LMFDB - Embedded newform 1900.2.i.c.201.3

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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1783323.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 $ x^6 - x^5 + 5x^4 - 2x^3 + 19x^2 - 12x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 380)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			201.3
Root			$-0.956115 - 1.65604i$ of defining polynomial
Character	$\chi$	$=$	1900.201
Dual form			1900.2.i.c.501.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.28442 - 2.22469i) q^{3} -3.56885 q^{7} +(-1.79949 - 3.11682i) q^{9} +O(q^{10})$	$q+(1.28442 - 2.22469i) q^{3} -3.56885 q^{7} +(-1.79949 - 3.11682i) q^{9} +4.56885 q^{11} +(-0.500000 - 0.866025i) q^{13} +(2.86834 - 4.96812i) q^{17} +(-4.35327 + 0.221364i) q^{19} +(-4.58392 + 7.93958i) q^{21} +(-2.79949 - 4.84887i) q^{23} -1.53871 q^{27} +(-3.38341 - 5.86024i) q^{29} +4.59899 q^{31} +(5.86834 - 10.1643i) q^{33} -3.56885 q^{37} -2.56885 q^{39} +(-5.35327 + 9.27214i) q^{41} +(-5.65277 + 9.79088i) q^{43} +(-3.38341 - 5.86024i) q^{47} +5.73669 q^{49} +(-7.36834 - 12.7623i) q^{51} +(-1.70051 - 2.94536i) q^{53} +(-5.09899 + 9.96901i) q^{57} +(3.38341 - 5.86024i) q^{59} +(-4.06885 - 7.04745i) q^{61} +(6.42212 + 11.1234i) q^{63} +(-3.16784 - 5.48686i) q^{67} -14.3830 q^{69} +(0.515069 - 0.892126i) q^{71} +(-6.36834 + 11.0303i) q^{73} -16.3055 q^{77} +(-2.43115 + 4.21088i) q^{79} +(3.42212 - 5.92729i) q^{81} +9.40101 q^{83} -17.3830 q^{87} +(-6.13770 - 10.6308i) q^{89} +(1.78442 + 3.09071i) q^{91} +(5.90705 - 10.2313i) q^{93} +(1.31456 - 2.27689i) q^{97} +(-8.22162 - 14.2403i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{3} - 4 q^{7} - 8 q^{9}+O(q^{10}) $ 6 * q - q^3 - 4 * q^7 - 8 * q^9	$ 6 q - q^{3} - 4 q^{7} - 8 q^{9} + 10 q^{11} - 3 q^{13} - 3 q^{17} - 16 q^{21} - 14 q^{23} + 20 q^{27} - 6 q^{29} + 22 q^{31} + 15 q^{33} - 4 q^{37} + 2 q^{39} - 6 q^{41} - 5 q^{43} - 6 q^{47} - 6 q^{49} - 24 q^{51} - 13 q^{53} - 25 q^{57} + 6 q^{59} - 7 q^{61} - 5 q^{63} + 4 q^{67} + 30 q^{69} + 9 q^{71} - 18 q^{73} - 40 q^{77} - 32 q^{79} - 23 q^{81} + 62 q^{83} + 12 q^{87} - 2 q^{89} + 2 q^{91} - 14 q^{93} + 11 q^{97} - 3 q^{99}+O(q^{100}) $ 6 * q - q^3 - 4 * q^7 - 8 * q^9 + 10 * q^11 - 3 * q^13 - 3 * q^17 - 16 * q^21 - 14 * q^23 + 20 * q^27 - 6 * q^29 + 22 * q^31 + 15 * q^33 - 4 * q^37 + 2 * q^39 - 6 * q^41 - 5 * q^43 - 6 * q^47 - 6 * q^49 - 24 * q^51 - 13 * q^53 - 25 * q^57 + 6 * q^59 - 7 * q^61 - 5 * q^63 + 4 * q^67 + 30 * q^69 + 9 * q^71 - 18 * q^73 - 40 * q^77 - 32 * q^79 - 23 * q^81 + 62 * q^83 + 12 * q^87 - 2 * q^89 + 2 * q^91 - 14 * q^93 + 11 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$	$951$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$3$	1.28442	−	2.22469i	0.741563	−	1.28442i	−0.210220	−	0.977654i	$-0.567418\pi$
$3$	1.28442	−	2.22469i	0.741563	−	1.28442i	0.951783	−	0.306771i	$-0.0992485\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−3.56885			−1.34890			−0.674449	−	0.738321i	$-0.735619\pi$
$7$	−3.56885			−1.34890			−0.674449	+	0.738321i	$0.735619\pi$
$8$		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
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	0.788320	−	0.615265i	$-0.210951\pi$
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	−0.926995	+	0.375073i	$0.877618\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.86834	−	4.96812i	0.695676	−	1.20495i	−0.274277	−	0.961651i	$-0.588438\pi$
$17$	2.86834	−	4.96812i	0.695676	−	1.20495i	0.969952	−	0.243295i	$-0.0782282\pi$
$18$		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
$23$	−2.79949	−	4.84887i	−0.583735	−	1.01106i	−0.995032	−	0.0995571i	$-0.968257\pi$
$23$	−2.79949	−	4.84887i	−0.583735	−	1.01106i	0.411297	−	0.911501i	$-0.365076\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−1.53871			−0.296125
$28$		0			0
$29$	−3.38341	−	5.86024i	−0.628284	−	1.08822i	−0.987896	−	0.155118i	$-0.950424\pi$
$29$	−3.38341	−	5.86024i	−0.628284	−	1.08822i	0.359612	−	0.933102i	$-0.382909\pi$
$30$		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
$33$	5.86834	−	10.1643i	1.02155	−	1.76937i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.56885			−0.586715			−0.293358	−	0.956003i	$-0.594773\pi$
$37$	−3.56885			−0.586715			−0.293358	+	0.956003i	$0.594773\pi$
$38$		0			0
$39$	−2.56885			−0.411345
$40$		0			0
$41$	−5.35327	+	9.27214i	−0.836041	+	1.44807i	0.0571390	+	0.998366i	$0.481802\pi$
$41$	−5.35327	+	9.27214i	−0.836041	+	1.44807i	−0.893180	+	0.449699i	$0.851531\pi$
$42$		0			0
$43$	−5.65277	+	9.79088i	−0.862039	+	1.49310i	0.00791826	+	0.999969i	$0.497480\pi$
$43$	−5.65277	+	9.79088i	−0.862039	+	1.49310i	−0.869957	+	0.493127i	$0.835854\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.38341	−	5.86024i	−0.493522	−	0.854804i	0.506451	−	0.862269i	$-0.330957\pi$
$47$	−3.38341	−	5.86024i	−0.493522	−	0.854804i	−0.999972	+	0.00746461i	$0.997624\pi$
$48$		0			0
$49$	5.73669			0.819527
$50$		0			0
$51$	−7.36834	−	12.7623i	−1.03177	−	1.78709i
$52$		0			0
$53$	−1.70051	−	2.94536i	−0.233582	−	0.404577i	0.725277	−	0.688457i	$-0.241712\pi$
$53$	−1.70051	−	2.94536i	−0.233582	−	0.404577i	−0.958860	+	0.283880i	$0.908378\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−5.09899	+	9.96901i	−0.675378	+	1.32043i
$58$		0			0
$59$	3.38341	−	5.86024i	0.440483	−	0.762939i	−0.557242	−	0.830350i	$-0.688141\pi$
$59$	3.38341	−	5.86024i	0.440483	−	0.762939i	0.997725	+	0.0674112i	$0.0214739\pi$
$60$		0			0
$61$	−4.06885	−	7.04745i	−0.520963	−	0.902334i	−0.999703	−	0.0243773i	$-0.992240\pi$
$61$	−4.06885	−	7.04745i	−0.520963	−	0.902334i	0.478740	−	0.877957i	$-0.341094\pi$
$62$		0			0
$63$	6.42212	+	11.1234i	0.809112	+	1.40142i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−3.16784	−	5.48686i	−0.387013	−	0.670326i	0.605033	−	0.796200i	$-0.293160\pi$
$67$	−3.16784	−	5.48686i	−0.387013	−	0.670326i	−0.992046	+	0.125874i	$0.959826\pi$
$68$		0			0
$69$	−14.3830			−1.73150
$70$		0			0
$71$	0.515069	−	0.892126i	0.0611275	−	0.105876i	−0.833842	−	0.552003i	$-0.813864\pi$
$71$	0.515069	−	0.892126i	0.0611275	−	0.105876i	0.894970	+	0.446127i	$0.147197\pi$
$72$		0			0
$73$	−6.36834	+	11.0303i	−0.745358	+	1.29100i	0.204669	+	0.978831i	$0.434388\pi$
$73$	−6.36834	+	11.0303i	−0.745358	+	1.29100i	−0.950027	+	0.312167i	$0.898945\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−16.3055			−1.85819
$78$		0			0
$79$	−2.43115	+	4.21088i	−0.273526	+	0.473761i	−0.969762	−	0.244052i	$-0.921523\pi$
$79$	−2.43115	+	4.21088i	−0.273526	+	0.473761i	0.696236	+	0.717813i	$0.254857\pi$
$80$		0			0
$81$	3.42212	−	5.92729i	0.380236	−	0.658588i
$82$		0			0
$83$	9.40101			1.03190			0.515948	−	0.856620i	$-0.327440\pi$
$83$	9.40101			1.03190			0.515948	+	0.856620i	$0.327440\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−17.3830			−1.86365
$88$		0			0
$89$	−6.13770	−	10.6308i	−0.650595	−	1.12686i	−0.982979	−	0.183719i	$-0.941186\pi$
$89$	−6.13770	−	10.6308i	−0.650595	−	1.12686i	0.332384	−	0.943144i	$-0.392147\pi$
$90$		0			0
$91$	1.78442	+	3.09071i	0.187059	+	0.323995i
$92$		0			0
$93$	5.90705	−	10.2313i	0.612533	−	1.06094i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	1.31456	−	2.27689i	0.133474	−	0.231183i	−0.791540	−	0.611118i	$-0.790720\pi$
$97$	1.31456	−	2.27689i	0.133474	−	0.231183i	0.925013	+	0.379935i	$0.124053\pi$
$98$		0			0
$99$	−8.22162	−	14.2403i	−0.826304	−	1.43120i
$100$		0			0
$101$	−4.43719	−	7.68544i	−0.441517	−	0.764730i	0.556285	−	0.830992i	$-0.312226\pi$
$101$	−4.43719	−	7.68544i	−0.441517	−	0.764730i	−0.997802	+	0.0662612i	$0.978893\pi$
$102$		0			0
$103$	4.40101			0.433645			0.216822	−	0.976211i	$-0.430431\pi$
$103$	4.40101			0.433645			0.216822	+	0.976211i	$0.430431\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	13.9347			1.34711			0.673557	−	0.739135i	$-0.264765\pi$
$107$	13.9347			1.34711			0.673557	+	0.739135i	$0.264765\pi$
$108$		0			0
$109$	−1.91608	+	3.31875i	−0.183527	+	0.317879i	−0.943079	−	0.332568i	$-0.892085\pi$
$109$	−1.91608	+	3.31875i	−0.183527	+	0.317879i	0.759552	+	0.650447i	$0.225418\pi$
$110$		0			0
$111$	−4.58392	+	7.93958i	−0.435086	+	0.753592i
$112$		0			0
$113$	1.70655			0.160539			0.0802693	−	0.996773i	$-0.474422\pi$
$113$	1.70655			0.160539			0.0802693	+	0.996773i	$0.474422\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1.79949	+	3.11682i	−0.166363	+	0.288150i
$118$		0			0
$119$	−10.2367	+	17.7305i	−0.938396	+	1.62535i
$120$		0			0
$121$	9.87439			0.897672
$122$		0			0
$123$	13.7518	+	23.8187i	1.23995	+	2.14766i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	7.53871	+	13.0574i	0.668952	+	1.15866i	0.978197	+	0.207677i	$0.0665904\pi$
$127$	7.53871	+	13.0574i	0.668952	+	1.15866i	−0.309245	+	0.950982i	$0.600076\pi$
$128$		0			0
$129$	14.5211	+	25.1513i	1.27851	+	2.21445i
$130$		0			0
$131$	6.78442	−	11.7510i	0.592758	−	1.02669i	−0.401101	−	0.916034i	$-0.631372\pi$
$131$	6.78442	−	11.7510i	0.592758	−	1.02669i	0.993859	−	0.110653i	$-0.0352943\pi$
$132$		0			0
$133$	15.5362	−	0.790014i	1.34716	−	0.0685029i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.51507	+	6.08828i	0.300313	+	0.520157i	0.976207	−	0.216842i	$-0.0695757\pi$
$137$	3.51507	+	6.08828i	0.300313	+	0.520157i	−0.675894	+	0.736999i	$0.736242\pi$
$138$		0			0
$139$	6.09899	+	10.5638i	0.517309	+	0.896006i	0.999798	+	0.0201039i	$0.00639970\pi$
$139$	6.09899	+	10.5638i	0.517309	+	0.896006i	−0.482488	+	0.875902i	$0.660267\pi$
$140$		0			0
$141$	−17.3830			−1.46391
$142$		0			0
$143$	−2.28442	−	3.95674i	−0.191033	−	0.330879i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	7.36834	−	12.7623i	0.607731	−	1.05262i
$148$		0			0
$149$	−4.76936	+	8.26077i	−0.390721	+	0.676748i	−0.992545	−	0.121880i	$-0.961108\pi$
$149$	−4.76936	+	8.26077i	−0.390721	+	0.676748i	0.601824	+	0.798629i	$0.294441\pi$
$150$		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
$153$	−20.6463			−1.66915
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−7.15277	+	12.3890i	−0.570853	+	0.988747i	0.425626	+	0.904899i	$0.360054\pi$
$157$	−7.15277	+	12.3890i	−0.570853	+	0.988747i	−0.996479	+	0.0838472i	$0.973279\pi$
$158$		0			0
$159$	−8.73669			−0.692864
$160$		0			0
$161$	9.99097	+	17.3049i	0.787399	+	1.36382i
$162$		0			0
$163$	−2.53871			−0.198847			−0.0994236	−	0.995045i	$-0.531700\pi$
$163$	−2.53871			−0.198847			−0.0994236	+	0.995045i	$0.531700\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.78442	−	11.7510i	−0.524995	−	0.909317i	−0.999576	−	0.0291058i	$-0.990734\pi$
$167$	−6.78442	−	11.7510i	−0.524995	−	0.909317i	0.474582	−	0.880211i	$-0.342599\pi$
$168$		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
$173$	1.18544	−	2.05324i	0.0901271	−	0.156105i	−0.817437	−	0.576017i	$-0.804606\pi$
$173$	1.18544	−	2.05324i	0.0901271	−	0.156105i	0.907564	+	0.419913i	$0.137939\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−8.69148	−	15.0541i	−0.653292	−	1.13153i
$178$		0			0
$179$	17.8744			1.33599			0.667997	−	0.744164i	$-0.267152\pi$
$179$	17.8744			1.33599			0.667997	+	0.744164i	$0.267152\pi$
$180$		0			0
$181$	−13.2065	−	22.8744i	−0.981635	−	1.70024i	−0.656028	−	0.754737i	$-0.727765\pi$
$181$	−13.2065	−	22.8744i	−0.981635	−	1.70024i	−0.325607	−	0.945505i	$-0.605569\pi$
$182$		0			0
$183$	−20.9045			−1.54531
$184$		0			0
$185$		0			0
$186$		0			0
$187$	13.1050	−	22.6986i	0.958335	−	1.65988i
$188$		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
$193$	−2.67037	+	4.62521i	−0.192217	+	0.332930i	−0.945985	−	0.324211i	$-0.894901\pi$
$193$	−2.67037	+	4.62521i	−0.192217	+	0.332930i	0.753767	+	0.657141i	$0.228234\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	4.43115			0.315706			0.157853	−	0.987463i	$-0.449543\pi$
$197$	4.43115			0.315706			0.157853	+	0.987463i	$0.449543\pi$
$198$		0			0
$199$	−6.08392	−	10.5377i	−0.431278	−	0.746995i	0.565706	−	0.824607i	$-0.308604\pi$
$199$	−6.08392	−	10.5377i	−0.431278	−	0.746995i	−0.996984	+	0.0776123i	$0.975270\pi$
$200$		0			0
$201$	−16.2754			−1.14798
$202$		0			0
$203$	12.0749	+	20.9143i	0.847491	+	1.46790i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−10.0753	+	17.4510i	−0.700285	+	1.21293i
$208$		0			0
$209$	−19.8895	+	1.01138i	−1.37578	+	0.0699584i
$210$		0			0
$211$	10.3357	−	17.9019i	0.711537	−	1.23242i	−0.252743	−	0.967534i	$-0.581333\pi$
$211$	10.3357	−	17.9019i	0.711537	−	1.23242i	0.964280	−	0.264885i	$-0.0853341\pi$
$212$		0			0
$213$	−1.32314	−	2.29174i	−0.0906598	−	0.157027i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−16.4131			−1.11419
$218$		0			0
$219$	16.3593	+	28.3352i	1.10546	+	1.91471i
$220$		0			0
$221$	−5.73669			−0.385891
$222$		0			0
$223$	2.25429	−	3.90454i	0.150958	−	0.261467i	−0.780622	−	0.625004i	$-0.785097\pi$
$223$	2.25429	−	3.90454i	0.150958	−	0.261467i	0.931580	+	0.363536i	$0.118431\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	16.6714			1.10652			0.553258	−	0.833010i	$-0.313384\pi$
$227$	16.6714			1.10652			0.553258	+	0.833010i	$0.313384\pi$
$228$		0			0
$229$	5.31060			0.350934			0.175467	−	0.984485i	$-0.443856\pi$
$229$	5.31060			0.350934			0.175467	+	0.984485i	$0.443856\pi$
$230$		0			0
$231$	−20.9432	+	36.2747i	−1.37796	+	2.38670i
$232$		0			0
$233$	−1.38594	+	2.40052i	−0.0907961	+	0.157263i	−0.907846	−	0.419303i	$-0.862274\pi$
$233$	−1.38594	+	2.40052i	−0.0907961	+	0.157263i	0.817050	+	0.576566i	$0.195608\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	6.24526	+	10.8171i	0.405673	+	0.702647i
$238$		0			0
$239$	−8.59899			−0.556222			−0.278111	−	0.960549i	$-0.589708\pi$
$239$	−8.59899			−0.556222			−0.278111	+	0.960549i	$0.589708\pi$
$240$		0			0
$241$	−2.83216	−	4.90545i	−0.182436	−	0.315988i	0.760274	−	0.649603i	$-0.225065\pi$
$241$	−2.83216	−	4.90545i	−0.182436	−	0.315988i	−0.942709	+	0.333615i	$0.891731\pi$
$242$		0			0
$243$	−11.0990	−	19.2240i	−0.712000	−	1.23322i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	2.36834	+	3.65936i	0.150694	+	0.232840i
$248$		0			0
$249$	12.0749	−	20.9143i	0.765215	−	1.32539i
$250$		0			0
$251$	11.5598	+	20.0222i	0.729650	+	1.26379i	0.957031	+	0.289984i	$0.0936501\pi$
$251$	11.5598	+	20.0222i	0.729650	+	1.26379i	−0.227382	+	0.973806i	$0.573017\pi$
$252$		0			0
$253$	−12.7905	−	22.1537i	−0.804130	−	1.39279i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−5.28442	−	9.15289i	−0.329633	−	0.570942i	0.652806	−	0.757525i	$-0.273592\pi$
$257$	−5.28442	−	9.15289i	−0.329633	−	0.570942i	−0.982439	+	0.186584i	$0.940258\pi$
$258$		0			0
$259$	12.7367			0.791419
$260$		0			0
$261$	−12.1769	+	21.0909i	−0.753729	+	1.30550i
$262$		0			0
$263$	4.43115	−	7.67498i	0.273236	−	0.473259i	−0.696452	−	0.717603i	$-0.745239\pi$
$263$	4.43115	−	7.67498i	0.273236	−	0.473259i	0.969689	+	0.244344i	$0.0785725\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−31.5337			−1.92983
$268$		0			0
$269$	−2.66784	+	4.62083i	−0.162661	+	0.281737i	−0.935822	−	0.352472i	$-0.885341\pi$
$269$	−2.66784	+	4.62083i	−0.162661	+	0.281737i	0.773161	+	0.634210i	$0.218674\pi$
$270$		0			0
$271$	−2.23064	+	3.86359i	−0.135502	+	0.234696i	−0.925789	−	0.378040i	$-0.876598\pi$
$271$	−2.23064	+	3.86359i	−0.135502	+	0.234696i	0.790287	+	0.612737i	$0.209931\pi$
$272$		0			0
$273$	9.16784			0.554863
$274$		0			0
$275$		0			0
$276$		0			0
$277$	23.0774			1.38659			0.693294	−	0.720655i	$-0.256159\pi$
$277$	23.0774			1.38659			0.693294	+	0.720655i	$0.256159\pi$
$278$		0			0
$279$	−8.27585	−	14.3342i	−0.495462	−	0.858166i
$280$		0			0
$281$	−2.01507	−	3.49020i	−0.120209	−	0.208208i	0.799641	−	0.600478i	$-0.205023\pi$
$281$	−2.01507	−	3.49020i	−0.120209	−	0.208208i	−0.919850	+	0.392270i	$0.871690\pi$
$282$		0			0
$283$	15.9196	−	27.5735i	0.946322	−	1.63908i	0.193239	−	0.981152i	$-0.438101\pi$
$283$	15.9196	−	27.5735i	0.946322	−	1.63908i	0.753083	−	0.657925i	$-0.228566\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	19.1050	−	33.0909i	1.12773	−	1.95329i
$288$		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
$293$	18.6764			1.09109			0.545544	−	0.838082i	$-0.316323\pi$
$293$	18.6764			1.09109			0.545544	+	0.838082i	$0.316323\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−7.03014			−0.407930
$298$		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
$303$	−22.7970			−1.30965
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−15.8955	+	27.5318i	−0.907204	+	1.57132i	−0.0892730	+	0.996007i	$0.528454\pi$
$307$	−15.8955	+	27.5318i	−0.907204	+	1.57132i	−0.817931	+	0.575316i	$0.804879\pi$
$308$		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
$313$	−6.10503	−	10.5742i	−0.345077	−	0.597691i	0.640291	−	0.768132i	$-0.278814\pi$
$313$	−6.10503	−	10.5742i	−0.345077	−	0.597691i	−0.985368	+	0.170442i	$0.945480\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	14.2216	+	24.6326i	0.798766	+	1.38350i	0.920420	+	0.390930i	$0.127847\pi$
$317$	14.2216	+	24.6326i	0.798766	+	1.38350i	−0.121655	+	0.992572i	$0.538820\pi$
$318$		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
$323$	−11.3869	+	22.2625i	−0.633586	+	1.23872i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	4.92212	+	8.52537i	0.272194	+	0.471454i
$328$		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
$333$	6.42212	+	11.1234i	0.351930	+	0.609561i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	5.83216	−	10.1016i	0.317698	−	0.550269i	−0.662309	−	0.749231i	$-0.730423\pi$
$337$	5.83216	−	10.1016i	0.317698	−	0.550269i	0.980007	+	0.198961i	$0.0637568\pi$
$338$		0			0
$339$	2.19193	−	3.79654i	0.119049	−	0.206200i
$340$		0			0
$341$	21.0121			1.13787
$342$		0			0
$343$	4.50857			0.243440
$344$		0			0
$345$		0			0
$346$		0			0
$347$	15.1613	−	26.2602i	0.813903	−	1.40972i	−0.0962092	−	0.995361i	$-0.530672\pi$
$347$	15.1613	−	26.2602i	0.813903	−	1.40972i	0.910113	−	0.414361i	$-0.135995\pi$
$348$		0			0
$349$	3.44324			0.184312			0.0921561	−	0.995745i	$-0.470624\pi$
$349$	3.44324			0.184312			0.0921561	+	0.995745i	$0.470624\pi$
$350$		0			0
$351$	0.769355	+	1.33256i	0.0410652	+	0.0711269i
$352$		0			0
$353$	6.53871			0.348020			0.174010	−	0.984744i	$-0.444327\pi$
$353$	6.53871			0.348020			0.174010	+	0.984744i	$0.444327\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	26.2965	+	45.5469i	1.39176	+	2.41060i
$358$		0			0
$359$	11.2392	−	19.4669i	0.593183	−	1.02742i	−0.400617	−	0.916245i	$-0.631204\pi$
$359$	11.2392	−	19.4669i	0.593183	−	1.02742i	0.993801	−	0.111178i	$-0.0354623\pi$
$360$		0			0
$361$	18.9020	−	1.92731i	0.994842	−	0.101438i
$362$		0			0
$363$	12.6829	−	21.9674i	0.665680	−	1.15299i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	4.29696	+	7.44256i	0.224300	+	0.388499i	0.956109	−	0.293011i	$-0.0946572\pi$
$367$	4.29696	+	7.44256i	0.224300	+	0.388499i	−0.731809	+	0.681509i	$0.761324\pi$
$368$		0			0
$369$	38.5327			2.00593
$370$		0			0
$371$	6.06885	+	10.5116i	0.315079	+	0.545733i
$372$		0			0
$373$	−37.2453			−1.92849			−0.964243	−	0.265019i	$-0.914622\pi$
$373$	−37.2453			−1.92849			−0.964243	+	0.265019i	$0.914622\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−3.38341	+	5.86024i	−0.174255	+	0.301818i
$378$		0			0
$379$	12.1678			0.625020			0.312510	−	0.949914i	$-0.398830\pi$
$379$	12.1678			0.625020			0.312510	+	0.949914i	$0.398830\pi$
$380$		0			0
$381$	38.7316			1.98428
$382$		0			0
$383$	−12.5272	+	21.6977i	−0.640108	+	1.10870i	0.345301	+	0.938492i	$0.387777\pi$
$383$	−12.5272	+	21.6977i	−0.640108	+	1.10870i	−0.985408	+	0.170207i	$0.945556\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	40.6885			2.06831
$388$		0			0
$389$	−11.0211	−	19.0891i	−0.558793	−	0.967857i	−0.997598	−	0.0692748i	$-0.977931\pi$
$389$	−11.0211	−	19.0891i	−0.558793	−	0.967857i	0.438805	−	0.898582i	$-0.355402\pi$
$390$		0			0
$391$	−32.1196			−1.62436
$392$		0			0
$393$	−17.4282	−	30.1865i	−0.879135	−	1.52271i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	18.0900	−	31.3327i	0.907909	−	1.57254i	0.0909453	−	0.995856i	$-0.471011\pi$
$397$	18.0900	−	31.3327i	0.907909	−	1.57254i	0.816964	−	0.576689i	$-0.195656\pi$
$398$		0			0
$399$	18.1975	−	35.5779i	0.911016	−	1.78112i
$400$		0			0
$401$	−13.9583	+	24.1765i	−0.697045	+	1.20732i	0.272442	+	0.962172i	$0.412169\pi$
$401$	−13.9583	+	24.1765i	−0.697045	+	1.20732i	−0.969487	+	0.245144i	$0.921165\pi$
$402$		0			0
$403$	−2.29949	−	3.98284i	−0.114546	−	0.198399i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−16.3055			−0.808235
$408$		0			0
$409$	−4.06281	−	7.03699i	−0.200893	−	0.347957i	0.747924	−	0.663785i	$-0.231051\pi$
$409$	−4.06281	−	7.03699i	−0.200893	−	0.347957i	−0.948816	+	0.315828i	$0.897718\pi$
$410$		0			0
$411$	18.0594			0.890803
$412$		0			0
$413$	−12.0749	+	20.9143i	−0.594167	+	1.02913i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	31.3348			1.53447
$418$		0			0
$419$	−2.87439			−0.140423			−0.0702115	−	0.997532i	$-0.522367\pi$
$419$	−2.87439			−0.140423			−0.0702115	+	0.997532i	$0.522367\pi$
$420$		0			0
$421$	3.48240	−	6.03170i	0.169722	−	0.293967i	−0.768600	−	0.639729i	$-0.779046\pi$
$421$	3.48240	−	6.03170i	0.169722	−	0.293967i	0.938322	+	0.345763i	$0.112380\pi$
$422$		0			0
$423$	−12.1769	+	21.0909i	−0.592059	+	1.02548i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	14.5211	+	25.1513i	0.702726	+	1.21716i
$428$		0			0
$429$	−11.7367			−0.566653
$430$		0			0
$431$	5.08996	+	8.81607i	0.245175	+	0.424655i	0.962181	−	0.272412i	$-0.0878213\pi$
$431$	5.08996	+	8.81607i	0.245175	+	0.424655i	−0.717006	+	0.697067i	$0.754488\pi$
$432$		0			0
$433$	−9.88341	−	17.1186i	−0.474967	−	0.822666i	0.524622	−	0.851335i	$-0.324207\pi$
$433$	−9.88341	−	17.1186i	−0.474967	−	0.822666i	−0.999589	+	0.0286689i	$0.990873\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	13.2603	+	20.4887i	0.634328	+	0.980109i
$438$		0			0
$439$	−19.3266	+	33.4747i	−0.922411	+	1.59766i	−0.126737	+	0.991936i	$0.540450\pi$
$439$	−19.3266	+	33.4747i	−0.922411	+	1.59766i	−0.795673	+	0.605726i	$0.792883\pi$
$440$		0			0
$441$	−10.3231	−	17.8802i	−0.491578	−	0.851438i
$442$		0			0
$443$	5.35327	+	9.27214i	0.254342	+	0.440533i	0.964717	−	0.263291i	$-0.0848079\pi$
$443$	5.35327	+	9.27214i	0.254342	+	0.440533i	−0.710375	+	0.703824i	$0.751475\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	12.2518	+	21.2207i	0.579488	+	1.00370i
$448$		0			0
$449$	23.0724			1.08885			0.544426	−	0.838809i	$-0.316747\pi$
$449$	23.0724			1.08885			0.544426	+	0.838809i	$0.316747\pi$
$450$		0			0
$451$	−24.4583	+	42.3630i	−1.15170	+	1.99480i
$452$		0			0
$453$	26.2191	−	45.4128i	1.23188	−	2.13368i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	6.87439			0.321570			0.160785	−	0.986989i	$-0.448597\pi$
$457$	6.87439			0.321570			0.160785	+	0.986989i	$0.448597\pi$
$458$		0			0
$459$	−4.41355	+	7.64450i	−0.206007	+	0.356815i
$460$		0			0
$461$	1.41355	−	2.44834i	0.0658357	−	0.114031i	−0.831229	−	0.555931i	$-0.812362\pi$
$461$	1.41355	−	2.44834i	0.0658357	−	0.114031i	0.897064	+	0.441900i	$0.145695\pi$
$462$		0			0
$463$	23.9347			1.11234			0.556169	−	0.831069i	$-0.312271\pi$
$463$	23.9347			1.11234			0.556169	+	0.831069i	$0.312271\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−33.5508			−1.55255			−0.776273	−	0.630397i	$-0.782892\pi$
$467$	−33.5508			−1.55255			−0.776273	+	0.630397i	$0.782892\pi$
$468$		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
$473$	−25.8266	+	44.7331i	−1.18751	+	2.05683i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−6.12010	+	10.6003i	−0.280220	+	0.485356i
$478$		0			0
$479$	18.4583	+	31.9707i	0.843382	+	1.46078i	0.887019	+	0.461732i	$0.152772\pi$
$479$	18.4583	+	31.9707i	0.843382	+	1.46078i	−0.0436379	+	0.999047i	$0.513895\pi$
$480$		0			0
$481$	1.78442	+	3.09071i	0.0813628	+	0.140924i
$482$		0			0
$483$	51.3306			2.33562
$484$		0			0
$485$		0			0
$486$		0			0
$487$	12.8744			0.583394			0.291697	−	0.956511i	$-0.405780\pi$
$487$	12.8744			0.583394			0.291697	+	0.956511i	$0.405780\pi$
$488$		0			0
$489$	−3.26078	+	5.64784i	−0.147458	+	0.255404i
$490$		0			0
$491$	12.3382	−	21.3704i	0.556815	−	0.964433i	−0.440944	−	0.897534i	$-0.645356\pi$
$491$	12.3382	−	21.3704i	0.556815	−	0.964433i	0.997760	−	0.0668981i	$-0.0213103\pi$
$492$		0			0
$493$	−38.8192			−1.74833
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.83821	+	3.18386i	−0.0824548	+	0.142816i
$498$		0			0
$499$	−15.7603	+	27.2977i	−0.705529	+	1.22201i	0.260971	+	0.965347i	$0.415957\pi$
$499$	−15.7603	+	27.2977i	−0.705529	+	1.22201i	−0.966500	+	0.256666i	$0.917376\pi$
$500$		0			0
$501$	−34.8563			−1.55727
$502$		0			0
$503$	6.08645	+	10.5420i	0.271381	+	0.470046i	0.969216	−	0.246213i	$-0.0791862\pi$
$503$	6.08645	+	10.5420i	0.271381	+	0.470046i	−0.697834	+	0.716259i	$0.745853\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−15.4131	−	26.6963i	−0.684520	−	1.18562i
$508$		0			0
$509$	4.70051	+	8.14151i	0.208346	+	0.360866i	0.951194	−	0.308594i	$-0.0998586\pi$
$509$	4.70051	+	8.14151i	0.208346	+	0.360866i	−0.742847	+	0.669461i	$0.766525\pi$
$510$		0			0
$511$	22.7277	−	39.3655i	1.00541	−	1.74143i
$512$		0			0
$513$	6.69843	−	0.340615i	0.295743	−	0.0150385i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−15.4583	−	26.7746i	−0.679856	−	1.17754i
$518$		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
$523$	11.2191	+	19.4320i	0.490577	+	0.849703i	0.999941	−	0.0108473i	$-0.00345288\pi$
$523$	11.2191	+	19.4320i	0.490577	+	0.849703i	−0.509365	+	0.860551i	$0.670120\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	13.1915	−	22.8483i	0.574630	−	0.995288i
$528$		0			0
$529$	−4.17434	+	7.23016i	−0.181493	+	0.314355i
$530$		0			0
$531$	−24.3537			−1.05686
$532$		0			0
$533$	10.7065			0.463752
$534$		0			0
$535$		0			0
$536$		0			0
$537$	22.9583	−	39.7650i	0.990724	−	1.71598i
$538$		0			0
$539$	26.2101			1.12895
$540$		0			0
$541$	13.7603	+	23.8336i	0.591603	+	1.02469i	0.994017	+	0.109228i	$0.0348379\pi$
$541$	13.7603	+	23.8336i	0.591603	+	1.02469i	−0.402414	+	0.915458i	$0.631829\pi$
$542$		0			0
$543$	−67.8513			−2.91178
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−0.425107	−	0.736308i	−0.0181763	−	0.0314822i	0.856794	−	0.515659i	$-0.172453\pi$
$547$	−0.425107	−	0.736308i	−0.0181763	−	0.0314822i	−0.874970	+	0.484176i	$0.839119\pi$
$548$		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
$553$	8.67641	−	15.0280i	0.368958	−	0.639055i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−19.6950	−	34.1127i	−0.834504	−	1.44540i	−0.894434	−	0.447200i	$-0.852421\pi$
$557$	−19.6950	−	34.1127i	−0.834504	−	1.44540i	0.0599303	−	0.998203i	$-0.480912\pi$
$558$		0			0
$559$	11.3055			0.478173
$560$		0			0
$561$	−33.6649	−	58.3092i	−1.42133	−	2.46182i
$562$		0			0
$563$	22.0774			0.930452			0.465226	−	0.885192i	$-0.345973\pi$
$563$	22.0774			0.930452			0.465226	+	0.885192i	$0.345973\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−12.2130	+	21.1536i	−0.512900	+	0.888368i
$568$		0			0
$569$	−7.53365			−0.315827			−0.157914	−	0.987453i	$-0.550477\pi$
$569$	−7.53365			−0.315827			−0.157914	+	0.987453i	$0.550477\pi$
$570$		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
$573$	0.676410	−	1.17158i	0.0282574	−	0.0489433i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	3.21006			0.133637			0.0668183	−	0.997765i	$-0.478715\pi$
$577$	3.21006			0.133637			0.0668183	+	0.997765i	$0.478715\pi$
$578$		0			0
$579$	6.85977	+	11.8815i	0.285082	+	0.493777i
$580$		0			0
$581$	−33.5508			−1.39192
$582$		0			0
$583$	−7.76936	−	13.4569i	−0.321774	−	0.557329i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.24824	+	2.16202i	−0.0515205	+	0.0892361i	−0.890636	−	0.454718i	$-0.849740\pi$
$587$	−1.24824	+	2.16202i	−0.0515205	+	0.0892361i	0.839115	+	0.543954i	$0.183073\pi$
$588$		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
$593$	7.03014	+	12.1766i	0.288693	+	0.500031i	0.973498	−	0.228695i	$-0.0734459\pi$
$593$	7.03014	+	12.1766i	0.288693	+	0.500031i	−0.684805	+	0.728726i	$0.740113\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−31.2573			−1.27928
$598$		0			0
$599$	11.6678	+	20.2093i	0.476735	+	0.825729i	0.999645	−	0.0266590i	$-0.00848682\pi$
$599$	11.6678	+	20.2093i	0.476735	+	0.825729i	−0.522910	+	0.852388i	$0.675153\pi$
$600$		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
$603$	−11.4010	+	19.7471i	−0.464285	+	0.804165i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−11.1929			−0.454307			−0.227153	−	0.973859i	$-0.572942\pi$
$607$	−11.1929			−0.454307			−0.227153	+	0.973859i	$0.572942\pi$
$608$		0			0
$609$	62.0372			2.51387
$610$		0			0
$611$	−3.38341	+	5.86024i	−0.136878	+	0.237080i
$612$		0			0
$613$	16.9794	−	29.4092i	0.685792	−	1.18783i	−0.287395	−	0.957812i	$-0.592789\pi$
$613$	16.9794	−	29.4092i	0.685792	−	1.18783i	0.973187	−	0.230015i	$-0.0738775\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	8.27287	+	14.3290i	0.333053	+	0.576865i	0.983109	−	0.183022i	$-0.0585878\pi$
$617$	8.27287	+	14.3290i	0.333053	+	0.576865i	−0.650056	+	0.759887i	$0.725254\pi$
$618$		0			0
$619$	21.4312			0.861391			0.430695	−	0.902497i	$-0.358268\pi$
$619$	21.4312			0.861391			0.430695	+	0.902497i	$0.358268\pi$
$620$		0			0
$621$	4.30761	+	7.46100i	0.172859	+	0.299400i
$622$		0			0
$623$	21.9045	+	37.9398i	0.877586	+	1.52002i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−23.2965	+	45.5469i	−0.930373	+	1.81897i
$628$		0			0
$629$	−10.2367	+	17.7305i	−0.408163	+	0.706960i
$630$		0			0
$631$	−10.5035	−	18.1926i	−0.418138	−	0.724237i	0.577614	−	0.816310i	$-0.303984\pi$
$631$	−10.5035	−	18.1926i	−0.418138	−	0.724237i	−0.995752	+	0.0920733i	$0.970651\pi$
$632$		0			0
$633$	−26.5508	−	45.9873i	−1.05530	−	1.82783i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−2.86834	−	4.96812i	−0.113648	−	0.196844i
$638$		0			0
$639$	−3.70746			−0.146665
$640$		0			0
$641$	15.9106	−	27.5579i	0.628430	−	1.08847i	−0.359437	−	0.933169i	$-0.617031\pi$
$641$	15.9106	−	27.5579i	0.628430	−	1.08847i	0.987867	−	0.155303i	$-0.0496353\pi$
$642$		0			0
$643$	−4.44369	+	7.69670i	−0.175242	+	0.303528i	−0.940245	−	0.340499i	$-0.889404\pi$
$643$	−4.44369	+	7.69670i	−0.175242	+	0.303528i	0.765003	+	0.644027i	$0.222737\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.37593			−0.0540934			−0.0270467	−	0.999634i	$-0.508610\pi$
$647$	−1.37593			−0.0540934			−0.0270467	+	0.999634i	$0.508610\pi$
$648$		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
$653$	24.7237			0.967513			0.483756	−	0.875203i	$-0.339272\pi$
$653$	24.7237			0.967513			0.483756	+	0.875203i	$0.339272\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	45.8392			1.78836
$658$		0			0
$659$	20.9020	+	36.2033i	0.814226	+	1.41028i	0.909882	+	0.414867i	$0.136172\pi$
$659$	20.9020	+	36.2033i	0.814226	+	1.41028i	−0.0956561	+	0.995414i	$0.530495\pi$
$660$		0			0
$661$	11.5211	+	19.9552i	0.448119	+	0.776165i	0.998264	−	0.0589041i	$-0.0187606\pi$
$661$	11.5211	+	19.9552i	0.448119	+	0.776165i	−0.550144	+	0.835070i	$0.685427\pi$
$662$		0			0
$663$	−7.36834	+	12.7623i	−0.286163	+	0.495648i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−18.9437	+	32.8114i	−0.733503	+	1.27046i
$668$		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
$673$	−29.5156			−1.13774			−0.568871	−	0.822427i	$-0.692620\pi$
$673$	−29.5156			−1.13774			−0.568871	+	0.822427i	$0.692620\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−12.5035			−0.480549			−0.240275	−	0.970705i	$-0.577237\pi$
$677$	−12.5035			−0.480549			−0.240275	+	0.970705i	$0.577237\pi$
$678$		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
$683$	−12.9045			−0.493778			−0.246889	−	0.969044i	$-0.579408\pi$
$683$	−12.9045			−0.493778			−0.246889	+	0.969044i	$0.579408\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	6.82106	−	11.8144i	0.260240	−	0.450748i
$688$		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
$693$	29.3417	+	50.8213i	1.11460	+	1.93054i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	30.7101	+	53.1914i	1.16323	+	2.01477i
$698$		0			0
$699$	3.56028	+	6.16658i	0.134662	+	0.233242i
$700$		0			0
$701$	5.82314	−	10.0860i	0.219937	−	0.380942i	−0.734852	−	0.678228i	$-0.762748\pi$
$701$	5.82314	−	10.0860i	0.219937	−	0.380942i	0.954788	+	0.297286i	$0.0960816\pi$
$702$		0			0
$703$	15.5362	−	0.790014i	0.585958	−	0.0297959i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	15.8357	+	27.4282i	0.595562	+	1.03154i
$708$		0			0
$709$	6.58645	+	11.4081i	0.247359	+	0.428439i	0.962792	−	0.270243i	$-0.0871039\pi$
$709$	6.58645	+	11.4081i	0.247359	+	0.428439i	−0.715433	+	0.698681i	$0.753771\pi$
$710$		0			0
$711$	17.4994			0.656277
$712$		0			0
$713$	−12.8748	−	22.2999i	−0.482167	−	0.835137i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−11.0448	+	19.1301i	−0.412474	+	0.714426i
$718$		0			0
$719$	2.43972	−	4.22572i	0.0909863	−	0.157593i	−0.816940	−	0.576723i	$-0.804331\pi$
$719$	2.43972	−	4.22572i	0.0909863	−	0.157593i	0.907926	+	0.419130i	$0.137665\pi$
$720$		0			0
$721$	−15.7065			−0.584942
$722$		0			0
$723$	−14.5508			−0.541150
$724$		0			0
$725$		0			0
$726$		0			0
$727$	24.9884	−	43.2813i	0.926770	−	1.60521i	0.138081	−	0.990421i	$-0.455907\pi$
$727$	24.9884	−	43.2813i	0.926770	−	1.60521i	0.788689	−	0.614792i	$-0.210760\pi$
$728$		0			0
$729$	−36.4905			−1.35150
$730$		0			0
$731$	32.4282	+	56.1672i	1.19940	+	2.07742i
$732$		0			0
$733$	39.0493			1.44232			0.721159	−	0.692770i	$-0.243610\pi$
$733$	39.0493			1.44232			0.721159	+	0.692770i	$0.243610\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−14.4734	−	25.0686i	−0.533134	−	0.923415i
$738$		0			0
$739$	12.4020	−	21.4809i	0.456215	−	0.790187i	−0.542542	−	0.840028i	$-0.682538\pi$
$739$	12.4020	−	21.4809i	0.456215	−	0.790187i	0.998757	+	0.0498412i	$0.0158715\pi$
$740$		0			0
$741$	11.1829	−	0.568650i	0.410814	−	0.0208899i
$742$		0			0
$743$	−9.92817	+	17.1961i	−0.364229	+	0.630863i	−0.988652	−	0.150223i	$-0.952001\pi$
$743$	−9.92817	+	17.1961i	−0.364229	+	0.630863i	0.624423	+	0.781086i	$0.285334\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−16.9171	−	29.3012i	−0.618963	−	1.07208i
$748$		0			0
$749$	−49.7307			−1.81712
$750$		0			0
$751$	13.7191	+	23.7622i	0.500617	+	0.867094i	1.00000		0.000712212i	$0.000226704\pi$
$751$	13.7191	+	23.7622i	0.500617	+	0.867094i	−0.499383	+	0.866381i	$0.666440\pi$
$752$		0			0
$753$	59.3909			2.16432
$754$		0			0
$755$		0			0
$756$		0			0
$757$	5.77540	−	10.0033i	0.209910	−	0.363576i	−0.741776	−	0.670648i	$-0.766016\pi$
$757$	5.77540	−	10.0033i	0.209910	−	0.363576i	0.951686	+	0.307073i	$0.0993494\pi$
$758$		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
$763$	6.83821	−	11.8441i	0.247560	−	0.428786i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−6.76683			−0.244336
$768$		0			0
$769$	6.43719	+	11.1495i	0.232131	+	0.402063i	0.958435	−	0.285311i	$-0.0920968\pi$
$769$	6.43719	+	11.1495i	0.232131	+	0.402063i	−0.726304	+	0.687374i	$0.758763\pi$
$770$		0			0
$771$	−27.1498			−0.977776
$772$		0			0
$773$	−14.0151	−	24.2748i	−0.504087	−	0.873104i	−0.999989	−	0.00472572i	$-0.998496\pi$
$773$	−14.0151	−	24.2748i	−0.504087	−	0.873104i	0.495902	−	0.868379i	$-0.334838\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	16.3593	−	28.3352i	0.586887	−	1.01652i
$778$		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
$783$	5.20609	+	9.01722i	0.186051	+	0.322249i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−22.3478			−0.796612			−0.398306	−	0.917253i	$-0.630402\pi$
$787$	−22.3478			−0.796612			−0.398306	+	0.917253i	$0.630402\pi$
$788$		0			0
$789$	−11.3830	−	19.7159i	−0.405244	−	0.701903i
$790$		0			0
$791$	−6.09042			−0.216550
$792$		0			0
$793$	−4.06885	+	7.04745i	−0.144489	+	0.250262i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−16.3176			−0.578000			−0.289000	−	0.957329i	$-0.593323\pi$
$797$	−16.3176			−0.578000			−0.289000	+	0.957329i	$0.593323\pi$
$798$		0			0
$799$	−38.8192			−1.37332
$800$		0			0
$801$	−22.0895	+	38.2601i	−0.780494	+	1.35186i
$802$		0			0
$803$	−29.0960	+	50.3958i	−1.02678	+	1.77843i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	6.85327	+	11.8702i	0.241247	+	0.417852i
$808$		0			0
$809$	−17.1859			−0.604224			−0.302112	−	0.953272i	$-0.597692\pi$
$809$	−17.1859			−0.604224			−0.302112	+	0.953272i	$0.597692\pi$
$810$		0			0
$811$	−18.5774	−	32.1770i	−0.652342	−	1.12989i	−0.982553	−	0.185982i	$-0.940453\pi$
$811$	−18.5774	−	32.1770i	−0.652342	−	1.12989i	0.330212	−	0.943907i	$-0.392880\pi$
$812$		0			0
$813$	5.73019	+	9.92498i	0.200967	+	0.348084i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	22.4407	−	43.8737i	0.785101	−	1.53495i
$818$		0			0
$819$	6.42212	−	11.1234i	0.224407	−	0.388685i
$820$		0			0
$821$	22.7638	+	39.4281i	0.794464	+	1.37605i	0.923179	+	0.384370i	$0.125581\pi$
$821$	22.7638	+	39.4281i	0.794464	+	1.37605i	−0.128716	+	0.991682i	$0.541085\pi$
$822$		0			0
$823$	−8.00000	−	13.8564i	−0.278862	−	0.483004i	0.692240	−	0.721668i	$-0.256624\pi$
$823$	−8.00000	−	13.8564i	−0.278862	−	0.483004i	−0.971102	+	0.238664i	$0.923291\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−6.58996	−	11.4141i	−0.229155	−	0.396909i	0.728403	−	0.685149i	$-0.240263\pi$
$827$	−6.58996	−	11.4141i	−0.229155	−	0.396909i	−0.957558	+	0.288240i	$0.906930\pi$
$828$		0			0
$829$	−33.4503			−1.16178			−0.580888	−	0.813984i	$-0.697295\pi$
$829$	−33.4503			−1.16178			−0.580888	+	0.813984i	$0.697295\pi$
$830$		0			0
$831$	29.6412	−	51.3401i	1.02824	−	1.78097i
$832$		0			0
$833$	16.4548	−	28.5005i	0.570125	−	0.987485i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−7.07651			−0.244600
$838$		0			0
$839$	22.6774	−	39.2784i	0.782911	−	1.35604i	−0.147329	−	0.989088i	$-0.547068\pi$
$839$	22.6774	−	39.2784i	0.782911	−	1.35604i	0.930239	−	0.366953i	$-0.119599\pi$
$840$		0			0
$841$	−8.39497	+	14.5405i	−0.289482	+	0.501397i
$842$		0			0
$843$	−10.3528			−0.356570
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−35.2402			−1.21087
$848$		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
$853$	−5.56632	+	9.64115i	−0.190587	+	0.330107i	−0.945445	−	0.325782i	$-0.894373\pi$
$853$	−5.56632	+	9.64115i	−0.190587	+	0.330107i	0.754858	+	0.655888i	$0.227706\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−7.27585	+	12.6021i	−0.248538	+	0.430481i	−0.963120	−	0.269070i	$-0.913284\pi$
$857$	−7.27585	+	12.6021i	−0.248538	+	0.430481i	0.714582	+	0.699552i	$0.246617\pi$
$858$		0			0
$859$	5.68797	+	9.85185i	0.194071	+	0.336141i	0.946596	−	0.322423i	$-0.104497\pi$
$859$	5.68797	+	9.85185i	0.194071	+	0.336141i	−0.752525	+	0.658564i	$0.771164\pi$
$860$		0			0
$861$	−49.0780	−	85.0055i	−1.67257	−	2.89698i
$862$		0			0
$863$	−0.778912			−0.0265145			−0.0132572	−	0.999912i	$-0.504220\pi$
$863$	−0.778912			−0.0265145			−0.0132572	+	0.999912i	$0.504220\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−40.8693			−1.38800
$868$		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
$873$	−9.46220			−0.320247
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−5.69401	+	9.86231i	−0.192273	+	0.333027i	−0.946003	−	0.324157i	$-0.894919\pi$
$877$	−5.69401	+	9.86231i	−0.192273	+	0.333027i	0.753730	+	0.657184i	$0.228253\pi$
$878$		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
$883$	17.3171	+	29.9941i	0.582767	+	1.00938i	0.995150	+	0.0983709i	$0.0313631\pi$
$883$	17.3171	+	29.9941i	0.582767	+	1.00938i	−0.412383	+	0.911010i	$0.635304\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	5.41608	+	9.38093i	0.181854	+	0.314981i	0.942512	−	0.334172i	$-0.108457\pi$
$887$	5.41608	+	9.38093i	0.181854	+	0.314981i	−0.760658	+	0.649153i	$0.775123\pi$
$888$		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
$893$	16.0262	+	24.7623i	0.536295	+	0.828638i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	7.19148	+	12.4560i	0.240117	+	0.415894i
$898$		0			0
$899$	−15.5603	−	26.9512i	−0.518964	−	0.898873i
$900$		0			0
$901$	−19.5105			−0.649990
$902$		0			0
$903$	−51.8237	−	89.7612i	−1.72458	−	2.98707i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−5.00000	+	8.66025i	−0.166022	+	0.287559i	−0.937018	−	0.349281i	$-0.886426\pi$
$907$	−5.00000	+	8.66025i	−0.166022	+	0.287559i	0.770996	+	0.636841i	$0.219759\pi$
$908$		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
$913$	42.9518			1.42150
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−24.2126	+	41.9374i	−0.799570	+	1.38490i
$918$		0			0
$919$	−10.1146			−0.333649			−0.166825	−	0.985987i	$-0.553351\pi$
$919$	−10.1146			−0.333649			−0.166825	+	0.985987i	$0.553351\pi$
$920$		0			0
$921$	40.8331	+	70.7251i	1.34550	+	2.33047i
$922$		0			0
$923$	−1.03014			−0.0339074
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−7.91959	−	13.7171i	−0.260114	−	0.450530i
$928$		0			0
$929$	−9.16134	+	15.8679i	−0.300574	+	0.520609i	−0.976266	−	0.216575i	$-0.930512\pi$
$929$	−9.16134	+	15.8679i	−0.300574	+	0.520609i	0.675692	+	0.737184i	$0.263845\pi$
$930$		0			0
$931$	−24.9734	+	1.26989i	−0.818469	+	0.0416191i
$932$		0			0
$933$	3.04521	−	5.27446i	0.0996956	−	0.172678i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−7.01507	−	12.1505i	−0.229172	−	0.396938i	0.728391	−	0.685162i	$-0.240269\pi$
$937$	−7.01507	−	12.1505i	−0.229172	−	0.396938i	−0.957563	+	0.288224i	$0.906935\pi$
$938$		0			0
$939$	−31.3658			−1.02358
$940$		0			0
$941$	6.67641	+	11.5639i	0.217645	+	0.376972i	0.954087	−	0.299528i	$-0.0968292\pi$
$941$	6.67641	+	11.5639i	0.217645	+	0.376972i	−0.736443	+	0.676500i	$0.763496\pi$
$942$		0			0
$943$	59.9458			1.95211
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−13.9247	+	24.1182i	−0.452490	+	0.783736i	−0.998540	−	0.0540164i	$-0.982798\pi$
$947$	−13.9247	+	24.1182i	−0.452490	+	0.783736i	0.546050	+	0.837753i	$0.316131\pi$
$948$		0			0
$949$	12.7367			0.413450
$950$		0			0
$951$	73.0664			2.36934
$952$		0			0
$953$	−23.5598	+	40.8068i	−0.763178	+	1.32186i	0.178027	+	0.984026i	$0.443028\pi$
$953$	−23.5598	+	40.8068i	−0.763178	+	1.32186i	−0.941205	+	0.337837i	$0.890305\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−79.4201			−2.56729
$958$		0			0
$959$	−12.5448	−	21.7282i	−0.405091	−	0.701639i
$960$		0			0
$961$	−9.84931			−0.317720
$962$		0			0
$963$	−25.0753	−	43.4318i	−0.808042	−	1.39957i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	6.19798	−	10.7352i	0.199313	−	0.345221i	−0.748993	−	0.662578i	$-0.769462\pi$
$967$	6.19798	−	10.7352i	0.199313	−	0.345221i	0.948306	+	0.317357i	$0.102795\pi$
$968$		0			0
$969$	34.9015	+	53.9269i	1.12120	+	1.73238i
$970$		0			0
$971$	24.0925	−	41.7294i	0.773165	−	1.33916i	−0.162655	−	0.986683i	$-0.552006\pi$
$971$	24.0925	−	41.7294i	0.773165	−	1.33916i	0.935820	−	0.352478i	$-0.114661\pi$
$972$		0			0
$973$	−21.7664	−	37.7005i	−0.697798	−	1.20862i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−4.86736			−0.155721			−0.0778603	−	0.996964i	$-0.524809\pi$
$977$	−4.86736			−0.155721			−0.0778603	+	0.996964i	$0.524809\pi$
$978$		0			0
$979$	−28.0422	−	48.5706i	−0.896233	−	1.55232i
$980$		0			0
$981$	13.7919			0.440342
$982$		0			0
$983$	11.7251	−	20.3085i	0.373974	−	0.647741i	−0.616199	−	0.787590i	$-0.711328\pi$
$983$	11.7251	−	20.3085i	0.373974	−	0.647741i	0.990173	+	0.139849i	$0.0446617\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	62.0372			1.97466
$988$		0			0
$989$	63.2996			2.01281
$990$		0			0
$991$	−23.5688	+	40.8224i	−0.748689	+	1.29677i	0.199762	+	0.979844i	$0.435983\pi$
$991$	−23.5688	+	40.8224i	−0.748689	+	1.29677i	−0.948451	+	0.316923i	$0.897350\pi$
$992$		0			0
$993$	−41.8633	+	72.5093i	−1.32849	+	2.30101i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−8.74526	−	15.1472i	−0.276965	−	0.479718i	0.693664	−	0.720299i	$-0.255995\pi$
$997$	−8.74526	−	15.1472i	−0.276965	−	0.479718i	−0.970629	+	0.240581i	$0.922662\pi$
$998$		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.i.c.201.3		6
5.2	odd	4		1900.2.s.c.49.2		12
5.3	odd	4		1900.2.s.c.49.5		12
5.4	even	2		380.2.i.b.201.1	yes	6
15.14	odd	2		3420.2.t.v.3241.3		6
19.7	even	3	inner	1900.2.i.c.501.3		6
20.19	odd	2		1520.2.q.i.961.3		6
95.7	odd	12		1900.2.s.c.349.5		12
95.49	even	6		7220.2.a.n.1.3		3
95.64	even	6		380.2.i.b.121.1	✓	6
95.83	odd	12		1900.2.s.c.349.2		12
95.84	odd	6		7220.2.a.o.1.1		3
285.254	odd	6		3420.2.t.v.1261.3		6
380.159	odd	6		1520.2.q.i.881.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.i.b.121.1	✓	6	95.64	even	6
380.2.i.b.201.1	yes	6	5.4	even	2
1520.2.q.i.881.3		6	380.159	odd	6
1520.2.q.i.961.3		6	20.19	odd	2
1900.2.i.c.201.3		6	1.1	even	1	trivial
1900.2.i.c.501.3		6	19.7	even	3	inner
1900.2.s.c.49.2		12	5.2	odd	4
1900.2.s.c.49.5		12	5.3	odd	4
1900.2.s.c.349.2		12	95.83	odd	12
1900.2.s.c.349.5		12	95.7	odd	12
3420.2.t.v.1261.3		6	285.254	odd	6
3420.2.t.v.3241.3		6	15.14	odd	2
7220.2.a.n.1.3		3	95.49	even	6
7220.2.a.o.1.1		3	95.84	odd	6

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)

\(f(q)\)	\(=\)	\(q+(1.28442 - 2.22469i) q^{3} -3.56885 q^{7} +(-1.79949 - 3.11682i) q^{9} +O(q^{10})\)	\(q+(1.28442 - 2.22469i) q^{3} -3.56885 q^{7} +(-1.79949 - 3.11682i) q^{9} +4.56885 q^{11} +(-0.500000 - 0.866025i) q^{13} +(2.86834 - 4.96812i) q^{17} +(-4.35327 + 0.221364i) q^{19} +(-4.58392 + 7.93958i) q^{21} +(-2.79949 - 4.84887i) q^{23} -1.53871 q^{27} +(-3.38341 - 5.86024i) q^{29} +4.59899 q^{31} +(5.86834 - 10.1643i) q^{33} -3.56885 q^{37} -2.56885 q^{39} +(-5.35327 + 9.27214i) q^{41} +(-5.65277 + 9.79088i) q^{43} +(-3.38341 - 5.86024i) q^{47} +5.73669 q^{49} +(-7.36834 - 12.7623i) q^{51} +(-1.70051 - 2.94536i) q^{53} +(-5.09899 + 9.96901i) q^{57} +(3.38341 - 5.86024i) q^{59} +(-4.06885 - 7.04745i) q^{61} +(6.42212 + 11.1234i) q^{63} +(-3.16784 - 5.48686i) q^{67} -14.3830 q^{69} +(0.515069 - 0.892126i) q^{71} +(-6.36834 + 11.0303i) q^{73} -16.3055 q^{77} +(-2.43115 + 4.21088i) q^{79} +(3.42212 - 5.92729i) q^{81} +9.40101 q^{83} -17.3830 q^{87} +(-6.13770 - 10.6308i) q^{89} +(1.78442 + 3.09071i) q^{91} +(5.90705 - 10.2313i) q^{93} +(1.31456 - 2.27689i) q^{97} +(-8.22162 - 14.2403i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{3} - 4 q^{7} - 8 q^{9}+O(q^{10}) \) 6 * q - q^3 - 4 * q^7 - 8 * q^9	\( 6 q - q^{3} - 4 q^{7} - 8 q^{9} + 10 q^{11} - 3 q^{13} - 3 q^{17} - 16 q^{21} - 14 q^{23} + 20 q^{27} - 6 q^{29} + 22 q^{31} + 15 q^{33} - 4 q^{37} + 2 q^{39} - 6 q^{41} - 5 q^{43} - 6 q^{47} - 6 q^{49} - 24 q^{51} - 13 q^{53} - 25 q^{57} + 6 q^{59} - 7 q^{61} - 5 q^{63} + 4 q^{67} + 30 q^{69} + 9 q^{71} - 18 q^{73} - 40 q^{77} - 32 q^{79} - 23 q^{81} + 62 q^{83} + 12 q^{87} - 2 q^{89} + 2 q^{91} - 14 q^{93} + 11 q^{97} - 3 q^{99}+O(q^{100}) \) 6 * q - q^3 - 4 * q^7 - 8 * q^9 + 10 * q^11 - 3 * q^13 - 3 * q^17 - 16 * q^21 - 14 * q^23 + 20 * q^27 - 6 * q^29 + 22 * q^31 + 15 * q^33 - 4 * q^37 + 2 * q^39 - 6 * q^41 - 5 * q^43 - 6 * q^47 - 6 * q^49 - 24 * q^51 - 13 * q^53 - 25 * q^57 + 6 * q^59 - 7 * q^61 - 5 * q^63 + 4 * q^67 + 30 * q^69 + 9 * q^71 - 18 * q^73 - 40 * q^77 - 32 * q^79 - 23 * q^81 + 62 * q^83 + 12 * q^87 - 2 * q^89 + 2 * q^91 - 14 * q^93 + 11 * q^97 - 3 * q^99

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