LMFDB - Embedded newform 1900.2.s.d.349.4

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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 17x^{14} + 215x^{12} - 1176x^{10} + 4775x^{8} - 2898x^{6} + 1385x^{4} - 164x^{2} + 16 $ x^16 - 17x^14 + 215x^12 - 1176x^10 + 4775x^8 - 2898x^6 + 1385x^4 - 164*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 380)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			349.4
Root			$-0.306096 - 0.176725i$ of defining polynomial
Character	$\chi$	$=$	1900.349
Dual form			1900.2.s.d.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.306096 + 0.176725i) q^{3} +4.30507i q^{7} +(-1.43754 + 2.48989i) q^{9} +O(q^{10})$	\(q+(-0.306096 + 0.176725i) q^{3} +4.30507i q^{7} +(-1.43754 + 2.48989i) q^{9} +6.01196 q^{11} +(5.15425 + 2.97581i) q^{13} +(-3.35591 + 1.93754i) q^{17} +(-4.19835 + 1.17212i) q^{19} +(-0.760812 - 1.31776i) q^{21} +(-0.678480 - 0.391721i) q^{23} -2.07654i q^{27} +(3.98179 - 6.89666i) q^{29} -4.49034 q^{31} +(-1.84024 + 1.06246i) q^{33} +0.988035i q^{37} -2.10360 q^{39} +(-3.15253 - 5.46035i) q^{41} +(-1.35967 + 0.785004i) q^{43} +(-1.09277 - 0.630909i) q^{47} -11.5336 q^{49} +(0.684822 - 1.18615i) q^{51} +(7.05712 + 4.07443i) q^{53} +(1.07796 - 1.10073i) q^{57} +(2.62834 + 4.55242i) q^{59} +(-2.80507 + 4.85852i) q^{61} +(-10.7191 - 6.18869i) q^{63} +(6.09963 + 3.52162i) q^{67} +0.276907 q^{69} +(2.90736 + 5.03570i) q^{71} +(-8.00250 + 4.62024i) q^{73} +25.8819i q^{77} +(-6.99743 - 12.1199i) q^{79} +(-3.94563 - 6.83404i) q^{81} +6.58197i q^{83} +2.81472i q^{87} +(-1.69237 + 2.93126i) q^{89} +(-12.8110 + 22.1894i) q^{91} +(1.37448 - 0.793555i) q^{93} +(6.40573 - 3.69835i) q^{97} +(-8.64242 + 14.9691i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 10 q^{9}+O(q^{10}) $ 16 * q + 10 * q^9	$ 16 q + 10 q^{9} + 8 q^{11} - 6 q^{19} + 16 q^{21} - 10 q^{29} - 40 q^{31} + 108 q^{39} - 16 q^{41} - 40 q^{49} + 24 q^{51} - 22 q^{59} + 24 q^{61} - 12 q^{69} + 28 q^{71} - 26 q^{79} - 48 q^{81} - 10 q^{89} - 92 q^{91} - 48 q^{99}+O(q^{100}) $ 16 * q + 10 * q^9 + 8 * q^11 - 6 * q^19 + 16 * q^21 - 10 * q^29 - 40 * q^31 + 108 * q^39 - 16 * q^41 - 40 * q^49 + 24 * q^51 - 22 * q^59 + 24 * q^61 - 12 * q^69 + 28 * q^71 - 26 * q^79 - 48 * q^81 - 10 * q^89 - 92 * q^91 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.306096	+	0.176725i	−0.176725	+	0.102032i	−0.585753	−	0.810490i	$-0.699201\pi$
$3$	−0.306096	+	0.176725i	−0.176725	+	0.102032i	0.409028	+	0.912522i	$0.365868\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$			4.30507i			1.62716i	0.581452	+	0.813581i	$0.302485\pi$
$7$			4.30507i			1.62716i	−0.581452	+	0.813581i	$0.697515\pi$
$8$		0			0
$9$	−1.43754	+	2.48989i	−0.479179	+	0.829962i
$10$		0			0
$11$	6.01196			1.81268			0.906338	−	0.422554i	$-0.138866\pi$
$11$	6.01196			1.81268			0.906338	+	0.422554i	$0.138866\pi$
$12$		0			0
$13$	5.15425	+	2.97581i	1.42953	+	0.825341i	0.997084	−	0.0763181i	$-0.0243164\pi$
$13$	5.15425	+	2.97581i	1.42953	+	0.825341i	0.432448	+	0.901659i	$0.357650\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.35591	+	1.93754i	−0.813928	+	0.469922i	−0.848318	−	0.529487i	$-0.822385\pi$
$17$	−3.35591	+	1.93754i	−0.813928	+	0.469922i	0.0343900	+	0.999408i	$0.489051\pi$
$18$		0			0
$19$	−4.19835	+	1.17212i	−0.963167	+	0.268903i
$19$	−4.19835	+	1.17212i	−0.963167	+	0.268903i
$20$		0			0
$21$	−0.760812	−	1.31776i	−0.166023	−	0.287560i
$22$		0			0
$23$	−0.678480	−	0.391721i	−0.141473	−	0.0816794i	0.427593	−	0.903971i	$-0.359362\pi$
$23$	−0.678480	−	0.391721i	−0.141473	−	0.0816794i	−0.569066	+	0.822292i	$0.692695\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	2.07654i		−	0.399631i
$28$		0			0
$29$	3.98179	−	6.89666i	0.739400	−	1.28068i	−0.213366	−	0.976972i	$-0.568443\pi$
$29$	3.98179	−	6.89666i	0.739400	−	1.28068i	0.952766	−	0.303706i	$-0.0982240\pi$
$30$		0			0
$31$	−4.49034			−0.806489			−0.403245	−	0.915092i	$-0.632118\pi$
$31$	−4.49034			−0.806489			−0.403245	+	0.915092i	$0.632118\pi$
$32$		0			0
$33$	−1.84024	+	1.06246i	−0.320345	+	0.184951i
$34$		0			0
$35$		0			0
$36$		0			0
$37$			0.988035i			0.162432i	0.996697	+	0.0812160i	$0.0258804\pi$
$37$			0.988035i			0.162432i	−0.996697	+	0.0812160i	$0.974120\pi$
$38$		0			0
$39$	−2.10360			−0.336845
$40$		0			0
$41$	−3.15253	−	5.46035i	−0.492343	−	0.852763i	0.507618	−	0.861582i	$-0.330526\pi$
$41$	−3.15253	−	5.46035i	−0.492343	−	0.852763i	−0.999961	+	0.00881921i	$0.997193\pi$
$42$		0			0
$43$	−1.35967	+	0.785004i	−0.207347	+	0.119712i	−0.600078	−	0.799942i	$-0.704864\pi$
$43$	−1.35967	+	0.785004i	−0.207347	+	0.119712i	0.392731	+	0.919654i	$0.371530\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.09277	−	0.630909i	−0.159396	−	0.0920275i	0.418180	−	0.908364i	$-0.362668\pi$
$47$	−1.09277	−	0.630909i	−0.159396	−	0.0920275i	−0.577576	+	0.816337i	$0.696001\pi$
$48$		0			0
$49$	−11.5336			−1.64766
$50$		0			0
$51$	0.684822	−	1.18615i	0.0958942	−	0.166094i
$52$		0			0
$53$	7.05712	+	4.07443i	0.969369	+	0.559666i	0.899044	−	0.437858i	$-0.144263\pi$
$53$	7.05712	+	4.07443i	0.969369	+	0.559666i	0.0703255	+	0.997524i	$0.477596\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	1.07796	−	1.10073i	0.142779	−	0.145796i
$58$		0			0
$59$	2.62834	+	4.55242i	0.342181	+	0.592675i	0.984837	−	0.173480i	$-0.0555011\pi$
$59$	2.62834	+	4.55242i	0.342181	+	0.592675i	−0.642657	+	0.766154i	$0.722168\pi$
$60$		0			0
$61$	−2.80507	+	4.85852i	−0.359152	+	0.622069i	−0.987819	−	0.155605i	$-0.950267\pi$
$61$	−2.80507	+	4.85852i	−0.359152	+	0.622069i	0.628668	+	0.777674i	$0.283601\pi$
$62$		0			0
$63$	−10.7191	−	6.18869i	−1.35048	−	0.779702i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	6.09963	+	3.52162i	0.745189	+	0.430235i	0.823953	−	0.566658i	$-0.191764\pi$
$67$	6.09963	+	3.52162i	0.745189	+	0.430235i	−0.0787642	+	0.996893i	$0.525097\pi$
$68$		0			0
$69$	0.276907			0.0333357
$70$		0			0
$71$	2.90736	+	5.03570i	0.345040	+	0.597628i	0.985361	−	0.170480i	$-0.0545319\pi$
$71$	2.90736	+	5.03570i	0.345040	+	0.597628i	−0.640321	+	0.768108i	$0.721199\pi$
$72$		0			0
$73$	−8.00250	+	4.62024i	−0.936621	+	0.540759i	−0.888900	−	0.458102i	$-0.848529\pi$
$73$	−8.00250	+	4.62024i	−0.936621	+	0.540759i	−0.0477218	+	0.998861i	$0.515196\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			25.8819i			2.94952i
$78$		0			0
$79$	−6.99743	−	12.1199i	−0.787273	−	1.36360i	−0.927632	−	0.373495i	$-0.878159\pi$
$79$	−6.99743	−	12.1199i	−0.787273	−	1.36360i	0.140359	−	0.990101i	$-0.455174\pi$
$80$		0			0
$81$	−3.94563	−	6.83404i	−0.438404	−	0.759338i
$82$		0			0
$83$			6.58197i			0.722465i	0.932476	+	0.361233i	$0.117644\pi$
$83$			6.58197i			0.722465i	−0.932476	+	0.361233i	$0.882356\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$			2.81472i			0.301770i
$88$		0			0
$89$	−1.69237	+	2.93126i	−0.179390	+	0.310713i	−0.941672	−	0.336532i	$-0.890746\pi$
$89$	−1.69237	+	2.93126i	−0.179390	+	0.310713i	0.762281	+	0.647246i	$0.224079\pi$
$90$		0			0
$91$	−12.8110	+	22.1894i	−1.34296	+	2.32608i
$92$		0			0
$93$	1.37448	−	0.793555i	0.142527	−	0.0822878i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	6.40573	−	3.69835i	0.650403	−	0.375510i	−0.138208	−	0.990403i	$-0.544134\pi$
$97$	6.40573	−	3.69835i	0.650403	−	0.375510i	0.788611	+	0.614893i	$0.210801\pi$
$98$		0			0
$99$	−8.64242	+	14.9691i	−0.868596	+	1.50445i
$100$		0			0
$101$	4.90369	−	8.49343i	0.487935	−	0.845128i	−0.511969	−	0.859004i	$-0.671084\pi$
$101$	4.90369	−	8.49343i	0.487935	−	0.845128i	0.999904	+	0.0138759i	$0.00441699\pi$
$102$		0			0
$103$			14.4368i			1.42250i	0.702938	+	0.711251i	$0.251871\pi$
$103$			14.4368i			1.42250i	−0.702938	+	0.711251i	$0.748129\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			9.49034i			0.917466i	0.888574	+	0.458733i	$0.151697\pi$
$107$			9.49034i			0.917466i	−0.888574	+	0.458733i	$0.848303\pi$
$108$		0			0
$109$	−1.30920	−	2.26759i	−0.125398	−	0.217196i	0.796490	−	0.604651i	$-0.206688\pi$
$109$	−1.30920	−	2.26759i	−0.125398	−	0.217196i	−0.921889	+	0.387455i	$0.873354\pi$
$110$		0			0
$111$	−0.174610	−	0.302434i	−0.0165733	−	0.0287058i
$112$		0			0
$113$		−	13.6705i		−	1.28601i	−0.765862	−	0.643005i	$-0.777687\pi$
$113$		−	13.6705i		−	1.28601i	0.765862	−	0.643005i	$-0.222313\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−14.8188	+	8.55567i	−1.37000	+	0.790972i
$118$		0			0
$119$	−8.34122	−	14.4474i	−0.764639	−	1.32439i
$120$		0			0
$121$	25.1437			2.28579
$122$		0			0
$123$	1.92996	+	1.11426i	0.174018	+	0.100470i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	11.3165	+	6.53359i	1.00418	+	0.579762i	0.909482	−	0.415744i	$-0.136479\pi$
$127$	11.3165	+	6.53359i	1.00418	+	0.579762i	0.0946960	+	0.995506i	$0.469812\pi$
$128$		0			0
$129$	0.277459	−	0.480574i	0.0244289	−	0.0423122i
$130$		0			0
$131$	3.75070	+	6.49640i	0.327700	+	0.567593i	0.982055	−	0.188594i	$-0.0603931\pi$
$131$	3.75070	+	6.49640i	0.327700	+	0.567593i	−0.654355	+	0.756188i	$0.727060\pi$
$132$		0			0
$133$	−5.04606	−	18.0742i	−0.437549	−	1.56723i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−7.30059	−	4.21500i	−0.623731	−	0.360111i	0.154589	−	0.987979i	$-0.450595\pi$
$137$	−7.30059	−	4.21500i	−0.623731	−	0.360111i	−0.778320	+	0.627867i	$0.783928\pi$
$138$		0			0
$139$	4.38961	−	7.60302i	0.372322	−	0.644880i	−0.617601	−	0.786492i	$-0.711895\pi$
$139$	4.38961	−	7.60302i	0.372322	−	0.644880i	0.989922	+	0.141612i	$0.0452285\pi$
$140$		0			0
$141$	0.445989			0.0375591
$142$		0			0
$143$	30.9872	+	17.8905i	2.59128	+	1.49607i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	3.53039	−	2.03827i	0.291182	−	0.168114i
$148$		0			0
$149$	−0.915913	−	1.58641i	−0.0750345	−	0.129964i	0.826067	−	0.563572i	$-0.190573\pi$
$149$	−0.915913	−	1.58641i	−0.0750345	−	0.129964i	−0.901101	+	0.433609i	$0.857240\pi$
$150$		0			0
$151$	−0.389869			−0.0317271			−0.0158635	−	0.999874i	$-0.505050\pi$
$151$	−0.389869			−0.0317271			−0.0158635	+	0.999874i	$0.505050\pi$
$152$		0			0
$153$		−	11.1411i		−	0.900706i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	2.38344	−	1.37608i	0.190219	−	0.109823i	−0.401866	−	0.915698i	$-0.631638\pi$
$157$	2.38344	−	1.37608i	0.190219	−	0.109823i	0.592085	+	0.805875i	$0.298305\pi$
$158$		0			0
$159$	−2.88021			−0.228416
$160$		0			0
$161$	1.68638	−	2.92090i	0.132906	−	0.230199i
$162$		0			0
$163$		−	15.0953i		−	1.18236i	−0.806540	−	0.591179i	$-0.798663\pi$
$163$		−	15.0953i		−	1.18236i	0.806540	−	0.591179i	$-0.201337\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.58771	+	1.49402i	0.200243	+	0.115611i	0.596769	−	0.802413i	$-0.296451\pi$
$167$	2.58771	+	1.49402i	0.200243	+	0.115611i	−0.396526	+	0.918024i	$0.629784\pi$
$168$		0			0
$169$	11.2109	+	19.4178i	0.862374	+	1.49368i
$170$		0			0
$171$	3.11683	−	12.1384i	0.238350	−	0.928245i
$172$		0			0
$173$	−20.0822	+	11.5945i	−1.52682	+	0.881513i	−0.527332	+	0.849659i	$0.676808\pi$
$173$	−20.0822	+	11.5945i	−1.52682	+	0.881513i	−0.999493	+	0.0318535i	$0.989859\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1.60905	−	0.928986i	−0.120944	−	0.0698269i
$178$		0			0
$179$	13.5091			1.00972			0.504860	−	0.863201i	$-0.331544\pi$
$179$	13.5091			1.00972			0.504860	+	0.863201i	$0.331544\pi$
$180$		0			0
$181$	10.1559	−	17.5906i	0.754886	−	1.30750i	−0.190546	−	0.981678i	$-0.561026\pi$
$181$	10.1559	−	17.5906i	0.754886	−	1.30750i	0.945431	−	0.325822i	$-0.105641\pi$
$182$		0			0
$183$		−	1.98290i		−	0.146580i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−20.1756	+	11.6484i	−1.47539	+	0.851816i
$188$		0			0
$189$	8.93965			0.650264
$190$		0			0
$191$	−7.04838			−0.510003			−0.255002	−	0.966941i	$-0.582076\pi$
$191$	−7.04838			−0.510003			−0.255002	+	0.966941i	$0.582076\pi$
$192$		0			0
$193$	−20.5926	+	11.8892i	−1.48229	+	0.855800i	−0.999798	−	0.0201010i	$-0.993601\pi$
$193$	−20.5926	+	11.8892i	−1.48229	+	0.855800i	−0.482491	+	0.875901i	$0.660268\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	23.7428i		−	1.69160i	−0.533497	−	0.845802i	$-0.679122\pi$
$197$		−	23.7428i		−	1.69160i	0.533497	−	0.845802i	$-0.320878\pi$
$198$		0			0
$199$	−11.4893	+	19.9001i	−0.814457	+	1.41068i	0.0952595	+	0.995452i	$0.469632\pi$
$199$	−11.4893	+	19.9001i	−0.814457	+	1.41068i	−0.909717	+	0.415229i	$0.863701\pi$
$200$		0			0
$201$	−2.48943			−0.175591
$202$		0			0
$203$	29.6906	+	17.1419i	2.08387	+	1.20312i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.95068	−	1.12623i	0.135582	−	0.0782781i
$208$		0			0
$209$	−25.2403	+	7.04675i	−1.74591	+	0.487434i
$210$		0			0
$211$	0.692366	+	1.19921i	0.0476645	+	0.0825573i	0.888873	−	0.458153i	$-0.151489\pi$
$211$	0.692366	+	1.19921i	0.0476645	+	0.0825573i	−0.841209	+	0.540710i	$0.818156\pi$
$212$		0			0
$213$	−1.77987	−	1.02761i	−0.121954	−	0.0704104i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		−	19.3312i		−	1.31229i
$218$		0			0
$219$	1.63302	−	2.82848i	0.110349	−	0.191131i
$220$		0			0
$221$	−23.0629			−1.55138
$222$		0			0
$223$	−20.1783	+	11.6500i	−1.35124	+	0.780139i	−0.988423	−	0.151721i	$-0.951519\pi$
$223$	−20.1783	+	11.6500i	−1.35124	+	0.780139i	−0.362818	+	0.931860i	$0.618185\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$			4.48943i			0.297974i	0.988839	+	0.148987i	$0.0476013\pi$
$227$			4.48943i			0.297974i	−0.988839	+	0.148987i	$0.952399\pi$
$228$		0			0
$229$	−9.20830			−0.608501			−0.304251	−	0.952592i	$-0.598406\pi$
$229$	−9.20830			−0.608501			−0.304251	+	0.952592i	$0.598406\pi$
$230$		0			0
$231$	−4.57397	−	7.92236i	−0.300945	−	0.521253i
$232$		0			0
$233$	−3.74581	+	2.16265i	−0.245396	+	0.141680i	−0.617654	−	0.786450i	$-0.711917\pi$
$233$	−3.74581	+	2.16265i	−0.245396	+	0.141680i	0.372258	+	0.928129i	$0.378584\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	4.28378	+	2.47324i	0.278261	+	0.160654i
$238$		0			0
$239$	14.8267			0.959059			0.479529	−	0.877526i	$-0.340807\pi$
$239$	14.8267			0.959059			0.479529	+	0.877526i	$0.340807\pi$
$240$		0			0
$241$	−1.44453	+	2.50199i	−0.0930500	+	0.161167i	−0.908793	−	0.417247i	$-0.862995\pi$
$241$	−1.44453	+	2.50199i	−0.0930500	+	0.161167i	0.815743	+	0.578414i	$0.196328\pi$
$242$		0			0
$243$	7.81050	+	4.50940i	0.501044	+	0.289278i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−25.1273	−	6.45207i	−1.59881	−	0.410535i
$248$		0			0
$249$	−1.16320	−	2.01472i	−0.0737147	−	0.127678i
$250$		0			0
$251$	−7.65253	+	13.2546i	−0.483024	+	0.836621i	−0.999810	−	0.0194930i	$-0.993795\pi$
$251$	−7.65253	+	13.2546i	−0.483024	+	0.836621i	0.516786	+	0.856114i	$0.327128\pi$
$252$		0			0
$253$	−4.07900	−	2.35501i	−0.256445	−	0.148058i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	11.3313	+	6.54214i	0.706828	+	0.408087i	0.809886	−	0.586588i	$-0.199529\pi$
$257$	11.3313	+	6.54214i	0.706828	+	0.408087i	−0.103057	+	0.994675i	$0.532863\pi$
$258$		0			0
$259$	−4.25356			−0.264303
$260$		0			0
$261$	11.4479	+	19.8284i	0.708610	+	1.22735i
$262$		0			0
$263$	16.7832	−	9.68980i	1.03490	−	0.597499i	0.116514	−	0.993189i	$-0.462828\pi$
$263$	16.7832	−	9.68980i	1.03490	−	0.597499i	0.918384	+	0.395691i	$0.129495\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	1.19633i		−	0.0732144i
$268$		0			0
$269$	−0.728523	−	1.26184i	−0.0444188	−	0.0769357i	0.842961	−	0.537974i	$-0.180810\pi$
$269$	−0.728523	−	1.26184i	−0.0444188	−	0.0769357i	−0.887380	+	0.461039i	$0.847477\pi$
$270$		0			0
$271$	−6.28133	−	10.8796i	−0.381563	−	0.660887i	0.609722	−	0.792615i	$-0.291281\pi$
$271$	−6.28133	−	10.8796i	−0.381563	−	0.660887i	−0.991286	+	0.131728i	$0.957948\pi$
$272$		0			0
$273$		−	9.05612i		−	0.548101i
$274$		0			0
$275$		0			0
$276$		0			0
$277$			4.39448i			0.264039i	0.991247	+	0.132019i	$0.0421461\pi$
$277$			4.39448i			0.264039i	−0.991247	+	0.132019i	$0.957854\pi$
$278$		0			0
$279$	6.45503	−	11.1804i	0.386453	−	0.669355i
$280$		0			0
$281$	−2.16265	+	3.74581i	−0.129013	+	0.223456i	−0.923294	−	0.384093i	$-0.874514\pi$
$281$	−2.16265	+	3.74581i	−0.129013	+	0.223456i	0.794282	+	0.607550i	$0.207847\pi$
$282$		0			0
$283$	6.49319	−	3.74885i	0.385980	−	0.222846i	−0.294437	−	0.955671i	$-0.595132\pi$
$283$	6.49319	−	3.74885i	0.385980	−	0.222846i	0.680417	+	0.732825i	$0.261799\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	23.5072	−	13.5719i	1.38758	−	0.801122i
$288$		0			0
$289$	−0.991903	+	1.71803i	−0.0583472	+	0.101060i
$290$		0			0
$291$	−1.30718	+	2.26410i	−0.0766282	+	0.132724i
$292$		0			0
$293$		−	22.2837i		−	1.30183i	−0.759151	−	0.650915i	$-0.774385\pi$
$293$		−	22.2837i		−	1.30183i	0.759151	−	0.650915i	$-0.225615\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		−	12.4841i		−	0.724401i
$298$		0			0
$299$	−2.33137	−	4.03805i	−0.134827	−	0.233527i
$300$		0			0
$301$	−3.37949	−	5.85345i	−0.194791	−	0.337387i
$302$		0			0
$303$			3.46641i			0.199140i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	26.2238	−	15.1403i	1.49667	−	0.864103i	0.496677	−	0.867935i	$-0.334553\pi$
$307$	26.2238	−	15.1403i	1.49667	−	0.864103i	0.999993	+	0.00383236i	$0.00121988\pi$
$308$		0			0
$309$	−2.55134	−	4.41906i	−0.145141	−	0.251391i
$310$		0			0
$311$	−5.37224			−0.304632			−0.152316	−	0.988332i	$-0.548673\pi$
$311$	−5.37224			−0.304632			−0.152316	+	0.988332i	$0.548673\pi$
$312$		0			0
$313$	4.16331	+	2.40369i	0.235324	+	0.135864i	0.613026	−	0.790063i	$-0.289952\pi$
$313$	4.16331	+	2.40369i	0.235324	+	0.135864i	−0.377702	+	0.925927i	$0.623286\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−25.7824	−	14.8855i	−1.44808	−	0.836052i	−0.449717	−	0.893171i	$-0.648475\pi$
$317$	−25.7824	−	14.8855i	−1.44808	−	0.836052i	−0.998367	+	0.0571197i	$0.981808\pi$
$318$		0			0
$319$	23.9384	−	41.4625i	1.34029	−	2.32145i
$320$		0			0
$321$	−1.67718	−	2.90496i	−0.0936110	−	0.162139i
$322$		0			0
$323$	11.8183	−	12.0680i	0.657586	−	0.671481i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	0.801480	+	0.462735i	0.0443220	+	0.0255893i
$328$		0			0
$329$	2.71610	−	4.70443i	0.149744	−	0.259364i
$330$		0			0
$331$	30.8042			1.69315			0.846577	−	0.532266i	$-0.178659\pi$
$331$	30.8042			1.69315			0.846577	+	0.532266i	$0.178659\pi$
$332$		0			0
$333$	−2.46010	−	1.42034i	−0.134812	−	0.0778340i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	5.75957	−	3.32529i	0.313744	−	0.181140i	−0.334857	−	0.942269i	$-0.608688\pi$
$337$	5.75957	−	3.32529i	0.313744	−	0.181140i	0.648601	+	0.761129i	$0.275355\pi$
$338$		0			0
$339$	2.41591	+	4.18448i	0.131214	+	0.227270i
$340$		0			0
$341$	−26.9958			−1.46190
$342$		0			0
$343$		−	19.5174i		−	1.05384i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−13.3460	+	7.70534i	−0.716453	+	0.413644i	−0.813446	−	0.581641i	$-0.802411\pi$
$347$	−13.3460	+	7.70534i	−0.716453	+	0.413644i	0.0969930	+	0.995285i	$0.469078\pi$
$348$		0			0
$349$	27.0157			1.44612			0.723058	−	0.690788i	$-0.242736\pi$
$349$	27.0157			1.44612			0.723058	+	0.690788i	$0.242736\pi$
$350$		0			0
$351$	6.17939	−	10.7030i	0.329832	−	0.571285i
$352$		0			0
$353$			19.7783i			1.05269i	0.850270	+	0.526346i	$0.176439\pi$
$353$			19.7783i			1.05269i	−0.850270	+	0.526346i	$0.823561\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	5.10644	+	2.94820i	0.270261	+	0.156035i
$358$		0			0
$359$	17.8408	+	30.9011i	0.941600	+	1.63090i	0.762420	+	0.647082i	$0.224011\pi$
$359$	17.8408	+	30.9011i	0.941600	+	1.63090i	0.179179	+	0.983816i	$0.442656\pi$
$360$		0			0
$361$	16.2523	−	9.84195i	0.855382	−	0.517997i
$362$		0			0
$363$	−7.69640	+	4.44352i	−0.403956	+	0.233224i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−1.82272	−	1.05235i	−0.0951454	−	0.0549322i	0.451672	−	0.892184i	$-0.350828\pi$
$367$	−1.82272	−	1.05235i	−0.0951454	−	0.0549322i	−0.546818	+	0.837252i	$0.684161\pi$
$368$		0			0
$369$	18.1275			0.943681
$370$		0			0
$371$	−17.5407	+	30.3813i	−0.910667	+	1.57732i
$372$		0			0
$373$		−	32.0208i		−	1.65797i	−0.559268	−	0.828987i	$-0.688918\pi$
$373$		−	32.0208i		−	1.65797i	0.559268	−	0.828987i	$-0.311082\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	41.0463	−	23.6981i	2.11399	−	1.22051i
$378$		0			0
$379$	2.24784			0.115464			0.0577319	−	0.998332i	$-0.481613\pi$
$379$	2.24784			0.115464			0.0577319	+	0.998332i	$0.481613\pi$
$380$		0			0
$381$	−4.61859			−0.236617
$382$		0			0
$383$	2.31192	−	1.33479i	0.118133	−	0.0682044i	−0.439769	−	0.898111i	$-0.644940\pi$
$383$	2.31192	−	1.33479i	0.118133	−	0.0682044i	0.557902	+	0.829907i	$0.311606\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$		−	4.51389i		−	0.229454i
$388$		0			0
$389$	7.76036	−	13.4413i	0.393466	−	0.681503i	−0.599438	−	0.800421i	$-0.704609\pi$
$389$	7.76036	−	13.4413i	0.393466	−	0.681503i	0.992904	+	0.118918i	$0.0379427\pi$
$390$		0			0
$391$	3.03589			0.153532
$392$		0			0
$393$	−2.29615	−	1.32568i	−0.115825	−	0.0668719i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−2.16228	+	1.24839i	−0.108522	+	0.0626551i	−0.553278	−	0.832996i	$-0.686623\pi$
$397$	−2.16228	+	1.24839i	−0.108522	+	0.0626551i	0.444757	+	0.895651i	$0.353290\pi$
$398$		0			0
$399$	4.73873	+	4.64067i	0.237233	+	0.232324i
$400$		0			0
$401$	10.8590	+	18.8083i	0.542271	+	0.939242i	0.998773	+	0.0495192i	$0.0157689\pi$
$401$	10.8590	+	18.8083i	0.542271	+	0.939242i	−0.456502	+	0.889723i	$0.650898\pi$
$402$		0			0
$403$	−23.1443	−	13.3624i	−1.15290	−	0.665628i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			5.94003i			0.294437i
$408$		0			0
$409$	12.1200	−	20.9924i	0.599294	−	1.03801i	−0.393631	−	0.919269i	$-0.628781\pi$
$409$	12.1200	−	20.9924i	0.599294	−	1.03801i	0.992925	−	0.118740i	$-0.0378855\pi$
$410$		0			0
$411$	2.97958			0.146972
$412$		0			0
$413$	−19.5985	+	11.3152i	−0.964377	+	0.556784i
$414$		0			0
$415$		0			0
$416$		0			0
$417$			3.10301i			0.151955i
$418$		0			0
$419$	37.6543			1.83953			0.919766	−	0.392467i	$-0.128378\pi$
$419$	37.6543			1.83953			0.919766	+	0.392467i	$0.128378\pi$
$420$		0			0
$421$	18.6884	+	32.3693i	0.910818	+	1.57758i	0.812911	+	0.582388i	$0.197881\pi$
$421$	18.6884	+	32.3693i	0.910818	+	1.57758i	0.0979071	+	0.995196i	$0.468785\pi$
$422$		0			0
$423$	3.14178	−	1.81391i	0.152759	−	0.0881953i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−20.9162	−	12.0760i	−1.01221	−	0.584398i
$428$		0			0
$429$	−12.6467			−0.610591
$430$		0			0
$431$	−5.41491	+	9.37889i	−0.260827	+	0.451765i	−0.966462	−	0.256810i	$-0.917329\pi$
$431$	−5.41491	+	9.37889i	−0.260827	+	0.451765i	0.705635	+	0.708576i	$0.250662\pi$
$432$		0			0
$433$	−9.89055	−	5.71031i	−0.475310	−	0.274420i	0.243150	−	0.969989i	$-0.421819\pi$
$433$	−9.89055	−	5.71031i	−0.475310	−	0.274420i	−0.718460	+	0.695569i	$0.755153\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	3.30764	+	0.849319i	0.158226	+	0.0406284i
$438$		0			0
$439$	15.0612	+	26.0868i	0.718832	+	1.24505i	0.961463	+	0.274934i	$0.0886561\pi$
$439$	15.0612	+	26.0868i	0.718832	+	1.24505i	−0.242631	+	0.970119i	$0.578011\pi$
$440$		0			0
$441$	16.5800	−	28.7173i	0.789522	−	1.36749i
$442$		0			0
$443$	17.8479	+	10.3045i	0.847981	+	0.489582i	0.859969	−	0.510346i	$-0.170483\pi$
$443$	17.8479	+	10.3045i	0.847981	+	0.489582i	−0.0119880	+	0.999928i	$0.503816\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	0.560715	+	0.323729i	0.0265209	+	0.0153119i
$448$		0			0
$449$	3.61436			0.170572			0.0852861	−	0.996357i	$-0.472820\pi$
$449$	3.61436			0.170572			0.0852861	+	0.996357i	$0.472820\pi$
$450$		0			0
$451$	−18.9529	−	32.8274i	−0.892458	−	1.54578i
$452$		0			0
$453$	0.119338	−	0.0688995i	0.00560697	−	0.00323718i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	5.50452i		−	0.257491i	−0.991678	−	0.128745i	$-0.958905\pi$
$457$		−	5.50452i		−	0.257491i	0.991678	−	0.128745i	$-0.0410950\pi$
$458$		0			0
$459$	4.02338	+	6.96869i	0.187795	+	0.325271i
$460$		0			0
$461$	−9.66053	−	16.7325i	−0.449936	−	0.779312i	0.548446	−	0.836186i	$-0.315220\pi$
$461$	−9.66053	−	16.7325i	−0.449936	−	0.779312i	−0.998381	+	0.0568746i	$0.981886\pi$
$462$		0			0
$463$			1.05722i			0.0491334i	0.999698	+	0.0245667i	$0.00782061\pi$
$463$			1.05722i			0.0491334i	−0.999698	+	0.0245667i	$0.992179\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	21.9413i		−	1.01532i	−0.861556	−	0.507662i	$-0.830510\pi$
$467$		−	21.9413i		−	1.01532i	0.861556	−	0.507662i	$-0.169490\pi$
$468$		0			0
$469$	−15.1608	+	26.2593i	−0.700062	+	1.21254i
$470$		0			0
$471$	−0.486375	+	0.842426i	−0.0224110	+	0.0388169i
$472$		0			0
$473$	−8.17427	+	4.71942i	−0.375853	+	0.216999i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−20.2897	+	11.7143i	−0.929003	+	0.536360i
$478$		0			0
$479$	−6.60203	+	11.4351i	−0.301655	+	0.522481i	−0.976511	−	0.215468i	$-0.930872\pi$
$479$	−6.60203	+	11.4351i	−0.301655	+	0.522481i	0.674856	+	0.737949i	$0.264206\pi$
$480$		0			0
$481$	−2.94020	+	5.09258i	−0.134062	+	0.232202i
$482$		0			0
$483$			1.19210i			0.0542426i
$484$		0			0
$485$		0			0
$486$		0			0
$487$		−	15.5627i		−	0.705211i	−0.935772	−	0.352606i	$-0.885296\pi$
$487$		−	15.5627i		−	0.705211i	0.935772	−	0.352606i	$-0.114704\pi$
$488$		0			0
$489$	2.66772	+	4.62063i	0.120638	+	0.208952i
$490$		0			0
$491$	14.7978	+	25.6306i	0.667816	+	1.15669i	0.978514	+	0.206182i	$0.0661040\pi$
$491$	14.7978	+	25.6306i	0.667816	+	1.15669i	−0.310698	+	0.950509i	$0.600563\pi$
$492$		0			0
$493$			30.8595i			1.38984i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−21.6790	+	12.5164i	−0.972437	+	0.561437i
$498$		0			0
$499$	−2.92190	−	5.06087i	−0.130802	−	0.226556i	0.793184	−	0.608982i	$-0.208422\pi$
$499$	−2.92190	−	5.06087i	−0.130802	−	0.226556i	−0.923986	+	0.382426i	$0.875089\pi$
$500$		0			0
$501$	−1.05612			−0.0471840
$502$		0			0
$503$	−5.44807	−	3.14544i	−0.242917	−	0.140248i	0.373600	−	0.927590i	$-0.378123\pi$
$503$	−5.44807	−	3.14544i	−0.242917	−	0.140248i	−0.616517	+	0.787342i	$0.711457\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−6.86321	−	3.96248i	−0.304806	−	0.175980i
$508$		0			0
$509$	−1.84591	+	3.19720i	−0.0818183	+	0.141713i	−0.904031	−	0.427467i	$-0.859406\pi$
$509$	−1.84591	+	3.19720i	−0.0818183	+	0.141713i	0.822213	+	0.569180i	$0.192739\pi$
$510$		0			0
$511$	−19.8905	−	34.4513i	−0.879902	−	1.52403i
$512$		0			0
$513$	2.43396	+	8.71805i	0.107462	+	0.384911i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−6.56967	−	3.79300i	−0.288934	−	0.166816i
$518$		0			0
$519$	4.09807	−	7.09806i	0.179885	−	0.311570i
$520$		0			0
$521$	29.0510			1.27275			0.636373	−	0.771381i	$-0.280434\pi$
$521$	29.0510			1.27275			0.636373	+	0.771381i	$0.280434\pi$
$522$		0			0
$523$	−15.9640	−	9.21685i	−0.698059	−	0.403025i	0.108565	−	0.994089i	$-0.465374\pi$
$523$	−15.9640	−	9.21685i	−0.698059	−	0.403025i	−0.806624	+	0.591065i	$0.798708\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	15.0692	−	8.70020i	0.656424	−	0.378987i
$528$		0			0
$529$	−11.1931	−	19.3870i	−0.486657	−	0.842915i
$530$		0			0
$531$	−15.1133			−0.655863
$532$		0			0
$533$		−	37.5253i		−	1.62540i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−4.13510	+	2.38740i	−0.178443	+	0.103024i
$538$		0			0
$539$	−69.3395			−2.98666
$540$		0			0
$541$	21.0875	−	36.5246i	0.906622	−	1.57032i	0.0878981	−	0.996129i	$-0.471985\pi$
$541$	21.0875	−	36.5246i	0.906622	−	1.57032i	0.818724	−	0.574187i	$-0.194682\pi$
$542$		0			0
$543$			7.17923i			0.308090i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	13.6437	+	7.87719i	0.583362	+	0.336804i	0.762468	−	0.647025i	$-0.223987\pi$
$547$	13.6437	+	7.87719i	0.583362	+	0.336804i	−0.179106	+	0.983830i	$0.557321\pi$
$548$		0			0
$549$	−8.06477	−	13.9686i	−0.344196	−	0.596165i
$550$		0			0
$551$	−8.63321	+	33.6217i	−0.367787	+	1.43233i
$552$		0			0
$553$	52.1770	−	30.1244i	2.21879	−	1.28102i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	20.0786	+	11.5924i	0.850757	+	0.491185i	0.860906	−	0.508764i	$-0.169897\pi$
$557$	20.0786	+	11.5924i	0.850757	+	0.491185i	−0.0101493	+	0.999948i	$0.503231\pi$
$558$		0			0
$559$	−9.34408			−0.395213
$560$		0			0
$561$	4.11712	−	7.13107i	0.173825	−	0.301074i
$562$		0			0
$563$		−	0.970934i		−	0.0409200i	−0.999791	−	0.0204600i	$-0.993487\pi$
$563$		−	0.970934i		−	0.0409200i	0.999791	−	0.0204600i	$-0.00651307\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	29.4210	−	16.9862i	1.23556	−	0.713354i
$568$		0			0
$569$	30.1395			1.26351			0.631757	−	0.775167i	$-0.282334\pi$
$569$	30.1395			1.26351			0.631757	+	0.775167i	$0.282334\pi$
$570$		0			0
$571$	−31.8976			−1.33487			−0.667436	−	0.744667i	$-0.732608\pi$
$571$	−31.8976			−1.33487			−0.667436	+	0.744667i	$0.732608\pi$
$572$		0			0
$573$	2.15748	−	1.24562i	0.0901302	−	0.0520367i
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	23.2889i		−	0.969528i	−0.874645	−	0.484764i	$-0.838905\pi$
$577$		−	23.2889i		−	0.969528i	0.874645	−	0.484764i	$-0.161095\pi$
$578$		0			0
$579$	4.20222	−	7.27845i	0.174638	−	0.302482i
$580$		0			0
$581$	−28.3358			−1.17557
$582$		0			0
$583$	42.4271	+	24.4953i	1.75715	+	1.01449i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−8.21094	+	4.74059i	−0.338902	+	0.195665i	−0.659786	−	0.751453i	$-0.729353\pi$
$587$	−8.21094	+	4.74059i	−0.338902	+	0.195665i	0.320885	+	0.947118i	$0.396020\pi$
$588$		0			0
$589$	18.8520	−	5.26323i	0.776784	−	0.216867i
$590$		0			0
$591$	4.19594	+	7.26758i	0.172598	+	0.298948i
$592$		0			0
$593$	36.7600	+	21.2234i	1.50955	+	0.871540i	0.999938	+	0.0111366i	$0.00354497\pi$
$593$	36.7600	+	21.2234i	1.50955	+	0.871540i	0.509614	+	0.860403i	$0.329788\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		−	8.12180i		−	0.332403i
$598$		0			0
$599$	−12.8961	+	22.3368i	−0.526922	+	0.912656i	0.472586	+	0.881285i	$0.343321\pi$
$599$	−12.8961	+	22.3368i	−0.526922	+	0.912656i	−0.999508	+	0.0313711i	$0.990013\pi$
$600$		0			0
$601$	0.206080			0.00840619			0.00420310	−	0.999991i	$-0.498662\pi$
$601$	0.206080			0.00840619			0.00420310	+	0.999991i	$0.498662\pi$
$602$		0			0
$603$	−17.5369	+	10.1249i	−0.714157	+	0.412319i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		−	0.100472i		−	0.00407802i	−0.999998	−	0.00203901i	$-0.999351\pi$
$607$		−	0.100472i		−	0.00407802i	0.999998	−	0.00203901i	$-0.000649038\pi$
$608$		0			0
$609$	−12.1176			−0.491029
$610$		0			0
$611$	−3.75493	−	6.50373i	−0.151908	−	0.263113i
$612$		0			0
$613$	−34.1907	+	19.7400i	−1.38095	+	0.797292i	−0.992272	−	0.124081i	$-0.960402\pi$
$613$	−34.1907	+	19.7400i	−1.38095	+	0.797292i	−0.388679	+	0.921373i	$0.627068\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−24.5359	−	14.1658i	−0.987777	−	0.570294i	−0.0831682	−	0.996536i	$-0.526504\pi$
$617$	−24.5359	−	14.1658i	−0.987777	−	0.570294i	−0.904609	+	0.426242i	$0.859837\pi$
$618$		0			0
$619$	1.39670			0.0561380			0.0280690	−	0.999606i	$-0.491064\pi$
$619$	1.39670			0.0561380			0.0280690	+	0.999606i	$0.491064\pi$
$620$		0			0
$621$	−0.813425	+	1.40889i	−0.0326416	+	0.0565369i
$622$		0			0
$623$	−12.6193	−	7.28575i	−0.505581	−	0.291897i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	6.48063	−	6.61758i	0.258812	−	0.264281i
$628$		0			0
$629$	−1.91435	−	3.31576i	−0.0763303	−	0.132208i
$630$		0			0
$631$	−4.07397	+	7.05633i	−0.162182	+	0.280908i	−0.935651	−	0.352926i	$-0.885187\pi$
$631$	−4.07397	+	7.05633i	−0.162182	+	0.280908i	0.773469	+	0.633834i	$0.218520\pi$
$632$		0			0
$633$	−0.423862	−	0.244717i	−0.0168470	−	0.00972661i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−59.4470	−	34.3217i	−2.35538	−	1.35988i
$638$		0			0
$639$	−16.7178			−0.661344
$640$		0			0
$641$	−9.76367	−	16.9112i	−0.385642	−	0.667951i	0.606216	−	0.795300i	$-0.292687\pi$
$641$	−9.76367	−	16.9112i	−0.385642	−	0.667951i	−0.991858	+	0.127349i	$0.959353\pi$
$642$		0			0
$643$	37.4028	−	21.5945i	1.47502	−	0.851604i	0.475417	−	0.879761i	$-0.342297\pi$
$643$	37.4028	−	21.5945i	1.47502	−	0.851604i	0.999604	+	0.0281570i	$0.00896384\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	27.4390i		−	1.07874i	−0.842069	−	0.539370i	$-0.818662\pi$
$647$		−	27.4390i		−	1.07874i	0.842069	−	0.539370i	$-0.181338\pi$
$648$		0			0
$649$	15.8015	+	27.3690i	0.620263	+	1.07433i
$650$		0			0
$651$	3.41630	+	5.91721i	0.133896	+	0.231914i
$652$		0			0
$653$		−	3.40515i		−	0.133254i	−0.997778	−	0.0666270i	$-0.978776\pi$
$653$		−	3.40515i		−	0.133254i	0.997778	−	0.0666270i	$-0.0212238\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		−	26.5671i		−	1.03648i
$658$		0			0
$659$	6.09862	−	10.5631i	0.237569	−	0.411481i	−0.722448	−	0.691426i	$-0.756983\pi$
$659$	6.09862	−	10.5631i	0.237569	−	0.411481i	0.960016	+	0.279945i	$0.0903162\pi$
$660$		0			0
$661$	19.0683	−	33.0272i	0.741670	−	1.28461i	−0.210064	−	0.977688i	$-0.567367\pi$
$661$	19.0683	−	33.0272i	0.741670	−	1.28461i	0.951734	−	0.306923i	$-0.0992994\pi$
$662$		0			0
$663$	7.05948	−	4.07580i	0.274168	−	0.158291i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−5.40313	+	3.11950i	−0.209210	+	0.120788i
$668$		0			0
$669$	4.11768	−	7.13202i	0.159199	−	0.275740i
$670$		0			0
$671$	−16.8640	+	29.2092i	−0.651026	+	1.12761i
$672$		0			0
$673$		−	37.9505i		−	1.46288i	−0.681903	−	0.731442i	$-0.738848\pi$
$673$		−	37.9505i		−	1.46288i	0.681903	−	0.731442i	$-0.261152\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			32.4499i			1.24715i	0.781763	+	0.623575i	$0.214321\pi$
$677$			32.4499i			1.24715i	−0.781763	+	0.623575i	$0.785679\pi$
$678$		0			0
$679$	15.9216	+	27.5771i	0.611016	+	1.05831i
$680$		0			0
$681$	−0.793394	−	1.37420i	−0.0304029	−	0.0526594i
$682$		0			0
$683$			40.5283i			1.55077i	0.631488	+	0.775385i	$0.282444\pi$
$683$			40.5283i			1.55077i	−0.631488	+	0.775385i	$0.717556\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	2.81863	−	1.62733i	0.107537	−	0.0620867i
$688$		0			0
$689$	24.2494	+	42.0012i	0.923830	+	1.60012i
$690$		0			0
$691$	1.78657			0.0679642			0.0339821	−	0.999422i	$-0.489181\pi$
$691$	1.78657			0.0679642			0.0339821	+	0.999422i	$0.489181\pi$
$692$		0			0
$693$	−64.4430	−	37.2062i	−2.44799	−	1.41335i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	21.1592	+	12.2163i	0.801464	+	0.462725i
$698$		0			0
$699$	0.764386	−	1.32396i	0.0289117	−	0.0500766i
$700$		0			0
$701$	21.8614	+	37.8650i	0.825693	+	1.43014i	0.901388	+	0.433011i	$0.142549\pi$
$701$	21.8614	+	37.8650i	0.825693	+	1.43014i	−0.0756952	+	0.997131i	$0.524118\pi$
$702$		0			0
$703$	−1.15810	−	4.14812i	−0.0436785	−	0.156449i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	36.5648	+	21.1107i	1.37516	+	0.793949i
$708$		0			0
$709$	7.32015	−	12.6789i	0.274914	−	0.476165i	−0.695199	−	0.718817i	$-0.744684\pi$
$709$	7.32015	−	12.6789i	0.274914	−	0.476165i	0.970113	+	0.242652i	$0.0780173\pi$
$710$		0			0
$711$	40.2363			1.50898
$712$		0			0
$713$	3.04661	+	1.75896i	0.114096	+	0.0658736i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−4.53840	+	2.62024i	−0.169489	+	0.0978548i
$718$		0			0
$719$	−11.1778	−	19.3606i	−0.416863	−	0.722028i	0.578759	−	0.815499i	$-0.303537\pi$
$719$	−11.1778	−	19.3606i	−0.416863	−	0.722028i	−0.995622	+	0.0934709i	$0.970204\pi$
$720$		0			0
$721$	−62.1515			−2.31464
$722$		0			0
$723$		−	1.02113i		−	0.0379764i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−7.18874	+	4.15042i	−0.266615	+	0.153930i	−0.627349	−	0.778739i	$-0.715860\pi$
$727$	−7.18874	+	4.15042i	−0.266615	+	0.153930i	0.360733	+	0.932669i	$0.382527\pi$
$728$		0			0
$729$	20.4861			0.758745
$730$		0			0
$731$	3.04195	−	5.26881i	0.112511	−	0.194874i
$732$		0			0
$733$			35.7912i			1.32198i	0.750396	+	0.660989i	$0.229863\pi$
$733$			35.7912i			1.32198i	−0.750396	+	0.660989i	$0.770137\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	36.6708	+	21.1719i	1.35079	+	0.779876i
$738$		0			0
$739$	−16.6216	−	28.7895i	−0.611437	−	1.05904i	−0.990998	−	0.133873i	$-0.957258\pi$
$739$	−16.6216	−	28.7895i	−0.611437	−	1.05904i	0.379561	−	0.925167i	$-0.376075\pi$
$740$		0			0
$741$	8.83163	−	2.46567i	0.324438	−	0.0905787i
$742$		0			0
$743$	−16.0638	+	9.27444i	−0.589324	+	0.340246i	−0.764830	−	0.644232i	$-0.777177\pi$
$743$	−16.0638	+	9.27444i	−0.589324	+	0.340246i	0.175506	+	0.984478i	$0.443844\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−16.3884	−	9.46183i	−0.599619	−	0.346190i
$748$		0			0
$749$	−40.8565			−1.49287
$750$		0			0
$751$	−21.5748	+	37.3687i	−0.787276	+	1.36360i	0.140353	+	0.990101i	$0.455176\pi$
$751$	−21.5748	+	37.3687i	−0.787276	+	1.36360i	−0.927630	+	0.373501i	$0.878157\pi$
$752$		0			0
$753$		−	5.40957i		−	0.197136i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−8.26940	+	4.77434i	−0.300556	+	0.173526i	−0.642693	−	0.766124i	$-0.722183\pi$
$757$	−8.26940	+	4.77434i	−0.300556	+	0.173526i	0.342136	+	0.939650i	$0.388849\pi$
$758$		0			0
$759$	1.66476			0.0604268
$760$		0			0
$761$	35.8512			1.29960			0.649802	−	0.760103i	$-0.274852\pi$
$761$	35.8512			1.29960			0.649802	+	0.760103i	$0.274852\pi$
$762$		0			0
$763$	9.76214	−	5.63617i	0.353413	−	0.204043i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			31.2857i			1.12966i
$768$		0			0
$769$	−8.93698	+	15.4793i	−0.322276	+	0.558198i	−0.980957	−	0.194224i	$-0.937781\pi$
$769$	−8.93698	+	15.4793i	−0.322276	+	0.558198i	0.658681	+	0.752422i	$0.271114\pi$
$770$		0			0
$771$	−4.62463			−0.166552
$772$		0			0
$773$	−1.60521	−	0.926769i	−0.0577354	−	0.0333336i	0.470854	−	0.882211i	$-0.343946\pi$
$773$	−1.60521	−	0.926769i	−0.0577354	−	0.0333336i	−0.528590	+	0.848877i	$0.677279\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	1.30200	−	0.751709i	0.0467089	−	0.0269674i
$778$		0			0
$779$	19.6356	+	19.2293i	0.703519	+	0.688961i
$780$		0			0
$781$	17.4790	+	30.2744i	0.625446	+	1.08330i
$782$		0			0
$783$	−14.3212	−	8.26836i	−0.511798	−	0.295487i
$784$		0			0
$785$		0			0
$786$		0			0
$787$			53.8501i			1.91955i	0.280773	+	0.959774i	$0.409409\pi$
$787$			53.8501i			1.91955i	−0.280773	+	0.959774i	$0.590591\pi$
$788$		0			0
$789$	−3.42486	+	5.93202i	−0.121928	+	0.211186i
$790$		0			0
$791$	58.8523			2.09255
$792$		0			0
$793$	−28.9160	+	16.6947i	−1.02684	+	0.592845i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			44.2766i			1.56836i	0.620535	+	0.784179i	$0.286915\pi$
$797$			44.2766i			1.56836i	−0.620535	+	0.784179i	$0.713085\pi$
$798$		0			0
$799$	4.88964			0.172983
$800$		0			0
$801$	−4.86568	−	8.42760i	−0.171920	−	0.297775i
$802$		0			0
$803$	−48.1107	+	27.7767i	−1.69779	+	0.980220i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	0.445996	+	0.257496i	0.0156998	+	0.00906429i
$808$		0			0
$809$	16.7641			0.589395			0.294698	−	0.955591i	$-0.404781\pi$
$809$	16.7641			0.589395			0.294698	+	0.955591i	$0.404781\pi$
$810$		0			0
$811$	13.7203	−	23.7642i	0.481784	−	0.834474i	−0.517998	−	0.855382i	$-0.673322\pi$
$811$	13.7203	−	23.7642i	0.481784	−	0.834474i	0.999781	+	0.0209083i	$0.00665581\pi$
$812$		0			0
$813$	3.84538	+	2.22013i	0.134863	+	0.0778635i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	4.78823	−	4.88942i	0.167519	−	0.171059i
$818$		0			0
$819$	−36.8327	−	63.7961i	−1.28704	−	2.22922i
$820$		0			0
$821$	11.9404	−	20.6814i	0.416723	−	0.721785i	−0.578885	−	0.815409i	$-0.696512\pi$
$821$	11.9404	−	20.6814i	0.416723	−	0.721785i	0.995608	+	0.0936244i	$0.0298453\pi$
$822$		0			0
$823$	19.6431	+	11.3410i	0.684716	+	0.395321i	0.801630	−	0.597821i	$-0.203967\pi$
$823$	19.6431	+	11.3410i	0.684716	+	0.395321i	−0.116913	+	0.993142i	$0.537300\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	27.9071	+	16.1121i	0.970423	+	0.560274i	0.899365	−	0.437198i	$-0.144029\pi$
$827$	27.9071	+	16.1121i	0.970423	+	0.560274i	0.0710581	+	0.997472i	$0.477362\pi$
$828$		0			0
$829$	0.593350			0.0206079			0.0103040	−	0.999947i	$-0.496720\pi$
$829$	0.593350			0.0206079			0.0103040	+	0.999947i	$0.496720\pi$
$830$		0			0
$831$	−0.776614	−	1.34513i	−0.0269404	−	0.0466622i
$832$		0			0
$833$	38.7057	−	22.3468i	1.34107	−	0.774269i
$834$		0			0
$835$		0			0
$836$		0			0
$837$			9.32438i			0.322298i
$838$		0			0
$839$	−10.9777	−	19.0139i	−0.378991	−	0.656431i	0.611925	−	0.790916i	$-0.290396\pi$
$839$	−10.9777	−	19.0139i	−0.378991	−	0.656431i	−0.990916	+	0.134484i	$0.957062\pi$
$840$		0			0
$841$	−17.2093	−	29.8074i	−0.593424	−	1.02784i
$842$		0			0
$843$		−	1.52877i		−	0.0526537i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			108.245i			3.71935i
$848$		0			0
$849$	−1.32503	+	2.29502i	−0.0454749	+	0.0787648i
$850$		0			0
$851$	0.387034	−	0.670363i	0.0132674	−	0.0229797i
$852$		0			0
$853$	16.9117	−	9.76396i	0.579045	−	0.334312i	−0.181709	−	0.983352i	$-0.558163\pi$
$853$	16.9117	−	9.76396i	0.579045	−	0.334312i	0.760754	+	0.649041i	$0.224829\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	0.730413	−	0.421704i	0.0249504	−	0.0144051i	−0.487473	−	0.873138i	$-0.662081\pi$
$857$	0.730413	−	0.421704i	0.0249504	−	0.0144051i	0.512423	+	0.858733i	$0.328748\pi$
$858$		0			0
$859$	16.7147	−	28.9508i	0.570299	−	0.987787i	−0.426236	−	0.904612i	$-0.640161\pi$
$859$	16.7147	−	28.9508i	0.570299	−	0.987787i	0.996535	−	0.0831752i	$-0.0265061\pi$
$860$		0			0
$861$	−4.79697	+	8.30859i	−0.163480	+	0.283156i
$862$		0			0
$863$		−	7.13064i		−	0.242730i	−0.992608	−	0.121365i	$-0.961273\pi$
$863$		−	7.13064i		−	0.242730i	0.992608	−	0.121365i	$-0.0387271\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		−	0.701176i		−	0.0238132i
$868$		0			0
$869$	−42.0683	−	72.8645i	−1.42707	−	2.47176i
$870$		0			0
$871$	20.9594	+	36.3027i	0.710181	+	1.23007i
$872$		0			0
$873$			21.2660i			0.719747i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−13.8835	+	8.01564i	−0.468812	+	0.270669i	−0.715742	−	0.698364i	$-0.753912\pi$
$877$	−13.8835	+	8.01564i	−0.468812	+	0.270669i	0.246930	+	0.969033i	$0.420578\pi$
$878$		0			0
$879$	3.93809	+	6.82097i	0.132828	+	0.230066i
$880$		0			0
$881$	−23.0319			−0.775963			−0.387982	−	0.921667i	$-0.626828\pi$
$881$	−23.0319			−0.775963			−0.387982	+	0.921667i	$0.626828\pi$
$882$		0			0
$883$	−35.5590	−	20.5300i	−1.19666	−	0.690890i	−0.236848	−	0.971547i	$-0.576114\pi$
$883$	−35.5590	−	20.5300i	−1.19666	−	0.690890i	−0.959808	+	0.280657i	$0.909448\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	8.77977	+	5.06900i	0.294796	+	0.170200i	0.640103	−	0.768289i	$-0.278892\pi$
$887$	8.77977	+	5.06900i	0.294796	+	0.170200i	−0.345307	+	0.938490i	$0.612225\pi$
$888$		0			0
$889$	−28.1275	+	48.7183i	−0.943367	+	1.63396i
$890$		0			0
$891$	−23.7210	−	41.0860i	−0.794684	−	1.37643i
$892$		0			0
$893$	5.32732	+	1.36792i	0.178272	+	0.0457757i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	1.42725	+	0.824023i	0.0476545	+	0.0275133i
$898$		0			0
$899$	−17.8796	+	30.9684i	−0.596318	+	1.03285i
$900$		0			0
$901$	−31.5774			−1.05200
$902$		0			0
$903$	2.06890	+	1.19448i	0.0688487	+	0.0397498i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−33.0677	+	19.0916i	−1.09799	+	0.633927i	−0.935693	−	0.352814i	$-0.885225\pi$
$907$	−33.0677	+	19.0916i	−1.09799	+	0.633927i	−0.162301	+	0.986741i	$0.551891\pi$
$908$		0			0
$909$	14.0985	+	24.4192i	0.467616	+	0.809935i
$910$		0			0
$911$	−14.4138			−0.477550			−0.238775	−	0.971075i	$-0.576746\pi$
$911$	−14.4138			−0.477550			−0.238775	+	0.971075i	$0.576746\pi$
$912$		0			0
$913$			39.5706i			1.30960i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−27.9674	+	16.1470i	−0.923566	+	0.533221i
$918$		0			0
$919$	−5.20920			−0.171836			−0.0859179	−	0.996302i	$-0.527382\pi$
$919$	−5.20920			−0.171836			−0.0859179	+	0.996302i	$0.527382\pi$
$920$		0			0
$921$	−5.35134	+	9.26878i	−0.176332	+	0.305417i
$922$		0			0
$923$			34.6070i			1.13910i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−35.9460	−	20.7535i	−1.18062	−	0.681633i
$928$		0			0
$929$	−19.1769	−	33.2154i	−0.629174	−	1.08976i	−0.987718	−	0.156249i	$-0.950060\pi$
$929$	−19.1769	−	33.2154i	−0.629174	−	1.08976i	0.358544	−	0.933513i	$-0.383273\pi$
$930$		0			0
$931$	48.4220	−	13.5188i	1.58697	−	0.443060i
$932$		0			0
$933$	1.64442	−	0.949408i	0.0538360	−	0.0310822i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	52.3580	+	30.2289i	1.71046	+	0.987536i	0.933929	+	0.357459i	$0.116357\pi$
$937$	52.3580	+	30.2289i	1.71046	+	0.987536i	0.776533	+	0.630077i	$0.216977\pi$
$938$		0			0
$939$	−1.69916			−0.0554501
$940$		0			0
$941$	12.0859	−	20.9335i	0.393990	−	0.682411i	−0.598981	−	0.800763i	$-0.704428\pi$
$941$	12.0859	−	20.9335i	0.393990	−	0.682411i	0.992972	+	0.118352i	$0.0377610\pi$
$942$		0			0
$943$			4.93965i			0.160857i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−8.51112	+	4.91390i	−0.276574	+	0.159680i	−0.631872	−	0.775073i	$-0.717713\pi$
$947$	−8.51112	+	4.91390i	−0.276574	+	0.159680i	0.355297	+	0.934753i	$0.384380\pi$
$948$		0			0
$949$	−54.9958			−1.78524
$950$		0			0
$951$	10.5225			0.341216
$952$		0			0
$953$	−1.81636	+	1.04867i	−0.0588375	+	0.0339699i	−0.529130	−	0.848541i	$-0.677482\pi$
$953$	−1.81636	+	1.04867i	−0.0588375	+	0.0339699i	0.470293	+	0.882511i	$0.344148\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			16.9220i			0.547011i
$958$		0			0
$959$	18.1458	−	31.4295i	0.585960	−	1.01491i
$960$		0			0
$961$	−10.8368			−0.349575
$962$		0			0
$963$	−23.6299	−	13.6427i	−0.761462	−	0.439630i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	33.2156	−	19.1770i	1.06814	−	0.616691i	0.140468	−	0.990085i	$-0.455139\pi$
$967$	33.2156	−	19.1770i	1.06814	−	0.616691i	0.927673	+	0.373394i	$0.121806\pi$
$968$		0			0
$969$	−1.48481	+	5.78255i	−0.0476990	+	0.185762i
$970$		0			0
$971$	−9.56818	−	16.5726i	−0.307058	−	0.531839i	0.670660	−	0.741765i	$-0.266011\pi$
$971$	−9.56818	−	16.5726i	−0.307058	−	0.531839i	−0.977717	+	0.209926i	$0.932678\pi$
$972$		0			0
$973$	32.7315	+	18.8975i	1.04932	+	0.605827i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	19.8444i		−	0.634878i	−0.948279	−	0.317439i	$-0.897177\pi$
$977$		−	19.8444i		−	0.634878i	0.948279	−	0.317439i	$-0.102823\pi$
$978$		0			0
$979$	−10.1744	+	17.6227i	−0.325177	+	0.563223i
$980$		0			0
$981$	7.52807			0.240353
$982$		0			0
$983$	36.0406	−	20.8080i	1.14952	−	0.663673i	0.200746	−	0.979643i	$-0.435663\pi$
$983$	36.0406	−	20.8080i	1.14952	−	0.663673i	0.948769	+	0.315970i	$0.102330\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$			1.92001i			0.0611147i
$988$		0			0
$989$	1.23001			0.0391120
$990$		0			0
$991$	5.96872	+	10.3381i	0.189603	+	0.328401i	0.945118	−	0.326730i	$-0.105947\pi$
$991$	5.96872	+	10.3381i	0.189603	+	0.328401i	−0.755515	+	0.655131i	$0.772613\pi$
$992$		0			0
$993$	−9.42907	+	5.44387i	−0.299222	+	0.172756i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−16.6925	−	9.63745i	−0.528658	−	0.305221i	0.211812	−	0.977311i	$-0.432064\pi$
$997$	−16.6925	−	9.63745i	−0.528658	−	0.305221i	−0.740470	+	0.672089i	$0.765397\pi$
$998$		0			0
$999$	2.05170			0.0649128

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1900.2.s.d.349.4		16
5.2	odd	4		380.2.i.c.121.3	✓	8
5.3	odd	4		1900.2.i.d.501.2		8
5.4	even	2	inner	1900.2.s.d.349.5		16
15.2	even	4		3420.2.t.w.1261.1		8
19.11	even	3	inner	1900.2.s.d.49.5		16
20.7	even	4		1520.2.q.m.881.2		8
95.7	odd	12		7220.2.a.r.1.2		4
95.12	even	12		7220.2.a.p.1.3		4
95.49	even	6	inner	1900.2.s.d.49.4		16
95.68	odd	12		1900.2.i.d.201.2		8
95.87	odd	12		380.2.i.c.201.3	yes	8
285.182	even	12		3420.2.t.w.3241.1		8
380.87	even	12		1520.2.q.m.961.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.i.c.121.3	✓	8	5.2	odd	4
380.2.i.c.201.3	yes	8	95.87	odd	12
1520.2.q.m.881.2		8	20.7	even	4
1520.2.q.m.961.2		8	380.87	even	12
1900.2.i.d.201.2		8	95.68	odd	12
1900.2.i.d.501.2		8	5.3	odd	4
1900.2.s.d.49.4		16	95.49	even	6	inner
1900.2.s.d.49.5		16	19.11	even	3	inner
1900.2.s.d.349.4		16	1.1	even	1	trivial
1900.2.s.d.349.5		16	5.4	even	2	inner
3420.2.t.w.1261.1		8	15.2	even	4
3420.2.t.w.3241.1		8	285.182	even	12
7220.2.a.p.1.3		4	95.12	even	12
7220.2.a.r.1.2		4	95.7	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.306096 + 0.176725i) q^{3} +4.30507i q^{7} +(-1.43754 + 2.48989i) q^{9} +O(q^{10})\)	\(q+(-0.306096 + 0.176725i) q^{3} +4.30507i q^{7} +(-1.43754 + 2.48989i) q^{9} +6.01196 q^{11} +(5.15425 + 2.97581i) q^{13} +(-3.35591 + 1.93754i) q^{17} +(-4.19835 + 1.17212i) q^{19} +(-0.760812 - 1.31776i) q^{21} +(-0.678480 - 0.391721i) q^{23} -2.07654i q^{27} +(3.98179 - 6.89666i) q^{29} -4.49034 q^{31} +(-1.84024 + 1.06246i) q^{33} +0.988035i q^{37} -2.10360 q^{39} +(-3.15253 - 5.46035i) q^{41} +(-1.35967 + 0.785004i) q^{43} +(-1.09277 - 0.630909i) q^{47} -11.5336 q^{49} +(0.684822 - 1.18615i) q^{51} +(7.05712 + 4.07443i) q^{53} +(1.07796 - 1.10073i) q^{57} +(2.62834 + 4.55242i) q^{59} +(-2.80507 + 4.85852i) q^{61} +(-10.7191 - 6.18869i) q^{63} +(6.09963 + 3.52162i) q^{67} +0.276907 q^{69} +(2.90736 + 5.03570i) q^{71} +(-8.00250 + 4.62024i) q^{73} +25.8819i q^{77} +(-6.99743 - 12.1199i) q^{79} +(-3.94563 - 6.83404i) q^{81} +6.58197i q^{83} +2.81472i q^{87} +(-1.69237 + 2.93126i) q^{89} +(-12.8110 + 22.1894i) q^{91} +(1.37448 - 0.793555i) q^{93} +(6.40573 - 3.69835i) q^{97} +(-8.64242 + 14.9691i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 10 q^{9}+O(q^{10}) \) 16 * q + 10 * q^9	\( 16 q + 10 q^{9} + 8 q^{11} - 6 q^{19} + 16 q^{21} - 10 q^{29} - 40 q^{31} + 108 q^{39} - 16 q^{41} - 40 q^{49} + 24 q^{51} - 22 q^{59} + 24 q^{61} - 12 q^{69} + 28 q^{71} - 26 q^{79} - 48 q^{81} - 10 q^{89} - 92 q^{91} - 48 q^{99}+O(q^{100}) \) 16 * q + 10 * q^9 + 8 * q^11 - 6 * q^19 + 16 * q^21 - 10 * q^29 - 40 * q^31 + 108 * q^39 - 16 * q^41 - 40 * q^49 + 24 * q^51 - 22 * q^59 + 24 * q^61 - 12 * q^69 + 28 * q^71 - 26 * q^79 - 48 * q^81 - 10 * q^89 - 92 * q^91 - 48 * q^99

Introduction

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