LMFDB - Embedded newform 3900.2.cd.o.2701.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3900,2,Mod(901,3900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3900, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))

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

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

chi := DirichletCharacter("3900.901");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3900.cd (of order $6$, degree $2$, 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:	$31.1416567883$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 26x^{10} + 239x^{8} + 924x^{6} + 1407x^{4} + 538x^{2} + 49 $ x^12 + 26x^10 + 239x^8 + 924x^6 + 1407x^4 + 538*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 780)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2701.2
Root			$-3.11341i$ of defining polynomial
Character	$\chi$	$=$	3900.2701
Dual form			3900.2.cd.o.901.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{3} +(-1.43544 - 0.828751i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	$q+(0.500000 + 0.866025i) q^{3} +(-1.43544 - 0.828751i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(5.23601 - 3.02301i) q^{11} +(-2.95768 - 2.06206i) q^{13} +(-0.573383 + 0.993129i) q^{17} +(-1.97958 - 1.14291i) q^{19} -1.65750i q^{21} +(3.87395 + 6.70988i) q^{23} -1.00000 q^{27} +(-3.60753 - 6.24842i) q^{29} +4.26033i q^{31} +(5.23601 + 3.02301i) q^{33} +(-2.74387 + 1.58417i) q^{37} +(0.306957 - 3.59246i) q^{39} +(9.30618 - 5.37292i) q^{41} +(1.23357 - 2.13661i) q^{43} -10.5431i q^{47} +(-2.12634 - 3.68294i) q^{49} -1.14677 q^{51} -4.38252 q^{53} -2.28582i q^{57} +(5.77915 + 3.33660i) q^{59} +(0.365010 - 0.632216i) q^{61} +(1.43544 - 0.828751i) q^{63} +(-3.12741 + 1.80561i) q^{67} +(-3.87395 + 6.70988i) q^{69} +(-10.6742 - 6.16273i) q^{71} -12.4953i q^{73} -10.0213 q^{77} -1.33438 q^{79} +(-0.500000 - 0.866025i) q^{81} -6.54486i q^{83} +(3.60753 - 6.24842i) q^{87} +(5.19861 - 3.00142i) q^{89} +(2.53664 + 5.41115i) q^{91} +(-3.68956 + 2.13017i) q^{93} +(-5.17274 - 2.98648i) q^{97} +6.04602i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} + 6 q^{7} - 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^3 + 6 * q^7 - 6 * q^9	$ 12 q + 6 q^{3} + 6 q^{7} - 6 q^{9} + 6 q^{11} - 8 q^{13} + 2 q^{17} - 12 q^{19} + 4 q^{23} - 12 q^{27} - 2 q^{29} + 6 q^{33} - 6 q^{37} - 4 q^{39} + 36 q^{41} + 16 q^{43} + 4 q^{49} + 4 q^{51} - 18 q^{59} + 22 q^{61} - 6 q^{63} + 6 q^{67} - 4 q^{69} + 6 q^{71} - 24 q^{77} - 4 q^{79} - 6 q^{81} + 2 q^{87} + 2 q^{91} - 6 q^{93} + 48 q^{97}+O(q^{100}) $ 12 * q + 6 * q^3 + 6 * q^7 - 6 * q^9 + 6 * q^11 - 8 * q^13 + 2 * q^17 - 12 * q^19 + 4 * q^23 - 12 * q^27 - 2 * q^29 + 6 * q^33 - 6 * q^37 - 4 * q^39 + 36 * q^41 + 16 * q^43 + 4 * q^49 + 4 * q^51 - 18 * q^59 + 22 * q^61 - 6 * q^63 + 6 * q^67 - 4 * q^69 + 6 * q^71 - 24 * q^77 - 4 * q^79 - 6 * q^81 + 2 * q^87 + 2 * q^91 - 6 * q^93 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3900\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1951$	$3277$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.43544	−	0.828751i	−0.542545	−	0.313238i	0.203565	−	0.979061i	$-0.434747\pi$
$7$	−1.43544	−	0.828751i	−0.542545	−	0.313238i	−0.746110	+	0.665823i	$0.768081\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	5.23601	−	3.02301i	1.57872	−	0.911472i	0.583677	−	0.811986i	$-0.301613\pi$
$11$	5.23601	−	3.02301i	1.57872	−	0.911472i	0.995039	−	0.0994860i	$-0.0317199\pi$
$12$		0			0
$13$	−2.95768	−	2.06206i	−0.820314	−	0.571913i
$13$	−2.95768	−	2.06206i	−0.820314	−	0.571913i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.573383	+	0.993129i	−0.139066	+	0.240869i	−0.927143	−	0.374707i	$-0.877743\pi$
$17$	−0.573383	+	0.993129i	−0.139066	+	0.240869i	0.788077	+	0.615576i	$0.211077\pi$
$18$		0			0
$19$	−1.97958	−	1.14291i	−0.454146	−	0.262201i	0.255433	−	0.966827i	$-0.417782\pi$
$19$	−1.97958	−	1.14291i	−0.454146	−	0.262201i	−0.709580	+	0.704625i	$0.751115\pi$
$20$		0			0
$21$		−	1.65750i		−	0.361697i
$22$		0			0
$23$	3.87395	+	6.70988i	0.807775	+	1.39911i	0.914402	+	0.404808i	$0.132662\pi$
$23$	3.87395	+	6.70988i	0.807775	+	1.39911i	−0.106627	+	0.994299i	$0.534005\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−3.60753	−	6.24842i	−0.669901	−	1.16030i	−0.977931	−	0.208926i	$-0.933003\pi$
$29$	−3.60753	−	6.24842i	−0.669901	−	1.16030i	0.308031	−	0.951376i	$-0.400330\pi$
$30$		0			0
$31$			4.26033i			0.765178i	0.923919	+	0.382589i	$0.124967\pi$
$31$			4.26033i			0.765178i	−0.923919	+	0.382589i	$0.875033\pi$
$32$		0			0
$33$	5.23601	+	3.02301i	0.911472	+	0.526239i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.74387	+	1.58417i	−0.451089	+	0.260436i	−0.708290	−	0.705922i	$-0.750533\pi$
$37$	−2.74387	+	1.58417i	−0.451089	+	0.260436i	0.257201	+	0.966358i	$0.417200\pi$
$38$		0			0
$39$	0.306957	−	3.59246i	0.0491524	−	0.575254i
$40$		0			0
$41$	9.30618	−	5.37292i	1.45338	−	0.839110i	0.454709	−	0.890640i	$-0.349743\pi$
$41$	9.30618	−	5.37292i	1.45338	−	0.839110i	0.998671	+	0.0515301i	$0.0164098\pi$
$42$		0			0
$43$	1.23357	−	2.13661i	0.188118	−	0.325830i	−0.756505	−	0.653988i	$-0.773095\pi$
$43$	1.23357	−	2.13661i	0.188118	−	0.325830i	0.944623	+	0.328158i	$0.106428\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	10.5431i		−	1.53787i	−0.639326	−	0.768935i	$-0.720787\pi$
$47$		−	10.5431i		−	1.53787i	0.639326	−	0.768935i	$-0.279213\pi$
$48$		0			0
$49$	−2.12634	−	3.68294i	−0.303763	−	0.526134i
$50$		0			0
$51$	−1.14677			−0.160579
$52$		0			0
$53$	−4.38252			−0.601985			−0.300992	−	0.953627i	$-0.597318\pi$
$53$	−4.38252			−0.601985			−0.300992	+	0.953627i	$0.597318\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	2.28582i		−	0.302764i
$58$		0			0
$59$	5.77915	+	3.33660i	0.752382	+	0.434388i	0.826554	−	0.562858i	$-0.190298\pi$
$59$	5.77915	+	3.33660i	0.752382	+	0.434388i	−0.0741721	+	0.997245i	$0.523631\pi$
$60$		0			0
$61$	0.365010	−	0.632216i	0.0467347	−	0.0809469i	−0.841712	−	0.539927i	$-0.818452\pi$
$61$	0.365010	−	0.632216i	0.0467347	−	0.0809469i	0.888446	+	0.458980i	$0.151785\pi$
$62$		0			0
$63$	1.43544	−	0.828751i	0.180848	−	0.104413i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−3.12741	+	1.80561i	−0.382075	+	0.220591i	−0.678720	−	0.734397i	$-0.737465\pi$
$67$	−3.12741	+	1.80561i	−0.382075	+	0.220591i	0.296646	+	0.954988i	$0.404132\pi$
$68$		0			0
$69$	−3.87395	+	6.70988i	−0.466369	+	0.807775i
$70$		0			0
$71$	−10.6742	−	6.16273i	−1.26679	−	0.731382i	−0.292411	−	0.956293i	$-0.594458\pi$
$71$	−10.6742	−	6.16273i	−1.26679	−	0.731382i	−0.974379	+	0.224911i	$0.927791\pi$
$72$		0			0
$73$		−	12.4953i		−	1.46247i	−0.682126	−	0.731235i	$-0.738944\pi$
$73$		−	12.4953i		−	1.46247i	0.682126	−	0.731235i	$-0.261056\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−10.0213			−1.14203
$78$		0			0
$79$	−1.33438			−0.150129			−0.0750646	−	0.997179i	$-0.523916\pi$
$79$	−1.33438			−0.150129			−0.0750646	+	0.997179i	$0.523916\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	6.54486i		−	0.718392i	−0.933262	−	0.359196i	$-0.883051\pi$
$83$		−	6.54486i		−	0.718392i	0.933262	−	0.359196i	$-0.116949\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	3.60753	−	6.24842i	0.386767	−	0.669901i
$88$		0			0
$89$	5.19861	−	3.00142i	0.551051	−	0.318150i	−0.198495	−	0.980102i	$-0.563605\pi$
$89$	5.19861	−	3.00142i	0.551051	−	0.318150i	0.749546	+	0.661952i	$0.230272\pi$
$90$		0			0
$91$	2.53664	+	5.41115i	0.265912	+	0.567242i
$92$		0			0
$93$	−3.68956	+	2.13017i	−0.382589	+	0.220888i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−5.17274	−	2.98648i	−0.525212	−	0.303231i	0.213853	−	0.976866i	$-0.431399\pi$
$97$	−5.17274	−	2.98648i	−0.525212	−	0.303231i	−0.739064	+	0.673635i	$0.764732\pi$
$98$		0			0
$99$			6.04602i			0.607648i
$100$		0			0
$101$	−0.102016	−	0.176697i	−0.0101510	−	0.0175820i	0.860905	−	0.508765i	$-0.169898\pi$
$101$	−0.102016	−	0.176697i	−0.0101510	−	0.0175820i	−0.871056	+	0.491183i	$0.836565\pi$
$102$		0			0
$103$	−3.25947			−0.321165			−0.160582	−	0.987022i	$-0.551337\pi$
$103$	−3.25947			−0.321165			−0.160582	+	0.987022i	$0.551337\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.75400	−	3.03801i	−0.169565	−	0.293695i	0.768702	−	0.639607i	$-0.220903\pi$
$107$	−1.75400	−	3.03801i	−0.169565	−	0.293695i	−0.938267	+	0.345912i	$0.887570\pi$
$108$		0			0
$109$		−	11.5163i		−	1.10307i	−0.834153	−	0.551533i	$-0.814043\pi$
$109$		−	11.5163i		−	1.10307i	0.834153	−	0.551533i	$-0.185957\pi$
$110$		0			0
$111$	−2.74387	−	1.58417i	−0.260436	−	0.150363i
$112$		0			0
$113$	−0.0964457	+	0.167049i	−0.00907284	+	0.0157146i	−0.870526	−	0.492122i	$-0.836221\pi$
$113$	−0.0964457	+	0.167049i	−0.00907284	+	0.0157146i	0.861453	+	0.507837i	$0.169555\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	3.26464	−	1.53040i	0.301816	−	0.141485i
$118$		0			0
$119$	1.64611	−	0.950384i	0.150899	−	0.0871215i
$120$		0			0
$121$	12.7772	−	22.1307i	1.16156	−	2.01189i
$122$		0			0
$123$	9.30618	+	5.37292i	0.839110	+	0.484460i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	9.63368	+	16.6860i	0.854851	+	1.48064i	0.876783	+	0.480885i	$0.159685\pi$
$127$	9.63368	+	16.6860i	0.854851	+	1.48064i	−0.0219328	+	0.999759i	$0.506982\pi$
$128$		0			0
$129$	2.46715			0.217220
$130$		0			0
$131$	−3.62693			−0.316886			−0.158443	−	0.987368i	$-0.550647\pi$
$131$	−3.62693			−0.316886			−0.158443	+	0.987368i	$0.550647\pi$
$132$		0			0
$133$	1.89437	+	3.28115i	0.164263	+	0.284512i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	7.78830	+	4.49658i	0.665400	+	0.384169i	0.794331	−	0.607485i	$-0.207821\pi$
$137$	7.78830	+	4.49658i	0.665400	+	0.384169i	−0.128932	+	0.991653i	$0.541155\pi$
$138$		0			0
$139$	5.32861	−	9.22941i	0.451966	−	0.782829i	−0.546542	−	0.837432i	$-0.684056\pi$
$139$	5.32861	−	9.22941i	0.451966	−	0.782829i	0.998508	+	0.0546031i	$0.0173894\pi$
$140$		0			0
$141$	9.13060	−	5.27156i	0.768935	−	0.443945i
$142$		0			0
$143$	−21.7201	−	1.85587i	−1.81633	−	0.155195i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	2.12634	−	3.68294i	0.175378	−	0.303763i
$148$		0			0
$149$	18.7162	+	10.8058i	1.53329	+	0.885245i	0.999207	+	0.0398134i	$0.0126764\pi$
$149$	18.7162	+	10.8058i	1.53329	+	0.885245i	0.534083	+	0.845432i	$0.320657\pi$
$150$		0			0
$151$		−	17.2597i		−	1.40458i	−0.711892	−	0.702289i	$-0.752162\pi$
$151$		−	17.2597i		−	1.40458i	0.711892	−	0.702289i	$-0.247838\pi$
$152$		0			0
$153$	−0.573383	−	0.993129i	−0.0463553	−	0.0802897i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	21.4448			1.71148			0.855741	−	0.517405i	$-0.173102\pi$
$157$	21.4448			1.71148			0.855741	+	0.517405i	$0.173102\pi$
$158$		0			0
$159$	−2.19126	−	3.79537i	−0.173778	−	0.300992i
$160$		0			0
$161$		−	12.8422i		−	1.01210i
$162$		0			0
$163$	−12.2954	−	7.09876i	−0.963051	−	0.556018i	−0.0659406	−	0.997824i	$-0.521005\pi$
$163$	−12.2954	−	7.09876i	−0.963051	−	0.556018i	−0.897111	+	0.441806i	$0.854338\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	5.51973	−	3.18682i	0.427129	−	0.246603i	−0.270994	−	0.962581i	$-0.587352\pi$
$167$	5.51973	−	3.18682i	0.427129	−	0.246603i	0.698123	+	0.715978i	$0.254019\pi$
$168$		0			0
$169$	4.49579	+	12.1979i	0.345830	+	0.938297i
$170$		0			0
$171$	1.97958	−	1.14291i	0.151382	−	0.0874005i
$172$		0			0
$173$	−8.64924	+	14.9809i	−0.657589	+	1.13898i	0.323648	+	0.946177i	$0.395090\pi$
$173$	−8.64924	+	14.9809i	−0.657589	+	1.13898i	−0.981238	+	0.192801i	$0.938243\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$			6.67319i			0.501588i
$178$		0			0
$179$	−5.19861	−	9.00425i	−0.388562	−	0.673010i	0.603694	−	0.797216i	$-0.293695\pi$
$179$	−5.19861	−	9.00425i	−0.388562	−	0.673010i	−0.992256	+	0.124206i	$0.960361\pi$
$180$		0			0
$181$	−10.0711			−0.748582			−0.374291	−	0.927311i	$-0.622114\pi$
$181$	−10.0711			−0.748582			−0.374291	+	0.927311i	$0.622114\pi$
$182$		0			0
$183$	0.730020			0.0539646
$184$		0			0
$185$		0			0
$186$		0			0
$187$			6.93337i			0.507018i
$188$		0			0
$189$	1.43544	+	0.828751i	0.104413	+	0.0602828i
$190$		0			0
$191$	10.3999	−	18.0132i	0.752513	−	1.30339i	−0.194088	−	0.980984i	$-0.562175\pi$
$191$	10.3999	−	18.0132i	0.752513	−	1.30339i	0.946601	−	0.322407i	$-0.104492\pi$
$192$		0			0
$193$	23.8195	−	13.7522i	1.71456	−	0.989904i	0.786414	−	0.617700i	$-0.211935\pi$
$193$	23.8195	−	13.7522i	1.71456	−	0.989904i	0.928151	−	0.372205i	$-0.121398\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−18.5448	+	10.7068i	−1.32126	+	0.762831i	−0.983930	−	0.178555i	$-0.942858\pi$
$197$	−18.5448	+	10.7068i	−1.32126	+	0.762831i	−0.337332	+	0.941386i	$0.609525\pi$
$198$		0			0
$199$	12.6961	−	21.9903i	0.900005	−	1.55885i	0.0725188	−	0.997367i	$-0.476896\pi$
$199$	12.6961	−	21.9903i	0.900005	−	1.55885i	0.827486	−	0.561487i	$-0.189770\pi$
$200$		0			0
$201$	−3.12741	−	1.80561i	−0.220591	−	0.127358i
$202$		0			0
$203$			11.9590i			0.839355i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−7.74791			−0.538517
$208$		0			0
$209$	−13.8201			−0.955957
$210$		0			0
$211$	−0.926303	−	1.60440i	−0.0637693	−	0.110452i	0.832378	−	0.554208i	$-0.186979\pi$
$211$	−0.926303	−	1.60440i	−0.0637693	−	0.110452i	−0.896147	+	0.443756i	$0.853646\pi$
$212$		0			0
$213$		−	12.3255i		−	0.844527i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	3.53075	−	6.11544i	0.239683	−	0.415143i
$218$		0			0
$219$	10.8213	−	6.24767i	0.731235	−	0.422179i
$220$		0			0
$221$	3.74378	−	1.75501i	0.251834	−	0.118055i
$222$		0			0
$223$	9.09160	−	5.24904i	0.608819	−	0.351502i	−0.163684	−	0.986513i	$-0.552338\pi$
$223$	9.09160	−	5.24904i	0.608819	−	0.351502i	0.772503	+	0.635011i	$0.219005\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	8.46169	+	4.88536i	0.561622	+	0.324252i	0.753796	−	0.657108i	$-0.228221\pi$
$227$	8.46169	+	4.88536i	0.561622	+	0.324252i	−0.192174	+	0.981361i	$0.561554\pi$
$228$		0			0
$229$			16.9351i			1.11910i	0.828796	+	0.559550i	$0.189026\pi$
$229$			16.9351i			1.11910i	−0.828796	+	0.559550i	$0.810974\pi$
$230$		0			0
$231$	−5.01065	−	8.67869i	−0.329676	−	0.571016i
$232$		0			0
$233$	−19.7938			−1.29674			−0.648368	−	0.761327i	$-0.724548\pi$
$233$	−19.7938			−1.29674			−0.648368	+	0.761327i	$0.724548\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−0.667188	−	1.15560i	−0.0433385	−	0.0750646i
$238$		0			0
$239$			1.00847i			0.0652328i	0.999468	+	0.0326164i	$0.0103840\pi$
$239$			1.00847i			0.0652328i	−0.999468	+	0.0326164i	$0.989616\pi$
$240$		0			0
$241$	7.67505	+	4.43119i	0.494393	+	0.285438i	0.726395	−	0.687277i	$-0.241194\pi$
$241$	7.67505	+	4.43119i	0.494393	+	0.285438i	−0.232002	+	0.972715i	$0.574528\pi$
$242$		0			0
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	3.49821	+	7.46238i	0.222586	+	0.474820i
$248$		0			0
$249$	5.66801	−	3.27243i	0.359196	−	0.207382i
$250$		0			0
$251$	1.40347	−	2.43088i	0.0885863	−	0.153436i	−0.818327	−	0.574752i	$-0.805098\pi$
$251$	1.40347	−	2.43088i	0.0885863	−	0.153436i	0.906914	+	0.421316i	$0.138432\pi$
$252$		0			0
$253$	40.5681	+	23.4220i	2.55049	+	1.47253i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−0.197590	−	0.342236i	−0.0123253	−	0.0213481i	0.859797	−	0.510636i	$-0.170590\pi$
$257$	−0.197590	−	0.342236i	−0.0123253	−	0.0213481i	−0.872122	+	0.489288i	$0.837257\pi$
$258$		0			0
$259$	5.25154			0.326315
$260$		0			0
$261$	7.21505			0.446601
$262$		0			0
$263$	−12.2704	−	21.2529i	−0.756623	−	1.31051i	−0.944563	−	0.328330i	$-0.893514\pi$
$263$	−12.2704	−	21.2529i	−0.756623	−	1.31051i	0.187940	−	0.982181i	$-0.439819\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	5.19861	+	3.00142i	0.318150	+	0.183684i
$268$		0			0
$269$	−6.07730	+	10.5262i	−0.370540	+	0.641793i	−0.989649	−	0.143512i	$-0.954161\pi$
$269$	−6.07730	+	10.5262i	−0.370540	+	0.641793i	0.619109	+	0.785305i	$0.287494\pi$
$270$		0			0
$271$	−3.19227	+	1.84306i	−0.193917	+	0.111958i	−0.593815	−	0.804602i	$-0.702379\pi$
$271$	−3.19227	+	1.84306i	−0.193917	+	0.111958i	0.399898	+	0.916560i	$0.369046\pi$
$272$		0			0
$273$	−3.41787	+	4.90237i	−0.206859	+	0.296705i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−0.402900	+	0.697843i	−0.0242079	+	0.0419293i	−0.877876	−	0.478889i	$-0.841040\pi$
$277$	−0.402900	+	0.697843i	−0.0242079	+	0.0419293i	0.853668	+	0.520818i	$0.174373\pi$
$278$		0			0
$279$	−3.68956	−	2.13017i	−0.220888	−	0.127530i
$280$		0			0
$281$		−	0.360243i		−	0.0214903i	−0.999942	−	0.0107452i	$-0.996580\pi$
$281$		−	0.360243i		−	0.0214903i	0.999942	−	0.0107452i	$-0.00342036\pi$
$282$		0			0
$283$	10.1636	+	17.6039i	0.604163	+	1.04644i	0.992183	+	0.124790i	$0.0398256\pi$
$283$	10.1636	+	17.6039i	0.604163	+	1.04644i	−0.388021	+	0.921651i	$0.626841\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−17.8113			−1.05137
$288$		0			0
$289$	7.84246	+	13.5835i	0.461321	+	0.799032i
$290$		0			0
$291$		−	5.97296i		−	0.350141i
$292$		0			0
$293$	−14.7008	−	8.48753i	−0.858832	−	0.495847i	0.00478898	−	0.999989i	$-0.498476\pi$
$293$	−14.7008	−	8.48753i	−0.858832	−	0.495847i	−0.863621	+	0.504142i	$0.831809\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−5.23601	+	3.02301i	−0.303824	+	0.175413i
$298$		0			0
$299$	2.37827	−	27.8340i	0.137539	−	1.60968i
$300$		0			0
$301$	−3.54144	+	2.04465i	−0.204125	+	0.117852i
$302$		0			0
$303$	0.102016	−	0.176697i	0.00586067	−	0.0101510i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	17.1770i		−	0.980346i	−0.871625	−	0.490173i	$-0.836934\pi$
$307$		−	17.1770i		−	0.980346i	0.871625	−	0.490173i	$-0.163066\pi$
$308$		0			0
$309$	−1.62973	−	2.82278i	−0.0927123	−	0.160582i
$310$		0			0
$311$	−18.4174			−1.04435			−0.522176	−	0.852837i	$-0.674880\pi$
$311$	−18.4174			−1.04435			−0.522176	+	0.852837i	$0.674880\pi$
$312$		0			0
$313$	−8.10571			−0.458162			−0.229081	−	0.973407i	$-0.573572\pi$
$313$	−8.10571			−0.458162			−0.229081	+	0.973407i	$0.573572\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			4.06294i			0.228197i	0.993469	+	0.114099i	$0.0363980\pi$
$317$			4.06294i			0.228197i	−0.993469	+	0.114099i	$0.963602\pi$
$318$		0			0
$319$	−37.7781	−	21.8112i	−2.11517	−	1.22119i
$320$		0			0
$321$	1.75400	−	3.03801i	0.0978985	−	0.169565i
$322$		0			0
$323$	2.27011	−	1.31065i	0.126312	−	0.0729265i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	9.97344	−	5.75817i	0.551533	−	0.318428i
$328$		0			0
$329$	−8.73761	+	15.1340i	−0.481720	+	0.834364i
$330$		0			0
$331$	17.3971	+	10.0442i	0.956233	+	0.552081i	0.895012	−	0.446043i	$-0.147167\pi$
$331$	17.3971	+	10.0442i	0.956233	+	0.552081i	0.0612213	+	0.998124i	$0.480500\pi$
$332$		0			0
$333$		−	3.16834i		−	0.173624i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−3.81854			−0.208009			−0.104005	−	0.994577i	$-0.533166\pi$
$337$	−3.81854			−0.208009			−0.104005	+	0.994577i	$0.533166\pi$
$338$		0			0
$339$	−0.192891			−0.0104764
$340$		0			0
$341$	12.8790	+	22.3071i	0.697438	+	1.20800i
$342$		0			0
$343$			18.6513i			1.00708i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	16.2317	−	28.1142i	0.871365	−	1.50925i	0.0107803	−	0.999942i	$-0.496568\pi$
$347$	16.2317	−	28.1142i	0.871365	−	1.50925i	0.860585	−	0.509307i	$-0.170098\pi$
$348$		0			0
$349$	12.6256	−	7.28941i	0.675834	−	0.390193i	−0.122449	−	0.992475i	$-0.539075\pi$
$349$	12.6256	−	7.28941i	0.675834	−	0.390193i	0.798284	+	0.602282i	$0.205742\pi$
$350$		0			0
$351$	2.95768	+	2.06206i	0.157870	+	0.110065i
$352$		0			0
$353$	−17.8982	+	10.3335i	−0.952626	+	0.549999i	−0.893896	−	0.448275i	$-0.852038\pi$
$353$	−17.8982	+	10.3335i	−0.952626	+	0.549999i	−0.0587300	+	0.998274i	$0.518705\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	1.64611	+	0.950384i	0.0871215	+	0.0502996i
$358$		0			0
$359$		−	5.82021i		−	0.307179i	−0.988135	−	0.153589i	$-0.950917\pi$
$359$		−	5.82021i		−	0.307179i	0.988135	−	0.153589i	$-0.0490833\pi$
$360$		0			0
$361$	−6.88751	−	11.9295i	−0.362501	−	0.627870i
$362$		0			0
$363$	25.5544			1.34126
$364$		0			0
$365$		0			0
$366$		0			0
$367$	7.11095	+	12.3165i	0.371189	+	0.642918i	0.989749	−	0.142820i	$-0.0456170\pi$
$367$	7.11095	+	12.3165i	0.371189	+	0.642918i	−0.618560	+	0.785738i	$0.712284\pi$
$368$		0			0
$369$			10.7458i			0.559407i
$370$		0			0
$371$	6.29083	+	3.63201i	0.326604	+	0.188565i
$372$		0			0
$373$	−16.2862	+	28.2085i	−0.843266	+	1.46058i	0.0438524	+	0.999038i	$0.486037\pi$
$373$	−16.2862	+	28.2085i	−0.843266	+	1.46058i	−0.887119	+	0.461542i	$0.847296\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.21471	+	25.9198i	−0.114063	+	1.33494i
$378$		0			0
$379$	−25.5125	+	14.7296i	−1.31049	+	0.756611i	−0.982177	−	0.187959i	$-0.939813\pi$
$379$	−25.5125	+	14.7296i	−1.31049	+	0.756611i	−0.328311	+	0.944570i	$0.606480\pi$
$380$		0			0
$381$	−9.63368	+	16.6860i	−0.493548	+	0.854851i
$382$		0			0
$383$	27.3433	+	15.7867i	1.39718	+	0.806660i	0.994096	−	0.108504i	$-0.0346061\pi$
$383$	27.3433	+	15.7867i	1.39718	+	0.806660i	0.403081	+	0.915164i	$0.367939\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	1.23357	+	2.13661i	0.0627061	+	0.108610i
$388$		0			0
$389$	−22.6754			−1.14969			−0.574843	−	0.818263i	$-0.694937\pi$
$389$	−22.6754			−1.14969			−0.574843	+	0.818263i	$0.694937\pi$
$390$		0			0
$391$	−8.88504			−0.449336
$392$		0			0
$393$	−1.81346	−	3.14101i	−0.0914772	−	0.158443i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−10.5951	−	6.11707i	−0.531752	−	0.307007i	0.209978	−	0.977706i	$-0.432661\pi$
$397$	−10.5951	−	6.11707i	−0.531752	−	0.307007i	−0.741730	+	0.670699i	$0.765994\pi$
$398$		0			0
$399$	−1.89437	+	3.28115i	−0.0948374	+	0.164263i
$400$		0			0
$401$	−15.1495	+	8.74659i	−0.756532	+	0.436784i	−0.828049	−	0.560656i	$-0.810549\pi$
$401$	−15.1495	+	8.74659i	−0.756532	+	0.436784i	0.0715175	+	0.997439i	$0.477216\pi$
$402$		0			0
$403$	8.78507	−	12.6007i	0.437616	−	0.627686i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−9.57794	+	16.5895i	−0.474761	+	0.822310i
$408$		0			0
$409$	31.6025	+	18.2457i	1.56264	+	0.902192i	0.996989	+	0.0775493i	$0.0247095\pi$
$409$	31.6025	+	18.2457i	1.56264	+	0.902192i	0.565654	+	0.824643i	$0.308624\pi$
$410$		0			0
$411$			8.99316i			0.443600i
$412$		0			0
$413$	−5.53041	−	9.57896i	−0.272134	−	0.471350i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	10.6572			0.521886
$418$		0			0
$419$	0.105105	+	0.182048i	0.00513472	+	0.00889360i	0.868581	−	0.495547i	$-0.165032\pi$
$419$	0.105105	+	0.182048i	0.00513472	+	0.00889360i	−0.863447	+	0.504440i	$0.831699\pi$
$420$		0			0
$421$			8.61066i			0.419658i	0.977738	+	0.209829i	$0.0672907\pi$
$421$			8.61066i			0.419658i	−0.977738	+	0.209829i	$0.932709\pi$
$422$		0			0
$423$	9.13060	+	5.27156i	0.443945	+	0.256312i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−1.04790	+	0.605005i	−0.0507114	+	0.0292782i
$428$		0			0
$429$	−9.25282	−	19.7381i	−0.446730	−	0.952964i
$430$		0			0
$431$	15.3283	−	8.84980i	0.738338	−	0.426280i	−0.0831267	−	0.996539i	$-0.526491\pi$
$431$	15.3283	−	8.84980i	0.738338	−	0.426280i	0.821465	+	0.570259i	$0.193157\pi$
$432$		0			0
$433$	4.65382	−	8.06065i	0.223648	−	0.387370i	−0.732265	−	0.681020i	$-0.761537\pi$
$433$	4.65382	−	8.06065i	0.223648	−	0.387370i	0.955913	+	0.293650i	$0.0948700\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		−	17.7103i		−	0.847199i
$438$		0			0
$439$	−6.22475	−	10.7816i	−0.297091	−	0.514577i	0.678378	−	0.734713i	$-0.262683\pi$
$439$	−6.22475	−	10.7816i	−0.297091	−	0.514577i	−0.975469	+	0.220136i	$0.929350\pi$
$440$		0			0
$441$	4.25269			0.202509
$442$		0			0
$443$	−3.86088			−0.183436			−0.0917180	−	0.995785i	$-0.529236\pi$
$443$	−3.86088			−0.183436			−0.0917180	+	0.995785i	$0.529236\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$			21.6116i			1.02219i
$448$		0			0
$449$	9.65851	+	5.57634i	0.455813	+	0.263164i	0.710282	−	0.703917i	$-0.248567\pi$
$449$	9.65851	+	5.57634i	0.455813	+	0.263164i	−0.254469	+	0.967081i	$0.581901\pi$
$450$		0			0
$451$	32.4848	−	56.2654i	1.52965	−	2.64943i
$452$		0			0
$453$	14.9474	−	8.62987i	0.702289	−	0.405467i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.12068	−	0.647022i	0.0524230	−	0.0302664i	−0.473559	−	0.880762i	$-0.657031\pi$
$457$	1.12068	−	0.647022i	0.0524230	−	0.0302664i	0.525982	+	0.850495i	$0.323698\pi$
$458$		0			0
$459$	0.573383	−	0.993129i	0.0267632	−	0.0463553i
$460$		0			0
$461$	13.9344	+	8.04505i	0.648991	+	0.374695i	0.788070	−	0.615586i	$-0.211081\pi$
$461$	13.9344	+	8.04505i	0.648991	+	0.374695i	−0.139078	+	0.990281i	$0.544414\pi$
$462$		0			0
$463$		−	18.9707i		−	0.881645i	−0.897594	−	0.440823i	$-0.854687\pi$
$463$		−	18.9707i		−	0.881645i	0.897594	−	0.440823i	$-0.145313\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−33.7236			−1.56054			−0.780272	−	0.625441i	$-0.784919\pi$
$467$	−33.7236			−1.56054			−0.780272	+	0.625441i	$0.784919\pi$
$468$		0			0
$469$	5.98562			0.276390
$470$		0			0
$471$	10.7224	+	18.5717i	0.494062	+	0.855741i
$472$		0			0
$473$		−	14.9164i		−	0.685858i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	2.19126	−	3.79537i	0.100331	−	0.173778i
$478$		0			0
$479$	−2.68929	+	1.55266i	−0.122877	+	0.0709429i	−0.560179	−	0.828372i	$-0.689267\pi$
$479$	−2.68929	+	1.55266i	−0.122877	+	0.0709429i	0.437302	+	0.899315i	$0.355934\pi$
$480$		0			0
$481$	11.3822	+	0.972544i	0.518982	+	0.0443442i
$482$		0			0
$483$	11.1216	−	6.42108i	0.506052	−	0.292169i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−2.74404	−	1.58427i	−0.124344	−	0.0717902i	0.436538	−	0.899686i	$-0.356205\pi$
$487$	−2.74404	−	1.58427i	−0.124344	−	0.0717902i	−0.560882	+	0.827896i	$0.689538\pi$
$488$		0			0
$489$		−	14.1975i		−	0.642034i
$490$		0			0
$491$	−13.0168	−	22.5458i	−0.587440	−	1.01748i	−0.994566	−	0.104105i	$-0.966802\pi$
$491$	−13.0168	−	22.5458i	−0.587440	−	1.01748i	0.407126	−	0.913372i	$-0.366531\pi$
$492$		0			0
$493$	8.27398			0.372641
$494$		0			0
$495$		0			0
$496$		0			0
$497$	10.2147	+	17.6924i	0.458194	+	0.793615i
$498$		0			0
$499$		−	19.4095i		−	0.868888i	−0.900699	−	0.434444i	$-0.856945\pi$
$499$		−	19.4095i		−	0.868888i	0.900699	−	0.434444i	$-0.143055\pi$
$500$		0			0
$501$	5.51973	+	3.18682i	0.246603	+	0.142376i
$502$		0			0
$503$	−19.0723	+	33.0342i	−0.850391	+	1.47292i	0.0304646	+	0.999536i	$0.490301\pi$
$503$	−19.0723	+	33.0342i	−0.850391	+	1.47292i	−0.880856	+	0.473385i	$0.843032\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−8.31576	+	9.99240i	−0.369316	+	0.443778i
$508$		0			0
$509$	35.6333	−	20.5729i	1.57942	−	0.911878i	0.584479	−	0.811409i	$-0.301299\pi$
$509$	35.6333	−	20.5729i	1.57942	−	0.911878i	0.994940	−	0.100470i	$-0.0320345\pi$
$510$		0			0
$511$	−10.3555	+	17.9363i	−0.458102	+	0.793455i
$512$		0			0
$513$	1.97958	+	1.14291i	0.0874005	+	0.0504607i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−31.8719	−	55.2038i	−1.40173	−	2.42786i
$518$		0			0
$519$	−17.2985			−0.759319
$520$		0			0
$521$	30.4270			1.33303			0.666516	−	0.745490i	$-0.267785\pi$
$521$	30.4270			1.33303			0.666516	+	0.745490i	$0.267785\pi$
$522$		0			0
$523$	−6.60990	−	11.4487i	−0.289031	−	0.500616i	0.684548	−	0.728968i	$-0.260000\pi$
$523$	−6.60990	−	11.4487i	−0.289031	−	0.500616i	−0.973579	+	0.228352i	$0.926666\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−4.23106	−	2.44280i	−0.184308	−	0.106410i
$528$		0			0
$529$	−18.5150	+	32.0690i	−0.805001	+	1.39430i
$530$		0			0
$531$	−5.77915	+	3.33660i	−0.250794	+	0.144796i
$532$		0			0
$533$	−38.6040	−	3.29851i	−1.67213	−	0.142874i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	5.19861	−	9.00425i	0.224337	−	0.388562i
$538$		0			0
$539$	−22.2671	−	12.8559i	−0.959112	−	0.553744i
$540$		0			0
$541$			13.9179i			0.598378i	0.954194	+	0.299189i	$0.0967161\pi$
$541$			13.9179i			0.598378i	−0.954194	+	0.299189i	$0.903284\pi$
$542$		0			0
$543$	−5.03557	−	8.72186i	−0.216097	−	0.374291i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	20.7737			0.888219			0.444109	−	0.895973i	$-0.353520\pi$
$547$	20.7737			0.888219			0.444109	+	0.895973i	$0.353520\pi$
$548$		0			0
$549$	0.365010	+	0.632216i	0.0155782	+	0.0269823i
$550$		0			0
$551$			16.4923i			0.702596i
$552$		0			0
$553$	1.91542	+	1.10587i	0.0814518	+	0.0470262i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−13.6876	+	7.90255i	−0.579963	+	0.334842i	−0.761119	−	0.648613i	$-0.775350\pi$
$557$	−13.6876	+	7.90255i	−0.579963	+	0.334842i	0.181156	+	0.983454i	$0.442016\pi$
$558$		0			0
$559$	−8.05435	+	3.77572i	−0.340663	+	0.159696i
$560$		0			0
$561$	−6.00448	+	3.46669i	−0.253509	+	0.146364i
$562$		0			0
$563$	20.1334	−	34.8721i	0.848521	−	1.46968i	−0.0340062	−	0.999422i	$-0.510827\pi$
$563$	20.1334	−	34.8721i	0.848521	−	1.46968i	0.882528	−	0.470261i	$-0.155840\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$			1.65750i			0.0696085i
$568$		0			0
$569$	7.65461	+	13.2582i	0.320898	+	0.555812i	0.980674	−	0.195651i	$-0.0626819\pi$
$569$	7.65461	+	13.2582i	0.320898	+	0.555812i	−0.659775	+	0.751463i	$0.729349\pi$
$570$		0			0
$571$	−3.13351			−0.131133			−0.0655666	−	0.997848i	$-0.520885\pi$
$571$	−3.13351			−0.131133			−0.0655666	+	0.997848i	$0.520885\pi$
$572$		0			0
$573$	20.7999			0.868927
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	29.1801i		−	1.21478i	−0.794403	−	0.607391i	$-0.792216\pi$
$577$		−	29.1801i		−	1.21478i	0.794403	−	0.607391i	$-0.207784\pi$
$578$		0			0
$579$	23.8195	+	13.7522i	0.989904	+	0.571522i
$580$		0			0
$581$	−5.42406	+	9.39474i	−0.225028	+	0.389760i
$582$		0			0
$583$	−22.9469	+	13.2484i	−0.950363	+	0.548692i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	3.93311	−	2.27078i	0.162337	−	0.0937252i	−0.416631	−	0.909076i	$-0.636789\pi$
$587$	3.93311	−	2.27078i	0.162337	−	0.0937252i	0.578967	+	0.815351i	$0.303456\pi$
$588$		0			0
$589$	4.86917	−	8.43366i	0.200631	−	0.347503i
$590$		0			0
$591$	−18.5448	−	10.7068i	−0.762831	−	0.440421i
$592$		0			0
$593$			3.21321i			0.131951i	0.997821	+	0.0659754i	$0.0210159\pi$
$593$			3.21321i			0.131951i	−0.997821	+	0.0659754i	$0.978984\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	25.3923			1.03924
$598$		0			0
$599$	−4.32402			−0.176675			−0.0883373	−	0.996091i	$-0.528155\pi$
$599$	−4.32402			−0.176675			−0.0883373	+	0.996091i	$0.528155\pi$
$600$		0			0
$601$	1.14660	+	1.98597i	0.0467709	+	0.0810096i	0.888463	−	0.458948i	$-0.151774\pi$
$601$	1.14660	+	1.98597i	0.0467709	+	0.0810096i	−0.841692	+	0.539958i	$0.818440\pi$
$602$		0			0
$603$		−	3.61123i		−	0.147061i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	2.77184	−	4.80097i	0.112506	−	0.194865i	−0.804274	−	0.594258i	$-0.797446\pi$
$607$	2.77184	−	4.80097i	0.112506	−	0.194865i	0.916780	+	0.399393i	$0.130779\pi$
$608$		0			0
$609$	−10.3568	+	5.97948i	−0.419677	+	0.242301i
$610$		0			0
$611$	−21.7406	+	31.1832i	−0.879529	+	1.26154i
$612$		0			0
$613$	6.35569	−	3.66946i	0.256704	−	0.148208i	−0.366126	−	0.930565i	$-0.619316\pi$
$613$	6.35569	−	3.66946i	0.256704	−	0.148208i	0.622830	+	0.782357i	$0.285983\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−29.3650	−	16.9539i	−1.18219	−	0.682537i	−0.225669	−	0.974204i	$-0.572457\pi$
$617$	−29.3650	−	16.9539i	−1.18219	−	0.682537i	−0.956520	+	0.291667i	$0.905790\pi$
$618$		0			0
$619$			44.9279i			1.80580i	0.429847	+	0.902902i	$0.358568\pi$
$619$			44.9279i			1.80580i	−0.429847	+	0.902902i	$0.641432\pi$
$620$		0			0
$621$	−3.87395	−	6.70988i	−0.155456	−	0.269258i
$622$		0			0
$623$	−9.94971			−0.398627
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−6.91006	−	11.9686i	−0.275961	−	0.477979i
$628$		0			0
$629$		−	3.63335i		−	0.144871i
$630$		0			0
$631$	−34.6730	−	20.0185i	−1.38031	−	0.796923i	−0.388115	−	0.921611i	$-0.626874\pi$
$631$	−34.6730	−	20.0185i	−1.38031	−	0.796923i	−0.992196	+	0.124688i	$0.960207\pi$
$632$		0			0
$633$	0.926303	−	1.60440i	0.0368172	−	0.0637693i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−1.30539	+	15.2776i	−0.0517215	+	0.605321i
$638$		0			0
$639$	10.6742	−	6.16273i	0.422263	−	0.243794i
$640$		0			0
$641$	−13.7186	+	23.7614i	−0.541854	+	0.938519i	0.456944	+	0.889496i	$0.348944\pi$
$641$	−13.7186	+	23.7614i	−0.541854	+	0.938519i	−0.998798	+	0.0490230i	$0.984389\pi$
$642$		0			0
$643$	11.6665	+	6.73564i	0.460081	+	0.265628i	0.712078	−	0.702100i	$-0.247754\pi$
$643$	11.6665	+	6.73564i	0.460081	+	0.265628i	−0.251998	+	0.967728i	$0.581087\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	16.9621	+	29.3793i	0.666851	+	1.15502i	0.978780	+	0.204914i	$0.0656914\pi$
$647$	16.9621	+	29.3793i	0.666851	+	1.15502i	−0.311929	+	0.950105i	$0.600975\pi$
$648$		0			0
$649$	40.3463			1.58373
$650$		0			0
$651$	7.06151			0.276762
$652$		0			0
$653$	−1.57766	−	2.73259i	−0.0617386	−	0.106934i	0.833504	−	0.552513i	$-0.186331\pi$
$653$	−1.57766	−	2.73259i	−0.0617386	−	0.106934i	−0.895243	+	0.445579i	$0.852998\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	10.8213	+	6.24767i	0.422179	+	0.243745i
$658$		0			0
$659$	−5.37780	+	9.31463i	−0.209489	+	0.362846i	−0.951554	−	0.307482i	$-0.900514\pi$
$659$	−5.37780	+	9.31463i	−0.209489	+	0.362846i	0.742064	+	0.670329i	$0.233847\pi$
$660$		0			0
$661$	−33.5544	+	19.3727i	−1.30512	+	0.753509i	−0.981277	−	0.192603i	$-0.938307\pi$
$661$	−33.5544	+	19.3727i	−1.30512	+	0.753509i	−0.323839	+	0.946112i	$0.604974\pi$
$662$		0			0
$663$	3.39177	+	2.36470i	0.131726	+	0.0918375i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	27.9508	−	48.4122i	1.08226	−	1.87453i
$668$		0			0
$669$	9.09160	+	5.24904i	0.351502	+	0.202940i
$670$		0			0
$671$		−	4.41372i		−	0.170390i
$672$		0			0
$673$	−9.90782	−	17.1608i	−0.381918	−	0.661502i	0.609418	−	0.792849i	$-0.291403\pi$
$673$	−9.90782	−	17.1608i	−0.381918	−	0.661502i	−0.991336	+	0.131347i	$0.958070\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	19.5883			0.752841			0.376421	−	0.926449i	$-0.377155\pi$
$677$	19.5883			0.752841			0.376421	+	0.926449i	$0.377155\pi$
$678$		0			0
$679$	4.95010	+	8.57382i	0.189967	+	0.329033i
$680$		0			0
$681$			9.77071i			0.374415i
$682$		0			0
$683$	−22.5656	−	13.0282i	−0.863447	−	0.498511i	0.00171806	−	0.999999i	$-0.499453\pi$
$683$	−22.5656	−	13.0282i	−0.863447	−	0.498511i	−0.865165	+	0.501487i	$0.832786\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−14.6662	+	8.46753i	−0.559550	+	0.323057i
$688$		0			0
$689$	12.9621	+	9.03702i	0.493817	+	0.344283i
$690$		0			0
$691$	−6.99020	+	4.03579i	−0.265920	+	0.153529i	−0.627032	−	0.778994i	$-0.715730\pi$
$691$	−6.99020	+	4.03579i	−0.265920	+	0.153529i	0.361112	+	0.932522i	$0.382397\pi$
$692$		0			0
$693$	5.01065	−	8.67869i	0.190339	−	0.329676i
$694$		0			0
$695$		0			0
$696$		0			0
$697$			12.3230i			0.466766i
$698$		0			0
$699$	−9.89691	−	17.1419i	−0.374335	−	0.648368i
$700$		0			0
$701$	−15.9799			−0.603551			−0.301775	−	0.953379i	$-0.597579\pi$
$701$	−15.9799			−0.603551			−0.301775	+	0.953379i	$0.597579\pi$
$702$		0			0
$703$	7.24226			0.273147
$704$		0			0
$705$		0			0
$706$		0			0
$707$			0.338183i			0.0127187i
$708$		0			0
$709$	−21.5086	−	12.4180i	−0.807772	−	0.466367i	0.0384099	−	0.999262i	$-0.487771\pi$
$709$	−21.5086	−	12.4180i	−0.807772	−	0.466367i	−0.846181	+	0.532895i	$0.821104\pi$
$710$		0			0
$711$	0.667188	−	1.15560i	0.0250215	−	0.0433385i
$712$		0			0
$713$	−28.5863	+	16.5043i	−1.07057	+	0.618092i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−0.873364	+	0.504237i	−0.0326164	+	0.0188311i
$718$		0			0
$719$	−10.8491	+	18.7912i	−0.404603	+	0.700794i	−0.994275	−	0.106849i	$-0.965924\pi$
$719$	−10.8491	+	18.7912i	−0.404603	+	0.700794i	0.589672	+	0.807643i	$0.299257\pi$
$720$		0			0
$721$	4.67877	+	2.70129i	0.174246	+	0.100601i
$722$		0			0
$723$			8.86238i			0.329596i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−34.2453			−1.27009			−0.635044	−	0.772476i	$-0.719018\pi$
$727$	−34.2453			−1.27009			−0.635044	+	0.772476i	$0.719018\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	1.41462	+	2.45019i	0.0523216	+	0.0906237i
$732$		0			0
$733$			16.9049i			0.624397i	0.950017	+	0.312199i	$0.101065\pi$
$733$			16.9049i			0.624397i	−0.950017	+	0.312199i	$0.898935\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−10.9168	+	18.9084i	−0.402125	+	0.696501i
$738$		0			0
$739$	−17.0843	+	9.86363i	−0.628456	+	0.362839i	−0.780154	−	0.625588i	$-0.784859\pi$
$739$	−17.0843	+	9.86363i	−0.628456	+	0.362839i	0.151698	+	0.988427i	$0.451526\pi$
$740$		0			0
$741$	−4.71350	+	6.76073i	−0.173155	+	0.248362i
$742$		0			0
$743$	−22.0040	+	12.7040i	−0.807247	+	0.466064i	−0.845999	−	0.533185i	$-0.820995\pi$
$743$	−22.0040	+	12.7040i	−0.807247	+	0.466064i	0.0387519	+	0.999249i	$0.487662\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	5.66801	+	3.27243i	0.207382	+	0.119732i
$748$		0			0
$749$			5.81450i			0.212457i
$750$		0			0
$751$	22.0169	+	38.1343i	0.803407	+	1.39154i	0.917361	+	0.398056i	$0.130315\pi$
$751$	22.0169	+	38.1343i	0.803407	+	1.39154i	−0.113954	+	0.993486i	$0.536352\pi$
$752$		0			0
$753$	2.80694			0.102291
$754$		0			0
$755$		0			0
$756$		0			0
$757$	10.2160	+	17.6946i	0.371306	+	0.643121i	0.989767	−	0.142695i	$-0.0455767\pi$
$757$	10.2160	+	17.6946i	0.371306	+	0.643121i	−0.618461	+	0.785816i	$0.712243\pi$
$758$		0			0
$759$			46.8440i			1.70033i
$760$		0			0
$761$	−11.4379	−	6.60370i	−0.414625	−	0.239384i	0.278150	−	0.960538i	$-0.410279\pi$
$761$	−11.4379	−	6.60370i	−0.414625	−	0.239384i	−0.692775	+	0.721154i	$0.743612\pi$
$762$		0			0
$763$	−9.54418	+	16.5310i	−0.345522	+	0.598462i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−10.2126	−	21.7856i	−0.368757	−	0.786632i
$768$		0			0
$769$	8.23441	−	4.75414i	0.296940	−	0.171439i	−0.344127	−	0.938923i	$-0.611825\pi$
$769$	8.23441	−	4.75414i	0.296940	−	0.171439i	0.641068	+	0.767484i	$0.278492\pi$
$770$		0			0
$771$	0.197590	−	0.342236i	0.00711604	−	0.0123253i
$772$		0			0
$773$	5.39516	+	3.11490i	0.194050	+	0.112035i	0.593877	−	0.804556i	$-0.297596\pi$
$773$	5.39516	+	3.11490i	0.194050	+	0.112035i	−0.399827	+	0.916591i	$0.630930\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	2.62577	+	4.54796i	0.0941989	+	0.163157i
$778$		0			0
$779$	−24.5631			−0.880063
$780$		0			0
$781$	−74.5200			−2.66654
$782$		0			0
$783$	3.60753	+	6.24842i	0.128922	+	0.223300i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	39.4276	+	22.7635i	1.40544	+	0.811433i	0.994944	−	0.100428i	$-0.0320213\pi$
$787$	39.4276	+	22.7635i	1.40544	+	0.811433i	0.410499	+	0.911861i	$0.365355\pi$
$788$		0			0
$789$	12.2704	−	21.2529i	0.436837	−	0.756623i
$790$		0			0
$791$	0.276884	−	0.159859i	0.00984485	−	0.00568393i
$792$		0			0
$793$	−2.38325	+	1.11722i	−0.0846318	+	0.0396737i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	11.5541	−	20.0123i	0.409267	−	0.708871i	−0.585541	−	0.810643i	$-0.699118\pi$
$797$	11.5541	−	20.0123i	0.409267	−	0.708871i	0.994808	+	0.101772i	$0.0324511\pi$
$798$		0			0
$799$	10.4707	+	6.04524i	0.370426	+	0.213865i
$800$		0			0
$801$			6.00284i			0.212100i
$802$		0			0
$803$	−37.7736	−	65.4257i	−1.33300	−	2.30882i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−12.1546			−0.427862
$808$		0			0
$809$	4.03014	+	6.98041i	0.141692	+	0.245418i	0.928134	−	0.372246i	$-0.121412\pi$
$809$	4.03014	+	6.98041i	0.141692	+	0.245418i	−0.786442	+	0.617664i	$0.788079\pi$
$810$		0			0
$811$			48.6471i			1.70823i	0.520084	+	0.854115i	$0.325901\pi$
$811$			48.6471i			1.70823i	−0.520084	+	0.854115i	$0.674099\pi$
$812$		0			0
$813$	−3.19227	−	1.84306i	−0.111958	−	0.0646389i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−4.88391	+	2.81973i	−0.170866	+	0.0986497i
$818$		0			0
$819$	−5.95451	−	0.508781i	−0.208067	−	0.0177783i
$820$		0			0
$821$	−41.7461	+	24.1021i	−1.45695	+	0.841169i	−0.998860	−	0.0477380i	$-0.984799\pi$
$821$	−41.7461	+	24.1021i	−1.45695	+	0.841169i	−0.458088	+	0.888907i	$0.651465\pi$
$822$		0			0
$823$	24.3042	−	42.0960i	0.847190	−	1.46738i	−0.0365160	−	0.999333i	$-0.511626\pi$
$823$	24.3042	−	42.0960i	0.847190	−	1.46738i	0.883706	−	0.468043i	$-0.155041\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	20.1081i		−	0.699229i	−0.936894	−	0.349614i	$-0.886313\pi$
$827$		−	20.1081i		−	0.699229i	0.936894	−	0.349614i	$-0.113687\pi$
$828$		0			0
$829$	10.5726	+	18.3123i	0.367203	+	0.636014i	0.989127	−	0.147063i	$-0.0469821\pi$
$829$	10.5726	+	18.3123i	0.367203	+	0.636014i	−0.621924	+	0.783077i	$0.713649\pi$
$830$		0			0
$831$	−0.805800			−0.0279529
$832$		0			0
$833$	4.87684			0.168972
$834$		0			0
$835$		0			0
$836$		0			0
$837$		−	4.26033i		−	0.147259i
$838$		0			0
$839$	12.3127	+	7.10874i	0.425082	+	0.245421i	0.697249	−	0.716829i	$-0.254407\pi$
$839$	12.3127	+	7.10874i	0.425082	+	0.245421i	−0.272167	+	0.962250i	$0.587740\pi$
$840$		0			0
$841$	−11.5285	+	19.9679i	−0.397534	+	0.688549i
$842$		0			0
$843$	0.311980	−	0.180122i	0.0107452	−	0.00620372i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−36.6817	+	21.1782i	−1.26040	+	0.727692i
$848$		0			0
$849$	−10.1636	+	17.6039i	−0.348813	+	0.604163i
$850$		0			0
$851$	−21.2592	−	12.2740i	−0.728757	−	0.420748i
$852$		0			0
$853$			26.1008i			0.893676i	0.894615	+	0.446838i	$0.147450\pi$
$853$			26.1008i			0.893676i	−0.894615	+	0.446838i	$0.852550\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	27.1782			0.928390			0.464195	−	0.885733i	$-0.346344\pi$
$857$	27.1782			0.928390			0.464195	+	0.885733i	$0.346344\pi$
$858$		0			0
$859$	−33.8502			−1.15495			−0.577477	−	0.816407i	$-0.695963\pi$
$859$	−33.8502			−1.15495			−0.577477	+	0.816407i	$0.695963\pi$
$860$		0			0
$861$	−8.90563	−	15.4250i	−0.303503	−	0.525683i
$862$		0			0
$863$			49.9350i			1.69981i	0.526938	+	0.849904i	$0.323340\pi$
$863$			49.9350i			1.69981i	−0.526938	+	0.849904i	$0.676660\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−7.84246	+	13.5835i	−0.266344	+	0.461321i
$868$		0			0
$869$	−6.98681	+	4.03384i	−0.237011	+	0.136839i
$870$		0			0
$871$	12.9732	+	1.10849i	0.439580	+	0.0375598i
$872$		0			0
$873$	5.17274	−	2.98648i	0.175071	−	0.101077i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−11.9224	−	6.88339i	−0.402590	−	0.232436i	0.285011	−	0.958524i	$-0.408003\pi$
$877$	−11.9224	−	6.88339i	−0.402590	−	0.232436i	−0.687601	+	0.726089i	$0.741336\pi$
$878$		0			0
$879$		−	16.9751i		−	0.572555i
$880$		0			0
$881$	−6.98061	−	12.0908i	−0.235183	−	0.407348i	0.724143	−	0.689650i	$-0.242235\pi$
$881$	−6.98061	−	12.0908i	−0.235183	−	0.407348i	−0.959326	+	0.282302i	$0.908902\pi$
$882$		0			0
$883$	5.95089			0.200263			0.100132	−	0.994974i	$-0.468074\pi$
$883$	5.95089			0.200263			0.100132	+	0.994974i	$0.468074\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−9.86299	−	17.0832i	−0.331167	−	0.573598i	0.651574	−	0.758585i	$-0.274109\pi$
$887$	−9.86299	−	17.0832i	−0.331167	−	0.573598i	−0.982741	+	0.184987i	$0.940776\pi$
$888$		0			0
$889$		−	31.9357i		−	1.07109i
$890$		0			0
$891$	−5.23601	−	3.02301i	−0.175413	−	0.101275i
$892$		0			0
$893$	−12.0498	+	20.8709i	−0.403232	+	0.698418i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	25.2941	−	11.8574i	0.844546	−	0.395906i
$898$		0			0
$899$	26.6203	−	15.3693i	0.887838	−	0.512593i
$900$		0			0
$901$	2.51286	−	4.35240i	0.0837155	−	0.145000i
$902$		0			0
$903$	−3.54144	−	2.04465i	−0.117852	−	0.0680417i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	8.07493	+	13.9862i	0.268124	+	0.464404i	0.968377	−	0.249490i	$-0.0802631\pi$
$907$	8.07493	+	13.9862i	0.268124	+	0.464404i	−0.700254	+	0.713894i	$0.746930\pi$
$908$		0			0
$909$	0.204032			0.00676732
$910$		0			0
$911$	35.1748			1.16539			0.582696	−	0.812690i	$-0.301998\pi$
$911$	35.1748			1.16539			0.582696	+	0.812690i	$0.301998\pi$
$912$		0			0
$913$	−19.7852	−	34.2689i	−0.654794	−	1.13414i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	5.20623	+	3.00582i	0.171925	+	0.0992610i
$918$		0			0
$919$	−7.24395	+	12.5469i	−0.238956	+	0.413884i	−0.960415	−	0.278573i	$-0.910139\pi$
$919$	−7.24395	+	12.5469i	−0.238956	+	0.413884i	0.721459	+	0.692457i	$0.243472\pi$
$920$		0			0
$921$	14.8758	−	8.58852i	0.490173	−	0.283001i
$922$		0			0
$923$	18.8629	+	40.2382i	0.620879	+	1.32446i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	1.62973	−	2.82278i	0.0535275	−	0.0927123i
$928$		0			0
$929$	32.4260	+	18.7212i	1.06386	+	0.614222i	0.926499	−	0.376298i	$-0.122803\pi$
$929$	32.4260	+	18.7212i	1.06386	+	0.614222i	0.137365	+	0.990520i	$0.456137\pi$
$930$		0			0
$931$			9.72088i			0.318589i
$932$		0			0
$933$	−9.20868	−	15.9499i	−0.301479	−	0.522176i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	56.2285			1.83690			0.918452	−	0.395533i	$-0.129440\pi$
$937$	56.2285			1.83690			0.918452	+	0.395533i	$0.129440\pi$
$938$		0			0
$939$	−4.05286	−	7.01975i	−0.132260	−	0.229081i
$940$		0			0
$941$			37.7863i			1.23180i	0.787826	+	0.615898i	$0.211207\pi$
$941$			37.7863i			1.23180i	−0.787826	+	0.615898i	$0.788793\pi$
$942$		0			0
$943$	72.1034	+	41.6289i	2.34801	+	1.35562i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−8.68360	+	5.01348i	−0.282179	+	0.162916i	−0.634409	−	0.772997i	$-0.718757\pi$
$947$	−8.68360	+	5.01348i	−0.282179	+	0.162916i	0.352230	+	0.935913i	$0.385423\pi$
$948$		0			0
$949$	−25.7662	+	36.9573i	−0.836406	+	1.19968i
$950$		0			0
$951$	−3.51861	+	2.03147i	−0.114099	+	0.0658749i
$952$		0			0
$953$	−0.289497	+	0.501424i	−0.00937773	+	0.0162427i	−0.870676	−	0.491857i	$-0.836318\pi$
$953$	−0.289497	+	0.501424i	−0.00937773	+	0.0162427i	0.861298	+	0.508099i	$0.169652\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		−	43.6224i		−	1.41011i
$958$		0			0
$959$	−7.45309	−	12.9091i	−0.240673	−	0.416857i
$960$		0			0
$961$	12.8496			0.414502
$962$		0			0
$963$	3.50799			0.113043
$964$		0			0
$965$		0			0
$966$		0			0
$967$			17.0784i			0.549205i	0.961558	+	0.274602i	$0.0885462\pi$
$967$			17.0784i			0.549205i	−0.961558	+	0.274602i	$0.911454\pi$
$968$		0			0
$969$	2.27011	+	1.31065i	0.0729265	+	0.0421042i
$970$		0			0
$971$	−21.5819	+	37.3810i	−0.692597	+	1.19961i	0.278387	+	0.960469i	$0.410200\pi$
$971$	−21.5819	+	37.3810i	−0.692597	+	1.19961i	−0.970984	+	0.239144i	$0.923133\pi$
$972$		0			0
$973$	−15.2978	+	8.83217i	−0.490424	+	0.283146i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−36.9032	+	21.3061i	−1.18064	+	0.681641i	−0.956162	−	0.292838i	$-0.905400\pi$
$977$	−36.9032	+	21.3061i	−1.18064	+	0.681641i	−0.224476	+	0.974480i	$0.572067\pi$
$978$		0			0
$979$	18.1466	−	31.4309i	0.579969	−	1.00454i
$980$		0			0
$981$	9.97344	+	5.75817i	0.318428	+	0.183844i
$982$		0			0
$983$		−	45.6346i		−	1.45552i	−0.685834	−	0.727758i	$-0.740562\pi$
$983$		−	45.6346i		−	1.45552i	0.685834	−	0.727758i	$-0.259438\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−17.4752			−0.556243
$988$		0			0
$989$	19.1152			0.607829
$990$		0			0
$991$	3.76168	+	6.51542i	0.119494	+	0.206969i	0.919567	−	0.392933i	$-0.128540\pi$
$991$	3.76168	+	6.51542i	0.119494	+	0.206969i	−0.800073	+	0.599902i	$0.795206\pi$
$992$		0			0
$993$			20.0885i			0.637489i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−17.4852	+	30.2852i	−0.553760	+	0.959141i	0.444239	+	0.895909i	$0.353474\pi$
$997$	−17.4852	+	30.2852i	−0.553760	+	0.959141i	−0.997999	+	0.0632324i	$0.979859\pi$
$998$		0			0
$999$	2.74387	−	1.58417i	0.0868121	−	0.0501210i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3900.2.cd.o.2701.2		12
5.2	odd	4		780.2.bv.a.49.9	yes	24
5.3	odd	4		780.2.bv.a.49.4	✓	24
5.4	even	2		3900.2.cd.n.2701.5		12
13.4	even	6	inner	3900.2.cd.o.901.2		12
15.2	even	4		2340.2.cr.b.829.8		24
15.8	even	4		2340.2.cr.b.829.5		24
65.4	even	6		3900.2.cd.n.901.5		12
65.17	odd	12		780.2.bv.a.589.4	yes	24
65.43	odd	12		780.2.bv.a.589.9	yes	24
195.17	even	12		2340.2.cr.b.1369.5		24
195.173	even	12		2340.2.cr.b.1369.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
780.2.bv.a.49.4	✓	24	5.3	odd	4
780.2.bv.a.49.9	yes	24	5.2	odd	4
780.2.bv.a.589.4	yes	24	65.17	odd	12
780.2.bv.a.589.9	yes	24	65.43	odd	12
2340.2.cr.b.829.5		24	15.8	even	4
2340.2.cr.b.829.8		24	15.2	even	4
2340.2.cr.b.1369.5		24	195.17	even	12
2340.2.cr.b.1369.8		24	195.173	even	12
3900.2.cd.n.901.5		12	65.4	even	6
3900.2.cd.n.2701.5		12	5.4	even	2
3900.2.cd.o.901.2		12	13.4	even	6	inner
3900.2.cd.o.2701.2		12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3900.cd (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{3} +(-1.43544 - 0.828751i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{3} +(-1.43544 - 0.828751i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(5.23601 - 3.02301i) q^{11} +(-2.95768 - 2.06206i) q^{13} +(-0.573383 + 0.993129i) q^{17} +(-1.97958 - 1.14291i) q^{19} -1.65750i q^{21} +(3.87395 + 6.70988i) q^{23} -1.00000 q^{27} +(-3.60753 - 6.24842i) q^{29} +4.26033i q^{31} +(5.23601 + 3.02301i) q^{33} +(-2.74387 + 1.58417i) q^{37} +(0.306957 - 3.59246i) q^{39} +(9.30618 - 5.37292i) q^{41} +(1.23357 - 2.13661i) q^{43} -10.5431i q^{47} +(-2.12634 - 3.68294i) q^{49} -1.14677 q^{51} -4.38252 q^{53} -2.28582i q^{57} +(5.77915 + 3.33660i) q^{59} +(0.365010 - 0.632216i) q^{61} +(1.43544 - 0.828751i) q^{63} +(-3.12741 + 1.80561i) q^{67} +(-3.87395 + 6.70988i) q^{69} +(-10.6742 - 6.16273i) q^{71} -12.4953i q^{73} -10.0213 q^{77} -1.33438 q^{79} +(-0.500000 - 0.866025i) q^{81} -6.54486i q^{83} +(3.60753 - 6.24842i) q^{87} +(5.19861 - 3.00142i) q^{89} +(2.53664 + 5.41115i) q^{91} +(-3.68956 + 2.13017i) q^{93} +(-5.17274 - 2.98648i) q^{97} +6.04602i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} + 6 q^{7} - 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^3 + 6 * q^7 - 6 * q^9	\( 12 q + 6 q^{3} + 6 q^{7} - 6 q^{9} + 6 q^{11} - 8 q^{13} + 2 q^{17} - 12 q^{19} + 4 q^{23} - 12 q^{27} - 2 q^{29} + 6 q^{33} - 6 q^{37} - 4 q^{39} + 36 q^{41} + 16 q^{43} + 4 q^{49} + 4 q^{51} - 18 q^{59} + 22 q^{61} - 6 q^{63} + 6 q^{67} - 4 q^{69} + 6 q^{71} - 24 q^{77} - 4 q^{79} - 6 q^{81} + 2 q^{87} + 2 q^{91} - 6 q^{93} + 48 q^{97}+O(q^{100}) \) 12 * q + 6 * q^3 + 6 * q^7 - 6 * q^9 + 6 * q^11 - 8 * q^13 + 2 * q^17 - 12 * q^19 + 4 * q^23 - 12 * q^27 - 2 * q^29 + 6 * q^33 - 6 * q^37 - 4 * q^39 + 36 * q^41 + 16 * q^43 + 4 * q^49 + 4 * q^51 - 18 * q^59 + 22 * q^61 - 6 * q^63 + 6 * q^67 - 4 * q^69 + 6 * q^71 - 24 * q^77 - 4 * q^79 - 6 * q^81 + 2 * q^87 + 2 * q^91 - 6 * q^93 + 48 * q^97

Introduction

L-functions

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