LMFDB - Embedded newform 390.2.t.a.307.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(307,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("390.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.t (of order $4$, degree $2$, 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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 6x^{10} - 24x^{9} + 18x^{8} + 40x^{7} - 82x^{6} + 12x^{5} + 228x^{4} - 284x^{3} + 124x^{2} - 16x + 2 $ x^12 + 6x^10 - 24x^9 + 18x^8 + 40x^7 - 82x^6 + 12x^5 + 228x^4 - 284x^3 + 124x^2 - 16x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.2
Root			$0.563963 - 1.36153i$ of defining polynomial
Character	$\chi$	$=$	390.307
Dual form			390.2.t.a.343.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(1.04698 - 1.97581i) q^{5} +(0.707107 + 0.707107i) q^{6} +2.54214 q^{7} +1.00000i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(1.04698 - 1.97581i) q^{5} +(0.707107 + 0.707107i) q^{6} +2.54214 q^{7} +1.00000i q^{8} -1.00000i q^{9} +(-1.97581 - 1.04698i) q^{10} +(-1.89487 + 1.89487i) q^{11} +(0.707107 - 0.707107i) q^{12} +(1.52886 - 3.26536i) q^{13} -2.54214i q^{14} +(0.656785 + 2.13744i) q^{15} +1.00000 q^{16} +(-1.27822 + 1.27822i) q^{17} -1.00000 q^{18} +(6.13392 - 6.13392i) q^{19} +(-1.04698 + 1.97581i) q^{20} +(-1.79756 + 1.79756i) q^{21} +(1.89487 + 1.89487i) q^{22} +(-0.312184 - 0.312184i) q^{23} +(-0.707107 - 0.707107i) q^{24} +(-2.80767 - 4.13727i) q^{25} +(-3.26536 - 1.52886i) q^{26} +(0.707107 + 0.707107i) q^{27} -2.54214 q^{28} -10.6134i q^{29} +(2.13744 - 0.656785i) q^{30} +(1.00000 + 1.00000i) q^{31} -1.00000i q^{32} -2.67974i q^{33} +(1.27822 + 1.27822i) q^{34} +(2.66157 - 5.02279i) q^{35} +1.00000i q^{36} -3.18391 q^{37} +(-6.13392 - 6.13392i) q^{38} +(1.22789 + 3.39003i) q^{39} +(1.97581 + 1.04698i) q^{40} +(4.77370 + 4.77370i) q^{41} +(1.79756 + 1.79756i) q^{42} +(5.88519 + 5.88519i) q^{43} +(1.89487 - 1.89487i) q^{44} +(-1.97581 - 1.04698i) q^{45} +(-0.312184 + 0.312184i) q^{46} -5.18357 q^{47} +(-0.707107 + 0.707107i) q^{48} -0.537526 q^{49} +(-4.13727 + 2.80767i) q^{50} -1.80767i q^{51} +(-1.52886 + 3.26536i) q^{52} +(-6.13727 + 6.13727i) q^{53} +(0.707107 - 0.707107i) q^{54} +(1.76001 + 5.72778i) q^{55} +2.54214i q^{56} +8.67468i q^{57} -10.6134 q^{58} +(7.78281 + 7.78281i) q^{59} +(-0.656785 - 2.13744i) q^{60} +6.41410 q^{61} +(1.00000 - 1.00000i) q^{62} -2.54214i q^{63} -1.00000 q^{64} +(-4.85106 - 6.43950i) q^{65} -2.67974 q^{66} +11.3845i q^{67} +(1.27822 - 1.27822i) q^{68} +0.441495 q^{69} +(-5.02279 - 2.66157i) q^{70} +(-7.30734 - 7.30734i) q^{71} +1.00000 q^{72} +14.5716i q^{73} +3.18391i q^{74} +(4.91081 + 0.940168i) q^{75} +(-6.13392 + 6.13392i) q^{76} +(-4.81701 + 4.81701i) q^{77} +(3.39003 - 1.22789i) q^{78} -3.04259i q^{79} +(1.04698 - 1.97581i) q^{80} -1.00000 q^{81} +(4.77370 - 4.77370i) q^{82} -3.42655 q^{83} +(1.79756 - 1.79756i) q^{84} +(1.18725 + 3.86378i) q^{85} +(5.88519 - 5.88519i) q^{86} +(7.50483 + 7.50483i) q^{87} +(-1.89487 - 1.89487i) q^{88} +(-2.37506 - 2.37506i) q^{89} +(-1.04698 + 1.97581i) q^{90} +(3.88657 - 8.30101i) q^{91} +(0.312184 + 0.312184i) q^{92} -1.41421 q^{93} +5.18357i q^{94} +(-5.69740 - 18.5416i) q^{95} +(0.707107 + 0.707107i) q^{96} -7.40145i q^{97} +0.537526i q^{98} +(1.89487 + 1.89487i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4} - 4 q^{5}+O(q^{10}) $ 12 * q - 12 * q^4 - 4 * q^5	$ 12 q - 12 q^{4} - 4 q^{5} + 4 q^{11} + 20 q^{13} - 4 q^{15} + 12 q^{16} + 8 q^{17} - 12 q^{18} - 4 q^{19} + 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{25} - 4 q^{26} + 4 q^{30} + 12 q^{31} - 8 q^{34} + 12 q^{35} - 16 q^{37} + 4 q^{38} - 12 q^{39} + 8 q^{41} + 8 q^{42} + 16 q^{43} - 4 q^{44} + 32 q^{47} - 20 q^{49} + 8 q^{50} - 20 q^{52} - 16 q^{53} - 12 q^{55} - 40 q^{58} + 20 q^{59} + 4 q^{60} + 16 q^{61} + 12 q^{62} - 12 q^{64} - 32 q^{65} - 16 q^{66} - 8 q^{68} - 32 q^{69} - 20 q^{70} - 32 q^{71} + 12 q^{72} + 4 q^{76} + 16 q^{77} - 4 q^{80} - 12 q^{81} + 8 q^{82} + 32 q^{83} + 8 q^{84} + 12 q^{85} + 16 q^{86} + 20 q^{87} + 4 q^{88} + 16 q^{89} + 4 q^{90} - 28 q^{91} - 8 q^{95} - 4 q^{99}+O(q^{100}) $ 12 * q - 12 * q^4 - 4 * q^5 + 4 * q^11 + 20 * q^13 - 4 * q^15 + 12 * q^16 + 8 * q^17 - 12 * q^18 - 4 * q^19 + 4 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^25 - 4 * q^26 + 4 * q^30 + 12 * q^31 - 8 * q^34 + 12 * q^35 - 16 * q^37 + 4 * q^38 - 12 * q^39 + 8 * q^41 + 8 * q^42 + 16 * q^43 - 4 * q^44 + 32 * q^47 - 20 * q^49 + 8 * q^50 - 20 * q^52 - 16 * q^53 - 12 * q^55 - 40 * q^58 + 20 * q^59 + 4 * q^60 + 16 * q^61 + 12 * q^62 - 12 * q^64 - 32 * q^65 - 16 * q^66 - 8 * q^68 - 32 * q^69 - 20 * q^70 - 32 * q^71 + 12 * q^72 + 4 * q^76 + 16 * q^77 - 4 * q^80 - 12 * q^81 + 8 * q^82 + 32 * q^83 + 8 * q^84 + 12 * q^85 + 16 * q^86 + 20 * q^87 + 4 * q^88 + 16 * q^89 + 4 * q^90 - 28 * q^91 - 8 * q^95 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	−1.00000			−0.500000
$5$	1.04698	−	1.97581i	0.468223	−	0.883610i
$5$	1.04698	−	1.97581i	0.468223	−	0.883610i
$6$	0.707107	+	0.707107i	0.288675	+	0.288675i
$7$	2.54214			0.960838			0.480419	−	0.877039i	$-0.340485\pi$
$7$	2.54214			0.960838			0.480419	+	0.877039i	$0.340485\pi$
$8$			1.00000i			0.353553i
$9$		−	1.00000i		−	0.333333i
$10$	−1.97581	−	1.04698i	−0.624807	−	0.331084i
$11$	−1.89487	+	1.89487i	−0.571323	+	0.571323i	−0.932498	−	0.361175i	$-0.882376\pi$
$11$	−1.89487	+	1.89487i	−0.571323	+	0.571323i	0.361175	+	0.932498i	$0.382376\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	1.52886	−	3.26536i	0.424029	−	0.905649i
$13$	1.52886	−	3.26536i	0.424029	−	0.905649i
$14$		−	2.54214i		−	0.679415i
$15$	0.656785	+	2.13744i	0.169581	+	0.551884i
$16$	1.00000			0.250000
$17$	−1.27822	+	1.27822i	−0.310013	+	0.310013i	−0.844914	−	0.534902i	$-0.820349\pi$
$17$	−1.27822	+	1.27822i	−0.310013	+	0.310013i	0.534902	+	0.844914i	$0.320349\pi$
$18$	−1.00000			−0.235702
$19$	6.13392	−	6.13392i	1.40722	−	1.40722i	0.633369	−	0.773850i	$-0.281672\pi$
$19$	6.13392	−	6.13392i	1.40722	−	1.40722i	0.773850	−	0.633369i	$-0.218328\pi$
$20$	−1.04698	+	1.97581i	−0.234112	+	0.441805i
$21$	−1.79756	+	1.79756i	−0.392261	+	0.392261i
$22$	1.89487	+	1.89487i	0.403987	+	0.403987i
$23$	−0.312184	−	0.312184i	−0.0650949	−	0.0650949i	0.673810	−	0.738905i	$-0.264657\pi$
$23$	−0.312184	−	0.312184i	−0.0650949	−	0.0650949i	−0.738905	+	0.673810i	$0.764657\pi$
$24$	−0.707107	−	0.707107i	−0.144338	−	0.144338i
$25$	−2.80767	−	4.13727i	−0.561534	−	0.827454i
$26$	−3.26536	−	1.52886i	−0.640390	−	0.299834i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−2.54214			−0.480419
$29$		−	10.6134i		−	1.97086i	−0.170069	−	0.985432i	$-0.554399\pi$
$29$		−	10.6134i		−	1.97086i	0.170069	−	0.985432i	$-0.445601\pi$
$30$	2.13744	−	0.656785i	0.390241	−	0.119912i
$31$	1.00000	+	1.00000i	0.179605	+	0.179605i	0.791184	−	0.611578i	$-0.209465\pi$
$31$	1.00000	+	1.00000i	0.179605	+	0.179605i	−0.611578	+	0.791184i	$0.709465\pi$
$32$		−	1.00000i		−	0.176777i
$33$		−	2.67974i		−	0.466484i
$34$	1.27822	+	1.27822i	0.219212	+	0.219212i
$35$	2.66157	−	5.02279i	0.449887	−	0.849007i
$36$			1.00000i			0.166667i
$37$	−3.18391			−0.523431			−0.261716	−	0.965145i	$-0.584288\pi$
$37$	−3.18391			−0.523431			−0.261716	+	0.965145i	$0.584288\pi$
$38$	−6.13392	−	6.13392i	−0.995054	−	0.995054i
$39$	1.22789	+	3.39003i	0.196620	+	0.542839i
$40$	1.97581	+	1.04698i	0.312403	+	0.165542i
$41$	4.77370	+	4.77370i	0.745527	+	0.745527i	0.973636	−	0.228109i	$-0.0732541\pi$
$41$	4.77370	+	4.77370i	0.745527	+	0.745527i	−0.228109	+	0.973636i	$0.573254\pi$
$42$	1.79756	+	1.79756i	0.277370	+	0.277370i
$43$	5.88519	+	5.88519i	0.897483	+	0.897483i	0.995213	−	0.0977303i	$-0.0311583\pi$
$43$	5.88519	+	5.88519i	0.897483	+	0.897483i	−0.0977303	+	0.995213i	$0.531158\pi$
$44$	1.89487	−	1.89487i	0.285662	−	0.285662i
$45$	−1.97581	−	1.04698i	−0.294537	−	0.156074i
$46$	−0.312184	+	0.312184i	−0.0460291	+	0.0460291i
$47$	−5.18357			−0.756101			−0.378051	−	0.925785i	$-0.623406\pi$
$47$	−5.18357			−0.756101			−0.378051	+	0.925785i	$0.623406\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$	−0.537526			−0.0767894
$50$	−4.13727	+	2.80767i	−0.585098	+	0.397065i
$51$		−	1.80767i		−	0.253124i
$52$	−1.52886	+	3.26536i	−0.212015	+	0.452824i
$53$	−6.13727	+	6.13727i	−0.843019	+	0.843019i	−0.989250	−	0.146232i	$-0.953285\pi$
$53$	−6.13727	+	6.13727i	−0.843019	+	0.843019i	0.146232	+	0.989250i	$0.453285\pi$
$54$	0.707107	−	0.707107i	0.0962250	−	0.0962250i
$55$	1.76001	+	5.72778i	0.237320	+	0.772334i
$56$			2.54214i			0.339708i
$57$			8.67468i			1.14899i
$58$	−10.6134			−1.39361
$59$	7.78281	+	7.78281i	1.01324	+	1.01324i	0.999911	+	0.0133238i	$0.00424123\pi$
$59$	7.78281	+	7.78281i	1.01324	+	1.01324i	0.0133238	+	0.999911i	$0.495759\pi$
$60$	−0.656785	−	2.13744i	−0.0847905	−	0.275942i
$61$	6.41410			0.821241			0.410621	−	0.911806i	$-0.365312\pi$
$61$	6.41410			0.821241			0.410621	+	0.911806i	$0.365312\pi$
$62$	1.00000	−	1.00000i	0.127000	−	0.127000i
$63$		−	2.54214i		−	0.320279i
$64$	−1.00000			−0.125000
$65$	−4.85106	−	6.43950i	−0.601700	−	0.798722i
$66$	−2.67974			−0.329854
$67$			11.3845i			1.39084i	0.718603	+	0.695420i	$0.244782\pi$
$67$			11.3845i			1.39084i	−0.718603	+	0.695420i	$0.755218\pi$
$68$	1.27822	−	1.27822i	0.155006	−	0.155006i
$69$	0.441495			0.0531498
$70$	−5.02279	−	2.66157i	−0.600338	−	0.318118i
$71$	−7.30734	−	7.30734i	−0.867222	−	0.867222i	0.124942	−	0.992164i	$-0.460126\pi$
$71$	−7.30734	−	7.30734i	−0.867222	−	0.867222i	−0.992164	+	0.124942i	$0.960126\pi$
$72$	1.00000			0.117851
$73$			14.5716i			1.70547i	0.522340	+	0.852737i	$0.325059\pi$
$73$			14.5716i			1.70547i	−0.522340	+	0.852737i	$0.674941\pi$
$74$			3.18391i			0.370122i
$75$	4.91081	+	0.940168i	0.567052	+	0.108561i
$76$	−6.13392	+	6.13392i	−0.703609	+	0.703609i
$77$	−4.81701	+	4.81701i	−0.548950	+	0.548950i
$78$	3.39003	−	1.22789i	0.383845	−	0.139032i
$79$		−	3.04259i		−	0.342318i	−0.985243	−	0.171159i	$-0.945249\pi$
$79$		−	3.04259i		−	0.342318i	0.985243	−	0.171159i	$-0.0547512\pi$
$80$	1.04698	−	1.97581i	0.117056	−	0.220903i
$81$	−1.00000			−0.111111
$82$	4.77370	−	4.77370i	0.527167	−	0.527167i
$83$	−3.42655			−0.376112			−0.188056	−	0.982158i	$-0.560219\pi$
$83$	−3.42655			−0.376112			−0.188056	+	0.982158i	$0.560219\pi$
$84$	1.79756	−	1.79756i	0.196130	−	0.196130i
$85$	1.18725	+	3.86378i	0.128775	+	0.419086i
$86$	5.88519	−	5.88519i	0.634616	−	0.634616i
$87$	7.50483	+	7.50483i	0.804602	+	0.804602i
$88$	−1.89487	−	1.89487i	−0.201993	−	0.201993i
$89$	−2.37506	−	2.37506i	−0.251756	−	0.251756i	0.569935	−	0.821690i	$-0.306969\pi$
$89$	−2.37506	−	2.37506i	−0.251756	−	0.251756i	−0.821690	+	0.569935i	$0.806969\pi$
$90$	−1.04698	+	1.97581i	−0.110361	+	0.208269i
$91$	3.88657	−	8.30101i	0.407423	−	0.870182i
$92$	0.312184	+	0.312184i	0.0325475	+	0.0325475i
$93$	−1.41421			−0.146647
$94$			5.18357i			0.534644i
$95$	−5.69740	−	18.5416i	−0.584540	−	1.90233i
$96$	0.707107	+	0.707107i	0.0721688	+	0.0721688i
$97$		−	7.40145i		−	0.751503i	−0.926720	−	0.375751i	$-0.877385\pi$
$97$		−	7.40145i		−	0.751503i	0.926720	−	0.375751i	$-0.122615\pi$
$98$			0.537526i			0.0542983i
$99$	1.89487	+	1.89487i	0.190441	+	0.190441i
$100$	2.80767	+	4.13727i	0.280767	+	0.413727i
$101$			1.83957i			0.183044i	0.995803	+	0.0915218i	$0.0291731\pi$
$101$			1.83957i			0.183044i	−0.995803	+	0.0915218i	$0.970827\pi$
$102$	−1.80767			−0.178986
$103$	1.21254	+	1.21254i	0.119475	+	0.119475i	0.764317	−	0.644841i	$-0.223077\pi$
$103$	1.21254	+	1.21254i	0.119475	+	0.119475i	−0.644841	+	0.764317i	$0.723077\pi$
$104$	3.26536	+	1.52886i	0.320195	+	0.149917i
$105$	1.66964	+	5.43366i	0.162940	+	0.530271i
$106$	6.13727	+	6.13727i	0.596104	+	0.596104i
$107$	14.2793	+	14.2793i	1.38043	+	1.38043i	0.843851	+	0.536578i	$0.180283\pi$
$107$	14.2793	+	14.2793i	1.38043	+	1.38043i	0.536578	+	0.843851i	$0.319717\pi$
$108$	−0.707107	−	0.707107i	−0.0680414	−	0.0680414i
$109$	−4.17757	+	4.17757i	−0.400139	+	0.400139i	−0.878282	−	0.478143i	$-0.841310\pi$
$109$	−4.17757	+	4.17757i	−0.400139	+	0.400139i	0.478143	+	0.878282i	$0.341310\pi$
$110$	5.72778	−	1.76001i	0.546123	−	0.167811i
$111$	2.25136	−	2.25136i	0.213690	−	0.213690i
$112$	2.54214			0.240210
$113$	−6.49114	+	6.49114i	−0.610635	+	0.610635i	−0.943112	−	0.332476i	$-0.892116\pi$
$113$	−6.49114	+	6.49114i	−0.610635	+	0.610635i	0.332476	+	0.943112i	$0.392116\pi$
$114$	8.67468			0.812458
$115$	−0.943668	+	0.289967i	−0.0879975	+	0.0270396i
$116$			10.6134i			0.985432i
$117$	−3.26536	−	1.52886i	−0.301883	−	0.141343i
$118$	7.78281	−	7.78281i	0.716465	−	0.716465i
$119$	−3.24940	+	3.24940i	−0.297872	+	0.297872i
$120$	−2.13744	+	0.656785i	−0.195120	+	0.0599560i
$121$			3.81897i			0.347179i
$122$		−	6.41410i		−	0.580705i
$123$	−6.75103			−0.608720
$124$	−1.00000	−	1.00000i	−0.0898027	−	0.0898027i
$125$	−11.1140	+	1.21580i	−0.994070	+	0.108744i
$126$	−2.54214			−0.226472
$127$	7.48269	−	7.48269i	0.663981	−	0.663981i	−0.292335	−	0.956316i	$-0.594432\pi$
$127$	7.48269	−	7.48269i	0.663981	−	0.663981i	0.956316	+	0.292335i	$0.0944322\pi$
$128$			1.00000i			0.0883883i
$129$	−8.32291			−0.732791
$130$	−6.43950	+	4.85106i	−0.564782	+	0.425466i
$131$	8.80803			0.769561			0.384781	−	0.923008i	$-0.374277\pi$
$131$	8.80803			0.769561			0.384781	+	0.923008i	$0.374277\pi$
$132$			2.67974i			0.233242i
$133$	15.5933	−	15.5933i	1.35211	−	1.35211i
$134$	11.3845			0.983473
$135$	2.13744	−	0.656785i	0.183961	−	0.0565270i
$136$	−1.27822	−	1.27822i	−0.109606	−	0.109606i
$137$	−1.55709			−0.133031			−0.0665155	−	0.997785i	$-0.521188\pi$
$137$	−1.55709			−0.133031			−0.0665155	+	0.997785i	$0.521188\pi$
$138$		−	0.441495i		−	0.0375826i
$139$		−	0.0179185i		−	0.00151983i	−1.00000		0.000759913i	$-0.999758\pi$
$139$		−	0.0179185i		−	0.00151983i	1.00000		0.000759913i	$-0.000241888\pi$
$140$	−2.66157	+	5.02279i	−0.224943	+	0.424503i
$141$	3.66534	−	3.66534i	0.308677	−	0.308677i
$142$	−7.30734	+	7.30734i	−0.613219	+	0.613219i
$143$	3.29044	+	9.08440i	0.275161	+	0.759676i
$144$		−	1.00000i		−	0.0833333i
$145$	−20.9701	−	11.1120i	−1.74148	−	0.922804i
$146$	14.5716			1.20595
$147$	0.380088	−	0.380088i	0.0313491	−	0.0313491i
$148$	3.18391			0.261716
$149$	10.2158	−	10.2158i	0.836912	−	0.836912i	−0.151539	−	0.988451i	$-0.548423\pi$
$149$	10.2158	−	10.2158i	0.836912	−	0.836912i	0.988451	+	0.151539i	$0.0484229\pi$
$150$	0.940168	−	4.91081i	0.0767644	−	0.400966i
$151$	−3.29704	+	3.29704i	−0.268310	+	0.268310i	−0.828419	−	0.560109i	$-0.810759\pi$
$151$	−3.29704	+	3.29704i	−0.268310	+	0.268310i	0.560109	+	0.828419i	$0.310759\pi$
$152$	6.13392	+	6.13392i	0.497527	+	0.497527i
$153$	1.27822	+	1.27822i	0.103338	+	0.103338i
$154$	4.81701	+	4.81701i	0.388166	+	0.388166i
$155$	3.02279	−	0.928834i	0.242796	−	0.0746057i
$156$	−1.22789	−	3.39003i	−0.0983102	−	0.271419i
$157$	−12.2613	−	12.2613i	−0.978560	−	0.978560i	0.0212147	−	0.999775i	$-0.493247\pi$
$157$	−12.2613	−	12.2613i	−0.978560	−	0.978560i	−0.999775	+	0.0212147i	$0.993247\pi$
$158$	−3.04259			−0.242056
$159$		−	8.67941i		−	0.688322i
$160$	−1.97581	−	1.04698i	−0.156202	−	0.0827709i
$161$	−0.793616	−	0.793616i	−0.0625457	−	0.0625457i
$162$			1.00000i			0.0785674i
$163$			13.8216i			1.08259i	0.840832	+	0.541296i	$0.182066\pi$
$163$			13.8216i			1.08259i	−0.840832	+	0.541296i	$0.817934\pi$
$164$	−4.77370	−	4.77370i	−0.372764	−	0.372764i
$165$	−5.29467	−	2.80564i	−0.412190	−	0.218418i
$166$			3.42655i			0.265952i
$167$	−17.5562			−1.35854			−0.679268	−	0.733890i	$-0.737703\pi$
$167$	−17.5562			−1.35854			−0.679268	+	0.733890i	$0.737703\pi$
$168$	−1.79756	−	1.79756i	−0.138685	−	0.138685i
$169$	−8.32518	−	9.98455i	−0.640399	−	0.768043i
$170$	3.86378	−	1.18725i	0.296338	−	0.0910579i
$171$	−6.13392	−	6.13392i	−0.469073	−	0.469073i
$172$	−5.88519	−	5.88519i	−0.448741	−	0.448741i
$173$	−1.23037	−	1.23037i	−0.0935431	−	0.0935431i	0.658787	−	0.752330i	$-0.271070\pi$
$173$	−1.23037	−	1.23037i	−0.0935431	−	0.0935431i	−0.752330	+	0.658787i	$0.771070\pi$
$174$	7.50483	−	7.50483i	0.568940	−	0.568940i
$175$	−7.13749	−	10.5175i	−0.539544	−	0.795049i
$176$	−1.89487	+	1.89487i	−0.142831	+	0.142831i
$177$	−11.0065			−0.827303
$178$	−2.37506	+	2.37506i	−0.178018	+	0.178018i
$179$	−0.271184			−0.0202692			−0.0101346	−	0.999949i	$-0.503226\pi$
$179$	−0.271184			−0.0202692			−0.0101346	+	0.999949i	$0.503226\pi$
$180$	1.97581	+	1.04698i	0.147268	+	0.0780372i
$181$			23.7110i			1.76242i	0.472723	+	0.881211i	$0.343271\pi$
$181$			23.7110i			1.76242i	−0.472723	+	0.881211i	$0.656729\pi$
$182$	−8.30101	−	3.88657i	−0.615312	−	0.288092i
$183$	−4.53545	+	4.53545i	−0.335270	+	0.335270i
$184$	0.312184	−	0.312184i	0.0230145	−	0.0230145i
$185$	−3.33348	+	6.29080i	−0.245083	+	0.462509i
$186$			1.41421i			0.103695i
$187$		−	4.84409i		−	0.354235i
$188$	5.18357			0.378051
$189$	1.79756	+	1.79756i	0.130754	+	0.130754i
$190$	−18.5416	+	5.69740i	−1.34515	+	0.413333i
$191$	8.88620			0.642983			0.321492	−	0.946912i	$-0.395816\pi$
$191$	8.88620			0.642983			0.321492	+	0.946912i	$0.395816\pi$
$192$	0.707107	−	0.707107i	0.0510310	−	0.0510310i
$193$		−	18.6866i		−	1.34509i	−0.740057	−	0.672544i	$-0.765201\pi$
$193$		−	18.6866i		−	1.34509i	0.740057	−	0.672544i	$-0.234799\pi$
$194$	−7.40145			−0.531393
$195$	7.98363	+	1.12320i	0.571720	+	0.0804339i
$196$	0.537526			0.0383947
$197$			5.31391i			0.378600i	0.981919	+	0.189300i	$0.0606219\pi$
$197$			5.31391i			0.378600i	−0.981919	+	0.189300i	$0.939378\pi$
$198$	1.89487	−	1.89487i	0.134662	−	0.134662i
$199$	−14.0316			−0.994671			−0.497335	−	0.867558i	$-0.665688\pi$
$199$	−14.0316			−0.994671			−0.497335	+	0.867558i	$0.665688\pi$
$200$	4.13727	−	2.80767i	0.292549	−	0.198532i
$201$	−8.05007	−	8.05007i	−0.567808	−	0.567808i
$202$	1.83957			0.129431
$203$		−	26.9808i		−	1.89368i
$204$			1.80767i			0.126562i
$205$	14.4299	−	4.43398i	1.00783	−	0.309682i
$206$	1.21254	−	1.21254i	0.0844818	−	0.0844818i
$207$	−0.312184	+	0.312184i	−0.0216983	+	0.0216983i
$208$	1.52886	−	3.26536i	0.106007	−	0.226412i
$209$			23.2459i			1.60795i
$210$	5.43366	−	1.66964i	0.374958	−	0.115216i
$211$	−12.1389			−0.835676			−0.417838	−	0.908522i	$-0.637212\pi$
$211$	−12.1389			−0.835676			−0.417838	+	0.908522i	$0.637212\pi$
$212$	6.13727	−	6.13727i	0.421509	−	0.421509i
$213$	10.3341			0.708084
$214$	14.2793	−	14.2793i	0.976110	−	0.976110i
$215$	17.7897	−	5.46636i	1.21325	−	0.372803i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	2.54214	+	2.54214i	0.172572	+	0.172572i
$218$	4.17757	+	4.17757i	0.282941	+	0.282941i
$219$	−10.3037	−	10.3037i	−0.696257	−	0.696257i
$220$	−1.76001	−	5.72778i	−0.118660	−	0.386167i
$221$	2.21963	+	6.12805i	0.149308	+	0.412217i
$222$	−2.25136	−	2.25136i	−0.151102	−	0.151102i
$223$	14.0062			0.937922			0.468961	−	0.883219i	$-0.344628\pi$
$223$	14.0062			0.937922			0.468961	+	0.883219i	$0.344628\pi$
$224$		−	2.54214i		−	0.169854i
$225$	−4.13727	+	2.80767i	−0.275818	+	0.187178i
$226$	6.49114	+	6.49114i	0.431784	+	0.431784i
$227$			7.16607i			0.475628i	0.971311	+	0.237814i	$0.0764309\pi$
$227$			7.16607i			0.475628i	−0.971311	+	0.237814i	$0.923569\pi$
$228$		−	8.67468i		−	0.574495i
$229$	−1.54327	−	1.54327i	−0.101982	−	0.101982i	0.654275	−	0.756257i	$-0.272974\pi$
$229$	−1.54327	−	1.54327i	−0.101982	−	0.101982i	−0.756257	+	0.654275i	$0.772974\pi$
$230$	0.289967	+	0.943668i	0.0191199	+	0.0622236i
$231$		−	6.81228i		−	0.448215i
$232$	10.6134			0.696806
$233$	4.01556	+	4.01556i	0.263068	+	0.263068i	0.826299	−	0.563231i	$-0.190442\pi$
$233$	4.01556	+	4.01556i	0.263068	+	0.263068i	−0.563231	+	0.826299i	$0.690442\pi$
$234$	−1.52886	+	3.26536i	−0.0999446	+	0.213463i
$235$	−5.42709	+	10.2418i	−0.354024	+	0.668099i
$236$	−7.78281	−	7.78281i	−0.506618	−	0.506618i
$237$	2.15144	+	2.15144i	0.139751	+	0.139751i
$238$	3.24940	+	3.24940i	0.210628	+	0.210628i
$239$	0.248851	−	0.248851i	0.0160969	−	0.0160969i	−0.699013	−	0.715109i	$-0.746377\pi$
$239$	0.248851	−	0.248851i	0.0160969	−	0.0160969i	0.715109	+	0.699013i	$0.246377\pi$
$240$	0.656785	+	2.13744i	0.0423953	+	0.137971i
$241$	16.0560	−	16.0560i	1.03426	−	1.03426i	0.0348663	−	0.999392i	$-0.488899\pi$
$241$	16.0560	−	16.0560i	1.03426	−	1.03426i	0.999392	−	0.0348663i	$-0.0111005\pi$
$242$	3.81897			0.245493
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−6.41410			−0.410621
$245$	−0.562778	+	1.06205i	−0.0359546	+	0.0678519i
$246$			6.75103i			0.430430i
$247$	−10.6516	−	29.4074i	−0.677744	−	1.87115i
$248$	−1.00000	+	1.00000i	−0.0635001	+	0.0635001i
$249$	2.42293	−	2.42293i	0.153547	−	0.153547i
$250$	1.21580	+	11.1140i	0.0768938	+	0.702913i
$251$		−	20.4132i		−	1.28847i	−0.764827	−	0.644236i	$-0.777175\pi$
$251$		−	20.4132i		−	1.28847i	0.764827	−	0.644236i	$-0.222825\pi$
$252$			2.54214i			0.160140i
$253$	1.18309			0.0743805
$254$	−7.48269	−	7.48269i	−0.469506	−	0.469506i
$255$	−3.57162	−	1.89259i	−0.223663	−	0.118519i
$256$	1.00000			0.0625000
$257$	−12.5444	+	12.5444i	−0.782500	+	0.782500i	−0.980252	−	0.197752i	$-0.936636\pi$
$257$	−12.5444	+	12.5444i	−0.782500	+	0.782500i	0.197752	+	0.980252i	$0.436636\pi$
$258$			8.32291i			0.518162i
$259$	−8.09394			−0.502933
$260$	4.85106	+	6.43950i	0.300850	+	0.399361i
$261$	−10.6134			−0.656955
$262$		−	8.80803i		−	0.544162i
$263$	−3.40213	+	3.40213i	−0.209785	+	0.209785i	−0.804176	−	0.594391i	$-0.797393\pi$
$263$	−3.40213	+	3.40213i	−0.209785	+	0.209785i	0.594391	+	0.804176i	$0.297393\pi$
$264$	2.67974			0.164927
$265$	5.70050	+	18.5517i	0.350179	+	1.13962i
$266$	−15.5933	−	15.5933i	−0.956086	−	0.956086i
$267$	3.35884			0.205558
$268$		−	11.3845i		−	0.695420i
$269$			11.6328i			0.709262i	0.935006	+	0.354631i	$0.115394\pi$
$269$			11.6328i			0.709262i	−0.935006	+	0.354631i	$0.884606\pi$
$270$	−0.656785	−	2.13744i	−0.0399706	−	0.130080i
$271$	−15.4392	+	15.4392i	−0.937863	+	0.937863i	−0.998179	−	0.0603160i	$-0.980789\pi$
$271$	−15.4392	+	15.4392i	−0.937863	+	0.937863i	0.0603160	+	0.998179i	$0.480789\pi$
$272$	−1.27822	+	1.27822i	−0.0775032	+	0.0775032i
$273$	3.12148	+	8.61792i	0.188920	+	0.521580i
$274$			1.55709i			0.0940671i
$275$	13.1597	+	2.51941i	0.793561	+	0.151926i
$276$	−0.441495			−0.0265749
$277$	11.5065	−	11.5065i	0.691357	−	0.691357i	−0.271173	−	0.962531i	$-0.587412\pi$
$277$	11.5065	−	11.5065i	0.691357	−	0.691357i	0.962531	+	0.271173i	$0.0874116\pi$
$278$	−0.0179185			−0.00107468
$279$	1.00000	−	1.00000i	0.0598684	−	0.0598684i
$280$	5.02279	+	2.66157i	0.300169	+	0.159059i
$281$	15.8122	−	15.8122i	0.943276	−	0.943276i	−0.0551994	−	0.998475i	$-0.517579\pi$
$281$	15.8122	−	15.8122i	0.943276	−	0.943276i	0.998475	+	0.0551994i	$0.0175795\pi$
$282$	−3.66534	−	3.66534i	−0.218268	−	0.218268i
$283$	7.26001	+	7.26001i	0.431563	+	0.431563i	0.889160	−	0.457597i	$-0.151290\pi$
$283$	7.26001	+	7.26001i	0.431563	+	0.431563i	−0.457597	+	0.889160i	$0.651290\pi$
$284$	7.30734	+	7.30734i	0.433611	+	0.433611i
$285$	17.1395	+	9.08221i	1.01526	+	0.537983i
$286$	9.08440	−	3.29044i	0.537172	−	0.194568i
$287$	12.1354	+	12.1354i	0.716331	+	0.716331i
$288$	−1.00000			−0.0589256
$289$			13.7323i			0.807784i
$290$	−11.1120	+	20.9701i	−0.652521	+	1.23141i
$291$	5.23361	+	5.23361i	0.306800	+	0.306800i
$292$		−	14.5716i		−	0.852737i
$293$		−	9.22562i		−	0.538966i	−0.963005	−	0.269483i	$-0.913147\pi$
$293$		−	9.22562i		−	0.538966i	0.963005	−	0.269483i	$-0.0868529\pi$
$294$	−0.380088	−	0.380088i	−0.0221672	−	0.0221672i
$295$	23.5258	−	7.22893i	1.36973	−	0.420885i
$296$		−	3.18391i		−	0.185061i
$297$	−2.67974			−0.155495
$298$	−10.2158	−	10.2158i	−0.591786	−	0.591786i
$299$	−1.49668	+	0.542109i	−0.0865553	+	0.0313510i
$300$	−4.91081	−	0.940168i	−0.283526	−	0.0542806i
$301$	14.9610	+	14.9610i	0.862336	+	0.862336i
$302$	3.29704	+	3.29704i	0.189724	+	0.189724i
$303$	−1.30077	−	1.30077i	−0.0747273	−	0.0747273i
$304$	6.13392	−	6.13392i	0.351805	−	0.351805i
$305$	6.71543	−	12.6731i	0.384524	−	0.725657i
$306$	1.27822	−	1.27822i	0.0730707	−	0.0730707i
$307$	−20.3901			−1.16373			−0.581863	−	0.813287i	$-0.697676\pi$
$307$	−20.3901			−1.16373			−0.581863	+	0.813287i	$0.697676\pi$
$308$	4.81701	−	4.81701i	0.274475	−	0.274475i
$309$	−1.71479			−0.0975512
$310$	−0.928834	−	3.02279i	−0.0527542	−	0.171683i
$311$			19.1186i			1.08412i	0.840340	+	0.542059i	$0.182355\pi$
$311$			19.1186i			1.08412i	−0.840340	+	0.542059i	$0.817645\pi$
$312$	−3.39003	+	1.22789i	−0.191922	+	0.0695158i
$313$	1.87309	−	1.87309i	0.105873	−	0.105873i	−0.652186	−	0.758059i	$-0.726148\pi$
$313$	1.87309	−	1.87309i	0.105873	−	0.105873i	0.758059	+	0.652186i	$0.226148\pi$
$314$	−12.2613	+	12.2613i	−0.691947	+	0.691947i
$315$	−5.02279	−	2.66157i	−0.283002	−	0.149962i
$316$			3.04259i			0.171159i
$317$		−	10.7007i		−	0.601014i	−0.953780	−	0.300507i	$-0.902844\pi$
$317$		−	10.7007i		−	0.601014i	0.953780	−	0.300507i	$-0.0971558\pi$
$318$	−8.67941			−0.486717
$319$	20.1110	+	20.1110i	1.12600	+	1.12600i
$320$	−1.04698	+	1.97581i	−0.0585279	+	0.110451i
$321$	−20.1939			−1.12712
$322$	−0.793616	+	0.793616i	−0.0442265	+	0.0442265i
$323$			15.6810i			0.872512i
$324$	1.00000			0.0555556
$325$	−17.8022	+	2.84276i	−0.987489	+	0.157688i
$326$	13.8216			0.765508
$327$		−	5.90798i		−	0.326712i
$328$	−4.77370	+	4.77370i	−0.263584	+	0.263584i
$329$	−13.1774			−0.726491
$330$	−2.80564	+	5.29467i	−0.154445	+	0.291462i
$331$	5.98236	+	5.98236i	0.328820	+	0.328820i	0.852138	−	0.523317i	$-0.175306\pi$
$331$	5.98236	+	5.98236i	0.328820	+	0.328820i	−0.523317	+	0.852138i	$0.675306\pi$
$332$	3.42655			0.188056
$333$			3.18391i			0.174477i
$334$			17.5562i			0.960630i
$335$	22.4937	+	11.9194i	1.22896	+	0.651224i
$336$	−1.79756	+	1.79756i	−0.0980652	+	0.0980652i
$337$	14.5767	−	14.5767i	0.794042	−	0.794042i	−0.188107	−	0.982149i	$-0.560235\pi$
$337$	14.5767	−	14.5767i	0.794042	−	0.794042i	0.982149	+	0.188107i	$0.0602351\pi$
$338$	−9.98455	+	8.32518i	−0.543088	+	0.452830i
$339$		−	9.17986i		−	0.498582i
$340$	−1.18725	−	3.86378i	−0.0643877	−	0.209543i
$341$	−3.78973			−0.205225
$342$	−6.13392	+	6.13392i	−0.331685	+	0.331685i
$343$	−19.1614			−1.03462
$344$	−5.88519	+	5.88519i	−0.317308	+	0.317308i
$345$	0.462236	−	0.872312i	0.0248860	−	0.0469637i
$346$	−1.23037	+	1.23037i	−0.0661450	+	0.0661450i
$347$	13.7628	+	13.7628i	0.738826	+	0.738826i	0.972351	−	0.233525i	$-0.0750259\pi$
$347$	13.7628	+	13.7628i	0.738826	+	0.738826i	−0.233525	+	0.972351i	$0.575026\pi$
$348$	−7.50483	−	7.50483i	−0.402301	−	0.402301i
$349$	−13.0900	−	13.0900i	−0.700689	−	0.700689i	0.263869	−	0.964559i	$-0.415001\pi$
$349$	−13.0900	−	13.0900i	−0.700689	−	0.700689i	−0.964559	+	0.263869i	$0.915001\pi$
$350$	−10.5175	+	7.13749i	−0.562185	+	0.381515i
$351$	3.39003	−	1.22789i	0.180946	−	0.0655401i
$352$	1.89487	+	1.89487i	0.100997	+	0.100997i
$353$	−31.4265			−1.67267			−0.836333	−	0.548222i	$-0.815305\pi$
$353$	−31.4265			−1.67267			−0.836333	+	0.548222i	$0.815305\pi$
$354$			11.0065i			0.584992i
$355$	−22.0886	+	6.78731i	−1.17234	+	0.360233i
$356$	2.37506	+	2.37506i	0.125878	+	0.125878i
$357$		−	4.59535i		−	0.243212i
$358$			0.271184i			0.0143325i
$359$	19.6376	+	19.6376i	1.03643	+	1.03643i	0.999311	+	0.0371233i	$0.0118194\pi$
$359$	19.6376	+	19.6376i	1.03643	+	1.03643i	0.0371233	+	0.999311i	$0.488181\pi$
$360$	1.04698	−	1.97581i	0.0551806	−	0.104134i
$361$		−	56.2501i		−	2.96053i
$362$	23.7110			1.24622
$363$	−2.70042	−	2.70042i	−0.141735	−	0.141735i
$364$	−3.88657	+	8.30101i	−0.203712	+	0.435091i
$365$	28.7907	+	15.2561i	1.50697	+	0.798543i
$366$	4.53545	+	4.53545i	0.237072	+	0.237072i
$367$	6.26943	+	6.26943i	0.327261	+	0.327261i	0.851544	−	0.524283i	$-0.175667\pi$
$367$	6.26943	+	6.26943i	0.327261	+	0.327261i	−0.524283	+	0.851544i	$0.675667\pi$
$368$	−0.312184	−	0.312184i	−0.0162737	−	0.0162737i
$369$	4.77370	−	4.77370i	0.248509	−	0.248509i
$370$	6.29080	+	3.33348i	0.327043	+	0.173300i
$371$	−15.6018	+	15.6018i	−0.810005	+	0.810005i
$372$	1.41421			0.0733236
$373$	12.7183	−	12.7183i	0.658530	−	0.658530i	−0.296502	−	0.955032i	$-0.595820\pi$
$373$	12.7183	−	12.7183i	0.658530	−	0.658530i	0.955032	+	0.296502i	$0.0958202\pi$
$374$	−4.84409			−0.250482
$375$	6.99911	−	8.71851i	0.361433	−	0.450222i
$376$		−	5.18357i		−	0.267322i
$377$	−34.6567	−	16.2264i	−1.78491	−	0.835704i
$378$	1.79756	−	1.79756i	0.0924567	−	0.0924567i
$379$	−8.37591	+	8.37591i	−0.430242	+	0.430242i	−0.888711	−	0.458469i	$-0.848398\pi$
$379$	−8.37591	+	8.37591i	−0.430242	+	0.430242i	0.458469	+	0.888711i	$0.348398\pi$
$380$	5.69740	+	18.5416i	0.292270	+	0.951163i
$381$			10.5821i			0.542138i
$382$		−	8.88620i		−	0.454658i
$383$	1.62824			0.0831991			0.0415995	−	0.999134i	$-0.486755\pi$
$383$	1.62824			0.0831991			0.0415995	+	0.999134i	$0.486755\pi$
$384$	−0.707107	−	0.707107i	−0.0360844	−	0.0360844i
$385$	4.47420	+	14.5608i	0.228027	+	0.742088i
$386$	−18.6866			−0.951121
$387$	5.88519	−	5.88519i	0.299161	−	0.299161i
$388$			7.40145i			0.375751i
$389$	5.38166			0.272861			0.136430	−	0.990650i	$-0.456437\pi$
$389$	5.38166			0.272861			0.136430	+	0.990650i	$0.456437\pi$
$390$	1.12320	−	7.98363i	0.0568753	−	0.404267i
$391$	0.798078			0.0403605
$392$		−	0.537526i		−	0.0271492i
$393$	−6.22822	+	6.22822i	−0.314172	+	0.314172i
$394$	5.31391			0.267711
$395$	−6.01159	−	3.18553i	−0.302476	−	0.160281i
$396$	−1.89487	−	1.89487i	−0.0952206	−	0.0952206i
$397$	11.3423			0.569254			0.284627	−	0.958638i	$-0.408130\pi$
$397$	11.3423			0.569254			0.284627	+	0.958638i	$0.408130\pi$
$398$			14.0316i			0.703338i
$399$			22.0522i			1.10399i
$400$	−2.80767	−	4.13727i	−0.140384	−	0.206863i
$401$	−15.9787	+	15.9787i	−0.797936	+	0.797936i	−0.982770	−	0.184833i	$-0.940825\pi$
$401$	−15.9787	+	15.9787i	−0.797936	+	0.797936i	0.184833	+	0.982770i	$0.440825\pi$
$402$	−8.05007	+	8.05007i	−0.401501	+	0.401501i
$403$	4.79422	−	1.73650i	0.238817	−	0.0865014i
$404$		−	1.83957i		−	0.0915218i
$405$	−1.04698	+	1.97581i	−0.0520248	+	0.0981789i
$406$	−26.9808			−1.33904
$407$	6.03307	−	6.03307i	0.299048	−	0.299048i
$408$	1.80767			0.0894930
$409$	−9.21508	+	9.21508i	−0.455657	+	0.455657i	−0.897227	−	0.441570i	$-0.854422\pi$
$409$	−9.21508	+	9.21508i	−0.455657	+	0.455657i	0.441570	+	0.897227i	$0.354422\pi$
$410$	−4.43398	−	14.4299i	−0.218978	−	0.712642i
$411$	1.10103	−	1.10103i	0.0543097	−	0.0543097i
$412$	−1.21254	−	1.21254i	−0.0597377	−	0.0597377i
$413$	19.7850	+	19.7850i	0.973555	+	0.973555i
$414$	0.312184	+	0.312184i	0.0153430	+	0.0153430i
$415$	−3.58752	+	6.77022i	−0.176105	+	0.332337i
$416$	−3.26536	−	1.52886i	−0.160098	−	0.0749585i
$417$	0.0126703	+	0.0126703i	0.000620466	+	0.000620466i
$418$	23.2459			1.13700
$419$		−	22.6047i		−	1.10431i	−0.833740	−	0.552157i	$-0.813805\pi$
$419$		−	22.6047i		−	1.10431i	0.833740	−	0.552157i	$-0.186195\pi$
$420$	−1.66964	−	5.43366i	−0.0814700	−	0.265136i
$421$	0.328119	+	0.328119i	0.0159916	+	0.0159916i	0.715057	−	0.699066i	$-0.246401\pi$
$421$	0.328119	+	0.328119i	0.0159916	+	0.0159916i	−0.699066	+	0.715057i	$0.746401\pi$
$422$			12.1389i			0.590912i
$423$			5.18357i			0.252034i
$424$	−6.13727	−	6.13727i	−0.298052	−	0.298052i
$425$	8.87713	+	1.69951i	0.430604	+	0.0824385i
$426$		−	10.3341i		−	0.500691i
$427$	16.3055			0.789080
$428$	−14.2793	−	14.2793i	−0.690214	−	0.690214i
$429$	−8.75034	−	4.09695i	−0.422470	−	0.197803i
$430$	−5.46636	−	17.7897i	−0.263611	−	0.857895i
$431$	−1.62855	−	1.62855i	−0.0784446	−	0.0784446i	0.666796	−	0.745240i	$-0.267665\pi$
$431$	−1.62855	−	1.62855i	−0.0784446	−	0.0784446i	−0.745240	+	0.666796i	$0.767665\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$	24.3982	+	24.3982i	1.17250	+	1.17250i	0.981611	+	0.190891i	$0.0611376\pi$
$433$	24.3982	+	24.3982i	1.17250	+	1.17250i	0.190891	+	0.981611i	$0.438862\pi$
$434$	2.54214	−	2.54214i	0.122027	−	0.122027i
$435$	22.6855	−	6.97074i	1.08769	−	0.334221i
$436$	4.17757	−	4.17757i	0.200069	−	0.200069i
$437$	−3.82983			−0.183206
$438$	−10.3037	+	10.3037i	−0.492328	+	0.492328i
$439$	−26.5637			−1.26782			−0.633909	−	0.773407i	$-0.718551\pi$
$439$	−26.5637			−1.26782			−0.633909	+	0.773407i	$0.718551\pi$
$440$	−5.72778	+	1.76001i	−0.273061	+	0.0839054i
$441$			0.537526i			0.0255965i
$442$	6.12805	−	2.21963i	0.291482	−	0.105577i
$443$	17.7803	−	17.7803i	0.844765	−	0.844765i	−0.144709	−	0.989474i	$-0.546225\pi$
$443$	17.7803	−	17.7803i	0.844765	−	0.844765i	0.989474	+	0.144709i	$0.0462246\pi$
$444$	−2.25136	+	2.25136i	−0.106845	+	0.106845i
$445$	−7.17930	+	2.20603i	−0.340332	+	0.104576i
$446$		−	14.0062i		−	0.663211i
$447$			14.4473i			0.683336i
$448$	−2.54214			−0.120105
$449$	0.365829	+	0.365829i	0.0172646	+	0.0172646i	0.715686	−	0.698422i	$-0.246114\pi$
$449$	0.365829	+	0.365829i	0.0172646	+	0.0172646i	−0.698422	+	0.715686i	$0.746114\pi$
$450$	2.80767	+	4.13727i	0.132355	+	0.195033i
$451$	−18.0910			−0.851874
$452$	6.49114	−	6.49114i	0.305318	−	0.305318i
$453$		−	4.66272i		−	0.219074i
$454$	7.16607			0.336320
$455$	−12.3321	−	16.3701i	−0.578137	−	0.767443i
$456$	−8.67468			−0.406229
$457$			13.6966i			0.640700i	0.947299	+	0.320350i	$0.103801\pi$
$457$			13.6966i			0.640700i	−0.947299	+	0.320350i	$0.896199\pi$
$458$	−1.54327	+	1.54327i	−0.0721123	+	0.0721123i
$459$	−1.80767			−0.0843748
$460$	0.943668	−	0.289967i	0.0439987	−	0.0135198i
$461$	6.04660	+	6.04660i	0.281618	+	0.281618i	0.833754	−	0.552136i	$-0.186187\pi$
$461$	6.04660	+	6.04660i	0.281618	+	0.281618i	−0.552136	+	0.833754i	$0.686187\pi$
$462$	−6.81228			−0.316936
$463$			10.1801i			0.473108i	0.971618	+	0.236554i	$0.0760181\pi$
$463$			10.1801i			0.473108i	−0.971618	+	0.236554i	$0.923982\pi$
$464$		−	10.6134i		−	0.492716i
$465$	−1.48065	+	2.79422i	−0.0686636	+	0.129579i
$466$	4.01556	−	4.01556i	0.186017	−	0.186017i
$467$	18.6160	−	18.6160i	0.861447	−	0.861447i	−0.130059	−	0.991506i	$-0.541517\pi$
$467$	18.6160	−	18.6160i	0.861447	−	0.861447i	0.991506	+	0.130059i	$0.0415168\pi$
$468$	3.26536	+	1.52886i	0.150941	+	0.0706715i
$469$			28.9410i			1.33637i
$470$	10.2418	+	5.42709i	0.472417	+	0.250333i
$471$	17.3401			0.798991
$472$	−7.78281	+	7.78281i	−0.358233	+	0.358233i
$473$	−22.3033			−1.02551
$474$	2.15144	−	2.15144i	0.0988188	−	0.0988188i
$475$	−42.5997	−	8.15565i	−1.95461	−	0.374207i
$476$	3.24940	−	3.24940i	0.148936	−	0.148936i
$477$	6.13727	+	6.13727i	0.281006	+	0.281006i
$478$	−0.248851	−	0.248851i	−0.0113822	−	0.0113822i
$479$	−19.0736	−	19.0736i	−0.871495	−	0.871495i	0.121140	−	0.992635i	$-0.461345\pi$
$479$	−19.0736	−	19.0736i	−0.871495	−	0.871495i	−0.992635	+	0.121140i	$0.961345\pi$
$480$	2.13744	−	0.656785i	0.0975602	−	0.0299780i
$481$	−4.86774	+	10.3966i	−0.221950	+	0.474045i
$482$	−16.0560	−	16.0560i	−0.731331	−	0.731331i
$483$	1.12234			0.0510684
$484$		−	3.81897i		−	0.173590i
$485$	−14.6239	−	7.74916i	−0.664036	−	0.351871i
$486$	−0.707107	−	0.707107i	−0.0320750	−	0.0320750i
$487$		−	0.609311i		−	0.0276105i	−0.999905	−	0.0138053i	$-0.995606\pi$
$487$		−	0.609311i		−	0.0276105i	0.999905	−	0.0138053i	$-0.00439449\pi$
$488$			6.41410i			0.290353i
$489$	−9.77335	−	9.77335i	−0.441966	−	0.441966i
$490$	1.06205	+	0.562778i	0.0479785	+	0.0254237i
$491$			5.96894i			0.269374i	0.990888	+	0.134687i	$0.0430030\pi$
$491$			5.96894i			0.269374i	−0.990888	+	0.134687i	$0.956997\pi$
$492$	6.75103			0.304360
$493$	13.5663	+	13.5663i	0.610993	+	0.610993i
$494$	−29.4074	+	10.6516i	−1.32310	+	0.479237i
$495$	5.72778	−	1.76001i	0.257445	−	0.0791068i
$496$	1.00000	+	1.00000i	0.0449013	+	0.0449013i
$497$	−18.5763	−	18.5763i	−0.833260	−	0.833260i
$498$	−2.42293	−	2.42293i	−0.108574	−	0.108574i
$499$	−30.0733	+	30.0733i	−1.34627	+	1.34627i	−0.456587	+	0.889679i	$0.650928\pi$
$499$	−30.0733	+	30.0733i	−1.34627	+	1.34627i	−0.889679	+	0.456587i	$0.849072\pi$
$500$	11.1140	−	1.21580i	0.497035	−	0.0543721i
$501$	12.4141	−	12.4141i	0.554620	−	0.554620i
$502$	−20.4132			−0.911088
$503$	7.94020	−	7.94020i	0.354036	−	0.354036i	−0.507573	−	0.861609i	$-0.669457\pi$
$503$	7.94020	−	7.94020i	0.354036	−	0.354036i	0.861609	+	0.507573i	$0.169457\pi$
$504$	2.54214			0.113236
$505$	3.63464	+	1.92599i	0.161739	+	0.0857053i
$506$		−	1.18309i		−	0.0525950i
$507$	12.9469	+	1.17335i	0.574994	+	0.0521104i
$508$	−7.48269	+	7.48269i	−0.331991	+	0.331991i
$509$	22.1730	−	22.1730i	0.982803	−	0.982803i	−0.0170515	−	0.999855i	$-0.505428\pi$
$509$	22.1730	−	22.1730i	0.982803	−	0.982803i	0.999855	+	0.0170515i	$0.00542792\pi$
$510$	−1.89259	+	3.57162i	−0.0838054	+	0.158154i
$511$			37.0430i			1.63869i
$512$		−	1.00000i		−	0.0441942i
$513$	8.67468			0.382996
$514$	12.5444	+	12.5444i	0.553311	+	0.553311i
$515$	3.66526	−	1.12625i	0.161511	−	0.0496285i
$516$	8.32291			0.366396
$517$	9.82217	−	9.82217i	0.431978	−	0.431978i
$518$			8.09394i			0.355627i
$519$	1.74000			0.0763776
$520$	6.43950	−	4.85106i	0.282391	−	0.212733i
$521$	10.9719			0.480686			0.240343	−	0.970688i	$-0.422740\pi$
$521$	10.9719			0.480686			0.240343	+	0.970688i	$0.422740\pi$
$522$			10.6134i			0.464537i
$523$	−13.4112	+	13.4112i	−0.586431	+	0.586431i	−0.936663	−	0.350232i	$-0.886103\pi$
$523$	−13.4112	+	13.4112i	−0.586431	+	0.586431i	0.350232	+	0.936663i	$0.386103\pi$
$524$	−8.80803			−0.384781
$525$	12.4840	+	2.39004i	0.544845	+	0.104310i
$526$	3.40213	+	3.40213i	0.148340	+	0.148340i
$527$	−2.55643			−0.111360
$528$		−	2.67974i		−	0.116621i
$529$		−	22.8051i		−	0.991525i
$530$	18.5517	−	5.70050i	0.805834	−	0.247614i
$531$	7.78281	−	7.78281i	0.337745	−	0.337745i
$532$	−15.5933	+	15.5933i	−0.676055	+	0.676055i
$533$	22.8862	−	8.28955i	0.991311	−	0.359060i
$534$		−	3.35884i		−	0.145351i
$535$	43.1632	−	13.2631i	1.86611	−	0.573412i
$536$	−11.3845			−0.491736
$537$	0.191756	−	0.191756i	0.00827488	−	0.00827488i
$538$	11.6328			0.501524
$539$	1.01854	−	1.01854i	0.0438716	−	0.0438716i
$540$	−2.13744	+	0.656785i	−0.0919806	+	0.0282635i
$541$	25.6187	−	25.6187i	1.10143	−	1.10143i	0.107194	−	0.994238i	$-0.465813\pi$
$541$	25.6187	−	25.6187i	1.10143	−	1.10143i	0.994238	−	0.107194i	$-0.0341867\pi$
$542$	15.4392	+	15.4392i	0.663170	+	0.663170i
$543$	−16.7662	−	16.7662i	−0.719506	−	0.719506i
$544$	1.27822	+	1.27822i	0.0548031	+	0.0548031i
$545$	3.88027	+	12.6279i	0.166212	+	0.540921i
$546$	8.61792	−	3.12148i	0.368813	−	0.133587i
$547$	−2.33129	−	2.33129i	−0.0996787	−	0.0996787i	0.655509	−	0.755188i	$-0.272454\pi$
$547$	−2.33129	−	2.33129i	−0.0996787	−	0.0996787i	−0.755188	+	0.655509i	$0.772454\pi$
$548$	1.55709			0.0665155
$549$		−	6.41410i		−	0.273747i
$550$	2.51941	−	13.1597i	0.107428	−	0.561132i
$551$	−65.1020	−	65.1020i	−2.77344	−	2.77344i
$552$			0.441495i			0.0187913i
$553$		−	7.73469i		−	0.328913i
$554$	−11.5065	−	11.5065i	−0.488864	−	0.488864i
$555$	−2.09114	−	6.80540i	−0.0887640	−	0.288873i
$556$			0.0179185i			0.000759913i
$557$	18.8191			0.797390			0.398695	−	0.917084i	$-0.369463\pi$
$557$	18.8191			0.797390			0.398695	+	0.917084i	$0.369463\pi$
$558$	−1.00000	−	1.00000i	−0.0423334	−	0.0423334i
$559$	28.2149	−	10.2197i	1.19336	−	0.432245i
$560$	2.66157	−	5.02279i	0.112472	−	0.212252i
$561$	3.42529	+	3.42529i	0.144616	+	0.144616i
$562$	−15.8122	−	15.8122i	−0.666997	−	0.666997i
$563$	24.6636	+	24.6636i	1.03945	+	1.03945i	0.999189	+	0.0402560i	$0.0128173\pi$
$563$	24.6636	+	24.6636i	1.03945	+	1.03945i	0.0402560	+	0.999189i	$0.487183\pi$
$564$	−3.66534	+	3.66534i	−0.154339	+	0.154339i
$565$	6.02919	+	19.6214i	0.253650	+	0.825477i
$566$	7.26001	−	7.26001i	0.305161	−	0.305161i
$567$	−2.54214			−0.106760
$568$	7.30734	−	7.30734i	0.306609	−	0.306609i
$569$	21.7286			0.910912			0.455456	−	0.890258i	$-0.349476\pi$
$569$	21.7286			0.910912			0.455456	+	0.890258i	$0.349476\pi$
$570$	9.08221	−	17.1395i	0.380412	−	0.717896i
$571$		−	38.0193i		−	1.59106i	−0.605916	−	0.795529i	$-0.707193\pi$
$571$		−	38.0193i		−	1.59106i	0.605916	−	0.795529i	$-0.292807\pi$
$572$	−3.29044	−	9.08440i	−0.137580	−	0.379838i
$573$	−6.28350	+	6.28350i	−0.262497	+	0.262497i
$574$	12.1354	−	12.1354i	0.506523	−	0.506523i
$575$	−0.415080	+	2.16810i	−0.0173100	+	0.0904160i
$576$			1.00000i			0.0416667i
$577$			3.70152i			0.154096i	0.997027	+	0.0770481i	$0.0245495\pi$
$577$			3.70152i			0.154096i	−0.997027	+	0.0770481i	$0.975450\pi$
$578$	13.7323			0.571190
$579$	13.2134	+	13.2134i	0.549130	+	0.549130i
$580$	20.9701	+	11.1120i	0.870738	+	0.461402i
$581$	−8.71076			−0.361383
$582$	5.23361	−	5.23361i	0.216940	−	0.216940i
$583$		−	23.2586i		−	0.963272i
$584$	−14.5716			−0.602976
$585$	−6.43950	+	4.85106i	−0.266241	+	0.200567i
$586$	−9.22562			−0.381107
$587$			16.4699i			0.679784i	0.940464	+	0.339892i	$0.110391\pi$
$587$			16.4699i			0.679784i	−0.940464	+	0.339892i	$0.889609\pi$
$588$	−0.380088	+	0.380088i	−0.0156746	+	0.0156746i
$589$	12.2678			0.505488
$590$	−7.22893	−	23.5258i	−0.297610	−	0.968542i
$591$	−3.75750	−	3.75750i	−0.154563	−	0.154563i
$592$	−3.18391			−0.130858
$593$		−	45.4038i		−	1.86451i	−0.361800	−	0.932256i	$-0.617838\pi$
$593$		−	45.4038i		−	1.86451i	0.361800	−	0.932256i	$-0.382162\pi$
$594$			2.67974i			0.109951i
$595$	3.01816	+	9.82227i	0.123732	+	0.402674i
$596$	−10.2158	+	10.2158i	−0.418456	+	0.418456i
$597$	9.92181	−	9.92181i	0.406073	−	0.406073i
$598$	0.542109	+	1.49668i	0.0221685	+	0.0612038i
$599$		−	27.0486i		−	1.10517i	−0.833455	−	0.552587i	$-0.813641\pi$
$599$		−	27.0486i		−	1.10517i	0.833455	−	0.552587i	$-0.186359\pi$
$600$	−0.940168	+	4.91081i	−0.0383822	+	0.200483i
$601$	20.2837			0.827391			0.413696	−	0.910415i	$-0.364238\pi$
$601$	20.2837			0.827391			0.413696	+	0.910415i	$0.364238\pi$
$602$	14.9610	−	14.9610i	0.609763	−	0.609763i
$603$	11.3845			0.463614
$604$	3.29704	−	3.29704i	0.134155	−	0.134155i
$605$	7.54557	+	3.99838i	0.306771	+	0.162557i
$606$	−1.30077	+	1.30077i	−0.0528401	+	0.0528401i
$607$	2.23846	+	2.23846i	0.0908562	+	0.0908562i	0.751074	−	0.660218i	$-0.229536\pi$
$607$	2.23846	+	2.23846i	0.0908562	+	0.0908562i	−0.660218	+	0.751074i	$0.729536\pi$
$608$	−6.13392	−	6.13392i	−0.248763	−	0.248763i
$609$	19.0783	+	19.0783i	0.773093	+	0.773093i
$610$	−12.6731	−	6.71543i	−0.513117	−	0.271900i
$611$	−7.92495	+	16.9262i	−0.320609	+	0.684762i
$612$	−1.27822	−	1.27822i	−0.0516688	−	0.0516688i
$613$	−22.1399			−0.894224			−0.447112	−	0.894478i	$-0.647547\pi$
$613$	−22.1399			−0.894224			−0.447112	+	0.894478i	$0.647547\pi$
$614$			20.3901i			0.822878i
$615$	−7.06819	+	13.3388i	−0.285017	+	0.537871i
$616$	−4.81701	−	4.81701i	−0.194083	−	0.194083i
$617$			24.8208i			0.999249i	0.866242	+	0.499625i	$0.166529\pi$
$617$			24.8208i			0.999249i	−0.866242	+	0.499625i	$0.833471\pi$
$618$			1.71479i			0.0689791i
$619$	−2.19943	−	2.19943i	−0.0884025	−	0.0884025i	0.661523	−	0.749925i	$-0.269911\pi$
$619$	−2.19943	−	2.19943i	−0.0884025	−	0.0884025i	−0.749925	+	0.661523i	$0.769911\pi$
$620$	−3.02279	+	0.928834i	−0.121398	+	0.0373029i
$621$		−	0.441495i		−	0.0177166i
$622$	19.1186			0.766587
$623$	−6.03773	−	6.03773i	−0.241896	−	0.241896i
$624$	1.22789	+	3.39003i	0.0491551	+	0.135710i
$625$	−9.23397	+	23.2322i	−0.369359	+	0.929287i
$626$	−1.87309	−	1.87309i	−0.0748638	−	0.0748638i
$627$	−16.4373	−	16.4373i	−0.656445	−	0.656445i
$628$	12.2613	+	12.2613i	0.489280	+	0.489280i
$629$	4.06972	−	4.06972i	0.162270	−	0.162270i
$630$	−2.66157	+	5.02279i	−0.106039	+	0.200113i
$631$	−23.0251	+	23.0251i	−0.916616	+	0.916616i	−0.996782	−	0.0801660i	$-0.974455\pi$
$631$	−23.0251	+	23.0251i	−0.916616	+	0.916616i	0.0801660	+	0.996782i	$0.474455\pi$
$632$	3.04259			0.121028
$633$	8.58349	−	8.58349i	0.341163	−	0.341163i
$634$	−10.7007			−0.424981
$635$	−6.95017	−	22.6186i	−0.275809	−	0.897592i
$636$			8.67941i			0.344161i
$637$	−0.821801	+	1.75522i	−0.0325609	+	0.0695442i
$638$	20.1110	−	20.1110i	0.796203	−	0.796203i
$639$	−7.30734	+	7.30734i	−0.289074	+	0.289074i
$640$	1.97581	+	1.04698i	0.0781008	+	0.0413855i
$641$		−	23.0969i		−	0.912275i	−0.889909	−	0.456137i	$-0.849233\pi$
$641$		−	23.0969i		−	0.912275i	0.889909	−	0.456137i	$-0.150767\pi$
$642$			20.1939i			0.796991i
$643$	−41.5694			−1.63934			−0.819669	−	0.572838i	$-0.805842\pi$
$643$	−41.5694			−1.63934			−0.819669	+	0.572838i	$0.805842\pi$
$644$	0.793616	+	0.793616i	0.0312729	+	0.0312729i
$645$	−8.71391	+	16.4445i	−0.343110	+	0.647502i
$646$	15.6810			0.616959
$647$	−30.3385	+	30.3385i	−1.19273	+	1.19273i	−0.216432	+	0.976298i	$0.569442\pi$
$647$	−30.3385	+	30.3385i	−1.19273	+	1.19273i	−0.976298	+	0.216432i	$0.930558\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	−29.4947			−1.15777
$650$	2.84276	+	17.8022i	0.111502	+	0.698260i
$651$	−3.59513			−0.140904
$652$		−	13.8216i		−	0.541296i
$653$	16.6272	−	16.6272i	0.650673	−	0.650673i	−0.302482	−	0.953155i	$-0.597815\pi$
$653$	16.6272	−	16.6272i	0.650673	−	0.650673i	0.953155	+	0.302482i	$0.0978153\pi$
$654$	−5.90798			−0.231020
$655$	9.22182	−	17.4030i	0.360326	−	0.679992i
$656$	4.77370	+	4.77370i	0.186382	+	0.186382i
$657$	14.5716			0.568491
$658$			13.1774i			0.513707i
$659$		−	22.8052i		−	0.888365i	−0.895936	−	0.444182i	$-0.853494\pi$
$659$		−	22.8052i		−	0.888365i	0.895936	−	0.444182i	$-0.146506\pi$
$660$	5.29467	+	2.80564i	0.206095	+	0.109209i
$661$	−3.97661	+	3.97661i	−0.154672	+	0.154672i	−0.780201	−	0.625529i	$-0.784883\pi$
$661$	−3.97661	+	3.97661i	−0.154672	+	0.154672i	0.625529	+	0.780201i	$0.284883\pi$
$662$	5.98236	−	5.98236i	0.232511	−	0.232511i
$663$	−5.90270	−	2.76367i	−0.229242	−	0.107332i
$664$		−	3.42655i		−	0.132976i
$665$	−14.4836	−	47.1353i	−0.561649	−	1.82783i
$666$	3.18391			0.123374
$667$	−3.31335	+	3.31335i	−0.128293	+	0.128293i
$668$	17.5562			0.679268
$669$	−9.90386	+	9.90386i	−0.382905	+	0.382905i
$670$	11.9194	−	22.4937i	0.460485	−	0.869007i
$671$	−12.1539	+	12.1539i	−0.469194	+	0.469194i
$672$	1.79756	+	1.79756i	0.0693425	+	0.0693425i
$673$	−9.80835	−	9.80835i	−0.378084	−	0.378084i	0.492327	−	0.870411i	$-0.336147\pi$
$673$	−9.80835	−	9.80835i	−0.378084	−	0.378084i	−0.870411	+	0.492327i	$0.836147\pi$
$674$	−14.5767	−	14.5767i	−0.561472	−	0.561472i
$675$	0.940168	−	4.91081i	0.0361871	−	0.189017i
$676$	8.32518	+	9.98455i	0.320199	+	0.384021i
$677$	−13.0375	−	13.0375i	−0.501071	−	0.501071i	0.410700	−	0.911771i	$-0.365285\pi$
$677$	−13.0375	−	13.0375i	−0.501071	−	0.501071i	−0.911771	+	0.410700i	$0.865285\pi$
$678$	−9.17986			−0.352550
$679$		−	18.8155i		−	0.722073i
$680$	−3.86378	+	1.18725i	−0.148169	+	0.0455290i
$681$	−5.06717	−	5.06717i	−0.194174	−	0.194174i
$682$			3.78973i			0.145116i
$683$			4.09726i			0.156777i	0.996923	+	0.0783887i	$0.0249775\pi$
$683$			4.09726i			0.156777i	−0.996923	+	0.0783887i	$0.975022\pi$
$684$	6.13392	+	6.13392i	0.234536	+	0.234536i
$685$	−1.63024	+	3.07651i	−0.0622882	+	0.117548i
$686$			19.1614i			0.731587i
$687$	2.18251			0.0832681
$688$	5.88519	+	5.88519i	0.224371	+	0.224371i
$689$	10.6574	+	29.4234i	0.406014	+	1.12094i
$690$	−0.872312	−	0.462236i	−0.0332083	−	0.0175970i
$691$	9.86360	+	9.86360i	0.375229	+	0.375229i	0.869377	−	0.494149i	$-0.164520\pi$
$691$	9.86360	+	9.86360i	0.375229	+	0.375229i	−0.494149	+	0.869377i	$0.664520\pi$
$692$	1.23037	+	1.23037i	0.0467715	+	0.0467715i
$693$	4.81701	+	4.81701i	0.182983	+	0.182983i
$694$	13.7628	−	13.7628i	0.522429	−	0.522429i
$695$	−0.0354035	−	0.0187603i	−0.00134293	−	0.000711617i
$696$	−7.50483	+	7.50483i	−0.284470	+	0.284470i
$697$	−12.2036			−0.462246
$698$	−13.0900	+	13.0900i	−0.495462	+	0.495462i
$699$	−5.67886			−0.214794
$700$	7.13749	+	10.5175i	0.269772	+	0.397525i
$701$			20.4861i			0.773749i	0.922132	+	0.386875i	$0.126445\pi$
$701$			20.4861i			0.773749i	−0.922132	+	0.386875i	$0.873555\pi$
$702$	−1.22789	−	3.39003i	−0.0463439	−	0.127948i
$703$	−19.5298	+	19.5298i	−0.736582	+	0.736582i
$704$	1.89487	−	1.89487i	0.0714154	−	0.0714154i
$705$	−3.40449	−	11.0796i	−0.128220	−	0.417280i
$706$			31.4265i			1.18275i
$707$			4.67643i			0.175875i
$708$	11.0065			0.413651
$709$	12.6265	+	12.6265i	0.474198	+	0.474198i	0.903270	−	0.429072i	$-0.141159\pi$
$709$	12.6265	+	12.6265i	0.474198	+	0.474198i	−0.429072	+	0.903270i	$0.641159\pi$
$710$	6.78731	+	22.0886i	0.254723	+	0.828969i
$711$	−3.04259			−0.114106
$712$	2.37506	−	2.37506i	0.0890090	−	0.0890090i
$713$		−	0.624369i		−	0.0233828i
$714$	−4.59535			−0.171977
$715$	21.3941	+	3.00988i	0.800094	+	0.112563i
$716$	0.271184			0.0101346
$717$			0.351929i			0.0131430i
$718$	19.6376	−	19.6376i	0.732870	−	0.732870i
$719$	−26.6297			−0.993121			−0.496560	−	0.868002i	$-0.665404\pi$
$719$	−26.6297			−0.993121			−0.496560	+	0.868002i	$0.665404\pi$
$720$	−1.97581	−	1.04698i	−0.0736342	−	0.0390186i
$721$	3.08245	+	3.08245i	0.114796	+	0.114796i
$722$	−56.2501			−2.09341
$723$			22.7066i			0.844468i
$724$		−	23.7110i		−	0.881211i
$725$	−43.9106	+	29.7990i	−1.63080	+	1.10671i
$726$	−2.70042	+	2.70042i	−0.100222	+	0.100222i
$727$	−16.2441	+	16.2441i	−0.602459	+	0.602459i	−0.940964	−	0.338506i	$-0.890079\pi$
$727$	−16.2441	+	16.2441i	−0.602459	+	0.602459i	0.338506	+	0.940964i	$0.390079\pi$
$728$	8.30101	+	3.88657i	0.307656	+	0.144046i
$729$			1.00000i			0.0370370i
$730$	15.2561	−	28.7907i	0.564655	−	1.06559i
$731$	−15.0451			−0.556462
$732$	4.53545	−	4.53545i	0.167635	−	0.167635i
$733$	−11.8939			−0.439312			−0.219656	−	0.975577i	$-0.570493\pi$
$733$	−11.8939			−0.439312			−0.219656	+	0.975577i	$0.570493\pi$
$734$	6.26943	−	6.26943i	0.231409	−	0.231409i
$735$	−0.353039	−	1.14893i	−0.0130220	−	0.0423788i
$736$	−0.312184	+	0.312184i	−0.0115073	+	0.0115073i
$737$	−21.5721	−	21.5721i	−0.794620	−	0.794620i
$738$	−4.77370	−	4.77370i	−0.175722	−	0.175722i
$739$	−13.3121	−	13.3121i	−0.489693	−	0.489693i	0.418517	−	0.908209i	$-0.362550\pi$
$739$	−13.3121	−	13.3121i	−0.489693	−	0.489693i	−0.908209	+	0.418517i	$0.862550\pi$
$740$	3.33348	−	6.29080i	0.122541	−	0.231255i
$741$	28.3260	+	13.2624i	1.04058	+	0.487205i
$742$	15.6018	+	15.6018i	0.572760	+	0.572760i
$743$	−45.7126			−1.67703			−0.838515	−	0.544878i	$-0.816576\pi$
$743$	−45.7126			−1.67703			−0.838515	+	0.544878i	$0.816576\pi$
$744$		−	1.41421i		−	0.0518476i
$745$	−9.48880	−	30.8803i	−0.347643	−	1.13137i
$746$	−12.7183	−	12.7183i	−0.465651	−	0.465651i
$747$			3.42655i			0.125371i
$748$			4.84409i			0.177118i
$749$	36.2999	+	36.2999i	1.32637	+	1.32637i
$750$	−8.71851	−	6.99911i	−0.318355	−	0.255571i
$751$		−	26.7596i		−	0.976471i	−0.872712	−	0.488236i	$-0.837641\pi$
$751$		−	26.7596i		−	0.976471i	0.872712	−	0.488236i	$-0.162359\pi$
$752$	−5.18357			−0.189025
$753$	14.4343	+	14.4343i	0.526017	+	0.526017i
$754$	−16.2264	+	34.6567i	−0.590932	+	1.26212i
$755$	3.06240	+	9.96627i	0.111452	+	0.362710i
$756$	−1.79756	−	1.79756i	−0.0653768	−	0.0653768i
$757$	−8.63345	−	8.63345i	−0.313788	−	0.313788i	0.532587	−	0.846375i	$-0.321220\pi$
$757$	−8.63345	−	8.63345i	−0.313788	−	0.313788i	−0.846375	+	0.532587i	$0.821220\pi$
$758$	8.37591	+	8.37591i	0.304227	+	0.304227i
$759$	−0.836574	+	0.836574i	−0.0303657	+	0.0303657i
$760$	18.5416	−	5.69740i	0.672574	−	0.206666i
$761$	4.99238	−	4.99238i	0.180973	−	0.180973i	−0.610806	−	0.791780i	$-0.709155\pi$
$761$	4.99238	−	4.99238i	0.180973	−	0.180973i	0.791780	+	0.610806i	$0.209155\pi$
$762$	10.5821			0.383350
$763$	−10.6200	+	10.6200i	−0.384469	+	0.384469i
$764$	−8.88620			−0.321492
$765$	3.86378	−	1.18725i	0.139695	−	0.0429251i
$766$		−	1.62824i		−	0.0588306i
$767$	37.3125	−	13.5149i	1.34728	−	0.487994i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	−34.2212	+	34.2212i	−1.23405	+	1.23405i	−0.271653	+	0.962395i	$0.587570\pi$
$769$	−34.2212	+	34.2212i	−1.23405	+	1.23405i	−0.962395	+	0.271653i	$0.912430\pi$
$770$	14.5608	−	4.47420i	0.524736	−	0.161239i
$771$		−	17.7405i		−	0.638908i
$772$			18.6866i			0.672544i
$773$	16.3484			0.588010			0.294005	−	0.955804i	$-0.405012\pi$
$773$	16.3484			0.588010			0.294005	+	0.955804i	$0.405012\pi$
$774$	−5.88519	−	5.88519i	−0.211539	−	0.211539i
$775$	1.32960	−	6.94494i	0.0477606	−	0.249470i
$776$	7.40145			0.265696
$777$	5.72328	−	5.72328i	0.205321	−	0.205321i
$778$		−	5.38166i		−	0.192942i
$779$	58.5631			2.09824
$780$	−7.98363	−	1.12320i	−0.285860	−	0.0402169i
$781$	27.6929			0.990928
$782$		−	0.798078i		−	0.0285392i
$783$	7.50483	−	7.50483i	0.268201	−	0.268201i
$784$	−0.537526			−0.0191974
$785$	−37.0634	+	11.3887i	−1.32285	+	0.406481i
$786$	6.22822	+	6.22822i	0.222153	+	0.222153i
$787$	−21.5385			−0.767766			−0.383883	−	0.923382i	$-0.625413\pi$
$787$	−21.5385			−0.767766			−0.383883	+	0.923382i	$0.625413\pi$
$788$		−	5.31391i		−	0.189300i
$789$		−	4.81134i		−	0.171288i
$790$	−3.18553	+	6.01159i	−0.113336	+	0.213883i
$791$	−16.5014	+	16.5014i	−0.586722	+	0.586722i
$792$	−1.89487	+	1.89487i	−0.0673311	+	0.0673311i
$793$	9.80625	−	20.9444i	0.348230	−	0.743756i
$794$		−	11.3423i		−	0.402523i
$795$	−17.1489	−	9.08716i	−0.608208	−	0.322288i
$796$	14.0316			0.497335
$797$	28.9089	−	28.9089i	1.02401	−	1.02401i	0.0243011	−	0.999705i	$-0.492264\pi$
$797$	28.9089	−	28.9089i	1.02401	−	1.02401i	0.999705	−	0.0243011i	$-0.00773604\pi$
$798$	22.0522			0.780641
$799$	6.62572	−	6.62572i	0.234401	−	0.234401i
$800$	−4.13727	+	2.80767i	−0.146275	+	0.0992661i
$801$	−2.37506	+	2.37506i	−0.0839185	+	0.0839185i
$802$	15.9787	+	15.9787i	0.564226	+	0.564226i
$803$	−27.6112	−	27.6112i	−0.974377	−	0.974377i
$804$	8.05007	+	8.05007i	0.283904	+	0.283904i
$805$	−2.39894	+	0.737137i	−0.0845514	+	0.0259807i
$806$	−1.73650	−	4.79422i	−0.0611657	−	0.168869i
$807$	−8.22561	−	8.22561i	−0.289555	−	0.289555i
$808$	−1.83957			−0.0647157
$809$			2.34413i			0.0824152i	0.999151	+	0.0412076i	$0.0131205\pi$
$809$			2.34413i			0.0824152i	−0.999151	+	0.0412076i	$0.986880\pi$
$810$	1.97581	+	1.04698i	0.0694230	+	0.0367871i
$811$	14.4497	+	14.4497i	0.507397	+	0.507397i	0.913727	−	0.406329i	$-0.133191\pi$
$811$	14.4497	+	14.4497i	0.507397	+	0.507397i	−0.406329	+	0.913727i	$0.633191\pi$
$812$			26.9808i			0.946841i
$813$		−	21.8343i		−	0.765762i
$814$	−6.03307	−	6.03307i	−0.211459	−	0.211459i
$815$	27.3089	+	14.4709i	0.956589	+	0.506894i
$816$		−	1.80767i		−	0.0632811i
$817$	72.1986			2.52591
$818$	9.21508	+	9.21508i	0.322198	+	0.322198i
$819$	−8.30101	−	3.88657i	−0.290061	−	0.135808i
$820$	−14.4299	+	4.43398i	−0.503914	+	0.154841i
$821$	25.0645	+	25.0645i	0.874757	+	0.874757i	0.992986	−	0.118230i	$-0.0377219\pi$
$821$	25.0645	+	25.0645i	0.874757	+	0.874757i	−0.118230	+	0.992986i	$0.537722\pi$
$822$	−1.10103	−	1.10103i	−0.0384027	−	0.0384027i
$823$	14.0958	+	14.0958i	0.491350	+	0.491350i	0.908731	−	0.417381i	$-0.137052\pi$
$823$	14.0958	+	14.0958i	0.491350	+	0.491350i	−0.417381	+	0.908731i	$0.637052\pi$
$824$	−1.21254	+	1.21254i	−0.0422409	+	0.0422409i
$825$	−11.0868	+	7.52384i	−0.385994	+	0.261946i
$826$	19.7850	−	19.7850i	0.688408	−	0.688408i
$827$	−15.8830			−0.552308			−0.276154	−	0.961113i	$-0.589060\pi$
$827$	−15.8830			−0.552308			−0.276154	+	0.961113i	$0.589060\pi$
$828$	0.312184	−	0.312184i	0.0108492	−	0.0108492i
$829$	32.4225			1.12608			0.563040	−	0.826429i	$-0.309632\pi$
$829$	32.4225			1.12608			0.563040	+	0.826429i	$0.309632\pi$
$830$	6.77022	+	3.58752i	0.234998	+	0.124525i
$831$			16.2726i			0.564491i
$832$	−1.52886	+	3.26536i	−0.0530036	+	0.113206i
$833$	0.687074	−	0.687074i	0.0238057	−	0.0238057i
$834$	0.0126703	−	0.0126703i	0.000438736	−	0.000438736i
$835$	−18.3809	+	34.6877i	−0.636098	+	1.20042i
$836$		−	23.2459i		−	0.803977i
$837$			1.41421i			0.0488824i
$838$	−22.6047			−0.780868
$839$	−11.9605	−	11.9605i	−0.412922	−	0.412922i	0.469833	−	0.882755i	$-0.344314\pi$
$839$	−11.9605	−	11.9605i	−0.412922	−	0.412922i	−0.882755	+	0.469833i	$0.844314\pi$
$840$	−5.43366	+	1.66964i	−0.187479	+	0.0576080i
$841$	−83.6449			−2.88431
$842$	0.328119	−	0.328119i	0.0113077	−	0.0113077i
$843$			22.3618i			0.770182i
$844$	12.1389			0.417838
$845$	−28.4439	+	5.99539i	−0.978500	+	0.206248i
$846$	5.18357			0.178215
$847$			9.70836i			0.333583i
$848$	−6.13727	+	6.13727i	−0.210755	+	0.210755i
$849$	−10.2672			−0.352369
$850$	1.69951	−	8.87713i	0.0582928	−	0.304483i
$851$	0.993966	+	0.993966i	0.0340727	+	0.0340727i
$852$	−10.3341			−0.354042
$853$		−	27.1504i		−	0.929611i	−0.885413	−	0.464806i	$-0.846124\pi$
$853$		−	27.1504i		−	0.929611i	0.885413	−	0.464806i	$-0.153876\pi$
$854$		−	16.3055i		−	0.557964i
$855$	−18.5416	+	5.69740i	−0.634108	+	0.194847i
$856$	−14.2793	+	14.2793i	−0.488055	+	0.488055i
$857$	5.31779	−	5.31779i	0.181652	−	0.181652i	−0.610423	−	0.792075i	$-0.709001\pi$
$857$	5.31779	−	5.31779i	0.181652	−	0.181652i	0.792075	+	0.610423i	$0.209001\pi$
$858$	−4.09695	+	8.75034i	−0.139868	+	0.298732i
$859$			9.67551i			0.330124i	0.986283	+	0.165062i	$0.0527824\pi$
$859$			9.67551i			0.330124i	−0.986283	+	0.165062i	$0.947218\pi$
$860$	−17.7897	+	5.46636i	−0.606623	+	0.186401i
$861$	−17.1621			−0.584882
$862$	−1.62855	+	1.62855i	−0.0554687	+	0.0554687i
$863$	11.6460			0.396435			0.198217	−	0.980158i	$-0.436485\pi$
$863$	11.6460			0.396435			0.198217	+	0.980158i	$0.436485\pi$
$864$	0.707107	−	0.707107i	0.0240563	−	0.0240563i
$865$	−3.71914	+	1.14281i	−0.126455	+	0.0388566i
$866$	24.3982	−	24.3982i	0.829084	−	0.829084i
$867$	−9.71022	−	9.71022i	−0.329776	−	0.329776i
$868$	−2.54214	−	2.54214i	−0.0862858	−	0.0862858i
$869$	5.76530	+	5.76530i	0.195574	+	0.195574i
$870$	−6.97074	−	22.6855i	−0.236330	−	0.769111i
$871$	37.1746	+	17.4053i	1.25961	+	0.589757i
$872$	−4.17757	−	4.17757i	−0.141470	−	0.141470i
$873$	−7.40145			−0.250501
$874$			3.82983i			0.129546i
$875$	−28.2534	+	3.09073i	−0.955140	+	0.104486i
$876$	10.3037	+	10.3037i	0.348129	+	0.348129i
$877$			47.1519i			1.59221i	0.605160	+	0.796104i	$0.293109\pi$
$877$			47.1519i			1.59221i	−0.605160	+	0.796104i	$0.706891\pi$
$878$			26.5637i			0.896483i
$879$	6.52350	+	6.52350i	0.220032	+	0.220032i
$880$	1.76001	+	5.72778i	0.0593301	+	0.193084i
$881$			31.6068i			1.06486i	0.846474	+	0.532430i	$0.178721\pi$
$881$			31.6068i			1.06486i	−0.846474	+	0.532430i	$0.821279\pi$
$882$	0.537526			0.0180994
$883$	−3.02122	−	3.02122i	−0.101672	−	0.101672i	0.654441	−	0.756113i	$-0.272904\pi$
$883$	−3.02122	−	3.02122i	−0.101672	−	0.101672i	−0.756113	+	0.654441i	$0.772904\pi$
$884$	−2.21963	−	6.12805i	−0.0746541	−	0.206109i
$885$	−11.5236	+	21.7469i	−0.387362	+	0.731013i
$886$	−17.7803	−	17.7803i	−0.597339	−	0.597339i
$887$	20.4002	+	20.4002i	0.684972	+	0.684972i	0.961116	−	0.276144i	$-0.0890566\pi$
$887$	20.4002	+	20.4002i	0.684972	+	0.684972i	−0.276144	+	0.961116i	$0.589057\pi$
$888$	2.25136	+	2.25136i	0.0755508	+	0.0755508i
$889$	19.0220	−	19.0220i	0.637979	−	0.637979i
$890$	2.20603	+	7.17930i	0.0739464	+	0.240651i
$891$	1.89487	−	1.89487i	0.0634804	−	0.0634804i
$892$	−14.0062			−0.468961
$893$	−31.7956	+	31.7956i	−1.06400	+	1.06400i
$894$	14.4473			0.483192
$895$	−0.283924	+	0.535809i	−0.00949053	+	0.0179101i
$896$			2.54214i			0.0849269i
$897$	0.674984	−	1.44164i	0.0225371	−	0.0481350i
$898$	0.365829	−	0.365829i	0.0122079	−	0.0122079i
$899$	10.6134	−	10.6134i	0.353978	−	0.353978i
$900$	4.13727	−	2.80767i	0.137909	−	0.0935890i
$901$		−	15.6895i		−	0.522693i
$902$			18.0910i			0.602366i
$903$	−21.1580			−0.704094
$904$	−6.49114	−	6.49114i	−0.215892	−	0.215892i
$905$	46.8484	+	24.8249i	1.55729	+	0.825207i
$906$	−4.66272			−0.154909
$907$	23.6195	−	23.6195i	0.784274	−	0.784274i	−0.196275	−	0.980549i	$-0.562884\pi$
$907$	23.6195	−	23.6195i	0.784274	−	0.784274i	0.980549	+	0.196275i	$0.0628845\pi$
$908$		−	7.16607i		−	0.237814i
$909$	1.83957			0.0610145
$910$	−16.3701	+	12.3321i	−0.542664	+	0.408804i
$911$	27.6160			0.914959			0.457479	−	0.889220i	$-0.348752\pi$
$911$	27.6160			0.914959			0.457479	+	0.889220i	$0.348752\pi$
$912$			8.67468i			0.287247i
$913$	6.49285	−	6.49285i	0.214882	−	0.214882i
$914$	13.6966			0.453043
$915$	4.21268	+	13.7097i	0.139267	+	0.453230i
$916$	1.54327	+	1.54327i	0.0509911	+	0.0509911i
$917$	22.3912			0.739424
$918$			1.80767i			0.0596620i
$919$		−	43.2829i		−	1.42777i	−0.700262	−	0.713886i	$-0.746934\pi$
$919$		−	43.2829i		−	1.42777i	0.700262	−	0.713886i	$-0.253066\pi$
$920$	−0.289967	−	0.943668i	−0.00955994	−	0.0311118i
$921$	14.4180	−	14.4180i	0.475089	−	0.475089i
$922$	6.04660	−	6.04660i	0.199134	−	0.199134i
$923$	−35.0330	+	12.6892i	−1.15313	+	0.417671i
$924$			6.81228i			0.224108i
$925$	8.93936	+	13.1727i	0.293924	+	0.433115i
$926$	10.1801			0.334538
$927$	1.21254	−	1.21254i	0.0398251	−	0.0398251i
$928$	−10.6134			−0.348403
$929$	−25.4271	+	25.4271i	−0.834234	+	0.834234i	−0.988093	−	0.153858i	$-0.950830\pi$
$929$	−25.4271	+	25.4271i	−0.834234	+	0.834234i	0.153858	+	0.988093i	$0.450830\pi$
$930$	2.79422	+	1.48065i	0.0916261	+	0.0485525i
$931$	−3.29714	+	3.29714i	−0.108060	+	0.108060i
$932$	−4.01556	−	4.01556i	−0.131534	−	0.131534i
$933$	−13.5189	−	13.5189i	−0.442589	−	0.442589i
$934$	−18.6160	−	18.6160i	−0.609135	−	0.609135i
$935$	−9.57102	−	5.07166i	−0.313006	−	0.165861i
$936$	1.52886	−	3.26536i	0.0499723	−	0.106732i
$937$	−27.4781	−	27.4781i	−0.897670	−	0.897670i	0.0975600	−	0.995230i	$-0.468896\pi$
$937$	−27.4781	−	27.4781i	−0.897670	−	0.897670i	−0.995230	+	0.0975600i	$0.968896\pi$
$938$	28.9410			0.944959
$939$			2.64895i			0.0864452i
$940$	5.42709	−	10.2418i	0.177012	−	0.334049i
$941$	25.6263	+	25.6263i	0.835394	+	0.835394i	0.988249	−	0.152854i	$-0.0488465\pi$
$941$	25.6263	+	25.6263i	0.835394	+	0.835394i	−0.152854	+	0.988249i	$0.548847\pi$
$942$		−	17.3401i		−	0.564972i
$943$		−	2.98055i		−	0.0970600i
$944$	7.78281	+	7.78281i	0.253309	+	0.253309i
$945$	5.43366	−	1.66964i	0.176757	−	0.0543133i
$946$			22.3033i			0.725142i
$947$	−25.4751			−0.827828			−0.413914	−	0.910316i	$-0.635839\pi$
$947$	−25.4751			−0.827828			−0.413914	+	0.910316i	$0.635839\pi$
$948$	−2.15144	−	2.15144i	−0.0698754	−	0.0698754i
$949$	47.5815	+	22.2779i	1.54456	+	0.723171i
$950$	−8.15565	+	42.5997i	−0.264604	+	1.38212i
$951$	7.56657	+	7.56657i	0.245363	+	0.245363i
$952$	−3.24940	−	3.24940i	−0.105314	−	0.105314i
$953$	−3.21451	−	3.21451i	−0.104128	−	0.104128i	0.653123	−	0.757252i	$-0.273458\pi$
$953$	−3.21451	−	3.21451i	−0.104128	−	0.104128i	−0.757252	+	0.653123i	$0.773458\pi$
$954$	6.13727	−	6.13727i	0.198701	−	0.198701i
$955$	9.30367	−	17.5575i	0.301060	−	0.568147i
$956$	−0.248851	+	0.248851i	−0.00804843	+	0.00804843i
$957$	−28.4413			−0.919376
$958$	−19.0736	+	19.0736i	−0.616240	+	0.616240i
$959$	−3.95833			−0.127821
$960$	−0.656785	−	2.13744i	−0.0211976	−	0.0689855i
$961$		−	29.0000i		−	0.935484i
$962$	10.3966	+	4.86774i	0.335200	+	0.156942i
$963$	14.2793	−	14.2793i	0.460143	−	0.460143i
$964$	−16.0560	+	16.0560i	−0.517129	+	0.517129i
$965$	−36.9212	−	19.5644i	−1.18853	−	0.629802i
$966$		−	1.12234i		−	0.0361108i
$967$			45.0288i			1.44803i	0.689785	+	0.724014i	$0.257705\pi$
$967$			45.0288i			1.44803i	−0.689785	+	0.724014i	$0.742295\pi$
$968$	−3.81897			−0.122746
$969$	−11.0881	−	11.0881i	−0.356202	−	0.356202i
$970$	−7.74916	+	14.6239i	−0.248810	+	0.469544i
$971$	−4.63059			−0.148603			−0.0743013	−	0.997236i	$-0.523673\pi$
$971$	−4.63059			−0.148603			−0.0743013	+	0.997236i	$0.523673\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$		−	0.0455513i		−	0.00146031i
$974$	−0.609311			−0.0195236
$975$	10.5779	−	14.5982i	0.338765	−	0.467517i
$976$	6.41410			0.205310
$977$		−	51.1169i		−	1.63538i	−0.575662	−	0.817688i	$-0.695256\pi$
$977$		−	51.1169i		−	1.63538i	0.575662	−	0.817688i	$-0.304744\pi$
$978$	−9.77335	+	9.77335i	−0.312517	+	0.312517i
$979$	9.00083			0.287668
$980$	0.562778	−	1.06205i	0.0179773	−	0.0339260i
$981$	4.17757	+	4.17757i	0.133380	+	0.133380i
$982$	5.96894			0.190476
$983$		−	29.8942i		−	0.953478i	−0.879045	−	0.476739i	$-0.841819\pi$
$983$		−	29.8942i		−	0.953478i	0.879045	−	0.476739i	$-0.158181\pi$
$984$		−	6.75103i		−	0.215215i
$985$	10.4993	+	5.56355i	0.334535	+	0.177269i
$986$	13.5663	−	13.5663i	0.432038	−	0.432038i
$987$	9.31780	−	9.31780i	0.296589	−	0.296589i
$988$	10.6516	+	29.4074i	0.338872	+	0.935574i
$989$		−	3.67453i		−	0.116843i
$990$	−1.76001	−	5.72778i	−0.0559369	−	0.182041i
$991$	11.5138			0.365749			0.182874	−	0.983136i	$-0.441460\pi$
$991$	11.5138			0.365749			0.182874	+	0.983136i	$0.441460\pi$
$992$	1.00000	−	1.00000i	0.0317500	−	0.0317500i
$993$	−8.46034			−0.268481
$994$	−18.5763	+	18.5763i	−0.589204	+	0.589204i
$995$	−14.6907	+	27.7237i	−0.465728	+	0.878901i
$996$	−2.42293	+	2.42293i	−0.0767736	+	0.0767736i
$997$	−21.2452	−	21.2452i	−0.672841	−	0.672841i	0.285529	−	0.958370i	$-0.407831\pi$
$997$	−21.2452	−	21.2452i	−0.672841	−	0.672841i	−0.958370	+	0.285529i	$0.907831\pi$
$998$	30.0733	+	30.0733i	0.951954	+	0.951954i
$999$	−2.25136	−	2.25136i	−0.0712299	−	0.0712299i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.t.a.307.2	yes	12
3.2	odd	2		1170.2.w.f.307.2		12
5.2	odd	4		1950.2.j.c.1243.6		12
5.3	odd	4		390.2.j.a.73.1	✓	12
5.4	even	2		1950.2.t.b.307.4		12
13.5	odd	4		390.2.j.a.187.1	yes	12
15.8	even	4		1170.2.m.f.73.5		12
39.5	even	4		1170.2.m.f.577.5		12
65.18	even	4	inner	390.2.t.a.343.2	yes	12
65.44	odd	4		1950.2.j.c.1357.4		12
65.57	even	4		1950.2.t.b.343.4		12
195.83	odd	4		1170.2.w.f.343.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.j.a.73.1	✓	12	5.3	odd	4
390.2.j.a.187.1	yes	12	13.5	odd	4
390.2.t.a.307.2	yes	12	1.1	even	1	trivial
390.2.t.a.343.2	yes	12	65.18	even	4	inner
1170.2.m.f.73.5		12	15.8	even	4
1170.2.m.f.577.5		12	39.5	even	4
1170.2.w.f.307.2		12	3.2	odd	2
1170.2.w.f.343.2		12	195.83	odd	4
1950.2.j.c.1243.6		12	5.2	odd	4
1950.2.j.c.1357.4		12	65.44	odd	4
1950.2.t.b.307.4		12	5.4	even	2
1950.2.t.b.343.4		12	65.57	even	4

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(1.04698 - 1.97581i) q^{5} +(0.707107 + 0.707107i) q^{6} +2.54214 q^{7} +1.00000i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.707107 + 0.707107i) q^{3} -1.00000 q^{4} +(1.04698 - 1.97581i) q^{5} +(0.707107 + 0.707107i) q^{6} +2.54214 q^{7} +1.00000i q^{8} -1.00000i q^{9} +(-1.97581 - 1.04698i) q^{10} +(-1.89487 + 1.89487i) q^{11} +(0.707107 - 0.707107i) q^{12} +(1.52886 - 3.26536i) q^{13} -2.54214i q^{14} +(0.656785 + 2.13744i) q^{15} +1.00000 q^{16} +(-1.27822 + 1.27822i) q^{17} -1.00000 q^{18} +(6.13392 - 6.13392i) q^{19} +(-1.04698 + 1.97581i) q^{20} +(-1.79756 + 1.79756i) q^{21} +(1.89487 + 1.89487i) q^{22} +(-0.312184 - 0.312184i) q^{23} +(-0.707107 - 0.707107i) q^{24} +(-2.80767 - 4.13727i) q^{25} +(-3.26536 - 1.52886i) q^{26} +(0.707107 + 0.707107i) q^{27} -2.54214 q^{28} -10.6134i q^{29} +(2.13744 - 0.656785i) q^{30} +(1.00000 + 1.00000i) q^{31} -1.00000i q^{32} -2.67974i q^{33} +(1.27822 + 1.27822i) q^{34} +(2.66157 - 5.02279i) q^{35} +1.00000i q^{36} -3.18391 q^{37} +(-6.13392 - 6.13392i) q^{38} +(1.22789 + 3.39003i) q^{39} +(1.97581 + 1.04698i) q^{40} +(4.77370 + 4.77370i) q^{41} +(1.79756 + 1.79756i) q^{42} +(5.88519 + 5.88519i) q^{43} +(1.89487 - 1.89487i) q^{44} +(-1.97581 - 1.04698i) q^{45} +(-0.312184 + 0.312184i) q^{46} -5.18357 q^{47} +(-0.707107 + 0.707107i) q^{48} -0.537526 q^{49} +(-4.13727 + 2.80767i) q^{50} -1.80767i q^{51} +(-1.52886 + 3.26536i) q^{52} +(-6.13727 + 6.13727i) q^{53} +(0.707107 - 0.707107i) q^{54} +(1.76001 + 5.72778i) q^{55} +2.54214i q^{56} +8.67468i q^{57} -10.6134 q^{58} +(7.78281 + 7.78281i) q^{59} +(-0.656785 - 2.13744i) q^{60} +6.41410 q^{61} +(1.00000 - 1.00000i) q^{62} -2.54214i q^{63} -1.00000 q^{64} +(-4.85106 - 6.43950i) q^{65} -2.67974 q^{66} +11.3845i q^{67} +(1.27822 - 1.27822i) q^{68} +0.441495 q^{69} +(-5.02279 - 2.66157i) q^{70} +(-7.30734 - 7.30734i) q^{71} +1.00000 q^{72} +14.5716i q^{73} +3.18391i q^{74} +(4.91081 + 0.940168i) q^{75} +(-6.13392 + 6.13392i) q^{76} +(-4.81701 + 4.81701i) q^{77} +(3.39003 - 1.22789i) q^{78} -3.04259i q^{79} +(1.04698 - 1.97581i) q^{80} -1.00000 q^{81} +(4.77370 - 4.77370i) q^{82} -3.42655 q^{83} +(1.79756 - 1.79756i) q^{84} +(1.18725 + 3.86378i) q^{85} +(5.88519 - 5.88519i) q^{86} +(7.50483 + 7.50483i) q^{87} +(-1.89487 - 1.89487i) q^{88} +(-2.37506 - 2.37506i) q^{89} +(-1.04698 + 1.97581i) q^{90} +(3.88657 - 8.30101i) q^{91} +(0.312184 + 0.312184i) q^{92} -1.41421 q^{93} +5.18357i q^{94} +(-5.69740 - 18.5416i) q^{95} +(0.707107 + 0.707107i) q^{96} -7.40145i q^{97} +0.537526i q^{98} +(1.89487 + 1.89487i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4} - 4 q^{5}+O(q^{10}) \) 12 * q - 12 * q^4 - 4 * q^5	\( 12 q - 12 q^{4} - 4 q^{5} + 4 q^{11} + 20 q^{13} - 4 q^{15} + 12 q^{16} + 8 q^{17} - 12 q^{18} - 4 q^{19} + 4 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{25} - 4 q^{26} + 4 q^{30} + 12 q^{31} - 8 q^{34} + 12 q^{35} - 16 q^{37} + 4 q^{38} - 12 q^{39} + 8 q^{41} + 8 q^{42} + 16 q^{43} - 4 q^{44} + 32 q^{47} - 20 q^{49} + 8 q^{50} - 20 q^{52} - 16 q^{53} - 12 q^{55} - 40 q^{58} + 20 q^{59} + 4 q^{60} + 16 q^{61} + 12 q^{62} - 12 q^{64} - 32 q^{65} - 16 q^{66} - 8 q^{68} - 32 q^{69} - 20 q^{70} - 32 q^{71} + 12 q^{72} + 4 q^{76} + 16 q^{77} - 4 q^{80} - 12 q^{81} + 8 q^{82} + 32 q^{83} + 8 q^{84} + 12 q^{85} + 16 q^{86} + 20 q^{87} + 4 q^{88} + 16 q^{89} + 4 q^{90} - 28 q^{91} - 8 q^{95} - 4 q^{99}+O(q^{100}) \) 12 * q - 12 * q^4 - 4 * q^5 + 4 * q^11 + 20 * q^13 - 4 * q^15 + 12 * q^16 + 8 * q^17 - 12 * q^18 - 4 * q^19 + 4 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^25 - 4 * q^26 + 4 * q^30 + 12 * q^31 - 8 * q^34 + 12 * q^35 - 16 * q^37 + 4 * q^38 - 12 * q^39 + 8 * q^41 + 8 * q^42 + 16 * q^43 - 4 * q^44 + 32 * q^47 - 20 * q^49 + 8 * q^50 - 20 * q^52 - 16 * q^53 - 12 * q^55 - 40 * q^58 + 20 * q^59 + 4 * q^60 + 16 * q^61 + 12 * q^62 - 12 * q^64 - 32 * q^65 - 16 * q^66 - 8 * q^68 - 32 * q^69 - 20 * q^70 - 32 * q^71 + 12 * q^72 + 4 * q^76 + 16 * q^77 - 4 * q^80 - 12 * q^81 + 8 * q^82 + 32 * q^83 + 8 * q^84 + 12 * q^85 + 16 * q^86 + 20 * q^87 + 4 * q^88 + 16 * q^89 + 4 * q^90 - 28 * q^91 - 8 * q^95 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more