LMFDB - Embedded newform 96.6.o.a.35.74

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [96,6,Mod(11,96)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("96.11"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(96, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([4, 5, 4])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 96 = 2^{5} \cdot 3 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	96.o (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.3968467020$
Analytic rank:	$0$
Dimension:	$312$
Relative dimension:	$78$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			35.74
Character	$\chi$	$=$	96.35
Dual form			96.6.o.a.11.74

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(5.55856 - 1.04998i) q^{2} +(12.6621 - 9.09239i) q^{3} +(29.7951 - 11.6727i) q^{4} +(-18.4880 + 7.65797i) q^{5} +(60.8361 - 63.8355i) q^{6} +(-168.744 - 168.744i) q^{7} +(153.362 - 96.1675i) q^{8} +(77.6568 - 230.257i) q^{9} +(-94.7257 + 61.9791i) q^{10} +(-370.212 + 153.347i) q^{11} +(271.135 - 418.709i) q^{12} +(217.625 - 525.392i) q^{13} +(-1115.15 - 760.794i) q^{14} +(-164.467 + 265.066i) q^{15} +(751.496 - 695.578i) q^{16} +1243.80 q^{17} +(189.895 - 1361.44i) q^{18} +(1864.33 + 772.230i) q^{19} +(-461.462 + 443.974i) q^{20} +(-3670.93 - 602.363i) q^{21} +(-1896.83 + 1241.10i) q^{22} +(2096.69 + 2096.69i) q^{23} +(1067.49 - 2612.11i) q^{24} +(-1926.55 + 1926.55i) q^{25} +(658.030 - 3148.92i) q^{26} +(-1110.29 - 3621.62i) q^{27} +(-6997.43 - 3058.04i) q^{28} +(471.407 - 1138.08i) q^{29} +(-635.887 + 1646.07i) q^{30} +4342.93i q^{31} +(3446.90 - 4655.46i) q^{32} +(-3293.37 + 5307.80i) q^{33} +(6913.75 - 1305.96i) q^{34} +(4411.96 + 1827.49i) q^{35} +(-373.930 - 7767.00i) q^{36} +(-2241.70 - 5411.95i) q^{37} +(11173.8 + 2334.99i) q^{38} +(-2021.49 - 8631.29i) q^{39} +(-2098.90 + 2952.38i) q^{40} +(8063.32 - 8063.32i) q^{41} +(-21037.5 + 506.116i) q^{42} +(1557.93 + 3761.17i) q^{43} +(-9240.54 + 8890.36i) q^{44} +(327.586 + 4851.68i) q^{45} +(13856.0 + 9453.10i) q^{46} -6200.25i q^{47} +(3191.04 - 15640.4i) q^{48} +40141.8i q^{49} +(-8686.00 + 12731.7i) q^{50} +(15749.2 - 11309.2i) q^{51} +(351.404 - 18194.4i) q^{52} +(-8867.88 - 21409.0i) q^{53} +(-9974.24 - 18965.2i) q^{54} +(5670.14 - 5670.14i) q^{55} +(-42106.5 - 9651.17i) q^{56} +(30627.7 - 7173.16i) q^{57} +(1425.39 - 6821.03i) q^{58} +(19289.2 + 46568.2i) q^{59} +(-1806.28 + 9817.43i) q^{60} +(7630.87 + 3160.81i) q^{61} +(4559.97 + 24140.4i) q^{62} +(-51958.6 + 25750.4i) q^{63} +(14271.6 - 29496.8i) q^{64} +11380.0i q^{65} +(-12733.3 + 32961.7i) q^{66} +(-15696.3 + 37894.2i) q^{67} +(37059.3 - 14518.5i) q^{68} +(45612.4 + 7484.54i) q^{69} +(26442.9 + 5525.78i) q^{70} +(-23598.6 + 23598.6i) q^{71} +(-10233.7 - 42780.7i) q^{72} +(-52850.5 - 52850.5i) q^{73} +(-18143.1 - 27728.9i) q^{74} +(-6877.19 + 41911.1i) q^{75} +(64561.9 + 1246.94i) q^{76} +(88347.2 + 36594.6i) q^{77} +(-20299.2 - 45855.0i) q^{78} +46031.8 q^{79} +(-8566.92 + 18614.8i) q^{80} +(-46987.8 - 35762.1i) q^{81} +(36354.1 - 53286.7i) q^{82} +(-1184.00 + 2858.44i) q^{83} +(-116407. + 24902.2i) q^{84} +(-22995.4 + 9525.01i) q^{85} +(12609.0 + 19270.9i) q^{86} +(-4378.84 - 18696.6i) q^{87} +(-42029.4 + 59119.9i) q^{88} +(82758.3 + 82758.3i) q^{89} +(6915.05 + 26624.4i) q^{90} +(-125379. + 51933.9i) q^{91} +(86945.1 + 37997.1i) q^{92} +(39487.6 + 54990.6i) q^{93} +(-6510.11 - 34464.5i) q^{94} -40381.4 q^{95} +(1315.58 - 90288.4i) q^{96} +55557.4 q^{97} +(42147.9 + 223131. i) q^{98} +(6559.73 + 97152.5i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 312 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 4 q^{9} + 192 q^{10} - 4 q^{12} - 8 q^{13} - 8 q^{15} - 6696 q^{16} - 4 q^{18} - 8 q^{19} - 4 q^{21} + 5576 q^{22} - 11024 q^{24} - 8 q^{25} + 7460 q^{27}+ \cdots + 339516 q^{99}+O(q^{100}) $ 312 * q - 4 * q^3 - 8 * q^4 - 4 * q^6 - 8 * q^7 - 4 * q^9 + 192 * q^10 - 4 * q^12 - 8 * q^13 - 8 * q^15 - 6696 * q^16 - 4 * q^18 - 8 * q^19 - 4 * q^21 + 5576 * q^22 - 11024 * q^24 - 8 * q^25 + 7460 * q^27 - 8 * q^28 + 32564 * q^30 - 8 * q^33 - 264 * q^34 + 3264 * q^36 - 8 * q^37 + 44900 * q^39 - 60136 * q^40 - 7264 * q^42 - 8 * q^43 - 4 * q^45 + 63320 * q^46 + 112368 * q^48 - 976 * q^51 - 55024 * q^52 - 115328 * q^54 - 110056 * q^55 - 4 * q^57 - 123568 * q^58 + 44648 * q^60 - 96168 * q^61 + 187432 * q^64 + 17564 * q^66 + 97848 * q^67 - 4 * q^69 - 143480 * q^70 + 179936 * q^72 - 8 * q^73 + 12496 * q^75 - 234928 * q^76 - 708428 * q^78 + 355344 * q^79 + 251552 * q^82 + 387560 * q^84 - 25008 * q^85 - 282188 * q^87 + 111632 * q^88 + 453536 * q^90 + 200104 * q^91 + 968 * q^93 - 671008 * q^94 - 911336 * q^96 - 16 * q^97 + 339516 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/96\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$65$
$\chi(n)$	$-1$	$e\left(\frac{3}{8}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	5.55856	−	1.04998i	0.982623	−	0.185611i
$2$	5.55856	−	1.04998i	0.982623	−	0.185611i
$3$	12.6621	−	9.09239i	0.812273	−	0.583277i
$3$	12.6621	−	9.09239i	0.812273	−	0.583277i
$4$	29.7951	−	11.6727i	0.931097	−	0.364772i
$5$	−18.4880	+	7.65797i	−0.330723	+	0.136990i	−0.541865	−	0.840465i	$-0.682282\pi$
$5$	−18.4880	+	7.65797i	−0.330723	+	0.136990i	0.211142	+	0.977455i	$0.432282\pi$
$6$	60.8361	−	63.8355i	0.689896	−	0.723909i
$7$	−168.744	−	168.744i	−1.30161	−	1.30161i	−0.927303	−	0.374311i	$-0.877879\pi$
$7$	−168.744	−	168.744i	−1.30161	−	1.30161i	−0.374311	−	0.927303i	$-0.622121\pi$
$8$	153.362	−	96.1675i	0.847212	−	0.531255i
$9$	77.6568	−	230.257i	0.319575	−	0.947561i
$10$	−94.7257	+	61.9791i	−0.299549	+	0.195995i
$11$	−370.212	+	153.347i	−0.922505	+	0.382114i	−0.792830	−	0.609442i	$-0.791393\pi$
$11$	−370.212	+	153.347i	−0.922505	+	0.382114i	−0.129675	+	0.991557i	$0.541393\pi$
$12$	271.135	−	418.709i	0.543542	−	0.839382i
$13$	217.625	−	525.392i	0.357149	−	0.862235i	−0.638549	−	0.769581i	$-0.720465\pi$
$13$	217.625	−	525.392i	0.357149	−	0.862235i	0.995698	−	0.0926536i	$-0.0295349\pi$
$14$	−1115.15	−	760.794i	−1.52059	−	1.03740i
$15$	−164.467	+	265.066i	−0.188734	+	0.304176i
$16$	751.496	−	695.578i	0.733883	−	0.679276i
$17$	1243.80			1.04383			0.521915	−	0.852998i	$-0.325218\pi$
$17$	1243.80			1.04383			0.521915	+	0.852998i	$0.325218\pi$
$18$	189.895	−	1361.44i	0.138144	−	0.990412i
$19$	1864.33	+	772.230i	1.18478	+	0.490753i	0.886053	−	0.463585i	$-0.153437\pi$
$19$	1864.33	+	772.230i	1.18478	+	0.490753i	0.298730	+	0.954338i	$0.403437\pi$
$20$	−461.462	+	443.974i	−0.257965	+	0.248189i
$21$	−3670.93	−	602.363i	−1.81647	−	0.298064i
$22$	−1896.83	+	1241.10i	−0.835550	+	0.546702i
$23$	2096.69	+	2096.69i	0.826446	+	0.826446i	0.987023	−	0.160577i	$-0.0513355\pi$
$23$	2096.69	+	2096.69i	0.826446	+	0.826446i	−0.160577	+	0.987023i	$0.551335\pi$
$24$	1067.49	−	2612.11i	0.378298	−	0.925684i
$25$	−1926.55	+	1926.55i	−0.616495	+	0.616495i
$26$	658.030	−	3148.92i	0.190903	−	0.913543i
$27$	−1110.29	−	3621.62i	−0.293108	−	0.956079i
$28$	−6997.43	−	3058.04i	−1.68672	−	0.737137i
$29$	471.407	−	1138.08i	0.104088	−	0.251291i	−0.863252	−	0.504773i	$-0.831576\pi$
$29$	471.407	−	1138.08i	0.104088	−	0.251291i	0.967340	+	0.253483i	$0.0815761\pi$
$30$	−635.887	+	1646.07i	−0.128996	+	0.333922i
$31$			4342.93i			0.811669i	0.913947	+	0.405834i	$0.133019\pi$
$31$			4342.93i			0.811669i	−0.913947	+	0.405834i	$0.866981\pi$
$32$	3446.90	−	4655.46i	0.595050	−	0.803689i
$33$	−3293.37	+	5307.80i	−0.526448	+	0.848457i
$34$	6913.75	−	1305.96i	1.02569	−	0.193746i
$35$	4411.96	+	1827.49i	0.608781	+	0.252166i
$36$	−373.930	−	7767.00i	−0.0480877	−	0.998843i
$37$	−2241.70	−	5411.95i	−0.269199	−	0.649905i	0.730247	−	0.683183i	$-0.239405\pi$
$37$	−2241.70	−	5411.95i	−0.269199	−	0.649905i	−0.999446	+	0.0332789i	$0.989405\pi$
$38$	11173.8	+	2334.99i	1.25528	+	0.262316i
$39$	−2021.49	−	8631.29i	−0.212819	−	0.908687i
$40$	−2098.90	+	2952.38i	−0.207416	+	0.291758i
$41$	8063.32	−	8063.32i	0.749125	−	0.749125i	−0.225190	−	0.974315i	$-0.572300\pi$
$41$	8063.32	−	8063.32i	0.749125	−	0.749125i	0.974315	+	0.225190i	$0.0723003\pi$
$42$	−21037.5	+	506.116i	−1.84023	+	0.0442717i
$43$	1557.93	+	3761.17i	0.128492	+	0.310207i	0.975013	−	0.222148i	$-0.0713069\pi$
$43$	1557.93	+	3761.17i	0.128492	+	0.310207i	−0.846521	+	0.532356i	$0.821307\pi$
$44$	−9240.54	+	8890.36i	−0.719557	+	0.692289i
$45$	327.586	+	4851.68i	0.0241153	+	0.357159i
$46$	13856.0	+	9453.10i	0.965483	+	0.658688i
$47$		−	6200.25i		−	0.409416i	−0.978823	−	0.204708i	$-0.934376\pi$
$47$		−	6200.25i		−	0.409416i	0.978823	−	0.204708i	$-0.0656245\pi$
$48$	3191.04	−	15640.4i	0.199908	−	0.979815i
$49$			40141.8i			2.38840i
$50$	−8686.00	+	12731.7i	−0.491354	+	0.720211i
$51$	15749.2	−	11309.2i	0.847875	−	0.608842i
$52$	351.404	−	18194.4i	0.0180218	−	0.933102i
$53$	−8867.88	−	21409.0i	−0.433641	−	1.04690i	−0.978104	−	0.208117i	$-0.933267\pi$
$53$	−8867.88	−	21409.0i	−0.433641	−	1.04690i	0.544463	−	0.838785i	$-0.316733\pi$
$54$	−9974.24	−	18965.2i	−0.465474	−	0.885062i
$55$	5670.14	−	5670.14i	0.252748	−	0.252748i
$56$	−42106.5	−	9651.17i	−1.79423	−	0.411254i
$57$	30627.7	−	7173.16i	1.24861	−	0.292431i
$58$	1425.39	−	6821.03i	0.0556369	−	0.266244i
$59$	19289.2	+	46568.2i	0.721413	+	1.74165i	0.669286	+	0.743005i	$0.266600\pi$
$59$	19289.2	+	46568.2i	0.721413	+	1.74165i	0.0521273	+	0.998640i	$0.483400\pi$
$60$	−1806.28	+	9817.43i	−0.0647749	+	0.352062i
$61$	7630.87	+	3160.81i	0.262573	+	0.108761i	0.510086	−	0.860123i	$-0.329613\pi$
$61$	7630.87	+	3160.81i	0.262573	+	0.108761i	−0.247514	+	0.968884i	$0.579613\pi$
$62$	4559.97	+	24140.4i	0.150655	+	0.797565i
$63$	−51958.6	+	25750.4i	−1.64932	+	0.817395i
$64$	14271.6	−	29496.8i	0.435536	−	0.900171i
$65$			11380.0i			0.334086i
$66$	−12733.3	+	32961.7i	−0.359817	+	0.931429i
$67$	−15696.3	+	37894.2i	−0.427179	+	1.03130i	0.552999	+	0.833182i	$0.313483\pi$
$67$	−15696.3	+	37894.2i	−0.427179	+	1.03130i	−0.980178	+	0.198120i	$0.936517\pi$
$68$	37059.3	−	14518.5i	0.971907	−	0.380760i
$69$	45612.4	+	7484.54i	1.15335	+	0.189253i
$70$	26442.9	+	5525.78i	0.645008	+	0.134787i
$71$	−23598.6	+	23598.6i	−0.555572	+	0.555572i	−0.928043	−	0.372472i	$-0.878510\pi$
$71$	−23598.6	+	23598.6i	−0.555572	+	0.555572i	0.372472	+	0.928043i	$0.378510\pi$
$72$	−10233.7	−	42780.7i	−0.232649	−	0.972561i
$73$	−52850.5	−	52850.5i	−1.16076	−	1.16076i	−0.984310	−	0.176450i	$-0.943539\pi$
$73$	−52850.5	−	52850.5i	−1.16076	−	1.16076i	−0.176450	−	0.984310i	$-0.556461\pi$
$74$	−18143.1	−	27728.9i	−0.385151	−	0.588645i
$75$	−6877.19	+	41911.1i	−0.141175	+	0.860350i
$76$	64561.9	+	1246.94i	1.28216	+	0.0247635i
$77$	88347.2	+	36594.6i	1.69811	+	0.703381i
$78$	−20299.2	−	45855.0i	−0.377783	−	0.853396i
$79$	46031.8			0.829831			0.414916	−	0.909860i	$-0.363811\pi$
$79$	46031.8			0.829831			0.414916	+	0.909860i	$0.363811\pi$
$80$	−8566.92	+	18614.8i	−0.149658	+	0.325186i
$81$	−46987.8	−	35762.1i	−0.795743	−	0.605634i
$82$	36354.1	−	53286.7i	0.597062	−	0.875153i
$83$	−1184.00	+	2858.44i	−0.0188650	+	0.0455442i	−0.933031	−	0.359795i	$-0.882847\pi$
$83$	−1184.00	+	2858.44i	−0.0188650	+	0.0455442i	0.914166	+	0.405339i	$0.132847\pi$
$84$	−116407.	+	24902.2i	−1.80003	+	0.385069i
$85$	−22995.4	+	9525.01i	−0.345218	+	0.142994i
$86$	12609.0	+	19270.9i	0.183837	+	0.280967i
$87$	−4378.84	−	18696.6i	−0.0620242	−	0.264829i
$88$	−42029.4	+	59119.9i	−0.578557	+	0.813817i
$89$	82758.3	+	82758.3i	1.10748	+	1.10748i	0.993481	+	0.114001i	$0.0363667\pi$
$89$	82758.3	+	82758.3i	1.10748	+	1.10748i	0.114001	+	0.993481i	$0.463633\pi$
$90$	6915.05	+	26624.4i	0.0899889	+	0.346476i
$91$	−125379.	+	51933.9i	−1.58717	+	0.657426i
$92$	86945.1	+	37997.1i	1.07097	+	0.468037i
$93$	39487.6	+	54990.6i	0.473428	+	0.659297i
$94$	−6510.11	−	34464.5i	−0.0759922	−	0.402302i
$95$	−40381.4			−0.459063
$96$	1315.58	−	90288.4i	0.0145693	−	0.999894i
$97$	55557.4			0.599532			0.299766	−	0.954013i	$-0.403091\pi$
$97$	55557.4			0.599532			0.299766	+	0.954013i	$0.403091\pi$
$98$	42147.9	+	223131.i	0.443314	+	2.34690i
$99$	6559.73	+	97152.5i	0.0672664	+	0.996244i
$100$	−34913.7	+	79889.7i	−0.349137	+	0.798897i
$101$	−6031.72	+	2498.42i	−0.0588353	+	0.0243704i	−0.411907	−	0.911226i	$-0.635137\pi$
$101$	−6031.72	+	2498.42i	−0.0588353	+	0.0243704i	0.353072	+	0.935596i	$0.385137\pi$
$102$	75668.2	−	79398.8i	0.720134	−	0.755637i
$103$	26649.1	+	26649.1i	0.247509	+	0.247509i	0.819947	−	0.572439i	$-0.194003\pi$
$103$	26649.1	+	26649.1i	0.247509	+	0.247509i	−0.572439	+	0.819947i	$0.694003\pi$
$104$	−17150.4	−	101504.i	−0.155486	−	0.920233i
$105$	72480.9	−	16975.4i	0.641579	−	0.150261i
$106$	−71771.5	−	109692.i	−0.620422	−	0.948221i
$107$	23917.3	−	9906.85i	0.201954	−	0.0836520i	−0.279414	−	0.960171i	$-0.590140\pi$
$107$	23917.3	−	9906.85i	0.201954	−	0.0836520i	0.481368	+	0.876519i	$0.340140\pi$
$108$	−75355.4	−	94946.6i	−0.621663	−	0.783285i
$109$	63476.0	−	153245.i	0.511733	−	1.23543i	−0.431141	−	0.902284i	$-0.641889\pi$
$109$	63476.0	−	153245.i	0.511733	−	1.23543i	0.942874	−	0.333149i	$-0.108111\pi$
$110$	25564.3	−	37471.3i	0.201443	−	0.295269i
$111$	−77592.2	−	48144.1i	−0.597738	−	0.370882i
$112$	−244185.	−	9435.82i	−1.83939	−	0.0710779i
$113$	74209.6			0.546719			0.273359	−	0.961912i	$-0.411865\pi$
$113$	74209.6			0.546719			0.273359	+	0.961912i	$0.411865\pi$
$114$	162714.	−	72030.8i	1.17264	−	0.519106i
$115$	−54819.9	−	22707.2i	−0.386539	−	0.160110i
$116$	761.192	−	39411.7i	0.00525229	−	0.271944i
$117$	−104075.	−	90910.0i	−0.702884	−	0.613970i
$118$	156116.	+	238599.i	1.03215	+	1.57748i
$119$	−209884.	−	209884.i	−1.35866	−	1.35866i
$120$	267.750	+	56467.3i	0.00169737	+	0.357968i
$121$	−338.537	+	338.537i	−0.00210205	+	0.00210205i
$122$	45735.4	+	9557.32i	0.278197	+	0.0581348i
$123$	28783.6	−	175413.i	0.171547	−	1.04544i
$124$	50693.7	+	129398.i	0.296074	+	0.755742i
$125$	44795.7	−	108146.i	0.256425	−	0.619065i
$126$	−261777.	+	197690.i	−1.46895	+	1.10932i
$127$		−	234610.i		−	1.29074i	−0.763871	−	0.645369i	$-0.776704\pi$
$127$		−	234610.i		−	1.29074i	0.763871	−	0.645369i	$-0.223296\pi$
$128$	48358.8	−	178945.i	0.260886	−	0.965370i
$129$	53924.6	+	33459.0i	0.285307	+	0.177026i
$130$	11948.7	+	63256.4i	0.0620102	+	0.328281i
$131$	−199418.	−	82601.8i	−1.01528	−	0.420544i	−0.187903	−	0.982188i	$-0.560169\pi$
$131$	−199418.	−	82601.8i	−1.01528	−	0.420544i	−0.827379	+	0.561644i	$0.810169\pi$
$132$	−36169.8	+	196589.i	−0.180681	+	0.982029i
$133$	−184285.	−	444903.i	−0.903359	−	2.18090i
$134$	−47460.8	+	227118.i	−0.228335	+	1.09267i
$135$	48261.3	+	58453.9i	0.227911	+	0.276044i
$136$	190752.	−	119613.i	0.884345	−	0.554540i
$137$	89634.0	−	89634.0i	0.408010	−	0.408010i	−0.473034	−	0.881044i	$-0.656841\pi$
$137$	89634.0	−	89634.0i	0.408010	−	0.408010i	0.881044	+	0.473034i	$0.156841\pi$
$138$	261398.	−	6288.64i	1.16843	−	0.0281099i
$139$	−73183.1	−	176680.i	−0.321273	−	0.775620i	−0.999181	−	0.0404738i	$-0.987113\pi$
$139$	−73183.1	−	176680.i	−0.321273	−	0.775620i	0.677908	−	0.735147i	$-0.262887\pi$
$140$	152787.	+	2950.90i	0.658817	+	0.0127243i
$141$	−56375.1	−	78508.1i	−0.238803	−	0.332558i
$142$	−106396.	+	155952.i	−0.442797	+	0.649038i
$143$			227879.i			0.931888i
$144$	−101803.	−	227054.i	−0.409124	−	0.912479i
$145$			24650.7i			0.0973665i
$146$	−349264.	−	238281.i	−1.35604	−	0.925139i
$147$	364985.	+	508279.i	1.39310	+	1.94003i
$148$	−129964.	−	135083.i	−0.487717	−	0.506928i
$149$	155603.	+	375659.i	0.574186	+	1.38621i	0.897962	+	0.440073i	$0.145048\pi$
$149$	155603.	+	375659.i	0.574186	+	1.38621i	−0.323776	+	0.946134i	$0.604952\pi$
$150$	5778.33	+	240186.i	0.0209688	+	0.871604i
$151$	−160775.	+	160775.i	−0.573821	+	0.573821i	−0.933194	−	0.359373i	$-0.882991\pi$
$151$	−160775.	+	160775.i	−0.573821	+	0.573821i	0.359373	+	0.933194i	$0.382991\pi$
$152$	360180.	−	60857.2i	1.26448	−	0.213650i
$153$	96589.9	−	286395.i	0.333582	−	0.989092i
$154$	529507.	+	110651.i	1.79916	+	0.375970i
$155$	−33258.0	−	80292.0i	−0.111190	−	0.268437i
$156$	−160981.	−	233574.i	−0.529619	−	0.768446i
$157$	−266686.	−	110465.i	−0.863477	−	0.357664i	−0.0934106	−	0.995628i	$-0.529777\pi$
$157$	−266686.	−	110465.i	−0.863477	−	0.357664i	−0.770066	+	0.637964i	$0.779777\pi$
$158$	255870.	−	48332.2i	0.815412	−	0.154026i
$159$	−306944.	−	190452.i	−0.962869	−	0.597437i
$160$	−28074.7	+	112466.i	−0.0866992	+	0.347314i
$161$		−	707606.i		−	2.15143i
$162$	−298734.	−	149450.i	−0.894328	−	0.447412i
$163$	−96367.8	+	232652.i	−0.284094	+	0.685865i	−0.999923	−	0.0124115i	$-0.996049\pi$
$163$	−96367.8	+	232652.i	−0.284094	+	0.685865i	0.715829	+	0.698276i	$0.246049\pi$
$164$	146127.	−	334368.i	0.424248	−	0.970767i
$165$	20240.7	−	123351.i	0.0578782	−	0.352722i
$166$	−3580.06	+	17131.9i	−0.0100837	+	0.0482544i
$167$	−243174.	+	243174.i	−0.674722	+	0.674722i	−0.958801	−	0.284079i	$-0.908312\pi$
$167$	−243174.	+	243174.i	−0.674722	+	0.674722i	0.284079	+	0.958801i	$0.408312\pi$
$168$	−620908.	+	260645.i	−1.69728	+	0.712485i
$169$	33867.0	+	33867.0i	0.0912138	+	0.0912138i
$170$	−117820.	+	77089.9i	−0.312678	+	0.204586i
$171$	322590.	−	369306.i	0.843646	−	0.965821i
$172$	90321.6	+	93879.2i	0.232793	+	0.241963i
$173$	47789.8	+	19795.2i	0.121400	+	0.0502856i	0.442557	−	0.896741i	$-0.354072\pi$
$173$	47789.8	+	19795.2i	0.121400	+	0.0502856i	−0.321156	+	0.947026i	$0.604072\pi$
$174$	−43971.0	−	99328.6i	−0.110102	−	0.248715i
$175$	650186.			1.60488
$176$	−171548.	+	372751.i	−0.417450	+	0.907063i
$177$	667658.	+	414266.i	1.60185	+	0.993908i
$178$	546911.	+	373123.i	1.29380	+	0.882676i
$179$	−209677.	+	506205.i	−0.489123	+	1.18085i	0.466039	+	0.884764i	$0.345681\pi$
$179$	−209677.	+	506205.i	−0.489123	+	1.18085i	−0.955162	+	0.296084i	$0.904319\pi$
$180$	66392.6	+	140733.i	0.152735	+	0.323753i
$181$	−392962.	+	162770.i	−0.891567	+	0.369299i	−0.780972	−	0.624567i	$-0.785276\pi$
$181$	−392962.	+	162770.i	−0.891567	+	0.369299i	−0.110595	+	0.993866i	$0.535276\pi$
$182$	−642399.	+	420323.i	−1.43756	+	0.940599i
$183$	125362.	−	29360.4i	0.276719	−	0.0648089i
$184$	523185.	+	119919.i	1.13923	+	0.261121i
$185$	82889.1	+	82889.1i	0.178061	+	0.178061i
$186$	277233.	+	264207.i	0.587574	+	0.559967i
$187$	−460471.	+	190733.i	−0.962938	+	0.398862i
$188$	−72373.7	−	184737.i	−0.149343	−	0.381206i
$189$	−423771.	+	798481.i	−0.862933	+	1.62596i
$190$	−224462.	+	42399.4i	−0.451086	+	0.0852072i
$191$	576967.			1.14437			0.572187	−	0.820123i	$-0.306095\pi$
$191$	576967.			1.14437			0.572187	+	0.820123i	$0.306095\pi$
$192$	−87487.9	−	503255.i	−0.171275	−	0.985223i
$193$	11.0193			2.12942e−5			1.06471e−5	−	1.00000i	$-0.499997\pi$
$193$	11.0193			2.12942e−5			1.06471e−5		1.00000i	$0.499997\pi$
$194$	308819.	−	58333.9i	0.589114	−	0.111280i
$195$	103471.	+	144095.i	0.194865	+	0.271369i
$196$	468563.	+	1.19603e6i	0.871221	+	2.22383i
$197$	−790380.	+	327386.i	−1.45101	+	0.601028i	−0.962439	−	0.271496i	$-0.912482\pi$
$197$	−790380.	+	327386.i	−1.45101	+	0.601028i	−0.488571	+	0.872524i	$0.662482\pi$
$198$	138470.	+	533140.i	0.251012	+	0.966447i
$199$	−536917.	−	536917.i	−0.961112	−	0.961112i	0.0381594	−	0.999272i	$-0.487851\pi$
$199$	−536917.	−	536917.i	−0.961112	−	0.961112i	−0.999272	+	0.0381594i	$0.987851\pi$
$200$	−110188.	+	480730.i	−0.194786	+	0.849819i
$201$	145801.	+	622537.i	0.254549	+	1.08686i
$202$	−30904.4	+	20220.8i	−0.0532895	+	0.0348674i
$203$	−271590.	+	112496.i	−0.462566	+	0.191601i
$204$	337239.	−	520792.i	0.567365	−	0.876172i
$205$	−87325.7	+	210823.i	−0.145130	+	0.350375i
$206$	176112.	+	120150.i	0.289148	+	0.197267i
$207$	645601.	−	319956.i	1.04722	−	0.518996i
$208$	−201907.	−	546206.i	−0.323589	−	0.875382i
$209$	−808616.			−1.28049
$210$	385065.	−	170462.i	0.602541	−	0.266734i
$211$	418799.	+	173472.i	0.647589	+	0.268240i	0.682205	−	0.731161i	$-0.261021\pi$
$211$	418799.	+	173472.i	0.647589	+	0.268240i	−0.0346165	+	0.999401i	$0.511021\pi$
$212$	−514120.	−	534370.i	−0.785642	−	0.816587i
$213$	−84239.7	+	513375.i	−0.127224	+	0.775328i
$214$	122544.	−	80180.3i	0.182918	−	0.119683i
$215$	−57605.8	−	57605.8i	−0.0849905	−	0.0849905i
$216$	−518559.	−	448645.i	−0.756247	−	0.654287i
$217$	732842.	−	732842.i	1.05648	−	1.05648i
$218$	191932.	−	918468.i	0.273531	−	1.30895i
$219$	−1.14974e6	−	188660.i	−1.61990	−	0.265809i
$220$	102757.	−	235128.i	0.143137	−	0.327528i
$221$	270682.	−	653485.i	0.372803	−	0.900026i
$222$	−481851.	−	186142.i	−0.656191	−	0.253491i
$223$		−	381783.i		−	0.514109i	−0.966397	−	0.257054i	$-0.917248\pi$
$223$		−	381783.i		−	0.514109i	0.966397	−	0.257054i	$-0.0827519\pi$
$224$	−1.36722e6	+	203938.i	−1.82062	+	0.271568i
$225$	293992.	+	593211.i	0.387150	+	0.781184i
$226$	412498.	−	77918.3i	0.537219	−	0.101477i
$227$	378191.	+	156652.i	0.487132	+	0.201777i	0.612711	−	0.790307i	$-0.290079\pi$
$227$	378191.	+	156652.i	0.487132	+	0.201777i	−0.125579	+	0.992084i	$0.540079\pi$
$228$	828826.	−	571233.i	1.05591	−	0.727740i
$229$	347552.	+	839064.i	0.437956	+	1.05732i	0.976654	+	0.214820i	$0.0689166\pi$
$229$	347552.	+	839064.i	0.437956	+	1.05732i	−0.538698	+	0.842499i	$0.681083\pi$
$230$	−328562.	−	68659.4i	−0.409541	−	0.0855816i
$231$	1.45139e6	−	339923.i	1.78960	−	0.419132i
$232$	−37150.2	−	219871.i	−0.0453149	−	0.268194i
$233$	863124.	−	863124.i	1.04156	−	1.04156i	0.0424600	−	0.999098i	$-0.486480\pi$
$233$	863124.	−	863124.i	1.04156	−	1.04156i	0.999098	−	0.0424600i	$-0.0135195\pi$
$234$	−673962.	−	396052.i	−0.804629	−	0.472838i
$235$	47481.3	+	114630.i	0.0560858	+	0.135403i
$236$	1.11830e6	+	1.16235e6i	1.30701	+	1.35849i
$237$	582858.	−	418539.i	0.674050	−	0.484022i
$238$	−1.38703e6	−	946279.i	−1.58724	−	1.08287i
$239$		−	696357.i		−	0.788565i	−0.918989	−	0.394282i	$-0.870993\pi$
$239$		−	696357.i		−	0.788565i	0.918989	−	0.394282i	$-0.129007\pi$
$240$	60777.6	+	313596.i	0.0681107	+	0.351432i
$241$			667571.i			0.740380i	0.928956	+	0.370190i	$0.120707\pi$
$241$			667571.i			0.740380i	−0.928956	+	0.370190i	$0.879293\pi$
$242$	−1526.32	+	2237.23i	−0.00167536	+	0.00245569i
$243$	−920127.	−	25591.1i	−0.999613	−	0.0278018i
$244$	264258.	+	5103.84i	0.284154	+	0.00548810i
$245$	−307405.	−	742141.i	−0.327187	−	0.789898i
$246$	−24184.5	−	1.00527e6i	−0.0254799	−	1.05912i
$247$	811448.	−	811448.i	0.846288	−	0.846288i
$248$	417649.	+	666040.i	0.431203	+	0.687655i
$249$	10998.1	+	46959.2i	0.0112413	+	0.0479979i
$250$	135448.	−	648172.i	0.137064	−	0.655904i
$251$	610977.	+	1.47503e6i	0.612126	+	1.47780i	0.860661	+	0.509179i	$0.170051\pi$
$251$	610977.	+	1.47503e6i	0.612126	+	1.47780i	−0.248535	+	0.968623i	$0.579949\pi$
$252$	−1.24753e6	+	1.37373e6i	−1.23752	+	1.36270i
$253$	−1.09774e6	−	454699.i	−1.07820	−	0.446604i
$254$	−246335.	−	1.30410e6i	−0.239575	−	1.26831i
$255$	−204565.	+	329690.i	−0.197006	+	0.317508i
$256$	80917.6	−	1.04545e6i	0.0771690	−	0.997018i
$257$		−	1.70812e6i		−	1.61319i	−0.591103	−	0.806596i	$-0.701307\pi$
$257$		−	1.70812e6i		−	1.61319i	0.591103	−	0.806596i	$-0.298693\pi$
$258$	334874.	+	129364.i	0.313208	+	0.120994i
$259$	−534959.	+	1.29151e6i	−0.495531	+	1.19632i
$260$	132835.	+	339068.i	0.121865	+	0.311067i
$261$	−225442.	−	196924.i	−0.204849	−	0.178936i
$262$	−1.19521e6	−	249762.i	−1.07570	−	0.224788i
$263$	−61706.3	+	61706.3i	−0.0550098	+	0.0550098i	−0.734077	−	0.679067i	$-0.762385\pi$
$263$	−61706.3	+	61706.3i	−0.0550098	+	0.0550098i	0.679067	+	0.734077i	$0.262385\pi$
$264$	5361.56	+	1.13073e6i	0.00473458	+	0.998501i
$265$	327898.	+	327898.i	0.286830	+	0.286830i
$266$	−1.49149e6	−	2.27952e6i	−1.29246	−	1.97533i
$267$	1.80036e6	+	295422.i	1.54555	+	0.253609i
$268$	−25345.2	+	1.31228e6i	−0.0215555	+	1.11606i
$269$	403100.	+	166970.i	0.339651	+	0.140688i	0.545988	−	0.837793i	$-0.316154\pi$
$269$	403100.	+	166970.i	0.339651	+	0.140688i	−0.206337	+	0.978481i	$0.566154\pi$
$270$	329638.	+	274246.i	0.275187	+	0.228945i
$271$	−2.13103e6			−1.76265			−0.881325	−	0.472511i	$-0.843348\pi$
$271$	−2.13103e6			−1.76265			−0.881325	+	0.472511i	$0.843348\pi$
$272$	934714.	−	865163.i	0.766049	−	0.709048i
$273$	−1.11536e6	+	1.79759e6i	−0.905752	+	1.45977i
$274$	404122.	−	592349.i	0.325189	−	0.476652i
$275$	417801.	−	1.00866e6i	0.333149	−	0.804292i
$276$	1.44639e6	−	309417.i	1.14291	−	0.244496i
$277$	−959369.	+	397384.i	−0.751253	+	0.311179i	−0.725253	−	0.688483i	$-0.758277\pi$
$277$	−959369.	+	397384.i	−0.751253	+	0.311179i	−0.0260003	+	0.999662i	$0.508277\pi$
$278$	−592301.	−	905243.i	−0.459654	−	0.702511i
$279$	999992.	+	337258.i	0.769105	+	0.259389i
$280$	852371.	−	144019.i	0.649731	−	0.109781i
$281$	1.12869e6	+	1.12869e6i	0.852725	+	0.852725i	0.990468	−	0.137743i	$-0.0439847\pi$
$281$	1.12869e6	+	1.12869e6i	0.852725	+	0.852725i	−0.137743	+	0.990468i	$0.543985\pi$
$282$	−395796.	−	377199.i	−0.296380	−	0.282454i
$283$	−179653.	+	74414.7i	−0.133342	+	0.0552322i	−0.448357	−	0.893855i	$-0.647991\pi$
$283$	−179653.	+	74414.7i	−0.133342	+	0.0552322i	0.315014	+	0.949087i	$0.397991\pi$
$284$	−427663.	+	978581.i	−0.314634	+	0.719948i
$285$	−511312.	+	367163.i	−0.372884	+	0.267761i
$286$	239267.	+	1.26668e6i	0.172969	+	0.915695i
$287$	−2.72127e6			−1.95014
$288$	−804280.	−	1.15520e6i	−0.571381	−	0.820685i
$289$	127191.			0.0895802
$290$	25882.7	+	137022.i	0.0180723	+	0.0956746i
$291$	703472.	−	505150.i	0.486984	−	0.349693i
$292$	−2.19160e6	−	957779.i	−1.50419	−	0.657367i
$293$	−1.56641e6	+	648828.i	−1.06595	+	0.441531i	−0.845559	−	0.533881i	$-0.820733\pi$
$293$	−1.56641e6	+	648828.i	−1.06595	+	0.441531i	−0.220390	+	0.975412i	$0.570733\pi$
$294$	2.56247e6	+	2.44207e6i	1.72898	+	1.64775i
$295$	−713236.	−	713236.i	−0.477175	−	0.477175i
$296$	−864245.	−	614407.i	−0.573334	−	0.407593i
$297$	966408.	+	1.17051e6i	0.635725	+	0.769987i
$298$	1.25936e6	+	1.92474e6i	0.821504	+	1.25554i
$299$	1.55788e6	−	645294.i	1.00776	−	0.417426i
$300$	284308.	+	1.32902e6i	0.182384	+	0.852566i
$301$	371783.	−	897564.i	0.236523	−	0.571017i
$302$	−724868.	+	1.06249e6i	−0.457342	+	0.670358i
$303$	−53657.5	+	86478.0i	−0.0335756	+	0.0541127i
$304$	1.93818e6	−	716459.i	1.20285	−	0.444639i
$305$	−165285.			−0.101738
$306$	236193.	−	1.69336e6i	0.144199	−	1.03382i
$307$	−699138.	−	289592.i	−0.423367	−	0.175364i	0.160820	−	0.986984i	$-0.448586\pi$
$307$	−699138.	−	289592.i	−0.423367	−	0.175364i	−0.584186	+	0.811620i	$0.698586\pi$
$308$	3.05947e6	+	59090.2i	1.83768	+	0.0354927i
$309$	579738.	+	95129.3i	0.345411	+	0.0566785i
$310$	−269171.	−	411387.i	−0.159083	−	0.243135i
$311$	1.89796e6	+	1.89796e6i	1.11272	+	1.11272i	0.992781	+	0.119942i	$0.0382708\pi$
$311$	1.89796e6	+	1.89796e6i	1.11272	+	1.11272i	0.119942	+	0.992781i	$0.461729\pi$
$312$	−1.14007e6	−	1.12931e6i	−0.663048	−	0.656789i
$313$	−1.01009e6	+	1.01009e6i	−0.582770	+	0.582770i	−0.935664	−	0.352893i	$-0.885198\pi$
$313$	−1.01009e6	+	1.01009e6i	−0.582770	+	0.582770i	0.352893	+	0.935664i	$0.385198\pi$
$314$	−1.59837e6	−	334012.i	−0.914859	−	0.191178i
$315$	763412.	−	873968.i	0.433494	−	0.496272i
$316$	1.37152e6	−	537315.i	0.772653	−	0.302699i
$317$	−327431.	+	790489.i	−0.183009	+	0.441822i	−0.988584	−	0.150671i	$-0.951857\pi$
$317$	−327431.	+	790489.i	−0.183009	+	0.441822i	0.805575	+	0.592494i	$0.201857\pi$
$318$	−1.90614e6	−	736353.i	−1.05703	−	0.408337i
$319$			493618.i			0.271590i
$320$	−37967.9	+	654628.i	−0.0207273	+	0.357371i
$321$	212765.	−	342907.i	0.115249	−	0.185743i
$322$	−742969.	−	3.93327e6i	−0.399329	−	2.11404i
$323$	2.31886e6	+	960503.i	1.23671	+	0.512262i
$324$	−1.81745e6	−	517061.i	−0.961832	−	0.273640i
$325$	592930.	+	1.43146e6i	0.311383	+	0.751745i
$326$	−291386.	+	1.39439e6i	−0.151854	+	0.726678i
$327$	−589622.	−	2.51755e6i	−0.304933	−	1.30199i
$328$	461176.	−	2.01203e6i	0.236691	−	1.03264i
$329$	−1.04625e6	+	1.04625e6i	−0.532902	+	0.532902i
$330$	−17006.6	−	706906.i	−0.00859670	−	0.357336i
$331$	−63229.3	−	152649.i	−0.0317211	−	0.0765816i	0.907225	−	0.420645i	$-0.138196\pi$
$331$	−63229.3	−	152649.i	−0.0317211	−	0.0765816i	−0.938946	+	0.344064i	$0.888196\pi$
$332$	−1911.84	+	98987.9i	−0.000951932	+	0.0492875i
$333$	−1.42022e6	+	95893.6i	−0.701854	+	0.0473892i
$334$	−1.09637e6	+	1.60702e6i	−0.537762	+	0.788234i
$335$		−	820788.i		−	0.399594i
$336$	−3.17768e6	+	2.10075e6i	−1.53554	+	1.01514i
$337$		−	989412.i		−	0.474573i	−0.971440	−	0.237286i	$-0.923742\pi$
$337$		−	989412.i		−	0.474573i	0.971440	−	0.237286i	$-0.0762579\pi$
$338$	223811.	+	152692.i	0.106559	+	0.0726985i
$339$	939649.	−	674743.i	0.444085	−	0.318889i
$340$	−573968.	+	552217.i	−0.269271	+	0.259067i
$341$	−665975.	−	1.60781e6i	−0.310150	−	0.748769i
$342$	1.40537e6	−	2.39152e6i	0.649719	−	1.10563i
$343$	3.93761e6	−	3.93761e6i	1.80716	−	1.80716i
$344$	600629.	+	426998.i	0.273659	+	0.194549i
$345$	−900597.	+	210924.i	−0.407364	+	0.0954067i
$346$	286426.	+	59854.5i	0.128624	+	0.0268786i
$347$	−56693.8	−	136871.i	−0.0252762	−	0.0610222i	0.910737	−	0.412986i	$-0.135514\pi$
$347$	−56693.8	−	136871.i	−0.0252762	−	0.0610222i	−0.936014	+	0.351964i	$0.885514\pi$
$348$	−348708.	−	505955.i	−0.154353	−	0.223957i
$349$	688922.	+	285361.i	0.302766	+	0.125410i	0.528894	−	0.848688i	$-0.322607\pi$
$349$	688922.	+	285361.i	0.302766	+	0.125410i	−0.226128	+	0.974097i	$0.572607\pi$
$350$	3.61409e6	−	682679.i	1.57699	−	0.297883i
$351$	−2.14440e6	−	204816.i	−0.929048	−	0.0887351i
$352$	−562181.	+	2.25208e6i	−0.241835	+	0.968784i
$353$		−	378061.i		−	0.161482i	−0.996735	−	0.0807411i	$-0.974271\pi$
$353$		−	378061.i		−	0.161482i	0.996735	−	0.0807411i	$-0.0257287\pi$
$354$	4.14618e6	+	1.60170e6i	1.75849	+	0.679317i
$355$	255573.	−	617007.i	0.107633	−	0.259848i
$356$	3.43180e6	+	1.49978e6i	1.43515	+	0.627195i
$357$	−4.56592e6	−	749222.i	−1.89608	−	0.311129i
$358$	−633999.	+	3.03393e6i	−0.261445	+	1.25112i
$359$	−1.03916e6	+	1.03916e6i	−0.425544	+	0.425544i	−0.887107	−	0.461563i	$-0.847289\pi$
$359$	−1.03916e6	+	1.03916e6i	−0.425544	+	0.425544i	0.461563	+	0.887107i	$0.347289\pi$
$360$	516813.	+	712559.i	0.210173	+	0.289778i
$361$	1.12852e6	+	1.12852e6i	0.455764	+	0.455764i
$362$	−2.01340e6	+	1.31737e6i	−0.807528	+	0.528366i
$363$	−1208.47	+	7364.70i	−0.000481361	+	0.00293352i
$364$	−3.12949e6	+	3.01089e6i	−1.23800	+	1.19108i
$365$	1.38183e6	+	572371.i	0.542902	+	0.224877i
$366$	666004.	−	294829.i	0.259881	−	0.115045i
$367$	5.12336e6			1.98559			0.992795	−	0.119829i	$-0.0382346\pi$
$367$	5.12336e6			1.98559			0.992795	+	0.119829i	$0.0382346\pi$
$368$	3.03407e6	+	117243.i	1.16790	+	0.0451302i
$369$	−1.23047e6	−	2.48281e6i	−0.470439	−	0.949243i
$370$	547775.	+	373712.i	0.208017	+	0.141916i
$371$	−2.11623e6	+	5.10902e6i	−0.798229	+	1.92710i
$372$	1.81843e6	+	1.17752e6i	0.681300	+	0.441176i
$373$	1.25392e6	−	519391.i	0.466657	−	0.193296i	−0.136949	−	0.990578i	$-0.543730\pi$
$373$	1.25392e6	−	519391.i	0.466657	−	0.193296i	0.603607	+	0.797282i	$0.293730\pi$
$374$	−2.35929e6	+	1.54369e6i	−0.872172	+	0.570663i
$375$	−416102.	−	1.77666e6i	−0.152799	−	0.652417i
$376$	−596263.	−	950881.i	−0.217504	−	0.346862i
$377$	−495347.	−	495347.i	−0.179497	−	0.179497i
$378$	−1.51717e6	+	4.88335e6i	−0.546142	+	1.75788i
$379$	−1.89851e6	+	786389.i	−0.678914	+	0.281215i	−0.695373	−	0.718649i	$-0.744761\pi$
$379$	−1.89851e6	+	786389.i	−0.678914	+	0.281215i	0.0164588	+	0.999865i	$0.494761\pi$
$380$	−1.20317e6	+	471359.i	−0.427432	+	0.167453i
$381$	−2.13317e6	−	2.97066e6i	−0.752858	−	1.04843i
$382$	3.20711e6	−	605802.i	1.12449	−	0.212409i
$383$	−2.20522e6			−0.768166			−0.384083	−	0.923299i	$-0.625482\pi$
$383$	−2.20522e6			−0.768166			−0.384083	+	0.923299i	$0.625482\pi$
$384$	−1.01471e6	−	2.70551e6i	−0.351168	−	0.936313i
$385$	−1.91360e6			−0.657960
$386$	61.2515	−	11.5700i	2.09242e−5	−	3.95244e-6i
$387$	987020.	−	66643.6i	0.335003	−	0.0226194i
$388$	1.65534e6	−	648505.i	0.558223	−	0.218692i
$389$	29537.5	−	12234.8i	0.00989690	−	0.00409943i	−0.377729	−	0.925916i	$-0.623295\pi$
$389$	29537.5	−	12234.8i	0.00989690	−	0.00409943i	0.387626	+	0.921817i	$0.373295\pi$
$390$	726447.	+	692315.i	0.241848	+	0.230485i
$391$	2.60787e6	+	2.60787e6i	0.862669	+	0.862669i
$392$	3.86034e6	+	6.15622e6i	1.26885	+	2.02348i
$393$	−3.27610e6	+	767279.i	−1.06998	+	0.250595i
$394$	−4.04962e6	+	2.64967e6i	−1.31424	+	0.859908i
$395$	−851033.	+	352510.i	−0.274444	+	0.113678i
$396$	1.32948e6	+	2.81810e6i	0.426033	+	0.903063i
$397$	189961.	−	458606.i	0.0604906	−	0.146037i	−0.890744	−	0.454505i	$-0.849816\pi$
$397$	189961.	−	458606.i	0.0604906	−	0.146037i	0.951235	+	0.308468i	$0.0998162\pi$
$398$	−3.54823e6	−	2.42073e6i	−1.12280	−	0.766018i
$399$	−6.37866e6	−	3.95781e6i	−2.00584	−	1.24458i
$400$	−107729.	+	2.78786e6i	−0.0336653	+	0.871206i
$401$	1.90486e6			0.591564			0.295782	−	0.955255i	$-0.404420\pi$
$401$	1.90486e6			0.591564			0.295782	+	0.955255i	$0.404420\pi$
$402$	1.46409e6	+	3.30732e6i	0.451859	+	1.02073i
$403$	2.28174e6	+	945129.i	0.699849	+	0.289887i
$404$	−150552.	+	144847.i	−0.0458917	+	0.0441526i
$405$	1.14257e6	+	301337.i	0.346136	+	0.0912883i
$406$	−1.39153e6	+	910479.i	−0.418965	+	0.274129i
$407$	1.65981e6	+	1.65981e6i	0.496676	+	0.496676i
$408$	1.32774e6	−	3.24895e6i	0.394879	−	0.966256i
$409$	1.85007e6	−	1.85007e6i	0.546864	−	0.546864i	−0.378668	−	0.925532i	$-0.623618\pi$
$409$	1.85007e6	−	1.85007e6i	0.546864	−	0.546864i	0.925532	+	0.378668i	$0.123618\pi$
$410$	−264046.	+	1.26356e6i	−0.0775747	+	0.371225i
$411$	319966.	−	1.94994e6i	0.0934327	−	0.569399i
$412$	1.10508e6	+	482947.i	0.320739	+	0.140170i
$413$	4.60316e6	−	1.11130e7i	1.32795	−	3.20595i
$414$	3.25266e6	−	2.45636e6i	0.932691	−	0.704354i
$415$		−	61913.7i		−	0.0176468i
$416$	−1.69582e6	−	2.82412e6i	−0.480447	−	0.800109i
$417$	−2.53309e6	−	1.57172e6i	−0.713363	−	0.442625i
$418$	−4.49474e6	+	849027.i	−1.25824	+	0.237674i
$419$	−1.64567e6	−	681658.i	−0.457939	−	0.189684i	0.141775	−	0.989899i	$-0.454719\pi$
$419$	−1.64567e6	−	681658.i	−0.457939	−	0.189684i	−0.599714	+	0.800214i	$0.704719\pi$
$420$	1.96143e6	−	1.35183e6i	0.542562	−	0.373938i
$421$	1.85058e6	+	4.46769e6i	0.508864	+	1.22851i	0.944538	+	0.328402i	$0.106510\pi$
$421$	1.85058e6	+	4.46769e6i	0.508864	+	1.22851i	−0.435674	+	0.900105i	$0.643490\pi$
$422$	2.51006e6	+	524527.i	0.686124	+	0.143379i
$423$	−1.42765e6	−	481492.i	−0.387946	−	0.130839i
$424$	−3.41884e6	−	2.43051e6i	−0.923558	−	0.656573i
$425$	−2.39625e6	+	2.39625e6i	−0.643516	+	0.643516i
$426$	70779.6	+	2.94207e6i	0.0188966	+	0.785470i
$427$	−754294.	−	1.82103e6i	−0.200203	−	0.483333i
$428$	596978.	−	574355.i	0.157525	−	0.151555i
$429$	2.07196e6	+	2.88542e6i	0.543549	+	0.756948i
$430$	−380690.	−	259720.i	−0.0992888	−	0.0677384i
$431$			1.95392e6i			0.506656i	0.967380	+	0.253328i	$0.0815252\pi$
$431$			1.95392e6i			0.506656i	−0.967380	+	0.253328i	$0.918475\pi$
$432$	−3.35350e6	−	1.94934e6i	−0.864549	−	0.502549i
$433$		−	3.02038e6i		−	0.774180i	−0.922042	−	0.387090i	$-0.873480\pi$
$433$		−	3.02038e6i		−	0.774180i	0.922042	−	0.387090i	$-0.126520\pi$
$434$	3.30408e6	−	4.84301e6i	0.842027	−	1.23422i
$435$	224134.	+	312130.i	0.0567917	+	0.0790882i
$436$	102496.	−	5.30688e6i	0.0258221	−	1.33697i
$437$	2.28979e6	+	5.52805e6i	0.573578	+	1.38474i
$438$	−6.58896e6	+	158516.i	−1.64109	+	0.0394809i
$439$	113807.	−	113807.i	0.0281844	−	0.0281844i	−0.692874	−	0.721059i	$-0.743656\pi$
$439$	113807.	−	113807.i	0.0281844	−	0.0281844i	0.721059	+	0.692874i	$0.243656\pi$
$440$	324300.	−	1.41487e6i	0.0798573	−	0.348404i
$441$	9.24295e6	+	3.11729e6i	2.26315	+	0.763274i
$442$	818460.	−	3.91664e6i	0.199270	−	0.953583i
$443$	−2.04246e6	−	4.93093e6i	−0.494475	−	1.19377i	−0.952420	−	0.304787i	$-0.901415\pi$
$443$	−2.04246e6	−	4.93093e6i	−0.494475	−	1.19377i	0.457946	−	0.888980i	$-0.348585\pi$
$444$	−2.87384e6	−	528749.i	−0.691839	−	0.127289i
$445$	−2.16379e6	−	896272.i	−0.517983	−	0.214556i
$446$	−400863.	−	2.12216e6i	−0.0954243	−	0.505175i
$447$	5.38590e6	+	3.34182e6i	1.27494	+	0.791069i
$448$	−7.38565e6	+	2.56915e6i	−1.73858	+	0.604776i
$449$		−	5.35385e6i		−	1.25329i	−0.779307	−	0.626643i	$-0.784428\pi$
$449$		−	5.35385e6i		−	1.25329i	0.779307	−	0.626643i	$-0.215572\pi$
$450$	2.25703e6	+	2.98871e6i	0.525419	+	0.695750i
$451$	−1.74865e6	+	4.22162e6i	−0.404820	+	0.977323i
$452$	2.21108e6	−	866226.i	0.509048	−	0.199428i
$453$	−573918.	+	3.49758e6i	−0.131403	+	0.800796i
$454$	2.26668e6	+	473667.i	0.516119	+	0.107853i
$455$	1.92030e6	−	1.92030e6i	0.434852	−	0.434852i
$456$	4.00729e6	−	4.04548e6i	0.902483	−	0.911083i
$457$	796376.	+	796376.i	0.178372	+	0.178372i	0.790646	−	0.612274i	$-0.209745\pi$
$457$	796376.	+	796376.i	0.178372	+	0.178372i	−0.612274	+	0.790646i	$0.709745\pi$
$458$	2.81288e6	+	4.29906e6i	0.626596	+	0.957657i
$459$	−1.38099e6	−	4.50459e6i	−0.305955	−	0.997984i
$460$	−1.89842e6	−	36665.8i	−0.418309	−	0.00807917i
$461$	−598697.	−	247988.i	−0.131206	−	0.0543474i	0.316114	−	0.948721i	$-0.397622\pi$
$461$	−598697.	−	247988.i	−0.131206	−	0.0543474i	−0.447321	+	0.894374i	$0.647622\pi$
$462$	7.71074e6	−	3.41341e6i	1.68070	−	0.744018i
$463$	−3.81533e6			−0.827142			−0.413571	−	0.910472i	$-0.635719\pi$
$463$	−3.81533e6			−0.827142			−0.413571	+	0.910472i	$0.635719\pi$
$464$	−437361.	−	1.18316e6i	−0.0943072	−	0.255122i
$465$	−1.15116e6	−	714269.i	−0.246890	−	0.153190i
$466$	3.89147e6	−	5.70398e6i	0.830134	−	1.21678i
$467$	−2.72402e6	+	6.57636e6i	−0.577987	+	1.39538i	0.316630	+	0.948549i	$0.397449\pi$
$467$	−2.72402e6	+	6.57636e6i	−0.577987	+	1.39538i	−0.894617	+	0.446834i	$0.852551\pi$
$468$	−4.16210e6	−	1.49383e6i	−0.878412	−	0.315273i
$469$	9.04306e6	−	3.74576e6i	1.89838	−	0.786335i
$470$	384286.	+	587323.i	0.0802436	+	0.122640i
$471$	−4.38119e6	+	1.02610e6i	−0.909996	+	0.213126i
$472$	7.43657e6	+	5.28679e6i	1.53645	+	1.09229i
$473$	−1.15353e6	−	1.15353e6i	−0.237069	−	0.237069i
$474$	2.80039e6	−	2.93846e6i	0.572497	−	0.600722i
$475$	−5.07946e6	+	2.10398e6i	−1.03296	+	0.427866i
$476$	−8.70343e6	−	3.80360e6i	−1.76065	−	0.769446i
$477$	−5.61822e6	+	379342.i	−1.13058	+	0.0763370i
$478$	−731158.	−	3.87074e6i	−0.146366	−	0.774862i
$479$	−5.08710e6			−1.01305			−0.506525	−	0.862225i	$-0.669070\pi$
$479$	−5.08710e6			−1.01305			−0.506525	+	0.862225i	$0.669070\pi$
$480$	667103.	+	1.67932e6i	0.132157	+	0.332683i
$481$	−3.33125e6			−0.656515
$482$	700933.	+	3.71073e6i	0.137423	+	0.727515i
$483$	−6.43383e6	−	8.95977e6i	−1.25488	−	1.74755i
$484$	−6135.11	+	14038.4i	−0.00119044	+	0.00272398i
$485$	−1.02714e6	+	425457.i	−0.198279	+	0.0821298i
$486$	−5.14145e6	+	823861.i	−0.987404	+	0.158221i
$487$	−2.54195e6	−	2.54195e6i	−0.485674	−	0.485674i	0.421264	−	0.906938i	$-0.361587\pi$
$487$	−2.54195e6	−	2.54195e6i	−0.485674	−	0.485674i	−0.906938	+	0.421264i	$0.861587\pi$
$488$	1.47425e6	−	249094.i	0.280235	−	0.0473493i
$489$	895149.	+	3.82208e6i	0.169287	+	0.722815i
$490$	−2.48796e6	−	3.80246e6i	−0.468115	−	0.715443i
$491$	2.57999e6	−	1.06867e6i	0.482963	−	0.200050i	−0.127899	−	0.991787i	$-0.540823\pi$
$491$	2.57999e6	−	1.06867e6i	0.482963	−	0.200050i	0.610861	+	0.791738i	$0.290823\pi$
$492$	−1.18994e6	−	5.56244e6i	−0.221621	−	1.03598i
$493$	586337.	−	1.41554e6i	0.108650	−	0.262305i
$494$	3.65848e6	−	5.36248e6i	0.674502	−	0.988663i
$495$	−865266.	−	1.74592e6i	−0.158722	−	0.320266i
$496$	3.02085e6	+	3.26370e6i	0.551347	+	0.595670i
$497$	7.96422e6			1.44628
$498$	110439.	+	249477.i	0.0199549	+	0.0450773i
$499$	−838843.	−	347460.i	−0.150810	−	0.0624674i	0.306002	−	0.952031i	$-0.401009\pi$
$499$	−838843.	−	347460.i	−0.150810	−	0.0624674i	−0.456812	+	0.889563i	$0.651009\pi$
$500$	72332.6	−	3.74512e6i	0.0129393	−	0.669947i
$501$	−868055.	+	5.29011e6i	−0.154509	+	0.941609i
$502$	4.94489e6	+	7.55752e6i	0.875785	+	1.33851i
$503$	5.77046e6	+	5.77046e6i	1.01693	+	1.01693i	0.999854	+	0.0170747i	$0.00543530\pi$
$503$	5.77046e6	+	5.77046e6i	1.01693	+	1.01693i	0.0170747	+	0.999854i	$0.494565\pi$
$504$	−5.49211e6	+	8.94584e6i	−0.963081	+	1.56872i
$505$	92381.4	−	92381.4i	0.0161197	−	0.0161197i
$506$	−6.57928e6	−	1.37487e6i	−1.14236	−	0.238718i
$507$	736760.	+	120895.i	0.127293	+	0.0208876i
$508$	−2.73854e6	−	6.99024e6i	−0.470825	−	1.20180i
$509$	−1.52095e6	+	3.67189e6i	−0.260207	+	0.628196i	−0.998951	−	0.0457904i	$-0.985419\pi$
$509$	−1.52095e6	+	3.67189e6i	−0.260207	+	0.628196i	0.738744	+	0.673986i	$0.235419\pi$
$510$	−790918.	+	2.04739e6i	−0.134650	+	0.348557i
$511$			1.78364e7i			3.02172i
$512$	−647911.	−	5.89615e6i	−0.109230	−	0.994017i
$513$	726779.	−	7.60930e6i	0.121929	−	1.27659i
$514$	−1.79349e6	−	9.49470e6i	−0.299427	−	1.58516i
$515$	−696767.	−	288610.i	−0.115763	−	0.0479505i
$516$	1.99725e6	+	367468.i	0.330223	+	0.0607568i
$517$	950789.	+	2.29541e6i	0.156444	+	0.377688i
$518$	−1.61755e6	+	7.74060e6i	−0.264871	+	1.26751i
$519$	785103.	−	183875.i	0.127941	−	0.0299643i
$520$	1.09439e6	+	1.74526e6i	0.177485	+	0.283042i
$521$	6.00952e6	−	6.00952e6i	0.969942	−	0.969942i	−0.0296192	−	0.999561i	$-0.509429\pi$
$521$	6.00952e6	−	6.00952e6i	0.969942	−	0.969942i	0.999561	+	0.0296192i	$0.00942947\pi$
$522$	−1.45990e6	−	857905.i	−0.234502	−	0.137804i
$523$	2.59345e6	+	6.26115e6i	0.414595	+	1.00092i	0.983888	+	0.178786i	$0.0572171\pi$
$523$	2.59345e6	+	6.26115e6i	0.414595	+	1.00092i	−0.569293	+	0.822135i	$0.692783\pi$
$524$	−6.90587e6	−	133379.i	−1.09873	−	0.0212207i
$525$	8.23271e6	−	5.91174e6i	1.30360	−	0.936089i
$526$	−278208.	+	407788.i	−0.0438435	+	0.0642643i
$527$			5.40176e6i			0.847244i
$528$	1.21704e6	+	6.27959e6i	0.189985	+	0.980272i
$529$			2.35588e6i			0.366027i
$530$	2.16693e6	+	1.47836e6i	0.335084	+	0.228607i
$531$	1.22206e7	−	825136.i	1.88086	−	0.126996i
$532$	−1.06840e7	−	1.11048e7i	−1.63665	−	1.70111i
$533$	−2.48163e6	−	5.99119e6i	−0.378372	−	0.913471i
$534$	1.03176e7	−	248218.i	1.56576	−	0.0376687i
$535$	−366315.	+	366315.i	−0.0553312	+	0.0553312i
$536$	1.23698e6	+	7.32099e6i	0.185973	+	1.10067i
$537$	1.94767e6	+	8.31608e6i	0.291460	+	1.24447i
$538$	2.41597e6	+	504865.i	0.359862	+	0.0752003i
$539$	−6.15563e6	−	1.48610e7i	−0.912642	−	2.20331i
$540$	2.12026e6	+	1.17830e6i	0.312900	+	0.173889i
$541$	3.09896e6	+	1.28363e6i	0.455221	+	0.188559i	0.598499	−	0.801124i	$-0.295764\pi$
$541$	3.09896e6	+	1.28363e6i	0.455221	+	0.188559i	−0.143278	+	0.989683i	$0.545764\pi$
$542$	−1.18454e7	+	2.23753e6i	−1.73202	+	0.327167i
$543$	−3.49575e6	+	5.63397e6i	−0.508792	+	0.820002i
$544$	4.28726e6	−	5.79048e6i	0.621130	−	0.838914i
$545$			3.31928e6i			0.478688i
$546$	−4.31238e6	+	1.11631e7i	−0.619064	+	1.60252i
$547$	4.07870e6	−	9.84685e6i	0.582845	−	1.40711i	−0.307378	−	0.951588i	$-0.599451\pi$
$547$	4.07870e6	−	9.84685e6i	0.582845	−	1.40711i	0.890223	−	0.455525i	$-0.150549\pi$
$548$	1.62438e6	−	3.71692e6i	0.231067	−	0.528728i
$549$	1.32039e6	−	1.51161e6i	0.186970	−	0.214046i
$550$	1.26330e6	−	6.04538e6i	0.178074	−	0.852152i
$551$	1.75771e6	−	1.75771e6i	0.246643	−	0.246643i
$552$	7.71497e6	−	3.23859e6i	1.07767	−	0.452385i
$553$	−7.76757e6	−	7.76757e6i	−1.08012	−	1.08012i
$554$	−4.91546e6	+	3.21619e6i	−0.680440	+	0.445213i
$555$	1.80321e6	+	295889.i	0.248493	+	0.0407752i
$556$	−4.24282e6	−	4.40994e6i	−0.582060	−	0.604987i
$557$	1.06173e7	+	4.39784e6i	1.45003	+	0.600623i	0.962207	−	0.272319i	$-0.0877905\pi$
$557$	1.06173e7	+	4.39784e6i	1.45003	+	0.600623i	0.487825	+	0.872942i	$0.337791\pi$
$558$	5.91262e6	+	824703.i	0.803886	+	0.112127i
$559$	2.31513e6			0.313362
$560$	4.58674e6	−	1.69551e6i	0.618064	−	0.228470i
$561$	−4.09630e6	+	6.60187e6i	−0.549522	+	0.885645i
$562$	7.45899e6	+	5.08879e6i	0.996183	+	0.679632i
$563$	−4.17325e6	+	1.00751e7i	−0.554885	+	1.33961i	0.358886	+	0.933381i	$0.383157\pi$
$563$	−4.17325e6	+	1.00751e7i	−0.554885	+	1.33961i	−0.913771	+	0.406229i	$0.866843\pi$
$564$	−2.59610e6	−	1.68111e6i	−0.343656	−	0.222535i
$565$	−1.37198e6	+	568295.i	−0.180812	+	0.0748949i
$566$	−920478.	+	602270.i	−0.120774	+	0.0790223i
$567$	1.89427e6	+	1.39635e7i	0.247448	+	1.82405i
$568$	−1.34970e6	+	5.88854e6i	−0.175537	+	0.765837i
$569$	941652.	+	941652.i	0.121930	+	0.121930i	0.765439	−	0.643509i	$-0.222522\pi$
$569$	941652.	+	941652.i	0.121930	+	0.121930i	−0.643509	+	0.765439i	$0.722522\pi$
$570$	−2.45665e6	+	2.57776e6i	−0.316705	+	0.332319i
$571$	3.80749e6	−	1.57711e6i	0.488706	−	0.202429i	−0.124703	−	0.992194i	$-0.539798\pi$
$571$	3.80749e6	−	1.57711e6i	0.488706	−	0.202429i	0.613409	+	0.789765i	$0.289798\pi$
$572$	2.65996e6	+	6.78967e6i	0.339926	+	0.867678i
$573$	7.30561e6	−	5.24601e6i	0.929544	−	0.667487i
$574$	−1.51263e7	+	2.85726e6i	−1.91626	+	0.361968i
$575$	−8.07875e6			−1.01900
$576$	−5.68357e6	−	5.57678e6i	−0.713781	−	0.700369i
$577$	−7.00890e6			−0.876417			−0.438208	−	0.898873i	$-0.644387\pi$
$577$	−7.00890e6			−0.876417			−0.438208	+	0.898873i	$0.644387\pi$
$578$	706999.	−	133547.i	0.0880236	−	0.0166271i
$579$	139.527	−	100.192i	1.72967e−5	−	1.24204e-5i
$580$	287740.	+	734471.i	0.0355166	+	0.0906577i
$581$	682136.	−	282550.i	0.0838360	−	0.0347260i
$582$	3.37990e6	−	3.54653e6i	0.413615	−	0.434007i
$583$	6.56599e6	+	6.56599e6i	0.800072	+	0.800072i
$584$	−1.31878e7	−	3.02275e6i	−1.60007	−	0.366750i
$585$	2.62033e6	+	883735.i	0.316567	+	0.106766i
$586$	−8.02573e6	+	5.25124e6i	−0.965473	+	0.631710i
$587$	−7.92115e6	+	3.28105e6i	−0.948840	+	0.393022i	−0.802795	−	0.596256i	$-0.796654\pi$
$587$	−7.92115e6	+	3.28105e6i	−0.948840	+	0.393022i	−0.146045	+	0.989278i	$0.546654\pi$
$588$	1.68078e7	+	1.08839e7i	2.00478	+	1.29820i
$589$	−3.35374e6	+	8.09665e6i	−0.398329	+	0.961651i
$590$	−4.71344e6	−	3.21568e6i	−0.557453	−	0.380315i
$591$	−7.03114e6	+	1.13318e7i	−0.828051	+	1.33454i
$592$	−5.44907e6	−	2.50778e6i	−0.639025	−	0.294093i
$593$	−1.06003e7			−1.23789			−0.618944	−	0.785435i	$-0.712439\pi$
$593$	−1.06003e7			−1.23789			−0.618944	+	0.785435i	$0.712439\pi$
$594$	6.60084e6	+	5.49164e6i	0.767597	+	0.638610i
$595$	5.48761e6	+	2.27304e6i	0.635464	+	0.263218i
$596$	9.02116e6	+	9.37649e6i	1.04027	+	1.08125i
$597$	−1.16803e7	−	1.91663e6i	−1.34128	−	0.220091i
$598$	7.98200e6	−	5.22263e6i	0.912765	−	0.597223i
$599$	7.75639e6	+	7.75639e6i	0.883268	+	0.883268i	0.993865	−	0.110598i	$-0.0352765\pi$
$599$	7.75639e6	+	7.75639e6i	0.883268	+	0.883268i	−0.110598	+	0.993865i	$0.535276\pi$
$600$	2.97578e6	+	7.08891e6i	0.337461	+	0.803899i
$601$	4.91544e6	−	4.91544e6i	0.555107	−	0.555107i	−0.372804	−	0.927910i	$-0.621604\pi$
$601$	4.91544e6	−	4.91544e6i	0.555107	−	0.555107i	0.927910	+	0.372804i	$0.121604\pi$
$602$	1.12416e6	−	5.37952e6i	0.126426	−	0.604996i
$603$	7.50649e6	+	6.55693e6i	0.840705	+	0.734357i
$604$	−2.91363e6	+	6.66699e6i	−0.324969	+	0.743597i
$605$	3666.36	−	8851.37i	0.000407236	−	0.000983155i
$606$	−207459.	+	537032.i	−0.0229483	+	0.0594044i
$607$		−	1.50924e7i		−	1.66260i	−0.555827	−	0.831298i	$-0.687598\pi$
$607$		−	1.50924e7i		−	1.66260i	0.555827	−	0.831298i	$-0.312402\pi$
$608$	1.00212e7	−	6.01752e6i	1.09942	−	0.660174i
$609$	−2.41604e6	+	3.89384e6i	−0.263973	+	0.425437i
$610$	−918744.	+	173545.i	−0.0999701	+	0.0188837i
$611$	−3.25757e6	−	1.34933e6i	−0.353013	−	0.146223i
$612$	−465095.	−	9.66063e6i	−0.0501953	−	1.04262i
$613$	5.36641e6	+	1.29556e7i	0.576809	+	1.39254i	0.895661	+	0.444736i	$0.146703\pi$
$613$	5.36641e6	+	1.29556e7i	0.576809	+	1.39254i	−0.318852	+	0.947804i	$0.603297\pi$
$614$	−4.19026e6	−	875638.i	−0.448560	−	0.0937354i
$615$	811159.	+	3.46346e6i	0.0864805	+	0.369251i
$616$	1.70683e7	−	2.88392e6i	1.81233	−	0.306218i
$617$	−5.19729e6	+	5.19729e6i	−0.549622	+	0.549622i	−0.926332	−	0.376709i	$-0.877056\pi$
$617$	−5.19729e6	+	5.19729e6i	−0.549622	+	0.549622i	0.376709	+	0.926332i	$0.377056\pi$
$618$	3.32239e6	−	79929.2i	0.349929	−	0.00841850i
$619$	−4.98631e6	−	1.20380e7i	−0.523061	−	1.26278i	−0.935993	−	0.352019i	$-0.885495\pi$
$619$	−4.98631e6	−	1.20380e7i	−0.523061	−	1.26278i	0.412932	−	0.910762i	$-0.364505\pi$
$620$	−1.92815e6	−	2.00410e6i	−0.201447	−	0.209382i
$621$	5.26549e6	−	9.92136e6i	0.547910	−	1.03239i
$622$	1.25428e7	+	8.55712e6i	1.29992	+	0.886853i
$623$		−	2.79299e7i		−	2.88303i
$624$	−7.52288e6	−	5.08028e6i	−0.773433	−	0.522307i
$625$		−	6.17177e6i		−	0.631990i
$626$	−4.55405e6	+	6.67519e6i	−0.464475	+	0.680812i
$627$	−1.02388e7	+	7.35226e6i	−1.04011	+	0.746882i
$628$	−9.23535e6	−	178370.i	−0.934446	−	0.0180478i
$629$	−2.78824e6	−	6.73141e6i	−0.280998	−	0.678390i
$630$	3.32583e6	−	5.65957e6i	0.333848	−	0.568109i
$631$	1.10644e6	−	1.10644e6i	0.110625	−	0.110625i	−0.649628	−	0.760253i	$-0.725075\pi$
$631$	1.10644e6	−	1.10644e6i	0.110625	−	0.110625i	0.760253	+	0.649628i	$0.225075\pi$
$632$	7.05951e6	−	4.42676e6i	0.703043	−	0.440852i
$633$	6.88015e6	−	1.61136e6i	0.682478	−	0.159840i
$634$	−990051.	+	4.73777e6i	−0.0978216	+	0.468114i
$635$	1.79664e6	+	4.33747e6i	0.176818	+	0.426876i
$636$	−1.13685e7	−	2.09166e6i	−1.11445	−	0.205045i
$637$	2.10902e7	+	8.73586e6i	2.05936	+	0.853015i
$638$	518287.	+	2.74380e6i	0.0504102	+	0.266871i
$639$	3.60115e6	+	7.26634e6i	0.348891	+	0.703985i
$640$	476296.	+	3.67865e6i	0.0459650	+	0.355008i
$641$			6.70198e6i			0.644256i	0.946696	+	0.322128i	$0.104398\pi$
$641$			6.70198e6i			0.644256i	−0.946696	+	0.322128i	$0.895602\pi$
$642$	822625.	−	2.12946e6i	0.0787707	−	0.203907i
$643$	−5.84445e6	+	1.41097e7i	−0.557463	+	1.34583i	0.354305	+	0.935130i	$0.384717\pi$
$643$	−5.84445e6	+	1.41097e7i	−0.557463	+	1.34583i	−0.911768	+	0.410705i	$0.865283\pi$
$644$	−8.25967e6	−	2.10832e7i	−0.784780	−	2.00319i
$645$	−1.25318e6	−	205635.i	−0.118608	−	0.0194625i
$646$	1.38980e7	+	2.90427e6i	1.31030	+	0.273814i
$647$	5.28905e6	−	5.28905e6i	0.496727	−	0.496727i	−0.413691	−	0.910417i	$-0.635761\pi$
$647$	5.28905e6	−	5.28905e6i	0.496727	−	0.496727i	0.910417	+	0.413691i	$0.135761\pi$
$648$	−1.06453e7	−	965837.i	−0.995909	−	0.0903580i
$649$	−1.42822e7	−	1.42822e7i	−1.33101	−	1.33101i
$650$	4.79883e6	+	7.33428e6i	0.445504	+	0.680886i
$651$	2.61602e6	−	1.59426e7i	0.241930	−	1.47437i
$652$	−155607.	+	8.05677e6i	−0.0143354	+	0.742236i
$653$	1.88498e6	+	780786.i	0.172991	+	0.0716554i	0.467498	−	0.883994i	$-0.345155\pi$
$653$	1.88498e6	+	780786.i	0.172991	+	0.0716554i	−0.294507	+	0.955649i	$0.595155\pi$
$654$	−5.92081e6	−	1.33748e7i	−0.541298	−	1.22277i
$655$	4.31940e6			0.393387
$656$	450885.	−	1.16682e7i	0.0409078	−	1.05863i
$657$	−1.62734e7	+	8.06501e6i	−1.47084	+	0.728940i
$658$	−4.71712e6	+	6.91420e6i	−0.424729	+	0.622554i
$659$	5.83455e6	−	1.40858e7i	0.523352	−	1.26348i	−0.412458	−	0.910977i	$-0.635329\pi$
$659$	5.83455e6	−	1.40858e7i	0.523352	−	1.26348i	0.935809	−	0.352506i	$-0.114671\pi$
$660$	−836765.	−	3.91152e6i	−0.0747728	−	0.349531i
$661$	−1.71212e7	+	7.09182e6i	−1.52416	+	0.631327i	−0.978419	−	0.206629i	$-0.933751\pi$
$661$	−1.71212e7	+	7.09182e6i	−1.52416	+	0.631327i	−0.545738	+	0.837956i	$0.683751\pi$
$662$	−511742.	−	782120.i	−0.0453843	−	0.0693630i
$663$	−2.51434e6	−	1.07356e7i	−0.222147	−	0.948515i
$664$	93307.8	+	552237.i	0.00821292	+	0.0486077i
$665$	6.81410e6	+	6.81410e6i	0.597523	+	0.597523i
$666$	−7.79371e6	+	2.02423e6i	−0.680862	+	0.176838i
$667$	3.37459e6	−	1.39780e6i	0.293701	−	0.121655i
$668$	−4.40689e6	+	1.00839e7i	−0.382112	+	0.874352i
$669$	−3.47132e6	−	4.83417e6i	−0.299868	−	0.417597i
$670$	−861808.	−	4.56240e6i	−0.0741691	−	0.392651i
$671$	−3.30974e6			−0.283784
$672$	−1.54576e7	+	1.50136e7i	−1.32044	+	1.28251i
$673$	−1.62878e7			−1.38619			−0.693096	−	0.720845i	$-0.743754\pi$
$673$	−1.62878e7			−1.38619			−0.693096	+	0.720845i	$0.743754\pi$
$674$	−1.03886e6	−	5.49970e6i	−0.0880860	−	0.466326i
$675$	9.11626e6	+	4.83820e6i	0.770118	+	0.408719i
$676$	1.40439e6	+	613752.i	0.118201	+	0.0516567i
$677$	−5.83406e6	+	2.41655e6i	−0.489214	+	0.202639i	−0.613634	−	0.789591i	$-0.710293\pi$
$677$	−5.83406e6	+	2.41655e6i	−0.489214	+	0.202639i	0.124420	+	0.992230i	$0.460293\pi$
$678$	4.51463e6	−	4.73720e6i	0.377179	−	0.395775i
$679$	−9.37496e6	−	9.37496e6i	−0.780360	−	0.780360i
$680$	−2.61062e6	+	3.67218e6i	−0.216507	+	0.304545i
$681$	6.21303e6	−	1.45512e6i	0.513376	−	0.120235i
$682$	−5.39002e6	−	8.23782e6i	−0.443741	−	0.678190i
$683$	5.35342e6	−	2.21746e6i	0.439116	−	0.181888i	−0.152162	−	0.988356i	$-0.548624\pi$
$683$	5.35342e6	−	2.21746e6i	0.439116	−	0.181888i	0.591278	+	0.806468i	$0.298624\pi$
$684$	5.30079e6	−	1.47690e7i	0.433212	−	1.20701i
$685$	−970736.	+	2.34356e6i	−0.0790450	+	0.190832i
$686$	1.77530e7	−	2.60218e7i	1.44033	−	2.11119i
$687$	1.20298e7	+	7.46422e6i	0.972450	+	0.603382i
$688$	3.78697e6	+	1.74284e6i	0.305014	+	0.140374i
$689$	−1.31780e7			−1.05755
$690$	−4.78455e6	+	2.11804e6i	−0.382577	+	0.169360i
$691$	−9.67785e6	−	4.00870e6i	−0.771052	−	0.319380i	−0.0377538	−	0.999287i	$-0.512020\pi$
$691$	−9.67785e6	−	4.00870e6i	−0.771052	−	0.319380i	−0.733299	+	0.679907i	$0.762020\pi$
$692$	1.65496e6	+	31963.7i	0.131378	+	0.00253742i
$693$	1.52869e7	−	1.75008e7i	1.20917	−	1.38428i
$694$	−458847.	−	701278.i	−0.0361634	−	0.0552703i
$695$	2.70601e6	+	2.70601e6i	0.212504	+	0.212504i
$696$	−2.46955e6	−	2.44625e6i	−0.193239	−	0.191415i
$697$	1.00292e7	−	1.00292e7i	0.781959	−	0.781959i
$698$	4.12903e6	+	862843.i	0.320782	+	0.0670337i
$699$	3.08109e6	−	1.87768e7i	0.238513	−	1.45355i
$700$	1.93723e7	−	7.58942e6i	1.49430	−	0.585414i
$701$	3.30858e6	−	7.98763e6i	0.254300	−	0.613936i	−0.744242	−	0.667910i	$-0.767189\pi$
$701$	3.30858e6	−	7.98763e6i	0.254300	−	0.613936i	0.998542	+	0.0539746i	$0.0171890\pi$
$702$	−1.21348e7	+	1.11309e6i	−0.929375	+	0.0852485i
$703$		−	1.18208e7i		−	0.902106i
$704$	−760289.	+	1.31086e7i	−0.0578158	+	0.996837i
$705$	1.64347e6	+	1.01974e6i	0.124535	+	0.0772708i
$706$	−396954.	−	2.10147e6i	−0.0299729	−	0.158676i
$707$	1.43941e6	+	596222.i	0.108302	+	0.0448600i
$708$	2.47285e7	+	4.54973e6i	1.85402	+	0.341116i
$709$	1.05030e6	+	2.53566e6i	0.0784691	+	0.189441i	0.958246	−	0.285946i	$-0.0923079\pi$
$709$	1.05030e6	+	2.53566e6i	0.0784691	+	0.189441i	−0.879777	+	0.475387i	$0.842308\pi$
$710$	772773.	−	3.69801e6i	0.0575315	−	0.275310i
$711$	3.57468e6	−	1.05991e7i	0.265194	−	0.786316i
$712$	2.06506e7	+	4.73330e6i	1.52663	+	0.349916i
$713$	−9.10578e6	+	9.10578e6i	−0.670801	+	0.670801i
$714$	−2.61666e7	+	629509.i	−1.92088	+	0.0462122i
$715$	−1.74509e6	−	4.21301e6i	−0.127659	−	0.308197i
$716$	−338571.	+	1.75299e7i	−0.0246812	+	1.27790i
$717$	−6.33155e6	−	8.81734e6i	−0.459952	−	0.640530i
$718$	−4.68512e6	+	6.86729e6i	−0.339164	+	0.497135i
$719$			1.12076e7i			0.808521i	0.914644	+	0.404260i	$0.132471\pi$
$719$			1.12076e7i			0.808521i	−0.914644	+	0.404260i	$0.867529\pi$
$720$	3.62090e6	+	3.41816e6i	0.260307	+	0.245732i
$721$		−	8.99375e6i		−	0.644321i
$722$	7.45784e6	+	5.08801e6i	0.532439	+	0.363250i
$723$	6.06981e6	+	8.45284e6i	0.431847	+	0.601391i
$724$	−9.80837e6	+	9.43667e6i	−0.695425	+	0.669071i
$725$	1.28437e6	+	3.10075e6i	0.0907498	+	0.219089i
$726$	1015.38	+	42206.0i	7.14969e−5	+	0.00297189i
$727$	−5.28359e6	+	5.28359e6i	−0.370760	+	0.370760i	−0.867754	−	0.496994i	$-0.834437\pi$
$727$	−5.28359e6	+	5.28359e6i	−0.370760	+	0.370760i	0.496994	+	0.867754i	$0.334437\pi$
$728$	−1.42341e7	+	2.00221e7i	−0.995406	+	1.40017i
$729$	−1.18834e7	+	8.04212e6i	−0.828175	+	0.560469i
$730$	8.28194e6	+	1.73067e6i	0.575208	+	0.120201i
$731$	1.93776e6	+	4.67816e6i	0.134124	+	0.323803i
$732$	3.39246e6	−	2.33811e6i	0.234011	−	0.161282i
$733$	9.64955e6	+	3.99698e6i	0.663357	+	0.274771i	0.688850	−	0.724904i	$-0.258116\pi$
$733$	9.64955e6	+	3.99698e6i	0.663357	+	0.274771i	−0.0254935	+	0.999675i	$0.508116\pi$
$734$	2.84785e7	−	5.37940e6i	1.95109	−	0.368548i
$735$	−1.06402e7	−	6.60201e6i	−0.726494	−	0.450773i
$736$	1.69881e7	−	2.53400e6i	1.15598	−	0.172429i
$737$		−	1.64359e7i		−	1.11461i
$738$	−9.44651e6	−	1.25089e7i	−0.638455	−	0.845430i
$739$	4.38276e6	−	1.05809e7i	0.295214	−	0.712709i	−0.704781	−	0.709425i	$-0.748955\pi$
$739$	4.38276e6	−	1.05809e7i	0.295214	−	0.712709i	0.999995	−	0.00328377i	$-0.00104526\pi$
$740$	3.43723e6	+	1.50215e6i	0.230743	+	0.100840i
$741$	2.89662e6	−	1.76526e7i	0.193797	−	1.18104i
$742$	−6.39882e6	+	3.06208e7i	−0.426668	+	2.04177i
$743$	−1.14722e7	+	1.14722e7i	−0.762386	+	0.762386i	−0.976753	−	0.214367i	$-0.931231\pi$
$743$	−1.14722e7	+	1.14722e7i	−0.762386	+	0.762386i	0.214367	+	0.976753i	$0.431231\pi$
$744$	1.13442e7	+	4.63602e6i	0.751348	+	0.307053i
$745$	−5.75357e6	−	5.75357e6i	−0.379793	−	0.379793i
$746$	6.42464e6	−	4.20365e6i	0.422671	−	0.276554i
$747$	566230.	+	494602.i	0.0371271	+	0.0324306i
$748$	−1.14934e7	+	1.10579e7i	−0.751095	+	0.722632i
$749$	−5.70760e6	−	2.36417e6i	−0.371749	−	0.153983i
$750$	−4.17837e6	−	9.43875e6i	−0.271240	−	0.612719i
$751$	−5.19828e6			−0.336326			−0.168163	−	0.985759i	$-0.553783\pi$
$751$	−5.19828e6			−0.336326			−0.168163	+	0.985759i	$0.553783\pi$
$752$	−4.31276e6	−	4.65947e6i	−0.278106	−	0.300463i
$753$	2.11478e7	+	1.31217e7i	1.35918	+	0.843340i
$754$	−3.27352e6	−	2.23331e6i	−0.209694	−	0.143061i
$755$	1.74119e6	−	4.20362e6i	0.111168	−	0.268383i
$756$	−3.30589e6	+	2.87374e7i	−0.210370	+	1.82870i
$757$	1.49143e6	−	617771.i	0.0945939	−	0.0391821i	−0.334885	−	0.942259i	$-0.608697\pi$
$757$	1.49143e6	−	617771.i	0.0945939	−	0.0391821i	0.429479	+	0.903077i	$0.358697\pi$
$758$	−9.72729e6	+	6.36457e6i	−0.614920	+	0.402343i
$759$	−1.80340e7	+	4.22365e6i	−1.13629	+	0.266124i
$760$	−6.19296e6	+	3.88337e6i	−0.388923	+	0.243879i
$761$	−4.59587e6	−	4.59587e6i	−0.287678	−	0.287678i	0.548484	−	0.836161i	$-0.315205\pi$
$761$	−4.59587e6	−	4.59587e6i	−0.287678	−	0.287678i	−0.836161	+	0.548484i	$0.815205\pi$
$762$	−1.49765e7	−	1.42728e7i	−0.934376	−	0.890474i
$763$	−3.65702e7	+	1.51479e7i	−2.27414	+	0.941978i
$764$	1.71908e7	−	6.73476e6i	1.06552	−	0.417435i
$765$	407452.	+	6.03454e6i	0.0251723	+	0.372813i
$766$	−1.22578e7	+	2.31543e6i	−0.754818	+	0.142580i
$767$	2.86644e7			1.75936
$768$	−8.48105e6	−	1.39733e7i	−0.518856	−	0.854862i
$769$	−2.25660e6			−0.137607			−0.0688033	−	0.997630i	$-0.521918\pi$
$769$	−2.25660e6			−0.137607			−0.0688033	+	0.997630i	$0.521918\pi$
$770$	−1.06369e7	+	2.00923e6i	−0.646527	+	0.122125i
$771$	−1.55309e7	−	2.16284e7i	−0.940938	−	1.31035i
$772$	328.322	−	128.625i	1.98270e−5	−	7.76752e-6i
$773$	−2.32853e7	+	9.64507e6i	−1.40163	+	0.580573i	−0.950173	−	0.311722i	$-0.899094\pi$
$773$	−2.32853e7	+	9.64507e6i	−1.40163	+	0.580573i	−0.451453	+	0.892295i	$0.649094\pi$
$774$	5.41643e6	−	1.40679e6i	0.324983	−	0.0844067i
$775$	−8.36687e6	−	8.36687e6i	−0.500390	−	0.500390i
$776$	8.52038e6	−	5.34281e6i	0.507931	−	0.318505i
$777$	4.96918e6	+	2.12172e7i	0.295279	+	1.26077i
$778$	151339.	−	99021.5i	0.00896402	−	0.00586517i
$779$	2.12594e7	−	8.80594e6i	1.25519	−	0.519915i
$780$	4.76491e6	+	3.08552e6i	0.280426	+	0.181590i
$781$	5.11771e6	−	1.23552e7i	0.300226	−	0.724810i
$782$	1.72342e7	+	1.17578e7i	1.00780	+	0.687558i
$783$	−4.64508e6	−	443661.i	−0.270763	−	0.0258611i
$784$	2.79218e7	+	3.01664e7i	1.62238	+	1.75281i
$785$	5.77641e6			0.334568
$786$	−1.74048e7	+	7.70478e6i	−1.00487	+	0.444840i
$787$	2.75357e7	+	1.14057e7i	1.58474	+	0.656423i	0.989156	−	0.146867i	$-0.0469189\pi$
$787$	2.75357e7	+	1.14057e7i	1.58474	+	0.656423i	0.595588	+	0.803290i	$0.296919\pi$
$788$	−1.97280e7	+	1.89804e7i	−1.13179	+	1.08890i
$789$	−220272.	+	1.34239e6i	−0.0125970	+	0.0767689i
$790$	−4.36039e6	+	2.85301e6i	−0.248575	+	0.162643i
$791$	−1.25224e7	−	1.25224e7i	−0.711617	−	0.711617i
$792$	1.03489e7	+	1.42686e7i	0.586249	+	0.808294i
$793$	3.32133e6	−	3.32133e6i	0.187555	−	0.187555i
$794$	574384.	−	2.74864e6i	0.0323334	−	0.154727i
$795$	7.13325e6	+	1.17050e6i	0.400285	+	0.0656829i
$796$	−2.22647e7	−	9.73022e6i	−1.24548	−	0.544302i
$797$	1.27743e6	−	3.08399e6i	0.0712347	−	0.171976i	−0.884252	−	0.467010i	$-0.845331\pi$
$797$	1.27743e6	−	3.08399e6i	0.0712347	−	0.171976i	0.955487	+	0.295034i	$0.0953311\pi$
$798$	−3.96117e7	−	1.53023e7i	−2.20200	−	0.850645i
$799$		−	7.71190e6i		−	0.427360i
$800$	2.32837e6	+	1.56096e7i	0.128625	+	0.862316i
$801$	2.54824e7	−	1.26290e7i	1.40333	−	0.695482i
$802$	1.05883e7	−	2.00006e6i	0.581285	−	0.109801i
$803$	2.76704e7	+	1.14614e7i	1.51435	+	0.627264i
$804$	1.16108e7	+	1.68466e7i	0.633466	+	0.919122i
$805$	5.41882e6	+	1.30822e7i	0.294724	+	0.711527i
$806$	1.36756e7	+	2.85778e6i	0.741494	+	0.154950i
$807$	6.62225e6	−	1.55096e6i	0.357949	−	0.0838335i
$808$	−684768.	+	963217.i	−0.0368990	+	0.0519034i
$809$	−1.02672e7	+	1.02672e7i	−0.551543	+	0.551543i	−0.926886	−	0.375343i	$-0.877525\pi$
$809$	−1.02672e7	+	1.02672e7i	−0.551543	+	0.551543i	0.375343	+	0.926886i	$0.377525\pi$
$810$	6.66746e6	+	475325.i	0.357066	+	0.0254553i
$811$	−713606.	−	1.72280e6i	−0.0380984	−	0.0919776i	0.903685	−	0.428198i	$-0.140851\pi$
$811$	−713606.	−	1.72280e6i	−0.0380984	−	0.0919776i	−0.941783	+	0.336220i	$0.890851\pi$
$812$	−6.77892e6	+	6.52202e6i	−0.360803	+	0.347130i
$813$	−2.69833e7	+	1.93761e7i	−1.43175	+	1.02811i
$814$	1.09689e7	+	7.48339e6i	0.580233	+	0.395856i
$815$		−	5.03925e6i		−	0.265749i
$816$	3.96903e6	−	1.94536e7i	0.208669	−	1.02276i
$817$			8.21514e6i			0.430586i
$818$	8.34118e6	−	1.22262e7i	0.435857	−	0.638865i
$819$	2.22158e6	+	3.29025e7i	0.115732	+	1.71404i
$820$	−141007.	+	7.30082e6i	−0.00732329	+	0.379173i
$821$	3.87720e6	+	9.36038e6i	0.200752	+	0.484658i	0.991908	−	0.126956i	$-0.0405206\pi$
$821$	3.87720e6	+	9.36038e6i	0.200752	+	0.484658i	−0.791156	+	0.611614i	$0.790521\pi$
$822$	−268841.	−	1.11748e7i	−0.0138776	−	0.576847i
$823$	1.87095e7	−	1.87095e7i	0.962859	−	0.962859i	−0.0364752	−	0.999335i	$-0.511613\pi$
$823$	1.87095e7	−	1.87095e7i	0.962859	−	0.962859i	0.999335	+	0.0364752i	$0.0116130\pi$
$824$	6.64974e6	+	1.52418e6i	0.341182	+	0.0782020i
$825$	−3.88091e6	−	1.65706e7i	−0.198517	−	0.847623i
$826$	1.39186e7	−	6.66056e7i	0.709813	−	3.39673i
$827$	−4.64811e6	−	1.12215e7i	−0.236326	−	0.570542i	0.760571	−	0.649255i	$-0.224919\pi$
$827$	−4.64811e6	−	1.12215e7i	−0.236326	−	0.570542i	−0.996897	+	0.0787124i	$0.974919\pi$
$828$	1.55010e7	−	1.70690e7i	0.785748	−	0.865232i
$829$	−3.25191e7	−	1.34699e7i	−1.64343	−	0.680732i	−0.646796	−	0.762663i	$-0.723891\pi$
$829$	−3.25191e7	−	1.34699e7i	−1.64343	−	0.680732i	−0.996638	+	0.0819309i	$0.973891\pi$
$830$	−65007.9	−	344151.i	−0.00327545	−	0.0173402i
$831$	−8.53444e6	+	1.37547e7i	−0.428719	+	0.690951i
$832$	−1.23915e7	−	1.39174e7i	−0.620608	−	0.697030i
$833$			4.99286e7i			2.49308i
$834$	−1.57306e7	−	6.07683e6i	−0.783123	−	0.302525i
$835$	2.63357e6	−	6.35800e6i	0.130716	−	0.315576i
$836$	−2.40928e7	+	9.43873e6i	−1.19226	+	0.467087i
$837$	1.57285e7	−	4.82192e6i	0.776020	−	0.237907i
$838$	−9.86327e6	−	2.06112e6i	−0.485189	−	0.101390i
$839$	−7.78914e6	+	7.78914e6i	−0.382019	+	0.382019i	−0.871829	−	0.489810i	$-0.837066\pi$
$839$	−7.78914e6	+	7.78914e6i	−0.382019	+	0.382019i	0.489810	+	0.871829i	$0.337066\pi$
$840$	9.48332e6	−	9.57368e6i	0.463727	−	0.468145i
$841$	1.34306e7	+	1.34306e7i	0.654794	+	0.654794i
$842$	1.49775e7	+	2.28908e7i	0.728046	+	1.11271i
$843$	2.45541e7	+	4.02908e6i	1.19002	+	0.195271i
$844$	1.45030e7	+	280110.i	0.700815	+	0.0135354i
$845$	−885485.	−	366780.i	−0.0426618	−	0.0176711i
$846$	−8.44125e6	−	1.17740e6i	−0.405490	−	0.0565585i
$847$	114252.			0.00547212
$848$	−2.15558e7	−	9.92045e6i	−1.02938	−	0.473742i
$849$	−1.59817e6	+	2.57572e6i	−0.0760948	+	0.122639i
$850$	−1.08037e7	+	1.58357e7i	−0.512890	+	0.751778i
$851$	6.64703e6	−	1.60473e7i	0.314632	−	0.759590i
$852$	3.48254e6	+	1.62794e7i	0.164360	+	0.768313i
$853$	3.08620e7	−	1.27834e7i	1.45228	−	0.601555i	0.489541	−	0.871980i	$-0.337164\pi$
$853$	3.08620e7	−	1.27834e7i	1.45228	−	0.601555i	0.962741	+	0.270425i	$0.0871643\pi$
$854$	−6.10482e6	−	9.33030e6i	−0.286436	−	0.437775i
$855$	−3.13589e6	+	9.29810e6i	−0.146705	+	0.434990i
$856$	2.71528e6	−	3.81939e6i	0.126657	−	0.178160i
$857$	1.96691e6	+	1.96691e6i	0.0914814	+	0.0914814i	0.751367	−	0.659885i	$-0.229395\pi$
$857$	1.96691e6	+	1.96691e6i	0.0914814	+	0.0914814i	−0.659885	+	0.751367i	$0.729395\pi$
$858$	1.45467e7	+	1.38633e7i	0.674602	+	0.642905i
$859$	−4.56584e6	+	1.89123e6i	−0.211124	+	0.0874504i	−0.485739	−	0.874104i	$-0.661450\pi$
$859$	−4.56584e6	+	1.89123e6i	−0.211124	+	0.0874504i	0.274615	+	0.961554i	$0.411450\pi$
$860$	−2.38879e6	−	1.04396e6i	−0.110136	−	0.0481322i
$861$	−3.44569e7	+	2.47428e7i	−1.58405	+	1.13747i
$862$	2.05157e6	+	1.08610e7i	0.0940410	+	0.497852i
$863$	3.84318e7			1.75656			0.878282	−	0.478143i	$-0.158690\pi$
$863$	3.84318e7			1.75656			0.878282	+	0.478143i	$0.158690\pi$
$864$	−2.06874e7	−	7.31443e6i	−0.942804	−	0.333347i
$865$	−1.03513e6			−0.0470384
$866$	−3.17133e6	−	1.67890e7i	−0.143697	−	0.760728i
$867$	1.61050e6	−	1.15647e6i	0.0727636	−	0.0522501i
$868$	1.32809e7	−	3.03894e7i	0.598311	−	1.36906i
$869$	−1.70415e7	+	7.05882e6i	−0.765524	+	0.317090i
$870$	1.57359e6	+	1.49965e6i	0.0704845	+	0.0671727i
$871$	1.64934e7	+	1.64934e7i	0.736657	+	0.736657i
$872$	−5.00236e6	−	2.96062e7i	−0.222784	−	1.31853i
$873$	4.31441e6	−	1.27925e7i	0.191596	−	0.568093i
$874$	1.85323e7	+	2.83237e7i	0.820634	+	1.25422i
$875$	−2.58080e7	+	1.06900e7i	−1.13955	+	0.472018i
$876$	−3.64587e7	+	7.79936e6i	−1.60524	+	0.343399i
$877$	−2.76064e6	+	6.66478e6i	−0.121202	+	0.292608i	−0.972823	−	0.231550i	$-0.925620\pi$
$877$	−2.76064e6	+	6.66478e6i	−0.121202	+	0.292608i	0.851621	+	0.524159i	$0.175620\pi$
$878$	513109.	−	752098.i	0.0224633	−	0.0329260i
$879$	−1.39346e7	+	2.24579e7i	−0.608307	+	0.980387i
$880$	317063.	−	8.20512e6i	0.0138019	−	0.357173i
$881$	780159.			0.0338644			0.0169322	−	0.999857i	$-0.494610\pi$
$881$	780159.			0.0338644			0.0169322	+	0.999857i	$0.494610\pi$
$882$	5.46505e7	+	7.62275e6i	2.36550	+	0.329944i
$883$	−4.03465e7	−	1.67121e7i	−1.74142	−	0.721321i	−0.998659	−	0.0517659i	$-0.983515\pi$
$883$	−4.03465e7	−	1.67121e7i	−1.74142	−	0.721321i	−0.742763	−	0.669555i	$-0.766485\pi$
$884$	437078.	−	2.26303e7i	0.0188117	−	0.974000i
$885$	−1.55161e7	−	2.54603e6i	−0.665922	−	0.109271i
$886$	−1.65305e7	−	2.52643e7i	−0.707459	−	1.08124i
$887$	7.36115e6	+	7.36115e6i	0.314150	+	0.314150i	0.846515	−	0.532365i	$-0.178697\pi$
$887$	7.36115e6	+	7.36115e6i	0.314150	+	0.314150i	−0.532365	+	0.846515i	$0.678697\pi$
$888$	−1.65296e7	+	78378.0i	−0.703444	+	0.00333551i
$889$	−3.95890e7	+	3.95890e7i	−1.68004	+	1.68004i
$890$	−1.29686e7	−	2.71005e6i	−0.548806	−	0.114684i
$891$	2.28795e7	+	6.03413e6i	0.965499	+	0.254636i
$892$	−4.45644e6	−	1.13753e7i	−0.187532	−	0.478685i
$893$	4.78802e6	−	1.15593e7i	0.200922	−	0.485069i
$894$	3.34467e7	+	1.29207e7i	1.39962	+	0.540680i
$895$		−	1.09644e7i		−	0.457538i
$896$	−3.83560e7	+	2.20355e7i	−1.59611	+	0.916966i
$897$	1.38587e7	−	2.23356e7i	0.575098	−	0.926865i
$898$	−5.62141e6	−	2.97597e7i	−0.232624	−	1.23151i
$899$	4.94259e6	+	2.04729e6i	0.203965	+	0.0844849i
$900$	1.56839e7	+	1.42431e7i	0.645428	+	0.586136i
$901$	−1.10299e7	−	2.66285e7i	−0.452647	−	1.09279i
$902$	−5.28739e6	+	2.53022e7i	−0.216384	+	1.03548i
$903$	−3.45345e6	−	1.47454e7i	−0.140940	−	0.601780i
$904$	1.13809e7	−	7.13655e6i	0.463187	−	0.290447i
$905$	6.01857e6	−	6.01857e6i	0.244271	−	0.244271i
$906$	482216.	+	2.00441e7i	0.0195174	+	0.811271i
$907$	−4.69550e6	−	1.13359e7i	−0.189524	−	0.457550i	0.800345	−	0.599540i	$-0.204650\pi$
$907$	−4.69550e6	−	1.13359e7i	−0.189524	−	0.457550i	−0.989868	+	0.141990i	$0.954650\pi$
$908$	1.30968e7	+	252950.i	0.527170	+	0.0101817i
$909$	106875.	+	1.58287e6i	0.00429010	+	0.0635382i
$910$	8.65784e6	−	1.26904e7i	0.346582	−	0.508009i
$911$		−	1.20997e7i		−	0.483037i	−0.970396	−	0.241518i	$-0.922355\pi$
$911$		−	1.20997e7i		−	0.483037i	0.970396	−	0.241518i	$-0.0776454\pi$
$912$	1.80271e7	−	2.66946e7i	0.717694	−	1.06276i
$913$		−	1.23979e6i		−	0.0492234i
$914$	5.26288e6	+	3.59053e6i	0.208381	+	0.142165i
$915$	−2.09285e6	+	1.50283e6i	−0.0826390	+	0.0593414i
$916$	2.01495e7	+	2.09431e7i	0.793460	+	0.824713i
$917$	1.97120e7	+	4.75891e7i	0.774120	+	1.86889i
$918$	−1.24060e7	−	2.35890e7i	−0.485875	−	0.923854i
$919$	2.26697e7	−	2.26697e7i	0.885435	−	0.885435i	−0.108646	−	0.994081i	$-0.534651\pi$
$919$	2.26697e7	−	2.26697e7i	0.885435	−	0.885435i	0.994081	+	0.108646i	$0.0346515\pi$
$920$	−1.05910e7	+	1.78948e6i	−0.412540	+	0.0697041i
$921$	−1.14856e7	+	2.68999e6i	−0.446175	+	0.104496i
$922$	−3.58827e6	−	749840.i	−0.139014	−	0.0290497i
$923$	7.26288e6	+	1.75342e7i	0.280611	+	0.677455i
$924$	3.92766e7	−	2.70697e7i	1.51340	−	1.04305i
$925$	1.47451e7	+	6.10764e6i	0.566623	+	0.234703i
$926$	−2.12078e7	+	4.00601e6i	−0.812769	+	0.153527i
$927$	8.20565e6	−	4.06667e6i	0.313627	−	0.155432i
$928$	−3.67338e6	−	6.11744e6i	−0.140022	−	0.233185i
$929$		−	3.83298e7i		−	1.45712i	−0.684979	−	0.728562i	$-0.740189\pi$
$929$		−	3.83298e7i		−	1.45712i	0.684979	−	0.728562i	$-0.259811\pi$
$930$	−7.14876e6	−	2.76161e6i	−0.271034	−	0.104702i
$931$	−3.09988e7	+	7.48376e7i	−1.17211	+	2.82973i
$932$	1.56419e7	−	3.57919e7i	0.589861	−	1.34972i
$933$	4.12892e7	+	6.77515e6i	1.55286	+	0.254809i
$934$	−8.23659e6	+	3.94152e7i	−0.308944	+	1.47842i
$935$	7.05254e6	−	7.05254e6i	0.263826	−	0.263826i
$936$	−2.47038e7	−	3.93345e6i	−0.921666	−	0.146752i
$937$	1.35550e7	+	1.35550e7i	0.504373	+	0.504373i	0.912794	−	0.408421i	$-0.133920\pi$
$937$	1.35550e7	+	1.35550e7i	0.504373	+	0.504373i	−0.408421	+	0.912794i	$0.633920\pi$
$938$	4.63334e7	−	3.03160e7i	1.71944	−	1.12503i
$939$	−3.60570e6	+	2.19739e7i	−0.133452	+	0.813285i
$940$	2.75275e6	+	2.86118e6i	0.101613	+	0.105615i
$941$	6.91126e6	+	2.86274e6i	0.254439	+	0.105392i	0.506257	−	0.862383i	$-0.331029\pi$
$941$	6.91126e6	+	2.86274e6i	0.254439	+	0.105392i	−0.251819	+	0.967774i	$0.581029\pi$
$942$	−2.32757e7	+	1.03038e7i	−0.854625	+	0.378328i
$943$	3.38126e7			1.23822
$944$	4.68876e7	+	2.15787e7i	1.71249	+	0.788126i
$945$	1.71993e6	−	1.80075e7i	0.0626515	−	0.655955i
$946$	−7.62312e6	−	5.20077e6i	−0.276952	−	0.188947i
$947$	9.75213e6	−	2.35437e7i	0.353366	−	0.853100i	−0.642834	−	0.766005i	$-0.722242\pi$
$947$	9.75213e6	−	2.35437e7i	0.353366	−	0.853100i	0.996200	−	0.0870951i	$-0.0277584\pi$
$948$	1.24808e7	−	1.92739e7i	0.451048	−	0.696545i
$949$	−3.92689e7	+	1.62657e7i	−1.41541	+	0.586283i
$950$	−2.60253e7	+	1.70284e7i	−0.935594	+	0.612160i
$951$	3.04147e6	+	1.29864e7i	0.109052	+	0.465625i
$952$	−5.23722e7	−	1.20042e7i	−1.87287	−	0.429279i
$953$	−1.25256e7	−	1.25256e7i	−0.446752	−	0.446752i	0.447521	−	0.894273i	$-0.352307\pi$
$953$	−1.25256e7	−	1.25256e7i	−0.446752	−	0.446752i	−0.894273	+	0.447521i	$0.852307\pi$
$954$	−3.08309e7	+	8.00759e6i	−1.09677	+	0.284860i
$955$	−1.06670e7	+	4.41840e6i	−0.378470	+	0.156768i
$956$	−8.12837e6	−	2.07480e7i	−0.287646	−	0.734230i
$957$	4.48817e6	+	6.25024e6i	0.158412	+	0.220606i
$958$	−2.82769e7	+	5.34133e6i	−0.995447	+	0.188034i
$959$	−3.02503e7			−1.06214
$960$	5.47138e6	+	8.63417e6i	0.191610	+	0.302373i
$961$	9.76809e6			0.341194
$962$	−1.85169e7	+	3.49773e6i	−0.645106	+	0.121856i
$963$	−423787.	−	6.27646e6i	−0.0147259	−	0.218097i
$964$	7.79235e6	+	1.98903e7i	0.270070	+	0.689366i
$965$	−203.725	+	84.3855i	−7.04248e−6	+	2.91709e-6i
$966$	−4.51704e7	−	4.30480e7i	−1.55744	−	1.48426i
$967$	2.74100e7	+	2.74100e7i	0.942633	+	0.942633i	0.998441	−	0.0558085i	$-0.0177736\pi$
$967$	2.74100e7	+	2.74100e7i	0.942633	+	0.942633i	−0.0558085	+	0.998441i	$0.517774\pi$
$968$	−19362.4	+	84474.9i	−0.000664157	+	0.00289761i
$969$	3.80949e7	−	8.92201e6i	1.30334	−	0.305248i
$970$	−5.26271e6	+	3.44340e6i	−0.179589	+	0.117505i
$971$	−4.28562e7	+	1.77516e7i	−1.45870	+	0.604213i	−0.964250	−	0.264993i	$-0.914630\pi$
$971$	−4.28562e7	+	1.77516e7i	−1.45870	+	0.604213i	−0.494450	+	0.869206i	$0.664630\pi$
$972$	−2.77140e7	+	9.97787e6i	−0.940878	+	0.338745i
$973$	−1.74644e7	+	4.21627e7i	−0.591386	+	1.42773i
$974$	−1.67986e7	−	1.14606e7i	−0.567381	−	0.387088i
$975$	2.05231e7	+	1.27341e7i	0.691403	+	0.429000i
$976$	7.93316e6	−	2.93253e6i	0.266576	−	0.0985412i
$977$	5.33300e7			1.78745			0.893727	−	0.448611i	$-0.148081\pi$
$977$	5.33300e7			1.78745			0.893727	+	0.448611i	$0.148081\pi$
$978$	8.98883e6	+	2.03053e7i	0.300508	+	0.678834i
$979$	−4.33288e7	−	1.79474e7i	−1.44484	−	0.598473i
$980$	−1.78219e7	−	1.85239e7i	−0.592775	−	0.616123i
$981$	−3.03564e7	−	2.65163e7i	−1.00711	−	0.879712i
$982$	1.32189e7	−	8.64916e6i	0.437439	−	0.286217i
$983$	−3.86757e7	−	3.86757e7i	−1.27660	−	1.27660i	−0.942558	−	0.334042i	$-0.891587\pi$
$983$	−3.86757e7	−	3.86757e7i	−1.27660	−	1.27660i	−0.334042	−	0.942558i	$-0.608413\pi$
$984$	−1.24548e7	−	2.96697e7i	−0.410060	−	0.976845i
$985$	1.21054e7	−	1.21054e7i	0.397547	−	0.397547i
$986$	1.77290e6	−	8.48402e6i	0.0580755	−	0.277913i
$987$	−3.73480e6	+	2.27607e7i	−0.122032	+	0.743691i
$988$	1.47054e7	−	3.36490e7i	0.479275	−	1.09668i
$989$	−4.61952e6	+	1.11525e7i	−0.150178	+	0.362561i
$990$	−6.64280e6	−	8.79627e6i	−0.215409	−	0.285240i
$991$			1.90287e7i			0.615495i	0.951468	+	0.307747i	$0.0995752\pi$
$991$			1.90287e7i			0.615495i	−0.951468	+	0.307747i	$0.900425\pi$
$992$	2.02184e7	+	1.49696e7i	0.652329	+	0.482983i
$993$	−2.18856e6	−	1.35795e6i	−0.0704345	−	0.0437030i
$994$	4.42696e7	−	8.36224e6i	1.42115	−	0.268446i
$995$	1.40382e7	+	5.81481e6i	0.449524	+	0.186199i
$996$	875829.	+	1.27078e6i	0.0279750	+	0.0405902i
$997$	−1.04269e7	−	2.51728e7i	−0.332214	−	0.802035i	−0.998416	−	0.0562636i	$-0.982081\pi$
$997$	−1.04269e7	−	2.51728e7i	−0.332214	−	0.802035i	0.666202	−	0.745771i	$-0.267919\pi$
$998$	−5.02758e6	−	1.05061e6i	−0.159784	−	0.0333900i
$999$	−1.71111e7	+	1.41275e7i	−0.542456	+	0.447868i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	96.6.o.a.35.74	yes	312
3.2	odd	2	inner	96.6.o.a.35.5	yes	312
32.11	odd	8	inner	96.6.o.a.11.5	✓	312
96.11	even	8	inner	96.6.o.a.11.74	yes	312

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.6.o.a.11.5	✓	312	32.11	odd	8	inner
96.6.o.a.11.74	yes	312	96.11	even	8	inner
96.6.o.a.35.5	yes	312	3.2	odd	2	inner
96.6.o.a.35.74	yes	312	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 96 = 2^{5} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	96.o (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(5.55856 - 1.04998i) q^{2} +(12.6621 - 9.09239i) q^{3} +(29.7951 - 11.6727i) q^{4} +(-18.4880 + 7.65797i) q^{5} +(60.8361 - 63.8355i) q^{6} +(-168.744 - 168.744i) q^{7} +(153.362 - 96.1675i) q^{8} +(77.6568 - 230.257i) q^{9} +(-94.7257 + 61.9791i) q^{10} +(-370.212 + 153.347i) q^{11} +(271.135 - 418.709i) q^{12} +(217.625 - 525.392i) q^{13} +(-1115.15 - 760.794i) q^{14} +(-164.467 + 265.066i) q^{15} +(751.496 - 695.578i) q^{16} +1243.80 q^{17} +(189.895 - 1361.44i) q^{18} +(1864.33 + 772.230i) q^{19} +(-461.462 + 443.974i) q^{20} +(-3670.93 - 602.363i) q^{21} +(-1896.83 + 1241.10i) q^{22} +(2096.69 + 2096.69i) q^{23} +(1067.49 - 2612.11i) q^{24} +(-1926.55 + 1926.55i) q^{25} +(658.030 - 3148.92i) q^{26} +(-1110.29 - 3621.62i) q^{27} +(-6997.43 - 3058.04i) q^{28} +(471.407 - 1138.08i) q^{29} +(-635.887 + 1646.07i) q^{30} +4342.93i q^{31} +(3446.90 - 4655.46i) q^{32} +(-3293.37 + 5307.80i) q^{33} +(6913.75 - 1305.96i) q^{34} +(4411.96 + 1827.49i) q^{35} +(-373.930 - 7767.00i) q^{36} +(-2241.70 - 5411.95i) q^{37} +(11173.8 + 2334.99i) q^{38} +(-2021.49 - 8631.29i) q^{39} +(-2098.90 + 2952.38i) q^{40} +(8063.32 - 8063.32i) q^{41} +(-21037.5 + 506.116i) q^{42} +(1557.93 + 3761.17i) q^{43} +(-9240.54 + 8890.36i) q^{44} +(327.586 + 4851.68i) q^{45} +(13856.0 + 9453.10i) q^{46} -6200.25i q^{47} +(3191.04 - 15640.4i) q^{48} +40141.8i q^{49} +(-8686.00 + 12731.7i) q^{50} +(15749.2 - 11309.2i) q^{51} +(351.404 - 18194.4i) q^{52} +(-8867.88 - 21409.0i) q^{53} +(-9974.24 - 18965.2i) q^{54} +(5670.14 - 5670.14i) q^{55} +(-42106.5 - 9651.17i) q^{56} +(30627.7 - 7173.16i) q^{57} +(1425.39 - 6821.03i) q^{58} +(19289.2 + 46568.2i) q^{59} +(-1806.28 + 9817.43i) q^{60} +(7630.87 + 3160.81i) q^{61} +(4559.97 + 24140.4i) q^{62} +(-51958.6 + 25750.4i) q^{63} +(14271.6 - 29496.8i) q^{64} +11380.0i q^{65} +(-12733.3 + 32961.7i) q^{66} +(-15696.3 + 37894.2i) q^{67} +(37059.3 - 14518.5i) q^{68} +(45612.4 + 7484.54i) q^{69} +(26442.9 + 5525.78i) q^{70} +(-23598.6 + 23598.6i) q^{71} +(-10233.7 - 42780.7i) q^{72} +(-52850.5 - 52850.5i) q^{73} +(-18143.1 - 27728.9i) q^{74} +(-6877.19 + 41911.1i) q^{75} +(64561.9 + 1246.94i) q^{76} +(88347.2 + 36594.6i) q^{77} +(-20299.2 - 45855.0i) q^{78} +46031.8 q^{79} +(-8566.92 + 18614.8i) q^{80} +(-46987.8 - 35762.1i) q^{81} +(36354.1 - 53286.7i) q^{82} +(-1184.00 + 2858.44i) q^{83} +(-116407. + 24902.2i) q^{84} +(-22995.4 + 9525.01i) q^{85} +(12609.0 + 19270.9i) q^{86} +(-4378.84 - 18696.6i) q^{87} +(-42029.4 + 59119.9i) q^{88} +(82758.3 + 82758.3i) q^{89} +(6915.05 + 26624.4i) q^{90} +(-125379. + 51933.9i) q^{91} +(86945.1 + 37997.1i) q^{92} +(39487.6 + 54990.6i) q^{93} +(-6510.11 - 34464.5i) q^{94} -40381.4 q^{95} +(1315.58 - 90288.4i) q^{96} +55557.4 q^{97} +(42147.9 + 223131. i) q^{98} +(6559.73 + 97152.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 312 q - 4 q^{3} - 8 q^{4} - 4 q^{6} - 8 q^{7} - 4 q^{9} + 192 q^{10} - 4 q^{12} - 8 q^{13} - 8 q^{15} - 6696 q^{16} - 4 q^{18} - 8 q^{19} - 4 q^{21} + 5576 q^{22} - 11024 q^{24} - 8 q^{25} + 7460 q^{27}+ \cdots + 339516 q^{99}+O(q^{100}) \) 312 * q - 4 * q^3 - 8 * q^4 - 4 * q^6 - 8 * q^7 - 4 * q^9 + 192 * q^10 - 4 * q^12 - 8 * q^13 - 8 * q^15 - 6696 * q^16 - 4 * q^18 - 8 * q^19 - 4 * q^21 + 5576 * q^22 - 11024 * q^24 - 8 * q^25 + 7460 * q^27 - 8 * q^28 + 32564 * q^30 - 8 * q^33 - 264 * q^34 + 3264 * q^36 - 8 * q^37 + 44900 * q^39 - 60136 * q^40 - 7264 * q^42 - 8 * q^43 - 4 * q^45 + 63320 * q^46 + 112368 * q^48 - 976 * q^51 - 55024 * q^52 - 115328 * q^54 - 110056 * q^55 - 4 * q^57 - 123568 * q^58 + 44648 * q^60 - 96168 * q^61 + 187432 * q^64 + 17564 * q^66 + 97848 * q^67 - 4 * q^69 - 143480 * q^70 + 179936 * q^72 - 8 * q^73 + 12496 * q^75 - 234928 * q^76 - 708428 * q^78 + 355344 * q^79 + 251552 * q^82 + 387560 * q^84 - 25008 * q^85 - 282188 * q^87 + 111632 * q^88 + 453536 * q^90 + 200104 * q^91 + 968 * q^93 - 671008 * q^94 - 911336 * q^96 - 16 * q^97 + 339516 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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