LMFDB - Embedded newform 1900.2.s.c.349.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1900,2,Mod(49,1900)]

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, 3, 4]))

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

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

chi := DirichletCharacter("1900.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1900 = 2^{2} \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1900.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.1715763840$
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} - 9x^{10} + 59x^{8} - 180x^{6} + 403x^{4} - 198x^{2} + 81 $ x^12 - 9x^10 + 59x^8 - 180x^6 + 403x^4 - 198*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 380)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.2
Root			$-1.65604 - 0.956115i$ of defining polynomial
Character	$\chi$	$=$	1900.349
Dual form			1900.2.s.c.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.22469 + 1.28442i) q^{3} +3.56885i q^{7} +(1.79949 - 3.11682i) q^{9} +O(q^{10})$	$q+(-2.22469 + 1.28442i) q^{3} +3.56885i q^{7} +(1.79949 - 3.11682i) q^{9} +4.56885 q^{11} +(-0.866025 - 0.500000i) q^{13} +(4.96812 - 2.86834i) q^{17} +(4.35327 + 0.221364i) q^{19} +(-4.58392 - 7.93958i) q^{21} +(-4.84887 - 2.79949i) q^{23} +1.53871i q^{27} +(3.38341 - 5.86024i) q^{29} +4.59899 q^{31} +(-10.1643 + 5.86834i) q^{33} +3.56885i q^{37} +2.56885 q^{39} +(-5.35327 - 9.27214i) q^{41} +(9.79088 - 5.65277i) q^{43} +(5.86024 + 3.38341i) q^{47} -5.73669 q^{49} +(-7.36834 + 12.7623i) q^{51} +(-2.94536 - 1.70051i) q^{53} +(-9.96901 + 5.09899i) q^{57} +(-3.38341 - 5.86024i) q^{59} +(-4.06885 + 7.04745i) q^{61} +(11.1234 + 6.42212i) q^{63} +(5.48686 + 3.16784i) q^{67} +14.3830 q^{69} +(0.515069 + 0.892126i) q^{71} +(11.0303 - 6.36834i) q^{73} +16.3055i q^{77} +(2.43115 + 4.21088i) q^{79} +(3.42212 + 5.92729i) q^{81} +9.40101i q^{83} +17.3830i q^{87} +(6.13770 - 10.6308i) q^{89} +(1.78442 - 3.09071i) q^{91} +(-10.2313 + 5.90705i) q^{93} +(2.27689 - 1.31456i) q^{97} +(8.22162 - 14.2403i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 16 q^{9}+O(q^{10}) $ 12 * q + 16 * q^9	$ 12 q + 16 q^{9} + 20 q^{11} - 32 q^{21} + 12 q^{29} + 44 q^{31} - 4 q^{39} - 12 q^{41} + 12 q^{49} - 48 q^{51} - 12 q^{59} - 14 q^{61} - 60 q^{69} + 18 q^{71} + 64 q^{79} - 46 q^{81} + 4 q^{89} + 4 q^{91} + 6 q^{99}+O(q^{100}) $ 12 * q + 16 * q^9 + 20 * q^11 - 32 * q^21 + 12 * q^29 + 44 * q^31 - 4 * q^39 - 12 * q^41 + 12 * q^49 - 48 * q^51 - 12 * q^59 - 14 * q^61 - 60 * q^69 + 18 * q^71 + 64 * q^79 - 46 * q^81 + 4 * q^89 + 4 * q^91 + 6 * 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
$3$	−2.22469	+	1.28442i	−1.28442	+	0.741563i	−0.977654	−	0.210220i	$-0.932582\pi$
$3$	−2.22469	+	1.28442i	−1.28442	+	0.741563i	−0.306771	+	0.951783i	$0.599249\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$			3.56885i			1.34890i	0.738321	+	0.674449i	$0.235619\pi$
$7$			3.56885i			1.34890i	−0.738321	+	0.674449i	$0.764381\pi$
$8$		0			0
$9$	1.79949	−	3.11682i	0.599831	−	1.03894i
$10$		0			0
$11$	4.56885			1.37756			0.688780	−	0.724970i	$-0.258147\pi$
$11$	4.56885			1.37756			0.688780	+	0.724970i	$0.258147\pi$
$12$		0			0
$13$	−0.866025	−	0.500000i	−0.240192	−	0.138675i	0.375073	−	0.926995i	$-0.377618\pi$
$13$	−0.866025	−	0.500000i	−0.240192	−	0.138675i	−0.615265	+	0.788320i	$0.710951\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	4.96812	−	2.86834i	1.20495	−	0.695676i	0.243295	−	0.969952i	$-0.421772\pi$
$17$	4.96812	−	2.86834i	1.20495	−	0.695676i	0.961651	+	0.274277i	$0.0884385\pi$
$18$		0			0
$19$	4.35327	+	0.221364i	0.998710	+	0.0507843i
$19$	4.35327	+	0.221364i	0.998710	+	0.0507843i
$20$		0			0
$21$	−4.58392	−	7.93958i	−1.00029	−	1.73256i
$22$		0			0
$23$	−4.84887	−	2.79949i	−1.01106	−	0.583735i	−0.0995571	−	0.995032i	$-0.531743\pi$
$23$	−4.84887	−	2.79949i	−1.01106	−	0.583735i	−0.911501	+	0.411297i	$0.865076\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			1.53871i			0.296125i
$28$		0			0
$29$	3.38341	−	5.86024i	0.628284	−	1.08822i	−0.359612	−	0.933102i	$-0.617091\pi$
$29$	3.38341	−	5.86024i	0.628284	−	1.08822i	0.987896	−	0.155118i	$-0.0495758\pi$
$30$		0			0
$31$	4.59899			0.826003			0.413001	−	0.910730i	$-0.364480\pi$
$31$	4.59899			0.826003			0.413001	+	0.910730i	$0.364480\pi$
$32$		0			0
$33$	−10.1643	+	5.86834i	−1.76937	+	1.02155i
$34$		0			0
$35$		0			0
$36$		0			0
$37$			3.56885i			0.586715i	0.956003	+	0.293358i	$0.0947727\pi$
$37$			3.56885i			0.586715i	−0.956003	+	0.293358i	$0.905227\pi$
$38$		0			0
$39$	2.56885			0.411345
$40$		0			0
$41$	−5.35327	−	9.27214i	−0.836041	−	1.44807i	−0.893180	−	0.449699i	$-0.851531\pi$
$41$	−5.35327	−	9.27214i	−0.836041	−	1.44807i	0.0571390	−	0.998366i	$-0.481802\pi$
$42$		0			0
$43$	9.79088	−	5.65277i	1.49310	−	0.862039i	0.493127	−	0.869957i	$-0.335854\pi$
$43$	9.79088	−	5.65277i	1.49310	−	0.862039i	0.999969	+	0.00791826i	$0.00252049\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.86024	+	3.38341i	0.854804	+	0.493522i	0.862269	−	0.506451i	$-0.169043\pi$
$47$	5.86024	+	3.38341i	0.854804	+	0.493522i	−0.00746461	+	0.999972i	$0.502376\pi$
$48$		0			0
$49$	−5.73669			−0.819527
$50$		0			0
$51$	−7.36834	+	12.7623i	−1.03177	+	1.78709i
$52$		0			0
$53$	−2.94536	−	1.70051i	−0.404577	−	0.233582i	0.283880	−	0.958860i	$-0.408378\pi$
$53$	−2.94536	−	1.70051i	−0.404577	−	0.233582i	−0.688457	+	0.725277i	$0.741712\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−9.96901	+	5.09899i	−1.32043	+	0.675378i
$58$		0			0
$59$	−3.38341	−	5.86024i	−0.440483	−	0.762939i	0.557242	−	0.830350i	$-0.311859\pi$
$59$	−3.38341	−	5.86024i	−0.440483	−	0.762939i	−0.997725	+	0.0674112i	$0.978526\pi$
$60$		0			0
$61$	−4.06885	+	7.04745i	−0.520963	+	0.902334i	0.478740	+	0.877957i	$0.341094\pi$
$61$	−4.06885	+	7.04745i	−0.520963	+	0.902334i	−0.999703	+	0.0243773i	$0.992240\pi$
$62$		0			0
$63$	11.1234	+	6.42212i	1.40142	+	0.809112i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	5.48686	+	3.16784i	0.670326	+	0.387013i	0.796200	−	0.605033i	$-0.206840\pi$
$67$	5.48686	+	3.16784i	0.670326	+	0.387013i	−0.125874	+	0.992046i	$0.540174\pi$
$68$		0			0
$69$	14.3830			1.73150
$70$		0			0
$71$	0.515069	+	0.892126i	0.0611275	+	0.105876i	0.894970	−	0.446127i	$-0.147197\pi$
$71$	0.515069	+	0.892126i	0.0611275	+	0.105876i	−0.833842	+	0.552003i	$0.813864\pi$
$72$		0			0
$73$	11.0303	−	6.36834i	1.29100	−	0.745358i	0.312167	−	0.950027i	$-0.398945\pi$
$73$	11.0303	−	6.36834i	1.29100	−	0.745358i	0.978831	+	0.204669i	$0.0656118\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			16.3055i			1.85819i
$78$		0			0
$79$	2.43115	+	4.21088i	0.273526	+	0.473761i	0.969762	−	0.244052i	$-0.0784768\pi$
$79$	2.43115	+	4.21088i	0.273526	+	0.473761i	−0.696236	+	0.717813i	$0.745143\pi$
$80$		0			0
$81$	3.42212	+	5.92729i	0.380236	+	0.658588i
$82$		0			0
$83$			9.40101i			1.03190i	0.856620	+	0.515948i	$0.172560\pi$
$83$			9.40101i			1.03190i	−0.856620	+	0.515948i	$0.827440\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$			17.3830i			1.86365i
$88$		0			0
$89$	6.13770	−	10.6308i	0.650595	−	1.12686i	−0.332384	−	0.943144i	$-0.607853\pi$
$89$	6.13770	−	10.6308i	0.650595	−	1.12686i	0.982979	−	0.183719i	$-0.0588137\pi$
$90$		0			0
$91$	1.78442	−	3.09071i	0.187059	−	0.323995i
$92$		0			0
$93$	−10.2313	+	5.90705i	−1.06094	+	0.612533i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	2.27689	−	1.31456i	0.231183	−	0.133474i	−0.379935	−	0.925013i	$-0.624053\pi$
$97$	2.27689	−	1.31456i	0.231183	−	0.133474i	0.611118	+	0.791540i	$0.290720\pi$
$98$		0			0
$99$	8.22162	−	14.2403i	0.826304	−	1.43120i
$100$		0			0
$101$	−4.43719	+	7.68544i	−0.441517	+	0.764730i	−0.997802	−	0.0662612i	$-0.978893\pi$
$101$	−4.43719	+	7.68544i	−0.441517	+	0.764730i	0.556285	+	0.830992i	$0.312226\pi$
$102$		0			0
$103$			4.40101i			0.433645i	0.976211	+	0.216822i	$0.0695692\pi$
$103$			4.40101i			0.433645i	−0.976211	+	0.216822i	$0.930431\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	13.9347i		−	1.34711i	−0.739135	−	0.673557i	$-0.764765\pi$
$107$		−	13.9347i		−	1.34711i	0.739135	−	0.673557i	$-0.235235\pi$
$108$		0			0
$109$	1.91608	+	3.31875i	0.183527	+	0.317879i	0.943079	−	0.332568i	$-0.107915\pi$
$109$	1.91608	+	3.31875i	0.183527	+	0.317879i	−0.759552	+	0.650447i	$0.774582\pi$
$110$		0			0
$111$	−4.58392	−	7.93958i	−0.435086	−	0.753592i
$112$		0			0
$113$			1.70655i			0.160539i	0.996773	+	0.0802693i	$0.0255780\pi$
$113$			1.70655i			0.160539i	−0.996773	+	0.0802693i	$0.974422\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−3.11682	+	1.79949i	−0.288150	+	0.166363i
$118$		0			0
$119$	10.2367	+	17.7305i	0.938396	+	1.62535i
$120$		0			0
$121$	9.87439			0.897672
$122$		0			0
$123$	23.8187	+	13.7518i	2.14766	+	1.23995i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−13.0574	−	7.53871i	−1.15866	−	0.668952i	−0.207677	−	0.978197i	$-0.566590\pi$
$127$	−13.0574	−	7.53871i	−1.15866	−	0.668952i	−0.950982	+	0.309245i	$0.899924\pi$
$128$		0			0
$129$	−14.5211	+	25.1513i	−1.27851	+	2.21445i
$130$		0			0
$131$	6.78442	+	11.7510i	0.592758	+	1.02669i	0.993859	+	0.110653i	$0.0352943\pi$
$131$	6.78442	+	11.7510i	0.592758	+	1.02669i	−0.401101	+	0.916034i	$0.631372\pi$
$132$		0			0
$133$	−0.790014	+	15.5362i	−0.0685029	+	1.34716i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.08828	−	3.51507i	−0.520157	−	0.300313i	0.216842	−	0.976207i	$-0.430424\pi$
$137$	−6.08828	−	3.51507i	−0.520157	−	0.300313i	−0.736999	+	0.675894i	$0.763758\pi$
$138$		0			0
$139$	−6.09899	+	10.5638i	−0.517309	+	0.896006i	0.482488	+	0.875902i	$0.339733\pi$
$139$	−6.09899	+	10.5638i	−0.517309	+	0.896006i	−0.999798	+	0.0201039i	$0.993600\pi$
$140$		0			0
$141$	−17.3830			−1.46391
$142$		0			0
$143$	−3.95674	−	2.28442i	−0.330879	−	0.191033i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	12.7623	−	7.36834i	1.05262	−	0.607731i
$148$		0			0
$149$	4.76936	+	8.26077i	0.390721	+	0.676748i	0.992545	−	0.121880i	$-0.0388925\pi$
$149$	4.76936	+	8.26077i	0.390721	+	0.676748i	−0.601824	+	0.798629i	$0.705559\pi$
$150$		0			0
$151$	20.4131			1.66119			0.830597	−	0.556874i	$-0.187999\pi$
$151$	20.4131			1.66119			0.830597	+	0.556874i	$0.187999\pi$
$152$		0			0
$153$		−	20.6463i		−	1.66915i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−12.3890	+	7.15277i	−0.988747	+	0.570853i	−0.904899	−	0.425626i	$-0.860054\pi$
$157$	−12.3890	+	7.15277i	−0.988747	+	0.570853i	−0.0838472	+	0.996479i	$0.526721\pi$
$158$		0			0
$159$	8.73669			0.692864
$160$		0			0
$161$	9.99097	−	17.3049i	0.787399	−	1.36382i
$162$		0			0
$163$		−	2.53871i		−	0.198847i	−0.995045	−	0.0994236i	$-0.968300\pi$
$163$		−	2.53871i		−	0.198847i	0.995045	−	0.0994236i	$-0.0316999\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	11.7510	+	6.78442i	0.909317	+	0.524995i	0.880211	−	0.474582i	$-0.157401\pi$
$167$	11.7510	+	6.78442i	0.909317	+	0.524995i	0.0291058	+	0.999576i	$0.490734\pi$
$168$		0			0
$169$	−6.00000	−	10.3923i	−0.461538	−	0.799408i
$170$		0			0
$171$	8.52364	−	13.1700i	0.651819	−	1.00714i
$172$		0			0
$173$	−2.05324	+	1.18544i	−0.156105	+	0.0901271i	−0.576017	−	0.817437i	$-0.695394\pi$
$173$	−2.05324	+	1.18544i	−0.156105	+	0.0901271i	0.419913	+	0.907564i	$0.362061\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	15.0541	+	8.69148i	1.13153	+	0.653292i
$178$		0			0
$179$	−17.8744			−1.33599			−0.667997	−	0.744164i	$-0.732848\pi$
$179$	−17.8744			−1.33599			−0.667997	+	0.744164i	$0.732848\pi$
$180$		0			0
$181$	−13.2065	+	22.8744i	−0.981635	+	1.70024i	−0.325607	+	0.945505i	$0.605569\pi$
$181$	−13.2065	+	22.8744i	−0.981635	+	1.70024i	−0.656028	+	0.754737i	$0.727765\pi$
$182$		0			0
$183$		−	20.9045i		−	1.54531i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	22.6986	−	13.1050i	1.65988	−	0.958335i
$188$		0			0
$189$	−5.49143			−0.399443
$190$		0			0
$191$	0.526625			0.0381052			0.0190526	−	0.999818i	$-0.493935\pi$
$191$	0.526625			0.0381052			0.0190526	+	0.999818i	$0.493935\pi$
$192$		0			0
$193$	4.62521	−	2.67037i	0.332930	−	0.192217i	−0.324211	−	0.945985i	$-0.605099\pi$
$193$	4.62521	−	2.67037i	0.332930	−	0.192217i	0.657141	+	0.753767i	$0.271766\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	4.43115i		−	0.315706i	−0.987463	−	0.157853i	$-0.949543\pi$
$197$		−	4.43115i		−	0.315706i	0.987463	−	0.157853i	$-0.0504573\pi$
$198$		0			0
$199$	6.08392	−	10.5377i	0.431278	−	0.746995i	−0.565706	−	0.824607i	$-0.691396\pi$
$199$	6.08392	−	10.5377i	0.431278	−	0.746995i	0.996984	+	0.0776123i	$0.0247296\pi$
$200$		0			0
$201$	−16.2754			−1.14798
$202$		0			0
$203$	20.9143	+	12.0749i	1.46790	+	0.847491i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−17.4510	+	10.0753i	−1.21293	+	0.700285i
$208$		0			0
$209$	19.8895	+	1.01138i	1.37578	+	0.0699584i
$210$		0			0
$211$	10.3357	+	17.9019i	0.711537	+	1.23242i	0.964280	+	0.264885i	$0.0853341\pi$
$211$	10.3357	+	17.9019i	0.711537	+	1.23242i	−0.252743	+	0.967534i	$0.581333\pi$
$212$		0			0
$213$	−2.29174	−	1.32314i	−0.157027	−	0.0906598i
$214$		0			0
$215$		0			0
$216$		0			0
$217$			16.4131i			1.11419i
$218$		0			0
$219$	−16.3593	+	28.3352i	−1.10546	+	1.91471i
$220$		0			0
$221$	−5.73669			−0.385891
$222$		0			0
$223$	−3.90454	+	2.25429i	−0.261467	+	0.150958i	−0.625004	−	0.780622i	$-0.714903\pi$
$223$	−3.90454	+	2.25429i	−0.261467	+	0.150958i	0.363536	+	0.931580i	$0.381569\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		−	16.6714i		−	1.10652i	−0.833010	−	0.553258i	$-0.813384\pi$
$227$		−	16.6714i		−	1.10652i	0.833010	−	0.553258i	$-0.186616\pi$
$228$		0			0
$229$	−5.31060			−0.350934			−0.175467	−	0.984485i	$-0.556144\pi$
$229$	−5.31060			−0.350934			−0.175467	+	0.984485i	$0.556144\pi$
$230$		0			0
$231$	−20.9432	−	36.2747i	−1.37796	−	2.38670i
$232$		0			0
$233$	2.40052	−	1.38594i	0.157263	−	0.0907961i	−0.419303	−	0.907846i	$-0.637726\pi$
$233$	2.40052	−	1.38594i	0.157263	−	0.0907961i	0.576566	+	0.817050i	$0.304392\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−10.8171	−	6.24526i	−0.702647	−	0.405673i
$238$		0			0
$239$	8.59899			0.556222			0.278111	−	0.960549i	$-0.410292\pi$
$239$	8.59899			0.556222			0.278111	+	0.960549i	$0.410292\pi$
$240$		0			0
$241$	−2.83216	+	4.90545i	−0.182436	+	0.315988i	−0.942709	−	0.333615i	$-0.891731\pi$
$241$	−2.83216	+	4.90545i	−0.182436	+	0.315988i	0.760274	+	0.649603i	$0.225065\pi$
$242$		0			0
$243$	−19.2240	−	11.0990i	−1.23322	−	0.712000i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−3.65936	−	2.36834i	−0.232840	−	0.150694i
$248$		0			0
$249$	−12.0749	−	20.9143i	−0.765215	−	1.32539i
$250$		0			0
$251$	11.5598	−	20.0222i	0.729650	−	1.26379i	−0.227382	−	0.973806i	$-0.573017\pi$
$251$	11.5598	−	20.0222i	0.729650	−	1.26379i	0.957031	−	0.289984i	$-0.0936501\pi$
$252$		0			0
$253$	−22.1537	−	12.7905i	−1.39279	−	0.804130i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	9.15289	+	5.28442i	0.570942	+	0.329633i	0.757525	−	0.652806i	$-0.226408\pi$
$257$	9.15289	+	5.28442i	0.570942	+	0.329633i	−0.186584	+	0.982439i	$0.559742\pi$
$258$		0			0
$259$	−12.7367			−0.791419
$260$		0			0
$261$	−12.1769	−	21.0909i	−0.753729	−	1.30550i
$262$		0			0
$263$	−7.67498	+	4.43115i	−0.473259	+	0.273236i	−0.717603	−	0.696452i	$-0.754761\pi$
$263$	−7.67498	+	4.43115i	−0.473259	+	0.273236i	0.244344	+	0.969689i	$0.421427\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			31.5337i			1.92983i
$268$		0			0
$269$	2.66784	+	4.62083i	0.162661	+	0.281737i	0.935822	−	0.352472i	$-0.114659\pi$
$269$	2.66784	+	4.62083i	0.162661	+	0.281737i	−0.773161	+	0.634210i	$0.781326\pi$
$270$		0			0
$271$	−2.23064	−	3.86359i	−0.135502	−	0.234696i	0.790287	−	0.612737i	$-0.209931\pi$
$271$	−2.23064	−	3.86359i	−0.135502	−	0.234696i	−0.925789	+	0.378040i	$0.876598\pi$
$272$		0			0
$273$			9.16784i			0.554863i
$274$		0			0
$275$		0			0
$276$		0			0
$277$		−	23.0774i		−	1.38659i	−0.720655	−	0.693294i	$-0.756159\pi$
$277$		−	23.0774i		−	1.38659i	0.720655	−	0.693294i	$-0.243841\pi$
$278$		0			0
$279$	8.27585	−	14.3342i	0.495462	−	0.858166i
$280$		0			0
$281$	−2.01507	+	3.49020i	−0.120209	+	0.208208i	−0.919850	−	0.392270i	$-0.871690\pi$
$281$	−2.01507	+	3.49020i	−0.120209	+	0.208208i	0.799641	+	0.600478i	$0.205023\pi$
$282$		0			0
$283$	−27.5735	+	15.9196i	−1.63908	+	0.946322i	−0.657925	+	0.753083i	$0.728566\pi$
$283$	−27.5735	+	15.9196i	−1.63908	+	0.946322i	−0.981152	+	0.193239i	$0.938101\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	33.0909	−	19.1050i	1.95329	−	1.12773i
$288$		0			0
$289$	7.95479	−	13.7781i	0.467929	−	0.810477i
$290$		0			0
$291$	−3.37692	+	5.84899i	−0.197958	+	0.342874i
$292$		0			0
$293$			18.6764i			1.09109i	0.838082	+	0.545544i	$0.183677\pi$
$293$			18.6764i			1.09109i	−0.838082	+	0.545544i	$0.816323\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$			7.03014i			0.407930i
$298$		0			0
$299$	2.79949	+	4.84887i	0.161899	+	0.280417i
$300$		0			0
$301$	20.1739	+	34.9422i	1.16280	+	2.01403i
$302$		0			0
$303$		−	22.7970i		−	1.30965i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−27.5318	+	15.8955i	−1.57132	+	0.907204i	−0.575316	+	0.817931i	$0.695121\pi$
$307$	−27.5318	+	15.8955i	−1.57132	+	0.907204i	−0.996007	+	0.0892730i	$0.971546\pi$
$308$		0			0
$309$	−5.65277	−	9.79088i	−0.321575	−	0.556984i
$310$		0			0
$311$	2.37087			0.134440			0.0672199	−	0.997738i	$-0.478587\pi$
$311$	2.37087			0.134440			0.0672199	+	0.997738i	$0.478587\pi$
$312$		0			0
$313$	−10.5742	−	6.10503i	−0.597691	−	0.345077i	0.170442	−	0.985368i	$-0.445480\pi$
$313$	−10.5742	−	6.10503i	−0.597691	−	0.345077i	−0.768132	+	0.640291i	$0.778814\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−24.6326	−	14.2216i	−1.38350	−	0.798766i	−0.390930	−	0.920420i	$-0.627847\pi$
$317$	−24.6326	−	14.2216i	−1.38350	−	0.798766i	−0.992572	+	0.121655i	$0.961180\pi$
$318$		0			0
$319$	15.4583	−	26.7746i	0.865499	−	1.49909i
$320$		0			0
$321$	17.8980	+	31.0003i	0.998971	+	1.73027i
$322$		0			0
$323$	22.2625	−	11.3869i	1.23872	−	0.633586i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−8.52537	−	4.92212i	−0.471454	−	0.272194i
$328$		0			0
$329$	−12.0749	+	20.9143i	−0.665710	+	1.15304i
$330$		0			0
$331$	−32.5930			−1.79147			−0.895737	−	0.444584i	$-0.853352\pi$
$331$	−32.5930			−1.79147			−0.895737	+	0.444584i	$0.853352\pi$
$332$		0			0
$333$	11.1234	+	6.42212i	0.609561	+	0.351930i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	10.1016	−	5.83216i	0.550269	−	0.317698i	−0.198961	−	0.980007i	$-0.563757\pi$
$337$	10.1016	−	5.83216i	0.550269	−	0.317698i	0.749231	+	0.662309i	$0.230423\pi$
$338$		0			0
$339$	−2.19193	−	3.79654i	−0.119049	−	0.206200i
$340$		0			0
$341$	21.0121			1.13787
$342$		0			0
$343$			4.50857i			0.243440i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	26.2602	−	15.1613i	1.40972	−	0.813903i	0.414361	−	0.910113i	$-0.364005\pi$
$347$	26.2602	−	15.1613i	1.40972	−	0.813903i	0.995361	+	0.0962092i	$0.0306718\pi$
$348$		0			0
$349$	−3.44324			−0.184312			−0.0921561	−	0.995745i	$-0.529376\pi$
$349$	−3.44324			−0.184312			−0.0921561	+	0.995745i	$0.529376\pi$
$350$		0			0
$351$	0.769355	−	1.33256i	0.0410652	−	0.0711269i
$352$		0			0
$353$			6.53871i			0.348020i	0.984744	+	0.174010i	$0.0556726\pi$
$353$			6.53871i			0.348020i	−0.984744	+	0.174010i	$0.944327\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−45.5469	−	26.2965i	−2.41060	−	1.39176i
$358$		0			0
$359$	−11.2392	−	19.4669i	−0.593183	−	1.02742i	−0.993801	−	0.111178i	$-0.964538\pi$
$359$	−11.2392	−	19.4669i	−0.593183	−	1.02742i	0.400617	−	0.916245i	$-0.368796\pi$
$360$		0			0
$361$	18.9020	+	1.92731i	0.994842	+	0.101438i
$362$		0			0
$363$	−21.9674	+	12.6829i	−1.15299	+	0.665680i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−7.44256	−	4.29696i	−0.388499	−	0.224300i	0.293011	−	0.956109i	$-0.405343\pi$
$367$	−7.44256	−	4.29696i	−0.388499	−	0.224300i	−0.681509	+	0.731809i	$0.738676\pi$
$368$		0			0
$369$	−38.5327			−2.00593
$370$		0			0
$371$	6.06885	−	10.5116i	0.315079	−	0.545733i
$372$		0			0
$373$		−	37.2453i		−	1.92849i	−0.265019	−	0.964243i	$-0.585378\pi$
$373$		−	37.2453i		−	1.92849i	0.265019	−	0.964243i	$-0.414622\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−5.86024	+	3.38341i	−0.301818	+	0.174255i
$378$		0			0
$379$	−12.1678			−0.625020			−0.312510	−	0.949914i	$-0.601170\pi$
$379$	−12.1678			−0.625020			−0.312510	+	0.949914i	$0.601170\pi$
$380$		0			0
$381$	38.7316			1.98428
$382$		0			0
$383$	21.6977	−	12.5272i	1.10870	−	0.640108i	0.170207	−	0.985408i	$-0.445556\pi$
$383$	21.6977	−	12.5272i	1.10870	−	0.640108i	0.938492	+	0.345301i	$0.112223\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		−	40.6885i		−	2.06831i
$388$		0			0
$389$	11.0211	−	19.0891i	0.558793	−	0.967857i	−0.438805	−	0.898582i	$-0.644598\pi$
$389$	11.0211	−	19.0891i	0.558793	−	0.967857i	0.997598	−	0.0692748i	$-0.0220685\pi$
$390$		0			0
$391$	−32.1196			−1.62436
$392$		0			0
$393$	−30.1865	−	17.4282i	−1.52271	−	0.879135i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	31.3327	−	18.0900i	1.57254	−	0.907909i	0.576689	−	0.816964i	$-0.304344\pi$
$397$	31.3327	−	18.0900i	1.57254	−	0.907909i	0.995856	−	0.0909453i	$-0.0289889\pi$
$398$		0			0
$399$	−18.1975	−	35.5779i	−0.911016	−	1.78112i
$400$		0			0
$401$	−13.9583	−	24.1765i	−0.697045	−	1.20732i	−0.969487	−	0.245144i	$-0.921165\pi$
$401$	−13.9583	−	24.1765i	−0.697045	−	1.20732i	0.272442	−	0.962172i	$-0.412169\pi$
$402$		0			0
$403$	−3.98284	−	2.29949i	−0.198399	−	0.114546i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			16.3055i			0.808235i
$408$		0			0
$409$	4.06281	−	7.03699i	0.200893	−	0.347957i	−0.747924	−	0.663785i	$-0.768949\pi$
$409$	4.06281	−	7.03699i	0.200893	−	0.347957i	0.948816	+	0.315828i	$0.102282\pi$
$410$		0			0
$411$	18.0594			0.890803
$412$		0			0
$413$	20.9143	−	12.0749i	1.02913	−	0.594167i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		−	31.3348i		−	1.53447i
$418$		0			0
$419$	2.87439			0.140423			0.0702115	−	0.997532i	$-0.477633\pi$
$419$	2.87439			0.140423			0.0702115	+	0.997532i	$0.477633\pi$
$420$		0			0
$421$	3.48240	+	6.03170i	0.169722	+	0.293967i	0.938322	−	0.345763i	$-0.112380\pi$
$421$	3.48240	+	6.03170i	0.169722	+	0.293967i	−0.768600	+	0.639729i	$0.779046\pi$
$422$		0			0
$423$	21.0909	−	12.1769i	1.02548	−	0.592059i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−25.1513	−	14.5211i	−1.21716	−	0.702726i
$428$		0			0
$429$	11.7367			0.566653
$430$		0			0
$431$	5.08996	−	8.81607i	0.245175	−	0.424655i	−0.717006	−	0.697067i	$-0.754488\pi$
$431$	5.08996	−	8.81607i	0.245175	−	0.424655i	0.962181	+	0.272412i	$0.0878213\pi$
$432$		0			0
$433$	−17.1186	−	9.88341i	−0.822666	−	0.474967i	0.0286689	−	0.999589i	$-0.490873\pi$
$433$	−17.1186	−	9.88341i	−0.822666	−	0.474967i	−0.851335	+	0.524622i	$0.824207\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−20.4887	−	13.2603i	−0.980109	−	0.634328i
$438$		0			0
$439$	19.3266	+	33.4747i	0.922411	+	1.59766i	0.795673	+	0.605726i	$0.207117\pi$
$439$	19.3266	+	33.4747i	0.922411	+	1.59766i	0.126737	+	0.991936i	$0.459550\pi$
$440$		0			0
$441$	−10.3231	+	17.8802i	−0.491578	+	0.851438i
$442$		0			0
$443$	9.27214	+	5.35327i	0.440533	+	0.254342i	0.703824	−	0.710375i	$-0.251475\pi$
$443$	9.27214	+	5.35327i	0.440533	+	0.254342i	−0.263291	+	0.964717i	$0.584808\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−21.2207	−	12.2518i	−1.00370	−	0.579488i
$448$		0			0
$449$	−23.0724			−1.08885			−0.544426	−	0.838809i	$-0.683253\pi$
$449$	−23.0724			−1.08885			−0.544426	+	0.838809i	$0.683253\pi$
$450$		0			0
$451$	−24.4583	−	42.3630i	−1.15170	−	1.99480i
$452$		0			0
$453$	−45.4128	+	26.2191i	−2.13368	+	1.23188i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	6.87439i		−	0.321570i	−0.986989	−	0.160785i	$-0.948597\pi$
$457$		−	6.87439i		−	0.321570i	0.986989	−	0.160785i	$-0.0514026\pi$
$458$		0			0
$459$	4.41355	+	7.64450i	0.206007	+	0.356815i
$460$		0			0
$461$	1.41355	+	2.44834i	0.0658357	+	0.114031i	0.897064	−	0.441900i	$-0.145695\pi$
$461$	1.41355	+	2.44834i	0.0658357	+	0.114031i	−0.831229	+	0.555931i	$0.812362\pi$
$462$		0			0
$463$			23.9347i			1.11234i	0.831069	+	0.556169i	$0.187729\pi$
$463$			23.9347i			1.11234i	−0.831069	+	0.556169i	$0.812271\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			33.5508i			1.55255i	0.630397	+	0.776273i	$0.282892\pi$
$467$			33.5508i			1.55255i	−0.630397	+	0.776273i	$0.717108\pi$
$468$		0			0
$469$	−11.3055	+	19.5818i	−0.522041	+	0.904202i
$470$		0			0
$471$	18.3744	−	31.8254i	0.846647	−	1.46644i
$472$		0			0
$473$	44.7331	−	25.8266i	2.05683	−	1.18751i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−10.6003	+	6.12010i	−0.485356	+	0.280220i
$478$		0			0
$479$	−18.4583	+	31.9707i	−0.843382	+	1.46078i	0.0436379	+	0.999047i	$0.486105\pi$
$479$	−18.4583	+	31.9707i	−0.843382	+	1.46078i	−0.887019	+	0.461732i	$0.847228\pi$
$480$		0			0
$481$	1.78442	−	3.09071i	0.0813628	−	0.140924i
$482$		0			0
$483$			51.3306i			2.33562i
$484$		0			0
$485$		0			0
$486$		0			0
$487$		−	12.8744i		−	0.583394i	−0.956511	−	0.291697i	$-0.905780\pi$
$487$		−	12.8744i		−	0.583394i	0.956511	−	0.291697i	$-0.0942199\pi$
$488$		0			0
$489$	3.26078	+	5.64784i	0.147458	+	0.255404i
$490$		0			0
$491$	12.3382	+	21.3704i	0.556815	+	0.964433i	0.997760	+	0.0668981i	$0.0213103\pi$
$491$	12.3382	+	21.3704i	0.556815	+	0.964433i	−0.440944	+	0.897534i	$0.645356\pi$
$492$		0			0
$493$		−	38.8192i		−	1.74833i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−3.18386	+	1.83821i	−0.142816	+	0.0824548i
$498$		0			0
$499$	15.7603	+	27.2977i	0.705529	+	1.22201i	0.966500	+	0.256666i	$0.0826240\pi$
$499$	15.7603	+	27.2977i	0.705529	+	1.22201i	−0.260971	+	0.965347i	$0.584043\pi$
$500$		0			0
$501$	−34.8563			−1.55727
$502$		0			0
$503$	10.5420	+	6.08645i	0.470046	+	0.271381i	0.716259	−	0.697834i	$-0.245853\pi$
$503$	10.5420	+	6.08645i	0.470046	+	0.271381i	−0.246213	+	0.969216i	$0.579186\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	26.6963	+	15.4131i	1.18562	+	0.684520i
$508$		0			0
$509$	−4.70051	+	8.14151i	−0.208346	+	0.360866i	−0.951194	−	0.308594i	$-0.900141\pi$
$509$	−4.70051	+	8.14151i	−0.208346	+	0.360866i	0.742847	+	0.669461i	$0.233475\pi$
$510$		0			0
$511$	22.7277	+	39.3655i	1.00541	+	1.74143i
$512$		0			0
$513$	−0.340615	+	6.69843i	−0.0150385	+	0.295743i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	26.7746	+	15.4583i	1.17754	+	0.679856i
$518$		0			0
$519$	3.04521	−	5.27446i	0.133670	−	0.231523i
$520$		0			0
$521$	8.49649			0.372238			0.186119	−	0.982527i	$-0.440409\pi$
$521$	8.49649			0.372238			0.186119	+	0.982527i	$0.440409\pi$
$522$		0			0
$523$	19.4320	+	11.2191i	0.849703	+	0.490577i	0.860551	−	0.509365i	$-0.170120\pi$
$523$	19.4320	+	11.2191i	0.849703	+	0.490577i	−0.0108473	+	0.999941i	$0.503453\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	22.8483	−	13.1915i	0.995288	−	0.574630i
$528$		0			0
$529$	4.17434	+	7.23016i	0.181493	+	0.314355i
$530$		0			0
$531$	−24.3537			−1.05686
$532$		0			0
$533$			10.7065i			0.463752i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	39.7650	−	22.9583i	1.71598	−	0.990724i
$538$		0			0
$539$	−26.2101			−1.12895
$540$		0			0
$541$	13.7603	−	23.8336i	0.591603	−	1.02469i	−0.402414	−	0.915458i	$-0.631829\pi$
$541$	13.7603	−	23.8336i	0.591603	−	1.02469i	0.994017	−	0.109228i	$-0.0348379\pi$
$542$		0			0
$543$		−	67.8513i		−	2.91178i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.736308	+	0.425107i	0.0314822	+	0.0181763i	0.515659	−	0.856794i	$-0.327547\pi$
$547$	0.736308	+	0.425107i	0.0314822	+	0.0181763i	−0.484176	+	0.874970i	$0.660881\pi$
$548$		0			0
$549$	14.6437	+	25.3637i	0.624980	+	1.08250i
$550$		0			0
$551$	16.0262	−	24.7623i	0.682738	−	1.05491i
$552$		0			0
$553$	−15.0280	+	8.67641i	−0.639055	+	0.368958i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	34.1127	+	19.6950i	1.44540	+	0.834504i	0.998203	−	0.0599303i	$-0.0190878\pi$
$557$	34.1127	+	19.6950i	1.44540	+	0.834504i	0.447200	+	0.894434i	$0.352421\pi$
$558$		0			0
$559$	−11.3055			−0.478173
$560$		0			0
$561$	−33.6649	+	58.3092i	−1.42133	+	2.46182i
$562$		0			0
$563$			22.0774i			0.930452i	0.885192	+	0.465226i	$0.154027\pi$
$563$			22.0774i			0.930452i	−0.885192	+	0.465226i	$0.845973\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−21.1536	+	12.2130i	−0.888368	+	0.512900i
$568$		0			0
$569$	7.53365			0.315827			0.157914	−	0.987453i	$-0.449523\pi$
$569$	7.53365			0.315827			0.157914	+	0.987453i	$0.449523\pi$
$570$		0			0
$571$	−38.2824			−1.60207			−0.801035	−	0.598618i	$-0.795717\pi$
$571$	−38.2824			−1.60207			−0.801035	+	0.598618i	$0.795717\pi$
$572$		0			0
$573$	−1.17158	+	0.676410i	−0.0489433	+	0.0282574i
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	3.21006i		−	0.133637i	−0.997765	−	0.0668183i	$-0.978715\pi$
$577$		−	3.21006i		−	0.133637i	0.997765	−	0.0668183i	$-0.0212848\pi$
$578$		0			0
$579$	−6.85977	+	11.8815i	−0.285082	+	0.493777i
$580$		0			0
$581$	−33.5508			−1.39192
$582$		0			0
$583$	−13.4569	−	7.76936i	−0.557329	−	0.321774i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2.16202	+	1.24824i	−0.0892361	+	0.0515205i	−0.543954	−	0.839115i	$-0.683073\pi$
$587$	−2.16202	+	1.24824i	−0.0892361	+	0.0515205i	0.454718	+	0.890636i	$0.349740\pi$
$588$		0			0
$589$	20.0207	+	1.01805i	0.824937	+	0.0419480i
$590$		0			0
$591$	5.69148	+	9.85793i	0.234116	+	0.405501i
$592$		0			0
$593$	12.1766	+	7.03014i	0.500031	+	0.288693i	0.728726	−	0.684805i	$-0.240113\pi$
$593$	12.1766	+	7.03014i	0.500031	+	0.288693i	−0.228695	+	0.973498i	$0.573446\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$			31.2573i			1.27928i
$598$		0			0
$599$	−11.6678	+	20.2093i	−0.476735	+	0.825729i	−0.999645	−	0.0266590i	$-0.991513\pi$
$599$	−11.6678	+	20.2093i	−0.476735	+	0.825729i	0.522910	+	0.852388i	$0.324847\pi$
$600$		0			0
$601$	46.6111			1.90131			0.950653	−	0.310257i	$-0.100415\pi$
$601$	46.6111			1.90131			0.950653	+	0.310257i	$0.100415\pi$
$602$		0			0
$603$	19.7471	−	11.4010i	0.804165	−	0.464285i
$604$		0			0
$605$		0			0
$606$		0			0
$607$			11.1929i			0.454307i	0.973859	+	0.227153i	$0.0729418\pi$
$607$			11.1929i			0.454307i	−0.973859	+	0.227153i	$0.927058\pi$
$608$		0			0
$609$	−62.0372			−2.51387
$610$		0			0
$611$	−3.38341	−	5.86024i	−0.136878	−	0.237080i
$612$		0			0
$613$	−29.4092	+	16.9794i	−1.18783	+	0.685792i	−0.957812	−	0.287395i	$-0.907211\pi$
$613$	−29.4092	+	16.9794i	−1.18783	+	0.685792i	−0.230015	+	0.973187i	$0.573877\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−14.3290	−	8.27287i	−0.576865	−	0.333053i	0.183022	−	0.983109i	$-0.441412\pi$
$617$	−14.3290	−	8.27287i	−0.576865	−	0.333053i	−0.759887	+	0.650056i	$0.774746\pi$
$618$		0			0
$619$	−21.4312			−0.861391			−0.430695	−	0.902497i	$-0.641732\pi$
$619$	−21.4312			−0.861391			−0.430695	+	0.902497i	$0.641732\pi$
$620$		0			0
$621$	4.30761	−	7.46100i	0.172859	−	0.299400i
$622$		0			0
$623$	37.9398	+	21.9045i	1.52002	+	0.877586i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−45.5469	+	23.2965i	−1.81897	+	0.930373i
$628$		0			0
$629$	10.2367	+	17.7305i	0.408163	+	0.706960i
$630$		0			0
$631$	−10.5035	+	18.1926i	−0.418138	+	0.724237i	−0.995752	−	0.0920733i	$-0.970651\pi$
$631$	−10.5035	+	18.1926i	−0.418138	+	0.724237i	0.577614	+	0.816310i	$0.303984\pi$
$632$		0			0
$633$	−45.9873	−	26.5508i	−1.82783	−	1.05530i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	4.96812	+	2.86834i	0.196844	+	0.113648i
$638$		0			0
$639$	3.70746			0.146665
$640$		0			0
$641$	15.9106	+	27.5579i	0.628430	+	1.08847i	0.987867	+	0.155303i	$0.0496353\pi$
$641$	15.9106	+	27.5579i	0.628430	+	1.08847i	−0.359437	+	0.933169i	$0.617031\pi$
$642$		0			0
$643$	7.69670	−	4.44369i	0.303528	−	0.175242i	−0.340499	−	0.940245i	$-0.610596\pi$
$643$	7.69670	−	4.44369i	0.303528	−	0.175242i	0.644027	+	0.765003i	$0.277263\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			1.37593i			0.0540934i	0.999634	+	0.0270467i	$0.00861029\pi$
$647$			1.37593i			0.0540934i	−0.999634	+	0.0270467i	$0.991390\pi$
$648$		0			0
$649$	−15.4583	−	26.7746i	−0.606792	−	1.05099i
$650$		0			0
$651$	−21.0814	−	36.5140i	−0.826245	−	1.43110i
$652$		0			0
$653$			24.7237i			0.967513i	0.875203	+	0.483756i	$0.160728\pi$
$653$			24.7237i			0.967513i	−0.875203	+	0.483756i	$0.839272\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	45.8392i		−	1.78836i
$658$		0			0
$659$	−20.9020	+	36.2033i	−0.814226	+	1.41028i	0.0956561	+	0.995414i	$0.469505\pi$
$659$	−20.9020	+	36.2033i	−0.814226	+	1.41028i	−0.909882	+	0.414867i	$0.863828\pi$
$660$		0			0
$661$	11.5211	−	19.9552i	0.448119	−	0.776165i	−0.550144	−	0.835070i	$-0.685427\pi$
$661$	11.5211	−	19.9552i	0.448119	−	0.776165i	0.998264	+	0.0589041i	$0.0187606\pi$
$662$		0			0
$663$	12.7623	−	7.36834i	0.495648	−	0.286163i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−32.8114	+	18.9437i	−1.27046	+	0.733503i
$668$		0			0
$669$	5.79092	−	10.0302i	0.223890	−	0.387789i
$670$		0			0
$671$	−18.5900	+	32.1988i	−0.717658	+	1.24302i
$672$		0			0
$673$		−	29.5156i		−	1.13774i	−0.822427	−	0.568871i	$-0.807380\pi$
$673$		−	29.5156i		−	1.13774i	0.822427	−	0.568871i	$-0.192620\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			12.5035i			0.480549i	0.970705	+	0.240275i	$0.0772375\pi$
$677$			12.5035i			0.480549i	−0.970705	+	0.240275i	$0.922763\pi$
$678$		0			0
$679$	4.69148	+	8.12588i	0.180042	+	0.311843i
$680$		0			0
$681$	21.4131	+	37.0886i	0.820552	+	1.42124i
$682$		0			0
$683$		−	12.9045i		−	0.493778i	−0.969044	−	0.246889i	$-0.920592\pi$
$683$		−	12.9045i		−	0.493778i	0.969044	−	0.246889i	$-0.0794083\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	11.8144	−	6.82106i	0.450748	−	0.260240i
$688$		0			0
$689$	1.70051	+	2.94536i	0.0647841	+	0.112209i
$690$		0			0
$691$	23.3779			0.889337			0.444669	−	0.895695i	$-0.353321\pi$
$691$	23.3779			0.889337			0.444669	+	0.895695i	$0.353321\pi$
$692$		0			0
$693$	50.8213	+	29.3417i	1.93054	+	1.11460i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−53.1914	−	30.7101i	−2.01477	−	1.16323i
$698$		0			0
$699$	−3.56028	+	6.16658i	−0.134662	+	0.233242i
$700$		0			0
$701$	5.82314	+	10.0860i	0.219937	+	0.380942i	0.954788	−	0.297286i	$-0.0960816\pi$
$701$	5.82314	+	10.0860i	0.219937	+	0.380942i	−0.734852	+	0.678228i	$0.762748\pi$
$702$		0			0
$703$	−0.790014	+	15.5362i	−0.0297959	+	0.585958i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−27.4282	−	15.8357i	−1.03154	−	0.595562i
$708$		0			0
$709$	−6.58645	+	11.4081i	−0.247359	+	0.428439i	−0.962792	−	0.270243i	$-0.912896\pi$
$709$	−6.58645	+	11.4081i	−0.247359	+	0.428439i	0.715433	+	0.698681i	$0.246229\pi$
$710$		0			0
$711$	17.4994			0.656277
$712$		0			0
$713$	−22.2999	−	12.8748i	−0.835137	−	0.482167i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−19.1301	+	11.0448i	−0.714426	+	0.412474i
$718$		0			0
$719$	−2.43972	−	4.22572i	−0.0909863	−	0.157593i	0.816940	−	0.576723i	$-0.195669\pi$
$719$	−2.43972	−	4.22572i	−0.0909863	−	0.157593i	−0.907926	+	0.419130i	$0.862335\pi$
$720$		0			0
$721$	−15.7065			−0.584942
$722$		0			0
$723$		−	14.5508i		−	0.541150i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	43.2813	−	24.9884i	1.60521	−	0.926770i	0.614792	−	0.788689i	$-0.289240\pi$
$727$	43.2813	−	24.9884i	1.60521	−	0.926770i	0.990421	−	0.138081i	$-0.0440934\pi$
$728$		0			0
$729$	36.4905			1.35150
$730$		0			0
$731$	32.4282	−	56.1672i	1.19940	−	2.07742i
$732$		0			0
$733$			39.0493i			1.44232i	0.692770	+	0.721159i	$0.256390\pi$
$733$			39.0493i			1.44232i	−0.692770	+	0.721159i	$0.743610\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	25.0686	+	14.4734i	0.923415	+	0.533134i
$738$		0			0
$739$	−12.4020	−	21.4809i	−0.456215	−	0.790187i	0.542542	−	0.840028i	$-0.317462\pi$
$739$	−12.4020	−	21.4809i	−0.456215	−	0.790187i	−0.998757	+	0.0498412i	$0.984128\pi$
$740$		0			0
$741$	11.1829	+	0.568650i	0.410814	+	0.0208899i
$742$		0			0
$743$	17.1961	−	9.92817i	0.630863	−	0.364229i	−0.150223	−	0.988652i	$-0.547999\pi$
$743$	17.1961	−	9.92817i	0.630863	−	0.364229i	0.781086	+	0.624423i	$0.214666\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	29.3012	+	16.9171i	1.07208	+	0.618963i
$748$		0			0
$749$	49.7307			1.81712
$750$		0			0
$751$	13.7191	−	23.7622i	0.500617	−	0.867094i	−0.499383	−	0.866381i	$-0.666440\pi$
$751$	13.7191	−	23.7622i	0.500617	−	0.867094i	1.00000		0.000712212i	$-0.000226704\pi$
$752$		0			0
$753$			59.3909i			2.16432i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	10.0033	−	5.77540i	0.363576	−	0.209910i	−0.307073	−	0.951686i	$-0.599349\pi$
$757$	10.0033	−	5.77540i	0.363576	−	0.209910i	0.670648	+	0.741776i	$0.266016\pi$
$758$		0			0
$759$	65.7136			2.38525
$760$		0			0
$761$	−46.9940			−1.70353			−0.851766	−	0.523922i	$-0.824468\pi$
$761$	−46.9940			−1.70353			−0.851766	+	0.523922i	$0.824468\pi$
$762$		0			0
$763$	−11.8441	+	6.83821i	−0.428786	+	0.247560i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			6.76683i			0.244336i
$768$		0			0
$769$	−6.43719	+	11.1495i	−0.232131	+	0.402063i	−0.958435	−	0.285311i	$-0.907903\pi$
$769$	−6.43719	+	11.1495i	−0.232131	+	0.402063i	0.726304	+	0.687374i	$0.241237\pi$
$770$		0			0
$771$	−27.1498			−0.977776
$772$		0			0
$773$	−24.2748	−	14.0151i	−0.873104	−	0.504087i	−0.00472572	−	0.999989i	$-0.501504\pi$
$773$	−24.2748	−	14.0151i	−0.873104	−	0.504087i	−0.868379	+	0.495902i	$0.834838\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	28.3352	−	16.3593i	1.01652	−	0.586887i
$778$		0			0
$779$	−21.2518	−	41.5492i	−0.761423	−	1.48865i
$780$		0			0
$781$	2.35327	+	4.07599i	0.0842068	+	0.145850i
$782$		0			0
$783$	9.01722	+	5.20609i	0.322249	+	0.186051i
$784$		0			0
$785$		0			0
$786$		0			0
$787$			22.3478i			0.796612i	0.917253	+	0.398306i	$0.130402\pi$
$787$			22.3478i			0.796612i	−0.917253	+	0.398306i	$0.869598\pi$
$788$		0			0
$789$	11.3830	−	19.7159i	0.405244	−	0.701903i
$790$		0			0
$791$	−6.09042			−0.216550
$792$		0			0
$793$	7.04745	−	4.06885i	0.250262	−	0.144489i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			16.3176i			0.578000i	0.957329	+	0.289000i	$0.0933227\pi$
$797$			16.3176i			0.578000i	−0.957329	+	0.289000i	$0.906677\pi$
$798$		0			0
$799$	38.8192			1.37332
$800$		0			0
$801$	−22.0895	−	38.2601i	−0.780494	−	1.35186i
$802$		0			0
$803$	50.3958	−	29.0960i	1.77843	−	1.02678i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−11.8702	−	6.85327i	−0.417852	−	0.241247i
$808$		0			0
$809$	17.1859			0.604224			0.302112	−	0.953272i	$-0.402308\pi$
$809$	17.1859			0.604224			0.302112	+	0.953272i	$0.402308\pi$
$810$		0			0
$811$	−18.5774	+	32.1770i	−0.652342	+	1.12989i	0.330212	+	0.943907i	$0.392880\pi$
$811$	−18.5774	+	32.1770i	−0.652342	+	1.12989i	−0.982553	+	0.185982i	$0.940453\pi$
$812$		0			0
$813$	9.92498	+	5.73019i	0.348084	+	0.200967i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	43.8737	−	22.4407i	1.53495	−	0.785101i
$818$		0			0
$819$	−6.42212	−	11.1234i	−0.224407	−	0.388685i
$820$		0			0
$821$	22.7638	−	39.4281i	0.794464	−	1.37605i	−0.128716	−	0.991682i	$-0.541085\pi$
$821$	22.7638	−	39.4281i	0.794464	−	1.37605i	0.923179	−	0.384370i	$-0.125581\pi$
$822$		0			0
$823$	−13.8564	−	8.00000i	−0.483004	−	0.278862i	0.238664	−	0.971102i	$-0.423291\pi$
$823$	−13.8564	−	8.00000i	−0.483004	−	0.278862i	−0.721668	+	0.692240i	$0.756624\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	11.4141	+	6.58996i	0.396909	+	0.229155i	0.685149	−	0.728403i	$-0.259737\pi$
$827$	11.4141	+	6.58996i	0.396909	+	0.229155i	−0.288240	+	0.957558i	$0.593070\pi$
$828$		0			0
$829$	33.4503			1.16178			0.580888	−	0.813984i	$-0.302705\pi$
$829$	33.4503			1.16178			0.580888	+	0.813984i	$0.302705\pi$
$830$		0			0
$831$	29.6412	+	51.3401i	1.02824	+	1.78097i
$832$		0			0
$833$	−28.5005	+	16.4548i	−0.987485	+	0.570125i
$834$		0			0
$835$		0			0
$836$		0			0
$837$			7.07651i			0.244600i
$838$		0			0
$839$	−22.6774	−	39.2784i	−0.782911	−	1.35604i	−0.930239	−	0.366953i	$-0.880401\pi$
$839$	−22.6774	−	39.2784i	−0.782911	−	1.35604i	0.147329	−	0.989088i	$-0.452932\pi$
$840$		0			0
$841$	−8.39497	−	14.5405i	−0.289482	−	0.501397i
$842$		0			0
$843$		−	10.3528i		−	0.356570i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			35.2402i			1.21087i
$848$		0			0
$849$	40.8950	−	70.8323i	1.40351	−	2.43096i
$850$		0			0
$851$	9.99097	−	17.3049i	0.342486	−	0.593203i
$852$		0			0
$853$	9.64115	−	5.56632i	0.330107	−	0.190587i	−0.325782	−	0.945445i	$-0.605627\pi$
$853$	9.64115	−	5.56632i	0.330107	−	0.190587i	0.655888	+	0.754858i	$0.272294\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−12.6021	+	7.27585i	−0.430481	+	0.248538i	−0.699552	−	0.714582i	$-0.746617\pi$
$857$	−12.6021	+	7.27585i	−0.430481	+	0.248538i	0.269070	+	0.963120i	$0.413284\pi$
$858$		0			0
$859$	−5.68797	+	9.85185i	−0.194071	+	0.336141i	−0.946596	−	0.322423i	$-0.895503\pi$
$859$	−5.68797	+	9.85185i	−0.194071	+	0.336141i	0.752525	+	0.658564i	$0.228836\pi$
$860$		0			0
$861$	−49.0780	+	85.0055i	−1.67257	+	2.89698i
$862$		0			0
$863$		−	0.778912i		−	0.0265145i	−0.999912	−	0.0132572i	$-0.995780\pi$
$863$		−	0.778912i		−	0.0265145i	0.999912	−	0.0132572i	$-0.00422003\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$			40.8693i			1.38800i
$868$		0			0
$869$	11.1076	+	19.2389i	0.376798	+	0.652634i
$870$		0			0
$871$	−3.16784	−	5.48686i	−0.107338	−	0.185915i
$872$		0			0
$873$		−	9.46220i		−	0.320247i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−9.86231	+	5.69401i	−0.333027	+	0.192273i	−0.657184	−	0.753730i	$-0.728253\pi$
$877$	−9.86231	+	5.69401i	−0.333027	+	0.192273i	0.324157	+	0.946003i	$0.394919\pi$
$878$		0			0
$879$	−23.9884	−	41.5492i	−0.809110	−	1.40142i
$880$		0			0
$881$	35.0171			1.17976			0.589879	−	0.807492i	$-0.299176\pi$
$881$	35.0171			1.17976			0.589879	+	0.807492i	$0.299176\pi$
$882$		0			0
$883$	29.9941	+	17.3171i	1.00938	+	0.582767i	0.911010	−	0.412383i	$-0.135304\pi$
$883$	29.9941	+	17.3171i	1.00938	+	0.582767i	0.0983709	+	0.995150i	$0.468637\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−9.38093	−	5.41608i	−0.314981	−	0.181854i	0.334172	−	0.942512i	$-0.391543\pi$
$887$	−9.38093	−	5.41608i	−0.314981	−	0.181854i	−0.649153	+	0.760658i	$0.724877\pi$
$888$		0			0
$889$	26.9045	−	46.6000i	0.902349	−	1.56291i
$890$		0			0
$891$	15.6352	+	27.0809i	0.523798	+	0.907245i
$892$		0			0
$893$	24.7623	+	16.0262i	0.828638	+	0.536295i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−12.4560	−	7.19148i	−0.415894	−	0.240117i
$898$		0			0
$899$	15.5603	−	26.9512i	0.518964	−	0.898873i
$900$		0			0
$901$	−19.5105			−0.649990
$902$		0			0
$903$	−89.7612	−	51.8237i	−2.98707	−	1.72458i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−8.66025	+	5.00000i	−0.287559	+	0.166022i	−0.636841	−	0.770996i	$-0.719759\pi$
$907$	−8.66025	+	5.00000i	−0.287559	+	0.166022i	0.349281	+	0.937018i	$0.386426\pi$
$908$		0			0
$909$	15.9694	+	27.6598i	0.529672	+	0.917418i
$910$		0			0
$911$	−40.8794			−1.35440			−0.677198	−	0.735801i	$-0.736806\pi$
$911$	−40.8794			−1.35440			−0.677198	+	0.735801i	$0.736806\pi$
$912$		0			0
$913$			42.9518i			1.42150i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−41.9374	+	24.2126i	−1.38490	+	0.799570i
$918$		0			0
$919$	10.1146			0.333649			0.166825	−	0.985987i	$-0.446649\pi$
$919$	10.1146			0.333649			0.166825	+	0.985987i	$0.446649\pi$
$920$		0			0
$921$	40.8331	−	70.7251i	1.34550	−	2.33047i
$922$		0			0
$923$		−	1.03014i		−	0.0339074i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	13.7171	+	7.91959i	0.450530	+	0.260114i
$928$		0			0
$929$	9.16134	+	15.8679i	0.300574	+	0.520609i	0.976266	−	0.216575i	$-0.0694885\pi$
$929$	9.16134	+	15.8679i	0.300574	+	0.520609i	−0.675692	+	0.737184i	$0.736155\pi$
$930$		0			0
$931$	−24.9734	−	1.26989i	−0.818469	−	0.0416191i
$932$		0			0
$933$	−5.27446	+	3.04521i	−0.172678	+	0.0996956i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	12.1505	+	7.01507i	0.396938	+	0.229172i	0.685162	−	0.728391i	$-0.259731\pi$
$937$	12.1505	+	7.01507i	0.396938	+	0.229172i	−0.288224	+	0.957563i	$0.593065\pi$
$938$		0			0
$939$	31.3658			1.02358
$940$		0			0
$941$	6.67641	−	11.5639i	0.217645	−	0.376972i	−0.736443	−	0.676500i	$-0.763496\pi$
$941$	6.67641	−	11.5639i	0.217645	−	0.376972i	0.954087	+	0.299528i	$0.0968292\pi$
$942$		0			0
$943$			59.9458i			1.95211i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−24.1182	+	13.9247i	−0.783736	+	0.452490i	−0.837753	−	0.546050i	$-0.816131\pi$
$947$	−24.1182	+	13.9247i	−0.783736	+	0.452490i	0.0540164	+	0.998540i	$0.482798\pi$
$948$		0			0
$949$	−12.7367			−0.413450
$950$		0			0
$951$	73.0664			2.36934
$952$		0			0
$953$	40.8068	−	23.5598i	1.32186	−	0.763178i	0.337837	−	0.941205i	$-0.390305\pi$
$953$	40.8068	−	23.5598i	1.32186	−	0.763178i	0.984026	+	0.178027i	$0.0569715\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			79.4201i			2.56729i
$958$		0			0
$959$	12.5448	−	21.7282i	0.405091	−	0.701639i
$960$		0			0
$961$	−9.84931			−0.317720
$962$		0			0
$963$	−43.4318	−	25.0753i	−1.39957	−	0.808042i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	10.7352	−	6.19798i	0.345221	−	0.199313i	−0.317357	−	0.948306i	$-0.602795\pi$
$967$	10.7352	−	6.19798i	0.345221	−	0.199313i	0.662578	+	0.748993i	$0.269462\pi$
$968$		0			0
$969$	−34.9015	+	53.9269i	−1.12120	+	1.73238i
$970$		0			0
$971$	24.0925	+	41.7294i	0.773165	+	1.33916i	0.935820	+	0.352478i	$0.114661\pi$
$971$	24.0925	+	41.7294i	0.773165	+	1.33916i	−0.162655	+	0.986683i	$0.552006\pi$
$972$		0			0
$973$	−37.7005	−	21.7664i	−1.20862	−	0.697798i
$974$		0			0
$975$		0			0
$976$		0			0
$977$			4.86736i			0.155721i	0.996964	+	0.0778603i	$0.0248088\pi$
$977$			4.86736i			0.155721i	−0.996964	+	0.0778603i	$0.975191\pi$
$978$		0			0
$979$	28.0422	−	48.5706i	0.896233	−	1.55232i
$980$		0			0
$981$	13.7919			0.440342
$982$		0			0
$983$	−20.3085	+	11.7251i	−0.647741	+	0.373974i	−0.787590	−	0.616199i	$-0.788672\pi$
$983$	−20.3085	+	11.7251i	−0.647741	+	0.373974i	0.139849	+	0.990173i	$0.455338\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		−	62.0372i		−	1.97466i
$988$		0			0
$989$	−63.2996			−2.01281
$990$		0			0
$991$	−23.5688	−	40.8224i	−0.748689	−	1.29677i	−0.948451	−	0.316923i	$-0.897350\pi$
$991$	−23.5688	−	40.8224i	−0.748689	−	1.29677i	0.199762	−	0.979844i	$-0.435983\pi$
$992$		0			0
$993$	72.5093	−	41.8633i	2.30101	−	1.32849i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	15.1472	+	8.74526i	0.479718	+	0.276965i	0.720299	−	0.693664i	$-0.244005\pi$
$997$	15.1472	+	8.74526i	0.479718	+	0.276965i	−0.240581	+	0.970629i	$0.577338\pi$
$998$		0			0
$999$	−5.49143			−0.173741

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1900.2.s.c.349.2		12
5.2	odd	4		1900.2.i.c.501.3		6
5.3	odd	4		380.2.i.b.121.1	✓	6
5.4	even	2	inner	1900.2.s.c.349.5		12
15.8	even	4		3420.2.t.v.1261.3		6
19.11	even	3	inner	1900.2.s.c.49.5		12
20.3	even	4		1520.2.q.i.881.3		6
95.49	even	6	inner	1900.2.s.c.49.2		12
95.68	odd	12		380.2.i.b.201.1	yes	6
95.83	odd	12		7220.2.a.n.1.3		3
95.87	odd	12		1900.2.i.c.201.3		6
95.88	even	12		7220.2.a.o.1.1		3
285.68	even	12		3420.2.t.v.3241.3		6
380.163	even	12		1520.2.q.i.961.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.i.b.121.1	✓	6	5.3	odd	4
380.2.i.b.201.1	yes	6	95.68	odd	12
1520.2.q.i.881.3		6	20.3	even	4
1520.2.q.i.961.3		6	380.163	even	12
1900.2.i.c.201.3		6	95.87	odd	12
1900.2.i.c.501.3		6	5.2	odd	4
1900.2.s.c.49.2		12	95.49	even	6	inner
1900.2.s.c.49.5		12	19.11	even	3	inner
1900.2.s.c.349.2		12	1.1	even	1	trivial
1900.2.s.c.349.5		12	5.4	even	2	inner
3420.2.t.v.1261.3		6	15.8	even	4
3420.2.t.v.3241.3		6	285.68	even	12
7220.2.a.n.1.3		3	95.83	odd	12
7220.2.a.o.1.1		3	95.88	even	12

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.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.22469 + 1.28442i) q^{3} +3.56885i q^{7} +(1.79949 - 3.11682i) q^{9} +O(q^{10})\)	\(q+(-2.22469 + 1.28442i) q^{3} +3.56885i q^{7} +(1.79949 - 3.11682i) q^{9} +4.56885 q^{11} +(-0.866025 - 0.500000i) q^{13} +(4.96812 - 2.86834i) q^{17} +(4.35327 + 0.221364i) q^{19} +(-4.58392 - 7.93958i) q^{21} +(-4.84887 - 2.79949i) q^{23} +1.53871i q^{27} +(3.38341 - 5.86024i) q^{29} +4.59899 q^{31} +(-10.1643 + 5.86834i) q^{33} +3.56885i q^{37} +2.56885 q^{39} +(-5.35327 - 9.27214i) q^{41} +(9.79088 - 5.65277i) q^{43} +(5.86024 + 3.38341i) q^{47} -5.73669 q^{49} +(-7.36834 + 12.7623i) q^{51} +(-2.94536 - 1.70051i) q^{53} +(-9.96901 + 5.09899i) q^{57} +(-3.38341 - 5.86024i) q^{59} +(-4.06885 + 7.04745i) q^{61} +(11.1234 + 6.42212i) q^{63} +(5.48686 + 3.16784i) q^{67} +14.3830 q^{69} +(0.515069 + 0.892126i) q^{71} +(11.0303 - 6.36834i) q^{73} +16.3055i q^{77} +(2.43115 + 4.21088i) q^{79} +(3.42212 + 5.92729i) q^{81} +9.40101i q^{83} +17.3830i q^{87} +(6.13770 - 10.6308i) q^{89} +(1.78442 - 3.09071i) q^{91} +(-10.2313 + 5.90705i) q^{93} +(2.27689 - 1.31456i) q^{97} +(8.22162 - 14.2403i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 16 q^{9}+O(q^{10}) \) 12 * q + 16 * q^9	\( 12 q + 16 q^{9} + 20 q^{11} - 32 q^{21} + 12 q^{29} + 44 q^{31} - 4 q^{39} - 12 q^{41} + 12 q^{49} - 48 q^{51} - 12 q^{59} - 14 q^{61} - 60 q^{69} + 18 q^{71} + 64 q^{79} - 46 q^{81} + 4 q^{89} + 4 q^{91} + 6 q^{99}+O(q^{100}) \) 12 * q + 16 * q^9 + 20 * q^11 - 32 * q^21 + 12 * q^29 + 44 * q^31 - 4 * q^39 - 12 * q^41 + 12 * q^49 - 48 * q^51 - 12 * q^59 - 14 * q^61 - 60 * q^69 + 18 * q^71 + 64 * q^79 - 46 * q^81 + 4 * q^89 + 4 * q^91 + 6 * q^99

Introduction

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