LMFDB - Embedded newform 930.2.bg.a.391.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(121,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bg (of order $15$, degree $8$, 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:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			391.1
Root			$0.669131 - 0.743145i$ of defining polynomial
Character	$\chi$	$=$	930.391
Dual form			930.2.bg.a.421.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-2.44512 + 2.71559i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-2.44512 + 2.71559i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.669131 + 0.743145i) q^{9} +(-0.913545 + 0.406737i) q^{10} +(-4.12260 - 0.876286i) q^{11} +(0.104528 - 0.994522i) q^{12} +(-0.492608 - 4.68685i) q^{13} +(3.57433 - 0.759747i) q^{14} +(-0.809017 + 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(6.16157 - 1.30968i) q^{17} +(-0.104528 - 0.994522i) q^{18} +(-0.488830 + 4.65090i) q^{19} +(0.978148 + 0.207912i) q^{20} +(3.33826 - 1.48629i) q^{21} +(2.82019 + 3.13214i) q^{22} +(0.0646021 - 0.198825i) q^{23} +(-0.669131 + 0.743145i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.35634 + 4.08129i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(-3.33826 - 1.48629i) q^{28} +(7.23968 + 5.25994i) q^{29} +1.00000 q^{30} +(1.82019 + 5.26184i) q^{31} +1.00000 q^{32} +(3.40977 + 2.47734i) q^{33} +(-5.75463 - 2.56213i) q^{34} +(1.12920 + 3.47533i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-0.469210 - 0.812696i) q^{37} +(3.12920 - 3.47533i) q^{38} +(-1.45630 + 4.48202i) q^{39} +(-0.669131 - 0.743145i) q^{40} +(-4.10219 + 1.82641i) q^{41} +(-3.57433 - 0.759747i) q^{42} +(-0.868460 + 8.26285i) q^{43} +(-0.440557 - 4.19162i) q^{44} +(0.978148 - 0.207912i) q^{45} +(-0.169131 + 0.122881i) q^{46} +(6.16157 - 4.47665i) q^{47} +(0.978148 - 0.207912i) q^{48} +(-0.664074 - 6.31824i) q^{49} +(-0.104528 + 0.994522i) q^{50} +(-6.16157 - 1.30968i) q^{51} +(4.30524 - 1.91682i) q^{52} +(5.61048 + 6.23107i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-2.82019 + 3.13214i) q^{55} +(1.82709 + 3.16461i) q^{56} +(2.33826 - 4.04999i) q^{57} +(-2.76531 - 8.51076i) q^{58} +(3.15563 + 1.40497i) q^{59} +(-0.809017 - 0.587785i) q^{60} +6.42941 q^{61} +(1.62027 - 5.32679i) q^{62} -3.65418 q^{63} +(-0.809017 - 0.587785i) q^{64} +(-4.30524 - 1.91682i) q^{65} +(-1.30242 - 4.00842i) q^{66} +(5.06677 - 8.77591i) q^{67} +(3.14961 + 5.45529i) q^{68} +(-0.139886 + 0.155360i) q^{69} +(1.12920 - 3.47533i) q^{70} +(6.53818 + 7.26139i) q^{71} +(0.913545 - 0.406737i) q^{72} +(-0.618034 - 0.131367i) q^{73} +(-0.0980917 + 0.933280i) q^{74} +(0.104528 + 0.994522i) q^{75} +(-4.57433 + 0.972304i) q^{76} +(12.4599 - 9.05265i) q^{77} +(3.81263 - 2.77004i) q^{78} +(2.09805 - 0.445954i) q^{79} +(0.104528 + 0.994522i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(4.39228 + 0.933609i) q^{82} +(7.22851 - 3.21834i) q^{83} +(2.44512 + 2.71559i) q^{84} +(1.94657 - 5.99092i) q^{85} +(5.55938 - 6.17432i) q^{86} +(-4.47437 - 7.74983i) q^{87} +(-2.10735 + 3.65004i) q^{88} +(4.52498 + 13.9264i) q^{89} +(-0.913545 - 0.406737i) q^{90} +(13.9320 + 10.1222i) q^{91} +0.209057 q^{92} +(0.477358 - 5.54726i) q^{93} -7.61612 q^{94} +(3.78339 + 2.74879i) q^{95} +(-0.913545 - 0.406737i) q^{96} +(-0.0901699 - 0.277515i) q^{97} +(-3.17652 + 5.50190i) q^{98} +(-2.10735 - 3.65004i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - q^{3} - 2 q^{4} + 4 q^{5} + 4 q^{6} + 2 q^{7} - 2 q^{8} + q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - q^3 - 2 * q^4 + 4 * q^5 + 4 * q^6 + 2 * q^7 - 2 * q^8 + q^9	\( 8 q - 2 q^{2} - q^{3} - 2 q^{4} + 4 q^{5} + 4 q^{6} + 2 q^{7} - 2 q^{8} + q^{9} - q^{10} - 23 q^{11} - q^{12} - 17 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} + 11 q^{17} + q^{18} - q^{20} + 18 q^{21} + 22 q^{22} - 2 q^{23} - q^{24} - 4 q^{25} - 2 q^{26} + 2 q^{27} - 18 q^{28} + 10 q^{29} + 8 q^{30} + 14 q^{31} + 8 q^{32} + 4 q^{33} - 19 q^{34} + 4 q^{35} - 4 q^{36} - q^{37} + 20 q^{38} + 6 q^{39} - q^{40} - 42 q^{41} - 2 q^{42} - 23 q^{43} + 17 q^{44} - q^{45} + 3 q^{46} + 11 q^{47} - q^{48} - 3 q^{49} + q^{50} - 11 q^{51} + 13 q^{52} + 2 q^{53} + 2 q^{54} - 22 q^{55} + 2 q^{56} + 10 q^{57} + 28 q^{59} - 2 q^{60} - 4 q^{61} + 14 q^{62} - 4 q^{63} - 2 q^{64} - 13 q^{65} - q^{66} - 20 q^{67} + q^{68} - q^{69} + 4 q^{70} + 42 q^{71} + q^{72} + 4 q^{73} - 41 q^{74} - q^{75} - 10 q^{76} + 52 q^{77} - 4 q^{78} - 42 q^{79} - q^{80} + q^{81} - 2 q^{82} + 6 q^{83} - 2 q^{84} + 22 q^{85} - 3 q^{86} - 10 q^{87} - 3 q^{88} + 16 q^{89} - q^{90} + 28 q^{91} - 2 q^{92} + 13 q^{93} + 6 q^{94} - q^{96} + 44 q^{97} - 8 q^{98} - 3 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - q^3 - 2 * q^4 + 4 * q^5 + 4 * q^6 + 2 * q^7 - 2 * q^8 + q^9 - q^10 - 23 * q^11 - q^12 - 17 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 + 11 * q^17 + q^18 - q^20 + 18 * q^21 + 22 * q^22 - 2 * q^23 - q^24 - 4 * q^25 - 2 * q^26 + 2 * q^27 - 18 * q^28 + 10 * q^29 + 8 * q^30 + 14 * q^31 + 8 * q^32 + 4 * q^33 - 19 * q^34 + 4 * q^35 - 4 * q^36 - q^37 + 20 * q^38 + 6 * q^39 - q^40 - 42 * q^41 - 2 * q^42 - 23 * q^43 + 17 * q^44 - q^45 + 3 * q^46 + 11 * q^47 - q^48 - 3 * q^49 + q^50 - 11 * q^51 + 13 * q^52 + 2 * q^53 + 2 * q^54 - 22 * q^55 + 2 * q^56 + 10 * q^57 + 28 * q^59 - 2 * q^60 - 4 * q^61 + 14 * q^62 - 4 * q^63 - 2 * q^64 - 13 * q^65 - q^66 - 20 * q^67 + q^68 - q^69 + 4 * q^70 + 42 * q^71 + q^72 + 4 * q^73 - 41 * q^74 - q^75 - 10 * q^76 + 52 * q^77 - 4 * q^78 - 42 * q^79 - q^80 + q^81 - 2 * q^82 + 6 * q^83 - 2 * q^84 + 22 * q^85 - 3 * q^86 - 10 * q^87 - 3 * q^88 + 16 * q^89 - q^90 + 28 * q^91 - 2 * q^92 + 13 * q^93 + 6 * q^94 - q^96 + 44 * q^97 - 8 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{15}\right)$

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
$3$	−0.913545	−	0.406737i	−0.527436	−	0.234830i
$3$	−0.913545	−	0.406737i	−0.527436	−	0.234830i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	−2.44512	+	2.71559i	−0.924170	+	1.02640i	0.0754020	+	0.997153i	$0.475976\pi$
$7$	−2.44512	+	2.71559i	−0.924170	+	1.02640i	−0.999572	+	0.0292419i	$0.990691\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	0.669131	+	0.743145i	0.223044	+	0.247715i
$10$	−0.913545	+	0.406737i	−0.288888	+	0.128621i
$11$	−4.12260	−	0.876286i	−1.24301	−	0.264210i	−0.460958	−	0.887422i	$-0.652494\pi$
$11$	−4.12260	−	0.876286i	−1.24301	−	0.264210i	−0.782053	+	0.623212i	$0.785828\pi$
$12$	0.104528	−	0.994522i	0.0301748	−	0.287094i
$13$	−0.492608	−	4.68685i	−0.136625	−	1.29990i	−0.821067	−	0.570832i	$-0.806621\pi$
$13$	−0.492608	−	4.68685i	−0.136625	−	1.29990i	0.684442	−	0.729067i	$-0.260046\pi$
$14$	3.57433	−	0.759747i	0.955280	−	0.203051i
$15$	−0.809017	+	0.587785i	−0.208887	+	0.151765i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	6.16157	−	1.30968i	1.49440	−	0.317645i	0.613026	−	0.790062i	$-0.289952\pi$
$17$	6.16157	−	1.30968i	1.49440	−	0.317645i	0.881375	+	0.472418i	$0.156619\pi$
$18$	−0.104528	−	0.994522i	−0.0246376	−	0.234411i
$19$	−0.488830	+	4.65090i	−0.112145	+	1.06699i	0.783247	+	0.621711i	$0.213562\pi$
$19$	−0.488830	+	4.65090i	−0.112145	+	1.06699i	−0.895392	+	0.445279i	$0.853104\pi$
$20$	0.978148	+	0.207912i	0.218720	+	0.0464905i
$21$	3.33826	−	1.48629i	0.728468	−	0.324335i
$22$	2.82019	+	3.13214i	0.601266	+	0.667773i
$23$	0.0646021	−	0.198825i	0.0134705	−	0.0414579i	−0.944095	−	0.329673i	$-0.893062\pi$
$23$	0.0646021	−	0.198825i	0.0134705	−	0.0414579i	0.957566	+	0.288215i	$0.0930617\pi$
$24$	−0.669131	+	0.743145i	−0.136586	+	0.151694i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−2.35634	+	4.08129i	−0.462115	+	0.800407i
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	−3.33826	−	1.48629i	−0.630872	−	0.280882i
$29$	7.23968	+	5.25994i	1.34438	+	0.976746i	0.999271	+	0.0381813i	$0.0121564\pi$
$29$	7.23968	+	5.25994i	1.34438	+	0.976746i	0.345104	+	0.938564i	$0.387844\pi$
$30$	1.00000			0.182574
$31$	1.82019	+	5.26184i	0.326915	+	0.945054i
$31$	1.82019	+	5.26184i	0.326915	+	0.945054i
$32$	1.00000			0.176777
$33$	3.40977	+	2.47734i	0.593564	+	0.431250i
$34$	−5.75463	−	2.56213i	−0.986911	−	0.439401i
$35$	1.12920	+	3.47533i	0.190870	+	0.587439i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−0.469210	−	0.812696i	−0.0771377	−	0.133606i	0.824876	−	0.565313i	$-0.191245\pi$
$37$	−0.469210	−	0.812696i	−0.0771377	−	0.133606i	−0.902014	+	0.431707i	$0.857911\pi$
$38$	3.12920	−	3.47533i	0.507624	−	0.563774i
$39$	−1.45630	+	4.48202i	−0.233194	+	0.717697i
$40$	−0.669131	−	0.743145i	−0.105799	−	0.117502i
$41$	−4.10219	+	1.82641i	−0.640655	+	0.285238i	−0.701240	−	0.712925i	$-0.747370\pi$
$41$	−4.10219	+	1.82641i	−0.640655	+	0.285238i	0.0605853	+	0.998163i	$0.480703\pi$
$42$	−3.57433	−	0.759747i	−0.551531	−	0.117232i
$43$	−0.868460	+	8.26285i	−0.132439	+	1.26007i	0.703279	+	0.710914i	$0.251718\pi$
$43$	−0.868460	+	8.26285i	−0.132439	+	1.26007i	−0.835718	+	0.549159i	$0.814948\pi$
$44$	−0.440557	−	4.19162i	−0.0664164	−	0.631910i
$45$	0.978148	−	0.207912i	0.145814	−	0.0309936i
$46$	−0.169131	+	0.122881i	−0.0249369	+	0.0181178i
$47$	6.16157	−	4.47665i	0.898758	−	0.652986i	−0.0393888	−	0.999224i	$-0.512541\pi$
$47$	6.16157	−	4.47665i	0.898758	−	0.652986i	0.938147	+	0.346238i	$0.112541\pi$
$48$	0.978148	−	0.207912i	0.141183	−	0.0300095i
$49$	−0.664074	−	6.31824i	−0.0948677	−	0.902606i
$50$	−0.104528	+	0.994522i	−0.0147826	+	0.140647i
$51$	−6.16157	−	1.30968i	−0.862793	−	0.183392i
$52$	4.30524	−	1.91682i	0.597029	−	0.265815i
$53$	5.61048	+	6.23107i	0.770658	+	0.855903i	0.992883	−	0.119093i	$-0.0379986\pi$
$53$	5.61048	+	6.23107i	0.770658	+	0.855903i	−0.222225	+	0.974995i	$0.571332\pi$
$54$	−0.309017	+	0.951057i	−0.0420519	+	0.129422i
$55$	−2.82019	+	3.13214i	−0.380274	+	0.422337i
$56$	1.82709	+	3.16461i	0.244155	+	0.422889i
$57$	2.33826	−	4.04999i	0.309710	−	0.536434i
$58$	−2.76531	−	8.51076i	−0.363103	−	1.11752i
$59$	3.15563	+	1.40497i	0.410827	+	0.182912i	0.601735	−	0.798696i	$-0.294476\pi$
$59$	3.15563	+	1.40497i	0.410827	+	0.182912i	−0.190907	+	0.981608i	$0.561143\pi$
$60$	−0.809017	−	0.587785i	−0.104444	−	0.0758827i
$61$	6.42941			0.823201			0.411601	−	0.911364i	$-0.364970\pi$
$61$	6.42941			0.823201			0.411601	+	0.911364i	$0.364970\pi$
$62$	1.62027	−	5.32679i	0.205774	−	0.676504i
$63$	−3.65418			−0.460384
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−4.30524	−	1.91682i	−0.533999	−	0.237752i
$66$	−1.30242	−	4.00842i	−0.160316	−	0.493403i
$67$	5.06677	−	8.77591i	0.619005	−	1.07215i	−0.370663	−	0.928767i	$-0.620869\pi$
$67$	5.06677	−	8.77591i	0.619005	−	1.07215i	0.989668	−	0.143380i	$-0.0457972\pi$
$68$	3.14961	+	5.45529i	0.381947	+	0.661551i
$69$	−0.139886	+	0.155360i	−0.0168403	+	0.0187031i
$70$	1.12920	−	3.47533i	0.134966	−	0.415382i
$71$	6.53818	+	7.26139i	0.775939	+	0.861768i	0.993447	−	0.114291i	$-0.0364595\pi$
$71$	6.53818	+	7.26139i	0.775939	+	0.861768i	−0.217508	+	0.976059i	$0.569793\pi$
$72$	0.913545	−	0.406737i	0.107662	−	0.0479344i
$73$	−0.618034	−	0.131367i	−0.0723354	−	0.0153754i	0.171602	−	0.985166i	$-0.445106\pi$
$73$	−0.618034	−	0.131367i	−0.0723354	−	0.0153754i	−0.243937	+	0.969791i	$0.578439\pi$
$74$	−0.0980917	+	0.933280i	−0.0114029	+	0.108492i
$75$	0.104528	+	0.994522i	0.0120699	+	0.114837i
$76$	−4.57433	+	0.972304i	−0.524712	+	0.111531i
$77$	12.4599	−	9.05265i	1.41994	−	1.03165i
$78$	3.81263	−	2.77004i	0.431695	−	0.313645i
$79$	2.09805	−	0.445954i	0.236049	−	0.0501738i	−0.0883681	−	0.996088i	$-0.528165\pi$
$79$	2.09805	−	0.445954i	0.236049	−	0.0501738i	0.324417	+	0.945914i	$0.394832\pi$
$80$	0.104528	+	0.994522i	0.0116866	+	0.111191i
$81$	−0.104528	+	0.994522i	−0.0116143	+	0.110502i
$82$	4.39228	+	0.933609i	0.485047	+	0.103100i
$83$	7.22851	−	3.21834i	0.793432	−	0.353259i	0.0303327	−	0.999540i	$-0.490343\pi$
$83$	7.22851	−	3.21834i	0.793432	−	0.353259i	0.763099	+	0.646281i	$0.223677\pi$
$84$	2.44512	+	2.71559i	0.266785	+	0.296295i
$85$	1.94657	−	5.99092i	0.211135	−	0.649807i
$86$	5.55938	−	6.17432i	0.599483	−	0.665794i
$87$	−4.47437	−	7.74983i	−0.479703	−	0.830869i
$88$	−2.10735	+	3.65004i	−0.224644	+	0.389096i
$89$	4.52498	+	13.9264i	0.479647	+	1.47620i	0.839587	+	0.543225i	$0.182797\pi$
$89$	4.52498	+	13.9264i	0.479647	+	1.47620i	−0.359940	+	0.932975i	$0.617203\pi$
$90$	−0.913545	−	0.406737i	−0.0962961	−	0.0428738i
$91$	13.9320	+	10.1222i	1.46048	+	1.06110i
$92$	0.209057			0.0217957
$93$	0.477358	−	5.54726i	0.0494997	−	0.575224i
$94$	−7.61612			−0.785543
$95$	3.78339	+	2.74879i	0.388167	+	0.282020i
$96$	−0.913545	−	0.406737i	−0.0932383	−	0.0415124i
$97$	−0.0901699	−	0.277515i	−0.00915537	−	0.0281773i	0.946374	−	0.323072i	$-0.104716\pi$
$97$	−0.0901699	−	0.277515i	−0.00915537	−	0.0281773i	−0.955530	+	0.294894i	$0.904716\pi$
$98$	−3.17652	+	5.50190i	−0.320877	+	0.555776i
$99$	−2.10735	−	3.65004i	−0.211797	−	0.366843i
$100$	0.669131	−	0.743145i	0.0669131	−	0.0743145i
$101$	−1.50660	+	4.63684i	−0.149912	+	0.461383i	−0.997610	−	0.0690968i	$-0.977988\pi$
$101$	−1.50660	+	4.63684i	−0.149912	+	0.461383i	0.847697	+	0.530480i	$0.177988\pi$
$102$	4.21501	+	4.68124i	0.417348	+	0.463512i
$103$	−5.74257	+	2.55676i	−0.565832	+	0.251925i	−0.669656	−	0.742671i	$-0.733559\pi$
$103$	−5.74257	+	2.55676i	−0.565832	+	0.251925i	0.103824	+	0.994596i	$0.466892\pi$
$104$	−4.60969	−	0.979819i	−0.452017	−	0.0960792i
$105$	0.381966	−	3.63416i	0.0372761	−	0.354658i
$106$	−0.876443	−	8.33879i	−0.0851276	−	0.809935i
$107$	3.33635	−	0.709163i	0.322537	−	0.0685574i	−0.0437978	−	0.999040i	$-0.513946\pi$
$107$	3.33635	−	0.709163i	0.322537	−	0.0685574i	0.366335	+	0.930483i	$0.380612\pi$
$108$	0.809017	−	0.587785i	0.0778477	−	0.0565597i
$109$	−10.0047	+	7.26882i	−0.958274	+	0.696227i	−0.952749	−	0.303758i	$-0.901759\pi$
$109$	−10.0047	+	7.26882i	−0.958274	+	0.696227i	−0.00552447	+	0.999985i	$0.501759\pi$
$110$	4.12260	−	0.876286i	0.393075	−	0.0835506i
$111$	0.0980917	+	0.933280i	0.00931045	+	0.0885830i
$112$	0.381966	−	3.63416i	0.0360924	−	0.343396i
$113$	−5.28493	−	1.12335i	−0.497165	−	0.105676i	−0.0474966	−	0.998871i	$-0.515124\pi$
$113$	−5.28493	−	1.12335i	−0.497165	−	0.105676i	−0.449668	+	0.893196i	$0.648458\pi$
$114$	−4.27222	+	1.90211i	−0.400130	+	0.178149i
$115$	−0.139886	−	0.155360i	−0.0130445	−	0.0144874i
$116$	−2.76531	+	8.51076i	−0.256753	+	0.790204i
$117$	3.15339	−	3.50220i	0.291531	−	0.323778i
$118$	−1.72713	−	2.99148i	−0.158995	−	0.275388i
$119$	−11.5093	+	19.9346i	−1.05505	+	1.82740i
$120$	0.309017	+	0.951057i	0.0282093	+	0.0868192i
$121$	6.17897	+	2.75106i	0.561725	+	0.250096i
$122$	−5.20150	−	3.77911i	−0.470922	−	0.342145i
$123$	4.49041			0.404887
$124$	−4.44183	+	3.35710i	−0.398889	+	0.301476i
$125$	−1.00000			−0.0894427
$126$	2.95630	+	2.14787i	0.263368	+	0.191348i
$127$	−11.6161	−	5.17183i	−1.03076	−	0.458926i	−0.179553	−	0.983748i	$-0.557465\pi$
$127$	−11.6161	−	5.17183i	−1.03076	−	0.458926i	−0.851212	+	0.524823i	$0.824132\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	4.15418	−	7.19525i	0.365755	−	0.633507i
$130$	2.35634	+	4.08129i	0.206664	+	0.357953i
$131$	13.6230	−	15.1299i	1.19025	−	1.32191i	0.255411	−	0.966833i	$-0.417789\pi$
$131$	13.6230	−	15.1299i	1.19025	−	1.32191i	0.934838	−	0.355073i	$-0.115544\pi$
$132$	−1.30242	+	4.00842i	−0.113361	+	0.348888i
$133$	−11.4347	−	12.6995i	−0.991513	−	1.10119i
$134$	−9.25745	+	4.12168i	−0.799722	+	0.356059i
$135$	−0.978148	−	0.207912i	−0.0841855	−	0.0178942i
$136$	0.658449	−	6.26472i	0.0564615	−	0.537195i
$137$	0.913745	+	8.69370i	0.0780665	+	0.742753i	0.961613	+	0.274410i	$0.0884824\pi$
$137$	0.913745	+	8.69370i	0.0780665	+	0.742753i	−0.883546	+	0.468344i	$0.844851\pi$
$138$	0.204489	−	0.0434654i	0.0174072	−	0.00370002i
$139$	16.0028	−	11.6267i	1.35734	−	0.986163i	0.358727	−	0.933442i	$-0.383211\pi$
$139$	16.0028	−	11.6267i	1.35734	−	0.986163i	0.998609	−	0.0527201i	$-0.0167891\pi$
$140$	−2.95630	+	2.14787i	−0.249853	+	0.181529i
$141$	−7.44969	+	1.58348i	−0.627377	+	0.133353i
$142$	−1.02136	−	9.71763i	−0.0857110	−	0.815486i
$143$	−2.07620	+	19.7537i	−0.173620	+	1.65189i
$144$	−0.978148	−	0.207912i	−0.0815123	−	0.0173260i
$145$	8.17508	−	3.63978i	0.678903	−	0.302267i
$146$	0.422784	+	0.469550i	0.0349899	+	0.0388602i
$147$	−1.96320	+	6.04210i	−0.161922	+	0.498344i
$148$	0.627926	−	0.697383i	0.0516152	−	0.0573245i
$149$	−4.91121	−	8.50647i	−0.402342	−	0.696877i	0.591666	−	0.806183i	$-0.298470\pi$
$149$	−4.91121	−	8.50647i	−0.402342	−	0.696877i	−0.994008	+	0.109306i	$0.965137\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	−1.41686	−	4.36064i	−0.115302	−	0.354864i	0.876708	−	0.481023i	$-0.159735\pi$
$151$	−1.41686	−	4.36064i	−0.115302	−	0.354864i	−0.992010	+	0.126160i	$0.959735\pi$
$152$	4.27222	+	1.90211i	0.346522	+	0.154282i
$153$	5.09618	+	3.70259i	0.412002	+	0.299337i
$154$	−15.4013			−1.24107
$155$	5.46698	+	1.05459i	0.439118	+	0.0847067i
$156$	−4.71267			−0.377316
$157$	−0.776482	−	0.564148i	−0.0619700	−	0.0450239i	0.556369	−	0.830935i	$-0.312194\pi$
$157$	−0.776482	−	0.564148i	−0.0619700	−	0.0450239i	−0.618339	+	0.785911i	$0.712194\pi$
$158$	−1.95948	−	0.872418i	−0.155888	−	0.0694059i
$159$	−2.59102	−	7.97435i	−0.205481	−	0.632407i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	0.381966	+	0.661585i	0.0301031	+	0.0521402i
$162$	0.669131	−	0.743145i	0.0525719	−	0.0583870i
$163$	−3.78446	+	11.6474i	−0.296422	+	0.912294i	0.686318	+	0.727302i	$0.259226\pi$
$163$	−3.78446	+	11.6474i	−0.296422	+	0.912294i	−0.982740	+	0.184992i	$0.940774\pi$
$164$	−3.00467	−	3.33702i	−0.234625	−	0.260578i
$165$	3.85032	−	1.71427i	0.299747	−	0.133456i
$166$	−7.73968	−	1.64512i	−0.600716	−	0.127686i
$167$	0.568215	−	5.40621i	0.0439698	−	0.418345i	−0.950291	−	0.311363i	$-0.899215\pi$
$167$	0.568215	−	5.40621i	0.0439698	−	0.418345i	0.994261	−	0.106982i	$-0.0341188\pi$
$168$	−0.381966	−	3.63416i	−0.0294693	−	0.280382i
$169$	−9.00802	+	1.91471i	−0.692924	+	0.147286i
$170$	−5.09618	+	3.70259i	−0.390859	+	0.283976i
$171$	−3.78339	+	2.74879i	−0.289323	+	0.210205i
$172$	−8.12681	+	1.72741i	−0.619663	+	0.131713i
$173$	−2.11889	−	20.1599i	−0.161096	−	1.53273i	−0.714395	−	0.699743i	$-0.753298\pi$
$173$	−2.11889	−	20.1599i	−0.161096	−	1.53273i	0.553299	−	0.832983i	$-0.313369\pi$
$174$	−0.935398	+	8.89972i	−0.0709123	+	0.674686i
$175$	3.57433	+	0.759747i	0.270194	+	0.0574315i
$176$	3.85032	−	1.71427i	0.290229	−	0.129218i
$177$	−2.31135	−	2.56702i	−0.173732	−	0.192949i
$178$	4.52498	−	13.9264i	0.339161	−	1.04383i
$179$	4.82293	−	5.35640i	0.360482	−	0.400356i	−0.535435	−	0.844576i	$-0.679852\pi$
$179$	4.82293	−	5.35640i	0.360482	−	0.400356i	0.895918	+	0.444220i	$0.146519\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$	−1.50670	+	2.60969i	−0.111992	+	0.193977i	−0.916574	−	0.399866i	$-0.869057\pi$
$181$	−1.50670	+	2.60969i	−0.111992	+	0.193977i	0.804581	+	0.593843i	$0.202390\pi$
$182$	−5.32157	−	16.3781i	−0.394461	−	1.21403i
$183$	−5.87356	−	2.61508i	−0.434186	−	0.193312i
$184$	−0.169131	−	0.122881i	−0.0124685	−	0.00905888i
$185$	−0.938421			−0.0689941
$186$	−3.64679	+	4.20725i	−0.267396	+	0.308490i
$187$	−26.5494			−1.94148
$188$	6.16157	+	4.47665i	0.449379	+	0.326493i
$189$	3.33826	+	1.48629i	0.242823	+	0.108112i
$190$	−1.44512	−	4.44764i	−0.104840	−	0.322666i
$191$	−8.32315	+	14.4161i	−0.602242	+	1.04311i	0.390239	+	0.920714i	$0.372392\pi$
$191$	−8.32315	+	14.4161i	−0.602242	+	1.04311i	−0.992481	+	0.122400i	$0.960941\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−15.6822	+	17.4168i	−1.12883	+	1.25369i	−0.165252	+	0.986251i	$0.552844\pi$
$193$	−15.6822	+	17.4168i	−1.12883	+	1.25369i	−0.963575	+	0.267438i	$0.913823\pi$
$194$	−0.0901699	+	0.277515i	−0.00647382	+	0.0199244i
$195$	3.15339	+	3.50220i	0.225819	+	0.250798i
$196$	5.80380	−	2.58402i	0.414557	−	0.184573i
$197$	15.8465	+	3.36829i	1.12902	+	0.239981i	0.734303	−	0.678822i	$-0.237509\pi$
$197$	15.8465	+	3.36829i	1.12902	+	0.239981i	0.394717	+	0.918803i	$0.370843\pi$
$198$	−0.440557	+	4.19162i	−0.0313090	+	0.297885i
$199$	1.81493	+	17.2679i	0.128657	+	1.22409i	0.848213	+	0.529655i	$0.177679\pi$
$199$	1.81493	+	17.2679i	0.128657	+	1.22409i	−0.719556	+	0.694435i	$0.755655\pi$
$200$	−0.978148	+	0.207912i	−0.0691655	+	0.0147016i
$201$	−8.19821	+	5.95635i	−0.578257	+	0.420128i
$202$	3.94433	−	2.86573i	0.277522	−	0.201632i
$203$	−31.9857	+	6.79878i	−2.24496	+	0.477181i
$204$	−0.658449	−	6.26472i	−0.0461006	−	0.438618i
$205$	−0.469376	+	4.46581i	−0.0327826	+	0.311906i
$206$	6.14866	+	1.30694i	0.428397	+	0.0910587i
$207$	0.190983	−	0.0850311i	0.0132742	−	0.00591007i
$208$	3.15339	+	3.50220i	0.218648	+	0.242834i
$209$	6.09077	−	18.7455i	0.421308	−	1.29665i
$210$	−2.44512	+	2.71559i	−0.168730	+	0.187393i
$211$	2.27510	+	3.94059i	0.156625	+	0.271282i	0.933649	−	0.358188i	$-0.116605\pi$
$211$	2.27510	+	3.94059i	0.156625	+	0.271282i	−0.777025	+	0.629470i	$0.783272\pi$
$212$	−4.19236	+	7.26139i	−0.287933	+	0.498714i
$213$	−3.01945	−	9.29292i	−0.206890	−	0.636741i
$214$	−3.11600	−	1.38733i	−0.213005	−	0.0948361i
$215$	6.72161	+	4.88353i	0.458410	+	0.333054i
$216$	−1.00000			−0.0680414
$217$	−18.7396	−	7.92297i	−1.27212	−	0.537846i
$218$	12.3665			0.837562
$219$	0.511170	+	0.371387i	0.0345417	+	0.0250960i
$220$	−3.85032	−	1.71427i	−0.259589	−	0.115576i
$221$	−9.17353	−	28.2332i	−0.617079	−	1.89917i
$222$	0.469210	−	0.812696i	0.0314913	−	0.0545446i
$223$	−0.213727	−	0.370187i	−0.0143122	−	0.0247895i	0.858781	−	0.512344i	$-0.171223\pi$
$223$	−0.213727	−	0.370187i	−0.0143122	−	0.0247895i	−0.873093	+	0.487554i	$0.837889\pi$
$224$	−2.44512	+	2.71559i	−0.163372	+	0.181443i
$225$	0.309017	−	0.951057i	0.0206011	−	0.0634038i
$226$	3.61531	+	4.01521i	0.240487	+	0.267088i
$227$	1.35495	−	0.603265i	0.0899315	−	0.0400401i	−0.361278	−	0.932458i	$-0.617659\pi$
$227$	1.35495	−	0.603265i	0.0899315	−	0.0400401i	0.451209	+	0.892418i	$0.350993\pi$
$228$	4.57433	+	0.972304i	0.302942	+	0.0643924i
$229$	−3.04626	+	28.9832i	−0.201303	+	1.91527i	0.167700	+	0.985838i	$0.446366\pi$
$229$	−3.04626	+	28.9832i	−0.201303	+	1.91527i	−0.369003	+	0.929428i	$0.620301\pi$
$230$	0.0218524	+	0.207912i	0.00144090	+	0.0137093i
$231$	−15.0647	+	3.20211i	−0.991187	+	0.210683i
$232$	7.23968	−	5.25994i	0.475308	−	0.345332i
$233$	−1.23761	+	0.899179i	−0.0810787	+	0.0589072i	−0.627586	−	0.778547i	$-0.715957\pi$
$233$	−1.23761	+	0.899179i	−0.0810787	+	0.0589072i	0.546507	+	0.837454i	$0.315957\pi$
$234$	−4.60969	+	0.979819i	−0.301345	+	0.0640528i
$235$	−0.796102	−	7.57440i	−0.0519320	−	0.494100i
$236$	−0.361069	+	3.43534i	−0.0235036	+	0.223622i
$237$	−2.09805	−	0.445954i	−0.136283	−	0.0289678i
$238$	21.0285	−	9.36248i	1.36307	−	0.606879i
$239$	−18.8862	−	20.9753i	−1.22165	−	1.35678i	−0.914226	−	0.405205i	$-0.867200\pi$
$239$	−18.8862	−	20.9753i	−1.22165	−	1.35678i	−0.307422	−	0.951573i	$-0.599466\pi$
$240$	0.309017	−	0.951057i	0.0199470	−	0.0613904i
$241$	−13.9937	+	15.5416i	−0.901413	+	1.00112i	0.0985695	+	0.995130i	$0.468573\pi$
$241$	−13.9937	+	15.5416i	−0.901413	+	1.00112i	−0.999982	+	0.00598994i	$0.998093\pi$
$242$	−3.38186	−	5.85756i	−0.217394	−	0.376538i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	1.98680	+	6.11473i	0.127192	+	0.391455i
$245$	−5.80380	−	2.58402i	−0.370791	−	0.165087i
$246$	−3.63282	−	2.63940i	−0.231620	−	0.168282i
$247$	22.0389			1.40230
$248$	5.56677	−	0.105104i	0.353490	−	0.00667413i
$249$	−7.91259			−0.501440
$250$	0.809017	+	0.587785i	0.0511667	+	0.0371748i
$251$	−26.0298	−	11.5892i	−1.64299	−	0.731506i	−0.643564	−	0.765393i	$-0.722545\pi$
$251$	−26.0298	−	11.5892i	−1.64299	−	0.731506i	−0.999426	+	0.0338867i	$0.989211\pi$
$252$	−1.12920	−	3.47533i	−0.0711332	−	0.218925i
$253$	−0.440557	+	0.763066i	−0.0276976	+	0.0479736i
$254$	6.35772	+	11.0119i	0.398919	+	0.690947i
$255$	−4.21501	+	4.68124i	−0.263954	+	0.293150i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	0.455017	+	0.505348i	0.0283832	+	0.0315227i	0.757169	−	0.653219i	$-0.226582\pi$
$257$	0.455017	+	0.505348i	0.0283832	+	0.0315227i	−0.728786	+	0.684741i	$0.759915\pi$
$258$	−7.59007	+	3.37932i	−0.472537	+	0.210387i
$259$	3.35423	+	0.712963i	0.208421	+	0.0443013i
$260$	0.492608	−	4.68685i	0.0305503	−	0.290666i
$261$	0.935398	+	8.89972i	0.0578997	+	0.550879i
$262$	−19.9144	+	4.23294i	−1.23032	+	0.261512i
$263$	−20.0331	+	14.5549i	−1.23529	+	0.897494i	−0.997276	−	0.0737661i	$-0.976498\pi$
$263$	−20.0331	+	14.5549i	−1.23529	+	0.897494i	−0.238019	+	0.971260i	$0.576498\pi$
$264$	3.40977	−	2.47734i	0.209857	−	0.152470i
$265$	8.20150	−	1.74328i	0.503814	−	0.107089i
$266$	1.78627	+	16.9952i	0.109523	+	1.04205i
$267$	1.53062	−	14.5629i	0.0936727	−	0.891236i
$268$	9.91210	+	2.10688i	0.605478	+	0.128698i
$269$	1.50654	−	0.670754i	0.0918553	−	0.0408966i	−0.360295	−	0.932839i	$-0.617324\pi$
$269$	1.50654	−	0.670754i	0.0918553	−	0.0408966i	0.452150	+	0.891942i	$0.350657\pi$
$270$	0.669131	+	0.743145i	0.0407220	+	0.0452264i
$271$	−5.30475	+	16.3263i	−0.322241	+	0.991755i	0.650430	+	0.759566i	$0.274589\pi$
$271$	−5.30475	+	16.3263i	−0.322241	+	0.991755i	−0.972671	+	0.232189i	$0.925411\pi$
$272$	−4.21501	+	4.68124i	−0.255572	+	0.283842i
$273$	−8.61048	−	14.9138i	−0.521130	−	0.902623i
$274$	4.37080	−	7.57044i	0.264049	−	0.457347i
$275$	1.30242	+	4.00842i	0.0785386	+	0.241717i
$276$	−0.190983	−	0.0850311i	−0.0114958	−	0.00511827i
$277$	21.7972	+	15.8366i	1.30966	+	0.951527i	1.00000		0.000680528i	$0.000216619\pi$
$277$	21.7972	+	15.8366i	1.30966	+	0.951527i	0.309664	+	0.950846i	$0.399783\pi$
$278$	−19.7805			−1.18636
$279$	−2.69236	+	4.87352i	−0.161188	+	0.291770i
$280$	3.65418			0.218379
$281$	0.255318	+	0.185499i	0.0152310	+	0.0110660i	0.595375	−	0.803448i	$-0.297004\pi$
$281$	0.255318	+	0.185499i	0.0152310	+	0.0110660i	−0.580144	+	0.814514i	$0.697004\pi$
$282$	6.95768	+	3.09776i	0.414324	+	0.184469i
$283$	3.09365	+	9.52127i	0.183898	+	0.565980i	0.999928	−	0.0120299i	$-0.00382932\pi$
$283$	3.09365	+	9.52127i	0.183898	+	0.565980i	−0.816029	+	0.578010i	$0.803829\pi$
$284$	−4.88558	+	8.46207i	−0.289906	+	0.502132i
$285$	−2.33826	−	4.04999i	−0.138507	−	0.239901i
$286$	13.2906	−	14.7607i	0.785890	−	0.872820i
$287$	5.07059	−	15.6057i	0.299307	−	0.921174i
$288$	0.669131	+	0.743145i	0.0394289	+	0.0437902i
$289$	20.7194	−	9.22489i	1.21879	−	0.542641i
$290$	−8.75319	−	1.86055i	−0.514005	−	0.109255i
$291$	−0.0305010	+	0.290198i	−0.00178800	+	0.0170117i
$292$	−0.0660454	−	0.628380i	−0.00386501	−	0.0367732i
$293$	5.55955	−	1.18172i	0.324792	−	0.0690367i	−0.0426302	−	0.999091i	$-0.513574\pi$
$293$	5.55955	−	1.18172i	0.324792	−	0.0690367i	0.367422	+	0.930054i	$0.380240\pi$
$294$	5.13972	−	3.73423i	0.299755	−	0.217784i
$295$	2.79456	−	2.03036i	0.162705	−	0.118212i
$296$	−0.917914	+	0.195109i	−0.0533527	+	0.0113405i
$297$	0.440557	+	4.19162i	0.0255637	+	0.243222i
$298$	−1.02672	+	9.76861i	−0.0594764	+	0.565881i
$299$	−0.963687	−	0.204838i	−0.0557315	−	0.0118461i
$300$	−0.913545	+	0.406737i	−0.0527436	+	0.0234830i
$301$	−20.3150	−	22.5621i	−1.17094	−	1.30046i
$302$	−1.41686	+	4.36064i	−0.0815310	+	0.250927i
$303$	3.26232	−	3.62318i	0.187416	−	0.208146i
$304$	−2.33826	−	4.04999i	−0.134108	−	0.232283i
$305$	3.21470	−	5.56803i	0.184073	−	0.318824i
$306$	−1.94657	−	5.99092i	−0.111278	−	0.342478i
$307$	15.9389	+	7.09645i	0.909680	+	0.405016i	0.807580	−	0.589758i	$-0.200777\pi$
$307$	15.9389	+	7.09645i	0.909680	+	0.405016i	0.102100	+	0.994774i	$0.467444\pi$
$308$	12.4599	+	9.05265i	0.709969	+	0.515823i
$309$	6.28602			0.357599
$310$	−3.80301	−	4.06659i	−0.215996	−	0.230967i
$311$	27.8101			1.57696			0.788482	−	0.615058i	$-0.210867\pi$
$311$	27.8101			1.57696			0.788482	+	0.615058i	$0.210867\pi$
$312$	3.81263	+	2.77004i	0.215848	+	0.156823i
$313$	19.6913	+	8.76713i	1.11302	+	0.495548i	0.879066	−	0.476700i	$-0.158167\pi$
$313$	19.6913	+	8.76713i	1.11302	+	0.495548i	0.233953	+	0.972248i	$0.424834\pi$
$314$	0.296590	+	0.912810i	0.0167375	+	0.0515128i
$315$	−1.82709	+	3.16461i	−0.102945	+	0.178306i
$316$	1.07246	+	1.85756i	0.0603306	+	0.104496i
$317$	10.2173	−	11.3474i	0.573858	−	0.637334i	−0.384424	−	0.923157i	$-0.625600\pi$
$317$	10.2173	−	11.3474i	0.573858	−	0.637334i	0.958283	+	0.285822i	$0.0922667\pi$
$318$	−2.59102	+	7.97435i	−0.145297	+	0.447179i
$319$	−25.2371	−	28.0287i	−1.41301	−	1.56930i
$320$	−0.913545	+	0.406737i	−0.0510687	+	0.0227373i
$321$	−3.33635	−	0.709163i	−0.186217	−	0.0395816i
$322$	0.0798526	−	0.759747i	0.00445001	−	0.0423391i
$323$	3.07925	+	29.2971i	0.171334	+	1.63013i
$324$	−0.978148	+	0.207912i	−0.0543415	+	0.0115506i
$325$	−3.81263	+	2.77004i	−0.211487	+	0.153654i
$326$	9.90786	−	7.19848i	0.548745	−	0.398687i
$327$	12.0962	−	2.57113i	0.668922	−	0.142184i
$328$	0.469376	+	4.46581i	0.0259169	+	0.246583i
$329$	−2.90910	+	27.6782i	−0.160384	+	1.52595i
$330$	−4.12260	−	0.876286i	−0.226942	−	0.0482380i
$331$	23.9031	−	10.6424i	1.31383	−	0.584957i	0.374267	−	0.927321i	$-0.377894\pi$
$331$	23.9031	−	10.6424i	1.31383	−	0.584957i	0.939567	+	0.342364i	$0.111228\pi$
$332$	5.29456	+	5.88020i	0.290577	+	0.322718i
$333$	0.289988	−	0.892491i	0.0158912	−	0.0489082i
$334$	−3.63739	+	4.03973i	−0.199029	+	0.221044i
$335$	−5.06677	−	8.77591i	−0.276827	−	0.479479i
$336$	−1.82709	+	3.16461i	−0.0996760	+	0.172644i
$337$	−0.577819	−	1.77834i	−0.0314758	−	0.0968726i	0.934084	−	0.357052i	$-0.116218\pi$
$337$	−0.577819	−	1.77834i	−0.0314758	−	0.0968726i	−0.965560	+	0.260180i	$0.916218\pi$
$338$	8.41308	+	3.74574i	0.457611	+	0.203742i
$339$	4.37112	+	3.17580i	0.237407	+	0.172486i
$340$	6.29923			0.341624
$341$	−2.89303	−	23.2875i	−0.156667	−	1.26109i
$342$	4.67652			0.252877
$343$	−1.91259	−	1.38958i	−0.103270	−	0.0750302i
$344$	7.59007	+	3.37932i	0.409229	+	0.182201i
$345$	0.0646021	+	0.198825i	0.00347806	+	0.0107044i
$346$	−10.1355	+	17.5551i	−0.544885	+	0.943769i
$347$	14.1681	+	24.5399i	0.760584	+	1.31737i	0.942550	+	0.334065i	$0.108421\pi$
$347$	14.1681	+	24.5399i	0.760584	+	1.31737i	−0.181966	+	0.983305i	$0.558246\pi$
$348$	5.98787	−	6.65021i	0.320984	−	0.356489i
$349$	7.11251	−	21.8901i	0.380724	−	1.17175i	−0.558811	−	0.829295i	$-0.688742\pi$
$349$	7.11251	−	21.8901i	0.380724	−	1.17175i	0.939535	−	0.342453i	$-0.111258\pi$
$350$	−2.44512	−	2.71559i	−0.130697	−	0.145154i
$351$	−4.30524	+	1.91682i	−0.229797	+	0.102312i
$352$	−4.12260	−	0.876286i	−0.219735	−	0.0467062i
$353$	−2.00108	+	19.0390i	−0.106507	+	1.01334i	0.802526	+	0.596618i	$0.203489\pi$
$353$	−2.00108	+	19.0390i	−0.106507	+	1.01334i	−0.909032	+	0.416726i	$0.863178\pi$
$354$	0.361069	+	3.43534i	0.0191906	+	0.182586i
$355$	9.55764	−	2.03154i	0.507267	−	0.107823i
$356$	−11.8465	+	8.60702i	−0.627866	+	0.456171i
$357$	18.6224	−	13.5299i	0.985601	−	0.716081i
$358$	−7.05024	+	1.49858i	−0.372617	+	0.0792022i
$359$	−0.466819	−	4.44149i	−0.0246378	−	0.234413i	−0.999910	−	0.0134064i	$-0.995732\pi$
$359$	−0.466819	−	4.44149i	−0.0246378	−	0.234413i	0.975272	−	0.221006i	$-0.0709342\pi$
$360$	0.104528	−	0.994522i	0.00550913	−	0.0524159i
$361$	−2.80715	−	0.596678i	−0.147745	−	0.0314041i
$362$	2.75289	−	1.22566i	0.144688	−	0.0644194i
$363$	−4.52582	−	5.02643i	−0.237544	−	0.263819i
$364$	−5.32157	+	16.3781i	−0.278926	+	0.858446i
$365$	−0.422784	+	0.469550i	−0.0221295	+	0.0245773i
$366$	3.21470	+	5.56803i	0.168035	+	0.291046i
$367$	6.17291	−	10.6918i	0.322223	−	0.558107i	−0.658723	−	0.752385i	$-0.728903\pi$
$367$	6.17291	−	10.6918i	0.322223	−	0.558107i	0.980946	+	0.194278i	$0.0622365\pi$
$368$	0.0646021	+	0.198825i	0.00336762	+	0.0103645i
$369$	−4.10219	−	1.82641i	−0.213552	−	0.0950793i
$370$	0.759198	+	0.551590i	0.0394689	+	0.0286758i
$371$	−30.6393			−1.59071
$372$	5.42327	−	1.26020i	0.281184	−	0.0653386i
$373$	−30.1174			−1.55942			−0.779711	−	0.626140i	$-0.784634\pi$
$373$	−30.1174			−1.55942			−0.779711	+	0.626140i	$0.784634\pi$
$374$	21.4789	+	15.6053i	1.11065	+	0.806932i
$375$	0.913545	+	0.406737i	0.0471753	+	0.0210038i
$376$	−2.35351	−	7.24336i	−0.121373	−	0.373548i
$377$	21.0862	−	36.5224i	1.08600	−	1.88100i
$378$	−1.82709	−	3.16461i	−0.0939754	−	0.162770i
$379$	−12.0145	+	13.3434i	−0.617141	+	0.685405i	−0.967979	−	0.251032i	$-0.919230\pi$
$379$	−12.0145	+	13.3434i	−0.617141	+	0.685405i	0.350838	+	0.936436i	$0.385897\pi$
$380$	−1.44512	+	4.44764i	−0.0741333	+	0.228159i
$381$	8.50828	+	9.44941i	0.435893	+	0.484108i
$382$	15.2071	−	6.77066i	0.778065	−	0.346417i
$383$	−29.5586	−	6.28287i	−1.51037	−	0.321039i	−0.623047	−	0.782184i	$-0.714106\pi$
$383$	−29.5586	−	6.28287i	−1.51037	−	0.321039i	−0.887325	+	0.461145i	$0.847439\pi$
$384$	0.104528	−	0.994522i	0.00533420	−	0.0507515i
$385$	−1.60987	−	15.3169i	−0.0820468	−	0.780623i
$386$	22.9245	−	4.87275i	1.16683	−	0.248016i
$387$	−6.72161	+	4.88353i	−0.341679	+	0.248244i
$388$	0.236068	−	0.171513i	0.0119845	−	0.00870727i
$389$	−7.43241	+	1.57981i	−0.376838	+	0.0800994i	−0.392437	−	0.919779i	$-0.628368\pi$
$389$	−7.43241	+	1.57981i	−0.376838	+	0.0800994i	0.0155988	+	0.999878i	$0.495035\pi$
$390$	−0.492608	−	4.68685i	−0.0249442	−	0.237328i
$391$	0.137653	−	1.30968i	0.00696142	−	0.0662335i
$392$	−6.21422	−	1.32087i	−0.313865	−	0.0667141i
$393$	−18.5991	+	8.28087i	−0.938203	+	0.417715i
$394$	−10.8403	−	12.0394i	−0.546126	−	0.606535i
$395$	0.662817	−	2.03994i	0.0333500	−	0.102641i
$396$	2.82019	−	3.13214i	0.141720	−	0.157396i
$397$	−7.20908	−	12.4865i	−0.361813	−	0.626679i	0.626446	−	0.779465i	$-0.284509\pi$
$397$	−7.20908	−	12.4865i	−0.361813	−	0.626679i	−0.988259	+	0.152786i	$0.951176\pi$
$398$	8.68152	−	15.0368i	0.435165	−	0.753728i
$399$	5.28075	+	16.2525i	0.264368	+	0.813641i
$400$	0.913545	+	0.406737i	0.0456773	+	0.0203368i
$401$	−26.1530	−	19.0013i	−1.30602	−	0.948878i	−0.306023	−	0.952024i	$-0.598999\pi$
$401$	−26.1530	−	19.0013i	−1.30602	−	0.948878i	−0.999995	+	0.00314607i	$0.998999\pi$
$402$	10.1335			0.505415
$403$	23.7648	−	11.1230i	1.18381	−	0.554075i
$404$	−4.87547			−0.242564
$405$	0.809017	+	0.587785i	0.0402004	+	0.0292073i
$406$	29.8732	+	13.3004i	1.48258	+	0.660089i
$407$	1.22221	+	3.76159i	0.0605829	+	0.186455i
$408$	−3.14961	+	5.45529i	−0.155929	+	0.270077i
$409$	−1.02429	−	1.77412i	−0.0506479	−	0.0877247i	0.839590	−	0.543221i	$-0.182795\pi$
$409$	−1.02429	−	1.77412i	−0.0506479	−	0.0877247i	−0.890238	+	0.455496i	$0.849462\pi$
$410$	3.00467	−	3.33702i	0.148390	−	0.164804i
$411$	2.70130	−	8.31375i	0.133245	−	0.410087i
$412$	−4.20617	−	4.67143i	−0.207223	−	0.230145i
$413$	−11.5312	+	5.13403i	−0.567415	+	0.252629i
$414$	−0.204489	−	0.0434654i	−0.0100501	−	0.00213621i
$415$	0.827091	−	7.86924i	0.0406003	−	0.386286i
$416$	−0.492608	−	4.68685i	−0.0241521	−	0.229792i
$417$	−19.3482	+	4.11260i	−0.947488	+	0.201395i
$418$	−15.9459	+	11.5853i	−0.779937	+	0.566657i
$419$	14.9975	−	10.8963i	0.732674	−	0.532319i	−0.157734	−	0.987482i	$-0.550419\pi$
$419$	14.9975	−	10.8963i	0.732674	−	0.532319i	0.890408	+	0.455163i	$0.150419\pi$
$420$	3.57433	−	0.759747i	0.174409	−	0.0370719i
$421$	−2.59781	−	24.7165i	−0.126609	−	1.20461i	−0.854698	−	0.519125i	$-0.826258\pi$
$421$	−2.59781	−	24.7165i	−0.126609	−	1.20461i	0.728089	−	0.685483i	$-0.240409\pi$
$422$	0.475626	−	4.52528i	0.0231531	−	0.220287i
$423$	7.44969	+	1.58348i	0.362216	+	0.0769915i
$424$	7.65983	−	3.41038i	0.371994	−	0.165622i
$425$	−4.21501	−	4.68124i	−0.204458	−	0.227073i
$426$	−3.01945	+	9.29292i	−0.146293	+	0.450244i
$427$	−15.7207	+	17.4596i	−0.760778	+	0.844930i
$428$	1.70544	+	2.95391i	0.0824357	+	0.142783i
$429$	9.93125	−	17.2014i	0.479485	−	0.830493i
$430$	−2.56743	−	7.90172i	−0.123812	−	0.381055i
$431$	33.2424	+	14.8005i	1.60123	+	0.712913i	0.996506	−	0.0835236i	$-0.0266174\pi$
$431$	33.2424	+	14.8005i	1.60123	+	0.712913i	0.604722	+	0.796436i	$0.293284\pi$
$432$	0.809017	+	0.587785i	0.0389238	+	0.0282798i
$433$	39.4360			1.89517			0.947586	−	0.319501i	$-0.103515\pi$
$433$	39.4360			1.89517			0.947586	+	0.319501i	$0.103515\pi$
$434$	10.5036	+	17.4247i	0.504190	+	0.836410i
$435$	−8.94874			−0.429059
$436$	−10.0047	−	7.26882i	−0.479137	−	0.348113i
$437$	0.893136	+	0.397650i	0.0427245	+	0.0190222i
$438$	−0.195250	−	0.600917i	−0.00932939	−	0.0287129i
$439$	−0.921569	+	1.59620i	−0.0439841	+	0.0761827i	−0.887179	−	0.461425i	$-0.847338\pi$
$439$	−0.921569	+	1.59620i	−0.0439841	+	0.0761827i	0.843195	+	0.537607i	$0.180672\pi$
$440$	2.10735	+	3.65004i	0.100464	+	0.174009i
$441$	4.25102	−	4.72123i	0.202429	−	0.224821i
$442$	−9.17353	+	28.2332i	−0.436341	+	1.34292i
$443$	6.55041	+	7.27497i	0.311219	+	0.345644i	0.878380	−	0.477963i	$-0.158625\pi$
$443$	6.55041	+	7.27497i	0.311219	+	0.345644i	−0.567161	+	0.823607i	$0.691958\pi$
$444$	−0.857290	+	0.381690i	−0.0406852	+	0.0181142i
$445$	14.3231	+	3.04448i	0.678982	+	0.144322i
$446$	−0.0446812	+	0.425113i	−0.00211572	+	0.0201297i
$447$	1.02672	+	9.76861i	0.0485623	+	0.462040i
$448$	3.57433	−	0.759747i	0.168871	−	0.0358947i
$449$	19.7815	−	14.3721i	0.933546	−	0.678261i	−0.0133128	−	0.999911i	$-0.504238\pi$
$449$	19.7815	−	14.3721i	0.933546	−	0.678261i	0.946858	+	0.321651i	$0.104238\pi$
$450$	−0.809017	+	0.587785i	−0.0381374	+	0.0277085i
$451$	18.5122	−	3.93488i	0.871704	−	0.185286i
$452$	−0.564767	−	5.37340i	−0.0265644	−	0.252744i
$453$	−0.479268	+	4.55993i	−0.0225180	+	0.214244i
$454$	−1.45077	−	0.308371i	−0.0680881	−	0.0144726i
$455$	15.7321	−	7.00439i	0.737533	−	0.328371i
$456$	−3.12920	−	3.47533i	−0.146538	−	0.162747i
$457$	−1.63355	+	5.02754i	−0.0764141	+	0.235178i	−0.981966	−	0.189057i	$-0.939457\pi$
$457$	−1.63355	+	5.02754i	−0.0764141	+	0.235178i	0.905552	+	0.424235i	$0.139457\pi$
$458$	19.5004	−	21.6574i	0.911194	−	1.01198i
$459$	−3.14961	−	5.45529i	−0.147011	−	0.254631i
$460$	0.104528	−	0.181049i	0.00487366	−	0.00844143i
$461$	−3.32440	−	10.2315i	−0.154833	−	0.476527i	0.843311	−	0.537426i	$-0.180603\pi$
$461$	−3.32440	−	10.2315i	−0.154833	−	0.476527i	−0.998144	+	0.0608991i	$0.980603\pi$
$462$	14.0698	+	6.26427i	0.654586	+	0.291440i
$463$	−14.6029	−	10.6096i	−0.678655	−	0.493072i	0.194256	−	0.980951i	$-0.437771\pi$
$463$	−14.6029	−	10.6096i	−0.678655	−	0.493072i	−0.872911	+	0.487879i	$0.837771\pi$
$464$	−8.94874			−0.415435
$465$	−4.56539	−	3.18704i	−0.211715	−	0.147795i
$466$	1.52977			0.0708654
$467$	−31.9684	−	23.2264i	−1.47932	−	1.07479i	−0.977775	−	0.209659i	$-0.932765\pi$
$467$	−31.9684	−	23.2264i	−1.47932	−	1.07479i	−0.501546	−	0.865131i	$-0.667235\pi$
$468$	4.30524	+	1.91682i	0.199010	+	0.0886048i
$469$	11.4428	+	35.2174i	0.528381	+	1.62619i
$470$	−3.80806	+	6.59576i	−0.175653	+	0.304240i
$471$	0.479893	+	0.831198i	0.0221123	+	0.0382996i
$472$	2.31135	−	2.56702i	0.106389	−	0.118157i
$473$	10.8209	−	33.3034i	0.497547	−	1.53129i
$474$	1.43523	+	1.59399i	0.0659224	+	0.0732143i
$475$	4.27222	−	1.90211i	0.196023	−	0.0872749i
$476$	−22.5155	−	4.78582i	−1.03200	−	0.219358i
$477$	−0.876443	+	8.33879i	−0.0401295	+	0.381807i
$478$	2.95032	+	28.0704i	0.134944	+	1.28391i
$479$	−11.8545	+	2.51975i	−0.541646	+	0.115130i	−0.470607	−	0.882343i	$-0.655965\pi$
$479$	−11.8545	+	2.51975i	−0.541646	+	0.115130i	−0.0710393	+	0.997474i	$0.522632\pi$
$480$	−0.809017	+	0.587785i	−0.0369264	+	0.0268286i
$481$	−3.57785	+	2.59946i	−0.163136	+	0.118525i
$482$	20.4562	−	4.34811i	0.931756	−	0.198051i
$483$	−0.0798526	−	0.759747i	−0.00363342	−	0.0345697i
$484$	−0.707002	+	6.72668i	−0.0321365	+	0.305758i
$485$	−0.285420	−	0.0606678i	−0.0129602	−	0.00275478i
$486$	−0.913545	+	0.406737i	−0.0414393	+	0.0184499i
$487$	−11.1889	−	12.4266i	−0.507019	−	0.563102i	0.434235	−	0.900799i	$-0.357019\pi$
$487$	−11.1889	−	12.4266i	−0.507019	−	0.563102i	−0.941255	+	0.337697i	$0.890352\pi$
$488$	1.98680	−	6.11473i	0.0899380	−	0.276801i
$489$	8.19470	−	9.10113i	0.370577	−	0.411568i
$490$	3.17652	+	5.50190i	0.143501	+	0.248550i
$491$	−0.688325	+	1.19221i	−0.0310637	+	0.0538038i	−0.881139	−	0.472857i	$-0.843223\pi$
$491$	−0.688325	+	1.19221i	−0.0310637	+	0.0538038i	0.850076	+	0.526661i	$0.176556\pi$
$492$	1.38761	+	4.27063i	0.0625584	+	0.192535i
$493$	51.4967	+	22.9278i	2.31929	+	1.03262i
$494$	−17.8299	−	12.9541i	−0.802203	−	0.582835i
$495$	−4.21470			−0.189437
$496$	−4.56539	−	3.18704i	−0.204992	−	0.143102i
$497$	−35.7056			−1.60161
$498$	6.40142	+	4.65090i	0.286854	+	0.208412i
$499$	3.91548	+	1.74328i	0.175281	+	0.0780400i	0.492501	−	0.870312i	$-0.336083\pi$
$499$	3.91548	+	1.74328i	0.175281	+	0.0780400i	−0.317220	+	0.948352i	$0.602749\pi$
$500$	−0.309017	−	0.951057i	−0.0138197	−	0.0425325i
$501$	−2.71799	+	4.70770i	−0.121431	+	0.210325i
$502$	14.2466	+	24.6758i	0.635857	+	1.10134i
$503$	6.86476	−	7.62408i	0.306084	−	0.339941i	−0.570404	−	0.821364i	$-0.693213\pi$
$503$	6.86476	−	7.62408i	0.306084	−	0.339941i	0.876488	+	0.481423i	$0.159880\pi$
$504$	−1.12920	+	3.47533i	−0.0502988	+	0.154804i
$505$	3.26232	+	3.62318i	0.145171	+	0.161229i
$506$	0.804937	−	0.358381i	0.0357838	−	0.0159320i
$507$	9.00802	+	1.91471i	0.400060	+	0.0850354i
$508$	1.32912	−	12.6458i	0.0589704	−	0.561066i
$509$	−0.726512	−	6.91230i	−0.0322021	−	0.306382i	−0.998754	−	0.0499102i	$-0.984106\pi$
$509$	−0.726512	−	6.91230i	−0.0322021	−	0.306382i	0.966552	−	0.256472i	$-0.0825602\pi$
$510$	6.16157	−	1.30968i	0.272839	−	0.0579937i
$511$	1.86791	−	1.35712i	0.0826314	−	0.0600353i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	4.57433	−	0.972304i	0.201962	−	0.0429283i
$514$	−0.0710806	−	0.676287i	−0.00313523	−	0.0298297i
$515$	−0.657068	+	6.25159i	−0.0289539	+	0.275478i
$516$	8.12681	+	1.72741i	0.357763	+	0.0760448i
$517$	−29.3245	+	13.0561i	−1.28969	+	0.574208i
$518$	−2.29456	−	2.54836i	−0.100817	−	0.111969i
$519$	−6.26406	+	19.2788i	−0.274962	+	0.846245i
$520$	−3.15339	+	3.50220i	−0.138285	+	0.153581i
$521$	16.5827	+	28.7221i	0.726503	+	1.25834i	0.958352	+	0.285588i	$0.0921890\pi$
$521$	16.5827	+	28.7221i	0.726503	+	1.25834i	−0.231850	+	0.972752i	$0.574478\pi$
$522$	4.47437	−	7.74983i	0.195838	−	0.339201i
$523$	−4.25047	−	13.0816i	−0.185860	−	0.572018i	0.814102	−	0.580722i	$-0.197229\pi$
$523$	−4.25047	−	13.0816i	−0.185860	−	0.572018i	−0.999962	+	0.00870368i	$0.997229\pi$
$524$	18.5991	+	8.28087i	0.812507	+	0.361752i
$525$	−2.95630	−	2.14787i	−0.129023	−	0.0937409i
$526$	24.7623			1.07969
$527$	18.1066	+	30.0373i	0.788734	+	1.30845i
$528$	−4.21470			−0.183421
$529$	18.5720	+	13.4934i	0.807480	+	0.586668i
$530$	−7.65983	−	3.41038i	−0.332722	−	0.148137i
$531$	1.06743	+	3.28520i	0.0463223	+	0.142565i
$532$	8.54443	−	14.7994i	0.370448	−	0.641635i
$533$	10.5809	+	18.3267i	0.458310	+	0.793816i
$534$	−9.79817	+	10.8820i	−0.424008	+	0.470909i
$535$	1.05402	−	3.24395i	0.0455693	−	0.140248i
$536$	−6.78066	−	7.53069i	−0.292880	−	0.325276i
$537$	−6.58461	+	2.93166i	−0.284147	+	0.126510i
$538$	−1.61307	−	0.342870i	−0.0695446	−	0.0147822i
$539$	−2.79888	+	26.6295i	−0.120556	+	1.14701i
$540$	−0.104528	−	0.994522i	−0.00449819	−	0.0427974i
$541$	33.0151	−	7.01757i	1.41943	−	0.301709i	0.566640	−	0.823966i	$-0.308243\pi$
$541$	33.0151	−	7.01757i	1.41943	−	0.301709i	0.852788	+	0.522257i	$0.174910\pi$
$542$	13.8880	−	10.0902i	0.596541	−	0.433413i
$543$	2.43790	−	1.77124i	0.104620	−	0.0760110i
$544$	6.16157	−	1.30968i	0.264175	−	0.0561522i
$545$	1.29265	+	12.2987i	0.0553709	+	0.526819i
$546$	−1.80008	+	17.1266i	−0.0770363	+	0.732951i
$547$	19.6672	+	4.18038i	0.840907	+	0.178740i	0.608177	−	0.793801i	$-0.291901\pi$
$547$	19.6672	+	4.18038i	0.840907	+	0.178740i	0.232730	+	0.972541i	$0.425234\pi$
$548$	−7.98584	+	3.55553i	−0.341138	+	0.151885i
$549$	4.30211	+	4.77798i	0.183610	+	0.203919i
$550$	1.30242	−	4.00842i	0.0555352	−	0.170920i
$551$	−28.0024	+	31.0998i	−1.19294	+	1.32490i
$552$	0.104528	+	0.181049i	0.00444903	+	0.00770594i
$553$	−3.91897	+	6.78785i	−0.166651	+	0.288649i
$554$	−8.32577	−	25.6241i	−0.353728	−	1.08866i
$555$	0.857290	+	0.381690i	0.0363899	+	0.0162018i
$556$	16.0028	+	11.6267i	0.678668	+	0.493081i
$557$	−3.98173			−0.168711			−0.0843556	−	0.996436i	$-0.526883\pi$
$557$	−3.98173			−0.168711			−0.0843556	+	0.996436i	$0.526883\pi$
$558$	5.04275	−	2.36023i	0.213477	−	0.0999164i
$559$	39.1546			1.65606
$560$	−2.95630	−	2.14787i	−0.124926	−	0.0907643i
$561$	24.2541	+	10.7986i	1.02401	+	0.455917i
$562$	−0.0975228	−	0.300144i	−0.00411375	−	0.0126608i
$563$	1.36527	−	2.36472i	0.0575394	−	0.0996611i	−0.835821	−	0.549002i	$-0.815008\pi$
$563$	1.36527	−	2.36472i	0.0575394	−	0.0996611i	0.893360	+	0.449341i	$0.148341\pi$
$564$	−3.80806	−	6.59576i	−0.160348	−	0.277731i
$565$	−3.61531	+	4.01521i	−0.152097	+	0.168921i
$566$	3.09365	−	9.52127i	0.130036	−	0.400209i
$567$	−2.44512	−	2.71559i	−0.102686	−	0.114044i
$568$	8.92640	−	3.97429i	0.374543	−	0.166757i
$569$	−0.582285	−	0.123769i	−0.0244107	−	0.00518865i	0.195690	−	0.980666i	$-0.437305\pi$
$569$	−0.582285	−	0.123769i	−0.0244107	−	0.00518865i	−0.220101	+	0.975477i	$0.570639\pi$
$570$	−0.488830	+	4.65090i	−0.0204748	+	0.194805i
$571$	−0.366453	−	3.48657i	−0.0153356	−	0.145908i	0.984175	−	0.177201i	$-0.0567043\pi$
$571$	−0.366453	−	3.48657i	−0.0153356	−	0.145908i	−0.999510	+	0.0312927i	$0.990038\pi$
$572$	−19.4285	+	4.12965i	−0.812345	+	0.172669i
$573$	13.4671	−	9.78445i	0.562598	−	0.408751i
$574$	−13.2750	+	9.64483i	−0.554087	+	0.402568i
$575$	−0.204489	+	0.0434654i	−0.00852776	+	0.00181263i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	−4.53253	+	43.1242i	−0.188692	+	1.79528i	0.333805	+	0.942642i	$0.391667\pi$
$577$	−4.53253	+	43.1242i	−0.188692	+	1.79528i	−0.522497	+	0.852641i	$0.674999\pi$
$578$	−22.1846	−	4.71549i	−0.922759	−	0.196139i
$579$	21.4104	−	9.53254i	0.889787	−	0.396159i
$580$	5.98787	+	6.65021i	0.248633	+	0.276135i
$581$	−8.93493	+	27.4989i	−0.370683	+	1.14085i
$582$	0.195250	−	0.216847i	0.00809336	−	0.00898859i
$583$	−17.6696	−	30.6046i	−0.731799	−	1.26751i
$584$	−0.315921	+	0.547191i	−0.0130729	+	0.0226429i
$585$	−1.45630	−	4.48202i	−0.0602104	−	0.185309i
$586$	−5.19236	−	2.31179i	−0.214495	−	0.0954991i
$587$	−6.77425	−	4.92178i	−0.279603	−	0.203144i	0.439141	−	0.898418i	$-0.355283\pi$
$587$	−6.77425	−	4.92178i	−0.279603	−	0.203144i	−0.718744	+	0.695274i	$0.755283\pi$
$588$	−6.35304			−0.261995
$589$	−25.3621	+	5.89337i	−1.04503	+	0.242832i
$590$	−3.45426			−0.142210
$591$	−13.1065	−	9.52245i	−0.539131	−	0.391701i
$592$	0.857290	+	0.381690i	0.0352344	+	0.0156874i
$593$	−3.28916	−	10.1230i	−0.135070	−	0.415701i	0.860531	−	0.509398i	$-0.170132\pi$
$593$	−3.28916	−	10.1230i	−0.135070	−	0.415701i	−0.995601	+	0.0936962i	$0.970132\pi$
$594$	2.10735	−	3.65004i	0.0864657	−	0.149763i
$595$	11.5093	+	19.9346i	0.471834	+	0.817240i
$596$	6.57248	−	7.29948i	0.269219	−	0.298998i
$597$	5.36547	−	16.5132i	0.219594	−	0.675841i
$598$	0.659238	+	0.732158i	0.0269583	+	0.0299402i
$599$	25.7906	−	11.4827i	1.05378	−	0.469171i	0.194617	−	0.980879i	$-0.437654\pi$
$599$	25.7906	−	11.4827i	1.05378	−	0.469171i	0.859159	+	0.511708i	$0.170987\pi$
$600$	0.978148	+	0.207912i	0.0399327	+	0.00848796i
$601$	1.86781	−	17.7710i	0.0761894	−	0.724894i	−0.888029	−	0.459787i	$-0.847926\pi$
$601$	1.86781	−	17.7710i	0.0761894	−	0.724894i	0.964219	−	0.265107i	$-0.0854074\pi$
$602$	3.17351	+	30.1940i	0.129343	+	1.23061i
$603$	9.91210	−	2.10688i	0.403652	−	0.0857989i
$604$	3.70938	−	2.69502i	0.150933	−	0.109659i
$605$	5.47197	−	3.97562i	0.222467	−	0.161632i
$606$	−4.76893	+	1.01367i	−0.193724	+	0.0411774i
$607$	3.84675	+	36.5994i	0.156135	+	1.48552i	0.739414	+	0.673251i	$0.235103\pi$
$607$	3.84675	+	36.5994i	0.156135	+	1.48552i	−0.583279	+	0.812272i	$0.698231\pi$
$608$	−0.488830	+	4.65090i	−0.0198247	+	0.188619i
$609$	31.9857	+	6.79878i	1.29613	+	0.275500i
$610$	−5.87356	+	2.61508i	−0.237813	+	0.105881i
$611$	−24.0166	−	26.6732i	−0.971609	−	1.07908i
$612$	−1.94657	+	5.99092i	−0.0786854	+	0.242169i
$613$	2.70810	−	3.00765i	0.109379	−	0.121478i	−0.685969	−	0.727631i	$-0.740621\pi$
$613$	2.70810	−	3.00765i	0.109379	−	0.121478i	0.795348	+	0.606153i	$0.207288\pi$
$614$	−8.72364	−	15.1098i	−0.352057	−	0.609781i
$615$	2.24520	−	3.88881i	0.0905354	−	0.156812i
$616$	−4.75926	−	14.6475i	−0.191756	−	0.590165i
$617$	17.4698	+	7.77807i	0.703309	+	0.313133i	0.727050	−	0.686585i	$-0.240891\pi$
$617$	17.4698	+	7.77807i	0.703309	+	0.313133i	−0.0237410	+	0.999718i	$0.507558\pi$
$618$	−5.08550	−	3.69483i	−0.204569	−	0.148628i
$619$	−41.6686			−1.67480			−0.837402	−	0.546588i	$-0.815927\pi$
$619$	−41.6686			−1.67480			−0.837402	+	0.546588i	$0.815927\pi$
$620$	0.686415	+	5.52529i	0.0275671	+	0.221901i
$621$	−0.209057			−0.00838917
$622$	−22.4988	−	16.3463i	−0.902120	−	0.655429i
$623$	−48.8826	−	21.7639i	−1.95844	−	0.871954i
$624$	−1.45630	−	4.48202i	−0.0582985	−	0.179424i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−10.7774	−	18.6670i	−0.430752	−	0.746084i
$627$	−13.1887	+	14.6475i	−0.526705	+	0.584965i
$628$	0.296590	−	0.912810i	0.0118352	−	0.0364251i
$629$	−3.95545	−	4.39297i	−0.157714	−	0.175159i
$630$	3.33826	−	1.48629i	0.133000	−	0.0592152i
$631$	−26.9394	−	5.72614i	−1.07244	−	0.227954i	−0.362333	−	0.932049i	$-0.618020\pi$
$631$	−26.9394	−	5.72614i	−1.07244	−	0.227954i	−0.710106	+	0.704095i	$0.751353\pi$
$632$	0.224205	−	2.13317i	0.00891841	−	0.0848530i
$633$	−0.475626	−	4.52528i	−0.0189044	−	0.179864i
$634$	−14.9358	+	3.17470i	−0.593176	+	0.126083i
$635$	−10.2870	+	7.47394i	−0.408227	+	0.296594i
$636$	6.78339	−	4.92842i	0.268979	−	0.195425i
$637$	−29.2855	+	6.22484i	−1.16034	+	0.246637i
$638$	3.94242	+	37.5097i	0.156082	+	1.48502i
$639$	−1.02136	+	9.71763i	−0.0404045	+	0.384424i
$640$	0.978148	+	0.207912i	0.0386647	+	0.00821843i
$641$	38.1000	−	16.9632i	1.50486	−	0.670006i	0.521761	−	0.853092i	$-0.325275\pi$
$641$	38.1000	−	16.9632i	1.50486	−	0.670006i	0.983097	+	0.183086i	$0.0586087\pi$
$642$	2.28233	+	2.53478i	0.0900763	+	0.100040i
$643$	−10.0587	+	30.9575i	−0.396676	+	1.22084i	0.530973	+	0.847389i	$0.321827\pi$
$643$	−10.0587	+	30.9575i	−0.396676	+	1.22084i	−0.927649	+	0.373454i	$0.878173\pi$
$644$	−0.511170	+	0.567712i	−0.0201429	+	0.0223710i
$645$	−4.15418	−	7.19525i	−0.163571	−	0.283313i
$646$	14.7292	−	25.5118i	0.579514	−	1.00375i
$647$	2.54200	+	7.82347i	0.0999363	+	0.307572i	0.988509	−	0.151164i	$-0.0483022\pi$
$647$	2.54200	+	7.82347i	0.0999363	+	0.307572i	−0.888572	+	0.458736i	$0.848302\pi$
$648$	0.913545	+	0.406737i	0.0358875	+	0.0159781i
$649$	−11.7782	−	8.55738i	−0.462336	−	0.335907i
$650$	4.71267			0.184846
$651$	13.8969	+	14.8601i	0.544661	+	0.582412i
$652$	−12.2468			−0.479621
$653$	−21.2505	−	15.4394i	−0.831597	−	0.604191i	0.0884136	−	0.996084i	$-0.471820\pi$
$653$	−21.2505	−	15.4394i	−0.831597	−	0.604191i	−0.920011	+	0.391893i	$0.871820\pi$
$654$	−11.2973	−	5.02989i	−0.441760	−	0.196684i
$655$	−6.29137	−	19.3628i	−0.245824	−	0.756569i
$656$	2.24520	−	3.88881i	0.0876605	−	0.151832i
$657$	−0.315921	−	0.547191i	−0.0123252	−	0.0213479i
$658$	18.6224	−	20.6822i	0.725976	−	0.806278i
$659$	13.7338	−	42.2682i	0.534992	−	1.64654i	−0.208675	−	0.977985i	$-0.566915\pi$
$659$	13.7338	−	42.2682i	0.534992	−	1.64654i	0.743667	−	0.668550i	$-0.233085\pi$
$660$	2.82019	+	3.13214i	0.109776	+	0.121918i
$661$	40.0070	−	17.8123i	1.55609	−	0.692816i	0.564888	−	0.825168i	$-0.308919\pi$
$661$	40.0070	−	17.8123i	1.55609	−	0.692816i	0.991203	+	0.132351i	$0.0422527\pi$
$662$	−25.5935	−	5.44006i	−0.994718	−	0.211434i
$663$	−3.10305	+	29.5236i	−0.120513	+	1.14660i
$664$	−0.827091	−	7.86924i	−0.0320974	−	0.305386i
$665$	−16.7154	+	3.55297i	−0.648197	+	0.137778i
$666$	−0.759198	+	0.551590i	−0.0294183	+	0.0213737i
$667$	1.51351	−	1.09963i	0.0586032	−	0.0425777i
$668$	5.31720	−	1.13021i	0.205729	−	0.0437290i
$669$	0.0446812	+	0.425113i	0.00172747	+	0.0164358i
$670$	−1.05924	+	10.0780i	−0.0409222	+	0.389348i
$671$	−26.5059	−	5.63400i	−1.02325	−	0.217498i
$672$	3.33826	−	1.48629i	0.128776	−	0.0573349i
$673$	−13.6117	−	15.1174i	−0.524694	−	0.582731i	0.421298	−	0.906922i	$-0.361575\pi$
$673$	−13.6117	−	15.1174i	−0.524694	−	0.582731i	−0.945992	+	0.324191i	$0.894908\pi$
$674$	−0.577819	+	1.77834i	−0.0222568	+	0.0684993i
$675$	−0.669131	+	0.743145i	−0.0257548	+	0.0286037i
$676$	−4.60463	−	7.97545i	−0.177101	−	0.306748i
$677$	20.5746	−	35.6363i	0.790746	−	1.36961i	−0.134759	−	0.990878i	$-0.543026\pi$
$677$	20.5746	−	35.6363i	0.790746	−	1.36961i	0.925505	−	0.378734i	$-0.123641\pi$
$678$	−1.66962	−	5.13856i	−0.0641213	−	0.197345i
$679$	0.974091	+	0.433693i	0.0373822	+	0.0166436i
$680$	−5.09618	−	3.70259i	−0.195430	−	0.141988i
$681$	−1.48318			−0.0568357
$682$	−11.3475	+	20.5404i	−0.434519	+	0.786534i
$683$	−9.04418			−0.346066			−0.173033	−	0.984916i	$-0.555357\pi$
$683$	−9.04418			−0.346066			−0.173033	+	0.984916i	$0.555357\pi$
$684$	−3.78339	−	2.74879i	−0.144661	−	0.105103i
$685$	7.98584	+	3.55553i	0.305123	+	0.135850i
$686$	0.730545	+	2.24838i	0.0278923	+	0.0858437i
$687$	14.5714	−	25.2385i	0.555935	−	0.962908i
$688$	−4.15418	−	7.19525i	−0.158377	−	0.274316i
$689$	26.4403	−	29.3650i	1.00730	−	1.11872i
$690$	0.0646021	−	0.198825i	0.00245936	−	0.00756914i
$691$	16.3103	+	18.1144i	0.620474	+	0.689106i	0.968680	−	0.248312i	$-0.0798758\pi$
$691$	16.3103	+	18.1144i	0.620474	+	0.689106i	−0.348206	+	0.937418i	$0.613209\pi$
$692$	18.5184	−	8.24492i	0.703964	−	0.313425i
$693$	15.0647	+	3.20211i	0.572262	+	0.121638i
$694$	2.96194	−	28.1810i	0.112434	−	1.06974i
$695$	−2.06763	−	19.6721i	−0.0784295	−	0.746207i
$696$	−8.75319	+	1.86055i	−0.331789	+	0.0705239i
$697$	−22.8839	+	16.6262i	−0.866791	+	0.629761i
$698$	−18.6208	+	13.5288i	−0.704807	+	0.512073i
$699$	1.49634	−	0.318058i	0.0565970	−	0.0120301i
$700$	0.381966	+	3.63416i	0.0144370	+	0.137358i
$701$	−0.635272	+	6.04421i	−0.0239939	+	0.228287i	0.975953	+	0.217981i	$0.0699471\pi$
$701$	−0.635272	+	6.04421i	−0.0239939	+	0.228287i	−0.999947	+	0.0103056i	$0.996720\pi$
$702$	4.60969	+	0.979819i	0.173981	+	0.0369809i
$703$	4.00914	−	1.78498i	0.151207	−	0.0673219i
$704$	2.82019	+	3.13214i	0.106290	+	0.118047i
$705$	−2.35351	+	7.24336i	−0.0886384	+	0.272801i
$706$	12.8097	−	14.2267i	0.482101	−	0.535427i
$707$	−8.90792	−	15.4290i	−0.335017	−	0.580266i
$708$	1.72713	−	2.99148i	0.0649096	−	0.112427i
$709$	−1.80377	−	5.55145i	−0.0677422	−	0.208489i	0.911455	−	0.411400i	$-0.134960\pi$
$709$	−1.80377	−	5.55145i	−0.0677422	−	0.208489i	−0.979197	+	0.202911i	$0.934960\pi$
$710$	−8.92640	−	3.97429i	−0.335002	−	0.149152i
$711$	1.73528	+	1.26075i	0.0650780	+	0.0472819i
$712$	14.6431			0.548775
$713$	1.16377	−	0.0219728i	0.0435836	−	0.000822887i
$714$	−23.0185			−0.861446
$715$	16.0691	+	11.6749i	0.600951	+	0.436616i
$716$	6.58461	+	2.93166i	0.246078	+	0.109561i
$717$	8.72201	+	26.8436i	0.325729	+	1.00249i
$718$	−2.23298	+	3.86763i	−0.0833340	+	0.144339i
$719$	1.30272	+	2.25637i	0.0485831	+	0.0841485i	0.889294	−	0.457335i	$-0.151196\pi$
$719$	1.30272	+	2.25637i	0.0485831	+	0.0841485i	−0.840711	+	0.541484i	$0.817863\pi$
$720$	−0.669131	+	0.743145i	−0.0249370	+	0.0276954i
$721$	7.09820	−	21.8460i	0.264351	−	0.813589i
$722$	1.92031	+	2.13272i	0.0714666	+	0.0793717i
$723$	19.1052	−	8.50618i	0.710530	−	0.316348i
$724$	−2.94756	−	0.626523i	−0.109545	−	0.0232845i
$725$	0.935398	−	8.89972i	0.0347398	−	0.330527i
$726$	0.707002	+	6.72668i	0.0262393	+	0.249650i
$727$	−48.0185	+	10.2066i	−1.78091	+	0.378543i	−0.976497	−	0.215532i	$-0.930851\pi$
$727$	−48.0185	+	10.2066i	−1.78091	+	0.378543i	−0.804409	+	0.594075i	$0.797518\pi$
$728$	13.9320	−	10.1222i	0.516356	−	0.375155i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	0.618034	−	0.131367i	0.0228745	−	0.00486212i
$731$	5.47063	+	52.0496i	0.202339	+	1.92512i
$732$	0.672056	−	6.39419i	0.0248399	−	0.236336i
$733$	−32.2869	−	6.86279i	−1.19254	−	0.253483i	−0.431457	−	0.902133i	$-0.642000\pi$
$733$	−32.2869	−	6.86279i	−1.19254	−	0.253483i	−0.761086	+	0.648650i	$0.775334\pi$
$734$	−11.2785	+	5.02150i	−0.416296	+	0.185347i
$735$	4.25102	+	4.72123i	0.156801	+	0.174145i
$736$	0.0646021	−	0.198825i	0.00238127	−	0.00732878i
$737$	−28.5785	+	31.7396i	−1.05270	+	1.16914i
$738$	2.24520	+	3.88881i	0.0826471	+	0.143149i
$739$	−12.4193	+	21.5108i	−0.456851	+	0.791289i	−0.998793	−	0.0491269i	$-0.984356\pi$
$739$	−12.4193	+	21.5108i	−0.456851	+	0.791289i	0.541941	+	0.840416i	$0.317689\pi$
$740$	−0.289988	−	0.892491i	−0.0106602	−	0.0328086i
$741$	−20.1335	−	8.96403i	−0.739624	−	0.329302i
$742$	24.7877	+	18.0093i	0.909986	+	0.661144i
$743$	−28.9212			−1.06102			−0.530508	−	0.847680i	$-0.677999\pi$
$743$	−28.9212			−1.06102			−0.530508	+	0.847680i	$0.677999\pi$
$744$	−5.12825	−	2.16819i	−0.188011	−	0.0794898i
$745$	−9.82242			−0.359866
$746$	24.3655	+	17.7026i	0.892085	+	0.648137i
$747$	7.22851	+	3.21834i	0.264477	+	0.117753i
$748$	−8.20421	−	25.2500i	−0.299976	−	0.923230i
$749$	−6.23200	+	10.7941i	−0.227712	+	0.394409i
$750$	−0.500000	−	0.866025i	−0.0182574	−	0.0316228i
$751$	35.6380	−	39.5800i	1.30045	−	1.44430i	0.474820	−	0.880083i	$-0.342513\pi$
$751$	35.6380	−	39.5800i	1.30045	−	1.44430i	0.825629	−	0.564213i	$-0.190820\pi$
$752$	−2.35351	+	7.24336i	−0.0858237	+	0.264138i
$753$	19.0657	+	21.1746i	0.694792	+	0.771645i
$754$	−38.5265	+	17.1531i	−1.40305	+	0.624678i
$755$	−4.48485	−	0.953285i	−0.163220	−	0.0346936i
$756$	−0.381966	+	3.63416i	−0.0138920	+	0.132173i
$757$	1.41225	+	13.4366i	0.0513290	+	0.488362i	0.989744	+	0.142852i	$0.0456274\pi$
$757$	1.41225	+	13.4366i	0.0513290	+	0.488362i	−0.938415	+	0.345510i	$0.887706\pi$
$758$	17.5630	−	3.73312i	0.637915	−	0.135593i
$759$	0.712835	−	0.517905i	0.0258743	−	0.0187988i
$760$	3.78339	−	2.74879i	0.137238	−	0.0997091i
$761$	−1.82709	+	0.388360i	−0.0662320	+	0.0140780i	−0.240908	−	0.970548i	$-0.577445\pi$
$761$	−1.82709	+	0.388360i	−0.0662320	+	0.0140780i	0.174677	+	0.984626i	$0.444112\pi$
$762$	−1.32912	−	12.6458i	−0.0481491	−	0.458108i
$763$	4.72356	−	44.9417i	0.171005	−	1.62700i
$764$	−16.2825	−	3.46096i	−0.589081	−	0.125213i
$765$	5.75463	−	2.56213i	0.208059	−	0.0926339i
$766$	20.2204	+	22.4570i	0.730593	+	0.811406i
$767$	5.03042	−	15.4821i	0.181638	−	0.559025i
$768$	−0.669131	+	0.743145i	−0.0241452	+	0.0268159i
$769$	16.5812	+	28.7195i	0.597935	+	1.03565i	0.993126	+	0.117054i	$0.0373451\pi$
$769$	16.5812	+	28.7195i	0.597935	+	1.03565i	−0.395191	+	0.918599i	$0.629322\pi$
$770$	−7.70065	+	13.3379i	−0.277512	+	0.480665i
$771$	−0.210135	−	0.646730i	−0.00756784	−	0.0232914i
$772$	−21.4104	−	9.53254i	−0.770578	−	0.343084i
$773$	32.3607	+	23.5114i	1.16393	+	0.845647i	0.990270	−	0.139159i	$-0.0444398\pi$
$773$	32.3607	+	23.5114i	1.16393	+	0.845647i	0.173663	+	0.984805i	$0.444440\pi$
$774$	8.30836			0.298638
$775$	3.64679	−	4.20725i	0.130997	−	0.151129i
$776$	−0.291796			−0.0104749
$777$	−2.77425	−	2.01561i	−0.0995256	−	0.0723096i
$778$	6.94153	+	3.09057i	0.248866	+	0.110802i
$779$	−6.48920	−	19.9717i	−0.232500	−	0.715561i
$780$	−2.35634	+	4.08129i	−0.0843703	+	0.146134i
$781$	−20.5913	−	35.6651i	−0.736814	−	1.27620i
$782$	−0.881176	+	0.978645i	−0.0315108	+	0.0349963i
$783$	2.76531	−	8.51076i	0.0988242	−	0.304150i
$784$	4.25102	+	4.72123i	0.151822	+	0.168615i
$785$	−0.876807	+	0.390380i	−0.0312946	+	0.0139333i
$786$	19.9144	+	4.23294i	0.710323	+	0.150984i
$787$	−3.50200	+	33.3193i	−0.124833	+	1.18770i	0.735339	+	0.677700i	$0.237023\pi$
$787$	−3.50200	+	33.3193i	−0.124833	+	1.18770i	−0.860172	+	0.510005i	$0.829644\pi$
$788$	1.69342	+	16.1118i	0.0603256	+	0.573960i
$789$	24.2212	−	5.14837i	0.862297	−	0.183287i
$790$	−1.73528	+	1.26075i	−0.0617384	+	0.0448556i
$791$	15.9729	−	11.6050i	0.567930	−	0.412625i
$792$	−4.12260	+	0.876286i	−0.146490	+	0.0311375i
$793$	−3.16718	−	30.1337i	−0.112470	−	1.07008i
$794$	−1.50711	+	14.3392i	−0.0534853	+	0.508878i
$795$	−8.20150	−	1.74328i	−0.290877	−	0.0618279i
$796$	−15.8619	+	7.06218i	−0.562211	+	0.250312i
$797$	30.9835	+	34.4106i	1.09749	+	1.21889i	0.974002	+	0.226540i	$0.0727415\pi$
$797$	30.9835	+	34.4106i	1.09749	+	1.21889i	0.123488	+	0.992346i	$0.460592\pi$
$798$	5.28075	−	16.2525i	0.186936	−	0.575331i
$799$	32.1020	−	35.6529i	1.13569	−	1.26131i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−7.32157	+	12.6813i	−0.258695	+	0.448073i
$802$	9.98956	+	30.7447i	0.352744	+	1.08563i
$803$	2.43279	+	1.08315i	0.0858514	+	0.0382235i
$804$	−8.19821	−	5.95635i	−0.289129	−	0.210064i
$805$	0.763932			0.0269251
$806$	−25.7641	−	4.96993i	−0.907500	−	0.175058i
$807$	−1.64911			−0.0580515
$808$	3.94433	+	2.86573i	0.138761	+	0.100816i
$809$	−32.3230	−	14.3911i	−1.13642	−	0.505965i	−0.249721	−	0.968318i	$-0.580339\pi$
$809$	−32.3230	−	14.3911i	−1.13642	−	0.505965i	−0.886696	+	0.462353i	$0.847005\pi$
$810$	−0.309017	−	0.951057i	−0.0108578	−	0.0334167i
$811$	−27.7145	+	48.0028i	−0.973186	+	1.68561i	−0.287391	+	0.957813i	$0.592788\pi$
$811$	−27.7145	+	48.0028i	−0.973186	+	1.68561i	−0.685795	+	0.727794i	$0.740546\pi$
$812$	−16.3502	−	28.3193i	−0.573778	−	0.993813i
$813$	11.4867	−	12.7572i	0.402854	−	0.447415i
$814$	1.22221	−	3.76159i	0.0428386	−	0.131844i
$815$	8.19470	+	9.10113i	0.287048	+	0.318799i
$816$	5.75463	−	2.56213i	0.201452	−	0.0896924i
$817$	−38.0052	−	8.07825i	−1.32963	−	0.282622i
$818$	−0.214135	+	2.03736i	−0.00748705	+	0.0712345i
$819$	1.80008	+	17.1266i	0.0628999	+	0.598452i
$820$	−4.39228	+	0.933609i	−0.153385	+	0.0326030i
$821$	−32.0363	+	23.2757i	−1.11807	+	0.812329i	−0.983916	−	0.178631i	$-0.942833\pi$
$821$	−32.0363	+	23.2757i	−1.11807	+	0.812329i	−0.134159	+	0.990960i	$0.542833\pi$
$822$	−7.07210	+	5.13818i	−0.246668	+	0.179215i
$823$	−1.74159	+	0.370187i	−0.0607081	+	0.0129039i	−0.238166	−	0.971225i	$-0.576546\pi$
$823$	−1.74159	+	0.370187i	−0.0607081	+	0.0129039i	0.177458	+	0.984128i	$0.443213\pi$
$824$	0.657068	+	6.25159i	0.0228901	+	0.217784i
$825$	0.440557	−	4.19162i	0.0153382	−	0.145933i
$826$	12.3467	+	2.62437i	0.429596	+	0.0913134i
$827$	35.9949	−	16.0260i	1.25166	−	0.557277i	0.329529	−	0.944145i	$-0.393110\pi$
$827$	35.9949	−	16.0260i	1.25166	−	0.557277i	0.922135	+	0.386868i	$0.126443\pi$
$828$	0.139886	+	0.155360i	0.00486139	+	0.00539912i
$829$	−10.5992	+	32.6211i	−0.368126	+	1.13298i	0.579874	+	0.814706i	$0.303102\pi$
$829$	−10.5992	+	32.6211i	−0.368126	+	1.13298i	−0.948000	+	0.318270i	$0.896898\pi$
$830$	−5.29456	+	5.88020i	−0.183777	+	0.204105i
$831$	−13.4714	−	23.3331i	−0.467317	−	0.809417i
$832$	−2.35634	+	4.08129i	−0.0816912	+	0.141493i
$833$	−12.3666	−	38.0606i	−0.428478	−	1.31872i
$834$	18.0704	+	8.04545i	0.625726	+	0.278591i
$835$	−4.39781	−	3.19519i	−0.152192	−	0.110574i
$836$	19.7102			0.681690
$837$	4.44183	−	3.35710i	0.153532	−	0.116038i
$838$	−18.5379			−0.640381
$839$	−29.1027	−	21.1444i	−1.00474	−	0.729984i	−0.0416385	−	0.999133i	$-0.513258\pi$
$839$	−29.1027	−	21.1444i	−1.00474	−	0.729984i	−0.963099	+	0.269148i	$0.913258\pi$
$840$	−3.33826	−	1.48629i	−0.115181	−	0.0512819i
$841$	15.7846	+	48.5799i	0.544295	+	1.67517i
$842$	−12.4263	+	21.5230i	−0.428239	+	0.741732i
$843$	−0.157795	−	0.273309i	−0.00543475	−	0.00941327i
$844$	−3.04468	+	3.38146i	−0.104802	+	0.116395i
$845$	−2.84582	+	8.75853i	−0.0978991	+	0.301303i
$846$	−5.09618	−	5.65988i	−0.175210	−	0.194591i
$847$	−22.5791	+	10.0529i	−0.775827	+	0.345420i
$848$	−8.20150	−	1.74328i	−0.281641	−	0.0598646i
$849$	1.04646	−	9.95641i	0.0359144	−	0.341703i
$850$	0.658449	+	6.26472i	0.0225846	+	0.214878i
$851$	−0.191896	+	0.0407888i	−0.00657812	+	0.00139822i
$852$	7.90503	−	5.74334i	0.270822	−	0.196764i
$853$	−26.8950	+	19.5404i	−0.920869	+	0.669050i	−0.943740	−	0.330688i	$-0.892719\pi$
$853$	−26.8950	+	19.5404i	−0.920869	+	0.669050i	0.0228713	+	0.999738i	$0.492719\pi$
$854$	22.9808	−	4.88472i	0.786387	−	0.167152i
$855$	0.488830	+	4.65090i	0.0167176	+	0.159058i
$856$	0.356535	−	3.39220i	0.0121861	−	0.115943i
$857$	−54.3496	−	11.5524i	−1.85655	−	0.394621i	−0.862731	−	0.505663i	$-0.831248\pi$
$857$	−54.3496	−	11.5524i	−1.85655	−	0.394621i	−0.993816	+	0.111042i	$0.964581\pi$
$858$	−18.1453	+	8.07881i	−0.619470	+	0.275806i
$859$	28.1779	+	31.2947i	0.961417	+	1.06776i	0.997657	+	0.0684190i	$0.0217955\pi$
$859$	28.1779	+	31.2947i	0.961417	+	1.06776i	−0.0362393	+	0.999343i	$0.511538\pi$
$860$	−2.56743	+	7.90172i	−0.0875485	+	0.269447i
$861$	−10.9796	+	12.1941i	−0.374184	+	0.415574i
$862$	−18.1941	−	31.5132i	−0.619695	−	1.07334i
$863$	14.3454	−	24.8469i	0.488322	−	0.845798i	−0.511588	−	0.859231i	$-0.670943\pi$
$863$	14.3454	−	24.8469i	0.488322	−	0.845798i	0.999910	+	0.0134326i	$0.00427587\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	−18.5184	−	8.24492i	−0.629644	−	0.280336i
$866$	−31.9044	−	23.1799i	−1.08415	−	0.787685i
$867$	−22.6803			−0.770262
$868$	1.74435	−	20.2707i	0.0592072	−	0.688033i
$869$	−9.04021			−0.306668
$870$	7.23968	+	5.25994i	0.245448	+	0.178329i
$871$	−43.6273	−	19.4241i	−1.47826	−	0.658162i
$872$	3.82144	+	11.7612i	0.129410	+	0.398284i
$873$	0.145898	−	0.252703i	0.00493790	−	0.00855269i
$874$	−0.488830	−	0.846678i	−0.0165349	−	0.0286393i
$875$	2.44512	−	2.71559i	0.0826603	−	0.0918036i
$876$	−0.195250	+	0.600917i	−0.00659688	+	0.0203031i
$877$	−25.3284	−	28.1300i	−0.855278	−	0.949882i	0.143934	−	0.989587i	$-0.454025\pi$
$877$	−25.3284	−	28.1300i	−0.855278	−	0.949882i	−0.999211	+	0.0397051i	$0.987358\pi$
$878$	1.68379	−	0.749672i	0.0568252	−	0.0253002i
$879$	−5.55955	−	1.18172i	−0.187519	−	0.0398584i
$880$	0.440557	−	4.19162i	0.0148512	−	0.141299i
$881$	−5.39131	−	51.2949i	−0.181638	−	1.72817i	−0.583194	−	0.812333i	$-0.698197\pi$
$881$	−5.39131	−	51.2949i	−0.181638	−	1.72817i	0.401556	−	0.915835i	$-0.368470\pi$
$882$	−6.21422	+	1.32087i	−0.209244	+	0.0444761i
$883$	18.7820	−	13.6460i	0.632066	−	0.459223i	−0.225049	−	0.974347i	$-0.572254\pi$
$883$	18.7820	−	13.6460i	0.632066	−	0.459223i	0.857115	+	0.515124i	$0.172254\pi$
$884$	24.0166	−	17.4491i	0.807766	−	0.586877i
$885$	−3.37878	+	0.718181i	−0.113576	+	0.0241414i
$886$	−1.02327	−	9.73580i	−0.0343776	−	0.327081i
$887$	−1.34336	+	12.7813i	−0.0451057	+	0.429153i	0.948545	+	0.316643i	$0.102556\pi$
$887$	−1.34336	+	12.7813i	−0.0451057	+	0.429153i	−0.993651	+	0.112510i	$0.964111\pi$
$888$	0.917914	+	0.195109i	0.0308032	+	0.00654742i
$889$	42.4474	−	18.8988i	1.42364	−	0.633846i
$890$	−9.79817	−	10.8820i	−0.328435	−	0.364764i
$891$	1.30242	−	4.00842i	0.0436325	−	0.134287i
$892$	0.286023	−	0.317661i	0.00957676	−	0.0106361i
$893$	17.8085	+	30.8452i	0.595938	+	1.03220i
$894$	4.91121	−	8.50647i	0.164255	−	0.284499i
$895$	−2.22732	−	6.85498i	−0.0744510	−	0.229137i
$896$	−3.33826	−	1.48629i	−0.111523	−	0.0496535i
$897$	0.797057	+	0.579096i	0.0266130	+	0.0193354i
$898$	−24.4512			−0.815949
$899$	−14.4993	+	47.6681i	−0.483580	+	1.58982i
$900$	1.00000			0.0333333
$901$	42.7301	+	31.0452i	1.42355	+	1.03427i
$902$	−17.2895	−	7.69779i	−0.575678	−	0.256309i
$903$	9.38184	+	28.8743i	0.312208	+	0.960878i
$904$	−2.70150	+	4.67914i	−0.0898506	+	0.155626i
$905$	1.50670	+	2.60969i	0.0500845	+	0.0867490i
$906$	3.06799	−	3.40735i	0.101927	−	0.113202i
$907$	16.1326	−	49.6511i	0.535675	−	1.64864i	−0.206512	−	0.978444i	$-0.566211\pi$
$907$	16.1326	−	49.6511i	0.535675	−	1.64864i	0.742187	−	0.670193i	$-0.233789\pi$
$908$	0.992443	+	1.10222i	0.0329354	+	0.0365784i
$909$	−4.45396	+	1.98303i	−0.147729	+	0.0657730i
$910$	−16.8446	−	3.58044i	−0.558394	−	0.118690i
$911$	−5.59898	+	53.2707i	−0.185502	+	1.76494i	0.365858	+	0.930671i	$0.380776\pi$
$911$	−5.59898	+	53.2707i	−0.185502	+	1.76494i	−0.551360	+	0.834267i	$0.685891\pi$
$912$	0.488830	+	4.65090i	0.0161868	+	0.154007i
$913$	−32.6205	+	6.93369i	−1.07958	+	0.229472i
$914$	4.27668	−	3.10719i	0.141460	−	0.102777i
$915$	−5.20150	+	3.77911i	−0.171956	+	0.124934i
$916$	−28.5060	+	6.05915i	−0.941866	+	0.200200i
$917$	7.77656	+	73.9890i	0.256805	+	2.44333i
$918$	−0.658449	+	6.26472i	−0.0217320	+	0.206767i
$919$	−34.0895	−	7.24594i	−1.12451	−	0.239022i	−0.392123	−	0.919913i	$-0.628259\pi$
$919$	−34.0895	−	7.24594i	−1.12451	−	0.239022i	−0.732385	+	0.680891i	$0.761593\pi$
$920$	−0.190983	+	0.0850311i	−0.00629652	+	0.00280339i
$921$	−11.6745	−	12.9659i	−0.384688	−	0.427240i
$922$	−3.32440	+	10.2315i	−0.109483	+	0.336955i
$923$	30.8123	−	34.2205i	1.01420	−	1.12638i
$924$	−7.70065	−	13.3379i	−0.253333	−	0.438785i
$925$	−0.469210	+	0.812696i	−0.0154275	+	0.0267213i
$926$	5.57782	+	17.1668i	0.183299	+	0.564135i
$927$	−5.74257	−	2.55676i	−0.188611	−	0.0839749i
$928$	7.23968	+	5.25994i	0.237654	+	0.172666i
$929$	45.3826			1.48896			0.744478	−	0.667647i	$-0.232699\pi$
$929$	45.3826			1.48896			0.744478	+	0.667647i	$0.232699\pi$
$930$	1.82019	+	5.26184i	0.0596863	+	0.172542i
$931$	29.7102			0.973711
$932$	−1.23761	−	0.899179i	−0.0405394	−	0.0294536i
$933$	−25.4058	−	11.3114i	−0.831747	−	0.370318i
$934$	12.2108	+	37.5811i	0.399551	+	1.22969i
$935$	−13.2747	+	22.9924i	−0.434129	+	0.751933i
$936$	−2.35634	−	4.08129i	−0.0770192	−	0.133401i
$937$	2.43932	−	2.70914i	0.0796890	−	0.0885036i	−0.701982	−	0.712195i	$-0.747701\pi$
$937$	2.43932	−	2.70914i	0.0796890	−	0.0885036i	0.781671	+	0.623691i	$0.214368\pi$
$938$	11.4428	−	35.2174i	0.373622	−	1.14989i
$939$	−14.4230	−	16.0184i	−0.470676	−	0.522739i
$940$	6.95768	−	3.09776i	0.226934	−	0.101038i
$941$	−41.5749	−	8.83702i	−1.35530	−	0.288079i	−0.527719	−	0.849419i	$-0.676953\pi$
$941$	−41.5749	−	8.83702i	−1.35530	−	0.288079i	−0.827585	+	0.561340i	$0.810286\pi$
$942$	0.100325	−	0.954527i	0.00326876	−	0.0311002i
$943$	0.0981262	+	0.933609i	0.00319543	+	0.0304025i
$944$	−3.37878	+	0.718181i	−0.109970	+	0.0233748i
$945$	2.95630	−	2.14787i	0.0961683	−	0.0698704i
$946$	−28.3296	+	20.5826i	−0.921074	+	0.669200i
$947$	36.6878	−	7.79822i	1.19219	−	0.253408i	0.431253	−	0.902231i	$-0.358072\pi$
$947$	36.6878	−	7.79822i	1.19219	−	0.253408i	0.760939	+	0.648823i	$0.224738\pi$
$948$	−0.224205	−	2.13317i	−0.00728185	−	0.0692822i
$949$	−0.311250	+	2.96135i	−0.0101036	+	0.0961294i
$950$	−4.57433	−	0.972304i	−0.148411	−	0.0315457i
$951$	−13.9493	+	6.21065i	−0.452338	+	0.201394i
$952$	15.4024	+	17.1061i	0.499195	+	0.554412i
$953$	−4.31418	+	13.2777i	−0.139750	+	0.430107i	−0.996299	−	0.0859599i	$-0.972604\pi$
$953$	−4.31418	+	13.2777i	−0.139750	+	0.430107i	0.856548	+	0.516067i	$0.172604\pi$
$954$	5.61048	−	6.23107i	0.181646	−	0.201738i
$955$	8.32315	+	14.4161i	0.269331	+	0.466494i
$956$	14.1125	−	24.4436i	0.456431	−	0.790562i
$957$	11.6550	+	35.8703i	0.376752	+	1.15952i
$958$	11.0716	+	4.92938i	0.357706	+	0.159261i
$959$	−25.8427	−	18.7758i	−0.834505	−	0.606303i
$960$	1.00000			0.0322749
$961$	−24.3738	+	19.1551i	−0.786253	+	0.617905i
$962$	4.42247			0.142586
$963$	2.75947	+	2.00487i	0.0889225	+	0.0646060i
$964$	−19.1052	−	8.50618i	−0.615337	−	0.273966i
$965$	7.24232	+	22.2896i	0.233138	+	0.717526i
$966$	−0.381966	+	0.661585i	−0.0122896	+	0.0212861i
$967$	−21.8174	−	37.7889i	−0.701601	−	1.21521i	−0.967904	−	0.251319i	$-0.919136\pi$
$967$	−21.8174	−	37.7889i	−0.701601	−	1.21521i	0.266303	−	0.963889i	$-0.414198\pi$
$968$	4.52582	−	5.02643i	0.145465	−	0.161556i
$969$	9.10317	−	28.0167i	0.292436	−	0.900025i
$970$	0.195250	+	0.216847i	0.00626909	+	0.00696253i
$971$	−3.16624	+	1.40970i	−0.101610	+	0.0452395i	−0.456912	−	0.889512i	$-0.651045\pi$
$971$	−3.16624	+	1.40970i	−0.101610	+	0.0452395i	0.355302	+	0.934751i	$0.384378\pi$
$972$	0.978148	+	0.207912i	0.0313741	+	0.00666877i
$973$	−7.55548	+	71.8856i	−0.242218	+	2.30455i
$974$	1.74788	+	16.6300i	0.0560058	+	0.532860i
$975$	4.60969	−	0.979819i	0.147628	−	0.0313793i
$976$	−5.20150	+	3.77911i	−0.166496	+	0.120966i
$977$	12.9355	−	9.39816i	0.413842	−	0.300674i	−0.361313	−	0.932444i	$-0.617672\pi$
$977$	12.9355	−	9.39816i	0.413842	−	0.300674i	0.775155	+	0.631771i	$0.217672\pi$
$978$	−11.9792	+	2.54625i	−0.383051	+	0.0814201i
$979$	−6.45113	−	61.3784i	−0.206179	−	1.96166i
$980$	0.664074	−	6.31824i	0.0212131	−	0.201829i
$981$	−12.0962	−	2.57113i	−0.386202	−	0.0820899i
$982$	1.25763	−	0.559934i	0.0401326	−	0.0178682i
$983$	14.8458	+	16.4880i	0.473509	+	0.525885i	0.931827	−	0.362904i	$-0.118215\pi$
$983$	14.8458	+	16.4880i	0.473509	+	0.525885i	−0.458318	+	0.888788i	$0.651548\pi$
$984$	1.38761	−	4.27063i	0.0442355	−	0.136143i
$985$	10.8403	−	12.0394i	0.345401	−	0.383606i
$986$	−28.1851	−	48.8180i	−0.897595	−	1.55468i
$987$	13.9154	−	24.1021i	0.442930	−	0.767178i
$988$	6.81040	+	20.9602i	0.216668	+	0.666834i
$989$	1.58676	+	0.706469i	0.0504559	+	0.0224644i
$990$	3.40977	+	2.47734i	0.108370	+	0.0787351i
$991$	34.5087			1.09620			0.548102	−	0.836411i	$-0.315350\pi$
$991$	34.5087			1.09620			0.548102	+	0.836411i	$0.315350\pi$
$992$	1.82019	+	5.26184i	0.0577910	+	0.167063i
$993$	−26.1652			−0.830328
$994$	28.8864	+	20.9872i	0.916222	+	0.665674i
$995$	15.8619	+	7.06218i	0.502857	+	0.223886i
$996$	−2.44512	−	7.52532i	−0.0774767	−	0.238449i
$997$	11.2951	−	19.5637i	0.357719	−	0.619587i	−0.629860	−	0.776708i	$-0.716888\pi$
$997$	11.2951	−	19.5637i	0.357719	−	0.619587i	0.987579	+	0.157121i	$0.0502212\pi$
$998$	−2.14301	−	3.71180i	−0.0678358	−	0.117495i
$999$	−0.627926	+	0.697383i	−0.0198667	+	0.0220642i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.a.391.1	✓	8
31.18	even	15	inner	930.2.bg.a.421.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.a.391.1	✓	8	1.1	even	1	trivial
930.2.bg.a.421.1	yes	8	31.18	even	15	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.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-2.44512 + 2.71559i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.913545 - 0.406737i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-2.44512 + 2.71559i) q^{7} +(0.309017 - 0.951057i) q^{8} +(0.669131 + 0.743145i) q^{9} +(-0.913545 + 0.406737i) q^{10} +(-4.12260 - 0.876286i) q^{11} +(0.104528 - 0.994522i) q^{12} +(-0.492608 - 4.68685i) q^{13} +(3.57433 - 0.759747i) q^{14} +(-0.809017 + 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(6.16157 - 1.30968i) q^{17} +(-0.104528 - 0.994522i) q^{18} +(-0.488830 + 4.65090i) q^{19} +(0.978148 + 0.207912i) q^{20} +(3.33826 - 1.48629i) q^{21} +(2.82019 + 3.13214i) q^{22} +(0.0646021 - 0.198825i) q^{23} +(-0.669131 + 0.743145i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.35634 + 4.08129i) q^{26} +(-0.309017 - 0.951057i) q^{27} +(-3.33826 - 1.48629i) q^{28} +(7.23968 + 5.25994i) q^{29} +1.00000 q^{30} +(1.82019 + 5.26184i) q^{31} +1.00000 q^{32} +(3.40977 + 2.47734i) q^{33} +(-5.75463 - 2.56213i) q^{34} +(1.12920 + 3.47533i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-0.469210 - 0.812696i) q^{37} +(3.12920 - 3.47533i) q^{38} +(-1.45630 + 4.48202i) q^{39} +(-0.669131 - 0.743145i) q^{40} +(-4.10219 + 1.82641i) q^{41} +(-3.57433 - 0.759747i) q^{42} +(-0.868460 + 8.26285i) q^{43} +(-0.440557 - 4.19162i) q^{44} +(0.978148 - 0.207912i) q^{45} +(-0.169131 + 0.122881i) q^{46} +(6.16157 - 4.47665i) q^{47} +(0.978148 - 0.207912i) q^{48} +(-0.664074 - 6.31824i) q^{49} +(-0.104528 + 0.994522i) q^{50} +(-6.16157 - 1.30968i) q^{51} +(4.30524 - 1.91682i) q^{52} +(5.61048 + 6.23107i) q^{53} +(-0.309017 + 0.951057i) q^{54} +(-2.82019 + 3.13214i) q^{55} +(1.82709 + 3.16461i) q^{56} +(2.33826 - 4.04999i) q^{57} +(-2.76531 - 8.51076i) q^{58} +(3.15563 + 1.40497i) q^{59} +(-0.809017 - 0.587785i) q^{60} +6.42941 q^{61} +(1.62027 - 5.32679i) q^{62} -3.65418 q^{63} +(-0.809017 - 0.587785i) q^{64} +(-4.30524 - 1.91682i) q^{65} +(-1.30242 - 4.00842i) q^{66} +(5.06677 - 8.77591i) q^{67} +(3.14961 + 5.45529i) q^{68} +(-0.139886 + 0.155360i) q^{69} +(1.12920 - 3.47533i) q^{70} +(6.53818 + 7.26139i) q^{71} +(0.913545 - 0.406737i) q^{72} +(-0.618034 - 0.131367i) q^{73} +(-0.0980917 + 0.933280i) q^{74} +(0.104528 + 0.994522i) q^{75} +(-4.57433 + 0.972304i) q^{76} +(12.4599 - 9.05265i) q^{77} +(3.81263 - 2.77004i) q^{78} +(2.09805 - 0.445954i) q^{79} +(0.104528 + 0.994522i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(4.39228 + 0.933609i) q^{82} +(7.22851 - 3.21834i) q^{83} +(2.44512 + 2.71559i) q^{84} +(1.94657 - 5.99092i) q^{85} +(5.55938 - 6.17432i) q^{86} +(-4.47437 - 7.74983i) q^{87} +(-2.10735 + 3.65004i) q^{88} +(4.52498 + 13.9264i) q^{89} +(-0.913545 - 0.406737i) q^{90} +(13.9320 + 10.1222i) q^{91} +0.209057 q^{92} +(0.477358 - 5.54726i) q^{93} -7.61612 q^{94} +(3.78339 + 2.74879i) q^{95} +(-0.913545 - 0.406737i) q^{96} +(-0.0901699 - 0.277515i) q^{97} +(-3.17652 + 5.50190i) q^{98} +(-2.10735 - 3.65004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - q^{3} - 2 q^{4} + 4 q^{5} + 4 q^{6} + 2 q^{7} - 2 q^{8} + q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - q^3 - 2 * q^4 + 4 * q^5 + 4 * q^6 + 2 * q^7 - 2 * q^8 + q^9	\( 8 q - 2 q^{2} - q^{3} - 2 q^{4} + 4 q^{5} + 4 q^{6} + 2 q^{7} - 2 q^{8} + q^{9} - q^{10} - 23 q^{11} - q^{12} - 17 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} + 11 q^{17} + q^{18} - q^{20} + 18 q^{21} + 22 q^{22} - 2 q^{23} - q^{24} - 4 q^{25} - 2 q^{26} + 2 q^{27} - 18 q^{28} + 10 q^{29} + 8 q^{30} + 14 q^{31} + 8 q^{32} + 4 q^{33} - 19 q^{34} + 4 q^{35} - 4 q^{36} - q^{37} + 20 q^{38} + 6 q^{39} - q^{40} - 42 q^{41} - 2 q^{42} - 23 q^{43} + 17 q^{44} - q^{45} + 3 q^{46} + 11 q^{47} - q^{48} - 3 q^{49} + q^{50} - 11 q^{51} + 13 q^{52} + 2 q^{53} + 2 q^{54} - 22 q^{55} + 2 q^{56} + 10 q^{57} + 28 q^{59} - 2 q^{60} - 4 q^{61} + 14 q^{62} - 4 q^{63} - 2 q^{64} - 13 q^{65} - q^{66} - 20 q^{67} + q^{68} - q^{69} + 4 q^{70} + 42 q^{71} + q^{72} + 4 q^{73} - 41 q^{74} - q^{75} - 10 q^{76} + 52 q^{77} - 4 q^{78} - 42 q^{79} - q^{80} + q^{81} - 2 q^{82} + 6 q^{83} - 2 q^{84} + 22 q^{85} - 3 q^{86} - 10 q^{87} - 3 q^{88} + 16 q^{89} - q^{90} + 28 q^{91} - 2 q^{92} + 13 q^{93} + 6 q^{94} - q^{96} + 44 q^{97} - 8 q^{98} - 3 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - q^3 - 2 * q^4 + 4 * q^5 + 4 * q^6 + 2 * q^7 - 2 * q^8 + q^9 - q^10 - 23 * q^11 - q^12 - 17 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 + 11 * q^17 + q^18 - q^20 + 18 * q^21 + 22 * q^22 - 2 * q^23 - q^24 - 4 * q^25 - 2 * q^26 + 2 * q^27 - 18 * q^28 + 10 * q^29 + 8 * q^30 + 14 * q^31 + 8 * q^32 + 4 * q^33 - 19 * q^34 + 4 * q^35 - 4 * q^36 - q^37 + 20 * q^38 + 6 * q^39 - q^40 - 42 * q^41 - 2 * q^42 - 23 * q^43 + 17 * q^44 - q^45 + 3 * q^46 + 11 * q^47 - q^48 - 3 * q^49 + q^50 - 11 * q^51 + 13 * q^52 + 2 * q^53 + 2 * q^54 - 22 * q^55 + 2 * q^56 + 10 * q^57 + 28 * q^59 - 2 * q^60 - 4 * q^61 + 14 * q^62 - 4 * q^63 - 2 * q^64 - 13 * q^65 - q^66 - 20 * q^67 + q^68 - q^69 + 4 * q^70 + 42 * q^71 + q^72 + 4 * q^73 - 41 * q^74 - q^75 - 10 * q^76 + 52 * q^77 - 4 * q^78 - 42 * q^79 - q^80 + q^81 - 2 * q^82 + 6 * q^83 - 2 * q^84 + 22 * q^85 - 3 * q^86 - 10 * q^87 - 3 * q^88 + 16 * q^89 - q^90 + 28 * q^91 - 2 * q^92 + 13 * q^93 + 6 * q^94 - q^96 + 44 * q^97 - 8 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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