LMFDB - Embedded newform 21.6.g.c.17.6

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			17.6
Root			$3.16536 - 1.82752i$ of defining polynomial
Character	$\chi$	$=$	21.17
Dual form			21.6.g.c.5.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.16536 - 1.82752i) q^{2} +(-8.54605 + 13.0371i) q^{3} +(-9.32032 + 16.1433i) q^{4} +(37.1622 + 64.3668i) q^{5} +(-3.22580 + 56.8851i) q^{6} +(45.3051 - 121.468i) q^{7} +185.094i q^{8} +(-96.9302 - 222.831i) q^{9} +O(q^{10})$	\(q+(3.16536 - 1.82752i) q^{2} +(-8.54605 + 13.0371i) 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} +(-96.9302 - 222.831i) q^{9} +(235.264 + 135.830i) q^{10} +(34.1140 + 19.6957i) q^{11} +(-130.809 - 259.471i) 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} +(-714.048 - 528.198i) q^{18} +(2396.97 - 1383.89i) q^{19} -1385.45 q^{20} +(1196.41 + 1628.72i) q^{21} +143.977 q^{22} +(-401.189 + 231.627i) q^{23} +(-2413.08 - 1581.82i) 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} +(-3781.39 + 1906.34i) q^{30} +(2465.35 + 1423.37i) q^{31} +(-4876.16 - 2815.25i) q^{32} +(-548.314 + 276.426i) 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} +(-7682.59 - 5036.09i) q^{39} +(-11913.9 + 6878.49i) q^{40} -12162.5 q^{41} +(6763.57 + 2969.02i) q^{42} +5350.18 q^{43} +(-635.906 + 367.140i) q^{44} +(10740.8 - 14520.0i) 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} +(8684.11 + 17225.7i) q^{51} +(-9513.04 - 5492.35i) q^{52} +(-13866.6 - 8005.88i) q^{53} +(12988.4 - 4795.08i) 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} +(11840.2 - 18062.2i) q^{60} +(4864.96 - 2808.79i) q^{61} +10405.0 q^{62} +(-31458.2 + 1678.54i) q^{63} -23140.6 q^{64} +(-37930.6 + 21899.2i) q^{65} +(-1230.44 + 1877.04i) 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} +(41244.6 - 17941.2i) q^{72} +(44722.8 + 25820.7i) q^{73} +(-24839.0 - 14340.8i) q^{74} +(-16835.5 - 33394.7i) 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} +(-40258.1 + 43198.0i) q^{81} +(-38498.7 + 22227.2i) q^{82} +8712.06 q^{83} +(-37443.7 + 4133.74i) q^{84} +91977.1 q^{85} +(16935.3 - 9777.57i) q^{86} +(-69025.7 - 45247.7i) 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} +(-39625.5 + 19976.7i) q^{93} +(21385.2 + 12346.7i) q^{94} +(178153. + 102857. i) q^{95} +(78374.5 - 39511.5i) 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 $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

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

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	$-0.561954\pi$
$2$	3.16536	−	1.82752i	0.559562	−	0.323064i	0.752970	+	0.658055i	$0.228621\pi$
$3$	−8.54605	+	13.0371i	−0.548229	+	0.836328i
$3$	−8.54605	+	13.0371i	−0.548229	+	0.836328i
$4$	−9.32032	+	16.1433i	−0.291260	+	0.504477i
$5$	37.1622	+	64.3668i	0.664777	+	1.15143i	0.979346	+	0.202193i	$0.0648069\pi$
$5$	37.1622	+	64.3668i	0.664777	+	1.15143i	−0.314568	+	0.949235i	$0.601860\pi$
$6$	−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
$9$	−96.9302	−	222.831i	−0.398890	−	0.916999i
$10$	235.264	+	135.830i	0.743969	+	0.429531i
$11$	34.1140	+	19.6957i	0.0850062	+	0.0490783i	0.541901	−	0.840443i	$-0.317705\pi$
$11$	34.1140	+	19.6957i	0.0850062	+	0.0490783i	−0.456894	+	0.889521i	$0.651038\pi$
$12$	−130.809	−	259.471i	−0.262231	−	0.520158i
$13$			589.288i			0.967096i	0.875318	+	0.483548i	$0.160652\pi$
$13$			589.288i			0.967096i	−0.875318	+	0.483548i	$0.839348\pi$
$14$	−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	−0.480475	−	0.877008i	$-0.659536\pi$
$17$	618.755	−	1071.71i	0.519274	−	0.899409i	0.999749	−	0.0224003i	$-0.00713083\pi$
$18$	−714.048	−	528.198i	−0.519453	−	0.384251i
$19$	2396.97	−	1383.89i	1.52328	−	0.879465i	0.523657	−	0.851929i	$-0.324567\pi$
$19$	2396.97	−	1383.89i	1.52328	−	0.879465i	0.999621	−	0.0275354i	$-0.00876591\pi$
$20$	−1385.45			−0.774492
$21$	1196.41	+	1628.72i	0.592012	+	0.805929i
$22$	143.977			0.0634217
$23$	−401.189	+	231.627i	−0.158136	+	0.0912997i	−0.576980	−	0.816759i	$-0.695769\pi$
$23$	−401.189	+	231.627i	−0.158136	+	0.0912997i	0.418844	+	0.908058i	$0.362435\pi$
$24$	−2413.08	−	1581.82i	−0.855153	−	0.560569i
$25$	−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	$0.801279\pi$
$30$	−3781.39	+	1906.34i	−0.767094	+	0.386721i
$31$	2465.35	+	1423.37i	0.460759	+	0.266019i	0.712363	−	0.701811i	$-0.247625\pi$
$31$	2465.35	+	1423.37i	0.460759	+	0.266019i	−0.251604	+	0.967830i	$0.580958\pi$
$32$	−4876.16	−	2815.25i	−0.841788	−	0.486007i
$33$	−548.314	+	276.426i	−0.0876485	+	0.0441869i
$34$		−	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	0.528288	−	0.849065i	$-0.322834\pi$
$37$	−3923.56	−	6795.80i	−0.471168	−	0.816087i	−0.999456	+	0.0329784i	$0.989501\pi$
$38$	5058.19	−	8761.05i	0.568246	−	0.984231i
$39$	−7682.59	−	5036.09i	−0.808809	−	0.530190i
$40$	−11913.9	+	6878.49i	−1.17735	+	0.679741i
$41$	−12162.5			−1.12996			−0.564980	−	0.825105i	$-0.691116\pi$
$41$	−12162.5			−1.12996			−0.564980	+	0.825105i	$0.691116\pi$
$42$	6763.57	+	2969.02i	0.591634	+	0.259710i
$43$	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
$45$	10740.8	−	14520.0i	0.790686	−	1.06889i
$46$	−846.606	+	1466.37i	−0.0589912	+	0.102176i
$47$	3377.99	+	5850.86i	0.223056	+	0.386345i	0.955734	−	0.294230i	$-0.0950633\pi$
$47$	3377.99	+	5850.86i	0.223056	+	0.386345i	−0.732678	+	0.680575i	$0.761730\pi$
$48$	−1245.49	−	70.6281i	−0.0780253	−	0.00442460i
$49$	−12701.9	−	11006.2i	−0.755751	−	0.654860i
$50$			8768.86i			0.496042i
$51$	8684.11	+	17225.7i	0.467520	+	0.927365i
$52$	−9513.04	−	5492.35i	−0.487878	−	0.281676i
$53$	−13866.6	−	8005.88i	−0.678078	−	0.391489i	0.121052	−	0.992646i	$-0.461373\pi$
$53$	−13866.6	−	8005.88i	−0.678078	−	0.391489i	−0.799131	+	0.601157i	$0.794706\pi$
$54$	12988.4	−	4795.08i	0.606139	−	0.223775i
$55$			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	$-0.787060\pi$
$59$	3873.32	−	6708.79i	0.144862	−	0.250908i	0.929321	+	0.369272i	$0.120393\pi$
$60$	11840.2	−	18062.2i	0.424599	−	0.647730i
$61$	4864.96	−	2808.79i	0.167400	−	0.0966484i	−0.413959	−	0.910295i	$-0.635854\pi$
$61$	4864.96	−	2808.79i	0.167400	−	0.0966484i	0.581359	+	0.813647i	$0.302521\pi$
$62$	10405.0			0.343765
$63$	−31458.2	+	1678.54i	−0.998580	+	0.0532819i
$64$	−23140.6			−0.706195
$65$	−37930.6	+	21899.2i	−1.11354	+	0.642903i
$66$	−1230.44	+	1877.04i	−0.0347696	+	0.0530413i
$67$	6443.69	−	11160.8i	0.175367	−	0.303745i	−0.764921	−	0.644124i	$-0.777222\pi$
$67$	6443.69	−	11160.8i	0.175367	−	0.303745i	0.940288	+	0.340379i	$0.110555\pi$
$68$	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	$-0.253020\pi$
$72$	41244.6	−	17941.2i	0.937640	−	0.407868i
$73$	44722.8	+	25820.7i	0.982249	+	0.567101i	0.902948	−	0.429749i	$-0.141398\pi$
$73$	44722.8	+	25820.7i	0.982249	+	0.567101i	0.0793003	+	0.996851i	$0.474731\pi$
$74$	−24839.0	−	14340.8i	−0.527296	−	0.304434i
$75$	−16835.5	−	33394.7i	−0.345600	−	0.685528i
$76$			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	−0.991688	−	0.128665i	$-0.958931\pi$
$79$	−33686.1	−	58346.0i	−0.607272	−	1.05183i	0.384417	−	0.923160i	$-0.374403\pi$
$80$	−2973.95	+	5151.04i	−0.0519528	+	0.0899849i
$81$	−40258.1	+	43198.0i	−0.681774	+	0.731563i
$82$	−38498.7	+	22227.2i	−0.632283	+	0.365049i
$83$	8712.06			0.138812			0.0694058	−	0.997589i	$-0.477890\pi$
$83$	8712.06			0.138812			0.0694058	+	0.997589i	$0.477890\pi$
$84$	−37443.7	+	4133.74i	−0.579002	+	0.0639213i
$85$	91977.1			1.38081
$86$	16935.3	−	9777.57i	0.246914	−	0.142556i
$87$	−69025.7	−	45247.7i	−0.977716	−	0.640912i
$88$	−3645.55	+	6314.28i	−0.0501830	+	0.0869196i
$89$	−9056.02	−	15685.5i	−0.121189	−	0.209905i	0.799048	−	0.601267i	$-0.205337\pi$
$89$	−9056.02	−	15685.5i	−0.121189	−	0.209905i	−0.920237	+	0.391362i	$0.872004\pi$
$90$	7462.85	−	65589.9i	0.0971177	−	0.853554i
$91$	71579.6	+	26697.8i	0.906120	+	0.337965i
$92$		−	8635.34i		−	0.106368i
$93$	−39625.5	+	19976.7i	−0.475081	+	0.239506i
$94$	21385.2	+	12346.7i	0.249628	+	0.144123i
$95$	178153.	+	102857.i	2.02528	+	1.16930i
$96$	78374.5	−	39511.5i	0.867954	−	0.437568i
$97$		−	18641.1i		−	0.201160i	−0.994929	−	0.100580i	$-0.967930\pi$
$97$		−	18641.1i		−	0.201160i	0.994929	−	0.100580i	$-0.0320698\pi$
$98$	−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	0.0643885	+	0.997925i	$0.479490\pi$
$101$	−85299.1	+	147742.i	−0.832034	+	1.44113i	−0.896423	+	0.443200i	$0.853843\pi$
$102$	58968.7	+	38655.1i	0.561204	+	0.367880i
$103$	−50998.3	+	29443.9i	−0.473656	+	0.273465i	−0.717769	−	0.696282i	$-0.754837\pi$
$103$	−50998.3	+	29443.9i	−0.473656	+	0.273465i	0.244113	+	0.969747i	$0.421503\pi$
$104$	−109074.			−0.988864
$105$	−60374.2	+	137535.i	−0.534414	+	1.21742i
$106$	−58523.7			−0.505903
$107$	127810.	−	73791.2i	1.07921	−	0.623082i	0.148526	−	0.988908i	$-0.452547\pi$
$107$	127810.	−	73791.2i	1.07921	−	0.623082i	0.930683	+	0.365827i	$0.119214\pi$
$108$	−45138.7	+	54298.8i	−0.372383	+	0.447951i
$109$	−13078.0	+	22651.8i	−0.105433	+	0.182615i	−0.913915	−	0.405906i	$-0.866956\pi$
$109$	−13078.0	+	22651.8i	−0.105433	+	0.182615i	0.808482	+	0.588521i	$0.200289\pi$
$110$	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	$-0.0224072\pi$
$114$	70990.8	+	140816.i	0.511611	+	1.01482i
$115$	−29818.1	−	17215.5i	−0.210250	−	0.121388i
$116$	−85471.7	−	49347.1i	−0.589763	−	0.340500i
$117$	131312.	−	57119.8i	0.886826	−	0.385764i
$118$		−	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
$123$	103941.	−	158563.i	0.619477	−	0.945017i
$124$	−45955.7	+	26532.5i	−0.268401	+	0.154962i
$125$	53951.2			0.308835
$126$	−96509.1	+	62803.8i	−0.541554	+	0.352419i
$127$	−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
$129$	−45722.9	+	69750.6i	−0.241913	+	0.369040i
$130$	−80042.7	+	138638.i	−0.415397	+	0.719489i
$131$	−141536.	−	245147.i	−0.720590	−	1.24810i	−0.960763	−	0.277369i	$-0.910538\pi$
$131$	−141536.	−	245147.i	−0.720590	−	1.24810i	0.240173	−	0.970730i	$-0.422796\pi$
$132$	648.048	−	11427.9i	0.00323722	−	0.0570865i
$133$	−59503.5	−	353853.i	−0.291685	−	1.73458i
$134$		−	47104.0i		−	0.226619i
$135$	97506.6	+	264116.i	0.460468	+	1.24727i
$136$	198368.	+	114528.i	0.919653	+	0.530962i
$137$	228359.	+	131843.i	1.03948	+	0.600145i	0.919686	−	0.392654i	$-0.128443\pi$
$137$	228359.	+	131843.i	1.03948	+	0.600145i	0.119795	+	0.992799i	$0.461776\pi$
$138$	−11882.0	−	23568.9i	−0.0531117	−	0.105352i
$139$			363744.i			1.59683i	0.602108	+	0.798415i	$0.294328\pi$
$139$			363744.i			1.59683i	−0.602108	+	0.798415i	$0.705672\pi$
$140$	−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
$144$	11564.8	−	15633.9i	0.0464762	−	0.0628291i
$145$	−340795.	+	196758.i	−1.34609	+	0.777163i
$146$	188752.			0.732839
$147$	252040.	−	71535.8i	0.962002	−	0.273042i
$148$	146275.			0.548929
$149$	−334179.	+	192939.i	−1.23314	+	0.711957i	−0.967684	−	0.252165i	$-0.918857\pi$
$149$	−334179.	+	192939.i	−1.23314	+	0.711957i	−0.265461	+	0.964122i	$0.585524\pi$
$150$	−114320.	−	74939.1i	−0.414854	−	0.271945i
$151$	138266.	−	239484.i	0.493485	−	0.854741i	−0.506487	−	0.862248i	$-0.669056\pi$
$151$	138266.	−	239484.i	0.493485	−	0.854741i	0.999972	+	0.00750641i	$0.00238939\pi$
$152$	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
$156$	152903.	−	77084.2i	0.503042	−	0.253603i
$157$	328216.	+	189496.i	1.06270	+	0.613550i	0.926178	−	0.377087i	$-0.123074\pi$
$157$	328216.	+	189496.i	1.06270	+	0.613550i	0.136522	+	0.990637i	$0.456408\pi$
$158$	−213257.	−	123124.i	−0.679613	−	0.392375i
$159$	222878.	−	112361.i	0.699155	−	0.352470i
$160$		−	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	0.984666	−	0.174453i	$-0.0558156\pi$
$163$	115756.	+	200496.i	0.341252	+	0.591067i	−0.643413	+	0.765519i	$0.722482\pi$
$164$	113358.	−	196342.i	0.329112	−	0.570038i
$165$	−38169.2	−	25020.6i	−0.109145	−	0.0715465i
$166$	27576.8	−	15921.5i	0.0776737	−	0.0448449i
$167$	173708.			0.481981			0.240990	−	0.970527i	$-0.422528\pi$
$167$	173708.			0.481981			0.240990	+	0.970527i	$0.422528\pi$
$168$	−301465.	+	221447.i	−0.824070	+	0.605337i
$169$	24032.3			0.0647260
$170$	291141.	−	168090.i	0.772647	−	0.446088i
$171$	−540713.	−	399978.i	−1.41409	−	1.04603i
$172$	−49865.4	+	86369.3i	−0.128522	+	0.222607i
$173$	−245255.	−	424794.i	−0.623021	−	1.07910i	−0.988920	−	0.148450i	$-0.952572\pi$
$173$	−245255.	−	424794.i	−0.623021	−	1.07910i	0.365899	−	0.930655i	$-0.380762\pi$
$174$	−301183.	−	17079.2i	−0.754148	−	0.0427657i
$175$	198027.	+	239838.i	0.488798	+	0.592000i
$176$			3152.35i			0.00767101i
$177$	54361.3	+	107830.i	0.130424	+	0.258707i
$178$	−57331.2	−	33100.2i	−0.135625	−	0.0783034i
$179$	−555400.	−	320660.i	−1.29561	−	0.748019i	−0.315965	−	0.948771i	$-0.602328\pi$
$179$	−555400.	−	320660.i	−1.29561	−	0.748019i	−0.979642	+	0.200752i	$0.935661\pi$
$180$	134292.	+	308722.i	0.308937	+	0.710208i
$181$			46939.3i			0.106498i	0.998581	+	0.0532489i	$0.0169577\pi$
$181$			46939.3i			0.106498i	−0.998581	+	0.0532489i	$0.983042\pi$
$182$	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
$186$	−88921.3	+	135650.i	−0.188462	+	0.287500i
$187$	42216.4	−	24373.6i	0.0882829	−	0.0509702i
$188$	−125936.			−0.259869
$189$	246960.	−	424468.i	0.502889	−	0.864351i
$190$	751894.			1.51103
$191$	−659392.	+	380700.i	−1.30786	+	0.755091i	−0.981738	−	0.190238i	$-0.939074\pi$
$191$	−659392.	+	380700.i	−1.30786	+	0.755091i	−0.326118	+	0.945329i	$0.605741\pi$
$192$	197761.	−	301685.i	0.387157	−	0.590611i
$193$	−278157.	+	481782.i	−0.537522	+	0.931015i	0.461515	+	0.887133i	$0.347306\pi$
$193$	−278157.	+	481782.i	−0.537522	+	0.931015i	−0.999037	+	0.0438828i	$0.986027\pi$
$194$	−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	$0.832933\pi$
$198$	−13955.8	−	32082.6i	−0.0252982	−	0.0581576i
$199$	−182905.	−	105600.i	−0.327411	−	0.189031i	0.327280	−	0.944927i	$-0.393868\pi$
$199$	−182905.	−	105600.i	−0.327411	−	0.189031i	−0.654691	+	0.755897i	$0.727201\pi$
$200$	−384568.	−	222030.i	−0.679827	−	0.392498i
$201$	90436.0	+	179388.i	0.157889	+	0.313186i
$202$			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
$207$	90500.9	+	66945.7i	0.146800	+	0.108592i
$208$	−40840.5	+	23579.3i	−0.0654535	+	0.0377896i
$209$	109027.			0.172651
$210$	60243.1	+	545685.i	0.0942668	+	0.853873i
$211$	−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
$213$	790538.	+	518213.i	1.19392	+	0.782634i
$214$	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
$219$	−718829.	+	362389.i	−1.01278	+	0.510581i
$220$	−47263.3	−	27287.5i	−0.0658366	−	0.0380108i
$221$	631549.	+	364625.i	0.869814	+	0.502187i
$222$	399237.	−	201270.i	0.543686	−	0.274092i
$223$		−	18729.0i		−	0.0252204i	−0.999920	−	0.0126102i	$-0.995986\pi$
$223$		−	18729.0i		−	0.0252204i	0.999920	−	0.0126102i	$-0.00401406\pi$
$224$	−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	$-0.740373\pi$
$227$	223523.	−	387154.i	0.287911	−	0.498677i	0.973311	+	0.229490i	$0.0737059\pi$
$228$	−672625.	−	440919.i	−0.856911	−	0.561722i
$229$	−19052.9	+	11000.2i	−0.0240089	+	0.0138616i	−0.511956	−	0.859011i	$-0.671079\pi$
$229$	−19052.9	+	11000.2i	−0.0240089	+	0.0138616i	0.487948	+	0.872873i	$0.337746\pi$
$230$	−125847.			−0.156864
$231$	8735.43	+	79126.0i	0.0107710	+	0.0975639i
$232$	−979993.			−1.19537
$233$	461670.	−	266545.i	0.557111	−	0.321648i	−0.194874	−	0.980828i	$-0.562430\pi$
$233$	461670.	−	266545.i	0.557111	−	0.321648i	0.751985	+	0.659180i	$0.229097\pi$
$234$	311261.	−	420780.i	0.371608	−	0.502360i
$235$	−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	$0.951316\pi$
$240$	−41738.9	−	82792.6i	−0.0467749	−	0.0927819i
$241$	−231077.	−	133412.i	−0.256279	−	0.147963i	0.366357	−	0.930474i	$-0.380605\pi$
$241$	−231077.	−	133412.i	−0.256279	−	0.147963i	−0.622636	+	0.782512i	$0.713938\pi$
$242$	−504873.	−	291489.i	−0.554171	−	0.319951i
$243$	−219128.	−	894020.i	−0.238058	−	0.971251i
$244$			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
$249$	−74453.6	+	113580.i	−0.0761005	+	0.116092i
$250$	170775.	−	98597.0i	0.172812	−	0.0997732i
$251$	−947580.			−0.949361			−0.474681	−	0.880158i	$-0.657436\pi$
$251$	−947580.			−0.949361			−0.474681	+	0.880158i	$0.657436\pi$
$252$	266103.	−	523483.i	0.263967	−	0.519279i
$253$	−18248.2			−0.0179233
$254$	−133509.	+	77081.5i	−0.129845	+	0.0749662i
$255$	−786041.	+	1.19911e6i	−0.756998	+	1.15481i
$256$	544954.	−	943888.i	0.519708	−	0.900161i
$257$	−263158.	−	455804.i	−0.248533	−	0.430472i	0.714586	−	0.699548i	$-0.246615\pi$
$257$	−263158.	−	455804.i	−0.248533	−	0.430472i	−0.963119	+	0.269076i	$0.913282\pi$
$258$	−17258.6	+	304346.i	−0.0161420	+	0.284654i
$259$	−1.00323e6	+	168702.i	−0.929288	+	0.156268i
$260$		−	816432.i		−	0.749008i
$261$	1.17979e6	−	513204.i	1.07203	−	0.466325i
$262$	−896025.	−	517320.i	−0.806431	−	0.465593i
$263$	1.18245e6	+	682687.i	1.05413	+	0.608601i	0.923802	−	0.382871i	$-0.125065\pi$
$263$	1.18245e6	+	682687.i	1.05413	+	0.608601i	0.130325	+	0.991471i	$0.458398\pi$
$264$	−51164.7	−	101490.i	−0.0451815	−	0.0896213i
$265$		−	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	$-0.837253\pi$
$269$	−14614.5	+	25313.1i	−0.0123141	+	0.0213287i	0.859803	+	0.510626i	$0.170586\pi$
$270$	791322.	+	657828.i	0.660608	+	0.549165i
$271$	366956.	−	211862.i	0.303522	−	0.175239i	−0.340502	−	0.940244i	$-0.610597\pi$
$271$	366956.	−	211862.i	0.303522	−	0.175239i	0.644024	+	0.765005i	$0.277264\pi$
$272$	99033.3			0.0811632
$273$	−959783.	+	705028.i	−0.779411	+	0.572532i
$274$	963785.			0.775540
$275$	−81843.2	+	47252.2i	−0.0652606	+	0.0376782i
$276$	112579.	+	73798.0i	0.0889583	+	0.0583139i
$277$	373490.	−	646904.i	0.292469	−	0.506571i	−0.681924	−	0.731423i	$-0.738856\pi$
$277$	373490.	−	646904.i	0.292469	−	0.506571i	0.974393	+	0.224852i	$0.0721898\pi$
$278$	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	$-0.103023\pi$
$282$	−343724.	+	173284.i	−0.257387	+	0.129758i
$283$	1.20615e6	+	696372.i	0.895233	+	0.516863i	0.875650	−	0.482945i	$-0.160433\pi$
$283$	1.20615e6	+	696372.i	0.895233	+	0.516863i	0.0195823	+	0.999808i	$0.493766\pi$
$284$	978890.	+	565163.i	0.720175	+	0.415793i
$285$	−2.86346e6	+	1.44358e6i	−2.08823	+	1.05276i
$286$			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
$291$	243025.	+	159307.i	0.168236	+	0.110282i
$292$	−833661.	+	481314.i	−0.572179	+	0.330348i
$293$	−537097.			−0.365497			−0.182748	−	0.983160i	$-0.558499\pi$
$293$	−537097.			−0.365497			−0.182748	+	0.983160i	$0.558499\pi$
$294$	667064.	−	687046.i	0.450090	−	0.463572i
$295$	575764.			0.385203
$296$	1.25786e6	−	726226.i	0.834456	−	0.481773i
$297$	114744.	+	95387.2i	0.0754814	+	0.0627479i
$298$	−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
$303$	−1.19716e6	−	2.37466e6i	−0.749108	−	1.48592i
$304$	191821.	+	110748.i	0.119045	+	0.0687308i
$305$	361585.	+	208761.i	0.222567	+	0.128499i
$306$	−1.00790e6	+	438430.i	−0.615337	+	0.267668i
$307$		−	511397.i		−	0.309679i	−0.987940	−	0.154840i	$-0.950514\pi$
$307$		−	511397.i		−	0.309679i	0.987940	−	0.154840i	$-0.0494861\pi$
$308$	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	0.258507	+	0.966009i	$0.416769\pi$
$311$	−1.20650e6	+	2.08971e6i	−0.707335	+	1.22514i	−0.965842	+	0.259131i	$0.916564\pi$
$312$	932149.	−	1.42200e6i	0.542124	−	0.827015i
$313$	2.35700e6	−	1.36081e6i	1.35987	−	0.785124i	0.370268	−	0.928925i	$-0.379266\pi$
$313$	2.35700e6	−	1.36081e6i	1.35987	−	0.785124i	0.989607	+	0.143801i	$0.0459326\pi$
$314$	1.38523e6			0.792862
$315$	−1.27710e6	−	1.96249e6i	−0.725183	−	1.11437i
$316$	1.25586e6			0.707495
$317$	−1.42964e6	+	825402.i	−0.799057	+	0.461336i	−0.843141	−	0.537692i	$-0.819296\pi$
$317$	−1.42964e6	+	825402.i	−0.799057	+	0.461336i	0.0440842	+	0.999028i	$0.485963\pi$
$318$	500146.	−	762977.i	0.277351	−	0.423101i
$319$	−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
$324$	−322139.	−	1.05252e6i	−0.170483	−	0.557014i
$325$	−1.22436e6	−	706884.i	−0.642985	−	0.371227i
$326$	732822.	+	423095.i	0.381904	+	0.220492i
$327$	−183547.	−	364082.i	−0.0949246	−	0.188291i
$328$		−	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	0.980970	+	0.194160i	$0.0621983\pi$
$331$	1.31284e6	+	2.27391e6i	0.658633	+	1.14079i	−0.322337	+	0.946625i	$0.604468\pi$
$332$	−81199.1	+	140641.i	−0.0404302	+	0.0700272i
$333$	−1.13400e6	+	1.53301e6i	−0.560407	+	0.757589i
$334$	549850.	−	317456.i	0.269698	−	0.155710i
$335$	957847.			0.466320
$336$	−65005.9	+	148087.i	−0.0314126	+	0.0715596i
$337$	−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
$339$	248934.	+	163181.i	0.117648	+	0.0771207i
$340$	−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
$345$	479267.	−	241616.i	0.216785	−	0.109290i
$346$	−1.55264e6	−	896419.i	−0.697238	−	0.402551i
$347$	−2.51975e6	−	1.45478e6i	−1.12340	−	0.648595i	−0.181133	−	0.983459i	$-0.557976\pi$
$347$	−2.51975e6	−	1.45478e6i	−1.12340	−	0.648595i	−0.942267	+	0.334864i	$0.891310\pi$
$348$	1.37379e6	−	692578.i	0.608095	−	0.306563i
$349$			3.93286e6i			1.72840i	0.503147	+	0.864201i	$0.332176\pi$
$349$			3.93286e6i			1.72840i	−0.503147	+	0.864201i	$0.667824\pi$
$350$	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	$-0.697653\pi$
$353$	967991.	−	1.67661e6i	0.413461	−	0.716136i	0.995266	+	0.0971931i	$0.0309864\pi$
$354$	369136.	+	241976.i	0.156559	+	0.102627i
$355$	3.90305e6	−	2.25343e6i	1.64374	−	0.949015i
$356$	337620.			0.141190
$357$	2.48580e6	−	274430.i	1.03228	−	0.113962i
$358$	−2.34406e6			−0.966631
$359$	1.20595e6	−	696256.i	0.493848	−	0.285123i	−0.232321	−	0.972639i	$-0.574632\pi$
$359$	1.20595e6	−	696256.i	0.493848	−	0.285123i	0.726169	+	0.687516i	$0.241299\pi$
$360$	2.68756e6	+	1.98805e6i	1.09295	+	0.808483i
$361$	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
$366$	144085.	+	285805.i	0.0562232	+	0.111524i
$367$	−853243.	−	492620.i	−0.330680	−	0.190918i	0.325463	−	0.945555i	$-0.394480\pi$
$367$	−853243.	−	492620.i	−0.330680	−	0.190918i	−0.656143	+	0.754637i	$0.727813\pi$
$368$	−32105.7	−	18536.2i	−0.0123584	−	0.00713513i
$369$	1.17891e6	+	2.71018e6i	0.450729	+	1.03617i
$370$		−	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	0.531190	−	0.847253i	$-0.321745\pi$
$373$	−1.25793e6	−	2.17879e6i	−0.468148	−	0.810856i	−0.999337	+	0.0363971i	$0.988412\pi$
$374$	89086.7	−	154303.i	0.0329332	−	0.0570420i
$375$	−461069.	+	703365.i	−0.169312	+	0.258287i
$376$	−1.08296e6	+	625246.i	−0.395041	+	0.228077i
$377$	−3.12003e6			−1.13059
$378$	5994.02	−	1.79492e6i	0.00215769	−	0.646123i
$379$	−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
$381$	360456.	−	549879.i	0.127215	−	0.194068i
$382$	−1.39148e6	+	2.41011e6i	−0.487885	+	0.845041i
$383$	1.55261e6	+	2.68921e6i	0.540837	+	0.936758i	0.998856	+	0.0478152i	$0.0152259\pi$
$383$	1.55261e6	+	2.68921e6i	0.540837	+	0.936758i	−0.458019	+	0.888942i	$0.651441\pi$
$384$	−84369.5	+	1.48781e6i	−0.0291983	+	0.514895i
$385$	355627.	+	132642.i	0.122276	+	0.0456066i
$386$			2.03335e6i			0.694615i
$387$	−518594.	−	1.19218e6i	−0.176015	−	0.404637i
$388$	300928.	+	173741.i	0.101481	+	0.0585898i
$389$	580056.	+	334895.i	0.194355	+	0.112211i	0.594020	−	0.804450i	$-0.297540\pi$
$389$	580056.	+	334895.i	0.194355	+	0.112211i	−0.399665	+	0.916661i	$0.630873\pi$
$390$	−1.12338e6	−	2.22833e6i	−0.373996	−	0.741853i
$391$			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
$396$	143449.	+	106112.i	0.0459683	+	0.0340039i
$397$	−3.02652e6	+	1.74736e6i	−0.963757	+	0.556425i	−0.897327	−	0.441366i	$-0.854494\pi$
$397$	−3.02652e6	+	1.74736e6i	−0.963757	+	0.556425i	−0.0664294	+	0.997791i	$0.521161\pi$
$398$	−771949.			−0.244276
$399$	5.12172e6	+	2.24829e6i	1.61058	+	0.707001i
$400$	−191992.			−0.0599975
$401$	2.43480e6	−	1.40573e6i	0.756140	−	0.436558i	−0.0717682	−	0.997421i	$-0.522864\pi$
$401$	2.43480e6	−	1.40573e6i	0.756140	−	0.436558i	0.827908	+	0.560864i	$0.189531\pi$
$402$	614098.	+	402553.i	0.189528	+	0.124239i
$403$	−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
$408$	−3.18837e6	+	1.60738e6i	−0.948239	+	0.478043i
$409$	−2.41651e6	−	1.39517e6i	−0.714300	−	0.412402i	0.0983509	−	0.995152i	$-0.468643\pi$
$409$	−2.41651e6	−	1.39517e6i	−0.714300	−	0.412402i	−0.812651	+	0.582750i	$0.801977\pi$
$410$	−2.86139e6	−	1.65202e6i	−0.840654	−	0.485352i
$411$	−3.67041e6	+	1.85039e6i	−1.07179	+	0.540331i
$412$		−	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
$417$	−4.74215e6	−	3.10857e6i	−1.33547	−	0.875428i
$418$	345110.	−	199249.i	0.0966088	−	0.0557771i
$419$	3.40729e6			0.948144			0.474072	−	0.880486i	$-0.342784\pi$
$419$	3.40729e6			0.948144			0.474072	+	0.880486i	$0.342784\pi$
$420$	−1.65756e6	−	2.25651e6i	−0.458508	−	0.624186i
$421$	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
$423$	976321.	−	1.31985e6i	0.265303	−	0.358651i
$424$	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
$429$	−162894.	−	323115.i	−0.0427329	−	0.0847644i
$430$	1.25870e6	+	726712.i	0.328286	+	0.189536i
$431$	−2.60415e6	−	1.50351e6i	−0.675263	−	0.389863i	0.122805	−	0.992431i	$-0.460811\pi$
$431$	−2.60415e6	−	1.50351e6i	−0.675263	−	0.389863i	−0.798068	+	0.602568i	$0.794144\pi$
$432$	104987.	+	284378.i	0.0270661	+	0.0733141i
$433$		−	1.50880e6i		−	0.386734i	−0.981126	−	0.193367i	$-0.938059\pi$
$433$		−	1.50880e6i		−	0.386734i	0.981126	−	0.193367i	$-0.0619408\pi$
$434$	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
$438$	−1.61308e6	+	2.46077e6i	−0.401764	+	0.612894i
$439$	−1.70748e6	+	985817.i	−0.422859	+	0.244138i	−0.696300	−	0.717751i	$-0.745172\pi$
$439$	−1.70748e6	+	985817.i	−0.422859	+	0.244138i	0.273441	+	0.961889i	$0.411838\pi$
$440$	−541907.			−0.133442
$441$	−1.22133e6	+	3.89721e6i	−0.299045	+	0.954239i
$442$	2.66544e6			0.648954
$443$	1.85053e6	−	1.06840e6i	0.448009	−	0.258658i	−0.258980	−	0.965883i	$-0.583386\pi$
$443$	1.85053e6	−	1.06840e6i	0.448009	−	0.258658i	0.706989	+	0.707225i	$0.250053\pi$
$444$	−1.25007e6	+	1.90700e6i	−0.300939	+	0.459085i
$445$	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	$0.756666\pi$
$450$	1.95397e6	−	849967.i	0.454870	−	0.197866i
$451$	−414911.	−	239549.i	−0.0960535	−	0.0554565i
$452$	308245.	+	177966.i	0.0709660	+	0.0409723i
$453$	1.94054e6	+	3.84923e6i	0.444301	+	0.881310i
$454$		−	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	0.888164	+	0.459526i	$0.151981\pi$
$457$	3.75946e6	+	6.51157e6i	0.842044	+	1.45846i	−0.0461206	+	0.998936i	$0.514686\pi$
$458$	−40206.2	+	69639.3i	−0.00895632	+	0.0155128i
$459$	2.99666e6	−	3.60477e6i	0.663904	−	0.798631i
$460$	555829.	−	320908.i	0.122475	−	0.0707109i
$461$	−929187.			−0.203634			−0.101817	−	0.994803i	$-0.532466\pi$
$461$	−929187.			−0.203634			−0.101817	+	0.994803i	$0.532466\pi$
$462$	172255.	+	234498.i	0.0375464	+	0.0511134i
$463$	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
$465$	−2.75841e6	−	1.80819e6i	−0.591597	−	0.387803i
$466$	974235.	−	1.68742e6i	0.207826	−	0.359964i
$467$	−1.51559e6	−	2.62507e6i	−0.321580	−	0.556992i	0.659234	−	0.751937i	$-0.270880\pi$
$467$	−1.51559e6	−	2.62507e6i	−0.321580	−	0.556992i	−0.980814	+	0.194945i	$0.937547\pi$
$468$	−301765.	+	2.65217e6i	−0.0636876	+	0.559741i
$469$	−1.06375e6	−	1.28834e6i	−0.223309	−	0.270458i
$470$			1.83532e6i			0.383238i
$471$	−5.27542e6	+	2.65954e6i	−1.09573	+	0.552400i
$472$	1.24176e6	+	716928.i	0.256555	+	0.148122i
$473$	182516.	+	105376.i	0.0375100	+	0.0216564i
$474$	3.42769e6	−	1.72803e6i	0.700737	−	0.353268i
$475$			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	$-0.835929\pi$
$479$	−40952.6	+	70932.0i	−0.00815535	+	0.0141255i	0.861919	+	0.507046i	$0.169263\pi$
$480$	5.45580e6	+	3.57638e6i	1.08082	+	0.708501i
$481$	4.00469e6	−	2.31211e6i	0.789234	−	0.455664i
$482$	−975255.			−0.191206
$483$	−857239.	−	376304.i	−0.167199	−	0.0733957i
$484$	2.97317e6			0.576907
$485$	1.19987e6	−	692743.i	0.231621	−	0.133727i
$486$	−2.32746e6	−	2.42944e6i	−0.446984	−	0.466568i
$487$	−2.20758e6	+	3.82364e6i	−0.421787	+	0.730557i	−0.996114	−	0.0880688i	$-0.971930\pi$
$487$	−2.20758e6	+	3.82364e6i	−0.421787	+	0.730557i	0.574327	+	0.818626i	$0.305264\pi$
$488$	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	$-0.355906\pi$
$492$	1.59096e6	+	3.15581e6i	0.296311	+	0.587757i
$493$	5.67427e6	+	3.27604e6i	1.05146	+	0.607061i
$494$	5.16278e6	+	2.98073e6i	0.951845	+	0.549548i
$495$	652391.	−	283786.i	0.119673	−	0.0520569i
$496$			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	−0.820703	−	0.571356i	$-0.806418\pi$
$499$	−5.03473e6	−	8.72042e6i	−0.905160	−	1.56778i	−0.0844572	−	0.996427i	$-0.526916\pi$
$500$	−502842.	+	870948.i	−0.0899512	+	0.155800i
$501$	−1.48452e6	+	2.26465e6i	−0.264236	+	0.403094i
$502$	−2.99943e6	+	1.73172e6i	−0.531227	+	0.306704i
$503$	2.68345e6			0.472904			0.236452	−	0.971643i	$-0.424015\pi$
$503$	2.68345e6			0.472904			0.236452	+	0.971643i	$0.424015\pi$
$504$	−310687.	−	5.82272e6i	−0.0544812	−	1.02106i
$505$	−1.26796e7			−2.21247
$506$	−57762.2	+	33349.0i	−0.0100292	+	0.00579038i
$507$	−205381.	+	313311.i	−0.0354847	+	0.0541322i
$508$	393113.	−	680893.i	0.0675863	−	0.117063i
$509$	−3.75644e6	−	6.50634e6i	−0.642661	−	1.11312i	−0.984837	−	0.173485i	$-0.944497\pi$
$509$	−3.75644e6	−	6.50634e6i	−0.642661	−	1.11312i	0.342176	−	0.939636i	$-0.388836\pi$
$510$	−296700.	+	5.23213e6i	−0.0505117	+	0.890745i
$511$	5.16255e6	−	4.26257e6i	0.874606	−	0.722137i
$512$		−	924585.i		−	0.155873i
$513$	9.83550e6	−	3.63108e6i	1.65007	−	0.609175i
$514$	−1.66598e6	−	961856.i	−0.278140	−	0.160584i
$515$	−3.79042e6	−	2.18840e6i	−0.629751	−	0.363587i
$516$	−699851.	−	1.38821e6i	−0.115713	−	0.229526i
$517$			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	0.177627	+	0.984098i	$0.443158\pi$
$521$	−4.73009e6	+	8.19276e6i	−0.763440	+	1.32232i	−0.941067	+	0.338220i	$0.890175\pi$
$522$	2.79658e6	−	3.78058e6i	0.449212	−	0.607270i
$523$	−1.14824e6	+	662937.i	−0.183560	+	0.105979i	−0.588964	−	0.808159i	$-0.700464\pi$
$523$	−1.14824e6	+	662937.i	−0.183560	+	0.105979i	0.405404	+	0.914138i	$0.367131\pi$
$524$	5.27664e6			0.839517
$525$	−4.81912e6	+	532027.i	−0.763080	+	0.0842433i
$526$	4.99051e6			0.786466
$527$	3.05089e6	−	1.76143e6i	0.478520	−	0.276274i
$528$	−41097.4	−	26940.1i	−0.00641548	−	0.00420547i
$529$	−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
$534$	921485.	−	464555.i	0.139841	−	0.0704992i
$535$	9.49940e6	+	5.48448e6i	1.43487	+	0.828421i
$536$	2.06580e6	+	1.19269e6i	0.310582	+	0.179314i
$537$	8.92694e6	−	4.50041e6i	1.33588	−	0.673467i
$538$			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	−0.999952	−	0.00981149i	$-0.996877\pi$
$541$	−3.46147e6	−	5.99545e6i	−0.508473	−	0.880701i	0.491479	−	0.870889i	$-0.336456\pi$
$542$	774365.	−	1.34124e6i	0.113226	−	0.196114i
$543$	−611951.	−	401146.i	−0.0890671	−	0.0583852i
$544$	−6.03430e6	+	3.48390e6i	−0.874237	+	0.504741i
$545$	−1.94403e6			−0.280357
$546$	−1.74961e6	+	3.98569e6i	−0.251165	+	0.572166i
$547$	−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
$549$	−1.09745e6	−	811807.i	−0.155401	−	0.114953i
$550$	−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
$555$	4.09277e6	+	8.11837e6i	0.564008	+	1.11876i
$556$	−5.87201e6	−	3.39021e6i	−0.805564	−	0.465092i
$557$	1.08587e7	+	6.26929e6i	1.48300	+	0.856210i	0.999814	−	0.0193079i	$-0.00614627\pi$
$557$	1.08587e7	+	6.26929e6i	1.48300	+	0.856210i	0.483186	+	0.875518i	$0.339480\pi$
$558$	−1.00855e6	−	2.31855e6i	−0.137124	−	0.315232i
$559$			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	$-0.984468\pi$
$563$	−3.43830e6	+	5.95530e6i	−0.457164	+	0.791832i	0.541645	+	0.840607i	$0.317802\pi$
$564$	1.07625e6	−	1.64183e6i	0.142468	−	0.217336i
$565$	1.22904e6	−	709588.i	0.161974	−	0.0935159i
$566$	5.09055e6			0.667918
$567$	3.42328e6	+	6.84716e6i	0.447182	+	0.894443i
$568$	1.12237e7			1.45970
$569$	−2.29442e6	+	1.32468e6i	−0.297093	+	0.171526i	−0.641136	−	0.767427i	$-0.721537\pi$
$569$	−2.29442e6	+	1.32468e6i	−0.297093	+	0.171526i	0.344043	+	0.938954i	$0.388203\pi$
$570$	−6.42572e6	+	9.80249e6i	−0.828390	+	1.26372i
$571$	−547786.	+	948793.i	−0.0703105	+	0.121781i	−0.899037	−	0.437872i	$-0.855732\pi$
$571$	−547786.	+	948793.i	−0.0703105	+	0.121781i	0.828727	+	0.559653i	$0.189066\pi$
$572$	−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
$576$	2.24302e6	+	5.15644e6i	0.281694	+	0.647580i
$577$	−2.51518e6	−	1.45214e6i	−0.314507	−	0.181581i	0.334435	−	0.942419i	$-0.391455\pi$
$577$	−2.51518e6	−	1.45214e6i	−0.314507	−	0.181581i	−0.648942	+	0.760838i	$0.724788\pi$
$578$	−353171.	−	203903.i	−0.0439709	−	0.0253866i
$579$	−3.90388e6	−	7.74367e6i	−0.483949	−	0.959955i
$580$		−	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
$585$	8.55644e6	+	6.32941e6i	1.03372	+	0.764669i
$586$	−1.70011e6	+	981557.i	−0.204518	+	0.118079i
$587$	2.80932e6			0.336516			0.168258	−	0.985743i	$-0.446186\pi$
$587$	2.80932e6			0.336516			0.168258	+	0.985743i	$0.446186\pi$
$588$	−1.19427e6	+	4.73548e6i	−0.142449	+	0.564834i
$589$	7.87916e6			0.935819
$590$	1.82250e6	−	1.05222e6i	0.215545	−	0.124445i
$591$	−7.11688e6	−	4.66525e6i	−0.838148	−	0.549422i
$592$	313988.	−	543843.i	0.0368221	−	0.0637777i
$593$	−235612.	−	408091.i	−0.0275144	−	0.0476563i	0.851940	−	0.523639i	$-0.175426\pi$
$593$	−235612.	−	408091.i	−0.0275144	−	0.0476563i	−0.879455	+	0.475983i	$0.842093\pi$
$594$	537529.	+	92237.3i	0.0625081	+	0.0107261i
$595$	4.16703e6	−	1.11723e7i	0.482541	−	1.29375i
$596$		−	7.19300e6i		−	0.829458i
$597$	2.93984e6	−	1.48208e6i	0.337588	−	0.170191i
$598$	−864112.	−	498895.i	−0.0988137	−	0.0570501i
$599$	1.50232e6	+	867362.i	0.171078	+	0.0987719i	0.583094	−	0.812405i	$-0.301842\pi$
$599$	1.50232e6	+	867362.i	0.171078	+	0.0987719i	−0.412016	+	0.911177i	$0.635175\pi$
$600$	6.18116e6	−	3.11616e6i	0.700958	−	0.353379i
$601$		−	3.42903e6i		−	0.387244i	−0.981076	−	0.193622i	$-0.937976\pi$
$601$		−	3.42903e6i		−	0.387244i	0.981076	−	0.193622i	$-0.0620235\pi$
$602$	−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
$606$	−8.12919e6	−	5.32884e6i	−0.899220	−	0.589456i
$607$	−8.49975e6	+	4.90733e6i	−0.936341	+	0.540597i	−0.888812	−	0.458273i	$-0.848468\pi$
$607$	−8.49975e6	+	4.90733e6i	−0.936341	+	0.540597i	−0.0475299	+	0.998870i	$0.515135\pi$
$608$	−1.55840e7			−1.70970
$609$	−8.62336e6	+	6.33446e6i	−0.942178	+	0.692096i
$610$	1.52607e6			0.166054
$611$	−3.44784e6	+	1.99061e6i	−0.373632	+	0.215717i
$612$	3.33360e6	−	4.50654e6i	0.359778	−	0.486368i
$613$	1.37890e6	−	2.38832e6i	0.148211	−	0.256709i	−0.782355	−	0.622833i	$-0.785982\pi$
$613$	1.37890e6	−	2.38832e6i	0.148211	−	0.256709i	0.930566	+	0.366123i	$0.119315\pi$
$614$	−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	$0.906703\pi$
$618$	−1.51041e6	−	2.99603e6i	−0.159083	−	0.315555i
$619$	3.67533e6	+	2.12195e6i	0.385540	+	0.222591i	0.680226	−	0.733003i	$-0.261882\pi$
$619$	3.67533e6	+	2.12195e6i	0.385540	+	0.222591i	−0.294686	+	0.955594i	$0.595215\pi$
$620$	−3.41562e6	−	1.97201e6i	−0.356854	−	0.206030i
$621$	−1.64620e6	+	607745.i	−0.171299	+	0.0632401i
$622$			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
$627$	−931750.	+	1.42139e6i	−0.0946521	+	0.144393i
$628$	−6.11815e6	+	3.53232e6i	−0.619044	+	0.357405i
$629$	−9.71088e6			−0.978660
$630$	−7.62897e6	−	3.87805e6i	−0.765798	−	0.389280i
$631$	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
$633$	5.73132e6	−	8.74318e6i	0.568520	−	0.867282i
$634$	−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
$639$	−1.35119e7	+	5.87762e6i	−1.30908	+	0.569442i
$640$	6.15322e6	+	3.55256e6i	0.593817	+	0.342840i
$641$	−5.95229e6	−	3.43656e6i	−0.572189	−	0.330353i	0.185834	−	0.982581i	$-0.440501\pi$
$641$	−5.95229e6	−	3.43656e6i	−0.572189	−	0.330353i	−0.758023	+	0.652228i	$0.773835\pi$
$642$	3.78533e6	+	7.50853e6i	0.362465	+	0.718981i
$643$			4.81869e6i			0.459623i	0.973235	+	0.229811i	$0.0738109\pi$
$643$			4.81869e6i			0.459623i	−0.973235	+	0.229811i	$0.926189\pi$
$644$	−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	$-0.947959\pi$
$647$	−3.75204e6	+	6.49872e6i	−0.352376	+	0.610333i	0.634289	+	0.773096i	$0.281293\pi$
$648$	−7.99569e6	−	7.45153e6i	−0.748029	−	0.697120i
$649$	264269.	−	152576.i	0.0246283	−	0.0142191i
$650$	−5.16739e6			−0.479720
$651$	631292.	+	5.71828e6i	0.0583819	+	0.528826i
$652$	−4.31554e6			−0.397573
$653$	1.21493e7	−	7.01440e6i	1.11498	−	0.643735i	0.174867	−	0.984592i	$-0.444050\pi$
$653$	1.21493e7	−	7.01440e6i	1.11498	−	0.643735i	0.940115	+	0.340857i	$0.110717\pi$
$654$	−1.24636e6	−	817015.i	−0.113946	−	0.0746939i
$655$	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	$0.928966\pi$
$660$	759663.	−	382975.i	0.0678830	−	0.0342224i
$661$	1.59100e7	+	9.18563e6i	1.41633	+	0.817721i	0.995975	−	0.0896367i	$-0.0285706\pi$
$661$	1.59100e7	+	9.18563e6i	1.41633	+	0.817721i	0.420360	+	0.907358i	$0.361904\pi$
$662$	8.31126e6	+	4.79851e6i	0.737092	+	0.425560i
$663$	−1.01509e7	+	5.11744e6i	−0.896851	+	0.452136i
$664$			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
$669$	244171.	+	160059.i	0.0210925	+	0.0138266i
$670$	3.03193e6	−	1.75049e6i	0.260935	−	0.150651i
$671$	221284.			0.0189734
$672$	−1.24862e6	−	1.13101e7i	−0.106661	−	0.966144i
$673$	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
$675$	−5.80950e6	+	6.98843e6i	−0.490772	+	0.590365i
$676$	−223989.	+	387960.i	−0.0188521	+	0.0326528i
$677$	6.85310e6	+	1.18699e7i	0.574666	+	0.995351i	0.996078	+	0.0884815i	$0.0282014\pi$
$677$	6.85310e6	+	1.18699e7i	0.574666	+	0.995351i	−0.421412	+	0.906869i	$0.638465\pi$
$678$	1.08619e6	+	61594.6i	0.0907465	+	0.00514599i
$679$	−2.26429e6	−	844535.i	−0.188477	−	0.0702980i
$680$			1.70244e7i			1.41189i
$681$	3.13711e6	+	6.22272e6i	0.259216	+	0.514177i
$682$	354954.	+	204933.i	0.0292221	+	0.0168714i
$683$	−1.35604e7	−	7.82911e6i	−1.11230	−	0.642186i	−0.172875	−	0.984944i	$-0.555306\pi$
$683$	−1.35604e7	−	7.82911e6i	−1.11230	−	0.642186i	−0.939424	+	0.342758i	$0.888639\pi$
$684$	1.14966e7	−	5.00095e6i	0.939568	−	0.408707i
$685$			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
$690$	1.07549e6	−	1.64068e6i	0.0859974	−	0.131190i
$691$	3.65594e6	−	2.11076e6i	0.291275	−	0.168168i	−0.347242	−	0.937776i	$-0.612882\pi$
$691$	3.65594e6	−	2.11076e6i	0.291275	−	0.168168i	0.638517	+	0.769608i	$0.279548\pi$
$692$	9.14342e6			0.725844
$693$	−1.10622e6	−	562330.i	−0.0875004	−	0.0444793i
$694$	−1.06346e7			−0.838150
$695$	−2.34130e7	+	1.35175e7i	−1.83863	+	1.06154i
$696$	8.37507e6	−	1.27762e7i	0.655338	−	0.999723i
$697$	−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	$0.703148\pi$
$702$	2.82568e6	+	7.65393e6i	0.216412	+	0.586195i
$703$	−1.88093e7	−	1.08596e7i	−1.43544	−	0.828751i
$704$	−789417.	−	455770.i	−0.0600309	−	0.0346589i
$705$	−3.52368e6	−	6.98953e6i	−0.267008	−	0.529633i
$706$		−	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	0.824960	−	0.565191i	$-0.191197\pi$
$709$	−1.03050e6	−	1.78488e6i	−0.0769895	−	0.133350i	−0.901950	+	0.431841i	$0.857864\pi$
$710$	8.23639e6	−	1.42658e7i	0.613184	−	1.06207i
$711$	−9.73609e6	+	1.31618e7i	−0.722288	+	0.976429i
$712$	2.90329e6	−	1.67621e6i	0.214630	−	0.123917i
$713$	−1.31876e6			−0.0971499
$714$	7.36693e6	−	5.41153e6i	0.540806	−	0.397260i
$715$	−1.72528e6			−0.126210
$716$	1.03530e7	−	5.97731e6i	0.754717	−	0.435736i
$717$	−3.50786e6	−	2.29947e6i	−0.254826	−	0.167044i
$718$	2.54485e6	−	4.40781e6i	0.184226	−	0.319089i
$719$	−1.12467e7	−	1.94798e7i	−0.811339	−	1.40528i	−0.911927	−	0.410353i	$-0.865406\pi$
$719$	−1.12467e7	−	1.94798e7i	−0.811339	−	1.40528i	0.100588	−	0.994928i	$-0.467928\pi$
$720$	1.43607e6	+	163397.i	0.103239	+	0.0117466i
$721$	1.26601e6	+	7.52862e6i	0.0906979	+	0.539358i
$722$		−	1.89497e7i		−	1.35288i
$723$	3.71410e6	−	1.87242e6i	0.264245	−	0.133216i
$724$	−757754.	−	437489.i	−0.0537257	−	0.0310185i
$725$	−1.10005e7	−	6.35114e6i	−0.777261	−	0.448752i
$726$	8.11483e6	−	4.09099e6i	0.571397	−	0.288063i
$727$		−	2.23831e7i		−	1.57067i	−0.619073	−	0.785334i	$-0.712491\pi$
$727$		−	2.23831e7i		−	1.57067i	0.619073	−	0.785334i	$-0.287509\pi$
$728$	−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
$732$	−1.36518e6	−	894901.i	−0.0941699	−	0.0617302i
$733$	1.07715e7	−	6.21894e6i	0.740487	−	0.427520i	−0.0817596	−	0.996652i	$-0.526054\pi$
$733$	1.07715e7	−	6.21894e6i	0.740487	−	0.427520i	0.822246	+	0.569132i	$0.192721\pi$
$734$	−3.60110e6			−0.246715
$735$	1.39709e7	+	1.35646e7i	0.953906	+	0.926164i
$736$	2.60835e6			0.177489
$737$	439640.	−	253826.i	0.0298146	−	0.0172134i
$738$	8.68459e6	+	6.42420e6i	0.586960	+	0.434189i
$739$	6.72742e6	−	1.16522e7i	0.453145	−	0.784871i	−0.545434	−	0.838154i	$-0.683635\pi$
$739$	6.72742e6	−	1.16522e7i	0.453145	−	0.784871i	0.998579	+	0.0532829i	$0.0169685\pi$
$740$	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	$-0.204454\pi$
$744$	−3.69757e6	−	7.33444e6i	−0.244897	−	0.485775i
$745$	−2.48377e7	−	1.43400e7i	−1.63953	−	0.946585i
$746$	−7.96359e6	−	4.59778e6i	−0.523916	−	0.302483i
$747$	−844461.	−	1.94131e6i	−0.0553705	−	0.127290i
$748$			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	0.701392	−	0.712776i	$-0.252562\pi$
$751$	−4.12037e6	−	7.13669e6i	−0.266586	−	0.461740i	−0.967978	+	0.251036i	$0.919229\pi$
$752$	−270328.	+	468222.i	−0.0174320	+	0.0301931i
$753$	8.09806e6	−	1.23537e7i	0.520467	−	0.793977i
$754$	−9.87603e6	+	5.70193e6i	−0.632636	+	0.365253i
$755$	2.05531e7			1.31223
$756$	4.55055e6	+	7.94292e6i	0.289574	+	0.505447i
$757$	−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
$759$	155950.	−	237903.i	0.00982610	−	0.0149898i
$760$	−1.90382e7	+	3.29751e7i	−1.19562	+	2.07087i
$761$	−6.12100e6	−	1.06019e7i	−0.383143	−	0.663623i	0.608367	−	0.793656i	$-0.291825\pi$
$761$	−6.12100e6	−	1.06019e7i	−0.383143	−	0.663623i	−0.991510	+	0.130033i	$0.958492\pi$
$762$	136058.	−	2.39931e6i	0.00848862	−	0.149692i
$763$	2.15896e6	+	2.61480e6i	0.134256	+	0.162602i
$764$		−	1.41930e7i		−	0.879711i
$765$	−8.91536e6	−	2.04953e7i	−0.550789	−	1.26620i
$766$	9.82918e6	+	5.67488e6i	0.605264	+	0.349450i
$767$	3.95341e6	+	2.28250e6i	0.242652	+	0.140095i
$768$	7.64832e6	+	1.51711e7i	0.467911	+	0.928141i
$769$		−	2.89879e6i		−	0.176767i	−0.996087	−	0.0883834i	$-0.971830\pi$
$769$		−	2.89879e6i		−	0.176767i	0.996087	−	0.0883834i	$-0.0281701\pi$
$770$	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	$-0.799742\pi$
$773$	1.74994e6	−	3.03099e6i	0.105336	−	0.182447i	0.913875	+	0.405995i	$0.133075\pi$
$774$	−3.82028e6	−	2.82595e6i	−0.229215	−	0.169556i
$775$	−5.91464e6	+	3.41482e6i	−0.353732	+	0.204227i
$776$	3.45035e6			0.205688
$777$	6.37426e6	−	1.45209e7i	0.378771	−	0.862861i
$778$	2.44812e6			0.145005
$779$	−2.91532e7	+	1.68316e7i	−1.72124	+	0.993759i
$780$	1.06439e7	+	6.97726e6i	0.626416	+	0.410628i
$781$	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
$786$	1.44018e7	−	7.26050e6i	0.831497	−	0.419189i
$787$	2.15310e7	+	1.24309e7i	1.23916	+	0.715429i	0.968922	−	0.247365i	$-0.0795646\pi$
$787$	2.15310e7	+	1.24309e7i	1.23916	+	0.715429i	0.270237	+	0.962794i	$0.412898\pi$
$788$	−8.81254e6	−	5.08792e6i	−0.505575	−	0.291894i
$789$	−1.90055e7	+	9.58139e6i	−1.08689	+	0.547944i
$790$		−	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
$795$	1.55149e7	+	1.01703e7i	0.870627	+	0.570713i
$796$	3.40947e6	−	1.96846e6i	0.190723	−	0.110114i
$797$	4.51523e6			0.251787			0.125894	−	0.992044i	$-0.459820\pi$
$797$	4.51523e6			0.251787			0.125894	+	0.992044i	$0.459820\pi$
$798$	2.03209e7	−	2.24341e6i	1.12963	−	0.124710i
$799$	8.36060e6			0.463309
$800$	1.16985e7	−	6.75410e6i	0.646254	−	0.373115i
$801$	−2.61741e6	+	3.53836e6i	−0.144142	+	0.194859i
$802$	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
$807$	−205112.	−	406857.i	−0.0110868	−	0.0219917i
$808$	−2.73462e7	−	1.57883e7i	−1.47356	−	0.850762i
$809$	2.79806e7	+	1.61546e7i	1.50309	+	0.867811i	0.999994	+	0.00358270i	$0.00114041\pi$
$809$	2.79806e7	+	1.61546e7i	1.50309	+	0.867811i	0.503099	+	0.864228i	$0.332193\pi$
$810$	−1.53388e7	+	4.69469e6i	−0.821447	+	0.251417i
$811$			1.64891e7i			0.880329i	0.897917	+	0.440164i	$0.145080\pi$
$811$			1.64891e7i			0.880329i	−0.897917	+	0.440164i	$0.854920\pi$
$812$	−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
$816$	−846344.	+	1.29110e6i	−0.0444960	+	0.0678791i
$817$	1.28242e7	−	7.40407e6i	0.672165	−	0.388075i
$818$	−1.01989e7			−0.532928
$819$	−989143.	−	1.85380e7i	−0.0515287	−	0.965722i
$820$	1.68506e7			0.875145
$821$	1.50775e7	−	8.70500e6i	0.780678	−	0.450724i	−0.0559928	−	0.998431i	$-0.517832\pi$
$821$	1.50775e7	−	8.70500e6i	0.780678	−	0.450724i	0.836670	+	0.547707i	$0.184499\pi$
$822$	−8.23656e6	+	1.25649e7i	−0.425173	+	0.648606i
$823$	−7.90254e6	+	1.36876e7i	−0.406693	+	0.704413i	−0.994517	−	0.104576i	$-0.966652\pi$
$823$	−7.90254e6	+	1.36876e7i	−0.406693	+	0.704413i	0.587824	+	0.808989i	$0.299985\pi$
$824$	−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	$-0.0576061\pi$
$828$	−1.92422e6	+	837025.i	−0.0975391	+	0.0424290i
$829$	186922.	+	107920.i	0.00944659	+	0.00545399i	0.504716	−	0.863286i	$-0.331597\pi$
$829$	186922.	+	107920.i	0.00944659	+	0.00545399i	−0.495269	+	0.868740i	$0.664931\pi$
$830$	2.04963e6	+	1.18335e6i	0.103271	+	0.0596238i
$831$	5.24187e6	+	1.03977e7i	0.263320	+	0.522317i
$832$		−	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
$837$	8.29234e6	+	6.89344e6i	0.409132	+	0.340112i
$838$	1.07853e7	−	6.22690e6i	0.530546	−	0.306311i
$839$	2.60061e7			1.27547			0.637735	−	0.770256i	$-0.279871\pi$
$839$	2.60061e7			1.27547			0.637735	+	0.770256i	$0.279871\pi$
$840$	−2.54570e7	−	1.11749e7i	−1.24483	−	0.546443i
$841$	−7.52137e6			−0.366697
$842$	1.19365e7	−	6.89157e6i	0.580227	−	0.334994i
$843$	1.09762e7	+	7.19509e6i	0.531964	+	0.348713i
$844$	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
$849$	−1.93865e7	+	9.77345e6i	−0.923060	+	0.465349i
$850$	9.39772e6	+	5.42578e6i	0.446144	+	0.257582i
$851$	3.14818e6	+	1.81760e6i	0.149017	+	0.0860349i
$852$	−1.57337e7	+	7.93195e6i	−0.742561	+	0.374353i
$853$			2.81393e7i			1.32416i	0.749433	+	0.662080i	$0.230326\pi$
$853$			2.81393e7i			1.32416i	−0.749433	+	0.662080i	$0.769674\pi$
$854$	−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	$-0.820559\pi$
$857$	862650.	−	1.49415e6i	0.0401220	−	0.0694933i	0.885389	+	0.464851i	$0.153892\pi$
$858$	−1.10612e6	−	725083.i	−0.0512960	−	0.0336255i
$859$	3.41000e7	−	1.96876e7i	1.57678	−	0.910354i	0.581475	−	0.813564i	$-0.302476\pi$
$859$	3.41000e7	−	1.96876e7i	1.57678	−	0.910354i	0.995305	−	0.0967905i	$-0.0308577\pi$
$860$	−7.41242e6			−0.341754
$861$	−1.45513e7	−	1.98092e7i	−0.668949	−	0.910667i
$862$	−1.09908e7			−0.503802
$863$	3.20069e7	−	1.84792e7i	1.46291	−	0.844610i	0.463763	−	0.885959i	$-0.346499\pi$
$863$	3.20069e7	−	1.84792e7i	1.46291	−	0.844610i	0.999145	+	0.0413494i	$0.0131657\pi$
$864$	−1.64012e7	−	1.36344e7i	−0.747468	−	0.621372i
$865$	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
$870$	−1.00933e7	−	2.00209e7i	−0.452099	−	0.896777i
$871$	6.57693e6	+	3.79719e6i	0.293750	+	0.169597i
$872$	−4.19270e6	−	2.42066e6i	−0.186725	−	0.107806i
$873$	−4.15380e6	+	1.80688e6i	−0.184463	+	0.0802406i
$874$			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	0.940788	+	0.338996i	$0.110087\pi$
$877$	1.74011e7	+	3.01396e7i	0.763973	+	1.32324i	−0.176815	+	0.984244i	$0.556579\pi$
$878$	−3.60321e6	+	6.24094e6i	−0.157744	+	0.273221i
$879$	4.59006e6	−	7.00217e6i	0.200376	−	0.305675i
$880$	−202907.	+	117148.i	−0.00883262	+	0.00509951i
$881$	−2.98621e7			−1.29623			−0.648114	−	0.761544i	$-0.724442\pi$
$881$	−2.98621e7			−1.29623			−0.648114	+	0.761544i	$0.724442\pi$
$882$	3.25629e6	+	1.45681e7i	0.140946	+	0.630567i
$883$	−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
$885$	−4.92051e6	+	7.50627e6i	−0.211179	+	0.322156i
$886$	3.90506e6	−	6.76377e6i	0.167126	−	0.289471i
$887$	−1.50058e7	−	2.59908e7i	−0.640398	−	1.10920i	−0.985344	−	0.170579i	$-0.945436\pi$
$887$	−1.50058e7	−	2.59908e7i	−0.640398	−	1.10920i	0.344946	−	0.938622i	$-0.387897\pi$
$888$	−1.28188e6	+	2.26052e7i	−0.0545525	+	0.962001i
$889$	−1.91088e6	+	5.12329e6i	−0.0810923	+	0.217417i
$890$		−	4.92030e6i		−	0.208217i
$891$	−2.22418e6	+	680745.i	−0.0938589	+	0.0287270i
$892$	302347.	+	174560.i	0.0127231	+	0.00734570i
$893$	1.61939e7	+	9.34956e6i	0.679553	+	0.392340i
$894$	−9.89734e6	−	1.96322e7i	−0.414166	−	0.821535i
$895$		−	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
$900$	−6.46272e6	+	8.73666e6i	−0.265955	+	0.359533i
$901$	−1.71600e7	+	9.90735e6i	−0.704217	+	0.406580i
$902$	−1.75112e6			−0.0716639
$903$	6.40098e6	+	8.71392e6i	0.261233	+	0.355626i
$904$	3.53425e6			0.143839
$905$	−3.02133e6	+	1.74437e6i	−0.122624	+	0.0707973i
$906$	1.31771e7	+	8.63783e6i	0.533333	+	0.349610i
$907$	−5.32535e6	+	9.22377e6i	−0.214946	+	0.372298i	−0.953256	−	0.302164i	$-0.902291\pi$
$907$	−5.32535e6	+	9.22377e6i	−0.214946	+	0.372298i	0.738310	+	0.674462i	$0.235624\pi$
$908$	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	$-0.0856509\pi$
$912$	−3.08314e6	+	1.55432e6i	−0.122746	+	0.0618806i
$913$	297203.	+	171590.i	0.0117998	+	0.00681264i
$914$	2.38001e7	+	1.37410e7i	0.942352	+	0.544067i
$915$	−5.81176e6	+	2.92993e6i	−0.229485	+	0.115692i
$916$		−	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	0.854242	−	0.519875i	$-0.174022\pi$
$919$	−591537.	−	1.02457e6i	−0.0231043	−	0.0400178i	−0.877346	+	0.479858i	$0.840688\pi$
$920$	3.18649e6	−	5.51916e6i	0.124120	−	0.214982i
$921$	6.66711e6	+	4.37042e6i	0.258993	+	0.169775i
$922$	−2.94121e6	+	1.69811e6i	−0.113946	+	0.0657868i
$923$	3.57331e7			1.38059
$924$	−1.35877e6	−	596461.i	−0.0523559	−	0.0229828i
$925$	1.88261e7			0.723446
$926$	3.84579e6	−	2.22037e6i	0.147387	−	0.0850937i
$927$	1.15043e7	+	8.50999e6i	0.439704	+	0.325259i
$928$	1.49056e7	−	2.58172e7i	0.568170	−	0.984100i
$929$	−4.74229e6	−	8.21389e6i	−0.180281	−	0.312255i	0.761695	−	0.647935i	$-0.224367\pi$
$929$	−4.74229e6	−	8.21389e6i	−0.180281	−	0.312255i	−0.941976	+	0.335680i	$0.891034\pi$
$930$	−1.20359e7	−	682522.i	−0.456321	−	0.0258767i
$931$	−4.56775e7	−	8.80355e6i	−1.72714	−	0.332877i
$932$			9.93714e6i			0.374733i
$933$	−1.69330e7	−	3.35880e7i	−0.636838	−	1.26322i
$934$	−9.59477e6	−	5.53954e6i	−0.359888	−	0.207781i
$935$	3.13770e6	+	1.81155e6i	0.117377	+	0.0677676i
$936$	1.05725e7	+	2.43050e7i	0.394447	+	0.906787i
$937$			1.67626e7i			0.623723i	0.950128	+	0.311861i	$0.100952\pi$
$937$			1.67626e7i			0.623723i	−0.950128	+	0.311861i	$0.899048\pi$
$938$	−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	0.186381	+	0.982477i	$0.440324\pi$
$941$	−2.05801e7	+	3.56458e7i	−0.757660	+	1.31231i	−0.944041	+	0.329828i	$0.893009\pi$
$942$	−1.18382e7	+	1.80593e7i	−0.434670	+	0.663093i
$943$	4.87946e6	−	2.81716e6i	0.178687	−	0.103165i
$944$	619935.			0.0226421
$945$	3.64992e7	+	121887.i	1.32955	+	0.00443994i
$946$	770305.			0.0279856
$947$	−1.94640e7	+	1.12376e7i	−0.705274	+	0.407190i	−0.809309	−	0.587383i	$-0.800158\pi$
$947$	−1.94640e7	+	1.12376e7i	−0.705274	+	0.407190i	0.104034	+	0.994574i	$0.466825\pi$
$948$	−1.07326e7	+	1.63727e7i	−0.387870	+	0.591698i
$949$	−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	$-0.0214603\pi$
$954$	5.67271e6	+	1.30409e7i	0.201799	+	0.463912i
$955$	−4.90089e7	−	2.82953e7i	−1.73887	−	1.00393i
$956$	−4.34364e6	−	2.50780e6i	−0.153713	−	0.0887460i
$957$	−1.46356e6	−	2.90309e6i	−0.0516570	−	0.102466i
$958$			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
$963$	−2.88316e7	−	2.13274e7i	−1.00185	−	0.741093i
$964$	4.30742e6	−	2.48689e6i	0.149288	−	0.0861913i
$965$	−4.13476e7			−1.42933
$966$	−3.40118e6	+	375487.i	−0.117270	+	0.0129465i
$967$	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
$969$	4.46541e7	+	2.92716e7i	1.52775	+	1.00147i
$970$	2.53201e6	−	4.38556e6i	0.0864043	−	0.149657i
$971$	1.89586e7	+	3.28373e7i	0.645296	+	1.11769i	0.984233	+	0.176877i	$0.0565995\pi$
$971$	1.89586e7	+	3.28373e7i	0.645296	+	1.11769i	−0.338937	+	0.940809i	$0.610067\pi$
$972$	1.64747e7	+	4.79510e6i	0.559311	+	0.162792i
$973$	4.41832e7	+	1.64794e7i	1.49615	+	0.558033i
$974$			1.61376e7i			0.545056i
$975$	1.96791e7	−	9.92099e6i	0.662971	−	0.334228i
$976$	389325.	+	224777.i	0.0130824	+	0.00755314i
$977$	−2.21992e7	−	1.28167e7i	−0.744050	−	0.429577i	0.0794903	−	0.996836i	$-0.474671\pi$
$977$	−2.21992e7	−	1.28167e7i	−0.744050	−	0.429577i	−0.823540	+	0.567258i	$0.808004\pi$
$978$	−1.17786e7	+	5.93806e6i	−0.393775	+	0.198517i
$979$		−	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	−0.419348	−	0.907826i	$-0.637741\pi$
$983$	1.74664e7	−	3.02526e7i	0.576526	−	0.998572i	0.995874	−	0.0907467i	$-0.0289254\pi$
$984$	2.93491e7	+	1.92389e7i	0.966288	+	0.633420i
$985$	−3.51375e7	+	2.02867e7i	−1.15393	+	0.666224i
$986$	2.39482e7			0.784477
$987$	−5.48793e6	+	1.25018e7i	−0.179315	+	0.408488i
$988$	−3.04033e7			−0.990897
$989$	−2.14643e6	+	1.23924e6i	−0.0697793	+	0.0402871i
$990$	1.54643e6	−	2.09055e6i	0.0501466	−	0.0677910i
$991$	−2.48035e7	+	4.29610e7i	−0.802286	+	1.38960i	0.115822	+	0.993270i	$0.463050\pi$
$991$	−2.48035e7	+	4.29610e7i	−0.802286	+	1.38960i	−0.918108	+	0.396330i	$0.870283\pi$
$992$	−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
$996$	−1.13961e6	−	2.26052e6i	−0.0364007	−	0.0722039i
$997$	−7.82003e6	−	4.51490e6i	−0.249155	−	0.143850i	0.370222	−	0.928943i	$-0.379282\pi$
$997$	−7.82003e6	−	4.51490e6i	−0.249155	−	0.143850i	−0.619377	+	0.785093i	$0.712615\pi$
$998$	−3.18735e7	−	1.84022e7i	−1.01299	−	0.584848i
$999$	−1.02947e7	−	2.78852e7i	−0.326362	−	0.884016i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.g.c.5.3	✓	16	7.5	odd	6	inner
21.6.g.c.5.6	yes	16	21.5	even	6	inner
21.6.g.c.17.3	yes	16	3.2	odd	2	inner
21.6.g.c.17.6	yes	16	1.1	even	1	trivial
147.6.c.c.146.5		16	21.11	odd	6
147.6.c.c.146.6		16	21.17	even	6
147.6.c.c.146.11		16	7.3	odd	6
147.6.c.c.146.12		16	7.4	even	3

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)

\(f(q)\)	\(=\)	\(q+(3.16536 - 1.82752i) q^{2} +(-8.54605 + 13.0371i) q^{3} +(-9.32032 + 16.1433i) q^{4} +(37.1622 + 64.3668i) q^{5} +(-3.22580 + 56.8851i) q^{6} +(45.3051 - 121.468i) q^{7} +185.094i q^{8} +(-96.9302 - 222.831i) q^{9} +O(q^{10})\)	\(q+(3.16536 - 1.82752i) q^{2} +(-8.54605 + 13.0371i) 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} +(-96.9302 - 222.831i) q^{9} +(235.264 + 135.830i) q^{10} +(34.1140 + 19.6957i) q^{11} +(-130.809 - 259.471i) 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} +(-714.048 - 528.198i) q^{18} +(2396.97 - 1383.89i) q^{19} -1385.45 q^{20} +(1196.41 + 1628.72i) q^{21} +143.977 q^{22} +(-401.189 + 231.627i) q^{23} +(-2413.08 - 1581.82i) 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} +(-3781.39 + 1906.34i) q^{30} +(2465.35 + 1423.37i) q^{31} +(-4876.16 - 2815.25i) q^{32} +(-548.314 + 276.426i) 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} +(-7682.59 - 5036.09i) q^{39} +(-11913.9 + 6878.49i) q^{40} -12162.5 q^{41} +(6763.57 + 2969.02i) q^{42} +5350.18 q^{43} +(-635.906 + 367.140i) q^{44} +(10740.8 - 14520.0i) 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} +(8684.11 + 17225.7i) q^{51} +(-9513.04 - 5492.35i) q^{52} +(-13866.6 - 8005.88i) q^{53} +(12988.4 - 4795.08i) 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} +(11840.2 - 18062.2i) q^{60} +(4864.96 - 2808.79i) q^{61} +10405.0 q^{62} +(-31458.2 + 1678.54i) q^{63} -23140.6 q^{64} +(-37930.6 + 21899.2i) q^{65} +(-1230.44 + 1877.04i) 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} +(41244.6 - 17941.2i) q^{72} +(44722.8 + 25820.7i) q^{73} +(-24839.0 - 14340.8i) q^{74} +(-16835.5 - 33394.7i) 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} +(-40258.1 + 43198.0i) q^{81} +(-38498.7 + 22227.2i) q^{82} +8712.06 q^{83} +(-37443.7 + 4133.74i) q^{84} +91977.1 q^{85} +(16935.3 - 9777.57i) q^{86} +(-69025.7 - 45247.7i) 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} +(-39625.5 + 19976.7i) q^{93} +(21385.2 + 12346.7i) q^{94} +(178153. + 102857. i) q^{95} +(78374.5 - 39511.5i) 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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