LMFDB - Embedded newform 97.6.k.a.2.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [97,6,Mod(2,97)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(97, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([17])) N = Newforms(chi, 6, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("97.2"); S:= CuspForms(chi, 6); N := Newforms(S);

Level:	$ N $	$=$	$ 97 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	97.k (of order $48$, degree $16$, 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:	$15.5572305219$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$40$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			2.7
Character	$\chi$	$=$	97.2
Dual form			97.6.k.a.49.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-7.92337 - 1.04313i) q^{2} +(5.32344 - 4.08482i) q^{3} +(30.7820 + 8.24802i) q^{4} +(42.3505 + 85.8783i) q^{5} +(-46.4406 + 26.8125i) q^{6} +(187.048 - 12.2598i) q^{7} +(0.975199 + 0.403941i) q^{8} +(-51.2397 + 191.229i) q^{9} +(-245.976 - 724.623i) q^{10} +(14.4808 + 109.992i) q^{11} +(197.558 - 81.8313i) q^{12} +(-428.086 + 211.109i) q^{13} +(-1494.84 - 97.9771i) q^{14} +(576.248 + 284.174i) q^{15} +(-890.455 - 514.105i) q^{16} +(14.7833 - 225.550i) q^{17} +(605.469 - 1461.73i) q^{18} +(780.528 - 1168.14i) q^{19} +(595.309 + 2992.82i) q^{20} +(945.663 - 829.324i) q^{21} -886.617i q^{22} +(276.925 + 315.772i) q^{23} +(6.84144 - 1.83316i) q^{24} +(-3679.14 + 4794.75i) q^{25} +(3612.10 - 1226.14i) q^{26} +(1132.35 + 2733.73i) q^{27} +(5858.85 + 1165.40i) q^{28} +(-2243.51 + 6609.17i) q^{29} +(-4269.40 - 2852.72i) q^{30} +(-3607.02 - 4700.76i) q^{31} +(6492.33 + 4981.74i) q^{32} +(526.388 + 526.388i) q^{33} +(-352.412 + 1771.70i) q^{34} +(8974.45 + 15544.2i) q^{35} +(-3154.53 + 5463.80i) q^{36} +(7468.46 + 6549.66i) q^{37} +(-7402.94 + 8441.43i) q^{38} +(-1416.55 + 2872.48i) q^{39} +(6.61042 + 100.856i) q^{40} +(-8040.07 - 2729.23i) q^{41} +(-8357.93 + 5584.59i) q^{42} +(-1020.72 - 3809.38i) q^{43} +(-461.473 + 3505.23i) q^{44} +(-18592.5 + 3698.28i) q^{45} +(-1864.78 - 2790.85i) q^{46} +(13361.0 - 13361.0i) q^{47} +(-6840.32 + 900.545i) q^{48} +(18173.6 - 2392.60i) q^{49} +(34152.8 - 34152.8i) q^{50} +(-842.634 - 1261.09i) q^{51} +(-14918.6 + 2967.49i) q^{52} +(-1773.18 + 13468.6i) q^{53} +(-6120.37 - 22841.5i) q^{54} +(-8832.71 + 5901.82i) q^{55} +(187.362 + 63.6007i) q^{56} +(-616.558 - 9406.86i) q^{57} +(24670.4 - 50026.6i) q^{58} +(12385.2 - 14122.6i) q^{59} +(15394.2 + 13500.4i) q^{60} +(-12193.8 + 21120.3i) q^{61} +(23676.2 + 41008.5i) q^{62} +(-7239.88 + 36397.3i) q^{63} +(-22978.8 - 22978.8i) q^{64} +(-36259.3 - 27822.8i) q^{65} +(-3621.67 - 4719.85i) q^{66} +(-6947.82 - 4642.38i) q^{67} +(2315.41 - 6820.96i) q^{68} +(2764.06 + 549.807i) q^{69} +(-54893.2 - 132524. i) q^{70} +(55751.3 - 18925.0i) q^{71} +(-127.214 + 165.789i) q^{72} +(-77228.3 + 20693.3i) q^{73} +(-52343.2 - 59686.0i) q^{74} +40553.3i q^{75} +(33661.1 - 29520.0i) q^{76} +(4057.09 + 20396.4i) q^{77} +(14220.2 - 21282.1i) q^{78} +(-18787.3 + 45356.6i) q^{79} +(6439.21 - 98243.4i) q^{80} +(-24467.9 - 14126.6i) q^{81} +(60857.5 + 30011.6i) q^{82} +(49685.4 + 3256.55i) q^{83} +(35949.7 - 17728.4i) q^{84} +(19996.0 - 8282.60i) q^{85} +(4113.86 + 31247.9i) q^{86} +(15054.1 + 44347.9i) q^{87} +(-30.3088 + 113.114i) q^{88} +(-45060.6 - 18664.7i) q^{89} +(151173. - 9908.40i) q^{90} +(-77484.7 + 44735.8i) q^{91} +(5919.81 + 12004.2i) q^{92} +(-38403.5 - 10290.2i) q^{93} +(-119801. + 91926.6i) q^{94} +(133374. + 17559.0i) q^{95} +54911.1 q^{96} +(-6969.04 + 92405.5i) q^{97} -146492. q^{98} +(-21775.8 - 2866.84i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 16 q^{2} + 72 q^{3} - 16 q^{4} - 16 q^{5} - 24 q^{6} - 16 q^{7} - 16 q^{8} - 280 q^{9} - 3984 q^{10} - 16 q^{11} - 4496 q^{12} - 16 q^{13} - 11008 q^{14} - 7664 q^{15} - 24 q^{16} - 2904 q^{17}+ \cdots - 1255776 q^{99}+O(q^{100}) $ 640 * q - 16 * q^2 + 72 * q^3 - 16 * q^4 - 16 * q^5 - 24 * q^6 - 16 * q^7 - 16 * q^8 - 280 * q^9 - 3984 * q^10 - 16 * q^11 - 4496 * q^12 - 16 * q^13 - 11008 * q^14 - 7664 * q^15 - 24 * q^16 - 2904 * q^17 + 14080 * q^18 + 11880 * q^19 - 11528 * q^20 - 16 * q^21 + 11128 * q^23 - 8208 * q^24 + 20216 * q^25 + 23944 * q^26 + 42048 * q^27 + 4344 * q^28 + 5664 * q^29 - 25016 * q^30 + 17720 * q^31 + 38288 * q^32 + 29992 * q^33 + 43504 * q^34 - 78408 * q^35 + 383608 * q^36 + 36792 * q^37 - 16 * q^38 + 32064 * q^39 - 68368 * q^40 - 62256 * q^41 - 62224 * q^42 - 6168 * q^43 + 73448 * q^44 + 302312 * q^45 - 16 * q^46 - 130528 * q^47 - 123216 * q^48 - 200400 * q^49 + 56408 * q^50 - 36624 * q^51 - 15184 * q^52 + 28608 * q^53 + 26160 * q^54 - 106768 * q^55 - 16 * q^56 - 16 * q^57 - 353424 * q^58 + 108448 * q^59 - 415744 * q^60 - 178616 * q^61 + 246008 * q^62 + 9648 * q^63 - 8208 * q^64 - 273528 * q^65 + 143104 * q^66 - 128800 * q^67 - 480600 * q^68 + 475104 * q^69 - 736096 * q^70 - 510680 * q^71 - 1088528 * q^72 - 239248 * q^73 - 249680 * q^74 + 1175984 * q^76 - 16 * q^77 - 62224 * q^78 - 450336 * q^79 - 882928 * q^80 - 626184 * q^81 + 164136 * q^82 - 45248 * q^83 + 2157472 * q^84 + 1060392 * q^85 + 1314208 * q^86 + 567200 * q^87 + 744432 * q^88 + 382432 * q^89 + 758960 * q^90 - 299688 * q^91 + 569608 * q^92 - 513336 * q^93 - 1447312 * q^94 - 1202720 * q^95 - 2188832 * q^96 - 754896 * q^97 + 3555136 * q^98 - 1255776 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/97\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{17}{48}\right)$

Coefficient data

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

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

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

$2$	−7.92337	−	1.04313i	−1.40067	−	0.184401i	−0.607942	−	0.793981i	$-0.708005\pi$
$2$	−7.92337	−	1.04313i	−1.40067	−	0.184401i	−0.792725	+	0.609580i	$0.791338\pi$
$3$	5.32344	−	4.08482i	0.341499	−	0.262042i	−0.423745	−	0.905781i	$-0.639285\pi$
$3$	5.32344	−	4.08482i	0.341499	−	0.262042i	0.765244	+	0.643740i	$0.222618\pi$
$4$	30.7820	+	8.24802i	0.961939	+	0.257751i
$5$	42.3505	+	85.8783i	0.757589	+	1.53624i	0.841799	+	0.539791i	$0.181497\pi$
$5$	42.3505	+	85.8783i	0.757589	+	1.53624i	−0.0842104	+	0.996448i	$0.526837\pi$
$6$	−46.4406	+	26.8125i	−0.526647	+	0.304060i
$7$	187.048	−	12.2598i	1.44281	−	0.0945667i	0.676218	−	0.736702i	$-0.263618\pi$
$7$	187.048	−	12.2598i	1.44281	−	0.0945667i	0.766591	+	0.642135i	$0.221951\pi$
$8$	0.975199	+	0.403941i	0.00538726	+	0.00223148i
$9$	−51.2397	+	191.229i	−0.210863	+	0.786952i
$10$	−245.976	−	724.623i	−0.777846	−	2.29146i
$11$	14.4808	+	109.992i	0.0360837	+	0.274083i	0.999970	+	0.00776799i	$0.00247265\pi$
$11$	14.4808	+	109.992i	0.0360837	+	0.274083i	−0.963886	+	0.266315i	$0.914194\pi$
$12$	197.558	−	81.8313i	0.396043	−	0.164046i
$13$	−428.086	+	211.109i	−0.702543	+	0.346456i	−0.758225	−	0.651993i	$-0.773933\pi$
$13$	−428.086	+	211.109i	−0.702543	+	0.346456i	0.0556824	+	0.998449i	$0.482267\pi$
$14$	−1494.84	−	97.9771i	−2.03833	−	0.133599i
$15$	576.248	+	284.174i	0.661274	+	0.326104i
$16$	−890.455	−	514.105i	−0.869585	−	0.502055i
$17$	14.7833	−	225.550i	0.0124065	−	0.189287i	−0.987157	−	0.159752i	$-0.948931\pi$
$17$	14.7833	−	225.550i	0.0124065	−	0.189287i	0.999564	−	0.0295352i	$-0.00940273\pi$
$18$	605.469	−	1461.73i	0.440464	−	1.06337i
$19$	780.528	−	1168.14i	0.496026	−	0.742355i	−0.496009	−	0.868317i	$-0.665202\pi$
$19$	780.528	−	1168.14i	0.496026	−	0.742355i	0.992035	+	0.125962i	$0.0402017\pi$
$20$	595.309	+	2992.82i	0.332788	+	1.67304i
$21$	945.663	−	829.324i	0.467938	−	0.410370i
$22$		−	886.617i		−	0.390552i
$23$	276.925	+	315.772i	0.109155	+	0.124467i	0.803837	−	0.594850i	$-0.202788\pi$
$23$	276.925	+	315.772i	0.109155	+	0.124467i	−0.694682	+	0.719317i	$0.744455\pi$
$24$	6.84144	−	1.83316i	0.00242449	−	0.000649639i
$25$	−3679.14	+	4794.75i	−1.17733	+	1.53432i
$26$	3612.10	−	1226.14i	1.04792	−	0.355719i
$27$	1132.35	+	2733.73i	0.298931	+	0.721682i
$28$	5858.85	+	1165.40i	1.41227	+	0.280918i
$29$	−2243.51	+	6609.17i	−0.495374	+	1.45932i	0.355861	+	0.934539i	$0.384188\pi$
$29$	−2243.51	+	6609.17i	−0.495374	+	1.45932i	−0.851235	+	0.524785i	$0.824146\pi$
$30$	−4269.40	−	2852.72i	−0.866091	−	0.578704i
$31$	−3607.02	−	4700.76i	−0.674131	−	0.878545i	0.323578	−	0.946202i	$-0.395114\pi$
$31$	−3607.02	−	4700.76i	−0.674131	−	0.878545i	−0.997709	+	0.0676569i	$0.978448\pi$
$32$	6492.33	+	4981.74i	1.12079	+	0.860015i
$33$	526.388	+	526.388i	0.0841435	+	0.0841435i
$34$	−352.412	+	1771.70i	−0.0522822	+	0.262840i
$35$	8974.45	+	15544.2i	1.23833	+	2.14486i
$36$	−3154.53	+	5463.80i	−0.405675	+	0.702650i
$37$	7468.46	+	6549.66i	0.896864	+	0.786529i	0.977658	−	0.210202i	$-0.0674121\pi$
$37$	7468.46	+	6549.66i	0.896864	+	0.786529i	−0.0807936	+	0.996731i	$0.525745\pi$
$38$	−7402.94	+	8441.43i	−0.831659	+	0.948325i
$39$	−1416.55	+	2872.48i	−0.149132	+	0.302410i
$40$	6.61042	+	100.856i	0.000653250	+	0.00996667i
$41$	−8040.07	−	2729.23i	−0.746964	−	0.253560i	−0.0781009	−	0.996945i	$-0.524886\pi$
$41$	−8040.07	−	2729.23i	−0.746964	−	0.253560i	−0.668864	+	0.743385i	$0.733219\pi$
$42$	−8357.93	+	5584.59i	−0.731098	+	0.488504i
$43$	−1020.72	−	3809.38i	−0.0841853	−	0.314184i	0.910973	−	0.412465i	$-0.135332\pi$
$43$	−1020.72	−	3809.38i	−0.0841853	−	0.314184i	−0.995159	+	0.0982815i	$0.968665\pi$
$44$	−461.473	+	3505.23i	−0.0359347	+	0.272951i
$45$	−18592.5	+	3698.28i	−1.36869	+	0.272250i
$46$	−1864.78	−	2790.85i	−0.129937	−	0.194465i
$47$	13361.0	−	13361.0i	0.882252	−	0.882252i	−0.111511	−	0.993763i	$-0.535569\pi$
$47$	13361.0	−	13361.0i	0.882252	−	0.882252i	0.993763	+	0.111511i	$0.0355690\pi$
$48$	−6840.32	+	900.545i	−0.428522	+	0.0564160i
$49$	18173.6	−	2392.60i	1.08131	−	0.142357i
$50$	34152.8	−	34152.8i	1.93197	−	1.93197i
$51$	−842.634	−	1261.09i	−0.0453643	−	0.0678924i
$52$	−14918.6	+	2967.49i	−0.765103	+	0.152188i
$53$	−1773.18	+	13468.6i	−0.0867086	+	0.658617i	0.891803	+	0.452424i	$0.149441\pi$
$53$	−1773.18	+	13468.6i	−0.0867086	+	0.658617i	−0.978511	+	0.206193i	$0.933893\pi$
$54$	−6120.37	−	22841.5i	−0.285623	−	1.06596i
$55$	−8832.71	+	5901.82i	−0.393720	+	0.263075i
$56$	187.362	+	63.6007i	0.00798382	+	0.00271014i
$57$	−616.558	−	9406.86i	−0.0251355	−	0.383493i
$58$	24670.4	−	50026.6i	0.962955	−	1.95268i
$59$	12385.2	−	14122.6i	0.463204	−	0.528183i	−0.472329	−	0.881423i	$-0.656586\pi$
$59$	12385.2	−	14122.6i	0.463204	−	0.528183i	0.935533	+	0.353239i	$0.114920\pi$
$60$	15394.2	+	13500.4i	0.552052	+	0.484136i
$61$	−12193.8	+	21120.3i	−0.419581	+	0.726735i	−0.995897	−	0.0904913i	$-0.971156\pi$
$61$	−12193.8	+	21120.3i	−0.419581	+	0.726735i	0.576316	+	0.817227i	$0.304490\pi$
$62$	23676.2	+	41008.5i	0.782229	+	1.35486i
$63$	−7239.88	+	36397.3i	−0.229816	+	1.15536i
$64$	−22978.8	−	22978.8i	−0.701258	−	0.701258i
$65$	−36259.3	−	27822.8i	−1.06448	−	0.816802i
$66$	−3621.67	−	4719.85i	−0.102341	−	0.133373i
$67$	−6947.82	−	4642.38i	−0.189087	−	0.126344i	0.457424	−	0.889249i	$-0.348772\pi$
$67$	−6947.82	−	4642.38i	−0.189087	−	0.126344i	−0.646510	+	0.762905i	$0.723772\pi$
$68$	2315.41	−	6820.96i	0.0607232	−	0.178885i
$69$	2764.06	+	549.807i	0.0698917	+	0.0139023i
$70$	−54893.2	−	132524.i	−1.33898	−	3.23258i
$71$	55751.3	−	18925.0i	1.31253	−	0.445544i	0.424541	−	0.905409i	$-0.360436\pi$
$71$	55751.3	−	18925.0i	1.31253	−	0.445544i	0.887989	+	0.459865i	$0.152102\pi$
$72$	−127.214	+	165.789i	−0.00289204	+	0.00376898i
$73$	−77228.3	+	20693.3i	−1.69617	+	0.454487i	−0.971970	−	0.235104i	$-0.924457\pi$
$73$	−77228.3	+	20693.3i	−1.69617	+	0.454487i	−0.724199	+	0.689591i	$0.757790\pi$
$74$	−52343.2	−	59686.0i	−1.11117	−	1.26705i
$75$			40553.3i			0.832478i
$76$	33661.1	−	29520.0i	0.668489	−	0.586250i
$77$	4057.09	+	20396.4i	0.0779809	+	0.392036i
$78$	14220.2	−	21282.1i	0.264649	−	0.396075i
$79$	−18787.3	+	45356.6i	−0.338686	+	0.817661i	0.659156	+	0.752006i	$0.270914\pi$
$79$	−18787.3	+	45356.6i	−0.338686	+	0.817661i	−0.997842	+	0.0656546i	$0.979086\pi$
$80$	6439.21	−	98243.4i	0.112488	−	1.71624i
$81$	−24467.9	−	14126.6i	−0.414366	−	0.239235i
$82$	60857.5	+	30011.6i	0.999492	+	0.492895i
$83$	49685.4	+	3256.55i	0.791650	+	0.0518875i	0.455862	−	0.890050i	$-0.349331\pi$
$83$	49685.4	+	3256.55i	0.791650	+	0.0518875i	0.335788	+	0.941938i	$0.390998\pi$
$84$	35949.7	−	17728.4i	0.555901	−	0.274140i
$85$	19996.0	−	8282.60i	0.300189	−	0.124342i
$86$	4113.86	+	31247.9i	0.0599796	+	0.455591i
$87$	15054.1	+	44347.9i	0.213234	+	0.628166i
$88$	−30.3088	+	113.114i	−0.000417217	+	0.00155707i
$89$	−45060.6	−	18664.7i	−0.603006	−	0.249773i	0.0602287	−	0.998185i	$-0.480817\pi$
$89$	−45060.6	−	18664.7i	−0.603006	−	0.249773i	−0.663235	+	0.748411i	$0.730817\pi$
$90$	151173.	−	9908.40i	1.96729	−	0.128943i
$91$	−77484.7	+	44735.8i	−0.980872	+	0.566307i
$92$	5919.81	+	12004.2i	0.0729186	+	0.147864i
$93$	−38403.5	−	10290.2i	−0.460430	−	0.123372i
$94$	−119801.	+	91926.6i	−1.39843	+	1.07305i
$95$	133374.	+	17559.0i	1.51622	+	0.199614i
$96$	54911.1			0.608110
$97$	−6969.04	+	92405.5i	−0.0752045	+	0.997168i
$97$	−6969.04	+	92405.5i	−0.0752045	+	0.997168i
$98$	−146492.			−1.54081
$99$	−21775.8	−	2866.84i	−0.223298	−	0.0293978i
$100$	−152799.	+	117247.i	−1.52799	+	1.17247i
$101$	−31928.2	−	8555.14i	−0.311438	−	0.0834495i	0.0997147	−	0.995016i	$-0.468207\pi$
$101$	−31928.2	−	8555.14i	−0.311438	−	0.0834495i	−0.411153	+	0.911567i	$0.634874\pi$
$102$	5361.02	+	10871.1i	0.0510208	+	0.103460i
$103$	95940.5	−	55391.3i	0.891064	−	0.514456i	0.0167736	−	0.999859i	$-0.494661\pi$
$103$	95940.5	−	55391.3i	0.891064	−	0.514456i	0.874290	+	0.485403i	$0.161327\pi$
$104$	−502.744	+	32.9516i	−0.00455789	+	0.000298740i
$105$	111270.	+	46089.7i	0.984931	+	0.407972i
$106$	28099.0	−	104867.i	0.242900	−	0.906514i
$107$	47036.0	+	138564.i	0.397165	+	1.17001i	0.943194	+	0.332243i	$0.107806\pi$
$107$	47036.0	+	138564.i	0.397165	+	1.17001i	−0.546029	+	0.837766i	$0.683861\pi$
$108$	12308.1	+	93489.4i	0.101539	+	0.771264i
$109$	38231.8	−	15836.1i	0.308218	−	0.127668i	−0.223213	−	0.974770i	$-0.571654\pi$
$109$	38231.8	−	15836.1i	0.308218	−	0.127668i	0.531431	+	0.847102i	$0.321654\pi$
$110$	76141.2	−	37548.7i	0.599981	−	0.295878i
$111$	66512.2	+	4359.44i	0.512382	+	0.0335833i
$112$	−172861.	−	85245.6i	−1.30212	−	0.642136i
$113$	179323.	+	103532.i	1.32111	+	0.762743i	0.983906	−	0.178688i	$-0.0571853\pi$
$113$	179323.	+	103532.i	1.32111	+	0.762743i	0.337204	+	0.941431i	$0.390519\pi$
$114$	−4927.37	+	75177.2i	−0.0355102	+	0.541781i
$115$	−15390.1	+	37154.9i	−0.108517	+	0.261982i
$116$	−123572.	+	184939.i	−0.852661	+	1.27610i
$117$	−18435.2	−	92679.8i	−0.124504	−	0.625922i
$118$	−112864.	+	98979.3i	−0.746193	+	0.654394i
$119$		−	42370.0i		−	0.274278i
$120$	447.167	+	509.897i	0.00283476	+	0.00323243i
$121$	143675.	−	38497.5i	0.892107	−	0.239039i
$122$	118648.	−	154624.i	0.721704	−	0.940543i
$123$	−53949.3	+	18313.3i	−0.321531	+	0.109145i
$124$	−72259.5	−	174450.i	−0.422027	−	1.01886i
$125$	−274100.	−	54522.0i	−1.56904	−	0.312102i
$126$	95331.4	−	280837.i	0.534946	−	1.57590i
$127$	−169894.	−	113520.i	−0.934694	−	0.624542i	−0.00784164	−	0.999969i	$-0.502496\pi$
$127$	−169894.	−	113520.i	−0.934694	−	0.624542i	−0.926852	+	0.375427i	$0.877496\pi$
$128$	−1315.99	−	1715.03i	−0.00709948	−	0.00925222i
$129$	−20994.4	−	16109.6i	−0.111078	−	0.0852334i
$130$	258273.	+	258273.i	1.34036	+	1.34036i
$131$	−15802.0	+	79442.0i	−0.0804514	+	0.404456i	0.919484	+	0.393126i	$0.128607\pi$
$131$	−15802.0	+	79442.0i	−0.0804514	+	0.404456i	−0.999936	+	0.0113300i	$0.996393\pi$
$132$	11861.6	+	20544.9i	0.0592529	+	0.102629i
$133$	131675.	−	228068.i	0.645469	−	1.11798i
$134$	50207.5	+	44030.8i	0.241550	+	0.211833i
$135$	−186813.	+	213019.i	−0.882210	+	1.00597i
$136$	105.526	−	213.985i	0.000489227	−	0.000992054i
$137$	3728.27	+	56882.4i	0.0169709	+	0.258926i	0.997910	+	0.0646128i	$0.0205812\pi$
$137$	3728.27	+	56882.4i	0.0169709	+	0.258926i	−0.980939	+	0.194313i	$0.937752\pi$
$138$	−21327.2	−	7239.61i	−0.0953314	−	0.0323606i
$139$	−8119.41	+	5425.22i	−0.0356441	+	0.0238166i	−0.573265	−	0.819370i	$-0.694323\pi$
$139$	−8119.41	+	5425.22i	−0.0356441	+	0.0238166i	0.537621	+	0.843187i	$0.319323\pi$
$140$	148043.	+	552504.i	0.638363	+	2.38240i
$141$	16549.2	−	125703.i	0.0701017	−	0.532475i
$142$	−461479.	+	91794.0i	−1.92058	+	0.382026i
$143$	−29419.4	−	44029.2i	−0.120308	−	0.180053i
$144$	143939.	−	143939.i	0.578457	−	0.578457i
$145$	−662598.	+	87232.7i	−2.61716	+	0.344556i
$146$	633494.	−	83401.1i	2.45958	−	0.323809i
$147$	86972.7	−	86972.7i	0.331963	−	0.331963i
$148$	175873.	+	263212.i	0.660000	+	0.987760i
$149$	287547.	−	57196.7i	1.06107	−	0.211060i	0.366450	−	0.930438i	$-0.380573\pi$
$149$	287547.	−	57196.7i	1.06107	−	0.211060i	0.694619	+	0.719378i	$0.255573\pi$
$150$	42302.4	−	321319.i	0.153510	−	1.16602i
$151$	105585.	+	394049.i	0.376843	+	1.40640i	0.850634	+	0.525758i	$0.176218\pi$
$151$	105585.	+	394049.i	0.376843	+	1.40640i	−0.473791	+	0.880637i	$0.657115\pi$
$152$	1233.03	−	823.885i	0.00432877	−	0.00289239i
$153$	42374.3	+	14384.1i	0.146344	+	0.0496770i
$154$	−10869.7	−	165840.i	−0.0369332	−	0.563492i
$155$	250934.	−	508845.i	0.838940	−	1.70120i
$156$	−67296.6	+	76737.1i	−0.221402	+	0.252461i
$157$	−395122.	−	346513.i	−1.27933	−	1.12194i	−0.986145	−	0.165884i	$-0.946952\pi$
$157$	−395122.	−	346513.i	−1.27933	−	1.12194i	−0.293183	−	0.956056i	$-0.594714\pi$
$158$	196172.	−	339780.i	0.625164	−	1.08282i
$159$	45577.5	+	78942.5i	0.142974	+	0.247638i
$160$	−152870.	+	768530.i	−0.472088	+	2.37334i
$161$	55669.6	+	55669.6i	0.169260	+	0.169260i
$162$	179133.	+	137453.i	0.536274	+	0.411498i
$163$	−237138.	−	309044.i	−0.699088	−	0.911069i	0.299993	−	0.953941i	$-0.403016\pi$
$163$	−237138.	−	309044.i	−0.699088	−	0.911069i	−0.999081	+	0.0428725i	$0.986349\pi$
$164$	−224979.	−	150326.i	−0.653179	−	0.436440i
$165$	−22912.5	+	67498.1i	−0.0655183	+	0.193011i
$166$	−390279.	−	77631.2i	−1.09927	−	0.218658i
$167$	−225382.	−	544121.i	−0.625358	−	1.50975i	−0.845331	−	0.534243i	$-0.820597\pi$
$167$	−225382.	−	544121.i	−0.625358	−	1.50975i	0.219973	−	0.975506i	$-0.429403\pi$
$168$	1257.21	−	426.764i	0.00343664	−	0.00116658i
$169$	−87338.0	+	113821.i	−0.235227	+	0.306553i
$170$	−167075.	+	44767.7i	−0.443394	+	0.118807i
$171$	183389.	+	209115.i	0.479604	+	0.546884i
$172$		−	125680.i		−	0.323924i
$173$	−409952.	+	359519.i	−1.04140	+	0.913285i	−0.996321	−	0.0856988i	$-0.972688\pi$
$173$	−409952.	+	359519.i	−1.04140	+	0.913285i	−0.0450804	+	0.998983i	$0.514354\pi$
$174$	−73018.3	−	367088.i	−0.182835	−	0.919173i
$175$	−629395.	+	941957.i	−1.55356	+	2.32507i
$176$	43653.2	−	105388.i	0.106227	−	0.256454i
$177$	8243.55	−	125772.i	0.0197779	−	0.301753i
$178$	337562.	+	194892.i	0.798553	+	0.461045i
$179$	616424.	+	303987.i	1.43796	+	0.709124i	0.983376	−	0.181580i	$-0.0581211\pi$
$179$	616424.	+	303987.i	1.43796	+	0.709124i	0.454585	+	0.890704i	$0.349788\pi$
$180$	−602818.	−	39510.8i	−1.38677	−	0.0908939i
$181$	700355.	−	345377.i	1.58899	−	0.783604i	0.589288	−	0.807923i	$-0.299408\pi$
$181$	700355.	−	345377.i	1.58899	−	0.783604i	0.999704	+	0.0243193i	$0.00774182\pi$
$182$	660605.	−	273632.i	1.47830	−	0.612333i
$183$	21359.6	+	162243.i	0.0471483	+	0.358127i
$184$	142.503	+	419.802i	0.000310299	+	0.000914112i
$185$	−246181.	+	918761.i	−0.528842	+	1.97366i
$186$	293552.	+	121593.i	0.622160	+	0.257707i
$187$	25022.9	−	1640.09i	0.0523280	−	0.00342976i
$188$	521479.	−	301076.i	1.07607	−	0.621272i
$189$	245319.	+	497457.i	0.499547	+	1.01298i
$190$	−1.03845e6	−	278253.i	−2.08691	−	0.559186i
$191$	269509.	−	206801.i	0.534552	−	0.410176i	−0.305899	−	0.952064i	$-0.598957\pi$
$191$	269509.	−	206801.i	0.534552	−	0.410176i	0.840451	+	0.541888i	$0.182290\pi$
$192$	−216191.	−	28462.1i	−0.423237	−	0.0557203i
$193$	849334.			1.64129			0.820645	−	0.571438i	$-0.193614\pi$
$193$	849334.			1.64129			0.820645	+	0.571438i	$0.193614\pi$
$194$	151609.	−	724893.i	0.289216	−	1.38283i
$195$	−306676.			−0.577554
$196$	579154.	+	76247.1i	1.07685	+	0.141770i
$197$	710089.	−	544871.i	1.30361	−	1.00029i	0.304755	−	0.952431i	$-0.401425\pi$
$197$	710089.	−	544871.i	1.30361	−	1.00029i	0.998854	−	0.0478634i	$-0.0152412\pi$
$198$	169547.	+	45430.0i	0.307346	+	0.0823531i
$199$	−367933.	−	746095.i	−0.658622	−	1.33555i	−0.928022	−	0.372526i	$-0.878492\pi$
$199$	−367933.	−	746095.i	−0.658622	−	1.33555i	0.269399	−	0.963029i	$-0.413175\pi$
$200$	−5524.69	+	3189.68i	−0.00976637	+	0.00563862i
$201$	−55949.6	+	3667.13i	−0.0976803	+	0.00640231i
$202$	244055.	+	101091.i	0.420833	+	0.174315i
$203$	−338618.	+	1.26374e6i	−0.576726	+	2.15237i
$204$	−15536.5	−	45769.0i	−0.0261383	−	0.0770010i
$205$	−106119.	−	806052.i	−0.176363	−	1.33961i
$206$	−817952.	+	338807.i	−1.34295	+	0.556268i
$207$	−74574.4	+	36776.0i	−0.120966	+	0.0596539i
$208$	489723.	+	32098.2i	0.784861	+	0.0514425i
$209$	139790.	+	68936.6i	0.221365	+	0.109165i
$210$	−833558.	−	481255.i	−1.30433	−	0.753055i
$211$	29699.1	−	453120.i	0.0459237	−	0.700660i	−0.911378	−	0.411570i	$-0.864981\pi$
$211$	29699.1	−	453120.i	0.0459237	−	0.700660i	0.957302	−	0.289090i	$-0.0933528\pi$
$212$	−165671.	+	399966.i	−0.253167	+	0.611200i
$213$	219484.	−	328480.i	0.331477	−	0.496090i
$214$	−228144.	−	1.14695e6i	−0.340544	−	1.71203i
$215$	283915.	−	248987.i	0.418883	−	0.367351i
$216$			3123.33i			0.00455495i
$217$	−732318.	−	835048.i	−1.05572	−	1.20382i
$218$	−319444.	+	85594.7i	−0.455253	+	0.121985i
$219$	−326592.	+	425623.i	−0.460146	+	0.599674i
$220$	−320567.	+	108818.i	−0.446542	+	0.151581i
$221$	41287.1	+	99675.8i	0.0568635	+	0.137281i
$222$	−522453.	−	103922.i	−0.711483	−	0.141523i
$223$	384129.	−	1.13161e6i	0.517267	−	1.52382i	−0.303656	−	0.952782i	$-0.598207\pi$
$223$	384129.	−	1.13161e6i	0.517267	−	1.52382i	0.820923	−	0.571039i	$-0.193459\pi$
$224$	1.27546e6	+	852232.i	1.69842	+	1.13485i
$225$	−728379.	−	949242.i	−0.959183	−	1.25003i
$226$	−1.31284e6	−	1.00738e6i	−1.70978	−	1.31196i
$227$	−1.03170e6	−	1.03170e6i	−1.32889	−	1.32889i	−0.906335	−	0.422560i	$-0.861132\pi$
$227$	−1.03170e6	−	1.03170e6i	−1.32889	−	1.32889i	−0.422560	−	0.906335i	$-0.638868\pi$
$228$	58609.1	−	294648.i	0.0746669	−	0.375376i
$229$	565820.	+	980028.i	0.713000	+	1.23495i	0.963726	+	0.266894i	$0.0859973\pi$
$229$	565820.	+	980028.i	0.713000	+	1.23495i	−0.250726	+	0.968058i	$0.580669\pi$
$230$	160699.	−	278338.i	0.200305	−	0.346939i
$231$	104913.	+	92006.5i	0.129360	+	0.113446i
$232$	−4857.58	+	5539.01i	−0.00592516	+	0.00675635i
$233$	96019.8	−	194709.i	0.115870	−	0.234961i	−0.831210	−	0.555958i	$-0.812351\pi$
$233$	96019.8	−	194709.i	0.115870	−	0.234961i	0.947080	+	0.320997i	$0.104018\pi$
$234$	49391.4	+	753566.i	0.0589673	+	0.899667i
$235$	1.71326e6	+	581573.i	2.02373	+	0.686965i
$236$	497725.	−	332569.i	0.581714	−	0.388689i
$237$	85260.5	+	318196.i	0.0986000	+	0.367980i
$238$	−44197.5	+	335714.i	−0.0505773	+	0.384173i
$239$	−585429.	+	116449.i	−0.662949	+	0.131869i	−0.515085	−	0.857139i	$-0.672240\pi$
$239$	−585429.	+	116449.i	−0.662949	+	0.131869i	−0.147864	+	0.989008i	$0.547240\pi$
$240$	−367028.	−	549296.i	−0.411312	−	0.615572i
$241$	64135.9	−	64135.9i	0.0711309	−	0.0711309i	−0.670646	−	0.741777i	$-0.733983\pi$
$241$	64135.9	−	64135.9i	0.0711309	−	0.0711309i	0.741777	+	0.670646i	$0.233983\pi$
$242$	−1.17855e6	+	155158.i	−1.29362	+	0.170309i
$243$	−900836.	+	118597.i	−0.978656	+	0.128842i
$244$	−549552.	+	549552.i	−0.590928	+	0.590928i
$245$	975133.	+	1.45939e6i	1.03788	+	1.55330i
$246$	446563.	−	88827.0i	0.470484	−	0.0935852i
$247$	−87528.1	+	664842.i	−0.0912862	+	0.693388i
$248$	−1618.73	−	6041.20i	−0.00167127	−	0.00623726i
$249$	277800.	−	185620.i	0.283944	−	0.189726i
$250$	2.11493e6	+	717921.i	2.14015	+	0.726484i
$251$	11239.8	+	171486.i	0.0112609	+	0.171809i	0.999785	+	0.0207440i	$0.00660351\pi$
$251$	11239.8	+	171486.i	0.0112609	+	0.171809i	−0.988524	+	0.151065i	$0.951730\pi$
$252$	−523064.	+	1.06067e6i	−0.518864	+	1.05215i
$253$	−30722.5	+	35032.2i	−0.0301755	+	0.0344086i
$254$	1.22772e6	+	1.07668e6i	1.19403	+	1.04713i
$255$	72614.5	−	125772.i	0.0699315	−	0.121125i
$256$	528589.	+	915543.i	0.504102	+	0.873130i
$257$	−8547.72	+	42972.3i	−0.00807268	+	0.0405841i	−0.984612	−	0.174757i	$-0.944086\pi$
$257$	−8547.72	+	42972.3i	−0.00807268	+	0.0405841i	0.976539	+	0.215341i	$0.0690862\pi$
$258$	149542.	+	149542.i	0.139867	+	0.139867i
$259$	1.47726e6	+	1.13354e6i	1.36838	+	1.05000i
$260$	−886654.	−	1.15551e6i	−0.813431	−	1.06008i
$261$	−1.14891e6	−	767677.i	−1.04396	−	0.697553i
$262$	208073.	−	612965.i	0.187268	−	0.551673i
$263$	−654673.	−	130223.i	−0.583627	−	0.116091i	−0.105558	−	0.994413i	$-0.533663\pi$
$263$	−654673.	−	130223.i	−0.583627	−	0.116091i	−0.478069	+	0.878323i	$0.658663\pi$
$264$	300.703	+	725.962i	0.000265539	+	0.000641068i
$265$	−1.23176e6	+	418125.i	−1.07748	+	0.365756i
$266$	−1.28122e6	+	1.66972e6i	−1.11024	+	1.44690i
$267$	−316120.	+	84704.0i	−0.271377	+	0.0727153i
$268$	−175578.	−	200208.i	−0.149325	−	0.170272i
$269$			1.04998e6i			0.884706i	0.896841	+	0.442353i	$0.145856\pi$
$269$			1.04998e6i			0.884706i	−0.896841	+	0.442353i	$0.854144\pi$
$270$	1.70239e6	−	1.49296e6i	1.42118	−	1.24635i
$271$	−277403.	−	1.39460e6i	−0.229450	−	1.15352i	−0.908001	−	0.418968i	$-0.862392\pi$
$271$	−277403.	−	1.39460e6i	−0.229450	−	1.15352i	0.678551	−	0.734553i	$-0.262608\pi$
$272$	−129120.	+	193242.i	−0.105821	+	0.158372i
$273$	−229748.	+	554660.i	−0.186571	+	0.450422i
$274$	29795.3	−	454589.i	0.0239757	−	0.365799i
$275$	−580664.	−	335247.i	−0.463013	−	0.267321i
$276$	80548.8	+	39722.3i	0.0636482	+	0.0313878i
$277$	−556607.	−	36481.9i	−0.435862	−	0.0285679i	−0.154107	−	0.988054i	$-0.549250\pi$
$277$	−556607.	−	36481.9i	−0.435862	−	0.0285679i	−0.281755	+	0.959486i	$0.590917\pi$
$278$	69992.3	−	34516.4i	0.0543173	−	0.0267863i
$279$	1.08375e6	−	448902.i	0.833522	−	0.345256i
$280$	2472.94	+	18783.8i	0.00188503	+	0.0143182i
$281$	497264.	+	1.46489e6i	0.375682	+	1.10672i	0.956260	+	0.292519i	$0.0944936\pi$
$281$	497264.	+	1.46489e6i	0.375682	+	1.10672i	−0.580577	+	0.814205i	$0.697173\pi$
$282$	−262250.	+	978732.i	−0.196378	+	0.732894i
$283$	1.38471e6	+	573567.i	1.02777	+	0.425714i	0.831905	−	0.554917i	$-0.187250\pi$
$283$	1.38471e6	+	573567.i	1.02777	+	0.425714i	0.195860	+	0.980632i	$0.437250\pi$
$284$	1.87223e6	−	122713.i	1.37741	−	0.0902804i
$285$	781734.	−	451334.i	0.570095	−	0.329144i
$286$	187173.	+	379548.i	0.135309	+	0.274380i
$287$	−1.53734e6	−	411929.i	−1.10171	−	0.295201i
$288$	−1.28532e6	+	986261.i	−0.913125	+	0.700665i
$289$	1.35706e6	+	178660.i	0.955769	+	0.125829i
$290$	5.34101e6			3.72931
$291$	340361.	+	520383.i	0.235617	+	0.360239i
$292$	−2.54792e6			−1.74876
$293$	2.29177e6	+	301718.i	1.55956	+	0.205320i	0.860391	−	0.509634i	$-0.170219\pi$
$293$	2.29177e6	+	301718.i	1.55956	+	0.205320i	0.699171	+	0.714954i	$0.253552\pi$
$294$	−779841.	+	598393.i	−0.526184	+	0.403755i
$295$	1.73735e6	+	465520.i	1.16233	+	0.311447i
$296$	4637.56	+	9404.04i	0.00307652	+	0.00623857i
$297$	−284292.	+	164136.i	−0.187014	+	0.107973i
$298$	−2.33801e6	+	153241.i	−1.52512	+	0.0999620i
$299$	−185210.	−	76716.4i	−0.119808	−	0.0496261i
$300$	−334484.	+	1.24831e6i	−0.214572	+	0.800793i
$301$	−237627.	−	700025.i	−0.151175	−	0.445346i
$302$	−425545.	−	3.23233e6i	−0.268490	−	2.03938i
$303$	−204914.	+	84878.3i	−0.128223	+	0.0531117i
$304$	−1.29557e6	+	638906.i	−0.804040	+	0.396509i
$305$	−2.33019e6	−	152729.i	−1.43431	−	0.0940096i
$306$	−320743.	−	158173.i	−0.195818	−	0.0965669i
$307$	−1.38908e6	−	801983.i	−0.841162	−	0.485645i	0.0164968	−	0.999864i	$-0.494749\pi$
$307$	−1.38908e6	−	801983.i	−0.841162	−	0.485645i	−0.857659	+	0.514219i	$0.828082\pi$
$308$	−43344.3	+	661306.i	−0.0260348	+	0.397215i
$309$	284470.	−	686772.i	0.169489	−	0.409182i
$310$	−2.51904e6	+	3.77001e6i	−1.48878	+	2.22812i
$311$	−159843.	−	803586.i	−0.0937115	−	0.471120i	−0.998933	−	0.0461798i	$-0.985295\pi$
$311$	−159843.	−	803586.i	−0.0937115	−	0.471120i	0.905222	−	0.424940i	$-0.139705\pi$
$312$	−2541.73	+	2229.04i	−0.00147823	+	0.00129638i
$313$		−	636506.i		−	0.367233i	−0.982998	−	0.183616i	$-0.941220\pi$
$313$		−	636506.i		−	0.367233i	0.982998	−	0.183616i	$-0.0587804\pi$
$314$	2.76924e6	+	3.15771e6i	1.58503	+	1.80737i
$315$	−3.43235e6	+	919697.i	−1.94902	+	0.522238i
$316$	−952415.	+	1.24121e6i	−0.536548	+	0.699243i
$317$	−474411.	+	161041.i	−0.265159	+	0.0900093i	−0.450853	−	0.892598i	$-0.648880\pi$
$317$	−474411.	+	161041.i	−0.265159	+	0.0900093i	0.185694	+	0.982608i	$0.440547\pi$
$318$	−278780.	−	673034.i	−0.154594	−	0.373223i
$319$	−759447.	−	151063.i	−0.417850	−	0.0831156i
$320$	1.00022e6	−	2.94655e6i	0.546034	−	1.60856i
$321$	816401.	+	545502.i	0.442223	+	0.295484i
$322$	−383020.	−	499162.i	−0.205865	−	0.268288i
$323$	−251936.	−	193317.i	−0.134364	−	0.103101i
$324$	−636657.	−	636657.i	−0.336932	−	0.336932i
$325$	562776.	−	2.82927e6i	0.295548	−	1.48582i
$326$	1.55656e6	+	2.69604e6i	0.811187	+	1.40502i
$327$	138837.	−	240473.i	0.0718019	−	0.124365i
$328$	−6738.21	−	5909.26i	−0.00345828	−	0.00303283i
$329$	2.33534e6	−	2.66295e6i	1.18949	−	1.35635i
$330$	251954.	−	510911.i	0.127361	−	0.258262i
$331$	−121226.	−	1.84956e6i	−0.0608173	−	0.927893i	−0.913854	−	0.406042i	$-0.866909\pi$
$331$	−121226.	−	1.84956e6i	−0.0608173	−	0.927893i	0.853037	−	0.521851i	$-0.174758\pi$
$332$	1.50256e6	+	510049.i	0.748145	+	0.253961i
$333$	−1.63517e6	+	1.09259e6i	−0.808076	+	0.539939i
$334$	1.21820e6	+	4.54638e6i	0.597519	+	2.22997i
$335$	104437.	−	793274.i	0.0508441	−	0.386199i
$336$	−1.26843e6	+	252306.i	−0.612940	+	0.121921i
$337$	256476.	+	383843.i	0.123019	+	0.184111i	0.887867	−	0.460099i	$-0.152186\pi$
$337$	256476.	+	383843.i	0.123019	+	0.184111i	−0.764849	+	0.644210i	$0.777186\pi$
$338$	810742.	−	810742.i	0.386003	−	0.386003i
$339$	1.37752e6	−	181354.i	0.651028	−	0.0857095i
$340$	683832.	−	90028.2i	0.320813	−	0.0422358i
$341$	464816.	−	464816.i	0.216469	−	0.216469i
$342$	−1.23492e6	−	1.84820e6i	−0.570920	−	0.854442i
$343$	280075.	−	55710.4i	0.128540	−	0.0255682i
$344$	543.358	−	4127.22i	0.000247566	−	0.00188045i
$345$	69843.1	+	260658.i	0.0315919	+	0.117903i
$346$	3.62323e6	−	2.42096e6i	1.62707	−	1.08717i
$347$	−1.92810e6	−	654501.i	−0.859618	−	0.291801i	−0.143389	−	0.989666i	$-0.545800\pi$
$347$	−1.92810e6	−	654501.i	−0.859618	−	0.291801i	−0.716229	+	0.697865i	$0.754133\pi$
$348$	97612.9	+	1.48928e6i	0.0432075	+	0.659219i
$349$	1.27043e6	−	2.57618e6i	0.558325	−	1.13217i	−0.416487	−	0.909142i	$-0.636739\pi$
$349$	1.27043e6	−	2.57618e6i	0.558325	−	1.13217i	0.974812	−	0.223029i	$-0.0715944\pi$
$350$	5.96952e6	−	6.80693e6i	2.60477	−	2.97017i
$351$	−1.06186e6	−	931223.i	−0.460043	−	0.403447i
$352$	−453940.	+	786247.i	−0.195273	+	0.338222i
$353$	−649477.	−	1.12493e6i	−0.277413	−	0.480494i	0.693328	−	0.720622i	$-0.256144\pi$
$353$	−649477.	−	1.12493e6i	−0.277413	−	0.480494i	−0.970741	+	0.240129i	$0.922810\pi$
$354$	−196514.	+	987941.i	−0.0833460	+	0.419008i
$355$	3.98635e6	+	3.98635e6i	1.67882	+	1.67882i
$356$	−1.23311e6	−	946199.i	−0.515676	−	0.395692i
$357$	−173074.	−	225555.i	−0.0718723	−	0.0936658i
$358$	−4.56706e6	−	3.05161e6i	−1.88334	−	1.25841i
$359$	205048.	−	604052.i	0.0839692	−	0.247365i	−0.896833	−	0.442368i	$-0.854138\pi$
$359$	205048.	−	604052.i	0.0839692	−	0.247365i	0.980803	+	0.195003i	$0.0624717\pi$
$360$	−19625.3	−	3903.71i	−0.00798103	−	0.00158753i
$361$	192229.	+	464081.i	0.0776337	+	0.187424i
$362$	−5.90944e6	+	2.00599e6i	−2.37015	+	0.804556i
$363$	607589.	−	791825.i	0.242015	−	0.315401i
$364$	−2.75412e6	+	737964.i	−1.08950	+	0.291932i
$365$	−5.04776e6	−	5.75587e6i	−1.98320	−	2.26141i
$366$		−	1.30779e6i		−	0.510311i
$367$	−83844.2	+	73529.4i	−0.0324944	+	0.0284968i	−0.675439	−	0.737416i	$-0.736046\pi$
$367$	−83844.2	+	73529.4i	−0.0324944	+	0.0284968i	0.642945	+	0.765913i	$0.277713\pi$
$368$	−84249.1	−	423549.i	−0.0324299	−	0.163036i
$369$	933880.	−	1.39765e6i	0.357047	−	0.534359i
$370$	2.90897e6	−	7.02288e6i	1.10468	−	2.66693i
$371$	−166547.	+	2.54102e6i	−0.0628207	+	0.958458i
$372$	−1.09727e6	−	633507.i	−0.411107	−	0.237353i
$373$	3.32774e6	+	1.64106e6i	1.23845	+	0.610735i	0.939177	−	0.343433i	$-0.111590\pi$
$373$	3.32774e6	+	1.64106e6i	1.23845	+	0.610735i	0.299271	+	0.954168i	$0.403257\pi$
$374$	−199977.	−	13107.2i	−0.0739265	−	0.00484540i
$375$	−1.68187e6	+	829407.i	−0.617610	+	0.304572i
$376$	18426.6	−	7632.56i	0.00672165	−	0.00278420i
$377$	−434837.	−	3.30292e6i	−0.157570	−	1.19686i
$378$	−1.42484e6	−	4.19744e6i	−0.512904	−	1.51097i
$379$	−472910.	+	1.76492e6i	−0.169114	+	0.631143i	0.828365	+	0.560188i	$0.189271\pi$
$379$	−472910.	+	1.76492e6i	−0.169114	+	0.631143i	−0.997480	+	0.0709547i	$0.977395\pi$
$380$	3.96070e6	+	1.64057e6i	1.40706	+	0.582823i
$381$	−1.36813e6	+	89672.0i	−0.482853	+	0.0316479i
$382$	−2.35114e6	+	1.35743e6i	−0.824366	+	0.475948i
$383$	1.86527e6	+	3.78240e6i	0.649749	+	1.31756i	0.933470	+	0.358654i	$0.116764\pi$
$383$	1.86527e6	+	3.78240e6i	0.649749	+	1.31756i	−0.283721	+	0.958907i	$0.591569\pi$
$384$	−14011.2	−	3754.28i	−0.00484893	−	0.00129927i
$385$	−1.57979e6	+	1.21221e6i	−0.543184	+	0.416800i
$386$	−6.72959e6	−	885967.i	−2.29890	−	0.302656i
$387$	780767.			0.264999
$388$	−976684.	+	2.78695e6i	−0.329363	+	0.939831i
$389$	1.58259e6			0.530266			0.265133	−	0.964212i	$-0.414584\pi$
$389$	1.58259e6			0.530266			0.265133	+	0.964212i	$0.414584\pi$
$390$	2.42990e6	+	319903.i	0.808961	+	0.106502i
$391$	75316.3	−	57792.2i	0.0249142	−	0.0191173i
$392$	18689.3	+	5007.79i	0.00614297	+	0.00164600i
$393$	240385.	+	487453.i	0.0785103	+	0.159203i
$394$	−6.19467e6	+	3.57649e6i	−2.01038	+	1.16069i
$395$	−4.69081e6	+	307452.i	−1.51271	+	0.0991480i
$396$	−646657.	−	267854.i	−0.207222	−	0.0858343i
$397$	813524.	−	3.03611e6i	0.259056	−	0.966812i	−0.706732	−	0.707481i	$-0.749831\pi$
$397$	813524.	−	3.03611e6i	0.259056	−	0.966812i	0.965789	−	0.259331i	$-0.0835019\pi$
$398$	2.13700e6	+	6.29539e6i	0.676233	+	1.99212i
$399$	−230652.	−	1.75198e6i	−0.0725314	−	0.550930i
$400$	5.74112e6	−	2.37805e6i	1.79410	−	0.743140i
$401$	3.46842e6	−	1.71043e6i	1.07714	−	0.531185i	0.184901	−	0.982757i	$-0.440803\pi$
$401$	3.46842e6	−	1.71043e6i	1.07714	−	0.531185i	0.892234	+	0.451572i	$0.149137\pi$
$402$	447135.	+	29306.8i	0.137998	+	0.00904488i
$403$	2.53649e6	+	1.25086e6i	0.777983	+	0.383659i
$404$	−912253.	−	526690.i	−0.278075	−	0.160547i
$405$	176937.	−	2.69953e6i	0.0536019	−	0.817807i
$406$	4.00124e6	−	9.65985e6i	1.20470	−	2.90841i
$407$	−612265.	+	916319.i	−0.183212	+	0.274196i
$408$	−312.330	−	1570.19i	−9.28888e−5	−	0.000466984i
$409$	−102690.	+	90056.5i	−0.0303542	+	0.0266199i	−0.674389	−	0.738377i	$-0.735593\pi$
$409$	−102690.	+	90056.5i	−0.0303542	+	0.0266199i	0.644034	+	0.764997i	$0.277259\pi$
$410$			6.49734e6i			1.90887i
$411$	252202.	+	287581.i	0.0736450	+	0.0839760i
$412$	3.41011e6	−	913737.i	0.989751	−	0.265203i
$413$	2.14349e6	−	2.79345e6i	0.618367	−	0.805872i
$414$	629243.	−	213599.i	0.180434	−	0.0612489i
$415$	1.82453e6	+	4.40481e6i	0.520034	+	1.25547i
$416$	−3.83097e6	−	762026.i	−1.08536	−	0.215892i
$417$	−21062.2	+	62047.2i	−0.00593148	+	0.0174736i
$418$	−1.03569e6	−	692029.i	−0.289929	−	0.193724i
$419$	3.85209e6	+	5.02014e6i	1.07192	+	1.39695i	0.912180	+	0.409790i	$0.134398\pi$
$419$	3.85209e6	+	5.02014e6i	1.07192	+	1.39695i	0.159738	+	0.987160i	$0.448935\pi$
$420$	3.04498e6	+	2.33649e6i	0.842289	+	0.646311i
$421$	−657950.	−	657950.i	−0.180920	−	0.180920i	0.610836	−	0.791757i	$-0.290833\pi$
$421$	−657950.	−	657950.i	−0.180920	−	0.180920i	−0.791757	+	0.610836i	$0.790833\pi$
$422$	−707981.	+	3.55926e6i	−0.193527	+	0.972924i
$423$	1.87039e6	+	3.23962e6i	0.508256	+	0.880325i
$424$	−7169.71	+	12418.3i	−0.00193681	+	0.00335465i
$425$	1.02707e6	+	900714.i	0.275821	+	0.241888i
$426$	−2.08170e6	+	2.37372e6i	−0.555768	+	0.633732i
$427$	−2.02191e6	+	4.10002e6i	−0.536650	+	1.08822i
$428$	304988.	+	4.65322e6i	0.0804774	+	1.22785i
$429$	−336464.	−	114214.i	−0.0882664	−	0.0299624i
$430$	−2.50929e6	+	1.67666e6i	−0.654456	+	0.437293i
$431$	−846373.	−	3.15871e6i	−0.219467	−	0.819060i	−0.984546	−	0.175125i	$-0.943967\pi$
$431$	−846373.	−	3.15871e6i	−0.219467	−	0.819060i	0.765080	−	0.643936i	$-0.222700\pi$
$432$	397118.	−	3.01641e6i	0.102379	−	0.777644i
$433$	−3.37381e6	+	671093.i	−0.864771	+	0.172014i	−0.607494	−	0.794324i	$-0.707825\pi$
$433$	−3.37381e6	+	671093.i	−0.864771	+	0.172014i	−0.257277	+	0.966338i	$0.582825\pi$
$434$	4.93136e6	+	7.38030e6i	1.25673	+	1.88083i
$435$	−3.17097e6	+	3.17097e6i	−0.803470	+	0.803470i
$436$	1.30747e6	−	172132.i	0.329394	−	0.0433655i
$437$	585014.	−	77018.6i	0.146542	−	0.0192926i
$438$	3.03169e6	−	3.03169e6i	0.755092	−	0.755092i
$439$	676169.	+	1.01196e6i	0.167453	+	0.250612i	0.905700	−	0.423919i	$-0.139346\pi$
$439$	676169.	+	1.01196e6i	0.167453	+	0.250612i	−0.738247	+	0.674531i	$0.764346\pi$
$440$	−10997.6	+	2187.56i	−0.00270812	+	0.000538678i
$441$	−473675.	+	3.59792e6i	−0.115980	+	0.880957i
$442$	−223158.	−	832836.i	−0.0543321	−	0.202770i
$443$	−4.00658e6	+	2.67711e6i	−0.969985	+	0.648123i	−0.936260	−	0.351308i	$-0.885737\pi$
$443$	−4.00658e6	+	2.67711e6i	−0.969985	+	0.648123i	−0.0337248	+	0.999431i	$0.510737\pi$
$444$	2.01142e6	+	682786.i	0.484224	+	0.164372i
$445$	−305445.	−	4.66019e6i	−0.0731194	−	1.11559i
$446$	−4.22401e6	+	8.56545e6i	−1.00551	+	2.03898i
$447$	1.29710e6	−	1.47906e6i	0.307048	−	0.350121i
$448$	−4.57987e6	−	4.01643e6i	−1.07810	−	0.945465i
$449$	2.11799e6	−	3.66846e6i	0.495801	−	0.858753i	−0.504187	−	0.863594i	$-0.668208\pi$
$449$	2.11799e6	−	3.66846e6i	0.495801	−	0.858753i	0.999988	+	0.00484158i	$0.00154113\pi$
$450$	4.78103e6	+	8.28099e6i	1.11299	+	1.92775i
$451$	183769.	−	923868.i	0.0425432	−	0.213879i
$452$	4.66598e6	+	4.66598e6i	1.07423	+	1.07423i
$453$	2.17169e6	+	1.66640e6i	0.497225	+	0.381534i
$454$	7.09837e6	+	9.25078e6i	1.61629	+	2.10639i
$455$	−7.12335e6	−	4.75967e6i	−1.61308	−	1.07783i
$456$	3198.55	−	9422.61i	0.000720345	−	0.00212207i
$457$	6.44308e6	+	1.28161e6i	1.44312	+	0.287055i	0.853698	−	0.520769i	$-0.174355\pi$
$457$	6.44308e6	+	1.28161e6i	1.44312	+	0.287055i	0.589424	+	0.807824i	$0.299355\pi$
$458$	−3.46090e6	−	8.35535e6i	−0.770949	−	1.86123i
$459$	633333.	−	214988.i	0.140314	−	0.0476301i
$460$	−780193.	+	1.01677e6i	−0.171912	+	0.224041i
$461$	−6.13599e6	+	1.64413e6i	−1.34472	+	0.360317i	−0.858184	−	0.513342i	$-0.828407\pi$
$461$	−6.13599e6	+	1.64413e6i	−1.34472	+	0.360317i	−0.486538	+	0.873659i	$0.661741\pi$
$462$	−735292.	−	838440.i	−0.160271	−	0.182754i
$463$		−	4.20429e6i		−	0.911466i	−0.890116	−	0.455733i	$-0.849377\pi$
$463$		−	4.20429e6i		−	0.911466i	0.890116	−	0.455733i	$-0.150623\pi$
$464$	5.39555e6	−	4.73177e6i	1.16343	−	1.02030i
$465$	−742705.	−	3.73383e6i	−0.159288	−	0.800796i
$466$	−963908.	+	1.44259e6i	−0.205622	+	0.307736i
$467$	−2.57563e6	+	6.21812e6i	−0.546501	+	1.31937i	0.373564	+	0.927604i	$0.378136\pi$
$467$	−2.57563e6	+	6.21812e6i	−0.546501	+	1.31937i	−0.920065	+	0.391766i	$0.871864\pi$
$468$	196953.	−	3.00493e6i	0.0415670	−	0.634190i
$469$	−1.35649e6	−	783171.i	−0.284764	−	0.164409i
$470$	−1.29681e7	−	6.39518e6i	−2.70790	−	1.33539i
$471$	−3.51885e6	−	230638.i	−0.730884	−	0.0479047i
$472$	17782.7	−	8769.47i	0.00367403	−	0.00181183i
$473$	404223.	−	167435.i	0.0830745	−	0.0344106i
$474$	−343630.	−	2.61013e6i	−0.0702497	−	0.533600i
$475$	2.72928e6	+	8.04021e6i	0.555027	+	1.63506i
$476$	349469.	−	1.30424e6i	0.0706955	−	0.263839i
$477$	−2.48473e6	−	1.02921e6i	−0.500016	−	0.207113i
$478$	4.76005e6	−	311990.i	0.952887	−	0.0624555i
$479$	620194.	−	358069.i	0.123506	−	0.0713063i	−0.436974	−	0.899474i	$-0.643950\pi$
$479$	620194.	−	358069.i	0.123506	−	0.0713063i	0.560480	+	0.828168i	$0.310617\pi$
$480$	2.32551e6	+	4.71567e6i	0.460697	+	0.934202i
$481$	−4.57984e6	−	1.22716e6i	−0.902583	−	0.241846i
$482$	−575074.	+	441270.i	−0.112747	+	0.0865141i
$483$	523754.	+	68953.6i	0.102155	+	0.0134490i
$484$	4.74013e6			0.919765
$485$	−8.23077e6	+	3.31493e6i	−1.58886	+	0.639912i
$486$	7.26137e6			1.39453
$487$	−252750.	−	33275.2i	−0.0482913	−	0.00635767i	0.106342	−	0.994330i	$-0.466086\pi$
$487$	−252750.	−	33275.2i	−0.0482913	−	0.00635767i	−0.154633	+	0.987972i	$0.549420\pi$
$488$	−20422.8	+	15670.9i	−0.00388209	+	0.00297883i
$489$	−2.52478e6	−	676513.i	−0.477476	−	0.127939i
$490$	−6.20401e6	−	1.25805e7i	−1.16730	−	2.36705i
$491$	7.32375e6	−	4.22837e6i	1.37098	−	0.791533i	0.379925	−	0.925017i	$-0.375950\pi$
$491$	7.32375e6	−	4.22837e6i	1.37098	−	0.791533i	0.991051	+	0.133484i	$0.0426165\pi$
$492$	−1.81172e6	+	118746.i	−0.337425	+	0.0221160i
$493$	1.45753e6	+	603730.i	0.270085	+	0.111873i
$494$	1.38704e6	−	5.17649e6i	0.255723	−	0.954372i
$495$	−676016.	−	1.99148e6i	−0.124006	−	0.365311i
$496$	795208.	+	6.04020e6i	0.145136	+	1.10242i
$497$	1.01962e7	−	4.22339e6i	1.85160	−	0.766956i
$498$	−2.39474e6	+	1.18095e6i	−0.432697	+	0.213383i
$499$	535218.	+	35080.1i	0.0962232	+	0.00630680i	0.113439	−	0.993545i	$-0.463813\pi$
$499$	535218.	+	35080.1i	0.0962232	+	0.00630680i	−0.0172155	+	0.999852i	$0.505480\pi$
$500$	−7.98767e6	−	3.93908e6i	−1.42888	−	0.704645i
$501$	−3.42245e6	−	1.97595e6i	−0.609176	−	0.351708i
$502$	89825.6	−	1.37047e6i	0.0159089	−	0.242723i
$503$	−667605.	+	1.61174e6i	−0.117652	+	0.284037i	−0.971725	−	0.236116i	$-0.924125\pi$
$503$	−667605.	+	1.61174e6i	−0.117652	+	0.284037i	0.854073	+	0.520154i	$0.174125\pi$
$504$	−21762.7	+	32570.2i	−0.00381624	+	0.00571141i
$505$	−617475.	−	3.10426e6i	−0.107744	−	0.541663i
$506$	279969.	−	245526.i	0.0486108	−	0.0426306i
$507$			962681.i			0.166327i
$508$	−4.29338e6	−	4.89566e6i	−0.738142	−	0.841690i
$509$	5.87509e6	−	1.57423e6i	1.00512	−	0.269322i	0.281534	−	0.959551i	$-0.409157\pi$
$509$	5.87509e6	−	1.57423e6i	1.00512	−	0.269322i	0.723591	+	0.690229i	$0.242490\pi$
$510$	−706548.	+	920791.i	−0.120286	+	0.156760i
$511$	−1.41917e7	+	4.81744e6i	−2.40427	+	0.816140i
$512$	−3.20670e6	−	7.74167e6i	−0.540610	−	1.30515i
$513$	4.07722e6	+	811009.i	0.684022	+	0.136061i
$514$	112553.	−	331569.i	0.0187909	−	0.0553562i
$515$	8.82004e6	+	5.89336e6i	1.46539	+	0.979141i
$516$	−513379.	−	669048.i	−0.0848816	−	0.110620i
$517$	1.66308e6	+	1.27613e6i	0.273645	+	0.209975i
$518$	−1.05225e7	−	1.05225e7i	−1.72303	−	1.72303i
$519$	−713789.	+	3.58846e6i	−0.116319	+	0.584776i
$520$	−24121.3	−	41779.3i	−0.00391194	−	0.00677569i
$521$	−40580.3	+	70287.1i	−0.00654969	+	0.0113444i	−0.869282	−	0.494317i	$-0.835418\pi$
$521$	−40580.3	+	70287.1i	−0.00654969	+	0.0113444i	0.862732	+	0.505661i	$0.168752\pi$
$522$	8.30245e6	+	7.28105e6i	1.33361	+	1.16955i
$523$	3.62183e6	−	4.12990e6i	0.578993	−	0.660216i	−0.385997	−	0.922500i	$-0.626143\pi$
$523$	3.62183e6	−	4.12990e6i	0.578993	−	0.660216i	0.964991	+	0.262284i	$0.0844759\pi$
$524$	−1.14166e6	+	2.31505e6i	−0.181638	+	0.368326i
$525$	497175.	+	7.58542e6i	0.0787247	+	1.20111i
$526$	5.05138e6	+	1.71471e6i	0.796060	+	0.270226i
$527$	−1.11358e6	+	744071.i	−0.174661	+	0.116705i
$528$	−198106.	−	739343.i	−0.0309253	−	0.115415i
$529$	817087.	−	6.20639e6i	0.126949	−	0.964273i
$530$	1.01958e7	−	2.02807e6i	1.57664	−	0.313613i
$531$	2.06604e6	+	3.09205e6i	0.317982	+	0.475894i
$532$	5.93435e6	−	5.93435e6i	0.909063	−	0.909063i
$533$	4.01801e6	−	528980.i	0.612622	−	0.0806532i
$534$	2.59309e6	−	341387.i	0.393518	−	0.0518076i
$535$	−9.90761e6	+	9.90761e6i	−1.49653	+	1.49653i
$536$	−4900.26	−	7333.75i	−0.000736727	−	0.00110259i
$537$	4.52323e6	−	899727.i	0.676882	−	0.134640i
$538$	1.09526e6	−	8.31936e6i	0.163141	−	1.23918i
$539$	526336.	+	1.96431e6i	0.0780353	+	0.291232i
$540$	−7.50746e6	+	5.01633e6i	−1.10792	+	0.740289i
$541$	1.37578e6	+	467016.i	0.202096	+	0.0686023i	0.420652	−	0.907222i	$-0.361801\pi$
$541$	1.37578e6	+	467016.i	0.202096	+	0.0686023i	−0.218556	+	0.975824i	$0.570135\pi$
$542$	743215.	+	1.13393e7i	0.108672	+	1.65801i
$543$	2.31750e6	−	4.69942e6i	0.337303	−	0.683982i
$544$	1.21961e6	−	1.39070e6i	0.176695	−	0.201482i
$545$	2.97912e6	+	2.61261e6i	0.429631	+	0.376777i
$546$	2.39896e6	−	4.15512e6i	0.344382	−	0.596488i
$547$	2.95822e6	+	5.12379e6i	0.422729	+	0.732189i	0.996205	−	0.0870336i	$-0.0277387\pi$
$547$	2.95822e6	+	5.12379e6i	0.422729	+	0.732189i	−0.573476	+	0.819222i	$0.694405\pi$
$548$	−354403.	+	1.78171e6i	−0.0504135	+	0.253446i
$549$	−3.41402e6	−	3.41402e6i	−0.483432	−	0.483432i
$550$	4.25111e6	+	3.26199e6i	0.599233	+	0.459807i
$551$	5.96933e6	+	7.77938e6i	0.837619	+	1.09161i
$552$	2473.42	+	1652.69i	0.000345502	+	0.000230857i
$553$	−2.95808e6	+	8.71421e6i	−0.411336	+	1.21176i
$554$	4.37215e6	+	869674.i	0.605230	+	0.120388i
$555$	2.44244e6	+	5.89658e6i	0.336583	+	0.812583i
$556$	−294679.	+	100030.i	−0.0404262	+	0.0137228i
$557$	−4.12100e6	+	5.37059e6i	−0.562814	+	0.733473i	−0.984908	−	0.173079i	$-0.944629\pi$
$557$	−4.12100e6	+	5.37059e6i	−0.562814	+	0.733473i	0.422094	+	0.906552i	$0.361295\pi$
$558$	−9.05519e6	+	2.42633e6i	−1.23115	+	0.329886i
$559$	1.24115e6	+	1.41526e6i	0.167994	+	0.191561i
$560$		−	1.84552e7i		−	2.48685i
$561$	126509.	−	110945.i	0.0169712	−	0.0148834i
$562$	−2.41193e6	−	1.21256e7i	−0.322124	−	1.61943i
$563$	−1.98750e6	+	2.97451e6i	−0.264263	+	0.395498i	−0.939744	−	0.341880i	$-0.888936\pi$
$563$	−1.98750e6	+	2.97451e6i	−0.264263	+	0.395498i	0.675480	+	0.737378i	$0.263936\pi$
$564$	1.54622e6	−	3.73291e6i	0.204679	−	0.494140i
$565$	−1.29675e6	+	1.97846e7i	−0.170897	+	2.60739i
$566$	−1.03733e7	−	5.98903e6i	−1.36106	−	0.785806i
$567$	−4.74987e6	−	2.34238e6i	−0.620475	−	0.305985i
$568$	62013.2	+	4064.56i	0.00806516	+	0.000528619i
$569$	382016.	−	188389.i	0.0494653	−	0.0243936i	−0.417388	−	0.908728i	$-0.637054\pi$
$569$	382016.	−	188389.i	0.0494653	−	0.0243936i	0.466853	+	0.884335i	$0.345388\pi$
$570$	−6.66477e6	+	2.76064e6i	−0.859208	+	0.355895i
$571$	−1.61205e6	−	1.22447e7i	−0.206913	−	1.57166i	−0.707969	−	0.706244i	$-0.750388\pi$
$571$	−1.61205e6	−	1.22447e7i	−0.206913	−	1.57166i	0.501056	−	0.865415i	$-0.332945\pi$
$572$	−542435.	−	1.59796e6i	−0.0693199	−	0.204210i
$573$	589968.	−	2.20179e6i	0.0750658	−	0.280149i
$574$	1.17512e7	+	4.86752e6i	1.48869	+	0.616634i
$575$	−2.53289e6	+	166015.i	−0.319483	+	0.0209400i
$576$	5.57165e6	−	3.21679e6i	0.699725	−	0.403987i
$577$	−4.24131e6	−	8.60052e6i	−0.530347	−	1.07544i	−0.982975	−	0.183738i	$-0.941180\pi$
$577$	−4.24131e6	−	8.60052e6i	−0.530347	−	1.07544i	0.452628	−	0.891699i	$-0.350487\pi$
$578$	−1.05661e7	−	2.83117e6i	−1.31551	−	0.352490i
$579$	4.52138e6	−	3.46938e6i	0.560499	−	0.430086i
$580$	−2.11156e7	−	2.77992e6i	−2.60636	−	0.343133i
$581$	9.33349e6			1.14711
$582$	−2.15398e6	−	4.47823e6i	−0.263593	−	0.548023i
$583$	−1.50712e6			−0.183644
$584$	−83671.8	−	11015.6i	−0.0101519	−	0.00133652i
$585$	7.17845e6	−	5.50822e6i	0.867243	−	0.665459i
$586$	−1.78438e7	−	4.78125e6i	−2.14657	−	0.575171i
$587$	382230.	+	775087.i	0.0457857	+	0.0928442i	0.918563	−	0.395274i	$-0.129350\pi$
$587$	382230.	+	775087.i	0.0457857	+	0.0928442i	−0.872778	+	0.488118i	$0.837684\pi$
$588$	3.39455e6	−	1.95985e6i	0.404892	−	0.233765i
$589$	−8.30654e6	+	544439.i	−0.986579	+	0.0646638i
$590$	−1.32800e7	−	5.50077e6i	−1.57061	−	0.650569i
$591$	1.55442e6	−	5.80118e6i	0.183063	−	0.683199i
$592$	−3.28312e6	−	9.67175e6i	−0.385019	−	1.13423i
$593$	1.26761e6	+	9.62849e6i	0.148030	+	1.12440i	0.890650	+	0.454689i	$0.150249\pi$
$593$	1.26761e6	+	9.62849e6i	0.148030	+	1.12440i	−0.742620	+	0.669713i	$0.766417\pi$
$594$	2.42377e6	−	1.00396e6i	0.281855	−	0.116748i
$595$	3.63867e6	−	1.79439e6i	0.421357	−	0.207790i
$596$	9.32306e6	+	611065.i	1.07508	+	0.0704648i
$597$	−5.00634e6	−	2.46885e6i	−0.574890	−	0.283504i
$598$	1.38746e6	+	801051.i	0.158660	+	0.0916024i
$599$	392989.	−	5.99586e6i	0.0447521	−	0.682786i	−0.915266	−	0.402849i	$-0.868020\pi$
$599$	392989.	−	5.99586e6i	0.0447521	−	0.682786i	0.960018	−	0.279937i	$-0.0903134\pi$
$600$	−16381.1	+	39547.5i	−0.00185766	+	0.00448478i
$601$	−6.16701e6	+	9.22958e6i	−0.696447	+	1.04231i	0.299650	+	0.954049i	$0.403130\pi$
$601$	−6.16701e6	+	9.22958e6i	−0.696447	+	1.04231i	−0.996098	+	0.0882579i	$0.971870\pi$
$602$	1.15258e6	+	5.79444e6i	0.129623	+	0.651658i
$603$	1.24376e6	−	1.09075e6i	0.139298	−	0.122161i
$604$			1.30005e7i			1.45000i
$605$	9.39080e6	+	1.07082e7i	1.04307	+	1.18940i
$606$	1.71215e6	−	458770.i	0.189392	−	0.0507473i
$607$	−3.58409e6	+	4.67087e6i	−0.394827	+	0.514549i	−0.947893	−	0.318589i	$-0.896791\pi$
$607$	−3.58409e6	+	4.67087e6i	−0.394827	+	0.514549i	0.553066	+	0.833137i	$0.313458\pi$
$608$	1.08868e7	−	3.69558e6i	1.19438	−	0.405437i
$609$	3.35954e6	+	8.11064e6i	0.367059	+	0.886159i
$610$	1.83037e7	+	3.64083e6i	1.99165	+	0.396165i
$611$	−2.89903e6	+	8.54025e6i	−0.314159	+	0.925481i
$612$	1.18573e6	+	792278.i	0.127969	+	0.0855065i
$613$	3.51906e6	+	4.58613e6i	0.378247	+	0.492942i	0.943220	−	0.332168i	$-0.107780\pi$
$613$	3.51906e6	+	4.58613e6i	0.378247	+	0.492942i	−0.564973	+	0.825109i	$0.691113\pi$
$614$	1.01696e7	+	7.80340e6i	1.08863	+	0.835339i
$615$	−3.85750e6	−	3.85750e6i	−0.411261	−	0.411261i
$616$	−4282.46	+	21529.4i	−0.000454717	+	0.00228602i
$617$	−4.85012e6	−	8.40066e6i	−0.512908	−	0.888383i	−0.999888	−	0.0149699i	$-0.995235\pi$
$617$	−4.85012e6	−	8.40066e6i	−0.512908	−	0.888383i	0.486980	−	0.873413i	$-0.338099\pi$
$618$	−2.97036e6	+	5.14481e6i	−0.312851	+	0.541874i
$619$	−5.38213e6	−	4.72000e6i	−0.564583	−	0.495126i	0.328814	−	0.944395i	$-0.393351\pi$
$619$	−5.38213e6	−	4.72000e6i	−0.564583	−	0.495126i	−0.893397	+	0.449269i	$0.851685\pi$
$620$	1.19212e7	−	1.35936e7i	1.24550	−	1.42022i
$621$	−549660.	+	1.11460e6i	−0.0571959	+	0.115982i
$622$	428251.	+	6.53384e6i	0.0443836	+	0.677162i
$623$	−8.65734e6	−	2.93877e6i	−0.893643	−	0.303351i
$624$	2.73813e6	−	1.82956e6i	0.281509	−	0.188099i
$625$	−2.03787e6	−	7.60544e6i	−0.208678	−	0.778797i
$626$	−663959.	+	5.04327e6i	−0.0677182	+	0.514371i
$627$	1.02576e6	−	204036.i	0.104202	−	0.0207270i
$628$	−9.30461e6	−	1.39253e7i	−0.941454	−	1.40899i
$629$	1.58769e6	−	1.58769e6i	0.160007	−	0.160007i
$630$	2.81552e7	−	3.70670e6i	2.82623	−	0.372080i
$631$	1.47073e7	−	1.93625e6i	1.47048	−	0.193592i	0.647674	−	0.761918i	$-0.275742\pi$
$631$	1.47073e7	−	1.93625e6i	1.47048	−	0.193592i	0.822804	+	0.568325i	$0.192409\pi$
$632$	−36642.8	+	36642.8i	−0.00364918	+	0.00364918i
$633$	−1.69282e6	−	2.53348e6i	−0.167919	−	0.251309i
$634$	3.92692e6	−	781112.i	0.387997	−	0.0771774i
$635$	2.55378e6	−	1.93979e7i	0.251332	−	1.90906i
$636$	751848.	+	2.80593e6i	0.0737033	+	0.275065i
$637$	−7.27476e6	+	4.86084e6i	−0.710346	+	0.474638i
$638$	5.85980e6	+	1.98913e6i	0.569942	+	0.193469i
$639$	762336.	+	1.16310e7i	0.0738574	+	1.12685i
$640$	91550.9	−	185647.i	0.00883513	−	0.0179159i
$641$	−1.27748e7	+	1.45669e7i	−1.22803	+	1.40030i	−0.340059	+	0.940404i	$0.610447\pi$
$641$	−1.27748e7	+	1.45669e7i	−1.22803	+	1.40030i	−0.887972	+	0.459897i	$0.847886\pi$
$642$	−5.89962e6	−	5.17383e6i	−0.564919	−	0.495421i
$643$	3.91028e6	−	6.77280e6i	0.372975	−	0.646012i	−0.617046	−	0.786927i	$-0.711671\pi$
$643$	3.91028e6	−	6.77280e6i	0.372975	−	0.646012i	0.990022	+	0.140914i	$0.0450043\pi$
$644$	1.25446e6	+	2.17279e6i	0.119191	+	0.206444i
$645$	494340.	−	2.48521e6i	0.0467871	−	0.235215i
$646$	1.79453e6	+	1.79453e6i	0.169188	+	0.169188i
$647$	−1.64060e7	−	1.25887e7i	−1.54078	−	1.18228i	−0.915793	−	0.401650i	$-0.868437\pi$
$647$	−1.64060e7	−	1.25887e7i	−1.54078	−	1.18228i	−0.624988	−	0.780634i	$-0.714896\pi$
$648$	−18154.8	−	23659.8i	−0.00169845	−	0.00221347i
$649$	1.73273e6	+	1.15777e6i	0.161480	+	0.107897i
$650$	−7.41038e6	+	2.18303e7i	−0.687951	+	2.02664i
$651$	−7.30948e6	−	1.45395e6i	−0.675980	−	0.134461i
$652$	−4.75058e6	−	1.14689e7i	−0.437651	−	1.05658i
$653$	9.61726e6	−	3.26462e6i	0.882609	−	0.299605i	0.156906	−	0.987614i	$-0.449848\pi$
$653$	9.61726e6	−	3.26462e6i	0.882609	−	0.299605i	0.725703	+	0.688008i	$0.241515\pi$
$654$	−1.35090e6	+	1.76053e6i	−0.123504	+	0.160953i
$655$	−7.49157e6	+	2.00736e6i	−0.682291	+	0.182819i
$656$	5.75621e6	+	6.56370e6i	0.522248	+	0.595510i
$657$		−	1.58286e7i		−	1.43064i
$658$	−2.12816e7	+	1.86635e7i	−1.91619	+	1.68046i
$659$	−2.23760e6	−	1.12492e7i	−0.200710	−	1.00904i	−0.941426	−	0.337220i	$-0.890513\pi$
$659$	−2.23760e6	−	1.12492e7i	−0.200710	−	1.00904i	0.740715	−	0.671819i	$-0.234487\pi$
$660$	−1.26202e6	+	1.88875e6i	−0.112773	+	0.168777i
$661$	7.18937e6	−	1.73567e7i	0.640011	−	1.54512i	−0.186653	−	0.982426i	$-0.559764\pi$
$661$	7.18937e6	−	1.73567e7i	0.640011	−	1.54512i	0.826664	−	0.562697i	$-0.190236\pi$
$662$	−968810.	+	1.47812e7i	−0.0859199	+	1.31088i
$663$	626947.	+	361968.i	0.0553920	+	0.0319806i
$664$	47137.7	+	23245.7i	0.00414904	+	0.00204608i
$665$	2.51626e7	+	1.64925e6i	2.20649	+	0.144621i
$666$	1.40958e7	−	6.95126e6i	1.23141	−	0.607265i
$667$	−2.70827e6	+	1.12180e6i	−0.235710	+	0.0976342i
$668$	−2.44981e6	−	1.86081e7i	−0.212418	−	1.61347i
$669$	−2.57753e6	−	7.59315e6i	−0.222658	−	0.655929i
$670$	−1.65498e6	+	6.17646e6i	−0.142431	+	0.531561i
$671$	−2.49966e6	−	1.03539e6i	−0.214325	−	0.0887765i
$672$	1.02710e7	−	673199.i	0.877386	−	0.0575069i
$673$	−4.99354e6	+	2.88302e6i	−0.424982	+	0.245364i	−0.697207	−	0.716870i	$-0.745574\pi$
$673$	−4.99354e6	+	2.88302e6i	−0.424982	+	0.245364i	0.272224	+	0.962234i	$0.412241\pi$
$674$	−1.63175e6	−	3.30887e6i	−0.138358	−	0.280563i
$675$	−1.72736e7	−	4.62846e6i	−1.45923	−	0.391000i
$676$	−3.62724e6	+	2.78328e6i	−0.305288	+	0.234256i
$677$	1.18971e7	+	1.56629e6i	0.997633	+	0.131341i	0.611619	−	0.791152i	$-0.290518\pi$
$677$	1.18971e7	+	1.56629e6i	0.997633	+	0.131341i	0.386013	+	0.922493i	$0.373852\pi$
$678$	−1.11038e7			−0.927679
$679$	−170675.	+	1.73697e7i	−0.0142068	+	1.44584i
$680$	22845.7			0.00189467
$681$	−9.70655e6	−	1.27789e6i	−0.802042	−	0.105591i
$682$	−4.16777e6	+	3.19804e6i	−0.343118	+	0.263283i
$683$	6.94914e6	+	1.86202e6i	0.570006	+	0.152733i	0.532299	−	0.846556i	$-0.321328\pi$
$683$	6.94914e6	+	1.86202e6i	0.570006	+	0.152733i	0.0377066	+	0.999289i	$0.487995\pi$
$684$	3.92030e6	+	7.94959e6i	0.320390	+	0.649687i
$685$	−4.72707e6	+	2.72917e6i	−0.384916	+	0.222231i
$686$	−2.27725e6	+	149259.i	−0.184757	+	0.0121096i
$687$	7.01535e6	+	2.90585e6i	0.567097	+	0.234899i
$688$	−1.04951e6	+	3.91684e6i	−0.0845313	+	0.315475i
$689$	−2.08427e6	−	6.14005e6i	−0.167265	−	0.492747i
$690$	−281492.	−	2.13814e6i	−0.0225083	−	0.170968i
$691$	1.30281e7	−	5.39640e6i	1.03797	−	0.429941i	0.202387	−	0.979306i	$-0.435130\pi$
$691$	1.30281e7	−	5.39640e6i	1.03797	−	0.429941i	0.835583	+	0.549364i	$0.185130\pi$
$692$	−1.55845e7	+	7.68542e6i	−1.23716	+	0.610102i
$693$	−4.10827e6	−	269270.i	−0.324957	−	0.0212988i
$694$	1.45943e7	+	7.19712e6i	1.15023	+	0.567231i
$695$	−809770.	−	467521.i	−0.0635916	−	0.0367146i
$696$	−3233.19	+	49329.0i	−0.000252993	+	0.00385992i
$697$	−734438.	+	1.77309e6i	−0.0572629	+	0.138245i
$698$	−1.27534e7	+	1.90868e7i	−0.990801	+	1.48284i
$699$	−284195.	−	1.42875e6i	−0.0220001	−	0.110602i
$700$	−2.71434e7	+	2.38041e7i	−2.09372	+	1.83614i
$701$			3.76125e6i			0.289093i	0.989498	+	0.144547i	$0.0461723\pi$
$701$			3.76125e6i			0.289093i	−0.989498	+	0.144547i	$0.953828\pi$
$702$	7.44209e6	+	8.48608e6i	0.569971	+	0.649927i
$703$	1.34803e7	−	3.61203e6i	1.02875	−	0.275653i
$704$	2.19475e6	−	2.86025e6i	0.166899	−	0.217506i
$705$	1.14961e7	−	3.90239e6i	0.871117	−	0.295704i
$706$	3.97260e6	+	9.59070e6i	0.299960	+	0.724167i
$707$	−6.07701e6	−	1.20879e6i	−0.457237	−	0.0909501i
$708$	1.29113e6	−	3.80353e6i	0.0968022	−	0.285170i
$709$	−1.77557e7	−	1.18640e7i	−1.32654	−	0.886369i	−0.328241	−	0.944594i	$-0.606456\pi$
$709$	−1.77557e7	−	1.18640e7i	−1.32654	−	0.886369i	−0.998303	+	0.0582253i	$0.981456\pi$
$710$	−2.74270e7	−	3.57436e7i	−2.04189	−	2.66104i
$711$	−7.71086e6	−	5.91675e6i	−0.572043	−	0.438944i
$712$	−36403.6	−	36403.6i	−0.00269119	−	0.00269119i
$713$	485496.	−	2.44075e6i	0.0357653	−	0.179804i
$714$	1.13605e6	+	1.96769e6i	0.0833971	+	0.144448i
$715$	2.53523e6	−	4.39115e6i	0.185461	−	0.321228i
$716$	1.64675e7	+	1.44416e7i	1.20045	+	1.05277i
$717$	−2.64083e6	+	3.01129e6i	−0.191841	+	0.218753i
$718$	−2.25478e6	+	4.57224e6i	−0.163227	+	0.330992i
$719$	1.01993e6	+	1.55611e7i	0.0735780	+	1.12258i	0.861819	+	0.507217i	$0.169326\pi$
$719$	1.01993e6	+	1.55611e7i	0.0735780	+	1.12258i	−0.788241	+	0.615367i	$0.789008\pi$
$720$	1.84571e7	+	6.26533e6i	1.32688	+	0.450415i
$721$	1.72664e7	−	1.15371e7i	1.23698	−	0.826527i
$722$	−1.03900e6	−	3.87761e6i	−0.0741776	−	0.276835i
$723$	79440.1	−	603407.i	0.00565189	−	0.0429304i
$724$	2.44070e7	−	4.85486e6i	1.73049	−	0.344215i
$725$	−2.34351e7	−	3.50732e7i	−1.65586	−	2.47816i
$726$	−5.64013e6	+	5.64013e6i	−0.397143	+	0.397143i
$727$	1.25543e7	−	1.65280e6i	0.880961	−	0.115981i	0.323544	−	0.946213i	$-0.395126\pi$
$727$	1.25543e7	−	1.65280e6i	0.880961	−	0.115981i	0.557417	+	0.830233i	$0.311792\pi$
$728$	−93633.6	+	12327.1i	−0.00654792	+	0.000862050i
$729$	543547.	−	543547.i	0.0378807	−	0.0378807i
$730$	3.39911e7	+	5.08713e7i	2.36080	+	3.53318i
$731$	−874297.	+	173908.i	−0.0605153	+	0.0120373i
$732$	−680687.	+	5.17033e6i	−0.0469537	+	0.356649i
$733$	−1.14328e6	−	4.26677e6i	−0.0785944	−	0.293318i	0.915430	−	0.402478i	$-0.131851\pi$
$733$	−1.14328e6	−	4.26677e6i	−0.0785944	−	0.293318i	−0.994024	+	0.109159i	$0.965184\pi$
$734$	741030.	−	495140.i	0.0507686	−	0.0339225i
$735$	1.11524e7	+	3.78574e6i	0.761466	+	0.258483i
$736$	224792.	+	3.42966e6i	0.0152963	+	0.233376i
$737$	410017.	−	831433.i	0.0278057	−	0.0563844i
$738$	−8.85741e6	+	1.00999e7i	−0.598640	+	0.682619i
$739$	−2.70813e6	−	2.37497e6i	−0.182414	−	0.159973i	0.563269	−	0.826274i	$-0.309543\pi$
$739$	−2.70813e6	−	2.37497e6i	−0.182414	−	0.159973i	−0.745683	+	0.666301i	$0.767877\pi$
$740$	−1.51559e7	+	2.62508e7i	−1.01743	+	1.76223i
$741$	2.24981e6	+	3.89679e6i	0.150522	+	0.260712i
$742$	3.97023e6	−	1.99597e7i	0.264732	−	1.33090i
$743$	−1.77486e7	−	1.77486e7i	−1.17949	−	1.17949i	−0.979875	−	0.199610i	$-0.936032\pi$
$743$	−1.77486e7	−	1.77486e7i	−1.17949	−	1.17949i	−0.199610	−	0.979875i	$-0.563968\pi$
$744$	−33294.5	−	25547.7i	−0.00220516	−	0.00169208i
$745$	1.70897e7	+	2.22718e7i	1.12809	+	1.47016i
$746$	−2.46551e7	−	1.64740e7i	−1.62203	−	1.08381i
$747$	−3.16861e6	+	9.33443e6i	−0.207763	+	0.612049i
$748$	783784.	+	155904.i	0.0512203	+	0.0101884i
$749$	1.04968e7	+	2.53414e7i	0.683677	+	1.65054i
$750$	1.41913e7	−	4.81729e6i	0.921230	−	0.312715i
$751$	4.00311e6	−	5.21696e6i	0.258999	−	0.337534i	−0.645696	−	0.763595i	$-0.723432\pi$
$751$	4.00311e6	−	5.21696e6i	0.258999	−	0.337534i	0.904694	+	0.426061i	$0.140099\pi$
$752$	−1.87663e7	+	5.02840e6i	−1.21013	+	0.324254i
$753$	760326.	+	866985.i	0.0488666	+	0.0557217i
$754$			2.66238e7i			1.70546i
$755$	−2.93687e7	+	2.57556e7i	−1.87507	+	1.64439i
$756$	3.44838e6	+	1.73362e7i	0.219437	+	1.10318i
$757$	−3.89490e6	+	5.82913e6i	−0.247034	+	0.369712i	−0.934177	−	0.356810i	$-0.883864\pi$
$757$	−3.89490e6	+	5.82913e6i	−0.247034	+	0.369712i	0.687143	+	0.726522i	$0.258864\pi$
$758$	5.58809e6	−	1.34908e7i	0.353256	−	0.852837i
$759$	−20448.8	+	311988.i	−0.00128844	+	0.0196577i
$760$	122973.	+	70998.7i	0.00772284	+	0.00445878i
$761$	−3.50914e6	−	1.73052e6i	−0.219654	−	0.108321i	0.329133	−	0.944284i	$-0.393244\pi$
$761$	−3.50914e6	−	1.73052e6i	−0.219654	−	0.108321i	−0.548787	+	0.835962i	$0.684910\pi$
$762$	1.09337e7	+	716635.i	0.682152	+	0.0447106i
$763$	6.95705e6	−	3.43084e6i	0.432627	−	0.213348i
$764$	1.00017e7	−	4.14286e6i	0.619929	−	0.256783i
$765$	559288.	+	4.24821e6i	0.0345527	+	0.262454i
$766$	−1.08337e7	−	3.19151e7i	−0.667122	−	1.96528i
$767$	−2.32052e6	+	8.66031e6i	−0.142429	+	0.531551i
$768$	6.55375e6	+	2.71465e6i	0.400947	+	0.166078i
$769$	1.61920e7	−	1.06128e6i	0.987378	−	0.0647162i	0.436851	−	0.899534i	$-0.356094\pi$
$769$	1.61920e7	−	1.06128e6i	0.987378	−	0.0647162i	0.550527	+	0.834818i	$0.314427\pi$
$770$	1.37817e7	−	7.95689e6i	0.837679	−	0.483634i
$771$	130031.	+	263677.i	0.00787790	+	0.0159748i
$772$	2.61442e7	+	7.00533e6i	1.57882	+	0.423044i
$773$	−1.08899e7	+	8.35615e6i	−0.655507	+	0.502988i	−0.882137	−	0.470993i	$-0.843896\pi$
$773$	−1.08899e7	+	8.35615e6i	−0.655507	+	0.502988i	0.226630	+	0.973981i	$0.427229\pi$
$774$	−6.18631e6	−	814443.i	−0.371175	−	0.0488662i
$775$	3.58097e7			2.14164
$776$	−44122.5	+	87298.6i	−0.00263030	+	0.00520419i
$777$	1.24944e7			0.742445
$778$	−1.25394e7	−	1.65085e6i	−0.742726	−	0.0977817i
$779$	−9.46363e6	+	7.26170e6i	−0.558746	+	0.428741i
$780$	−9.44010e6	−	2.52947e6i	−0.555572	−	0.148865i
$781$	2.88893e6	+	5.85818e6i	0.169477	+	0.343665i
$782$	−657044.	+	379344.i	−0.0384218	+	0.0221828i
$783$	−2.06081e7	+	1.35073e6i	−1.20125	+	0.0787341i
$784$	−1.74128e7	−	7.21262e6i	−1.01176	−	0.419086i
$785$	1.30243e7	−	4.86074e7i	0.754363	−	2.81532i
$786$	−1.39618e6	−	4.11303e6i	−0.0806095	−	0.237468i
$787$	−3.26490e6	−	2.47994e7i	−0.187903	−	1.42726i	−0.782205	−	0.623021i	$-0.785905\pi$
$787$	−3.26490e6	−	2.47994e7i	−0.187903	−	1.42726i	0.594302	−	0.804242i	$-0.297428\pi$
$788$	2.63521e7	−	1.09154e7i	1.51182	−	0.626216i
$789$	−4.01705e6	+	1.98099e6i	−0.229729	+	0.113290i
$790$	3.74877e7	+	2.45707e6i	2.13708	+	0.140072i
$791$	3.48113e7	+	1.71670e7i	1.97824	+	0.975560i
$792$	−20077.7	−	11591.9i	−0.00113737	−	0.000656659i
$793$	761323.	−	1.16155e7i	0.0429918	−	0.655929i
$794$	−9.61292e6	+	2.32076e7i	−0.541133	+	1.30641i
$795$	−4.84922e6	+	7.25737e6i	−0.272116	+	0.407250i
$796$	−5.17193e6	−	2.60011e7i	−0.289314	−	1.45448i
$797$	−2.30476e6	+	2.02122e6i	−0.128523	+	0.112712i	−0.721194	−	0.692733i	$-0.756407\pi$
$797$	−2.30476e6	+	2.02122e6i	−0.128523	+	0.112712i	0.592672	+	0.805444i	$0.298073\pi$
$798$			1.41222e7i			0.785045i
$799$	−2.81605e6	−	3.21109e6i	−0.156053	−	0.177945i
$800$	−4.77724e7	+	1.28006e7i	−2.63908	+	0.707139i
$801$	5.87813e6	−	7.66053e6i	0.323711	−	0.421869i
$802$	−2.92658e7	+	9.93439e6i	−1.60666	+	0.545388i
$803$	−3.39443e6	−	8.19488e6i	−0.185771	−	0.448491i
$804$	−1.75249e6	−	348592.i	−0.0956127	−	0.0190186i
$805$	−2.42318e6	+	7.13845e6i	−0.131794	+	0.388252i
$806$	−1.87927e7	−	1.25569e7i	−1.01895	−	0.680839i
$807$	4.28897e6	+	5.58950e6i	0.231830	+	0.302126i
$808$	−27680.6	−	21240.1i	−0.00149158	−	0.00114453i
$809$	−7.71126e6	−	7.71126e6i	−0.414242	−	0.414242i	0.468971	−	0.883213i	$-0.344625\pi$
$809$	−7.71126e6	−	7.71126e6i	−0.414242	−	0.414242i	−0.883213	+	0.468971i	$0.844625\pi$
$810$	−4.21790e6	+	2.12048e7i	−0.225883	+	1.13559i
$811$	−491300.	−	850956.i	−0.0262298	−	0.0454313i	0.852613	−	0.522544i	$-0.175017\pi$
$811$	−491300.	−	850956.i	−0.0262298	−	0.0454313i	−0.878842	+	0.477112i	$0.841683\pi$
$812$	−2.08467e7	+	3.61075e7i	−1.10955	+	1.92180i
$813$	−7.17342e6	−	6.29092e6i	−0.380627	−	0.333801i
$814$	5.80704e6	−	6.62166e6i	0.307181	−	0.350272i
$815$	1.64973e7	−	3.34532e7i	0.869998	−	1.76418i
$816$	101995.	+	1.55615e6i	0.00536235	+	0.0818136i
$817$	−5.24661e6	−	1.78098e6i	−0.274994	−	0.0933479i
$818$	907590.	−	606432.i	0.0474249	−	0.0316883i
$819$	−4.58450e6	−	1.71096e7i	−0.238826	−	0.891312i
$820$	3.38178e6	−	2.56872e7i	0.175635	−	1.33408i
$821$	−8.12503e6	+	1.61617e6i	−0.420695	+	0.0836814i	−0.400898	−	0.916123i	$-0.631302\pi$
$821$	−8.12503e6	+	1.61617e6i	−0.420695	+	0.0836814i	−0.0197967	+	0.999804i	$0.506302\pi$
$822$	−1.69830e6	−	2.54169e6i	−0.0876668	−	0.131203i
$823$	3.38113e6	−	3.38113e6i	0.174005	−	0.174005i	−0.614731	−	0.788737i	$-0.710736\pi$
$823$	3.38113e6	−	3.38113e6i	0.174005	−	0.174005i	0.788737	+	0.614731i	$0.210736\pi$
$824$	115936.	−	15263.2i	0.00594839	−	0.000783121i
$825$	−4.46056e6	+	587243.i	−0.228168	+	0.0300388i
$826$	−1.98976e7	+	1.98976e7i	−1.01473	+	1.01473i
$827$	2.00363e6	+	2.99865e6i	0.101872	+	0.152462i	0.878904	−	0.476999i	$-0.158276\pi$
$827$	2.00363e6	+	2.99865e6i	0.101872	+	0.152462i	−0.777032	+	0.629461i	$0.783276\pi$
$828$	−2.59888e6	+	516950.i	−0.131738	+	0.0262043i
$829$	−3.90260e6	+	2.96432e7i	−0.197228	+	1.49809i	0.550919	+	0.834559i	$0.314277\pi$
$829$	−3.90260e6	+	2.96432e7i	−0.197228	+	1.49809i	−0.748146	+	0.663534i	$0.769056\pi$
$830$	−9.86165e6	−	3.68042e7i	−0.496883	−	1.85439i
$831$	−3.11209e6	+	2.07943e6i	−0.156333	+	0.104458i
$832$	1.46879e7	+	4.98588e6i	0.735618	+	0.249709i
$833$	−270985.	−	4.13443e6i	−0.0135311	−	0.206444i
$834$	231607.	−	469652.i	0.0115302	−	0.0233809i
$835$	3.71832e7	−	4.23993e7i	1.84557	−	2.10447i
$836$	3.73442e6	+	3.27500e6i	0.184802	+	0.162067i
$837$	8.76621e6	−	1.51835e7i	0.432512	−	0.749133i
$838$	−2.52849e7	−	4.37947e7i	−1.24380	−	2.15432i
$839$	−7.15472e6	+	3.59692e7i	−0.350904	+	1.76411i	0.253403	+	0.967361i	$0.418450\pi$
$839$	−7.15472e6	+	3.59692e7i	−0.350904	+	1.76411i	−0.604307	+	0.796752i	$0.706550\pi$
$840$	89893.2	+	89893.2i	0.00439570	+	0.00439570i
$841$	−2.23752e7	−	1.71691e7i	−1.09088	−	0.837060i
$842$	4.52685e6	+	5.89951e6i	0.220047	+	0.286771i
$843$	8.63098e6	+	5.76703e6i	0.418303	+	0.279501i
$844$	4.65155e6	−	1.37030e7i	0.224772	−	0.662156i
$845$	−1.34736e7	−	2.68006e6i	−0.649144	−	0.129123i
$846$	−1.14405e7	−	2.76198e7i	−0.549564	−	1.32676i
$847$	2.64021e7	−	8.96232e6i	1.26453	−	0.429252i
$848$	8.50320e6	−	1.10816e7i	0.406062	−	0.529191i
$849$	9.71437e6	−	2.60296e6i	0.462536	−	0.123936i
$850$	−7.19828e6	−	8.20806e6i	−0.341728	−	0.389667i
$851$			4.17209e6i			0.197483i
$852$	9.46547e6	−	8.30099e6i	0.446728	−	0.391770i
$853$	−6.99597e6	−	3.51711e7i	−0.329212	−	1.65506i	−0.691042	−	0.722815i	$-0.742848\pi$
$853$	−6.99597e6	−	3.51711e7i	−0.329212	−	1.65506i	0.361830	−	0.932244i	$-0.382152\pi$
$854$	2.02972e7	−	3.03769e7i	0.952337	−	1.42527i
$855$	−1.01918e7	+	2.46053e7i	−0.476801	+	1.15110i
$856$	−10102.0	+	154127.i	−0.000471219	+	0.00718942i
$857$	9.93165e6	+	5.73404e6i	0.461923	+	0.266691i	0.712852	−	0.701314i	$-0.247403\pi$
$857$	9.93165e6	+	5.73404e6i	0.461923	+	0.266691i	−0.250930	+	0.968005i	$0.580736\pi$
$858$	2.54679e6	+	1.25594e6i	0.118107	+	0.0582438i
$859$	1.65746e7	+	1.08635e6i	0.766406	+	0.0502329i	0.443591	−	0.896229i	$-0.353704\pi$
$859$	1.65746e7	+	1.08635e6i	0.766406	+	0.0502329i	0.322815	+	0.946462i	$0.395371\pi$
$860$	1.07932e7	−	5.32259e6i	0.497625	−	0.245401i
$861$	−9.86661e6	+	4.08688e6i	−0.453586	+	0.187882i
$862$	3.41118e6	+	2.59105e7i	0.156364	+	1.18770i
$863$	1.03009e7	+	3.03454e7i	0.470811	+	1.38696i	0.880199	+	0.474604i	$0.157409\pi$
$863$	1.03009e7	+	3.03454e7i	0.470811	+	1.38696i	−0.409389	+	0.912360i	$0.634258\pi$
$864$	−6.26715e6	+	2.33893e7i	−0.285618	+	1.06594i
$865$	−4.82366e7	−	1.99802e7i	−2.19198	−	0.907947i
$866$	2.74320e7	−	1.79799e6i	1.24298	−	0.0814689i
$867$	7.95400e6	−	4.59225e6i	0.359367	−	0.207481i
$868$	−1.56547e7	−	3.17447e7i	−0.705256	−	1.43012i
$869$	−5.26094e6	−	1.40967e6i	−0.236328	−	0.0633238i
$870$	2.84325e7	−	2.18171e7i	1.27355	−	0.977233i
$871$	3.95431e6	+	520595.i	0.176614	+	0.0232517i
$872$	43680.4			0.00194534
$873$	−1.73135e7	−	6.06752e6i	−0.768866	−	0.269448i
$874$	−4.71562e6			−0.208814
$875$	−5.19385e7	−	6.83783e6i	−2.29334	−	0.301924i
$876$	−1.35637e7	+	1.04078e7i	−0.597199	+	0.458247i
$877$	3.44630e7	+	9.23434e6i	1.51305	+	0.405422i	0.917448	−	0.397855i	$-0.130245\pi$
$877$	3.44630e7	+	9.23434e6i	1.51305	+	0.405422i	0.595606	+	0.803277i	$0.296912\pi$
$878$	−4.30193e6	−	8.72346e6i	−0.188333	−	0.381902i
$879$	1.34326e7	−	7.75532e6i	0.586392	−	0.338554i
$880$	1.08993e7	−	714377.i	0.474451	−	0.0310972i
$881$	−1.62589e7	−	6.73464e6i	−0.705749	−	0.292331i	0.000795019	−	1.00000i	$-0.499747\pi$
$881$	−1.62589e7	−	6.73464e6i	−0.705749	−	0.292331i	−0.706544	+	0.707669i	$0.749747\pi$
$882$	7.50620e6	−	2.80135e7i	0.324899	−	1.21254i
$883$	−1.17457e6	−	3.46017e6i	−0.0506964	−	0.149347i	0.918633	−	0.395112i	$-0.129294\pi$
$883$	−1.17457e6	−	3.46017e6i	−0.0506964	−	0.149347i	−0.969329	+	0.245765i	$0.920961\pi$
$884$	448772.	+	3.40876e6i	0.0193150	+	0.146712i
$885$	1.11502e7	−	4.61858e6i	0.478548	−	0.198221i
$886$	3.45382e7	−	1.70324e7i	1.47814	−	0.728938i
$887$	−1.22652e7	−	803904.i	−0.523439	−	0.0343080i	−0.198606	−	0.980079i	$-0.563641\pi$
$887$	−1.22652e7	−	803904.i	−0.523439	−	0.0343080i	−0.324833	+	0.945771i	$0.605308\pi$
$888$	63101.6	+	31118.3i	0.00268539	+	0.00132429i
$889$	−3.31702e7	−	1.91508e7i	−1.40765	−	0.812704i
$890$	−2.44104e6	+	3.72430e7i	−0.103300	+	1.57605i
$891$	1.19950e6	−	2.89585e6i	0.0506182	−	0.122203i
$892$	2.11578e7	−	3.16649e7i	0.890346	−	1.33250i
$893$	−5.17890e6	−	2.60361e7i	−0.217325	−	1.09257i
$894$	−1.18203e7	+	1.03661e7i	−0.494635	+	0.433783i
$895$			6.58115e7i			2.74628i
$896$	−267179.	−	304659.i	−0.0111181	−	0.0126778i
$897$	−1.29933e6	+	348154.i	−0.0539184	+	0.0144474i
$898$	−2.06083e7	+	2.68572e7i	−0.852808	+	1.11140i
$899$	3.91605e7	−	1.32932e7i	1.61603	−	0.548568i
$900$	−1.45916e7	−	3.52273e7i	−0.600479	−	1.44968i
$901$	3.01163e6	+	599051.i	0.123592	+	0.0245840i
$902$	−2.41978e6	+	7.12846e6i	−0.0990285	+	0.291729i
$903$	−4.12447e6	−	2.75588e6i	−0.168325	−	0.112471i
$904$	133054.	+	173400.i	0.00541512	+	0.00705713i
$905$	5.93208e7	+	4.55184e7i	2.40761	+	1.84742i
$906$	−1.54689e7	−	1.54689e7i	−0.626092	−	0.626092i
$907$	−4.34788e6	+	2.18583e7i	−0.175493	+	0.882261i	0.788235	+	0.615374i	$0.210995\pi$
$907$	−4.34788e6	+	2.18583e7i	−0.175493	+	0.882261i	−0.963728	+	0.266887i	$0.914005\pi$
$908$	−2.32485e7	−	4.02675e7i	−0.935792	−	1.62084i
$909$	3.27199e6	−	5.66725e6i	0.131342	−	0.227490i
$910$	5.14760e7	+	4.51432e7i	2.06064	+	1.80713i
$911$	1.55675e6	−	1.77513e6i	0.0621474	−	0.0708655i	−0.719931	−	0.694046i	$-0.755826\pi$
$911$	1.55675e6	−	1.77513e6i	0.0621474	−	0.0708655i	0.782078	+	0.623180i	$0.214160\pi$
$912$	−4.28709e6	+	8.69336e6i	−0.170677	+	0.346099i
$913$	361287.	+	5.51217e6i	0.0143442	+	0.218850i
$914$	−4.97140e7	−	1.68756e7i	−1.96840	−	0.668182i
$915$	−1.30285e7	+	8.70539e6i	−0.514450	+	0.343744i
$916$	9.33379e6	+	3.48342e7i	0.367552	+	1.37172i
$917$	−1.98179e6	+	1.50532e7i	−0.0778279	+	0.591161i
$918$	−5.24239e6	+	1.04278e6i	−0.205316	+	0.0408399i
$919$	−3.86824e6	−	5.78923e6i	−0.151086	−	0.226116i	0.748204	−	0.663469i	$-0.230916\pi$
$919$	−3.86824e6	−	5.78923e6i	−0.151086	−	0.226116i	−0.899290	+	0.437352i	$0.855916\pi$
$920$	−30016.8	+	30016.8i	−0.00116921	+	0.00116921i
$921$	−1.06706e7	+	1.40481e6i	−0.414515	+	0.0545720i
$922$	5.03328e7	−	6.62644e6i	1.94995	−	0.256716i
$923$	−1.98711e7	+	1.98711e7i	−0.767747	+	0.767747i
$924$	2.47058e6	+	3.69748e6i	0.0951959	+	0.142471i
$925$	−5.88816e7	+	1.17123e7i	−2.26269	+	0.450077i
$926$	−4.38563e6	+	3.33122e7i	−0.168076	+	1.27666i
$927$	5.67647e6	+	2.11849e7i	0.216960	+	0.809704i
$928$	−4.74908e7	+	3.17323e7i	−1.81025	+	1.20957i
$929$	−1.26786e6	−	430381.i	−0.0481984	−	0.0163612i	0.297236	−	0.954804i	$-0.403935\pi$
$929$	−1.26786e6	−	430381.i	−0.0481984	−	0.0163612i	−0.345435	+	0.938443i	$0.612268\pi$
$930$	1.98985e6	+	3.03592e7i	0.0754420	+	1.15102i
$931$	1.13901e7	−	2.30968e7i	0.430679	−	0.873330i
$932$	4.56165e6	−	5.20157e6i	0.172021	−	0.196153i
$933$	−4.13342e6	−	3.62491e6i	−0.155455	−	0.136331i
$934$	2.68940e7	−	4.65817e7i	1.00876	−	1.74722i
$935$	1.20058e6	+	2.07947e6i	0.0449120	+	0.0777899i
$936$	19459.2	−	97827.9i	0.000725997	−	0.00364983i
$937$	−1.86680e7	−	1.86680e7i	−0.694622	−	0.694622i	0.268623	−	0.963245i	$-0.413431\pi$
$937$	−1.86680e7	−	1.86680e7i	−0.694622	−	0.694622i	−0.963245	+	0.268623i	$0.913431\pi$
$938$	9.93104e6	+	7.62036e6i	0.368543	+	0.282793i
$939$	−2.60001e6	−	3.38840e6i	−0.0962302	−	0.125410i
$940$	4.79408e7	+	3.20330e7i	1.76964	+	1.18244i
$941$	−1.44739e6	+	4.26388e6i	−0.0532859	+	0.156975i	−0.970315	−	0.241846i	$-0.922247\pi$
$941$	−1.44739e6	+	4.26388e6i	−0.0532859	+	0.156975i	0.917029	+	0.398821i	$0.130581\pi$
$942$	2.76406e7	+	5.49805e6i	1.01489	+	0.201875i
$943$	−1.36468e6	−	3.29462e6i	−0.0499747	−	0.120650i
$944$	−1.82890e7	+	6.20826e6i	−0.667973	+	0.226746i
$945$	−3.23314e7	+	4.21352e7i	−1.17773	+	1.53485i
$946$	−3.37746e6	+	904988.i	−0.122705	+	0.0328787i
$947$	−1.08302e7	−	1.23495e7i	−0.392430	−	0.447481i	0.521562	−	0.853214i	$-0.325350\pi$
$947$	−1.08302e7	−	1.23495e7i	−0.392430	−	0.447481i	−0.913992	+	0.405733i	$0.867016\pi$
$948$			1.04980e7i			0.379389i
$949$	2.86918e7	−	2.51621e7i	1.03417	−	0.906944i
$950$	−1.32381e7	−	6.65525e7i	−0.475902	−	2.39252i
$951$	−1.86768e6	+	2.79517e6i	−0.0669654	+	0.100221i
$952$	17115.0	−	41319.2i	0.000612046	−	0.00147761i
$953$	−2.74671e6	+	4.19067e7i	−0.0979673	+	1.49469i	0.612225	+	0.790684i	$0.290275\pi$
$953$	−2.74671e6	+	4.19067e7i	−0.0979673	+	1.49469i	−0.710192	+	0.704008i	$0.751392\pi$
$954$	1.86139e7	+	1.07467e7i	0.662164	+	0.382301i
$955$	2.91736e7	+	1.43868e7i	1.03510	+	0.510454i
$956$	−1.89812e7	−	1.24409e6i	−0.671705	−	0.0440259i
$957$	−4.65994e6	+	2.29803e6i	−0.164475	+	0.0811102i
$958$	−5.28754e6	+	2.19017e6i	−0.186140	+	0.0771017i
$959$	1.39473e6	+	1.05940e7i	0.0489716	+	0.371976i
$960$	−6.71152e6	−	1.97715e7i	−0.235040	−	0.692407i
$961$	−1.67678e6	+	6.25784e6i	−0.0585691	+	0.218583i
$962$	3.50076e7	+	1.45006e7i	1.21962	+	0.505184i
$963$	−2.89075e7	+	1.89470e6i	−1.00449	+	0.0658377i
$964$	2.50323e6	−	1.44524e6i	0.0867576	−	0.0500896i
$965$	3.59697e7	+	7.29394e7i	1.24342	+	2.52141i
$966$	−4.07797e6	−	1.09269e6i	−0.140605	−	0.0376751i
$967$	−2.32124e7	+	1.78115e7i	−0.798278	+	0.612541i	−0.925247	−	0.379366i	$-0.876142\pi$
$967$	−2.32124e7	+	1.78115e7i	−0.798278	+	0.612541i	0.126968	+	0.991907i	$0.459475\pi$
$968$	155662.	+	20493.3i	0.00533942	+	0.000702949i
$969$	−2.13083e6			−0.0729021
$970$	6.86734e7	−	1.76796e7i	2.34347	−	0.603315i
$971$	−1.47443e7			−0.501853			−0.250927	−	0.968006i	$-0.580735\pi$
$971$	−1.47443e7			−0.501853			−0.250927	+	0.968006i	$0.580735\pi$
$972$	−2.87078e7	−	3.77945e6i	−0.974616	−	0.128311i
$973$	−1.45221e6	+	1.11432e6i	−0.0491754	+	0.0377336i
$974$	1.96792e6	+	527303.i	0.0664676	+	0.0178099i
$975$	−8.56115e6	−	1.73603e7i	−0.288417	−	0.584851i
$976$	2.17161e7	−	1.25378e7i	0.729723	−	0.421306i
$977$	3.82341e7	−	2.50600e6i	1.28149	−	0.0839932i	0.590606	−	0.806960i	$-0.298889\pi$
$977$	3.82341e7	−	2.50600e6i	1.28149	−	0.0839932i	0.690883	+	0.722967i	$0.257222\pi$
$978$	1.92991e7	+	7.99394e6i	0.645192	+	0.267247i
$979$	1.40046e6	−	5.22661e6i	0.0466999	−	0.174286i
$980$	1.79795e7	+	5.29659e7i	0.598016	+	1.76170i
$981$	1.06934e6	+	8.12248e6i	0.0354768	+	0.269473i
$982$	−6.24395e7	+	2.58633e7i	−2.06624	+	0.855865i
$983$	1.30666e7	−	6.44374e6i	0.431300	−	0.212693i	−0.213663	−	0.976907i	$-0.568539\pi$
$983$	1.30666e7	−	6.44374e6i	0.431300	−	0.212693i	0.644963	+	0.764214i	$0.276873\pi$
$984$	−60008.8	−	3933.18i	−0.00197573	−	0.000129496i
$985$	7.68652e7	+	3.79057e7i	2.52429	+	1.24484i
$986$	−1.09188e7	−	6.30397e6i	−0.357670	−	0.206501i
$987$	1.55440e6	−	2.37155e7i	0.0507889	−	0.774889i
$988$	−8.17793e6	+	1.97433e7i	−0.266533	+	0.643467i
$989$	920234.	−	1.37723e6i	0.0299163	−	0.0447729i
$990$	3.27895e6	+	1.64844e7i	0.106328	+	0.534546i
$991$	−5.53915e6	+	4.85771e6i	−0.179167	+	0.157126i	−0.744232	−	0.667921i	$-0.767184\pi$
$991$	−5.53915e6	+	4.85771e6i	−0.179167	+	0.157126i	0.565065	+	0.825046i	$0.308851\pi$
$992$		−	4.84881e7i		−	1.56443i
$993$	−8.20046e6	−	9.35083e6i	−0.263916	−	0.300938i
$994$	−8.51936e7	+	2.28276e7i	−2.73490	+	0.732814i
$995$	4.84913e7	−	6.31950e7i	1.55276	−	2.02360i
$996$	1.00822e7	−	3.42246e6i	0.322039	−	0.109318i
$997$	−104859.	−	253152.i	−0.00334093	−	0.00806573i	0.922200	−	0.386713i	$-0.126389\pi$
$997$	−104859.	−	253152.i	−0.00334093	−	0.00806573i	−0.925541	+	0.378647i	$0.876389\pi$
$998$	−4.20414e6	−	836255.i	−0.133614	−	0.0265774i
$999$	−9.44812e6	+	2.78333e7i	−0.299524	+	0.882369i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	97.6.k.a.2.7	✓	640
97.49	even	48	inner	97.6.k.a.49.7	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
97.6.k.a.2.7	✓	640	1.1	even	1	trivial
97.6.k.a.49.7	yes	640	97.49	even	48	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:	\( N \)	\(=\)	\( 97 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	97.k (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.92337 - 1.04313i) q^{2} +(5.32344 - 4.08482i) q^{3} +(30.7820 + 8.24802i) q^{4} +(42.3505 + 85.8783i) q^{5} +(-46.4406 + 26.8125i) q^{6} +(187.048 - 12.2598i) q^{7} +(0.975199 + 0.403941i) q^{8} +(-51.2397 + 191.229i) q^{9} +(-245.976 - 724.623i) q^{10} +(14.4808 + 109.992i) q^{11} +(197.558 - 81.8313i) q^{12} +(-428.086 + 211.109i) q^{13} +(-1494.84 - 97.9771i) q^{14} +(576.248 + 284.174i) q^{15} +(-890.455 - 514.105i) q^{16} +(14.7833 - 225.550i) q^{17} +(605.469 - 1461.73i) q^{18} +(780.528 - 1168.14i) q^{19} +(595.309 + 2992.82i) q^{20} +(945.663 - 829.324i) q^{21} -886.617i q^{22} +(276.925 + 315.772i) q^{23} +(6.84144 - 1.83316i) q^{24} +(-3679.14 + 4794.75i) q^{25} +(3612.10 - 1226.14i) q^{26} +(1132.35 + 2733.73i) q^{27} +(5858.85 + 1165.40i) q^{28} +(-2243.51 + 6609.17i) q^{29} +(-4269.40 - 2852.72i) q^{30} +(-3607.02 - 4700.76i) q^{31} +(6492.33 + 4981.74i) q^{32} +(526.388 + 526.388i) q^{33} +(-352.412 + 1771.70i) q^{34} +(8974.45 + 15544.2i) q^{35} +(-3154.53 + 5463.80i) q^{36} +(7468.46 + 6549.66i) q^{37} +(-7402.94 + 8441.43i) q^{38} +(-1416.55 + 2872.48i) q^{39} +(6.61042 + 100.856i) q^{40} +(-8040.07 - 2729.23i) q^{41} +(-8357.93 + 5584.59i) q^{42} +(-1020.72 - 3809.38i) q^{43} +(-461.473 + 3505.23i) q^{44} +(-18592.5 + 3698.28i) q^{45} +(-1864.78 - 2790.85i) q^{46} +(13361.0 - 13361.0i) q^{47} +(-6840.32 + 900.545i) q^{48} +(18173.6 - 2392.60i) q^{49} +(34152.8 - 34152.8i) q^{50} +(-842.634 - 1261.09i) q^{51} +(-14918.6 + 2967.49i) q^{52} +(-1773.18 + 13468.6i) q^{53} +(-6120.37 - 22841.5i) q^{54} +(-8832.71 + 5901.82i) q^{55} +(187.362 + 63.6007i) q^{56} +(-616.558 - 9406.86i) q^{57} +(24670.4 - 50026.6i) q^{58} +(12385.2 - 14122.6i) q^{59} +(15394.2 + 13500.4i) q^{60} +(-12193.8 + 21120.3i) q^{61} +(23676.2 + 41008.5i) q^{62} +(-7239.88 + 36397.3i) q^{63} +(-22978.8 - 22978.8i) q^{64} +(-36259.3 - 27822.8i) q^{65} +(-3621.67 - 4719.85i) q^{66} +(-6947.82 - 4642.38i) q^{67} +(2315.41 - 6820.96i) q^{68} +(2764.06 + 549.807i) q^{69} +(-54893.2 - 132524. i) q^{70} +(55751.3 - 18925.0i) q^{71} +(-127.214 + 165.789i) q^{72} +(-77228.3 + 20693.3i) q^{73} +(-52343.2 - 59686.0i) q^{74} +40553.3i q^{75} +(33661.1 - 29520.0i) q^{76} +(4057.09 + 20396.4i) q^{77} +(14220.2 - 21282.1i) q^{78} +(-18787.3 + 45356.6i) q^{79} +(6439.21 - 98243.4i) q^{80} +(-24467.9 - 14126.6i) q^{81} +(60857.5 + 30011.6i) q^{82} +(49685.4 + 3256.55i) q^{83} +(35949.7 - 17728.4i) q^{84} +(19996.0 - 8282.60i) q^{85} +(4113.86 + 31247.9i) q^{86} +(15054.1 + 44347.9i) q^{87} +(-30.3088 + 113.114i) q^{88} +(-45060.6 - 18664.7i) q^{89} +(151173. - 9908.40i) q^{90} +(-77484.7 + 44735.8i) q^{91} +(5919.81 + 12004.2i) q^{92} +(-38403.5 - 10290.2i) q^{93} +(-119801. + 91926.6i) q^{94} +(133374. + 17559.0i) q^{95} +54911.1 q^{96} +(-6969.04 + 92405.5i) q^{97} -146492. q^{98} +(-21775.8 - 2866.84i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 16 q^{2} + 72 q^{3} - 16 q^{4} - 16 q^{5} - 24 q^{6} - 16 q^{7} - 16 q^{8} - 280 q^{9} - 3984 q^{10} - 16 q^{11} - 4496 q^{12} - 16 q^{13} - 11008 q^{14} - 7664 q^{15} - 24 q^{16} - 2904 q^{17}+ \cdots - 1255776 q^{99}+O(q^{100}) \) 640 * q - 16 * q^2 + 72 * q^3 - 16 * q^4 - 16 * q^5 - 24 * q^6 - 16 * q^7 - 16 * q^8 - 280 * q^9 - 3984 * q^10 - 16 * q^11 - 4496 * q^12 - 16 * q^13 - 11008 * q^14 - 7664 * q^15 - 24 * q^16 - 2904 * q^17 + 14080 * q^18 + 11880 * q^19 - 11528 * q^20 - 16 * q^21 + 11128 * q^23 - 8208 * q^24 + 20216 * q^25 + 23944 * q^26 + 42048 * q^27 + 4344 * q^28 + 5664 * q^29 - 25016 * q^30 + 17720 * q^31 + 38288 * q^32 + 29992 * q^33 + 43504 * q^34 - 78408 * q^35 + 383608 * q^36 + 36792 * q^37 - 16 * q^38 + 32064 * q^39 - 68368 * q^40 - 62256 * q^41 - 62224 * q^42 - 6168 * q^43 + 73448 * q^44 + 302312 * q^45 - 16 * q^46 - 130528 * q^47 - 123216 * q^48 - 200400 * q^49 + 56408 * q^50 - 36624 * q^51 - 15184 * q^52 + 28608 * q^53 + 26160 * q^54 - 106768 * q^55 - 16 * q^56 - 16 * q^57 - 353424 * q^58 + 108448 * q^59 - 415744 * q^60 - 178616 * q^61 + 246008 * q^62 + 9648 * q^63 - 8208 * q^64 - 273528 * q^65 + 143104 * q^66 - 128800 * q^67 - 480600 * q^68 + 475104 * q^69 - 736096 * q^70 - 510680 * q^71 - 1088528 * q^72 - 239248 * q^73 - 249680 * q^74 + 1175984 * q^76 - 16 * q^77 - 62224 * q^78 - 450336 * q^79 - 882928 * q^80 - 626184 * q^81 + 164136 * q^82 - 45248 * q^83 + 2157472 * q^84 + 1060392 * q^85 + 1314208 * q^86 + 567200 * q^87 + 744432 * q^88 + 382432 * q^89 + 758960 * q^90 - 299688 * q^91 + 569608 * q^92 - 513336 * q^93 - 1447312 * q^94 - 1202720 * q^95 - 2188832 * q^96 - 754896 * q^97 + 3555136 * q^98 - 1255776 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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