LMFDB - Embedded newform 230.2.g.b.141.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(31,230)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 6]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("230.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.g (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 5 x^{19} + 12 x^{18} + 16 x^{17} - 49 x^{16} + 59 x^{15} - 197 x^{14} + 42 x^{13} + 1625 x^{12} + \cdots + 529 $ x^20 - 5x^19 + 12x^18 + 16x^17 - 49x^16 + 59x^15 - 197x^14 + 42x^13 + 1625x^12 - 5910x^11 + 14651x^10 - 22501x^9 + 26003x^8 - 19607x^7 + 13040x^6 + 348x^5 + 7193x^4 + 10771x^3 + 8781x^2 + 3105*x + 529
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			141.2
Root			$-0.905632 - 1.98306i$ of defining polynomial
Character	$\chi$	$=$	230.141
Dual form			230.2.g.b.31.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 + 0.989821i) q^{2} +(1.40549 - 3.07760i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(3.24630 + 0.953198i) q^{6} +(2.97617 - 1.91267i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-5.53162 - 6.38383i) q^{9} +O(q^{10})$	\(q+(0.142315 + 0.989821i) q^{2} +(1.40549 - 3.07760i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(3.24630 + 0.953198i) q^{6} +(2.97617 - 1.91267i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-5.53162 - 6.38383i) q^{9} +(-0.841254 - 0.540641i) q^{10} +(-0.474502 + 3.30023i) q^{11} +(-0.481500 + 3.34891i) q^{12} +(-2.04439 - 1.31385i) q^{13} +(2.31676 + 2.67368i) q^{14} +(1.40549 + 3.07760i) q^{15} +(0.841254 - 0.540641i) q^{16} +(4.17723 + 1.22655i) q^{17} +(5.53162 - 6.38383i) q^{18} +(-1.70877 + 0.501740i) q^{19} +(0.415415 - 0.909632i) q^{20} +(-1.70344 - 11.8477i) q^{21} -3.33417 q^{22} +(4.72437 + 0.824821i) q^{23} -3.38334 q^{24} +(-0.142315 - 0.989821i) q^{25} +(1.00953 - 2.21057i) q^{26} +(-17.6826 + 5.19209i) q^{27} +(-2.31676 + 2.67368i) q^{28} +(4.26170 + 1.25135i) q^{29} +(-2.84625 + 1.82917i) q^{30} +(0.962566 + 2.10773i) q^{31} +(0.654861 + 0.755750i) q^{32} +(9.48988 + 6.09877i) q^{33} +(-0.619580 + 4.30927i) q^{34} +(-0.503479 + 3.50177i) q^{35} +(7.10608 + 4.56680i) q^{36} +(2.47799 + 2.85975i) q^{37} +(-0.739816 - 1.61997i) q^{38} +(-6.91689 + 4.44521i) q^{39} +(0.959493 + 0.281733i) q^{40} +(-5.45570 + 6.29621i) q^{41} +(11.4847 - 3.37221i) q^{42} +(-1.86625 + 4.08651i) q^{43} +(-0.474502 - 3.30023i) q^{44} +8.44702 q^{45} +(-0.144077 + 4.79367i) q^{46} -6.54226 q^{47} +(-0.481500 - 3.34891i) q^{48} +(2.29140 - 5.01746i) q^{49} +(0.959493 - 0.281733i) q^{50} +(9.64588 - 11.1319i) q^{51} +(2.33174 + 0.684660i) q^{52} +(-6.75825 + 4.34326i) q^{53} +(-7.65574 - 16.7637i) q^{54} +(-2.18342 - 2.51980i) q^{55} +(-2.97617 - 1.91267i) q^{56} +(-0.857508 + 5.96410i) q^{57} +(-0.632108 + 4.39641i) q^{58} +(11.7107 + 7.52602i) q^{59} +(-2.21562 - 2.55696i) q^{60} +(-4.41893 - 9.67611i) q^{61} +(-1.94929 + 1.25273i) q^{62} +(-28.6732 - 8.41922i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(2.33174 - 0.684660i) q^{65} +(-4.68615 + 10.2612i) q^{66} +(0.522775 + 3.63598i) q^{67} -4.35358 q^{68} +(9.17853 - 13.3804i) q^{69} -3.53778 q^{70} +(-1.28444 - 8.93348i) q^{71} +(-3.50902 + 7.68368i) q^{72} +(-2.35015 + 0.690068i) q^{73} +(-2.47799 + 2.85975i) q^{74} +(-3.24630 - 0.953198i) q^{75} +(1.49820 - 0.962832i) q^{76} +(4.90006 + 10.7296i) q^{77} +(-5.38434 - 6.21386i) q^{78} +(-1.93484 - 1.24344i) q^{79} +(-0.142315 + 0.989821i) q^{80} +(-5.26722 + 36.6343i) q^{81} +(-7.00855 - 4.50412i) q^{82} +(0.921369 + 1.06332i) q^{83} +(4.97233 + 10.8879i) q^{84} +(-3.66247 + 2.35373i) q^{85} +(-4.31051 - 1.26568i) q^{86} +(9.84093 - 11.3570i) q^{87} +(3.19911 - 0.939344i) q^{88} +(6.81581 - 14.9245i) q^{89} +(1.20214 + 8.36104i) q^{90} -8.59744 q^{91} +(-4.76538 + 0.539599i) q^{92} +7.83961 q^{93} +(-0.931060 - 6.47567i) q^{94} +(0.739816 - 1.61997i) q^{95} +(3.24630 - 0.953198i) q^{96} +(7.51574 - 8.67363i) q^{97} +(5.29248 + 1.55401i) q^{98} +(23.6929 - 15.2265i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9	\( 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9} + 2 q^{10} + 7 q^{11} + 8 q^{12} + 8 q^{13} + 3 q^{14} - 3 q^{15} - 2 q^{16} + 8 q^{17} + 27 q^{18} - q^{19} - 2 q^{20} - 31 q^{21} - 18 q^{22} - 9 q^{23} - 8 q^{24} - 2 q^{25} - 8 q^{26} - 18 q^{27} - 3 q^{28} + 20 q^{29} + 3 q^{30} - 17 q^{31} + 2 q^{32} + 17 q^{33} + 3 q^{34} - 3 q^{35} + 17 q^{36} + 6 q^{37} - 21 q^{38} - 75 q^{39} + 2 q^{40} - 2 q^{41} + 42 q^{42} - 18 q^{43} + 7 q^{44} + 28 q^{45} - 2 q^{46} + 42 q^{47} + 8 q^{48} - 19 q^{49} + 2 q^{50} + 26 q^{51} + 19 q^{52} + 19 q^{53} - 26 q^{54} - 15 q^{55} - 19 q^{56} + 7 q^{57} - 9 q^{58} + 25 q^{59} - 3 q^{60} - 49 q^{61} - 38 q^{62} - 87 q^{63} - 2 q^{64} + 19 q^{65} - 6 q^{66} + 19 q^{67} - 36 q^{68} + 36 q^{69} + 14 q^{70} + 7 q^{71} - 17 q^{72} - 10 q^{73} - 6 q^{74} - 3 q^{75} - q^{76} - 29 q^{77} - 2 q^{78} - 33 q^{79} - 2 q^{80} + 72 q^{81} + 2 q^{82} - 41 q^{83} + 13 q^{84} - 14 q^{85} - 48 q^{86} - 16 q^{87} - 7 q^{88} + 55 q^{89} + 5 q^{90} + 13 q^{92} + 10 q^{93} + 13 q^{94} + 21 q^{95} + 3 q^{96} - 9 q^{97} + 41 q^{98} + 59 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9 + 2 * q^10 + 7 * q^11 + 8 * q^12 + 8 * q^13 + 3 * q^14 - 3 * q^15 - 2 * q^16 + 8 * q^17 + 27 * q^18 - q^19 - 2 * q^20 - 31 * q^21 - 18 * q^22 - 9 * q^23 - 8 * q^24 - 2 * q^25 - 8 * q^26 - 18 * q^27 - 3 * q^28 + 20 * q^29 + 3 * q^30 - 17 * q^31 + 2 * q^32 + 17 * q^33 + 3 * q^34 - 3 * q^35 + 17 * q^36 + 6 * q^37 - 21 * q^38 - 75 * q^39 + 2 * q^40 - 2 * q^41 + 42 * q^42 - 18 * q^43 + 7 * q^44 + 28 * q^45 - 2 * q^46 + 42 * q^47 + 8 * q^48 - 19 * q^49 + 2 * q^50 + 26 * q^51 + 19 * q^52 + 19 * q^53 - 26 * q^54 - 15 * q^55 - 19 * q^56 + 7 * q^57 - 9 * q^58 + 25 * q^59 - 3 * q^60 - 49 * q^61 - 38 * q^62 - 87 * q^63 - 2 * q^64 + 19 * q^65 - 6 * q^66 + 19 * q^67 - 36 * q^68 + 36 * q^69 + 14 * q^70 + 7 * q^71 - 17 * q^72 - 10 * q^73 - 6 * q^74 - 3 * q^75 - q^76 - 29 * q^77 - 2 * q^78 - 33 * q^79 - 2 * q^80 + 72 * q^81 + 2 * q^82 - 41 * q^83 + 13 * q^84 - 14 * q^85 - 48 * q^86 - 16 * q^87 - 7 * q^88 + 55 * q^89 + 5 * q^90 + 13 * q^92 + 10 * q^93 + 13 * q^94 + 21 * q^95 + 3 * q^96 - 9 * q^97 + 41 * q^98 + 59 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{8}{11}\right)$

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 $

$2$	0.142315	+	0.989821i	0.100632	+	0.699909i
$2$	0.142315	+	0.989821i	0.100632	+	0.699909i
$3$	1.40549	−	3.07760i	0.811461	−	1.77685i	0.210463	−	0.977602i	$-0.432503\pi$
$3$	1.40549	−	3.07760i	0.811461	−	1.77685i	0.600998	−	0.799250i	$-0.294770\pi$
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	−0.654861	+	0.755750i	−0.292863	+	0.337981i
$5$	−0.654861	+	0.755750i	−0.292863	+	0.337981i
$6$	3.24630	+	0.953198i	1.32529	+	0.389142i
$7$	2.97617	−	1.91267i	1.12489	−	0.722922i	0.160401	−	0.987052i	$-0.448721\pi$
$7$	2.97617	−	1.91267i	1.12489	−	0.722922i	0.964487	+	0.264130i	$0.0850849\pi$
$8$	−0.415415	−	0.909632i	−0.146871	−	0.321603i
$9$	−5.53162	−	6.38383i	−1.84387	−	2.12794i
$10$	−0.841254	−	0.540641i	−0.266028	−	0.170966i
$11$	−0.474502	+	3.30023i	−0.143068	+	0.995057i	0.784160	+	0.620559i	$0.213094\pi$
$11$	−0.474502	+	3.30023i	−0.143068	+	0.995057i	−0.927228	+	0.374498i	$0.877815\pi$
$12$	−0.481500	+	3.34891i	−0.138997	+	0.966746i
$13$	−2.04439	−	1.31385i	−0.567013	−	0.364397i	0.225509	−	0.974241i	$-0.427596\pi$
$13$	−2.04439	−	1.31385i	−0.567013	−	0.364397i	−0.792521	+	0.609844i	$0.791232\pi$
$14$	2.31676	+	2.67368i	0.619179	+	0.714571i
$15$	1.40549	+	3.07760i	0.362896	+	0.794632i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	4.17723	+	1.22655i	1.01313	+	0.297481i	0.745833	−	0.666133i	$-0.232052\pi$
$17$	4.17723	+	1.22655i	1.01313	+	0.297481i	0.267295	+	0.963615i	$0.413870\pi$
$18$	5.53162	−	6.38383i	1.30382	−	1.50468i
$19$	−1.70877	+	0.501740i	−0.392019	+	0.115107i	−0.471801	−	0.881705i	$-0.656396\pi$
$19$	−1.70877	+	0.501740i	−0.392019	+	0.115107i	0.0797820	+	0.996812i	$0.474578\pi$
$20$	0.415415	−	0.909632i	0.0928896	−	0.203400i
$21$	−1.70344	−	11.8477i	−0.371722	−	2.58538i
$22$	−3.33417			−0.710847
$23$	4.72437	+	0.824821i	0.985099	+	0.171987i
$23$	4.72437	+	0.824821i	0.985099	+	0.171987i
$24$	−3.38334			−0.690622
$25$	−0.142315	−	0.989821i	−0.0284630	−	0.197964i
$26$	1.00953	−	2.21057i	0.197985	−	0.433528i
$27$	−17.6826	+	5.19209i	−3.40302	+	0.999218i
$28$	−2.31676	+	2.67368i	−0.437826	+	0.505278i
$29$	4.26170	+	1.25135i	0.791378	+	0.232370i	0.652349	−	0.757919i	$-0.273784\pi$
$29$	4.26170	+	1.25135i	0.791378	+	0.232370i	0.139029	+	0.990288i	$0.455602\pi$
$30$	−2.84625	+	1.82917i	−0.519652	+	0.333960i
$31$	0.962566	+	2.10773i	0.172882	+	0.378559i	0.976162	−	0.217043i	$-0.0696411\pi$
$31$	0.962566	+	2.10773i	0.172882	+	0.378559i	−0.803280	+	0.595601i	$0.796914\pi$
$32$	0.654861	+	0.755750i	0.115764	+	0.133599i
$33$	9.48988	+	6.09877i	1.65198	+	1.06166i
$34$	−0.619580	+	4.30927i	−0.106257	+	0.739034i
$35$	−0.503479	+	3.50177i	−0.0851035	+	0.591908i
$36$	7.10608	+	4.56680i	1.18435	+	0.761134i
$37$	2.47799	+	2.85975i	0.407379	+	0.470140i	0.921951	−	0.387307i	$-0.126595\pi$
$37$	2.47799	+	2.85975i	0.407379	+	0.470140i	−0.514572	+	0.857447i	$0.672049\pi$
$38$	−0.739816	−	1.61997i	−0.120014	−	0.262794i
$39$	−6.91689	+	4.44521i	−1.10759	+	0.711804i
$40$	0.959493	+	0.281733i	0.151709	+	0.0445458i
$41$	−5.45570	+	6.29621i	−0.852036	+	0.983303i	−0.999984	−	0.00569272i	$-0.998188\pi$
$41$	−5.45570	+	6.29621i	−0.852036	+	0.983303i	0.147947	+	0.988995i	$0.452733\pi$
$42$	11.4847	−	3.37221i	1.77213	−	0.520343i
$43$	−1.86625	+	4.08651i	−0.284600	+	0.623187i	−0.996899	−	0.0786889i	$-0.974927\pi$
$43$	−1.86625	+	4.08651i	−0.284600	+	0.623187i	0.712299	+	0.701876i	$0.247654\pi$
$44$	−0.474502	−	3.30023i	−0.0715338	−	0.497529i
$45$	8.44702			1.25921
$46$	−0.144077	+	4.79367i	−0.0212431	+	0.706788i
$47$	−6.54226			−0.954286			−0.477143	−	0.878826i	$-0.658328\pi$
$47$	−6.54226			−0.954286			−0.477143	+	0.878826i	$0.658328\pi$
$48$	−0.481500	−	3.34891i	−0.0694986	−	0.483373i
$49$	2.29140	−	5.01746i	0.327342	−	0.716779i
$50$	0.959493	−	0.281733i	0.135693	−	0.0398430i
$51$	9.64588	−	11.1319i	1.35069	−	1.55878i
$52$	2.33174	+	0.684660i	0.323354	+	0.0949452i
$53$	−6.75825	+	4.34326i	−0.928317	+	0.596593i	−0.915059	−	0.403319i	$-0.867856\pi$
$53$	−6.75825	+	4.34326i	−0.928317	+	0.596593i	−0.0132574	+	0.999912i	$0.504220\pi$
$54$	−7.65574	−	16.7637i	−1.04181	−	2.28126i
$55$	−2.18342	−	2.51980i	−0.294412	−	0.339769i
$56$	−2.97617	−	1.91267i	−0.397708	−	0.255591i
$57$	−0.857508	+	5.96410i	−0.113580	+	0.789964i
$58$	−0.632108	+	4.39641i	−0.0829999	+	0.577277i
$59$	11.7107	+	7.52602i	1.52461	+	0.979805i	0.990969	+	0.134092i	$0.0428116\pi$
$59$	11.7107	+	7.52602i	1.52461	+	0.979805i	0.533637	+	0.845713i	$0.320825\pi$
$60$	−2.21562	−	2.55696i	−0.286035	−	0.330102i
$61$	−4.41893	−	9.67611i	−0.565786	−	1.23890i	−0.949011	−	0.315244i	$-0.897914\pi$
$61$	−4.41893	−	9.67611i	−0.565786	−	1.23890i	0.383224	−	0.923655i	$-0.374814\pi$
$62$	−1.94929	+	1.25273i	−0.247559	+	0.159097i
$63$	−28.6732	−	8.41922i	−3.61249	−	1.06072i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	2.33174	−	0.684660i	0.289216	−	0.0849216i
$66$	−4.68615	+	10.2612i	−0.576825	+	1.26307i
$67$	0.522775	+	3.63598i	0.0638671	+	0.444205i	0.996515	+	0.0834168i	$0.0265833\pi$
$67$	0.522775	+	3.63598i	0.0638671	+	0.444205i	−0.932648	+	0.360788i	$0.882508\pi$
$68$	−4.35358			−0.527950
$69$	9.17853	−	13.3804i	1.10497	−	1.61081i
$70$	−3.53778			−0.422846
$71$	−1.28444	−	8.93348i	−0.152435	−	1.06021i	−0.912122	−	0.409920i	$-0.865557\pi$
$71$	−1.28444	−	8.93348i	−0.152435	−	1.06021i	0.759687	−	0.650289i	$-0.225352\pi$
$72$	−3.50902	+	7.68368i	−0.413542	+	0.905530i
$73$	−2.35015	+	0.690068i	−0.275065	+	0.0807663i	−0.416356	−	0.909202i	$-0.636693\pi$
$73$	−2.35015	+	0.690068i	−0.275065	+	0.0807663i	0.141291	+	0.989968i	$0.454875\pi$
$74$	−2.47799	+	2.85975i	−0.288060	+	0.332439i
$75$	−3.24630	−	0.953198i	−0.374850	−	0.110066i
$76$	1.49820	−	0.962832i	0.171855	−	0.110444i
$77$	4.90006	+	10.7296i	0.558413	+	1.22275i
$78$	−5.38434	−	6.21386i	−0.609657	−	0.703582i
$79$	−1.93484	−	1.24344i	−0.217686	−	0.139898i	0.427254	−	0.904132i	$-0.359481\pi$
$79$	−1.93484	−	1.24344i	−0.217686	−	0.139898i	−0.644940	+	0.764234i	$0.723117\pi$
$80$	−0.142315	+	0.989821i	−0.0159113	+	0.110665i
$81$	−5.26722	+	36.6343i	−0.585247	+	4.07048i
$82$	−7.00855	−	4.50412i	−0.773965	−	0.497397i
$83$	0.921369	+	1.06332i	0.101133	+	0.116714i	0.804060	−	0.594548i	$-0.202669\pi$
$83$	0.921369	+	1.06332i	0.101133	+	0.116714i	−0.702926	+	0.711263i	$0.748124\pi$
$84$	4.97233	+	10.8879i	0.542525	+	1.18796i
$85$	−3.66247	+	2.35373i	−0.397250	+	0.255297i
$86$	−4.31051	−	1.26568i	−0.464814	−	0.136482i
$87$	9.84093	−	11.3570i	1.05506	−	1.21760i
$88$	3.19911	−	0.939344i	0.341026	−	0.100134i
$89$	6.81581	−	14.9245i	0.722474	−	1.58200i	−0.0879306	−	0.996127i	$-0.528025\pi$
$89$	6.81581	−	14.9245i	0.722474	−	1.58200i	0.810405	−	0.585871i	$-0.199247\pi$
$90$	1.20214	+	8.36104i	0.126716	+	0.881331i
$91$	−8.59744			−0.901256
$92$	−4.76538	+	0.539599i	−0.496825	+	0.0562571i
$93$	7.83961			0.812930
$94$	−0.931060	−	6.47567i	−0.0960315	−	0.667914i
$95$	0.739816	−	1.61997i	0.0759035	−	0.166206i
$96$	3.24630	−	0.953198i	0.331324	−	0.0972854i
$97$	7.51574	−	8.67363i	0.763108	−	0.880673i	−0.232662	−	0.972558i	$-0.574744\pi$
$97$	7.51574	−	8.67363i	0.763108	−	0.880673i	0.995770	+	0.0918844i	$0.0292890\pi$
$98$	5.29248	+	1.55401i	0.534622	+	0.156979i
$99$	23.6929	−	15.2265i	2.38122	−	1.53032i
$100$	0.415415	+	0.909632i	0.0415415	+	0.0909632i
$101$	−4.98657	−	5.75481i	−0.496182	−	0.572625i	0.451325	−	0.892360i	$-0.350952\pi$
$101$	−4.98657	−	5.75481i	−0.496182	−	0.572625i	−0.947507	+	0.319735i	$0.896406\pi$
$102$	12.3914	+	7.96346i	1.22693	+	0.788500i
$103$	1.45754	−	10.1374i	0.143616	−	0.998869i	−0.782775	−	0.622305i	$-0.786196\pi$
$103$	1.45754	−	10.1374i	0.143616	−	0.998869i	0.926391	−	0.376564i	$-0.122894\pi$
$104$	−0.345850	+	2.40544i	−0.0339134	+	0.235873i
$105$	10.0694	+	6.47122i	0.982675	+	0.631527i
$106$	−5.26085	−	6.07135i	−0.510979	−	0.589701i
$107$	−0.662403	−	1.45046i	−0.0640369	−	0.140221i	0.874908	−	0.484290i	$-0.160922\pi$
$107$	−0.662403	−	1.45046i	−0.0640369	−	0.140221i	−0.938944	+	0.344069i	$0.888195\pi$
$108$	15.5036	−	9.96354i	1.49183	−	0.958742i
$109$	−5.70566	−	1.67533i	−0.546503	−	0.160468i	−0.00318548	−	0.999995i	$-0.501014\pi$
$109$	−5.70566	−	1.67533i	−0.546503	−	0.160468i	−0.543318	+	0.839527i	$0.682832\pi$
$110$	2.18342	−	2.51980i	0.208181	−	0.240253i
$111$	12.2840	−	3.60689i	1.16594	−	0.342351i
$112$	1.46965	−	3.21808i	0.138869	−	0.304080i
$113$	1.03394	+	7.19123i	0.0972651	+	0.676494i	0.978867	+	0.204499i	$0.0655566\pi$
$113$	1.03394	+	7.19123i	0.0972651	+	0.676494i	−0.881602	+	0.471994i	$0.843534\pi$
$114$	−6.02543			−0.564333
$115$	−3.71716	+	3.03030i	−0.346627	+	0.282577i
$116$	−4.44162			−0.412394
$117$	2.92140	+	20.3188i	0.270084	+	1.87847i
$118$	−5.78281	+	12.6626i	−0.532351	+	1.16569i
$119$	14.7782	−	4.33926i	1.35471	−	0.397779i
$120$	2.21562	−	2.55696i	0.202257	−	0.233418i
$121$	−0.111955	−	0.0328728i	−0.0101777	−	0.00298844i
$122$	8.94874	−	5.75101i	0.810181	−	0.520672i
$123$	11.7093	+	25.6397i	1.05579	+	2.31185i
$124$	−1.51739	−	1.75116i	−0.136266	−	0.157259i
$125$	0.841254	+	0.540641i	0.0752440	+	0.0483564i
$126$	4.25290	−	29.5796i	0.378878	−	2.63516i
$127$	−0.907193	+	6.30967i	−0.0805004	+	0.559892i	0.909158	+	0.416450i	$0.136726\pi$
$127$	−0.907193	+	6.30967i	−0.0805004	+	0.559892i	−0.989659	+	0.143442i	$0.954183\pi$
$128$	−0.841254	−	0.540641i	−0.0743570	−	0.0477863i
$129$	9.95364	+	11.4871i	0.876369	+	1.01138i
$130$	1.00953	+	2.21057i	0.0885418	+	0.193879i
$131$	−8.42656	+	5.41542i	−0.736232	+	0.473147i	−0.854249	−	0.519864i	$-0.825983\pi$
$131$	−8.42656	+	5.41542i	−0.736232	+	0.473147i	0.118017	+	0.993012i	$0.462346\pi$
$132$	−10.8237	−	3.17812i	−0.942082	−	0.276620i
$133$	−4.12593	+	4.76158i	−0.357764	+	0.412881i
$134$	−3.52457	+	1.03491i	−0.304476	+	0.0894023i
$135$	7.65574	−	16.7637i	0.658901	−	1.44279i
$136$	−0.619580	−	4.30927i	−0.0531285	−	0.369517i
$137$	7.61920			0.650952			0.325476	−	0.945550i	$-0.394475\pi$
$137$	7.61920			0.650952			0.325476	+	0.945550i	$0.394475\pi$
$138$	14.5505	+	7.18087i	1.23862	+	0.611276i
$139$	−15.1421			−1.28434			−0.642170	−	0.766563i	$-0.721966\pi$
$139$	−15.1421			−1.28434			−0.642170	+	0.766563i	$0.721966\pi$
$140$	−0.503479	−	3.50177i	−0.0425518	−	0.295954i
$141$	−9.19509	+	20.1344i	−0.774366	+	1.69563i
$142$	8.65976	−	2.54273i	0.726711	−	0.213382i
$143$	5.30608	−	6.12355i	0.443717	−	0.512077i
$144$	−8.10485	−	2.37980i	−0.675405	−	0.198317i
$145$	−3.73653	+	2.40132i	−0.310302	+	0.199419i
$146$	−1.01751	−	2.22803i	−0.0842094	−	0.184393i
$147$	−12.2212	−	14.1040i	−1.00799	−	1.16328i
$148$	−3.18330	−	2.04578i	−0.261665	−	0.168162i
$149$	−0.638482	+	4.44074i	−0.0523065	+	0.363800i	0.946811	+	0.321791i	$0.104285\pi$
$149$	−0.638482	+	4.44074i	−0.0523065	+	0.363800i	−0.999117	+	0.0420088i	$0.986624\pi$
$150$	0.481500	−	3.34891i	0.0393143	−	0.273437i
$151$	−7.89187	−	5.07180i	−0.642231	−	0.412737i	0.178589	−	0.983924i	$-0.442847\pi$
$151$	−7.89187	−	5.07180i	−0.642231	−	0.412737i	−0.820820	+	0.571187i	$0.806483\pi$
$152$	1.16625	+	1.34592i	0.0945951	+	0.109169i
$153$	−15.2768	−	33.4515i	−1.23506	−	2.70440i
$154$	−9.92306	+	6.37717i	−0.799623	+	0.513887i
$155$	−2.22326	−	0.652808i	−0.178577	−	0.0524348i
$156$	5.38434	−	6.21386i	0.431093	−	0.497507i
$157$	−2.71487	+	0.797157i	−0.216670	+	0.0636200i	−0.388266	−	0.921547i	$-0.626926\pi$
$157$	−2.71487	+	0.797157i	−0.216670	+	0.0636200i	0.171596	+	0.985167i	$0.445108\pi$
$158$	0.955431	−	2.09210i	0.0760100	−	0.166439i
$159$	3.86815	+	26.9036i	0.306764	+	2.13359i
$160$	−1.00000			−0.0790569
$161$	15.6382	−	6.58135i	1.23246	−	0.518683i
$162$	−37.0111			−2.90786
$163$	−1.01255	−	7.04242i	−0.0793088	−	0.551605i	−0.990275	−	0.139124i	$-0.955571\pi$
$163$	−1.01255	−	7.04242i	−0.0793088	−	0.551605i	0.910966	−	0.412481i	$-0.135338\pi$
$164$	3.46085	−	7.57821i	0.270247	−	0.591759i
$165$	−10.8237	+	3.17812i	−0.842624	+	0.247417i
$166$	−0.921369	+	1.06332i	−0.0715121	+	0.0825294i
$167$	−3.82944	−	1.12442i	−0.296331	−	0.0870106i	0.130188	−	0.991489i	$-0.458442\pi$
$167$	−3.82944	−	1.12442i	−0.296331	−	0.0870106i	−0.426519	+	0.904479i	$0.640260\pi$
$168$	−10.0694	+	6.47122i	−0.776873	+	0.499266i
$169$	−2.94706	−	6.45315i	−0.226697	−	0.496396i
$170$	−2.85099	−	3.29022i	−0.218661	−	0.252348i
$171$	12.6553	+	8.13306i	0.967774	+	0.621951i
$172$	0.639348	−	4.44676i	0.0487498	−	0.339062i
$173$	3.61524	−	25.1445i	0.274861	−	1.91170i	−0.119658	−	0.992815i	$-0.538180\pi$
$173$	3.61524	−	25.1445i	0.274861	−	1.91170i	0.394519	−	0.918888i	$-0.370911\pi$
$174$	12.6420	+	8.12449i	0.958384	+	0.615916i
$175$	−2.31676	−	2.67368i	−0.175130	−	0.202111i
$176$	1.38506	+	3.03287i	0.104403	+	0.228611i
$177$	39.6214	−	25.4631i	2.97813	−	1.91393i
$178$	15.7426	+	4.62245i	1.17996	+	0.346467i
$179$	−12.8875	+	14.8730i	−0.963257	+	1.11166i	0.0304372	+	0.999537i	$0.490310\pi$
$179$	−12.8875	+	14.8730i	−0.963257	+	1.11166i	−0.993695	+	0.112122i	$0.964235\pi$
$180$	−8.10485	+	2.37980i	−0.604100	+	0.177380i
$181$	3.53497	−	7.74051i	0.262752	−	0.575348i	−0.731569	−	0.681768i	$-0.761212\pi$
$181$	3.53497	−	7.74051i	0.262752	−	0.575348i	0.994321	+	0.106420i	$0.0339388\pi$
$182$	−1.22354	−	8.50993i	−0.0906950	−	0.630798i
$183$	−35.9900			−2.66045
$184$	−1.21229	−	4.64008i	−0.0893713	−	0.342071i
$185$	−3.78399			−0.278205
$186$	1.11569	+	7.75982i	0.0818066	+	0.568977i
$187$	−6.02999	+	13.2038i	−0.440957	+	0.965560i
$188$	6.27725	−	1.84317i	0.457815	−	0.134427i
$189$	−42.6958	+	49.2736i	−3.10566	+	3.58413i
$190$	1.70877	+	0.501740i	0.123967	+	0.0364000i
$191$	−16.2244	+	10.4268i	−1.17396	+	0.754457i	−0.974266	−	0.225402i	$-0.927631\pi$
$191$	−16.2244	+	10.4268i	−1.17396	+	0.754457i	−0.199692	+	0.979859i	$0.563994\pi$
$192$	1.40549	+	3.07760i	0.101433	+	0.222107i
$193$	9.11317	+	10.5172i	0.655980	+	0.757041i	0.982115	−	0.188282i	$-0.0602918\pi$
$193$	9.11317	+	10.5172i	0.655980	+	0.757041i	−0.326135	+	0.945323i	$0.605746\pi$
$194$	9.65494	+	6.20485i	0.693184	+	0.445483i
$195$	1.17013	−	8.13843i	0.0837947	−	0.582805i
$196$	−0.784997	+	5.45977i	−0.0560712	+	0.389984i
$197$	5.73032	+	3.68265i	0.408269	+	0.262378i	0.728617	−	0.684922i	$-0.240164\pi$
$197$	5.73032	+	3.68265i	0.408269	+	0.262378i	−0.320348	+	0.947300i	$0.603800\pi$
$198$	18.4434	+	21.2848i	1.31071	+	1.51264i
$199$	−9.16447	−	20.0674i	−0.649652	−	1.42254i	−0.891858	−	0.452315i	$-0.850598\pi$
$199$	−9.16447	−	20.0674i	−0.649652	−	1.42254i	0.242206	−	0.970225i	$-0.422129\pi$
$200$	−0.841254	+	0.540641i	−0.0594856	+	0.0382291i
$201$	11.9248	+	3.50145i	0.841113	+	0.246973i
$202$	4.98657	−	5.75481i	0.350854	−	0.404907i
$203$	15.0770	−	4.42700i	1.05820	−	0.310714i
$204$	−6.11893	+	13.3986i	−0.428411	+	0.938088i
$205$	−1.18564	−	8.24628i	−0.0828084	−	0.575945i
$206$	10.2417			0.713570
$207$	−20.8679	−	34.7222i	−1.45042	−	2.41336i
$208$	−2.43018			−0.168502
$209$	−0.845044	−	5.87741i	−0.0584529	−	0.406549i
$210$	−4.97233	+	10.8879i	−0.343123	+	0.751335i
$211$	−2.89011	+	0.848613i	−0.198963	+	0.0584209i	−0.379696	−	0.925111i	$-0.623971\pi$
$211$	−2.89011	+	0.848613i	−0.198963	+	0.0584209i	0.180732	+	0.983532i	$0.442153\pi$
$212$	5.26085	−	6.07135i	0.361317	−	0.416982i
$213$	−29.2989	−	8.60294i	−2.00753	−	0.589464i
$214$	1.34143	−	0.862082i	0.0916980	−	0.0589307i
$215$	−1.86625	−	4.08651i	−0.127277	−	0.278698i
$216$	12.0685	+	13.9278i	0.821159	+	0.947668i
$217$	6.89615	+	4.43189i	0.468141	+	0.300856i
$218$	0.846281	−	5.88601i	0.0573174	−	0.398651i
$219$	−1.17937	+	8.20272i	−0.0796946	+	0.554288i
$220$	2.80488	+	1.80259i	0.189105	+	0.121530i
$221$	−6.92841	−	7.99581i	−0.466055	−	0.537856i
$222$	5.31837	+	11.6456i	0.356946	+	0.781602i
$223$	−1.69953	+	1.09222i	−0.113809	+	0.0731407i	−0.596307	−	0.802756i	$-0.703366\pi$
$223$	−1.69953	+	1.09222i	−0.113809	+	0.0731407i	0.482498	+	0.875897i	$0.339730\pi$
$224$	3.39448	+	0.996709i	0.226803	+	0.0665954i
$225$	−5.53162	+	6.38383i	−0.368775	+	0.425589i
$226$	−6.97089	+	2.04684i	−0.463696	+	0.136154i
$227$	−5.14764	+	11.2718i	−0.341661	+	0.748132i	−0.999989	−	0.00459808i	$-0.998536\pi$
$227$	−5.14764	+	11.2718i	−0.341661	+	0.748132i	0.658329	+	0.752730i	$0.271264\pi$
$228$	−0.857508	−	5.96410i	−0.0567898	−	0.394982i
$229$	26.1155			1.72576			0.862880	−	0.505409i	$-0.168658\pi$
$229$	26.1155			1.72576			0.862880	+	0.505409i	$0.168658\pi$
$230$	−3.52846	−	3.24807i	−0.232660	−	0.214171i
$231$	39.9085			2.62578
$232$	−0.632108	−	4.39641i	−0.0414999	−	0.288638i
$233$	5.86662	−	12.8461i	0.384335	−	0.841577i	−0.614286	−	0.789083i	$-0.710556\pi$
$233$	5.86662	−	12.8461i	0.384335	−	0.841577i	0.998621	−	0.0524933i	$-0.0167168\pi$
$234$	−19.6962	+	5.78333i	−1.28758	+	0.378068i
$235$	4.28427	−	4.94431i	0.279475	−	0.322531i
$236$	−13.3567	−	3.92188i	−0.869446	−	0.255292i
$237$	−6.54621	+	4.20700i	−0.425222	+	0.273274i
$238$	6.39824	+	14.0102i	0.414736	+	0.908146i
$239$	−3.26621	−	3.76940i	−0.211273	−	0.243822i	0.640215	−	0.768196i	$-0.278845\pi$
$239$	−3.26621	−	3.76940i	−0.211273	−	0.243822i	−0.851489	+	0.524373i	$0.824300\pi$
$240$	2.84625	+	1.82917i	0.183725	+	0.118073i
$241$	0.239778	−	1.66769i	0.0154454	−	0.107425i	−0.980640	−	0.195818i	$-0.937264\pi$
$241$	0.239778	−	1.66769i	0.0154454	−	0.107425i	0.996086	+	0.0883925i	$0.0281730\pi$
$242$	0.0166054	−	0.115493i	0.00106744	−	0.00742419i
$243$	58.8320	+	37.8090i	3.77408	+	2.42545i
$244$	6.96601	+	8.03920i	0.445953	+	0.514657i
$245$	2.29140	+	5.01746i	0.146392	+	0.320553i
$246$	−23.7123	+	15.2390i	−1.51184	+	0.971603i
$247$	4.15261	+	1.21932i	0.264224	+	0.0775832i
$248$	1.51739	−	1.75116i	0.0963544	−	0.111199i
$249$	4.56744	−	1.34112i	0.289450	−	0.0849901i
$250$	−0.415415	+	0.909632i	−0.0262732	+	0.0575302i
$251$	3.36584	+	23.4099i	0.212450	+	1.47762i	0.764940	+	0.644102i	$0.222769\pi$
$251$	3.36584	+	23.4099i	0.212450	+	1.47762i	−0.552490	+	0.833519i	$0.686322\pi$
$252$	29.8837			1.88250
$253$	−4.96382	+	15.2001i	−0.312073	+	0.955624i
$254$	−6.37455			−0.399975
$255$	2.09625	+	14.5797i	0.131272	+	0.913019i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	−15.6685	+	4.60068i	−0.977372	+	0.286982i	−0.731139	−	0.682228i	$-0.761011\pi$
$257$	−15.6685	+	4.60068i	−0.977372	+	0.286982i	−0.246233	+	0.969211i	$0.579193\pi$
$258$	−9.95364	+	11.4871i	−0.619687	+	0.715157i
$259$	12.8447	+	3.77154i	0.798130	+	0.234352i
$260$	−2.04439	+	1.31385i	−0.126788	+	0.0814816i
$261$	−15.5857	−	34.1280i	−0.964732	−	2.11247i
$262$	−6.55952	−	7.57009i	−0.405249	−	0.467682i
$263$	1.27661	+	0.820427i	0.0787191	+	0.0505897i	0.579408	−	0.815037i	$-0.303284\pi$
$263$	1.27661	+	0.820427i	0.0787191	+	0.0505897i	−0.500689	+	0.865627i	$0.666920\pi$
$264$	1.60540	−	11.1658i	0.0988057	−	0.687209i
$265$	1.14329	−	7.95177i	0.0702319	−	0.488474i
$266$	−5.30029	−	3.40629i	−0.324982	−	0.208853i
$267$	−36.3522	−	41.9526i	−2.22472	−	2.56746i
$268$	−1.52597	−	3.34141i	−0.0932136	−	0.204109i
$269$	−17.3777	+	11.1680i	−1.05954	+	0.680924i	−0.949743	−	0.313031i	$-0.898656\pi$
$269$	−17.3777	+	11.1680i	−1.05954	+	0.680924i	−0.109795	+	0.993954i	$0.535019\pi$
$270$	17.6826	+	5.19209i	1.07613	+	0.315980i
$271$	7.56829	−	8.73427i	0.459741	−	0.530569i	−0.477789	−	0.878475i	$-0.658562\pi$
$271$	7.56829	−	8.73427i	0.459741	−	0.530569i	0.937530	+	0.347906i	$0.113107\pi$
$272$	4.17723	−	1.22655i	0.253282	−	0.0743703i
$273$	−12.0836	+	26.4595i	−0.731334	+	1.60140i
$274$	1.08433	+	7.54165i	0.0655065	+	0.455608i
$275$	3.33417			0.201058
$276$	−5.03703	+	15.4243i	−0.303194	+	0.928435i
$277$	1.27581			0.0766562			0.0383281	−	0.999265i	$-0.487797\pi$
$277$	1.27581			0.0766562			0.0383281	+	0.999265i	$0.487797\pi$
$278$	−2.15495	−	14.9880i	−0.129245	−	0.898921i
$279$	8.13082	−	17.8040i	0.486779	−	1.06590i
$280$	3.39448	−	0.996709i	0.202859	−	0.0595648i
$281$	−3.58023	+	4.13181i	−0.213579	+	0.246483i	−0.852423	−	0.522853i	$-0.824868\pi$
$281$	−3.58023	+	4.13181i	−0.213579	+	0.246483i	0.638844	+	0.769336i	$0.279413\pi$
$282$	−21.2381	−	6.23607i	−1.26471	−	0.371352i
$283$	−0.279134	+	0.179389i	−0.0165928	+	0.0106635i	−0.548911	−	0.835881i	$-0.684957\pi$
$283$	−0.279134	+	0.179389i	−0.0165928	+	0.0106635i	0.532318	+	0.846544i	$0.321321\pi$
$284$	3.74926	+	8.20974i	0.222478	+	0.487159i
$285$	−3.94582	−	4.55371i	−0.233730	−	0.269739i
$286$	6.81635	+	4.38060i	0.403059	+	0.259031i
$287$	−4.19452	+	29.1736i	−0.247595	+	1.72206i
$288$	1.20214	−	8.36104i	0.0708365	−	0.492679i
$289$	1.64355	+	1.05625i	0.0966796	+	0.0621322i
$290$	−2.90864	−	3.35675i	−0.170801	−	0.197115i
$291$	−16.1306	−	35.3211i	−0.945594	−	2.07056i
$292$	2.06054	−	1.32423i	0.120584	−	0.0774947i
$293$	15.4125	+	4.52552i	0.900409	+	0.264384i	0.698999	−	0.715123i	$-0.253629\pi$
$293$	15.4125	+	4.52552i	0.900409	+	0.264384i	0.201410	+	0.979507i	$0.435448\pi$
$294$	12.2212	−	14.1040i	0.712753	−	0.822561i
$295$	−13.3567	+	3.92188i	−0.777656	+	0.228340i
$296$	1.57193	−	3.44204i	0.0913664	−	0.200065i
$297$	−8.74466	−	60.8204i	−0.507416	−	3.52916i
$298$	−4.48641			−0.259891
$299$	−8.57478	−	7.89338i	−0.495892	−	0.456486i
$300$	3.38334			0.195337
$301$	2.26187	+	15.7317i	0.130372	+	0.906759i
$302$	3.89704	−	8.53333i	0.224250	−	0.491038i
$303$	−24.7196	+	7.25832i	−1.42010	+	0.416980i
$304$	−1.16625	+	1.34592i	−0.0668889	+	0.0771939i
$305$	10.2065	+	2.99690i	0.584423	+	0.171602i
$306$	30.9369	−	19.8820i	1.76855	−	1.13658i
$307$	13.5141	+	29.5917i	0.771288	+	1.68888i	0.723797	+	0.690013i	$0.242395\pi$
$307$	13.5141	+	29.5917i	0.771288	+	1.68888i	0.0474912	+	0.998872i	$0.484877\pi$
$308$	−7.72446	−	8.91450i	−0.440142	−	0.507951i
$309$	−29.1503	−	18.7338i	−1.65830	−	1.06573i
$310$	0.329761	−	2.29353i	0.0187291	−	0.130264i
$311$	0.282669	−	1.96601i	0.0160287	−	0.111482i	−0.980236	−	0.197830i	$-0.936611\pi$
$311$	0.282669	−	1.96601i	0.0160287	−	0.111482i	0.996265	+	0.0863480i	$0.0275197\pi$
$312$	6.91689	+	4.44521i	0.391592	+	0.251661i
$313$	2.53433	+	2.92477i	0.143249	+	0.165318i	0.822840	−	0.568273i	$-0.192388\pi$
$313$	2.53433	+	2.92477i	0.143249	+	0.165318i	−0.679591	+	0.733591i	$0.737843\pi$
$314$	−1.17541	−	2.57379i	−0.0663321	−	0.145247i
$315$	25.1398	−	16.1564i	1.41647	−	0.910308i
$316$	2.20678	+	0.647969i	0.124141	+	0.0364511i
$317$	1.36805	−	1.57881i	0.0768373	−	0.0886750i	−0.716029	−	0.698070i	$-0.754042\pi$
$317$	1.36805	−	1.57881i	0.0768373	−	0.0886750i	0.792867	+	0.609395i	$0.208588\pi$
$318$	−26.0793	+	7.65756i	−1.46245	+	0.429415i
$319$	−6.15192	+	13.4708i	−0.344442	+	0.754222i
$320$	−0.142315	−	0.989821i	−0.00795564	−	0.0553327i
$321$	−5.39493			−0.301116
$322$	8.73991	+	14.5424i	0.487056	+	0.810414i
$323$	−7.75334			−0.431407
$324$	−5.26722	−	36.6343i	−0.292624	−	2.03524i
$325$	−1.00953	+	2.21057i	−0.0559987	+	0.122620i
$326$	6.82664	−	2.00448i	0.378093	−	0.111018i
$327$	−13.1753	+	15.2051i	−0.728594	+	0.840842i
$328$	7.99361	+	2.34714i	0.441373	+	0.129599i
$329$	−19.4709	+	12.5132i	−1.07346	+	0.689874i
$330$	−4.68615	−	10.2612i	−0.257964	−	0.564862i
$331$	−8.39176	−	9.68461i	−0.461253	−	0.532314i	0.476705	−	0.879063i	$-0.341831\pi$
$331$	−8.39176	−	9.68461i	−0.461253	−	0.532314i	−0.937958	+	0.346749i	$0.887286\pi$
$332$	−1.18362	−	0.760665i	−0.0649595	−	0.0417469i
$333$	4.54887	−	31.6381i	0.249277	−	1.73376i
$334$	0.567993	−	3.95048i	0.0310792	−	0.216161i
$335$	−3.09023	−	1.98597i	−0.168837	−	0.108505i
$336$	−7.83838	−	9.04598i	−0.427619	−	0.493498i
$337$	4.78442	+	10.4764i	0.260624	+	0.570687i	0.994030	−	0.109103i	$-0.0347980\pi$
$337$	4.78442	+	10.4764i	0.260624	+	0.570687i	−0.733406	+	0.679791i	$0.762071\pi$
$338$	5.96806	−	3.83544i	0.324620	−	0.208620i
$339$	23.5849	+	6.92515i	1.28096	+	0.376123i
$340$	2.85099	−	3.29022i	0.154617	−	0.178437i
$341$	−7.41272	+	2.17657i	−0.401422	+	0.117868i
$342$	−6.24924	+	13.6839i	−0.337920	+	0.739942i
$343$	0.747204	+	5.19692i	0.0403452	+	0.280607i
$344$	4.49249			0.242219
$345$	4.10160	+	15.6990i	0.220823	+	0.845205i
$346$	25.4031			1.36568
$347$	0.612508	+	4.26009i	0.0328812	+	0.228694i	0.999635	−	0.0270152i	$-0.00860026\pi$
$347$	0.612508	+	4.26009i	0.0328812	+	0.228694i	−0.966754	+	0.255709i	$0.917691\pi$
$348$	−6.24266	+	13.6695i	−0.334642	+	0.732763i
$349$	9.23442	−	2.71147i	0.494307	−	0.145142i	−0.0250720	−	0.999686i	$-0.507982\pi$
$349$	9.23442	−	2.71147i	0.494307	−	0.145142i	0.519379	+	0.854544i	$0.326163\pi$
$350$	2.31676	−	2.67368i	0.123836	−	0.142914i
$351$	42.9719	+	12.6177i	2.29367	+	0.673482i
$352$	−2.80488	+	1.80259i	−0.149501	+	0.0960782i
$353$	−12.0667	−	26.4224i	−0.642245	−	1.40632i	−0.898181	−	0.439627i	$-0.855111\pi$
$353$	−12.0667	−	26.4224i	−0.642245	−	1.40632i	0.255935	−	0.966694i	$-0.417617\pi$
$354$	30.8427	+	35.5943i	1.63927	+	1.89182i
$355$	7.59260	+	4.87947i	0.402974	+	0.258975i
$356$	−2.33499	+	16.2402i	−0.123754	+	0.860730i
$357$	7.41608	−	51.5800i	0.392501	−	2.72990i
$358$	−16.5557	−	10.6397i	−0.874994	−	0.562325i
$359$	16.2996	+	18.8108i	0.860262	+	0.992796i	0.999997	+	0.00260652i	$0.000829684\pi$
$359$	16.2996	+	18.8108i	0.860262	+	0.992796i	−0.139734	+	0.990189i	$0.544625\pi$
$360$	−3.50902	−	7.68368i	−0.184941	−	0.404965i
$361$	−13.3157	+	8.55746i	−0.700825	+	0.450393i
$362$	8.16480	+	2.39740i	0.429132	+	0.126005i
$363$	−0.258521	+	0.298349i	−0.0135688	+	0.0156592i
$364$	8.24918	−	2.42218i	0.432375	−	0.126957i
$365$	1.01751	−	2.22803i	0.0532587	−	0.116620i
$366$	−5.12191	−	35.6236i	−0.267726	−	1.86208i
$367$	32.1217			1.67674			0.838369	−	0.545104i	$-0.183510\pi$
$367$	32.1217			1.67674			0.838369	+	0.545104i	$0.183510\pi$
$368$	4.42032	−	1.86030i	0.230425	−	0.0969750i
$369$	70.3728			3.66346
$370$	−0.538518	−	3.74548i	−0.0279962	−	0.194718i
$371$	−11.8065	+	25.8526i	−0.612962	+	1.34220i
$372$	−7.52205	+	2.20867i	−0.390000	+	0.114514i
$373$	−13.5420	+	15.6283i	−0.701180	+	0.809205i	−0.988912	−	0.148506i	$-0.952554\pi$
$373$	−13.5420	+	15.6283i	−0.701180	+	0.809205i	0.287731	+	0.957711i	$0.407099\pi$
$374$	−13.9276	−	4.08951i	−0.720179	−	0.211464i
$375$	2.84625	−	1.82917i	0.146980	−	0.0944581i
$376$	2.71775	+	5.95105i	0.140157	+	0.306902i
$377$	−7.06851	−	8.15749i	−0.364047	−	0.420132i
$378$	−54.8483	−	35.2489i	−2.82109	−	1.81301i
$379$	3.70937	−	25.7992i	0.190537	−	1.32522i	−0.640052	−	0.768331i	$-0.721087\pi$
$379$	3.70937	−	25.7992i	0.190537	−	1.32522i	0.830590	−	0.556885i	$-0.188004\pi$
$380$	−0.253450	+	1.76278i	−0.0130017	+	0.0904288i
$381$	18.1436	+	11.6602i	0.929523	+	0.597368i
$382$	−12.6297	−	14.5754i	−0.646189	−	0.745742i
$383$	4.54089	+	9.94317i	0.232029	+	0.508072i	0.989454	−	0.144850i	$-0.0462700\pi$
$383$	4.54089	+	9.94317i	0.232029	+	0.508072i	−0.757425	+	0.652922i	$0.773543\pi$
$384$	−2.84625	+	1.82917i	−0.145247	+	0.0933446i
$385$	−11.3178	−	3.32320i	−0.576807	−	0.169366i
$386$	−9.11317	+	10.5172i	−0.463848	+	0.535309i
$387$	36.4110	−	10.6912i	1.85087	−	0.543465i
$388$	−4.76766	+	10.4397i	−0.242041	+	0.529996i
$389$	−4.61944	−	32.1289i	−0.234215	−	1.62900i	−0.679545	−	0.733634i	$-0.737823\pi$
$389$	−4.61944	−	32.1289i	−0.234215	−	1.62900i	0.445330	−	0.895367i	$-0.353086\pi$
$390$	8.22212			0.416343
$391$	18.7231	+	9.24013i	0.946869	+	0.467293i
$392$	−5.51592			−0.278596
$393$	4.82303	+	33.5449i	0.243290	+	1.69212i
$394$	−2.82966	+	6.19609i	−0.142556	+	0.312155i
$395$	2.20678	−	0.647969i	0.111035	−	0.0326029i
$396$	−18.4434	+	21.2848i	−0.926814	+	1.06960i
$397$	−13.2937	−	3.90337i	−0.667189	−	0.195904i	−0.0694383	−	0.997586i	$-0.522121\pi$
$397$	−13.2937	−	3.90337i	−0.667189	−	0.195904i	−0.597751	+	0.801682i	$0.703939\pi$
$398$	18.5589	−	11.9271i	0.930273	−	0.597850i
$399$	8.85526	+	19.3903i	0.443318	+	0.970730i
$400$	−0.654861	−	0.755750i	−0.0327430	−	0.0377875i
$401$	−13.9669	−	8.97599i	−0.697474	−	0.448239i	0.143262	−	0.989685i	$-0.454241\pi$
$401$	−13.9669	−	8.97599i	−0.697474	−	0.448239i	−0.840736	+	0.541445i	$0.817877\pi$
$402$	−1.76873	+	12.3018i	−0.0882160	+	0.613556i
$403$	0.801376	−	5.57369i	0.0399194	−	0.277645i
$404$	6.40590	+	4.11682i	0.318705	+	0.204819i
$405$	−24.2371	−	27.9711i	−1.20435	−	1.38989i
$406$	6.52762	+	14.2935i	0.323960	+	0.709374i
$407$	−10.6136	+	6.82098i	−0.526099	+	0.338103i
$408$	−14.1330	−	4.14983i	−0.699689	−	0.205447i
$409$	19.9343	−	23.0055i	0.985690	−	1.13755i	−0.00480359	−	0.999988i	$-0.501529\pi$
$409$	19.9343	−	23.0055i	0.985690	−	1.13755i	0.990494	−	0.137558i	$-0.0439255\pi$
$410$	7.99361	−	2.34714i	0.394776	−	0.115917i
$411$	10.7087	−	23.4488i	0.528222	−	1.15665i
$412$	1.45754	+	10.1374i	0.0718078	+	0.499434i
$413$	49.2480			2.42333
$414$	31.3989	−	25.5970i	1.54317	−	1.25802i
$415$	−1.40697			−0.0690654
$416$	−0.345850	−	2.40544i	−0.0169567	−	0.117936i
$417$	−21.2822	+	46.6014i	−1.04219	+	2.28208i
$418$	5.69733	−	1.67289i	0.278665	−	0.0818235i
$419$	−12.8289	+	14.8054i	−0.626735	+	0.723291i	−0.976971	−	0.213371i	$-0.931556\pi$
$419$	−12.8289	+	14.8054i	−0.626735	+	0.723291i	0.350236	+	0.936661i	$0.386101\pi$
$420$	−11.4847	−	3.37221i	−0.560396	−	0.164547i
$421$	3.33622	−	2.14406i	0.162597	−	0.104495i	−0.456812	−	0.889563i	$-0.651009\pi$
$421$	3.33622	−	2.14406i	0.162597	−	0.104495i	0.619409	+	0.785069i	$0.287372\pi$
$422$	−1.25128	−	2.73992i	−0.0609114	−	0.133377i
$423$	36.1893	+	41.7647i	1.75958	+	2.03067i
$424$	6.75825	+	4.34326i	0.328210	+	0.210927i
$425$	0.619580	−	4.30927i	0.0300540	−	0.209030i
$426$	4.34571	−	30.2250i	0.210550	−	1.46441i
$427$	−31.6587	−	20.3458i	−1.53207	−	0.984604i
$428$	1.04421	+	1.20509i	0.0504739	+	0.0582500i
$429$	−11.3882	−	24.9366i	−0.549826	−	1.20395i
$430$	3.77932	−	2.42882i	0.182255	−	0.117128i
$431$	4.81999	+	1.41528i	0.232171	+	0.0681715i	0.395748	−	0.918359i	$-0.370485\pi$
$431$	4.81999	+	1.41528i	0.232171	+	0.0681715i	−0.163578	+	0.986530i	$0.552303\pi$
$432$	−12.0685	+	13.9278i	−0.580647	+	0.670102i
$433$	−3.65110	+	1.07206i	−0.175461	+	0.0515199i	−0.368283	−	0.929714i	$-0.620054\pi$
$433$	−3.65110	+	1.07206i	−0.175461	+	0.0515199i	0.192822	+	0.981234i	$0.438236\pi$
$434$	−3.40535	+	7.45668i	−0.163462	+	0.357932i
$435$	2.13864	+	14.8746i	0.102540	+	0.713181i
$436$	5.94654			0.284788
$437$	−8.48670	+	0.960976i	−0.405974	+	0.0459697i
$438$	−8.28707			−0.395971
$439$	3.35462	+	23.3319i	0.160107	+	1.11357i	0.898428	+	0.439120i	$0.144710\pi$
$439$	3.35462	+	23.3319i	0.160107	+	1.11357i	−0.738321	+	0.674449i	$0.764381\pi$
$440$	−1.38506	+	3.03287i	−0.0660303	+	0.144586i
$441$	−44.7057	+	13.1268i	−2.12884	+	0.625085i
$442$	6.92841	−	7.99581i	0.329551	−	0.380322i
$443$	−2.67495	−	0.785437i	−0.127091	−	0.0373172i	0.217569	−	0.976045i	$-0.430187\pi$
$443$	−2.67495	−	0.785437i	−0.127091	−	0.0373172i	−0.344659	+	0.938728i	$0.612006\pi$
$444$	−10.7702	+	6.92158i	−0.511131	+	0.328484i
$445$	6.81581	+	14.9245i	0.323100	+	0.707491i
$446$	−1.32298	−	1.52680i	−0.0626447	−	0.0722959i
$447$	12.7694	+	8.20642i	0.603974	+	0.388150i
$448$	−0.503479	+	3.50177i	−0.0237872	+	0.165443i
$449$	−2.77765	+	19.3190i	−0.131086	+	0.911720i	0.813057	+	0.582184i	$0.197802\pi$
$449$	−2.77765	+	19.3190i	−0.131086	+	0.911720i	−0.944143	+	0.329536i	$0.893108\pi$
$450$	−7.10608	−	4.56680i	−0.334984	−	0.215281i
$451$	−18.1902	−	20.9926i	−0.856543	−	0.988504i
$452$	−3.01806	−	6.60864i	−0.141958	−	0.310844i
$453$	−26.7009	+	17.1596i	−1.25452	+	0.806230i
$454$	−11.8896	−	3.49110i	−0.558007	−	0.163846i
$455$	5.63012	−	6.49751i	0.263944	−	0.304608i
$456$	5.78135	−	1.69756i	0.270737	−	0.0794955i
$457$	1.32739	−	2.90658i	0.0620927	−	0.135964i	−0.876042	−	0.482235i	$-0.839825\pi$
$457$	1.32739	−	2.90658i	0.0620927	−	0.135964i	0.938134	+	0.346271i	$0.112552\pi$
$458$	3.71662	+	25.8497i	0.173666	+	1.20788i
$459$	−80.2328			−3.74495
$460$	2.71286	−	3.95479i	0.126488	−	0.184393i
$461$	−13.2998			−0.619436			−0.309718	−	0.950829i	$-0.600235\pi$
$461$	−13.2998			−0.619436			−0.309718	+	0.950829i	$0.600235\pi$
$462$	5.67957	+	39.5023i	0.264237	+	1.83781i
$463$	8.20700	−	17.9708i	0.381412	−	0.835175i	−0.617410	−	0.786642i	$-0.711818\pi$
$463$	8.20700	−	17.9708i	0.381412	−	0.835175i	0.998822	−	0.0485337i	$-0.0154548\pi$
$464$	4.26170	−	1.25135i	0.197844	−	0.0580924i
$465$	−5.13386	+	5.92478i	−0.238077	+	0.274755i
$466$	13.5503	+	3.97872i	0.627704	+	0.184310i
$467$	−6.84846	+	4.40124i	−0.316909	+	0.203665i	−0.689418	−	0.724363i	$-0.742134\pi$
$467$	−6.84846	+	4.40124i	−0.316909	+	0.203665i	0.372509	+	0.928028i	$0.378497\pi$
$468$	−8.52753	−	18.6727i	−0.394185	−	0.863145i
$469$	8.51029	+	9.82140i	0.392969	+	0.453510i
$470$	5.50370	+	3.53701i	0.253867	+	0.163150i
$471$	−1.36239	+	9.47566i	−0.0627758	+	0.436616i
$472$	1.98110	−	13.7789i	0.0911876	−	0.634224i
$473$	−12.6009	−	8.09810i	−0.579390	−	0.372351i
$474$	−5.09580	−	5.88087i	−0.234058	−	0.270117i
$475$	0.739816	+	1.61997i	0.0339451	+	0.0743294i
$476$	−12.9570	+	8.32697i	−0.593884	+	0.381666i
$477$	65.1107	+	19.1182i	2.98121	+	0.875364i
$478$	3.26621	−	3.76940i	0.149393	−	0.172409i
$479$	−5.28119	+	1.55070i	−0.241304	+	0.0708532i	−0.400148	−	0.916450i	$-0.631041\pi$
$479$	−5.28119	+	1.55070i	−0.241304	+	0.0708532i	0.158844	+	0.987304i	$0.449223\pi$
$480$	−1.40549	+	3.07760i	−0.0641516	+	0.140472i
$481$	−1.30869	−	9.10217i	−0.0596713	−	0.415023i
$482$	1.68484			0.0767423
$483$	1.72454	−	57.3780i	0.0784694	−	2.61079i
$484$	0.116681			0.00530368
$485$	1.63333	+	11.3600i	0.0741655	+	0.515833i
$486$	−29.0515	+	63.6140i	−1.31780	+	2.88559i
$487$	28.7103	−	8.43010i	1.30099	−	0.382004i	0.443391	−	0.896328i	$-0.353775\pi$
$487$	28.7103	−	8.43010i	1.30099	−	0.382004i	0.857596	+	0.514324i	$0.171957\pi$
$488$	−6.96601	+	8.03920i	−0.315336	+	0.363918i
$489$	−23.0969	−	6.78185i	−1.04448	−	0.306686i
$490$	−4.64029	+	2.98213i	−0.209627	+	0.134719i
$491$	12.2961	+	26.9247i	0.554916	+	1.21510i	0.954448	+	0.298377i	$0.0964453\pi$
$491$	12.2961	+	26.9247i	0.554916	+	1.21510i	−0.399532	+	0.916719i	$0.630827\pi$
$492$	−18.4585	−	21.3022i	−0.832173	−	0.960379i
$493$	16.2673	+	10.4543i	0.732642	+	0.470840i
$494$	−0.615927	+	4.28387i	−0.0277119	+	0.192740i
$495$	−4.00812	+	27.8771i	−0.180152	+	1.25298i
$496$	1.94929	+	1.25273i	0.0875255	+	0.0562492i
$497$	−20.9095	−	24.1309i	−0.937920	−	1.08242i
$498$	1.97748	+	4.33009i	0.0886132	+	0.194036i
$499$	−17.1162	+	10.9999i	−0.766227	+	0.492424i	−0.864437	−	0.502742i	$-0.832325\pi$
$499$	−17.1162	+	10.9999i	−0.766227	+	0.492424i	0.0982098	+	0.995166i	$0.468688\pi$
$500$	−0.959493	−	0.281733i	−0.0429098	−	0.0125995i
$501$	−8.84277	+	10.2051i	−0.395066	+	0.455930i
$502$	−22.6926	+	6.66316i	−1.01282	+	0.297391i
$503$	2.90113	−	6.35260i	0.129355	−	0.283248i	−0.833862	−	0.551973i	$-0.813875\pi$
$503$	2.90113	−	6.35260i	0.129355	−	0.283248i	0.963217	+	0.268725i	$0.0866023\pi$
$504$	4.25290	+	29.5796i	0.189439	+	1.31758i
$505$	7.61470			0.338850
$506$	−15.7518	−	2.75009i	−0.700255	−	0.122257i
$507$	−24.0023			−1.06598
$508$	−0.907193	−	6.30967i	−0.0402502	−	0.279946i
$509$	15.5440	−	34.0367i	0.688978	−	1.50865i	−0.163865	−	0.986483i	$-0.552396\pi$
$509$	15.5440	−	34.0367i	0.688978	−	1.50865i	0.852843	−	0.522168i	$-0.174877\pi$
$510$	−14.1330	+	4.14983i	−0.625821	+	0.183758i
$511$	−5.67460	+	6.54883i	−0.251029	+	0.289703i
$512$	0.959493	+	0.281733i	0.0424040	+	0.0124509i
$513$	27.6105	−	17.7442i	1.21903	−	0.783424i
$514$	−6.78371	−	14.8542i	−0.299216	−	0.655193i
$515$	6.70686	+	7.74013i	0.295539	+	0.341071i
$516$	−12.7867	−	8.21754i	−0.562905	−	0.361757i
$517$	3.10431	−	21.5910i	0.136527	−	0.949569i
$518$	−1.90516	+	13.2507i	−0.0837080	+	0.582202i
$519$	−72.3036	−	46.4667i	−3.17377	−	2.03966i
$520$	−1.59143	−	1.83660i	−0.0697887	−	0.0805404i
$521$	2.54875	+	5.58099i	0.111663	+	0.244507i	0.957211	−	0.289392i	$-0.0934532\pi$
$521$	2.54875	+	5.58099i	0.111663	+	0.244507i	−0.845548	+	0.533900i	$0.820726\pi$
$522$	31.5625	−	20.2840i	1.38145	−	0.887806i
$523$	32.7567	+	9.61823i	1.43235	+	0.420576i	0.903664	−	0.428242i	$-0.140867\pi$
$523$	32.7567	+	9.61823i	1.43235	+	0.420576i	0.528686	+	0.848818i	$0.322685\pi$
$524$	6.55952	−	7.57009i	0.286554	−	0.330701i
$525$	−11.4847	+	3.37221i	−0.501233	+	0.147175i
$526$	−0.630396	+	1.38037i	−0.0274866	+	0.0601872i
$527$	1.43564	+	9.98510i	0.0625375	+	0.434958i
$528$	11.2806			0.490927
$529$	21.6393	+	7.79352i	0.940841	+	0.338849i
$530$	8.03354			0.348955
$531$	−16.7344	−	116.390i	−0.726212	−	5.05091i
$532$	2.61731	−	5.73111i	0.113475	−	0.248475i
$533$	19.4259	−	5.70395i	0.841428	−	0.247066i
$534$	36.3522	−	41.9526i	1.57311	−	1.81547i
$535$	1.52997	+	0.449238i	0.0661462	+	0.0194223i
$536$	3.09023	−	1.98597i	0.133478	−	0.0857809i
$537$	27.6597	+	60.5664i	1.19361	+	2.61363i
$538$	−13.5274	−	15.6115i	−0.583208	−	0.673058i
$539$	15.4715	+	9.94293i	0.666404	+	0.428272i
$540$	−2.62274	+	18.2416i	−0.112865	+	0.784992i
$541$	0.736079	−	5.11954i	0.0316465	−	0.220106i	−0.967861	−	0.251486i	$-0.919081\pi$
$541$	0.736079	−	5.11954i	0.0316465	−	0.220106i	0.999508	+	0.0313794i	$0.00999000\pi$
$542$	9.72245	+	6.24824i	0.417615	+	0.268385i
$543$	−18.8538	−	21.7584i	−0.809094	−	0.933744i
$544$	1.80854	+	3.96016i	0.0775407	+	0.169790i
$545$	5.00255	−	3.21494i	0.214286	−	0.137713i
$546$	−27.9098	−	8.19506i	−1.19443	−	0.350716i
$547$	0.343860	−	0.396836i	0.0147024	−	0.0169675i	−0.748351	−	0.663303i	$-0.769154\pi$
$547$	0.343860	−	0.396836i	0.0147024	−	0.0169675i	0.763053	+	0.646336i	$0.223699\pi$
$548$	−7.31057	+	2.14658i	−0.312292	+	0.0916972i
$549$	−37.3268	+	81.7343i	−1.59307	+	3.48833i
$550$	0.474502	+	3.30023i	0.0202328	+	0.140722i
$551$	−7.91011			−0.336982
$552$	−15.9842	−	2.79065i	−0.680331	−	0.118778i
$553$	−8.13670			−0.346008
$554$	0.181567	+	1.26283i	0.00771405	+	0.0536524i
$555$	−5.31837	+	11.6456i	−0.225752	+	0.494329i
$556$	14.5288	−	4.26603i	0.616157	−	0.180920i
$557$	5.14454	−	5.93712i	0.217981	−	0.251564i	−0.636218	−	0.771509i	$-0.719502\pi$
$557$	5.14454	−	5.93712i	0.217981	−	0.251564i	0.854200	+	0.519945i	$0.174048\pi$
$558$	18.7799	+	5.51428i	0.795017	+	0.233438i
$559$	9.18441	−	5.90246i	0.388459	−	0.249648i
$560$	1.46965	+	3.21808i	0.0621040	+	0.135989i
$561$	32.1610	+	37.1158i	1.35784	+	1.56703i
$562$	−4.59927	−	2.95577i	−0.194009	−	0.124682i
$563$	1.28394	−	8.92997i	0.0541114	−	0.376353i	−0.944714	−	0.327896i	$-0.893660\pi$
$563$	1.28394	−	8.92997i	0.0541114	−	0.376353i	0.998825	−	0.0484572i	$-0.0154305\pi$
$564$	3.15010	−	21.9094i	0.132643	−	0.922552i
$565$	−6.11185	−	3.92785i	−0.257128	−	0.165246i
$566$	−0.217288	−	0.250763i	−0.00913328	−	0.0105404i
$567$	54.3933	+	119.105i	2.28430	+	5.00192i
$568$	−7.59260	+	4.87947i	−0.318579	+	0.204738i
$569$	−34.9157	−	10.2522i	−1.46374	−	0.429793i	−0.549682	−	0.835374i	$-0.685251\pi$
$569$	−34.9157	−	10.2522i	−1.46374	−	0.429793i	−0.914059	+	0.405581i	$0.867069\pi$
$570$	3.94582	−	4.55371i	0.165272	−	0.190734i
$571$	23.0743	−	6.77521i	0.965628	−	0.283534i	0.239348	−	0.970934i	$-0.423066\pi$
$571$	23.0743	−	6.77521i	0.965628	−	0.283534i	0.726279	+	0.687400i	$0.241248\pi$
$572$	−3.36595	+	7.37040i	−0.140737	+	0.308172i
$573$	9.28622	+	64.5870i	0.387937	+	2.69816i
$574$	−29.4736			−1.23020
$575$	0.144077	−	4.79367i	0.00600845	−	0.199910i
$576$	8.44702			0.351959
$577$	1.51041	+	10.5051i	0.0628791	+	0.437333i	0.996805	+	0.0798681i	$0.0254499\pi$
$577$	1.51041	+	10.5051i	0.0628791	+	0.437333i	−0.933926	+	0.357465i	$0.883641\pi$
$578$	−0.811594	+	1.77714i	−0.0337579	+	0.0739194i
$579$	45.1761	−	13.2649i	1.87745	−	0.551270i
$580$	2.90864	−	3.35675i	0.120775	−	0.139381i
$581$	4.77593	+	1.40234i	0.198139	+	0.0581788i
$582$	32.6660	−	20.9932i	1.35405	−	0.870194i
$583$	−11.1270	−	24.3647i	−0.460832	−	1.00908i
$584$	1.60400	+	1.85111i	0.0663739	+	0.0765995i
$585$	−17.2690	−	11.0981i	−0.713987	−	0.458851i
$586$	−2.28603	+	15.8997i	−0.0944350	+	0.656810i
$587$	−4.57225	+	31.8007i	−0.188717	+	1.31256i	0.646617	+	0.762814i	$0.276183\pi$
$587$	−4.57225	+	31.8007i	−0.188717	+	1.31256i	−0.835335	+	0.549742i	$0.814726\pi$
$588$	15.6997	+	10.0896i	0.647444	+	0.416087i
$589$	−2.70233	−	3.11866i	−0.111348	−	0.128502i
$590$	−5.78281	−	12.6626i	−0.238075	−	0.521311i
$591$	19.3877	−	12.4597i	0.797501	−	0.512523i
$592$	3.63071	+	1.06607i	0.149221	+	0.0438154i
$593$	−15.2607	+	17.6118i	−0.626682	+	0.723229i	−0.976961	−	0.213416i	$-0.931541\pi$
$593$	−15.2607	+	17.6118i	−0.626682	+	0.723229i	0.350280	+	0.936645i	$0.386086\pi$
$594$	58.9569	−	17.3113i	2.41903	−	0.710291i
$595$	−6.39824	+	14.0102i	−0.262302	+	0.574362i
$596$	−0.638482	−	4.44074i	−0.0261533	−	0.181900i
$597$	−74.6399			−3.05481
$598$	6.59272	−	9.61085i	0.269596	−	0.393017i
$599$	9.23034			0.377141			0.188571	−	0.982060i	$-0.439615\pi$
$599$	9.23034			0.377141			0.188571	+	0.982060i	$0.439615\pi$
$600$	0.481500	+	3.34891i	0.0196572	+	0.136719i
$601$	16.2641	−	35.6133i	0.663425	−	1.45270i	−0.215871	−	0.976422i	$-0.569259\pi$
$601$	16.2641	−	35.6133i	0.663425	−	1.45270i	0.879296	−	0.476276i	$-0.158014\pi$
$602$	−15.2497	+	4.47770i	−0.621530	+	0.182498i
$603$	20.3197	−	23.4501i	0.827481	−	0.954964i
$604$	9.00108	+	2.64296i	0.366249	+	0.107540i
$605$	0.0981583	−	0.0630825i	0.00399070	−	0.00256467i
$606$	−10.7024	−	23.4350i	−0.434756	−	0.951982i
$607$	0.419175	+	0.483753i	0.0170138	+	0.0196349i	0.764193	−	0.644988i	$-0.223138\pi$
$607$	0.419175	+	0.483753i	0.0170138	+	0.0196349i	−0.747179	+	0.664623i	$0.768592\pi$
$608$	−1.49820	−	0.962832i	−0.0607599	−	0.0390480i
$609$	7.56604	−	52.6230i	0.306592	−	2.13239i
$610$	−1.51386	+	10.5291i	−0.0612943	+	0.426312i
$611$	13.3749	+	8.59556i	0.541092	+	0.347739i
$612$	24.0824	+	27.7925i	0.973472	+	1.12345i
$613$	−1.91972	−	4.20361i	−0.0775369	−	0.169782i	0.866894	−	0.498493i	$-0.166113\pi$
$613$	−1.91972	−	4.20361i	−0.0775369	−	0.169782i	−0.944431	+	0.328711i	$0.893386\pi$
$614$	−27.3672	+	17.5878i	−1.10445	+	0.709787i
$615$	−27.0451	−	7.94117i	−1.09057	−	0.320219i
$616$	7.72446	−	8.91450i	0.311227	−	0.359175i
$617$	23.3444	−	6.85452i	0.939809	−	0.275953i	0.224271	−	0.974527i	$-0.428000\pi$
$617$	23.3444	−	6.85452i	0.939809	−	0.275953i	0.715538	+	0.698574i	$0.246182\pi$
$618$	14.3946	−	31.5197i	0.579034	−	1.26791i
$619$	−5.29251	−	36.8102i	−0.212724	−	1.47953i	−0.764007	−	0.645208i	$-0.776771\pi$
$619$	−5.29251	−	36.8102i	−0.212724	−	1.47953i	0.551283	−	0.834318i	$-0.314138\pi$
$620$	2.31712			0.0930578
$621$	−87.8218	+	9.94434i	−3.52417	+	0.399053i
$622$	1.98622			0.0796404
$623$	−8.26069	−	57.4544i	−0.330958	−	2.30186i
$624$	−3.41559	+	7.47910i	−0.136733	+	0.299404i
$625$	−0.959493	+	0.281733i	−0.0383797	+	0.0112693i
$626$	−2.53433	+	2.92477i	−0.101292	+	0.116897i
$627$	−19.2760	−	5.65995i	−0.769810	−	0.226037i
$628$	2.38031	−	1.52973i	0.0949847	−	0.0610430i
$629$	6.84352	+	14.9852i	0.272869	+	0.597500i
$630$	19.5697	+	22.5846i	0.779675	+	0.899793i
$631$	30.7487	+	19.7610i	1.22409	+	0.786672i	0.982960	−	0.183822i	$-0.0588470\pi$
$631$	30.7487	+	19.7610i	1.22409	+	0.786672i	0.241126	+	0.970494i	$0.422483\pi$
$632$	−0.327316	+	2.27653i	−0.0130199	+	0.0905556i
$633$	−1.45034	+	10.0873i	−0.0576457	+	0.400935i
$634$	1.75744	+	1.12944i	0.0697967	+	0.0448556i
$635$	−4.17444	−	4.81756i	−0.165658	−	0.191179i
$636$	−11.2911	−	24.7240i	−0.447721	−	0.980371i
$637$	−11.2767	+	7.24710i	−0.446799	+	0.287141i
$638$	−14.2092	−	4.17221i	−0.562549	−	0.165179i
$639$	−49.9248	+	57.6163i	−1.97499	+	2.27926i
$640$	0.959493	−	0.281733i	0.0379273	−	0.0111365i
$641$	4.62164	−	10.1200i	0.182544	−	0.399715i	−0.796133	−	0.605122i	$-0.793124\pi$
$641$	4.62164	−	10.1200i	0.182544	−	0.399715i	0.978677	+	0.205407i	$0.0658517\pi$
$642$	−0.767779	−	5.34002i	−0.0303018	−	0.210754i
$643$	−9.80294			−0.386590			−0.193295	−	0.981141i	$-0.561917\pi$
$643$	−9.80294			−0.386590			−0.193295	+	0.981141i	$0.561917\pi$
$644$	−13.1505	+	10.7205i	−0.518203	+	0.422448i
$645$	−15.1996			−0.598485
$646$	−1.10341	−	7.67442i	−0.0434133	−	0.301946i
$647$	10.5963	−	23.2027i	0.416584	−	0.912191i	−0.578733	−	0.815517i	$-0.696452\pi$
$647$	10.5963	−	23.2027i	0.416584	−	0.912191i	0.995316	−	0.0966734i	$-0.0308202\pi$
$648$	35.5119	−	10.4272i	1.39504	−	0.409620i
$649$	−30.3944	+	35.0770i	−1.19308	+	1.37689i
$650$	−2.33174	−	0.684660i	−0.0914582	−	0.0268546i
$651$	23.3321	−	14.9946i	0.914455	−	0.587685i
$652$	2.95561	+	6.47189i	0.115751	+	0.253459i
$653$	−27.8364	−	32.1249i	−1.08932	−	1.25715i	−0.964249	−	0.264999i	$-0.914629\pi$
$653$	−27.8364	−	32.1249i	−1.08932	−	1.25715i	−0.125074	−	0.992147i	$-0.539917\pi$
$654$	−16.9253	−	10.8773i	−0.661833	−	0.425334i
$655$	1.42552	−	9.91471i	0.0556997	−	0.387400i
$656$	−1.18564	+	8.24628i	−0.0462913	+	0.321963i
$657$	17.4054	+	11.1858i	0.679051	+	0.436399i
$658$	−15.1568	−	17.4919i	−0.590874	−	0.681905i
$659$	−13.8736	−	30.3789i	−0.540437	−	1.18339i	−0.961106	−	0.276179i	$-0.910932\pi$
$659$	−13.8736	−	30.3789i	−0.540437	−	1.18339i	0.420669	−	0.907214i	$-0.361795\pi$
$660$	9.48988	−	6.09877i	0.369393	−	0.237394i
$661$	28.1443	+	8.26392i	1.09469	+	0.321429i	0.778739	−	0.627348i	$-0.215859\pi$
$661$	28.1443	+	8.26392i	1.09469	+	0.321429i	0.315947	+	0.948777i	$0.397678\pi$
$662$	8.39176	−	9.68461i	0.326155	−	0.376403i
$663$	−34.3457	+	10.0848i	−1.33388	+	0.391662i
$664$	0.584476	−	1.27982i	0.0226821	−	0.0496668i
$665$	−0.896650	−	6.23634i	−0.0347706	−	0.241835i
$666$	31.9635			1.23856
$667$	19.1017	+	9.42697i	0.739621	+	0.365014i
$668$	3.99110			0.154420
$669$	0.972746	+	6.76560i	0.0376085	+	0.261573i
$670$	1.52597	−	3.34141i	0.0589534	−	0.129090i
$671$	34.0302	−	9.99217i	1.31372	−	0.385743i
$672$	7.83838	−	9.04598i	0.302372	−	0.348956i
$673$	37.1884	+	10.9195i	1.43351	+	0.420916i	0.904053	−	0.427421i	$-0.140578\pi$
$673$	37.1884	+	10.9195i	1.43351	+	0.420916i	0.529456	+	0.848337i	$0.322396\pi$
$674$	−9.68889	+	6.22667i	−0.373202	+	0.239843i
$675$	7.65574	+	16.7637i	0.294670	+	0.645236i
$676$	4.64574	+	5.36147i	0.178682	+	0.206211i
$677$	−5.19887	−	3.34111i	−0.199809	−	0.128409i	0.436911	−	0.899505i	$-0.356073\pi$
$677$	−5.19887	−	3.34111i	−0.199809	−	0.128409i	−0.636719	+	0.771096i	$0.719709\pi$
$678$	−3.49818	+	24.3304i	−0.134347	+	0.934403i
$679$	5.77836	−	40.1893i	0.221753	−	1.54233i
$680$	3.66247	+	2.35373i	0.140449	+	0.0902612i
$681$	27.4550	+	31.6847i	1.05208	+	1.21416i
$682$	−3.20936	−	7.02752i	−0.122893	−	0.269097i
$683$	−11.9685	+	7.69168i	−0.457961	+	0.294314i	−0.749209	−	0.662334i	$-0.769566\pi$
$683$	−11.9685	+	7.69168i	−0.457961	+	0.294314i	0.291248	+	0.956648i	$0.405930\pi$
$684$	−14.4340	−	4.23821i	−0.551898	−	0.162052i
$685$	−4.98951	+	5.75821i	−0.190640	+	0.220010i
$686$	−5.03769	+	1.47920i	−0.192340	+	0.0564760i
$687$	36.7051	−	80.3730i	1.40039	−	3.06642i
$688$	0.639348	+	4.44676i	0.0243749	+	0.169531i
$689$	19.5229			0.743764
$690$	−14.9555	+	6.29405i	−0.569345	+	0.239610i
$691$	−18.7466			−0.713153			−0.356576	−	0.934266i	$-0.616056\pi$
$691$	−18.7466			−0.713153			−0.356576	+	0.934266i	$0.616056\pi$
$692$	3.61524	+	25.1445i	0.137431	+	0.955851i
$693$	41.3909	−	90.6334i	1.57231	−	3.44288i
$694$	−4.12956	+	1.21255i	−0.156756	+	0.0460277i
$695$	9.91599	−	11.4437i	0.376135	−	0.434083i
$696$	−14.4188	−	4.23374i	−0.546543	−	0.160480i
$697$	−30.5123	+	19.6091i	−1.15574	+	0.742746i
$698$	3.99806	+	8.75454i	0.151329	+	0.331364i
$699$	−31.2897	−	36.1102i	−1.18348	−	1.36581i
$700$	2.97617	+	1.91267i	0.112489	+	0.0722922i
$701$	−6.53534	+	45.4543i	−0.246836	+	1.71678i	0.369441	+	0.929254i	$0.379549\pi$
$701$	−6.53534	+	45.4543i	−0.246836	+	1.71678i	−0.616277	+	0.787530i	$0.711360\pi$
$702$	−6.37372	+	44.3302i	−0.240560	+	1.67313i
$703$	−5.66916	−	3.64335i	−0.213816	−	0.137411i
$704$	−2.18342	−	2.51980i	−0.0822906	−	0.0949684i
$705$	−9.19509	−	20.1344i	−0.346307	−	0.758307i
$706$	24.4362	−	15.7042i	0.919667	−	0.591034i
$707$	−25.8480	−	7.58964i	−0.972112	−	0.285438i
$708$	−30.8427	+	35.5943i	−1.15914	+	1.33772i
$709$	2.24684	−	0.659733i	0.0843820	−	0.0247768i	−0.239269	−	0.970953i	$-0.576908\pi$
$709$	2.24684	−	0.659733i	0.0843820	−	0.0247768i	0.323651	+	0.946177i	$0.395090\pi$
$710$	−3.74926	+	8.20974i	−0.140707	+	0.308106i
$711$	2.76484	+	19.2299i	0.103690	+	0.721178i
$712$	−16.4072			−0.614887
$713$	2.80902	+	10.7516i	0.105199	+	0.402651i
$714$	52.1104			1.95018
$715$	1.15312	+	8.02014i	0.0431243	+	0.299936i
$716$	8.17527	−	17.9013i	0.305524	−	0.669005i
$717$	−16.1913	+	4.75421i	−0.604677	+	0.177549i
$718$	−16.2996	+	18.8108i	−0.608297	+	0.702012i
$719$	−9.05495	−	2.65877i	−0.337693	−	0.0991555i	0.108490	−	0.994098i	$-0.465399\pi$
$719$	−9.05495	−	2.65877i	−0.337693	−	0.0991555i	−0.446182	+	0.894942i	$0.647217\pi$
$720$	7.10608	−	4.56680i	0.264828	−	0.170195i
$721$	−15.0516	−	32.9585i	−0.560552	−	1.22744i
$722$	−10.3654	−	11.9623i	−0.385759	−	0.445190i
$723$	−4.79547	−	3.08186i	−0.178346	−	0.114616i
$724$	−1.21103	+	8.42288i	−0.0450075	+	0.313034i
$725$	0.632108	−	4.39641i	0.0234759	−	0.163278i
$726$	−0.332103	−	0.213430i	−0.0123255	−	0.00792112i
$727$	12.8019	+	14.7741i	0.474795	+	0.547943i	0.941739	−	0.336344i	$-0.109191\pi$
$727$	12.8019	+	14.7741i	0.474795	+	0.547943i	−0.466944	+	0.884287i	$0.654645\pi$
$728$	3.57150	+	7.82050i	0.132369	+	0.289847i
$729$	105.642	−	67.8919i	3.91266	−	2.51452i
$730$	2.35015	+	0.690068i	0.0869831	+	0.0255405i
$731$	−12.8080	+	14.7813i	−0.473723	+	0.546705i
$732$	34.5321	−	10.1395i	1.27634	−	0.374768i
$733$	−1.39238	+	3.04890i	−0.0514289	+	0.112614i	−0.933602	−	0.358312i	$-0.883353\pi$
$733$	−1.39238	+	3.04890i	−0.0514289	+	0.112614i	0.882173	+	0.470925i	$0.156080\pi$
$734$	4.57139	+	31.7947i	0.168733	+	1.17356i
$735$	18.6622			0.688367
$736$	2.47045	+	4.11058i	0.0910619	+	0.151518i
$737$	−12.2476			−0.451147
$738$	10.0151	+	69.6565i	0.368660	+	2.56409i
$739$	−12.2408	+	26.8035i	−0.450284	+	0.985984i	0.539312	+	0.842106i	$0.318684\pi$
$739$	−12.2408	+	26.8035i	−0.450284	+	0.985984i	−0.989595	+	0.143878i	$0.954043\pi$
$740$	3.63071	−	1.06607i	0.133468	−	0.0391897i
$741$	9.58902	−	11.0663i	0.352262	−	0.406532i
$742$	−27.2697	−	8.00711i	−1.00110	−	0.293950i
$743$	−21.6886	+	13.9384i	−0.795677	+	0.511350i	−0.874202	−	0.485562i	$-0.838615\pi$
$743$	−21.6886	+	13.9384i	−0.795677	+	0.511350i	0.0785257	+	0.996912i	$0.474979\pi$
$744$	−3.25669	−	7.13116i	−0.119396	−	0.261441i
$745$	−2.93797	−	3.39060i	−0.107639	−	0.124222i
$746$	−17.3965	−	11.1801i	−0.636931	−	0.409331i
$747$	1.69137	−	11.7637i	0.0618839	−	0.430412i
$748$	2.06578	−	14.3678i	0.0755325	−	0.525340i
$749$	−4.74568	−	3.04986i	−0.173403	−	0.111439i
$750$	2.21562	+	2.55696i	0.0809030	+	0.0933670i
$751$	1.58875	+	3.47887i	0.0579741	+	0.126946i	0.936402	−	0.350930i	$-0.114134\pi$
$751$	1.58875	+	3.47887i	0.0579741	+	0.126946i	−0.878428	+	0.477875i	$0.841407\pi$
$752$	−5.50370	+	3.53701i	−0.200699	+	0.128982i
$753$	76.7770	+	22.5438i	2.79791	+	0.821540i
$754$	7.06851	−	8.15749i	0.257420	−	0.297078i
$755$	9.00108	−	2.64296i	0.327583	−	0.0961870i
$756$	27.0844	−	59.3065i	0.985049	−	2.15696i
$757$	−4.27139	−	29.7081i	−0.155246	−	1.07976i	−0.907247	−	0.420599i	$-0.861820\pi$
$757$	−4.27139	−	29.7081i	−0.155246	−	1.07976i	0.752001	−	0.659162i	$-0.229089\pi$
$758$	26.0645			0.946705
$759$	39.8033	+	36.6403i	1.44477	+	1.32996i
$760$	−1.78091			−0.0646003
$761$	−6.80297	−	47.3157i	−0.246607	−	1.71519i	−0.617546	−	0.786535i	$-0.711873\pi$
$761$	−6.80297	−	47.3157i	−0.246607	−	1.71519i	0.370939	−	0.928657i	$-0.379036\pi$
$762$	−8.95938	+	19.6183i	−0.324564	+	0.710696i
$763$	−20.1854	+	5.92697i	−0.730761	+	0.214571i
$764$	12.6297	−	14.5754i	0.456925	−	0.527319i
$765$	35.2852	+	10.3607i	1.27574	+	0.374590i
$766$	−9.19573	+	5.90973i	−0.332255	+	0.213527i
$767$	−14.0532	−	30.7723i	−0.507433	−	1.11112i
$768$	−2.21562	−	2.55696i	−0.0799493	−	0.0922664i
$769$	29.7917	+	19.1460i	1.07432	+	0.690421i	0.953238	−	0.302221i	$-0.0977282\pi$
$769$	29.7917	+	19.1460i	1.07432	+	0.690421i	0.121079	+	0.992643i	$0.461365\pi$
$770$	1.67868	−	11.6755i	0.0604956	−	0.420756i
$771$	−7.86287	+	54.6875i	−0.283174	+	1.96952i
$772$	−11.7070	−	7.52366i	−0.421346	−	0.270782i
$773$	9.14989	+	10.5595i	0.329099	+	0.379800i	0.896052	−	0.443950i	$-0.146423\pi$
$773$	9.14989	+	10.5595i	0.329099	+	0.379800i	−0.566953	+	0.823750i	$0.691878\pi$
$774$	15.7642	+	34.5188i	0.566633	+	1.24075i
$775$	1.94929	−	1.25273i	0.0700204	−	0.0449994i
$776$	−11.0120	−	3.23340i	−0.395306	−	0.116072i
$777$	29.6604	−	34.2299i	1.06406	−	1.22799i
$778$	31.1445	−	9.14484i	1.11658	−	0.327859i
$779$	6.16347	−	13.4961i	0.220829	−	0.483548i
$780$	1.17013	+	8.13843i	0.0418974	+	0.291403i
$781$	30.0920			1.07678
$782$	−6.48150	+	19.8475i	−0.231778	+	0.709747i
$783$	−81.8552			−2.92527
$784$	−0.784997	−	5.45977i	−0.0280356	−	0.194992i
$785$	1.17541	−	2.57379i	0.0419521	−	0.0918623i
$786$	−32.5171	+	9.54787i	−1.15985	+	0.340561i
$787$	−23.5270	+	27.1516i	−0.838647	+	0.967850i	−0.999818	−	0.0190767i	$-0.993927\pi$
$787$	−23.5270	+	27.1516i	−0.838647	+	0.967850i	0.161171	+	0.986926i	$0.448473\pi$
$788$	−6.53573	−	1.91906i	−0.232826	−	0.0683638i
$789$	4.31921	−	2.77579i	0.153768	−	0.0988207i
$790$	0.955431	+	2.09210i	0.0339927	+	0.0744336i
$791$	16.8316	+	19.4247i	0.598464	+	0.690665i
$792$	−23.6929	−	15.2265i	−0.841890	−	0.541050i
$793$	−3.67894	+	25.5876i	−0.130643	+	0.908643i
$794$	1.97175	−	13.7139i	0.0699749	−	0.486686i
$795$	−22.8655	−	14.6948i	−0.810955	−	0.521169i
$796$	14.4469	+	16.6726i	0.512056	+	0.590944i
$797$	−14.6498	−	32.0787i	−0.518924	−	1.13628i	−0.969845	−	0.243721i	$-0.921632\pi$
$797$	−14.6498	−	32.0787i	−0.518924	−	1.13628i	0.450922	−	0.892563i	$-0.351095\pi$
$798$	−17.9327	+	11.5247i	−0.634811	+	0.407968i
$799$	−27.3285	−	8.02438i	−0.966814	−	0.283882i
$800$	0.654861	−	0.755750i	0.0231528	−	0.0267198i
$801$	−132.978	+	39.0459i	−4.69855	+	1.37962i
$802$	6.89693	−	15.1022i	0.243539	−	0.533276i
$803$	−1.16223	−	8.08349i	−0.0410142	−	0.285260i
$804$	−12.4283			−0.438311
$805$	−5.26696	+	16.1284i	−0.185636	+	0.568451i
$806$	5.63101			0.198344
$807$	9.94631	+	69.1781i	0.350127	+	2.43518i
$808$	−3.16326	+	6.92658i	−0.111283	+	0.243676i
$809$	5.73260	−	1.68324i	0.201548	−	0.0591797i	−0.179401	−	0.983776i	$-0.557416\pi$
$809$	5.73260	−	1.68324i	0.201548	−	0.0591797i	0.380948	+	0.924596i	$0.375598\pi$
$810$	24.2371	−	27.9711i	0.851605	−	0.982804i
$811$	−31.3203	−	9.19648i	−1.09981	−	0.322932i	−0.319031	−	0.947744i	$-0.603357\pi$
$811$	−31.3203	−	9.19648i	−1.09981	−	0.322932i	−0.780775	+	0.624812i	$0.785176\pi$
$812$	−13.2190	+	8.49535i	−0.463897	+	0.298128i
$813$	−16.2434	−	35.5681i	−0.569681	−	1.24743i
$814$	−8.26203	−	9.53489i	−0.289584	−	0.334198i
$815$	5.98538	+	3.84657i	0.209659	+	0.134740i
$816$	2.09625	−	14.5797i	0.0733835	−	0.510393i
$817$	1.13862	−	7.91927i	0.0398353	−	0.277060i
$818$	25.6083	+	16.4574i	0.895372	+	0.575420i
$819$	47.5578	+	54.8846i	1.66180	+	1.91782i
$820$	3.46085	+	7.57821i	0.120858	+	0.264643i
$821$	5.18848	−	3.33443i	0.181079	−	0.116373i	−0.446961	−	0.894553i	$-0.647494\pi$
$821$	5.18848	−	3.33443i	0.181079	−	0.116373i	0.628040	+	0.778181i	$0.283857\pi$
$822$	24.7342	+	7.26261i	0.862703	+	0.253313i
$823$	−21.8802	+	25.2511i	−0.762697	+	0.880200i	−0.995734	−	0.0922684i	$-0.970588\pi$
$823$	−21.8802	+	25.2511i	−0.762697	+	0.880200i	0.233037	+	0.972468i	$0.425134\pi$
$824$	−9.82680	+	2.88541i	−0.342333	+	0.100518i
$825$	4.68615	−	10.2612i	0.163151	−	0.357250i
$826$	7.00871	+	48.7467i	0.243864	+	1.69611i
$827$	41.1796			1.43196			0.715978	−	0.698123i	$-0.245981\pi$
$827$	41.1796			1.43196			0.715978	+	0.698123i	$0.245981\pi$
$828$	29.8050	+	27.4365i	1.03579	+	0.953485i
$829$	1.03538			0.0359601			0.0179800	−	0.999838i	$-0.494276\pi$
$829$	1.03538			0.0359601			0.0179800	+	0.999838i	$0.494276\pi$
$830$	−0.200233	−	1.39265i	−0.00695018	−	0.0483395i
$831$	1.79315	−	3.92644i	0.0622035	−	0.136207i
$832$	2.33174	−	0.684660i	0.0808384	−	0.0237363i
$833$	15.7258	−	18.1486i	0.544868	−	0.628811i
$834$	−49.1558	−	14.4335i	−1.70213	−	0.499790i
$835$	3.35753	−	2.15775i	0.116192	−	0.0746722i
$836$	2.46667	+	5.40126i	0.0853116	+	0.186806i
$837$	−27.9642	−	32.2724i	−0.966584	−	1.11550i
$838$	−16.4804	−	10.5913i	−0.569307	−	0.365872i
$839$	1.31747	−	9.16322i	0.0454842	−	0.316350i	−0.954359	−	0.298661i	$-0.903460\pi$
$839$	1.31747	−	9.16322i	0.0454842	−	0.316350i	0.999844	−	0.0176888i	$-0.00563083\pi$
$840$	1.70344	−	11.8477i	0.0587744	−	0.408785i
$841$	−7.80013	−	5.01284i	−0.268970	−	0.172857i
$842$	2.59703	+	2.99713i	0.0894994	+	0.103288i
$843$	7.68406	+	16.8257i	0.264653	+	0.579509i
$844$	2.53396	−	1.62848i	0.0872225	−	0.0560545i
$845$	6.80688	+	1.99868i	0.234164	+	0.0687567i
$846$	−36.1893	+	41.7647i	−1.24421	+	1.43590i
$847$	−0.396071	+	0.116297i	−0.0136092	+	0.00399601i
$848$	−3.33726	+	7.30757i	−0.114602	+	0.250943i
$849$	0.159765	+	1.11119i	0.00548313	+	0.0381360i
$850$	4.35358			0.149327
$851$	9.34815	+	15.5544i	0.320450	+	0.533199i
$852$	30.5359			1.04614
$853$	−3.30389	−	22.9791i	−0.113123	−	0.786789i	−0.964850	−	0.262802i	$-0.915353\pi$
$853$	−3.30389	−	22.9791i	−0.113123	−	0.786789i	0.851727	−	0.523986i	$-0.175556\pi$
$854$	15.6332	−	34.2320i	0.534958	−	1.17139i
$855$	−14.4340	+	4.23821i	−0.493633	+	0.144944i
$856$	−1.04421	+	1.20509i	−0.0356904	+	0.0411890i
$857$	−11.7174	−	3.44053i	−0.400258	−	0.117526i	0.0754071	−	0.997153i	$-0.475974\pi$
$857$	−11.7174	−	3.44053i	−0.400258	−	0.117526i	−0.475665	+	0.879626i	$0.657793\pi$
$858$	23.0621	−	14.8211i	0.787326	−	0.505984i
$859$	−17.9109	−	39.2194i	−0.611111	−	1.33815i	−0.921811	−	0.387639i	$-0.873291\pi$
$859$	−17.9109	−	39.2194i	−0.611111	−	1.33815i	0.310700	−	0.950508i	$-0.399437\pi$
$860$	2.94195	+	3.39520i	0.100320	+	0.115775i
$861$	83.8891	+	53.9123i	2.85893	+	1.83732i
$862$	−0.714915	+	4.97234i	−0.0243501	+	0.169359i
$863$	−0.734051	+	5.10544i	−0.0249874	+	0.173791i	−0.998494	−	0.0548698i	$-0.982526\pi$
$863$	−0.734051	+	5.10544i	−0.0249874	+	0.173791i	0.973506	+	0.228661i	$0.0734347\pi$
$864$	−15.5036	−	9.96354i	−0.527442	−	0.338967i
$865$	16.6355	+	19.1984i	0.565624	+	0.652764i
$866$	−1.58075	−	3.46137i	−0.0537162	−	0.117622i
$867$	5.56070	−	3.57365i	0.188851	−	0.121367i
$868$	−7.86541	−	2.30949i	−0.266970	−	0.0783893i
$869$	5.02173	−	5.79539i	0.170351	−	0.196595i
$870$	−14.4188	+	4.23374i	−0.488843	+	0.143537i
$871$	3.70838	−	8.12022i	0.125654	−	0.275143i
$872$	0.846281	+	5.88601i	0.0286587	+	0.199326i
$873$	−96.9452			−3.28110
$874$	−2.15898	−	8.26356i	−0.0730286	−	0.279519i
$875$	3.53778			0.119599
$876$	−1.17937	−	8.20272i	−0.0398473	−	0.277144i
$877$	22.1532	−	48.5087i	0.748060	−	1.63802i	−0.0217607	−	0.999763i	$-0.506927\pi$
$877$	22.1532	−	48.5087i	0.748060	−	1.63802i	0.769821	−	0.638260i	$-0.220346\pi$
$878$	−22.6170	+	6.64094i	−0.763286	+	0.224121i
$879$	35.5899	−	41.0730i	1.20042	−	1.38536i
$880$	−3.19911	−	0.939344i	−0.107842	−	0.0316653i
$881$	30.9764	−	19.9074i	1.04362	−	0.670696i	0.0977428	−	0.995212i	$-0.468838\pi$
$881$	30.9764	−	19.9074i	1.04362	−	0.670696i	0.945880	+	0.324516i	$0.105201\pi$
$882$	−19.3555	−	42.3825i	−0.651732	−	1.42709i
$883$	−11.6056	−	13.3936i	−0.390561	−	0.450731i	0.526085	−	0.850432i	$-0.323659\pi$
$883$	−11.6056	−	13.3936i	−0.390561	−	0.450731i	−0.916646	+	0.399701i	$0.869114\pi$
$884$	8.90044	+	5.71997i	0.299354	+	0.192383i
$885$	−6.70275	+	46.6187i	−0.225311	+	1.56707i
$886$	0.396757	−	2.75950i	0.0133293	−	0.0927074i
$887$	−17.2351	−	11.0763i	−0.578697	−	0.371906i	0.218307	−	0.975880i	$-0.429947\pi$
$887$	−17.2351	−	11.0763i	−0.578697	−	0.371906i	−0.797004	+	0.603974i	$0.793583\pi$
$888$	−8.38389	−	9.67552i	−0.281345	−	0.324689i
$889$	9.36835	+	20.5138i	0.314204	+	0.688011i
$890$	−13.8026	+	8.87041i	−0.462665	+	0.297337i
$891$	−118.403	−	34.7661i	−3.96663	−	1.16471i
$892$	1.32298	−	1.52680i	0.0442965	−	0.0511209i
$893$	11.1792	−	3.28251i	0.374098	−	0.109845i
$894$	−6.30561	+	13.8074i	−0.210891	+	0.461787i
$895$	−2.80072	−	19.4795i	−0.0936178	−	0.651126i
$896$	−3.53778			−0.118189
$897$	−36.3444	+	15.2956i	−1.21351	+	0.510707i
$898$	−19.5177			−0.651313
$899$	1.46467	+	10.1870i	0.0488495	+	0.339756i
$900$	3.50902	−	7.68368i	0.116967	−	0.256123i
$901$	−33.5580	+	9.85352i	−1.11798	+	0.328268i
$902$	18.1902	−	20.9926i	0.605668	−	0.698978i
$903$	51.5948	+	15.1496i	1.71697	+	0.504147i
$904$	6.11185	−	3.92785i	0.203277	−	0.130638i
$905$	3.53497	+	7.74051i	0.117506	+	0.257303i
$906$	−20.7849	−	23.9871i	−0.690532	−	0.796917i
$907$	23.4683	+	15.0822i	0.779253	+	0.500796i	0.868786	−	0.495188i	$-0.164901\pi$
$907$	23.4683	+	15.0822i	0.779253	+	0.500796i	−0.0895324	+	0.995984i	$0.528537\pi$
$908$	1.76350	−	12.2654i	0.0585239	−	0.407042i
$909$	−9.15391	+	63.6668i	−0.303616	+	2.11170i
$910$	7.23262	+	4.64813i	0.239759	+	0.154084i
$911$	16.6903	+	19.2617i	0.552976	+	0.638168i	0.961574	−	0.274546i	$-0.0885277\pi$
$911$	16.6903	+	19.2617i	0.552976	+	0.638168i	−0.408598	+	0.912714i	$0.633982\pi$
$912$	2.50305	+	5.48092i	0.0828844	+	0.181491i
$913$	−3.94638	+	2.53619i	−0.130606	+	0.0839355i
$914$	3.06590	+	0.900231i	0.101411	+	0.0297770i
$915$	23.5684	−	27.1994i	0.779148	−	0.899184i
$916$	−25.0576	+	7.35758i	−0.827927	+	0.243101i
$917$	−14.7210	+	32.2345i	−0.486130	+	1.06448i
$918$	−11.4183	−	79.4161i	−0.376861	−	2.62112i
$919$	−45.4554			−1.49944			−0.749718	−	0.661758i	$-0.769811\pi$
$919$	−45.4554			−1.49944			−0.749718	+	0.661758i	$0.769811\pi$
$920$	4.30062	+	2.12242i	0.141787	+	0.0699741i
$921$	110.065			3.62677
$922$	−1.89277	−	13.1645i	−0.0623349	−	0.433549i
$923$	−9.11137	+	19.9511i	−0.299904	+	0.656699i
$924$	−38.2919	+	11.2435i	−1.25971	+	0.369885i
$925$	2.47799	−	2.85975i	0.0814757	−	0.0940280i
$926$	18.9559	+	5.56595i	0.622929	+	0.182909i
$927$	−72.7781	+	46.7716i	−2.39035	+	1.53618i
$928$	1.84511	+	4.04024i	0.0605689	+	0.132627i
$929$	−14.7633	−	17.0377i	−0.484367	−	0.558989i	0.459985	−	0.887927i	$-0.347855\pi$
$929$	−14.7633	−	17.0377i	−0.484367	−	0.558989i	−0.944352	+	0.328938i	$0.893309\pi$
$930$	−6.59510	−	4.23842i	−0.216262	−	0.138983i
$931$	−1.39801	+	9.72336i	−0.0458179	+	0.318670i
$932$	−2.00982	+	13.9786i	−0.0658337	+	0.457883i
$933$	−5.65329	−	3.63315i	−0.185081	−	0.118944i
$934$	−5.33108	−	6.15239i	−0.174438	−	0.201312i
$935$	−6.02999	−	13.2038i	−0.197202	−	0.431812i
$936$	17.2690	−	11.0981i	0.564456	−	0.362754i
$937$	18.8432	+	5.53285i	0.615579	+	0.180750i	0.574633	−	0.818411i	$-0.305145\pi$
$937$	18.8432	+	5.53285i	0.615579	+	0.180750i	0.0409458	+	0.999161i	$0.486963\pi$
$938$	−8.51029	+	9.82140i	−0.277871	+	0.320680i
$939$	12.5632	−	3.68890i	0.409986	−	0.120383i
$940$	−2.71775	+	5.95105i	−0.0886433	+	0.194102i
$941$	0.802738	+	5.58316i	0.0261685	+	0.182006i	0.998713	−	0.0507091i	$-0.0161481\pi$
$941$	0.802738	+	5.58316i	0.0261685	+	0.182006i	−0.972545	+	0.232715i	$0.925239\pi$
$942$	−9.57310			−0.311909
$943$	−30.9680	+	25.2456i	−1.00846	+	0.822111i
$944$	13.9206			0.453076
$945$	−9.27869	−	64.5347i	−0.301836	−	2.09931i
$946$	6.22238	−	13.6251i	0.202307	−	0.442991i
$947$	−0.927954	+	0.272472i	−0.0301544	+	0.00885414i	−0.296775	−	0.954947i	$-0.595911\pi$
$947$	−0.927954	+	0.272472i	−0.0301544	+	0.00885414i	0.266621	+	0.963802i	$0.414093\pi$
$948$	5.09580	−	5.88087i	0.165504	−	0.191002i
$949$	5.71129	+	1.67699i	0.185396	+	0.0544372i
$950$	−1.49820	+	0.962832i	−0.0486079	+	0.0312384i
$951$	−2.93617	−	6.42931i	−0.0952118	−	0.208485i
$952$	−10.0862	−	11.6401i	−0.326895	−	0.377257i
$953$	−27.4641	−	17.6501i	−0.889649	−	0.571743i	0.0140544	−	0.999901i	$-0.495526\pi$
$953$	−27.4641	−	17.6501i	−0.889649	−	0.571743i	−0.903704	+	0.428158i	$0.859163\pi$
$954$	−9.65741	+	67.1688i	−0.312670	+	2.17467i
$955$	2.74469	−	19.0897i	0.0888159	−	0.617728i
$956$	4.19587	+	2.69652i	0.135704	+	0.0872117i
$957$	32.8113	+	37.8663i	1.06064	+	1.22404i
$958$	−2.28650	−	5.00675i	−0.0738736	−	0.161761i
$959$	22.6761	−	14.5730i	0.732248	−	0.470587i
$960$	−3.24630	−	0.953198i	−0.104774	−	0.0307643i
$961$	16.7847	−	19.3706i	0.541442	−	0.624858i
$962$	8.82327	−	2.59075i	0.284474	−	0.0835290i
$963$	−5.59533	+	12.2521i	−0.180307	+	0.394817i
$964$	0.239778	+	1.66769i	0.00772272	+	0.0537127i
$965$	−13.9162			−0.447978
$966$	57.0394	−	6.45875i	1.83521	−	0.207807i
$967$	−40.2297			−1.29370			−0.646851	−	0.762617i	$-0.723914\pi$
$967$	−40.2297			−1.29370			−0.646851	+	0.762617i	$0.723914\pi$
$968$	0.0166054	+	0.115493i	0.000533719	+	0.00371210i
$969$	−10.8973	+	23.8617i	−0.350070	+	0.766547i
$970$	−11.0120	+	3.23340i	−0.353573	+	0.103818i
$971$	−0.758179	+	0.874985i	−0.0243311	+	0.0280796i	−0.767785	−	0.640708i	$-0.778641\pi$
$971$	−0.758179	+	0.874985i	−0.0243311	+	0.0280796i	0.743454	+	0.668788i	$0.233186\pi$
$972$	−67.1009	−	19.7026i	−2.15226	−	0.631962i
$973$	−45.0656	+	28.9619i	−1.44474	+	0.928477i
$974$	12.4302	+	27.2183i	0.398289	+	0.872132i
$975$	5.38434	+	6.21386i	0.172437	+	0.199003i
$976$	−8.94874	−	5.75101i	−0.286442	−	0.184085i
$977$	−7.87917	+	54.8009i	−0.252077	+	1.75323i	0.333623	+	0.942707i	$0.391729\pi$
$977$	−7.87917	+	54.8009i	−0.252077	+	1.75323i	−0.585700	+	0.810528i	$0.699180\pi$
$978$	3.42580	−	23.8269i	0.109545	−	0.761901i
$979$	46.0203	+	29.5755i	1.47082	+	0.945236i
$980$	−3.61216	−	4.16865i	−0.115386	−	0.133163i
$981$	20.8665	+	45.6913i	0.666217	+	1.45881i
$982$	−24.9008	+	16.0027i	−0.794615	+	0.510668i
$983$	1.23462	+	0.362516i	0.0393781	+	0.0115625i	0.301362	−	0.953510i	$-0.402559\pi$
$983$	1.23462	+	0.362516i	0.0393781	+	0.0115625i	−0.261984	+	0.965072i	$0.584377\pi$
$984$	18.4585	−	21.3022i	0.588435	−	0.679091i
$985$	−6.53573	+	1.91906i	−0.208246	+	0.0611464i
$986$	−8.03286	+	17.5895i	−0.255818	+	0.560164i
$987$	11.1444	+	77.5108i	0.354729	+	2.46719i
$988$	−4.32792			−0.137689
$989$	−12.1875	+	17.7669i	−0.387539	+	0.564954i
$990$	−28.1638			−0.895104
$991$	1.55111	+	10.7882i	0.0492725	+	0.342698i	0.999514	+	0.0311828i	$0.00992741\pi$
$991$	1.55111	+	10.7882i	0.0492725	+	0.342698i	−0.950241	+	0.311515i	$0.899163\pi$
$992$	−0.962566	+	2.10773i	−0.0305615	+	0.0669204i
$993$	−41.5999	+	12.2148i	−1.32013	+	0.387626i
$994$	20.9095	−	24.1309i	0.663210	−	0.765385i
$995$	21.1674	+	6.21530i	0.671051	+	0.197038i
$996$	−4.00459	+	2.57359i	−0.126890	+	0.0815474i
$997$	−2.85596	−	6.25368i	−0.0904491	−	0.198056i	0.859001	−	0.511974i	$-0.171086\pi$
$997$	−2.85596	−	6.25368i	−0.0904491	−	0.198056i	−0.949450	+	0.313918i	$0.898358\pi$
$998$	−13.3239	−	15.3765i	−0.421759	−	0.486736i
$999$	−58.6654	−	37.7020i	−1.85609	−	1.19284i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.g.b.141.2	yes	20
23.8	even	11	inner	230.2.g.b.31.2	✓	20
23.10	odd	22		5290.2.a.bi.1.10		10
23.13	even	11		5290.2.a.bj.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.g.b.31.2	✓	20	23.8	even	11	inner
230.2.g.b.141.2	yes	20	1.1	even	1	trivial
5290.2.a.bi.1.10		10	23.10	odd	22
5290.2.a.bj.1.10		10	23.13	even	11

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 + 0.989821i) q^{2} +(1.40549 - 3.07760i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(3.24630 + 0.953198i) q^{6} +(2.97617 - 1.91267i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-5.53162 - 6.38383i) q^{9} +O(q^{10})\)	\(q+(0.142315 + 0.989821i) q^{2} +(1.40549 - 3.07760i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.654861 + 0.755750i) q^{5} +(3.24630 + 0.953198i) q^{6} +(2.97617 - 1.91267i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-5.53162 - 6.38383i) q^{9} +(-0.841254 - 0.540641i) q^{10} +(-0.474502 + 3.30023i) q^{11} +(-0.481500 + 3.34891i) q^{12} +(-2.04439 - 1.31385i) q^{13} +(2.31676 + 2.67368i) q^{14} +(1.40549 + 3.07760i) q^{15} +(0.841254 - 0.540641i) q^{16} +(4.17723 + 1.22655i) q^{17} +(5.53162 - 6.38383i) q^{18} +(-1.70877 + 0.501740i) q^{19} +(0.415415 - 0.909632i) q^{20} +(-1.70344 - 11.8477i) q^{21} -3.33417 q^{22} +(4.72437 + 0.824821i) q^{23} -3.38334 q^{24} +(-0.142315 - 0.989821i) q^{25} +(1.00953 - 2.21057i) q^{26} +(-17.6826 + 5.19209i) q^{27} +(-2.31676 + 2.67368i) q^{28} +(4.26170 + 1.25135i) q^{29} +(-2.84625 + 1.82917i) q^{30} +(0.962566 + 2.10773i) q^{31} +(0.654861 + 0.755750i) q^{32} +(9.48988 + 6.09877i) q^{33} +(-0.619580 + 4.30927i) q^{34} +(-0.503479 + 3.50177i) q^{35} +(7.10608 + 4.56680i) q^{36} +(2.47799 + 2.85975i) q^{37} +(-0.739816 - 1.61997i) q^{38} +(-6.91689 + 4.44521i) q^{39} +(0.959493 + 0.281733i) q^{40} +(-5.45570 + 6.29621i) q^{41} +(11.4847 - 3.37221i) q^{42} +(-1.86625 + 4.08651i) q^{43} +(-0.474502 - 3.30023i) q^{44} +8.44702 q^{45} +(-0.144077 + 4.79367i) q^{46} -6.54226 q^{47} +(-0.481500 - 3.34891i) q^{48} +(2.29140 - 5.01746i) q^{49} +(0.959493 - 0.281733i) q^{50} +(9.64588 - 11.1319i) q^{51} +(2.33174 + 0.684660i) q^{52} +(-6.75825 + 4.34326i) q^{53} +(-7.65574 - 16.7637i) q^{54} +(-2.18342 - 2.51980i) q^{55} +(-2.97617 - 1.91267i) q^{56} +(-0.857508 + 5.96410i) q^{57} +(-0.632108 + 4.39641i) q^{58} +(11.7107 + 7.52602i) q^{59} +(-2.21562 - 2.55696i) q^{60} +(-4.41893 - 9.67611i) q^{61} +(-1.94929 + 1.25273i) q^{62} +(-28.6732 - 8.41922i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(2.33174 - 0.684660i) q^{65} +(-4.68615 + 10.2612i) q^{66} +(0.522775 + 3.63598i) q^{67} -4.35358 q^{68} +(9.17853 - 13.3804i) q^{69} -3.53778 q^{70} +(-1.28444 - 8.93348i) q^{71} +(-3.50902 + 7.68368i) q^{72} +(-2.35015 + 0.690068i) q^{73} +(-2.47799 + 2.85975i) q^{74} +(-3.24630 - 0.953198i) q^{75} +(1.49820 - 0.962832i) q^{76} +(4.90006 + 10.7296i) q^{77} +(-5.38434 - 6.21386i) q^{78} +(-1.93484 - 1.24344i) q^{79} +(-0.142315 + 0.989821i) q^{80} +(-5.26722 + 36.6343i) q^{81} +(-7.00855 - 4.50412i) q^{82} +(0.921369 + 1.06332i) q^{83} +(4.97233 + 10.8879i) q^{84} +(-3.66247 + 2.35373i) q^{85} +(-4.31051 - 1.26568i) q^{86} +(9.84093 - 11.3570i) q^{87} +(3.19911 - 0.939344i) q^{88} +(6.81581 - 14.9245i) q^{89} +(1.20214 + 8.36104i) q^{90} -8.59744 q^{91} +(-4.76538 + 0.539599i) q^{92} +7.83961 q^{93} +(-0.931060 - 6.47567i) q^{94} +(0.739816 - 1.61997i) q^{95} +(3.24630 - 0.953198i) q^{96} +(7.51574 - 8.67363i) q^{97} +(5.29248 + 1.55401i) q^{98} +(23.6929 - 15.2265i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9	\( 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9} + 2 q^{10} + 7 q^{11} + 8 q^{12} + 8 q^{13} + 3 q^{14} - 3 q^{15} - 2 q^{16} + 8 q^{17} + 27 q^{18} - q^{19} - 2 q^{20} - 31 q^{21} - 18 q^{22} - 9 q^{23} - 8 q^{24} - 2 q^{25} - 8 q^{26} - 18 q^{27} - 3 q^{28} + 20 q^{29} + 3 q^{30} - 17 q^{31} + 2 q^{32} + 17 q^{33} + 3 q^{34} - 3 q^{35} + 17 q^{36} + 6 q^{37} - 21 q^{38} - 75 q^{39} + 2 q^{40} - 2 q^{41} + 42 q^{42} - 18 q^{43} + 7 q^{44} + 28 q^{45} - 2 q^{46} + 42 q^{47} + 8 q^{48} - 19 q^{49} + 2 q^{50} + 26 q^{51} + 19 q^{52} + 19 q^{53} - 26 q^{54} - 15 q^{55} - 19 q^{56} + 7 q^{57} - 9 q^{58} + 25 q^{59} - 3 q^{60} - 49 q^{61} - 38 q^{62} - 87 q^{63} - 2 q^{64} + 19 q^{65} - 6 q^{66} + 19 q^{67} - 36 q^{68} + 36 q^{69} + 14 q^{70} + 7 q^{71} - 17 q^{72} - 10 q^{73} - 6 q^{74} - 3 q^{75} - q^{76} - 29 q^{77} - 2 q^{78} - 33 q^{79} - 2 q^{80} + 72 q^{81} + 2 q^{82} - 41 q^{83} + 13 q^{84} - 14 q^{85} - 48 q^{86} - 16 q^{87} - 7 q^{88} + 55 q^{89} + 5 q^{90} + 13 q^{92} + 10 q^{93} + 13 q^{94} + 21 q^{95} + 3 q^{96} - 9 q^{97} + 41 q^{98} + 59 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9 + 2 * q^10 + 7 * q^11 + 8 * q^12 + 8 * q^13 + 3 * q^14 - 3 * q^15 - 2 * q^16 + 8 * q^17 + 27 * q^18 - q^19 - 2 * q^20 - 31 * q^21 - 18 * q^22 - 9 * q^23 - 8 * q^24 - 2 * q^25 - 8 * q^26 - 18 * q^27 - 3 * q^28 + 20 * q^29 + 3 * q^30 - 17 * q^31 + 2 * q^32 + 17 * q^33 + 3 * q^34 - 3 * q^35 + 17 * q^36 + 6 * q^37 - 21 * q^38 - 75 * q^39 + 2 * q^40 - 2 * q^41 + 42 * q^42 - 18 * q^43 + 7 * q^44 + 28 * q^45 - 2 * q^46 + 42 * q^47 + 8 * q^48 - 19 * q^49 + 2 * q^50 + 26 * q^51 + 19 * q^52 + 19 * q^53 - 26 * q^54 - 15 * q^55 - 19 * q^56 + 7 * q^57 - 9 * q^58 + 25 * q^59 - 3 * q^60 - 49 * q^61 - 38 * q^62 - 87 * q^63 - 2 * q^64 + 19 * q^65 - 6 * q^66 + 19 * q^67 - 36 * q^68 + 36 * q^69 + 14 * q^70 + 7 * q^71 - 17 * q^72 - 10 * q^73 - 6 * q^74 - 3 * q^75 - q^76 - 29 * q^77 - 2 * q^78 - 33 * q^79 - 2 * q^80 + 72 * q^81 + 2 * q^82 - 41 * q^83 + 13 * q^84 - 14 * q^85 - 48 * q^86 - 16 * q^87 - 7 * q^88 + 55 * q^89 + 5 * q^90 + 13 * q^92 + 10 * q^93 + 13 * q^94 + 21 * q^95 + 3 * q^96 - 9 * q^97 + 41 * q^98 + 59 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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