LMFDB - Embedded newform 605.2.j.g.124.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(9,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 6]))

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

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

chi := DirichletCharacter("605.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.j (of order $10$, degree $4$, 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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{14} + 25x^{12} - 57x^{10} + 194x^{8} - 303x^{6} + 235x^{4} - 33x^{2} + 121 $ x^16 - 7x^14 + 25x^12 - 57x^10 + 194x^8 - 303x^6 + 235x^4 - 33*x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			124.4
Root			$0.972539 - 1.33858i$ of defining polynomial
Character	$\chi$	$=$	605.124
Dual form			605.2.j.g.444.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.972539 + 1.33858i) q^{2} +(-1.87813 + 0.610243i) q^{3} +(-0.227943 + 0.701538i) q^{4} +(-1.51945 - 1.64051i) q^{5} +(-2.64342 - 1.92056i) q^{6} +(2.13329 + 0.693148i) q^{7} +(1.98645 - 0.645437i) q^{8} +(0.727943 - 0.528882i) q^{9} +O(q^{10})$	\(q+(0.972539 + 1.33858i) q^{2} +(-1.87813 + 0.610243i) q^{3} +(-0.227943 + 0.701538i) q^{4} +(-1.51945 - 1.64051i) q^{5} +(-2.64342 - 1.92056i) q^{6} +(2.13329 + 0.693148i) q^{7} +(1.98645 - 0.645437i) q^{8} +(0.727943 - 0.528882i) q^{9} +(0.718246 - 3.62937i) q^{10} -1.45668i q^{12} +(2.17466 + 2.99317i) q^{13} +(1.14687 + 3.52970i) q^{14} +(3.85484 + 2.15387i) q^{15} +(3.98940 + 2.89847i) q^{16} +(1.30759 - 1.79974i) q^{17} +(1.41591 + 0.460056i) q^{18} +(1.63372 + 5.02809i) q^{19} +(1.49723 - 0.692004i) q^{20} -4.42960 q^{21} +3.85415i q^{23} +(-3.33695 + 2.42443i) q^{24} +(-0.382569 + 4.98534i) q^{25} +(-1.89166 + 5.82194i) q^{26} +(2.43782 - 3.35538i) q^{27} +(-0.972539 + 1.33858i) q^{28} +(0.0582308 - 0.179216i) q^{29} +(0.865834 + 7.25475i) q^{30} +(-0.555687 + 0.403730i) q^{31} +3.98166i q^{32} +3.68079 q^{34} +(-2.10430 - 4.55289i) q^{35} +(0.205101 + 0.631235i) q^{36} +(2.46624 + 0.801331i) q^{37} +(-5.14166 + 7.07689i) q^{38} +(-5.91087 - 4.29450i) q^{39} +(-4.07715 - 2.27809i) q^{40} +(-2.44619 - 7.52860i) q^{41} +(-4.30795 - 5.92939i) q^{42} +8.41368i q^{43} +(-1.97371 - 0.390594i) q^{45} +(-5.15911 + 3.74831i) q^{46} +(11.4252 - 3.71227i) q^{47} +(-9.26140 - 3.00921i) q^{48} +(-1.59265 - 1.15713i) q^{49} +(-7.04537 + 4.33634i) q^{50} +(-1.35755 + 4.17811i) q^{51} +(-2.59552 + 0.843335i) q^{52} +(7.43935 + 10.2394i) q^{53} +6.86233 q^{54} +4.68506 q^{56} +(-6.13671 - 8.44645i) q^{57} +(0.296528 - 0.0963477i) q^{58} +(0.106206 - 0.326867i) q^{59} +(-2.38971 + 2.21335i) q^{60} +(1.40233 + 1.01885i) q^{61} +(-1.08085 - 0.351191i) q^{62} +(1.91951 - 0.623686i) q^{63} +(2.64900 - 1.92461i) q^{64} +(1.60605 - 8.11552i) q^{65} +0.650461i q^{67} +(0.964532 + 1.32756i) q^{68} +(-2.35197 - 7.23862i) q^{69} +(4.04792 - 7.24465i) q^{70} +(-3.75999 - 2.73179i) q^{71} +(1.10466 - 1.52044i) q^{72} +(-8.42484 - 2.73740i) q^{73} +(1.32587 + 4.08060i) q^{74} +(-2.32375 - 9.59661i) q^{75} -3.89979 q^{76} -12.0888i q^{78} +(5.85264 - 4.25219i) q^{79} +(-1.30670 - 10.9487i) q^{80} +(-3.36512 + 10.3568i) q^{81} +(7.69865 - 10.5963i) q^{82} +(1.87013 - 2.57401i) q^{83} +(1.00970 - 3.10753i) q^{84} +(-4.93932 + 0.589494i) q^{85} +(-11.2624 + 8.18263i) q^{86} +0.372127i q^{87} -9.92195 q^{89} +(-1.39666 - 3.02184i) q^{90} +(2.56448 + 7.89265i) q^{91} +(-2.70383 - 0.878529i) q^{92} +(0.797281 - 1.09736i) q^{93} +(16.0806 + 11.6833i) q^{94} +(5.76629 - 10.3200i) q^{95} +(-2.42978 - 7.47810i) q^{96} +(-1.33316 - 1.83494i) q^{97} -3.25724i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{4} - 2 q^{5} - 12 q^{6} + 2 q^{9}+O(q^{10}) $ 16 * q + 6 * q^4 - 2 * q^5 - 12 * q^6 + 2 * q^9	$ 16 q + 6 q^{4} - 2 q^{5} - 12 q^{6} + 2 q^{9} + 8 q^{14} + 24 q^{15} + 6 q^{16} - 6 q^{19} + 12 q^{20} - 8 q^{21} + 4 q^{24} + 24 q^{25} - 50 q^{26} - 22 q^{29} + 4 q^{30} - 22 q^{31} - 16 q^{34} + 8 q^{35} - 30 q^{36} - 12 q^{40} - 18 q^{41} + 12 q^{45} - 38 q^{46} - 20 q^{49} + 12 q^{50} + 12 q^{51} + 40 q^{54} - 20 q^{56} - 8 q^{59} - 2 q^{60} - 20 q^{61} + 22 q^{64} + 40 q^{65} + 6 q^{69} + 26 q^{70} + 6 q^{71} + 52 q^{74} + 40 q^{75} - 56 q^{76} + 22 q^{79} - 6 q^{80} - 32 q^{81} + 18 q^{84} + 62 q^{85} - 68 q^{86} + 24 q^{89} + 32 q^{90} + 56 q^{94} + 22 q^{95} - 94 q^{96}+O(q^{100}) $ 16 * q + 6 * q^4 - 2 * q^5 - 12 * q^6 + 2 * q^9 + 8 * q^14 + 24 * q^15 + 6 * q^16 - 6 * q^19 + 12 * q^20 - 8 * q^21 + 4 * q^24 + 24 * q^25 - 50 * q^26 - 22 * q^29 + 4 * q^30 - 22 * q^31 - 16 * q^34 + 8 * q^35 - 30 * q^36 - 12 * q^40 - 18 * q^41 + 12 * q^45 - 38 * q^46 - 20 * q^49 + 12 * q^50 + 12 * q^51 + 40 * q^54 - 20 * q^56 - 8 * q^59 - 2 * q^60 - 20 * q^61 + 22 * q^64 + 40 * q^65 + 6 * q^69 + 26 * q^70 + 6 * q^71 + 52 * q^74 + 40 * q^75 - 56 * q^76 + 22 * q^79 - 6 * q^80 - 32 * q^81 + 18 * q^84 + 62 * q^85 - 68 * q^86 + 24 * q^89 + 32 * q^90 + 56 * q^94 + 22 * q^95 - 94 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$122$	$486$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.972539	+	1.33858i	0.687689	+	0.946522i	0.999994	−	0.00345950i	$-0.00110120\pi$
$2$	0.972539	+	1.33858i	0.687689	+	0.946522i	−0.312305	+	0.949982i	$0.601101\pi$
$3$	−1.87813	+	0.610243i	−1.08434	+	0.352324i	−0.796058	−	0.605221i	$-0.793085\pi$
$3$	−1.87813	+	0.610243i	−1.08434	+	0.352324i	−0.288284	+	0.957545i	$0.593085\pi$
$4$	−0.227943	+	0.701538i	−0.113972	+	0.350769i
$5$	−1.51945	−	1.64051i	−0.679517	−	0.733660i
$5$	−1.51945	−	1.64051i	−0.679517	−	0.733660i
$6$	−2.64342	−	1.92056i	−1.07917	−	0.784064i
$7$	2.13329	+	0.693148i	0.806308	+	0.261985i	0.683033	−	0.730387i	$-0.260660\pi$
$7$	2.13329	+	0.693148i	0.806308	+	0.261985i	0.123275	+	0.992373i	$0.460660\pi$
$8$	1.98645	−	0.645437i	0.702316	−	0.228196i
$9$	0.727943	−	0.528882i	0.242648	−	0.176294i
$10$	0.718246	−	3.62937i	0.227129	−	1.14771i
$11$		0			0
$11$		0			0
$12$		−	1.45668i		−	0.420508i
$13$	2.17466	+	2.99317i	0.603143	+	0.830155i	0.995991	−	0.0894482i	$-0.0285104\pi$
$13$	2.17466	+	2.99317i	0.603143	+	0.830155i	−0.392849	+	0.919603i	$0.628510\pi$
$14$	1.14687	+	3.52970i	0.306514	+	0.943353i
$15$	3.85484	+	2.15387i	0.995314	+	0.556128i
$16$	3.98940	+	2.89847i	0.997350	+	0.724617i
$17$	1.30759	−	1.79974i	0.317137	−	0.436502i	−0.620453	−	0.784244i	$-0.713051\pi$
$17$	1.30759	−	1.79974i	0.317137	−	0.436502i	0.937591	+	0.347741i	$0.113051\pi$
$18$	1.41591	+	0.460056i	0.333732	+	0.108436i
$19$	1.63372	+	5.02809i	0.374802	+	1.15352i	0.943612	+	0.331053i	$0.107404\pi$
$19$	1.63372	+	5.02809i	0.374802	+	1.15352i	−0.568810	+	0.822469i	$0.692596\pi$
$20$	1.49723	−	0.692004i	0.334791	−	0.154737i
$21$	−4.42960			−0.966617
$22$		0			0
$23$			3.85415i			0.803647i	0.915717	+	0.401823i	$0.131623\pi$
$23$			3.85415i			0.803647i	−0.915717	+	0.401823i	$0.868377\pi$
$24$	−3.33695	+	2.42443i	−0.681152	+	0.494886i
$25$	−0.382569	+	4.98534i	−0.0765139	+	0.997069i
$26$	−1.89166	+	5.82194i	−0.370986	+	1.14178i
$27$	2.43782	−	3.35538i	0.469159	−	0.645743i
$28$	−0.972539	+	1.33858i	−0.183793	+	0.252969i
$29$	0.0582308	−	0.179216i	0.0108132	−	0.0332796i	−0.945504	−	0.325609i	$-0.894431\pi$
$29$	0.0582308	−	0.179216i	0.0108132	−	0.0332796i	0.956318	+	0.292330i	$0.0944305\pi$
$30$	0.865834	+	7.25475i	0.158079	+	1.32453i
$31$	−0.555687	+	0.403730i	−0.0998043	+	0.0725121i	−0.636568	−	0.771220i	$-0.719647\pi$
$31$	−0.555687	+	0.403730i	−0.0998043	+	0.0725121i	0.536764	+	0.843733i	$0.319647\pi$
$32$			3.98166i			0.703866i
$33$		0			0
$34$	3.68079			0.631251
$35$	−2.10430	−	4.55289i	−0.355692	−	0.769579i
$36$	0.205101	+	0.631235i	0.0341834	+	0.105206i
$37$	2.46624	+	0.801331i	0.405448	+	0.131738i	0.504639	−	0.863330i	$-0.331626\pi$
$37$	2.46624	+	0.801331i	0.405448	+	0.131738i	−0.0991914	+	0.995068i	$0.531626\pi$
$38$	−5.14166	+	7.07689i	−0.834087	+	1.14802i
$39$	−5.91087	−	4.29450i	−0.946496	−	0.687670i
$40$	−4.07715	−	2.27809i	−0.644654	−	0.360198i
$41$	−2.44619	−	7.52860i	−0.382031	−	1.17577i	−0.938611	−	0.344976i	$-0.887887\pi$
$41$	−2.44619	−	7.52860i	−0.382031	−	1.17577i	0.556581	−	0.830793i	$-0.312113\pi$
$42$	−4.30795	−	5.92939i	−0.664732	−	0.914924i
$43$			8.41368i			1.28307i	0.767092	+	0.641537i	$0.221703\pi$
$43$			8.41368i			1.28307i	−0.767092	+	0.641537i	$0.778297\pi$
$44$		0			0
$45$	−1.97371	−	0.390594i	−0.294223	−	0.0582263i
$46$	−5.15911	+	3.74831i	−0.760669	+	0.552659i
$47$	11.4252	−	3.71227i	1.66654	−	0.541491i	0.684311	−	0.729190i	$-0.260103\pi$
$47$	11.4252	−	3.71227i	1.66654	−	0.541491i	0.982227	+	0.187699i	$0.0601031\pi$
$48$	−9.26140	−	3.00921i	−1.33677	−	0.434342i
$49$	−1.59265	−	1.15713i	−0.227521	−	0.165304i
$50$	−7.04537	+	4.33634i	−0.996365	+	0.613251i
$51$	−1.35755	+	4.17811i	−0.190095	+	0.585053i
$52$	−2.59552	+	0.843335i	−0.359934	+	0.116950i
$53$	7.43935	+	10.2394i	1.02187	+	1.40649i	0.910882	+	0.412667i	$0.135403\pi$
$53$	7.43935	+	10.2394i	1.02187	+	1.40649i	0.110991	+	0.993821i	$0.464597\pi$
$54$	6.86233			0.933845
$55$		0			0
$56$	4.68506			0.626067
$57$	−6.13671	−	8.44645i	−0.812827	−	1.11876i
$58$	0.296528	−	0.0963477i	0.0389360	−	0.0126511i
$59$	0.106206	−	0.326867i	0.0138268	−	0.0425545i	−0.943905	−	0.330217i	$-0.892878\pi$
$59$	0.106206	−	0.326867i	0.0138268	−	0.0425545i	0.957732	+	0.287662i	$0.0928781\pi$
$60$	−2.38971	+	2.21335i	−0.308510	+	0.285742i
$61$	1.40233	+	1.01885i	0.179550	+	0.130451i	0.673930	−	0.738795i	$-0.264605\pi$
$61$	1.40233	+	1.01885i	0.179550	+	0.130451i	−0.494380	+	0.869246i	$0.664605\pi$
$62$	−1.08085	−	0.351191i	−0.137269	−	0.0446013i
$63$	1.91951	−	0.623686i	0.241835	−	0.0785770i
$64$	2.64900	−	1.92461i	0.331125	−	0.240577i
$65$	1.60605	−	8.11552i	0.199206	−	1.00661i
$66$		0			0
$67$			0.650461i			0.0794664i	0.999210	+	0.0397332i	$0.0126508\pi$
$67$			0.650461i			0.0794664i	−0.999210	+	0.0397332i	$0.987349\pi$
$68$	0.964532	+	1.32756i	0.116967	+	0.160991i
$69$	−2.35197	−	7.23862i	−0.283144	−	0.871428i
$70$	4.04792	−	7.24465i	0.483819	−	0.865901i
$71$	−3.75999	−	2.73179i	−0.446229	−	0.324204i	0.341876	−	0.939745i	$-0.388938\pi$
$71$	−3.75999	−	2.73179i	−0.446229	−	0.324204i	−0.788105	+	0.615541i	$0.788938\pi$
$72$	1.10466	−	1.52044i	0.130186	−	0.179185i
$73$	−8.42484	−	2.73740i	−0.986053	−	0.320388i	−0.228774	−	0.973479i	$-0.573472\pi$
$73$	−8.42484	−	2.73740i	−0.986053	−	0.320388i	−0.757279	+	0.653091i	$0.773472\pi$
$74$	1.32587	+	4.08060i	0.154129	+	0.474360i
$75$	−2.32375	−	9.59661i	−0.268324	−	1.10812i
$76$	−3.89979			−0.447336
$77$		0			0
$78$		−	12.0888i		−	1.36878i
$79$	5.85264	−	4.25219i	0.658473	−	0.478409i	−0.207674	−	0.978198i	$-0.566589\pi$
$79$	5.85264	−	4.25219i	0.658473	−	0.478409i	0.866147	+	0.499789i	$0.166589\pi$
$80$	−1.30670	−	10.9487i	−0.146093	−	1.22410i
$81$	−3.36512	+	10.3568i	−0.373902	+	1.15075i
$82$	7.69865	−	10.5963i	0.850174	−	1.17016i
$83$	1.87013	−	2.57401i	0.205273	−	0.282534i	−0.693951	−	0.720022i	$-0.744132\pi$
$83$	1.87013	−	2.57401i	0.205273	−	0.282534i	0.899224	+	0.437488i	$0.144132\pi$
$84$	1.00970	−	3.10753i	0.110167	−	0.339059i
$85$	−4.93932	+	0.589494i	−0.535744	+	0.0639396i
$86$	−11.2624	+	8.18263i	−1.21446	+	0.882356i
$87$			0.372127i			0.0398962i
$88$		0			0
$89$	−9.92195			−1.05172			−0.525862	−	0.850570i	$-0.676257\pi$
$89$	−9.92195			−1.05172			−0.525862	+	0.850570i	$0.676257\pi$
$90$	−1.39666	−	3.02184i	−0.147221	−	0.318530i
$91$	2.56448	+	7.89265i	0.268830	+	0.827375i
$92$	−2.70383	−	0.878529i	−0.281894	−	0.0915930i
$93$	0.797281	−	1.09736i	0.0826742	−	0.113791i
$94$	16.0806	+	11.6833i	1.65859	+	1.20504i
$95$	5.76629	−	10.3200i	0.591609	−	1.05881i
$96$	−2.42978	−	7.47810i	−0.247989	−	0.763231i
$97$	−1.33316	−	1.83494i	−0.135362	−	0.186310i	0.735955	−	0.677031i	$-0.236734\pi$
$97$	−1.33316	−	1.83494i	−0.135362	−	0.186310i	−0.871317	+	0.490721i	$0.836734\pi$
$98$		−	3.25724i		−	0.329031i
$99$		0			0
$100$	−3.41020	−	1.40476i	−0.341020	−	0.140476i
$101$	8.00673	−	5.81723i	0.796699	−	0.578836i	−0.113245	−	0.993567i	$-0.536124\pi$
$101$	8.00673	−	5.81723i	0.796699	−	0.578836i	0.909944	+	0.414731i	$0.136124\pi$
$102$	−6.91303	+	2.24618i	−0.684492	+	0.222405i
$103$	−9.73989	−	3.16468i	−0.959700	−	0.311825i	−0.213049	−	0.977041i	$-0.568339\pi$
$103$	−9.73989	−	3.16468i	−0.959700	−	0.311825i	−0.746651	+	0.665216i	$0.768339\pi$
$104$	6.25176	+	4.54217i	0.613035	+	0.445396i
$105$	6.73053	+	7.26681i	0.656832	+	0.709168i
$106$	−6.47123	+	19.9164i	−0.628542	+	1.93445i
$107$	9.55508	−	3.10463i	0.923724	−	0.300136i	0.191731	−	0.981448i	$-0.438590\pi$
$107$	9.55508	−	3.10463i	0.923724	−	0.300136i	0.731994	+	0.681311i	$0.238590\pi$
$108$	1.79824	+	2.47506i	0.173035	+	0.238163i
$109$	−8.80173			−0.843053			−0.421527	−	0.906816i	$-0.638506\pi$
$109$	−8.80173			−0.843053			−0.421527	+	0.906816i	$0.638506\pi$
$110$		0			0
$111$	−5.12094			−0.486058
$112$	6.50148	+	8.94851i	0.614332	+	0.845555i
$113$	0.220029	−	0.0714918i	0.0206986	−	0.00672538i	−0.298649	−	0.954363i	$-0.596536\pi$
$113$	0.220029	−	0.0714918i	0.0206986	−	0.00672538i	0.319348	+	0.947638i	$0.396536\pi$
$114$	5.33811	−	16.4290i	0.499960	−	1.53872i
$115$	6.32279	−	5.85618i	0.589603	−	0.546091i
$116$	0.112453	+	0.0817022i	0.0104410	+	0.00758586i
$117$	3.16606	+	1.02872i	0.292703	+	0.0951048i
$118$	0.540828	−	0.175726i	0.0497873	−	0.0161769i
$119$	4.03696	−	2.93302i	0.370068	−	0.268870i
$120$	9.04763	+	1.79051i	0.825932	+	0.163451i
$121$		0			0
$122$			2.86801i			0.259658i
$123$	9.18855	+	12.6470i	0.828504	+	1.14034i
$124$	−0.156567	−	0.481863i	−0.0140601	−	0.0432726i
$125$	8.75982	−	6.94735i	0.783502	−	0.621390i
$126$	2.70165	+	1.96286i	0.240682	+	0.174866i
$127$	1.42852	−	1.96619i	0.126761	−	0.174471i	−0.740920	−	0.671594i	$-0.765610\pi$
$127$	1.42852	−	1.96619i	0.126761	−	0.174471i	0.867680	+	0.497123i	$0.165610\pi$
$128$	12.7261	+	4.13496i	1.12484	+	0.365482i
$129$	−5.13439	−	15.8020i	−0.452058	−	1.39129i
$130$	12.4253	−	5.74282i	1.08977	−	0.503679i
$131$	−1.58846			−0.138785			−0.0693924	−	0.997589i	$-0.522106\pi$
$131$	−1.58846			−0.138785			−0.0693924	+	0.997589i	$0.522106\pi$
$132$		0			0
$133$			11.8588i			1.02829i
$134$	−0.870697	+	0.632598i	−0.0752167	+	0.0546482i
$135$	−9.20868	+	1.09903i	−0.792557	+	0.0945894i
$136$	1.43584	−	4.41907i	0.123123	−	0.378932i
$137$	−10.9927	+	15.1301i	−0.939169	+	1.29266i	0.0170046	+	0.999855i	$0.494587\pi$
$137$	−10.9927	+	15.1301i	−0.939169	+	1.29266i	−0.956174	+	0.292800i	$0.905413\pi$
$138$	7.40212	−	10.1881i	0.630111	−	0.867273i
$139$	3.59306	−	11.0583i	0.304759	−	0.937953i	−0.675008	−	0.737811i	$-0.735860\pi$
$139$	3.59306	−	11.0583i	0.304759	−	0.937953i	0.979767	−	0.200142i	$-0.0641403\pi$
$140$	3.67369	−	0.438444i	0.310483	−	0.0370553i
$141$	−19.1927	+	13.9443i	−1.61632	+	1.17432i
$142$		−	7.68984i		−	0.645317i
$143$		0			0
$144$	4.43700			0.369750
$145$	−0.382485	+	0.176781i	−0.0317636	+	0.0146808i
$146$	−4.52925	−	13.9396i	−0.374843	−	1.15365i
$147$	3.69733	+	1.20134i	0.304951	+	0.0990846i
$148$	−1.12433	+	1.54750i	−0.0924191	+	0.127204i
$149$	−4.78576	−	3.47706i	−0.392065	−	0.284852i	0.374236	−	0.927333i	$-0.377905\pi$
$149$	−4.78576	−	3.47706i	−0.392065	−	0.284852i	−0.766301	+	0.642482i	$0.777905\pi$
$150$	10.5859	−	12.4436i	0.864338	−	1.01602i
$151$	−3.94858	−	12.1525i	−0.321331	−	0.988954i	−0.973070	−	0.230511i	$-0.925960\pi$
$151$	−3.94858	−	12.1525i	−0.321331	−	0.988954i	0.651739	−	0.758443i	$-0.274040\pi$
$152$	6.49062	+	8.93357i	0.526459	+	0.724609i
$153$		−	2.00167i		−	0.161826i
$154$		0			0
$155$	1.50666	+	0.298166i	0.121018	+	0.0239492i
$156$	4.36009	−	3.16779i	0.349087	−	0.253627i
$157$	−13.6464	+	4.43398i	−1.08910	+	0.353870i	−0.797899	−	0.602791i	$-0.794055\pi$
$157$	−13.6464	+	4.43398i	−1.08910	+	0.353870i	−0.291202	+	0.956662i	$0.594055\pi$
$158$	11.3838	+	3.69883i	0.905649	+	0.294263i
$159$	−20.2206	−	14.6911i	−1.60360	−	1.16508i
$160$	6.53197	−	6.04992i	0.516398	−	0.478288i
$161$	−2.67150	+	8.22203i	−0.210544	+	0.647986i
$162$	−17.1361	+	5.56786i	−1.34634	+	0.437452i
$163$	−2.13199	−	2.93443i	−0.166990	−	0.229843i	0.717318	−	0.696746i	$-0.245370\pi$
$163$	−2.13199	−	2.93443i	−0.166990	−	0.229843i	−0.884308	+	0.466903i	$0.845370\pi$
$164$	5.83919			0.455964
$165$		0			0
$166$	5.26430			0.408589
$167$	−2.24575	−	3.09101i	−0.173781	−	0.239190i	0.713238	−	0.700922i	$-0.247228\pi$
$167$	−2.24575	−	3.09101i	−0.173781	−	0.239190i	−0.887019	+	0.461733i	$0.847228\pi$
$168$	−8.79917	+	2.85902i	−0.678871	+	0.220578i
$169$	−0.212666	+	0.654519i	−0.0163589	+	0.0503476i
$170$	−5.59277	−	6.03839i	−0.428946	−	0.463124i
$171$	3.84852	+	2.79611i	0.294304	+	0.213824i
$172$	−5.90252	−	1.91784i	−0.450063	−	0.146234i
$173$	−2.00401	+	0.651143i	−0.152362	+	0.0495055i	−0.384205	−	0.923248i	$-0.625524\pi$
$173$	−2.00401	+	0.651143i	−0.152362	+	0.0495055i	0.231843	+	0.972753i	$0.425524\pi$
$174$	−0.498123	+	0.361908i	−0.0377626	+	0.0274362i
$175$	−4.27171	+	10.3700i	−0.322911	+	0.783899i
$176$		0			0
$177$			0.678711i			0.0510151i
$178$	−9.64948	−	13.2814i	−0.723259	−	0.995481i
$179$	−1.55249	−	4.77808i	−0.116039	−	0.357131i	0.876124	−	0.482087i	$-0.160121\pi$
$179$	−1.55249	−	4.77808i	−0.116039	−	0.357131i	−0.992162	+	0.124956i	$0.960121\pi$
$180$	0.723910	−	1.29560i	0.0539571	−	0.0965681i
$181$	12.6592	+	9.19743i	0.940949	+	0.683640i	0.948649	−	0.316331i	$-0.102451\pi$
$181$	12.6592	+	9.19743i	0.940949	+	0.683640i	−0.00769972	+	0.999970i	$0.502451\pi$
$182$	−8.07093	+	11.1087i	−0.598257	+	0.823430i
$183$	−3.25552	−	1.05778i	−0.240655	−	0.0781934i
$184$	2.48761	+	7.65608i	0.183389	+	0.564414i
$185$	−2.43273	−	5.26348i	−0.178858	−	0.386979i
$186$	2.24430			0.164560
$187$		0			0
$188$			8.86140i			0.646284i
$189$	7.52636	−	5.46822i	0.547462	−	0.397754i
$190$	19.4222	−	2.31798i	1.40903	−	0.168164i
$191$	0.962852	−	2.96335i	0.0696695	−	0.214421i	−0.910160	−	0.414258i	$-0.864041\pi$
$191$	0.962852	−	2.96335i	0.0696695	−	0.214421i	0.979829	+	0.199837i	$0.0640413\pi$
$192$	−3.80070	+	5.23122i	−0.274292	+	0.377530i
$193$	−5.66412	+	7.79599i	−0.407712	+	0.561168i	−0.962659	−	0.270718i	$-0.912739\pi$
$193$	−5.66412	+	7.79599i	−0.407712	+	0.561168i	0.554946	+	0.831886i	$0.312739\pi$
$194$	1.15967	−	3.56910i	0.0832595	−	0.256246i
$195$	1.93606	+	16.2221i	0.138644	+	1.16169i
$196$	1.17480	−	0.853543i	0.0839143	−	0.0609673i
$197$		−	14.3974i		−	1.02577i	−0.858457	−	0.512885i	$-0.828577\pi$
$197$		−	14.3974i		−	1.02577i	0.858457	−	0.512885i	$-0.171423\pi$
$198$		0			0
$199$	−14.7978			−1.04899			−0.524493	−	0.851415i	$-0.675745\pi$
$199$	−14.7978			−1.04899			−0.524493	+	0.851415i	$0.675745\pi$
$200$	2.45777	+	10.1501i	0.173790	+	0.717717i
$201$	−0.396939	−	1.22165i	−0.0279979	−	0.0861688i
$202$	15.5737	+	5.06020i	1.09576	+	0.356035i
$203$	0.248446	−	0.341957i	0.0174375	−	0.0240007i
$204$	−2.62166	−	1.90475i	−0.183553	−	0.133359i
$205$	−8.63391	+	15.4523i	−0.603019	+	1.07924i
$206$	−5.23623	−	16.1154i	−0.364825	−	1.12282i
$207$	2.03839	+	2.80561i	0.141678	+	0.195003i
$208$			18.2441i			1.26500i
$209$		0			0
$210$	−3.18154	+	16.0766i	−0.219547	+	1.10939i
$211$	−5.47824	+	3.98017i	−0.377137	+	0.274006i	−0.760164	−	0.649731i	$-0.774882\pi$
$211$	−5.47824	+	3.98017i	−0.377137	+	0.274006i	0.383027	+	0.923737i	$0.374882\pi$
$212$	−8.87907	+	2.88498i	−0.609817	+	0.198141i
$213$	8.72883	+	2.83617i	0.598089	+	0.194331i
$214$	13.4485	+	9.77090i	0.919320	+	0.667925i
$215$	13.8028	−	12.7841i	0.941340	−	0.871871i
$216$	2.67693	−	8.23875i	0.182142	−	0.560576i
$217$	−1.46529	+	0.476100i	−0.0994701	+	0.0323198i
$218$	−8.56003	−	11.7819i	−0.579758	−	0.797969i
$219$	17.4935			1.18210
$220$		0			0
$221$	8.23051			0.553644
$222$	−4.98031	−	6.85481i	−0.334257	−	0.460065i
$223$	8.29062	−	2.69379i	0.555181	−	0.180389i	−0.0179708	−	0.999839i	$-0.505721\pi$
$223$	8.29062	−	2.69379i	0.555181	−	0.180389i	0.573152	+	0.819449i	$0.305721\pi$
$224$	−2.75988	+	8.49404i	−0.184402	+	0.567532i
$225$	2.35817	+	3.83138i	0.157211	+	0.255425i
$226$	0.309684	+	0.224999i	0.0205999	+	0.0149667i
$227$	3.62109	+	1.17656i	0.240340	+	0.0780912i	0.426710	−	0.904388i	$-0.359672\pi$
$227$	3.62109	+	1.17656i	0.240340	+	0.0780912i	−0.186370	+	0.982480i	$0.559672\pi$
$228$	7.32433	−	2.37982i	0.485065	−	0.157607i
$229$	−2.19540	+	1.59505i	−0.145076	+	0.105404i	−0.657956	−	0.753056i	$-0.728579\pi$
$229$	−2.19540	+	1.59505i	−0.145076	+	0.105404i	0.512880	+	0.858461i	$0.328579\pi$
$230$	13.9881	+	2.76823i	0.922351	+	0.182532i
$231$		0			0
$232$		−	0.393588i		−	0.0258403i
$233$	−6.17808	−	8.50340i	−0.404740	−	0.557076i	0.557186	−	0.830388i	$-0.311881\pi$
$233$	−6.17808	−	8.50340i	−0.404740	−	0.557076i	−0.961926	+	0.273312i	$0.911881\pi$
$234$	1.70209	+	5.23851i	0.111269	+	0.342452i
$235$	−23.4500	−	13.1026i	−1.52971	−	0.854720i
$236$	0.205101	+	0.149014i	0.0133509	+	0.00970001i
$237$	−8.39717	+	11.5577i	−0.545455	+	0.750755i
$238$	7.85220	+	2.55133i	0.508983	+	0.165378i
$239$	6.19258	+	19.0588i	0.400565	+	1.23281i	0.924542	+	0.381079i	$0.124448\pi$
$239$	6.19258	+	19.0588i	0.400565	+	1.23281i	−0.523978	+	0.851732i	$0.675552\pi$
$240$	9.13554	+	19.7658i	0.589697	+	1.27588i
$241$	−28.4450			−1.83230			−0.916152	−	0.400832i	$-0.868721\pi$
$241$	−28.4450			−1.83230			−0.916152	+	0.400832i	$0.868721\pi$
$242$		0			0
$243$		−	9.06251i		−	0.581361i
$244$	−1.03442	+	0.751547i	−0.0662217	+	0.0481129i
$245$	0.521660	+	4.37095i	0.0333277	+	0.279250i
$246$	−7.99280	+	24.5993i	−0.509602	+	1.56839i
$247$	−11.4971	+	15.8244i	−0.731543	+	1.00688i
$248$	−0.843262	+	1.16065i	−0.0535472	+	0.0737014i
$249$	−1.94158	+	5.97557i	−0.123043	+	0.378687i
$250$	17.8189	+	4.96919i	1.12696	+	0.314279i
$251$	19.2845	−	14.0110i	1.21723	−	0.884369i	0.221362	−	0.975192i	$-0.428950\pi$
$251$	19.2845	−	14.0110i	1.21723	−	0.884369i	0.995867	+	0.0908228i	$0.0289497\pi$
$252$			1.48877i			0.0937838i
$253$		0			0
$254$	4.02120			0.252313
$255$	8.91697	−	4.12133i	0.558403	−	0.258088i
$256$	4.81797	+	14.8282i	0.301123	+	0.926761i
$257$	−23.4686	−	7.62540i	−1.46393	−	0.475660i	−0.534662	−	0.845066i	$-0.679561\pi$
$257$	−23.4686	−	7.62540i	−1.46393	−	0.475660i	−0.929268	+	0.369407i	$0.879561\pi$
$258$	16.1590	−	22.2409i	1.00601	−	1.38466i
$259$	4.70577	+	3.41894i	0.292402	+	0.212443i
$260$	5.32725	+	2.97658i	0.330382	+	0.184600i
$261$	−0.0523954	−	0.161256i	−0.00324319	−	0.00998152i
$262$	−1.54484	−	2.12629i	−0.0954407	−	0.131363i
$263$		−	5.44098i		−	0.335505i	−0.985829	−	0.167753i	$-0.946349\pi$
$263$		−	5.44098i		−	0.335505i	0.985829	−	0.167753i	$-0.0536510\pi$
$264$		0			0
$265$	5.49416	−	27.7625i	0.337504	−	1.70544i
$266$	−15.8740	+	11.5331i	−0.973296	+	0.707141i
$267$	18.6348	−	6.05480i	1.14043	−	0.370548i
$268$	−0.456323	−	0.148268i	−0.0278743	−	0.00905692i
$269$	−5.42492	−	3.94143i	−0.330763	−	0.240314i	0.409991	−	0.912089i	$-0.365532\pi$
$269$	−5.42492	−	3.94143i	−0.330763	−	0.240314i	−0.740754	+	0.671776i	$0.765532\pi$
$270$	−10.4269	−	11.2578i	−0.634564	−	0.685125i
$271$	1.56357	−	4.81219i	0.0949804	−	0.292319i	−0.892268	−	0.451506i	$-0.850887\pi$
$271$	1.56357	−	4.81219i	0.0949804	−	0.292319i	0.987249	+	0.159186i	$0.0508870\pi$
$272$	10.4330	−	3.38989i	0.632594	−	0.205542i
$273$	−9.63287	−	13.2585i	−0.583008	−	0.802442i
$274$	−30.9438			−1.86938
$275$		0			0
$276$	5.61428			0.337940
$277$	6.28559	+	8.65138i	0.377665	+	0.519811i	0.954964	−	0.296722i	$-0.0958934\pi$
$277$	6.28559	+	8.65138i	0.377665	+	0.519811i	−0.577299	+	0.816533i	$0.695893\pi$
$278$	18.2969	−	5.94501i	1.09737	−	0.356558i
$279$	−0.190983	+	0.587785i	−0.0114339	+	0.0351898i
$280$	−7.11869	−	7.68590i	−0.425423	−	0.459320i
$281$	−11.0995	−	8.06425i	−0.662140	−	0.481073i	0.205245	−	0.978711i	$-0.434201\pi$
$281$	−11.0995	−	8.06425i	−0.662140	−	0.481073i	−0.867385	+	0.497638i	$0.834201\pi$
$282$	−37.3313	−	12.1297i	−2.22304	−	0.722311i
$283$	−20.8940	+	6.78888i	−1.24202	+	0.403557i	−0.855055	−	0.518537i	$-0.826477\pi$
$283$	−20.8940	+	6.78888i	−1.24202	+	0.403557i	−0.386965	+	0.922094i	$0.626477\pi$
$284$	2.77352	−	2.01508i	0.164578	−	0.119573i
$285$	−4.53213	+	22.9013i	−0.268460	+	1.35655i
$286$		0			0
$287$		−	17.7563i		−	1.04812i
$288$	2.10583	+	2.89843i	0.124087	+	0.170791i
$289$	3.72400	+	11.4613i	0.219059	+	0.674194i
$290$	−0.608617	−	0.340063i	−0.0357392	−	0.0199692i
$291$	3.62361	+	2.63271i	0.212420	+	0.154332i
$292$	3.84078	−	5.28637i	0.224764	−	0.309362i
$293$	−13.3510	−	4.33799i	−0.779971	−	0.253428i	−0.108143	−	0.994135i	$-0.534491\pi$
$293$	−13.3510	−	4.33799i	−0.779971	−	0.253428i	−0.671828	+	0.740707i	$0.734491\pi$
$294$	1.98771	+	6.11754i	0.115926	+	0.356782i
$295$	−0.697603	+	0.322425i	−0.0406160	+	0.0187723i
$296$	5.41627			0.314815
$297$		0			0
$298$		−	9.78772i		−	0.566988i
$299$	−11.5361	+	8.38148i	−0.667151	+	0.484714i
$300$	7.26206	+	0.557282i	0.419276	+	0.0321747i
$301$	−5.83193	+	17.9488i	−0.336147	+	1.03455i
$302$	12.4270	−	17.1042i	0.715091	−	0.984239i
$303$	−11.4878	+	15.8116i	−0.659956	+	0.908352i
$304$	−8.05617	+	24.7943i	−0.462053	+	1.42205i
$305$	−0.459324	−	3.84864i	−0.0263008	−	0.220372i
$306$	2.67941	−	1.94670i	0.153172	−	0.111286i
$307$		−	6.86951i		−	0.392064i	−0.980598	−	0.196032i	$-0.937194\pi$
$307$		−	6.86951i		−	0.392064i	0.980598	−	0.196032i	$-0.0628056\pi$
$308$		0			0
$309$	20.2241			1.15051
$310$	1.06617	+	2.30677i	0.0605541	+	0.131016i
$311$	−1.70008	−	5.23231i	−0.0964027	−	0.296697i	0.891214	−	0.453583i	$-0.149854\pi$
$311$	−1.70008	−	5.23231i	−0.0964027	−	0.296697i	−0.987617	+	0.156886i	$0.949854\pi$
$312$	−14.5135	−	4.71571i	−0.821664	−	0.266975i
$313$	8.36536	−	11.5139i	0.472838	−	0.650806i	−0.504271	−	0.863546i	$-0.668239\pi$
$313$	8.36536	−	11.5139i	0.472838	−	0.650806i	0.977109	+	0.212740i	$0.0682387\pi$
$314$	−19.2069	−	13.9546i	−1.08391	−	0.787506i
$315$	−3.93975	−	2.20132i	−0.221980	−	0.124030i
$316$	1.64900	+	5.07510i	0.0927636	+	0.285497i
$317$	10.9836	+	15.1176i	0.616900	+	0.849090i	0.997123	−	0.0758046i	$-0.0241525\pi$
$317$	10.9836	+	15.1176i	0.616900	+	0.849090i	−0.380222	+	0.924895i	$0.624153\pi$
$318$		−	41.3547i		−	2.31906i
$319$		0			0
$320$	−7.18237	−	1.42138i	−0.401506	−	0.0794575i
$321$	−16.0511	+	11.6618i	−0.895888	+	0.650900i
$322$	−13.6040	+	4.42021i	−0.758122	+	0.246329i
$323$	11.1855	+	3.63439i	0.622379	+	0.202223i
$324$	−6.49860	−	4.72151i	−0.361033	−	0.262306i
$325$	−15.7539	+	9.69634i	−0.873870	+	0.537856i
$326$	1.85454	−	5.70770i	0.102714	−	0.316120i
$327$	16.5308	−	5.37120i	0.914158	−	0.297028i
$328$	−9.71847	−	13.3763i	−0.536613	−	0.738584i
$329$	26.9464			1.48560
$330$		0			0
$331$	0.468249			0.0257373			0.0128686	−	0.999917i	$-0.495904\pi$
$331$	0.468249			0.0257373			0.0128686	+	0.999917i	$0.495904\pi$
$332$	1.37948	+	1.89869i	0.0757089	+	0.104204i
$333$	2.21909	−	0.721027i	0.121606	−	0.0395120i
$334$	1.95350	−	6.01226i	0.106891	−	0.328976i
$335$	1.06709	−	0.988340i	0.0583013	−	0.0539988i
$336$	−17.6714	−	12.8390i	−0.964055	−	0.700427i
$337$	32.4189	+	10.5335i	1.76597	+	0.573798i	0.997790	−	0.0664400i	$-0.0211641\pi$
$337$	32.4189	+	10.5335i	1.76597	+	0.573798i	0.768177	+	0.640238i	$0.221164\pi$
$338$	−1.08295	+	0.351873i	−0.0589050	+	0.0191394i
$339$	−0.369617	+	0.268542i	−0.0200748	+	0.0145852i
$340$	0.712333	−	3.59949i	0.0386317	−	0.195210i
$341$		0			0
$342$			7.87090i			0.425610i
$343$	−11.8246	−	16.2752i	−0.638470	−	0.878779i
$344$	5.43050	+	16.7134i	0.292793	+	0.901124i
$345$	−8.30136	+	14.8571i	−0.446930	+	0.799881i
$346$	−2.82059	−	2.04928i	−0.151636	−	0.110170i
$347$	2.11187	−	2.90673i	0.113371	−	0.156042i	−0.748561	−	0.663066i	$-0.769255\pi$
$347$	2.11187	−	2.90673i	0.113371	−	0.156042i	0.861932	+	0.507025i	$0.169255\pi$
$348$	−0.261061	−	0.0848239i	−0.0139943	−	0.00454704i
$349$	−1.96878	−	6.05927i	−0.105386	−	0.324346i	0.884435	−	0.466664i	$-0.154544\pi$
$349$	−1.96878	−	6.05927i	−0.105386	−	0.324346i	−0.989821	+	0.142319i	$0.954544\pi$
$350$	−18.0355	+	4.36718i	−0.964040	+	0.233436i
$351$	15.3446			0.819037
$352$		0			0
$353$		−	12.1971i		−	0.649186i	−0.945854	−	0.324593i	$-0.894773\pi$
$353$		−	12.1971i		−	0.649186i	0.945854	−	0.324593i	$-0.105227\pi$
$354$	−0.908513	+	0.660073i	−0.0482869	+	0.0350825i
$355$	1.23156	+	10.3191i	0.0653643	+	0.547682i
$356$	2.26164	−	6.96062i	0.119867	−	0.368912i
$357$	−5.79210	+	7.97214i	−0.306550	+	0.421930i
$358$	4.88601	−	6.72501i	0.258234	−	0.355428i
$359$	7.45190	−	22.9346i	0.393296	−	1.21044i	−0.536984	−	0.843593i	$-0.680436\pi$
$359$	7.45190	−	22.9346i	0.393296	−	1.21044i	0.930280	−	0.366850i	$-0.119564\pi$
$360$	−4.17278	+	0.498009i	−0.219925	+	0.0262474i
$361$	−7.24126	+	5.26109i	−0.381119	+	0.276899i
$362$			25.8902i			1.36076i
$363$		0			0
$364$	−6.12155			−0.320856
$365$	8.31036	+	17.9804i	0.434984	+	0.941137i
$366$	−1.75019	−	5.38652i	−0.0914837	−	0.281558i
$367$	19.3920	+	6.30083i	1.01225	+	0.328901i	0.767751	−	0.640748i	$-0.221376\pi$
$367$	19.3920	+	6.30083i	1.01225	+	0.328901i	0.244501	+	0.969649i	$0.421376\pi$
$368$	−11.1711	+	15.3758i	−0.582336	+	0.801517i
$369$	−5.76243	−	4.18665i	−0.299980	−	0.217948i
$370$	4.67969	−	8.37535i	0.243286	−	0.435414i
$371$	8.77288	+	27.0002i	0.455465	+	1.40178i
$372$	0.588107	+	0.809460i	0.0304919	+	0.0419685i
$373$		−	7.51997i		−	0.389369i	−0.980866	−	0.194685i	$-0.937632\pi$
$373$		−	7.51997i		−	0.389369i	0.980866	−	0.194685i	$-0.0623684\pi$
$374$		0			0
$375$	−12.2125	+	18.3937i	−0.630653	+	0.949845i
$376$	20.2996	−	14.7485i	1.04687	−	0.760596i
$377$	0.663056	−	0.215440i	0.0341491	−	0.0110957i
$378$	14.6393	+	4.75661i	0.752967	+	0.244654i
$379$	18.7621	+	13.6315i	0.963745	+	0.700202i	0.954017	−	0.299751i	$-0.0969036\pi$
$379$	18.7621	+	13.6315i	0.963745	+	0.700202i	0.00972738	+	0.999953i	$0.496904\pi$
$380$	5.92552	+	6.39765i	0.303973	+	0.328193i
$381$	−1.48310	+	4.56452i	−0.0759816	+	0.233847i
$382$	4.90311	−	1.59312i	0.250865	−	0.0815109i
$383$	−1.43443	−	1.97432i	−0.0732958	−	0.100883i	0.770795	−	0.637083i	$-0.219859\pi$
$383$	−1.43443	−	1.97432i	−0.0732958	−	0.100883i	−0.844091	+	0.536200i	$0.819859\pi$
$384$	−26.4246			−1.34848
$385$		0			0
$386$	−15.9442			−0.811537
$387$	4.44984	+	6.12468i	0.226198	+	0.311335i
$388$	1.59116	−	0.517000i	0.0807791	−	0.0262467i
$389$	−10.4983	+	32.3104i	−0.532284	+	1.63820i	0.217162	+	0.976136i	$0.430320\pi$
$389$	−10.4983	+	32.3104i	−0.532284	+	1.63820i	−0.749446	+	0.662066i	$0.769680\pi$
$390$	−19.8318	+	18.3682i	−1.00422	+	0.930111i
$391$	6.93649	+	5.03966i	0.350794	+	0.254866i
$392$	−3.91057	−	1.27062i	−0.197513	−	0.0641760i
$393$	2.98335	−	0.969349i	0.150490	−	0.0488972i
$394$	19.2721	−	14.0020i	0.970915	−	0.705411i
$395$	−15.8685	−	3.14036i	−0.798433	−	0.158009i
$396$		0			0
$397$			27.4961i			1.37999i	0.723814	+	0.689995i	$0.242387\pi$
$397$			27.4961i			1.37999i	−0.723814	+	0.689995i	$0.757613\pi$
$398$	−14.3914	−	19.8081i	−0.721376	−	0.992888i
$399$	−7.23674	−	22.2724i	−0.362290	−	1.11501i
$400$	−15.9761	+	18.7797i	−0.798804	+	0.938983i
$401$	1.52696	+	1.10940i	0.0762527	+	0.0554008i	0.625259	−	0.780418i	$-0.284994\pi$
$401$	1.52696	+	1.10940i	0.0762527	+	0.0554008i	−0.549006	+	0.835819i	$0.684994\pi$
$402$	1.24925	−	1.71944i	0.0623068	−	0.0857579i
$403$	−2.41686	−	0.785286i	−0.120392	−	0.0391179i
$404$	2.25592	+	6.94302i	0.112236	+	0.345428i
$405$	22.1035	−	10.2160i	1.09833	−	0.507638i
$406$	0.699363			0.0347088
$407$		0			0
$408$			9.17582i			0.454271i
$409$	−10.9682	+	7.96888i	−0.542344	+	0.394036i	−0.824955	−	0.565199i	$-0.808799\pi$
$409$	−10.9682	+	7.96888i	−0.542344	+	0.394036i	0.282611	+	0.959235i	$0.408799\pi$
$410$	−29.0810	+	3.47074i	−1.43621	+	0.171408i
$411$	11.4127	−	35.1247i	0.562947	−	1.73257i
$412$	4.44029	−	6.11153i	0.218757	−	0.301094i
$413$	0.453134	−	0.623686i	0.0222973	−	0.0306896i
$414$	−1.77313	+	5.45712i	−0.0871444	+	0.268203i
$415$	−7.06426	+	0.843099i	−0.346771	+	0.0413861i
$416$	−11.9178	+	8.65878i	−0.584317	+	0.424531i
$417$			22.9616i			1.12444i
$418$		0			0
$419$	22.1368			1.08145			0.540727	−	0.841198i	$-0.318149\pi$
$419$	22.1368			1.08145			0.540727	+	0.841198i	$0.318149\pi$
$420$	−6.63212	+	3.06530i	−0.323614	+	0.149571i
$421$	5.53219	+	17.0263i	0.269623	+	0.829813i	0.990592	+	0.136846i	$0.0436967\pi$
$421$	5.53219	+	17.0263i	0.269623	+	0.829813i	−0.720970	+	0.692967i	$0.756303\pi$
$422$	−10.6556	−	3.46221i	−0.518706	−	0.168538i
$423$	6.35355	−	8.74491i	0.308920	−	0.425192i
$424$	21.3868	+	15.5384i	1.03863	+	0.754612i
$425$	8.47210	+	7.20732i	0.410957	+	0.349606i
$426$	4.69267	+	14.4426i	0.227361	+	0.699744i
$427$	2.28536	+	3.14553i	0.110596	+	0.152223i
$428$			7.41093i			0.358221i
$429$		0			0
$430$	30.5364	+	6.04310i	1.47259	+	0.291424i
$431$	27.0581	−	19.6589i	1.30334	−	0.946934i	0.303361	−	0.952876i	$-0.401891\pi$
$431$	27.0581	−	19.6589i	1.30334	−	0.946934i	0.999982	+	0.00594140i	$0.00189122\pi$
$432$	19.4509	−	6.31998i	0.935832	−	0.304070i
$433$	29.9501	+	9.73138i	1.43931	+	0.467660i	0.921682	−	0.387946i	$-0.126815\pi$
$433$	29.9501	+	9.73138i	1.43931	+	0.467660i	0.517628	+	0.855606i	$0.326815\pi$
$434$	−2.06235	−	1.49838i	−0.0989958	−	0.0719247i
$435$	0.610479	−	0.565427i	0.0292702	−	0.0271101i
$436$	2.00630	−	6.17475i	0.0960842	−	0.295717i
$437$	−19.3790	+	6.29662i	−0.927024	+	0.301208i
$438$	17.0131	+	23.4165i	0.812916	+	1.11888i
$439$	35.6208			1.70009			0.850045	−	0.526710i	$-0.176575\pi$
$439$	35.6208			1.70009			0.850045	+	0.526710i	$0.176575\pi$
$440$		0			0
$441$	−1.77134			−0.0843495
$442$	8.00448	+	11.0172i	0.380734	+	0.524036i
$443$	−22.3380	+	7.25806i	−1.06131	+	0.344841i	−0.787098	−	0.616828i	$-0.788417\pi$
$443$	−22.3380	+	7.25806i	−1.06131	+	0.344841i	−0.274213	+	0.961669i	$0.588417\pi$
$444$	1.16728	−	3.59253i	0.0553969	−	0.170494i
$445$	15.0759	+	16.2771i	0.714665	+	0.771608i
$446$	11.6688	+	8.47789i	0.552534	+	0.401439i
$447$	11.1102	+	3.60991i	0.525492	+	0.170743i
$448$	6.98513	−	2.26961i	0.330016	−	0.107229i
$449$	−25.3966	+	18.4517i	−1.19854	+	0.870792i	−0.994141	−	0.108096i	$-0.965525\pi$
$449$	−25.3966	+	18.4517i	−1.19854	+	0.870792i	−0.204401	+	0.978887i	$0.565525\pi$
$450$	−2.83522	+	6.88277i	−0.133653	+	0.324457i
$451$		0			0
$452$			0.170655i			0.00802692i
$453$	14.8319	+	20.4144i	0.696864	+	0.959151i
$454$	1.94672	+	5.99138i	0.0913640	+	0.281190i
$455$	9.05142	−	16.1995i	0.424337	−	0.759445i
$456$	−17.6419	−	12.8176i	−0.826158	−	0.600239i
$457$	22.9887	−	31.6412i	1.07536	−	1.48011i	0.210839	−	0.977521i	$-0.432380\pi$
$457$	22.9887	−	31.6412i	1.07536	−	1.48011i	0.864525	−	0.502591i	$-0.167620\pi$
$458$	−4.27023	−	1.38748i	−0.199535	−	0.0648328i
$459$	−2.85115	−	8.77492i	−0.133080	−	0.409578i
$460$	2.66709	+	5.77055i	0.124354	+	0.269053i
$461$	8.88399			0.413769			0.206884	−	0.978365i	$-0.433668\pi$
$461$	8.88399			0.413769			0.206884	+	0.978365i	$0.433668\pi$
$462$		0			0
$463$			4.21081i			0.195693i	0.995202	+	0.0978464i	$0.0311954\pi$
$463$			4.21081i			0.195693i	−0.995202	+	0.0978464i	$0.968805\pi$
$464$	0.751758	−	0.546184i	0.0348995	−	0.0253560i
$465$	−3.01167	+	0.359434i	−0.139663	+	0.0166683i
$466$	5.37410	−	16.5398i	0.248950	−	0.766190i
$467$	3.95488	−	5.44342i	0.183010	−	0.251891i	−0.707649	−	0.706565i	$-0.750244\pi$
$467$	3.95488	−	5.44342i	0.183010	−	0.251891i	0.890658	+	0.454673i	$0.150244\pi$
$468$	−1.44337	+	1.98662i	−0.0667196	+	0.0918317i
$469$	−0.450866	+	1.38762i	−0.0208190	+	0.0640744i
$470$	−5.26710	−	44.1326i	−0.242953	−	2.03569i
$471$	22.9240	−	16.6552i	1.05628	−	0.767433i
$472$		−	0.717854i		−	0.0330419i
$473$		0			0
$474$	−23.6376			−1.08571
$475$	−25.6917	+	6.22108i	−1.17882	+	0.285443i
$476$	1.13743	+	3.50064i	0.0521339	+	0.160452i
$477$	10.8309	+	3.51916i	0.495911	+	0.161131i
$478$	−19.4893	+	26.8247i	−0.891420	+	1.22693i
$479$	−16.8352	−	12.2315i	−0.769218	−	0.558870i	0.132506	−	0.991182i	$-0.457698\pi$
$479$	−16.8352	−	12.2315i	−0.769218	−	0.558870i	−0.901724	+	0.432313i	$0.857698\pi$
$480$	−8.57601	+	15.3487i	−0.391439	+	0.700567i
$481$	2.96473	+	9.12450i	0.135180	+	0.416041i
$482$	−27.6639	−	38.0760i	−1.26005	−	1.73432i
$483$		−	17.0723i		−	0.776818i
$484$		0			0
$485$	−0.984576	+	4.97516i	−0.0447073	+	0.225910i
$486$	12.1309	−	8.81365i	0.550271	−	0.399795i
$487$	−15.0071	+	4.87610i	−0.680036	+	0.220957i	−0.628611	−	0.777720i	$-0.716376\pi$
$487$	−15.0071	+	4.87610i	−0.680036	+	0.220957i	−0.0514249	+	0.998677i	$0.516376\pi$
$488$	3.44327	+	1.11879i	0.155869	+	0.0506450i
$489$	5.79489	+	4.21023i	0.262054	+	0.190393i
$490$	−5.34355	+	4.94920i	−0.241397	+	0.223582i
$491$	−5.97340	+	18.3842i	−0.269576	+	0.829669i	0.721028	+	0.692906i	$0.243670\pi$
$491$	−5.97340	+	18.3842i	−0.269576	+	0.829669i	−0.990604	+	0.136763i	$0.956330\pi$
$492$	−10.9668	+	3.56332i	−0.494421	+	0.160647i
$493$	−0.246401	−	0.339142i	−0.0110973	−	0.0152742i
$494$	−32.3637			−1.45611
$495$		0			0
$496$	−3.38705			−0.152083
$497$	−6.12761	−	8.43394i	−0.274861	−	0.378314i
$498$	−9.88707	+	3.21250i	−0.443050	+	0.143956i
$499$	12.8117	−	39.4305i	0.573532	−	1.76515i	−0.0675920	−	0.997713i	$-0.521532\pi$
$499$	12.8117	−	39.4305i	0.573532	−	1.76515i	0.641124	−	0.767437i	$-0.278468\pi$
$500$	2.87708	+	7.72894i	0.128667	+	0.345649i
$501$	6.10409	+	4.43488i	0.272711	+	0.198136i
$502$	37.5099	+	12.1877i	1.67415	+	0.543964i
$503$	−31.0628	+	10.0929i	−1.38502	+	0.450020i	−0.904317	−	0.426862i	$-0.859619\pi$
$503$	−31.0628	+	10.0929i	−1.38502	+	0.450020i	−0.480704	+	0.876883i	$0.659619\pi$
$504$	3.41046	−	2.47784i	0.151914	−	0.110372i
$505$	−21.7090	−	4.29618i	−0.966039	−	0.191178i
$506$		0			0
$507$		−	1.35905i		−	0.0603576i
$508$	1.05373	+	1.45034i	0.0467519	+	0.0643485i
$509$	−5.14365	−	15.8305i	−0.227988	−	0.701675i	−0.997975	−	0.0636149i	$-0.979737\pi$
$509$	−5.14365	−	15.8305i	−0.227988	−	0.701675i	0.769986	−	0.638060i	$-0.220263\pi$
$510$	14.1889	+	7.92797i	0.628293	+	0.351056i
$511$	−16.0752	−	11.6793i	−0.711126	−	0.516663i
$512$	0.567200	−	0.780684i	0.0250669	−	0.0345017i
$513$	20.8539	+	6.77583i	0.920720	+	0.299160i
$514$	−12.6169	−	38.8307i	−0.556505	−	1.71275i
$515$	9.60753	+	20.7870i	0.423358	+	0.915984i
$516$	12.2561			0.539543
$517$		0			0
$518$			9.62412i			0.422860i
$519$	3.36645	−	2.44587i	0.147771	−	0.107362i
$520$	−2.04772	−	17.1577i	−0.0897984	−	0.752414i
$521$	4.34362	−	13.3683i	0.190298	−	0.585676i	−0.809702	−	0.586842i	$-0.800371\pi$
$521$	4.34362	−	13.3683i	0.190298	−	0.585676i	0.999999	+	0.00116602i	$0.000371156\pi$
$522$	0.164899	−	0.226964i	0.00721742	−	0.00993393i
$523$	9.20925	−	12.6754i	0.402692	−	0.554258i	−0.558725	−	0.829353i	$-0.688709\pi$
$523$	9.20925	−	12.6754i	0.402692	−	0.554258i	0.961417	+	0.275095i	$0.0887092\pi$
$524$	0.362080	−	1.11437i	0.0158175	−	0.0486814i
$525$	1.69463	−	22.0830i	0.0739596	−	0.963783i
$526$	7.28322	−	5.29157i	0.317563	−	0.230723i
$527$			1.52801i			0.0665611i
$528$		0			0
$529$	8.14550			0.354152
$530$	42.5058	−	19.6457i	1.84633	−	0.853357i
$531$	−0.0955624	−	0.294111i	−0.00414705	−	0.0127633i
$532$	−8.31938	−	2.70313i	−0.360691	−	0.117196i
$533$	17.2147	−	23.6940i	0.745652	−	1.02630i
$534$	26.2279	+	19.0557i	1.13499	+	0.824620i
$535$	−19.6116	−	10.9579i	−0.847884	−	0.473752i
$536$	0.419831	+	1.29211i	0.0181339	+	0.0558106i
$537$	5.83158	+	8.02648i	0.251651	+	0.346368i
$538$		−	11.0949i		−	0.478336i
$539$		0			0
$540$	1.32805	−	6.71075i	0.0571501	−	0.288785i
$541$	−32.0681	+	23.2989i	−1.37872	+	1.00170i	−0.381718	+	0.924279i	$0.624667\pi$
$541$	−32.0681	+	23.2989i	−1.37872	+	1.00170i	−0.996999	+	0.0774172i	$0.975333\pi$
$542$	7.96215	−	2.58706i	0.342004	−	0.111124i
$543$	−29.3883	−	9.54884i	−1.26117	−	0.409780i
$544$	7.16598	+	5.20639i	0.307239	+	0.223222i
$545$	13.3738	+	14.4394i	0.572869	+	0.618514i
$546$	8.37930	−	25.7888i	0.358601	−	1.10366i
$547$	39.1516	−	12.7211i	1.67400	−	0.543916i	0.690269	−	0.723553i	$-0.257492\pi$
$547$	39.1516	−	12.7211i	1.67400	−	0.543916i	0.983733	+	0.179637i	$0.0574923\pi$
$548$	−8.10865	−	11.1606i	−0.346385	−	0.476757i
$549$	1.55967			0.0665651
$550$		0			0
$551$	0.996247			0.0424415
$552$	−9.34414	−	12.8611i	−0.397713	−	0.547405i
$553$	15.4328	−	5.01441i	0.656268	−	0.213234i
$554$	−5.46762	+	16.8276i	−0.232297	+	0.714936i
$555$	7.78099	+	8.40097i	0.330285	+	0.356601i
$556$	6.93880	+	5.04133i	0.294271	+	0.213800i
$557$	−28.4137	−	9.23218i	−1.20393	−	0.391180i	−0.362724	−	0.931897i	$-0.618153\pi$
$557$	−28.4137	−	9.23218i	−1.20393	−	0.391180i	−0.841205	+	0.540717i	$0.818153\pi$
$558$	−0.972539	+	0.315997i	−0.0411708	+	0.0133772i
$559$	−25.1836	+	18.2969i	−1.06515	+	0.773877i
$560$	4.80152	−	24.2625i	0.202901	−	1.02528i
$561$		0			0
$562$		−	22.7004i		−	0.957558i
$563$	−1.26832	−	1.74569i	−0.0534533	−	0.0735721i	0.781454	−	0.623963i	$-0.214479\pi$
$563$	−1.26832	−	1.74569i	−0.0534533	−	0.0735721i	−0.834907	+	0.550391i	$0.814479\pi$
$564$	−5.40761	−	16.6429i	−0.227701	−	0.700793i
$565$	−0.451605	−	0.252333i	−0.0189992	−	0.0106157i
$566$	−29.4077	−	21.3660i	−1.23610	−	0.898079i
$567$	−14.3575	+	19.7615i	−0.602960	+	0.829903i
$568$	−9.23223	−	2.99973i	−0.387376	−	0.125866i
$569$	0.221654	+	0.682181i	0.00929222	+	0.0285985i	0.955595	−	0.294683i	$-0.0952140\pi$
$569$	0.221654	+	0.682181i	0.00929222	+	0.0285985i	−0.946303	+	0.323281i	$0.895214\pi$
$570$	−35.0630	+	16.2057i	−1.46863	+	0.678784i
$571$	21.6311			0.905235			0.452617	−	0.891705i	$-0.350490\pi$
$571$	21.6311			0.905235			0.452617	+	0.891705i	$0.350490\pi$
$572$		0			0
$573$			6.15315i			0.257051i
$574$	23.7682	−	17.2686i	0.992068	−	0.720779i
$575$	−19.2143	−	1.47448i	−0.801291	−	0.0614901i
$576$	0.910431	−	2.80202i	0.0379346	−	0.116751i
$577$	13.7704	−	18.9533i	0.573269	−	0.789037i	−0.419668	−	0.907677i	$-0.637854\pi$
$577$	13.7704	−	18.9533i	0.573269	−	0.789037i	0.992937	+	0.118641i	$0.0378537\pi$
$578$	−11.7202	+	16.1314i	−0.487495	+	0.670980i
$579$	5.88053	−	18.0984i	0.244387	−	0.752145i
$580$	−0.0368333	−	0.308624i	−0.00152942	−	0.0128149i
$581$	5.77370	−	4.19484i	0.239533	−	0.174031i
$582$			7.41093i			0.307193i
$583$		0			0
$584$	−18.5023			−0.765633
$585$	−3.12304	−	6.75705i	−0.129122	−	0.279369i
$586$	−7.17756	−	22.0903i	−0.296502	−	0.912540i
$587$	−2.13735	−	0.694466i	−0.0882177	−	0.0286637i	0.264576	−	0.964365i	$-0.414768\pi$
$587$	−2.13735	−	0.694466i	−0.0882177	−	0.0286637i	−0.352793	+	0.935701i	$0.614768\pi$
$588$	−1.68557	+	2.31998i	−0.0695116	+	0.0956745i
$589$	−2.93783	−	2.13446i	−0.121051	−	0.0879488i
$590$	−1.11004	−	0.620230i	−0.0456996	−	0.0255345i
$591$	8.78590	+	27.0402i	0.361404	+	1.11229i
$592$	7.51619	+	10.3451i	0.308914	+	0.425183i
$593$			25.4034i			1.04319i	0.853193	+	0.521596i	$0.174663\pi$
$593$			25.4034i			1.04319i	−0.853193	+	0.521596i	$0.825337\pi$
$594$		0			0
$595$	−10.9456	−	2.16612i	−0.448726	−	0.0888022i
$596$	3.53017	−	2.56482i	0.144601	−	0.105059i
$597$	27.7922	−	9.03023i	1.13746	−	0.369583i
$598$	−22.4387	−	7.29076i	−0.917585	−	0.298141i
$599$	−14.7446	−	10.7126i	−0.602448	−	0.437704i	0.244299	−	0.969700i	$-0.421442\pi$
$599$	−14.7446	−	10.7126i	−0.602448	−	0.437704i	−0.846747	+	0.531996i	$0.821442\pi$
$600$	−10.8100	−	17.5633i	−0.441317	−	0.717020i
$601$	10.7043	−	32.9444i	0.436637	−	1.34383i	−0.454762	−	0.890613i	$-0.650276\pi$
$601$	10.7043	−	32.9444i	0.436637	−	1.34383i	0.891400	−	0.453218i	$-0.149724\pi$
$602$	−29.6978	+	9.64940i	−1.21039	+	0.393280i
$603$	0.344017	+	0.473499i	0.0140095	+	0.0192824i
$604$	9.42547			0.383517
$605$		0			0
$606$	−32.3375			−1.31362
$607$	14.9581	+	20.5881i	0.607131	+	0.835644i	0.996338	−	0.0855067i	$-0.0272509\pi$
$607$	14.9581	+	20.5881i	0.607131	+	0.835644i	−0.389207	+	0.921150i	$0.627251\pi$
$608$	−20.0201	+	6.50494i	−0.811924	+	0.263810i
$609$	−0.257939	+	0.793855i	−0.0104522	+	0.0321686i
$610$	4.70502	−	4.35779i	0.190501	−	0.176442i
$611$	35.9574	+	26.1246i	1.45468	+	1.05689i
$612$	1.40425	+	0.456268i	0.0567634	+	0.0184436i
$613$	35.2477	−	11.4527i	1.42364	−	0.462569i	0.506884	−	0.862014i	$-0.330797\pi$
$613$	35.2477	−	11.4527i	1.42364	−	0.462569i	0.916757	+	0.399445i	$0.130797\pi$
$614$	9.19542	−	6.68086i	0.371097	−	0.269618i
$615$	6.78600	−	34.2903i	0.273638	−	1.38272i
$616$		0			0
$617$		−	27.5937i		−	1.11088i	−0.831557	−	0.555439i	$-0.812550\pi$
$617$		−	27.5937i		−	1.11088i	0.831557	−	0.555439i	$-0.187450\pi$
$618$	19.6687	+	27.0716i	0.791190	+	1.08898i
$619$	−6.31739	−	19.4429i	−0.253917	−	0.781477i	−0.994041	−	0.109006i	$-0.965233\pi$
$619$	−6.31739	−	19.4429i	−0.253917	−	0.781477i	0.740124	−	0.672471i	$-0.234767\pi$
$620$	−0.552608	+	0.989014i	−0.0221933	+	0.0397198i
$621$	12.9321	+	9.39575i	0.518949	+	0.377038i
$622$	5.35049	−	7.36432i	0.214535	−	0.295282i
$623$	−21.1664	−	6.87738i	−0.848014	−	0.275536i
$624$	−11.1333	−	34.2649i	−0.445691	−	1.37169i
$625$	−24.7073	−	3.81448i	−0.988291	−	0.152579i
$626$	23.5480			0.941167
$627$		0			0
$628$		−	10.5842i		−	0.422354i
$629$	4.66703	−	3.39079i	0.186087	−	0.135200i
$630$	−0.884907	−	7.41456i	−0.0352555	−	0.295403i
$631$	0.234586	−	0.721982i	0.00933873	−	0.0287417i	−0.946279	−	0.323353i	$-0.895190\pi$
$631$	0.234586	−	0.721982i	0.00933873	−	0.0287417i	0.955617	+	0.294611i	$0.0951900\pi$
$632$	8.88145	−	12.2243i	0.353285	−	0.486255i
$633$	7.86000	−	10.8184i	0.312407	−	0.429991i
$634$	−9.55425	+	29.4050i	−0.379448	+	1.16782i
$635$	−5.39612	+	0.644012i	−0.214139	+	0.0255568i
$636$	14.9155	−	10.8368i	0.591440	−	0.429706i
$637$		−	7.28342i		−	0.288579i
$638$		0			0
$639$	−4.18186			−0.165432
$640$	−12.5531	−	27.1602i	−0.496207	−	1.07360i
$641$	−4.60590	−	14.1755i	−0.181922	−	0.559899i	0.817960	−	0.575276i	$-0.195105\pi$
$641$	−4.60590	−	14.1755i	−0.181922	−	0.559899i	−0.999882	+	0.0153768i	$0.995105\pi$
$642$	−31.2207	−	10.1442i	−1.23218	−	0.400361i
$643$	−16.2432	+	22.3568i	−0.640569	+	0.881667i	−0.998646	−	0.0520249i	$-0.983432\pi$
$643$	−16.2432	+	22.3568i	−0.640569	+	0.881667i	0.358077	+	0.933692i	$0.383432\pi$
$644$	−5.15911	−	3.74831i	−0.203297	−	0.147704i
$645$	−18.1220	+	32.4334i	−0.713554	+	1.27706i
$646$	6.01340	+	18.5073i	0.236594	+	0.728162i
$647$	−14.6820	−	20.2081i	−0.577210	−	0.794461i	0.416176	−	0.909284i	$-0.363370\pi$
$647$	−14.6820	−	20.2081i	−0.577210	−	0.794461i	−0.993386	+	0.114823i	$0.963370\pi$
$648$			22.7452i			0.893514i
$649$		0			0
$650$	−28.3007	−	11.6579i	−1.11004	−	0.457260i
$651$	2.46147	−	1.78836i	0.0964725	−	0.0700914i
$652$	2.54459	−	0.826787i	0.0996538	−	0.0323795i
$653$	−26.4042	−	8.57923i	−1.03327	−	0.335731i	−0.257191	−	0.966361i	$-0.582797\pi$
$653$	−26.4042	−	8.57923i	−1.03327	−	0.335731i	−0.776084	+	0.630629i	$0.782797\pi$
$654$	23.2667	+	16.9042i	0.909800	+	0.661008i
$655$	2.41358	+	2.60590i	0.0943066	+	0.101821i
$656$	12.0626	−	37.1248i	0.470964	−	1.44948i
$657$	−7.58057	+	2.46308i	−0.295746	+	0.0960938i
$658$	26.2064	+	36.0701i	1.02163	+	1.40616i
$659$	−21.5863			−0.840883			−0.420442	−	0.907320i	$-0.638125\pi$
$659$	−21.5863			−0.840883			−0.420442	+	0.907320i	$0.638125\pi$
$660$		0			0
$661$	−16.0174			−0.623003			−0.311502	−	0.950246i	$-0.600832\pi$
$661$	−16.0174			−0.623003			−0.311502	+	0.950246i	$0.600832\pi$
$662$	0.455390	+	0.626791i	0.0176992	+	0.0243609i
$663$	−15.4580	+	5.02261i	−0.600339	+	0.195062i
$664$	2.05356	−	6.32019i	0.0796934	−	0.245271i
$665$	19.4545	−	18.0188i	0.754412	−	0.698738i
$666$	3.12331	+	2.26922i	0.121026	+	0.0879304i
$667$	0.690726	+	0.224431i	0.0267450	+	0.00868999i
$668$	2.68036	−	0.870903i	0.103706	−	0.0336963i
$669$	−13.9270	+	10.1186i	−0.538450	+	0.391207i
$670$	2.36076	+	0.467191i	0.0912042	+	0.0180492i
$671$		0			0
$672$		−	17.6372i		−	0.680368i
$673$	−18.4253	−	25.3602i	−0.710242	−	0.977564i	−0.999792	−	0.0204009i	$-0.993506\pi$
$673$	−18.4253	−	25.3602i	−0.710242	−	0.977564i	0.289550	−	0.957163i	$-0.406494\pi$
$674$	17.4286	+	53.6396i	0.671324	+	2.06612i
$675$	15.7951	+	13.4371i	0.607952	+	0.517192i
$676$	−0.410694	−	0.298386i	−0.0157959	−	0.0114764i
$677$	18.0252	−	24.8096i	0.692766	−	0.953510i	−0.307232	−	0.951635i	$-0.599403\pi$
$677$	18.0252	−	24.8096i	0.692766	−	0.953510i	0.999998	−	0.00187591i	$-0.000597121\pi$
$678$	−0.718933	−	0.233596i	−0.0276105	−	0.00897118i
$679$	−1.57213	−	4.83853i	−0.0603330	−	0.185686i
$680$	−9.43123	+	4.35902i	−0.361671	+	0.167161i
$681$	−7.51888			−0.288124
$682$		0			0
$683$			3.27236i			0.125213i	0.998038	+	0.0626066i	$0.0199414\pi$
$683$			3.27236i			0.125213i	−0.998038	+	0.0626066i	$0.980059\pi$
$684$	−2.83882	+	2.06253i	−0.108545	+	0.0788627i
$685$	41.5240	−	4.95577i	1.58655	−	0.189350i
$686$	10.2858	−	31.6566i	0.392715	−	1.20865i
$687$	3.14989	−	4.33546i	0.120176	−	0.165408i
$688$	−24.3868	+	33.5655i	−0.929737	+	1.27967i
$689$	−14.4701	+	44.5344i	−0.551267	+	1.69663i
$690$	−27.9609	+	3.33706i	−1.06445	+	0.127040i
$691$	29.5247	−	21.4510i	1.12317	−	0.816034i	0.138487	−	0.990364i	$-0.455776\pi$
$691$	29.5247	−	21.4510i	1.12317	−	0.816034i	0.984687	+	0.174330i	$0.0557761\pi$
$692$		−	1.55431i		−	0.0590862i
$693$		0			0
$694$	5.94478			0.225661
$695$	−23.6008	+	10.9080i	−0.895228	+	0.413765i
$696$	0.240184	+	0.739212i	0.00910417	+	0.0280197i
$697$	−16.7482	−	5.44181i	−0.634382	−	0.206123i
$698$	6.19614	−	8.52825i	0.234527	−	0.322799i
$699$	16.7924	+	12.2004i	0.635147	+	0.461461i
$700$	−6.30124	−	5.36054i	−0.238164	−	0.202609i
$701$	−14.3880	−	44.2818i	−0.543429	−	1.67250i	−0.724696	−	0.689068i	$-0.758020\pi$
$701$	−14.3880	−	44.2818i	−0.543429	−	1.67250i	0.181267	−	0.983434i	$-0.441980\pi$
$702$	14.9233	+	20.5401i	0.563242	+	0.775236i
$703$			13.7096i			0.517068i
$704$		0			0
$705$	52.0381	+	10.2983i	1.95987	+	0.387855i
$706$	16.3268	−	11.8621i	0.614469	−	0.446438i
$707$	21.1129	−	6.85999i	0.794031	−	0.257996i
$708$	−0.476142	−	0.154708i	−0.0178945	−	0.00581427i
$709$	−28.7982	−	20.9231i	−1.08154	−	0.785785i	−0.103590	−	0.994620i	$-0.533033\pi$
$709$	−28.7982	−	20.9231i	−1.08154	−	0.785785i	−0.977951	+	0.208835i	$0.933033\pi$
$710$	−12.6153	+	11.6843i	−0.473443	+	0.438504i
$711$	2.01148	−	6.19071i	0.0754365	−	0.232170i
$712$	−19.7095	+	6.40399i	−0.738643	+	0.240000i
$713$	−1.55604	−	2.14170i	−0.0582741	−	0.0802074i
$714$	−16.3044			−0.610178
$715$		0			0
$716$	3.70588			0.138495
$717$	−23.2610	−	32.0160i	−0.868698	−	1.19566i
$718$	37.9472	−	12.3298i	1.41618	−	0.460143i
$719$	−6.82658	+	21.0101i	−0.254589	+	0.783543i	0.739322	+	0.673352i	$0.235146\pi$
$719$	−6.82658	+	21.0101i	−0.254589	+	0.783543i	−0.993910	+	0.110191i	$0.964854\pi$
$720$	−6.74179	−	7.27896i	−0.251251	−	0.271271i
$721$	−18.5844	−	13.5024i	−0.692120	−	0.502855i
$722$	−14.0848	−	4.57644i	−0.524183	−	0.170317i
$723$	53.4235	−	17.3584i	1.98684	−	0.645564i
$724$	−9.33792	+	6.78440i	−0.347041	+	0.252140i
$725$	0.871176	+	0.358863i	0.0323547	+	0.0133278i
$726$		0			0
$727$			45.5415i			1.68904i	0.535522	+	0.844521i	$0.320115\pi$
$727$			45.5415i			1.68904i	−0.535522	+	0.844521i	$0.679885\pi$
$728$	10.1884	+	14.0232i	0.377608	+	0.519733i
$729$	−4.56501	−	14.0497i	−0.169075	−	0.520358i
$730$	−15.9861	+	28.6107i	−0.591674	+	1.05893i
$731$	15.1425	+	11.0017i	0.560065	+	0.406911i
$732$	1.48415	−	2.04275i	0.0548556	−	0.0755023i
$733$	10.8220	+	3.51627i	0.399719	+	0.129877i	0.501976	−	0.864881i	$-0.332607\pi$
$733$	10.8220	+	3.51627i	0.399719	+	0.129877i	−0.102257	+	0.994758i	$0.532607\pi$
$734$	10.4252	+	32.0856i	0.384803	+	1.18430i
$735$	−3.64709	−	7.89089i	−0.134525	−	0.291060i
$736$	−15.3459			−0.565659
$737$		0			0
$738$		−	11.7852i		−	0.433818i
$739$	3.50933	−	2.54968i	0.129093	−	0.0937915i	−0.521365	−	0.853334i	$-0.674577\pi$
$739$	3.50933	−	2.54968i	0.129093	−	0.0937915i	0.650458	+	0.759542i	$0.274577\pi$
$740$	4.24705	−	0.506874i	0.156125	−	0.0186330i
$741$	11.9364	−	36.7364i	0.438494	−	1.34954i
$742$	−27.6100	+	38.0019i	−1.01360	+	1.39510i
$743$	10.1654	−	13.9915i	0.372934	−	0.513300i	−0.580761	−	0.814074i	$-0.697245\pi$
$743$	10.1654	−	13.9915i	0.372934	−	0.513300i	0.953695	+	0.300774i	$0.0972451\pi$
$744$	0.875481	−	2.69445i	0.0320967	−	0.0987834i
$745$	1.56754	+	13.1343i	0.0574303	+	0.481204i
$746$	10.0661	−	7.31346i	0.368547	−	0.267765i
$747$		−	2.86281i		−	0.104745i
$748$		0			0
$749$	22.5357			0.823437
$750$	−36.4987	+	1.54103i	−1.33274	+	0.0562706i
$751$	−9.73806	−	29.9707i	−0.355347	−	1.09365i	−0.955808	−	0.293991i	$-0.905016\pi$
$751$	−9.73806	−	29.9707i	−0.355347	−	1.09365i	0.600461	−	0.799654i	$-0.294984\pi$
$752$	56.3396	+	18.3058i	2.05449	+	0.667546i
$753$	−27.6688	+	38.0829i	−1.00831	+	1.38782i
$754$	0.933232	+	0.678033i	0.0339863	+	0.0246925i
$755$	−13.9366	+	24.9427i	−0.507206	+	0.907758i
$756$	2.12058	+	6.52647i	0.0771247	+	0.237365i
$757$	−5.45311	−	7.50556i	−0.198197	−	0.272794i	0.698338	−	0.715768i	$-0.253923\pi$
$757$	−5.45311	−	7.50556i	−0.198197	−	0.272794i	−0.896534	+	0.442974i	$0.853923\pi$
$758$			38.3718i			1.39373i
$759$		0			0
$760$	4.79350	−	24.2220i	0.173879	−	0.878626i
$761$	−3.36397	+	2.44407i	−0.121944	+	0.0885975i	−0.647086	−	0.762417i	$-0.724012\pi$
$761$	−3.36397	+	2.44407i	−0.121944	+	0.0885975i	0.525142	+	0.851015i	$0.324012\pi$
$762$	−7.55236	+	2.45391i	−0.273593	+	0.0888958i
$763$	−18.7767	−	6.10090i	−0.679760	−	0.220868i
$764$	1.85943	+	1.35095i	0.0672717	+	0.0488758i
$765$	−3.28377	+	3.04143i	−0.118725	+	0.109963i
$766$	1.24776	−	3.84020i	0.0450833	−	0.138752i
$767$	1.20933	−	0.392935i	0.0436663	−	0.0141880i
$768$	−18.0976	−	24.9092i	−0.653040	−	0.898833i
$769$	16.8800			0.608709			0.304355	−	0.952559i	$-0.401559\pi$
$769$	16.8800			0.608709			0.304355	+	0.952559i	$0.401559\pi$
$770$		0			0
$771$	48.7305			1.75499
$772$	−4.17808	−	5.75064i	−0.150373	−	0.206970i
$773$	−8.06267	+	2.61972i	−0.289994	+	0.0942248i	−0.450402	−	0.892826i	$-0.648719\pi$
$773$	−8.06267	+	2.61972i	−0.289994	+	0.0942248i	0.160407	+	0.987051i	$0.448719\pi$
$774$	−3.87076	+	11.9130i	−0.139132	+	0.428203i
$775$	−1.80014	−	2.92474i	−0.0646631	−	0.105060i
$776$	−3.83259	−	2.78454i	−0.137582	−	0.0999593i
$777$	−10.9245	−	3.54957i	−0.391913	−	0.127340i
$778$	−53.4602	+	17.3703i	−1.91664	+	0.622754i
$779$	33.8580	−	24.5993i	1.21309	−	0.881361i
$780$	−11.8217	−	2.33950i	−0.423286	−	0.0837676i
$781$		0			0
$782$			14.1863i			0.507303i
$783$	−0.459381	−	0.632284i	−0.0164169	−	0.0225960i
$784$	−2.99981	−	9.23247i	−0.107136	−	0.329731i
$785$	28.0090	+	15.6499i	0.999683	+	0.558569i
$786$	4.19898	+	3.05074i	0.149773	+	0.108816i
$787$	−31.5150	+	43.3767i	−1.12339	+	1.54621i	−0.323336	+	0.946284i	$0.604804\pi$
$787$	−31.5150	+	43.3767i	−1.12339	+	1.54621i	−0.800054	+	0.599928i	$0.795196\pi$
$788$	10.1003	+	3.28179i	0.359808	+	0.116909i
$789$	3.32032	+	10.2189i	0.118207	+	0.363803i
$790$	−11.2291	−	24.2955i	−0.399515	−	0.864395i
$791$	0.518940			0.0184514
$792$		0			0
$793$			6.41307i			0.227735i
$794$	−36.8059	+	26.7410i	−1.30619	+	0.949004i
$795$	6.62312	+	55.4946i	0.234898	+	1.96819i
$796$	3.37305	−	10.3812i	0.119555	−	0.367951i
$797$	16.7782	−	23.0932i	0.594315	−	0.818004i	−0.400858	−	0.916140i	$-0.631288\pi$
$797$	16.7782	−	23.0932i	0.594315	−	0.818004i	0.995173	+	0.0981362i	$0.0312881\pi$
$798$	22.7755	−	31.3477i	0.806243	−	1.10970i
$799$	8.25835	−	25.4166i	0.292159	−	0.899174i
$800$	−19.8500	−	1.52326i	−0.701802	−	0.0538555i
$801$	−7.22262	+	5.24754i	−0.255199	+	0.185413i
$802$			3.12290i			0.110273i
$803$		0			0
$804$	0.947515			0.0334163
$805$	17.5475	−	8.11029i	0.618470	−	0.285850i
$806$	−1.29932	−	3.99890i	−0.0457666	−	0.140855i
$807$	12.5940	+	4.09203i	0.443329	+	0.144046i
$808$	12.1503	−	16.7235i	0.427446	−	0.588330i
$809$	−29.8900	−	21.7163i	−1.05088	−	0.763506i	−0.0784966	−	0.996914i	$-0.525012\pi$
$809$	−29.8900	−	21.7163i	−1.05088	−	0.763506i	−0.972379	+	0.233409i	$0.925012\pi$
$810$	35.1715	+	19.6520i	1.23580	+	0.690499i
$811$	11.8591	+	36.4985i	0.416428	+	1.28163i	0.910967	+	0.412479i	$0.135337\pi$
$811$	11.8591	+	36.4985i	0.416428	+	1.28163i	−0.494539	+	0.869156i	$0.664663\pi$
$812$	0.183264	+	0.252241i	0.00643131	+	0.00885194i
$813$			9.99209i			0.350438i
$814$		0			0
$815$	−1.57453	+	7.95628i	−0.0551535	+	0.278696i
$816$	−17.5259	+	12.7333i	−0.613530	+	0.445756i
$817$	−42.3047	+	13.7456i	−1.48005	+	0.480899i
$818$	−21.3340	−	6.93185i	−0.745927	−	0.242366i
$819$	6.04108	+	4.38910i	0.211092	+	0.153368i
$820$	−8.87233	−	9.57927i	−0.309835	−	0.334522i
$821$	3.16732	−	9.74799i	0.110540	−	0.340207i	−0.880451	−	0.474138i	$-0.842760\pi$
$821$	3.16732	−	9.74799i	0.110540	−	0.340207i	0.990991	+	0.133930i	$0.0427599\pi$
$822$	58.1166	−	18.8832i	2.02705	−	0.658629i
$823$	14.8296	+	20.4112i	0.516926	+	0.711488i	0.985068	−	0.172165i	$-0.0550763\pi$
$823$	14.8296	+	20.4112i	0.516926	+	0.711488i	−0.468142	+	0.883653i	$0.655076\pi$
$824$	−21.3904			−0.745170
$825$		0			0
$826$	1.27555			0.0443820
$827$	−10.7850	−	14.8443i	−0.375031	−	0.516186i	0.579229	−	0.815165i	$-0.303354\pi$
$827$	−10.7850	−	14.8443i	−0.375031	−	0.516186i	−0.954260	+	0.298979i	$0.903354\pi$
$828$	−2.43288	+	0.790489i	−0.0845483	+	0.0274714i
$829$	−7.53463	+	23.1892i	−0.261689	+	0.805395i	0.730749	+	0.682646i	$0.239171\pi$
$829$	−7.53463	+	23.1892i	−0.261689	+	0.805395i	−0.992438	+	0.122749i	$0.960829\pi$
$830$	−7.99882	−	8.63616i	−0.277643	−	0.299766i
$831$	−17.0846	−	12.4127i	−0.592659	−	0.430592i
$832$	11.5214	+	3.74352i	0.399432	+	0.129783i
$833$	−4.16506	+	1.35331i	−0.144311	+	0.0468894i
$834$	−30.7361	+	22.3311i	−1.06430	+	0.773262i
$835$	−1.65855	+	8.38081i	−0.0573964	+	0.290030i
$836$		0			0
$837$			2.84876i			0.0984676i
$838$	21.5289	+	29.6320i	0.743704	+	1.02362i
$839$	13.0655	+	40.2114i	0.451071	+	1.38825i	0.875687	+	0.482880i	$0.160409\pi$
$839$	13.0655	+	40.2114i	0.451071	+	1.38825i	−0.424616	+	0.905374i	$0.639591\pi$
$840$	18.0601	+	10.0910i	0.623134	+	0.348173i
$841$	23.4328	+	17.0249i	0.808026	+	0.587066i
$842$	−17.4109	+	23.9641i	−0.600020	+	0.825857i
$843$	25.7675	+	8.37236i	0.887479	+	0.288359i
$844$	−1.54351	−	4.75044i	−0.0531299	−	0.163517i
$845$	1.39688	−	0.645624i	0.0480542	−	0.0222101i
$846$	17.8849			0.614895
$847$		0			0
$848$			62.4117i			2.14323i
$849$	35.0989	−	25.5009i	1.20459	−	0.875187i
$850$	−1.40816	+	18.3500i	−0.0482994	+	0.629400i
$851$	−3.08845	+	9.50527i	−0.105871	+	0.325837i
$852$	−3.97936	+	5.47712i	−0.136331	+	0.187643i
$853$	9.04511	−	12.4495i	0.309699	−	0.426264i	−0.625589	−	0.780153i	$-0.715141\pi$
$853$	9.04511	−	12.4495i	0.309699	−	0.426264i	0.935287	+	0.353890i	$0.115141\pi$
$854$	−1.98796	+	6.11831i	−0.0680265	+	0.209364i
$855$	−1.26056	−	10.5621i	−0.0431101	−	0.361216i
$856$	16.9768	−	12.3344i	0.580256	−	0.421581i
$857$		−	36.1038i		−	1.23328i	−0.787245	−	0.616641i	$-0.788493\pi$
$857$		−	36.1038i		−	1.23328i	0.787245	−	0.616641i	$-0.211507\pi$
$858$		0			0
$859$	−48.3509			−1.64971			−0.824855	−	0.565344i	$-0.808743\pi$
$859$	−48.3509			−1.64971			−0.824855	+	0.565344i	$0.808743\pi$
$860$	5.82230	+	12.5972i	0.198539	+	0.429561i
$861$	10.8356	+	33.3486i	0.369277	+	1.13652i
$862$	52.6301	+	17.1006i	1.79259	+	0.582447i
$863$	−21.8590	+	30.0863i	−0.744088	+	1.02415i	0.254286	+	0.967129i	$0.418160\pi$
$863$	−21.8590	+	30.0863i	−0.744088	+	1.02415i	−0.998373	+	0.0570194i	$0.981840\pi$
$864$	13.3600	+	9.70660i	0.454516	+	0.330225i
$865$	4.11320	+	2.29823i	0.139853	+	0.0781423i
$866$	16.1014	+	49.5549i	0.547146	+	1.68394i
$867$	−13.9884	−	19.2533i	−0.475070	−	0.653877i
$868$		−	1.13648i		−	0.0385745i
$869$		0			0
$870$	1.35059	+	0.267279i	0.0457892	+	0.00906160i
$871$	−1.94694	+	1.41453i	−0.0659694	+	0.0479296i
$872$	−17.4842	+	5.68096i	−0.592090	+	0.192382i
$873$	−1.94093	−	0.630647i	−0.0656906	−	0.0213442i
$874$	−27.2754	−	19.8167i	−0.922604	−	0.670311i
$875$	23.5028	−	8.74886i	0.794538	−	0.295765i
$876$	−3.98752	+	12.2723i	−0.134726	+	0.414644i
$877$	−24.5308	+	7.97055i	−0.828347	+	0.269146i	−0.692349	−	0.721563i	$-0.743424\pi$
$877$	−24.5308	+	7.97055i	−0.828347	+	0.269146i	−0.135998	+	0.990709i	$0.543424\pi$
$878$	34.6426	+	47.6815i	1.16913	+	1.60917i
$879$	27.7221			0.935044
$880$		0			0
$881$	−45.6820			−1.53906			−0.769532	−	0.638608i	$-0.779511\pi$
$881$	−45.6820			−1.53906			−0.769532	+	0.638608i	$0.779511\pi$
$882$	−1.72270	−	2.37109i	−0.0580062	−	0.0798387i
$883$	−4.72324	+	1.53467i	−0.158950	+	0.0516459i	−0.387411	−	0.921907i	$-0.626631\pi$
$883$	−4.72324	+	1.53467i	−0.158950	+	0.0516459i	0.228461	+	0.973553i	$0.426631\pi$
$884$	−1.87609	+	5.77401i	−0.0630997	+	0.194201i
$885$	1.11344	−	1.03127i	0.0374277	−	0.0346656i
$886$	−31.4401	−	22.8426i	−1.05625	−	0.767411i
$887$	−27.5076	−	8.93777i	−0.923615	−	0.300101i	−0.191666	−	0.981460i	$-0.561389\pi$
$887$	−27.5076	−	8.93777i	−0.923615	−	0.300101i	−0.731949	+	0.681359i	$0.761389\pi$
$888$	−10.1725	+	3.30524i	−0.341367	+	0.110917i
$889$	4.41031	−	3.20428i	0.147917	−	0.107468i
$890$	−7.12641	+	36.0104i	−0.238878	+	1.20707i
$891$		0			0
$892$			6.43021i			0.215299i
$893$	37.3313	+	51.3821i	1.24924	+	1.71944i
$894$	5.97289	+	18.3827i	0.199763	+	0.614808i
$895$	−5.47958	+	9.80692i	−0.183162	+	0.327809i
$896$	24.2823	+	17.6421i	0.811215	+	0.589382i
$897$	16.5517	−	22.7814i	0.552644	−	0.760649i
$898$	−49.3984	−	16.0505i	−1.64845	−	0.535613i
$899$	0.0399968	+	0.123098i	0.00133397	+	0.00410553i
$900$	−3.22539	+	0.781006i	−0.107513	+	0.0260335i
$901$	28.1559			0.938010
$902$		0			0
$903$		−	37.2692i		−	1.24024i
$904$	0.390933	−	0.284030i	0.0130022	−	0.00944668i
$905$	−4.14642	−	34.7425i	−0.137832	−	1.15488i
$906$	−12.9018	+	39.7076i	−0.428633	+	1.31920i
$907$	−7.78974	+	10.7217i	−0.258654	+	0.356007i	−0.918519	−	0.395378i	$-0.870614\pi$
$907$	−7.78974	+	10.7217i	−0.258654	+	0.356007i	0.659864	+	0.751385i	$0.270614\pi$
$908$	−1.65081	+	2.27214i	−0.0547839	+	0.0754036i
$909$	2.75182	−	8.46923i	0.0912720	−	0.280906i
$910$	30.4873	−	3.63857i	1.01064	−	0.120617i
$911$	−11.1099	+	8.07183i	−0.368088	+	0.267431i	−0.756418	−	0.654089i	$-0.773052\pi$
$911$	−11.1099	+	8.07183i	−0.368088	+	0.267431i	0.388330	+	0.921520i	$0.373052\pi$
$912$		−	51.4833i		−	1.70478i
$913$		0			0
$914$	64.7117			2.14047
$915$	3.21128	+	6.94796i	0.106162	+	0.229692i
$916$	−0.618563	−	1.90374i	−0.0204379	−	0.0629014i
$917$	−3.38865	−	1.10104i	−0.111903	−	0.0363596i
$918$	8.97313	−	12.3505i	0.296157	−	0.407626i
$919$	−48.0394	−	34.9027i	−1.58467	−	1.15133i	−0.911079	−	0.412232i	$-0.864749\pi$
$919$	−48.0394	−	34.9027i	−1.58467	−	1.15133i	−0.673595	−	0.739101i	$-0.735251\pi$
$920$	8.78012	−	15.7140i	0.289472	−	0.518074i
$921$	4.19207	+	12.9019i	0.138133	+	0.425131i
$922$	8.64002	+	11.8920i	0.284544	+	0.391641i
$923$		−	17.1950i		−	0.565981i
$924$		0			0
$925$	−4.93842	+	11.9885i	−0.162374	+	0.394179i
$926$	−5.63652	+	4.09517i	−0.185228	+	0.134576i
$927$	−8.76383	+	2.84754i	−0.287842	+	0.0935255i
$928$	0.713578	+	0.231856i	0.0234244	+	0.00761103i
$929$	15.8471	+	11.5136i	0.519926	+	0.377749i	0.816576	−	0.577238i	$-0.195869\pi$
$929$	15.8471	+	11.5136i	0.519926	+	0.377749i	−0.296650	+	0.954986i	$0.595869\pi$
$930$	−3.41009	−	3.68181i	−0.111821	−	0.120731i
$931$	3.21618	−	9.89839i	0.105406	−	0.324407i
$932$	7.37371	−	2.39586i	0.241534	−	0.0784791i
$933$	6.38596	+	8.78952i	0.209067	+	0.287756i
$934$	11.1327			0.364275
$935$		0			0
$936$	6.95320			0.227272
$937$	23.8319	+	32.8018i	0.778554	+	1.07159i	0.995440	+	0.0953903i	$0.0304099\pi$
$937$	23.8319	+	32.8018i	0.778554	+	1.07159i	−0.216886	+	0.976197i	$0.569590\pi$
$938$	−2.29593	+	0.745994i	−0.0749649	+	0.0243576i
$939$	−8.68498	+	26.7296i	−0.283424	+	0.872288i
$940$	14.5372	−	13.4644i	0.474153	−	0.439161i
$941$	−0.331447	−	0.240811i	−0.0108049	−	0.00785020i	0.582370	−	0.812924i	$-0.302126\pi$
$941$	−0.331447	−	0.240811i	−0.0108049	−	0.00785020i	−0.593175	+	0.805074i	$0.702126\pi$
$942$	44.5889	+	14.4878i	1.45278	+	0.472038i
$943$	29.0164	−	9.42799i	0.944903	−	0.307018i
$944$	1.37111	−	0.996169i	0.0446258	−	0.0324225i
$945$	−20.4066	−	4.03843i	−0.663826	−	0.131370i
$946$		0			0
$947$			2.45729i			0.0798511i	0.999203	+	0.0399256i	$0.0127121\pi$
$947$			2.45729i			0.0798511i	−0.999203	+	0.0399256i	$0.987288\pi$
$948$	−6.19409	−	8.52544i	−0.201175	−	0.276893i
$949$	−10.1277	−	31.1699i	−0.328759	−	1.01182i
$950$	−33.3137	−	28.3403i	−1.08084	−	0.919482i
$951$	−29.8541	−	21.6903i	−0.968086	−	0.703355i
$952$	6.12614	−	8.43191i	0.198549	−	0.273280i
$953$	58.0396	+	18.8582i	1.88009	+	0.610877i	0.986935	+	0.161122i	$0.0515112\pi$
$953$	58.0396	+	18.8582i	1.88009	+	0.610877i	0.893152	+	0.449755i	$0.148489\pi$
$954$	5.82273	+	17.9205i	0.188518	+	0.580199i
$955$	−6.32442	+	2.92308i	−0.204653	+	0.0945887i
$956$	−14.7820			−0.478085
$957$		0			0
$958$		−	34.4309i		−	1.11241i
$959$	−33.9380	+	24.6574i	−1.09592	+	0.796230i
$960$	14.3568	−	1.71345i	0.463365	−	0.0553013i
$961$	−9.43374	+	29.0341i	−0.304314	+	0.936582i
$962$	−9.33060	+	12.8425i	−0.300830	+	0.414058i
$963$	5.31357	−	7.31350i	0.171227	−	0.235674i
$964$	6.48385	−	19.9552i	0.208831	−	0.642715i
$965$	21.3958	−	2.55352i	0.688754	−	0.0822008i
$966$	22.8528	−	16.6035i	0.735276	−	0.534209i
$967$		−	17.1997i		−	0.553106i	−0.960999	−	0.276553i	$-0.910808\pi$
$967$		−	17.1997i		−	0.553106i	0.960999	−	0.276553i	$-0.0891921\pi$
$968$		0			0
$969$	−23.2258			−0.746119
$970$	−7.61721	+	3.52060i	−0.244574	+	0.113040i
$971$	8.40803	+	25.8773i	0.269827	+	0.830441i	0.990542	+	0.137210i	$0.0438134\pi$
$971$	8.40803	+	25.8773i	0.269827	+	0.830441i	−0.720715	+	0.693231i	$0.756187\pi$
$972$	6.35769	+	2.06574i	0.203923	+	0.0662586i
$973$	15.3301	−	21.1000i	0.491460	−	0.676436i
$974$	−21.1220	−	15.3461i	−0.676794	−	0.491720i
$975$	23.6709	−	27.8248i	0.758074	−	0.891106i
$976$	2.64135	+	8.12923i	0.0845474	+	0.260210i
$977$	11.2692	+	15.5107i	0.360532	+	0.496230i	0.950297	−	0.311345i	$-0.100780\pi$
$977$	11.2692	+	15.5107i	0.360532	+	0.496230i	−0.589765	+	0.807575i	$0.700780\pi$
$978$			11.8516i			0.378971i
$979$		0			0
$980$	−3.18529	−	0.630365i	−0.101750	−	0.0201363i
$981$	−6.40716	+	4.65508i	−0.204565	+	0.148625i
$982$	−30.4182	+	9.88348i	−0.970685	+	0.315395i
$983$	22.9494	+	7.45672i	0.731973	+	0.237832i	0.651206	−	0.758901i	$-0.274263\pi$
$983$	22.9494	+	7.45672i	0.731973	+	0.237832i	0.0807665	+	0.996733i	$0.474263\pi$
$984$	26.4154	+	19.1919i	0.842092	+	0.611816i
$985$	−23.6191	+	21.8760i	−0.752567	+	0.697028i
$986$	0.214336	−	0.659657i	0.00682584	−	0.0210078i
$987$	−50.6090	+	16.4439i	−1.61090	+	0.523414i
$988$	−8.48072	−	11.6727i	−0.269808	−	0.371358i
$989$	−32.4276			−1.03114
$990$		0			0
$991$	27.7081			0.880177			0.440089	−	0.897954i	$-0.354947\pi$
$991$	27.7081			0.880177			0.440089	+	0.897954i	$0.354947\pi$
$992$	−1.60752	−	2.21256i	−0.0510387	−	0.0702488i
$993$	−0.879435	+	0.285746i	−0.0279080	+	0.00906786i
$994$	5.33020	−	16.4047i	0.169064	−	0.520324i
$995$	22.4844	+	24.2759i	0.712803	+	0.769599i
$996$	−3.74952	−	2.72418i	−0.118808	−	0.0863191i
$997$	−31.8520	−	10.3494i	−1.00876	−	0.327767i	−0.242402	−	0.970176i	$-0.577935\pi$
$997$	−31.8520	−	10.3494i	−1.00876	−	0.327767i	−0.766362	+	0.642408i	$0.777935\pi$
$998$	65.2409	−	21.1981i	2.06517	−	0.671013i
$999$	8.70103	−	6.32167i	0.275288	−	0.200009i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.j.g.124.4		16
5.4	even	2	inner	605.2.j.g.124.1		16
11.2	odd	10		605.2.b.g.364.7		8
11.3	even	5		605.2.j.d.269.4		16
11.4	even	5	inner	605.2.j.g.444.1		16
11.5	even	5		605.2.j.d.9.1		16
11.6	odd	10		55.2.j.a.9.4	yes	16
11.7	odd	10		605.2.j.h.444.4		16
11.8	odd	10		55.2.j.a.49.1	yes	16
11.9	even	5		605.2.b.f.364.2		8
11.10	odd	2		605.2.j.h.124.1		16
33.8	even	10		495.2.ba.a.379.4		16
33.17	even	10		495.2.ba.a.64.1		16
44.19	even	10		880.2.cd.c.49.1		16
44.39	even	10		880.2.cd.c.449.4		16
55.2	even	20		3025.2.a.bl.1.2		8
55.4	even	10	inner	605.2.j.g.444.4		16
55.8	even	20		275.2.h.d.126.4		16
55.9	even	10		605.2.b.f.364.7		8
55.13	even	20		3025.2.a.bl.1.7		8
55.14	even	10		605.2.j.d.269.1		16
55.17	even	20		275.2.h.d.251.1		16
55.19	odd	10		55.2.j.a.49.4	yes	16
55.24	odd	10		605.2.b.g.364.2		8
55.28	even	20		275.2.h.d.251.4		16
55.29	odd	10		605.2.j.h.444.1		16
55.39	odd	10		55.2.j.a.9.1	✓	16
55.42	odd	20		3025.2.a.bk.1.7		8
55.49	even	10		605.2.j.d.9.4		16
55.52	even	20		275.2.h.d.126.1		16
55.53	odd	20		3025.2.a.bk.1.2		8
55.54	odd	2		605.2.j.h.124.4		16
165.74	even	10		495.2.ba.a.379.1		16
165.149	even	10		495.2.ba.a.64.4		16
220.19	even	10		880.2.cd.c.49.4		16
220.39	even	10		880.2.cd.c.449.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.j.a.9.1	✓	16	55.39	odd	10
55.2.j.a.9.4	yes	16	11.6	odd	10
55.2.j.a.49.1	yes	16	11.8	odd	10
55.2.j.a.49.4	yes	16	55.19	odd	10
275.2.h.d.126.1		16	55.52	even	20
275.2.h.d.126.4		16	55.8	even	20
275.2.h.d.251.1		16	55.17	even	20
275.2.h.d.251.4		16	55.28	even	20
495.2.ba.a.64.1		16	33.17	even	10
495.2.ba.a.64.4		16	165.149	even	10
495.2.ba.a.379.1		16	165.74	even	10
495.2.ba.a.379.4		16	33.8	even	10
605.2.b.f.364.2		8	11.9	even	5
605.2.b.f.364.7		8	55.9	even	10
605.2.b.g.364.2		8	55.24	odd	10
605.2.b.g.364.7		8	11.2	odd	10
605.2.j.d.9.1		16	11.5	even	5
605.2.j.d.9.4		16	55.49	even	10
605.2.j.d.269.1		16	55.14	even	10
605.2.j.d.269.4		16	11.3	even	5
605.2.j.g.124.1		16	5.4	even	2	inner
605.2.j.g.124.4		16	1.1	even	1	trivial
605.2.j.g.444.1		16	11.4	even	5	inner
605.2.j.g.444.4		16	55.4	even	10	inner
605.2.j.h.124.1		16	11.10	odd	2
605.2.j.h.124.4		16	55.54	odd	2
605.2.j.h.444.1		16	55.29	odd	10
605.2.j.h.444.4		16	11.7	odd	10
880.2.cd.c.49.1		16	44.19	even	10
880.2.cd.c.49.4		16	220.19	even	10
880.2.cd.c.449.1		16	220.39	even	10
880.2.cd.c.449.4		16	44.39	even	10
3025.2.a.bk.1.2		8	55.53	odd	20
3025.2.a.bk.1.7		8	55.42	odd	20
3025.2.a.bl.1.2		8	55.2	even	20
3025.2.a.bl.1.7		8	55.13	even	20

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.j (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.972539 + 1.33858i) q^{2} +(-1.87813 + 0.610243i) q^{3} +(-0.227943 + 0.701538i) q^{4} +(-1.51945 - 1.64051i) q^{5} +(-2.64342 - 1.92056i) q^{6} +(2.13329 + 0.693148i) q^{7} +(1.98645 - 0.645437i) q^{8} +(0.727943 - 0.528882i) q^{9} +O(q^{10})\)	\(q+(0.972539 + 1.33858i) q^{2} +(-1.87813 + 0.610243i) q^{3} +(-0.227943 + 0.701538i) q^{4} +(-1.51945 - 1.64051i) q^{5} +(-2.64342 - 1.92056i) q^{6} +(2.13329 + 0.693148i) q^{7} +(1.98645 - 0.645437i) q^{8} +(0.727943 - 0.528882i) q^{9} +(0.718246 - 3.62937i) q^{10} -1.45668i q^{12} +(2.17466 + 2.99317i) q^{13} +(1.14687 + 3.52970i) q^{14} +(3.85484 + 2.15387i) q^{15} +(3.98940 + 2.89847i) q^{16} +(1.30759 - 1.79974i) q^{17} +(1.41591 + 0.460056i) q^{18} +(1.63372 + 5.02809i) q^{19} +(1.49723 - 0.692004i) q^{20} -4.42960 q^{21} +3.85415i q^{23} +(-3.33695 + 2.42443i) q^{24} +(-0.382569 + 4.98534i) q^{25} +(-1.89166 + 5.82194i) q^{26} +(2.43782 - 3.35538i) q^{27} +(-0.972539 + 1.33858i) q^{28} +(0.0582308 - 0.179216i) q^{29} +(0.865834 + 7.25475i) q^{30} +(-0.555687 + 0.403730i) q^{31} +3.98166i q^{32} +3.68079 q^{34} +(-2.10430 - 4.55289i) q^{35} +(0.205101 + 0.631235i) q^{36} +(2.46624 + 0.801331i) q^{37} +(-5.14166 + 7.07689i) q^{38} +(-5.91087 - 4.29450i) q^{39} +(-4.07715 - 2.27809i) q^{40} +(-2.44619 - 7.52860i) q^{41} +(-4.30795 - 5.92939i) q^{42} +8.41368i q^{43} +(-1.97371 - 0.390594i) q^{45} +(-5.15911 + 3.74831i) q^{46} +(11.4252 - 3.71227i) q^{47} +(-9.26140 - 3.00921i) q^{48} +(-1.59265 - 1.15713i) q^{49} +(-7.04537 + 4.33634i) q^{50} +(-1.35755 + 4.17811i) q^{51} +(-2.59552 + 0.843335i) q^{52} +(7.43935 + 10.2394i) q^{53} +6.86233 q^{54} +4.68506 q^{56} +(-6.13671 - 8.44645i) q^{57} +(0.296528 - 0.0963477i) q^{58} +(0.106206 - 0.326867i) q^{59} +(-2.38971 + 2.21335i) q^{60} +(1.40233 + 1.01885i) q^{61} +(-1.08085 - 0.351191i) q^{62} +(1.91951 - 0.623686i) q^{63} +(2.64900 - 1.92461i) q^{64} +(1.60605 - 8.11552i) q^{65} +0.650461i q^{67} +(0.964532 + 1.32756i) q^{68} +(-2.35197 - 7.23862i) q^{69} +(4.04792 - 7.24465i) q^{70} +(-3.75999 - 2.73179i) q^{71} +(1.10466 - 1.52044i) q^{72} +(-8.42484 - 2.73740i) q^{73} +(1.32587 + 4.08060i) q^{74} +(-2.32375 - 9.59661i) q^{75} -3.89979 q^{76} -12.0888i q^{78} +(5.85264 - 4.25219i) q^{79} +(-1.30670 - 10.9487i) q^{80} +(-3.36512 + 10.3568i) q^{81} +(7.69865 - 10.5963i) q^{82} +(1.87013 - 2.57401i) q^{83} +(1.00970 - 3.10753i) q^{84} +(-4.93932 + 0.589494i) q^{85} +(-11.2624 + 8.18263i) q^{86} +0.372127i q^{87} -9.92195 q^{89} +(-1.39666 - 3.02184i) q^{90} +(2.56448 + 7.89265i) q^{91} +(-2.70383 - 0.878529i) q^{92} +(0.797281 - 1.09736i) q^{93} +(16.0806 + 11.6833i) q^{94} +(5.76629 - 10.3200i) q^{95} +(-2.42978 - 7.47810i) q^{96} +(-1.33316 - 1.83494i) q^{97} -3.25724i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{4} - 2 q^{5} - 12 q^{6} + 2 q^{9}+O(q^{10}) \) 16 * q + 6 * q^4 - 2 * q^5 - 12 * q^6 + 2 * q^9	\( 16 q + 6 q^{4} - 2 q^{5} - 12 q^{6} + 2 q^{9} + 8 q^{14} + 24 q^{15} + 6 q^{16} - 6 q^{19} + 12 q^{20} - 8 q^{21} + 4 q^{24} + 24 q^{25} - 50 q^{26} - 22 q^{29} + 4 q^{30} - 22 q^{31} - 16 q^{34} + 8 q^{35} - 30 q^{36} - 12 q^{40} - 18 q^{41} + 12 q^{45} - 38 q^{46} - 20 q^{49} + 12 q^{50} + 12 q^{51} + 40 q^{54} - 20 q^{56} - 8 q^{59} - 2 q^{60} - 20 q^{61} + 22 q^{64} + 40 q^{65} + 6 q^{69} + 26 q^{70} + 6 q^{71} + 52 q^{74} + 40 q^{75} - 56 q^{76} + 22 q^{79} - 6 q^{80} - 32 q^{81} + 18 q^{84} + 62 q^{85} - 68 q^{86} + 24 q^{89} + 32 q^{90} + 56 q^{94} + 22 q^{95} - 94 q^{96}+O(q^{100}) \) 16 * q + 6 * q^4 - 2 * q^5 - 12 * q^6 + 2 * q^9 + 8 * q^14 + 24 * q^15 + 6 * q^16 - 6 * q^19 + 12 * q^20 - 8 * q^21 + 4 * q^24 + 24 * q^25 - 50 * q^26 - 22 * q^29 + 4 * q^30 - 22 * q^31 - 16 * q^34 + 8 * q^35 - 30 * q^36 - 12 * q^40 - 18 * q^41 + 12 * q^45 - 38 * q^46 - 20 * q^49 + 12 * q^50 + 12 * q^51 + 40 * q^54 - 20 * q^56 - 8 * q^59 - 2 * q^60 - 20 * q^61 + 22 * q^64 + 40 * q^65 + 6 * q^69 + 26 * q^70 + 6 * q^71 + 52 * q^74 + 40 * q^75 - 56 * q^76 + 22 * q^79 - 6 * q^80 - 32 * q^81 + 18 * q^84 + 62 * q^85 - 68 * q^86 + 24 * q^89 + 32 * q^90 + 56 * q^94 + 22 * q^95 - 94 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more