LMFDB - Embedded newform 546.2.by.b.535.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(19,546)]

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, 10, 5]))

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

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

chi := DirichletCharacter("546.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.by (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			535.1
Character	$\chi$	$=$	546.535
Dual form			546.2.by.b.397.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} -1.00000i q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.13407 + 4.23240i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(0.0297166 - 2.64558i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} -1.00000i q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.13407 + 4.23240i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(0.0297166 - 2.64558i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +4.38171 q^{10} +(-2.28221 - 2.28221i) q^{11} +(0.500000 + 0.866025i) q^{12} +(2.90215 - 2.13951i) q^{13} +(-2.56313 + 0.656024i) q^{14} +(4.23240 + 1.13407i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.17072 - 5.49185i) q^{17} +(0.258819 + 0.965926i) q^{18} +(-3.82276 - 3.82276i) q^{19} +(-1.13407 - 4.23240i) q^{20} +(-2.64558 - 0.0297166i) q^{21} +(-1.61377 + 2.79513i) q^{22} +(1.71950 + 0.992755i) q^{23} +(0.707107 - 0.707107i) q^{24} +(-12.2970 - 7.09968i) q^{25} +(-2.81774 - 2.24952i) q^{26} +1.00000i q^{27} +(1.29706 + 2.30600i) q^{28} +(-1.73874 - 3.01158i) q^{29} -4.38171i q^{30} +(8.25065 - 2.21076i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-2.28221 + 2.28221i) q^{33} +(-4.48408 + 4.48408i) q^{34} +(11.1635 + 3.12605i) q^{35} +(0.866025 - 0.500000i) q^{36} +(-0.173808 + 0.0465718i) q^{37} +(-2.70310 + 4.68191i) q^{38} +(-2.13951 - 2.90215i) q^{39} +(-3.79467 + 2.19085i) q^{40} +(0.00297886 - 0.0111173i) q^{41} +(0.656024 + 2.56313i) q^{42} +(-2.69459 - 1.55572i) q^{43} +(3.11756 + 0.835348i) q^{44} +(1.13407 - 4.23240i) q^{45} +(0.513888 - 1.91786i) q^{46} +(3.71124 + 0.994423i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(-6.99823 - 0.157236i) q^{49} +(-3.67507 + 13.7155i) q^{50} +(-5.49185 + 3.17072i) q^{51} +(-1.44358 + 3.30395i) q^{52} +(-6.19883 + 10.7367i) q^{53} +(0.965926 - 0.258819i) q^{54} +(12.2474 - 7.07106i) q^{55} +(1.89172 - 1.84970i) q^{56} +(-3.82276 + 3.82276i) q^{57} +(-2.45895 + 2.45895i) q^{58} +(6.22342 + 1.66756i) q^{59} +(-4.23240 + 1.13407i) q^{60} -5.70985i q^{61} +(-4.27085 - 7.39733i) q^{62} +(-0.0297166 + 2.64558i) q^{63} +1.00000i q^{64} +(5.76403 + 14.7094i) q^{65} +(2.79513 + 1.61377i) q^{66} +(-3.75578 + 3.75578i) q^{67} +(5.49185 + 3.17072i) q^{68} +(0.992755 - 1.71950i) q^{69} +(0.130210 - 11.5922i) q^{70} +(1.61017 + 6.00925i) q^{71} +(-0.707107 - 0.707107i) q^{72} +(0.931045 + 3.47471i) q^{73} +(0.0899699 + 0.155832i) q^{74} +(-7.09968 + 12.2970i) q^{75} +(5.22199 + 1.39923i) q^{76} +(-6.10560 + 5.96997i) q^{77} +(-2.24952 + 2.81774i) q^{78} +(-7.63746 - 13.2285i) q^{79} +(3.09834 + 3.09834i) q^{80} +1.00000 q^{81} -0.0115094 q^{82} +(1.17696 + 1.17696i) q^{83} +(2.30600 - 1.29706i) q^{84} +(26.8396 - 7.19164i) q^{85} +(-0.805301 + 3.00543i) q^{86} +(-3.01158 + 1.73874i) q^{87} -3.22754i q^{88} +(-4.61404 - 17.2198i) q^{89} -4.38171 q^{90} +(-5.57401 - 7.74147i) q^{91} -1.98551 q^{92} +(-2.21076 - 8.25065i) q^{93} -3.84215i q^{94} +(20.5148 - 11.8442i) q^{95} +(-0.258819 + 0.965926i) q^{96} +(-2.25048 + 0.603015i) q^{97} +(1.65940 + 6.80047i) q^{98} +(2.28221 + 2.28221i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) $ 40 * q - 4 * q^7 - 40 * q^9	$ 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) $ 40 * q - 4 * q^7 - 40 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^21 - 4 * q^22 + 24 * q^23 + 24 * q^25 - 8 * q^26 + 4 * q^28 - 12 * q^29 + 24 * q^31 - 4 * q^33 + 8 * q^34 + 28 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 - 20 * q^41 - 12 * q^42 - 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 + 4 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^52 - 4 * q^53 - 24 * q^55 + 12 * q^56 + 8 * q^57 + 24 * q^58 - 12 * q^59 - 32 * q^62 + 4 * q^63 - 4 * q^65 - 24 * q^67 + 24 * q^68 + 8 * q^69 + 52 * q^70 - 28 * q^71 + 108 * q^73 + 20 * q^74 - 36 * q^75 - 4 * q^76 + 12 * q^77 + 4 * q^78 + 40 * q^81 - 48 * q^82 - 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^87 - 60 * q^89 - 40 * q^91 - 16 * q^92 - 48 * q^95 + 48 * q^97 - 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{12}\right)$

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
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−1.13407	+	4.23240i	−0.507171	+	1.89279i	−0.0603236	+	0.998179i	$0.519213\pi$
$5$	−1.13407	+	4.23240i	−0.507171	+	1.89279i	−0.446848	+	0.894610i	$0.647453\pi$
$6$	−0.965926	+	0.258819i	−0.394338	+	0.105662i
$7$	0.0297166	−	2.64558i	0.0112318	−	0.999937i
$7$	0.0297166	−	2.64558i	0.0112318	−	0.999937i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−1.00000			−0.333333
$10$	4.38171			1.38562
$11$	−2.28221	−	2.28221i	−0.688113	−	0.688113i	0.273702	−	0.961815i	$-0.411752\pi$
$11$	−2.28221	−	2.28221i	−0.688113	−	0.688113i	−0.961815	+	0.273702i	$0.911752\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	2.90215	−	2.13951i	0.804913	−	0.593393i
$13$	2.90215	−	2.13951i	0.804913	−	0.593393i
$14$	−2.56313	+	0.656024i	−0.685025	+	0.175330i
$15$	4.23240	+	1.13407i	1.09280	+	0.292815i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−3.17072	−	5.49185i	−0.769013	−	1.33197i	−0.938098	−	0.346369i	$-0.887415\pi$
$17$	−3.17072	−	5.49185i	−0.769013	−	1.33197i	0.169085	−	0.985601i	$-0.445919\pi$
$18$	0.258819	+	0.965926i	0.0610042	+	0.227671i
$19$	−3.82276	−	3.82276i	−0.877002	−	0.877002i	0.116221	−	0.993223i	$-0.462922\pi$
$19$	−3.82276	−	3.82276i	−0.877002	−	0.877002i	−0.993223	+	0.116221i	$0.962922\pi$
$20$	−1.13407	−	4.23240i	−0.253586	−	0.946394i
$21$	−2.64558	−	0.0297166i	−0.577314	−	0.00648470i
$22$	−1.61377	+	2.79513i	−0.344056	+	0.595923i
$23$	1.71950	+	0.992755i	0.358541	+	0.207004i	0.668441	−	0.743766i	$-0.266962\pi$
$23$	1.71950	+	0.992755i	0.358541	+	0.207004i	−0.309900	+	0.950769i	$0.600295\pi$
$24$	0.707107	−	0.707107i	0.144338	−	0.144338i
$25$	−12.2970	−	7.09968i	−2.45940	−	1.41994i
$26$	−2.81774	−	2.24952i	−0.552604	−	0.441167i
$27$			1.00000i			0.192450i
$28$	1.29706	+	2.30600i	0.245121	+	0.435793i
$29$	−1.73874	−	3.01158i	−0.322876	−	0.559237i	0.658204	−	0.752839i	$-0.271316\pi$
$29$	−1.73874	−	3.01158i	−0.322876	−	0.559237i	−0.981080	+	0.193602i	$0.937983\pi$
$30$		−	4.38171i		−	0.799987i
$31$	8.25065	−	2.21076i	1.48186	−	0.397063i	0.574881	−	0.818237i	$-0.305048\pi$
$31$	8.25065	−	2.21076i	1.48186	−	0.397063i	0.906980	+	0.421174i	$0.138382\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	−2.28221	+	2.28221i	−0.397282	+	0.397282i
$34$	−4.48408	+	4.48408i	−0.769013	+	0.769013i
$35$	11.1635	+	3.12605i	1.88697	+	0.528399i
$36$	0.866025	−	0.500000i	0.144338	−	0.0833333i
$37$	−0.173808	+	0.0465718i	−0.0285739	+	0.00765636i	−0.273078	−	0.961992i	$-0.588042\pi$
$37$	−0.173808	+	0.0465718i	−0.0285739	+	0.00765636i	0.244504	+	0.969648i	$0.421375\pi$
$38$	−2.70310	+	4.68191i	−0.438501	+	0.759506i
$39$	−2.13951	−	2.90215i	−0.342596	−	0.464717i
$40$	−3.79467	+	2.19085i	−0.599990	+	0.346404i
$41$	0.00297886	−	0.0111173i	0.000465220	−	0.00173623i	−0.965693	−	0.259687i	$-0.916381\pi$
$41$	0.00297886	−	0.0111173i	0.000465220	−	0.00173623i	0.966158	+	0.257951i	$0.0830473\pi$
$42$	0.656024	+	2.56313i	0.101227	+	0.395499i
$43$	−2.69459	−	1.55572i	−0.410921	−	0.237245i	0.280264	−	0.959923i	$-0.409578\pi$
$43$	−2.69459	−	1.55572i	−0.410921	−	0.237245i	−0.691185	+	0.722677i	$0.742911\pi$
$44$	3.11756	+	0.835348i	0.469990	+	0.125933i
$45$	1.13407	−	4.23240i	0.169057	−	0.630930i
$46$	0.513888	−	1.91786i	0.0757687	−	0.282772i
$47$	3.71124	+	0.994423i	0.541339	+	0.145051i	0.519120	−	0.854702i	$-0.326260\pi$
$47$	3.71124	+	0.994423i	0.541339	+	0.145051i	0.0222199	+	0.999753i	$0.492927\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	−6.99823	−	0.157236i	−0.999748	−	0.0224622i
$50$	−3.67507	+	13.7155i	−0.519733	+	1.93967i
$51$	−5.49185	+	3.17072i	−0.769013	+	0.443990i
$52$	−1.44358	+	3.30395i	−0.200189	+	0.458175i
$53$	−6.19883	+	10.7367i	−0.851475	+	1.47480i	0.0284016	+	0.999597i	$0.490958\pi$
$53$	−6.19883	+	10.7367i	−0.851475	+	1.47480i	−0.879877	+	0.475202i	$0.842375\pi$
$54$	0.965926	−	0.258819i	0.131446	−	0.0352208i
$55$	12.2474	−	7.07106i	1.65144	−	0.953461i
$56$	1.89172	−	1.84970i	0.252792	−	0.247176i
$57$	−3.82276	+	3.82276i	−0.506337	+	0.506337i
$58$	−2.45895	+	2.45895i	−0.322876	+	0.322876i
$59$	6.22342	+	1.66756i	0.810220	+	0.217098i	0.640066	−	0.768320i	$-0.278907\pi$
$59$	6.22342	+	1.66756i	0.810220	+	0.217098i	0.170154	+	0.985418i	$0.445574\pi$
$60$	−4.23240	+	1.13407i	−0.546401	+	0.146408i
$61$		−	5.70985i		−	0.731071i	−0.930797	−	0.365535i	$-0.880886\pi$
$61$		−	5.70985i		−	0.731071i	0.930797	−	0.365535i	$-0.119114\pi$
$62$	−4.27085	−	7.39733i	−0.542399	−	0.939462i
$63$	−0.0297166	+	2.64558i	−0.00374394	+	0.333312i
$64$			1.00000i			0.125000i
$65$	5.76403	+	14.7094i	0.714940	+	1.82448i
$66$	2.79513	+	1.61377i	0.344056	+	0.198641i
$67$	−3.75578	+	3.75578i	−0.458842	+	0.458842i	−0.898275	−	0.439433i	$-0.855179\pi$
$67$	−3.75578	+	3.75578i	−0.458842	+	0.458842i	0.439433	+	0.898275i	$0.355179\pi$
$68$	5.49185	+	3.17072i	0.665985	+	0.384507i
$69$	0.992755	−	1.71950i	0.119514	−	0.207004i
$70$	0.130210	−	11.5922i	0.0155630	−	1.38553i
$71$	1.61017	+	6.00925i	0.191092	+	0.713167i	0.993244	+	0.116046i	$0.0370220\pi$
$71$	1.61017	+	6.00925i	0.191092	+	0.713167i	−0.802151	+	0.597121i	$0.796311\pi$
$72$	−0.707107	−	0.707107i	−0.0833333	−	0.0833333i
$73$	0.931045	+	3.47471i	0.108971	+	0.406684i	0.998765	−	0.0496772i	$-0.0158193\pi$
$73$	0.931045	+	3.47471i	0.108971	+	0.406684i	−0.889795	+	0.456361i	$0.849153\pi$
$74$	0.0899699	+	0.155832i	0.0104588	+	0.0181151i
$75$	−7.09968	+	12.2970i	−0.819801	+	1.41994i
$76$	5.22199	+	1.39923i	0.599004	+	0.160503i
$77$	−6.10560	+	5.96997i	−0.695798	+	0.680341i
$78$	−2.24952	+	2.81774i	−0.254708	+	0.319046i
$79$	−7.63746	−	13.2285i	−0.859282	−	1.48832i	−0.872615	−	0.488408i	$-0.837578\pi$
$79$	−7.63746	−	13.2285i	−0.859282	−	1.48832i	0.0133334	−	0.999911i	$-0.495756\pi$
$80$	3.09834	+	3.09834i	0.346404	+	0.346404i
$81$	1.00000			0.111111
$82$	−0.0115094			−0.00127101
$83$	1.17696	+	1.17696i	0.129188	+	0.129188i	0.768744	−	0.639556i	$-0.220882\pi$
$83$	1.17696	+	1.17696i	0.129188	+	0.129188i	−0.639556	+	0.768744i	$0.720882\pi$
$84$	2.30600	−	1.29706i	0.251605	−	0.141521i
$85$	26.8396	−	7.19164i	2.91116	−	0.780043i
$86$	−0.805301	+	3.00543i	−0.0868379	+	0.324083i
$87$	−3.01158	+	1.73874i	−0.322876	+	0.186412i
$88$		−	3.22754i		−	0.344056i
$89$	−4.61404	−	17.2198i	−0.489088	−	1.82530i	−0.560902	−	0.827882i	$-0.689546\pi$
$89$	−4.61404	−	17.2198i	−0.489088	−	1.82530i	0.0718142	−	0.997418i	$-0.477121\pi$
$90$	−4.38171			−0.461873
$91$	−5.57401	−	7.74147i	−0.584315	−	0.811527i
$92$	−1.98551			−0.207004
$93$	−2.21076	−	8.25065i	−0.229245	−	0.855553i
$94$		−	3.84215i		−	0.396288i
$95$	20.5148	−	11.8442i	2.10477	−	1.21519i
$96$	−0.258819	+	0.965926i	−0.0264156	+	0.0985844i
$97$	−2.25048	+	0.603015i	−0.228502	+	0.0612269i	−0.371253	−	0.928532i	$-0.621072\pi$
$97$	−2.25048	+	0.603015i	−0.228502	+	0.0612269i	0.142751	+	0.989759i	$0.454405\pi$
$98$	1.65940	+	6.80047i	0.167625	+	0.686951i
$99$	2.28221	+	2.28221i	0.229371	+	0.229371i
$100$	14.1994			1.41994
$101$	−8.32192			−0.828062			−0.414031	−	0.910263i	$-0.635879\pi$
$101$	−8.32192			−0.828062			−0.414031	+	0.910263i	$0.635879\pi$
$102$	4.48408	+	4.48408i	0.443990	+	0.443990i
$103$	−1.19202	−	2.06463i	−0.117453	−	0.203434i	0.801305	−	0.598256i	$-0.204140\pi$
$103$	−1.19202	−	2.06463i	−0.117453	−	0.203434i	−0.918758	+	0.394822i	$0.870806\pi$
$104$	3.56499	+	0.539271i	0.349576	+	0.0528798i
$105$	3.12605	−	11.1635i	0.305071	−	1.08944i
$106$	11.9752	+	3.20875i	1.16314	+	0.311662i
$107$	2.13236	−	3.69335i	0.206143	−	0.357050i	−0.744353	−	0.667786i	$-0.767242\pi$
$107$	2.13236	−	3.69335i	0.206143	−	0.357050i	0.950496	+	0.310736i	$0.100576\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	4.84556	+	18.0839i	0.464120	+	1.73212i	0.659789	+	0.751451i	$0.270646\pi$
$109$	4.84556	+	18.0839i	0.464120	+	1.73212i	−0.195668	+	0.980670i	$0.562688\pi$
$110$	−9.99999	−	9.99999i	−0.953461	−	0.953461i
$111$	0.0465718	+	0.173808i	0.00442040	+	0.0164972i
$112$	−2.27629	−	1.34853i	−0.215089	−	0.127424i
$113$	3.88176	−	6.72341i	0.365166	−	0.632486i	−0.623637	−	0.781714i	$-0.714346\pi$
$113$	3.88176	−	6.72341i	0.365166	−	0.632486i	0.988803	+	0.149228i	$0.0476790\pi$
$114$	4.68191	+	2.70310i	0.438501	+	0.253169i
$115$	−6.15178	+	6.15178i	−0.573656	+	0.573656i
$116$	3.01158	+	1.73874i	0.279619	+	0.161438i
$117$	−2.90215	+	2.13951i	−0.268304	+	0.197798i
$118$		−	6.44295i		−	0.593122i
$119$	−14.6234	+	8.22522i	−1.34052	+	0.754005i
$120$	2.19085	+	3.79467i	0.199997	+	0.346404i
$121$		−	0.583014i		−	0.0530013i
$122$	−5.51529	+	1.47782i	−0.499331	+	0.133795i
$123$	−0.0111173	−	0.00297886i	−0.00100241	−	0.000268595i
$124$	−6.03990	+	6.03990i	−0.542399	+	0.542399i
$125$	28.5027	−	28.5027i	2.54936	−	2.54936i
$126$	2.56313	−	0.656024i	0.228342	−	0.0584432i
$127$	−0.607656	+	0.350830i	−0.0539207	+	0.0311311i	−0.526718	−	0.850040i	$-0.676578\pi$
$127$	−0.607656	+	0.350830i	−0.0539207	+	0.0311311i	0.472797	+	0.881171i	$0.343244\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	−1.55572	+	2.69459i	−0.136974	+	0.237245i
$130$	12.7164	−	9.37471i	1.11530	−	0.822216i
$131$	6.17726	−	3.56644i	0.539710	−	0.311602i	−0.205252	−	0.978709i	$-0.565801\pi$
$131$	6.17726	−	3.56644i	0.539710	−	0.311602i	0.744961	+	0.667108i	$0.232468\pi$
$132$	0.835348	−	3.11756i	0.0727077	−	0.271349i
$133$	−10.2270	+	9.99985i	−0.886797	+	0.867097i
$134$	4.59988	+	2.65574i	0.397369	+	0.229421i
$135$	−4.23240	−	1.13407i	−0.364267	−	0.0976052i
$136$	1.64129	−	6.12537i	0.140739	−	0.525246i
$137$	−0.234204	+	0.874063i	−0.0200094	+	0.0746762i	−0.975209	−	0.221287i	$-0.928974\pi$
$137$	−0.234204	+	0.874063i	−0.0200094	+	0.0746762i	0.955199	+	0.295964i	$0.0956408\pi$
$138$	−1.91786	−	0.513888i	−0.163259	−	0.0437451i
$139$	17.7912	+	10.2718i	1.50903	+	0.871239i	0.999945	+	0.0105224i	$0.00334944\pi$
$139$	17.7912	+	10.2718i	1.50903	+	0.871239i	0.509085	+	0.860716i	$0.329984\pi$
$140$	−11.2309	+	2.87450i	−0.949183	+	0.242940i
$141$	0.994423	−	3.71124i	0.0837455	−	0.312542i
$142$	5.38775	−	3.11062i	0.452130	−	0.261037i
$143$	−11.5061	−	1.74052i	−0.962192	−	0.145549i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	14.7181	−	3.94370i	1.22227	−	0.327507i
$146$	3.11534	−	1.79864i	0.257827	−	0.148857i
$147$	−0.157236	+	6.99823i	−0.0129686	+	0.577205i
$148$	0.127237	−	0.127237i	0.0104588	−	0.0104588i
$149$	−5.11347	+	5.11347i	−0.418912	+	0.418912i	−0.884829	−	0.465917i	$-0.845725\pi$
$149$	−5.11347	+	5.11347i	−0.418912	+	0.418912i	0.465917	+	0.884829i	$0.345725\pi$
$150$	13.7155	+	3.67507i	1.11987	+	0.300068i
$151$	−3.27255	+	0.876878i	−0.266317	+	0.0713593i	−0.389506	−	0.921024i	$-0.627354\pi$
$151$	−3.27255	+	0.876878i	−0.266317	+	0.0713593i	0.123190	+	0.992383i	$0.460688\pi$
$152$		−	5.40620i		−	0.438501i
$153$	3.17072	+	5.49185i	0.256338	+	0.443990i
$154$	7.34679	+	4.35242i	0.592021	+	0.350728i
$155$			37.4272i			3.00623i
$156$	3.30395	+	1.44358i	0.264527	+	0.115579i
$157$	−1.58306	−	0.913980i	−0.126342	−	0.0729436i	0.435497	−	0.900190i	$-0.356573\pi$
$157$	−1.58306	−	0.913980i	−0.126342	−	0.0729436i	−0.561839	+	0.827247i	$0.689906\pi$
$158$	−10.8010	+	10.8010i	−0.859282	+	0.859282i
$159$	10.7367	+	6.19883i	0.851475	+	0.491599i
$160$	2.19085	−	3.79467i	0.173202	−	0.299995i
$161$	2.67752	−	4.51959i	0.211018	−	0.356193i
$162$	−0.258819	−	0.965926i	−0.0203347	−	0.0758903i
$163$	8.10494	+	8.10494i	0.634828	+	0.634828i	0.949275	−	0.314447i	$-0.101819\pi$
$163$	8.10494	+	8.10494i	0.634828	+	0.634828i	−0.314447	+	0.949275i	$0.601819\pi$
$164$	0.00297886	+	0.0111173i	0.000232610	+	0.000868113i
$165$	−7.07106	−	12.2474i	−0.550481	−	0.953461i
$166$	0.832238	−	1.44148i	0.0645942	−	0.111880i
$167$	−9.75066	−	2.61268i	−0.754529	−	0.202175i	−0.139003	−	0.990292i	$-0.544390\pi$
$167$	−9.75066	−	2.61268i	−0.754529	−	0.202175i	−0.615526	+	0.788117i	$0.711056\pi$
$168$	−1.84970	−	1.89172i	−0.142707	−	0.145950i
$169$	3.84499	−	12.4184i	0.295769	−	0.955260i
$170$	−13.8932	−	24.0637i	−1.06556	−	1.84560i
$171$	3.82276	+	3.82276i	0.292334	+	0.292334i
$172$	3.11145			0.237245
$173$	−10.9280			−0.830842			−0.415421	−	0.909629i	$-0.636366\pi$
$173$	−10.9280			−0.830842			−0.415421	+	0.909629i	$0.636366\pi$
$174$	2.45895	+	2.45895i	0.186412	+	0.186412i
$175$	−19.1482	+	32.3218i	−1.44747	+	2.44330i
$176$	−3.11756	+	0.835348i	−0.234995	+	0.0629667i
$177$	1.66756	−	6.22342i	0.125341	−	0.467781i
$178$	−15.4389	+	8.91365i	−1.15719	+	0.668106i
$179$			10.0398i			0.750411i	0.926942	+	0.375205i	$0.122428\pi$
$179$			10.0398i			0.750411i	−0.926942	+	0.375205i	$0.877572\pi$
$180$	1.13407	+	4.23240i	0.0845285	+	0.315465i
$181$	−0.280875			−0.0208773			−0.0104386	−	0.999946i	$-0.503323\pi$
$181$	−0.280875			−0.0208773			−0.0104386	+	0.999946i	$0.503323\pi$
$182$	−6.03503	+	7.38772i	−0.447346	+	0.547614i
$183$	−5.70985			−0.422084
$184$	0.513888	+	1.91786i	0.0378843	+	0.141386i
$185$		−	0.788443i		−	0.0579675i
$186$	−7.39733	+	4.27085i	−0.542399	+	0.313154i
$187$	−5.29731	+	19.7698i	−0.387378	+	1.44571i
$188$	−3.71124	+	0.994423i	−0.270670	+	0.0725257i
$189$	2.64558	+	0.0297166i	0.192438	+	0.00216157i
$190$	−16.7502	−	16.7502i	−1.21519	−	1.21519i
$191$	3.98098			0.288053			0.144027	−	0.989574i	$-0.453995\pi$
$191$	3.98098			0.288053			0.144027	+	0.989574i	$0.453995\pi$
$192$	1.00000			0.0721688
$193$	17.3308	+	17.3308i	1.24750	+	1.24750i	0.956822	+	0.290675i	$0.0938799\pi$
$193$	17.3308	+	17.3308i	1.24750	+	1.24750i	0.290675	+	0.956822i	$0.406120\pi$
$194$	1.16494	+	2.01773i	0.0836375	+	0.144864i
$195$	14.7094	−	5.76403i	1.05337	−	0.412771i
$196$	6.13927	−	3.36295i	0.438519	−	0.240210i
$197$	3.65004	+	0.978025i	0.260054	+	0.0696814i	0.386491	−	0.922293i	$-0.373687\pi$
$197$	3.65004	+	0.978025i	0.260054	+	0.0696814i	−0.126436	+	0.991975i	$0.540354\pi$
$198$	1.61377	−	2.79513i	0.114685	−	0.198641i
$199$	−1.78708	−	3.09532i	−0.126683	−	0.219421i	0.795707	−	0.605682i	$-0.207100\pi$
$199$	−1.78708	−	3.09532i	−0.126683	−	0.219421i	−0.922390	+	0.386261i	$0.873766\pi$
$200$	−3.67507	−	13.7155i	−0.259866	−	0.969835i
$201$	3.75578	+	3.75578i	0.264913	+	0.264913i
$202$	2.15387	+	8.03835i	0.151546	+	0.565577i
$203$	−8.01907	+	4.51049i	−0.562828	+	0.316574i
$204$	3.17072	−	5.49185i	0.221995	−	0.384507i
$205$	0.0436746	+	0.0252155i	0.00305036	+	0.00176113i
$206$	−1.68576	+	1.68576i	−0.117453	+	0.117453i
$207$	−1.71950	−	0.992755i	−0.119514	−	0.0690013i
$208$	−0.401793	−	3.58309i	−0.0278593	−	0.248443i
$209$			17.4487i			1.20695i
$210$	−11.5922	−	0.130210i	−0.799936	−	0.00898531i
$211$	−7.71910	−	13.3699i	−0.531405	−	0.920420i	−0.999328	−	0.0366508i	$-0.988331\pi$
$211$	−7.71910	−	13.3699i	−0.531405	−	0.920420i	0.467924	−	0.883769i	$-0.345002\pi$
$212$		−	12.3977i		−	0.851475i
$213$	6.00925	−	1.61017i	0.411747	−	0.110327i
$214$	−4.11940	−	1.10379i	−0.281596	−	0.0754535i
$215$	9.64030	−	9.64030i	0.657463	−	0.657463i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	−5.60356	−	21.8935i	−0.380394	−	1.48623i
$218$	16.2136	−	9.36090i	1.09812	−	0.634000i
$219$	3.47471	−	0.931045i	0.234799	−	0.0629142i
$220$	−7.07106	+	12.2474i	−0.476731	+	0.825722i
$221$	−20.9518	−	9.15441i	−1.40937	−	0.615792i
$222$	0.155832	−	0.0899699i	0.0104588	−	0.00603838i
$223$	5.78209	−	21.5790i	0.387197	−	1.44504i	−0.447477	−	0.894295i	$-0.647677\pi$
$223$	5.78209	−	21.5790i	0.387197	−	1.44504i	0.834674	−	0.550744i	$-0.185656\pi$
$224$	−0.713432	+	2.54775i	−0.0476682	+	0.170229i
$225$	12.2970	+	7.09968i	0.819801	+	0.473312i
$226$	−7.49899	−	2.00935i	−0.498826	−	0.133660i
$227$	5.98281	−	22.3281i	0.397093	−	1.48197i	−0.421093	−	0.907017i	$-0.638354\pi$
$227$	5.98281	−	22.3281i	0.397093	−	1.48197i	0.818186	−	0.574953i	$-0.194980\pi$
$228$	1.39923	−	5.22199i	0.0926662	−	0.345835i
$229$	13.7806	+	3.69250i	0.910646	+	0.244007i	0.683583	−	0.729873i	$-0.260421\pi$
$229$	13.7806	+	3.69250i	0.910646	+	0.244007i	0.227064	+	0.973880i	$0.427087\pi$
$230$	7.53436	+	4.34996i	0.496801	+	0.286828i
$231$	5.96997	+	6.10560i	0.392795	+	0.401719i
$232$	0.900038	−	3.35899i	0.0590904	−	0.220528i
$233$	1.76570	−	1.01943i	0.115675	−	0.0667851i	−0.441046	−	0.897484i	$-0.645392\pi$
$233$	1.76570	−	1.01943i	0.115675	−	0.0667851i	0.556721	+	0.830699i	$0.312059\pi$
$234$	2.81774	+	2.24952i	0.184201	+	0.147056i
$235$	−8.41760	+	14.5797i	−0.549104	+	0.951075i
$236$	−6.22342	+	1.66756i	−0.405110	+	0.108549i
$237$	−13.2285	+	7.63746i	−0.859282	+	0.496107i
$238$	11.7298	+	11.9963i	0.760328	+	0.777602i
$239$	7.26823	−	7.26823i	0.470143	−	0.470143i	−0.431818	−	0.901961i	$-0.642128\pi$
$239$	7.26823	−	7.26823i	0.470143	−	0.470143i	0.901961	+	0.431818i	$0.142128\pi$
$240$	3.09834	−	3.09834i	0.199997	−	0.199997i
$241$	10.6061	+	2.84189i	0.683198	+	0.183062i	0.583693	−	0.811975i	$-0.301607\pi$
$241$	10.6061	+	2.84189i	0.683198	+	0.183062i	0.0995053	+	0.995037i	$0.468274\pi$
$242$	−0.563149	+	0.150895i	−0.0362006	+	0.00969991i
$243$		−	1.00000i		−	0.0641500i
$244$	2.85492	+	4.94487i	0.182768	+	0.316563i
$245$	8.60197	−	29.4410i	0.549560	−	1.88092i
$246$			0.0115094i			0.000733816i
$247$	−19.2731	−	2.91541i	−1.22632	−	0.185503i
$248$	7.39733	+	4.27085i	0.469731	+	0.271199i
$249$	1.17696	−	1.17696i	0.0745869	−	0.0745869i
$250$	−34.9086	−	20.1545i	−2.20781	−	1.27468i
$251$	−6.53973	+	11.3271i	−0.412784	+	0.714963i	−0.995193	−	0.0979333i	$-0.968777\pi$
$251$	−6.53973	+	11.3271i	−0.412784	+	0.714963i	0.582409	+	0.812896i	$0.302110\pi$
$252$	−1.29706	−	2.30600i	−0.0817069	−	0.145264i
$253$	−1.65859	−	6.18995i	−0.104275	−	0.389159i
$254$	0.496149	+	0.496149i	0.0311311	+	0.0311311i
$255$	−7.19164	−	26.8396i	−0.450358	−	1.68076i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.0323063	−	0.0559561i	0.00201521	−	0.00349044i	−0.865016	−	0.501744i	$-0.832692\pi$
$257$	0.0323063	−	0.0559561i	0.00201521	−	0.00349044i	0.867031	+	0.498254i	$0.166025\pi$
$258$	3.00543	+	0.805301i	0.187110	+	0.0501359i
$259$	0.118045	+	0.461209i	0.00733494	+	0.0286581i
$260$	−12.3465	−	9.85674i	−0.765698	−	0.611289i
$261$	1.73874	+	3.01158i	0.107625	+	0.186412i
$262$	−5.04371	−	5.04371i	−0.311602	−	0.311602i
$263$	−3.99899			−0.246588			−0.123294	−	0.992370i	$-0.539346\pi$
$263$	−3.99899			−0.246588			−0.123294	+	0.992370i	$0.539346\pi$
$264$	−3.22754			−0.198641
$265$	−38.4121	−	38.4121i	−2.35964	−	2.35964i
$266$	12.3061	+	7.29042i	0.754533	+	0.447004i
$267$	−17.2198	+	4.61404i	−1.05384	+	0.282375i
$268$	1.37471	−	5.13050i	0.0839739	−	0.313395i
$269$	−3.72107	+	2.14836i	−0.226878	+	0.130988i	−0.609131	−	0.793070i	$-0.708482\pi$
$269$	−3.72107	+	2.14836i	−0.226878	+	0.130988i	0.382253	+	0.924058i	$0.375148\pi$
$270$			4.38171i			0.266662i
$271$	1.97318	+	7.36399i	0.119862	+	0.447331i	0.999605	−	0.0281194i	$-0.00895187\pi$
$271$	1.97318	+	7.36399i	0.119862	+	0.447331i	−0.879743	+	0.475450i	$0.842285\pi$
$272$	−6.34145			−0.384507
$273$	−7.74147	+	5.57401i	−0.468535	+	0.337355i
$274$	0.904896			0.0546668
$275$	11.8614	+	44.2674i	0.715270	+	2.66942i
$276$			1.98551i			0.119514i
$277$	−1.10751	+	0.639421i	−0.0665438	+	0.0384191i	−0.532903	−	0.846176i	$-0.678899\pi$
$277$	−1.10751	+	0.639421i	−0.0665438	+	0.0384191i	0.466359	+	0.884596i	$0.345566\pi$
$278$	5.31705	−	19.8435i	0.318895	−	1.19013i
$279$	−8.25065	+	2.21076i	−0.493954	+	0.132354i
$280$	5.68332	+	10.1042i	0.339644	+	0.603843i
$281$	7.17377	+	7.17377i	0.427951	+	0.427951i	0.887930	−	0.459979i	$-0.152143\pi$
$281$	7.17377	+	7.17377i	0.427951	+	0.427951i	−0.459979	+	0.887930i	$0.652143\pi$
$282$	−3.84215			−0.228797
$283$	−4.33819			−0.257878			−0.128939	−	0.991653i	$-0.541157\pi$
$283$	−4.33819			−0.257878			−0.128939	+	0.991653i	$0.541157\pi$
$284$	−4.39908	−	4.39908i	−0.261037	−	0.261037i
$285$	−11.8442	−	20.5148i	−0.701590	−	1.21519i
$286$	1.29680	+	11.5646i	0.0766815	+	0.683827i
$287$	−0.0293232	−	0.00821120i	−0.00173089	−	0.000484692i
$288$	0.965926	+	0.258819i	0.0569177	+	0.0152511i
$289$	−11.6070	+	20.1039i	−0.682763	+	1.18258i
$290$	−7.61865	−	13.1959i	−0.447382	−	0.774889i
$291$	0.603015	+	2.25048i	0.0353494	+	0.131926i
$292$	−2.54366	−	2.54366i	−0.148857	−	0.148857i
$293$	4.70535	+	17.5606i	0.274890	+	1.02590i	0.955915	+	0.293643i	$0.0948676\pi$
$293$	4.70535	+	17.5606i	0.274890	+	1.02590i	−0.681026	+	0.732260i	$0.738466\pi$
$294$	6.80047	−	1.65940i	0.396611	−	0.0967781i
$295$	−14.1156	+	24.4489i	−0.821840	+	1.42347i
$296$	−0.155832	−	0.0899699i	−0.00905757	−	0.00522939i
$297$	2.28221	−	2.28221i	0.132427	−	0.132427i
$298$	6.26270	+	3.61577i	0.362789	+	0.209456i
$299$	7.11427	−	0.797765i	0.411429	−	0.0461359i
$300$		−	14.1994i		−	0.819801i
$301$	−4.19587	+	7.08254i	−0.241846	+	0.408231i
$302$	1.69400	+	2.93409i	0.0974786	+	0.168838i
$303$			8.32192i			0.478082i
$304$	−5.22199	+	1.39923i	−0.299502	+	0.0802513i
$305$	24.1664	+	6.47536i	1.38376	+	0.370778i
$306$	4.48408	−	4.48408i	0.256338	−	0.256338i
$307$	7.72652	−	7.72652i	0.440976	−	0.440976i	−0.451364	−	0.892340i	$-0.649062\pi$
$307$	7.72652	−	7.72652i	0.440976	−	0.440976i	0.892340	+	0.451364i	$0.149062\pi$
$308$	2.30263	−	8.22294i	0.131204	−	0.468546i
$309$	−2.06463	+	1.19202i	−0.117453	+	0.0678114i
$310$	36.1519	−	9.68688i	2.05329	−	0.550178i
$311$	5.76925	−	9.99263i	0.327144	−	0.566630i	−0.654800	−	0.755802i	$-0.727247\pi$
$311$	5.76925	−	9.99263i	0.327144	−	0.566630i	0.981944	+	0.189172i	$0.0605804\pi$
$312$	0.539271	−	3.56499i	0.0305302	−	0.201828i
$313$	−15.6924	+	9.06000i	−0.886986	+	0.512101i	−0.872955	−	0.487800i	$-0.837799\pi$
$313$	−15.6924	+	9.06000i	−0.886986	+	0.512101i	−0.0140304	+	0.999902i	$0.504466\pi$
$314$	−0.473111	+	1.76567i	−0.0266992	+	0.0996428i
$315$	−11.1635	−	3.12605i	−0.628991	−	0.176133i
$316$	13.2285	+	7.63746i	0.744160	+	0.429641i
$317$	−23.9680	−	6.42219i	−1.34617	−	0.360706i	−0.487453	−	0.873149i	$-0.662074\pi$
$317$	−23.9680	−	6.42219i	−1.34617	−	0.360706i	−0.858721	+	0.512443i	$0.828741\pi$
$318$	3.20875	−	11.9752i	0.179938	−	0.671537i
$319$	−2.90490	+	10.8412i	−0.162643	+	0.606993i
$320$	−4.23240	−	1.13407i	−0.236599	−	0.0633964i
$321$	−3.69335	−	2.13236i	−0.206143	−	0.119017i
$322$	−5.05858	−	1.41653i	−0.281904	−	0.0789399i
$323$	−8.87314	+	33.1150i	−0.493714	+	1.84257i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	−50.8777	+	5.70521i	−2.82218	+	0.316468i
$326$	5.73106	−	9.92648i	0.317414	−	0.549777i
$327$	18.0839	−	4.84556i	1.00004	−	0.267960i
$328$	0.00996747	−	0.00575472i	0.000550362	−	0.000317751i
$329$	2.74111	−	9.78884i	0.151123	−	0.539676i
$330$	−9.99999	+	9.99999i	−0.550481	+	0.550481i
$331$	9.11773	−	9.11773i	0.501156	−	0.501156i	−0.410641	−	0.911797i	$-0.634695\pi$
$331$	9.11773	−	9.11773i	0.501156	−	0.501156i	0.911797	+	0.410641i	$0.134695\pi$
$332$	−1.60776	−	0.430798i	−0.0882373	−	0.0236431i
$333$	0.173808	−	0.0465718i	0.00952464	−	0.00255212i
$334$			10.0946i			0.552354i
$335$	−11.6367	−	20.1553i	−0.635780	−	1.10120i
$336$	−1.34853	+	2.27629i	−0.0735682	+	0.124182i
$337$			10.2939i			0.560743i	0.959892	+	0.280372i	$0.0904577\pi$
$337$			10.2939i			0.560743i	−0.959892	+	0.280372i	$0.909542\pi$
$338$	−12.9904	−	0.499867i	−0.706584	−	0.0271892i
$339$	−6.72341	−	3.88176i	−0.365166	−	0.210829i
$340$	−19.6479	+	19.6479i	−1.06556	+	1.06556i
$341$	−23.8752	−	13.7843i	−1.29291	−	0.746463i
$342$	2.70310	−	4.68191i	0.146167	−	0.253169i
$343$	−0.623944	+	18.5097i	−0.0336898	+	0.999432i
$344$	−0.805301	−	3.00543i	−0.0434189	−	0.162042i
$345$	6.15178	+	6.15178i	0.331201	+	0.331201i
$346$	2.82838	+	10.5557i	0.152055	+	0.567475i
$347$	−13.6113	−	23.5755i	−0.730694	−	1.26560i	−0.956587	−	0.291447i	$-0.905863\pi$
$347$	−13.6113	−	23.5755i	−0.730694	−	1.26560i	0.225893	−	0.974152i	$-0.427470\pi$
$348$	1.73874	−	3.01158i	0.0932062	−	0.161438i
$349$	20.4872	+	5.48954i	1.09666	+	0.293848i	0.761402	−	0.648280i	$-0.224511\pi$
$349$	20.4872	+	5.48954i	1.09666	+	0.293848i	0.335254	+	0.942128i	$0.391178\pi$
$350$	36.1764	+	10.1303i	1.93371	+	0.541486i
$351$	2.13951	+	2.90215i	0.114199	+	0.154906i
$352$	1.61377	+	2.79513i	0.0860141	+	0.148981i
$353$	2.52442	+	2.52442i	0.134362	+	0.134362i	0.771089	−	0.636727i	$-0.219712\pi$
$353$	2.52442	+	2.52442i	0.134362	+	0.134362i	−0.636727	+	0.771089i	$0.719712\pi$
$354$	−6.44295			−0.342439
$355$	−27.2596			−1.44679
$356$	12.6058	+	12.6058i	0.668106	+	0.668106i
$357$	8.22522	+	14.6234i	0.435325	+	0.773952i
$358$	9.69771	−	2.59849i	0.512540	−	0.137335i
$359$	4.70401	−	17.5556i	0.248268	−	0.926549i	−0.723444	−	0.690383i	$-0.757442\pi$
$359$	4.70401	−	17.5556i	0.248268	−	0.926549i	0.971713	−	0.236167i	$-0.0758911\pi$
$360$	3.79467	−	2.19085i	0.199997	−	0.115468i
$361$			10.2270i			0.538266i
$362$	0.0726959	+	0.271305i	0.00382081	+	0.0142595i
$363$	−0.583014			−0.0306003
$364$	8.69797	+	3.91731i	0.455898	+	0.205323i
$365$	−15.7622			−0.825033
$366$	1.47782	+	5.51529i	0.0772467	+	0.288289i
$367$			0.354772i			0.0185190i	0.999957	+	0.00925948i	$0.00294743\pi$
$367$			0.354772i			0.0185190i	−0.999957	+	0.00925948i	$0.997053\pi$
$368$	1.71950	−	0.992755i	0.0896353	−	0.0517510i
$369$	−0.00297886	+	0.0111173i	−0.000155073	+	0.000578742i
$370$	−0.761578	+	0.204064i	−0.0395925	+	0.0106088i
$371$	28.2206	+	16.7186i	1.46514	+	0.867986i
$372$	6.03990	+	6.03990i	0.313154	+	0.313154i
$373$	21.2008			1.09773			0.548867	−	0.835909i	$-0.315059\pi$
$373$	21.2008			1.09773			0.548867	+	0.835909i	$0.315059\pi$
$374$	20.4672			1.05834
$375$	−28.5027	−	28.5027i	−1.47187	−	1.47187i
$376$	1.92108	+	3.32740i	0.0990720	+	0.171598i
$377$	−11.4894	−	5.02003i	−0.591734	−	0.258545i
$378$	−0.656024	−	2.56313i	−0.0337422	−	0.131833i
$379$	10.3631	+	2.77679i	0.532317	+	0.142634i	0.514958	−	0.857215i	$-0.327807\pi$
$379$	10.3631	+	2.77679i	0.532317	+	0.142634i	0.0173592	+	0.999849i	$0.494474\pi$
$380$	−11.8442	+	20.5148i	−0.607595	+	1.05239i
$381$	0.350830	+	0.607656i	0.0179736	+	0.0311311i
$382$	−1.03035	−	3.84533i	−0.0527174	−	0.196744i
$383$	−10.3753	−	10.3753i	−0.530153	−	0.530153i	0.390465	−	0.920618i	$-0.372314\pi$
$383$	−10.3753	−	10.3753i	−0.530153	−	0.530153i	−0.920618	+	0.390465i	$0.872314\pi$
$384$	−0.258819	−	0.965926i	−0.0132078	−	0.0492922i
$385$	−18.3431	−	32.6117i	−0.934853	−	1.66205i
$386$	12.2547	−	21.2258i	0.623748	−	1.08036i
$387$	2.69459	+	1.55572i	0.136974	+	0.0790818i
$388$	1.64747	−	1.64747i	0.0836375	−	0.0836375i
$389$	6.90619	+	3.98729i	0.350158	+	0.202164i	0.664755	−	0.747062i	$-0.268536\pi$
$389$	6.90619	+	3.98729i	0.350158	+	0.202164i	−0.314597	+	0.949225i	$0.601869\pi$
$390$	−9.37471	−	12.7164i	−0.474707	−	0.643919i
$391$		−	12.5910i		−	0.636755i
$392$	−4.83732	−	5.05968i	−0.244321	−	0.255552i
$393$	−3.56644	−	6.17726i	−0.179903	−	0.311602i
$394$		−	3.77880i		−	0.190373i
$395$	64.6497	−	17.3228i	3.25288	−	0.871606i
$396$	−3.11756	−	0.835348i	−0.156663	−	0.0419778i
$397$	15.2081	−	15.2081i	0.763274	−	0.763274i	−0.213638	−	0.976913i	$-0.568531\pi$
$397$	15.2081	−	15.2081i	0.763274	−	0.763274i	0.976913	+	0.213638i	$0.0685315\pi$
$398$	−2.52732	+	2.52732i	−0.126683	+	0.126683i
$399$	9.99985	+	10.2270i	0.500618	+	0.511993i
$400$	−12.2970	+	7.09968i	−0.614850	+	0.354984i
$401$	−21.0329	+	5.63574i	−1.05033	+	0.281436i	−0.742389	−	0.669969i	$-0.766307\pi$
$401$	−21.0329	+	5.63574i	−1.05033	+	0.281436i	−0.307943	+	0.951405i	$0.599641\pi$
$402$	2.65574	−	4.59988i	0.132456	−	0.229421i
$403$	19.2147	−	24.0683i	0.957154	−	1.19893i
$404$	7.20699	−	4.16096i	0.358561	−	0.207015i
$405$	−1.13407	+	4.23240i	−0.0563524	+	0.210310i
$406$	6.43228	+	6.57843i	0.319229	+	0.326482i
$407$	0.502955	+	0.290381i	0.0249305	+	0.0143936i
$408$	−6.12537	−	1.64129i	−0.303251	−	0.0812558i
$409$	8.36755	−	31.2281i	0.413749	−	1.54413i	−0.373580	−	0.927598i	$-0.621870\pi$
$409$	8.36755	−	31.2281i	0.413749	−	1.54413i	0.787329	−	0.616534i	$-0.211464\pi$
$410$	0.0130525	−	0.0487126i	0.000644618	−	0.00240575i
$411$	0.874063	+	0.234204i	0.0431143	+	0.0115525i
$412$	2.06463	+	1.19202i	0.101717	+	0.0587264i
$413$	4.59661	−	16.4150i	0.226184	−	0.807730i
$414$	−0.513888	+	1.91786i	−0.0252562	+	0.0942575i
$415$	−6.31614	+	3.64662i	−0.310047	+	0.179006i
$416$	−3.35701	+	1.31548i	−0.164591	+	0.0644965i
$417$	10.2718	−	17.7912i	0.503010	−	0.871239i
$418$	16.8542	−	4.51606i	0.824364	−	0.220888i
$419$	4.47379	−	2.58295i	0.218559	−	0.126185i	−0.386724	−	0.922196i	$-0.626393\pi$
$419$	4.47379	−	2.58295i	0.218559	−	0.126185i	0.605283	+	0.796010i	$0.293060\pi$
$420$	2.87450	+	11.2309i	0.140261	+	0.548011i
$421$	10.2156	−	10.2156i	0.497877	−	0.497877i	−0.412899	−	0.910777i	$-0.635484\pi$
$421$	10.2156	−	10.2156i	0.497877	−	0.497877i	0.910777	+	0.412899i	$0.135484\pi$
$422$	−10.9165	+	10.9165i	−0.531405	+	0.531405i
$423$	−3.71124	−	0.994423i	−0.180446	−	0.0483505i
$424$	−11.9752	+	3.20875i	−0.581568	+	0.155831i
$425$			90.0445i			4.36780i
$426$	−3.11062	−	5.38775i	−0.150710	−	0.261037i
$427$	−15.1059	−	0.169677i	−0.731025	−	0.00821126i
$428$			4.26472i			0.206143i
$429$	−1.74052	+	11.5061i	−0.0840329	+	0.555522i
$430$	−11.8069	−	6.81672i	−0.569380	−	0.328732i
$431$	−3.04921	+	3.04921i	−0.146875	+	0.146875i	−0.776720	−	0.629845i	$-0.783118\pi$
$431$	−3.04921	+	3.04921i	−0.146875	+	0.146875i	0.629845	+	0.776720i	$0.283118\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	−19.0775	+	33.0433i	−0.916808	+	1.58796i	−0.112575	+	0.993643i	$0.535910\pi$
$433$	−19.0775	+	33.0433i	−0.916808	+	1.58796i	−0.804233	+	0.594314i	$0.797424\pi$
$434$	−19.6972	+	11.0791i	−0.945495	+	0.531813i
$435$	−3.94370	−	14.7181i	−0.189086	−	0.705679i
$436$	−13.2383	−	13.2383i	−0.634000	−	0.634000i
$437$	−2.77818	−	10.3683i	−0.132899	−	0.495984i
$438$	−1.79864	−	3.11534i	−0.0859424	−	0.148857i
$439$	9.88117	−	17.1147i	0.471602	−	0.816839i	−0.527870	−	0.849325i	$-0.677009\pi$
$439$	9.88117	−	17.1147i	0.471602	−	0.816839i	0.999472	+	0.0324860i	$0.0103424\pi$
$440$	13.6602	+	3.66025i	0.651226	+	0.174496i
$441$	6.99823	+	0.157236i	0.333249	+	0.00748741i
$442$	−3.41976	+	22.6072i	−0.162661	+	1.07532i
$443$	−13.7162	−	23.7572i	−0.651677	−	1.12874i	−0.982716	−	0.185120i	$-0.940733\pi$
$443$	−13.7162	−	23.7572i	−0.651677	−	1.12874i	0.331039	−	0.943617i	$-0.392601\pi$
$444$	−0.127237	−	0.127237i	−0.00603838	−	0.00603838i
$445$	78.1140			3.70296
$446$	−22.3403			−1.05784
$447$	5.11347	+	5.11347i	0.241859	+	0.241859i
$448$	2.64558	+	0.0297166i	0.124992	+	0.00140398i
$449$	−21.2137	+	5.68419i	−1.00114	+	0.268253i	−0.721921	−	0.691975i	$-0.756741\pi$
$449$	−21.2137	+	5.68419i	−1.00114	+	0.268253i	−0.279214	+	0.960229i	$0.590074\pi$
$450$	3.67507	−	13.7155i	0.173244	−	0.646556i
$451$	−0.0321704	+	0.0185736i	−0.00151484	+	0.000874596i
$452$			7.76353i			0.365166i
$453$	0.876878	+	3.27255i	0.0411993	+	0.153758i
$454$	−23.1158			−1.08488
$455$	39.0864	−	14.8121i	1.83240	−	0.694402i
$456$	−5.40620			−0.253169
$457$	−2.30088	−	8.58700i	−0.107631	−	0.401683i	0.891000	−	0.454004i	$-0.150005\pi$
$457$	−2.30088	−	8.58700i	−0.107631	−	0.401683i	−0.998630	+	0.0523209i	$0.983338\pi$
$458$		−	14.2667i		−	0.666639i
$459$	5.49185	−	3.17072i	0.256338	−	0.147997i
$460$	2.25171	−	8.40349i	0.104986	−	0.391815i
$461$	12.8354	−	3.43922i	0.597802	−	0.160181i	0.0527857	−	0.998606i	$-0.483190\pi$
$461$	12.8354	−	3.43922i	0.597802	−	0.160181i	0.545017	+	0.838425i	$0.316523\pi$
$462$	4.35242	−	7.34679i	0.202493	−	0.341804i
$463$	16.8995	+	16.8995i	0.785385	+	0.785385i	0.980734	−	0.195349i	$-0.0625838\pi$
$463$	16.8995	+	16.8995i	0.785385	+	0.785385i	−0.195349	+	0.980734i	$0.562584\pi$
$464$	−3.47748			−0.161438
$465$	37.4272			1.73565
$466$	−1.44169	−	1.44169i	−0.0667851	−	0.0667851i
$467$	5.72210	+	9.91096i	0.264787	+	0.458625i	0.967508	−	0.252841i	$-0.0813650\pi$
$467$	5.72210	+	9.91096i	0.264787	+	0.458625i	−0.702721	+	0.711466i	$0.748032\pi$
$468$	1.44358	−	3.30395i	0.0667297	−	0.152725i
$469$	9.82463	+	10.0479i	0.453659	+	0.463967i
$470$	16.2616	+	4.35727i	0.750089	+	0.200986i
$471$	−0.913980	+	1.58306i	−0.0421140	+	0.0729436i
$472$	3.22148	+	5.57976i	0.148280	+	0.256829i
$473$	2.59914	+	9.70012i	0.119509	+	0.446012i
$474$	10.8010	+	10.8010i	0.496107	+	0.496107i
$475$	19.8682	+	74.1490i	0.911614	+	3.40219i
$476$	8.55162	−	14.4349i	0.391963	−	0.661624i
$477$	6.19883	−	10.7367i	0.283825	−	0.491599i
$478$	−8.90173	−	5.13942i	−0.407156	−	0.235071i
$479$	23.3756	−	23.3756i	1.06806	−	1.06806i	0.0705478	−	0.997508i	$-0.477525\pi$
$479$	23.3756	−	23.3756i	1.06806	−	1.06806i	0.997508	−	0.0705478i	$-0.0224747\pi$
$480$	−3.79467	−	2.19085i	−0.173202	−	0.0999983i
$481$	−0.404778	+	0.507024i	−0.0184563	+	0.0231183i
$482$		−	10.9802i		−	0.500136i
$483$	−4.51959	−	2.67752i	−0.205648	−	0.121831i
$484$	0.291507	+	0.504905i	0.0132503	+	0.0229502i
$485$		−	10.2088i		−	0.463559i
$486$	−0.965926	+	0.258819i	−0.0438153	+	0.0117403i
$487$	−36.3247	−	9.73317i	−1.64603	−	0.441052i	−0.687532	−	0.726154i	$-0.741306\pi$
$487$	−36.3247	−	9.73317i	−1.64603	−	0.441052i	−0.958497	+	0.285102i	$0.907972\pi$
$488$	4.03747	−	4.03747i	0.182768	−	0.182768i
$489$	8.10494	−	8.10494i	0.366518	−	0.366518i
$490$	−30.6642	−	0.688960i	−1.38527	−	0.0311241i
$491$	−14.7584	+	8.52076i	−0.666036	+	0.384536i	−0.794573	−	0.607168i	$-0.792305\pi$
$491$	−14.7584	+	8.52076i	−0.666036	+	0.384536i	0.128537	+	0.991705i	$0.458972\pi$
$492$	0.0111173	−	0.00297886i	0.000501205	−	0.000134298i
$493$	−11.0261	+	19.0978i	−0.496592	+	0.860122i
$494$	2.17218	+	19.3709i	0.0977308	+	0.871540i
$495$	−12.2474	+	7.07106i	−0.550481	+	0.317820i
$496$	2.21076	−	8.25065i	0.0992658	−	0.370465i
$497$	15.9458	−	4.08128i	0.715268	−	0.183070i
$498$	−1.44148	−	0.832238i	−0.0645942	−	0.0372935i
$499$	−0.641641	−	0.171927i	−0.0287238	−	0.00769651i	0.244429	−	0.969667i	$-0.421400\pi$
$499$	−0.641641	−	0.171927i	−0.0287238	−	0.00769651i	−0.273152	+	0.961971i	$0.588066\pi$
$500$	−10.4327	+	38.9354i	−0.466565	+	1.74125i
$501$	−2.61268	+	9.75066i	−0.116726	+	0.435628i
$502$	12.6338	+	3.38521i	0.563873	+	0.151089i
$503$	28.3846	+	16.3878i	1.26561	+	0.730698i	0.974153	−	0.225888i	$-0.0725282\pi$
$503$	28.3846	+	16.3878i	1.26561	+	0.730698i	0.291452	+	0.956585i	$0.405862\pi$
$504$	−1.89172	+	1.84970i	−0.0842641	+	0.0823921i
$505$	9.43763	−	35.2217i	0.419969	−	1.56735i
$506$	−5.54976	+	3.20415i	−0.246717	+	0.142442i
$507$	−12.4184	−	3.84499i	−0.551519	−	0.170762i
$508$	0.350830	−	0.607656i	0.0155656	−	0.0269604i
$509$	29.7239	−	7.96450i	1.31749	−	0.353020i	0.469452	−	0.882958i	$-0.344451\pi$
$509$	29.7239	−	7.96450i	1.31749	−	0.353020i	0.848036	+	0.529938i	$0.177785\pi$
$510$	−24.0637	+	13.8932i	−1.06556	+	0.615201i
$511$	9.22030	−	2.35990i	0.407882	−	0.104396i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	3.82276	−	3.82276i	0.168779	−	0.168779i
$514$	−0.0624109	−	0.0167230i	−0.00275283	−	0.000737618i
$515$	10.0902	−	2.70366i	0.444627	−	0.119137i
$516$		−	3.11145i		−	0.136974i
$517$	−6.20034	−	10.7393i	−0.272691	−	0.472314i
$518$	0.414941	−	0.233392i	0.0182315	−	0.0102547i
$519$			10.9280i			0.479687i
$520$	−6.32536	+	14.4769i	−0.277386	+	0.634855i
$521$	−25.3802	−	14.6533i	−1.11193	−	0.641972i	−0.172600	−	0.984992i	$-0.555217\pi$
$521$	−25.3802	−	14.6533i	−1.11193	−	0.641972i	−0.939328	+	0.343020i	$0.888550\pi$
$522$	2.45895	−	2.45895i	0.107625	−	0.107625i
$523$	30.5087	+	17.6142i	1.33405	+	0.770217i	0.985918	−	0.167227i	$-0.0534814\pi$
$523$	30.5087	+	17.6142i	1.33405	+	0.770217i	0.348136	+	0.937444i	$0.386815\pi$
$524$	−3.56644	+	6.17726i	−0.155801	+	0.269855i
$525$	32.3218	+	19.1482i	1.41064	+	0.835697i
$526$	1.03501	+	3.86273i	0.0451288	+	0.168423i
$527$	−38.3017	−	38.3017i	−1.66845	−	1.66845i
$528$	0.835348	+	3.11756i	0.0363538	+	0.135674i
$529$	−9.52887	−	16.5045i	−0.414299	−	0.717587i
$530$	−27.1615	+	47.0451i	−1.17982	+	2.04351i
$531$	−6.22342	−	1.66756i	−0.270073	−	0.0723659i
$532$	3.85696	−	13.7736i	0.167220	−	0.597163i
$533$	−0.0151404	−	0.0386373i	−0.000655803	−	0.00167357i
$534$	8.91365	+	15.4389i	0.385731	+	0.668106i
$535$	13.2135	+	13.2135i	0.571270	+	0.571270i
$536$	−5.31148			−0.229421
$537$	10.0398			0.433250
$538$	3.03824	+	3.03824i	0.130988	+	0.130988i
$539$	15.6126	+	16.3303i	0.672483	+	0.703396i
$540$	4.23240	−	1.13407i	0.182134	−	0.0488026i
$541$	0.956053	−	3.56804i	0.0411039	−	0.153402i	−0.942324	−	0.334703i	$-0.891364\pi$
$541$	0.956053	−	3.56804i	0.0411039	−	0.153402i	0.983428	+	0.181301i	$0.0580308\pi$
$542$	6.60238	−	3.81188i	0.283596	−	0.163734i
$543$			0.280875i			0.0120535i
$544$	1.64129	+	6.12537i	0.0703696	+	0.262623i
$545$	−82.0335			−3.51393
$546$	7.38772	+	6.03503i	0.316165	+	0.258275i
$547$	−21.9784			−0.939729			−0.469864	−	0.882739i	$-0.655697\pi$
$547$	−21.9784			−0.939729			−0.469864	+	0.882739i	$0.655697\pi$
$548$	−0.234204	−	0.874063i	−0.0100047	−	0.0373381i
$549$			5.70985i			0.243690i
$550$	39.6890	−	22.9145i	1.69235	−	0.977076i
$551$	−4.86579	+	18.1594i	−0.207290	+	0.773615i
$552$	1.91786	−	0.513888i	0.0816294	−	0.0218725i
$553$	−35.2240	+	19.8124i	−1.49788	+	0.842511i
$554$	0.904278	+	0.904278i	0.0384191	+	0.0384191i
$555$	−0.788443			−0.0334676
$556$	−20.5435			−0.871239
$557$	−5.80587	−	5.80587i	−0.246002	−	0.246002i	0.573325	−	0.819328i	$-0.305653\pi$
$557$	−5.80587	−	5.80587i	−0.246002	−	0.246002i	−0.819328	+	0.573325i	$0.805653\pi$
$558$	4.27085	+	7.39733i	0.180800	+	0.313154i
$559$	−11.1486	+	1.25016i	−0.471536	+	0.0528760i
$560$	8.28898	−	8.10484i	0.350273	−	0.342492i
$561$	19.7698	+	5.29731i	0.834683	+	0.223653i
$562$	5.07262	−	8.78604i	0.213976	−	0.370617i
$563$	4.82462	+	8.35649i	0.203334	+	0.352184i	0.949601	−	0.313463i	$-0.101489\pi$
$563$	4.82462	+	8.35649i	0.203334	+	0.352184i	−0.746267	+	0.665647i	$0.768156\pi$
$564$	0.994423	+	3.71124i	0.0418727	+	0.156271i
$565$	24.0540	+	24.0540i	1.01196	+	1.01196i
$566$	1.12281	+	4.19037i	0.0471950	+	0.176134i
$567$	0.0297166	−	2.64558i	0.00124798	−	0.111104i
$568$	−3.11062	+	5.38775i	−0.130519	+	0.226065i
$569$	21.0536	+	12.1553i	0.882613	+	0.509577i	0.871519	−	0.490362i	$-0.163135\pi$
$569$	21.0536	+	12.1553i	0.882613	+	0.509577i	0.0110936	+	0.999938i	$0.496469\pi$
$570$	−16.7502	+	16.7502i	−0.701590	+	0.701590i
$571$	17.5708	+	10.1445i	0.735315	+	0.424534i	0.820363	−	0.571843i	$-0.193771\pi$
$571$	17.5708	+	10.1445i	0.735315	+	0.424534i	−0.0850485	+	0.996377i	$0.527105\pi$
$572$	10.8349	−	4.24574i	0.453029	−	0.177523i
$573$		−	3.98098i		−	0.166308i
$574$	−0.000342022		0.0304492i	−1.42757e−5		0.00127093i
$575$	−14.0965	−	24.4158i	−0.587864	−	1.01821i
$576$		−	1.00000i		−	0.0416667i
$577$	−31.4207	+	8.41915i	−1.30806	+	0.350494i	−0.844492	−	0.535568i	$-0.820098\pi$
$577$	−31.4207	+	8.41915i	−1.30806	+	0.350494i	−0.463568	+	0.886061i	$0.653431\pi$
$578$	22.4230	+	6.00821i	0.932672	+	0.249909i
$579$	17.3308	−	17.3308i	0.720243	−	0.720243i
$580$	−10.7744	+	10.7744i	−0.447382	+	0.447382i
$581$	3.14873	−	3.07878i	0.130631	−	0.127729i
$582$	2.01773	−	1.16494i	0.0836375	−	0.0482882i
$583$	38.6505	−	10.3564i	1.60074	−	0.428917i
$584$	−1.79864	+	3.11534i	−0.0744283	+	0.128914i
$585$	−5.76403	−	14.7094i	−0.238313	−	0.608161i
$586$	15.7444	−	9.09005i	0.650396	−	0.375506i
$587$	9.53490	−	35.5847i	0.393548	−	1.46874i	−0.430692	−	0.902499i	$-0.641731\pi$
$587$	9.53490	−	35.5847i	0.393548	−	1.46874i	0.824240	−	0.566241i	$-0.191603\pi$
$588$	−3.36295	−	6.13927i	−0.138686	−	0.253179i
$589$	−39.9915	−	23.0891i	−1.64782	−	0.951370i
$590$	27.2692	+	7.30676i	1.12265	+	0.300814i
$591$	0.978025	−	3.65004i	0.0402306	−	0.150142i
$592$	−0.0465718	+	0.173808i	−0.00191409	+	0.00714348i
$593$	−32.4894	−	8.70551i	−1.33418	−	0.357493i	−0.479908	−	0.877319i	$-0.659330\pi$
$593$	−32.4894	−	8.70551i	−1.33418	−	0.357493i	−0.854272	+	0.519826i	$0.825997\pi$
$594$	−2.79513	−	1.61377i	−0.114685	−	0.0662137i
$595$	−18.2285	−	71.2201i	−0.747296	−	2.91974i
$596$	1.87166	−	6.98514i	0.0766662	−	0.286122i
$597$	−3.09532	+	1.78708i	−0.126683	+	0.0731405i
$598$	−2.61189	−	6.66538i	−0.106808	−	0.272568i
$599$	−4.56535	+	7.90742i	−0.186535	+	0.323088i	−0.944093	−	0.329680i	$-0.893059\pi$
$599$	−4.56535	+	7.90742i	−0.186535	+	0.323088i	0.757558	+	0.652768i	$0.226393\pi$
$600$	−13.7155	+	3.67507i	−0.559934	+	0.150034i
$601$	39.0133	−	22.5243i	1.59139	−	0.918787i	0.598316	−	0.801260i	$-0.295837\pi$
$601$	39.0133	−	22.5243i	1.59139	−	0.918787i	0.993070	−	0.117527i	$-0.0374968\pi$
$602$	7.92718	+	2.21980i	0.323088	+	0.0904724i
$603$	3.75578	−	3.75578i	0.152947	−	0.152947i
$604$	2.39568	−	2.39568i	0.0974786	−	0.0974786i
$605$	2.46755	+	0.661179i	0.100320	+	0.0268807i
$606$	8.03835	−	2.15387i	0.326536	−	0.0874950i
$607$		−	19.4589i		−	0.789811i	−0.918722	−	0.394906i	$-0.870777\pi$
$607$		−	19.4589i		−	0.789811i	0.918722	−	0.394906i	$-0.129223\pi$
$608$	2.70310	+	4.68191i	0.109625	+	0.189877i
$609$	4.51049	+	8.01907i	0.182774	+	0.324949i
$610$		−	25.0189i		−	1.01298i
$611$	12.8982	−	5.05426i	0.521803	−	0.204473i
$612$	−5.49185	−	3.17072i	−0.221995	−	0.128169i
$613$	−10.2738	+	10.2738i	−0.414956	+	0.414956i	−0.883461	−	0.468505i	$-0.844793\pi$
$613$	−10.2738	+	10.2738i	−0.414956	+	0.414956i	0.468505	+	0.883461i	$0.344793\pi$
$614$	−9.46302	−	5.46348i	−0.381896	−	0.220488i
$615$	0.0252155	−	0.0436746i	0.00101679	−	0.00176113i
$616$	−8.53872	−	0.0959114i	−0.344035	−	0.00386438i
$617$	4.14330	+	15.4630i	0.166803	+	0.622518i	0.997803	+	0.0662456i	$0.0211021\pi$
$617$	4.14330	+	15.4630i	0.166803	+	0.622518i	−0.831000	+	0.556272i	$0.812231\pi$
$618$	1.68576	+	1.68576i	0.0678114	+	0.0678114i
$619$	11.1300	+	41.5376i	0.447351	+	1.66954i	0.709652	+	0.704552i	$0.248852\pi$
$619$	11.1300	+	41.5376i	0.447351	+	1.66954i	−0.262301	+	0.964986i	$0.584481\pi$
$620$	−18.7136	−	32.4129i	−0.751557	−	1.30174i
$621$	−0.992755	+	1.71950i	−0.0398379	+	0.0690013i
$622$	−11.1453	−	2.98638i	−0.446887	−	0.119743i
$623$	−45.6937	+	11.6951i	−1.83068	+	0.468555i
$624$	−3.58309	+	0.401793i	−0.143439	+	0.0160846i
$625$	52.8126	+	91.4740i	2.11250	+	3.65896i
$626$	12.8128	+	12.8128i	0.512101	+	0.512101i
$627$	17.4487			0.696835
$628$	1.82796			0.0729436
$629$	0.806864	+	0.806864i	0.0321718	+	0.0321718i
$630$	−0.130210	+	11.5922i	−0.00518767	+	0.461843i
$631$	−4.52314	+	1.21197i	−0.180063	+	0.0482478i	−0.347724	−	0.937597i	$-0.613045\pi$
$631$	−4.52314	+	1.21197i	−0.180063	+	0.0482478i	0.167661	+	0.985845i	$0.446379\pi$
$632$	3.95344	−	14.7544i	0.157259	−	0.586900i
$633$	−13.3699	+	7.71910i	−0.531405	+	0.306807i
$634$			24.8135i			0.985468i
$635$	−0.795731	−	2.96971i	−0.0315776	−	0.117849i
$636$	−12.3977			−0.491599
$637$	−20.6464	+	14.5165i	−0.818039	+	0.575163i
$638$	11.2237			0.444350
$639$	−1.61017	−	6.00925i	−0.0636975	−	0.237722i
$640$			4.38171i			0.173202i
$641$	6.21840	−	3.59019i	0.245612	−	0.141804i	−0.372141	−	0.928176i	$-0.621376\pi$
$641$	6.21840	−	3.59019i	0.245612	−	0.141804i	0.617753	+	0.786372i	$0.288043\pi$
$642$	−1.10379	+	4.11940i	−0.0435631	+	0.162580i
$643$	−29.2307	+	7.83235i	−1.15275	+	0.308878i	−0.784066	−	0.620678i	$-0.786858\pi$
$643$	−29.2307	+	7.83235i	−1.15275	+	0.308878i	−0.368682	+	0.929556i	$0.620191\pi$
$644$	−0.0590026	+	5.25284i	−0.00232503	+	0.206991i
$645$	−9.64030	−	9.64030i	−0.379586	−	0.379586i
$646$	34.2832			1.34885
$647$	18.5164			0.727956			0.363978	−	0.931408i	$-0.381418\pi$
$647$	18.5164			0.727956			0.363978	+	0.931408i	$0.381418\pi$
$648$	0.707107	+	0.707107i	0.0277778	+	0.0277778i
$649$	−10.3974	−	18.0089i	−0.408135	−	0.706910i
$650$	18.6789	+	47.6674i	0.732647	+	1.86967i
$651$	−21.8935	+	5.60356i	−0.858074	+	0.219621i
$652$	−11.0716	−	2.96661i	−0.433595	−	0.116182i
$653$	4.68214	−	8.10970i	0.183226	−	0.317357i	−0.759751	−	0.650214i	$-0.774679\pi$
$653$	4.68214	−	8.10970i	0.183226	−	0.317357i	0.942977	+	0.332857i	$0.108013\pi$
$654$	−9.36090	−	16.2136i	−0.366040	−	0.634000i
$655$	8.08919	+	30.1893i	0.316071	+	1.17959i
$656$	−0.00813841	−	0.00813841i	−0.000317751	−	0.000317751i
$657$	−0.931045	−	3.47471i	−0.0363235	−	0.135561i
$658$	−10.1647	−	0.114176i	−0.396263	−	0.00445104i
$659$	16.2208	−	28.0953i	0.631874	−	1.09444i	−0.355294	−	0.934754i	$-0.615619\pi$
$659$	16.2208	−	28.0953i	0.631874	−	1.09444i	0.987168	−	0.159683i	$-0.0510473\pi$
$660$	12.2474	+	7.07106i	0.476731	+	0.275241i
$661$	−2.95795	+	2.95795i	−0.115051	+	0.115051i	−0.762288	−	0.647238i	$-0.775924\pi$
$661$	−2.95795	+	2.95795i	−0.115051	+	0.115051i	0.647238	+	0.762288i	$0.275924\pi$
$662$	−11.1669	−	6.44721i	−0.434014	−	0.250578i
$663$	−9.15441	+	20.9518i	−0.355528	+	0.813701i
$664$			1.66448i			0.0645942i
$665$	−30.7252	−	54.6255i	−1.19147	−	2.11829i
$666$	−0.0899699	−	0.155832i	−0.00348626	−	0.00603838i
$667$		−	6.90457i		−	0.267346i
$668$	9.75066	−	2.61268i	0.377264	−	0.101088i
$669$	−21.5790	−	5.78209i	−0.834294	−	0.223548i
$670$	−16.4567	+	16.4567i	−0.635780	+	0.635780i
$671$	−13.0311	+	13.0311i	−0.503059	+	0.503059i
$672$	2.54775	+	0.713432i	0.0982815	+	0.0275212i
$673$	24.5261	−	14.1601i	0.945412	−	0.545834i	0.0537590	−	0.998554i	$-0.482880\pi$
$673$	24.5261	−	14.1601i	0.945412	−	0.545834i	0.891653	+	0.452720i	$0.149546\pi$
$674$	9.94312	−	2.66425i	0.382995	−	0.102623i
$675$	7.09968	−	12.2970i	0.273267	−	0.473312i
$676$	2.87932	+	12.6771i	0.110743	+	0.487582i
$677$	23.0893	−	13.3306i	0.887395	−	0.512337i	0.0143051	−	0.999898i	$-0.495446\pi$
$677$	23.0893	−	13.3306i	0.887395	−	0.512337i	0.873089	+	0.487560i	$0.162113\pi$
$678$	−2.00935	+	7.49899i	−0.0771686	+	0.287997i
$679$	1.52845	+	5.97176i	0.0586566	+	0.229175i
$680$	24.0637	+	13.8932i	0.922801	+	0.532779i
$681$	−22.3281	−	5.98281i	−0.855616	−	0.229262i
$682$	−7.13529	+	26.6293i	−0.273224	+	1.01969i
$683$	7.10257	−	26.5071i	0.271772	−	1.01427i	−0.686201	−	0.727412i	$-0.740723\pi$
$683$	7.10257	−	26.5071i	0.271772	−	1.01427i	0.957974	−	0.286856i	$-0.0926102\pi$
$684$	−5.22199	−	1.39923i	−0.199668	−	0.0535008i
$685$	−3.43378	−	1.98250i	−0.131198	−	0.0757473i
$686$	18.0405	−	4.18799i	0.688791	−	0.159898i
$687$	3.69250	−	13.7806i	0.140877	−	0.525762i
$688$	−2.69459	+	1.55572i	−0.102730	+	0.0593114i
$689$	4.98130	+	44.4220i	0.189772	+	1.69234i
$690$	4.34996	−	7.53436i	0.165600	−	0.286828i
$691$	17.7212	−	4.74839i	0.674148	−	0.180637i	0.0945254	−	0.995522i	$-0.469867\pi$
$691$	17.7212	−	4.74839i	0.674148	−	0.180637i	0.579623	+	0.814885i	$0.303200\pi$
$692$	9.46394	−	5.46401i	0.359765	−	0.207710i
$693$	6.10560	−	5.96997i	0.231933	−	0.226780i
$694$	−19.2493	+	19.2493i	−0.730694	+	0.730694i
$695$	−63.6507	+	63.6507i	−2.41441	+	2.41441i
$696$	−3.35899	−	0.900038i	−0.127322	−	0.0341158i
$697$	−0.0704996	+	0.0188903i	−0.00267036	+	0.000715522i
$698$		−	21.2099i		−	0.802808i
$699$	−1.01943	−	1.76570i	−0.0385584	−	0.0667851i
$700$	0.421957	−	37.5656i	0.0159485	−	1.41985i
$701$		−	41.7640i		−	1.57740i	−0.614775	−	0.788702i	$-0.710753\pi$
$701$		−	41.7640i		−	1.57740i	0.614775	−	0.788702i	$-0.289247\pi$
$702$	2.24952	−	2.81774i	0.0849026	−	0.106349i
$703$	0.842462	+	0.486396i	0.0317740	+	0.0183448i
$704$	2.28221	−	2.28221i	0.0860141	−	0.0860141i
$705$	14.5797	+	8.41760i	0.549104	+	0.317025i
$706$	1.78504	−	3.09178i	0.0671808	−	0.116361i
$707$	−0.247299	+	22.0163i	−0.00930064	+	0.828009i
$708$	1.66756	+	6.22342i	0.0626707	+	0.233890i
$709$	6.08452	+	6.08452i	0.228509	+	0.228509i	0.812070	−	0.583561i	$-0.198341\pi$
$709$	6.08452	+	6.08452i	0.228509	+	0.228509i	−0.583561	+	0.812070i	$0.698341\pi$
$710$	7.05531	+	26.3308i	0.264781	+	0.988176i
$711$	7.63746	+	13.2285i	0.286427	+	0.496107i
$712$	8.91365	−	15.4389i	0.334053	−	0.578597i
$713$	16.3818	+	4.38948i	0.613502	+	0.164387i
$714$	11.9963	−	11.7298i	0.448949	−	0.438975i
$715$	20.4153	−	46.7248i	0.763490	−	1.74741i
$716$	−5.01990	−	8.69473i	−0.187603	−	0.324937i
$717$	−7.26823	−	7.26823i	−0.271437	−	0.271437i
$718$	−18.1749			−0.678281
$719$	−17.1045			−0.637891			−0.318946	−	0.947773i	$-0.603329\pi$
$719$	−17.1045			−0.637891			−0.318946	+	0.947773i	$0.603329\pi$
$720$	−3.09834	−	3.09834i	−0.115468	−	0.115468i
$721$	−5.49758	+	3.09222i	−0.204741	+	0.115160i
$722$	9.87857	−	2.64696i	0.367642	−	0.0985095i
$723$	2.84189	−	10.6061i	0.105691	−	0.394444i
$724$	0.243245	−	0.140438i	0.00904013	−	0.00521932i
$725$			49.3780i			1.83385i
$726$	0.150895	+	0.563149i	0.00560025	+	0.0209004i
$727$	45.6775			1.69409			0.847043	−	0.531525i	$-0.178381\pi$
$727$	45.6775			1.69409			0.847043	+	0.531525i	$0.178381\pi$
$728$	1.53263	−	9.41547i	0.0568029	−	0.348961i
$729$	−1.00000			−0.0370370
$730$	4.07957	+	15.2252i	0.150992	+	0.563508i
$731$			19.7311i			0.729780i
$732$	4.94487	−	2.85492i	0.182768	−	0.105521i
$733$	8.90463	−	33.2325i	0.328900	−	1.22747i	−0.581433	−	0.813594i	$-0.697508\pi$
$733$	8.90463	−	33.2325i	0.328900	−	1.22747i	0.910333	−	0.413877i	$-0.135826\pi$
$734$	0.342684	−	0.0918218i	0.0126487	−	0.00338920i
$735$	−29.4410	−	8.60197i	−1.08595	−	0.317288i
$736$	−1.40397	−	1.40397i	−0.0517510	−	0.0517510i
$737$	17.1430			0.631470
$738$	0.0115094			0.000423669
$739$	1.55885	+	1.55885i	0.0573432	+	0.0573432i	0.735197	−	0.677854i	$-0.237090\pi$
$739$	1.55885	+	1.55885i	0.0573432	+	0.0573432i	−0.677854	+	0.735197i	$0.737090\pi$
$740$	0.394222	+	0.682812i	0.0144919	+	0.0251007i
$741$	−2.91541	+	19.2731i	−0.107100	+	0.708015i
$742$	8.84489	−	31.5861i	0.324706	−	1.15956i
$743$	−22.1382	−	5.93191i	−0.812172	−	0.217621i	−0.171251	−	0.985227i	$-0.554781\pi$
$743$	−22.1382	−	5.93191i	−0.812172	−	0.217621i	−0.640921	+	0.767607i	$0.721447\pi$
$744$	4.27085	−	7.39733i	0.156577	−	0.271199i
$745$	−15.8433	−	27.4413i	−0.580452	−	1.00537i
$746$	−5.48717	−	20.4784i	−0.200899	−	0.749767i
$747$	−1.17696	−	1.17696i	−0.0430628	−	0.0430628i
$748$	−5.29731	−	19.7698i	−0.193689	−	0.722857i
$749$	−9.70771	−	5.75109i	−0.354712	−	0.210140i
$750$	−20.1545	+	34.9086i	−0.735937	+	1.27468i
$751$	−32.6576	−	18.8548i	−1.19169	−	0.688023i	−0.233001	−	0.972476i	$-0.574855\pi$
$751$	−32.6576	−	18.8548i	−1.19169	−	0.688023i	−0.958690	+	0.284453i	$0.908188\pi$
$752$	2.71681	−	2.71681i	0.0990720	−	0.0990720i
$753$	11.3271	+	6.53973i	0.412784	+	0.238321i
$754$	−1.87530	+	12.3972i	−0.0682945	+	0.451479i
$755$		−	14.8452i		−	0.540273i
$756$	−2.30600	+	1.29706i	−0.0838685	+	0.0471735i
$757$	−14.6011	−	25.2898i	−0.530685	−	0.919173i	−0.999359	−	0.0358019i	$-0.988601\pi$
$757$	−14.6011	−	25.2898i	−0.530685	−	0.919173i	0.468674	−	0.883371i	$-0.344732\pi$
$758$		−	10.7287i		−	0.389683i
$759$	−6.18995	+	1.65859i	−0.224681	+	0.0602031i
$760$	22.8812	+	6.13101i	0.829990	+	0.222395i
$761$	−21.3286	+	21.3286i	−0.773161	+	0.773161i	−0.978658	−	0.205497i	$-0.934119\pi$
$761$	−21.3286	+	21.3286i	−0.773161	+	0.773161i	0.205497	+	0.978658i	$0.434119\pi$
$762$	0.496149	−	0.496149i	0.0179736	−	0.0179736i
$763$	47.9864	−	12.2819i	1.73722	−	0.444636i
$764$	−3.44763	+	1.99049i	−0.124731	+	0.0720133i
$765$	−26.8396	+	7.19164i	−0.970387	+	0.260014i
$766$	−7.33644	+	12.7071i	−0.265076	+	0.459126i
$767$	21.6291	−	8.47555i	0.780980	−	0.306034i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$	−5.78494	+	21.5897i	−0.208610	+	0.778544i	0.779709	+	0.626143i	$0.215367\pi$
$769$	−5.78494	+	21.5897i	−0.208610	+	0.778544i	−0.988319	+	0.152401i	$0.951299\pi$
$770$	−26.7530	+	26.1586i	−0.964110	+	0.942692i
$771$	−0.0559561	−	0.0323063i	−0.00201521	−	0.00116348i
$772$	−23.6743	−	6.34351i	−0.852056	−	0.228308i
$773$	0.119844	−	0.447264i	0.00431049	−	0.0160870i	−0.963737	−	0.266854i	$-0.914016\pi$
$773$	0.119844	−	0.447264i	0.00431049	−	0.0160870i	0.968048	+	0.250767i	$0.0806827\pi$
$774$	0.805301	−	3.00543i	0.0289460	−	0.108028i
$775$	−117.154	−	31.3913i	−4.20830	−	1.12761i
$776$	−2.01773	−	1.16494i	−0.0724322	−	0.0418188i
$777$	0.461209	−	0.118045i	0.0165458	−	0.00423483i
$778$	2.06397	−	7.70285i	0.0739970	−	0.276161i
$779$	−0.0538862	+	0.0311112i	−0.00193067	+	0.00111467i
$780$	−9.85674	+	12.3465i	−0.352928	+	0.442076i
$781$	10.0396	−	17.3891i	0.359246	−	0.622232i
$782$	−12.1620	+	3.25879i	−0.434912	+	0.116534i
$783$	3.01158	−	1.73874i	0.107625	−	0.0621375i
$784$	−3.63529	+	5.98203i	−0.129832	+	0.213644i
$785$	5.66363	−	5.66363i	0.202144	−	0.202144i
$786$	−5.04371	+	5.04371i	−0.179903	+	0.179903i
$787$	−21.0823	−	5.64900i	−0.751505	−	0.201365i	−0.137319	−	0.990527i	$-0.543849\pi$
$787$	−21.0823	−	5.64900i	−0.751505	−	0.201365i	−0.614185	+	0.789162i	$0.710515\pi$
$788$	−3.65004	+	0.978025i	−0.130027	+	0.0348407i
$789$			3.99899i			0.142368i
$790$	−33.4651	−	57.9633i	−1.19064	−	2.06224i
$791$	−17.6720	−	10.4693i	−0.628344	−	0.372247i
$792$			3.22754i			0.114685i
$793$	−12.2163	−	16.5709i	−0.433813	−	0.588448i
$794$	−18.6261	−	10.7538i	−0.661015	−	0.381637i
$795$	−38.4121	+	38.4121i	−1.36234	+	1.36234i
$796$	3.09532	+	1.78708i	0.109711	+	0.0633415i
$797$	−8.23632	+	14.2657i	−0.291745	+	0.505318i	−0.974223	−	0.225589i	$-0.927569\pi$
$797$	−8.23632	+	14.2657i	−0.291745	+	0.505318i	0.682477	+	0.730907i	$0.260903\pi$
$798$	7.29042	−	12.3061i	0.258078	−	0.435630i
$799$	−6.30608	−	23.5346i	−0.223093	−	0.832595i
$800$	10.0405	+	10.0405i	0.354984	+	0.354984i
$801$	4.61404	+	17.2198i	0.163029	+	0.608433i
$802$	10.8874	+	18.8576i	0.384448	+	0.665884i
$803$	5.80518	−	10.0549i	0.204860	−	0.354828i
$804$	−5.13050	−	1.37471i	−0.180939	−	0.0484824i
$805$	16.0922	+	16.4579i	0.567177	+	0.580063i
$806$	−28.2213	−	12.3307i	−0.994054	−	0.434329i
$807$	2.14836	+	3.72107i	0.0756259	+	0.130988i
$808$	−5.88448	−	5.88448i	−0.207015	−	0.207015i
$809$	17.0828			0.600601			0.300300	−	0.953845i	$-0.402913\pi$
$809$	17.0828			0.600601			0.300300	+	0.953845i	$0.402913\pi$
$810$	4.38171			0.153958
$811$	18.8226	+	18.8226i	0.660952	+	0.660952i	0.955604	−	0.294653i	$-0.0952040\pi$
$811$	18.8226	+	18.8226i	0.660952	+	0.660952i	−0.294653	+	0.955604i	$0.595204\pi$
$812$	4.68948	−	7.91573i	0.164568	−	0.277788i
$813$	7.36399	−	1.97318i	0.258267	−	0.0692023i
$814$	0.150312	−	0.560973i	0.00526844	−	0.0196621i
$815$	−43.4949	+	25.1118i	−1.52356	+	0.879629i
$816$			6.34145i			0.221995i
$817$	4.35362	+	16.2479i	0.152314	+	0.568444i
$818$	−32.3297			−1.13038
$819$	5.57401	+	7.74147i	0.194772	+	0.270509i
$820$	−0.0504310			−0.00176113
$821$	−0.988460	−	3.68898i	−0.0344975	−	0.128746i	0.946530	−	0.322617i	$-0.104563\pi$
$821$	−0.988460	−	3.68898i	−0.0344975	−	0.128746i	−0.981027	+	0.193870i	$0.937896\pi$
$822$		−	0.904896i		−	0.0315619i
$823$	15.7907	−	9.11678i	0.550430	−	0.317791i	−0.198865	−	0.980027i	$-0.563726\pi$
$823$	15.7907	−	9.11678i	0.550430	−	0.317791i	0.749295	+	0.662236i	$0.230392\pi$
$824$	0.617033	−	2.30280i	0.0214954	−	0.0802217i
$825$	44.2674	−	11.8614i	1.54119	−	0.412961i
$826$	−17.0454	−	0.191463i	−0.593085	−	0.00666184i
$827$	0.844609	+	0.844609i	0.0293699	+	0.0293699i	0.721639	−	0.692269i	$-0.243389\pi$
$827$	0.844609	+	0.844609i	0.0293699	+	0.0293699i	−0.692269	+	0.721639i	$0.743389\pi$
$828$	1.98551			0.0690013
$829$	22.0384			0.765426			0.382713	−	0.923867i	$-0.374990\pi$
$829$	22.0384			0.765426			0.382713	+	0.923867i	$0.374990\pi$
$830$	5.15710	+	5.15710i	0.179006	+	0.179006i
$831$	0.639421	+	1.10751i	0.0221813	+	0.0384191i
$832$	2.13951	+	2.90215i	0.0741742	+	0.100614i
$833$	21.3260	+	38.9318i	0.738900	+	1.34891i
$834$	−19.8435	−	5.31705i	−0.687124	−	0.184114i
$835$	22.1159	−	38.3058i	0.765351	−	1.32563i
$836$	−8.72436	−	15.1110i	−0.301738	−	0.522626i
$837$	2.21076	+	8.25065i	0.0764149	+	0.285184i
$838$	−3.65284	−	3.65284i	−0.126185	−	0.126185i
$839$	−12.2092	−	45.5653i	−0.421508	−	1.57309i	−0.771433	−	0.636311i	$-0.780460\pi$
$839$	−12.2092	−	45.5653i	−0.421508	−	1.57309i	0.349925	−	0.936778i	$-0.386207\pi$
$840$	10.1042	−	5.68332i	0.348629	−	0.196093i
$841$	8.45357	−	14.6420i	0.291502	−	0.504897i
$842$	−12.5115	−	7.22351i	−0.431174	−	0.248939i
$843$	7.17377	−	7.17377i	0.247078	−	0.247078i
$844$	13.3699	+	7.71910i	0.460210	+	0.265702i
$845$	48.1991	+	30.3569i	1.65810	+	1.04431i
$846$			3.84215i			0.132096i
$847$	−1.54241	−	0.0173252i	−0.0529980	−	0.000595301i
$848$	6.19883	+	10.7367i	0.212869	+	0.368700i
$849$			4.33819i			0.148886i
$850$	86.9763	−	23.3052i	2.98326	−	0.799363i
$851$	−0.345099	−	0.0924689i	−0.0118298	−	0.00316979i
$852$	−4.39908	+	4.39908i	−0.150710	+	0.150710i
$853$	−17.7773	+	17.7773i	−0.608682	+	0.608682i	−0.942602	−	0.333919i	$-0.891629\pi$
$853$	−17.7773	+	17.7773i	−0.608682	+	0.608682i	0.333919	+	0.942602i	$0.391629\pi$
$854$	3.74579	+	14.6351i	0.128178	+	0.500802i
$855$	−20.5148	+	11.8442i	−0.701590	+	0.405063i
$856$	4.11940	−	1.10379i	0.140798	−	0.0377267i
$857$	6.86537	−	11.8912i	0.234517	−	0.406195i	−0.724616	−	0.689153i	$-0.757983\pi$
$857$	6.86537	−	11.8912i	0.234517	−	0.406195i	0.959132	+	0.282959i	$0.0913160\pi$
$858$	11.5646	−	1.29680i	0.394808	−	0.0442721i
$859$	27.2083	−	15.7087i	0.928334	−	0.535974i	0.0420501	−	0.999116i	$-0.486611\pi$
$859$	27.2083	−	15.7087i	0.928334	−	0.535974i	0.886284	+	0.463141i	$0.153278\pi$
$860$	−3.52860	+	13.1689i	−0.120324	+	0.449056i
$861$	−0.00821120	+	0.0293232i	−0.000279837	+	0.000999331i
$862$	3.73450	+	2.15611i	0.127198	+	0.0734375i
$863$	55.8578	+	14.9670i	1.90142	+	0.509484i	0.996468	+	0.0839709i	$0.0267603\pi$
$863$	55.8578	+	14.9670i	1.90142	+	0.509484i	0.904952	+	0.425513i	$0.139906\pi$
$864$	0.258819	−	0.965926i	0.00880520	−	0.0328615i
$865$	12.3931	−	46.2518i	0.421379	−	1.57261i
$866$	36.8550	+	9.87526i	1.25238	+	0.335575i
$867$	20.1039	+	11.6070i	0.682763	+	0.394194i
$868$	15.7996	+	16.1585i	0.536272	+	0.548457i
$869$	−12.7599	+	47.6205i	−0.432849	+	1.61541i
$870$	−13.1959	+	7.61865i	−0.447382	+	0.258296i
$871$	−2.86432	+	18.9354i	−0.0970539	+	0.641601i
$872$	−9.36090	+	16.2136i	−0.317000	+	0.549060i
$873$	2.25048	−	0.603015i	0.0761673	−	0.0204090i
$874$	−9.29598	+	5.36704i	−0.314441	+	0.181543i
$875$	−74.5593	−	76.2533i	−2.52057	−	2.57783i
$876$	−2.54366	+	2.54366i	−0.0859424	+	0.0859424i
$877$	−25.5733	+	25.5733i	−0.863548	+	0.863548i	−0.991748	−	0.128200i	$-0.959080\pi$
$877$	−25.5733	+	25.5733i	−0.863548	+	0.863548i	0.128200	+	0.991748i	$0.459080\pi$
$878$	−19.0890	−	5.11487i	−0.644221	−	0.172618i
$879$	17.5606	−	4.70535i	0.592305	−	0.158708i
$880$		−	14.1421i		−	0.476731i
$881$	−8.96533	−	15.5284i	−0.302050	−	0.523165i	0.674550	−	0.738229i	$-0.264337\pi$
$881$	−8.96533	−	15.5284i	−0.302050	−	0.523165i	−0.976600	+	0.215063i	$0.931004\pi$
$882$	−1.65940	−	6.80047i	−0.0558748	−	0.228984i
$883$		−	15.9776i		−	0.537689i	−0.963184	−	0.268844i	$-0.913358\pi$
$883$		−	15.9776i		−	0.537689i	0.963184	−	0.268844i	$-0.0866417\pi$
$884$	22.7220	−	2.54795i	0.764224	−	0.0856968i
$885$	24.4489	+	14.1156i	0.821840	+	0.474490i
$886$	−19.3976	+	19.3976i	−0.651677	+	0.651677i
$887$	26.4145	+	15.2504i	0.886910	+	0.512058i	0.872931	−	0.487844i	$-0.162217\pi$
$887$	26.4145	+	15.2504i	0.886910	+	0.512058i	0.0139798	+	0.999902i	$0.495550\pi$
$888$	−0.0899699	+	0.155832i	−0.00301919	+	0.00522939i
$889$	0.910093	+	1.61803i	0.0305235	+	0.0542670i
$890$	−20.2174	−	75.4523i	−0.677689	−	2.52917i
$891$	−2.28221	−	2.28221i	−0.0764570	−	0.0764570i
$892$	5.78209	+	21.5790i	0.193599	+	0.722520i
$893$	−10.3857	−	17.9886i	−0.347545	−	0.601966i
$894$	3.61577	−	6.26270i	0.120930	−	0.209456i
$895$	−42.4925	−	11.3858i	−1.42037	−	0.380587i
$896$	−0.656024	−	2.56313i	−0.0219162	−	0.0856281i
$897$	−0.797765	−	7.11427i	−0.0266366	−	0.237539i
$898$	10.9810	+	19.0197i	0.366441	+	0.634694i
$899$	−21.0036	−	21.0036i	−0.700510	−	0.700510i
$900$	−14.1994			−0.473312
$901$	78.6192			2.61918
$902$	0.0262670	+	0.0262670i	0.000874596	+	0.000874596i
$903$	7.08254	+	4.19587i	0.235692	+	0.139630i
$904$	7.49899	−	2.00935i	0.249413	−	0.0668300i
$905$	0.318532	−	1.18878i	0.0105884	−	0.0395163i
$906$	2.93409	−	1.69400i	0.0974786	−	0.0562793i
$907$		−	8.03721i		−	0.266871i	−0.991057	−	0.133436i	$-0.957399\pi$
$907$		−	8.03721i		−	0.266871i	0.991057	−	0.133436i	$-0.0426009\pi$
$908$	5.98281	+	22.3281i	0.198546	+	0.740985i
$909$	8.32192			0.276021
$910$	−24.4237	−	33.9209i	−0.809638	−	1.12447i
$911$	−35.0854			−1.16243			−0.581216	−	0.813750i	$-0.697423\pi$
$911$	−35.0854			−1.16243			−0.581216	+	0.813750i	$0.697423\pi$
$912$	1.39923	+	5.22199i	0.0463331	+	0.172917i
$913$		−	5.37215i		−	0.177792i
$914$	−7.69890	+	4.44496i	−0.254657	+	0.147026i
$915$	6.47536	−	24.1664i	0.214069	−	0.798916i
$916$	−13.7806	+	3.69250i	−0.455323	+	0.122003i
$917$	−9.25176	−	16.4484i	−0.305520	−	0.543175i
$918$	−4.48408	−	4.48408i	−0.147997	−	0.147997i
$919$	3.32817			0.109786			0.0548932	−	0.998492i	$-0.482518\pi$
$919$	3.32817			0.109786			0.0548932	+	0.998492i	$0.482518\pi$
$920$	−8.69993			−0.286828
$921$	−7.72652	−	7.72652i	−0.254598	−	0.254598i
$922$	−6.64407	−	11.5079i	−0.218811	−	0.378992i
$923$	17.5298	+	13.9948i	0.577001	+	0.460644i
$924$	−8.22294	−	2.30263i	−0.270515	−	0.0757508i
$925$	2.46797	+	0.661290i	0.0811463	+	0.0217431i
$926$	11.9497	−	20.6975i	0.392693	−	0.680164i
$927$	1.19202	+	2.06463i	0.0391509	+	0.0678114i
$928$	0.900038	+	3.35899i	0.0295452	+	0.110264i
$929$	−19.7186	−	19.7186i	−0.646948	−	0.646948i	0.305306	−	0.952254i	$-0.401241\pi$
$929$	−19.7186	−	19.7186i	−0.646948	−	0.646948i	−0.952254	+	0.305306i	$0.901241\pi$
$930$	−9.68688	−	36.1519i	−0.317645	−	1.18547i
$931$	26.1515	+	27.3537i	0.857082	+	0.896480i
$932$	−1.01943	+	1.76570i	−0.0333925	+	0.0578376i
$933$	−9.99263	−	5.76925i	−0.327144	−	0.188877i
$934$	8.09226	−	8.09226i	0.264787	−	0.264787i
$935$	−77.6665	−	44.8407i	−2.53996	−	1.46645i
$936$	−3.56499	−	0.539271i	−0.116525	−	0.0176266i
$937$			18.5913i			0.607351i	0.952776	+	0.303676i	$0.0982139\pi$
$937$			18.5913i			0.607351i	−0.952776	+	0.303676i	$0.901786\pi$
$938$	7.16268	−	12.0904i	0.233870	−	0.394767i
$939$	9.06000	+	15.6924i	0.295662	+	0.512101i
$940$		−	16.8352i		−	0.549104i
$941$	−27.0611	+	7.25100i	−0.882167	+	0.236376i	−0.671342	−	0.741148i	$-0.734282\pi$
$941$	−27.0611	+	7.25100i	−0.882167	+	0.236376i	−0.210825	+	0.977524i	$0.567615\pi$
$942$	1.76567	+	0.473111i	0.0575288	+	0.0154148i
$943$	0.0161589	−	0.0161589i	0.000526206	−	0.000526206i
$944$	4.55586	−	4.55586i	0.148280	−	0.148280i
$945$	−3.12605	+	11.1635i	−0.101690	+	0.363148i
$946$	8.69689	−	5.02115i	0.282760	−	0.163252i
$947$	−29.2741	+	7.84398i	−0.951282	+	0.254895i	−0.700906	−	0.713254i	$-0.747221\pi$
$947$	−29.2741	+	7.84398i	−0.951282	+	0.254895i	−0.250376	+	0.968149i	$0.580554\pi$
$948$	7.63746	−	13.2285i	0.248053	−	0.429641i
$949$	10.1362	+	8.09215i	0.329035	+	0.262682i
$950$	66.4801	−	38.3823i	2.15690	−	1.24529i
$951$	−6.42219	+	23.9680i	−0.208254	+	0.777214i
$952$	−16.1564	−	4.52419i	−0.523632	−	0.146630i
$953$	−23.0230	−	13.2923i	−0.745789	−	0.430581i	0.0783816	−	0.996923i	$-0.475025\pi$
$953$	−23.0230	−	13.2923i	−0.745789	−	0.430581i	−0.824170	+	0.566342i	$0.808358\pi$
$954$	−11.9752	−	3.20875i	−0.387712	−	0.103887i
$955$	−4.51470	+	16.8491i	−0.146092	+	0.545224i
$956$	−2.66036	+	9.92859i	−0.0860421	+	0.321113i
$957$	10.8412	+	2.90490i	0.350448	+	0.0939022i
$958$	−28.6291	−	16.5290i	−0.924964	−	0.534028i
$959$	2.30545	+	0.645582i	0.0744468	+	0.0208469i
$960$	−1.13407	+	4.23240i	−0.0366019	+	0.136600i
$961$	36.3390	−	20.9803i	1.17223	−	0.676785i
$962$	0.594511	+	0.259758i	0.0191678	+	0.00837494i
$963$	−2.13236	+	3.69335i	−0.0687143	+	0.119017i
$964$	−10.6061	+	2.84189i	−0.341599	+	0.0915312i
$965$	−93.0052	+	53.6966i	−2.99394	+	1.72855i
$966$	−1.41653	+	5.05858i	−0.0455760	+	0.162757i
$967$	24.4165	−	24.4165i	0.785182	−	0.785182i	−0.195518	−	0.980700i	$-0.562639\pi$
$967$	24.4165	−	24.4165i	0.785182	−	0.785182i	0.980700	+	0.195518i	$0.0626387\pi$
$968$	0.412253	−	0.412253i	0.0132503	−	0.0132503i
$969$	33.1150	+	8.87314i	1.06381	+	0.285046i
$970$	−9.86096	+	2.64224i	−0.316616	+	0.0848371i
$971$		−	28.1935i		−	0.904772i	−0.891822	−	0.452386i	$-0.850573\pi$
$971$		−	28.1935i		−	0.904772i	0.891822	−	0.452386i	$-0.149427\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	27.7035	−	46.7629i	0.888133	−	1.49915i
$974$			37.6061i			1.20498i
$975$	5.70521	+	50.8777i	0.182713	+	1.62939i
$976$	−4.94487	−	2.85492i	−0.158281	−	0.0913839i
$977$	−11.1254	+	11.1254i	−0.355932	+	0.355932i	−0.862311	−	0.506379i	$-0.830984\pi$
$977$	−11.1254	+	11.1254i	−0.355932	+	0.355932i	0.506379	+	0.862311i	$0.330984\pi$
$978$	−9.92648	−	5.73106i	−0.317414	−	0.183259i
$979$	−28.7691	+	49.8296i	−0.919465	+	1.59256i
$980$	7.27100	+	29.7977i	0.232264	+	0.951852i
$981$	−4.84556	−	18.0839i	−0.154707	−	0.577374i
$982$	12.0502	+	12.0502i	0.384536	+	0.384536i
$983$	12.3821	+	46.2105i	0.394926	+	1.47388i	0.821906	+	0.569624i	$0.192911\pi$
$983$	12.3821	+	46.2105i	0.394926	+	1.47388i	−0.426979	+	0.904261i	$0.640422\pi$
$984$	−0.00575472	−	0.00996747i	−0.000183454	−	0.000317751i
$985$	−8.27879	+	14.3393i	−0.263784	+	0.456888i
$986$	21.3008	+	5.70754i	0.678357	+	0.181765i
$987$	−9.78884	−	2.74111i	−0.311582	−	0.0872506i
$988$	18.1487	−	7.11173i	0.577387	−	0.226254i
$989$	−3.08890	−	5.35014i	−0.0982214	−	0.170125i
$990$	9.99999	+	9.99999i	0.317820	+	0.317820i
$991$	−8.86301			−0.281543			−0.140771	−	0.990042i	$-0.544958\pi$
$991$	−8.86301			−0.281543			−0.140771	+	0.990042i	$0.544958\pi$
$992$	−8.54170			−0.271199
$993$	−9.11773	−	9.11773i	−0.289343	−	0.289343i
$994$	−8.06929	−	14.3462i	−0.255942	−	0.455033i
$995$	15.1273	−	4.05335i	0.479568	−	0.128500i
$996$	−0.430798	+	1.60776i	−0.0136504	+	0.0509438i
$997$	−18.1663	+	10.4883i	−0.575334	+	0.332169i	−0.759277	−	0.650768i	$-0.774447\pi$
$997$	−18.1663	+	10.4883i	−0.575334	+	0.332169i	0.183943	+	0.982937i	$0.441114\pi$
$998$			0.664275i			0.0210273i
$999$	−0.0465718	−	0.173808i	−0.00147347	−	0.00549906i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.by.b.535.1	yes	40
7.5	odd	6		546.2.cg.b.145.1	yes	40
13.7	odd	12		546.2.cg.b.241.1	yes	40
91.33	even	12	inner	546.2.by.b.397.1	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.397.1	✓	40	91.33	even	12	inner
546.2.by.b.535.1	yes	40	1.1	even	1	trivial
546.2.cg.b.145.1	yes	40	7.5	odd	6
546.2.cg.b.241.1	yes	40	13.7	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.by (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} -1.00000i q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.13407 + 4.23240i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(0.0297166 - 2.64558i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} -1.00000i q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.13407 + 4.23240i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(0.0297166 - 2.64558i) q^{7} +(0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +4.38171 q^{10} +(-2.28221 - 2.28221i) q^{11} +(0.500000 + 0.866025i) q^{12} +(2.90215 - 2.13951i) q^{13} +(-2.56313 + 0.656024i) q^{14} +(4.23240 + 1.13407i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.17072 - 5.49185i) q^{17} +(0.258819 + 0.965926i) q^{18} +(-3.82276 - 3.82276i) q^{19} +(-1.13407 - 4.23240i) q^{20} +(-2.64558 - 0.0297166i) q^{21} +(-1.61377 + 2.79513i) q^{22} +(1.71950 + 0.992755i) q^{23} +(0.707107 - 0.707107i) q^{24} +(-12.2970 - 7.09968i) q^{25} +(-2.81774 - 2.24952i) q^{26} +1.00000i q^{27} +(1.29706 + 2.30600i) q^{28} +(-1.73874 - 3.01158i) q^{29} -4.38171i q^{30} +(8.25065 - 2.21076i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-2.28221 + 2.28221i) q^{33} +(-4.48408 + 4.48408i) q^{34} +(11.1635 + 3.12605i) q^{35} +(0.866025 - 0.500000i) q^{36} +(-0.173808 + 0.0465718i) q^{37} +(-2.70310 + 4.68191i) q^{38} +(-2.13951 - 2.90215i) q^{39} +(-3.79467 + 2.19085i) q^{40} +(0.00297886 - 0.0111173i) q^{41} +(0.656024 + 2.56313i) q^{42} +(-2.69459 - 1.55572i) q^{43} +(3.11756 + 0.835348i) q^{44} +(1.13407 - 4.23240i) q^{45} +(0.513888 - 1.91786i) q^{46} +(3.71124 + 0.994423i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(-6.99823 - 0.157236i) q^{49} +(-3.67507 + 13.7155i) q^{50} +(-5.49185 + 3.17072i) q^{51} +(-1.44358 + 3.30395i) q^{52} +(-6.19883 + 10.7367i) q^{53} +(0.965926 - 0.258819i) q^{54} +(12.2474 - 7.07106i) q^{55} +(1.89172 - 1.84970i) q^{56} +(-3.82276 + 3.82276i) q^{57} +(-2.45895 + 2.45895i) q^{58} +(6.22342 + 1.66756i) q^{59} +(-4.23240 + 1.13407i) q^{60} -5.70985i q^{61} +(-4.27085 - 7.39733i) q^{62} +(-0.0297166 + 2.64558i) q^{63} +1.00000i q^{64} +(5.76403 + 14.7094i) q^{65} +(2.79513 + 1.61377i) q^{66} +(-3.75578 + 3.75578i) q^{67} +(5.49185 + 3.17072i) q^{68} +(0.992755 - 1.71950i) q^{69} +(0.130210 - 11.5922i) q^{70} +(1.61017 + 6.00925i) q^{71} +(-0.707107 - 0.707107i) q^{72} +(0.931045 + 3.47471i) q^{73} +(0.0899699 + 0.155832i) q^{74} +(-7.09968 + 12.2970i) q^{75} +(5.22199 + 1.39923i) q^{76} +(-6.10560 + 5.96997i) q^{77} +(-2.24952 + 2.81774i) q^{78} +(-7.63746 - 13.2285i) q^{79} +(3.09834 + 3.09834i) q^{80} +1.00000 q^{81} -0.0115094 q^{82} +(1.17696 + 1.17696i) q^{83} +(2.30600 - 1.29706i) q^{84} +(26.8396 - 7.19164i) q^{85} +(-0.805301 + 3.00543i) q^{86} +(-3.01158 + 1.73874i) q^{87} -3.22754i q^{88} +(-4.61404 - 17.2198i) q^{89} -4.38171 q^{90} +(-5.57401 - 7.74147i) q^{91} -1.98551 q^{92} +(-2.21076 - 8.25065i) q^{93} -3.84215i q^{94} +(20.5148 - 11.8442i) q^{95} +(-0.258819 + 0.965926i) q^{96} +(-2.25048 + 0.603015i) q^{97} +(1.65940 + 6.80047i) q^{98} +(2.28221 + 2.28221i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) \) 40 * q - 4 * q^7 - 40 * q^9	\( 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) 40 * q - 4 * q^7 - 40 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^21 - 4 * q^22 + 24 * q^23 + 24 * q^25 - 8 * q^26 + 4 * q^28 - 12 * q^29 + 24 * q^31 - 4 * q^33 + 8 * q^34 + 28 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 - 20 * q^41 - 12 * q^42 - 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 + 4 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^52 - 4 * q^53 - 24 * q^55 + 12 * q^56 + 8 * q^57 + 24 * q^58 - 12 * q^59 - 32 * q^62 + 4 * q^63 - 4 * q^65 - 24 * q^67 + 24 * q^68 + 8 * q^69 + 52 * q^70 - 28 * q^71 + 108 * q^73 + 20 * q^74 - 36 * q^75 - 4 * q^76 + 12 * q^77 + 4 * q^78 + 40 * q^81 - 48 * q^82 - 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^87 - 60 * q^89 - 40 * q^91 - 16 * q^92 - 48 * q^95 + 48 * q^97 - 8 * q^98 + 4 * q^99

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