LMFDB - Embedded newform 833.2.v.b.508.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [833,2,Mod(128,833)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [8,4,4,0,0,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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			508.1
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	833.508
Dual form			833.2.v.b.569.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.624844 + 2.33195i) q^{2} +(-1.07313 - 0.141281i) q^{3} +(-3.31552 - 1.91421i) q^{4} +(0.607206 + 0.465926i) q^{5} +(1.00000 - 2.41421i) q^{6} +(3.12132 - 3.12132i) q^{8} +(-1.76612 - 0.473232i) q^{9} +(-1.46593 + 1.12484i) q^{10} +(-1.59077 - 2.07313i) q^{11} +(3.28754 + 2.52262i) q^{12} -1.41421i q^{13} +(-0.585786 - 0.585786i) q^{15} +(1.50000 + 2.59808i) q^{16} +(1.18386 + 3.94949i) q^{17} +(2.20711 - 3.82282i) q^{18} +(0.214413 - 0.800199i) q^{19} +(-1.12132 - 2.70711i) q^{20} +(5.82843 - 2.41421i) q^{22} +(4.73703 - 0.623642i) q^{23} +(-3.79057 + 2.90861i) q^{24} +(-1.14248 - 4.26380i) q^{25} +(3.29788 + 0.883663i) q^{26} +(4.82843 + 2.00000i) q^{27} +(-0.292893 + 0.121320i) q^{29} +(1.73205 - 1.00000i) q^{30} +(7.77231 + 1.02324i) q^{31} +(1.53175 - 0.410432i) q^{32} +(1.41421 + 2.44949i) q^{33} +(-9.94975 + 0.292893i) q^{34} +(4.94975 + 4.94975i) q^{36} +(5.62422 - 7.32963i) q^{37} +(1.73205 + 1.00000i) q^{38} +(-0.199801 + 1.51764i) q^{39} +(3.34959 - 0.440982i) q^{40} +(1.12132 + 0.464466i) q^{41} +(-0.585786 + 0.585786i) q^{43} +(1.30581 + 9.91858i) q^{44} +(-0.851911 - 1.11023i) q^{45} +(-1.50561 + 11.4362i) q^{46} +(-4.47871 + 2.58579i) q^{47} +(-1.24264 - 3.00000i) q^{48} +10.6569 q^{50} +(-0.712455 - 4.40558i) q^{51} +(-2.70711 + 4.68885i) q^{52} +(1.36603 - 0.366025i) q^{53} +(-7.68092 + 10.0100i) q^{54} -2.00000i q^{55} +(-0.343146 + 0.828427i) q^{57} +(-0.0999004 - 0.758819i) q^{58} +(1.55291 + 5.79555i) q^{59} +(0.820863 + 3.06350i) q^{60} +(0.499502 + 3.79410i) q^{61} +(-7.24264 + 17.4853i) q^{62} +9.82843i q^{64} +(0.658919 - 0.858719i) q^{65} +(-6.59575 + 1.76733i) q^{66} +(-0.585786 + 1.01461i) q^{67} +(3.63505 - 15.3608i) q^{68} -5.17157 q^{69} +(-2.07107 - 5.00000i) q^{71} +(-6.98975 + 4.03553i) q^{72} +(1.68827 - 12.8237i) q^{73} +(13.5781 + 17.6953i) q^{74} +(0.623642 + 4.73703i) q^{75} +(-2.24264 + 2.24264i) q^{76} +(-3.41421 - 1.41421i) q^{78} +(-4.73703 + 0.623642i) q^{79} +(-0.299701 + 2.27646i) q^{80} +(-0.148586 - 0.0857864i) q^{81} +(-1.78376 + 2.32465i) q^{82} +(8.24264 + 8.24264i) q^{83} +(-1.12132 + 2.94975i) q^{85} +(-1.00000 - 1.73205i) q^{86} +(0.331453 - 0.0888127i) q^{87} +(-11.4362 - 1.50561i) q^{88} +(5.70346 - 3.29289i) q^{89} +(3.12132 - 1.29289i) q^{90} +(-16.8995 - 7.00000i) q^{92} +(-8.19615 - 2.19615i) q^{93} +(-3.23143 - 12.0599i) q^{94} +(0.503026 - 0.385986i) q^{95} +(-1.70176 + 0.224041i) 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} - 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}+ \cdots - 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

Character values

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

$n$	$52$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{8}\right)$

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 $

$2$	−0.624844	+	2.33195i	−0.441832	+	1.64894i	0.282337	+	0.959315i	$0.408890\pi$
$2$	−0.624844	+	2.33195i	−0.441832	+	1.64894i	−0.724168	+	0.689623i	$0.757776\pi$
$3$	−1.07313	−	0.141281i	−0.619573	−	0.0815684i	−0.185796	−	0.982588i	$-0.559486\pi$
$3$	−1.07313	−	0.141281i	−0.619573	−	0.0815684i	−0.433777	+	0.901020i	$0.642820\pi$
$4$	−3.31552	−	1.91421i	−1.65776	−	0.957107i
$5$	0.607206	+	0.465926i	0.271551	+	0.208368i	0.735556	−	0.677464i	$-0.236921\pi$
$5$	0.607206	+	0.465926i	0.271551	+	0.208368i	−0.464005	+	0.885833i	$0.653588\pi$
$6$	1.00000	−	2.41421i	0.408248	−	0.985599i
$7$		0			0
$7$		0			0
$8$	3.12132	−	3.12132i	1.10355	−	1.10355i
$9$	−1.76612	−	0.473232i	−0.588708	−	0.157744i
$10$	−1.46593	+	1.12484i	−0.463566	+	0.355707i
$11$	−1.59077	−	2.07313i	−0.479635	−	0.625073i	0.489381	−	0.872070i	$-0.337223\pi$
$11$	−1.59077	−	2.07313i	−0.479635	−	0.625073i	−0.969016	+	0.246997i	$0.920556\pi$
$12$	3.28754	+	2.52262i	0.949032	+	0.728218i
$13$		−	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
$17$	1.18386	+	3.94949i	0.287129	+	0.957892i
$17$	1.18386	+	3.94949i	0.287129	+	0.957892i
$18$	2.20711	−	3.82282i	0.520220	−	0.901048i
$19$	0.214413	−	0.800199i	0.0491897	−	0.183578i	−0.936960	−	0.349437i	$-0.886373\pi$
$19$	0.214413	−	0.800199i	0.0491897	−	0.183578i	0.986150	+	0.165859i	$0.0530396\pi$
$20$	−1.12132	−	2.70711i	−0.250735	−	0.605327i
$21$		0			0
$22$	5.82843	−	2.41421i	1.24262	−	0.514712i
$23$	4.73703	−	0.623642i	0.987740	−	0.130038i	0.380691	−	0.924702i	$-0.375686\pi$
$23$	4.73703	−	0.623642i	0.987740	−	0.130038i	0.607049	+	0.794664i	$0.292353\pi$
$24$	−3.79057	+	2.90861i	−0.773747	+	0.593717i
$25$	−1.14248	−	4.26380i	−0.228497	−	0.852761i
$26$	3.29788	+	0.883663i	0.646767	+	0.173301i
$27$	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
$31$	7.77231	+	1.02324i	1.39595	+	0.183780i	0.790674	−	0.612237i	$-0.209730\pi$
$31$	7.77231	+	1.02324i	1.39595	+	0.183780i	0.605274	+	0.796017i	$0.293064\pi$
$32$	1.53175	−	0.410432i	0.270778	−	0.0725548i
$33$	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
$37$	5.62422	−	7.32963i	0.924616	−	1.20498i	−0.0538440	−	0.998549i	$-0.517147\pi$
$37$	5.62422	−	7.32963i	0.924616	−	1.20498i	0.978460	−	0.206434i	$-0.0661860\pi$
$38$	1.73205	+	1.00000i	0.280976	+	0.162221i
$39$	−0.199801	+	1.51764i	−0.0319937	+	0.243017i
$40$	3.34959	−	0.440982i	0.529617	−	0.0697253i
$41$	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	$0.270120\pi$
$44$	1.30581	+	9.91858i	0.196858	+	1.49528i
$45$	−0.851911	−	1.11023i	−0.126995	−	0.165504i
$46$	−1.50561	+	11.4362i	−0.221990	+	1.68618i
$47$	−4.47871	+	2.58579i	−0.653288	+	0.377176i	−0.789715	−	0.613474i	$-0.789771\pi$
$47$	−4.47871	+	2.58579i	−0.653288	+	0.377176i	0.136427	+	0.990650i	$0.456438\pi$
$48$	−1.24264	−	3.00000i	−0.179360	−	0.433013i
$49$		0			0
$50$	10.6569			1.50711
$51$	−0.712455	−	4.40558i	−0.0997637	−	0.616905i
$52$	−2.70711	+	4.68885i	−0.375408	+	0.650226i
$53$	1.36603	−	0.366025i	0.187638	−	0.0502775i	−0.163776	−	0.986498i	$-0.552368\pi$
$53$	1.36603	−	0.366025i	0.187638	−	0.0502775i	0.351414	+	0.936220i	$0.385701\pi$
$54$	−7.68092	+	10.0100i	−1.04524	+	1.36218i
$55$		−	2.00000i		−	0.269680i
$56$		0			0
$57$	−0.343146	+	0.828427i	−0.0454508	+	0.109728i
$58$	−0.0999004	−	0.758819i	−0.0131176	−	0.0996378i
$59$	1.55291	+	5.79555i	0.202172	+	0.754517i	0.990293	+	0.138996i	$0.0443876\pi$
$59$	1.55291	+	5.79555i	0.202172	+	0.754517i	−0.788121	+	0.615521i	$0.788946\pi$
$60$	0.820863	+	3.06350i	0.105973	+	0.395497i
$61$	0.499502	+	3.79410i	0.0639547	+	0.485784i	0.993209	+	0.116344i	$0.0371173\pi$
$61$	0.499502	+	3.79410i	0.0639547	+	0.485784i	−0.929254	+	0.369441i	$0.879549\pi$
$62$	−7.24264	+	17.4853i	−0.919816	+	2.22063i
$63$		0			0
$64$			9.82843i			1.22855i
$65$	0.658919	−	0.858719i	0.0817288	−	0.106511i
$66$	−6.59575	+	1.76733i	−0.811881	+	0.217543i
$67$	−0.585786	+	1.01461i	−0.0715652	+	0.123955i	−0.899587	−	0.436741i	$-0.856133\pi$
$67$	−0.585786	+	1.01461i	−0.0715652	+	0.123955i	0.828022	+	0.560695i	$0.189466\pi$
$68$	3.63505	−	15.3608i	0.440815	−	1.86277i
$69$	−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
$73$	1.68827	−	12.8237i	0.197597	−	1.50090i	−0.549114	−	0.835747i	$-0.685035\pi$
$73$	1.68827	−	12.8237i	0.197597	−	1.50090i	0.746711	−	0.665149i	$-0.231632\pi$
$74$	13.5781	+	17.6953i	1.57842	+	2.05704i
$75$	0.623642	+	4.73703i	0.0720120	+	0.546986i
$76$	−2.24264	+	2.24264i	−0.257249	+	0.257249i
$77$		0			0
$78$	−3.41421	−	1.41421i	−0.386584	−	0.160128i
$79$	−4.73703	+	0.623642i	−0.532958	+	0.0701653i	−0.392202	−	0.919879i	$-0.628287\pi$
$79$	−4.73703	+	0.623642i	−0.532958	+	0.0701653i	−0.140756	+	0.990044i	$0.544953\pi$
$80$	−0.299701	+	2.27646i	−0.0335076	+	0.254516i
$81$	−0.148586	−	0.0857864i	−0.0165096	−	0.00953183i
$82$	−1.78376	+	2.32465i	−0.196984	+	0.256714i
$83$	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
$87$	0.331453	−	0.0888127i	0.0355355	−	0.00952172i
$88$	−11.4362	−	1.50561i	−1.21910	−	0.160498i
$89$	5.70346	−	3.29289i	0.604565	−	0.349046i	−0.166270	−	0.986080i	$-0.553172\pi$
$89$	5.70346	−	3.29289i	0.604565	−	0.349046i	0.770835	+	0.637034i	$0.219839\pi$
$90$	3.12132	−	1.29289i	0.329016	−	0.136283i
$91$		0			0
$92$	−16.8995	−	7.00000i	−1.76189	−	0.729800i
$93$	−8.19615	−	2.19615i	−0.849901	−	0.227730i
$94$	−3.23143	−	12.0599i	−0.333296	−	1.24388i
$95$	0.503026	−	0.385986i	0.0516094	−	0.0396013i
$96$	−1.70176	+	0.224041i	−0.173685	+	0.0228661i
$97$	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
$100$	−4.37391	+	16.3237i	−0.437391	+	1.63237i
$101$	5.29289	−	9.16756i	0.526663	−	0.912206i	−0.472855	−	0.881140i	$-0.656776\pi$
$101$	5.29289	−	9.16756i	0.526663	−	0.912206i	0.999517	−	0.0310659i	$-0.00989019\pi$
$102$	10.7188	+	1.09139i	1.06132	+	0.108064i
$103$	−6.24264	−	10.8126i	−0.615106	−	1.06539i	−0.990366	−	0.138475i	$-0.955780\pi$
$103$	−6.24264	−	10.8126i	−0.615106	−	1.06539i	0.375260	−	0.926919i	$-0.377553\pi$
$104$	−4.41421	−	4.41421i	−0.432849	−	0.432849i
$105$		0			0
$106$			3.41421i			0.331618i
$107$	−0.355693	−	0.272933i	−0.0343862	−	0.0263854i	0.591425	−	0.806360i	$-0.298565\pi$
$107$	−0.355693	−	0.272933i	−0.0343862	−	0.0263854i	−0.625812	+	0.779974i	$0.715232\pi$
$108$	−12.1803	−	15.8737i	−1.17205	−	1.52744i
$109$	−12.3346	+	9.46468i	−1.18144	+	0.906552i	−0.997084	−	0.0763072i	$-0.975687\pi$
$109$	−12.3346	+	9.46468i	−1.18144	+	0.906552i	−0.184357	+	0.982859i	$0.559020\pi$
$110$	4.66390	+	1.24969i	0.444686	+	0.119153i
$111$	−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	$-0.0881645\pi$
$114$	−1.71744	−	1.31784i	−0.160853	−	0.123427i
$115$	3.16693	+	1.82843i	0.295318	+	0.170502i
$116$	1.20332	+	0.158421i	0.111726	+	0.0147090i
$117$	−0.669251	+	2.49768i	−0.0618723	+	0.230910i
$118$	−14.4853			−1.33348
$119$		0			0
$120$	−3.65685			−0.333824
$121$	1.07968	−	4.02943i	0.0981530	−	0.366312i
$122$	−9.15976	−	1.20590i	−0.829285	−	0.109177i
$123$	−1.13770	−	0.656854i	−0.102583	−	0.0592266i
$124$	−23.8105	−	18.2704i	−2.13825	−	1.64073i
$125$	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	$0.325757\pi$
$128$	−19.8559	−	5.32037i	−1.75503	−	0.470259i
$129$	0.711386	−	0.545866i	0.0626341	−	0.0480608i
$130$	1.59077	+	2.07313i	0.139520	+	0.181826i
$131$	12.0831	+	9.27169i	1.05571	+	0.810071i	0.982316	−	0.187232i	$-0.0599517\pi$
$131$	12.0831	+	9.27169i	1.05571	+	0.810071i	0.0733896	+	0.997303i	$0.476618\pi$
$132$		−	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
$136$	16.0228	+	8.63241i	1.37395	+	0.740223i
$137$	8.36396	−	14.4868i	0.714581	−	1.23769i	−0.248539	−	0.968622i	$-0.579951\pi$
$137$	8.36396	−	14.4868i	0.714581	−	1.23769i	0.963121	−	0.269070i	$-0.0867161\pi$
$138$	3.23143	−	12.0599i	0.275077	−	1.02660i
$139$	−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
$142$	12.9539	−	1.70541i	1.08706	−	0.143115i
$143$	−2.93185	+	2.24969i	−0.245174	+	0.188128i
$144$	−1.41970	−	5.29837i	−0.118308	−	0.441531i
$145$	−0.234373	−	0.0628000i	−0.0194636	−	0.00521526i
$146$	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	$-0.422008\pi$
$149$	14.6969	−	8.48528i	1.20402	−	0.695141i	0.961447	+	0.274992i	$0.0886751\pi$
$150$	−11.4362	−	1.50561i	−0.933763	−	0.122932i
$151$	−6.92721	+	1.85614i	−0.563728	+	0.151051i	−0.529419	−	0.848361i	$-0.677590\pi$
$151$	−6.92721	+	1.85614i	−0.563728	+	0.151051i	−0.0343096	+	0.999411i	$0.510923\pi$
$152$	−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
$156$	3.56753	−	4.64929i	0.285631	−	0.372241i
$157$	8.36308	+	4.82843i	0.667447	+	0.385350i	0.795108	−	0.606467i	$-0.207414\pi$
$157$	8.36308	+	4.82843i	0.667447	+	0.385350i	−0.127662	+	0.991818i	$0.540747\pi$
$158$	1.50561	−	11.4362i	0.119780	−	0.909816i
$159$	−1.51764	+	0.199801i	−0.120357	+	0.0158452i
$160$	1.12132	+	0.464466i	0.0886482	+	0.0367193i
$161$		0			0
$162$	0.292893	−	0.292893i	0.0230119	−	0.0230119i
$163$	1.10600	+	8.40094i	0.0866289	+	0.658012i	0.978578	+	0.205876i	$0.0660045\pi$
$163$	1.10600	+	8.40094i	0.0866289	+	0.658012i	−0.891949	+	0.452136i	$0.850662\pi$
$164$	−2.82867	−	3.68639i	−0.220882	−	0.287859i
$165$	−0.282561	+	2.14626i	−0.0219973	+	0.167086i
$166$	−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
$170$	−6.17802	−	4.45800i	−0.473832	−	0.341913i
$171$	−0.757359	+	1.31178i	−0.0579167	+	0.100315i
$172$	3.06350	−	0.820863i	0.233590	−	0.0625903i
$173$	1.78376	−	2.32465i	0.135617	−	0.176740i	−0.720608	−	0.693343i	$-0.756137\pi$
$173$	1.78376	−	2.32465i	0.135617	−	0.176740i	0.856225	+	0.516603i	$0.172804\pi$
$174$			0.828427i			0.0628029i
$175$		0			0
$176$	3.00000	−	7.24264i	0.226134	−	0.545935i
$177$	−0.847683	−	6.43879i	−0.0637158	−	0.483969i
$178$	4.11509	+	15.3577i	0.308439	+	1.15111i
$179$	−1.55291	−	5.79555i	−0.116070	−	0.433180i	0.883294	−	0.468819i	$-0.155320\pi$
$179$	−1.55291	−	5.79555i	−0.116070	−	0.433180i	−0.999365	+	0.0356385i	$0.988654\pi$
$180$	0.699303	+	5.31173i	0.0521230	+	0.395913i
$181$	−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
$184$	12.8392	−	16.7324i	0.946519	−	1.23353i
$185$	6.83013	−	1.83013i	0.502161	−	0.134554i
$186$	10.2426	−	17.7408i	0.751027	−	1.30082i
$187$	6.30456	−	8.73703i	0.461035	−	0.638915i
$188$	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	$-0.409164\pi$
$191$	17.3205	−	10.0000i	1.25327	−	0.723575i	0.971757	+	0.235983i	$0.0758311\pi$
$192$	1.38857	−	10.5472i	0.100211	−	0.761179i
$193$	1.39778	+	1.82162i	0.100614	+	0.131123i	0.840947	−	0.541118i	$-0.181999\pi$
$193$	1.39778	+	1.82162i	0.100614	+	0.131123i	−0.740333	+	0.672241i	$0.765332\pi$
$194$	3.25239	+	24.7044i	0.233508	+	1.77367i
$195$	−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	$0.677933\pi$
$198$	−11.4362	+	1.50561i	−0.812736	+	0.106999i
$199$	−1.50561	+	11.4362i	−0.106730	+	0.810692i	0.851432	+	0.524465i	$0.175734\pi$
$199$	−1.50561	+	11.4362i	−0.106730	+	0.810692i	−0.958162	+	0.286227i	$0.907599\pi$
$200$	−16.8747	−	9.74264i	−1.19322	−	0.688909i
$201$	0.771971	−	1.00605i	0.0544506	−	0.0709615i
$202$	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
$206$	29.1151	−	7.80136i	2.02854	−	0.543546i
$207$	−8.66132	−	1.14028i	−0.602004	−	0.0792553i
$208$	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	$0.887824\pi$
$212$	−5.22973	−	1.40130i	−0.359179	−	0.0962418i
$213$	1.51613	+	5.65826i	0.103883	+	0.387698i
$214$	0.858719	−	0.658919i	0.0587009	−	0.0450427i
$215$	−0.628626	+	0.0827602i	−0.0428720	+	0.00564420i
$216$	21.3137	−	8.82843i	1.45021	−	0.600698i
$217$		0			0
$218$	−14.3640	−	34.6777i	−0.972850	−	2.34867i
$219$	−3.62347	+	13.5230i	−0.244851	+	0.913797i
$220$	−3.82843	+	6.63103i	−0.258113	+	0.447064i
$221$	5.58542	−	1.67423i	0.375716	−	0.112621i
$222$	−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
$226$	25.2764	+	19.3953i	1.68136	+	1.29016i
$227$	10.5895	+	13.8005i	0.702852	+	0.915974i	0.999236	−	0.0390949i	$-0.0124475\pi$
$227$	10.5895	+	13.8005i	0.702852	+	0.915974i	−0.296384	+	0.955069i	$0.595781\pi$
$228$	2.72349	−	2.08981i	0.180368	−	0.138401i
$229$	16.5865	+	4.44433i	1.09606	+	0.293690i	0.761161	−	0.648563i	$-0.224630\pi$
$229$	16.5865	+	4.44433i	1.09606	+	0.293690i	0.334903	+	0.942252i	$0.391296\pi$
$230$	−6.24264	+	6.24264i	−0.411628	+	0.411628i
$231$		0			0
$232$	−0.535534	+	1.29289i	−0.0351595	+	0.0848826i
$233$	−6.97394	−	5.35129i	−0.456878	−	0.350575i	0.354540	−	0.935041i	$-0.384637\pi$
$233$	−6.97394	−	5.35129i	−0.456878	−	0.350575i	−0.811418	+	0.584466i	$0.801304\pi$
$234$	−5.40629	−	3.12132i	−0.353420	−	0.204047i
$235$	−3.92429	−	0.516642i	−0.255992	−	0.0337020i
$236$	5.94522	−	22.1879i	0.387001	−	1.44431i
$237$	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	$0.340787\pi$
$240$	0.643238	−	2.40060i	0.0415208	−	0.154958i
$241$	3.53371	+	0.465222i	0.227626	+	0.0299676i	0.243476	−	0.969907i	$-0.421712\pi$
$241$	3.53371	+	0.465222i	0.227626	+	0.0299676i	−0.0158502	+	0.999874i	$0.505045\pi$
$242$	8.72180	+	5.03553i	0.560659	+	0.323696i
$243$	−12.2915	−	9.43157i	−0.788498	−	0.605035i
$244$	5.60660	−	13.5355i	0.358926	−	0.866524i
$245$		0			0
$246$	2.24264	−	2.24264i	0.142986	−	0.142986i
$247$	−1.13165	−	0.303225i	−0.0720053	−	0.0192938i
$248$	27.4537	−	21.0660i	1.74331	−	1.33769i
$249$	−7.68092	−	10.0100i	−0.486758	−	0.634356i
$250$	13.8005	+	10.5895i	0.872823	+	0.669740i
$251$		−	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
$255$	1.62007	−	3.00705i	0.101453	−	0.188309i
$256$	14.9853	−	25.9553i	0.936580	−	1.62220i
$257$	−1.58970	+	5.93285i	−0.0991629	+	0.370081i	−0.997618	−	0.0689851i	$-0.978024\pi$
$257$	−1.58970	+	5.93285i	−0.0991629	+	0.370081i	0.898455	+	0.439066i	$0.144691\pi$
$258$	0.828427	+	2.00000i	0.0515756	+	0.124515i
$259$		0			0
$260$	−3.82843	+	1.58579i	−0.237429	+	0.0983463i
$261$	0.574699	−	0.0756605i	0.0355730	−	0.00468327i
$262$	−29.1712	+	22.3838i	−1.80220	+	1.38288i
$263$	−2.71379	−	10.1280i	−0.167339	−	0.624519i	−0.997730	−	0.0673380i	$-0.978549\pi$
$263$	−2.71379	−	10.1280i	−0.167339	−	0.624519i	0.830391	−	0.557182i	$-0.188117\pi$
$264$	12.0599	+	3.23143i	0.742233	+	0.198881i
$265$	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
$269$	−26.2220	−	3.45219i	−1.59878	−	0.210484i	−0.722183	−	0.691702i	$-0.756861\pi$
$269$	−26.2220	−	3.45219i	−1.59878	−	0.210484i	−0.876601	+	0.481218i	$0.840195\pi$
$270$	−9.32780	+	2.49938i	−0.567672	+	0.152107i
$271$	−11.0711	−	19.1757i	−0.672519	−	1.16484i	−0.977187	−	0.212379i	$-0.931879\pi$
$271$	−11.0711	−	19.1757i	−0.672519	−	1.16484i	0.304668	−	0.952459i	$-0.401455\pi$
$272$	−8.48528	+	9.00000i	−0.514496	+	0.545705i
$273$		0			0
$274$	28.5563	+	28.5563i	1.72515	+	1.72515i
$275$	−7.02200	+	9.15125i	−0.423443	+	0.551841i
$276$	17.1464	+	9.89949i	1.03209	+	0.595880i
$277$	2.60451	−	19.7832i	0.156490	−	1.18866i	−0.715314	−	0.698803i	$-0.753716\pi$
$277$	2.60451	−	19.7832i	0.156490	−	1.18866i	0.871804	−	0.489855i	$-0.162950\pi$
$278$	51.1105	−	6.72883i	3.06540	−	0.403568i
$279$	−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	$0.268044\pi$
$282$	1.76393	+	13.3984i	0.105040	+	0.797861i
$283$	−11.3615	−	14.8066i	−0.675371	−	0.880160i	0.322420	−	0.946597i	$-0.395504\pi$
$283$	−11.3615	−	14.8066i	−0.675371	−	0.880160i	−0.997791	+	0.0664363i	$0.978837\pi$
$284$	−2.70441	+	20.5420i	−0.160477	+	1.21895i
$285$	−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
$289$	−14.1969	+	9.35131i	−0.835114	+	0.550077i
$290$	0.292893	−	0.507306i	0.0171993	−	0.0297900i
$291$	−10.7909	+	2.89142i	−0.632574	+	0.169498i
$292$	−30.1447	+	39.2853i	−1.76408	+	2.29900i
$293$		−	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
$296$	−5.32312	−	40.4331i	−0.309400	−	2.35013i
$297$	−3.53465	−	13.1915i	−0.205101	−	0.765449i
$298$	10.6040	+	39.5745i	0.614271	+	2.29249i
$299$	−0.881964	−	6.69918i	−0.0510053	−	0.387424i
$300$	7.00000	−	16.8995i	0.404145	−	0.975693i
$301$		0			0
$302$		−	17.3137i		−	0.996292i
$303$	−6.97517	+	9.09022i	−0.400713	+	0.522220i
$304$	2.40060	−	0.643238i	0.137684	−	0.0368922i
$305$	−1.46447	+	2.53653i	−0.0838551	+	0.145241i
$306$	17.7111	+	4.19125i	1.01248	+	0.239598i
$307$	−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
$311$	−3.35229	+	25.4632i	−0.190091	+	1.44389i	0.584485	+	0.811405i	$0.301297\pi$
$311$	−3.35229	+	25.4632i	−0.190091	+	1.44389i	−0.774576	+	0.632481i	$0.782037\pi$
$312$	4.11339	+	5.36068i	0.232875	+	0.303489i
$313$	1.28866	+	9.78838i	0.0728397	+	0.553272i	0.988489	+	0.151294i	$0.0483439\pi$
$313$	1.28866	+	9.78838i	0.0728397	+	0.553272i	−0.915649	+	0.401978i	$0.868323\pi$
$314$	−16.4853	+	16.4853i	−0.930318	+	0.930318i
$315$		0			0
$316$	16.8995	+	7.00000i	0.950671	+	0.393781i
$317$	−19.0783	+	2.51171i	−1.07155	+	0.141072i	−0.645599	−	0.763677i	$-0.723392\pi$
$317$	−19.0783	+	2.51171i	−1.07155	+	0.141072i	−0.425947	+	0.904748i	$0.640059\pi$
$318$	0.482362	−	3.66390i	0.0270495	−	0.205461i
$319$	0.717439	+	0.414214i	0.0401689	+	0.0231915i
$320$	−4.57932	+	5.96788i	−0.255992	+	0.333615i
$321$	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
$325$	−6.02993	+	1.61571i	−0.334480	+	0.0896237i
$326$	−20.2817	−	2.67013i	−1.12330	−	0.147885i
$327$	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
$331$	21.0562	+	5.64199i	1.15735	+	0.310112i	0.785909	−	0.618343i	$-0.212196\pi$
$331$	21.0562	+	5.64199i	1.15735	+	0.310112i	0.371445	+	0.928455i	$0.378862\pi$
$332$	−11.5504	−	43.1068i	−0.633912	−	2.36579i
$333$	−13.4017	+	10.2835i	−0.734408	+	0.563531i
$334$	−4.73703	+	0.623642i	−0.259199	+	0.0341242i
$335$	−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	$0.923918\pi$
$338$	−6.87329	+	25.6515i	−0.373858	+	1.39526i
$339$	−7.14214	+	12.3705i	−0.387908	+	0.671876i
$340$	9.36420	−	7.63349i	0.507845	−	0.413984i
$341$	−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
$345$	−3.14021	−	2.40957i	−0.169063	−	0.129727i
$346$	4.30638	+	5.61219i	0.231513	+	0.301713i
$347$	−13.2975	+	10.2035i	−0.713848	+	0.547755i	−0.900598	−	0.434653i	$-0.856871\pi$
$347$	−13.2975	+	10.2035i	−0.713848	+	0.547755i	0.186750	+	0.982407i	$0.440204\pi$
$348$	−1.26894	−	0.340013i	−0.0680226	−	0.0182266i
$349$	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
$352$	−3.28754	−	2.52262i	−0.175227	−	0.134456i
$353$	−12.1244	−	7.00000i	−0.645314	−	0.372572i	0.141344	−	0.989960i	$-0.454858\pi$
$353$	−12.1244	−	7.00000i	−0.645314	−	0.372572i	−0.786659	+	0.617388i	$0.788191\pi$
$354$	15.5446	+	2.04649i	0.826187	+	0.108770i
$355$	1.07206	−	4.00100i	0.0568992	−	0.212351i
$356$	−25.2132			−1.33630
$357$		0			0
$358$	14.4853			0.765571
$359$	−7.46135	+	27.8461i	−0.393795	+	1.46966i	0.430028	+	0.902815i	$0.358504\pi$
$359$	−7.46135	+	27.8461i	−0.393795	+	1.46966i	−0.823823	+	0.566847i	$0.808163\pi$
$360$	−6.12448	−	0.806303i	−0.322788	−	0.0424959i
$361$	15.8601	+	9.15685i	0.834744	+	0.481940i
$362$	−22.3446	−	17.1456i	−1.17441	−	0.901153i
$363$	−1.72792	+	4.17157i	−0.0906924	+	0.218951i
$364$		0			0
$365$	7.00000	−	7.00000i	0.366397	−	0.366397i
$366$	9.65926	+	2.58819i	0.504898	+	0.135287i
$367$	3.49591	−	2.68250i	0.182485	−	0.140025i	−0.513480	−	0.858102i	$-0.671644\pi$
$367$	3.49591	−	2.68250i	0.182485	−	0.140025i	0.695964	+	0.718076i	$0.254977\pi$
$368$	8.72582	+	11.3717i	0.454865	+	0.592792i
$369$	−1.76059	−	1.35095i	−0.0916527	−	0.0703276i
$370$			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	0.676767	−	0.736198i	$-0.263381\pi$
$373$	−5.77817	−	10.0081i	−0.299183	−	0.518199i	−0.975949	+	0.217998i	$0.930047\pi$
$374$	16.4350	+	20.1612i	0.849832	+	1.04251i
$375$	−3.89949	+	6.75412i	−0.201369	+	0.348781i
$376$	−5.90843	+	22.0506i	−0.304704	+	1.13717i
$377$	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	$0.396379\pi$
$380$	−2.40665	+	0.316841i	−0.123459	+	0.0162536i
$381$	4.56298	−	3.50130i	0.233769	−	0.179377i
$382$	12.4969	+	46.6390i	0.639396	+	2.38626i
$383$	21.7191	+	5.81962i	1.10979	+	0.297369i	0.766747	−	0.641949i	$-0.221874\pi$
$383$	21.7191	+	5.81962i	1.10979	+	0.297369i	0.343048	+	0.939318i	$0.388541\pi$
$384$	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
$388$	−39.1759	−	5.15760i	−1.98885	−	0.261838i
$389$	11.7284	−	3.14262i	0.594654	−	0.159337i	0.0510744	−	0.998695i	$-0.483735\pi$
$389$	11.7284	−	3.14262i	0.594654	−	0.159337i	0.543579	+	0.839358i	$0.317069\pi$
$390$	−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
$394$	6.82901	−	8.89974i	0.344040	−	0.448362i
$395$	−3.16693	−	1.82843i	−0.159345	−	0.0919982i
$396$	2.38757	−	18.1354i	0.119980	−	0.911338i
$397$	−17.6370	+	2.32195i	−0.885174	+	0.116535i	−0.559386	−	0.828908i	$-0.688963\pi$
$397$	−17.6370	+	2.32195i	−0.885174	+	0.116535i	−0.325788	+	0.945443i	$0.605630\pi$
$398$	−25.7279	−	10.6569i	−1.28962	−	0.534180i
$399$		0			0
$400$	9.36396	−	9.36396i	0.468198	−	0.468198i
$401$	0.0756605	+	0.574699i	0.00377831	+	0.0286991i	0.993230	−	0.116163i	$-0.0370595\pi$
$401$	0.0756605	+	0.574699i	0.00377831	+	0.0286991i	−0.989452	+	0.144862i	$0.953726\pi$
$402$	1.86370	+	2.42883i	0.0929531	+	0.121139i
$403$	1.44709	−	10.9917i	0.0720845	−	0.547536i
$404$	−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
$408$	−15.9750	−	11.5274i	−0.790882	−	0.570693i
$409$	1.65685	−	2.86976i	0.0819262	−	0.141900i	−0.822151	−	0.569269i	$-0.807226\pi$
$409$	1.65685	−	2.86976i	0.0819262	−	0.141900i	0.904077	+	0.427369i	$0.140559\pi$
$410$	−2.16622	+	0.580438i	−0.106982	+	0.0286658i
$411$	−11.0223	+	14.3646i	−0.543692	+	0.708553i
$412$			47.7990i			2.35489i
$413$		0			0
$414$	8.07107	−	19.4853i	0.396671	−	0.957649i
$415$	1.16452	+	8.84544i	0.0571643	+	0.434206i
$416$	−0.580438	−	2.16622i	−0.0284583	−	0.106208i
$417$	5.98201	+	22.3252i	0.292940	+	1.09327i
$418$	−0.682163	−	5.18154i	−0.0333657	−	0.253437i
$419$	−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	$-0.115667\pi$
$422$	31.3826	−	40.8986i	1.52768	−	1.99091i
$423$	9.13364	−	2.44735i	0.444093	−	0.118994i
$424$	3.12132	−	5.40629i	0.151585	−	0.262552i
$425$	15.4873	−	9.55998i	0.751245	−	0.463727i
$426$	−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
$430$	0.199801	−	1.51764i	0.00963525	−	0.0731870i
$431$	4.45255	+	5.80268i	0.214472	+	0.279505i	0.888183	−	0.459489i	$-0.151968\pi$
$431$	4.45255	+	5.80268i	0.214472	+	0.279505i	−0.673711	+	0.738995i	$0.735301\pi$
$432$	2.04649	+	15.5446i	0.0984617	+	0.747891i
$433$	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
$436$	59.0130	−	7.76921i	2.82621	−	0.372078i
$437$	0.516642	−	3.92429i	0.0247144	−	0.187724i
$438$	−29.2708	−	16.8995i	−1.39861	−	0.807489i
$439$	−6.47613	+	8.43986i	−0.309089	+	0.402813i	−0.921907	−	0.387412i	$-0.873369\pi$
$439$	−6.47613	+	8.43986i	−0.309089	+	0.402813i	0.612818	+	0.790224i	$0.290036\pi$
$440$	−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	0.997016	+	0.0771965i	$0.0245969\pi$
$443$	11.8995	+	20.6105i	0.565362	+	0.979236i	−0.431654	+	0.902039i	$0.642070\pi$
$444$	36.9798	−	9.90870i	1.75498	−	0.470246i
$445$	4.99742	+	0.657923i	0.236900	+	0.0311885i
$446$	−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	$0.532721\pi$
$450$	−18.8213	−	5.04316i	−0.887246	−	0.237737i
$451$	−0.820863	−	3.06350i	−0.0386530	−	0.144255i
$452$	−40.0830	+	30.7568i	−1.88535	+	1.44668i
$453$	7.69605	−	1.01320i	0.361592	−	0.0476045i
$454$	−38.7990	+	16.0711i	−1.82093	+	0.754253i
$455$		0			0
$456$	1.51472	+	3.65685i	0.0709332	+	0.171248i
$457$	3.40905	−	12.7228i	0.159469	−	0.595146i	−0.839212	−	0.543804i	$-0.816984\pi$
$457$	3.40905	−	12.7228i	0.159469	−	0.595146i	0.998681	−	0.0513418i	$-0.0163498\pi$
$458$	−20.7279	+	35.9018i	−0.968552	+	1.67758i
$459$	−2.18278	+	21.4375i	−0.101884	+	1.00062i
$460$	−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	$0.889608\pi$
$464$	−0.754539	−	0.578978i	−0.0350286	−	0.0268784i
$465$	−3.95351	−	5.15232i	−0.183340	−	0.238933i
$466$	16.8366	−	12.9192i	0.779939	−	0.598468i
$467$	−31.5157	−	8.44460i	−1.45837	−	0.390769i	−0.559444	−	0.828868i	$-0.688985\pi$
$467$	−31.5157	−	8.44460i	−1.45837	−	0.390769i	−0.898927	+	0.438099i	$0.855652\pi$
$468$	7.00000	−	7.00000i	0.323575	−	0.323575i
$469$		0			0
$470$	3.65685	−	8.82843i	0.168678	−	0.407225i
$471$	−8.29253	−	6.36308i	−0.382100	−	0.293195i
$472$	22.9369	+	13.2426i	1.05576	+	0.609542i
$473$	2.14626	+	0.282561i	0.0986853	+	0.0129922i
$474$	−3.23143	+	12.0599i	−0.148424	+	0.553928i
$475$	−3.65685			−0.167788
$476$		0			0
$477$	−2.58579			−0.118395
$478$	−9.26546	+	34.5792i	−0.423792	+	1.58161i
$479$	−5.10528	−	0.672122i	−0.233266	−	0.0307100i	0.0129869	−	0.999916i	$-0.495866\pi$
$479$	−5.10528	−	0.672122i	−0.233266	−	0.0307100i	−0.246253	+	0.969206i	$0.579199\pi$
$480$	−1.13770	−	0.656854i	−0.0519289	−	0.0299812i
$481$	−10.3657	−	7.95385i	−0.472633	−	0.362664i
$482$	−3.29289	+	7.94975i	−0.149987	+	0.362101i
$483$		0			0
$484$	−11.2929	+	11.2929i	−0.513313	+	0.513313i
$485$	7.63033	+	2.04454i	0.346475	+	0.0928378i
$486$	29.6742	−	22.7698i	1.34605	−	1.03286i
$487$	16.0208	+	20.8787i	0.725970	+	0.946102i	0.999877	−	0.0156538i	$-0.00498297\pi$
$487$	16.0208	+	20.8787i	0.725970	+	0.946102i	−0.273908	+	0.961756i	$0.588316\pi$
$488$	13.4017	+	10.2835i	0.606666	+	0.465511i
$489$		−	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
$493$	−0.825899	−	1.01315i	−0.0371966	−	0.0456301i
$494$	1.41421	−	2.44949i	0.0636285	−	0.110208i
$495$	−0.946464	+	3.53225i	−0.0425404	+	0.158763i
$496$	9.00000	+	21.7279i	0.404112	+	0.975613i
$497$		0			0
$498$	28.1421	−	11.6569i	1.26108	−	0.522356i
$499$	21.2785	−	2.80137i	0.952558	−	0.125407i	0.361800	−	0.932256i	$-0.382162\pi$
$499$	21.2785	−	2.80137i	0.952558	−	0.125407i	0.590758	+	0.806849i	$0.298829\pi$
$500$	−21.8847	+	16.7927i	−0.978714	+	0.750994i
$501$	−0.554425	−	2.06914i	−0.0247699	−	0.0924425i
$502$	47.7707	+	12.8001i	2.13211	+	0.571297i
$503$	−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
$507$	−11.8045	−	1.55409i	−0.524254	−	0.0690194i
$508$	19.6500	−	5.26519i	0.871826	−	0.233605i
$509$	18.4853	+	32.0174i	0.819346	+	1.41915i	0.906165	+	0.422924i	$0.138996\pi$
$509$	18.4853	+	32.0174i	0.819346	+	1.41915i	−0.0868193	+	0.996224i	$0.527670\pi$
$510$	6.00000	+	5.65685i	0.265684	+	0.250490i
$511$		0			0
$512$	22.0919	+	22.0919i	0.976333	+	0.976333i
$513$	2.63567	−	3.43488i	0.116368	−	0.151654i
$514$	−12.8418	−	7.41421i	−0.566427	−	0.327027i
$515$	1.24728	−	9.47407i	0.0549619	−	0.417477i
$516$	−3.40352	+	0.448082i	−0.149831	+	0.0197257i
$517$	12.4853	+	5.17157i	0.549102	+	0.227446i
$518$		0			0
$519$	−2.24264	+	2.24264i	−0.0984410	+	0.0984410i
$520$	−0.623642	−	4.73703i	−0.0273485	−	0.207733i
$521$	11.3284	+	14.7634i	0.496306	+	0.646798i	0.972599	−	0.232488i	$-0.0746867\pi$
$521$	11.3284	+	14.7634i	0.496306	+	0.646798i	−0.476294	+	0.879286i	$0.658020\pi$
$522$	−0.182661	+	1.38745i	−0.00799484	+	0.0607268i
$523$	−1.01461	+	0.585786i	−0.0443659	+	0.0256147i	−0.522019	−	0.852934i	$-0.674821\pi$
$523$	−1.01461	+	0.585786i	−0.0443659	+	0.0256147i	0.477653	+	0.878549i	$0.341488\pi$
$524$	−22.3137	−	53.8701i	−0.974779	−	2.35332i
$525$		0			0
$526$	25.3137			1.10373
$527$	5.16006	+	31.9080i	0.224776	+	1.38994i
$528$	−4.24264	+	7.34847i	−0.184637	+	0.319801i
$529$	−0.165727	+	0.0444063i	−0.00720551	+	0.00193071i
$530$	−1.59077	+	2.07313i	−0.0690986	+	0.0900511i
$531$		−	10.9706i		−	0.476082i
$532$		0			0
$533$	0.656854	−	1.58579i	0.0284515	−	0.0686880i
$534$	−2.24629	−	17.0623i	−0.0972064	−	0.738356i
$535$	−0.0888127	−	0.331453i	−0.00383971	−	0.0143300i
$536$	1.33850	+	4.99536i	0.0578145	+	0.215767i
$537$	0.847683	+	6.43879i	0.0365802	+	0.277854i
$538$	24.4350	−	58.9914i	1.05347	−	2.54330i
$539$		0			0
$540$		−	15.3137i		−	0.658997i
$541$	−11.2153	+	14.6161i	−0.482185	+	0.628395i	−0.969577	−	0.244788i	$-0.921282\pi$
$541$	−11.2153	+	14.6161i	−0.482185	+	0.628395i	0.487392	+	0.873183i	$0.337948\pi$
$542$	51.6344	−	13.8354i	2.21789	−	0.594281i
$543$	6.31371	−	10.9357i	0.270947	−	0.469294i
$544$	3.43438	+	5.56374i	0.147248	+	0.238544i
$545$	−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
$549$	0.913303	−	6.93723i	0.0389788	−	0.296074i
$550$	−16.9526	−	22.0931i	−0.722862	−	0.942052i
$551$	0.0342804	+	0.260386i	0.00146039	+	0.0110928i
$552$	−16.1421	+	16.1421i	−0.687055	+	0.687055i
$553$		0			0
$554$	44.5061	+	18.4350i	1.89088	+	0.783229i
$555$	−7.58819	+	0.999004i	−0.322101	+	0.0424054i
$556$	−10.6705	+	81.0504i	−0.452529	+	3.43730i
$557$	−17.1104	−	9.87868i	−0.724990	−	0.418573i	0.0915966	−	0.995796i	$-0.470803\pi$
$557$	−17.1104	−	9.87868i	−0.724990	−	0.418573i	−0.816586	+	0.577223i	$0.804136\pi$
$558$	21.0660	−	27.4537i	0.891795	−	1.16221i
$559$	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
$563$	−33.5848	+	8.99902i	−1.41543	+	0.379264i	−0.883861	−	0.467751i	$-0.845065\pi$
$563$	−33.5848	+	8.99902i	−1.41543	+	0.379264i	−0.531570	+	0.847014i	$0.678398\pi$
$564$	−21.2469	−	2.79721i	−0.894657	−	0.117784i
$565$	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
$569$	−11.6313	−	3.11660i	−0.487610	−	0.130655i	0.00663368	−	0.999978i	$-0.497888\pi$
$569$	−11.6313	−	3.11660i	−0.487610	−	0.130655i	−0.494244	+	0.869323i	$0.664555\pi$
$570$	−0.428825	−	1.60040i	−0.0179615	−	0.0670333i
$571$	3.37385	−	2.58885i	0.141191	−	0.108340i	−0.535751	−	0.844376i	$-0.679971\pi$
$571$	3.37385	−	2.58885i	0.141191	−	0.108340i	0.676942	+	0.736036i	$0.263305\pi$
$572$	14.0270	−	1.84669i	0.586498	−	0.0772139i
$573$	−20.0000	+	8.28427i	−0.835512	+	0.346080i
$574$		0			0
$575$	−8.07107	−	19.4853i	−0.336587	−	0.812592i
$576$	4.65112	−	17.3582i	0.193797	−	0.723260i
$577$	13.5355	−	23.4442i	0.563492	−	0.975996i	−0.433697	−	0.901059i	$-0.642791\pi$
$577$	13.5355	−	23.4442i	0.563492	−	0.975996i	0.997188	−	0.0749372i	$-0.0238756\pi$
$578$	−12.9359	−	38.9497i	−0.538063	−	1.62009i
$579$	−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
$583$	−2.93185	−	2.24969i	−0.121425	−	0.0931726i
$584$	−34.7571	−	45.2964i	−1.43826	−	1.87438i
$585$	−1.57011	+	1.20478i	−0.0649159	+	0.0498117i
$586$	28.7836	+	7.71255i	1.18904	+	0.318602i
$587$	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
$590$	−8.79555	−	6.74907i	−0.362107	−	0.277855i
$591$	4.35562	+	2.51472i	0.179166	+	0.103442i
$592$	27.4793	+	3.61771i	1.12939	+	0.148687i
$593$	3.34625	−	12.4884i	0.137414	−	0.512837i	−0.862562	−	0.505951i	$-0.831142\pi$
$593$	3.34625	−	12.4884i	0.137414	−	0.512837i	0.999976	−	0.00688551i	$-0.00219174\pi$
$594$	32.9706			1.35280
$595$		0			0
$596$	−64.9706			−2.66130
$597$	3.23143	−	12.0599i	0.132254	−	0.493577i
$598$	16.1732	+	2.12925i	0.661373	+	0.0870714i
$599$	9.20361	+	5.31371i	0.376049	+	0.217112i	0.676098	−	0.736812i	$-0.263670\pi$
$599$	9.20361	+	5.31371i	0.376049	+	0.217112i	−0.300049	+	0.953924i	$0.597003\pi$
$600$	16.7324	+	12.8392i	0.683097	+	0.524159i
$601$	−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
$604$	26.5203	+	7.10610i	1.07910	+	0.289143i
$605$	2.53301	−	1.94364i	0.102981	−	0.0790203i
$606$	−16.8396	−	21.9457i	−0.684060	−	0.891485i
$607$	−13.0028	−	9.97744i	−0.527769	−	0.404972i	0.310215	−	0.950667i	$-0.399599\pi$
$607$	−13.0028	−	9.97744i	−0.527769	−	0.404972i	−0.837984	+	0.545695i	$0.816266\pi$
$608$		−	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
$612$	−13.6892	+	25.4088i	−0.553351	+	1.02709i
$613$	−2.65685	+	4.60181i	−0.107309	+	0.185865i	−0.914679	−	0.404180i	$-0.867557\pi$
$613$	−2.65685	+	4.60181i	−0.107309	+	0.185865i	0.807370	+	0.590045i	$0.200890\pi$
$614$	16.3348	−	60.9622i	0.659218	−	2.46023i
$615$	−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	$0.393785\pi$
$618$	−32.3465	+	4.25850i	−1.30117	+	0.171302i
$619$	−22.5961	+	17.3386i	−0.908214	+	0.696897i	−0.953280	−	0.302087i	$-0.902317\pi$
$619$	−22.5961	+	17.3386i	−0.908214	+	0.696897i	0.0450666	+	0.998984i	$0.485650\pi$
$620$	−5.94522	−	22.1879i	−0.238766	−	0.891086i
$621$	24.1197	+	6.46286i	0.967891	+	0.259346i
$622$	−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
$626$	−23.6312	−	3.11111i	−0.944495	−	0.124345i
$627$	2.26330	−	0.606451i	0.0903877	−	0.0242193i
$628$	−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	$0.948309\pi$
$632$	−12.8392	+	16.7324i	−0.510717	+	0.665579i
$633$	20.0162	+	11.5563i	0.795572	+	0.459324i
$634$	6.06380	−	46.0592i	0.240824	−	1.82924i
$635$	−4.03214	+	0.530842i	−0.160011	+	0.0210658i
$636$	5.41421	+	2.24264i	0.214688	+	0.0889265i
$637$		0			0
$638$	−1.41421	+	1.41421i	−0.0559893	+	0.0559893i
$639$	1.29161	+	9.81072i	0.0510951	+	0.388106i
$640$	−9.57773	−	12.4819i	−0.378593	−	0.493392i
$641$	5.40588	−	41.0617i	0.213519	−	1.62184i	−0.463653	−	0.886017i	$-0.653461\pi$
$641$	5.40588	−	41.0617i	0.213519	−	1.62184i	0.677172	−	0.735824i	$-0.263205\pi$
$642$	−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
$646$	−1.89898	+	8.02458i	−0.0747143	+	0.315723i
$647$	1.41421	−	2.44949i	0.0555985	−	0.0962994i	−0.836887	−	0.547376i	$-0.815627\pi$
$647$	1.41421	−	2.44949i	0.0555985	−	0.0962994i	0.892485	+	0.451077i	$0.148960\pi$
$648$	−0.731553	+	0.196019i	−0.0287381	+	0.00770035i
$649$	9.54462	−	12.4388i	0.374659	−	0.488265i
$650$		−	15.0711i		−	0.591136i
$651$		0			0
$652$	12.4142	−	29.9706i	0.486178	−	1.17374i
$653$	−1.24019	−	9.42014i	−0.0485322	−	0.368639i	−0.998427	−	0.0560686i	$-0.982143\pi$
$653$	−1.24019	−	9.42014i	−0.0485322	−	0.368639i	0.949895	−	0.312570i	$-0.101190\pi$
$654$	10.5151	+	39.2431i	0.411175	+	1.53453i
$655$	3.01702	+	11.2597i	0.117885	+	0.439951i
$656$	0.475262	+	3.60997i	0.0185559	+	0.140946i
$657$	−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	$0.947151\pi$
$660$	5.04524	−	6.57509i	0.196386	−	0.255935i
$661$	−1.17186	+	0.314000i	−0.0455802	+	0.0122132i	−0.281537	−	0.959550i	$-0.590844\pi$
$661$	−1.17186	+	0.314000i	−0.0455802	+	0.0122132i	0.235957	+	0.971764i	$0.424178\pi$
$662$	−26.3137	+	45.5767i	−1.02271	+	1.77139i
$663$	−6.23043	+	1.00756i	−0.241970	+	0.0391305i
$664$	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
$668$	0.988964	−	7.51193i	0.0382642	−	0.290645i
$669$	−3.18154	−	4.14626i	−0.123005	−	0.160304i
$670$	−0.282561	−	2.14626i	−0.0109163	−	0.0829174i
$671$	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	$0.597599\pi$
$674$	13.4523	−	1.77103i	0.518163	−	0.0682174i
$675$	3.01121	−	22.8724i	0.115902	−	0.880360i
$676$	−36.4707	−	21.0563i	−1.40272	−	0.809860i
$677$	−23.1889	+	30.2204i	−0.891223	+	1.16146i	0.0949069	+	0.995486i	$0.469745\pi$
$677$	−23.1889	+	30.2204i	−0.891223	+	1.16146i	−0.986129	+	0.165978i	$0.946922\pi$
$678$	−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
$682$	47.7707	−	12.8001i	1.82923	−	0.490142i
$683$	23.5773	+	3.10401i	0.902161	+	0.118772i	0.567315	−	0.823501i	$-0.307982\pi$
$683$	23.5773	+	3.10401i	0.902161	+	0.118772i	0.334846	+	0.942273i	$0.391316\pi$
$684$	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
$688$	−2.40060	−	0.643238i	−0.0915219	−	0.0245232i
$689$	−0.517638	−	1.93185i	−0.0197204	−	0.0735977i
$690$	7.58114	−	5.81722i	0.288609	−	0.221458i
$691$	19.7609	−	2.60157i	0.751740	−	0.0989684i	0.255087	−	0.966918i	$-0.417896\pi$
$691$	19.7609	−	2.60157i	0.751740	−	0.0989684i	0.496652	+	0.867950i	$0.334562\pi$
$692$	−10.3640	+	4.29289i	−0.393979	+	0.163191i
$693$		0			0
$694$	−15.4853	−	37.3848i	−0.587813	−	1.41911i
$695$	4.22992	−	15.7863i	0.160450	−	0.598807i
$696$	0.757359	−	1.31178i	0.0287076	−	0.0497231i
$697$	−0.506915	+	4.97851i	−0.0192008	+	0.188574i
$698$	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	$0.747823\pi$
$702$	14.1562	+	10.8625i	0.534293	+	0.409977i
$703$	−4.65926	−	6.07206i	−0.175727	−	0.229012i
$704$	20.3756	−	15.6348i	0.767935	−	0.589258i
$705$	4.13829	+	1.10885i	0.155857	+	0.0417617i
$706$	23.8995	−	23.8995i	0.899469	−	0.899469i
$707$		0			0
$708$	−9.51472	+	22.9706i	−0.357585	+	0.863287i
$709$	−19.2654	−	14.7829i	−0.723527	−	0.555182i	0.180024	−	0.983662i	$-0.442382\pi$
$709$	−19.2654	−	14.7829i	−0.723527	−	0.555182i	−0.903551	+	0.428480i	$0.859049\pi$
$710$	8.66025	+	5.00000i	0.325014	+	0.187647i
$711$	8.66132	+	1.14028i	0.324825	+	0.0427640i
$712$	7.52415	−	28.0805i	0.281979	−	1.05236i
$713$	37.4558			1.40273
$714$		0			0
$715$	−2.82843			−0.105777
$716$	−5.94522	+	22.1879i	−0.222183	+	0.829199i
$717$	−15.9129	−	2.09497i	−0.594277	−	0.0782380i
$718$	−60.2736	−	34.7990i	−2.24939	−	1.29869i
$719$	26.9507	+	20.6800i	1.00509	+	0.771234i	0.973598	−	0.228270i	$-0.0733068\pi$
$719$	26.9507	+	20.6800i	1.00509	+	0.771234i	0.0314942	+	0.999504i	$0.489973\pi$
$720$	1.60660	−	3.87868i	0.0598745	−	0.144550i
$721$		0			0
$722$	−31.2635	+	31.2635i	−1.16351	+	1.16351i
$723$	−3.72641	−	0.998489i	−0.138587	−	0.0371342i
$724$	35.4337	−	27.1893i	1.31688	−	1.01048i
$725$	0.851911	+	1.11023i	0.0316392	+	0.0412330i
$726$	−8.64822	−	6.63601i	−0.320966	−	0.246286i
$727$			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
$731$	−3.00705	−	1.62007i	−0.111220	−	0.0599203i
$732$	−7.92893	+	13.7333i	−0.293062	+	0.507598i
$733$	−9.32826	+	34.8135i	−0.344547	+	1.28587i	0.548593	+	0.836089i	$0.315164\pi$
$733$	−9.32826	+	34.8135i	−0.344547	+	1.28587i	−0.893140	+	0.449778i	$0.851503\pi$
$734$	4.07107	+	9.82843i	0.150266	+	0.362774i
$735$		0			0
$736$	7.00000	−	2.89949i	0.258023	−	0.106877i
$737$	3.03528	−	0.399602i	0.111806	−	0.0147195i
$738$	4.25044	−	3.26148i	0.156461	−	0.120057i
$739$	5.76759	+	21.5250i	0.212164	+	0.791808i	0.987146	+	0.159824i	$0.0510926\pi$
$739$	5.76759	+	21.5250i	0.212164	+	0.791808i	−0.774981	+	0.631984i	$0.782241\pi$
$740$	−26.1486	−	7.00651i	−0.961243	−	0.257564i
$741$	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
$745$	12.8776	+	1.69537i	0.471798	+	0.0621134i
$746$	26.9488	−	7.22092i	0.986667	−	0.264377i
$747$	−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
$751$	28.9730	−	37.7584i	1.05724	−	1.37782i	0.135161	−	0.990824i	$-0.456845\pi$
$751$	28.9730	−	37.7584i	1.05724	−	1.37782i	0.922080	−	0.386999i	$-0.126488\pi$
$752$	−13.4361	−	7.75736i	−0.489966	−	0.282882i
$753$	−2.89417	+	21.9834i	−0.105469	+	0.801120i
$754$	−1.07313	+	0.141281i	−0.0390812	+	0.00514513i
$755$	−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	$0.264722\pi$
$758$	−0.823443	−	6.25467i	−0.0299088	−	0.227180i
$759$	8.22678	+	10.7214i	0.298613	+	0.389161i
$760$	0.365321	−	2.77489i	0.0132516	−	0.100656i
$761$	−32.6478	+	18.8492i	−1.18348	+	0.683285i	−0.956818	−	0.290688i	$-0.906116\pi$
$761$	−32.6478	+	18.8492i	−1.18348	+	0.683285i	−0.226666	+	0.973973i	$0.572782\pi$
$762$	5.31371	+	12.8284i	0.192495	+	0.464725i
$763$		0			0
$764$	−76.5685			−2.77015
$765$	3.37631	−	4.67898i	0.122071	−	0.169169i
$766$	−27.1421	+	47.0116i	−0.980685	+	1.69860i
$767$	8.19615	−	2.19615i	0.295946	−	0.0792985i
$768$	−19.7482	+	25.7363i	−0.712600	+	0.928679i
$769$			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
$772$	−1.14738	−	8.71525i	−0.0412953	−	0.313669i
$773$	−0.214413	−	0.800199i	−0.00771189	−	0.0287812i	0.961963	−	0.273181i	$-0.0880758\pi$
$773$	−0.214413	−	0.800199i	−0.00771189	−	0.0287812i	−0.969675	+	0.244400i	$0.921409\pi$
$774$	0.946464	+	3.53225i	0.0340199	+	0.126964i
$775$	−4.51682	−	34.3086i	−0.162249	−	1.23240i
$776$	17.4350	−	42.0919i	0.625881	−	1.51101i
$777$		0			0
$778$			29.3137i			1.05095i
$779$	0.612091	−	0.797692i	0.0219304	−	0.0285803i
$780$	4.33245	−	1.16088i	0.155127	−	0.0415660i
$781$	−7.07107	+	12.2474i	−0.253023	+	0.438248i
$782$	−46.9496	+	7.59253i	−1.67892	+	0.271508i
$783$	−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
$787$	2.68433	−	20.3895i	0.0956860	−	0.726808i	−0.874600	−	0.484846i	$-0.838876\pi$
$787$	2.68433	−	20.3895i	0.0956860	−	0.726808i	0.970286	−	0.241962i	$-0.0777909\pi$
$788$	10.8293	+	14.1131i	0.385779	+	0.502758i
$789$	1.48137	+	11.2521i	0.0527380	+	0.400585i
$790$	6.24264	−	6.24264i	0.222103	−	0.222103i
$791$		0			0
$792$	19.4853	+	8.07107i	0.692379	+	0.286793i
$793$	5.36566	−	0.706403i	0.190540	−	0.0250851i
$794$	5.60568	−	42.5794i	0.198938	−	1.51109i
$795$	−1.01461	−	0.585786i	−0.0359846	−	0.0207757i
$796$	26.8832	−	35.0349i	0.952850	−	1.24178i
$797$	−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
$801$	−11.6313	+	3.11660i	−0.410973	+	0.110120i
$802$	−1.38745	−	0.182661i	−0.0489924	−	0.00644997i
$803$	−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
$807$	27.6520	+	7.40932i	0.973395	+	0.260820i
$808$	−12.0941	−	45.1357i	−0.425468	−	1.58787i
$809$	27.9999	−	21.4851i	0.984425	−	0.755376i	0.0147794	−	0.999891i	$-0.495295\pi$
$809$	27.9999	−	21.4851i	0.984425	−	0.755376i	0.969646	+	0.244515i	$0.0786287\pi$
$810$	0.314313	−	0.0413801i	0.0110438	−	0.00145395i
$811$	−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
$814$	15.0851	−	56.2983i	0.528732	−	1.97325i
$815$	−3.24264	+	5.61642i	−0.113585	+	0.196735i
$816$	10.3774	−	8.45938i	0.363280	−	0.296138i
$817$	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
$821$	−30.4898	−	23.3956i	−1.06410	−	0.816513i	−0.0804785	−	0.996756i	$-0.525645\pi$
$821$	−30.4898	−	23.3956i	−1.06410	−	0.816513i	−0.983622	+	0.180243i	$0.942311\pi$
$822$	−26.6103	−	34.6792i	−0.928140	−	1.20958i
$823$	−7.72848	+	5.93027i	−0.269398	+	0.206716i	−0.734622	−	0.678477i	$-0.762640\pi$
$823$	−7.72848	+	5.93027i	−0.269398	+	0.206716i	0.465224	+	0.885193i	$0.345974\pi$
$824$	−53.2348	−	14.2642i	−1.85452	−	0.496918i
$825$	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	$0.821969\pi$
$828$	26.5340	+	20.3603i	0.922120	+	0.707568i
$829$	46.7144	+	26.9706i	1.62246	+	0.936726i	0.986260	+	0.165200i	$0.0528270\pi$
$829$	46.7144	+	26.9706i	1.62246	+	0.936726i	0.636198	+	0.771526i	$0.280506\pi$
$830$	−21.3548	−	2.81141i	−0.741236	−	0.0975855i
$831$	−5.58997	+	20.8620i	−0.193914	+	0.723696i
$832$	13.8995			0.481878
$833$		0			0
$834$	−55.7990			−1.93216
$835$	−0.392038	+	1.46311i	−0.0135670	+	0.0506329i
$836$	8.21682	+	1.08176i	0.284185	+	0.0374136i
$837$	35.4815	+	20.4853i	1.22642	+	0.708075i
$838$	−25.5279	−	19.5883i	−0.881848	−	0.676666i
$839$	−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
$842$	34.0133	+	9.11385i	1.17218	+	0.314084i
$843$	1.63113	−	1.25161i	0.0561792	−	0.0431078i
$844$	49.7661	+	64.8564i	1.71302	+	2.23245i
$845$	6.67927	+	5.12518i	0.229774	+	0.176312i
$846$			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
$850$	12.6163	+	42.0891i	0.432734	+	1.44365i
$851$	22.0711	−	38.2282i	0.756586	−	1.31045i
$852$	5.80438	−	21.6622i	0.198855	−	0.742136i
$853$	−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
$856$	−1.96214	+	0.258321i	−0.0670647	+	0.00882924i
$857$	7.32963	−	5.62422i	0.250375	−	0.192120i	−0.475947	−	0.879474i	$-0.657895\pi$
$857$	7.32963	−	5.62422i	0.250375	−	0.192120i	0.726322	+	0.687354i	$0.241228\pi$
$858$	2.49938	+	9.32780i	0.0853274	+	0.318446i
$859$	−33.7790	−	9.05105i	−1.15252	−	0.308818i	−0.368548	−	0.929609i	$-0.620145\pi$
$859$	−33.7790	−	9.05105i	−1.15252	−	0.308818i	−0.783976	+	0.620791i	$0.786812\pi$
$860$	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	$-0.608772\pi$
$863$	9.20361	−	5.31371i	0.313295	−	0.180881i	0.648400	+	0.761300i	$0.275439\pi$
$864$	8.21682	+	1.08176i	0.279542	+	0.0368024i
$865$	2.16622	−	0.580438i	0.0736538	−	0.0197355i
$866$	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
$870$	−0.385986	+	0.503026i	−0.0130861	+	0.0170542i
$871$	1.43488	+	0.828427i	0.0486190	+	0.0280702i
$872$	−8.95798	+	68.0426i	−0.303355	+	2.30421i
$873$	−18.7101	+	2.46323i	−0.633241	+	0.0833677i
$874$	8.82843	+	3.65685i	0.298626	+	0.123695i
$875$		0			0
$876$	37.8995	−	37.8995i	1.28051	−	1.28051i
$877$	−6.55621	−	49.7993i	−0.221387	−	1.68160i	−0.636065	−	0.771636i	$-0.719439\pi$
$877$	−6.55621	−	49.7993i	−0.221387	−	1.68160i	0.414678	−	0.909968i	$-0.363894\pi$
$878$	−15.6348	−	20.3756i	−0.527648	−	0.687644i
$879$	−1.74385	+	13.2458i	−0.0588185	+	0.446771i
$880$	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	$0.457022\pi$
$884$	−21.7234	−	5.14074i	−0.730637	−	0.172902i
$885$	2.48528	−	4.30463i	0.0835418	−	0.144699i
$886$	−55.4981	+	14.8707i	−1.86449	+	0.499590i
$887$	26.8170	−	34.9486i	0.900426	−	1.17346i	−0.0837890	−	0.996484i	$-0.526702\pi$
$887$	26.8170	−	34.9486i	0.900426	−	1.17346i	0.984215	−	0.176975i	$-0.0566312\pi$
$888$			44.1421i			1.48131i
$889$		0			0
$890$	−4.65685	+	11.2426i	−0.156098	+	0.376854i
$891$	0.0585203	+	0.444506i	0.00196050	+	0.0148915i
$892$	−4.78434	−	17.8554i	−0.160192	−	0.597843i
$893$	1.10885	+	4.13829i	0.0371063	+	0.138483i
$894$	−5.78834	−	43.9668i	−0.193591	−	1.47047i
$895$	1.75736	−	4.24264i	0.0587420	−	0.141816i
$896$		0			0
$897$			7.31371i			0.244198i
$898$	−17.8045	+	23.2033i	−0.594144	+	0.774304i
$899$	−2.40060	+	0.643238i	−0.0800644	+	0.0214532i
$900$	15.4497	−	26.7597i	0.514992	−	0.891992i
$901$	3.06280	+	4.96178i	0.102037	+	0.165301i
$902$	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
$906$	−2.44609	+	18.5799i	−0.0812659	+	0.617276i
$907$	8.17996	+	10.6603i	0.271611	+	0.353970i	0.909166	−	0.416435i	$-0.136721\pi$
$907$	8.17996	+	10.6603i	0.271611	+	0.353970i	−0.637555	+	0.770405i	$0.720054\pi$
$908$	−8.69255	−	66.0265i	−0.288473	−	2.19117i
$909$	−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	$0.595033\pi$
$912$	−2.66704	+	0.351122i	−0.0883144	+	0.0116268i
$913$	3.97594	−	30.2002i	0.131584	−	0.999482i
$914$	27.5387	+	15.8995i	0.910900	+	0.525909i
$915$	1.92993	−	2.51513i	0.0638015	−	0.0831477i
$916$	−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	0.661636	−	0.749826i	$-0.269863\pi$
$919$	−9.65685	−	16.7262i	−0.318550	−	0.551745i	−0.980186	+	0.198080i	$0.936529\pi$
$920$	15.5921	−	4.17789i	0.514057	−	0.137741i
$921$	28.0540	+	3.69337i	0.924410	+	0.121701i
$922$	−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
$926$	−34.1104	−	9.13986i	−1.12094	−	0.300354i
$927$	5.90843	+	22.0506i	0.194058	+	0.724236i
$928$	−0.398846	+	0.306045i	−0.0130928	+	0.0100464i
$929$	−17.1925	+	2.26343i	−0.564066	+	0.0742607i	−0.407167	−	0.913354i	$-0.633483\pi$
$929$	−17.1925	+	2.26343i	−0.564066	+	0.0742607i	−0.156899	+	0.987615i	$0.550150\pi$
$930$	14.4853	−	6.00000i	0.474991	−	0.196748i
$931$		0			0
$932$	12.8787	+	31.0919i	0.421855	+	1.01845i
$933$	7.19491	−	26.8518i	0.235551	−	0.879087i
$934$	39.3848	−	68.2164i	1.28871	−	2.23211i
$935$	7.89898	−	2.36773i	0.258324	−	0.0774329i
$936$	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
$940$	12.0221	+	9.22486i	0.392117	+	0.300882i
$941$	−24.2807	−	31.6432i	−0.791527	−	1.03154i	−0.998583	−	0.0532087i	$-0.983055\pi$
$941$	−24.2807	−	31.6432i	−0.791527	−	1.03154i	0.207057	−	0.978329i	$-0.433612\pi$
$942$	20.0199	−	15.3618i	0.652285	−	0.500516i
$943$	5.60139	+	1.50089i	0.182406	+	0.0488757i
$944$	−12.7279	+	12.7279i	−0.414259	+	0.414259i
$945$		0			0
$946$	−2.00000	+	4.82843i	−0.0650256	+	0.156986i
$947$	−24.3135	−	18.6564i	−0.790084	−	0.606253i	0.132883	−	0.991132i	$-0.457576\pi$
$947$	−24.3135	−	18.6564i	−0.790084	−	0.606253i	−0.922967	+	0.384879i	$0.874243\pi$
$948$	−17.1464	−	9.89949i	−0.556890	−	0.321521i
$949$	−18.1354	−	2.38757i	−0.588700	−	0.0775038i
$950$	2.28497	−	8.52761i	0.0741341	−	0.276672i
$951$	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	$0.202194\pi$
$954$	1.61571	−	6.02993i	0.0523107	−	0.195226i
$955$	15.1764	+	1.99801i	0.491096	+	0.0646540i
$956$	−49.1639	−	28.3848i	−1.59007	−	0.918029i
$957$	−0.711386	−	0.545866i	−0.0229959	−	0.0176453i
$958$	4.75736	−	11.4853i	0.153703	−	0.371073i
$959$		0			0
$960$	5.75736	−	5.75736i	0.185818	−	0.185818i
$961$	29.4181	+	7.88255i	0.948971	+	0.254276i
$962$	25.0249	−	19.2023i	0.806836	−	0.619107i
$963$	0.499038	+	0.650359i	0.0160813	+	0.0209575i
$964$	−10.8255	−	8.30672i	−0.348667	−	0.267542i
$965$			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
$969$	−3.67810	−	0.374507i	−0.118158	−	0.0120309i
$970$	−9.53553	+	16.5160i	−0.306168	+	0.530298i
$971$	−13.3913	+	49.9771i	−0.429748	+	1.60384i	0.323583	+	0.946200i	$0.395113\pi$
$971$	−13.3913	+	49.9771i	−0.429748	+	1.60384i	−0.753331	+	0.657642i	$0.771554\pi$
$972$	22.6985	+	54.7990i	0.728054	+	1.75768i
$973$		0			0
$974$	−58.6985	+	24.3137i	−1.88082	+	0.779061i
$975$	6.69918	−	0.881964i	0.214545	−	0.0282454i
$976$	−9.10810	+	6.98889i	−0.291543	+	0.223709i
$977$	−9.93471	−	37.0768i	−0.317840	−	1.18619i	−0.921317	−	0.388813i	$-0.872885\pi$
$977$	−9.93471	−	37.0768i	−0.317840	−	1.18619i	0.603477	−	0.797380i	$-0.293781\pi$
$978$	21.3877	+	5.73081i	0.683902	+	0.183251i
$979$	−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
$983$	−9.65819	−	1.27152i	−0.308048	−	0.0405553i	−0.0250827	−	0.999685i	$-0.507985\pi$
$983$	−9.65819	−	1.27152i	−0.308048	−	0.0405553i	−0.282966	+	0.959130i	$0.591318\pi$
$984$	−5.60139	+	1.50089i	−0.178566	+	0.0478466i
$985$	−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
$989$	−2.40957	+	3.14021i	−0.0766198	+	0.0998529i
$990$	−7.64564	−	4.41421i	−0.242994	−	0.140293i
$991$	−5.33022	+	40.4870i	−0.169320	+	1.28611i	0.669953	+	0.742403i	$0.266314\pi$
$991$	−5.33022	+	40.4870i	−0.169320	+	1.28611i	−0.839273	+	0.543710i	$0.817019\pi$
$992$	12.3252	−	1.62265i	0.391326	−	0.0515191i
$993$	−21.7990	−	9.02944i	−0.691770	−	0.286541i
$994$		0			0
$995$	−6.24264	+	6.24264i	−0.197905	+	0.197905i
$996$	6.30499	+	47.8911i	0.199781	+	1.51749i
$997$	−4.57932	−	5.96788i	−0.145028	−	0.189005i	0.715191	−	0.698930i	$-0.246340\pi$
$997$	−4.57932	−	5.96788i	−0.145028	−	0.189005i	−0.860219	+	0.509925i	$0.829673\pi$
$998$	−6.76311	+	51.3709i	−0.214082	+	1.62612i
$999$	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.508.1		8
7.2	even	3	inner	833.2.v.b.814.1		8
7.3	odd	6		833.2.l.a.491.1		4
7.4	even	3		17.2.d.a.15.1	yes	4
7.5	odd	6		833.2.v.a.814.1		8
7.6	odd	2		833.2.v.a.508.1		8
17.8	even	8	inner	833.2.v.b.263.1		8
21.11	odd	6		153.2.l.c.100.1		4
28.11	odd	6		272.2.v.d.49.1		4
35.4	even	6		425.2.m.a.151.1		4
35.18	odd	12		425.2.n.a.49.1		4
35.32	odd	12		425.2.n.b.49.1		4
119.4	even	12		289.2.d.c.155.1		4
119.11	odd	48		289.2.c.c.251.1		8
119.25	even	24		17.2.d.a.8.1	✓	4
119.32	even	24		289.2.d.b.179.1		4
119.39	odd	48		289.2.a.f.1.3		4
119.46	odd	48		289.2.a.f.1.4		4
119.53	even	24		289.2.d.c.179.1		4
119.59	odd	24		833.2.l.a.246.1		4
119.60	even	24		289.2.d.a.110.1		4
119.67	even	6		289.2.d.a.134.1		4
119.74	odd	48		289.2.c.c.251.2		8
119.76	odd	8		833.2.v.a.263.1		8
119.81	even	12		289.2.d.b.155.1		4
119.88	odd	48		289.2.b.b.288.2		4
119.93	even	24	inner	833.2.v.b.569.1		8
119.95	odd	48		289.2.c.c.38.3		8
119.109	odd	48		289.2.c.c.38.4		8
119.110	odd	24		833.2.v.a.569.1		8
119.116	odd	48		289.2.b.b.288.1		4
357.158	even	48		2601.2.a.bb.1.1		4
357.263	odd	24		153.2.l.c.127.1		4
357.284	even	48		2601.2.a.bb.1.2		4
476.39	even	48		4624.2.a.bp.1.3		4
476.263	odd	24		272.2.v.d.161.1		4
476.403	even	48		4624.2.a.bp.1.2		4
595.39	odd	48		7225.2.a.u.1.2		4
595.144	even	24		425.2.m.a.76.1		4
595.263	odd	24		425.2.n.b.399.1		4
595.284	odd	48		7225.2.a.u.1.1		4
595.382	odd	24		425.2.n.a.399.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.2.d.a.8.1	✓	4	119.25	even	24
17.2.d.a.15.1	yes	4	7.4	even	3
153.2.l.c.100.1		4	21.11	odd	6
153.2.l.c.127.1		4	357.263	odd	24
272.2.v.d.49.1		4	28.11	odd	6
272.2.v.d.161.1		4	476.263	odd	24
289.2.a.f.1.3		4	119.39	odd	48
289.2.a.f.1.4		4	119.46	odd	48
289.2.b.b.288.1		4	119.116	odd	48
289.2.b.b.288.2		4	119.88	odd	48
289.2.c.c.38.3		8	119.95	odd	48
289.2.c.c.38.4		8	119.109	odd	48
289.2.c.c.251.1		8	119.11	odd	48
289.2.c.c.251.2		8	119.74	odd	48
289.2.d.a.110.1		4	119.60	even	24
289.2.d.a.134.1		4	119.67	even	6
289.2.d.b.155.1		4	119.81	even	12
289.2.d.b.179.1		4	119.32	even	24
289.2.d.c.155.1		4	119.4	even	12
289.2.d.c.179.1		4	119.53	even	24
425.2.m.a.76.1		4	595.144	even	24
425.2.m.a.151.1		4	35.4	even	6
425.2.n.a.49.1		4	35.18	odd	12
425.2.n.a.399.1		4	595.382	odd	24
425.2.n.b.49.1		4	35.32	odd	12
425.2.n.b.399.1		4	595.263	odd	24
833.2.l.a.246.1		4	119.59	odd	24
833.2.l.a.491.1		4	7.3	odd	6
833.2.v.a.263.1		8	119.76	odd	8
833.2.v.a.508.1		8	7.6	odd	2
833.2.v.a.569.1		8	119.110	odd	24
833.2.v.a.814.1		8	7.5	odd	6
833.2.v.b.263.1		8	17.8	even	8	inner
833.2.v.b.508.1		8	1.1	even	1	trivial
833.2.v.b.569.1		8	119.93	even	24	inner
833.2.v.b.814.1		8	7.2	even	3	inner
2601.2.a.bb.1.1		4	357.158	even	48
2601.2.a.bb.1.2		4	357.284	even	48
4624.2.a.bp.1.2		4	476.403	even	48
4624.2.a.bp.1.3		4	476.39	even	48
7225.2.a.u.1.1		4	595.284	odd	48
7225.2.a.u.1.2		4	595.39	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 $\F_{q}$
Belyi maps

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+(-0.624844 + 2.33195i) q^{2} +(-1.07313 - 0.141281i) q^{3} +(-3.31552 - 1.91421i) q^{4} +(0.607206 + 0.465926i) q^{5} +(1.00000 - 2.41421i) q^{6} +(3.12132 - 3.12132i) q^{8} +(-1.76612 - 0.473232i) q^{9} +(-1.46593 + 1.12484i) q^{10} +(-1.59077 - 2.07313i) q^{11} +(3.28754 + 2.52262i) q^{12} -1.41421i q^{13} +(-0.585786 - 0.585786i) q^{15} +(1.50000 + 2.59808i) q^{16} +(1.18386 + 3.94949i) q^{17} +(2.20711 - 3.82282i) q^{18} +(0.214413 - 0.800199i) q^{19} +(-1.12132 - 2.70711i) q^{20} +(5.82843 - 2.41421i) q^{22} +(4.73703 - 0.623642i) q^{23} +(-3.79057 + 2.90861i) q^{24} +(-1.14248 - 4.26380i) q^{25} +(3.29788 + 0.883663i) q^{26} +(4.82843 + 2.00000i) q^{27} +(-0.292893 + 0.121320i) q^{29} +(1.73205 - 1.00000i) q^{30} +(7.77231 + 1.02324i) q^{31} +(1.53175 - 0.410432i) q^{32} +(1.41421 + 2.44949i) q^{33} +(-9.94975 + 0.292893i) q^{34} +(4.94975 + 4.94975i) q^{36} +(5.62422 - 7.32963i) q^{37} +(1.73205 + 1.00000i) q^{38} +(-0.199801 + 1.51764i) q^{39} +(3.34959 - 0.440982i) q^{40} +(1.12132 + 0.464466i) q^{41} +(-0.585786 + 0.585786i) q^{43} +(1.30581 + 9.91858i) q^{44} +(-0.851911 - 1.11023i) q^{45} +(-1.50561 + 11.4362i) q^{46} +(-4.47871 + 2.58579i) q^{47} +(-1.24264 - 3.00000i) q^{48} +10.6569 q^{50} +(-0.712455 - 4.40558i) q^{51} +(-2.70711 + 4.68885i) q^{52} +(1.36603 - 0.366025i) q^{53} +(-7.68092 + 10.0100i) q^{54} -2.00000i q^{55} +(-0.343146 + 0.828427i) q^{57} +(-0.0999004 - 0.758819i) q^{58} +(1.55291 + 5.79555i) q^{59} +(0.820863 + 3.06350i) q^{60} +(0.499502 + 3.79410i) q^{61} +(-7.24264 + 17.4853i) q^{62} +9.82843i q^{64} +(0.658919 - 0.858719i) q^{65} +(-6.59575 + 1.76733i) q^{66} +(-0.585786 + 1.01461i) q^{67} +(3.63505 - 15.3608i) q^{68} -5.17157 q^{69} +(-2.07107 - 5.00000i) q^{71} +(-6.98975 + 4.03553i) q^{72} +(1.68827 - 12.8237i) q^{73} +(13.5781 + 17.6953i) q^{74} +(0.623642 + 4.73703i) q^{75} +(-2.24264 + 2.24264i) q^{76} +(-3.41421 - 1.41421i) q^{78} +(-4.73703 + 0.623642i) q^{79} +(-0.299701 + 2.27646i) q^{80} +(-0.148586 - 0.0857864i) q^{81} +(-1.78376 + 2.32465i) q^{82} +(8.24264 + 8.24264i) q^{83} +(-1.12132 + 2.94975i) q^{85} +(-1.00000 - 1.73205i) q^{86} +(0.331453 - 0.0888127i) q^{87} +(-11.4362 - 1.50561i) q^{88} +(5.70346 - 3.29289i) q^{89} +(3.12132 - 1.29289i) q^{90} +(-16.8995 - 7.00000i) q^{92} +(-8.19615 - 2.19615i) q^{93} +(-3.23143 - 12.0599i) q^{94} +(0.503026 - 0.385986i) q^{95} +(-1.70176 + 0.224041i) q^{96} +(9.53553 - 3.94975i) q^{97} +(1.82843 + 4.41421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 4 q^{3} + 8 q^{6} + 8 q^{8} - 8 q^{9} - 4 q^{10} + 4 q^{11} + 4 q^{12} - 16 q^{15} + 12 q^{16} + 12 q^{18} - 8 q^{19} + 8 q^{20} + 24 q^{22} - 4 q^{23} - 12 q^{24} + 4 q^{25} + 4 q^{26}+ \cdots - 8 q^{99}+O(q^{100}) \) 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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