LMFDB - Embedded newform 390.2.bd.a.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(7,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 11]))

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

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

chi := DirichletCharacter("390.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bd (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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.2
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	390.37
Dual form			390.2.bd.a.253.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.965926 + 0.258819i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.12132 - 0.707107i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(2.29788 - 3.98004i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.965926 + 0.258819i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.12132 - 0.707107i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(2.29788 - 3.98004i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +(2.19067 - 0.448288i) q^{10} +(-3.47323 - 0.930650i) q^{11} +(0.707107 - 0.707107i) q^{12} +(-3.53553 + 0.707107i) q^{13} +4.59575i q^{14} +(-1.86603 - 1.23205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.401302 - 1.49768i) q^{17} -1.00000 q^{18} +(-1.97506 - 7.37101i) q^{19} +(-1.67303 + 1.48356i) q^{20} +(3.24969 - 3.24969i) q^{21} +(3.47323 - 0.930650i) q^{22} +(0.298499 - 1.11401i) q^{23} +(-0.258819 + 0.965926i) q^{24} +(4.00000 + 3.00000i) q^{25} +(2.70831 - 2.38014i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-2.29788 - 3.98004i) q^{28} +(4.97589 - 2.87283i) q^{29} +(2.23205 + 0.133975i) q^{30} +(-0.351414 - 0.351414i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-3.11401 - 1.79788i) q^{33} +(1.09638 + 1.09638i) q^{34} +(-7.68885 + 6.81809i) q^{35} +(0.866025 - 0.500000i) q^{36} +(5.11219 + 8.85457i) q^{37} +(5.39595 + 5.39595i) q^{38} +(-3.59808 - 0.232051i) q^{39} +(0.707107 - 2.12132i) q^{40} +(1.93720 - 7.22973i) q^{41} +(-1.18947 + 4.43916i) q^{42} +(1.38014 - 0.369807i) q^{43} +(-2.54258 + 2.54258i) q^{44} +(-1.48356 - 1.67303i) q^{45} +(0.298499 + 1.11401i) q^{46} +6.76733 q^{47} +(-0.258819 - 0.965926i) q^{48} +(-7.06048 - 12.2291i) q^{49} +(-4.96410 - 0.598076i) q^{50} -1.55051i q^{51} +(-1.15539 + 3.41542i) q^{52} +(-8.92820 + 8.92820i) q^{53} +(-0.965926 - 0.258819i) q^{54} +(6.70977 + 4.43015i) q^{55} +(3.98004 + 2.29788i) q^{56} -7.63103i q^{57} +(-2.87283 + 4.97589i) q^{58} +(8.74786 - 2.34398i) q^{59} +(-2.00000 + 1.00000i) q^{60} +(0.721719 - 1.25005i) q^{61} +(0.480040 + 0.128626i) q^{62} +(3.98004 - 2.29788i) q^{63} -1.00000 q^{64} +(8.00000 + 1.00000i) q^{65} +3.59575 q^{66} +(-0.210133 + 0.121320i) q^{67} +(-1.49768 - 0.401302i) q^{68} +(0.576656 - 0.998798i) q^{69} +(3.24969 - 9.74907i) q^{70} +(-7.94182 + 2.12800i) q^{71} +(-0.500000 + 0.866025i) q^{72} -3.79655i q^{73} +(-8.85457 - 5.11219i) q^{74} +(3.08725 + 3.93305i) q^{75} +(-7.37101 - 1.97506i) q^{76} +(-11.6851 + 11.6851i) q^{77} +(3.23205 - 1.59808i) q^{78} -2.76393i q^{79} +(0.448288 + 2.19067i) q^{80} +(0.500000 + 0.866025i) q^{81} +(1.93720 + 7.22973i) q^{82} -8.75611 q^{83} +(-1.18947 - 4.43916i) q^{84} +(-0.207729 + 3.46082i) q^{85} +(-1.01033 + 1.01033i) q^{86} +(5.54989 - 1.48709i) q^{87} +(0.930650 - 3.47323i) q^{88} +(0.166225 - 0.620358i) q^{89} +(2.12132 + 0.707107i) q^{90} +(-5.30991 + 15.6964i) q^{91} +(-0.815515 - 0.815515i) q^{92} +(-0.248487 - 0.430392i) q^{93} +(-5.86068 + 3.38366i) q^{94} +(-1.02236 + 17.0328i) q^{95} +(0.707107 + 0.707107i) q^{96} +(4.87662 + 2.81552i) q^{97} +(12.2291 + 7.06048i) q^{98} +(-2.54258 - 2.54258i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} - 4 q^{7}+O(q^{10}) $ 8 * q + 4 * q^4 - 4 * q^7	$ 8 q + 4 q^{4} - 4 q^{7} - 16 q^{11} - 8 q^{15} - 4 q^{16} + 12 q^{17} - 8 q^{18} - 24 q^{19} + 8 q^{21} + 16 q^{22} + 16 q^{23} + 32 q^{25} + 4 q^{28} - 24 q^{29} + 4 q^{30} - 4 q^{31} - 12 q^{33} - 24 q^{35} + 8 q^{37} - 8 q^{39} + 28 q^{41} - 8 q^{42} - 8 q^{43} - 8 q^{44} + 16 q^{46} + 32 q^{47} - 20 q^{49} - 12 q^{50} - 16 q^{53} - 4 q^{55} + 12 q^{56} - 8 q^{58} + 32 q^{59} - 16 q^{60} - 8 q^{61} - 16 q^{62} + 12 q^{63} - 8 q^{64} + 64 q^{65} - 16 q^{66} + 12 q^{68} + 8 q^{70} + 8 q^{71} - 4 q^{72} - 24 q^{74} - 24 q^{76} - 24 q^{77} + 12 q^{78} + 4 q^{81} + 28 q^{82} - 32 q^{83} - 8 q^{84} - 32 q^{85} - 8 q^{86} + 28 q^{87} + 8 q^{88} - 4 q^{89} - 8 q^{91} + 20 q^{92} - 12 q^{94} + 4 q^{95} + 12 q^{97} + 24 q^{98} - 8 q^{99}+O(q^{100}) $ 8 * q + 4 * q^4 - 4 * q^7 - 16 * q^11 - 8 * q^15 - 4 * q^16 + 12 * q^17 - 8 * q^18 - 24 * q^19 + 8 * q^21 + 16 * q^22 + 16 * q^23 + 32 * q^25 + 4 * q^28 - 24 * q^29 + 4 * q^30 - 4 * q^31 - 12 * q^33 - 24 * q^35 + 8 * q^37 - 8 * q^39 + 28 * q^41 - 8 * q^42 - 8 * q^43 - 8 * q^44 + 16 * q^46 + 32 * q^47 - 20 * q^49 - 12 * q^50 - 16 * q^53 - 4 * q^55 + 12 * q^56 - 8 * q^58 + 32 * q^59 - 16 * q^60 - 8 * q^61 - 16 * q^62 + 12 * q^63 - 8 * q^64 + 64 * q^65 - 16 * q^66 + 12 * q^68 + 8 * q^70 + 8 * q^71 - 4 * q^72 - 24 * q^74 - 24 * q^76 - 24 * q^77 + 12 * q^78 + 4 * q^81 + 28 * q^82 - 32 * q^83 - 8 * q^84 - 32 * q^85 - 8 * q^86 + 28 * q^87 + 8 * q^88 - 4 * q^89 - 8 * q^91 + 20 * q^92 - 12 * q^94 + 4 * q^95 + 12 * q^97 + 24 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{12}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−2.12132	−	0.707107i	−0.948683	−	0.316228i
$5$	−2.12132	−	0.707107i	−0.948683	−	0.316228i
$6$	−0.965926	+	0.258819i	−0.394338	+	0.105662i
$7$	2.29788	−	3.98004i	0.868516	−	1.50431i	0.00500265	−	0.999987i	$-0.498408\pi$
$7$	2.29788	−	3.98004i	0.868516	−	1.50431i	0.863513	−	0.504326i	$-0.168259\pi$
$8$			1.00000i			0.353553i
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$	2.19067	−	0.448288i	0.692751	−	0.141761i
$11$	−3.47323	−	0.930650i	−1.04722	−	0.280601i	−0.306117	−	0.951994i	$-0.599030\pi$
$11$	−3.47323	−	0.930650i	−1.04722	−	0.280601i	−0.741102	+	0.671393i	$0.765696\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	−3.53553	+	0.707107i	−0.980581	+	0.196116i
$13$	−3.53553	+	0.707107i	−0.980581	+	0.196116i
$14$			4.59575i			1.22827i
$15$	−1.86603	−	1.23205i	−0.481806	−	0.318114i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.401302	−	1.49768i	−0.0973299	−	0.363240i	0.900032	−	0.435823i	$-0.143543\pi$
$17$	−0.401302	−	1.49768i	−0.0973299	−	0.363240i	−0.997362	+	0.0725826i	$0.976876\pi$
$18$	−1.00000			−0.235702
$19$	−1.97506	−	7.37101i	−0.453109	−	1.69103i	−0.693589	−	0.720371i	$-0.743971\pi$
$19$	−1.97506	−	7.37101i	−0.453109	−	1.69103i	0.240480	−	0.970654i	$-0.422695\pi$
$20$	−1.67303	+	1.48356i	−0.374101	+	0.331735i
$21$	3.24969	−	3.24969i	0.709140	−	0.709140i
$22$	3.47323	−	0.930650i	0.740495	−	0.198415i
$23$	0.298499	−	1.11401i	0.0622414	−	0.232288i	−0.927797	−	0.373085i	$-0.878300\pi$
$23$	0.298499	−	1.11401i	0.0622414	−	0.232288i	0.990038	+	0.140797i	$0.0449666\pi$
$24$	−0.258819	+	0.965926i	−0.0528312	+	0.197169i
$25$	4.00000	+	3.00000i	0.800000	+	0.600000i
$26$	2.70831	−	2.38014i	0.531143	−	0.466784i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−2.29788	−	3.98004i	−0.434258	−	0.752157i
$29$	4.97589	−	2.87283i	0.924000	−	0.533472i	0.0390912	−	0.999236i	$-0.487554\pi$
$29$	4.97589	−	2.87283i	0.924000	−	0.533472i	0.884909	+	0.465764i	$0.154220\pi$
$30$	2.23205	+	0.133975i	0.407515	+	0.0244603i
$31$	−0.351414	−	0.351414i	−0.0631157	−	0.0631157i	0.674844	−	0.737960i	$-0.264211\pi$
$31$	−0.351414	−	0.351414i	−0.0631157	−	0.0631157i	−0.737960	+	0.674844i	$0.764211\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−3.11401	−	1.79788i	−0.542080	−	0.312970i
$34$	1.09638	+	1.09638i	0.188027	+	0.188027i
$35$	−7.68885	+	6.81809i	−1.29965	+	1.15247i
$36$	0.866025	−	0.500000i	0.144338	−	0.0833333i
$37$	5.11219	+	8.85457i	0.840439	+	1.45568i	0.889524	+	0.456888i	$0.151036\pi$
$37$	5.11219	+	8.85457i	0.840439	+	1.45568i	−0.0490852	+	0.998795i	$0.515631\pi$
$38$	5.39595	+	5.39595i	0.875339	+	0.875339i
$39$	−3.59808	−	0.232051i	−0.576153	−	0.0371579i
$40$	0.707107	−	2.12132i	0.111803	−	0.335410i
$41$	1.93720	−	7.22973i	0.302540	−	1.12909i	−0.632503	−	0.774558i	$-0.717972\pi$
$41$	1.93720	−	7.22973i	0.302540	−	1.12909i	0.935042	−	0.354536i	$-0.115361\pi$
$42$	−1.18947	+	4.43916i	−0.183539	+	0.684977i
$43$	1.38014	−	0.369807i	0.210469	−	0.0563951i	−0.152044	−	0.988374i	$-0.548585\pi$
$43$	1.38014	−	0.369807i	0.210469	−	0.0563951i	0.362513	+	0.931979i	$0.381919\pi$
$44$	−2.54258	+	2.54258i	−0.383309	+	0.383309i
$45$	−1.48356	−	1.67303i	−0.221157	−	0.249401i
$46$	0.298499	+	1.11401i	0.0440113	+	0.164252i
$47$	6.76733			0.987116			0.493558	−	0.869713i	$-0.335696\pi$
$47$	6.76733			0.987116			0.493558	+	0.869713i	$0.335696\pi$
$48$	−0.258819	−	0.965926i	−0.0373573	−	0.139419i
$49$	−7.06048	−	12.2291i	−1.00864	−	1.74702i
$50$	−4.96410	−	0.598076i	−0.702030	−	0.0845807i
$51$		−	1.55051i		−	0.217115i
$52$	−1.15539	+	3.41542i	−0.160224	+	0.473633i
$53$	−8.92820	+	8.92820i	−1.22638	+	1.22638i	−0.261061	+	0.965322i	$0.584072\pi$
$53$	−8.92820	+	8.92820i	−1.22638	+	1.22638i	−0.965322	+	0.261061i	$0.915928\pi$
$54$	−0.965926	−	0.258819i	−0.131446	−	0.0352208i
$55$	6.70977	+	4.43015i	0.904745	+	0.597362i
$56$	3.98004	+	2.29788i	0.531855	+	0.307067i
$57$		−	7.63103i		−	1.01075i
$58$	−2.87283	+	4.97589i	−0.377222	+	0.653367i
$59$	8.74786	−	2.34398i	1.13887	−	0.305161i	0.360376	−	0.932807i	$-0.382648\pi$
$59$	8.74786	−	2.34398i	1.13887	−	0.305161i	0.778499	+	0.627646i	$0.215982\pi$
$60$	−2.00000	+	1.00000i	−0.258199	+	0.129099i
$61$	0.721719	−	1.25005i	0.0924066	−	0.160053i	−0.816117	−	0.577887i	$-0.803877\pi$
$61$	0.721719	−	1.25005i	0.0924066	−	0.160053i	0.908523	+	0.417834i	$0.137211\pi$
$62$	0.480040	+	0.128626i	0.0609651	+	0.0163356i
$63$	3.98004	−	2.29788i	0.501438	−	0.289505i
$64$	−1.00000			−0.125000
$65$	8.00000	+	1.00000i	0.992278	+	0.124035i
$66$	3.59575			0.442607
$67$	−0.210133	+	0.121320i	−0.0256718	+	0.0148216i	−0.512781	−	0.858519i	$-0.671385\pi$
$67$	−0.210133	+	0.121320i	−0.0256718	+	0.0148216i	0.487109	+	0.873341i	$0.338051\pi$
$68$	−1.49768	−	0.401302i	−0.181620	−	0.0486650i
$69$	0.576656	−	0.998798i	0.0694213	−	0.120241i
$70$	3.24969	−	9.74907i	0.388412	−	1.16524i
$71$	−7.94182	+	2.12800i	−0.942521	+	0.252548i	−0.697186	−	0.716891i	$-0.745565\pi$
$71$	−7.94182	+	2.12800i	−0.942521	+	0.252548i	−0.245335	+	0.969438i	$0.578898\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$		−	3.79655i		−	0.444353i	−0.975007	−	0.222176i	$-0.928684\pi$
$73$		−	3.79655i		−	0.444353i	0.975007	−	0.222176i	$-0.0713161\pi$
$74$	−8.85457	−	5.11219i	−1.02932	−	0.594280i
$75$	3.08725	+	3.93305i	0.356484	+	0.454150i
$76$	−7.37101	−	1.97506i	−0.845513	−	0.226554i
$77$	−11.6851	+	11.6851i	−1.33164	+	1.33164i
$78$	3.23205	−	1.59808i	0.365958	−	0.180946i
$79$		−	2.76393i		−	0.310966i	−0.987839	−	0.155483i	$-0.950307\pi$
$79$		−	2.76393i		−	0.310966i	0.987839	−	0.155483i	$-0.0496934\pi$
$80$	0.448288	+	2.19067i	0.0501201	+	0.244924i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	1.93720	+	7.22973i	0.213928	+	0.798390i
$83$	−8.75611			−0.961108			−0.480554	−	0.876965i	$-0.659564\pi$
$83$	−8.75611			−0.961108			−0.480554	+	0.876965i	$0.659564\pi$
$84$	−1.18947	−	4.43916i	−0.129782	−	0.484352i
$85$	−0.207729	+	3.46082i	−0.0225314	+	0.375378i
$86$	−1.01033	+	1.01033i	−0.108947	+	0.108947i
$87$	5.54989	−	1.48709i	0.595010	−	0.159433i
$88$	0.930650	−	3.47323i	0.0992076	−	0.370248i
$89$	0.166225	−	0.620358i	0.0176198	−	0.0657579i	−0.956556	−	0.291548i	$-0.905830\pi$
$89$	0.166225	−	0.620358i	0.0176198	−	0.0657579i	0.974176	+	0.225790i	$0.0724964\pi$
$90$	2.12132	+	0.707107i	0.223607	+	0.0745356i
$91$	−5.30991	+	15.6964i	−0.556630	+	1.64543i
$92$	−0.815515	−	0.815515i	−0.0850233	−	0.0850233i
$93$	−0.248487	−	0.430392i	−0.0257669	−	0.0446296i
$94$	−5.86068	+	3.38366i	−0.604483	+	0.348998i
$95$	−1.02236	+	17.0328i	−0.104892	+	1.74753i
$96$	0.707107	+	0.707107i	0.0721688	+	0.0721688i
$97$	4.87662	+	2.81552i	0.495145	+	0.285872i	0.726706	−	0.686948i	$-0.241050\pi$
$97$	4.87662	+	2.81552i	0.495145	+	0.285872i	−0.231561	+	0.972820i	$0.574383\pi$
$98$	12.2291	+	7.06048i	1.23533	+	0.713216i
$99$	−2.54258	−	2.54258i	−0.255539	−	0.255539i
$100$	4.59808	−	1.96410i	0.459808	−	0.196410i
$101$	−4.31747	+	2.49269i	−0.429605	+	0.248032i	−0.699178	−	0.714947i	$-0.746451\pi$
$101$	−4.31747	+	2.49269i	−0.429605	+	0.248032i	0.269574	+	0.962980i	$0.413117\pi$
$102$	0.775255	+	1.34278i	0.0767617	+	0.132955i
$103$	13.4741	+	13.4741i	1.32764	+	1.32764i	0.907425	+	0.420215i	$0.138045\pi$
$103$	13.4741	+	13.4741i	1.32764	+	1.32764i	0.420215	+	0.907425i	$0.361955\pi$
$104$	−0.707107	−	3.53553i	−0.0693375	−	0.346688i
$105$	−9.19151	+	4.59575i	−0.896999	+	0.448500i
$106$	3.26795	−	12.1962i	0.317411	−	1.18460i
$107$	0.525566	−	1.96144i	0.0508084	−	0.189620i	−0.935857	−	0.352379i	$-0.885373\pi$
$107$	0.525566	−	1.96144i	0.0508084	−	0.189620i	0.986666	+	0.162759i	$0.0520395\pi$
$108$	0.965926	−	0.258819i	0.0929463	−	0.0249049i
$109$	−12.4777	+	12.4777i	−1.19515	+	1.19515i	−0.219547	+	0.975602i	$0.570458\pi$
$109$	−12.4777	+	12.4777i	−1.19515	+	1.19515i	−0.975602	+	0.219547i	$0.929542\pi$
$110$	−8.02591	−	0.481740i	−0.765240	−	0.0459321i
$111$	2.64626	+	9.87599i	0.251172	+	0.937388i
$112$	−4.59575			−0.434258
$113$	1.92367	+	7.17922i	0.180963	+	0.675364i	0.995459	+	0.0951941i	$0.0303472\pi$
$113$	1.92367	+	7.17922i	0.180963	+	0.675364i	−0.814495	+	0.580170i	$0.802986\pi$
$114$	3.81552	+	6.60867i	0.357356	+	0.618958i
$115$	−1.42094	+	2.15211i	−0.132503	+	0.200685i
$116$		−	5.74567i		−	0.533472i
$117$	−3.41542	−	1.15539i	−0.315755	−	0.106816i
$118$	−6.40388	+	6.40388i	−0.589525	+	0.589525i
$119$	−6.88296	−	1.84428i	−0.630960	−	0.169065i
$120$	1.23205	−	1.86603i	0.112470	−	0.170344i
$121$	1.67095	+	0.964724i	0.151905	+	0.0877022i
$122$			1.44344i			0.130683i
$123$	3.74238	−	6.48200i	0.337439	−	0.584462i
$124$	−0.480040	+	0.128626i	−0.0431088	+	0.0115510i
$125$	−6.36396	−	9.19239i	−0.569210	−	0.822192i
$126$	−2.29788	+	3.98004i	−0.204711	+	0.354570i
$127$	7.79555	+	2.08881i	0.691744	+	0.185352i	0.587530	−	0.809203i	$-0.300101\pi$
$127$	7.79555	+	2.08881i	0.691744	+	0.185352i	0.104214	+	0.994555i	$0.466767\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	1.42883			0.125801
$130$	−7.42820	+	3.13397i	−0.651497	+	0.274868i
$131$	19.0528			1.66465			0.832326	−	0.554287i	$-0.187009\pi$
$131$	19.0528			1.66465			0.832326	+	0.554287i	$0.187009\pi$
$132$	−3.11401	+	1.79788i	−0.271040	+	0.156485i
$133$	−33.8753	−	9.07687i	−2.93737	−	0.787065i
$134$	0.121320	−	0.210133i	0.0104805	−	0.0181527i
$135$	−1.00000	−	2.00000i	−0.0860663	−	0.172133i
$136$	1.49768	−	0.401302i	0.128425	−	0.0344113i
$137$	8.64332	−	14.9707i	0.738449	−	1.27903i	−0.214745	−	0.976670i	$-0.568892\pi$
$137$	8.64332	−	14.9707i	0.738449	−	1.27903i	0.953194	−	0.302360i	$-0.0977746\pi$
$138$			1.15331i			0.0981765i
$139$	1.66354	+	0.960444i	0.141099	+	0.0814638i	0.568888	−	0.822415i	$-0.307374\pi$
$139$	1.66354	+	0.960444i	0.141099	+	0.0814638i	−0.427788	+	0.903879i	$0.640707\pi$
$140$	2.06022	+	10.0678i	0.174120	+	0.850883i
$141$	6.53674	+	1.75151i	0.550492	+	0.147504i
$142$	5.81382	−	5.81382i	0.487885	−	0.487885i
$143$	12.9378	+	0.834398i	1.08191	+	0.0697758i
$144$		−	1.00000i		−	0.0833333i
$145$	−12.5869	+	2.57571i	−1.04528	+	0.213901i
$146$	1.89828	+	3.28791i	0.157102	+	0.272109i
$147$	−3.65477	−	13.6398i	−0.301441	−	1.12499i
$148$	10.2244			0.840439
$149$	1.16296	+	4.34022i	0.0952732	+	0.355565i	0.997061	−	0.0766151i	$-0.0244113\pi$
$149$	1.16296	+	4.34022i	0.0952732	+	0.355565i	−0.901787	+	0.432180i	$0.857745\pi$
$150$	−4.64016	−	1.86250i	−0.378868	−	0.152073i
$151$	8.06450	−	8.06450i	0.656280	−	0.656280i	−0.298218	−	0.954498i	$-0.596392\pi$
$151$	8.06450	−	8.06450i	0.656280	−	0.656280i	0.954498	+	0.298218i	$0.0963923\pi$
$152$	7.37101	−	1.97506i	0.597868	−	0.160198i
$153$	0.401302	−	1.49768i	0.0324433	−	0.121080i
$154$	4.27704	−	15.9621i	0.344653	−	1.28626i
$155$	0.496974	+	0.993948i	0.0399179	+	0.0798358i
$156$	−2.00000	+	3.00000i	−0.160128	+	0.240192i
$157$	−6.34330	−	6.34330i	−0.506250	−	0.506250i	0.407123	−	0.913373i	$-0.366532\pi$
$157$	−6.34330	−	6.34330i	−0.506250	−	0.506250i	−0.913373	+	0.407123i	$0.866532\pi$
$158$	1.38196	+	2.39363i	0.109943	+	0.190427i
$159$	−10.9348	+	6.31319i	−0.867184	+	0.500669i
$160$	−1.48356	−	1.67303i	−0.117286	−	0.132265i
$161$	−3.74791	−	3.74791i	−0.295376	−	0.295376i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	7.85217	+	4.53345i	0.615029	+	0.355087i	0.774931	−	0.632046i	$-0.217784\pi$
$163$	7.85217	+	4.53345i	0.615029	+	0.355087i	−0.159902	+	0.987133i	$0.551118\pi$
$164$	−5.29253	−	5.29253i	−0.413277	−	0.413277i
$165$	5.33453	+	6.01581i	0.415293	+	0.468330i
$166$	7.58302	−	4.37806i	0.588556	−	0.339803i
$167$	−0.699801	−	1.21209i	−0.0541522	−	0.0937944i	0.837679	−	0.546164i	$-0.183912\pi$
$167$	−0.699801	−	1.21209i	−0.0541522	−	0.0937944i	−0.891831	+	0.452369i	$0.850579\pi$
$168$	3.24969	+	3.24969i	0.250719	+	0.250719i
$169$	12.0000	−	5.00000i	0.923077	−	0.384615i
$170$	−1.55051	−	3.10102i	−0.118919	−	0.237837i
$171$	1.97506	−	7.37101i	0.151036	−	0.563675i
$172$	0.369807	−	1.38014i	0.0281975	−	0.105235i
$173$	22.3242	−	5.98174i	1.69727	−	0.454783i	0.725023	−	0.688724i	$-0.241829\pi$
$173$	22.3242	−	5.98174i	1.69727	−	0.454783i	0.972251	+	0.233941i	$0.0751623\pi$
$174$	−4.06280	+	4.06280i	−0.308000	+	0.308000i
$175$	21.1316	−	9.02653i	1.59740	−	0.682341i
$176$	0.930650	+	3.47323i	0.0701504	+	0.261805i
$177$	9.05646			0.680725
$178$	0.166225	+	0.620358i	0.0124591	+	0.0464978i
$179$	−3.61193	−	6.25605i	−0.269969	−	0.467599i	0.698885	−	0.715234i	$-0.253680\pi$
$179$	−3.61193	−	6.25605i	−0.269969	−	0.467599i	−0.968853	+	0.247635i	$0.920347\pi$
$180$	−2.19067	+	0.448288i	−0.163283	+	0.0334134i
$181$		−	7.02118i		−	0.521880i	−0.965355	−	0.260940i	$-0.915967\pi$
$181$		−	7.02118i		−	0.521880i	0.965355	−	0.260940i	$-0.0840325\pi$
$182$	−3.24969	−	16.2484i	−0.240883	−	1.20441i
$183$	1.02066	−	1.02066i	0.0754497	−	0.0754497i
$184$	1.11401	+	0.298499i	0.0821262	+	0.0220057i
$185$	−4.58346	−	22.3983i	−0.336983	−	1.64675i
$186$	0.430392	+	0.248487i	0.0315579	+	0.0182199i
$187$			5.57525i			0.407703i
$188$	3.38366	−	5.86068i	0.246779	−	0.427434i
$189$	4.43916	−	1.18947i	0.322901	−	0.0865211i
$190$	−7.63103	−	15.2621i	−0.553613	−	1.10723i
$191$	10.3967	−	18.0075i	0.752276	−	1.30298i	−0.194442	−	0.980914i	$-0.562289\pi$
$191$	10.3967	−	18.0075i	0.752276	−	1.30298i	0.946717	−	0.322066i	$-0.104377\pi$
$192$	−0.965926	−	0.258819i	−0.0697097	−	0.0186787i
$193$	−22.0657	+	12.7396i	−1.58832	+	0.917018i	−0.594737	+	0.803920i	$0.702744\pi$
$193$	−22.0657	+	12.7396i	−1.58832	+	0.917018i	−0.993584	+	0.113097i	$0.963923\pi$
$194$	−5.63103			−0.404284
$195$	7.46859	+	3.03648i	0.534837	+	0.217447i
$196$	−14.1210			−1.00864
$197$	3.38927	−	1.95680i	0.241475	−	0.139416i	−0.374379	−	0.927276i	$-0.622144\pi$
$197$	3.38927	−	1.95680i	0.241475	−	0.139416i	0.615855	+	0.787860i	$0.288811\pi$
$198$	3.47323	+	0.930650i	0.246832	+	0.0661384i
$199$	−5.06110	+	8.76608i	−0.358772	+	0.621411i	−0.987756	−	0.156007i	$-0.950138\pi$
$199$	−5.06110	+	8.76608i	−0.358772	+	0.621411i	0.628984	+	0.777418i	$0.283471\pi$
$200$	−3.00000	+	4.00000i	−0.212132	+	0.282843i
$201$	−0.234373	+	0.0628000i	−0.0165314	+	0.00442957i
$202$	2.49269	−	4.31747i	0.175385	−	0.303776i
$203$		−	26.4057i		−	1.85331i
$204$	−1.34278	−	0.775255i	−0.0940135	−	0.0542787i
$205$	−9.22161	+	13.9668i	−0.644065	+	0.975481i
$206$	−18.4059	−	4.93185i	−1.28240	−	0.343618i
$207$	0.815515	−	0.815515i	0.0566822	−	0.0566822i
$208$	2.38014	+	2.70831i	0.165033	+	0.187787i
$209$			27.4393i			1.89802i
$210$	5.66220	−	8.57579i	0.390729	−	0.591786i
$211$	2.10066	+	3.63844i	0.144615	+	0.250481i	0.929229	−	0.369504i	$-0.120472\pi$
$211$	2.10066	+	3.63844i	0.144615	+	0.250481i	−0.784614	+	0.619984i	$0.787139\pi$
$212$	3.26795	+	12.1962i	0.224444	+	0.837635i
$213$	−8.22198			−0.563361
$214$	0.525566	+	1.96144i	0.0359270	+	0.134081i
$215$	−3.18921	−	0.191426i	−0.217502	−	0.0130552i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	−2.20614	+	0.591135i	−0.149763	+	0.0401288i
$218$	4.56716	−	17.0449i	0.309327	−	1.15442i
$219$	0.982620	−	3.66719i	0.0663993	−	0.247805i
$220$	7.19151	−	3.59575i	0.484851	−	0.242426i
$221$	2.47783	+	5.01133i	0.166677	+	0.337098i
$222$	−7.22973	−	7.22973i	−0.485228	−	0.485228i
$223$	9.24969	+	16.0209i	0.619405	+	1.07284i	0.989594	+	0.143885i	$0.0459594\pi$
$223$	9.24969	+	16.0209i	0.619405	+	1.07284i	−0.370189	+	0.928956i	$0.620707\pi$
$224$	3.98004	−	2.29788i	0.265928	−	0.153533i
$225$	1.96410	+	4.59808i	0.130940	+	0.306538i
$226$	−5.25555	−	5.25555i	−0.349594	−	0.349594i
$227$	−4.48440	−	2.58907i	−0.297640	−	0.171843i	0.343742	−	0.939064i	$-0.388305\pi$
$227$	−4.48440	−	2.58907i	−0.297640	−	0.171843i	−0.641382	+	0.767221i	$0.721639\pi$
$228$	−6.60867	−	3.81552i	−0.437670	−	0.252689i
$229$	−8.55583	−	8.55583i	−0.565385	−	0.565385i	0.365447	−	0.930832i	$-0.380916\pi$
$229$	−8.55583	−	8.55583i	−0.565385	−	0.565385i	−0.930832	+	0.365447i	$0.880916\pi$
$230$	0.154515	−	2.57425i	0.0101884	−	0.169741i
$231$	−14.3112	+	8.26260i	−0.941611	+	0.543639i
$232$	2.87283	+	4.97589i	0.188611	+	0.326683i
$233$	−16.4531	−	16.4531i	−1.07788	−	1.07788i	−0.996699	−	0.0811798i	$-0.974131\pi$
$233$	−16.4531	−	16.4531i	−1.07788	−	1.07788i	−0.0811798	−	0.996699i	$-0.525869\pi$
$234$	3.53553	−	0.707107i	0.231125	−	0.0462250i
$235$	−14.3557	−	4.78522i	−0.936461	−	0.312154i
$236$	2.34398	−	8.74786i	0.152580	−	0.569437i
$237$	0.715357	−	2.66975i	0.0464674	−	0.173419i
$238$	6.88296	−	1.84428i	0.446156	−	0.119547i
$239$	7.30714	−	7.30714i	0.472660	−	0.472660i	−0.430115	−	0.902774i	$-0.641527\pi$
$239$	7.30714	−	7.30714i	0.472660	−	0.472660i	0.902774	+	0.430115i	$0.141527\pi$
$240$	−0.133975	+	2.23205i	−0.00864802	+	0.144078i
$241$	0.575712	+	2.14859i	0.0370849	+	0.138403i	0.981986	−	0.188953i	$-0.0605093\pi$
$241$	0.575712	+	2.14859i	0.0370849	+	0.138403i	−0.944901	+	0.327355i	$0.893843\pi$
$242$	−1.92945			−0.124030
$243$	0.258819	+	0.965926i	0.0166032	+	0.0619642i
$244$	−0.721719	−	1.25005i	−0.0462033	−	0.0800265i
$245$	6.33025	+	30.9344i	0.404425	+	1.97632i
$246$			7.48477i			0.477211i
$247$	12.1950	+	24.6639i	0.775947	+	1.56932i
$248$	0.351414	−	0.351414i	0.0223148	−	0.0223148i
$249$	−8.45776	−	2.26625i	−0.535989	−	0.143618i
$250$	10.1075	+	4.77886i	0.639257	+	0.302242i
$251$	8.49693	+	4.90571i	0.536322	+	0.309645i	0.743587	−	0.668639i	$-0.233123\pi$
$251$	8.49693	+	4.90571i	0.536322	+	0.309645i	−0.207265	+	0.978285i	$0.566456\pi$
$252$		−	4.59575i		−	0.289505i
$253$	−2.07351	+	3.59143i	−0.130361	+	0.225791i
$254$	−7.79555	+	2.08881i	−0.489137	+	0.131064i
$255$	−1.09638	+	3.28913i	−0.0686577	+	0.205973i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−8.78788	−	2.35471i	−0.548173	−	0.146883i	−0.0259059	−	0.999664i	$-0.508247\pi$
$257$	−8.78788	−	2.35471i	−0.548173	−	0.146883i	−0.522267	+	0.852782i	$0.674914\pi$
$258$	−1.23740	+	0.714413i	−0.0770371	+	0.0444774i
$259$	46.9887			2.91974
$260$	4.86603	−	6.42820i	0.301778	−	0.398660i
$261$	5.74567			0.355648
$262$	−16.5002	+	9.52640i	−1.01939	+	0.588543i
$263$	−7.86238	−	2.10672i	−0.484815	−	0.129906i	0.00812880	−	0.999967i	$-0.497412\pi$
$263$	−7.86238	−	2.10672i	−0.484815	−	0.129906i	−0.492944	+	0.870061i	$0.664079\pi$
$264$	1.79788	−	3.11401i	0.110652	−	0.191654i
$265$	25.2528	−	12.6264i	1.55127	−	0.775633i
$266$	33.8753	−	9.07687i	2.07703	−	0.556539i
$267$	0.321121	−	0.556198i	0.0196523	−	0.0340388i
$268$			0.242641i			0.0148216i
$269$	7.88108	+	4.55015i	0.480518	+	0.277427i	0.720632	−	0.693317i	$-0.243852\pi$
$269$	7.88108	+	4.55015i	0.480518	+	0.277427i	−0.240114	+	0.970745i	$0.577185\pi$
$270$	1.86603	+	1.23205i	0.113563	+	0.0749802i
$271$	−18.2045	−	4.87788i	−1.10584	−	0.296310i	−0.340702	−	0.940171i	$-0.610665\pi$
$271$	−18.2045	−	4.87788i	−1.10584	−	0.296310i	−0.765142	+	0.643861i	$0.777331\pi$
$272$	−1.09638	+	1.09638i	−0.0664776	+	0.0664776i
$273$	−9.19151	+	13.7873i	−0.556295	+	0.834443i
$274$			17.2866i			1.04432i
$275$	−11.1010	−	14.1423i	−0.669414	−	0.852812i
$276$	−0.576656	−	0.998798i	−0.0347106	−	0.0601206i
$277$	1.18274	+	4.41406i	0.0710641	+	0.265215i	0.992312	−	0.123761i	$-0.0394956\pi$
$277$	1.18274	+	4.41406i	0.0710641	+	0.265215i	−0.921248	+	0.388976i	$0.872829\pi$
$278$	−1.92089			−0.115207
$279$	−0.128626	−	0.480040i	−0.00770065	−	0.0287392i
$280$	−6.81809	−	7.68885i	−0.407459	−	0.459496i
$281$	8.50454	−	8.50454i	0.507338	−	0.507338i	−0.406370	−	0.913708i	$-0.633206\pi$
$281$	8.50454	−	8.50454i	0.507338	−	0.507338i	0.913708	+	0.406370i	$0.133206\pi$
$282$	−6.53674	+	1.75151i	−0.389257	+	0.104301i
$283$	0.323932	−	1.20893i	0.0192558	−	0.0718635i	−0.955629	−	0.294572i	$-0.904823\pi$
$283$	0.323932	−	1.20893i	0.0192558	−	0.0718635i	0.974885	+	0.222708i	$0.0714897\pi$
$284$	−2.12800	+	7.94182i	−0.126274	+	0.471260i
$285$	−5.39595	+	16.1879i	−0.319629	+	0.958886i
$286$	−11.6217	+	5.74629i	−0.687203	+	0.339785i
$287$	−24.3232	−	24.3232i	−1.43575	−	1.43575i
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	12.6404	−	7.29796i	0.743555	−	0.429292i
$290$	9.61269	−	8.52406i	0.564476	−	0.500550i
$291$	3.98174	+	3.98174i	0.233414	+	0.233414i
$292$	−3.28791	−	1.89828i	−0.192410	−	0.111088i
$293$	8.47370	+	4.89230i	0.495039	+	0.285811i	0.726663	−	0.686995i	$-0.241070\pi$
$293$	8.47370	+	4.89230i	0.495039	+	0.285811i	−0.231623	+	0.972806i	$0.574404\pi$
$294$	9.98502	+	9.98502i	0.582338	+	0.582338i
$295$	−20.2145	−	1.21334i	−1.17693	−	0.0706431i
$296$	−8.85457	+	5.11219i	−0.514662	+	0.297140i
$297$	−1.79788	−	3.11401i	−0.104323	−	0.180693i
$298$	−3.17726	−	3.17726i	−0.184054	−	0.184054i
$299$	−0.267627	+	4.14971i	−0.0154773	+	0.239984i
$300$	4.94975	−	0.707107i	0.285774	−	0.0408248i
$301$	1.69954	−	6.34278i	0.0979600	−	0.365592i
$302$	−2.95181	+	11.0163i	−0.169858	+	0.633918i
$303$	−4.81552	+	1.29031i	−0.276644	+	0.0741266i
$304$	−5.39595	+	5.39595i	−0.309479	+	0.309479i
$305$	−2.41492	+	2.14143i	−0.138278	+	0.122618i
$306$	0.401302	+	1.49768i	0.0229409	+	0.0856165i
$307$	17.2613			0.985156			0.492578	−	0.870268i	$-0.336055\pi$
$307$	17.2613			0.985156			0.492578	+	0.870268i	$0.336055\pi$
$308$	4.27704	+	15.9621i	0.243707	+	0.909526i
$309$	9.52761	+	16.5023i	0.542007	+	0.938783i
$310$	−0.927366	−	0.612297i	−0.0526708	−	0.0347761i
$311$			9.94495i			0.563927i	0.959425	+	0.281963i	$0.0909856\pi$
$311$			9.94495i			0.563927i	−0.959425	+	0.281963i	$0.909014\pi$
$312$	0.232051	−	3.59808i	0.0131373	−	0.203701i
$313$	14.3777	−	14.3777i	0.812675	−	0.812675i	−0.172359	−	0.985034i	$-0.555139\pi$
$313$	14.3777	−	14.3777i	0.812675	−	0.812675i	0.985034	+	0.172359i	$0.0551389\pi$
$314$	8.66510	+	2.32181i	0.489000	+	0.131027i
$315$	−10.0678	+	2.06022i	−0.567255	+	0.116080i
$316$	−2.39363	−	1.38196i	−0.134652	−	0.0777415i
$317$		−	1.20080i		−	0.0674435i	−0.999431	−	0.0337217i	$-0.989264\pi$
$317$		−	1.20080i		−	0.0674435i	0.999431	−	0.0337217i	$-0.0107360\pi$
$318$	6.31319	−	10.9348i	0.354026	−	0.613192i
$319$	−19.9560	+	5.34720i	−1.11732	+	0.299386i
$320$	2.12132	+	0.707107i	0.118585	+	0.0395285i
$321$	1.01532	−	1.75858i	0.0566694	−	0.0981543i
$322$	5.11974	+	1.37183i	0.285312	+	0.0764491i
$323$	−10.2468	+	5.91600i	−0.570147	+	0.329175i
$324$	1.00000			0.0555556
$325$	−16.2635	−	7.77817i	−0.902134	−	0.431455i
$326$	−9.06690			−0.502169
$327$	−15.2820	+	8.82308i	−0.845098	+	0.487917i
$328$	7.22973	+	1.93720i	0.399195	+	0.106964i
$329$	15.5505	−	26.9342i	0.857326	−	1.48493i
$330$	−7.62775	−	2.54258i	−0.419894	−	0.139965i
$331$	0.819503	−	0.219585i	0.0450440	−	0.0120695i	−0.236227	−	0.971698i	$-0.575911\pi$
$331$	0.819503	−	0.219585i	0.0450440	−	0.0120695i	0.281271	+	0.959628i	$0.409244\pi$
$332$	−4.37806	+	7.58302i	−0.240277	+	0.416172i
$333$			10.2244i			0.560293i
$334$	1.21209	+	0.699801i	0.0663226	+	0.0382914i
$335$	0.531546	−	0.108773i	0.0290415	−	0.00594290i
$336$	−4.43916	−	1.18947i	−0.242176	−	0.0648908i
$337$	−5.62622	+	5.62622i	−0.306480	+	0.306480i	−0.843542	−	0.537063i	$-0.819534\pi$
$337$	−5.62622	+	5.62622i	−0.306480	+	0.306480i	0.537063	+	0.843542i	$0.319534\pi$
$338$	−7.89230	+	10.3301i	−0.429285	+	0.561885i
$339$			7.43247i			0.403677i
$340$	2.89329	+	1.91031i	0.156911	+	0.103601i
$341$	0.893498	+	1.54758i	0.0483856	+	0.0838063i
$342$	1.97506	+	7.37101i	0.106799	+	0.398579i
$343$	−32.7262			−1.76705
$344$	0.369807	+	1.38014i	0.0199387	+	0.0744121i
$345$	−1.92953	+	1.71101i	−0.103882	+	0.0921178i
$346$	−16.3424	+	16.3424i	−0.878574	+	0.878574i
$347$	2.73910	−	0.733939i	0.147043	−	0.0393999i	−0.184547	−	0.982824i	$-0.559082\pi$
$347$	2.73910	−	0.733939i	0.147043	−	0.0393999i	0.331589	+	0.943424i	$0.392415\pi$
$348$	1.48709	−	5.54989i	0.0797163	−	0.297505i
$349$	8.23873	−	30.7473i	0.441009	−	1.64587i	−0.285255	−	0.958452i	$-0.592078\pi$
$349$	8.23873	−	30.7473i	0.441009	−	1.64587i	0.726264	−	0.687416i	$-0.241255\pi$
$350$	−13.7873	+	18.3830i	−0.736960	+	0.982614i
$351$	−3.00000	−	2.00000i	−0.160128	−	0.106752i
$352$	−2.54258	−	2.54258i	−0.135520	−	0.135520i
$353$	4.22803	+	7.32316i	0.225035	+	0.389773i	0.956330	−	0.292289i	$-0.0944169\pi$
$353$	4.22803	+	7.32316i	0.225035	+	0.389773i	−0.731295	+	0.682062i	$0.761084\pi$
$354$	−7.84312	+	4.52823i	−0.416857	+	0.240673i
$355$	18.3519	+	1.10154i	0.974016	+	0.0584635i
$356$	−0.454134	−	0.454134i	−0.0240691	−	0.0240691i
$357$	−6.17109	−	3.56288i	−0.326609	−	0.188568i
$358$	6.25605	+	3.61193i	0.330643	+	0.190897i
$359$	18.1981	+	18.1981i	0.960458	+	0.960458i	0.999247	−	0.0387897i	$-0.0123502\pi$
$359$	18.1981	+	18.1981i	0.960458	+	0.960458i	−0.0387897	+	0.999247i	$0.512350\pi$
$360$	1.67303	−	1.48356i	0.0881766	−	0.0781907i
$361$	−33.9764	+	19.6163i	−1.78823	+	1.03244i
$362$	3.51059	+	6.08052i	0.184513	+	0.319585i
$363$	1.36433	+	1.36433i	0.0716085	+	0.0716085i
$364$	10.9385	+	12.4467i	0.573335	+	0.652385i
$365$	−2.68457	+	8.05370i	−0.140517	+	0.421550i
$366$	−0.373589	+	1.39425i	−0.0195278	+	0.0728788i
$367$	9.44193	−	35.2377i	0.492865	−	1.83940i	−0.0488113	−	0.998808i	$-0.515543\pi$
$367$	9.44193	−	35.2377i	0.492865	−	1.83940i	0.541676	−	0.840587i	$-0.317790\pi$
$368$	−1.11401	+	0.298499i	−0.0580720	+	0.0155603i
$369$	5.29253	−	5.29253i	0.275518	−	0.275518i
$370$	15.1685	+	17.1057i	0.788574	+	0.889284i
$371$	15.0187	+	56.0505i	0.779732	+	2.91000i
$372$	−0.496974			−0.0257669
$373$	−7.79259	−	29.0824i	−0.403485	−	1.50583i	−0.806833	−	0.590780i	$-0.798820\pi$
$373$	−7.79259	−	29.0824i	−0.403485	−	1.50583i	0.403347	−	0.915047i	$-0.367847\pi$
$374$	−2.78763	−	4.82831i	−0.144145	−	0.249666i
$375$	−3.76795	−	10.5263i	−0.194576	−	0.543575i
$376$			6.76733i			0.348998i
$377$	−15.5610	+	13.6755i	−0.801434	+	0.704323i
$378$	−3.24969	+	3.24969i	−0.167146	+	0.167146i
$379$	−23.1719	−	6.20889i	−1.19026	−	0.318929i	−0.391271	−	0.920275i	$-0.627965\pi$
$379$	−23.1719	−	6.20889i	−1.19026	−	0.318929i	−0.798989	+	0.601346i	$0.794631\pi$
$380$	14.2397	+	9.40182i	0.730481	+	0.482303i
$381$	6.98930	+	4.03528i	0.358073	+	0.206733i
$382$			20.7933i			1.06388i
$383$	−0.360784	+	0.624896i	−0.0184352	+	0.0319307i	−0.875096	−	0.483950i	$-0.839202\pi$
$383$	−0.360784	+	0.624896i	−0.0184352	+	0.0319307i	0.856661	+	0.515880i	$0.172535\pi$
$384$	0.965926	−	0.258819i	0.0492922	−	0.0132078i
$385$	33.0504	−	16.5252i	1.68440	−	0.842202i
$386$	12.7396	−	22.0657i	0.648429	−	1.12311i
$387$	1.38014	+	0.369807i	0.0701564	+	0.0187984i
$388$	4.87662	−	2.81552i	0.247573	−	0.142936i
$389$	−34.5417			−1.75133			−0.875666	−	0.482918i	$-0.839577\pi$
$389$	−34.5417			−1.75133			−0.875666	+	0.482918i	$0.839577\pi$
$390$	−7.98623	+	1.10463i	−0.404398	+	0.0559349i
$391$	−1.78822			−0.0904343
$392$	12.2291	−	7.06048i	0.617663	−	0.356608i
$393$	18.4036	+	4.93123i	0.928339	+	0.248748i
$394$	−1.95680	+	3.38927i	−0.0985819	+	0.170749i
$395$	−1.95439	+	5.86317i	−0.0983361	+	0.295008i
$396$	−3.47323	+	0.930650i	−0.174536	+	0.0467669i
$397$	−14.9619	+	25.9148i	−0.750917	+	1.30063i	0.196462	+	0.980511i	$0.437055\pi$
$397$	−14.9619	+	25.9148i	−0.750917	+	1.30063i	−0.947379	+	0.320115i	$0.896279\pi$
$398$		−	10.1222i		−	0.507380i
$399$	−30.3718	−	17.5352i	−1.52049	−	0.877856i
$400$	0.598076	−	4.96410i	0.0299038	−	0.248205i
$401$	6.61965	+	1.77373i	0.330570	+	0.0885759i	0.420287	−	0.907391i	$-0.361930\pi$
$401$	6.61965	+	1.77373i	0.330570	+	0.0885759i	−0.0897168	+	0.995967i	$0.528596\pi$
$402$	0.171573	−	0.171573i	0.00855728	−	0.00855728i
$403$	1.49092	+	0.993948i	0.0742681	+	0.0495121i
$404$			4.98539i			0.248032i
$405$	−0.448288	−	2.19067i	−0.0222756	−	0.108855i
$406$	13.2028	+	22.8680i	0.655246	+	1.13492i
$407$	−9.51532	−	35.5116i	−0.471657	−	1.76025i
$408$	1.55051			0.0767617
$409$	3.63827	+	13.5782i	0.179901	+	0.671399i	0.995665	+	0.0930139i	$0.0296501\pi$
$409$	3.63827	+	13.5782i	0.179901	+	0.671399i	−0.815764	+	0.578385i	$0.803683\pi$
$410$	1.00277	−	16.7064i	0.0495232	−	0.825069i
$411$	12.2235	−	12.2235i	0.602941	−	0.602941i
$412$	18.4059	−	4.93185i	0.906795	−	0.242975i
$413$	10.7724	−	40.2030i	0.530074	−	1.97826i
$414$	−0.298499	+	1.11401i	−0.0146704	+	0.0547508i
$415$	18.5745	+	6.19151i	0.911788	+	0.303929i
$416$	−3.41542	−	1.15539i	−0.167455	−	0.0566479i
$417$	1.35827	+	1.35827i	0.0665149	+	0.0665149i
$418$	−13.7197	−	23.7631i	−0.671050	−	1.16229i
$419$	21.8412	−	12.6100i	1.06701	−	0.616039i	0.139647	−	0.990201i	$-0.455403\pi$
$419$	21.8412	−	12.6100i	1.06701	−	0.616039i	0.927363	+	0.374162i	$0.122070\pi$
$420$	−0.615714	+	10.2580i	−0.0300438	+	0.500537i
$421$	0.532765	+	0.532765i	0.0259654	+	0.0259654i	0.719970	−	0.694005i	$-0.244155\pi$
$421$	0.532765	+	0.532765i	0.0259654	+	0.0259654i	−0.694005	+	0.719970i	$0.744155\pi$
$422$	−3.63844	−	2.10066i	−0.177117	−	0.102258i
$423$	5.86068	+	3.38366i	0.284956	+	0.164519i
$424$	−8.92820	−	8.92820i	−0.433592	−	0.433592i
$425$	2.88783	−	7.19462i	0.140080	−	0.348990i
$426$	7.12044	−	4.11099i	0.344986	−	0.199178i
$427$	−3.31684	−	5.74494i	−0.160513	−	0.278017i
$428$	−1.43587	−	1.43587i	−0.0694056	−	0.0694056i
$429$	12.2810	+	4.15451i	0.592932	+	0.200582i
$430$	2.85765	−	1.42883i	0.137808	−	0.0689041i
$431$	−6.29012	+	23.4751i	−0.302985	+	1.13075i	0.631682	+	0.775228i	$0.282365\pi$
$431$	−6.29012	+	23.4751i	−0.302985	+	1.13075i	−0.934666	+	0.355526i	$0.884302\pi$
$432$	0.258819	−	0.965926i	0.0124524	−	0.0464731i
$433$	22.0934	−	5.91991i	1.06174	−	0.284493i	0.314646	−	0.949209i	$-0.398114\pi$
$433$	22.0934	−	5.91991i	1.06174	−	0.284493i	0.747096	+	0.664716i	$0.231448\pi$
$434$	1.61501	−	1.61501i	0.0775230	−	0.0775230i
$435$	−12.8246	−	0.769773i	−0.614893	−	0.0369078i
$436$	4.56716	+	17.0449i	0.218727	+	0.816302i
$437$	−8.80096			−0.421007
$438$	0.982620	+	3.66719i	0.0469514	+	0.175225i
$439$	9.38839	+	16.2612i	0.448083	+	0.776103i	0.998261	−	0.0589443i	$-0.0187734\pi$
$439$	9.38839	+	16.2612i	0.448083	+	0.776103i	−0.550178	+	0.835047i	$0.685440\pi$
$440$	−4.43015	+	6.70977i	−0.211199	+	0.319876i
$441$		−	14.1210i		−	0.672426i
$442$	−4.65153	−	3.10102i	−0.221251	−	0.147501i
$443$	−4.60332	+	4.60332i	−0.218710	+	0.218710i	−0.807955	−	0.589245i	$-0.799425\pi$
$443$	−4.60332	+	4.60332i	−0.218710	+	0.218710i	0.589245	+	0.807955i	$0.299425\pi$
$444$	9.87599	+	2.64626i	0.468694	+	0.125586i
$445$	−0.791275	+	1.19844i	−0.0375100	+	0.0568115i
$446$	−16.0209	−	9.24969i	−0.758613	−	0.437985i
$447$			4.49333i			0.212527i
$448$	−2.29788	+	3.98004i	−0.108564	+	0.188039i
$449$	5.98074	−	1.60254i	0.282249	−	0.0756283i	−0.114917	−	0.993375i	$-0.536660\pi$
$449$	5.98074	−	1.60254i	0.282249	−	0.0756283i	0.397166	+	0.917747i	$0.369994\pi$
$450$	−4.00000	−	3.00000i	−0.188562	−	0.141421i
$451$	−13.4567	+	23.3077i	−0.633651	+	1.09752i
$452$	7.17922	+	1.92367i	0.337682	+	0.0904816i
$453$	9.87695	−	5.70246i	0.464060	−	0.267925i
$454$	5.17814			0.243022
$455$	22.3631	−	29.5424i	1.04840	−	1.38497i
$456$	7.63103			0.357356
$457$	14.5333	−	8.39079i	0.679838	−	0.392505i	−0.119956	−	0.992779i	$-0.538275\pi$
$457$	14.5333	−	8.39079i	0.679838	−	0.392505i	0.799794	+	0.600274i	$0.204942\pi$
$458$	11.6875	+	3.13165i	0.546120	+	0.146333i
$459$	0.775255	−	1.34278i	0.0361858	−	0.0626757i
$460$	1.15331	+	2.30663i	0.0537735	+	0.107547i
$461$	−35.5676	+	9.53032i	−1.65655	+	0.443871i	−0.961436	−	0.275028i	$-0.911313\pi$
$461$	−35.5676	+	9.53032i	−1.65655	+	0.443871i	−0.695114	+	0.718900i	$0.744646\pi$
$462$	8.26260	−	14.3112i	0.384411	−	0.665819i
$463$			26.8683i			1.24868i	0.781154	+	0.624338i	$0.214631\pi$
$463$			26.8683i			1.24868i	−0.781154	+	0.624338i	$0.785369\pi$
$464$	−4.97589	−	2.87283i	−0.231000	−	0.133368i
$465$	0.222787	+	1.08871i	0.0103315	+	0.0504875i
$466$	22.4754	+	6.02226i	1.04115	+	0.278976i
$467$	−7.00532	+	7.00532i	−0.324168	+	0.324168i	−0.850363	−	0.526196i	$-0.823618\pi$
$467$	−7.00532	+	7.00532i	−0.324168	+	0.324168i	0.526196	+	0.850363i	$0.323618\pi$
$468$	−2.70831	+	2.38014i	−0.125192	+	0.110022i
$469$			1.11512i			0.0514913i
$470$	14.8250	−	3.03371i	0.683826	−	0.139935i
$471$	−4.48539	−	7.76892i	−0.206676	−	0.357973i
$472$	2.34398	+	8.74786i	0.107891	+	0.402653i
$473$	−5.13770			−0.236232
$474$	0.715357	+	2.66975i	0.0328574	+	0.122626i
$475$	14.2128	−	35.4092i	0.652128	−	1.62469i
$476$	−5.03868	+	5.03868i	−0.230947	+	0.230947i
$477$	−12.1962	+	3.26795i	−0.558423	+	0.149629i
$478$	−2.67460	+	9.98174i	−0.122333	+	0.456554i
$479$	−9.29474	+	34.6885i	−0.424688	+	1.58496i	0.339916	+	0.940456i	$0.389601\pi$
$479$	−9.29474	+	34.6885i	−0.424688	+	1.58496i	−0.764604	+	0.644500i	$0.777065\pi$
$480$	−1.00000	−	2.00000i	−0.0456435	−	0.0912871i
$481$	−24.3355	−	27.6908i	−1.10960	−	1.26259i
$482$	−1.57287	−	1.57287i	−0.0716425	−	0.0716425i
$483$	−2.65017	−	4.59023i	−0.120587	−	0.208863i
$484$	1.67095	−	0.964724i	0.0759523	−	0.0438511i
$485$	−8.35399	−	9.42090i	−0.379335	−	0.427781i
$486$	−0.707107	−	0.707107i	−0.0320750	−	0.0320750i
$487$	−8.64927	−	4.99366i	−0.391936	−	0.226284i	0.291063	−	0.956704i	$-0.405991\pi$
$487$	−8.64927	−	4.99366i	−0.391936	−	0.226284i	−0.682998	+	0.730420i	$0.739324\pi$
$488$	1.25005	+	0.721719i	0.0565873	+	0.0326707i
$489$	6.41127	+	6.41127i	0.289928	+	0.289928i
$490$	−20.9493	−	23.6248i	−0.946395	−	1.06726i
$491$	3.69150	−	2.13129i	0.166595	−	0.0961837i	−0.414384	−	0.910102i	$-0.636003\pi$
$491$	3.69150	−	2.13129i	0.166595	−	0.0961837i	0.580979	+	0.813918i	$0.302670\pi$
$492$	−3.74238	−	6.48200i	−0.168720	−	0.292231i
$493$	−6.29941	−	6.29941i	−0.283711	−	0.283711i
$494$	−22.8931	−	15.2621i	−1.03001	−	0.686673i
$495$	3.59575	+	7.19151i	0.161617	+	0.323234i
$496$	−0.128626	+	0.480040i	−0.00577549	+	0.0215544i
$497$	−9.77978	+	36.4986i	−0.438683	+	1.63719i
$498$	8.45776	−	2.26625i	0.379001	−	0.101553i
$499$	−7.38839	+	7.38839i	−0.330750	+	0.330750i	−0.852871	−	0.522121i	$-0.825141\pi$
$499$	−7.38839	+	7.38839i	−0.330750	+	0.330750i	0.522121	+	0.852871i	$0.325141\pi$
$500$	−11.1428	+	0.915158i	−0.498322	+	0.0409271i
$501$	−0.362244	−	1.35191i	−0.0161838	−	0.0603989i
$502$	−9.81141			−0.437905
$503$	1.54189	+	5.75442i	0.0687495	+	0.256577i	0.991743	−	0.128238i	$-0.0409321\pi$
$503$	1.54189	+	5.75442i	0.0687495	+	0.256577i	−0.922994	+	0.384815i	$0.874265\pi$
$504$	2.29788	+	3.98004i	0.102356	+	0.177285i
$505$	10.9213	−	2.23489i	0.485993	−	0.0994512i
$506$		−	4.14703i		−	0.184358i
$507$	12.8852	−	1.72380i	0.572252	−	0.0765567i
$508$	5.70674	−	5.70674i	0.253196	−	0.253196i
$509$	20.9261	+	5.60714i	0.927534	+	0.248532i	0.690803	−	0.723043i	$-0.257257\pi$
$509$	20.9261	+	5.60714i	0.927534	+	0.248532i	0.236731	+	0.971575i	$0.423924\pi$
$510$	−0.695075	−	3.39666i	−0.0307784	−	0.150407i
$511$	−15.1104	−	8.72401i	−0.668446	−	0.385927i
$512$		−	1.00000i		−	0.0441942i
$513$	3.81552	−	6.60867i	0.168459	−	0.291780i
$514$	8.78788	−	2.35471i	0.387617	−	0.103862i
$515$	−19.0552	−	38.1104i	−0.839673	−	1.67935i
$516$	0.714413	−	1.23740i	0.0314503	−	0.0544735i
$517$	−23.5045	−	6.29801i	−1.03373	−	0.276986i
$518$	−40.6934	+	23.4944i	−1.78797	+	1.03228i
$519$	23.1117			1.01449
$520$	−1.00000	+	8.00000i	−0.0438529	+	0.350823i
$521$	14.6016			0.639707			0.319854	−	0.947467i	$-0.396366\pi$
$521$	14.6016			0.639707			0.319854	+	0.947467i	$0.396366\pi$
$522$	−4.97589	+	2.87283i	−0.217789	+	0.125741i
$523$	−36.1910	−	9.69735i	−1.58252	−	0.424035i	−0.642816	−	0.766021i	$-0.722234\pi$
$523$	−36.1910	−	9.69735i	−1.58252	−	0.424035i	−0.939705	+	0.341985i	$0.888901\pi$
$524$	9.52640	−	16.5002i	0.416163	−	0.720815i
$525$	22.7478	−	3.24969i	0.992796	−	0.141828i
$526$	7.86238	−	2.10672i	0.342816	−	0.0918573i
$527$	−0.385281	+	0.667327i	−0.0167831	+	0.0290692i
$528$			3.59575i			0.156485i
$529$	18.7667	+	10.8349i	0.815942	+	0.471084i
$530$	−15.5563	+	23.5612i	−0.675725	+	1.02343i
$531$	8.74786	+	2.34398i	0.379625	+	0.101720i
$532$	−24.7985	+	24.7985i	−1.07515	+	1.07515i
$533$	−1.73685	+	26.9308i	−0.0752312	+	1.16650i
$534$			0.642242i			0.0277925i
$535$	−2.50184	+	3.78921i	−0.108164	+	0.163822i
$536$	−0.121320	−	0.210133i	−0.00524024	−	0.00907636i
$537$	−1.86967	−	6.97772i	−0.0806824	−	0.301111i
$538$	−9.10029			−0.392341
$539$	13.1417	+	49.0454i	0.566051	+	2.11253i
$540$	−2.23205	−	0.133975i	−0.0960522	−	0.00576535i
$541$	19.1127	−	19.1127i	0.821718	−	0.821718i	−0.164637	−	0.986354i	$-0.552645\pi$
$541$	19.1127	−	19.1127i	0.821718	−	0.821718i	0.986354	+	0.164637i	$0.0526452\pi$
$542$	18.2045	−	4.87788i	0.781950	−	0.209523i
$543$	1.81722	−	6.78194i	0.0779842	−	0.291041i
$544$	0.401302	−	1.49768i	0.0172057	−	0.0642124i
$545$	35.2923	−	17.6462i	1.51176	−	0.755878i
$546$	1.06645	−	16.5359i	0.0456398	−	0.707670i
$547$	9.72084	+	9.72084i	0.415633	+	0.415633i	0.883695	−	0.468062i	$-0.155048\pi$
$547$	9.72084	+	9.72084i	0.415633	+	0.415633i	−0.468062	+	0.883695i	$0.655048\pi$
$548$	−8.64332	−	14.9707i	−0.369224	−	0.639515i
$549$	1.25005	−	0.721719i	0.0533510	−	0.0308022i
$550$	16.6849	+	6.69710i	0.711446	+	0.285565i
$551$	−31.0034	−	31.0034i	−1.32079	−	1.32079i
$552$	0.998798	+	0.576656i	0.0425117	+	0.0245441i
$553$	−11.0005	−	6.35116i	−0.467791	−	0.270079i
$554$	−3.23131	−	3.23131i	−0.137285	−	0.137285i
$555$	1.36981	−	22.8213i	0.0581451	−	0.968712i
$556$	1.66354	−	0.960444i	0.0705497	−	0.0407319i
$557$	13.4746	+	23.3387i	0.570936	+	0.988891i	0.996470	+	0.0839484i	$0.0267531\pi$
$557$	13.4746	+	23.3387i	0.570936	+	0.988891i	−0.425534	+	0.904943i	$0.639914\pi$
$558$	0.351414	+	0.351414i	0.0148765	+	0.0148765i
$559$	−4.61804	+	2.28337i	−0.195322	+	0.0965763i
$560$	9.74907	+	3.24969i	0.411973	+	0.137324i
$561$	−1.44298	+	5.38528i	−0.0609227	+	0.227367i
$562$	−3.11288	+	11.6174i	−0.131309	+	0.490051i
$563$	3.68352	−	0.986997i	0.155242	−	0.0415970i	−0.180361	−	0.983600i	$-0.557727\pi$
$563$	3.68352	−	0.986997i	0.155242	−	0.0415970i	0.335603	+	0.942004i	$0.391060\pi$
$564$	4.78522	−	4.78522i	0.201494	−	0.201494i
$565$	0.995763	−	16.5897i	0.0418921	−	0.697932i
$566$	0.323932	+	1.20893i	0.0136159	+	0.0508152i
$567$	4.59575			0.193004
$568$	−2.12800	−	7.94182i	−0.0892891	−	0.333231i
$569$	8.28497	+	14.3500i	0.347324	+	0.601582i	0.985773	−	0.168081i	$-0.0537571\pi$
$569$	8.28497	+	14.3500i	0.347324	+	0.601582i	−0.638449	+	0.769664i	$0.720424\pi$
$570$	−3.42090	−	16.7171i	−0.143286	−	0.700201i
$571$		−	22.4047i		−	0.937608i	−0.883302	−	0.468804i	$-0.844685\pi$
$571$		−	22.4047i		−	0.937608i	0.883302	−	0.468804i	$-0.155315\pi$
$572$	7.19151	−	10.7873i	0.300692	−	0.451038i
$573$	14.7031	−	14.7031i	0.614231	−	0.614231i
$574$	33.2261	+	8.90289i	1.38683	+	0.371600i
$575$	4.53604	−	3.56056i	0.189166	−	0.148486i
$576$	−0.866025	−	0.500000i	−0.0360844	−	0.0208333i
$577$			9.87100i			0.410935i	0.978664	+	0.205468i	$0.0658715\pi$
$577$			9.87100i			0.410935i	−0.978664	+	0.205468i	$0.934128\pi$
$578$	−7.29796	+	12.6404i	−0.303555	+	0.525773i
$579$	−24.6110	+	6.59451i	−1.02280	+	0.274058i
$580$	−4.06280	+	12.1884i	−0.168699	+	0.506096i
$581$	−20.1205	+	34.8497i	−0.834738	+	1.44581i
$582$	−5.43916	−	1.45742i	−0.225460	−	0.0604119i
$583$	39.3187	−	22.7007i	1.62842	−	0.940167i
$584$	3.79655			0.157102
$585$	6.42820	+	4.86603i	0.265773	+	0.201185i
$586$	−9.78459			−0.404198
$587$	22.8800	−	13.2098i	0.944358	−	0.545225i	0.0530344	−	0.998593i	$-0.483111\pi$
$587$	22.8800	−	13.2098i	0.944358	−	0.545225i	0.891324	+	0.453367i	$0.149777\pi$
$588$	−13.6398	−	3.65477i	−0.562496	−	0.150720i
$589$	−1.89621	+	3.28433i	−0.0781320	+	0.135329i
$590$	18.1129	−	9.05646i	0.745697	−	0.372848i
$591$	3.78024	−	1.01291i	0.155498	−	0.0416656i
$592$	5.11219	−	8.85457i	0.210110	−	0.363921i
$593$		−	4.74643i		−	0.194913i	−0.995240	−	0.0974563i	$-0.968929\pi$
$593$		−	4.74643i		−	0.194913i	0.995240	−	0.0974563i	$-0.0310706\pi$
$594$	3.11401	+	1.79788i	0.127770	+	0.0737678i
$595$	13.2969	+	8.77930i	0.545118	+	0.359916i
$596$	4.34022	+	1.16296i	0.177782	+	0.0476366i
$597$	−7.15748	+	7.15748i	−0.292936	+	0.292936i
$598$	−1.84308	−	3.72756i	−0.0753692	−	0.152431i
$599$		−	6.53789i		−	0.267131i	−0.991040	−	0.133565i	$-0.957357\pi$
$599$		−	6.53789i		−	0.267131i	0.991040	−	0.133565i	$-0.0426426\pi$
$600$	−3.93305	+	3.08725i	−0.160566	+	0.126036i
$601$	−12.5745	−	21.7796i	−0.512923	−	0.888409i	−0.999888	−	0.0149873i	$-0.995229\pi$
$601$	−12.5745	−	21.7796i	−0.512923	−	0.888409i	0.486964	−	0.873422i	$-0.338104\pi$
$602$	1.69954	+	6.34278i	0.0692682	+	0.258512i
$603$	−0.242641			−0.00988109
$604$	−2.95181	−	11.0163i	−0.120108	−	0.448247i
$605$	−2.86246	−	3.22803i	−0.116376	−	0.131238i
$606$	3.52520	−	3.52520i	0.143202	−	0.143202i
$607$	16.7839	−	4.49722i	0.681236	−	0.182537i	0.0984251	−	0.995144i	$-0.468620\pi$
$607$	16.7839	−	4.49722i	0.681236	−	0.182537i	0.582811	+	0.812608i	$0.301953\pi$
$608$	1.97506	−	7.37101i	0.0800991	−	0.298934i
$609$	6.83429	−	25.5059i	0.276939	−	1.03355i
$610$	1.02066	−	3.06199i	0.0413255	−	0.123976i
$611$	−23.9261	+	4.78522i	−0.967947	+	0.193589i
$612$	−1.09638	−	1.09638i	−0.0443184	−	0.0443184i
$613$	−4.45826	−	7.72192i	−0.180067	−	0.311886i	0.761836	−	0.647770i	$-0.224298\pi$
$613$	−4.45826	−	7.72192i	−0.180067	−	0.311886i	−0.941903	+	0.335884i	$0.890965\pi$
$614$	−14.9488	+	8.63067i	−0.603283	+	0.348305i
$615$	−12.5223	+	11.1041i	−0.504946	+	0.447762i
$616$	−11.6851	−	11.6851i	−0.470805	−	0.470805i
$617$	−20.9147	−	12.0751i	−0.841993	−	0.486125i	0.0159483	−	0.999873i	$-0.494923\pi$
$617$	−20.9147	−	12.0751i	−0.841993	−	0.486125i	−0.857941	+	0.513748i	$0.828257\pi$
$618$	−16.5023	−	9.52761i	−0.663820	−	0.383257i
$619$	−28.9712	−	28.9712i	−1.16445	−	1.16445i	−0.983490	−	0.180961i	$-0.942079\pi$
$619$	−28.9712	−	28.9712i	−1.16445	−	1.16445i	−0.180961	−	0.983490i	$-0.557921\pi$
$620$	1.10927	+	0.0665819i	0.0445494	+	0.00267399i
$621$	0.998798	−	0.576656i	0.0400804	−	0.0231404i
$622$	−4.97248	−	8.61258i	−0.199378	−	0.345333i
$623$	−2.08709	−	2.08709i	−0.0836174	−	0.0836174i
$624$	1.59808	+	3.23205i	0.0639742	+	0.129386i
$625$	7.00000	+	24.0000i	0.280000	+	0.960000i
$626$	−5.26260	+	19.6403i	−0.210336	+	0.784984i
$627$	−7.10182	+	26.5043i	−0.283619	+	1.05848i
$628$	−8.66510	+	2.32181i	−0.345775	+	0.0926502i
$629$	11.2098	−	11.2098i	0.446963	−	0.446963i
$630$	7.68885	−	6.81809i	0.306331	−	0.271639i
$631$	−2.11445	−	7.89123i	−0.0841748	−	0.314145i	0.910982	−	0.412447i	$-0.135326\pi$
$631$	−2.11445	−	7.89123i	−0.0841748	−	0.314145i	−0.995157	+	0.0983017i	$0.968659\pi$
$632$	2.76393			0.109943
$633$	1.08738	+	4.05816i	0.0432195	+	0.161297i
$634$	0.600398	+	1.03992i	0.0238449	+	0.0413005i
$635$	−15.0599	−	9.94333i	−0.597632	−	0.394589i
$636$			12.6264i			0.500669i
$637$	33.6098	+	38.2439i	1.33167	+	1.51528i
$638$	14.6088	−	14.6088i	0.578369	−	0.578369i
$639$	−7.94182	−	2.12800i	−0.314174	−	0.0841825i
$640$	−2.19067	+	0.448288i	−0.0865939	+	0.0177201i
$641$	−19.4025	−	11.2020i	−0.766351	−	0.442453i	0.0652203	−	0.997871i	$-0.479225\pi$
$641$	−19.4025	−	11.2020i	−0.766351	−	0.442453i	−0.831571	+	0.555418i	$0.812558\pi$
$642$			2.03063i			0.0801427i
$643$	−18.7280	+	32.4379i	−0.738562	+	1.27923i	0.214581	+	0.976706i	$0.431161\pi$
$643$	−18.7280	+	32.4379i	−0.738562	+	1.27923i	−0.953143	+	0.302520i	$0.902172\pi$
$644$	−5.11974	+	1.37183i	−0.201746	+	0.0540576i
$645$	−3.03100	−	1.01033i	−0.119345	−	0.0397818i
$646$	5.91600	−	10.2468i	0.232762	−	0.403155i
$647$	−21.4617	−	5.75064i	−0.843745	−	0.226081i	−0.189044	−	0.981969i	$-0.560539\pi$
$647$	−21.4617	−	5.75064i	−0.843745	−	0.226081i	−0.654701	+	0.755888i	$0.727206\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	−32.5648			−1.27828
$650$	17.9737	−	1.39563i	0.704985	−	0.0547412i
$651$	−2.28397			−0.0895158
$652$	7.85217	−	4.53345i	0.307515	−	0.177544i
$653$	16.6871	+	4.47130i	0.653018	+	0.174976i	0.570093	−	0.821580i	$-0.306907\pi$
$653$	16.6871	+	4.47130i	0.653018	+	0.174976i	0.0829247	+	0.996556i	$0.473574\pi$
$654$	8.82308	−	15.2820i	0.345010	−	0.597574i
$655$	−40.4171	−	13.4724i	−1.57923	−	0.526409i
$656$	−7.22973	+	1.93720i	−0.282273	+	0.0756350i
$657$	1.89828	−	3.28791i	0.0740588	−	0.128274i
$658$			31.1010i			1.21244i
$659$	−2.04351	−	1.17982i	−0.0796040	−	0.0459594i	0.459670	−	0.888090i	$-0.347968\pi$
$659$	−2.04351	−	1.17982i	−0.0796040	−	0.0459594i	−0.539274	+	0.842131i	$0.681301\pi$
$660$	7.87711	−	1.61193i	0.306616	−	0.0627444i
$661$	−15.6842	−	4.20257i	−0.610045	−	0.163461i	−0.0594467	−	0.998231i	$-0.518934\pi$
$661$	−15.6842	−	4.20257i	−0.610045	−	0.163461i	−0.550598	+	0.834770i	$0.685600\pi$
$662$	−0.599918	+	0.599918i	−0.0233165	+	0.0233165i
$663$	1.09638	+	5.48188i	0.0425797	+	0.212899i
$664$		−	8.75611i		−	0.339803i
$665$	65.4421	+	43.2084i	2.53774	+	1.67555i
$666$	−5.11219	−	8.85457i	−0.198093	−	0.343108i
$667$	−1.71508	−	6.40076i	−0.0664081	−	0.247838i
$668$	−1.39960			−0.0541522
$669$	4.78799	+	17.8690i	0.185114	+	0.690856i
$670$	−0.405946	+	0.359973i	−0.0156831	+	0.0139070i
$671$	−3.67006	+	3.67006i	−0.141681	+	0.141681i
$672$	4.43916	−	1.18947i	0.171244	−	0.0458848i
$673$	−8.05524	+	30.0626i	−0.310507	+	1.15883i	0.617594	+	0.786497i	$0.288107\pi$
$673$	−8.05524	+	30.0626i	−0.310507	+	1.15883i	−0.928101	+	0.372329i	$0.878559\pi$
$674$	2.05934	−	7.68556i	0.0793228	−	0.296037i
$675$	0.707107	+	4.94975i	0.0272166	+	0.190516i
$676$	1.66987	−	12.8923i	0.0642259	−	0.495858i
$677$	12.3115	+	12.3115i	0.473170	+	0.473170i	0.902939	−	0.429769i	$-0.141405\pi$
$677$	12.3115	+	12.3115i	0.473170	+	0.473170i	−0.429769	+	0.902939i	$0.641405\pi$
$678$	−3.71624	−	6.43671i	−0.142721	−	0.247200i
$679$	22.4117	−	12.9394i	0.860083	−	0.496569i
$680$	−3.46082	−	0.207729i	−0.132716	−	0.00796604i
$681$	−3.66150	−	3.66150i	−0.140309	−	0.140309i
$682$	−1.54758	−	0.893498i	−0.0592600	−	0.0342138i
$683$	−25.4290	−	14.6814i	−0.973013	−	0.561769i	−0.0728597	−	0.997342i	$-0.523213\pi$
$683$	−25.4290	−	14.6814i	−0.973013	−	0.561769i	−0.900154	+	0.435573i	$0.856546\pi$
$684$	−5.39595	−	5.39595i	−0.206319	−	0.206319i
$685$	−28.9211	+	25.6458i	−1.10502	+	0.979877i
$686$	28.3417	−	16.3631i	1.08209	−	0.624745i
$687$	−6.04989	−	10.4787i	−0.230818	−	0.399788i
$688$	−1.01033	−	1.01033i	−0.0385186	−	0.0385186i
$689$	25.2528	−	37.8792i	0.962054	−	1.44308i
$690$	0.815515	−	2.44655i	0.0310461	−	0.0931384i
$691$	0.344305	−	1.28497i	0.0130980	−	0.0488824i	−0.959068	−	0.283177i	$-0.908611\pi$
$691$	0.344305	−	1.28497i	0.0130980	−	0.0488824i	0.972166	+	0.234295i	$0.0752782\pi$
$692$	5.98174	−	22.3242i	0.227392	−	0.848637i
$693$	−15.9621	+	4.27704i	−0.606351	+	0.162471i
$694$	−2.00516	+	2.00516i	−0.0761148	+	0.0761148i
$695$	−2.84976	−	3.21371i	−0.108098	−	0.121903i
$696$	1.48709	+	5.54989i	0.0563679	+	0.210368i
$697$	−11.6052			−0.439579
$698$	8.23873	+	30.7473i	0.311840	+	1.16380i
$699$	−11.6341	−	20.1509i	−0.440042	−	0.762176i
$700$	2.74861	−	22.8138i	0.103888	−	0.862280i
$701$		−	28.0942i		−	1.06110i	−0.847653	−	0.530551i	$-0.821985\pi$
$701$		−	28.0942i		−	1.06110i	0.847653	−	0.530551i	$-0.178015\pi$
$702$	3.59808	+	0.232051i	0.135801	+	0.00875819i
$703$	55.1703	−	55.1703i	2.08079	−	2.08079i
$704$	3.47323	+	0.930650i	0.130902	+	0.0350752i
$705$	−12.6280	−	8.33769i	−0.475598	−	0.314016i
$706$	−7.32316	−	4.22803i	−0.275611	−	0.159124i
$707$			22.9116i			0.861680i
$708$	4.52823	−	7.84312i	0.170181	−	0.294763i
$709$	−5.40393	+	1.44798i	−0.202949	+	0.0543800i	−0.358861	−	0.933391i	$-0.616835\pi$
$709$	−5.40393	+	1.44798i	−0.202949	+	0.0543800i	0.155912	+	0.987771i	$0.450168\pi$
$710$	−16.4440	+	8.22198i	−0.617131	+	0.308565i
$711$	1.38196	−	2.39363i	0.0518277	−	0.0897682i
$712$	0.620358	+	0.166225i	0.0232489	+	0.00622953i
$713$	−0.496376	+	0.286583i	−0.0185894	+	0.0107326i
$714$	7.12576			0.266675
$715$	−26.8552	−	10.9184i	−1.00433	−	0.408326i
$716$	−7.22386			−0.269969
$717$	8.94938	−	5.16693i	0.334221	−	0.192962i
$718$	−24.8590	−	6.66096i	−0.927731	−	0.248585i
$719$	−21.6317	+	37.4673i	−0.806728	+	1.39729i	0.108391	+	0.994108i	$0.465430\pi$
$719$	−21.6317	+	37.4673i	−0.806728	+	1.39729i	−0.915119	+	0.403185i	$0.867903\pi$
$720$	−0.707107	+	2.12132i	−0.0263523	+	0.0790569i
$721$	84.5891	−	22.6656i	3.15026	−	0.844110i
$722$	19.6163	−	33.9764i	0.730044	−	1.26447i
$723$			2.22438i			0.0827256i
$724$	−6.08052	−	3.51059i	−0.225981	−	0.130470i
$725$	28.5221	+	3.43635i	1.05928	+	0.127623i
$726$	−1.86370	−	0.499378i	−0.0691685	−	0.0185336i
$727$	6.37185	−	6.37185i	0.236319	−	0.236319i	−0.579005	−	0.815324i	$-0.696559\pi$
$727$	6.37185	−	6.37185i	0.236319	−	0.236319i	0.815324	+	0.579005i	$0.196559\pi$
$728$	−15.6964	−	5.30991i	−0.581748	−	0.196798i
$729$			1.00000i			0.0370370i
$730$	−1.70195	−	8.31699i	−0.0629919	−	0.307826i
$731$	−1.10770	−	1.91860i	−0.0409699	−	0.0709620i
$732$	−0.373589	−	1.39425i	−0.0138082	−	0.0515331i
$733$	33.1154			1.22315			0.611573	−	0.791188i	$-0.290537\pi$
$733$	33.1154			1.22315			0.611573	+	0.791188i	$0.290537\pi$
$734$	9.44193	+	35.2377i	0.348508	+	1.30065i
$735$	−1.89185	+	31.5187i	−0.0697819	+	1.16258i
$736$	0.815515	−	0.815515i	0.0300603	−	0.0300603i
$737$	0.842747	−	0.225813i	0.0310430	−	0.00831795i
$738$	−1.93720	+	7.22973i	−0.0713093	+	0.266130i
$739$	1.14653	−	4.27891i	0.0421758	−	0.157402i	−0.941626	−	0.336660i	$-0.890703\pi$
$739$	1.14653	−	4.27891i	0.0421758	−	0.157402i	0.983802	+	0.179257i	$0.0573695\pi$
$740$	−21.6892	−	7.22973i	−0.797310	−	0.265770i
$741$	5.39595	+	26.9798i	0.198225	+	0.991126i
$742$	−41.0318	−	41.0318i	−1.50633	−	1.50633i
$743$	19.8071	+	34.3069i	0.726653	+	1.25860i	0.958290	+	0.285797i	$0.0922583\pi$
$743$	19.8071	+	34.3069i	0.726653	+	1.25860i	−0.231638	+	0.972802i	$0.574408\pi$
$744$	0.430392	−	0.248487i	0.0157789	−	0.00910997i
$745$	0.601991	−	10.0293i	0.0220553	−	0.367446i
$746$	21.2898	+	21.2898i	0.779474	+	0.779474i
$747$	−7.58302	−	4.37806i	−0.277448	−	0.160185i
$748$	4.82831	+	2.78763i	0.176541	+	0.101926i
$749$	−6.59892	−	6.59892i	−0.241119	−	0.241119i
$750$	8.52628	+	7.23205i	0.311336	+	0.264077i
$751$	39.5124	−	22.8125i	1.44183	−	0.832440i	0.443856	−	0.896098i	$-0.353610\pi$
$751$	39.5124	−	22.8125i	1.44183	−	0.832440i	0.997972	+	0.0636587i	$0.0202769\pi$
$752$	−3.38366	−	5.86068i	−0.123390	−	0.213717i
$753$	6.93772	+	6.93772i	0.252824	+	0.252824i
$754$	6.63851	−	19.6238i	0.241760	−	0.714658i
$755$	−22.8099	+	11.4049i	−0.830135	+	0.415068i
$756$	1.18947	−	4.43916i	0.0432606	−	0.161451i
$757$	−10.3317	+	38.5585i	−0.375513	+	1.40143i	0.477081	+	0.878859i	$0.341695\pi$
$757$	−10.3317	+	38.5585i	−0.375513	+	1.40143i	−0.852594	+	0.522574i	$0.824972\pi$
$758$	23.1719	−	6.20889i	0.841641	−	0.225517i
$759$	−2.93239	+	2.93239i	−0.106439	+	0.106439i
$760$	−17.0328	−	1.02236i	−0.617846	−	0.0370850i
$761$	2.17385	+	8.11291i	0.0788019	+	0.294093i	0.994068	−	0.108756i	$-0.0346867\pi$
$761$	2.17385	+	8.11291i	0.0788019	+	0.294093i	−0.915267	+	0.402849i	$0.868020\pi$
$762$	−8.07055			−0.292365
$763$	20.9896	+	78.3341i	0.759873	+	2.83588i
$764$	−10.3967	−	18.0075i	−0.376138	−	0.651490i
$765$	−1.91031	+	2.89329i	−0.0690673	+	0.104607i
$766$		−	0.721568i		−	0.0260713i
$767$	−29.2709	+	14.4729i	−1.05691	+	0.522586i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	−33.6872	−	9.02645i	−1.21479	−	0.325502i	−0.406150	−	0.913806i	$-0.633129\pi$
$769$	−33.6872	−	9.02645i	−1.21479	−	0.325502i	−0.808640	+	0.588304i	$0.799796\pi$
$770$	−20.3599	+	30.8364i	−0.733719	+	1.11127i
$771$	−7.87900	−	4.54894i	−0.283755	−	0.163826i
$772$			25.4792i			0.917018i
$773$	17.1633	−	29.7277i	0.617320	−	1.06923i	−0.372652	−	0.927971i	$-0.621552\pi$
$773$	17.1633	−	29.7277i	0.617320	−	1.06923i	0.989973	−	0.141259i	$-0.0451151\pi$
$774$	−1.38014	+	0.369807i	−0.0496081	+	0.0132924i
$775$	−0.351414	−	2.45989i	−0.0126231	−	0.0883620i
$776$	−2.81552	+	4.87662i	−0.101071	+	0.175060i
$777$	45.3876	+	12.1616i	1.62827	+	0.436294i
$778$	29.9139	−	17.2708i	1.07247	−	0.619189i
$779$	−57.1165			−2.04641
$780$	6.36396	−	4.94975i	0.227866	−	0.177229i
$781$	29.5642			1.05789
$782$	1.54865	−	0.894111i	0.0553795	−	0.0319734i
$783$	5.54989	+	1.48709i	0.198337	+	0.0531442i
$784$	−7.06048	+	12.2291i	−0.252160	+	0.436754i
$785$	8.97078	+	17.9416i	0.320181	+	0.640361i
$786$	−18.4036	+	4.93123i	−0.656435	+	0.175891i
$787$	26.0748	−	45.1629i	0.929467	−	1.60988i	0.145252	−	0.989395i	$-0.453601\pi$
$787$	26.0748	−	45.1629i	0.929467	−	1.60988i	0.784215	−	0.620490i	$-0.213066\pi$
$788$		−	3.91359i		−	0.139416i
$789$	−7.04921	−	4.06987i	−0.250959	−	0.144891i
$790$	−1.23903	−	6.05485i	−0.0440829	−	0.215422i
$791$	32.9939	+	8.84069i	1.17313	+	0.314339i
$792$	2.54258	−	2.54258i	0.0903467	−	0.0903467i
$793$	−1.66774	+	4.92994i	−0.0592232	+	0.175067i
$794$		−	29.9238i		−	1.06196i
$795$	27.6603	−	5.66025i	0.981008	−	0.200749i
$796$	5.06110	+	8.76608i	0.179386	+	0.310706i
$797$	8.61098	+	32.1366i	0.305017	+	1.13834i	0.932931	+	0.360055i	$0.117242\pi$
$797$	8.61098	+	32.1366i	0.305017	+	1.13834i	−0.627915	+	0.778282i	$0.716091\pi$
$798$	35.0703			1.24148
$799$	−2.71574	−	10.1353i	−0.0960759	−	0.358560i
$800$	1.96410	+	4.59808i	0.0694415	+	0.162567i
$801$	0.454134	−	0.454134i	0.0160460	−	0.0160460i
$802$	−6.61965	+	1.77373i	−0.233748	+	0.0626326i
$803$	−3.53326	+	13.1863i	−0.124686	+	0.465334i
$804$	−0.0628000	+	0.234373i	−0.00221479	+	0.00826570i
$805$	5.30034	+	10.6007i	0.186812	+	0.373625i
$806$	−1.78815	−	0.115323i	−0.0629849	−	0.00406209i
$807$	6.43488	+	6.43488i	0.226518	+	0.226518i
$808$	−2.49269	−	4.31747i	−0.0876927	−	0.151888i
$809$	−2.57136	+	1.48458i	−0.0904043	+	0.0521950i	−0.544521	−	0.838747i	$-0.683288\pi$
$809$	−2.57136	+	1.48458i	−0.0904043	+	0.0521950i	0.454116	+	0.890942i	$0.349955\pi$
$810$	1.48356	+	1.67303i	0.0521271	+	0.0587844i
$811$	22.2623	+	22.2623i	0.781735	+	0.781735i	0.980124	−	0.198388i	$-0.0635707\pi$
$811$	22.2623	+	22.2623i	0.781735	+	0.781735i	−0.198388	+	0.980124i	$0.563571\pi$
$812$	−22.8680	−	13.2028i	−0.802509	−	0.463329i
$813$	−16.3217	−	9.42334i	−0.572427	−	0.330491i
$814$	25.9963	+	25.9963i	0.911171	+	0.911171i
$815$	−13.4513	−	15.1692i	−0.471180	−	0.531355i
$816$	−1.34278	+	0.775255i	−0.0470067	+	0.0271394i
$817$	−5.45171	−	9.44263i	−0.190731	−	0.330356i
$818$	−9.93993	−	9.93993i	−0.347542	−	0.347542i
$819$	−12.4467	+	10.9385i	−0.434924	+	0.382223i
$820$	7.48477	+	14.9695i	0.261379	+	0.522759i
$821$	−14.2761	+	53.2791i	−0.498239	+	1.85945i	0.0128385	+	0.999918i	$0.495913\pi$
$821$	−14.2761	+	53.2791i	−0.498239	+	1.85945i	−0.511077	+	0.859535i	$0.670753\pi$
$822$	−4.47411	+	16.6976i	−0.156053	+	0.582396i
$823$	−3.11563	+	0.834831i	−0.108604	+	0.0291004i	−0.312712	−	0.949848i	$-0.601237\pi$
$823$	−3.11563	+	0.834831i	−0.108604	+	0.0291004i	0.204108	+	0.978948i	$0.434571\pi$
$824$	−13.4741	+	13.4741i	−0.469391	+	0.469391i
$825$	−7.06243	−	16.5336i	−0.245882	−	0.575624i
$826$	10.7724	+	40.2030i	0.374819	+	1.39884i
$827$	36.5493			1.27094			0.635471	−	0.772125i	$-0.280806\pi$
$827$	36.5493			1.27094			0.635471	+	0.772125i	$0.280806\pi$
$828$	−0.298499	−	1.11401i	−0.0103736	−	0.0387147i
$829$	19.3877	+	33.5804i	0.673361	+	1.16630i	0.976945	+	0.213491i	$0.0684835\pi$
$829$	19.3877	+	33.5804i	0.673361	+	1.16630i	−0.303584	+	0.952805i	$0.598183\pi$
$830$	−19.1818	+	3.92526i	−0.665809	+	0.136248i
$831$			4.56977i			0.158523i
$832$	3.53553	−	0.707107i	0.122573	−	0.0245145i
$833$	−15.4819	+	15.4819i	−0.536415	+	0.536415i
$834$	−1.85544	−	0.497162i	−0.0642485	−	0.0172153i
$835$	0.627424	+	3.06607i	0.0217129	+	0.106106i
$836$	23.7631	+	13.7197i	0.821865	+	0.474504i
$837$		−	0.496974i		−	0.0171779i
$838$	−12.6100	+	21.8412i	−0.435605	+	0.754490i
$839$	−31.0861	+	8.32950i	−1.07321	+	0.287566i	−0.751812	−	0.659377i	$-0.770820\pi$
$839$	−31.0861	+	8.32950i	−1.07321	+	0.287566i	−0.321400	+	0.946943i	$0.604153\pi$
$840$	−4.59575	−	9.19151i	−0.158569	−	0.317137i
$841$	2.00634	−	3.47509i	0.0691843	−	0.119831i
$842$	−0.727771	−	0.195006i	−0.0250806	−	0.00672034i
$843$	10.4159	−	6.01362i	0.358742	−	0.207120i
$844$	4.20131			0.144615
$845$	−28.9914	+	2.12132i	−0.997334	+	0.0729756i
$846$	−6.76733			−0.232665
$847$	7.67928	−	4.43363i	0.263863	−	0.152341i
$848$	12.1962	+	3.26795i	0.418818	+	0.112222i
$849$	0.625789	−	1.08390i	0.0214770	−	0.0371993i
$850$	1.09638	+	7.67463i	0.0376054	+	0.263238i
$851$	11.3901	−	3.05197i	0.390448	−	0.104620i
$852$	−4.11099	+	7.12044i	−0.140840	+	0.243942i
$853$			22.7906i			0.780334i	0.920744	+	0.390167i	$0.127583\pi$
$853$			22.7906i			0.780334i	−0.920744	+	0.390167i	$0.872417\pi$
$854$	5.74494	+	3.31684i	0.196588	+	0.113500i
$855$	−9.40182	+	14.2397i	−0.321535	+	0.486987i
$856$	1.96144	+	0.525566i	0.0670406	+	0.0179635i
$857$	−23.9484	+	23.9484i	−0.818063	+	0.818063i	−0.985827	−	0.167764i	$-0.946345\pi$
$857$	−23.9484	+	23.9484i	−0.818063	+	0.818063i	0.167764	+	0.985827i	$0.446345\pi$
$858$	−12.7129	+	2.54258i	−0.434012	+	0.0868023i
$859$			6.91162i			0.235821i	0.993024	+	0.117911i	$0.0376197\pi$
$859$			6.91162i			0.235821i	−0.993024	+	0.117911i	$0.962380\pi$
$860$	−1.76039	+	2.66622i	−0.0600286	+	0.0909175i
$861$	−17.1991	−	29.7897i	−0.586143	−	1.01523i
$862$	−6.29012	−	23.4751i	−0.214242	−	0.799564i
$863$	−24.3385			−0.828491			−0.414245	−	0.910165i	$-0.635954\pi$
$863$	−24.3385			−0.828491			−0.414245	+	0.910165i	$0.635954\pi$
$864$	0.258819	+	0.965926i	0.00880520	+	0.0328615i
$865$	−51.5864	−	3.09638i	−1.75399	−	0.105280i
$866$	−16.1735	+	16.1735i	−0.549598	+	0.549598i
$867$	14.0986	−	3.77770i	0.478813	−	0.128297i
$868$	−0.591135	+	2.20614i	−0.0200644	+	0.0748814i
$869$	−2.57225	+	9.59976i	−0.0872575	+	0.325650i
$870$	11.4913	−	5.74567i	0.389593	−	0.194796i
$871$	0.657146	−	0.577519i	0.0222665	−	0.0195685i
$872$	−12.4777	−	12.4777i	−0.422549	−	0.422549i
$873$	2.81552	+	4.87662i	0.0952908	+	0.165048i
$874$	7.62186	−	4.40048i	0.257813	−	0.148849i
$875$	−51.2097	+	4.20584i	−1.73120	+	0.142183i
$876$	−2.68457	−	2.68457i	−0.0907031	−	0.0907031i
$877$	−39.6098	−	22.8687i	−1.33753	−	0.772221i	−0.351086	−	0.936343i	$-0.614188\pi$
$877$	−39.6098	−	22.8687i	−1.33753	−	0.772221i	−0.986440	+	0.164122i	$0.947521\pi$
$878$	−16.2612	−	9.38839i	−0.548788	−	0.316843i
$879$	6.91875	+	6.91875i	0.233364	+	0.233364i
$880$	0.481740	−	8.02591i	0.0162394	−	0.270553i
$881$	−10.7076	+	6.18206i	−0.360749	+	0.208279i	−0.669409	−	0.742894i	$-0.733453\pi$
$881$	−10.7076	+	6.18206i	−0.360749	+	0.208279i	0.308660	+	0.951172i	$0.400119\pi$
$882$	7.06048	+	12.2291i	0.237739	+	0.411775i
$883$	9.47873	+	9.47873i	0.318985	+	0.318985i	0.848377	−	0.529392i	$-0.177580\pi$
$883$	9.47873	+	9.47873i	0.318985	+	0.318985i	−0.529392	+	0.848377i	$0.677580\pi$
$884$	5.57885	+	0.359797i	0.187637	+	0.0121013i
$885$	−19.2116	−	6.40388i	−0.645792	−	0.215264i
$886$	1.68493	−	6.28825i	0.0566064	−	0.211258i
$887$	5.60688	−	20.9252i	0.188261	−	0.702599i	−0.805648	−	0.592394i	$-0.798183\pi$
$887$	5.60688	−	20.9252i	0.188261	−	0.702599i	0.993909	−	0.110204i	$-0.0351505\pi$
$888$	−9.87599	+	2.64626i	−0.331417	+	0.0888028i
$889$	26.2268	−	26.2268i	0.879618	−	0.879618i
$890$	0.0860442	−	1.43352i	0.00288421	−	0.0480516i
$891$	−0.930650	−	3.47323i	−0.0311779	−	0.116358i
$892$	18.4994			0.619405
$893$	−13.3658	−	49.8820i	−0.447271	−	1.66924i
$894$	−2.24666	−	3.89133i	−0.0751396	−	0.130146i
$895$	3.23837	+	15.8251i	0.108247	+	0.528975i
$896$		−	4.59575i		−	0.153533i
$897$	−1.33253	+	3.93904i	−0.0444919	+	0.131521i
$898$	−4.37821	+	4.37821i	−0.146103	+	0.146103i
$899$	−2.75815	−	0.739044i	−0.0919894	−	0.0246485i
$900$	4.96410	+	0.598076i	0.165470	+	0.0199359i
$901$	16.9545	+	9.78867i	0.564835	+	0.326108i
$902$		−	26.9134i		−	0.896117i
$903$	3.28327	−	5.68678i	0.109260	−	0.189244i
$904$	−7.17922	+	1.92367i	−0.238777	+	0.0639802i
$905$	−4.96472	+	14.8942i	−0.165033	+	0.495099i
$906$	−5.70246	+	9.87695i	−0.189452	+	0.328140i
$907$	−41.2099	−	11.0422i	−1.36835	−	0.366649i	−0.501475	−	0.865172i	$-0.667209\pi$
$907$	−41.2099	−	11.0422i	−1.36835	−	0.366649i	−0.866876	+	0.498523i	$0.833876\pi$
$908$	−4.48440	+	2.58907i	−0.148820	+	0.0859213i
$909$	−4.98539			−0.165355
$910$	−4.59575	+	36.7660i	−0.152348	+	1.21878i
$911$	36.6088			1.21290			0.606451	−	0.795121i	$-0.292592\pi$
$911$	36.6088			1.21290			0.606451	+	0.795121i	$0.292592\pi$
$912$	−6.60867	+	3.81552i	−0.218835	+	0.126344i
$913$	30.4120	+	8.14888i	1.00649	+	0.269688i
$914$	−8.39079	+	14.5333i	−0.277543	+	0.480718i
$915$	−2.88687	+	1.44344i	−0.0954371	+	0.0477186i
$916$	−11.6875	+	3.13165i	−0.386165	+	0.103473i
$917$	43.7810	−	75.8309i	1.44578	−	2.50416i
$918$			1.55051i			0.0511745i
$919$	14.6408	+	8.45289i	0.482957	+	0.278835i	0.721648	−	0.692260i	$-0.243385\pi$
$919$	14.6408	+	8.45289i	0.482957	+	0.278835i	−0.238691	+	0.971096i	$0.576718\pi$
$920$	−2.15211	−	1.42094i	−0.0709530	−	0.0468470i
$921$	16.6732	+	4.46756i	0.549399	+	0.147211i
$922$	26.0373	−	26.0373i	0.857493	−	0.857493i
$923$	26.5738	−	13.1393i	0.874689	−	0.432487i
$924$			16.5252i			0.543639i
$925$	−6.11496	+	50.7549i	−0.201059	+	1.66881i
$926$	−13.4341	−	23.2686i	−0.441474	−	0.764655i
$927$	4.93185	+	18.4059i	0.161983	+	0.604530i
$928$	5.74567			0.188611
$929$	−0.593290	−	2.21419i	−0.0194652	−	0.0726452i	0.955510	−	0.294959i	$-0.0953059\pi$
$929$	−0.593290	−	2.21419i	−0.0194652	−	0.0726452i	−0.974975	+	0.222313i	$0.928639\pi$
$930$	−0.737292	−	0.831453i	−0.0241768	−	0.0272644i
$931$	−76.1960	+	76.1960i	−2.49722	+	2.49722i
$932$	−22.4754	+	6.02226i	−0.736205	+	0.197266i
$933$	−2.57394	+	9.60609i	−0.0842671	+	0.314489i
$934$	2.56413	−	9.56945i	0.0839008	−	0.313122i
$935$	3.94230	−	11.8269i	0.128927	−	0.386781i
$936$	1.15539	−	3.41542i	0.0377653	−	0.111636i
$937$	−27.0807	−	27.0807i	−0.884687	−	0.884687i	0.109319	−	0.994007i	$-0.465133\pi$
$937$	−27.0807	−	27.0807i	−0.884687	−	0.884687i	−0.994007	+	0.109319i	$0.965133\pi$
$938$	−0.557558	−	0.965720i	−0.0182049	−	0.0315319i
$939$	17.6090	−	10.1666i	0.574648	−	0.331773i
$940$	−11.3220	+	10.0398i	−0.369282	+	0.327461i
$941$	11.6289	+	11.6289i	0.379091	+	0.379091i	0.870774	−	0.491683i	$-0.163618\pi$
$941$	11.6289	+	11.6289i	0.379091	+	0.379091i	−0.491683	+	0.870774i	$0.663618\pi$
$942$	7.76892	+	4.48539i	0.253125	+	0.146142i
$943$	−7.47577	−	4.31614i	−0.243445	−	0.140553i
$944$	−6.40388	−	6.40388i	−0.208429	−	0.208429i
$945$	−10.2580	−	0.615714i	−0.333691	−	0.0200292i
$946$	4.44938	−	2.56885i	0.144662	−	0.0835206i
$947$	12.6948	+	21.9880i	0.412525	+	0.714514i	0.995165	−	0.0982160i	$-0.0313136\pi$
$947$	12.6948	+	21.9880i	0.412525	+	0.714514i	−0.582640	+	0.812730i	$0.697980\pi$
$948$	−1.95439	−	1.95439i	−0.0634757	−	0.0634757i
$949$	2.68457	+	13.4228i	0.0871447	+	0.435724i
$950$	5.39595	+	37.7717i	0.175068	+	1.22547i
$951$	0.310789	−	1.15988i	0.0100780	−	0.0376117i
$952$	1.84428	−	6.88296i	0.0597736	−	0.223078i
$953$	8.09473	−	2.16898i	0.262214	−	0.0702601i	−0.125317	−	0.992117i	$-0.539995\pi$
$953$	8.09473	−	2.16898i	0.262214	−	0.0702601i	0.387531	+	0.921857i	$0.373328\pi$
$954$	8.92820	−	8.92820i	0.289061	−	0.289061i
$955$	−34.7879	+	30.8482i	−1.12571	+	0.998225i
$956$	−2.67460	−	9.98174i	−0.0865027	−	0.322833i
$957$	−20.6600			−0.667843
$958$	−9.29474	−	34.6885i	−0.300300	−	1.12073i
$959$	−39.7226	−	68.8015i	−1.28271	−	2.22172i
$960$	1.86603	+	1.23205i	0.0602257	+	0.0397643i
$961$		−	30.7530i		−	0.992033i
$962$	34.9205	+	11.8132i	1.12588	+	0.380873i
$963$	1.43587	−	1.43587i	0.0462704	−	0.0462704i
$964$	2.14859	+	0.575712i	0.0692013	+	0.0185424i
$965$	55.8166	−	11.4220i	1.79680	−	0.367688i
$966$	4.59023	+	2.65017i	0.147688	+	0.0852678i
$967$			17.2490i			0.554690i	0.960770	+	0.277345i	$0.0894545\pi$
$967$			17.2490i			0.554690i	−0.960770	+	0.277345i	$0.910545\pi$
$968$	−0.964724	+	1.67095i	−0.0310074	+	0.0537064i
$969$	−11.4288	+	3.06234i	−0.367147	+	0.0983767i
$970$	11.9452	+	3.98174i	0.383538	+	0.127846i
$971$	−2.05077	+	3.55203i	−0.0658123	+	0.113990i	−0.897054	−	0.441921i	$-0.854297\pi$
$971$	−2.05077	+	3.55203i	−0.0658123	+	0.113990i	0.831242	+	0.555911i	$0.187631\pi$
$972$	0.965926	+	0.258819i	0.0309821	+	0.00830162i
$973$	7.64521	−	4.41396i	0.245094	−	0.141505i
$974$	9.98731			0.320014
$975$	−13.6962	−	11.7224i	−0.438628	−	0.375418i
$976$	−1.44344			−0.0462033
$977$	−28.2766	+	16.3255i	−0.904647	+	0.522298i	−0.878705	−	0.477365i	$-0.841592\pi$
$977$	−28.2766	+	16.3255i	−0.904647	+	0.522298i	−0.0259424	+	0.999663i	$0.508259\pi$
$978$	−8.75796	−	2.34669i	−0.280049	−	0.0750388i
$979$	−1.15467	+	1.99995i	−0.0369035	+	0.0639187i
$980$	29.9551	+	9.98502i	0.956880	+	0.318960i
$981$	−17.0449	+	4.56716i	−0.544201	+	0.145818i
$982$	−2.13129	+	3.69150i	−0.0680121	+	0.117800i
$983$			43.4739i			1.38660i	0.720648	+	0.693301i	$0.243844\pi$
$983$			43.4739i			1.38660i	−0.720648	+	0.693301i	$0.756156\pi$
$984$	6.48200	+	3.74238i	0.206639	+	0.119303i
$985$	−8.57339	+	1.75442i	−0.273171	+	0.0559003i
$986$	8.60516	+	2.30575i	0.274044	+	0.0734299i
$987$	21.9917	−	21.9917i	0.700004	−	0.700004i
$988$	27.4570	+	1.77079i	0.873524	+	0.0563362i
$989$		−	1.64788i		−	0.0523996i
$990$	−6.70977	−	4.43015i	−0.213250	−	0.140799i
$991$	2.24028	+	3.88028i	0.0711649	+	0.123261i	0.899412	−	0.437102i	$-0.143995\pi$
$991$	2.24028	+	3.88028i	0.0711649	+	0.123261i	−0.828247	+	0.560363i	$0.810662\pi$
$992$	−0.128626	−	0.480040i	−0.00408389	−	0.0152413i
$993$	0.848412			0.0269235
$994$	−9.77978	−	36.4986i	−0.310196	−	1.15767i
$995$	16.9348	−	15.0169i	0.536868	−	0.476069i
$996$	−6.19151	+	6.19151i	−0.196185	+	0.196185i
$997$	4.81529	−	1.29025i	0.152502	−	0.0408627i	−0.181760	−	0.983343i	$-0.558180\pi$
$997$	4.81529	−	1.29025i	0.152502	−	0.0408627i	0.334262	+	0.942480i	$0.391513\pi$
$998$	2.70434	−	10.0927i	0.0856043	−	0.319480i
$999$	−2.64626	+	9.87599i	−0.0837241	+	0.312463i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bd.a.37.2	✓	8
5.3	odd	4		390.2.bn.a.193.1	yes	8
13.6	odd	12		390.2.bn.a.97.1	yes	8
65.58	even	12	inner	390.2.bd.a.253.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bd.a.37.2	✓	8	1.1	even	1	trivial
390.2.bd.a.253.2	yes	8	65.58	even	12	inner
390.2.bn.a.97.1	yes	8	13.6	odd	12
390.2.bn.a.193.1	yes	8	5.3	odd	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.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.965926 + 0.258819i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.12132 - 0.707107i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(2.29788 - 3.98004i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.965926 + 0.258819i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.12132 - 0.707107i) q^{5} +(-0.965926 + 0.258819i) q^{6} +(2.29788 - 3.98004i) q^{7} +1.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +(2.19067 - 0.448288i) q^{10} +(-3.47323 - 0.930650i) q^{11} +(0.707107 - 0.707107i) q^{12} +(-3.53553 + 0.707107i) q^{13} +4.59575i q^{14} +(-1.86603 - 1.23205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.401302 - 1.49768i) q^{17} -1.00000 q^{18} +(-1.97506 - 7.37101i) q^{19} +(-1.67303 + 1.48356i) q^{20} +(3.24969 - 3.24969i) q^{21} +(3.47323 - 0.930650i) q^{22} +(0.298499 - 1.11401i) q^{23} +(-0.258819 + 0.965926i) q^{24} +(4.00000 + 3.00000i) q^{25} +(2.70831 - 2.38014i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-2.29788 - 3.98004i) q^{28} +(4.97589 - 2.87283i) q^{29} +(2.23205 + 0.133975i) q^{30} +(-0.351414 - 0.351414i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-3.11401 - 1.79788i) q^{33} +(1.09638 + 1.09638i) q^{34} +(-7.68885 + 6.81809i) q^{35} +(0.866025 - 0.500000i) q^{36} +(5.11219 + 8.85457i) q^{37} +(5.39595 + 5.39595i) q^{38} +(-3.59808 - 0.232051i) q^{39} +(0.707107 - 2.12132i) q^{40} +(1.93720 - 7.22973i) q^{41} +(-1.18947 + 4.43916i) q^{42} +(1.38014 - 0.369807i) q^{43} +(-2.54258 + 2.54258i) q^{44} +(-1.48356 - 1.67303i) q^{45} +(0.298499 + 1.11401i) q^{46} +6.76733 q^{47} +(-0.258819 - 0.965926i) q^{48} +(-7.06048 - 12.2291i) q^{49} +(-4.96410 - 0.598076i) q^{50} -1.55051i q^{51} +(-1.15539 + 3.41542i) q^{52} +(-8.92820 + 8.92820i) q^{53} +(-0.965926 - 0.258819i) q^{54} +(6.70977 + 4.43015i) q^{55} +(3.98004 + 2.29788i) q^{56} -7.63103i q^{57} +(-2.87283 + 4.97589i) q^{58} +(8.74786 - 2.34398i) q^{59} +(-2.00000 + 1.00000i) q^{60} +(0.721719 - 1.25005i) q^{61} +(0.480040 + 0.128626i) q^{62} +(3.98004 - 2.29788i) q^{63} -1.00000 q^{64} +(8.00000 + 1.00000i) q^{65} +3.59575 q^{66} +(-0.210133 + 0.121320i) q^{67} +(-1.49768 - 0.401302i) q^{68} +(0.576656 - 0.998798i) q^{69} +(3.24969 - 9.74907i) q^{70} +(-7.94182 + 2.12800i) q^{71} +(-0.500000 + 0.866025i) q^{72} -3.79655i q^{73} +(-8.85457 - 5.11219i) q^{74} +(3.08725 + 3.93305i) q^{75} +(-7.37101 - 1.97506i) q^{76} +(-11.6851 + 11.6851i) q^{77} +(3.23205 - 1.59808i) q^{78} -2.76393i q^{79} +(0.448288 + 2.19067i) q^{80} +(0.500000 + 0.866025i) q^{81} +(1.93720 + 7.22973i) q^{82} -8.75611 q^{83} +(-1.18947 - 4.43916i) q^{84} +(-0.207729 + 3.46082i) q^{85} +(-1.01033 + 1.01033i) q^{86} +(5.54989 - 1.48709i) q^{87} +(0.930650 - 3.47323i) q^{88} +(0.166225 - 0.620358i) q^{89} +(2.12132 + 0.707107i) q^{90} +(-5.30991 + 15.6964i) q^{91} +(-0.815515 - 0.815515i) q^{92} +(-0.248487 - 0.430392i) q^{93} +(-5.86068 + 3.38366i) q^{94} +(-1.02236 + 17.0328i) q^{95} +(0.707107 + 0.707107i) q^{96} +(4.87662 + 2.81552i) q^{97} +(12.2291 + 7.06048i) q^{98} +(-2.54258 - 2.54258i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 4 q^{7}+O(q^{10}) \) 8 * q + 4 * q^4 - 4 * q^7	\( 8 q + 4 q^{4} - 4 q^{7} - 16 q^{11} - 8 q^{15} - 4 q^{16} + 12 q^{17} - 8 q^{18} - 24 q^{19} + 8 q^{21} + 16 q^{22} + 16 q^{23} + 32 q^{25} + 4 q^{28} - 24 q^{29} + 4 q^{30} - 4 q^{31} - 12 q^{33} - 24 q^{35} + 8 q^{37} - 8 q^{39} + 28 q^{41} - 8 q^{42} - 8 q^{43} - 8 q^{44} + 16 q^{46} + 32 q^{47} - 20 q^{49} - 12 q^{50} - 16 q^{53} - 4 q^{55} + 12 q^{56} - 8 q^{58} + 32 q^{59} - 16 q^{60} - 8 q^{61} - 16 q^{62} + 12 q^{63} - 8 q^{64} + 64 q^{65} - 16 q^{66} + 12 q^{68} + 8 q^{70} + 8 q^{71} - 4 q^{72} - 24 q^{74} - 24 q^{76} - 24 q^{77} + 12 q^{78} + 4 q^{81} + 28 q^{82} - 32 q^{83} - 8 q^{84} - 32 q^{85} - 8 q^{86} + 28 q^{87} + 8 q^{88} - 4 q^{89} - 8 q^{91} + 20 q^{92} - 12 q^{94} + 4 q^{95} + 12 q^{97} + 24 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q + 4 * q^4 - 4 * q^7 - 16 * q^11 - 8 * q^15 - 4 * q^16 + 12 * q^17 - 8 * q^18 - 24 * q^19 + 8 * q^21 + 16 * q^22 + 16 * q^23 + 32 * q^25 + 4 * q^28 - 24 * q^29 + 4 * q^30 - 4 * q^31 - 12 * q^33 - 24 * q^35 + 8 * q^37 - 8 * q^39 + 28 * q^41 - 8 * q^42 - 8 * q^43 - 8 * q^44 + 16 * q^46 + 32 * q^47 - 20 * q^49 - 12 * q^50 - 16 * q^53 - 4 * q^55 + 12 * q^56 - 8 * q^58 + 32 * q^59 - 16 * q^60 - 8 * q^61 - 16 * q^62 + 12 * q^63 - 8 * q^64 + 64 * q^65 - 16 * q^66 + 12 * q^68 + 8 * q^70 + 8 * q^71 - 4 * q^72 - 24 * q^74 - 24 * q^76 - 24 * q^77 + 12 * q^78 + 4 * q^81 + 28 * q^82 - 32 * q^83 - 8 * q^84 - 32 * q^85 - 8 * q^86 + 28 * q^87 + 8 * q^88 - 4 * q^89 - 8 * q^91 + 20 * q^92 - 12 * q^94 + 4 * q^95 + 12 * q^97 + 24 * q^98 - 8 * q^99

Introduction

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