LMFDB - Embedded newform 930.2.n.b.481.2

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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.1816890625.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 8x^{6} - 15x^{5} + 41x^{4} + 15x^{3} + 62x^{2} + 133x + 361 $ x^8 - x^7 + 8x^6 - 15x^5 + 41x^4 + 15x^3 + 62x^2 + 133x + 361
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			481.2
Root			$-0.903072 - 2.77937i$ of defining polynomial
Character	$\chi$	$=$	930.481
Dual form			930.2.n.b.901.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{4} -1.00000 q^{5} +1.00000 q^{6} +(0.712089 - 2.19158i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{4} -1.00000 q^{5} +1.00000 q^{6} +(0.712089 - 2.19158i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-0.809017 + 0.587785i) q^{10} +(0.594055 - 1.82831i) q^{11} +(0.809017 - 0.587785i) q^{12} +(0.253761 + 0.184368i) q^{13} +(-0.712089 - 2.19158i) q^{14} +(-0.809017 - 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.05813 + 3.25659i) q^{17} +(0.809017 + 0.587785i) q^{18} +(6.53756 - 4.74982i) q^{19} +(-0.309017 + 0.951057i) q^{20} +(1.86427 - 1.35447i) q^{21} +(-0.594055 - 1.82831i) q^{22} +(-1.96120 - 6.03596i) q^{23} +(0.309017 - 0.951057i) q^{24} +1.00000 q^{25} +0.313665 q^{26} +(-0.309017 + 0.951057i) q^{27} +(-1.86427 - 1.35447i) q^{28} +(2.71209 - 1.97045i) q^{29} -1.00000 q^{30} +(-4.67329 - 3.02661i) q^{31} -1.00000 q^{32} +(1.55526 - 1.12996i) q^{33} +(2.77022 + 2.01268i) q^{34} +(-0.712089 + 2.19158i) q^{35} +1.00000 q^{36} +1.00575 q^{37} +(2.49713 - 7.68537i) q^{38} +(0.0969280 + 0.298314i) q^{39} +(0.309017 + 0.951057i) q^{40} +(-6.28668 + 4.56754i) q^{41} +(0.712089 - 2.19158i) q^{42} +(1.90772 - 1.38604i) q^{43} +(-1.55526 - 1.12996i) q^{44} +(-0.309017 - 0.951057i) q^{45} +(-5.13449 - 3.73043i) q^{46} +(4.93599 + 3.58620i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(1.36715 + 0.993290i) q^{49} +(0.809017 - 0.587785i) q^{50} +(-1.05813 + 3.25659i) q^{51} +(0.253761 - 0.184368i) q^{52} +(0.705803 + 2.17224i) q^{53} +(0.309017 + 0.951057i) q^{54} +(-0.594055 + 1.82831i) q^{55} -2.30437 q^{56} +8.08087 q^{57} +(1.03593 - 3.18825i) q^{58} +(-3.16864 - 2.30215i) q^{59} +(-0.809017 + 0.587785i) q^{60} +4.99070 q^{61} +(-5.55977 + 0.298314i) q^{62} +2.30437 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-0.253761 - 0.184368i) q^{65} +(0.594055 - 1.82831i) q^{66} +2.91311 q^{67} +3.42418 q^{68} +(1.96120 - 6.03596i) q^{69} +(0.712089 + 2.19158i) q^{70} +(0.936125 + 2.88110i) q^{71} +(0.809017 - 0.587785i) q^{72} +(-0.0249911 + 0.0769148i) q^{73} +(0.813665 - 0.591163i) q^{74} +(0.809017 + 0.587785i) q^{75} +(-2.49713 - 7.68537i) q^{76} +(-3.58388 - 2.60384i) q^{77} +(0.253761 + 0.184368i) q^{78} +(0.728684 + 2.24266i) q^{79} +(0.809017 + 0.587785i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-2.40130 + 7.39043i) q^{82} +(-6.41953 + 4.66406i) q^{83} +(-0.712089 - 2.19158i) q^{84} +(-1.05813 - 3.25659i) q^{85} +(0.728684 - 2.24266i) q^{86} +3.35233 q^{87} -1.92240 q^{88} +(-1.34106 + 4.12735i) q^{89} +(-0.809017 - 0.587785i) q^{90} +(0.584758 - 0.424852i) q^{91} -6.34658 q^{92} +(-2.00178 - 5.19547i) q^{93} +6.10122 q^{94} +(-6.53756 + 4.74982i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(-2.65218 + 8.16258i) q^{97} +1.68989 q^{98} +1.92240 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 8 q^{6} - 7 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 8 * q^6 - 7 * q^7 + 2 * q^8 - 2 * q^9	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 8 q^{6} - 7 q^{7} + 2 q^{8} - 2 q^{9} - 2 q^{10} + q^{11} + 2 q^{12} + 11 q^{13} + 7 q^{14} - 2 q^{15} - 2 q^{16} + 7 q^{17} + 2 q^{18} + 12 q^{19} + 2 q^{20} - 3 q^{21} - q^{22} - 6 q^{23} - 2 q^{24} + 8 q^{25} + 4 q^{26} + 2 q^{27} + 3 q^{28} + 9 q^{29} - 8 q^{30} - 15 q^{31} - 8 q^{32} - q^{33} + 8 q^{34} + 7 q^{35} + 8 q^{36} + 32 q^{37} + 8 q^{38} + 9 q^{39} - 2 q^{40} - 13 q^{41} - 7 q^{42} + 13 q^{43} + q^{44} + 2 q^{45} - 9 q^{46} - 15 q^{47} + 2 q^{48} + 5 q^{49} + 2 q^{50} - 7 q^{51} + 11 q^{52} + 25 q^{53} - 2 q^{54} - q^{55} - 8 q^{56} + 8 q^{57} + 6 q^{58} + 3 q^{59} - 2 q^{60} + 28 q^{61} - 5 q^{62} + 8 q^{63} - 2 q^{64} - 11 q^{65} + q^{66} - 8 q^{67} + 2 q^{68} + 6 q^{69} - 7 q^{70} - 15 q^{71} + 2 q^{72} - 24 q^{73} + 8 q^{74} + 2 q^{75} - 8 q^{76} - 16 q^{77} + 11 q^{78} + 2 q^{79} + 2 q^{80} - 2 q^{81} - 17 q^{82} - 20 q^{83} + 7 q^{84} - 7 q^{85} + 2 q^{86} + 6 q^{87} + 4 q^{88} + 37 q^{89} - 2 q^{90} - 11 q^{91} - 6 q^{92} - 10 q^{93} + 10 q^{94} - 12 q^{95} - 2 q^{96} - 16 q^{97} - 4 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 8 * q^6 - 7 * q^7 + 2 * q^8 - 2 * q^9 - 2 * q^10 + q^11 + 2 * q^12 + 11 * q^13 + 7 * q^14 - 2 * q^15 - 2 * q^16 + 7 * q^17 + 2 * q^18 + 12 * q^19 + 2 * q^20 - 3 * q^21 - q^22 - 6 * q^23 - 2 * q^24 + 8 * q^25 + 4 * q^26 + 2 * q^27 + 3 * q^28 + 9 * q^29 - 8 * q^30 - 15 * q^31 - 8 * q^32 - q^33 + 8 * q^34 + 7 * q^35 + 8 * q^36 + 32 * q^37 + 8 * q^38 + 9 * q^39 - 2 * q^40 - 13 * q^41 - 7 * q^42 + 13 * q^43 + q^44 + 2 * q^45 - 9 * q^46 - 15 * q^47 + 2 * q^48 + 5 * q^49 + 2 * q^50 - 7 * q^51 + 11 * q^52 + 25 * q^53 - 2 * q^54 - q^55 - 8 * q^56 + 8 * q^57 + 6 * q^58 + 3 * q^59 - 2 * q^60 + 28 * q^61 - 5 * q^62 + 8 * q^63 - 2 * q^64 - 11 * q^65 + q^66 - 8 * q^67 + 2 * q^68 + 6 * q^69 - 7 * q^70 - 15 * q^71 + 2 * q^72 - 24 * q^73 + 8 * q^74 + 2 * q^75 - 8 * q^76 - 16 * q^77 + 11 * q^78 + 2 * q^79 + 2 * q^80 - 2 * q^81 - 17 * q^82 - 20 * q^83 + 7 * q^84 - 7 * q^85 + 2 * q^86 + 6 * q^87 + 4 * q^88 + 37 * q^89 - 2 * q^90 - 11 * q^91 - 6 * q^92 - 10 * q^93 + 10 * q^94 - 12 * q^95 - 2 * q^96 - 16 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	1.00000			0.408248
$7$	0.712089	−	2.19158i	0.269144	−	0.828341i	−0.721565	−	0.692346i	$-0.756577\pi$
$7$	0.712089	−	2.19158i	0.269144	−	0.828341i	0.990710	−	0.135995i	$-0.0434230\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$	−0.809017	+	0.587785i	−0.255834	+	0.185874i
$11$	0.594055	−	1.82831i	0.179114	−	0.551257i	−0.820683	−	0.571384i	$-0.806407\pi$
$11$	0.594055	−	1.82831i	0.179114	−	0.551257i	0.999797	+	0.0201264i	$0.00640686\pi$
$12$	0.809017	−	0.587785i	0.233543	−	0.169679i
$13$	0.253761	+	0.184368i	0.0703806	+	0.0511345i	0.622419	−	0.782684i	$-0.286150\pi$
$13$	0.253761	+	0.184368i	0.0703806	+	0.0511345i	−0.552039	+	0.833819i	$0.686150\pi$
$14$	−0.712089	−	2.19158i	−0.190314	−	0.585726i
$15$	−0.809017	−	0.587785i	−0.208887	−	0.151765i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	1.05813	+	3.25659i	0.256634	+	0.789838i	0.993503	+	0.113803i	$0.0363033\pi$
$17$	1.05813	+	3.25659i	0.256634	+	0.789838i	−0.736869	+	0.676035i	$0.763697\pi$
$18$	0.809017	+	0.587785i	0.190687	+	0.138542i
$19$	6.53756	−	4.74982i	1.49982	−	1.08968i	0.529367	−	0.848393i	$-0.322430\pi$
$19$	6.53756	−	4.74982i	1.49982	−	1.08968i	0.970453	−	0.241290i	$-0.0775705\pi$
$20$	−0.309017	+	0.951057i	−0.0690983	+	0.212663i
$21$	1.86427	−	1.35447i	0.406818	−	0.295570i
$22$	−0.594055	−	1.82831i	−0.126653	−	0.389798i
$23$	−1.96120	−	6.03596i	−0.408939	−	1.25858i	−0.917561	−	0.397594i	$-0.869845\pi$
$23$	−1.96120	−	6.03596i	−0.408939	−	1.25858i	0.508623	−	0.860990i	$-0.330155\pi$
$24$	0.309017	−	0.951057i	0.0630778	−	0.194134i
$25$	1.00000			0.200000
$26$	0.313665			0.0615149
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$	−1.86427	−	1.35447i	−0.352315	−	0.255971i
$29$	2.71209	−	1.97045i	0.503622	−	0.365903i	−0.306777	−	0.951782i	$-0.599250\pi$
$29$	2.71209	−	1.97045i	0.503622	−	0.365903i	0.810399	+	0.585879i	$0.199250\pi$
$30$	−1.00000			−0.182574
$31$	−4.67329	−	3.02661i	−0.839348	−	0.543595i
$31$	−4.67329	−	3.02661i	−0.839348	−	0.543595i
$32$	−1.00000			−0.176777
$33$	1.55526	−	1.12996i	0.270735	−	0.196701i
$34$	2.77022	+	2.01268i	0.475089	+	0.345172i
$35$	−0.712089	+	2.19158i	−0.120365	+	0.370445i
$36$	1.00000			0.166667
$37$	1.00575			0.165344			0.0826718	−	0.996577i	$-0.473655\pi$
$37$	1.00575			0.165344			0.0826718	+	0.996577i	$0.473655\pi$
$38$	2.49713	−	7.68537i	0.405088	−	1.24673i
$39$	0.0969280	+	0.298314i	0.0155209	+	0.0477684i
$40$	0.309017	+	0.951057i	0.0488599	+	0.150375i
$41$	−6.28668	+	4.56754i	−0.981814	+	0.713329i	−0.958113	−	0.286390i	$-0.907545\pi$
$41$	−6.28668	+	4.56754i	−0.981814	+	0.713329i	−0.0237006	+	0.999719i	$0.507545\pi$
$42$	0.712089	−	2.19158i	0.109878	−	0.338169i
$43$	1.90772	−	1.38604i	0.290925	−	0.211369i	−0.432744	−	0.901517i	$-0.642455\pi$
$43$	1.90772	−	1.38604i	0.290925	−	0.211369i	0.723668	+	0.690148i	$0.242455\pi$
$44$	−1.55526	−	1.12996i	−0.234464	−	0.170348i
$45$	−0.309017	−	0.951057i	−0.0460655	−	0.141775i
$46$	−5.13449	−	3.73043i	−0.757039	−	0.550021i
$47$	4.93599	+	3.58620i	0.719988	+	0.523102i	0.886380	−	0.462958i	$-0.153212\pi$
$47$	4.93599	+	3.58620i	0.719988	+	0.523102i	−0.166393	+	0.986060i	$0.553212\pi$
$48$	−0.309017	−	0.951057i	−0.0446028	−	0.137273i
$49$	1.36715	+	0.993290i	0.195307	+	0.141899i
$50$	0.809017	−	0.587785i	0.114412	−	0.0831254i
$51$	−1.05813	+	3.25659i	−0.148168	+	0.456013i
$52$	0.253761	−	0.184368i	0.0351903	−	0.0255672i
$53$	0.705803	+	2.17224i	0.0969495	+	0.298380i	0.987757	−	0.156001i	$-0.0498604\pi$
$53$	0.705803	+	2.17224i	0.0969495	+	0.298380i	−0.890807	+	0.454381i	$0.849860\pi$
$54$	0.309017	+	0.951057i	0.0420519	+	0.129422i
$55$	−0.594055	+	1.82831i	−0.0801024	+	0.246530i
$56$	−2.30437			−0.307934
$57$	8.08087			1.07034
$58$	1.03593	−	3.18825i	0.136024	−	0.418638i
$59$	−3.16864	−	2.30215i	−0.412522	−	0.299715i	0.362100	−	0.932139i	$-0.382060\pi$
$59$	−3.16864	−	2.30215i	−0.412522	−	0.299715i	−0.774622	+	0.632424i	$0.782060\pi$
$60$	−0.809017	+	0.587785i	−0.104444	+	0.0758827i
$61$	4.99070			0.638994			0.319497	−	0.947587i	$-0.396486\pi$
$61$	4.99070			0.638994			0.319497	+	0.947587i	$0.396486\pi$
$62$	−5.55977	+	0.298314i	−0.706091	+	0.0378859i
$63$	2.30437			0.290323
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−0.253761	−	0.184368i	−0.0314751	−	0.0228680i
$66$	0.594055	−	1.82831i	0.0731231	−	0.225050i
$67$	2.91311			0.355892			0.177946	−	0.984040i	$-0.443055\pi$
$67$	2.91311			0.355892			0.177946	+	0.984040i	$0.443055\pi$
$68$	3.42418			0.415243
$69$	1.96120	−	6.03596i	0.236101	−	0.726644i
$70$	0.712089	+	2.19158i	0.0851109	+	0.261944i
$71$	0.936125	+	2.88110i	0.111098	+	0.341923i	0.991113	−	0.133022i	$-0.0424680\pi$
$71$	0.936125	+	2.88110i	0.111098	+	0.341923i	−0.880016	+	0.474945i	$0.842468\pi$
$72$	0.809017	−	0.587785i	0.0953436	−	0.0692712i
$73$	−0.0249911	+	0.0769148i	−0.00292499	+	0.00900220i	−0.952508	−	0.304512i	$-0.901506\pi$
$73$	−0.0249911	+	0.0769148i	−0.00292499	+	0.00900220i	0.949583	+	0.313515i	$0.101506\pi$
$74$	0.813665	−	0.591163i	0.0945867	−	0.0687213i
$75$	0.809017	+	0.587785i	0.0934172	+	0.0678716i
$76$	−2.49713	−	7.68537i	−0.286440	−	0.881572i
$77$	−3.58388	−	2.60384i	−0.408421	−	0.296736i
$78$	0.253761	+	0.184368i	0.0287327	+	0.0208756i
$79$	0.728684	+	2.24266i	0.0819834	+	0.252319i	0.983643	−	0.180127i	$-0.0576508\pi$
$79$	0.728684	+	2.24266i	0.0819834	+	0.252319i	−0.901660	+	0.432446i	$0.857651\pi$
$80$	0.809017	+	0.587785i	0.0904508	+	0.0657164i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−2.40130	+	7.39043i	−0.265179	+	0.816137i
$83$	−6.41953	+	4.66406i	−0.704635	+	0.511947i	−0.881438	−	0.472299i	$-0.843424\pi$
$83$	−6.41953	+	4.66406i	−0.704635	+	0.511947i	0.176804	+	0.984246i	$0.443424\pi$
$84$	−0.712089	−	2.19158i	−0.0776953	−	0.239121i
$85$	−1.05813	−	3.25659i	−0.114770	−	0.353226i
$86$	0.728684	−	2.24266i	0.0785761	−	0.241832i
$87$	3.35233			0.359407
$88$	−1.92240			−0.204929
$89$	−1.34106	+	4.12735i	−0.142152	+	0.437498i	−0.996634	−	0.0819828i	$-0.973875\pi$
$89$	−1.34106	+	4.12735i	−0.142152	+	0.437498i	0.854482	+	0.519481i	$0.173875\pi$
$90$	−0.809017	−	0.587785i	−0.0852779	−	0.0619580i
$91$	0.584758	−	0.424852i	0.0612993	−	0.0445366i
$92$	−6.34658			−0.661677
$93$	−2.00178	−	5.19547i	−0.207574	−	0.538745i
$94$	6.10122			0.629292
$95$	−6.53756	+	4.74982i	−0.670740	+	0.487321i
$96$	−0.809017	−	0.587785i	−0.0825700	−	0.0599906i
$97$	−2.65218	+	8.16258i	−0.269289	+	0.828785i	0.721386	+	0.692533i	$0.243505\pi$
$97$	−2.65218	+	8.16258i	−0.269289	+	0.828785i	−0.990674	+	0.136251i	$0.956495\pi$
$98$	1.68989			0.170704
$99$	1.92240			0.193209
$100$	0.309017	−	0.951057i	0.0309017	−	0.0951057i
$101$	2.15109	+	6.62036i	0.214041	+	0.658751i	0.999220	+	0.0394822i	$0.0125708\pi$
$101$	2.15109	+	6.62036i	0.214041	+	0.658751i	−0.785179	+	0.619269i	$0.787429\pi$
$102$	1.05813	+	3.25659i	0.104770	+	0.322450i
$103$	−3.61339	+	2.62528i	−0.356037	+	0.258676i	−0.751397	−	0.659850i	$-0.770620\pi$
$103$	−3.61339	+	2.62528i	−0.356037	+	0.258676i	0.395360	+	0.918526i	$0.370620\pi$
$104$	0.0969280	−	0.298314i	0.00950457	−	0.0292521i
$105$	−1.86427	+	1.35447i	−0.181934	+	0.132183i
$106$	1.84782	+	1.34252i	0.179476	+	0.130397i
$107$	4.15669	+	12.7930i	0.401843	+	1.23675i	0.923503	+	0.383592i	$0.125313\pi$
$107$	4.15669	+	12.7930i	0.401843	+	1.23675i	−0.521660	+	0.853154i	$0.674687\pi$
$108$	0.809017	+	0.587785i	0.0778477	+	0.0565597i
$109$	−11.5465	−	8.38902i	−1.10595	−	0.803523i	−0.123932	−	0.992291i	$-0.539551\pi$
$109$	−11.5465	−	8.38902i	−1.10595	−	0.803523i	−0.982022	+	0.188768i	$0.939551\pi$
$110$	0.594055	+	1.82831i	0.0566409	+	0.174323i
$111$	0.813665	+	0.591163i	0.0772297	+	0.0561107i
$112$	−1.86427	+	1.35447i	−0.176157	+	0.127986i
$113$	−1.41612	+	4.35836i	−0.133217	+	0.410000i	−0.995308	−	0.0967530i	$-0.969154\pi$
$113$	−1.41612	+	4.35836i	−0.133217	+	0.410000i	0.862091	+	0.506753i	$0.169154\pi$
$114$	6.53756	−	4.74982i	0.612299	−	0.444861i
$115$	1.96120	+	6.03596i	0.182883	+	0.562856i
$116$	−1.03593	−	3.18825i	−0.0961833	−	0.296022i
$117$	−0.0969280	+	0.298314i	−0.00896099	+	0.0275791i
$118$	−3.91666			−0.360557
$119$	7.89057			0.723327
$120$	−0.309017	+	0.951057i	−0.0282093	+	0.0868192i
$121$	5.90936	+	4.29340i	0.537214	+	0.390309i
$122$	4.03756	−	2.93346i	0.365544	−	0.265583i
$123$	−7.77076			−0.700666
$124$	−4.32260	+	3.50929i	−0.388181	+	0.315144i
$125$	−1.00000			−0.0894427
$126$	1.86427	−	1.35447i	0.166083	−	0.120666i
$127$	−8.67958	−	6.30608i	−0.770188	−	0.559574i	0.131830	−	0.991272i	$-0.457915\pi$
$127$	−8.67958	−	6.30608i	−0.770188	−	0.559574i	−0.902018	+	0.431698i	$0.857915\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	2.35807			0.207617
$130$	−0.313665			−0.0275103
$131$	−4.79406	+	14.7546i	−0.418859	+	1.28912i	0.489895	+	0.871782i	$0.337035\pi$
$131$	−4.79406	+	14.7546i	−0.418859	+	1.28912i	−0.908753	+	0.417333i	$0.862965\pi$
$132$	−0.594055	−	1.82831i	−0.0517059	−	0.159134i
$133$	−5.75430	−	17.7099i	−0.498961	−	1.53564i
$134$	2.35675	−	1.71228i	0.203592	−	0.147919i
$135$	0.309017	−	0.951057i	0.0265959	−	0.0818539i
$136$	2.77022	−	2.01268i	0.237544	−	0.172586i
$137$	0.0940550	+	0.0683350i	0.00803567	+	0.00583825i	0.591796	−	0.806088i	$-0.298419\pi$
$137$	0.0940550	+	0.0683350i	0.00803567	+	0.00583825i	−0.583760	+	0.811926i	$0.698419\pi$
$138$	−1.96120	−	6.03596i	−0.166949	−	0.513815i
$139$	1.71009	+	1.24245i	0.145048	+	0.105384i	0.657943	−	0.753068i	$-0.271427\pi$
$139$	1.71009	+	1.24245i	0.145048	+	0.105384i	−0.512895	+	0.858452i	$0.671427\pi$
$140$	1.86427	+	1.35447i	0.157560	+	0.114474i
$141$	1.88538	+	5.80260i	0.158778	+	0.488667i
$142$	2.45081	+	1.78062i	0.205667	+	0.149426i
$143$	0.487830	−	0.354429i	0.0407944	−	0.0296389i
$144$	0.309017	−	0.951057i	0.0257514	−	0.0792547i
$145$	−2.71209	+	1.97045i	−0.225227	+	0.163637i
$146$	0.0249911	+	0.0769148i	0.00206828	+	0.00636552i
$147$	0.522203	+	1.60718i	0.0430706	+	0.132558i
$148$	0.310793	−	0.956521i	0.0255470	−	0.0786256i
$149$	−6.23252			−0.510588			−0.255294	−	0.966864i	$-0.582172\pi$
$149$	−6.23252			−0.510588			−0.255294	+	0.966864i	$0.582172\pi$
$150$	1.00000			0.0816497
$151$	3.94010	−	12.1264i	0.320640	−	0.986830i	−0.652730	−	0.757591i	$-0.726376\pi$
$151$	3.94010	−	12.1264i	0.320640	−	0.986830i	0.973370	−	0.229239i	$-0.0736237\pi$
$152$	−6.53756	−	4.74982i	−0.530266	−	0.385261i
$153$	−2.77022	+	2.01268i	−0.223959	+	0.162716i
$154$	−4.42992			−0.356973
$155$	4.67329	+	3.02661i	0.375368	+	0.243103i
$156$	0.313665			0.0251133
$157$	−12.7690	+	9.27721i	−1.01908	+	0.740402i	−0.966093	−	0.258194i	$-0.916873\pi$
$157$	−12.7690	+	9.27721i	−1.01908	+	0.740402i	−0.0529826	+	0.998595i	$0.516873\pi$
$158$	1.90772	+	1.38604i	0.151770	+	0.110267i
$159$	−0.705803	+	2.17224i	−0.0559738	+	0.172270i
$160$	1.00000			0.0790569
$161$	−14.6249			−1.15260
$162$	−0.309017	+	0.951057i	−0.0242787	+	0.0747221i
$163$	2.92186	+	8.99257i	0.228858	+	0.704352i	0.997877	+	0.0651264i	$0.0207451\pi$
$163$	2.92186	+	8.99257i	0.228858	+	0.704352i	−0.769019	+	0.639226i	$0.779255\pi$
$164$	2.40130	+	7.39043i	0.187510	+	0.577096i
$165$	−1.55526	+	1.12996i	−0.121077	+	0.0879673i
$166$	−2.45204	+	7.54661i	−0.190315	+	0.585731i
$167$	2.17616	−	1.58108i	0.168397	−	0.122347i	−0.500395	−	0.865797i	$-0.666812\pi$
$167$	2.17616	−	1.58108i	0.168397	−	0.122347i	0.668792	+	0.743450i	$0.266812\pi$
$168$	−1.86427	−	1.35447i	−0.143832	−	0.104500i
$169$	−3.98682	−	12.2702i	−0.306678	−	0.943859i
$170$	−2.77022	−	2.01268i	−0.212466	−	0.154366i
$171$	6.53756	+	4.74982i	0.499940	+	0.363228i
$172$	−0.728684	−	2.24266i	−0.0555617	−	0.171001i
$173$	3.29397	+	2.39321i	0.250436	+	0.181953i	0.705920	−	0.708291i	$-0.250534\pi$
$173$	3.29397	+	2.39321i	0.250436	+	0.181953i	−0.455484	+	0.890244i	$0.650534\pi$
$174$	2.71209	−	1.97045i	0.205603	−	0.149379i
$175$	0.712089	−	2.19158i	0.0538289	−	0.165668i
$176$	−1.55526	+	1.12996i	−0.117232	+	0.0851739i
$177$	−1.21031	−	3.72496i	−0.0909727	−	0.279985i
$178$	1.34106	+	4.12735i	0.100517	+	0.309358i
$179$	1.30513	−	4.01678i	0.0975501	−	0.300228i	−0.890360	−	0.455258i	$-0.849547\pi$
$179$	1.30513	−	4.01678i	0.0975501	−	0.300228i	0.987910	+	0.155029i	$0.0495472\pi$
$180$	−1.00000			−0.0745356
$181$	6.95357			0.516855			0.258427	−	0.966031i	$-0.416796\pi$
$181$	6.95357			0.516855			0.258427	+	0.966031i	$0.416796\pi$
$182$	0.223358	−	0.687424i	0.0165564	−	0.0509553i
$183$	4.03756	+	2.93346i	0.298465	+	0.216848i
$184$	−5.13449	+	3.73043i	−0.378520	+	0.275011i
$185$	−1.00575			−0.0739439
$186$	−4.67329	−	3.02661i	−0.342662	−	0.221922i
$187$	6.58265			0.481371
$188$	4.93599	−	3.58620i	0.359994	−	0.261551i
$189$	1.86427	+	1.35447i	0.135606	+	0.0985235i
$190$	−2.49713	+	7.68537i	−0.181161	+	0.557555i
$191$	−19.8423			−1.43574			−0.717870	−	0.696177i	$-0.754883\pi$
$191$	−19.8423			−1.43574			−0.717870	+	0.696177i	$0.754883\pi$
$192$	−1.00000			−0.0721688
$193$	3.41155	−	10.4997i	0.245569	−	0.755784i	−0.749973	−	0.661468i	$-0.769934\pi$
$193$	3.41155	−	10.4997i	0.245569	−	0.755784i	0.995542	−	0.0943155i	$-0.0300663\pi$
$194$	2.65218	+	8.16258i	0.190416	+	0.586039i
$195$	−0.0969280	−	0.298314i	−0.00694116	−	0.0213627i
$196$	1.36715	−	0.993290i	0.0976533	−	0.0709493i
$197$	−6.71651	+	20.6713i	−0.478532	+	1.47277i	0.362603	+	0.931944i	$0.381888\pi$
$197$	−6.71651	+	20.6713i	−0.478532	+	1.47277i	−0.841135	+	0.540826i	$0.818112\pi$
$198$	1.55526	−	1.12996i	0.110527	−	0.0803028i
$199$	11.7647	+	8.54755i	0.833977	+	0.605920i	0.920682	−	0.390314i	$-0.127634\pi$
$199$	11.7647	+	8.54755i	0.833977	+	0.605920i	−0.0867046	+	0.996234i	$0.527634\pi$
$200$	−0.309017	−	0.951057i	−0.0218508	−	0.0672499i
$201$	2.35675	+	1.71228i	0.166232	+	0.120775i
$202$	5.63162	+	4.09161i	0.396239	+	0.287885i
$203$	−2.38715	−	7.34691i	−0.167545	−	0.515652i
$204$	2.77022	+	2.01268i	0.193954	+	0.140916i
$205$	6.28668	−	4.56754i	0.439080	−	0.319011i
$206$	−1.38019	+	4.24779i	−0.0961624	+	0.295958i
$207$	5.13449	−	3.73043i	0.356872	−	0.259283i
$208$	−0.0969280	−	0.298314i	−0.00672074	−	0.0206843i
$209$	−4.80048	−	14.7744i	−0.332056	−	1.02196i
$210$	−0.712089	+	2.19158i	−0.0491388	+	0.151234i
$211$	16.0455			1.10462			0.552308	−	0.833640i	$-0.313747\pi$
$211$	16.0455			1.10462			0.552308	+	0.833640i	$0.313747\pi$
$212$	2.28403			0.156868
$213$	−0.936125	+	2.88110i	−0.0641422	+	0.197409i
$214$	10.8824	+	7.90650i	0.743903	+	0.540477i
$215$	−1.90772	+	1.38604i	−0.130105	+	0.0945271i
$216$	1.00000			0.0680414
$217$	−9.96087	+	8.08670i	−0.676188	+	0.548961i
$218$	−14.2723			−0.966639
$219$	−0.0654277	+	0.0475360i	−0.00442119	+	0.00321218i
$220$	1.55526	+	1.12996i	0.104855	+	0.0761819i
$221$	−0.331899	+	1.02148i	−0.0223259	+	0.0687121i
$222$	1.00575			0.0675012
$223$	26.8459			1.79773			0.898867	−	0.438222i	$-0.144392\pi$
$223$	26.8459			1.79773			0.898867	+	0.438222i	$0.144392\pi$
$224$	−0.712089	+	2.19158i	−0.0475785	+	0.146431i
$225$	0.309017	+	0.951057i	0.0206011	+	0.0634038i
$226$	1.41612	+	4.35836i	0.0941987	+	0.289914i
$227$	−21.0279	+	15.2777i	−1.39567	+	1.01402i	−0.400457	+	0.916316i	$0.631149\pi$
$227$	−21.0279	+	15.2777i	−1.39567	+	1.01402i	−0.995216	+	0.0977002i	$0.968851\pi$
$228$	2.49713	−	7.68537i	0.165376	−	0.508976i
$229$	10.9961	−	7.98915i	0.726644	−	0.527938i	−0.161856	−	0.986814i	$-0.551748\pi$
$229$	10.9961	−	7.98915i	0.726644	−	0.527938i	0.888500	+	0.458877i	$0.151748\pi$
$230$	5.13449	+	3.73043i	0.338558	+	0.245977i
$231$	−1.36892	−	4.21311i	−0.0900684	−	0.277202i
$232$	−2.71209	−	1.97045i	−0.178057	−	0.129366i
$233$	22.8681	+	16.6146i	1.49814	+	1.08846i	0.971115	+	0.238610i	$0.0766918\pi$
$233$	22.8681	+	16.6146i	1.49814	+	1.08846i	0.527023	+	0.849851i	$0.323308\pi$
$234$	0.0969280	+	0.298314i	0.00633638	+	0.0195014i
$235$	−4.93599	−	3.58620i	−0.321988	−	0.233938i
$236$	−3.16864	+	2.30215i	−0.206261	+	0.149857i
$237$	−0.728684	+	2.24266i	−0.0473331	+	0.145676i
$238$	6.38360	−	4.63796i	0.413788	−	0.300634i
$239$	−8.98913	−	27.6657i	−0.581459	−	1.78955i	−0.613049	−	0.790045i	$-0.710057\pi$
$239$	−8.98913	−	27.6657i	−0.581459	−	1.78955i	0.0315900	−	0.999501i	$-0.489943\pi$
$240$	0.309017	+	0.951057i	0.0199470	+	0.0613904i
$241$	−0.234345	+	0.721240i	−0.0150955	+	0.0464591i	−0.958321	−	0.285695i	$-0.907775\pi$
$241$	−0.234345	+	0.721240i	−0.0150955	+	0.0464591i	0.943225	+	0.332154i	$0.107775\pi$
$242$	7.30437			0.469543
$243$	−1.00000			−0.0641500
$244$	1.54221	−	4.74644i	0.0987300	−	0.303860i
$245$	−1.36715	−	0.993290i	−0.0873438	−	0.0634590i
$246$	−6.28668	+	4.56754i	−0.400824	+	0.291216i
$247$	2.53469			0.161279
$248$	−1.43435	+	5.37984i	−0.0910813	+	0.341620i
$249$	−7.93497			−0.502859
$250$	−0.809017	+	0.587785i	−0.0511667	+	0.0371748i
$251$	−18.3280	−	13.3161i	−1.15685	−	0.840504i	−0.167477	−	0.985876i	$-0.553562\pi$
$251$	−18.3280	−	13.3161i	−1.15685	−	0.840504i	−0.989377	+	0.145372i	$0.953562\pi$
$252$	0.712089	−	2.19158i	0.0448574	−	0.138057i
$253$	−12.2007			−0.767050
$254$	−10.7285			−0.673169
$255$	1.05813	−	3.25659i	0.0662626	−	0.203935i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−4.33477	−	13.3411i	−0.270396	−	0.832192i	−0.990401	−	0.138224i	$-0.955861\pi$
$257$	−4.33477	−	13.3411i	−0.270396	−	0.832192i	0.720005	−	0.693968i	$-0.244139\pi$
$258$	1.90772	−	1.38604i	0.118769	−	0.0862911i
$259$	0.716181	−	2.20418i	0.0445013	−	0.136961i
$260$	−0.253761	+	0.184368i	−0.0157376	+	0.0114340i
$261$	2.71209	+	1.97045i	0.167874	+	0.121968i
$262$	4.79406	+	14.7546i	0.296178	+	0.911542i
$263$	16.4110	+	11.9233i	1.01195	+	0.735221i	0.964616	−	0.263658i	$-0.0849290\pi$
$263$	16.4110	+	11.9233i	1.01195	+	0.735221i	0.0473291	+	0.998879i	$0.484929\pi$
$264$	−1.55526	−	1.12996i	−0.0957194	−	0.0695442i
$265$	−0.705803	−	2.17224i	−0.0433571	−	0.133439i
$266$	−15.0650	−	10.9453i	−0.923692	−	0.671101i
$267$	−3.51093	+	2.55084i	−0.214866	+	0.156109i
$268$	0.900199	−	2.77053i	0.0549884	−	0.169237i
$269$	13.0054	−	9.44898i	0.792954	−	0.576115i	−0.115885	−	0.993263i	$-0.536970\pi$
$269$	13.0054	−	9.44898i	0.792954	−	0.576115i	0.908839	+	0.417148i	$0.136970\pi$
$270$	−0.309017	−	0.951057i	−0.0188062	−	0.0578795i
$271$	4.52009	+	13.9114i	0.274576	+	0.845058i	0.989331	+	0.145684i	$0.0465382\pi$
$271$	4.52009	+	13.9114i	0.274576	+	0.845058i	−0.714755	+	0.699375i	$0.753462\pi$
$272$	1.05813	−	3.25659i	0.0641585	−	0.197460i
$273$	0.722801			0.0437459
$274$	0.116258			0.00702343
$275$	0.594055	−	1.82831i	0.0358229	−	0.110251i
$276$	−5.13449	−	3.73043i	−0.309060	−	0.224545i
$277$	−20.7440	+	15.0714i	−1.24639	+	0.905552i	−0.998007	−	0.0631107i	$-0.979898\pi$
$277$	−20.7440	+	15.0714i	−1.24639	+	0.905552i	−0.248379	+	0.968663i	$0.579898\pi$
$278$	2.11379			0.126777
$279$	1.43435	−	5.37984i	0.0858723	−	0.322082i
$280$	2.30437			0.137712
$281$	−6.64489	+	4.82779i	−0.396401	+	0.288002i	−0.768073	−	0.640362i	$-0.778784\pi$
$281$	−6.64489	+	4.82779i	−0.396401	+	0.288002i	0.371673	+	0.928364i	$0.378784\pi$
$282$	4.93599	+	3.58620i	0.293934	+	0.213555i
$283$	−6.89842	+	21.2312i	−0.410069	+	1.26206i	0.506519	+	0.862229i	$0.330932\pi$
$283$	−6.89842	+	21.2312i	−0.410069	+	1.26206i	−0.916588	+	0.399833i	$0.869068\pi$
$284$	3.02936			0.179760
$285$	−8.08087			−0.478670
$286$	0.186335	−	0.573479i	0.0110182	−	0.0339105i
$287$	5.53347	+	17.0303i	0.326631	+	1.00527i
$288$	−0.309017	−	0.951057i	−0.0182090	−	0.0560415i
$289$	4.26757	−	3.10057i	0.251033	−	0.182386i
$290$	−1.03593	+	3.18825i	−0.0608317	+	0.187221i
$291$	−6.94351	+	5.04475i	−0.407036	+	0.295729i
$292$	0.0654277	+	0.0475360i	0.00382886	+	0.00278183i
$293$	−1.22336	−	3.76511i	−0.0714693	−	0.219960i	0.908941	−	0.416924i	$-0.136892\pi$
$293$	−1.22336	−	3.76511i	−0.0714693	−	0.219960i	−0.980411	+	0.196964i	$0.936892\pi$
$294$	1.36715	+	0.993290i	0.0797336	+	0.0579298i
$295$	3.16864	+	2.30215i	0.184485	+	0.134037i
$296$	−0.310793	−	0.956521i	−0.0180644	−	0.0555967i
$297$	1.55526	+	1.12996i	0.0902451	+	0.0655669i
$298$	−5.04221	+	3.66338i	−0.292088	+	0.212214i
$299$	0.615161	−	1.89327i	0.0355757	−	0.109491i
$300$	0.809017	−	0.587785i	0.0467086	−	0.0339358i
$301$	−1.67916	−	5.16792i	−0.0967850	−	0.297874i
$302$	−3.94010	−	12.1264i	−0.226727	−	0.697794i
$303$	−2.15109	+	6.62036i	−0.123577	+	0.380330i
$304$	−8.08087			−0.463470
$305$	−4.99070			−0.285767
$306$	−1.05813	+	3.25659i	−0.0604892	+	0.186167i
$307$	12.5647	+	9.12881i	0.717107	+	0.521009i	0.885459	−	0.464718i	$-0.153844\pi$
$307$	12.5647	+	9.12881i	0.717107	+	0.521009i	−0.168351	+	0.985727i	$0.553844\pi$
$308$	−3.58388	+	2.60384i	−0.204211	+	0.148368i
$309$	−4.46639			−0.254084
$310$	5.55977	−	0.298314i	0.315774	−	0.0169431i
$311$	12.5994			0.714449			0.357224	−	0.934019i	$-0.383723\pi$
$311$	12.5994			0.714449			0.357224	+	0.934019i	$0.383723\pi$
$312$	0.253761	−	0.184368i	0.0143664	−	0.0104378i
$313$	−4.55438	−	3.30895i	−0.257429	−	0.187033i	0.451584	−	0.892229i	$-0.350859\pi$
$313$	−4.55438	−	3.30895i	−0.257429	−	0.187033i	−0.709013	+	0.705196i	$0.750859\pi$
$314$	−4.87732	+	15.0108i	−0.275243	+	0.847111i
$315$	−2.30437			−0.129836
$316$	2.35807			0.132652
$317$	−7.85320	+	24.1697i	−0.441080	+	1.35750i	0.445647	+	0.895209i	$0.352974\pi$
$317$	−7.85320	+	24.1697i	−0.441080	+	1.35750i	−0.886726	+	0.462295i	$0.847026\pi$
$318$	0.705803	+	2.17224i	0.0395795	+	0.121813i
$319$	−1.99147	−	6.12910i	−0.111501	−	0.343164i
$320$	0.809017	−	0.587785i	0.0452254	−	0.0328582i
$321$	−4.15669	+	12.7930i	−0.232004	+	0.714035i
$322$	−11.8318	+	8.59628i	−0.659358	+	0.479052i
$323$	22.3858	+	16.2642i	1.24558	+	0.904966i
$324$	0.309017	+	0.951057i	0.0171676	+	0.0528365i
$325$	0.253761	+	0.184368i	0.0140761	+	0.0102269i
$326$	7.64953	+	5.55771i	0.423669	+	0.307813i
$327$	−4.41037	−	13.5737i	−0.243894	−	0.750629i
$328$	6.28668	+	4.56754i	0.347124	+	0.252200i
$329$	11.3743	−	8.26394i	0.627087	−	0.455606i
$330$	−0.594055	+	1.82831i	−0.0327017	+	0.100645i
$331$	16.5036	−	11.9906i	0.907120	−	0.659061i	−0.0331652	−	0.999450i	$-0.510559\pi$
$331$	16.5036	−	11.9906i	0.907120	−	0.659061i	0.940285	+	0.340389i	$0.110559\pi$
$332$	2.45204	+	7.54661i	0.134573	+	0.414174i
$333$	0.310793	+	0.956521i	0.0170313	+	0.0524170i
$334$	0.831220	−	2.55823i	0.0454824	−	0.139980i
$335$	−2.91311			−0.159160
$336$	−2.30437			−0.125714
$337$	0.631894	−	1.94477i	0.0344215	−	0.105938i	−0.932370	−	0.361507i	$-0.882263\pi$
$337$	0.631894	−	1.94477i	0.0344215	−	0.105938i	0.966791	+	0.255568i	$0.0822625\pi$
$338$	−10.4376	−	7.58338i	−0.567732	−	0.412481i
$339$	−3.70744	+	2.69361i	−0.201361	+	0.146297i
$340$	−3.42418			−0.185702
$341$	−8.30978	+	6.74627i	−0.450000	+	0.365331i
$342$	8.08087			0.436964
$343$	16.2003	−	11.7702i	0.874735	−	0.635532i
$344$	−1.90772	−	1.38604i	−0.102857	−	0.0747303i
$345$	−1.96120	+	6.03596i	−0.105588	+	0.324965i
$346$	4.07158			0.218889
$347$	16.1929			0.869281			0.434641	−	0.900604i	$-0.356875\pi$
$347$	16.1929			0.869281			0.434641	+	0.900604i	$0.356875\pi$
$348$	1.03593	−	3.18825i	0.0555315	−	0.170908i
$349$	−5.95253	−	18.3200i	−0.318632	−	0.980647i	−0.974234	−	0.225541i	$-0.927585\pi$
$349$	−5.95253	−	18.3200i	−0.318632	−	0.980647i	0.655602	−	0.755107i	$-0.272415\pi$
$350$	−0.712089	−	2.19158i	−0.0380628	−	0.117145i
$351$	−0.253761	+	0.184368i	−0.0135447	+	0.00984083i
$352$	−0.594055	+	1.82831i	−0.0316632	+	0.0974494i
$353$	18.6211	−	13.5290i	0.991100	−	0.720077i	0.0309386	−	0.999521i	$-0.490150\pi$
$353$	18.6211	−	13.5290i	0.991100	−	0.720077i	0.960162	+	0.279445i	$0.0901504\pi$
$354$	−3.16864	−	2.30215i	−0.168411	−	0.122358i
$355$	−0.936125	−	2.88110i	−0.0496844	−	0.152913i
$356$	3.51093	+	2.55084i	0.186079	+	0.135194i
$357$	6.38360	+	4.63796i	0.337856	+	0.245467i
$358$	−1.30513	−	4.01678i	−0.0689784	−	0.212294i
$359$	−12.7454	−	9.26008i	−0.672677	−	0.488728i	0.198243	−	0.980153i	$-0.436476\pi$
$359$	−12.7454	−	9.26008i	−0.672677	−	0.488728i	−0.870920	+	0.491424i	$0.836476\pi$
$360$	−0.809017	+	0.587785i	−0.0426389	+	0.0309790i
$361$	14.3076	−	44.0344i	0.753034	−	2.31760i
$362$	5.62556	−	4.08721i	0.295673	−	0.214819i
$363$	2.25717	+	6.94687i	0.118471	+	0.364616i
$364$	−0.223358	−	0.687424i	−0.0117071	−	0.0360308i
$365$	0.0249911	−	0.0769148i	0.00130810	−	0.00402591i
$366$	4.99070			0.260868
$367$	27.0022			1.40950			0.704751	−	0.709455i	$-0.251059\pi$
$367$	27.0022			1.40950			0.704751	+	0.709455i	$0.251059\pi$
$368$	−1.96120	+	6.03596i	−0.102235	+	0.314646i
$369$	−6.28668	−	4.56754i	−0.327271	−	0.237776i
$370$	−0.813665	+	0.591163i	−0.0423005	+	0.0307331i
$371$	5.26324			0.273254
$372$	−5.55977	+	0.298314i	−0.288260	+	0.0154668i
$373$	−30.7055			−1.58987			−0.794934	−	0.606696i	$-0.792495\pi$
$373$	−30.7055			−1.58987			−0.794934	+	0.606696i	$0.792495\pi$
$374$	5.32547	−	3.86918i	0.275374	−	0.200071i
$375$	−0.809017	−	0.587785i	−0.0417775	−	0.0303531i
$376$	1.88538	−	5.80260i	0.0972310	−	0.299246i
$377$	1.05151			0.0541555
$378$	2.30437			0.118524
$379$	1.06215	−	3.26897i	0.0545591	−	0.167916i	−0.920064	−	0.391768i	$-0.871863\pi$
$379$	1.06215	−	3.26897i	0.0545591	−	0.167916i	0.974623	+	0.223853i	$0.0718635\pi$
$380$	2.49713	+	7.68537i	0.128100	+	0.394251i
$381$	−3.31530	−	10.2035i	−0.169848	−	0.522739i
$382$	−16.0528	+	11.6630i	−0.821332	+	0.596733i
$383$	5.20643	−	16.0237i	0.266036	−	0.818775i	−0.725417	−	0.688310i	$-0.758353\pi$
$383$	5.20643	−	16.0237i	0.266036	−	0.818775i	0.991453	−	0.130465i	$-0.0416470\pi$
$384$	−0.809017	+	0.587785i	−0.0412850	+	0.0299953i
$385$	3.58388	+	2.60384i	0.182652	+	0.132704i
$386$	−3.41155	−	10.4997i	−0.173643	−	0.534420i
$387$	1.90772	+	1.38604i	0.0969749	+	0.0704564i
$388$	6.94351	+	5.04475i	0.352503	+	0.256109i
$389$	−5.69651	−	17.5320i	−0.288824	−	0.888910i	−0.985226	−	0.171258i	$-0.945217\pi$
$389$	−5.69651	−	17.5320i	−0.288824	−	0.888910i	0.696402	−	0.717652i	$-0.254783\pi$
$390$	−0.253761	−	0.184368i	−0.0128497	−	0.00933583i
$391$	17.5814	−	12.7736i	0.889130	−	0.645991i
$392$	0.522203	−	1.60718i	0.0263753	−	0.0811747i
$393$	−12.5510	+	9.11884i	−0.633115	+	0.459985i
$394$	6.71651	+	20.6713i	0.338373	+	1.04141i
$395$	−0.728684	−	2.24266i	−0.0366641	−	0.112840i
$396$	0.594055	−	1.82831i	0.0298524	−	0.0918762i
$397$	−32.0109			−1.60658			−0.803291	−	0.595587i	$-0.796919\pi$
$397$	−32.0109			−1.60658			−0.803291	+	0.595587i	$0.796919\pi$
$398$	14.5420			0.728923
$399$	5.75430	−	17.7099i	0.288075	−	0.886605i
$400$	−0.809017	−	0.587785i	−0.0404508	−	0.0293893i
$401$	−19.9425	+	14.4890i	−0.995879	+	0.723548i	−0.961201	−	0.275850i	$-0.911041\pi$
$401$	−19.9425	+	14.4890i	−0.995879	+	0.723548i	−0.0346780	+	0.999399i	$0.511041\pi$
$402$	2.91311			0.145293
$403$	−0.627888	−	1.62964i	−0.0312773	−	0.0811781i
$404$	6.96106			0.346326
$405$	0.809017	−	0.587785i	0.0402004	−	0.0292073i
$406$	−6.24965	−	4.54064i	−0.310165	−	0.225348i
$407$	0.597468	−	1.83882i	0.0296154	−	0.0911469i
$408$	3.42418			0.169522
$409$	7.92021			0.391629			0.195815	−	0.980641i	$-0.437265\pi$
$409$	7.92021			0.391629			0.195815	+	0.980641i	$0.437265\pi$
$410$	2.40130	−	7.39043i	0.118592	−	0.364987i
$411$	0.0359258	+	0.110568i	0.00177209	+	0.00545393i
$412$	1.38019	+	4.24779i	0.0679971	+	0.209274i
$413$	−7.30172	+	5.30501i	−0.359294	+	0.261042i
$414$	1.96120	−	6.03596i	0.0963878	−	0.296651i
$415$	6.41953	−	4.66406i	0.315122	−	0.228950i
$416$	−0.253761	−	0.184368i	−0.0124416	−	0.00903938i
$417$	0.653196	+	2.01033i	0.0319872	+	0.0984464i
$418$	−12.5678	−	9.13106i	−0.614713	−	0.446615i
$419$	10.0848	+	7.32703i	0.492674	+	0.357949i	0.806212	−	0.591627i	$-0.201514\pi$
$419$	10.0848	+	7.32703i	0.492674	+	0.357949i	−0.313538	+	0.949576i	$0.601514\pi$
$420$	0.712089	+	2.19158i	0.0347464	+	0.106938i
$421$	16.7753	+	12.1879i	0.817577	+	0.594004i	0.916017	−	0.401139i	$-0.131385\pi$
$421$	16.7753	+	12.1879i	0.817577	+	0.594004i	−0.0984407	+	0.995143i	$0.531385\pi$
$422$	12.9811	−	9.43130i	0.631909	−	0.459109i
$423$	−1.88538	+	5.80260i	−0.0916703	+	0.282132i
$424$	1.84782	−	1.34252i	0.0897379	−	0.0651984i
$425$	1.05813	+	3.25659i	0.0513268	+	0.157968i
$426$	0.936125	+	2.88110i	0.0453554	+	0.139590i
$427$	3.55382	−	10.9375i	0.171982	−	0.529305i
$428$	13.4513			0.650195
$429$	0.602991			0.0291127
$430$	−0.728684	+	2.24266i	−0.0351403	+	0.108151i
$431$	12.5773	+	9.13798i	0.605830	+	0.440161i	0.847943	−	0.530087i	$-0.177841\pi$
$431$	12.5773	+	9.13798i	0.605830	+	0.440161i	−0.242114	+	0.970248i	$0.577841\pi$
$432$	0.809017	−	0.587785i	0.0389238	−	0.0282798i
$433$	−28.9049			−1.38908			−0.694540	−	0.719454i	$-0.744392\pi$
$433$	−28.9049			−1.38908			−0.694540	+	0.719454i	$0.744392\pi$
$434$	−3.30527	+	12.3971i	−0.158658	+	0.595081i
$435$	−3.35233			−0.160732
$436$	−11.5465	+	8.38902i	−0.552977	+	0.401761i
$437$	−41.4912	−	30.1451i	−1.98479	−	1.44204i
$438$	−0.0249911	+	0.0769148i	−0.00119412	+	0.00367513i
$439$	11.8701			0.566527			0.283263	−	0.959042i	$-0.408583\pi$
$439$	11.8701			0.566527			0.283263	+	0.959042i	$0.408583\pi$
$440$	1.92240			0.0916469
$441$	−0.522203	+	1.60718i	−0.0248668	+	0.0765322i
$442$	0.331899	+	1.02148i	0.0157868	+	0.0485868i
$443$	−8.12643	−	25.0106i	−0.386098	−	1.18829i	−0.935680	−	0.352849i	$-0.885213\pi$
$443$	−8.12643	−	25.0106i	−0.386098	−	1.18829i	0.549582	−	0.835440i	$-0.314787\pi$
$444$	0.813665	−	0.591163i	0.0386149	−	0.0280553i
$445$	1.34106	−	4.12735i	0.0635722	−	0.195655i
$446$	21.7188	−	15.7796i	1.02841	−	0.747186i
$447$	−5.04221	−	3.66338i	−0.238488	−	0.173272i
$448$	0.712089	+	2.19158i	0.0336430	+	0.103543i
$449$	−5.44241	−	3.95414i	−0.256843	−	0.186608i	0.451911	−	0.892063i	$-0.350742\pi$
$449$	−5.44241	−	3.95414i	−0.256843	−	0.186608i	−0.708754	+	0.705455i	$0.750742\pi$
$450$	0.809017	+	0.587785i	0.0381374	+	0.0277085i
$451$	4.61626	+	14.2074i	0.217371	+	0.669000i
$452$	3.70744	+	2.69361i	0.174383	+	0.126697i
$453$	10.3153	−	7.49451i	0.484655	−	0.352123i
$454$	−8.03196	+	24.7198i	−0.376958	+	1.16016i
$455$	−0.584758	+	0.424852i	−0.0274139	+	0.0199174i
$456$	−2.49713	−	7.68537i	−0.116939	−	0.359900i
$457$	3.11398	+	9.58384i	0.145666	+	0.448313i	0.997096	−	0.0761547i	$-0.0242643\pi$
$457$	3.11398	+	9.58384i	0.145666	+	0.448313i	−0.851430	+	0.524468i	$0.824264\pi$
$458$	4.20014	−	12.9267i	0.196260	−	0.604025i
$459$	−3.42418			−0.159827
$460$	6.34658			0.295911
$461$	7.90606	−	24.3323i	0.368222	−	1.13327i	−0.579717	−	0.814818i	$-0.696837\pi$
$461$	7.90606	−	24.3323i	0.368222	−	1.13327i	0.947939	−	0.318452i	$-0.103163\pi$
$462$	−3.58388	−	2.60384i	−0.166737	−	0.121142i
$463$	−26.2218	+	19.0513i	−1.21863	+	0.885388i	−0.995986	−	0.0895115i	$-0.971469\pi$
$463$	−26.2218	+	19.0513i	−1.21863	+	0.885388i	−0.222646	+	0.974899i	$0.571469\pi$
$464$	−3.35233			−0.155628
$465$	2.00178	+	5.19547i	0.0928301	+	0.240934i
$466$	28.2665			1.30942
$467$	5.58694	−	4.05915i	0.258533	−	0.187835i	−0.450967	−	0.892540i	$-0.648921\pi$
$467$	5.58694	−	4.05915i	0.258533	−	0.187835i	0.709500	+	0.704706i	$0.248921\pi$
$468$	0.253761	+	0.184368i	0.0117301	+	0.00852241i
$469$	2.07439	−	6.38432i	0.0957865	−	0.294800i
$470$	−6.10122			−0.281428
$471$	−15.7833			−0.727258
$472$	−1.21031	+	3.72496i	−0.0557092	+	0.171455i
$473$	−1.40082	−	4.31130i	−0.0644100	−	0.198234i
$474$	0.728684	+	2.24266i	0.0334696	+	0.103009i
$475$	6.53756	−	4.74982i	0.299964	−	0.217937i
$476$	2.43832	−	7.50438i	0.111760	−	0.343963i
$477$	−1.84782	+	1.34252i	−0.0846057	+	0.0614696i
$478$	−23.5339	−	17.0983i	−1.07641	−	0.782060i
$479$	−6.34721	−	19.5347i	−0.290011	−	0.892563i	−0.984852	−	0.173399i	$-0.944525\pi$
$479$	−6.34721	−	19.5347i	−0.290011	−	0.892563i	0.694840	−	0.719164i	$-0.255475\pi$
$480$	0.809017	+	0.587785i	0.0369264	+	0.0268286i
$481$	0.255219	+	0.185427i	0.0116370	+	0.00845476i
$482$	0.234345	+	0.721240i	0.0106741	+	0.0328516i
$483$	−11.8318	−	8.59628i	−0.538364	−	0.391144i
$484$	5.90936	−	4.29340i	0.268607	−	0.195155i
$485$	2.65218	−	8.16258i	0.120429	−	0.370644i
$486$	−0.809017	+	0.587785i	−0.0366978	+	0.0266625i
$487$	−4.18067	−	12.8668i	−0.189444	−	0.583050i	0.810552	−	0.585666i	$-0.199167\pi$
$487$	−4.18067	−	12.8668i	−0.189444	−	0.583050i	−0.999997	+	0.00261649i	$0.999167\pi$
$488$	−1.54221	−	4.74644i	−0.0698127	−	0.214861i
$489$	−2.92186	+	8.99257i	−0.132131	+	0.406658i
$490$	−1.68989			−0.0763413
$491$	−34.8122			−1.57105			−0.785527	−	0.618827i	$-0.787608\pi$
$491$	−34.8122			−1.57105			−0.785527	+	0.618827i	$0.787608\pi$
$492$	−2.40130	+	7.39043i	−0.108259	+	0.333186i
$493$	9.28668	+	6.74716i	0.418251	+	0.303877i
$494$	2.05061	−	1.48985i	0.0922612	−	0.0670317i
$495$	−1.92240			−0.0864056
$496$	2.00178	+	5.19547i	0.0898824	+	0.233283i
$497$	6.98077			0.313130
$498$	−6.41953	+	4.66406i	−0.287666	+	0.209002i
$499$	−34.0629	−	24.7482i	−1.52487	−	1.10788i	−0.959009	−	0.283377i	$-0.908545\pi$
$499$	−34.0629	−	24.7482i	−1.52487	−	1.10788i	−0.565858	−	0.824503i	$-0.691455\pi$
$500$	−0.309017	+	0.951057i	−0.0138197	+	0.0425325i
$501$	2.68989			0.120175
$502$	−22.6547			−1.01113
$503$	4.38571	−	13.4978i	0.195549	−	0.601839i	−0.804420	−	0.594060i	$-0.797524\pi$
$503$	4.38571	−	13.4978i	0.195549	−	0.601839i	0.999970	−	0.00777846i	$-0.00247599\pi$
$504$	−0.712089	−	2.19158i	−0.0317190	−	0.0976209i
$505$	−2.15109	−	6.62036i	−0.0957221	−	0.294602i
$506$	−9.87056	+	7.17138i	−0.438800	+	0.318807i
$507$	3.98682	−	12.2702i	0.177061	−	0.544937i
$508$	−8.67958	+	6.30608i	−0.385094	+	0.279787i
$509$	13.6980	+	9.95220i	0.607155	+	0.441124i	0.848411	−	0.529338i	$-0.177560\pi$
$509$	13.6980	+	9.95220i	0.607155	+	0.441124i	−0.241257	+	0.970461i	$0.577560\pi$
$510$	−1.05813	−	3.25659i	−0.0468547	−	0.144204i
$511$	0.150769	+	0.109540i	0.00666965	+	0.00484578i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	2.49713	+	7.68537i	0.110251	+	0.339317i
$514$	−11.3486	−	8.24523i	−0.500564	−	0.363681i
$515$	3.61339	−	2.62528i	0.159225	−	0.115684i
$516$	0.728684	−	2.24266i	0.0320785	−	0.0987276i
$517$	9.48895	−	6.89413i	0.417324	−	0.303203i
$518$	−0.716181	−	2.20418i	−0.0314672	−	0.0968460i
$519$	1.25819	+	3.87230i	0.0552282	+	0.169975i
$520$	−0.0969280	+	0.298314i	−0.00425057	+	0.0130819i
$521$	9.67965			0.424073			0.212036	−	0.977262i	$-0.431990\pi$
$521$	9.67965			0.424073			0.212036	+	0.977262i	$0.431990\pi$
$522$	3.35233			0.146727
$523$	2.91899	−	8.98372i	0.127638	−	0.392831i	−0.866734	−	0.498771i	$-0.833785\pi$
$523$	2.91899	−	8.98372i	0.127638	−	0.392831i	0.994373	+	0.105940i	$0.0337850\pi$
$524$	12.5510	+	9.11884i	0.548293	+	0.398359i
$525$	1.86427	−	1.35447i	0.0813636	−	0.0591141i
$526$	20.2851			0.884473
$527$	4.91147	−	18.4215i	0.213947	−	0.802454i
$528$	−1.92240			−0.0836618
$529$	−13.9791	+	10.1564i	−0.607786	+	0.441582i
$530$	−1.84782	−	1.34252i	−0.0802640	−	0.0583152i
$531$	1.21031	−	3.72496i	0.0525231	−	0.161650i
$532$	−18.6213			−0.807336
$533$	−2.43742			−0.105576
$534$	−1.34106	+	4.12735i	−0.0580332	+	0.178608i
$535$	−4.15669	−	12.7930i	−0.179710	−	0.553089i
$536$	−0.900199	−	2.77053i	−0.0388827	−	0.119669i
$537$	3.41688	−	2.48251i	0.147449	−	0.107128i
$538$	4.96763	−	15.2888i	0.214170	−	0.659146i
$539$	2.62821	−	1.90950i	0.113205	−	0.0822481i
$540$	−0.809017	−	0.587785i	−0.0348145	−	0.0252942i
$541$	−1.98954	−	6.12317i	−0.0855369	−	0.263255i	0.899135	−	0.437671i	$-0.144196\pi$
$541$	−1.98954	−	6.12317i	−0.0855369	−	0.263255i	−0.984672	+	0.174415i	$0.944196\pi$
$542$	11.8338	+	8.59773i	0.508303	+	0.369304i
$543$	5.62556	+	4.08721i	0.241416	+	0.175399i
$544$	−1.05813	−	3.25659i	−0.0453669	−	0.139625i
$545$	11.5465	+	8.38902i	0.494598	+	0.359346i
$546$	0.584758	−	0.424852i	0.0250253	−	0.0181820i
$547$	−9.60793	+	29.5702i	−0.410805	+	1.26433i	0.505144	+	0.863035i	$0.331439\pi$
$547$	−9.60793	+	29.5702i	−0.410805	+	1.26433i	−0.915949	+	0.401294i	$0.868561\pi$
$548$	0.0940550	−	0.0683350i	0.00401783	−	0.00291913i
$549$	1.54221	+	4.74644i	0.0658200	+	0.202573i
$550$	−0.594055	−	1.82831i	−0.0253306	−	0.0779595i
$551$	8.37119	−	25.7639i	0.356624	−	1.09758i
$552$	−6.34658			−0.270128
$553$	5.43387			0.231072
$554$	−7.92350	+	24.3860i	−0.336637	+	1.03606i
$555$	−0.813665	−	0.591163i	−0.0345382	−	0.0250935i
$556$	1.71009	−	1.24245i	0.0725240	−	0.0526918i
$557$	−9.71067			−0.411454			−0.205727	−	0.978609i	$-0.565956\pi$
$557$	−9.71067			−0.411454			−0.205727	+	0.978609i	$0.565956\pi$
$558$	−2.00178	−	5.19547i	−0.0847419	−	0.219942i
$559$	0.739646			0.0312837
$560$	1.86427	−	1.35447i	0.0787799	−	0.0572370i
$561$	5.32547	+	3.86918i	0.224842	+	0.163357i
$562$	−2.53812	+	7.81153i	−0.107064	+	0.329510i
$563$	20.2212			0.852222			0.426111	−	0.904671i	$-0.359883\pi$
$563$	20.2212			0.852222			0.426111	+	0.904671i	$0.359883\pi$
$564$	6.10122			0.256908
$565$	1.41612	−	4.35836i	0.0595765	−	0.183357i
$566$	6.89842	+	21.2312i	0.289962	+	0.892412i
$567$	0.712089	+	2.19158i	0.0299049	+	0.0920379i
$568$	2.45081	−	1.78062i	0.102834	−	0.0747130i
$569$	4.34869	−	13.3839i	0.182307	−	0.561082i	−0.817585	−	0.575808i	$-0.804688\pi$
$569$	4.34869	−	13.3839i	0.182307	−	0.561082i	0.999892	+	0.0147260i	$0.00468760\pi$
$570$	−6.53756	+	4.74982i	−0.273828	+	0.198948i
$571$	2.82460	+	2.05219i	0.118206	+	0.0858816i	0.645318	−	0.763914i	$-0.276725\pi$
$571$	2.82460	+	2.05219i	0.118206	+	0.0858816i	−0.527112	+	0.849796i	$0.676725\pi$
$572$	−0.186335	−	0.573479i	−0.00779104	−	0.0239784i
$573$	−16.0528	−	11.6630i	−0.670615	−	0.487230i
$574$	14.4868	+	10.5253i	0.604668	+	0.439317i
$575$	−1.96120	−	6.03596i	−0.0817877	−	0.251717i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	−12.9031	+	9.37466i	−0.537164	+	0.390272i	−0.823031	−	0.567997i	$-0.807718\pi$
$577$	−12.9031	+	9.37466i	−0.537164	+	0.390272i	0.285867	+	0.958269i	$0.407718\pi$
$578$	1.63007	−	5.01683i	0.0678018	−	0.208673i
$579$	8.93156	−	6.48916i	0.371183	−	0.269680i
$580$	1.03593	+	3.18825i	0.0430145	+	0.132385i
$581$	5.65041	+	17.3902i	0.234418	+	0.721466i
$582$	−2.65218	+	8.16258i	−0.109937	+	0.338350i
$583$	4.39082			0.181849
$584$	0.0808730			0.00334655
$585$	0.0969280	−	0.298314i	0.00400748	−	0.0123337i
$586$	−3.20279	−	2.32696i	−0.132306	−	0.0961260i
$587$	25.2062	−	18.3134i	1.04037	−	0.755875i	0.0700148	−	0.997546i	$-0.477695\pi$
$587$	25.2062	−	18.3134i	1.04037	−	0.755875i	0.970358	+	0.241671i	$0.0776953\pi$
$588$	1.68989			0.0696897
$589$	−44.9278	+	2.41063i	−1.85122	+	0.0993284i
$590$	3.91666			0.161246
$591$	−17.5841	+	12.7756i	−0.723312	+	0.525517i
$592$	−0.813665	−	0.591163i	−0.0334414	−	0.0242966i
$593$	−2.88620	+	8.88280i	−0.118522	+	0.364773i	−0.992665	−	0.120895i	$-0.961424\pi$
$593$	−2.88620	+	8.88280i	−0.118522	+	0.364773i	0.874143	+	0.485668i	$0.161424\pi$
$594$	1.92240			0.0788771
$595$	−7.89057			−0.323482
$596$	−1.92595	+	5.92748i	−0.0788901	+	0.242799i
$597$	4.49371	+	13.8302i	0.183915	+	0.566034i
$598$	−0.615161	−	1.89327i	−0.0251558	−	0.0774216i
$599$	18.6098	−	13.5208i	0.760377	−	0.552446i	−0.138649	−	0.990342i	$-0.544276\pi$
$599$	18.6098	−	13.5208i	0.760377	−	0.552446i	0.899026	+	0.437896i	$0.144276\pi$
$600$	0.309017	−	0.951057i	0.0126156	−	0.0388267i
$601$	2.77861	−	2.01878i	0.113342	−	0.0823478i	−0.529670	−	0.848204i	$-0.677684\pi$
$601$	2.77861	−	2.01878i	0.113342	−	0.0823478i	0.643012	+	0.765856i	$0.277684\pi$
$602$	−4.39609	−	3.19395i	−0.179171	−	0.130176i
$603$	0.900199	+	2.77053i	0.0366589	+	0.112825i
$604$	−10.3153	−	7.49451i	−0.419724	−	0.304947i
$605$	−5.90936	−	4.29340i	−0.240250	−	0.174552i
$606$	2.15109	+	6.62036i	0.0873819	+	0.268934i
$607$	−2.54008	−	1.84547i	−0.103098	−	0.0749054i	0.535042	−	0.844826i	$-0.320296\pi$
$607$	−2.54008	−	1.84547i	−0.103098	−	0.0749054i	−0.638140	+	0.769920i	$0.720296\pi$
$608$	−6.53756	+	4.74982i	−0.265133	+	0.192631i
$609$	2.38715	−	7.34691i	0.0967324	−	0.297712i
$610$	−4.03756	+	2.93346i	−0.163476	+	0.118772i
$611$	0.591378	+	1.82008i	0.0239246	+	0.0736324i
$612$	1.05813	+	3.25659i	0.0427723	+	0.131640i
$613$	9.90897	−	30.4967i	0.400220	−	1.23175i	−0.524602	−	0.851348i	$-0.675786\pi$
$613$	9.90897	−	30.4967i	0.400220	−	1.23175i	0.924821	−	0.380402i	$-0.124214\pi$
$614$	15.5309			0.626775
$615$	7.77076			0.313347
$616$	−1.36892	+	4.21311i	−0.0551554	+	0.169751i
$617$	13.9005	+	10.0993i	0.559612	+	0.406582i	0.831317	−	0.555799i	$-0.187588\pi$
$617$	13.9005	+	10.0993i	0.559612	+	0.406582i	−0.271705	+	0.962381i	$0.587588\pi$
$618$	−3.61339	+	2.62528i	−0.145352	+	0.105604i
$619$	−26.5820			−1.06842			−0.534210	−	0.845352i	$-0.679391\pi$
$619$	−26.5820			−1.06842			−0.534210	+	0.845352i	$0.679391\pi$
$620$	4.32260	−	3.50929i	0.173600	−	0.140936i
$621$	6.34658			0.254680
$622$	10.1932	−	7.40577i	0.408709	−	0.296944i
$623$	8.09049	+	5.87808i	0.324139	+	0.235500i
$624$	0.0969280	−	0.298314i	0.00388022	−	0.0119421i
$625$	1.00000			0.0400000
$626$	−5.62953			−0.225001
$627$	4.80048	−	14.7744i	0.191713	−	0.590031i
$628$	4.87732	+	15.0108i	0.194626	+	0.598998i
$629$	1.06421	+	3.27530i	0.0424328	+	0.130595i
$630$	−1.86427	+	1.35447i	−0.0742744	+	0.0539635i
$631$	8.74585	−	26.9170i	0.348167	−	1.07155i	−0.611700	−	0.791090i	$-0.709514\pi$
$631$	8.74585	−	26.9170i	0.348167	−	1.07155i	0.959866	−	0.280457i	$-0.0904861\pi$
$632$	1.90772	−	1.38604i	0.0758850	−	0.0551337i
$633$	12.9811	+	9.43130i	0.515951	+	0.374861i
$634$	7.85320	+	24.1697i	0.311890	+	0.959900i
$635$	8.67958	+	6.30608i	0.344438	+	0.250249i
$636$	1.84782	+	1.34252i	0.0732707	+	0.0532343i
$637$	0.163797	+	0.504116i	0.00648988	+	0.0199738i
$638$	−5.21373	−	3.78799i	−0.206413	−	0.149968i
$639$	−2.45081	+	1.78062i	−0.0969524	+	0.0704401i
$640$	0.309017	−	0.951057i	0.0122150	−	0.0375938i
$641$	30.3127	−	22.0235i	1.19728	−	0.869874i	0.203265	−	0.979124i	$-0.434845\pi$
$641$	30.3127	−	22.0235i	1.19728	−	0.869874i	0.994014	+	0.109249i	$0.0348447\pi$
$642$	4.15669	+	12.7930i	0.164052	+	0.504899i
$643$	9.94903	+	30.6200i	0.392351	+	1.20753i	0.931005	+	0.365006i	$0.118933\pi$
$643$	9.94903	+	30.6200i	0.392351	+	1.20753i	−0.538654	+	0.842527i	$0.681067\pi$
$644$	−4.51933	+	13.9091i	−0.178087	+	0.548094i
$645$	−2.35807			−0.0928490
$646$	27.6703			1.08868
$647$	2.26303	−	6.96489i	0.0889689	−	0.273818i	−0.896666	−	0.442707i	$-0.854018\pi$
$647$	2.26303	−	6.96489i	0.0889689	−	0.273818i	0.985635	+	0.168889i	$0.0540180\pi$
$648$	0.809017	+	0.587785i	0.0317812	+	0.0230904i
$649$	−6.09141	+	4.42566i	−0.239109	+	0.173723i
$650$	0.313665			0.0123030
$651$	−12.8118	+	0.687424i	−0.502132	+	0.0269423i
$652$	9.45534			0.370300
$653$	−17.3289	+	12.5902i	−0.678132	+	0.492692i	−0.872737	−	0.488190i	$-0.837657\pi$
$653$	−17.3289	+	12.5902i	−0.678132	+	0.492692i	0.194606	+	0.980882i	$0.437657\pi$
$654$	−11.5465	−	8.38902i	−0.451504	−	0.328037i
$655$	4.79406	−	14.7546i	0.187319	−	0.576510i
$656$	7.77076			0.303397
$657$	−0.0808730			−0.00315516
$658$	4.34461	−	13.3713i	0.169370	−	0.521269i
$659$	7.64816	+	23.5386i	0.297930	+	0.916934i	0.982221	+	0.187726i	$0.0601116\pi$
$659$	7.64816	+	23.5386i	0.297930	+	0.916934i	−0.684291	+	0.729209i	$0.739888\pi$
$660$	0.594055	+	1.82831i	0.0231236	+	0.0711670i
$661$	22.4870	−	16.3378i	0.874643	−	0.635465i	−0.0571859	−	0.998364i	$-0.518213\pi$
$661$	22.4870	−	16.3378i	0.874643	−	0.635465i	0.931829	+	0.362898i	$0.118213\pi$
$662$	6.30381	−	19.4011i	0.245005	−	0.754047i
$663$	−0.868922	+	0.631309i	−0.0337461	+	0.0245180i
$664$	6.41953	+	4.66406i	0.249126	+	0.181001i
$665$	5.75430	+	17.7099i	0.223142	+	0.686761i
$666$	0.813665	+	0.591163i	0.0315289	+	0.0229071i
$667$	−17.2125	−	12.5056i	−0.666470	−	0.484219i
$668$	−0.831220	−	2.55823i	−0.0321609	−	0.0989810i
$669$	21.7188	+	15.7796i	0.839696	+	0.610075i
$670$	−2.35675	+	1.71228i	−0.0910493	+	0.0661512i
$671$	2.96475	−	9.12457i	0.114453	−	0.352250i
$672$	−1.86427	+	1.35447i	−0.0719159	+	0.0522500i
$673$	10.3084	+	31.7259i	0.397359	+	1.22294i	0.927109	+	0.374791i	$0.122285\pi$
$673$	10.3084	+	31.7259i	0.397359	+	1.22294i	−0.529751	+	0.848153i	$0.677715\pi$
$674$	−0.631894	−	1.94477i	−0.0243397	−	0.0749098i
$675$	−0.309017	+	0.951057i	−0.0118941	+	0.0366062i
$676$	−12.9016			−0.496216
$677$	−9.54754			−0.366942			−0.183471	−	0.983025i	$-0.558733\pi$
$677$	−9.54754			−0.366942			−0.183471	+	0.983025i	$0.558733\pi$
$678$	−1.41612	+	4.35836i	−0.0543856	+	0.167382i
$679$	16.0004	+	11.6250i	0.614039	+	0.446126i
$680$	−2.77022	+	2.01268i	−0.106233	+	0.0771828i
$681$	−25.9920			−0.996014
$682$	−2.75740	+	10.3422i	−0.105586	+	0.396024i
$683$	42.2623			1.61712			0.808561	−	0.588413i	$-0.200247\pi$
$683$	42.2623			1.61712			0.808561	+	0.588413i	$0.200247\pi$
$684$	6.53756	−	4.74982i	0.249970	−	0.181614i
$685$	−0.0940550	−	0.0683350i	−0.00359366	−	0.00261095i
$686$	6.18797	−	19.0446i	0.236258	−	0.727127i
$687$	13.5919			0.518565
$688$	−2.35807			−0.0899007
$689$	−0.221386	+	0.681356i	−0.00843413	+	0.0259576i
$690$	1.96120	+	6.03596i	0.0746617	+	0.229785i
$691$	8.29166	+	25.5191i	0.315430	+	0.970792i	0.975577	+	0.219657i	$0.0704937\pi$
$691$	8.29166	+	25.5191i	0.315430	+	0.970792i	−0.660148	+	0.751136i	$0.729506\pi$
$692$	3.29397	−	2.39321i	0.125218	−	0.0909763i
$693$	1.36892	−	4.21311i	0.0520010	−	0.160043i
$694$	13.1003	−	9.51796i	0.497282	−	0.361297i
$695$	−1.71009	−	1.24245i	−0.0648674	−	0.0471289i
$696$	−1.03593	−	3.18825i	−0.0392667	−	0.120850i
$697$	−21.5267	−	15.6401i	−0.815382	−	0.592410i
$698$	−15.5839	−	11.3224i	−0.589860	−	0.428559i
$699$	8.73483	+	26.8831i	0.330382	+	1.01681i
$700$	−1.86427	−	1.35447i	−0.0704629	−	0.0511943i
$701$	25.0040	−	18.1665i	0.944390	−	0.686139i	−0.00508375	−	0.999987i	$-0.501618\pi$
$701$	25.0040	−	18.1665i	0.944390	−	0.686139i	0.949473	+	0.313848i	$0.101618\pi$
$702$	−0.0969280	+	0.298314i	−0.00365831	+	0.0112591i
$703$	6.57513	−	4.77711i	0.247986	−	0.180172i
$704$	0.594055	+	1.82831i	0.0223893	+	0.0689072i
$705$	−1.88538	−	5.80260i	−0.0710075	−	0.218539i
$706$	7.11262	−	21.8904i	0.267687	−	0.823856i
$707$	16.0409			0.603278
$708$	−3.91666			−0.147197
$709$	−8.53805	+	26.2774i	−0.320653	+	0.986869i	0.652711	+	0.757607i	$0.273631\pi$
$709$	−8.53805	+	26.2774i	−0.320653	+	0.986869i	−0.973365	+	0.229263i	$0.926369\pi$
$710$	−2.45081	−	1.78062i	−0.0919771	−	0.0668253i
$711$	−1.90772	+	1.38604i	−0.0715451	+	0.0519806i
$712$	4.33975			0.162639
$713$	−9.10321	+	34.1436i	−0.340918	+	1.27869i
$714$	7.89057			0.295297
$715$	−0.487830	+	0.354429i	−0.0182438	+	0.0132549i
$716$	−3.41688	−	2.48251i	−0.127695	−	0.0927757i
$717$	8.98913	−	27.6657i	0.335705	−	1.03319i
$718$	−15.7542			−0.587941
$719$	18.6893			0.696995			0.348497	−	0.937310i	$-0.386692\pi$
$719$	18.6893			0.696995			0.348497	+	0.937310i	$0.386692\pi$
$720$	−0.309017	+	0.951057i	−0.0115164	+	0.0354438i
$721$	3.18047	+	9.78847i	0.118447	+	0.364542i
$722$	−14.3076	−	44.0344i	−0.532475	−	1.63879i
$723$	−0.613523	+	0.445751i	−0.0228172	+	0.0165776i
$724$	2.14877	−	6.61324i	0.0798584	−	0.245779i
$725$	2.71209	−	1.97045i	0.100724	−	0.0731806i
$726$	5.90936	+	4.29340i	0.219317	+	0.159343i
$727$	13.7078	+	42.1882i	0.508394	+	1.56467i	0.794990	+	0.606623i	$0.207476\pi$
$727$	13.7078	+	42.1882i	0.508394	+	1.56467i	−0.286596	+	0.958052i	$0.592524\pi$
$728$	−0.584758	−	0.424852i	−0.0216726	−	0.0157460i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−0.0249911	−	0.0769148i	−0.000924964	−	0.00284675i
$731$	6.53237	+	4.74605i	0.241609	+	0.175539i
$732$	4.03756	−	2.93346i	0.149233	−	0.108424i
$733$	−2.91721	+	8.97826i	−0.107750	+	0.331620i	−0.990366	−	0.138475i	$-0.955780\pi$
$733$	−2.91721	+	8.97826i	−0.107750	+	0.331620i	0.882616	+	0.470094i	$0.155780\pi$
$734$	21.8452	−	15.8715i	0.806321	−	0.585827i
$735$	−0.522203	−	1.60718i	−0.0192618	−	0.0592816i
$736$	1.96120	+	6.03596i	0.0722908	+	0.222488i
$737$	1.73055	−	5.32607i	0.0637454	−	0.196188i
$738$	−7.77076			−0.286046
$739$	−33.9509			−1.24891			−0.624453	−	0.781063i	$-0.714678\pi$
$739$	−33.9509			−1.24891			−0.624453	+	0.781063i	$0.714678\pi$
$740$	−0.310793	+	0.956521i	−0.0114250	+	0.0351624i
$741$	2.05061	+	1.48985i	0.0753310	+	0.0547311i
$742$	4.25805	−	3.09365i	0.156318	−	0.113572i
$743$	−51.7186			−1.89737			−0.948685	−	0.316222i	$-0.897586\pi$
$743$	−51.7186			−1.89737			−0.948685	+	0.316222i	$0.897586\pi$
$744$	−4.32260	+	3.50929i	−0.158474	+	0.128657i
$745$	6.23252			0.228342
$746$	−24.8412	+	18.0482i	−0.909502	+	0.660792i
$747$	−6.41953	−	4.66406i	−0.234878	−	0.170649i
$748$	2.03415	−	6.26047i	0.0743759	−	0.228905i
$749$	30.9969			1.13260
$750$	−1.00000			−0.0365148
$751$	0.936491	−	2.88222i	0.0341731	−	0.105174i	−0.932515	−	0.361131i	$-0.882391\pi$
$751$	0.936491	−	2.88222i	0.0341731	−	0.105174i	0.966688	+	0.255957i	$0.0823907\pi$
$752$	−1.88538	−	5.80260i	−0.0687527	−	0.211599i
$753$	−7.00068	−	21.5459i	−0.255119	−	0.785175i
$754$	0.850689	−	0.618061i	0.0309803	−	0.0225085i
$755$	−3.94010	+	12.1264i	−0.143395	+	0.441324i
$756$	1.86427	−	1.35447i	0.0678030	−	0.0492617i
$757$	−38.4860	−	27.9617i	−1.39880	−	1.01629i	−0.994834	−	0.101511i	$-0.967632\pi$
$757$	−38.4860	−	27.9617i	−1.39880	−	1.01629i	−0.403963	−	0.914775i	$-0.632368\pi$
$758$	−1.06215	−	3.26897i	−0.0385791	−	0.118734i
$759$	−9.87056	−	7.17138i	−0.358279	−	0.260305i
$760$	6.53756	+	4.74982i	0.237142	+	0.172294i
$761$	5.13779	+	15.8125i	0.186245	+	0.573203i	0.999968	−	0.00805045i	$-0.00256257\pi$
$761$	5.13779	+	15.8125i	0.186245	+	0.573203i	−0.813723	+	0.581253i	$0.802563\pi$
$762$	−8.67958	−	6.30608i	−0.314428	−	0.228445i
$763$	−26.6074	+	19.3314i	−0.963252	+	0.699844i
$764$	−6.13162	+	18.8712i	−0.221834	+	0.682735i
$765$	2.77022	−	2.01268i	0.100157	−	0.0727686i
$766$	−5.20643	−	16.0237i	−0.188116	−	0.578961i
$767$	−0.379634	−	1.16839i	−0.0137078	−	0.0421882i
$768$	−0.309017	+	0.951057i	−0.0111507	+	0.0343183i
$769$	−50.4063			−1.81770			−0.908848	−	0.417127i	$-0.863037\pi$
$769$	−50.4063			−1.81770			−0.908848	+	0.417127i	$0.863037\pi$
$770$	4.42992			0.159643
$771$	4.33477	−	13.3411i	0.156113	−	0.480466i
$772$	−8.93156	−	6.48916i	−0.321454	−	0.233550i
$773$	1.89842	−	1.37929i	0.0682816	−	0.0496095i	−0.553121	−	0.833101i	$-0.686563\pi$
$773$	1.89842	−	1.37929i	0.0682816	−	0.0496095i	0.621402	+	0.783492i	$0.286563\pi$
$774$	2.35807			0.0847592
$775$	−4.67329	−	3.02661i	−0.167870	−	0.108719i
$776$	8.58265			0.308099
$777$	1.87499	−	1.36226i	0.0672647	−	0.0488707i
$778$	−14.9136	−	10.8354i	−0.534680	−	0.388468i
$779$	−19.4046	+	59.7211i	−0.695241	+	2.13973i
$780$	−0.313665			−0.0112310
$781$	5.82366			0.208387
$782$	6.71550	−	20.6682i	0.240146	−	0.739093i
$783$	1.03593	+	3.18825i	0.0370210	+	0.113939i
$784$	−0.522203	−	1.60718i	−0.0186501	−	0.0573992i
$785$	12.7690	−	9.27721i	0.455745	−	0.331118i
$786$	−4.79406	+	14.7546i	−0.170998	+	0.526279i
$787$	8.93280	−	6.49006i	0.318420	−	0.231346i	−0.417081	−	0.908869i	$-0.636947\pi$
$787$	8.93280	−	6.49006i	0.318420	−	0.231346i	0.735501	+	0.677524i	$0.236947\pi$
$788$	17.5841	+	12.7756i	0.626406	+	0.455111i
$789$	6.26844	+	19.2923i	0.223162	+	0.686823i
$790$	−1.90772	−	1.38604i	−0.0678736	−	0.0493131i
$791$	8.54331	+	6.20708i	0.303765	+	0.220698i
$792$	−0.594055	−	1.82831i	−0.0211088	−	0.0649663i
$793$	1.26644	+	0.920126i	0.0449728	+	0.0326746i
$794$	−25.8974	+	18.8155i	−0.919063	+	0.667739i
$795$	0.705803	−	2.17224i	0.0250322	−	0.0770413i
$796$	11.7647	−	8.54755i	0.416989	−	0.302960i
$797$	−6.56614	−	20.2085i	−0.232585	−	0.715822i	−0.997433	−	0.0716110i	$-0.977186\pi$
$797$	−6.56614	−	20.2085i	−0.232585	−	0.715822i	0.764848	−	0.644211i	$-0.222814\pi$
$798$	−5.75430	−	17.7099i	−0.203700	−	0.626924i
$799$	−6.45587	+	19.8691i	−0.228392	+	0.702920i
$800$	−1.00000			−0.0353553
$801$	−4.33975			−0.153338
$802$	−7.61734	+	23.4438i	−0.268978	+	0.827828i
$803$	0.125778	+	0.0913833i	0.00443862	+	0.00322485i
$804$	2.35675	−	1.71228i	0.0831162	−	0.0603875i
$805$	14.6249			0.515459
$806$	−1.46585	−	0.949342i	−0.0516324	−	0.0334392i
$807$	16.0756			0.565887
$808$	5.63162	−	4.09161i	0.198120	−	0.143942i
$809$	−15.6990	−	11.4060i	−0.551949	−	0.401014i	0.276555	−	0.960998i	$-0.410807\pi$
$809$	−15.6990	−	11.4060i	−0.551949	−	0.401014i	−0.828504	+	0.559984i	$0.810807\pi$
$810$	0.309017	−	0.951057i	0.0108578	−	0.0334167i
$811$	−35.6174			−1.25069			−0.625347	−	0.780346i	$-0.715043\pi$
$811$	−35.6174			−1.25069			−0.625347	+	0.780346i	$0.715043\pi$
$812$	−7.72500			−0.271094
$813$	−4.52009	+	13.9114i	−0.158527	+	0.487895i
$814$	−0.597468	−	1.83882i	−0.0209413	−	0.0644506i
$815$	−2.92186	−	8.99257i	−0.102348	−	0.314996i
$816$	2.77022	−	2.01268i	0.0969770	−	0.0704579i
$817$	5.88841	−	18.1227i	0.206009	−	0.634031i
$818$	6.40758	−	4.65538i	0.224036	−	0.162772i
$819$	0.584758	+	0.424852i	0.0204331	+	0.0148455i
$820$	−2.40130	−	7.39043i	−0.0838569	−	0.258085i
$821$	6.55881	+	4.76525i	0.228904	+	0.166308i	0.696326	−	0.717726i	$-0.254817\pi$
$821$	6.55881	+	4.76525i	0.228904	+	0.166308i	−0.467422	+	0.884035i	$0.654817\pi$
$822$	0.0940550	+	0.0683350i	0.00328055	+	0.00238346i
$823$	12.5935	+	38.7588i	0.438982	+	1.35105i	0.888951	+	0.458003i	$0.151435\pi$
$823$	12.5935	+	38.7588i	0.438982	+	1.35105i	−0.449969	+	0.893044i	$0.648565\pi$
$824$	3.61339	+	2.62528i	0.125878	+	0.0914559i
$825$	1.55526	−	1.12996i	0.0541471	−	0.0393402i
$826$	−2.78901	+	8.58368i	−0.0970420	+	0.298665i
$827$	1.20115	−	0.872690i	0.0417682	−	0.0303464i	−0.566705	−	0.823921i	$-0.691782\pi$
$827$	1.20115	−	0.872690i	0.0417682	−	0.0303464i	0.608473	+	0.793574i	$0.291782\pi$
$828$	−1.96120	−	6.03596i	−0.0681565	−	0.209764i
$829$	9.56633	+	29.4422i	0.332253	+	1.02257i	0.968060	+	0.250720i	$0.0806674\pi$
$829$	9.56633	+	29.4422i	0.332253	+	1.02257i	−0.635807	+	0.771848i	$0.719333\pi$
$830$	2.45204	−	7.54661i	0.0851116	−	0.261947i
$831$	−25.6410			−0.889476
$832$	−0.313665			−0.0108744
$833$	−1.78812	+	5.50326i	−0.0619546	+	0.190677i
$834$	1.71009	+	1.24245i	0.0592156	+	0.0430226i
$835$	−2.17616	+	1.58108i	−0.0753092	+	0.0547154i
$836$	−15.5347			−0.537279
$837$	4.32260	−	3.50929i	0.149411	−	0.121299i
$838$	12.4655			0.430613
$839$	41.3600	−	30.0498i	1.42790	−	1.03743i	0.437502	−	0.899217i	$-0.355863\pi$
$839$	41.3600	−	30.0498i	1.42790	−	1.03743i	0.990402	−	0.138216i	$-0.0441368\pi$
$840$	1.86427	+	1.35447i	0.0643235	+	0.0467338i
$841$	−5.48873	+	16.8926i	−0.189267	+	0.582503i
$842$	20.7354			0.714588
$843$	−8.21353			−0.282889
$844$	4.95833	−	15.2602i	0.170673	−	0.525277i
$845$	3.98682	+	12.2702i	0.137151	+	0.422106i
$846$	1.88538	+	5.80260i	0.0648207	+	0.199498i
$847$	13.6173	−	9.89358i	0.467897	−	0.339947i
$848$	0.705803	−	2.17224i	0.0242374	−	0.0745949i
$849$	−18.0603	+	13.1216i	−0.619828	+	0.450332i
$850$	2.77022	+	2.01268i	0.0950177	+	0.0690344i
$851$	−1.97247	−	6.07064i	−0.0676154	−	0.208099i
$852$	2.45081	+	1.78062i	0.0839633	+	0.0610029i
$853$	−1.59273	−	1.15718i	−0.0545339	−	0.0396212i	0.560184	−	0.828368i	$-0.310730\pi$
$853$	−1.59273	−	1.15718i	−0.0545339	−	0.0396212i	−0.614718	+	0.788747i	$0.710730\pi$
$854$	−3.55382	−	10.9375i	−0.121609	−	0.374275i
$855$	−6.53756	−	4.74982i	−0.223580	−	0.162440i
$856$	10.8824	−	7.90650i	0.371952	−	0.270239i
$857$	−10.1134	+	31.1258i	−0.345467	+	1.06324i	0.615867	+	0.787850i	$0.288806\pi$
$857$	−10.1134	+	31.1258i	−0.345467	+	1.06324i	−0.961334	+	0.275387i	$0.911194\pi$
$858$	0.487830	−	0.354429i	0.0166542	−	0.0121000i
$859$	11.7633	+	36.2038i	0.401359	+	1.23526i	0.923897	+	0.382641i	$0.124985\pi$
$859$	11.7633	+	36.2038i	0.401359	+	1.23526i	−0.522538	+	0.852616i	$0.675015\pi$
$860$	0.728684	+	2.24266i	0.0248479	+	0.0764741i
$861$	−5.53347	+	17.0303i	−0.188580	+	0.580390i
$862$	15.5465			0.529514
$863$	−35.5989			−1.21180			−0.605901	−	0.795540i	$-0.707187\pi$
$863$	−35.5989			−1.21180			−0.605901	+	0.795540i	$0.707187\pi$
$864$	0.309017	−	0.951057i	0.0105130	−	0.0323556i
$865$	−3.29397	−	2.39321i	−0.111998	−	0.0813717i
$866$	−23.3845	+	16.9899i	−0.794639	+	0.577339i
$867$	5.27500			0.179149
$868$	4.61283	+	11.9723i	0.156570	+	0.406365i
$869$	4.53316			0.153777
$870$	−2.71209	+	1.97045i	−0.0919484	+	0.0668044i
$871$	0.739232	+	0.537083i	0.0250479	+	0.0181984i
$872$	−4.41037	+	13.5737i	−0.149354	+	0.459664i
$873$	−8.58265			−0.290479
$874$	−51.2859			−1.73477
$875$	−0.712089	+	2.19158i	−0.0240730	+	0.0740891i
$876$	0.0249911	+	0.0769148i	0.000844372	+	0.00259871i
$877$	−8.98767	−	27.6612i	−0.303492	−	0.934052i	−0.980236	−	0.197833i	$-0.936609\pi$
$877$	−8.98767	−	27.6612i	−0.303492	−	0.934052i	0.676744	−	0.736219i	$-0.263391\pi$
$878$	9.60308	−	6.97704i	0.324088	−	0.235464i
$879$	1.22336	−	3.76511i	0.0412628	−	0.126994i
$880$	1.55526	−	1.12996i	0.0524277	−	0.0380909i
$881$	21.4009	+	15.5487i	0.721015	+	0.523848i	0.886708	−	0.462329i	$-0.152986\pi$
$881$	21.4009	+	15.5487i	0.721015	+	0.523848i	−0.165693	+	0.986177i	$0.552986\pi$
$882$	0.522203	+	1.60718i	0.0175835	+	0.0541165i
$883$	−23.4267	−	17.0205i	−0.788370	−	0.572784i	0.119109	−	0.992881i	$-0.461996\pi$
$883$	−23.4267	−	17.0205i	−0.788370	−	0.572784i	−0.907479	+	0.420097i	$0.861996\pi$
$884$	0.868922	+	0.631309i	0.0292250	+	0.0212332i
$885$	1.21031	+	3.72496i	0.0406842	+	0.125213i
$886$	−21.2753	−	15.4574i	−0.714757	−	0.519301i
$887$	15.9345	−	11.5771i	0.535027	−	0.388720i	−0.287208	−	0.957868i	$-0.592727\pi$
$887$	15.9345	−	11.5771i	0.535027	−	0.388720i	0.822235	+	0.569149i	$0.192727\pi$
$888$	0.310793	−	0.956521i	0.0104295	−	0.0320987i
$889$	−20.0009	+	14.5315i	−0.670810	+	0.487372i
$890$	−1.34106	−	4.12735i	−0.0449524	−	0.138349i
$891$	0.594055	+	1.82831i	0.0199016	+	0.0612508i
$892$	8.29583	−	25.5320i	0.277765	−	0.854873i
$893$	49.3031			1.64987
$894$	−6.23252			−0.208447
$895$	−1.30513	+	4.01678i	−0.0436257	+	0.134266i
$896$	1.86427	+	1.35447i	0.0622810	+	0.0452498i
$897$	1.61051	−	1.17011i	0.0537735	−	0.0390687i
$898$	−6.72719			−0.224489
$899$	−18.6382	+	1.00004i	−0.621617	+	0.0333534i
$900$	1.00000			0.0333333
$901$	−6.32725	+	4.59702i	−0.210791	+	0.153149i
$902$	12.0855	+	8.78065i	0.402404	+	0.292364i
$903$	1.67916	−	5.16792i	0.0558789	−	0.171977i
$904$	4.58265			0.152417
$905$	−6.95357			−0.231144
$906$	3.94010	−	12.1264i	0.130901	−	0.402872i
$907$	15.1535	+	46.6377i	0.503164	+	1.54858i	0.803835	+	0.594852i	$0.202789\pi$
$907$	15.1535	+	46.6377i	0.503164	+	1.54858i	−0.300671	+	0.953728i	$0.597211\pi$
$908$	8.03196	+	24.7198i	0.266550	+	0.820356i
$909$	−5.63162	+	4.09161i	−0.186789	+	0.135710i
$910$	−0.223358	+	0.687424i	−0.00740424	+	0.0227879i
$911$	−30.7124	+	22.3139i	−1.01755	+	0.739291i	−0.965779	−	0.259368i	$-0.916486\pi$
$911$	−30.7124	+	22.3139i	−1.01755	+	0.739291i	−0.0517685	+	0.998659i	$0.516486\pi$
$912$	−6.53756	−	4.74982i	−0.216480	−	0.157282i
$913$	4.71381	+	14.5076i	0.156004	+	0.480132i
$914$	8.15250	+	5.92314i	0.269661	+	0.195920i
$915$	−4.03756	−	2.93346i	−0.133478	−	0.0969773i
$916$	−4.20014	−	12.9267i	−0.138777	−	0.427110i
$917$	28.9222	+	21.0132i	0.955094	+	0.693916i
$918$	−2.77022	+	2.01268i	−0.0914308	+	0.0664284i
$919$	−11.7890	+	36.2828i	−0.388883	+	1.19686i	0.544741	+	0.838604i	$0.316628\pi$
$919$	−11.7890	+	36.2828i	−0.388883	+	1.19686i	−0.933624	+	0.358254i	$0.883372\pi$
$920$	5.13449	−	3.73043i	0.169279	−	0.122989i
$921$	4.79930	+	14.7707i	0.158142	+	0.486712i
$922$	−7.90606	−	24.3323i	−0.260372	−	0.801343i
$923$	−0.293630	+	0.903700i	−0.00966495	+	0.0297457i
$924$	−4.42992			−0.145734
$925$	1.00575			0.0330687
$926$	−10.0158	+	30.8256i	−0.329141	+	1.01299i
$927$	−3.61339	−	2.62528i	−0.118679	−	0.0862255i
$928$	−2.71209	+	1.97045i	−0.0890287	+	0.0646831i
$929$	−37.0630			−1.21600			−0.607999	−	0.793938i	$-0.708027\pi$
$929$	−37.0630			−1.21600			−0.607999	+	0.793938i	$0.708027\pi$
$930$	4.67329	+	3.02661i	0.153243	+	0.0992464i
$931$	13.6558			0.447549
$932$	22.8681	−	16.6146i	0.749069	−	0.544231i
$933$	10.1932	+	7.40577i	0.333709	+	0.242454i
$934$	2.13402	−	6.56784i	0.0698273	−	0.214906i
$935$	−6.58265			−0.215276
$936$	0.313665			0.0102525
$937$	8.10466	−	24.9436i	0.264768	−	0.814871i	−0.726979	−	0.686659i	$-0.759076\pi$
$937$	8.10466	−	24.9436i	0.264768	−	0.814871i	0.991747	−	0.128211i	$-0.0409236\pi$
$938$	−2.07439	−	6.38432i	−0.0677313	−	0.208455i
$939$	−1.73962	−	5.35400i	−0.0567703	−	0.174721i
$940$	−4.93599	+	3.58620i	−0.160994	+	0.116969i
$941$	2.28690	−	7.03835i	0.0745508	−	0.229444i	−0.906837	−	0.421482i	$-0.861510\pi$
$941$	2.28690	−	7.03835i	0.0745508	−	0.229444i	0.981387	+	0.192039i	$0.0615099\pi$
$942$	−12.7690	+	9.27721i	−0.416036	+	0.302268i
$943$	39.8989	+	28.9882i	1.29929	+	0.943987i
$944$	1.21031	+	3.72496i	0.0393923	+	0.121237i
$945$	−1.86427	−	1.35447i	−0.0606448	−	0.0440610i
$946$	−3.66741	−	2.66453i	−0.119238	−	0.0866312i
$947$	12.7502	+	39.2412i	0.414327	+	1.27517i	0.912852	+	0.408291i	$0.133875\pi$
$947$	12.7502	+	39.2412i	0.414327	+	1.27517i	−0.498525	+	0.866875i	$0.666125\pi$
$948$	1.90772	+	1.38604i	0.0619599	+	0.0450165i
$949$	−0.0205224	+	0.0149104i	−0.000666185	+	0.000484012i
$950$	2.49713	−	7.68537i	0.0810175	−	0.249346i
$951$	−20.5599	+	14.9377i	−0.666702	+	0.484387i
$952$	−2.43832	−	7.50438i	−0.0790264	−	0.243218i
$953$	2.29151	+	7.05256i	0.0742294	+	0.228455i	0.981287	−	0.192553i	$-0.0616766\pi$
$953$	2.29151	+	7.05256i	0.0742294	+	0.228455i	−0.907057	+	0.421007i	$0.861677\pi$
$954$	−0.705803	+	2.17224i	−0.0228512	+	0.0703288i
$955$	19.8423			0.642083
$956$	−29.0894			−0.940820
$957$	1.99147	−	6.12910i	0.0643750	−	0.198126i
$958$	−16.6172	−	12.0731i	−0.536877	−	0.390064i
$959$	0.216737	−	0.157469i	0.00699882	−	0.00508494i
$960$	1.00000			0.0322749
$961$	12.6793	+	28.2884i	0.409009	+	0.912530i
$962$	0.315468			0.0101711
$963$	−10.8824	+	7.90650i	−0.350679	+	0.254784i
$964$	0.613523	+	0.445751i	0.0197603	+	0.0143567i
$965$	−3.41155	+	10.4997i	−0.109822	+	0.337997i
$966$	−14.6249			−0.470547
$967$	−17.7594			−0.571105			−0.285553	−	0.958363i	$-0.592177\pi$
$967$	−17.7594			−0.571105			−0.285553	+	0.958363i	$0.592177\pi$
$968$	2.25717	−	6.94687i	0.0725483	−	0.223281i
$969$	8.55061	+	26.3161i	0.274685	+	0.845394i
$970$	−2.65218	−	8.16258i	−0.0851565	−	0.262085i
$971$	−39.3383	+	28.5809i	−1.26242	+	0.917205i	−0.998874	−	0.0474404i	$-0.984894\pi$
$971$	−39.3383	+	28.5809i	−1.26242	+	0.917205i	−0.263551	+	0.964646i	$0.584894\pi$
$972$	−0.309017	+	0.951057i	−0.00991172	+	0.0305052i
$973$	3.94068	−	2.86307i	0.126332	−	0.0917858i
$974$	−10.9451	−	7.95211i	−0.350705	−	0.254802i
$975$	0.0969280	+	0.298314i	0.00310418	+	0.00955368i
$976$	−4.03756	−	2.93346i	−0.129239	−	0.0938978i
$977$	−18.0341	−	13.1025i	−0.576961	−	0.419187i	0.260666	−	0.965429i	$-0.416058\pi$
$977$	−18.0341	−	13.1025i	−0.576961	−	0.419187i	−0.837627	+	0.546242i	$0.816058\pi$
$978$	2.92186	+	8.99257i	0.0934308	+	0.287551i
$979$	6.74943	+	4.90375i	0.215713	+	0.156724i
$980$	−1.36715	+	0.993290i	−0.0436719	+	0.0317295i
$981$	4.41037	−	13.5737i	0.140812	−	0.433376i
$982$	−28.1637	+	20.4621i	−0.898740	+	0.652973i
$983$	−13.6689	−	42.0686i	−0.435970	−	1.34178i	−0.892089	−	0.451860i	$-0.850761\pi$
$983$	−13.6689	−	42.0686i	−0.435970	−	1.34178i	0.456119	−	0.889919i	$-0.349239\pi$
$984$	2.40130	+	7.39043i	0.0765505	+	0.235598i
$985$	6.71651	−	20.6713i	0.214006	−	0.658643i
$986$	11.4790			0.365565
$987$	14.0594			0.447517
$988$	0.783263	−	2.41063i	0.0249189	−	0.0766925i
$989$	−12.1075	−	8.79662i	−0.384996	−	0.279716i
$990$	−1.55526	+	1.12996i	−0.0494293	+	0.0359125i
$991$	−50.3829			−1.60047			−0.800233	−	0.599689i	$-0.795291\pi$
$991$	−50.3829			−1.60047			−0.800233	+	0.599689i	$0.795291\pi$
$992$	4.67329	+	3.02661i	0.148377	+	0.0960949i
$993$	20.3996			0.647361
$994$	5.64756	−	4.10319i	0.179130	−	0.130145i
$995$	−11.7647	−	8.54755i	−0.372966	−	0.270976i
$996$	−2.45204	+	7.54661i	−0.0776959	+	0.239123i
$997$	−20.8925			−0.661673			−0.330837	−	0.943688i	$-0.607331\pi$
$997$	−20.8925			−0.661673			−0.330837	+	0.943688i	$0.607331\pi$
$998$	−42.1041			−1.33278
$999$	−0.310793	+	0.956521i	−0.00983304	+	0.0302630i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.b.481.2	✓	8
31.2	even	5	inner	930.2.n.b.901.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.b.481.2	✓	8	1.1	even	1	trivial
930.2.n.b.901.2	yes	8	31.2	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)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{4} -1.00000 q^{5} +1.00000 q^{6} +(0.712089 - 2.19158i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.809017 + 0.587785i) q^{3} +(0.309017 - 0.951057i) q^{4} -1.00000 q^{5} +1.00000 q^{6} +(0.712089 - 2.19158i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.309017 + 0.951057i) q^{9} +(-0.809017 + 0.587785i) q^{10} +(0.594055 - 1.82831i) q^{11} +(0.809017 - 0.587785i) q^{12} +(0.253761 + 0.184368i) q^{13} +(-0.712089 - 2.19158i) q^{14} +(-0.809017 - 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.05813 + 3.25659i) q^{17} +(0.809017 + 0.587785i) q^{18} +(6.53756 - 4.74982i) q^{19} +(-0.309017 + 0.951057i) q^{20} +(1.86427 - 1.35447i) q^{21} +(-0.594055 - 1.82831i) q^{22} +(-1.96120 - 6.03596i) q^{23} +(0.309017 - 0.951057i) q^{24} +1.00000 q^{25} +0.313665 q^{26} +(-0.309017 + 0.951057i) q^{27} +(-1.86427 - 1.35447i) q^{28} +(2.71209 - 1.97045i) q^{29} -1.00000 q^{30} +(-4.67329 - 3.02661i) q^{31} -1.00000 q^{32} +(1.55526 - 1.12996i) q^{33} +(2.77022 + 2.01268i) q^{34} +(-0.712089 + 2.19158i) q^{35} +1.00000 q^{36} +1.00575 q^{37} +(2.49713 - 7.68537i) q^{38} +(0.0969280 + 0.298314i) q^{39} +(0.309017 + 0.951057i) q^{40} +(-6.28668 + 4.56754i) q^{41} +(0.712089 - 2.19158i) q^{42} +(1.90772 - 1.38604i) q^{43} +(-1.55526 - 1.12996i) q^{44} +(-0.309017 - 0.951057i) q^{45} +(-5.13449 - 3.73043i) q^{46} +(4.93599 + 3.58620i) q^{47} +(-0.309017 - 0.951057i) q^{48} +(1.36715 + 0.993290i) q^{49} +(0.809017 - 0.587785i) q^{50} +(-1.05813 + 3.25659i) q^{51} +(0.253761 - 0.184368i) q^{52} +(0.705803 + 2.17224i) q^{53} +(0.309017 + 0.951057i) q^{54} +(-0.594055 + 1.82831i) q^{55} -2.30437 q^{56} +8.08087 q^{57} +(1.03593 - 3.18825i) q^{58} +(-3.16864 - 2.30215i) q^{59} +(-0.809017 + 0.587785i) q^{60} +4.99070 q^{61} +(-5.55977 + 0.298314i) q^{62} +2.30437 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-0.253761 - 0.184368i) q^{65} +(0.594055 - 1.82831i) q^{66} +2.91311 q^{67} +3.42418 q^{68} +(1.96120 - 6.03596i) q^{69} +(0.712089 + 2.19158i) q^{70} +(0.936125 + 2.88110i) q^{71} +(0.809017 - 0.587785i) q^{72} +(-0.0249911 + 0.0769148i) q^{73} +(0.813665 - 0.591163i) q^{74} +(0.809017 + 0.587785i) q^{75} +(-2.49713 - 7.68537i) q^{76} +(-3.58388 - 2.60384i) q^{77} +(0.253761 + 0.184368i) q^{78} +(0.728684 + 2.24266i) q^{79} +(0.809017 + 0.587785i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-2.40130 + 7.39043i) q^{82} +(-6.41953 + 4.66406i) q^{83} +(-0.712089 - 2.19158i) q^{84} +(-1.05813 - 3.25659i) q^{85} +(0.728684 - 2.24266i) q^{86} +3.35233 q^{87} -1.92240 q^{88} +(-1.34106 + 4.12735i) q^{89} +(-0.809017 - 0.587785i) q^{90} +(0.584758 - 0.424852i) q^{91} -6.34658 q^{92} +(-2.00178 - 5.19547i) q^{93} +6.10122 q^{94} +(-6.53756 + 4.74982i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(-2.65218 + 8.16258i) q^{97} +1.68989 q^{98} +1.92240 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 8 q^{6} - 7 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 8 * q^6 - 7 * q^7 + 2 * q^8 - 2 * q^9	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 8 q^{6} - 7 q^{7} + 2 q^{8} - 2 q^{9} - 2 q^{10} + q^{11} + 2 q^{12} + 11 q^{13} + 7 q^{14} - 2 q^{15} - 2 q^{16} + 7 q^{17} + 2 q^{18} + 12 q^{19} + 2 q^{20} - 3 q^{21} - q^{22} - 6 q^{23} - 2 q^{24} + 8 q^{25} + 4 q^{26} + 2 q^{27} + 3 q^{28} + 9 q^{29} - 8 q^{30} - 15 q^{31} - 8 q^{32} - q^{33} + 8 q^{34} + 7 q^{35} + 8 q^{36} + 32 q^{37} + 8 q^{38} + 9 q^{39} - 2 q^{40} - 13 q^{41} - 7 q^{42} + 13 q^{43} + q^{44} + 2 q^{45} - 9 q^{46} - 15 q^{47} + 2 q^{48} + 5 q^{49} + 2 q^{50} - 7 q^{51} + 11 q^{52} + 25 q^{53} - 2 q^{54} - q^{55} - 8 q^{56} + 8 q^{57} + 6 q^{58} + 3 q^{59} - 2 q^{60} + 28 q^{61} - 5 q^{62} + 8 q^{63} - 2 q^{64} - 11 q^{65} + q^{66} - 8 q^{67} + 2 q^{68} + 6 q^{69} - 7 q^{70} - 15 q^{71} + 2 q^{72} - 24 q^{73} + 8 q^{74} + 2 q^{75} - 8 q^{76} - 16 q^{77} + 11 q^{78} + 2 q^{79} + 2 q^{80} - 2 q^{81} - 17 q^{82} - 20 q^{83} + 7 q^{84} - 7 q^{85} + 2 q^{86} + 6 q^{87} + 4 q^{88} + 37 q^{89} - 2 q^{90} - 11 q^{91} - 6 q^{92} - 10 q^{93} + 10 q^{94} - 12 q^{95} - 2 q^{96} - 16 q^{97} - 4 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 8 * q^6 - 7 * q^7 + 2 * q^8 - 2 * q^9 - 2 * q^10 + q^11 + 2 * q^12 + 11 * q^13 + 7 * q^14 - 2 * q^15 - 2 * q^16 + 7 * q^17 + 2 * q^18 + 12 * q^19 + 2 * q^20 - 3 * q^21 - q^22 - 6 * q^23 - 2 * q^24 + 8 * q^25 + 4 * q^26 + 2 * q^27 + 3 * q^28 + 9 * q^29 - 8 * q^30 - 15 * q^31 - 8 * q^32 - q^33 + 8 * q^34 + 7 * q^35 + 8 * q^36 + 32 * q^37 + 8 * q^38 + 9 * q^39 - 2 * q^40 - 13 * q^41 - 7 * q^42 + 13 * q^43 + q^44 + 2 * q^45 - 9 * q^46 - 15 * q^47 + 2 * q^48 + 5 * q^49 + 2 * q^50 - 7 * q^51 + 11 * q^52 + 25 * q^53 - 2 * q^54 - q^55 - 8 * q^56 + 8 * q^57 + 6 * q^58 + 3 * q^59 - 2 * q^60 + 28 * q^61 - 5 * q^62 + 8 * q^63 - 2 * q^64 - 11 * q^65 + q^66 - 8 * q^67 + 2 * q^68 + 6 * q^69 - 7 * q^70 - 15 * q^71 + 2 * q^72 - 24 * q^73 + 8 * q^74 + 2 * q^75 - 8 * q^76 - 16 * q^77 + 11 * q^78 + 2 * q^79 + 2 * q^80 - 2 * q^81 - 17 * q^82 - 20 * q^83 + 7 * q^84 - 7 * q^85 + 2 * q^86 + 6 * q^87 + 4 * q^88 + 37 * q^89 - 2 * q^90 - 11 * q^91 - 6 * q^92 - 10 * q^93 + 10 * q^94 - 12 * q^95 - 2 * q^96 - 16 * q^97 - 4 * q^99

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