LMFDB - Embedded newform 930.2.n.h.721.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(481,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("930.481");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.n (of order $5$, degree $4$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 5 x^{14} - 60 x^{13} + 480 x^{12} - 1202 x^{11} - 147 x^{10} - 2185 x^{9} + \cdots + 12851 $ x^16 - 4x^15 + 5x^14 - 60x^13 + 480x^12 - 1202x^11 - 147x^10 - 2185x^9 + 62400x^8 - 289745x^7 + 699483x^6 - 1042897x^5 + 1014415x^4 - 652345x^3 + 274580x^2 - 73519*x + 12851
Coefficient ring:	$\Z[a_1, \ldots, a_{31}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			721.4
Root			$2.05406 + 2.30144i$ of defining polynomial
Character	$\chi$	$=$	930.721
Dual form			930.2.n.h.841.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(1.31796 + 0.957557i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(1.31796 + 0.957557i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(0.309017 - 0.951057i) q^{10} +(-0.438591 - 0.318655i) q^{11} +(0.309017 - 0.951057i) q^{12} +(-1.26948 - 3.90705i) q^{13} +(-1.31796 + 0.957557i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-4.63894 + 3.37039i) q^{17} +(-0.309017 - 0.951057i) q^{18} +(-1.96388 + 6.04420i) q^{19} +(0.809017 + 0.587785i) q^{20} +(-0.503417 + 1.54936i) q^{21} +(0.438591 - 0.318655i) q^{22} +(-6.13886 + 4.46015i) q^{23} +(0.809017 + 0.587785i) q^{24} +1.00000 q^{25} +4.10812 q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.503417 - 1.54936i) q^{28} +(-0.0513096 + 0.157915i) q^{29} +1.00000 q^{30} +(-5.47576 + 1.00798i) q^{31} -1.00000 q^{32} +(0.167527 - 0.515594i) q^{33} +(-1.77192 - 5.45340i) q^{34} +(-1.31796 - 0.957557i) q^{35} +1.00000 q^{36} +3.76990 q^{37} +(-5.14150 - 3.73552i) q^{38} +(3.32354 - 2.41469i) q^{39} +(-0.809017 + 0.587785i) q^{40} +(2.66998 - 8.21736i) q^{41} +(-1.31796 - 0.957557i) q^{42} +(0.369599 - 1.13751i) q^{43} +(0.167527 + 0.515594i) q^{44} +(0.809017 - 0.587785i) q^{45} +(-2.34484 - 7.21667i) q^{46} +(0.679710 + 2.09193i) q^{47} +(-0.809017 + 0.587785i) q^{48} +(-1.34301 - 4.13335i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(-4.63894 - 3.37039i) q^{51} +(-1.26948 + 3.90705i) q^{52} +(-11.3745 + 8.26405i) q^{53} +(0.809017 - 0.587785i) q^{54} +(0.438591 + 0.318655i) q^{55} +1.62909 q^{56} -6.35525 q^{57} +(-0.134330 - 0.0975966i) q^{58} +(-1.83265 - 5.64033i) q^{59} +(-0.309017 + 0.951057i) q^{60} +10.3419 q^{61} +(0.733458 - 5.51924i) q^{62} -1.62909 q^{63} +(0.309017 - 0.951057i) q^{64} +(1.26948 + 3.90705i) q^{65} +(0.438591 + 0.318655i) q^{66} -7.49953 q^{67} +5.73404 q^{68} +(-6.13886 - 4.46015i) q^{69} +(1.31796 - 0.957557i) q^{70} +(-8.09841 + 5.88384i) q^{71} +(-0.309017 + 0.951057i) q^{72} +(-5.10048 - 3.70571i) q^{73} +(-1.16496 + 3.58538i) q^{74} +(0.309017 + 0.951057i) q^{75} +(5.14150 - 3.73552i) q^{76} +(-0.272917 - 0.839951i) q^{77} +(1.26948 + 3.90705i) q^{78} +(4.55240 - 3.30751i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(0.309017 - 0.951057i) q^{81} +(6.99010 + 5.07861i) q^{82} +(-3.17470 + 9.77074i) q^{83} +(1.31796 - 0.957557i) q^{84} +(4.63894 - 3.37039i) q^{85} +(0.967622 + 0.703018i) q^{86} -0.166041 q^{87} -0.542128 q^{88} +(2.10428 + 1.52885i) q^{89} +(0.309017 + 0.951057i) q^{90} +(2.06810 - 6.36495i) q^{91} +7.58805 q^{92} +(-2.65075 - 4.89628i) q^{93} -2.19959 q^{94} +(1.96388 - 6.04420i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(15.1329 + 10.9947i) q^{97} +4.34606 q^{98} +0.542128 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 4 q^{3} - 4 q^{4} - 16 q^{5} - 16 q^{6} - 7 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 - 4 * q^3 - 4 * q^4 - 16 * q^5 - 16 * q^6 - 7 * q^7 + 4 * q^8 - 4 * q^9	\( 16 q + 4 q^{2} - 4 q^{3} - 4 q^{4} - 16 q^{5} - 16 q^{6} - 7 q^{7} + 4 q^{8} - 4 q^{9} - 4 q^{10} + 4 q^{11} - 4 q^{12} + 2 q^{13} + 7 q^{14} + 4 q^{15} - 4 q^{16} + 5 q^{17} + 4 q^{18} - 2 q^{19} + 4 q^{20} + 8 q^{21} - 4 q^{22} - 4 q^{23} + 4 q^{24} + 16 q^{25} + 8 q^{26} - 4 q^{27} + 8 q^{28} + 5 q^{29} + 16 q^{30} - q^{31} - 16 q^{32} - q^{33} - 5 q^{34} + 7 q^{35} + 16 q^{36} - 20 q^{37} - 3 q^{38} + 2 q^{39} - 4 q^{40} - 17 q^{41} + 7 q^{42} - 4 q^{43} - q^{44} + 4 q^{45} - 6 q^{46} + 2 q^{47} - 4 q^{48} - 21 q^{49} + 4 q^{50} + 5 q^{51} + 2 q^{52} + 9 q^{53} + 4 q^{54} - 4 q^{55} + 2 q^{56} - 2 q^{57} - 5 q^{58} - 3 q^{59} + 4 q^{60} + 70 q^{61} - 4 q^{62} - 2 q^{63} - 4 q^{64} - 2 q^{65} - 4 q^{66} - 66 q^{67} - 20 q^{68} - 4 q^{69} - 7 q^{70} - 25 q^{71} + 4 q^{72} - 10 q^{73} - 15 q^{74} - 4 q^{75} + 3 q^{76} + 26 q^{77} - 2 q^{78} + 14 q^{79} + 4 q^{80} - 4 q^{81} + 17 q^{82} + 20 q^{83} - 7 q^{84} - 5 q^{85} - 6 q^{86} - 20 q^{87} + 6 q^{88} - 13 q^{89} - 4 q^{90} - 4 q^{91} - 4 q^{92} + 4 q^{93} - 12 q^{94} + 2 q^{95} + 4 q^{96} + 55 q^{97} - 14 q^{98} - 6 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 4 * q^3 - 4 * q^4 - 16 * q^5 - 16 * q^6 - 7 * q^7 + 4 * q^8 - 4 * q^9 - 4 * q^10 + 4 * q^11 - 4 * q^12 + 2 * q^13 + 7 * q^14 + 4 * q^15 - 4 * q^16 + 5 * q^17 + 4 * q^18 - 2 * q^19 + 4 * q^20 + 8 * q^21 - 4 * q^22 - 4 * q^23 + 4 * q^24 + 16 * q^25 + 8 * q^26 - 4 * q^27 + 8 * q^28 + 5 * q^29 + 16 * q^30 - q^31 - 16 * q^32 - q^33 - 5 * q^34 + 7 * q^35 + 16 * q^36 - 20 * q^37 - 3 * q^38 + 2 * q^39 - 4 * q^40 - 17 * q^41 + 7 * q^42 - 4 * q^43 - q^44 + 4 * q^45 - 6 * q^46 + 2 * q^47 - 4 * q^48 - 21 * q^49 + 4 * q^50 + 5 * q^51 + 2 * q^52 + 9 * q^53 + 4 * q^54 - 4 * q^55 + 2 * q^56 - 2 * q^57 - 5 * q^58 - 3 * q^59 + 4 * q^60 + 70 * q^61 - 4 * q^62 - 2 * q^63 - 4 * q^64 - 2 * q^65 - 4 * q^66 - 66 * q^67 - 20 * q^68 - 4 * q^69 - 7 * q^70 - 25 * q^71 + 4 * q^72 - 10 * q^73 - 15 * q^74 - 4 * q^75 + 3 * q^76 + 26 * q^77 - 2 * q^78 + 14 * q^79 + 4 * q^80 - 4 * q^81 + 17 * q^82 + 20 * q^83 - 7 * q^84 - 5 * q^85 - 6 * q^86 - 20 * q^87 + 6 * q^88 - 13 * q^89 - 4 * q^90 - 4 * q^91 - 4 * q^92 + 4 * q^93 - 12 * q^94 + 2 * q^95 + 4 * q^96 + 55 * q^97 - 14 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−1.00000			−0.408248
$7$	1.31796	+	0.957557i	0.498144	+	0.361922i	0.808307	−	0.588761i	$-0.200384\pi$
$7$	1.31796	+	0.957557i	0.498144	+	0.361922i	−0.310164	+	0.950683i	$0.600384\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	0.309017	−	0.951057i	0.0977198	−	0.300750i
$11$	−0.438591	−	0.318655i	−0.132240	−	0.0960781i	0.519699	−	0.854350i	$-0.326044\pi$
$11$	−0.438591	−	0.318655i	−0.132240	−	0.0960781i	−0.651939	+	0.758271i	$0.726044\pi$
$12$	0.309017	−	0.951057i	0.0892055	−	0.274546i
$13$	−1.26948	−	3.90705i	−0.352090	−	1.08362i	−0.957678	−	0.287843i	$-0.907062\pi$
$13$	−1.26948	−	3.90705i	−0.352090	−	1.08362i	0.605587	−	0.795779i	$-0.292938\pi$
$14$	−1.31796	+	0.957557i	−0.352241	+	0.255918i
$15$	−0.309017	−	0.951057i	−0.0797878	−	0.245562i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−4.63894	+	3.37039i	−1.12511	+	0.817439i	−0.984975	−	0.172694i	$-0.944753\pi$
$17$	−4.63894	+	3.37039i	−1.12511	+	0.817439i	−0.140132	+	0.990133i	$0.544753\pi$
$18$	−0.309017	−	0.951057i	−0.0728360	−	0.224166i
$19$	−1.96388	+	6.04420i	−0.450545	+	1.38663i	0.425742	+	0.904845i	$0.360013\pi$
$19$	−1.96388	+	6.04420i	−0.450545	+	1.38663i	−0.876287	+	0.481790i	$0.839987\pi$
$20$	0.809017	+	0.587785i	0.180902	+	0.131433i
$21$	−0.503417	+	1.54936i	−0.109855	+	0.338098i
$22$	0.438591	−	0.318655i	0.0935079	−	0.0679374i
$23$	−6.13886	+	4.46015i	−1.28004	+	0.930005i	−0.999554	−	0.0298530i	$-0.990496\pi$
$23$	−6.13886	+	4.46015i	−1.28004	+	0.930005i	−0.280487	+	0.959858i	$0.590496\pi$
$24$	0.809017	+	0.587785i	0.165140	+	0.119981i
$25$	1.00000			0.200000
$26$	4.10812			0.805669
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−0.503417	−	1.54936i	−0.0951369	−	0.292801i
$29$	−0.0513096	+	0.157915i	−0.00952795	+	0.0293240i	−0.955707	−	0.294318i	$-0.904907\pi$
$29$	−0.0513096	+	0.157915i	−0.00952795	+	0.0293240i	0.946180	+	0.323642i	$0.104907\pi$
$30$	1.00000			0.182574
$31$	−5.47576	+	1.00798i	−0.983476	+	0.181039i
$31$	−5.47576	+	1.00798i	−0.983476	+	0.181039i
$32$	−1.00000			−0.176777
$33$	0.167527	−	0.515594i	0.0291627	−	0.0897535i
$34$	−1.77192	−	5.45340i	−0.303881	−	0.935250i
$35$	−1.31796	−	0.957557i	−0.222777	−	0.161857i
$36$	1.00000			0.166667
$37$	3.76990			0.619767			0.309884	−	0.950775i	$-0.399710\pi$
$37$	3.76990			0.619767			0.309884	+	0.950775i	$0.399710\pi$
$38$	−5.14150	−	3.73552i	−0.834062	−	0.605981i
$39$	3.32354	−	2.41469i	0.532192	−	0.386660i
$40$	−0.809017	+	0.587785i	−0.127917	+	0.0929370i
$41$	2.66998	−	8.21736i	0.416981	−	1.28334i	−0.493486	−	0.869754i	$-0.664277\pi$
$41$	2.66998	−	8.21736i	0.416981	−	1.28334i	0.910467	−	0.413582i	$-0.135723\pi$
$42$	−1.31796	−	0.957557i	−0.203366	−	0.147754i
$43$	0.369599	−	1.13751i	0.0563633	−	0.173468i	−0.918912	−	0.394463i	$-0.870930\pi$
$43$	0.369599	−	1.13751i	0.0563633	−	0.173468i	0.975275	+	0.220995i	$0.0709305\pi$
$44$	0.167527	+	0.515594i	0.0252556	+	0.0777288i
$45$	0.809017	−	0.587785i	0.120601	−	0.0876219i
$46$	−2.34484	−	7.21667i	−0.345727	−	1.06404i
$47$	0.679710	+	2.09193i	0.0991460	+	0.305140i	0.988312	−	0.152445i	$-0.0487146\pi$
$47$	0.679710	+	2.09193i	0.0991460	+	0.305140i	−0.889166	+	0.457585i	$0.848715\pi$
$48$	−0.809017	+	0.587785i	−0.116772	+	0.0848395i
$49$	−1.34301	−	4.13335i	−0.191858	−	0.590478i
$50$	−0.309017	+	0.951057i	−0.0437016	+	0.134500i
$51$	−4.63894	−	3.37039i	−0.649581	−	0.471948i
$52$	−1.26948	+	3.90705i	−0.176045	+	0.541811i
$53$	−11.3745	+	8.26405i	−1.56241	+	1.13515i	−0.628405	+	0.777886i	$0.716292\pi$
$53$	−11.3745	+	8.26405i	−1.56241	+	1.13515i	−0.934002	+	0.357268i	$0.883708\pi$
$54$	0.809017	−	0.587785i	0.110093	−	0.0799874i
$55$	0.438591	+	0.318655i	0.0591396	+	0.0429674i
$56$	1.62909			0.217697
$57$	−6.35525			−0.841773
$58$	−0.134330	−	0.0975966i	−0.0176384	−	0.0128151i
$59$	−1.83265	−	5.64033i	−0.238591	−	0.734308i	−0.996625	−	0.0820926i	$-0.973840\pi$
$59$	−1.83265	−	5.64033i	−0.238591	−	0.734308i	0.758034	−	0.652216i	$-0.226160\pi$
$60$	−0.309017	+	0.951057i	−0.0398939	+	0.122781i
$61$	10.3419			1.32415			0.662075	−	0.749438i	$-0.269676\pi$
$61$	10.3419			1.32415			0.662075	+	0.749438i	$0.269676\pi$
$62$	0.733458	−	5.51924i	0.0931492	−	0.700945i
$63$	−1.62909			−0.205246
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	1.26948	+	3.90705i	0.157459	+	0.484610i
$66$	0.438591	+	0.318655i	0.0539868	+	0.0392237i
$67$	−7.49953			−0.916213			−0.458107	−	0.888897i	$-0.651472\pi$
$67$	−7.49953			−0.916213			−0.458107	+	0.888897i	$0.651472\pi$
$68$	5.73404			0.695355
$69$	−6.13886	−	4.46015i	−0.739032	−	0.536938i
$70$	1.31796	−	0.957557i	0.157527	−	0.114450i
$71$	−8.09841	+	5.88384i	−0.961105	+	0.698283i	−0.953407	−	0.301687i	$-0.902450\pi$
$71$	−8.09841	+	5.88384i	−0.961105	+	0.698283i	−0.00769766	+	0.999970i	$0.502450\pi$
$72$	−0.309017	+	0.951057i	−0.0364180	+	0.112083i
$73$	−5.10048	−	3.70571i	−0.596966	−	0.433721i	0.247835	−	0.968802i	$-0.420281\pi$
$73$	−5.10048	−	3.70571i	−0.596966	−	0.433721i	−0.844801	+	0.535081i	$0.820281\pi$
$74$	−1.16496	+	3.58538i	−0.135424	+	0.416792i
$75$	0.309017	+	0.951057i	0.0356822	+	0.109819i
$76$	5.14150	−	3.73552i	0.589771	−	0.428494i
$77$	−0.272917	−	0.839951i	−0.0311017	−	0.0957213i
$78$	1.26948	+	3.90705i	0.143740	+	0.442387i
$79$	4.55240	−	3.30751i	0.512185	−	0.372124i	−0.301467	−	0.953477i	$-0.597476\pi$
$79$	4.55240	−	3.30751i	0.512185	−	0.372124i	0.813652	+	0.581352i	$0.197476\pi$
$80$	−0.309017	−	0.951057i	−0.0345492	−	0.106331i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	6.99010	+	5.07861i	0.771928	+	0.560838i
$83$	−3.17470	+	9.77074i	−0.348469	+	1.07248i	0.611231	+	0.791452i	$0.290675\pi$
$83$	−3.17470	+	9.77074i	−0.348469	+	1.07248i	−0.959700	+	0.281026i	$0.909325\pi$
$84$	1.31796	−	0.957557i	0.143802	−	0.104478i
$85$	4.63894	−	3.37039i	0.503163	−	0.365570i
$86$	0.967622	+	0.703018i	0.104341	+	0.0758084i
$87$	−0.166041			−0.0178015
$88$	−0.542128			−0.0577910
$89$	2.10428	+	1.52885i	0.223053	+	0.162058i	0.693700	−	0.720264i	$-0.255979\pi$
$89$	2.10428	+	1.52885i	0.223053	+	0.162058i	−0.470647	+	0.882322i	$0.655979\pi$
$90$	0.309017	+	0.951057i	0.0325733	+	0.100250i
$91$	2.06810	−	6.36495i	0.216796	−	0.667228i
$92$	7.58805			0.791109
$93$	−2.65075	−	4.89628i	−0.274870	−	0.507720i
$94$	−2.19959			−0.226870
$95$	1.96388	−	6.04420i	0.201490	−	0.620122i
$96$	−0.309017	−	0.951057i	−0.0315389	−	0.0970668i
$97$	15.1329	+	10.9947i	1.53651	+	1.11634i	0.952477	+	0.304609i	$0.0985259\pi$
$97$	15.1329	+	10.9947i	1.53651	+	1.11634i	0.584032	+	0.811730i	$0.301474\pi$
$98$	4.34606			0.439018
$99$	0.542128			0.0544859
$100$	−0.809017	−	0.587785i	−0.0809017	−	0.0587785i
$101$	−11.6072	+	8.43315i	−1.15496	+	0.839129i	−0.989133	−	0.147025i	$-0.953030\pi$
$101$	−11.6072	+	8.43315i	−1.15496	+	0.839129i	−0.165830	+	0.986154i	$0.553030\pi$
$102$	4.63894	−	3.37039i	0.459323	−	0.333718i
$103$	0.180501	−	0.555526i	0.0177853	−	0.0547376i	−0.941770	−	0.336258i	$-0.890839\pi$
$103$	0.180501	−	0.555526i	0.0177853	−	0.0547376i	0.959555	+	0.281520i	$0.0908386\pi$
$104$	−3.32354	−	2.41469i	−0.325900	−	0.236780i
$105$	0.503417	−	1.54936i	0.0491285	−	0.151202i
$106$	−4.34467	−	13.3715i	−0.421992	−	1.29876i
$107$	16.1673	−	11.7462i	1.56295	−	1.13555i	0.629414	−	0.777070i	$-0.283295\pi$
$107$	16.1673	−	11.7462i	1.56295	−	1.13555i	0.933537	−	0.358480i	$-0.116705\pi$
$108$	0.309017	+	0.951057i	0.0297352	+	0.0915155i
$109$	−3.21234	−	9.88656i	−0.307686	−	0.946961i	−0.978661	−	0.205481i	$-0.934124\pi$
$109$	−3.21234	−	9.88656i	−0.307686	−	0.946961i	0.670975	−	0.741480i	$-0.265876\pi$
$110$	−0.438591	+	0.318655i	−0.0418180	+	0.0303825i
$111$	1.16496	+	3.58538i	0.110573	+	0.340310i
$112$	−0.503417	+	1.54936i	−0.0475685	+	0.146401i
$113$	−7.87621	−	5.72240i	−0.740932	−	0.538318i	0.152071	−	0.988370i	$-0.451406\pi$
$113$	−7.87621	−	5.72240i	−0.740932	−	0.538318i	−0.893003	+	0.450051i	$0.851406\pi$
$114$	1.96388	−	6.04420i	0.183934	−	0.566091i
$115$	6.13886	−	4.46015i	0.572452	−	0.415911i
$116$	0.134330	−	0.0975966i	0.0124722	−	0.00906162i
$117$	3.32354	+	2.41469i	0.307261	+	0.223238i
$118$	5.93059			0.545955
$119$	−9.34129			−0.856314
$120$	−0.809017	−	0.587785i	−0.0738528	−	0.0536572i
$121$	−3.30837	−	10.1821i	−0.300761	−	0.925646i
$122$	−3.19583	+	9.83577i	−0.289337	+	0.890489i
$123$	8.64024			0.779064
$124$	5.02246	+	2.40310i	0.451030	+	0.215805i
$125$	−1.00000			−0.0894427
$126$	0.503417	−	1.54936i	0.0448480	−	0.138028i
$127$	4.82199	+	14.8405i	0.427882	+	1.31689i	0.900207	+	0.435461i	$0.143415\pi$
$127$	4.82199	+	14.8405i	0.427882	+	1.31689i	−0.472325	+	0.881424i	$0.656585\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	1.19605			0.105306
$130$	−4.10812			−0.360306
$131$	10.9744	+	7.97334i	0.958834	+	0.696634i	0.952880	−	0.303348i	$-0.0981046\pi$
$131$	10.9744	+	7.97334i	0.958834	+	0.696634i	0.00595456	+	0.999982i	$0.498105\pi$
$132$	−0.438591	+	0.318655i	−0.0381744	+	0.0277353i
$133$	−8.37599	+	6.08551i	−0.726290	+	0.527681i
$134$	2.31748	−	7.13248i	0.200200	−	0.616152i
$135$	0.809017	+	0.587785i	0.0696291	+	0.0505885i
$136$	−1.77192	+	5.45340i	−0.151941	+	0.467625i
$137$	4.78270	+	14.7196i	0.408613	+	1.25758i	0.917840	+	0.396950i	$0.129931\pi$
$137$	4.78270	+	14.7196i	0.408613	+	1.25758i	−0.509227	+	0.860632i	$0.670069\pi$
$138$	6.13886	−	4.46015i	0.522575	−	0.379673i
$139$	4.06461	+	12.5096i	0.344755	+	1.06105i	0.961715	+	0.274053i	$0.0883644\pi$
$139$	4.06461	+	12.5096i	0.344755	+	1.06105i	−0.616959	+	0.786995i	$0.711636\pi$
$140$	0.503417	+	1.54936i	0.0425465	+	0.130945i
$141$	−1.77950	+	1.29289i	−0.149861	+	0.108881i
$142$	−3.09332	−	9.52025i	−0.259585	−	0.798922i
$143$	−0.688220	+	2.11812i	−0.0575519	+	0.177126i
$144$	−0.809017	−	0.587785i	−0.0674181	−	0.0489821i
$145$	0.0513096	−	0.157915i	0.00426103	−	0.0131141i
$146$	5.10048	−	3.70571i	0.422119	−	0.306687i
$147$	3.51603	−	2.55455i	0.289998	−	0.210696i
$148$	−3.04991	−	2.21589i	−0.250701	−	0.182145i
$149$	−10.0423			−0.822694			−0.411347	−	0.911479i	$-0.634941\pi$
$149$	−10.0423			−0.822694			−0.411347	+	0.911479i	$0.634941\pi$
$150$	−1.00000			−0.0816497
$151$	5.01888	+	3.64643i	0.408431	+	0.296742i	0.772966	−	0.634447i	$-0.218772\pi$
$151$	5.01888	+	3.64643i	0.408431	+	0.296742i	−0.364536	+	0.931189i	$0.618772\pi$
$152$	1.96388	+	6.04420i	0.159292	+	0.490249i
$153$	1.77192	−	5.45340i	0.143251	−	0.440881i
$154$	0.883177			0.0711684
$155$	5.47576	−	1.00798i	0.439824	−	0.0809629i
$156$	−4.10812			−0.328913
$157$	−4.41111	+	13.5760i	−0.352045	+	1.08348i	0.605658	+	0.795725i	$0.292910\pi$
$157$	−4.41111	+	13.5760i	−0.352045	+	1.08348i	−0.957703	+	0.287759i	$0.907090\pi$
$158$	1.73886	+	5.35167i	0.138336	+	0.425756i
$159$	−11.3745	−	8.26405i	−0.902056	−	0.655382i
$160$	1.00000			0.0790569
$161$	−12.3616			−0.974234
$162$	0.809017	+	0.587785i	0.0635624	+	0.0461808i
$163$	12.3147	−	8.94714i	0.964561	−	0.700794i	0.0103551	−	0.999946i	$-0.496704\pi$
$163$	12.3147	−	8.94714i	0.964561	−	0.700794i	0.954205	+	0.299152i	$0.0967038\pi$
$164$	−6.99010	+	5.07861i	−0.545835	+	0.396573i
$165$	−0.167527	+	0.515594i	−0.0130419	+	0.0401390i
$166$	−8.31149	−	6.03865i	−0.645096	−	0.468690i
$167$	−4.15781	+	12.7964i	−0.321741	+	0.990218i	0.651149	+	0.758950i	$0.274287\pi$
$167$	−4.15781	+	12.7964i	−0.321741	+	0.990218i	−0.972890	+	0.231268i	$0.925713\pi$
$168$	0.503417	+	1.54936i	0.0388395	+	0.119536i
$169$	−3.13627	+	2.27864i	−0.241252	+	0.175280i
$170$	1.77192	+	5.45340i	0.135900	+	0.418257i
$171$	−1.96388	−	6.04420i	−0.150182	−	0.462211i
$172$	−0.967622	+	0.703018i	−0.0737805	+	0.0536047i
$173$	−2.36286	−	7.27214i	−0.179645	−	0.552891i	0.820170	−	0.572120i	$-0.193879\pi$
$173$	−2.36286	−	7.27214i	−0.179645	−	0.552891i	−0.999815	+	0.0192291i	$0.993879\pi$
$174$	0.0513096	−	0.157915i	0.00388977	−	0.0119715i
$175$	1.31796	+	0.957557i	0.0996287	+	0.0723845i
$176$	0.167527	−	0.515594i	0.0126278	−	0.0388644i
$177$	4.79795	−	3.48591i	0.360636	−	0.262017i
$178$	−2.10428	+	1.52885i	−0.157723	+	0.114592i
$179$	8.17292	+	5.93797i	0.610873	+	0.443825i	0.849721	−	0.527232i	$-0.176770\pi$
$179$	8.17292	+	5.93797i	0.610873	+	0.443825i	−0.238849	+	0.971057i	$0.576770\pi$
$180$	−1.00000			−0.0745356
$181$	5.10679			0.379584			0.189792	−	0.981824i	$-0.439219\pi$
$181$	5.10679			0.379584			0.189792	+	0.981824i	$0.439219\pi$
$182$	5.41435	+	3.93376i	0.401339	+	0.291590i
$183$	3.19583	+	9.83577i	0.236243	+	0.727081i
$184$	−2.34484	+	7.21667i	−0.172864	+	0.532020i
$185$	−3.76990			−0.277168
$186$	5.47576	−	1.00798i	0.401502	−	0.0739087i
$187$	3.10858			0.227322
$188$	0.679710	−	2.09193i	0.0495730	−	0.152570i
$189$	−0.503417	−	1.54936i	−0.0366182	−	0.112699i
$190$	5.14150	+	3.73552i	0.373004	+	0.271003i
$191$	5.52582			0.399835			0.199917	−	0.979813i	$-0.435933\pi$
$191$	5.52582			0.399835			0.199917	+	0.979813i	$0.435933\pi$
$192$	1.00000			0.0721688
$193$	−14.0871	−	10.2349i	−1.01401	−	0.736722i	−0.0489644	−	0.998801i	$-0.515592\pi$
$193$	−14.0871	−	10.2349i	−1.01401	−	0.736722i	−0.965047	+	0.262078i	$0.915592\pi$
$194$	−15.1329	+	10.9947i	−1.08648	+	0.789371i
$195$	−3.32354	+	2.41469i	−0.238004	+	0.172920i
$196$	−1.34301	+	4.13335i	−0.0959289	+	0.295239i
$197$	18.4444	+	13.4007i	1.31411	+	0.954758i	0.999986	+	0.00537650i	$0.00171140\pi$
$197$	18.4444	+	13.4007i	1.31411	+	0.954758i	0.314126	+	0.949381i	$0.398289\pi$
$198$	−0.167527	+	0.515594i	−0.0119056	+	0.0366417i
$199$	−0.820882	−	2.52642i	−0.0581908	−	0.179093i	0.917736	−	0.397191i	$-0.130015\pi$
$199$	−0.820882	−	2.52642i	−0.0581908	−	0.179093i	−0.975927	+	0.218098i	$0.930015\pi$
$200$	0.809017	−	0.587785i	0.0572061	−	0.0415627i
$201$	−2.31748	−	7.13248i	−0.163463	−	0.503086i
$202$	−4.43357	−	13.6451i	−0.311945	−	0.960067i
$203$	−0.218836	+	0.158994i	−0.0153593	+	0.0111592i
$204$	1.77192	+	5.45340i	0.124059	+	0.381814i
$205$	−2.66998	+	8.21736i	−0.186480	+	0.573925i
$206$	0.472559	+	0.343334i	0.0329247	+	0.0239212i
$207$	2.34484	−	7.21667i	0.162977	−	0.501593i
$208$	3.32354	−	2.41469i	0.230446	−	0.167429i
$209$	2.78735	−	2.02513i	0.192805	−	0.140081i
$210$	1.31796	+	0.957557i	0.0909481	+	0.0660777i
$211$	−14.3277			−0.986357			−0.493178	−	0.869928i	$-0.664165\pi$
$211$	−14.3277			−0.986357			−0.493178	+	0.869928i	$0.664165\pi$
$212$	14.0596			0.965620
$213$	−8.09841	−	5.88384i	−0.554894	−	0.403154i
$214$	6.17536	+	19.0058i	0.422139	+	1.29921i
$215$	−0.369599	+	1.13751i	−0.0252064	+	0.0775774i
$216$	−1.00000			−0.0680414
$217$	−8.18206	−	3.91487i	−0.555434	−	0.265759i
$218$	10.3953			0.704062
$219$	1.94821	−	5.99597i	0.131648	−	0.405170i
$220$	−0.167527	−	0.515594i	−0.0112947	−	0.0347614i
$221$	19.0573	+	13.8459i	1.28193	+	0.931379i
$222$	−3.76990			−0.253019
$223$	−12.6546			−0.847415			−0.423707	−	0.905799i	$-0.639271\pi$
$223$	−12.6546			−0.847415			−0.423707	+	0.905799i	$0.639271\pi$
$224$	−1.31796	−	0.957557i	−0.0880602	−	0.0639795i
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$	7.87621	−	5.72240i	0.523918	−	0.380649i
$227$	3.03424	−	9.33842i	0.201389	−	0.619813i	−0.798453	−	0.602057i	$-0.794348\pi$
$227$	3.03424	−	9.33842i	0.201389	−	0.619813i	0.999842	−	0.0177556i	$-0.00565209\pi$
$228$	5.14150	+	3.73552i	0.340504	+	0.247391i
$229$	−0.322524	+	0.992628i	−0.0213130	+	0.0655947i	−0.961147	−	0.276036i	$-0.910979\pi$
$229$	−0.322524	+	0.992628i	−0.0213130	+	0.0655947i	0.939834	+	0.341631i	$0.110979\pi$
$230$	2.34484	+	7.21667i	0.154614	+	0.475853i
$231$	0.714505	−	0.519118i	0.0470110	−	0.0341555i
$232$	0.0513096	+	0.157915i	0.00336864	+	0.0103676i
$233$	7.41181	+	22.8112i	0.485564	+	1.49441i	0.831163	+	0.556029i	$0.187676\pi$
$233$	7.41181	+	22.8112i	0.485564	+	1.49441i	−0.345600	+	0.938382i	$0.612324\pi$
$234$	−3.32354	+	2.41469i	−0.217267	+	0.157853i
$235$	−0.679710	−	2.09193i	−0.0443394	−	0.136463i
$236$	−1.83265	+	5.64033i	−0.119296	+	0.367154i
$237$	4.55240	+	3.30751i	0.295710	+	0.214846i
$238$	2.88662	−	8.88409i	0.187112	−	0.575870i
$239$	1.64370	−	1.19422i	0.106322	−	0.0772474i	−0.533354	−	0.845892i	$-0.679069\pi$
$239$	1.64370	−	1.19422i	0.106322	−	0.0772474i	0.639676	+	0.768645i	$0.279069\pi$
$240$	0.809017	−	0.587785i	0.0522218	−	0.0379414i
$241$	−2.65800	−	1.93115i	−0.171217	−	0.124397i	0.498877	−	0.866673i	$-0.333746\pi$
$241$	−2.65800	−	1.93115i	−0.171217	−	0.124397i	−0.670094	+	0.742277i	$0.733746\pi$
$242$	10.7061			0.688214
$243$	1.00000			0.0641500
$244$	−8.36680	−	6.07884i	−0.535630	−	0.389158i
$245$	1.34301	+	4.13335i	0.0858015	+	0.264070i
$246$	−2.66998	+	8.21736i	−0.170232	+	0.523920i
$247$	26.1081			1.66122
$248$	−3.83751	+	4.03405i	−0.243682	+	0.256162i
$249$	−10.2736			−0.651060
$250$	0.309017	−	0.951057i	0.0195440	−	0.0601501i
$251$	5.84254	+	17.9815i	0.368778	+	1.13498i	0.947582	+	0.319514i	$0.103520\pi$
$251$	5.84254	+	17.9815i	0.368778	+	1.13498i	−0.578804	+	0.815467i	$0.696480\pi$
$252$	1.31796	+	0.957557i	0.0830239	+	0.0603204i
$253$	4.11370			0.258626
$254$	−15.6043			−0.979099
$255$	4.63894	+	3.37039i	0.290502	+	0.211062i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−15.8658	+	11.5272i	−0.989683	+	0.719047i	−0.959852	−	0.280508i	$-0.909497\pi$
$257$	−15.8658	+	11.5272i	−0.989683	+	0.719047i	−0.0298312	+	0.999555i	$0.509497\pi$
$258$	−0.369599	+	1.13751i	−0.0230102	+	0.0708181i
$259$	4.96859	+	3.60989i	0.308733	+	0.224308i
$260$	1.26948	−	3.90705i	0.0787297	−	0.242305i
$261$	−0.0513096	−	0.157915i	−0.00317598	−	0.00977467i
$262$	−10.9744	+	7.97334i	−0.677998	+	0.492595i
$263$	−1.46774	−	4.51724i	−0.0905047	−	0.278545i	0.895551	−	0.444958i	$-0.146781\pi$
$263$	−1.46774	−	4.51724i	−0.0905047	−	0.278545i	−0.986056	+	0.166413i	$0.946781\pi$
$264$	−0.167527	−	0.515594i	−0.0103106	−	0.0317326i
$265$	11.3745	−	8.26405i	0.698729	−	0.507657i
$266$	−3.19934	−	9.84656i	−0.196164	−	0.603731i
$267$	−0.803764	+	2.47373i	−0.0491896	+	0.151390i
$268$	6.06725	+	4.40811i	0.370616	+	0.269268i
$269$	9.54466	−	29.3754i	0.581948	−	1.79105i	−0.0292467	−	0.999572i	$-0.509311\pi$
$269$	9.54466	−	29.3754i	0.581948	−	1.79105i	0.611195	−	0.791480i	$-0.290689\pi$
$270$	−0.809017	+	0.587785i	−0.0492352	+	0.0357715i
$271$	5.32325	−	3.86757i	0.323364	−	0.234938i	−0.414245	−	0.910165i	$-0.635954\pi$
$271$	5.32325	−	3.86757i	0.323364	−	0.234938i	0.737610	+	0.675227i	$0.235954\pi$
$272$	−4.63894	−	3.37039i	−0.281277	−	0.204360i
$273$	6.69251			0.405049
$274$	−15.4771			−0.935008
$275$	−0.438591	−	0.318655i	−0.0264480	−	0.0192156i
$276$	2.34484	+	7.21667i	0.141143	+	0.434392i
$277$	−4.94338	+	15.2141i	−0.297019	+	0.914130i	0.685517	+	0.728056i	$0.259576\pi$
$277$	−4.94338	+	15.2141i	−0.297019	+	0.914130i	−0.982536	+	0.186073i	$0.940424\pi$
$278$	−13.1533			−0.788885
$279$	3.83751	−	4.03405i	0.229746	−	0.241512i
$280$	−1.62909			−0.0973569
$281$	3.72032	−	11.4500i	0.221936	−	0.683048i	−0.776653	−	0.629929i	$-0.783084\pi$
$281$	3.72032	−	11.4500i	0.221936	−	0.683048i	0.998588	−	0.0531185i	$-0.0169161\pi$
$282$	−0.679710	−	2.09193i	−0.0404762	−	0.124573i
$283$	26.5821	+	19.3130i	1.58014	+	1.14804i	0.916530	+	0.399965i	$0.130978\pi$
$283$	26.5821	+	19.3130i	1.58014	+	1.14804i	0.663613	+	0.748076i	$0.269022\pi$
$284$	10.0102			0.593995
$285$	6.35525			0.376452
$286$	−1.80178	−	1.30907i	−0.106542	−	0.0774071i
$287$	11.3875	−	8.27352i	0.672184	−	0.488371i
$288$	0.809017	−	0.587785i	0.0476718	−	0.0346356i
$289$	4.90696	−	15.1021i	0.288644	−	0.888356i
$290$	0.134330	+	0.0975966i	0.00788814	+	0.00573107i
$291$	−5.78024	+	17.7898i	−0.338844	+	1.04285i
$292$	1.94821	+	5.99597i	0.114010	+	0.350888i
$293$	2.44794	−	1.77853i	0.143010	−	0.103903i	−0.513980	−	0.857802i	$-0.671829\pi$
$293$	2.44794	−	1.77853i	0.143010	−	0.103903i	0.656990	+	0.753899i	$0.271829\pi$
$294$	1.34301	+	4.13335i	0.0783257	+	0.241062i
$295$	1.83265	+	5.64033i	0.106701	+	0.328393i
$296$	3.04991	−	2.21589i	0.177272	−	0.128796i
$297$	0.167527	+	0.515594i	0.00972089	+	0.0299178i
$298$	3.10323	−	9.55075i	0.179765	−	0.553260i
$299$	25.2192	+	18.3228i	1.45846	+	1.05964i
$300$	0.309017	−	0.951057i	0.0178411	−	0.0549093i
$301$	1.57635	−	1.14528i	0.0908591	−	0.0660130i
$302$	−5.01888	+	3.64643i	−0.288804	+	0.209828i
$303$	−11.6072	−	8.43315i	−0.666818	−	0.484472i
$304$	−6.35525			−0.364498
$305$	−10.3419			−0.592178
$306$	4.63894	+	3.37039i	0.265190	+	0.192672i
$307$	9.06677	+	27.9046i	0.517468	+	1.59260i	0.778747	+	0.627339i	$0.215856\pi$
$307$	9.06677	+	27.9046i	0.517468	+	1.59260i	−0.261279	+	0.965263i	$0.584144\pi$
$308$	−0.272917	+	0.839951i	−0.0155509	+	0.0478607i
$309$	0.584115			0.0332291
$310$	−0.733458	+	5.51924i	−0.0416576	+	0.313472i
$311$	−10.6760			−0.605380			−0.302690	−	0.953089i	$-0.597885\pi$
$311$	−10.6760			−0.605380			−0.302690	+	0.953089i	$0.597885\pi$
$312$	1.26948	−	3.90705i	0.0718701	−	0.221193i
$313$	9.05134	+	27.8572i	0.511612	+	1.57458i	0.789363	+	0.613927i	$0.210411\pi$
$313$	9.05134	+	27.8572i	0.511612	+	1.57458i	−0.277751	+	0.960653i	$0.589589\pi$
$314$	−11.5484	−	8.39044i	−0.651717	−	0.473500i
$315$	1.62909			0.0917890
$316$	−5.62708			−0.316548
$317$	−11.1210	−	8.07988i	−0.624618	−	0.453811i	0.229914	−	0.973211i	$-0.426156\pi$
$317$	−11.1210	−	8.07988i	−0.624618	−	0.453811i	−0.854531	+	0.519400i	$0.826156\pi$
$318$	11.3745	−	8.26405i	0.637850	−	0.463425i
$319$	0.0728241	−	0.0529098i	0.00407737	−	0.00296238i
$320$	−0.309017	+	0.951057i	−0.0172746	+	0.0531657i
$321$	16.1673	+	11.7462i	0.902370	+	0.655610i
$322$	3.81996	−	11.7566i	0.212878	−	0.655171i
$323$	−11.2610	−	34.6577i	−0.626577	−	1.92841i
$324$	−0.809017	+	0.587785i	−0.0449454	+	0.0326547i
$325$	−1.26948	−	3.90705i	−0.0704180	−	0.216724i
$326$	4.70379	+	14.4768i	0.260519	+	0.801795i
$327$	8.41001	−	6.11023i	0.465075	−	0.337897i
$328$	−2.66998	−	8.21736i	−0.147425	−	0.453728i
$329$	−1.10731	+	3.40795i	−0.0610481	+	0.187887i
$330$	−0.438591	−	0.318655i	−0.0241436	−	0.0175414i
$331$	4.06527	−	12.5116i	0.223447	−	0.687700i	−0.774998	−	0.631963i	$-0.782249\pi$
$331$	4.06527	−	12.5116i	0.223447	−	0.687700i	0.998446	−	0.0557366i	$-0.0177507\pi$
$332$	8.31149	−	6.03865i	0.456152	−	0.331414i
$333$	−3.04991	+	2.21589i	−0.167134	+	0.121430i
$334$	−10.8853	−	7.90863i	−0.595617	−	0.432741i
$335$	7.49953			0.409743
$336$	−1.62909			−0.0888743
$337$	−29.4245	−	21.3781i	−1.60285	−	1.16454i	−0.881755	−	0.471708i	$-0.843638\pi$
$337$	−29.4245	−	21.3781i	−1.60285	−	1.16454i	−0.721098	−	0.692833i	$-0.756362\pi$
$338$	−1.19795	−	3.68691i	−0.0651599	−	0.200542i
$339$	3.00844	−	9.25904i	0.163396	−	0.502882i
$340$	−5.73404			−0.310972
$341$	2.72282	+	1.30279i	0.147449	+	0.0705499i
$342$	6.35525			0.343652
$343$	5.71180	−	17.5791i	0.308408	−	0.949183i
$344$	−0.369599	−	1.13751i	−0.0199274	−	0.0613303i
$345$	6.13886	+	4.46015i	0.330505	+	0.240126i
$346$	7.64638			0.411072
$347$	1.87275			0.100535			0.0502673	−	0.998736i	$-0.483993\pi$
$347$	1.87275			0.100535			0.0502673	+	0.998736i	$0.483993\pi$
$348$	0.134330	+	0.0975966i	0.00720085	+	0.00523173i
$349$	−18.8907	+	13.7249i	−1.01120	+	0.734676i	−0.964459	−	0.264231i	$-0.914882\pi$
$349$	−18.8907	+	13.7249i	−1.01120	+	0.734676i	−0.0467357	+	0.998907i	$0.514882\pi$
$350$	−1.31796	+	0.957557i	−0.0704481	+	0.0511836i
$351$	−1.26948	+	3.90705i	−0.0677598	+	0.208543i
$352$	0.438591	+	0.318655i	0.0233770	+	0.0169844i
$353$	−0.327063	+	1.00660i	−0.0174078	+	0.0535758i	−0.959383	−	0.282106i	$-0.908967\pi$
$353$	−0.327063	+	1.00660i	−0.0174078	+	0.0535758i	0.941975	+	0.335682i	$0.108967\pi$
$354$	1.83265	+	5.64033i	0.0974045	+	0.299780i
$355$	8.09841	−	5.88384i	0.429819	−	0.312282i
$356$	−0.803764	−	2.47373i	−0.0425994	−	0.131108i
$357$	−2.88662	−	8.88409i	−0.152776	−	0.470196i
$358$	−8.17292	+	5.93797i	−0.431952	+	0.313832i
$359$	−10.1712	−	31.3036i	−0.536813	−	1.65214i	−0.739698	−	0.672939i	$-0.765032\pi$
$359$	−10.1712	−	31.3036i	−0.536813	−	1.65214i	0.202884	−	0.979203i	$-0.434968\pi$
$360$	0.309017	−	0.951057i	0.0162866	−	0.0501251i
$361$	−17.3042	−	12.5722i	−0.910747	−	0.661696i
$362$	−1.57808	+	4.85684i	−0.0829422	+	0.255270i
$363$	8.66141	−	6.29289i	0.454606	−	0.330291i
$364$	−5.41435	+	3.93376i	−0.283789	+	0.206185i
$365$	5.10048	+	3.70571i	0.266971	+	0.193966i
$366$	−10.3419			−0.540582
$367$	16.5155			0.862101			0.431050	−	0.902328i	$-0.358143\pi$
$367$	16.5155			0.862101			0.431050	+	0.902328i	$0.358143\pi$
$368$	−6.13886	−	4.46015i	−0.320010	−	0.232501i
$369$	2.66998	+	8.21736i	0.138994	+	0.427779i
$370$	1.16496	−	3.58538i	0.0605635	−	0.186395i
$371$	−22.9045			−1.18914
$372$	−0.733458	+	5.51924i	−0.0380280	+	0.286159i
$373$	−1.74350			−0.0902748			−0.0451374	−	0.998981i	$-0.514373\pi$
$373$	−1.74350			−0.0902748			−0.0451374	+	0.998981i	$0.514373\pi$
$374$	−0.960606	+	2.95644i	−0.0496717	+	0.152874i
$375$	−0.309017	−	0.951057i	−0.0159576	−	0.0491123i
$376$	1.77950	+	1.29289i	0.0917710	+	0.0666755i
$377$	0.682117			0.0351308
$378$	1.62909			0.0837915
$379$	5.17094	+	3.75691i	0.265614	+	0.192980i	0.712618	−	0.701552i	$-0.247509\pi$
$379$	5.17094	+	3.75691i	0.265614	+	0.192980i	−0.447005	+	0.894532i	$0.647509\pi$
$380$	−5.14150	+	3.73552i	−0.263754	+	0.191628i
$381$	−12.6241	+	9.17196i	−0.646754	+	0.469894i
$382$	−1.70757	+	5.25537i	−0.0873671	+	0.268888i
$383$	−13.8489	−	10.0618i	−0.707645	−	0.514134i	0.174768	−	0.984610i	$-0.444082\pi$
$383$	−13.8489	−	10.0618i	−0.707645	−	0.514134i	−0.882413	+	0.470476i	$0.844082\pi$
$384$	−0.309017	+	0.951057i	−0.0157695	+	0.0485334i
$385$	0.272917	+	0.839951i	0.0139091	+	0.0428079i
$386$	14.0871	−	10.2349i	0.717014	−	0.520941i
$387$	0.369599	+	1.13751i	0.0187878	+	0.0578228i
$388$	−5.78024	−	17.7898i	−0.293447	−	0.903138i
$389$	6.35159	−	4.61470i	0.322038	−	0.233975i	−0.415006	−	0.909818i	$-0.636221\pi$
$389$	6.35159	−	4.61470i	0.322038	−	0.233975i	0.737045	+	0.675844i	$0.236221\pi$
$390$	−1.26948	−	3.90705i	−0.0642826	−	0.197841i
$391$	13.4454	−	41.3807i	0.679963	−	2.09271i
$392$	−3.51603	−	2.55455i	−0.177587	−	0.129024i
$393$	−4.19183	+	12.9011i	−0.211450	+	0.650776i
$394$	−18.4444	+	13.4007i	−0.929217	+	0.675116i
$395$	−4.55240	+	3.30751i	−0.229056	+	0.166419i
$396$	−0.438591	−	0.318655i	−0.0220400	−	0.0160130i
$397$	−10.7508			−0.539569			−0.269784	−	0.962921i	$-0.586952\pi$
$397$	−10.7508			−0.539569			−0.269784	+	0.962921i	$0.586952\pi$
$398$	2.65643			0.133155
$399$	−8.37599	−	6.08551i	−0.419324	−	0.304657i
$400$	0.309017	+	0.951057i	0.0154508	+	0.0475528i
$401$	1.75898	−	5.41359i	0.0878394	−	0.270342i	−0.897482	−	0.441051i	$-0.854606\pi$
$401$	1.75898	−	5.41359i	0.0878394	−	0.270342i	0.985321	+	0.170709i	$0.0546058\pi$
$402$	7.49953			0.374043
$403$	10.8896	+	20.1145i	0.542449	+	1.00197i
$404$	14.3473			0.713806
$405$	−0.309017	+	0.951057i	−0.0153552	+	0.0472584i
$406$	−0.0835880	−	0.257258i	−0.00414840	−	0.0127675i
$407$	−1.65344	−	1.20130i	−0.0819581	−	0.0595460i
$408$	−5.73404			−0.283877
$409$	−9.29072			−0.459396			−0.229698	−	0.973262i	$-0.573774\pi$
$409$	−9.29072			−0.459396			−0.229698	+	0.973262i	$0.573774\pi$
$410$	−6.99010	−	5.07861i	−0.345217	−	0.250815i
$411$	−12.5213	+	9.09723i	−0.617628	+	0.448733i
$412$	−0.472559	+	0.343334i	−0.0232813	+	0.0169149i
$413$	2.98556	−	9.18862i	0.146910	−	0.452142i
$414$	6.13886	+	4.46015i	0.301709	+	0.219204i
$415$	3.17470	−	9.77074i	0.155840	−	0.479627i
$416$	1.26948	+	3.90705i	0.0622413	+	0.191559i
$417$	−10.6413	+	7.73134i	−0.521106	+	0.378605i
$418$	1.06467	+	3.27673i	0.0520749	+	0.160270i
$419$	0.949588	+	2.92253i	0.0463904	+	0.142775i	0.971569	−	0.236758i	$-0.0760848\pi$
$419$	0.949588	+	2.92253i	0.0463904	+	0.142775i	−0.925178	+	0.379533i	$0.876085\pi$
$420$	−1.31796	+	0.957557i	−0.0643101	+	0.0467240i
$421$	5.04910	+	15.5395i	0.246078	+	0.757351i	0.995457	+	0.0952096i	$0.0303521\pi$
$421$	5.04910	+	15.5395i	0.246078	+	0.757351i	−0.749379	+	0.662141i	$0.769648\pi$
$422$	4.42749	−	13.6264i	0.215527	−	0.663323i
$423$	−1.77950	−	1.29289i	−0.0865225	−	0.0628623i
$424$	−4.34467	+	13.3715i	−0.210996	+	0.649378i
$425$	−4.63894	+	3.37039i	−0.225022	+	0.163488i
$426$	8.09841	−	5.88384i	0.392369	−	0.285073i
$427$	13.6303	+	9.90299i	0.659616	+	0.479239i
$428$	−19.9839			−0.965957
$429$	−2.22713			−0.107527
$430$	−0.967622	−	0.703018i	−0.0466629	−	0.0339026i
$431$	−0.434709	−	1.33790i	−0.0209392	−	0.0644443i	0.940041	−	0.341062i	$-0.110787\pi$
$431$	−0.434709	−	1.33790i	−0.0209392	−	0.0644443i	−0.960980	+	0.276617i	$0.910787\pi$
$432$	0.309017	−	0.951057i	0.0148676	−	0.0457577i
$433$	−12.9610			−0.622866			−0.311433	−	0.950268i	$-0.600809\pi$
$433$	−12.9610			−0.622866			−0.311433	+	0.950268i	$0.600809\pi$
$434$	6.25166	−	6.57183i	0.300089	−	0.315458i
$435$	0.166041			0.00796107
$436$	−3.21234	+	9.88656i	−0.153843	+	0.473481i
$437$	−14.9020	−	45.8637i	−0.712860	−	2.19396i
$438$	5.10048	+	3.70571i	0.243710	+	0.177066i
$439$	−12.7365			−0.607881			−0.303941	−	0.952691i	$-0.598302\pi$
$439$	−12.7365			−0.607881			−0.303941	+	0.952691i	$0.598302\pi$
$440$	0.542128			0.0258449
$441$	3.51603	+	2.55455i	0.167430	+	0.121645i
$442$	−19.0573	+	13.8459i	−0.906464	+	0.658585i
$443$	3.05518	−	2.21972i	0.145156	−	0.105462i	−0.512837	−	0.858486i	$-0.671406\pi$
$443$	3.05518	−	2.21972i	0.145156	−	0.105462i	0.657993	+	0.753024i	$0.271406\pi$
$444$	1.16496	−	3.58538i	0.0552866	−	0.170155i
$445$	−2.10428	−	1.52885i	−0.0997525	−	0.0724745i
$446$	3.91049	−	12.0352i	0.185167	−	0.569885i
$447$	−3.10323	−	9.55075i	−0.146778	−	0.451735i
$448$	1.31796	−	0.957557i	0.0622679	−	0.0452403i
$449$	−6.33400	−	19.4940i	−0.298920	−	0.919981i	−0.981877	−	0.189522i	$-0.939306\pi$
$449$	−6.33400	−	19.4940i	−0.298920	−	0.919981i	0.682957	−	0.730459i	$-0.260694\pi$
$450$	−0.309017	−	0.951057i	−0.0145672	−	0.0448332i
$451$	−3.78953	+	2.75326i	−0.178442	+	0.129646i
$452$	3.00844	+	9.25904i	0.141505	+	0.435509i
$453$	−1.91704	+	5.90005i	−0.0900704	+	0.277208i
$454$	7.94374	+	5.77146i	0.372818	+	0.270868i
$455$	−2.06810	+	6.36495i	−0.0969540	+	0.298394i
$456$	−5.14150	+	3.73552i	−0.240773	+	0.174932i
$457$	8.28261	−	6.01767i	0.387444	−	0.281495i	−0.376963	−	0.926228i	$-0.623032\pi$
$457$	8.28261	−	6.01767i	0.387444	−	0.281495i	0.764407	+	0.644734i	$0.223032\pi$
$458$	−0.844380	−	0.613478i	−0.0394553	−	0.0286659i
$459$	5.73404			0.267642
$460$	−7.58805			−0.353795
$461$	−3.29015	−	2.39044i	−0.153238	−	0.111334i	0.508524	−	0.861048i	$-0.330191\pi$
$461$	−3.29015	−	2.39044i	−0.153238	−	0.111334i	−0.661762	+	0.749714i	$0.730191\pi$
$462$	0.272917	+	0.839951i	0.0126972	+	0.0390781i
$463$	−2.50379	+	7.70586i	−0.116361	+	0.358122i	−0.992228	−	0.124430i	$-0.960290\pi$
$463$	−2.50379	+	7.70586i	−0.116361	+	0.358122i	0.875868	+	0.482552i	$0.160290\pi$
$464$	−0.166041			−0.00770827
$465$	2.65075	+	4.89628i	0.122926	+	0.227059i
$466$	−23.9851			−1.11109
$467$	5.49959	−	16.9260i	0.254491	−	0.783242i	−0.739439	−	0.673224i	$-0.764909\pi$
$467$	5.49959	−	16.9260i	0.254491	−	0.783242i	0.993930	−	0.110018i	$-0.0350909\pi$
$468$	−1.26948	−	3.90705i	−0.0586817	−	0.180604i
$469$	−9.88411	−	7.18123i	−0.456406	−	0.331598i
$470$	2.19959			0.101459
$471$	−14.2747			−0.657742
$472$	−4.79795	−	3.48591i	−0.220844	−	0.160452i
$473$	−0.524575	+	0.381126i	−0.0241200	+	0.0175242i
$474$	−4.55240	+	3.30751i	−0.209099	+	0.151919i
$475$	−1.96388	+	6.04420i	−0.0901090	+	0.277327i
$476$	7.55726	+	5.49067i	0.346386	+	0.251665i
$477$	4.34467	−	13.3715i	0.198929	−	0.612240i
$478$	0.627836	+	1.93228i	0.0287166	+	0.0883805i
$479$	10.4823	−	7.61581i	0.478947	−	0.347975i	−0.321971	−	0.946750i	$-0.604345\pi$
$479$	10.4823	−	7.61581i	0.478947	−	0.347975i	0.800918	+	0.598774i	$0.204345\pi$
$480$	0.309017	+	0.951057i	0.0141046	+	0.0434096i
$481$	−4.78580	−	14.7292i	−0.218214	−	0.671593i
$482$	2.65800	−	1.93115i	0.121069	−	0.0879616i
$483$	−3.81996	−	11.7566i	−0.173814	−	0.534945i
$484$	−3.30837	+	10.1821i	−0.150380	+	0.462823i
$485$	−15.1329	−	10.9947i	−0.687148	−	0.499242i
$486$	−0.309017	+	0.951057i	−0.0140173	+	0.0431408i
$487$	−17.9368	+	13.0318i	−0.812793	+	0.590529i	−0.914639	−	0.404272i	$-0.867525\pi$
$487$	−17.9368	+	13.0318i	−0.812793	+	0.590529i	0.101846	+	0.994800i	$0.467525\pi$
$488$	8.36680	−	6.07884i	0.378747	−	0.275176i
$489$	12.3147	+	8.94714i	0.556889	+	0.404604i
$490$	−4.34606			−0.196335
$491$	24.9634			1.12658			0.563292	−	0.826258i	$-0.309535\pi$
$491$	24.9634			1.12658			0.563292	+	0.826258i	$0.309535\pi$
$492$	−6.99010	−	5.07861i	−0.315138	−	0.228961i
$493$	−0.294211	−	0.905489i	−0.0132506	−	0.0407812i
$494$	−8.06785	+	24.8303i	−0.362990	+	1.11717i
$495$	−0.542128			−0.0243668
$496$	−2.65075	−	4.89628i	−0.119022	−	0.219849i
$497$	−16.3075			−0.731493
$498$	3.17470	−	9.77074i	0.142262	−	0.437837i
$499$	5.40646	+	16.6394i	0.242027	+	0.744881i	0.996111	+	0.0881039i	$0.0280808\pi$
$499$	5.40646	+	16.6394i	0.242027	+	0.744881i	−0.754085	+	0.656777i	$0.771919\pi$
$500$	0.809017	+	0.587785i	0.0361803	+	0.0262866i
$501$	−13.4550			−0.601124
$502$	−18.9068			−0.843854
$503$	−4.82791	−	3.50768i	−0.215266	−	0.156400i	0.474927	−	0.880025i	$-0.342474\pi$
$503$	−4.82791	−	3.50768i	−0.215266	−	0.156400i	−0.690193	+	0.723625i	$0.742474\pi$
$504$	−1.31796	+	0.957557i	−0.0587068	+	0.0426530i
$505$	11.6072	−	8.43315i	0.516515	−	0.375270i
$506$	−1.27120	+	3.91236i	−0.0565118	+	0.173926i
$507$	−3.13627	−	2.27864i	−0.139287	−	0.101198i
$508$	4.82199	−	14.8405i	0.213941	−	0.658443i
$509$	7.42754	+	22.8596i	0.329220	+	1.01323i	0.969500	+	0.245093i	$0.0788185\pi$
$509$	7.42754	+	22.8596i	0.329220	+	1.01323i	−0.640280	+	0.768142i	$0.721182\pi$
$510$	−4.63894	+	3.37039i	−0.205416	+	0.149243i
$511$	−3.17381	−	9.76800i	−0.140401	−	0.432111i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	5.14150	−	3.73552i	0.227003	−	0.164927i
$514$	−6.06020	−	18.6514i	−0.267304	−	0.822678i
$515$	−0.180501	+	0.555526i	−0.00795385	+	0.0244794i
$516$	−0.967622	−	0.703018i	−0.0425972	−	0.0309487i
$517$	0.368490	−	1.13410i	0.0162062	−	0.0498775i
$518$	−4.96859	+	3.60989i	−0.218307	+	0.158609i
$519$	6.18605	−	4.49443i	0.271538	−	0.197284i
$520$	3.32354	+	2.41469i	0.145747	+	0.105891i
$521$	36.4908			1.59869			0.799345	−	0.600873i	$-0.205180\pi$
$521$	36.4908			1.59869			0.799345	+	0.600873i	$0.205180\pi$
$522$	0.166041			0.00726743
$523$	−15.6790	−	11.3914i	−0.685594	−	0.498113i	0.189615	−	0.981859i	$-0.439276\pi$
$523$	−15.6790	−	11.3914i	−0.685594	−	0.498113i	−0.875209	+	0.483746i	$0.839276\pi$
$524$	−4.19183	−	12.9011i	−0.183121	−	0.563589i
$525$	−0.503417	+	1.54936i	−0.0219709	+	0.0676196i
$526$	4.74970			0.207097
$527$	22.0044	−	23.1314i	0.958528	−	1.00762i
$528$	0.542128			0.0235931
$529$	10.6854	−	32.8862i	0.464581	−	1.42983i
$530$	4.34467	+	13.3715i	0.188720	+	0.580822i
$531$	4.79795	+	3.48591i	0.208213	+	0.151276i
$532$	10.3533			0.448872
$533$	−35.4952			−1.53747
$534$	−2.10428	−	1.52885i	−0.0910612	−	0.0661598i
$535$	−16.1673	+	11.7462i	−0.698973	+	0.507834i
$536$	−6.06725	+	4.40811i	−0.262065	+	0.190402i
$537$	−3.12178	+	9.60784i	−0.134715	+	0.414609i
$538$	24.9882	+	18.1550i	1.07732	+	0.782719i
$539$	−0.728081	+	2.24080i	−0.0313607	+	0.0965182i
$540$	−0.309017	−	0.951057i	−0.0132980	−	0.0409270i
$541$	−21.7421	+	15.7965i	−0.934765	+	0.679147i	−0.947155	−	0.320777i	$-0.896056\pi$
$541$	−21.7421	+	15.7965i	−0.934765	+	0.679147i	0.0123897	+	0.999923i	$0.496056\pi$
$542$	2.03330	+	6.25786i	0.0873378	+	0.268798i
$543$	1.57808	+	4.85684i	0.0677221	+	0.208427i
$544$	4.63894	−	3.37039i	0.198893	−	0.144504i
$545$	3.21234	+	9.88656i	0.137602	+	0.423494i
$546$	−2.06810	+	6.36495i	−0.0885065	+	0.272395i
$547$	27.9279	+	20.2908i	1.19411	+	0.867572i	0.993693	−	0.112139i	$-0.0357701\pi$
$547$	27.9279	+	20.2908i	1.19411	+	0.867572i	0.200418	+	0.979711i	$0.435770\pi$
$548$	4.78270	−	14.7196i	0.204307	−	0.628791i
$549$	−8.36680	+	6.07884i	−0.357086	+	0.259439i
$550$	0.438591	−	0.318655i	0.0187016	−	0.0135875i
$551$	−0.853701	−	0.620250i	−0.0363689	−	0.0264236i
$552$	−7.58805			−0.322969
$553$	9.16703			0.389822
$554$	−12.9419	−	9.40286i	−0.549850	−	0.399489i
$555$	−1.16496	−	3.58538i	−0.0494499	−	0.152191i
$556$	4.06461	−	12.5096i	0.172378	−	0.530524i
$557$	24.4943			1.03786			0.518929	−	0.854817i	$-0.326331\pi$
$557$	24.4943			1.03786			0.518929	+	0.854817i	$0.326331\pi$
$558$	2.65075	+	4.89628i	0.112215	+	0.207276i
$559$	−4.91350			−0.207819
$560$	0.503417	−	1.54936i	0.0212733	−	0.0654724i
$561$	0.960606	+	2.95644i	0.0405568	+	0.124821i
$562$	9.73992	+	7.07647i	0.410854	+	0.298503i
$563$	−16.4803			−0.694563			−0.347282	−	0.937761i	$-0.612895\pi$
$563$	−16.4803			−0.694563			−0.347282	+	0.937761i	$0.612895\pi$
$564$	2.19959			0.0926194
$565$	7.87621	+	5.72240i	0.331355	+	0.240743i
$566$	−26.5821	+	19.3130i	−1.11733	+	0.811788i
$567$	1.31796	−	0.957557i	0.0553493	−	0.0402136i
$568$	−3.09332	+	9.52025i	−0.129793	+	0.399461i
$569$	−36.8969	−	26.8072i	−1.54680	−	1.12382i	−0.945885	−	0.324501i	$-0.894803\pi$
$569$	−36.8969	−	26.8072i	−1.54680	−	1.12382i	−0.600914	−	0.799314i	$-0.705197\pi$
$570$	−1.96388	+	6.04420i	−0.0822578	+	0.253164i
$571$	3.98413	+	12.2619i	0.166730	+	0.513144i	0.999160	−	0.0409878i	$-0.0130505\pi$
$571$	3.98413	+	12.2619i	0.166730	+	0.513144i	−0.832429	+	0.554131i	$0.813050\pi$
$572$	1.80178	−	1.30907i	0.0753363	−	0.0547351i
$573$	1.70757	+	5.25537i	0.0713349	+	0.219546i
$574$	4.34965	+	13.3868i	0.181551	+	0.558756i
$575$	−6.13886	+	4.46015i	−0.256008	+	0.186001i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	−2.70847	+	8.33580i	−0.112755	+	0.347024i	−0.991472	−	0.130319i	$-0.958400\pi$
$577$	−2.70847	+	8.33580i	−0.112755	+	0.347024i	0.878717	+	0.477343i	$0.158400\pi$
$578$	12.8466	+	9.33358i	0.534347	+	0.388226i
$579$	5.38079	−	16.5604i	0.223618	−	0.688225i
$580$	−0.134330	+	0.0975966i	−0.00557776	+	0.00405248i
$581$	−13.5402	+	9.83752i	−0.561741	+	0.408129i
$582$	−15.1329	−	10.9947i	−0.627277	−	0.455744i
$583$	7.62213			0.315676
$584$	−6.30454			−0.260884
$585$	−3.32354	−	2.41469i	−0.137411	−	0.0998352i
$586$	0.935031	+	2.87773i	0.0386258	+	0.118878i
$587$	13.9325	−	42.8798i	0.575056	−	1.76984i	−0.0609336	−	0.998142i	$-0.519408\pi$
$587$	13.9325	−	42.8798i	0.575056	−	1.76984i	0.635989	−	0.771698i	$-0.280592\pi$
$588$	−4.34606			−0.179228
$589$	4.66130	−	35.0761i	0.192066	−	1.44529i
$590$	−5.93059			−0.244159
$591$	−7.04515	+	21.6827i	−0.289799	+	0.891908i
$592$	1.16496	+	3.58538i	0.0478796	+	0.147358i
$593$	29.6865	+	21.5685i	1.21908	+	0.885712i	0.996023	−	0.0890943i	$-0.0283972\pi$
$593$	29.6865	+	21.5685i	1.21908	+	0.885712i	0.223054	+	0.974806i	$0.428397\pi$
$594$	−0.542128			−0.0222438
$595$	9.34129			0.382955
$596$	8.12435	+	5.90269i	0.332787	+	0.241784i
$597$	2.14910	−	1.56141i	0.0879567	−	0.0639043i
$598$	−25.2192	+	18.3228i	−1.03129	+	0.749276i
$599$	9.43434	−	29.0359i	0.385477	−	1.18638i	−0.550657	−	0.834731i	$-0.685623\pi$
$599$	9.43434	−	29.0359i	0.385477	−	1.18638i	0.936134	−	0.351644i	$-0.114377\pi$
$600$	0.809017	+	0.587785i	0.0330280	+	0.0239962i
$601$	1.93917	−	5.96817i	0.0791006	−	0.243447i	−0.903685	−	0.428199i	$-0.859148\pi$
$601$	1.93917	−	5.96817i	0.0791006	−	0.243447i	0.982785	+	0.184752i	$0.0591483\pi$
$602$	0.602111	+	1.85311i	0.0245402	+	0.0755270i
$603$	6.06725	−	4.40811i	0.247077	−	0.179512i
$604$	−1.91704	−	5.90005i	−0.0780033	−	0.240069i
$605$	3.30837	+	10.1821i	0.134504	+	0.413961i
$606$	11.6072	−	8.43315i	0.471512	−	0.342573i
$607$	−7.18446	−	22.1115i	−0.291608	−	0.897478i	−0.984340	−	0.176282i	$-0.943593\pi$
$607$	−7.18446	−	22.1115i	−0.291608	−	0.897478i	0.692731	−	0.721196i	$-0.256407\pi$
$608$	1.96388	−	6.04420i	0.0796458	−	0.245125i
$609$	−0.218836	−	0.158994i	−0.00886770	−	0.00644276i
$610$	3.19583	−	9.83577i	0.129396	−	0.398239i
$611$	7.31042	−	5.31133i	0.295748	−	0.214873i
$612$	−4.63894	+	3.37039i	−0.187518	+	0.136240i
$613$	4.44177	+	3.22714i	0.179401	+	0.130343i	0.673862	−	0.738857i	$-0.264634\pi$
$613$	4.44177	+	3.22714i	0.179401	+	0.130343i	−0.494460	+	0.869200i	$0.664634\pi$
$614$	−29.3407			−1.18409
$615$	−8.64024			−0.348408
$616$	−0.714505	−	0.519118i	−0.0287882	−	0.0209159i
$617$	−8.74373	−	26.9104i	−0.352009	−	1.08337i	−0.957723	−	0.287691i	$-0.907112\pi$
$617$	−8.74373	−	26.9104i	−0.352009	−	1.08337i	0.605714	−	0.795683i	$-0.292888\pi$
$618$	−0.180501	+	0.555526i	−0.00726083	+	0.0223466i
$619$	18.8165			0.756300			0.378150	−	0.925744i	$-0.376560\pi$
$619$	18.8165			0.756300			0.378150	+	0.925744i	$0.376560\pi$
$620$	−5.02246	−	2.40310i	−0.201707	−	0.0965108i
$621$	7.58805			0.304498
$622$	3.29906	−	10.1535i	0.132280	−	0.407117i
$623$	1.30941	+	4.02994i	0.0524603	+	0.161456i
$624$	3.32354	+	2.41469i	0.133048	+	0.0966651i
$625$	1.00000			0.0400000
$626$	−29.2908			−1.17069
$627$	2.78735	+	2.02513i	0.111316	+	0.0808759i
$628$	11.5484	−	8.39044i	0.460833	−	0.334815i
$629$	−17.4883	+	12.7060i	−0.697305	+	0.506622i
$630$	−0.503417	+	1.54936i	−0.0200566	+	0.0617280i
$631$	5.07790	+	3.68931i	0.202148	+	0.146869i	0.684254	−	0.729244i	$-0.260128\pi$
$631$	5.07790	+	3.68931i	0.202148	+	0.146869i	−0.482106	+	0.876113i	$0.660128\pi$
$632$	1.73886	−	5.35167i	0.0691682	−	0.212878i
$633$	−4.42749	−	13.6264i	−0.175977	−	0.541601i
$634$	11.1210	−	8.07988i	0.441671	−	0.320893i
$635$	−4.82199	−	14.8405i	−0.191355	−	0.588929i
$636$	4.34467	+	13.3715i	0.172277	+	0.530215i
$637$	−14.4443	+	10.4944i	−0.572303	+	0.415803i
$638$	0.0278163	+	0.0856099i	0.00110126	+	0.00338933i
$639$	3.09332	−	9.52025i	0.122370	−	0.376615i
$640$	−0.809017	−	0.587785i	−0.0319792	−	0.0232343i
$641$	−11.8172	+	36.3697i	−0.466752	+	1.43652i	0.390013	+	0.920809i	$0.372470\pi$
$641$	−11.8172	+	36.3697i	−0.466752	+	1.43652i	−0.856765	+	0.515706i	$0.827530\pi$
$642$	−16.1673	+	11.7462i	−0.638072	+	0.463587i
$643$	−35.5748	+	25.8466i	−1.40293	+	1.01929i	−0.408630	+	0.912700i	$0.633993\pi$
$643$	−35.5748	+	25.8466i	−1.40293	+	1.01929i	−0.994303	+	0.106590i	$0.966007\pi$
$644$	10.0008	+	7.26599i	0.394086	+	0.286320i
$645$	−1.19605			−0.0470943
$646$	36.4413			1.43376
$647$	−38.2402	−	27.7831i	−1.50338	−	1.09227i	−0.969012	−	0.247012i	$-0.920551\pi$
$647$	−38.2402	−	27.7831i	−1.50338	−	1.09227i	−0.534364	−	0.845255i	$-0.679449\pi$
$648$	−0.309017	−	0.951057i	−0.0121393	−	0.0373610i
$649$	−0.993533	+	3.05778i	−0.0389996	+	0.120028i
$650$	4.10812			0.161134
$651$	1.19487	−	8.99136i	0.0468307	−	0.352399i
$652$	−15.2218			−0.596131
$653$	−2.13174	+	6.56083i	−0.0834215	+	0.256745i	−0.984064	−	0.177817i	$-0.943097\pi$
$653$	−2.13174	+	6.56083i	−0.0834215	+	0.256745i	0.900642	+	0.434561i	$0.143097\pi$
$654$	3.21234	+	9.88656i	0.125612	+	0.386595i
$655$	−10.9744	−	7.97334i	−0.428804	−	0.311544i
$656$	8.64024			0.337345
$657$	6.30454			0.245963
$658$	−2.89898	−	2.10623i	−0.113014	−	0.0821095i
$659$	−4.68274	+	3.40221i	−0.182414	+	0.132531i	−0.675245	−	0.737594i	$-0.735962\pi$
$659$	−4.68274	+	3.40221i	−0.182414	+	0.132531i	0.492831	+	0.870125i	$0.335962\pi$
$660$	0.438591	−	0.318655i	0.0170721	−	0.0124036i
$661$	8.01677	−	24.6731i	0.311816	−	0.959672i	−0.665229	−	0.746639i	$-0.731666\pi$
$661$	8.01677	−	24.6731i	0.311816	−	0.959672i	0.977045	−	0.213032i	$-0.0683340\pi$
$662$	10.6430	+	7.73260i	0.413652	+	0.300536i
$663$	−7.27925	+	22.4032i	−0.282702	+	0.870069i
$664$	3.17470	+	9.77074i	0.123202	+	0.379178i
$665$	8.37599	−	6.08551i	0.324807	−	0.235986i
$666$	−1.16496	−	3.58538i	−0.0451414	−	0.138931i
$667$	−0.389340	−	1.19826i	−0.0150753	−	0.0463970i
$668$	10.8853	−	7.90863i	0.421165	−	0.305994i
$669$	−3.91049	−	12.0352i	−0.151188	−	0.465309i
$670$	−2.31748	+	7.13248i	−0.0895322	+	0.275552i
$671$	−4.53588	−	3.29551i	−0.175106	−	0.127222i
$672$	0.503417	−	1.54936i	0.0194197	−	0.0597678i
$673$	−20.3097	+	14.7558i	−0.782880	+	0.568796i	−0.905842	−	0.423616i	$-0.860761\pi$
$673$	−20.3097	+	14.7558i	−0.782880	+	0.568796i	0.122962	+	0.992411i	$0.460761\pi$
$674$	29.4245	−	21.3781i	1.13339	−	0.823455i
$675$	−0.809017	−	0.587785i	−0.0311391	−	0.0226239i
$676$	3.87665			0.149102
$677$	5.12239			0.196869			0.0984347	−	0.995144i	$-0.468616\pi$
$677$	5.12239			0.196869			0.0984347	+	0.995144i	$0.468616\pi$
$678$	7.87621	+	5.72240i	0.302484	+	0.219768i
$679$	9.41655	+	28.9812i	0.361374	+	1.11219i
$680$	1.77192	−	5.45340i	0.0679499	−	0.209128i
$681$	9.81900			0.376265
$682$	−2.08042	+	2.18697i	−0.0796634	+	0.0837434i
$683$	−2.37302			−0.0908012			−0.0454006	−	0.998969i	$-0.514456\pi$
$683$	−2.37302			−0.0908012			−0.0454006	+	0.998969i	$0.514456\pi$
$684$	−1.96388	+	6.04420i	−0.0750908	+	0.231106i
$685$	−4.78270	−	14.7196i	−0.182737	−	0.562408i
$686$	14.9537	+	10.8645i	0.570935	+	0.414808i
$687$	−1.04371			−0.0398201
$688$	1.19605			0.0455988
$689$	46.7278	+	33.9497i	1.78019	+	1.29338i
$690$	−6.13886	+	4.46015i	−0.233703	+	0.169795i
$691$	−31.9491	+	23.2124i	−1.21540	+	0.883040i	−0.995710	−	0.0925295i	$-0.970505\pi$
$691$	−31.9491	+	23.2124i	−1.21540	+	0.883040i	−0.219690	+	0.975570i	$0.570505\pi$
$692$	−2.36286	+	7.27214i	−0.0898226	+	0.276445i
$693$	0.714505	+	0.519118i	0.0271418	+	0.0197197i
$694$	−0.578713	+	1.78109i	−0.0219676	+	0.0676094i
$695$	−4.06461	−	12.5096i	−0.154179	−	0.474515i
$696$	−0.134330	+	0.0975966i	−0.00509177	+	0.00369939i
$697$	15.3098	+	47.1187i	0.579900	+	1.78475i
$698$	−7.21560	−	22.2073i	−0.273114	−	0.840560i
$699$	−19.4044	+	14.0981i	−0.733940	+	0.533239i
$700$	−0.503417	−	1.54936i	−0.0190274	−	0.0585603i
$701$	−2.57155	+	7.91443i	−0.0971262	+	0.298924i	−0.987802	−	0.155715i	$-0.950232\pi$
$701$	−2.57155	+	7.91443i	−0.0971262	+	0.298924i	0.890676	+	0.454639i	$0.150232\pi$
$702$	−3.32354	−	2.41469i	−0.125439	−	0.0911367i
$703$	−7.40362	+	22.7860i	−0.279233	+	0.859390i
$704$	−0.438591	+	0.318655i	−0.0165300	+	0.0120098i
$705$	1.77950	−	1.29289i	0.0670200	−	0.0486929i
$706$	−0.856263	−	0.622112i	−0.0322259	−	0.0234135i
$707$	−23.3731			−0.879037
$708$	−5.93059			−0.222885
$709$	11.3290	+	8.23103i	0.425471	+	0.309123i	0.779835	−	0.625985i	$-0.215303\pi$
$709$	11.3290	+	8.23103i	0.425471	+	0.309123i	−0.354364	+	0.935107i	$0.615303\pi$
$710$	3.09332	+	9.52025i	0.116090	+	0.357289i
$711$	−1.73886	+	5.35167i	−0.0652124	+	0.200703i
$712$	2.60104			0.0974779
$713$	29.1192	−	30.6106i	1.09052	−	1.14637i
$714$	9.34129			0.349589
$715$	0.688220	−	2.11812i	0.0257380	−	0.0792133i
$716$	−3.12178	−	9.60784i	−0.116666	−	0.359062i
$717$	1.64370	+	1.19422i	0.0613850	+	0.0445988i
$718$	32.9146			1.22836
$719$	34.4930			1.28637			0.643186	−	0.765710i	$-0.277612\pi$
$719$	34.4930			1.28637			0.643186	+	0.765710i	$0.277612\pi$
$720$	0.809017	+	0.587785i	0.0301503	+	0.0219055i
$721$	0.769843	−	0.559323i	0.0286704	−	0.0208303i
$722$	17.3042	−	12.5722i	0.643995	−	0.467890i
$723$	1.01527	−	3.12467i	0.0377582	−	0.116208i
$724$	−4.13148	−	3.00169i	−0.153545	−	0.111557i
$725$	−0.0513096	+	0.157915i	−0.00190559	+	0.00586480i
$726$	3.30837	+	10.1821i	0.122785	+	0.377893i
$727$	5.95922	−	4.32963i	0.221015	−	0.160577i	−0.471768	−	0.881723i	$-0.656384\pi$
$727$	5.95922	−	4.32963i	0.221015	−	0.160577i	0.692784	+	0.721146i	$0.256384\pi$
$728$	−2.06810	−	6.36495i	−0.0766488	−	0.235901i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−5.10048	+	3.70571i	−0.188777	+	0.137155i
$731$	2.11929	+	6.52252i	0.0783849	+	0.241244i
$732$	3.19583	−	9.83577i	0.118121	−	0.363540i
$733$	−1.38248	−	1.00443i	−0.0510629	−	0.0370994i	0.561961	−	0.827164i	$-0.310047\pi$
$733$	−1.38248	−	1.00443i	−0.0510629	−	0.0370994i	−0.613024	+	0.790064i	$0.710047\pi$
$734$	−5.10356	+	15.7072i	−0.188376	+	0.579762i
$735$	−3.51603	+	2.55455i	−0.129691	+	0.0942259i
$736$	6.13886	−	4.46015i	0.226282	−	0.164403i
$737$	3.28922	+	2.38976i	0.121160	+	0.0880280i
$738$	−8.64024			−0.318052
$739$	53.4787			1.96725			0.983623	−	0.180240i	$-0.0576874\pi$
$739$	53.4787			1.96725			0.983623	+	0.180240i	$0.0576874\pi$
$740$	3.04991	+	2.21589i	0.112117	+	0.0814577i
$741$	8.06785	+	24.8303i	0.296380	+	0.912164i
$742$	7.07787	−	21.7834i	0.259837	−	0.799695i
$743$	16.7415			0.614185			0.307092	−	0.951680i	$-0.400644\pi$
$743$	16.7415			0.614185			0.307092	+	0.951680i	$0.400644\pi$
$744$	−5.02246	−	2.40310i	−0.184132	−	0.0881019i
$745$	10.0423			0.367920
$746$	0.538770	−	1.65816i	0.0197258	−	0.0607097i
$747$	−3.17470	−	9.77074i	−0.116156	−	0.357493i
$748$	−2.51490	−	1.82718i	−0.0919538	−	0.0668083i
$749$	32.5556			1.18956
$750$	1.00000			0.0365148
$751$	−3.28600	−	2.38742i	−0.119908	−	0.0871182i	0.526215	−	0.850352i	$-0.323611\pi$
$751$	−3.28600	−	2.38742i	−0.119908	−	0.0871182i	−0.646123	+	0.763233i	$0.723611\pi$
$752$	−1.77950	+	1.29289i	−0.0648919	+	0.0471467i
$753$	−15.2960	+	11.1132i	−0.557416	+	0.404986i
$754$	−0.210786	+	0.648732i	−0.00767637	+	0.0236254i
$755$	−5.01888	−	3.64643i	−0.182656	−	0.132707i
$756$	−0.503417	+	1.54936i	−0.0183091	+	0.0563497i
$757$	−6.46217	−	19.8885i	−0.234872	−	0.722860i	−0.997138	−	0.0755975i	$-0.975914\pi$
$757$	−6.46217	−	19.8885i	−0.234872	−	0.722860i	0.762267	−	0.647263i	$-0.224086\pi$
$758$	−5.17094	+	3.75691i	−0.187817	+	0.136457i
$759$	1.27120	+	3.91236i	0.0461417	+	0.142010i
$760$	−1.96388	−	6.04420i	−0.0712374	−	0.219246i
$761$	−6.62267	+	4.81165i	−0.240072	+	0.174422i	−0.701315	−	0.712851i	$-0.747403\pi$
$761$	−6.62267	+	4.81165i	−0.240072	+	0.174422i	0.461243	+	0.887274i	$0.347403\pi$
$762$	−4.82199	−	14.8405i	−0.174682	−	0.537616i
$763$	5.23320	−	16.1061i	0.189455	−	0.583081i
$764$	−4.47048	−	3.24800i	−0.161736	−	0.117508i
$765$	−1.77192	+	5.45340i	−0.0640638	+	0.197168i
$766$	13.8489	−	10.0618i	0.500380	−	0.363548i
$767$	−19.7106	+	14.3206i	−0.711707	+	0.517085i
$768$	−0.809017	−	0.587785i	−0.0291929	−	0.0212099i
$769$	31.5731			1.13855			0.569277	−	0.822146i	$-0.307223\pi$
$769$	31.5731			1.13855			0.569277	+	0.822146i	$0.307223\pi$
$770$	−0.883177			−0.0318275
$771$	−15.8658	−	11.5272i	−0.571394	−	0.415142i
$772$	5.38079	+	16.5604i	0.193659	+	0.596021i
$773$	−16.8499	+	51.8586i	−0.606048	+	1.86522i	−0.116631	+	0.993175i	$0.537209\pi$
$773$	−16.8499	+	51.8586i	−0.606048	+	1.86522i	−0.489417	+	0.872050i	$0.662791\pi$
$774$	−1.19605			−0.0429910
$775$	−5.47576	+	1.00798i	−0.196695	+	0.0362077i
$776$	18.7053			0.671479
$777$	−1.89783	+	5.84092i	−0.0680843	+	0.209542i
$778$	2.42609	+	7.46674i	0.0869796	+	0.267696i
$779$	44.4238	+	32.2758i	1.59165	+	1.15640i
$780$	4.10812			0.147094
$781$	5.42680			0.194186
$782$	35.2005	+	25.5747i	1.25877	+	0.914548i
$783$	0.134330	−	0.0975966i	0.00480057	−	0.00348782i
$784$	3.51603	−	2.55455i	0.125573	−	0.0912338i
$785$	4.41111	−	13.5760i	0.157439	−	0.484549i
$786$	−10.9744	−	7.97334i	−0.391442	−	0.284400i
$787$	−11.9010	+	36.6274i	−0.424223	+	1.30563i	0.479512	+	0.877535i	$0.340814\pi$
$787$	−11.9010	+	36.6274i	−0.424223	+	1.30563i	−0.903736	+	0.428090i	$0.859186\pi$
$788$	−7.04515	−	21.6827i	−0.250973	−	0.772415i
$789$	3.84259	−	2.79181i	0.136800	−	0.0993909i
$790$	−1.73886	−	5.35167i	−0.0618660	−	0.190404i
$791$	−4.90104	−	15.0838i	−0.174261	−	0.536320i
$792$	0.438591	−	0.318655i	0.0155846	−	0.0113229i
$793$	−13.1289	−	40.4065i	−0.466220	−	1.43488i
$794$	3.32219	−	10.2246i	0.117900	−	0.362859i
$795$	11.3745	+	8.26405i	0.403412	+	0.293096i
$796$	−0.820882	+	2.52642i	−0.0290954	+	0.0895465i
$797$	−16.1842	+	11.7585i	−0.573273	+	0.416507i	−0.836293	−	0.548283i	$-0.815282\pi$
$797$	−16.1842	+	11.7585i	−0.573273	+	0.416507i	0.263020	+	0.964790i	$0.415282\pi$
$798$	8.37599	−	6.08551i	0.296507	−	0.215425i
$799$	−10.2038	−	7.41346i	−0.360983	−	0.262269i
$800$	−1.00000			−0.0353553
$801$	−2.60104			−0.0919031
$802$	4.60508	+	3.34578i	0.162611	+	0.118144i
$803$	1.05618	+	3.25058i	0.0372717	+	0.114711i
$804$	−2.31748	+	7.13248i	−0.0817313	+	0.251543i
$805$	12.3616			0.435691
$806$	−22.4951	+	4.14090i	−0.792356	+	0.145857i
$807$	30.8872			1.08728
$808$	−4.43357	+	13.6451i	−0.155972	+	0.480034i
$809$	−3.20301	−	9.85786i	−0.112612	−	0.346584i	0.878830	−	0.477136i	$-0.158325\pi$
$809$	−3.20301	−	9.85786i	−0.112612	−	0.346584i	−0.991441	+	0.130552i	$0.958325\pi$
$810$	−0.809017	−	0.587785i	−0.0284260	−	0.0206527i
$811$	−9.48510			−0.333067			−0.166533	−	0.986036i	$-0.553257\pi$
$811$	−9.48510			−0.333067			−0.166533	+	0.986036i	$0.553257\pi$
$812$	0.270497			0.00949257
$813$	5.32325	+	3.86757i	0.186695	+	0.135642i
$814$	1.65344	−	1.20130i	0.0579531	−	0.0421054i
$815$	−12.3147	+	8.94714i	−0.431365	+	0.313405i
$816$	1.77192	−	5.45340i	0.0620295	−	0.190907i
$817$	6.14948	+	4.46786i	0.215143	+	0.156310i
$818$	2.87099	−	8.83600i	0.100382	−	0.308943i
$819$	2.06810	+	6.36495i	0.0722652	+	0.222409i
$820$	6.99010	−	5.07861i	0.244105	−	0.177353i
$821$	−10.7016	−	32.9362i	−0.373489	−	1.14948i	−0.944493	−	0.328533i	$-0.893446\pi$
$821$	−10.7016	−	32.9362i	−0.373489	−	1.14948i	0.571004	−	0.820948i	$-0.306554\pi$
$822$	−4.78270	−	14.7196i	−0.166816	−	0.513406i
$823$	−3.28002	+	2.38307i	−0.114334	+	0.0830687i	−0.643483	−	0.765460i	$-0.722511\pi$
$823$	−3.28002	+	2.38307i	−0.114334	+	0.0830687i	0.529149	+	0.848529i	$0.322511\pi$
$824$	−0.180501	−	0.555526i	−0.00628807	−	0.0193527i
$825$	0.167527	−	0.515594i	0.00583253	−	0.0179507i
$826$	7.81631	+	5.67888i	0.271964	+	0.197593i
$827$	−11.1079	+	34.1865i	−0.386258	+	1.18878i	0.549306	+	0.835622i	$0.314892\pi$
$827$	−11.1079	+	34.1865i	−0.386258	+	1.18878i	−0.935564	+	0.353158i	$0.885108\pi$
$828$	−6.13886	+	4.46015i	−0.213340	+	0.155001i
$829$	−36.4100	+	26.4534i	−1.26457	+	0.918766i	−0.998973	−	0.0453179i	$-0.985570\pi$
$829$	−36.4100	+	26.4534i	−1.26457	+	0.918766i	−0.265600	+	0.964083i	$0.585570\pi$
$830$	8.31149	+	6.03865i	0.288496	+	0.209605i
$831$	−15.9971			−0.554933
$832$	−4.10812			−0.142423
$833$	20.1611	+	14.6479i	0.698540	+	0.507519i
$834$	−4.06461	−	12.5096i	−0.140746	−	0.433171i
$835$	4.15781	−	12.7964i	0.143887	−	0.442839i
$836$	−3.44536			−0.119160
$837$	5.02246	+	2.40310i	0.173602	+	0.0830633i
$838$	−3.07293			−0.106153
$839$	1.66637	−	5.12856i	0.0575295	−	0.177058i	−0.918162	−	0.396204i	$-0.870327\pi$
$839$	1.66637	−	5.12856i	0.0575295	−	0.177058i	0.975692	+	0.219146i	$0.0703273\pi$
$840$	−0.503417	−	1.54936i	−0.0173696	−	0.0534580i
$841$	23.4392	+	17.0296i	0.808248	+	0.587226i
$842$	−16.3392			−0.563087
$843$	12.0392			0.414652
$844$	11.5913	+	8.42159i	0.398990	+	0.289883i
$845$	3.13627	−	2.27864i	0.107891	−	0.0783875i
$846$	1.77950	−	1.29289i	0.0611806	−	0.0444503i
$847$	5.38964	−	16.5876i	0.185190	−	0.569956i
$848$	−11.3745	−	8.26405i	−0.390602	−	0.283789i
$849$	−10.1535	+	31.2492i	−0.348466	+	1.07247i
$850$	−1.77192	−	5.45340i	−0.0607762	−	0.187050i
$851$	−23.1429	+	16.8143i	−0.793328	+	0.576386i
$852$	3.09332	+	9.52025i	0.105975	+	0.326159i
$853$	−1.36909	−	4.21364i	−0.0468769	−	0.144272i	0.924878	−	0.380263i	$-0.124167\pi$
$853$	−1.36909	−	4.21364i	−0.0468769	−	0.144272i	−0.971755	+	0.235991i	$0.924167\pi$
$854$	−13.6303	+	9.90299i	−0.466419	+	0.338873i
$855$	1.96388	+	6.04420i	0.0671633	+	0.206707i
$856$	6.17536	−	19.0058i	0.211069	−	0.649605i
$857$	−37.1574	−	26.9965i	−1.26927	−	0.922181i	−0.270100	−	0.962832i	$-0.587057\pi$
$857$	−37.1574	−	26.9965i	−1.26927	−	0.922181i	−0.999173	+	0.0406507i	$0.987057\pi$
$858$	0.688220	−	2.11812i	0.0234954	−	0.0723115i
$859$	12.6445	−	9.18677i	0.431425	−	0.313448i	−0.350794	−	0.936453i	$-0.614088\pi$
$859$	12.6445	−	9.18677i	0.431425	−	0.313448i	0.782218	+	0.623004i	$0.214088\pi$
$860$	0.967622	−	0.703018i	0.0329956	−	0.0239727i
$861$	11.3875	+	8.27352i	0.388086	+	0.281961i
$862$	1.40675			0.0479141
$863$	25.4461			0.866196			0.433098	−	0.901347i	$-0.357420\pi$
$863$	25.4461			0.866196			0.433098	+	0.901347i	$0.357420\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$	2.36286	+	7.27214i	0.0803397	+	0.247260i
$866$	4.00517	−	12.3267i	0.136101	−	0.418877i
$867$	15.8792			0.539287
$868$	4.31832	+	7.97649i	0.146573	+	0.270740i
$869$	−3.05060			−0.103484
$870$	−0.0513096	+	0.157915i	−0.00173956	+	0.00535381i
$871$	9.52050	+	29.3011i	0.322590	+	0.992829i
$872$	−8.41001	−	6.11023i	−0.284799	−	0.206919i
$873$	−18.7053			−0.633077
$874$	48.2240			1.63120
$875$	−1.31796	−	0.957557i	−0.0445553	−	0.0323713i
$876$	−5.10048	+	3.70571i	−0.172329	+	0.125205i
$877$	−18.7640	+	13.6328i	−0.633614	+	0.460347i	−0.857650	−	0.514233i	$-0.828076\pi$
$877$	−18.7640	+	13.6328i	−0.633614	+	0.460347i	0.224037	+	0.974581i	$0.428076\pi$
$878$	3.93580	−	12.1132i	0.132827	−	0.408799i
$879$	2.44794	+	1.77853i	0.0825670	+	0.0599885i
$880$	−0.167527	+	0.515594i	−0.00564733	+	0.0173807i
$881$	−1.33582	−	4.11122i	−0.0450048	−	0.138511i	0.926029	−	0.377452i	$-0.123200\pi$
$881$	−1.33582	−	4.11122i	−0.0450048	−	0.138511i	−0.971034	+	0.238941i	$0.923200\pi$
$882$	−3.51603	+	2.55455i	−0.118391	+	0.0860161i
$883$	6.84457	+	21.0654i	0.230338	+	0.708908i	0.997706	+	0.0677003i	$0.0215662\pi$
$883$	6.84457	+	21.0654i	0.230338	+	0.708908i	−0.767368	+	0.641207i	$0.778434\pi$
$884$	−7.27925	−	22.4032i	−0.244828	−	0.753502i
$885$	−4.79795	+	3.48591i	−0.161281	+	0.117178i
$886$	1.16697	+	3.59158i	0.0392053	+	0.120661i
$887$	−14.2820	+	43.9555i	−0.479543	+	1.47588i	0.360189	+	0.932879i	$0.382712\pi$
$887$	−14.2820	+	43.9555i	−0.479543	+	1.47588i	−0.839732	+	0.543001i	$0.817288\pi$
$888$	3.04991	+	2.21589i	0.102348	+	0.0743604i
$889$	−7.85546	+	24.1766i	−0.263464	+	0.810858i
$890$	2.10428	−	1.52885i	0.0705357	−	0.0512472i
$891$	−0.438591	+	0.318655i	−0.0146933	+	0.0106753i
$892$	10.2378	+	7.43819i	0.342786	+	0.249049i
$893$	−13.9789			−0.467787
$894$	10.0423			0.335863
$895$	−8.17292	−	5.93797i	−0.273191	−	0.198485i
$896$	0.503417	+	1.54936i	0.0168180	+	0.0517605i
$897$	−9.63287	+	29.6469i	−0.321632	+	0.989882i
$898$	20.4972			0.684002
$899$	0.121784	−	0.916422i	0.00406173	−	0.0305644i
$900$	1.00000			0.0333333
$901$	24.9125	−	76.6728i	0.829956	−	2.55434i
$902$	−1.44747	−	4.45486i	−0.0481955	−	0.148331i
$903$	1.57635	+	1.14528i	0.0524575	+	0.0381126i
$904$	−9.73553			−0.323799
$905$	−5.10679			−0.169755
$906$	−5.01888	−	3.64643i	−0.166741	−	0.121144i
$907$	30.2445	−	21.9739i	1.00425	−	0.729632i	0.0412565	−	0.999149i	$-0.486864\pi$
$907$	30.2445	−	21.9739i	1.00425	−	0.729632i	0.962996	+	0.269517i	$0.0868639\pi$
$908$	−7.94374	+	5.77146i	−0.263622	+	0.191533i
$909$	4.43357	−	13.6451i	0.147052	−	0.452580i
$910$	−5.41435	−	3.93376i	−0.179484	−	0.130403i
$911$	−0.0534117	+	0.164384i	−0.00176961	+	0.00544629i	−0.951937	−	0.306293i	$-0.900911\pi$
$911$	−0.0534117	+	0.164384i	−0.00176961	+	0.00544629i	0.950168	+	0.311739i	$0.100911\pi$
$912$	−1.96388	−	6.04420i	−0.0650305	−	0.200143i
$913$	4.50589	−	3.27372i	0.149123	−	0.108344i
$914$	3.16367	+	9.73679i	0.104645	+	0.322064i
$915$	−3.19583	−	9.83577i	−0.105651	−	0.325160i
$916$	0.844380	−	0.613478i	0.0278991	−	0.0202699i
$917$	6.82888	+	21.0171i	0.225510	+	0.694047i
$918$	−1.77192	+	5.45340i	−0.0584820	+	0.179989i
$919$	−42.3317	−	30.7558i	−1.39639	−	1.01454i	−0.995129	−	0.0985767i	$-0.968571\pi$
$919$	−42.3317	−	30.7558i	−1.39639	−	1.01454i	−0.401264	−	0.915962i	$-0.631429\pi$
$920$	2.34484	−	7.21667i	0.0773070	−	0.237926i
$921$	−23.7371	+	17.2460i	−0.782164	+	0.568276i
$922$	3.29015	−	2.39044i	0.108355	−	0.0787248i
$923$	33.2692	+	24.1715i	1.09507	+	0.795615i
$924$	−0.883177			−0.0290544
$925$	3.76990			0.123953
$926$	−6.55500	−	4.76249i	−0.215411	−	0.156505i
$927$	0.180501	+	0.555526i	0.00592845	+	0.0182459i
$928$	0.0513096	−	0.157915i	0.00168432	−	0.00518380i
$929$	6.07495			0.199313			0.0996563	−	0.995022i	$-0.468226\pi$
$929$	6.07495			0.199313			0.0996563	+	0.995022i	$0.468226\pi$
$930$	−5.47576	+	1.00798i	−0.179557	+	0.0330530i
$931$	27.6203			0.905217
$932$	7.41181	−	22.8112i	0.242782	−	0.747205i
$933$	−3.29906	−	10.1535i	−0.108006	−	0.332410i
$934$	14.3981	+	10.4608i	0.471121	+	0.342289i
$935$	−3.10858			−0.101662
$936$	4.10812			0.134278
$937$	−38.5197	−	27.9862i	−1.25838	−	0.914269i	−0.259705	−	0.965688i	$-0.583625\pi$
$937$	−38.5197	−	27.9862i	−1.25838	−	0.914269i	−0.998677	+	0.0514194i	$0.983625\pi$
$938$	9.88411	−	7.18123i	0.322728	−	0.234475i
$939$	−23.6967	+	17.2167i	−0.773313	+	0.561845i
$940$	−0.679710	+	2.09193i	−0.0221697	+	0.0682314i
$941$	34.6726	+	25.1911i	1.13029	+	0.821206i	0.985737	−	0.168291i	$-0.0538248\pi$
$941$	34.6726	+	25.1911i	1.13029	+	0.821206i	0.144555	+	0.989497i	$0.453825\pi$
$942$	4.41111	−	13.5760i	0.143722	−	0.442330i
$943$	20.2600	+	62.3538i	0.659755	+	2.03052i
$944$	4.79795	−	3.48591i	0.156160	−	0.113457i
$945$	0.503417	+	1.54936i	0.0163762	+	0.0504007i
$946$	−0.200370	−	0.616675i	−0.00651458	−	0.0200498i
$947$	16.5195	−	12.0021i	0.536810	−	0.390015i	−0.286089	−	0.958203i	$-0.592355\pi$
$947$	16.5195	−	12.0021i	0.536810	−	0.390015i	0.822899	+	0.568188i	$0.192355\pi$
$948$	−1.73886	−	5.35167i	−0.0564756	−	0.173814i
$949$	−8.00348	+	24.6322i	−0.259804	+	0.799594i
$950$	−5.14150	−	3.73552i	−0.166812	−	0.121196i
$951$	4.24785	−	13.0735i	0.137746	−	0.423938i
$952$	−7.55726	+	5.49067i	−0.244932	+	0.177954i
$953$	14.4964	−	10.5322i	0.469583	−	0.341172i	−0.327696	−	0.944783i	$-0.606272\pi$
$953$	14.4964	−	10.5322i	0.469583	−	0.341172i	0.797279	+	0.603611i	$0.206272\pi$
$954$	11.3745	+	8.26405i	0.368263	+	0.267559i
$955$	−5.52582			−0.178811
$956$	−2.03172			−0.0657106
$957$	0.0728241	+	0.0529098i	0.00235407	+	0.00171033i
$958$	4.00387	+	12.3226i	0.129359	+	0.398126i
$959$	−7.79146	+	23.9796i	−0.251599	+	0.774343i
$960$	−1.00000			−0.0322749
$961$	28.9680	−	11.0389i	0.934450	−	0.356094i
$962$	15.4872			0.499327
$963$	−6.17536	+	19.0058i	−0.198998	+	0.612453i
$964$	1.01527	+	3.12467i	0.0326996	+	0.100639i
$965$	14.0871	+	10.2349i	0.453480	+	0.329472i
$966$	12.3616			0.397729
$967$	−38.9111			−1.25130			−0.625649	−	0.780105i	$-0.715166\pi$
$967$	−38.9111			−1.25130			−0.625649	+	0.780105i	$0.715166\pi$
$968$	−8.66141	−	6.29289i	−0.278388	−	0.202261i
$969$	29.4816	−	21.4196i	0.947085	−	0.688098i
$970$	15.1329	−	10.9947i	0.485887	−	0.353018i
$971$	0.646228	−	1.98889i	0.0207384	−	0.0638264i	−0.940152	−	0.340756i	$-0.889317\pi$
$971$	0.646228	−	1.98889i	0.0207384	−	0.0638264i	0.960890	+	0.276930i	$0.0893169\pi$
$972$	−0.809017	−	0.587785i	−0.0259492	−	0.0188532i
$973$	−6.62162	+	20.3793i	−0.212279	+	0.653329i
$974$	−6.85124	−	21.0859i	−0.219528	−	0.675637i
$975$	3.32354	−	2.41469i	0.106438	−	0.0773320i
$976$	3.19583	+	9.83577i	0.102296	+	0.314835i
$977$	−8.95041	−	27.5465i	−0.286349	−	0.881291i	−0.985991	−	0.166798i	$-0.946657\pi$
$977$	−8.95041	−	27.5465i	−0.286349	−	0.881291i	0.699642	−	0.714493i	$-0.253343\pi$
$978$	−12.3147	+	8.94714i	−0.393780	+	0.286098i
$979$	−0.435743	−	1.34108i	−0.0139264	−	0.0428611i
$980$	1.34301	−	4.13335i	0.0429007	−	0.132035i
$981$	8.41001	+	6.11023i	0.268511	+	0.195085i
$982$	−7.71413	+	23.7416i	−0.246168	+	0.757626i
$983$	−18.3038	+	13.2985i	−0.583802	+	0.424157i	−0.840093	−	0.542443i	$-0.817499\pi$
$983$	−18.3038	+	13.2985i	−0.583802	+	0.424157i	0.256291	+	0.966600i	$0.417499\pi$
$984$	6.99010	−	5.07861i	0.222836	−	0.161900i
$985$	−18.4444	−	13.4007i	−0.587688	−	0.426981i
$986$	0.952087			0.0303206
$987$	−3.58334			−0.114059
$988$	−21.1219	−	15.3460i	−0.671977	−	0.488220i
$989$	2.80453	+	8.63147i	0.0891790	+	0.274465i
$990$	0.167527	−	0.515594i	0.00532435	−	0.0163867i
$991$	−40.1289			−1.27474			−0.637368	−	0.770559i	$-0.719977\pi$
$991$	−40.1289			−1.27474			−0.637368	+	0.770559i	$0.719977\pi$
$992$	5.47576	−	1.00798i	0.173856	−	0.0320034i
$993$	13.1555			0.417477
$994$	5.03930	−	15.5094i	0.159837	−	0.491928i
$995$	0.820882	+	2.52642i	0.0260237	+	0.0800928i
$996$	8.31149	+	6.03865i	0.263359	+	0.191342i
$997$	−36.1111			−1.14365			−0.571825	−	0.820376i	$-0.693764\pi$
$997$	−36.1111			−1.14365			−0.571825	+	0.820376i	$0.693764\pi$
$998$	−17.4957			−0.553816
$999$	−3.04991	−	2.21589i	−0.0964949	−	0.0701076i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.h.721.4	✓	16
31.4	even	5	inner	930.2.n.h.841.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.h.721.4	✓	16	1.1	even	1	trivial
930.2.n.h.841.4	yes	16	31.4	even	5	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(1.31796 + 0.957557i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(1.31796 + 0.957557i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(0.309017 - 0.951057i) q^{10} +(-0.438591 - 0.318655i) q^{11} +(0.309017 - 0.951057i) q^{12} +(-1.26948 - 3.90705i) q^{13} +(-1.31796 + 0.957557i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-4.63894 + 3.37039i) q^{17} +(-0.309017 - 0.951057i) q^{18} +(-1.96388 + 6.04420i) q^{19} +(0.809017 + 0.587785i) q^{20} +(-0.503417 + 1.54936i) q^{21} +(0.438591 - 0.318655i) q^{22} +(-6.13886 + 4.46015i) q^{23} +(0.809017 + 0.587785i) q^{24} +1.00000 q^{25} +4.10812 q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.503417 - 1.54936i) q^{28} +(-0.0513096 + 0.157915i) q^{29} +1.00000 q^{30} +(-5.47576 + 1.00798i) q^{31} -1.00000 q^{32} +(0.167527 - 0.515594i) q^{33} +(-1.77192 - 5.45340i) q^{34} +(-1.31796 - 0.957557i) q^{35} +1.00000 q^{36} +3.76990 q^{37} +(-5.14150 - 3.73552i) q^{38} +(3.32354 - 2.41469i) q^{39} +(-0.809017 + 0.587785i) q^{40} +(2.66998 - 8.21736i) q^{41} +(-1.31796 - 0.957557i) q^{42} +(0.369599 - 1.13751i) q^{43} +(0.167527 + 0.515594i) q^{44} +(0.809017 - 0.587785i) q^{45} +(-2.34484 - 7.21667i) q^{46} +(0.679710 + 2.09193i) q^{47} +(-0.809017 + 0.587785i) q^{48} +(-1.34301 - 4.13335i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(-4.63894 - 3.37039i) q^{51} +(-1.26948 + 3.90705i) q^{52} +(-11.3745 + 8.26405i) q^{53} +(0.809017 - 0.587785i) q^{54} +(0.438591 + 0.318655i) q^{55} +1.62909 q^{56} -6.35525 q^{57} +(-0.134330 - 0.0975966i) q^{58} +(-1.83265 - 5.64033i) q^{59} +(-0.309017 + 0.951057i) q^{60} +10.3419 q^{61} +(0.733458 - 5.51924i) q^{62} -1.62909 q^{63} +(0.309017 - 0.951057i) q^{64} +(1.26948 + 3.90705i) q^{65} +(0.438591 + 0.318655i) q^{66} -7.49953 q^{67} +5.73404 q^{68} +(-6.13886 - 4.46015i) q^{69} +(1.31796 - 0.957557i) q^{70} +(-8.09841 + 5.88384i) q^{71} +(-0.309017 + 0.951057i) q^{72} +(-5.10048 - 3.70571i) q^{73} +(-1.16496 + 3.58538i) q^{74} +(0.309017 + 0.951057i) q^{75} +(5.14150 - 3.73552i) q^{76} +(-0.272917 - 0.839951i) q^{77} +(1.26948 + 3.90705i) q^{78} +(4.55240 - 3.30751i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(0.309017 - 0.951057i) q^{81} +(6.99010 + 5.07861i) q^{82} +(-3.17470 + 9.77074i) q^{83} +(1.31796 - 0.957557i) q^{84} +(4.63894 - 3.37039i) q^{85} +(0.967622 + 0.703018i) q^{86} -0.166041 q^{87} -0.542128 q^{88} +(2.10428 + 1.52885i) q^{89} +(0.309017 + 0.951057i) q^{90} +(2.06810 - 6.36495i) q^{91} +7.58805 q^{92} +(-2.65075 - 4.89628i) q^{93} -2.19959 q^{94} +(1.96388 - 6.04420i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(15.1329 + 10.9947i) q^{97} +4.34606 q^{98} +0.542128 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 4 q^{3} - 4 q^{4} - 16 q^{5} - 16 q^{6} - 7 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 - 4 * q^3 - 4 * q^4 - 16 * q^5 - 16 * q^6 - 7 * q^7 + 4 * q^8 - 4 * q^9	\( 16 q + 4 q^{2} - 4 q^{3} - 4 q^{4} - 16 q^{5} - 16 q^{6} - 7 q^{7} + 4 q^{8} - 4 q^{9} - 4 q^{10} + 4 q^{11} - 4 q^{12} + 2 q^{13} + 7 q^{14} + 4 q^{15} - 4 q^{16} + 5 q^{17} + 4 q^{18} - 2 q^{19} + 4 q^{20} + 8 q^{21} - 4 q^{22} - 4 q^{23} + 4 q^{24} + 16 q^{25} + 8 q^{26} - 4 q^{27} + 8 q^{28} + 5 q^{29} + 16 q^{30} - q^{31} - 16 q^{32} - q^{33} - 5 q^{34} + 7 q^{35} + 16 q^{36} - 20 q^{37} - 3 q^{38} + 2 q^{39} - 4 q^{40} - 17 q^{41} + 7 q^{42} - 4 q^{43} - q^{44} + 4 q^{45} - 6 q^{46} + 2 q^{47} - 4 q^{48} - 21 q^{49} + 4 q^{50} + 5 q^{51} + 2 q^{52} + 9 q^{53} + 4 q^{54} - 4 q^{55} + 2 q^{56} - 2 q^{57} - 5 q^{58} - 3 q^{59} + 4 q^{60} + 70 q^{61} - 4 q^{62} - 2 q^{63} - 4 q^{64} - 2 q^{65} - 4 q^{66} - 66 q^{67} - 20 q^{68} - 4 q^{69} - 7 q^{70} - 25 q^{71} + 4 q^{72} - 10 q^{73} - 15 q^{74} - 4 q^{75} + 3 q^{76} + 26 q^{77} - 2 q^{78} + 14 q^{79} + 4 q^{80} - 4 q^{81} + 17 q^{82} + 20 q^{83} - 7 q^{84} - 5 q^{85} - 6 q^{86} - 20 q^{87} + 6 q^{88} - 13 q^{89} - 4 q^{90} - 4 q^{91} - 4 q^{92} + 4 q^{93} - 12 q^{94} + 2 q^{95} + 4 q^{96} + 55 q^{97} - 14 q^{98} - 6 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 4 * q^3 - 4 * q^4 - 16 * q^5 - 16 * q^6 - 7 * q^7 + 4 * q^8 - 4 * q^9 - 4 * q^10 + 4 * q^11 - 4 * q^12 + 2 * q^13 + 7 * q^14 + 4 * q^15 - 4 * q^16 + 5 * q^17 + 4 * q^18 - 2 * q^19 + 4 * q^20 + 8 * q^21 - 4 * q^22 - 4 * q^23 + 4 * q^24 + 16 * q^25 + 8 * q^26 - 4 * q^27 + 8 * q^28 + 5 * q^29 + 16 * q^30 - q^31 - 16 * q^32 - q^33 - 5 * q^34 + 7 * q^35 + 16 * q^36 - 20 * q^37 - 3 * q^38 + 2 * q^39 - 4 * q^40 - 17 * q^41 + 7 * q^42 - 4 * q^43 - q^44 + 4 * q^45 - 6 * q^46 + 2 * q^47 - 4 * q^48 - 21 * q^49 + 4 * q^50 + 5 * q^51 + 2 * q^52 + 9 * q^53 + 4 * q^54 - 4 * q^55 + 2 * q^56 - 2 * q^57 - 5 * q^58 - 3 * q^59 + 4 * q^60 + 70 * q^61 - 4 * q^62 - 2 * q^63 - 4 * q^64 - 2 * q^65 - 4 * q^66 - 66 * q^67 - 20 * q^68 - 4 * q^69 - 7 * q^70 - 25 * q^71 + 4 * q^72 - 10 * q^73 - 15 * q^74 - 4 * q^75 + 3 * q^76 + 26 * q^77 - 2 * q^78 + 14 * q^79 + 4 * q^80 - 4 * q^81 + 17 * q^82 + 20 * q^83 - 7 * q^84 - 5 * q^85 - 6 * q^86 - 20 * q^87 + 6 * q^88 - 13 * q^89 - 4 * q^90 - 4 * q^91 - 4 * q^92 + 4 * q^93 - 12 * q^94 + 2 * q^95 + 4 * q^96 + 55 * q^97 - 14 * q^98 - 6 * q^99

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