LMFDB - Embedded newform 409.3.p.a.21.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [409,3,Mod(21,409)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(409, base_ring=CyclotomicField(408)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("409.21"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 409 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	409.p (of order $408$, degree $128$, 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:	$11.1444428123$
Analytic rank:	$0$
Dimension:	$8576$
Relative dimension:	$67$ over $\Q(\zeta_{408})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{408}]$

Embedding invariants

Embedding label			21.18
Character	$\chi$	$=$	409.21
Dual form			409.3.p.a.39.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.87616 - 1.37196i) q^{2} +(-2.27472 - 1.77344i) q^{3} +(0.425102 + 1.33628i) q^{4} +(-5.80963 - 1.08601i) q^{5} +(1.83464 + 6.44810i) q^{6} +(-7.01076 + 5.37954i) q^{7} +(-1.91878 + 5.72485i) q^{8} +(-0.165999 - 0.660008i) q^{9} +(9.40985 + 10.0081i) q^{10} +(-1.29784 - 11.1867i) q^{11} +(1.40284 - 3.79356i) q^{12} +(-17.9706 + 14.2343i) q^{13} +(20.5339 - 0.474415i) q^{14} +(11.2893 + 12.7734i) q^{15} +(16.0323 - 11.3491i) q^{16} +(-8.21313 + 12.3949i) q^{17} +(-0.594065 + 1.46603i) q^{18} +(5.21713 - 4.98150i) q^{19} +(-1.01847 - 8.22497i) q^{20} +(25.4878 + 0.196259i) q^{21} +(-12.9128 + 22.7686i) q^{22} +(-3.52372 - 17.3653i) q^{23} +(14.5174 - 9.61956i) q^{24} +(9.26056 + 3.58756i) q^{25} +(53.2447 - 2.05093i) q^{26} +(-11.2783 + 25.5429i) q^{27} +(-10.1689 - 7.08150i) q^{28} +(3.73942 - 4.57443i) q^{29} +(-3.65590 - 39.4535i) q^{30} +(-21.9932 - 9.10988i) q^{31} +(-21.5012 - 0.331144i) q^{32} +(-16.8868 + 27.7482i) q^{33} +(32.4144 - 11.9867i) q^{34} +(46.5721 - 23.6394i) q^{35} +(0.811392 - 0.502393i) q^{36} +(-46.2756 - 42.8428i) q^{37} +(-16.6226 + 2.18841i) q^{38} +(66.1218 - 0.509146i) q^{39} +(17.3646 - 31.1754i) q^{40} +(-14.3272 + 15.2381i) q^{41} +(-47.5500 - 35.3365i) q^{42} +(-26.5546 + 27.8107i) q^{43} +(14.3969 - 6.48976i) q^{44} +(0.247617 + 4.01468i) q^{45} +(-17.2134 + 37.4145i) q^{46} +(13.0450 - 57.4449i) q^{47} +(-56.5959 - 2.61659i) q^{48} +(7.52909 - 28.0990i) q^{49} +(-12.4523 - 19.4360i) q^{50} +(40.6641 - 13.6292i) q^{51} +(-26.6604 - 17.9628i) q^{52} +(44.8714 - 77.7195i) q^{53} +(56.2039 - 32.4493i) q^{54} +(-4.60889 + 66.3999i) q^{55} +(-17.3450 - 50.4576i) q^{56} +(-20.7019 + 2.07920i) q^{57} +(-13.2917 + 3.45204i) q^{58} +(-3.24530 + 8.98810i) q^{59} +(-12.2698 + 20.5157i) q^{60} +(2.64502 - 1.55438i) q^{61} +(28.7644 + 47.2655i) q^{62} +(4.71432 + 3.73416i) q^{63} +(-22.8154 - 17.2294i) q^{64} +(119.861 - 63.1798i) q^{65} +(69.7518 - 28.8921i) q^{66} +(37.9166 - 15.0257i) q^{67} +(-20.0545 - 5.70598i) q^{68} +(-22.7809 + 45.7501i) q^{69} +(-119.809 - 19.5437i) q^{70} +(64.2285 + 74.9678i) q^{71} +(4.09696 + 0.316090i) q^{72} +(-15.8918 - 22.8203i) q^{73} +(28.0419 + 143.869i) q^{74} +(-14.7028 - 24.5838i) q^{75} +(8.87450 + 4.85391i) q^{76} +(69.2781 + 71.4454i) q^{77} +(-124.754 - 89.7613i) q^{78} +(-12.0307 - 57.0317i) q^{79} +(-105.467 + 48.5225i) q^{80} +(65.5577 - 35.2037i) q^{81} +(47.7862 - 8.93279i) q^{82} +(-46.0119 - 92.4044i) q^{83} +(10.5727 + 34.1424i) q^{84} +(61.1761 - 63.0900i) q^{85} +(87.9760 - 15.7455i) q^{86} +(-16.6186 + 3.77387i) q^{87} +(66.5323 + 14.0348i) q^{88} +(-52.7485 + 48.0866i) q^{89} +(5.04342 - 7.87192i) q^{90} +(49.4134 - 196.467i) q^{91} +(21.7070 - 12.0907i) q^{92} +(33.8724 + 59.7261i) q^{93} +(-103.287 + 89.8789i) q^{94} +(-35.7195 + 23.2748i) q^{95} +(48.3219 + 38.8845i) q^{96} +(23.5545 + 7.69343i) q^{97} +(-52.6765 + 42.3886i) q^{98} +(-7.16787 + 2.71356i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8576 q - 124 q^{2} - 112 q^{3} - 124 q^{4} - 120 q^{5} - 120 q^{6} - 144 q^{7} + 8 q^{8} - 292 q^{9} - 96 q^{10} - 160 q^{11} + 36 q^{12} - 164 q^{13} - 16 q^{14} - 80 q^{15} - 204 q^{16} - 148 q^{17} - 148 q^{18}+ \cdots + 1180 q^{99}+O(q^{100}) $ 8576 * q - 124 * q^2 - 112 * q^3 - 124 * q^4 - 120 * q^5 - 120 * q^6 - 144 * q^7 + 8 * q^8 - 292 * q^9 - 96 * q^10 - 160 * q^11 + 36 * q^12 - 164 * q^13 - 16 * q^14 - 80 * q^15 - 204 * q^16 - 148 * q^17 - 148 * q^18 - 96 * q^19 + 68 * q^20 - 144 * q^21 - 256 * q^22 - 128 * q^23 - 1156 * q^24 - 2496 * q^25 - 280 * q^26 - 100 * q^27 - 92 * q^28 - 80 * q^29 + 672 * q^30 - 168 * q^31 + 2112 * q^32 - 96 * q^33 + 92 * q^34 + 64 * q^35 - 2344 * q^36 - 152 * q^37 - 2972 * q^39 + 112 * q^40 - 196 * q^41 + 488 * q^42 - 452 * q^43 + 92 * q^44 - 244 * q^45 - 124 * q^46 + 16 * q^47 - 188 * q^48 + 16 * q^49 + 96 * q^50 + 8 * q^51 - 828 * q^52 - 256 * q^53 + 240 * q^54 - 1016 * q^55 + 76 * q^56 - 92 * q^57 - 800 * q^58 + 48 * q^59 - 64 * q^60 + 428 * q^61 - 52 * q^62 + 1604 * q^63 - 136 * q^64 + 136 * q^65 + 224 * q^66 + 600 * q^67 - 136 * q^68 + 2808 * q^69 - 20 * q^70 - 188 * q^71 + 560 * q^72 + 144 * q^73 - 996 * q^74 + 1152 * q^75 + 992 * q^76 - 3084 * q^77 - 4900 * q^78 - 560 * q^79 - 292 * q^80 - 3128 * q^81 + 1488 * q^82 + 120 * q^83 + 6560 * q^84 + 288 * q^85 + 3248 * q^86 - 632 * q^87 + 144 * q^88 + 608 * q^89 + 268 * q^90 + 404 * q^91 - 5128 * q^92 - 104 * q^93 - 624 * q^94 + 84 * q^95 + 140 * q^96 - 840 * q^97 - 72 * q^98 + 1180 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/409\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{408}\right)$

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 $

$2$	−1.87616	−	1.37196i	−0.938082	−	0.685981i	0.0113559	−	0.999936i	$-0.496385\pi$
$2$	−1.87616	−	1.37196i	−0.938082	−	0.685981i	−0.949438	+	0.313955i	$0.898346\pi$
$3$	−2.27472	−	1.77344i	−0.758238	−	0.591148i	0.160027	−	0.987113i	$-0.448842\pi$
$3$	−2.27472	−	1.77344i	−0.758238	−	0.591148i	−0.918266	+	0.395964i	$0.870410\pi$
$4$	0.425102	+	1.33628i	0.106276	+	0.334071i
$5$	−5.80963	−	1.08601i	−1.16193	−	0.217202i	−0.432741	−	0.901518i	$-0.642453\pi$
$5$	−5.80963	−	1.08601i	−1.16193	−	0.217202i	−0.729185	+	0.684317i	$0.760101\pi$
$6$	1.83464	+	6.44810i	0.305774	+	1.07468i
$7$	−7.01076	+	5.37954i	−1.00154	+	0.768506i	−0.972934	−	0.231085i	$-0.925773\pi$
$7$	−7.01076	+	5.37954i	−1.00154	+	0.768506i	−0.0286030	+	0.999591i	$0.509106\pi$
$8$	−1.91878	+	5.72485i	−0.239847	+	0.715606i
$9$	−0.165999	−	0.660008i	−0.0184443	−	0.0733343i
$10$	9.40985	+	10.0081i	0.940985	+	1.00081i
$11$	−1.29784	−	11.1867i	−0.117985	−	1.01697i	−0.912316	−	0.409487i	$-0.865708\pi$
$11$	−1.29784	−	11.1867i	−0.117985	−	1.01697i	0.794331	−	0.607485i	$-0.207822\pi$
$12$	1.40284	−	3.79356i	0.116903	−	0.316130i
$13$	−17.9706	+	14.2343i	−1.38235	+	1.09495i	−0.398265	+	0.917271i	$0.630387\pi$
$13$	−17.9706	+	14.2343i	−1.38235	+	1.09495i	−0.984089	+	0.177676i	$0.943142\pi$
$14$	20.5339	−	0.474415i	1.46670	−	0.0338868i
$15$	11.2893	+	12.7734i	0.752618	+	0.851561i
$16$	16.0323	−	11.3491i	1.00202	−	0.709316i
$17$	−8.21313	+	12.3949i	−0.483125	+	0.729109i	−0.991224	−	0.132190i	$-0.957799\pi$
$17$	−8.21313	+	12.3949i	−0.483125	+	0.729109i	0.508099	+	0.861298i	$0.330348\pi$
$18$	−0.594065	+	1.46603i	−0.0330036	+	0.0814460i
$19$	5.21713	−	4.98150i	0.274586	−	0.262184i	−0.540736	−	0.841192i	$-0.681854\pi$
$19$	5.21713	−	4.98150i	0.274586	−	0.262184i	0.815322	+	0.579008i	$0.196560\pi$
$20$	−1.01847	−	8.22497i	−0.0509236	−	0.411249i
$21$	25.4878	+	0.196259i	1.21370	+	0.00934569i
$22$	−12.9128	+	22.7686i	−0.586943	+	1.03494i
$23$	−3.52372	−	17.3653i	−0.153205	−	0.755011i	−0.981004	−	0.193986i	$-0.937858\pi$
$23$	−3.52372	−	17.3653i	−0.153205	−	0.755011i	0.827799	−	0.561025i	$-0.189593\pi$
$24$	14.5174	−	9.61956i	0.604890	−	0.400815i
$25$	9.26056	+	3.58756i	0.370422	+	0.143502i
$26$	53.2447	−	2.05093i	2.04787	−	0.0788819i
$27$	−11.2783	+	25.5429i	−0.417715	+	0.946035i
$28$	−10.1689	−	7.08150i	−0.363174	−	0.252911i
$29$	3.73942	−	4.57443i	0.128946	−	0.157739i	−0.705730	−	0.708481i	$-0.749381\pi$
$29$	3.73942	−	4.57443i	0.128946	−	0.157739i	0.834675	+	0.550742i	$0.185655\pi$
$30$	−3.65590	−	39.4535i	−0.121863	−	1.31512i
$31$	−21.9932	−	9.10988i	−0.709458	−	0.293867i	−0.00137767	−	0.999999i	$-0.500439\pi$
$31$	−21.9932	−	9.10988i	−0.709458	−	0.293867i	−0.708080	+	0.706132i	$0.750439\pi$
$32$	−21.5012	−	0.331144i	−0.671913	−	0.0103483i
$33$	−16.8868	+	27.7482i	−0.511720	+	0.840854i
$34$	32.4144	−	11.9867i	0.953366	−	0.352549i
$35$	46.5721	−	23.6394i	1.33063	−	0.675412i
$36$	0.811392	−	0.502393i	0.0225387	−	0.0139553i
$37$	−46.2756	−	42.8428i	−1.25069	−	1.15791i	−0.980798	−	0.195024i	$-0.937521\pi$
$37$	−46.2756	−	42.8428i	−1.25069	−	1.15791i	−0.269893	−	0.962890i	$-0.586988\pi$
$38$	−16.6226	+	2.18841i	−0.437437	+	0.0575897i
$39$	66.1218	−	0.509146i	1.69543	−	0.0130550i
$40$	17.3646	−	31.1754i	0.434115	−	0.779386i
$41$	−14.3272	+	15.2381i	−0.349443	+	0.371660i	−0.879170	−	0.476508i	$-0.841902\pi$
$41$	−14.3272	+	15.2381i	−0.349443	+	0.371660i	0.529727	+	0.848168i	$0.322294\pi$
$42$	−47.5500	−	35.3365i	−1.13214	−	0.841345i
$43$	−26.5546	+	27.8107i	−0.617549	+	0.646760i	−0.955704	−	0.294331i	$-0.904903\pi$
$43$	−26.5546	+	27.8107i	−0.617549	+	0.646760i	0.338154	+	0.941091i	$0.390197\pi$
$44$	14.3969	−	6.48976i	0.327202	−	0.147495i
$45$	0.247617	+	4.01468i	0.00550260	+	0.0892151i
$46$	−17.2134	+	37.4145i	−0.374204	+	0.813358i
$47$	13.0450	−	57.4449i	0.277552	−	1.22223i	−0.621157	−	0.783686i	$-0.713337\pi$
$47$	13.0450	−	57.4449i	0.277552	−	1.22223i	0.898709	−	0.438545i	$-0.144506\pi$
$48$	−56.5959	−	2.61659i	−1.17908	−	0.0545122i
$49$	7.52909	−	28.0990i	0.153655	−	0.573448i
$50$	−12.4523	−	19.4360i	−0.249047	−	0.388720i
$51$	40.6641	−	13.6292i	0.797335	−	0.267240i
$52$	−26.6604	−	17.9628i	−0.512700	−	0.345438i
$53$	44.8714	−	77.7195i	0.846630	−	1.46641i	−0.0375683	−	0.999294i	$-0.511961\pi$
$53$	44.8714	−	77.7195i	0.846630	−	1.46641i	0.884198	−	0.467112i	$-0.154705\pi$
$54$	56.2039	−	32.4493i	1.04081	−	0.600914i
$55$	−4.60889	+	66.3999i	−0.0837979	+	1.20727i
$56$	−17.3450	−	50.4576i	−0.309732	−	0.901029i
$57$	−20.7019	+	2.07920i	−0.363191	+	0.0364772i
$58$	−13.2917	+	3.45204i	−0.229168	+	0.0595178i
$59$	−3.24530	+	8.98810i	−0.0550051	+	0.152341i	−0.964981	−	0.262321i	$-0.915512\pi$
$59$	−3.24530	+	8.98810i	−0.0550051	+	0.152341i	0.909976	+	0.414662i	$0.136100\pi$
$60$	−12.2698	+	20.5157i	−0.204497	+	0.341928i
$61$	2.64502	−	1.55438i	0.0433609	−	0.0254816i	−0.484813	−	0.874618i	$-0.661112\pi$
$61$	2.64502	−	1.55438i	0.0433609	−	0.0254816i	0.528174	+	0.849136i	$0.322877\pi$
$62$	28.7644	+	47.2655i	0.463943	+	0.762346i
$63$	4.71432	+	3.73416i	0.0748305	+	0.0592724i
$64$	−22.8154	−	17.2294i	−0.356491	−	0.269209i
$65$	119.861	−	63.1798i	1.84402	−	0.971997i
$66$	69.7518	−	28.8921i	1.05685	−	0.437760i
$67$	37.9166	−	15.0257i	0.565919	−	0.224265i	−0.0679720	−	0.997687i	$-0.521653\pi$
$67$	37.9166	−	15.0257i	0.565919	−	0.224265i	0.633891	+	0.773422i	$0.281457\pi$
$68$	−20.0545	−	5.70598i	−0.294918	−	0.0839115i
$69$	−22.7809	+	45.7501i	−0.330157	+	0.663046i
$70$	−119.809	−	19.5437i	−1.71156	−	0.279196i
$71$	64.2285	+	74.9678i	0.904626	+	1.05588i	0.998182	+	0.0602702i	$0.0191962\pi$
$71$	64.2285	+	74.9678i	0.904626	+	1.05588i	−0.0935558	+	0.995614i	$0.529823\pi$
$72$	4.09696	+	0.316090i	0.0569022	+	0.00439014i
$73$	−15.8918	−	22.8203i	−0.217696	−	0.312607i	0.696750	−	0.717314i	$-0.254629\pi$
$73$	−15.8918	−	22.8203i	−0.217696	−	0.312607i	−0.914447	+	0.404707i	$0.867374\pi$
$74$	28.0419	+	143.869i	0.378944	+	1.94417i
$75$	−14.7028	−	24.5838i	−0.196037	−	0.327783i
$76$	8.87450	+	4.85391i	0.116770	+	0.0638673i
$77$	69.2781	+	71.4454i	0.899715	+	0.927862i
$78$	−124.754	−	89.7613i	−1.59941	−	1.15079i
$79$	−12.0307	−	57.0317i	−0.152287	−	0.721921i	−0.985597	−	0.169114i	$-0.945910\pi$
$79$	−12.0307	−	57.0317i	−0.152287	−	0.721921i	0.833309	−	0.552807i	$-0.186443\pi$
$80$	−105.467	+	48.5225i	−1.31834	+	0.606532i
$81$	65.5577	−	35.2037i	0.809354	−	0.434614i
$82$	47.7862	−	8.93279i	0.582758	−	0.108936i
$83$	−46.0119	−	92.4044i	−0.554361	−	1.11331i	−0.978219	−	0.207577i	$-0.933442\pi$
$83$	−46.0119	−	92.4044i	−0.554361	−	1.11331i	0.423858	−	0.905729i	$-0.360676\pi$
$84$	10.5727	+	34.1424i	0.125865	+	0.406457i
$85$	61.1761	−	63.0900i	0.719719	−	0.742235i
$86$	87.9760	−	15.7455i	1.02298	−	0.183087i
$87$	−16.6186	+	3.77387i	−0.191019	+	0.0433778i
$88$	66.5323	+	14.0348i	0.756049	+	0.159487i
$89$	−52.7485	+	48.0866i	−0.592680	+	0.540299i	−0.913499	−	0.406841i	$-0.866630\pi$
$89$	−52.7485	+	48.0866i	−0.592680	+	0.540299i	0.320819	+	0.947141i	$0.396042\pi$
$90$	5.04342	−	7.87192i	0.0560380	−	0.0874658i
$91$	49.4134	−	196.467i	0.543004	−	2.15898i
$92$	21.7070	−	12.0907i	0.235945	−	0.131421i
$93$	33.8724	+	59.7261i	0.364219	+	0.642216i
$94$	−103.287	+	89.8789i	−1.09879	+	0.956158i
$95$	−35.7195	+	23.2748i	−0.375995	+	0.244998i
$96$	48.3219	+	38.8845i	0.503353	+	0.405047i
$97$	23.5545	+	7.69343i	0.242829	+	0.0793137i	0.429353	−	0.903137i	$-0.358742\pi$
$97$	23.5545	+	7.69343i	0.242829	+	0.0793137i	−0.186524	+	0.982450i	$0.559722\pi$
$98$	−52.6765	+	42.3886i	−0.537515	+	0.432537i
$99$	−7.16787	+	2.71356i	−0.0724027	+	0.0274097i
$100$	−0.857311	+	13.8998i	−0.00857311	+	0.138998i
$101$	−34.0391	−	18.2786i	−0.337021	−	0.180976i	0.295849	−	0.955235i	$-0.404398\pi$
$101$	−34.0391	−	18.2786i	−0.337021	−	0.180976i	−0.632870	+	0.774258i	$0.718123\pi$
$102$	−94.9913	−	30.2189i	−0.931288	−	0.296264i
$103$	−126.600	+	86.7229i	−1.22912	+	0.841969i	−0.991591	−	0.129410i	$-0.958692\pi$
$103$	−126.600	+	86.7229i	−1.22912	+	0.841969i	−0.237533	+	0.971380i	$0.576339\pi$
$104$	−47.0077	−	130.191i	−0.451997	−	1.25184i
$105$	−147.861	−	28.8201i	−1.40820	−	0.274477i
$106$	−190.814	+	84.2528i	−1.80013	+	0.794837i
$107$	62.4435	+	127.861i	0.583584	+	1.19497i	0.962940	+	0.269716i	$0.0869298\pi$
$107$	62.4435	+	127.861i	0.583584	+	1.19497i	−0.379356	+	0.925251i	$0.623854\pi$
$108$	−38.9270	−	4.21266i	−0.360436	−	0.0390061i
$109$	21.8658	+	19.3252i	0.200604	+	0.177296i	0.756577	−	0.653904i	$-0.226870\pi$
$109$	21.8658	+	19.3252i	0.200604	+	0.177296i	−0.555974	+	0.831200i	$0.687654\pi$
$110$	99.7452	−	118.254i	0.906775	−	1.07504i
$111$	29.2844	+	179.522i	0.263823	+	1.61732i
$112$	−51.3460	+	165.812i	−0.458447	+	1.48046i
$113$	95.0680	+	173.815i	0.841310	+	1.53818i	0.842827	+	0.538184i	$0.180889\pi$
$113$	95.0680	+	173.815i	0.841310	+	1.53818i	−0.00151764	+	0.999999i	$0.500483\pi$
$114$	41.6927	+	24.5013i	0.365726	+	0.214923i
$115$	1.61270	+	104.712i	0.0140234	+	0.910543i
$116$	7.70237	+	3.05233i	0.0663998	+	0.0263132i
$117$	12.3779	+	9.49787i	0.105794	+	0.0811784i
$118$	18.4200	−	12.4107i	0.156102	−	0.105176i
$119$	−9.09840	−	131.080i	−0.0764572	−	1.10151i
$120$	−94.7874	+	40.1201i	−0.789895	+	0.334334i
$121$	−5.67159	+	1.33395i	−0.0468727	+	0.0110244i
$122$	−7.09503	−	0.712593i	−0.0581560	−	0.00584092i
$123$	59.6141	−	9.25382i	0.484668	−	0.0752343i
$124$	2.82402	−	33.2618i	0.0227744	−	0.268240i
$125$	75.7209	+	46.8844i	0.605767	+	0.375075i
$126$	−3.72171	−	13.4738i	−0.0295374	−	0.106935i
$127$	5.58775	+	103.569i	0.0439980	+	0.815502i	0.933502	+	0.358573i	$0.116737\pi$
$127$	5.58775	+	103.569i	0.0439980	+	0.815502i	−0.889504	+	0.456928i	$0.848950\pi$
$128$	43.9777	+	145.986i	0.343576	+	1.14052i
$129$	109.725	−	16.1682i	0.850581	−	0.125335i
$130$	−311.559	−	45.9090i	−2.39661	−	0.353146i
$131$	−33.5618	−	10.1103i	−0.256197	−	0.0771782i	0.157751	−	0.987479i	$-0.449576\pi$
$131$	−33.5618	−	10.1103i	−0.256197	−	0.0771782i	−0.413947	+	0.910301i	$0.635850\pi$
$132$	−44.2580	−	10.7697i	−0.335288	−	0.0815886i
$133$	−9.77783	+	62.9898i	−0.0735175	+	0.473608i
$134$	−91.7525	−	23.8293i	−0.684720	−	0.177831i
$135$	93.2626	−	136.147i	0.690834	−	1.00849i
$136$	−55.1995	−	70.8018i	−0.405879	−	0.520602i
$137$	8.21853	−	0.253210i	0.0599893	−	0.00184825i	−0.000786541	−	1.00000i	$-0.500250\pi$
$137$	8.21853	−	0.253210i	0.0599893	−	0.00184825i	0.0607758	+	0.998151i	$0.480643\pi$
$138$	105.508	−	54.5803i	0.764551	−	0.395509i
$139$	79.6940	+	226.155i	0.573338	+	1.62702i	0.763896	+	0.645340i	$0.223284\pi$
$139$	79.6940	+	226.155i	0.573338	+	1.62702i	−0.190558	+	0.981676i	$0.561030\pi$
$140$	51.3869	+	52.1844i	0.367049	+	0.372746i
$141$	−131.549	+	107.536i	−0.932971	+	0.762669i
$142$	−17.6502	−	228.771i	−0.124297	−	1.61106i
$143$	182.558	+	182.558i	1.27663	+	1.27663i
$144$	−10.1518	−	8.69754i	−0.0704987	−	0.0603996i
$145$	−26.6925	+	22.5147i	−0.184086	+	0.155274i
$146$	−1.49293	+	64.6176i	−0.0102255	+	0.442586i
$147$	−66.9585	+	50.5647i	−0.455500	+	0.343978i
$148$	37.5783	−	80.0499i	0.253908	−	0.540878i
$149$	99.6769	−	101.224i	0.668973	−	0.679355i	−0.291867	−	0.956459i	$-0.594277\pi$
$149$	99.6769	−	101.224i	0.668973	−	0.679355i	0.960840	+	0.277104i	$0.0893746\pi$
$150$	−6.14312	+	66.2948i	−0.0409541	+	0.441966i
$151$	18.3463	−	34.8055i	0.121498	−	0.230500i	−0.816340	−	0.577572i	$-0.804000\pi$
$151$	18.3463	−	34.8055i	0.121498	−	0.230500i	0.937839	+	0.347072i	$0.112824\pi$
$152$	18.5078	+	39.4256i	0.121762	+	0.259379i
$153$	9.54408	+	3.36320i	0.0623796	+	0.0219817i
$154$	−31.9567	−	229.090i	−0.207511	−	1.48760i
$155$	117.879	+	76.8098i	0.760509	+	0.495547i
$156$	28.7889	+	88.1410i	0.184544	+	0.565006i
$157$	−213.248	−	80.7297i	−1.35826	−	0.514202i	−0.435717	−	0.900084i	$-0.643505\pi$
$157$	−213.248	−	80.7297i	−1.35826	−	0.514202i	−0.922548	+	0.385882i	$0.873897\pi$
$158$	−55.6738	+	123.507i	−0.352366	+	0.781687i
$159$	−239.901	+	97.2129i	−1.50881	+	0.611402i
$160$	124.555	+	25.2743i	0.778466	+	0.157965i
$161$	118.121	+	102.788i	0.733671	+	0.638432i
$162$	−171.295	−	23.8946i	−1.05738	−	0.147498i
$163$	−44.6839	+	86.3776i	−0.274135	+	0.529924i	−0.984818	−	0.173587i	$-0.944464\pi$
$163$	−44.6839	+	86.3776i	−0.274135	+	0.529924i	0.710684	+	0.703511i	$0.248386\pi$
$164$	−26.4529	−	12.6674i	−0.161298	−	0.0772404i
$165$	128.241	−	142.867i	0.777215	−	0.865863i
$166$	−40.4494	+	236.492i	−0.243671	+	1.42465i
$167$	23.7096	−	56.0162i	0.141974	−	0.335426i	−0.834518	−	0.550981i	$-0.814254\pi$
$167$	23.7096	−	56.0162i	0.141974	−	0.335426i	0.976492	+	0.215554i	$0.0691558\pi$
$168$	−50.0289	+	145.537i	−0.297791	+	0.866293i
$169$	81.6341	−	347.087i	0.483042	−	2.05377i
$170$	−201.333	+	34.4358i	−1.18431	+	0.202564i
$171$	−4.15387	−	2.61642i	−0.0242916	−	0.0153007i
$172$	−48.4514	−	23.6621i	−0.281694	−	0.137570i
$173$	6.66691	−	173.081i	0.0385371	−	1.00047i	−0.845765	−	0.533556i	$-0.820856\pi$
$173$	6.66691	−	173.081i	0.0385371	−	1.00047i	0.884302	−	0.466915i	$-0.154635\pi$
$174$	36.3569	+	15.7197i	0.208948	+	0.0903433i
$175$	−84.2229	+	24.6661i	−0.481274	+	0.140949i
$176$	−147.766	−	164.619i	−0.839577	−	0.935338i
$177$	23.3220	−	14.6900i	0.131763	−	0.0829944i
$178$	164.938	−	17.8495i	0.926617	−	0.100278i
$179$	128.290	+	90.8148i	0.716705	+	0.507345i	0.877460	−	0.479649i	$-0.159236\pi$
$179$	128.290	+	90.8148i	0.716705	+	0.507345i	−0.160755	+	0.986994i	$0.551393\pi$
$180$	−5.25949	+	2.03754i	−0.0292194	+	0.0113196i
$181$	−56.4616	+	24.4125i	−0.311942	+	0.134875i	−0.547065	−	0.837090i	$-0.684255\pi$
$181$	−56.4616	+	24.4125i	−0.311942	+	0.134875i	0.235122	+	0.971966i	$0.424451\pi$
$182$	−362.253	+	300.811i	−1.99040	+	1.65281i
$183$	−8.77326	−	1.15502i	−0.0479413	−	0.00631159i
$184$	106.175	+	13.1473i	0.577036	+	0.0714526i
$185$	222.316	+	299.157i	1.20171	+	1.61706i
$186$	18.3918	−	158.528i	0.0988804	−	0.852299i
$187$	149.317	+	75.7912i	0.798485	+	0.405301i
$188$	82.3081	−	6.98820i	0.437809	−	0.0371713i
$189$	−58.3398	−	239.747i	−0.308676	−	1.26851i
$190$	98.9478	+	5.33844i	0.520778	+	0.0280971i
$191$	−152.412	+	33.3788i	−0.797971	+	0.174758i	−0.594260	−	0.804273i	$-0.702555\pi$
$191$	−152.412	+	33.3788i	−0.797971	+	0.174758i	−0.203711	+	0.979031i	$0.565300\pi$
$192$	21.3432	+	79.6538i	0.111162	+	0.414864i
$193$	−172.958	+	189.726i	−0.896156	+	0.983037i	−0.999933	−	0.0115640i	$-0.996319\pi$
$193$	−172.958	+	189.726i	−0.896156	+	0.983037i	0.103777	+	0.994601i	$0.466907\pi$
$194$	−33.6369	−	46.7499i	−0.173386	−	0.240979i
$195$	−384.696	−	68.8508i	−1.97280	−	0.353081i
$196$	40.7488	−	1.88393i	0.207902	−	0.00961189i
$197$	80.3832	−	367.041i	0.408036	−	1.86315i	−0.0899201	−	0.995949i	$-0.528661\pi$
$197$	80.3832	−	367.041i	0.408036	−	1.86315i	0.497957	−	0.867202i	$-0.334084\pi$
$198$	17.1710	+	4.74296i	0.0867222	+	0.0239543i
$199$	−48.0811	+	44.5144i	−0.241614	+	0.223691i	−0.790903	−	0.611942i	$-0.790389\pi$
$199$	−48.0811	+	44.5144i	−0.241614	+	0.223691i	0.549289	+	0.835632i	$0.314899\pi$
$200$	−38.3071	+	46.1315i	−0.191536	+	0.230658i
$201$	−112.897	−	33.0637i	−0.561675	−	0.164496i
$202$	38.7854	+	80.9941i	0.192007	+	0.400961i
$203$	−1.60785	+	52.1866i	−0.00792045	+	0.257077i
$204$	35.4989	+	48.5450i	0.174014	+	0.237965i
$205$	99.7842	−	72.9681i	0.486752	−	0.355942i
$206$	356.502	+	10.9837i	1.73059	+	0.0533190i
$207$	−10.8763	+	5.20830i	−0.0525424	+	0.0251609i
$208$	−126.565	+	432.158i	−0.608484	+	2.07768i
$209$	−62.4974	−	51.8972i	−0.299031	−	0.248312i
$210$	237.872	+	256.932i	1.13273	+	1.22348i
$211$	52.8185	−	191.220i	0.250325	−	0.906254i	−0.725594	−	0.688123i	$-0.758435\pi$
$211$	52.8185	−	191.220i	0.250325	−	0.906254i	0.975919	−	0.218132i	$-0.0699962\pi$
$212$	122.930	+	26.9221i	0.579860	+	0.126991i
$213$	−13.1503	−	284.436i	−0.0617384	−	1.33538i
$214$	58.2668	−	325.559i	0.272275	−	1.52130i
$215$	184.475	−	132.731i	0.858024	−	0.617354i
$216$	−124.589	−	113.578i	−0.576800	−	0.525823i
$217$	203.196	−	54.4462i	0.936387	−	0.250904i
$218$	−14.5104	−	66.2564i	−0.0665613	−	0.303928i
$219$	−4.32119	+	80.0930i	−0.0197314	+	0.365721i
$220$	−90.6884	+	22.0680i	−0.412220	+	0.100309i
$221$	−28.8374	−	339.651i	−0.130486	−	1.53688i
$222$	191.356	−	376.991i	0.861962	−	1.69816i
$223$	−199.763	−	23.1757i	−0.895798	−	0.103927i	−0.345036	−	0.938589i	$-0.612133\pi$
$223$	−199.763	−	23.1757i	−0.895798	−	0.103927i	−0.550762	+	0.834662i	$0.685663\pi$
$224$	152.521	−	113.345i	0.680899	−	0.506005i
$225$	0.830578	−	6.70757i	0.00369146	−	0.0298114i
$226$	60.1039	−	456.535i	0.265947	−	2.02006i
$227$	56.4901	+	68.0284i	0.248855	+	0.299685i	0.879028	−	0.476770i	$-0.158193\pi$
$227$	56.4901	+	68.0284i	0.248855	+	0.299685i	−0.630173	+	0.776455i	$0.717016\pi$
$228$	−11.5788	−	26.7797i	−0.0507843	−	0.117455i
$229$	−88.5133	−	228.479i	−0.386521	−	0.997725i	−0.981068	−	0.193665i	$-0.937963\pi$
$229$	−88.5133	−	228.479i	−0.386521	−	0.997725i	0.594547	−	0.804061i	$-0.297331\pi$
$230$	140.636	−	198.670i	0.611460	−	0.863784i
$231$	−30.8835	−	285.379i	−0.133695	−	1.23541i
$232$	19.0128	+	30.1849i	0.0819517	+	0.130107i
$233$	140.477	−	126.095i	0.602907	−	0.541181i	−0.309272	−	0.950974i	$-0.600085\pi$
$233$	140.477	−	126.095i	0.602907	−	0.541181i	0.912179	+	0.409793i	$0.134399\pi$
$234$	−10.1922	−	34.8015i	−0.0435564	−	0.148724i
$235$	−138.172	+	319.567i	−0.587966	+	1.35986i
$236$	−13.3902	−	0.515777i	−0.0567383	−	0.00218550i
$237$	−73.7762	+	151.067i	−0.311292	+	0.637413i
$238$	−162.767	+	258.411i	−0.683894	+	1.08576i
$239$	−19.3658	−	113.225i	−0.0810286	−	0.473744i	−0.997316	−	0.0732217i	$-0.976672\pi$
$239$	−19.3658	−	113.225i	−0.0810286	−	0.473744i	0.916287	−	0.400522i	$-0.131171\pi$
$240$	325.959	+	76.6650i	1.35816	+	0.319437i
$241$	45.6906	+	15.7063i	0.189588	+	0.0651714i	0.418239	−	0.908337i	$-0.362647\pi$
$241$	45.6906	+	15.7063i	0.189588	+	0.0651714i	−0.228652	+	0.973508i	$0.573432\pi$
$242$	12.4710	+	5.27851i	0.0515329	+	0.0218120i
$243$	36.1447	+	6.18214i	0.148743	+	0.0254409i
$244$	3.20149	+	2.87372i	0.0131209	+	0.0117775i
$245$	−74.2569	+	155.068i	−0.303089	+	0.632930i
$246$	−124.542	−	64.4266i	−0.506267	−	0.261897i
$247$	−22.8467	+	163.783i	−0.0924968	+	0.663088i
$248$	94.3527	−	108.428i	0.380454	−	0.437209i
$249$	−59.2101	+	291.793i	−0.237791	+	1.17186i
$250$	−77.7412	−	191.849i	−0.310965	−	0.767396i
$251$	112.330	+	50.6358i	0.447531	+	0.201736i	0.622147	−	0.782900i	$-0.286261\pi$
$251$	112.330	+	50.6358i	0.447531	+	0.201736i	−0.174616	+	0.984637i	$0.555868\pi$
$252$	−2.98583	+	7.88707i	−0.0118485	+	0.0312979i
$253$	−189.686	+	61.9560i	−0.749749	+	0.244885i
$254$	131.609	−	201.978i	0.518145	−	0.795189i
$255$	−251.045	+	35.0193i	−0.984489	+	0.137330i
$256$	79.7699	−	226.370i	0.311601	−	0.884260i
$257$	332.301	−	155.994i	1.29300	−	0.606981i	0.349061	−	0.937100i	$-0.386501\pi$
$257$	332.301	−	155.994i	1.29300	−	0.606981i	0.943939	+	0.330119i	$0.107089\pi$
$258$	−228.044	−	120.204i	−0.883892	−	0.465908i
$259$	554.902	+	51.4192i	2.14248	+	0.198530i
$260$	135.379	+	133.310i	0.520690	+	0.512732i
$261$	−3.63990	−	1.70870i	−0.0139460	−	0.00654675i
$262$	49.0964	+	65.0142i	0.187391	+	0.248146i
$263$	−45.7611	−	1.05727i	−0.173997	−	0.00402003i	−0.0639881	−	0.997951i	$-0.520382\pi$
$263$	−45.7611	−	1.05727i	−0.173997	−	0.00402003i	−0.110009	+	0.993931i	$0.535088\pi$
$264$	−126.452	−	149.917i	−0.478985	−	0.567866i
$265$	−345.090	+	402.791i	−1.30223	+	1.51997i
$266$	104.764	−	104.764i	0.393851	−	0.393851i
$267$	205.267	−	15.8368i	0.768789	−	0.0593139i
$268$	36.1971	+	44.2798i	0.135064	+	0.165223i
$269$	−321.026	+	316.120i	−1.19340	+	1.17517i	−0.213236	+	0.977001i	$0.568400\pi$
$269$	−321.026	+	316.120i	−1.19340	+	1.17517i	−0.980169	+	0.198166i	$0.936502\pi$
$270$	−361.764	+	127.481i	−1.33987	+	0.472151i
$271$	233.631	+	451.627i	0.862106	+	1.66652i	0.738567	+	0.674180i	$0.235503\pi$
$271$	233.631	+	451.627i	0.862106	+	1.66652i	0.123539	+	0.992340i	$0.460576\pi$
$272$	8.99425	+	291.930i	0.0330671	+	1.07327i
$273$	−460.825	+	359.274i	−1.68800	+	1.31602i
$274$	−15.7667	−	10.8005i	−0.0575428	−	0.0394177i
$275$	28.1142	−	108.251i	0.102234	−	0.393640i
$276$	−70.8194	−	10.9932i	−0.256592	−	0.0398304i
$277$	32.0354	−	131.649i	0.115651	−	0.475268i	−0.884314	−	0.466893i	$-0.845373\pi$
$277$	32.0354	−	131.649i	0.115651	−	0.475268i	0.999965	−	0.00837512i	$-0.00266591\pi$
$278$	160.757	−	533.641i	0.578263	−	1.91957i
$279$	−2.36175	+	16.0279i	−0.00846507	+	0.0574478i
$280$	45.9706	+	311.977i	0.164181	+	1.11420i
$281$	−443.854	+	133.709i	−1.57955	+	0.475833i	−0.952854	−	0.303429i	$-0.901868\pi$
$281$	−443.854	+	133.709i	−1.57955	+	0.475833i	−0.626698	+	0.779262i	$0.715594\pi$
$282$	394.343	−	21.2756i	1.39838	−	0.0754456i
$283$	327.383	−	90.4294i	1.15683	−	0.319539i	0.365431	−	0.930839i	$-0.380922\pi$
$283$	327.383	−	90.4294i	1.15683	−	0.319539i	0.791399	+	0.611300i	$0.209353\pi$
$284$	−72.8745	+	117.696i	−0.256600	+	0.414424i
$285$	122.528	+	10.4030i	0.429924	+	0.0365018i
$286$	−92.0460	−	592.970i	−0.321839	−	2.07332i
$287$	18.4705	−	183.904i	0.0643571	−	0.640781i
$288$	3.35062	+	14.2460i	0.0116341	+	0.0494651i
$289$	26.4712	+	62.5407i	0.0915959	+	0.216404i
$290$	80.9689	−	5.62013i	0.279203	−	0.0193798i
$291$	−39.9358	−	59.2729i	−0.137236	−	0.203687i
$292$	23.7388	−	30.9369i	0.0812971	−	0.105948i
$293$	73.2824	−	184.924i	0.250111	−	0.631139i	−0.749410	−	0.662106i	$-0.769663\pi$
$293$	73.2824	−	184.924i	0.250111	−	0.631139i	0.999520	+	0.0309673i	$0.00985877\pi$
$294$	194.998	−	3.00320i	0.663258	−	0.0102150i
$295$	28.6151	−	48.6931i	0.0970004	−	0.165061i
$296$	334.061	−	182.715i	1.12858	−	0.617280i
$297$	300.378	+	93.0164i	1.01137	+	0.313187i
$298$	−325.886	+	53.1597i	−1.09358	+	0.178388i
$299$	310.506	+	261.906i	1.03848	+	0.875941i
$300$	26.6007	−	30.0977i	0.0886689	−	0.100326i
$301$	36.5592	−	337.826i	0.121459	−	1.12234i
$302$	−82.1724	+	40.1304i	−0.272094	+	0.132882i
$303$	45.0132	+	101.945i	0.148558	+	0.336453i
$304$	27.1074	−	139.074i	0.0891691	−	0.457482i
$305$	−17.0546	+	6.15785i	−0.0559168	+	0.0201897i
$306$	−13.2921	−	19.4040i	−0.0434381	−	0.0634119i
$307$	41.2749	−	129.745i	0.134446	−	0.422623i	−0.861995	−	0.506917i	$-0.830785\pi$
$307$	41.2749	−	129.745i	0.134446	−	0.422623i	0.996441	+	0.0842939i	$0.0268635\pi$
$308$	−66.0210	+	122.947i	−0.214354	+	0.399178i
$309$	441.777	+	27.2478i	1.42970	+	0.0881807i
$310$	−115.780	−	305.833i	−0.373484	−	0.986558i
$311$	−330.675	−	410.931i	−1.06326	−	1.32132i	−0.944541	−	0.328395i	$-0.893492\pi$
$311$	−330.675	−	410.931i	−1.06326	−	1.32132i	−0.118723	−	0.992927i	$-0.537880\pi$
$312$	−123.958	+	379.514i	−0.397301	+	1.21639i
$313$	−249.661	+	310.254i	−0.797638	+	0.991228i	0.202291	+	0.979325i	$0.435161\pi$
$313$	−249.661	+	310.254i	−0.797638	+	0.991228i	−0.999929	+	0.0119023i	$0.996211\pi$
$314$	289.329	+	444.030i	0.921431	+	1.41411i
$315$	−23.3331	−	26.8139i	−0.0740734	−	0.0851234i
$316$	71.0963	−	40.3208i	0.224988	−	0.127597i
$317$	−105.868	−	190.070i	−0.333969	−	0.599590i	0.653588	−	0.756851i	$-0.273263\pi$
$317$	−105.868	−	190.070i	−0.333969	−	0.599590i	−0.987557	+	0.157261i	$0.949734\pi$
$318$	583.466	+	146.748i	1.83480	+	0.461470i
$319$	−56.0259	−	35.8949i	−0.175630	−	0.112523i
$320$	113.838	+	124.874i	0.355743	+	0.390231i
$321$	84.7141	−	401.588i	0.263907	−	1.25105i
$322$	−80.5939	−	354.904i	−0.250292	−	1.10219i
$323$	18.8960	+	105.579i	0.0585015	+	0.326870i
$324$	74.9109	+	72.6384i	0.231206	+	0.224193i
$325$	−217.484	+	67.3471i	−0.669182	+	0.207222i
$326$	202.341	−	100.754i	0.620678	−	0.309061i
$327$	−15.4663	−	82.7372i	−0.0472974	−	0.253019i
$328$	−59.7450	−	111.259i	−0.182149	−	0.339205i
$329$	217.572	+	472.908i	0.661314	+	1.43741i
$330$	−436.609	+	92.1016i	−1.32306	+	0.279096i
$331$	−202.578	+	281.551i	−0.612019	+	0.850609i	−0.997394	−	0.0721516i	$-0.977013\pi$
$331$	−202.578	+	281.551i	−0.612019	+	0.850609i	0.385374	+	0.922760i	$0.374072\pi$
$332$	103.919	−	100.766i	0.313008	−	0.303513i
$333$	−20.5949	+	37.6541i	−0.0618467	+	0.113075i
$334$	−121.335	+	72.5669i	−0.363279	+	0.217266i
$335$	−236.599	+	46.1163i	−0.706266	+	0.137661i
$336$	410.856	−	286.116i	1.22279	−	0.851535i
$337$	39.3708	−	510.299i	0.116827	−	1.51424i	−0.590318	−	0.807171i	$-0.700997\pi$
$337$	39.3708	−	510.299i	0.116827	−	1.51424i	0.707145	−	0.707069i	$-0.249983\pi$
$338$	−629.349	+	539.193i	−1.86198	+	1.59525i
$339$	91.9980	−	563.977i	0.271381	−	1.66365i
$340$	110.312	+	54.9289i	0.324448	+	0.161556i
$341$	−73.3658	+	257.854i	−0.215149	+	0.756171i
$342$	4.20370	+	10.6078i	0.0122915	+	0.0310169i
$343$	−67.3295	−	162.548i	−0.196296	−	0.473900i
$344$	−108.260	−	205.384i	−0.314708	−	0.597045i
$345$	182.033	−	241.051i	0.527633	−	0.698699i
$346$	−249.969	+	315.582i	−0.722455	+	0.912088i
$347$	367.478	−	223.637i	1.05902	−	0.644487i	0.121557	−	0.992584i	$-0.461211\pi$
$347$	367.478	−	223.637i	1.05902	−	0.644487i	0.937458	+	0.348097i	$0.113172\pi$
$348$	−12.1076	−	20.6029i	−0.0347919	−	0.0592038i
$349$	−458.038	−	273.939i	−1.31243	−	0.784924i	−0.325418	−	0.945570i	$-0.605505\pi$
$349$	−458.038	−	273.939i	−1.31243	−	0.784924i	−0.987012	+	0.160646i	$0.948642\pi$
$350$	191.857	+	69.2731i	0.548163	+	0.197923i
$351$	−160.908	−	619.561i	−0.458428	−	1.76513i
$352$	24.2007	+	240.957i	0.0687519	+	0.684538i
$353$	−214.139	+	73.6112i	−0.606627	+	0.208530i	−0.611222	−	0.791459i	$-0.709322\pi$
$353$	−214.139	+	73.6112i	−0.606627	+	0.208530i	0.00459475	+	0.999989i	$0.498537\pi$
$354$	−63.9101	−	4.43606i	−0.180537	−	0.0125312i
$355$	−291.728	−	505.288i	−0.821769	−	1.42335i
$356$	−86.6809	−	50.0452i	−0.243486	−	0.140576i
$357$	−211.767	+	314.306i	−0.593185	+	0.880408i
$358$	−116.099	−	346.393i	−0.324299	−	0.967577i
$359$	58.9293	−	37.7551i	0.164148	−	0.105167i	−0.454819	−	0.890584i	$-0.650296\pi$
$359$	58.9293	−	37.7551i	0.164148	−	0.105167i	0.618968	+	0.785416i	$0.287551\pi$
$360$	−23.4585	−	6.28570i	−0.0651626	−	0.0174603i
$361$	−14.2691	+	308.637i	−0.0395267	+	0.854949i
$362$	139.424	+	31.6613i	0.385150	+	0.0874623i
$363$	15.2669	+	7.02391i	0.0420577	+	0.0193496i
$364$	283.541	−	17.4882i	0.778959	−	0.0480446i
$365$	67.5425	+	149.836i	0.185048	+	0.410510i
$366$	14.8754	+	14.2036i	0.0406433	+	0.0388076i
$367$	−276.586	+	372.183i	−0.753639	+	1.01412i	0.245362	+	0.969432i	$0.421093\pi$
$367$	−276.586	+	372.183i	−0.753639	+	1.01412i	−0.999001	+	0.0446918i	$0.985769\pi$
$368$	−253.573	−	238.415i	−0.689056	−	0.647866i
$369$	12.4355	+	6.92656i	0.0337007	+	0.0187712i
$370$	−6.67044	−	866.276i	−0.0180282	−	2.34129i
$371$	103.513	+	786.260i	0.279011	+	2.11930i
$372$	−65.4118	+	70.6528i	−0.175838	+	0.189927i
$373$	−47.8186	−	77.2297i	−0.128200	−	0.207050i	0.779791	−	0.626040i	$-0.215325\pi$
$373$	−47.8186	−	77.2297i	−0.128200	−	0.207050i	−0.907991	+	0.418990i	$0.862384\pi$
$374$	−176.160	−	347.053i	−0.471016	−	0.927950i
$375$	−89.0966	−	240.935i	−0.237591	−	0.642494i
$376$	303.833	+	184.904i	0.808066	+	0.491767i
$377$	−2.08583	+	135.433i	−0.00553272	+	0.359240i
$378$	−219.469	+	529.846i	−0.580606	+	1.40171i
$379$	212.209	−	19.6640i	0.559917	−	0.0518840i	0.191412	−	0.981510i	$-0.438693\pi$
$379$	212.209	−	19.6640i	0.559917	−	0.0518840i	0.368505	+	0.929626i	$0.379870\pi$
$380$	−46.2862	−	37.8372i	−0.121806	−	0.0995716i
$381$	170.963	−	245.499i	0.448721	−	0.644354i
$382$	331.745	+	146.480i	0.868443	+	0.383455i
$383$	25.5994	+	664.593i	0.0668392	+	1.73523i	0.529165	+	0.848519i	$0.322505\pi$
$383$	25.5994	+	664.593i	0.0668392	+	1.73523i	−0.462326	+	0.886710i	$0.652985\pi$
$384$	158.862	−	410.069i	0.413702	−	1.06789i
$385$	−324.890	−	490.308i	−0.843869	−	1.27353i
$386$	584.795	−	118.665i	1.51501	−	0.307423i
$387$	22.7633	+	12.9097i	0.0588200	+	0.0333585i
$388$	−0.267548	+	34.7459i	−0.000689557	+	0.0895513i
$389$	118.578	−	14.6831i	0.304827	−	0.0377458i	0.0309833	−	0.999520i	$-0.490136\pi$
$389$	118.578	−	14.6831i	0.304827	−	0.0377458i	0.273844	+	0.961774i	$0.411705\pi$
$390$	627.292	+	656.963i	1.60844	+	1.68452i
$391$	244.181	+	98.9471i	0.624503	+	0.253062i
$392$	146.416	+	97.0185i	0.373509	+	0.247496i
$393$	58.4134	+	82.5181i	0.148635	+	0.209970i
$394$	−654.378	+	578.346i	−1.66086	+	1.46788i
$395$	7.95701	+	344.399i	0.0201443	+	0.871895i
$396$	−6.67316	−	8.42476i	−0.0168514	−	0.0212747i
$397$	570.358	+	210.915i	1.43667	+	0.531273i	0.941348	−	0.337436i	$-0.109560\pi$
$397$	570.358	+	210.915i	1.43667	+	0.531273i	0.495322	+	0.868709i	$0.335050\pi$
$398$	151.280	−	17.5509i	0.380101	−	0.0440978i
$399$	133.951	−	125.943i	0.335716	−	0.315648i
$400$	189.184	−	47.5816i	0.472959	−	0.118954i
$401$	−216.178	−	72.4556i	−0.539097	−	0.180687i	0.0351306	−	0.999383i	$-0.488815\pi$
$401$	−216.178	−	72.4556i	−0.539097	−	0.180687i	−0.574228	+	0.818696i	$0.694698\pi$
$402$	166.451	+	216.923i	0.414057	+	0.539609i
$403$	524.904	−	149.348i	1.30249	−	0.370591i
$404$	9.95531	−	53.2562i	0.0246419	−	0.131822i
$405$	−419.097	+	133.324i	−1.03481	+	0.329196i
$406$	74.6146	−	95.7047i	0.183780	−	0.235726i
$407$	−419.211	+	573.273i	−1.03000	+	1.40853i
$408$			258.947i			0.634675i
$409$	−309.985	−	266.816i	−0.757909	−	0.652361i
$409$	−309.985	−	266.816i	−0.757909	−	0.652361i
$410$	−287.321			−0.700783
$411$	−19.1439	−	13.9991i	−0.0465788	−	0.0340612i
$412$	−169.704	−	132.307i	−0.411903	−	0.321134i
$413$	−25.5998	−	80.4716i	−0.0619851	−	0.194846i
$414$	27.5513	+	5.15023i	0.0665490	+	0.0124402i
$415$	166.960	+	586.804i	0.402314	+	1.41399i
$416$	391.104	−	300.104i	0.940153	−	0.721405i
$417$	219.792	−	655.772i	0.527080	−	1.57259i
$418$	46.0544	+	183.112i	0.110178	+	0.438066i
$419$	−16.7316	−	17.7954i	−0.0399322	−	0.0424710i	0.708271	−	0.705940i	$-0.249475\pi$
$419$	−16.7316	−	17.7954i	−0.0399322	−	0.0424710i	−0.748203	+	0.663469i	$0.769083\pi$
$420$	−24.3444	−	209.836i	−0.0579628	−	0.499610i
$421$	159.961	−	432.567i	0.379955	−	1.02748i	−0.594736	−	0.803921i	$-0.702743\pi$
$421$	159.961	−	432.567i	0.379955	−	1.02748i	0.974691	−	0.223555i	$-0.0717663\pi$
$422$	−361.442	+	286.294i	−0.856498	+	0.678423i
$423$	−40.0796	+	0.926000i	−0.0947507	+	0.00218913i
$424$	358.834	+	406.008i	0.846307	+	0.957566i
$425$	−120.525	+	85.3181i	−0.283589	+	0.200749i
$426$	−365.563	+	551.690i	−0.858130	+	1.29505i
$427$	−10.1817	+	25.1263i	−0.0238448	+	0.0588439i
$428$	−144.314	+	137.796i	−0.337183	+	0.321954i
$429$	−91.5108	−	739.023i	−0.213312	−	1.72266i
$430$	−528.208	−	4.06727i	−1.22839	−	0.00945877i
$431$	−125.489	+	221.271i	−0.291158	+	0.513390i	−0.976691	−	0.214652i	$-0.931138\pi$
$431$	−125.489	+	221.271i	−0.291158	+	0.513390i	0.685532	+	0.728042i	$0.259570\pi$
$432$	109.071	+	537.511i	0.252478	+	1.24424i
$433$	−185.366	+	122.828i	−0.428097	+	0.283667i	−0.747893	−	0.663819i	$-0.768935\pi$
$433$	−185.366	+	122.828i	−0.428097	+	0.283667i	0.319796	+	0.947486i	$0.396385\pi$
$434$	−455.927	−	176.627i	−1.05052	−	0.406975i
$435$	100.646	−	3.87680i	0.231371	−	0.00891218i
$436$	−16.5288	+	37.4341i	−0.0379100	+	0.0858581i
$437$	−104.889	−	73.0433i	−0.240020	−	0.167147i
$438$	117.992	−	144.339i	0.269388	−	0.329541i
$439$	23.8576	+	257.465i	0.0543454	+	0.586480i	0.978749	+	0.205063i	$0.0657401\pi$
$439$	23.8576	+	257.465i	0.0543454	+	0.586480i	−0.924403	+	0.381416i	$0.875436\pi$
$440$	−371.286	−	153.792i	−0.843832	−	0.349527i
$441$	−19.7954	−	0.304872i	−0.0448875	−	0.000691320i
$442$	−411.885	+	676.805i	−0.931866	+	1.53123i
$443$	−456.345	+	168.754i	−1.03012	+	0.380934i	−0.804923	−	0.593379i	$-0.797794\pi$
$443$	−456.345	+	168.754i	−1.03012	+	0.380934i	−0.225200	+	0.974313i	$0.572303\pi$
$444$	−227.444	+	115.448i	−0.512261	+	0.260017i
$445$	358.672	−	222.080i	0.806004	−	0.499056i
$446$	342.992	+	317.549i	0.769040	+	0.711993i
$447$	−406.252	+	53.4840i	−0.908840	+	0.119651i
$448$	252.639	−	1.94536i	0.563927	−	0.00434232i
$449$	83.5067	−	149.923i	0.185984	−	0.333905i	−0.764530	−	0.644589i	$-0.777029\pi$
$449$	83.5067	−	149.923i	0.185984	−	0.333905i	0.950513	+	0.310684i	$0.100558\pi$
$450$	−10.7608	+	11.4450i	−0.0239130	+	0.0254333i
$451$	189.058	+	140.497i	0.419197	+	0.311524i
$452$	−191.852	+	200.927i	−0.424451	+	0.444528i
$453$	−103.458	+	46.6364i	−0.228384	+	0.102950i
$454$	−12.6523	−	205.135i	−0.0278685	−	0.451839i
$455$	−500.438	+	1087.74i	−1.09986	+	2.39063i
$456$	27.8191	−	122.505i	0.0610069	−	0.268651i
$457$	−354.045	−	16.3685i	−0.774716	−	0.0358173i	−0.344788	−	0.938680i	$-0.612049\pi$
$457$	−354.045	−	16.3685i	−0.774716	−	0.0358173i	−0.429928	+	0.902863i	$0.641461\pi$
$458$	−147.399	+	550.101i	−0.321832	+	1.20109i
$459$	−223.971	−	349.580i	−0.487954	−	0.761613i
$460$	−139.240	+	46.6685i	−0.302696	+	0.101453i
$461$	−420.451	−	283.284i	−0.912040	−	0.614498i	0.0106907	−	0.999943i	$-0.496597\pi$
$461$	−420.451	−	283.284i	−0.912040	−	0.614498i	−0.922731	+	0.385445i	$0.874048\pi$
$462$	−333.586	+	577.788i	−0.722048	+	1.25062i
$463$	43.1054	−	24.8869i	0.0931003	−	0.0537515i	−0.452727	−	0.891649i	$-0.649549\pi$
$463$	43.1054	−	24.8869i	0.0931003	−	0.0537515i	0.545827	+	0.837898i	$0.316215\pi$
$464$	8.03624	−	115.778i	0.0173195	−	0.249521i
$465$	−131.923	−	383.772i	−0.283705	−	0.825316i
$466$	−436.556	+	43.8457i	−0.936816	+	0.0940895i
$467$	300.785	−	78.1179i	0.644080	−	0.167276i	0.0849881	−	0.996382i	$-0.472915\pi$
$467$	300.785	−	78.1179i	0.644080	−	0.167276i	0.559091	+	0.829106i	$0.311150\pi$
$468$	−7.42998	+	20.5779i	−0.0158760	+	0.0439699i
$469$	−184.992	+	309.316i	−0.394440	+	0.659522i
$470$	697.666	−	409.993i	1.48440	−	0.872325i
$471$	341.908	+	561.820i	0.725919	+	1.19282i
$472$	−45.2285	−	35.8250i	−0.0958230	−	0.0759004i
$473$	345.573	+	260.965i	0.730598	+	0.551722i
$474$	345.674	−	182.208i	0.729270	−	0.384405i
$475$	66.1849	−	27.4147i	0.139337	−	0.0577151i
$476$	171.292	−	67.8805i	0.359858	−	0.142606i
$477$	−58.7441	−	16.7141i	−0.123153	−	0.0350401i
$478$	−119.007	+	238.997i	−0.248968	+	0.499995i
$479$	531.665	+	86.7273i	1.10995	+	0.181059i	0.688106	−	0.725610i	$-0.258442\pi$
$479$	531.665	+	86.7273i	1.10995	+	0.181059i	0.421843	+	0.906669i	$0.361384\pi$
$480$	−238.503	−	278.382i	−0.496882	−	0.579963i
$481$	1441.44	+	111.210i	2.99675	+	0.231207i
$482$	−64.1747	−	92.1534i	−0.133142	−	0.191190i
$483$	−86.4037	−	443.294i	−0.178890	−	0.917792i
$484$	−4.19354	−	7.01179i	−0.00866434	−	0.0144872i
$485$	−128.487	−	70.2763i	−0.264923	−	0.144900i
$486$	−59.3317	−	61.1878i	−0.122082	−	0.125901i
$487$	135.014	+	97.1438i	0.277237	+	0.199474i	0.714081	−	0.700063i	$-0.246845\pi$
$487$	135.014	+	97.1438i	0.277237	+	0.199474i	−0.436844	+	0.899537i	$0.643904\pi$
$488$	3.82338	+	18.1248i	0.00783480	+	0.0371410i
$489$	254.829	−	117.240i	0.521123	−	0.239755i
$490$	352.065	−	189.055i	0.718501	−	0.385827i
$491$	−930.695	+	173.977i	−1.89551	+	0.354332i	−0.996500	−	0.0835962i	$-0.973359\pi$
$491$	−930.695	+	173.977i	−1.89551	+	0.354332i	−0.899010	+	0.437928i	$0.855712\pi$
$492$	37.7078	+	75.7275i	0.0766419	+	0.153918i
$493$	25.9870	+	83.9200i	0.0527120	+	0.170223i
$494$	267.568	−	275.938i	0.541635	−	0.558580i
$495$	44.5896	−	7.98041i	0.0900800	−	0.0161220i
$496$	−455.991	+	103.549i	−0.919336	+	0.208769i
$497$	−853.582	−	180.061i	−1.71747	−	0.362296i
$498$	511.417	−	466.218i	1.02694	−	0.936181i
$499$	−398.200	+	621.523i	−0.797996	+	1.24554i	0.167694	+	0.985839i	$0.446368\pi$
$499$	−398.200	+	621.523i	−0.797996	+	1.24554i	−0.965690	+	0.259698i	$0.916377\pi$
$500$	−30.4617	+	121.115i	−0.0609234	+	0.242230i
$501$	−153.274	+	85.3732i	−0.305937	+	0.170406i
$502$	−141.280	−	249.114i	−0.281434	−	0.496243i
$503$	−693.810	+	603.746i	−1.37934	+	1.20029i	−0.423687	+	0.905809i	$0.639264\pi$
$503$	−693.810	+	603.746i	−1.37934	+	1.20029i	−0.955657	+	0.294481i	$0.904853\pi$
$504$	−30.4232	+	19.8237i	−0.0603635	+	0.0393328i
$505$	177.904	+	143.159i	0.352285	+	0.283483i
$506$	440.884	+	144.003i	0.871313	+	0.284591i
$507$	−801.234	+	644.751i	−1.58034	+	1.27170i
$508$	−136.022	+	51.4941i	−0.267759	+	0.101366i
$509$	47.9257	−	777.033i	0.0941567	−	1.52659i	−0.596034	−	0.802959i	$-0.703258\pi$
$509$	47.9257	−	777.033i	0.0941567	−	1.52659i	0.690191	−	0.723628i	$-0.257527\pi$
$510$	519.046	+	278.722i	1.01774	+	0.546514i
$511$	234.177	+	74.4969i	0.458271	+	0.145787i
$512$	42.9049	−	29.3905i	0.0837986	−	0.0574034i
$513$	68.4017	+	189.444i	0.133337	+	0.369286i
$514$	−837.470	−	163.234i	−1.62932	−	0.317575i
$515$	829.679	−	366.339i	1.61103	−	0.711338i
$516$	68.2497	+	139.750i	0.132267	+	0.270834i
$517$	−659.548	−	71.3758i	−1.27572	−	0.138058i
$518$	−970.542	−	857.775i	−1.87363	−	1.65594i
$519$	−322.116	+	381.888i	−0.620647	+	0.735814i
$520$	131.708	+	807.414i	0.253286	+	1.55272i
$521$	−29.5162	+	95.3166i	−0.0566529	+	0.182949i	−0.979185	−	0.202972i	$-0.934940\pi$
$521$	−29.5162	+	95.3166i	−0.0566529	+	0.182949i	0.922532	+	0.385921i	$0.126116\pi$
$522$	4.48478	+	8.19961i	0.00859154	+	0.0157081i
$523$	−321.977	−	189.214i	−0.615634	−	0.361785i	0.165444	−	0.986219i	$-0.447094\pi$
$523$	−321.977	−	189.214i	−0.615634	−	0.361785i	−0.781078	+	0.624434i	$0.785330\pi$
$524$	−0.756906	−	49.1460i	−0.00144448	−	0.0937901i
$525$	235.327	+	93.2564i	0.448242	+	0.177631i
$526$	84.4049	+	64.7661i	0.160466	+	0.123130i
$527$	293.549	−	197.782i	0.557018	−	0.375298i
$528$	44.1812	+	636.517i	0.0836766	+	1.20552i
$529$	198.023	−	83.8161i	0.374335	−	0.158443i
$530$	1200.06	−	282.251i	2.26426	−	0.532550i
$531$	6.47093	+	0.649911i	0.0121863	+	0.00122394i
$532$	−88.3288	+	13.7112i	−0.166032	+	0.0257729i
$533$	40.5645	−	477.775i	0.0761059	−	0.896388i
$534$	−406.842	−	251.906i	−0.761876	−	0.471734i
$535$	−223.915	−	810.641i	−0.418532	−	1.51522i
$536$	13.2667	+	245.898i	0.0247513	+	0.458764i
$537$	−130.769	−	434.093i	−0.243517	−	0.808367i
$538$	1036.00	−	152.657i	1.92565	−	0.283750i
$539$	−324.106	−	47.7578i	−0.601309	−	0.0886044i
$540$	221.577	+	66.7490i	0.410327	+	0.123609i
$541$	−64.3263	−	15.6531i	−0.118903	−	0.0289336i	0.176545	−	0.984293i	$-0.443508\pi$
$541$	−64.3263	−	15.6531i	−0.118903	−	0.0289336i	−0.295447	+	0.955359i	$0.595469\pi$
$542$	181.285	−	1167.86i	0.334475	−	2.15472i
$543$	171.728	+	44.6001i	0.316258	+	0.0821364i
$544$	180.697	−	263.785i	0.332163	−	0.484899i
$545$	−106.045	−	136.019i	−0.194578	−	0.249576i
$546$	1357.49	−	41.8239i	2.48625	−	0.0766006i
$547$	202.410	−	104.709i	0.370037	−	0.191424i	−0.264373	−	0.964421i	$-0.585165\pi$
$547$	202.410	−	104.709i	0.370037	−	0.191424i	0.634410	+	0.772997i	$0.281243\pi$
$548$	3.83208	+	10.8747i	0.00699285	+	0.0198443i
$549$	−1.46497	−	1.48771i	−0.00266844	−	0.00270985i
$550$	−201.263	+	164.525i	−0.365933	+	0.299136i
$551$	−3.27846	−	42.4933i	−0.00595002	−	0.0771203i
$552$	−218.201	−	218.201i	−0.395292	−	0.395292i
$553$	391.149	+	335.116i	0.707322	+	0.605996i
$554$	−240.721	+	203.044i	−0.434515	+	0.366506i
$555$	24.8314	−	1074.76i	0.0447412	−	1.93651i
$556$	−268.329	+	202.633i	−0.482607	+	0.364448i
$557$	−76.6654	+	163.314i	−0.137640	+	0.293203i	−0.962090	−	0.272732i	$-0.912073\pi$
$557$	−76.6654	+	163.314i	−0.137640	+	0.293203i	0.824450	+	0.565935i	$0.191485\pi$
$558$	26.4207	−	26.8308i	0.0473490	−	0.0480838i
$559$	81.3366	−	877.761i	0.145504	−	1.57024i
$560$	478.375	−	907.544i	0.854240	−	1.62061i
$561$	−205.241	−	437.208i	−0.365849	−	0.779337i
$562$	1016.19	+	358.090i	1.80816	+	0.637172i
$563$	24.2469	+	173.820i	0.0430672	+	0.308739i	0.999840	+	0.0179016i	$0.00569856\pi$
$563$	24.2469	+	173.820i	0.0430672	+	0.308739i	−0.956773	+	0.290837i	$0.906066\pi$
$564$	−199.621	−	130.073i	−0.353937	−	0.230625i
$565$	−363.546	−	1113.04i	−0.643444	−	1.96999i
$566$	−738.290	−	279.496i	−1.30440	−	0.493810i
$567$	−270.229	+	599.475i	−0.476594	+	1.05728i
$568$	−552.419	+	223.852i	−0.972569	+	0.394105i
$569$	−187.932	−	38.1347i	−0.330284	−	0.0670206i	0.0308789	−	0.999523i	$-0.490169\pi$
$569$	−187.932	−	38.1347i	−0.330284	−	0.0670206i	−0.361163	+	0.932503i	$0.617620\pi$
$570$	−215.611	−	187.622i	−0.378264	−	0.329161i
$571$	656.577	+	91.5886i	1.14987	+	0.160400i	0.687431	−	0.726249i	$-0.258738\pi$
$571$	656.577	+	91.5886i	1.14987	+	0.160400i	0.462441	+	0.886650i	$0.346974\pi$
$572$	−166.343	+	321.554i	−0.290810	+	0.562158i
$573$	405.890	+	194.368i	0.708360	+	0.339210i
$574$	−286.963	+	319.693i	−0.499936	+	0.556957i
$575$	29.6673	−	173.453i	0.0515953	−	0.301658i
$576$	−7.58421	+	17.9184i	−0.0131670	+	0.0311084i
$577$	304.746	−	886.523i	0.528155	−	1.53644i	−0.287432	−	0.957801i	$-0.592801\pi$
$577$	304.746	−	886.523i	0.528155	−	1.53644i	0.815587	−	0.578635i	$-0.196414\pi$
$578$	36.1391	−	153.654i	0.0625244	−	0.265838i
$579$	729.899	−	124.841i	1.26062	−	0.215615i
$580$	−41.4331	−	26.0977i	−0.0714363	−	0.0449961i
$581$	819.672	+	400.302i	1.41079	+	0.688987i
$582$	−6.39399	+	165.996i	−0.0109862	+	0.285217i
$583$	−927.660	−	401.095i	−1.59118	−	0.687985i
$584$	161.136	−	47.1912i	0.275917	−	0.0808068i
$585$	−61.5960	−	68.6215i	−0.105292	−	0.117302i
$586$	−391.198	+	246.407i	−0.667574	+	0.420489i
$587$	534.851	−	57.8811i	0.911159	−	0.0986050i	0.359950	−	0.932972i	$-0.382794\pi$
$587$	534.851	−	57.8811i	0.911159	−	0.0986050i	0.551210	+	0.834367i	$0.314166\pi$
$588$	−96.0330	−	67.9803i	−0.163321	−	0.115613i
$589$	−160.122	+	62.0316i	−0.271854	+	0.105317i
$590$	−120.492	+	52.0974i	−0.204223	+	0.0883006i
$591$	−833.775	+	692.358i	−1.41079	+	1.17150i
$592$	−1228.13	−	161.687i	−2.07455	−	0.273119i
$593$	−240.702	−	29.8054i	−0.405906	−	0.0502621i	−0.0826619	−	0.996578i	$-0.526342\pi$
$593$	−240.702	−	29.8054i	−0.405906	−	0.0502621i	−0.323244	+	0.946316i	$0.604774\pi$
$594$	−435.944	−	586.622i	−0.733912	−	0.987578i
$595$	−89.4957	+	771.408i	−0.150413	+	1.29648i
$596$	177.637	+	90.1661i	0.298048	+	0.151285i
$597$	188.315	−	15.9885i	0.315435	−	0.0267814i
$598$	−223.234	−	917.381i	−0.373302	−	1.53408i
$599$	−972.631	−	52.4755i	−1.62376	−	0.0876052i	−0.780515	−	0.625137i	$-0.785043\pi$
$599$	−972.631	−	52.4755i	−1.62376	−	0.0876052i	−0.843243	+	0.537532i	$0.819357\pi$
$600$	168.950	−	37.0005i	0.281583	−	0.0616676i
$601$	271.735	+	1014.13i	0.452139	+	1.68740i	0.696366	+	0.717687i	$0.254799\pi$
$601$	271.735	+	1014.13i	0.452139	+	1.68740i	−0.244227	+	0.969718i	$0.578534\pi$
$602$	−532.075	+	583.659i	−0.883846	+	0.969533i
$603$	−16.2112	−	22.5310i	−0.0268843	−	0.0373648i
$604$	54.3090	+	9.71993i	0.0899156	+	0.0160926i
$605$	34.3985	−	1.59034i	0.0568571	−	0.00262866i
$606$	55.4127	−	253.022i	0.0914401	−	0.417528i
$607$	887.889	+	245.252i	1.46275	+	0.404040i	0.904801	−	0.425836i	$-0.140020\pi$
$607$	887.889	+	245.252i	1.46275	+	0.404040i	0.557949	+	0.829875i	$0.311588\pi$
$608$	−113.824	+	105.381i	−0.187211	+	0.173323i
$609$	96.2075	−	115.858i	0.157976	−	0.190243i
$610$	40.4456	+	11.8452i	0.0663043	+	0.0194183i
$611$	583.263	+	1218.00i	0.954603	+	1.99346i
$612$	−0.436983	+	14.1833i	−0.000714024	+	0.0231753i
$613$	52.9237	+	72.3734i	0.0863356	+	0.118064i	0.848209	−	0.529661i	$-0.177681\pi$
$613$	52.9237	+	72.3734i	0.0863356	+	0.118064i	−0.761874	+	0.647726i	$0.775720\pi$
$614$	−255.444	+	186.796i	−0.416033	+	0.304228i
$615$	−356.386	−	10.9801i	−0.579489	−	0.0178539i
$616$	−541.943	+	259.519i	−0.879777	+	0.421297i
$617$	327.382	−	1117.86i	0.530603	−	1.81176i	−0.0515364	−	0.998671i	$-0.516412\pi$
$617$	327.382	−	1117.86i	0.530603	−	1.81176i	0.582140	−	0.813089i	$-0.302216\pi$
$618$	−791.462	−	657.222i	−1.28068	−	1.06347i
$619$	111.784	+	120.740i	0.180587	+	0.195057i	0.817583	−	0.575810i	$-0.195313\pi$
$619$	111.784	+	120.740i	0.180587	+	0.195057i	−0.636996	+	0.770867i	$0.719823\pi$
$620$	−52.5291	+	190.172i	−0.0847243	+	0.306728i
$621$	483.301	+	105.845i	0.778263	+	0.170442i
$622$	56.6189	+	1224.65i	0.0910272	+	1.96889i
$623$	111.123	−	620.886i	0.178367	−	0.996607i
$624$	1054.31	−	758.582i	1.68960	−	1.21568i
$625$	−572.474	−	521.879i	−0.915959	−	0.835007i
$626$	894.061	−	239.563i	1.42821	−	0.382689i
$627$	50.1270	+	228.887i	0.0799474	+	0.365051i
$628$	17.2257	−	319.278i	0.0274295	−	0.508404i
$629$	911.098	−	221.705i	1.44849	−	0.352473i
$630$	6.98916	+	82.3194i	0.0110939	+	0.130666i
$631$	−302.846	+	596.638i	−0.479946	+	0.945543i	0.516085	+	0.856537i	$0.327389\pi$
$631$	−302.846	+	596.638i	−0.479946	+	0.945543i	−0.996031	+	0.0890061i	$0.971631\pi$
$632$	349.582	+	40.5572i	0.553136	+	0.0641727i
$633$	−459.265	+	341.300i	−0.725537	+	0.539178i
$634$	−62.1425	+	501.850i	−0.0980165	+	0.791561i
$635$	80.0136	−	607.764i	0.126006	−	0.957109i
$636$	−231.886	−	279.250i	−0.364601	−	0.439073i
$637$	264.667	+	612.126i	0.415490	+	0.960952i
$638$	55.8673	+	144.210i	0.0875663	+	0.226035i
$639$	38.8175	−	54.8359i	0.0607473	−	0.0858152i
$640$	−96.9521	−	895.886i	−0.151488	−	1.39982i
$641$	−192.914	−	306.272i	−0.300957	−	0.477803i	0.661233	−	0.750180i	$-0.270033\pi$
$641$	−192.914	−	306.272i	−0.300957	−	0.477803i	−0.962191	+	0.272377i	$0.912190\pi$
$642$	−709.902	+	637.221i	−1.10577	+	0.992557i
$643$	−248.621	−	848.922i	−0.386657	−	1.32025i	−0.889919	−	0.456118i	$-0.849239\pi$
$643$	−248.621	−	848.922i	−0.386657	−	1.32025i	0.503262	−	0.864134i	$-0.332133\pi$
$644$	−87.1398	+	201.538i	−0.135310	+	0.312948i
$645$	−655.020	−	25.2307i	−1.01553	−	0.0391173i
$646$	109.399	−	224.008i	0.169348	−	0.346762i
$647$	667.497	−	1059.73i	1.03168	−	1.63791i	0.303084	−	0.952964i	$-0.401984\pi$
$647$	667.497	−	1059.73i	1.03168	−	1.63791i	0.728596	−	0.684943i	$-0.240173\pi$
$648$	75.7455	+	442.856i	0.116891	+	0.683419i
$649$	104.759	+	24.6391i	0.161416	+	0.0379647i
$650$	500.434	+	172.026i	0.769898	+	0.264655i
$651$	−558.770	−	236.507i	−0.858326	−	0.363298i
$652$	−134.420	−	22.9911i	−0.206166	−	0.0352624i
$653$	143.484	+	128.794i	0.219731	+	0.197235i	0.770531	−	0.637402i	$-0.219991\pi$
$653$	143.484	+	128.794i	0.219731	+	0.197235i	−0.550800	+	0.834637i	$0.685677\pi$
$654$	−84.4950	+	176.448i	−0.129197	+	0.269798i
$655$	184.002	+	95.1857i	0.280918	+	0.145322i
$656$	−56.7603	+	406.902i	−0.0865249	+	0.620277i
$657$	−12.4236	+	14.2769i	−0.0189096	+	0.0217304i
$658$	240.611	−	1185.75i	0.365670	−	1.80206i
$659$	452.809	+	1117.44i	0.687115	+	1.69566i	0.717916	+	0.696130i	$0.245096\pi$
$659$	452.809	+	1117.44i	0.687115	+	1.69566i	−0.0308004	+	0.999526i	$0.509806\pi$
$660$	245.427	+	110.632i	0.371859	+	0.167625i
$661$	−19.7116	+	52.0683i	−0.0298209	+	0.0787721i	−0.949307	−	0.314351i	$-0.898213\pi$
$661$	−19.7116	+	52.0683i	−0.0298209	+	0.0787721i	0.919486	+	0.393123i	$0.128605\pi$
$662$	766.348	−	250.307i	1.15763	−	0.378107i
$663$	−536.756	+	823.751i	−0.809586	+	1.24246i
$664$	617.288	−	86.1079i	0.929650	−	0.129681i
$665$	125.213	−	355.328i	0.188290	−	0.534329i
$666$	90.2995	−	42.3899i	0.135585	−	0.0636485i
$667$	−92.6128	−	48.8171i	−0.138850	−	0.0731890i
$668$	84.9325	+	7.87016i	0.127145	+	0.0117817i
$669$	413.303	+	406.987i	0.617792	+	0.608351i
$670$	507.169	+	238.083i	0.756968	+	0.355348i
$671$	−20.8211	−	27.5716i	−0.0310300	−	0.0410904i
$672$	−547.954	−	12.6600i	−0.815408	−	0.0188392i
$673$	718.559	+	851.895i	1.06770	+	1.26582i	0.962476	+	0.271368i	$0.0874761\pi$
$673$	718.559	+	851.895i	1.06770	+	1.26582i	0.105220	+	0.994449i	$0.466445\pi$
$674$	−773.977	+	903.389i	−1.14833	+	1.34034i
$675$	−196.080	+	196.080i	−0.290489	+	0.290489i
$676$	498.510	−	38.4612i	0.737440	−	0.0568952i
$677$	564.066	+	690.020i	0.833184	+	1.01923i	0.999450	+	0.0331514i	$0.0105543\pi$
$677$	564.066	+	690.020i	0.833184	+	1.01923i	−0.166266	+	0.986081i	$0.553171\pi$
$678$	−946.358	+	931.895i	−1.39581	+	1.37448i
$679$	−206.522	+	72.7754i	−0.304156	+	0.107180i
$680$	243.797	+	471.279i	0.358525	+	0.693058i
$681$	−7.85423	−	254.927i	−0.0115334	−	0.374343i
$682$	491.412	−	383.122i	0.720546	−	0.561762i
$683$	−474.311	−	324.911i	−0.694452	−	0.475711i	0.165418	−	0.986224i	$-0.447103\pi$
$683$	−474.311	−	324.911i	−0.694452	−	0.475711i	−0.859870	+	0.510513i	$0.829456\pi$
$684$	1.73047	−	6.66299i	0.00252992	−	0.00974121i
$685$	−48.0216	−	7.45433i	−0.0701045	−	0.0108822i
$686$	−96.6881	+	397.340i	−0.140945	+	0.579212i
$687$	−203.853	+	676.698i	−0.296729	+	0.985005i
$688$	−110.108	+	747.240i	−0.160040	+	1.08610i
$689$	299.918	+	2035.38i	0.435295	+	2.95411i
$690$	−672.237	+	202.509i	−0.974257	+	0.293491i
$691$	813.411	−	43.8853i	1.17715	−	0.0635098i	0.545055	−	0.838400i	$-0.316509\pi$
$691$	813.411	−	43.8853i	1.17715	−	0.0635098i	0.632096	+	0.774890i	$0.282195\pi$
$692$	234.120	−	64.6684i	0.338324	−	0.0934515i
$693$	35.6545	−	57.5840i	0.0514495	−	0.0830937i
$694$	−996.271	−	84.5863i	−1.43555	−	0.121882i
$695$	−217.386	−	1400.43i	−0.312786	−	2.01500i
$696$	10.2826	−	102.380i	0.0147739	−	0.147098i
$697$	−71.2027	−	302.735i	−0.102156	−	0.434341i
$698$	483.521	+	1142.36i	0.692724	+	1.63663i
$699$	−543.168	+	37.7019i	−0.777065	+	0.0539368i
$700$	−68.7642	−	102.060i	−0.0982346	−	0.145800i
$701$	406.586	−	529.874i	0.580009	−	0.755882i	−0.407541	−	0.913187i	$-0.633614\pi$
$701$	406.586	−	529.874i	0.580009	−	0.755882i	0.987550	+	0.157304i	$0.0502804\pi$
$702$	−548.124	+	1383.16i	−0.780803	+	1.97031i
$703$	−454.847	+	7.00518i	−0.647009	+	0.00996470i
$704$	−163.129	+	277.590i	−0.231718	+	0.394303i
$705$	881.035	−	481.883i	1.24970	−	0.683521i
$706$	502.752	+	155.684i	0.712114	+	0.220516i
$707$	336.971	−	54.9679i	0.476620	−	0.0777481i
$708$	29.5443	+	24.9201i	0.0417292	+	0.0351978i
$709$	513.567	−	581.082i	0.724353	−	0.819580i	−0.265132	−	0.964212i	$-0.585416\pi$
$709$	513.567	−	581.082i	0.724353	−	0.819580i	0.989485	+	0.144632i	$0.0461999\pi$
$710$	−145.906	+	1348.24i	−0.205501	+	1.89893i
$711$	−35.6444	+	17.4076i	−0.0501327	+	0.0244832i
$712$	−174.076	−	394.245i	−0.244489	−	0.553714i
$713$	−80.6976	+	414.018i	−0.113180	+	0.580671i
$714$	828.525	−	299.152i	1.16040	−	0.418981i
$715$	−862.333	−	1258.85i	−1.20606	−	1.76063i
$716$	−66.8178	+	210.038i	−0.0933209	+	0.293349i
$717$	−156.746	+	291.898i	−0.218614	+	0.407111i
$718$	−162.360	−	10.0140i	−0.226127	−	0.0139471i
$719$	75.2799	+	198.852i	0.104701	+	0.276567i	0.977297	−	0.211876i	$-0.0679572\pi$
$719$	75.2799	+	198.852i	0.104701	+	0.276567i	−0.872596	+	0.488443i	$0.837565\pi$
$720$	49.5327	+	61.5544i	0.0687954	+	0.0854923i
$721$	421.031	−	1289.04i	0.583954	−	1.78785i
$722$	450.209	−	559.476i	0.623558	−	0.774898i
$723$	−76.0789	−	116.757i	−0.105227	−	0.161490i
$724$	−56.6239	−	65.0709i	−0.0782098	−	0.0898769i
$725$	51.0402	−	28.9464i	0.0704003	−	0.0399260i
$726$	−19.0068	−	34.1237i	−0.0261801	−	0.0470023i
$727$	1062.30	+	267.179i	1.46121	+	0.367509i	0.891005	−	0.453993i	$-0.150001\pi$
$727$	1062.30	+	267.179i	1.46121	+	0.367509i	0.570205	+	0.821502i	$0.306864\pi$
$728$	1029.93	+	659.860i	1.41474	+	0.906401i
$729$	−522.433	−	573.082i	−0.716643	−	0.786120i
$730$	78.8486	−	373.783i	0.108012	−	0.512032i
$731$	−126.613	−	557.553i	−0.173205	−	0.762727i
$732$	−2.18610	−	12.2146i	−0.00298647	−	0.0166866i
$733$	929.173	+	900.986i	1.26763	+	1.22918i	0.960746	+	0.277429i	$0.0894824\pi$
$733$	929.173	+	900.986i	1.26763	+	1.22918i	0.306884	+	0.951747i	$0.400714\pi$
$734$	1029.54	−	318.812i	1.40264	−	0.434349i
$735$	443.918	−	221.045i	0.603969	−	0.300741i
$736$	70.0139	+	374.541i	0.0951276	+	0.508888i
$737$	−217.298	−	404.660i	−0.294841	−	0.549064i
$738$	−13.8282	−	30.0565i	−0.0187373	−	0.0407269i
$739$	−405.787	+	85.5997i	−0.549103	+	0.115832i	−0.472664	−	0.881242i	$-0.656708\pi$
$739$	−405.787	+	85.5997i	−0.549103	+	0.115832i	−0.0764382	+	0.997074i	$0.524355\pi$
$740$	−305.251	+	424.250i	−0.412501	+	0.573310i
$741$	342.429	−	332.042i	0.462118	−	0.448099i
$742$	884.511	−	1617.17i	1.19206	−	2.17947i
$743$	−181.899	+	108.788i	−0.244817	+	0.146418i	−0.630438	−	0.776240i	$-0.717125\pi$
$743$	−181.899	+	108.788i	−0.244817	+	0.146418i	0.385621	+	0.922657i	$0.373987\pi$
$744$	−406.916	+	79.3133i	−0.546931	+	0.106604i
$745$	−689.016	+	479.823i	−0.924853	+	0.644058i
$746$	−16.2406	+	210.501i	−0.0217703	+	0.282173i
$747$	−53.3498	+	45.7073i	−0.0714187	+	0.0611878i
$748$	−37.8037	+	231.748i	−0.0505397	+	0.309824i
$749$	−1125.61	−	560.488i	−1.50282	−	0.748315i
$750$	−163.394	+	574.271i	−0.217859	+	0.765695i
$751$	220.419	+	556.214i	0.293501	+	0.740632i	0.999475	+	0.0323944i	$0.0103132\pi$
$751$	220.419	+	556.214i	0.293501	+	0.740632i	−0.705974	+	0.708237i	$0.749491\pi$
$752$	−442.804	−	1069.02i	−0.588835	−	1.42157i
$753$	−165.720	−	314.394i	−0.220079	−	0.417521i
$754$	189.723	−	251.234i	0.251622	−	0.333201i
$755$	−144.384	+	182.283i	−0.191237	+	0.241434i
$756$	295.570	−	179.876i	0.390966	−	0.237931i
$757$	326.657	+	555.858i	0.431515	+	0.734290i	0.995826	−	0.0912722i	$-0.0290933\pi$
$757$	326.657	+	555.858i	0.431515	+	0.734290i	−0.564311	+	0.825562i	$0.690858\pi$
$758$	−425.117	−	254.249i	−0.560840	−	0.335421i
$759$	541.358	+	195.466i	0.713252	+	0.257531i
$760$	−64.7070	−	249.148i	−0.0851407	−	0.327826i
$761$	−20.3364	−	202.482i	−0.0267232	−	0.266074i	−0.999422	−	0.0340015i	$-0.989175\pi$
$761$	−20.3364	−	202.482i	−0.0267232	−	0.266074i	0.972699	−	0.232072i	$-0.0745506\pi$
$762$	−657.569	+	226.042i	−0.862952	+	0.296643i
$763$	−257.257	−	17.8564i	−0.337165	−	0.0234029i
$764$	−109.394	−	189.477i	−0.143186	−	0.248006i
$765$	−51.7951	−	29.9039i	−0.0677060	−	0.0390901i
$766$	863.767	−	1282.01i	1.12763	−	1.67364i
$767$	−69.6194	−	207.716i	−0.0907684	−	0.270816i
$768$	−582.909	+	373.461i	−0.758996	+	0.486277i
$769$	600.090	+	160.794i	0.780352	+	0.209095i	0.626940	−	0.779068i	$-0.284307\pi$
$769$	600.090	+	160.794i	0.780352	+	0.209095i	0.153412	+	0.988162i	$0.450974\pi$
$770$	−63.1371	+	1365.63i	−0.0819962	+	1.77355i
$771$	−1032.54	−	234.475i	−1.33922	−	0.304118i
$772$	−327.053	−	150.468i	−0.423643	−	0.194907i
$773$	−977.971	+	60.3192i	−1.26516	+	0.0780326i	−0.680200	−	0.733027i	$-0.738107\pi$
$773$	−977.971	+	60.3192i	−1.26516	+	0.0780326i	−0.584964	+	0.811059i	$0.698891\pi$
$774$	−24.9961	−	55.4512i	−0.0322947	−	0.0716424i
$775$	−170.987	−	163.264i	−0.220628	−	0.210664i
$776$	−89.2394	+	120.084i	−0.114999	+	0.154747i
$777$	−1171.05	−	1101.05i	−1.50715	−	1.41705i
$778$	−242.616	−	135.136i	−0.311846	−	0.173697i
$779$	1.16172	+	150.870i	0.00149129	+	0.193671i
$780$	−71.5309	−	543.331i	−0.0917063	−	0.696578i
$781$	755.283	−	815.800i	0.967072	−	1.04456i
$782$	−322.371	−	520.647i	−0.412239	−	0.665789i
$783$	74.6700	+	147.108i	0.0953640	+	0.187877i
$784$	−198.188	−	535.940i	−0.252790	−	0.683597i
$785$	1151.22	+	700.598i	1.46652	+	0.892482i
$786$	3.61864	−	234.958i	0.00460387	−	0.298929i
$787$	262.123	−	632.821i	0.333066	−	0.804093i	−0.665280	−	0.746594i	$-0.731688\pi$
$787$	262.123	−	632.821i	0.333066	−	0.804093i	0.998346	−	0.0574982i	$-0.0183124\pi$
$788$	524.642	−	48.6152i	0.665789	−	0.0616944i
$789$	102.219	+	83.5598i	0.129555	+	0.105906i
$790$	457.573	−	657.065i	0.579207	−	0.831728i
$791$	−1601.54	−	707.150i	−2.02471	−	0.893995i
$792$	−1.78118	−	46.2417i	−0.00224896	−	0.0583859i
$793$	−25.4070	+	65.5831i	−0.0320391	+	0.0827025i
$794$	−780.718	−	1178.22i	−0.983272	−	1.48391i
$795$	1499.31	−	304.236i	1.88592	−	0.382687i
$796$	−79.9233	−	45.3268i	−0.100406	−	0.0569432i
$797$	−6.83980	+	888.270i	−0.00858193	+	1.11452i	0.826012	+	0.563652i	$0.190604\pi$
$797$	−6.83980	+	888.270i	−0.00858193	+	1.11452i	−0.834594	+	0.550865i	$0.814298\pi$
$798$	−424.103	+	52.5153i	−0.531458	+	0.0658087i
$799$	604.881	+	633.492i	0.757048	+	0.792857i
$800$	−197.925	−	80.2035i	−0.247407	−	0.100254i
$801$	40.4938	+	26.8321i	0.0505540	+	0.0334983i
$802$	306.179	+	432.526i	0.381769	+	0.539310i
$803$	−234.659	+	207.394i	−0.292228	+	0.258274i
$804$	−3.81026	−	164.917i	−0.00473913	−	0.205121i
$805$	−574.611	−	725.438i	−0.713803	−	0.901165i
$806$	−1189.71	−	439.947i	−1.47606	−	0.545839i
$807$	1290.86	−	149.761i	1.59958	−	0.185577i
$808$	169.956	−	159.796i	0.210341	−	0.197768i
$809$	1178.12	−	296.308i	1.45626	−	0.366265i	0.567022	−	0.823703i	$-0.308095\pi$
$809$	1178.12	−	296.308i	1.45626	−	0.366265i	0.889242	+	0.457438i	$0.151233\pi$
$810$	969.211	+	324.847i	1.19656	+	0.401045i
$811$	713.835	+	930.288i	0.880191	+	1.14709i	0.988235	+	0.152942i	$0.0488747\pi$
$811$	713.835	+	930.288i	0.880191	+	1.14709i	−0.108044	+	0.994146i	$0.534459\pi$
$812$	−70.4196	+	20.0361i	−0.0867237	+	0.0246750i
$813$	269.492	−	1441.65i	0.331478	−	1.77325i
$814$	1573.02	−	500.413i	1.93246	−	0.614758i
$815$	353.404	−	453.295i	0.433624	−	0.556190i
$816$	497.261	−	680.007i	0.609389	−	0.833342i
$817$			277.374i			0.339503i
$818$	215.521	+	925.877i	0.263473	+	1.13188i
$819$	−137.872			−0.168342
$820$	139.925	+	102.321i	0.170640	+	0.124782i
$821$	−71.5895	−	55.8135i	−0.0871979	−	0.0679824i	0.570313	−	0.821428i	$-0.306822\pi$
$821$	−71.5895	−	55.8135i	−0.0871979	−	0.0679824i	−0.657511	+	0.753445i	$0.728391\pi$
$822$	16.7108	+	52.5293i	0.0203294	+	0.0639043i
$823$	−574.111	−	107.320i	−0.697583	−	0.130401i	−0.176999	−	0.984211i	$-0.556639\pi$
$823$	−574.111	−	107.320i	−0.697583	−	0.130401i	−0.520584	+	0.853810i	$0.674286\pi$
$824$	−253.559	−	891.166i	−0.307717	−	1.08151i
$825$	−255.929	+	196.381i	−0.310217	+	0.238038i
$826$	−62.3744	+	186.100i	−0.0755138	+	0.225303i
$827$	−147.401	−	586.065i	−0.178236	−	0.708664i	−0.991867	−	0.127281i	$-0.959375\pi$
$827$	−147.401	−	586.065i	−0.178236	−	0.708664i	0.813631	−	0.581382i	$-0.197488\pi$
$828$	−11.5833	−	12.3197i	−0.0139895	−	0.0148789i
$829$	133.594	+	1151.52i	0.161151	+	1.38904i	0.790759	+	0.612128i	$0.209686\pi$
$829$	133.594	+	1151.52i	0.161151	+	1.38904i	−0.629607	+	0.776913i	$0.716784\pi$
$830$	491.828	−	1330.00i	0.592564	−	1.60242i
$831$	−306.344	+	242.652i	−0.368645	+	0.292000i
$832$	655.255	−	15.1390i	0.787566	−	0.0181960i
$833$	286.445	+	324.102i	0.343872	+	0.389078i
$834$	−1312.06	+	928.788i	−1.57321	+	1.11366i
$835$	−198.578	+	299.684i	−0.237818	+	0.358903i
$836$	42.7816	−	105.576i	0.0511741	−	0.126287i
$837$	480.739	−	459.027i	0.574360	−	0.548419i
$838$	6.97667	+	56.3421i	0.00832538	+	0.0672341i
$839$	−416.890	−	3.21011i	−0.496889	−	0.00382611i	−0.240986	−	0.970529i	$-0.577471\pi$
$839$	−416.890	−	3.21011i	−0.496889	−	0.00382611i	−0.255903	+	0.966702i	$0.582373\pi$
$840$	448.704	−	791.185i	0.534171	−	0.941887i
$841$	160.303	+	789.991i	0.190610	+	0.939347i
$842$	−893.579	+	592.107i	−1.06126	+	0.703215i
$843$	1246.77	+	483.000i	1.47897	+	0.572954i
$844$	277.977	−	10.7074i	0.329357	−	0.0126865i
$845$	−851.203	+	1927.79i	−1.00734	+	2.28141i
$846$	76.4663	+	53.2503i	0.0903857	+	0.0629436i
$847$	32.5861	−	39.8626i	0.0384724	−	0.0470632i
$848$	−162.650	−	1755.27i	−0.191804	−	2.06990i
$849$	−905.074	−	374.894i	−1.06605	−	0.441571i
$850$	343.179	+	5.28536i	0.403740	+	0.00621807i
$851$	−580.915	+	954.554i	−0.682626	+	1.12168i
$852$	374.497	−	138.487i	0.439550	−	0.162543i
$853$	−168.417	+	85.4863i	−0.197441	+	0.100218i	−0.548556	−	0.836114i	$-0.684822\pi$
$853$	−168.417	+	85.4863i	−0.197441	+	0.100218i	0.351115	+	0.936332i	$0.385803\pi$
$854$	53.5750	−	33.1722i	0.0627341	−	0.0388433i
$855$	21.2910	+	19.7116i	0.0249017	+	0.0230545i
$856$	−851.802	+	112.142i	−0.995096	+	0.131007i
$857$	1296.96	−	9.98678i	1.51337	−	0.0116532i	0.751653	−	0.659558i	$-0.229257\pi$
$857$	1296.96	−	9.98678i	1.51337	−	0.0116532i	0.761721	+	0.647905i	$0.224355\pi$
$858$	−842.221	+	1512.08i	−0.981610	+	1.76233i
$859$	1117.66	−	1188.72i	1.30112	−	1.38384i	0.422473	−	0.906376i	$-0.361162\pi$
$859$	1117.66	−	1188.72i	1.30112	−	1.38384i	0.878649	−	0.477469i	$-0.158446\pi$
$860$	255.787	+	190.087i	0.297427	+	0.221031i
$861$	−368.159	+	385.573i	−0.427594	+	0.447820i
$862$	539.014	−	242.975i	0.625307	−	0.281873i
$863$	−52.0269	−	843.527i	−0.0602861	−	0.977435i	−0.900410	−	0.435041i	$-0.856734\pi$
$863$	−52.0269	−	843.527i	−0.0602861	−	0.977435i	0.840124	−	0.542394i	$-0.182482\pi$
$864$	250.956	−	545.470i	0.290458	−	0.631331i
$865$	−226.700	+	998.298i	−0.262081	+	1.15410i
$866$	516.292	+	23.8696i	0.596180	+	0.0275631i
$867$	50.6980	−	189.208i	0.0584752	−	0.218232i
$868$	159.135	+	248.382i	0.183335	+	0.286155i
$869$	−622.382	+	208.602i	−0.716205	+	0.240048i
$870$	−194.148	−	130.810i	−0.223159	−	0.150356i
$871$	−467.502	+	809.738i	−0.536742	+	0.929665i
$872$	−152.590	+	88.0976i	−0.174988	+	0.101029i
$873$	1.16772	−	16.8232i	0.00133759	−	0.0192706i
$874$	96.5757	+	280.945i	0.110498	+	0.321447i
$875$	−783.077	+	78.6487i	−0.894945	+	0.0898842i
$876$	−108.864	+	28.2734i	−0.124274	+	0.0322756i
$877$	68.8481	−	190.680i	0.0785041	−	0.217423i	−0.895012	−	0.446043i	$-0.852833\pi$
$877$	68.8481	−	190.680i	0.0785041	−	0.217423i	0.973516	+	0.228620i	$0.0734212\pi$
$878$	308.471	−	515.778i	0.351334	−	0.587446i
$879$	−494.649	+	290.687i	−0.562740	+	0.330702i
$880$	679.685	+	1116.85i	0.772370	+	1.26915i
$881$	844.185	+	668.670i	0.958213	+	0.758990i	0.970541	−	0.240934i	$-0.0774539\pi$
$881$	844.185	+	668.670i	0.958213	+	0.758990i	−0.0123287	+	0.999924i	$0.503924\pi$
$882$	36.7211	+	27.7305i	0.0416339	+	0.0314405i
$883$	−658.321	+	347.007i	−0.745550	+	0.392986i	−0.795649	−	0.605758i	$-0.792870\pi$
$883$	−658.321	+	347.007i	−0.745550	+	0.392986i	0.0500985	+	0.998744i	$0.484046\pi$
$884$	441.611	−	182.921i	0.499560	−	0.206925i
$885$	−151.446	+	60.0156i	−0.171125	+	0.0678142i
$886$	1087.70	+	309.478i	1.22765	+	0.349298i
$887$	234.376	−	470.691i	0.264235	−	0.530655i	−0.722820	−	0.691036i	$-0.757155\pi$
$887$	234.376	−	470.691i	0.264235	−	0.530655i	0.987055	+	0.160381i	$0.0512722\pi$
$888$	−1083.93	−	176.815i	−1.22064	−	0.199116i
$889$	−596.327	−	696.035i	−0.670784	−	0.782942i
$890$	−977.612	−	75.4251i	−1.09844	−	0.0847473i
$891$	−478.896	−	687.685i	−0.537482	−	0.771812i
$892$	−53.9504	−	276.792i	−0.0604825	−	0.310305i
$893$	−218.104	−	364.681i	−0.244238	−	0.408377i
$894$	835.573	+	457.017i	0.934645	+	0.511205i
$895$	−646.693	−	666.924i	−0.722562	−	0.745167i
$896$	−1093.66	−	786.894i	−1.22060	−	0.878230i
$897$	−241.836	−	1146.43i	−0.269605	−	1.27807i
$898$	−362.361	+	166.713i	−0.403520	+	0.185649i
$899$	−123.914	+	66.5406i	−0.137836	+	0.0740163i
$900$	9.31630	−	1.74152i	0.0103514	−	0.00193502i
$901$	594.788	+	1194.49i	0.660142	+	1.32574i
$902$	−161.947	−	522.976i	−0.179542	−	0.579796i
$903$	−682.277	+	703.622i	−0.755567	+	0.779204i
$904$	−1177.48	+	210.738i	−1.30252	+	0.233118i
$905$	354.533	−	80.5096i	0.391749	−	0.0889609i
$906$	258.088	+	54.4430i	0.284865	+	0.0600916i
$907$	302.675	−	275.925i	0.333710	−	0.304217i	−0.489444	−	0.872035i	$-0.662800\pi$
$907$	302.675	−	275.925i	0.333710	−	0.304217i	0.823154	+	0.567818i	$0.192212\pi$
$908$	−66.8912	+	104.406i	−0.0736687	+	0.114984i
$909$	−6.41359	+	25.5003i	−0.00705566	+	0.0280532i
$910$	2431.24	−	1354.19i	2.67169	−	1.48812i
$911$	−136.179	−	240.120i	−0.149483	−	0.263579i	0.785067	−	0.619411i	$-0.212629\pi$
$911$	−136.179	−	240.120i	−0.149483	−	0.263579i	−0.934550	+	0.355833i	$0.884197\pi$
$912$	−308.302	+	268.281i	−0.338051	+	0.294168i
$913$	−973.983	+	634.647i	−1.06679	+	0.695122i
$914$	641.790	+	516.447i	0.702178	+	0.565040i
$915$	49.7150	+	16.2381i	0.0543334	+	0.0177465i
$916$	267.686	−	215.406i	0.292233	−	0.235159i
$917$	289.683	−	109.666i	0.315902	−	0.119592i
$918$	−59.4050	+	963.149i	−0.0647114	+	1.04918i
$919$	755.183	+	405.525i	0.821745	+	0.441267i	0.829368	−	0.558703i	$-0.188701\pi$
$919$	755.183	+	405.525i	0.821745	+	0.441267i	−0.00762297	+	0.999971i	$0.502426\pi$
$920$	−602.557	−	191.687i	−0.654954	−	0.208356i
$921$	−323.985	+	221.935i	−0.351775	+	0.240972i
$922$	400.180	+	1108.33i	0.434035	+	1.20209i
$923$	−2221.34	−	432.968i	−2.40665	−	0.469088i
$924$	368.218	−	162.584i	0.398505	−	0.175957i
$925$	−274.836	−	562.765i	−0.297120	−	0.608394i
$926$	−115.017	−	12.4470i	−0.124208	−	0.0134417i
$927$	78.2532	+	69.1610i	0.0844156	+	0.0746074i
$928$	−81.9170	+	97.1176i	−0.0882727	+	0.104653i
$929$	−281.518	−	1725.80i	−0.303034	−	1.85769i	−0.485172	−	0.874419i	$-0.661243\pi$
$929$	−281.518	−	1725.80i	−0.303034	−	1.85769i	0.182139	−	0.983273i	$-0.441698\pi$
$930$	−279.011	+	901.013i	−0.300012	+	0.968831i
$931$	−100.695	−	184.102i	−0.108157	−	0.197746i
$932$	228.216	+	134.114i	0.244867	+	0.143899i
$933$	23.4281	+	1521.19i	0.0251105	+	1.63042i
$934$	−671.497	−	266.104i	−0.718948	−	0.284908i
$935$	−785.164	−	602.478i	−0.839748	−	0.644361i
$936$	−78.1242	+	52.6371i	−0.0834660	+	0.0562362i
$937$	−46.0561	−	663.527i	−0.0491527	−	0.708140i	−0.957228	−	0.289334i	$-0.906566\pi$
$937$	−46.0561	−	663.527i	−0.0491527	−	0.708140i	0.908076	−	0.418806i	$-0.137551\pi$
$938$	771.445	−	326.525i	0.822436	−	0.348107i
$939$	1118.13	−	262.981i	1.19076	−	0.280065i
$940$	−485.769	−	48.7884i	−0.516775	−	0.0519025i
$941$	1055.93	−	163.910i	1.12213	−	0.174187i	0.434797	−	0.900528i	$-0.356820\pi$
$941$	1055.93	−	163.910i	1.12213	−	0.174187i	0.687334	+	0.726341i	$0.258781\pi$
$942$	129.320	−	1523.15i	0.137282	−	1.61693i
$943$	315.098	+	195.100i	0.334144	+	0.206893i
$944$	49.9767	+	180.931i	0.0529414	+	0.191664i
$945$	78.5651	+	1456.20i	0.0831377	+	1.54095i
$946$	−290.318	−	963.725i	−0.306890	−	1.01874i
$947$	−1051.30	+	154.911i	−1.11013	+	0.163581i	−0.675738	−	0.737142i	$-0.736175\pi$
$947$	−1051.30	+	154.911i	−1.11013	+	0.163581i	−0.434395	+	0.900723i	$0.643038\pi$
$948$	−233.230	−	34.3671i	−0.246024	−	0.0362522i
$949$	610.417	+	183.886i	0.643221	+	0.193768i
$950$	−161.786	−	39.3687i	−0.170301	−	0.0414407i
$951$	−96.2584	+	620.107i	−0.101218	+	0.652058i
$952$	767.872	+	199.426i	0.806588	+	0.209481i
$953$	−463.379	+	676.450i	−0.486232	+	0.709811i	−0.987873	−	0.155265i	$-0.950377\pi$
$953$	−463.379	+	676.450i	−0.486232	+	0.709811i	0.501641	+	0.865076i	$0.332730\pi$
$954$	87.2825	+	111.953i	0.0914911	+	0.117351i
$955$	921.709	−	28.3975i	0.965140	−	0.0297357i
$956$	143.068	−	74.0103i	0.149653	−	0.0774167i
$957$	63.7853	+	181.010i	0.0666513	+	0.189143i
$958$	−878.505	−	892.139i	−0.917020	−	0.931252i
$959$	−56.2560	+	45.9871i	−0.0586611	+	0.0479532i
$960$	−37.4912	−	485.938i	−0.0390534	−	0.506185i
$961$	−278.819	−	278.819i	−0.290134	−	0.290134i
$962$	−2551.80	−	2186.25i	−2.65260	−	2.27261i
$963$	74.0241	−	62.4381i	0.0768682	−	0.0648370i
$964$	−1.56489	+	67.7324i	−0.00162333	+	0.0702619i
$965$	1210.87	−	914.404i	1.25478	−	0.947569i
$966$	−446.074	+	950.234i	−0.461775	+	0.983680i
$967$	378.595	−	384.470i	0.391515	−	0.397591i	−0.488479	−	0.872575i	$-0.662448\pi$
$967$	378.595	−	384.470i	0.391515	−	0.397591i	0.879994	+	0.474984i	$0.157546\pi$
$968$	3.24587	−	35.0286i	0.00335318	−	0.0361865i
$969$	144.256	−	273.674i	0.148871	−	0.282429i
$970$	144.647	+	308.130i	0.149121	+	0.317660i
$971$	−1342.13	−	472.950i	−1.38222	−	0.487075i	−0.464947	−	0.885338i	$-0.653927\pi$
$971$	−1342.13	−	472.950i	−1.38222	−	0.487075i	−0.917271	+	0.398263i	$0.869613\pi$
$972$	7.10409	+	50.9276i	0.00730874	+	0.0523946i
$973$	−1775.33	−	1156.80i	−1.82459	−	1.18890i
$974$	−120.031	−	367.492i	−0.123236	−	0.377302i
$975$	614.151	+	232.501i	0.629898	+	0.238462i
$976$	24.7651	−	54.9387i	0.0253740	−	0.0562897i
$977$	−1554.04	+	629.729i	−1.59062	+	0.644554i	−0.988137	−	0.153576i	$-0.950921\pi$
$977$	−1554.04	+	629.729i	−1.59062	+	0.644554i	−0.602486	+	0.798130i	$0.705823\pi$
$978$	−638.950	−	129.654i	−0.653323	−	0.132571i
$979$	606.389	+	527.673i	0.619396	+	0.538991i
$980$	−238.781	−	33.3086i	−0.243654	−	0.0339883i
$981$	9.12512	−	17.6396i	0.00930185	−	0.0179812i
$982$	1984.83	+	950.469i	2.02121	+	0.967891i
$983$	432.801	−	482.165i	0.440285	−	0.490504i	−0.482458	−	0.875919i	$-0.660256\pi$
$983$	432.801	−	482.165i	0.440285	−	0.490504i	0.922743	+	0.385416i	$0.125942\pi$
$984$	−61.4094	+	359.038i	−0.0624079	+	0.364876i
$985$	−865.605	+	2045.07i	−0.878787	+	2.07622i
$986$	66.3791	−	193.101i	0.0673216	−	0.195843i
$987$	343.761	−	1461.58i	0.348289	−	1.48083i
$988$	−228.572	+	39.0947i	−0.231348	+	0.0395696i
$989$	576.511	+	363.131i	0.582923	+	0.367170i
$990$	−94.6062	−	46.2027i	−0.0955618	−	0.0466694i
$991$	2.93926	−	76.3068i	0.00296595	−	0.0769998i	−0.997034	−	0.0769617i	$-0.975478\pi$
$991$	2.93926	−	76.3068i	0.00296595	−	0.0769998i	1.00000		3.80720e-5i	$-1.21187e-5\pi$
$992$	469.864	+	203.157i	0.473653	+	0.204795i
$993$	960.124	−	281.188i	0.966892	−	0.283170i
$994$	1354.42	+	1508.91i	1.36260	+	1.51801i
$995$	327.676	−	206.396i	0.329323	−	0.207433i
$996$	−415.089	+	44.9206i	−0.416756	+	0.0451010i
$997$	−11.2547	−	7.96705i	−0.0112886	−	0.00799102i	0.572116	−	0.820173i	$-0.306123\pi$
$997$	−11.2547	−	7.96705i	−0.0112886	−	0.00799102i	−0.583404	+	0.812182i	$0.698280\pi$
$998$	1599.79	−	619.764i	1.60300	−	0.621006i
$999$	1616.24	−	698.820i	1.61786	−	0.699519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	409.3.p.a.21.18	✓	8576
409.39	odd	408	inner	409.3.p.a.39.18	yes	8576

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
409.3.p.a.21.18	✓	8576	1.1	even	1	trivial
409.3.p.a.39.18	yes	8576	409.39	odd	408	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:	\( N \)	\(=\)	\( 409 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	409.p (of order \(408\), degree \(128\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.87616 - 1.37196i) q^{2} +(-2.27472 - 1.77344i) q^{3} +(0.425102 + 1.33628i) q^{4} +(-5.80963 - 1.08601i) q^{5} +(1.83464 + 6.44810i) q^{6} +(-7.01076 + 5.37954i) q^{7} +(-1.91878 + 5.72485i) q^{8} +(-0.165999 - 0.660008i) q^{9} +(9.40985 + 10.0081i) q^{10} +(-1.29784 - 11.1867i) q^{11} +(1.40284 - 3.79356i) q^{12} +(-17.9706 + 14.2343i) q^{13} +(20.5339 - 0.474415i) q^{14} +(11.2893 + 12.7734i) q^{15} +(16.0323 - 11.3491i) q^{16} +(-8.21313 + 12.3949i) q^{17} +(-0.594065 + 1.46603i) q^{18} +(5.21713 - 4.98150i) q^{19} +(-1.01847 - 8.22497i) q^{20} +(25.4878 + 0.196259i) q^{21} +(-12.9128 + 22.7686i) q^{22} +(-3.52372 - 17.3653i) q^{23} +(14.5174 - 9.61956i) q^{24} +(9.26056 + 3.58756i) q^{25} +(53.2447 - 2.05093i) q^{26} +(-11.2783 + 25.5429i) q^{27} +(-10.1689 - 7.08150i) q^{28} +(3.73942 - 4.57443i) q^{29} +(-3.65590 - 39.4535i) q^{30} +(-21.9932 - 9.10988i) q^{31} +(-21.5012 - 0.331144i) q^{32} +(-16.8868 + 27.7482i) q^{33} +(32.4144 - 11.9867i) q^{34} +(46.5721 - 23.6394i) q^{35} +(0.811392 - 0.502393i) q^{36} +(-46.2756 - 42.8428i) q^{37} +(-16.6226 + 2.18841i) q^{38} +(66.1218 - 0.509146i) q^{39} +(17.3646 - 31.1754i) q^{40} +(-14.3272 + 15.2381i) q^{41} +(-47.5500 - 35.3365i) q^{42} +(-26.5546 + 27.8107i) q^{43} +(14.3969 - 6.48976i) q^{44} +(0.247617 + 4.01468i) q^{45} +(-17.2134 + 37.4145i) q^{46} +(13.0450 - 57.4449i) q^{47} +(-56.5959 - 2.61659i) q^{48} +(7.52909 - 28.0990i) q^{49} +(-12.4523 - 19.4360i) q^{50} +(40.6641 - 13.6292i) q^{51} +(-26.6604 - 17.9628i) q^{52} +(44.8714 - 77.7195i) q^{53} +(56.2039 - 32.4493i) q^{54} +(-4.60889 + 66.3999i) q^{55} +(-17.3450 - 50.4576i) q^{56} +(-20.7019 + 2.07920i) q^{57} +(-13.2917 + 3.45204i) q^{58} +(-3.24530 + 8.98810i) q^{59} +(-12.2698 + 20.5157i) q^{60} +(2.64502 - 1.55438i) q^{61} +(28.7644 + 47.2655i) q^{62} +(4.71432 + 3.73416i) q^{63} +(-22.8154 - 17.2294i) q^{64} +(119.861 - 63.1798i) q^{65} +(69.7518 - 28.8921i) q^{66} +(37.9166 - 15.0257i) q^{67} +(-20.0545 - 5.70598i) q^{68} +(-22.7809 + 45.7501i) q^{69} +(-119.809 - 19.5437i) q^{70} +(64.2285 + 74.9678i) q^{71} +(4.09696 + 0.316090i) q^{72} +(-15.8918 - 22.8203i) q^{73} +(28.0419 + 143.869i) q^{74} +(-14.7028 - 24.5838i) q^{75} +(8.87450 + 4.85391i) q^{76} +(69.2781 + 71.4454i) q^{77} +(-124.754 - 89.7613i) q^{78} +(-12.0307 - 57.0317i) q^{79} +(-105.467 + 48.5225i) q^{80} +(65.5577 - 35.2037i) q^{81} +(47.7862 - 8.93279i) q^{82} +(-46.0119 - 92.4044i) q^{83} +(10.5727 + 34.1424i) q^{84} +(61.1761 - 63.0900i) q^{85} +(87.9760 - 15.7455i) q^{86} +(-16.6186 + 3.77387i) q^{87} +(66.5323 + 14.0348i) q^{88} +(-52.7485 + 48.0866i) q^{89} +(5.04342 - 7.87192i) q^{90} +(49.4134 - 196.467i) q^{91} +(21.7070 - 12.0907i) q^{92} +(33.8724 + 59.7261i) q^{93} +(-103.287 + 89.8789i) q^{94} +(-35.7195 + 23.2748i) q^{95} +(48.3219 + 38.8845i) q^{96} +(23.5545 + 7.69343i) q^{97} +(-52.6765 + 42.3886i) q^{98} +(-7.16787 + 2.71356i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8576 q - 124 q^{2} - 112 q^{3} - 124 q^{4} - 120 q^{5} - 120 q^{6} - 144 q^{7} + 8 q^{8} - 292 q^{9} - 96 q^{10} - 160 q^{11} + 36 q^{12} - 164 q^{13} - 16 q^{14} - 80 q^{15} - 204 q^{16} - 148 q^{17} - 148 q^{18}+ \cdots + 1180 q^{99}+O(q^{100}) \) 8576 * q - 124 * q^2 - 112 * q^3 - 124 * q^4 - 120 * q^5 - 120 * q^6 - 144 * q^7 + 8 * q^8 - 292 * q^9 - 96 * q^10 - 160 * q^11 + 36 * q^12 - 164 * q^13 - 16 * q^14 - 80 * q^15 - 204 * q^16 - 148 * q^17 - 148 * q^18 - 96 * q^19 + 68 * q^20 - 144 * q^21 - 256 * q^22 - 128 * q^23 - 1156 * q^24 - 2496 * q^25 - 280 * q^26 - 100 * q^27 - 92 * q^28 - 80 * q^29 + 672 * q^30 - 168 * q^31 + 2112 * q^32 - 96 * q^33 + 92 * q^34 + 64 * q^35 - 2344 * q^36 - 152 * q^37 - 2972 * q^39 + 112 * q^40 - 196 * q^41 + 488 * q^42 - 452 * q^43 + 92 * q^44 - 244 * q^45 - 124 * q^46 + 16 * q^47 - 188 * q^48 + 16 * q^49 + 96 * q^50 + 8 * q^51 - 828 * q^52 - 256 * q^53 + 240 * q^54 - 1016 * q^55 + 76 * q^56 - 92 * q^57 - 800 * q^58 + 48 * q^59 - 64 * q^60 + 428 * q^61 - 52 * q^62 + 1604 * q^63 - 136 * q^64 + 136 * q^65 + 224 * q^66 + 600 * q^67 - 136 * q^68 + 2808 * q^69 - 20 * q^70 - 188 * q^71 + 560 * q^72 + 144 * q^73 - 996 * q^74 + 1152 * q^75 + 992 * q^76 - 3084 * q^77 - 4900 * q^78 - 560 * q^79 - 292 * q^80 - 3128 * q^81 + 1488 * q^82 + 120 * q^83 + 6560 * q^84 + 288 * q^85 + 3248 * q^86 - 632 * q^87 + 144 * q^88 + 608 * q^89 + 268 * q^90 + 404 * q^91 - 5128 * q^92 - 104 * q^93 - 624 * q^94 + 84 * q^95 + 140 * q^96 - 840 * q^97 - 72 * q^98 + 1180 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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