LMFDB - Embedded newform 546.2.bx.a.97.4

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			97.4
Character	$\chi$	$=$	546.97
Dual form			546.2.bx.a.349.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.258819 - 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.413783 + 0.413783i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(-2.23784 + 1.41140i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.292588 - 0.506778i) q^{10} +(3.08054 - 0.825428i) q^{11} +1.00000 q^{12} +(3.19595 - 1.66911i) q^{13} +(1.94250 + 1.79629i) q^{14} +(-0.151455 - 0.565237i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.52328 - 2.63841i) q^{17} +(0.707107 - 0.707107i) q^{18} +(0.927951 - 3.46316i) q^{19} +(-0.565237 - 0.151455i) q^{20} +(2.64373 - 0.103386i) q^{21} +(-1.59460 - 2.76194i) q^{22} +(6.31658 + 3.64688i) q^{23} +(-0.258819 - 0.965926i) q^{24} -4.65757i q^{25} +(-2.43941 - 2.65505i) q^{26} -1.00000i q^{27} +(1.23233 - 2.34123i) q^{28} +(0.955316 - 1.65466i) q^{29} +(-0.506778 + 0.292588i) q^{30} +(-1.43220 - 1.43220i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-3.08054 - 0.825428i) q^{33} +(-2.15425 + 2.15425i) q^{34} +(-1.50999 - 0.341968i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(8.56639 - 2.29536i) q^{37} -3.58533 q^{38} +(-3.60233 - 0.152479i) q^{39} +0.585177i q^{40} +(2.53250 - 0.678581i) q^{41} +(-0.784111 - 2.52689i) q^{42} +(-4.19550 + 2.42227i) q^{43} +(-2.25511 + 2.25511i) q^{44} +(-0.151455 + 0.565237i) q^{45} +(1.88776 - 7.04523i) q^{46} +(-6.97884 + 6.97884i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(3.01590 - 6.31699i) q^{49} +(-4.49887 + 1.20547i) q^{50} +3.04657i q^{51} +(-1.93321 + 3.04347i) q^{52} +1.08877 q^{53} +(-0.965926 + 0.258819i) q^{54} +(1.61622 + 0.933126i) q^{55} +(-2.58041 - 0.584385i) q^{56} +(-2.53521 + 2.53521i) q^{57} +(-1.84553 - 0.494508i) q^{58} +(-0.426056 - 0.114161i) q^{59} +(0.413783 + 0.413783i) q^{60} +(12.5873 - 7.26727i) q^{61} +(-1.01272 + 1.75408i) q^{62} +(-2.34123 - 1.23233i) q^{63} +1.00000i q^{64} +(2.01308 + 0.631777i) q^{65} +3.18921i q^{66} +(-3.77898 - 14.1033i) q^{67} +(2.63841 + 1.52328i) q^{68} +(-3.64688 - 6.31658i) q^{69} +(0.0604991 + 1.54705i) q^{70} +(3.82702 + 1.02545i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(0.831214 - 0.831214i) q^{73} +(-4.43429 - 7.68041i) q^{74} +(-2.32878 + 4.03357i) q^{75} +(0.927951 + 3.46316i) q^{76} +(-5.72876 + 6.19505i) q^{77} +(0.785067 + 3.51904i) q^{78} +3.09358 q^{79} +(0.565237 - 0.151455i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.31092 - 2.27058i) q^{82} +(8.79143 + 8.79143i) q^{83} +(-2.23784 + 1.41140i) q^{84} +(0.461418 - 1.72203i) q^{85} +(3.42561 + 3.42561i) q^{86} +(-1.65466 + 0.955316i) q^{87} +(2.76194 + 1.59460i) q^{88} +(0.813298 + 3.03527i) q^{89} +0.585177 q^{90} +(-4.79624 + 8.24597i) q^{91} -7.29376 q^{92} +(0.524220 + 1.95642i) q^{93} +(8.54730 + 4.93479i) q^{94} +(1.81696 - 1.04903i) q^{95} +(0.707107 + 0.707107i) q^{96} +(-3.09651 + 11.5563i) q^{97} +(-6.88232 - 1.27818i) q^{98} +(2.25511 + 2.25511i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

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
$5$	0.413783	+	0.413783i	0.185049	+	0.185049i	0.793552	−	0.608503i	$-0.208230\pi$
$5$	0.413783	+	0.413783i	0.185049	+	0.185049i	−0.608503	+	0.793552i	$0.708230\pi$
$6$	−0.258819	+	0.965926i	−0.105662	+	0.394338i
$7$	−2.23784	+	1.41140i	−0.845826	+	0.533459i
$7$	−2.23784	+	1.41140i	−0.845826	+	0.533459i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.292588	−	0.506778i	0.0925246	−	0.160257i
$11$	3.08054	−	0.825428i	0.928817	−	0.248876i	0.237467	−	0.971396i	$-0.423683\pi$
$11$	3.08054	−	0.825428i	0.928817	−	0.248876i	0.691350	+	0.722520i	$0.257016\pi$
$12$	1.00000			0.288675
$13$	3.19595	−	1.66911i	0.886396	−	0.462928i
$13$	3.19595	−	1.66911i	0.886396	−	0.462928i
$14$	1.94250	+	1.79629i	0.519156	+	0.480080i
$15$	−0.151455	−	0.565237i	−0.0391055	−	0.145944i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.52328	−	2.63841i	−0.369451	−	0.639907i	0.620029	−	0.784579i	$-0.287121\pi$
$17$	−1.52328	−	2.63841i	−0.369451	−	0.639907i	−0.989480	+	0.144671i	$0.953787\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	0.927951	−	3.46316i	0.212886	−	0.794503i	−0.774013	−	0.633169i	$-0.781754\pi$
$19$	0.927951	−	3.46316i	0.212886	−	0.794503i	0.986900	−	0.161334i	$-0.0515796\pi$
$20$	−0.565237	−	0.151455i	−0.126391	−	0.0338663i
$21$	2.64373	−	0.103386i	0.576909	−	0.0225607i
$22$	−1.59460	−	2.76194i	−0.339971	−	0.588847i
$23$	6.31658	+	3.64688i	1.31710	+	0.760427i	0.983261	−	0.182204i	$-0.0583230\pi$
$23$	6.31658	+	3.64688i	1.31710	+	0.760427i	0.333838	+	0.942631i	$0.391656\pi$
$24$	−0.258819	−	0.965926i	−0.0528312	−	0.197169i
$25$		−	4.65757i		−	0.931514i
$26$	−2.43941	−	2.65505i	−0.478408	−	0.520698i
$27$		−	1.00000i		−	0.192450i
$28$	1.23233	−	2.34123i	0.232889	−	0.442451i
$29$	0.955316	−	1.65466i	0.177398	−	0.307262i	−0.763591	−	0.645701i	$-0.776565\pi$
$29$	0.955316	−	1.65466i	0.177398	−	0.307262i	0.940988	+	0.338439i	$0.109899\pi$
$30$	−0.506778	+	0.292588i	−0.0925246	+	0.0534191i
$31$	−1.43220	−	1.43220i	−0.257230	−	0.257230i	0.566697	−	0.823927i	$-0.308221\pi$
$31$	−1.43220	−	1.43220i	−0.257230	−	0.257230i	−0.823927	+	0.566697i	$0.808221\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	−3.08054	−	0.825428i	−0.536253	−	0.143689i
$34$	−2.15425	+	2.15425i	−0.369451	+	0.369451i
$35$	−1.50999	−	0.341968i	−0.255236	−	0.0578032i
$36$	−0.866025	−	0.500000i	−0.144338	−	0.0833333i
$37$	8.56639	−	2.29536i	1.40831	−	0.377354i	0.526985	−	0.849874i	$-0.323322\pi$
$37$	8.56639	−	2.29536i	1.40831	−	0.377354i	0.881320	+	0.472520i	$0.156656\pi$
$38$	−3.58533			−0.581617
$39$	−3.60233	−	0.152479i	−0.576834	−	0.0244162i
$40$			0.585177i			0.0925246i
$41$	2.53250	−	0.678581i	0.395510	−	0.105977i	−0.0555817	−	0.998454i	$-0.517701\pi$
$41$	2.53250	−	0.678581i	0.395510	−	0.105977i	0.451092	+	0.892478i	$0.351035\pi$
$42$	−0.784111	−	2.52689i	−0.120991	−	0.389907i
$43$	−4.19550	+	2.42227i	−0.639808	+	0.369393i	−0.784540	−	0.620078i	$-0.787101\pi$
$43$	−4.19550	+	2.42227i	−0.639808	+	0.369393i	0.144733	+	0.989471i	$0.453768\pi$
$44$	−2.25511	+	2.25511i	−0.339971	+	0.339971i
$45$	−0.151455	+	0.565237i	−0.0225776	+	0.0842606i
$46$	1.88776	−	7.04523i	0.278336	−	1.03876i
$47$	−6.97884	+	6.97884i	−1.01797	+	1.01797i	−0.0181334	+	0.999836i	$0.505772\pi$
$47$	−6.97884	+	6.97884i	−1.01797	+	1.01797i	−0.999836	+	0.0181334i	$0.994228\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	3.01590	−	6.31699i	0.430843	−	0.902427i
$50$	−4.49887	+	1.20547i	−0.636236	+	0.170479i
$51$			3.04657i			0.426605i
$52$	−1.93321	+	3.04347i	−0.268089	+	0.422053i
$53$	1.08877			0.149555			0.0747774	−	0.997200i	$-0.476175\pi$
$53$	1.08877			0.149555			0.0747774	+	0.997200i	$0.476175\pi$
$54$	−0.965926	+	0.258819i	−0.131446	+	0.0352208i
$55$	1.61622	+	0.933126i	0.217931	+	0.125823i
$56$	−2.58041	−	0.584385i	−0.344821	−	0.0780917i
$57$	−2.53521	+	2.53521i	−0.335797	+	0.335797i
$58$	−1.84553	−	0.494508i	−0.242330	−	0.0649321i
$59$	−0.426056	−	0.114161i	−0.0554678	−	0.0148626i	0.230978	−	0.972959i	$-0.425807\pi$
$59$	−0.426056	−	0.114161i	−0.0554678	−	0.0148626i	−0.286446	+	0.958096i	$0.592474\pi$
$60$	0.413783	+	0.413783i	0.0534191	+	0.0534191i
$61$	12.5873	−	7.26727i	1.61164	−	0.930478i	0.622644	−	0.782505i	$-0.286058\pi$
$61$	12.5873	−	7.26727i	1.61164	−	0.930478i	0.988991	−	0.147973i	$-0.0472750\pi$
$62$	−1.01272	+	1.75408i	−0.128615	+	0.222768i
$63$	−2.34123	−	1.23233i	−0.294967	−	0.155259i
$64$			1.00000i			0.125000i
$65$	2.01308	+	0.631777i	0.249691	+	0.0783623i
$66$			3.18921i			0.392564i
$67$	−3.77898	−	14.1033i	−0.461676	−	1.72300i	−0.667682	−	0.744447i	$-0.732713\pi$
$67$	−3.77898	−	14.1033i	−0.461676	−	1.72300i	0.206006	−	0.978551i	$-0.433953\pi$
$68$	2.63841	+	1.52328i	0.319954	+	0.184725i
$69$	−3.64688	−	6.31658i	−0.439033	−	0.760427i
$70$	0.0604991	+	1.54705i	0.00723103	+	0.184908i
$71$	3.82702	+	1.02545i	0.454184	+	0.121698i	0.478656	−	0.878002i	$-0.341124\pi$
$71$	3.82702	+	1.02545i	0.454184	+	0.121698i	−0.0244725	+	0.999701i	$0.507791\pi$
$72$	−0.258819	+	0.965926i	−0.0305021	+	0.113835i
$73$	0.831214	−	0.831214i	0.0972862	−	0.0972862i	−0.656789	−	0.754075i	$-0.728086\pi$
$73$	0.831214	−	0.831214i	0.0972862	−	0.0972862i	0.754075	+	0.656789i	$0.228086\pi$
$74$	−4.43429	−	7.68041i	−0.515476	−	0.892830i
$75$	−2.32878	+	4.03357i	−0.268905	+	0.465757i
$76$	0.927951	+	3.46316i	0.106443	+	0.397252i
$77$	−5.72876	+	6.19505i	−0.652853	+	0.705992i
$78$	0.785067	+	3.51904i	0.0888913	+	0.398453i
$79$	3.09358			0.348055			0.174028	−	0.984741i	$-0.444322\pi$
$79$	3.09358			0.348055			0.174028	+	0.984741i	$0.444322\pi$
$80$	0.565237	−	0.151455i	0.0631955	−	0.0169332i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.31092	−	2.27058i	−0.144767	−	0.250743i
$83$	8.79143	+	8.79143i	0.964984	+	0.964984i	0.999407	−	0.0344229i	$-0.0109593\pi$
$83$	8.79143	+	8.79143i	0.964984	+	0.964984i	−0.0344229	+	0.999407i	$0.510959\pi$
$84$	−2.23784	+	1.41140i	−0.244169	+	0.153996i
$85$	0.461418	−	1.72203i	0.0500478	−	0.186781i
$86$	3.42561	+	3.42561i	0.369393	+	0.369393i
$87$	−1.65466	+	0.955316i	−0.177398	+	0.102421i
$88$	2.76194	+	1.59460i	0.294423	+	0.169985i
$89$	0.813298	+	3.03527i	0.0862095	+	0.321738i	0.995540	−	0.0943354i	$-0.0300726\pi$
$89$	0.813298	+	3.03527i	0.0862095	+	0.321738i	−0.909331	+	0.416073i	$0.863406\pi$
$90$	0.585177			0.0616831
$91$	−4.79624	+	8.24597i	−0.502783	+	0.864413i
$92$	−7.29376			−0.760427
$93$	0.524220	+	1.95642i	0.0543591	+	0.202871i
$94$	8.54730	+	4.93479i	0.881587	+	0.508984i
$95$	1.81696	−	1.04903i	0.186417	−	0.107628i
$96$	0.707107	+	0.707107i	0.0721688	+	0.0721688i
$97$	−3.09651	+	11.5563i	−0.314403	+	1.17337i	0.610142	+	0.792292i	$0.291112\pi$
$97$	−3.09651	+	11.5563i	−0.314403	+	1.17337i	−0.924544	+	0.381074i	$0.875554\pi$
$98$	−6.88232	−	1.27818i	−0.695219	−	0.129115i
$99$	2.25511	+	2.25511i	0.226647	+	0.226647i
$100$	2.32878	+	4.03357i	0.232878	+	0.403357i
$101$	0.0718530	−	0.124453i	0.00714964	−	0.0123835i	−0.862428	−	0.506179i	$-0.831058\pi$
$101$	0.0718530	−	0.124453i	0.00714964	−	0.0123835i	0.869578	+	0.493795i	$0.164391\pi$
$102$	2.94276	−	0.788510i	0.291377	−	0.0780741i
$103$	0.649727			0.0640195			0.0320097	−	0.999488i	$-0.489809\pi$
$103$	0.649727			0.0640195			0.0320097	+	0.999488i	$0.489809\pi$
$104$	3.44011	+	1.07963i	0.337331	+	0.105867i
$105$	1.13671	+	1.05115i	0.110931	+	0.102582i
$106$	−0.281796	−	1.05168i	−0.0273704	−	0.102148i
$107$	−5.26658	+	9.12199i	−0.509140	+	0.881856i	0.490804	+	0.871270i	$0.336703\pi$
$107$	−5.26658	+	9.12199i	−0.509140	+	0.881856i	−0.999944	+	0.0105862i	$0.996630\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−4.72622	+	4.72622i	−0.452690	+	0.452690i	−0.896246	−	0.443556i	$-0.853717\pi$
$109$	−4.72622	+	4.72622i	−0.452690	+	0.452690i	0.443556	+	0.896246i	$0.353717\pi$
$110$	0.483021	−	1.80266i	0.0460543	−	0.171877i
$111$	−8.56639	−	2.29536i	−0.813085	−	0.217866i
$112$	0.103386	+	2.64373i	0.00976906	+	0.249809i
$113$	−1.76024	−	3.04882i	−0.165589	−	0.286809i	0.771275	−	0.636502i	$-0.219619\pi$
$113$	−1.76024	−	3.04882i	−0.165589	−	0.286809i	−0.936864	+	0.349693i	$0.886286\pi$
$114$	3.10498	+	1.79266i	0.290808	+	0.167898i
$115$	1.10468	+	4.12271i	0.103012	+	0.384444i
$116$			1.91063i			0.177398i
$117$	3.04347	+	1.93321i	0.281369	+	0.178726i
$118$			0.441086i			0.0406053i
$119$	7.13272	+	3.75438i	0.653855	+	0.344163i
$120$	0.292588	−	0.506778i	0.0267095	−	0.0462623i
$121$	−0.717890	+	0.414474i	−0.0652627	+	0.0376795i
$122$	−10.2775	−	10.2775i	−0.930478	−	0.930478i
$123$	−2.53250	−	0.678581i	−0.228348	−	0.0611856i
$124$	1.95642	+	0.524220i	0.175691	+	0.0470764i
$125$	3.99613	−	3.99613i	0.357425	−	0.357425i
$126$	−0.584385	+	2.58041i	−0.0520611	+	0.229881i
$127$	−10.7470	−	6.20481i	−0.953646	−	0.550588i	−0.0594340	−	0.998232i	$-0.518930\pi$
$127$	−10.7470	−	6.20481i	−0.953646	−	0.550588i	−0.894211	+	0.447645i	$0.852263\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	4.84455			0.426539
$130$	0.0892274	−	2.10800i	0.00782576	−	0.184884i
$131$			15.3073i			1.33740i	0.743530	+	0.668702i	$0.233150\pi$
$131$			15.3073i			1.33740i	−0.743530	+	0.668702i	$0.766850\pi$
$132$	3.08054	−	0.825428i	0.268127	−	0.0718443i
$133$	2.81129	+	9.05972i	0.243770	+	0.785578i
$134$	−12.6447	+	7.30043i	−1.09234	+	0.630661i
$135$	0.413783	−	0.413783i	0.0356127	−	0.0356127i
$136$	0.788510	−	2.94276i	0.0676142	−	0.252340i
$137$	−0.640302	+	2.38964i	−0.0547047	+	0.204161i	−0.987869	−	0.155289i	$-0.950369\pi$
$137$	−0.640302	+	2.38964i	−0.0547047	+	0.204161i	0.933164	+	0.359450i	$0.117036\pi$
$138$	−5.15747	+	5.15747i	−0.439033	+	0.439033i
$139$	15.0580	−	8.69372i	1.27720	−	0.737392i	0.300867	−	0.953666i	$-0.402724\pi$
$139$	15.0580	−	8.69372i	1.27720	−	0.737392i	0.976333	+	0.216274i	$0.0693905\pi$
$140$	1.47868	−	0.458844i	0.124971	−	0.0387794i
$141$	9.53328	−	2.55443i	0.802847	−	0.215122i
$142$		−	3.96202i		−	0.332486i
$143$	8.46750	−	7.77979i	0.708088	−	0.650578i
$144$	1.00000			0.0833333
$145$	1.07996	−	0.289375i	0.0896858	−	0.0240312i
$146$	−1.01802	−	0.587757i	−0.0842523	−	0.0486431i
$147$	−5.77034	+	3.96272i	−0.475930	+	0.326840i
$148$	−6.27103	+	6.27103i	−0.515476	+	0.515476i
$149$	20.6475	+	5.53249i	1.69151	+	0.453240i	0.970780	−	0.239973i	$-0.0771385\pi$
$149$	20.6475	+	5.53249i	1.69151	+	0.453240i	0.720733	+	0.693212i	$0.243805\pi$
$150$	4.49887	+	1.20547i	0.367331	+	0.0984260i
$151$	−3.92626	−	3.92626i	−0.319515	−	0.319515i	0.529066	−	0.848581i	$-0.322542\pi$
$151$	−3.92626	−	3.92626i	−0.319515	−	0.319515i	−0.848581	+	0.529066i	$0.822542\pi$
$152$	3.10498	−	1.79266i	0.251847	−	0.145404i
$153$	1.52328	−	2.63841i	0.123150	−	0.213302i
$154$	7.46667	+	3.93016i	0.601682	+	0.316701i
$155$		−	1.18524i		−	0.0952004i
$156$	3.19595	−	1.66911i	0.255880	−	0.133636i
$157$		−	3.78771i		−	0.302292i	−0.988511	−	0.151146i	$-0.951704\pi$
$157$		−	3.78771i		−	0.302292i	0.988511	−	0.151146i	$-0.0482964\pi$
$158$	−0.800679	−	2.98817i	−0.0636986	−	0.237726i
$159$	−0.942907	−	0.544387i	−0.0747774	−	0.0431727i
$160$	−0.292588	−	0.506778i	−0.0231311	−	0.0400643i
$161$	−19.2827	+	0.754073i	−1.51969	+	0.0594293i
$162$	0.965926	+	0.258819i	0.0758903	+	0.0203347i
$163$	−6.52705	+	24.3593i	−0.511238	+	1.90797i	−0.104200	+	0.994556i	$0.533228\pi$
$163$	−6.52705	+	24.3593i	−0.511238	+	1.90797i	−0.407038	+	0.913411i	$0.633438\pi$
$164$	−1.85392	+	1.85392i	−0.144767	+	0.144767i
$165$	−0.933126	−	1.61622i	−0.0726437	−	0.125823i
$166$	6.21648	−	10.7673i	0.482492	−	0.835701i
$167$	2.72930	+	10.1859i	0.211200	+	0.788208i	0.987470	+	0.157807i	$0.0504425\pi$
$167$	2.72930	+	10.1859i	0.211200	+	0.788208i	−0.776270	+	0.630400i	$0.782891\pi$
$168$	1.94250	+	1.79629i	0.149867	+	0.138587i
$169$	7.42813	−	10.6688i	0.571395	−	0.820675i
$170$	−1.78278			−0.136733
$171$	3.46316	−	0.927951i	0.264834	−	0.0709622i
$172$	2.42227	−	4.19550i	0.184697	−	0.319904i
$173$	−3.47513	−	6.01909i	−0.264209	−	0.457623i	0.703147	−	0.711044i	$-0.251778\pi$
$173$	−3.47513	−	6.01909i	−0.264209	−	0.457623i	−0.967356	+	0.253421i	$0.918444\pi$
$174$	1.35102	+	1.35102i	0.102421	+	0.102421i
$175$	6.57369	+	10.4229i	0.496924	+	0.787898i
$176$	0.825428	−	3.08054i	0.0622190	−	0.232204i
$177$	0.311895	+	0.311895i	0.0234435	+	0.0234435i
$178$	2.72135	−	1.57117i	0.203974	−	0.117764i
$179$	−20.7557	−	11.9833i	−1.55136	−	0.895676i	−0.998032	−	0.0627103i	$-0.980026\pi$
$179$	−20.7557	−	11.9833i	−1.55136	−	0.895676i	−0.553325	−	0.832966i	$-0.686641\pi$
$180$	−0.151455	−	0.565237i	−0.0112888	−	0.0421303i
$181$	−19.5793			−1.45532			−0.727660	−	0.685937i	$-0.759392\pi$
$181$	−19.5793			−1.45532			−0.727660	+	0.685937i	$0.759392\pi$
$182$	9.20636	+	2.49860i	0.682420	+	0.185209i
$183$	−14.5345			−1.07442
$184$	1.88776	+	7.04523i	0.139168	+	0.519381i
$185$	4.49440	+	2.59484i	0.330435	+	0.190777i
$186$	1.75408	−	1.01272i	0.128615	−	0.0742559i
$187$	−6.87035	−	6.87035i	−0.502410	−	0.502410i
$188$	2.55443	−	9.53328i	0.186301	−	0.695286i
$189$	1.41140	+	2.23784i	0.102664	+	0.162779i
$190$	−1.48355	−	1.48355i	−0.107628	−	0.107628i
$191$	−7.93587	−	13.7453i	−0.574219	−	0.994577i	−0.996126	−	0.0879377i	$-0.971972\pi$
$191$	−7.93587	−	13.7453i	−0.574219	−	0.994577i	0.421907	−	0.906639i	$-0.361361\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−1.19526	+	0.320268i	−0.0860364	+	0.0230534i	−0.301580	−	0.953441i	$-0.597514\pi$
$193$	−1.19526	+	0.320268i	−0.0860364	+	0.0230534i	0.215544	+	0.976494i	$0.430848\pi$
$194$	11.9640			0.858964
$195$	−1.42749	−	1.55367i	−0.102224	−	0.111261i
$196$	0.546650	+	6.97862i	0.0390464	+	0.498473i
$197$	−5.00414	−	18.6757i	−0.356530	−	1.33059i	−0.878548	−	0.477654i	$-0.841487\pi$
$197$	−5.00414	−	18.6757i	−0.356530	−	1.33059i	0.522018	−	0.852935i	$-0.325179\pi$
$198$	1.59460	−	2.76194i	0.113324	−	0.196282i
$199$	2.75691	+	4.77511i	0.195432	+	0.338499i	0.947042	−	0.321109i	$-0.104056\pi$
$199$	2.75691	+	4.77511i	0.195432	+	0.338499i	−0.751610	+	0.659608i	$0.770722\pi$
$200$	3.29340	−	3.29340i	0.232878	−	0.232878i
$201$	−3.77898	+	14.1033i	−0.266549	+	0.994773i
$202$	−0.138809	−	0.0371938i	−0.00976659	−	0.00261695i
$203$	0.197533	+	5.05120i	0.0138641	+	0.354524i
$204$	−1.52328	−	2.63841i	−0.106651	−	0.184725i
$205$	1.32869	+	0.767119i	0.0927997	+	0.0535779i
$206$	−0.168162	−	0.627588i	−0.0117164	−	0.0437261i
$207$			7.29376i			0.506951i
$208$	0.152479	−	3.60233i	0.0105725	−	0.249776i
$209$		−	11.4344i		−	0.790931i
$210$	0.721131	−	1.37003i	0.0497628	−	0.0945413i
$211$	6.03031	−	10.4448i	0.415144	−	0.719050i	−0.580300	−	0.814403i	$-0.697065\pi$
$211$	6.03031	−	10.4448i	0.415144	−	0.719050i	0.995444	+	0.0953529i	$0.0303980\pi$
$212$	−0.942907	+	0.544387i	−0.0647591	+	0.0373887i
$213$	−2.80157	−	2.80157i	−0.191961	−	0.191961i
$214$	10.1743	+	2.72618i	0.695498	+	0.186358i
$215$	−2.73832	−	0.733730i	−0.186752	−	0.0500400i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	5.22644	+	1.18363i	0.354794	+	0.0803501i
$218$	5.78842	+	3.34194i	0.392041	+	0.226345i
$219$	−1.13546	+	0.304245i	−0.0767272	+	0.0205590i
$220$	−1.86625			−0.125823
$221$	−9.27213	−	5.88967i	−0.623711	−	0.396182i
$222$			8.86858i			0.595220i
$223$	−16.2388	+	4.35117i	−1.08743	+	0.291376i	−0.757637	−	0.652677i	$-0.773646\pi$
$223$	−16.2388	+	4.35117i	−1.08743	+	0.291376i	−0.329794	+	0.944053i	$0.606979\pi$
$224$	2.52689	−	0.784111i	0.168835	−	0.0523906i
$225$	4.03357	−	2.32878i	0.268905	−	0.155252i
$226$	−2.48935	+	2.48935i	−0.165589	+	0.165589i
$227$	−6.82989	+	25.4895i	−0.453316	+	1.69180i	0.239676	+	0.970853i	$0.422959\pi$
$227$	−6.82989	+	25.4895i	−0.453316	+	1.69180i	−0.692992	+	0.720945i	$0.743708\pi$
$228$	0.927951	−	3.46316i	0.0614550	−	0.229353i
$229$	−9.22201	+	9.22201i	−0.609407	+	0.609407i	−0.942791	−	0.333384i	$-0.891810\pi$
$229$	−9.22201	+	9.22201i	−0.609407	+	0.609407i	0.333384	+	0.942791i	$0.391810\pi$
$230$	3.69632	−	2.13407i	0.243728	−	0.140716i
$231$	8.05878	−	2.50069i	0.530229	−	0.164534i
$232$	1.84553	−	0.494508i	0.121165	−	0.0324660i
$233$			4.85744i			0.318221i	0.987261	+	0.159111i	$0.0508627\pi$
$233$			4.85744i			0.318221i	−0.987261	+	0.159111i	$0.949137\pi$
$234$	1.07963	−	3.44011i	0.0705779	−	0.224887i
$235$	−5.77545			−0.376749
$236$	0.426056	−	0.114161i	0.0277339	−	0.00743128i
$237$	−2.67912	−	1.54679i	−0.174028	−	0.100475i
$238$	1.78037	−	7.86138i	0.115404	−	0.509578i
$239$	17.8540	−	17.8540i	1.15488	−	1.15488i	0.169319	−	0.985561i	$-0.445843\pi$
$239$	17.8540	−	17.8540i	1.15488	−	1.15488i	0.985561	−	0.169319i	$-0.0541568\pi$
$240$	−0.565237	−	0.151455i	−0.0364859	−	0.00977637i
$241$	−10.8213	−	2.89956i	−0.697061	−	0.186777i	−0.107147	−	0.994243i	$-0.534172\pi$
$241$	−10.8213	−	2.89956i	−0.697061	−	0.186777i	−0.589914	+	0.807466i	$0.700838\pi$
$242$	0.586155	+	0.586155i	0.0376795	+	0.0376795i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−7.26727	+	12.5873i	−0.465239	+	0.805818i
$245$	3.86179	−	1.36593i	0.246720	−	0.0872663i
$246$			2.62184i			0.167162i
$247$	−2.81472	−	12.6169i	−0.179096	−	0.802795i
$248$		−	2.02543i		−	0.128615i
$249$	−3.21789	−	12.0093i	−0.203925	−	0.761059i
$250$	−4.89424	−	2.82569i	−0.309539	−	0.178712i
$251$	−11.2234	−	19.4395i	−0.708414	−	1.22701i	−0.965445	−	0.260606i	$-0.916078\pi$
$251$	−11.2234	−	19.4395i	−0.708414	−	1.22701i	0.257031	−	0.966403i	$-0.417256\pi$
$252$	2.64373	−	0.103386i	0.166539	−	0.00651271i
$253$	22.4687	+	6.02047i	1.41260	+	0.378504i
$254$	−3.21184	+	11.9868i	−0.201529	+	0.752117i
$255$	−1.26062	+	1.26062i	−0.0789429	+	0.0789429i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.64611	+	4.58320i	−0.165060	+	0.285892i	−0.936677	−	0.350196i	$-0.886115\pi$
$257$	−2.64611	+	4.58320i	−0.165060	+	0.285892i	0.771617	+	0.636088i	$0.219448\pi$
$258$	−1.25386	−	4.67947i	−0.0780620	−	0.291331i
$259$	−15.9306	+	17.2273i	−0.989878	+	1.07045i
$260$	−2.05926	+	0.459403i	−0.127710	+	0.0284910i
$261$	1.91063			0.118265
$262$	14.7857	−	3.96182i	0.913465	−	0.244762i
$263$	8.05322	−	13.9486i	0.496583	−	0.860107i	−0.503409	−	0.864048i	$-0.667921\pi$
$263$	8.05322	−	13.9486i	0.496583	−	0.860107i	0.999992	+	0.00394107i	$0.00125448\pi$
$264$	−1.59460	−	2.76194i	−0.0981411	−	0.169985i
$265$	0.450516	+	0.450516i	0.0276750	+	0.0276750i
$266$	8.02340	−	5.06033i	0.491946	−	0.310269i
$267$	0.813298	−	3.03527i	0.0497731	−	0.185756i
$268$	10.3244	+	10.3244i	0.630661	+	0.630661i
$269$	−12.9505	+	7.47700i	−0.789609	+	0.455881i	−0.839825	−	0.542857i	$-0.817342\pi$
$269$	−12.9505	+	7.47700i	−0.789609	+	0.455881i	0.0502159	+	0.998738i	$0.484009\pi$
$270$	−0.506778	−	0.292588i	−0.0308415	−	0.0178064i
$271$	−6.42824	−	23.9905i	−0.390488	−	1.45732i	−0.829332	−	0.558756i	$-0.811279\pi$
$271$	−6.42824	−	23.9905i	−0.390488	−	1.45732i	0.438844	−	0.898563i	$-0.355388\pi$
$272$	−3.04657			−0.184725
$273$	8.27666	−	4.74310i	0.500926	−	0.287065i
$274$	2.47394			0.149456
$275$	−3.84449	−	14.3478i	−0.231831	−	0.865206i
$276$	6.31658	+	3.64688i	0.380214	+	0.219516i
$277$	−19.5039	+	11.2606i	−1.17187	+	0.676582i	−0.954121	−	0.299421i	$-0.903206\pi$
$277$	−19.5039	+	11.2606i	−1.17187	+	0.676582i	−0.217754	+	0.976004i	$0.569873\pi$
$278$	−12.2948	−	12.2948i	−0.737392	−	0.737392i
$279$	0.524220	−	1.95642i	0.0313842	−	0.117128i
$280$	−0.825919	−	1.30954i	−0.0493581	−	0.0782597i
$281$	11.9422	+	11.9422i	0.712409	+	0.712409i	0.967039	−	0.254629i	$-0.0819535\pi$
$281$	11.9422	+	11.9422i	0.712409	+	0.712409i	−0.254629	+	0.967039i	$0.581954\pi$
$282$	−4.93479	−	8.54730i	−0.293862	−	0.508984i
$283$	−4.01787	+	6.95916i	−0.238838	+	0.413679i	−0.960381	−	0.278690i	$-0.910100\pi$
$283$	−4.01787	+	6.95916i	−0.238838	+	0.413679i	0.721543	+	0.692369i	$0.243433\pi$
$284$	−3.82702	+	1.02545i	−0.227092	+	0.0608491i
$285$	−2.09805			−0.124278
$286$	−9.70625	−	6.16542i	−0.573942	−	0.364569i
$287$	−4.70959	+	5.09293i	−0.277998	+	0.300626i
$288$	−0.258819	−	0.965926i	−0.0152511	−	0.0569177i
$289$	3.85921	−	6.68435i	0.227012	−	0.393197i
$290$	−0.559029	−	0.968266i	−0.0328273	−	0.0568585i
$291$	8.45981	−	8.45981i	0.495923	−	0.495923i
$292$	−0.304245	+	1.13546i	−0.0178046	+	0.0664477i
$293$	16.8911	+	4.52596i	0.986789	+	0.264409i	0.715901	−	0.698201i	$-0.246016\pi$
$293$	16.8911	+	4.52596i	0.986789	+	0.264409i	0.270888	+	0.962611i	$0.412683\pi$
$294$	5.32117	+	4.54809i	0.310337	+	0.265250i
$295$	−0.129057	−	0.223533i	−0.00751397	−	0.0130146i
$296$	7.68041	+	4.43429i	0.446415	+	0.257738i
$297$	−0.825428	−	3.08054i	−0.0478962	−	0.178751i
$298$		−	21.3759i		−	1.23827i
$299$	26.2745	+	1.11215i	1.51949	+	0.0643172i
$300$		−	4.65757i		−	0.268905i
$301$	5.97008	−	11.3422i	0.344110	−	0.653754i
$302$	−2.77629	+	4.80867i	−0.159757	+	0.276708i
$303$	−0.124453	+	0.0718530i	−0.00714964	+	0.00412785i
$304$	−2.53521	−	2.53521i	−0.145404	−	0.145404i
$305$	8.21546	+	2.20133i	0.470416	+	0.126048i
$306$	−2.94276	−	0.788510i	−0.168226	−	0.0450761i
$307$	−21.8073	+	21.8073i	−1.24461	+	1.24461i	−0.286539	+	0.958068i	$0.592505\pi$
$307$	−21.8073	+	21.8073i	−1.24461	+	1.24461i	−0.958068	+	0.286539i	$0.907495\pi$
$308$	1.86372	−	8.22945i	0.106196	−	0.468917i
$309$	−0.562680	−	0.324863i	−0.0320097	−	0.0184808i
$310$	−1.14485	+	0.306762i	−0.0650231	+	0.0174229i
$311$	2.00881			0.113909			0.0569547	−	0.998377i	$-0.481861\pi$
$311$	2.00881			0.113909			0.0569547	+	0.998377i	$0.481861\pi$
$312$	−2.43941	−	2.65505i	−0.138104	−	0.150312i
$313$		−	30.0011i		−	1.69576i	−0.530185	−	0.847882i	$-0.677878\pi$
$313$		−	30.0011i		−	1.69576i	0.530185	−	0.847882i	$-0.322122\pi$
$314$	−3.65865	+	0.980332i	−0.206470	+	0.0553234i
$315$	−0.458844	−	1.47868i	−0.0258529	−	0.0833140i
$316$	−2.67912	+	1.54679i	−0.150712	+	0.0870139i
$317$	−3.18003	+	3.18003i	−0.178608	+	0.178608i	−0.790749	−	0.612141i	$-0.790309\pi$
$317$	−3.18003	+	3.18003i	−0.178608	+	0.178608i	0.612141	+	0.790749i	$0.290309\pi$
$318$	−0.281796	+	1.05168i	−0.0158023	+	0.0589750i
$319$	1.57709	−	5.88578i	0.0883000	−	0.329540i
$320$	−0.413783	+	0.413783i	−0.0231311	+	0.0231311i
$321$	9.12199	−	5.26658i	0.509140	−	0.293952i
$322$	5.71912	+	18.4305i	0.318714	+	1.02709i
$323$	−10.5508	+	2.82707i	−0.587060	+	0.157302i
$324$		−	1.00000i		−	0.0555556i
$325$	−7.77400	−	14.8853i	−0.431224	−	0.825690i
$326$	25.2186			1.39673
$327$	6.45614	−	1.72992i	0.357025	−	0.0956647i
$328$	2.27058	+	1.31092i	0.125372	+	0.0723834i
$329$	5.76763	−	25.4675i	0.317980	−	1.40407i
$330$	−1.31964	+	1.31964i	−0.0726437	+	0.0726437i
$331$	3.44973	+	0.924353i	0.189614	+	0.0508070i	0.352377	−	0.935858i	$-0.385374\pi$
$331$	3.44973	+	0.924353i	0.189614	+	0.0508070i	−0.162762	+	0.986665i	$0.552040\pi$
$332$	−12.0093	−	3.21789i	−0.659097	−	0.176604i
$333$	6.27103	+	6.27103i	0.343650	+	0.343650i
$334$	9.13242	−	5.27260i	0.499704	−	0.288504i
$335$	4.27204	−	7.39939i	0.233407	−	0.404272i
$336$	1.23233	−	2.34123i	0.0672291	−	0.127725i
$337$		−	7.81434i		−	0.425674i	−0.977088	−	0.212837i	$-0.931730\pi$
$337$		−	7.81434i		−	0.425674i	0.977088	−	0.212837i	$-0.0682703\pi$
$338$	−12.2278	−	4.41374i	−0.665104	−	0.240076i
$339$			3.52047i			0.191206i
$340$	0.461418	+	1.72203i	0.0250239	+	0.0933904i
$341$	−5.59411	−	3.22976i	−0.302938	−	0.174901i
$342$	−1.79266	−	3.10498i	−0.0969361	−	0.167898i
$343$	2.16669	+	18.3931i	0.116990	+	0.993133i
$344$	−4.67947	−	1.25386i	−0.252300	−	0.0676036i
$345$	1.10468	−	4.12271i	0.0594738	−	0.221959i
$346$	−4.91457	+	4.91457i	−0.264209	+	0.264209i
$347$	−15.2294	−	26.3780i	−0.817556	−	1.41605i	−0.907478	−	0.420099i	$-0.861995\pi$
$347$	−15.2294	−	26.3780i	−0.817556	−	1.41605i	0.0899227	−	0.995949i	$-0.471338\pi$
$348$	0.955316	−	1.65466i	0.0512103	−	0.0886988i
$349$	3.50154	+	13.0679i	0.187433	+	0.699509i	0.994097	+	0.108498i	$0.0346043\pi$
$349$	3.50154	+	13.0679i	0.187433	+	0.699509i	−0.806664	+	0.591011i	$0.798729\pi$
$350$	8.36637	−	9.04735i	0.447201	−	0.483601i
$351$	−1.66911	−	3.19595i	−0.0890906	−	0.170587i
$352$	−3.18921			−0.169985
$353$	11.5893	−	3.10534i	0.616835	−	0.165280i	0.0631465	−	0.998004i	$-0.479886\pi$
$353$	11.5893	−	3.10534i	0.616835	−	0.165280i	0.553689	+	0.832724i	$0.313220\pi$
$354$	0.220543	−	0.381992i	0.0117217	−	0.0203026i
$355$	1.15924	+	2.00787i	0.0615262	+	0.106567i
$356$	−2.22197	−	2.22197i	−0.117764	−	0.117764i
$357$	−4.29993	−	6.81775i	−0.227576	−	0.360833i
$358$	−6.20303	+	23.1500i	−0.327840	+	1.22352i
$359$	7.55100	+	7.55100i	0.398526	+	0.398526i	0.877713	−	0.479187i	$-0.159068\pi$
$359$	7.55100	+	7.55100i	0.398526	+	0.398526i	−0.479187	+	0.877713i	$0.659068\pi$
$360$	−0.506778	+	0.292588i	−0.0267095	+	0.0154208i
$361$	5.32210	+	3.07272i	0.280111	+	0.161722i
$362$	5.06751	+	18.9122i	0.266342	+	0.994003i
$363$	0.828948			0.0435085
$364$	0.0306841	−	9.53934i	0.00160828	−	0.499997i
$365$	0.687884			0.0360055
$366$	3.76181	+	14.0393i	0.196633	+	0.733845i
$367$	2.75791	+	1.59228i	0.143962	+	0.0831163i	0.570251	−	0.821471i	$-0.306846\pi$
$367$	2.75791	+	1.59228i	0.143962	+	0.0831163i	−0.426289	+	0.904587i	$0.640179\pi$
$368$	6.31658	−	3.64688i	0.329275	−	0.190107i
$369$	1.85392	+	1.85392i	0.0965112	+	0.0965112i
$370$	1.34319	−	5.01285i	0.0698291	−	0.260606i
$371$	−2.43651	+	1.53670i	−0.126497	+	0.0797813i
$372$	−1.43220	−	1.43220i	−0.0742559	−	0.0742559i
$373$	11.7464	+	20.3453i	0.608203	+	1.05344i	0.991536	+	0.129829i	$0.0414428\pi$
$373$	11.7464	+	20.3453i	0.608203	+	1.05344i	−0.383333	+	0.923610i	$0.625224\pi$
$374$	−4.85807	+	8.41443i	−0.251205	+	0.435100i
$375$	−5.45882	+	1.46269i	−0.281892	+	0.0755328i
$376$	−9.86958			−0.508984
$377$	0.291332	−	6.88272i	0.0150044	−	0.354478i
$378$	1.79629	−	1.94250i	0.0923914	−	0.0999117i
$379$	2.37161	+	8.85097i	0.121821	+	0.454644i	0.999706	−	0.0242276i	$-0.00771264\pi$
$379$	2.37161	+	8.85097i	0.121821	+	0.454644i	−0.877885	+	0.478872i	$0.841046\pi$
$380$	−1.04903	+	1.81696i	−0.0538138	+	0.0932083i
$381$	6.20481	+	10.7470i	0.317882	+	0.550588i
$382$	−11.2230	+	11.2230i	−0.574219	+	0.574219i
$383$	−7.18759	+	26.8245i	−0.367269	+	1.37067i	0.497050	+	0.867722i	$0.334416\pi$
$383$	−7.18759	+	26.8245i	−0.367269	+	1.37067i	−0.864319	+	0.502944i	$0.832250\pi$
$384$	−0.965926	−	0.258819i	−0.0492922	−	0.0132078i
$385$	−4.93387	+	0.192944i	−0.251453	+	0.00983336i
$386$	0.618710	+	1.07164i	0.0314915	+	0.0545449i
$387$	−4.19550	−	2.42227i	−0.213269	−	0.123131i
$388$	−3.09651	−	11.5563i	−0.157201	−	0.586683i
$389$			20.0005i			1.01406i	0.861927	+	0.507032i	$0.169257\pi$
$389$			20.0005i			1.01406i	−0.861927	+	0.507032i	$0.830743\pi$
$390$	−1.13127	+	1.78097i	−0.0572842	+	0.0901827i
$391$		−	22.2209i		−	1.12376i
$392$	6.59935	−	2.33422i	0.333317	−	0.117896i
$393$	7.65365	−	13.2565i	0.386076	−	0.668702i
$394$	−16.7442	+	9.66726i	−0.843559	+	0.487029i
$395$	1.28007	+	1.28007i	0.0644074	+	0.0644074i
$396$	−3.08054	−	0.825428i	−0.154803	−	0.0414793i
$397$	0.642083	+	0.172046i	0.0322252	+	0.00863472i	0.274896	−	0.961474i	$-0.411357\pi$
$397$	0.642083	+	0.172046i	0.0322252	+	0.00863472i	−0.242670	+	0.970109i	$0.578023\pi$
$398$	3.89886	−	3.89886i	0.195432	−	0.195432i
$399$	2.09521	−	9.25160i	0.104892	−	0.463159i
$400$	−4.03357	−	2.32878i	−0.201679	−	0.116439i
$401$	4.30263	−	1.15289i	0.214863	−	0.0575724i	−0.149782	−	0.988719i	$-0.547857\pi$
$401$	4.30263	−	1.15289i	0.214863	−	0.0575724i	0.364645	+	0.931147i	$0.381190\pi$
$402$	14.6009			0.728224
$403$	−6.96772	−	2.18673i	−0.347087	−	0.108929i
$404$			0.143706i			0.00714964i
$405$	−0.565237	+	0.151455i	−0.0280869	+	0.00752586i
$406$	4.82795	−	1.49815i	0.239607	−	0.0743518i
$407$	24.4944	−	14.1419i	1.21414	−	0.700986i
$408$	−2.15425	+	2.15425i	−0.106651	+	0.106651i
$409$	−0.0722585	+	0.269672i	−0.00357295	+	0.0133344i	−0.967689	−	0.252146i	$-0.918864\pi$
$409$	−0.0722585	+	0.269672i	−0.00357295	+	0.0133344i	0.964116	+	0.265480i	$0.0855305\pi$
$410$	0.397090	−	1.48196i	0.0196109	−	0.0731888i
$411$	1.74934	−	1.74934i	0.0862884	−	0.0862884i
$412$	−0.562680	+	0.324863i	−0.0277212	+	0.0160049i
$413$	1.11458	−	0.345860i	0.0548447	−	0.0170187i
$414$	7.04523	−	1.88776i	0.346254	−	0.0927785i
$415$			7.27548i			0.357139i
$416$	−3.51904	+	0.785067i	−0.172535	+	0.0384911i
$417$	−17.3874			−0.851467
$418$	−11.0447	+	2.95943i	−0.540216	+	0.144750i
$419$	28.5481	+	16.4822i	1.39466	+	0.805210i	0.993827	−	0.110939i	$-0.0353859\pi$
$419$	28.5481	+	16.4822i	1.39466	+	0.805210i	0.400837	+	0.916149i	$0.368719\pi$
$420$	−1.50999	−	0.341968i	−0.0736802	−	0.0166863i
$421$	−4.07006	+	4.07006i	−0.198363	+	0.198363i	−0.799298	−	0.600935i	$-0.794795\pi$
$421$	−4.07006	+	4.07006i	−0.198363	+	0.198363i	0.600935	+	0.799298i	$0.294795\pi$
$422$	−11.6497	−	3.12152i	−0.567097	−	0.151953i
$423$	−9.53328	−	2.55443i	−0.463524	−	0.124201i
$424$	0.769880	+	0.769880i	0.0373887	+	0.0373887i
$425$	−12.2886	+	7.09480i	−0.596082	+	0.344148i
$426$	−1.98101	+	3.43121i	−0.0959804	+	0.166243i
$427$	−17.9113	+	34.0287i	−0.866791	+	1.64676i
$428$		−	10.5332i		−	0.509140i
$429$	−11.2230	+	2.50374i	−0.541850	+	0.120882i
$430$			2.83492i			0.136712i
$431$	5.87139	+	21.9123i	0.282815	+	1.05548i	0.950421	+	0.310965i	$0.100652\pi$
$431$	5.87139	+	21.9123i	0.282815	+	1.05548i	−0.667606	+	0.744515i	$0.732681\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$	2.44283	+	4.23110i	0.117395	+	0.203334i	0.918735	−	0.394876i	$-0.129212\pi$
$433$	2.44283	+	4.23110i	0.117395	+	0.203334i	−0.801340	+	0.598210i	$0.795879\pi$
$434$	−0.209401	−	5.35470i	−0.0100516	−	0.257034i
$435$	−1.07996	−	0.289375i	−0.0517801	−	0.0138744i
$436$	1.72992	−	6.45614i	0.0828480	−	0.309193i
$437$	18.4912	−	18.4912i	0.884554	−	0.884554i
$438$	0.587757	+	1.01802i	0.0280841	+	0.0486431i
$439$	10.6909	−	18.5172i	0.510249	−	0.883777i	−0.489680	−	0.871902i	$-0.662887\pi$
$439$	10.6909	−	18.5172i	0.510249	−	0.883777i	0.999929	−	0.0118753i	$-0.00378012\pi$
$440$	0.483021	+	1.80266i	0.0230271	+	0.0859385i
$441$	6.97862	−	0.546650i	0.332315	−	0.0260309i
$442$	−3.28918	+	10.4805i	−0.156450	+	0.498509i
$443$	−14.6858			−0.697742			−0.348871	−	0.937171i	$-0.613435\pi$
$443$	−14.6858			−0.697742			−0.348871	+	0.937171i	$0.613435\pi$
$444$	8.56639	−	2.29536i	0.406543	−	0.108933i
$445$	−0.919413	+	1.59247i	−0.0435844	+	0.0754904i
$446$	8.40582	+	14.5593i	0.398027	+	0.689404i
$447$	−15.1151	−	15.1151i	−0.714918	−	0.714918i
$448$	−1.41140	−	2.23784i	−0.0666824	−	0.105728i
$449$	−8.03608	+	29.9911i	−0.379246	+	1.41537i	0.467794	+	0.883837i	$0.345049\pi$
$449$	−8.03608	+	29.9911i	−0.379246	+	1.41537i	−0.847040	+	0.531529i	$0.821618\pi$
$450$	−3.29340	−	3.29340i	−0.155252	−	0.155252i
$451$	7.24135	−	4.18079i	0.340982	−	0.196866i
$452$	3.04882	+	1.76024i	0.143404	+	0.0827945i
$453$	1.43711	+	5.36338i	0.0675214	+	0.251993i
$454$	26.3887			1.23848
$455$	−5.39664	+	1.42744i	−0.252998	+	0.0669193i
$456$	−3.58533			−0.167898
$457$	−4.06816	−	15.1826i	−0.190300	−	0.710211i	−0.993434	−	0.114411i	$-0.963502\pi$
$457$	−4.06816	−	15.1826i	−0.190300	−	0.710211i	0.803133	−	0.595800i	$-0.203165\pi$
$458$	11.2946	+	6.52094i	0.527762	+	0.304704i
$459$	−2.63841	+	1.52328i	−0.123150	+	0.0711008i
$460$	−3.01803	−	3.01803i	−0.140716	−	0.140716i
$461$	−10.0811	+	37.6232i	−0.469524	+	1.75229i	0.171912	+	0.985112i	$0.445006\pi$
$461$	−10.0811	+	37.6232i	−0.469524	+	1.75229i	−0.641436	+	0.767176i	$0.721661\pi$
$462$	−4.50125	−	7.13695i	−0.209417	−	0.332041i
$463$	10.1505	+	10.1505i	0.471733	+	0.471733i	0.902475	−	0.430742i	$-0.141748\pi$
$463$	10.1505	+	10.1505i	0.471733	+	0.471733i	−0.430742	+	0.902475i	$0.641748\pi$
$464$	−0.955316	−	1.65466i	−0.0443494	−	0.0768155i
$465$	−0.592618	+	1.02644i	−0.0274820	+	0.0476002i
$466$	4.69192	−	1.25720i	0.217349	−	0.0582385i
$467$	−4.53821			−0.210003			−0.105002	−	0.994472i	$-0.533485\pi$
$467$	−4.53821			−0.210003			−0.105002	+	0.994472i	$0.533485\pi$
$468$	−3.60233	−	0.152479i	−0.166518	−	0.00704836i
$469$	28.3622	+	26.2274i	1.30965	+	1.21107i
$470$	1.49480	+	5.57865i	0.0689498	+	0.257324i
$471$	−1.89386	+	3.28026i	−0.0872643	+	0.151146i
$472$	−0.220543	−	0.381992i	−0.0101513	−	0.0175826i
$473$	−10.9250	+	10.9250i	−0.502332	+	0.502332i
$474$	−0.800679	+	2.98817i	−0.0367764	+	0.137251i
$475$	−16.1299	−	4.32199i	−0.740091	−	0.198307i
$476$	−8.05431	+	0.314973i	−0.369169	+	0.0144368i
$477$	0.544387	+	0.942907i	0.0249258	+	0.0431727i
$478$	−21.8666	−	12.6247i	−1.00016	−	0.577440i
$479$	−4.25607	−	15.8839i	−0.194465	−	0.725752i	−0.992405	−	0.123015i	$-0.960744\pi$
$479$	−4.25607	−	15.8839i	−0.194465	−	0.725752i	0.797940	−	0.602737i	$-0.205923\pi$
$480$			0.585177i			0.0267095i
$481$	23.5465	−	21.6341i	1.07363	−	0.986430i
$482$			11.2030i			0.510284i
$483$	17.0764	+	8.98832i	0.777002	+	0.408983i
$484$	0.414474	−	0.717890i	0.0188397	−	0.0326314i
$485$	−6.06308	+	3.50052i	−0.275310	+	0.158951i
$486$	−0.707107	−	0.707107i	−0.0320750	−	0.0320750i
$487$	15.2701	+	4.09162i	0.691956	+	0.185409i	0.587625	−	0.809133i	$-0.300063\pi$
$487$	15.2701	+	4.09162i	0.691956	+	0.185409i	0.104331	+	0.994543i	$0.466730\pi$
$488$	14.0393	+	3.76181i	0.635529	+	0.170289i
$489$	17.8322	−	17.8322i	0.806402	−	0.806402i
$490$	−2.31889	−	3.37667i	−0.104757	−	0.152542i
$491$	10.2725	+	5.93081i	0.463590	+	0.267654i	0.713552	−	0.700602i	$-0.247085\pi$
$491$	10.2725	+	5.93081i	0.463590	+	0.267654i	−0.249963	+	0.968255i	$0.580418\pi$
$492$	2.53250	−	0.678581i	0.114174	−	0.0305928i
$493$	−5.82087			−0.262159
$494$	−11.4585	+	5.98431i	−0.515543	+	0.269247i
$495$			1.86625i			0.0838818i
$496$	−1.95642	+	0.524220i	−0.0878457	+	0.0235382i
$497$	−10.0116	+	3.10667i	−0.449081	+	0.139353i
$498$	−10.7673	+	6.21648i	−0.482492	+	0.278567i
$499$	−11.5210	+	11.5210i	−0.515751	+	0.515751i	−0.916283	−	0.400532i	$-0.868825\pi$
$499$	−11.5210	+	11.5210i	−0.515751	+	0.515751i	0.400532	+	0.916283i	$0.368825\pi$
$500$	−1.46269	+	5.45882i	−0.0654133	+	0.244126i
$501$	2.72930	−	10.1859i	0.121936	−	0.455072i
$502$	−15.8723	+	15.8723i	−0.708414	+	0.708414i
$503$	16.5119	−	9.53312i	0.736227	−	0.425061i	−0.0844688	−	0.996426i	$-0.526919\pi$
$503$	16.5119	−	9.53312i	0.736227	−	0.425061i	0.820696	+	0.571365i	$0.193586\pi$
$504$	−0.784111	−	2.52689i	−0.0349271	−	0.112557i
$505$	0.0812280	−	0.0217650i	0.00361460	−	0.000968529i
$506$		−	23.2613i		−	1.03409i
$507$	−11.7673	+	5.52537i	−0.522606	+	0.245390i
$508$	12.4096			0.550588
$509$	7.52946	−	2.01751i	0.333738	−	0.0894247i	−0.0880588	−	0.996115i	$-0.528066\pi$
$509$	7.52946	−	2.01751i	0.333738	−	0.0894247i	0.421796	+	0.906691i	$0.361400\pi$
$510$	1.54393	+	0.891391i	0.0683665	+	0.0394714i
$511$	−0.686952	+	3.03330i	−0.0303890	+	0.134185i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−3.46316	−	0.927951i	−0.152902	−	0.0409700i
$514$	5.11190	+	1.36973i	0.225476	+	0.0604161i
$515$	0.268845	+	0.268845i	0.0118467	+	0.0118467i
$516$	−4.19550	+	2.42227i	−0.184697	+	0.106635i
$517$	−15.7381	+	27.2591i	−0.692159	+	1.19886i
$518$	20.7634	+	10.9290i	0.912291	+	0.480193i
$519$			6.95025i			0.305082i
$520$	0.976726	+	1.87019i	0.0428323	+	0.0820134i
$521$		−	37.4573i		−	1.64103i	−0.571623	−	0.820516i	$-0.693686\pi$
$521$		−	37.4573i		−	1.64103i	0.571623	−	0.820516i	$-0.306314\pi$
$522$	−0.494508	−	1.84553i	−0.0216440	−	0.0807766i
$523$	−20.0250	−	11.5615i	−0.875633	−	0.505547i	−0.00641691	−	0.999979i	$-0.502043\pi$
$523$	−20.0250	−	11.5615i	−0.875633	−	0.505547i	−0.869216	+	0.494432i	$0.835376\pi$
$524$	−7.65365	−	13.2565i	−0.334351	−	0.579113i
$525$	−0.481528	−	12.3134i	−0.0210156	−	0.537399i
$526$	−15.5576	−	4.16866i	−0.678345	−	0.181762i
$527$	−1.59707	+	5.96036i	−0.0695696	+	0.259637i
$528$	−2.25511	+	2.25511i	−0.0981411	+	0.0981411i
$529$	15.0995	+	26.1531i	0.656499	+	1.13709i
$530$	0.318563	−	0.551767i	0.0138375	−	0.0239672i
$531$	−0.114161	−	0.426056i	−0.00495419	−	0.0184893i
$532$	−6.96451	−	6.44030i	−0.301950	−	0.279223i
$533$	6.96110	−	6.39574i	0.301519	−	0.277030i
$534$	−3.14234			−0.135983
$535$	−5.95374	+	1.59530i	−0.257403	+	0.0689708i
$536$	7.30043	−	12.6447i	0.315330	−	0.546168i
$537$	11.9833	+	20.7557i	0.517119	+	0.895676i
$538$	10.5741	+	10.5741i	0.455881	+	0.455881i
$539$	4.07637	−	21.9491i	0.175582	−	0.945416i
$540$	−0.151455	+	0.565237i	−0.00651758	+	0.0243239i
$541$	−22.3187	−	22.3187i	−0.959557	−	0.959557i	0.0396567	−	0.999213i	$-0.487374\pi$
$541$	−22.3187	−	22.3187i	−0.959557	−	0.959557i	−0.999213	+	0.0396567i	$0.987374\pi$
$542$	−21.5093	+	12.4184i	−0.923904	+	0.533416i
$543$	16.9562	+	9.78967i	0.727660	+	0.420115i
$544$	0.788510	+	2.94276i	0.0338071	+	0.126170i
$545$	−3.91126			−0.167540
$546$	−6.72364	−	6.76703i	−0.287745	−	0.289602i
$547$	7.95300			0.340046			0.170023	−	0.985440i	$-0.445616\pi$
$547$	7.95300			0.340046			0.170023	+	0.985440i	$0.445616\pi$
$548$	−0.640302	−	2.38964i	−0.0273523	−	0.102080i
$549$	12.5873	+	7.26727i	0.537212	+	0.310159i
$550$	−12.8639	+	7.42698i	−0.548519	+	0.316687i
$551$	−4.84385	−	4.84385i	−0.206355	−	0.206355i
$552$	1.88776	−	7.04523i	0.0803486	−	0.299865i
$553$	−6.92296	+	4.36629i	−0.294394	+	0.185673i
$554$	15.9249	+	15.9249i	0.676582	+	0.676582i
$555$	−2.59484	−	4.49440i	−0.110145	−	0.190777i
$556$	−8.69372	+	15.0580i	−0.368696	+	0.638600i
$557$	−24.0373	+	6.44076i	−1.01849	+	0.272904i	−0.729173	−	0.684329i	$-0.760095\pi$
$557$	−24.0373	+	6.44076i	−1.01849	+	0.272904i	−0.289318	+	0.957233i	$0.593428\pi$
$558$	−2.02543			−0.0857434
$559$	−9.36554	+	14.7442i	−0.396120	+	0.623614i
$560$	−1.05115	+	1.13671i	−0.0444192	+	0.0480347i
$561$	2.51472	+	9.38507i	0.106172	+	0.396238i
$562$	8.44438	−	14.6261i	0.356205	−	0.616964i
$563$	19.8692	+	34.4144i	0.837385	+	1.45039i	0.892073	+	0.451891i	$0.149250\pi$
$563$	19.8692	+	34.4144i	0.837385	+	1.45039i	−0.0546879	+	0.998503i	$0.517416\pi$
$564$	−6.97884	+	6.97884i	−0.293862	+	0.293862i
$565$	0.533193	−	1.98990i	0.0224316	−	0.0837158i
$566$	7.76194	+	2.07980i	0.326259	+	0.0874207i
$567$	−0.103386	−	2.64373i	−0.00434181	−	0.111026i
$568$	1.98101	+	3.43121i	0.0831214	+	0.143971i
$569$	−5.23407	−	3.02189i	−0.219424	−	0.126684i	0.386260	−	0.922390i	$-0.373767\pi$
$569$	−5.23407	−	3.02189i	−0.219424	−	0.126684i	−0.605683	+	0.795706i	$0.707100\pi$
$570$	0.543015	+	2.02656i	0.0227444	+	0.0848833i
$571$			5.37374i			0.224884i	0.993658	+	0.112442i	$0.0358672\pi$
$571$			5.37374i			0.224884i	−0.993658	+	0.112442i	$0.964133\pi$
$572$	−3.44318	+	10.9712i	−0.143967	+	0.458731i
$573$			15.8717i			0.663051i
$574$	6.13833	+	3.23097i	0.256209	+	0.134858i
$575$	16.9856	−	29.4199i	0.708348	−	1.22690i
$576$	−0.866025	+	0.500000i	−0.0360844	+	0.0208333i
$577$	21.0241	+	21.0241i	0.875243	+	0.875243i	0.993038	−	0.117795i	$-0.0375826\pi$
$577$	21.0241	+	21.0241i	0.875243	+	0.875243i	−0.117795	+	0.993038i	$0.537583\pi$
$578$	−7.45542	−	1.99767i	−0.310105	−	0.0830923i
$579$	1.19526	+	0.320268i	0.0496732	+	0.0133099i
$580$	−0.790586	+	0.790586i	−0.0328273	+	0.0328273i
$581$	−32.0821	−	7.26563i	−1.33099	−	0.301429i
$582$	−10.3611	−	5.98199i	−0.429482	−	0.247961i
$583$	3.35401	−	0.898705i	0.138909	−	0.0372206i
$584$	1.17551			0.0486431
$585$	0.459403	+	2.05926i	0.0189940	+	0.0851401i
$586$		−	17.4870i		−	0.722380i
$587$	13.3130	−	3.56722i	0.549488	−	0.147235i	0.0266156	−	0.999646i	$-0.491527\pi$
$587$	13.3130	−	3.56722i	0.549488	−	0.147235i	0.522873	+	0.852411i	$0.324860\pi$
$588$	3.01590	−	6.31699i	0.124374	−	0.260508i
$589$	−6.28893	+	3.63092i	−0.259131	+	0.149609i
$590$	−0.182514	+	0.182514i	−0.00751397	+	0.00751397i
$591$	−5.00414	+	18.6757i	−0.205843	+	0.768216i
$592$	2.29536	−	8.56639i	0.0943386	−	0.352076i
$593$	−33.5971	+	33.5971i	−1.37967	+	1.37967i	−0.534497	+	0.845170i	$0.679499\pi$
$593$	−33.5971	+	33.5971i	−1.37967	+	1.37967i	−0.845170	+	0.534497i	$0.820501\pi$
$594$	−2.76194	+	1.59460i	−0.113324	+	0.0654274i
$595$	1.39790	+	4.50489i	0.0573083	+	0.184683i
$596$	−20.6475	+	5.53249i	−0.845757	+	0.226620i
$597$		−	5.51382i		−	0.225666i
$598$	−5.72609	−	25.6671i	−0.234157	−	1.04960i
$599$	15.4553			0.631486			0.315743	−	0.948845i	$-0.397746\pi$
$599$	15.4553			0.631486			0.315743	+	0.948845i	$0.397746\pi$
$600$	−4.49887	+	1.20547i	−0.183665	+	0.0492130i
$601$	26.0350	+	15.0313i	1.06199	+	0.613140i	0.925982	−	0.377568i	$-0.123240\pi$
$601$	26.0350	+	15.0313i	1.06199	+	0.613140i	0.136007	+	0.990708i	$0.456573\pi$
$602$	−12.5009	−	2.83108i	−0.509499	−	0.115386i
$603$	10.3244	−	10.3244i	0.420441	−	0.420441i
$604$	5.36338	+	1.43711i	0.218233	+	0.0584753i
$605$	−0.468553	−	0.125548i	−0.0190494	−	0.00510426i
$606$	0.101615	+	0.101615i	0.00412785	+	0.00412785i
$607$	26.8881	−	15.5239i	1.09136	−	0.630094i	0.157418	−	0.987532i	$-0.449683\pi$
$607$	26.8881	−	15.5239i	1.09136	−	0.630094i	0.933937	+	0.357438i	$0.116350\pi$
$608$	−1.79266	+	3.10498i	−0.0727021	+	0.125924i
$609$	2.35453	−	4.47323i	0.0954103	−	0.181264i
$610$		−	8.50527i		−	0.344368i
$611$	−10.6555	+	33.9525i	−0.431077	+	1.37357i
$612$			3.04657i			0.123150i
$613$	3.94356	+	14.7176i	0.159279	+	0.594436i	0.998701	+	0.0509564i	$0.0162270\pi$
$613$	3.94356	+	14.7176i	0.159279	+	0.594436i	−0.839422	+	0.543480i	$0.817106\pi$
$614$	26.7084	+	15.4201i	1.07786	+	0.622304i
$615$	−0.767119	−	1.32869i	−0.0309332	−	0.0535779i
$616$	−8.43141	+	0.329720i	−0.339711	+	0.0132848i
$617$	−25.4820	−	6.82787i	−1.02587	−	0.274880i	−0.293621	−	0.955922i	$-0.594860\pi$
$617$	−25.4820	−	6.82787i	−1.02587	−	0.274880i	−0.732244	+	0.681042i	$0.761527\pi$
$618$	−0.168162	+	0.627588i	−0.00676445	+	0.0252453i
$619$	17.3034	−	17.3034i	0.695481	−	0.695481i	−0.267952	−	0.963432i	$-0.586347\pi$
$619$	17.3034	−	17.3034i	0.695481	−	0.695481i	0.963432	+	0.267952i	$0.0863467\pi$
$620$	0.592618	+	1.02644i	0.0238001	+	0.0412230i
$621$	3.64688	−	6.31658i	0.146344	−	0.253476i
$622$	−0.519920	−	1.94037i	−0.0208469	−	0.0778016i
$623$	−6.10402	−	5.64458i	−0.244552	−	0.226145i
$624$	−1.93321	+	3.04347i	−0.0773905	+	0.121836i
$625$	−19.9808			−0.799231
$626$	−28.9789	+	7.76486i	−1.15823	+	0.310346i
$627$	−5.71718	+	9.90244i	−0.228322	+	0.395465i
$628$	1.89386	+	3.28026i	0.0755731	+	0.130896i
$629$	−19.1051	−	19.1051i	−0.761771	−	0.761771i
$630$	−1.30954	+	0.825919i	−0.0521731	+	0.0329054i
$631$	−0.637828	+	2.38041i	−0.0253915	+	0.0947625i	−0.977459	−	0.211126i	$-0.932287\pi$
$631$	−0.637828	+	2.38041i	−0.0253915	+	0.0947625i	0.952067	+	0.305889i	$0.0989536\pi$
$632$	2.18749	+	2.18749i	0.0870139	+	0.0870139i
$633$	−10.4448	+	6.03031i	−0.415144	+	0.239683i
$634$	3.89473	+	2.24862i	0.154679	+	0.0893042i
$635$	−1.87950	−	7.01438i	−0.0745856	−	0.278357i
$636$	1.08877			0.0431727
$637$	−0.905115	−	25.2226i	−0.0358619	−	0.999357i
$638$	−6.09340			−0.241240
$639$	1.02545	+	3.82702i	0.0405661	+	0.151395i
$640$	0.506778	+	0.292588i	0.0200322	+	0.0115656i
$641$	−7.33245	+	4.23339i	−0.289614	+	0.167209i	−0.637768	−	0.770229i	$-0.720142\pi$
$641$	−7.33245	+	4.23339i	−0.289614	+	0.167209i	0.348154	+	0.937438i	$0.386809\pi$
$642$	−7.44807	−	7.44807i	−0.293952	−	0.293952i
$643$	−5.58735	+	20.8523i	−0.220343	+	0.822333i	0.763873	+	0.645366i	$0.223295\pi$
$643$	−5.58735	+	20.8523i	−0.220343	+	0.822333i	−0.984217	+	0.176967i	$0.943371\pi$
$644$	16.3223	−	10.2944i	0.643189	−	0.405657i
$645$	2.00459	+	2.00459i	0.0789306	+	0.0789306i
$646$	5.46147	+	9.45955i	0.214879	+	0.372181i
$647$	−1.49876	+	2.59593i	−0.0589223	+	0.102056i	−0.893982	−	0.448103i	$-0.852100\pi$
$647$	−1.49876	+	2.59593i	−0.0589223	+	0.102056i	0.835060	+	0.550160i	$0.185433\pi$
$648$	−0.965926	+	0.258819i	−0.0379452	+	0.0101674i
$649$	−1.40672			−0.0552184
$650$	−12.3661	+	11.3617i	−0.485037	+	0.445643i
$651$	−3.93441	−	3.63827i	−0.154202	−	0.142595i
$652$	−6.52705	−	24.3593i	−0.255619	−	0.953984i
$653$	12.4468	−	21.5584i	0.487080	−	0.843647i	−0.512810	−	0.858502i	$-0.671395\pi$
$653$	12.4468	−	21.5584i	0.487080	−	0.843647i	0.999890	+	0.0148552i	$0.00472873\pi$
$654$	−3.34194	−	5.78842i	−0.130680	−	0.226345i
$655$	−6.33389	+	6.33389i	−0.247486	+	0.247486i
$656$	0.678581	−	2.53250i	0.0264942	−	0.0988775i
$657$	1.13546	+	0.304245i	0.0442985	+	0.0118697i
$658$	−26.0925	+	1.02038i	−1.01719	+	0.0397784i
$659$	3.11188	+	5.38993i	0.121222	+	0.209962i	0.920250	−	0.391332i	$-0.127985\pi$
$659$	3.11188	+	5.38993i	0.121222	+	0.209962i	−0.799028	+	0.601294i	$0.794652\pi$
$660$	1.61622	+	0.933126i	0.0629113	+	0.0363219i
$661$	−6.68650	−	24.9543i	−0.260075	−	0.970611i	−0.965197	−	0.261525i	$-0.915774\pi$
$661$	−6.68650	−	24.9543i	−0.260075	−	0.970611i	0.705122	−	0.709086i	$-0.250892\pi$
$662$		−	3.57142i		−	0.138807i
$663$	5.08506	+	9.73667i	0.197488	+	0.378141i
$664$			12.4330i			0.482492i
$665$	−2.58549	+	4.91202i	−0.100261	+	0.190480i
$666$	4.43429	−	7.68041i	0.171825	−	0.297610i
$667$	12.0687	−	6.96784i	0.467300	−	0.269796i
$668$	−7.45659	−	7.45659i	−0.288504	−	0.288504i
$669$	16.2388	+	4.35117i	0.627829	+	0.168226i
$670$	−8.25295	−	2.21137i	−0.318839	−	0.0854327i
$671$	32.7770	−	32.7770i	1.26534	−	1.26534i
$672$	−2.58041	−	0.584385i	−0.0995413	−	0.0225431i
$673$	−2.44380	−	1.41093i	−0.0942014	−	0.0543872i	0.452159	−	0.891937i	$-0.350654\pi$
$673$	−2.44380	−	1.41093i	−0.0942014	−	0.0543872i	−0.546361	+	0.837550i	$0.683987\pi$
$674$	−7.54807	+	2.02250i	−0.290741	+	0.0779037i
$675$	−4.65757			−0.179270
$676$	−1.09856	+	12.9535i	−0.0422523	+	0.498212i
$677$		−	28.6749i		−	1.10207i	−0.834483	−	0.551033i	$-0.814234\pi$
$677$		−	28.6749i		−	1.10207i	0.834483	−	0.551033i	$-0.185766\pi$
$678$	3.40051	−	0.911165i	0.130596	−	0.0349931i
$679$	−9.38109	−	30.2317i	−0.360013	−	1.16018i
$680$	1.54393	−	0.891391i	0.0592072	−	0.0341833i
$681$	18.6596	−	18.6596i	0.715038	−	0.715038i
$682$	−1.67185	+	6.23942i	−0.0640184	+	0.238920i
$683$	−3.09642	+	11.5560i	−0.118481	+	0.442178i	−0.999524	−	0.0308593i	$-0.990176\pi$
$683$	−3.09642	+	11.5560i	−0.118481	+	0.442178i	0.881043	+	0.473037i	$0.156842\pi$
$684$	−2.53521	+	2.53521i	−0.0969361	+	0.0969361i
$685$	−1.25374	+	0.723845i	−0.0479028	+	0.0276567i
$686$	17.2056	−	6.85334i	0.656912	−	0.261662i
$687$	12.5975	−	3.37549i	0.480624	−	0.128783i
$688$			4.84455i			0.184697i
$689$	3.47966	−	1.81729i	0.132565	−	0.0692331i
$690$	−4.26814			−0.162485
$691$	19.0611	−	5.10741i	0.725118	−	0.194295i	0.122664	−	0.992448i	$-0.460856\pi$
$691$	19.0611	−	5.10741i	0.725118	−	0.194295i	0.602454	+	0.798153i	$0.294190\pi$
$692$	6.01909	+	3.47513i	0.228812	+	0.132104i
$693$	−8.22945	−	1.86372i	−0.312611	−	0.0707970i
$694$	−21.5376	+	21.5376i	−0.817556	+	0.817556i
$695$	9.82803	+	2.63341i	0.372799	+	0.0998911i
$696$	−1.84553	−	0.494508i	−0.0699546	−	0.0187443i
$697$	−5.64809	−	5.64809i	−0.213937	−	0.213937i
$698$	11.7164	−	6.76445i	0.443471	−	0.256038i
$699$	2.42872	−	4.20666i	0.0918626	−	0.159111i
$700$	−10.9044	−	5.73966i	−0.412149	−	0.216939i
$701$			51.6721i			1.95163i	0.218603	+	0.975814i	$0.429850\pi$
$701$			51.6721i			1.95163i	−0.218603	+	0.975814i	$0.570150\pi$
$702$	−2.65505	+	2.43941i	−0.100208	+	0.0920696i
$703$		−	31.7967i		−	1.19924i
$704$	0.825428	+	3.08054i	0.0311095	+	0.116102i
$705$	5.00168	+	2.88772i	0.188374	+	0.108758i
$706$	−5.99905	−	10.3907i	−0.225777	−	0.391058i
$707$	0.0148572	+	0.379920i	0.000558762	+	0.0142884i
$708$	−0.426056	−	0.114161i	−0.0160122	−	0.00429045i
$709$	4.69715	−	17.5300i	0.176405	−	0.658353i	−0.819903	−	0.572503i	$-0.805973\pi$
$709$	4.69715	−	17.5300i	0.176405	−	0.658353i	0.996308	−	0.0858504i	$-0.0273607\pi$
$710$	1.63942	−	1.63942i	0.0615262	−	0.0615262i
$711$	1.54679	+	2.67912i	0.0580092	+	0.100475i
$712$	−1.57117	+	2.72135i	−0.0588822	+	0.101987i
$713$	−3.82354	−	14.2696i	−0.143193	−	0.534402i
$714$	−5.47254	+	5.91797i	−0.204804	+	0.221475i
$715$	6.72284	+	0.284565i	0.251420	+	0.0106421i
$716$	23.9667			0.895676
$717$	−24.3890	+	6.53502i	−0.910825	+	0.244055i
$718$	5.33936	−	9.24804i	0.199263	−	0.345134i
$719$	−7.75311	−	13.4288i	−0.289142	−	0.500809i	0.684463	−	0.729048i	$-0.260037\pi$
$719$	−7.75311	−	13.4288i	−0.289142	−	0.500809i	−0.973605	+	0.228239i	$0.926703\pi$
$720$	0.413783	+	0.413783i	0.0154208	+	0.0154208i
$721$	−1.45399	+	0.917024i	−0.0541493	+	0.0341518i
$722$	1.59056	−	5.93603i	0.0591944	−	0.220916i
$723$	7.92174	+	7.92174i	0.294613	+	0.294613i
$724$	16.9562	−	9.78967i	0.630172	−	0.363830i
$725$	−7.70667	−	4.44945i	−0.286219	−	0.165248i
$726$	−0.214548	−	0.800702i	−0.00796261	−	0.0297169i
$727$	−2.17120			−0.0805253			−0.0402627	−	0.999189i	$-0.512819\pi$
$727$	−2.17120			−0.0805253			−0.0402627	+	0.999189i	$0.512819\pi$
$728$	−9.22224	+	2.43933i	−0.341799	+	0.0904074i
$729$	−1.00000			−0.0370370
$730$	−0.178037	−	0.664445i	−0.00658946	−	0.0245922i
$731$	12.7819	+	7.37962i	0.472755	+	0.272945i
$732$	12.5873	−	7.26727i	0.465239	−	0.268606i
$733$	14.3408	+	14.3408i	0.529689	+	0.529689i	0.920480	−	0.390790i	$-0.127798\pi$
$733$	14.3408	+	14.3408i	0.529689	+	0.529689i	−0.390790	+	0.920480i	$0.627798\pi$
$734$	0.824225	−	3.07605i	0.0304227	−	0.113539i
$735$	−4.02737	−	0.747960i	−0.148552	−	0.0275889i
$736$	−5.15747	−	5.15747i	−0.190107	−	0.190107i
$737$	−23.2826	−	40.3266i	−0.857625	−	1.48545i
$738$	1.31092	−	2.27058i	0.0482556	−	0.0835811i
$739$	0.533221	−	0.142876i	0.0196149	−	0.00525578i	−0.248998	−	0.968504i	$-0.580101\pi$
$739$	0.533221	−	0.142876i	0.0196149	−	0.00525578i	0.268613	+	0.963248i	$0.413435\pi$
$740$	−5.18969			−0.190777
$741$	−3.87084	+	12.3339i	−0.142199	+	0.453098i
$742$	2.11495	+	1.95576i	0.0776423	+	0.0717982i
$743$	1.75925	+	6.56561i	0.0645406	+	0.240869i	0.990659	−	0.136365i	$-0.0435420\pi$
$743$	1.75925	+	6.56561i	0.0645406	+	0.240869i	−0.926118	+	0.377234i	$0.876875\pi$
$744$	−1.01272	+	1.75408i	−0.0371280	+	0.0643075i
$745$	6.25435	+	10.8328i	0.229141	+	0.396885i
$746$	16.6119	−	16.6119i	0.608203	−	0.608203i
$747$	−3.21789	+	12.0093i	−0.117736	+	0.439398i
$748$	9.38507	+	2.51472i	0.343152	+	0.0919474i
$749$	−1.08898	−	27.8469i	−0.0397906	−	1.01750i
$750$	2.82569	+	4.89424i	0.103180	+	0.178712i
$751$	−10.4450	−	6.03043i	−0.381144	−	0.220054i	0.297172	−	0.954824i	$-0.403957\pi$
$751$	−10.4450	−	6.03043i	−0.381144	−	0.220054i	−0.678316	+	0.734770i	$0.737290\pi$
$752$	2.55443	+	9.53328i	0.0931506	+	0.347643i
$753$			22.4468i			0.818006i
$754$	−6.72360	+	1.49997i	−0.244859	+	0.0546258i
$755$		−	3.24924i		−	0.118252i
$756$	−2.34123	−	1.23233i	−0.0851497	−	0.0448194i
$757$	3.91592	−	6.78257i	0.142327	−	0.246517i	−0.786046	−	0.618168i	$-0.787875\pi$
$757$	3.91592	−	6.78257i	0.142327	−	0.246517i	0.928372	+	0.371651i	$0.121208\pi$
$758$	7.93556	−	4.58160i	0.288233	−	0.166411i
$759$	−16.4482	−	16.4482i	−0.597033	−	0.597033i
$760$	2.02656	+	0.543015i	0.0735111	+	0.0196972i
$761$	7.49643	+	2.00866i	0.271745	+	0.0728140i	0.392118	−	0.919915i	$-0.371742\pi$
$761$	7.49643	+	2.00866i	0.271745	+	0.0728140i	−0.120373	+	0.992729i	$0.538409\pi$
$762$	8.77492	−	8.77492i	0.317882	−	0.317882i
$763$	3.90596	−	17.2471i	0.141405	−	0.624389i
$764$	13.7453	+	7.93587i	0.497288	+	0.287110i
$765$	1.72203	−	0.461418i	0.0622603	−	0.0166826i
$766$	27.7707			1.00340
$767$	−1.55220	+	0.346282i	−0.0560467	+	0.0125035i
$768$			1.00000i			0.0360844i
$769$	8.11098	−	2.17333i	0.292489	−	0.0783723i	−0.109591	−	0.993977i	$-0.534954\pi$
$769$	8.11098	−	2.17333i	0.292489	−	0.0783723i	0.402080	+	0.915605i	$0.368287\pi$
$770$	1.46335	+	4.71581i	0.0527354	+	0.169946i
$771$	4.58320	−	2.64611i	0.165060	−	0.0952974i
$772$	0.874988	−	0.874988i	0.0314915	−	0.0314915i
$773$	9.20420	−	34.3505i	0.331052	−	1.23550i	−0.577035	−	0.816720i	$-0.695790\pi$
$773$	9.20420	−	34.3505i	0.331052	−	1.23550i	0.908086	−	0.418783i	$-0.137543\pi$
$774$	−1.25386	+	4.67947i	−0.0450691	+	0.168200i
$775$	−6.67055	+	6.67055i	−0.239613	+	0.239613i
$776$	−10.3611	+	5.98199i	−0.371942	+	0.214741i
$777$	22.4099	−	6.95395i	0.803951	−	0.249472i
$778$	19.3190	−	5.17650i	0.692619	−	0.185587i
$779$		−	9.40014i		−	0.336795i
$780$	2.01308	+	0.631777i	0.0720797	+	0.0226212i
$781$	12.6357			0.452142
$782$	−21.4638	+	5.75120i	−0.767543	+	0.205663i
$783$	−1.65466	−	0.955316i	−0.0591326	−	0.0341402i
$784$	−3.96272	−	5.77034i	−0.141526	−	0.206084i
$785$	1.56729	−	1.56729i	0.0559390	−	0.0559390i
$786$	−14.7857	−	3.96182i	−0.527389	−	0.141313i
$787$	−2.35283	−	0.630439i	−0.0838693	−	0.0224727i	0.216640	−	0.976251i	$-0.430490\pi$
$787$	−2.35283	−	0.630439i	−0.0838693	−	0.0224727i	−0.300510	+	0.953779i	$0.597157\pi$
$788$	13.6716	+	13.6716i	0.487029	+	0.487029i
$789$	−13.9486	+	8.05322i	−0.496583	+	0.286702i
$790$	0.905147	−	1.56776i	0.0322037	−	0.0557784i
$791$	8.24224	+	4.33838i	0.293060	+	0.154255i
$792$			3.18921i			0.113324i
$793$	28.0984	−	44.2354i	0.997802	−	1.57084i
$794$		−	0.664733i		−	0.0235905i
$795$	−0.164900	−	0.615416i	−0.00584841	−	0.0218266i
$796$	−4.77511	−	2.75691i	−0.169249	−	0.0977161i
$797$	−14.4210	−	24.9779i	−0.510819	−	0.884764i	−0.999921	−	0.0125380i	$-0.996009\pi$
$797$	−14.4210	−	24.9779i	−0.510819	−	0.884764i	0.489102	−	0.872226i	$-0.337324\pi$
$798$	−9.47864	+	0.370673i	−0.335540	+	0.0131217i
$799$	29.0438	+	7.78226i	1.02750	+	0.275317i
$800$	−1.20547	+	4.49887i	−0.0426197	+	0.159059i
$801$	−2.22197	+	2.22197i	−0.0785095	+	0.0785095i
$802$	−2.22721	−	3.85763i	−0.0786454	−	0.136218i
$803$	1.87448	−	3.24669i	0.0661490	−	0.114573i
$804$	−3.77898	−	14.1033i	−0.133274	−	0.497387i
$805$	−8.29088	−	7.66684i	−0.292215	−	0.270221i
$806$	−0.308837	+	7.29626i	−0.0108783	+	0.257000i
$807$	14.9540			0.526406
$808$	0.138809	−	0.0371938i	0.00488330	−	0.00130847i
$809$	−23.8475	+	41.3052i	−0.838435	+	1.45221i	0.0527677	+	0.998607i	$0.483196\pi$
$809$	−23.8475	+	41.3052i	−0.838435	+	1.45221i	−0.891203	+	0.453605i	$0.850138\pi$
$810$	0.292588	+	0.506778i	0.0102805	+	0.0178064i
$811$	30.3760	+	30.3760i	1.06665	+	1.06665i	0.997615	+	0.0690307i	$0.0219907\pi$
$811$	30.3760	+	30.3760i	1.06665	+	1.06665i	0.0690307	+	0.997615i	$0.478009\pi$
$812$	−2.69667	−	4.27570i	−0.0946344	−	0.150048i
$813$	−6.42824	+	23.9905i	−0.225448	+	0.841384i
$814$	−19.9996	−	19.9996i	−0.700986	−	0.700986i
$815$	−12.7802	+	7.37867i	−0.447672	+	0.258464i
$816$	2.63841	+	1.52328i	0.0923627	+	0.0533256i
$817$	4.49550	+	16.7774i	0.157278	+	0.586968i
$818$	0.279185			0.00976148
$819$	−9.53934	−	0.0306841i	−0.333332	−	0.00107219i
$820$	−1.53424			−0.0535779
$821$	1.58999	+	5.93391i	0.0554909	+	0.207095i	0.988105	−	0.153780i	$-0.0491447\pi$
$821$	1.58999	+	5.93391i	0.0554909	+	0.207095i	−0.932614	+	0.360875i	$0.882478\pi$
$822$	−2.14249	−	1.23697i	−0.0747280	−	0.0431442i
$823$	15.5553	−	8.98085i	0.542223	−	0.313053i	−0.203756	−	0.979022i	$-0.565315\pi$
$823$	15.5553	−	8.98085i	0.542223	−	0.313053i	0.745980	+	0.665969i	$0.231982\pi$
$824$	0.459426	+	0.459426i	0.0160049	+	0.0160049i
$825$	−3.84449	+	14.3478i	−0.133848	+	0.499527i
$826$	−0.622549	−	0.987082i	−0.0216612	−	0.0343450i
$827$	−16.9993	−	16.9993i	−0.591124	−	0.591124i	0.346811	−	0.937935i	$-0.387265\pi$
$827$	−16.9993	−	16.9993i	−0.591124	−	0.591124i	−0.937935	+	0.346811i	$0.887265\pi$
$828$	−3.64688	−	6.31658i	−0.126738	−	0.219516i
$829$	−6.27999	+	10.8773i	−0.218113	+	0.377783i	−0.954231	−	0.299070i	$-0.903324\pi$
$829$	−6.27999	+	10.8773i	−0.218113	+	0.377783i	0.736118	+	0.676853i	$0.236657\pi$
$830$	7.02757	−	1.88303i	0.243931	−	0.0653610i
$831$	22.5211			0.781250
$832$	1.66911	+	3.19595i	0.0578660	+	0.110799i
$833$	−21.2609	+	1.66541i	−0.736645	+	0.0577029i
$834$	4.50020	+	16.7950i	0.155829	+	0.581563i
$835$	−3.08541	+	5.34408i	−0.106775	+	0.184939i
$836$	5.71718	+	9.90244i	0.197733	+	0.342483i
$837$	−1.43220	+	1.43220i	−0.0495040	+	0.0495040i
$838$	8.53183	−	31.8412i	0.294727	−	1.09994i
$839$	−54.8442	−	14.6955i	−1.89343	−	0.507344i	−0.998077	−	0.0619909i	$-0.980255\pi$
$839$	−54.8442	−	14.6955i	−1.89343	−	0.507344i	−0.895355	−	0.445353i	$-0.853078\pi$
$840$	0.0604991	+	1.54705i	0.00208742	+	0.0533783i
$841$	12.6747	+	21.9533i	0.437060	+	0.757010i
$842$	4.98479	+	2.87797i	0.171787	+	0.0991814i
$843$	−4.37113	−	16.3133i	−0.150550	−	0.561859i
$844$			12.0606i			0.415144i
$845$	7.48819	−	1.34092i	0.257601	−	0.0461292i
$846$			9.86958i			0.339323i
$847$	1.02154	−	1.94076i	0.0351005	−	0.0666853i
$848$	0.544387	−	0.942907i	0.0186943	−	0.0323795i
$849$	6.95916	−	4.01787i	0.238838	−	0.137893i
$850$	10.0336	+	10.0336i	0.344148	+	0.344148i
$851$	62.4812	+	16.7418i	2.14183	+	0.573901i
$852$	3.82702	+	1.02545i	0.131112	+	0.0351312i
$853$	35.1436	−	35.1436i	1.20330	−	1.20330i	0.230137	−	0.973158i	$-0.426082\pi$
$853$	35.1436	−	35.1436i	1.20330	−	1.20330i	0.973158	−	0.230137i	$-0.0739175\pi$
$854$	37.5050	+	8.49376i	1.28339	+	0.290650i
$855$	1.81696	+	1.04903i	0.0621389	+	0.0358759i
$856$	−10.1743	+	2.72618i	−0.347749	+	0.0931791i
$857$	−28.2924			−0.966449			−0.483225	−	0.875496i	$-0.660535\pi$
$857$	−28.2924			−0.966449			−0.483225	+	0.875496i	$0.660535\pi$
$858$	5.32315	+	10.1925i	0.181729	+	0.347967i
$859$		−	3.57208i		−	0.121878i	−0.998141	−	0.0609390i	$-0.980590\pi$
$859$		−	3.57208i		−	0.121878i	0.998141	−	0.0609390i	$-0.0194095\pi$
$860$	2.73832	−	0.733730i	0.0933759	−	0.0250200i
$861$	6.62509	−	2.05581i	0.225783	−	0.0700619i
$862$	19.6461	−	11.3427i	0.669147	−	0.386332i
$863$	22.5019	−	22.5019i	0.765974	−	0.765974i	−0.211421	−	0.977395i	$-0.567809\pi$
$863$	22.5019	−	22.5019i	0.765974	−	0.765974i	0.977395	+	0.211421i	$0.0678091\pi$
$864$	−0.258819	+	0.965926i	−0.00880520	+	0.0328615i
$865$	1.05265	−	3.92854i	0.0357912	−	0.133574i
$866$	3.45468	−	3.45468i	0.117395	−	0.117395i
$867$	−6.68435	+	3.85921i	−0.227012	+	0.131066i
$868$	−5.11804	+	1.58816i	−0.173718	+	0.0539058i
$869$	9.52991	−	2.55353i	0.323280	−	0.0866226i
$870$			1.11806i			0.0379057i
$871$	−35.6175	−	38.7660i	−1.20685	−	1.31353i
$872$	−6.68389			−0.226345
$873$	−11.5563	+	3.09651i	−0.391122	+	0.104801i
$874$	−22.6470	−	13.0753i	−0.766046	−	0.442277i
$875$	−3.30258	+	14.5829i	−0.111648	+	0.492991i
$876$	0.831214	−	0.831214i	0.0280841	−	0.0280841i
$877$	11.7229	+	3.14115i	0.395855	+	0.106069i	0.451255	−	0.892395i	$-0.350977\pi$
$877$	11.7229	+	3.14115i	0.395855	+	0.106069i	−0.0553994	+	0.998464i	$0.517643\pi$
$878$	−20.6532	−	5.53402i	−0.697013	−	0.186764i
$879$	−12.3652	−	12.3652i	−0.417066	−	0.417066i
$880$	1.61622	−	0.933126i	0.0544828	−	0.0314557i
$881$	−12.6411	+	21.8950i	−0.425889	+	0.737661i	−0.996503	−	0.0835575i	$-0.973372\pi$
$881$	−12.6411	+	21.8950i	−0.425889	+	0.737661i	0.570614	+	0.821218i	$0.306705\pi$
$882$	−2.33422	−	6.59935i	−0.0785974	−	0.222212i
$883$		−	48.8278i		−	1.64319i	−0.570074	−	0.821594i	$-0.693085\pi$
$883$		−	48.8278i		−	1.64319i	0.570074	−	0.821594i	$-0.306915\pi$
$884$	10.9747	+	0.464539i	0.369120	+	0.0156241i
$885$			0.258113i			0.00867638i
$886$	3.80095	+	14.1854i	0.127696	+	0.476566i
$887$	−41.3523	−	23.8748i	−1.38847	−	0.801636i	−0.395331	−	0.918539i	$-0.629370\pi$
$887$	−41.3523	−	23.8748i	−1.38847	−	0.801636i	−0.993143	+	0.116903i	$0.962703\pi$
$888$	−4.43429	−	7.68041i	−0.148805	−	0.257738i
$889$	32.8077	−	1.28298i	1.10033	−	0.0430298i
$890$	1.77617	+	0.475923i	0.0595374	+	0.0159530i
$891$	−0.825428	+	3.08054i	−0.0276529	+	0.103202i
$892$	11.8876	−	11.8876i	0.398027	−	0.398027i
$893$	17.6928	+	30.6449i	0.592068	+	1.02549i
$894$	−10.6880	+	18.5121i	−0.357459	+	0.619137i
$895$	−3.62987	−	13.5469i	−0.121333	−	0.452821i
$896$	−1.79629	+	1.94250i	−0.0600100	+	0.0648945i
$897$	−22.1983	−	14.1004i	−0.741180	−	0.470799i
$898$	31.0490			1.03612
$899$	−3.73799	+	1.00159i	−0.124669	+	0.0334050i
$900$	−2.32878	+	4.03357i	−0.0776261	+	0.134452i
$901$	−1.65851	−	2.87263i	−0.0552531	−	0.0957012i
$902$	−5.91253	−	5.91253i	−0.196866	−	0.196866i
$903$	−10.8413	+	6.83759i	−0.360777	+	0.227541i
$904$	0.911165	−	3.40051i	0.0303049	−	0.113099i
$905$	−8.10159	−	8.10159i	−0.269306	−	0.269306i
$906$	4.80867	−	2.77629i	0.159757	−	0.0922360i
$907$	28.0265	+	16.1811i	0.930603	+	0.537284i	0.887002	−	0.461765i	$-0.152784\pi$
$907$	28.0265	+	16.1811i	0.930603	+	0.537284i	0.0436008	+	0.999049i	$0.486117\pi$
$908$	−6.82989	−	25.4895i	−0.226658	−	0.845899i
$909$	0.143706			0.00476643
$910$	2.77555	+	4.84331i	0.0920086	+	0.160554i
$911$	−34.9265			−1.15717			−0.578584	−	0.815623i	$-0.696394\pi$
$911$	−34.9265			−1.15717			−0.578584	+	0.815623i	$0.696394\pi$
$912$	0.927951	+	3.46316i	0.0307275	+	0.114677i
$913$	34.3390	+	19.8256i	1.13646	+	0.656133i
$914$	−13.6123	+	7.85908i	−0.450255	+	0.259955i
$915$	−6.01414	−	6.01414i	−0.198821	−	0.198821i
$916$	3.37549	−	12.5975i	0.111529	−	0.416233i
$917$	−21.6047	−	34.2554i	−0.713451	−	1.13121i
$918$	2.15425	+	2.15425i	0.0711008	+	0.0711008i
$919$	20.3000	+	35.1606i	0.669635	+	1.15984i	0.978006	+	0.208576i	$0.0668830\pi$
$919$	20.3000	+	35.1606i	0.669635	+	1.15984i	−0.308371	+	0.951266i	$0.599784\pi$
$920$	−2.13407	+	3.69632i	−0.0703582	+	0.121864i
$921$	29.7893	−	7.98202i	0.981591	−	0.263017i
$922$	38.9504			1.28276
$923$	13.9425	−	3.11045i	0.458924	−	0.102382i
$924$	−5.72876	+	6.19505i	−0.188462	+	0.203802i
$925$	−10.6908	−	39.8985i	−0.351511	−	1.31186i
$926$	7.17747	−	12.4317i	0.235866	−	0.408532i
$927$	0.324863	+	0.562680i	0.0106699	+	0.0184808i
$928$	−1.35102	+	1.35102i	−0.0443494	+	0.0443494i
$929$	1.54087	−	5.75060i	0.0505542	−	0.188671i	−0.936031	−	0.351917i	$-0.885530\pi$
$929$	1.54087	−	5.75060i	0.0505542	−	0.188671i	0.986585	+	0.163246i	$0.0521965\pi$
$930$	1.14485	+	0.306762i	0.0375411	+	0.0100591i
$931$	−19.0781	−	16.3064i	−0.625261	−	0.534420i
$932$	−2.42872	−	4.20666i	−0.0795553	−	0.137794i
$933$	−1.73968	−	1.00441i	−0.0569547	−	0.0328828i
$934$	1.17457	+	4.38357i	0.0384332	+	0.143435i
$935$		−	5.68566i		−	0.185941i
$936$	0.785067	+	3.51904i	0.0256607	+	0.115024i
$937$			24.7605i			0.808889i	0.914563	+	0.404444i	$0.132535\pi$
$937$			24.7605i			0.808889i	−0.914563	+	0.404444i	$0.867465\pi$
$938$	17.9931	−	34.1840i	0.587495	−	1.11615i
$939$	−15.0006	+	25.9817i	−0.489525	+	0.847882i
$940$	5.00168	−	2.88772i	0.163137	−	0.0941872i
$941$	32.4734	+	32.4734i	1.05860	+	1.05860i	0.998172	+	0.0604314i	$0.0192476\pi$
$941$	32.4734	+	32.4734i	1.05860	+	1.05860i	0.0604314	+	0.998172i	$0.480752\pi$
$942$	3.65865	+	0.980332i	0.119205	+	0.0319410i
$943$	18.4715	+	4.94941i	0.601513	+	0.161175i
$944$	−0.311895	+	0.311895i	−0.0101513	+	0.0101513i
$945$	−0.341968	+	1.50999i	−0.0111242	+	0.0491201i
$946$	13.3803	+	7.72513i	0.435032	+	0.251166i
$947$	−10.1728	+	2.72579i	−0.330571	+	0.0885761i	−0.420287	−	0.907391i	$-0.638071\pi$
$947$	−10.1728	+	2.72579i	−0.330571	+	0.0885761i	0.0897164	+	0.995967i	$0.471404\pi$
$948$	3.09358			0.100475
$949$	1.26913	−	4.04390i	0.0411975	−	0.131271i
$950$			16.6989i			0.541784i
$951$	4.34401	−	1.16397i	0.140864	−	0.0377444i
$952$	2.38885	+	7.69834i	0.0774230	+	0.249505i
$953$	−24.7720	+	14.3021i	−0.802442	+	0.463290i	−0.844324	−	0.535832i	$-0.819998\pi$
$953$	−24.7720	+	14.3021i	−0.802442	+	0.463290i	0.0418822	+	0.999123i	$0.486665\pi$
$954$	0.769880	−	0.769880i	0.0249258	−	0.0249258i
$955$	2.40385	−	8.97130i	0.0777868	−	0.290304i
$956$	−6.53502	+	24.3890i	−0.211358	+	0.788798i
$957$	−4.30869	+	4.30869i	−0.139280	+	0.139280i
$958$	−14.2411	+	8.22209i	−0.460108	+	0.265644i
$959$	−1.93984	−	6.25136i	−0.0626407	−	0.201867i
$960$	0.565237	−	0.151455i	0.0182430	−	0.00488819i
$961$		−	26.8976i		−	0.867665i
$962$	−26.9912	−	17.1449i	−0.870231	−	0.552772i
$963$	−10.5332			−0.339427
$964$	10.8213	−	2.89956i	0.348531	−	0.0933885i
$965$	−0.627098	−	0.362055i	−0.0201870	−	0.0116550i
$966$	4.26236	−	18.8209i	0.137139	−	0.605551i
$967$	12.0359	−	12.0359i	0.387047	−	0.387047i	−0.486586	−	0.873633i	$-0.661758\pi$
$967$	12.0359	−	12.0359i	0.387047	−	0.387047i	0.873633	+	0.486586i	$0.161758\pi$
$968$	−0.800702	−	0.214548i	−0.0257356	−	0.00689582i
$969$	10.5508	+	2.82707i	0.338939	+	0.0908184i
$970$	4.95049	+	4.95049i	0.158951	+	0.158951i
$971$	−43.7408	+	25.2537i	−1.40371	+	0.810431i	−0.994771	−	0.102131i	$-0.967434\pi$
$971$	−43.7408	+	25.2537i	−1.40371	+	0.810431i	−0.408937	+	0.912563i	$0.634100\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	−21.4271	+	40.7080i	−0.686920	+	1.30504i
$974$		−	15.8088i		−	0.506547i
$975$	−0.710183	+	16.7781i	−0.0227441	+	0.537328i
$976$		−	14.5345i		−	0.465239i
$977$	14.7282	+	54.9664i	0.471197	+	1.75853i	0.635480	+	0.772117i	$0.280802\pi$
$977$	14.7282	+	54.9664i	0.471197	+	1.75853i	−0.164283	+	0.986413i	$0.552531\pi$
$978$	−21.8399	−	12.6093i	−0.698365	−	0.403201i
$979$	5.01079	+	8.67895i	0.160146	+	0.277380i
$980$	−2.66144	+	3.11383i	−0.0850165	+	0.0994675i
$981$	−6.45614	−	1.72992i	−0.206129	−	0.0552320i
$982$	3.07001	−	11.4574i	0.0979680	−	0.365622i
$983$	25.3767	−	25.3767i	0.809391	−	0.809391i	−0.175151	−	0.984542i	$-0.556041\pi$
$983$	25.3767	−	25.3767i	0.809391	−	0.809391i	0.984542	+	0.175151i	$0.0560414\pi$
$984$	−1.31092	−	2.27058i	−0.0417906	−	0.0723834i
$985$	5.65705	−	9.79831i	0.180249	−	0.312200i
$986$	1.50655	+	5.62253i	0.0479784	+	0.179058i
$987$	−17.7287	+	19.1717i	−0.564310	+	0.610242i
$988$	8.74608	+	9.51921i	0.278250	+	0.302847i
$989$	−35.3350			−1.12359
$990$	1.80266	−	0.483021i	0.0572923	−	0.0153514i
$991$	2.90165	−	5.02581i	0.0921740	−	0.159650i	−0.816252	−	0.577696i	$-0.803952\pi$
$991$	2.90165	−	5.02581i	0.0921740	−	0.159650i	0.908426	+	0.418046i	$0.137285\pi$
$992$	1.01272	+	1.75408i	0.0321538	+	0.0556919i
$993$	−2.52538	−	2.52538i	−0.0801405	−	0.0801405i
$994$	5.59200	+	8.86640i	0.177368	+	0.281225i
$995$	−0.835095	+	3.11662i	−0.0264743	+	0.0988034i
$996$	8.79143	+	8.79143i	0.278567	+	0.278567i
$997$	−23.2950	+	13.4494i	−0.737759	+	0.425945i	−0.821254	−	0.570563i	$-0.806725\pi$
$997$	−23.2950	+	13.4494i	−0.737759	+	0.425945i	0.0834950	+	0.996508i	$0.473392\pi$
$998$	14.1103	+	8.14658i	0.446654	+	0.257876i
$999$	−2.29536	−	8.56639i	−0.0726219	−	0.271028i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bx.a.97.4	✓	40
7.6	odd	2		546.2.bx.b.97.2	yes	40
13.11	odd	12		546.2.bx.b.349.2	yes	40
91.76	even	12	inner	546.2.bx.a.349.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bx.a.97.4	✓	40	1.1	even	1	trivial
546.2.bx.a.349.4	yes	40	91.76	even	12	inner
546.2.bx.b.97.2	yes	40	7.6	odd	2
546.2.bx.b.349.2	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} +(0.413783 + 0.413783i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(-2.23784 + 1.41140i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.292588 - 0.506778i) q^{10} +(3.08054 - 0.825428i) q^{11} +1.00000 q^{12} +(3.19595 - 1.66911i) q^{13} +(1.94250 + 1.79629i) q^{14} +(-0.151455 - 0.565237i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.52328 - 2.63841i) q^{17} +(0.707107 - 0.707107i) q^{18} +(0.927951 - 3.46316i) q^{19} +(-0.565237 - 0.151455i) q^{20} +(2.64373 - 0.103386i) q^{21} +(-1.59460 - 2.76194i) q^{22} +(6.31658 + 3.64688i) q^{23} +(-0.258819 - 0.965926i) q^{24} -4.65757i q^{25} +(-2.43941 - 2.65505i) q^{26} -1.00000i q^{27} +(1.23233 - 2.34123i) q^{28} +(0.955316 - 1.65466i) q^{29} +(-0.506778 + 0.292588i) q^{30} +(-1.43220 - 1.43220i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-3.08054 - 0.825428i) q^{33} +(-2.15425 + 2.15425i) q^{34} +(-1.50999 - 0.341968i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(8.56639 - 2.29536i) q^{37} -3.58533 q^{38} +(-3.60233 - 0.152479i) q^{39} +0.585177i q^{40} +(2.53250 - 0.678581i) q^{41} +(-0.784111 - 2.52689i) q^{42} +(-4.19550 + 2.42227i) q^{43} +(-2.25511 + 2.25511i) q^{44} +(-0.151455 + 0.565237i) q^{45} +(1.88776 - 7.04523i) q^{46} +(-6.97884 + 6.97884i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(3.01590 - 6.31699i) q^{49} +(-4.49887 + 1.20547i) q^{50} +3.04657i q^{51} +(-1.93321 + 3.04347i) q^{52} +1.08877 q^{53} +(-0.965926 + 0.258819i) q^{54} +(1.61622 + 0.933126i) q^{55} +(-2.58041 - 0.584385i) q^{56} +(-2.53521 + 2.53521i) q^{57} +(-1.84553 - 0.494508i) q^{58} +(-0.426056 - 0.114161i) q^{59} +(0.413783 + 0.413783i) q^{60} +(12.5873 - 7.26727i) q^{61} +(-1.01272 + 1.75408i) q^{62} +(-2.34123 - 1.23233i) q^{63} +1.00000i q^{64} +(2.01308 + 0.631777i) q^{65} +3.18921i q^{66} +(-3.77898 - 14.1033i) q^{67} +(2.63841 + 1.52328i) q^{68} +(-3.64688 - 6.31658i) q^{69} +(0.0604991 + 1.54705i) q^{70} +(3.82702 + 1.02545i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(0.831214 - 0.831214i) q^{73} +(-4.43429 - 7.68041i) q^{74} +(-2.32878 + 4.03357i) q^{75} +(0.927951 + 3.46316i) q^{76} +(-5.72876 + 6.19505i) q^{77} +(0.785067 + 3.51904i) q^{78} +3.09358 q^{79} +(0.565237 - 0.151455i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.31092 - 2.27058i) q^{82} +(8.79143 + 8.79143i) q^{83} +(-2.23784 + 1.41140i) q^{84} +(0.461418 - 1.72203i) q^{85} +(3.42561 + 3.42561i) q^{86} +(-1.65466 + 0.955316i) q^{87} +(2.76194 + 1.59460i) q^{88} +(0.813298 + 3.03527i) q^{89} +0.585177 q^{90} +(-4.79624 + 8.24597i) q^{91} -7.29376 q^{92} +(0.524220 + 1.95642i) q^{93} +(8.54730 + 4.93479i) q^{94} +(1.81696 - 1.04903i) q^{95} +(0.707107 + 0.707107i) q^{96} +(-3.09651 + 11.5563i) q^{97} +(-6.88232 - 1.27818i) q^{98} +(2.25511 + 2.25511i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 8 q^{7} + 20 q^{9} + 8 q^{11} + 40 q^{12} - 8 q^{14} + 20 q^{16} + 16 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 32 q^{26} + 8 q^{28} - 8 q^{33} + 16 q^{34} - 32 q^{35} + 40 q^{37} - 16 q^{38} - 16 q^{39}+ \cdots - 8 q^{99}+O(q^{100}) \) 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

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