LMFDB - Embedded newform 546.2.bx.b.97.2

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			97.2
Character	$\chi$	$=$	546.97
Dual form			546.2.bx.b.349.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.413783 - 0.413783i) q^{5} +(0.258819 - 0.965926i) q^{6} +(1.23233 + 2.34123i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.413783 - 0.413783i) q^{5} +(0.258819 - 0.965926i) q^{6} +(1.23233 + 2.34123i) 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} +(-0.103386 + 2.64373i) 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} +(-2.23784 - 1.41140i) 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} +(0.458844 - 1.47868i) 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} +(2.58041 - 0.584385i) 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} +(-3.96272 + 5.77034i) 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} +(-0.784111 + 2.52689i) 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} +(-1.41140 + 2.23784i) 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} +(-1.54705 - 0.0604991i) 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} +(-1.23233 - 2.34123i) 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} +(-7.84624 - 5.42555i) 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} +(6.59935 + 2.33422i) q^{98} +(2.25511 + 2.25511i) 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} + 40 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} - 20 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} - 20 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} + 32 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 + 40 * 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 - 20 * 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 - 20 * 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 + 32 * 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
$5$	−0.413783	−	0.413783i	−0.185049	−	0.185049i	0.608503	−	0.793552i	$-0.291770\pi$
$5$	−0.413783	−	0.413783i	−0.185049	−	0.185049i	−0.793552	+	0.608503i	$0.791770\pi$
$6$	0.258819	−	0.965926i	0.105662	−	0.394338i
$7$	1.23233	+	2.34123i	0.465777	+	0.884902i
$7$	1.23233	+	2.34123i	0.465777	+	0.884902i
$8$	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	0.989480	−	0.144671i	$-0.0462125\pi$
$17$	1.52328	+	2.63841i	0.369451	+	0.639907i	−0.620029	+	0.784579i	$0.712879\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	−0.927951	+	3.46316i	−0.212886	+	0.794503i	0.774013	+	0.633169i	$0.218246\pi$
$19$	−0.927951	+	3.46316i	−0.212886	+	0.794503i	−0.986900	+	0.161334i	$0.948420\pi$
$20$	0.565237	+	0.151455i	0.126391	+	0.0338663i
$21$	−0.103386	+	2.64373i	−0.0225607	+	0.576909i
$22$	−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
$28$	−2.23784	−	1.41140i	−0.422913	−	0.266730i
$29$	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	0.823927	−	0.566697i	$-0.191779\pi$
$31$	1.43220	+	1.43220i	0.257230	+	0.257230i	−0.566697	+	0.823927i	$0.691779\pi$
$32$	−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
$35$	0.458844	−	1.47868i	0.0775587	−	0.249942i
$36$	−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	−0.451092	−	0.892478i	$-0.648965\pi$
$41$	−2.53250	+	0.678581i	−0.395510	+	0.105977i	0.0555817	+	0.998454i	$0.482299\pi$
$42$	2.58041	−	0.584385i	0.398165	−	0.0901725i
$43$	−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	$-0.494228\pi$
$47$	6.97884	−	6.97884i	1.01797	−	1.01797i	0.999836	−	0.0181334i	$-0.00577235\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	−3.96272	+	5.77034i	−0.566103	+	0.824334i
$50$	−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
$56$	−0.784111	+	2.52689i	−0.104781	+	0.337670i
$57$	−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	0.286446	−	0.958096i	$-0.407526\pi$
$59$	0.426056	+	0.114161i	0.0554678	+	0.0148626i	−0.230978	+	0.972959i	$0.574193\pi$
$60$	0.413783	+	0.413783i	0.0534191	+	0.0534191i
$61$	−12.5873	+	7.26727i	−1.61164	+	0.930478i	−0.622644	+	0.782505i	$0.713942\pi$
$61$	−12.5873	+	7.26727i	−1.61164	+	0.930478i	−0.988991	+	0.147973i	$0.952725\pi$
$62$	1.01272	−	1.75408i	0.128615	−	0.222768i
$63$	−1.41140	+	2.23784i	−0.177820	+	0.281942i
$64$			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
$70$	−1.54705	−	0.0604991i	−0.184908	−	0.00723103i
$71$	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	−0.754075	−	0.656789i	$-0.771914\pi$
$73$	−0.831214	+	0.831214i	−0.0972862	+	0.0972862i	0.656789	+	0.754075i	$0.271914\pi$
$74$	−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	0.0344229	−	0.999407i	$-0.489041\pi$
$83$	−8.79143	−	8.79143i	−0.964984	−	0.964984i	−0.999407	+	0.0344229i	$0.989041\pi$
$84$	−1.23233	−	2.34123i	−0.134458	−	0.255449i
$85$	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	0.909331	−	0.416073i	$-0.136594\pi$
$89$	−0.813298	−	3.03527i	−0.0862095	−	0.321738i	−0.995540	+	0.0943354i	$0.969927\pi$
$90$	−0.585177			−0.0616831
$91$	−7.84624	−	5.42555i	−0.822509	−	0.568752i
$92$	−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	$-0.708888\pi$
$97$	3.09651	−	11.5563i	0.314403	−	1.17337i	0.924544	−	0.381074i	$-0.124446\pi$
$98$	6.59935	+	2.33422i	0.666635	+	0.235792i
$99$	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	−0.869578	−	0.493795i	$-0.835609\pi$
$101$	−0.0718530	+	0.124453i	−0.00714964	+	0.0123835i	0.862428	+	0.506179i	$0.168942\pi$
$102$	2.94276	−	0.788510i	0.291377	−	0.0780741i
$103$	−0.649727			−0.0640195			−0.0320097	−	0.999488i	$-0.510191\pi$
$103$	−0.649727			−0.0640195			−0.0320097	+	0.999488i	$0.510191\pi$
$104$	−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
$112$	2.64373	+	0.103386i	0.249809	+	0.00976906i
$113$	−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
$119$	−4.29993	+	6.81775i	−0.394174	+	0.624982i
$120$	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
$126$	2.52689	+	0.784111i	0.225113	+	0.0698542i
$127$	−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	$-0.766850\pi$
$131$		−	15.3073i		−	1.33740i	0.743530	−	0.668702i	$-0.233150\pi$
$132$	−3.08054	+	0.825428i	−0.268127	+	0.0718443i
$133$	−9.25160	+	2.09521i	−0.802215	+	0.181678i
$134$	−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	−0.976333	−	0.216274i	$-0.930609\pi$
$139$	−15.0580	+	8.69372i	−1.27720	+	0.737392i	−0.300867	+	0.953666i	$0.597276\pi$
$140$	0.341968	+	1.50999i	0.0289016	+	0.127618i
$141$	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
$147$	−6.31699	+	3.01590i	−0.521017	+	0.248747i
$148$	−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
$154$	4.50125	−	7.13695i	0.362721	−	0.575112i
$155$		−	1.18524i		−	0.0952004i
$156$	3.19595	−	1.66911i	0.255880	−	0.133636i
$157$			3.78771i			0.302292i	0.988511	+	0.151146i	$0.0482964\pi$
$157$			3.78771i			0.302292i	−0.988511	+	0.151146i	$0.951704\pi$
$158$	−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
$161$	−0.754073	+	19.2827i	−0.0594293	+	1.51969i
$162$	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	$-0.949557\pi$
$167$	−2.72930	−	10.1859i	−0.211200	−	0.788208i	0.776270	−	0.630400i	$-0.217109\pi$
$168$	−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	0.967356	−	0.253421i	$-0.0815558\pi$
$173$	3.47513	+	6.01909i	0.264209	+	0.457623i	−0.703147	+	0.711044i	$0.748222\pi$
$174$	−1.35102	−	1.35102i	−0.102421	−	0.102421i
$175$	10.9044	−	5.73966i	0.824298	−	0.433878i
$176$	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	$-0.240608\pi$
$181$	19.5793			1.45532			0.727660	+	0.685937i	$0.240608\pi$
$182$	−3.20992	+	8.98312i	−0.237935	+	0.665873i
$183$	−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
$189$	−2.34123	+	1.23233i	−0.170299	+	0.0896388i
$190$	−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	0.751610	−	0.659608i	$-0.229278\pi$
$199$	−2.75691	−	4.77511i	−0.195432	−	0.338499i	−0.947042	+	0.321109i	$0.895944\pi$
$200$	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
$203$	5.05120	+	0.197533i	0.354524	+	0.0138641i
$204$	−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
$210$	−1.30954	−	0.825919i	−0.0903665	−	0.0569938i
$211$	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
$217$	−1.58816	+	5.11804i	−0.107812	+	0.347435i
$218$	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	0.329794	−	0.944053i	$-0.393021\pi$
$223$	16.2388	−	4.35117i	1.08743	−	0.291376i	0.757637	+	0.652677i	$0.226354\pi$
$224$	−0.584385	−	2.58041i	−0.0390458	−	0.172411i
$225$	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	$-0.577041\pi$
$227$	6.82989	−	25.4895i	0.453316	−	1.69180i	0.692992	−	0.720945i	$-0.256292\pi$
$228$	0.927951	−	3.46316i	0.0614550	−	0.229353i
$229$	9.22201	−	9.22201i	0.609407	−	0.609407i	−0.333384	−	0.942791i	$-0.608190\pi$
$229$	9.22201	−	9.22201i	0.609407	−	0.609407i	0.942791	+	0.333384i	$0.108190\pi$
$230$	−3.69632	+	2.13407i	−0.243728	+	0.140716i
$231$	1.86372	+	8.22945i	0.122624	+	0.541458i
$232$	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
$238$	7.69834	+	2.38885i	0.499009	+	0.154846i
$239$	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	0.589914	−	0.807466i	$-0.299162\pi$
$241$	10.8213	+	2.89956i	0.697061	+	0.186777i	0.107147	+	0.994243i	$0.465828\pi$
$242$	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
$245$	4.02737	−	0.747960i	0.257299	−	0.0477854i
$246$			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	$0.0839224\pi$
$251$	11.2234	+	19.4395i	0.708414	+	1.22701i	−0.257031	+	0.966403i	$0.582744\pi$
$252$	0.103386	−	2.64373i	0.00651271	−	0.166539i
$253$	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	−0.771617	−	0.636088i	$-0.780552\pi$
$257$	2.64611	−	4.58320i	0.165060	−	0.285892i	0.936677	+	0.350196i	$0.113885\pi$
$258$	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
$266$	4.41831	+	8.39408i	0.270904	+	0.514674i
$267$	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	−0.0502159	−	0.998738i	$-0.515991\pi$
$269$	12.9505	−	7.47700i	0.789609	−	0.455881i	0.839825	+	0.542857i	$0.182658\pi$
$270$	−0.506778	−	0.292588i	−0.0308415	−	0.0178064i
$271$	6.42824	+	23.9905i	0.390488	+	1.45732i	0.829332	+	0.558756i	$0.188721\pi$
$271$	6.42824	+	23.9905i	0.390488	+	1.45732i	−0.438844	+	0.898563i	$0.644612\pi$
$272$	3.04657			0.184725
$273$	−4.08227	−	8.62178i	−0.247070	−	0.521814i
$274$	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
$280$	1.37003	−	0.721131i	0.0818752	−	0.0430958i
$281$	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	−0.721543	−	0.692369i	$-0.756567\pi$
$283$	4.01787	−	6.95916i	0.238838	−	0.413679i	0.960381	+	0.278690i	$0.0899002\pi$
$284$	−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	−0.270888	−	0.962611i	$-0.587317\pi$
$293$	−16.8911	−	4.52596i	−0.986789	−	0.264409i	−0.715901	+	0.698201i	$0.753984\pi$
$294$	4.54809	+	5.32117i	0.265250	+	0.310337i
$295$	−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
$301$	−10.8413	−	6.83759i	−0.624885	−	0.394112i
$302$	−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	$-0.407495\pi$
$307$	21.8073	−	21.8073i	1.24461	−	1.24461i	0.958068	−	0.286539i	$-0.0925049\pi$
$308$	−8.05878	−	2.50069i	−0.459191	−	0.142490i
$309$	−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	$-0.518139\pi$
$311$	−2.00881			−0.113909			−0.0569547	+	0.998377i	$0.518139\pi$
$312$	−2.43941	−	2.65505i	−0.138104	−	0.150312i
$313$			30.0011i			1.69576i	0.530185	+	0.847882i	$0.322122\pi$
$313$			30.0011i			1.69576i	−0.530185	+	0.847882i	$0.677878\pi$
$314$	3.65865	−	0.980332i	0.206470	−	0.0553234i
$315$	1.50999	−	0.341968i	0.0850785	−	0.0192677i
$316$	−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
$322$	18.8209	−	4.26236i	1.04885	−	0.237532i
$323$	−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
$329$	24.9393	+	7.73884i	1.37495	+	0.426656i
$330$	−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
$336$	2.23784	+	1.41140i	0.122084	+	0.0769982i
$337$		−	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
$343$	−18.3931	−	2.16669i	−0.993133	−	0.116990i
$344$	−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	$-0.965396\pi$
$349$	−3.50154	−	13.0679i	−0.187433	−	0.699509i	0.806664	−	0.591011i	$-0.201271\pi$
$350$	−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	−0.553689	−	0.832724i	$-0.686780\pi$
$353$	−11.5893	+	3.10534i	−0.616835	+	0.165280i	−0.0631465	+	0.998004i	$0.520114\pi$
$354$	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
$357$	−7.13272	+	3.75438i	−0.377504	+	0.198703i
$358$	−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
$364$	9.50781	+	0.775545i	0.498345	+	0.0406496i
$365$	0.687884			0.0360055
$366$	3.76181	+	14.0393i	0.196633	+	0.733845i
$367$	−2.75791	−	1.59228i	−0.143962	−	0.0831163i	0.426289	−	0.904587i	$-0.359821\pi$
$367$	−2.75791	−	1.59228i	−0.143962	−	0.0831163i	−0.570251	+	0.821471i	$0.693154\pi$
$368$	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
$371$	1.34173	+	2.54907i	0.0696592	+	0.132341i
$372$	−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	$-0.665584\pi$
$383$	7.18759	−	26.8245i	0.367269	−	1.37067i	0.864319	−	0.502944i	$-0.167750\pi$
$384$	0.965926	+	0.258819i	0.0492922	+	0.0132078i
$385$	0.192944	−	4.93387i	0.00983336	−	0.251453i
$386$	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
$392$	−6.88232	+	1.27818i	−0.347609	+	0.0645577i
$393$	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	0.242670	−	0.970109i	$-0.421977\pi$
$397$	−0.642083	−	0.172046i	−0.0322252	−	0.00863472i	−0.274896	+	0.961474i	$0.588643\pi$
$398$	−3.89886	+	3.89886i	−0.195432	+	0.195432i
$399$	−9.05972	−	2.81129i	−0.453553	−	0.140741i
$400$	−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
$406$	−1.11654	−	4.93021i	−0.0554131	−	0.244682i
$407$	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	−0.964116	−	0.265480i	$-0.914470\pi$
$409$	0.0722585	−	0.269672i	0.00357295	−	0.0133344i	0.967689	+	0.252146i	$0.0811362\pi$
$410$	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
$413$	0.257764	+	1.13818i	0.0126837	+	0.0560062i
$414$	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	−0.400837	−	0.916149i	$-0.631281\pi$
$419$	−28.5481	−	16.4822i	−1.39466	−	0.805210i	−0.993827	+	0.110939i	$0.964614\pi$
$420$	−0.458844	+	1.47868i	−0.0223893	+	0.0721521i
$421$	−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
$427$	−32.5260	−	20.5140i	−1.57405	−	0.992744i
$428$		−	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	0.801340	−	0.598210i	$-0.204121\pi$
$433$	−2.44283	−	4.23110i	−0.117395	−	0.203334i	−0.918735	+	0.394876i	$0.870788\pi$
$434$	5.35470	+	0.209401i	0.257034	+	0.0100516i
$435$	−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	$0.337113\pi$
$439$	−10.6909	+	18.5172i	−0.510249	+	0.883777i	−0.999929	+	0.0118753i	$0.996220\pi$
$440$	−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
$448$	−2.34123	+	1.23233i	−0.110613	+	0.0582221i
$449$	−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
$455$	1.00164	+	5.49163i	0.0469575	+	0.257452i
$456$	−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	$-0.554994\pi$
$461$	10.0811	−	37.6232i	0.469524	−	1.75229i	0.641436	−	0.767176i	$-0.278339\pi$
$462$	7.46667	−	3.93016i	0.347381	−	0.182848i
$463$	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	$-0.466515\pi$
$467$	4.53821			0.210003			0.105002	+	0.994472i	$0.466515\pi$
$468$	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
$476$	0.314973	−	8.05431i	0.0144368	−	0.369169i
$477$	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	$0.0392564\pi$
$479$	4.25607	+	15.8839i	0.194465	+	0.725752i	−0.797940	+	0.602737i	$0.794077\pi$
$480$			0.585177i			0.0267095i
$481$	−23.5465	+	21.6341i	−1.07363	+	0.986430i
$482$		−	11.2030i		−	0.510284i
$483$	−10.2944	+	16.3223i	−0.468412	+	0.742691i
$484$	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
$490$	−1.76483	−	3.69656i	−0.0797271	−	0.166993i
$491$	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
$497$	2.31535	+	10.2236i	0.103857	+	0.458593i
$498$	−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	−0.820696	−	0.571365i	$-0.806414\pi$
$503$	−16.5119	+	9.53312i	−0.736227	+	0.425061i	0.0844688	+	0.996426i	$0.473081\pi$
$504$	−2.58041	+	0.584385i	−0.114940	+	0.0260306i
$505$	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	−0.421796	−	0.906691i	$-0.638600\pi$
$509$	−7.52946	+	2.01751i	−0.333738	+	0.0894247i	0.0880588	+	0.996115i	$0.471934\pi$
$510$	−1.54393	−	0.891391i	−0.0683665	−	0.0394714i
$511$	−2.97039	−	0.921734i	−0.131402	−	0.0407751i
$512$	−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
$518$	12.5171	−	19.8465i	0.549970	−	0.872005i
$519$			6.95025i			0.305082i
$520$	0.976726	+	1.87019i	0.0428323	+	0.0820134i
$521$			37.4573i			1.64103i	0.571623	+	0.820516i	$0.306314\pi$
$521$			37.4573i			1.64103i	−0.571623	+	0.820516i	$0.693686\pi$
$522$	−0.494508	−	1.84553i	−0.0216440	−	0.0807766i
$523$	20.0250	+	11.5615i	0.875633	+	0.505547i	0.869216	−	0.494432i	$-0.164624\pi$
$523$	20.0250	+	11.5615i	0.875633	+	0.505547i	0.00641691	+	0.999979i	$0.497957\pi$
$524$	7.65365	+	13.2565i	0.334351	+	0.579113i
$525$	12.3134	+	0.481528i	0.537399	+	0.0210156i
$526$	−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
$539$	−7.44433	+	21.0467i	−0.320650	+	0.906546i
$540$	−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
$546$	−7.27143	+	6.17465i	−0.311189	+	0.264250i
$547$	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
$553$	3.81232	+	7.24280i	0.162116	+	0.307995i
$554$	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	$-0.850750\pi$
$563$	−19.8692	−	34.4144i	−0.837385	−	1.45039i	0.0546879	−	0.998503i	$-0.482584\pi$
$564$	−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
$567$	−2.64373	−	0.103386i	−0.111026	−	0.00434181i
$568$	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
$574$	−3.70046	+	5.86727i	−0.154454	+	0.244895i
$575$	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	0.117795	−	0.993038i	$-0.462417\pi$
$577$	−21.0241	−	21.0241i	−0.875243	−	0.875243i	−0.993038	+	0.117795i	$0.962417\pi$
$578$	−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
$581$	9.74882	−	31.4167i	0.404449	−	1.30338i
$582$	−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	−0.522873	−	0.852411i	$-0.675140\pi$
$587$	−13.3130	+	3.56722i	−0.549488	+	0.147235i	−0.0266156	+	0.999646i	$0.508473\pi$
$588$	3.96272	−	5.77034i	0.163420	−	0.237965i
$589$	−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	$-0.320501\pi$
$593$	33.5971	−	33.5971i	1.37967	−	1.37967i	0.845170	−	0.534497i	$-0.179499\pi$
$594$	2.76194	−	1.59460i	0.113324	−	0.0654274i
$595$	4.60030	−	1.04183i	0.188594	−	0.0427109i
$596$	−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	−0.136007	−	0.990708i	$-0.543427\pi$
$601$	−26.0350	−	15.0313i	−1.06199	−	0.613140i	−0.925982	+	0.377568i	$0.876760\pi$
$602$	−3.79866	+	12.2416i	−0.154822	+	0.498932i
$603$	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	−0.933937	−	0.357438i	$-0.883650\pi$
$607$	−26.8881	+	15.5239i	−1.09136	+	0.630094i	−0.157418	+	0.987532i	$0.550317\pi$
$608$	1.79266	−	3.10498i	0.0727021	−	0.125924i
$609$	4.27570	+	2.69667i	0.173260	+	0.109274i
$610$		−	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
$616$	−0.329720	+	8.43141i	−0.0132848	+	0.339711i
$617$	−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	−0.963432	−	0.267952i	$-0.913653\pi$
$619$	−17.3034	+	17.3034i	−0.695481	+	0.695481i	0.267952	+	0.963432i	$0.413653\pi$
$620$	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
$630$	−0.721131	−	1.37003i	−0.0287306	−	0.0545835i
$631$	−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
$637$	3.03331	−	25.0559i	0.120184	−	0.992752i
$638$	−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	$-0.776705\pi$
$643$	5.58735	−	20.8523i	0.220343	−	0.822333i	0.984217	−	0.176967i	$-0.0566285\pi$
$644$	−8.98832	−	17.0764i	−0.354190	−	0.672904i
$645$	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	−0.835060	−	0.550160i	$-0.814567\pi$
$647$	1.49876	−	2.59593i	0.0589223	−	0.102056i	0.893982	+	0.448103i	$0.147900\pi$
$648$	−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
$658$	1.02038	−	26.0925i	0.0397784	−	1.01719i
$659$	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	$0.0842255\pi$
$661$	6.68650	+	24.9543i	0.260075	+	0.970611i	−0.705122	+	0.709086i	$0.749108\pi$
$662$		−	3.57142i		−	0.138807i
$663$	−5.08506	−	9.73667i	−0.197488	−	0.378141i
$664$		−	12.4330i		−	0.482492i
$665$	4.69511	+	2.96119i	0.182069	+	0.114830i
$666$	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
$672$	0.784111	−	2.52689i	0.0302477	−	0.0974769i
$673$	−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	$0.185766\pi$
$677$			28.6749i			1.10207i	−0.834483	+	0.551033i	$0.814234\pi$
$678$	−3.40051	+	0.911165i	−0.130596	+	0.0349931i
$679$	30.8719	−	6.99156i	1.18476	−	0.268312i
$680$	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
$686$	2.66762	+	18.3271i	0.101850	+	0.699733i
$687$	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	−0.602454	−	0.798153i	$-0.705810\pi$
$691$	−19.0611	+	5.10741i	−0.725118	+	0.194295i	−0.122664	+	0.992448i	$0.539144\pi$
$692$	−6.01909	−	3.47513i	−0.228812	−	0.132104i
$693$	−2.50069	+	8.05878i	−0.0949935	+	0.306128i
$694$	−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
$700$	−6.57369	+	10.4229i	−0.248462	+	0.393949i
$701$			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
$707$	−0.379920	−	0.0148572i	−0.0142884	−	0.000558762i
$708$	−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	0.973605	−	0.228239i	$-0.0732966\pi$
$719$	7.75311	+	13.4288i	0.289142	+	0.500809i	−0.684463	+	0.729048i	$0.739963\pi$
$720$	−0.413783	−	0.413783i	−0.0154208	−	0.0154208i
$721$	−0.800678	−	1.52116i	−0.0298188	−	0.0566510i
$722$	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	$-0.487181\pi$
$727$	2.17120			0.0805253			0.0402627	+	0.999189i	$0.487181\pi$
$728$	−1.71168	−	9.38457i	−0.0634393	−	0.347815i
$729$	−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	0.390790	−	0.920480i	$-0.372202\pi$
$733$	−14.3408	−	14.3408i	−0.529689	−	0.529689i	−0.920480	+	0.390790i	$0.872202\pi$
$734$	−0.824225	+	3.07605i	−0.0304227	+	0.113539i
$735$	3.86179	+	1.36593i	0.142444	+	0.0503832i
$736$	−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
$749$	−27.8469	−	1.08898i	−1.01750	−	0.0397906i
$750$	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
$756$	1.41140	−	2.23784i	0.0513321	−	0.0813896i
$757$	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	0.120373	−	0.992729i	$-0.461591\pi$
$761$	−7.49643	−	2.00866i	−0.271745	−	0.0728140i	−0.392118	+	0.919915i	$0.628258\pi$
$762$	−8.77492	+	8.77492i	−0.317882	+	0.317882i
$763$	−16.8894	−	5.24091i	−0.611439	−	0.189734i
$764$	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	−0.402080	−	0.915605i	$-0.631713\pi$
$769$	−8.11098	+	2.17333i	−0.292489	+	0.0783723i	0.109591	+	0.993977i	$0.465046\pi$
$770$	−4.81569	+	1.09061i	−0.173545	+	0.0393028i
$771$	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	$0.304210\pi$
$773$	−9.20420	+	34.3505i	−0.331052	+	1.23550i	−0.908086	+	0.418783i	$0.862457\pi$
$774$	−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
$777$	5.18266	+	22.8845i	0.185927	+	0.820978i
$778$	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
$784$	3.01590	+	6.31699i	0.107711	+	0.225607i
$785$	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	0.300510	−	0.953779i	$-0.402843\pi$
$787$	2.35283	+	0.630439i	0.0838693	+	0.0224727i	−0.216640	+	0.976251i	$0.569510\pi$
$788$	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
$791$	4.96879	−	7.87827i	0.176670	−	0.280119i
$792$			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	$0.00399108\pi$
$797$	14.4210	+	24.9779i	0.510819	+	0.884764i	−0.489102	+	0.872226i	$0.662676\pi$
$798$	−0.370673	+	9.47864i	−0.0131217	+	0.335540i
$799$	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	$-0.978009\pi$
$811$	−30.3760	−	30.3760i	−1.06665	−	1.06665i	−0.0690307	−	0.997615i	$-0.521991\pi$
$812$	−4.47323	+	2.35453i	−0.156980	+	0.0826278i
$813$	−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
$819$	0.775545	−	9.50781i	0.0270997	−	0.332230i
$820$	−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
$826$	1.03268	−	0.543564i	0.0359317	−	0.0189130i
$827$	−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	−0.736118	−	0.676853i	$-0.763343\pi$
$829$	6.27999	−	10.8773i	0.218113	−	0.377783i	0.954231	+	0.299070i	$0.0966765\pi$
$830$	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	$0.0197450\pi$
$839$	54.8442	+	14.6955i	1.89343	+	0.507344i	0.895355	+	0.445353i	$0.146922\pi$
$840$	1.54705	+	0.0604991i	0.0533783	+	0.00208742i
$841$	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
$847$	−1.85506	−	1.16998i	−0.0637405	−	0.0402009i
$848$	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	$0.573918\pi$
$853$	−35.1436	+	35.1436i	−1.20330	+	1.20330i	−0.973158	+	0.230137i	$0.926082\pi$
$854$	−11.3967	+	36.7272i	−0.389987	+	1.25678i
$855$	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	$-0.339465\pi$
$857$	28.2924			0.966449			0.483225	+	0.875496i	$0.339465\pi$
$858$	5.32315	+	10.1925i	0.181729	+	0.347967i
$859$			3.57208i			0.121878i	0.998141	+	0.0609390i	$0.0194095\pi$
$859$			3.57208i			0.121878i	−0.998141	+	0.0609390i	$0.980590\pi$
$860$	−2.73832	+	0.733730i	−0.0933759	+	0.0250200i
$861$	−1.53216	−	6.76540i	−0.0522159	−	0.230564i
$862$	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
$868$	−1.18363	−	5.22644i	−0.0401751	−	0.177397i
$869$	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
$875$	−14.2804	−	4.43131i	−0.482767	−	0.149806i
$876$	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	−0.570614	−	0.821218i	$-0.693295\pi$
$881$	12.6411	−	21.8950i	0.425889	−	0.737661i	0.996503	+	0.0835575i	$0.0266282\pi$
$882$	1.27818	+	6.88232i	0.0430385	+	0.231740i
$883$		−	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	0.993143	−	0.116903i	$-0.0372966\pi$
$887$	41.3523	+	23.8748i	1.38847	+	0.801636i	0.395331	+	0.918539i	$0.370630\pi$
$888$	4.43429	+	7.68041i	0.148805	+	0.257738i
$889$	1.28298	−	32.8077i	0.0430298	−	1.10033i
$890$	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
$903$	−5.97008	−	11.3422i	−0.198672	−	0.377445i
$904$	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
$910$	5.04527	−	2.38885i	0.167249	−	0.0791895i
$911$	−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
$917$	35.8379	−	18.8636i	1.18347	−	0.622933i
$918$	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	−0.986585	−	0.163246i	$-0.947803\pi$
$929$	−1.54087	+	5.75060i	−0.0505542	+	0.188671i	0.936031	+	0.351917i	$0.114470\pi$
$930$	−1.14485	−	0.306762i	−0.0375411	−	0.0100591i
$931$	−16.3064	−	19.0781i	−0.534420	−	0.625261i
$932$	−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	$-0.867465\pi$
$937$		−	24.7605i		−	0.808889i	0.914563	−	0.404444i	$-0.132535\pi$
$938$	−32.6744	−	20.6076i	−1.06686	−	0.672864i
$939$	−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	$-0.980752\pi$
$941$	−32.4734	−	32.4734i	−1.05860	−	1.05860i	−0.0604314	−	0.998172i	$-0.519248\pi$
$942$	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
$945$	1.47868	+	0.458844i	0.0481014	+	0.0149262i
$946$	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
$952$	−7.86138	+	1.78037i	−0.254789	+	0.0577020i
$953$	−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
$959$	−6.38376	+	1.44573i	−0.206142	+	0.0466851i
$960$	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
$966$	18.4305	+	5.71912i	0.592992	+	0.184010i
$967$	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	0.408937	−	0.912563i	$-0.365900\pi$
$971$	43.7408	−	25.2537i	1.40371	−	0.810431i	0.994771	+	0.102131i	$0.0325662\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−38.9104	−	24.5406i	−1.24741	−	0.786737i
$974$		−	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
$980$	−3.11383	+	2.66144i	−0.0994675	+	0.0850165i
$981$	−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	−0.984542	−	0.175151i	$-0.943959\pi$
$983$	−25.3767	+	25.3767i	−0.809391	+	0.809391i	0.175151	+	0.984542i	$0.443959\pi$
$984$	−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
$994$	9.27601	−	4.88252i	0.294217	−	0.154864i
$995$	−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	−0.0834950	−	0.996508i	$-0.526608\pi$
$997$	23.2950	−	13.4494i	0.737759	−	0.425945i	0.821254	+	0.570563i	$0.193275\pi$
$998$	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.b.97.2	yes	40
7.6	odd	2		546.2.bx.a.97.4	✓	40
13.11	odd	12		546.2.bx.a.349.4	yes	40
91.76	even	12	inner	546.2.bx.b.349.2	yes	40

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.413783 - 0.413783i) q^{5} +(0.258819 - 0.965926i) q^{6} +(1.23233 + 2.34123i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-0.413783 - 0.413783i) q^{5} +(0.258819 - 0.965926i) q^{6} +(1.23233 + 2.34123i) 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} +(-0.103386 + 2.64373i) 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} +(-2.23784 - 1.41140i) 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} +(0.458844 - 1.47868i) 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} +(2.58041 - 0.584385i) 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} +(-3.96272 + 5.77034i) 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} +(-0.784111 + 2.52689i) 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} +(-1.41140 + 2.23784i) 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} +(-1.54705 - 0.0604991i) 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} +(-1.23233 - 2.34123i) 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} +(-7.84624 - 5.42555i) 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} +(6.59935 + 2.33422i) q^{98} +(2.25511 + 2.25511i) 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	\( 40 q + 8 q^{7} + 20 q^{9} + 8 q^{11} - 40 q^{12} - 8 q^{14} + 20 q^{16} - 16 q^{17} - 16 q^{19} + 4 q^{21} + 8 q^{22} - 32 q^{26} - 8 q^{28} + 8 q^{33} - 16 q^{34} + 40 q^{35} + 40 q^{37} + 16 q^{38} - 16 q^{39} + 4 q^{41} - 12 q^{42} + 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} - 20 q^{49} - 16 q^{50} + 8 q^{52} + 32 q^{53} + 72 q^{55} + 12 q^{56} + 8 q^{57} - 36 q^{58} - 84 q^{59} + 48 q^{61} + 4 q^{62} + 4 q^{63} - 16 q^{65} - 12 q^{68} + 8 q^{69} - 20 q^{70} - 40 q^{71} + 48 q^{73} + 8 q^{74} - 36 q^{75} - 16 q^{76} + 24 q^{77} - 8 q^{78} - 48 q^{79} - 20 q^{81} - 36 q^{83} - 8 q^{84} + 8 q^{85} - 8 q^{86} - 12 q^{89} + 32 q^{91} - 16 q^{92} - 24 q^{93} - 96 q^{95} - 8 q^{98} - 8 q^{99}+O(q^{100}) \) 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 + 40 * 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 - 20 * 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 - 20 * 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 + 32 * q^91 - 16 * q^92 - 24 * q^93 - 96 * q^95 - 8 * q^98 - 8 * q^99

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