LMFDB - Embedded newform 1900.2.i.e.501.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1900,2,Mod(201,1900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1900, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("1900.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1900 = 2^{2} \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1900.i (of order $3$, 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:	$15.1715763840$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
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} - 3 x^{11} + 15 x^{10} - 16 x^{9} + 79 x^{8} - 65 x^{7} + 298 x^{6} + 13 x^{5} + 233 x^{4} + \cdots + 9 $ x^12 - 3x^11 + 15x^10 - 16x^9 + 79x^8 - 65x^7 + 298x^6 + 13x^5 + 233x^4 + 14x^3 + 145x^2 + 33*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			501.3
Root			$-0.126563 - 0.219213i$ of defining polynomial
Character	$\chi$	$=$	1900.501
Dual form			1900.2.i.e.201.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.626563 - 1.08524i) q^{3} +2.18534 q^{7} +(0.714838 - 1.23814i) q^{9} +O(q^{10})$	$q+(-0.626563 - 1.08524i) q^{3} +2.18534 q^{7} +(0.714838 - 1.23814i) q^{9} +2.12964 q^{11} +(2.58011 - 4.46889i) q^{13} +(1.31355 + 2.27514i) q^{17} +(2.80353 + 3.33770i) q^{19} +(-1.36925 - 2.37161i) q^{21} +(1.27261 - 2.20422i) q^{23} -5.55094 q^{27} +(-3.08011 + 5.33491i) q^{29} -1.05063 q^{31} +(-1.33435 - 2.31116i) q^{33} +2.25927 q^{37} -6.46641 q^{39} +(5.02728 + 8.70750i) q^{41} +(0.840080 + 1.45506i) q^{43} +(3.24455 - 5.61972i) q^{47} -2.22430 q^{49} +(1.64604 - 2.85103i) q^{51} +(3.63184 - 6.29053i) q^{53} +(1.86561 - 5.13378i) q^{57} +(3.53663 + 6.12563i) q^{59} +(5.41986 - 9.38748i) q^{61} +(1.56216 - 2.70574i) q^{63} +(-1.41877 + 2.45739i) q^{67} -3.18947 q^{69} +(-3.11236 - 5.39076i) q^{71} +(-7.78260 - 13.4799i) q^{73} +4.65397 q^{77} +(2.80671 + 4.86136i) q^{79} +(1.33350 + 2.30969i) q^{81} +7.55136 q^{83} +7.71954 q^{87} +(-7.73341 + 13.3947i) q^{89} +(5.63842 - 9.76603i) q^{91} +(0.658285 + 1.14018i) q^{93} +(-6.63073 - 11.4848i) q^{97} +(1.52234 - 2.63678i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 - 3 * q^9	$ 12 q - 3 q^{3} - 3 q^{9} + 2 q^{11} - 7 q^{13} + q^{17} + q^{21} + 2 q^{23} + 24 q^{27} + q^{29} + 2 q^{31} - 10 q^{33} - 20 q^{37} + 36 q^{39} - 7 q^{41} - 19 q^{43} + 14 q^{47} + 8 q^{49} + 11 q^{51} - 6 q^{53} + 28 q^{57} - 5 q^{61} + 11 q^{63} - 14 q^{67} - 14 q^{69} + 8 q^{71} + 9 q^{73} - 2 q^{77} + q^{79} + 2 q^{81} + 26 q^{83} - 30 q^{87} - 8 q^{89} + 3 q^{91} - 9 q^{93} + 11 q^{97} - 18 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 - 3 * q^9 + 2 * q^11 - 7 * q^13 + q^17 + q^21 + 2 * q^23 + 24 * q^27 + q^29 + 2 * q^31 - 10 * q^33 - 20 * q^37 + 36 * q^39 - 7 * q^41 - 19 * q^43 + 14 * q^47 + 8 * q^49 + 11 * q^51 - 6 * q^53 + 28 * q^57 - 5 * q^61 + 11 * q^63 - 14 * q^67 - 14 * q^69 + 8 * q^71 + 9 * q^73 - 2 * q^77 + q^79 + 2 * q^81 + 26 * q^83 - 30 * q^87 - 8 * q^89 + 3 * q^91 - 9 * q^93 + 11 * q^97 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times$.

$n$	$77$	$401$	$951$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

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
$3$	−0.626563	−	1.08524i	−0.361746	−	0.626563i	0.626502	−	0.779420i	$-0.284486\pi$
$3$	−0.626563	−	1.08524i	−0.361746	−	0.626563i	−0.988248	+	0.152857i	$0.951153\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.18534			0.825980			0.412990	−	0.910736i	$-0.364484\pi$
$7$	2.18534			0.825980			0.412990	+	0.910736i	$0.364484\pi$
$8$		0			0
$9$	0.714838	−	1.23814i	0.238279	−	0.412712i
$10$		0			0
$11$	2.12964			0.642109			0.321055	−	0.947061i	$-0.395963\pi$
$11$	2.12964			0.642109			0.321055	+	0.947061i	$0.395963\pi$
$12$		0			0
$13$	2.58011	−	4.46889i	0.715595	−	1.23945i	−0.247135	−	0.968981i	$-0.579489\pi$
$13$	2.58011	−	4.46889i	0.715595	−	1.23945i	0.962730	−	0.270465i	$-0.0871775\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.31355	+	2.27514i	0.318583	+	0.551801i	0.980193	−	0.198047i	$-0.0634598\pi$
$17$	1.31355	+	2.27514i	0.318583	+	0.551801i	−0.661610	+	0.749848i	$0.730126\pi$
$18$		0			0
$19$	2.80353	+	3.33770i	0.643174	+	0.765720i
$19$	2.80353	+	3.33770i	0.643174	+	0.765720i
$20$		0			0
$21$	−1.36925	−	2.37161i	−0.298795	−	0.517528i
$22$		0			0
$23$	1.27261	−	2.20422i	0.265357	−	0.459611i	−0.702300	−	0.711881i	$-0.747844\pi$
$23$	1.27261	−	2.20422i	0.265357	−	0.459611i	0.967657	+	0.252269i	$0.0811769\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−5.55094			−1.06828
$28$		0			0
$29$	−3.08011	+	5.33491i	−0.571963	+	0.990668i	0.424402	+	0.905474i	$0.360484\pi$
$29$	−3.08011	+	5.33491i	−0.571963	+	0.990668i	−0.996364	+	0.0851943i	$0.972849\pi$
$30$		0			0
$31$	−1.05063			−0.188699			−0.0943493	−	0.995539i	$-0.530077\pi$
$31$	−1.05063			−0.188699			−0.0943493	+	0.995539i	$0.530077\pi$
$32$		0			0
$33$	−1.33435	−	2.31116i	−0.232281	−	0.402322i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	2.25927			0.371422			0.185711	−	0.982604i	$-0.440541\pi$
$37$	2.25927			0.371422			0.185711	+	0.982604i	$0.440541\pi$
$38$		0			0
$39$	−6.46641			−1.03545
$40$		0			0
$41$	5.02728	+	8.70750i	0.785129	+	1.35988i	0.928922	+	0.370275i	$0.120736\pi$
$41$	5.02728	+	8.70750i	0.785129	+	1.35988i	−0.143794	+	0.989608i	$0.545930\pi$
$42$		0			0
$43$	0.840080	+	1.45506i	0.128111	+	0.221895i	0.922945	−	0.384933i	$-0.125775\pi$
$43$	0.840080	+	1.45506i	0.128111	+	0.221895i	−0.794834	+	0.606827i	$0.792442\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.24455	−	5.61972i	0.473266	−	0.819720i	−0.526266	−	0.850320i	$-0.676408\pi$
$47$	3.24455	−	5.61972i	0.473266	−	0.819720i	0.999532	+	0.0305997i	$0.00974171\pi$
$48$		0			0
$49$	−2.22430			−0.317757
$50$		0			0
$51$	1.64604	−	2.85103i	0.230492	−	0.399224i
$52$		0			0
$53$	3.63184	−	6.29053i	0.498871	−	0.864071i	−0.501128	−	0.865373i	$-0.667081\pi$
$53$	3.63184	−	6.29053i	0.498871	−	0.864071i	0.999999	+	0.00130277i	$0.000414685\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	1.86561	−	5.13378i	0.247106	−	0.679985i
$58$		0			0
$59$	3.53663	+	6.12563i	0.460430	+	0.797489i	0.998982	−	0.0451035i	$-0.0143618\pi$
$59$	3.53663	+	6.12563i	0.460430	+	0.797489i	−0.538552	+	0.842592i	$0.681028\pi$
$60$		0			0
$61$	5.41986	−	9.38748i	0.693943	−	1.20194i	−0.276593	−	0.960987i	$-0.589205\pi$
$61$	5.41986	−	9.38748i	0.693943	−	1.20194i	0.970536	−	0.240957i	$-0.0774612\pi$
$62$		0			0
$63$	1.56216	−	2.70574i	0.196814	−	0.340892i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−1.41877	+	2.45739i	−0.173331	+	0.300218i	−0.939582	−	0.342323i	$-0.888786\pi$
$67$	−1.41877	+	2.45739i	−0.173331	+	0.300218i	0.766251	+	0.642541i	$0.222120\pi$
$68$		0			0
$69$	−3.18947			−0.383967
$70$		0			0
$71$	−3.11236	−	5.39076i	−0.369369	−	0.639766i	0.620098	−	0.784524i	$-0.287093\pi$
$71$	−3.11236	−	5.39076i	−0.369369	−	0.639766i	−0.989467	+	0.144759i	$0.953759\pi$
$72$		0			0
$73$	−7.78260	−	13.4799i	−0.910885	−	1.57770i	−0.812817	−	0.582519i	$-0.802067\pi$
$73$	−7.78260	−	13.4799i	−0.910885	−	1.57770i	−0.0980678	−	0.995180i	$-0.531266\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.65397			0.530370
$78$		0			0
$79$	2.80671	+	4.86136i	0.315779	+	0.546946i	0.979603	−	0.200943i	$-0.0644007\pi$
$79$	2.80671	+	4.86136i	0.315779	+	0.546946i	−0.663823	+	0.747889i	$0.731067\pi$
$80$		0			0
$81$	1.33350	+	2.30969i	0.148167	+	0.256632i
$82$		0			0
$83$	7.55136			0.828869			0.414435	−	0.910079i	$-0.363979\pi$
$83$	7.55136			0.828869			0.414435	+	0.910079i	$0.363979\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	7.71954			0.827621
$88$		0			0
$89$	−7.73341	+	13.3947i	−0.819740	+	1.41983i	0.0861333	+	0.996284i	$0.472549\pi$
$89$	−7.73341	+	13.3947i	−0.819740	+	1.41983i	−0.905874	+	0.423548i	$0.860784\pi$
$90$		0			0
$91$	5.63842	−	9.76603i	0.591067	−	1.02376i
$92$		0			0
$93$	0.658285	+	1.14018i	0.0682610	+	0.118232i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−6.63073	−	11.4848i	−0.673248	−	1.16610i	−0.976978	−	0.213342i	$-0.931565\pi$
$97$	−6.63073	−	11.4848i	−0.673248	−	1.16610i	0.303729	−	0.952758i	$-0.401768\pi$
$98$		0			0
$99$	1.52234	−	2.63678i	0.153001	−	0.265006i
$100$		0			0
$101$	2.08748	−	3.61562i	0.207712	−	0.359767i	−0.743282	−	0.668979i	$-0.766732\pi$
$101$	2.08748	−	3.61562i	0.207712	−	0.359767i	0.950993	+	0.309211i	$0.100065\pi$
$102$		0			0
$103$	15.8667			1.56340			0.781699	−	0.623656i	$-0.214354\pi$
$103$	15.8667			1.56340			0.781699	+	0.623656i	$0.214354\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.02114			0.388739			0.194369	−	0.980928i	$-0.437734\pi$
$107$	4.02114			0.388739			0.194369	+	0.980928i	$0.437734\pi$
$108$		0			0
$109$	−2.21086	−	3.82932i	−0.211762	−	0.366783i	0.740504	−	0.672052i	$-0.234587\pi$
$109$	−2.21086	−	3.82932i	−0.211762	−	0.366783i	−0.952266	+	0.305269i	$0.901254\pi$
$110$		0			0
$111$	−1.41558	−	2.45185i	−0.134361	−	0.232719i
$112$		0			0
$113$	−6.04226			−0.568408			−0.284204	−	0.958764i	$-0.591729\pi$
$113$	−6.04226			−0.568408			−0.284204	+	0.958764i	$0.591729\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−3.68873	−	6.38906i	−0.341023	−	0.590669i
$118$		0			0
$119$	2.87055	+	4.97194i	0.263143	+	0.455777i
$120$		0			0
$121$	−6.46465			−0.587695
$122$		0			0
$123$	6.29981	−	10.9116i	0.568035	−	0.983865i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−3.88488	+	6.72881i	−0.344727	+	0.597085i	−0.985304	−	0.170809i	$-0.945362\pi$
$127$	−3.88488	+	6.72881i	−0.344727	+	0.597085i	0.640577	+	0.767894i	$0.278695\pi$
$128$		0			0
$129$	1.05273	−	1.82338i	0.0926874	−	0.160539i
$130$		0			0
$131$	−8.18596	−	14.1785i	−0.715211	−	1.23878i	−0.962878	−	0.269937i	$-0.912997\pi$
$131$	−8.18596	−	14.1785i	−0.715211	−	1.23878i	0.247667	−	0.968845i	$-0.420336\pi$
$132$		0			0
$133$	6.12666	+	7.29399i	0.531249	+	0.632470i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.255662	−	0.442820i	0.0218427	−	0.0378326i	−0.854897	−	0.518797i	$-0.826380\pi$
$137$	0.255662	−	0.442820i	0.0218427	−	0.0378326i	0.876740	+	0.480964i	$0.159713\pi$
$138$		0			0
$139$	3.83289	−	6.63877i	0.325102	−	0.563093i	−0.656431	−	0.754386i	$-0.727935\pi$
$139$	3.83289	−	6.63877i	0.325102	−	0.563093i	0.981533	+	0.191293i	$0.0612681\pi$
$140$		0			0
$141$	−8.13165			−0.684808
$142$		0			0
$143$	5.49470	−	9.51710i	0.459490	−	0.795860i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	1.39366	+	2.41390i	0.114947	+	0.199095i
$148$		0			0
$149$	−6.96176	−	12.0581i	−0.570330	−	0.987840i	−0.996532	−	0.0832122i	$-0.973482\pi$
$149$	−6.96176	−	12.0581i	−0.570330	−	0.987840i	0.426202	−	0.904628i	$-0.359851\pi$
$150$		0			0
$151$	0.617238			0.0502301			0.0251151	−	0.999685i	$-0.492005\pi$
$151$	0.617238			0.0502301			0.0251151	+	0.999685i	$0.492005\pi$
$152$		0			0
$153$	3.75590			0.303647
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−9.52408	−	16.4962i	−0.760104	−	1.31654i	−0.942796	−	0.333369i	$-0.891815\pi$
$157$	−9.52408	−	16.4962i	−0.760104	−	1.31654i	0.182692	−	0.983170i	$-0.441519\pi$
$158$		0			0
$159$	−9.10230			−0.721859
$160$		0			0
$161$	2.78107	−	4.81696i	0.219179	−	0.379630i
$162$		0			0
$163$	0.523410			0.0409967			0.0204983	−	0.999790i	$-0.493475\pi$
$163$	0.523410			0.0409967			0.0204983	+	0.999790i	$0.493475\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−10.4720	+	18.1381i	−0.810349	+	1.40357i	0.102270	+	0.994757i	$0.467389\pi$
$167$	−10.4720	+	18.1381i	−0.810349	+	1.40357i	−0.912620	+	0.408810i	$0.865944\pi$
$168$		0			0
$169$	−6.81397	−	11.8021i	−0.524151	−	0.907857i
$170$		0			0
$171$	6.13659	−	1.08524i	0.469277	−	0.0829903i
$172$		0			0
$173$	−0.896215	−	1.55229i	−0.0681380	−	0.118018i	0.829944	−	0.557847i	$-0.188372\pi$
$173$	−0.896215	−	1.55229i	−0.0681380	−	0.118018i	−0.898082	+	0.439829i	$0.855039\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	4.43185	−	7.67618i	0.333118	−	0.576977i
$178$		0			0
$179$	26.6492			1.99186			0.995928	−	0.0901537i	$-0.0287358\pi$
$179$	26.6492			1.99186			0.995928	+	0.0901537i	$0.0287358\pi$
$180$		0			0
$181$	−5.21515	+	9.03290i	−0.387639	+	0.671410i	−0.992131	−	0.125200i	$-0.960043\pi$
$181$	−5.21515	+	9.03290i	−0.387639	+	0.671410i	0.604492	+	0.796611i	$0.293376\pi$
$182$		0			0
$183$	−13.5835			−1.00412
$184$		0			0
$185$		0			0
$186$		0			0
$187$	2.79738	+	4.84521i	0.204565	+	0.354317i
$188$		0			0
$189$	−12.1307			−0.882377
$190$		0			0
$191$	5.07372			0.367122			0.183561	−	0.983008i	$-0.441238\pi$
$191$	5.07372			0.367122			0.183561	+	0.983008i	$0.441238\pi$
$192$		0			0
$193$	3.25345	+	5.63515i	0.234189	+	0.405627i	0.959037	−	0.283282i	$-0.0914233\pi$
$193$	3.25345	+	5.63515i	0.234189	+	0.405627i	−0.724848	+	0.688909i	$0.758090\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	6.78955			0.483735			0.241868	−	0.970309i	$-0.422240\pi$
$197$	6.78955			0.483735			0.241868	+	0.970309i	$0.422240\pi$
$198$		0			0
$199$	−6.90024	+	11.9516i	−0.489145	+	0.847224i	−0.999922	−	0.0124890i	$-0.996025\pi$
$199$	−6.90024	+	11.9516i	−0.489145	+	0.847224i	0.510777	+	0.859713i	$0.329358\pi$
$200$		0			0
$201$	3.55581			0.250807
$202$		0			0
$203$	−6.73109	+	11.6586i	−0.472430	+	0.818272i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.81941	−	3.15132i	−0.126458	−	0.219032i
$208$		0			0
$209$	5.97050	+	7.10808i	0.412988	+	0.491676i
$210$		0			0
$211$	−2.06131	−	3.57030i	−0.141907	−	0.245789i	0.786308	−	0.617835i	$-0.211990\pi$
$211$	−2.06131	−	3.57030i	−0.141907	−	0.245789i	−0.928215	+	0.372045i	$0.878657\pi$
$212$		0			0
$213$	−3.90018	+	6.75530i	−0.267236	+	0.462866i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−2.29598			−0.155861
$218$		0			0
$219$	−9.75258	+	16.8920i	−0.659018	+	1.14145i
$220$		0			0
$221$	13.5564			0.911904
$222$		0			0
$223$	−2.53146	−	4.38462i	−0.169519	−	0.293616i	0.768732	−	0.639571i	$-0.220888\pi$
$223$	−2.53146	−	4.38462i	−0.169519	−	0.293616i	−0.938251	+	0.345956i	$0.887555\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.05466			−0.335489			−0.167745	−	0.985830i	$-0.553648\pi$
$227$	−5.05466			−0.335489			−0.167745	+	0.985830i	$0.553648\pi$
$228$		0			0
$229$	1.01317			0.0669523			0.0334761	−	0.999440i	$-0.489342\pi$
$229$	1.01317			0.0669523			0.0334761	+	0.999440i	$0.489342\pi$
$230$		0			0
$231$	−2.91601	−	5.05067i	−0.191859	−	0.332310i
$232$		0			0
$233$	−5.73375	−	9.93114i	−0.375630	−	0.650611i	0.614791	−	0.788690i	$-0.289240\pi$
$233$	−5.73375	−	9.93114i	−0.375630	−	0.650611i	−0.990421	+	0.138079i	$0.955907\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	3.51716	−	6.09190i	0.228464	−	0.395711i
$238$		0			0
$239$	18.0027			1.16450			0.582250	−	0.813010i	$-0.302172\pi$
$239$	18.0027			1.16450			0.582250	+	0.813010i	$0.302172\pi$
$240$		0			0
$241$	−1.52915	+	2.64856i	−0.0985012	+	0.170609i	−0.911064	−	0.412264i	$-0.864738\pi$
$241$	−1.52915	+	2.64856i	−0.0985012	+	0.170609i	0.812563	+	0.582873i	$0.198071\pi$
$242$		0			0
$243$	−6.65537	+	11.5274i	−0.426942	+	0.739485i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	22.1492	−	3.91703i	1.40932	−	0.249234i
$248$		0			0
$249$	−4.73140	−	8.19503i	−0.299840	−	0.519339i
$250$		0			0
$251$	−0.789341	+	1.36718i	−0.0498228	+	0.0862956i	−0.889861	−	0.456231i	$-0.849199\pi$
$251$	−0.789341	+	1.36718i	−0.0498228	+	0.0862956i	0.840038	+	0.542527i	$0.182532\pi$
$252$		0			0
$253$	2.71019	−	4.69418i	0.170388	−	0.295121i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−7.07800	+	12.2595i	−0.441513	+	0.764724i	−0.997802	−	0.0662654i	$-0.978892\pi$
$257$	−7.07800	+	12.2595i	−0.441513	+	0.764724i	0.556289	+	0.830989i	$0.312225\pi$
$258$		0			0
$259$	4.93727			0.306787
$260$		0			0
$261$	4.40356	+	7.62719i	0.272574	+	0.472112i
$262$		0			0
$263$	9.04170	+	15.6607i	0.557535	+	0.965679i	0.997701	+	0.0677628i	$0.0215861\pi$
$263$	9.04170	+	15.6607i	0.557535	+	0.965679i	−0.440166	+	0.897916i	$0.645081\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	19.3819			1.18615
$268$		0			0
$269$	3.29767	+	5.71172i	0.201062	+	0.348250i	0.948871	−	0.315664i	$-0.102227\pi$
$269$	3.29767	+	5.71172i	0.201062	+	0.348250i	−0.747809	+	0.663914i	$0.768894\pi$
$270$		0			0
$271$	12.4587	+	21.5791i	0.756811	+	1.31084i	0.944469	+	0.328601i	$0.106577\pi$
$271$	12.4587	+	21.5791i	0.756811	+	1.31084i	−0.187657	+	0.982235i	$0.560089\pi$
$272$		0			0
$273$	−14.1313			−0.855265
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−17.5130			−1.05226			−0.526128	−	0.850406i	$-0.676357\pi$
$277$	−17.5130			−1.05226			−0.526128	+	0.850406i	$0.676357\pi$
$278$		0			0
$279$	−0.751029	+	1.30082i	−0.0449630	+	0.0778781i
$280$		0			0
$281$	−8.43050	+	14.6021i	−0.502922	+	0.871086i	0.497073	+	0.867709i	$0.334408\pi$
$281$	−8.43050	+	14.6021i	−0.502922	+	0.871086i	−0.999994	+	0.00337702i	$0.998925\pi$
$282$		0			0
$283$	1.90656	+	3.30226i	0.113333	+	0.196299i	0.917112	−	0.398629i	$-0.130514\pi$
$283$	1.90656	+	3.30226i	0.113333	+	0.196299i	−0.803779	+	0.594928i	$0.797181\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	10.9863	+	19.0288i	0.648501	+	1.12324i
$288$		0			0
$289$	5.04917	−	8.74542i	0.297010	−	0.514437i
$290$		0			0
$291$	−8.30913	+	14.3918i	−0.487090	+	0.843665i
$292$		0			0
$293$	12.6667			0.739996			0.369998	−	0.929033i	$-0.379358\pi$
$293$	12.6667			0.739996			0.369998	+	0.929033i	$0.379358\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−11.8215			−0.685952
$298$		0			0
$299$	−6.56694	−	11.3743i	−0.379776	−	0.657791i
$300$		0			0
$301$	1.83586	+	3.17980i	0.105817	+	0.183281i
$302$		0			0
$303$	−5.23174			−0.300556
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−7.64480	−	13.2412i	−0.436312	−	0.755714i	0.561090	−	0.827755i	$-0.310382\pi$
$307$	−7.64480	−	13.2412i	−0.436312	−	0.755714i	−0.997402	+	0.0720410i	$0.977049\pi$
$308$		0			0
$309$	−9.94152	−	17.2192i	−0.565553	−	0.979567i
$310$		0			0
$311$	−27.9152			−1.58292			−0.791462	−	0.611218i	$-0.790680\pi$
$311$	−27.9152			−1.58292			−0.791462	+	0.611218i	$0.790680\pi$
$312$		0			0
$313$	−1.95539	+	3.38684i	−0.110525	+	0.191436i	−0.915982	−	0.401219i	$-0.868587\pi$
$313$	−1.95539	+	3.38684i	−0.110525	+	0.191436i	0.805457	+	0.592654i	$0.201920\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.70175	+	8.14366i	−0.264076	+	0.457394i	−0.967321	−	0.253554i	$-0.918400\pi$
$317$	−4.70175	+	8.14366i	−0.264076	+	0.457394i	0.703245	+	0.710948i	$0.251734\pi$
$318$		0			0
$319$	−6.55952	+	11.3614i	−0.367263	+	0.636118i
$320$		0			0
$321$	−2.51950	−	4.36390i	−0.140625	−	0.243569i
$322$		0			0
$323$	−3.91113	+	10.7626i	−0.217621	+	0.598849i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−2.77049	+	4.79863i	−0.153208	+	0.265365i
$328$		0			0
$329$	7.09043	−	12.2810i	0.390908	−	0.677073i
$330$		0			0
$331$	1.46413			0.0804757			0.0402379	−	0.999190i	$-0.487188\pi$
$331$	1.46413			0.0804757			0.0402379	+	0.999190i	$0.487188\pi$
$332$		0			0
$333$	1.61501	−	2.79729i	0.0885022	−	0.153290i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−15.6121	−	27.0410i	−0.850447	−	1.47302i	−0.880806	−	0.473478i	$-0.842998\pi$
$337$	−15.6121	−	27.0410i	−0.850447	−	1.47302i	0.0303589	−	0.999539i	$-0.490335\pi$
$338$		0			0
$339$	3.78585	+	6.55729i	0.205619	+	0.356143i
$340$		0			0
$341$	−2.23746			−0.121165
$342$		0			0
$343$	−20.1582			−1.08844
$344$		0			0
$345$		0			0
$346$		0			0
$347$	15.1197	+	26.1882i	0.811670	+	1.40585i	0.911694	+	0.410869i	$0.134775\pi$
$347$	15.1197	+	26.1882i	0.811670	+	1.40585i	−0.100024	+	0.994985i	$0.531892\pi$
$348$		0			0
$349$	17.1752			0.919367			0.459683	−	0.888083i	$-0.347963\pi$
$349$	17.1752			0.919367			0.459683	+	0.888083i	$0.347963\pi$
$350$		0			0
$351$	−14.3221	+	24.8065i	−0.764455	+	1.32407i
$352$		0			0
$353$	−10.6712			−0.567970			−0.283985	−	0.958829i	$-0.591657\pi$
$353$	−10.6712			−0.567970			−0.283985	+	0.958829i	$0.591657\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	3.59716	−	6.23047i	0.190382	−	0.329751i
$358$		0			0
$359$	−0.751774	−	1.30211i	−0.0396771	−	0.0687228i	0.845505	−	0.533968i	$-0.179300\pi$
$359$	−0.751774	−	1.30211i	−0.0396771	−	0.0687228i	−0.885182	+	0.465245i	$0.845966\pi$
$360$		0			0
$361$	−3.28043	+	18.7147i	−0.172654	+	0.984982i
$362$		0			0
$363$	4.05051	+	7.01569i	0.212597	+	0.368228i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−17.9857	+	31.1522i	−0.938846	+	1.62613i	−0.171218	+	0.985233i	$0.554770\pi$
$367$	−17.9857	+	31.1522i	−0.938846	+	1.62613i	−0.767628	+	0.640896i	$0.778563\pi$
$368$		0			0
$369$	14.3747			0.748320
$370$		0			0
$371$	7.93679	−	13.7469i	0.412058	−	0.713705i
$372$		0			0
$373$	−18.0175			−0.932911			−0.466455	−	0.884545i	$-0.654469\pi$
$373$	−18.0175			−0.932911			−0.466455	+	0.884545i	$0.654469\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	15.8941	+	27.5294i	0.818587	+	1.41783i
$378$		0			0
$379$	−14.1538			−0.727032			−0.363516	−	0.931588i	$-0.618424\pi$
$379$	−14.1538			−0.727032			−0.363516	+	0.931588i	$0.618424\pi$
$380$		0			0
$381$	9.73649			0.498815
$382$		0			0
$383$	8.80446	+	15.2498i	0.449887	+	0.779227i	0.998378	−	0.0569291i	$-0.0181309\pi$
$383$	8.80446	+	15.2498i	0.449887	+	0.779227i	−0.548491	+	0.836156i	$0.684798\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	2.40208			0.122105
$388$		0			0
$389$	5.72023	−	9.90774i	0.290027	−	0.502342i	−0.683789	−	0.729680i	$-0.739669\pi$
$389$	5.72023	−	9.90774i	0.290027	−	0.502342i	0.973816	+	0.227338i	$0.0730023\pi$
$390$		0			0
$391$	6.68653			0.338152
$392$		0			0
$393$	−10.2580	+	17.7674i	−0.517450	+	0.896249i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	8.97852	+	15.5513i	0.450619	+	0.780495i	0.998425	−	0.0561107i	$-0.0178700\pi$
$397$	8.97852	+	15.5513i	0.450619	+	0.780495i	−0.547806	+	0.836606i	$0.684537\pi$
$398$		0			0
$399$	4.07699	−	11.2190i	0.204105	−	0.561654i
$400$		0			0
$401$	−4.69150	−	8.12592i	−0.234282	−	0.405789i	0.724782	−	0.688979i	$-0.241941\pi$
$401$	−4.69150	−	8.12592i	−0.234282	−	0.405789i	−0.959064	+	0.283190i	$0.908607\pi$
$402$		0			0
$403$	−2.71074	+	4.69514i	−0.135032	+	0.233882i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	4.81143			0.238494
$408$		0			0
$409$	19.4232	−	33.6420i	0.960415	−	1.66349i	0.238956	−	0.971030i	$-0.423195\pi$
$409$	19.4232	−	33.6420i	0.960415	−	1.66349i	0.721459	−	0.692457i	$-0.243472\pi$
$410$		0			0
$411$	−0.640753			−0.0316060
$412$		0			0
$413$	7.72874	+	13.3866i	0.380306	+	0.658710i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−9.60620			−0.470418
$418$		0			0
$419$	40.0512			1.95663			0.978314	−	0.207128i	$-0.0664118\pi$
$419$	40.0512			1.95663			0.978314	+	0.207128i	$0.0664118\pi$
$420$		0			0
$421$	18.7255	+	32.4336i	0.912627	+	1.58072i	0.810339	+	0.585962i	$0.199283\pi$
$421$	18.7255	+	32.4336i	0.912627	+	1.58072i	0.102289	+	0.994755i	$0.467383\pi$
$422$		0			0
$423$	−4.63865	−	8.03438i	−0.225539	−	0.390645i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	11.8442	−	20.5148i	0.573183	−	0.992782i
$428$		0			0
$429$	−13.7711			−0.664875
$430$		0			0
$431$	7.38909	−	12.7983i	0.355920	−	0.616472i	−0.631355	−	0.775494i	$-0.717501\pi$
$431$	7.38909	−	12.7983i	0.355920	−	0.616472i	0.987275	+	0.159022i	$0.0508342\pi$
$432$		0			0
$433$	−4.84501	+	8.39180i	−0.232836	+	0.403284i	−0.958642	−	0.284616i	$-0.908134\pi$
$433$	−4.84501	+	8.39180i	−0.232836	+	0.403284i	0.725805	+	0.687900i	$0.241467\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	10.9248	−	1.93202i	0.522604	−	0.0924211i
$438$		0			0
$439$	−2.80499	−	4.85838i	−0.133875	−	0.231878i	0.791292	−	0.611438i	$-0.209409\pi$
$439$	−2.80499	−	4.85838i	−0.133875	−	0.231878i	−0.925167	+	0.379560i	$0.876075\pi$
$440$		0			0
$441$	−1.59001	+	2.75398i	−0.0757149	+	0.131142i
$442$		0			0
$443$	−2.68171	+	4.64485i	−0.127412	+	0.220684i	−0.922673	−	0.385583i	$-0.874000\pi$
$443$	−2.68171	+	4.64485i	−0.127412	+	0.220684i	0.795261	+	0.606267i	$0.207334\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−8.72396	+	15.1103i	−0.412629	+	0.714695i
$448$		0			0
$449$	6.14784			0.290134			0.145067	−	0.989422i	$-0.453660\pi$
$449$	6.14784			0.290134			0.145067	+	0.989422i	$0.453660\pi$
$450$		0			0
$451$	10.7063	+	18.5438i	0.504138	+	0.873193i
$452$		0			0
$453$	−0.386738	−	0.669851i	−0.0181706	−	0.0314723i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−31.6775			−1.48181			−0.740906	−	0.671608i	$-0.765604\pi$
$457$	−31.6775			−1.48181			−0.740906	+	0.671608i	$0.765604\pi$
$458$		0			0
$459$	−7.29144	−	12.6291i	−0.340335	−	0.589478i
$460$		0			0
$461$	4.34077	+	7.51844i	0.202170	+	0.350169i	0.949227	−	0.314591i	$-0.101867\pi$
$461$	4.34077	+	7.51844i	0.202170	+	0.350169i	−0.747057	+	0.664760i	$0.768534\pi$
$462$		0			0
$463$	−0.258854			−0.0120300			−0.00601499	−	0.999982i	$-0.501915\pi$
$463$	−0.258854			−0.0120300			−0.00601499	+	0.999982i	$0.501915\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−22.8060			−1.05534			−0.527668	−	0.849451i	$-0.676934\pi$
$467$	−22.8060			−1.05534			−0.527668	+	0.849451i	$0.676934\pi$
$468$		0			0
$469$	−3.10050	+	5.37023i	−0.143168	+	0.247974i
$470$		0			0
$471$	−11.9349	+	20.6718i	−0.549930	+	0.952506i
$472$		0			0
$473$	1.78907	+	3.09875i	0.0822613	+	0.142481i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−5.19235	−	8.99342i	−0.237741	−	0.411780i
$478$		0			0
$479$	−3.10389	+	5.37609i	−0.141820	+	0.245640i	−0.928182	−	0.372126i	$-0.878629\pi$
$479$	−3.10389	+	5.37609i	−0.141820	+	0.245640i	0.786362	+	0.617766i	$0.211962\pi$
$480$		0			0
$481$	5.82918	−	10.0964i	0.265788	−	0.460358i
$482$		0			0
$483$	−6.97007			−0.317149
$484$		0			0
$485$		0			0
$486$		0			0
$487$	21.5698			0.977420			0.488710	−	0.872446i	$-0.337468\pi$
$487$	21.5698			0.977420			0.488710	+	0.872446i	$0.337468\pi$
$488$		0			0
$489$	−0.327950	−	0.568025i	−0.0148304	−	0.0256870i
$490$		0			0
$491$	−18.2548	−	31.6182i	−0.823828	−	1.42691i	−0.902812	−	0.430036i	$-0.858501\pi$
$491$	−18.2548	−	31.6182i	−0.823828	−	1.42691i	0.0789841	−	0.996876i	$-0.474832\pi$
$492$		0			0
$493$	−16.1835			−0.728870
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−6.80155	−	11.7806i	−0.305091	−	0.528434i
$498$		0			0
$499$	−18.5178	−	32.0737i	−0.828969	−	1.43582i	−0.898848	−	0.438260i	$-0.855595\pi$
$499$	−18.5178	−	32.0737i	−0.828969	−	1.43582i	0.0698794	−	0.997555i	$-0.477739\pi$
$500$		0			0
$501$	26.2455			1.17256
$502$		0			0
$503$	−17.0971	+	29.6130i	−0.762321	+	1.32038i	0.179330	+	0.983789i	$0.442607\pi$
$503$	−17.0971	+	29.6130i	−0.762321	+	1.32038i	−0.941651	+	0.336590i	$0.890726\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−8.53876	+	14.7896i	−0.379220	+	0.656827i
$508$		0			0
$509$	−17.0016	+	29.4476i	−0.753581	+	1.30524i	0.192495	+	0.981298i	$0.438342\pi$
$509$	−17.0016	+	29.4476i	−0.753581	+	1.30524i	−0.946077	+	0.323943i	$0.894991\pi$
$510$		0			0
$511$	−17.0076	−	29.4581i	−0.752373	−	1.30315i
$512$		0			0
$513$	−15.5622	−	18.5274i	−0.687089	−	0.818003i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	6.90970	−	11.9680i	0.303888	−	0.526350i
$518$		0			0
$519$	−1.12307	+	1.94522i	−0.0492973	+	0.0853855i
$520$		0			0
$521$	−33.6165			−1.47277			−0.736383	−	0.676565i	$-0.763468\pi$
$521$	−33.6165			−1.47277			−0.736383	+	0.676565i	$0.763468\pi$
$522$		0			0
$523$	−11.6947	+	20.2557i	−0.511372	+	0.885722i	0.488541	+	0.872541i	$0.337529\pi$
$523$	−11.6947	+	20.2557i	−0.511372	+	0.885722i	−0.999913	+	0.0131810i	$0.995804\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.38005	−	2.39032i	−0.0601161	−	0.104124i
$528$		0			0
$529$	8.26095	+	14.3084i	0.359172	+	0.622103i
$530$		0			0
$531$	10.1125			0.438844
$532$		0			0
$533$	51.8838			2.24734
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−16.6974	−	28.9208i	−0.720546	−	1.24802i
$538$		0			0
$539$	−4.73695			−0.204035
$540$		0			0
$541$	−18.0050	+	31.1856i	−0.774097	+	1.34077i	0.161204	+	0.986921i	$0.448462\pi$
$541$	−18.0050	+	31.1856i	−0.774097	+	1.34077i	−0.935301	+	0.353854i	$0.884871\pi$
$542$		0			0
$543$	13.0705			0.560908
$544$		0			0
$545$		0			0
$546$		0			0
$547$	6.61701	−	11.4610i	0.282923	−	0.490037i	−0.689180	−	0.724590i	$-0.742029\pi$
$547$	6.61701	−	11.4610i	0.282923	−	0.490037i	0.972103	+	0.234553i	$0.0753626\pi$
$548$		0			0
$549$	−7.74865	−	13.4211i	−0.330704	−	0.572797i
$550$		0			0
$551$	−26.4415	+	4.67611i	−1.12645	+	0.199209i
$552$		0			0
$553$	6.13361	+	10.6237i	0.260827	+	0.451766i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−9.03385	+	15.6471i	−0.382776	+	0.662988i	−0.991458	−	0.130427i	$-0.958365\pi$
$557$	−9.03385	+	15.6471i	−0.382776	+	0.662988i	0.608682	+	0.793415i	$0.291699\pi$
$558$		0			0
$559$	8.67001			0.366702
$560$		0			0
$561$	3.50547	−	6.07166i	0.148001	−	0.256346i
$562$		0			0
$563$	24.4686			1.03123			0.515613	−	0.856821i	$-0.327564\pi$
$563$	24.4686			1.03123			0.515613	+	0.856821i	$0.327564\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	2.91415	+	5.04745i	0.122383	+	0.211973i
$568$		0			0
$569$	−18.4580			−0.773801			−0.386900	−	0.922122i	$-0.626454\pi$
$569$	−18.4580			−0.773801			−0.386900	+	0.922122i	$0.626454\pi$
$570$		0			0
$571$	−19.5131			−0.816598			−0.408299	−	0.912848i	$-0.633878\pi$
$571$	−19.5131			−0.816598			−0.408299	+	0.912848i	$0.633878\pi$
$572$		0			0
$573$	−3.17901	−	5.50620i	−0.132805	−	0.230025i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	5.03750			0.209714			0.104857	−	0.994487i	$-0.466562\pi$
$577$	5.03750			0.209714			0.104857	+	0.994487i	$0.466562\pi$
$578$		0			0
$579$	4.07699	−	7.06155i	0.169434	−	0.293468i
$580$		0			0
$581$	16.5023			0.684630
$582$		0			0
$583$	7.73449	−	13.3965i	0.320330	−	0.554828i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	14.8436	+	25.7099i	0.612662	+	1.06116i	0.990790	+	0.135409i	$0.0432348\pi$
$587$	14.8436	+	25.7099i	0.612662	+	1.06116i	−0.378128	+	0.925754i	$0.623432\pi$
$588$		0			0
$589$	−2.94547	−	3.50668i	−0.121366	−	0.144490i
$590$		0			0
$591$	−4.25408	−	7.36828i	−0.174989	−	0.303091i
$592$		0			0
$593$	−17.2178	+	29.8222i	−0.707052	+	1.22465i	0.258894	+	0.965906i	$0.416642\pi$
$593$	−17.2178	+	29.8222i	−0.707052	+	1.22465i	−0.965946	+	0.258744i	$0.916692\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	17.2937			0.707786
$598$		0			0
$599$	−0.909784	+	1.57579i	−0.0371728	+	0.0643851i	−0.884013	−	0.467462i	$-0.845169\pi$
$599$	−0.909784	+	1.57579i	−0.0371728	+	0.0643851i	0.846840	+	0.531847i	$0.178502\pi$
$600$		0			0
$601$	−9.14106			−0.372872			−0.186436	−	0.982467i	$-0.559694\pi$
$601$	−9.14106			−0.372872			−0.186436	+	0.982467i	$0.559694\pi$
$602$		0			0
$603$	2.02839	+	3.51327i	0.0826023	+	0.143071i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−27.7363			−1.12578			−0.562890	−	0.826532i	$-0.690311\pi$
$607$	−27.7363			−1.12578			−0.562890	+	0.826532i	$0.690311\pi$
$608$		0			0
$609$	16.8698			0.683599
$610$		0			0
$611$	−16.7426	−	28.9990i	−0.677333	−	1.17317i
$612$		0			0
$613$	−11.1937	−	19.3881i	−0.452109	−	0.783076i	0.546407	−	0.837519i	$-0.315995\pi$
$613$	−11.1937	−	19.3881i	−0.452109	−	0.783076i	−0.998517	+	0.0544430i	$0.982662\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	21.8234	−	37.7993i	0.878578	−	1.52174i	0.0256759	−	0.999670i	$-0.491826\pi$
$617$	21.8234	−	37.7993i	0.878578	−	1.52174i	0.852902	−	0.522071i	$-0.174840\pi$
$618$		0			0
$619$	27.7258			1.11440			0.557198	−	0.830380i	$-0.311876\pi$
$619$	27.7258			1.11440			0.557198	+	0.830380i	$0.311876\pi$
$620$		0			0
$621$	−7.06416	+	12.2355i	−0.283475	+	0.490993i
$622$		0			0
$623$	−16.9001	+	29.2719i	−0.677089	+	1.17275i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	3.97307	−	10.9331i	0.158669	−	0.436625i
$628$		0			0
$629$	2.96767	+	5.14015i	0.118329	+	0.204951i
$630$		0			0
$631$	−5.83973	+	10.1147i	−0.232476	+	0.402660i	−0.958536	−	0.284971i	$-0.908016\pi$
$631$	−5.83973	+	10.1147i	−0.232476	+	0.402660i	0.726060	+	0.687631i	$0.241349\pi$
$632$		0			0
$633$	−2.58308	+	4.47403i	−0.102668	+	0.177827i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−5.73894	+	9.94014i	−0.227385	+	0.393843i
$638$		0			0
$639$	−8.89932			−0.352052
$640$		0			0
$641$	−9.87218	−	17.0991i	−0.389928	−	0.675374i	0.602512	−	0.798110i	$-0.294167\pi$
$641$	−9.87218	−	17.0991i	−0.389928	−	0.675374i	−0.992439	+	0.122736i	$0.960833\pi$
$642$		0			0
$643$	9.48677	+	16.4316i	0.374122	+	0.647998i	0.990195	−	0.139691i	$-0.0446109\pi$
$643$	9.48677	+	16.4316i	0.374122	+	0.647998i	−0.616073	+	0.787689i	$0.711278\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	6.83157			0.268577			0.134288	−	0.990942i	$-0.457125\pi$
$647$	6.83157			0.268577			0.134288	+	0.990942i	$0.457125\pi$
$648$		0			0
$649$	7.53174	+	13.0454i	0.295647	+	0.512075i
$650$		0			0
$651$	1.43858	+	2.49169i	0.0563822	+	0.0976569i
$652$		0			0
$653$	18.7904			0.735325			0.367663	−	0.929959i	$-0.380158\pi$
$653$	18.7904			0.735325			0.367663	+	0.929959i	$0.380158\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−22.2532			−0.868180
$658$		0			0
$659$	−17.7289	+	30.7073i	−0.690619	+	1.19619i	0.281016	+	0.959703i	$0.409329\pi$
$659$	−17.7289	+	30.7073i	−0.690619	+	1.19619i	−0.971635	+	0.236485i	$0.924005\pi$
$660$		0			0
$661$	11.8550	−	20.5335i	0.461108	−	0.798662i	−0.537909	−	0.843003i	$-0.680786\pi$
$661$	11.8550	−	20.5335i	0.461108	−	0.798662i	0.999016	+	0.0443412i	$0.0141189\pi$
$662$		0			0
$663$	−8.49396	−	14.7120i	−0.329878	−	0.571365i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	7.83954	+	13.5785i	0.303548	+	0.525761i
$668$		0			0
$669$	−3.17224	+	5.49448i	−0.122646	+	0.212429i
$670$		0			0
$671$	11.5423	−	19.9919i	0.445587	−	0.771779i
$672$		0			0
$673$	2.76230			0.106479			0.0532394	−	0.998582i	$-0.483045\pi$
$673$	2.76230			0.106479			0.0532394	+	0.998582i	$0.483045\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	17.0981			0.657132			0.328566	−	0.944481i	$-0.393435\pi$
$677$	17.0981			0.657132			0.328566	+	0.944481i	$0.393435\pi$
$678$		0			0
$679$	−14.4904	−	25.0981i	−0.556090	−	0.963175i
$680$		0			0
$681$	3.16706	+	5.48551i	0.121362	+	0.210205i
$682$		0			0
$683$	−17.4864			−0.669098			−0.334549	−	0.942378i	$-0.608584\pi$
$683$	−17.4864			−0.669098			−0.334549	+	0.942378i	$0.608584\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−0.634816	−	1.09953i	−0.0242197	−	0.0419498i
$688$		0			0
$689$	−18.7411	−	32.4605i	−0.713979	−	1.23665i
$690$		0			0
$691$	20.2781			0.771416			0.385708	−	0.922621i	$-0.373957\pi$
$691$	20.2781			0.771416			0.385708	+	0.922621i	$0.373957\pi$
$692$		0			0
$693$	3.32684	−	5.76225i	0.126376	−	0.218890i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−13.2072	+	22.8755i	−0.500257	+	0.866470i
$698$		0			0
$699$	−7.18511	+	12.4450i	−0.271766	+	0.470712i
$700$		0			0
$701$	24.2078	+	41.9292i	0.914317	+	1.58364i	0.807899	+	0.589321i	$0.200605\pi$
$701$	24.2078	+	41.9292i	0.914317	+	1.58364i	0.106418	+	0.994322i	$0.466062\pi$
$702$		0			0
$703$	6.33394	+	7.54077i	0.238889	+	0.284405i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	4.56184	−	7.90134i	0.171566	−	0.297161i
$708$		0			0
$709$	9.60392	−	16.6345i	0.360683	−	0.624721i	−0.627391	−	0.778705i	$-0.715877\pi$
$709$	9.60392	−	16.6345i	0.360683	−	0.624721i	0.988073	+	0.153984i	$0.0492104\pi$
$710$		0			0
$711$	8.02537			0.300975
$712$		0			0
$713$	−1.33704	+	2.31582i	−0.0500724	+	0.0867280i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−11.2799	−	19.5373i	−0.421254	−	0.729633i
$718$		0			0
$719$	25.0395	+	43.3698i	0.933817	+	1.61742i	0.776729	+	0.629835i	$0.216877\pi$
$719$	25.0395	+	43.3698i	0.933817	+	1.61742i	0.157088	+	0.987585i	$0.449789\pi$
$720$		0			0
$721$	34.6742			1.29133
$722$		0			0
$723$	3.83243			0.142530
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−22.2320	−	38.5070i	−0.824540	−	1.42815i	−0.902270	−	0.431171i	$-0.858101\pi$
$727$	−22.2320	−	38.5070i	−0.824540	−	1.42815i	0.0777303	−	0.996974i	$-0.475233\pi$
$728$		0			0
$729$	24.6810			0.914112
$730$		0			0
$731$	−2.20697	+	3.82259i	−0.0816279	+	0.141384i
$732$		0			0
$733$	40.6973			1.50319			0.751594	−	0.659626i	$-0.229285\pi$
$733$	40.6973			1.50319			0.751594	+	0.659626i	$0.229285\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.02147	+	5.23335i	−0.111297	+	0.192773i
$738$		0			0
$739$	−20.0899	−	34.7967i	−0.739019	−	1.28002i	−0.952938	−	0.303167i	$-0.901956\pi$
$739$	−20.0899	−	34.7967i	−0.739019	−	1.28002i	0.213919	−	0.976851i	$-0.431377\pi$
$740$		0			0
$741$	−18.1288	−	21.5829i	−0.665978	−	0.792868i
$742$		0			0
$743$	−14.7584	−	25.5623i	−0.541432	−	0.937788i	−0.998822	−	0.0485220i	$-0.984549\pi$
$743$	−14.7584	−	25.5623i	−0.541432	−	0.937788i	0.457390	−	0.889266i	$-0.348784\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	5.39800	−	9.34961i	0.197502	−	0.342084i
$748$		0			0
$749$	8.78756			0.321090
$750$		0			0
$751$	−0.886284	+	1.53509i	−0.0323410	+	0.0560162i	−0.881743	−	0.471730i	$-0.843630\pi$
$751$	−0.886284	+	1.53509i	−0.0323410	+	0.0560162i	0.849402	+	0.527747i	$0.176963\pi$
$752$		0			0
$753$	1.97829			0.0720928
$754$		0			0
$755$		0			0
$756$		0			0
$757$	5.33238	+	9.23595i	0.193809	+	0.335686i	0.946509	−	0.322677i	$-0.104583\pi$
$757$	5.33238	+	9.23595i	0.193809	+	0.335686i	−0.752701	+	0.658363i	$0.771249\pi$
$758$		0			0
$759$	−6.79241			−0.246549
$760$		0			0
$761$	−26.5852			−0.963713			−0.481856	−	0.876250i	$-0.660037\pi$
$761$	−26.5852			−0.963713			−0.481856	+	0.876250i	$0.660037\pi$
$762$		0			0
$763$	−4.83148	−	8.36837i	−0.174911	−	0.302955i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	36.4997			1.31793
$768$		0			0
$769$	−3.28351	+	5.68721i	−0.118406	+	0.205086i	−0.919136	−	0.393940i	$-0.871112\pi$
$769$	−3.28351	+	5.68721i	−0.118406	+	0.205086i	0.800730	+	0.599026i	$0.204445\pi$
$770$		0			0
$771$	17.7392			0.638863
$772$		0			0
$773$	−10.8126	+	18.7279i	−0.388902	+	0.673597i	−0.992302	−	0.123841i	$-0.960479\pi$
$773$	−10.8126	+	18.7279i	−0.388902	+	0.673597i	0.603400	+	0.797438i	$0.293812\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−3.09351	−	5.35812i	−0.110979	−	0.192222i
$778$		0			0
$779$	−14.9689	+	41.1913i	−0.536315	+	1.47583i
$780$		0			0
$781$	−6.62819	−	11.4804i	−0.237175	−	0.410800i
$782$		0			0
$783$	17.0975	−	29.6138i	0.611016	−	1.05831i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	46.4649			1.65630			0.828148	−	0.560509i	$-0.189395\pi$
$787$	46.4649			1.65630			0.828148	+	0.560509i	$0.189395\pi$
$788$		0			0
$789$	11.3304	−	19.6248i	0.403372	−	0.698662i
$790$		0			0
$791$	−13.2044			−0.469494
$792$		0			0
$793$	−27.9677	−	48.4415i	−0.993163	−	1.72021i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−36.8012			−1.30357			−0.651783	−	0.758405i	$-0.725979\pi$
$797$	−36.8012			−1.30357			−0.651783	+	0.758405i	$0.725979\pi$
$798$		0			0
$799$	17.0475			0.603097
$800$		0			0
$801$	11.0563	+	19.1500i	0.390654	+	0.676633i
$802$		0			0
$803$	−16.5741	−	28.7072i	−0.584888	−	1.01306i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	4.13239	−	7.15751i	0.145467	−	0.251956i
$808$		0			0
$809$	−1.18674			−0.0417234			−0.0208617	−	0.999782i	$-0.506641\pi$
$809$	−1.18674			−0.0417234			−0.0208617	+	0.999782i	$0.506641\pi$
$810$		0			0
$811$	23.3332	−	40.4144i	0.819341	−	1.41914i	−0.0868272	−	0.996223i	$-0.527673\pi$
$811$	23.3332	−	40.4144i	0.819341	−	1.41914i	0.906168	−	0.422917i	$-0.138994\pi$
$812$		0			0
$813$	15.6123	−	27.0413i	0.547547	−	0.948380i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−2.50136	+	6.88324i	−0.0875116	+	0.240814i
$818$		0			0
$819$	−8.06111	−	13.9623i	−0.281678	−	0.487881i
$820$		0			0
$821$	23.4760	−	40.6617i	0.819319	−	1.41910i	−0.0868660	−	0.996220i	$-0.527685\pi$
$821$	23.4760	−	40.6617i	0.819319	−	1.41910i	0.906185	−	0.422882i	$-0.138981\pi$
$822$		0			0
$823$	16.5603	−	28.6833i	0.577257	−	0.999838i	−0.418536	−	0.908200i	$-0.637457\pi$
$823$	16.5603	−	28.6833i	0.577257	−	0.999838i	0.995792	−	0.0916375i	$-0.0292101\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−6.36751	+	11.0288i	−0.221420	+	0.383511i	−0.955239	−	0.295834i	$-0.904402\pi$
$827$	−6.36751	+	11.0288i	−0.221420	+	0.383511i	0.733819	+	0.679345i	$0.237736\pi$
$828$		0			0
$829$	−21.1725			−0.735352			−0.367676	−	0.929954i	$-0.619846\pi$
$829$	−21.1725			−0.735352			−0.367676	+	0.929954i	$0.619846\pi$
$830$		0			0
$831$	10.9730	+	19.0058i	0.380649	+	0.659304i
$832$		0			0
$833$	−2.92173	−	5.06058i	−0.101232	−	0.175339i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	5.83198			0.201583
$838$		0			0
$839$	5.20388	+	9.01338i	0.179658	+	0.311177i	0.941763	−	0.336276i	$-0.109168\pi$
$839$	5.20388	+	9.01338i	0.179658	+	0.311177i	−0.762106	+	0.647453i	$0.775834\pi$
$840$		0			0
$841$	−4.47419	−	7.74953i	−0.154283	−	0.267225i
$842$		0			0
$843$	21.1290			0.727720
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−14.1274			−0.485425
$848$		0			0
$849$	2.38916	−	4.13815i	0.0819959	−	0.142021i
$850$		0			0
$851$	2.87516	−	4.97993i	0.0985594	−	0.170710i
$852$		0			0
$853$	−12.2168	−	21.1602i	−0.418296	−	0.724511i	0.577472	−	0.816411i	$-0.304039\pi$
$853$	−12.2168	−	21.1602i	−0.418296	−	0.724511i	−0.995768	+	0.0918999i	$0.970706\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	25.9649	+	44.9725i	0.886944	+	1.53623i	0.843469	+	0.537178i	$0.180510\pi$
$857$	25.9649	+	44.9725i	0.886944	+	1.53623i	0.0434759	+	0.999054i	$0.486157\pi$
$858$		0			0
$859$	−28.7960	+	49.8761i	−0.982505	+	1.70175i	−0.329970	+	0.943992i	$0.607039\pi$
$859$	−28.7960	+	49.8761i	−0.982505	+	1.70175i	−0.652536	+	0.757758i	$0.726295\pi$
$860$		0			0
$861$	13.7672	−	23.8455i	0.469185	−	0.812653i
$862$		0			0
$863$	44.2381			1.50588			0.752941	−	0.658089i	$-0.228635\pi$
$863$	44.2381			1.50588			0.752941	+	0.658089i	$0.228635\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−12.6545			−0.429769
$868$		0			0
$869$	5.97727	+	10.3529i	0.202765	+	0.351199i
$870$		0			0
$871$	7.32120	+	12.6807i	0.248069	+	0.429669i
$872$		0			0
$873$	−18.9596			−0.641684
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.601541	−	1.04190i	−0.0203126	−	0.0351825i	0.855690	−	0.517488i	$-0.173133\pi$
$877$	−0.601541	−	1.04190i	−0.0203126	−	0.0351825i	−0.876003	+	0.482306i	$0.839799\pi$
$878$		0			0
$879$	−7.93648	−	13.7464i	−0.267691	−	0.463654i
$880$		0			0
$881$	−39.5743			−1.33329			−0.666646	−	0.745374i	$-0.732271\pi$
$881$	−39.5743			−1.33329			−0.666646	+	0.745374i	$0.732271\pi$
$882$		0			0
$883$	16.7178	−	28.9561i	0.562598	−	0.974449i	−0.434670	−	0.900590i	$-0.643135\pi$
$883$	16.7178	−	28.9561i	0.562598	−	0.974449i	0.997269	−	0.0738592i	$-0.0235315\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−18.7869	+	32.5399i	−0.630803	+	1.09258i	0.356585	+	0.934263i	$0.383941\pi$
$887$	−18.7869	+	32.5399i	−0.630803	+	1.09258i	−0.987388	+	0.158319i	$0.949392\pi$
$888$		0			0
$889$	−8.48978	+	14.7047i	−0.284738	+	0.493181i
$890$		0			0
$891$	2.83987	+	4.91880i	0.0951392	+	0.164786i
$892$		0			0
$893$	27.8531	−	4.92574i	0.932068	−	0.164834i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−8.22920	+	14.2534i	−0.274765	+	0.475907i
$898$		0			0
$899$	3.23606	−	5.60501i	0.107929	−	0.186938i
$900$		0			0
$901$	19.0824			0.635727
$902$		0			0
$903$	2.30056	−	3.98469i	0.0765579	−	0.132602i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−16.2915	−	28.2178i	−0.540951	−	0.936955i	−0.998850	−	0.0479506i	$-0.984731\pi$
$907$	−16.2915	−	28.2178i	−0.540951	−	0.936955i	0.457898	−	0.889005i	$-0.348602\pi$
$908$		0			0
$909$	−2.98442	−	5.16916i	−0.0989868	−	0.171450i
$910$		0			0
$911$	3.37691			0.111882			0.0559410	−	0.998434i	$-0.482184\pi$
$911$	3.37691			0.111882			0.0559410	+	0.998434i	$0.482184\pi$
$912$		0			0
$913$	16.0816			0.532225
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−17.8891	−	30.9848i	−0.590750	−	1.02321i
$918$		0			0
$919$	14.8096			0.488523			0.244262	−	0.969709i	$-0.421454\pi$
$919$	14.8096			0.488523			0.244262	+	0.969709i	$0.421454\pi$
$920$		0			0
$921$	−9.57989	+	16.5929i	−0.315668	+	0.546753i
$922$		0			0
$923$	−32.1209			−1.05727
$924$		0			0
$925$		0			0
$926$		0			0
$927$	11.3422	−	19.6452i	0.372525	−	0.645233i
$928$		0			0
$929$	25.5943	+	44.3307i	0.839723	+	1.45444i	0.890126	+	0.455714i	$0.150616\pi$
$929$	25.5943	+	44.3307i	0.839723	+	1.45444i	−0.0504032	+	0.998729i	$0.516051\pi$
$930$		0			0
$931$	−6.23589	−	7.42403i	−0.204373	−	0.243313i
$932$		0			0
$933$	17.4906	+	30.2946i	0.572617	+	0.991802i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	0.296297	−	0.513202i	0.00967961	−	0.0167656i	−0.861145	−	0.508359i	$-0.830252\pi$
$937$	0.296297	−	0.513202i	0.00967961	−	0.0167656i	0.870825	+	0.491594i	$0.163586\pi$
$938$		0			0
$939$	4.90071			0.159929
$940$		0			0
$941$	18.0480	−	31.2601i	0.588348	−	1.01905i	−0.406101	−	0.913828i	$-0.633112\pi$
$941$	18.0480	−	31.2601i	0.588348	−	1.01905i	0.994449	−	0.105220i	$-0.0335548\pi$
$942$		0			0
$943$	25.5910			0.833357
$944$		0			0
$945$		0			0
$946$		0			0
$947$	17.4620	+	30.2450i	0.567438	+	0.982831i	0.996818	+	0.0797073i	$0.0253986\pi$
$947$	17.4620	+	30.2450i	0.567438	+	0.982831i	−0.429381	+	0.903124i	$0.641268\pi$
$948$		0			0
$949$	−80.3200			−2.60730
$950$		0			0
$951$	11.7838			0.382115
$952$		0			0
$953$	−14.8329	−	25.6914i	−0.480485	−	0.832225i	0.519264	−	0.854614i	$-0.326206\pi$
$953$	−14.8329	−	25.6914i	−0.480485	−	0.832225i	−0.999749	+	0.0223888i	$0.992873\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	16.4398			0.531424
$958$		0			0
$959$	0.558708	−	0.967710i	0.0180416	−	0.0312490i
$960$		0			0
$961$	−29.8962			−0.964393
$962$		0			0
$963$	2.87447	−	4.97872i	0.0926284	−	0.160437i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−13.5515	−	23.4719i	−0.435788	−	0.754807i	0.561572	−	0.827428i	$-0.310197\pi$
$967$	−13.5515	−	23.4719i	−0.435788	−	0.754807i	−0.997360	+	0.0726212i	$0.976864\pi$
$968$		0			0
$969$	14.1306	−	2.49896i	0.453941	−	0.0802781i
$970$		0			0
$971$	23.4010	+	40.5316i	0.750973	+	1.30072i	0.947352	+	0.320195i	$0.103748\pi$
$971$	23.4010	+	40.5316i	0.750973	+	1.30072i	−0.196379	+	0.980528i	$0.562918\pi$
$972$		0			0
$973$	8.37617	−	14.5080i	0.268528	−	0.465104i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	42.0640			1.34575			0.672874	−	0.739757i	$-0.265060\pi$
$977$	42.0640			1.34575			0.672874	+	0.739757i	$0.265060\pi$
$978$		0			0
$979$	−16.4694	+	28.5258i	−0.526363	+	0.911687i
$980$		0			0
$981$	−6.32163			−0.201834
$982$		0			0
$983$	−8.61466	−	14.9210i	−0.274765	−	0.475907i	0.695311	−	0.718709i	$-0.255267\pi$
$983$	−8.61466	−	14.9210i	−0.274765	−	0.475907i	−0.970076	+	0.242802i	$0.921933\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−17.7704			−0.565638
$988$		0			0
$989$	4.27637			0.135981
$990$		0			0
$991$	3.75314	+	6.50063i	0.119223	+	0.206499i	0.919460	−	0.393184i	$-0.128626\pi$
$991$	3.75314	+	6.50063i	0.119223	+	0.206499i	−0.800237	+	0.599684i	$0.795293\pi$
$992$		0			0
$993$	−0.917368	−	1.58893i	−0.0291118	−	0.0504231i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	29.5433	−	51.1705i	0.935646	−	1.62059i	0.162167	−	0.986763i	$-0.448152\pi$
$997$	29.5433	−	51.1705i	0.935646	−	1.62059i	0.773478	−	0.633823i	$-0.218515\pi$
$998$		0			0
$999$	−12.5411			−0.396782

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1900.2.i.e.501.3	yes	12
5.2	odd	4		1900.2.s.e.349.5		24
5.3	odd	4		1900.2.s.e.349.8		24
5.4	even	2		1900.2.i.f.501.4	yes	12
19.11	even	3	inner	1900.2.i.e.201.3	✓	12
95.49	even	6		1900.2.i.f.201.4	yes	12
95.68	odd	12		1900.2.s.e.49.5		24
95.87	odd	12		1900.2.s.e.49.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1900.2.i.e.201.3	✓	12	19.11	even	3	inner
1900.2.i.e.501.3	yes	12	1.1	even	1	trivial
1900.2.i.f.201.4	yes	12	95.49	even	6
1900.2.i.f.501.4	yes	12	5.4	even	2
1900.2.s.e.49.5		24	95.68	odd	12
1900.2.s.e.49.8		24	95.87	odd	12
1900.2.s.e.349.5		24	5.2	odd	4
1900.2.s.e.349.8		24	5.3	odd	4

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:	\( N \)	\(=\)	\( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1900.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.626563 - 1.08524i) q^{3} +2.18534 q^{7} +(0.714838 - 1.23814i) q^{9} +O(q^{10})\)	\(q+(-0.626563 - 1.08524i) q^{3} +2.18534 q^{7} +(0.714838 - 1.23814i) q^{9} +2.12964 q^{11} +(2.58011 - 4.46889i) q^{13} +(1.31355 + 2.27514i) q^{17} +(2.80353 + 3.33770i) q^{19} +(-1.36925 - 2.37161i) q^{21} +(1.27261 - 2.20422i) q^{23} -5.55094 q^{27} +(-3.08011 + 5.33491i) q^{29} -1.05063 q^{31} +(-1.33435 - 2.31116i) q^{33} +2.25927 q^{37} -6.46641 q^{39} +(5.02728 + 8.70750i) q^{41} +(0.840080 + 1.45506i) q^{43} +(3.24455 - 5.61972i) q^{47} -2.22430 q^{49} +(1.64604 - 2.85103i) q^{51} +(3.63184 - 6.29053i) q^{53} +(1.86561 - 5.13378i) q^{57} +(3.53663 + 6.12563i) q^{59} +(5.41986 - 9.38748i) q^{61} +(1.56216 - 2.70574i) q^{63} +(-1.41877 + 2.45739i) q^{67} -3.18947 q^{69} +(-3.11236 - 5.39076i) q^{71} +(-7.78260 - 13.4799i) q^{73} +4.65397 q^{77} +(2.80671 + 4.86136i) q^{79} +(1.33350 + 2.30969i) q^{81} +7.55136 q^{83} +7.71954 q^{87} +(-7.73341 + 13.3947i) q^{89} +(5.63842 - 9.76603i) q^{91} +(0.658285 + 1.14018i) q^{93} +(-6.63073 - 11.4848i) q^{97} +(1.52234 - 2.63678i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 - 3 * q^9	\( 12 q - 3 q^{3} - 3 q^{9} + 2 q^{11} - 7 q^{13} + q^{17} + q^{21} + 2 q^{23} + 24 q^{27} + q^{29} + 2 q^{31} - 10 q^{33} - 20 q^{37} + 36 q^{39} - 7 q^{41} - 19 q^{43} + 14 q^{47} + 8 q^{49} + 11 q^{51} - 6 q^{53} + 28 q^{57} - 5 q^{61} + 11 q^{63} - 14 q^{67} - 14 q^{69} + 8 q^{71} + 9 q^{73} - 2 q^{77} + q^{79} + 2 q^{81} + 26 q^{83} - 30 q^{87} - 8 q^{89} + 3 q^{91} - 9 q^{93} + 11 q^{97} - 18 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 - 3 * q^9 + 2 * q^11 - 7 * q^13 + q^17 + q^21 + 2 * q^23 + 24 * q^27 + q^29 + 2 * q^31 - 10 * q^33 - 20 * q^37 + 36 * q^39 - 7 * q^41 - 19 * q^43 + 14 * q^47 + 8 * q^49 + 11 * q^51 - 6 * q^53 + 28 * q^57 - 5 * q^61 + 11 * q^63 - 14 * q^67 - 14 * q^69 + 8 * q^71 + 9 * q^73 - 2 * q^77 + q^79 + 2 * q^81 + 26 * q^83 - 30 * q^87 - 8 * q^89 + 3 * q^91 - 9 * q^93 + 11 * q^97 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more