LMFDB - Embedded newform 605.2.m.b.578.1

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			578.1
Root			$0.453990 + 0.891007i$ of defining polynomial
Character	$\chi$	$=$	605.578
Dual form			605.2.m.b.112.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.01515 + 1.99235i) q^{2} +(0.221232 + 1.39680i) q^{3} +(-1.76336 - 2.42705i) q^{4} +(-1.56909 + 1.59310i) q^{5} +(-3.00750 - 0.977198i) q^{6} +(2.20854 - 0.349798i) q^{8} +(0.951057 - 0.309017i) q^{9} +O(q^{10})$	\(q+(-1.01515 + 1.99235i) q^{2} +(0.221232 + 1.39680i) q^{3} +(-1.76336 - 2.42705i) q^{4} +(-1.56909 + 1.59310i) q^{5} +(-3.00750 - 0.977198i) q^{6} +(2.20854 - 0.349798i) q^{8} +(0.951057 - 0.309017i) q^{9} +(-1.58114 - 4.74342i) q^{10} +(3.00000 - 3.00000i) q^{12} +(-3.98470 - 2.03031i) q^{13} +(-2.57237 - 1.83927i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-3.98470 + 2.03031i) q^{17} +(-0.349798 + 2.20854i) q^{18} +(-5.11667 - 3.71748i) q^{19} +(6.63339 + 0.999068i) q^{20} +(-1.00000 - 1.00000i) q^{23} +(0.977198 + 3.00750i) q^{24} +(-0.0759100 - 4.99942i) q^{25} +(8.09017 - 5.87785i) q^{26} +(2.56816 + 5.04029i) q^{27} +(5.11667 - 3.71748i) q^{29} +(6.27582 - 3.25793i) q^{30} +(0.618034 + 1.90211i) q^{31} +(4.74342 + 4.74342i) q^{32} -10.0000i q^{34} +(-2.42705 - 1.76336i) q^{36} +(-0.663695 + 4.19041i) q^{37} +(12.6007 - 6.42040i) q^{38} +(1.95440 - 6.01501i) q^{39} +(-2.90813 + 4.06728i) q^{40} +(-3.71748 + 5.11667i) q^{41} +(-1.00000 + 2.00000i) q^{45} +(3.00750 - 0.977198i) q^{46} +(-4.19041 + 0.663695i) q^{47} +(1.39680 + 0.221232i) q^{48} +(-6.65740 - 2.16312i) q^{49} +(10.0377 + 4.92394i) q^{50} +(-3.71748 - 5.11667i) q^{51} +(2.09879 + 13.2512i) q^{52} +(0.642040 - 1.26007i) q^{53} -12.6491 q^{54} +(4.06061 - 7.96940i) q^{57} +(2.21232 + 13.9680i) q^{58} +(-3.52671 - 4.85410i) q^{59} +(0.0720166 + 9.48656i) q^{60} +(6.01501 + 1.95440i) q^{61} +(-4.41708 - 0.699596i) q^{62} +(-12.3637 + 4.01722i) q^{64} +(9.48683 - 3.16228i) q^{65} +(3.00000 - 3.00000i) q^{67} +(11.9541 + 6.09092i) q^{68} +(1.17557 - 1.61803i) q^{69} +(-2.47214 + 7.60845i) q^{71} +(1.99235 - 1.01515i) q^{72} +(-0.699596 + 4.41708i) q^{73} +(-7.67501 - 5.57622i) q^{74} +(6.96641 - 1.21206i) q^{75} +18.9737i q^{76} +(10.0000 + 10.0000i) q^{78} +(-1.95440 - 6.01501i) q^{79} +(1.03025 + 1.98459i) q^{80} +(-4.04508 + 2.93893i) q^{81} +(-6.42040 - 12.6007i) q^{82} +(4.06061 + 7.96940i) q^{83} +(3.01788 - 9.53375i) q^{85} +(6.32456 + 6.32456i) q^{87} +6.00000i q^{89} +(-2.96955 - 4.02266i) q^{90} +(-0.663695 + 4.19041i) q^{92} +(-2.52015 + 1.28408i) q^{93} +(2.93159 - 9.02251i) q^{94} +(13.9508 - 2.31829i) q^{95} +(-5.57622 + 7.67501i) q^{96} +(-8.82051 - 4.49428i) 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 $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−1.01515	+	1.99235i	−0.717822	+	1.40881i	0.186717	+	0.982414i	$0.440215\pi$
$2$	−1.01515	+	1.99235i	−0.717822	+	1.40881i	−0.904539	+	0.426391i	$0.859785\pi$
$3$	0.221232	+	1.39680i	0.127728	+	0.806444i	0.965496	+	0.260418i	$0.0838602\pi$
$3$	0.221232	+	1.39680i	0.127728	+	0.806444i	−0.837768	+	0.546027i	$0.816140\pi$
$4$	−1.76336	−	2.42705i	−0.881678	−	1.21353i
$5$	−1.56909	+	1.59310i	−0.701719	+	0.712454i
$5$	−1.56909	+	1.59310i	−0.701719	+	0.712454i
$6$	−3.00750	−	0.977198i	−1.22781	−	0.398939i
$7$		0			0		0.156434	−	0.987688i	$-0.450000\pi$
$7$		0			0		−0.156434	+	0.987688i	$0.550000\pi$
$8$	2.20854	−	0.349798i	0.780836	−	0.123672i
$9$	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
$13$	−3.98470	−	2.03031i	−1.10516	−	0.563106i	−0.196439	−	0.980516i	$-0.562938\pi$
$13$	−3.98470	−	2.03031i	−1.10516	−	0.563106i	−0.908718	+	0.417410i	$0.862938\pi$
$14$		0			0
$15$	−2.57237	−	1.83927i	−0.664184	−	0.474896i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−3.98470	+	2.03031i	−0.966432	+	0.492422i	−0.864644	−	0.502384i	$-0.832456\pi$
$17$	−3.98470	+	2.03031i	−0.966432	+	0.492422i	−0.101788	+	0.994806i	$0.532456\pi$
$18$	−0.349798	+	2.20854i	−0.0824482	+	0.520557i
$19$	−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	$0.958380\pi$
$20$	6.63339	+	0.999068i	1.48327	+	0.223398i
$21$		0			0
$22$		0			0
$23$	−1.00000	−	1.00000i	−0.208514	−	0.208514i	0.595121	−	0.803636i	$-0.297104\pi$
$23$	−1.00000	−	1.00000i	−0.208514	−	0.208514i	−0.803636	+	0.595121i	$0.797104\pi$
$24$	0.977198	+	3.00750i	0.199470	+	0.613904i
$25$	−0.0759100	−	4.99942i	−0.0151820	−	0.999885i
$26$	8.09017	−	5.87785i	1.58661	−	1.15274i
$27$	2.56816	+	5.04029i	0.494242	+	0.970005i
$28$		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	$0.100222\pi$
$30$	6.27582	−	3.25793i	1.14580	−	0.594814i
$31$	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
$37$	−0.663695	+	4.19041i	−0.109111	+	0.688899i	0.871124	+	0.491063i	$0.163391\pi$
$37$	−0.663695	+	4.19041i	−0.109111	+	0.688899i	−0.980235	+	0.197836i	$0.936609\pi$
$38$	12.6007	−	6.42040i	2.04411	−	1.04153i
$39$	1.95440	−	6.01501i	0.312954	−	0.963172i
$40$	−2.90813	+	4.06728i	−0.459816	+	0.643093i
$41$	−3.71748	+	5.11667i	−0.580573	+	0.799090i	−0.993758	−	0.111557i	$-0.964416\pi$
$41$	−3.71748	+	5.11667i	−0.580573	+	0.799090i	0.413185	+	0.910647i	$0.364416\pi$
$42$		0			0
$43$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$43$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$44$		0			0
$45$	−1.00000	+	2.00000i	−0.149071	+	0.298142i
$46$	3.00750	−	0.977198i	0.443432	−	0.144080i
$47$	−4.19041	+	0.663695i	−0.611234	+	0.0968099i	−0.454374	−	0.890811i	$-0.650137\pi$
$47$	−4.19041	+	0.663695i	−0.611234	+	0.0968099i	−0.156860	+	0.987621i	$0.550137\pi$
$48$	1.39680	+	0.221232i	0.201611	+	0.0319321i
$49$	−6.65740	−	2.16312i	−0.951057	−	0.309017i
$50$	10.0377	+	4.92394i	1.41954	+	0.696351i
$51$	−3.71748	−	5.11667i	−0.520551	−	0.716477i
$52$	2.09879	+	13.2512i	0.291050	+	1.83761i
$53$	0.642040	−	1.26007i	0.0881909	−	0.173084i	−0.842698	−	0.538386i	$-0.819034\pi$
$53$	0.642040	−	1.26007i	0.0881909	−	0.173084i	0.930889	+	0.365302i	$0.119034\pi$
$54$	−12.6491			−1.72133
$55$		0			0
$56$		0			0
$57$	4.06061	−	7.96940i	0.537842	−	1.05557i
$58$	2.21232	+	13.9680i	0.290492	+	1.83409i
$59$	−3.52671	−	4.85410i	−0.459139	−	0.631950i	0.515191	−	0.857075i	$-0.327721\pi$
$59$	−3.52671	−	4.85410i	−0.459139	−	0.631950i	−0.974330	+	0.225125i	$0.927721\pi$
$60$	0.0720166	+	9.48656i	0.00929730	+	1.22471i
$61$	6.01501	+	1.95440i	0.770143	+	0.250235i	0.667626	−	0.744497i	$-0.267310\pi$
$61$	6.01501	+	1.95440i	0.770143	+	0.250235i	0.102517	+	0.994731i	$0.467310\pi$
$62$	−4.41708	−	0.699596i	−0.560969	−	0.0888488i
$63$		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	−0.499694	−	0.866202i	$-0.666554\pi$
$67$	3.00000	−	3.00000i	0.366508	−	0.366508i	0.866202	+	0.499694i	$0.166554\pi$
$68$	11.9541	+	6.09092i	1.44965	+	0.738633i
$69$	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	$0.942552\pi$
$72$	1.99235	−	1.01515i	0.234801	−	0.119637i
$73$	−0.699596	+	4.41708i	−0.0818815	+	0.516980i	0.912323	+	0.409472i	$0.134287\pi$
$73$	−0.699596	+	4.41708i	−0.0818815	+	0.516980i	−0.994204	+	0.107508i	$0.965713\pi$
$74$	−7.67501	−	5.57622i	−0.892202	−	0.648222i
$75$	6.96641	−	1.21206i	0.804412	−	0.139957i
$76$			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	$-0.215786\pi$
$80$	1.03025	+	1.98459i	0.115185	+	0.221884i
$81$	−4.04508	+	2.93893i	−0.449454	+	0.326547i
$82$	−6.42040	−	12.6007i	−0.709014	−	1.39152i
$83$	4.06061	+	7.96940i	0.445710	+	0.874756i	0.999124	+	0.0418492i	$0.0133249\pi$
$83$	4.06061	+	7.96940i	0.445710	+	0.874756i	−0.553414	+	0.832907i	$0.686675\pi$
$84$		0			0
$85$	3.01788	−	9.53375i	0.327335	−	1.03408i
$86$		0			0
$87$	6.32456	+	6.32456i	0.678064	+	0.678064i
$88$		0			0
$89$			6.00000i			0.635999i	0.948091	+	0.317999i	$0.103011\pi$
$89$			6.00000i			0.635999i	−0.948091	+	0.317999i	$0.896989\pi$
$90$	−2.96955	−	4.02266i	−0.313018	−	0.424025i
$91$		0			0
$92$	−0.663695	+	4.19041i	−0.0691950	+	0.436880i
$93$	−2.52015	+	1.28408i	−0.261327	+	0.133153i
$94$	2.93159	−	9.02251i	0.302371	−	0.930601i
$95$	13.9508	−	2.31829i	1.43132	−	0.237851i
$96$	−5.57622	+	7.67501i	−0.569121	+	0.783327i
$97$	−8.82051	−	4.49428i	−0.895588	−	0.456325i	−0.0553026	−	0.998470i	$-0.517612\pi$
$97$	−8.82051	−	4.49428i	−0.895588	−	0.456325i	−0.840285	+	0.542145i	$0.817612\pi$
$98$	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	$0.400000\pi$
$102$	13.9680	−	2.21232i	1.38304	−	0.219052i
$103$	−12.5712	−	1.99109i	−1.23868	−	0.196188i	−0.497482	−	0.867475i	$-0.665742\pi$
$103$	−12.5712	−	1.99109i	−1.23868	−	0.196188i	−0.741198	+	0.671287i	$0.765742\pi$
$104$	−9.51057	−	3.09017i	−0.932588	−	0.303016i
$105$		0			0
$106$	1.85874	+	2.55834i	0.180537	+	0.248488i
$107$		0			0		0.987688	−	0.156434i	$-0.0500000\pi$
$107$		0			0		−0.987688	+	0.156434i	$0.950000\pi$
$108$	7.70447	−	15.1209i	0.741363	−	1.45501i
$109$	−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
$113$	−1.99109	−	12.5712i	−0.187306	−	1.18260i	−0.884786	−	0.465997i	$-0.845696\pi$
$113$	−1.99109	−	12.5712i	−0.187306	−	1.18260i	0.697481	−	0.716604i	$-0.254304\pi$
$114$	11.7557	+	16.1803i	1.10102	+	1.51543i
$115$	3.16219	−	0.0240055i	0.294875	−	0.00223853i
$116$	−18.0450	−	5.86319i	−1.67544	−	0.544383i
$117$	−4.41708	−	0.699596i	−0.408359	−	0.0646777i
$118$	13.2512	−	2.09879i	1.21987	−	0.193209i
$119$		0			0
$120$	−6.32456	−	3.16228i	−0.577350	−	0.288675i
$121$		0			0
$122$	−10.0000	+	10.0000i	−0.905357	+	0.905357i
$123$	−7.96940	−	4.06061i	−0.718577	−	0.366133i
$124$	3.52671	−	4.85410i	0.316708	−	0.435911i
$125$	8.08367	+	7.72362i	0.723026	+	0.690821i
$126$		0			0
$127$	−7.96940	+	4.06061i	−0.707170	+	0.360321i	−0.770298	−	0.637684i	$-0.779892\pi$
$127$	−7.96940	+	4.06061i	−0.707170	+	0.360321i	0.0631276	+	0.998005i	$0.479892\pi$
$128$	2.44859	−	15.4598i	0.216427	−	1.36646i
$129$		0			0
$130$	−3.33023	+	22.1113i	−0.292080	+	1.93929i
$131$		−	12.6491i		−	1.10516i	−0.833461	−	0.552579i	$-0.813644\pi$
$131$		−	12.6491i		−	1.10516i	0.833461	−	0.552579i	$-0.186356\pi$
$132$		0			0
$133$		0			0
$134$	2.93159	+	9.02251i	0.253251	+	0.779427i
$135$	−12.0593	−	3.81736i	−1.03790	−	0.328546i
$136$	−8.09017	+	5.87785i	−0.693726	+	0.504022i
$137$	−8.34651	−	16.3810i	−0.713091	−	1.39952i	−0.908115	−	0.418721i	$-0.862479\pi$
$137$	−8.34651	−	16.3810i	−0.713091	−	1.39952i	0.195024	−	0.980798i	$-0.437521\pi$
$138$	2.03031	+	3.98470i	0.172831	+	0.339200i
$139$	−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
$145$	−2.10622	+	13.9844i	−0.174912	+	1.16134i
$146$	−8.09017	−	5.87785i	−0.669547	−	0.486455i
$147$	1.54862	−	9.77762i	0.127728	−	0.806444i
$148$	11.3407	−	5.77836i	0.932197	−	0.474978i
$149$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$149$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$150$	−4.65712	+	15.1100i	−0.380253	+	1.23372i
$151$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$151$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$152$	−12.6007	−	6.42040i	−1.02205	−	0.520763i
$153$	−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
$157$	9.77762	−	1.54862i	0.780339	−	0.123594i	0.246458	−	0.969153i	$-0.420733\pi$
$157$	9.77762	−	1.54862i	0.780339	−	0.123594i	0.533881	+	0.845560i	$0.320733\pi$
$158$	13.9680	+	2.21232i	1.11124	+	0.176003i
$159$	1.90211	+	0.618034i	0.150847	+	0.0490133i
$160$	−14.9996	+	0.113868i	−1.18582	+	0.00900207i
$161$		0			0
$162$	−1.74899	−	11.0427i	−0.137414	−	0.867596i
$163$	0.642040	−	1.26007i	0.0502884	−	0.0986966i	−0.864495	−	0.502642i	$-0.832361\pi$
$163$	0.642040	−	1.26007i	0.0502884	−	0.0986966i	0.914783	+	0.403945i	$0.132361\pi$
$164$	18.9737			1.48159
$165$		0			0
$166$	−20.0000			−1.55230
$167$	−8.12123	+	15.9388i	−0.628440	+	1.23338i	0.328886	+	0.944370i	$0.393327\pi$
$167$	−8.12123	+	15.9388i	−0.628440	+	1.23338i	−0.957325	+	0.289012i	$0.906673\pi$
$168$		0			0
$169$	4.11450	+	5.66312i	0.316500	+	0.435625i
$170$	15.9310	+	15.6909i	1.22185	+	1.20344i
$171$	−6.01501	−	1.95440i	−0.459979	−	0.149456i
$172$		0			0
$173$	−4.41708	+	0.699596i	−0.335824	+	0.0531893i	−0.322069	−	0.946716i	$-0.604378\pi$
$173$	−4.41708	+	0.699596i	−0.335824	+	0.0531893i	−0.0137548	+	0.999905i	$0.504378\pi$
$174$	−19.0211	+	6.18034i	−1.44199	+	0.468530i
$175$		0			0
$176$		0			0
$177$	6.00000	−	6.00000i	0.450988	−	0.450988i
$178$	−11.9541	−	6.09092i	−0.895998	−	0.456534i
$179$	−2.35114	+	3.23607i	−0.175733	+	0.241875i	−0.887793	−	0.460243i	$-0.847762\pi$
$179$	−2.35114	+	3.23607i	−0.175733	+	0.241875i	0.712060	+	0.702118i	$0.247762\pi$
$180$	6.61746	−	1.09966i	0.493236	−	0.0819639i
$181$	−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
$183$	−1.39919	+	8.83415i	−0.103431	+	0.653039i
$184$	−2.55834	−	1.85874i	−0.188603	−	0.137028i
$185$	−5.63432	−	7.63246i	−0.414244	−	0.561149i
$186$		−	6.32456i		−	0.463739i
$187$		0			0
$188$	9.00000	+	9.00000i	0.656392	+	0.656392i
$189$		0			0
$190$	−9.54339	+	30.1484i	−0.692350	+	2.18719i
$191$	−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	$0.593019\pi$
$192$	−8.34651	−	16.3810i	−0.602358	−	1.18219i
$193$	−10.1515	−	19.9235i	−0.730724	−	1.43413i	−0.894241	−	0.447585i	$-0.852284\pi$
$193$	−10.1515	−	19.9235i	−0.730724	−	1.43413i	0.163518	−	0.986540i	$-0.447716\pi$
$194$	17.9084	−	13.0112i	1.28574	−	0.934148i
$195$	6.51587	+	12.5516i	0.466611	+	0.898841i
$196$	6.48936	+	19.9722i	0.463525	+	1.42658i
$197$	3.16228	+	3.16228i	0.225303	+	0.225303i	0.810727	−	0.585424i	$-0.199072\pi$
$197$	3.16228	+	3.16228i	0.225303	+	0.225303i	−0.585424	+	0.810727i	$0.699072\pi$
$198$		0			0
$199$			6.00000i			0.425329i	0.977125	+	0.212664i	$0.0682141\pi$
$199$			6.00000i			0.425329i	−0.977125	+	0.212664i	$0.931786\pi$
$200$	−1.91644	−	11.0149i	−0.135513	−	0.778869i
$201$	4.85410	+	3.52671i	0.342382	+	0.248755i
$202$		0			0
$203$		0			0
$204$	−5.86319	+	18.0450i	−0.410505	+	1.26340i
$205$	−2.31829	−	13.9508i	−0.161916	−	0.974368i
$206$	16.7287	−	23.0250i	1.16554	−	1.60423i
$207$	−1.26007	−	0.642040i	−0.0875812	−	0.0446248i
$208$	−3.16228	+	3.16228i	−0.219265	+	0.219265i
$209$		0			0
$210$		0			0
$211$	24.0600	−	7.81758i	1.65636	−	0.538184i	0.676257	−	0.736666i	$-0.263601\pi$
$211$	24.0600	−	7.81758i	1.65636	−	0.538184i	0.980105	+	0.198482i	$0.0636010\pi$
$212$	−4.19041	+	0.663695i	−0.287798	+	0.0455828i
$213$	−11.1744	−	1.76985i	−0.765659	−	0.121268i
$214$		0			0
$215$		0			0
$216$	7.43496	+	10.2333i	0.505885	+	0.696291i
$217$		0			0
$218$	12.8408	−	25.2015i	0.869688	−	1.70686i
$219$	−6.32456			−0.427374
$220$		0			0
$221$	20.0000			1.34535
$222$	6.09092	−	11.9541i	0.408796	−	0.802307i
$223$	2.43355	+	15.3648i	0.162963	+	1.02890i	0.924611	+	0.380914i	$0.124391\pi$
$223$	2.43355	+	15.3648i	0.162963	+	1.02890i	−0.761648	+	0.647991i	$0.775609\pi$
$224$		0			0
$225$	−1.61710	−	4.73128i	−0.107807	−	0.315418i
$226$	27.0675	+	8.79478i	1.80051	+	0.585020i
$227$	8.83415	+	1.39919i	0.586343	+	0.0928677i	0.442556	−	0.896741i	$-0.354072\pi$
$227$	8.83415	+	1.39919i	0.586343	+	0.0928677i	0.143787	+	0.989609i	$0.454072\pi$
$228$	−26.5025	+	4.19758i	−1.75517	+	0.277991i
$229$	3.80423	−	1.23607i	0.251390	−	0.0816817i	−0.180611	−	0.983555i	$-0.557808\pi$
$229$	3.80423	−	1.23607i	0.251390	−	0.0816817i	0.432001	+	0.901873i	$0.357808\pi$
$230$	−3.16228	+	6.32456i	−0.208514	+	0.417029i
$231$		0			0
$232$	10.0000	−	10.0000i	0.656532	−	0.656532i
$233$	11.9541	+	6.09092i	0.783140	+	0.399030i	0.799370	−	0.600839i	$-0.205167\pi$
$233$	11.9541	+	6.09092i	0.783140	+	0.399030i	−0.0162307	+	0.999868i	$0.505167\pi$
$234$	5.87785	−	8.09017i	0.384247	−	0.528871i
$235$	5.51780	−	7.71712i	0.359941	−	0.503409i
$236$	−5.56231	+	17.1190i	−0.362075	+	1.11435i
$237$	7.96940	−	4.06061i	0.517668	−	0.263765i
$238$		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	$0.489700\pi$
$240$	−2.54415	+	1.87811i	−0.164224	+	0.121231i
$241$		−	6.32456i		−	0.407400i	−0.979033	−	0.203700i	$-0.934703\pi$
$241$		−	6.32456i		−	0.407400i	0.979033	−	0.203700i	$-0.0652968\pi$
$242$		0			0
$243$	7.00000	+	7.00000i	0.449050	+	0.449050i
$244$	−5.86319	−	18.0450i	−0.375352	−	1.15521i
$245$	13.8921	−	7.21174i	0.887535	−	0.460741i
$246$	16.1803	−	11.7557i	1.03162	−	0.749516i
$247$	12.8408	+	25.2015i	0.817040	+	1.60353i
$248$	2.03031	+	3.98470i	0.128925	+	0.253029i
$249$	−10.2333	+	7.43496i	−0.648512	+	0.471171i
$250$	−23.5943	+	8.26486i	−1.49224	+	0.522715i
$251$	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
$255$	13.9844	+	2.10622i	0.875738	+	0.131897i
$256$	7.28115	+	5.29007i	0.455072	+	0.330629i
$257$	1.54862	−	9.77762i	0.0966004	−	0.609911i	−0.891131	−	0.453747i	$-0.850087\pi$
$257$	1.54862	−	9.77762i	0.0966004	−	0.609911i	0.987731	−	0.156164i	$-0.0499129\pi$
$258$		0			0
$259$		0			0
$260$	−24.4037	−	17.4488i	−1.51345	−	1.08213i
$261$	3.71748	−	5.11667i	0.230106	−	0.316714i
$262$	25.2015	+	12.8408i	1.55695	+	0.793307i
$263$	−18.9737	+	18.9737i	−1.16997	+	1.16997i	−0.187749	+	0.982217i	$0.560119\pi$
$263$	−18.9737	+	18.9737i	−1.16997	+	1.16997i	−0.982217	+	0.187749i	$0.939881\pi$
$264$		0			0
$265$	1.00000	+	3.00000i	0.0614295	+	0.184289i
$266$		0			0
$267$	−8.38081	+	1.32739i	−0.512897	+	0.0812350i
$268$	−12.5712	−	1.99109i	−0.767909	−	0.121625i
$269$	−22.8254	−	7.41641i	−1.39169	−	0.452186i	−0.485193	−	0.874407i	$-0.661251\pi$
$269$	−22.8254	−	7.41641i	−1.39169	−	0.452186i	−0.906493	+	0.422221i	$0.861251\pi$
$270$	19.8476	−	20.1512i	1.20789	−	1.22637i
$271$	−7.43496	−	10.2333i	−0.451642	−	0.621631i	0.521108	−	0.853491i	$-0.325519\pi$
$271$	−7.43496	−	10.2333i	−0.451642	−	0.621631i	−0.972749	+	0.231860i	$0.925519\pi$
$272$	0.699596	+	4.41708i	0.0424193	+	0.267825i
$273$		0			0
$274$	41.1096			2.48352
$275$		0			0
$276$	−6.00000			−0.361158
$277$	−6.09092	+	11.9541i	−0.365968	+	0.718253i	−0.998411	−	0.0563544i	$-0.982052\pi$
$277$	−6.09092	+	11.9541i	−0.365968	+	0.718253i	0.632443	+	0.774607i	$0.282052\pi$
$278$	−4.42463	−	27.9360i	−0.265372	−	1.67549i
$279$	1.17557	+	1.61803i	0.0703796	+	0.0968692i
$280$		0			0
$281$	18.0450	+	5.86319i	1.07648	+	0.349768i	0.793007	−	0.609213i	$-0.208515\pi$
$281$	18.0450	+	5.86319i	1.07648	+	0.349768i	0.283469	+	0.958981i	$0.408515\pi$
$282$	13.2512	+	2.09879i	0.789099	+	0.124981i
$283$	8.83415	−	1.39919i	0.525136	−	0.0831734i	0.111762	−	0.993735i	$-0.464350\pi$
$283$	8.83415	−	1.39919i	0.525136	−	0.0831734i	0.413373	+	0.910562i	$0.364350\pi$
$284$	22.8254	−	7.41641i	1.35444	−	0.440083i
$285$	6.32456	+	18.9737i	0.374634	+	1.12390i
$286$		0			0
$287$		0			0
$288$	5.97705	+	3.04546i	0.352201	+	0.179456i
$289$	1.76336	−	2.42705i	0.103727	−	0.142768i
$290$	−25.7237	−	18.3927i	−1.51055	−	1.08005i
$291$	4.32624	−	13.3148i	0.253609	−	0.780527i
$292$	11.9541	−	6.09092i	0.699561	−	0.356444i
$293$	−3.49798	+	22.0854i	−0.204354	+	1.29024i	0.645718	+	0.763576i	$0.276558\pi$
$293$	−3.49798	+	22.0854i	−0.204354	+	1.29024i	−0.850072	+	0.526666i	$0.823442\pi$
$294$	17.9084	+	13.0112i	1.04444	+	0.758827i
$295$	13.2668	+	1.99814i	0.772422	+	0.116336i
$296$			9.48683i			0.551411i
$297$		0			0
$298$		0			0
$299$	1.95440	+	6.01501i	0.113026	+	0.347857i
$300$	−15.2260	−	14.7705i	−0.879074	−	0.852778i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−5.11667	+	3.71748i	−0.293461	+	0.213212i
$305$	−12.5516	+	6.51587i	−0.718704	+	0.373097i
$306$	−3.09017	−	9.51057i	−0.176653	−	0.543683i
$307$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$307$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$308$		0			0
$309$		−	18.0000i		−	1.02398i
$310$	8.04532	−	5.93910i	0.456943	−	0.337318i
$311$	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	$0.627167\pi$
$312$	2.21232	−	13.9680i	0.125248	−	0.790784i
$313$	11.3407	−	5.77836i	0.641012	−	0.326612i	−0.103096	−	0.994671i	$-0.532875\pi$
$313$	11.3407	−	5.77836i	0.641012	−	0.326612i	0.744108	+	0.668059i	$0.232875\pi$
$314$	−6.84038	+	21.0525i	−0.386025	+	1.18806i
$315$		0			0
$316$	−11.1524	+	15.3500i	−0.627374	+	0.863506i
$317$	−21.4212	−	10.9147i	−1.20314	−	0.613029i	−0.266671	−	0.963788i	$-0.585924\pi$
$317$	−21.4212	−	10.9147i	−1.20314	−	0.613029i	−0.936466	+	0.350758i	$0.885924\pi$
$318$	−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
$323$	27.9360	+	4.42463i	1.55440	+	0.246193i
$324$	14.2658	+	4.63525i	0.792547	+	0.257514i
$325$	−9.84789	+	20.0753i	−0.546263	+	1.11358i
$326$	1.85874	+	2.55834i	0.102946	+	0.141693i
$327$	−2.79838	−	17.6683i	−0.154751	−	0.977060i
$328$	−6.42040	+	12.6007i	−0.354507	+	0.695759i
$329$		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	$0.664716\pi$
$332$	12.1818	−	23.9082i	0.668566	−	1.31213i
$333$	0.663695	+	4.19041i	0.0363703	+	0.229633i
$334$	−23.5114	−	32.3607i	−1.28649	−	1.77070i
$335$	0.0720166	+	9.48656i	0.00393469	+	0.518306i
$336$		0			0
$337$	13.2512	+	2.09879i	0.721840	+	0.114328i	0.506536	−	0.862219i	$-0.330926\pi$
$337$	13.2512	+	2.09879i	0.721840	+	0.114328i	0.215304	+	0.976547i	$0.430926\pi$
$338$	−15.4598	+	2.44859i	−0.840901	+	0.133186i
$339$	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
$345$	0.733107	+	4.41164i	0.0394692	+	0.237515i
$346$	3.09017	−	9.51057i	0.166129	−	0.511291i
$347$	23.9082	−	12.1818i	1.28346	−	0.653956i	0.326781	−	0.945100i	$-0.394036\pi$
$347$	23.9082	−	12.1818i	1.28346	−	0.653956i	0.956679	+	0.291144i	$0.0940360\pi$
$348$	4.19758	−	26.5025i	0.225014	−	1.42068i
$349$	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	−0.992076	−	0.125642i	$-0.959901\pi$
$353$	−21.0000	−	21.0000i	−1.11772	−	1.11772i	−0.125642	−	0.992076i	$-0.540099\pi$
$354$	5.86319	+	18.0450i	0.311625	+	0.959082i
$355$	−8.24199	−	15.8767i	−0.437439	−	0.842648i
$356$	14.5623	−	10.5801i	0.771801	−	0.560746i
$357$		0			0
$358$	−4.06061	−	7.96940i	−0.214610	−	0.421196i
$359$	−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	$0.466923\pi$
$360$	−1.50894	+	4.76687i	−0.0795282	+	0.251236i
$361$	6.48936	+	19.9722i	0.341545	+	1.05117i
$362$	−12.6491	−	12.6491i	−0.664822	−	0.664822i
$363$		0			0
$364$		0			0
$365$	−5.93910	−	8.04532i	−0.310867	−	0.421111i
$366$	−16.1803	−	11.7557i	−0.845760	−	0.614481i
$367$	−0.663695	+	4.19041i	−0.0346446	+	0.218737i	−0.998937	−	0.0461037i	$-0.985320\pi$
$367$	−0.663695	+	4.19041i	−0.0346446	+	0.218737i	0.964292	+	0.264841i	$0.0853195\pi$
$368$	−1.26007	+	0.642040i	−0.0656859	+	0.0334686i
$369$	−1.95440	+	6.01501i	−0.101742	+	0.313129i
$370$	20.9262	−	3.47743i	1.08790	−	0.180783i
$371$		0			0
$372$	7.56044	+	3.85224i	0.391991	+	0.199729i
$373$	3.16228	−	3.16228i	0.163737	−	0.163737i	−0.620483	−	0.784220i	$-0.713063\pi$
$373$	3.16228	−	3.16228i	0.163737	−	0.163737i	0.784220	+	0.620483i	$0.213063\pi$
$374$		0			0
$375$	−9.00000	+	13.0000i	−0.464758	+	0.671317i
$376$	−9.02251	+	2.93159i	−0.465301	+	0.151185i
$377$	−27.9360	+	4.42463i	−1.43878	+	0.227880i
$378$		0			0
$379$	24.7275	+	8.03444i	1.27016	+	0.412702i	0.865106	−	0.501589i	$-0.167251\pi$
$379$	24.7275	+	8.03444i	1.27016	+	0.412702i	0.405059	+	0.914291i	$0.367251\pi$
$380$	−30.2269	−	29.7714i	−1.55061	−	1.52724i
$381$	−7.43496	−	10.2333i	−0.380905	−	0.524270i
$382$	−7.69556	−	48.5878i	−0.393739	−	2.48597i
$383$	−12.1988	+	23.9414i	−0.623327	+	1.22335i	0.336216	+	0.941785i	$0.390853\pi$
$383$	−12.1988	+	23.9414i	−0.623327	+	1.22335i	−0.959543	+	0.281563i	$0.909147\pi$
$384$	22.1359			1.12962
$385$		0			0
$386$	50.0000			2.54493
$387$		0			0
$388$	4.64587	+	29.3328i	0.235858	+	1.48915i
$389$	−9.40456	−	12.9443i	−0.476830	−	0.656301i	0.501062	−	0.865412i	$-0.332943\pi$
$389$	−9.40456	−	12.9443i	−0.476830	−	0.656301i	−0.977892	+	0.209111i	$0.932943\pi$
$390$	−31.6219	+	0.240055i	−1.60124	+	0.0121557i
$391$	6.01501	+	1.95440i	0.304192	+	0.0988380i
$392$	−15.4598	−	2.44859i	−0.780836	−	0.123672i
$393$	17.6683	−	2.79838i	0.891248	−	0.141160i
$394$	−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	−0.301131	−	0.953583i	$-0.597364\pi$
$397$	13.0000	−	13.0000i	0.652451	−	0.652451i	0.953583	+	0.301131i	$0.0973643\pi$
$398$	−11.9541	−	6.09092i	−0.599205	−	0.305310i
$399$		0			0
$400$	−4.77819	−	1.47271i	−0.238910	−	0.0736356i
$401$	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	$0.00313820\pi$
$402$	−11.9541	+	6.09092i	−0.596217	+	0.303788i
$403$	1.39919	−	8.83415i	0.0696987	−	0.440061i
$404$		0			0
$405$	1.66511	−	11.0557i	0.0827401	−	0.549360i
$406$		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	$-0.201243\pi$
$410$	30.1484	+	9.54339i	1.48892	+	0.471314i
$411$	21.0344	−	15.2824i	1.03755	−	0.753826i
$412$	17.3351	+	34.0220i	0.854037	+	1.67614i
$413$		0			0
$414$	2.55834	−	1.85874i	0.125735	−	0.0913521i
$415$	−19.0675	−	6.03577i	−0.935987	−	0.296284i
$416$	−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	$0.342028\pi$
$419$			36.0000i			1.75872i	−0.476162	+	0.879358i	$0.657972\pi$
$420$		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	$0.460972\pi$
$422$	−8.84927	+	55.8721i	−0.430776	+	2.71981i
$423$	−3.78022	+	1.92612i	−0.183801	+	0.0936511i
$424$	0.977198	−	3.00750i	0.0474569	−	0.146057i
$425$	10.4528	+	19.7671i	0.507037	+	0.958845i
$426$	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	−0.709465	−	0.704741i	$-0.751063\pi$
$431$	−18.0450	+	5.86319i	−0.869198	+	0.282420i	−0.159733	+	0.987160i	$0.551063\pi$
$432$	5.58721	−	0.884927i	0.268815	−	0.0425761i
$433$	1.39680	+	0.221232i	0.0671260	+	0.0106317i	0.189907	−	0.981802i	$-0.439181\pi$
$433$	1.39680	+	0.221232i	0.0671260	+	0.0106317i	−0.122781	+	0.992434i	$0.539181\pi$
$434$		0			0
$435$	−19.9994	+	0.151824i	−0.958899	+	0.00727942i
$436$	22.3049	+	30.7000i	1.06821	+	1.47027i
$437$	1.39919	+	8.83415i	0.0669324	+	0.422595i
$438$	6.42040	−	12.6007i	0.306778	−	0.602086i
$439$	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
$442$	−20.3031	+	39.8470i	−0.965719	+	1.89533i
$443$	2.43355	+	15.3648i	0.115621	+	0.730005i	0.975581	+	0.219642i	$0.0704889\pi$
$443$	2.43355	+	15.3648i	0.115621	+	0.730005i	−0.859959	+	0.510363i	$0.829511\pi$
$444$	10.5801	+	14.5623i	0.502111	+	0.691096i
$445$	−9.55858	−	9.41454i	−0.453120	−	0.446292i
$446$	−33.0826	−	10.7492i	−1.56650	−	0.508988i
$447$		0			0
$448$		0			0
$449$	−5.70634	+	1.85410i	−0.269299	+	0.0875005i	−0.440554	−	0.897726i	$-0.645218\pi$
$449$	−5.70634	+	1.85410i	−0.269299	+	0.0875005i	0.171255	+	0.985227i	$0.445218\pi$
$450$	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
$457$	−19.9235	+	10.1515i	−0.931983	+	0.474869i	−0.852944	−	0.522003i	$-0.825185\pi$
$457$	−19.9235	+	10.1515i	−0.931983	+	0.474869i	−0.0790387	+	0.996872i	$0.525185\pi$
$458$	−1.39919	+	8.83415i	−0.0653800	+	0.412793i
$459$	−20.4667	−	14.8699i	−0.955303	−	0.694068i
$460$	−5.63432	−	7.63246i	−0.262702	−	0.355865i
$461$		−	25.2982i		−	1.17826i	−0.808040	−	0.589128i	$-0.799471\pi$
$461$		−	25.2982i		−	1.17826i	0.808040	−	0.589128i	$-0.200529\pi$
$462$		0			0
$463$	9.00000	+	9.00000i	0.418265	+	0.418265i	0.884606	−	0.466340i	$-0.154428\pi$
$463$	9.00000	+	9.00000i	0.418265	+	0.418265i	−0.466340	+	0.884606i	$0.654428\pi$
$464$	−1.95440	−	6.01501i	−0.0907305	−	0.279240i
$465$	1.90868	−	6.02967i	0.0885128	−	0.279619i
$466$	−24.2705	+	17.6336i	−1.12431	+	0.816859i
$467$	4.49428	+	8.82051i	0.207970	+	0.408165i	0.971305	−	0.237839i	$-0.0764391\pi$
$467$	4.49428	+	8.82051i	0.207970	+	0.408165i	−0.763334	+	0.646004i	$0.776439\pi$
$468$	6.09092	+	11.9541i	0.281553	+	0.552579i
$469$		0			0
$470$	9.77380	+	18.8275i	0.450832	+	0.868446i
$471$	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
$475$	−18.1969	+	25.8626i	−0.834929	+	1.18666i
$476$		0			0
$477$	0.221232	−	1.39680i	0.0101295	−	0.0639552i
$478$	−37.8022	+	19.2612i	−1.72903	+	0.880986i
$479$	−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	$0.146154\pi$
$480$	−3.47743	−	20.9262i	−0.158722	−	0.955148i
$481$	11.1524	−	15.3500i	0.508508	−	0.699901i
$482$	12.6007	+	6.42040i	0.573948	+	0.292441i
$483$		0			0
$484$		0			0
$485$	21.0000	−	7.00000i	0.953561	−	0.317854i
$486$	−21.0525	+	6.84038i	−0.954962	+	0.310286i
$487$	−4.19041	+	0.663695i	−0.189885	+	0.0300749i	−0.250653	−	0.968077i	$-0.580645\pi$
$487$	−4.19041	+	0.663695i	−0.189885	+	0.0300749i	0.0607673	+	0.998152i	$0.480645\pi$
$488$	13.9680	+	2.21232i	0.632303	+	0.100147i
$489$	1.90211	+	0.618034i	0.0860165	+	0.0279485i
$490$	0.265693	+	34.9990i	0.0120028	+	1.58109i
$491$	3.71748	+	5.11667i	0.167768	+	0.230912i	0.884620	−	0.466313i	$-0.154418\pi$
$491$	3.71748	+	5.11667i	0.167768	+	0.230912i	−0.716852	+	0.697225i	$0.754418\pi$
$492$	4.19758	+	26.5025i	0.189241	+	1.19482i
$493$	−12.8408	+	25.2015i	−0.578320	+	1.13502i
$494$	−63.2456			−2.84555
$495$		0			0
$496$	2.00000			0.0898027
$497$		0			0
$498$	−4.42463	−	27.9360i	−0.198273	−	1.25184i
$499$	19.9847	+	27.5066i	0.894638	+	1.23136i	0.972147	+	0.234372i	$0.0753033\pi$
$499$	19.9847	+	27.5066i	0.894638	+	1.23136i	−0.0775090	+	0.996992i	$0.524697\pi$
$500$	4.49122	−	33.2390i	0.200854	−	1.48649i
$501$	−24.0600	−	7.81758i	−1.07492	−	0.349264i
$502$	−26.5025	−	4.19758i	−1.18286	−	0.187347i
$503$	−8.83415	+	1.39919i	−0.393895	+	0.0623869i	−0.350241	−	0.936660i	$-0.613900\pi$
$503$	−8.83415	+	1.39919i	−0.393895	+	0.0623869i	−0.0436548	+	0.999047i	$0.513900\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−7.00000	+	7.00000i	−0.310881	+	0.310881i
$508$	23.9082	+	12.1818i	1.06076	+	0.540482i
$509$	−2.35114	+	3.23607i	−0.104212	+	0.143436i	−0.857938	−	0.513753i	$-0.828255\pi$
$509$	−2.35114	+	3.23607i	−0.104212	+	0.143436i	0.753726	+	0.657189i	$0.228255\pi$
$510$	−18.3927	+	25.7237i	−0.814441	+	1.13907i
$511$		0			0
$512$	9.96176	−	5.07577i	0.440252	−	0.224319i
$513$	5.59677	−	35.3366i	0.247103	−	1.56015i
$514$	17.9084	+	13.0112i	0.789904	+	0.573899i
$515$	22.8974	−	16.9030i	1.00898	−	0.744834i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−1.95440	−	6.01501i	−0.0857884	−	0.264030i
$520$	19.8459	−	10.3025i	0.870299	−	0.451794i
$521$	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	$0.0898211\pi$
$522$	6.42040	+	12.6007i	0.281013	+	0.551519i
$523$	−12.1818	−	23.9082i	−0.532675	−	1.04543i	−0.987905	−	0.155059i	$-0.950443\pi$
$523$	−12.1818	−	23.9082i	−0.532675	−	1.04543i	0.455230	−	0.890374i	$-0.349557\pi$
$524$	−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
$530$	−6.99221	−	1.05311i	−0.303722	−	0.0457442i
$531$	−4.85410	−	3.52671i	−0.210650	−	0.153046i
$532$		0			0
$533$	25.2015	−	12.8408i	1.09160	−	0.556196i
$534$	5.86319	−	18.0450i	0.253725	−	0.780885i
$535$		0			0
$536$	5.57622	−	7.67501i	0.240856	−	0.331510i
$537$	−5.04029	−	2.56816i	−0.217505	−	0.110824i
$538$	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	0.597076	−	0.802185i	$-0.296329\pi$
$541$	36.0901	−	11.7264i	1.55163	−	0.504156i	0.954557	+	0.298029i	$0.0963291\pi$
$542$	27.9360	−	4.42463i	1.19996	−	0.190054i
$543$	−11.1744	−	1.76985i	−0.479540	−	0.0759517i
$544$	−28.5317	−	9.27051i	−1.22329	−	0.397470i
$545$	19.8476	−	20.1512i	0.850178	−	0.863185i
$546$		0			0
$547$	2.79838	+	17.6683i	0.119650	+	0.755442i	0.972434	+	0.233178i	$0.0749125\pi$
$547$	2.79838	+	17.6683i	0.119650	+	0.755442i	−0.852784	+	0.522264i	$0.825088\pi$
$548$	−25.0395	+	49.1429i	−1.06964	+	2.09928i
$549$	6.32456			0.269925
$550$		0			0
$551$	−40.0000			−1.70406
$552$	2.03031	−	3.98470i	0.0864156	−	0.169600i
$553$		0			0
$554$	−17.6336	−	24.2705i	−0.749178	−	1.03116i
$555$	9.41454	−	9.55858i	0.399625	−	0.405739i
$556$	36.0901	+	11.7264i	1.53056	+	0.497309i
$557$	22.0854	+	3.49798i	0.935788	+	0.148214i	0.605661	−	0.795723i	$-0.292909\pi$
$557$	22.0854	+	3.49798i	0.935788	+	0.148214i	0.330126	+	0.943937i	$0.392909\pi$
$558$	−4.41708	+	0.699596i	−0.186990	+	0.0296163i
$559$		0			0
$560$		0			0
$561$		0			0
$562$	−30.0000	+	30.0000i	−1.26547	+	1.26547i
$563$	−23.9082	−	12.1818i	−1.00761	−	0.513403i	−0.129357	−	0.991598i	$-0.541291\pi$
$563$	−23.9082	−	12.1818i	−1.00761	−	0.513403i	−0.878254	+	0.478195i	$0.841291\pi$
$564$	−10.5801	+	14.5623i	−0.445504	+	0.613184i
$565$	23.1514	+	16.5534i	0.973985	+	0.696406i
$566$	−6.18034	+	19.0211i	−0.259779	+	0.799518i
$567$		0			0
$568$	−2.79838	+	17.6683i	−0.117418	+	0.741346i
$569$	−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	$0.992748\pi$
$570$	−44.2226	−	6.66045i	−1.85228	−	0.278976i
$571$			44.2719i			1.85272i	0.376638	+	0.926360i	$0.377080\pi$
$571$			44.2719i			1.85272i	−0.376638	+	0.926360i	$0.622920\pi$
$572$		0			0
$573$	−22.0000	−	22.0000i	−0.919063	−	0.919063i
$574$		0			0
$575$	−4.92351	+	5.07533i	−0.205325	+	0.211656i
$576$	−10.5172	+	7.64121i	−0.438218	+	0.318384i
$577$	−14.7669	−	28.9817i	−0.614754	−	1.20652i	−0.963097	−	0.269156i	$-0.913255\pi$
$577$	−14.7669	−	28.9817i	−0.614754	−	1.20652i	0.348342	−	0.937367i	$-0.386745\pi$
$578$	3.04546	+	5.97705i	0.126674	+	0.248613i
$579$	25.5834	−	18.5874i	1.06321	−	0.772466i
$580$	37.6549	−	19.5476i	1.56353	−	0.811670i
$581$		0			0
$582$	22.1359	+	22.1359i	0.917564	+	0.917564i
$583$		0			0
$584$			10.0000i			0.413803i
$585$	8.04532	−	5.93910i	0.332633	−	0.245551i
$586$	−40.4508	−	29.3893i	−1.67101	−	1.21406i
$587$	1.54862	−	9.77762i	0.0639185	−	0.403565i	−0.934898	−	0.354918i	$-0.884509\pi$
$587$	1.54862	−	9.77762i	0.0639185	−	0.403565i	0.998816	−	0.0486476i	$-0.0154911\pi$
$588$	−26.4615	+	13.4828i	−1.09126	+	0.556023i
$589$	3.90879	−	12.0300i	0.161059	−	0.495688i
$590$	−17.4488	+	24.4037i	−0.718356	+	1.00468i
$591$	−3.71748	+	5.11667i	−0.152917	+	0.210472i
$592$	3.78022	+	1.92612i	0.155366	+	0.0791630i
$593$	−15.8114	+	15.8114i	−0.649296	+	0.649296i	−0.952823	−	0.303527i	$-0.901836\pi$
$593$	−15.8114	+	15.8114i	−0.649296	+	0.649296i	0.303527	+	0.952823i	$0.401836\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−8.38081	+	1.32739i	−0.343004	+	0.0543265i
$598$	−13.9680	−	2.21232i	−0.571195	−	0.0904684i
$599$	15.2169	+	4.94427i	0.621746	+	0.202017i	0.602915	−	0.797805i	$-0.294006\pi$
$599$	15.2169	+	4.94427i	0.621746	+	0.202017i	0.0188306	+	0.999823i	$0.494006\pi$
$600$	14.9616	−	5.11372i	0.610805	−	0.208767i
$601$	−18.5874	−	25.5834i	−0.758196	−	1.04357i	−0.997362	−	0.0725885i	$-0.976874\pi$
$601$	−18.5874	−	25.5834i	−0.758196	−	1.04357i	0.239166	−	0.970979i	$-0.423126\pi$
$602$		0			0
$603$	1.92612	−	3.78022i	0.0784376	−	0.153942i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	20.3031	−	39.8470i	0.824076	−	1.61734i	0.0379461	−	0.999280i	$-0.487918\pi$
$607$	20.3031	−	39.8470i	0.824076	−	1.61734i	0.786130	−	0.618061i	$-0.212082\pi$
$608$	−6.63695	−	41.9041i	−0.269164	−	1.69943i
$609$		0			0
$610$	−0.240055	−	31.6219i	−0.00971956	−	1.28033i
$611$	18.0450	+	5.86319i	0.730024	+	0.237199i
$612$	13.2512	+	2.09879i	0.535649	+	0.0848385i
$613$	−39.7537	+	6.29637i	−1.60564	+	0.254308i	−0.893942	−	0.448182i	$-0.852072\pi$
$613$	−39.7537	+	6.29637i	−1.60564	+	0.254308i	−0.711694	+	0.702490i	$0.752072\pi$
$614$		0			0
$615$	18.9737	−	6.32456i	0.765092	−	0.255031i
$616$		0			0
$617$	−17.0000	+	17.0000i	−0.684394	+	0.684394i	−0.960987	−	0.276593i	$-0.910795\pi$
$617$	−17.0000	+	17.0000i	−0.684394	+	0.684394i	0.276593	+	0.960987i	$0.410795\pi$
$618$	35.8623	+	18.2728i	1.44259	+	0.735038i
$619$	21.1603	−	29.1246i	0.850503	−	1.17062i	−0.133249	−	0.991083i	$-0.542541\pi$
$619$	21.1603	−	29.1246i	0.850503	−	1.17062i	0.983752	−	0.179534i	$-0.0574591\pi$
$620$	2.19932	+	13.2349i	0.0883269	+	0.531527i
$621$	2.47214	−	7.60845i	0.0992034	−	0.305317i
$622$	−15.9388	+	8.12123i	−0.639088	+	0.325632i
$623$		0			0
$624$	−5.11667	−	3.71748i	−0.204831	−	0.148818i
$625$	−24.9885	+	0.759012i	−0.999539	+	0.0303605i
$626$			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	$0.519804\pi$
$632$	−6.42040	−	12.6007i	−0.255390	−	0.501230i
$633$	16.2425	+	31.8776i	0.645580	+	1.26702i
$634$	43.4917	−	31.5986i	1.72728	−	1.25494i
$635$	6.03577	−	19.0675i	0.239522	−	0.756671i
$636$	−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
$640$	20.7868	+	28.1586i	0.821672	+	1.11307i
$641$	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
$643$	−13.8608	+	7.06243i	−0.546617	+	0.278515i	−0.705413	−	0.708796i	$-0.749239\pi$
$643$	−13.8608	+	7.06243i	−0.546617	+	0.278515i	0.158796	+	0.987311i	$0.449239\pi$
$644$		0			0
$645$		0			0
$646$	−37.1748	+	51.1667i	−1.46262	+	2.01313i
$647$	16.3810	+	8.34651i	0.644002	+	0.328135i	0.745308	−	0.666720i	$-0.232302\pi$
$647$	16.3810	+	8.34651i	0.644002	+	0.328135i	−0.101307	+	0.994855i	$0.532302\pi$
$648$	−7.90569	+	7.90569i	−0.310565	+	0.310565i
$649$		0			0
$650$	−30.0000	−	40.0000i	−1.17670	−	1.56893i
$651$		0			0
$652$	−4.19041	+	0.663695i	−0.164109	+	0.0259923i
$653$	1.39680	+	0.221232i	0.0546611	+	0.00865747i	0.183705	−	0.982981i	$-0.441191\pi$
$653$	1.39680	+	0.221232i	0.0546611	+	0.00865747i	−0.129044	+	0.991639i	$0.541191\pi$
$654$	38.0423	+	12.3607i	1.48757	+	0.483341i
$655$	20.1512	+	19.8476i	0.787374	+	0.775510i
$656$	3.71748	+	5.11667i	0.145143	+	0.199773i
$657$	0.699596	+	4.41708i	0.0272938	+	0.172327i
$658$		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	$0.195743\pi$
$662$	18.2728	−	35.8623i	0.710191	−	1.39383i
$663$	4.42463	+	27.9360i	0.171839	+	1.08495i
$664$	11.7557	+	16.1803i	0.456210	+	0.627919i
$665$		0			0
$666$	−9.02251	−	2.93159i	−0.349615	−	0.113597i
$667$	−8.83415	−	1.39919i	−0.342060	−	0.0541769i
$668$	53.0049	−	8.39515i	2.05082	−	0.324818i
$669$	−20.9232	+	6.79837i	−0.808939	+	0.262840i
$670$	−18.9737	−	9.48683i	−0.733017	−	0.366508i
$671$		0			0
$672$		0			0
$673$	−35.8623	−	18.2728i	−1.38239	−	0.704363i	−0.404707	−	0.914446i	$-0.632627\pi$
$673$	−35.8623	−	18.2728i	−1.38239	−	0.704363i	−0.977684	+	0.210083i	$0.932627\pi$
$674$	−17.6336	+	24.2705i	−0.679219	+	0.934865i
$675$	25.0036	−	13.2219i	0.962390	−	0.508912i
$676$	6.48936	−	19.9722i	0.249591	−	0.768161i
$677$	11.9541	−	6.09092i	0.459434	−	0.234093i	−0.208926	−	0.977931i	$-0.566997\pi$
$677$	11.9541	−	6.09092i	0.459434	−	0.234093i	0.668360	+	0.743838i	$0.266997\pi$
$678$	−6.29637	+	39.7537i	−0.241810	+	1.52673i
$679$		0			0
$680$	3.33023	−	22.1113i	0.127708	−	0.847930i
$681$			12.6491i			0.484715i
$682$		0			0
$683$	29.0000	+	29.0000i	1.10965	+	1.10965i	0.993196	+	0.116459i	$0.0371542\pi$
$683$	29.0000	+	29.0000i	1.10965	+	1.10965i	0.116459	+	0.993196i	$0.462846\pi$
$684$	5.86319	+	18.0450i	0.224184	+	0.689969i
$685$	39.1929	+	12.4064i	1.49748	+	0.474024i
$686$		0			0
$687$	2.56816	+	5.04029i	0.0979813	+	0.192299i
$688$		0			0
$689$	−5.11667	+	3.71748i	−0.194930	+	0.141625i
$690$	−9.53375	−	3.01788i	−0.362944	−	0.114889i
$691$	−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
$695$	4.21244	−	27.9688i	0.159787	−	1.06092i
$696$	16.1803	+	11.7557i	0.613314	+	0.445599i
$697$	4.42463	−	27.9360i	0.167595	−	1.05815i
$698$	−63.0037	+	32.1020i	−2.38472	+	1.21508i
$699$	−5.86319	+	18.0450i	−0.221766	+	0.682526i
$700$		0			0
$701$	−18.5874	+	25.5834i	−0.702036	+	0.966270i	0.297895	+	0.954599i	$0.403715\pi$
$701$	−18.5874	+	25.5834i	−0.702036	+	0.966270i	−0.999932	+	0.0116718i	$0.996285\pi$
$702$	50.4029	+	25.6816i	1.90234	+	0.969289i
$703$	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
$708$	−25.1424	−	3.98217i	−0.944911	−	0.149659i
$709$	5.70634	+	1.85410i	0.214306	+	0.0696323i	0.414202	−	0.910185i	$-0.364061\pi$
$709$	5.70634	+	1.85410i	0.214306	+	0.0696323i	−0.199896	+	0.979817i	$0.564061\pi$
$710$	39.9988	−	0.303649i	1.50113	−	0.0113957i
$711$	−3.71748	−	5.11667i	−0.139416	−	0.191890i
$712$	2.09879	+	13.2512i	0.0786554	+	0.496611i
$713$	1.28408	−	2.52015i	0.0480891	−	0.0943802i
$714$		0			0
$715$		0			0
$716$	12.0000			0.448461
$717$	−12.1818	+	23.9082i	−0.454939	+	0.892869i
$718$	−6.63695	−	41.9041i	−0.247689	−	1.56385i
$719$	14.1068	+	19.4164i	0.526097	+	0.724110i	0.986529	−	0.163585i	$-0.0523057\pi$
$719$	14.1068	+	19.4164i	0.526097	+	0.724110i	−0.460433	+	0.887695i	$0.652306\pi$
$720$	1.59310	+	1.56909i	0.0593712	+	0.0584766i
$721$		0			0
$722$	−46.3793	−	7.34576i	−1.72606	−	0.273381i
$723$	8.83415	−	1.39919i	0.328546	−	0.0520365i
$724$	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	−0.137482	−	0.990504i	$-0.543901\pi$
$727$	23.0000	−	23.0000i	0.853023	−	0.853023i	0.990504	+	0.137482i	$0.0439008\pi$
$728$		0			0
$729$	−17.0458	+	23.4615i	−0.631325	+	0.868944i
$730$	22.0582	−	3.66554i	0.816410	−	0.135668i
$731$		0			0
$732$	23.9082	−	12.1818i	0.883673	−	0.450254i
$733$	−2.09879	+	13.2512i	−0.0775205	+	0.489445i	0.918130	+	0.396279i	$0.129699\pi$
$733$	−2.09879	+	13.2512i	−0.0775205	+	0.489445i	−0.995651	+	0.0931661i	$0.970301\pi$
$734$	−7.67501	−	5.57622i	−0.283290	−	0.205822i
$735$	13.1468	+	17.8091i	0.484925	+	0.656897i
$736$		−	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	$0.825260\pi$
$740$	−8.58905	+	27.1335i	−0.315740	+	0.997448i
$741$	−32.3607	+	23.5114i	−1.18880	+	0.863713i
$742$		0			0
$743$		0			0		0.891007	−	0.453990i	$-0.150000\pi$
$743$		0			0		−0.891007	+	0.453990i	$0.850000\pi$
$744$	−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
$750$	−16.7642	−	31.1282i	−0.612141	−	1.13664i
$751$	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	$0.653372\pi$
$752$	−0.663695	+	4.19041i	−0.0242025	+	0.152808i
$753$	−15.1209	+	7.70447i	−0.551036	+	0.280767i
$754$	19.5440	−	60.1501i	0.711749	−	2.19054i
$755$		0			0
$756$		0			0
$757$	−34.0220	−	17.3351i	−1.23655	−	0.630054i	−0.291372	−	0.956610i	$-0.594112\pi$
$757$	−34.0220	−	17.3351i	−1.23655	−	0.630054i	−0.945178	+	0.326556i	$0.894112\pi$
$758$	−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	−0.878449	−	0.477836i	$-0.841421\pi$
$761$	−36.0901	+	11.7264i	−1.30826	+	0.425081i	−0.429815	+	0.902917i	$0.641421\pi$
$762$	27.9360	−	4.42463i	1.01202	−	0.160288i
$763$		0			0
$764$	62.7697	+	20.3951i	2.27093	+	0.737870i
$765$	−0.0759122	−	9.99971i	−0.00274461	−	0.361540i
$766$	−35.3161	−	48.6084i	−1.27602	−	1.75629i
$767$	4.19758	+	26.5025i	0.151566	+	0.956948i
$768$	−5.77836	+	11.3407i	−0.208508	+	0.409221i
$769$	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
$772$	−30.4546	+	59.7705i	−1.09609	+	2.15119i
$773$	2.43355	+	15.3648i	0.0875287	+	0.552634i	0.992014	+	0.126129i	$0.0402554\pi$
$773$	2.43355	+	15.3648i	0.0875287	+	0.552634i	−0.904485	+	0.426505i	$0.859745\pi$
$774$		0			0
$775$	9.46255	−	3.23420i	0.339905	−	0.116176i
$776$	−21.0525	−	6.84038i	−0.755742	−	0.245555i
$777$		0			0
$778$	35.3366	−	5.59677i	1.26688	−	0.200654i
$779$	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
$783$	31.8776	+	16.2425i	1.13921	+	0.580458i
$784$	−4.11450	+	5.66312i	−0.146946	+	0.202254i
$785$	−12.8749	+	18.0066i	−0.459523	+	0.642683i
$786$	−12.3607	+	38.0423i	−0.440891	+	1.35692i
$787$	−31.8776	+	16.2425i	−1.13631	+	0.578981i	−0.917875	−	0.396869i	$-0.870097\pi$
$787$	−31.8776	+	16.2425i	−1.13631	+	0.578981i	−0.218439	+	0.975851i	$0.570097\pi$
$788$	2.09879	−	13.2512i	0.0747662	−	0.472056i
$789$	−30.7000	−	22.3049i	−1.09295	−	0.794075i
$790$	−25.4415	+	18.7811i	−0.905169	+	0.668201i
$791$		0			0
$792$		0			0
$793$	−20.0000	−	20.0000i	−0.710221	−	0.710221i
$794$	12.7036	+	39.0976i	0.450833	+	1.38752i
$795$	−3.96917	+	2.06050i	−0.140772	+	0.0730783i
$796$	14.5623	−	10.5801i	0.516147	−	0.375003i
$797$	−8.34651	−	16.3810i	−0.295649	−	0.580243i	0.694626	−	0.719371i	$-0.255570\pi$
$797$	−8.34651	−	16.3810i	−0.295649	−	0.580243i	−0.990274	+	0.139128i	$0.955570\pi$
$798$		0			0
$799$	15.3500	−	11.1524i	0.543045	−	0.394545i
$800$	23.3543	−	24.0744i	0.825698	−	0.851159i
$801$	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
$807$	5.30956	−	33.5233i	0.186905	−	1.18007i
$808$		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	$-0.00824298\pi$
$810$	20.3364	+	14.5407i	0.714548	+	0.510907i
$811$	3.71748	−	5.11667i	0.130538	−	0.179671i	−0.738745	−	0.673986i	$-0.764581\pi$
$811$	3.71748	−	5.11667i	0.130538	−	0.179671i	0.869283	+	0.494315i	$0.164581\pi$
$812$		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
$818$	27.9360	+	4.42463i	0.976761	+	0.154704i
$819$		0			0
$820$	−29.7714	+	30.2269i	−1.03966	+	1.05557i
$821$	11.1524	+	15.3500i	0.389223	+	0.535719i	0.957998	−	0.286773i	$-0.0925827\pi$
$821$	11.1524	+	15.3500i	0.389223	+	0.535719i	−0.568776	+	0.822493i	$0.692583\pi$
$822$	9.09475	+	57.4220i	0.317216	+	2.00282i
$823$	7.06243	−	13.8608i	0.246181	−	0.483157i	−0.734541	−	0.678564i	$-0.762603\pi$
$823$	7.06243	−	13.8608i	0.246181	−	0.483157i	0.980722	+	0.195407i	$0.0626026\pi$
$824$	−28.4605			−0.991468
$825$		0			0
$826$		0			0
$827$	4.06061	−	7.96940i	0.141201	−	0.277123i	−0.809566	−	0.587029i	$-0.800297\pi$
$827$	4.06061	−	7.96940i	0.141201	−	0.277123i	0.950767	+	0.309906i	$0.100297\pi$
$828$	0.663695	+	4.19041i	0.0230650	+	0.145627i
$829$	−3.52671	−	4.85410i	−0.122488	−	0.168590i	0.743370	−	0.668881i	$-0.233226\pi$
$829$	−3.52671	−	4.85410i	−0.122488	−	0.168590i	−0.865857	+	0.500291i	$0.833226\pi$
$830$	31.3818	−	31.8619i	1.08928	−	1.10594i
$831$	−18.0450	−	5.86319i	−0.625975	−	0.203392i
$832$	57.4220	+	9.09475i	1.99075	+	0.315304i
$833$	30.9195	−	4.89717i	1.07130	−	0.169677i
$834$	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
$838$	−71.7246	−	36.5455i	−2.47769	−	1.26244i
$839$	3.52671	−	4.85410i	0.121756	−	0.167582i	−0.743788	−	0.668415i	$-0.766973\pi$
$839$	3.52671	−	4.85410i	0.121756	−	0.167582i	0.865544	+	0.500833i	$0.166973\pi$
$840$		0			0
$841$	3.39919	−	10.4616i	0.117213	−	0.360746i
$842$	−55.7858	+	28.4243i	−1.92251	+	0.979566i
$843$	−4.19758	+	26.5025i	−0.144572	+	0.912793i
$844$	−61.4001	−	44.6098i	−2.11348	−	1.53553i
$845$	−15.4779	−	2.33116i	−0.532456	−	0.0801943i
$846$		−	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
$850$	−49.9942	+	0.759100i	−1.71479	+	0.0260369i
$851$	4.85410	−	3.52671i	0.166396	−	0.120894i
$852$	15.4089	+	30.2418i	0.527902	+	1.03607i
$853$	6.09092	+	11.9541i	0.208549	+	0.409301i	0.971460	−	0.237203i	$-0.0762306\pi$
$853$	6.09092	+	11.9541i	0.208549	+	0.409301i	−0.762911	+	0.646504i	$0.776231\pi$
$854$		0			0
$855$	12.5516	−	6.51587i	0.429257	−	0.222838i
$856$		0			0
$857$	15.8114	+	15.8114i	0.540107	+	0.540107i	0.923560	−	0.383453i	$-0.125265\pi$
$857$	15.8114	+	15.8114i	0.540107	+	0.540107i	−0.383453	+	0.923560i	$0.625265\pi$
$858$		0			0
$859$		−	44.0000i		−	1.50126i	−0.660722	−	0.750630i	$-0.729750\pi$
$859$		−	44.0000i		−	1.50126i	0.660722	−	0.750630i	$-0.270250\pi$
$860$		0			0
$861$		0			0
$862$	6.63695	−	41.9041i	0.226055	−	1.42726i
$863$	−1.26007	+	0.642040i	−0.0428934	+	0.0218553i	−0.475306	−	0.879821i	$-0.657663\pi$
$863$	−1.26007	+	0.642040i	−0.0428934	+	0.0218553i	0.432412	+	0.901676i	$0.357663\pi$
$864$	−11.7264	+	36.0901i	−0.398939	+	1.22781i
$865$	5.81627	−	8.13456i	0.197759	−	0.276583i
$866$	−1.85874	+	2.55834i	−0.0631626	+	0.0869358i
$867$	3.78022	+	1.92612i	0.128383	+	0.0654144i
$868$		0			0
$869$		0			0
$870$	20.0000	−	40.0000i	0.678064	−	1.35613i
$871$	−18.0450	+	5.86319i	−0.611432	+	0.198666i
$872$	−27.9360	+	4.42463i	−0.946034	+	0.149837i
$873$	−9.77762	−	1.54862i	−0.330922	−	0.0524129i
$874$	−19.0211	−	6.18034i	−0.643399	−	0.209053i
$875$		0			0
$876$	11.1524	+	15.3500i	0.376806	+	0.518629i
$877$	−9.09475	−	57.4220i	−0.307108	−	1.93900i	−0.342221	−	0.939620i	$-0.611179\pi$
$877$	−9.09475	−	57.4220i	−0.307108	−	1.93900i	0.0351127	−	0.999383i	$-0.488821\pi$
$878$	−12.8408	+	25.2015i	−0.433356	+	0.850508i
$879$	−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	$0.489274\pi$
$882$	7.10608	−	13.9465i	0.239274	−	0.469602i
$883$	−4.20340	−	26.5392i	−0.141456	−	0.893117i	−0.951701	−	0.307026i	$-0.900666\pi$
$883$	−4.20340	−	26.5392i	−0.141456	−	0.893117i	0.810245	−	0.586091i	$-0.199334\pi$
$884$	−35.2671	−	48.5410i	−1.18616	−	1.63261i
$885$	0.144033	+	18.9731i	0.00484162	+	0.637774i
$886$	−33.0826	−	10.7492i	−1.11143	−	0.361126i
$887$	−8.83415	−	1.39919i	−0.296622	−	0.0469803i	0.00634986	−	0.999980i	$-0.497979\pi$
$887$	−8.83415	−	1.39919i	−0.296622	−	0.0469803i	−0.302972	+	0.953000i	$0.597979\pi$
$888$	−13.2512	+	2.09879i	−0.444682	+	0.0704307i
$889$		0			0
$890$	28.4605	−	9.48683i	0.953998	−	0.317999i
$891$		0			0
$892$	33.0000	−	33.0000i	1.10492	−	1.10492i
$893$	23.9082	+	12.1818i	0.800058	+	0.407650i
$894$		0			0
$895$	−1.46621	−	8.82328i	−0.0490101	−	0.294930i
$896$		0			0
$897$	−7.96940	+	4.06061i	−0.266091	+	0.135580i
$898$	2.09879	−	13.2512i	0.0700375	−	0.442199i
$899$	10.2333	+	7.43496i	0.341301	+	0.247970i
$900$	−8.63153	+	12.2677i	−0.287718	+	0.408924i
$901$			6.32456i			0.210701i
$902$		0			0
$903$		0			0
$904$	−8.79478	−	27.0675i	−0.292510	−	0.900253i
$905$	−8.24199	−	15.8767i	−0.273973	−	0.527759i
$906$		0			0
$907$	10.9147	+	21.4212i	0.362416	+	0.711281i	0.998161	−	0.0606180i	$-0.0193071\pi$
$907$	10.9147	+	21.4212i	0.362416	+	0.711281i	−0.635745	+	0.771899i	$0.719307\pi$
$908$	−12.1818	−	23.9082i	−0.404269	−	0.793422i
$909$		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
$915$	−11.8782	−	16.0906i	−0.392681	−	0.531940i
$916$	−9.70820	−	7.05342i	−0.320768	−	0.233052i
$917$		0			0
$918$	50.4029	−	25.6816i	1.66354	−	0.847618i
$919$	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	$-0.115261\pi$
$920$	6.97541	−	1.15914i	0.229973	−	0.0382158i
$921$		0			0
$922$	50.4029	+	25.6816i	1.65993	+	0.845778i
$923$	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
$927$	−12.5712	+	1.99109i	−0.412893	+	0.0653958i
$928$	41.9041	+	6.63695i	1.37557	+	0.217869i
$929$	−3.80423	−	1.23607i	−0.124813	−	0.0405541i	0.245945	−	0.969284i	$-0.420902\pi$
$929$	−3.80423	−	1.23607i	−0.124813	−	0.0405541i	−0.370757	+	0.928730i	$0.620902\pi$
$930$	10.0756	+	9.92380i	0.330393	+	0.325414i
$931$	26.0224	+	35.8167i	0.852848	+	1.17385i
$932$	−6.29637	−	39.7537i	−0.206244	−	1.30218i
$933$	−5.13632	+	10.0806i	−0.168155	+	0.330024i
$934$	−22.1359			−0.724310
$935$		0			0
$936$	−10.0000			−0.326860
$937$	6.09092	−	11.9541i	0.198982	−	0.390524i	−0.769857	−	0.638217i	$-0.779672\pi$
$937$	6.09092	−	11.9541i	0.198982	−	0.390524i	0.968839	+	0.247693i	$0.0796724\pi$
$938$		0			0
$939$	10.5801	+	14.5623i	0.345270	+	0.475223i
$940$	−28.4597	+	0.216050i	−0.928252	+	0.00704677i
$941$	−36.0901	−	11.7264i	−1.17650	−	0.382269i	−0.345436	−	0.938442i	$-0.612269\pi$
$941$	−36.0901	−	11.7264i	−1.17650	−	0.382269i	−0.831066	+	0.556174i	$0.812269\pi$
$942$	−30.9195	−	4.89717i	−1.00741	−	0.159559i
$943$	8.83415	−	1.39919i	0.287680	−	0.0455640i
$944$	−5.70634	+	1.85410i	−0.185726	+	0.0603459i
$945$		0			0
$946$		0			0
$947$	−7.00000	+	7.00000i	−0.227469	+	0.227469i	−0.811635	−	0.584165i	$-0.801422\pi$
$947$	−7.00000	+	7.00000i	−0.227469	+	0.227469i	0.584165	+	0.811635i	$0.301422\pi$
$948$	−23.9082	−	12.1818i	−0.776503	−	0.395648i
$949$	11.7557	−	16.1803i	0.381606	−	0.525236i
$950$	−33.0548	−	62.5090i	−1.07244	−	2.02806i
$951$	10.5066	−	32.3359i	0.340699	−	1.04856i
$952$		0			0
$953$	2.09879	−	13.2512i	0.0679864	−	0.429249i	−0.930094	−	0.367321i	$-0.880275\pi$
$953$	2.09879	−	13.2512i	0.0679864	−	0.429249i	0.998081	−	0.0619283i	$-0.0197250\pi$
$954$	2.55834	+	1.85874i	0.0828292	+	0.0601789i
$955$	7.32650	−	48.6449i	0.237080	−	1.57411i
$956$		−	56.9210i		−	1.84096i
$957$		0			0
$958$	−10.0000	−	10.0000i	−0.323085	−	0.323085i
$959$		0			0
$960$	39.1929	+	12.4064i	1.26494	+	0.400415i
$961$	21.8435	−	15.8702i	0.704628	−	0.511942i
$962$	19.2612	+	37.8022i	0.621006	+	1.21879i
$963$		0			0
$964$	−15.3500	+	11.1524i	−0.494391	+	0.359196i
$965$	47.6687	+	15.0894i	1.53451	+	0.485746i
$966$		0			0
$967$	−18.9737	−	18.9737i	−0.610152	−	0.610152i	0.332834	−	0.942986i	$-0.391995\pi$
$967$	−18.9737	−	18.9737i	−0.610152	−	0.610152i	−0.942986	+	0.332834i	$0.891995\pi$
$968$		0			0
$969$			40.0000i			1.28499i
$970$	−7.37177	+	48.9454i	−0.236693	+	1.57154i
$971$	−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	$0.935392\pi$
$972$	4.64587	−	29.3328i	0.149016	−	0.940852i
$973$		0			0
$974$	2.93159	−	9.02251i	0.0939343	−	0.289100i
$975$	−30.2199	−	9.31425i	−0.967813	−	0.298295i
$976$	3.71748	−	5.11667i	0.118994	−	0.163781i
$977$	−21.4212	−	10.9147i	−0.685326	−	0.349191i	0.0764116	−	0.997076i	$-0.475654\pi$
$977$	−21.4212	−	10.9147i	−0.685326	−	0.349191i	−0.761738	+	0.647885i	$0.775654\pi$
$978$	−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
$982$	−13.9680	+	2.21232i	−0.445738	+	0.0705979i
$983$	−40.5073	−	6.41572i	−1.29198	−	0.204630i	−0.527655	−	0.849459i	$-0.676928\pi$
$983$	−40.5073	−	6.41572i	−1.29198	−	0.204630i	−0.764327	+	0.644829i	$0.776928\pi$
$984$	−19.0211	−	6.18034i	−0.606371	−	0.197022i
$985$	−9.99971	+	0.0759122i	−0.318617	+	0.00241876i
$986$	−37.1748	−	51.1667i	−1.18389	−	1.62948i
$987$		0			0
$988$	38.5224	−	75.6044i	1.22556	−	2.40530i
$989$		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	$0.872802\pi$
$992$	−6.09092	+	11.9541i	−0.193387	+	0.379543i
$993$	−3.98217	−	25.1424i	−0.126370	−	0.797871i
$994$		0			0
$995$	−9.55858	−	9.41454i	−0.303027	−	0.298461i
$996$	36.0901	+	11.7264i	1.14356	+	0.371564i
$997$	−48.5878	−	7.69556i	−1.53879	−	0.243721i	−0.671305	−	0.741181i	$-0.734266\pi$
$997$	−48.5878	−	7.69556i	−1.53879	−	0.243721i	−0.867487	+	0.497460i	$0.834266\pi$
$998$	−75.0903	+	11.8931i	−2.37694	+	0.376471i
$999$	−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.578.1		16
5.2	odd	4	inner	605.2.m.b.457.1		16
11.2	odd	10	inner	605.2.m.b.233.1		16
11.3	even	5		55.2.e.a.43.2	yes	4
11.4	even	5	inner	605.2.m.b.118.1		16
11.5	even	5	inner	605.2.m.b.403.1		16
11.6	odd	10	inner	605.2.m.b.403.2		16
11.7	odd	10	inner	605.2.m.b.118.2		16
11.8	odd	10		55.2.e.a.43.1	yes	4
11.9	even	5	inner	605.2.m.b.233.2		16
11.10	odd	2	inner	605.2.m.b.578.2		16
33.8	even	10		495.2.k.b.208.2		4
33.14	odd	10		495.2.k.b.208.1		4
44.3	odd	10		880.2.bd.e.593.1		4
44.19	even	10		880.2.bd.e.593.2		4
55.2	even	20	inner	605.2.m.b.112.1		16
55.3	odd	20		275.2.e.b.32.2		4
55.7	even	20	inner	605.2.m.b.602.1		16
55.8	even	20		275.2.e.b.32.1		4
55.14	even	10		275.2.e.b.43.1		4
55.17	even	20	inner	605.2.m.b.282.1		16
55.19	odd	10		275.2.e.b.43.2		4
55.27	odd	20	inner	605.2.m.b.282.2		16
55.32	even	4	inner	605.2.m.b.457.2		16
55.37	odd	20	inner	605.2.m.b.602.2		16
55.42	odd	20	inner	605.2.m.b.112.2		16
55.47	odd	20		55.2.e.a.32.1	✓	4
55.52	even	20		55.2.e.a.32.2	yes	4
165.47	even	20		495.2.k.b.307.2		4
165.107	odd	20		495.2.k.b.307.1		4
220.47	even	20		880.2.bd.e.417.1		4
220.107	odd	20		880.2.bd.e.417.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.e.a.32.1	✓	4	55.47	odd	20
55.2.e.a.32.2	yes	4	55.52	even	20
55.2.e.a.43.1	yes	4	11.8	odd	10
55.2.e.a.43.2	yes	4	11.3	even	5
275.2.e.b.32.1		4	55.8	even	20
275.2.e.b.32.2		4	55.3	odd	20
275.2.e.b.43.1		4	55.14	even	10
275.2.e.b.43.2		4	55.19	odd	10
495.2.k.b.208.1		4	33.14	odd	10
495.2.k.b.208.2		4	33.8	even	10
495.2.k.b.307.1		4	165.107	odd	20
495.2.k.b.307.2		4	165.47	even	20
605.2.m.b.112.1		16	55.2	even	20	inner
605.2.m.b.112.2		16	55.42	odd	20	inner
605.2.m.b.118.1		16	11.4	even	5	inner
605.2.m.b.118.2		16	11.7	odd	10	inner
605.2.m.b.233.1		16	11.2	odd	10	inner
605.2.m.b.233.2		16	11.9	even	5	inner
605.2.m.b.282.1		16	55.17	even	20	inner
605.2.m.b.282.2		16	55.27	odd	20	inner
605.2.m.b.403.1		16	11.5	even	5	inner
605.2.m.b.403.2		16	11.6	odd	10	inner
605.2.m.b.457.1		16	5.2	odd	4	inner
605.2.m.b.457.2		16	55.32	even	4	inner
605.2.m.b.578.1		16	1.1	even	1	trivial
605.2.m.b.578.2		16	11.10	odd	2	inner
605.2.m.b.602.1		16	55.7	even	20	inner
605.2.m.b.602.2		16	55.37	odd	20	inner
880.2.bd.e.417.1		4	220.47	even	20
880.2.bd.e.417.2		4	220.107	odd	20
880.2.bd.e.593.1		4	44.3	odd	10
880.2.bd.e.593.2		4	44.19	even	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.m (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.01515 + 1.99235i) q^{2} +(0.221232 + 1.39680i) q^{3} +(-1.76336 - 2.42705i) q^{4} +(-1.56909 + 1.59310i) q^{5} +(-3.00750 - 0.977198i) q^{6} +(2.20854 - 0.349798i) q^{8} +(0.951057 - 0.309017i) q^{9} +O(q^{10})\)	\(q+(-1.01515 + 1.99235i) q^{2} +(0.221232 + 1.39680i) q^{3} +(-1.76336 - 2.42705i) q^{4} +(-1.56909 + 1.59310i) q^{5} +(-3.00750 - 0.977198i) q^{6} +(2.20854 - 0.349798i) q^{8} +(0.951057 - 0.309017i) q^{9} +(-1.58114 - 4.74342i) q^{10} +(3.00000 - 3.00000i) q^{12} +(-3.98470 - 2.03031i) q^{13} +(-2.57237 - 1.83927i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-3.98470 + 2.03031i) q^{17} +(-0.349798 + 2.20854i) q^{18} +(-5.11667 - 3.71748i) q^{19} +(6.63339 + 0.999068i) q^{20} +(-1.00000 - 1.00000i) q^{23} +(0.977198 + 3.00750i) q^{24} +(-0.0759100 - 4.99942i) q^{25} +(8.09017 - 5.87785i) q^{26} +(2.56816 + 5.04029i) q^{27} +(5.11667 - 3.71748i) q^{29} +(6.27582 - 3.25793i) q^{30} +(0.618034 + 1.90211i) q^{31} +(4.74342 + 4.74342i) q^{32} -10.0000i q^{34} +(-2.42705 - 1.76336i) q^{36} +(-0.663695 + 4.19041i) q^{37} +(12.6007 - 6.42040i) q^{38} +(1.95440 - 6.01501i) q^{39} +(-2.90813 + 4.06728i) q^{40} +(-3.71748 + 5.11667i) q^{41} +(-1.00000 + 2.00000i) q^{45} +(3.00750 - 0.977198i) q^{46} +(-4.19041 + 0.663695i) q^{47} +(1.39680 + 0.221232i) q^{48} +(-6.65740 - 2.16312i) q^{49} +(10.0377 + 4.92394i) q^{50} +(-3.71748 - 5.11667i) q^{51} +(2.09879 + 13.2512i) q^{52} +(0.642040 - 1.26007i) q^{53} -12.6491 q^{54} +(4.06061 - 7.96940i) q^{57} +(2.21232 + 13.9680i) q^{58} +(-3.52671 - 4.85410i) q^{59} +(0.0720166 + 9.48656i) q^{60} +(6.01501 + 1.95440i) q^{61} +(-4.41708 - 0.699596i) q^{62} +(-12.3637 + 4.01722i) q^{64} +(9.48683 - 3.16228i) q^{65} +(3.00000 - 3.00000i) q^{67} +(11.9541 + 6.09092i) q^{68} +(1.17557 - 1.61803i) q^{69} +(-2.47214 + 7.60845i) q^{71} +(1.99235 - 1.01515i) q^{72} +(-0.699596 + 4.41708i) q^{73} +(-7.67501 - 5.57622i) q^{74} +(6.96641 - 1.21206i) q^{75} +18.9737i q^{76} +(10.0000 + 10.0000i) q^{78} +(-1.95440 - 6.01501i) q^{79} +(1.03025 + 1.98459i) q^{80} +(-4.04508 + 2.93893i) q^{81} +(-6.42040 - 12.6007i) q^{82} +(4.06061 + 7.96940i) q^{83} +(3.01788 - 9.53375i) q^{85} +(6.32456 + 6.32456i) q^{87} +6.00000i q^{89} +(-2.96955 - 4.02266i) q^{90} +(-0.663695 + 4.19041i) q^{92} +(-2.52015 + 1.28408i) q^{93} +(2.93159 - 9.02251i) q^{94} +(13.9508 - 2.31829i) q^{95} +(-5.57622 + 7.67501i) q^{96} +(-8.82051 - 4.49428i) 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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