	2.53745e6i	0.0709855	+	0.122951i
$124$	−8.64563e6	−	4.99156e6i	−0.407212	−	0.235104i
$125$			2.33707e7i			1.07025i
$126$	6.34296e6	−	3.66211e6i	0.282485	−	0.163093i
$127$	5.54893e6	+	9.61103e6i	0.240379	+	0.416348i	0.960822	−	0.277165i	$-0.0893950\pi$
$127$	5.54893e6	+	9.61103e6i	0.240379	+	0.416348i	−0.720443	+	0.693514i	$0.756062\pi$
$128$	1.53880e7	−	8.88425e6i	0.648555	−	0.374443i
$129$	4.24111e6	+	2.44861e6i	0.173946	+	0.100428i
$130$	1.66450e6	+	960998.i	0.0664479	+	0.0383637i
$131$	−3.69353e7	+	2.13246e7i	−1.43546	+	0.828765i	−0.997530	−	0.0702423i	$-0.977623\pi$
$131$	−3.69353e7	+	2.13246e7i	−1.43546	+	0.828765i	−0.437933	+	0.899007i	$0.644289\pi$
$132$	3.37113e6	+	5.83897e6i	0.127575	+	0.220967i
$133$	5.25904e7	−	3.03631e7i	1.93832	−	1.11909i
$134$		−	9.01046e6i		−	0.323504i
$135$	−5.18432e6	−	2.99317e6i	−0.181353	−	0.104704i
$136$	6.30062e6	+	1.09130e7i	0.214782	+	0.372013i
$137$	−1.19480e6			−0.0396985			−0.0198493	−	0.999803i	$-0.506319\pi$
$137$	−1.19480e6			−0.0396985			−0.0198493	+	0.999803i	$0.506319\pi$
$138$	88445.6			0.00286483
$139$	−1.70968e6	−	2.96126e6i	−0.0539962	−	0.0935242i	0.837764	−	0.546033i	$-0.183863\pi$
$139$	−1.70968e6	−	2.96126e6i	−0.0539962	−	0.0935242i	−0.891760	+	0.452508i	$0.850529\pi$
$140$		−	3.59252e7i		−	1.10650i
$141$	908856.	−	1.57418e6i	0.0273041	−	0.0472921i
$142$		−	7.99462e6i		−	0.234309i
$143$	−2.79507e7	−	1.61373e7i	−0.799312	−	0.461483i
$144$	1.52588e7	−	2.64290e7i	0.425845	−	0.737584i
$145$	−1.34293e7	+	2.32602e7i	−0.365818	+	0.633615i
$146$	−5.57010e6	+	3.21590e6i	−0.148125	+	0.0855199i
$147$	−8.54095e6			−0.221766
$148$	3.05892e7	+	2.20439e7i	0.775626	+	0.558948i
$149$	−4.74254e7			−1.17452			−0.587258	−	0.809400i	$-0.699793\pi$
$149$	−4.74254e7			−1.17452			−0.587258	+	0.809400i	$0.699793\pi$
$150$	−512304.	+	295779.i	−0.0123939	+	0.00715562i
$151$	−1.74572e7	+	3.02367e7i	−0.412624	+	0.714686i	−0.995176	−	0.0981076i	$-0.968721\pi$
$151$	−1.74572e7	+	3.02367e7i	−0.412624	+	0.714686i	0.582552	+	0.812794i	$0.302054\pi$
$152$	−1.25022e7	+	2.16544e7i	−0.288757	+	0.500143i
$153$	3.93386e7	+	2.27121e7i	0.887970	+	0.512670i
$154$		−	2.77366e7i		−	0.611971i
$155$	8.30221e6	−	1.43799e7i	0.179074	−	0.310166i
$156$		−	3.31074e6i		−	0.0698214i
$157$	1.89268e7	+	3.27821e7i	0.390326	+	0.676065i	0.992492	−	0.122306i	$-0.0390288\pi$
$157$	1.89268e7	+	3.27821e7i	0.390326	+	0.676065i	−0.602166	+	0.798371i	$0.705695\pi$
$158$	1.78419e7			0.359866
$159$	1.28537e6			0.0253593
$160$	1.11774e7	+	1.93598e7i	0.215735	+	0.373664i
$161$	6.85345e6	+	3.95684e6i	0.129425	+	0.0747236i
$162$			1.06316e7i			0.196469i
$163$	−2.94985e7	+	1.70310e7i	−0.533510	+	0.308022i	−0.742445	−	0.669907i	$-0.766334\pi$
$163$	−2.94985e7	+	1.70310e7i	−0.533510	+	0.308022i	0.208934	+	0.977930i	$0.433001\pi$
$164$	−2.63802e7	−	4.56919e7i	−0.467009	−	0.808883i
$165$	−9.71168e6	+	5.60704e6i	−0.168306	+	0.0971717i
$166$	−1.70155e7	−	9.82392e6i	−0.288714	−	0.166689i
$167$	4.87449e7	+	2.81429e7i	0.809882	+	0.467586i	0.846915	−	0.531729i	$-0.178457\pi$
$167$	4.87449e7	+	2.81429e7i	0.809882	+	0.467586i	−0.0370330	+	0.999314i	$0.511791\pi$
$168$	5.04136e6	−	2.91063e6i	0.0820286	−	0.0473592i
$169$	−2.34501e7	−	4.06168e7i	−0.373716	−	0.647296i
$170$	−8.87159e6	+	5.12201e6i	−0.138494	+	0.0799594i
$171$			9.01343e7i			1.37849i
$172$	−7.63696e7	−	4.40920e7i	−1.14438	−	0.660709i
$173$	−4.95119e7	−	8.57571e7i	−0.727023	−	1.25924i	−0.958136	−	0.286314i	$-0.907570\pi$
$173$	−4.95119e7	−	8.57571e7i	−0.727023	−	1.25924i	0.231113	−	0.972927i	$-0.425763\pi$
$174$	−2.12716e6			−0.0306110
$175$	−5.29296e7			−0.746562
$176$	−5.77845e7	−	1.00086e8i	−0.798946	−	1.38381i
$177$			8.36255e6i			0.113353i
$178$	−9.56336e6	+	1.65642e7i	−0.127098	+	0.220141i
$179$			8.51133e7i			1.10921i	0.832115	+	0.554603i	$0.187130\pi$
$179$			8.51133e7i			1.10921i	−0.832115	+	0.554603i	$0.812870\pi$
$180$	4.61789e7	+	2.66614e7i	0.590187	+	0.340744i
$181$	−7.38388e7	+	1.27893e8i	−0.925571	+	1.60314i	−0.134931	+	0.990855i	$0.543081\pi$
$181$	−7.38388e7	+	1.27893e8i	−0.925571	+	1.60314i	−0.790640	+	0.612281i	$0.790252\pi$
$182$	−6.80993e6	+	1.17951e7i	−0.0837322	+	0.145028i
$183$	1.19551e7	−	6.90229e6i	0.144203	−	0.0832557i
$184$	−3.25850e6			−0.0385617
$185$	−3.66645e7	+	5.08776e7i	−0.425740	+	0.590779i
$186$	1.31505e6			0.0149846
$187$	1.48974e8	−	8.60101e7i	1.66596	−	0.961843i
$188$	−1.63658e7	+	2.83463e7i	−0.179632	+	0.311132i
$189$	2.12105e7	−	3.67377e7i	0.228525	−	0.395818i
$190$	−1.76037e7	−	1.01635e7i	−0.186194	−	0.107499i
$191$		−	1.21050e8i		−	1.25704i	−0.777793	−	0.628521i	$-0.783661\pi$
$191$		−	1.21050e8i		−	1.25704i	0.777793	−	0.628521i	$-0.216339\pi$
$192$	5.31484e6	−	9.20558e6i	0.0541921	−	0.0938635i
$193$			1.15128e8i			1.15274i	0.817189	+	0.576370i	$0.195531\pi$
$193$			1.15128e8i			1.15274i	−0.817189	+	0.576370i	$0.804469\pi$
$194$	−3.36658e6	−	5.83109e6i	−0.0331042	−	0.0573381i
$195$	5.50659e6			0.0531816
$196$	1.53797e8			1.45899
$197$	−5.31513e7	−	9.20607e7i	−0.495315	−	0.857911i	0.504670	−	0.863312i	$-0.331614\pi$
$197$	−5.31513e7	−	9.20607e7i	−0.495315	−	0.857911i	−0.999985	+	0.00540107i	$0.998281\pi$
$198$	3.56531e7	+	2.05843e7i	0.326415	+	0.188456i
$199$			1.51824e7i			0.136570i	0.997666	+	0.0682849i	$0.0217527\pi$
$199$			1.51824e7i			0.136570i	−0.997666	+	0.0682849i	$0.978247\pi$
$200$	1.88742e7	−	1.08970e7i	0.166826	−	0.0963171i
$201$	−1.29077e7	−	2.23567e7i	−0.112114	−	0.194188i
$202$	−9.28360e6	+	5.35989e6i	−0.0792477	+	0.0457537i
$203$	−1.64829e8	−	9.51639e7i	−1.38292	−	0.798429i
$204$	1.52818e7	+	8.82293e6i	0.126028	+	0.0727624i
$205$	7.59972e7	−	4.38770e7i	0.616111	−	0.355712i
$206$	−7.71141e6	−	1.33566e7i	−0.0614609	−	0.106453i
$207$	−1.01724e7	+	5.87303e6i	−0.0797126	+	0.0460221i
$208$			5.67494e7i			0.437260i
$209$	2.95605e8	+	1.70668e8i	2.23975	+	1.29312i
$210$	2.36616e6	+	4.09831e6i	0.0176310	+	0.0305378i
$211$	8.19130e7			0.600294			0.300147	−	0.953893i	$-0.402964\pi$
$211$	8.19130e7			0.600294			0.300147	+	0.953893i	$0.402964\pi$
$212$	−2.31455e7			−0.166837
$213$	−1.14524e7	−	1.98362e7i	−0.0812025	−	0.140647i
$214$			9.08825e6i			0.0633916i
$215$	7.33361e7	−	1.27022e8i	0.503249	−	0.871654i
$216$			1.74671e7i			0.117932i
$217$	1.01900e8	+	5.88320e7i	0.676964	+	0.390845i
$218$	2.24189e6	−	3.88308e6i	0.0146561	−	0.0253851i
$219$	−9.21366e6	+	1.59585e7i	−0.0592759	+	0.102669i
$220$	1.74878e8	−	1.00966e8i	1.10728	−	0.639286i
$221$	−8.44693e7			−0.526412
$222$	−4.94148e6	−	500029.i	−0.0303125	−	0.00306732i
$223$	4.03286e7			0.243526			0.121763	−	0.992559i	$-0.461145\pi$
$223$	4.03286e7			0.243526			0.121763	+	0.992559i	$0.461145\pi$
$224$	−1.37190e8	+	7.92064e7i	−0.815555	+	0.470861i
$225$	3.92810e7	−	6.80367e7i	0.229903	−	0.398203i
$226$	−1.22678e7	+	2.12485e7i	−0.0706949	+	0.122447i
$227$	−2.75996e8	−	1.59347e8i	−1.56608	−	0.904175i	−0.996620	−	0.0821531i	$-0.973820\pi$
$227$	−2.75996e8	−	1.59347e8i	−1.56608	−	0.904175i	−0.569457	−	0.822021i	$-0.692846\pi$
$228$			3.50143e7i			0.195647i
$229$	−7.85925e7	+	1.36126e8i	−0.432471	+	0.749062i	−0.997085	−	0.0762932i	$-0.975692\pi$
$229$	−7.85925e7	+	1.36126e8i	−0.432471	+	0.749062i	0.564615	+	0.825355i	$0.309025\pi$
$230$		−	2.64896e6i		−	0.0143558i
$231$	−3.97332e7	−	6.88199e7i	−0.212086	−	0.367343i
$232$	7.83686e7			0.412035
$233$	1.27865e8			0.662227			0.331114	−	0.943591i	$-0.392576\pi$
$233$	1.27865e8			0.662227			0.331114	+	0.943591i	$0.392576\pi$
$234$	−1.01078e7	−	1.75072e7i	−0.0515704	−	0.0893226i
$235$	−4.71471e7	−	2.72204e7i	−0.236983	−	0.136822i
$236$		−	1.50584e8i		−	0.745741i
$237$	4.42692e7	−	2.55588e7i	0.216014	−	0.124716i
$238$	−3.62961e7	−	6.28668e7i	−0.174518	−	0.302275i
$239$	1.08505e8	−	6.26454e7i	0.514111	−	0.296822i	−0.220411	−	0.975407i	$-0.570740\pi$
$239$	1.08505e8	−	6.26454e7i	0.514111	−	0.296822i	0.734522	+	0.678585i	$0.237406\pi$
$240$	1.70763e7	+	9.85900e6i	0.0797359	+	0.0460356i
$241$	8.51658e7	+	4.91705e7i	0.391927	+	0.226279i	0.682995	−	0.730423i	$-0.260677\pi$
$241$	8.51658e7	+	4.91705e7i	0.391927	+	0.226279i	−0.291067	+	0.956703i	$0.594010\pi$
$242$	9.49864e7	−	5.48404e7i	0.430832	−	0.248741i
$243$	4.73912e7	+	8.20840e7i	0.211873	+	0.366975i
$244$	−2.15275e8	+	1.24289e8i	−0.948703	+	0.547734i
$245$			2.55803e8i			1.11128i
$246$	6.01887e6	+	3.47500e6i	0.0257776	+	0.0148827i
$247$	−8.38052e7	−	1.45155e8i	−0.353860	−	0.612904i
$248$	−4.84488e7			−0.201698
$249$	−5.62918e7			−0.231072
$250$	2.77178e7	+	4.80086e7i	0.112194	+	0.194325i
$251$			3.34855e7i			0.133659i	0.997764	+	0.0668296i	$0.0212884\pi$
$251$			3.34855e7i			0.133659i	−0.997764	+	0.0668296i	$0.978712\pi$
$252$	−1.88931e8	+	3.27237e8i	−0.743705	+	1.28813i
$253$			4.44820e7i			0.172688i
$254$	2.27975e7	+	1.31621e7i	0.0872908	+	0.0503973i
$255$	−1.46748e7	+	2.54174e7i	−0.0554218	+	0.0959933i
$256$	−7.90310e7	+	1.36886e8i	−0.294413	+	0.509939i
$257$	1.18797e7	−	6.85876e6i	0.0436556	−	0.0252046i	−0.478013	−	0.878353i	$-0.658643\pi$
$257$	1.18797e7	−	6.85876e6i	0.0436556	−	0.0252046i	0.521669	+	0.853148i	$0.325310\pi$
$258$	1.16162e7			0.0421111
$259$	−3.60534e8	−	2.59816e8i	−1.28943	−	0.929216i
$260$	−9.91571e7			−0.349878
$261$	2.44651e8	−	1.41249e8i	0.851736	−	0.491750i
$262$	−5.05822e7	+	8.76109e7i	−0.173757	+	0.300956i
$263$	−7.03066e7	+	1.21775e8i	−0.238315	+	0.412774i	−0.960231	−	0.279207i	$-0.909928\pi$
$263$	−7.03066e7	+	1.21775e8i	−0.238315	+	0.412774i	0.721916	+	0.691981i	$0.243262\pi$
$264$	2.83370e7	+	1.63604e7i	0.0947850	+	0.0547242i
$265$		−	3.84969e7i		−	0.127076i
$266$	7.20216e7	−	1.24745e8i	0.234626	−	0.406385i
$267$			5.47987e7i			0.176190i
$268$	2.32428e8	+	4.02577e8i	0.737592	+	1.27755i
$269$	−4.58204e8			−1.43525			−0.717623	−	0.696432i	$-0.754770\pi$
$269$	−4.58204e8			−1.43525			−0.717623	+	0.696432i	$0.754770\pi$
$270$	−1.41997e7			−0.0439040
$271$	−2.32765e8	−	4.03161e8i	−0.710436	−	1.23051i	−0.964694	−	0.263375i	$-0.915164\pi$
$271$	−2.32765e8	−	4.03161e8i	−0.710436	−	1.23051i	0.254258	−	0.967136i	$-0.418169\pi$
$272$	−2.61945e8	−	1.51234e8i	−0.789257	−	0.455678i
$273$			3.90214e7i			0.116074i
$274$	−2.45439e6	+	1.41704e6i	−0.00720803	+	0.00416156i
$275$	−1.48756e8	−	2.57653e8i	−0.431331	−	0.747086i
$276$	−3.95165e6	+	2.28148e6i	−0.0113135	+	0.00653184i
$277$	4.16103e7	+	2.40237e7i	0.117631	+	0.0679143i	0.557661	−	0.830069i	$-0.311699\pi$
$277$	4.16103e7	+	2.40237e7i	0.117631	+	0.0679143i	−0.440030	+	0.897983i	$0.645032\pi$
$278$	−7.02413e6	−	4.05538e6i	−0.0196081	−	0.0113207i
$279$	−1.51247e8	+	8.73228e7i	−0.416940	+	0.240720i
$280$	−8.71738e7	−	1.50990e8i	−0.237319	−	0.411049i
$281$	1.49172e8	−	8.61244e7i	0.401065	−	0.231555i	−0.285879	−	0.958266i	$-0.592285\pi$
$281$	1.49172e8	−	8.61244e7i	0.401065	−	0.231555i	0.686943	+	0.726711i	$0.258952\pi$
$282$		−	4.31163e6i		−	0.0114491i
$283$	8.35922e7	+	4.82620e7i	0.219237	+	0.126576i	0.605597	−	0.795772i	$-0.292934\pi$
$283$	8.35922e7	+	4.82620e7i	0.219237	+	0.126576i	−0.386360	+	0.922348i	$0.626268\pi$
$284$	2.06224e8	+	3.57190e8i	0.534226	+	0.925306i
$285$	−5.82375e7			−0.149021
$286$	−7.65558e7			−0.193507
$287$	3.10926e8	+	5.38539e8i	0.776372	+	1.34472i
$288$		−	2.35128e8i		−	0.580003i
$289$	1.99366e7	−	3.45312e7i	0.0485858	−	0.0841530i
$290$			6.37087e7i			0.153393i
$291$	−1.67063e7	−	9.64538e6i	−0.0397424	−	0.0229453i
$292$	1.65910e8	−	2.87365e8i	0.389972	−	0.675451i
$293$	1.72976e8	−	2.99602e8i	0.401743	−	0.695839i	−0.592194	−	0.805796i	$-0.701738\pi$
$293$	1.72976e8	−	2.99602e8i	0.401743	−	0.695839i	0.993936	+	0.109957i	$0.0350713\pi$
$294$	−1.75450e7	+	1.01296e7i	−0.0402659	+	0.0232475i
$295$	2.50460e8			0.568016
$296$	1.82053e8	+	1.84220e7i	0.408017	+	0.0412872i
$297$	2.38444e8			0.528128
$298$	−9.74222e7	+	5.62468e7i	−0.213256	+	0.123123i
$299$	1.09213e7	−	1.89162e7i	0.0236279	−	0.0409247i
$300$	1.52594e7	−	2.64301e7i	0.0326297	−	0.0565163i
$301$	9.00116e8	+	5.19682e8i	1.90246	+	1.09839i
$302$			8.28172e7i			0.173020i
$303$	−1.53563e7	+	2.65979e7i	−0.0317130	+	0.0549285i
$304$		−	6.00180e8i		−	1.22525i
$305$	−2.06724e8	−	3.58057e8i	−0.417198	−	0.722609i
$306$	1.07747e8			0.214971
$307$	−6.16594e8			−1.21623			−0.608114	−	0.793850i	$-0.708074\pi$
$307$	−6.16594e8			−1.21623			−0.608114	+	0.793850i	$0.708074\pi$
$308$	7.15475e8	+	1.23924e9i	1.39530	+	2.41673i
$309$	−3.82670e7	−	2.20935e7i	−0.0737853	−	0.0426000i
$310$		−	3.93859e7i		−	0.0750887i
$311$	2.02904e8	−	1.17147e8i	0.382498	−	0.220835i	−0.296407	−	0.955062i	$-0.595788\pi$
$311$	2.02904e8	−	1.17147e8i	0.382498	−	0.220835i	0.678904	+	0.734227i	$0.262455\pi$
$312$	−8.03364e6	−	1.39147e7i	−0.0149751	−	0.0259377i
$313$	1.51828e8	−	8.76578e7i	0.279863	−	0.161579i	−0.353498	−	0.935435i	$-0.615008\pi$
$313$	1.51828e8	−	8.76578e7i	0.279863	−	0.161579i	0.633362	+	0.773856i	$0.281675\pi$
$314$	7.77596e7	+	4.48945e7i	0.141742	+	0.0818351i
$315$	−5.44278e8	−	3.14239e8i	−0.981147	−	0.566466i
$316$	−7.97155e8	+	4.60237e8i	−1.42114	+	0.820497i
$317$	4.37166e7	+	7.57193e7i	0.0770794	+	0.133506i	0.901989	−	0.431760i	$-0.142107\pi$
$317$	4.37166e7	+	7.57193e7i	0.0770794	+	0.133506i	−0.824909	+	0.565265i	$0.808774\pi$
$318$	2.64042e6	−	1.52445e6i	0.00460446	−	0.00265839i
$319$		−	1.06981e9i		−	1.84519i
$320$	−2.75708e8	−	1.59180e8i	−0.470354	−	0.271559i
$321$	1.30191e7	+	2.25497e7i	0.0219691	+	0.0380516i
$322$	1.87713e7			0.0313328
$323$	8.93345e8			1.47506
$324$	−2.74245e8	−	4.75005e8i	−0.447951	−	0.775874i
$325$			1.46091e8i			0.236065i
$326$	−4.03976e7	+	6.99707e7i	−0.0645794	+	0.111855i
$327$		−	1.28462e7i		−	0.0203169i
$328$	−2.21746e8	−	1.28025e8i	−0.346975	−	0.200326i
$329$	1.92892e8	−	3.34098e8i	0.298626	−	0.517236i
$330$	−1.33000e7	+	2.30362e7i	−0.0203728	+	0.0352868i
$331$	3.23203e8	−	1.86601e8i	0.489866	−	0.282824i	−0.234653	−	0.972079i	$-0.575395\pi$
$331$	3.23203e8	−	1.86601e8i	0.489866	−	0.282824i	0.724519	+	0.689255i	$0.242062\pi$
$332$	1.01365e9			1.52021
$333$	6.01538e8	−	2.70618e8i	0.892705	−	0.401608i
$334$	1.33510e8			0.196066
$335$	−6.69587e8	+	3.86586e8i	−0.973083	+	0.561810i
$336$	−6.98639e7	+	1.21008e8i	−0.100477	+	0.174031i
$337$	2.09237e8	−	3.62409e8i	0.297806	−	0.515816i	−0.677827	−	0.735221i	$-0.737078\pi$
$337$	2.09237e8	−	3.62409e8i	0.297806	−	0.515816i	0.975634	+	0.219405i	$0.0704117\pi$
$338$	−9.63435e7	−	5.56240e7i	−0.135711	−	0.0783526i
$339$			7.02956e7i			0.0980007i
$340$	2.64248e8	−	4.57691e8i	0.364616	−	0.631533i
$341$			6.61378e8i			0.903252i
$342$	1.06900e8	+	1.85156e8i	0.144506	+	0.250291i
$343$	−6.24873e8			−0.836108
$344$	−4.27964e8			−0.566830
$345$	−3.79468e6	−	6.57258e6i	−0.00497518	−	0.00861726i
$346$	−2.03417e8	−	1.17443e8i	−0.264010	−	0.152426i
$347$			1.15282e9i			1.48118i	0.671955	+	0.740592i	$0.265455\pi$
$347$			1.15282e9i			1.48118i	−0.671955	+	0.740592i	$0.734545\pi$
$348$	9.50390e7	−	5.48708e7i	0.120886	−	0.0697933i
$349$	4.57102e8	+	7.91724e8i	0.575605	+	0.996977i	0.995976	+	0.0896243i	$0.0285666\pi$
$349$	4.57102e8	+	7.91724e8i	0.575605	+	0.996977i	−0.420371	+	0.907352i	$0.638100\pi$
$350$	−1.08729e8	+	6.27748e7i	−0.135553	+	0.0782614i
$351$	−1.01400e8	−	5.85431e7i	−0.125159	−	0.0722605i
$352$	−7.71128e8	−	4.45211e8i	−0.942383	−	0.544085i
$353$	−5.77692e8	+	3.33530e8i	−0.699012	+	0.403575i	−0.806979	−	0.590580i	$-0.798899\pi$
$353$	−5.77692e8	+	3.33530e8i	−0.699012	+	0.403575i	0.107967	+	0.994154i	$0.465566\pi$
$354$	9.91803e6	+	1.71785e7i	0.0118827	+	0.0205814i
$355$	−5.94098e8	+	3.43002e8i	−0.704788	+	0.406910i
$356$		−	9.86760e8i		−	1.15914i
$357$	−1.80116e8	−	1.03990e8i	−0.209514	−	0.120963i
$358$	1.00945e8	+	1.74842e8i	0.116277	+	0.201398i
$359$	−4.64434e8			−0.529777			−0.264889	−	0.964279i	$-0.585335\pi$
$359$	−4.64434e8			−0.529777			−0.264889	+	0.964279i	$0.585335\pi$
$360$	2.58780e8			0.292329
$361$	4.39386e8	+	7.61039e8i	0.491554	+	0.851396i
$362$			3.50293e8i			0.388107i
$363$	1.57120e8	−	2.72139e8i	0.172408	−	0.298620i
$364$		−	7.02657e8i		−	0.763640i
$365$	4.77960e8	+	2.75951e8i	0.514478	+	0.297034i
$366$	1.63723e7	−	2.83576e7i	0.0174552	−	0.0302333i
$367$	−1.19808e8	+	2.07514e8i	−0.126519	+	0.219137i	−0.922326	−	0.386414i	$-0.873714\pi$
$367$	−1.19808e8	+	2.07514e8i	−0.126519	+	0.219137i	0.795807	+	0.605551i	$0.207047\pi$
$368$	6.77352e7	−	3.91069e7i	0.0708511	−	0.0409059i
$369$	−9.22997e8			−0.956331
$370$	−1.49759e7	+	1.47998e8i	−0.0153705	+	0.151897i
$371$	2.72801e8			0.277355
$372$	−5.87548e7	+	3.39221e7i	−0.0591756	+	0.0341651i
$373$	−1.51267e8	+	2.62002e8i	−0.150926	+	0.261411i	−0.931568	−	0.363567i	$-0.881559\pi$
$373$	−1.51267e8	+	2.62002e8i	−0.150926	+	0.261411i	0.780642	+	0.624978i	$0.214892\pi$
$374$	2.04017e8	−	3.53368e8i	0.201658	−	0.349282i
$375$	1.37546e8	+	7.94124e7i	0.134691	+	0.0777641i
$376$			1.58849e8i			0.154108i
$377$	−2.62662e8	+	4.54944e8i	−0.252466	+	0.437284i
$378$		−	1.00623e8i		−	0.0958244i
$379$	−8.34534e8	−	1.44546e9i	−0.787421	−	1.36385i	−0.927542	−	0.373719i	$-0.878082\pi$
$379$	−8.34534e8	−	1.44546e9i	−0.787421	−	1.36385i	0.140121	−	0.990134i	$-0.455251\pi$
$380$	1.04868e9			0.980396
$381$	7.54199e7			0.0698632
$382$	−1.43566e8	−	2.48664e8i	−0.131774	−	0.228240i
$383$	−3.49237e8	−	2.01632e8i	−0.317632	−	0.183385i	0.332704	−	0.943031i	$-0.392039\pi$
$383$	−3.49237e8	−	2.01632e8i	−0.317632	−	0.183385i	−0.650337	+	0.759646i	$0.725372\pi$
$384$		−	1.20753e8i		−	0.108827i
$385$	−2.06117e9	+	1.19001e9i	−1.84077	+	1.06277i
$386$	1.36543e8	+	2.36499e8i	0.120841	+	0.209302i
$387$	−1.33602e9	+	7.71350e8i	−1.17172	+	0.676493i
$388$	3.00830e8	+	1.73684e8i	0.261463	+	0.150956i
$389$	8.53242e8	+	4.92619e8i	0.734934	+	0.424315i	0.820225	−	0.572042i	$-0.193848\pi$
$389$	8.53242e8	+	4.92619e8i	0.734934	+	0.424315i	−0.0852902	+	0.996356i	$0.527182\pi$
$390$	1.13118e7	−	6.53084e6i	0.00965615	−	0.00557498i
$391$	5.82092e7	+	1.00821e8i	0.0492462	+	0.0852970i
$392$	6.46391e8	−	3.73194e8i	0.541993	−	0.312920i
$393$			2.89840e8i			0.240871i
$394$	−2.18369e8	−	1.26075e8i	−0.179868	−	0.103847i
$395$	−7.65491e8	−	1.32587e9i	−0.624957	−	1.08246i
$396$	−2.12392e9			−1.71872
$397$	1.90017e9			1.52415			0.762073	−	0.647491i	$-0.224182\pi$
$397$	1.90017e9			1.52415			0.762073	+	0.647491i	$0.224182\pi$
$398$	1.80064e7	+	3.11880e7i	0.0143165	+	0.0247969i
$399$		−	4.12689e8i		−	0.325250i
$400$	−2.61562e8	+	4.53038e8i	−0.204345	+	0.353936i
$401$		−	2.72303e7i		−	0.0210886i	−0.999944	−	0.0105443i	$-0.996644\pi$
$401$		−	2.72303e7i		−	0.0210886i	0.999944	−	0.0105443i	$-0.00335642\pi$
$402$	−5.30303e7	−	3.06171e7i	−0.0407130	−	0.0235057i
$403$	1.62382e8	−	2.81254e8i	0.123587	−	0.214058i
$404$	2.76520e8	−	4.78947e8i	0.208637	−	0.361371i
$405$	7.90054e8	−	4.56138e8i	0.590968	−	0.341196i
$406$	−4.51460e8			−0.334794
$407$	2.51480e8	−	2.48522e9i	0.184894	−	1.82719i
$408$	8.56368e7			0.0624237
$409$	−393982.	+	227466.i	−0.000284738	+	0.000164393i	−0.500142	−	0.865943i	$-0.666719\pi$
$409$	−393982.	+	227466.i	−0.000284738	+	0.000164393i	0.499858	+	0.866108i	$0.333386\pi$
$410$	1.04077e8	−	1.80266e8i	0.0745778	−	0.129173i
$411$	−4.05988e6	+	7.03191e6i	−0.00288447	+	0.00499605i
$412$	6.89074e8	+	3.97837e8i	0.485429	+	0.280262i
$413$			1.77483e9i			1.23975i
$414$	−1.39309e7	+	2.41290e7i	−0.00964890	+	0.0167124i
$415$			1.68595e9i			1.15791i
$416$	2.18618e8	+	3.78657e8i	0.148888	+	0.257881i
$417$	−2.32376e7			−0.0156934
$418$	8.09652e8			0.542227
$419$	4.29941e8	+	7.44680e8i	0.285535	+	0.494562i	0.972739	−	0.231903i	$-0.0744952\pi$
$419$	4.29941e8	+	7.44680e8i	0.285535	+	0.494562i	−0.687203	+	0.726465i	$0.741162\pi$
$420$	−2.11435e8	−	1.22072e8i	−0.139253	−	0.0803976i
$421$			8.46966e8i			0.553195i	0.960986	+	0.276598i	$0.0892069\pi$
$421$			8.46966e8i			0.553195i	−0.960986	+	0.276598i	$0.910793\pi$
$422$	1.68267e8	−	9.71492e7i	0.108995	−	0.0629283i
$423$	2.86304e8	+	4.95893e8i	0.183923	+	0.318564i
$424$	−9.72782e7	+	5.61636e7i	−0.0619776	+	0.0357828i
$425$	−6.74330e8	−	3.89325e8i	−0.426100	−	0.246009i
$426$	−4.70517e7	−	2.71653e7i	−0.0294878	−	0.0170248i
$427$	2.53730e9	−	1.46491e9i	1.57716	−	0.910572i
$428$	−2.34434e8	−	4.06052e8i	−0.144533	−	0.250339i
$429$	−1.89950e8	+	1.09668e8i	−0.116155	+	0.0670622i
$430$		−	3.47908e8i		−	0.211021i
$431$	2.12711e9	+	1.22809e9i	1.27973	+	0.738854i	0.976799	−	0.214158i	$-0.0687009\pi$
$431$	2.12711e9	+	1.22809e9i	1.27973	+	0.738854i	0.302933	+	0.953012i	$0.402034\pi$
$432$	−2.09631e8	−	3.63092e8i	−0.125102	−	0.216682i
$433$	1.85255e9			1.09663			0.548316	−	0.836271i	$-0.315269\pi$
$433$	1.85255e9			1.09663			0.548316	+	0.836271i	$0.315269\pi$
$434$	2.79100e8			0.163888
$435$	9.12639e7	+	1.58074e8i	0.0531602	+	0.0920762i
$436$			2.31322e8i			0.133664i
$437$	−1.15503e8	+	2.00057e8i	−0.0662077	+	0.114675i
$438$			4.37098e7i			0.0248553i
$439$	−2.62590e9	−	1.51606e9i	−1.48133	−	0.855246i	−0.481553	−	0.876417i	$-0.659927\pi$
$439$	−2.62590e9	−	1.51606e9i	−1.48133	−	0.855246i	−0.999776	+	0.0211708i	$0.993261\pi$
$440$	4.89995e8	−	8.48697e8i	0.274225	−	0.474972i
$441$	1.34527e9	−	2.33007e9i	0.746920	−	1.29370i
$442$	−1.73519e8	+	1.00181e8i	−0.0955803	+	0.0551833i
$443$	2.46715e8			0.134829			0.0674143	−	0.997725i	$-0.478525\pi$
$443$	2.46715e8			0.134829			0.0674143	+	0.997725i	$0.478525\pi$
$444$	2.33678e8	−	1.05126e8i	0.126700	−	0.0569996i
$445$	1.64123e9			0.882896
$446$	8.28438e7	−	4.78299e7i	0.0442168	−	0.0255286i
$447$	−1.61149e8	+	2.79118e8i	−0.0853398	+	0.147813i
$448$	1.12800e9	−	1.95375e9i	0.592702	−	1.02659i
$449$	−1.79628e9	−	1.03708e9i	−0.936509	−	0.540694i	−0.0476448	−	0.998864i	$-0.515172\pi$
$449$	−1.79628e9	−	1.03708e9i	−0.936509	−	0.540694i	−0.888864	+	0.458171i	$0.848505\pi$
$450$		−	1.86350e8i		−	0.0964019i
$451$	−1.74768e9	+	3.02707e9i	−0.897107	+	1.55384i
$452$		−	1.26581e9i		−	0.644740i
$453$	1.18637e8	+	2.05486e8i	0.0599621	+	0.103857i
$454$	−7.55943e8			−0.379135
$455$	1.16870e9			0.581650
$456$	8.49635e7	+	1.47161e8i	0.0419619	+	0.0726802i
$457$	−2.79558e9	−	1.61403e9i	−1.37014	−	0.791052i	−0.379196	−	0.925316i	$-0.623800\pi$
$457$	−2.79558e9	−	1.61403e9i	−1.37014	−	0.791052i	−0.990946	+	0.134264i	$0.957133\pi$
$458$			3.72844e8i			0.181342i
$459$	5.40449e8	−	3.12028e8i	0.260862	−	0.150609i
$460$	6.83308e7	+	1.18352e8i	0.0327314	+	0.0566924i
$461$	3.46762e8	−	2.00203e8i	0.164846	−	0.0951737i	−0.415307	−	0.909681i	$-0.636326\pi$
$461$	3.46762e8	−	2.00203e8i	0.164846	−	0.0951737i	0.580153	+	0.814507i	$0.302993\pi$
$462$	−1.63241e8	−	9.42475e7i	−0.0770165	−	0.0444655i
$463$	2.80717e9	+	1.62072e9i	1.31442	+	0.758884i	0.982826	−	0.184537i	$-0.0590785\pi$
$463$	2.80717e9	+	1.62072e9i	1.31442	+	0.758884i	0.331599	+	0.943420i	$0.392412\pi$
$464$	−1.62906e9	+	9.40540e8i	−0.757051	+	0.437083i
$465$	−5.64210e7	−	9.77240e7i	−0.0260229	−	0.0450729i
$466$	2.62664e8	−	1.51649e8i	0.120240	−	0.0694207i
$467$			3.60008e9i			1.63570i	0.575432	+	0.817849i	$0.304834\pi$
$467$			3.60008e9i			1.63570i	−0.575432	+	0.817849i	$0.695166\pi$
$468$	9.03209e8	+	5.21468e8i	0.407312	+	0.235162i
$469$	−2.73947e9	−	4.74490e9i	−1.22620	−	2.12384i
$470$	−1.29134e8			−0.0573717
$471$	2.57249e8			0.113444
$472$	−3.65399e8	−	6.32889e8i	−0.159945	−	0.277033i
$473$			5.84216e9i			2.53840i
$474$	6.06258e7	−	1.05007e8i	0.0261477	−	0.0452891i
$475$		−	1.54506e9i		−	0.661480i
$476$	3.24334e9	+	1.87254e9i	1.37838	+	0.795806i
$477$	−2.02455e8	+	3.50663e8i	−0.0854112	+	0.147937i
$478$	1.48596e8	−	2.57375e8i	0.0622312	−	0.107788i
$479$	4.13814e8	−	2.38915e8i	0.172040	−	0.0993276i	−0.411507	−	0.911407i	$-0.634997\pi$
$479$	4.13814e8	−	2.38915e8i	0.172040	−	0.0993276i	0.583548	+	0.812079i	$0.301664\pi$
$480$	1.51921e8			0.0627008
$481$	−7.17118e8	+	9.95110e8i	−0.293821	+	0.407721i
$482$	2.33266e8			0.0948826
$483$	4.65753e7	−	2.68903e7i	0.0188079	−	0.0108588i
$484$	−2.82925e9	+	4.90041e9i	−1.13426	+	1.96460i
$485$	−2.88880e8	+	5.00356e8i	−0.114980	+	0.199151i
$486$	1.94704e8	+	1.12413e8i	0.0769393	+	0.0444209i
$487$		−	3.62950e9i		−	1.42395i	−0.702204	−	0.711976i	$-0.747801\pi$
$487$		−	3.62950e9i		−	1.42395i	0.702204	−	0.711976i	$-0.252199\pi$
$488$	−6.03186e8	+	1.04475e9i	−0.234953	+	0.406951i
$489$			2.31481e8i			0.0895230i
$490$	3.03383e8	+	5.25475e8i	0.116495	+	0.201774i
$491$	1.60624e9			0.612387			0.306194	−	0.951969i	$-0.400944\pi$
$491$	1.60624e9			0.612387			0.306194	+	0.951969i	$0.400944\pi$
$492$	−3.58555e8			−0.135731
$493$	−1.39996e9	−	2.42480e9i	−0.526200	−	0.911406i
$494$	−3.44309e8	−	1.98787e8i	−0.128500	−	0.0741897i
$495$		−	3.53261e9i		−	1.30912i
$496$	1.00712e9	−	5.81459e8i	0.370590	−	0.213960i
$497$	−2.43062e9	−	4.20996e9i	−0.888116	−	1.53826i
$498$	−1.15636e8	+	6.67624e7i	−0.0419556	+	0.0242231i
$499$	−2.03399e9	−	1.17432e9i	−0.732818	−	0.423093i	0.0866343	−	0.996240i	$-0.472389\pi$
$499$	−2.03399e9	−	1.17432e9i	−0.732818	−	0.423093i	−0.819452	+	0.573148i	$0.805722\pi$
$500$	−2.47679e9	−	1.42998e9i	−0.886125	−	0.511604i
$501$	3.31265e8	−	1.91256e8i	0.117691	−	0.0679490i
$502$	3.97140e7	+	6.87866e7i	0.0140114	+	0.0242684i
$503$	−4.55533e9	+	2.63002e9i	−1.59600	+	0.921449i	−0.603748	+	0.797175i	$0.706327\pi$
$503$	−4.55533e9	+	2.63002e9i	−1.59600	+	0.921449i	−0.992248	+	0.124274i	$0.960340\pi$
$504$			1.83379e9i			0.638033i
$505$	7.96610e8	+	4.59923e8i	0.275249	+	0.158915i
$506$	5.27559e7	+	9.13759e7i	0.0181027	+	0.0313548i
$507$	−3.18729e8			−0.108616
$508$	−1.35808e9			−0.459625
$509$	−9.82672e8	−	1.70204e9i	−0.330291	−	0.572080i	0.652278	−	0.757980i	$-0.273813\pi$
$509$	−9.82672e8	−	1.70204e9i	−0.330291	−	0.572080i	−0.982569	+	0.185899i	$0.940480\pi$
$510$			6.96173e7i			0.0232392i
$511$	−1.95547e9	+	3.38697e9i	−0.648303	+	1.12289i
$512$			2.64929e9i			0.872339i
$513$	1.07240e9	+	6.19150e8i	0.350708	+	0.202482i
$514$	1.62690e7	−	2.81788e7i	0.00528434	−	0.00915275i
$515$	−6.61703e8	+	1.14610e9i	−0.213470	+	0.369742i
$516$	−5.19000e8	+	2.99645e8i	−0.166300	+	0.0960136i
$517$	2.16845e9			0.690133
$518$	−1.04876e9	−	1.06124e8i	−0.331529	−	0.0335475i
$519$	−6.72955e8			−0.211300
$520$	−4.16746e8	+	2.40609e8i	−0.129975	+	0.0750411i
$521$	7.17523e8	−	1.24279e9i	0.222282	−	0.385004i	−0.733219	−	0.679993i	$-0.761983\pi$
$521$	7.17523e8	−	1.24279e9i	0.222282	−	0.385004i	0.955501	+	0.294989i	$0.0953161\pi$
$522$	3.35045e8	−	5.80314e8i	0.103099	−	0.178573i
$523$	4.47318e9	+	2.58259e9i	1.36729	+	0.789406i	0.990581	−	0.136926i	$-0.0437221\pi$
$523$	4.47318e9	+	2.58259e9i	1.36729	+	0.789406i	0.376710	+	0.926331i	$0.377055\pi$
$524$		−	5.21914e9i		−	1.58467i
$525$	−1.79852e8	+	3.11513e8i	−0.0542448	+	0.0939548i
$526$			3.33536e8i			0.0999293i
$527$	8.65479e8	+	1.49905e9i	0.257584	+	0.446149i
$528$	−7.85395e8			−0.232204
$529$	3.37472e9			0.991158
$530$	−4.56575e7	−	7.90811e7i	−0.0133213	−	0.0230732i
$531$	−2.28140e9	−	1.31717e9i	−0.661259	−	0.381778i
$532$			7.43128e9i			2.13980i
$533$	1.48642e9	−	8.58186e8i	0.425204	−	0.245491i
$534$	6.49916e7	+	1.12569e8i	0.0184698	+	0.0319907i
$535$	6.75367e8	−	3.89923e8i	0.190678	−	0.110088i
$536$	1.95374e9	+	1.12799e9i	0.548011	+	0.316394i
$537$	5.00928e8	+	2.89211e8i	0.139593	+	0.0805943i
$538$	−9.41253e8	+	5.43433e8i	−0.260596	+	0.150455i
$539$	−5.09449e9	−	8.82392e9i	−1.40133	−	2.42717i
$540$	6.34424e8	−	3.66285e8i	0.173381	−	0.100102i
$541$			1.43722e9i			0.390240i	0.980779	+	0.195120i	$0.0625096\pi$
$541$			1.43722e9i			0.390240i	−0.980779	+	0.195120i	$0.937490\pi$
$542$	−9.56301e8	−	5.52121e8i	−0.257987	−	0.148949i
$543$	5.01801e8	+	8.69145e8i	0.134503	+	0.232966i
$544$	−2.33042e9			−0.620636
$545$	−3.84746e8			−0.101809
$546$	4.62796e7	+	8.01585e7i	0.0121679	+	0.0210754i
$547$			2.96420e9i			0.774376i	0.922001	+	0.387188i	$0.126553\pi$
$547$			2.96420e9i			0.774376i	−0.922001	+	0.387188i	$0.873447\pi$
$548$	7.31061e7	−	1.26624e8i	0.0189767	−	0.0328687i
$549$			4.34866e9i			1.12164i
$550$	−6.11156e8	−	3.52851e8i	−0.156633	−	0.0904319i
$551$	2.77791e9	−	4.81147e9i	0.707436	−	1.22531i
$552$	−1.10722e7	+	1.91777e7i	−0.00280187	+	0.00485298i
$553$	9.39551e9	−	5.42450e9i	2.36256	−	1.36402i
$554$	1.13969e8			0.0284776
$555$	1.74852e8	+	3.88665e8i	0.0434155	+	0.0965051i
$556$	4.18440e8			0.103246
$557$	−3.01495e9	+	1.74068e9i	−0.739242	+	0.426802i	−0.821794	−	0.569785i	$-0.807026\pi$
$557$	−3.01495e9	+	1.74068e9i	−0.739242	+	0.426802i	0.0825515	+	0.996587i	$0.473693\pi$
$558$	−2.07131e8	+	3.58761e8i	−0.0504690	+	0.0874148i
$559$	1.43437e9	−	2.48441e9i	0.347313	−	0.601564i
$560$	3.62420e9	+	2.09243e9i	0.872076	+	0.503493i
$561$		−	1.16903e9i		−	0.279548i
$562$	2.04288e8	−	3.53837e8i	0.0485473	−	0.0840864i
$563$		−	5.08782e9i		−	1.20158i	−0.799407	−	0.600790i	$-0.794853\pi$
$563$		−	5.08782e9i		−	1.20158i	0.799407	−	0.600790i	$-0.205147\pi$
$564$	1.11220e8	+	1.92639e8i	0.0261039	+	0.0452133i
$565$	2.10536e9			0.491086
$566$	2.28956e8			0.0530755
$567$	3.23233e9	+	5.59856e9i	0.744689	+	1.28984i
$568$	1.73347e9	+	1.00082e9i	0.396915	+	0.229159i
$569$			1.43935e9i			0.327547i	0.986498	+	0.163774i	$0.0523667\pi$
$569$			1.43935e9i			0.327547i	−0.986498	+	0.163774i	$0.947633\pi$
$570$	−1.19633e8	+	6.90700e7i	−0.0270575	+	0.0156217i
$571$	−1.99014e9	−	3.44703e9i	−0.447361	−	0.774852i	0.550852	−	0.834603i	$-0.314303\pi$
$571$	−1.99014e9	−	3.44703e9i	−0.447361	−	0.774852i	−0.998213	+	0.0597507i	$0.980969\pi$
$572$	3.42042e9	−	1.97478e9i	0.764177	−	0.441198i
$573$	−7.12433e8	−	4.11323e8i	−0.158199	−	0.0913360i
$574$	1.27742e9	+	7.37519e8i	0.281930	+	0.162773i
$575$	1.74372e8	−	1.00674e8i	0.0382507	−	0.0220841i
$576$	1.67426e9	+	2.89990e9i	0.365043	+	0.632274i
$577$	5.70513e9	−	3.29386e9i	1.23637	−	0.713821i	0.268023	−	0.963412i	$-0.413630\pi$
$577$	5.70513e9	−	3.29386e9i	1.23637	−	0.713821i	0.968351	+	0.249591i	$0.0802963\pi$
$578$		−	9.45797e7i		−	0.0203728i
$579$	6.77578e8	+	3.91200e8i	0.145072	+	0.0837575i
$580$	−1.64339e9	−	2.84643e9i	−0.349737	−	0.605763i
$581$	−1.19471e10			−2.52725
$582$	−4.57579e7			−0.00962133
$583$	7.66692e8	+	1.32795e9i	0.160244	+	0.277550i
$584$		−	1.61035e9i		−	0.334561i
$585$	−8.67332e8	+	1.50226e9i	−0.179118	+	0.310242i
$586$		−	8.20599e8i		−	0.168457i
$587$	3.42040e9	+	1.97477e9i	0.697980	+	0.402979i	0.806595	−	0.591105i	$-0.201308\pi$
$587$	3.42040e9	+	1.97477e9i	0.697980	+	0.402979i	−0.108614	+	0.994084i	$0.534641\pi$
$588$	5.22593e8	−	9.05158e8i	0.106009	−	0.183613i
$589$	−1.71735e9	+	2.97454e9i	−0.346302	+	0.599813i
$590$	5.14500e8	−	2.97046e8i	0.103134	−	0.0595446i
$591$	−7.22421e8			−0.143957
$592$	−4.00547e9	+	1.80197e9i	−0.793465	+	0.356962i
$593$	1.31988e9			0.259921			0.129961	−	0.991519i	$-0.458515\pi$
$593$	1.31988e9			0.259921			0.129961	+	0.991519i	$0.458515\pi$
$594$	4.89817e8	−	2.82796e8i	0.0958917	−	0.0553631i
$595$	−3.11451e9	+	5.39449e9i	−0.606150	+	1.04988i
$596$	2.90181e9	−	5.02608e9i	0.561444	−	0.972450i
$597$	8.93548e7	+	5.15890e7i	0.0171873	+	0.00992309i
$598$		−	5.18108e7i		−	0.00990754i
$599$	1.67788e9	−	2.90618e9i	0.318983	−	0.552496i	−0.661293	−	0.750128i	$-0.729992\pi$
$599$	1.67788e9	−	2.90618e9i	0.318983	−	0.552496i	0.980276	+	0.197632i	$0.0633252\pi$
$600$		−	1.48110e8i		−	0.0279934i
$601$	4.66006e8	+	8.07146e8i	0.0875651	+	0.151667i	0.906481	−	0.422246i	$-0.138758\pi$
$601$	4.66006e8	+	8.07146e8i	0.0875651	+	0.151667i	−0.818916	+	0.573913i	$0.805425\pi$
$602$	2.46538e9			0.460571
$603$	8.13223e9			1.51043
$604$	−2.13630e9	−	3.70017e9i	−0.394487	−	0.683271i
$605$	−8.15062e9	−	4.70576e9i	−1.49640	−	0.863945i
$606$			7.28505e7i			0.0132978i
$607$	−3.24955e9	+	1.87613e9i	−0.589744	+	0.340489i	−0.764996	−	0.644035i	$-0.777259\pi$
$607$	−3.24955e9	+	1.87613e9i	−0.589744	+	0.340489i	0.175252	+	0.984524i	$0.443926\pi$
$608$	−2.31209e9	−	4.00467e9i	−0.417199	−	0.722610i
$609$	−1.12016e9	+	6.46724e8i	−0.200964	+	0.116027i
$610$	−8.49316e8	−	4.90353e8i	−0.151501	−	0.0874690i
$611$	−9.22146e8	−	5.32401e8i	−0.163552	−	0.0944267i
$612$	−4.81400e9	+	2.77936e9i	−0.848938	+	0.490135i
$613$	−2.52146e9	−	4.36730e9i	−0.442121	−	0.765776i	0.555726	−	0.831366i	$-0.312440\pi$
$613$	−2.52146e9	−	4.36730e9i	−0.442121	−	0.765776i	−0.997847	+	0.0655899i	$0.979107\pi$
$614$	−1.26662e9	+	7.31284e8i	−0.220830	+	0.127496i
$615$		−	5.96367e8i		−	0.103383i
$616$	6.01412e9	+	3.47226e9i	1.03667	+	0.598521i
$617$	3.79950e9	+	6.58092e9i	0.651220	+	1.12795i	0.982827	+	0.184529i	$0.0590760\pi$
$617$	3.79950e9	+	6.58092e9i	0.651220	+	1.12795i	−0.331607	+	0.943418i	$0.607591\pi$
$618$	−1.04812e8			−0.0178629
$619$	6.16859e9			1.04537			0.522683	−	0.852527i	$-0.324931\pi$
$619$	6.16859e9			1.04537			0.522683	+	0.852527i	$0.324931\pi$
$620$	1.01597e9	+	1.75971e9i	0.171203	+	0.296532i
$621$			1.61372e8i			0.0270401i
$622$	2.77873e8	−	4.81290e8i	0.0462999	−	0.0801938i
$623$			1.16303e10i			1.92700i
$624$	3.33994e8	+	1.92831e8i	0.0550291	+	0.0317711i
$625$	9.44927e8	−	1.63666e9i	0.154817	−	0.268151i
$626$	2.07925e8	−	3.60137e8i	0.0338764	−	0.0586756i
$627$	2.00890e9	−	1.15984e9i	0.325479	−	0.187915i
$628$	−4.63227e9			−0.746338
$629$	−2.68217e9	−	5.96200e9i	−0.429743	−	0.955245i
$630$	−1.49076e9			−0.237528
$631$	−2.74341e8	+	1.58391e8i	−0.0434699	+	0.0250974i	−0.521577	−	0.853204i	$-0.674656\pi$
$631$	−2.74341e8	+	1.58391e8i	−0.0434699	+	0.0250974i	0.478108	+	0.878301i	$0.341323\pi$
$632$	−2.23357e9	+	3.86865e9i	−0.351957	+	0.609607i
$633$	2.78336e8	−	4.82092e8i	0.0436171	−	0.0755470i
$634$	1.79607e8	+	1.03696e8i	0.0279905	+	0.0161603i
$635$		−	2.25884e9i		−	0.350088i
$636$	−7.86474e7	+	1.36221e8i	−0.0121223	+	0.0209964i
$637$			5.00323e9i			0.766941i
$638$	−1.26880e9	−	2.19763e9i	−0.193429	−	0.335029i
$639$	7.21541e9			1.09398
$640$	−3.61657e9			−0.545339
$641$	−7.09912e8	−	1.22960e9i	−0.106464	−	0.184400i	0.807872	−	0.589359i	$-0.200619\pi$
$641$	−7.09912e8	−	1.22960e9i	−0.106464	−	0.184400i	−0.914335	+	0.404958i	$0.867286\pi$
$642$	5.34881e7	+	3.08814e7i	0.00797783	+	0.00460600i
$643$			1.11136e10i			1.64860i	0.566150	+	0.824302i	$0.308432\pi$
$643$			1.11136e10i			1.64860i	−0.566150	+	0.824302i	$0.691568\pi$
$644$	−8.38681e8	+	4.84213e8i	−0.123736	+	0.0714391i
$645$	−4.98385e8	−	8.63227e8i	−0.0731317	−	0.126668i
$646$	1.83513e9	−	1.05951e9i	0.267826	−	0.154629i
$647$	−1.14188e10	−	6.59263e9i	−1.65750	−	0.956959i	−0.973862	−	0.227140i	$-0.927063\pi$
$647$	−1.14188e10	−	6.59263e9i	−1.65750	−	0.956959i	−0.683640	−	0.729819i	$-0.739604\pi$
$648$	−2.30524e9	−	1.33093e9i	−0.332815	−	0.192151i
$649$	−8.63961e9	+	4.98808e9i	−1.24062	+	0.716270i
$650$	1.73265e8	+	3.00104e8i	0.0247465	+	0.0428622i
$651$	6.92502e8	−	3.99816e8i	0.0983756	−	0.0567972i
$652$		−	4.16828e9i		−	0.588966i
$653$	−9.44132e8	−	5.45095e8i	−0.132690	−	0.0766083i	0.432186	−	0.901785i	$-0.357742\pi$
$653$	−9.44132e8	−	5.45095e8i	−0.132690	−	0.0766083i	−0.564875	+	0.825176i	$0.691076\pi$
$654$	−1.52357e7	−	2.63890e7i	−0.00212980	−	0.00368893i
$655$	8.68074e9			1.20701
$656$	6.14599e9			0.850018
$657$	−2.90245e9	−	5.02719e9i	−0.399288	−	0.691587i
$658$		−	9.15083e8i		−	0.125219i
$659$	−3.36248e9	+	5.82399e9i	−0.457679	+	0.792723i	−0.998838	−	0.0481972i	$-0.984652\pi$
$659$	−3.36248e9	+	5.82399e9i	−0.457679	+	0.792723i	0.541159	+	0.840920i	$0.317986\pi$
$660$		−	1.37231e9i		−	0.185801i
$661$	−1.21783e10	−	7.03114e9i	−1.64014	−	0.946937i	−0.980781	−	0.195110i	$-0.937494\pi$
$661$	−1.21783e10	−	7.03114e9i	−1.64014	−	0.946937i	−0.659361	−	0.751827i	$-0.729173\pi$
$662$	4.42620e8	−	7.66641e8i	0.0592964	−	0.102704i
$663$	−2.87022e8	+	4.97137e8i	−0.0382488	+	0.0662489i
$664$	4.26024e9	−	2.45965e9i	0.564736	−	0.326051i
$665$	−1.23601e10			−1.62984
$666$	9.14736e8	−	1.26934e9i	0.119988	−	0.166501i
$667$	7.24019e8			0.0944734
$668$	−5.96509e9	+	3.44395e9i	−0.774282	+	0.447032i
$669$	1.37034e8	−	2.37350e8i	0.0176945	−	0.0306477i
$670$	−9.16986e8	+	1.58827e9i	−0.117788	+	0.204015i
$671$	1.42619e10	+	8.23412e9i	1.82242	+	1.05218i
$672$			1.07656e9i			0.136850i
$673$	−3.93651e9	+	6.81823e9i	−0.497804	+	0.862222i	−0.999997	−	0.00253386i	$-0.999193\pi$
$673$	−3.93651e9	+	6.81823e9i	−0.497804	+	0.862222i	0.502193	+	0.864756i	$0.332527\pi$
$674$		−	9.92625e8i		−	0.124875i
$675$	−5.39658e8	−	9.34716e8i	−0.0675392	−	0.116981i
$676$	5.73935e9			0.714578
$677$	−6.97478e9			−0.863913			−0.431957	−	0.901894i	$-0.642177\pi$
$677$	−6.97478e9			−0.863913			−0.431957	+	0.901894i	$0.642177\pi$
$678$	8.33709e7	+	1.44403e8i	0.0102733	+	0.0177939i
$679$	−3.54567e9	−	2.04709e9i	−0.434665	−	0.250954i
$680$		−	2.56483e9i		−	0.312808i
$681$	−1.87564e9	+	1.08290e9i	−0.227581	+	0.131394i
$682$	7.84397e8	+	1.35862e9i	0.0946871	+	0.164003i
$683$	−1.06037e10	+	6.12202e9i	−1.27345	+	0.735229i	−0.975636	−	0.219394i	$-0.929592\pi$
$683$	−1.06037e10	+	6.12202e9i	−1.27345	+	0.735229i	−0.297817	+	0.954623i	$0.596259\pi$
$684$	−9.55231e9	−	5.51503e9i	−1.14133	−	0.658948i
$685$	2.10607e8	+	1.21594e8i	0.0250355	+	0.0144542i
$686$	−1.28363e9	+	7.41103e8i	−0.151812	+	0.0876484i
$687$	5.34106e8	+	9.25099e8i	0.0628462	+	0.108853i
$688$	8.89618e9	−	5.13621e9i	1.04146	−	0.601289i
$689$		−	7.52957e8i		−	0.0877007i
$690$	−1.55902e7	−	9.00103e6i	−0.00180668	−	0.00104309i
$691$	−1.27740e9	−	2.21252e9i	−0.147284	−	0.255103i	0.782939	−	0.622098i	$-0.213720\pi$
$691$	−1.27740e9	−	2.21252e9i	−0.147284	−	0.255103i	−0.930223	+	0.366996i	$0.880386\pi$
$692$	1.21179e10			1.39013
$693$	2.50332e10			2.85726
$694$	1.36725e9	+	2.36815e9i	0.155271	+	0.268937i
$695$			6.95971e8i			0.0786401i
$696$	2.66292e8	−	4.61232e8i	0.0299382	−	0.0518545i
$697$			9.14807e9i			1.02333i
$698$	1.87798e9	+	1.08425e9i	0.209024	+	0.120680i
$699$	4.34480e8	−	7.52541e8i	0.0481171	−	0.0833413i
$700$	3.23859e9	−	5.60941e9i	0.356873	−	0.618122i
$701$	1.30507e10	−	7.53482e9i	1.43094	−	0.826152i	0.433745	−	0.901036i	$-0.357192\pi$
$701$	1.30507e10	−	7.53482e9i	1.43094	−	0.826152i	0.997192	+	0.0748842i	$0.0238587\pi$
$702$	−2.77730e8			−0.0303000
$703$	7.58422e9	−	1.05243e10i	0.823317	−	1.14248i
$704$	1.26808e10			1.36975
$705$	−3.20407e8	+	1.84987e8i	−0.0344381	+	0.0198829i
$706$	−7.91138e8	+	1.37029e9i	−0.0846127	+	0.146553i
$707$	−3.25915e9	+	5.64502e9i	−0.346846	+	0.600755i
$708$	−8.86252e8	−	5.11678e8i	−0.0938514	−	0.0541851i
$709$		−	2.12346e8i		−	0.0223760i	−0.999937	−	0.0111880i	$-0.996439\pi$
$709$		−	2.12346e8i		−	0.0223760i	0.999937	−	0.0111880i	$-0.00356133\pi$
$710$	−8.13605e8	+	1.40921e9i	−0.0853119	+	0.147764i
$711$			1.61029e10i			1.68020i
$712$	−2.39441e9	−	4.14724e9i	−0.248610	−	0.430605i
$713$	−4.47601e8			−0.0462464
$714$	−4.93330e8			−0.0507217
$715$	3.28456e9	+	5.68903e9i	0.336052	+	0.582059i
$716$	−9.02020e9	−	5.20781e9i	−0.918376	−	0.530224i
$717$		−	8.51463e8i		−	0.0862678i
$718$	−9.54050e8	+	5.50821e8i	−0.0961912	+	0.0555360i
$719$	−4.17954e9	−	7.23917e9i	−0.419350	−	0.726336i	0.576524	−	0.817080i	$-0.304409\pi$
$719$	−4.17954e9	−	7.23917e9i	−0.419350	−	0.726336i	−0.995874	+	0.0907443i	$0.971075\pi$
$720$	−5.37930e9	+	3.10574e9i	−0.537109	+	0.310100i
$721$	−8.12164e9	−	4.68903e9i	−0.806994	−	0.465918i
$722$	1.80519e9	+	1.04223e9i	0.178502	+	0.103058i
$723$	5.78778e8	−	3.34158e8i	0.0569545	−	0.0328827i
$724$	−9.03592e9	−	1.56507e10i	−0.884886	−	1.53267i
$725$	−4.19373e9	+	2.42125e9i	−0.408713	+	0.235970i
$726$		−	7.45379e8i		−	0.0722935i
$727$	5.74964e9	+	3.31956e9i	0.554971	+	0.320412i	0.751124	−	0.660161i	$-0.229512\pi$
$727$	5.74964e9	+	3.31956e9i	0.554971	+	0.320412i	−0.196154	+	0.980573i	$0.562845\pi$
$728$	−1.70503e9	−	2.95319e9i	−0.163784	−	0.283682i
$729$	−9.15819e9			−0.875515
$730$	1.30911e9			0.124551
$731$	7.64506e9	+	1.32416e10i	0.723886	+	1.25381i
$732$			1.68931e9i			0.159192i
$733$	1.26122e9	−	2.18449e9i	0.118284	−	0.204874i	−0.800804	−	0.598927i	$-0.795594\pi$
$733$	1.26122e9	−	2.18449e9i	0.118284	−	0.204874i	0.919088	+	0.394053i	$0.128927\pi$
$734$			5.68372e8i			0.0530513i
$735$	1.50551e9	+	8.69205e8i	0.139855	+	0.0807451i
$736$	3.01306e8	−	5.21878e8i	0.0278571	−	0.0482499i
$737$	1.53983e10	−	2.66706e10i	1.41689	−	2.45412i
$738$	−1.89604e9	+	1.09468e9i	−0.173640	+	0.100251i
$739$	3.77805e8			0.0344359			0.0172180	−	0.999852i	$-0.494519\pi$
$739$	3.77805e8			0.0344359			0.0172180	+	0.999852i	$0.494519\pi$
$740$	−3.14855e9	−	6.99869e9i	−0.285627	−	0.634901i
$741$	−1.13906e9			−0.102845
$742$	5.60393e8	−	3.23543e8i	0.0503592	−	0.0290749i
$743$	−2.36451e9	+	4.09545e9i	−0.211485	+	0.366303i	−0.952180	−	0.305539i	$-0.901163\pi$
$743$	−2.36451e9	+	4.09545e9i	−0.211485	+	0.366303i	0.740694	+	0.671842i	$0.234497\pi$
$744$	−1.64627e8	+	2.85142e8i	−0.0146553	+	0.0253837i
$745$	8.35963e9	+	4.82644e9i	0.740697	+	0.427641i
$746$			7.17614e8i			0.0632856i
$747$	8.86641e9	−	1.53571e10i	0.778262	−	1.34799i
$748$			2.10507e10i			1.83913i
$749$	2.76312e9	+	4.78586e9i	0.240277	+	0.416172i
$750$	3.76734e8			0.0326077
$751$	2.46663e9			0.212503			0.106251	−	0.994339i	$-0.466115\pi$
$751$	2.46663e9			0.212503			0.106251	+	0.994339i	$0.466115\pi$
$752$	−1.90642e9	−	3.30202e9i	−0.163477	−	0.283150i
$753$	1.97076e8	+	1.13782e8i	0.0168210	+	0.00971161i
$754$			1.24607e9i			0.105863i
$755$	6.15432e9	−	3.55320e9i	0.520434	−	0.300473i
$756$	2.59560e9	+	4.49572e9i	0.218480	+	0.378419i
$757$	2.16903e9	−	1.25229e9i	0.181731	−	0.104923i	−0.406375	−	0.913707i	$-0.633207\pi$
$757$	2.16903e9	−	1.25229e9i	0.181731	−	0.104923i	0.588106	+	0.808784i	$0.299874\pi$
$758$	−3.42864e9	−	1.97952e9i	−0.285943	−	0.165089i
$759$	2.61795e8	+	1.51148e8i	0.0217328	+	0.0125474i
$760$	4.40750e9	−	2.54467e9i	0.364204	−	0.210273i
$761$	−1.56453e9	−	2.70985e9i	−0.128688	−	0.222894i	0.794480	−	0.607290i	$-0.207743\pi$
$761$	−1.56453e9	−	2.70985e9i	−0.128688	−	0.222894i	−0.923169	+	0.384395i	$0.874410\pi$
$762$	1.54929e8	−	8.94484e7i	0.0126850	−	0.00732369i
$763$		−	2.72643e9i		−	0.222207i
$764$	1.28288e10	+	7.40669e9i	1.04078	+	0.600893i
$765$	−4.62278e9	−	8.00689e9i	−0.373326	−	0.646620i
$766$	−9.56547e8			−0.0768963
$767$	4.89872e9			0.392012
$768$	5.37086e8	+	9.30261e8i	0.0427839	+	0.0741038i
$769$			1.72330e10i			1.36653i	0.730171	+	0.683264i	$0.239440\pi$
$769$			1.72330e10i			1.36653i	−0.730171	+	0.683264i	$0.760560\pi$
$770$	−2.82273e9	+	4.88911e9i	−0.222819	+	0.385933i
$771$		−	9.32228e7i		−	0.00732541i
$772$	−1.22011e10	−	7.04432e9i	−0.954420	−	0.551035i
$773$	−2.77719e9	+	4.81024e9i	−0.216261	+	0.374575i	−0.953662	−	0.300880i	$-0.902719\pi$
$773$	−2.77719e9	+	4.81024e9i	−0.216261	+	0.374575i	0.737401	+	0.675455i	$0.236053\pi$
$774$	−1.82965e9	+	3.16905e9i	−0.141832	+	0.245660i
$775$	2.59264e9	−	1.49686e9i	0.200072	−	0.115512i
$776$	1.68581e9			0.129506
$777$	−2.75420e9	+	1.23905e9i	−0.210631	+	0.0947581i
$778$	2.33700e9			0.177922
$779$	−1.57204e10	+	9.07615e9i	−1.19146	+	0.687893i
$780$	−3.36931e8	+	5.83581e8i	−0.0254220	+	0.0440322i
$781$	1.36623e10	−	2.36637e10i	1.02623	−	1.77748i
$782$	2.39149e8	+	1.38073e8i	0.0178832	+	0.0103249i
$783$		−	3.88108e9i		−	0.288926i
$784$	−8.95777e9	+	1.55153e10i	−0.663887	+	1.14989i
$785$		−	7.70464e9i		−	0.568471i
$786$	3.43751e8	+	5.95395e8i	0.0252502	+	0.0437347i
$787$	−8.55823e9			−0.625853			−0.312926	−	0.949777i	$-0.601309\pi$
$787$	−8.55823e9			−0.625853			−0.312926	+	0.949777i	$0.601309\pi$
$788$	1.30086e10			0.947086
$789$	4.77797e8	+	8.27568e8i	0.0346317	+	0.0599838i
$790$	−3.14497e9	−	1.81575e9i	−0.226946	−	0.131027i
$791$			1.49192e10i			1.07184i
$792$	−8.92660e9	+	5.15378e9i	−0.638481	+	0.368627i
$793$	−4.04331e9	−	7.00321e9i	−0.287926	−	0.498702i
$794$	3.90338e9	−	2.25362e9i	0.276738	−	0.159775i
$795$	−2.26570e8	−	1.30810e8i	−0.0159926	−	0.00923331i
$796$	−1.60901e9	−	9.28962e8i	−0.113074	−	0.0652833i
$797$	−6.32718e9	+	3.65300e9i	−0.442696	+	0.255591i	−0.704741	−	0.709465i	$-0.748937\pi$
$797$	−6.32718e9	+	3.65300e9i	−0.442696	+	0.255591i	0.262044	+	0.965056i	$0.415603\pi$
$798$	−4.89451e8	−	8.47754e8i	−0.0340957	−	0.0590554i
$799$	4.91493e9	−	2.83764e9i	0.340882	−	0.196808i
$800$			4.03050e9i			0.278319i
$801$	−1.49497e10	−	8.63124e9i	−1.02783	−	0.593416i
$802$	−3.22953e7	−	5.59371e7i	−0.00221070	−	0.00382904i
$803$	−2.19830e10			−1.49824
$804$	3.15911e9			0.214372
$805$	−8.05368e8	−	1.39494e9i	−0.0544138	−	0.0942474i
$806$		−	7.70345e8i		−	0.0518218i
$807$	−1.55695e9	+	2.69672e9i	−0.104284	+	0.180626i
$808$		−	2.68395e9i		−	0.178992i
$809$	1.68394e10	+	9.72224e9i	1.11817	+	0.645575i	0.940933	−	0.338594i	$-0.109951\pi$
$809$	1.68394e10	+	9.72224e9i	1.11817	+	0.645575i	0.177236	+	0.984168i	$0.443284\pi$
$810$	1.08196e9	−	1.87402e9i	0.0715344	−	0.123901i
$811$	−6.80630e9	+	1.17889e10i	−0.448062	+	0.776066i	−0.998260	−	0.0589681i	$-0.981219\pi$
$811$	−6.80630e9	+	1.17889e10i	−0.448062	+	0.776066i	0.550198	+	0.835034i	$0.314552\pi$
$812$	2.01707e10	−	1.16455e10i	1.32213	−	0.763333i
$813$	−3.16369e9			−0.206480
$814$	−2.43089e9	−	5.40345e9i	−0.157972	−	0.351144i
$815$	6.93289e9			0.448604
$816$	−1.78015e9	+	1.02777e9i	−0.114694	+	0.0662186i
$817$	−1.51699e10	+	2.62751e10i	−0.973208	+	1.68565i
$818$	−539551.	+	934530.i	−3.44664e−5	+	5.96976e-5i
$819$	−1.06455e10	−	6.14618e9i	−0.677130	−	0.390941i
$820$			1.07388e10i			0.680152i
$821$	−2.28891e9	+	3.96451e9i	−0.144354	+	0.250028i	−0.929132	−	0.369749i	$-0.879444\pi$
$821$	−2.28891e9	+	3.96451e9i	−0.144354	+	0.250028i	0.784778	+	0.619777i	$0.212777\pi$
$822$			1.92601e7i			0.00120951i
$823$	1.60784e9	+	2.78486e9i	0.100541	+	0.174142i	0.911908	−	0.410396i	$-0.134609\pi$
$823$	1.60784e9	+	2.78486e9i	0.100541	+	0.174142i	−0.811367	+	0.584537i	$0.801276\pi$
$824$	3.86147e9			0.240440
$825$	−2.02186e9			−0.125361
$826$	2.10496e9	+	3.64590e9i	0.129961	+	0.225100i
$827$	−2.54210e10	−	1.46768e10i	−1.56287	−	0.902324i	−0.996965	−	0.0778552i	$-0.975193\pi$
$827$	−2.54210e10	−	1.46768e10i	−1.56287	−	0.902324i	−0.565907	−	0.824469i	$-0.691474\pi$
$828$		−	1.43741e9i		−	0.0879982i
$829$	2.82519e9	−	1.63113e9i	0.172229	−	0.0994367i	−0.411407	−	0.911452i	$-0.634963\pi$
$829$	2.82519e9	−	1.63113e9i	0.172229	−	0.0994367i	0.583637	+	0.812015i	$0.301629\pi$
$830$	1.99954e9	+	3.46331e9i	0.121383	+	0.210241i
$831$	2.82779e8	−	1.63263e8i	0.0170940	−	0.00986924i
$832$	−5.39256e9	−	3.11340e9i	−0.324611	−	0.187414i
$833$	−2.30940e10	−	1.33333e10i	−1.38434	−	0.799246i
$834$	−4.77352e7	+	2.75600e7i	−0.00284943	+	0.00164512i
$835$	−5.72815e9	−	9.92145e9i	−0.340496	−	0.589756i
$836$	−3.61743e10	+	2.08852e10i	−2.14130	+	1.23628i
$837$			2.39935e9i			0.141434i
$838$	1.76639e9	+	1.01982e9i	0.103689	+	0.0598648i
$839$	9.19959e9	+	1.59342e10i	0.537776	+	0.931456i	0.999023	+	0.0441844i	$0.0140689\pi$
$839$	9.19959e9	+	1.59342e10i	0.537776	+	0.931456i	−0.461247	+	0.887272i	$0.652598\pi$
$840$	−1.18485e9			−0.0689740
$841$	−1.63125e8			−0.00945662
$842$	1.00451e9	+	1.73985e9i	0.0579909	+	0.100443i
$843$		−	1.17058e9i		−	0.0672986i
$844$	−5.01199e9	+	8.68103e9i	−0.286954	+	0.497019i
$845$			9.54599e9i			0.544280i
$846$	1.17626e9	+	6.79116e8i	0.0667896	+	0.0385610i
$847$	3.33465e10	−	5.77577e10i	1.88564	−	3.26602i
$848$	1.34809e9	−	2.33497e9i	0.0759163	−	0.131491i
$849$	5.68084e8	−	3.27983e8i	0.0318592	−	0.0183939i
$850$	−1.84696e9			−0.103155
$851$	1.68193e9	+	1.70194e8i	0.0935521	+	0.00946654i
$852$	2.80295e9			0.155266
$853$	4.39641e9	−	2.53827e9i	0.242536	−	0.140028i	−0.373806	−	0.927507i	$-0.621947\pi$
$853$	4.39641e9	−	2.53827e9i	0.242536	−	0.140028i	0.616342	+	0.787479i	$0.288614\pi$
$854$	3.47479e9	−	6.01851e9i	0.190909	−	0.330664i
$855$	9.17288e9	−	1.58879e10i	0.501908	−	0.869330i
$856$	−1.97060e9	−	1.13773e9i	−0.107384	−	0.0619984i
$857$		−	2.48505e10i		−	1.34866i	−0.738430	−	0.674330i	$-0.764432\pi$
$857$		−	2.48505e10i		−	1.34866i	0.738430	−	0.674330i	$-0.235568\pi$
$858$	−2.60133e8	+	4.50563e8i	−0.0140601	+	0.0243529i
$859$		−	9.87012e9i		−	0.531308i	−0.964068	−	0.265654i	$-0.914412\pi$
$859$		−	9.87012e9i		−	0.531308i	0.964068	−	0.265654i	$-0.0855879\pi$
$860$	8.97440e9	+	1.55441e10i	0.481128	+	0.833339i
$861$	4.22604e9			0.225643
$862$	5.82606e9			0.309813
$863$	−5.96227e9	−	1.03270e10i	−0.315772	−	0.546933i	0.663829	−	0.747884i	$-0.268930\pi$
$863$	−5.96227e9	−	1.03270e10i	−0.315772	−	0.546933i	−0.979601	+	0.200951i	$0.935597\pi$
$864$	−2.79751e9	−	1.61514e9i	−0.147561	−	0.0851946i
$865$			2.01551e10i			1.05884i
$866$	3.80554e9	−	2.19713e9i	0.199115	−	0.114959i
$867$	−1.35487e8	−	2.34671e8i	−0.00706043	−	0.0122290i
$868$	−1.24699e10	+	7.19948e9i	−0.647207	+	0.373665i
$869$	5.28112e10	+	3.04906e10i	2.72996	+	1.57615i
$870$	3.74953e8	+	2.16479e8i	0.0193045	+	0.0111455i
$871$	−1.30964e10	+	7.56121e9i	−0.671565	+	0.387728i
$872$	5.61311e8	+	9.72220e8i	0.0286679	+	0.0496543i
$873$	5.26275e9	−	3.03845e9i	0.267709	−	0.154562i
$874$			5.47949e8i			0.0277620i
$875$	2.91923e10	+	1.68542e10i	1.47313	+	0.850509i
$876$	−1.12751e9	−	1.95290e9i	−0.0566703	−	0.0981558i
$877$	−3.62805e10			−1.81625			−0.908123	−	0.418703i	$-0.862485\pi$
$877$	−3.62805e10			−1.81625			−0.908123	+	0.418703i	$0.862485\pi$
$878$	−7.19223e9			−0.358618
$879$	−1.17552e9	−	2.03607e9i	−0.0583808	−	0.101119i
$880$			2.35227e10i			1.16358i
$881$	−2.86314e9	+	4.95910e9i	−0.141067	+	0.244336i	−0.927899	−	0.372832i	$-0.878387\pi$
$881$	−2.86314e9	+	4.95910e9i	−0.141067	+	0.244336i	0.786832	+	0.617168i	$0.211720\pi$
$882$		−	6.38198e9i		−	0.313195i
$883$	2.17306e9	+	1.25462e9i	0.106221	+	0.0613267i	0.552169	−	0.833732i	$-0.313800\pi$
$883$	2.17306e9	+	1.25462e9i	0.106221	+	0.0613267i	−0.445948	+	0.895059i	$0.647134\pi$
$884$	5.16841e9	−	8.95194e9i	0.251637	−	0.435847i
$885$	8.51049e8	−	1.47406e9i	0.0412718	−	0.0714848i
$886$	5.06807e8	−	2.92605e8i	0.0244807	−	0.0141340i
$887$	2.04725e10			0.985004			0.492502	−	0.870311i	$-0.336082\pi$
$887$	2.04725e10			0.985004			0.492502	+	0.870311i	$0.336082\pi$
$888$	7.27029e8	−	1.00886e9i	0.0348423	−	0.0483490i
$889$	1.60068e10			0.764097
$890$	3.37145e9	−	1.94651e9i	0.160307	−	0.0925531i
$891$	−1.81686e10	+	3.14689e10i	−0.860497	+	1.49043i
$892$	−2.46757e9	+	4.27396e9i	−0.116411	+	0.201629i
$893$	9.75258e9	+	5.63066e9i	0.458289	+	0.264593i
$894$			7.64494e8i			0.0357843i
$895$	8.66190e9	−	1.50029e10i	0.403862	−	0.699509i
$896$		−	2.56281e10i		−	1.19025i
$897$	−7.42199e7	−	1.28553e8i	−0.00343358	−	0.00594713i
$898$	−4.91994e9			−0.226722
$899$	1.07650e10			0.494147
$900$	4.80696e9	+	8.32590e9i	0.219797	+	0.380699i
$901$	3.47551e9	+	2.00659e9i	0.158300	+	0.0913948i
$902$			8.29103e9i			0.376171i
$903$	6.11709e9	−	3.53170e9i	0.276464	−	0.159616i
$904$	−3.07154e9	−	5.32006e9i	−0.138282	−	0.239512i
$905$	2.60310e10	−	1.50290e10i	1.16740	−	0.674001i
$906$	4.87414e8	+	2.81408e8i	0.0217745	+	0.0125715i
$907$	8.06045e9	+	4.65371e9i	0.358702	+	0.207097i	0.668511	−	0.743702i	$-0.266932\pi$
$907$	8.06045e9	+	4.65371e9i	0.358702	+	0.207097i	−0.309809	+	0.950799i	$0.600265\pi$
$908$	3.37747e10	−	1.94998e10i	1.49724	−	0.864430i
$909$	−4.83747e9	−	8.37875e9i	−0.213622	−	0.370003i
$910$	2.40076e9	−	1.38608e9i	0.105610	−	0.0609738i
$911$		−	5.58627e9i		−	0.244798i	−0.992481	−	0.122399i	$-0.960941\pi$
$911$		−	5.58627e9i		−	0.244798i	0.992481	−	0.122399i	$-0.0390587\pi$
$912$	−3.53231e9	−	2.03938e9i	−0.154197	−	0.0890258i
$913$	−3.35768e10	−	5.81568e10i	−1.46013	−	2.52902i
$914$	−7.65699e9			−0.331701
$915$	−2.80976e9			−0.121254
$916$	−9.61764e9	−	1.66582e10i	−0.413461	−	0.716135i
$917$			6.15144e10i			2.63441i
$918$	7.40134e8	−	1.28195e9i	0.0315763	−	0.0546917i
$919$		−	1.50013e10i		−	0.637566i	−0.947828	−	0.318783i	$-0.896726\pi$
$919$		−	1.50013e10i		−	0.637566i	0.947828	−	0.318783i	$-0.103274\pi$
$920$	5.74374e8	+	3.31615e8i	0.0243185	+	0.0140403i
$921$	−2.09515e9	+	3.62891e9i	−0.0883705	+	0.153062i
$922$	4.74883e8	−	8.22522e8i	0.0199539	−	0.0345612i
$923$	−1.16199e10	+	6.70876e9i	−0.486403	+	0.280825i
$924$	9.72458e9			0.405526
$925$	−1.03114e10	+	4.63886e9i	−0.428372	+	0.192715i
$926$	7.68874e9			0.318212
$927$	1.20547e10	−	6.95980e9i	0.497025	−	0.286958i
$928$	−7.24656e9	+	1.25514e10i	−0.297655	+	0.515554i
$929$	1.80398e10	−	3.12459e10i	0.738205	−	1.27861i	−0.215098	−	0.976593i	$-0.569007\pi$
$929$	1.80398e10	−	3.12459e10i	0.738205	−	1.27861i	0.953303	−	0.302016i	$-0.0976597\pi$
$930$	−2.31802e8	−	1.33831e8i	−0.00944991	−	0.00545591i
$931$		−	5.29140e10i		−	2.14905i
$932$	−7.82367e9	+	1.35510e10i	−0.316559	+	0.548296i
$933$		−	1.59223e9i		−	0.0641831i
$934$	4.26972e9	+	7.39536e9i	0.171469	+	0.296993i
$935$	−3.50127e10			−1.40083
$936$	5.06145e9			0.201748
$937$	1.31151e10	+	2.27160e10i	0.520815	+	0.902078i	0.999707	+	0.0242043i	$0.00770521\pi$
$937$	1.31151e10	+	2.27160e10i	0.520815	+	0.902078i	−0.478892	+	0.877874i	$0.658961\pi$
$938$	−1.12549e10	−	6.49804e9i	−0.445280	−	0.257083i
$939$		−	1.19143e9i		−	0.0469610i
$940$	5.76955e9	−	3.33105e9i	0.226566	−	0.130808i
$941$	−1.17514e10	−	2.03540e10i	−0.459753	−	0.796316i	0.539194	−	0.842181i	$-0.318729\pi$
$941$	−1.17514e10	−	2.03540e10i	−0.459753	−	0.796316i	−0.998948	+	0.0458653i	$0.985395\pi$
$942$	5.28446e8	−	3.05098e8i	0.0205979	−	0.0118922i
$943$	−2.04864e9	−	1.18278e9i	−0.0795562	−	0.0459318i
$944$	1.51912e10	+	8.77067e9i	0.587748	+	0.339337i
$945$	−7.47751e9	+	4.31714e9i	−0.288234	+	0.166412i
$946$	6.92883e9	+	1.20011e10i	0.266098	+	0.460895i
$947$	−2.40817e10	+	1.39036e10i	−0.921430	+	0.531988i	−0.884091	−	0.467315i	$-0.845222\pi$
$947$	−2.40817e10	+	1.39036e10i	−0.921430	+	0.531988i	−0.0373392	+	0.999303i	$0.511888\pi$
$948$			6.25545e9i			0.238468i
$949$	9.34839e9	+	5.39729e9i	0.355063	+	0.204995i
$950$	−1.83244e9	−	3.17389e9i	−0.0693423	−	0.120104i
$951$	5.94186e8			0.0224022
$952$	1.81752e10			0.682731
$953$	1.45166e10	+	2.51435e10i	0.543300	+	0.941023i	0.998712	+	0.0507419i	$0.0161586\pi$
$953$	1.45166e10	+	2.51435e10i	0.543300	+	0.941023i	−0.455412	+	0.890281i	$0.650508\pi$
$954$			9.60452e8i			0.0358143i
$955$	−1.23192e10	+	2.13375e10i	−0.457689	+	0.792741i
$956$			1.53323e10i			0.567550i
$957$	−6.29630e9	−	3.63517e9i	−0.232217	−	0.134070i
$958$	5.66710e8	−	9.81570e8i	0.0208248	−	0.0360697i
$959$	−8.61651e8	+	1.49242e9i	−0.0315476	+	0.0546421i
$960$	−1.87369e9	+	1.08177e9i	−0.0683514	+	0.0394627i
$961$	2.08575e10			0.758106
$962$	−2.92913e8	+	2.89468e9i	−0.0106078	+	0.104831i
$963$	−8.20244e9			−0.295972
$964$	−1.04220e10	+	6.01717e9i	−0.374700	+	0.216333i
$965$	1.17165e10	−	2.02936e10i	0.419712	−	0.726963i
$966$	6.37840e7	−	1.10477e8i	0.00227663	−	0.00394323i
$967$	2.46820e10	+	1.42501e10i	0.877783	+	0.506788i	0.869927	−	0.493181i	$-0.164166\pi$
$967$	2.46820e10	+	1.42501e10i	0.877783	+	0.506788i	0.00785630	+	0.999969i	$0.497499\pi$
$968$			2.74612e10i			0.973095i
$969$	3.03554e9	−	5.25771e9i	0.107177	−	0.185636i
$970$			1.37045e9i			0.0482129i
$971$	1.68772e10	+	2.92322e10i	0.591607	+	1.02469i	0.994016	+	0.109234i	$0.0348397\pi$
$971$	1.68772e10	+	2.92322e10i	0.591607	+	1.02469i	−0.402409	+	0.915460i	$0.631827\pi$
$972$	−1.15989e10			−0.405120
$973$	−4.93186e9			−0.171639
$974$	−4.30460e9	−	7.45579e9i	−0.149271	−	0.258546i
$975$	8.59808e8	+	4.96410e8i	0.0297088	+	0.0171524i
$976$		−	2.89565e10i		−	0.996948i
$977$	−6.53104e9	+	3.77070e9i	−0.224053	+	0.129357i	−0.607826	−	0.794070i	$-0.707958\pi$
$977$	−6.53104e9	+	3.77070e9i	−0.224053	+	0.129357i	0.383772	+	0.923428i	$0.374625\pi$
$978$	2.74538e8	+	4.75513e8i	0.00938461	+	0.0162546i
$979$	−5.66142e10	+	3.26862e10i	−1.92835	+	1.11333i
$980$	−2.71096e10	−	1.56518e10i	−0.920094	−	0.531217i
$981$	3.50460e9	+	2.02338e9i	0.118521	+	0.0684284i
$982$	3.29958e9	−	1.90501e9i	0.111191	−	0.0641960i
$983$	−2.88458e10	−	4.99624e10i	−0.968603	−	1.67767i	−0.699607	−	0.714528i	$-0.746642\pi$
$983$	−2.88458e10	−	4.99624e10i	−0.968603	−	1.67767i	−0.268996	−	0.963141i	$-0.586692\pi$
$984$	−1.50697e9	+	8.70047e8i	−0.0504220	+	0.0291112i
$985$			2.16366e10i			0.721377i
$986$	−5.75165e9	−	3.32072e9i	−0.191084	−	0.110322i
$987$	−1.31087e9	−	2.27050e9i	−0.0433961	−	0.0751642i
$988$	2.05111e10			0.676612
$989$	−3.95381e9			−0.129966
$990$	−4.18970e9	−	7.25677e9i	−0.137233	−	0.237695i
$991$		−	3.21962e10i		−	1.05086i	−0.850836	−	0.525432i	$-0.823904\pi$
$991$		−	3.21962e10i		−	1.05086i	0.850836	−	0.525432i	$-0.176096\pi$
$992$	4.47995e9	−	7.75950e9i	0.145708	−	0.252373i
$993$		−	2.53625e9i		−	0.0821995i
$994$	−9.98606e9	−	5.76545e9i	−0.322509	−	0.186201i
$995$	1.54510e9	−	2.67619e9i	0.0497251	−	0.0861263i
$996$	3.44431e9	−	5.96573e9i	0.110457	−	0.191318i
$997$	−3.69344e10	+	2.13241e10i	−1.18031	+	0.681455i	−0.956087	−	0.293082i	$-0.905319\pi$
$997$	−3.69344e10	+	2.13241e10i	−1.18031	+	0.681455i	−0.224227	+	0.974537i	$0.571986\pi$
$998$	−5.57101e9			−0.177410
$999$	9.12320e8	−	9.01591e9i	0.0289513	−	0.286108i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.8.e.a.11.11	✓	40
37.27	even	6	inner	37.8.e.a.27.11	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.8.e.a.11.11	✓	40	1.1	even	1	trivial
37.8.e.a.27.11	yes	40	37.27	even	6	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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	37.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.05422 - 1.18601i) q^{2} +(3.39795 - 5.88542i) q^{3} +(-61.1868 + 105.979i) q^{4} +(-176.269 - 101.769i) q^{5} -16.1199i q^{6} +(721.166 - 1249.10i) q^{7} +593.889i q^{8} +(1070.41 + 1854.00i) q^{9} +O(q^{10})\)	\(q+(2.05422 - 1.18601i) q^{2} +(3.39795 - 5.88542i) q^{3} +(-61.1868 + 105.979i) q^{4} +(-176.269 - 101.769i) q^{5} -16.1199i q^{6} +(721.166 - 1249.10i) q^{7} +593.889i q^{8} +(1070.41 + 1854.00i) q^{9} -482.794 q^{10} +8107.21 q^{11} +(415.819 + 720.220i) q^{12} +(-3447.63 - 1990.49i) q^{13} -3421.23i q^{14} +(-1197.91 + 691.612i) q^{15} +(-7127.55 - 12345.3i) q^{16} +(18375.5 - 10609.1i) q^{17} +(4397.71 + 2539.02i) q^{18} +(36462.1 + 21051.4i) q^{19} +(21570.7 - 12453.8i) q^{20} +(-4900.97 - 8488.73i) q^{21} +(16654.0 - 9615.19i) q^{22} +5486.72i q^{23} +(3495.28 + 2018.00i) q^{24} +(-18348.6 - 31780.8i) q^{25} -9442.93 q^{26} +29411.4 q^{27} +(88251.7 + 152856. i) q^{28} -131958. i q^{29} +(-1640.51 + 2841.45i) q^{30} +81579.0i q^{31} +(-95116.4 - 54915.5i) q^{32} +(27547.9 - 47714.3i) q^{33} +(25164.9 - 43586.9i) q^{34} +(-254239. + 146785. i) q^{35} -261979. q^{36} +(31019.3 - 306545. i) q^{37} +99868.2 q^{38} +(-23429.8 + 13527.2i) q^{39} +(60439.5 - 104684. i) q^{40} +(-215571. + 373381. i) q^{41} +(-20135.4 - 11625.2i) q^{42} +720613. i q^{43} +(-496054. + 859190. i) q^{44} -435738. i q^{45} +(6507.28 + 11270.9i) q^{46} +267472. q^{47} -96876.2 q^{48} +(-628390. - 1.08840e6i) q^{49} +(-75384.3 - 43523.1i) q^{50} -144197. i q^{51} +(421899. - 243584. i) q^{52} +(94569.2 + 163799. i) q^{53} +(60417.5 - 34882.0i) q^{54} +(-1.42905e6 - 825063. i) q^{55} +(741824. + 428293. i) q^{56} +(247792. - 143063. i) q^{57} +(-156503. - 271072. i) q^{58} +(-1.06567e6 + 615265. i) q^{59} -169270. i q^{60} +(1.75917e6 + 1.01566e6i) q^{61} +(96753.1 + 167581. i) q^{62} +3.08777e6 q^{63} +1.56413e6 q^{64} +(405141. + 701725. i) q^{65} -130688. i q^{66} +(1.89933e6 - 3.28974e6i) q^{67} +2.59655e6i q^{68} +(32291.7 + 18643.6i) q^{69} +(-348175. + 603057. i) q^{70} +(1.68520e6 - 2.91885e6i) q^{71} +(-1.10107e6 + 635703. i) q^{72} -2.71154e6 q^{73} +(-299843. - 666500. i) q^{74} -249391. q^{75} +(-4.46199e6 + 2.57613e6i) q^{76} +(5.84664e6 - 1.01267e7i) q^{77} +(-32086.6 + 55575.6i) q^{78} +(6.51411e6 + 3.76092e6i) q^{79} +2.90146e6i q^{80} +(-2.24104e6 + 3.88160e6i) q^{81} +1.02267e6i q^{82} +(-4.14160e6 - 7.17347e6i) q^{83} +1.19950e6 q^{84} -4.31871e6 q^{85} +(854651. + 1.48030e6i) q^{86} +(-776630. - 448388. i) q^{87} +4.81478e6i q^{88} +(-6.98320e6 + 4.03175e6i) q^{89} +(-516787. - 895101. i) q^{90} +(-4.97264e6 + 2.87095e6i) q^{91} +(-581475. - 335715. i) q^{92} +(480126. + 277201. i) q^{93} +(549447. - 317223. i) q^{94} +(-4.28476e6 - 7.42142e6i) q^{95} +(-646401. + 373200. i) q^{96} -2.83859e6i q^{97} +(-2.58171e6 - 1.49055e6i) q^{98} +(8.67802e6 + 1.50308e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 18 q^{2} - 42 q^{3} + 1114 q^{4} - 672 q^{5} + 156 q^{7} - 9128 q^{9}+O(q^{10}) \) 40 * q + 18 * q^2 - 42 * q^3 + 1114 * q^4 - 672 * q^5 + 156 * q^7 - 9128 * q^9	\( 40 q + 18 q^{2} - 42 q^{3} + 1114 q^{4} - 672 q^{5} + 156 q^{7} - 9128 q^{9} - 5124 q^{10} + 12468 q^{11} + 6926 q^{12} + 10512 q^{13} + 36402 q^{15} - 31094 q^{16} - 22440 q^{17} - 153504 q^{18} + 49086 q^{19} + 28662 q^{20} + 7736 q^{21} + 132018 q^{22} + 2754 q^{24} + 72328 q^{25} - 680244 q^{26} + 42984 q^{27} + 105488 q^{28} + 382084 q^{30} + 523656 q^{32} + 9228 q^{33} + 276914 q^{34} - 904452 q^{35} - 204828 q^{36} + 1333776 q^{37} + 50208 q^{38} + 122040 q^{39} - 1205236 q^{40} - 871440 q^{41} + 1436094 q^{42} - 994326 q^{44} - 987942 q^{46} - 586932 q^{47} + 3984388 q^{48} - 1766072 q^{49} + 1818708 q^{50} - 2745228 q^{52} + 1661988 q^{53} + 1102554 q^{54} - 2733258 q^{55} - 5943924 q^{56} + 3920592 q^{57} + 5021672 q^{58} + 5296632 q^{59} - 4588524 q^{61} - 8143398 q^{62} - 2503648 q^{63} + 10662964 q^{64} - 1652736 q^{65} + 1940622 q^{67} - 10266552 q^{69} - 5038546 q^{70} + 6420528 q^{71} - 6576036 q^{72} - 3313032 q^{73} + 16192386 q^{74} - 5168536 q^{75} + 10328022 q^{76} - 8599404 q^{77} + 18210222 q^{78} - 15094374 q^{79} + 1733956 q^{81} - 191670 q^{83} + 1175224 q^{84} - 18053592 q^{85} + 18575940 q^{86} - 3762762 q^{87} - 14873004 q^{89} + 37293212 q^{90} - 76496700 q^{91} + 27846618 q^{92} + 26687652 q^{93} + 35421402 q^{94} + 14310774 q^{95} - 30894534 q^{96} - 13793868 q^{98} - 37141758 q^{99}+O(q^{100}) \) 40 * q + 18 * q^2 - 42 * q^3 + 1114 * q^4 - 672 * q^5 + 156 * q^7 - 9128 * q^9 - 5124 * q^10 + 12468 * q^11 + 6926 * q^12 + 10512 * q^13 + 36402 * q^15 - 31094 * q^16 - 22440 * q^17 - 153504 * q^18 + 49086 * q^19 + 28662 * q^20 + 7736 * q^21 + 132018 * q^22 + 2754 * q^24 + 72328 * q^25 - 680244 * q^26 + 42984 * q^27 + 105488 * q^28 + 382084 * q^30 + 523656 * q^32 + 9228 * q^33 + 276914 * q^34 - 904452 * q^35 - 204828 * q^36 + 1333776 * q^37 + 50208 * q^38 + 122040 * q^39 - 1205236 * q^40 - 871440 * q^41 + 1436094 * q^42 - 994326 * q^44 - 987942 * q^46 - 586932 * q^47 + 3984388 * q^48 - 1766072 * q^49 + 1818708 * q^50 - 2745228 * q^52 + 1661988 * q^53 + 1102554 * q^54 - 2733258 * q^55 - 5943924 * q^56 + 3920592 * q^57 + 5021672 * q^58 + 5296632 * q^59 - 4588524 * q^61 - 8143398 * q^62 - 2503648 * q^63 + 10662964 * q^64 - 1652736 * q^65 + 1940622 * q^67 - 10266552 * q^69 - 5038546 * q^70 + 6420528 * q^71 - 6576036 * q^72 - 3313032 * q^73 + 16192386 * q^74 - 5168536 * q^75 + 10328022 * q^76 - 8599404 * q^77 + 18210222 * q^78 - 15094374 * q^79 + 1733956 * q^81 - 191670 * q^83 + 1175224 * q^84 - 18053592 * q^85 + 18575940 * q^86 - 3762762 * q^87 - 14873004 * q^89 + 37293212 * q^90 - 76496700 * q^91 + 27846618 * q^92 + 26687652 * q^93 + 35421402 * q^94 + 14310774 * q^95 - 30894534 * q^96 - 13793868 * q^98 - 37141758 * q^99

Introduction

L-functions

Modular forms

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