LMFDB - Embedded newform 546.2.bx.a.97.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(97,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 5]))

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

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

chi := DirichletCharacter("546.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bx (of order $12$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			97.7
Character	$\chi$	$=$	546.97
Dual form			546.2.bx.a.349.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.52143 - 1.52143i) q^{5} +(0.258819 - 0.965926i) q^{6} +(2.42509 + 1.05779i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.52143 - 1.52143i) q^{5} +(0.258819 - 0.965926i) q^{6} +(2.42509 + 1.05779i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(1.07582 - 1.86337i) q^{10} +(-2.31526 + 0.620373i) q^{11} +1.00000 q^{12} +(-0.713225 - 3.53430i) q^{13} +(-0.394087 + 2.61624i) q^{14} +(0.556883 + 2.07832i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.44046 - 2.49495i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(1.65268 - 6.16787i) q^{19} +(2.07832 + 0.556883i) q^{20} +(-1.57130 - 2.12862i) q^{21} +(-1.19847 - 2.07581i) q^{22} +(0.0337181 + 0.0194671i) q^{23} +(0.258819 + 0.965926i) q^{24} -0.370480i q^{25} +(3.22928 - 1.60367i) q^{26} -1.00000i q^{27} +(-2.62909 + 0.296473i) q^{28} +(3.82269 - 6.62110i) q^{29} +(-1.86337 + 1.07582i) q^{30} +(-0.864576 - 0.864576i) q^{31} +(0.965926 + 0.258819i) q^{32} +(2.31526 + 0.620373i) q^{33} +(2.03711 - 2.03711i) q^{34} +(-2.08026 - 5.29898i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(5.90397 - 1.58196i) q^{37} +6.38545 q^{38} +(-1.14948 + 3.41741i) q^{39} +2.15163i q^{40} +(-4.54549 + 1.21796i) q^{41} +(1.64941 - 2.06868i) q^{42} +(1.31731 - 0.760547i) q^{43} +(1.69489 - 1.69489i) q^{44} +(0.556883 - 2.07832i) q^{45} +(-0.0100769 + 0.0376076i) q^{46} +(3.10268 - 3.10268i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(4.76216 + 5.13048i) q^{49} +(0.357856 - 0.0958873i) q^{50} +2.88092i q^{51} +(2.38482 + 2.70419i) q^{52} -11.5264 q^{53} +(0.965926 - 0.258819i) q^{54} +(4.46638 + 2.57866i) q^{55} +(-0.966829 - 2.46277i) q^{56} +(-4.51520 + 4.51520i) q^{57} +(7.38488 + 1.97877i) q^{58} +(-1.12417 - 0.301220i) q^{59} +(-1.52143 - 1.52143i) q^{60} +(-4.42383 + 2.55410i) q^{61} +(0.611348 - 1.05889i) q^{62} +(0.296473 + 2.62909i) q^{63} +1.00000i q^{64} +(-4.29209 + 6.46233i) q^{65} +2.39694i q^{66} +(0.334985 + 1.25018i) q^{67} +(2.49495 + 1.44046i) q^{68} +(-0.0194671 - 0.0337181i) q^{69} +(4.58001 - 3.38085i) q^{70} +(-4.09800 - 1.09806i) q^{71} +(0.258819 - 0.965926i) q^{72} +(-9.09290 + 9.09290i) q^{73} +(3.05612 + 5.29336i) q^{74} +(-0.185240 + 0.320845i) q^{75} +(1.65268 + 6.16787i) q^{76} +(-6.27096 - 0.944603i) q^{77} +(-3.59847 - 0.225823i) q^{78} +11.5267 q^{79} +(-2.07832 + 0.556883i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.35292 - 4.07538i) q^{82} +(5.24816 + 5.24816i) q^{83} +(2.42509 + 1.05779i) q^{84} +(-1.60433 + 5.98746i) q^{85} +(1.07558 + 1.07558i) q^{86} +(-6.62110 + 3.82269i) q^{87} +(2.07581 + 1.19847i) q^{88} +(0.0380409 + 0.141971i) q^{89} +2.15163 q^{90} +(2.00892 - 9.32546i) q^{91} -0.0389343 q^{92} +(0.316457 + 1.18103i) q^{93} +(3.79999 + 2.19392i) q^{94} +(-11.8984 + 6.86957i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(2.46917 - 9.21508i) q^{97} +(-3.72313 + 5.92776i) q^{98} +(-1.69489 - 1.69489i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 8 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q - 8 * q^7 + 20 * q^9	$ 40 q - 8 q^{7} + 20 q^{9} + 8 q^{11} + 40 q^{12} - 8 q^{14} + 20 q^{16} + 16 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 32 q^{26} + 8 q^{28} - 8 q^{33} + 16 q^{34} - 32 q^{35} + 40 q^{37} - 16 q^{38} - 16 q^{39} - 4 q^{41} + 12 q^{42} + 24 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} - 4 q^{49} - 16 q^{50} - 8 q^{52} + 32 q^{53} - 72 q^{55} + 12 q^{56} + 8 q^{57} - 36 q^{58} + 84 q^{59} - 48 q^{61} - 4 q^{62} - 4 q^{63} - 16 q^{65} + 12 q^{68} - 8 q^{69} + 36 q^{70} - 40 q^{71} - 48 q^{73} + 8 q^{74} + 36 q^{75} + 16 q^{76} - 24 q^{77} - 8 q^{78} - 48 q^{79} - 20 q^{81} + 36 q^{83} - 8 q^{84} + 8 q^{85} - 8 q^{86} + 12 q^{89} - 48 q^{91} - 16 q^{92} - 24 q^{93} - 96 q^{95} + 8 q^{98} - 8 q^{99}+O(q^{100}) $ 40 * q - 8 * q^7 + 20 * q^9 + 8 * q^11 + 40 * q^12 - 8 * q^14 + 20 * q^16 + 16 * q^17 + 16 * q^19 + 4 * q^21 + 8 * q^22 + 32 * q^26 + 8 * q^28 - 8 * q^33 + 16 * q^34 - 32 * q^35 + 40 * q^37 - 16 * q^38 - 16 * q^39 - 4 * q^41 + 12 * q^42 + 24 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 - 4 * q^49 - 16 * q^50 - 8 * q^52 + 32 * q^53 - 72 * q^55 + 12 * q^56 + 8 * q^57 - 36 * q^58 + 84 * q^59 - 48 * q^61 - 4 * q^62 - 4 * q^63 - 16 * q^65 + 12 * q^68 - 8 * q^69 + 36 * q^70 - 40 * q^71 - 48 * q^73 + 8 * q^74 + 36 * q^75 + 16 * q^76 - 24 * q^77 - 8 * q^78 - 48 * q^79 - 20 * q^81 + 36 * q^83 - 8 * q^84 + 8 * q^85 - 8 * q^86 + 12 * q^89 - 48 * q^91 - 16 * q^92 - 24 * q^93 - 96 * q^95 + 8 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−1.52143	−	1.52143i	−0.680406	−	0.680406i	0.279686	−	0.960092i	$-0.409770\pi$
$5$	−1.52143	−	1.52143i	−0.680406	−	0.680406i	−0.960092	+	0.279686i	$0.909770\pi$
$6$	0.258819	−	0.965926i	0.105662	−	0.394338i
$7$	2.42509	+	1.05779i	0.916599	+	0.399807i
$7$	2.42509	+	1.05779i	0.916599	+	0.399807i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	1.07582	−	1.86337i	0.340203	−	0.589249i
$11$	−2.31526	+	0.620373i	−0.698079	+	0.187050i	−0.590370	−	0.807133i	$-0.701018\pi$
$11$	−2.31526	+	0.620373i	−0.698079	+	0.187050i	−0.107709	+	0.994182i	$0.534351\pi$
$12$	1.00000			0.288675
$13$	−0.713225	−	3.53430i	−0.197813	−	0.980240i
$13$	−0.713225	−	3.53430i	−0.197813	−	0.980240i
$14$	−0.394087	+	2.61624i	−0.105324	+	0.699219i
$15$	0.556883	+	2.07832i	0.143787	+	0.536619i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.44046	−	2.49495i	−0.349362	−	0.605113i	0.636774	−	0.771051i	$-0.280268\pi$
$17$	−1.44046	−	2.49495i	−0.349362	−	0.605113i	−0.986136	+	0.165937i	$0.946935\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	1.65268	−	6.16787i	0.379150	−	1.41501i	−0.468035	−	0.883710i	$-0.655038\pi$
$19$	1.65268	−	6.16787i	0.379150	−	1.41501i	0.847185	−	0.531297i	$-0.178295\pi$
$20$	2.07832	+	0.556883i	0.464726	+	0.124523i
$21$	−1.57130	−	2.12862i	−0.342885	−	0.464503i
$22$	−1.19847	−	2.07581i	−0.255515	−	0.442564i
$23$	0.0337181	+	0.0194671i	0.00703071	+	0.00405918i	0.503511	−	0.863989i	$-0.332041\pi$
$23$	0.0337181	+	0.0194671i	0.00703071	+	0.00405918i	−0.496481	+	0.868048i	$0.665375\pi$
$24$	0.258819	+	0.965926i	0.0528312	+	0.197169i
$25$		−	0.370480i		−	0.0740960i
$26$	3.22928	−	1.60367i	0.633314	−	0.314505i
$27$		−	1.00000i		−	0.192450i
$28$	−2.62909	+	0.296473i	−0.496851	+	0.0560281i
$29$	3.82269	−	6.62110i	0.709857	−	1.22951i	−0.255054	−	0.966927i	$-0.582093\pi$
$29$	3.82269	−	6.62110i	0.709857	−	1.22951i	0.964910	−	0.262581i	$-0.0845736\pi$
$30$	−1.86337	+	1.07582i	−0.340203	+	0.196416i
$31$	−0.864576	−	0.864576i	−0.155283	−	0.155283i	0.625190	−	0.780473i	$-0.285021\pi$
$31$	−0.864576	−	0.864576i	−0.155283	−	0.155283i	−0.780473	+	0.625190i	$0.785021\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	2.31526	+	0.620373i	0.403036	+	0.107993i
$34$	2.03711	−	2.03711i	0.349362	−	0.349362i
$35$	−2.08026	−	5.29898i	−0.351628	−	0.895691i
$36$	−0.866025	−	0.500000i	−0.144338	−	0.0833333i
$37$	5.90397	−	1.58196i	0.970607	−	0.260073i	0.261523	−	0.965197i	$-0.415775\pi$
$37$	5.90397	−	1.58196i	0.970607	−	0.260073i	0.709084	+	0.705124i	$0.249109\pi$
$38$	6.38545			1.03586
$39$	−1.14948	+	3.41741i	−0.184064	+	0.547224i
$40$			2.15163i			0.340203i
$41$	−4.54549	+	1.21796i	−0.709886	+	0.190213i	−0.595655	−	0.803241i	$-0.703107\pi$
$41$	−4.54549	+	1.21796i	−0.709886	+	0.190213i	−0.114232	+	0.993454i	$0.536441\pi$
$42$	1.64941	−	2.06868i	0.254509	−	0.319205i
$43$	1.31731	−	0.760547i	0.200887	−	0.115982i	−0.396182	−	0.918172i	$-0.629665\pi$
$43$	1.31731	−	0.760547i	0.200887	−	0.115982i	0.597069	+	0.802190i	$0.296332\pi$
$44$	1.69489	−	1.69489i	0.255515	−	0.255515i
$45$	0.556883	−	2.07832i	0.0830153	−	0.309817i
$46$	−0.0100769	+	0.0376076i	−0.00148576	+	0.00554494i
$47$	3.10268	−	3.10268i	0.452572	−	0.452572i	−0.443636	−	0.896207i	$-0.646312\pi$
$47$	3.10268	−	3.10268i	0.452572	−	0.452572i	0.896207	+	0.443636i	$0.146312\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	4.76216	+	5.13048i	0.680308	+	0.732926i
$50$	0.357856	−	0.0958873i	0.0506085	−	0.0135605i
$51$			2.88092i			0.403409i
$52$	2.38482	+	2.70419i	0.330715	+	0.375003i
$53$	−11.5264			−1.58328			−0.791638	−	0.610990i	$-0.790772\pi$
$53$	−11.5264			−1.58328			−0.791638	+	0.610990i	$0.790772\pi$
$54$	0.965926	−	0.258819i	0.131446	−	0.0352208i
$55$	4.46638	+	2.57866i	0.602246	+	0.347707i
$56$	−0.966829	−	2.46277i	−0.129198	−	0.329102i
$57$	−4.51520	+	4.51520i	−0.598052	+	0.598052i
$58$	7.38488	+	1.97877i	0.969682	+	0.259826i
$59$	−1.12417	−	0.301220i	−0.146354	−	0.0392155i	0.184898	−	0.982758i	$-0.440804\pi$
$59$	−1.12417	−	0.301220i	−0.146354	−	0.0392155i	−0.331252	+	0.943542i	$0.607471\pi$
$60$	−1.52143	−	1.52143i	−0.196416	−	0.196416i
$61$	−4.42383	+	2.55410i	−0.566414	+	0.327019i	−0.755716	−	0.654900i	$-0.772711\pi$
$61$	−4.42383	+	2.55410i	−0.566414	+	0.327019i	0.189302	+	0.981919i	$0.439378\pi$
$62$	0.611348	−	1.05889i	0.0776413	−	0.134479i
$63$	0.296473	+	2.62909i	0.0373521	+	0.331234i
$64$			1.00000i			0.125000i
$65$	−4.29209	+	6.46233i	−0.532368	+	0.801554i
$66$			2.39694i			0.295043i
$67$	0.334985	+	1.25018i	0.0409249	+	0.152734i	0.983365	−	0.181642i	$-0.0581412\pi$
$67$	0.334985	+	1.25018i	0.0409249	+	0.152734i	−0.942440	+	0.334376i	$0.891475\pi$
$68$	2.49495	+	1.44046i	0.302557	+	0.174681i
$69$	−0.0194671	−	0.0337181i	−0.00234357	−	0.00405918i
$70$	4.58001	−	3.38085i	0.547416	−	0.404089i
$71$	−4.09800	−	1.09806i	−0.486343	−	0.130315i	0.00731140	−	0.999973i	$-0.497673\pi$
$71$	−4.09800	−	1.09806i	−0.486343	−	0.130315i	−0.493655	+	0.869658i	$0.664339\pi$
$72$	0.258819	−	0.965926i	0.0305021	−	0.113835i
$73$	−9.09290	+	9.09290i	−1.06424	+	1.06424i	−0.0664534	+	0.997790i	$0.521168\pi$
$73$	−9.09290	+	9.09290i	−1.06424	+	1.06424i	−0.997790	+	0.0664534i	$0.978832\pi$
$74$	3.05612	+	5.29336i	0.355267	+	0.615340i
$75$	−0.185240	+	0.320845i	−0.0213897	+	0.0370480i
$76$	1.65268	+	6.16787i	0.189575	+	0.707504i
$77$	−6.27096	−	0.944603i	−0.714642	−	0.107648i
$78$	−3.59847	−	0.225823i	−0.407447	−	0.0255695i
$79$	11.5267			1.29686			0.648430	−	0.761274i	$-0.275426\pi$
$79$	11.5267			1.29686			0.648430	+	0.761274i	$0.275426\pi$
$80$	−2.07832	+	0.556883i	−0.232363	+	0.0622614i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.35292	−	4.07538i	−0.259836	−	0.450050i
$83$	5.24816	+	5.24816i	0.576061	+	0.576061i	0.933816	−	0.357755i	$-0.116458\pi$
$83$	5.24816	+	5.24816i	0.576061	+	0.576061i	−0.357755	+	0.933816i	$0.616458\pi$
$84$	2.42509	+	1.05779i	0.264599	+	0.115414i
$85$	−1.60433	+	5.98746i	−0.174014	+	0.649431i
$86$	1.07558	+	1.07558i	0.115982	+	0.115982i
$87$	−6.62110	+	3.82269i	−0.709857	+	0.409836i
$88$	2.07581	+	1.19847i	0.221282	+	0.127757i
$89$	0.0380409	+	0.141971i	0.00403233	+	0.0150489i	0.967913	−	0.251287i	$-0.0808537\pi$
$89$	0.0380409	+	0.141971i	0.00403233	+	0.0150489i	−0.963880	+	0.266336i	$0.914187\pi$
$90$	2.15163			0.226802
$91$	2.00892	−	9.32546i	0.210592	−	0.977574i
$92$	−0.0389343			−0.00405918
$93$	0.316457	+	1.18103i	0.0328151	+	0.122467i
$94$	3.79999	+	2.19392i	0.391939	+	0.226286i
$95$	−11.8984	+	6.86957i	−1.22075	+	0.704803i
$96$	−0.707107	−	0.707107i	−0.0721688	−	0.0721688i
$97$	2.46917	−	9.21508i	0.250707	−	0.935650i	−0.719722	−	0.694262i	$-0.755731\pi$
$97$	2.46917	−	9.21508i	0.250707	−	0.935650i	0.970429	−	0.241388i	$-0.0776025\pi$
$98$	−3.72313	+	5.92776i	−0.376093	+	0.598794i
$99$	−1.69489	−	1.69489i	−0.170343	−	0.170343i
$100$	0.185240	+	0.320845i	0.0185240	+	0.0320845i
$101$	−0.629935	+	1.09108i	−0.0626809	+	0.108566i	−0.895663	−	0.444734i	$-0.853298\pi$
$101$	−0.629935	+	1.09108i	−0.0626809	+	0.108566i	0.832982	+	0.553300i	$0.186632\pi$
$102$	−2.78275	+	0.745636i	−0.275533	+	0.0738289i
$103$	−13.3063			−1.31111			−0.655553	−	0.755149i	$-0.727564\pi$
$103$	−13.3063			−1.31111			−0.655553	+	0.755149i	$0.727564\pi$
$104$	−1.99480	+	3.00346i	−0.195607	+	0.294513i
$105$	−0.847931	+	5.62918i	−0.0827496	+	0.549352i
$106$	−2.98326	−	11.1337i	−0.289760	−	1.08140i
$107$	8.86720	−	15.3584i	0.857225	−	1.48476i	−0.0173405	−	0.999850i	$-0.505520\pi$
$107$	8.86720	−	15.3584i	0.857225	−	1.48476i	0.874565	−	0.484907i	$-0.161147\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	0.595782	−	0.595782i	0.0570656	−	0.0570656i	−0.677998	−	0.735064i	$-0.737152\pi$
$109$	0.595782	−	0.595782i	0.0570656	−	0.0570656i	0.735064	+	0.677998i	$0.237152\pi$
$110$	−1.33482	+	4.98160i	−0.127270	+	0.474977i
$111$	−5.90397	−	1.58196i	−0.560380	−	0.150153i
$112$	2.12862	−	1.57130i	0.201136	−	0.148474i
$113$	−1.70513	−	2.95338i	−0.160406	−	0.277831i	0.774609	−	0.632441i	$-0.217947\pi$
$113$	−1.70513	−	2.95338i	−0.160406	−	0.277831i	−0.935014	+	0.354610i	$0.884614\pi$
$114$	−5.52996	−	3.19273i	−0.517929	−	0.299026i
$115$	−0.0216819	−	0.0809178i	−0.00202184	−	0.00754562i
$116$			7.64539i			0.709857i
$117$	2.70419	−	2.38482i	0.250002	−	0.220477i
$118$		−	1.16382i		−	0.107139i
$119$	−0.854113	−	7.57418i	−0.0782964	−	0.694324i
$120$	1.07582	−	1.86337i	0.0982081	−	0.170101i
$121$	−4.55069	+	2.62734i	−0.413699	+	0.238849i
$122$	−3.61205	−	3.61205i	−0.327019	−	0.327019i
$123$	4.54549	+	1.21796i	0.409853	+	0.109820i
$124$	1.18103	+	0.316457i	0.106060	+	0.0284187i
$125$	−8.17083	+	8.17083i	−0.730821	+	0.730821i
$126$	−2.46277	+	0.966829i	−0.219401	+	0.0861319i
$127$	18.7769	+	10.8408i	1.66618	+	0.961969i	0.969669	+	0.244422i	$0.0785981\pi$
$127$	18.7769	+	10.8408i	1.66618	+	0.961969i	0.696510	+	0.717547i	$0.254735\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	−1.52109			−0.133925
$130$	−7.35301	−	2.47326i	−0.644902	−	0.216919i
$131$			4.96588i			0.433871i	0.976186	+	0.216936i	$0.0696062\pi$
$131$			4.96588i			0.433871i	−0.976186	+	0.216936i	$0.930394\pi$
$132$	−2.31526	+	0.620373i	−0.201518	+	0.0539966i
$133$	10.5322	−	13.2095i	0.913259	−	1.14541i
$134$	−1.12088	+	0.647141i	−0.0968293	+	0.0559044i
$135$	−1.52143	+	1.52143i	−0.130944	+	0.130944i
$136$	−0.745636	+	2.78275i	−0.0639377	+	0.238619i
$137$	−4.26704	+	15.9248i	−0.364558	+	1.36055i	0.503461	+	0.864018i	$0.332060\pi$
$137$	−4.26704	+	15.9248i	−0.364558	+	1.36055i	−0.868019	+	0.496531i	$0.834607\pi$
$138$	0.0275307	−	0.0275307i	0.00234357	−	0.00234357i
$139$	14.1828	−	8.18843i	1.20297	−	0.694534i	0.241754	−	0.970338i	$-0.422277\pi$
$139$	14.1828	−	8.18843i	1.20297	−	0.694534i	0.961214	+	0.275804i	$0.0889440\pi$
$140$	4.45105	+	3.54892i	0.376182	+	0.299938i
$141$	−4.23833	+	1.13566i	−0.356932	+	0.0956397i
$142$		−	4.24256i		−	0.356028i
$143$	3.84389	+	7.74039i	0.321442	+	0.647284i
$144$	1.00000			0.0833333
$145$	−15.8895	+	4.25759i	−1.31955	+	0.353574i
$146$	−11.1365	−	6.42965i	−0.921661	−	0.532121i
$147$	−1.55891	−	6.82421i	−0.128576	−	0.562851i
$148$	−4.32201	+	4.32201i	−0.355267	+	0.355267i
$149$	21.2876	+	5.70398i	1.74395	+	0.467289i	0.983317	−	0.181899i	$-0.0582245\pi$
$149$	21.2876	+	5.70398i	1.74395	+	0.467289i	0.760628	+	0.649188i	$0.224891\pi$
$150$	−0.357856	−	0.0958873i	−0.0292188	−	0.00782917i
$151$	0.584300	+	0.584300i	0.0475497	+	0.0475497i	0.730482	−	0.682932i	$-0.239296\pi$
$151$	0.584300	+	0.584300i	0.0475497	+	0.0475497i	−0.682932	+	0.730482i	$0.739296\pi$
$152$	−5.52996	+	3.19273i	−0.448539	+	0.258964i
$153$	1.44046	−	2.49495i	0.116454	−	0.201704i
$154$	−0.710627	−	6.30176i	−0.0572640	−	0.507810i
$155$			2.63079i			0.211310i
$156$	−0.713225	−	3.53430i	−0.0571037	−	0.282971i
$157$		−	9.18712i		−	0.733212i	−0.930376	−	0.366606i	$-0.880520\pi$
$157$		−	9.18712i		−	0.733212i	0.930376	−	0.366606i	$-0.119480\pi$
$158$	2.98334	+	11.1340i	0.237342	+	0.885772i
$159$	9.98218	+	5.76321i	0.791638	+	0.457053i
$160$	−1.07582	−	1.86337i	−0.0850507	−	0.147312i
$161$	0.0611773	+	0.0828763i	0.00482145	+	0.00653157i
$162$	−0.965926	−	0.258819i	−0.0758903	−	0.0203347i
$163$	−0.199027	+	0.742780i	−0.0155890	+	0.0581790i	−0.973282	−	0.229612i	$-0.926254\pi$
$163$	−0.199027	+	0.742780i	−0.0155890	+	0.0581790i	0.957693	+	0.287791i	$0.0929209\pi$
$164$	3.32753	−	3.32753i	0.259836	−	0.259836i
$165$	−2.57866	−	4.46638i	−0.200749	−	0.347707i
$166$	−3.71101	+	6.42766i	−0.288030	+	0.498883i
$167$	−1.28092	−	4.78045i	−0.0991204	−	0.369922i	0.898492	−	0.438991i	$-0.144664\pi$
$167$	−1.28092	−	4.78045i	−0.0991204	−	0.369922i	−0.997612	+	0.0690685i	$0.977997\pi$
$168$	−0.394087	+	2.61624i	−0.0304045	+	0.201847i
$169$	−11.9826	+	5.04151i	−0.921740	+	0.387808i
$170$	−6.19867			−0.475416
$171$	6.16787	−	1.65268i	0.471669	−	0.126383i
$172$	−0.760547	+	1.31731i	−0.0579912	+	0.100444i
$173$	6.84166	+	11.8501i	0.520161	+	0.900946i	0.999725	+	0.0234390i	$0.00746156\pi$
$173$	6.84166	+	11.8501i	0.520161	+	0.900946i	−0.479564	+	0.877507i	$0.659205\pi$
$174$	−5.40611	−	5.40611i	−0.409836	−	0.409836i
$175$	0.391891	−	0.898449i	0.0296241	−	0.0679164i
$176$	−0.620373	+	2.31526i	−0.0467624	+	0.174520i
$177$	0.822948	+	0.822948i	0.0618565	+	0.0618565i
$178$	−0.127287	+	0.0734894i	−0.00954059	+	0.00550826i
$179$	−12.5427	−	7.24152i	−0.937484	−	0.541256i	−0.0483131	−	0.998832i	$-0.515385\pi$
$179$	−12.5427	−	7.24152i	−0.937484	−	0.541256i	−0.889171	+	0.457576i	$0.848718\pi$
$180$	0.556883	+	2.07832i	0.0415076	+	0.154909i
$181$	−17.4769			−1.29905			−0.649524	−	0.760341i	$-0.725032\pi$
$181$	−17.4769			−1.29905			−0.649524	+	0.760341i	$0.725032\pi$
$182$	9.52765	−	0.473140i	0.706237	−	0.0350714i
$183$	5.10820			0.377609
$184$	−0.0100769	−	0.0376076i	−0.000742881	−	0.00277247i
$185$	−11.3894	−	6.57565i	−0.837362	−	0.483451i
$186$	−1.05889	+	0.611348i	−0.0776413	+	0.0448262i
$187$	4.88284	+	4.88284i	0.357069	+	0.357069i
$188$	−1.13566	+	4.23833i	−0.0828264	+	0.309112i
$189$	1.05779	−	2.42509i	0.0769430	−	0.176400i
$190$	−9.71504	−	9.71504i	−0.704803	−	0.704803i
$191$	1.81273	+	3.13973i	0.131164	+	0.227183i	0.924126	−	0.382089i	$-0.124795\pi$
$191$	1.81273	+	3.13973i	0.131164	+	0.227183i	−0.792961	+	0.609272i	$0.791462\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−18.1806	+	4.87149i	−1.30867	+	0.350657i	−0.844722	−	0.535205i	$-0.820235\pi$
$193$	−18.1806	+	4.87149i	−1.30867	+	0.350657i	−0.463949	+	0.885862i	$0.653568\pi$
$194$	9.54016			0.684943
$195$	6.94822	−	3.45050i	0.497573	−	0.247096i
$196$	−6.68939	−	2.06205i	−0.477814	−	0.147289i
$197$	−2.51822	−	9.39811i	−0.179415	−	0.669587i	−0.995757	−	0.0920185i	$-0.970668\pi$
$197$	−2.51822	−	9.39811i	−0.179415	−	0.669587i	0.816342	−	0.577569i	$-0.195999\pi$
$198$	1.19847	−	2.07581i	0.0851715	−	0.147521i
$199$	7.78591	+	13.4856i	0.551929	+	0.955969i	0.998135	+	0.0610386i	$0.0194413\pi$
$199$	7.78591	+	13.4856i	0.551929	+	0.955969i	−0.446207	+	0.894930i	$0.647225\pi$
$200$	−0.261969	+	0.261969i	−0.0185240	+	0.0185240i
$201$	0.334985	−	1.25018i	0.0236280	−	0.0881809i
$202$	−1.21694	−	0.326078i	−0.0856236	−	0.0229428i
$203$	16.2741	−	12.0132i	1.14222	−	0.843160i
$204$	−1.44046	−	2.49495i	−0.100852	−	0.174681i
$205$	8.76871	+	5.06262i	0.612433	+	0.353588i
$206$	−3.44392	−	12.8529i	−0.239949	−	0.895502i
$207$			0.0389343i			0.00270612i
$208$	−3.41741	−	1.14948i	−0.236955	−	0.0797022i
$209$			15.3055i			1.05871i
$210$	−5.65683	+	0.637900i	−0.390358	+	0.0440193i
$211$	7.40701	−	12.8293i	0.509919	−	0.883206i	−0.490015	−	0.871714i	$-0.663009\pi$
$211$	7.40701	−	12.8293i	0.509919	−	0.883206i	0.999934	−	0.0114920i	$-0.00365809\pi$
$212$	9.98218	−	5.76321i	0.685579	−	0.395819i
$213$	2.99995	+	2.99995i	0.205553	+	0.205553i
$214$	17.1301	+	4.59000i	1.17099	+	0.313766i
$215$	−3.16132	−	0.847072i	−0.215600	−	0.0577698i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	−1.18214	−	3.01122i	−0.0802487	−	0.204415i
$218$	0.729681	+	0.421282i	0.0494202	+	0.0285328i
$219$	12.4211	−	3.32823i	0.839342	−	0.224901i
$220$	−5.15733			−0.347707
$221$	−7.79053	+	6.87047i	−0.524048	+	0.462158i
$222$		−	6.11224i		−	0.410227i
$223$	17.9491	−	4.80944i	1.20196	−	0.322064i	0.398357	−	0.917231i	$-0.369581\pi$
$223$	17.9491	−	4.80944i	1.20196	−	0.322064i	0.803602	+	0.595167i	$0.202914\pi$
$224$	2.06868	+	1.64941i	0.138220	+	0.110206i
$225$	0.320845	−	0.185240i	0.0213897	−	0.0123493i
$226$	2.41143	−	2.41143i	0.160406	−	0.160406i
$227$	−0.784280	+	2.92697i	−0.0520545	+	0.194270i	−0.987057	−	0.160372i	$-0.948731\pi$
$227$	−0.784280	+	2.92697i	−0.0520545	+	0.194270i	0.935002	+	0.354642i	$0.115397\pi$
$228$	1.65268	−	6.16787i	0.109451	−	0.408477i
$229$	−12.8469	+	12.8469i	−0.848945	+	0.848945i	−0.990002	−	0.141056i	$-0.954950\pi$
$229$	−12.8469	+	12.8469i	−0.848945	+	0.848945i	0.141056	+	0.990002i	$0.454950\pi$
$230$	0.0725489	−	0.0418861i	0.00478373	−	0.00276189i
$231$	4.95851	+	3.95353i	0.326246	+	0.260123i
$232$	−7.38488	+	1.97877i	−0.484841	+	0.129913i
$233$		−	19.6049i		−	1.28436i	−0.766555	−	0.642179i	$-0.778031\pi$
$233$		−	19.6049i		−	1.28436i	0.766555	−	0.642179i	$-0.221969\pi$
$234$	3.00346	+	1.99480i	0.196342	+	0.130404i
$235$	−9.44103			−0.615865
$236$	1.12417	−	0.301220i	0.0731771	−	0.0196077i
$237$	−9.98245	−	5.76337i	−0.648430	−	0.374371i
$238$	7.09504	−	2.78535i	0.459903	−	0.180548i
$239$	−10.1590	+	10.1590i	−0.657130	+	0.657130i	−0.954700	−	0.297570i	$-0.903824\pi$
$239$	−10.1590	+	10.1590i	−0.657130	+	0.657130i	0.297570	+	0.954700i	$0.403824\pi$
$240$	2.07832	+	0.556883i	0.134155	+	0.0359467i
$241$	17.6926	+	4.74073i	1.13968	+	0.305377i	0.778824	−	0.627243i	$-0.215817\pi$
$241$	17.6926	+	4.74073i	1.13968	+	0.305377i	0.360859	+	0.932620i	$0.382483\pi$
$242$	−3.71562	−	3.71562i	−0.238849	−	0.238849i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	2.55410	−	4.42383i	0.163510	−	0.283207i
$245$	0.560387	−	15.0510i	0.0358018	−	0.961573i
$246$			4.70584i			0.300033i
$247$	−22.9779	−	1.44198i	−1.46205	−	0.0917512i
$248$			1.22270i			0.0776413i
$249$	−1.92096	−	7.16912i	−0.121736	−	0.454325i
$250$	−10.0072	−	5.77765i	−0.632910	−	0.365411i
$251$	8.37788	+	14.5109i	0.528807	+	0.915921i	0.999436	+	0.0335896i	$0.0106939\pi$
$251$	8.37788	+	14.5109i	0.528807	+	0.915921i	−0.470628	+	0.882332i	$0.655973\pi$
$252$	−1.57130	−	2.12862i	−0.0989824	−	0.134090i
$253$	−0.0901432	−	0.0241538i	−0.00566725	−	0.00151854i
$254$	−5.61163	+	20.9429i	−0.352105	+	1.31407i
$255$	4.38312	−	4.38312i	0.274482	−	0.274482i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	13.7403	−	23.7990i	0.857098	−	1.48454i	−0.0175861	−	0.999845i	$-0.505598\pi$
$257$	13.7403	−	23.7990i	0.857098	−	1.48454i	0.874685	−	0.484693i	$-0.161069\pi$
$258$	−0.393688	−	1.46926i	−0.0245100	−	0.0914724i
$259$	15.9911	+	2.40876i	0.993637	+	0.149673i
$260$	0.485889	−	7.74259i	0.0301335	−	0.480175i
$261$	7.64539			0.473238
$262$	−4.79667	+	1.28527i	−0.296340	+	0.0794039i
$263$	14.5204	−	25.1500i	0.895365	−	1.55082i	0.0620133	−	0.998075i	$-0.480248\pi$
$263$	14.5204	−	25.1500i	0.895365	−	1.55082i	0.833352	−	0.552743i	$-0.186419\pi$
$264$	−1.19847	−	2.07581i	−0.0737607	−	0.127757i
$265$	17.5367	+	17.5367i	1.07727	+	1.07727i
$266$	15.4853	+	6.75447i	0.949466	+	0.414143i
$267$	0.0380409	−	0.141971i	0.00232807	−	0.00868846i
$268$	−0.915195	−	0.915195i	−0.0559044	−	0.0559044i
$269$	17.7908	−	10.2715i	1.08473	−	0.626267i	0.152559	−	0.988294i	$-0.451249\pi$
$269$	17.7908	−	10.2715i	1.08473	−	0.626267i	0.932168	+	0.362027i	$0.117915\pi$
$270$	−1.86337	−	1.07582i	−0.113401	−	0.0654721i
$271$	−0.577838	−	2.15652i	−0.0351012	−	0.130999i	0.946152	−	0.323723i	$-0.104935\pi$
$271$	−0.577838	−	2.15652i	−0.0351012	−	0.130999i	−0.981253	+	0.192724i	$0.938268\pi$
$272$	−2.88092			−0.174681
$273$	−6.40251	+	7.07163i	−0.387497	+	0.427994i
$274$	−16.4866			−0.995991
$275$	0.229836	+	0.857760i	0.0138596	+	0.0517249i
$276$	0.0337181	+	0.0194671i	0.00202959	+	0.00117178i
$277$	−10.5983	+	6.11895i	−0.636792	+	0.367652i	−0.783378	−	0.621546i	$-0.786505\pi$
$277$	−10.5983	+	6.11895i	−0.636792	+	0.367652i	0.146586	+	0.989198i	$0.453172\pi$
$278$	11.5802	+	11.5802i	0.694534	+	0.694534i
$279$	0.316457	−	1.18103i	0.0189458	−	0.0707066i
$280$	−2.27598	+	5.21791i	−0.136016	+	0.311830i
$281$	22.6960	+	22.6960i	1.35393	+	1.35393i	0.881218	+	0.472709i	$0.156724\pi$
$281$	22.6960	+	22.6960i	1.35393	+	1.35393i	0.472709	+	0.881218i	$0.343276\pi$
$282$	−2.19392	−	3.79999i	−0.130646	−	0.226286i
$283$	7.46543	−	12.9305i	0.443774	−	0.768638i	−0.554192	−	0.832389i	$-0.686973\pi$
$283$	7.46543	−	12.9305i	0.443774	−	0.768638i	0.997966	+	0.0637502i	$0.0203061\pi$
$284$	4.09800	−	1.09806i	0.243172	−	0.0651577i
$285$	13.7391			0.813837
$286$	−6.48177	+	5.71627i	−0.383275	+	0.338010i
$287$	−12.3116	−	1.85451i	−0.726730	−	0.109468i
$288$	0.258819	+	0.965926i	0.0152511	+	0.0569177i
$289$	4.35016	−	7.53470i	0.255892	−	0.443218i
$290$	−8.22503	−	14.2462i	−0.482990	−	0.836564i
$291$	−6.74591	+	6.74591i	−0.395452	+	0.395452i
$292$	3.32823	−	12.4211i	0.194770	−	0.726891i
$293$	−8.70333	−	2.33205i	−0.508454	−	0.136240i	−0.00453323	−	0.999990i	$-0.501443\pi$
$293$	−8.70333	−	2.33205i	−0.508454	−	0.136240i	−0.503921	+	0.863750i	$0.668110\pi$
$294$	6.18820	−	3.27202i	0.360903	−	0.190828i
$295$	1.25206	+	2.16863i	0.0728978	+	0.126263i
$296$	−5.29336	−	3.05612i	−0.307670	−	0.177633i
$297$	0.620373	+	2.31526i	0.0359977	+	0.134345i
$298$			22.0385i			1.27666i
$299$	0.0447542	−	0.133054i	0.00258821	−	0.00769474i
$300$		−	0.370480i		−	0.0213897i
$301$	3.99909	−	0.450963i	0.230504	−	0.0259931i
$302$	−0.413163	+	0.715619i	−0.0237748	+	0.0411792i
$303$	1.09108	−	0.629935i	0.0626809	−	0.0361888i
$304$	−4.51520	−	4.51520i	−0.258964	−	0.258964i
$305$	10.6165	+	2.84467i	0.607897	+	0.162886i
$306$	2.78275	+	0.745636i	0.159079	+	0.0426252i
$307$	12.6883	−	12.6883i	0.724162	−	0.724162i	−0.245288	−	0.969450i	$-0.578883\pi$
$307$	12.6883	−	12.6883i	0.724162	−	0.724162i	0.969450	+	0.245288i	$0.0788827\pi$
$308$	5.90311	−	2.31743i	0.336361	−	0.132048i
$309$	11.5236	+	6.65313i	0.655553	+	0.378484i
$310$	−2.54115	+	0.680899i	−0.144328	+	0.0386725i
$311$	19.7846			1.12188			0.560940	−	0.827856i	$-0.310440\pi$
$311$	19.7846			1.12188			0.560940	+	0.827856i	$0.310440\pi$
$312$	3.22928	−	1.60367i	0.182822	−	0.0907898i
$313$		−	29.2248i		−	1.65188i	−0.563756	−	0.825941i	$-0.690644\pi$
$313$		−	29.2248i		−	1.65188i	0.563756	−	0.825941i	$-0.309356\pi$
$314$	8.87408	−	2.37780i	0.500793	−	0.134187i
$315$	3.54892	−	4.45105i	0.199959	−	0.250788i
$316$	−9.98245	+	5.76337i	−0.561557	+	0.324215i
$317$	−7.03786	+	7.03786i	−0.395285	+	0.395285i	−0.876566	−	0.481281i	$-0.840172\pi$
$317$	−7.03786	+	7.03786i	−0.395285	+	0.395285i	0.481281	+	0.876566i	$0.340172\pi$
$318$	−2.98326	+	11.1337i	−0.167293	+	0.624346i
$319$	−4.74300	+	17.7011i	−0.265557	+	0.991071i
$320$	1.52143	−	1.52143i	0.0850507	−	0.0850507i
$321$	−15.3584	+	8.86720i	−0.857225	+	0.494919i
$322$	−0.0642185	+	0.0805427i	−0.00357876	+	0.00448847i
$323$	−17.7691	+	4.76122i	−0.988700	+	0.264921i
$324$		−	1.00000i		−	0.0555556i
$325$	−1.30939	+	0.264236i	−0.0726319	+	0.0146572i
$326$	−0.768982			−0.0425900
$327$	−0.813854	+	0.218071i	−0.0450062	+	0.0120594i
$328$	4.07538	+	2.35292i	0.225025	+	0.129918i
$329$	10.8063	−	4.24230i	0.595768	−	0.233885i
$330$	3.64678	−	3.64678i	0.200749	−	0.200749i
$331$	2.10322	+	0.563556i	0.115603	+	0.0309758i	0.316157	−	0.948707i	$-0.397607\pi$
$331$	2.10322	+	0.563556i	0.115603	+	0.0309758i	−0.200554	+	0.979683i	$0.564274\pi$
$332$	−7.16912	−	1.92096i	−0.393457	−	0.105426i
$333$	4.32201	+	4.32201i	0.236845	+	0.236845i
$334$	4.28604	−	2.47454i	0.234521	−	0.135401i
$335$	1.39241	−	2.41172i	0.0760754	−	0.131766i
$336$	−2.62909	+	0.296473i	−0.143429	+	0.0161739i
$337$			12.7100i			0.692357i	0.938169	+	0.346179i	$0.112521\pi$
$337$			12.7100i			0.692357i	−0.938169	+	0.346179i	$0.887479\pi$
$338$	−7.97105	−	10.2695i	−0.433568	−	0.558586i
$339$			3.41027i			0.185220i
$340$	−1.60433	−	5.98746i	−0.0870072	−	0.324715i
$341$	2.53808	+	1.46536i	0.137445	+	0.0793539i
$342$	3.19273	+	5.52996i	0.172643	+	0.299026i
$343$	6.12169	+	17.4793i	0.330540	+	0.943792i
$344$	−1.46926	−	0.393688i	−0.0792174	−	0.0212262i
$345$	−0.0216819	+	0.0809178i	−0.00116731	+	0.00435647i
$346$	−9.67556	+	9.67556i	−0.520161	+	0.520161i
$347$	−2.58028	−	4.46917i	−0.138517	−	0.239918i	0.788419	−	0.615139i	$-0.210900\pi$
$347$	−2.58028	−	4.46917i	−0.138517	−	0.239918i	−0.926935	+	0.375221i	$0.877567\pi$
$348$	3.82269	−	6.62110i	0.204918	−	0.354928i
$349$	5.61458	+	20.9539i	0.300542	+	1.12164i	0.936716	+	0.350091i	$0.113849\pi$
$349$	5.61458	+	20.9539i	0.300542	+	1.12164i	−0.636174	+	0.771546i	$0.719484\pi$
$350$	0.969264	+	0.146002i	0.0518093	+	0.00780411i
$351$	−3.53430	+	0.713225i	−0.188647	+	0.0380691i
$352$	−2.39694			−0.127757
$353$	16.9352	−	4.53778i	0.901371	−	0.241522i	0.221766	−	0.975100i	$-0.428818\pi$
$353$	16.9352	−	4.53778i	0.901371	−	0.241522i	0.679605	+	0.733578i	$0.262151\pi$
$354$	−0.581912	+	1.00790i	−0.0309283	+	0.0535693i
$355$	4.56422	+	7.90546i	0.242244	+	0.419578i
$356$	−0.103930	−	0.103930i	−0.00550826	−	0.00550826i
$357$	−3.04741	+	6.98649i	−0.161286	+	0.369764i
$358$	3.74849	−	13.9895i	0.198114	−	0.739370i
$359$	−11.4946	−	11.4946i	−0.606660	−	0.606660i	0.335412	−	0.942072i	$-0.391125\pi$
$359$	−11.4946	−	11.4946i	−0.606660	−	0.606660i	−0.942072	+	0.335412i	$0.891125\pi$
$360$	−1.86337	+	1.07582i	−0.0982081	+	0.0567005i
$361$	−18.8568	−	10.8870i	−0.992465	−	0.573000i
$362$	−4.52336	−	16.8814i	−0.237742	−	0.887266i
$363$	5.25469			0.275799
$364$	2.92296	+	9.08055i	0.153204	+	0.475950i
$365$	27.6685			1.44823
$366$	1.32210	+	4.93415i	0.0691073	+	0.257912i
$367$	−30.9396	−	17.8630i	−1.61503	−	0.932440i	−0.988179	−	0.153303i	$-0.951009\pi$
$367$	−30.9396	−	17.8630i	−1.61503	−	0.932440i	−0.626854	−	0.779137i	$-0.715658\pi$
$368$	0.0337181	−	0.0194671i	0.00175768	−	0.00101479i
$369$	−3.32753	−	3.32753i	−0.173224	−	0.173224i
$370$	3.40381	−	12.7032i	0.176955	−	0.660407i
$371$	−27.9527	−	12.1926i	−1.45123	−	0.633006i
$372$	−0.864576	−	0.864576i	−0.0448262	−	0.0448262i
$373$	−16.7914	−	29.0836i	−0.869427	−	1.50589i	−0.862583	−	0.505916i	$-0.831155\pi$
$373$	−16.7914	−	29.0836i	−0.869427	−	1.50589i	−0.00684428	−	0.999977i	$-0.502179\pi$
$374$	−3.45269	+	5.98023i	−0.178534	+	0.309230i
$375$	11.1616	−	2.99073i	0.576380	−	0.154441i
$376$	−4.38785			−0.226286
$377$	−26.1274	−	8.78823i	−1.34563	−	0.452617i
$378$	2.61624	+	0.394087i	0.134565	+	0.0202697i
$379$	3.54733	+	13.2388i	0.182214	+	0.680032i	0.995210	+	0.0977624i	$0.0311685\pi$
$379$	3.54733	+	13.2388i	0.182214	+	0.680032i	−0.812996	+	0.582270i	$0.802165\pi$
$380$	6.86957	−	11.8984i	0.352402	−	0.610377i
$381$	−10.8408	−	18.7769i	−0.555393	−	0.961969i
$382$	−2.56358	+	2.56358i	−0.131164	+	0.131164i
$383$	−3.55206	+	13.2564i	−0.181502	+	0.677373i	0.813851	+	0.581074i	$0.197367\pi$
$383$	−3.55206	+	13.2564i	−0.181502	+	0.677373i	−0.995352	+	0.0962992i	$0.969299\pi$
$384$	0.965926	+	0.258819i	0.0492922	+	0.0132078i
$385$	8.10370	+	10.9780i	0.413003	+	0.559491i
$386$	−9.41099	−	16.3003i	−0.479007	−	0.829664i
$387$	1.31731	+	0.760547i	0.0669624	+	0.0386608i
$388$	2.46917	+	9.21508i	0.125353	+	0.467825i
$389$		−	32.6089i		−	1.65334i	−0.562688	−	0.826669i	$-0.690233\pi$
$389$		−	32.6089i		−	1.65334i	0.562688	−	0.826669i	$-0.309767\pi$
$390$	5.13126	+	5.81841i	0.259832	+	0.294627i
$391$		−	0.112166i		−	0.00567250i
$392$	0.260448	−	6.99515i	0.0131546	−	0.353309i
$393$	2.48294	−	4.30058i	0.125248	−	0.216936i
$394$	8.42611	−	4.86482i	0.424501	−	0.245086i
$395$	−17.5372	−	17.5372i	−0.882391	−	0.882391i
$396$	2.31526	+	0.620373i	0.116346	+	0.0311749i
$397$	−13.3833	−	3.58604i	−0.671687	−	0.179978i	−0.0931723	−	0.995650i	$-0.529701\pi$
$397$	−13.3833	−	3.58604i	−0.671687	−	0.179978i	−0.578515	+	0.815672i	$0.696367\pi$
$398$	−11.0109	+	11.0109i	−0.551929	+	0.551929i
$399$	−15.7259	+	6.17364i	−0.787280	+	0.309068i
$400$	−0.320845	−	0.185240i	−0.0160423	−	0.00926200i
$401$	35.9398	−	9.63003i	1.79475	−	0.480901i	0.801608	−	0.597849i	$-0.203978\pi$
$401$	35.9398	−	9.63003i	1.79475	−	0.480901i	0.993138	+	0.116949i	$0.0373113\pi$
$402$	1.29428			0.0645529
$403$	−2.43904	+	3.67231i	−0.121497	+	0.182931i
$404$		−	1.25987i		−	0.0626809i
$405$	2.07832	−	0.556883i	0.103272	−	0.0276718i
$406$	15.8159	+	12.6104i	0.784930	+	0.625842i
$407$	−12.6878	+	7.32533i	−0.628913	+	0.363103i
$408$	2.03711	−	2.03711i	0.100852	−	0.100852i
$409$	1.01886	−	3.80245i	0.0503795	−	0.188019i	−0.936150	−	0.351600i	$-0.885638\pi$
$409$	1.01886	−	3.80245i	0.0503795	−	0.188019i	0.986530	+	0.163581i	$0.0523045\pi$
$410$	−2.62060	+	9.78022i	−0.129422	+	0.483011i
$411$	11.6578	−	11.6578i	0.575036	−	0.575036i
$412$	11.5236	−	6.65313i	0.567725	−	0.327776i
$413$	−2.40758	−	1.91962i	−0.118469	−	0.0944584i
$414$	−0.0376076	+	0.0100769i	−0.00184831	+	0.000495254i
$415$		−	15.9695i		−	0.783910i
$416$	0.225823	−	3.59847i	0.0110719	−	0.176430i
$417$	−16.3769			−0.801979
$418$	−14.7840	+	3.96136i	−0.723110	+	0.193757i
$419$	7.57088	+	4.37105i	0.369862	+	0.213540i	0.673398	−	0.739280i	$-0.264834\pi$
$419$	7.57088	+	4.37105i	0.369862	+	0.213540i	−0.303536	+	0.952820i	$0.598167\pi$
$420$	−2.08026	−	5.29898i	−0.101506	−	0.258564i
$421$	−9.92724	+	9.92724i	−0.483824	+	0.483824i	−0.906351	−	0.422527i	$-0.861143\pi$
$421$	−9.92724	+	9.92724i	−0.483824	+	0.483824i	0.422527	+	0.906351i	$0.361143\pi$
$422$	14.3092	+	3.83415i	0.696563	+	0.186643i
$423$	4.23833	+	1.13566i	0.206075	+	0.0552176i
$424$	8.15042	+	8.15042i	0.395819	+	0.395819i
$425$	−0.924328	+	0.533661i	−0.0448365	+	0.0258864i
$426$	−2.12128	+	3.67417i	−0.102776	+	0.178014i
$427$	−13.4299	+	1.51444i	−0.649919	+	0.0732890i
$428$			17.7344i			0.857225i
$429$	0.541285	−	8.62532i	0.0261335	−	0.416434i
$430$		−	3.27283i		−	0.157830i
$431$	−2.65831	−	9.92095i	−0.128046	−	0.477875i	0.871884	−	0.489713i	$-0.162898\pi$
$431$	−2.65831	−	9.92095i	−0.128046	−	0.477875i	−0.999930	+	0.0118379i	$0.996232\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$	−6.08844	−	10.5455i	−0.292592	−	0.506784i	0.681830	−	0.731511i	$-0.261184\pi$
$433$	−6.08844	−	10.5455i	−0.292592	−	0.506784i	−0.974422	+	0.224727i	$0.927851\pi$
$434$	2.60266	−	1.92122i	0.124931	−	0.0922214i
$435$	15.8895	+	4.25759i	0.761845	+	0.204136i
$436$	−0.218071	+	0.813854i	−0.0104437	+	0.0389765i
$437$	0.175796	−	0.175796i	0.00840946	−	0.00840946i
$438$	6.42965	+	11.1365i	0.307220	+	0.532121i
$439$	−20.0669	+	34.7569i	−0.957741	+	1.65886i	−0.229772	+	0.973244i	$0.573798\pi$
$439$	−20.0669	+	34.7569i	−0.957741	+	1.65886i	−0.727968	+	0.685611i	$0.759535\pi$
$440$	−1.33482	−	4.98160i	−0.0636348	−	0.237488i
$441$	−2.06205	+	6.68939i	−0.0981929	+	0.318542i
$442$	−8.65271	−	5.74686i	−0.411567	−	0.273350i
$443$	−21.7143			−1.03168			−0.515839	−	0.856685i	$-0.672520\pi$
$443$	−21.7143			−1.03168			−0.515839	+	0.856685i	$0.672520\pi$
$444$	5.90397	−	1.58196i	0.280190	−	0.0750767i
$445$	0.158122	−	0.273875i	0.00749571	−	0.0129829i
$446$	9.29112	+	16.0927i	0.439948	+	0.762011i
$447$	−15.5836	−	15.5836i	−0.737078	−	0.737078i
$448$	−1.05779	+	2.42509i	−0.0499759	+	0.114575i
$449$	3.21778	−	12.0089i	0.151857	−	0.566736i	−0.847498	−	0.530799i	$-0.821892\pi$
$449$	3.21778	−	12.0089i	0.151857	−	0.566736i	0.999354	−	0.0359369i	$-0.0114415\pi$
$450$	0.261969	+	0.261969i	0.0123493	+	0.0123493i
$451$	9.76842	−	5.63980i	0.459977	−	0.265568i
$452$	2.95338	+	1.70513i	0.138915	+	0.0802028i
$453$	−0.213869	−	0.798169i	−0.0100484	−	0.0375013i
$454$	−3.03023			−0.142216
$455$	−17.2445	+	11.1316i	−0.808435	+	0.521859i
$456$	6.38545			0.299026
$457$	2.09389	+	7.81451i	0.0979481	+	0.365547i	0.997450	−	0.0713697i	$-0.0227370\pi$
$457$	2.09389	+	7.81451i	0.0979481	+	0.365547i	−0.899502	+	0.436917i	$0.856070\pi$
$458$	−15.7341	−	9.08411i	−0.735208	−	0.424473i
$459$	−2.49495	+	1.44046i	−0.116454	+	0.0672348i
$460$	0.0592359	+	0.0592359i	0.00276189	+	0.00276189i
$461$	−6.42020	+	23.9605i	−0.299019	+	1.11595i	0.638954	+	0.769245i	$0.279367\pi$
$461$	−6.42020	+	23.9605i	−0.299019	+	1.11595i	−0.937973	+	0.346708i	$0.887299\pi$
$462$	−2.53546	+	5.81280i	−0.117960	+	0.270436i
$463$	25.1995	+	25.1995i	1.17112	+	1.17112i	0.981943	+	0.189177i	$0.0605821\pi$
$463$	25.1995	+	25.1995i	1.17112	+	1.17112i	0.189177	+	0.981943i	$0.439418\pi$
$464$	−3.82269	−	6.62110i	−0.177464	−	0.307377i
$465$	1.31540	−	2.27833i	0.0610000	−	0.105655i
$466$	18.9369	−	5.07412i	0.877233	−	0.235054i
$467$	19.4236			0.898817			0.449408	−	0.893326i	$-0.351635\pi$
$467$	19.4236			0.898817			0.449408	+	0.893326i	$0.351635\pi$
$468$	−1.14948	+	3.41741i	−0.0531348	+	0.157970i
$469$	−0.510060	+	3.38615i	−0.0235524	+	0.156358i
$470$	−2.44352	−	9.11933i	−0.112711	−	0.420644i
$471$	−4.59356	+	7.95628i	−0.211660	+	0.366606i
$472$	0.581912	+	1.00790i	0.0267847	+	0.0463924i
$473$	−2.57809	+	2.57809i	−0.118541	+	0.118541i
$474$	2.98334	−	11.1340i	0.137029	−	0.511401i
$475$	−2.28507	−	0.612284i	−0.104846	−	0.0280935i
$476$	4.52677	+	6.13238i	0.207484	+	0.281077i
$477$	−5.76321	−	9.98218i	−0.263879	−	0.457053i
$478$	−12.4422	−	7.18348i	−0.569091	−	0.328565i
$479$	7.23040	+	26.9842i	0.330366	+	1.23294i	0.908807	+	0.417217i	$0.136995\pi$
$479$	7.23040	+	26.9842i	0.330366	+	1.23294i	−0.578441	+	0.815724i	$0.696339\pi$
$480$			2.15163i			0.0982081i
$481$	−9.80200	−	19.7381i	−0.446933	−	0.899982i
$482$			18.3168i			0.834306i
$483$	−0.0115430	−	0.102362i	−0.000525223	−	0.00465762i
$484$	2.62734	−	4.55069i	0.119425	−	0.206850i
$485$	−17.7768	+	10.2635i	−0.807204	+	0.466039i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	4.74639	+	1.27179i	0.215079	+	0.0576304i	0.364750	−	0.931106i	$-0.381155\pi$
$487$	4.74639	+	1.27179i	0.215079	+	0.0576304i	−0.149670	+	0.988736i	$0.547821\pi$
$488$	4.93415	+	1.32210i	0.223358	+	0.0598487i
$489$	0.543752	−	0.543752i	0.0245893	−	0.0245893i
$490$	14.6832	−	3.35419i	0.663319	−	0.151527i
$491$	22.4925	+	12.9861i	1.01507	+	0.586053i	0.912673	−	0.408690i	$-0.134014\pi$
$491$	22.4925	+	12.9861i	1.01507	+	0.586053i	0.102401	+	0.994743i	$0.467348\pi$
$492$	−4.54549	+	1.21796i	−0.204927	+	0.0549099i
$493$	−22.0257			−0.991989
$494$	−4.55426	−	22.5681i	−0.204906	−	1.01539i
$495$			5.15733i			0.231805i
$496$	−1.18103	+	0.316457i	−0.0530300	+	0.0142093i
$497$	−8.77652	−	6.99772i	−0.393681	−	0.313891i
$498$	6.42766	−	3.71101i	0.288030	−	0.166294i
$499$	−23.7752	+	23.7752i	−1.06432	+	1.06432i	−0.0665382	+	0.997784i	$0.521195\pi$
$499$	−23.7752	+	23.7752i	−1.06432	+	1.06432i	−0.997784	+	0.0665382i	$0.978805\pi$
$500$	2.99073	−	11.1616i	0.133750	−	0.499160i
$501$	−1.28092	+	4.78045i	−0.0572272	+	0.213575i
$502$	−11.8481	+	11.8481i	−0.528807	+	0.528807i
$503$	−17.9853	+	10.3838i	−0.801925	+	0.462992i	−0.844144	−	0.536117i	$-0.819891\pi$
$503$	−17.9853	+	10.3838i	−0.801925	+	0.462992i	0.0422185	+	0.999108i	$0.486557\pi$
$504$	1.64941	−	2.06868i	0.0734705	−	0.0921465i
$505$	2.61841	−	0.701600i	0.116518	−	0.0312208i
$506$		−	0.0933231i		−	0.00414872i
$507$	12.8980	+	1.62524i	0.572821	+	0.0721794i
$508$	−21.6817			−0.961969
$509$	5.41041	−	1.44971i	0.239812	−	0.0642575i	−0.136911	−	0.990583i	$-0.543717\pi$
$509$	5.41041	−	1.44971i	0.239812	−	0.0642575i	0.376723	+	0.926326i	$0.377051\pi$
$510$	5.36821	+	3.09934i	0.237708	+	0.137241i
$511$	−31.6695	+	12.4327i	−1.40098	+	0.549992i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−6.16787	−	1.65268i	−0.272318	−	0.0729674i
$514$	26.5443	+	7.11252i	1.17082	+	0.313720i
$515$	20.2446	+	20.2446i	0.892084	+	0.892084i
$516$	1.31731	−	0.760547i	0.0579912	−	0.0334812i
$517$	−5.25870	+	9.10833i	−0.231277	+	0.400584i
$518$	1.81211	+	16.0696i	0.0796197	+	0.706059i
$519$		−	13.6833i		−	0.600631i
$520$	7.60452	−	1.53460i	0.333480	−	0.0672965i
$521$			37.6571i			1.64979i	0.565287	+	0.824894i	$0.308765\pi$
$521$			37.6571i			1.64979i	−0.565287	+	0.824894i	$0.691235\pi$
$522$	1.97877	+	7.38488i	0.0866085	+	0.323227i
$523$	12.3073	+	7.10564i	0.538162	+	0.310708i	0.744334	−	0.667808i	$-0.232767\pi$
$523$	12.3073	+	7.10564i	0.538162	+	0.310708i	−0.206172	+	0.978516i	$0.566101\pi$
$524$	−2.48294	−	4.30058i	−0.108468	−	0.187872i
$525$	−0.788612	+	0.582134i	−0.0344178	+	0.0254064i
$526$	28.0512	+	7.51630i	1.22309	+	0.327726i
$527$	−0.911686	+	3.40246i	−0.0397137	+	0.148213i
$528$	1.69489	−	1.69489i	0.0737607	−	0.0737607i
$529$	−11.4992	−	19.9173i	−0.499967	−	0.865968i
$530$	−12.4003	+	21.4780i	−0.538635	+	0.932944i
$531$	−0.301220	−	1.12417i	−0.0130718	−	0.0487847i
$532$	−2.51643	+	16.7059i	−0.109101	+	0.724291i
$533$	7.54660	+	15.1965i	0.326880	+	0.658232i
$534$	0.146979			0.00636039
$535$	−36.8577	+	9.87600i	−1.59350	+	0.426977i
$536$	0.647141	−	1.12088i	0.0279522	−	0.0484147i
$537$	7.24152	+	12.5427i	0.312495	+	0.541256i
$538$	14.5262	+	14.5262i	0.626267	+	0.626267i
$539$	−14.2085	−	8.92412i	−0.612002	−	0.384389i
$540$	0.556883	−	2.07832i	0.0239644	−	0.0894365i
$541$	0.350415	+	0.350415i	0.0150655	+	0.0150655i	0.714599	−	0.699534i	$-0.246609\pi$
$541$	0.350415	+	0.350415i	0.0150655	+	0.0150655i	−0.699534	+	0.714599i	$0.746609\pi$
$542$	1.93348	−	1.11630i	0.0830502	−	0.0479491i
$543$	15.1354	+	8.73845i	0.649524	+	0.375003i
$544$	−0.745636	−	2.78275i	−0.0319689	−	0.119309i
$545$	−1.81289			−0.0776555
$546$	−8.48776	−	4.35407i	−0.363243	−	0.186337i
$547$	15.4047			0.658659			0.329329	−	0.944215i	$-0.393177\pi$
$547$	15.4047			0.658659			0.329329	+	0.944215i	$0.393177\pi$
$548$	−4.26704	−	15.9248i	−0.182279	−	0.680274i
$549$	−4.42383	−	2.55410i	−0.188805	−	0.109006i
$550$	−0.769046	+	0.444009i	−0.0327922	+	0.0189326i
$551$	−34.5204	−	34.5204i	−1.47062	−	1.47062i
$552$	−0.0100769	+	0.0376076i	−0.000428903	+	0.00160069i
$553$	27.9534	+	12.1929i	1.18870	+	0.518494i
$554$	−8.65351	−	8.65351i	−0.367652	−	0.367652i
$555$	6.57565	+	11.3894i	0.279121	+	0.483451i
$556$	−8.18843	+	14.1828i	−0.347267	+	0.601484i
$557$	−10.4167	+	2.79114i	−0.441369	+	0.118264i	−0.472658	−	0.881246i	$-0.656705\pi$
$557$	−10.4167	+	2.79114i	−0.441369	+	0.118264i	0.0312892	+	0.999510i	$0.490039\pi$
$558$	1.22270			0.0517608
$559$	−3.62754	−	4.11332i	−0.153429	−	0.173975i
$560$	−5.62918	−	0.847931i	−0.237876	−	0.0358316i
$561$	−1.78724	−	6.67008i	−0.0754575	−	0.281611i
$562$	−16.0485	+	27.7968i	−0.676964	+	1.17254i
$563$	4.24963	+	7.36058i	0.179101	+	0.310211i	0.941573	−	0.336810i	$-0.109348\pi$
$563$	4.24963	+	7.36058i	0.179101	+	0.310211i	−0.762472	+	0.647021i	$0.776015\pi$
$564$	3.10268	−	3.10268i	0.130646	−	0.130646i
$565$	−1.89912	+	7.08762i	−0.0798967	+	0.298178i
$566$	14.4221	+	3.86439i	0.606206	+	0.162432i
$567$	−2.12862	+	1.57130i	−0.0893937	+	0.0659883i
$568$	2.12128	+	3.67417i	0.0890070	+	0.154165i
$569$	34.7466	+	20.0610i	1.45665	+	0.841000i	0.998845	−	0.0480500i	$-0.0153007\pi$
$569$	34.7466	+	20.0610i	1.45665	+	0.841000i	0.457810	+	0.889050i	$0.348634\pi$
$570$	3.55595	+	13.2710i	0.148942	+	0.555861i
$571$		−	20.5233i		−	0.858873i	−0.903097	−	0.429436i	$-0.858712\pi$
$571$		−	20.5233i		−	0.858873i	0.903097	−	0.429436i	$-0.141288\pi$
$572$	−7.19910	−	4.78142i	−0.301010	−	0.199921i
$573$		−	3.62545i		−	0.151455i
$574$	−1.39515	−	12.3721i	−0.0582325	−	0.516400i
$575$	0.00721219	−	0.0124919i	0.000300769	−	0.000520947i
$576$	−0.866025	+	0.500000i	−0.0360844	+	0.0208333i
$577$	1.68654	+	1.68654i	0.0702115	+	0.0702115i	0.741341	−	0.671129i	$-0.234190\pi$
$577$	1.68654	+	1.68654i	0.0702115	+	0.0702115i	−0.671129	+	0.741341i	$0.734190\pi$
$578$	8.40387	+	2.25181i	0.349555	+	0.0936629i
$579$	18.1806	+	4.87149i	0.755562	+	0.202452i
$580$	11.6320	−	11.6320i	0.482990	−	0.482990i
$581$	7.17583	+	18.2787i	0.297703	+	0.758330i
$582$	−8.26202	−	4.77008i	−0.342472	−	0.197726i
$583$	26.6867	−	7.15069i	1.10525	−	0.296151i
$584$	12.8593			0.532121
$585$	−7.74259	−	0.485889i	−0.320117	−	0.0200890i
$586$		−	9.01035i		−	0.372214i
$587$	21.6179	−	5.79249i	0.892265	−	0.239082i	0.216573	−	0.976266i	$-0.430512\pi$
$587$	21.6179	−	5.79249i	0.892265	−	0.239082i	0.675691	+	0.737185i	$0.263845\pi$
$588$	4.76216	+	5.13048i	0.196388	+	0.211578i
$589$	−6.76146	+	3.90373i	−0.278601	+	0.160850i
$590$	−1.77068	+	1.77068i	−0.0728978	+	0.0728978i
$591$	−2.51822	+	9.39811i	−0.103586	+	0.386587i
$592$	1.58196	−	5.90397i	0.0650183	−	0.242652i
$593$	2.97376	−	2.97376i	0.122118	−	0.122118i	−0.643407	−	0.765525i	$-0.722480\pi$
$593$	2.97376	−	2.97376i	0.122118	−	0.122118i	0.765525	+	0.643407i	$0.222480\pi$
$594$	−2.07581	+	1.19847i	−0.0851715	+	0.0491738i
$595$	−10.2241	+	12.8231i	−0.419149	+	0.525695i
$596$	−21.2876	+	5.70398i	−0.871973	+	0.233644i
$597$		−	15.5718i		−	0.637312i
$598$	0.140104	+	0.00879227i	0.00572928	+	0.000359543i
$599$	47.1190			1.92523			0.962615	−	0.270872i	$-0.0873120\pi$
$599$	47.1190			1.92523			0.962615	+	0.270872i	$0.0873120\pi$
$600$	0.357856	−	0.0958873i	0.0146094	−	0.00391458i
$601$	−3.34359	−	1.93042i	−0.136388	−	0.0787436i	0.430254	−	0.902708i	$-0.358424\pi$
$601$	−3.34359	−	1.93042i	−0.136388	−	0.0787436i	−0.566641	+	0.823965i	$0.691758\pi$
$602$	1.47064	+	3.74611i	0.0599387	+	0.152680i
$603$	−0.915195	+	0.915195i	−0.0372696	+	0.0372696i
$604$	−0.798169	−	0.213869i	−0.0324770	−	0.00870220i
$605$	10.9209	+	2.92625i	0.443998	+	0.118969i
$606$	0.890862	+	0.890862i	0.0361888	+	0.0361888i
$607$	−31.0344	+	17.9177i	−1.25965	+	0.727259i	−0.973006	−	0.230779i	$-0.925873\pi$
$607$	−31.0344	+	17.9177i	−1.25965	+	0.727259i	−0.286643	+	0.958038i	$0.592539\pi$
$608$	3.19273	−	5.52996i	0.129482	−	0.224270i
$609$	−20.1004	+	2.26665i	−0.814509	+	0.0918493i
$610$			10.9910i			0.445011i
$611$	−13.1787	−	8.75290i	−0.533153	−	0.354104i
$612$			2.88092i			0.116454i
$613$	−6.46670	−	24.1340i	−0.261187	−	0.974765i	−0.964543	−	0.263926i	$-0.914982\pi$
$613$	−6.46670	−	24.1340i	−0.261187	−	0.974765i	0.703355	−	0.710838i	$-0.251684\pi$
$614$	15.5400	+	8.97201i	0.627142	+	0.362081i
$615$	−5.06262	−	8.76871i	−0.204144	−	0.353588i
$616$	3.76630	+	5.10217i	0.151749	+	0.205572i
$617$	15.8325	+	4.24230i	0.637392	+	0.170789i	0.563022	−	0.826442i	$-0.309639\pi$
$617$	15.8325	+	4.24230i	0.637392	+	0.170789i	0.0743701	+	0.997231i	$0.476305\pi$
$618$	−3.44392	+	12.8529i	−0.138535	+	0.517018i
$619$	−23.0434	+	23.0434i	−0.926191	+	0.926191i	−0.997457	−	0.0712663i	$-0.977296\pi$
$619$	−23.0434	+	23.0434i	−0.926191	+	0.926191i	0.0712663	+	0.997457i	$0.477296\pi$
$620$	−1.31540	−	2.27833i	−0.0528276	−	0.0915000i
$621$	0.0194671	−	0.0337181i	0.000781189	−	0.00135306i
$622$	5.12063	+	19.1104i	0.205318	+	0.766259i
$623$	−0.0579225	+	0.384531i	−0.00232061	+	0.0154059i
$624$	2.38482	+	2.70419i	0.0954693	+	0.108254i
$625$	23.0103			0.920414
$626$	28.2290	−	7.56393i	1.12826	−	0.302315i
$627$	7.65277	−	13.2550i	0.305622	−	0.529353i
$628$	4.59356	+	7.95628i	0.183303	+	0.317490i
$629$	−12.4513	−	12.4513i	−0.496467	−	0.496467i
$630$	5.21791	+	2.27598i	0.207886	+	0.0906771i
$631$	10.0475	−	37.4979i	0.399986	−	1.49277i	−0.413132	−	0.910671i	$-0.635565\pi$
$631$	10.0475	−	37.4979i	0.399986	−	1.49277i	0.813118	−	0.582098i	$-0.197768\pi$
$632$	−8.15064	−	8.15064i	−0.324215	−	0.324215i
$633$	−12.8293	+	7.40701i	−0.509919	+	0.294402i
$634$	−8.61958	−	4.97652i	−0.342327	−	0.197643i
$635$	−12.0742	−	45.0614i	−0.479149	−	1.78821i
$636$	−11.5264			−0.457053
$637$	14.7362	−	20.4901i	0.583870	−	0.811847i
$638$	−18.3255			−0.725515
$639$	−1.09806	−	4.09800i	−0.0434384	−	0.162114i
$640$	1.86337	+	1.07582i	0.0736561	+	0.0425254i
$641$	7.00206	−	4.04264i	0.276565	−	0.159675i	−0.355302	−	0.934751i	$-0.615622\pi$
$641$	7.00206	−	4.04264i	0.276565	−	0.159675i	0.631867	+	0.775077i	$0.282289\pi$
$642$	−12.5401	−	12.5401i	−0.494919	−	0.494919i
$643$	10.2143	−	38.1203i	0.402813	−	1.50332i	−0.405242	−	0.914210i	$-0.632813\pi$
$643$	10.2143	−	38.1203i	0.402813	−	1.50332i	0.808054	−	0.589108i	$-0.200521\pi$
$644$	−0.0944193	−	0.0411843i	−0.00372064	−	0.00162289i
$645$	2.31424	+	2.31424i	0.0911233	+	0.0911233i
$646$	−9.19797	−	15.9314i	−0.361889	−	0.626811i
$647$	0.155537	−	0.269397i	0.00611478	−	0.0105911i	−0.862952	−	0.505286i	$-0.831387\pi$
$647$	0.155537	−	0.269397i	0.00611478	−	0.0105911i	0.869067	+	0.494695i	$0.164720\pi$
$648$	0.965926	−	0.258819i	0.0379452	−	0.0101674i
$649$	2.78961			0.109502
$650$	−0.594127	−	1.19638i	−0.0233036	−	0.0469260i
$651$	−0.481849	+	3.19886i	−0.0188851	+	0.125373i
$652$	−0.199027	−	0.742780i	−0.00779451	−	0.0290895i
$653$	−21.4956	+	37.2315i	−0.841188	+	1.45698i	0.0477023	+	0.998862i	$0.484810\pi$
$653$	−21.4956	+	37.2315i	−0.841188	+	1.45698i	−0.888891	+	0.458119i	$0.848523\pi$
$654$	−0.421282	−	0.729681i	−0.0164734	−	0.0285328i
$655$	7.55526	−	7.55526i	0.295208	−	0.295208i
$656$	−1.21796	+	4.54549i	−0.0475534	+	0.177472i
$657$	−12.4211	−	3.32823i	−0.484594	−	0.129847i
$658$	6.89461	+	9.34006i	0.268780	+	0.364113i
$659$	−8.12809	−	14.0783i	−0.316626	−	0.548412i	0.663156	−	0.748481i	$-0.269217\pi$
$659$	−8.12809	−	14.0783i	−0.316626	−	0.548412i	−0.979782	+	0.200069i	$0.935883\pi$
$660$	4.46638	+	2.57866i	0.173854	+	0.100374i
$661$	8.96825	+	33.4700i	0.348824	+	1.30183i	0.888080	+	0.459688i	$0.152039\pi$
$661$	8.96825	+	33.4700i	0.348824	+	1.30183i	−0.539256	+	0.842142i	$0.681294\pi$
$662$			2.17741i			0.0846275i
$663$	10.1820	−	2.05474i	0.395437	−	0.0797995i
$664$		−	7.42202i		−	0.288030i
$665$	−36.1214	+	4.07328i	−1.40073	+	0.157955i
$666$	−3.05612	+	5.29336i	−0.118422	+	0.205113i
$667$	0.257788	−	0.148834i	0.00998158	−	0.00576287i
$668$	3.49953	+	3.49953i	0.135401	+	0.135401i
$669$	−17.9491	−	4.80944i	−0.693951	−	0.185944i
$670$	2.68993	+	0.720764i	0.103921	+	0.0278455i
$671$	8.65785	−	8.65785i	0.334233	−	0.334233i
$672$	−0.966829	−	2.46277i	−0.0372962	−	0.0950035i
$673$	−23.1587	−	13.3707i	−0.892703	−	0.515403i	−0.0178776	−	0.999840i	$-0.505691\pi$
$673$	−23.1587	−	13.3707i	−0.892703	−	0.515403i	−0.874826	+	0.484438i	$0.839024\pi$
$674$	−12.2769	+	3.28959i	−0.472889	+	0.126710i
$675$	−0.370480			−0.0142598
$676$	7.85650	−	10.3574i	0.302173	−	0.398361i
$677$		−	9.16406i		−	0.352203i	−0.984372	−	0.176102i	$-0.943651\pi$
$677$		−	9.16406i		−	0.352203i	0.984372	−	0.176102i	$-0.0563488\pi$
$678$	−3.29407	+	0.882643i	−0.126508	+	0.0338977i
$679$	15.7356	−	19.7356i	0.603877	−	0.757382i
$680$	5.36821	−	3.09934i	0.205861	−	0.118854i
$681$	2.14269	−	2.14269i	0.0821082	−	0.0821082i
$682$	−0.758528	+	2.83086i	−0.0290455	+	0.108399i
$683$	−1.95099	+	7.28118i	−0.0746525	+	0.278607i	−0.993154	−	0.116810i	$-0.962733\pi$
$683$	−1.95099	+	7.28118i	−0.0746525	+	0.278607i	0.918502	+	0.395417i	$0.129400\pi$
$684$	−4.51520	+	4.51520i	−0.172643	+	0.172643i
$685$	30.7206	−	17.7365i	1.17377	−	0.677678i
$686$	−15.2993	+	10.4371i	−0.584129	+	0.398489i
$687$	17.5492	−	4.70228i	0.669542	−	0.179403i
$688$		−	1.52109i		−	0.0579912i
$689$	8.22093	+	40.7379i	0.313193	+	1.55199i
$690$	−0.0837722			−0.00318915
$691$	−20.5374	+	5.50298i	−0.781279	+	0.209343i	−0.627349	−	0.778739i	$-0.715860\pi$
$691$	−20.5374	+	5.50298i	−0.781279	+	0.209343i	−0.153931	+	0.988082i	$0.549193\pi$
$692$	−11.8501	−	6.84166i	−0.450473	−	0.260081i
$693$	−2.31743	−	5.90311i	−0.0880318	−	0.224241i
$694$	3.64907	−	3.64907i	0.138517	−	0.138517i
$695$	−34.0363	−	9.12000i	−1.29107	−	0.345941i
$696$	7.38488	+	1.97877i	0.279923	+	0.0750052i
$697$	9.58633	+	9.58633i	0.363108	+	0.363108i
$698$	−18.7868	+	10.8465i	−0.711089	+	0.410548i
$699$	−9.80244	+	16.9783i	−0.370762	+	0.642179i
$700$	0.109837	+	0.974025i	0.00415146	+	0.0368147i
$701$			29.8466i			1.12729i	0.826016	+	0.563646i	$0.190602\pi$
$701$			29.8466i			1.12729i	−0.826016	+	0.563646i	$0.809398\pi$
$702$	−1.60367	−	3.22928i	−0.0605265	−	0.121881i
$703$		−	39.0294i		−	1.47202i
$704$	−0.620373	−	2.31526i	−0.0233812	−	0.0872598i
$705$	8.17617	+	4.72051i	0.307932	+	0.177785i
$706$	8.76631	+	15.1837i	0.329925	+	0.571446i
$707$	−2.68178	+	1.97963i	−0.100859	+	0.0744516i
$708$	−1.12417	−	0.301220i	−0.0422488	−	0.0113205i
$709$	−10.7448	+	40.1002i	−0.403530	+	1.50599i	0.403221	+	0.915103i	$0.367891\pi$
$709$	−10.7448	+	40.1002i	−0.403530	+	1.50599i	−0.806751	+	0.590892i	$0.798776\pi$
$710$	−6.45478	+	6.45478i	−0.242244	+	0.242244i
$711$	5.76337	+	9.98245i	0.216143	+	0.374371i
$712$	0.0734894	−	0.127287i	0.00275413	−	0.00477029i
$713$	−0.0123210	−	0.0459827i	−0.000461426	−	0.00172207i
$714$	−7.53716	−	1.13533i	−0.282071	−	0.0424888i
$715$	5.92826	−	17.6247i	0.221704	−	0.659127i
$716$	14.4830			0.541256
$717$	13.8774	−	3.71844i	0.518262	−	0.138868i
$718$	8.12789	−	14.0779i	0.303330	−	0.525383i
$719$	15.1205	+	26.1894i	0.563898	+	0.976700i	0.997151	+	0.0754275i	$0.0240322\pi$
$719$	15.1205	+	26.1894i	0.563898	+	0.976700i	−0.433253	+	0.901272i	$0.642635\pi$
$720$	−1.52143	−	1.52143i	−0.0567005	−	0.0567005i
$721$	−32.2689	−	14.0752i	−1.20176	−	0.524190i
$722$	5.63552	−	21.0321i	0.209732	−	0.782732i
$723$	−12.9519	−	12.9519i	−0.481687	−	0.481687i
$724$	15.1354	−	8.73845i	0.562504	−	0.324762i
$725$	−2.45299	−	1.41623i	−0.0911016	−	0.0525975i
$726$	1.36001	+	5.07564i	0.0504748	+	0.188375i
$727$	−28.0253			−1.03940			−0.519701	−	0.854348i	$-0.673957\pi$
$727$	−28.0253			−1.03940			−0.519701	+	0.854348i	$0.673957\pi$
$728$	−8.01462	+	5.17358i	−0.297042	+	0.191746i
$729$	−1.00000			−0.0370370
$730$	7.16113	+	26.7257i	0.265045	+	0.989162i
$731$	−3.79505	−	2.19107i	−0.140365	−	0.0810397i
$732$	−4.42383	+	2.55410i	−0.163510	+	0.0944023i
$733$	14.4076	+	14.4076i	0.532158	+	0.532158i	0.921214	−	0.389056i	$-0.127199\pi$
$733$	14.4076	+	14.4076i	0.532158	+	0.532158i	−0.389056	+	0.921214i	$0.627199\pi$
$734$	9.24656	−	34.5086i	0.341297	−	1.27374i
$735$	−8.01081	+	12.7544i	−0.295483	+	0.470451i
$736$	0.0275307	+	0.0275307i	0.00101479	+	0.00101479i
$737$	−1.55116	−	2.68668i	−0.0571376	−	0.0989652i
$738$	2.35292	−	4.07538i	0.0866121	−	0.150017i
$739$	44.8971	−	12.0301i	1.65157	−	0.442536i	0.691515	−	0.722362i	$-0.256943\pi$
$739$	44.8971	−	12.0301i	1.65157	−	0.442536i	0.960051	+	0.279826i	$0.0902768\pi$
$740$	13.1513			0.483451
$741$	19.1784	+	12.7377i	0.704537	+	0.467932i
$742$	4.54242	−	30.1559i	0.166757	−	1.10706i
$743$	3.60806	+	13.4654i	0.132367	+	0.493999i	0.999995	−	0.00321437i	$-0.00102317\pi$
$743$	3.60806	+	13.4654i	0.132367	+	0.493999i	−0.867628	+	0.497214i	$0.834357\pi$
$744$	0.611348	−	1.05889i	0.0224131	−	0.0388206i
$745$	−23.7094	−	41.0658i	−0.868644	−	1.50454i
$746$	23.7467	−	23.7467i	0.869427	−	0.869427i
$747$	−1.92096	+	7.16912i	−0.0702843	+	0.262305i
$748$	−6.67008	−	1.78724i	−0.243882	−	0.0653481i
$749$	37.7498	−	27.8660i	1.37935	−	1.01820i
$750$	5.77765	+	10.0072i	0.210970	+	0.365411i
$751$	−18.3876	−	10.6161i	−0.670972	−	0.387386i	0.125473	−	0.992097i	$-0.459955\pi$
$751$	−18.3876	−	10.6161i	−0.670972	−	0.387386i	−0.796445	+	0.604711i	$0.793288\pi$
$752$	−1.13566	−	4.23833i	−0.0414132	−	0.154556i
$753$		−	16.7558i		−	0.610614i
$754$	1.72651	−	27.5117i	0.0628757	−	1.00192i
$755$		−	1.77795i		−	0.0647062i
$756$	0.296473	+	2.62909i	0.0107826	+	0.0956190i
$757$	10.3475	−	17.9224i	0.376087	−	0.651402i	−0.614402	−	0.788993i	$-0.710603\pi$
$757$	10.3475	−	17.9224i	0.376087	−	0.651402i	0.990489	+	0.137591i	$0.0439361\pi$
$758$	−11.8696	+	6.85291i	−0.431123	+	0.248909i
$759$	0.0659894	+	0.0659894i	0.00239526	+	0.00239526i
$760$	13.2710	+	3.55595i	0.481389	+	0.128988i
$761$	40.5742	+	10.8718i	1.47081	+	0.394103i	0.903210	−	0.429200i	$-0.141204\pi$
$761$	40.5742	+	10.8718i	1.47081	+	0.394103i	0.567603	+	0.823303i	$0.307871\pi$
$762$	15.3313	−	15.3313i	0.555393	−	0.555393i
$763$	2.07504	−	0.814614i	0.0751215	−	0.0294910i
$764$	−3.13973	−	1.81273i	−0.113592	−	0.0655821i
$765$	−5.98746	+	1.60433i	−0.216477	+	0.0580048i
$766$	−13.7241			−0.495871
$767$	−0.262819	+	4.18799i	−0.00948983	+	0.151220i
$768$			1.00000i			0.0360844i
$769$	46.1610	−	12.3688i	1.66461	−	0.446030i	0.700959	−	0.713202i	$-0.252756\pi$
$769$	46.1610	−	12.3688i	1.66461	−	0.446030i	0.963649	+	0.267172i	$0.0860891\pi$
$770$	−8.50654	+	10.6689i	−0.306554	+	0.384480i
$771$	−23.7990	+	13.7403i	−0.857098	+	0.494846i
$772$	13.3092	−	13.3092i	0.479007	−	0.479007i
$773$	5.91290	−	22.0672i	0.212672	−	0.793703i	−0.774301	−	0.632817i	$-0.781898\pi$
$773$	5.91290	−	22.0672i	0.212672	−	0.793703i	0.986973	−	0.160886i	$-0.0514350\pi$
$774$	−0.393688	+	1.46926i	−0.0141508	+	0.0528116i
$775$	−0.320308	+	0.320308i	−0.0115058	+	0.0115058i
$776$	−8.26202	+	4.77008i	−0.296589	+	0.171236i
$777$	−12.6443	−	10.0816i	−0.453612	−	0.361675i
$778$	31.4978	−	8.43981i	1.12925	−	0.302582i
$779$			30.0489i			1.07661i
$780$	−4.29209	+	6.46233i	−0.153681	+	0.231389i
$781$	10.1692			0.363881
$782$	0.108344	−	0.0290308i	0.00387439	−	0.00103814i
$783$	−6.62110	−	3.82269i	−0.236619	−	0.136612i
$784$	6.82421	−	1.55891i	0.243722	−	0.0556752i
$785$	−13.9776	+	13.9776i	−0.498882	+	0.498882i
$786$	4.79667	+	1.28527i	0.171092	+	0.0458439i
$787$	−4.25101	−	1.13906i	−0.151532	−	0.0406029i	0.182255	−	0.983251i	$-0.441660\pi$
$787$	−4.25101	−	1.13906i	−0.151532	−	0.0406029i	−0.333788	+	0.942648i	$0.608327\pi$
$788$	6.87989	+	6.87989i	0.245086	+	0.245086i
$789$	−25.1500	+	14.5204i	−0.895365	+	0.516939i
$790$	12.4007	−	21.4786i	0.441195	−	0.764173i
$791$	−1.01105	−	8.96590i	−0.0359489	−	0.318791i
$792$			2.39694i			0.0851715i
$793$	12.1822	+	13.8135i	0.432601	+	0.490533i
$794$		−	13.8554i		−	0.491709i
$795$	−6.41888	−	23.9556i	−0.227654	−	0.849617i
$796$	−13.4856	−	7.78591i	−0.477984	−	0.275964i
$797$	−23.8327	−	41.2795i	−0.844199	−	1.46220i	−0.886315	−	0.463083i	$-0.846743\pi$
$797$	−23.8327	−	41.2795i	−0.844199	−	1.46220i	0.0421161	−	0.999113i	$-0.486590\pi$
$798$	−10.0334	−	13.5922i	−0.355180	−	0.481159i
$799$	−12.2103	−	3.27174i	−0.431969	−	0.115746i
$800$	0.0958873	−	0.357856i	0.00339013	−	0.0126521i
$801$	−0.103930	+	0.103930i	−0.00367217	+	0.00367217i
$802$	18.6038	+	32.2227i	0.656923	+	1.13782i
$803$	15.4115	−	26.6935i	0.543859	−	0.941991i
$804$	0.334985	+	1.25018i	0.0118140	+	0.0440904i
$805$	0.0330136	−	0.219168i	0.00116358	−	0.00772466i
$806$	−4.17845	−	1.40547i	−0.147180	−	0.0495054i
$807$	−20.5431			−0.723151
$808$	1.21694	−	0.326078i	0.0428118	−	0.0114714i
$809$	−7.51199	+	13.0111i	−0.264107	+	0.457447i	−0.967329	−	0.253523i	$-0.918411\pi$
$809$	−7.51199	+	13.0111i	−0.264107	+	0.457447i	0.703222	+	0.710970i	$0.251744\pi$
$810$	1.07582	+	1.86337i	0.0378003	+	0.0654721i
$811$	2.89047	+	2.89047i	0.101498	+	0.101498i	0.756032	−	0.654534i	$-0.227135\pi$
$811$	2.89047	+	2.89047i	0.101498	+	0.101498i	−0.654534	+	0.756032i	$0.727135\pi$
$812$	−8.08722	+	18.5408i	−0.283806	+	0.650654i
$813$	−0.577838	+	2.15652i	−0.0202657	+	0.0756325i
$814$	−10.3596	−	10.3596i	−0.363103	−	0.363103i
$815$	1.43290	−	0.827283i	0.0501922	−	0.0289785i
$816$	2.49495	+	1.44046i	0.0873406	+	0.0504261i
$817$	−2.51388	−	9.38191i	−0.0879494	−	0.328232i
$818$	3.93658			0.137639
$819$	9.08055	−	2.92296i	0.317300	−	0.102136i
$820$	−10.1252			−0.353588
$821$	−0.373907	−	1.39544i	−0.0130494	−	0.0487011i	0.959094	−	0.283087i	$-0.0913586\pi$
$821$	−0.373907	−	1.39544i	−0.0130494	−	0.0487011i	−0.972144	+	0.234386i	$0.924692\pi$
$822$	14.2778	+	8.24329i	0.497995	+	0.287518i
$823$	32.8533	−	18.9679i	1.14519	−	0.661178i	0.197482	−	0.980306i	$-0.436724\pi$
$823$	32.8533	−	18.9679i	1.14519	−	0.661178i	0.947711	+	0.319129i	$0.103390\pi$
$824$	9.40895	+	9.40895i	0.327776	+	0.327776i
$825$	0.229836	−	0.857760i	0.00800186	−	0.0298634i
$826$	1.23108	−	2.82238i	0.0428348	−	0.0982032i
$827$	−20.6807	−	20.6807i	−0.719137	−	0.719137i	0.249291	−	0.968429i	$-0.419802\pi$
$827$	−20.6807	−	20.6807i	−0.719137	−	0.719137i	−0.968429	+	0.249291i	$0.919802\pi$
$828$	−0.0194671	−	0.0337181i	−0.000676530	−	0.00117178i
$829$	16.5981	−	28.7487i	0.576475	−	0.998483i	−0.419405	−	0.907799i	$-0.637761\pi$
$829$	16.5981	−	28.7487i	0.576475	−	0.998483i	0.995880	−	0.0906842i	$-0.0289054\pi$
$830$	15.4253	−	4.13320i	0.535421	−	0.143466i
$831$	12.2379			0.424528
$832$	3.53430	−	0.713225i	0.122530	−	0.0247266i
$833$	5.94060	−	19.2716i	0.205829	−	0.667720i
$834$	−4.23864	−	15.8188i	−0.146772	−	0.547762i
$835$	−5.32431	+	9.22197i	−0.184255	+	0.319139i
$836$	−7.65277	−	13.2550i	−0.264676	−	0.458433i
$837$	−0.864576	+	0.864576i	−0.0298841	+	0.0298841i
$838$	−2.26262	+	8.44422i	−0.0781610	+	0.291701i
$839$	−10.0733	−	2.69912i	−0.347767	−	0.0931840i	0.0807071	−	0.996738i	$-0.474282\pi$
$839$	−10.0733	−	2.69912i	−0.347767	−	0.0931840i	−0.428474	+	0.903554i	$0.640949\pi$
$840$	4.58001	−	3.38085i	0.158025	−	0.116650i
$841$	−14.7260	−	25.5062i	−0.507793	−	0.879522i
$842$	−12.1583	−	7.01962i	−0.419004	−	0.241912i
$843$	−8.30730	−	31.0033i	−0.286119	−	1.06781i
$844$			14.8140i			0.509919i
$845$	25.9011	+	10.5604i	0.891024	+	0.363290i
$846$			4.38785i			0.150857i
$847$	−13.8150	+	1.55787i	−0.474690	+	0.0535291i
$848$	−5.76321	+	9.98218i	−0.197910	+	0.342789i
$849$	−12.9305	+	7.46543i	−0.443774	+	0.256213i
$850$	−0.754711	−	0.754711i	−0.0258864	−	0.0258864i
$851$	0.229867	+	0.0615927i	0.00787974	+	0.00211137i
$852$	−4.09800	−	1.09806i	−0.140395	−	0.0376188i
$853$	−9.65024	+	9.65024i	−0.330418	+	0.330418i	−0.852745	−	0.522327i	$-0.825064\pi$
$853$	−9.65024	+	9.65024i	−0.330418	+	0.330418i	0.522327	+	0.852745i	$0.325064\pi$
$854$	−4.93876	−	12.5803i	−0.169001	−	0.430490i
$855$	−11.8984	−	6.86957i	−0.406918	−	0.234934i
$856$	−17.1301	+	4.59000i	−0.585496	+	0.156883i
$857$	−1.49546			−0.0510838			−0.0255419	−	0.999674i	$-0.508131\pi$
$857$	−1.49546			−0.0510838			−0.0255419	+	0.999674i	$0.508131\pi$
$858$	8.47151	−	1.70956i	0.289213	−	0.0583633i
$859$		−	11.7495i		−	0.400886i	−0.979705	−	0.200443i	$-0.935762\pi$
$859$		−	11.7495i		−	0.400886i	0.979705	−	0.200443i	$-0.0642382\pi$
$860$	3.16132	−	0.847072i	0.107800	−	0.0288849i
$861$	9.73489	+	7.76185i	0.331764	+	0.264523i
$862$	8.89488	−	5.13546i	0.302961	−	0.174914i
$863$	−27.1845	+	27.1845i	−0.925373	+	0.925373i	−0.997402	−	0.0720299i	$-0.977052\pi$
$863$	−27.1845	+	27.1845i	−0.925373	+	0.925373i	0.0720299	+	0.997402i	$0.477052\pi$
$864$	0.258819	−	0.965926i	0.00880520	−	0.0328615i
$865$	7.62001	−	28.4383i	0.259088	−	0.966930i
$866$	8.61036	−	8.61036i	0.292592	−	0.292592i
$867$	−7.53470	+	4.35016i	−0.255892	+	0.147739i
$868$	2.52937	+	2.01672i	0.0858524	+	0.0684521i
$869$	−26.6875	+	7.15088i	−0.905310	+	0.242577i
$870$			16.4501i			0.557709i
$871$	4.17960	−	2.07560i	0.141620	−	0.0703289i
$872$	−0.842563			−0.0285328
$873$	9.21508	−	2.46917i	0.311883	−	0.0835689i
$874$	0.215305	+	0.124306i	0.00728281	+	0.00420473i
$875$	−28.4581	+	11.1720i	−0.962058	+	0.377682i
$876$	−9.09290	+	9.09290i	−0.307220	+	0.307220i
$877$	−1.88382	−	0.504769i	−0.0636122	−	0.0170448i	0.226873	−	0.973924i	$-0.427150\pi$
$877$	−1.88382	−	0.504769i	−0.0636122	−	0.0170448i	−0.290485	+	0.956880i	$0.593817\pi$
$878$	−38.7663	−	10.3874i	−1.30830	−	0.350557i
$879$	6.37128	+	6.37128i	0.214898	+	0.214898i
$880$	4.46638	−	2.57866i	0.150562	−	0.0869268i
$881$	27.7429	−	48.0520i	0.934681	−	1.61891i	0.159478	−	0.987201i	$-0.449019\pi$
$881$	27.7429	−	48.0520i	0.934681	−	1.61891i	0.775202	−	0.631713i	$-0.217648\pi$
$882$	−6.99515	−	0.260448i	−0.235539	−	0.00876972i
$883$			13.4332i			0.452064i	0.974120	+	0.226032i	$0.0725755\pi$
$883$			13.4332i			0.452064i	−0.974120	+	0.226032i	$0.927425\pi$
$884$	3.31156	−	9.84527i	0.111380	−	0.331132i
$885$		−	2.50412i		−	0.0841751i
$886$	−5.62008	−	20.9744i	−0.188810	−	0.704650i
$887$	2.52468	+	1.45762i	0.0847703	+	0.0489422i	0.541786	−	0.840516i	$-0.317748\pi$
$887$	2.52468	+	1.45762i	0.0847703	+	0.0489422i	−0.457016	+	0.889459i	$0.651082\pi$
$888$	3.05612	+	5.29336i	0.102557	+	0.177633i
$889$	34.0684	+	46.1521i	1.14262	+	1.54789i
$890$	0.305468	+	0.0818500i	0.0102393	+	0.00274362i
$891$	0.620373	−	2.31526i	0.0207833	−	0.0775643i
$892$	−13.1396	+	13.1396i	−0.439948	+	0.439948i
$893$	−14.0092	−	24.2646i	−0.468800	−	0.811985i
$894$	11.0193	−	19.0859i	0.368539	−	0.638328i
$895$	8.06536	+	30.1003i	0.269595	+	1.00614i
$896$	−2.61624	−	0.394087i	−0.0874023	−	0.0131655i
$897$	−0.105286	+	0.0928514i	−0.00351538	+	0.00310022i
$898$	12.4326			0.414880
$899$	−9.02946	+	2.41944i	−0.301149	+	0.0806927i
$900$	−0.185240	+	0.320845i	−0.00617467	+	0.0106948i
$901$	16.6033	+	28.7578i	0.553137	+	0.958062i
$902$	7.97588	+	7.97588i	0.265568	+	0.265568i
$903$	−3.68880	−	1.60900i	−0.122755	−	0.0535442i
$904$	−0.882643	+	3.29407i	−0.0293563	+	0.109559i
$905$	26.5900	+	26.5900i	0.883880	+	0.883880i
$906$	0.715619	−	0.413163i	0.0237748	−	0.0137264i
$907$	31.5694	+	18.2266i	1.04824	+	0.605204i	0.922157	−	0.386816i	$-0.126425\pi$
$907$	31.5694	+	18.2266i	1.04824	+	0.605204i	0.126086	+	0.992019i	$0.459758\pi$
$908$	−0.784280	−	2.92697i	−0.0260272	−	0.0971350i
$909$	−1.25987			−0.0417872
$910$	−15.2155	−	13.7758i	−0.504390	−	0.456665i
$911$	24.6465			0.816574			0.408287	−	0.912854i	$-0.366126\pi$
$911$	24.6465			0.816574			0.408287	+	0.912854i	$0.366126\pi$
$912$	1.65268	+	6.16787i	0.0547256	+	0.204239i
$913$	−15.4067	−	8.89507i	−0.509888	−	0.294384i
$914$	−7.00630	+	4.04509i	−0.231748	+	0.133800i
$915$	−7.77179	−	7.77179i	−0.256928	−	0.256928i
$916$	4.70228	−	17.5492i	0.155368	−	0.579840i
$917$	−5.25287	+	12.0427i	−0.173465	+	0.397686i
$918$	−2.03711	−	2.03711i	−0.0672348	−	0.0672348i
$919$	18.5155	+	32.0698i	0.610771	+	1.05789i	0.991111	+	0.133040i	$0.0424737\pi$
$919$	18.5155	+	32.0698i	0.610771	+	1.05789i	−0.380340	+	0.924847i	$0.624193\pi$
$920$	−0.0418861	+	0.0725489i	−0.00138094	+	0.00239187i
$921$	−17.3326	+	4.64425i	−0.571128	+	0.153033i
$922$	−24.8058			−0.816934
$923$	−0.958070	+	15.2667i	−0.0315353	+	0.502511i
$924$	−6.27096	−	0.944603i	−0.206299	−	0.0310752i
$925$	−0.586086	−	2.18730i	−0.0192704	−	0.0719181i
$926$	−17.8187	+	30.8630i	−0.585560	+	1.01422i
$927$	−6.65313	−	11.5236i	−0.218518	−	0.378484i
$928$	5.40611	−	5.40611i	0.177464	−	0.177464i
$929$	−6.11544	+	22.8231i	−0.200641	+	0.748802i	0.790093	+	0.612987i	$0.210032\pi$
$929$	−6.11544	+	22.8231i	−0.200641	+	0.748802i	−0.990734	+	0.135816i	$0.956635\pi$
$930$	2.54115	+	0.680899i	0.0833276	+	0.0223276i
$931$	39.5145	−	20.8933i	1.29503	−	0.684752i
$932$	9.80244	+	16.9783i	0.321090	+	0.556143i
$933$	−17.1340	−	9.89229i	−0.560940	−	0.323859i
$934$	5.02720	+	18.7617i	0.164495	+	0.613903i
$935$		−	14.8578i		−	0.485903i
$936$	−3.59847	−	0.225823i	−0.117620	−	0.00738127i
$937$		−	5.43133i		−	0.177434i	−0.996057	−	0.0887169i	$-0.971723\pi$
$937$		−	5.43133i		−	0.177434i	0.996057	−	0.0887169i	$-0.0282766\pi$
$938$	−3.40278	+	0.383719i	−0.111105	+	0.0125289i
$939$	−14.6124	+	25.3094i	−0.476857	+	0.825941i
$940$	8.17617	−	4.72051i	0.266677	−	0.153966i
$941$	11.0955	+	11.0955i	0.361702	+	0.361702i	0.864439	−	0.502737i	$-0.167674\pi$
$941$	11.0955	+	11.0955i	0.361702	+	0.361702i	−0.502737	+	0.864439i	$0.667674\pi$
$942$	−8.87408	−	2.37780i	−0.289133	−	0.0774730i
$943$	−0.176975	−	0.0474204i	−0.00576311	−	0.00154422i
$944$	−0.822948	+	0.822948i	−0.0267847	+	0.0267847i
$945$	−5.29898	+	2.08026i	−0.172376	+	0.0676708i
$946$	−3.15750	−	1.82298i	−0.102659	−	0.0592703i
$947$	29.1250	−	7.80403i	0.946437	−	0.253597i	0.247587	−	0.968866i	$-0.420362\pi$
$947$	29.1250	−	7.80403i	0.946437	−	0.253597i	0.698850	+	0.715269i	$0.253696\pi$
$948$	11.5267			0.374371
$949$	38.6223	+	25.6518i	1.25373	+	0.832692i
$950$		−	2.36568i		−	0.0767529i
$951$	9.61389	−	2.57603i	0.311752	−	0.0835337i
$952$	−4.75181	+	5.95970i	−0.154007	+	0.193155i
$953$	27.2825	−	15.7515i	0.883765	−	0.510242i	0.0118673	−	0.999930i	$-0.496222\pi$
$953$	27.2825	−	15.7515i	0.883765	−	0.510242i	0.871898	+	0.489687i	$0.162889\pi$
$954$	8.15042	−	8.15042i	0.263879	−	0.263879i
$955$	2.01895	−	7.53484i	0.0653318	−	0.243822i
$956$	3.71844	−	13.8774i	0.120263	−	0.448828i
$957$	12.9581	−	12.9581i	0.418876	−	0.418876i
$958$	−24.1934	+	13.9681i	−0.781653	+	0.451288i
$959$	−27.1931	+	34.1055i	−0.878111	+	1.10132i
$960$	−2.07832	+	0.556883i	−0.0670774	+	0.0179733i
$961$		−	29.5050i		−	0.951775i
$962$	16.5286	−	14.5766i	0.532905	−	0.469969i
$963$	17.7344			0.571483
$964$	−17.6926	+	4.74073i	−0.569841	+	0.152689i
$965$	35.0723	+	20.2490i	1.12902	+	0.651838i
$966$	0.0958862	−	0.0376428i	0.00308509	−	0.00121114i
$967$	12.0337	−	12.0337i	0.386978	−	0.386978i	−0.486630	−	0.873608i	$-0.661774\pi$
$967$	12.0337	−	12.0337i	0.386978	−	0.386978i	0.873608	+	0.486630i	$0.161774\pi$
$968$	5.07564	+	1.36001i	0.163137	+	0.0437125i
$969$	17.7691	+	4.76122i	0.570826	+	0.152952i
$970$	−14.5147	−	14.5147i	−0.466039	−	0.466039i
$971$	17.9842	−	10.3832i	0.577140	−	0.333212i	−0.182856	−	0.983140i	$-0.558534\pi$
$971$	17.9842	−	10.3832i	0.577140	−	0.333212i	0.759996	+	0.649928i	$0.225201\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	43.0562	−	4.85529i	1.38032	−	0.155654i
$974$			4.91382i			0.157449i
$975$	1.26608	+	0.425860i	0.0405471	+	0.0136384i
$976$			5.10820i			0.163510i
$977$	5.39938	+	20.1508i	0.172741	+	0.644680i	0.996925	+	0.0783576i	$0.0249676\pi$
$977$	5.39938	+	20.1508i	0.172741	+	0.644680i	−0.824184	+	0.566322i	$0.808366\pi$
$978$	0.665958	+	0.384491i	0.0212950	+	0.0122947i
$979$	−0.176150	−	0.305100i	−0.00562976	−	0.00975104i
$980$	7.04019	+	13.3147i	0.224891	+	0.425324i
$981$	0.813854	+	0.218071i	0.0259843	+	0.00696248i
$982$	−6.72208	+	25.0872i	−0.214510	+	0.800563i
$983$	−26.7082	+	26.7082i	−0.851858	+	0.851858i	−0.990362	−	0.138503i	$-0.955771\pi$
$983$	−26.7082	+	26.7082i	−0.851858	+	0.851858i	0.138503	+	0.990362i	$0.455771\pi$
$984$	−2.35292	−	4.07538i	−0.0750083	−	0.129918i
$985$	−10.4673	+	18.1299i	−0.333516	+	0.577666i
$986$	−5.70068	−	21.2752i	−0.181546	−	0.677541i
$987$	−11.4796	−	1.72919i	−0.365401	−	0.0550409i
$988$	20.6204	−	10.2401i	0.656023	−	0.325782i
$989$	0.0592227			0.00188317
$990$	−4.98160	+	1.33482i	−0.158326	+	0.0424232i
$991$	−5.27410	+	9.13500i	−0.167537	+	0.290183i	−0.937553	−	0.347841i	$-0.886915\pi$
$991$	−5.27410	+	9.13500i	−0.167537	+	0.290183i	0.770016	+	0.638024i	$0.220248\pi$
$992$	−0.611348	−	1.05889i	−0.0194103	−	0.0336196i
$993$	−1.53966	−	1.53966i	−0.0488597	−	0.0488597i
$994$	4.48775	−	10.2886i	0.142343	−	0.326335i
$995$	8.67169	−	32.3632i	0.274911	−	1.02598i
$996$	5.24816	+	5.24816i	0.166294	+	0.166294i
$997$	38.8472	−	22.4285i	1.23030	−	0.710316i	0.263210	−	0.964738i	$-0.415219\pi$
$997$	38.8472	−	22.4285i	1.23030	−	0.710316i	0.967093	+	0.254422i	$0.0818853\pi$
$998$	−29.1185	−	16.8116i	−0.921730	−	0.532161i
$999$	−1.58196	−	5.90397i	−0.0500511	−	0.186793i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bx.a.97.7	✓	40
7.6	odd	2		546.2.bx.b.97.9	yes	40
13.11	odd	12		546.2.bx.b.349.9	yes	40
91.76	even	12	inner	546.2.bx.a.349.7	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bx.a.97.7	✓	40	1.1	even	1	trivial
546.2.bx.a.349.7	yes	40	91.76	even	12	inner
546.2.bx.b.97.9	yes	40	7.6	odd	2
546.2.bx.b.349.9	yes	40	13.11	odd	12

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bx (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.52143 - 1.52143i) q^{5} +(0.258819 - 0.965926i) q^{6} +(2.42509 + 1.05779i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.52143 - 1.52143i) q^{5} +(0.258819 - 0.965926i) q^{6} +(2.42509 + 1.05779i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(1.07582 - 1.86337i) q^{10} +(-2.31526 + 0.620373i) q^{11} +1.00000 q^{12} +(-0.713225 - 3.53430i) q^{13} +(-0.394087 + 2.61624i) q^{14} +(0.556883 + 2.07832i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.44046 - 2.49495i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(1.65268 - 6.16787i) q^{19} +(2.07832 + 0.556883i) q^{20} +(-1.57130 - 2.12862i) q^{21} +(-1.19847 - 2.07581i) q^{22} +(0.0337181 + 0.0194671i) q^{23} +(0.258819 + 0.965926i) q^{24} -0.370480i q^{25} +(3.22928 - 1.60367i) q^{26} -1.00000i q^{27} +(-2.62909 + 0.296473i) q^{28} +(3.82269 - 6.62110i) q^{29} +(-1.86337 + 1.07582i) q^{30} +(-0.864576 - 0.864576i) q^{31} +(0.965926 + 0.258819i) q^{32} +(2.31526 + 0.620373i) q^{33} +(2.03711 - 2.03711i) q^{34} +(-2.08026 - 5.29898i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(5.90397 - 1.58196i) q^{37} +6.38545 q^{38} +(-1.14948 + 3.41741i) q^{39} +2.15163i q^{40} +(-4.54549 + 1.21796i) q^{41} +(1.64941 - 2.06868i) q^{42} +(1.31731 - 0.760547i) q^{43} +(1.69489 - 1.69489i) q^{44} +(0.556883 - 2.07832i) q^{45} +(-0.0100769 + 0.0376076i) q^{46} +(3.10268 - 3.10268i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(4.76216 + 5.13048i) q^{49} +(0.357856 - 0.0958873i) q^{50} +2.88092i q^{51} +(2.38482 + 2.70419i) q^{52} -11.5264 q^{53} +(0.965926 - 0.258819i) q^{54} +(4.46638 + 2.57866i) q^{55} +(-0.966829 - 2.46277i) q^{56} +(-4.51520 + 4.51520i) q^{57} +(7.38488 + 1.97877i) q^{58} +(-1.12417 - 0.301220i) q^{59} +(-1.52143 - 1.52143i) q^{60} +(-4.42383 + 2.55410i) q^{61} +(0.611348 - 1.05889i) q^{62} +(0.296473 + 2.62909i) q^{63} +1.00000i q^{64} +(-4.29209 + 6.46233i) q^{65} +2.39694i q^{66} +(0.334985 + 1.25018i) q^{67} +(2.49495 + 1.44046i) q^{68} +(-0.0194671 - 0.0337181i) q^{69} +(4.58001 - 3.38085i) q^{70} +(-4.09800 - 1.09806i) q^{71} +(0.258819 - 0.965926i) q^{72} +(-9.09290 + 9.09290i) q^{73} +(3.05612 + 5.29336i) q^{74} +(-0.185240 + 0.320845i) q^{75} +(1.65268 + 6.16787i) q^{76} +(-6.27096 - 0.944603i) q^{77} +(-3.59847 - 0.225823i) q^{78} +11.5267 q^{79} +(-2.07832 + 0.556883i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.35292 - 4.07538i) q^{82} +(5.24816 + 5.24816i) q^{83} +(2.42509 + 1.05779i) q^{84} +(-1.60433 + 5.98746i) q^{85} +(1.07558 + 1.07558i) q^{86} +(-6.62110 + 3.82269i) q^{87} +(2.07581 + 1.19847i) q^{88} +(0.0380409 + 0.141971i) q^{89} +2.15163 q^{90} +(2.00892 - 9.32546i) q^{91} -0.0389343 q^{92} +(0.316457 + 1.18103i) q^{93} +(3.79999 + 2.19392i) q^{94} +(-11.8984 + 6.86957i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(2.46917 - 9.21508i) q^{97} +(-3.72313 + 5.92776i) q^{98} +(-1.69489 - 1.69489i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q - 8 * q^7 + 20 * q^9	\( 40 q - 8 q^{7} + 20 q^{9} + 8 q^{11} + 40 q^{12} - 8 q^{14} + 20 q^{16} + 16 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 32 q^{26} + 8 q^{28} - 8 q^{33} + 16 q^{34} - 32 q^{35} + 40 q^{37} - 16 q^{38} - 16 q^{39} - 4 q^{41} + 12 q^{42} + 24 q^{43} + 8 q^{44} - 4 q^{46} + 16 q^{47} - 4 q^{49} - 16 q^{50} - 8 q^{52} + 32 q^{53} - 72 q^{55} + 12 q^{56} + 8 q^{57} - 36 q^{58} + 84 q^{59} - 48 q^{61} - 4 q^{62} - 4 q^{63} - 16 q^{65} + 12 q^{68} - 8 q^{69} + 36 q^{70} - 40 q^{71} - 48 q^{73} + 8 q^{74} + 36 q^{75} + 16 q^{76} - 24 q^{77} - 8 q^{78} - 48 q^{79} - 20 q^{81} + 36 q^{83} - 8 q^{84} + 8 q^{85} - 8 q^{86} + 12 q^{89} - 48 q^{91} - 16 q^{92} - 24 q^{93} - 96 q^{95} + 8 q^{98} - 8 q^{99}+O(q^{100}) \) 40 * q - 8 * q^7 + 20 * q^9 + 8 * q^11 + 40 * q^12 - 8 * q^14 + 20 * q^16 + 16 * q^17 + 16 * q^19 + 4 * q^21 + 8 * q^22 + 32 * q^26 + 8 * q^28 - 8 * q^33 + 16 * q^34 - 32 * q^35 + 40 * q^37 - 16 * q^38 - 16 * q^39 - 4 * q^41 + 12 * q^42 + 24 * q^43 + 8 * q^44 - 4 * q^46 + 16 * q^47 - 4 * q^49 - 16 * q^50 - 8 * q^52 + 32 * q^53 - 72 * q^55 + 12 * q^56 + 8 * q^57 - 36 * q^58 + 84 * q^59 - 48 * q^61 - 4 * q^62 - 4 * q^63 - 16 * q^65 + 12 * q^68 - 8 * q^69 + 36 * q^70 - 40 * q^71 - 48 * q^73 + 8 * q^74 + 36 * q^75 + 16 * q^76 - 24 * q^77 - 8 * q^78 - 48 * q^79 - 20 * q^81 + 36 * q^83 - 8 * q^84 + 8 * q^85 - 8 * q^86 + 12 * q^89 - 48 * q^91 - 16 * q^92 - 24 * q^93 - 96 * q^95 + 8 * q^98 - 8 * q^99

Introduction

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