LMFDB - Embedded newform 833.2.v.b.814.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [833,2,Mod(128,833)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(833, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([8, 3]))

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

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

chi := DirichletCharacter("833.128");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.v (of order $24$, degree $8$, not 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:	$6.65153848837$
Analytic rank:	$0$
Dimension:	$8$
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:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			814.1
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	833.814
Dual form			833.2.v.b.263.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.33195 - 0.624844i) q^{2} +(0.658919 - 0.858719i) q^{3} +(3.31552 - 1.91421i) q^{4} +(0.0999004 - 0.758819i) q^{5} +(1.00000 - 2.41421i) q^{6} +(3.12132 - 3.12132i) q^{8} +(0.473232 + 1.76612i) q^{9} +O(q^{10})$	\(q+(2.33195 - 0.624844i) q^{2} +(0.658919 - 0.858719i) q^{3} +(3.31552 - 1.91421i) q^{4} +(0.0999004 - 0.758819i) q^{5} +(1.00000 - 2.41421i) q^{6} +(3.12132 - 3.12132i) q^{8} +(0.473232 + 1.76612i) q^{9} +(-0.241181 - 1.83195i) q^{10} +(2.59077 - 0.341081i) q^{11} +(0.540882 - 4.10841i) q^{12} -1.41421i q^{13} +(-0.585786 - 0.585786i) q^{15} +(1.50000 - 2.59808i) q^{16} +(-4.01229 - 0.949490i) q^{17} +(2.20711 + 3.82282i) q^{18} +(-0.800199 + 0.214413i) q^{19} +(-1.12132 - 2.70711i) q^{20} +(5.82843 - 2.41421i) q^{22} +(-2.90861 - 3.79057i) q^{23} +(-0.623642 - 4.73703i) q^{24} +(4.26380 + 1.14248i) q^{25} +(-0.883663 - 3.29788i) q^{26} +(4.82843 + 2.00000i) q^{27} +(-0.292893 + 0.121320i) q^{29} +(-1.73205 - 1.00000i) q^{30} +(-4.77231 + 6.21940i) q^{31} +(-0.410432 + 1.53175i) q^{32} +(1.41421 - 2.44949i) q^{33} +(-9.94975 + 0.292893i) q^{34} +(4.94975 + 4.94975i) q^{36} +(-9.15976 - 1.20590i) q^{37} +(-1.73205 + 1.00000i) q^{38} +(-1.21441 - 0.931852i) q^{39} +(-2.05670 - 2.68034i) q^{40} +(1.12132 + 0.464466i) q^{41} +(-0.585786 + 0.585786i) q^{43} +(7.93684 - 6.09015i) q^{44} +(1.38745 - 0.182661i) q^{45} +(-9.15125 - 7.02200i) q^{46} +(4.47871 + 2.58579i) q^{47} +(-1.24264 - 3.00000i) q^{48} +10.6569 q^{50} +(-3.45912 + 2.81979i) q^{51} +(-2.70711 - 4.68885i) q^{52} +(-0.366025 + 1.36603i) q^{53} +(12.5093 + 1.64689i) q^{54} -2.00000i q^{55} +(-0.343146 + 0.828427i) q^{57} +(-0.607206 + 0.465926i) q^{58} +(-5.79555 - 1.55291i) q^{59} +(-3.06350 - 0.820863i) q^{60} +(3.03603 - 2.32963i) q^{61} +(-7.24264 + 17.4853i) q^{62} +9.82843i q^{64} +(-1.07313 - 0.141281i) q^{65} +(1.76733 - 6.59575i) q^{66} +(-0.585786 - 1.01461i) q^{67} +(-15.1203 + 4.53233i) q^{68} -5.17157 q^{69} +(-2.07107 - 5.00000i) q^{71} +(6.98975 + 4.03553i) q^{72} +(10.2615 + 7.87391i) q^{73} +(-22.1136 + 2.91131i) q^{74} +(3.79057 - 2.90861i) q^{75} +(-2.24264 + 2.24264i) q^{76} +(-3.41421 - 1.41421i) q^{78} +(2.90861 + 3.79057i) q^{79} +(-1.82162 - 1.39778i) q^{80} +(0.148586 - 0.0857864i) q^{81} +(2.90508 + 0.382461i) q^{82} +(8.24264 + 8.24264i) q^{83} +(-1.12132 + 2.94975i) q^{85} +(-1.00000 + 1.73205i) q^{86} +(-0.0888127 + 0.331453i) q^{87} +(7.02200 - 9.15125i) q^{88} +(-5.70346 - 3.29289i) q^{89} +(3.12132 - 1.29289i) q^{90} +(-16.8995 - 7.00000i) q^{92} +(2.19615 + 8.19615i) q^{93} +(12.0599 + 3.23143i) q^{94} +(0.0827602 + 0.628626i) q^{95} +(1.04490 + 1.36175i) q^{96} +(9.53553 - 3.94975i) q^{97} +(1.82843 + 4.41421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 4 q^{3} + 8 q^{6} + 8 q^{8} - 8 q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 + 4 * q^3 + 8 * q^6 + 8 * q^8 - 8 * q^9	$ 8 q + 4 q^{2} + 4 q^{3} + 8 q^{6} + 8 q^{8} - 8 q^{9} - 4 q^{10} + 4 q^{11} + 4 q^{12} - 16 q^{15} + 12 q^{16} + 12 q^{18} - 8 q^{19} + 8 q^{20} + 24 q^{22} - 4 q^{23} - 12 q^{24} + 4 q^{25} + 4 q^{26} + 16 q^{27} - 8 q^{29} + 12 q^{31} - 4 q^{32} - 40 q^{34} + 8 q^{40} - 8 q^{41} - 16 q^{43} + 20 q^{44} - 12 q^{45} - 20 q^{46} + 24 q^{48} + 40 q^{50} - 28 q^{51} - 16 q^{52} + 4 q^{53} + 8 q^{54} - 48 q^{57} + 8 q^{60} - 24 q^{62} + 4 q^{65} - 8 q^{66} - 16 q^{67} - 12 q^{68} - 64 q^{69} + 40 q^{71} + 28 q^{73} - 20 q^{74} + 12 q^{75} + 16 q^{76} - 16 q^{78} + 4 q^{79} - 4 q^{82} + 32 q^{83} + 8 q^{85} - 8 q^{86} - 16 q^{87} - 12 q^{88} + 8 q^{90} - 56 q^{92} - 24 q^{93} + 24 q^{94} + 8 q^{95} + 20 q^{96} + 48 q^{97} - 8 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 + 4 * q^3 + 8 * q^6 + 8 * q^8 - 8 * q^9 - 4 * q^10 + 4 * q^11 + 4 * q^12 - 16 * q^15 + 12 * q^16 + 12 * q^18 - 8 * q^19 + 8 * q^20 + 24 * q^22 - 4 * q^23 - 12 * q^24 + 4 * q^25 + 4 * q^26 + 16 * q^27 - 8 * q^29 + 12 * q^31 - 4 * q^32 - 40 * q^34 + 8 * q^40 - 8 * q^41 - 16 * q^43 + 20 * q^44 - 12 * q^45 - 20 * q^46 + 24 * q^48 + 40 * q^50 - 28 * q^51 - 16 * q^52 + 4 * q^53 + 8 * q^54 - 48 * q^57 + 8 * q^60 - 24 * q^62 + 4 * q^65 - 8 * q^66 - 16 * q^67 - 12 * q^68 - 64 * q^69 + 40 * q^71 + 28 * q^73 - 20 * q^74 + 12 * q^75 + 16 * q^76 - 16 * q^78 + 4 * q^79 - 4 * q^82 + 32 * q^83 + 8 * q^85 - 8 * q^86 - 16 * q^87 - 12 * q^88 + 8 * q^90 - 56 * q^92 - 24 * q^93 + 24 * q^94 + 8 * q^95 + 20 * q^96 + 48 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

$n$	$52$	$785$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{8}\right)$

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 $

$2$	2.33195	−	0.624844i	1.64894	−	0.441832i	0.689623	−	0.724168i	$-0.257776\pi$
$2$	2.33195	−	0.624844i	1.64894	−	0.441832i	0.959315	+	0.282337i	$0.0911095\pi$
$3$	0.658919	−	0.858719i	0.380427	−	0.495782i	−0.563418	−	0.826172i	$-0.690514\pi$
$3$	0.658919	−	0.858719i	0.380427	−	0.495782i	0.943844	+	0.330390i	$0.107180\pi$
$4$	3.31552	−	1.91421i	1.65776	−	0.957107i
$5$	0.0999004	−	0.758819i	0.0446768	−	0.339354i	−0.954479	−	0.298278i	$-0.903588\pi$
$5$	0.0999004	−	0.758819i	0.0446768	−	0.339354i	0.999156	−	0.0410766i	$-0.0130788\pi$
$6$	1.00000	−	2.41421i	0.408248	−	0.985599i
$7$		0			0
$7$		0			0
$8$	3.12132	−	3.12132i	1.10355	−	1.10355i
$9$	0.473232	+	1.76612i	0.157744	+	0.588708i
$10$	−0.241181	−	1.83195i	−0.0762681	−	0.579314i
$11$	2.59077	−	0.341081i	0.781147	−	0.102840i	0.270602	−	0.962691i	$-0.412777\pi$
$11$	2.59077	−	0.341081i	0.781147	−	0.102840i	0.510544	+	0.859851i	$0.329444\pi$
$12$	0.540882	−	4.10841i	0.156139	−	1.18600i
$13$		−	1.41421i		−	0.392232i	−0.980581	−	0.196116i	$-0.937167\pi$
$13$		−	1.41421i		−	0.392232i	0.980581	−	0.196116i	$-0.0628330\pi$
$14$		0			0
$15$	−0.585786	−	0.585786i	−0.151249	−	0.151249i
$16$	1.50000	−	2.59808i	0.375000	−	0.649519i
$17$	−4.01229	−	0.949490i	−0.973123	−	0.230285i
$17$	−4.01229	−	0.949490i	−0.973123	−	0.230285i
$18$	2.20711	+	3.82282i	0.520220	+	0.901048i
$19$	−0.800199	+	0.214413i	−0.183578	+	0.0491897i	−0.349437	−	0.936960i	$-0.613627\pi$
$19$	−0.800199	+	0.214413i	−0.183578	+	0.0491897i	0.165859	+	0.986150i	$0.446960\pi$
$20$	−1.12132	−	2.70711i	−0.250735	−	0.605327i
$21$		0			0
$22$	5.82843	−	2.41421i	1.24262	−	0.514712i
$23$	−2.90861	−	3.79057i	−0.606487	−	0.790389i	0.384675	−	0.923052i	$-0.374314\pi$
$23$	−2.90861	−	3.79057i	−0.606487	−	0.790389i	−0.991161	+	0.132664i	$0.957647\pi$
$24$	−0.623642	−	4.73703i	−0.127300	−	0.966943i
$25$	4.26380	+	1.14248i	0.852761	+	0.228497i
$26$	−0.883663	−	3.29788i	−0.173301	−	0.646767i
$27$	4.82843	+	2.00000i	0.929231	+	0.384900i
$28$		0			0
$29$	−0.292893	+	0.121320i	−0.0543889	+	0.0225286i	−0.409712	−	0.912215i	$-0.634371\pi$
$29$	−0.292893	+	0.121320i	−0.0543889	+	0.0225286i	0.355323	+	0.934744i	$0.384371\pi$
$30$	−1.73205	−	1.00000i	−0.316228	−	0.182574i
$31$	−4.77231	+	6.21940i	−0.857132	+	1.11704i	0.134876	+	0.990863i	$0.456936\pi$
$31$	−4.77231	+	6.21940i	−0.857132	+	1.11704i	−0.992008	+	0.126174i	$0.959730\pi$
$32$	−0.410432	+	1.53175i	−0.0725548	+	0.270778i
$33$	1.41421	−	2.44949i	0.246183	−	0.426401i
$34$	−9.94975	+	0.292893i	−1.70637	+	0.0502308i
$35$		0			0
$36$	4.94975	+	4.94975i	0.824958	+	0.824958i
$37$	−9.15976	−	1.20590i	−1.50585	−	0.198250i	−0.668008	−	0.744155i	$-0.732853\pi$
$37$	−9.15976	−	1.20590i	−1.50585	−	0.198250i	−0.837847	+	0.545905i	$0.816186\pi$
$38$	−1.73205	+	1.00000i	−0.280976	+	0.162221i
$39$	−1.21441	−	0.931852i	−0.194462	−	0.149216i
$40$	−2.05670	−	2.68034i	−0.325192	−	0.423799i
$41$	1.12132	+	0.464466i	0.175121	+	0.0725374i	0.468521	−	0.883452i	$-0.344787\pi$
$41$	1.12132	+	0.464466i	0.175121	+	0.0725374i	−0.293400	+	0.955990i	$0.594787\pi$
$42$		0			0
$43$	−0.585786	+	0.585786i	−0.0893316	+	0.0893316i	−0.750360	−	0.661029i	$-0.770120\pi$
$43$	−0.585786	+	0.585786i	−0.0893316	+	0.0893316i	0.661029	+	0.750360i	$0.270120\pi$
$44$	7.93684	−	6.09015i	1.19652	−	0.918124i
$45$	1.38745	−	0.182661i	0.206828	−	0.0272294i
$46$	−9.15125	−	7.02200i	−1.34928	−	1.03534i
$47$	4.47871	+	2.58579i	0.653288	+	0.377176i	0.789715	−	0.613474i	$-0.210229\pi$
$47$	4.47871	+	2.58579i	0.653288	+	0.377176i	−0.136427	+	0.990650i	$0.543562\pi$
$48$	−1.24264	−	3.00000i	−0.179360	−	0.433013i
$49$		0			0
$50$	10.6569			1.50711
$51$	−3.45912	+	2.81979i	−0.484373	+	0.394850i
$52$	−2.70711	−	4.68885i	−0.375408	−	0.650226i
$53$	−0.366025	+	1.36603i	−0.0502775	+	0.187638i	−0.986498	−	0.163776i	$-0.947632\pi$
$53$	−0.366025	+	1.36603i	−0.0502775	+	0.187638i	0.936220	+	0.351414i	$0.114299\pi$
$54$	12.5093	+	1.64689i	1.70231	+	0.224113i
$55$		−	2.00000i		−	0.269680i
$56$		0			0
$57$	−0.343146	+	0.828427i	−0.0454508	+	0.109728i
$58$	−0.607206	+	0.465926i	−0.0797301	+	0.0611791i
$59$	−5.79555	−	1.55291i	−0.754517	−	0.202172i	−0.138996	−	0.990293i	$-0.544388\pi$
$59$	−5.79555	−	1.55291i	−0.754517	−	0.202172i	−0.615521	+	0.788121i	$0.711054\pi$
$60$	−3.06350	−	0.820863i	−0.395497	−	0.105973i
$61$	3.03603	−	2.32963i	0.388724	−	0.298278i	−0.395848	−	0.918316i	$-0.629549\pi$
$61$	3.03603	−	2.32963i	0.388724	−	0.298278i	0.784572	+	0.620038i	$0.212883\pi$
$62$	−7.24264	+	17.4853i	−0.919816	+	2.22063i
$63$		0			0
$64$			9.82843i			1.22855i
$65$	−1.07313	−	0.141281i	−0.133106	−	0.0175237i
$66$	1.76733	−	6.59575i	0.217543	−	0.811881i
$67$	−0.585786	−	1.01461i	−0.0715652	−	0.123955i	0.828022	−	0.560695i	$-0.189466\pi$
$67$	−0.585786	−	1.01461i	−0.0715652	−	0.123955i	−0.899587	+	0.436741i	$0.856133\pi$
$68$	−15.1203	+	4.53233i	−1.83361	+	0.549626i
$69$	−5.17157			−0.622584
$70$		0			0
$71$	−2.07107	−	5.00000i	−0.245791	−	0.593391i	0.752048	−	0.659109i	$-0.229066\pi$
$71$	−2.07107	−	5.00000i	−0.245791	−	0.593391i	−0.997838	+	0.0657178i	$0.979066\pi$
$72$	6.98975	+	4.03553i	0.823750	+	0.475592i
$73$	10.2615	+	7.87391i	1.20102	+	0.921572i	0.998336	−	0.0576734i	$-0.0183682\pi$
$73$	10.2615	+	7.87391i	1.20102	+	0.921572i	0.202680	+	0.979245i	$0.435035\pi$
$74$	−22.1136	+	2.91131i	−2.57065	+	0.338433i
$75$	3.79057	−	2.90861i	0.437697	−	0.335857i
$76$	−2.24264	+	2.24264i	−0.257249	+	0.257249i
$77$		0			0
$78$	−3.41421	−	1.41421i	−0.386584	−	0.160128i
$79$	2.90861	+	3.79057i	0.327244	+	0.426473i	0.927782	−	0.373124i	$-0.121713\pi$
$79$	2.90861	+	3.79057i	0.327244	+	0.426473i	−0.600538	+	0.799597i	$0.705047\pi$
$80$	−1.82162	−	1.39778i	−0.203663	−	0.156276i
$81$	0.148586	−	0.0857864i	0.0165096	−	0.00953183i
$82$	2.90508	+	0.382461i	0.320813	+	0.0422358i
$83$	8.24264	+	8.24264i	0.904747	+	0.904747i	0.995842	−	0.0910949i	$-0.0290366\pi$
$83$	8.24264	+	8.24264i	0.904747	+	0.904747i	−0.0910949	+	0.995842i	$0.529037\pi$
$84$		0			0
$85$	−1.12132	+	2.94975i	−0.121624	+	0.319945i
$86$	−1.00000	+	1.73205i	−0.107833	+	0.186772i
$87$	−0.0888127	+	0.331453i	−0.00952172	+	0.0355355i
$88$	7.02200	−	9.15125i	0.748548	−	0.975526i
$89$	−5.70346	−	3.29289i	−0.604565	−	0.349046i	0.166270	−	0.986080i	$-0.446828\pi$
$89$	−5.70346	−	3.29289i	−0.604565	−	0.349046i	−0.770835	+	0.637034i	$0.780161\pi$
$90$	3.12132	−	1.29289i	0.329016	−	0.136283i
$91$		0			0
$92$	−16.8995	−	7.00000i	−1.76189	−	0.729800i
$93$	2.19615	+	8.19615i	0.227730	+	0.849901i
$94$	12.0599	+	3.23143i	1.24388	+	0.333296i
$95$	0.0827602	+	0.628626i	0.00849102	+	0.0644957i
$96$	1.04490	+	1.36175i	0.106645	+	0.138983i
$97$	9.53553	−	3.94975i	0.968187	−	0.401036i	0.158150	−	0.987415i	$-0.449447\pi$
$97$	9.53553	−	3.94975i	0.968187	−	0.401036i	0.810037	+	0.586379i	$0.199447\pi$
$98$		0			0
$99$	1.82843	+	4.41421i	0.183764	+	0.443645i
$100$	16.3237	−	4.37391i	1.63237	−	0.437391i
$101$	5.29289	+	9.16756i	0.526663	+	0.912206i	0.999517	+	0.0310659i	$0.00989019\pi$
$101$	5.29289	+	9.16756i	0.526663	+	0.912206i	−0.472855	+	0.881140i	$0.656776\pi$
$102$	−6.30456	+	8.73703i	−0.624245	+	0.865095i
$103$	−6.24264	+	10.8126i	−0.615106	+	1.06539i	0.375260	+	0.926919i	$0.377553\pi$
$103$	−6.24264	+	10.8126i	−0.615106	+	1.06539i	−0.990366	+	0.138475i	$0.955780\pi$
$104$	−4.41421	−	4.41421i	−0.432849	−	0.432849i
$105$		0			0
$106$			3.41421i			0.331618i
$107$	−0.0585203	+	0.444506i	−0.00565737	+	0.0429720i	−0.994041	−	0.109010i	$-0.965232\pi$
$107$	−0.0585203	+	0.444506i	−0.00565737	+	0.0429720i	0.988383	+	0.151982i	$0.0485654\pi$
$108$	19.8372	−	2.61161i	1.90883	−	0.251302i
$109$	−2.02935	−	15.4144i	−0.194376	−	1.47643i	−0.759002	−	0.651088i	$-0.774313\pi$
$109$	−2.02935	−	15.4144i	−0.194376	−	1.47643i	0.564626	−	0.825347i	$-0.309020\pi$
$110$	−1.24969	−	4.66390i	−0.119153	−	0.444686i
$111$	−7.07107	+	7.07107i	−0.671156	+	0.671156i
$112$		0			0
$113$	5.05025	−	12.1924i	0.475088	−	1.14696i	−0.486799	−	0.873514i	$-0.661835\pi$
$113$	5.05025	−	12.1924i	0.475088	−	1.14696i	0.961886	−	0.273449i	$-0.0881645\pi$
$114$	−0.282561	+	2.14626i	−0.0264643	+	0.201016i
$115$	−3.16693	+	1.82843i	−0.295318	+	0.170502i
$116$	−0.738859	+	0.962900i	−0.0686013	+	0.0894030i
$117$	2.49768	−	0.669251i	0.230910	−	0.0618723i
$118$	−14.4853			−1.33348
$119$		0			0
$120$	−3.65685			−0.333824
$121$	−4.02943	+	1.07968i	−0.366312	+	0.0981530i
$122$	5.62422	−	7.32963i	0.509193	−	0.663593i
$123$	1.13770	−	0.656854i	0.102583	−	0.0592266i
$124$	−3.91742	+	29.7557i	−0.351794	+	2.67214i
$125$	2.75736	−	6.65685i	0.246626	−	0.595407i
$126$		0			0
$127$	−3.75736	+	3.75736i	−0.333412	+	0.333412i	−0.853881	−	0.520469i	$-0.825757\pi$
$127$	−3.75736	+	3.75736i	−0.333412	+	0.333412i	0.520469	+	0.853881i	$0.325757\pi$
$128$	5.32037	+	19.8559i	0.470259	+	1.75503i
$129$	0.117041	+	0.889012i	0.0103049	+	0.0782731i
$130$	−2.59077	+	0.341081i	−0.227226	+	0.0299148i
$131$	1.98797	−	15.1001i	0.173690	−	1.31930i	−0.653306	−	0.757094i	$-0.726618\pi$
$131$	1.98797	−	15.1001i	0.173690	−	1.31930i	0.826995	−	0.562209i	$-0.190048\pi$
$132$		−	10.8284i		−	0.942494i
$133$		0			0
$134$	−2.00000	−	2.00000i	−0.172774	−	0.172774i
$135$	2.00000	−	3.46410i	0.172133	−	0.298142i
$136$	−15.4873	+	9.55998i	−1.32803	+	0.819762i
$137$	8.36396	+	14.4868i	0.714581	+	1.23769i	0.963121	+	0.269070i	$0.0867161\pi$
$137$	8.36396	+	14.4868i	0.714581	+	1.23769i	−0.248539	+	0.968622i	$0.579951\pi$
$138$	−12.0599	+	3.23143i	−1.02660	+	0.275077i
$139$	−8.17157	−	19.7279i	−0.693104	−	1.67330i	−0.738432	−	0.674328i	$-0.764433\pi$
$139$	−8.17157	−	19.7279i	−0.693104	−	1.67330i	0.0453279	−	0.998972i	$-0.485567\pi$
$140$		0			0
$141$	5.17157	−	2.14214i	0.435525	−	0.180400i
$142$	−7.95385	−	10.3657i	−0.667472	−	0.869867i
$143$	−0.482362	−	3.66390i	−0.0403371	−	0.306391i
$144$	5.29837	+	1.41970i	0.441531	+	0.118308i
$145$	0.0628000	+	0.234373i	0.00521526	+	0.0194636i
$146$	28.8492	+	11.9497i	2.38758	+	0.988968i
$147$		0			0
$148$	−32.6777	+	13.5355i	−2.68609	+	1.11261i
$149$	−14.6969	−	8.48528i	−1.20402	−	0.695141i	−0.242574	−	0.970133i	$-0.577992\pi$
$149$	−14.6969	−	8.48528i	−1.20402	−	0.695141i	−0.961447	+	0.274992i	$0.911325\pi$
$150$	7.02200	−	9.15125i	0.573344	−	0.747196i
$151$	1.85614	−	6.92721i	0.151051	−	0.563728i	−0.848361	−	0.529419i	$-0.822410\pi$
$151$	1.85614	−	6.92721i	0.151051	−	0.563728i	0.999411	−	0.0343096i	$-0.0109232\pi$
$152$	−1.82843	+	3.16693i	−0.148305	+	0.256872i
$153$	−0.221825	−	7.53553i	−0.0179335	−	0.609212i
$154$		0			0
$155$	4.24264	+	4.24264i	0.340777	+	0.340777i
$156$	−5.81017	−	0.764923i	−0.465186	−	0.0612429i
$157$	−8.36308	+	4.82843i	−0.667447	+	0.385350i	−0.795108	−	0.606467i	$-0.792586\pi$
$157$	−8.36308	+	4.82843i	−0.667447	+	0.385350i	0.127662	+	0.991818i	$0.459253\pi$
$158$	9.15125	+	7.02200i	0.728034	+	0.558640i
$159$	0.931852	+	1.21441i	0.0739006	+	0.0963092i
$160$	1.12132	+	0.464466i	0.0886482	+	0.0367193i
$161$		0			0
$162$	0.292893	−	0.292893i	0.0230119	−	0.0230119i
$163$	6.72242	−	5.15830i	0.526541	−	0.404029i	−0.310995	−	0.950412i	$-0.600662\pi$
$163$	6.72242	−	5.15830i	0.526541	−	0.404029i	0.837536	+	0.546383i	$0.183996\pi$
$164$	4.60684	−	0.606502i	0.359734	−	0.0473599i
$165$	−1.71744	−	1.31784i	−0.133702	−	0.102593i
$166$	24.3718	+	14.0711i	1.89162	+	1.09213i
$167$	0.757359	+	1.82843i	0.0586062	+	0.141488i	0.950470	−	0.310816i	$-0.100602\pi$
$167$	0.757359	+	1.82843i	0.0586062	+	0.141488i	−0.891864	+	0.452304i	$0.850602\pi$
$168$		0			0
$169$	11.0000			0.846154
$170$	−0.771731	+	7.57932i	−0.0591891	+	0.581307i
$171$	−0.757359	−	1.31178i	−0.0579167	−	0.100315i
$172$	−0.820863	+	3.06350i	−0.0625903	+	0.233590i
$173$	−2.90508	−	0.382461i	−0.220869	−	0.0290780i	0.0192792	−	0.999814i	$-0.493863\pi$
$173$	−2.90508	−	0.382461i	−0.220869	−	0.0290780i	−0.240149	+	0.970736i	$0.577196\pi$
$174$			0.828427i			0.0628029i
$175$		0			0
$176$	3.00000	−	7.24264i	0.226134	−	0.545935i
$177$	−5.15232	+	3.95351i	−0.387272	+	0.297164i
$178$	−15.3577	−	4.11509i	−1.15111	−	0.308439i
$179$	5.79555	+	1.55291i	0.433180	+	0.116070i	0.468819	−	0.883294i	$-0.344680\pi$
$179$	5.79555	+	1.55291i	0.433180	+	0.116070i	−0.0356385	+	0.999365i	$0.511346\pi$
$180$	4.25044	−	3.26148i	0.316809	−	0.243096i
$181$	−4.46447	+	10.7782i	−0.331841	+	0.801135i	0.666605	+	0.745411i	$0.267747\pi$
$181$	−4.46447	+	10.7782i	−0.331841	+	0.801135i	−0.998446	+	0.0557243i	$0.982253\pi$
$182$		0			0
$183$		−	4.14214i		−	0.306195i
$184$	−20.9103	−	2.75289i	−1.54153	−	0.202946i
$185$	−1.83013	+	6.83013i	−0.134554	+	0.502161i
$186$	10.2426	+	17.7408i	0.751027	+	1.30082i
$187$	−10.7188	−	1.09139i	−0.783834	−	0.0798105i
$188$	19.7990			1.44399
$189$		0			0
$190$	0.585786	+	1.41421i	0.0424974	+	0.102598i
$191$	−17.3205	−	10.0000i	−1.25327	−	0.723575i	−0.281511	−	0.959558i	$-0.590836\pi$
$191$	−17.3205	−	10.0000i	−1.25327	−	0.723575i	−0.971757	+	0.235983i	$0.924169\pi$
$192$	8.43986	+	6.47613i	0.609095	+	0.467375i
$193$	−2.27646	+	0.299701i	−0.163863	+	0.0215730i	−0.212011	−	0.977267i	$-0.568001\pi$
$193$	−2.27646	+	0.299701i	−0.163863	+	0.0215730i	0.0481483	+	0.998840i	$0.484668\pi$
$194$	19.7684	−	15.1688i	1.41929	−	1.08906i
$195$	−0.828427	+	0.828427i	−0.0593249	+	0.0593249i
$196$		0			0
$197$	−4.29289	−	1.77817i	−0.305856	−	0.126690i	0.224476	−	0.974480i	$-0.427933\pi$
$197$	−4.29289	−	1.77817i	−0.305856	−	0.126690i	−0.530332	+	0.847790i	$0.677933\pi$
$198$	7.02200	+	9.15125i	0.499032	+	0.650351i
$199$	−9.15125	−	7.02200i	−0.648715	−	0.497776i	0.231201	−	0.972906i	$-0.425734\pi$
$199$	−9.15125	−	7.02200i	−0.648715	−	0.497776i	−0.879916	+	0.475130i	$0.842401\pi$
$200$	16.8747	−	9.74264i	1.19322	−	0.688909i
$201$	−1.25725	−	0.165520i	−0.0886798	−	0.0116749i
$202$	18.0711	+	18.0711i	1.27148	+	1.27148i
$203$		0			0
$204$	−6.07107	+	15.9706i	−0.425060	+	1.11816i
$205$	0.464466	−	0.804479i	0.0324397	−	0.0561872i
$206$	−7.80136	+	29.1151i	−0.543546	+	2.02854i
$207$	5.31818	−	6.93078i	0.369639	−	0.481723i
$208$	−3.67423	−	2.12132i	−0.254762	−	0.147087i
$209$	−2.00000	+	0.828427i	−0.138343	+	0.0573035i
$210$		0			0
$211$	−19.7279	−	8.17157i	−1.35813	−	0.562554i	−0.419583	−	0.907717i	$-0.637824\pi$
$211$	−19.7279	−	8.17157i	−1.35813	−	0.562554i	−0.938543	+	0.345163i	$0.887824\pi$
$212$	1.40130	+	5.22973i	0.0962418	+	0.359179i
$213$	−5.65826	−	1.51613i	−0.387698	−	0.103883i
$214$	0.141281	+	1.07313i	0.00965774	+	0.0733578i
$215$	0.385986	+	0.503026i	0.0263240	+	0.0343061i
$216$	21.3137	−	8.82843i	1.45021	−	0.600698i
$217$		0			0
$218$	−14.3640	−	34.6777i	−0.972850	−	2.34867i
$219$	13.5230	−	3.62347i	0.913797	−	0.244851i
$220$	−3.82843	−	6.63103i	−0.258113	−	0.447064i
$221$	−1.34278	+	5.67423i	−0.0903252	+	0.381690i
$222$	−12.0711	+	20.9077i	−0.810157	+	1.40323i
$223$	3.41421	+	3.41421i	0.228633	+	0.228633i	0.812121	−	0.583489i	$-0.198313\pi$
$223$	3.41421	+	3.41421i	0.228633	+	0.228633i	−0.583489	+	0.812121i	$0.698313\pi$
$224$		0			0
$225$			8.07107i			0.538071i
$226$	4.15860	−	31.5877i	0.276626	−	2.10118i
$227$	−17.2464	+	2.27053i	−1.14468	+	0.150700i	−0.678922	−	0.734210i	$-0.737553\pi$
$227$	−17.2464	+	2.27053i	−1.14468	+	0.150700i	−0.465761	+	0.884911i	$0.654219\pi$
$228$	0.448082	+	3.40352i	0.0296749	+	0.225403i
$229$	−4.44433	−	16.5865i	−0.293690	−	1.09606i	−0.942252	−	0.334903i	$-0.891296\pi$
$229$	−4.44433	−	16.5865i	−0.293690	−	1.09606i	0.648563	−	0.761161i	$-0.275370\pi$
$230$	−6.24264	+	6.24264i	−0.411628	+	0.411628i
$231$		0			0
$232$	−0.535534	+	1.29289i	−0.0351595	+	0.0848826i
$233$	−1.14738	+	8.71525i	−0.0751677	+	0.570955i	0.911872	+	0.410476i	$0.134637\pi$
$233$	−1.14738	+	8.71525i	−0.0751677	+	0.570955i	−0.987039	+	0.160479i	$0.948696\pi$
$234$	5.40629	−	3.12132i	0.353420	−	0.204047i
$235$	2.40957	−	3.14021i	0.157183	−	0.204845i
$236$	−22.1879	+	5.94522i	−1.44431	+	0.387001i
$237$	5.17157			0.335930
$238$		0			0
$239$	14.8284			0.959171			0.479586	−	0.877495i	$-0.340787\pi$
$239$	14.8284			0.959171			0.479586	+	0.877495i	$0.340787\pi$
$240$	−2.40060	+	0.643238i	−0.154958	+	0.0415208i
$241$	−2.16975	+	2.82767i	−0.139766	+	0.182146i	−0.857992	−	0.513664i	$-0.828288\pi$
$241$	−2.16975	+	2.82767i	−0.139766	+	0.182146i	0.718226	+	0.695810i	$0.244955\pi$
$242$	−8.72180	+	5.03553i	−0.560659	+	0.323696i
$243$	−2.02225	+	15.3605i	−0.129727	+	0.985377i
$244$	5.60660	−	13.5355i	0.358926	−	0.866524i
$245$		0			0
$246$	2.24264	−	2.24264i	0.142986	−	0.142986i
$247$	0.303225	+	1.13165i	0.0192938	+	0.0720053i
$248$	4.51682	+	34.3086i	0.286818	+	2.17860i
$249$	12.5093	−	1.64689i	0.792748	−	0.104367i
$250$	2.27053	−	17.2464i	0.143601	−	1.09076i
$251$		−	20.4853i		−	1.29302i	−0.762906	−	0.646510i	$-0.776228\pi$
$251$		−	20.4853i		−	1.29302i	0.762906	−	0.646510i	$-0.223772\pi$
$252$		0			0
$253$	−8.82843	−	8.82843i	−0.555038	−	0.555038i
$254$	−6.41421	+	11.1097i	−0.402464	+	0.697087i
$255$	1.79415	+	2.90654i	0.112354	+	0.182015i
$256$	14.9853	+	25.9553i	0.936580	+	1.62220i
$257$	5.93285	−	1.58970i	0.370081	−	0.0991629i	−0.0689851	−	0.997618i	$-0.521976\pi$
$257$	5.93285	−	1.58970i	0.370081	−	0.0991629i	0.439066	+	0.898455i	$0.355309\pi$
$258$	0.828427	+	2.00000i	0.0515756	+	0.124515i
$259$		0			0
$260$	−3.82843	+	1.58579i	−0.237429	+	0.0983463i
$261$	−0.352873	−	0.459873i	−0.0218423	−	0.0284654i
$262$	−4.79938	−	36.4549i	−0.296507	−	2.25219i
$263$	10.1280	+	2.71379i	0.624519	+	0.167339i	0.557182	−	0.830391i	$-0.311883\pi$
$263$	10.1280	+	2.71379i	0.624519	+	0.167339i	0.0673380	+	0.997730i	$0.478549\pi$
$264$	−3.23143	−	12.0599i	−0.198881	−	0.742233i
$265$	1.00000	+	0.414214i	0.0614295	+	0.0254449i
$266$		0			0
$267$	−6.58579	+	2.72792i	−0.403044	+	0.166946i
$268$	−3.88437	−	2.24264i	−0.237276	−	0.136991i
$269$	16.1007	−	20.9828i	0.981677	−	1.27935i	0.0215538	−	0.999768i	$-0.493139\pi$
$269$	16.1007	−	20.9828i	0.981677	−	1.27935i	0.960123	−	0.279578i	$-0.0901947\pi$
$270$	2.49938	−	9.32780i	0.152107	−	0.567672i
$271$	−11.0711	+	19.1757i	−0.672519	+	1.16484i	0.304668	+	0.952459i	$0.401455\pi$
$271$	−11.0711	+	19.1757i	−0.672519	+	1.16484i	−0.977187	+	0.212379i	$0.931879\pi$
$272$	−8.48528	+	9.00000i	−0.514496	+	0.545705i
$273$		0			0
$274$	28.5563	+	28.5563i	1.72515	+	1.72515i
$275$	11.4362	+	1.50561i	0.689630	+	0.0907915i
$276$	−17.1464	+	9.89949i	−1.03209	+	0.595880i
$277$	15.8305	+	12.1472i	0.951164	+	0.729854i	0.962838	−	0.270078i	$-0.0870496\pi$
$277$	15.8305	+	12.1472i	0.951164	+	0.729854i	−0.0116747	+	0.999932i	$0.503716\pi$
$278$	−31.3826	−	40.8986i	−1.88220	−	2.45293i
$279$	−13.2426	−	5.48528i	−0.792816	−	0.328395i
$280$		0			0
$281$	−1.34315	+	1.34315i	−0.0801254	+	0.0801254i	−0.746034	−	0.665908i	$-0.768044\pi$
$281$	−1.34315	+	1.34315i	−0.0801254	+	0.0801254i	0.665908	+	0.746034i	$0.268044\pi$
$282$	10.7214	−	8.22678i	0.638447	−	0.489898i
$283$	18.5036	−	2.43605i	1.09993	−	0.144808i	0.441360	−	0.897330i	$-0.354496\pi$
$283$	18.5036	−	2.43605i	1.09993	−	0.144808i	0.658567	+	0.752522i	$0.271163\pi$
$284$	−16.4377	−	12.6131i	−0.975399	−	0.748450i
$285$	0.594346	+	0.343146i	0.0352060	+	0.0203262i
$286$	−3.41421	−	8.24264i	−0.201887	−	0.487398i
$287$		0			0
$288$	−2.89949			−0.170854
$289$	15.1969	+	7.61926i	0.893938	+	0.448192i
$290$	0.292893	+	0.507306i	0.0171993	+	0.0297900i
$291$	2.89142	−	10.7909i	0.169498	−	0.632574i
$292$	49.0944	+	6.46341i	2.87303	+	0.378242i
$293$		−	12.3431i		−	0.721094i	−0.932741	−	0.360547i	$-0.882590\pi$
$293$		−	12.3431i		−	0.721094i	0.932741	−	0.360547i	$-0.117410\pi$
$294$		0			0
$295$	−1.75736	+	4.24264i	−0.102317	+	0.247016i
$296$	−32.3545	+	24.8265i	−1.88057	+	1.44301i
$297$	13.1915	+	3.53465i	0.765449	+	0.205101i
$298$	−39.5745	−	10.6040i	−2.29249	−	0.614271i
$299$	−5.36068	+	4.11339i	−0.310016	+	0.237884i
$300$	7.00000	−	16.8995i	0.404145	−	0.975693i
$301$		0			0
$302$		−	17.3137i		−	0.996292i
$303$	11.3599	+	1.49557i	0.652612	+	0.0859180i
$304$	−0.643238	+	2.40060i	−0.0368922	+	0.137684i
$305$	−1.46447	−	2.53653i	−0.0838551	−	0.145241i
$306$	−5.22582	−	17.4339i	−0.298740	−	0.996629i
$307$	−26.1421			−1.49201			−0.746005	−	0.665940i	$-0.768031\pi$
$307$	−26.1421			−1.49201			−0.746005	+	0.665940i	$0.768031\pi$
$308$		0			0
$309$	5.17157	+	12.4853i	0.294201	+	0.710263i
$310$	12.5446	+	7.24264i	0.712487	+	0.411354i
$311$	−20.3756	−	15.6348i	−1.15540	−	0.886566i	−0.160456	−	0.987043i	$-0.551297\pi$
$311$	−20.3756	−	15.6348i	−1.15540	−	0.886566i	−0.994939	+	0.100476i	$0.967963\pi$
$312$	−6.69918	+	0.881964i	−0.379266	+	0.0499314i
$313$	7.83266	−	6.01021i	0.442728	−	0.339717i	−0.363220	−	0.931703i	$-0.618323\pi$
$313$	7.83266	−	6.01021i	0.442728	−	0.339717i	0.805948	+	0.591986i	$0.201656\pi$
$314$	−16.4853	+	16.4853i	−0.930318	+	0.930318i
$315$		0			0
$316$	16.8995	+	7.00000i	0.950671	+	0.393781i
$317$	11.7144	+	15.2665i	0.657945	+	0.857450i	0.996508	−	0.0834934i	$-0.0266077\pi$
$317$	11.7144	+	15.2665i	0.657945	+	0.857450i	−0.338564	+	0.940943i	$0.609941\pi$
$318$	2.93185	+	2.24969i	0.164410	+	0.126156i
$319$	−0.717439	+	0.414214i	−0.0401689	+	0.0231915i
$320$	7.45800	+	0.981864i	0.416915	+	0.0548879i
$321$	0.343146	+	0.343146i	0.0191525	+	0.0191525i
$322$		0			0
$323$	3.41421	−	0.100505i	0.189972	−	0.00559225i
$324$	0.328427	−	0.568852i	0.0182460	−	0.0316029i
$325$	1.61571	−	6.02993i	0.0896237	−	0.334480i
$326$	12.4532	−	16.2294i	0.689721	−	0.898861i
$327$	−14.5738	−	8.41421i	−0.805935	−	0.465307i
$328$	4.94975	−	2.05025i	0.273304	−	0.113206i
$329$		0			0
$330$	−4.82843	−	2.00000i	−0.265796	−	0.110096i
$331$	−5.64199	−	21.0562i	−0.310112	−	1.15735i	−0.928455	−	0.371445i	$-0.878862\pi$
$331$	−5.64199	−	21.0562i	−0.310112	−	1.15735i	0.618343	−	0.785909i	$-0.287804\pi$
$332$	43.1068	+	11.5504i	2.36579	+	0.633912i
$333$	−2.20491	−	16.7479i	−0.120828	−	0.917782i
$334$	2.90861	+	3.79057i	0.159152	+	0.207411i
$335$	−0.828427	+	0.343146i	−0.0452618	+	0.0187481i
$336$		0			0
$337$	−2.15076	−	5.19239i	−0.117159	−	0.282847i	0.854411	−	0.519597i	$-0.173918\pi$
$337$	−2.15076	−	5.19239i	−0.117159	−	0.282847i	−0.971571	+	0.236750i	$0.923918\pi$
$338$	25.6515	−	6.87329i	1.39526	−	0.373858i
$339$	−7.14214	−	12.3705i	−0.387908	−	0.671876i
$340$	1.92869	+	11.9264i	0.104598	+	0.646799i
$341$	−10.2426	+	17.7408i	−0.554670	+	0.960717i
$342$	−2.58579	−	2.58579i	−0.139823	−	0.139823i
$343$		0			0
$344$			3.65685i			0.197164i
$345$	−0.516642	+	3.92429i	−0.0278151	+	0.211277i
$346$	−7.01349	+	0.923344i	−0.377048	+	0.0496393i
$347$	−2.18777	−	16.6178i	−0.117446	−	0.892088i	−0.944165	−	0.329473i	$-0.893129\pi$
$347$	−2.18777	−	16.6178i	−0.117446	−	0.892088i	0.826719	−	0.562615i	$-0.190204\pi$
$348$	0.340013	+	1.26894i	0.0182266	+	0.0680226i
$349$	3.00000	−	3.00000i	0.160586	−	0.160586i	−0.622240	−	0.782826i	$-0.713777\pi$
$349$	3.00000	−	3.00000i	0.160586	−	0.160586i	0.782826	+	0.622240i	$0.213777\pi$
$350$		0			0
$351$	2.82843	−	6.82843i	0.150970	−	0.364474i
$352$	−0.540882	+	4.10841i	−0.0288291	+	0.218979i
$353$	12.1244	−	7.00000i	0.645314	−	0.372572i	−0.141344	−	0.989960i	$-0.545142\pi$
$353$	12.1244	−	7.00000i	0.645314	−	0.372572i	0.786659	+	0.617388i	$0.211809\pi$
$354$	−9.54462	+	12.4388i	−0.507291	+	0.661114i
$355$	−4.00100	+	1.07206i	−0.212351	+	0.0568992i
$356$	−25.2132			−1.33630
$357$		0			0
$358$	14.4853			0.765571
$359$	27.8461	−	7.46135i	1.46966	−	0.393795i	0.566847	−	0.823823i	$-0.308163\pi$
$359$	27.8461	−	7.46135i	1.46966	−	0.393795i	0.902815	+	0.430028i	$0.141496\pi$
$360$	3.76052	−	4.90080i	0.198197	−	0.258295i
$361$	−15.8601	+	9.15685i	−0.834744	+	0.481940i
$362$	−3.67623	+	27.9238i	−0.193219	+	1.46764i
$363$	−1.72792	+	4.17157i	−0.0906924	+	0.218951i
$364$		0			0
$365$	7.00000	−	7.00000i	0.366397	−	0.366397i
$366$	−2.58819	−	9.65926i	−0.135287	−	0.504898i
$367$	0.575163	+	4.36879i	0.0300232	+	0.228049i	0.999878	−	0.0156355i	$-0.00497714\pi$
$367$	0.575163	+	4.36879i	0.0300232	+	0.228049i	−0.969855	+	0.243685i	$0.921644\pi$
$368$	−14.2111	+	1.87093i	−0.740805	+	0.0975288i
$369$	−0.289661	+	2.20019i	−0.0150791	+	0.114537i
$370$			17.0711i			0.887483i
$371$		0			0
$372$	22.9706	+	22.9706i	1.19097	+	1.19097i
$373$	−5.77817	+	10.0081i	−0.299183	+	0.518199i	−0.975949	−	0.217998i	$-0.930047\pi$
$373$	−5.77817	+	10.0081i	−0.299183	+	0.518199i	0.676767	+	0.736198i	$0.263381\pi$
$374$	−25.6776	+	4.15249i	−1.32776	+	0.214720i
$375$	−3.89949	−	6.75412i	−0.201369	−	0.348781i
$376$	22.0506	−	5.90843i	1.13717	−	0.304704i
$377$	0.171573	+	0.414214i	0.00883645	+	0.0213331i
$378$		0			0
$379$	−2.41421	+	1.00000i	−0.124010	+	0.0513665i	−0.443826	−	0.896113i	$-0.646379\pi$
$379$	−2.41421	+	1.00000i	−0.124010	+	0.0513665i	0.319816	+	0.947480i	$0.396379\pi$
$380$	1.47772	+	1.92580i	0.0758053	+	0.0987914i
$381$	0.750724	+	5.70231i	0.0384607	+	0.292138i
$382$	−46.6390	−	12.4969i	−2.38626	−	0.639396i
$383$	−5.81962	−	21.7191i	−0.297369	−	1.10979i	−0.939318	−	0.343048i	$-0.888541\pi$
$383$	−5.81962	−	21.7191i	−0.297369	−	1.10979i	0.641949	−	0.766747i	$-0.278126\pi$
$384$	20.5563	+	8.51472i	1.04901	+	0.434515i
$385$		0			0
$386$	−5.12132	+	2.12132i	−0.260668	+	0.107972i
$387$	−1.31178	−	0.757359i	−0.0666818	−	0.0384987i
$388$	24.0545	−	31.3485i	1.22118	−	1.59148i
$389$	−3.14262	+	11.7284i	−0.159337	+	0.594654i	0.839358	+	0.543579i	$0.182931\pi$
$389$	−3.14262	+	11.7284i	−0.159337	+	0.594654i	−0.998695	+	0.0510744i	$0.983735\pi$
$390$	−1.41421	+	2.44949i	−0.0716115	+	0.124035i
$391$	8.07107	+	17.9706i	0.408171	+	0.908810i
$392$		0			0
$393$	−11.6569	−	11.6569i	−0.588011	−	0.588011i
$394$	−11.1219	−	1.46423i	−0.560313	−	0.0737666i
$395$	3.16693	−	1.82843i	0.159345	−	0.0919982i
$396$	14.5119	+	11.1354i	0.729252	+	0.559574i
$397$	10.8293	+	14.1131i	0.543509	+	0.708315i	0.981672	−	0.190581i	$-0.0610371\pi$
$397$	10.8293	+	14.1131i	0.543509	+	0.708315i	−0.438162	+	0.898896i	$0.644370\pi$
$398$	−25.7279	−	10.6569i	−1.28962	−	0.534180i
$399$		0			0
$400$	9.36396	−	9.36396i	0.468198	−	0.468198i
$401$	0.459873	−	0.352873i	0.0229650	−	0.0176216i	−0.597215	−	0.802081i	$-0.703726\pi$
$401$	0.459873	−	0.352873i	0.0229650	−	0.0176216i	0.620180	+	0.784459i	$0.287059\pi$
$402$	−3.03528	+	0.399602i	−0.151386	+	0.0199303i
$403$	8.79555	+	6.74907i	0.438138	+	0.336195i
$404$	35.0973	+	20.2635i	1.74616	+	1.00814i
$405$	−0.0502525	−	0.121320i	−0.00249707	−	0.00602846i
$406$		0			0
$407$	−24.1421			−1.19668
$408$	−1.99553	+	19.5985i	−0.0987935	+	0.970270i
$409$	1.65685	+	2.86976i	0.0819262	+	0.141900i	0.904077	−	0.427369i	$-0.140559\pi$
$409$	1.65685	+	2.86976i	0.0819262	+	0.141900i	−0.822151	+	0.569269i	$0.807226\pi$
$410$	0.580438	−	2.16622i	0.0286658	−	0.106982i
$411$	17.9513	+	2.36333i	0.885471	+	0.116574i
$412$			47.7990i			2.35489i
$413$		0			0
$414$	8.07107	−	19.4853i	0.396671	−	0.957649i
$415$	7.07812	−	5.43123i	0.347451	−	0.266609i
$416$	2.16622	+	0.580438i	0.106208	+	0.0284583i
$417$	−22.3252	−	5.98201i	−1.09327	−	0.292940i
$418$	−4.14626	+	3.18154i	−0.202800	+	0.155614i
$419$	−5.10051	+	12.3137i	−0.249176	+	0.601564i	−0.998135	−	0.0610528i	$-0.980554\pi$
$419$	−5.10051	+	12.3137i	−0.249176	+	0.601564i	0.748959	+	0.662617i	$0.230554\pi$
$420$		0			0
$421$		−	14.5858i		−	0.710868i	−0.934701	−	0.355434i	$-0.884333\pi$
$421$		−	14.5858i		−	0.710868i	0.934701	−	0.355434i	$-0.115667\pi$
$422$	−51.1105	−	6.72883i	−2.48802	−	0.327554i
$423$	−2.44735	+	9.13364i	−0.118994	+	0.444093i
$424$	3.12132	+	5.40629i	0.151585	+	0.262552i
$425$	−16.0228	−	8.63241i	−0.777222	−	0.418733i
$426$	−14.1421			−0.685189
$427$		0			0
$428$	0.656854	+	1.58579i	0.0317502	+	0.0766519i
$429$	−3.46410	−	2.00000i	−0.167248	−	0.0965609i
$430$	1.21441	+	0.931852i	0.0585642	+	0.0449379i
$431$	−7.25154	+	0.954683i	−0.349294	+	0.0459855i	−0.303132	−	0.952948i	$-0.598032\pi$
$431$	−7.25154	+	0.954683i	−0.349294	+	0.0459855i	−0.0461621	+	0.998934i	$0.514699\pi$
$432$	12.4388	−	9.54462i	0.598462	−	0.459216i
$433$	14.7279	−	14.7279i	0.707779	−	0.707779i	−0.258289	−	0.966068i	$-0.583159\pi$
$433$	14.7279	−	14.7279i	0.707779	−	0.707779i	0.966068	+	0.258289i	$0.0831587\pi$
$434$		0			0
$435$	0.242641	+	0.100505i	0.0116337	+	0.00481885i
$436$	−36.2348	−	47.2222i	−1.73533	−	2.26153i
$437$	3.14021	+	2.40957i	0.150217	+	0.115265i
$438$	29.2708	−	16.8995i	1.39861	−	0.807489i
$439$	10.5472	+	1.38857i	0.503390	+	0.0662726i	0.377945	−	0.925828i	$-0.376631\pi$
$439$	10.5472	+	1.38857i	0.503390	+	0.0662726i	0.125445	+	0.992101i	$0.459964\pi$
$440$	−6.24264	−	6.24264i	−0.297606	−	0.297606i
$441$		0			0
$442$	0.414214	+	14.0711i	0.0197021	+	0.669292i
$443$	11.8995	−	20.6105i	0.565362	−	0.979236i	−0.431654	−	0.902039i	$-0.642070\pi$
$443$	11.8995	−	20.6105i	0.565362	−	0.979236i	0.997016	−	0.0771965i	$-0.0245969\pi$
$444$	−9.90870	+	36.9798i	−0.470246	+	1.75498i
$445$	−3.06849	+	3.99893i	−0.145460	+	0.189568i
$446$	10.0951	+	5.82843i	0.478018	+	0.275984i
$447$	−16.9706	+	7.02944i	−0.802680	+	0.332481i
$448$		0			0
$449$	11.1924	+	4.63604i	0.528201	+	0.218788i	0.630815	−	0.775933i	$-0.282721\pi$
$449$	11.1924	+	4.63604i	0.528201	+	0.218788i	−0.102614	+	0.994721i	$0.532721\pi$
$450$	5.04316	+	18.8213i	0.237737	+	0.887246i
$451$	3.06350	+	0.820863i	0.144255	+	0.0386530i
$452$	−6.59465	−	50.0913i	−0.310186	−	2.35610i
$453$	−4.72548	−	6.15837i	−0.222023	−	0.289345i
$454$	−38.7990	+	16.0711i	−1.82093	+	0.754253i
$455$		0			0
$456$	1.51472	+	3.65685i	0.0709332	+	0.171248i
$457$	−12.7228	+	3.40905i	−0.595146	+	0.159469i	−0.543804	−	0.839212i	$-0.683016\pi$
$457$	−12.7228	+	3.40905i	−0.595146	+	0.159469i	−0.0513418	+	0.998681i	$0.516350\pi$
$458$	−20.7279	−	35.9018i	−0.968552	−	1.67758i
$459$	−17.4741	−	12.6091i	−0.815620	−	0.588543i
$460$	−7.00000	+	12.1244i	−0.326377	+	0.565301i
$461$	17.0000	+	17.0000i	0.791769	+	0.791769i	0.981782	−	0.190013i	$-0.0608529\pi$
$461$	17.0000	+	17.0000i	0.791769	+	0.791769i	−0.190013	+	0.981782i	$0.560853\pi$
$462$		0			0
$463$			14.6274i			0.679794i	0.940463	+	0.339897i	$0.110392\pi$
$463$			14.6274i			0.679794i	−0.940463	+	0.339897i	$0.889608\pi$
$464$	−0.124140	+	0.942939i	−0.00576307	+	0.0437749i
$465$	6.43879	−	0.847683i	0.298592	−	0.0393104i
$466$	2.77003	+	21.0405i	0.128319	+	0.974681i
$467$	8.44460	+	31.5157i	0.390769	+	1.45837i	0.828868	+	0.559444i	$0.188985\pi$
$467$	8.44460	+	31.5157i	0.390769	+	1.45837i	−0.438099	+	0.898927i	$0.644348\pi$
$468$	7.00000	−	7.00000i	0.323575	−	0.323575i
$469$		0			0
$470$	3.65685	−	8.82843i	0.168678	−	0.407225i
$471$	−1.36433	+	10.3631i	−0.0628648	+	0.477506i
$472$	−22.9369	+	13.2426i	−1.05576	+	0.609542i
$473$	−1.31784	+	1.71744i	−0.0605942	+	0.0789679i
$474$	12.0599	−	3.23143i	0.553928	−	0.148424i
$475$	−3.65685			−0.167788
$476$		0			0
$477$	−2.58579			−0.118395
$478$	34.5792	−	9.26546i	1.58161	−	0.423792i
$479$	3.13471	−	4.08524i	0.143229	−	0.186659i	−0.716230	−	0.697864i	$-0.754134\pi$
$479$	3.13471	−	4.08524i	0.143229	−	0.186659i	0.859459	+	0.511205i	$0.170801\pi$
$480$	1.13770	−	0.656854i	0.0519289	−	0.0299812i
$481$	−1.70541	+	12.9539i	−0.0777599	+	0.590645i
$482$	−3.29289	+	7.94975i	−0.149987	+	0.362101i
$483$		0			0
$484$	−11.2929	+	11.2929i	−0.513313	+	0.513313i
$485$	−2.04454	−	7.63033i	−0.0928378	−	0.346475i
$486$	4.88214	+	37.0835i	0.221458	+	1.68214i
$487$	−26.0918	+	3.43505i	−1.18233	+	0.155657i	−0.695951	−	0.718089i	$-0.745017\pi$
$487$	−26.0918	+	3.43505i	−1.18233	+	0.155657i	−0.486382	+	0.873746i	$0.661684\pi$
$488$	2.20491	−	16.7479i	0.0998115	−	0.758144i
$489$		−	9.17157i		−	0.414753i
$490$		0			0
$491$	26.2426	+	26.2426i	1.18431	+	1.18431i	0.978615	+	0.205698i	$0.0659466\pi$
$491$	26.2426	+	26.2426i	1.18431	+	1.18431i	0.205698	+	0.978615i	$0.434053\pi$
$492$	2.51472	−	4.35562i	0.113372	−	0.196367i
$493$	1.29036	−	0.208673i	0.0581151	−	0.00939817i
$494$	1.41421	+	2.44949i	0.0636285	+	0.110208i
$495$	3.53225	−	0.946464i	0.158763	−	0.0425404i
$496$	9.00000	+	21.7279i	0.404112	+	0.975613i
$497$		0			0
$498$	28.1421	−	11.6569i	1.26108	−	0.522356i
$499$	−13.0653	−	17.0271i	−0.584884	−	0.762236i	0.403373	−	0.915036i	$-0.367838\pi$
$499$	−13.0653	−	17.0271i	−0.584884	−	0.762236i	−0.988257	+	0.152800i	$0.951171\pi$
$500$	−3.60057	−	27.3491i	−0.161023	−	1.22309i
$501$	2.06914	+	0.554425i	0.0924425	+	0.0247699i
$502$	−12.8001	−	47.7707i	−0.571297	−	2.13211i
$503$	−19.7279	−	8.17157i	−0.879625	−	0.364352i	−0.103273	−	0.994653i	$-0.532932\pi$
$503$	−19.7279	−	8.17157i	−0.879625	−	0.364352i	−0.776351	+	0.630301i	$0.782932\pi$
$504$		0			0
$505$	7.48528	−	3.10051i	0.333091	−	0.137971i
$506$	−26.1039	−	15.0711i	−1.16046	−	0.669991i
$507$	7.24810	−	9.44591i	0.321900	−	0.419508i
$508$	−5.26519	+	19.6500i	−0.233605	+	0.871826i
$509$	18.4853	−	32.0174i	0.819346	−	1.41915i	−0.0868193	−	0.996224i	$-0.527670\pi$
$509$	18.4853	−	32.0174i	0.819346	−	1.41915i	0.906165	−	0.422924i	$-0.138996\pi$
$510$	6.00000	+	5.65685i	0.265684	+	0.250490i
$511$		0			0
$512$	22.0919	+	22.0919i	0.976333	+	0.976333i
$513$	−4.29253	−	0.565122i	−0.189520	−	0.0249508i
$514$	12.8418	−	7.41421i	0.566427	−	0.327027i
$515$	7.58114	+	5.81722i	0.334065	+	0.256337i
$516$	2.08981	+	2.72349i	0.0919987	+	0.119895i
$517$	12.4853	+	5.17157i	0.549102	+	0.227446i
$518$		0			0
$519$	−2.24264	+	2.24264i	−0.0984410	+	0.0984410i
$520$	−3.79057	+	2.90861i	−0.166228	+	0.127551i
$521$	−18.4497	+	2.42895i	−0.808296	+	0.106414i	−0.523337	−	0.852126i	$-0.675313\pi$
$521$	−18.4497	+	2.42895i	−0.808296	+	0.106414i	−0.284959	+	0.958540i	$0.591980\pi$
$522$	−1.11023	−	0.851911i	−0.0485936	−	0.0372871i
$523$	1.01461	+	0.585786i	0.0443659	+	0.0256147i	0.522019	−	0.852934i	$-0.325179\pi$
$523$	1.01461	+	0.585786i	0.0443659	+	0.0256147i	−0.477653	+	0.878549i	$0.658512\pi$
$524$	−22.3137	−	53.8701i	−0.974779	−	2.35332i
$525$		0			0
$526$	25.3137			1.10373
$527$	25.0531	−	20.4228i	1.09133	−	0.889629i
$528$	−4.24264	−	7.34847i	−0.184637	−	0.319801i
$529$	0.0444063	−	0.165727i	0.00193071	−	0.00720551i
$530$	2.59077	+	0.341081i	0.112536	+	0.0148156i
$531$		−	10.9706i		−	0.476082i
$532$		0			0
$533$	0.656854	−	1.58579i	0.0284515	−	0.0686880i
$534$	−13.6532	+	10.4765i	−0.590832	+	0.453361i
$535$	0.331453	+	0.0888127i	0.0143300	+	0.00383971i
$536$	−4.99536	−	1.33850i	−0.215767	−	0.0578145i
$537$	5.15232	−	3.95351i	0.222339	−	0.170607i
$538$	24.4350	−	58.9914i	1.05347	−	2.54330i
$539$		0			0
$540$		−	15.3137i		−	0.658997i
$541$	18.2656	+	2.40471i	0.785299	+	0.103387i	0.512503	−	0.858685i	$-0.328718\pi$
$541$	18.2656	+	2.40471i	0.785299	+	0.103387i	0.272796	+	0.962072i	$0.412052\pi$
$542$	−13.8354	+	51.6344i	−0.594281	+	2.21789i
$543$	6.31371	+	10.9357i	0.270947	+	0.469294i
$544$	3.10115	−	5.75613i	0.132961	−	0.246792i
$545$	−11.8995			−0.509718
$546$		0			0
$547$	3.10051	+	7.48528i	0.132568	+	0.320048i	0.976199	−	0.216875i	$-0.0695866\pi$
$547$	3.10051	+	7.48528i	0.132568	+	0.320048i	−0.843631	+	0.536923i	$0.819587\pi$
$548$	55.4617	+	32.0208i	2.36921	+	1.36786i
$549$	5.55116	+	4.25956i	0.236918	+	0.181793i
$550$	27.6095	−	3.63485i	1.17727	−	0.154991i
$551$	0.208360	−	0.159880i	0.00887645	−	0.00681114i
$552$	−16.1421	+	16.1421i	−0.687055	+	0.687055i
$553$		0			0
$554$	44.5061	+	18.4350i	1.89088	+	0.783229i
$555$	4.65926	+	6.07206i	0.197774	+	0.257745i
$556$	−64.8564	−	49.7661i	−2.75053	−	2.11055i
$557$	17.1104	−	9.87868i	0.724990	−	0.418573i	−0.0915966	−	0.995796i	$-0.529197\pi$
$557$	17.1104	−	9.87868i	0.724990	−	0.418573i	0.816586	+	0.577223i	$0.195864\pi$
$558$	−34.3086	−	4.51682i	−1.45240	−	0.191212i
$559$	0.828427	+	0.828427i	0.0350387	+	0.0350387i
$560$		0			0
$561$	−8.00000	+	8.48528i	−0.337760	+	0.358249i
$562$	−2.29289	+	3.97141i	−0.0967199	+	0.167524i
$563$	8.99902	−	33.5848i	0.379264	−	1.41543i	−0.467751	−	0.883861i	$-0.654935\pi$
$563$	8.99902	−	33.5848i	0.379264	−	1.41543i	0.847014	−	0.531570i	$-0.178398\pi$
$564$	13.0459	−	17.0018i	0.549332	−	0.715904i
$565$	−8.74729	−	5.05025i	−0.368001	−	0.212466i
$566$	41.6274	−	17.2426i	1.74973	−	0.724762i
$567$		0			0
$568$	−22.0711	−	9.14214i	−0.926081	−	0.383595i
$569$	3.11660	+	11.6313i	0.130655	+	0.487610i	0.999978	−	0.00663368i	$-0.00211158\pi$
$569$	3.11660	+	11.6313i	0.130655	+	0.487610i	−0.869323	+	0.494244i	$0.835445\pi$
$570$	1.60040	+	0.428825i	0.0670333	+	0.0179615i
$571$	0.555082	+	4.21626i	0.0232294	+	0.176445i	0.999127	−	0.0417858i	$-0.0133047\pi$
$571$	0.555082	+	4.21626i	0.0232294	+	0.176445i	−0.975897	+	0.218231i	$0.929971\pi$
$572$	−8.61277	−	11.2244i	−0.360118	−	0.469315i
$573$	−20.0000	+	8.28427i	−0.835512	+	0.346080i
$574$		0			0
$575$	−8.07107	−	19.4853i	−0.336587	−	0.812592i
$576$	−17.3582	+	4.65112i	−0.723260	+	0.193797i
$577$	13.5355	+	23.4442i	0.563492	+	0.975996i	0.997188	+	0.0749372i	$0.0238756\pi$
$577$	13.5355	+	23.4442i	0.563492	+	0.975996i	−0.433697	+	0.901059i	$0.642791\pi$
$578$	40.1994	+	8.27201i	1.67207	+	0.344070i
$579$	−1.24264	+	2.15232i	−0.0516424	+	0.0894472i
$580$	0.656854	+	0.656854i	0.0272744	+	0.0272744i
$581$		0			0
$582$		−	26.9706i		−	1.11797i
$583$	−0.482362	+	3.66390i	−0.0199774	+	0.151743i
$584$	56.6064	−	7.45237i	2.34239	−	0.308381i
$585$	−0.258321	−	1.96214i	−0.0106803	−	0.0811247i
$586$	−7.71255	−	28.7836i	−0.318602	−	1.18904i
$587$	32.0416	−	32.0416i	1.32250	−	1.32250i	0.410753	−	0.911747i	$-0.365266\pi$
$587$	32.0416	−	32.0416i	1.32250	−	1.32250i	0.911747	−	0.410753i	$-0.134734\pi$
$588$		0			0
$589$	2.48528	−	6.00000i	0.102404	−	0.247226i
$590$	−1.44709	+	10.9917i	−0.0595756	+	0.452521i
$591$	−4.35562	+	2.51472i	−0.179166	+	0.103442i
$592$	−16.8727	+	21.9889i	−0.693462	+	0.903738i
$593$	−12.4884	+	3.34625i	−0.512837	+	0.137414i	−0.505951	−	0.862562i	$-0.668858\pi$
$593$	−12.4884	+	3.34625i	−0.512837	+	0.137414i	−0.00688551	+	0.999976i	$0.502192\pi$
$594$	32.9706			1.35280
$595$		0			0
$596$	−64.9706			−2.66130
$597$	−12.0599	+	3.23143i	−0.493577	+	0.132254i
$598$	−9.93061	+	12.9418i	−0.406093	+	0.529230i
$599$	−9.20361	+	5.31371i	−0.376049	+	0.217112i	−0.676098	−	0.736812i	$-0.736330\pi$
$599$	−9.20361	+	5.31371i	−0.376049	+	0.217112i	0.300049	+	0.953924i	$0.402997\pi$
$600$	2.75289	−	20.9103i	0.112386	−	0.853659i
$601$	−3.22183	+	7.77817i	−0.131421	+	0.317278i	−0.975868	−	0.218360i	$-0.929929\pi$
$601$	−3.22183	+	7.77817i	−0.131421	+	0.317278i	0.844447	+	0.535639i	$0.179929\pi$
$602$		0			0
$603$	1.51472	−	1.51472i	0.0616841	−	0.0616841i
$604$	−7.10610	−	26.5203i	−0.289143	−	1.07910i
$605$	0.416742	+	3.16547i	0.0169430	+	0.128695i
$606$	27.4253	−	3.61061i	1.11408	−	0.146671i
$607$	−2.13929	+	16.2495i	−0.0868311	+	0.659547i	0.891578	+	0.452868i	$0.149599\pi$
$607$	−2.13929	+	16.2495i	−0.0868311	+	0.659547i	−0.978409	+	0.206680i	$0.933734\pi$
$608$		−	1.31371i		−	0.0532779i
$609$		0			0
$610$	−5.00000	−	5.00000i	−0.202444	−	0.202444i
$611$	3.65685	−	6.33386i	0.147940	−	0.256240i
$612$	−15.1601	−	24.5596i	−0.612810	−	0.992761i
$613$	−2.65685	−	4.60181i	−0.107309	−	0.185865i	0.807370	−	0.590045i	$-0.200890\pi$
$613$	−2.65685	−	4.60181i	−0.107309	−	0.185865i	−0.914679	+	0.404180i	$0.867557\pi$
$614$	−60.9622	+	16.3348i	−2.46023	+	0.659218i
$615$	−0.384776	−	0.928932i	−0.0155157	−	0.0374582i
$616$		0			0
$617$	−2.70711	+	1.12132i	−0.108984	+	0.0451427i	−0.436509	−	0.899700i	$-0.643785\pi$
$617$	−2.70711	+	1.12132i	−0.108984	+	0.0451427i	0.327525	+	0.944842i	$0.393785\pi$
$618$	19.8612	+	25.8836i	0.798935	+	1.04119i
$619$	−3.71761	−	28.2381i	−0.149424	−	1.13498i	−0.887679	−	0.460463i	$-0.847683\pi$
$619$	−3.71761	−	28.2381i	−0.149424	−	1.13498i	0.738255	−	0.674521i	$-0.235650\pi$
$620$	22.1879	+	5.94522i	0.891086	+	0.238766i
$621$	−6.46286	−	24.1197i	−0.259346	−	0.967891i
$622$	−57.2843	−	23.7279i	−2.29689	−	0.951403i
$623$		0			0
$624$	−4.24264	+	1.75736i	−0.169842	+	0.0703507i
$625$	14.3382	+	8.27817i	0.573529	+	0.331127i
$626$	14.5099	−	18.9097i	0.579933	−	0.755784i
$627$	−0.606451	+	2.26330i	−0.0242193	+	0.0903877i
$628$	−18.4853	+	32.0174i	−0.737643	+	1.27764i
$629$	35.6066	+	13.5355i	1.41973	+	0.539697i
$630$		0			0
$631$	−20.7279	−	20.7279i	−0.825166	−	0.825166i	0.161678	−	0.986844i	$-0.448309\pi$
$631$	−20.7279	−	20.7279i	−0.825166	−	0.825166i	−0.986844	+	0.161678i	$0.948309\pi$
$632$	20.9103	+	2.75289i	0.831766	+	0.109504i
$633$	−20.0162	+	11.5563i	−0.795572	+	0.459324i
$634$	36.8565	+	28.2810i	1.46376	+	1.12318i
$635$	2.47579	+	3.22652i	0.0982489	+	0.128040i
$636$	5.41421	+	2.24264i	0.214688	+	0.0889265i
$637$		0			0
$638$	−1.41421	+	1.41421i	−0.0559893	+	0.0559893i
$639$	7.85053	−	6.02392i	0.310562	−	0.238303i
$640$	15.5985	−	2.05359i	0.616587	−	0.0811752i
$641$	32.8576	+	25.2125i	1.29780	+	0.995834i	0.999140	+	0.0414734i	$0.0132052\pi$
$641$	32.8576	+	25.2125i	1.29780	+	0.995834i	0.298657	+	0.954361i	$0.403461\pi$
$642$	1.01461	+	0.585786i	0.0400435	+	0.0231191i
$643$	11.0416	+	26.6569i	0.435439	+	1.05124i	0.977506	+	0.210908i	$0.0676421\pi$
$643$	11.0416	+	26.6569i	0.435439	+	1.05124i	−0.542066	+	0.840336i	$0.682358\pi$
$644$		0			0
$645$	0.686292			0.0270227
$646$	7.89898	−	2.36773i	0.310781	−	0.0931569i
$647$	1.41421	+	2.44949i	0.0555985	+	0.0962994i	0.892485	−	0.451077i	$-0.148960\pi$
$647$	1.41421	+	2.44949i	0.0555985	+	0.0962994i	−0.836887	+	0.547376i	$0.815627\pi$
$648$	0.196019	−	0.731553i	0.00770035	−	0.0287381i
$649$	−15.5446	−	2.04649i	−0.610180	−	0.0803317i
$650$		−	15.0711i		−	0.591136i
$651$		0			0
$652$	12.4142	−	29.9706i	0.486178	−	1.17374i
$653$	−7.53799	+	5.78410i	−0.294984	+	0.226349i	−0.745641	−	0.666348i	$-0.767857\pi$
$653$	−7.53799	+	5.78410i	−0.294984	+	0.226349i	0.450657	+	0.892697i	$0.351190\pi$
$654$	−39.2431	−	10.5151i	−1.53453	−	0.411175i
$655$	−11.2597	−	3.01702i	−0.439951	−	0.117885i
$656$	2.88870	−	2.21658i	0.112785	−	0.0865428i
$657$	−9.05025	+	21.8492i	−0.353084	+	0.852420i
$658$		0			0
$659$			8.48528i			0.330540i	0.986248	+	0.165270i	$0.0528495\pi$
$659$			8.48528i			0.330540i	−0.986248	+	0.165270i	$0.947151\pi$
$660$	−8.21682	−	1.08176i	−0.319839	−	0.0421076i
$661$	0.314000	−	1.17186i	0.0122132	−	0.0455802i	−0.959550	−	0.281537i	$-0.909156\pi$
$661$	0.314000	−	1.17186i	0.0122132	−	0.0455802i	0.971764	+	0.235957i	$0.0758224\pi$
$662$	−26.3137	−	45.5767i	−1.02271	−	1.77139i
$663$	3.98779	+	4.89193i	0.154873	+	0.189987i
$664$	51.4558			1.99687
$665$		0			0
$666$	−15.6066	−	37.6777i	−0.604744	−	1.45998i
$667$	1.31178	+	0.757359i	0.0507925	+	0.0293251i
$668$	6.01104	+	4.61243i	0.232574	+	0.178460i
$669$	5.18154	−	0.682163i	0.200330	−	0.0263739i
$670$	−1.71744	+	1.31784i	−0.0663505	+	0.0509125i
$671$	7.07107	−	7.07107i	0.272976	−	0.272976i
$672$		0			0
$673$	4.12132	+	1.70711i	0.158865	+	0.0658041i	0.460699	−	0.887556i	$-0.347599\pi$
$673$	4.12132	+	1.70711i	0.158865	+	0.0658041i	−0.301834	+	0.953361i	$0.597599\pi$
$674$	−8.25990	−	10.7645i	−0.318159	−	0.414633i
$675$	18.3025	+	14.0440i	0.704463	+	0.540554i
$676$	36.4707	−	21.0563i	1.40272	−	0.809860i
$677$	37.7661	+	4.97200i	1.45147	+	0.191089i	0.814663	−	0.579935i	$-0.196922\pi$
$677$	37.7661	+	4.97200i	1.45147	+	0.191089i	0.636806	+	0.771024i	$0.280255\pi$
$678$	−24.3848	−	24.3848i	−0.936492	−	0.936492i
$679$		0			0
$680$	5.70711	+	12.7071i	0.218858	+	0.487295i
$681$	−9.41421	+	16.3059i	−0.360753	+	0.624843i
$682$	−12.8001	+	47.7707i	−0.490142	+	1.82923i
$683$	−14.4768	+	18.8665i	−0.553940	+	0.721908i	−0.983455	−	0.181151i	$-0.942018\pi$
$683$	−14.4768	+	18.8665i	−0.553940	+	0.721908i	0.429515	+	0.903060i	$0.358684\pi$
$684$	−5.02207	−	2.89949i	−0.192024	−	0.110865i
$685$	11.8284	−	4.89949i	0.451941	−	0.187200i
$686$		0			0
$687$	−17.1716	−	7.11270i	−0.655136	−	0.271366i
$688$	0.643238	+	2.40060i	0.0245232	+	0.0915219i
$689$	1.93185	+	0.517638i	0.0735977	+	0.0197204i
$690$	1.24728	+	9.47407i	0.0474833	+	0.360672i
$691$	−12.1335	−	15.8126i	−0.461579	−	0.601541i	0.503340	−	0.864088i	$-0.332104\pi$
$691$	−12.1335	−	15.8126i	−0.461579	−	0.601541i	−0.964919	+	0.262547i	$0.915438\pi$
$692$	−10.3640	+	4.29289i	−0.393979	+	0.163191i
$693$		0			0
$694$	−15.4853	−	37.3848i	−0.587813	−	1.41911i
$695$	−15.7863	+	4.22992i	−0.598807	+	0.160450i
$696$	0.757359	+	1.31178i	0.0287076	+	0.0497231i
$697$	−4.05806	−	2.92825i	−0.153710	−	0.110916i
$698$	5.12132	−	8.87039i	0.193845	−	0.335749i
$699$	6.72792	+	6.72792i	0.254473	+	0.254473i
$700$		0			0
$701$			37.6985i			1.42385i	0.702254	+	0.711926i	$0.252177\pi$
$701$			37.6985i			1.42385i	−0.702254	+	0.711926i	$0.747823\pi$
$702$	2.32905	−	17.6909i	0.0879043	−	0.667699i
$703$	7.58819	−	0.999004i	0.286194	−	0.0376782i
$704$	3.35229	+	25.4632i	0.126344	+	0.959680i
$705$	−1.10885	−	4.13829i	−0.0417617	−	0.155857i
$706$	23.8995	−	23.8995i	0.899469	−	0.899469i
$707$		0			0
$708$	−9.51472	+	22.9706i	−0.357585	+	0.863287i
$709$	−3.16963	+	24.0758i	−0.119038	+	0.904184i	0.822850	+	0.568258i	$0.192382\pi$
$709$	−3.16963	+	24.0758i	−0.119038	+	0.904184i	−0.941888	+	0.335926i	$0.890951\pi$
$710$	−8.66025	+	5.00000i	−0.325014	+	0.187647i
$711$	−5.31818	+	6.93078i	−0.199447	+	0.259925i
$712$	−28.0805	+	7.52415i	−1.05236	+	0.281979i
$713$	37.4558			1.40273
$714$		0			0
$715$	−2.82843			−0.105777
$716$	22.1879	−	5.94522i	0.829199	−	0.222183i
$717$	9.77073	−	12.7335i	0.364894	−	0.475540i
$718$	60.2736	−	34.7990i	2.24939	−	1.29869i
$719$	4.43406	−	33.6800i	0.165362	−	1.25605i	−0.684486	−	0.729026i	$-0.739973\pi$
$719$	4.43406	−	33.6800i	0.165362	−	1.25605i	0.849849	−	0.527027i	$-0.176693\pi$
$720$	1.60660	−	3.87868i	0.0598745	−	0.144550i
$721$		0			0
$722$	−31.2635	+	31.2635i	−1.16351	+	1.16351i
$723$	0.998489	+	3.72641i	0.0371342	+	0.138587i
$724$	5.82972	+	44.2811i	0.216660	+	1.64570i
$725$	−1.38745	+	0.182661i	−0.0515284	+	0.00678385i
$726$	−1.42285	+	10.8076i	−0.0528068	+	0.401107i
$727$			43.1127i			1.59896i	0.600692	+	0.799481i	$0.294892\pi$
$727$			43.1127i			1.59896i	−0.600692	+	0.799481i	$0.705108\pi$
$728$		0			0
$729$	12.2218	+	12.2218i	0.452660	+	0.452660i
$730$	11.9497	−	20.6976i	0.442280	−	0.766051i
$731$	2.90654	−	1.79415i	0.107502	−	0.0663589i
$732$	−7.92893	−	13.7333i	−0.293062	−	0.507598i
$733$	34.8135	−	9.32826i	1.28587	−	0.344547i	0.449778	−	0.893140i	$-0.351503\pi$
$733$	34.8135	−	9.32826i	1.28587	−	0.344547i	0.836089	+	0.548593i	$0.184836\pi$
$734$	4.07107	+	9.82843i	0.150266	+	0.362774i
$735$		0			0
$736$	7.00000	−	2.89949i	0.258023	−	0.106877i
$737$	−1.86370	−	2.42883i	−0.0686504	−	0.0894669i
$738$	0.699303	+	5.31173i	0.0257417	+	0.195528i
$739$	−21.5250	−	5.76759i	−0.791808	−	0.212164i	−0.159824	−	0.987146i	$-0.551093\pi$
$739$	−21.5250	−	5.76759i	−0.791808	−	0.212164i	−0.631984	+	0.774981i	$0.717759\pi$
$740$	7.00651	+	26.1486i	0.257564	+	0.961243i
$741$	1.17157	+	0.485281i	0.0430388	+	0.0178273i
$742$		0			0
$743$	47.1421	−	19.5269i	1.72948	−	0.716373i	0.730020	−	0.683426i	$-0.239511\pi$
$743$	47.1421	−	19.5269i	1.72948	−	0.716373i	0.999457	−	0.0329473i	$-0.0104893\pi$
$744$	32.4377	+	18.7279i	1.18922	+	0.686599i
$745$	−7.90702	+	10.3046i	−0.289691	+	0.377533i
$746$	−7.22092	+	26.9488i	−0.264377	+	0.986667i
$747$	−10.6569	+	18.4582i	−0.389914	+	0.675351i
$748$	−37.6274	+	16.8995i	−1.37579	+	0.617907i
$749$		0			0
$750$	−13.3137	−	13.3137i	−0.486148	−	0.486148i
$751$	−47.1862	−	6.21218i	−1.72185	−	0.226686i	−0.796191	−	0.605045i	$-0.793155\pi$
$751$	−47.1862	−	6.21218i	−1.72185	−	0.226686i	−0.925659	+	0.378359i	$0.876488\pi$
$752$	13.4361	−	7.75736i	0.489966	−	0.282882i
$753$	−17.5911	−	13.4981i	−0.641056	−	0.491899i
$754$	0.658919	+	0.858719i	0.0239964	+	0.0312727i
$755$	−5.07107	−	2.10051i	−0.184555	−	0.0764452i
$756$		0			0
$757$	−1.79899	+	1.79899i	−0.0653854	+	0.0653854i	−0.739043	−	0.673658i	$-0.764722\pi$
$757$	−1.79899	+	1.79899i	−0.0653854	+	0.0653854i	0.673658	+	0.739043i	$0.264722\pi$
$758$	−5.00498	+	3.84046i	−0.181789	+	0.139492i
$759$	−13.3984	+	1.76393i	−0.486330	+	0.0640265i
$760$	2.22047	+	1.70382i	0.0805447	+	0.0618042i
$761$	32.6478	+	18.8492i	1.18348	+	0.683285i	0.956818	−	0.290688i	$-0.0938842\pi$
$761$	32.6478	+	18.8492i	1.18348	+	0.683285i	0.226666	+	0.973973i	$0.427218\pi$
$762$	5.31371	+	12.8284i	0.192495	+	0.464725i
$763$		0			0
$764$	−76.5685			−2.77015
$765$	−5.74027	−	0.584478i	−0.207540	−	0.0211318i
$766$	−27.1421	−	47.0116i	−0.980685	−	1.69860i
$767$	−2.19615	+	8.19615i	−0.0792985	+	0.295946i
$768$	32.1624	+	4.23426i	1.16056	+	0.152791i
$769$			12.7279i			0.458981i	0.973311	+	0.229490i	$0.0737059\pi$
$769$			12.7279i			0.458981i	−0.973311	+	0.229490i	$0.926294\pi$
$770$		0			0
$771$	2.54416	−	6.14214i	0.0916255	−	0.221204i
$772$	−6.97394	+	5.35129i	−0.250997	+	0.192597i
$773$	0.800199	+	0.214413i	0.0287812	+	0.00771189i	0.273181	−	0.961963i	$-0.411924\pi$
$773$	0.800199	+	0.214413i	0.0287812	+	0.00771189i	−0.244400	+	0.969675i	$0.578591\pi$
$774$	−3.53225	−	0.946464i	−0.126964	−	0.0340199i
$775$	−27.4537	+	21.0660i	−0.986168	+	0.756713i
$776$	17.4350	−	42.0919i	0.625881	−	1.51101i
$777$		0			0
$778$			29.3137i			1.05095i
$779$	−0.996867	−	0.131240i	−0.0357165	−	0.00470216i
$780$	−1.16088	+	4.33245i	−0.0415660	+	0.155127i
$781$	−7.07107	−	12.2474i	−0.253023	−	0.438248i
$782$	30.0501	+	36.8633i	1.07459	+	1.31823i
$783$	−1.65685			−0.0592111
$784$		0			0
$785$	2.82843	+	6.82843i	0.100951	+	0.243717i
$786$	−34.4669	−	19.8995i	−1.22939	−	0.709791i
$787$	16.3157	+	12.5195i	0.581591	+	0.446270i	0.857189	−	0.515003i	$-0.172209\pi$
$787$	16.3157	+	12.5195i	0.581591	+	0.446270i	−0.275598	+	0.961273i	$0.588876\pi$
$788$	−17.6370	+	2.32195i	−0.628291	+	0.0827160i
$789$	9.00392	−	6.90895i	0.320548	−	0.245965i
$790$	6.24264	−	6.24264i	0.222103	−	0.222103i
$791$		0			0
$792$	19.4853	+	8.07107i	0.692379	+	0.286793i
$793$	−3.29459	−	4.29360i	−0.116994	−	0.152470i
$794$	34.0720	+	26.1444i	1.20917	+	0.927828i
$795$	1.01461	−	0.585786i	0.0359846	−	0.0207757i
$796$	−43.7827	−	5.76410i	−1.55184	−	0.204303i
$797$	−17.8284	−	17.8284i	−0.631515	−	0.631515i	0.316933	−	0.948448i	$-0.397347\pi$
$797$	−17.8284	−	17.8284i	−0.631515	−	0.631515i	−0.948448	+	0.316933i	$0.897347\pi$
$798$		0			0
$799$	−15.5147	−	14.6274i	−0.548871	−	0.517481i
$800$	−3.50000	+	6.06218i	−0.123744	+	0.214330i
$801$	3.11660	−	11.6313i	0.110120	−	0.410973i
$802$	0.851911	−	1.11023i	0.0300820	−	0.0392037i
$803$	29.2708	+	16.8995i	1.03294	+	0.596370i
$804$	−4.48528	+	1.85786i	−0.158184	+	0.0655218i
$805$		0			0
$806$	24.7279	+	10.2426i	0.871004	+	0.360782i
$807$	−7.40932	−	27.6520i	−0.260820	−	0.973395i
$808$	45.1357	+	12.0941i	1.58787	+	0.425468i
$809$	4.60668	+	34.9912i	0.161962	+	1.23022i	0.858541	+	0.512745i	$0.171371\pi$
$809$	4.60668	+	34.9912i	0.161962	+	1.23022i	−0.696579	+	0.717480i	$0.745295\pi$
$810$	−0.192993	−	0.251513i	−0.00678108	−	0.00883727i
$811$	−50.9411	+	21.1005i	−1.78878	+	0.740939i	−0.798481	+	0.602020i	$0.794363\pi$
$811$	−50.9411	+	21.1005i	−1.78878	+	0.740939i	−0.990304	+	0.138919i	$0.955637\pi$
$812$		0			0
$813$	9.17157	+	22.1421i	0.321661	+	0.776559i
$814$	−56.2983	+	15.0851i	−1.97325	+	0.528732i
$815$	−3.24264	−	5.61642i	−0.113585	−	0.196735i
$816$	2.13737	+	13.2167i	0.0748228	+	0.462679i
$817$	0.343146	−	0.594346i	0.0120052	−	0.0207935i
$818$	5.65685	+	5.65685i	0.197787	+	0.197787i
$819$		0			0
$820$		−	3.55635i		−	0.124193i
$821$	−5.01632	+	38.1027i	−0.175071	+	1.32979i	0.647906	+	0.761720i	$0.275645\pi$
$821$	−5.01632	+	38.1027i	−0.175071	+	1.32979i	−0.822977	+	0.568075i	$0.807689\pi$
$822$	43.3382	−	5.70558i	1.51159	−	0.199005i
$823$	−1.27152	−	9.65819i	−0.0443226	−	0.336663i	−0.999212	−	0.0397005i	$-0.987360\pi$
$823$	−1.27152	−	9.65819i	−0.0443226	−	0.336663i	0.954889	−	0.296963i	$-0.0959737\pi$
$824$	14.2642	+	53.2348i	0.496918	+	1.85452i
$825$	8.82843	−	8.82843i	0.307366	−	0.307366i
$826$		0			0
$827$	−17.9289	+	43.2843i	−0.623450	+	1.50514i	0.224177	+	0.974549i	$0.428031\pi$
$827$	−17.9289	+	43.2843i	−0.623450	+	1.50514i	−0.847627	+	0.530593i	$0.821969\pi$
$828$	4.36550	−	33.1592i	0.151712	−	1.15236i
$829$	−46.7144	+	26.9706i	−1.62246	+	0.936726i	−0.636198	+	0.771526i	$0.719494\pi$
$829$	−46.7144	+	26.9706i	−1.62246	+	0.936726i	−0.986260	+	0.165200i	$0.947173\pi$
$830$	13.1121	−	17.0881i	0.455129	−	0.593136i
$831$	20.8620	−	5.58997i	0.723696	−	0.193914i
$832$	13.8995			0.481878
$833$		0			0
$834$	−55.7990			−1.93216
$835$	1.46311	−	0.392038i	0.0506329	−	0.0135670i
$836$	−5.04524	+	6.57509i	−0.174493	+	0.227404i
$837$	−35.4815	+	20.4853i	−1.22642	+	0.708075i
$838$	−4.19998	+	31.9020i	−0.145086	+	1.10204i
$839$	−6.41421	+	15.4853i	−0.221443	+	0.534611i	−0.995086	−	0.0990102i	$-0.968432\pi$
$839$	−6.41421	+	15.4853i	−0.221443	+	0.534611i	0.773643	+	0.633622i	$0.218432\pi$
$840$		0			0
$841$	−20.4350	+	20.4350i	−0.704656	+	0.704656i
$842$	−9.11385	−	34.0133i	−0.314084	−	1.17218i
$843$	0.268362	+	2.03841i	0.00924287	+	0.0702065i
$844$	−81.0504	+	10.6705i	−2.78987	+	0.367293i
$845$	1.09890	−	8.34701i	0.0378035	−	0.287146i
$846$			22.8284i			0.784857i
$847$		0			0
$848$	3.00000	+	3.00000i	0.103020	+	0.103020i
$849$	10.1005	−	17.4946i	0.346648	−	0.600413i
$850$	−42.7584	−	10.1186i	−1.46660	−	0.347064i
$851$	22.0711	+	38.2282i	0.756586	+	1.31045i
$852$	−21.6622	+	5.80438i	−0.742136	+	0.198855i
$853$	−7.33452	−	17.7071i	−0.251129	−	0.606280i	0.747166	−	0.664637i	$-0.231414\pi$
$853$	−7.33452	−	17.7071i	−0.251129	−	0.606280i	−0.998296	+	0.0583572i	$0.981414\pi$
$854$		0			0
$855$	−1.07107	+	0.443651i	−0.0366297	+	0.0151725i
$856$	1.20478	+	1.57011i	0.0411787	+	0.0536651i
$857$	1.20590	+	9.15976i	0.0411929	+	0.312891i	0.999620	+	0.0275547i	$0.00877205\pi$
$857$	1.20590	+	9.15976i	0.0411929	+	0.312891i	−0.958427	+	0.285337i	$0.907895\pi$
$858$	−9.32780	−	2.49938i	−0.318446	−	0.0853274i
$859$	9.05105	+	33.7790i	0.308818	+	1.15252i	0.929609	+	0.368548i	$0.120145\pi$
$859$	9.05105	+	33.7790i	0.308818	+	1.15252i	−0.620791	+	0.783976i	$0.713188\pi$
$860$	2.24264	+	0.928932i	0.0764734	+	0.0316763i
$861$		0			0
$862$	−16.3137	+	6.75736i	−0.555647	+	0.230157i
$863$	−9.20361	−	5.31371i	−0.313295	−	0.180881i	0.335105	−	0.942181i	$-0.391228\pi$
$863$	−9.20361	−	5.31371i	−0.313295	−	0.180881i	−0.648400	+	0.761300i	$0.724561\pi$
$864$	−5.04524	+	6.57509i	−0.171643	+	0.223689i
$865$	−0.580438	+	2.16622i	−0.0197355	+	0.0736538i
$866$	25.1421	−	43.5475i	0.854365	−	1.47980i
$867$	16.5563	−	8.02944i	0.562283	−	0.272694i
$868$		0			0
$869$	8.82843	+	8.82843i	0.299484	+	0.299484i
$870$	0.628626	+	0.0827602i	0.0213124	+	0.00280583i
$871$	−1.43488	+	0.828427i	−0.0486190	+	0.0280702i
$872$	−54.4476	−	41.7791i	−1.84383	−	1.41482i
$873$	11.4883	+	14.9718i	0.388819	+	0.506719i
$874$	8.82843	+	3.65685i	0.298626	+	0.123695i
$875$		0			0
$876$	37.8995	−	37.8995i	1.28051	−	1.28051i
$877$	−39.8494	+	30.5775i	−1.34562	+	1.03253i	−0.350224	+	0.936666i	$0.613894\pi$
$877$	−39.8494	+	30.5775i	−1.34562	+	1.03253i	−0.995395	+	0.0958630i	$0.969439\pi$
$878$	25.4632	−	3.35229i	0.859341	−	0.113134i
$879$	−10.5993	−	8.13313i	−0.357506	−	0.274324i
$880$	−5.19615	−	3.00000i	−0.175162	−	0.101130i
$881$	12.8787	+	31.0919i	0.433894	+	1.04751i	0.978020	+	0.208509i	$0.0668611\pi$
$881$	12.8787	+	31.0919i	0.433894	+	1.04751i	−0.544127	+	0.839003i	$0.683139\pi$
$882$		0			0
$883$	8.00000			0.269221			0.134611	−	0.990899i	$-0.457022\pi$
$883$	8.00000			0.269221			0.134611	+	0.990899i	$0.457022\pi$
$884$	6.40969	+	21.3834i	0.215581	+	0.719201i
$885$	2.48528	+	4.30463i	0.0835418	+	0.144699i
$886$	14.8707	−	55.4981i	0.499590	−	1.86449i
$887$	−43.6749	−	5.74990i	−1.46646	−	0.193063i	−0.645373	−	0.763868i	$-0.723298\pi$
$887$	−43.6749	−	5.74990i	−1.46646	−	0.193063i	−0.821086	+	0.570805i	$0.806631\pi$
$888$			44.1421i			1.48131i
$889$		0			0
$890$	−4.65685	+	11.2426i	−0.156098	+	0.376854i
$891$	0.355693	−	0.272933i	0.0119162	−	0.00914360i
$892$	17.8554	+	4.78434i	0.597843	+	0.160192i
$893$	−4.13829	−	1.10885i	−0.138483	−	0.0371063i
$894$	−35.1822	+	26.9963i	−1.17667	+	0.902890i
$895$	1.75736	−	4.24264i	0.0587420	−	0.141816i
$896$		0			0
$897$			7.31371i			0.244198i
$898$	28.9969	+	3.81752i	0.967639	+	0.127392i
$899$	0.643238	−	2.40060i	0.0214532	−	0.0800644i
$900$	15.4497	+	26.7597i	0.514992	+	0.891992i
$901$	2.76563	−	5.13335i	0.0921364	−	0.171017i
$902$	7.65685			0.254945
$903$		0			0
$904$	−22.2929	−	53.8198i	−0.741451	−	1.79002i
$905$	7.73268	+	4.46447i	0.257043	+	0.148404i
$906$	−14.8676	−	11.4083i	−0.493944	−	0.379016i
$907$	−13.3221	+	1.75389i	−0.442353	+	0.0582369i	−0.348413	−	0.937341i	$-0.613279\pi$
$907$	−13.3221	+	1.75389i	−0.442353	+	0.0582369i	−0.0939396	+	0.995578i	$0.529946\pi$
$908$	−52.8344	+	40.5412i	−1.75337	+	1.34541i
$909$	−13.6863	+	13.6863i	−0.453946	+	0.453946i
$910$		0			0
$911$	5.24264	+	2.17157i	0.173696	+	0.0719474i	0.467837	−	0.883815i	$-0.345033\pi$
$911$	5.24264	+	2.17157i	0.173696	+	0.0719474i	−0.294141	+	0.955762i	$0.595033\pi$
$912$	1.63760	+	2.13416i	0.0542263	+	0.0706691i
$913$	24.1662	+	18.5434i	0.799784	+	0.613696i
$914$	−27.5387	+	15.8995i	−0.910900	+	0.525909i
$915$	−3.14313	−	0.413801i	−0.103909	−	0.0136798i
$916$	−46.4853	−	46.4853i	−1.53592	−	1.53592i
$917$		0			0
$918$	−48.6274	−	18.4853i	−1.60494	−	0.610105i
$919$	−9.65685	+	16.7262i	−0.318550	+	0.551745i	−0.980186	−	0.198080i	$-0.936529\pi$
$919$	−9.65685	+	16.7262i	−0.318550	+	0.551745i	0.661636	+	0.749826i	$0.269863\pi$
$920$	−4.17789	+	15.5921i	−0.137741	+	0.514057i
$921$	−17.2255	+	22.4488i	−0.567601	+	0.739712i
$922$	50.2655	+	29.0208i	1.65541	+	0.955750i
$923$	−7.07107	+	2.92893i	−0.232747	+	0.0964070i
$924$		0			0
$925$	−37.6777	−	15.6066i	−1.23883	−	0.513142i
$926$	9.13986	+	34.1104i	0.300354	+	1.12094i
$927$	−22.0506	−	5.90843i	−0.724236	−	0.194058i
$928$	−0.0656200	−	0.498434i	−0.00215408	−	0.0163619i
$929$	10.5564	+	13.7574i	0.346345	+	0.451365i	0.933749	−	0.357928i	$-0.116517\pi$
$929$	10.5564	+	13.7574i	0.346345	+	0.451365i	−0.587404	+	0.809294i	$0.699850\pi$
$930$	14.4853	−	6.00000i	0.474991	−	0.196748i
$931$		0			0
$932$	12.8787	+	31.0919i	0.421855	+	1.01845i
$933$	−26.8518	+	7.19491i	−0.879087	+	0.235551i
$934$	39.3848	+	68.2164i	1.28871	+	2.23211i
$935$	−1.89898	+	8.02458i	−0.0621033	+	0.262432i
$936$	5.70711	−	9.88500i	0.186543	−	0.323101i
$937$	19.4853	+	19.4853i	0.636556	+	0.636556i	0.949704	−	0.313148i	$-0.101384\pi$
$937$	19.4853	+	19.4853i	0.636556	+	0.636556i	−0.313148	+	0.949704i	$0.601384\pi$
$938$		0			0
$939$		−	10.6863i		−	0.348734i
$940$	1.97793	−	15.0239i	0.0645129	−	0.490024i
$941$	39.5441	−	5.20608i	1.28910	−	0.169713i	0.545372	−	0.838194i	$-0.316388\pi$
$941$	39.5441	−	5.20608i	1.28910	−	0.169713i	0.743729	+	0.668481i	$0.233055\pi$
$942$	3.29377	+	25.0187i	0.107317	+	0.815153i
$943$	−1.50089	−	5.60139i	−0.0488757	−	0.182406i
$944$	−12.7279	+	12.7279i	−0.414259	+	0.414259i
$945$		0			0
$946$	−2.00000	+	4.82843i	−0.0650256	+	0.156986i
$947$	−4.00018	+	30.3844i	−0.129988	+	0.987359i	0.794799	+	0.606873i	$0.207576\pi$
$947$	−4.00018	+	30.3844i	−0.129988	+	0.987359i	−0.924787	+	0.380486i	$0.875757\pi$
$948$	17.1464	−	9.89949i	0.556890	−	0.321521i
$949$	11.1354	−	14.5119i	0.361470	−	0.471077i
$950$	−8.52761	+	2.28497i	−0.276672	+	0.0741341i
$951$	20.8284			0.675408
$952$		0			0
$953$	49.6985			1.60989			0.804946	−	0.593348i	$-0.202194\pi$
$953$	49.6985			1.60989			0.804946	+	0.593348i	$0.202194\pi$
$954$	−6.02993	+	1.61571i	−0.195226	+	0.0523107i
$955$	−9.31852	+	12.1441i	−0.301540	+	0.392975i
$956$	49.1639	−	28.3848i	1.59007	−	0.918029i
$957$	−0.117041	+	0.889012i	−0.00378339	+	0.0287377i
$958$	4.75736	−	11.4853i	0.153703	−	0.371073i
$959$		0			0
$960$	5.75736	−	5.75736i	0.185818	−	0.185818i
$961$	−7.88255	−	29.4181i	−0.254276	−	0.948971i
$962$	4.11722	+	31.2734i	0.132744	+	1.00829i
$963$	−0.812747	+	0.107000i	−0.0261904	+	0.00344803i
$964$	−1.78107	+	13.5286i	−0.0573643	+	0.435725i
$965$			1.75736i			0.0565714i
$966$		0			0
$967$	−30.8701	−	30.8701i	−0.992714	−	0.992714i	0.00725952	−	0.999974i	$-0.497689\pi$
$967$	−30.8701	−	30.8701i	−0.992714	−	0.992714i	−0.999974	+	0.00725952i	$0.997689\pi$
$968$	−9.20711	+	15.9472i	−0.295928	+	0.512562i
$969$	2.16338	−	2.99808i	0.0694979	−	0.0963121i
$970$	−9.53553	−	16.5160i	−0.306168	−	0.530298i
$971$	49.9771	−	13.3913i	1.60384	−	0.429748i	0.657642	−	0.753331i	$-0.271554\pi$
$971$	49.9771	−	13.3913i	1.60384	−	0.429748i	0.946200	+	0.323583i	$0.104887\pi$
$972$	22.6985	+	54.7990i	0.728054	+	1.75768i
$973$		0			0
$974$	−58.6985	+	24.3137i	−1.88082	+	0.779061i
$975$	−4.11339	−	5.36068i	−0.131734	−	0.171679i
$976$	−1.49851	−	11.3823i	−0.0479660	−	0.364338i
$977$	37.0768	+	9.93471i	1.18619	+	0.317840i	0.797380	−	0.603477i	$-0.206219\pi$
$977$	37.0768	+	9.93471i	1.18619	+	0.317840i	0.388813	+	0.921317i	$0.372885\pi$
$978$	−5.73081	−	21.3877i	−0.183251	−	0.683902i
$979$	−15.8995	−	6.58579i	−0.508150	−	0.210483i
$980$		0			0
$981$	26.2635	−	10.8787i	0.838528	−	0.347330i
$982$	77.5941	+	44.7990i	2.47613	+	1.42959i
$983$	5.93027	−	7.72848i	0.189146	−	0.246500i	−0.689148	−	0.724620i	$-0.742015\pi$
$983$	5.93027	−	7.72848i	0.189146	−	0.246500i	0.878294	+	0.478120i	$0.158682\pi$
$984$	1.50089	−	5.60139i	0.0478466	−	0.178566i
$985$	−1.77817	+	3.07989i	−0.0566574	+	0.0981334i
$986$	2.87868	−	1.29289i	0.0916758	−	0.0411741i
$987$		0			0
$988$	3.17157	+	3.17157i	0.100901	+	0.100901i
$989$	3.92429	+	0.516642i	0.124785	+	0.0164283i
$990$	7.64564	−	4.41421i	0.242994	−	0.140293i
$991$	−32.3977	−	24.8596i	−1.02915	−	0.789692i	−0.0512301	−	0.998687i	$-0.516314\pi$
$991$	−32.3977	−	24.8596i	−1.02915	−	0.789692i	−0.977917	+	0.208995i	$0.932981\pi$
$992$	−7.56787	−	9.86263i	−0.240280	−	0.313139i
$993$	−21.7990	−	9.02944i	−0.691770	−	0.286541i
$994$		0			0
$995$	−6.24264	+	6.24264i	−0.197905	+	0.197905i
$996$	38.3224	−	29.4058i	1.21429	−	0.931760i
$997$	7.45800	−	0.981864i	0.236197	−	0.0310959i	−0.0114983	−	0.999934i	$-0.503660\pi$
$997$	7.45800	−	0.981864i	0.236197	−	0.0310959i	0.247695	+	0.968838i	$0.420327\pi$
$998$	−41.1070	−	31.5425i	−1.30122	−	0.998460i
$999$	−41.8154	−	24.1421i	−1.32298	−	0.763823i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.v.b.814.1		8
7.2	even	3		17.2.d.a.15.1	yes	4
7.3	odd	6		833.2.v.a.508.1		8
7.4	even	3	inner	833.2.v.b.508.1		8
7.5	odd	6		833.2.l.a.491.1		4
7.6	odd	2		833.2.v.a.814.1		8
17.8	even	8	inner	833.2.v.b.569.1		8
21.2	odd	6		153.2.l.c.100.1		4
28.23	odd	6		272.2.v.d.49.1		4
35.2	odd	12		425.2.n.b.49.1		4
35.9	even	6		425.2.m.a.151.1		4
35.23	odd	12		425.2.n.a.49.1		4
119.2	even	24		289.2.d.c.179.1		4
119.9	even	24		289.2.d.a.110.1		4
119.16	even	6		289.2.d.a.134.1		4
119.23	odd	48		289.2.c.c.251.2		8
119.25	even	24	inner	833.2.v.b.263.1		8
119.30	even	12		289.2.d.b.155.1		4
119.37	odd	48		289.2.b.b.288.2		4
119.44	odd	48		289.2.c.c.38.3		8
119.58	odd	48		289.2.c.c.38.4		8
119.59	odd	24		833.2.v.a.263.1		8
119.65	odd	48		289.2.b.b.288.1		4
119.72	even	12		289.2.d.c.155.1		4
119.76	odd	8		833.2.v.a.569.1		8
119.79	odd	48		289.2.c.c.251.1		8
119.93	even	24		17.2.d.a.8.1	✓	4
119.100	even	24		289.2.d.b.179.1		4
119.107	odd	48		289.2.a.f.1.3		4
119.110	odd	24		833.2.l.a.246.1		4
119.114	odd	48		289.2.a.f.1.4		4
357.107	even	48		2601.2.a.bb.1.1		4
357.212	odd	24		153.2.l.c.127.1		4
357.233	even	48		2601.2.a.bb.1.2		4
476.107	even	48		4624.2.a.bp.1.3		4
476.331	odd	24		272.2.v.d.161.1		4
476.471	even	48		4624.2.a.bp.1.2		4
595.93	odd	24		425.2.n.b.399.1		4
595.114	odd	48		7225.2.a.u.1.1		4
595.212	odd	24		425.2.n.a.399.1		4
595.464	odd	48		7225.2.a.u.1.2		4
595.569	even	24		425.2.m.a.76.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.2.d.a.8.1	✓	4	119.93	even	24
17.2.d.a.15.1	yes	4	7.2	even	3
153.2.l.c.100.1		4	21.2	odd	6
153.2.l.c.127.1		4	357.212	odd	24
272.2.v.d.49.1		4	28.23	odd	6
272.2.v.d.161.1		4	476.331	odd	24
289.2.a.f.1.3		4	119.107	odd	48
289.2.a.f.1.4		4	119.114	odd	48
289.2.b.b.288.1		4	119.65	odd	48
289.2.b.b.288.2		4	119.37	odd	48
289.2.c.c.38.3		8	119.44	odd	48
289.2.c.c.38.4		8	119.58	odd	48
289.2.c.c.251.1		8	119.79	odd	48
289.2.c.c.251.2		8	119.23	odd	48
289.2.d.a.110.1		4	119.9	even	24
289.2.d.a.134.1		4	119.16	even	6
289.2.d.b.155.1		4	119.30	even	12
289.2.d.b.179.1		4	119.100	even	24
289.2.d.c.155.1		4	119.72	even	12
289.2.d.c.179.1		4	119.2	even	24
425.2.m.a.76.1		4	595.569	even	24
425.2.m.a.151.1		4	35.9	even	6
425.2.n.a.49.1		4	35.23	odd	12
425.2.n.a.399.1		4	595.212	odd	24
425.2.n.b.49.1		4	35.2	odd	12
425.2.n.b.399.1		4	595.93	odd	24
833.2.l.a.246.1		4	119.110	odd	24
833.2.l.a.491.1		4	7.5	odd	6
833.2.v.a.263.1		8	119.59	odd	24
833.2.v.a.508.1		8	7.3	odd	6
833.2.v.a.569.1		8	119.76	odd	8
833.2.v.a.814.1		8	7.6	odd	2
833.2.v.b.263.1		8	119.25	even	24	inner
833.2.v.b.508.1		8	7.4	even	3	inner
833.2.v.b.569.1		8	17.8	even	8	inner
833.2.v.b.814.1		8	1.1	even	1	trivial
2601.2.a.bb.1.1		4	357.107	even	48
2601.2.a.bb.1.2		4	357.233	even	48
4624.2.a.bp.1.2		4	476.471	even	48
4624.2.a.bp.1.3		4	476.107	even	48
7225.2.a.u.1.1		4	595.114	odd	48
7225.2.a.u.1.2		4	595.464	odd	48

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:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.v (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.33195 - 0.624844i) q^{2} +(0.658919 - 0.858719i) q^{3} +(3.31552 - 1.91421i) q^{4} +(0.0999004 - 0.758819i) q^{5} +(1.00000 - 2.41421i) q^{6} +(3.12132 - 3.12132i) q^{8} +(0.473232 + 1.76612i) q^{9} +O(q^{10})\)	\(q+(2.33195 - 0.624844i) q^{2} +(0.658919 - 0.858719i) q^{3} +(3.31552 - 1.91421i) q^{4} +(0.0999004 - 0.758819i) q^{5} +(1.00000 - 2.41421i) q^{6} +(3.12132 - 3.12132i) q^{8} +(0.473232 + 1.76612i) q^{9} +(-0.241181 - 1.83195i) q^{10} +(2.59077 - 0.341081i) q^{11} +(0.540882 - 4.10841i) q^{12} -1.41421i q^{13} +(-0.585786 - 0.585786i) q^{15} +(1.50000 - 2.59808i) q^{16} +(-4.01229 - 0.949490i) q^{17} +(2.20711 + 3.82282i) q^{18} +(-0.800199 + 0.214413i) q^{19} +(-1.12132 - 2.70711i) q^{20} +(5.82843 - 2.41421i) q^{22} +(-2.90861 - 3.79057i) q^{23} +(-0.623642 - 4.73703i) q^{24} +(4.26380 + 1.14248i) q^{25} +(-0.883663 - 3.29788i) q^{26} +(4.82843 + 2.00000i) q^{27} +(-0.292893 + 0.121320i) q^{29} +(-1.73205 - 1.00000i) q^{30} +(-4.77231 + 6.21940i) q^{31} +(-0.410432 + 1.53175i) q^{32} +(1.41421 - 2.44949i) q^{33} +(-9.94975 + 0.292893i) q^{34} +(4.94975 + 4.94975i) q^{36} +(-9.15976 - 1.20590i) q^{37} +(-1.73205 + 1.00000i) q^{38} +(-1.21441 - 0.931852i) q^{39} +(-2.05670 - 2.68034i) q^{40} +(1.12132 + 0.464466i) q^{41} +(-0.585786 + 0.585786i) q^{43} +(7.93684 - 6.09015i) q^{44} +(1.38745 - 0.182661i) q^{45} +(-9.15125 - 7.02200i) q^{46} +(4.47871 + 2.58579i) q^{47} +(-1.24264 - 3.00000i) q^{48} +10.6569 q^{50} +(-3.45912 + 2.81979i) q^{51} +(-2.70711 - 4.68885i) q^{52} +(-0.366025 + 1.36603i) q^{53} +(12.5093 + 1.64689i) q^{54} -2.00000i q^{55} +(-0.343146 + 0.828427i) q^{57} +(-0.607206 + 0.465926i) q^{58} +(-5.79555 - 1.55291i) q^{59} +(-3.06350 - 0.820863i) q^{60} +(3.03603 - 2.32963i) q^{61} +(-7.24264 + 17.4853i) q^{62} +9.82843i q^{64} +(-1.07313 - 0.141281i) q^{65} +(1.76733 - 6.59575i) q^{66} +(-0.585786 - 1.01461i) q^{67} +(-15.1203 + 4.53233i) q^{68} -5.17157 q^{69} +(-2.07107 - 5.00000i) q^{71} +(6.98975 + 4.03553i) q^{72} +(10.2615 + 7.87391i) q^{73} +(-22.1136 + 2.91131i) q^{74} +(3.79057 - 2.90861i) q^{75} +(-2.24264 + 2.24264i) q^{76} +(-3.41421 - 1.41421i) q^{78} +(2.90861 + 3.79057i) q^{79} +(-1.82162 - 1.39778i) q^{80} +(0.148586 - 0.0857864i) q^{81} +(2.90508 + 0.382461i) q^{82} +(8.24264 + 8.24264i) q^{83} +(-1.12132 + 2.94975i) q^{85} +(-1.00000 + 1.73205i) q^{86} +(-0.0888127 + 0.331453i) q^{87} +(7.02200 - 9.15125i) q^{88} +(-5.70346 - 3.29289i) q^{89} +(3.12132 - 1.29289i) q^{90} +(-16.8995 - 7.00000i) q^{92} +(2.19615 + 8.19615i) q^{93} +(12.0599 + 3.23143i) q^{94} +(0.0827602 + 0.628626i) q^{95} +(1.04490 + 1.36175i) q^{96} +(9.53553 - 3.94975i) q^{97} +(1.82843 + 4.41421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 4 q^{3} + 8 q^{6} + 8 q^{8} - 8 q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 + 4 * q^3 + 8 * q^6 + 8 * q^8 - 8 * q^9	\( 8 q + 4 q^{2} + 4 q^{3} + 8 q^{6} + 8 q^{8} - 8 q^{9} - 4 q^{10} + 4 q^{11} + 4 q^{12} - 16 q^{15} + 12 q^{16} + 12 q^{18} - 8 q^{19} + 8 q^{20} + 24 q^{22} - 4 q^{23} - 12 q^{24} + 4 q^{25} + 4 q^{26} + 16 q^{27} - 8 q^{29} + 12 q^{31} - 4 q^{32} - 40 q^{34} + 8 q^{40} - 8 q^{41} - 16 q^{43} + 20 q^{44} - 12 q^{45} - 20 q^{46} + 24 q^{48} + 40 q^{50} - 28 q^{51} - 16 q^{52} + 4 q^{53} + 8 q^{54} - 48 q^{57} + 8 q^{60} - 24 q^{62} + 4 q^{65} - 8 q^{66} - 16 q^{67} - 12 q^{68} - 64 q^{69} + 40 q^{71} + 28 q^{73} - 20 q^{74} + 12 q^{75} + 16 q^{76} - 16 q^{78} + 4 q^{79} - 4 q^{82} + 32 q^{83} + 8 q^{85} - 8 q^{86} - 16 q^{87} - 12 q^{88} + 8 q^{90} - 56 q^{92} - 24 q^{93} + 24 q^{94} + 8 q^{95} + 20 q^{96} + 48 q^{97} - 8 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 + 4 * q^3 + 8 * q^6 + 8 * q^8 - 8 * q^9 - 4 * q^10 + 4 * q^11 + 4 * q^12 - 16 * q^15 + 12 * q^16 + 12 * q^18 - 8 * q^19 + 8 * q^20 + 24 * q^22 - 4 * q^23 - 12 * q^24 + 4 * q^25 + 4 * q^26 + 16 * q^27 - 8 * q^29 + 12 * q^31 - 4 * q^32 - 40 * q^34 + 8 * q^40 - 8 * q^41 - 16 * q^43 + 20 * q^44 - 12 * q^45 - 20 * q^46 + 24 * q^48 + 40 * q^50 - 28 * q^51 - 16 * q^52 + 4 * q^53 + 8 * q^54 - 48 * q^57 + 8 * q^60 - 24 * q^62 + 4 * q^65 - 8 * q^66 - 16 * q^67 - 12 * q^68 - 64 * q^69 + 40 * q^71 + 28 * q^73 - 20 * q^74 + 12 * q^75 + 16 * q^76 - 16 * q^78 + 4 * q^79 - 4 * q^82 + 32 * q^83 + 8 * q^85 - 8 * q^86 - 16 * q^87 - 12 * q^88 + 8 * q^90 - 56 * q^92 - 24 * q^93 + 24 * q^94 + 8 * q^95 + 20 * q^96 + 48 * q^97 - 8 * q^99

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