LMFDB - Embedded newform 21.6.g.c.5.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,6,Mod(5,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("21.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	21.g (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:	$3.36806021607$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 171 x^{14} + 21495 x^{12} - 1128902 x^{10} + 42970860 x^{8} - 655075344 x^{6} + \cdots + 90230547456 $ x^16 - 171x^14 + 21495x^12 - 1128902x^10 + 42970860x^8 - 655075344x^6 + 7244325760x^4 - 29387167488*x^2 + 90230547456
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.3
Root			$-3.16536 - 1.82752i$ of defining polynomial
Character	$\chi$	$=$	21.5
Dual form			21.6.g.c.17.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.16536 - 1.82752i) q^{2} +(7.01741 + 13.9196i) q^{3} +(-9.32032 - 16.1433i) q^{4} +(-37.1622 + 64.3668i) q^{5} +(3.22580 - 56.8851i) q^{6} +(45.3051 + 121.468i) q^{7} +185.094i q^{8} +(-144.512 + 195.359i) q^{9} +O(q^{10})$	\(q+(-3.16536 - 1.82752i) q^{2} +(7.01741 + 13.9196i) q^{3} +(-9.32032 - 16.1433i) q^{4} +(-37.1622 + 64.3668i) q^{5} +(3.22580 - 56.8851i) q^{6} +(45.3051 + 121.468i) q^{7} +185.094i q^{8} +(-144.512 + 195.359i) q^{9} +(235.264 - 135.830i) q^{10} +(-34.1140 + 19.6957i) q^{11} +(159.304 - 243.019i) q^{12} -589.288i q^{13} +(78.5784 - 467.286i) q^{14} +(-1156.74 - 65.5958i) q^{15} +(40.0132 - 69.3048i) q^{16} +(-618.755 - 1071.71i) q^{17} +(814.457 - 354.284i) q^{18} +(2396.97 + 1383.89i) q^{19} +1385.45 q^{20} +(-1372.86 + 1483.02i) q^{21} +143.977 q^{22} +(401.189 + 231.627i) q^{23} +(-2576.44 + 1298.88i) q^{24} +(-1199.56 - 2077.69i) q^{25} +(-1076.94 + 1865.31i) q^{26} +(-3733.43 - 640.637i) q^{27} +(1538.63 - 1863.49i) q^{28} +5294.57i q^{29} +(3541.64 + 2321.61i) q^{30} +(2465.35 - 1423.37i) q^{31} +(4876.16 - 2815.25i) q^{32} +(-513.548 - 336.641i) q^{33} +4523.16i q^{34} +(-9502.13 - 1597.87i) q^{35} +(4500.64 + 512.084i) q^{36} +(-3923.56 + 6795.80i) q^{37} +(-5058.19 - 8761.05i) q^{38} +(8202.67 - 4135.28i) q^{39} +(-11913.9 - 6878.49i) q^{40} +12162.5 q^{41} +(7055.86 - 2185.35i) q^{42} +5350.18 q^{43} +(635.906 + 367.140i) q^{44} +(-7204.27 - 16561.8i) q^{45} +(-846.606 - 1466.37i) q^{46} +(-3377.99 + 5850.86i) q^{47} +(1245.49 + 70.6281i) q^{48} +(-12701.9 + 11006.2i) q^{49} +8768.86i q^{50} +(10575.8 - 16133.5i) q^{51} +(-9513.04 + 5492.35i) q^{52} +(13866.6 - 8005.88i) q^{53} +(10646.9 + 8850.78i) q^{54} -2927.74i q^{55} +(-22483.0 + 8385.69i) q^{56} +(-2442.74 + 43076.3i) q^{57} +(9675.96 - 16759.2i) q^{58} +(-3873.32 - 6708.79i) q^{59} +(9722.29 + 19285.0i) q^{60} +(4864.96 + 2808.79i) q^{61} -10405.0 q^{62} +(-30277.0 - 8702.80i) q^{63} -23140.6 q^{64} +(37930.6 + 21899.2i) q^{65} +(1010.35 + 2004.11i) q^{66} +(6443.69 + 11160.8i) q^{67} +(-11534.0 + 19977.4i) q^{68} +(-408.849 + 7209.82i) q^{69} +(27157.6 + 22423.2i) q^{70} -60637.7i q^{71} +(-36159.8 - 26748.3i) q^{72} +(44722.8 - 25820.7i) q^{73} +(24839.0 - 14340.8i) q^{74} +(20502.9 - 31277.4i) q^{75} -51593.3i q^{76} +(-3937.93 - 3251.44i) q^{77} +(-33521.7 - 1900.93i) q^{78} +(-33686.1 + 58346.0i) q^{79} +(2973.95 + 5151.04i) q^{80} +(-17281.6 - 56463.5i) q^{81} +(-38498.7 - 22227.2i) q^{82} -8712.06 q^{83} +(36736.3 + 8340.29i) q^{84} +91977.1 q^{85} +(-16935.3 - 9777.57i) q^{86} +(-73698.5 + 37154.2i) q^{87} +(-3645.55 - 6314.28i) q^{88} +(9056.02 - 15685.5i) q^{89} +(-7462.85 + 65589.9i) q^{90} +(71579.6 - 26697.8i) q^{91} -8635.34i q^{92} +(37113.1 + 24328.4i) q^{93} +(21385.2 - 12346.7i) q^{94} +(-178153. + 102857. i) q^{95} +(73405.3 + 48118.6i) q^{96} +18641.1i q^{97} +(60320.3 - 11625.7i) q^{98} +(1082.14 - 9510.75i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 18 q^{3} + 86 q^{4} - 616 q^{7} - 606 q^{9}+O(q^{10}) $ 16 * q + 18 * q^3 + 86 * q^4 - 616 * q^7 - 606 * q^9	$ 16 q + 18 q^{3} + 86 q^{4} - 616 q^{7} - 606 q^{9} - 546 q^{10} + 4128 q^{12} + 1188 q^{15} - 2858 q^{16} - 438 q^{18} + 3258 q^{19} + 882 q^{21} - 21900 q^{22} + 10374 q^{24} - 6578 q^{25} + 34006 q^{28} + 450 q^{30} - 9792 q^{31} + 17556 q^{33} - 15132 q^{36} - 10466 q^{37} - 17418 q^{39} - 60774 q^{40} - 56994 q^{42} + 111052 q^{43} - 31374 q^{45} + 81696 q^{46} - 51548 q^{49} + 31596 q^{51} + 126960 q^{52} + 7434 q^{54} - 31368 q^{57} - 41706 q^{58} + 60066 q^{60} - 128580 q^{61} - 123606 q^{63} - 158884 q^{64} - 160314 q^{66} - 102202 q^{67} + 234318 q^{70} + 330864 q^{72} + 345150 q^{73} + 428202 q^{75} - 277512 q^{78} - 251308 q^{79} + 179262 q^{81} - 534576 q^{82} + 106176 q^{84} + 205152 q^{85} - 551922 q^{87} - 359514 q^{88} + 65814 q^{91} + 17676 q^{93} + 276612 q^{94} + 1043910 q^{96} + 215472 q^{99}+O(q^{100}) $ 16 * q + 18 * q^3 + 86 * q^4 - 616 * q^7 - 606 * q^9 - 546 * q^10 + 4128 * q^12 + 1188 * q^15 - 2858 * q^16 - 438 * q^18 + 3258 * q^19 + 882 * q^21 - 21900 * q^22 + 10374 * q^24 - 6578 * q^25 + 34006 * q^28 + 450 * q^30 - 9792 * q^31 + 17556 * q^33 - 15132 * q^36 - 10466 * q^37 - 17418 * q^39 - 60774 * q^40 - 56994 * q^42 + 111052 * q^43 - 31374 * q^45 + 81696 * q^46 - 51548 * q^49 + 31596 * q^51 + 126960 * q^52 + 7434 * q^54 - 31368 * q^57 - 41706 * q^58 + 60066 * q^60 - 128580 * q^61 - 123606 * q^63 - 158884 * q^64 - 160314 * q^66 - 102202 * q^67 + 234318 * q^70 + 330864 * q^72 + 345150 * q^73 + 428202 * q^75 - 277512 * q^78 - 251308 * q^79 + 179262 * q^81 - 534576 * q^82 + 106176 * q^84 + 205152 * q^85 - 551922 * q^87 - 359514 * q^88 + 65814 * q^91 + 17676 * q^93 + 276612 * q^94 + 1043910 * q^96 + 215472 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−3.16536	−	1.82752i	−0.559562	−	0.323064i	0.193407	−	0.981119i	$-0.438046\pi$
$2$	−3.16536	−	1.82752i	−0.559562	−	0.323064i	−0.752970	+	0.658055i	$0.771379\pi$
$3$	7.01741	+	13.9196i	0.450167	+	0.892944i
$3$	7.01741	+	13.9196i	0.450167	+	0.892944i
$4$	−9.32032	−	16.1433i	−0.291260	−	0.504477i
$5$	−37.1622	+	64.3668i	−0.664777	+	1.15143i	0.314568	+	0.949235i	$0.398140\pi$
$5$	−37.1622	+	64.3668i	−0.664777	+	1.15143i	−0.979346	+	0.202193i	$0.935193\pi$
$6$	3.22580	−	56.8851i	0.0365813	−	0.645091i
$7$	45.3051	+	121.468i	0.349463	+	0.936950i
$7$	45.3051	+	121.468i	0.349463	+	0.936950i
$8$			185.094i			1.02251i
$9$	−144.512	+	195.359i	−0.594700	+	0.803948i
$10$	235.264	−	135.830i	0.743969	−	0.429531i
$11$	−34.1140	+	19.6957i	−0.0850062	+	0.0490783i	−0.541901	−	0.840443i	$-0.682295\pi$
$11$	−34.1140	+	19.6957i	−0.0850062	+	0.0490783i	0.456894	+	0.889521i	$0.348962\pi$
$12$	159.304	−	243.019i	0.319354	−	0.487178i
$13$		−	589.288i		−	0.967096i	−0.875318	−	0.483548i	$-0.839348\pi$
$13$		−	589.288i		−	0.967096i	0.875318	−	0.483548i	$-0.160652\pi$
$14$	78.5784	−	467.286i	0.107148	−	0.637181i
$15$	−1156.74	−	65.5958i	−1.32742	−	0.0752745i
$16$	40.0132	−	69.3048i	0.0390753	−	0.0676805i
$17$	−618.755	−	1071.71i	−0.519274	−	0.899409i	−0.999749	−	0.0224003i	$-0.992869\pi$
$17$	−618.755	−	1071.71i	−0.519274	−	0.899409i	0.480475	−	0.877008i	$-0.340464\pi$
$18$	814.457	−	354.284i	0.592498	−	0.257733i
$19$	2396.97	+	1383.89i	1.52328	+	0.879465i	0.999621	+	0.0275354i	$0.00876591\pi$
$19$	2396.97	+	1383.89i	1.52328	+	0.879465i	0.523657	+	0.851929i	$0.324567\pi$
$20$	1385.45			0.774492
$21$	−1372.86	+	1483.02i	−0.679327	+	0.733835i
$22$	143.977			0.0634217
$23$	401.189	+	231.627i	0.158136	+	0.0912997i	0.576980	−	0.816759i	$-0.304231\pi$
$23$	401.189	+	231.627i	0.158136	+	0.0912997i	−0.418844	+	0.908058i	$0.637565\pi$
$24$	−2576.44	+	1298.88i	−0.913044	+	0.460300i
$25$	−1199.56	−	2077.69i	−0.383858	−	0.664861i
$26$	−1076.94	+	1865.31i	−0.312433	+	0.541150i
$27$	−3733.43	−	640.637i	−0.985595	−	0.169123i
$28$	1538.63	−	1863.49i	0.370885	−	0.449192i
$29$			5294.57i			1.16906i	0.811373	+	0.584529i	$0.198721\pi$
$29$			5294.57i			1.16906i	−0.811373	+	0.584529i	$0.801279\pi$
$30$	3541.64	+	2321.61i	0.718457	+	0.470962i
$31$	2465.35	−	1423.37i	0.460759	−	0.266019i	−0.251604	−	0.967830i	$-0.580958\pi$
$31$	2465.35	−	1423.37i	0.460759	−	0.266019i	0.712363	+	0.701811i	$0.247625\pi$
$32$	4876.16	−	2815.25i	0.841788	−	0.486007i
$33$	−513.548	−	336.641i	−0.0820912	−	0.0538123i
$34$			4523.16i			0.671034i
$35$	−9502.13	−	1597.87i	−1.31115	−	0.220481i
$36$	4500.64	+	512.084i	0.578785	+	0.0658545i
$37$	−3923.56	+	6795.80i	−0.471168	+	0.816087i	−0.999456	−	0.0329784i	$-0.989501\pi$
$37$	−3923.56	+	6795.80i	−0.471168	+	0.816087i	0.528288	+	0.849065i	$0.322834\pi$
$38$	−5058.19	−	8761.05i	−0.568246	−	0.984231i
$39$	8202.67	−	4135.28i	0.863563	−	0.435354i
$40$	−11913.9	−	6878.49i	−1.17735	−	0.679741i
$41$	12162.5			1.12996			0.564980	−	0.825105i	$-0.308884\pi$
$41$	12162.5			1.12996			0.564980	+	0.825105i	$0.308884\pi$
$42$	7055.86	−	2185.35i	0.617201	−	0.191161i
$43$	5350.18			0.441262			0.220631	−	0.975357i	$-0.429188\pi$
$43$	5350.18			0.441262			0.220631	+	0.975357i	$0.429188\pi$
$44$	635.906	+	367.140i	0.0495178	+	0.0285891i
$45$	−7204.27	−	16561.8i	−0.530345	−	1.21920i
$46$	−846.606	−	1466.37i	−0.0589912	−	0.102176i
$47$	−3377.99	+	5850.86i	−0.223056	+	0.386345i	−0.955734	−	0.294230i	$-0.904937\pi$
$47$	−3377.99	+	5850.86i	−0.223056	+	0.386345i	0.732678	+	0.680575i	$0.238270\pi$
$48$	1245.49	+	70.6281i	0.0780253	+	0.00442460i
$49$	−12701.9	+	11006.2i	−0.755751	+	0.654860i
$50$			8768.86i			0.496042i
$51$	10575.8	−	16133.5i	0.569362	−	0.868567i
$52$	−9513.04	+	5492.35i	−0.487878	+	0.281676i
$53$	13866.6	−	8005.88i	0.678078	−	0.391489i	−0.121052	−	0.992646i	$-0.538627\pi$
$53$	13866.6	−	8005.88i	0.678078	−	0.391489i	0.799131	+	0.601157i	$0.205294\pi$
$54$	10646.9	+	8850.78i	0.496864	+	0.413045i
$55$		−	2927.74i		−	0.130505i
$56$	−22483.0	+	8385.69i	−0.958040	+	0.357329i
$57$	−2442.74	+	43076.3i	−0.0995841	+	1.75611i
$58$	9675.96	−	16759.2i	0.377680	−	0.654161i
$59$	−3873.32	−	6708.79i	−0.144862	−	0.250908i	0.784460	−	0.620180i	$-0.212940\pi$
$59$	−3873.32	−	6708.79i	−0.144862	−	0.250908i	−0.929321	+	0.369272i	$0.879607\pi$
$60$	9722.29	+	19285.0i	0.348651	+	0.691578i
$61$	4864.96	+	2808.79i	0.167400	+	0.0966484i	0.581359	−	0.813647i	$-0.302521\pi$
$61$	4864.96	+	2808.79i	0.167400	+	0.0966484i	−0.413959	+	0.910295i	$0.635854\pi$
$62$	−10405.0			−0.343765
$63$	−30277.0	−	8702.80i	−0.961085	−	0.276253i
$64$	−23140.6			−0.706195
$65$	37930.6	+	21899.2i	1.11354	+	0.642903i
$66$	1010.35	+	2004.11i	0.0285503	+	0.0566320i
$67$	6443.69	+	11160.8i	0.175367	+	0.303745i	0.940288	−	0.340379i	$-0.110555\pi$
$67$	6443.69	+	11160.8i	0.175367	+	0.303745i	−0.764921	+	0.644124i	$0.777222\pi$
$68$	−11534.0	+	19977.4i	−0.302487	+	0.523923i
$69$	−408.849	+	7209.82i	−0.0103381	+	0.182306i
$70$	27157.6	+	22423.2i	0.662439	+	0.546956i
$71$		−	60637.7i		−	1.42757i	−0.700366	−	0.713784i	$-0.746980\pi$
$71$		−	60637.7i		−	1.42757i	0.700366	−	0.713784i	$-0.253020\pi$
$72$	−36159.8	−	26748.3i	−0.822044	−	0.608086i
$73$	44722.8	−	25820.7i	0.982249	−	0.567101i	0.0793003	−	0.996851i	$-0.474731\pi$
$73$	44722.8	−	25820.7i	0.982249	−	0.567101i	0.902948	+	0.429749i	$0.141398\pi$
$74$	24839.0	−	14340.8i	0.527296	−	0.304434i
$75$	20502.9	−	31277.4i	0.420884	−	0.642062i
$76$		−	51593.3i		−	1.02461i
$77$	−3937.93	−	3251.44i	−0.0756905	−	0.0624954i
$78$	−33521.7	−	1900.93i	−0.623864	−	0.0353776i
$79$	−33686.1	+	58346.0i	−0.607272	+	1.05183i	0.384417	+	0.923160i	$0.374403\pi$
$79$	−33686.1	+	58346.0i	−0.607272	+	1.05183i	−0.991688	+	0.128665i	$0.958931\pi$
$80$	2973.95	+	5151.04i	0.0519528	+	0.0899849i
$81$	−17281.6	−	56463.5i	−0.292665	−	0.956215i
$82$	−38498.7	−	22227.2i	−0.632283	−	0.365049i
$83$	−8712.06			−0.138812			−0.0694058	−	0.997589i	$-0.522110\pi$
$83$	−8712.06			−0.138812			−0.0694058	+	0.997589i	$0.522110\pi$
$84$	36736.3	+	8340.29i	0.568064	+	0.128968i
$85$	91977.1			1.38081
$86$	−16935.3	−	9777.57i	−0.246914	−	0.142556i
$87$	−73698.5	+	37154.2i	−1.04390	+	0.526271i
$88$	−3645.55	−	6314.28i	−0.0501830	−	0.0869196i
$89$	9056.02	−	15685.5i	0.121189	−	0.209905i	−0.799048	−	0.601267i	$-0.794663\pi$
$89$	9056.02	−	15685.5i	0.121189	−	0.209905i	0.920237	+	0.391362i	$0.127996\pi$
$90$	−7462.85	+	65589.9i	−0.0971177	+	0.853554i
$91$	71579.6	−	26697.8i	0.906120	−	0.337965i
$92$		−	8635.34i		−	0.106368i
$93$	37113.1	+	24328.4i	0.444959	+	0.291679i
$94$	21385.2	−	12346.7i	0.249628	−	0.144123i
$95$	−178153.	+	102857.i	−2.02528	+	1.16930i
$96$	73405.3	+	48118.6i	0.812922	+	0.532886i
$97$			18641.1i			0.201160i	0.994929	+	0.100580i	$0.0320698\pi$
$97$			18641.1i			0.201160i	−0.994929	+	0.100580i	$0.967930\pi$
$98$	60320.3	−	11625.7i	0.634451	−	0.122279i
$99$	1082.14	−	9510.75i	0.0110967	−	0.0975274i
$100$	−22360.5	+	38729.5i	−0.223605	+	0.387295i
$101$	85299.1	+	147742.i	0.832034	+	1.44113i	0.896423	+	0.443200i	$0.146157\pi$
$101$	85299.1	+	147742.i	0.832034	+	1.44113i	−0.0643885	+	0.997925i	$0.520510\pi$
$102$	−62960.6	+	31740.8i	−0.599196	+	0.302077i
$103$	−50998.3	−	29443.9i	−0.473656	−	0.273465i	0.244113	−	0.969747i	$-0.421503\pi$
$103$	−50998.3	−	29443.9i	−0.473656	−	0.273465i	−0.717769	+	0.696282i	$0.754837\pi$
$104$	109074.			0.988864
$105$	−44438.6	−	143479.i	−0.393357	−	1.27003i
$106$	−58523.7			−0.505903
$107$	−127810.	−	73791.2i	−1.07921	−	0.623082i	−0.148526	−	0.988908i	$-0.547453\pi$
$107$	−127810.	−	73791.2i	−1.07921	−	0.623082i	−0.930683	+	0.365827i	$0.880786\pi$
$108$	24454.8	+	66240.7i	0.201746	+	0.546469i
$109$	−13078.0	−	22651.8i	−0.105433	−	0.182615i	0.808482	−	0.588521i	$-0.200289\pi$
$109$	−13078.0	−	22651.8i	−0.105433	−	0.182615i	−0.913915	+	0.405906i	$0.866956\pi$
$110$	−5350.52	+	9267.36i	−0.0421613	+	0.0730255i
$111$	−122128.	−	6925.56i	−0.940824	−	0.0533516i
$112$	10231.1	+	1720.45i	0.0770686	+	0.0129598i
$113$		−	19094.4i		−	0.140672i	−0.997523	−	0.0703362i	$-0.977593\pi$
$113$		−	19094.4i		−	0.140672i	0.997523	−	0.0703362i	$-0.0224072\pi$
$114$	86455.1	−	131888.i	0.623058	−	0.950480i
$115$	−29818.1	+	17215.5i	−0.210250	+	0.121388i
$116$	85471.7	−	49347.1i	0.589763	−	0.340500i
$117$	115123.	+	85159.2i	0.777495	+	0.575131i
$118$			28314.3i			0.187198i
$119$	102146.	−	123713.i	0.661234	−	0.800844i
$120$	12141.4	−	214106.i	0.0769688	−	1.35730i
$121$	−79749.7	+	138130.i	−0.495183	+	0.857681i
$122$	−10266.3	−	17781.7i	−0.0624471	−	0.108162i
$123$	85349.1	+	169297.i	0.508670	+	1.00899i
$124$	−45955.7	−	26532.5i	−0.268401	−	0.154962i
$125$	−53951.2			−0.308835
$126$	79933.2	+	82879.5i	0.448540	+	0.465072i
$127$	−42178.1			−0.232048			−0.116024	−	0.993246i	$-0.537015\pi$
$127$	−42178.1			−0.232048			−0.116024	+	0.993246i	$0.537015\pi$
$128$	−82788.7	−	47798.1i	−0.446628	−	0.257861i
$129$	37544.4	+	74472.5i	0.198642	+	0.394023i
$130$	−80042.7	−	138638.i	−0.415397	−	0.719489i
$131$	141536.	−	245147.i	0.720590	−	1.24810i	−0.240173	−	0.970730i	$-0.577204\pi$
$131$	141536.	−	245147.i	0.720590	−	1.24810i	0.960763	−	0.277369i	$-0.0894625\pi$
$132$	−648.048	+	11427.9i	−0.00323722	+	0.0570865i
$133$	−59503.5	+	353853.i	−0.291685	+	1.73458i
$134$		−	47104.0i		−	0.226619i
$135$	179978.	−	216501.i	0.849934	−	1.02241i
$136$	198368.	−	114528.i	0.919653	−	0.530962i
$137$	−228359.	+	131843.i	−1.03948	+	0.600145i	−0.919686	−	0.392654i	$-0.871557\pi$
$137$	−228359.	+	131843.i	−1.03948	+	0.600145i	−0.119795	+	0.992799i	$0.538224\pi$
$138$	14470.3	−	22074.5i	0.0646814	−	0.0986720i
$139$		−	363744.i		−	1.59683i	−0.602108	−	0.798415i	$-0.705672\pi$
$139$		−	363744.i		−	1.59683i	0.602108	−	0.798415i	$-0.294328\pi$
$140$	62768.1	+	168288.i	0.270657	+	0.725660i
$141$	−105147.	−	5962.57i	−0.445397	−	0.0252572i
$142$	−110817.	+	191940.i	−0.461195	+	0.798813i
$143$	11606.4	+	20103.0i	0.0474634	+	0.0822091i
$144$	7756.96	+	17832.3i	0.0311735	+	0.0716641i
$145$	−340795.	−	196758.i	−1.34609	−	0.777163i
$146$	−188752.			−0.732839
$147$	−242337.	−	99570.5i	−0.924967	−	0.380047i
$148$	146275.			0.548929
$149$	334179.	+	192939.i	1.23314	+	0.711957i	0.967684	−	0.252165i	$-0.0811426\pi$
$149$	334179.	+	192939.i	1.23314	+	0.711957i	0.265461	+	0.964122i	$0.414476\pi$
$150$	−122059.	+	61534.7i	−0.442938	+	0.223302i
$151$	138266.	+	239484.i	0.493485	+	0.854741i	0.999972	−	0.00750641i	$-0.00238939\pi$
$151$	138266.	+	239484.i	0.493485	+	0.854741i	−0.506487	+	0.862248i	$0.669056\pi$
$152$	−256150.	+	443665.i	−0.899260	+	1.55756i
$153$	298787.	+	33996.1i	1.03189	+	0.117409i
$154$	6522.91	+	17488.6i	0.0221636	+	0.0594229i
$155$			211582.i			0.707375i
$156$	−143208.	−	93875.8i	−0.471148	−	0.308846i
$157$	328216.	−	189496.i	1.06270	−	0.613550i	0.136522	−	0.990637i	$-0.456408\pi$
$157$	328216.	−	189496.i	1.06270	−	0.613550i	0.926178	+	0.377087i	$0.123074\pi$
$158$	213257.	−	123124.i	0.679613	−	0.392375i
$159$	208746.	+	136837.i	0.654826	+	0.429251i
$160$			418484.i			1.29235i
$161$	−9959.30	+	59225.5i	−0.0302806	+	0.180071i
$162$	−48486.0	+	210310.i	−0.145154	+	0.629611i
$163$	115756.	−	200496.i	0.341252	−	0.591067i	−0.643413	−	0.765519i	$-0.722482\pi$
$163$	115756.	−	200496.i	0.341252	−	0.591067i	0.984666	+	0.174453i	$0.0558156\pi$
$164$	−113358.	−	196342.i	−0.329112	−	0.570038i
$165$	40753.1	−	20545.2i	0.116533	−	0.0587489i
$166$	27576.8	+	15921.5i	0.0776737	+	0.0448449i
$167$	−173708.			−0.481981			−0.240990	−	0.970527i	$-0.577472\pi$
$167$	−173708.			−0.481981			−0.240990	+	0.970527i	$0.577472\pi$
$168$	−274498.	−	254109.i	−0.750353	−	0.694618i
$169$	24032.3			0.0647260
$170$	−291141.	−	168090.i	−0.772647	−	0.446088i
$171$	−616748.	+	268282.i	−1.61294	+	0.701619i
$172$	−49865.4	−	86369.3i	−0.128522	−	0.222607i
$173$	245255.	−	424794.i	0.623021	−	1.07910i	−0.365899	−	0.930655i	$-0.619238\pi$
$173$	245255.	−	424794.i	0.623021	−	1.07910i	0.988920	−	0.148450i	$-0.0474283\pi$
$174$	301183.	+	17079.2i	0.754148	+	0.0427657i
$175$	198027.	−	239838.i	0.488798	−	0.592000i
$176$			3152.35i			0.00767101i
$177$	66203.2	−	100993.i	0.158835	−	0.242304i
$178$	−57331.2	+	33100.2i	−0.135625	+	0.0783034i
$179$	555400.	−	320660.i	1.29561	−	0.748019i	0.315965	−	0.948771i	$-0.397672\pi$
$179$	555400.	−	320660.i	1.29561	−	0.748019i	0.979642	+	0.200752i	$0.0643385\pi$
$180$	−200215.	+	270661.i	−0.460590	+	0.622651i
$181$		−	46939.3i		−	0.106498i	−0.998581	−	0.0532489i	$-0.983042\pi$
$181$		−	46939.3i		−	0.106498i	0.998581	−	0.0532489i	$-0.0169577\pi$
$182$	−275366.	−	46305.3i	−0.616215	−	0.103622i
$183$	−4957.85	+	87428.9i	−0.0109437	+	0.192987i
$184$	−42872.7	+	74257.7i	−0.0933547	+	0.161695i
$185$	−291616.	−	505094.i	−0.626443	−	1.08503i
$186$	−73015.8	−	144833.i	−0.154751	−	0.306963i
$187$	42216.4	+	24373.6i	0.0882829	+	0.0509702i
$188$	125936.			0.259869
$189$	−91326.4	−	482516.i	−0.185970	−	0.982555i
$190$	751894.			1.51103
$191$	659392.	+	380700.i	1.30786	+	0.755091i	0.981738	−	0.190238i	$-0.0609259\pi$
$191$	659392.	+	380700.i	1.30786	+	0.755091i	0.326118	+	0.945329i	$0.394259\pi$
$192$	−162387.	−	322108.i	−0.317906	−	0.630593i
$193$	−278157.	−	481782.i	−0.537522	−	0.931015i	−0.999037	−	0.0438828i	$-0.986027\pi$
$193$	−278157.	−	481782.i	−0.537522	−	0.931015i	0.461515	−	0.887133i	$-0.347306\pi$
$194$	34067.0	−	59005.7i	0.0649874	−	0.112561i
$195$	−38654.8	+	681656.i	−0.0727976	+	1.28374i
$196$	296062.	+	102469.i	0.550481	+	0.190524i
$197$			545896.i			1.00218i	0.865396	+	0.501088i	$0.167067\pi$
$197$			545896.i			1.00218i	−0.865396	+	0.501088i	$0.832933\pi$
$198$	−20806.5	+	28127.3i	−0.0377168	+	0.0509877i
$199$	−182905.	+	105600.i	−0.327411	+	0.189031i	−0.654691	−	0.755897i	$-0.727201\pi$
$199$	−182905.	+	105600.i	−0.327411	+	0.189031i	0.327280	+	0.944927i	$0.393868\pi$
$200$	384568.	−	222030.i	0.679827	−	0.392498i
$201$	−110136.	+	168014.i	−0.192283	+	0.293329i
$202$		−	623544.i		−	1.07520i
$203$	−643121.	+	239871.i	−1.09535	+	0.408543i
$204$	−359017.	−	20358.9i	−0.604004	−	0.0342514i
$205$	−451985.	+	782860.i	−0.751171	+	1.30107i
$206$	107619.	+	186401.i	0.176693	+	0.306042i
$207$	−103227.	+	44903.2i	−0.167443	+	0.0728370i
$208$	−40840.5	−	23579.3i	−0.0654535	−	0.0377896i
$209$	−109027.			−0.172651
$210$	−121547.	+	535376.i	−0.190194	+	0.837743i
$211$	−670640.			−1.03701			−0.518506	−	0.855074i	$-0.673512\pi$
$211$	−670640.			−1.03701			−0.518506	+	0.855074i	$0.673512\pi$
$212$	−258482.	−	149235.i	−0.394994	−	0.228050i
$213$	844054.	−	425519.i	1.27474	−	0.642644i
$214$	269710.	+	467152.i	0.402590	+	0.697306i
$215$	−198824.	+	344374.i	−0.293341	+	0.508082i
$216$	118578.	−	691035.i	0.172930	−	1.00778i
$217$	284586.	+	234975.i	0.410265	+	0.338744i
$218$			95601.5i			0.136246i
$219$	673252.	+	441330.i	0.948566	+	0.621803i
$220$	−47263.3	+	27287.5i	−0.0658366	+	0.0380108i
$221$	−631549.	+	364625.i	−0.869814	+	0.502187i
$222$	373923.	+	245114.i	0.509214	+	0.333800i
$223$			18729.0i			0.0252204i	0.999920	+	0.0126102i	$0.00401406\pi$
$223$			18729.0i			0.0252204i	−0.999920	+	0.0126102i	$0.995986\pi$
$224$	562878.	+	464752.i	0.749538	+	0.618872i
$225$	579247.	+	65906.9i	0.762794	+	0.0867910i
$226$	−34895.4	+	60440.6i	−0.0454461	+	0.0787150i
$227$	−223523.	−	387154.i	−0.287911	−	0.498677i	0.685400	−	0.728167i	$-0.259627\pi$
$227$	−223523.	−	387154.i	−0.287911	−	0.498677i	−0.973311	+	0.229490i	$0.926294\pi$
$228$	718159.	−	362051.i	0.914921	−	0.461246i
$229$	−19052.9	−	11000.2i	−0.0240089	−	0.0138616i	0.487948	−	0.872873i	$-0.337746\pi$
$229$	−19052.9	−	11000.2i	−0.0240089	−	0.0138616i	−0.511956	+	0.859011i	$0.671079\pi$
$230$	125847.			0.156864
$231$	17624.7	−	77631.2i	0.0217316	−	0.0957208i
$232$	−979993.			−1.19537
$233$	−461670.	−	266545.i	−0.557111	−	0.321648i	0.194874	−	0.980828i	$-0.437570\pi$
$233$	−461670.	−	266545.i	−0.557111	−	0.321648i	−0.751985	+	0.659180i	$0.770903\pi$
$234$	−208776.	−	479950.i	−0.249253	−	0.573002i
$235$	−251067.	−	434861.i	−0.296565	−	0.513666i
$236$	−72201.2	+	125056.i	−0.0843848	+	0.146159i
$237$	−1.04854e6	−	59460.1i	−1.21259	−	0.0687629i
$238$	−549418.	+	204922.i	−0.628725	+	0.234502i
$239$			269068.i			0.304697i	0.988327	+	0.152348i	$0.0486836\pi$
$239$			269068.i			0.304697i	−0.988327	+	0.152348i	$0.951316\pi$
$240$	−50831.1	+	77543.2i	−0.0569641	+	0.0868992i
$241$	−231077.	+	133412.i	−0.256279	+	0.147963i	−0.622636	−	0.782512i	$-0.713938\pi$
$241$	−231077.	+	133412.i	−0.256279	+	0.147963i	0.366357	+	0.930474i	$0.380605\pi$
$242$	504873.	−	291489.i	0.554171	−	0.319951i
$243$	664680.	−	636781.i	0.722099	−	0.691790i
$244$		−	104715.i		−	0.112599i
$245$	−236405.	−	1.22660e6i	−0.251618	−	1.30553i
$246$	39233.8	−	691865.i	0.0413354	−	0.728926i
$247$	815512.	−	1.41251e6i	0.850527	−	1.47316i
$248$	263457.	+	456321.i	0.272007	+	0.471130i
$249$	−61136.0	−	121269.i	−0.0624883	−	0.123951i
$250$	170775.	+	98597.0i	0.172812	+	0.0997732i
$251$	947580.			0.949361			0.474681	−	0.880158i	$-0.342564\pi$
$251$	947580.			0.949361			0.474681	+	0.880158i	$0.342564\pi$
$252$	141700.	+	569883.i	0.140562	+	0.565307i
$253$	−18248.2			−0.0179233
$254$	133509.	+	77081.5i	0.129845	+	0.0749662i
$255$	645441.	+	1.28029e6i	0.621593	+	1.23298i
$256$	544954.	+	943888.i	0.519708	+	0.900161i
$257$	263158.	−	455804.i	0.248533	−	0.430472i	−0.714586	−	0.699548i	$-0.753385\pi$
$257$	263158.	−	455804.i	0.248533	−	0.430472i	0.963119	+	0.269076i	$0.0867182\pi$
$258$	17258.6	−	304346.i	0.0161420	−	0.284654i
$259$	−1.00323e6	−	168702.i	−0.929288	−	0.156268i
$260$		−	816432.i		−	0.749008i
$261$	−1.03434e6	−	765130.i	−0.939862	−	0.695238i
$262$	−896025.	+	517320.i	−0.806431	+	0.465593i
$263$	−1.18245e6	+	682687.i	−1.05413	+	0.608601i	−0.923802	−	0.382871i	$-0.874935\pi$
$263$	−1.18245e6	+	682687.i	−1.05413	+	0.608601i	−0.130325	+	0.991471i	$0.541602\pi$
$264$	62310.2	−	95054.7i	0.0550236	−	0.0839390i
$265$			1.19006e6i			1.04101i
$266$	835024.	−	1.01133e6i	0.723594	−	0.876371i
$267$	281886.	+	15985.0i	0.241989	+	0.0137225i
$268$	120115.	−	208045.i	0.102155	−	0.176937i
$269$	14614.5	+	25313.1i	0.0123141	+	0.0213287i	0.872117	−	0.489298i	$-0.162747\pi$
$269$	14614.5	+	25313.1i	0.0123141	+	0.0213287i	−0.859803	+	0.510626i	$0.829414\pi$
$270$	−965357.	+	356391.i	−0.805895	+	0.297521i
$271$	366956.	+	211862.i	0.303522	+	0.175239i	0.644024	−	0.765005i	$-0.277264\pi$
$271$	366956.	+	211862.i	0.303522	+	0.175239i	−0.340502	+	0.940244i	$0.610597\pi$
$272$	−99033.3			−0.0811632
$273$	873926.	+	809012.i	0.709689	+	0.656975i
$274$	963785.			0.775540
$275$	81843.2	+	47252.2i	0.0652606	+	0.0376782i
$276$	120201.	−	60597.7i	0.0949805	−	0.0478832i
$277$	373490.	+	646904.i	0.292469	+	0.506571i	0.974393	−	0.224852i	$-0.0721898\pi$
$277$	373490.	+	646904.i	0.292469	+	0.506571i	−0.681924	+	0.731423i	$0.738856\pi$
$278$	−664750.	+	1.15138e6i	−0.515877	+	0.893525i
$279$	−78203.9	+	687323.i	−0.0601475	+	0.528628i
$280$	295756.	−	1.75879e6i	0.225444	−	1.34066i
$281$		−	841921.i		−	0.636071i	−0.948079	−	0.318035i	$-0.896977\pi$
$281$		−	841921.i		−	0.636071i	0.948079	−	0.318035i	$-0.103023\pi$
$282$	321930.	+	211031.i	0.241068	+	0.158024i
$283$	1.20615e6	−	696372.i	0.895233	−	0.516863i	0.0195823	−	0.999808i	$-0.493766\pi$
$283$	1.20615e6	−	696372.i	0.895233	−	0.516863i	0.875650	+	0.482945i	$0.160433\pi$
$284$	−978890.	+	565163.i	−0.720175	+	0.415793i
$285$	−2.68191e6	−	1.75804e6i	−1.95583	−	1.28208i
$286$		−	84844.2i		−	0.0613348i
$287$	551022.	+	1.47735e6i	0.394879	+	1.05872i
$288$	−154678.	+	1.35944e6i	−0.109887	+	0.965782i
$289$	−55786.8	+	96625.6i	−0.0392905	+	0.0680531i
$290$	719159.	+	1.24562e6i	0.502146	+	0.869743i
$291$	−259477.	+	130812.i	−0.179625	+	0.0905555i
$292$	−833661.	−	481314.i	−0.572179	−	0.330348i
$293$	537097.			0.365497			0.182748	−	0.983160i	$-0.441501\pi$
$293$	537097.			0.365497			0.182748	+	0.983160i	$0.441501\pi$
$294$	585117.	+	758053.i	0.394797	+	0.511483i
$295$	575764.			0.385203
$296$	−1.25786e6	−	726226.i	−0.834456	−	0.481773i
$297$	139980.	−	51677.8i	0.0920819	−	0.0339949i
$298$	−705200.	−	1.22144e6i	−0.460014	−	0.796768i
$299$	136495.	−	236416.i	0.0882955	−	0.152932i
$300$	−696013.	−	39469.0i	−0.446492	−	0.0253194i
$301$	242390.	+	649875.i	0.154205	+	0.413441i
$302$		−	1.01074e6i		−	0.637708i
$303$	−1.45794e6	+	2.22410e6i	−0.912291	+	1.39171i
$304$	191821.	−	110748.i	0.119045	−	0.0687308i
$305$	−361585.	+	208761.i	−0.222567	+	0.128499i
$306$	−883641.	−	653650.i	−0.539476	−	0.399063i
$307$			511397.i			0.309679i	0.987940	+	0.154840i	$0.0494861\pi$
$307$			511397.i			0.309679i	−0.987940	+	0.154840i	$0.950514\pi$
$308$	−15786.0	+	93875.5i	−0.00948191	+	0.0563865i
$309$	51972.1	−	916497.i	0.0309652	−	0.546053i
$310$	386671.	−	669734.i	0.228527	−	0.395820i
$311$	1.20650e6	+	2.08971e6i	0.707335	+	1.22514i	0.965842	+	0.259131i	$0.0834361\pi$
$311$	1.20650e6	+	2.08971e6i	0.707335	+	1.22514i	−0.258507	+	0.966009i	$0.583231\pi$
$312$	765414.	+	1.51826e6i	0.445154	+	0.883000i
$313$	2.35700e6	+	1.36081e6i	1.35987	+	0.785124i	0.989607	−	0.143801i	$-0.0459326\pi$
$313$	2.35700e6	+	1.36081e6i	1.35987	+	0.785124i	0.370268	+	0.928925i	$0.379266\pi$
$314$	−1.38523e6			−0.792862
$315$	1.68533e6	−	1.62542e6i	0.956993	−	0.922973i
$316$	1.25586e6			0.707495
$317$	1.42964e6	+	825402.i	0.799057	+	0.461336i	0.843141	−	0.537692i	$-0.180704\pi$
$317$	1.42964e6	+	825402.i	0.799057	+	0.461336i	−0.0440842	+	0.999028i	$0.514037\pi$
$318$	−410685.	−	814628.i	−0.227741	−	0.451743i
$319$	−104280.	−	180619.i	−0.0573754	−	0.0993771i
$320$	859955.	−	1.48949e6i	0.469462	−	0.813133i
$321$	130250.	−	2.29689e6i	0.0705532	−	1.24416i
$322$	139761.	−	169269.i	0.0751183	−	0.0909785i
$323$		−	3.42516e6i		−	1.82673i
$324$	−750436.	+	805239.i	−0.397147	+	0.426150i
$325$	−1.22436e6	+	706884.i	−0.642985	+	0.371227i
$326$	−732822.	+	423095.i	−0.381904	+	0.220492i
$327$	223531.	−	340998.i	0.115603	−	0.176353i
$328$			2.25120e6i			1.15539i
$329$	−863732.	−	145244.i	−0.439936	−	0.0739791i
$330$	−166545.	−	9444.31i	−0.0841873	−	0.00477403i
$331$	1.31284e6	−	2.27391e6i	0.658633	−	1.14079i	−0.322337	−	0.946625i	$-0.604468\pi$
$331$	1.31284e6	−	2.27391e6i	0.658633	−	1.14079i	0.980970	−	0.194160i	$-0.0621983\pi$
$332$	81199.1	+	140641.i	0.0404302	+	0.0700272i
$333$	−760622.	−	1.74858e6i	−0.375888	−	0.864121i
$334$	549850.	+	317456.i	0.269698	+	0.155710i
$335$	−957847.			−0.466320
$336$	47847.8	+	154486.i	0.0231214	+	0.0746521i
$337$	−3.01254e6			−1.44497			−0.722483	−	0.691388i	$-0.756999\pi$
$337$	−3.01254e6			−1.44497			−0.722483	+	0.691388i	$0.756999\pi$
$338$	−76071.0	−	43919.6i	−0.0362182	−	0.0209106i
$339$	265786.	−	133993.i	0.125613	−	0.0633261i
$340$	−857256.	−	1.48481e6i	−0.402173	−	0.696585i
$341$	−56068.5	+	97113.5i	−0.0261116	+	0.0452266i
$342$	2.44252e6	+	277911.i	1.12921	+	0.128482i
$343$	−1.91236e6	−	1.04424e6i	−0.877678	−	0.479251i
$344$			990285.i			0.451195i
$345$	−448880.	−	294249.i	−0.203040	−	0.133097i
$346$	−1.55264e6	+	896419.i	−0.697238	+	0.402551i
$347$	2.51975e6	−	1.45478e6i	1.12340	−	0.648595i	0.181133	−	0.983459i	$-0.442024\pi$
$347$	2.51975e6	−	1.45478e6i	1.12340	−	0.648595i	0.942267	+	0.334864i	$0.108690\pi$
$348$	1.28668e6	+	843446.i	0.569539	+	0.373344i
$349$		−	3.93286e6i		−	1.72840i	−0.503147	−	0.864201i	$-0.667824\pi$
$349$		−	3.93286e6i		−	1.72840i	0.503147	−	0.864201i	$-0.332176\pi$
$350$	−1.06514e6	+	397274.i	−0.464766	+	0.173349i
$351$	−377520.	+	2.20007e6i	−0.163558	+	0.953165i
$352$	−110897.	+	192079.i	−0.0477048	+	0.0826271i
$353$	−967991.	−	1.67661e6i	−0.413461	−	0.716136i	0.581804	−	0.813329i	$-0.302347\pi$
$353$	−967991.	−	1.67661e6i	−0.413461	−	0.716136i	−0.995266	+	0.0971931i	$0.969014\pi$
$354$	−394125.	+	198693.i	−0.167157	+	0.0842703i
$355$	3.90305e6	+	2.25343e6i	1.64374	+	0.949015i
$356$	−337620.			−0.141190
$357$	2.43884e6	+	553693.i	1.01277	+	0.229931i
$358$	−2.34406e6			−0.966631
$359$	−1.20595e6	−	696256.i	−0.493848	−	0.285123i	0.232321	−	0.972639i	$-0.425368\pi$
$359$	−1.20595e6	−	696256.i	−0.493848	−	0.285123i	−0.726169	+	0.687516i	$0.758701\pi$
$360$	3.06548e6	−	1.33347e6i	1.24664	−	0.542283i
$361$	2.59227e6	+	4.48994e6i	1.04692	+	1.81331i
$362$	−85782.7	+	148580.i	−0.0344055	+	0.0595921i
$363$	−2.48236e6	−	140768.i	−0.988777	−	0.0560708i
$364$	−1.09813e6	−	906697.i	−0.434412	−	0.358681i
$365$			3.83821e6i			1.50798i
$366$	175472.	−	267684.i	0.0684707	−	0.104453i
$367$	−853243.	+	492620.i	−0.330680	+	0.190918i	−0.656143	−	0.754637i	$-0.727813\pi$
$367$	−853243.	+	492620.i	−0.330680	+	0.190918i	0.325463	+	0.945555i	$0.394480\pi$
$368$	32105.7	−	18536.2i	0.0123584	−	0.00713513i
$369$	−1.75763e6	+	2.37606e6i	−0.671986	+	0.908428i
$370$			2.13174e6i			0.809524i
$371$	1.60068e6	+	1.32164e6i	0.603769	+	0.498514i
$372$	46833.1	−	825875.i	0.0175467	−	0.309426i
$373$	−1.25793e6	+	2.17879e6i	−0.468148	+	0.810856i	−0.999337	−	0.0363971i	$-0.988412\pi$
$373$	−1.25793e6	+	2.17879e6i	−0.468148	+	0.810856i	0.531190	+	0.847253i	$0.321745\pi$
$374$	−89086.7	−	154303.i	−0.0329332	−	0.0570420i
$375$	−378597.	−	750980.i	−0.139027	−	0.275772i
$376$	−1.08296e6	−	625246.i	−0.395041	−	0.228077i
$377$	3.12003e6			1.13059
$378$	−592728.	+	1.69424e6i	−0.213366	+	0.609881i
$379$	−627888.			−0.224535			−0.112268	−	0.993678i	$-0.535811\pi$
$379$	−627888.			−0.224535			−0.112268	+	0.993678i	$0.535811\pi$
$380$	3.32089e6	+	1.91732e6i	1.17977	+	0.681138i
$381$	−295981.	−	587104.i	−0.104460	−	0.207206i
$382$	−1.39148e6	−	2.41011e6i	−0.487885	−	0.845041i
$383$	−1.55261e6	+	2.68921e6i	−0.540837	+	0.936758i	0.458019	+	0.888942i	$0.348559\pi$
$383$	−1.55261e6	+	2.68921e6i	−0.540837	+	0.936758i	−0.998856	+	0.0478152i	$0.984774\pi$
$384$	84369.5	−	1.48781e6i	0.0291983	−	0.514895i
$385$	355627.	−	132642.i	0.122276	−	0.0456066i
$386$			2.03335e6i			0.694615i
$387$	−773165.	+	1.04521e6i	−0.262419	+	0.354752i
$388$	300928.	−	173741.i	0.101481	−	0.0585898i
$389$	−580056.	+	334895.i	−0.194355	+	0.112211i	−0.594020	−	0.804450i	$-0.702460\pi$
$389$	−580056.	+	334895.i	−0.194355	+	0.112211i	0.399665	+	0.916661i	$0.369127\pi$
$390$	1.36810e6	−	2.08704e6i	0.455466	−	0.694817i
$391$		−	573281.i		−	0.189638i
$392$	−2.03718e6	−	2.35104e6i	−0.669600	−	0.772762i
$393$	4.40558e6	+	249828.i	1.43887	+	0.0815943i
$394$	997637.	−	1.72796e6i	0.323767	−	0.560780i
$395$	−2.50370e6	−	4.33653e6i	−0.807401	−	1.39846i
$396$	−163620.	+	71174.0i	−0.0524324	+	0.0228078i
$397$	−3.02652e6	−	1.74736e6i	−0.963757	−	0.556425i	−0.0664294	−	0.997791i	$-0.521161\pi$
$397$	−3.02652e6	−	1.74736e6i	−0.963757	−	0.556425i	−0.897327	+	0.441366i	$0.854494\pi$
$398$	771949.			0.244276
$399$	−5.34306e6	+	1.65486e6i	−1.68019	+	0.520390i
$400$	−191992.			−0.0599975
$401$	−2.43480e6	−	1.40573e6i	−0.756140	−	0.436558i	0.0717682	−	0.997421i	$-0.477136\pi$
$401$	−2.43480e6	−	1.40573e6i	−0.756140	−	0.436558i	−0.827908	+	0.560864i	$0.810469\pi$
$402$	655670.	−	330548.i	0.202358	−	0.102016i
$403$	−838775.	−	1.45280e6i	−0.257266	−	0.445598i
$404$	1.59003e6	−	2.75401e6i	0.484676	−	0.839484i
$405$	4.27660e6	+	985950.i	1.29557	+	0.298688i
$406$	2.47408e6	+	416039.i	0.744901	+	0.125262i
$407$		−	309109.i		−	0.0924965i
$408$	2.98621e6	+	1.95752e6i	0.888117	+	0.582178i
$409$	−2.41651e6	+	1.39517e6i	−0.714300	+	0.412402i	−0.812651	−	0.582750i	$-0.801977\pi$
$409$	−2.41651e6	+	1.39517e6i	−0.714300	+	0.412402i	0.0983509	+	0.995152i	$0.468643\pi$
$410$	2.86139e6	−	1.65202e6i	0.840654	−	0.485352i
$411$	−3.43770e6	−	2.25348e6i	−1.00384	−	0.658034i
$412$			1.09771e6i			0.318598i
$413$	639421.	−	774426.i	0.184464	−	0.223411i
$414$	408813.	+	46514.9i	0.117226	+	0.0133380i
$415$	323759.	−	560767.i	0.0922787	−	0.159831i
$416$	−1.65900e6	−	2.87346e6i	−0.470015	−	0.814090i
$417$	5.06318e6	−	2.55254e6i	1.42588	−	0.718839i
$418$	345110.	+	199249.i	0.0966088	+	0.0557771i
$419$	−3.40729e6			−0.948144			−0.474072	−	0.880486i	$-0.657216\pi$
$419$	−3.40729e6			−0.948144			−0.474072	+	0.880486i	$0.657216\pi$
$420$	−1.90204e6	+	2.05465e6i	−0.526134	+	0.568350i
$421$	3.77099e6			1.03693			0.518465	−	0.855099i	$-0.326504\pi$
$421$	3.77099e6			1.03693			0.518465	+	0.855099i	$0.326504\pi$
$422$	2.12282e6	+	1.22561e6i	0.580273	+	0.335021i
$423$	−654859.	−	1.50544e6i	−0.177950	−	0.409085i
$424$	1.48184e6	+	2.56662e6i	0.400301	+	0.693341i
$425$	−1.48446e6	+	2.57116e6i	−0.398655	+	0.690490i
$426$	−3.44938e6	−	195605.i	−0.920911	−	0.0522223i
$427$	−120770.	+	718189.i	−0.0320545	+	0.190620i
$428$			2.75103e6i			0.725915i
$429$	−198378.	+	302628.i	−0.0520417	+	0.0793900i
$430$	1.25870e6	−	726712.i	0.328286	−	0.189536i
$431$	2.60415e6	−	1.50351e6i	0.675263	−	0.389863i	−0.122805	−	0.992431i	$-0.539189\pi$
$431$	2.60415e6	−	1.50351e6i	0.675263	−	0.389863i	0.798068	+	0.602568i	$0.205856\pi$
$432$	−193785.	+	233111.i	−0.0499588	+	0.0600970i
$433$			1.50880e6i			0.386734i	0.981126	+	0.193367i	$0.0619408\pi$
$433$			1.50880e6i			0.386734i	−0.981126	+	0.193367i	$0.938059\pi$
$434$	−471398.	−	1.26387e6i	−0.120133	−	0.322090i
$435$	347302.	−	6.12447e6i	0.0880002	−	1.55183i
$436$	−243782.	+	422244.i	−0.0614167	+	0.106377i
$437$	641093.	+	1.11041e6i	0.160590	+	0.278149i
$438$	−1.32455e6	−	2.62735e6i	−0.329900	−	0.654385i
$439$	−1.70748e6	−	985817.i	−0.422859	−	0.244138i	0.273441	−	0.961889i	$-0.411838\pi$
$439$	−1.70748e6	−	985817.i	−0.422859	−	0.244138i	−0.696300	+	0.717751i	$0.745172\pi$
$440$	541907.			0.133442
$441$	−314592.	−	4.07197e6i	−0.0770285	−	0.997029i
$442$	2.66544e6			0.648954
$443$	−1.85053e6	−	1.06840e6i	−0.448009	−	0.258658i	0.258980	−	0.965883i	$-0.416614\pi$
$443$	−1.85053e6	−	1.06840e6i	−0.448009	−	0.258658i	−0.706989	+	0.707225i	$0.749947\pi$
$444$	1.02647e6	+	2.03610e6i	0.247110	+	0.490163i
$445$	673083.	+	1.16581e6i	0.161127	+	0.279080i
$446$	34227.7	−	59284.0i	0.00814779	−	0.0141124i
$447$	−340560.	+	6.00558e6i	−0.0806167	+	1.42163i
$448$	−1.04839e6	−	2.81084e6i	−0.246789	−	0.661669i
$449$			5.91347e6i			1.38429i	0.721759	+	0.692144i	$0.243334\pi$
$449$			5.91347e6i			1.38429i	−0.721759	+	0.692144i	$0.756666\pi$
$450$	−1.71308e6	−	1.26721e6i	−0.398792	−	0.294996i
$451$	−414911.	+	239549.i	−0.0960535	+	0.0554565i
$452$	−308245.	+	177966.i	−0.0709660	+	0.0409723i
$453$	−2.36326e6	+	3.60517e6i	−0.541086	+	0.825431i
$454$			1.63398e6i			0.372054i
$455$	−941606.	+	5.59950e6i	−0.213226	+	1.26800i
$456$	−7.97316e6	−	452136.i	−1.79564	−	0.101826i
$457$	3.75946e6	−	6.51157e6i	0.842044	−	1.45846i	−0.0461206	−	0.998936i	$-0.514686\pi$
$457$	3.75946e6	−	6.51157e6i	0.842044	−	1.45846i	0.888164	−	0.459526i	$-0.151981\pi$
$458$	40206.2	+	69639.3i	0.00895632	+	0.0155128i
$459$	1.62350e6	+	4.39757e6i	0.359683	+	0.974274i
$460$	555829.	+	320908.i	0.122475	+	0.0707109i
$461$	929187.			0.203634			0.101817	−	0.994803i	$-0.467534\pi$
$461$	929187.			0.203634			0.101817	+	0.994803i	$0.467534\pi$
$462$	−197661.	+	213521.i	−0.0430841	+	0.0465411i
$463$	1.21496e6			0.263396			0.131698	−	0.991290i	$-0.457957\pi$
$463$	1.21496e6			0.263396			0.131698	+	0.991290i	$0.457957\pi$
$464$	366939.	+	211853.i	0.0791224	+	0.0456813i
$465$	−2.94514e6	+	1.48476e6i	−0.631646	+	0.318437i
$466$	974235.	+	1.68742e6i	0.207826	+	0.359964i
$467$	1.51559e6	−	2.62507e6i	0.321580	−	0.556992i	−0.659234	−	0.751937i	$-0.729120\pi$
$467$	1.51559e6	−	2.62507e6i	0.321580	−	0.556992i	0.980814	+	0.194945i	$0.0624529\pi$
$468$	301765.	−	2.65217e6i	0.0636876	−	0.559741i
$469$	−1.06375e6	+	1.28834e6i	−0.223309	+	0.270458i
$470$			1.83532e6i			0.383238i
$471$	4.94093e6	+	3.23888e6i	1.02626	+	0.672732i
$472$	1.24176e6	−	716928.i	0.256555	−	0.148122i
$473$	−182516.	+	105376.i	−0.0375100	+	0.0216564i
$474$	3.21036e6	+	2.10445e6i	0.656308	+	0.430222i
$475$		−	6.64023e6i		−	1.35036i
$476$	−2.94917e6	−	495929.i	−0.596598	−	0.100323i
$477$	−439865.	+	3.86591e6i	−0.0885164	+	0.777958i
$478$	491729.	−	851699.i	0.0984364	−	0.170497i
$479$	40952.6	+	70932.0i	0.00815535	+	0.0141255i	0.870074	−	0.492921i	$-0.164071\pi$
$479$	40952.6	+	70932.0i	0.00815535	+	0.0141255i	−0.861919	+	0.507046i	$0.830737\pi$
$480$	−5.82514e6	+	2.93667e6i	−1.15399	+	0.581771i
$481$	4.00469e6	+	2.31211e6i	0.789234	+	0.455664i
$482$	975255.			0.191206
$483$	−894285.	+	276980.i	−0.174425	+	0.0540232i
$484$	2.97317e6			0.576907
$485$	−1.19987e6	−	692743.i	−0.231621	−	0.133727i
$486$	−3.26768e6	+	800924.i	−0.627551	+	0.153816i
$487$	−2.20758e6	−	3.82364e6i	−0.421787	−	0.730557i	0.574327	−	0.818626i	$-0.305264\pi$
$487$	−2.20758e6	−	3.82364e6i	−0.421787	−	0.730557i	−0.996114	+	0.0880688i	$0.971930\pi$
$488$	−519890.	+	900475.i	−0.0988238	+	0.171168i
$489$	3.60314e6	+	204324.i	0.681410	+	0.0386409i
$490$	−1.49332e6	+	4.31466e6i	−0.280973	+	0.811813i
$491$		−	9.60786e6i		−	1.79855i	−0.437381	−	0.899276i	$-0.644094\pi$
$491$		−	9.60786e6i		−	1.79855i	0.437381	−	0.899276i	$-0.355906\pi$
$492$	1.93753e6	−	2.95572e6i	0.360857	−	0.550491i
$493$	5.67427e6	−	3.27604e6i	1.05146	−	0.607061i
$494$	−5.16278e6	+	2.98073e6i	−0.951845	+	0.549548i
$495$	571962.	+	423094.i	0.104919	+	0.0776111i
$496$		−	227814.i		−	0.0415792i
$497$	7.36553e6	−	2.74720e6i	1.33756	−	0.498883i
$498$	−28103.4	+	495587.i	−0.00507791	+	0.0895460i
$499$	−5.03473e6	+	8.72042e6i	−0.905160	+	1.56778i	−0.0844572	+	0.996427i	$0.526916\pi$
$499$	−5.03473e6	+	8.72042e6i	−0.905160	+	1.56778i	−0.820703	+	0.571356i	$0.806418\pi$
$500$	502842.	+	870948.i	0.0899512	+	0.155800i
$501$	−1.21898e6	−	2.41796e6i	−0.216972	−	0.430382i
$502$	−2.99943e6	−	1.73172e6i	−0.531227	−	0.306704i
$503$	−2.68345e6			−0.472904			−0.236452	−	0.971643i	$-0.575985\pi$
$503$	−2.68345e6			−0.472904			−0.236452	+	0.971643i	$0.575985\pi$
$504$	1.61083e6	−	5.60409e6i	0.282472	−	0.982718i
$505$	−1.26796e7			−2.21247
$506$	57762.2	+	33349.0i	0.0100292	+	0.00579038i
$507$	168645.	+	334521.i	0.0291375	+	0.0577967i
$508$	393113.	+	680893.i	0.0675863	+	0.117063i
$509$	3.75644e6	−	6.50634e6i	0.642661	−	1.11312i	−0.342176	−	0.939636i	$-0.611164\pi$
$509$	3.75644e6	−	6.50634e6i	0.642661	−	1.11312i	0.984837	−	0.173485i	$-0.0555027\pi$
$510$	296700.	−	5.23213e6i	0.0505117	−	0.890745i
$511$	5.16255e6	+	4.26257e6i	0.874606	+	0.722137i
$512$		−	924585.i		−	0.155873i
$513$	−8.06235e6	−	6.70225e6i	−1.35260	−	1.12442i
$514$	−1.66598e6	+	961856.i	−0.278140	+	0.160584i
$515$	3.79042e6	−	2.18840e6i	0.629751	−	0.363587i
$516$	852303.	−	1.30020e6i	0.140919	−	0.214973i
$517$		−	266128.i		−	0.0437889i
$518$	2.86728e6	+	2.36743e6i	0.469510	+	0.387661i
$519$	7.63403e6	+	432905.i	1.24404	+	0.0705463i
$520$	−4.05342e6	+	7.02072e6i	−0.657374	+	1.13861i
$521$	4.73009e6	+	8.19276e6i	0.763440	+	1.32232i	0.941067	+	0.338220i	$0.109825\pi$
$521$	4.73009e6	+	8.19276e6i	0.763440	+	1.32232i	−0.177627	+	0.984098i	$0.556842\pi$
$522$	1.87578e6	+	4.31220e6i	0.301305	+	0.692664i
$523$	−1.14824e6	−	662937.i	−0.183560	−	0.105979i	0.405404	−	0.914138i	$-0.367131\pi$
$523$	−1.14824e6	−	662937.i	−0.183560	−	0.105979i	−0.588964	+	0.808159i	$0.700464\pi$
$524$	−5.27664e6			−0.839517
$525$	4.72808e6	+	1.07342e6i	0.748664	+	0.169970i
$526$	4.99051e6			0.786466
$527$	−3.05089e6	−	1.76143e6i	−0.478520	−	0.276274i
$528$	−43879.5	+	22121.3i	−0.00684979	+	0.00345323i
$529$	−3.11087e6	−	5.38818e6i	−0.483329	−	0.837150i
$530$	2.17487e6	−	3.76698e6i	0.336313	−	0.582511i
$531$	1.87037e6	+	212811.i	0.287866	+	0.0327535i
$532$	6.26693e6	−	2.33744e6i	0.960010	−	0.358064i
$533$		−	7.16721e6i		−	1.09278i
$534$	−863059.	−	565752.i	−0.130975	−	0.0858564i
$535$	9.49940e6	−	5.48448e6i	1.43487	−	0.828421i
$536$	−2.06580e6	+	1.19269e6i	−0.310582	+	0.179314i
$537$	8.36094e6	+	5.48076e6i	1.25118	+	0.820172i
$538$		−	106833.i		−	0.0159130i
$539$	216537.	−	625639.i	0.0321040	−	0.0927581i
$540$	−5.17249e6	−	887573.i	−0.763335	−	0.130984i
$541$	−3.46147e6	+	5.99545e6i	−0.508473	+	0.880701i	0.491479	+	0.870889i	$0.336456\pi$
$541$	−3.46147e6	+	5.99545e6i	−0.508473	+	0.880701i	−0.999952	+	0.00981149i	$0.996877\pi$
$542$	−774365.	−	1.34124e6i	−0.113226	−	0.196114i
$543$	653378.	−	329392.i	0.0950966	−	0.0479417i
$544$	−6.03430e6	−	3.48390e6i	−0.874237	−	0.504741i
$545$	1.94403e6			0.280357
$546$	−1.28780e6	−	4.15794e6i	−0.184871	−	0.596893i
$547$	−9.97756e6			−1.42579			−0.712896	−	0.701270i	$-0.752617\pi$
$547$	−9.97756e6			−1.42579			−0.712896	+	0.701270i	$0.752617\pi$
$548$	4.25676e6	+	2.45764e6i	0.605519	+	0.349596i
$549$	−1.25177e6	+	544513.i	−0.177253	+	0.0771040i
$550$	−172709.	−	299141.i	−0.0243449	−	0.0421666i
$551$	−7.32712e6	+	1.26909e7i	−1.02815	+	1.78080i
$552$	−1.33449e6	−	75675.5i	−0.186410	−	0.0105708i
$553$	−8.61332e6	−	1.44841e6i	−1.19773	−	0.201409i
$554$		−	2.73025e6i		−	0.377944i
$555$	4.98433e6	−	7.60363e6i	0.686869	−	1.04782i
$556$	−5.87201e6	+	3.39021e6i	−0.805564	+	0.465092i
$557$	−1.08587e7	+	6.26929e6i	−1.48300	+	0.856210i	−0.999814	−	0.0193079i	$-0.993854\pi$
$557$	−1.08587e7	+	6.26929e6i	−1.48300	+	0.856210i	−0.483186	+	0.875518i	$0.660520\pi$
$558$	1.50364e6	−	2.03271e6i	0.204437	−	0.276369i
$559$		−	3.15280e6i		−	0.426743i
$560$	−490950.	+	594608.i	−0.0661557	+	0.0801236i
$561$	−43022.4	+	758676.i	−0.00577149	+	0.101777i
$562$	−1.53863e6	+	2.66498e6i	−0.205491	+	0.355921i
$563$	3.43830e6	+	5.95530e6i	0.457164	+	0.791832i	0.998810	−	0.0487752i	$-0.0155318\pi$
$563$	3.43830e6	+	5.95530e6i	0.457164	+	0.791832i	−0.541645	+	0.840607i	$0.682198\pi$
$564$	883744.	+	1.75298e6i	0.116985	+	0.232049i
$565$	1.22904e6	+	709588.i	0.161974	+	0.0935159i
$566$	−5.09055e6			−0.667918
$567$	6.07557e6	−	4.65724e6i	0.793650	−	0.608374i
$568$	1.12237e7			1.45970
$569$	2.29442e6	+	1.32468e6i	0.297093	+	0.171526i	0.641136	−	0.767427i	$-0.278463\pi$
$569$	2.29442e6	+	1.32468e6i	0.297093	+	0.171526i	−0.344043	+	0.938954i	$0.611797\pi$
$570$	5.27635e6	+	1.04661e7i	0.680215	+	1.34926i
$571$	−547786.	−	948793.i	−0.0703105	−	0.121781i	0.828727	−	0.559653i	$-0.189066\pi$
$571$	−547786.	−	948793.i	−0.0703105	−	0.121781i	−0.899037	+	0.437872i	$0.855732\pi$
$572$	216352.	−	374732.i	0.0276484	−	0.0478884i
$573$	−671982.	+	1.18500e7i	−0.0855009	+	1.50776i
$574$	955709.	−	5.68336e6i	0.121073	−	0.719988i
$575$		−	1.11140e6i		−	0.140184i
$576$	3.34409e6	−	4.52073e6i	0.419974	−	0.567744i
$577$	−2.51518e6	+	1.45214e6i	−0.314507	+	0.181581i	−0.648942	−	0.760838i	$-0.724788\pi$
$577$	−2.51518e6	+	1.45214e6i	−0.314507	+	0.181581i	0.334435	+	0.942419i	$0.391455\pi$
$578$	353171.	−	203903.i	0.0439709	−	0.0253866i
$579$	4.75428e6	−	7.25269e6i	0.589370	−	0.899090i
$580$			7.33539e6i			0.905426i
$581$	−394700.	−	1.05824e6i	−0.0485095	−	0.130059i
$582$	1.06040e6	+	60132.3i	0.129766	+	0.00735869i
$583$	−315363.	+	546224.i	−0.0384272	+	0.0665579i
$584$	4.77925e6	+	8.27791e6i	0.579866	+	1.00436i
$585$	−9.75965e6	+	4.24539e6i	−1.17908	+	0.512895i
$586$	−1.70011e6	−	981557.i	−0.204518	−	0.118079i
$587$	−2.80932e6			−0.336516			−0.168258	−	0.985743i	$-0.553814\pi$
$587$	−2.80932e6			−0.336516			−0.168258	+	0.985743i	$0.553814\pi$
$588$	651264.	+	4.84014e6i	0.0776808	+	0.577317i
$589$	7.87916e6			0.935819
$590$	−1.82250e6	−	1.05222e6i	−0.215545	−	0.124445i
$591$	−7.59866e6	+	3.83077e6i	−0.894888	+	0.451146i
$592$	313988.	+	543843.i	0.0368221	+	0.0637777i
$593$	235612.	−	408091.i	0.0275144	−	0.0476563i	−0.851940	−	0.523639i	$-0.824574\pi$
$593$	235612.	−	408091.i	0.0275144	−	0.0476563i	0.879455	+	0.475983i	$0.157907\pi$
$594$	−537529.	−	92237.3i	−0.0625081	−	0.0107261i
$595$	4.16703e6	+	1.11723e7i	0.482541	+	1.29375i
$596$		−	7.19300e6i		−	0.829458i
$597$	−2.75344e6	−	1.80493e6i	−0.316184	−	0.207264i
$598$	−864112.	+	498895.i	−0.0988137	+	0.0570501i
$599$	−1.50232e6	+	867362.i	−0.171078	+	0.0987719i	−0.583094	−	0.812405i	$-0.698158\pi$
$599$	−1.50232e6	+	867362.i	−0.171078	+	0.0987719i	0.412016	+	0.911177i	$0.364825\pi$
$600$	5.78925e6	+	3.79497e6i	0.656514	+	0.430358i
$601$			3.42903e6i			0.387244i	0.981076	+	0.193622i	$0.0620235\pi$
$601$			3.42903e6i			0.387244i	−0.981076	+	0.193622i	$0.937976\pi$
$602$	420408.	−	2.50006e6i	0.0472803	−	0.281164i
$603$	−3.11156e6	−	354034.i	−0.348486	−	0.0396508i
$604$	2.57737e6	−	4.46414e6i	0.287465	−	0.497904i
$605$	−5.92734e6	−	1.02665e7i	−0.658372	−	1.14033i
$606$	8.67951e6	−	4.37567e6i	0.960093	−	0.484019i
$607$	−8.49975e6	−	4.90733e6i	−0.936341	−	0.540597i	−0.0475299	−	0.998870i	$-0.515135\pi$
$607$	−8.49975e6	−	4.90733e6i	−0.936341	−	0.540597i	−0.888812	+	0.458273i	$0.848468\pi$
$608$	1.55840e7			1.70970
$609$	−7.85196e6	−	7.26873e6i	−0.857896	−	0.794173i
$610$	1.52607e6			0.166054
$611$	3.44784e6	+	1.99061e6i	0.373632	+	0.215717i
$612$	−2.23598e6	−	5.14025e6i	−0.241318	−	0.554761i
$613$	1.37890e6	+	2.38832e6i	0.148211	+	0.256709i	0.930566	−	0.366123i	$-0.119315\pi$
$613$	1.37890e6	+	2.38832e6i	0.148211	+	0.256709i	−0.782355	+	0.622833i	$0.785982\pi$
$614$	934589.	−	1.61876e6i	0.100046	−	0.173285i
$615$	−1.40689e7	−	797808.i	−1.49993	−	0.0850571i
$616$	601821.	−	728887.i	0.0639021	−	0.0773942i
$617$			5.46419e6i			0.577847i	0.957352	+	0.288923i	$0.0932973\pi$
$617$			5.46419e6i			0.577847i	−0.957352	+	0.288923i	$0.906703\pi$
$618$	−1.83943e6	+	2.80607e6i	−0.193737	+	0.295547i
$619$	3.67533e6	−	2.12195e6i	0.385540	−	0.222591i	−0.294686	−	0.955594i	$-0.595215\pi$
$619$	3.67533e6	−	2.12195e6i	0.385540	−	0.222591i	0.680226	+	0.733003i	$0.261882\pi$
$620$	3.41562e6	−	1.97201e6i	0.356854	−	0.206030i
$621$	−1.34942e6	−	1.12178e6i	−0.140417	−	0.116729i
$622$		−	8.81960e6i		−	0.914057i
$623$	2.31557e6	+	389384.i	0.239022	+	0.0401937i
$624$	41620.3	−	733950.i	0.00427901	−	0.0754580i
$625$	5.75356e6	−	9.96545e6i	0.589164	−	1.02046i
$626$	−4.97384e6	−	8.61495e6i	−0.507290	−	0.878652i
$627$	−765087.	−	1.51761e6i	−0.0777216	−	0.154167i
$628$	−6.11815e6	−	3.53232e6i	−0.619044	−	0.357405i
$629$	9.71088e6			0.978660
$630$	−8.30518e6	+	2.06506e6i	−0.833676	+	0.207291i
$631$	1.97794e6			0.197761			0.0988804	−	0.995099i	$-0.468474\pi$
$631$	1.97794e6			0.197761			0.0988804	+	0.995099i	$0.468474\pi$
$632$	−1.07995e7	−	6.23509e6i	−1.07550	−	0.620940i
$633$	−4.70616e6	−	9.33506e6i	−0.466828	−	0.925994i
$634$	−3.01688e6	−	5.22539e6i	−0.298082	−	0.516292i
$635$	1.56743e6	−	2.71487e6i	0.154260	−	0.267187i
$636$	263417.	−	4.64521e6i	0.0258227	−	0.455368i
$637$	6.48584e6	+	7.48508e6i	0.633312	+	0.730883i
$638$			762299.i			0.0741436i
$639$	1.18461e7	+	8.76287e6i	1.14769	+	0.848974i
$640$	6.15322e6	−	3.55256e6i	0.593817	−	0.342840i
$641$	5.95229e6	−	3.43656e6i	0.572189	−	0.330353i	−0.185834	−	0.982581i	$-0.559499\pi$
$641$	5.95229e6	−	3.43656e6i	0.572189	−	0.330353i	0.758023	+	0.652228i	$0.226165\pi$
$642$	−4.60991e6	+	7.03246e6i	−0.441423	+	0.673395i
$643$		−	4.81869e6i		−	0.459623i	−0.973235	−	0.229811i	$-0.926189\pi$
$643$		−	4.81869e6i		−	0.459623i	0.973235	−	0.229811i	$-0.0738109\pi$
$644$	1.04892e6	−	391225.i	0.0996612	−	0.0371716i
$645$	−6.18878e6	−	350949.i	−0.585742	−	0.0332158i
$646$	−6.25956e6	+	1.08419e7i	−0.590150	+	1.02217i
$647$	3.75204e6	+	6.49872e6i	0.352376	+	0.610333i	0.986665	−	0.162763i	$-0.0520405\pi$
$647$	3.75204e6	+	6.49872e6i	0.352376	+	0.610333i	−0.634289	+	0.773096i	$0.718707\pi$
$648$	1.04511e7	−	3.19871e6i	0.977738	−	0.299252i
$649$	264269.	+	152576.i	0.0246283	+	0.0142191i
$650$	5.16739e6			0.479720
$651$	−1.27370e6	+	5.61025e6i	−0.117792	+	0.518836i
$652$	−4.31554e6			−0.397573
$653$	−1.21493e7	−	7.01440e6i	−1.11498	−	0.643735i	−0.174867	−	0.984592i	$-0.555950\pi$
$653$	−1.21493e7	−	7.01440e6i	−1.11498	−	0.643735i	−0.940115	+	0.340857i	$0.889283\pi$
$654$	−1.33074e6	+	670874.i	−0.121660	+	0.0613334i
$655$	1.05196e7	+	1.82204e7i	0.958064	+	1.65942i
$656$	486659.	−	842919.i	0.0441535	−	0.0764762i
$657$	−1.41866e6	+	1.24684e7i	−0.128223	+	1.12693i
$658$	2.46859e6	+	2.03824e6i	0.222271	+	0.183523i
$659$			4.93455e6i			0.442623i	0.975203	+	0.221311i	$0.0710337\pi$
$659$			4.93455e6i			0.442623i	−0.975203	+	0.221311i	$0.928966\pi$
$660$	−711497.	−	466400.i	−0.0635790	−	0.0416772i
$661$	1.59100e7	−	9.18563e6i	1.41633	−	0.817721i	0.420360	−	0.907358i	$-0.361904\pi$
$661$	1.59100e7	−	9.18563e6i	1.41633	−	0.817721i	0.995975	+	0.0896367i	$0.0285706\pi$
$662$	−8.31126e6	+	4.79851e6i	−0.737092	+	0.425560i
$663$	−9.50728e6	−	6.23221e6i	−0.839987	−	0.550628i
$664$		−	1.61255e6i		−	0.141936i
$665$	−2.05651e7	−	1.69800e7i	−1.80333	−	1.48896i
$666$	−787923.	+	6.92494e6i	−0.0688332	+	0.604965i
$667$	−1.22637e6	+	2.12413e6i	−0.106735	+	0.184870i
$668$	1.61902e6	+	2.80422e6i	0.140382	+	0.243148i
$669$	−260701.	+	131429.i	−0.0225204	+	0.0113534i
$670$	3.03193e6	+	1.75049e6i	0.260935	+	0.150651i
$671$	−221284.			−0.0189734
$672$	−2.51923e6	+	1.10964e7i	−0.215201	+	0.947892i
$673$	5.27763e6			0.449160			0.224580	−	0.974456i	$-0.427899\pi$
$673$	5.27763e6			0.449160			0.224580	+	0.974456i	$0.427899\pi$
$674$	9.53578e6	+	5.50548e6i	0.808549	+	0.466816i
$675$	3.14741e6	+	8.52539e6i	0.265885	+	0.720203i
$676$	−223989.	−	387960.i	−0.0188521	−	0.0326528i
$677$	−6.85310e6	+	1.18699e7i	−0.574666	+	0.995351i	0.421412	+	0.906869i	$0.361535\pi$
$677$	−6.85310e6	+	1.18699e7i	−0.574666	+	0.995351i	−0.996078	+	0.0884815i	$0.971799\pi$
$678$	−1.08619e6	−	61594.6i	−0.0907465	−	0.00514599i
$679$	−2.26429e6	+	844535.i	−0.188477	+	0.0702980i
$680$			1.70244e7i			1.41189i
$681$	3.82048e6	−	5.82818e6i	0.315683	−	0.481576i
$682$	354954.	−	204933.i	0.0292221	−	0.0168714i
$683$	1.35604e7	−	7.82911e6i	1.11230	−	0.642186i	0.172875	−	0.984944i	$-0.444694\pi$
$683$	1.35604e7	−	7.82911e6i	1.11230	−	0.642186i	0.939424	+	0.342758i	$0.111361\pi$
$684$	1.00792e7	+	7.45585e6i	0.823734	+	0.609336i
$685$		−	1.95983e7i		−	1.59585i
$686$	4.14496e6	+	6.80027e6i	0.336287	+	0.551717i
$687$	19416.7	−	342402.i	0.00156958	−	0.0276786i
$688$	214077.	−	370793.i	0.0172425	−	0.0298649i
$689$	−4.71777e6	−	8.17142e6i	−0.378607	−	0.655767i
$690$	883119.	+	1.75174e6i	0.0706150	+	0.140071i
$691$	3.65594e6	+	2.11076e6i	0.291275	+	0.168168i	0.638517	−	0.769608i	$-0.279548\pi$
$691$	3.65594e6	+	2.11076e6i	0.291275	+	0.168168i	−0.347242	+	0.937776i	$0.612882\pi$
$692$	−9.14342e6			−0.725844
$693$	1.20428e6	−	299440.i	0.0952562	−	0.0236852i
$694$	−1.06346e7			−0.838150
$695$	2.34130e7	+	1.35175e7i	1.83863	+	1.06154i
$696$	−6.87701e6	−	1.36411e7i	−0.538117	−	1.06740i
$697$	−7.52560e6	−	1.30347e7i	−0.586758	−	1.01630i
$698$	−7.18739e6	+	1.24489e7i	−0.558384	+	0.967149i
$699$	470485.	−	8.29673e6i	0.0364211	−	0.642264i
$700$	−5.71743e6	−	961438.i	−0.441018	−	0.0741611i
$701$			2.08992e7i			1.60633i	0.595758	+	0.803164i	$0.296852\pi$
$701$			2.08992e7i			1.60633i	−0.595758	+	0.803164i	$0.703148\pi$
$702$	5.21566e6	−	6.27408e6i	0.399454	−	0.480515i
$703$	−1.88093e7	+	1.08596e7i	−1.43544	+	0.828751i
$704$	789417.	−	455770.i	0.0600309	−	0.0346589i
$705$	4.29127e6	−	6.54636e6i	0.325172	−	0.496052i
$706$			7.07610e6i			0.534297i
$707$	−1.40815e7	+	1.70546e7i	−1.05950	+	1.28319i
$708$	−2.24740e6	−	127444.i	−0.168499	−	0.00955511i
$709$	−1.03050e6	+	1.78488e6i	−0.0769895	+	0.133350i	−0.901950	−	0.431841i	$-0.857864\pi$
$709$	−1.03050e6	+	1.78488e6i	−0.0769895	+	0.133350i	0.824960	+	0.565191i	$0.191197\pi$
$710$	−8.23639e6	−	1.42658e7i	−0.613184	−	1.06207i
$711$	−6.53040e6	−	1.50126e7i	−0.484469	−	1.11373i
$712$	2.90329e6	+	1.67621e6i	0.214630	+	0.123917i
$713$	1.31876e6			0.0971499
$714$	−6.70793e6	−	6.20968e6i	−0.492428	−	0.455852i
$715$	−1.72528e6			−0.126210
$716$	−1.03530e7	−	5.97731e6i	−0.754717	−	0.435736i
$717$	−3.74533e6	+	1.88816e6i	−0.272077	+	0.137164i
$718$	2.54485e6	+	4.40781e6i	0.184226	+	0.319089i
$719$	1.12467e7	−	1.94798e7i	0.811339	−	1.40528i	−0.100588	−	0.994928i	$-0.532072\pi$
$719$	1.12467e7	−	1.94798e7i	0.811339	−	1.40528i	0.911927	−	0.410353i	$-0.134594\pi$
$720$	−1.43607e6	−	163397.i	−0.103239	−	0.0117466i
$721$	1.26601e6	−	7.52862e6i	0.0906979	−	0.539358i
$722$		−	1.89497e7i		−	1.35288i
$723$	−3.47861e6	−	2.28029e6i	−0.247491	−	0.162235i
$724$	−757754.	+	437489.i	−0.0537257	+	0.0310185i
$725$	1.10005e7	−	6.35114e6i	0.777261	−	0.448752i
$726$	7.60031e6	+	4.98215e6i	0.535168	+	0.350813i
$727$			2.23831e7i			1.57067i	0.619073	+	0.785334i	$0.287509\pi$
$727$			2.23831e7i			1.57067i	−0.619073	+	0.785334i	$0.712491\pi$
$728$	4.94159e6	+	1.32489e7i	0.345572	+	0.926516i
$729$	1.35281e7	+	4.78355e6i	0.942795	+	0.333374i
$730$	7.01442e6	−	1.21493e7i	0.487175	−	0.843812i
$731$	−3.31045e6	−	5.73386e6i	−0.229136	−	0.396875i
$732$	1.45760e6	−	734829.i	0.100545	−	0.0506884i
$733$	1.07715e7	+	6.21894e6i	0.740487	+	0.427520i	0.822246	−	0.569132i	$-0.192721\pi$
$733$	1.07715e7	+	6.21894e6i	0.740487	+	0.427520i	−0.0817596	+	0.996652i	$0.526054\pi$
$734$	3.60110e6			0.246715
$735$	1.54148e7	−	1.18982e7i	1.05249	−	0.812386i
$736$	2.60835e6			0.177489
$737$	−439640.	−	253826.i	−0.0298146	−	0.0172134i
$738$	9.90582e6	−	4.30898e6i	0.669498	−	0.291228i
$739$	6.72742e6	+	1.16522e7i	0.453145	+	0.784871i	0.998579	−	0.0532829i	$-0.0169685\pi$
$739$	6.72742e6	+	1.16522e7i	0.453145	+	0.784871i	−0.545434	+	0.838154i	$0.683635\pi$
$740$	−5.43591e6	+	9.41527e6i	−0.364916	+	0.632053i
$741$	2.53844e7	+	1.43948e6i	1.69832	+	0.0963073i
$742$	−2.65142e6	−	7.10875e6i	−0.176795	−	0.474006i
$743$		−	1.80287e7i		−	1.19810i	−0.800713	−	0.599049i	$-0.795546\pi$
$743$		−	1.80287e7i		−	1.19810i	0.800713	−	0.599049i	$-0.204454\pi$
$744$	−4.50303e6	+	6.86941e6i	−0.298245	+	0.454975i
$745$	−2.48377e7	+	1.43400e7i	−1.63953	+	0.946585i
$746$	7.96359e6	−	4.59778e6i	0.523916	−	0.302483i
$747$	1.25900e6	−	1.70198e6i	0.0825511	−	0.111597i
$748$		−	908680.i		−	0.0593823i
$749$	3.17281e6	−	1.88679e7i	0.206652	−	1.22891i
$750$	−174036.	+	3.06902e6i	−0.0112976	+	0.199226i
$751$	−4.12037e6	+	7.13669e6i	−0.266586	+	0.461740i	−0.967978	−	0.251036i	$-0.919229\pi$
$751$	−4.12037e6	+	7.13669e6i	−0.266586	+	0.461740i	0.701392	+	0.712776i	$0.252562\pi$
$752$	270328.	+	468222.i	0.0174320	+	0.0301931i
$753$	6.64955e6	+	1.31900e7i	0.427371	+	0.847727i
$754$	−9.87603e6	−	5.70193e6i	−0.632636	−	0.365253i
$755$	−2.05531e7			−1.31223
$756$	−6.93819e6	+	5.97151e6i	−0.441511	+	0.379996i
$757$	−1.17983e7			−0.748308			−0.374154	−	0.927367i	$-0.622067\pi$
$757$	−1.17983e7			−0.748308			−0.374154	+	0.927367i	$0.622067\pi$
$758$	1.98749e6	+	1.14748e6i	0.125641	+	0.0725391i
$759$	−128055.	−	254008.i	−0.00806849	−	0.0160045i
$760$	−1.90382e7	−	3.29751e7i	−1.19562	−	2.07087i
$761$	6.12100e6	−	1.06019e7i	0.383143	−	0.663623i	−0.608367	−	0.793656i	$-0.708175\pi$
$761$	6.12100e6	−	1.06019e7i	0.383143	−	0.663623i	0.991510	+	0.130033i	$0.0415083\pi$
$762$	−136058.	+	2.39931e6i	−0.00848862	+	0.149692i
$763$	2.15896e6	−	2.61480e6i	0.134256	−	0.162602i
$764$		−	1.41930e7i		−	0.879711i
$765$	−1.32918e7	+	1.79686e7i	−0.821165	+	1.11010i
$766$	9.82918e6	−	5.67488e6i	0.605264	−	0.349450i
$767$	−3.95341e6	+	2.28250e6i	−0.242652	+	0.140095i
$768$	−9.31440e6	+	1.42092e7i	−0.569839	+	0.869294i
$769$			2.89879e6i			0.176767i	0.996087	+	0.0883834i	$0.0281701\pi$
$769$			2.89879e6i			0.176767i	−0.996087	+	0.0883834i	$0.971830\pi$
$770$	−1.36809e6	−	230057.i	−0.0831551	−	0.0139833i
$771$	8.19131e6	+	464507.i	0.496269	+	0.0281421i
$772$	−5.18502e6	+	8.98071e6i	−0.313117	+	0.542335i
$773$	−1.74994e6	−	3.03099e6i	−0.105336	−	0.182447i	0.808540	−	0.588442i	$-0.200258\pi$
$773$	−1.74994e6	−	3.03099e6i	−0.105336	−	0.182447i	−0.913875	+	0.405995i	$0.866925\pi$
$774$	4.35749e6	−	1.89548e6i	0.261447	−	0.113728i
$775$	−5.91464e6	−	3.41482e6i	−0.353732	−	0.204227i
$776$	−3.45035e6			−0.205688
$777$	−4.69179e6	−	1.51484e7i	−0.278796	−	0.900150i
$778$	2.44812e6			0.145005
$779$	2.91532e7	+	1.68316e7i	1.72124	+	0.993759i
$780$	1.13644e7	−	5.72923e6i	0.668822	−	0.337179i
$781$	1.19430e6	+	2.06859e6i	0.0700627	+	0.121352i
$782$	−1.04768e6	+	1.81464e6i	−0.0612651	+	0.106114i
$783$	3.39190e6	−	1.97669e7i	0.197715	−	1.15222i
$784$	254541.	+	1.32070e6i	0.0147900	+	0.0767384i
$785$			2.81683e7i			1.63150i
$786$	−1.34887e7	−	8.84209e6i	−0.778777	−	0.510503i
$787$	2.15310e7	−	1.24309e7i	1.23916	−	0.715429i	0.270237	−	0.962794i	$-0.412898\pi$
$787$	2.15310e7	−	1.24309e7i	1.23916	−	0.715429i	0.968922	+	0.247365i	$0.0795646\pi$
$788$	8.81254e6	−	5.08792e6i	0.505575	−	0.291894i
$789$	−1.78005e7	−	1.16686e7i	−1.01798	−	0.667305i
$790$			1.83023e7i			1.04337i
$791$	2.31935e6	−	865072.i	0.131803	−	0.0491599i
$792$	1.76038e6	+	200297.i	0.0997226	+	0.0113465i
$793$	1.65519e6	−	2.86687e6i	0.0934682	−	0.161892i
$794$	6.38669e6	+	1.10621e7i	0.359521	+	0.622709i
$795$	−1.65652e7	+	8.35116e6i	−0.929565	+	0.468629i
$796$	3.40947e6	+	1.96846e6i	0.190723	+	0.110114i
$797$	−4.51523e6			−0.251787			−0.125894	−	0.992044i	$-0.540180\pi$
$797$	−4.51523e6			−0.251787			−0.125894	+	0.992044i	$0.540180\pi$
$798$	1.99370e7	+	4.52632e6i	1.10829	+	0.251616i
$799$	8.36060e6			0.463309
$800$	−1.16985e7	−	6.75410e6i	−0.646254	−	0.373115i
$801$	1.75560e6	+	4.03592e6i	0.0966819	+	0.222260i
$802$	5.13801e6	+	8.89930e6i	0.282072	+	0.488562i
$803$	−1.01711e6	+	1.76169e6i	−0.0556648	+	0.0964142i
$804$	3.73879e6	+	212017.i	0.203982	+	0.0115673i
$805$	−3.44205e6	−	2.84200e6i	−0.187209	−	0.154573i
$806$			6.13152e6i			0.332453i
$807$	−249793.	+	381061.i	−0.0135019	+	0.0205973i
$808$	−2.73462e7	+	1.57883e7i	−1.47356	+	0.850762i
$809$	−2.79806e7	+	1.61546e7i	−1.50309	+	0.867811i	−0.503099	+	0.864228i	$0.667807\pi$
$809$	−2.79806e7	+	1.61546e7i	−1.50309	+	0.867811i	−0.999994	+	0.00358270i	$0.998860\pi$
$810$	−1.17351e7	−	1.09365e7i	−0.628457	−	0.585686i
$811$		−	1.64891e7i		−	0.880329i	−0.897917	−	0.440164i	$-0.854920\pi$
$811$		−	1.64891e7i		−	0.880329i	0.897917	−	0.440164i	$-0.145080\pi$
$812$	9.86639e6	+	8.14639e6i	0.525132	+	0.433586i
$813$	−373962.	+	6.59461e6i	−0.0198427	+	0.349915i
$814$	−564904.	+	978442.i	−0.0298823	+	0.0517576i
$815$	8.60352e6	+	1.49017e7i	0.453714	+	0.785855i
$816$	−694957.	−	1.37851e6i	−0.0365370	−	0.0724742i
$817$	1.28242e7	+	7.40407e6i	0.672165	+	0.388075i
$818$	1.01989e7			0.532928
$819$	−5.12846e6	+	1.78419e7i	−0.267163	+	0.929461i
$820$	1.68506e7			0.875145
$821$	−1.50775e7	−	8.70500e6i	−0.780678	−	0.450724i	0.0559928	−	0.998431i	$-0.482168\pi$
$821$	−1.50775e7	−	8.70500e6i	−0.780678	−	0.450724i	−0.836670	+	0.547707i	$0.815501\pi$
$822$	6.76327e6	+	1.34155e7i	0.349122	+	0.692514i
$823$	−7.90254e6	−	1.36876e7i	−0.406693	−	0.704413i	0.587824	−	0.808989i	$-0.299985\pi$
$823$	−7.90254e6	−	1.36876e7i	−0.406693	−	0.704413i	−0.994517	+	0.104576i	$0.966652\pi$
$824$	5.44988e6	−	9.43948e6i	0.279621	−	0.484317i
$825$	−83405.9	+	1.47081e6i	−0.00426640	+	0.0752355i
$826$	−3.43928e6	+	1.28278e6i	−0.175395	+	0.0654189i
$827$		−	7.08010e6i		−	0.359978i	−0.983669	−	0.179989i	$-0.942394\pi$
$827$		−	7.08010e6i		−	0.359978i	0.983669	−	0.179989i	$-0.0576061\pi$
$828$	1.68699e6	+	1.24791e6i	0.0855141	+	0.0632568i
$829$	186922.	−	107920.i	0.00944659	−	0.00545399i	−0.495269	−	0.868740i	$-0.664931\pi$
$829$	186922.	−	107920.i	0.00944659	−	0.00545399i	0.504716	+	0.863286i	$0.331597\pi$
$830$	−2.04963e6	+	1.18335e6i	−0.103271	+	0.0596238i
$831$	−6.38373e6	+	9.73844e6i	−0.320680	+	0.489200i
$832$			1.36365e7i			0.682958i
$833$	1.96549e7	+	6.80266e6i	0.981428	+	0.339677i
$834$	−2.06916e7	−	1.17336e6i	−1.03010	−	0.0584141i
$835$	6.45539e6	−	1.11811e7i	0.320410	−	0.554966i
$836$	1.01617e6	+	1.76005e6i	0.0502862	+	0.0870983i
$837$	−1.01161e7	+	3.73465e6i	−0.499112	+	0.184262i
$838$	1.07853e7	+	6.22690e6i	0.530546	+	0.306311i
$839$	−2.60061e7			−1.27547			−0.637735	−	0.770256i	$-0.720129\pi$
$839$	−2.60061e7			−1.27547			−0.637735	+	0.770256i	$0.720129\pi$
$840$	2.65571e7	−	8.22531e6i	1.29862	−	0.402211i
$841$	−7.52137e6			−0.366697
$842$	−1.19365e7	−	6.89157e6i	−0.580227	−	0.334994i
$843$	1.17192e7	−	5.90810e6i	0.567976	−	0.286338i
$844$	6.25058e6	+	1.08263e7i	0.302040	+	0.523148i
$845$	−893093.	+	1.54688e6i	−0.0430284	+	0.0745273i
$846$	−678363.	+	5.96204e6i	−0.0325864	+	0.286397i
$847$	−2.03915e7	−	3.42901e6i	−0.976653	−	0.164233i
$848$		−	1.28136e6i		−	0.0611902i
$849$	1.81573e7	+	1.19025e7i	0.864534	+	0.566719i
$850$	9.39772e6	−	5.42578e6i	0.446144	−	0.257582i
$851$	−3.14818e6	+	1.81760e6i	−0.149017	+	0.0860349i
$852$	−1.47361e7	−	9.65981e6i	−0.695479	−	0.455900i
$853$		−	2.81393e7i		−	1.32416i	−0.749433	−	0.662080i	$-0.769674\pi$
$853$		−	2.81393e7i		−	1.32416i	0.749433	−	0.662080i	$-0.230326\pi$
$854$	1.69479e6	−	2.05262e6i	0.0795190	−	0.0963083i
$855$	5.65125e6	−	4.96680e7i	0.264380	−	2.32360i
$856$	1.36583e7	−	2.36569e7i	0.637107	−	1.10350i
$857$	−862650.	−	1.49415e6i	−0.0401220	−	0.0694933i	0.845267	−	0.534344i	$-0.179441\pi$
$857$	−862650.	−	1.49415e6i	−0.0401220	−	0.0694933i	−0.885389	+	0.464851i	$0.846108\pi$
$858$	1.18100e6	−	595386.i	0.0547686	−	0.0276109i
$859$	3.41000e7	+	1.96876e7i	1.57678	+	0.910354i	0.995305	+	0.0967905i	$0.0308577\pi$
$859$	3.41000e7	+	1.96876e7i	1.57678	+	0.910354i	0.581475	+	0.813564i	$0.302476\pi$
$860$	7.41242e6			0.341754
$861$	−1.66974e7	+	1.80372e7i	−0.767612	+	0.829204i
$862$	−1.09908e7			−0.503802
$863$	−3.20069e7	−	1.84792e7i	−1.46291	−	0.844610i	−0.463763	−	0.885959i	$-0.653501\pi$
$863$	−3.20069e7	−	1.84792e7i	−1.46291	−	0.844610i	−0.999145	+	0.0413494i	$0.986834\pi$
$864$	−2.00083e7	+	7.38669e6i	−0.911857	+	0.336640i
$865$	1.82284e7	+	3.15726e7i	0.828341	+	1.43473i
$866$	2.75737e6	−	4.77591e6i	0.124940	−	0.216402i
$867$	−1.73647e6	−	98470.6i	−0.0784549	−	0.00444896i
$868$	1.14082e6	−	6.78419e6i	0.0513948	−	0.305632i
$869$		−	2.65389e6i		−	0.119215i
$870$	−1.22919e7	+	1.87515e7i	−0.550582	+	0.839918i
$871$	6.57693e6	−	3.79719e6i	0.293750	−	0.169597i
$872$	4.19270e6	−	2.42066e6i	0.186725	−	0.107806i
$873$	−3.64171e6	−	2.69386e6i	−0.161722	−	0.119630i
$874$		−	4.68645e6i		−	0.207523i
$875$	−2.44426e6	−	6.55334e6i	−0.107926	−	0.289363i
$876$	849578.	−	1.49818e7i	0.0374062	−	0.659636i
$877$	1.74011e7	−	3.01396e7i	0.763973	−	1.32324i	−0.176815	−	0.984244i	$-0.556579\pi$
$877$	1.74011e7	−	3.01396e7i	0.763973	−	1.32324i	0.940788	−	0.338996i	$-0.110087\pi$
$878$	3.60321e6	+	6.24094e6i	0.157744	+	0.273221i
$879$	3.76903e6	+	7.47619e6i	0.164535	+	0.326368i
$880$	−202907.	−	117148.i	−0.00883262	−	0.00509951i
$881$	2.98621e7			1.29623			0.648114	−	0.761544i	$-0.275558\pi$
$881$	2.98621e7			1.29623			0.648114	+	0.761544i	$0.275558\pi$
$882$	−6.44582e6	+	1.34642e7i	−0.279001	+	0.582785i
$883$	−3.38129e7			−1.45942			−0.729710	−	0.683757i	$-0.760345\pi$
$883$	−3.38129e7			−1.45942			−0.729710	+	0.683757i	$0.760345\pi$
$884$	1.17725e7	+	6.79684e6i	0.506684	+	0.292534i
$885$	4.04037e6	+	8.01442e6i	0.173406	+	0.343965i
$886$	3.90506e6	+	6.76377e6i	0.167126	+	0.289471i
$887$	1.50058e7	−	2.59908e7i	0.640398	−	1.10920i	−0.344946	−	0.938622i	$-0.612103\pi$
$887$	1.50058e7	−	2.59908e7i	0.640398	−	1.10920i	0.985344	−	0.170579i	$-0.0545637\pi$
$888$	1.28188e6	−	2.26052e7i	0.0545525	−	0.962001i
$889$	−1.91088e6	−	5.12329e6i	−0.0810923	−	0.217417i
$890$		−	4.92030e6i		−	0.208217i
$891$	1.70163e6	+	1.58582e6i	0.0718077	+	0.0669207i
$892$	302347.	−	174560.i	0.0127231	−	0.00734570i
$893$	−1.61939e7	+	9.34956e6i	−0.679553	+	0.392340i
$894$	1.20533e7	−	1.83875e7i	0.504387	−	0.769446i
$895$			4.76658e7i			1.98906i
$896$	2.05518e6	−	1.22217e7i	0.0855226	−	0.508581i
$897$	4.24866e6	+	240930.i	0.176308	+	0.00999793i
$898$	1.08070e7	−	1.87183e7i	0.447213	−	0.774596i
$899$	7.53613e6	+	1.30530e7i	0.310992	+	0.538654i
$900$	−4.33481e6	−	9.96521e6i	−0.178387	−	0.410091i
$901$	−1.71600e7	−	9.90735e6i	−0.704217	−	0.406580i
$902$	1.75112e6			0.0716639
$903$	−7.34506e6	+	7.93442e6i	−0.299762	+	0.323814i
$904$	3.53425e6			0.143839
$905$	3.02133e6	+	1.74437e6i	0.122624	+	0.0707973i
$906$	1.40691e7	−	7.09277e6i	0.569438	−	0.287075i
$907$	−5.32535e6	−	9.22377e6i	−0.214946	−	0.372298i	0.738310	−	0.674462i	$-0.235624\pi$
$907$	−5.32535e6	−	9.22377e6i	−0.214946	−	0.372298i	−0.953256	+	0.302164i	$0.902291\pi$
$908$	−4.16662e6	+	7.21680e6i	−0.167714	+	0.290489i
$909$	−4.11896e7	−	4.68657e6i	−1.65340	−	0.188125i
$910$	1.32137e7	−	1.60036e7i	0.528959	−	0.640642i
$911$		−	1.33185e7i		−	0.531690i	−0.964016	−	0.265845i	$-0.914349\pi$
$911$		−	1.33185e7i		−	0.531690i	0.964016	−	0.265845i	$-0.0856509\pi$
$912$	2.88765e6	+	1.89291e6i	0.114963	+	0.0753604i
$913$	297203.	−	171590.i	0.0117998	−	0.00681264i
$914$	−2.38001e7	+	1.37410e7i	−0.942352	+	0.544067i
$915$	−5.44327e6	−	3.56817e6i	−0.214935	−	0.140894i
$916$			410101.i			0.0161493i
$917$	3.61898e7	+	6.08565e6i	1.42123	+	0.238992i
$918$	2.89770e6	−	1.68869e7i	0.113487	−	0.661367i
$919$	−591537.	+	1.02457e6i	−0.0231043	+	0.0400178i	−0.877346	−	0.479858i	$-0.840688\pi$
$919$	−591537.	+	1.02457e6i	−0.0231043	+	0.0400178i	0.854242	+	0.519875i	$0.174022\pi$
$920$	−3.18649e6	−	5.51916e6i	−0.124120	−	0.214982i
$921$	−7.11845e6	+	3.58868e6i	−0.276526	+	0.139407i
$922$	−2.94121e6	−	1.69811e6i	−0.113946	−	0.0657868i
$923$	−3.57331e7			−1.38059
$924$	−1.41749e6	+	439027.i	−0.0546185	+	0.0169165i
$925$	1.88261e7			0.723446
$926$	−3.84579e6	−	2.22037e6i	−0.147387	−	0.0850937i
$927$	1.31220e7	−	5.70800e6i	0.501535	−	0.218165i
$928$	1.49056e7	+	2.58172e7i	0.568170	+	0.984100i
$929$	4.74229e6	−	8.21389e6i	0.180281	−	0.312255i	−0.761695	−	0.647935i	$-0.775633\pi$
$929$	4.74229e6	−	8.21389e6i	0.180281	−	0.312255i	0.941976	+	0.335680i	$0.108966\pi$
$930$	1.20359e7	+	682522.i	0.456321	+	0.0258767i
$931$	−4.56775e7	+	8.80355e6i	−1.72714	+	0.332877i
$932$			9.93714e6i			0.374733i
$933$	−2.06216e7	+	3.14584e7i	−0.775563	+	1.18313i
$934$	−9.59477e6	+	5.53954e6i	−0.359888	+	0.207781i
$935$	−3.13770e6	+	1.81155e6i	−0.117377	+	0.0677676i
$936$	−1.57625e7	+	2.13086e7i	−0.588077	+	0.794995i
$937$		−	1.67626e7i		−	0.623723i	−0.950128	−	0.311861i	$-0.899048\pi$
$937$		−	1.67626e7i		−	0.623723i	0.950128	−	0.311861i	$-0.100952\pi$
$938$	5.72162e6	−	2.13405e6i	0.212330	−	0.0791950i
$939$	−2.40200e6	+	4.23580e7i	−0.0889016	+	1.56773i
$940$	−4.68005e6	+	8.10609e6i	−0.172755	+	0.299221i
$941$	2.05801e7	+	3.56458e7i	0.757660	+	1.31231i	0.944041	+	0.329828i	$0.106991\pi$
$941$	2.05801e7	+	3.56458e7i	0.757660	+	1.31231i	−0.186381	+	0.982477i	$0.559676\pi$
$942$	−9.72072e6	−	1.92819e7i	−0.356920	−	0.707982i
$943$	4.87946e6	+	2.81716e6i	0.178687	+	0.103165i
$944$	−619935.			−0.0226421
$945$	3.44519e7	+	1.20530e7i	1.25497	+	0.439050i
$946$	770305.			0.0279856
$947$	1.94640e7	+	1.12376e7i	0.705274	+	0.407190i	0.809309	−	0.587383i	$-0.199842\pi$
$947$	1.94640e7	+	1.12376e7i	0.705274	+	0.407190i	−0.104034	+	0.994574i	$0.533175\pi$
$948$	8.81288e6	+	1.74811e7i	0.318491	+	0.631754i
$949$	−1.52158e7	−	2.63546e7i	−0.548441	−	0.949928i
$950$	−1.21352e7	+	2.10187e7i	−0.436251	+	0.755610i
$951$	−1.45693e6	+	2.56922e7i	−0.0522383	+	0.921192i
$952$	2.28985e7	+	1.89066e7i	0.818870	+	0.676117i
$953$		−	3.77762e6i		−	0.134737i	−0.997728	−	0.0673683i	$-0.978540\pi$
$953$		−	3.77762e6i		−	0.134737i	0.997728	−	0.0673683i	$-0.0214603\pi$
$954$	8.45738e6	−	1.14332e7i	0.300860	−	0.406720i
$955$	−4.90089e7	+	2.82953e7i	−1.73887	+	1.00393i
$956$	4.34364e6	−	2.50780e6i	0.153713	−	0.0887460i
$957$	1.78237e6	−	2.71902e6i	0.0629098	−	0.0959694i
$958$		−	299367.i		−	0.0105388i
$959$	−2.63605e7	−	2.17651e7i	−0.925566	−	0.764213i
$960$	2.67677e7	+	1.51793e6i	0.937419	+	0.0531585i
$961$	−1.02626e7	+	1.77754e7i	−0.358467	+	0.620884i
$962$	−8.45086e6	−	1.46373e7i	−0.294417	−	0.509945i
$963$	3.28859e7	−	1.43052e7i	1.14273	−	0.497082i
$964$	4.30742e6	+	2.48689e6i	0.149288	+	0.0861913i
$965$	4.13476e7			1.42933
$966$	3.33692e6	+	757586.i	0.115054	+	0.0261210i
$967$	3.72823e7			1.28214			0.641072	−	0.767481i	$-0.278490\pi$
$967$	3.72823e7			1.28214			0.641072	+	0.767481i	$0.278490\pi$
$968$	−2.55671e7	−	1.47612e7i	−0.876987	−	0.506329i
$969$	4.76770e7	−	2.40358e7i	1.63117	−	0.822334i
$970$	2.53201e6	+	4.38556e6i	0.0864043	+	0.149657i
$971$	−1.89586e7	+	3.28373e7i	−0.645296	+	1.11769i	0.338937	+	0.940809i	$0.389933\pi$
$971$	−1.89586e7	+	3.28373e7i	−0.645296	+	1.11769i	−0.984233	+	0.176877i	$0.943401\pi$
$972$	−1.64747e7	−	4.79510e6i	−0.559311	−	0.162792i
$973$	4.41832e7	−	1.64794e7i	1.49615	−	0.558033i
$974$			1.61376e7i			0.545056i
$975$	−1.84314e7	−	1.20821e7i	−0.620936	−	0.407035i
$976$	389325.	−	224777.i	0.0130824	−	0.00755314i
$977$	2.21992e7	−	1.28167e7i	0.744050	−	0.429577i	−0.0794903	−	0.996836i	$-0.525329\pi$
$977$	2.21992e7	−	1.28167e7i	0.744050	−	0.429577i	0.823540	+	0.567258i	$0.191996\pi$
$978$	−1.10318e7	−	7.23158e6i	−0.368808	−	0.241761i
$979$			713459.i			0.0237910i
$980$	−1.75979e7	+	1.52486e7i	−0.585323	+	0.507184i
$981$	6.31517e6	+	718542.i	0.209514	+	0.0238385i
$982$	−1.75586e7	+	3.04124e7i	−0.581047	+	1.00640i
$983$	−1.74664e7	−	3.02526e7i	−0.576526	−	0.998572i	−0.995874	−	0.0907467i	$-0.971075\pi$
$983$	−1.74664e7	−	3.02526e7i	−0.576526	−	0.998572i	0.419348	−	0.907826i	$-0.362259\pi$
$984$	−3.13359e7	+	1.57976e7i	−1.03170	+	0.520120i
$985$	−3.51375e7	−	2.02867e7i	−1.15393	−	0.666224i
$986$	−2.39482e7			−0.784477
$987$	−4.03941e6	−	1.30421e7i	−0.131985	−	0.426141i
$988$	−3.04033e7			−0.990897
$989$	2.14643e6	+	1.23924e6i	0.0697793	+	0.0402871i
$990$	−1.03725e6	−	2.38452e6i	−0.0336354	−	0.0773237i
$991$	−2.48035e7	−	4.29610e7i	−0.802286	−	1.38960i	−0.918108	−	0.396330i	$-0.870283\pi$
$991$	−2.48035e7	−	4.29610e7i	−0.802286	−	1.38960i	0.115822	−	0.993270i	$-0.463050\pi$
$992$	8.01429e6	−	1.38812e7i	0.258574	−	0.447864i
$993$	4.08648e7	+	2.31733e6i	1.31515	+	0.0745787i
$994$	−2.83351e7	−	4.76481e6i	−0.909619	−	0.152961i
$995$		−	1.56974e7i		−	0.502654i
$996$	−1.38786e6	+	2.11720e6i	−0.0443301	+	0.0676259i
$997$	−7.82003e6	+	4.51490e6i	−0.249155	+	0.143850i	−0.619377	−	0.785093i	$-0.712615\pi$
$997$	−7.82003e6	+	4.51490e6i	−0.249155	+	0.143850i	0.370222	+	0.928943i	$0.379282\pi$
$998$	3.18735e7	−	1.84022e7i	1.01299	−	0.584848i
$999$	1.90020e7	−	2.28581e7i	0.602400	−	0.724646i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.6.g.c.5.3	✓	16
3.2	odd	2	inner	21.6.g.c.5.6	yes	16
7.2	even	3		147.6.c.c.146.11		16
7.3	odd	6	inner	21.6.g.c.17.6	yes	16
7.5	odd	6		147.6.c.c.146.12		16
21.2	odd	6		147.6.c.c.146.6		16
21.5	even	6		147.6.c.c.146.5		16
21.17	even	6	inner	21.6.g.c.17.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.g.c.5.3	✓	16	1.1	even	1	trivial
21.6.g.c.5.6	yes	16	3.2	odd	2	inner
21.6.g.c.17.3	yes	16	21.17	even	6	inner
21.6.g.c.17.6	yes	16	7.3	odd	6	inner
147.6.c.c.146.5		16	21.5	even	6
147.6.c.c.146.6		16	21.2	odd	6
147.6.c.c.146.11		16	7.2	even	3
147.6.c.c.146.12		16	7.5	odd	6

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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	21.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.16536 - 1.82752i) q^{2} +(7.01741 + 13.9196i) q^{3} +(-9.32032 - 16.1433i) q^{4} +(-37.1622 + 64.3668i) q^{5} +(3.22580 - 56.8851i) q^{6} +(45.3051 + 121.468i) q^{7} +185.094i q^{8} +(-144.512 + 195.359i) q^{9} +O(q^{10})\)	\(q+(-3.16536 - 1.82752i) q^{2} +(7.01741 + 13.9196i) q^{3} +(-9.32032 - 16.1433i) q^{4} +(-37.1622 + 64.3668i) q^{5} +(3.22580 - 56.8851i) q^{6} +(45.3051 + 121.468i) q^{7} +185.094i q^{8} +(-144.512 + 195.359i) q^{9} +(235.264 - 135.830i) q^{10} +(-34.1140 + 19.6957i) q^{11} +(159.304 - 243.019i) q^{12} -589.288i q^{13} +(78.5784 - 467.286i) q^{14} +(-1156.74 - 65.5958i) q^{15} +(40.0132 - 69.3048i) q^{16} +(-618.755 - 1071.71i) q^{17} +(814.457 - 354.284i) q^{18} +(2396.97 + 1383.89i) q^{19} +1385.45 q^{20} +(-1372.86 + 1483.02i) q^{21} +143.977 q^{22} +(401.189 + 231.627i) q^{23} +(-2576.44 + 1298.88i) q^{24} +(-1199.56 - 2077.69i) q^{25} +(-1076.94 + 1865.31i) q^{26} +(-3733.43 - 640.637i) q^{27} +(1538.63 - 1863.49i) q^{28} +5294.57i q^{29} +(3541.64 + 2321.61i) q^{30} +(2465.35 - 1423.37i) q^{31} +(4876.16 - 2815.25i) q^{32} +(-513.548 - 336.641i) q^{33} +4523.16i q^{34} +(-9502.13 - 1597.87i) q^{35} +(4500.64 + 512.084i) q^{36} +(-3923.56 + 6795.80i) q^{37} +(-5058.19 - 8761.05i) q^{38} +(8202.67 - 4135.28i) q^{39} +(-11913.9 - 6878.49i) q^{40} +12162.5 q^{41} +(7055.86 - 2185.35i) q^{42} +5350.18 q^{43} +(635.906 + 367.140i) q^{44} +(-7204.27 - 16561.8i) q^{45} +(-846.606 - 1466.37i) q^{46} +(-3377.99 + 5850.86i) q^{47} +(1245.49 + 70.6281i) q^{48} +(-12701.9 + 11006.2i) q^{49} +8768.86i q^{50} +(10575.8 - 16133.5i) q^{51} +(-9513.04 + 5492.35i) q^{52} +(13866.6 - 8005.88i) q^{53} +(10646.9 + 8850.78i) q^{54} -2927.74i q^{55} +(-22483.0 + 8385.69i) q^{56} +(-2442.74 + 43076.3i) q^{57} +(9675.96 - 16759.2i) q^{58} +(-3873.32 - 6708.79i) q^{59} +(9722.29 + 19285.0i) q^{60} +(4864.96 + 2808.79i) q^{61} -10405.0 q^{62} +(-30277.0 - 8702.80i) q^{63} -23140.6 q^{64} +(37930.6 + 21899.2i) q^{65} +(1010.35 + 2004.11i) q^{66} +(6443.69 + 11160.8i) q^{67} +(-11534.0 + 19977.4i) q^{68} +(-408.849 + 7209.82i) q^{69} +(27157.6 + 22423.2i) q^{70} -60637.7i q^{71} +(-36159.8 - 26748.3i) q^{72} +(44722.8 - 25820.7i) q^{73} +(24839.0 - 14340.8i) q^{74} +(20502.9 - 31277.4i) q^{75} -51593.3i q^{76} +(-3937.93 - 3251.44i) q^{77} +(-33521.7 - 1900.93i) q^{78} +(-33686.1 + 58346.0i) q^{79} +(2973.95 + 5151.04i) q^{80} +(-17281.6 - 56463.5i) q^{81} +(-38498.7 - 22227.2i) q^{82} -8712.06 q^{83} +(36736.3 + 8340.29i) q^{84} +91977.1 q^{85} +(-16935.3 - 9777.57i) q^{86} +(-73698.5 + 37154.2i) q^{87} +(-3645.55 - 6314.28i) q^{88} +(9056.02 - 15685.5i) q^{89} +(-7462.85 + 65589.9i) q^{90} +(71579.6 - 26697.8i) q^{91} -8635.34i q^{92} +(37113.1 + 24328.4i) q^{93} +(21385.2 - 12346.7i) q^{94} +(-178153. + 102857. i) q^{95} +(73405.3 + 48118.6i) q^{96} +18641.1i q^{97} +(60320.3 - 11625.7i) q^{98} +(1082.14 - 9510.75i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 18 q^{3} + 86 q^{4} - 616 q^{7} - 606 q^{9}+O(q^{10}) \) 16 * q + 18 * q^3 + 86 * q^4 - 616 * q^7 - 606 * q^9	\( 16 q + 18 q^{3} + 86 q^{4} - 616 q^{7} - 606 q^{9} - 546 q^{10} + 4128 q^{12} + 1188 q^{15} - 2858 q^{16} - 438 q^{18} + 3258 q^{19} + 882 q^{21} - 21900 q^{22} + 10374 q^{24} - 6578 q^{25} + 34006 q^{28} + 450 q^{30} - 9792 q^{31} + 17556 q^{33} - 15132 q^{36} - 10466 q^{37} - 17418 q^{39} - 60774 q^{40} - 56994 q^{42} + 111052 q^{43} - 31374 q^{45} + 81696 q^{46} - 51548 q^{49} + 31596 q^{51} + 126960 q^{52} + 7434 q^{54} - 31368 q^{57} - 41706 q^{58} + 60066 q^{60} - 128580 q^{61} - 123606 q^{63} - 158884 q^{64} - 160314 q^{66} - 102202 q^{67} + 234318 q^{70} + 330864 q^{72} + 345150 q^{73} + 428202 q^{75} - 277512 q^{78} - 251308 q^{79} + 179262 q^{81} - 534576 q^{82} + 106176 q^{84} + 205152 q^{85} - 551922 q^{87} - 359514 q^{88} + 65814 q^{91} + 17676 q^{93} + 276612 q^{94} + 1043910 q^{96} + 215472 q^{99}+O(q^{100}) \) 16 * q + 18 * q^3 + 86 * q^4 - 616 * q^7 - 606 * q^9 - 546 * q^10 + 4128 * q^12 + 1188 * q^15 - 2858 * q^16 - 438 * q^18 + 3258 * q^19 + 882 * q^21 - 21900 * q^22 + 10374 * q^24 - 6578 * q^25 + 34006 * q^28 + 450 * q^30 - 9792 * q^31 + 17556 * q^33 - 15132 * q^36 - 10466 * q^37 - 17418 * q^39 - 60774 * q^40 - 56994 * q^42 + 111052 * q^43 - 31374 * q^45 + 81696 * q^46 - 51548 * q^49 + 31596 * q^51 + 126960 * q^52 + 7434 * q^54 - 31368 * q^57 - 41706 * q^58 + 60066 * q^60 - 128580 * q^61 - 123606 * q^63 - 158884 * q^64 - 160314 * q^66 - 102202 * q^67 + 234318 * q^70 + 330864 * q^72 + 345150 * q^73 + 428202 * q^75 - 277512 * q^78 - 251308 * q^79 + 179262 * q^81 - 534576 * q^82 + 106176 * q^84 + 205152 * q^85 - 551922 * q^87 - 359514 * q^88 + 65814 * q^91 + 17676 * q^93 + 276612 * q^94 + 1043910 * q^96 + 215472 * q^99

Introduction

L-functions

Modular forms

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