LMFDB - Embedded newform 605.2.m.b.457.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("605.112");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
Coefficient field:	$\Q(\zeta_{40})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{12} + x^{8} - x^{4} + 1 $ x^16 - x^12 + x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{4} $
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			457.2
Root			$-0.891007 + 0.453990i$ of defining polynomial
Character	$\chi$	$=$	605.457
Dual form			605.2.m.b.233.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.99235 + 1.01515i) q^{2} +(1.39680 - 0.221232i) q^{3} +(1.76336 + 2.42705i) q^{4} +(0.333023 + 2.21113i) q^{5} +(3.00750 + 0.977198i) q^{6} +(0.349798 + 2.20854i) q^{8} +(-0.951057 + 0.309017i) q^{9} +O(q^{10})$	\(q+(1.99235 + 1.01515i) q^{2} +(1.39680 - 0.221232i) q^{3} +(1.76336 + 2.42705i) q^{4} +(0.333023 + 2.21113i) q^{5} +(3.00750 + 0.977198i) q^{6} +(0.349798 + 2.20854i) q^{8} +(-0.951057 + 0.309017i) q^{9} +(-1.58114 + 4.74342i) q^{10} +(3.00000 + 3.00000i) q^{12} +(2.03031 - 3.98470i) q^{13} +(0.954339 + 3.01484i) q^{15} +(0.309017 - 0.951057i) q^{16} +(2.03031 + 3.98470i) q^{17} +(-2.20854 - 0.349798i) q^{18} +(-5.11667 - 3.71748i) q^{19} +(-4.77929 + 4.70727i) q^{20} +(-1.00000 + 1.00000i) q^{23} +(0.977198 + 3.00750i) q^{24} +(-4.77819 + 1.47271i) q^{25} +(8.09017 - 5.87785i) q^{26} +(-5.04029 + 2.56816i) q^{27} +(5.11667 - 3.71748i) q^{29} +(-1.15914 + 6.97541i) q^{30} +(0.618034 + 1.90211i) q^{31} +(4.74342 - 4.74342i) q^{32} +10.0000i q^{34} +(-2.42705 - 1.76336i) q^{36} +(-4.19041 - 0.663695i) q^{37} +(-6.42040 - 12.6007i) q^{38} +(1.95440 - 6.01501i) q^{39} +(-4.76687 + 1.50894i) q^{40} +(3.71748 - 5.11667i) q^{41} +(-1.00000 - 2.00000i) q^{45} +(-3.00750 + 0.977198i) q^{46} +(-0.663695 - 4.19041i) q^{47} +(0.221232 - 1.39680i) q^{48} +(6.65740 + 2.16312i) q^{49} +(-11.0149 - 1.91644i) q^{50} +(3.71748 + 5.11667i) q^{51} +(13.2512 - 2.09879i) q^{52} +(-1.26007 - 0.642040i) q^{53} -12.6491 q^{54} +(-7.96940 - 4.06061i) q^{57} +(13.9680 - 2.21232i) q^{58} +(3.52671 + 4.85410i) q^{59} +(-5.63432 + 7.63246i) q^{60} +(-6.01501 - 1.95440i) q^{61} +(-0.699596 + 4.41708i) q^{62} +(12.3637 - 4.01722i) q^{64} +(9.48683 + 3.16228i) q^{65} +(3.00000 + 3.00000i) q^{67} +(-6.09092 + 11.9541i) q^{68} +(-1.17557 + 1.61803i) q^{69} +(-2.47214 + 7.60845i) q^{71} +(-1.01515 - 1.99235i) q^{72} +(-4.41708 - 0.699596i) q^{73} +(-7.67501 - 5.57622i) q^{74} +(-6.34838 + 3.11418i) q^{75} -18.9737i q^{76} +(10.0000 - 10.0000i) q^{78} +(-1.95440 - 6.01501i) q^{79} +(2.20582 + 0.366554i) q^{80} +(-4.04508 + 2.93893i) q^{81} +(12.6007 - 6.42040i) q^{82} +(-7.96940 + 4.06061i) q^{83} +(-8.13456 + 5.81627i) q^{85} +(6.32456 - 6.32456i) q^{87} -6.00000i q^{89} +(0.0379561 - 4.99986i) q^{90} +(-4.19041 - 0.663695i) q^{92} +(1.28408 + 2.52015i) q^{93} +(2.93159 - 9.02251i) q^{94} +(6.51587 - 12.5516i) q^{95} +(5.57622 - 7.67501i) q^{96} +(4.49428 - 8.82051i) q^{97} +(11.0680 + 11.0680i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3} + 8 q^{5}+O(q^{10}) $ 16 * q + 4 * q^3 + 8 * q^5	$ 16 q + 4 q^{3} + 8 q^{5} + 48 q^{12} - 4 q^{15} - 4 q^{16} - 12 q^{20} - 16 q^{23} - 12 q^{25} + 40 q^{26} + 16 q^{27} - 8 q^{31} - 12 q^{36} - 12 q^{37} - 40 q^{38} - 16 q^{45} - 12 q^{47} + 4 q^{48} + 4 q^{53} + 40 q^{58} + 36 q^{60} + 48 q^{67} + 32 q^{71} - 4 q^{75} + 160 q^{78} + 8 q^{80} - 20 q^{81} - 40 q^{82} - 12 q^{92} + 8 q^{93} + 28 q^{97}+O(q^{100}) $ 16 * q + 4 * q^3 + 8 * q^5 + 48 * q^12 - 4 * q^15 - 4 * q^16 - 12 * q^20 - 16 * q^23 - 12 * q^25 + 40 * q^26 + 16 * q^27 - 8 * q^31 - 12 * q^36 - 12 * q^37 - 40 * q^38 - 16 * q^45 - 12 * q^47 + 4 * q^48 + 4 * q^53 + 40 * q^58 + 36 * q^60 + 48 * q^67 + 32 * q^71 - 4 * q^75 + 160 * q^78 + 8 * q^80 - 20 * q^81 - 40 * q^82 - 12 * q^92 + 8 * q^93 + 28 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{9}{10}\right)$

Coefficient data

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

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

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

$2$	1.99235	+	1.01515i	1.40881	+	0.717822i	0.982414	−	0.186717i	$-0.0597847\pi$
$2$	1.99235	+	1.01515i	1.40881	+	0.717822i	0.426391	+	0.904539i	$0.359785\pi$
$3$	1.39680	−	0.221232i	0.806444	−	0.127728i	0.260418	−	0.965496i	$-0.416140\pi$
$3$	1.39680	−	0.221232i	0.806444	−	0.127728i	0.546027	+	0.837768i	$0.316140\pi$
$4$	1.76336	+	2.42705i	0.881678	+	1.21353i
$5$	0.333023	+	2.21113i	0.148932	+	0.988847i
$5$	0.333023	+	2.21113i	0.148932	+	0.988847i
$6$	3.00750	+	0.977198i	1.22781	+	0.398939i
$7$		0			0		−0.987688	−	0.156434i	$-0.950000\pi$
$7$		0			0		0.987688	+	0.156434i	$0.0500000\pi$
$8$	0.349798	+	2.20854i	0.123672	+	0.780836i
$9$	−0.951057	+	0.309017i	−0.317019	+	0.103006i
$10$	−1.58114	+	4.74342i	−0.500000	+	1.50000i
$11$		0			0
$11$		0			0
$12$	3.00000	+	3.00000i	0.866025	+	0.866025i
$13$	2.03031	−	3.98470i	0.563106	−	1.10516i	−0.417410	−	0.908718i	$-0.637062\pi$
$13$	2.03031	−	3.98470i	0.563106	−	1.10516i	0.980516	−	0.196439i	$-0.0629379\pi$
$14$		0			0
$15$	0.954339	+	3.01484i	0.246409	+	0.778427i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	2.03031	+	3.98470i	0.492422	+	0.966432i	0.994806	+	0.101788i	$0.0324563\pi$
$17$	2.03031	+	3.98470i	0.492422	+	0.966432i	−0.502384	+	0.864644i	$0.667544\pi$
$18$	−2.20854	−	0.349798i	−0.520557	−	0.0824482i
$19$	−5.11667	−	3.71748i	−1.17385	−	0.852848i	−0.182381	−	0.983228i	$-0.558380\pi$
$19$	−5.11667	−	3.71748i	−1.17385	−	0.852848i	−0.991464	+	0.130379i	$0.958380\pi$
$20$	−4.77929	+	4.70727i	−1.06868	+	1.05258i
$21$		0			0
$22$		0			0
$23$	−1.00000	+	1.00000i	−0.208514	+	0.208514i	−0.803636	−	0.595121i	$-0.797104\pi$
$23$	−1.00000	+	1.00000i	−0.208514	+	0.208514i	0.595121	+	0.803636i	$0.297104\pi$
$24$	0.977198	+	3.00750i	0.199470	+	0.613904i
$25$	−4.77819	+	1.47271i	−0.955638	+	0.294542i
$26$	8.09017	−	5.87785i	1.58661	−	1.15274i
$27$	−5.04029	+	2.56816i	−0.970005	+	0.494242i
$28$		0			0
$29$	5.11667	−	3.71748i	0.950142	−	0.690319i	−0.000698242	−	1.00000i	$-0.500222\pi$
$29$	5.11667	−	3.71748i	0.950142	−	0.690319i	0.950841	+	0.309681i	$0.100222\pi$
$30$	−1.15914	+	6.97541i	−0.211630	+	1.27353i
$31$	0.618034	+	1.90211i	0.111002	+	0.341630i	0.991092	−	0.133177i	$-0.0425179\pi$
$31$	0.618034	+	1.90211i	0.111002	+	0.341630i	−0.880090	+	0.474807i	$0.842518\pi$
$32$	4.74342	−	4.74342i	0.838525	−	0.838525i
$33$		0			0
$34$			10.0000i			1.71499i
$35$		0			0
$36$	−2.42705	−	1.76336i	−0.404508	−	0.293893i
$37$	−4.19041	−	0.663695i	−0.688899	−	0.109111i	−0.197836	−	0.980235i	$-0.563391\pi$
$37$	−4.19041	−	0.663695i	−0.688899	−	0.109111i	−0.491063	+	0.871124i	$0.663391\pi$
$38$	−6.42040	−	12.6007i	−1.04153	−	2.04411i
$39$	1.95440	−	6.01501i	0.312954	−	0.963172i
$40$	−4.76687	+	1.50894i	−0.753709	+	0.238585i
$41$	3.71748	−	5.11667i	0.580573	−	0.799090i	−0.413185	−	0.910647i	$-0.635584\pi$
$41$	3.71748	−	5.11667i	0.580573	−	0.799090i	0.993758	+	0.111557i	$0.0355838\pi$
$42$		0			0
$43$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$43$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$44$		0			0
$45$	−1.00000	−	2.00000i	−0.149071	−	0.298142i
$46$	−3.00750	+	0.977198i	−0.443432	+	0.144080i
$47$	−0.663695	−	4.19041i	−0.0968099	−	0.611234i	−0.987621	−	0.156860i	$-0.949863\pi$
$47$	−0.663695	−	4.19041i	−0.0968099	−	0.611234i	0.890811	−	0.454374i	$-0.150137\pi$
$48$	0.221232	−	1.39680i	0.0319321	−	0.201611i
$49$	6.65740	+	2.16312i	0.951057	+	0.309017i
$50$	−11.0149	−	1.91644i	−1.55774	−	0.271025i
$51$	3.71748	+	5.11667i	0.520551	+	0.716477i
$52$	13.2512	−	2.09879i	1.83761	−	0.291050i
$53$	−1.26007	−	0.642040i	−0.173084	−	0.0881909i	0.365302	−	0.930889i	$-0.380966\pi$
$53$	−1.26007	−	0.642040i	−0.173084	−	0.0881909i	−0.538386	+	0.842698i	$0.680966\pi$
$54$	−12.6491			−1.72133
$55$		0			0
$56$		0			0
$57$	−7.96940	−	4.06061i	−1.05557	−	0.537842i
$58$	13.9680	−	2.21232i	1.83409	−	0.290492i
$59$	3.52671	+	4.85410i	0.459139	+	0.631950i	0.974330	−	0.225125i	$-0.0722791\pi$
$59$	3.52671	+	4.85410i	0.459139	+	0.631950i	−0.515191	+	0.857075i	$0.672279\pi$
$60$	−5.63432	+	7.63246i	−0.727388	+	0.985346i
$61$	−6.01501	−	1.95440i	−0.770143	−	0.250235i	−0.102517	−	0.994731i	$-0.532690\pi$
$61$	−6.01501	−	1.95440i	−0.770143	−	0.250235i	−0.667626	+	0.744497i	$0.732690\pi$
$62$	−0.699596	+	4.41708i	−0.0888488	+	0.560969i
$63$		0			0
$64$	12.3637	−	4.01722i	1.54547	−	0.502153i
$65$	9.48683	+	3.16228i	1.17670	+	0.392232i
$66$		0			0
$67$	3.00000	+	3.00000i	0.366508	+	0.366508i	0.866202	−	0.499694i	$-0.166554\pi$
$67$	3.00000	+	3.00000i	0.366508	+	0.366508i	−0.499694	+	0.866202i	$0.666554\pi$
$68$	−6.09092	+	11.9541i	−0.738633	+	1.44965i
$69$	−1.17557	+	1.61803i	−0.141522	+	0.194788i
$70$		0			0
$71$	−2.47214	+	7.60845i	−0.293389	+	0.902957i	0.690369	+	0.723457i	$0.257448\pi$
$71$	−2.47214	+	7.60845i	−0.293389	+	0.902957i	−0.983758	+	0.179500i	$0.942552\pi$
$72$	−1.01515	−	1.99235i	−0.119637	−	0.234801i
$73$	−4.41708	−	0.699596i	−0.516980	−	0.0818815i	−0.107508	−	0.994204i	$-0.534287\pi$
$73$	−4.41708	−	0.699596i	−0.516980	−	0.0818815i	−0.409472	+	0.912323i	$0.634287\pi$
$74$	−7.67501	−	5.57622i	−0.892202	−	0.648222i
$75$	−6.34838	+	3.11418i	−0.733048	+	0.359594i
$76$		−	18.9737i		−	2.17643i
$77$		0			0
$78$	10.0000	−	10.0000i	1.13228	−	1.13228i
$79$	−1.95440	−	6.01501i	−0.219887	−	0.676741i	−0.998770	−	0.0495733i	$-0.984214\pi$
$79$	−1.95440	−	6.01501i	−0.219887	−	0.676741i	0.778884	−	0.627168i	$-0.215786\pi$
$80$	2.20582	+	0.366554i	0.246618	+	0.0409819i
$81$	−4.04508	+	2.93893i	−0.449454	+	0.326547i
$82$	12.6007	−	6.42040i	1.39152	−	0.709014i
$83$	−7.96940	+	4.06061i	−0.874756	+	0.445710i	−0.832907	−	0.553414i	$-0.813325\pi$
$83$	−7.96940	+	4.06061i	−0.874756	+	0.445710i	−0.0418492	+	0.999124i	$0.513325\pi$
$84$		0			0
$85$	−8.13456	+	5.81627i	−0.882317	+	0.630863i
$86$		0			0
$87$	6.32456	−	6.32456i	0.678064	−	0.678064i
$88$		0			0
$89$		−	6.00000i		−	0.635999i	−0.948091	−	0.317999i	$-0.896989\pi$
$89$		−	6.00000i		−	0.635999i	0.948091	−	0.317999i	$-0.103011\pi$
$90$	0.0379561	−	4.99986i	0.00400092	−	0.527031i
$91$		0			0
$92$	−4.19041	−	0.663695i	−0.436880	−	0.0691950i
$93$	1.28408	+	2.52015i	0.133153	+	0.261327i
$94$	2.93159	−	9.02251i	0.302371	−	0.930601i
$95$	6.51587	−	12.5516i	0.668514	−	1.28777i
$96$	5.57622	−	7.67501i	0.569121	−	0.783327i
$97$	4.49428	−	8.82051i	0.456325	−	0.895588i	−0.542145	−	0.840285i	$-0.682388\pi$
$97$	4.49428	−	8.82051i	0.456325	−	0.895588i	0.998470	−	0.0553026i	$-0.0176124\pi$
$98$	11.0680	+	11.0680i	1.11803	+	1.11803i
$99$		0			0
$100$	−12.0000	−	9.00000i	−1.20000	−	0.900000i
$101$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$101$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$102$	2.21232	+	13.9680i	0.219052	+	1.38304i
$103$	−1.99109	+	12.5712i	−0.196188	+	1.23868i	0.671287	+	0.741198i	$0.265742\pi$
$103$	−1.99109	+	12.5712i	−0.196188	+	1.23868i	−0.867475	+	0.497482i	$0.834258\pi$
$104$	9.51057	+	3.09017i	0.932588	+	0.303016i
$105$		0			0
$106$	−1.85874	−	2.55834i	−0.180537	−	0.248488i
$107$		0			0		−0.156434	−	0.987688i	$-0.550000\pi$
$107$		0			0		0.156434	+	0.987688i	$0.450000\pi$
$108$	−15.1209	−	7.70447i	−1.45501	−	0.741363i
$109$	−12.6491			−1.21157			−0.605783	−	0.795630i	$-0.707140\pi$
$109$	−12.6491			−1.21157			−0.605783	+	0.795630i	$0.707140\pi$
$110$		0			0
$111$	−6.00000			−0.569495
$112$		0			0
$113$	−12.5712	+	1.99109i	−1.18260	+	0.187306i	−0.716604	−	0.697481i	$-0.754304\pi$
$113$	−12.5712	+	1.99109i	−1.18260	+	0.187306i	−0.465997	+	0.884786i	$0.654304\pi$
$114$	−11.7557	−	16.1803i	−1.10102	−	1.51543i
$115$	−2.54415	−	1.87811i	−0.237243	−	0.175134i
$116$	18.0450	+	5.86319i	1.67544	+	0.544383i
$117$	−0.699596	+	4.41708i	−0.0646777	+	0.408359i
$118$	2.09879	+	13.2512i	0.193209	+	1.21987i
$119$		0			0
$120$	−6.32456	+	3.16228i	−0.577350	+	0.288675i
$121$		0			0
$122$	−10.0000	−	10.0000i	−0.905357	−	0.905357i
$123$	4.06061	−	7.96940i	0.366133	−	0.718577i
$124$	−3.52671	+	4.85410i	−0.316708	+	0.435911i
$125$	−4.84760	−	10.0748i	−0.433583	−	0.901114i
$126$		0			0
$127$	4.06061	+	7.96940i	0.360321	+	0.707170i	0.998005	−	0.0631276i	$-0.0201075\pi$
$127$	4.06061	+	7.96940i	0.360321	+	0.707170i	−0.637684	+	0.770298i	$0.720108\pi$
$128$	15.4598	+	2.44859i	1.36646	+	0.216427i
$129$		0			0
$130$	15.6909	+	15.9310i	1.37618	+	1.39724i
$131$			12.6491i			1.10516i	0.833461	+	0.552579i	$0.186356\pi$
$131$			12.6491i			1.10516i	−0.833461	+	0.552579i	$0.813644\pi$
$132$		0			0
$133$		0			0
$134$	2.93159	+	9.02251i	0.253251	+	0.779427i
$135$	−7.35706	−	10.2895i	−0.633195	−	0.885578i
$136$	−8.09017	+	5.87785i	−0.693726	+	0.504022i
$137$	16.3810	−	8.34651i	1.39952	−	0.713091i	0.418721	−	0.908115i	$-0.362479\pi$
$137$	16.3810	−	8.34651i	1.39952	−	0.713091i	0.980798	+	0.195024i	$0.0624785\pi$
$138$	−3.98470	+	2.03031i	−0.339200	+	0.172831i
$139$	−10.2333	+	7.43496i	−0.867981	+	0.630625i	−0.930044	−	0.367447i	$-0.880232\pi$
$139$	−10.2333	+	7.43496i	−0.867981	+	0.630625i	0.0620634	+	0.998072i	$0.480232\pi$
$140$		0			0
$141$	−1.85410	−	5.70634i	−0.156144	−	0.480560i
$142$	−12.6491	+	12.6491i	−1.06149	+	1.06149i
$143$		0			0
$144$			1.00000i			0.0833333i
$145$	9.92380	+	10.0756i	0.824127	+	0.836735i
$146$	−8.09017	−	5.87785i	−0.669547	−	0.486455i
$147$	9.77762	+	1.54862i	0.806444	+	0.127728i
$148$	−5.77836	−	11.3407i	−0.474978	−	0.932197i
$149$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$149$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$150$	−15.8096	−	0.240048i	−1.29085	−	0.0195999i
$151$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$151$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$152$	6.42040	−	12.6007i	0.520763	−	1.02205i
$153$	−3.16228	−	3.16228i	−0.255655	−	0.255655i
$154$		0			0
$155$	−4.00000	+	2.00000i	−0.321288	+	0.160644i
$156$	18.0450	−	5.86319i	1.44476	−	0.469431i
$157$	1.54862	+	9.77762i	0.123594	+	0.780339i	0.969153	+	0.246458i	$0.0792668\pi$
$157$	1.54862	+	9.77762i	0.123594	+	0.780339i	−0.845560	+	0.533881i	$0.820733\pi$
$158$	2.21232	−	13.9680i	0.176003	−	1.11124i
$159$	−1.90211	−	0.618034i	−0.150847	−	0.0490133i
$160$	12.0680	+	8.90865i	0.954057	+	0.704290i
$161$		0			0
$162$	−11.0427	+	1.74899i	−0.867596	+	0.137414i
$163$	−1.26007	−	0.642040i	−0.0986966	−	0.0502884i	0.403945	−	0.914783i	$-0.367639\pi$
$163$	−1.26007	−	0.642040i	−0.0986966	−	0.0502884i	−0.502642	+	0.864495i	$0.667639\pi$
$164$	18.9737			1.48159
$165$		0			0
$166$	−20.0000			−1.55230
$167$	15.9388	+	8.12123i	1.23338	+	0.628440i	0.944370	−	0.328886i	$-0.106673\pi$
$167$	15.9388	+	8.12123i	1.23338	+	0.628440i	0.289012	+	0.957325i	$0.406673\pi$
$168$		0			0
$169$	−4.11450	−	5.66312i	−0.316500	−	0.435625i
$170$	−22.1113	+	3.33023i	−1.69586	+	0.255417i
$171$	6.01501	+	1.95440i	0.459979	+	0.149456i
$172$		0			0
$173$	−0.699596	−	4.41708i	−0.0531893	−	0.335824i	−0.999905	−	0.0137548i	$-0.995622\pi$
$173$	−0.699596	−	4.41708i	−0.0531893	−	0.335824i	0.946716	−	0.322069i	$-0.104378\pi$
$174$	19.0211	−	6.18034i	1.44199	−	0.468530i
$175$		0			0
$176$		0			0
$177$	6.00000	+	6.00000i	0.450988	+	0.450988i
$178$	6.09092	−	11.9541i	0.456534	−	0.895998i
$179$	2.35114	−	3.23607i	0.175733	−	0.241875i	−0.712060	−	0.702118i	$-0.752238\pi$
$179$	2.35114	−	3.23607i	0.175733	−	0.241875i	0.887793	+	0.460243i	$0.152238\pi$
$180$	3.09075	−	5.95376i	0.230371	−	0.443767i
$181$	−2.47214	+	7.60845i	−0.183752	+	0.565532i	−0.999925	−	0.0122769i	$-0.996092\pi$
$181$	−2.47214	+	7.60845i	−0.183752	+	0.565532i	0.816172	+	0.577809i	$0.196092\pi$
$182$		0			0
$183$	−8.83415	−	1.39919i	−0.653039	−	0.103431i
$184$	−2.55834	−	1.85874i	−0.188603	−	0.137028i
$185$	0.0720166	−	9.48656i	0.00529477	−	0.697466i
$186$			6.32456i			0.463739i
$187$		0			0
$188$	9.00000	−	9.00000i	0.656392	−	0.656392i
$189$		0			0
$190$	25.7237	−	18.3927i	1.86620	−	1.33434i
$191$	−17.7984	+	12.9313i	−1.28785	+	0.935674i	−0.999760	−	0.0219304i	$-0.993019\pi$
$191$	−17.7984	+	12.9313i	−1.28785	+	0.935674i	−0.288086	+	0.957605i	$0.593019\pi$
$192$	16.3810	−	8.34651i	1.18219	−	0.602358i
$193$	19.9235	−	10.1515i	1.43413	−	0.730724i	0.447585	−	0.894241i	$-0.352284\pi$
$193$	19.9235	−	10.1515i	1.43413	−	0.730724i	0.986540	+	0.163518i	$0.0522841\pi$
$194$	17.9084	−	13.0112i	1.28574	−	0.934148i
$195$	13.9508	+	2.31829i	0.999039	+	0.166016i
$196$	6.48936	+	19.9722i	0.463525	+	1.42658i
$197$	3.16228	−	3.16228i	0.225303	−	0.225303i	−0.585424	−	0.810727i	$-0.699072\pi$
$197$	3.16228	−	3.16228i	0.225303	−	0.225303i	0.810727	+	0.585424i	$0.199072\pi$
$198$		0			0
$199$		−	6.00000i		−	0.425329i	−0.977125	−	0.212664i	$-0.931786\pi$
$199$		−	6.00000i		−	0.425329i	0.977125	−	0.212664i	$-0.0682141\pi$
$200$	−4.92394	−	10.0377i	−0.348175	−	0.709770i
$201$	4.85410	+	3.52671i	0.342382	+	0.248755i
$202$		0			0
$203$		0			0
$204$	−5.86319	+	18.0450i	−0.410505	+	1.26340i
$205$	12.5516	+	6.51587i	0.876644	+	0.455088i
$206$	−16.7287	+	23.0250i	−1.16554	+	1.60423i
$207$	0.642040	−	1.26007i	0.0446248	−	0.0875812i
$208$	−3.16228	−	3.16228i	−0.219265	−	0.219265i
$209$		0			0
$210$		0			0
$211$	−24.0600	+	7.81758i	−1.65636	+	0.538184i	−0.980105	−	0.198482i	$-0.936399\pi$
$211$	−24.0600	+	7.81758i	−1.65636	+	0.538184i	−0.676257	+	0.736666i	$0.736399\pi$
$212$	−0.663695	−	4.19041i	−0.0455828	−	0.287798i
$213$	−1.76985	+	11.1744i	−0.121268	+	0.765659i
$214$		0			0
$215$		0			0
$216$	−7.43496	−	10.2333i	−0.505885	−	0.696291i
$217$		0			0
$218$	−25.2015	−	12.8408i	−1.70686	−	0.869688i
$219$	−6.32456			−0.427374
$220$		0			0
$221$	20.0000			1.34535
$222$	−11.9541	−	6.09092i	−0.802307	−	0.408796i
$223$	15.3648	−	2.43355i	1.02890	−	0.162963i	0.380914	−	0.924611i	$-0.375609\pi$
$223$	15.3648	−	2.43355i	1.02890	−	0.162963i	0.647991	+	0.761648i	$0.275609\pi$
$224$		0			0
$225$	4.08924	−	2.87718i	0.272616	−	0.191812i
$226$	−27.0675	−	8.79478i	−1.80051	−	0.585020i
$227$	1.39919	−	8.83415i	0.0928677	−	0.586343i	−0.896741	−	0.442556i	$-0.854072\pi$
$227$	1.39919	−	8.83415i	0.0928677	−	0.586343i	0.989609	−	0.143787i	$-0.0459282\pi$
$228$	−4.19758	−	26.5025i	−0.277991	−	1.75517i
$229$	−3.80423	+	1.23607i	−0.251390	+	0.0816817i	−0.432001	−	0.901873i	$-0.642192\pi$
$229$	−3.80423	+	1.23607i	−0.251390	+	0.0816817i	0.180611	+	0.983555i	$0.442192\pi$
$230$	−3.16228	−	6.32456i	−0.208514	−	0.417029i
$231$		0			0
$232$	10.0000	+	10.0000i	0.656532	+	0.656532i
$233$	−6.09092	+	11.9541i	−0.399030	+	0.783140i	−0.999868	−	0.0162307i	$-0.994833\pi$
$233$	−6.09092	+	11.9541i	−0.399030	+	0.783140i	0.600839	+	0.799370i	$0.294833\pi$
$234$	−5.87785	+	8.09017i	−0.384247	+	0.528871i
$235$	9.04451	−	2.86302i	0.589999	−	0.186763i
$236$	−5.56231	+	17.1190i	−0.362075	+	1.11435i
$237$	−4.06061	−	7.96940i	−0.263765	−	0.517668i
$238$		0			0
$239$	15.3500	+	11.1524i	0.992910	+	0.721391i	0.960556	−	0.278085i	$-0.0896997\pi$
$239$	15.3500	+	11.1524i	0.992910	+	0.721391i	0.0323537	+	0.999476i	$0.489700\pi$
$240$	3.16219	+	0.0240055i	0.204118	+	0.00154955i
$241$			6.32456i			0.407400i	0.979033	+	0.203700i	$0.0652968\pi$
$241$			6.32456i			0.407400i	−0.979033	+	0.203700i	$0.934703\pi$
$242$		0			0
$243$	7.00000	−	7.00000i	0.449050	−	0.449050i
$244$	−5.86319	−	18.0450i	−0.375352	−	1.15521i
$245$	−2.56587	+	15.4407i	−0.163928	+	0.986472i
$246$	16.1803	−	11.7557i	1.03162	−	0.749516i
$247$	−25.2015	+	12.8408i	−1.60353	+	0.817040i
$248$	−3.98470	+	2.03031i	−0.253029	+	0.128925i
$249$	−10.2333	+	7.43496i	−0.648512	+	0.471171i
$250$	0.569297	−	24.9935i	0.0360055	−	1.58073i
$251$	3.70820	+	11.4127i	0.234060	+	0.720362i	0.997245	+	0.0741818i	$0.0236345\pi$
$251$	3.70820	+	11.4127i	0.234060	+	0.720362i	−0.763185	+	0.646180i	$0.776365\pi$
$252$		0			0
$253$		0			0
$254$			20.0000i			1.25491i
$255$	−10.0756	+	9.92380i	−0.630960	+	0.621452i
$256$	7.28115	+	5.29007i	0.455072	+	0.330629i
$257$	9.77762	+	1.54862i	0.609911	+	0.0966004i	0.453747	−	0.891131i	$-0.350087\pi$
$257$	9.77762	+	1.54862i	0.609911	+	0.0966004i	0.156164	+	0.987731i	$0.450087\pi$
$258$		0			0
$259$		0			0
$260$	9.05365	+	28.6012i	0.561484	+	1.77377i
$261$	−3.71748	+	5.11667i	−0.230106	+	0.316714i
$262$	−12.8408	+	25.2015i	−0.793307	+	1.55695i
$263$	−18.9737	−	18.9737i	−1.16997	−	1.16997i	−0.982217	−	0.187749i	$-0.939881\pi$
$263$	−18.9737	−	18.9737i	−1.16997	−	1.16997i	−0.187749	−	0.982217i	$-0.560119\pi$
$264$		0			0
$265$	1.00000	−	3.00000i	0.0614295	−	0.184289i
$266$		0			0
$267$	−1.32739	−	8.38081i	−0.0812350	−	0.512897i
$268$	−1.99109	+	12.5712i	−0.121625	+	0.767909i
$269$	22.8254	+	7.41641i	1.39169	+	0.452186i	0.906493	−	0.422221i	$-0.138749\pi$
$269$	22.8254	+	7.41641i	1.39169	+	0.452186i	0.485193	+	0.874407i	$0.338749\pi$
$270$	−4.21244	−	27.9688i	−0.256361	−	1.70213i
$271$	7.43496	+	10.2333i	0.451642	+	0.621631i	0.972749	−	0.231860i	$-0.0744810\pi$
$271$	7.43496	+	10.2333i	0.451642	+	0.621631i	−0.521108	+	0.853491i	$0.674481\pi$
$272$	4.41708	−	0.699596i	0.267825	−	0.0424193i
$273$		0			0
$274$	41.1096			2.48352
$275$		0			0
$276$	−6.00000			−0.361158
$277$	11.9541	+	6.09092i	0.718253	+	0.365968i	0.774607	−	0.632443i	$-0.217948\pi$
$277$	11.9541	+	6.09092i	0.718253	+	0.365968i	−0.0563544	+	0.998411i	$0.517948\pi$
$278$	−27.9360	+	4.42463i	−1.67549	+	0.265372i
$279$	−1.17557	−	1.61803i	−0.0703796	−	0.0968692i
$280$		0			0
$281$	−18.0450	−	5.86319i	−1.07648	−	0.349768i	−0.283469	−	0.958981i	$-0.591485\pi$
$281$	−18.0450	−	5.86319i	−1.07648	−	0.349768i	−0.793007	+	0.609213i	$0.791485\pi$
$282$	2.09879	−	13.2512i	0.124981	−	0.789099i
$283$	1.39919	+	8.83415i	0.0831734	+	0.525136i	0.993735	+	0.111762i	$0.0356496\pi$
$283$	1.39919	+	8.83415i	0.0831734	+	0.525136i	−0.910562	+	0.413373i	$0.864350\pi$
$284$	−22.8254	+	7.41641i	−1.35444	+	0.440083i
$285$	6.32456	−	18.9737i	0.374634	−	1.12390i
$286$		0			0
$287$		0			0
$288$	−3.04546	+	5.97705i	−0.179456	+	0.352201i
$289$	−1.76336	+	2.42705i	−0.103727	+	0.142768i
$290$	9.54339	+	30.1484i	0.560407	+	1.77037i
$291$	4.32624	−	13.3148i	0.253609	−	0.780527i
$292$	−6.09092	−	11.9541i	−0.356444	−	0.699561i
$293$	−22.0854	−	3.49798i	−1.29024	−	0.204354i	−0.526666	−	0.850072i	$-0.676558\pi$
$293$	−22.0854	−	3.49798i	−1.29024	−	0.204354i	−0.763576	+	0.645718i	$0.776558\pi$
$294$	17.9084	+	13.0112i	1.04444	+	0.758827i
$295$	−9.55858	+	9.41454i	−0.556522	+	0.548136i
$296$		−	9.48683i		−	0.551411i
$297$		0			0
$298$		0			0
$299$	1.95440	+	6.01501i	0.113026	+	0.347857i
$300$	−18.7527	−	9.91644i	−1.08269	−	0.572526i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−5.11667	+	3.71748i	−0.293461	+	0.213212i
$305$	2.31829	−	13.9508i	0.132745	−	0.798822i
$306$	−3.09017	−	9.51057i	−0.176653	−	0.543683i
$307$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$307$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$308$		0			0
$309$			18.0000i			1.02398i
$310$	−9.99971	−	0.0759122i	−0.567945	−	0.00431152i
$311$	6.47214	+	4.70228i	0.367001	+	0.266642i	0.755966	−	0.654611i	$-0.227167\pi$
$311$	6.47214	+	4.70228i	0.367001	+	0.266642i	−0.388965	+	0.921252i	$0.627167\pi$
$312$	13.9680	+	2.21232i	0.790784	+	0.125248i
$313$	−5.77836	−	11.3407i	−0.326612	−	0.641012i	0.668059	−	0.744108i	$-0.267125\pi$
$313$	−5.77836	−	11.3407i	−0.326612	−	0.641012i	−0.994671	+	0.103096i	$0.967125\pi$
$314$	−6.84038	+	21.0525i	−0.386025	+	1.18806i
$315$		0			0
$316$	11.1524	−	15.3500i	0.627374	−	0.863506i
$317$	10.9147	−	21.4212i	0.613029	−	1.20314i	−0.350758	−	0.936466i	$-0.614076\pi$
$317$	10.9147	−	21.4212i	0.613029	−	1.20314i	0.963788	−	0.266671i	$-0.0859238\pi$
$318$	−3.16228	−	3.16228i	−0.177332	−	0.177332i
$319$		0			0
$320$	13.0000	+	26.0000i	0.726722	+	1.45344i
$321$		0			0
$322$		0			0
$323$	4.42463	−	27.9360i	0.246193	−	1.55440i
$324$	−14.2658	−	4.63525i	−0.792547	−	0.257514i
$325$	−3.83288	+	22.0297i	−0.212610	+	1.22199i
$326$	−1.85874	−	2.55834i	−0.102946	−	0.141693i
$327$	−17.6683	+	2.79838i	−0.977060	+	0.154751i
$328$	12.6007	+	6.42040i	0.695759	+	0.354507i
$329$		0			0
$330$		0			0
$331$	−18.0000			−0.989369			−0.494685	−	0.869072i	$-0.664716\pi$
$331$	−18.0000			−0.989369			−0.494685	+	0.869072i	$0.664716\pi$
$332$	−23.9082	−	12.1818i	−1.31213	−	0.668566i
$333$	4.19041	−	0.663695i	0.229633	−	0.0363703i
$334$	23.5114	+	32.3607i	1.28649	+	1.77070i
$335$	−5.63432	+	7.63246i	−0.307836	+	0.417006i
$336$		0			0
$337$	2.09879	−	13.2512i	0.114328	−	0.721840i	−0.862219	−	0.506536i	$-0.830926\pi$
$337$	2.09879	−	13.2512i	0.114328	−	0.721840i	0.976547	−	0.215304i	$-0.0690743\pi$
$338$	−2.44859	−	15.4598i	−0.133186	−	0.840901i
$339$	−17.1190	+	5.56231i	−0.929777	+	0.302103i
$340$	−28.4605	−	9.48683i	−1.54349	−	0.514496i
$341$		0			0
$342$	10.0000	+	10.0000i	0.540738	+	0.540738i
$343$		0			0
$344$		0			0
$345$	−3.96917	−	2.06050i	−0.213693	−	0.110933i
$346$	3.09017	−	9.51057i	0.166129	−	0.511291i
$347$	−12.1818	−	23.9082i	−0.653956	−	1.28346i	−0.945100	−	0.326781i	$-0.894036\pi$
$347$	−12.1818	−	23.9082i	−0.653956	−	1.28346i	0.291144	−	0.956679i	$-0.405964\pi$
$348$	26.5025	+	4.19758i	1.42068	+	0.225014i
$349$	25.5834	+	18.5874i	1.36945	+	0.994961i	0.997780	+	0.0665943i	$0.0212133\pi$
$349$	25.5834	+	18.5874i	1.36945	+	0.994961i	0.371666	+	0.928367i	$0.378787\pi$
$350$		0			0
$351$			25.2982i			1.35032i
$352$		0			0
$353$	−21.0000	+	21.0000i	−1.11772	+	1.11772i	−0.125642	+	0.992076i	$0.540099\pi$
$353$	−21.0000	+	21.0000i	−1.11772	+	1.11772i	−0.992076	+	0.125642i	$0.959901\pi$
$354$	5.86319	+	18.0450i	0.311625	+	0.959082i
$355$	−17.6466	−	2.93243i	−0.936582	−	0.155637i
$356$	14.5623	−	10.5801i	0.771801	−	0.560746i
$357$		0			0
$358$	7.96940	−	4.06061i	0.421196	−	0.214610i
$359$	−15.3500	+	11.1524i	−0.810143	+	0.588603i	−0.913872	−	0.406002i	$-0.866923\pi$
$359$	−15.3500	+	11.1524i	−0.810143	+	0.588603i	0.103729	+	0.994606i	$0.466923\pi$
$360$	4.06728	−	2.90813i	0.214364	−	0.153272i
$361$	6.48936	+	19.9722i	0.341545	+	1.05117i
$362$	−12.6491	+	12.6491i	−0.664822	+	0.664822i
$363$		0			0
$364$		0			0
$365$	0.0759122	−	9.99971i	0.00397342	−	0.523409i
$366$	−16.1803	−	11.7557i	−0.845760	−	0.614481i
$367$	−4.19041	−	0.663695i	−0.218737	−	0.0346446i	0.0461037	−	0.998937i	$-0.485320\pi$
$367$	−4.19041	−	0.663695i	−0.218737	−	0.0346446i	−0.264841	+	0.964292i	$0.585320\pi$
$368$	0.642040	+	1.26007i	0.0334686	+	0.0656859i
$369$	−1.95440	+	6.01501i	−0.101742	+	0.313129i
$370$	9.77380	−	18.8275i	0.508116	−	0.978793i
$371$		0			0
$372$	−3.85224	+	7.56044i	−0.199729	+	0.391991i
$373$	3.16228	+	3.16228i	0.163737	+	0.163737i	0.784220	−	0.620483i	$-0.213063\pi$
$373$	3.16228	+	3.16228i	0.163737	+	0.163737i	−0.620483	+	0.784220i	$0.713063\pi$
$374$		0			0
$375$	−9.00000	−	13.0000i	−0.464758	−	0.671317i
$376$	9.02251	−	2.93159i	0.465301	−	0.151185i
$377$	−4.42463	−	27.9360i	−0.227880	−	1.43878i
$378$		0			0
$379$	−24.7275	−	8.03444i	−1.27016	−	0.412702i	−0.405059	−	0.914291i	$-0.632749\pi$
$379$	−24.7275	−	8.03444i	−1.27016	−	0.412702i	−0.865106	+	0.501589i	$0.832749\pi$
$380$	41.9532	−	6.31866i	2.15216	−	0.324140i
$381$	7.43496	+	10.2333i	0.380905	+	0.524270i
$382$	−48.5878	+	7.69556i	−2.48597	+	0.393739i
$383$	23.9414	+	12.1988i	1.22335	+	0.623327i	0.941785	−	0.336216i	$-0.109147\pi$
$383$	23.9414	+	12.1988i	1.22335	+	0.623327i	0.281563	+	0.959543i	$0.409147\pi$
$384$	22.1359			1.12962
$385$		0			0
$386$	50.0000			2.54493
$387$		0			0
$388$	29.3328	−	4.64587i	1.48915	−	0.235858i
$389$	9.40456	+	12.9443i	0.476830	+	0.656301i	0.977892	−	0.209111i	$-0.0670570\pi$
$389$	9.40456	+	12.9443i	0.476830	+	0.656301i	−0.501062	+	0.865412i	$0.667057\pi$
$390$	25.4415	+	18.7811i	1.28828	+	0.951017i
$391$	−6.01501	−	1.95440i	−0.304192	−	0.0988380i
$392$	−2.44859	+	15.4598i	−0.123672	+	0.780836i
$393$	2.79838	+	17.6683i	0.141160	+	0.891248i
$394$	9.51057	−	3.09017i	0.479135	−	0.155681i
$395$	12.6491	−	6.32456i	0.636446	−	0.318223i
$396$		0			0
$397$	13.0000	+	13.0000i	0.652451	+	0.652451i	0.953583	−	0.301131i	$-0.0973643\pi$
$397$	13.0000	+	13.0000i	0.652451	+	0.652451i	−0.301131	+	0.953583i	$0.597364\pi$
$398$	6.09092	−	11.9541i	0.305310	−	0.599205i
$399$		0			0
$400$	−0.0759100	+	4.99942i	−0.00379550	+	0.249971i
$401$	3.70820	−	11.4127i	0.185179	−	0.569922i	−0.814773	−	0.579781i	$-0.803138\pi$
$401$	3.70820	−	11.4127i	0.185179	−	0.569922i	0.999951	+	0.00985880i	$0.00313820\pi$
$402$	6.09092	+	11.9541i	0.303788	+	0.596217i
$403$	8.83415	+	1.39919i	0.440061	+	0.0696987i
$404$		0			0
$405$	−7.84545	−	7.96548i	−0.389844	−	0.395808i
$406$		0			0
$407$		0			0
$408$	−10.0000	+	10.0000i	−0.495074	+	0.495074i
$409$	−3.90879	−	12.0300i	−0.193277	−	0.594846i	−0.999992	−	0.00390565i	$-0.998757\pi$
$409$	−3.90879	−	12.0300i	−0.193277	−	0.594846i	0.806715	−	0.590941i	$-0.201243\pi$
$410$	18.3927	+	25.7237i	0.908349	+	1.27040i
$411$	21.0344	−	15.2824i	1.03755	−	0.753826i
$412$	−34.0220	+	17.3351i	−1.67614	+	0.854037i
$413$		0			0
$414$	2.55834	−	1.85874i	0.125735	−	0.0913521i
$415$	−11.6325	−	16.2691i	−0.571019	−	0.798619i
$416$	−9.27051	−	28.5317i	−0.454524	−	1.39888i
$417$	−12.6491	+	12.6491i	−0.619430	+	0.619430i
$418$		0			0
$419$		−	36.0000i		−	1.75872i	−0.476162	−	0.879358i	$-0.657972\pi$
$419$		−	36.0000i		−	1.75872i	0.476162	−	0.879358i	$-0.342028\pi$
$420$		0			0
$421$	22.6525	+	16.4580i	1.10401	+	0.802113i	0.981711	−	0.190380i	$-0.0609719\pi$
$421$	22.6525	+	16.4580i	1.10401	+	0.802113i	0.122304	+	0.992493i	$0.460972\pi$
$422$	−55.8721	−	8.84927i	−2.71981	−	0.430776i
$423$	1.92612	+	3.78022i	0.0936511	+	0.183801i
$424$	0.977198	−	3.00750i	0.0474569	−	0.146057i
$425$	−15.5695	−	16.0496i	−0.755233	−	0.778521i
$426$	−14.8699	+	20.4667i	−0.720450	+	0.991614i
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$	18.0450	−	5.86319i	0.869198	−	0.282420i	0.159733	−	0.987160i	$-0.448937\pi$
$431$	18.0450	−	5.86319i	0.869198	−	0.282420i	0.709465	+	0.704741i	$0.248937\pi$
$432$	0.884927	+	5.58721i	0.0425761	+	0.268815i
$433$	0.221232	−	1.39680i	0.0106317	−	0.0671260i	−0.981802	−	0.189907i	$-0.939181\pi$
$433$	0.221232	−	1.39680i	0.0106317	−	0.0671260i	0.992434	+	0.122781i	$0.0391813\pi$
$434$		0			0
$435$	16.0906	+	11.8782i	0.771487	+	0.569516i
$436$	−22.3049	−	30.7000i	−1.06821	−	1.47027i
$437$	8.83415	−	1.39919i	0.422595	−	0.0669324i
$438$	−12.6007	−	6.42040i	−0.602086	−	0.306778i
$439$	12.6491			0.603709			0.301855	−	0.953354i	$-0.402394\pi$
$439$	12.6491			0.603709			0.301855	+	0.953354i	$0.402394\pi$
$440$		0			0
$441$	−7.00000			−0.333333
$442$	39.8470	+	20.3031i	1.89533	+	0.965719i
$443$	15.3648	−	2.43355i	0.730005	−	0.115621i	0.219642	−	0.975581i	$-0.429511\pi$
$443$	15.3648	−	2.43355i	0.730005	−	0.115621i	0.510363	+	0.859959i	$0.329511\pi$
$444$	−10.5801	−	14.5623i	−0.502111	−	0.691096i
$445$	13.2668	−	1.99814i	0.628906	−	0.0947207i
$446$	33.0826	+	10.7492i	1.56650	+	0.508988i
$447$		0			0
$448$		0			0
$449$	5.70634	−	1.85410i	0.269299	−	0.0875005i	−0.171255	−	0.985227i	$-0.554782\pi$
$449$	5.70634	−	1.85410i	0.269299	−	0.0875005i	0.440554	+	0.897726i	$0.354782\pi$
$450$	11.0680	−	1.58114i	0.521749	−	0.0745356i
$451$		0			0
$452$	−27.0000	−	27.0000i	−1.26997	−	1.26997i
$453$		0			0
$454$	11.7557	−	16.1803i	0.551723	−	0.759381i
$455$		0			0
$456$	6.18034	−	19.0211i	0.289421	−	0.890746i
$457$	10.1515	+	19.9235i	0.474869	+	0.931983i	0.996872	+	0.0790387i	$0.0251851\pi$
$457$	10.1515	+	19.9235i	0.474869	+	0.931983i	−0.522003	+	0.852944i	$0.674815\pi$
$458$	−8.83415	−	1.39919i	−0.412793	−	0.0653800i
$459$	−20.4667	−	14.8699i	−0.955303	−	0.694068i
$460$	0.0720166	−	9.48656i	0.00335779	−	0.442313i
$461$			25.2982i			1.17826i	0.808040	+	0.589128i	$0.200529\pi$
$461$			25.2982i			1.17826i	−0.808040	+	0.589128i	$0.799471\pi$
$462$		0			0
$463$	9.00000	−	9.00000i	0.418265	−	0.418265i	−0.466340	−	0.884606i	$-0.654428\pi$
$463$	9.00000	−	9.00000i	0.418265	−	0.418265i	0.884606	+	0.466340i	$0.154428\pi$
$464$	−1.95440	−	6.01501i	−0.0907305	−	0.279240i
$465$	−5.14475	+	3.67853i	−0.238582	+	0.170588i
$466$	−24.2705	+	17.6336i	−1.12431	+	0.816859i
$467$	−8.82051	+	4.49428i	−0.408165	+	0.207970i	−0.646004	−	0.763334i	$-0.723561\pi$
$467$	−8.82051	+	4.49428i	−0.408165	+	0.207970i	0.237839	+	0.971305i	$0.423561\pi$
$468$	−11.9541	+	6.09092i	−0.552579	+	0.281553i
$469$		0			0
$470$	20.9262	+	3.47743i	0.965255	+	0.160402i
$471$	4.32624	+	13.3148i	0.199343	+	0.613513i
$472$	−9.48683	+	9.48683i	−0.436667	+	0.436667i
$473$		0			0
$474$		−	20.0000i		−	0.918630i
$475$	29.9232	+	10.2274i	1.37297	+	0.469268i
$476$		0			0
$477$	1.39680	+	0.221232i	0.0639552	+	0.0101295i
$478$	19.2612	+	37.8022i	0.880986	+	1.72903i
$479$	−1.95440	+	6.01501i	−0.0892986	+	0.274833i	−0.985726	−	0.168358i	$-0.946154\pi$
$479$	−1.95440	+	6.01501i	−0.0892986	+	0.274833i	0.896427	+	0.443191i	$0.146154\pi$
$480$	18.8275	+	9.77380i	0.859352	+	0.446111i
$481$	−11.1524	+	15.3500i	−0.508508	+	0.699901i
$482$	−6.42040	+	12.6007i	−0.292441	+	0.573948i
$483$		0			0
$484$		0			0
$485$	21.0000	+	7.00000i	0.953561	+	0.317854i
$486$	21.0525	−	6.84038i	0.954962	−	0.310286i
$487$	−0.663695	−	4.19041i	−0.0300749	−	0.189885i	0.968077	−	0.250653i	$-0.0806452\pi$
$487$	−0.663695	−	4.19041i	−0.0300749	−	0.189885i	−0.998152	+	0.0607673i	$0.980645\pi$
$488$	2.21232	−	13.9680i	0.100147	−	0.632303i
$489$	−1.90211	−	0.618034i	−0.0860165	−	0.0279485i
$490$	−20.7868	+	28.1586i	−0.939054	+	1.27208i
$491$	−3.71748	−	5.11667i	−0.167768	−	0.230912i	0.716852	−	0.697225i	$-0.245582\pi$
$491$	−3.71748	−	5.11667i	−0.167768	−	0.230912i	−0.884620	+	0.466313i	$0.845582\pi$
$492$	26.5025	−	4.19758i	1.19482	−	0.189241i
$493$	25.2015	+	12.8408i	1.13502	+	0.578320i
$494$	−63.2456			−2.84555
$495$		0			0
$496$	2.00000			0.0898027
$497$		0			0
$498$	−27.9360	+	4.42463i	−1.25184	+	0.198273i
$499$	−19.9847	−	27.5066i	−0.894638	−	1.23136i	−0.972147	−	0.234372i	$-0.924697\pi$
$499$	−19.9847	−	27.5066i	−0.894638	−	1.23136i	0.0775090	−	0.996992i	$-0.475303\pi$
$500$	15.9039	−	29.5308i	0.711244	−	1.32066i
$501$	24.0600	+	7.81758i	1.07492	+	0.349264i
$502$	−4.19758	+	26.5025i	−0.187347	+	1.18286i
$503$	−1.39919	−	8.83415i	−0.0623869	−	0.393895i	−0.999047	−	0.0436548i	$-0.986100\pi$
$503$	−1.39919	−	8.83415i	−0.0623869	−	0.393895i	0.936660	−	0.350241i	$-0.113900\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−7.00000	−	7.00000i	−0.310881	−	0.310881i
$508$	−12.1818	+	23.9082i	−0.540482	+	1.06076i
$509$	2.35114	−	3.23607i	0.104212	−	0.143436i	−0.753726	−	0.657189i	$-0.771745\pi$
$509$	2.35114	−	3.23607i	0.104212	−	0.143436i	0.857938	+	0.513753i	$0.171745\pi$
$510$	−30.1484	+	9.54339i	−1.33499	+	0.422588i
$511$		0			0
$512$	−5.07577	−	9.96176i	−0.224319	−	0.440252i
$513$	35.3366	+	5.59677i	1.56015	+	0.247103i
$514$	17.9084	+	13.0112i	0.789904	+	0.573899i
$515$	−28.4597	−	0.216050i	−1.25408	−	0.00952029i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−1.95440	−	6.01501i	−0.0857884	−	0.264030i
$520$	−3.66554	+	22.0582i	−0.160744	+	0.967316i
$521$	22.6525	−	16.4580i	0.992423	−	0.721038i	0.0319726	−	0.999489i	$-0.489821\pi$
$521$	22.6525	−	16.4580i	0.992423	−	0.721038i	0.960450	+	0.278451i	$0.0898211\pi$
$522$	−12.6007	+	6.42040i	−0.551519	+	0.281013i
$523$	23.9082	−	12.1818i	1.04543	−	0.532675i	0.155059	−	0.987905i	$-0.450443\pi$
$523$	23.9082	−	12.1818i	1.04543	−	0.532675i	0.890374	+	0.455230i	$0.150443\pi$
$524$	−30.7000	+	22.3049i	−1.34114	+	0.974393i
$525$		0			0
$526$	−18.5410	−	57.0634i	−0.808427	−	2.48808i
$527$	−6.32456	+	6.32456i	−0.275502	+	0.275502i
$528$		0			0
$529$			21.0000i			0.913043i
$530$	5.03781	−	4.96190i	0.218829	−	0.215531i
$531$	−4.85410	−	3.52671i	−0.210650	−	0.153046i
$532$		0			0
$533$	−12.8408	−	25.2015i	−0.556196	−	1.09160i
$534$	5.86319	−	18.0450i	0.253725	−	0.780885i
$535$		0			0
$536$	−5.57622	+	7.67501i	−0.240856	+	0.331510i
$537$	2.56816	−	5.04029i	0.110824	−	0.217505i
$538$	37.9473	+	37.9473i	1.63603	+	1.63603i
$539$		0			0
$540$	12.0000	−	36.0000i	0.516398	−	1.54919i
$541$	−36.0901	+	11.7264i	−1.55163	+	0.504156i	−0.954557	−	0.298029i	$-0.903671\pi$
$541$	−36.0901	+	11.7264i	−1.55163	+	0.504156i	−0.597076	+	0.802185i	$0.703671\pi$
$542$	4.42463	+	27.9360i	0.190054	+	1.19996i
$543$	−1.76985	+	11.1744i	−0.0759517	+	0.479540i
$544$	28.5317	+	9.27051i	1.22329	+	0.397470i
$545$	−4.21244	−	27.9688i	−0.180441	−	1.19805i
$546$		0			0
$547$	17.6683	−	2.79838i	0.755442	−	0.119650i	0.233178	−	0.972434i	$-0.425088\pi$
$547$	17.6683	−	2.79838i	0.755442	−	0.119650i	0.522264	+	0.852784i	$0.325088\pi$
$548$	49.1429	+	25.0395i	2.09928	+	1.06964i
$549$	6.32456			0.269925
$550$		0			0
$551$	−40.0000			−1.70406
$552$	−3.98470	−	2.03031i	−0.169600	−	0.0864156i
$553$		0			0
$554$	17.6336	+	24.2705i	0.749178	+	1.03116i
$555$	−1.99814	−	13.2668i	−0.0848161	−	0.563143i
$556$	−36.0901	−	11.7264i	−1.53056	−	0.497309i
$557$	3.49798	−	22.0854i	0.148214	−	0.935788i	−0.795723	−	0.605661i	$-0.792909\pi$
$557$	3.49798	−	22.0854i	0.148214	−	0.935788i	0.943937	−	0.330126i	$-0.107091\pi$
$558$	−0.699596	−	4.41708i	−0.0296163	−	0.186990i
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−30.0000	−	30.0000i	−1.26547	−	1.26547i
$563$	12.1818	−	23.9082i	0.513403	−	1.00761i	−0.478195	−	0.878254i	$-0.658709\pi$
$563$	12.1818	−	23.9082i	0.513403	−	1.00761i	0.991598	−	0.129357i	$-0.0412914\pi$
$564$	10.5801	−	14.5623i	0.445504	−	0.613184i
$565$	−8.58905	−	27.1335i	−0.361344	−	1.14152i
$566$	−6.18034	+	19.0211i	−0.259779	+	0.799518i
$567$		0			0
$568$	−17.6683	−	2.79838i	−0.741346	−	0.117418i
$569$	−30.7000	−	22.3049i	−1.28701	−	0.935069i	−0.287272	−	0.957849i	$-0.592748\pi$
$569$	−30.7000	−	22.3049i	−1.28701	−	0.935069i	−0.999741	+	0.0227798i	$0.992748\pi$
$570$	31.8619	−	31.3818i	1.33455	−	1.31444i
$571$		−	44.2719i		−	1.85272i	−0.376638	−	0.926360i	$-0.622920\pi$
$571$		−	44.2719i		−	1.85272i	0.376638	−	0.926360i	$-0.377080\pi$
$572$		0			0
$573$	−22.0000	+	22.0000i	−0.919063	+	0.919063i
$574$		0			0
$575$	3.30548	−	6.25090i	0.137848	−	0.260681i
$576$	−10.5172	+	7.64121i	−0.438218	+	0.318384i
$577$	28.9817	−	14.7669i	1.20652	−	0.614754i	0.269156	−	0.963097i	$-0.413255\pi$
$577$	28.9817	−	14.7669i	1.20652	−	0.614754i	0.937367	+	0.348342i	$0.113255\pi$
$578$	−5.97705	+	3.04546i	−0.248613	+	0.126674i
$579$	25.5834	−	18.5874i	1.06321	−	0.772466i
$580$	−6.95486	+	41.8525i	−0.288785	+	1.73783i
$581$		0			0
$582$	22.1359	−	22.1359i	0.917564	−	0.917564i
$583$		0			0
$584$		−	10.0000i		−	0.413803i
$585$	−9.99971	−	0.0759122i	−0.413437	−	0.00313858i
$586$	−40.4508	−	29.3893i	−1.67101	−	1.21406i
$587$	9.77762	+	1.54862i	0.403565	+	0.0639185i	0.354918	−	0.934898i	$-0.384509\pi$
$587$	9.77762	+	1.54862i	0.403565	+	0.0639185i	0.0486476	+	0.998816i	$0.484509\pi$
$588$	13.4828	+	26.4615i	0.556023	+	1.09126i
$589$	3.90879	−	12.0300i	0.161059	−	0.495688i
$590$	−28.6012	+	9.05365i	−1.17749	+	0.372733i
$591$	3.71748	−	5.11667i	0.152917	−	0.210472i
$592$	−1.92612	+	3.78022i	−0.0791630	+	0.155366i
$593$	−15.8114	−	15.8114i	−0.649296	−	0.649296i	0.303527	−	0.952823i	$-0.401836\pi$
$593$	−15.8114	−	15.8114i	−0.649296	−	0.649296i	−0.952823	+	0.303527i	$0.901836\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1.32739	−	8.38081i	−0.0543265	−	0.343004i
$598$	−2.21232	+	13.9680i	−0.0904684	+	0.571195i
$599$	−15.2169	−	4.94427i	−0.621746	−	0.202017i	−0.0188306	−	0.999823i	$-0.505994\pi$
$599$	−15.2169	−	4.94427i	−0.621746	−	0.202017i	−0.602915	+	0.797805i	$0.705994\pi$
$600$	−9.09843	−	12.9313i	−0.371442	−	0.527918i
$601$	18.5874	+	25.5834i	0.758196	+	1.04357i	0.997362	+	0.0725885i	$0.0231260\pi$
$601$	18.5874	+	25.5834i	0.758196	+	1.04357i	−0.239166	+	0.970979i	$0.576874\pi$
$602$		0			0
$603$	−3.78022	−	1.92612i	−0.153942	−	0.0784376i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−39.8470	−	20.3031i	−1.61734	−	0.824076i	−0.999280	−	0.0379461i	$-0.987918\pi$
$607$	−39.8470	−	20.3031i	−1.61734	−	0.824076i	−0.618061	−	0.786130i	$-0.712082\pi$
$608$	−41.9041	+	6.63695i	−1.69943	+	0.269164i
$609$		0			0
$610$	18.7811	−	25.4415i	0.760423	−	1.03010i
$611$	−18.0450	−	5.86319i	−0.730024	−	0.237199i
$612$	2.09879	−	13.2512i	0.0848385	−	0.535649i
$613$	−6.29637	−	39.7537i	−0.254308	−	1.60564i	−0.702490	−	0.711694i	$-0.747928\pi$
$613$	−6.29637	−	39.7537i	−0.254308	−	1.60564i	0.448182	−	0.893942i	$-0.352072\pi$
$614$		0			0
$615$	18.9737	+	6.32456i	0.765092	+	0.255031i
$616$		0			0
$617$	−17.0000	−	17.0000i	−0.684394	−	0.684394i	0.276593	−	0.960987i	$-0.410795\pi$
$617$	−17.0000	−	17.0000i	−0.684394	−	0.684394i	−0.960987	+	0.276593i	$0.910795\pi$
$618$	−18.2728	+	35.8623i	−0.735038	+	1.44259i
$619$	−21.1603	+	29.1246i	−0.850503	+	1.17062i	0.133249	+	0.991083i	$0.457459\pi$
$619$	−21.1603	+	29.1246i	−0.850503	+	1.17062i	−0.983752	+	0.179534i	$0.942541\pi$
$620$	−11.9075	−	6.18149i	−0.478218	−	0.248255i
$621$	2.47214	−	7.60845i	0.0992034	−	0.305317i
$622$	8.12123	+	15.9388i	0.325632	+	0.639088i
$623$		0			0
$624$	−5.11667	−	3.71748i	−0.204831	−	0.148818i
$625$	20.6622	−	14.0738i	0.826489	−	0.562952i
$626$		−	28.4605i		−	1.13751i
$627$		0			0
$628$	−21.0000	+	21.0000i	−0.837991	+	0.837991i
$629$	−5.86319	−	18.0450i	−0.233781	−	0.719502i
$630$		0			0
$631$	−25.8885	+	18.8091i	−1.03061	+	0.748780i	−0.968430	−	0.249286i	$-0.919804\pi$
$631$	−25.8885	+	18.8091i	−1.03061	+	0.748780i	−0.0621766	+	0.998065i	$0.519804\pi$
$632$	12.6007	−	6.42040i	0.501230	−	0.255390i
$633$	−31.8776	+	16.2425i	−1.26702	+	0.645580i
$634$	43.4917	−	31.5986i	1.72728	−	1.25494i
$635$	−16.2691	+	11.6325i	−0.645620	+	0.461623i
$636$	−1.85410	−	5.70634i	−0.0735199	−	0.226271i
$637$	22.1359	−	22.1359i	0.877058	−	0.877058i
$638$		0			0
$639$		−	8.00000i		−	0.316475i
$640$	−0.265693	+	34.9990i	−0.0105024	+	1.38346i
$641$	6.47214	+	4.70228i	0.255634	+	0.185729i	0.708220	−	0.705992i	$-0.249498\pi$
$641$	6.47214	+	4.70228i	0.255634	+	0.185729i	−0.452586	+	0.891721i	$0.649498\pi$
$642$		0			0
$643$	7.06243	+	13.8608i	0.278515	+	0.546617i	0.987311	−	0.158796i	$-0.0507614\pi$
$643$	7.06243	+	13.8608i	0.278515	+	0.546617i	−0.708796	+	0.705413i	$0.750761\pi$
$644$		0			0
$645$		0			0
$646$	37.1748	−	51.1667i	1.46262	−	2.01313i
$647$	−8.34651	+	16.3810i	−0.328135	+	0.644002i	−0.994855	−	0.101307i	$-0.967698\pi$
$647$	−8.34651	+	16.3810i	−0.328135	+	0.644002i	0.666720	+	0.745308i	$0.267698\pi$
$648$	−7.90569	−	7.90569i	−0.310565	−	0.310565i
$649$		0			0
$650$	−30.0000	+	40.0000i	−1.17670	+	1.56893i
$651$		0			0
$652$	−0.663695	−	4.19041i	−0.0259923	−	0.164109i
$653$	0.221232	−	1.39680i	0.00865747	−	0.0546611i	−0.982981	−	0.183705i	$-0.941191\pi$
$653$	0.221232	−	1.39680i	0.00865747	−	0.0546611i	0.991639	+	0.129044i	$0.0411909\pi$
$654$	−38.0423	−	12.3607i	−1.48757	−	0.483341i
$655$	−27.9688	+	4.21244i	−1.09283	+	0.164594i
$656$	−3.71748	−	5.11667i	−0.145143	−	0.199773i
$657$	4.41708	−	0.699596i	0.172327	−	0.0272938i
$658$		0			0
$659$	−12.6491			−0.492739			−0.246370	−	0.969176i	$-0.579238\pi$
$659$	−12.6491			−0.492739			−0.246370	+	0.969176i	$0.579238\pi$
$660$		0			0
$661$	42.0000			1.63361			0.816805	−	0.576913i	$-0.195743\pi$
$661$	42.0000			1.63361			0.816805	+	0.576913i	$0.195743\pi$
$662$	−35.8623	−	18.2728i	−1.39383	−	0.710191i
$663$	27.9360	−	4.42463i	1.08495	−	0.171839i
$664$	−11.7557	−	16.1803i	−0.456210	−	0.627919i
$665$		0			0
$666$	9.02251	+	2.93159i	0.349615	+	0.113597i
$667$	−1.39919	+	8.83415i	−0.0541769	+	0.342060i
$668$	8.39515	+	53.0049i	0.324818	+	2.05082i
$669$	20.9232	−	6.79837i	0.808939	−	0.262840i
$670$	−18.9737	+	9.48683i	−0.733017	+	0.366508i
$671$		0			0
$672$		0			0
$673$	18.2728	−	35.8623i	0.704363	−	1.38239i	−0.210083	−	0.977684i	$-0.567373\pi$
$673$	18.2728	−	35.8623i	0.704363	−	1.38239i	0.914446	−	0.404707i	$-0.132627\pi$
$674$	17.6336	−	24.2705i	0.679219	−	0.934865i
$675$	20.3013	−	19.6941i	0.781399	−	0.758025i
$676$	6.48936	−	19.9722i	0.249591	−	0.768161i
$677$	−6.09092	−	11.9541i	−0.234093	−	0.459434i	0.743838	−	0.668360i	$-0.233003\pi$
$677$	−6.09092	−	11.9541i	−0.234093	−	0.459434i	−0.977931	+	0.208926i	$0.933003\pi$
$678$	−39.7537	−	6.29637i	−1.52673	−	0.241810i
$679$		0			0
$680$	−15.6909	−	15.9310i	−0.601719	−	0.610924i
$681$		−	12.6491i		−	0.484715i
$682$		0			0
$683$	29.0000	−	29.0000i	1.10965	−	1.10965i	0.116459	−	0.993196i	$-0.462846\pi$
$683$	29.0000	−	29.0000i	1.10965	−	1.10965i	0.993196	−	0.116459i	$-0.0371542\pi$
$684$	5.86319	+	18.0450i	0.224184	+	0.689969i
$685$	23.9105	+	33.4408i	0.913572	+	1.27771i
$686$		0			0
$687$	−5.04029	+	2.56816i	−0.192299	+	0.0979813i
$688$		0			0
$689$	−5.11667	+	3.71748i	−0.194930	+	0.141625i
$690$	−5.81627	−	8.13456i	−0.221422	−	0.309677i
$691$	−8.65248	−	26.6296i	−0.329156	−	1.01304i	−0.969530	−	0.244974i	$-0.921221\pi$
$691$	−8.65248	−	26.6296i	−0.329156	−	1.01304i	0.640374	−	0.768063i	$-0.278779\pi$
$692$	9.48683	−	9.48683i	0.360635	−	0.360635i
$693$		0			0
$694$		−	60.0000i		−	2.27757i
$695$	−19.8476	−	20.1512i	−0.752862	−	0.764380i
$696$	16.1803	+	11.7557i	0.613314	+	0.445599i
$697$	27.9360	+	4.42463i	1.05815	+	0.167595i
$698$	32.1020	+	63.0037i	1.21508	+	2.38472i
$699$	−5.86319	+	18.0450i	−0.221766	+	0.682526i
$700$		0			0
$701$	18.5874	−	25.5834i	0.702036	−	0.966270i	−0.297895	−	0.954599i	$-0.596285\pi$
$701$	18.5874	−	25.5834i	0.702036	−	0.966270i	0.999932	−	0.0116718i	$-0.00371533\pi$
$702$	−25.6816	+	50.4029i	−0.969289	+	1.90234i
$703$	18.9737	+	18.9737i	0.715605	+	0.715605i
$704$		0			0
$705$	12.0000	−	6.00000i	0.451946	−	0.225973i
$706$	−63.1576	+	20.5211i	−2.37697	+	0.772324i
$707$		0			0
$708$	−3.98217	+	25.1424i	−0.149659	+	0.944911i
$709$	−5.70634	−	1.85410i	−0.214306	−	0.0696323i	0.199896	−	0.979817i	$-0.435939\pi$
$709$	−5.70634	−	1.85410i	−0.214306	−	0.0696323i	−0.414202	+	0.910185i	$0.635939\pi$
$710$	−32.1813	−	23.7564i	−1.20774	−	0.891561i
$711$	3.71748	+	5.11667i	0.139416	+	0.191890i
$712$	13.2512	−	2.09879i	0.496611	−	0.0786554i
$713$	−2.52015	−	1.28408i	−0.0943802	−	0.0480891i
$714$		0			0
$715$		0			0
$716$	12.0000			0.448461
$717$	23.9082	+	12.1818i	0.892869	+	0.454939i
$718$	−41.9041	+	6.63695i	−1.56385	+	0.247689i
$719$	−14.1068	−	19.4164i	−0.526097	−	0.724110i	0.460433	−	0.887695i	$-0.347694\pi$
$719$	−14.1068	−	19.4164i	−0.526097	−	0.724110i	−0.986529	+	0.163585i	$0.947694\pi$
$720$	−2.21113	+	0.333023i	−0.0824040	+	0.0124110i
$721$		0			0
$722$	−7.34576	+	46.3793i	−0.273381	+	1.72606i
$723$	1.39919	+	8.83415i	0.0520365	+	0.328546i
$724$	−22.8254	+	7.41641i	−0.848298	+	0.275629i
$725$	−18.9737	+	25.2982i	−0.704664	+	0.939552i
$726$		0			0
$727$	23.0000	+	23.0000i	0.853023	+	0.853023i	0.990504	−	0.137482i	$-0.0439008\pi$
$727$	23.0000	+	23.0000i	0.853023	+	0.853023i	−0.137482	+	0.990504i	$0.543901\pi$
$728$		0			0
$729$	17.0458	−	23.4615i	0.631325	−	0.868944i
$730$	10.3025	−	19.8459i	0.381312	−	0.734529i
$731$		0			0
$732$	−12.1818	−	23.9082i	−0.450254	−	0.883673i
$733$	−13.2512	−	2.09879i	−0.489445	−	0.0775205i	−0.0931661	−	0.995651i	$-0.529699\pi$
$733$	−13.2512	−	2.09879i	−0.489445	−	0.0775205i	−0.396279	+	0.918130i	$0.629699\pi$
$734$	−7.67501	−	5.57622i	−0.283290	−	0.205822i
$735$	−0.168039	+	22.1353i	−0.00619820	+	0.816473i
$736$			9.48683i			0.349689i
$737$		0			0
$738$	−10.0000	+	10.0000i	−0.368105	+	0.368105i
$739$	3.90879	+	12.0300i	0.143787	+	0.442531i	0.996853	−	0.0792718i	$-0.0252595\pi$
$739$	3.90879	+	12.0300i	0.143787	+	0.442531i	−0.853066	+	0.521803i	$0.825260\pi$
$740$	23.1514	−	16.5534i	0.851061	−	0.608515i
$741$	−32.3607	+	23.5114i	−1.18880	+	0.863713i
$742$		0			0
$743$		0			0		−0.453990	−	0.891007i	$-0.650000\pi$
$743$		0			0		0.453990	+	0.891007i	$0.350000\pi$
$744$	−5.11667	+	3.71748i	−0.187586	+	0.136289i
$745$		0			0
$746$	3.09017	+	9.51057i	0.113139	+	0.348207i
$747$	6.32456	−	6.32456i	0.231403	−	0.231403i
$748$		0			0
$749$		0			0
$750$	−4.73416	−	35.0369i	−0.172867	−	1.27937i
$751$	6.47214	+	4.70228i	0.236172	+	0.171589i	0.699576	−	0.714558i	$-0.253372\pi$
$751$	6.47214	+	4.70228i	0.236172	+	0.171589i	−0.463404	+	0.886147i	$0.653372\pi$
$752$	−4.19041	−	0.663695i	−0.152808	−	0.0242025i
$753$	7.70447	+	15.1209i	0.280767	+	0.551036i
$754$	19.5440	−	60.1501i	0.711749	−	2.19054i
$755$		0			0
$756$		0			0
$757$	17.3351	−	34.0220i	0.630054	−	1.23655i	−0.326556	−	0.945178i	$-0.605888\pi$
$757$	17.3351	−	34.0220i	0.630054	−	1.23655i	0.956610	−	0.291372i	$-0.0941118\pi$
$758$	−41.1096	−	41.1096i	−1.49317	−	1.49317i
$759$		0			0
$760$	30.0000	+	10.0000i	1.08821	+	0.362738i
$761$	36.0901	−	11.7264i	1.30826	−	0.425081i	0.429815	−	0.902917i	$-0.358579\pi$
$761$	36.0901	−	11.7264i	1.30826	−	0.425081i	0.878449	+	0.477836i	$0.158579\pi$
$762$	4.42463	+	27.9360i	0.160288	+	1.01202i
$763$		0			0
$764$	−62.7697	−	20.3951i	−2.27093	−	0.737870i
$765$	5.93910	−	8.04532i	0.214729	−	0.290879i
$766$	35.3161	+	48.6084i	1.27602	+	1.75629i
$767$	26.5025	−	4.19758i	0.956948	−	0.151566i
$768$	11.3407	+	5.77836i	0.409221	+	0.208508i
$769$	6.32456			0.228069			0.114035	−	0.993477i	$-0.463623\pi$
$769$	6.32456			0.228069			0.114035	+	0.993477i	$0.463623\pi$
$770$		0			0
$771$	14.0000			0.504198
$772$	59.7705	+	30.4546i	2.15119	+	1.09609i
$773$	15.3648	−	2.43355i	0.552634	−	0.0875287i	0.126129	−	0.992014i	$-0.459745\pi$
$773$	15.3648	−	2.43355i	0.552634	−	0.0875287i	0.426505	+	0.904485i	$0.359745\pi$
$774$		0			0
$775$	−5.75435	−	8.17848i	−0.206702	−	0.293779i
$776$	21.0525	+	6.84038i	0.755742	+	0.245555i
$777$		0			0
$778$	5.59677	+	35.3366i	0.200654	+	1.26688i
$779$	−38.0423	+	12.3607i	−1.36301	+	0.442867i
$780$	18.9737	+	37.9473i	0.679366	+	1.35873i
$781$		0			0
$782$	−10.0000	−	10.0000i	−0.357599	−	0.357599i
$783$	−16.2425	+	31.8776i	−0.580458	+	1.13921i
$784$	4.11450	−	5.66312i	0.146946	−	0.202254i
$785$	−21.1039	+	6.68037i	−0.753229	+	0.238433i
$786$	−12.3607	+	38.0423i	−0.440891	+	1.35692i
$787$	16.2425	+	31.8776i	0.578981	+	1.13631i	0.975851	+	0.218439i	$0.0700966\pi$
$787$	16.2425	+	31.8776i	0.578981	+	1.13631i	−0.396869	+	0.917875i	$0.629903\pi$
$788$	13.2512	+	2.09879i	0.472056	+	0.0747662i
$789$	−30.7000	−	22.3049i	−1.09295	−	0.794075i
$790$	31.6219	+	0.240055i	1.12506	+	0.00854079i
$791$		0			0
$792$		0			0
$793$	−20.0000	+	20.0000i	−0.710221	+	0.710221i
$794$	12.7036	+	39.0976i	0.450833	+	1.38752i
$795$	0.733107	−	4.41164i	0.0260006	−	0.156465i
$796$	14.5623	−	10.5801i	0.516147	−	0.375003i
$797$	16.3810	−	8.34651i	0.580243	−	0.295649i	−0.139128	−	0.990274i	$-0.544430\pi$
$797$	16.3810	−	8.34651i	0.580243	−	0.295649i	0.719371	+	0.694626i	$0.244430\pi$
$798$		0			0
$799$	15.3500	−	11.1524i	0.543045	−	0.394545i
$800$	−15.6793	+	29.6506i	−0.554346	+	1.04831i
$801$	1.85410	+	5.70634i	0.0655115	+	0.201624i
$802$	18.9737	−	18.9737i	0.669983	−	0.669983i
$803$		0			0
$804$			18.0000i			0.634811i
$805$		0			0
$806$	16.1803	+	11.7557i	0.569928	+	0.414077i
$807$	33.5233	+	5.30956i	1.18007	+	0.186905i
$808$		0			0
$809$	5.86319	−	18.0450i	0.206139	−	0.634429i	−0.793526	−	0.608536i	$-0.791757\pi$
$809$	5.86319	−	18.0450i	0.206139	−	0.634429i	0.999665	−	0.0258932i	$-0.00824298\pi$
$810$	−7.54471	−	23.8344i	−0.265094	−	0.837455i
$811$	−3.71748	+	5.11667i	−0.130538	+	0.179671i	−0.869283	−	0.494315i	$-0.835419\pi$
$811$	−3.71748	+	5.11667i	−0.130538	+	0.179671i	0.738745	+	0.673986i	$0.235419\pi$
$812$		0			0
$813$	12.6491	+	12.6491i	0.443624	+	0.443624i
$814$		0			0
$815$	1.00000	−	3.00000i	0.0350285	−	0.105085i
$816$	6.01501	−	1.95440i	0.210567	−	0.0684175i
$817$		0			0
$818$	4.42463	−	27.9360i	0.154704	−	0.976761i
$819$		0			0
$820$	6.31866	+	41.9532i	0.220657	+	1.46507i
$821$	−11.1524	−	15.3500i	−0.389223	−	0.535719i	0.568776	−	0.822493i	$-0.307417\pi$
$821$	−11.1524	−	15.3500i	−0.389223	−	0.535719i	−0.957998	+	0.286773i	$0.907417\pi$
$822$	57.4220	−	9.09475i	2.00282	−	0.317216i
$823$	−13.8608	−	7.06243i	−0.483157	−	0.246181i	0.195407	−	0.980722i	$-0.437397\pi$
$823$	−13.8608	−	7.06243i	−0.483157	−	0.246181i	−0.678564	+	0.734541i	$0.737397\pi$
$824$	−28.4605			−0.991468
$825$		0			0
$826$		0			0
$827$	−7.96940	−	4.06061i	−0.277123	−	0.141201i	0.309906	−	0.950767i	$-0.399703\pi$
$827$	−7.96940	−	4.06061i	−0.277123	−	0.141201i	−0.587029	+	0.809566i	$0.699703\pi$
$828$	4.19041	−	0.663695i	0.145627	−	0.0230650i
$829$	3.52671	+	4.85410i	0.122488	+	0.168590i	0.865857	−	0.500291i	$-0.166774\pi$
$829$	3.52671	+	4.85410i	0.122488	+	0.168590i	−0.743370	+	0.668881i	$0.766774\pi$
$830$	−6.66045	−	44.2226i	−0.231188	−	1.53499i
$831$	18.0450	+	5.86319i	0.625975	+	0.203392i
$832$	9.09475	−	57.4220i	0.315304	−	1.99075i
$833$	4.89717	+	30.9195i	0.169677	+	1.07130i
$834$	−38.0423	+	12.3607i	−1.31730	+	0.428015i
$835$	−12.6491	+	37.9473i	−0.437741	+	1.31322i
$836$		0			0
$837$	−8.00000	−	8.00000i	−0.276520	−	0.276520i
$838$	36.5455	−	71.7246i	1.26244	−	2.47769i
$839$	−3.52671	+	4.85410i	−0.121756	+	0.167582i	−0.865544	−	0.500833i	$-0.833027\pi$
$839$	−3.52671	+	4.85410i	−0.121756	+	0.167582i	0.743788	+	0.668415i	$0.233027\pi$
$840$		0			0
$841$	3.39919	−	10.4616i	0.117213	−	0.360746i
$842$	28.4243	+	55.7858i	0.979566	+	1.92251i
$843$	−26.5025	−	4.19758i	−0.912793	−	0.144572i
$844$	−61.4001	−	44.6098i	−2.11348	−	1.53553i
$845$	11.1517	−	10.9836i	0.383629	−	0.377848i
$846$			9.48683i			0.326164i
$847$		0			0
$848$	−1.00000	+	1.00000i	−0.0343401	+	0.0343401i
$849$	3.90879	+	12.0300i	0.134149	+	0.412869i
$850$	−14.7271	−	47.7819i	−0.505136	−	1.63891i
$851$	4.85410	−	3.52671i	0.166396	−	0.120894i
$852$	−30.2418	+	15.4089i	−1.03607	+	0.527902i
$853$	−11.9541	+	6.09092i	−0.409301	+	0.208549i	−0.646504	−	0.762911i	$-0.723769\pi$
$853$	−11.9541	+	6.09092i	−0.409301	+	0.208549i	0.237203	+	0.971460i	$0.423769\pi$
$854$		0			0
$855$	−2.31829	+	13.9508i	−0.0792838	+	0.477108i
$856$		0			0
$857$	15.8114	−	15.8114i	0.540107	−	0.540107i	−0.383453	−	0.923560i	$-0.625265\pi$
$857$	15.8114	−	15.8114i	0.540107	−	0.540107i	0.923560	+	0.383453i	$0.125265\pi$
$858$		0			0
$859$			44.0000i			1.50126i	0.660722	+	0.750630i	$0.270250\pi$
$859$			44.0000i			1.50126i	−0.660722	+	0.750630i	$0.729750\pi$
$860$		0			0
$861$		0			0
$862$	41.9041	+	6.63695i	1.42726	+	0.226055i
$863$	0.642040	+	1.26007i	0.0218553	+	0.0428934i	0.901676	−	0.432412i	$-0.142337\pi$
$863$	0.642040	+	1.26007i	0.0218553	+	0.0428934i	−0.879821	+	0.475306i	$0.842337\pi$
$864$	−11.7264	+	36.0901i	−0.398939	+	1.22781i
$865$	9.53375	−	3.01788i	0.324157	−	0.102611i
$866$	1.85874	−	2.55834i	0.0631626	−	0.0869358i
$867$	−1.92612	+	3.78022i	−0.0654144	+	0.128383i
$868$		0			0
$869$		0			0
$870$	20.0000	+	40.0000i	0.678064	+	1.35613i
$871$	18.0450	−	5.86319i	0.611432	−	0.198666i
$872$	−4.42463	−	27.9360i	−0.149837	−	0.946034i
$873$	−1.54862	+	9.77762i	−0.0524129	+	0.330922i
$874$	19.0211	+	6.18034i	0.643399	+	0.209053i
$875$		0			0
$876$	−11.1524	−	15.3500i	−0.376806	−	0.518629i
$877$	−57.4220	+	9.09475i	−1.93900	+	0.307108i	−0.999383	−	0.0351127i	$-0.988821\pi$
$877$	−57.4220	+	9.09475i	−1.93900	+	0.307108i	−0.939620	+	0.342221i	$0.888821\pi$
$878$	25.2015	+	12.8408i	0.850508	+	0.433356i
$879$	−31.6228			−1.06661
$880$		0			0
$881$	2.00000			0.0673817			0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000			0.0673817			0.0336909	+	0.999432i	$0.489274\pi$
$882$	−13.9465	−	7.10608i	−0.469602	−	0.239274i
$883$	−26.5392	+	4.20340i	−0.893117	+	0.141456i	−0.586091	−	0.810245i	$-0.699334\pi$
$883$	−26.5392	+	4.20340i	−0.893117	+	0.141456i	−0.307026	+	0.951701i	$0.599334\pi$
$884$	35.2671	+	48.5410i	1.18616	+	1.63261i
$885$	−11.2686	+	15.2649i	−0.378791	+	0.513125i
$886$	33.0826	+	10.7492i	1.11143	+	0.361126i
$887$	−1.39919	+	8.83415i	−0.0469803	+	0.296622i	−0.999980	−	0.00634986i	$-0.997979\pi$
$887$	−1.39919	+	8.83415i	−0.0469803	+	0.296622i	0.953000	+	0.302972i	$0.0979788\pi$
$888$	−2.09879	−	13.2512i	−0.0704307	−	0.444682i
$889$		0			0
$890$	28.4605	+	9.48683i	0.953998	+	0.317999i
$891$		0			0
$892$	33.0000	+	33.0000i	1.10492	+	1.10492i
$893$	−12.1818	+	23.9082i	−0.407650	+	0.800058i
$894$		0			0
$895$	7.93835	+	4.12099i	0.265350	+	0.137750i
$896$		0			0
$897$	4.06061	+	7.96940i	0.135580	+	0.266091i
$898$	13.2512	+	2.09879i	0.442199	+	0.0700375i
$899$	10.2333	+	7.43496i	0.341301	+	0.247970i
$900$	14.1938	+	4.85130i	0.473128	+	0.161710i
$901$		−	6.32456i		−	0.210701i
$902$		0			0
$903$		0			0
$904$	−8.79478	−	27.0675i	−0.292510	−	0.900253i
$905$	−17.6466	−	2.93243i	−0.586591	−	0.0974772i
$906$		0			0
$907$	−21.4212	+	10.9147i	−0.711281	+	0.362416i	−0.771899	−	0.635745i	$-0.780693\pi$
$907$	−21.4212	+	10.9147i	−0.711281	+	0.362416i	0.0606180	+	0.998161i	$0.480693\pi$
$908$	23.9082	−	12.1818i	0.793422	−	0.404269i
$909$		0			0
$910$		0			0
$911$	12.9787	+	39.9444i	0.430004	+	1.32342i	0.898121	+	0.439749i	$0.144933\pi$
$911$	12.9787	+	39.9444i	0.430004	+	1.32342i	−0.468117	+	0.883667i	$0.655067\pi$
$912$	−6.32456	+	6.32456i	−0.209427	+	0.209427i
$913$		0			0
$914$			50.0000i			1.65385i
$915$	0.151824	−	19.9994i	0.00501916	−	0.661161i
$916$	−9.70820	−	7.05342i	−0.320768	−	0.233052i
$917$		0			0
$918$	−25.6816	−	50.4029i	−0.847618	−	1.66354i
$919$	11.7264	−	36.0901i	0.386817	−	1.19050i	−0.548336	−	0.836258i	$-0.684739\pi$
$919$	11.7264	−	36.0901i	0.386817	−	1.19050i	0.935153	−	0.354243i	$-0.115261\pi$
$920$	3.25793	−	6.27582i	0.107411	−	0.206908i
$921$		0			0
$922$	−25.6816	+	50.4029i	−0.845778	+	1.65993i
$923$	25.2982	+	25.2982i	0.832701	+	0.832701i
$924$		0			0
$925$	21.0000	−	3.00000i	0.690476	−	0.0986394i
$926$	27.0675	−	8.79478i	0.889495	−	0.289014i
$927$	−1.99109	−	12.5712i	−0.0653958	−	0.412893i
$928$	6.63695	−	41.9041i	0.217869	−	1.37557i
$929$	3.80423	+	1.23607i	0.124813	+	0.0405541i	0.370757	−	0.928730i	$-0.379098\pi$
$929$	3.80423	+	1.23607i	0.124813	+	0.0405541i	−0.245945	+	0.969284i	$0.579098\pi$
$930$	−13.9844	+	2.10622i	−0.458567	+	0.0690657i
$931$	−26.0224	−	35.8167i	−0.852848	−	1.17385i
$932$	−39.7537	+	6.29637i	−1.30218	+	0.206244i
$933$	10.0806	+	5.13632i	0.330024	+	0.168155i
$934$	−22.1359			−0.724310
$935$		0			0
$936$	−10.0000			−0.326860
$937$	−11.9541	−	6.09092i	−0.390524	−	0.198982i	0.247693	−	0.968839i	$-0.420328\pi$
$937$	−11.9541	−	6.09092i	−0.390524	−	0.198982i	−0.638217	+	0.769857i	$0.720328\pi$
$938$		0			0
$939$	−10.5801	−	14.5623i	−0.345270	−	0.475223i
$940$	22.8974	+	16.9030i	0.746830	+	0.551314i
$941$	36.0901	+	11.7264i	1.17650	+	0.382269i	0.831066	−	0.556174i	$-0.187731\pi$
$941$	36.0901	+	11.7264i	1.17650	+	0.382269i	0.345436	+	0.938442i	$0.387731\pi$
$942$	−4.89717	+	30.9195i	−0.159559	+	1.00741i
$943$	1.39919	+	8.83415i	0.0455640	+	0.287680i
$944$	5.70634	−	1.85410i	0.185726	−	0.0603459i
$945$		0			0
$946$		0			0
$947$	−7.00000	−	7.00000i	−0.227469	−	0.227469i	0.584165	−	0.811635i	$-0.301422\pi$
$947$	−7.00000	−	7.00000i	−0.227469	−	0.227469i	−0.811635	+	0.584165i	$0.801422\pi$
$948$	12.1818	−	23.9082i	0.395648	−	0.776503i
$949$	−11.7557	+	16.1803i	−0.381606	+	0.525236i
$950$	49.2351	+	50.7533i	1.59740	+	1.64666i
$951$	10.5066	−	32.3359i	0.340699	−	1.04856i
$952$		0			0
$953$	13.2512	+	2.09879i	0.429249	+	0.0679864i	0.367321	−	0.930094i	$-0.380275\pi$
$953$	13.2512	+	2.09879i	0.429249	+	0.0679864i	0.0619283	+	0.998081i	$0.480275\pi$
$954$	2.55834	+	1.85874i	0.0828292	+	0.0601789i
$955$	−34.5200	−	35.0481i	−1.11704	−	1.13413i
$956$			56.9210i			1.84096i
$957$		0			0
$958$	−10.0000	+	10.0000i	−0.323085	+	0.323085i
$959$		0			0
$960$	23.9105	+	33.4408i	0.771707	+	1.07930i
$961$	21.8435	−	15.8702i	0.704628	−	0.511942i
$962$	−37.8022	+	19.2612i	−1.21879	+	0.621006i
$963$		0			0
$964$	−15.3500	+	11.1524i	−0.494391	+	0.359196i
$965$	29.0813	+	40.6728i	0.936162	+	1.30930i
$966$		0			0
$967$	−18.9737	+	18.9737i	−0.610152	+	0.610152i	−0.942986	−	0.332834i	$-0.891995\pi$
$967$	−18.9737	+	18.9737i	−0.610152	+	0.610152i	0.332834	+	0.942986i	$0.391995\pi$
$968$		0			0
$969$		−	40.0000i		−	1.28499i
$970$	34.7333	+	35.2647i	1.11522	+	1.13228i
$971$	−33.9787	−	24.6870i	−1.09043	−	0.792243i	−0.110957	−	0.993825i	$-0.535392\pi$
$971$	−33.9787	−	24.6870i	−1.09043	−	0.792243i	−0.979472	+	0.201582i	$0.935392\pi$
$972$	29.3328	+	4.64587i	0.940852	+	0.149016i
$973$		0			0
$974$	2.93159	−	9.02251i	0.0939343	−	0.289100i
$975$	−0.480097	+	31.6191i	−0.0153754	+	1.01262i
$976$	−3.71748	+	5.11667i	−0.118994	+	0.163781i
$977$	10.9147	−	21.4212i	0.349191	−	0.685326i	−0.647885	−	0.761738i	$-0.724346\pi$
$977$	10.9147	−	21.4212i	0.349191	−	0.685326i	0.997076	+	0.0764116i	$0.0243463\pi$
$978$	−3.16228	−	3.16228i	−0.101118	−	0.101118i
$979$		0			0
$980$	−42.0000	+	21.0000i	−1.34164	+	0.670820i
$981$	12.0300	−	3.90879i	0.384089	−	0.124798i
$982$	−2.21232	−	13.9680i	−0.0705979	−	0.445738i
$983$	−6.41572	+	40.5073i	−0.204630	+	1.29198i	0.644829	+	0.764327i	$0.276928\pi$
$983$	−6.41572	+	40.5073i	−0.204630	+	1.29198i	−0.849459	+	0.527655i	$0.823072\pi$
$984$	19.0211	+	6.18034i	0.606371	+	0.197022i
$985$	8.04532	+	5.93910i	0.256345	+	0.189235i
$986$	37.1748	+	51.1667i	1.18389	+	1.62948i
$987$		0			0
$988$	−75.6044	−	38.5224i	−2.40530	−	1.22556i
$989$		0			0
$990$		0			0
$991$	−58.0000			−1.84243			−0.921215	−	0.389053i	$-0.872802\pi$
$991$	−58.0000			−1.84243			−0.921215	+	0.389053i	$0.872802\pi$
$992$	11.9541	+	6.09092i	0.379543	+	0.193387i
$993$	−25.1424	+	3.98217i	−0.797871	+	0.126370i
$994$		0			0
$995$	13.2668	−	1.99814i	0.420585	−	0.0633451i
$996$	−36.0901	−	11.7264i	−1.14356	−	0.371564i
$997$	−7.69556	+	48.5878i	−0.243721	+	1.53879i	0.497460	+	0.867487i	$0.334266\pi$
$997$	−7.69556	+	48.5878i	−0.243721	+	1.53879i	−0.741181	+	0.671305i	$0.765734\pi$
$998$	−11.8931	−	75.0903i	−0.376471	−	2.37694i
$999$	22.8254	−	7.41641i	0.722162	−	0.234645i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.m.b.457.2		16
5.3	odd	4	inner	605.2.m.b.578.2		16
11.2	odd	10	inner	605.2.m.b.112.2		16
11.3	even	5		55.2.e.a.32.2	yes	4
11.4	even	5	inner	605.2.m.b.602.1		16
11.5	even	5	inner	605.2.m.b.282.1		16
11.6	odd	10	inner	605.2.m.b.282.2		16
11.7	odd	10	inner	605.2.m.b.602.2		16
11.8	odd	10		55.2.e.a.32.1	✓	4
11.9	even	5	inner	605.2.m.b.112.1		16
11.10	odd	2	inner	605.2.m.b.457.1		16
33.8	even	10		495.2.k.b.307.2		4
33.14	odd	10		495.2.k.b.307.1		4
44.3	odd	10		880.2.bd.e.417.2		4
44.19	even	10		880.2.bd.e.417.1		4
55.3	odd	20		55.2.e.a.43.1	yes	4
55.8	even	20		55.2.e.a.43.2	yes	4
55.13	even	20	inner	605.2.m.b.233.2		16
55.14	even	10		275.2.e.b.32.1		4
55.18	even	20	inner	605.2.m.b.118.1		16
55.19	odd	10		275.2.e.b.32.2		4
55.28	even	20	inner	605.2.m.b.403.1		16
55.38	odd	20	inner	605.2.m.b.403.2		16
55.43	even	4	inner	605.2.m.b.578.1		16
55.47	odd	20		275.2.e.b.43.2		4
55.48	odd	20	inner	605.2.m.b.118.2		16
55.52	even	20		275.2.e.b.43.1		4
55.53	odd	20	inner	605.2.m.b.233.1		16
165.8	odd	20		495.2.k.b.208.1		4
165.113	even	20		495.2.k.b.208.2		4
220.3	even	20		880.2.bd.e.593.2		4
220.63	odd	20		880.2.bd.e.593.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.e.a.32.1	✓	4	11.8	odd	10
55.2.e.a.32.2	yes	4	11.3	even	5
55.2.e.a.43.1	yes	4	55.3	odd	20
55.2.e.a.43.2	yes	4	55.8	even	20
275.2.e.b.32.1		4	55.14	even	10
275.2.e.b.32.2		4	55.19	odd	10
275.2.e.b.43.1		4	55.52	even	20
275.2.e.b.43.2		4	55.47	odd	20
495.2.k.b.208.1		4	165.8	odd	20
495.2.k.b.208.2		4	165.113	even	20
495.2.k.b.307.1		4	33.14	odd	10
495.2.k.b.307.2		4	33.8	even	10
605.2.m.b.112.1		16	11.9	even	5	inner
605.2.m.b.112.2		16	11.2	odd	10	inner
605.2.m.b.118.1		16	55.18	even	20	inner
605.2.m.b.118.2		16	55.48	odd	20	inner
605.2.m.b.233.1		16	55.53	odd	20	inner
605.2.m.b.233.2		16	55.13	even	20	inner
605.2.m.b.282.1		16	11.5	even	5	inner
605.2.m.b.282.2		16	11.6	odd	10	inner
605.2.m.b.403.1		16	55.28	even	20	inner
605.2.m.b.403.2		16	55.38	odd	20	inner
605.2.m.b.457.1		16	11.10	odd	2	inner
605.2.m.b.457.2		16	1.1	even	1	trivial
605.2.m.b.578.1		16	55.43	even	4	inner
605.2.m.b.578.2		16	5.3	odd	4	inner
605.2.m.b.602.1		16	11.4	even	5	inner
605.2.m.b.602.2		16	11.7	odd	10	inner
880.2.bd.e.417.1		4	44.19	even	10
880.2.bd.e.417.2		4	44.3	odd	10
880.2.bd.e.593.1		4	220.63	odd	20
880.2.bd.e.593.2		4	220.3	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.m (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.99235 + 1.01515i) q^{2} +(1.39680 - 0.221232i) q^{3} +(1.76336 + 2.42705i) q^{4} +(0.333023 + 2.21113i) q^{5} +(3.00750 + 0.977198i) q^{6} +(0.349798 + 2.20854i) q^{8} +(-0.951057 + 0.309017i) q^{9} +O(q^{10})\)	\(q+(1.99235 + 1.01515i) q^{2} +(1.39680 - 0.221232i) q^{3} +(1.76336 + 2.42705i) q^{4} +(0.333023 + 2.21113i) q^{5} +(3.00750 + 0.977198i) q^{6} +(0.349798 + 2.20854i) q^{8} +(-0.951057 + 0.309017i) q^{9} +(-1.58114 + 4.74342i) q^{10} +(3.00000 + 3.00000i) q^{12} +(2.03031 - 3.98470i) q^{13} +(0.954339 + 3.01484i) q^{15} +(0.309017 - 0.951057i) q^{16} +(2.03031 + 3.98470i) q^{17} +(-2.20854 - 0.349798i) q^{18} +(-5.11667 - 3.71748i) q^{19} +(-4.77929 + 4.70727i) q^{20} +(-1.00000 + 1.00000i) q^{23} +(0.977198 + 3.00750i) q^{24} +(-4.77819 + 1.47271i) q^{25} +(8.09017 - 5.87785i) q^{26} +(-5.04029 + 2.56816i) q^{27} +(5.11667 - 3.71748i) q^{29} +(-1.15914 + 6.97541i) q^{30} +(0.618034 + 1.90211i) q^{31} +(4.74342 - 4.74342i) q^{32} +10.0000i q^{34} +(-2.42705 - 1.76336i) q^{36} +(-4.19041 - 0.663695i) q^{37} +(-6.42040 - 12.6007i) q^{38} +(1.95440 - 6.01501i) q^{39} +(-4.76687 + 1.50894i) q^{40} +(3.71748 - 5.11667i) q^{41} +(-1.00000 - 2.00000i) q^{45} +(-3.00750 + 0.977198i) q^{46} +(-0.663695 - 4.19041i) q^{47} +(0.221232 - 1.39680i) q^{48} +(6.65740 + 2.16312i) q^{49} +(-11.0149 - 1.91644i) q^{50} +(3.71748 + 5.11667i) q^{51} +(13.2512 - 2.09879i) q^{52} +(-1.26007 - 0.642040i) q^{53} -12.6491 q^{54} +(-7.96940 - 4.06061i) q^{57} +(13.9680 - 2.21232i) q^{58} +(3.52671 + 4.85410i) q^{59} +(-5.63432 + 7.63246i) q^{60} +(-6.01501 - 1.95440i) q^{61} +(-0.699596 + 4.41708i) q^{62} +(12.3637 - 4.01722i) q^{64} +(9.48683 + 3.16228i) q^{65} +(3.00000 + 3.00000i) q^{67} +(-6.09092 + 11.9541i) q^{68} +(-1.17557 + 1.61803i) q^{69} +(-2.47214 + 7.60845i) q^{71} +(-1.01515 - 1.99235i) q^{72} +(-4.41708 - 0.699596i) q^{73} +(-7.67501 - 5.57622i) q^{74} +(-6.34838 + 3.11418i) q^{75} -18.9737i q^{76} +(10.0000 - 10.0000i) q^{78} +(-1.95440 - 6.01501i) q^{79} +(2.20582 + 0.366554i) q^{80} +(-4.04508 + 2.93893i) q^{81} +(12.6007 - 6.42040i) q^{82} +(-7.96940 + 4.06061i) q^{83} +(-8.13456 + 5.81627i) q^{85} +(6.32456 - 6.32456i) q^{87} -6.00000i q^{89} +(0.0379561 - 4.99986i) q^{90} +(-4.19041 - 0.663695i) q^{92} +(1.28408 + 2.52015i) q^{93} +(2.93159 - 9.02251i) q^{94} +(6.51587 - 12.5516i) q^{95} +(5.57622 - 7.67501i) q^{96} +(4.49428 - 8.82051i) q^{97} +(11.0680 + 11.0680i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3} + 8 q^{5}+O(q^{10}) \) 16 * q + 4 * q^3 + 8 * q^5	\( 16 q + 4 q^{3} + 8 q^{5} + 48 q^{12} - 4 q^{15} - 4 q^{16} - 12 q^{20} - 16 q^{23} - 12 q^{25} + 40 q^{26} + 16 q^{27} - 8 q^{31} - 12 q^{36} - 12 q^{37} - 40 q^{38} - 16 q^{45} - 12 q^{47} + 4 q^{48} + 4 q^{53} + 40 q^{58} + 36 q^{60} + 48 q^{67} + 32 q^{71} - 4 q^{75} + 160 q^{78} + 8 q^{80} - 20 q^{81} - 40 q^{82} - 12 q^{92} + 8 q^{93} + 28 q^{97}+O(q^{100}) \) 16 * q + 4 * q^3 + 8 * q^5 + 48 * q^12 - 4 * q^15 - 4 * q^16 - 12 * q^20 - 16 * q^23 - 12 * q^25 + 40 * q^26 + 16 * q^27 - 8 * q^31 - 12 * q^36 - 12 * q^37 - 40 * q^38 - 16 * q^45 - 12 * q^47 + 4 * q^48 + 4 * q^53 + 40 * q^58 + 36 * q^60 + 48 * q^67 + 32 * q^71 - 4 * q^75 + 160 * q^78 + 8 * q^80 - 20 * q^81 - 40 * q^82 - 12 * q^92 + 8 * q^93 + 28 * q^97

Introduction

L-functions

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