LMFDB - Embedded newform 605.2.g.i.251.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(81,605)]

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([0, 2]))

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

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

chi := DirichletCharacter("605.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.g (of order $5$, 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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.324000000.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 $ x^8 + 3x^6 + 9x^4 + 27*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			251.2
Root			$-1.40126 + 1.01807i$ of defining polynomial
Character	$\chi$	$=$	605.251
Dual form			605.2.g.i.511.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.535233 - 1.64728i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.535233 - 1.64728i) q^{6} +(1.40126 + 1.01807i) q^{7} +(1.40126 - 1.01807i) q^{8} +(-0.618034 + 1.90211i) q^{9} +O(q^{10})$	\(q+(0.535233 - 1.64728i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.535233 - 1.64728i) q^{6} +(1.40126 + 1.01807i) q^{7} +(1.40126 - 1.01807i) q^{8} +(-0.618034 + 1.90211i) q^{9} -1.73205 q^{10} -1.00000 q^{12} +(1.07047 - 3.29456i) q^{13} +(2.42705 - 1.76336i) q^{14} +(-0.809017 - 0.587785i) q^{15} +(-1.54508 - 4.75528i) q^{16} +(-2.14093 - 6.58911i) q^{17} +(2.80252 + 2.03615i) q^{18} +(2.80252 - 2.03615i) q^{19} +(-0.309017 + 0.951057i) q^{20} +1.73205 q^{21} +(0.535233 - 1.64728i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(-4.85410 - 3.52671i) q^{26} +(1.54508 + 4.75528i) q^{27} +(-0.535233 - 1.64728i) q^{28} +(-1.40126 + 1.01807i) q^{30} +(-2.47214 + 7.60845i) q^{31} -5.19615 q^{32} -12.0000 q^{34} +(0.535233 - 1.64728i) q^{35} +(1.61803 - 1.17557i) q^{36} +(6.47214 + 4.70228i) q^{37} +(-1.85410 - 5.70634i) q^{38} +(-1.07047 - 3.29456i) q^{39} +(-1.40126 - 1.01807i) q^{40} +(-9.80881 + 7.12652i) q^{41} +(0.927051 - 2.85317i) q^{42} +8.66025 q^{43} +2.00000 q^{45} +(-7.28115 + 5.29007i) q^{47} +(-4.04508 - 2.93893i) q^{48} +(-1.23607 - 3.80423i) q^{49} +(0.535233 + 1.64728i) q^{50} +(-5.60503 - 4.07230i) q^{51} +(-2.80252 + 2.03615i) q^{52} +(1.85410 - 5.70634i) q^{53} +8.66025 q^{54} +3.00000 q^{56} +(1.07047 - 3.29456i) q^{57} +(9.70820 + 7.05342i) q^{59} +(0.309017 + 0.951057i) q^{60} +(2.67617 + 8.23639i) q^{61} +(11.2101 + 8.14459i) q^{62} +(-2.80252 + 2.03615i) q^{63} +(0.309017 - 0.951057i) q^{64} -3.46410 q^{65} -5.00000 q^{67} +(-2.14093 + 6.58911i) q^{68} +(-2.42705 - 1.76336i) q^{70} +(-3.70820 - 11.4127i) q^{71} +(1.07047 + 3.29456i) q^{72} +(11.2101 - 8.14459i) q^{74} +(-0.309017 + 0.951057i) q^{75} -3.46410 q^{76} -6.00000 q^{78} +(-3.21140 + 9.88367i) q^{79} +(-4.04508 + 2.93893i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(6.48936 + 19.9722i) q^{82} +(1.07047 + 3.29456i) q^{83} +(-1.40126 - 1.01807i) q^{84} +(-5.60503 + 4.07230i) q^{85} +(4.63525 - 14.2658i) q^{86} +3.00000 q^{89} +(1.07047 - 3.29456i) q^{90} +(4.85410 - 3.52671i) q^{91} +(2.47214 + 7.60845i) q^{93} +(4.81710 + 14.8255i) q^{94} +(-2.80252 - 2.03615i) q^{95} +(-4.20378 + 3.05422i) q^{96} +(-3.09017 + 9.51057i) q^{97} -6.92820 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 - 2 * q^4 + 2 * q^5 + 4 * q^9	$ 8 q + 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{9} - 8 q^{12} + 6 q^{14} - 2 q^{15} + 10 q^{16} + 2 q^{20} - 2 q^{25} - 12 q^{26} - 10 q^{27} + 16 q^{31} - 96 q^{34} + 4 q^{36} + 16 q^{37} + 12 q^{38} - 6 q^{42} + 16 q^{45} - 18 q^{47} - 10 q^{48} + 8 q^{49} - 12 q^{53} + 24 q^{56} + 24 q^{59} - 2 q^{60} - 2 q^{64} - 40 q^{67} - 6 q^{70} + 24 q^{71} + 2 q^{75} - 48 q^{78} - 10 q^{80} - 2 q^{81} - 42 q^{82} - 30 q^{86} + 24 q^{89} + 12 q^{91} - 16 q^{93} + 20 q^{97}+O(q^{100}) $ 8 * q + 2 * q^3 - 2 * q^4 + 2 * q^5 + 4 * q^9 - 8 * q^12 + 6 * q^14 - 2 * q^15 + 10 * q^16 + 2 * q^20 - 2 * q^25 - 12 * q^26 - 10 * q^27 + 16 * q^31 - 96 * q^34 + 4 * q^36 + 16 * q^37 + 12 * q^38 - 6 * q^42 + 16 * q^45 - 18 * q^47 - 10 * q^48 + 8 * q^49 - 12 * q^53 + 24 * q^56 + 24 * q^59 - 2 * q^60 - 2 * q^64 - 40 * q^67 - 6 * q^70 + 24 * q^71 + 2 * q^75 - 48 * q^78 - 10 * q^80 - 2 * q^81 - 42 * q^82 - 30 * q^86 + 24 * q^89 + 12 * q^91 - 16 * q^93 + 20 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.535233	−	1.64728i	0.378467	−	1.16480i	−0.562643	−	0.826700i	$-0.690215\pi$
$2$	0.535233	−	1.64728i	0.378467	−	1.16480i	0.941110	−	0.338101i	$-0.109785\pi$
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i	−0.329218	−	0.944254i	$-0.606785\pi$
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i	0.796305	+	0.604896i	$0.206785\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$6$	−0.535233	−	1.64728i	−0.218508	−	0.672499i
$7$	1.40126	+	1.01807i	0.529626	+	0.384796i	0.820218	−	0.572051i	$-0.193852\pi$
$7$	1.40126	+	1.01807i	0.529626	+	0.384796i	−0.290592	+	0.956847i	$0.593852\pi$
$8$	1.40126	−	1.01807i	0.495420	−	0.359943i
$9$	−0.618034	+	1.90211i	−0.206011	+	0.634038i
$10$	−1.73205			−0.547723
$11$		0			0
$11$		0			0
$12$	−1.00000			−0.288675
$13$	1.07047	−	3.29456i	0.296894	−	0.913746i	−0.685685	−	0.727899i	$-0.740497\pi$
$13$	1.07047	−	3.29456i	0.296894	−	0.913746i	0.982579	−	0.185847i	$-0.0595029\pi$
$14$	2.42705	−	1.76336i	0.648657	−	0.471277i
$15$	−0.809017	−	0.587785i	−0.208887	−	0.151765i
$16$	−1.54508	−	4.75528i	−0.386271	−	1.18882i
$17$	−2.14093	−	6.58911i	−0.519252	−	1.59809i	−0.775409	−	0.631459i	$-0.782456\pi$
$17$	−2.14093	−	6.58911i	−0.519252	−	1.59809i	0.256157	−	0.966635i	$-0.417544\pi$
$18$	2.80252	+	2.03615i	0.660560	+	0.479925i
$19$	2.80252	−	2.03615i	0.642942	−	0.467124i	−0.217918	−	0.975967i	$-0.569927\pi$
$19$	2.80252	−	2.03615i	0.642942	−	0.467124i	0.860859	+	0.508843i	$0.169927\pi$
$20$	−0.309017	+	0.951057i	−0.0690983	+	0.212663i
$21$	1.73205			0.377964
$22$		0			0
$23$		0			0			−	1.00000i	$-0.5\pi$
$23$		0			0				1.00000i	$0.5\pi$
$24$	0.535233	−	1.64728i	0.109254	−	0.336249i
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$	−4.85410	−	3.52671i	−0.951968	−	0.691645i
$27$	1.54508	+	4.75528i	0.297352	+	0.915155i
$28$	−0.535233	−	1.64728i	−0.101150	−	0.311306i
$29$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$29$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$30$	−1.40126	+	1.01807i	−0.255834	+	0.185874i
$31$	−2.47214	+	7.60845i	−0.444009	+	1.36652i	0.439558	+	0.898214i	$0.355135\pi$
$31$	−2.47214	+	7.60845i	−0.444009	+	1.36652i	−0.883567	+	0.468304i	$0.844865\pi$
$32$	−5.19615			−0.918559
$33$		0			0
$34$	−12.0000			−2.05798
$35$	0.535233	−	1.64728i	0.0904709	−	0.278441i
$36$	1.61803	−	1.17557i	0.269672	−	0.195928i
$37$	6.47214	+	4.70228i	1.06401	+	0.773050i	0.974827	−	0.222965i	$-0.0715734\pi$
$37$	6.47214	+	4.70228i	1.06401	+	0.773050i	0.0891861	+	0.996015i	$0.471573\pi$
$38$	−1.85410	−	5.70634i	−0.300775	−	0.925690i
$39$	−1.07047	−	3.29456i	−0.171412	−	0.527551i
$40$	−1.40126	−	1.01807i	−0.221558	−	0.160972i
$41$	−9.80881	+	7.12652i	−1.53188	+	1.11298i	−0.576696	+	0.816959i	$0.695658\pi$
$41$	−9.80881	+	7.12652i	−1.53188	+	1.11298i	−0.955183	+	0.296016i	$0.904342\pi$
$42$	0.927051	−	2.85317i	0.143047	−	0.440254i
$43$	8.66025			1.32068			0.660338	−	0.750968i	$-0.270413\pi$
$43$	8.66025			1.32068			0.660338	+	0.750968i	$0.270413\pi$
$44$		0			0
$45$	2.00000			0.298142
$46$		0			0
$47$	−7.28115	+	5.29007i	−1.06207	+	0.771636i	−0.974469	−	0.224520i	$-0.927918\pi$
$47$	−7.28115	+	5.29007i	−1.06207	+	0.771636i	−0.0875959	+	0.996156i	$0.527918\pi$
$48$	−4.04508	−	2.93893i	−0.583858	−	0.424197i
$49$	−1.23607	−	3.80423i	−0.176581	−	0.543461i
$50$	0.535233	+	1.64728i	0.0756934	+	0.232960i
$51$	−5.60503	−	4.07230i	−0.784862	−	0.570235i
$52$	−2.80252	+	2.03615i	−0.388639	+	0.282363i
$53$	1.85410	−	5.70634i	0.254680	−	0.783826i	−0.739212	−	0.673473i	$-0.764802\pi$
$53$	1.85410	−	5.70634i	0.254680	−	0.783826i	0.993892	−	0.110353i	$-0.0351982\pi$
$54$	8.66025			1.17851
$55$		0			0
$56$	3.00000			0.400892
$57$	1.07047	−	3.29456i	0.141787	−	0.436375i
$58$		0			0
$59$	9.70820	+	7.05342i	1.26390	+	0.918277i	0.998942	−	0.0459824i	$-0.0146418\pi$
$59$	9.70820	+	7.05342i	1.26390	+	0.918277i	0.264958	+	0.964260i	$0.414642\pi$
$60$	0.309017	+	0.951057i	0.0398939	+	0.122781i
$61$	2.67617	+	8.23639i	0.342648	+	1.05456i	0.962831	+	0.270105i	$0.0870583\pi$
$61$	2.67617	+	8.23639i	0.342648	+	1.05456i	−0.620183	+	0.784457i	$0.712942\pi$
$62$	11.2101	+	8.14459i	1.42368	+	1.03436i
$63$	−2.80252	+	2.03615i	−0.353084	+	0.256531i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−3.46410			−0.429669
$66$		0			0
$67$	−5.00000			−0.610847			−0.305424	−	0.952217i	$-0.598798\pi$
$67$	−5.00000			−0.610847			−0.305424	+	0.952217i	$0.598798\pi$
$68$	−2.14093	+	6.58911i	−0.259626	+	0.799047i
$69$		0			0
$70$	−2.42705	−	1.76336i	−0.290088	−	0.210761i
$71$	−3.70820	−	11.4127i	−0.440083	−	1.35444i	−0.887787	−	0.460254i	$-0.847758\pi$
$71$	−3.70820	−	11.4127i	−0.440083	−	1.35444i	0.447704	−	0.894182i	$-0.352242\pi$
$72$	1.07047	+	3.29456i	0.126156	+	0.388267i
$73$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$73$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$74$	11.2101	−	8.14459i	1.30314	−	0.946790i
$75$	−0.309017	+	0.951057i	−0.0356822	+	0.109819i
$76$	−3.46410			−0.397360
$77$		0			0
$78$	−6.00000			−0.679366
$79$	−3.21140	+	9.88367i	−0.361311	+	1.11200i	0.590949	+	0.806709i	$0.298754\pi$
$79$	−3.21140	+	9.88367i	−0.361311	+	1.11200i	−0.952259	+	0.305291i	$0.901246\pi$
$80$	−4.04508	+	2.93893i	−0.452254	+	0.328582i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	6.48936	+	19.9722i	0.716630	+	2.20556i
$83$	1.07047	+	3.29456i	0.117499	+	0.361625i	0.992460	−	0.122569i	$-0.0391132\pi$
$83$	1.07047	+	3.29456i	0.117499	+	0.361625i	−0.874961	+	0.484193i	$0.839113\pi$
$84$	−1.40126	−	1.01807i	−0.152890	−	0.111081i
$85$	−5.60503	+	4.07230i	−0.607951	+	0.441702i
$86$	4.63525	−	14.2658i	0.499832	−	1.53833i
$87$		0			0
$88$		0			0
$89$	3.00000			0.317999			0.159000	−	0.987279i	$-0.449173\pi$
$89$	3.00000			0.317999			0.159000	+	0.987279i	$0.449173\pi$
$90$	1.07047	−	3.29456i	0.112837	−	0.347277i
$91$	4.85410	−	3.52671i	0.508848	−	0.369700i
$92$		0			0
$93$	2.47214	+	7.60845i	0.256349	+	0.788960i
$94$	4.81710	+	14.8255i	0.496846	+	1.52913i
$95$	−2.80252	−	2.03615i	−0.287532	−	0.208904i
$96$	−4.20378	+	3.05422i	−0.429046	+	0.311720i
$97$	−3.09017	+	9.51057i	−0.313759	+	0.965652i	0.662503	+	0.749059i	$0.269494\pi$
$97$	−3.09017	+	9.51057i	−0.313759	+	0.965652i	−0.976262	+	0.216592i	$0.930506\pi$
$98$	−6.92820			−0.699854
$99$		0			0
$100$	1.00000			0.100000
$101$	−0.535233	+	1.64728i	−0.0532577	+	0.163910i	−0.974148	−	0.225912i	$-0.927464\pi$
$101$	−0.535233	+	1.64728i	−0.0532577	+	0.163910i	0.920890	+	0.389823i	$0.127464\pi$
$102$	−9.70820	+	7.05342i	−0.961255	+	0.698393i
$103$	3.23607	+	2.35114i	0.318859	+	0.231665i	0.735689	−	0.677320i	$-0.236859\pi$
$103$	3.23607	+	2.35114i	0.318859	+	0.231665i	−0.416829	+	0.908985i	$0.636859\pi$
$104$	−1.85410	−	5.70634i	−0.181810	−	0.559553i
$105$	−0.535233	−	1.64728i	−0.0522334	−	0.160758i
$106$	−8.40755	−	6.10844i	−0.816614	−	0.593304i
$107$	−1.40126	+	1.01807i	−0.135465	+	0.0984209i	−0.653454	−	0.756966i	$-0.726681\pi$
$107$	−1.40126	+	1.01807i	−0.135465	+	0.0984209i	0.517989	+	0.855387i	$0.326681\pi$
$108$	1.54508	−	4.75528i	0.148676	−	0.457577i
$109$	1.73205			0.165900			0.0829502	−	0.996554i	$-0.473566\pi$
$109$	1.73205			0.165900			0.0829502	+	0.996554i	$0.473566\pi$
$110$		0			0
$111$	8.00000			0.759326
$112$	2.67617	−	8.23639i	0.252874	−	0.778266i
$113$	4.85410	−	3.52671i	0.456636	−	0.331765i	−0.335575	−	0.942014i	$-0.608930\pi$
$113$	4.85410	−	3.52671i	0.456636	−	0.331765i	0.792210	+	0.610249i	$0.208930\pi$
$114$	−4.85410	−	3.52671i	−0.454628	−	0.330307i
$115$		0			0
$116$		0			0
$117$	5.60503	+	4.07230i	0.518186	+	0.376484i
$118$	16.8151	−	12.2169i	1.54796	−	1.12466i
$119$	3.70820	−	11.4127i	0.339930	−	1.04620i
$120$	−1.73205			−0.158114
$121$		0			0
$122$	15.0000			1.35804
$123$	−3.74663	+	11.5309i	−0.337822	+	1.03971i
$124$	6.47214	−	4.70228i	0.581215	−	0.422277i
$125$	0.809017	+	0.587785i	0.0723607	+	0.0525731i
$126$	1.85410	+	5.70634i	0.165177	+	0.508361i
$127$	0.535233	+	1.64728i	0.0474943	+	0.146172i	0.971991	−	0.235017i	$-0.0755146\pi$
$127$	0.535233	+	1.64728i	0.0474943	+	0.146172i	−0.924497	+	0.381189i	$0.875515\pi$
$128$	−9.80881	−	7.12652i	−0.866984	−	0.629901i
$129$	7.00629	−	5.09037i	0.616870	−	0.448182i
$130$	−1.85410	+	5.70634i	−0.162615	+	0.500479i
$131$	−3.46410			−0.302660			−0.151330	−	0.988483i	$-0.548356\pi$
$131$	−3.46410			−0.302660			−0.151330	+	0.988483i	$0.548356\pi$
$132$		0			0
$133$	6.00000			0.520266
$134$	−2.67617	+	8.23639i	−0.231186	+	0.711516i
$135$	4.04508	−	2.93893i	0.348145	−	0.252942i
$136$	−9.70820	−	7.05342i	−0.832472	−	0.604826i
$137$	5.56231	+	17.1190i	0.475220	+	1.46258i	0.845661	+	0.533720i	$0.179207\pi$
$137$	5.56231	+	17.1190i	0.475220	+	1.46258i	−0.370441	+	0.928856i	$0.620793\pi$
$138$		0			0
$139$	−11.2101	−	8.14459i	−0.950826	−	0.690815i	0.000176405	−	1.00000i	$-0.499944\pi$
$139$	−11.2101	−	8.14459i	−0.950826	−	0.690815i	−0.951002	+	0.309185i	$0.899944\pi$
$140$	−1.40126	+	1.01807i	−0.118428	+	0.0860430i
$141$	−2.78115	+	8.55951i	−0.234215	+	0.720841i
$142$	−20.7846			−1.74421
$143$		0			0
$144$	10.0000			0.833333
$145$		0			0
$146$		0			0
$147$	−3.23607	−	2.35114i	−0.266906	−	0.193919i
$148$	−2.47214	−	7.60845i	−0.203208	−	0.625411i
$149$	−5.88756	−	18.1201i	−0.482328	−	1.48445i	−0.835814	−	0.549013i	$-0.815004\pi$
$149$	−5.88756	−	18.1201i	−0.482328	−	1.48445i	0.353486	−	0.935440i	$-0.384996\pi$
$150$	1.40126	+	1.01807i	0.114412	+	0.0831254i
$151$	16.8151	−	12.2169i	1.36839	−	0.994196i	0.370533	−	0.928819i	$-0.379175\pi$
$151$	16.8151	−	12.2169i	1.36839	−	0.994196i	0.997861	−	0.0653769i	$-0.0208250\pi$
$152$	1.85410	−	5.70634i	0.150388	−	0.462845i
$153$	13.8564			1.12022
$154$		0			0
$155$	8.00000			0.642575
$156$	−1.07047	+	3.29456i	−0.0857059	+	0.263776i
$157$	−3.23607	+	2.35114i	−0.258266	+	0.187641i	−0.709382	−	0.704824i	$-0.751026\pi$
$157$	−3.23607	+	2.35114i	−0.258266	+	0.187641i	0.451116	+	0.892465i	$0.351026\pi$
$158$	14.5623	+	10.5801i	1.15851	+	0.841710i
$159$	−1.85410	−	5.70634i	−0.147040	−	0.452542i
$160$	1.60570	+	4.94183i	0.126942	+	0.390686i
$161$		0			0
$162$	−1.40126	+	1.01807i	−0.110093	+	0.0799874i
$163$	−5.87132	+	18.0701i	−0.459878	+	1.41536i	0.405435	+	0.914124i	$0.367120\pi$
$163$	−5.87132	+	18.0701i	−0.459878	+	1.41536i	−0.865312	+	0.501233i	$0.832880\pi$
$164$	12.1244			0.946753
$165$		0			0
$166$	6.00000			0.465690
$167$	−1.60570	+	4.94183i	−0.124253	+	0.382411i	−0.993764	−	0.111502i	$-0.964434\pi$
$167$	−1.60570	+	4.94183i	−0.124253	+	0.382411i	0.869511	+	0.493913i	$0.164434\pi$
$168$	2.42705	−	1.76336i	0.187251	−	0.136046i
$169$	0.809017	+	0.587785i	0.0622321	+	0.0452143i
$170$	3.70820	+	11.4127i	0.284406	+	0.875312i
$171$	2.14093	+	6.58911i	0.163721	+	0.503882i
$172$	−7.00629	−	5.09037i	−0.534225	−	0.388137i
$173$	−8.40755	+	6.10844i	−0.639214	+	0.464416i	−0.859580	−	0.511001i	$-0.829275\pi$
$173$	−8.40755	+	6.10844i	−0.639214	+	0.464416i	0.220366	+	0.975417i	$0.429275\pi$
$174$		0			0
$175$	−1.73205			−0.130931
$176$		0			0
$177$	12.0000			0.901975
$178$	1.60570	−	4.94183i	0.120352	−	0.370406i
$179$	14.5623	−	10.5801i	1.08844	−	0.790796i	0.109303	−	0.994008i	$-0.465138\pi$
$179$	14.5623	−	10.5801i	1.08844	−	0.790796i	0.979135	+	0.203212i	$0.0651381\pi$
$180$	−1.61803	−	1.17557i	−0.120601	−	0.0876219i
$181$	3.39919	+	10.4616i	0.252660	+	0.777606i	0.994282	+	0.106788i	$0.0340567\pi$
$181$	3.39919	+	10.4616i	0.252660	+	0.777606i	−0.741622	+	0.670818i	$0.765943\pi$
$182$	−3.21140	−	9.88367i	−0.238045	−	0.732626i
$183$	7.00629	+	5.09037i	0.517920	+	0.376291i
$184$		0			0
$185$	2.47214	−	7.60845i	0.181755	−	0.559385i
$186$	13.8564			1.01600
$187$		0			0
$188$	9.00000			0.656392
$189$	−2.67617	+	8.23639i	−0.194662	+	0.599109i
$190$	−4.85410	+	3.52671i	−0.352154	+	0.255855i
$191$	4.85410	+	3.52671i	0.351230	+	0.255184i	0.749385	−	0.662134i	$-0.230349\pi$
$191$	4.85410	+	3.52671i	0.351230	+	0.255184i	−0.398155	+	0.917318i	$0.630349\pi$
$192$	−0.309017	−	0.951057i	−0.0223014	−	0.0686366i
$193$	−1.07047	−	3.29456i	−0.0770538	−	0.237147i	0.905109	−	0.425180i	$-0.139789\pi$
$193$	−1.07047	−	3.29456i	−0.0770538	−	0.237147i	−0.982163	+	0.188032i	$0.939789\pi$
$194$	14.0126	+	10.1807i	1.00605	+	0.730934i
$195$	−2.80252	+	2.03615i	−0.200692	+	0.145812i
$196$	−1.23607	+	3.80423i	−0.0882906	+	0.271730i
$197$	−10.3923			−0.740421			−0.370211	−	0.928948i	$-0.620714\pi$
$197$	−10.3923			−0.740421			−0.370211	+	0.928948i	$0.620714\pi$
$198$		0			0
$199$	−14.0000			−0.992434			−0.496217	−	0.868199i	$-0.665278\pi$
$199$	−14.0000			−0.992434			−0.496217	+	0.868199i	$0.665278\pi$
$200$	−0.535233	+	1.64728i	−0.0378467	+	0.116480i
$201$	−4.04508	+	2.93893i	−0.285318	+	0.207296i
$202$	2.42705	+	1.76336i	0.170767	+	0.124069i
$203$		0			0
$204$	2.14093	+	6.58911i	0.149895	+	0.461330i
$205$	9.80881	+	7.12652i	0.685077	+	0.497738i
$206$	5.60503	−	4.07230i	0.390521	−	0.283730i
$207$		0			0
$208$	−17.3205			−1.20096
$209$		0			0
$210$	−3.00000			−0.207020
$211$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$211$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$212$	−4.85410	+	3.52671i	−0.333381	+	0.242216i
$213$	−9.70820	−	7.05342i	−0.665195	−	0.483293i
$214$	0.927051	+	2.85317i	0.0633719	+	0.195039i
$215$	−2.67617	−	8.23639i	−0.182513	−	0.561717i
$216$	7.00629	+	5.09037i	0.476718	+	0.346356i
$217$	−11.2101	+	8.14459i	−0.760989	+	0.552891i
$218$	0.927051	−	2.85317i	0.0627878	−	0.193241i
$219$		0			0
$220$		0			0
$221$	−24.0000			−1.61441
$222$	4.28187	−	13.1782i	0.287380	−	0.884465i
$223$	15.3713	−	11.1679i	1.02934	−	0.747859i	0.0611635	−	0.998128i	$-0.480519\pi$
$223$	15.3713	−	11.1679i	1.02934	−	0.747859i	0.968176	+	0.250269i	$0.0805189\pi$
$224$	−7.28115	−	5.29007i	−0.486492	−	0.353457i
$225$	−0.618034	−	1.90211i	−0.0412023	−	0.126808i
$226$	−3.21140	−	9.88367i	−0.213619	−	0.657452i
$227$	−15.4138	−	11.1988i	−1.02305	−	0.743291i	−0.0561463	−	0.998423i	$-0.517881\pi$
$227$	−15.4138	−	11.1988i	−1.02305	−	0.743291i	−0.966906	+	0.255131i	$0.917881\pi$
$228$	−2.80252	+	2.03615i	−0.185601	+	0.134847i
$229$	2.16312	−	6.65740i	0.142943	−	0.439933i	−0.853798	−	0.520605i	$-0.825707\pi$
$229$	2.16312	−	6.65740i	0.142943	−	0.439933i	0.996741	+	0.0806717i	$0.0257065\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.07047	+	3.29456i	−0.0701286	+	0.215834i	−0.979978	−	0.199104i	$-0.936197\pi$
$233$	−1.07047	+	3.29456i	−0.0701286	+	0.215834i	0.909850	+	0.414938i	$0.136197\pi$
$234$	9.70820	−	7.05342i	0.634645	−	0.461097i
$235$	7.28115	+	5.29007i	0.474970	+	0.345086i
$236$	−3.70820	−	11.4127i	−0.241384	−	0.742902i
$237$	3.21140	+	9.88367i	0.208603	+	0.642013i
$238$	−16.8151	−	12.2169i	−1.08996	−	0.791903i
$239$	−2.80252	+	2.03615i	−0.181280	+	0.131707i	−0.674724	−	0.738070i	$-0.735738\pi$
$239$	−2.80252	+	2.03615i	−0.181280	+	0.131707i	0.493445	+	0.869777i	$0.335738\pi$
$240$	−1.54508	+	4.75528i	−0.0997348	+	0.306952i
$241$	−19.0526			−1.22728			−0.613642	−	0.789585i	$-0.710296\pi$
$241$	−19.0526			−1.22728			−0.613642	+	0.789585i	$0.710296\pi$
$242$		0			0
$243$	−16.0000			−1.02640
$244$	2.67617	−	8.23639i	0.171324	−	0.527281i
$245$	−3.23607	+	2.35114i	−0.206745	+	0.150209i
$246$	16.9894	+	12.3435i	1.08320	+	0.786992i
$247$	−3.70820	−	11.4127i	−0.235947	−	0.726171i
$248$	4.28187	+	13.1782i	0.271899	+	0.836818i
$249$	2.80252	+	2.03615i	0.177602	+	0.129036i
$250$	1.40126	−	1.01807i	0.0886234	−	0.0643886i
$251$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$251$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$252$	3.46410			0.218218
$253$		0			0
$254$	3.00000			0.188237
$255$	−2.14093	+	6.58911i	−0.134070	+	0.412626i
$256$	−15.3713	+	11.1679i	−0.960708	+	0.697995i
$257$	−9.70820	−	7.05342i	−0.605581	−	0.439980i	0.242274	−	0.970208i	$-0.422107\pi$
$257$	−9.70820	−	7.05342i	−0.605581	−	0.439980i	−0.847856	+	0.530227i	$0.822107\pi$
$258$	−4.63525	−	14.2658i	−0.288578	−	0.888153i
$259$	4.28187	+	13.1782i	0.266062	+	0.818855i
$260$	2.80252	+	2.03615i	0.173805	+	0.126277i
$261$		0			0
$262$	−1.85410	+	5.70634i	−0.114547	+	0.352539i
$263$	24.2487			1.49524			0.747620	−	0.664127i	$-0.231197\pi$
$263$	24.2487			1.49524			0.747620	+	0.664127i	$0.231197\pi$
$264$		0			0
$265$	−6.00000			−0.368577
$266$	3.21140	−	9.88367i	0.196903	−	0.606007i
$267$	2.42705	−	1.76336i	0.148533	−	0.107916i
$268$	4.04508	+	2.93893i	0.247093	+	0.179523i
$269$	−4.63525	−	14.2658i	−0.282616	−	0.869804i	−0.987103	−	0.160087i	$-0.948823\pi$
$269$	−4.63525	−	14.2658i	−0.282616	−	0.869804i	0.704486	−	0.709717i	$-0.251177\pi$
$270$	−2.67617	−	8.23639i	−0.162866	−	0.501251i
$271$	11.2101	+	8.14459i	0.680963	+	0.494749i	0.873677	−	0.486506i	$-0.161729\pi$
$271$	11.2101	+	8.14459i	0.680963	+	0.494749i	−0.192714	+	0.981255i	$0.561729\pi$
$272$	−28.0252	+	20.3615i	−1.69928	+	1.23460i
$273$	1.85410	−	5.70634i	0.112215	−	0.345363i
$274$	31.1769			1.88347
$275$		0			0
$276$		0			0
$277$	3.21140	−	9.88367i	0.192954	−	0.593852i	−0.807040	−	0.590497i	$-0.798932\pi$
$277$	3.21140	−	9.88367i	0.192954	−	0.593852i	0.999994	−	0.00335552i	$-0.00106810\pi$
$278$	−19.4164	+	14.1068i	−1.16452	+	0.846072i
$279$	−12.9443	−	9.40456i	−0.774953	−	0.563037i
$280$	−0.927051	−	2.85317i	−0.0554019	−	0.170509i
$281$	−2.14093	−	6.58911i	−0.127717	−	0.393074i	0.866669	−	0.498884i	$-0.166256\pi$
$281$	−2.14093	−	6.58911i	−0.127717	−	0.393074i	−0.994386	+	0.105810i	$0.966256\pi$
$282$	12.6113	+	9.16267i	0.750994	+	0.545629i
$283$	4.20378	−	3.05422i	0.249889	−	0.181555i	−0.455789	−	0.890088i	$-0.650643\pi$
$283$	4.20378	−	3.05422i	0.249889	−	0.181555i	0.705677	+	0.708533i	$0.250643\pi$
$284$	−3.70820	+	11.4127i	−0.220041	+	0.677218i
$285$	−3.46410			−0.205196
$286$		0			0
$287$	−21.0000			−1.23959
$288$	3.21140	−	9.88367i	0.189233	−	0.582401i
$289$	−25.0795	+	18.2213i	−1.47527	+	1.07184i
$290$		0			0
$291$	3.09017	+	9.51057i	0.181149	+	0.557519i
$292$		0			0
$293$	5.60503	+	4.07230i	0.327450	+	0.237906i	0.739348	−	0.673324i	$-0.235134\pi$
$293$	5.60503	+	4.07230i	0.327450	+	0.237906i	−0.411898	+	0.911230i	$0.635134\pi$
$294$	−5.60503	+	4.07230i	−0.326892	+	0.237501i
$295$	3.70820	−	11.4127i	0.215900	−	0.664472i
$296$	13.8564			0.805387
$297$		0			0
$298$	−33.0000			−1.91164
$299$		0			0
$300$	0.809017	−	0.587785i	0.0467086	−	0.0339358i
$301$	12.1353	+	8.81678i	0.699464	+	0.508191i
$302$	−11.1246	−	34.2380i	−0.640149	−	1.97018i
$303$	0.535233	+	1.64728i	0.0307483	+	0.0946337i
$304$	−14.0126	−	10.1807i	−0.803677	−	0.583905i
$305$	7.00629	−	5.09037i	0.401179	−	0.291474i
$306$	7.41641	−	22.8254i	0.423968	−	1.30484i
$307$	−10.3923			−0.593120			−0.296560	−	0.955014i	$-0.595840\pi$
$307$	−10.3923			−0.593120			−0.296560	+	0.955014i	$0.595840\pi$
$308$		0			0
$309$	4.00000			0.227552
$310$	4.28187	−	13.1782i	0.243194	−	0.748473i
$311$	4.85410	−	3.52671i	0.275251	−	0.199981i	−0.441592	−	0.897216i	$-0.645586\pi$
$311$	4.85410	−	3.52671i	0.275251	−	0.199981i	0.716843	+	0.697234i	$0.245586\pi$
$312$	−4.85410	−	3.52671i	−0.274809	−	0.199661i
$313$	3.09017	+	9.51057i	0.174667	+	0.537569i	0.999618	−	0.0276348i	$-0.00879755\pi$
$313$	3.09017	+	9.51057i	0.174667	+	0.537569i	−0.824951	+	0.565204i	$0.808798\pi$
$314$	2.14093	+	6.58911i	0.120820	+	0.371845i
$315$	2.80252	+	2.03615i	0.157904	+	0.114724i
$316$	8.40755	−	6.10844i	0.472962	−	0.343627i
$317$	−1.85410	+	5.70634i	−0.104137	+	0.320500i	−0.989527	−	0.144349i	$-0.953891\pi$
$317$	−1.85410	+	5.70634i	−0.104137	+	0.320500i	0.885390	+	0.464849i	$0.153891\pi$
$318$	−10.3923			−0.582772
$319$		0			0
$320$	−1.00000			−0.0559017
$321$	−0.535233	+	1.64728i	−0.0298738	+	0.0919421i
$322$		0			0
$323$	−19.4164	−	14.1068i	−1.08036	−	0.784926i
$324$	0.309017	+	0.951057i	0.0171676	+	0.0528365i
$325$	1.07047	+	3.29456i	0.0593788	+	0.182749i
$326$	26.6239	+	19.3434i	1.47456	+	1.07133i
$327$	1.40126	−	1.01807i	0.0774898	−	0.0562996i
$328$	−6.48936	+	19.9722i	−0.358315	+	1.10278i
$329$	−15.5885			−0.859419
$330$		0			0
$331$	−34.0000			−1.86881			−0.934405	−	0.356214i	$-0.884068\pi$
$331$	−34.0000			−1.86881			−0.934405	+	0.356214i	$0.884068\pi$
$332$	1.07047	−	3.29456i	0.0587495	−	0.180812i
$333$	−12.9443	+	9.40456i	−0.709342	+	0.515367i
$334$	7.28115	+	5.29007i	0.398407	+	0.289460i
$335$	1.54508	+	4.75528i	0.0844170	+	0.259809i
$336$	−2.67617	−	8.23639i	−0.145997	−	0.449332i
$337$	−8.40755	−	6.10844i	−0.457988	−	0.332748i	0.334753	−	0.942306i	$-0.391347\pi$
$337$	−8.40755	−	6.10844i	−0.457988	−	0.332748i	−0.792742	+	0.609558i	$0.791347\pi$
$338$	1.40126	−	1.01807i	0.0762184	−	0.0553759i
$339$	1.85410	−	5.70634i	0.100701	−	0.309926i
$340$	6.92820			0.375735
$341$		0			0
$342$	12.0000			0.648886
$343$	5.88756	−	18.1201i	0.317899	−	0.978391i
$344$	12.1353	−	8.81678i	0.654289	−	0.475369i
$345$		0			0
$346$	5.56231	+	17.1190i	0.299031	+	0.920324i
$347$	−3.74663	−	11.5309i	−0.201130	−	0.619014i	−0.999850	−	0.0173113i	$-0.994489\pi$
$347$	−3.74663	−	11.5309i	−0.201130	−	0.619014i	0.798720	−	0.601702i	$-0.205511\pi$
$348$		0			0
$349$	−28.0252	+	20.3615i	−1.50015	+	1.08992i	−0.529833	+	0.848102i	$0.677745\pi$
$349$	−28.0252	+	20.3615i	−1.50015	+	1.08992i	−0.970320	+	0.241823i	$0.922255\pi$
$350$	−0.927051	+	2.85317i	−0.0495530	+	0.152508i
$351$	17.3205			0.924500
$352$		0			0
$353$	24.0000			1.27739			0.638696	−	0.769460i	$-0.279474\pi$
$353$	24.0000			1.27739			0.638696	+	0.769460i	$0.279474\pi$
$354$	6.42280	−	19.7673i	0.341368	−	1.05062i
$355$	−9.70820	+	7.05342i	−0.515258	+	0.374357i
$356$	−2.42705	−	1.76336i	−0.128633	−	0.0934577i
$357$	−3.70820	−	11.4127i	−0.196259	−	0.604023i
$358$	−9.63420	−	29.6510i	−0.509183	−	1.56710i
$359$	2.80252	+	2.03615i	0.147911	+	0.107464i	0.659280	−	0.751898i	$-0.270861\pi$
$359$	2.80252	+	2.03615i	0.147911	+	0.107464i	−0.511369	+	0.859361i	$0.670861\pi$
$360$	2.80252	−	2.03615i	0.147706	−	0.107314i
$361$	−2.16312	+	6.65740i	−0.113848	+	0.350389i
$362$	19.0526			1.00138
$363$		0			0
$364$	−6.00000			−0.314485
$365$		0			0
$366$	12.1353	−	8.81678i	0.634320	−	0.460860i
$367$	−13.7533	−	9.99235i	−0.717916	−	0.521596i	0.167802	−	0.985821i	$-0.446333\pi$
$367$	−13.7533	−	9.99235i	−0.717916	−	0.521596i	−0.885718	+	0.464224i	$0.846333\pi$
$368$		0			0
$369$	−7.49326	−	23.0619i	−0.390084	−	1.20055i
$370$	−11.2101	−	8.14459i	−0.582784	−	0.423417i
$371$	8.40755	−	6.10844i	0.436498	−	0.317135i
$372$	2.47214	−	7.60845i	0.128174	−	0.394480i
$373$	−13.8564			−0.717458			−0.358729	−	0.933442i	$-0.616790\pi$
$373$	−13.8564			−0.717458			−0.358729	+	0.933442i	$0.616790\pi$
$374$		0			0
$375$	1.00000			0.0516398
$376$	−4.81710	+	14.8255i	−0.248423	+	0.764567i
$377$		0			0
$378$	12.1353	+	8.81678i	0.624170	+	0.453486i
$379$	−10.5066	−	32.3359i	−0.539687	−	1.66098i	−0.733299	−	0.679907i	$-0.762020\pi$
$379$	−10.5066	−	32.3359i	−0.539687	−	1.66098i	0.193612	−	0.981078i	$-0.437980\pi$
$380$	1.07047	+	3.29456i	0.0549138	+	0.169007i
$381$	1.40126	+	1.01807i	0.0717886	+	0.0521575i
$382$	8.40755	−	6.10844i	0.430168	−	0.312535i
$383$	7.41641	−	22.8254i	0.378961	−	1.16632i	−0.561807	−	0.827269i	$-0.689894\pi$
$383$	7.41641	−	22.8254i	0.378961	−	1.16632i	0.940767	−	0.339053i	$-0.110106\pi$
$384$	−12.1244			−0.618718
$385$		0			0
$386$	−6.00000			−0.305392
$387$	−5.35233	+	16.4728i	−0.272074	+	0.837359i
$388$	8.09017	−	5.87785i	0.410716	−	0.298403i
$389$	−2.42705	−	1.76336i	−0.123056	−	0.0894057i	0.524555	−	0.851377i	$-0.324232\pi$
$389$	−2.42705	−	1.76336i	−0.123056	−	0.0894057i	−0.647611	+	0.761971i	$0.724232\pi$
$390$	1.85410	+	5.70634i	0.0938861	+	0.288952i
$391$		0			0
$392$	−5.60503	−	4.07230i	−0.283097	−	0.205682i
$393$	−2.80252	+	2.03615i	−0.141368	+	0.102710i
$394$	−5.56231	+	17.1190i	−0.280225	+	0.862444i
$395$	10.3923			0.522894
$396$		0			0
$397$	20.0000			1.00377			0.501886	−	0.864934i	$-0.332640\pi$
$397$	20.0000			1.00377			0.501886	+	0.864934i	$0.332640\pi$
$398$	−7.49326	+	23.0619i	−0.375603	+	1.15599i
$399$	4.85410	−	3.52671i	0.243009	−	0.176556i
$400$	4.04508	+	2.93893i	0.202254	+	0.146946i
$401$	8.34346	+	25.6785i	0.416652	+	1.28232i	0.910765	+	0.412926i	$0.135493\pi$
$401$	8.34346	+	25.6785i	0.416652	+	1.28232i	−0.494112	+	0.869398i	$0.664507\pi$
$402$	2.67617	+	8.23639i	0.133475	+	0.410794i
$403$	22.4201	+	16.2892i	1.11683	+	0.811422i
$404$	1.40126	−	1.01807i	0.0697152	−	0.0506511i
$405$	−0.309017	+	0.951057i	−0.0153552	+	0.0472584i
$406$		0			0
$407$		0			0
$408$	−12.0000			−0.594089
$409$	1.60570	−	4.94183i	0.0793967	−	0.244358i	−0.903478	−	0.428635i	$-0.858994\pi$
$409$	1.60570	−	4.94183i	0.0793967	−	0.244358i	0.982874	+	0.184277i	$0.0589945\pi$
$410$	16.9894	−	12.3435i	0.839045	−	0.609602i
$411$	14.5623	+	10.5801i	0.718306	+	0.521880i
$412$	−1.23607	−	3.80423i	−0.0608967	−	0.187421i
$413$	6.42280	+	19.7673i	0.316045	+	0.972687i
$414$		0			0
$415$	2.80252	−	2.03615i	0.137570	−	0.0999506i
$416$	−5.56231	+	17.1190i	−0.272714	+	0.839329i
$417$	−13.8564			−0.678551
$418$		0			0
$419$	18.0000			0.879358			0.439679	−	0.898155i	$-0.355092\pi$
$419$	18.0000			0.879358			0.439679	+	0.898155i	$0.355092\pi$
$420$	−0.535233	+	1.64728i	−0.0261167	+	0.0803789i
$421$	13.7533	−	9.99235i	0.670294	−	0.486997i	−0.199829	−	0.979831i	$-0.564039\pi$
$421$	13.7533	−	9.99235i	0.670294	−	0.486997i	0.870124	+	0.492833i	$0.164039\pi$
$422$		0			0
$423$	−5.56231	−	17.1190i	−0.270449	−	0.832355i
$424$	−3.21140	−	9.88367i	−0.155959	−	0.479993i
$425$	5.60503	+	4.07230i	0.271884	+	0.197535i
$426$	−16.8151	+	12.2169i	−0.814694	+	0.591910i
$427$	−4.63525	+	14.2658i	−0.224316	+	0.690373i
$428$	1.73205			0.0837218
$429$		0			0
$430$	−15.0000			−0.723364
$431$	11.7751	−	36.2401i	0.567188	−	1.74563i	−0.0941714	−	0.995556i	$-0.530020\pi$
$431$	11.7751	−	36.2401i	0.567188	−	1.74563i	0.661359	−	0.750069i	$-0.269980\pi$
$432$	20.2254	−	14.6946i	0.973096	−	0.706996i
$433$	−25.8885	−	18.8091i	−1.24412	−	0.903909i	−0.246258	−	0.969204i	$-0.579201\pi$
$433$	−25.8885	−	18.8091i	−1.24412	−	0.903909i	−0.997866	+	0.0652953i	$0.979201\pi$
$434$	7.41641	+	22.8254i	0.355999	+	1.09565i
$435$		0			0
$436$	−1.40126	−	1.01807i	−0.0671081	−	0.0487569i
$437$		0			0
$438$		0			0
$439$	−27.7128			−1.32266			−0.661330	−	0.750095i	$-0.730008\pi$
$439$	−27.7128			−1.32266			−0.661330	+	0.750095i	$0.730008\pi$
$440$		0			0
$441$	8.00000			0.380952
$442$	−12.8456	+	39.5347i	−0.611003	+	1.88047i
$443$	12.1353	−	8.81678i	0.576563	−	0.418898i	−0.260920	−	0.965360i	$-0.584026\pi$
$443$	12.1353	−	8.81678i	0.576563	−	0.418898i	0.837484	+	0.546463i	$0.184026\pi$
$444$	−6.47214	−	4.70228i	−0.307154	−	0.223160i
$445$	−0.927051	−	2.85317i	−0.0439464	−	0.135253i
$446$	−10.1694	−	31.2983i	−0.481536	−	1.48202i
$447$	−15.4138	−	11.1988i	−0.729050	−	0.529686i
$448$	1.40126	−	1.01807i	0.0662032	−	0.0480995i
$449$	−4.63525	+	14.2658i	−0.218751	+	0.673247i	0.780115	+	0.625636i	$0.215161\pi$
$449$	−4.63525	+	14.2658i	−0.218751	+	0.673247i	−0.998866	+	0.0476105i	$0.984839\pi$
$450$	−3.46410			−0.163299
$451$		0			0
$452$	−6.00000			−0.282216
$453$	6.42280	−	19.7673i	0.301769	−	0.928751i
$454$	−26.6976	+	19.3969i	−1.25298	+	0.910342i
$455$	−4.85410	−	3.52671i	−0.227564	−	0.165335i
$456$	−1.85410	−	5.70634i	−0.0868263	−	0.267224i
$457$	6.42280	+	19.7673i	0.300446	+	0.924677i	0.981338	+	0.192293i	$0.0615924\pi$
$457$	6.42280	+	19.7673i	0.300446	+	0.924677i	−0.680892	+	0.732384i	$0.738408\pi$
$458$	−9.80881	−	7.12652i	−0.458336	−	0.333000i
$459$	28.0252	−	20.3615i	1.30810	−	0.950392i
$460$		0			0
$461$	−12.1244			−0.564688			−0.282344	−	0.959313i	$-0.591112\pi$
$461$	−12.1244			−0.564688			−0.282344	+	0.959313i	$0.591112\pi$
$462$		0			0
$463$	41.0000			1.90543			0.952716	−	0.303863i	$-0.0982765\pi$
$463$	41.0000			1.90543			0.952716	+	0.303863i	$0.0982765\pi$
$464$		0			0
$465$	6.47214	−	4.70228i	0.300138	−	0.218063i
$466$	4.85410	+	3.52671i	0.224862	+	0.163372i
$467$	0.927051	+	2.85317i	0.0428988	+	0.132029i	0.970212	−	0.242257i	$-0.0778878\pi$
$467$	0.927051	+	2.85317i	0.0428988	+	0.132029i	−0.927313	+	0.374286i	$0.877888\pi$
$468$	−2.14093	−	6.58911i	−0.0989646	−	0.304582i
$469$	−7.00629	−	5.09037i	−0.323521	−	0.235051i
$470$	12.6113	−	9.16267i	0.581717	−	0.422642i
$471$	−1.23607	+	3.80423i	−0.0569550	+	0.175289i
$472$	20.7846			0.956689
$473$		0			0
$474$	18.0000			0.826767
$475$	−1.07047	+	3.29456i	−0.0491164	+	0.151165i
$476$	−9.70820	+	7.05342i	−0.444975	+	0.323293i
$477$	9.70820	+	7.05342i	0.444508	+	0.322954i
$478$	1.85410	+	5.70634i	0.0848047	+	0.261002i
$479$	3.21140	+	9.88367i	0.146733	+	0.451596i	0.997230	−	0.0743832i	$-0.0236988\pi$
$479$	3.21140	+	9.88367i	0.146733	+	0.451596i	−0.850497	+	0.525980i	$0.823699\pi$
$480$	4.20378	+	3.05422i	0.191875	+	0.139406i
$481$	22.4201	−	16.2892i	1.02227	−	0.742723i
$482$	−10.1976	+	31.3849i	−0.464486	+	1.42954i
$483$		0			0
$484$		0			0
$485$	10.0000			0.454077
$486$	−8.56373	+	26.3565i	−0.388459	+	1.19555i
$487$	16.1803	−	11.7557i	0.733201	−	0.532702i	−0.157373	−	0.987539i	$-0.550303\pi$
$487$	16.1803	−	11.7557i	0.733201	−	0.532702i	0.890575	+	0.454837i	$0.150303\pi$
$488$	12.1353	+	8.81678i	0.549337	+	0.399117i
$489$	5.87132	+	18.0701i	0.265510	+	0.817157i
$490$	2.14093	+	6.58911i	0.0967175	+	0.297666i
$491$	−19.6176	−	14.2530i	−0.885331	−	0.643230i	0.0493256	−	0.998783i	$-0.484293\pi$
$491$	−19.6176	−	14.2530i	−0.885331	−	0.643230i	−0.934656	+	0.355552i	$0.884293\pi$
$492$	9.80881	−	7.12652i	0.442215	−	0.321288i
$493$		0			0
$494$	−20.7846			−0.935144
$495$		0			0
$496$	40.0000			1.79605
$497$	6.42280	−	19.7673i	0.288102	−	0.886686i
$498$	4.85410	−	3.52671i	0.217518	−	0.158036i
$499$	30.7426	+	22.3358i	1.37623	+	0.999890i	0.997221	+	0.0744963i	$0.0237349\pi$
$499$	30.7426	+	22.3358i	1.37623	+	0.999890i	0.379009	+	0.925393i	$0.376265\pi$
$500$	−0.309017	−	0.951057i	−0.0138197	−	0.0425325i
$501$	1.60570	+	4.94183i	0.0717374	+	0.220785i
$502$		0			0
$503$	−7.00629	+	5.09037i	−0.312395	+	0.226968i	−0.732924	−	0.680311i	$-0.761845\pi$
$503$	−7.00629	+	5.09037i	−0.312395	+	0.226968i	0.420528	+	0.907279i	$0.361845\pi$
$504$	−1.85410	+	5.70634i	−0.0825883	+	0.254181i
$505$	1.73205			0.0770752
$506$		0			0
$507$	1.00000			0.0444116
$508$	0.535233	−	1.64728i	0.0237471	−	0.0730862i
$509$	−12.1353	+	8.81678i	−0.537886	+	0.390797i	−0.823299	−	0.567608i	$-0.807869\pi$
$509$	−12.1353	+	8.81678i	−0.537886	+	0.390797i	0.285413	+	0.958404i	$0.407869\pi$
$510$	9.70820	+	7.05342i	0.429886	+	0.312331i
$511$		0			0
$512$	2.67617	+	8.23639i	0.118271	+	0.364000i
$513$	14.0126	+	10.1807i	0.618671	+	0.449491i
$514$	−16.8151	+	12.2169i	−0.741682	+	0.538864i
$515$	1.23607	−	3.80423i	0.0544677	−	0.167634i
$516$	−8.66025			−0.381246
$517$		0			0
$518$	24.0000			1.05450
$519$	−3.21140	+	9.88367i	−0.140965	+	0.433845i
$520$	−4.85410	+	3.52671i	−0.212866	+	0.154657i
$521$	−12.1353	−	8.81678i	−0.531655	−	0.386270i	0.289321	−	0.957232i	$-0.406570\pi$
$521$	−12.1353	−	8.81678i	−0.531655	−	0.386270i	−0.820977	+	0.570962i	$0.806570\pi$
$522$		0			0
$523$	−5.35233	−	16.4728i	−0.234041	−	0.720304i	−0.997247	−	0.0741493i	$-0.976376\pi$
$523$	−5.35233	−	16.4728i	−0.234041	−	0.720304i	0.763206	−	0.646155i	$-0.223624\pi$
$524$	2.80252	+	2.03615i	0.122429	+	0.0889495i
$525$	−1.40126	+	1.01807i	−0.0611559	+	0.0444324i
$526$	12.9787	−	39.9444i	0.565899	−	1.74166i
$527$	55.4256			2.41438
$528$		0			0
$529$	−23.0000			−1.00000
$530$	−3.21140	+	9.88367i	−0.139494	+	0.429319i
$531$	−19.4164	+	14.1068i	−0.842600	+	0.612185i
$532$	−4.85410	−	3.52671i	−0.210452	−	0.152902i
$533$	12.9787	+	39.9444i	0.562170	+	1.73018i
$534$	−1.60570	−	4.94183i	−0.0694854	−	0.213854i
$535$	1.40126	+	1.01807i	0.0605817	+	0.0440152i
$536$	−7.00629	+	5.09037i	−0.302626	+	0.219870i
$537$	5.56231	−	17.1190i	0.240031	−	0.738740i
$538$	−25.9808			−1.12011
$539$		0			0
$540$	−5.00000			−0.215166
$541$	−1.60570	+	4.94183i	−0.0690344	+	0.212466i	−0.979622	−	0.200850i	$-0.935630\pi$
$541$	−1.60570	+	4.94183i	−0.0690344	+	0.212466i	0.910588	+	0.413316i	$0.135630\pi$
$542$	19.4164	−	14.1068i	0.834006	−	0.605941i
$543$	8.89919	+	6.46564i	0.381901	+	0.277467i
$544$	11.1246	+	34.2380i	0.476964	+	1.46794i
$545$	−0.535233	−	1.64728i	−0.0229269	−	0.0705616i
$546$	−8.40755	−	6.10844i	−0.359810	−	0.261417i
$547$	36.4327	−	26.4699i	1.55775	−	1.13177i	0.619927	−	0.784659i	$-0.287162\pi$
$547$	36.4327	−	26.4699i	1.55775	−	1.13177i	0.937823	−	0.347113i	$-0.112838\pi$
$548$	5.56231	−	17.1190i	0.237610	−	0.731288i
$549$	−17.3205			−0.739221
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−14.5623	+	10.5801i	−0.619252	+	0.449913i
$554$	−14.5623	−	10.5801i	−0.618693	−	0.449507i
$555$	−2.47214	−	7.60845i	−0.104936	−	0.322961i
$556$	4.28187	+	13.1782i	0.181592	+	0.558881i
$557$	5.60503	+	4.07230i	0.237493	+	0.172549i	0.700166	−	0.713980i	$-0.253109\pi$
$557$	5.60503	+	4.07230i	0.237493	+	0.172549i	−0.462673	+	0.886529i	$0.653109\pi$
$558$	−22.4201	+	16.2892i	−0.949120	+	0.689576i
$559$	9.27051	−	28.5317i	0.392101	−	1.20676i
$560$	−8.66025			−0.365963
$561$		0			0
$562$	−12.0000			−0.506189
$563$	−4.81710	+	14.8255i	−0.203016	+	0.624820i	0.796773	+	0.604279i	$0.206539\pi$
$563$	−4.81710	+	14.8255i	−0.203016	+	0.624820i	−0.999789	+	0.0205411i	$0.993461\pi$
$564$	7.28115	−	5.29007i	0.306592	−	0.222752i
$565$	−4.85410	−	3.52671i	−0.204214	−	0.148370i
$566$	−2.78115	−	8.55951i	−0.116901	−	0.359783i
$567$	−0.535233	−	1.64728i	−0.0224777	−	0.0691792i
$568$	−16.8151	−	12.2169i	−0.705546	−	0.512609i
$569$	1.40126	−	1.01807i	0.0587438	−	0.0426799i	−0.558026	−	0.829824i	$-0.688441\pi$
$569$	1.40126	−	1.01807i	0.0587438	−	0.0426799i	0.616770	+	0.787144i	$0.288441\pi$
$570$	−1.85410	+	5.70634i	−0.0776598	+	0.239012i
$571$	−3.46410			−0.144968			−0.0724841	−	0.997370i	$-0.523093\pi$
$571$	−3.46410			−0.144968			−0.0724841	+	0.997370i	$0.523093\pi$
$572$		0			0
$573$	6.00000			0.250654
$574$	−11.2399	+	34.5928i	−0.469144	+	1.44388i
$575$		0			0
$576$	1.61803	+	1.17557i	0.0674181	+	0.0489821i
$577$	−6.18034	−	19.0211i	−0.257291	−	0.791860i	−0.993370	−	0.114964i	$-0.963325\pi$
$577$	−6.18034	−	19.0211i	−0.257291	−	0.791860i	0.736079	−	0.676896i	$-0.236675\pi$
$578$	16.5922	+	51.0656i	0.690146	+	2.12405i
$579$	−2.80252	−	2.03615i	−0.116469	−	0.0846194i
$580$		0			0
$581$	−1.85410	+	5.70634i	−0.0769211	+	0.236739i
$582$	17.3205			0.717958
$583$		0			0
$584$		0			0
$585$	2.14093	−	6.58911i	0.0885167	−	0.272426i
$586$	9.70820	−	7.05342i	0.401042	−	0.291374i
$587$	−16.9894	−	12.3435i	−0.701226	−	0.509470i	0.179105	−	0.983830i	$-0.442680\pi$
$587$	−16.9894	−	12.3435i	−0.701226	−	0.509470i	−0.880331	+	0.474360i	$0.842680\pi$
$588$	1.23607	+	3.80423i	0.0509746	+	0.156884i
$589$	8.56373	+	26.3565i	0.352862	+	1.08600i
$590$	−16.8151	−	12.2169i	−0.692267	−	0.502961i
$591$	−8.40755	+	6.10844i	−0.345840	+	0.251268i
$592$	12.3607	−	38.0423i	0.508021	−	1.56353i
$593$	24.2487			0.995775			0.497888	−	0.867242i	$-0.334109\pi$
$593$	24.2487			0.995775			0.497888	+	0.867242i	$0.334109\pi$
$594$		0			0
$595$	−12.0000			−0.491952
$596$	−5.88756	+	18.1201i	−0.241164	+	0.742227i
$597$	−11.3262	+	8.22899i	−0.463552	+	0.336790i
$598$		0			0
$599$	9.27051	+	28.5317i	0.378783	+	1.16577i	0.940891	+	0.338710i	$0.109990\pi$
$599$	9.27051	+	28.5317i	0.378783	+	1.16577i	−0.562108	+	0.827064i	$0.690010\pi$
$600$	0.535233	+	1.64728i	0.0218508	+	0.0672499i
$601$	−16.8151	−	12.2169i	−0.685902	−	0.498337i	0.189408	−	0.981898i	$-0.439343\pi$
$601$	−16.8151	−	12.2169i	−0.685902	−	0.498337i	−0.875311	+	0.483561i	$0.839343\pi$
$602$	21.0189	−	15.2711i	0.856666	−	0.622404i
$603$	3.09017	−	9.51057i	0.125841	−	0.387300i
$604$	−20.7846			−0.845714
$605$		0			0
$606$	3.00000			0.121867
$607$	−1.07047	+	3.29456i	−0.0434489	+	0.133722i	−0.970428	−	0.241391i	$-0.922396\pi$
$607$	−1.07047	+	3.29456i	−0.0434489	+	0.133722i	0.926979	+	0.375113i	$0.122396\pi$
$608$	−14.5623	+	10.5801i	−0.590579	+	0.429081i
$609$		0			0
$610$	−4.63525	−	14.2658i	−0.187676	−	0.577607i
$611$	9.63420	+	29.6510i	0.389758	+	1.19955i
$612$	−11.2101	−	8.14459i	−0.453140	−	0.329226i
$613$	8.40755	−	6.10844i	0.339578	−	0.246718i	−0.404906	−	0.914358i	$-0.632696\pi$
$613$	8.40755	−	6.10844i	0.339578	−	0.246718i	0.744484	+	0.667641i	$0.232696\pi$
$614$	−5.56231	+	17.1190i	−0.224476	+	0.690867i
$615$	12.1244			0.488901
$616$		0			0
$617$	−36.0000			−1.44931			−0.724653	−	0.689114i	$-0.758000\pi$
$617$	−36.0000			−1.44931			−0.724653	+	0.689114i	$0.758000\pi$
$618$	2.14093	−	6.58911i	0.0861209	−	0.265053i
$619$	−16.1803	+	11.7557i	−0.650343	+	0.472502i	−0.863388	−	0.504541i	$-0.831662\pi$
$619$	−16.1803	+	11.7557i	−0.650343	+	0.472502i	0.213045	+	0.977042i	$0.431662\pi$
$620$	−6.47214	−	4.70228i	−0.259927	−	0.188848i
$621$		0			0
$622$	−3.21140	−	9.88367i	−0.128765	−	0.396299i
$623$	4.20378	+	3.05422i	0.168421	+	0.122365i
$624$	−14.0126	+	10.1807i	−0.560952	+	0.407556i
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	17.3205			0.692267
$627$		0			0
$628$	4.00000			0.159617
$629$	17.1275	−	52.7129i	0.682917	−	2.10180i
$630$	4.85410	−	3.52671i	0.193392	−	0.140508i
$631$	−22.6525	−	16.4580i	−0.901781	−	0.655182i	0.0371420	−	0.999310i	$-0.488175\pi$
$631$	−22.6525	−	16.4580i	−0.901781	−	0.655182i	−0.938923	+	0.344128i	$0.888175\pi$
$632$	5.56231	+	17.1190i	0.221257	+	0.680958i
$633$		0			0
$634$	8.40755	+	6.10844i	0.333907	+	0.242597i
$635$	1.40126	−	1.01807i	0.0556072	−	0.0404010i
$636$	−1.85410	+	5.70634i	−0.0735199	+	0.226271i
$637$	−13.8564			−0.549011
$638$		0			0
$639$	24.0000			0.949425
$640$	−3.74663	+	11.5309i	−0.148099	+	0.455801i
$641$	−24.2705	+	17.6336i	−0.958628	+	0.696484i	−0.952832	−	0.303500i	$-0.901845\pi$
$641$	−24.2705	+	17.6336i	−0.958628	+	0.696484i	−0.00579592	+	0.999983i	$0.501845\pi$
$642$	2.42705	+	1.76336i	0.0957881	+	0.0695941i
$643$	−9.57953	−	29.4828i	−0.377780	−	1.16269i	−0.941584	−	0.336778i	$-0.890663\pi$
$643$	−9.57953	−	29.4828i	−0.377780	−	1.16269i	0.563804	−	0.825908i	$-0.309337\pi$
$644$		0			0
$645$	−7.00629	−	5.09037i	−0.275873	−	0.200433i
$646$	−33.6302	+	24.4338i	−1.32316	+	0.961334i
$647$	10.1976	−	31.3849i	0.400907	−	1.23387i	−0.523357	−	0.852114i	$-0.675321\pi$
$647$	10.1976	−	31.3849i	0.400907	−	1.23387i	0.924264	−	0.381753i	$-0.124679\pi$
$648$	−1.73205			−0.0680414
$649$		0			0
$650$	6.00000			0.235339
$651$	−4.28187	+	13.1782i	−0.167820	+	0.516495i
$652$	15.3713	−	11.1679i	0.601987	−	0.437369i
$653$	24.2705	+	17.6336i	0.949778	+	0.690054i	0.950754	−	0.309945i	$-0.100311\pi$
$653$	24.2705	+	17.6336i	0.949778	+	0.690054i	−0.000976014		1.00000i	$0.500311\pi$
$654$	−0.927051	−	2.85317i	−0.0362506	−	0.111568i
$655$	1.07047	+	3.29456i	0.0418266	+	0.128729i
$656$	49.0440	+	35.6326i	1.91485	+	1.39122i
$657$		0			0
$658$	−8.34346	+	25.6785i	−0.325262	+	1.00105i
$659$	3.46410			0.134942			0.0674711	−	0.997721i	$-0.478507\pi$
$659$	3.46410			0.134942			0.0674711	+	0.997721i	$0.478507\pi$
$660$		0			0
$661$	37.0000			1.43913			0.719567	−	0.694423i	$-0.244340\pi$
$661$	37.0000			1.43913			0.719567	+	0.694423i	$0.244340\pi$
$662$	−18.1979	+	56.0075i	−0.707283	+	2.17679i
$663$	−19.4164	+	14.1068i	−0.754071	+	0.547865i
$664$	4.85410	+	3.52671i	0.188376	+	0.136863i
$665$	−1.85410	−	5.70634i	−0.0718990	−	0.221282i
$666$	8.56373	+	26.3565i	0.331838	+	1.02129i
$667$		0			0
$668$	4.20378	−	3.05422i	0.162649	−	0.118171i
$669$	5.87132	−	18.0701i	0.226998	−	0.698629i
$670$	8.66025			0.334575
$671$		0			0
$672$	−9.00000			−0.347183
$673$	−6.42280	+	19.7673i	−0.247581	+	0.761975i	0.747621	+	0.664126i	$0.231196\pi$
$673$	−6.42280	+	19.7673i	−0.247581	+	0.761975i	−0.995201	+	0.0978489i	$0.968804\pi$
$674$	−14.5623	+	10.5801i	−0.560919	+	0.407532i
$675$	−4.04508	−	2.93893i	−0.155695	−	0.113119i
$676$	−0.309017	−	0.951057i	−0.0118853	−	0.0365791i
$677$	8.56373	+	26.3565i	0.329131	+	1.01296i	0.969541	+	0.244928i	$0.0787643\pi$
$677$	8.56373	+	26.3565i	0.329131	+	1.01296i	−0.640410	+	0.768033i	$0.721236\pi$
$678$	−8.40755	−	6.10844i	−0.322890	−	0.234593i
$679$	−14.0126	+	10.1807i	−0.537754	+	0.390701i
$680$	−3.70820	+	11.4127i	−0.142203	+	0.437656i
$681$	−19.0526			−0.730096
$682$		0			0
$683$	−21.0000			−0.803543			−0.401771	−	0.915740i	$-0.631605\pi$
$683$	−21.0000			−0.803543			−0.401771	+	0.915740i	$0.631605\pi$
$684$	2.14093	−	6.58911i	0.0818606	−	0.251941i
$685$	14.5623	−	10.5801i	0.556397	−	0.404246i
$686$	−26.6976	−	19.3969i	−1.01932	−	0.740578i
$687$	−2.16312	−	6.65740i	−0.0825281	−	0.253995i
$688$	−13.3808	−	41.1820i	−0.510139	−	1.57005i
$689$	−16.8151	−	12.2169i	−0.640604	−	0.465426i
$690$		0			0
$691$	−3.09017	+	9.51057i	−0.117556	+	0.361799i	−0.992471	−	0.122476i	$-0.960917\pi$
$691$	−3.09017	+	9.51057i	−0.117556	+	0.361799i	0.874916	+	0.484275i	$0.160917\pi$
$692$	10.3923			0.395056
$693$		0			0
$694$	−21.0000			−0.797149
$695$	−4.28187	+	13.1782i	−0.162420	+	0.499879i
$696$		0			0
$697$	67.9574	+	49.3740i	2.57407	+	1.87017i
$698$	18.5410	+	57.0634i	0.701788	+	2.15988i
$699$	1.07047	+	3.29456i	0.0404888	+	0.124612i
$700$	1.40126	+	1.01807i	0.0529626	+	0.0384796i
$701$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$701$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$702$	9.27051	−	28.5317i	0.349893	−	1.07686i
$703$	27.7128			1.04521
$704$		0			0
$705$	9.00000			0.338960
$706$	12.8456	−	39.5347i	0.483450	−	1.48791i
$707$	−2.42705	+	1.76336i	−0.0912786	+	0.0663178i
$708$	−9.70820	−	7.05342i	−0.364857	−	0.265084i
$709$	7.72542	+	23.7764i	0.290134	+	0.892942i	0.984813	+	0.173621i	$0.0555468\pi$
$709$	7.72542	+	23.7764i	0.290134	+	0.892942i	−0.694678	+	0.719321i	$0.744453\pi$
$710$	6.42280	+	19.7673i	0.241043	+	0.741855i
$711$	−16.8151	−	12.2169i	−0.630616	−	0.458169i
$712$	4.20378	−	3.05422i	0.157543	−	0.114462i
$713$		0			0
$714$	−20.7846			−0.777844
$715$		0			0
$716$	−18.0000			−0.672692
$717$	−1.07047	+	3.29456i	−0.0399773	+	0.123037i
$718$	4.85410	−	3.52671i	0.181153	−	0.131616i
$719$	−4.85410	−	3.52671i	−0.181027	−	0.131524i	0.493581	−	0.869700i	$-0.335688\pi$
$719$	−4.85410	−	3.52671i	−0.181027	−	0.131524i	−0.674609	+	0.738176i	$0.735688\pi$
$720$	−3.09017	−	9.51057i	−0.115164	−	0.354438i
$721$	2.14093	+	6.58911i	0.0797325	+	0.245391i
$722$	9.80881	+	7.12652i	0.365046	+	0.265222i
$723$	−15.4138	+	11.1988i	−0.573247	+	0.416488i
$724$	3.39919	−	10.4616i	0.126330	−	0.388803i
$725$		0			0
$726$		0			0
$727$	1.00000			0.0370879			0.0185440	−	0.999828i	$-0.494097\pi$
$727$	1.00000			0.0370879			0.0185440	+	0.999828i	$0.494097\pi$
$728$	3.21140	−	9.88367i	0.119022	−	0.366313i
$729$	−10.5172	+	7.64121i	−0.389527	+	0.283008i
$730$		0			0
$731$	−18.5410	−	57.0634i	−0.685764	−	2.11057i
$732$	−2.67617	−	8.23639i	−0.0989139	−	0.304426i
$733$	16.8151	+	12.2169i	0.621080	+	0.451241i	0.853299	−	0.521423i	$-0.174598\pi$
$733$	16.8151	+	12.2169i	0.621080	+	0.451241i	−0.232219	+	0.972664i	$0.574598\pi$
$734$	−23.8214	+	17.3073i	−0.879264	+	0.638823i
$735$	−1.23607	+	3.80423i	−0.0455931	+	0.140321i
$736$		0			0
$737$		0			0
$738$	−42.0000			−1.54604
$739$	1.07047	−	3.29456i	0.0393777	−	0.121192i	−0.929435	−	0.368985i	$-0.879705\pi$
$739$	1.07047	−	3.29456i	0.0393777	−	0.121192i	0.968813	+	0.247793i	$0.0797053\pi$
$740$	−6.47214	+	4.70228i	−0.237920	+	0.172859i
$741$	−9.70820	−	7.05342i	−0.356640	−	0.259114i
$742$	−5.56231	−	17.1190i	−0.204199	−	0.628459i
$743$	1.60570	+	4.94183i	0.0589074	+	0.181298i	0.976180	−	0.216961i	$-0.0696144\pi$
$743$	1.60570	+	4.94183i	0.0589074	+	0.181298i	−0.917273	+	0.398259i	$0.869614\pi$
$744$	11.2101	+	8.14459i	0.410981	+	0.298595i
$745$	−15.4138	+	11.1988i	−0.564720	+	0.410293i
$746$	−7.41641	+	22.8254i	−0.271534	+	0.835696i
$747$	−6.92820			−0.253490
$748$		0			0
$749$	−3.00000			−0.109618
$750$	0.535233	−	1.64728i	0.0195440	−	0.0601501i
$751$	11.3262	−	8.22899i	0.413300	−	0.300280i	−0.361636	−	0.932319i	$-0.617782\pi$
$751$	11.3262	−	8.22899i	0.413300	−	0.300280i	0.774937	+	0.632039i	$0.217782\pi$
$752$	36.4058	+	26.4503i	1.32758	+	0.964545i
$753$		0			0
$754$		0			0
$755$	−16.8151	−	12.2169i	−0.611964	−	0.444618i
$756$	7.00629	−	5.09037i	0.254816	−	0.185135i
$757$	−0.618034	+	1.90211i	−0.0224628	+	0.0691335i	−0.961660	−	0.274246i	$-0.911572\pi$
$757$	−0.618034	+	1.90211i	−0.0224628	+	0.0691335i	0.939197	+	0.343380i	$0.111572\pi$
$758$	−58.8897			−2.13897
$759$		0			0
$760$	−6.00000			−0.217643
$761$	10.7047	−	32.9456i	0.388044	−	1.19428i	−0.546204	−	0.837652i	$-0.683928\pi$
$761$	10.7047	−	32.9456i	0.388044	−	1.19428i	0.934248	−	0.356624i	$-0.116072\pi$
$762$	2.42705	−	1.76336i	0.0879228	−	0.0638796i
$763$	2.42705	+	1.76336i	0.0878651	+	0.0638378i
$764$	−1.85410	−	5.70634i	−0.0670791	−	0.206448i
$765$	−4.28187	−	13.1782i	−0.154811	−	0.476460i
$766$	−33.6302	−	24.4338i	−1.21511	−	0.882828i
$767$	33.6302	−	24.4338i	1.21432	−	0.882252i
$768$	−5.87132	+	18.0701i	−0.211863	+	0.652048i
$769$	27.7128			0.999350			0.499675	−	0.866213i	$-0.333453\pi$
$769$	27.7128			0.999350			0.499675	+	0.866213i	$0.333453\pi$
$770$		0			0
$771$	−12.0000			−0.432169
$772$	−1.07047	+	3.29456i	−0.0385269	+	0.118574i
$773$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$773$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$774$	24.2705	+	17.6336i	0.872385	+	0.633825i
$775$	−2.47214	−	7.60845i	−0.0888017	−	0.273304i
$776$	5.35233	+	16.4728i	0.192137	+	0.591338i
$777$	11.2101	+	8.14459i	0.402159	+	0.292186i
$778$	−4.20378	+	3.05422i	−0.150713	+	0.109499i
$779$	−12.9787	+	39.9444i	−0.465011	+	1.43116i
$780$	3.46410			0.124035
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−16.1803	+	11.7557i	−0.577869	+	0.419847i
$785$	3.23607	+	2.35114i	0.115500	+	0.0839158i
$786$	1.85410	+	5.70634i	0.0661336	+	0.203538i
$787$	−8.02850	−	24.7092i	−0.286185	−	0.880787i	−0.986041	−	0.166503i	$-0.946752\pi$
$787$	−8.02850	−	24.7092i	−0.286185	−	0.880787i	0.699856	−	0.714284i	$-0.253248\pi$
$788$	8.40755	+	6.10844i	0.299507	+	0.217604i
$789$	19.6176	−	14.2530i	0.698406	−	0.507421i
$790$	5.56231	−	17.1190i	0.197898	−	0.609067i
$791$	10.3923			0.369508
$792$		0			0
$793$	30.0000			1.06533
$794$	10.7047	−	32.9456i	0.379894	−	1.16919i
$795$	−4.85410	+	3.52671i	−0.172157	+	0.125080i
$796$	11.3262	+	8.22899i	0.401448	+	0.291669i
$797$	−3.70820	−	11.4127i	−0.131351	−	0.404258i	0.863653	−	0.504086i	$-0.168171\pi$
$797$	−3.70820	−	11.4127i	−0.131351	−	0.404258i	−0.995005	+	0.0998284i	$0.968171\pi$
$798$	−3.21140	−	9.88367i	−0.113682	−	0.349878i
$799$	50.4453	+	36.6507i	1.78463	+	1.29661i
$800$	4.20378	−	3.05422i	0.148626	−	0.107983i
$801$	−1.85410	+	5.70634i	−0.0655115	+	0.201624i
$802$	46.7654			1.65134
$803$		0			0
$804$	5.00000			0.176336
$805$		0			0
$806$	38.8328	−	28.2137i	1.36783	−	0.993785i
$807$	−12.1353	−	8.81678i	−0.427181	−	0.310365i
$808$	0.927051	+	2.85317i	0.0326135	+	0.100374i
$809$	−14.9865	−	46.1238i	−0.526898	−	1.62163i	−0.760531	−	0.649301i	$-0.775061\pi$
$809$	−14.9865	−	46.1238i	−0.526898	−	1.62163i	0.233633	−	0.972325i	$-0.424939\pi$
$810$	1.40126	+	1.01807i	0.0492352	+	0.0357715i
$811$	−5.60503	+	4.07230i	−0.196819	+	0.142998i	−0.681830	−	0.731511i	$-0.738816\pi$
$811$	−5.60503	+	4.07230i	−0.196819	+	0.142998i	0.485011	+	0.874508i	$0.338816\pi$
$812$		0			0
$813$	13.8564			0.485965
$814$		0			0
$815$	19.0000			0.665541
$816$	−10.7047	+	32.9456i	−0.374738	+	1.15333i
$817$	24.2705	−	17.6336i	0.849118	−	0.616920i
$818$	−7.28115	−	5.29007i	−0.254580	−	0.184963i
$819$	3.70820	+	11.4127i	0.129575	+	0.398791i
$820$	−3.74663	−	11.5309i	−0.130838	−	0.402678i
$821$	−23.8214	−	17.3073i	−0.831372	−	0.604027i	0.0885749	−	0.996070i	$-0.471769\pi$
$821$	−23.8214	−	17.3073i	−0.831372	−	0.604027i	−0.919947	+	0.392042i	$0.871769\pi$
$822$	25.2227	−	18.3253i	0.879741	−	0.639169i
$823$	5.25329	−	16.1680i	0.183118	−	0.563580i	−0.816793	−	0.576931i	$-0.804250\pi$
$823$	5.25329	−	16.1680i	0.183118	−	0.563580i	0.999911	+	0.0133515i	$0.00425006\pi$
$824$	6.92820			0.241355
$825$		0			0
$826$	36.0000			1.25260
$827$	9.09896	−	28.0037i	0.316402	−	0.973785i	−0.658772	−	0.752343i	$-0.728924\pi$
$827$	9.09896	−	28.0037i	0.316402	−	0.973785i	0.975174	−	0.221442i	$-0.0710764\pi$
$828$		0			0
$829$	−23.4615	−	17.0458i	−0.814851	−	0.592024i	0.100382	−	0.994949i	$-0.467994\pi$
$829$	−23.4615	−	17.0458i	−0.814851	−	0.592024i	−0.915233	+	0.402925i	$0.867994\pi$
$830$	−1.85410	−	5.70634i	−0.0643568	−	0.198070i
$831$	−3.21140	−	9.88367i	−0.111402	−	0.342861i
$832$	−2.80252	−	2.03615i	−0.0971598	−	0.0705907i
$833$	−22.4201	+	16.2892i	−0.776812	+	0.564387i
$834$	−7.41641	+	22.8254i	−0.256809	+	0.790377i
$835$	5.19615			0.179820
$836$		0			0
$837$	−40.0000			−1.38260
$838$	9.63420	−	29.6510i	0.332808	−	1.02428i
$839$	33.9787	−	24.6870i	1.17308	−	0.852289i	0.181702	−	0.983354i	$-0.441839\pi$
$839$	33.9787	−	24.6870i	1.17308	−	0.852289i	0.991374	+	0.131064i	$0.0418395\pi$
$840$	−2.42705	−	1.76336i	−0.0837412	−	0.0608416i
$841$	−8.96149	−	27.5806i	−0.309017	−	0.951057i
$842$	−9.09896	−	28.0037i	−0.313571	−	0.965072i
$843$	−5.60503	−	4.07230i	−0.193048	−	0.140257i
$844$		0			0
$845$	0.309017	−	0.951057i	0.0106305	−	0.0327173i
$846$	−31.1769			−1.07188
$847$		0			0
$848$	−30.0000			−1.03020
$849$	1.60570	−	4.94183i	0.0551075	−	0.169603i
$850$	9.70820	−	7.05342i	0.332989	−	0.241930i
$851$		0			0
$852$	3.70820	+	11.4127i	0.127041	+	0.390992i
$853$	−10.7047	−	32.9456i	−0.366521	−	1.12803i	−0.949023	−	0.315206i	$-0.897926\pi$
$853$	−10.7047	−	32.9456i	−0.366521	−	1.12803i	0.582503	−	0.812829i	$-0.302074\pi$
$854$	21.0189	+	15.2711i	0.719251	+	0.522567i
$855$	5.60503	−	4.07230i	0.191688	−	0.139270i
$856$	−0.927051	+	2.85317i	−0.0316860	+	0.0975193i
$857$	−10.3923			−0.354994			−0.177497	−	0.984121i	$-0.556800\pi$
$857$	−10.3923			−0.354994			−0.177497	+	0.984121i	$0.556800\pi$
$858$		0			0
$859$	14.0000			0.477674			0.238837	−	0.971060i	$-0.423234\pi$
$859$	14.0000			0.477674			0.238837	+	0.971060i	$0.423234\pi$
$860$	−2.67617	+	8.23639i	−0.0912565	+	0.280859i
$861$	−16.9894	+	12.3435i	−0.578996	+	0.420665i
$862$	−53.3951	−	38.7938i	−1.81865	−	1.32132i
$863$	6.48936	+	19.9722i	0.220900	+	0.679861i	0.998682	+	0.0513266i	$0.0163449\pi$
$863$	6.48936	+	19.9722i	0.220900	+	0.679861i	−0.777782	+	0.628535i	$0.783655\pi$
$864$	−8.02850	−	24.7092i	−0.273135	−	0.840623i
$865$	8.40755	+	6.10844i	0.285865	+	0.207693i
$866$	−44.8403	+	32.5784i	−1.52373	+	1.10706i
$867$	−9.57953	+	29.4828i	−0.325338	+	1.00129i
$868$	13.8564			0.470317
$869$		0			0
$870$		0			0
$871$	−5.35233	+	16.4728i	−0.181357	+	0.558159i
$872$	2.42705	−	1.76336i	0.0821903	−	0.0597148i
$873$	−16.1803	−	11.7557i	−0.547622	−	0.397870i
$874$		0			0
$875$	0.535233	+	1.64728i	0.0180942	+	0.0556882i
$876$		0			0
$877$	22.4201	−	16.2892i	0.757074	−	0.550047i	−0.140937	−	0.990019i	$-0.545012\pi$
$877$	22.4201	−	16.2892i	0.757074	−	0.550047i	0.898012	+	0.439972i	$0.145012\pi$
$878$	−14.8328	+	45.6507i	−0.500583	+	1.54064i
$879$	6.92820			0.233682
$880$		0			0
$881$	−21.0000			−0.707508			−0.353754	−	0.935339i	$-0.615095\pi$
$881$	−21.0000			−0.707508			−0.353754	+	0.935339i	$0.615095\pi$
$882$	4.28187	−	13.1782i	0.144178	−	0.443734i
$883$	45.3050	−	32.9160i	1.52463	−	1.10771i	0.565503	−	0.824747i	$-0.308682\pi$
$883$	45.3050	−	32.9160i	1.52463	−	1.10771i	0.959130	−	0.282964i	$-0.0913178\pi$
$884$	19.4164	+	14.1068i	0.653044	+	0.474465i
$885$	−3.70820	−	11.4127i	−0.124650	−	0.383633i
$886$	−8.02850	−	24.7092i	−0.269723	−	0.830121i
$887$	26.6239	+	19.3434i	0.893943	+	0.649488i	0.936903	−	0.349589i	$-0.113679\pi$
$887$	26.6239	+	19.3434i	0.893943	+	0.649488i	−0.0429597	+	0.999077i	$0.513679\pi$
$888$	11.2101	−	8.14459i	0.376185	−	0.273315i
$889$	−0.927051	+	2.85317i	−0.0310923	+	0.0956922i
$890$	−5.19615			−0.174175
$891$		0			0
$892$	−19.0000			−0.636167
$893$	−9.63420	+	29.6510i	−0.322396	+	0.992233i
$894$	−26.6976	+	19.3969i	−0.892900	+	0.648730i
$895$	−14.5623	−	10.5801i	−0.486764	−	0.353655i
$896$	−6.48936	−	19.9722i	−0.216794	−	0.667224i
$897$		0			0
$898$	21.0189	+	15.2711i	0.701409	+	0.509604i
$899$		0			0
$900$	−0.618034	+	1.90211i	−0.0206011	+	0.0634038i
$901$	−41.5692			−1.38487
$902$		0			0
$903$	15.0000			0.499169
$904$	3.21140	−	9.88367i	0.106810	−	0.328726i
$905$	8.89919	−	6.46564i	0.295819	−	0.214925i
$906$	−29.1246	−	21.1603i	−0.967600	−	0.703003i
$907$	5.25329	+	16.1680i	0.174433	+	0.536848i	0.999607	−	0.0280296i	$-0.00892326\pi$
$907$	5.25329	+	16.1680i	0.174433	+	0.536848i	−0.825174	+	0.564878i	$0.808923\pi$
$908$	5.88756	+	18.1201i	0.195386	+	0.601335i
$909$	−2.80252	−	2.03615i	−0.0929536	−	0.0675348i
$910$	−8.40755	+	6.10844i	−0.278708	+	0.202493i
$911$	1.85410	−	5.70634i	0.0614291	−	0.189059i	−0.915632	−	0.402017i	$-0.868309\pi$
$911$	1.85410	−	5.70634i	0.0614291	−	0.189059i	0.977062	+	0.212957i	$0.0683094\pi$
$912$	−17.3205			−0.573539
$913$		0			0
$914$	36.0000			1.19077
$915$	2.67617	−	8.23639i	0.0884713	−	0.272287i
$916$	−5.66312	+	4.11450i	−0.187115	+	0.135947i
$917$	−4.85410	−	3.52671i	−0.160297	−	0.116462i
$918$	−18.5410	−	57.0634i	−0.611945	−	1.88337i
$919$	11.7751	+	36.2401i	0.388426	+	1.19545i	0.933965	+	0.357366i	$0.116325\pi$
$919$	11.7751	+	36.2401i	0.388426	+	1.19545i	−0.545539	+	0.838086i	$0.683675\pi$
$920$		0			0
$921$	−8.40755	+	6.10844i	−0.277038	+	0.201280i
$922$	−6.48936	+	19.9722i	−0.213716	+	0.657749i
$923$	−41.5692			−1.36827
$924$		0			0
$925$	−8.00000			−0.263038
$926$	21.9446	−	67.5384i	0.721143	−	2.21945i
$927$	−6.47214	+	4.70228i	−0.212573	+	0.154443i
$928$		0			0
$929$	5.56231	+	17.1190i	0.182493	+	0.561657i	0.999896	−	0.0144098i	$-0.00458693\pi$
$929$	5.56231	+	17.1190i	0.182493	+	0.561657i	−0.817403	+	0.576066i	$0.804587\pi$
$930$	−4.28187	−	13.1782i	−0.140408	−	0.432131i
$931$	−11.2101	−	8.14459i	−0.367395	−	0.266928i
$932$	2.80252	−	2.03615i	0.0917995	−	0.0666962i
$933$	1.85410	−	5.70634i	0.0607006	−	0.186817i
$934$	5.19615			0.170023
$935$		0			0
$936$	12.0000			0.392232
$937$	−7.49326	+	23.0619i	−0.244794	+	0.753399i	0.750876	+	0.660443i	$0.229632\pi$
$937$	−7.49326	+	23.0619i	−0.244794	+	0.753399i	−0.995670	+	0.0929560i	$0.970368\pi$
$938$	−12.1353	+	8.81678i	−0.396230	+	0.287878i
$939$	8.09017	+	5.87785i	0.264013	+	0.191816i
$940$	−2.78115	−	8.55951i	−0.0907112	−	0.279180i
$941$	−15.5218	−	47.7711i	−0.505995	−	1.55729i	−0.799091	−	0.601209i	$-0.794686\pi$
$941$	−15.5218	−	47.7711i	−0.505995	−	1.55729i	0.293097	−	0.956083i	$-0.405314\pi$
$942$	5.60503	+	4.07230i	0.182622	+	0.132683i
$943$		0			0
$944$	18.5410	−	57.0634i	0.603459	−	1.85726i
$945$	8.66025			0.281718
$946$		0			0
$947$	−12.0000			−0.389948			−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000			−0.389948			−0.194974	+	0.980808i	$0.562462\pi$
$948$	3.21140	−	9.88367i	0.104301	−	0.321007i
$949$		0			0
$950$	4.85410	+	3.52671i	0.157488	+	0.114422i
$951$	1.85410	+	5.70634i	0.0601234	+	0.185041i
$952$	−6.42280	−	19.7673i	−0.208164	−	0.640663i
$953$	−44.8403	−	32.5784i	−1.45252	−	1.05532i	−0.985235	−	0.171210i	$-0.945232\pi$
$953$	−44.8403	−	32.5784i	−1.45252	−	1.05532i	−0.467284	−	0.884107i	$-0.654768\pi$
$954$	16.8151	−	12.2169i	0.544409	−	0.395536i
$955$	1.85410	−	5.70634i	0.0599973	−	0.184653i
$956$	3.46410			0.112037
$957$		0			0
$958$	18.0000			0.581554
$959$	−9.63420	+	29.6510i	−0.311104	+	0.957481i
$960$	−0.809017	+	0.587785i	−0.0261109	+	0.0189707i
$961$	−26.6976	−	19.3969i	−0.861212	−	0.625707i
$962$	−14.8328	−	45.6507i	−0.478229	−	1.47184i
$963$	−1.07047	−	3.29456i	−0.0344953	−	0.106166i
$964$	15.4138	+	11.1988i	0.496446	+	0.360689i
$965$	−2.80252	+	2.03615i	−0.0902162	+	0.0655459i
$966$		0			0
$967$	38.1051			1.22538			0.612689	−	0.790324i	$-0.290088\pi$
$967$	38.1051			1.22538			0.612689	+	0.790324i	$0.290088\pi$
$968$		0			0
$969$	−24.0000			−0.770991
$970$	5.35233	−	16.4728i	0.171853	−	0.528909i
$971$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$971$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$972$	12.9443	+	9.40456i	0.415188	+	0.301652i
$973$	−7.41641	−	22.8254i	−0.237759	−	0.731747i
$974$	−10.7047	−	32.9456i	−0.343000	−	1.05564i
$975$	2.80252	+	2.03615i	0.0897524	+	0.0652089i
$976$	35.0315	−	25.4518i	1.12133	−	0.814694i
$977$	−7.41641	+	22.8254i	−0.237272	+	0.730248i	0.759540	+	0.650461i	$0.225424\pi$
$977$	−7.41641	+	22.8254i	−0.237272	+	0.730248i	−0.996812	+	0.0797873i	$0.974576\pi$
$978$	32.9090			1.05231
$979$		0			0
$980$	4.00000			0.127775
$981$	−1.07047	+	3.29456i	−0.0341774	+	0.105187i
$982$	−33.9787	+	24.6870i	−1.08430	+	0.787793i
$983$	2.42705	+	1.76336i	0.0774109	+	0.0562423i	0.625818	−	0.779969i	$-0.284765\pi$
$983$	2.42705	+	1.76336i	0.0774109	+	0.0562423i	−0.548407	+	0.836212i	$0.684765\pi$
$984$	6.48936	+	19.9722i	0.206873	+	0.636690i
$985$	3.21140	+	9.88367i	0.102324	+	0.314920i
$986$		0			0
$987$	−12.6113	+	9.16267i	−0.401423	+	0.291651i
$988$	−3.70820	+	11.4127i	−0.117974	+	0.363086i
$989$		0			0
$990$		0			0
$991$	−2.00000			−0.0635321			−0.0317660	−	0.999495i	$-0.510113\pi$
$991$	−2.00000			−0.0635321			−0.0317660	+	0.999495i	$0.510113\pi$
$992$	12.8456	−	39.5347i	0.407848	−	1.25523i
$993$	−27.5066	+	19.9847i	−0.872895	+	0.634195i
$994$	−29.1246	−	21.1603i	−0.923777	−	0.671163i
$995$	4.32624	+	13.3148i	0.137151	+	0.422107i
$996$	−1.07047	−	3.29456i	−0.0339190	−	0.104392i
$997$	36.4327	+	26.4699i	1.15384	+	0.838311i	0.988986	−	0.148008i	$-0.0472861\pi$
$997$	36.4327	+	26.4699i	1.15384	+	0.838311i	0.164850	+	0.986319i	$0.447286\pi$
$998$	53.2478	−	38.6868i	1.68553	−	1.22461i
$999$	−12.3607	+	38.0423i	−0.391075	+	1.20360i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.i.251.2		8
11.2	odd	10	inner	605.2.g.i.366.2		8
11.3	even	5	inner	605.2.g.i.81.1		8
11.4	even	5		605.2.a.e.1.2	yes	2
11.5	even	5	inner	605.2.g.i.511.2		8
11.6	odd	10	inner	605.2.g.i.511.1		8
11.7	odd	10		605.2.a.e.1.1	✓	2
11.8	odd	10	inner	605.2.g.i.81.2		8
11.9	even	5	inner	605.2.g.i.366.1		8
11.10	odd	2	inner	605.2.g.i.251.1		8
33.26	odd	10		5445.2.a.u.1.1		2
33.29	even	10		5445.2.a.u.1.2		2
44.7	even	10		9680.2.a.bu.1.1		2
44.15	odd	10		9680.2.a.bu.1.2		2
55.4	even	10		3025.2.a.l.1.1		2
55.29	odd	10		3025.2.a.l.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.a.e.1.1	✓	2	11.7	odd	10
605.2.a.e.1.2	yes	2	11.4	even	5
605.2.g.i.81.1		8	11.3	even	5	inner
605.2.g.i.81.2		8	11.8	odd	10	inner
605.2.g.i.251.1		8	11.10	odd	2	inner
605.2.g.i.251.2		8	1.1	even	1	trivial
605.2.g.i.366.1		8	11.9	even	5	inner
605.2.g.i.366.2		8	11.2	odd	10	inner
605.2.g.i.511.1		8	11.6	odd	10	inner
605.2.g.i.511.2		8	11.5	even	5	inner
3025.2.a.l.1.1		2	55.4	even	10
3025.2.a.l.1.2		2	55.29	odd	10
5445.2.a.u.1.1		2	33.26	odd	10
5445.2.a.u.1.2		2	33.29	even	10
9680.2.a.bu.1.1		2	44.7	even	10
9680.2.a.bu.1.2		2	44.15	odd	10

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.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.535233 - 1.64728i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.535233 - 1.64728i) q^{6} +(1.40126 + 1.01807i) q^{7} +(1.40126 - 1.01807i) q^{8} +(-0.618034 + 1.90211i) q^{9} +O(q^{10})\)	\(q+(0.535233 - 1.64728i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.309017 - 0.951057i) q^{5} +(-0.535233 - 1.64728i) q^{6} +(1.40126 + 1.01807i) q^{7} +(1.40126 - 1.01807i) q^{8} +(-0.618034 + 1.90211i) q^{9} -1.73205 q^{10} -1.00000 q^{12} +(1.07047 - 3.29456i) q^{13} +(2.42705 - 1.76336i) q^{14} +(-0.809017 - 0.587785i) q^{15} +(-1.54508 - 4.75528i) q^{16} +(-2.14093 - 6.58911i) q^{17} +(2.80252 + 2.03615i) q^{18} +(2.80252 - 2.03615i) q^{19} +(-0.309017 + 0.951057i) q^{20} +1.73205 q^{21} +(0.535233 - 1.64728i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(-4.85410 - 3.52671i) q^{26} +(1.54508 + 4.75528i) q^{27} +(-0.535233 - 1.64728i) q^{28} +(-1.40126 + 1.01807i) q^{30} +(-2.47214 + 7.60845i) q^{31} -5.19615 q^{32} -12.0000 q^{34} +(0.535233 - 1.64728i) q^{35} +(1.61803 - 1.17557i) q^{36} +(6.47214 + 4.70228i) q^{37} +(-1.85410 - 5.70634i) q^{38} +(-1.07047 - 3.29456i) q^{39} +(-1.40126 - 1.01807i) q^{40} +(-9.80881 + 7.12652i) q^{41} +(0.927051 - 2.85317i) q^{42} +8.66025 q^{43} +2.00000 q^{45} +(-7.28115 + 5.29007i) q^{47} +(-4.04508 - 2.93893i) q^{48} +(-1.23607 - 3.80423i) q^{49} +(0.535233 + 1.64728i) q^{50} +(-5.60503 - 4.07230i) q^{51} +(-2.80252 + 2.03615i) q^{52} +(1.85410 - 5.70634i) q^{53} +8.66025 q^{54} +3.00000 q^{56} +(1.07047 - 3.29456i) q^{57} +(9.70820 + 7.05342i) q^{59} +(0.309017 + 0.951057i) q^{60} +(2.67617 + 8.23639i) q^{61} +(11.2101 + 8.14459i) q^{62} +(-2.80252 + 2.03615i) q^{63} +(0.309017 - 0.951057i) q^{64} -3.46410 q^{65} -5.00000 q^{67} +(-2.14093 + 6.58911i) q^{68} +(-2.42705 - 1.76336i) q^{70} +(-3.70820 - 11.4127i) q^{71} +(1.07047 + 3.29456i) q^{72} +(11.2101 - 8.14459i) q^{74} +(-0.309017 + 0.951057i) q^{75} -3.46410 q^{76} -6.00000 q^{78} +(-3.21140 + 9.88367i) q^{79} +(-4.04508 + 2.93893i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(6.48936 + 19.9722i) q^{82} +(1.07047 + 3.29456i) q^{83} +(-1.40126 - 1.01807i) q^{84} +(-5.60503 + 4.07230i) q^{85} +(4.63525 - 14.2658i) q^{86} +3.00000 q^{89} +(1.07047 - 3.29456i) q^{90} +(4.85410 - 3.52671i) q^{91} +(2.47214 + 7.60845i) q^{93} +(4.81710 + 14.8255i) q^{94} +(-2.80252 - 2.03615i) q^{95} +(-4.20378 + 3.05422i) q^{96} +(-3.09017 + 9.51057i) q^{97} -6.92820 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 - 2 * q^4 + 2 * q^5 + 4 * q^9	\( 8 q + 2 q^{3} - 2 q^{4} + 2 q^{5} + 4 q^{9} - 8 q^{12} + 6 q^{14} - 2 q^{15} + 10 q^{16} + 2 q^{20} - 2 q^{25} - 12 q^{26} - 10 q^{27} + 16 q^{31} - 96 q^{34} + 4 q^{36} + 16 q^{37} + 12 q^{38} - 6 q^{42} + 16 q^{45} - 18 q^{47} - 10 q^{48} + 8 q^{49} - 12 q^{53} + 24 q^{56} + 24 q^{59} - 2 q^{60} - 2 q^{64} - 40 q^{67} - 6 q^{70} + 24 q^{71} + 2 q^{75} - 48 q^{78} - 10 q^{80} - 2 q^{81} - 42 q^{82} - 30 q^{86} + 24 q^{89} + 12 q^{91} - 16 q^{93} + 20 q^{97}+O(q^{100}) \) 8 * q + 2 * q^3 - 2 * q^4 + 2 * q^5 + 4 * q^9 - 8 * q^12 + 6 * q^14 - 2 * q^15 + 10 * q^16 + 2 * q^20 - 2 * q^25 - 12 * q^26 - 10 * q^27 + 16 * q^31 - 96 * q^34 + 4 * q^36 + 16 * q^37 + 12 * q^38 - 6 * q^42 + 16 * q^45 - 18 * q^47 - 10 * q^48 + 8 * q^49 - 12 * q^53 + 24 * q^56 + 24 * q^59 - 2 * q^60 - 2 * q^64 - 40 * q^67 - 6 * q^70 + 24 * q^71 + 2 * q^75 - 48 * q^78 - 10 * q^80 - 2 * q^81 - 42 * q^82 - 30 * q^86 + 24 * q^89 + 12 * q^91 - 16 * q^93 + 20 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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