LMFDB - Embedded newform 96.6.o.a.11.11

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			11.11
Character	$\chi$	$=$	96.11
Dual form			96.6.o.a.35.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.99058 - 2.66347i) q^{2} +(-10.7907 + 11.2499i) q^{3} +(17.8119 + 26.5845i) q^{4} +(-78.3856 - 32.4684i) q^{5} +(83.8158 - 27.4027i) q^{6} +(81.6131 - 81.6131i) q^{7} +(-18.0846 - 180.114i) q^{8} +(-10.1198 - 242.789i) q^{9} +(304.712 + 370.814i) q^{10} +(702.990 + 291.188i) q^{11} +(-491.276 - 86.4853i) q^{12} +(-338.008 - 816.025i) q^{13} +(-624.671 + 189.923i) q^{14} +(1211.10 - 531.471i) q^{15} +(-389.474 + 947.040i) q^{16} -524.376 q^{17} +(-596.158 + 1238.61i) q^{18} +(-2460.08 + 1019.00i) q^{19} +(-533.038 - 2662.17i) q^{20} +(37.4719 + 1798.80i) q^{21} +(-2732.76 - 3325.59i) q^{22} +(-105.025 + 105.025i) q^{23} +(2221.40 + 1740.11i) q^{24} +(2880.40 + 2880.40i) q^{25} +(-486.596 + 4972.72i) q^{26} +(2840.55 + 2506.03i) q^{27} +(3623.33 + 715.963i) q^{28} +(790.078 + 1907.42i) q^{29} +(-7459.68 - 573.387i) q^{30} +1081.48i q^{31} +(4466.12 - 3688.93i) q^{32} +(-10861.6 + 4766.42i) q^{33} +(2616.94 + 1396.66i) q^{34} +(-9047.13 + 3747.45i) q^{35} +(6274.18 - 4593.56i) q^{36} +(-1879.67 + 4537.93i) q^{37} +(14991.3 + 1466.95i) q^{38} +(12827.5 + 5002.96i) q^{39} +(-4430.43 + 14705.5i) q^{40} +(2149.04 + 2149.04i) q^{41} +(4604.05 - 9076.88i) q^{42} +(-2622.76 + 6331.90i) q^{43} +(4780.47 + 23875.2i) q^{44} +(-7089.73 + 19359.8i) q^{45} +(803.869 - 244.406i) q^{46} -25306.4i q^{47} +(-6451.38 - 14600.8i) q^{48} +3485.62i q^{49} +(-6703.02 - 22046.7i) q^{50} +(5658.41 - 5899.17i) q^{51} +(15673.1 - 23520.7i) q^{52} +(-10418.9 + 25153.4i) q^{53} +(-7501.27 - 20072.3i) q^{54} +(-45649.9 - 45649.9i) q^{55} +(-16175.6 - 13223.7i) q^{56} +(15082.5 - 38671.3i) q^{57} +(1137.39 - 11623.5i) q^{58} +(-9041.30 + 21827.6i) q^{59} +(35700.9 + 22730.1i) q^{60} +(-2285.96 + 946.877i) q^{61} +(2880.49 - 5397.22i) q^{62} +(-20640.7 - 18988.9i) q^{63} +(-32113.9 + 6514.57i) q^{64} +74939.2i q^{65} +(66901.0 + 5142.34i) q^{66} +(5560.64 + 13424.6i) q^{67} +(-9340.12 - 13940.3i) q^{68} +(-48.2214 - 2314.82i) q^{69} +(55131.7 + 5394.81i) q^{70} +(10278.6 + 10278.6i) q^{71} +(-43546.6 + 6213.45i) q^{72} +(16957.6 - 16957.6i) q^{73} +(21467.3 - 17640.5i) q^{74} +(-63485.8 + 1322.51i) q^{75} +(-70908.2 - 47249.8i) q^{76} +(81137.8 - 33608.4i) q^{77} +(-50691.7 - 59133.4i) q^{78} +9638.57 q^{79} +(61278.1 - 61588.7i) q^{80} +(-58844.2 + 4913.94i) q^{81} +(-5001.06 - 16448.8i) q^{82} +(38710.6 + 93455.6i) q^{83} +(-47152.9 + 33036.2i) q^{84} +(41103.6 + 17025.6i) q^{85} +(29953.9 - 24614.3i) q^{86} +(-29983.7 - 11694.2i) q^{87} +(39733.6 - 131884. i) q^{88} +(-45087.5 + 45087.5i) q^{89} +(86946.0 - 77733.2i) q^{90} +(-94184.2 - 39012.4i) q^{91} +(-4662.74 - 921.350i) q^{92} +(-12166.5 - 11670.0i) q^{93} +(-67402.8 + 126294. i) q^{94} +225920. q^{95} +(-6692.65 + 90049.6i) q^{96} +115610. q^{97} +(9283.84 - 17395.3i) q^{98} +(63583.2 - 173625. i) 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 $\left(\mathbb{Z}/96\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$65$
$\chi(n)$	$-1$	$e\left(\frac{5}{8}\right)$	$-1$

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 $

$2$	−4.99058	−	2.66347i	−0.882219	−	0.470839i
$2$	−4.99058	−	2.66347i	−0.882219	−	0.470839i
$3$	−10.7907	+	11.2499i	−0.692226	+	0.721680i
$3$	−10.7907	+	11.2499i	−0.692226	+	0.721680i
$4$	17.8119	+	26.5845i	0.556621	+	0.830767i
$5$	−78.3856	−	32.4684i	−1.40220	−	0.580812i	−0.451882	−	0.892078i	$-0.649247\pi$
$5$	−78.3856	−	32.4684i	−1.40220	−	0.580812i	−0.950323	+	0.311266i	$0.899247\pi$
$6$	83.8158	−	27.4027i	0.950491	−	0.310753i
$7$	81.6131	−	81.6131i	0.629527	−	0.629527i	−0.318422	−	0.947949i	$-0.603153\pi$
$7$	81.6131	−	81.6131i	0.629527	−	0.629527i	0.947949	+	0.318422i	$0.103153\pi$
$8$	−18.0846	−	180.114i	−0.0999043	−	0.994997i
$9$	−10.1198	−	242.789i	−0.0416451	−	0.999132i
$10$	304.712	+	370.814i	0.963582	+	1.17262i
$11$	702.990	+	291.188i	1.75173	+	0.725590i	0.997628	+	0.0688326i	$0.0219275\pi$
$11$	702.990	+	291.188i	1.75173	+	0.725590i	0.754102	+	0.656758i	$0.228073\pi$
$12$	−491.276	−	86.4853i	−0.984856	−	0.173376i
$13$	−338.008	−	816.025i	−0.554714	−	1.33920i	−0.913903	−	0.405933i	$-0.866947\pi$
$13$	−338.008	−	816.025i	−0.554714	−	1.33920i	0.359189	−	0.933265i	$-0.383053\pi$
$14$	−624.671	+	189.923i	−0.851787	+	0.258975i
$15$	1211.10	−	531.471i	1.38980	−	0.609890i
$16$	−389.474	+	947.040i	−0.380346	+	0.924844i
$17$	−524.376			−0.440069			−0.220034	−	0.975492i	$-0.570617\pi$
$17$	−524.376			−0.440069			−0.220034	+	0.975492i	$0.570617\pi$
$18$	−596.158	+	1238.61i	−0.433691	+	0.901062i
$19$	−2460.08	+	1019.00i	−1.56338	+	0.647574i	−0.985673	−	0.168669i	$-0.946053\pi$
$19$	−2460.08	+	1019.00i	−1.56338	+	0.647574i	−0.577709	+	0.816243i	$0.696053\pi$
$20$	−533.038	−	2662.17i	−0.297977	−	1.48820i
$21$	37.4719	+	1798.80i	0.0185421	+	0.890093i
$22$	−2732.76	−	3325.59i	−1.20377	−	1.46491i
$23$	−105.025	+	105.025i	−0.0413975	+	0.0413975i	−0.727503	−	0.686105i	$-0.759319\pi$
$23$	−105.025	+	105.025i	−0.0413975	+	0.0413975i	0.686105	+	0.727503i	$0.259319\pi$
$24$	2221.40	+	1740.11i	0.787226	+	0.616664i
$25$	2880.40	+	2880.40i	0.921728	+	0.921728i
$26$	−486.596	+	4972.72i	−0.141168	+	1.44265i
$27$	2840.55	+	2506.03i	0.749882	+	0.661571i
$28$	3623.33	+	715.963i	0.873398	+	0.172582i
$29$	790.078	+	1907.42i	0.174452	+	0.421163i	0.986786	−	0.162028i	$-0.0518036\pi$
$29$	790.078	+	1907.42i	0.174452	+	0.421163i	−0.812335	+	0.583192i	$0.801804\pi$
$30$	−7459.68	−	573.387i	−1.51327	−	0.116317i
$31$			1081.48i			0.202123i	0.994880	+	0.101061i	$0.0322238\pi$
$31$			1081.48i			0.202123i	−0.994880	+	0.101061i	$0.967776\pi$
$32$	4466.12	−	3688.93i	0.771001	−	0.636833i
$33$	−10861.6	+	4766.42i	−1.73624	+	0.761916i
$34$	2616.94	+	1396.66i	0.388237	+	0.207202i
$35$	−9047.13	+	3747.45i	−1.24836	+	0.517089i
$36$	6274.18	−	4593.56i	0.806865	−	0.590735i
$37$	−1879.67	+	4537.93i	−0.225724	+	0.544946i	−0.995648	−	0.0931891i	$-0.970294\pi$
$37$	−1879.67	+	4537.93i	−0.225724	+	0.544946i	0.769924	+	0.638135i	$0.220294\pi$
$38$	14991.3	+	1466.95i	1.68415	+	0.164799i
$39$	12827.5	+	5002.96i	1.35046	+	0.526702i
$40$	−4430.43	+	14705.5i	−0.437820	+	1.45321i
$41$	2149.04	+	2149.04i	0.199657	+	0.199657i	0.799853	−	0.600196i	$-0.204911\pi$
$41$	2149.04	+	2149.04i	0.199657	+	0.199657i	−0.600196	+	0.799853i	$0.704911\pi$
$42$	4604.05	−	9076.88i	0.402732	−	0.793987i
$43$	−2622.76	+	6331.90i	−0.216315	+	0.522232i	−0.994370	−	0.105965i	$-0.966207\pi$
$43$	−2622.76	+	6331.90i	−0.216315	+	0.522232i	0.778054	+	0.628197i	$0.216207\pi$
$44$	4780.47	+	23875.2i	0.372254	+	1.85916i
$45$	−7089.73	+	19359.8i	−0.521913	+	1.42518i
$46$	803.869	−	244.406i	0.0560132	−	0.0170301i
$47$		−	25306.4i		−	1.67103i	−0.549464	−	0.835517i	$-0.685168\pi$
$47$		−	25306.4i		−	1.67103i	0.549464	−	0.835517i	$-0.314832\pi$
$48$	−6451.38	−	14600.8i	−0.404156	−	0.914690i
$49$			3485.62i			0.207391i
$50$	−6703.02	−	22046.7i	−0.379180	−	1.24715i
$51$	5658.41	−	5899.17i	0.304627	−	0.317589i
$52$	15673.1	−	23520.7i	0.803796	−	1.20626i
$53$	−10418.9	+	25153.4i	−0.509485	+	1.23001i	0.434696	+	0.900577i	$0.356856\pi$
$53$	−10418.9	+	25153.4i	−0.509485	+	1.23001i	−0.944181	+	0.329428i	$0.893144\pi$
$54$	−7501.27	−	20072.3i	−0.350067	−	0.936725i
$55$	−45649.9	−	45649.9i	−2.03485	−	2.03485i
$56$	−16175.6	−	13223.7i	−0.689270	−	0.563485i
$57$	15082.5	−	38671.3i	0.614873	−	1.57653i
$58$	1137.39	−	11623.5i	0.0443957	−	0.453697i
$59$	−9041.30	+	21827.6i	−0.338143	+	0.816350i	0.659751	+	0.751484i	$0.270662\pi$
$59$	−9041.30	+	21827.6i	−0.338143	+	0.816350i	−0.997894	+	0.0648654i	$0.979338\pi$
$60$	35700.9	+	22730.1i	1.28027	+	0.815125i
$61$	−2285.96	+	946.877i	−0.0786583	+	0.0325813i	−0.421666	−	0.906751i	$-0.638554\pi$
$61$	−2285.96	+	946.877i	−0.0786583	+	0.0325813i	0.343007	+	0.939333i	$0.388554\pi$
$62$	2880.49	−	5397.22i	0.0951672	−	0.178316i
$63$	−20640.7	−	18988.9i	−0.655198	−	0.602764i
$64$	−32113.9	+	6514.57i	−0.980038	+	0.198809i
$65$			74939.2i			2.20001i
$66$	66901.0	+	5142.34i	1.89048	+	0.145312i
$67$	5560.64	+	13424.6i	0.151335	+	0.365354i	0.981307	−	0.192451i	$-0.0616437\pi$
$67$	5560.64	+	13424.6i	0.151335	+	0.365354i	−0.829972	+	0.557805i	$0.811644\pi$
$68$	−9340.12	−	13940.3i	−0.244952	−	0.365595i
$69$	−48.2214	−	2314.82i	−0.00121932	−	0.0585322i
$70$	55131.7	+	5394.81i	1.34480	+	0.131592i
$71$	10278.6	+	10278.6i	0.241985	+	0.241985i	0.817671	−	0.575686i	$-0.195265\pi$
$71$	10278.6	+	10278.6i	0.241985	+	0.241985i	−0.575686	+	0.817671i	$0.695265\pi$
$72$	−43546.6	+	6213.45i	−0.989973	+	0.141254i
$73$	16957.6	−	16957.6i	0.372440	−	0.372440i	−0.495925	−	0.868365i	$-0.665171\pi$
$73$	16957.6	−	16957.6i	0.372440	−	0.372440i	0.868365	+	0.495925i	$0.165171\pi$
$74$	21467.3	−	17640.5i	0.455720	−	0.374482i
$75$	−63485.8	+	1322.51i	−1.30324	+	0.0271485i
$76$	−70908.2	−	47249.8i	−1.40819	−	0.938352i
$77$	81137.8	−	33608.4i	1.55954	−	0.645983i
$78$	−50691.7	−	59133.4i	−0.943410	−	1.10052i
$79$	9638.57			0.173758			0.0868790	−	0.996219i	$-0.472311\pi$
$79$	9638.57			0.173758			0.0868790	+	0.996219i	$0.472311\pi$
$80$	61278.1	−	61588.7i	1.07048	−	1.07591i
$81$	−58844.2	+	4913.94i	−0.996531	+	0.0832180i
$82$	−5001.06	−	16448.8i	−0.0821348	−	0.270147i
$83$	38710.6	+	93455.6i	0.616786	+	1.48905i	0.855416	+	0.517942i	$0.173302\pi$
$83$	38710.6	+	93455.6i	0.616786	+	1.48905i	−0.238630	+	0.971111i	$0.576698\pi$
$84$	−47152.9	+	33036.2i	−0.729138	+	0.510848i
$85$	41103.6	+	17025.6i	0.617067	+	0.255597i
$86$	29953.9	−	24614.3i	0.436725	−	0.358873i
$87$	−29983.7	−	11694.2i	−0.424705	−	0.165642i
$88$	39733.6	−	131884.i	0.546955	−	1.81546i
$89$	−45087.5	+	45087.5i	−0.603367	+	0.603367i	−0.941204	−	0.337837i	$-0.890305\pi$
$89$	−45087.5	+	45087.5i	−0.603367	+	0.603367i	0.337837	+	0.941204i	$0.390305\pi$
$90$	86946.0	−	77733.2i	1.13147	−	1.01158i
$91$	−94184.2	−	39012.4i	−1.19227	−	0.493854i
$92$	−4662.74	−	921.350i	−0.0574344	−	0.0113489i
$93$	−12166.5	−	11670.0i	−0.145868	−	0.139915i
$94$	−67402.8	+	126294.i	−0.786789	+	1.47422i
$95$	225920.			2.56830
$96$	−6692.65	+	90049.6i	−0.0741174	+	0.997250i
$97$	115610.			1.24758			0.623788	−	0.781593i	$-0.285593\pi$
$97$	115610.			1.24758			0.623788	+	0.781593i	$0.285593\pi$
$98$	9283.84	−	17395.3i	0.0976478	−	0.182964i
$99$	63583.2	−	173625.i	0.652010	−	1.78043i
$100$	−25268.8	+	127879.i	−0.252688	+	1.27879i
$101$	−120479.	−	49904.0i	−1.17519	−	0.486779i	−0.292285	−	0.956331i	$-0.594415\pi$
$101$	−120479.	−	49904.0i	−1.17519	−	0.486779i	−0.882905	+	0.469552i	$0.844415\pi$
$102$	−43951.0	+	14369.3i	−0.418281	+	0.136753i
$103$	−91541.6	+	91541.6i	−0.850208	+	0.850208i	−0.990159	−	0.139950i	$-0.955306\pi$
$103$	−91541.6	+	91541.6i	−0.850208	+	0.850208i	0.139950	+	0.990159i	$0.455306\pi$
$104$	−140864.	+	75637.4i	−1.27708	+	0.685731i
$105$	55467.0	−	142217.i	0.490977	−	1.25886i
$106$	118992.	−	97779.8i	1.02861	−	0.845249i
$107$	−6009.99	−	2489.42i	−0.0507475	−	0.0210203i	0.357165	−	0.934041i	$-0.383743\pi$
$107$	−6009.99	−	2489.42i	−0.0507475	−	0.0210203i	−0.407913	+	0.913021i	$0.633743\pi$
$108$	−16026.1	+	120152.i	−0.132211	+	0.991222i
$109$	34583.0	+	83490.7i	0.278802	+	0.673088i	0.999803	−	0.0198461i	$-0.00631764\pi$
$109$	34583.0	+	83490.7i	0.278802	+	0.673088i	−0.721001	+	0.692934i	$0.756318\pi$
$110$	106233.	+	349407.i	0.837097	+	2.75327i
$111$	−30768.1	−	70113.7i	−0.237025	−	0.540127i
$112$	45504.7	+	109077.i	0.342776	+	0.821653i
$113$	17880.3			0.131728			0.0658641	−	0.997829i	$-0.479020\pi$
$113$	17880.3			0.131728			0.0658641	+	0.997829i	$0.479020\pi$
$114$	−178270.	+	152821.i	−1.28474	+	1.10134i
$115$	11642.5	−	4822.47i	0.0820919	−	0.0340036i
$116$	−36635.0	+	54978.5i	−0.252785	+	0.379357i
$117$	−194701.	+	90322.8i	−1.31494	+	0.610004i
$118$	103259.	−	84851.4i	0.682686	−	0.560988i
$119$	−42795.9	+	42795.9i	−0.277035	+	0.277035i
$120$	−117628.	−	208525.i	−0.745686	−	1.32192i
$121$	295524.	+	295524.i	1.83497	+	1.83497i
$122$	13930.3	+	1363.12i	0.0847344	+	0.00829153i
$123$	−47366.1	+	986.712i	−0.282296	+	0.00588068i
$124$	−28750.7	+	19263.2i	−0.167917	+	0.112506i
$125$	−30796.2	−	74348.7i	−0.176288	−	0.425597i
$126$	52432.8	+	149741.i	0.294223	+	0.840263i
$127$			202382.i			1.11343i	0.830705	+	0.556713i	$0.187938\pi$
$127$			202382.i			1.11343i	−0.830705	+	0.556713i	$0.812062\pi$
$128$	177618.	+	53022.8i	0.958215	+	0.286047i
$129$	−42931.7	−	97831.7i	−0.227145	−	0.517613i
$130$	199598.	−	373990.i	1.03585	−	1.94089i
$131$	−196046.	+	81204.8i	−0.998112	+	0.413431i	−0.821104	−	0.570778i	$-0.806642\pi$
$131$	−196046.	+	81204.8i	−0.998112	+	0.413431i	−0.177007	+	0.984210i	$0.556642\pi$
$132$	−320179.	−	203852.i	−1.59940	−	1.01831i
$133$	−117611.	+	283938.i	−0.576526	+	1.39186i
$134$	8005.09	−	81807.1i	0.0385127	−	0.393576i
$135$	−141292.	−	288665.i	−0.667239	−	1.36320i
$136$	9483.14	+	94447.4i	0.0439648	+	0.437867i
$137$	−79955.0	−	79955.0i	−0.363952	−	0.363952i	0.501314	−	0.865266i	$-0.332850\pi$
$137$	−79955.0	−	79955.0i	−0.363952	−	0.363952i	−0.865266	+	0.501314i	$0.832850\pi$
$138$	−5924.80	+	11680.8i	−0.0264835	+	0.0522123i
$139$	83828.3	−	202380.i	0.368005	−	0.888443i	−0.626072	−	0.779765i	$-0.715338\pi$
$139$	83828.3	−	202380.i	0.368005	−	0.888443i	0.994077	−	0.108678i	$-0.0346616\pi$
$140$	−260770.	−	173765.i	−1.12445	−	0.749276i
$141$	284694.	+	273075.i	1.20595	+	1.15673i
$142$	−23919.5	−	78673.0i	−0.0995477	−	0.327420i
$143$		−	672081.i		−	2.74841i
$144$	233873.	+	84976.4i	0.939881	+	0.341501i
$145$		−	175167.i		−	0.691881i
$146$	−129794.	+	39462.3i	−0.503934	+	0.153215i
$147$	−39212.8	−	37612.4i	−0.149670	−	0.143561i
$148$	−154119.	+	30858.8i	−0.578366	+	0.115804i
$149$	17832.2	−	43050.7i	0.0658019	−	0.158860i	−0.887558	−	0.460696i	$-0.847600\pi$
$149$	17832.2	−	43050.7i	0.0658019	−	0.158860i	0.953360	+	0.301837i	$0.0975997\pi$
$150$	320354.	+	162492.i	1.16252	+	0.589664i
$151$	28.0049	+	28.0049i	9.99519e−5	+	9.99519e-5i	0.707157	−	0.707057i	$-0.249978\pi$
$151$	28.0049	+	28.0049i	9.99519e−5	+	9.99519e-5i	−0.707057	+	0.707157i	$0.749978\pi$
$152$	228025.	+	424666.i	0.800523	+	1.49086i
$153$	5306.56	+	127313.i	0.0183267	+	0.439687i
$154$	−494440.	−	48382.5i	−1.68001	−	0.164394i
$155$	35113.9	−	84772.5i	0.117395	−	0.283417i
$156$	95481.4	+	430126.i	0.314128	+	1.41509i
$157$	191100.	−	79156.3i	0.618745	−	0.256293i	−0.0512173	−	0.998688i	$-0.516310\pi$
$157$	191100.	−	79156.3i	0.618745	−	0.256293i	0.669963	+	0.742395i	$0.266310\pi$
$158$	−48102.1	−	25672.0i	−0.153293	−	0.0818121i
$159$	−170545.	−	388635.i	−0.534992	−	1.21913i
$160$	−469853.	+	144152.i	−1.45098	+	0.445164i
$161$			17142.9i			0.0521217i
$162$	306755.	+	132206.i	0.918341	+	0.395789i
$163$	21736.6	+	52476.9i	0.0640801	+	0.154703i	0.952676	−	0.303988i	$-0.0983184\pi$
$163$	21736.6	+	52476.9i	0.0640801	+	0.154703i	−0.888596	+	0.458691i	$0.848318\pi$
$164$	−18852.8	+	95409.5i	−0.0547350	+	0.277001i
$165$	1.00615e6	−	20959.7i	2.87709	−	0.0599344i
$166$	55727.6	−	569503.i	0.156964	−	1.60408i
$167$	213181.	+	213181.i	0.591503	+	0.591503i	0.938037	−	0.346534i	$-0.112642\pi$
$167$	213181.	+	213181.i	0.591503	+	0.591503i	−0.346534	+	0.938037i	$0.612642\pi$
$168$	323311.	−	39279.8i	0.883787	−	0.107373i
$169$	−289103.	+	289103.i	−0.778638	+	0.778638i
$170$	−159783.	−	194446.i	−0.424043	−	0.516032i
$171$	272297.	+	586968.i	0.712119	+	1.53506i
$172$	−215047.	+	43058.2i	−0.554258	+	0.110977i
$173$	−201022.	+	83266.1i	−0.510656	+	0.211521i	−0.623107	−	0.782137i	$-0.714130\pi$
$173$	−201022.	+	83266.1i	−0.510656	+	0.211521i	0.112451	+	0.993657i	$0.464130\pi$
$174$	118489.	+	138221.i	0.296692	+	0.346101i
$175$	470156.			1.16051
$176$	−549563.	+	552349.i	−1.33732	+	1.34410i
$177$	−147996.	−	337250.i	−0.355072	−	0.809130i
$178$	345102.	−	104924.i	0.816391	−	0.248213i
$179$	−97875.2	−	236292.i	−0.228318	−	0.551208i	0.767655	−	0.640863i	$-0.221424\pi$
$179$	−97875.2	−	236292.i	−0.228318	−	0.551208i	−0.995973	+	0.0896550i	$0.971424\pi$
$180$	−640951.	+	156356.i	−1.47450	+	0.359695i
$181$	109359.	+	45297.9i	0.248117	+	0.102774i	0.503276	−	0.864126i	$-0.332128\pi$
$181$	109359.	+	45297.9i	0.248117	+	0.102774i	−0.255159	+	0.966899i	$0.582128\pi$
$182$	366126.	+	445551.i	0.819317	+	0.997055i
$183$	14015.0	−	35934.3i	0.0309360	−	0.0793198i
$184$	20815.8	+	17017.1i	0.0453262	+	0.0370546i
$185$	294678.	−	294678.i	0.633022	−	0.633022i
$186$	29635.5	+	90645.2i	0.0628102	+	0.192116i
$187$	−368631.	−	152692.i	−0.770882	−	0.319310i
$188$	672758.	−	450754.i	1.38824	−	0.930133i
$189$	436351.	−	27301.2i	0.888548	−	0.0555940i
$190$	−1.12747e6	−	601731.i	−2.26580	−	1.20926i
$191$	474533.			0.941202			0.470601	−	0.882346i	$-0.344037\pi$
$191$	474533.			0.941202			0.470601	+	0.882346i	$0.344037\pi$
$192$	273245.	−	431575.i	0.534932	−	0.844895i
$193$	−920467.			−1.77875			−0.889375	−	0.457178i	$-0.848860\pi$
$193$	−920467.			−1.77875			−0.889375	+	0.457178i	$0.848860\pi$
$194$	−576963.	−	307924.i	−1.10064	−	0.587408i
$195$	−843057.	−	808649.i	−1.58771	−	1.52291i
$196$	−92663.5	+	62085.4i	−0.172293	+	0.115438i
$197$	622403.	+	257808.i	1.14263	+	0.473293i	0.872056	−	0.489406i	$-0.162786\pi$
$197$	622403.	+	257808.i	1.14263	+	0.473293i	0.270575	+	0.962699i	$0.412786\pi$
$198$	−779762.	+	697139.i	−1.41351	+	1.26374i
$199$	421719.	−	421719.i	0.754902	−	0.754902i	−0.220487	−	0.975390i	$-0.570765\pi$
$199$	421719.	−	421719.i	0.754902	−	0.754902i	0.975390	+	0.220487i	$0.0707648\pi$
$200$	466708.	−	570890.i	0.825032	−	1.00920i
$201$	−211028.	−	82304.6i	−0.368427	−	0.143692i
$202$	468343.	+	569942.i	0.807580	+	0.982771i
$203$	220151.	+	91189.4i	0.374956	+	0.155312i
$204$	257614.	+	45350.8i	0.433404	+	0.0762974i
$205$	−98677.8	−	238229.i	−0.163997	−	0.395923i
$206$	700664.	−	213028.i	1.15038	−	0.349759i
$207$	26561.8	+	24436.2i	0.0430856	+	0.0396376i
$208$	904454.	−	2287.00i	1.44953	−	0.00366528i
$209$	−2.02613e6			−3.20850
$210$	−655603.	+	562011.i	−1.02587	+	0.879421i
$211$	118988.	−	49286.5i	0.183991	−	0.0762117i	−0.288786	−	0.957394i	$-0.593252\pi$
$211$	118988.	−	49286.5i	0.183991	−	0.0762117i	0.472777	+	0.881182i	$0.343252\pi$
$212$	−854271.	+	171048.i	−1.30544	+	0.261384i
$213$	−226547.	+	4719.33i	−0.342144	+	0.00712741i
$214$	23362.9	+	28431.1i	0.0348732	+	0.0424384i
$215$	411173.	−	411173.i	0.606637	−	0.606637i
$216$	400000.	−	556943.i	0.583345	−	0.812224i
$217$	88263.0	+	88263.0i	0.127242	+	0.127242i
$218$	49785.5	−	508778.i	0.0709516	−	0.725082i
$219$	7785.93	+	373756.i	0.0109698	+	0.526596i
$220$	400471.	−	2.02669e6i	0.557846	−	2.82313i
$221$	177244.	+	427904.i	0.244112	+	0.589340i
$222$	−33194.7	+	431858.i	−0.0452050	+	0.588110i
$223$		−	129578.i		−	0.174490i	−0.996187	−	0.0872448i	$-0.972194\pi$
$223$		−	129578.i		−	0.174490i	0.996187	−	0.0872448i	$-0.0278062\pi$
$224$	63428.4	−	665559.i	0.0844624	−	0.886270i
$225$	670181.	−	728479.i	0.882543	−	0.959314i
$226$	−89233.2	−	47623.6i	−0.116213	−	0.0620228i
$227$	−351961.	+	145787.i	−0.453346	+	0.187782i	−0.597659	−	0.801750i	$-0.703903\pi$
$227$	−351961.	+	145787.i	−0.453346	+	0.187782i	0.144314	+	0.989532i	$0.453903\pi$
$228$	1.29671e6	−	287849.i	1.65198	−	0.366714i
$229$	−307475.	+	742309.i	−0.387454	+	0.935397i	0.603023	+	0.797724i	$0.293963\pi$
$229$	−307475.	+	742309.i	−0.387454	+	0.935397i	−0.990478	+	0.137674i	$0.956037\pi$
$230$	−70947.2	−	6942.41i	−0.0884333	−	0.00865348i
$231$	−497447.	+	1.27545e6i	−0.613362	+	1.57266i
$232$	329264.	−	176799.i	0.401628	−	0.215655i
$233$	−175319.	−	175319.i	−0.211562	−	0.211562i	0.593369	−	0.804931i	$-0.297798\pi$
$233$	−175319.	−	175319.i	−0.211562	−	0.211562i	−0.804931	+	0.593369i	$0.797798\pi$
$234$	1.21225e6	+	67817.5i	1.44727	+	0.0809659i
$235$	−821657.	+	1.98366e6i	−0.970557	+	2.34313i
$236$	−741319.	+	148432.i	−0.866414	+	0.173479i
$237$	−104007.	+	108433.i	−0.120280	+	0.125398i
$238$	327562.	−	99591.1i	0.374845	−	0.113967i
$239$			770499.i			0.872524i	0.899820	+	0.436262i	$0.143698\pi$
$239$			770499.i			0.872524i	−0.899820	+	0.436262i	$0.856302\pi$
$240$	31630.4	+	1.35396e6i	0.0354468	+	1.51732i
$241$		−	58479.8i		−	0.0648579i	−0.999474	−	0.0324290i	$-0.989676\pi$
$241$		−	58479.8i		−	0.0648579i	0.999474	−	0.0324290i	$-0.0103243\pi$
$242$	−687718.	−	2.26195e6i	−0.754870	−	2.48282i
$243$	579691.	−	715015.i	0.629769	−	0.776783i
$244$	−65889.5	−	43905.6i	−0.0708503	−	0.0472112i
$245$	113172.	−	273222.i	0.120455	−	0.290804i
$246$	239013.	+	121234.i	0.251816	+	0.127728i
$247$	1.66305e6	+	1.66305e6i	1.73446	+	1.73446i
$248$	194790.	−	19558.2i	0.201111	−	0.0201929i
$249$	−1.46908e6	−	572966.i	−1.50158	−	0.585640i
$250$	−44334.2	+	453068.i	−0.0448630	+	0.458473i
$251$	−712905.	+	1.72110e6i	−0.714245	+	1.72434i	−0.0251336	+	0.999684i	$0.508001\pi$
$251$	−712905.	+	1.72110e6i	−0.714245	+	1.72434i	−0.689111	+	0.724656i	$0.741999\pi$
$252$	137161.	−	886950.i	0.136060	−	0.879828i
$253$	−104414.	+	43249.6i	−0.102555	+	0.0424796i
$254$	539037.	−	1.01000e6i	0.524245	−	0.982286i
$255$	−635074.	+	278691.i	−0.611609	+	0.268394i
$256$	−745195.	−	737696.i	−0.710674	−	0.703522i
$257$		−	1.24383e6i		−	1.17470i	−0.809332	−	0.587352i	$-0.800170\pi$
$257$		−	1.24383e6i		−	1.17470i	0.809332	−	0.587352i	$-0.199830\pi$
$258$	−46317.6	+	602585.i	−0.0433208	+	0.563597i
$259$	216949.	+	523760.i	0.200959	+	0.485158i
$260$	−1.99222e6	+	1.33481e6i	−1.82770	+	1.22457i
$261$	455105.	−	211125.i	0.413533	−	0.191840i
$262$	1.19467e6	+	116902.i	1.07521	+	0.105213i
$263$	−1.17303e6	−	1.17303e6i	−1.04573	−	1.04573i	−0.998903	−	0.0468299i	$-0.985088\pi$
$263$	−1.17303e6	−	1.17303e6i	−1.04573	−	1.04573i	−0.0468299	−	0.998903i	$-0.514912\pi$
$264$	1.05493e6	+	1.87013e6i	0.931562	+	1.65143i
$265$	1.63338e6	−	1.63338e6i	1.42880	−	1.42880i
$266$	1.34321e6	−	1.10376e6i	1.16396	−	0.956471i
$267$	−20701.6	−	993758.i	−0.0177715	−	0.853105i
$268$	−257841.	+	386944.i	−0.219288	+	0.329087i
$269$	456593.	−	189127.i	0.384724	−	0.159358i	−0.181935	−	0.983311i	$-0.558236\pi$
$269$	456593.	−	189127.i	0.384724	−	0.159358i	0.566658	+	0.823953i	$0.308236\pi$
$270$	−63722.1	+	1.81693e6i	−0.0531962	+	1.51680i
$271$	−1.89928e6			−1.57097			−0.785483	−	0.618884i	$-0.787585\pi$
$271$	−1.89928e6			−1.57097			−0.785483	+	0.618884i	$0.787585\pi$
$272$	204231.	−	496606.i	0.167379	−	0.406995i
$273$	1.45520e6	−	638589.i	1.18173	−	0.518579i
$274$	186065.	+	611980.i	0.149723	+	0.492448i
$275$	1.18615e6	+	2.86363e6i	0.945821	+	2.28341i
$276$	60679.5	−	42513.3i	0.0479479	−	0.0335932i
$277$	−411783.	−	170566.i	−0.322455	−	0.133565i	0.215584	−	0.976485i	$-0.430835\pi$
$277$	−411783.	−	170566.i	−0.322455	−	0.133565i	−0.538039	+	0.842920i	$0.680835\pi$
$278$	−957384.	+	786718.i	−0.742975	+	0.610530i
$279$	262572.	−	10944.3i	0.201947	−	0.00841741i
$280$	838580.	+	1.56174e6i	0.639219	+	1.19046i
$281$	−1.42515e6	+	1.42515e6i	−1.07670	+	1.07670i	−0.0798966	+	0.996803i	$0.525459\pi$
$281$	−1.42515e6	+	1.42515e6i	−1.07670	+	1.07670i	−0.996803	+	0.0798966i	$0.974541\pi$
$282$	−693463.	−	2.12108e6i	−0.519279	−	1.58830i
$283$	−2.06753e6	−	856400.i	−1.53457	−	0.635639i	−0.554124	−	0.832434i	$-0.686947\pi$
$283$	−2.06753e6	−	856400.i	−1.53457	−	0.635639i	−0.980445	+	0.196795i	$0.936947\pi$
$284$	−90170.7	+	456333.i	−0.0663391	+	0.335727i
$285$	−2.43784e6	+	2.54157e6i	−1.77784	+	1.85349i
$286$	−1.79007e6	+	3.35408e6i	−1.29406	+	2.42470i
$287$	350779.			0.251379
$288$	−940829.	−	1.04699e6i	−0.668389	−	0.743812i
$289$	−1.14489e6			−0.806339
$290$	−466551.	+	874184.i	−0.325764	+	0.610390i
$291$	−1.24752e6	+	1.30060e6i	−0.863605	+	0.900351i
$292$	752856.	+	148763.i	0.516719	+	0.102103i
$293$	695017.	+	287885.i	0.472962	+	0.195907i	0.606416	−	0.795148i	$-0.292607\pi$
$293$	695017.	+	287885.i	0.472962	+	0.195907i	−0.133454	+	0.991055i	$0.542607\pi$
$294$	95515.4	+	292150.i	0.0644473	+	0.197123i
$295$	1.41741e6	−	1.41741e6i	0.948292	−	0.948292i
$296$	851336.	+	256488.i	0.564770	+	0.170152i
$297$	1.26715e6	+	2.58885e6i	0.833561	+	1.70300i
$298$	−203657.	+	167353.i	−0.132849	+	0.109167i
$299$	121203.	+	50203.8i	0.0784032	+	0.0324757i
$300$	−1.16596e6	−	1.66418e6i	−0.747963	−	1.06757i
$301$	302715.	+	730818.i	0.192583	+	0.464936i
$302$	−65.1705	−	214.351i	−4.11182e−5	−	0.000135241i
$303$	1.86147e6	−	816873.i	1.16480	−	0.511150i
$304$	−6894.63	−	2.72667e6i	−0.00427885	−	1.69219i
$305$	209930.			0.129219
$306$	312611.	−	649500.i	0.190854	−	0.396529i
$307$	1.73162e6	−	717261.i	1.04859	−	0.434341i	0.209203	−	0.977872i	$-0.432913\pi$
$307$	1.73162e6	−	717261.i	1.04859	−	0.434341i	0.839389	+	0.543531i	$0.182913\pi$
$308$	2.33868e6	+	1.55838e6i	1.40473	+	0.936046i
$309$	−42030.5	−	2.01763e6i	−0.0250420	−	1.20212i
$310$	−401028.	+	329540.i	−0.237012	+	0.194762i
$311$	563331.	−	563331.i	0.330265	−	0.330265i	−0.522422	−	0.852687i	$-0.674971\pi$
$311$	563331.	−	563331.i	0.330265	−	0.330265i	0.852687	+	0.522422i	$0.174971\pi$
$312$	669120.	−	2.40089e6i	0.389150	−	1.39632i
$313$	1.37565e6	+	1.37565e6i	0.793684	+	0.793684i	0.982091	−	0.188407i	$-0.0603325\pi$
$313$	1.37565e6	+	1.37565e6i	0.793684	+	0.793684i	−0.188407	+	0.982091i	$0.560332\pi$
$314$	−1.16453e6	−	113953.i	−0.666542	−	0.0652232i
$315$	1.00139e6	+	2.15862e6i	0.568628	+	1.22575i
$316$	171681.	+	256237.i	0.0967174	+	0.144352i
$317$	−718574.	−	1.73479e6i	−0.401627	−	0.969614i	−0.987271	−	0.159046i	$-0.949158\pi$
$317$	−718574.	−	1.73479e6i	−0.401627	−	0.969614i	0.585644	−	0.810568i	$-0.300842\pi$
$318$	−183996.	+	2.39376e6i	−0.102033	+	1.32743i
$319$			1.57095e6i			0.864345i
$320$	2.72878e6	+	532038.i	1.48968	+	0.290447i
$321$	92857.9	−	40749.0i	0.0502987	−	0.0220727i
$322$	45659.5	−	85552.9i	0.0245409	−	0.0459828i
$323$	1.29001e6	−	534338.i	0.687996	−	0.284977i
$324$	−1.17876e6	−	1.47682e6i	−0.623825	−	0.781564i
$325$	1.37688e6	−	3.32408e6i	0.723081	−	1.74567i
$326$	31292.0	−	319785.i	0.0163076	−	0.166653i
$327$	−1.31244e6	−	511872.i	−0.678749	−	0.264723i
$328$	348206.	−	425935.i	0.178711	−	0.218605i
$329$	−2.06533e6	−	2.06533e6i	−1.05196	−	1.05196i
$330$	−5.07711e6	−	2.57525e6i	−2.56644	−	1.30177i
$331$	329887.	−	796418.i	0.165499	−	0.399550i	−0.819272	−	0.573405i	$-0.805622\pi$
$331$	329887.	−	796418.i	0.165499	−	0.399550i	0.984771	+	0.173855i	$0.0556223\pi$
$332$	−1.79497e6	+	2.69372e6i	−0.893739	+	1.34124i
$333$	1.12078e6	+	410441.i	0.553874	+	0.202834i
$334$	−496097.	−	1.63170e6i	−0.243333	−	0.800338i
$335$		−	1.23284e6i		−	0.600198i
$336$	−1.71813e6	−	665100.i	−0.830250	−	0.321395i
$337$			146197.i			0.0701236i	0.999385	+	0.0350618i	$0.0111628\pi$
$337$			146197.i			0.0701236i	−0.999385	+	0.0350618i	$0.988837\pi$
$338$	2.21281e6	−	672776.i	1.05354	−	0.320316i
$339$	−192942.	+	201151.i	−0.0911857	+	0.0950656i
$340$	279512.	+	1.39598e6i	0.131131	+	0.654909i
$341$	−314914.	+	760270.i	−0.146658	+	0.354064i
$342$	204450.	−	3.65457e6i	0.0945197	−	1.68955i
$343$	1.65614e6	+	1.65614e6i	0.760085	+	0.760085i
$344$	1.18789e6	+	357885.i	0.541230	+	0.163060i
$345$	−71378.7	+	183014.i	−0.0322865	+	0.0827823i
$346$	1.22499e6	+	119870.i	0.550103	+	0.0538293i
$347$	1.43619e6	−	3.46727e6i	0.640308	−	1.54584i	−0.185957	−	0.982558i	$-0.559539\pi$
$347$	1.43619e6	−	3.46727e6i	0.640308	−	1.54584i	0.826265	−	0.563282i	$-0.190461\pi$
$348$	−223183.	−	1.00540e6i	−0.0987900	−	0.445031i
$349$	−2.81710e6	+	1.16688e6i	−1.23805	+	0.512818i	−0.903105	−	0.429419i	$-0.858718\pi$
$349$	−2.81710e6	+	1.16688e6i	−1.23805	+	0.512818i	−0.334946	+	0.942237i	$0.608718\pi$
$350$	−2.34636e6	−	1.25225e6i	−1.02382	−	0.546411i
$351$	1.08485e6	−	3.16502e6i	0.470005	−	1.37122i
$352$	4.21381e6	−	1.29280e6i	1.81267	−	0.556129i
$353$		−	836601.i		−	0.357340i	−0.983909	−	0.178670i	$-0.942821\pi$
$353$		−	836601.i		−	0.357340i	0.983909	−	0.178670i	$-0.0571795\pi$
$354$	−159668.	+	2.07726e6i	−0.0677189	+	0.881012i
$355$	−471965.	−	1.13942e6i	−0.198765	−	0.479860i
$356$	−2.00172e6	−	395538.i	−0.837104	−	0.165410i
$357$	−19649.4	−	943249.i	−0.00815978	−	0.391702i
$358$	−140901.	+	1.43992e6i	−0.0581040	+	0.593788i
$359$	1.32566e6	+	1.32566e6i	0.542868	+	0.542868i	0.924369	−	0.381500i	$-0.124592\pi$
$359$	1.32566e6	+	1.32566e6i	0.542868	+	0.542868i	−0.381500	+	0.924369i	$0.624592\pi$
$360$	3.61517e6	+	926844.i	1.47019	+	0.376921i
$361$	3.26276e6	−	3.26276e6i	1.31770	−	1.31770i
$362$	−425114.	−	517336.i	−0.170504	−	0.207492i
$363$	−6.51353e6	+	135687.i	−2.59448	+	0.0540471i
$364$	−640471.	−	3.19872e6i	−0.253365	−	1.26539i
$365$	−1.87982e6	+	778645.i	−0.738555	+	0.305920i
$366$	−165653.	+	142005.i	−0.0646392	+	0.0554115i
$367$	−1.14080e6			−0.442125			−0.221063	−	0.975260i	$-0.570953\pi$
$367$	−1.14080e6			−0.442125			−0.221063	+	0.975260i	$0.570953\pi$
$368$	−58558.5	−	140368.i	−0.0225409	−	0.0540316i
$369$	500015.	−	543511.i	0.191169	−	0.207798i
$370$	−2.25548e6	+	685751.i	−0.856516	+	0.260413i
$371$	1.20253e6	+	2.90316e6i	0.453587	+	1.09506i
$372$	93532.2	−	531306.i	0.0350432	−	0.199061i
$373$	−2.59834e6	−	1.07627e6i	−0.966994	−	0.400542i	−0.157402	−	0.987535i	$-0.550312\pi$
$373$	−2.59834e6	−	1.07627e6i	−0.966994	−	0.400542i	−0.809592	+	0.586993i	$0.800312\pi$
$374$	1.43299e6	+	1.74386e6i	0.529743	+	0.644663i
$375$	1.16873e6	+	455824.i	0.429176	+	0.167386i
$376$	−4.55803e6	+	457656.i	−1.66267	+	0.166944i
$377$	1.28945e6	−	1.28945e6i	0.467251	−	0.467251i
$378$	−2.25036e6	−	1.02596e6i	−0.810070	−	0.369317i
$379$	619182.	+	256474.i	0.221422	+	0.0917160i	0.490637	−	0.871364i	$-0.336764\pi$
$379$	619182.	+	256474.i	0.221422	+	0.0917160i	−0.269215	+	0.963080i	$0.586764\pi$
$380$	4.02406e6	+	6.00598e6i	1.42957	+	2.13366i
$381$	−2.27677e6	−	2.18385e6i	−0.803538	−	0.770743i
$382$	−2.36820e6	−	1.26390e6i	−0.830346	−	0.443155i
$383$	3.14461e6			1.09539			0.547696	−	0.836678i	$-0.315505\pi$
$383$	3.14461e6			1.09539			0.547696	+	0.836678i	$0.315505\pi$
$384$	−2.51314e6	+	1.42603e6i	−0.869737	+	0.493516i
$385$	−7.45125e6			−2.56199
$386$	4.59367e6	+	2.45163e6i	1.56925	+	0.837505i
$387$	1.56386e6	+	572701.i	0.530787	+	0.194379i
$388$	2.05924e6	+	3.07345e6i	0.694427	+	1.03644i
$389$	1.00181e6	+	414961.i	0.335667	+	0.139038i	0.544150	−	0.838988i	$-0.316852\pi$
$389$	1.00181e6	+	414961.i	0.335667	+	0.139038i	−0.208482	+	0.978026i	$0.566852\pi$
$390$	2.05354e6	+	6.28109e6i	0.683661	+	2.09109i
$391$	55072.7	−	55072.7i	0.0182178	−	0.0182178i
$392$	627808.	−	63036.0i	0.206353	−	0.0207192i
$393$	1.20193e6	−	3.08175e6i	0.392554	−	1.00651i
$394$	−2.41949e6	−	2.94436e6i	−0.785206	−	0.955544i
$395$	−755525.	−	312949.i	−0.243644	−	0.100921i
$396$	5.74827e6	−	1.40226e6i	1.84204	−	0.449355i
$397$	176842.	+	426935.i	0.0563132	+	0.135952i	0.949532	−	0.313670i	$-0.101559\pi$
$397$	176842.	+	426935.i	0.0563132	+	0.135952i	−0.893219	+	0.449622i	$0.851559\pi$
$398$	−3.22786e6	+	981390.i	−1.02143	+	0.310552i
$399$	−1.92516e6	−	4.38701e6i	−0.605389	−	1.37955i
$400$	−3.84970e6	+	1.60601e6i	−1.20303	+	0.501879i
$401$	1.88679e6			0.585954			0.292977	−	0.956120i	$-0.405354\pi$
$401$	1.88679e6			0.585954			0.292977	+	0.956120i	$0.405354\pi$
$402$	833940.	+	972816.i	0.257377	+	0.300238i
$403$	882515.	−	365550.i	0.270682	−	0.112120i
$404$	−819281.	−	4.09176e6i	−0.249735	−	1.24726i
$405$	4.77208e6	+	1.52539e6i	1.44567	+	0.462109i
$406$	−855801.	−	1.04145e6i	−0.257666	−	0.313563i
$407$	−2.64278e6	+	2.64278e6i	−0.790815	+	0.790815i
$408$	−1.16485e6	−	912473.i	−0.346434	−	0.271375i
$409$	613890.	+	613890.i	0.181460	+	0.181460i	0.791992	−	0.610531i	$-0.209044\pi$
$409$	613890.	+	613890.i	0.181460	+	0.181460i	−0.610531	+	0.791992i	$0.709044\pi$
$410$	−142056.	+	1.45173e6i	−0.0417350	+	0.426507i
$411$	1.76226e6	−	36710.6i	0.514594	−	0.0107198i
$412$	−4.06412e6	−	803063.i	−1.17957	−	0.233081i
$413$	1.04353e6	+	2.51931e6i	0.301044	+	0.726785i
$414$	−67474.1	−	192697.i	−0.0193480	−	0.0552554i
$415$		−	8.58245e6i		−	2.44619i
$416$	−4.51985e6	−	2.39757e6i	−1.28053	−	0.679263i
$417$	1.37218e6	+	3.12688e6i	0.386429	+	0.880586i
$418$	1.01116e7	+	5.39653e6i	2.83060	+	1.51069i
$419$	1.52028e6	−	629721.i	0.423047	−	0.175232i	−0.160995	−	0.986955i	$-0.551470\pi$
$419$	1.52028e6	−	629721.i	0.423047	−	0.175232i	0.584042	+	0.811723i	$0.301470\pi$
$420$	4.76874e6	−	1.05859e6i	1.31911	−	0.292822i
$421$	640736.	−	1.54687e6i	0.176187	−	0.425353i	−0.810974	−	0.585082i	$-0.801062\pi$
$421$	640736.	−	1.54687e6i	0.176187	−	0.425353i	0.987161	+	0.159729i	$0.0510622\pi$
$422$	−725093.	−	70952.7i	−0.198204	−	0.0193949i
$423$	−6.14412e6	+	256095.i	−1.66959	+	0.0695904i
$424$	4.71889e6	+	1.42169e6i	1.27475	+	0.384053i
$425$	−1.51041e6	−	1.51041e6i	−0.405624	−	0.405624i
$426$	1.14317e6	+	579848.i	0.305202	+	0.154807i
$427$	−109287.	+	263842.i	−0.0290067	+	0.0700284i
$428$	−40869.1	−	204114.i	−0.0107842	−	0.0538596i
$429$	7.56083e6	+	7.25225e6i	1.98347	+	1.90252i
$430$	−3.14714e6	+	956848.i	−0.820815	+	0.249558i
$431$		−	974674.i		−	0.252736i	−0.991983	−	0.126368i	$-0.959668\pi$
$431$		−	974674.i		−	0.252736i	0.991983	−	0.126368i	$-0.0403320\pi$
$432$	−3.47963e6	+	1.71408e6i	−0.897065	+	0.441898i
$433$			2.65720e6i			0.681089i	0.940228	+	0.340545i	$0.110611\pi$
$433$			2.65720e6i			0.681089i	−0.940228	+	0.340545i	$0.889389\pi$
$434$	−205398.	−	675569.i	−0.0523446	−	0.172165i
$435$	1.97060e6	+	1.89018e6i	0.499317	+	0.478938i
$436$	−1.60357e6	+	2.40650e6i	−0.403992	+	0.606274i
$437$	151350.	−	365391.i	0.0379121	−	0.0915280i
$438$	956630.	−	1.88600e6i	0.238264	−	0.469738i
$439$	2.85086e6	+	2.85086e6i	0.706016	+	0.706016i	0.965695	−	0.259679i	$-0.0836168\pi$
$439$	2.85086e6	+	2.85086e6i	0.706016	+	0.706016i	−0.259679	+	0.965695i	$0.583617\pi$
$440$	−7.39661e6	+	9.04773e6i	−1.82138	+	2.22796i
$441$	846271.	−	35273.6i	0.207211	−	0.00863682i
$442$	255159.	−	2.60757e6i	0.0621235	−	0.634864i
$443$	493353.	−	1.19106e6i	0.119440	−	0.288353i	−0.852841	−	0.522171i	$-0.825122\pi$
$443$	493353.	−	1.19106e6i	0.119440	−	0.288353i	0.972280	+	0.233819i	$0.0751222\pi$
$444$	1.31590e6	−	2.06681e6i	0.316786	−	0.497558i
$445$	4.99813e6	−	2.07030e6i	1.19649	−	0.495601i
$446$	−345127.	+	646671.i	−0.0821565	+	0.153938i
$447$	291893.	+	665158.i	0.0690962	+	0.157455i
$448$	−2.08924e6	+	3.15259e6i	−0.491805	+	0.742116i
$449$		−	181497.i		−	0.0424866i	−0.999774	−	0.0212433i	$-0.993238\pi$
$449$		−	181497.i		−	0.0424866i	0.999774	−	0.0212433i	$-0.00676247\pi$
$450$	−5.28487e6	+	1.85053e6i	−1.23028	+	0.430789i
$451$	884977.	+	2.13652e6i	0.204876	+	0.494614i
$452$	318482.	+	475339.i	0.0733227	+	0.109435i
$453$	−617.244	+	12.8582i	−0.000141323	+	2.94398e-6i
$454$	2.14479e6	+	209874.i	0.488365	+	0.0477881i
$455$	6.11602e6	+	6.11602e6i	1.38497	+	1.38497i
$456$	−7.23800e6	−	2.01720e6i	−1.63007	−	0.454294i
$457$	−4.07066e6	+	4.07066e6i	−0.911747	+	0.911747i	−0.996410	−	0.0846624i	$-0.973019\pi$
$457$	−4.07066e6	+	4.07066e6i	−0.911747	+	0.911747i	0.0846624	+	0.996410i	$0.473019\pi$
$458$	3.51159e6	−	2.88561e6i	0.782241	−	0.642797i
$459$	−1.48952e6	−	1.31410e6i	−0.330000	−	0.291137i
$460$	335577.	+	223612.i	0.0739431	+	0.0492721i
$461$	−3.33694e6	+	1.38220e6i	−0.731300	+	0.302914i	−0.717086	−	0.696985i	$-0.754525\pi$
$461$	−3.33694e6	+	1.38220e6i	−0.731300	+	0.302914i	−0.0142139	+	0.999899i	$0.504525\pi$
$462$	5.87967e6	−	5.04031e6i	1.28159	−	1.09863i
$463$	−4.31322e6			−0.935080			−0.467540	−	0.883972i	$-0.654860\pi$
$463$	−4.31322e6			−0.935080			−0.467540	+	0.883972i	$0.654860\pi$
$464$	−2.11412e6	+	5345.74i	−0.455862	+	0.00115269i
$465$	574776.	+	1.30979e6i	0.123272	+	0.280911i
$466$	407987.	+	1.34190e6i	0.0870325	+	0.286256i
$467$	−1.97556e6	−	4.76941e6i	−0.419177	−	1.01198i	−0.982587	−	0.185804i	$-0.940511\pi$
$467$	−1.97556e6	−	4.76941e6i	−0.419177	−	1.01198i	0.563410	−	0.826177i	$-0.309489\pi$
$468$	−5.86919e6	−	3.56723e6i	−1.23869	−	0.752863i
$469$	1.54944e6	+	641800.i	0.325270	+	0.134731i
$470$	9.38396e6	−	7.71115e6i	1.95948	−	1.61018i
$471$	−1.17161e6	+	3.00401e6i	−0.243350	+	0.623949i
$472$	4.09496e6	+	1.23372e6i	0.846048	+	0.254895i
$473$	−3.68755e6	+	3.68755e6i	−0.757853	+	0.757853i
$474$	807865.	−	264123.i	0.165155	−	0.0539958i
$475$	−1.00211e7	−	4.15089e6i	−2.03790	−	0.844125i
$476$	−1.89999e6	−	375434.i	−0.384355	−	0.0759480i
$477$	6.21241e6	+	2.27504e6i	1.25016	+	0.457819i
$478$	2.05220e6	−	3.84524e6i	0.410818	−	0.769757i
$479$	−2.78621e6			−0.554849			−0.277424	−	0.960747i	$-0.589481\pi$
$479$	−2.78621e6			−0.554849			−0.277424	+	0.960747i	$0.589481\pi$
$480$	3.44837e6	−	6.84130e6i	0.683142	−	1.35530i
$481$	4.33841e6			0.855003
$482$	−155759.	+	291848.i	−0.0305377	+	0.0572189i
$483$	−192855.	−	184984.i	−0.0376152	−	0.0360800i
$484$	−2.59253e6	+	1.31202e7i	−0.503049	+	2.54581i
$485$	−9.06218e6	−	3.75368e6i	−1.74936	−	0.724607i
$486$	−4.79742e6	+	2.02435e6i	−0.921334	+	0.388773i
$487$	4.63188e6	−	4.63188e6i	0.884983	−	0.884983i	−0.109053	−	0.994036i	$-0.534782\pi$
$487$	4.63188e6	−	4.63188e6i	0.884983	−	0.884983i	0.994036	+	0.109053i	$0.0347818\pi$
$488$	211886.	+	394609.i	0.0402766	+	0.0750098i
$489$	−824913.	−	321730.i	−0.156004	−	0.0608442i
$490$	−1.29252e6	+	1.06211e6i	−0.243190	+	0.199838i
$491$	107039.	+	44337.2i	0.0200373	+	0.00829973i	0.392680	−	0.919675i	$-0.371548\pi$
$491$	107039.	+	44337.2i	0.0200373	+	0.00829973i	−0.372642	+	0.927975i	$0.621548\pi$
$492$	−869910.	−	1.24163e6i	−0.162017	−	0.231249i
$493$	−414298.	−	1.00020e6i	−0.0767707	−	0.185341i
$494$	−3.87012e6	−	1.27291e7i	−0.713522	−	2.34682i
$495$	−1.06213e7	+	1.15453e7i	−1.94834	+	2.11783i
$496$	−1.02421e6	−	421209.i	−0.186932	−	0.0768765i
$497$	1.67774e6			0.304672
$498$	5.80550e6	+	6.77228e6i	1.04898	+	1.22366i
$499$	−2.36750e6	+	980651.i	−0.425636	+	0.176304i	−0.585210	−	0.810882i	$-0.698988\pi$
$499$	−2.36750e6	+	980651.i	−0.425636	+	0.176304i	0.159574	+	0.987186i	$0.448988\pi$
$500$	1.42799e6	−	2.14299e6i	0.255446	−	0.383350i
$501$	−4.69864e6	+	97880.2i	−0.836330	+	0.0174221i
$502$	8.14192e6	−	6.69052e6i	1.44201	−	1.18495i
$503$	−2.98180e6	+	2.98180e6i	−0.525484	+	0.525484i	−0.919222	−	0.393739i	$-0.871181\pi$
$503$	−2.98180e6	+	2.98180e6i	−0.525484	+	0.525484i	0.393739	+	0.919222i	$0.371181\pi$
$504$	−3.04688e6	+	4.06107e6i	−0.534292	+	0.712139i
$505$	7.82352e6	+	7.82352e6i	1.36513	+	1.36513i
$506$	636279.	+	62262.0i	0.110477	+	0.0108105i
$507$	−132739.	−	6.37200e6i	−0.0229339	−	1.10092i
$508$	−5.38022e6	+	3.60479e6i	−0.924998	+	0.619757i
$509$	780028.	+	1.88315e6i	0.133449	+	0.322174i	0.976452	−	0.215734i	$-0.0692145\pi$
$509$	780028.	+	1.88315e6i	0.133449	+	0.322174i	−0.843003	+	0.537909i	$0.819214\pi$
$510$	3.91168e6	+	300671.i	0.665944	+	0.0511877i
$511$		−	2.76792e6i		−	0.468923i
$512$	1.75413e6	+	5.66634e6i	0.295724	+	0.955273i
$513$	−9.54161e6	−	3.27051e6i	−1.60077	−	0.548685i
$514$	−3.31290e6	+	6.20744e6i	−0.553097	+	1.03635i
$515$	1.01478e7	−	4.20334e6i	1.68598	−	0.698355i
$516$	1.83612e6	−	2.88388e6i	0.303582	−	0.476819i
$517$	7.36891e6	−	1.77901e7i	1.21249	−	2.92720i
$518$	312318.	−	3.19170e6i	0.0511415	−	0.522635i
$519$	1.23244e6	−	3.15998e6i	0.200839	−	0.514951i
$520$	1.34976e7	−	1.35525e6i	2.18901	−	0.219791i
$521$	7.65829e6	+	7.65829e6i	1.23605	+	1.23605i	0.961600	+	0.274454i	$0.0884973\pi$
$521$	7.65829e6	+	7.65829e6i	1.23605	+	1.23605i	0.274454	+	0.961600i	$0.411503\pi$
$522$	−2.83356e6	−	158520.i	−0.455152	−	0.0254629i
$523$	−1.07719e6	+	2.60056e6i	−0.172202	+	0.415732i	−0.986293	−	0.165006i	$-0.947236\pi$
$523$	−1.07719e6	+	2.60056e6i	−0.172202	+	0.415732i	0.814091	+	0.580737i	$0.197236\pi$
$524$	−5.65073e6	−	3.76537e6i	−0.899035	−	0.599073i
$525$	−5.07334e6	+	5.28920e6i	−0.803333	+	0.837514i
$526$	2.72978e6	+	8.97845e6i	0.430193	+	1.41494i
$527$		−	567103.i		−	0.0889478i
$528$	−283673.	−	1.21428e7i	−0.0442825	−	1.89554i
$529$			6.41428e6i			0.996572i
$530$	−1.25020e7	+	3.80107e6i	−1.93325	+	0.587781i
$531$	5.39101e6	+	1.97424e6i	0.829724	+	0.303853i
$532$	−9.64323e6	+	1.93084e6i	−1.47721	+	0.295778i
$533$	1.02727e6	−	2.48006e6i	0.156628	−	0.378133i
$534$	−2.54353e6	+	5.01457e6i	−0.385997	+	0.760993i
$535$	390269.	+	390269.i	0.0589495	+	0.0589495i
$536$	2.31739e6	−	1.24433e6i	0.348407	−	0.187078i
$537$	3.71440e6	+	1.44868e6i	0.555844	+	0.216788i
$538$	−2.78240e6	−	272267.i	−0.414442	−	0.0405545i
$539$	−1.01497e6	+	2.45035e6i	−0.150481	+	0.363293i
$540$	5.15735e6	−	8.89783e6i	0.761101	−	1.31311i
$541$	−8.51960e6	+	3.52893e6i	−1.25149	+	0.518382i	−0.907286	−	0.420514i	$-0.861850\pi$
$541$	−8.51960e6	+	3.52893e6i	−1.25149	+	0.518382i	−0.344200	+	0.938896i	$0.611850\pi$
$542$	9.47854e6	+	5.05868e6i	1.38594	+	0.739672i
$543$	−1.68966e6	+	741475.i	−0.245923	+	0.107919i
$544$	−2.34193e6	+	1.93439e6i	−0.339294	+	0.280251i
$545$		−	7.66732e6i		−	1.10574i
$546$	−8.96317e6	−	688953.i	−1.28671	−	0.0989026i
$547$	−4.75528e6	−	1.14803e7i	−0.679529	−	1.64053i	−0.764877	−	0.644176i	$-0.777200\pi$
$547$	−4.75528e6	−	1.14803e7i	−0.679529	−	1.64053i	0.0853482	−	0.996351i	$-0.472800\pi$
$548$	701418.	−	3.54971e6i	0.0997759	−	0.504943i
$549$	253025.	+	545425.i	0.0358288	+	0.0772332i
$550$	1.70758e6	−	1.74505e7i	0.240699	−	2.45980i
$551$	−3.88731e6	−	3.88731e6i	−0.545469	−	0.545469i
$552$	−416059.	+	50548.0i	−0.0581176	+	0.00706084i
$553$	786633.	−	786633.i	0.109385	−	0.109385i
$554$	1.60074e6	+	1.94800e6i	0.221588	+	0.269658i
$555$	135299.	+	6.49490e6i	0.0186450	+	0.895035i
$556$	6.87330e6	−	1.37622e6i	0.942928	−	0.188800i
$557$	−9.97377e6	+	4.13127e6i	−1.36214	+	0.564217i	−0.939646	−	0.342149i	$-0.888845\pi$
$557$	−9.97377e6	+	4.13127e6i	−1.36214	+	0.564217i	−0.422494	+	0.906366i	$0.638845\pi$
$558$	−1.33954e6	−	644733.i	−0.182125	−	0.0876586i
$559$	6.05351e6			0.819365
$560$	−25355.6	−	1.00275e7i	−0.00341667	−	1.35121i
$561$	5.69557e6	−	2.49940e6i	0.764064	−	0.335296i
$562$	1.09082e7	−	3.31649e6i	1.45684	−	0.442933i
$563$	−1.18762e6	−	2.86717e6i	−0.157909	−	0.381226i	0.825048	−	0.565063i	$-0.191148\pi$
$563$	−1.18762e6	−	2.86717e6i	−0.157909	−	0.381226i	−0.982957	+	0.183837i	$0.941148\pi$
$564$	−2.18863e6	+	1.24324e7i	−0.289718	+	1.64573i
$565$	−1.40156e6	−	580544.i	−0.184710	−	0.0765093i
$566$	8.03720e6	+	9.78075e6i	1.05454	+	1.28331i
$567$	−4.40141e6	+	5.20349e6i	−0.574956	+	0.679732i
$568$	1.66543e6	−	2.03720e6i	0.216599	−	0.264950i
$569$	−7.68808e6	+	7.68808e6i	−0.995490	+	0.995490i	−0.999990	−	0.00449949i	$-0.998568\pi$
$569$	−7.68808e6	+	7.68808e6i	−0.995490	+	0.995490i	0.00449949	+	0.999990i	$0.498568\pi$
$570$	1.89357e7	−	6.19082e6i	2.44114	−	0.798106i
$571$	588510.	+	243769.i	0.0755376	+	0.0312887i	0.420132	−	0.907463i	$-0.361984\pi$
$571$	588510.	+	243769.i	0.0755376	+	0.0312887i	−0.344595	+	0.938752i	$0.611984\pi$
$572$	1.78670e7	−	1.19710e7i	2.28329	−	1.52982i
$573$	−5.12056e6	+	5.33844e6i	−0.651525	+	0.679247i
$574$	−1.75059e6	−	934288.i	−0.221771	−	0.118359i
$575$	−605029.			−0.0763144
$576$	1.90665e6	+	7.73098e6i	0.239450	+	0.970909i
$577$	−4.35778e6			−0.544912			−0.272456	−	0.962168i	$-0.587836\pi$
$577$	−4.35778e6			−0.544912			−0.272456	+	0.962168i	$0.587836\pi$
$578$	5.71365e6	+	3.04937e6i	0.711368	+	0.379656i
$579$	9.93252e6	−	1.03551e7i	1.23130	−	1.28369i
$580$	4.65672e6	−	3.12004e6i	0.574791	−	0.385115i
$581$	1.07865e7	+	4.46791e6i	1.32568	+	0.549116i
$582$	9.68997e6	−	3.16803e6i	1.18581	−	0.387688i
$583$	−1.46487e7	+	1.46487e7i	−1.78496	+	1.78496i
$584$	−3.36096e6	−	2.74762e6i	−0.407786	−	0.333369i
$585$	1.81944e7	−	758367.i	2.19811	−	0.0916198i
$586$	−2.70177e6	−	3.28787e6i	−0.325015	−	0.395522i
$587$	8.75371e6	+	3.62590e6i	1.04857	+	0.434331i	0.839381	−	0.543544i	$-0.182918\pi$
$587$	8.75371e6	+	3.62590e6i	1.04857	+	0.434331i	0.209188	+	0.977875i	$0.432918\pi$
$588$	301455.	−	1.71240e6i	0.0359566	−	0.204250i
$589$	−1.10203e6	−	2.66053e6i	−0.130889	−	0.315995i
$590$	−1.08490e7	+	3.29849e6i	−1.28309	+	0.390108i
$591$	−9.61650e6	+	4.22002e6i	−1.13253	+	0.496988i
$592$	−3.56552e6	−	3.54753e6i	−0.418137	−	0.416028i
$593$	−1.04252e7			−1.21744			−0.608722	−	0.793384i	$-0.708317\pi$
$593$	−1.04252e7			−1.21744			−0.608722	+	0.793384i	$0.708317\pi$
$594$	571482.	−	1.62949e7i	0.0664563	−	1.89489i
$595$	4.74410e6	−	1.96507e6i	0.549366	−	0.227555i
$596$	1.46211e6	−	292753.i	0.168602	−	0.0337587i
$597$	193629.	+	9.29496e6i	0.0222348	+	1.06736i
$598$	−471156.	−	573365.i	−0.0538780	−	0.0655660i
$599$	5.10648e6	−	5.10648e6i	0.581507	−	0.581507i	−0.353811	−	0.935317i	$-0.615114\pi$
$599$	5.10648e6	−	5.10648e6i	0.581507	−	0.581507i	0.935317	+	0.353811i	$0.115114\pi$
$600$	1.38632e6	+	1.14107e7i	0.157212	+	1.29400i
$601$	1.29159e6	+	1.29159e6i	0.145860	+	0.145860i	0.776266	−	0.630406i	$-0.217111\pi$
$601$	1.29159e6	+	1.29159e6i	0.145860	+	0.145860i	−0.630406	+	0.776266i	$0.717111\pi$
$602$	435787.	−	4.45348e6i	0.0490098	−	0.500850i
$603$	3.20307e6	−	1.48592e6i	0.358735	−	0.166418i
$604$	−245.677	+	1243.31i	−2.74014e−5	+	0.000138672i
$605$	−1.35696e7	−	3.27600e7i	−1.50723	−	3.63878i
$606$	−1.14656e7	−	881298.i	−1.26827	−	0.0974858i
$607$		−	483682.i		−	0.0532829i	−0.999645	−	0.0266415i	$-0.991519\pi$
$607$		−	483682.i		−	0.0532829i	0.999645	−	0.0266415i	$-0.00848125\pi$
$608$	−7.22798e6	+	1.36260e7i	−0.792973	+	1.49489i
$609$	−3.40146e6	+	1.49267e6i	−0.371640	+	0.163087i
$610$	−1.04767e6	−	559142.i	−0.113999	−	0.0608412i
$611$	−2.06506e7	+	8.55377e6i	−2.23785	+	0.926947i
$612$	−3.29003e6	+	2.40875e6i	−0.355076	+	0.259964i
$613$	−3.26626e6	+	7.88544e6i	−0.351074	+	0.847568i	0.645414	+	0.763833i	$0.276685\pi$
$613$	−3.26626e6	+	7.88544e6i	−0.351074	+	0.847568i	−0.996488	+	0.0837352i	$0.973315\pi$
$614$	−1.05522e7	−	1.03257e6i	−1.12959	−	0.110534i
$615$	3.74486e6	+	1.46056e6i	0.399252	+	0.155715i
$616$	−7.52068e6	−	1.40062e7i	−0.798556	−	1.48720i
$617$	8.21785e6	+	8.21785e6i	0.869051	+	0.869051i	0.992367	−	0.123317i	$-0.0393531\pi$
$617$	8.21785e6	+	8.21785e6i	0.869051	+	0.869051i	−0.123317	+	0.992367i	$0.539353\pi$
$618$	−5.16415e6	+	1.01811e7i	−0.543910	+	1.07232i
$619$	−1.83176e6	+	4.42226e6i	−0.192151	+	0.463893i	−0.990365	−	0.138481i	$-0.955778\pi$
$619$	−1.83176e6	+	4.42226e6i	−0.192151	+	0.463893i	0.798214	+	0.602373i	$0.205778\pi$
$620$	2.87908e6	−	576470.i	0.300798	−	0.0602279i
$621$	−561526.	+	35133.1i	−0.0584307	+	0.00365584i
$622$	−4.31177e6	+	1.31094e6i	−0.446868	+	0.135864i
$623$			7.35946e6i			0.759672i
$624$	−9.73400e6	+	1.01997e7i	−1.00076	+	1.04864i
$625$		−	5.90191e6i		−	0.604356i
$626$	−3.20130e6	−	1.05293e7i	−0.326506	−	1.07390i
$627$	2.18634e7	−	2.27937e7i	2.22101	−	2.31551i
$628$	5.50818e6	+	3.67039e6i	0.557326	+	0.371375i
$629$	985655.	−	2.37958e6i	0.0993341	−	0.239814i
$630$	751882.	−	1.34400e7i	0.0754742	−	1.34911i
$631$	−1.16221e6	−	1.16221e6i	−0.116201	−	0.116201i	0.646615	−	0.762816i	$-0.276184\pi$
$631$	−1.16221e6	−	1.16221e6i	−0.116201	−	0.116201i	−0.762816	+	0.646615i	$0.776184\pi$
$632$	−174310.	−	1.73604e6i	−0.0173592	−	0.172889i
$633$	−729503.	+	1.87044e6i	−0.0723632	+	0.185539i
$634$	−1.03446e6	+	1.05715e7i	−0.102209	+	1.04451i
$635$	6.57100e6	−	1.58638e7i	0.646692	−	1.56125i
$636$	7.29395e6	−	1.14562e7i	0.715023	−	1.12305i
$637$	2.84435e6	−	1.17817e6i	0.277738	−	0.115043i
$638$	4.18419e6	−	7.83998e6i	0.406967	−	0.762541i
$639$	2.39152e6	−	2.59955e6i	0.231697	−	0.251852i
$640$	−1.22012e7	−	9.92321e6i	−1.17747	−	0.957640i
$641$			1.50860e7i			1.45020i	0.688641	+	0.725102i	$0.258208\pi$
$641$			1.50860e7i			1.45020i	−0.688641	+	0.725102i	$0.741792\pi$
$642$	−571949.	−	43962.8i	−0.0547671	−	0.00420967i
$643$	−3.34278e6	−	8.07018e6i	−0.318845	−	0.769761i	−0.999316	−	0.0369852i	$-0.988225\pi$
$643$	−3.34278e6	−	8.07018e6i	−0.318845	−	0.769761i	0.680471	−	0.732775i	$-0.261775\pi$
$644$	−455735.	+	305346.i	−0.0433010	+	0.0290120i
$645$	188787.	+	9.06252e6i	0.0178678	+	0.857728i
$646$	−7.86108e6	−	769232.i	−0.741141	−	0.0725230i
$647$	−538961.	−	538961.i	−0.0506170	−	0.0506170i	0.681345	−	0.731962i	$-0.261395\pi$
$647$	−538961.	−	538961.i	−0.0506170	−	0.0506170i	−0.731962	+	0.681345i	$0.761395\pi$
$648$	1.94924e6	+	1.05098e7i	0.182359	+	0.983232i
$649$	−1.27119e7	+	1.27119e7i	−1.18467	+	1.18467i
$650$	−1.57250e7	+	1.29218e7i	−1.45985	+	1.19961i
$651$	−1.94537e6	+	40525.2i	−0.179908	+	0.00374777i
$652$	−1.00790e6	+	1.51257e6i	−0.0928538	+	0.139347i
$653$	−5.83962e6	+	2.41885e6i	−0.535922	+	0.221986i	−0.634195	−	0.773173i	$-0.718668\pi$
$653$	−5.83962e6	+	2.41885e6i	−0.535922	+	0.221986i	0.0982726	+	0.995160i	$0.468668\pi$
$654$	5.18647e6	+	6.05018e6i	0.474163	+	0.553125i
$655$	1.80038e7			1.63968
$656$	−2.87222e6	+	1.19823e6i	−0.260590	+	0.108713i
$657$	−4.28872e6	−	3.94551e6i	−0.387628	−	0.356607i
$658$	4.80627e6	+	1.58082e7i	0.432756	+	1.42337i
$659$	−890551.	−	2.14998e6i	−0.0798814	−	0.192851i	0.878893	−	0.477019i	$-0.158283\pi$
$659$	−890551.	−	2.14998e6i	−0.0798814	−	0.192851i	−0.958774	+	0.284168i	$0.908283\pi$
$660$	1.84786e7	+	2.63747e7i	1.65124	+	2.35683i
$661$	2.45043e6	+	1.01500e6i	0.218142	+	0.0903574i	0.489078	−	0.872240i	$-0.337333\pi$
$661$	2.45043e6	+	1.01500e6i	0.218142	+	0.0903574i	−0.270936	+	0.962597i	$0.587333\pi$
$662$	−3.76756e6	+	3.09595e6i	−0.334130	+	0.274567i
$663$	−6.72646e6	−	2.62343e6i	−0.594296	−	0.231785i
$664$	1.61326e7	−	8.66241e6i	1.41998	−	0.762463i
$665$	1.84380e7	−	1.84380e7i	1.61681	−	1.61681i
$666$	−4.50016e6	−	5.03351e6i	−0.393136	−	0.439729i
$667$	−283305.	−	117349.i	−0.0246570	−	0.0102133i
$668$	−1.87016e6	+	9.46446e6i	−0.162158	+	0.820644i
$669$	1.45774e6	+	1.39824e6i	0.125926	+	0.120786i
$670$	−3.28363e6	+	6.15259e6i	−0.282597	+	0.529506i
$671$	−1.88273e6			−0.161429
$672$	6.80302e6	+	7.89543e6i	0.581137	+	0.674455i
$673$	1.10046e7			0.936566			0.468283	−	0.883579i	$-0.344873\pi$
$673$	1.10046e7			0.936566			0.468283	+	0.883579i	$0.344873\pi$
$674$	389391.	−	729609.i	0.0330169	−	0.0618643i
$675$	963552.	+	1.54003e7i	0.0813984	+	1.30098i
$676$	−1.28351e7	−	2.53620e6i	−1.08027	−	0.213460i
$677$	2.01046e7	+	8.32758e6i	1.68587	+	0.698308i	0.999579	−	0.0290228i	$-0.00923955\pi$
$677$	2.01046e7	+	8.32758e6i	1.68587	+	0.698308i	0.686287	+	0.727331i	$0.259240\pi$
$678$	1.49865e6	−	489968.i	0.125206	−	0.0409349i
$679$	9.43531e6	−	9.43531e6i	0.785383	−	0.785383i
$680$	2.32321e6	−	7.71122e6i	0.192671	−	0.639515i
$681$	2.15783e6	−	5.53266e6i	0.178299	−	0.457158i
$682$	3.59656e6	−	2.95543e6i	0.296092	−	0.243310i
$683$	−6.22108e6	−	2.57686e6i	−0.510286	−	0.211368i	0.112658	−	0.993634i	$-0.464064\pi$
$683$	−6.22108e6	−	2.57686e6i	−0.510286	−	0.211368i	−0.622944	+	0.782266i	$0.714064\pi$
$684$	−1.07542e7	+	1.76939e7i	−0.878893	+	1.44605i
$685$	3.67131e6	+	8.86333e6i	0.298947	+	0.721723i
$686$	−3.85404e6	−	1.26762e7i	−0.312684	−	1.02844i
$687$	−5.03301e6	−	1.14691e7i	−0.406852	−	0.927125i
$688$	−4.97507e6	−	4.94998e6i	−0.400708	−	0.398687i
$689$	2.40475e7			1.92984
$690$	843674.	−	723234.i	0.0674609	−	0.0578304i
$691$	8.04359e6	−	3.33176e6i	0.640848	−	0.265448i	−0.0385065	−	0.999258i	$-0.512260\pi$
$691$	8.04359e6	−	3.33176e6i	0.640848	−	0.265448i	0.679354	+	0.733811i	$0.262260\pi$
$692$	−5.79417e6	−	3.86095e6i	−0.459966	−	0.306499i
$693$	−8.98085e6	−	1.93593e7i	−0.710370	−	1.53129i
$694$	−1.64024e7	+	1.34785e7i	−1.29273	+	1.06229i
$695$	−1.31419e7	+	1.31419e7i	−1.03204	+	1.03204i
$696$	−1.56403e6	+	5.61197e6i	−0.122384	+	0.439129i
$697$	−1.12690e6	−	1.12690e6i	−0.0878628	−	0.0878628i
$698$	1.71669e7	+	1.67984e6i	1.33369	+	0.130506i
$699$	3.86413e6	−	80496.0i	0.299129	−	0.00623134i
$700$	8.37436e6	+	1.24989e7i	0.645962	+	0.964109i
$701$	−2.37514e6	−	5.73409e6i	−0.182555	−	0.440727i	0.805937	−	0.592002i	$-0.201662\pi$
$701$	−2.37514e6	−	5.73409e6i	−0.182555	−	0.440727i	−0.988492	+	0.151275i	$0.951662\pi$
$702$	−1.38440e7	+	1.29058e7i	−1.06027	+	0.988423i
$703$		−	1.30790e7i		−	0.998131i
$704$	−2.44727e7	−	4.77150e6i	−1.86102	−	0.362847i
$705$	−1.34496e7	−	3.06487e7i	−1.01915	−	2.32241i
$706$	−2.22826e6	+	4.17513e6i	−0.168250	+	0.315252i
$707$	−1.39055e7	+	5.75984e6i	−1.04625	+	0.433373i
$708$	6.32954e6	−	9.94145e6i	0.474558	−	0.745361i
$709$	9.52964e6	−	2.30066e7i	0.711969	−	1.71885i	0.0169474	−	0.999856i	$-0.494605\pi$
$709$	9.52964e6	−	2.30066e7i	0.711969	−	1.71885i	0.695022	−	0.718989i	$-0.255395\pi$
$710$	−679439.	+	6.94346e6i	−0.0505830	+	0.516928i
$711$	−97540.0	−	2.34014e6i	−0.00723617	−	0.173607i
$712$	8.93628e6	+	7.30549e6i	0.660627	+	0.540070i
$713$	−113583.	−	113583.i	−0.00836737	−	0.00836737i
$714$	−2.41425e6	+	4.75970e6i	−0.177230	+	0.349409i
$715$	−2.18214e7	+	5.26815e7i	−1.59631	+	3.85383i
$716$	4.53836e6	−	6.81076e6i	0.330839	−	0.496493i
$717$	−8.66802e6	−	8.31426e6i	−0.629683	−	0.603984i
$718$	−3.08495e6	−	1.01466e7i	−0.223325	−	0.734533i
$719$		−	1.73690e7i		−	1.25300i	−0.779420	−	0.626502i	$-0.784486\pi$
$719$		−	1.73690e7i		−	1.25300i	0.779420	−	0.626502i	$-0.215514\pi$
$720$	−1.55732e7	−	1.42544e7i	−1.11956	−	1.02475i
$721$			1.49420e7i			1.07046i
$722$	−2.49734e7	+	7.59283e6i	−1.78293	+	0.542077i
$723$	657891.	+	631040.i	0.0468067	+	0.0448964i
$724$	743661.	+	3.71409e6i	0.0527265	+	0.263333i
$725$	−3.21838e6	+	7.76986e6i	−0.227401	+	0.548995i
$726$	3.28677e7	+	1.66714e7i	2.31434	+	1.17390i
$727$	1.13829e7	+	1.13829e7i	0.798760	+	0.798760i	0.982900	−	0.184140i	$-0.0589499\pi$
$727$	1.13829e7	+	1.13829e7i	0.798760	+	0.798760i	−0.184140	+	0.982900i	$0.558950\pi$
$728$	−5.32338e6	+	1.76694e7i	−0.372271	+	1.23564i
$729$	1.78854e6	+	1.42370e7i	0.124646	+	0.992201i
$730$	1.14553e7	+	1.12094e6i	0.795607	+	0.0778526i
$731$	1.37531e6	−	3.32030e6i	0.0951937	−	0.229818i
$732$	1.20493e6	−	267476.i	0.0831159	−	0.0184504i
$733$	2.34457e7	−	9.71155e6i	1.61177	−	0.667619i	0.618756	−	0.785583i	$-0.287637\pi$
$733$	2.34457e7	−	9.71155e6i	1.61177	−	0.667619i	0.993018	+	0.117964i	$0.0376369\pi$
$734$	5.69327e6	+	3.03849e6i	0.390052	+	0.208170i
$735$	1.85251e6	+	4.22145e6i	0.126486	+	0.288233i
$736$	−81624.0	+	856486.i	−0.00555422	+	0.0582808i
$737$			1.10565e7i			0.749808i
$738$	−3.94299e6	+	1.38066e6i	−0.266492	+	0.0933139i
$739$	8.58725e6	+	2.07315e7i	0.578420	+	1.39643i	0.894231	+	0.447607i	$0.147724\pi$
$739$	8.58725e6	+	2.07315e7i	0.578420	+	1.39643i	−0.315811	+	0.948822i	$0.602276\pi$
$740$	1.30827e7	+	2.58511e6i	0.878247	+	0.173540i
$741$	−3.66548e7	+	763577.i	−2.45236	+	0.0510866i
$742$	1.73116e6	−	1.76914e7i	0.115432	−	1.17965i
$743$	1.44189e7	+	1.44189e7i	0.958211	+	0.958211i	0.999161	−	0.0409497i	$-0.0130383\pi$
$743$	1.44189e7	+	1.44189e7i	0.958211	+	0.958211i	−0.0409497	+	0.999161i	$0.513038\pi$
$744$	−1.88190e6	+	2.40241e6i	−0.124642	+	0.159116i
$745$	−2.79557e6	+	2.79557e6i	−0.184535	+	0.184535i
$746$	1.01006e7	+	1.22918e7i	0.664510	+	0.808665i
$747$	2.22983e7	−	1.03443e7i	1.46208	−	0.678263i
$748$	−2.50676e6	−	1.25196e7i	−0.163817	−	0.818157i
$749$	−693663.	+	287325.i	−0.0451798	+	0.0187141i
$750$	−4.61857e6	−	5.38770e6i	−0.299816	−	0.349744i
$751$	−1.31710e7			−0.852153			−0.426076	−	0.904687i	$-0.640105\pi$
$751$	−1.31710e7			−0.852153			−0.426076	+	0.904687i	$0.640105\pi$
$752$	2.39662e7	+	9.85619e6i	1.54545	+	0.635572i
$753$	−1.16694e7	−	2.65921e7i	−0.750003	−	1.70909i
$754$	−9.86949e6	+	3.00069e6i	−0.632217	+	0.192217i
$755$	−1285.91	−	3104.45i	−8.20997e−5	−	0.000198206i
$756$	8.49801e6	+	1.11139e7i	0.540770	+	0.707232i
$757$	−1.52951e7	−	6.33544e6i	−0.970092	−	0.401825i	−0.159346	−	0.987223i	$-0.550938\pi$
$757$	−1.52951e7	−	6.33544e6i	−0.970092	−	0.401825i	−0.810746	+	0.585398i	$0.800938\pi$
$758$	−2.40697e6	−	2.92913e6i	−0.152159	−	0.185168i
$759$	640149.	−	1.64134e6i	0.0403345	−	0.103417i
$760$	−4.08567e6	−	4.06913e7i	−0.256584	−	2.55545i
$761$	1.50107e7	−	1.50107e7i	0.939590	−	0.939590i	−0.0586863	−	0.998276i	$-0.518691\pi$
$761$	1.50107e7	−	1.50107e7i	0.939590	−	0.939590i	0.998276	+	0.0586863i	$0.0186912\pi$
$762$	5.54580e6	+	1.69628e7i	0.346001	+	1.05830i
$763$	9.63635e6	+	3.99151e6i	0.599241	+	0.248214i
$764$	8.45231e6	+	1.26152e7i	0.523893	+	0.781919i
$765$	3.71769e6	−	1.01518e7i	0.229678	−	0.627176i
$766$	−1.56934e7	−	8.37556e6i	−0.966375	−	0.515753i
$767$	2.08679e7			1.28083
$768$	1.63402e7	−	423073.i	0.999665	−	0.0258829i
$769$	−2.52669e7			−1.54076			−0.770381	−	0.637584i	$-0.779934\pi$
$769$	−2.52669e7			−1.54076			−0.770381	+	0.637584i	$0.779934\pi$
$770$	3.71861e7	+	1.98462e7i	2.26024	+	1.20628i
$771$	1.39930e7	+	1.34219e7i	0.847761	+	0.813161i
$772$	−1.63952e7	−	2.44702e7i	−0.990090	−	1.47773i
$773$	−1.96634e7	−	8.14483e6i	−1.18361	−	0.490267i	−0.297941	−	0.954584i	$-0.596300\pi$
$773$	−1.96634e7	−	8.14483e6i	−1.18361	−	0.490267i	−0.885669	+	0.464317i	$0.846300\pi$
$774$	−6.27920e6	−	7.02340e6i	−0.376749	−	0.421401i
$775$	−3.11510e6	+	3.11510e6i	−0.186302	+	0.186302i
$776$	−2.09077e6	−	2.08230e7i	−0.124638	−	1.24133i
$777$	−8.23328e6	−	3.21111e6i	−0.489238	−	0.190811i
$778$	−3.89436e6	−	4.73918e6i	−0.230668	−	0.280707i
$779$	−7.47666e6	−	3.09694e6i	−0.441432	−	0.182847i
$780$	6.48114e6	−	3.68158e7i	0.381430	−	2.16670i
$781$	4.23275e6	+	1.02188e7i	0.248310	+	0.599474i
$782$	−421530.	+	128161.i	−0.0246497	+	0.00749442i
$783$	−2.53579e6	+	7.39807e6i	−0.147812	+	0.431235i
$784$	−3.30102e6	−	1.35756e6i	−0.191804	−	0.0788803i
$785$	−1.75496e7			−1.01647
$786$	−1.42065e7	+	1.21784e7i	−0.820221	+	0.703129i
$787$	−2.53443e7	+	1.04979e7i	−1.45862	+	0.604181i	−0.964232	−	0.265059i	$-0.914609\pi$
$787$	−2.53443e7	+	1.04979e7i	−1.45862	+	0.604181i	−0.494390	+	0.869240i	$0.664609\pi$
$788$	4.23246e6	+	2.11383e7i	0.242816	+	1.21270i
$789$	2.58544e7	−	538588.i	1.47857	−	0.0308009i
$790$	2.93698e6	+	3.57411e6i	0.167430	+	0.203751i
$791$	1.45927e6	−	1.45927e6i	0.0829265	−	0.0829265i
$792$	−3.24221e7	−	8.31226e6i	−1.83666	−	0.470876i
$793$	1.54535e6	+	1.54535e6i	0.0872657	+	0.0872657i
$794$	254582.	−	2.60167e6i	0.0143310	−	0.146454i
$795$	749952.	+	3.60007e7i	0.0420839	+	2.02020i
$796$	1.87228e7	+	3.69960e6i	1.04734	+	0.206953i
$797$	5.20651e6	+	1.25696e7i	0.290336	+	0.700933i	0.999993	−	0.00361391i	$-0.00115035\pi$
$797$	5.20651e6	+	1.25696e7i	0.290336	+	0.700933i	−0.709658	+	0.704547i	$0.751150\pi$
$798$	−2.07699e6	+	2.70214e7i	−0.115459	+	1.50210i
$799$			1.32701e7i			0.735371i
$800$	2.34898e7	+	2.23860e6i	1.29764	+	0.123666i
$801$	1.14030e7	+	1.04905e7i	0.627971	+	0.577716i
$802$	−9.41620e6	−	5.02541e6i	−0.516939	−	0.275890i
$803$	1.68588e7	−	6.98316e6i	0.922654	−	0.382176i
$804$	−1.57078e6	−	7.07609e6i	−0.0856991	−	0.386059i
$805$	556601.	−	1.34375e6i	0.0302729	−	0.0730853i
$806$	−5.37790e6	−	526244.i	−0.291592	−	0.0285332i
$807$	−2.79932e6	+	7.17744e6i	−0.151311	+	0.387959i
$808$	−6.80959e6	+	2.26024e7i	−0.366938	+	1.21794i
$809$	−3.21739e6	−	3.21739e6i	−0.172835	−	0.172835i	0.615389	−	0.788224i	$-0.288999\pi$
$809$	−3.21739e6	−	3.21739e6i	−0.172835	−	0.172835i	−0.788224	+	0.615389i	$0.788999\pi$
$810$	−1.97527e7	−	2.03229e7i	−1.05782	−	1.08836i
$811$	1.21667e7	−	2.93730e7i	0.649563	−	1.56818i	−0.163844	−	0.986486i	$-0.552389\pi$
$811$	1.21667e7	−	2.93730e7i	0.649563	−	1.56818i	0.813406	−	0.581696i	$-0.197611\pi$
$812$	1.49707e6	+	7.47686e6i	0.0796804	+	0.397951i
$813$	2.04947e7	−	2.13667e7i	1.08746	−	1.13373i
$814$	2.02280e7	−	6.15006e6i	1.07002	−	0.325325i
$815$		−	4.81918e6i		−	0.254144i
$816$	3.38295e6	+	7.65632e6i	0.177857	+	0.402527i
$817$		−	1.82496e7i		−	0.956528i
$818$	−1.42859e6	−	4.69874e6i	−0.0746492	−	0.245527i
$819$	−8.51866e6	+	2.32617e7i	−0.443774	+	1.21180i
$820$	4.57558e6	−	6.86661e6i	0.237635	−	0.356622i
$821$	1.51527e6	−	3.65819e6i	0.0784572	−	0.189412i	−0.879784	−	0.475374i	$-0.842313\pi$
$821$	1.51527e6	−	3.65819e6i	0.0784572	−	0.189412i	0.958241	+	0.285961i	$0.0923129\pi$
$822$	−8.89248e6	−	4.51051e6i	−0.459032	−	0.232834i
$823$	6.52400e6	+	6.52400e6i	0.335749	+	0.335749i	0.854765	−	0.519016i	$-0.173701\pi$
$823$	6.52400e6	+	6.52400e6i	0.335749	+	0.335749i	−0.519016	+	0.854765i	$0.673701\pi$
$824$	1.81434e7	+	1.48324e7i	0.930894	+	0.761015i
$825$	−4.50150e7	−	1.75566e7i	−2.30262	−	0.898059i
$826$	1.50226e6	−	1.53522e7i	0.0766119	−	0.782927i
$827$	−9.65684e6	+	2.33137e7i	−0.490988	+	1.18535i	0.463229	+	0.886238i	$0.346691\pi$
$827$	−9.65684e6	+	2.33137e7i	−0.490988	+	1.18535i	−0.954218	+	0.299113i	$0.903309\pi$
$828$	−176508.	+	1.14139e6i	−0.00894723	+	0.0578572i
$829$	−2.94643e7	+	1.22045e7i	−1.48905	+	0.616785i	−0.971110	−	0.238632i	$-0.923301\pi$
$829$	−2.94643e7	+	1.22045e7i	−1.48905	+	0.616785i	−0.517940	+	0.855417i	$0.673301\pi$
$830$	−2.28591e7	+	4.28314e7i	−1.15176	+	2.15808i
$831$	6.36230e6	−	2.79198e6i	0.319603	−	0.140252i
$832$	1.61708e7	+	2.40037e7i	0.809886	+	1.20218i
$833$		−	1.82778e6i		−	0.0912663i
$834$	1.48040e6	−	1.92597e7i	0.0736992	−	0.958815i
$835$	−9.78868e6	−	2.36320e7i	−0.485856	−	1.17296i
$836$	−3.60892e7	−	5.38637e7i	−1.78592	−	2.66551i
$837$	−2.71022e6	+	3.07200e6i	−0.133718	+	0.151568i
$838$	−9.26433e6	−	906544.i	−0.455726	−	0.0445942i
$839$	−2.22614e7	−	2.22614e7i	−1.09181	−	1.09181i	−0.995335	−	0.0964766i	$-0.969243\pi$
$839$	−2.22614e7	−	2.22614e7i	−1.09181	−	1.09181i	−0.0964766	−	0.995335i	$-0.530757\pi$
$840$	−2.66183e7	−	7.41842e6i	−1.30161	−	0.362755i
$841$	1.14896e7	−	1.14896e7i	0.560162	−	0.560162i
$842$	−7.31769e6	+	6.01322e6i	−0.355708	+	0.292299i
$843$	−654345.	−	3.14112e7i	−0.0317130	−	1.52235i
$844$	3.42966e6	+	2.28536e6i	0.165728	+	0.110433i
$845$	3.20482e7	−	1.32748e7i	1.54405	−	0.639567i
$846$	3.13448e7	+	1.50866e7i	1.50571	+	0.724712i
$847$	4.82372e7			2.31033
$848$	−1.97634e7	−	1.96637e7i	−0.943783	−	0.939022i
$849$	3.19446e7	−	1.40183e7i	1.52100	−	0.667462i
$850$	3.51491e6	+	1.15608e7i	0.166865	+	0.548833i
$851$	−279184.	−	674010.i	−0.0132150	−	0.0319038i
$852$	−4.16068e6	−	5.93858e6i	−0.196366	−	0.280275i
$853$	−3.61221e7	−	1.49622e7i	−1.69981	−	0.704084i	−0.699860	−	0.714280i	$-0.746754\pi$
$853$	−3.61221e7	−	1.49622e7i	−1.69981	−	0.704084i	−0.999948	+	0.0101961i	$0.996754\pi$
$854$	1.24814e6	−	1.02564e6i	0.0585624	−	0.0481229i
$855$	−2.28626e6	−	5.48509e7i	−0.106957	−	2.56607i
$856$	−339690.	+	1.12750e6i	−0.0158452	+	0.0525936i
$857$	9.98293e6	−	9.98293e6i	0.464308	−	0.464308i	−0.435757	−	0.900065i	$-0.643519\pi$
$857$	9.98293e6	−	9.98293e6i	0.464308	−	0.464308i	0.900065	+	0.435757i	$0.143519\pi$
$858$	−1.84168e7	−	5.63310e7i	−0.854076	−	2.61234i
$859$	2.12790e7	+	8.81406e6i	0.983940	+	0.407561i	0.815884	−	0.578216i	$-0.196251\pi$
$859$	2.12790e7	+	8.81406e6i	0.983940	+	0.407561i	0.168057	+	0.985777i	$0.446251\pi$
$860$	1.82546e7	+	3.60708e6i	0.841641	+	0.166307i
$861$	−3.78516e6	+	3.94622e6i	−0.174011	+	0.181415i
$862$	−2.59601e6	+	4.86420e6i	−0.118998	+	0.222968i
$863$	−4.15721e7			−1.90009			−0.950046	−	0.312109i	$-0.898965\pi$
$863$	−4.15721e7			−1.90009			−0.950046	+	0.312109i	$0.898965\pi$
$864$	2.19308e7	+	713623.i	0.999471	+	0.0325226i
$865$	1.84608e7			0.838898
$866$	7.07736e6	−	1.32610e7i	0.320684	−	0.600870i
$867$	1.23542e7	−	1.28798e7i	0.558169	−	0.581919i
$868$	−774301.	+	3.91856e6i	−0.0348827	+	0.176533i
$869$	6.77581e6	+	2.80663e6i	0.304377	+	0.126077i
$870$	−4.80004e6	−	1.46817e7i	−0.215004	−	0.657626i
$871$	9.07525e6	−	9.07525e6i	0.405334	−	0.405334i
$872$	1.44124e7	−	7.73877e6i	0.641867	−	0.344652i
$873$	−1.16995e6	−	2.80689e7i	−0.0519555	−	1.24649i
$874$	−1.72853e6	+	1.42040e6i	−0.0765418	+	0.0628972i
$875$	−8.58120e6	−	3.55445e6i	−0.378903	−	0.156947i
$876$	−9.79744e6	+	6.86427e6i	−0.431372	+	0.302228i
$877$	−4.45536e6	−	1.07562e7i	−0.195607	−	0.472237i	0.795394	−	0.606093i	$-0.207264\pi$
$877$	−4.45536e6	−	1.07562e7i	−0.195607	−	0.472237i	−0.991001	+	0.133856i	$0.957264\pi$
$878$	−6.63428e6	−	2.18206e7i	−0.290441	−	0.955280i
$879$	−1.07384e7	+	4.71236e6i	−0.468779	+	0.205715i
$880$	6.10117e7	−	2.54528e7i	2.65587	−	1.10797i
$881$	1.25415e7			0.544387			0.272194	−	0.962242i	$-0.412251\pi$
$881$	1.25415e7			0.544387			0.272194	+	0.962242i	$0.412251\pi$
$882$	−4.31734e6	−	2.07798e6i	−0.186872	−	0.0899435i
$883$	3.57412e6	−	1.48045e6i	0.154265	−	0.0638987i	−0.304215	−	0.952603i	$-0.598394\pi$
$883$	3.57412e6	−	1.48045e6i	0.154265	−	0.0638987i	0.458480	+	0.888705i	$0.348394\pi$
$884$	−8.21858e6	+	1.23337e7i	−0.353726	+	0.530839i
$885$	650794.	+	3.12407e7i	0.0279309	+	1.34080i
$886$	−5.63446e6	+	4.63005e6i	−0.241139	+	0.198153i
$887$	−2.73725e7	+	2.73725e7i	−1.16817	+	1.16817i	−0.185529	+	0.982639i	$0.559400\pi$
$887$	−2.73725e7	+	2.73725e7i	−1.16817	+	1.16817i	−0.982639	+	0.185529i	$0.940600\pi$
$888$	−1.20720e7	+	6.80974e6i	−0.513745	+	0.289800i
$889$	1.65170e7	+	1.65170e7i	0.700932	+	0.700932i
$890$	−3.04578e7	−	2.98039e6i	−1.28891	−	0.126124i
$891$	−4.27977e7	−	1.36803e7i	−1.80604	−	0.577298i
$892$	3.44477e6	−	2.30803e6i	0.144960	−	0.0971246i
$893$	2.57872e7	+	6.22557e7i	1.08212	+	2.61247i
$894$	314914.	−	4.09698e6i	0.0131779	−	0.171443i
$895$			2.16997e7i			0.905517i
$896$	1.88233e7	−	1.01686e7i	0.783297	−	0.423148i
$897$	−1.87265e6	+	821779.i	−0.0777099	+	0.0341016i
$898$	−483410.	+	905774.i	−0.0200044	+	0.0374825i
$899$	−2.06283e6	+	854454.i	−0.0851266	+	0.0352606i
$900$	3.13034e7	+	4.84087e6i	1.28821	+	0.199213i
$901$	5.46341e6	−	1.31898e7i	0.224208	−	0.541287i
$902$	1.27401e6	−	1.30196e7i	0.0521383	−	0.532821i
$903$	−1.14881e7	−	4.48056e6i	−0.468846	−	0.182858i
$904$	−323358.	−	3.22049e6i	−0.0131602	−	0.131069i
$905$	−7.10140e6	−	7.10140e6i	−0.288219	−	0.288219i
$906$	3114.66	+	1579.84i	0.000126064	+	6.39430e-5i
$907$	1.21823e7	−	2.94107e7i	0.491713	−	1.18710i	−0.462135	−	0.886810i	$-0.652916\pi$
$907$	1.21823e7	−	2.94107e7i	0.491713	−	1.18710i	0.953848	−	0.300290i	$-0.0970835\pi$
$908$	−1.01448e7	−	6.75997e6i	−0.408345	−	0.272101i
$909$	−1.08969e7	+	2.97560e7i	−0.437416	+	1.19444i
$910$	−1.42327e7	−	4.68123e7i	−0.569748	−	1.87394i
$911$		−	6.10209e6i		−	0.243603i	−0.992554	−	0.121801i	$-0.961133\pi$
$911$		−	6.10209e6i		−	0.243603i	0.992554	−	0.121801i	$-0.0388671\pi$
$912$	3.07491e7	+	2.93452e7i	1.22418	+	1.16829i
$913$			7.69704e7i			3.05595i
$914$	3.11571e7	−	9.47290e6i	1.23365	−	0.375075i
$915$	−2.26530e6	+	2.36169e6i	−0.0894486	+	0.0932546i
$916$	−2.52106e7	+	5.04785e6i	−0.992762	+	0.198778i
$917$	−9.37252e6	+	2.26273e7i	−0.368072	+	0.888605i
$918$	3.93349e6	+	1.05254e7i	0.154053	+	0.412223i
$919$	1.86716e7	+	1.86716e7i	0.729275	+	0.729275i	0.970475	−	0.241200i	$-0.0775410\pi$
$919$	1.86716e7	+	1.86716e7i	0.729275	+	0.729275i	−0.241200	+	0.970475i	$0.577541\pi$
$920$	−1.07914e6	−	2.00976e6i	−0.0420348	−	0.0782841i
$921$	−1.06164e7	+	2.72203e7i	−0.412408	+	1.05741i
$922$	2.03347e7	+	1.98982e6i	0.787791	+	0.0770878i
$923$	4.91334e6	−	1.18618e7i	0.189833	−	0.458298i
$924$	−4.27677e7	+	9.49377e6i	−1.64792	+	0.365813i
$925$	−1.84853e7	+	7.65684e6i	−0.710348	+	0.294236i
$926$	2.15255e7	+	1.14881e7i	0.824945	+	0.440272i
$927$	2.31517e7	+	2.12989e7i	0.884878	+	0.814064i
$928$	1.05649e7	+	5.60420e6i	0.402713	+	0.213621i
$929$			3.03300e7i			1.15301i	0.817094	+	0.576505i	$0.195584\pi$
$929$			3.03300e7i			1.15301i	−0.817094	+	0.576505i	$0.804416\pi$
$930$	620107.	−	8.06750e6i	0.0235104	−	0.305866i
$931$	−3.55184e6	−	8.57490e6i	−0.134301	−	0.324231i
$932$	1.53801e6	−	7.78352e6i	0.0579989	−	0.293519i
$933$	258649.	+	1.24162e7i	0.00972760	+	0.466964i
$934$	−2.84400e6	+	2.90640e7i	−0.106675	+	1.09015i
$935$	2.39377e7	+	2.39377e7i	0.895475	+	0.895475i
$936$	1.97895e7	+	3.34349e7i	0.738320	+	1.24741i
$937$	−2.21579e7	+	2.21579e7i	−0.824480	+	0.824480i	−0.986747	−	0.162267i	$-0.948119\pi$
$937$	−2.21579e7	+	2.21579e7i	−0.824480	+	0.824480i	0.162267	+	0.986747i	$0.448119\pi$
$938$	−6.02321e6	−	7.32985e6i	−0.223522	−	0.272012i
$939$	−3.03202e7	+	631618.i	−1.12219	+	0.0233771i
$940$	−6.73698e7	+	1.34893e7i	−2.48683	+	0.497930i
$941$	2.09031e7	−	8.65836e6i	0.769550	−	0.318758i	0.0368601	−	0.999320i	$-0.488264\pi$
$941$	2.09031e7	−	8.65836e6i	0.769550	−	0.318758i	0.732690	+	0.680562i	$0.238264\pi$
$942$	1.38481e7	−	1.18712e7i	0.508468	−	0.435881i
$943$	−451406.			−0.0165306
$944$	−1.71503e7	−	1.70638e7i	−0.626385	−	0.623225i
$945$	−3.50900e7	−	1.20276e7i	−1.27822	−	0.438126i
$946$	2.82247e7	−	8.58135e6i	1.02542	−	0.311765i
$947$	1.14141e7	+	2.75561e7i	0.413587	+	0.998487i	0.984167	+	0.177245i	$0.0567184\pi$
$947$	1.14141e7	+	2.75561e7i	0.413587	+	0.998487i	−0.570580	+	0.821242i	$0.693282\pi$
$948$	−4.73520e6	−	833595.i	−0.171127	−	0.0301255i
$949$	−1.95696e7	−	8.10600e6i	−0.705370	−	0.292174i
$950$	3.89555e7	+	4.74063e7i	1.40043	+	1.70423i
$951$	2.72701e7	+	1.06358e7i	0.977769	+	0.381346i
$952$	8.48208e6	+	6.93419e6i	0.303326	+	0.247972i
$953$	−3.47949e6	+	3.47949e6i	−0.124103	+	0.124103i	−0.766431	−	0.642327i	$-0.777969\pi$
$953$	−3.47949e6	+	3.47949e6i	−0.124103	+	0.124103i	0.642327	+	0.766431i	$0.277969\pi$
$954$	−2.49440e7	−	2.79004e7i	−0.887352	−	0.992519i
$955$	−3.71965e7	−	1.54073e7i	−1.31976	−	0.546661i
$956$	−2.04834e7	+	1.37240e7i	−0.724864	+	0.485665i
$957$	−1.76731e7	−	1.69518e7i	−0.623781	−	0.598322i
$958$	1.39048e7	+	7.42098e6i	0.489498	+	0.261245i
$959$	−1.30507e7			−0.458236
$960$	−3.54310e7	+	2.49574e7i	−1.24081	+	0.874021i
$961$	2.74595e7			0.959146
$962$	−2.16512e7	−	1.15552e7i	−0.754300	−	0.402569i
$963$	−543585.	+	1.48435e6i	−0.0188887	+	0.0515788i
$964$	1.55466e6	−	1.04163e6i	0.0538818	−	0.0361013i
$965$	7.21514e7	+	2.98861e7i	2.49417	+	1.03312i
$966$	469761.	+	1.43684e6i	0.0161970	+	0.0495412i
$967$	1.07048e7	−	1.07048e7i	0.368139	−	0.368139i	−0.498659	−	0.866798i	$-0.666174\pi$
$967$	1.07048e7	−	1.07048e7i	0.368139	−	0.368139i	0.866798	+	0.498659i	$0.166174\pi$
$968$	4.78834e7	−	5.85723e7i	1.64247	−	2.00911i
$969$	−7.90889e6	+	2.02783e7i	−0.270586	+	0.693782i
$970$	3.52278e7	+	4.28699e7i	1.20214	+	1.46293i
$971$	1.31958e7	+	5.46587e6i	0.449145	+	0.186042i	0.595778	−	0.803149i	$-0.296844\pi$
$971$	1.31958e7	+	5.46587e6i	0.449145	+	0.186042i	−0.146633	+	0.989191i	$0.546844\pi$
$972$	2.93337e7	+	2.67506e6i	0.995868	+	0.0908170i
$973$	−9.67532e6	−	2.33583e7i	−0.327630	−	0.790968i
$974$	−3.54527e7	+	1.07789e7i	−1.19743	+	0.364064i
$975$	2.25379e7	+	5.13590e7i	0.759281	+	1.73023i
$976$	−6406.66	−	2.53368e6i	−0.000215282	−	0.0851389i
$977$	−5.16110e7			−1.72984			−0.864919	−	0.501911i	$-0.832631\pi$
$977$	−5.16110e7			−1.72984			−0.864919	+	0.501911i	$0.832631\pi$
$978$	3.25988e6	+	3.80275e6i	0.108982	+	0.127131i
$979$	−4.48250e7	+	1.85671e7i	−1.49473	+	0.619139i
$980$	9.27930e6	−	1.85797e6i	0.308638	−	0.0617978i
$981$	1.99207e7	−	9.24128e6i	0.660893	−	0.306591i
$982$	−416098.	−	506364.i	−0.0137695	−	0.0167565i
$983$	−9.86618e6	+	9.86618e6i	−0.325661	+	0.325661i	−0.850934	−	0.525273i	$-0.823963\pi$
$983$	−9.86618e6	+	9.86618e6i	−0.325661	+	0.325661i	0.525273	+	0.850934i	$0.323963\pi$
$984$	1.03432e6	+	8.51344e6i	0.0340538	+	0.280296i
$985$	−4.04168e7	−	4.04168e7i	−1.32731	−	1.32731i
$986$	−596422.	+	6.09507e6i	−0.0195372	+	0.199658i
$987$	4.55212e7	−	948279.i	1.48738	−	0.0309844i
$988$	−1.45894e7	+	7.38336e7i	−0.475494	+	2.40637i
$989$	−389554.	−	940466.i	−0.0126642	−	0.0305740i
$990$	8.37571e7	−	2.93280e7i	2.71602	−	0.951031i
$991$			1.92411e7i			0.622367i	0.950350	+	0.311184i	$0.100725\pi$
$991$			1.92411e7i			0.622367i	−0.950350	+	0.311184i	$0.899275\pi$
$992$	3.98951e6	+	4.83002e6i	0.128718	+	0.155837i
$993$	5.39988e6	+	1.23051e7i	0.173785	+	0.396016i
$994$	−8.37289e6	−	4.46860e6i	−0.268788	−	0.143452i
$995$	−4.67493e7	+	1.93642e7i	−1.49698	+	0.620071i
$996$	−1.09350e7	−	4.92604e7i	−0.349279	−	1.57344i
$997$	−1.42307e7	+	3.43559e7i	−0.453406	+	1.09462i	0.517612	+	0.855615i	$0.326821\pi$
$997$	−1.42307e7	+	3.43559e7i	−0.453406	+	1.09462i	−0.971018	+	0.239005i	$0.923179\pi$
$998$	1.44271e7	+	1.41174e6i	0.458516	+	0.0448672i
$999$	−1.67115e7	+	8.17970e6i	−0.529787	+	0.259313i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	96.6.o.a.11.11	✓	312
3.2	odd	2	inner	96.6.o.a.11.68	yes	312
32.3	odd	8	inner	96.6.o.a.35.68	yes	312
96.35	even	8	inner	96.6.o.a.35.11	yes	312

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
96.6.o.a.11.11	✓	312	1.1	even	1	trivial
96.6.o.a.11.68	yes	312	3.2	odd	2	inner
96.6.o.a.35.11	yes	312	96.35	even	8	inner
96.6.o.a.35.68	yes	312	32.3	odd	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
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+(-4.99058 - 2.66347i) q^{2} +(-10.7907 + 11.2499i) q^{3} +(17.8119 + 26.5845i) q^{4} +(-78.3856 - 32.4684i) q^{5} +(83.8158 - 27.4027i) q^{6} +(81.6131 - 81.6131i) q^{7} +(-18.0846 - 180.114i) q^{8} +(-10.1198 - 242.789i) q^{9} +(304.712 + 370.814i) q^{10} +(702.990 + 291.188i) q^{11} +(-491.276 - 86.4853i) q^{12} +(-338.008 - 816.025i) q^{13} +(-624.671 + 189.923i) q^{14} +(1211.10 - 531.471i) q^{15} +(-389.474 + 947.040i) q^{16} -524.376 q^{17} +(-596.158 + 1238.61i) q^{18} +(-2460.08 + 1019.00i) q^{19} +(-533.038 - 2662.17i) q^{20} +(37.4719 + 1798.80i) q^{21} +(-2732.76 - 3325.59i) q^{22} +(-105.025 + 105.025i) q^{23} +(2221.40 + 1740.11i) q^{24} +(2880.40 + 2880.40i) q^{25} +(-486.596 + 4972.72i) q^{26} +(2840.55 + 2506.03i) q^{27} +(3623.33 + 715.963i) q^{28} +(790.078 + 1907.42i) q^{29} +(-7459.68 - 573.387i) q^{30} +1081.48i q^{31} +(4466.12 - 3688.93i) q^{32} +(-10861.6 + 4766.42i) q^{33} +(2616.94 + 1396.66i) q^{34} +(-9047.13 + 3747.45i) q^{35} +(6274.18 - 4593.56i) q^{36} +(-1879.67 + 4537.93i) q^{37} +(14991.3 + 1466.95i) q^{38} +(12827.5 + 5002.96i) q^{39} +(-4430.43 + 14705.5i) q^{40} +(2149.04 + 2149.04i) q^{41} +(4604.05 - 9076.88i) q^{42} +(-2622.76 + 6331.90i) q^{43} +(4780.47 + 23875.2i) q^{44} +(-7089.73 + 19359.8i) q^{45} +(803.869 - 244.406i) q^{46} -25306.4i q^{47} +(-6451.38 - 14600.8i) q^{48} +3485.62i q^{49} +(-6703.02 - 22046.7i) q^{50} +(5658.41 - 5899.17i) q^{51} +(15673.1 - 23520.7i) q^{52} +(-10418.9 + 25153.4i) q^{53} +(-7501.27 - 20072.3i) q^{54} +(-45649.9 - 45649.9i) q^{55} +(-16175.6 - 13223.7i) q^{56} +(15082.5 - 38671.3i) q^{57} +(1137.39 - 11623.5i) q^{58} +(-9041.30 + 21827.6i) q^{59} +(35700.9 + 22730.1i) q^{60} +(-2285.96 + 946.877i) q^{61} +(2880.49 - 5397.22i) q^{62} +(-20640.7 - 18988.9i) q^{63} +(-32113.9 + 6514.57i) q^{64} +74939.2i q^{65} +(66901.0 + 5142.34i) q^{66} +(5560.64 + 13424.6i) q^{67} +(-9340.12 - 13940.3i) q^{68} +(-48.2214 - 2314.82i) q^{69} +(55131.7 + 5394.81i) q^{70} +(10278.6 + 10278.6i) q^{71} +(-43546.6 + 6213.45i) q^{72} +(16957.6 - 16957.6i) q^{73} +(21467.3 - 17640.5i) q^{74} +(-63485.8 + 1322.51i) q^{75} +(-70908.2 - 47249.8i) q^{76} +(81137.8 - 33608.4i) q^{77} +(-50691.7 - 59133.4i) q^{78} +9638.57 q^{79} +(61278.1 - 61588.7i) q^{80} +(-58844.2 + 4913.94i) q^{81} +(-5001.06 - 16448.8i) q^{82} +(38710.6 + 93455.6i) q^{83} +(-47152.9 + 33036.2i) q^{84} +(41103.6 + 17025.6i) q^{85} +(29953.9 - 24614.3i) q^{86} +(-29983.7 - 11694.2i) q^{87} +(39733.6 - 131884. i) q^{88} +(-45087.5 + 45087.5i) q^{89} +(86946.0 - 77733.2i) q^{90} +(-94184.2 - 39012.4i) q^{91} +(-4662.74 - 921.350i) q^{92} +(-12166.5 - 11670.0i) q^{93} +(-67402.8 + 126294. i) q^{94} +225920. q^{95} +(-6692.65 + 90049.6i) q^{96} +115610. q^{97} +(9283.84 - 17395.3i) q^{98} +(63583.2 - 173625. i) 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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