LMFDB - Embedded newform 605.2.m.g.112.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(112,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 2]))

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

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

chi := DirichletCharacter("605.112");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.m (of order $20$, 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$20$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			112.19
Character	$\chi$	$=$	605.112
Dual form			605.2.m.g.578.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.05904 + 2.07848i) q^{2} +(-0.318551 + 2.01125i) q^{3} +(-2.02296 + 2.78437i) q^{4} +(2.18295 + 0.484484i) q^{5} +(-4.51772 + 1.46790i) q^{6} +(-4.54674 + 0.720133i) q^{7} +(-3.32162 - 0.526094i) q^{8} +(-1.09050 - 0.354324i) q^{9} +O(q^{10})$	\(q+(1.05904 + 2.07848i) q^{2} +(-0.318551 + 2.01125i) q^{3} +(-2.02296 + 2.78437i) q^{4} +(2.18295 + 0.484484i) q^{5} +(-4.51772 + 1.46790i) q^{6} +(-4.54674 + 0.720133i) q^{7} +(-3.32162 - 0.526094i) q^{8} +(-1.09050 - 0.354324i) q^{9} +(1.30484 + 5.05032i) q^{10} +(-4.95565 - 4.95565i) q^{12} +(2.18403 - 1.11282i) q^{13} +(-6.31197 - 8.68769i) q^{14} +(-1.66980 + 4.23614i) q^{15} +(-0.297192 - 0.914662i) q^{16} +(-1.67563 - 0.853774i) q^{17} +(-0.418424 - 2.64182i) q^{18} +(1.38826 - 1.00863i) q^{19} +(-5.76500 + 5.09804i) q^{20} -9.37405i q^{21} +(0.313926 - 0.313926i) q^{23} +(2.11622 - 6.51304i) q^{24} +(4.53055 + 2.11521i) q^{25} +(4.62596 + 3.36096i) q^{26} +(-1.71340 + 3.36274i) q^{27} +(7.19277 - 14.1166i) q^{28} +(2.29174 + 1.66504i) q^{29} +(-10.5731 + 1.01558i) q^{30} +(0.725999 - 2.23440i) q^{31} +(-3.16967 + 3.16967i) q^{32} -4.38695i q^{34} +(-10.2742 - 0.630809i) q^{35} +(3.19260 - 2.31956i) q^{36} +(-0.287467 - 1.81500i) q^{37} +(3.56664 + 1.81730i) q^{38} +(1.54244 + 4.74714i) q^{39} +(-6.99606 - 2.75771i) q^{40} +(4.45234 + 6.12812i) q^{41} +(19.4838 - 9.92751i) q^{42} +(-4.63235 - 4.63235i) q^{43} +(-2.20884 - 1.30180i) q^{45} +(0.984950 + 0.320030i) q^{46} +(-2.17672 - 0.344758i) q^{47} +(1.93429 - 0.306361i) q^{48} +(13.4969 - 4.38541i) q^{49} +(0.401606 + 11.6568i) q^{50} +(2.25093 - 3.09814i) q^{51} +(-1.31971 + 8.33234i) q^{52} +(6.07129 + 11.9156i) q^{53} -8.80396 q^{54} +15.4814 q^{56} +(1.58638 + 3.11344i) q^{57} +(-1.03373 + 6.52669i) q^{58} +(2.43363 - 3.34961i) q^{59} +(-8.41701 - 13.2189i) q^{60} +(2.33575 - 0.758930i) q^{61} +(5.41302 - 0.857338i) q^{62} +(5.21337 + 0.825717i) q^{63} +(-11.7742 - 3.82568i) q^{64} +(5.30678 - 1.37110i) q^{65} +(8.24053 + 8.24053i) q^{67} +(5.76695 - 2.93841i) q^{68} +(0.531383 + 0.731386i) q^{69} +(-9.56968 - 22.0228i) q^{70} +(-2.88398 - 8.87597i) q^{71} +(3.43581 + 1.75063i) q^{72} +(-2.20858 - 13.9444i) q^{73} +(3.46801 - 2.51965i) q^{74} +(-5.69744 + 8.43828i) q^{75} +5.90584i q^{76} +(-8.23334 + 8.23334i) q^{78} +(0.657095 - 2.02233i) q^{79} +(-0.205616 - 2.14065i) q^{80} +(-9.00041 - 6.53918i) q^{81} +(-8.02199 + 15.7440i) q^{82} +(-6.77566 + 13.2980i) q^{83} +(26.1008 + 18.9633i) q^{84} +(-3.24417 - 2.67556i) q^{85} +(4.72242 - 14.5341i) q^{86} +(-4.07886 + 4.07886i) q^{87} -4.75744i q^{89} +(0.366523 - 5.96969i) q^{90} +(-9.12886 + 6.63251i) q^{91} +(0.239025 + 1.50914i) q^{92} +(4.26267 + 2.17194i) q^{93} +(-1.58866 - 4.88939i) q^{94} +(3.51917 - 1.52920i) q^{95} +(-5.36531 - 7.38471i) q^{96} +(-12.3234 + 6.27908i) q^{97} +(23.4088 + 23.4088i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 8 q^{3} + 4 q^{5}+O(q^{10}) $ 160 * q - 8 * q^3 + 4 * q^5	$ 160 q - 8 q^{3} + 4 q^{5} - 128 q^{12} - 32 q^{15} + 24 q^{16} - 32 q^{20} - 96 q^{23} + 52 q^{25} + 8 q^{26} - 32 q^{27} - 16 q^{31} + 40 q^{36} - 36 q^{37} - 32 q^{38} - 32 q^{42} + 256 q^{45} - 32 q^{47} + 16 q^{48} + 68 q^{53} + 320 q^{56} - 132 q^{58} + 64 q^{60} - 352 q^{67} + 8 q^{70} + 16 q^{75} - 992 q^{78} + 164 q^{80} + 40 q^{81} - 100 q^{82} + 80 q^{86} + 96 q^{91} + 56 q^{92} - 24 q^{93} + 68 q^{97}+O(q^{100}) $ 160 * q - 8 * q^3 + 4 * q^5 - 128 * q^12 - 32 * q^15 + 24 * q^16 - 32 * q^20 - 96 * q^23 + 52 * q^25 + 8 * q^26 - 32 * q^27 - 16 * q^31 + 40 * q^36 - 36 * q^37 - 32 * q^38 - 32 * q^42 + 256 * q^45 - 32 * q^47 + 16 * q^48 + 68 * q^53 + 320 * q^56 - 132 * q^58 + 64 * q^60 - 352 * q^67 + 8 * q^70 + 16 * q^75 - 992 * q^78 + 164 * q^80 + 40 * q^81 - 100 * q^82 + 80 * q^86 + 96 * q^91 + 56 * q^92 - 24 * q^93 + 68 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.05904	+	2.07848i	0.748855	+	1.46971i	0.878293	+	0.478123i	$0.158683\pi$
$2$	1.05904	+	2.07848i	0.748855	+	1.46971i	−0.129438	+	0.991588i	$0.541317\pi$
$3$	−0.318551	+	2.01125i	−0.183916	+	1.16120i	0.707062	+	0.707151i	$0.250020\pi$
$3$	−0.318551	+	2.01125i	−0.183916	+	1.16120i	−0.890978	+	0.454047i	$0.849980\pi$
$4$	−2.02296	+	2.78437i	−1.01148	+	1.39218i
$5$	2.18295	+	0.484484i	0.976245	+	0.216668i
$5$	2.18295	+	0.484484i	0.976245	+	0.216668i
$6$	−4.51772	+	1.46790i	−1.84435	+	0.599266i
$7$	−4.54674	+	0.720133i	−1.71851	+	0.272185i	−0.936394	−	0.350951i	$-0.885858\pi$
$7$	−4.54674	+	0.720133i	−1.71851	+	0.272185i	−0.782114	+	0.623136i	$0.785858\pi$
$8$	−3.32162	−	0.526094i	−1.17437	−	0.186002i
$9$	−1.09050	−	0.354324i	−0.363499	−	0.118108i
$10$	1.30484	+	5.05032i	0.412627	+	1.59705i
$11$		0			0
$11$		0			0
$12$	−4.95565	−	4.95565i	−1.43057	−	1.43057i
$13$	2.18403	−	1.11282i	0.605742	−	0.308641i	−0.124086	−	0.992271i	$-0.539600\pi$
$13$	2.18403	−	1.11282i	0.605742	−	0.308641i	0.729828	+	0.683631i	$0.239600\pi$
$14$	−6.31197	−	8.68769i	−1.68695	−	2.32188i
$15$	−1.66980	+	4.23614i	−0.431141	+	1.09377i
$16$	−0.297192	−	0.914662i	−0.0742979	−	0.228665i
$17$	−1.67563	−	0.853774i	−0.406399	−	0.207071i	0.238827	−	0.971062i	$-0.423237\pi$
$17$	−1.67563	−	0.853774i	−0.406399	−	0.207071i	−0.645226	+	0.763991i	$0.723237\pi$
$18$	−0.418424	−	2.64182i	−0.0986234	−	0.622684i
$19$	1.38826	−	1.00863i	0.318488	−	0.231395i	−0.417042	−	0.908887i	$-0.636933\pi$
$19$	1.38826	−	1.00863i	0.318488	−	0.231395i	0.735530	+	0.677492i	$0.236933\pi$
$20$	−5.76500	+	5.09804i	−1.28909	+	1.13996i
$21$		−	9.37405i		−	2.04559i
$22$		0			0
$23$	0.313926	−	0.313926i	0.0654581	−	0.0654581i	−0.673620	−	0.739078i	$-0.735261\pi$
$23$	0.313926	−	0.313926i	0.0654581	−	0.0654581i	0.739078	+	0.673620i	$0.235261\pi$
$24$	2.11622	−	6.51304i	0.431971	−	1.32947i
$25$	4.53055	+	2.11521i	0.906110	+	0.423042i
$26$	4.62596	+	3.36096i	0.907226	+	0.659138i
$27$	−1.71340	+	3.36274i	−0.329744	+	0.647159i
$28$	7.19277	−	14.1166i	1.35931	−	2.66779i
$29$	2.29174	+	1.66504i	0.425565	+	0.309191i	0.779873	−	0.625938i	$-0.215284\pi$
$29$	2.29174	+	1.66504i	0.425565	+	0.309191i	−0.354308	+	0.935129i	$0.615284\pi$
$30$	−10.5731	+	1.01558i	−1.93038	+	0.185419i
$31$	0.725999	−	2.23440i	0.130393	−	0.401309i	−0.864452	−	0.502716i	$-0.832334\pi$
$31$	0.725999	−	2.23440i	0.130393	−	0.401309i	0.994845	+	0.101406i	$0.0323343\pi$
$32$	−3.16967	+	3.16967i	−0.560324	+	0.560324i
$33$		0			0
$34$		−	4.38695i		−	0.752355i
$35$	−10.2742	−	0.630809i	−1.73666	−	0.106626i
$36$	3.19260	−	2.31956i	0.532100	−	0.386593i
$37$	−0.287467	−	1.81500i	−0.0472594	−	0.298384i	0.952726	−	0.303831i	$-0.0982660\pi$
$37$	−0.287467	−	1.81500i	−0.0472594	−	0.298384i	−0.999985	+	0.00544758i	$0.998266\pi$
$38$	3.56664	+	1.81730i	0.578586	+	0.294804i
$39$	1.54244	+	4.74714i	0.246988	+	0.760150i
$40$	−6.99606	−	2.75771i	−1.10617	−	0.436032i
$41$	4.45234	+	6.12812i	0.695338	+	0.957051i	0.999989	+	0.00458685i	$0.00146005\pi$
$41$	4.45234	+	6.12812i	0.695338	+	0.957051i	−0.304651	+	0.952464i	$0.598540\pi$
$42$	19.4838	−	9.92751i	3.00642	−	1.53185i
$43$	−4.63235	−	4.63235i	−0.706427	−	0.706427i	0.259355	−	0.965782i	$-0.416490\pi$
$43$	−4.63235	−	4.63235i	−0.706427	−	0.706427i	−0.965782	+	0.259355i	$0.916490\pi$
$44$		0			0
$45$	−2.20884	−	1.30180i	−0.329274	−	0.194061i
$46$	0.984950	+	0.320030i	0.145223	+	0.0471858i
$47$	−2.17672	−	0.344758i	−0.317507	−	0.0502882i	−0.00435305	−	0.999991i	$-0.501386\pi$
$47$	−2.17672	−	0.344758i	−0.317507	−	0.0502882i	−0.313154	+	0.949702i	$0.601386\pi$
$48$	1.93429	−	0.306361i	0.279190	−	0.0442194i
$49$	13.4969	−	4.38541i	1.92813	−	0.626486i
$50$	0.401606	+	11.6568i	0.0567956	+	1.64852i
$51$	2.25093	−	3.09814i	0.315193	−	0.433826i
$52$	−1.31971	+	8.33234i	−0.183011	+	1.15549i
$53$	6.07129	+	11.9156i	0.833956	+	1.63673i	0.769357	+	0.638819i	$0.220577\pi$
$53$	6.07129	+	11.9156i	0.833956	+	1.63673i	0.0645984	+	0.997911i	$0.479423\pi$
$54$	−8.80396			−1.19807
$55$		0			0
$56$	15.4814			2.06879
$57$	1.58638	+	3.11344i	0.210121	+	0.412385i
$58$	−1.03373	+	6.52669i	−0.135735	+	0.856997i
$59$	2.43363	−	3.34961i	0.316832	−	0.436081i	−0.620665	−	0.784076i	$-0.713137\pi$
$59$	2.43363	−	3.34961i	0.316832	−	0.436081i	0.937497	+	0.347995i	$0.113137\pi$
$60$	−8.41701	−	13.2189i	−1.08663	−	1.70655i
$61$	2.33575	−	0.758930i	0.299062	−	0.0971711i	−0.155643	−	0.987813i	$-0.549745\pi$
$61$	2.33575	−	0.758930i	0.299062	−	0.0971711i	0.454705	+	0.890642i	$0.349745\pi$
$62$	5.41302	−	0.857338i	0.687454	−	0.108882i
$63$	5.21337	+	0.825717i	0.656823	+	0.104031i
$64$	−11.7742	−	3.82568i	−1.47178	−	0.478210i
$65$	5.30678	−	1.37110i	0.658225	−	0.170064i
$66$		0			0
$67$	8.24053	+	8.24053i	1.00674	+	1.00674i	0.999977	+	0.00676329i	$0.00215284\pi$
$67$	8.24053	+	8.24053i	1.00674	+	1.00674i	0.00676329	+	0.999977i	$0.497847\pi$
$68$	5.76695	−	2.93841i	0.699345	−	0.356334i
$69$	0.531383	+	0.731386i	0.0639710	+	0.0880485i
$70$	−9.56968	−	22.0228i	−1.14380	−	2.63223i
$71$	−2.88398	−	8.87597i	−0.342265	−	1.05338i	−0.963032	−	0.269389i	$-0.913178\pi$
$71$	−2.88398	−	8.87597i	−0.342265	−	1.05338i	0.620766	−	0.783996i	$-0.286822\pi$
$72$	3.43581	+	1.75063i	0.404914	+	0.206314i
$73$	−2.20858	−	13.9444i	−0.258495	−	1.63207i	−0.685675	−	0.727908i	$-0.740493\pi$
$73$	−2.20858	−	13.9444i	−0.258495	−	1.63207i	0.427180	−	0.904167i	$-0.359507\pi$
$74$	3.46801	−	2.51965i	0.403148	−	0.292904i
$75$	−5.69744	+	8.43828i	−0.657883	+	0.974369i
$76$			5.90584i			0.677446i
$77$		0			0
$78$	−8.23334	+	8.23334i	−0.932243	+	0.932243i
$79$	0.657095	−	2.02233i	0.0739289	−	0.227530i	−0.907263	−	0.420563i	$-0.861833\pi$
$79$	0.657095	−	2.02233i	0.0739289	−	0.227530i	0.981192	+	0.193033i	$0.0618325\pi$
$80$	−0.205616	−	2.14065i	−0.0229885	−	0.239331i
$81$	−9.00041	−	6.53918i	−1.00005	−	0.726576i
$82$	−8.02199	+	15.7440i	−0.885880	+	1.73864i
$83$	−6.77566	+	13.2980i	−0.743725	+	1.45964i	0.139267	+	0.990255i	$0.455525\pi$
$83$	−6.77566	+	13.2980i	−0.743725	+	1.45964i	−0.882992	+	0.469388i	$0.844475\pi$
$84$	26.1008	+	18.9633i	2.84783	+	2.06907i
$85$	−3.24417	−	2.67556i	−0.351880	−	0.290205i
$86$	4.72242	−	14.5341i	0.509232	−	1.56725i
$87$	−4.07886	+	4.07886i	−0.437300	+	0.437300i
$88$		0			0
$89$		−	4.75744i		−	0.504288i	−0.967690	−	0.252144i	$-0.918864\pi$
$89$		−	4.75744i		−	0.504288i	0.967690	−	0.252144i	$-0.0811357\pi$
$90$	0.366523	−	5.96969i	0.0386349	−	0.629261i
$91$	−9.12886	+	6.63251i	−0.956965	+	0.695275i
$92$	0.239025	+	1.50914i	0.0249201	+	0.157339i
$93$	4.26267	+	2.17194i	0.442018	+	0.225219i
$94$	−1.58866	−	4.88939i	−0.163858	−	0.504302i
$95$	3.51917	−	1.52920i	0.361059	−	0.156892i
$96$	−5.36531	−	7.38471i	−0.547594	−	0.753699i
$97$	−12.3234	+	6.27908i	−1.25125	+	0.637544i	−0.948877	−	0.315646i	$-0.897779\pi$
$97$	−12.3234	+	6.27908i	−1.25125	+	0.637544i	−0.302373	+	0.953190i	$0.597779\pi$
$98$	23.4088	+	23.4088i	2.36464	+	2.36464i
$99$		0			0
$100$	−15.0546	+	8.33572i	−1.50546	+	0.833572i
$101$	2.99430	+	0.972906i	0.297944	+	0.0968078i	0.454174	−	0.890913i	$-0.349934\pi$
$101$	2.99430	+	0.972906i	0.297944	+	0.0968078i	−0.156231	+	0.987721i	$0.549934\pi$
$102$	8.82326	+	1.39747i	0.873633	+	0.138370i
$103$	9.59196	−	1.51922i	0.945124	−	0.149693i	0.335195	−	0.942149i	$-0.391198\pi$
$103$	9.59196	−	1.51922i	0.945124	−	0.149693i	0.609929	+	0.792456i	$0.291198\pi$
$104$	−7.83999	+	2.54737i	−0.768774	+	0.249790i
$105$	4.54158	−	20.4631i	0.443213	−	1.99699i
$106$	−18.3366	+	25.2382i	−1.78101	+	2.45135i
$107$	−1.71665	+	10.8385i	−0.165954	+	1.04780i	0.754316	+	0.656512i	$0.227969\pi$
$107$	−1.71665	+	10.8385i	−0.165954	+	1.04780i	−0.920270	+	0.391284i	$0.872031\pi$
$108$	−5.89695	−	11.5734i	−0.567435	−	1.11365i
$109$	−0.410178			−0.0392880			−0.0196440	−	0.999807i	$-0.506253\pi$
$109$	−0.410178			−0.0392880			−0.0196440	+	0.999807i	$0.506253\pi$
$110$		0			0
$111$	3.74200			0.355174
$112$	2.00993	+	3.94471i	0.189921	+	0.372740i
$113$	1.39128	−	8.78418i	0.130880	−	0.826346i	−0.831675	−	0.555262i	$-0.812618\pi$
$113$	1.39128	−	8.78418i	0.130880	−	0.826346i	0.962556	−	0.271084i	$-0.0873822\pi$
$114$	−4.79120	+	6.59452i	−0.448737	+	0.617634i
$115$	0.837377	−	0.533193i	0.0780858	−	0.0497205i
$116$	−9.27219	+	3.01272i	−0.860901	+	0.279724i
$117$	−2.77598	+	0.439672i	−0.256639	+	0.0406477i
$118$	9.53942	+	1.51090i	0.878175	+	0.139089i
$119$	8.23347	+	2.67522i	0.754761	+	0.245237i
$120$	7.77506	−	13.1924i	0.709763	−	1.20429i
$121$		0			0
$122$	4.05108	+	4.05108i	0.366767	+	0.366767i
$123$	−13.7435	+	7.00266i	−1.23921	+	0.631408i
$124$	4.75271	+	6.54154i	0.426806	+	0.587448i
$125$	8.86518	+	6.81238i	0.792926	+	0.609318i
$126$	3.80493	+	11.7104i	0.338970	+	1.04324i
$127$	11.8901	+	6.05832i	1.05508	+	0.537589i	0.893403	−	0.449256i	$-0.148311\pi$
$127$	11.8901	+	6.05832i	1.05508	+	0.537589i	0.161674	+	0.986844i	$0.448311\pi$
$128$	−3.11532	−	19.6693i	−0.275358	−	1.73854i
$129$	10.7925	−	7.84119i	0.950224	−	0.690378i
$130$	8.46992	+	9.57801i	0.742861	+	0.840047i
$131$		−	10.7318i		−	0.937642i	−0.883293	−	0.468821i	$-0.844679\pi$
$131$		−	10.7318i		−	0.937642i	0.883293	−	0.468821i	$-0.155321\pi$
$132$		0			0
$133$	−5.58571	+	5.58571i	−0.484343	+	0.484343i
$134$	−8.40075	+	25.8549i	−0.725715	+	2.23352i
$135$	−5.36946	+	6.51058i	−0.462130	+	0.560341i
$136$	5.11664	+	3.71745i	0.438748	+	0.318769i
$137$	−1.95436	+	3.83564i	−0.166972	+	0.327701i	−0.959297	−	0.282398i	$-0.908870\pi$
$137$	−1.95436	+	3.83564i	−0.166972	+	0.327701i	0.792326	+	0.610099i	$0.208870\pi$
$138$	−0.957418	+	1.87904i	−0.0815009	+	0.159954i
$139$	10.8791	+	7.90413i	0.922753	+	0.670419i	0.944208	−	0.329350i	$-0.106830\pi$
$139$	10.8791	+	7.90413i	0.922753	+	0.670419i	−0.0214546	+	0.999770i	$0.506830\pi$
$140$	22.5407	−	27.3311i	1.90504	−	2.30990i
$141$	1.38679	−	4.26811i	0.116789	−	0.359440i
$142$	15.3943	−	15.3943i	1.29186	−	1.29186i
$143$		0			0
$144$			1.10274i			0.0918948i
$145$	4.19606	+	4.74502i	0.348464	+	0.394053i
$146$	26.6443	−	19.3582i	2.20510	−	1.60210i
$147$	4.52071	+	28.5426i	0.372862	+	2.35416i
$148$	5.63516	+	2.87125i	0.463207	+	0.236016i
$149$	0.652676	+	2.00873i	0.0534693	+	0.164561i	0.974225	−	0.225578i	$-0.0724269\pi$
$149$	0.652676	+	2.00873i	0.0534693	+	0.164561i	−0.920756	+	0.390139i	$0.872427\pi$
$150$	−23.5727	−	2.90555i	−1.92470	−	0.237237i
$151$	−5.47883	−	7.54096i	−0.445861	−	0.613675i	0.525641	−	0.850706i	$-0.323826\pi$
$151$	−5.47883	−	7.54096i	−0.445861	−	0.613675i	−0.971502	+	0.237032i	$0.923826\pi$
$152$	−5.14191	+	2.61993i	−0.417064	+	0.212505i
$153$	1.52475	+	1.52475i	0.123269	+	0.123269i
$154$		0			0
$155$	2.66735	−	4.52584i	0.214247	−	0.363524i
$156$	−16.3381	−	5.30856i	−1.30809	−	0.425025i
$157$	3.34231	+	0.529370i	0.266745	+	0.0422483i	0.288374	−	0.957518i	$-0.406885\pi$
$157$	3.34231	+	0.529370i	0.266745	+	0.0422483i	−0.0216289	+	0.999766i	$0.506885\pi$
$158$	4.89927	−	0.775968i	0.389765	−	0.0617327i
$159$	−25.8993	+	8.41518i	−2.05395	+	0.667367i
$160$	−8.45489	+	5.38358i	−0.668417	+	0.425609i
$161$	−1.20127	+	1.65341i	−0.0946735	+	0.130307i
$162$	4.05979	−	25.6325i	0.318967	−	2.01388i
$163$	−7.71943	−	15.1502i	−0.604632	−	1.18666i	−0.967037	−	0.254637i	$-0.918044\pi$
$163$	−7.71943	−	15.1502i	−0.604632	−	1.18666i	0.362404	−	0.932021i	$-0.381956\pi$
$164$	−26.0698			−2.03571
$165$		0			0
$166$	−34.8153			−2.70219
$167$	6.06520	+	11.9036i	0.469339	+	0.921130i	0.997410	+	0.0719298i	$0.0229158\pi$
$167$	6.06520	+	11.9036i	0.469339	+	0.921130i	−0.528070	+	0.849201i	$0.677084\pi$
$168$	−4.93163	+	31.1371i	−0.380483	+	2.40228i
$169$	−4.10958	+	5.65635i	−0.316121	+	0.435104i
$170$	2.12541	−	9.57649i	0.163011	−	0.734483i
$171$	−1.87127	+	0.608014i	−0.143100	+	0.0464960i
$172$	22.2692	−	3.52710i	1.69801	−	0.268939i
$173$	−6.74334	−	1.06804i	−0.512687	−	0.0812016i	−0.105270	−	0.994444i	$-0.533571\pi$
$173$	−6.74334	−	1.06804i	−0.512687	−	0.0812016i	−0.407417	+	0.913242i	$0.633571\pi$
$174$	−12.7975	−	4.15817i	−0.970179	−	0.315230i
$175$	−22.1225	−	6.35472i	−1.67230	−	0.480372i
$176$		0			0
$177$	5.96167	+	5.96167i	0.448107	+	0.448107i
$178$	9.88828	−	5.03833i	0.741158	−	0.377639i
$179$	−3.69433	−	5.08481i	−0.276127	−	0.380056i	0.648319	−	0.761369i	$-0.275472\pi$
$179$	−3.69433	−	5.08481i	−0.276127	−	0.380056i	−0.924446	+	0.381312i	$0.875472\pi$
$180$	8.09308	−	3.51672i	0.603222	−	0.262121i
$181$	1.10130	+	3.38946i	0.0818591	+	0.251936i	0.983607	−	0.180326i	$-0.0577153\pi$
$181$	1.10130	+	3.38946i	0.0818591	+	0.251936i	−0.901748	+	0.432263i	$0.857715\pi$
$182$	−23.4534	−	11.9501i	−1.73848	−	0.885801i
$183$	0.782346	+	4.93954i	0.0578327	+	0.365141i
$184$	−1.20790	+	0.877589i	−0.0890474	+	0.0646967i
$185$	0.251810	−	4.10133i	0.0185135	−	0.301535i
$186$			11.1601i			0.818295i
$187$		0			0
$188$	5.36335	−	5.36335i	0.391163	−	0.391163i
$189$	5.36877	−	16.5234i	0.390521	−	1.20190i
$190$	6.90536	+	5.69505i	0.500967	+	0.413162i
$191$	−7.85051	−	5.70373i	−0.568043	−	0.412707i	0.266351	−	0.963876i	$-0.414182\pi$
$191$	−7.85051	−	5.70373i	−0.568043	−	0.412707i	−0.834394	+	0.551169i	$0.814182\pi$
$192$	11.4451	−	22.4623i	0.825980	−	1.62108i
$193$	6.06974	−	11.9125i	0.436910	−	0.857484i	−0.562617	−	0.826718i	$-0.690205\pi$
$193$	6.06974	−	11.9125i	0.436910	−	0.857484i	0.999527	−	0.0307659i	$-0.00979464\pi$
$194$	−26.1019	−	18.9642i	−1.87401	−	1.36155i
$195$	1.06715	+	11.1101i	0.0764205	+	0.795607i
$196$	−15.0931	+	46.4518i	−1.07808	+	3.31798i
$197$	6.37464	−	6.37464i	0.454174	−	0.454174i	−0.442563	−	0.896737i	$-0.645931\pi$
$197$	6.37464	−	6.37464i	0.454174	−	0.454174i	0.896737	+	0.442563i	$0.145931\pi$
$198$		0			0
$199$		−	18.6070i		−	1.31902i	−0.751698	−	0.659508i	$-0.770765\pi$
$199$		−	18.6070i		−	1.31902i	0.751698	−	0.659508i	$-0.229235\pi$
$200$	−13.9360	−	9.40943i	−0.985423	−	0.665347i
$201$	−19.1988	+	13.9488i	−1.35418	+	0.983869i
$202$	1.14891	+	7.25395i	0.0808372	+	0.510386i
$203$	−11.6190	−	5.92017i	−0.815494	−	0.415515i
$204$	4.07281	+	12.5348i	0.285154	+	0.877613i
$205$	6.75026	+	15.5345i	0.471458	+	1.08497i
$206$	13.3160	+	18.3278i	0.927766	+	1.27696i
$207$	−0.453567	+	0.231104i	−0.0315251	+	0.0160628i
$208$	−1.66693	−	1.66693i	−0.115581	−	0.115581i
$209$		0			0
$210$	47.3420	−	12.2317i	3.26691	−	0.844064i
$211$	24.8508	+	8.07452i	1.71080	+	0.555873i	0.990467	−	0.137753i	$-0.0439880\pi$
$211$	24.8508	+	8.07452i	1.71080	+	0.555873i	0.720335	+	0.693626i	$0.243988\pi$
$212$	−45.4593	−	7.20005i	−3.12216	−	0.494501i
$213$	18.7705	−	2.97296i	1.28614	−	0.203704i
$214$	−24.3456	+	7.91037i	−1.66423	+	0.540742i
$215$	−7.86789	−	12.3565i	−0.536586	−	0.842706i
$216$	7.46039	−	10.2683i	0.507615	−	0.698672i
$217$	−1.69187	+	10.6820i	−0.114852	+	0.725144i
$218$	−0.434396	−	0.852549i	−0.0294210	−	0.0577419i
$219$	28.7494			1.94270
$220$		0			0
$221$	−4.60972			−0.310083
$222$	3.96293	+	7.77768i	0.265974	+	0.522004i
$223$	2.99548	−	18.9127i	0.200592	−	1.26649i	−0.657681	−	0.753297i	$-0.728462\pi$
$223$	2.99548	−	18.9127i	0.200592	−	1.26649i	0.858273	−	0.513193i	$-0.171538\pi$
$224$	12.1291	−	16.6943i	0.810409	−	1.11543i
$225$	−4.19108	−	3.91191i	−0.279405	−	0.260794i
$226$	19.7312	−	6.41106i	1.31250	−	0.426457i
$227$	18.5357	−	2.93576i	1.23026	−	0.194853i	0.492736	−	0.870179i	$-0.335997\pi$
$227$	18.5357	−	2.93576i	1.23026	−	0.194853i	0.737520	+	0.675326i	$0.235997\pi$
$228$	−11.8781	−	1.88131i	−0.786649	−	0.124593i
$229$	20.9827	+	6.81771i	1.38658	+	0.450527i	0.904827	−	0.425780i	$-0.140000\pi$
$229$	20.9827	+	6.81771i	1.38658	+	0.450527i	0.481753	+	0.876307i	$0.340000\pi$
$230$	1.99505	+	1.17580i	0.131550	+	0.0775301i
$231$		0			0
$232$	−6.73632	−	6.73632i	−0.442261	−	0.442261i
$233$	16.5794	−	8.44763i	1.08615	−	0.553422i	0.183162	−	0.983083i	$-0.441367\pi$
$233$	16.5794	−	8.44763i	1.08615	−	0.553422i	0.902991	+	0.429660i	$0.141367\pi$
$234$	−3.85373	−	5.30420i	−0.251926	−	0.346747i
$235$	−4.58464	−	1.80718i	−0.299069	−	0.117887i
$236$	4.40339	+	13.5522i	0.286636	+	0.882176i
$237$	3.85810	+	1.96580i	0.250610	+	0.127692i
$238$	3.15919	+	19.9463i	0.204780	+	1.29293i
$239$	−3.15616	+	2.29308i	−0.204155	+	0.148327i	−0.685165	−	0.728388i	$-0.740270\pi$
$239$	−3.15616	+	2.29308i	−0.204155	+	0.148327i	0.481010	+	0.876715i	$0.340270\pi$
$240$	4.37088	+	0.268360i	0.282139	+	0.0173226i
$241$			9.09968i			0.586162i	0.956088	+	0.293081i	$0.0946806\pi$
$241$			9.09968i			0.586162i	−0.956088	+	0.293081i	$0.905319\pi$
$242$		0			0
$243$	8.01299	−	8.01299i	0.514034	−	0.514034i
$244$	−2.61198	+	8.03886i	−0.167215	+	0.514635i
$245$	31.5877	−	3.03410i	2.01806	−	0.193841i
$246$	−29.1098	−	21.1495i	−1.85598	−	1.34845i
$247$	1.90958	−	3.74776i	0.121504	−	0.238464i
$248$	−3.58700	+	7.03988i	−0.227775	+	0.447033i
$249$	−24.5872	−	17.8637i	−1.55815	−	1.13206i
$250$	−4.77084	+	25.6407i	−0.301734	+	1.62166i
$251$	3.71334	−	11.4285i	0.234384	−	0.721359i	−0.762819	−	0.646612i	$-0.776185\pi$
$251$	3.71334	−	11.4285i	0.234384	−	0.721359i	0.997203	−	0.0747465i	$-0.0238148\pi$
$252$	−12.8455	+	12.8455i	−0.809193	+	0.809193i
$253$		0			0
$254$			31.1294i			1.95323i
$255$	6.41467	−	5.67255i	0.401702	−	0.355229i
$256$	17.5516	−	12.7520i	1.09698	−	0.797000i
$257$	−4.21517	−	26.6136i	−0.262935	−	1.66011i	−0.666761	−	0.745272i	$-0.732320\pi$
$257$	−4.21517	−	26.6136i	−0.262935	−	1.66011i	0.403825	−	0.914836i	$-0.367680\pi$
$258$	27.7275	+	14.1278i	1.72624	+	0.879561i
$259$	2.61408	+	8.04532i	0.162431	+	0.499912i
$260$	−6.91776	+	17.5497i	−0.429021	+	1.08839i
$261$	−1.90917	−	2.62774i	−0.118174	−	0.162653i
$262$	22.3059	−	11.3654i	1.37806	−	0.702158i
$263$	3.51126	+	3.51126i	0.216513	+	0.216513i	0.807027	−	0.590514i	$-0.201075\pi$
$263$	3.51126	+	3.51126i	0.216513	+	0.216513i	−0.590514	+	0.807027i	$0.701075\pi$
$264$		0			0
$265$	7.48042	+	28.9526i	0.459518	+	1.77854i
$266$	−17.5253	−	5.69432i	−1.07455	−	0.349141i
$267$	9.56843	+	1.51549i	0.585578	+	0.0927465i
$268$	−39.6149	+	6.27438i	−2.41986	+	0.383269i
$269$	16.7033	−	5.42722i	1.01842	−	0.330904i	0.248216	−	0.968705i	$-0.420156\pi$
$269$	16.7033	−	5.42722i	1.01842	−	0.330904i	0.770201	+	0.637801i	$0.220156\pi$
$270$	−19.2186	−	4.26538i	−1.16961	−	0.259583i
$271$	−0.403270	+	0.555054i	−0.0244969	+	0.0337171i	−0.821090	−	0.570799i	$-0.806634\pi$
$271$	−0.403270	+	0.555054i	−0.0244969	+	0.0337171i	0.796593	+	0.604516i	$0.206634\pi$
$272$	−0.282932	+	1.78637i	−0.0171553	+	0.108314i
$273$	−10.4316	−	20.4732i	−0.631352	−	1.23910i
$274$	−10.0421			−0.606663
$275$		0			0
$276$	−3.11141			−0.187285
$277$	−9.60346	−	18.8479i	−0.577016	−	1.13246i	−0.976460	−	0.215700i	$-0.930797\pi$
$277$	−9.60346	−	18.8479i	−0.577016	−	1.13246i	0.399444	−	0.916758i	$-0.369203\pi$
$278$	−4.90720	+	30.9828i	−0.294314	+	1.85823i
$279$	−1.58340	+	2.17936i	−0.0947956	+	0.130475i
$280$	33.7952	+	7.50051i	2.01965	+	0.448241i
$281$	7.69935	−	2.50167i	0.459305	−	0.149237i	−0.0702202	−	0.997532i	$-0.522370\pi$
$281$	7.69935	−	2.50167i	0.459305	−	0.149237i	0.529525	+	0.848294i	$0.322370\pi$
$282$	10.3399	−	1.63768i	0.615731	−	0.0975221i
$283$	−4.29336	−	0.680002i	−0.255214	−	0.0404219i	0.0275165	−	0.999621i	$-0.491240\pi$
$283$	−4.29336	−	0.680002i	−0.255214	−	0.0404219i	−0.282730	+	0.959199i	$0.591240\pi$
$284$	30.5481	+	9.92569i	1.81270	+	0.588981i
$285$	1.95457	+	7.56507i	0.115779	+	0.448116i
$286$		0			0
$287$	−24.6567	−	24.6567i	−1.45544	−	1.45544i
$288$	4.57960	−	2.33342i	0.269856	−	0.137498i
$289$	−7.91356	−	10.8921i	−0.465503	−	0.640710i
$290$	−5.41865	+	13.7466i	−0.318194	+	0.807230i
$291$	−8.70319	−	26.7857i	−0.510190	−	1.57020i
$292$	43.2943	+	22.0596i	2.53361	+	1.29094i
$293$	−1.47710	−	9.32606i	−0.0862933	−	0.544834i	−0.992524	−	0.122051i	$-0.961053\pi$
$293$	−1.47710	−	9.32606i	−0.0862933	−	0.544834i	0.906231	−	0.422784i	$-0.138947\pi$
$294$	−54.5378	+	39.6241i	−3.18071	+	2.31092i
$295$	6.93533	−	6.13297i	0.403790	−	0.357075i
$296$			6.17998i			0.359204i
$297$		0			0
$298$	−3.48390	+	3.48390i	−0.201817	+	0.201817i
$299$	0.336281	−	1.03497i	0.0194477	−	0.0598537i
$300$	−11.9696	−	32.9341i	−0.691064	−	1.90145i
$301$	24.3980	+	17.7262i	1.40628	+	1.02172i
$302$	9.87147	−	19.3739i	0.568039	−	1.11484i
$303$	−2.91060	+	5.71237i	−0.167210	+	0.328167i
$304$	−1.33513	−	0.970031i	−0.0765751	−	0.0556351i
$305$	5.46651	−	0.525075i	0.313012	−	0.0300657i
$306$	−1.55440	+	4.78395i	−0.0888591	+	0.273480i
$307$	−13.6423	+	13.6423i	−0.778608	+	0.778608i	−0.979594	−	0.200986i	$-0.935585\pi$
$307$	−13.6423	+	13.6423i	−0.778608	+	0.778608i	0.200986	+	0.979594i	$0.435585\pi$
$308$		0			0
$309$			19.7758i			1.12501i
$310$	12.2317	+	0.750995i	0.694715	+	0.0426536i
$311$	5.58551	−	4.05811i	0.316725	−	0.230114i	−0.418052	−	0.908423i	$-0.637287\pi$
$311$	5.58551	−	4.05811i	0.316725	−	0.230114i	0.734777	+	0.678309i	$0.237287\pi$
$312$	−2.62596	−	16.5797i	−0.148666	−	0.938639i
$313$	−10.3012	−	5.24871i	−0.582257	−	0.296675i	0.137944	−	0.990440i	$-0.455951\pi$
$313$	−10.3012	−	5.24871i	−0.582257	−	0.296675i	−0.720201	+	0.693765i	$0.755951\pi$
$314$	2.43936	+	7.50757i	0.137661	+	0.423676i
$315$	10.9805	+	4.32829i	0.618680	+	0.243872i
$316$	4.30163	+	5.92068i	0.241985	+	0.333064i
$317$	−19.7704	+	10.0735i	−1.11042	+	0.565785i	−0.910284	−	0.413984i	$-0.864137\pi$
$317$	−19.7704	+	10.0735i	−1.11042	+	0.565785i	−0.200131	+	0.979769i	$0.564137\pi$
$318$	−44.9192	−	44.9192i	−2.51894	−	2.51894i
$319$		0			0
$320$	−23.8491	−	14.0557i	−1.33321	−	0.785738i
$321$	−21.2521	−	6.90522i	−1.18618	−	0.385412i
$322$	−4.70878	−	0.745798i	−0.262410	−	0.0415617i
$323$	−3.18735	+	0.504826i	−0.177349	+	0.0280893i
$324$	36.4150	−	11.8319i	2.02305	−	0.657330i
$325$	12.2487	−	0.422000i	0.679437	−	0.0234083i
$326$	23.3143	−	32.0894i	1.29126	−	1.77727i
$327$	0.130663	−	0.824973i	0.00722567	−	0.0456211i
$328$	−11.5650	−	22.6976i	−0.638572	−	1.25327i
$329$	10.1453			0.559326
$330$		0			0
$331$	10.8195			0.594695			0.297347	−	0.954769i	$-0.403898\pi$
$331$	10.8195			0.594695			0.297347	+	0.954769i	$0.403898\pi$
$332$	−23.3195	−	45.7672i	−1.27983	−	2.51180i
$333$	−0.329615	+	2.08111i	−0.0180628	+	0.114044i
$334$	−18.3182	+	25.2129i	−1.00233	+	1.37959i
$335$	13.9963	+	21.9811i	0.764697	+	1.20095i
$336$	−8.57409	+	2.78589i	−0.467755	+	0.151983i
$337$	−13.9556	+	2.21035i	−0.760209	+	0.120405i	−0.524491	−	0.851416i	$-0.675744\pi$
$337$	−13.9556	+	2.21035i	−0.760209	+	0.120405i	−0.235718	+	0.971821i	$0.575744\pi$
$338$	−16.1088	−	2.55139i	−0.876205	−	0.138777i
$339$	17.2240	+	5.59643i	0.935481	+	0.303956i
$340$	14.0126	−	3.62040i	0.759938	−	0.196344i
$341$		0			0
$342$	−3.24550	−	3.24550i	−0.175497	−	0.175497i
$343$	−29.4971	+	15.0295i	−1.59269	+	0.811518i
$344$	12.9499	+	17.8240i	0.698210	+	0.961004i
$345$	0.805638	+	1.85403i	0.0433741	+	0.0998174i
$346$	−4.92157	−	15.1470i	−0.264585	−	0.814310i
$347$	−2.37627	−	1.21077i	−0.127565	−	0.0649975i	0.389043	−	0.921219i	$-0.372806\pi$
$347$	−2.37627	−	1.21077i	−0.127565	−	0.0649975i	−0.516608	+	0.856222i	$0.672806\pi$
$348$	−3.10567	−	19.6084i	−0.166481	−	1.05112i
$349$	2.56746	−	1.86537i	0.137433	−	0.0998508i	−0.516945	−	0.856019i	$-0.672931\pi$
$349$	2.56746	−	1.86537i	0.137433	−	0.0998508i	0.654378	+	0.756168i	$0.272931\pi$
$350$	−10.2204	−	52.7111i	−0.546305	−	2.81753i
$351$			9.25104i			0.493784i
$352$		0			0
$353$	26.2495	−	26.2495i	1.39712	−	1.39712i	0.588950	−	0.808169i	$-0.299541\pi$
$353$	26.2495	−	26.2495i	1.39712	−	1.39712i	0.808169	−	0.588950i	$-0.200459\pi$
$354$	−6.07759	+	18.7049i	−0.323020	+	0.994154i
$355$	−1.99532	−	20.7731i	−0.105900	−	1.10252i
$356$	13.2465	+	9.62412i	0.702061	+	0.510077i
$357$	−8.00333	+	15.7074i	−0.423581	+	0.831324i
$358$	6.65625	−	13.0636i	0.351794	−	0.690434i
$359$	16.5672	+	12.0368i	0.874382	+	0.635276i	0.931759	−	0.363077i	$-0.118274\pi$
$359$	16.5672	+	12.0368i	0.874382	+	0.635276i	−0.0573771	+	0.998353i	$0.518274\pi$
$360$	6.65206	+	5.48614i	0.350594	+	0.289145i
$361$	−4.96139	+	15.2696i	−0.261126	+	0.803663i
$362$	−5.87861	+	5.87861i	−0.308973	+	0.308973i
$363$		0			0
$364$		−	38.8354i		−	2.03553i
$365$	1.93463	−	31.5101i	0.101263	−	1.64931i
$366$	−9.43822	+	6.85727i	−0.493344	+	0.358435i
$367$	−4.46975	−	28.2209i	−0.233319	−	1.47312i	−0.774694	−	0.632337i	$-0.782096\pi$
$367$	−4.46975	−	28.2209i	−0.233319	−	1.47312i	0.541374	−	0.840782i	$-0.317904\pi$
$368$	−0.380432	−	0.193840i	−0.0198314	−	0.0101046i
$369$	−2.68392	−	8.26026i	−0.139719	−	0.430012i
$370$	8.79122	−	3.82009i	0.457034	−	0.198597i
$371$	−36.1854	−	49.8049i	−1.87865	−	2.58574i
$372$	−14.6707	+	7.47508i	−0.760639	+	0.387565i
$373$	23.0751	+	23.0751i	1.19478	+	1.19478i	0.975708	+	0.219076i	$0.0703043\pi$
$373$	23.0751	+	23.0751i	1.19478	+	1.19478i	0.219076	+	0.975708i	$0.429696\pi$
$374$		0			0
$375$	−16.5254	+	15.6600i	−0.853370	+	0.808681i
$376$	7.04887	+	2.29032i	0.363518	+	0.118114i
$377$	6.85813	+	1.08622i	0.353212	+	0.0559432i
$378$	40.0294	−	6.34003i	2.05889	−	0.326096i
$379$	−21.8307	+	7.09324i	−1.12137	+	0.364355i	−0.810290	−	0.586029i	$-0.800691\pi$
$379$	−21.8307	+	7.09324i	−1.12137	+	0.364355i	−0.311080	+	0.950384i	$0.600691\pi$
$380$	−2.86129	+	12.8922i	−0.146781	+	0.661354i
$381$	−15.9724	+	21.9842i	−0.818292	+	1.12628i
$382$	3.54110	−	22.3577i	0.181179	−	1.14392i
$383$	14.1519	+	27.7747i	0.723128	+	1.41922i	0.900403	+	0.435057i	$0.143272\pi$
$383$	14.1519	+	27.7747i	0.723128	+	1.41922i	−0.177275	+	0.984161i	$0.556728\pi$
$384$	40.5524			2.06943
$385$		0			0
$386$	31.1881			1.58743
$387$	3.41021	+	6.69291i	0.173351	+	0.340220i
$388$	7.44647	−	47.0151i	0.378037	−	2.38683i
$389$	2.42848	−	3.34251i	0.123129	−	0.169472i	−0.743003	−	0.669288i	$-0.766599\pi$
$389$	2.42848	−	3.34251i	0.123129	−	0.169472i	0.866131	+	0.499816i	$0.166599\pi$
$390$	−21.9619	+	13.9841i	−1.11208	+	0.708110i
$391$	−0.794044	+	0.258001i	−0.0401565	+	0.0130477i
$392$	−47.1387	+	7.46604i	−2.38087	+	0.377092i
$393$	21.5844	+	3.41863i	1.08879	+	0.172447i
$394$	20.0006	+	6.49858i	1.00761	+	0.327394i
$395$	2.41419	−	4.09629i	0.121471	−	0.206107i
$396$		0			0
$397$	−9.17863	−	9.17863i	−0.460662	−	0.460662i	0.438210	−	0.898872i	$-0.355613\pi$
$397$	−9.17863	−	9.17863i	−0.460662	−	0.460662i	−0.898872	+	0.438210i	$0.855613\pi$
$398$	38.6744	−	19.7056i	1.93857	−	0.987751i
$399$	−9.45495	−	13.0136i	−0.473339	−	0.651496i
$400$	0.588260	−	4.77254i	0.0294130	−	0.238627i
$401$	−5.31060	−	16.3443i	−0.265199	−	0.816198i	−0.991648	−	0.128977i	$-0.958831\pi$
$401$	−5.31060	−	16.3443i	−0.265199	−	0.816198i	0.726449	−	0.687221i	$-0.241169\pi$
$402$	−49.3246	−	25.1321i	−2.46009	−	1.25348i
$403$	−0.900875	−	5.68790i	−0.0448758	−	0.283334i
$404$	−8.76627	+	6.36907i	−0.436138	+	0.316873i
$405$	−16.4793	−	18.6353i	−0.818864	−	0.925994i
$406$		−	30.4196i		−	1.50970i
$407$		0			0
$408$	−9.10665	+	9.10665i	−0.450846	+	0.450846i
$409$	−9.44065	+	29.0553i	−0.466810	+	1.43669i	0.389882	+	0.920865i	$0.372516\pi$
$409$	−9.44065	+	29.0553i	−0.466810	+	1.43669i	−0.856692	+	0.515829i	$0.827484\pi$
$410$	−25.1393	+	30.4819i	−1.24154	+	1.50540i
$411$	−7.09188	−	5.15255i	−0.349817	−	0.254157i
$412$	−15.1741	+	29.7809i	−0.747575	+	1.46720i
$413$	−8.65293	+	16.9823i	−0.425783	+	0.835646i
$414$	−0.960691	−	0.697983i	−0.0472154	−	0.0343040i
$415$	−21.2336	+	25.7461i	−1.04232	+	1.26383i
$416$	−3.39539	+	10.4499i	−0.166473	+	0.512350i
$417$	−19.3628	+	19.3628i	−0.948198	+	0.948198i
$418$		0			0
$419$			7.07861i			0.345813i	0.984938	+	0.172906i	$0.0553158\pi$
$419$			7.07861i			0.345813i	−0.984938	+	0.172906i	$0.944684\pi$
$420$	47.7893	+	54.0415i	2.33188	+	2.63695i
$421$	−29.4670	+	21.4090i	−1.43613	+	1.04341i	−0.447302	+	0.894383i	$0.647615\pi$
$421$	−29.4670	+	21.4090i	−1.43613	+	1.04341i	−0.988833	+	0.149030i	$0.952385\pi$
$422$	9.53527	+	60.2033i	0.464170	+	2.93065i
$423$	2.25155	+	1.14722i	0.109474	+	0.0557798i
$424$	−13.8978	−	42.7731i	−0.674938	−	2.07725i
$425$	−5.78560	−	7.41237i	−0.280643	−	0.359553i
$426$	26.0580	+	35.8658i	1.26251	+	1.73770i
$427$	−10.0735	+	5.13271i	−0.487491	+	0.248389i
$428$	−26.7056	−	26.7056i	−1.29086	−	1.29086i
$429$		0			0
$430$	17.3504	−	29.4393i	0.836709	−	1.41969i
$431$	8.44725	+	2.74468i	0.406889	+	0.132206i	0.505309	−	0.862939i	$-0.331379\pi$
$431$	8.44725	+	2.74468i	0.406889	+	0.132206i	−0.0984193	+	0.995145i	$0.531379\pi$
$432$	3.58498	+	0.567804i	0.172482	+	0.0273185i
$433$	−10.2057	+	1.61642i	−0.490453	+	0.0776801i	−0.396763	−	0.917921i	$-0.629866\pi$
$433$	−10.2057	+	1.61642i	−0.490453	+	0.0776801i	−0.0936904	+	0.995601i	$0.529866\pi$
$434$	−23.9942	+	7.79619i	−1.15176	+	0.374229i
$435$	−10.8801	+	6.92781i	−0.521661	+	0.332163i
$436$	0.829774	−	1.14209i	0.0397390	−	0.0546960i
$437$	0.119176	−	0.752445i	0.00570094	−	0.0359943i
$438$	30.4468	+	59.7551i	1.45480	+	2.85521i
$439$	−13.7787			−0.657620			−0.328810	−	0.944396i	$-0.606648\pi$
$439$	−13.7787			−0.657620			−0.328810	+	0.944396i	$0.606648\pi$
$440$		0			0
$441$	−16.2722			−0.774865
$442$	−4.88188	−	9.58123i	−0.232207	−	0.455733i
$443$	−1.28019	+	8.08279i	−0.0608236	+	0.384025i	0.938433	+	0.345462i	$0.112278\pi$
$443$	−1.28019	+	8.08279i	−0.0608236	+	0.384025i	−0.999256	+	0.0385626i	$0.987722\pi$
$444$	−7.56991	+	10.4191i	−0.359252	+	0.494468i
$445$	2.30491	−	10.3853i	0.109263	−	0.492309i
$446$	42.4821	−	13.8033i	2.01159	−	0.653605i
$447$	−4.24797	+	0.672813i	−0.200922	+	0.0318230i
$448$	56.2894	+	8.91537i	2.65943	+	0.421212i
$449$	−32.8026	−	10.6582i	−1.54805	−	0.502992i	−0.594467	−	0.804120i	$-0.702637\pi$
$449$	−32.8026	−	10.6582i	−1.54805	−	0.502992i	−0.953584	+	0.301127i	$0.902637\pi$
$450$	3.69232	−	12.8540i	0.174058	−	0.605942i
$451$		0			0
$452$	21.6439	+	21.6439i	1.01804	+	1.01804i
$453$	16.9121	−	8.61713i	0.794599	−	0.404868i
$454$	25.7320	+	35.4170i	1.20766	+	1.66220i
$455$	−23.1412	+	10.0556i	−1.08488	+	0.471416i
$456$	−3.63139	−	11.1763i	−0.170055	−	0.523377i
$457$	−31.5967	−	16.0993i	−1.47803	−	0.753094i	−0.485401	−	0.874292i	$-0.661326\pi$
$457$	−31.5967	−	16.0993i	−1.47803	−	0.753094i	−0.992628	+	0.121198i	$0.961326\pi$
$458$	8.05109	+	50.8326i	0.376203	+	2.37525i
$459$	5.74204	−	4.17184i	0.268015	−	0.194725i
$460$	−0.209377	+	3.41019i	−0.00976224	+	0.159001i
$461$		−	26.6036i		−	1.23905i	−0.784975	−	0.619527i	$-0.787324\pi$
$461$		−	26.6036i		−	1.23905i	0.784975	−	0.619527i	$-0.212676\pi$
$462$		0			0
$463$	−1.31785	+	1.31785i	−0.0612455	+	0.0612455i	−0.737066	−	0.675821i	$-0.763789\pi$
$463$	−1.31785	+	1.31785i	−0.0612455	+	0.0612455i	0.675821	+	0.737066i	$0.263789\pi$
$464$	0.841867	−	2.59100i	0.0390827	−	0.120284i
$465$	8.25292	+	6.80643i	0.382720	+	0.315641i
$466$	35.1165	+	25.5136i	1.62674	+	1.18190i
$467$	12.2555	−	24.0527i	0.567116	−	1.11303i	−0.412276	−	0.911059i	$-0.635266\pi$
$467$	12.2555	−	24.0527i	0.567116	−	1.11303i	0.979392	−	0.201969i	$-0.0647341\pi$
$468$	4.39149	−	8.61878i	0.202997	−	0.398403i
$469$	−43.4018	−	31.5333i	−2.00411	−	1.45607i
$470$	−1.09913	−	11.4430i	−0.0506992	−	0.527825i
$471$	−2.12939	+	6.55360i	−0.0981173	+	0.301974i
$472$	−9.84581	+	9.84581i	−0.453190	+	0.453190i
$473$		0			0
$474$			10.1009i			0.463948i
$475$	8.42304	−	1.63319i	0.386476	−	0.0749357i
$476$	−24.1048	+	17.5131i	−1.10484	+	0.802714i
$477$	−2.39875	−	15.1451i	−0.109831	−	0.693446i
$478$	−8.10863	−	4.13156i	−0.370880	−	0.188973i
$479$	−9.94286	−	30.6010i	−0.454301	−	1.39819i	−0.871954	−	0.489588i	$-0.837147\pi$
$479$	−9.94286	−	30.6010i	−0.454301	−	1.39819i	0.417653	−	0.908606i	$-0.362853\pi$
$480$	−8.13442	−	18.7199i	−0.371284	−	0.854441i
$481$	−2.64761	−	3.64412i	−0.120720	−	0.166157i
$482$	−18.9135	+	9.63693i	−0.861488	+	0.438950i
$483$	−2.94276	−	2.94276i	−0.133900	−	0.133900i
$484$		0			0
$485$	−29.9435	+	7.73644i	−1.35966	+	0.351293i
$486$	25.1410	+	8.16879i	1.14042	+	0.370544i
$487$	18.4096	+	2.91580i	0.834220	+	0.132128i	0.558910	−	0.829228i	$-0.311220\pi$
$487$	18.4096	+	2.91580i	0.834220	+	0.132128i	0.275310	+	0.961356i	$0.411220\pi$
$488$	−8.15774	+	1.29206i	−0.369284	+	0.0584888i
$489$	32.9300	−	10.6996i	1.48915	−	0.483853i
$490$	39.7590	+	62.4413i	1.79613	+	2.82081i
$491$	−1.79202	+	2.46651i	−0.0808728	+	0.111312i	−0.847537	−	0.530737i	$-0.821915\pi$
$491$	−1.79202	+	2.46651i	−0.0808728	+	0.111312i	0.766664	+	0.642049i	$0.221915\pi$
$492$	8.30457	−	52.4330i	0.374399	−	2.36386i
$493$	−2.41852	−	4.74662i	−0.108925	−	0.213777i
$494$	9.81199			0.441462
$495$		0			0
$496$	−2.25948			−0.101453
$497$	19.5046	+	38.2799i	0.874901	+	1.71709i
$498$	11.0905	−	70.0225i	0.496976	−	3.13778i
$499$	−8.78569	+	12.0925i	−0.393301	+	0.541333i	−0.959047	−	0.283247i	$-0.908588\pi$
$499$	−8.78569	+	12.0925i	−0.393301	+	0.541333i	0.565746	+	0.824580i	$0.308588\pi$
$500$	−36.9021	+	10.9027i	−1.65031	+	0.487585i
$501$	−25.8733	+	8.40674i	−1.15593	+	0.375586i
$502$	27.6865	−	4.38511i	1.23571	−	0.195717i
$503$	14.2334	+	2.25435i	0.634637	+	0.100517i	0.465460	−	0.885069i	$-0.345889\pi$
$503$	14.2334	+	2.25435i	0.634637	+	0.100517i	0.169177	+	0.985586i	$0.445889\pi$
$504$	−16.8824	−	5.48544i	−0.752004	−	0.244341i
$505$	6.06505	+	3.57450i	0.269891	+	0.159063i
$506$		0			0
$507$	−10.0672	−	10.0672i	−0.447102	−	0.447102i
$508$	−40.9218	+	20.8507i	−1.81561	+	0.925100i
$509$	20.0473	+	27.5928i	0.888583	+	1.22303i	0.973969	+	0.226681i	$0.0727875\pi$
$509$	20.0473	+	27.5928i	0.888583	+	1.22303i	−0.0853865	+	0.996348i	$0.527213\pi$
$510$	18.5837	+	7.32533i	0.822900	+	0.324371i
$511$	20.0837	+	61.8114i	0.888452	+	2.73437i
$512$	9.60479	+	4.89389i	0.424476	+	0.216281i
$513$	1.01311	+	6.39654i	0.0447300	+	0.282414i
$514$	50.8518	−	36.9460i	2.24298	−	1.62962i
$515$	21.6748	+	1.33078i	0.955107	+	0.0586410i
$516$			45.9126i			2.02119i
$517$		0			0
$518$	−13.9536	+	13.9536i	−0.613088	+	0.613088i
$519$	4.29620	−	13.2223i	0.188582	−	0.580397i
$520$	−18.3485	+	1.76243i	−0.804633	+	0.0772875i
$521$	−15.4260	−	11.2076i	−0.675823	−	0.491014i	0.196146	−	0.980575i	$-0.437157\pi$
$521$	−15.4260	−	11.2076i	−0.675823	−	0.491014i	−0.871969	+	0.489560i	$0.837157\pi$
$522$	3.43984	−	6.75106i	0.150558	−	0.295486i
$523$	−1.28390	+	2.51979i	−0.0561410	+	0.110183i	−0.917372	−	0.398030i	$-0.869694\pi$
$523$	−1.28390	+	2.51979i	−0.0561410	+	0.110183i	0.861231	+	0.508213i	$0.169694\pi$
$524$	29.8813	+	21.7100i	1.30537	+	0.948406i
$525$	19.8281	−	42.4696i	0.865369	−	1.85353i
$526$	−3.57953	+	11.0167i	−0.156075	+	0.480349i
$527$	−3.12417	+	3.12417i	−0.136091	+	0.136091i
$528$		0			0
$529$			22.8029i			0.991430i
$530$	−52.2554	+	46.2099i	−2.26983	+	2.00723i
$531$	−3.84071	+	2.79044i	−0.166673	+	0.121095i
$532$	−4.25299	−	26.8523i	−0.184391	−	1.16420i
$533$	16.5435	+	8.42936i	0.716580	+	0.365116i
$534$	6.98343	+	21.4928i	0.302203	+	0.930084i
$535$	−8.99843	+	22.8282i	−0.389036	+	0.986948i
$536$	−23.0366	−	31.7072i	−0.995031	−	1.36954i
$537$	11.4037	−	5.81046i	0.492105	−	0.250740i
$538$	28.9698	+	28.9698i	1.24898	+	1.24898i
$539$		0			0
$540$	−7.26562	−	28.1212i	−0.312663	−	1.21014i
$541$	−36.0711	−	11.7202i	−1.55082	−	0.503891i	−0.596482	−	0.802627i	$-0.703435\pi$
$541$	−36.0711	−	11.7202i	−1.55082	−	0.503891i	−0.954336	+	0.298736i	$0.903435\pi$
$542$	−1.58075	−	0.250366i	−0.0678991	−	0.0107542i
$543$	−7.16788	+	1.13528i	−0.307603	+	0.0487196i
$544$	8.01736	−	2.60500i	0.343742	−	0.111688i
$545$	−0.895399	−	0.198725i	−0.0383547	−	0.00851244i
$546$	31.5058	−	43.3640i	1.34832	−	1.85581i
$547$	−1.60044	+	10.1048i	−0.0684297	+	0.432048i	0.929560	+	0.368671i	$0.120187\pi$
$547$	−1.60044	+	10.1048i	−0.0684297	+	0.432048i	−0.997990	+	0.0633771i	$0.979813\pi$
$548$	−6.72624	−	13.2010i	−0.287331	−	0.563918i
$549$	−2.81603			−0.120185
$550$		0			0
$551$	4.86094			0.207083
$552$	−1.38028	−	2.70895i	−0.0587485	−	0.115300i
$553$	−1.53129	+	9.66821i	−0.0651172	+	0.411134i
$554$	29.0045	−	39.9213i	1.23228	−	1.69609i
$555$	8.16859	+	1.81294i	0.346737	+	0.0769549i
$556$	−44.0160	+	14.3017i	−1.86669	+	0.606525i
$557$	−3.27898	+	0.519340i	−0.138935	+	0.0220051i	−0.225515	−	0.974240i	$-0.572406\pi$
$557$	−3.27898	+	0.519340i	−0.138935	+	0.0220051i	0.0865796	+	0.996245i	$0.472406\pi$
$558$	−6.20665	−	0.983037i	−0.262749	−	0.0416153i
$559$	−15.2722	−	4.96223i	−0.645944	−	0.209880i
$560$	2.47643	+	9.58490i	0.104648	+	0.405036i
$561$		0			0
$562$	13.3536	+	13.3536i	0.563288	+	0.563288i
$563$	−19.1161	+	9.74013i	−0.805647	+	0.410498i	−0.807768	−	0.589500i	$-0.799325\pi$
$563$	−19.1161	+	9.74013i	−0.805647	+	0.410498i	0.00212144	+	0.999998i	$0.499325\pi$
$564$	9.07856	+	12.4956i	0.382276	+	0.526158i
$565$	7.29289	−	18.5014i	0.306814	−	0.778359i
$566$	−3.13347	−	9.64383i	−0.131710	−	0.405361i
$567$	45.6316	+	23.2505i	1.91635	+	0.976429i
$568$	4.90990	+	30.9999i	0.206015	+	1.30073i
$569$	−18.4510	+	13.4054i	−0.773504	+	0.561984i	−0.903022	−	0.429593i	$-0.858657\pi$
$569$	−18.4510	+	13.4054i	−0.773504	+	0.561984i	0.129518	+	0.991577i	$0.458657\pi$
$570$	−13.6539	+	12.0743i	−0.571899	+	0.505735i
$571$		−	10.1650i		−	0.425391i	−0.977119	−	0.212695i	$-0.931776\pi$
$571$		−	10.1650i		−	0.425391i	0.977119	−	0.212695i	$-0.0682242\pi$
$572$		0			0
$573$	13.9724	−	13.9724i	0.583707	−	0.583707i
$574$	25.1361	−	77.3610i	1.04916	−	3.22899i
$575$	2.08628	−	0.758238i	0.0870037	−	0.0316207i
$576$	11.4842	+	8.34379i	0.478510	+	0.347658i
$577$	−4.15568	+	8.15598i	−0.173003	+	0.339538i	−0.961185	−	0.275905i	$-0.911023\pi$
$577$	−4.15568	+	8.15598i	−0.173003	+	0.339538i	0.788182	+	0.615442i	$0.211023\pi$
$578$	14.2582	−	27.9834i	0.593064	−	1.16395i
$579$	22.0256	+	16.0026i	0.915354	+	0.665043i
$580$	−21.7003	+	2.08438i	−0.901058	+	0.0865494i
$581$	21.2309	−	65.3419i	0.880804	−	2.71084i
$582$	46.4566	−	46.4566i	1.92569	−	1.92569i
$583$		0			0
$584$			47.4801i			1.96474i
$585$	−6.27284	−	0.385136i	−0.259350	−	0.0159234i
$586$	17.8198	−	12.9468i	0.736128	−	0.534828i
$587$	3.68127	+	23.2426i	0.151942	+	0.959325i	0.939367	+	0.342914i	$0.111414\pi$
$587$	3.68127	+	23.2426i	0.151942	+	0.959325i	−0.787424	+	0.616411i	$0.788586\pi$
$588$	−88.6184	−	45.1533i	−3.65456	−	1.86209i
$589$	−1.24580	−	3.83418i	−0.0513324	−	0.157985i
$590$	20.0921	+	7.91991i	0.827178	+	0.326057i
$591$	10.7904	+	14.8517i	0.443856	+	0.610916i
$592$	−1.57468	+	0.802338i	−0.0647188	+	0.0329759i
$593$	−2.38701	−	2.38701i	−0.0980227	−	0.0980227i	0.656395	−	0.754418i	$-0.272081\pi$
$593$	−2.38701	−	2.38701i	−0.0980227	−	0.0980227i	−0.754418	+	0.656395i	$0.772081\pi$
$594$		0			0
$595$	16.6772	+	9.82886i	0.683697	+	0.402944i
$596$	−6.91337	−	2.24629i	−0.283183	−	0.0920117i
$597$	37.4234	+	5.92729i	1.53164	+	0.242588i
$598$	2.50730	−	0.397117i	0.102531	−	0.0162393i
$599$	−4.43601	+	1.44135i	−0.181250	+	0.0588918i	−0.398236	−	0.917283i	$-0.630378\pi$
$599$	−4.43601	+	1.44135i	−0.181250	+	0.0588918i	0.216986	+	0.976175i	$0.430378\pi$
$600$	23.3641	−	25.0314i	0.953834	−	1.02190i
$601$	7.58355	−	10.4379i	0.309340	−	0.425769i	−0.625836	−	0.779955i	$-0.715242\pi$
$601$	7.58355	−	10.4379i	0.309340	−	0.425769i	0.935175	+	0.354186i	$0.115242\pi$
$602$	−11.0051	+	69.4837i	−0.448536	+	2.83194i
$603$	−6.06645	−	11.9061i	−0.247045	−	0.484853i
$604$	32.0803			1.30533
$605$		0			0
$606$	−14.9555			−0.607526
$607$	−4.81442	−	9.44883i	−0.195411	−	0.383516i	0.772422	−	0.635110i	$-0.219045\pi$
$607$	−4.81442	−	9.44883i	−0.195411	−	0.383516i	−0.967833	+	0.251594i	$0.919045\pi$
$608$	−1.20330	+	7.59734i	−0.0488003	+	0.308113i
$609$	15.6082	−	21.4829i	0.632477	−	0.870530i
$610$	6.88062	+	10.8060i	0.278588	+	0.437522i
$611$	−5.13768	+	1.66933i	−0.207848	+	0.0675340i
$612$	−7.32998	+	1.16096i	−0.296297	+	0.0469288i
$613$	−30.3492	−	4.80684i	−1.22579	−	0.194146i	−0.490224	−	0.871597i	$-0.663085\pi$
$613$	−30.3492	−	4.80684i	−1.22579	−	0.194146i	−0.735569	+	0.677450i	$0.763085\pi$
$614$	−42.8031	−	13.9076i	−1.72739	−	0.561264i
$615$	−33.3940	+	8.62796i	−1.34658	+	0.347913i
$616$		0			0
$617$	−5.09052	−	5.09052i	−0.204936	−	0.204936i	0.597175	−	0.802111i	$-0.296290\pi$
$617$	−5.09052	−	5.09052i	−0.204936	−	0.204936i	−0.802111	+	0.597175i	$0.796290\pi$
$618$	−41.1037	+	20.9434i	−1.65344	+	0.842467i
$619$	−23.7900	−	32.7441i	−0.956200	−	1.31610i	−0.948718	−	0.316125i	$-0.897618\pi$
$619$	−23.7900	−	32.7441i	−0.956200	−	1.31610i	−0.00748244	−	0.999972i	$-0.502382\pi$
$620$	7.20565	+	16.5825i	0.289386	+	0.665968i
$621$	0.517770	+	1.59353i	0.0207774	+	0.0639462i
$622$	14.3500	+	7.31169i	0.575382	+	0.293172i
$623$	3.42600	+	21.6309i	0.137260	+	0.866623i
$624$	3.88362	−	2.82162i	0.155469	−	0.112955i
$625$	16.0518	+	19.1661i	0.642071	+	0.766645i
$626$		−	26.9694i		−	1.07792i
$627$		0			0
$628$	−8.23532	+	8.23532i	−0.328625	+	0.328625i
$629$	−1.06791	+	3.28669i	−0.0425804	+	0.131049i
$630$	2.63249	+	27.4066i	0.104881	+	1.09191i
$631$	−5.94401	−	4.31857i	−0.236627	−	0.171920i	0.463152	−	0.886279i	$-0.346718\pi$
$631$	−5.94401	−	4.31857i	−0.236627	−	0.171920i	−0.699779	+	0.714359i	$0.746718\pi$
$632$	−3.24656	+	6.37172i	−0.129141	+	0.253454i
$633$	−24.1562	+	47.4092i	−0.960122	+	1.88435i
$634$	−41.8753	−	30.4242i	−1.66308	−	1.20830i
$635$	23.0204	+	18.9856i	0.913536	+	0.753420i
$636$	28.9622	−	89.1366i	1.14843	−	3.53450i
$637$	24.5975	−	24.5975i	0.974588	−	0.974588i
$638$		0			0
$639$			10.7011i			0.423328i
$640$	2.72890	−	44.4465i	0.107869	−	1.75690i
$641$	−10.4344	+	7.58105i	−0.412135	+	0.299433i	−0.774465	−	0.632616i	$-0.781981\pi$
$641$	−10.4344	+	7.58105i	−0.412135	+	0.299433i	0.362331	+	0.932050i	$0.381981\pi$
$642$	−8.15443	−	51.4851i	−0.321830	−	2.03195i
$643$	17.9349	+	9.13827i	0.707282	+	0.360378i	0.770341	−	0.637632i	$-0.220086\pi$
$643$	17.9349	+	9.13827i	0.707282	+	0.360378i	−0.0630595	+	0.998010i	$0.520086\pi$
$644$	−2.17357	−	6.68956i	−0.0856507	−	0.263606i
$645$	27.3584	−	11.8882i	1.07723	−	0.468096i
$646$	−4.42480	−	6.09022i	−0.174091	−	0.239616i
$647$	27.5681	−	14.0466i	1.08381	−	0.552231i	0.181535	−	0.983384i	$-0.441893\pi$
$647$	27.5681	−	14.0466i	1.08381	−	0.552231i	0.902278	+	0.431154i	$0.141893\pi$
$648$	26.4558	+	26.4558i	1.03928	+	1.03928i
$649$		0			0
$650$	13.8490	+	25.0119i	0.543203	+	0.981046i
$651$	−20.9453	−	6.80555i	−0.820913	−	0.266731i
$652$	57.7999	+	9.15460i	2.26362	+	0.358522i
$653$	−26.7304	+	4.23368i	−1.04604	+	0.165677i	−0.655722	−	0.755003i	$-0.727636\pi$
$653$	−26.7304	+	4.23368i	−1.04604	+	0.165677i	−0.390320	+	0.920679i	$0.627636\pi$
$654$	1.85307	−	0.602099i	0.0724608	−	0.0235439i
$655$	5.19939	−	23.4270i	0.203157	−	0.915368i
$656$	4.28195	−	5.89360i	0.167182	−	0.230107i
$657$	−2.53240	+	15.9889i	−0.0987982	+	0.623788i
$658$	10.7442	+	21.0868i	0.418854	+	0.822047i
$659$	−18.9473			−0.738081			−0.369040	−	0.929413i	$-0.620314\pi$
$659$	−18.9473			−0.738081			−0.369040	+	0.929413i	$0.620314\pi$
$660$		0			0
$661$	−9.89812			−0.384992			−0.192496	−	0.981298i	$-0.561658\pi$
$661$	−9.89812			−0.384992			−0.192496	+	0.981298i	$0.561658\pi$
$662$	11.4583	+	22.4882i	0.445340	+	0.874029i
$663$	1.46843	−	9.27132i	0.0570292	−	0.360068i
$664$	29.5022	−	40.6062i	1.14491	−	1.57583i
$665$	−14.8995	+	9.48714i	−0.577779	+	0.367896i
$666$	−4.67462	+	1.51888i	−0.181138	+	0.0588553i
$667$	1.24214	−	0.196735i	0.0480957	−	0.00761761i
$668$	−45.4137	−	7.19283i	−1.75711	−	0.278299i
$669$	37.0841	+	12.0493i	1.43375	+	0.465855i
$670$	−30.8647	+	52.3699i	−1.19241	+	2.02322i
$671$		0			0
$672$	29.7126	+	29.7126i	1.14619	+	1.14619i
$673$	−2.32937	+	1.18687i	−0.0897906	+	0.0457506i	−0.498309	−	0.866999i	$-0.666046\pi$
$673$	−2.32937	+	1.18687i	−0.0897906	+	0.0457506i	0.408519	+	0.912750i	$0.366046\pi$
$674$	−19.3737	−	26.6656i	−0.746247	−	1.02712i
$675$	−14.8756	+	11.6109i	−0.572560	+	0.446902i
$676$	−7.43583	−	22.8851i	−0.285993	−	0.880197i
$677$	23.9844	+	12.2206i	0.921794	+	0.469678i	0.849430	−	0.527701i	$-0.176946\pi$
$677$	23.9844	+	12.2206i	0.921794	+	0.469678i	0.0723639	+	0.997378i	$0.476946\pi$
$678$	6.60886	+	41.7267i	0.253812	+	1.60251i
$679$	51.5095	−	37.4238i	1.97675	−	1.43620i
$680$	9.36832	+	10.5939i	0.359259	+	0.406259i
$681$			38.2151i			1.46441i
$682$		0			0
$683$	−30.8267	+	30.8267i	−1.17955	+	1.17955i	−0.199691	+	0.979859i	$0.563994\pi$
$683$	−30.8267	+	30.8267i	−1.17955	+	1.17955i	−0.979859	+	0.199691i	$0.936006\pi$
$684$	2.09258	−	6.44030i	0.0800118	−	0.246251i
$685$	−6.12457	+	7.42616i	−0.234008	+	0.283739i
$686$	−62.4772	−	45.3924i	−2.38539	−	1.73309i
$687$	−20.3962	+	40.0298i	−0.778164	+	1.52723i
$688$	−2.86034	+	5.61373i	−0.109049	+	0.214021i
$689$	26.5198	+	19.2678i	1.01032	+	0.734043i
$690$	−3.00036	+	3.63800i	−0.114222	+	0.138496i
$691$	4.67904	−	14.4006i	0.177999	−	0.547824i	−0.821759	−	0.569835i	$-0.807007\pi$
$691$	4.67904	−	14.4006i	0.177999	−	0.547824i	0.999758	+	0.0220111i	$0.00700693\pi$
$692$	16.6153	−	16.6153i	0.631620	−	0.631620i
$693$		0			0
$694$		−	6.22129i		−	0.236157i
$695$	19.9191	+	22.5251i	0.755575	+	0.854425i
$696$	15.6943	−	11.4026i	0.594891	−	0.432214i
$697$	−2.22842	−	14.0697i	−0.0844076	−	0.532929i
$698$	6.59618	+	3.36092i	0.249669	+	0.127213i
$699$	11.7089	+	36.0364i	0.442872	+	1.36302i
$700$	62.4468	−	48.7418i	2.36027	−	1.84227i
$701$	20.3541	+	28.0150i	0.768764	+	1.05811i	0.996434	+	0.0843745i	$0.0268892\pi$
$701$	20.3541	+	28.0150i	0.768764	+	1.05811i	−0.227670	+	0.973738i	$0.573111\pi$
$702$	−19.2282	+	9.79723i	−0.725720	+	0.369773i
$703$	−2.22974	−	2.22974i	−0.0840962	−	0.0840962i
$704$		0			0
$705$	5.09513	−	8.64520i	0.191894	−	0.325597i
$706$	82.3584	+	26.7599i	3.09960	+	1.00712i
$707$	−14.3149	−	2.26726i	−0.538368	−	0.0852691i
$708$	−28.6597	+	4.53925i	−1.07710	+	0.170595i
$709$	10.8917	−	3.53892i	0.409045	−	0.132907i	−0.0972644	−	0.995259i	$-0.531009\pi$
$709$	10.8917	−	3.53892i	0.409045	−	0.132907i	0.506310	+	0.862352i	$0.331009\pi$
$710$	41.0634	−	26.1467i	1.54108	−	0.981270i
$711$	−1.43312	+	1.97252i	−0.0537462	+	0.0739752i
$712$	−2.50286	+	15.8024i	−0.0937987	+	0.592222i
$713$	−0.473525	−	0.929344i	−0.0177336	−	0.0348042i
$714$	−41.1235			−1.53901
$715$		0			0
$716$	21.6314			0.808405
$717$	−3.60657	−	7.07830i	−0.134690	−	0.264344i
$718$	−7.47290	+	47.1820i	−0.278886	+	1.76082i
$719$	−11.3292	+	15.5934i	−0.422510	+	0.581535i	−0.966214	−	0.257742i	$-0.917021\pi$
$719$	−11.3292	+	15.5934i	−0.422510	+	0.581535i	0.543704	+	0.839277i	$0.317021\pi$
$720$	−0.534259	+	2.40722i	−0.0199106	+	0.0897119i
$721$	−42.5182	+	13.8150i	−1.58346	+	0.514497i
$722$	−36.9919	+	5.85895i	−1.37670	+	0.218047i
$723$	−18.3018	−	2.89872i	−0.680650	−	0.107804i
$724$	−11.6654	−	3.79031i	−0.433540	−	0.140866i
$725$	6.86091	+	12.3911i	0.254808	+	0.460193i
$726$		0			0
$727$	2.58958	+	2.58958i	0.0960422	+	0.0960422i	0.753495	−	0.657453i	$-0.228366\pi$
$727$	2.58958	+	2.58958i	0.0960422	+	0.0960422i	−0.657453	+	0.753495i	$0.728366\pi$
$728$	33.8120	−	17.2281i	1.25315	−	0.638514i
$729$	−6.05394	−	8.33253i	−0.224220	−	0.308612i
$730$	67.5421	−	29.3493i	2.49984	−	1.08627i
$731$	3.80711	+	11.7171i	0.140811	+	0.433371i
$732$	−15.3361	−	7.81415i	−0.566840	−	0.288819i
$733$	−5.61968	−	35.4813i	−0.207568	−	1.31053i	−0.842807	−	0.538215i	$-0.819099\pi$
$733$	−5.61968	−	35.4813i	−0.207568	−	1.31053i	0.635240	−	0.772315i	$-0.280901\pi$
$734$	53.9230	−	39.1774i	1.99034	−	1.44606i
$735$	−3.95997	+	64.4974i	−0.146066	+	2.37902i
$736$			1.99008i			0.0733554i
$737$		0			0
$738$	14.3264	−	14.3264i	0.527364	−	0.527364i
$739$	−2.72592	+	8.38951i	−0.100274	+	0.308613i	−0.988592	−	0.150616i	$-0.951874\pi$
$739$	−2.72592	+	8.38951i	−0.100274	+	0.308613i	0.888318	+	0.459229i	$0.151874\pi$
$740$	10.9102	+	8.99795i	0.401067	+	0.330771i
$741$	6.92940	+	5.03451i	0.254558	+	0.184947i
$742$	65.1970	−	127.956i	2.39346	−	4.69742i
$743$	1.25683	−	2.46666i	0.0461084	−	0.0904929i	−0.866803	−	0.498651i	$-0.833829\pi$
$743$	1.25683	−	2.46666i	0.0461084	−	0.0904929i	0.912911	+	0.408158i	$0.133829\pi$
$744$	−13.0163	−	9.45692i	−0.477202	−	0.346708i
$745$	0.451562	+	4.70117i	0.0165439	+	0.172237i
$746$	−23.5238	+	72.3987i	−0.861267	+	2.65071i
$747$	12.1006	−	12.1006i	0.442739	−	0.442739i
$748$		0			0
$749$		−	50.5160i		−	1.84581i
$750$	−50.0503	−	17.7633i	−1.82758	−	0.648622i
$751$	23.3576	−	16.9703i	0.852331	−	0.619255i	−0.0734567	−	0.997298i	$-0.523403\pi$
$751$	23.3576	−	16.9703i	0.852331	−	0.619255i	0.925788	+	0.378044i	$0.123403\pi$
$752$	0.331565	+	2.09342i	0.0120909	+	0.0763392i
$753$	21.8027	+	11.1090i	0.794533	+	0.404835i
$754$	5.00534	+	15.4049i	0.182284	+	0.561012i
$755$	−8.30654	−	19.1160i	−0.302306	−	0.695701i
$756$	35.1463	+	48.3748i	1.27826	+	1.75937i
$757$	−24.8245	+	12.6487i	−0.902263	+	0.459726i	−0.842629	−	0.538494i	$-0.818993\pi$
$757$	−24.8245	+	12.6487i	−0.902263	+	0.459726i	−0.0596341	+	0.998220i	$0.518993\pi$
$758$	−37.8628	−	37.8628i	−1.37524	−	1.37524i
$759$		0			0
$760$	−12.4939	+	3.22801i	−0.453200	+	0.117092i
$761$	7.10812	+	2.30957i	0.257669	+	0.0837218i	0.435003	−	0.900429i	$-0.356747\pi$
$761$	7.10812	+	2.30957i	0.257669	+	0.0837218i	−0.177334	+	0.984151i	$0.556747\pi$
$762$	−62.6092	−	9.91632i	−2.26809	−	0.359230i
$763$	1.86498	−	0.295383i	0.0675166	−	0.0106936i
$764$	31.7625	−	10.3203i	1.14913	−	0.373375i
$765$	2.58974	+	4.06718i	0.0936323	+	0.147049i
$766$	−42.7418	+	58.8290i	−1.54432	+	2.12558i
$767$	1.58762	−	10.0238i	0.0573257	−	0.361940i
$768$	20.0564	+	39.3629i	0.723723	+	1.42039i
$769$	−33.5984			−1.21159			−0.605794	−	0.795621i	$-0.707145\pi$
$769$	−33.5984			−1.21159			−0.605794	+	0.795621i	$0.707145\pi$
$770$		0			0
$771$	54.8694			1.97607
$772$	20.8900	+	40.9990i	0.751849	+	1.47559i
$773$	−6.05694	+	38.2420i	−0.217853	+	1.37547i	0.599980	+	0.800015i	$0.295175\pi$
$773$	−6.05694	+	38.2420i	−0.217853	+	1.37547i	−0.817833	+	0.575455i	$0.804825\pi$
$774$	−10.2996	+	14.1761i	−0.370210	+	0.509551i
$775$	8.01539	−	8.58740i	0.287921	−	0.308468i
$776$	44.2370	−	14.3735i	1.58802	−	0.515978i
$777$	−17.0139	+	2.69474i	−0.610370	+	0.0966731i
$778$	9.51922	+	1.50770i	0.341280	+	0.0540535i
$779$	12.3620	+	4.01666i	0.442914	+	0.143912i
$780$	−33.0933	−	19.5038i	−1.18493	−	0.698350i
$781$		0			0
$782$	−1.37718	−	1.37718i	−0.0492477	−	0.0492477i
$783$	−9.52578	+	4.85363i	−0.340423	+	0.173454i
$784$	−8.02232	−	11.0418i	−0.286512	−	0.394349i
$785$	7.03963	+	2.77489i	0.251255	+	0.0990399i
$786$	15.7532	+	48.4833i	0.561897	+	1.72934i
$787$	−0.843285	−	0.429675i	−0.0300599	−	0.0153163i	0.438896	−	0.898538i	$-0.355370\pi$
$787$	−0.843285	−	0.429675i	−0.0300599	−	0.0153163i	−0.468956	+	0.883222i	$0.655370\pi$
$788$	4.85368	+	30.6450i	0.172905	+	1.09168i
$789$	−8.18054	+	5.94351i	−0.291235	+	0.211595i
$790$	11.0708	+	0.679718i	0.393882	+	0.0241833i
$791$			40.9413i			1.45571i
$792$		0			0
$793$	4.25680	−	4.25680i	0.151163	−	0.151163i
$794$	9.35710	−	28.7982i	0.332071	−	1.02201i
$795$	−60.6138	+	5.82214i	−2.14975	+	0.206490i
$796$	51.8087	+	37.6412i	1.83631	+	1.33416i
$797$	6.39499	−	12.5509i	0.226522	−	0.444575i	−0.749572	−	0.661923i	$-0.769741\pi$
$797$	6.39499	−	12.5509i	0.226522	−	0.444575i	0.976094	+	0.217348i	$0.0697407\pi$
$798$	17.0354	−	33.4339i	0.603048	−	1.18355i
$799$	3.35302	+	2.43611i	0.118621	+	0.0861835i
$800$	−21.0649	+	7.65583i	−0.744755	+	0.270674i
$801$	−1.68568	+	5.18798i	−0.0595604	+	0.183308i
$802$	28.3473	−	28.3473i	1.00098	−	1.00098i
$803$		0			0
$804$		−	81.6743i		−	2.88043i
$805$	−3.42337	+	3.02731i	−0.120658	+	0.106699i
$806$	10.8681	−	7.89617i	0.382814	−	0.278131i
$807$	5.59467	+	35.3234i	0.196942	+	1.24344i
$808$	−9.43409	−	4.80691i	−0.331890	−	0.169106i
$809$	2.45527	+	7.55653i	0.0863226	+	0.265674i	0.984895	−	0.173151i	$-0.0553949\pi$
$809$	2.45527	+	7.55653i	0.0863226	+	0.265674i	−0.898573	+	0.438825i	$0.855395\pi$
$810$	21.2808	−	53.9875i	0.747733	−	1.89693i
$811$	−4.09252	−	5.63287i	−0.143708	−	0.197797i	0.731095	−	0.682275i	$-0.239009\pi$
$811$	−4.09252	−	5.63287i	−0.143708	−	0.197797i	−0.874803	+	0.484479i	$0.839009\pi$
$812$	39.9887	−	20.3753i	1.40333	−	0.715032i
$813$	−0.987892	−	0.987892i	−0.0346469	−	0.0346469i
$814$		0			0
$815$	−9.51109	−	36.8122i	−0.333159	−	1.28947i
$816$	−3.50271	−	1.13810i	−0.122619	−	0.0398414i
$817$	−11.1032	−	1.75858i	−0.388453	−	0.0615249i
$818$	−70.3891	+	11.1485i	−2.46110	+	0.389799i
$819$	12.3050	−	3.99815i	0.429973	−	0.139707i
$820$	−56.9091	−	12.6304i	−1.98735	−	0.441073i
$821$	23.9157	−	32.9172i	0.834665	−	1.14882i	−0.152372	−	0.988323i	$-0.548691\pi$
$821$	23.9157	−	32.9172i	0.834665	−	1.14882i	0.987037	−	0.160494i	$-0.0513088\pi$
$822$	3.19891	−	20.1971i	0.111575	−	0.704456i
$823$	−2.01224	−	3.94925i	−0.0701423	−	0.137662i	0.853273	−	0.521465i	$-0.174614\pi$
$823$	−2.01224	−	3.94925i	−0.0701423	−	0.137662i	−0.923415	+	0.383803i	$0.874614\pi$
$824$	−32.6602			−1.13777
$825$		0			0
$826$	−44.4613			−1.54701
$827$	−21.4959	−	42.1881i	−0.747487	−	1.46703i	−0.879561	−	0.475786i	$-0.842164\pi$
$827$	−21.4959	−	42.1881i	−0.747487	−	1.46703i	0.132074	−	0.991240i	$-0.457836\pi$
$828$	0.274070	−	1.73041i	0.00952459	−	0.0601359i
$829$	6.23413	−	8.58054i	0.216520	−	0.298015i	−0.686916	−	0.726737i	$-0.741036\pi$
$829$	6.23413	−	8.58054i	0.216520	−	0.298015i	0.903436	+	0.428722i	$0.141036\pi$
$830$	−76.0002	−	16.8675i	−2.63800	−	0.585479i
$831$	40.9670	−	13.3110i	1.42113	−	0.461753i
$832$	−29.9726	+	4.74720i	−1.03911	+	0.164579i
$833$	−26.3599	−	4.17500i	−0.913316	−	0.144655i
$834$	−60.7511	−	19.7392i	−2.10364	−	0.683514i
$835$	7.47292	+	28.9235i	0.258611	+	1.00094i
$836$		0			0
$837$	6.26976	+	6.26976i	0.216715	+	0.216715i
$838$	−14.7128	+	7.49654i	−0.508245	+	0.258964i
$839$	19.0162	+	26.1736i	0.656514	+	0.903614i	0.999360	−	0.0357779i	$-0.0113909\pi$
$839$	19.0162	+	26.1736i	0.656514	+	0.903614i	−0.342846	+	0.939392i	$0.611391\pi$
$840$	−25.8509	+	65.5814i	−0.891942	+	2.26277i
$841$	−6.48181	−	19.9489i	−0.223511	−	0.687895i
$842$	−75.7051	−	38.5737i	−2.60897	−	1.32934i
$843$	2.57886	+	16.2823i	0.0888205	+	0.560791i
$844$	−72.7547	+	52.8594i	−2.50432	+	1.81949i
$845$	−11.7114	+	10.3565i	−0.402885	+	0.356275i
$846$			5.89476i			0.202666i
$847$		0			0
$848$	9.09438	−	9.09438i	0.312302	−	0.312302i
$849$	2.73531	−	8.41842i	0.0938756	−	0.288920i
$850$	9.27931	−	19.8753i	0.318278	−	0.681716i
$851$	−0.660018	−	0.479531i	−0.0226251	−	0.0164381i
$852$	−29.6942	+	58.2782i	−1.01731	+	1.99658i
$853$	8.98357	−	17.6313i	0.307592	−	0.603683i	−0.684527	−	0.728988i	$-0.739991\pi$
$853$	8.98357	−	17.6313i	0.307592	−	0.603683i	0.992118	+	0.125305i	$0.0399910\pi$
$854$	−21.3365	−	15.5019i	−0.730121	−	0.530464i
$855$	−4.37947	+	0.420662i	−0.149775	+	0.0143863i
$856$	11.4041	−	35.0982i	0.389784	−	1.19963i
$857$	22.2530	−	22.2530i	0.760147	−	0.760147i	−0.216201	−	0.976349i	$-0.569367\pi$
$857$	22.2530	−	22.2530i	0.760147	−	0.760147i	0.976349	+	0.216201i	$0.0693668\pi$
$858$		0			0
$859$			18.3060i			0.624593i	0.949985	+	0.312296i	$0.101098\pi$
$859$			18.3060i			0.624593i	−0.949985	+	0.312296i	$0.898902\pi$
$860$	50.3214	+	3.08960i	1.71595	+	0.105355i
$861$	57.4453	−	41.7364i	1.95773	−	1.42237i
$862$	3.24121	+	20.4642i	0.110396	+	0.697013i
$863$	−37.7726	−	19.2461i	−1.28580	−	0.655146i	−0.328568	−	0.944480i	$-0.606566\pi$
$863$	−37.7726	−	19.2461i	−1.28580	−	0.655146i	−0.957228	+	0.289335i	$0.906566\pi$
$864$	−5.22785	−	16.0897i	−0.177855	−	0.547382i
$865$	−14.2029	−	5.59852i	−0.482914	−	0.190355i
$866$	−14.1679	−	19.5005i	−0.481446	−	0.662653i
$867$	24.4276	−	12.4465i	0.829605	−	0.422705i
$868$	−26.3201	−	26.3201i	−0.893363	−	0.893363i
$869$		0			0
$870$	−25.9218	−	15.2773i	−0.878832	−	0.517949i
$871$	27.1678	+	8.82736i	0.920546	+	0.299104i
$872$	1.36246	+	0.215792i	0.0461386	+	0.00730764i
$873$	15.6634	−	2.48084i	0.530127	−	0.0839639i
$874$	1.69016	−	0.549166i	0.0571704	−	0.0185758i
$875$	−45.2135	−	24.5900i	−1.52850	−	0.831295i
$876$	−58.1588	+	80.0488i	−1.96500	+	2.70460i
$877$	2.83578	−	17.9044i	0.0957576	−	0.604590i	−0.892412	−	0.451222i	$-0.850988\pi$
$877$	2.83578	−	17.9044i	0.0957576	−	0.604590i	0.988169	−	0.153367i	$-0.0490118\pi$
$878$	−14.5922	−	28.6388i	−0.492462	−	0.966511i
$879$	19.2276			0.648531
$880$		0			0
$881$	−37.5895			−1.26642			−0.633211	−	0.773979i	$-0.718264\pi$
$881$	−37.5895			−1.26642			−0.633211	+	0.773979i	$0.718264\pi$
$882$	−17.2329	−	33.8215i	−0.580262	−	1.13883i
$883$	1.80212	−	11.3781i	0.0606461	−	0.382904i	−0.938632	−	0.344920i	$-0.887906\pi$
$883$	1.80212	−	11.3781i	0.0606461	−	0.382904i	0.999278	−	0.0379846i	$-0.0120938\pi$
$884$	9.32528	−	12.8352i	0.313643	−	0.431693i
$885$	10.1257	+	15.9024i	0.340372	+	0.534552i
$886$	−18.1557	+	5.89915i	−0.609954	+	0.198186i
$887$	−9.29199	+	1.47171i	−0.311994	+	0.0494151i	−0.310468	−	0.950584i	$-0.600486\pi$
$887$	−9.29199	+	1.47171i	−0.311994	+	0.0494151i	−0.00152627	+	0.999999i	$0.500486\pi$
$888$	−12.4295	−	1.96864i	−0.417107	−	0.0660632i
$889$	−58.4241	−	18.9831i	−1.95948	−	0.636674i
$890$	24.0266	−	6.20771i	0.805374	−	0.208083i
$891$		0			0
$892$	46.6002	+	46.6002i	1.56029	+	1.56029i
$893$	−3.36958	+	1.71689i	−0.112759	+	0.0574535i
$894$	−5.89721	−	8.11681i	−0.197232	−	0.271467i
$895$	−5.60103	−	12.8897i	−0.187222	−	0.430856i
$896$	28.3291	+	87.1879i	0.946408	+	2.91274i
$897$	1.97446	+	1.00604i	0.0659253	+	0.0335906i
$898$	−12.5864	−	79.4672i	−0.420013	−	2.65186i
$899$	5.38417	−	3.91183i	0.179572	−	0.130467i
$900$	19.3706	−	3.75586i	0.645686	−	0.125195i
$901$		−	25.1496i		−	0.837853i
$902$		0			0
$903$	−43.4239	+	43.4239i	−1.44506	+	1.44506i
$904$	−9.24260	+	28.4458i	−0.307404	+	0.946094i
$905$	0.761949	+	7.93258i	0.0253280	+	0.263688i
$906$	35.8212	+	26.0256i	1.19008	+	0.864643i
$907$	−22.5376	+	44.2324i	−0.748347	+	1.46871i	0.130418	+	0.991459i	$0.458368\pi$
$907$	−22.5376	+	44.2324i	−0.748347	+	1.46871i	−0.878765	+	0.477255i	$0.841632\pi$
$908$	−29.3227	+	57.5490i	−0.973107	+	1.90983i
$909$	−2.92055	−	2.12190i	−0.0968685	−	0.0703791i
$910$	−45.4080	−	37.4493i	−1.50526	−	1.24143i
$911$	−7.96116	+	24.5019i	−0.263765	+	0.811785i	0.728210	+	0.685354i	$0.240352\pi$
$911$	−7.96116	+	24.5019i	−0.263765	+	0.811785i	−0.991975	+	0.126431i	$0.959648\pi$
$912$	2.37629	−	2.37629i	0.0786867	−	0.0786867i
$913$		0			0
$914$		−	82.7230i		−	2.73623i
$915$	−0.685305	+	11.1618i	−0.0226555	+	0.368998i
$916$	−61.4303	+	44.6317i	−2.02971	+	1.47467i
$917$	7.72833	+	48.7947i	0.255212	+	1.61134i
$918$	14.7522	+	7.51660i	0.486894	+	0.248085i
$919$	−2.47791	−	7.62622i	−0.0817387	−	0.251566i	0.901833	−	0.432085i	$-0.142222\pi$
$919$	−2.47791	−	7.62622i	−0.0817387	−	0.251566i	−0.983571	+	0.180520i	$0.942222\pi$
$920$	−3.06196	+	1.33053i	−0.100950	+	0.0438662i
$921$	−23.0924	−	31.7839i	−0.760920	−	1.04732i
$922$	55.2952	−	28.1743i	1.82105	−	0.927871i
$923$	−16.1761	−	16.1761i	−0.532442	−	0.532442i
$924$		0			0
$925$	2.53672	−	8.83100i	0.0834067	−	0.290361i
$926$	−4.13478	−	1.34347i	−0.135877	−	0.0441492i
$927$	−10.9983	−	1.74196i	−0.361232	−	0.0572135i
$928$	−12.5417	+	1.98641i	−0.411701	+	0.0652070i
$929$	14.1548	−	4.59918i	0.464405	−	0.150894i	−0.0674627	−	0.997722i	$-0.521490\pi$
$929$	14.1548	−	4.59918i	0.464405	−	0.150894i	0.531868	+	0.846827i	$0.321490\pi$
$930$	−5.40687	+	24.3619i	−0.177298	+	0.798857i
$931$	14.3139	−	19.7014i	0.469120	−	0.645689i
$932$	−10.0182	+	63.2523i	−0.328157	+	2.07190i
$933$	6.38261	+	12.5266i	0.208957	+	0.410102i
$934$	62.9723			2.06052
$935$		0			0
$936$	9.45207			0.308951
$937$	8.35552	+	16.3986i	0.272963	+	0.535720i	0.986272	−	0.165130i	$-0.0528043\pi$
$937$	8.35552	+	16.3986i	0.272963	+	0.535720i	−0.713309	+	0.700850i	$0.752804\pi$
$938$	19.5771	−	123.605i	0.639216	−	4.03585i
$939$	13.8379	−	19.0463i	0.451584	−	0.621552i
$940$	14.3064	−	9.10947i	0.466623	−	0.297118i
$941$	14.8709	−	4.83184i	0.484777	−	0.157514i	−0.0564239	−	0.998407i	$-0.517970\pi$
$941$	14.8709	−	4.83184i	0.484777	−	0.157514i	0.541201	+	0.840893i	$0.317970\pi$
$942$	−15.8767	+	2.51462i	−0.517290	+	0.0819307i
$943$	3.32148	+	0.526070i	0.108162	+	0.0171312i
$944$	−3.78701	−	1.23047i	−0.123257	−	0.0400485i
$945$	19.7251	−	33.4687i	0.641657	−	1.08874i
$946$		0			0
$947$	−23.9724	−	23.9724i	−0.778997	−	0.778997i	0.200664	−	0.979660i	$-0.435690\pi$
$947$	−23.9724	−	23.9724i	−0.778997	−	0.778997i	−0.979660	+	0.200664i	$0.935690\pi$
$948$	−13.2783	+	6.76562i	−0.431259	+	0.219737i
$949$	−20.3413	−	27.9974i	−0.660306	−	0.908833i
$950$	12.3149	+	15.7776i	0.399548	+	0.511891i
$951$	−13.9625	−	42.9722i	−0.452766	−	1.39347i
$952$	−25.9411	−	13.2176i	−0.840756	−	0.428386i
$953$	−3.25554	−	20.5547i	−0.105457	−	0.665831i	−0.982619	−	0.185636i	$-0.940566\pi$
$953$	−3.25554	−	20.5547i	−0.105457	−	0.665831i	0.877161	−	0.480196i	$-0.159434\pi$
$954$	28.9385	−	21.0250i	0.936918	−	0.680711i
$955$	−14.3739	−	16.2544i	−0.465129	−	0.525980i
$956$		−	13.4267i		−	0.434251i
$957$		0			0
$958$	53.0738	−	53.0738i	1.71474	−	1.71474i
$959$	6.12378	−	18.8471i	0.197747	−	0.608603i
$960$	35.8668	−	43.4891i	1.15759	−	1.40361i
$961$	20.6141	+	14.9770i	0.664970	+	0.483129i
$962$	4.77032	−	9.36228i	0.153801	−	0.301852i
$963$	5.71233	−	11.2111i	0.184077	−	0.361272i
$964$	−25.3368	−	18.4083i	−0.816045	−	0.592891i
$965$	19.0214	−	23.0638i	0.612320	−	0.742450i
$966$	2.99998	−	9.23298i	0.0965227	−	0.297066i
$967$	−16.5393	+	16.5393i	−0.531867	+	0.531867i	−0.921128	−	0.389261i	$-0.872730\pi$
$967$	−16.5393	+	16.5393i	−0.531867	+	0.531867i	0.389261	+	0.921128i	$0.372730\pi$
$968$		0			0
$969$		−	6.57137i		−	0.211103i
$970$	−47.7914	−	54.0438i	−1.53449	−	1.73524i
$971$	−11.2190	+	8.15111i	−0.360036	+	0.261582i	−0.753067	−	0.657944i	$-0.771426\pi$
$971$	−11.2190	+	8.15111i	−0.360036	+	0.261582i	0.393031	+	0.919525i	$0.371426\pi$
$972$	6.10114	+	38.5211i	0.195694	+	1.23556i
$973$	−55.1565	−	28.1036i	−1.76824	−	0.900961i
$974$	13.4361	+	41.3521i	0.430521	+	1.32501i
$975$	−3.05310	+	24.7697i	−0.0977774	+	0.793266i
$976$	−1.38833	−	1.91087i	−0.0444393	−	0.0611655i
$977$	−12.6310	+	6.43580i	−0.404101	+	0.205900i	−0.644214	−	0.764845i	$-0.722815\pi$
$977$	−12.6310	+	6.43580i	−0.404101	+	0.205900i	0.240113	+	0.970745i	$0.422815\pi$
$978$	57.1132	+	57.1132i	1.82628	+	1.82628i
$979$		0			0
$980$	−55.4526	+	94.0896i	−1.77137	+	3.00558i
$981$	0.447298	+	0.145336i	0.0142811	+	0.00464022i
$982$	−7.02442	−	1.11256i	−0.224158	−	0.0355032i
$983$	38.4702	−	6.09307i	1.22701	−	0.194339i	0.490908	−	0.871212i	$-0.336665\pi$
$983$	38.4702	−	6.09307i	1.22701	−	0.194339i	0.736100	+	0.676873i	$0.236665\pi$
$984$	49.3348	−	16.0298i	1.57273	−	0.511013i
$985$	17.0039	−	10.8271i	0.541790	−	0.344980i
$986$	7.30446	−	10.0537i	0.232621	−	0.320176i
$987$	−3.23178	+	20.4047i	−0.102869	+	0.649488i
$988$	6.57214	+	12.8985i	0.209088	+	0.410358i
$989$	−2.90843			−0.0924827
$990$		0			0
$991$	−21.6881			−0.688947			−0.344473	−	0.938796i	$-0.611942\pi$
$991$	−21.6881			−0.688947			−0.344473	+	0.938796i	$0.611942\pi$
$992$	4.78112	+	9.38347i	0.151801	+	0.297925i
$993$	−3.44657	+	21.7608i	−0.109374	+	0.690558i
$994$	−58.9081	+	81.0800i	−1.86845	+	2.57170i
$995$	9.01480	−	40.6182i	0.285788	−	1.28768i
$996$	99.4779	−	32.3223i	3.15208	−	1.02417i
$997$	5.86148	−	0.928367i	0.185635	−	0.0294017i	−0.0629247	−	0.998018i	$-0.520043\pi$
$997$	5.86148	−	0.928367i	0.185635	−	0.0294017i	0.248560	+	0.968617i	$0.420043\pi$
$998$	−34.4384	−	5.45451i	−1.09013	−	0.172659i
$999$	6.59591	+	2.14314i	0.208685	+	0.0678060i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.m.g.112.19		160
5.3	odd	4	inner	605.2.m.g.233.19		160
11.2	odd	10	inner	605.2.m.g.602.2		160
11.3	even	5	inner	605.2.m.g.282.19		160
11.4	even	5		605.2.e.c.362.2	✓	40
11.5	even	5	inner	605.2.m.g.457.2		160
11.6	odd	10	inner	605.2.m.g.457.19		160
11.7	odd	10		605.2.e.c.362.19	yes	40
11.8	odd	10	inner	605.2.m.g.282.2		160
11.9	even	5	inner	605.2.m.g.602.19		160
11.10	odd	2	inner	605.2.m.g.112.2		160
55.3	odd	20	inner	605.2.m.g.403.2		160
55.8	even	20	inner	605.2.m.g.403.19		160
55.13	even	20	inner	605.2.m.g.118.19		160
55.18	even	20		605.2.e.c.483.2	yes	40
55.28	even	20	inner	605.2.m.g.578.19		160
55.38	odd	20	inner	605.2.m.g.578.2		160
55.43	even	4	inner	605.2.m.g.233.2		160
55.48	odd	20		605.2.e.c.483.19	yes	40
55.53	odd	20	inner	605.2.m.g.118.2		160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.e.c.362.2	✓	40	11.4	even	5
605.2.e.c.362.19	yes	40	11.7	odd	10
605.2.e.c.483.2	yes	40	55.18	even	20
605.2.e.c.483.19	yes	40	55.48	odd	20
605.2.m.g.112.2		160	11.10	odd	2	inner
605.2.m.g.112.19		160	1.1	even	1	trivial
605.2.m.g.118.2		160	55.53	odd	20	inner
605.2.m.g.118.19		160	55.13	even	20	inner
605.2.m.g.233.2		160	55.43	even	4	inner
605.2.m.g.233.19		160	5.3	odd	4	inner
605.2.m.g.282.2		160	11.8	odd	10	inner
605.2.m.g.282.19		160	11.3	even	5	inner
605.2.m.g.403.2		160	55.3	odd	20	inner
605.2.m.g.403.19		160	55.8	even	20	inner
605.2.m.g.457.2		160	11.5	even	5	inner
605.2.m.g.457.19		160	11.6	odd	10	inner
605.2.m.g.578.2		160	55.38	odd	20	inner
605.2.m.g.578.19		160	55.28	even	20	inner
605.2.m.g.602.2		160	11.2	odd	10	inner
605.2.m.g.602.19		160	11.9	even	5	inner

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.m (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.05904 + 2.07848i) q^{2} +(-0.318551 + 2.01125i) q^{3} +(-2.02296 + 2.78437i) q^{4} +(2.18295 + 0.484484i) q^{5} +(-4.51772 + 1.46790i) q^{6} +(-4.54674 + 0.720133i) q^{7} +(-3.32162 - 0.526094i) q^{8} +(-1.09050 - 0.354324i) q^{9} +O(q^{10})\)	\(q+(1.05904 + 2.07848i) q^{2} +(-0.318551 + 2.01125i) q^{3} +(-2.02296 + 2.78437i) q^{4} +(2.18295 + 0.484484i) q^{5} +(-4.51772 + 1.46790i) q^{6} +(-4.54674 + 0.720133i) q^{7} +(-3.32162 - 0.526094i) q^{8} +(-1.09050 - 0.354324i) q^{9} +(1.30484 + 5.05032i) q^{10} +(-4.95565 - 4.95565i) q^{12} +(2.18403 - 1.11282i) q^{13} +(-6.31197 - 8.68769i) q^{14} +(-1.66980 + 4.23614i) q^{15} +(-0.297192 - 0.914662i) q^{16} +(-1.67563 - 0.853774i) q^{17} +(-0.418424 - 2.64182i) q^{18} +(1.38826 - 1.00863i) q^{19} +(-5.76500 + 5.09804i) q^{20} -9.37405i q^{21} +(0.313926 - 0.313926i) q^{23} +(2.11622 - 6.51304i) q^{24} +(4.53055 + 2.11521i) q^{25} +(4.62596 + 3.36096i) q^{26} +(-1.71340 + 3.36274i) q^{27} +(7.19277 - 14.1166i) q^{28} +(2.29174 + 1.66504i) q^{29} +(-10.5731 + 1.01558i) q^{30} +(0.725999 - 2.23440i) q^{31} +(-3.16967 + 3.16967i) q^{32} -4.38695i q^{34} +(-10.2742 - 0.630809i) q^{35} +(3.19260 - 2.31956i) q^{36} +(-0.287467 - 1.81500i) q^{37} +(3.56664 + 1.81730i) q^{38} +(1.54244 + 4.74714i) q^{39} +(-6.99606 - 2.75771i) q^{40} +(4.45234 + 6.12812i) q^{41} +(19.4838 - 9.92751i) q^{42} +(-4.63235 - 4.63235i) q^{43} +(-2.20884 - 1.30180i) q^{45} +(0.984950 + 0.320030i) q^{46} +(-2.17672 - 0.344758i) q^{47} +(1.93429 - 0.306361i) q^{48} +(13.4969 - 4.38541i) q^{49} +(0.401606 + 11.6568i) q^{50} +(2.25093 - 3.09814i) q^{51} +(-1.31971 + 8.33234i) q^{52} +(6.07129 + 11.9156i) q^{53} -8.80396 q^{54} +15.4814 q^{56} +(1.58638 + 3.11344i) q^{57} +(-1.03373 + 6.52669i) q^{58} +(2.43363 - 3.34961i) q^{59} +(-8.41701 - 13.2189i) q^{60} +(2.33575 - 0.758930i) q^{61} +(5.41302 - 0.857338i) q^{62} +(5.21337 + 0.825717i) q^{63} +(-11.7742 - 3.82568i) q^{64} +(5.30678 - 1.37110i) q^{65} +(8.24053 + 8.24053i) q^{67} +(5.76695 - 2.93841i) q^{68} +(0.531383 + 0.731386i) q^{69} +(-9.56968 - 22.0228i) q^{70} +(-2.88398 - 8.87597i) q^{71} +(3.43581 + 1.75063i) q^{72} +(-2.20858 - 13.9444i) q^{73} +(3.46801 - 2.51965i) q^{74} +(-5.69744 + 8.43828i) q^{75} +5.90584i q^{76} +(-8.23334 + 8.23334i) q^{78} +(0.657095 - 2.02233i) q^{79} +(-0.205616 - 2.14065i) q^{80} +(-9.00041 - 6.53918i) q^{81} +(-8.02199 + 15.7440i) q^{82} +(-6.77566 + 13.2980i) q^{83} +(26.1008 + 18.9633i) q^{84} +(-3.24417 - 2.67556i) q^{85} +(4.72242 - 14.5341i) q^{86} +(-4.07886 + 4.07886i) q^{87} -4.75744i q^{89} +(0.366523 - 5.96969i) q^{90} +(-9.12886 + 6.63251i) q^{91} +(0.239025 + 1.50914i) q^{92} +(4.26267 + 2.17194i) q^{93} +(-1.58866 - 4.88939i) q^{94} +(3.51917 - 1.52920i) q^{95} +(-5.36531 - 7.38471i) q^{96} +(-12.3234 + 6.27908i) q^{97} +(23.4088 + 23.4088i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 8 q^{3} + 4 q^{5}+O(q^{10}) \) 160 * q - 8 * q^3 + 4 * q^5	\( 160 q - 8 q^{3} + 4 q^{5} - 128 q^{12} - 32 q^{15} + 24 q^{16} - 32 q^{20} - 96 q^{23} + 52 q^{25} + 8 q^{26} - 32 q^{27} - 16 q^{31} + 40 q^{36} - 36 q^{37} - 32 q^{38} - 32 q^{42} + 256 q^{45} - 32 q^{47} + 16 q^{48} + 68 q^{53} + 320 q^{56} - 132 q^{58} + 64 q^{60} - 352 q^{67} + 8 q^{70} + 16 q^{75} - 992 q^{78} + 164 q^{80} + 40 q^{81} - 100 q^{82} + 80 q^{86} + 96 q^{91} + 56 q^{92} - 24 q^{93} + 68 q^{97}+O(q^{100}) \) 160 * q - 8 * q^3 + 4 * q^5 - 128 * q^12 - 32 * q^15 + 24 * q^16 - 32 * q^20 - 96 * q^23 + 52 * q^25 + 8 * q^26 - 32 * q^27 - 16 * q^31 + 40 * q^36 - 36 * q^37 - 32 * q^38 - 32 * q^42 + 256 * q^45 - 32 * q^47 + 16 * q^48 + 68 * q^53 + 320 * q^56 - 132 * q^58 + 64 * q^60 - 352 * q^67 + 8 * q^70 + 16 * q^75 - 992 * q^78 + 164 * q^80 + 40 * q^81 - 100 * q^82 + 80 * q^86 + 96 * q^91 + 56 * q^92 - 24 * q^93 + 68 * q^97

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