LMFDB - Embedded newform 1900.2.s.d.349.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("1900.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.1715763840$
Analytic rank:	$0$
Dimension:	$16$
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			349.2
Root			$-2.18309 - 1.26041i$ of defining polynomial
Character	$\chi$	$=$	1900.349
Dual form			1900.2.s.d.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.18309 + 1.26041i) q^{3} -2.72743i q^{7} +(1.67727 - 2.90511i) q^{9} +O(q^{10})$	\(q+(-2.18309 + 1.26041i) q^{3} -2.72743i q^{7} +(1.67727 - 2.90511i) q^{9} +3.31421 q^{11} +(-2.81306 - 1.62412i) q^{13} +(2.03909 - 1.17727i) q^{17} +(3.11494 + 3.04912i) q^{19} +(3.43768 + 5.95423i) q^{21} +(-1.86016 - 1.07396i) q^{23} +0.893714i q^{27} +(-1.96702 + 3.40697i) q^{29} -10.1896 q^{31} +(-7.23524 + 4.17727i) q^{33} +3.68579i q^{37} +8.18825 q^{39} +(0.363714 + 0.629971i) q^{41} +(-2.05499 + 1.18645i) q^{43} +(-9.54644 - 5.51164i) q^{47} -0.438860 q^{49} +(-2.96768 + 5.14017i) q^{51} +(7.77947 + 4.49148i) q^{53} +(-10.6434 - 2.73041i) q^{57} +(-5.48784 - 9.50521i) q^{59} +(4.22743 - 7.32212i) q^{61} +(-7.92348 - 4.57462i) q^{63} +(-8.44436 - 4.87535i) q^{67} +5.41453 q^{69} +(-3.45850 - 5.99029i) q^{71} +(-2.14818 + 1.24025i) q^{73} -9.03927i q^{77} +(5.99948 + 10.3914i) q^{79} +(3.90535 + 6.76427i) q^{81} +4.68711i q^{83} -9.91699i q^{87} +(4.27205 - 7.39941i) q^{89} +(-4.42968 + 7.67243i) q^{91} +(22.2448 - 12.8430i) q^{93} +(-6.26127 + 3.61494i) q^{97} +(5.55882 - 9.62816i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.18309	+	1.26041i	−1.26041	+	0.727698i	−0.973154	−	0.230156i	$-0.926076\pi$
$3$	−2.18309	+	1.26041i	−1.26041	+	0.727698i	−0.287256	+	0.957854i	$0.592743\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$		−	2.72743i		−	1.03087i	−0.856928	−	0.515435i	$-0.827630\pi$
$7$		−	2.72743i		−	1.03087i	0.856928	−	0.515435i	$-0.172370\pi$
$8$		0			0
$9$	1.67727	−	2.90511i	0.559089	−	0.968370i
$10$		0			0
$11$	3.31421			0.999273			0.499636	−	0.866235i	$-0.333467\pi$
$11$	3.31421			0.999273			0.499636	+	0.866235i	$0.333467\pi$
$12$		0			0
$13$	−2.81306	−	1.62412i	−0.780204	−	0.450451i	0.0562987	−	0.998414i	$-0.482070\pi$
$13$	−2.81306	−	1.62412i	−0.780204	−	0.450451i	−0.836502	+	0.547963i	$0.815403\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.03909	−	1.17727i	0.494551	−	0.285529i	−0.231910	−	0.972737i	$-0.574497\pi$
$17$	2.03909	−	1.17727i	0.494551	−	0.285529i	0.726460	+	0.687208i	$0.241164\pi$
$18$		0			0
$19$	3.11494	+	3.04912i	0.714617	+	0.699516i
$19$	3.11494	+	3.04912i	0.714617	+	0.699516i
$20$		0			0
$21$	3.43768	+	5.95423i	0.750163	+	1.29932i
$22$		0			0
$23$	−1.86016	−	1.07396i	−0.387870	−	0.223937i	0.293367	−	0.956000i	$-0.405224\pi$
$23$	−1.86016	−	1.07396i	−0.387870	−	0.223937i	−0.681237	+	0.732063i	$0.738558\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			0.893714i			0.171995i
$28$		0			0
$29$	−1.96702	+	3.40697i	−0.365266	+	0.632659i	−0.988819	−	0.149122i	$-0.952355\pi$
$29$	−1.96702	+	3.40697i	−0.365266	+	0.632659i	0.623553	+	0.781781i	$0.285689\pi$
$30$		0			0
$31$	−10.1896			−1.83010			−0.915050	−	0.403340i	$-0.867849\pi$
$31$	−10.1896			−1.83010			−0.915050	+	0.403340i	$0.867849\pi$
$32$		0			0
$33$	−7.23524	+	4.17727i	−1.25949	+	0.727169i
$34$		0			0
$35$		0			0
$36$		0			0
$37$			3.68579i			0.605940i	0.953000	+	0.302970i	$0.0979782\pi$
$37$			3.68579i			0.605940i	−0.953000	+	0.302970i	$0.902022\pi$
$38$		0			0
$39$	8.18825			1.31117
$40$		0			0
$41$	0.363714	+	0.629971i	0.0568025	+	0.0983849i	0.893028	−	0.450000i	$-0.148576\pi$
$41$	0.363714	+	0.629971i	0.0568025	+	0.0983849i	−0.836226	+	0.548385i	$0.815243\pi$
$42$		0			0
$43$	−2.05499	+	1.18645i	−0.313383	+	0.180931i	−0.648439	−	0.761267i	$-0.724578\pi$
$43$	−2.05499	+	1.18645i	−0.313383	+	0.180931i	0.335057	+	0.942198i	$0.391245\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−9.54644	−	5.51164i	−1.39249	−	0.803955i	−0.398901	−	0.916994i	$-0.630608\pi$
$47$	−9.54644	−	5.51164i	−1.39249	−	0.803955i	−0.993591	+	0.113039i	$0.963942\pi$
$48$		0			0
$49$	−0.438860			−0.0626942
$50$		0			0
$51$	−2.96768	+	5.14017i	−0.415558	+	0.719767i
$52$		0			0
$53$	7.77947	+	4.49148i	1.06859	+	0.616952i	0.927797	−	0.373087i	$-0.121701\pi$
$53$	7.77947	+	4.49148i	1.06859	+	0.616952i	0.140796	+	0.990039i	$0.455034\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−10.6434	−	2.73041i	−1.40975	−	0.361652i
$58$		0			0
$59$	−5.48784	−	9.50521i	−0.714456	−	1.23747i	−0.963169	−	0.268896i	$-0.913341\pi$
$59$	−5.48784	−	9.50521i	−0.714456	−	1.23747i	0.248714	−	0.968577i	$-0.419992\pi$
$60$		0			0
$61$	4.22743	−	7.32212i	0.541267	−	0.937501i	−0.457565	−	0.889176i	$-0.651278\pi$
$61$	4.22743	−	7.32212i	0.541267	−	0.937501i	0.998832	−	0.0483251i	$-0.0153884\pi$
$62$		0			0
$63$	−7.92348	−	4.57462i	−0.998264	−	0.576348i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−8.44436	−	4.87535i	−1.03164	−	0.595619i	−0.114188	−	0.993459i	$-0.536427\pi$
$67$	−8.44436	−	4.87535i	−1.03164	−	0.595619i	−0.917455	+	0.397840i	$0.869760\pi$
$68$		0			0
$69$	5.41453			0.651833
$70$		0			0
$71$	−3.45850	−	5.99029i	−0.410448	−	0.710917i	0.584491	−	0.811400i	$-0.301294\pi$
$71$	−3.45850	−	5.99029i	−0.410448	−	0.710917i	−0.994939	+	0.100484i	$0.967961\pi$
$72$		0			0
$73$	−2.14818	+	1.24025i	−0.251425	+	0.145160i	−0.620417	−	0.784272i	$-0.713036\pi$
$73$	−2.14818	+	1.24025i	−0.251425	+	0.145160i	0.368992	+	0.929433i	$0.379703\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		−	9.03927i		−	1.03012i
$78$		0			0
$79$	5.99948	+	10.3914i	0.674994	+	1.16912i	0.976471	+	0.215650i	$0.0691871\pi$
$79$	5.99948	+	10.3914i	0.674994	+	1.16912i	−0.301477	+	0.953474i	$0.597480\pi$
$80$		0			0
$81$	3.90535	+	6.76427i	0.433928	+	0.751586i
$82$		0			0
$83$			4.68711i			0.514477i	0.966348	+	0.257238i	$0.0828126\pi$
$83$			4.68711i			0.514477i	−0.966348	+	0.257238i	$0.917187\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		−	9.91699i		−	1.06321i
$88$		0			0
$89$	4.27205	−	7.39941i	0.452836	−	0.784336i	−0.545725	−	0.837965i	$-0.683746\pi$
$89$	4.27205	−	7.39941i	0.452836	−	0.784336i	0.998561	+	0.0536291i	$0.0170789\pi$
$90$		0			0
$91$	−4.42968	+	7.67243i	−0.464357	+	0.804289i
$92$		0			0
$93$	22.2448	−	12.8430i	2.30668	−	1.33176i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−6.26127	+	3.61494i	−0.635735	+	0.367042i	−0.782970	−	0.622060i	$-0.786296\pi$
$97$	−6.26127	+	3.61494i	−0.635735	+	0.367042i	0.147235	+	0.989102i	$0.452963\pi$
$98$		0			0
$99$	5.55882	−	9.62816i	0.558682	−	0.967666i
$100$		0			0
$101$	2.88818	−	5.00247i	0.287384	−	0.497764i	−0.685800	−	0.727790i	$-0.740548\pi$
$101$	2.88818	−	5.00247i	0.287384	−	0.497764i	0.973185	+	0.230026i	$0.0738810\pi$
$102$		0			0
$103$		−	15.0576i		−	1.48367i	−0.670581	−	0.741836i	$-0.733955\pi$
$103$		−	15.0576i		−	1.48367i	0.670581	−	0.741836i	$-0.266045\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			15.1896i			1.46843i	0.678917	+	0.734215i	$0.262450\pi$
$107$			15.1896i			1.46843i	−0.678917	+	0.734215i	$0.737550\pi$
$108$		0			0
$109$	−6.31057	−	10.9302i	−0.604443	−	1.04693i	−0.992139	−	0.125139i	$-0.960062\pi$
$109$	−6.31057	−	10.9302i	−0.604443	−	1.04693i	0.387696	−	0.921787i	$-0.373271\pi$
$110$		0			0
$111$	−4.64560	−	8.04642i	−0.440941	−	0.763732i
$112$		0			0
$113$		−	6.10761i		−	0.574555i	−0.957847	−	0.287278i	$-0.907250\pi$
$113$		−	6.10761i		−	0.574555i	0.957847	−	0.287278i	$-0.0927502\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−9.43652	+	5.44818i	−0.872406	+	0.503684i
$118$		0			0
$119$	−3.21091	−	5.56146i	−0.294344	−	0.509818i
$120$		0			0
$121$	−0.0159950			−0.00145409
$122$		0			0
$123$	−1.58804	−	0.916857i	−0.143189	−	0.0826702i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−7.90013	−	4.56114i	−0.701023	−	0.404736i	0.106705	−	0.994291i	$-0.465970\pi$
$127$	−7.90013	−	4.56114i	−0.701023	−	0.404736i	−0.807728	+	0.589555i	$0.799303\pi$
$128$		0			0
$129$	2.99082	−	5.18025i	0.263327	−	0.456096i
$130$		0			0
$131$	−11.1328	−	19.2825i	−0.972676	−	1.68472i	−0.687402	−	0.726277i	$-0.741249\pi$
$131$	−11.1328	−	19.2825i	−0.972676	−	1.68472i	−0.285274	−	0.958446i	$-0.592085\pi$
$132$		0			0
$133$	8.31625	−	8.49578i	0.721110	−	0.736678i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.60527	−	3.81355i	−0.564326	−	0.325814i	0.190554	−	0.981677i	$-0.438972\pi$
$137$	−6.60527	−	3.81355i	−0.564326	−	0.325814i	−0.754880	+	0.655863i	$0.772305\pi$
$138$		0			0
$139$	8.45916	−	14.6517i	0.717496	−	1.24274i	−0.244493	−	0.969651i	$-0.578621\pi$
$139$	8.45916	−	14.6517i	0.717496	−	1.24274i	0.961989	−	0.273089i	$-0.0880453\pi$
$140$		0			0
$141$	27.7877			2.34015
$142$		0			0
$143$	−9.32309	−	5.38269i	−0.779636	−	0.450123i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	0.958072	−	0.553143i	0.0790204	−	0.0456225i
$148$		0			0
$149$	−6.19809	−	10.7354i	−0.507767	−	0.879478i	−0.999960	−	0.00899193i	$-0.997138\pi$
$149$	−6.19809	−	10.7354i	−0.507767	−	0.879478i	0.492193	−	0.870486i	$-0.336196\pi$
$150$		0			0
$151$	−14.4549			−1.17632			−0.588160	−	0.808745i	$-0.700147\pi$
$151$	−14.4549			−1.17632			−0.588160	+	0.808745i	$0.700147\pi$
$152$		0			0
$153$		−	7.89836i		−	0.638544i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	15.7728	−	9.10642i	1.25881	−	0.726772i	0.285963	−	0.958241i	$-0.407687\pi$
$157$	15.7728	−	9.10642i	1.25881	−	0.726772i	0.972842	+	0.231469i	$0.0743532\pi$
$158$		0			0
$159$	−22.6444			−1.79582
$160$		0			0
$161$	−2.92916	+	5.07345i	−0.230850	+	0.399844i
$162$		0			0
$163$			19.2642i			1.50889i	0.656362	+	0.754446i	$0.272094\pi$
$163$			19.2642i			1.50889i	−0.656362	+	0.754446i	$0.727906\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	4.92404	+	2.84289i	0.381033	+	0.219990i	0.678268	−	0.734815i	$-0.262731\pi$
$167$	4.92404	+	2.84289i	0.381033	+	0.219990i	−0.297234	+	0.954805i	$0.596064\pi$
$168$		0			0
$169$	−1.22445	−	2.12080i	−0.0941881	−	0.163139i
$170$		0			0
$171$	14.0826	−	3.93507i	1.07692	−	0.300922i
$172$		0			0
$173$	−7.92864	+	4.57760i	−0.602804	+	0.348029i	−0.770144	−	0.637870i	$-0.779816\pi$
$173$	−7.92864	+	4.57760i	−0.602804	+	0.348029i	0.167340	+	0.985899i	$0.446482\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	23.9609	+	13.8338i	1.80101	+	1.03982i
$178$		0			0
$179$	−12.1810			−0.910448			−0.455224	−	0.890377i	$-0.650441\pi$
$179$	−12.1810			−0.910448			−0.455224	+	0.890377i	$0.650441\pi$
$180$		0			0
$181$	−7.70608	+	13.3473i	−0.572789	+	0.992099i	0.423489	+	0.905901i	$0.360805\pi$
$181$	−7.70608	+	13.3473i	−0.572789	+	0.992099i	−0.996278	+	0.0861980i	$0.972528\pi$
$182$		0			0
$183$			21.3132i			1.57551i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	6.75796	−	3.90171i	0.494191	−	0.285321i
$188$		0			0
$189$	2.43754			0.177305
$190$		0			0
$191$	−16.2482			−1.17568			−0.587841	−	0.808977i	$-0.700022\pi$
$191$	−16.2482			−1.17568			−0.587841	+	0.808977i	$0.700022\pi$
$192$		0			0
$193$	0.737011	−	0.425514i	0.0530512	−	0.0306292i	−0.473240	−	0.880934i	$-0.656916\pi$
$193$	0.737011	−	0.425514i	0.0530512	−	0.0306292i	0.526291	+	0.850305i	$0.323582\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	19.9843i		−	1.42382i	−0.702270	−	0.711910i	$-0.747830\pi$
$197$		−	19.9843i		−	1.42382i	0.702270	−	0.711910i	$-0.252170\pi$
$198$		0			0
$199$	−3.22861	+	5.59212i	−0.228870	+	0.396415i	−0.957474	−	0.288521i	$-0.906836\pi$
$199$	−3.22861	+	5.59212i	−0.228870	+	0.396415i	0.728603	+	0.684936i	$0.240170\pi$
$200$		0			0
$201$	24.5798			1.73372
$202$		0			0
$203$	9.29227	+	5.36490i	0.652190	+	0.376542i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−6.23996	+	3.60264i	−0.433707	+	0.250401i
$208$		0			0
$209$	10.3236	+	10.1054i	0.714097	+	0.699007i
$210$		0			0
$211$	−5.27205	−	9.13146i	−0.362943	−	0.628635i	0.625501	−	0.780223i	$-0.284895\pi$
$211$	−5.27205	−	9.13146i	−0.362943	−	0.628635i	−0.988444	+	0.151588i	$0.951561\pi$
$212$		0			0
$213$	15.1004	+	8.71825i	1.03467	+	0.597364i
$214$		0			0
$215$		0			0
$216$		0			0
$217$			27.7913i			1.88660i
$218$		0			0
$219$	3.12645	−	5.41516i	0.211266	−	0.365923i
$220$		0			0
$221$	−7.64811			−0.514467
$222$		0			0
$223$	8.42329	−	4.86319i	0.564065	−	0.325663i	−0.190710	−	0.981646i	$-0.561079\pi$
$223$	8.42329	−	4.86319i	0.564065	−	0.325663i	0.754776	+	0.655983i	$0.227746\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		−	22.5798i		−	1.49867i	−0.662190	−	0.749336i	$-0.730373\pi$
$227$		−	22.5798i		−	1.49867i	0.662190	−	0.749336i	$-0.269627\pi$
$228$		0			0
$229$	16.2239			1.07211			0.536053	−	0.844184i	$-0.319915\pi$
$229$	16.2239			1.07211			0.536053	+	0.844184i	$0.319915\pi$
$230$		0			0
$231$	11.3932	+	19.7336i	0.749617	+	1.29837i
$232$		0			0
$233$	−16.1624	+	9.33139i	−1.05884	+	0.611320i	−0.925110	−	0.379699i	$-0.876028\pi$
$233$	−16.1624	+	9.33139i	−1.05884	+	0.611320i	−0.133727	+	0.991018i	$0.542694\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−26.1948	−	15.1236i	−1.70154	−	0.982383i
$238$		0			0
$239$	−0.602780			−0.0389906			−0.0194953	−	0.999810i	$-0.506206\pi$
$239$	−0.602780			−0.0389906			−0.0194953	+	0.999810i	$0.506206\pi$
$240$		0			0
$241$	−10.9408	+	18.9500i	−0.704759	+	1.22068i	0.262020	+	0.965062i	$0.415611\pi$
$241$	−10.9408	+	18.9500i	−0.704759	+	1.22068i	−0.966779	+	0.255615i	$0.917722\pi$
$242$		0			0
$243$	−19.3734	−	11.1853i	−1.24281	−	0.717535i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−3.81039	−	13.6364i	−0.242449	−	0.867665i
$248$		0			0
$249$	−5.90768	−	10.2324i	−0.374384	−	0.648452i
$250$		0			0
$251$	−4.13629	+	7.16426i	−0.261080	+	0.452204i	−0.966529	−	0.256557i	$-0.917412\pi$
$251$	−4.13629	+	7.16426i	−0.261080	+	0.452204i	0.705449	+	0.708761i	$0.250745\pi$
$252$		0			0
$253$	−6.16496	−	3.55934i	−0.387588	−	0.223774i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	12.2897	+	7.09544i	0.766608	+	0.442602i	0.831663	−	0.555280i	$-0.187389\pi$
$257$	12.2897	+	7.09544i	0.766608	+	0.442602i	−0.0650550	+	0.997882i	$0.520722\pi$
$258$		0			0
$259$	10.0527			0.624645
$260$		0			0
$261$	6.59842	+	11.4288i	0.408432	+	0.707425i
$262$		0			0
$263$	−16.0588	+	9.27153i	−0.990225	+	0.571707i	−0.905342	−	0.424684i	$-0.860385\pi$
$263$	−16.0588	+	9.27153i	−0.990225	+	0.571707i	−0.0848836	+	0.996391i	$0.527052\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			21.5381i			1.31811i
$268$		0			0
$269$	3.33371	+	5.77416i	0.203260	+	0.352057i	0.949577	−	0.313534i	$-0.101513\pi$
$269$	3.33371	+	5.77416i	0.203260	+	0.352057i	−0.746317	+	0.665591i	$0.768180\pi$
$270$		0			0
$271$	−11.0331	−	19.1099i	−0.670214	−	1.16085i	−0.977843	−	0.209339i	$-0.932869\pi$
$271$	−11.0331	−	19.1099i	−0.670214	−	1.16085i	0.307629	−	0.951506i	$-0.400464\pi$
$272$		0			0
$273$		−	22.3328i		−	1.35165i
$274$		0			0
$275$		0			0
$276$		0			0
$277$			24.4624i			1.46980i	0.678173	+	0.734902i	$0.262772\pi$
$277$			24.4624i			1.46980i	−0.678173	+	0.734902i	$0.737228\pi$
$278$		0			0
$279$	−17.0906	+	29.6018i	−1.02319	+	1.77221i
$280$		0			0
$281$	−9.33139	+	16.1624i	−0.556664	+	0.964170i	0.441108	+	0.897454i	$0.354586\pi$
$281$	−9.33139	+	16.1624i	−0.556664	+	0.964170i	−0.997772	+	0.0667164i	$0.978748\pi$
$282$		0			0
$283$	3.89384	−	2.24811i	0.231465	−	0.133636i	−0.379783	−	0.925076i	$-0.624001\pi$
$283$	3.89384	−	2.24811i	0.231465	−	0.133636i	0.611248	+	0.791439i	$0.290668\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.71820	−	0.992002i	0.101422	−	0.0585561i
$288$		0			0
$289$	−5.72809	+	9.92134i	−0.336946	+	0.583608i
$290$		0			0
$291$	9.11262	−	15.7835i	0.534191	−	0.925246i
$292$		0			0
$293$			1.27021i			0.0742063i	0.999311	+	0.0371031i	$0.0118130\pi$
$293$			1.27021i			0.0742063i	−0.999311	+	0.0371031i	$0.988187\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$			2.96196i			0.171870i
$298$		0			0
$299$	3.48850	+	6.04225i	0.201745	+	0.349433i
$300$		0			0
$301$	3.23595	+	5.60483i	0.186517	+	0.323057i
$302$		0			0
$303$			14.5611i			0.836516i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	7.49350	−	4.32638i	0.427677	−	0.246919i	−0.270680	−	0.962669i	$-0.587248\pi$
$307$	7.49350	−	4.32638i	0.427677	−	0.246919i	0.698356	+	0.715750i	$0.253915\pi$
$308$		0			0
$309$	18.9788	+	32.8722i	1.07967	+	1.87004i
$310$		0			0
$311$	23.8497			1.35239			0.676196	−	0.736721i	$-0.263627\pi$
$311$	23.8497			1.35239			0.676196	+	0.736721i	$0.263627\pi$
$312$		0			0
$313$	0.672340	+	0.388175i	0.0380029	+	0.0219410i	0.518881	−	0.854846i	$-0.326349\pi$
$313$	0.672340	+	0.388175i	0.0380029	+	0.0219410i	−0.480878	+	0.876787i	$0.659682\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−11.9878	−	6.92116i	−0.673302	−	0.388731i	0.124025	−	0.992279i	$-0.460420\pi$
$317$	−11.9878	−	6.92116i	−0.673302	−	0.388731i	−0.797327	+	0.603548i	$0.793753\pi$
$318$		0			0
$319$	−6.51911	+	11.2914i	−0.365000	+	0.632199i
$320$		0			0
$321$	−19.1451	−	33.1603i	−1.06857	−	1.85082i
$322$		0			0
$323$	9.94126	+	2.55030i	0.553147	+	0.141902i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	27.5531	+	15.9078i	1.52369	+	0.879704i
$328$		0			0
$329$	−15.0326	+	26.0372i	−0.828774	+	1.43548i
$330$		0			0
$331$	28.6993			1.57746			0.788728	−	0.614742i	$-0.210740\pi$
$331$	28.6993			1.57746			0.788728	+	0.614742i	$0.210740\pi$
$332$		0			0
$333$	10.7076	+	6.18205i	0.586774	+	0.338774i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	30.5928	−	17.6628i	1.66650	−	0.962153i	0.696994	−	0.717077i	$-0.254520\pi$
$337$	30.5928	−	17.6628i	1.66650	−	0.962153i	0.969504	−	0.245076i	$-0.0788129\pi$
$338$		0			0
$339$	7.69809	+	13.3335i	0.418103	+	0.724175i
$340$		0			0
$341$	−33.7704			−1.82877
$342$		0			0
$343$		−	17.8950i		−	0.966241i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−22.5221	+	13.0031i	−1.20905	+	0.698044i	−0.962551	−	0.271100i	$-0.912613\pi$
$347$	−22.5221	+	13.0031i	−1.20905	+	0.698044i	−0.246496	+	0.969144i	$0.579279\pi$
$348$		0			0
$349$	−2.44757			−0.131015			−0.0655077	−	0.997852i	$-0.520867\pi$
$349$	−2.44757			−0.131015			−0.0655077	+	0.997852i	$0.520867\pi$
$350$		0			0
$351$	1.45150	−	2.51408i	0.0774755	−	0.134191i
$352$		0			0
$353$		−	4.85103i		−	0.258194i	−0.991632	−	0.129097i	$-0.958792\pi$
$353$		−	4.85103i		−	0.258194i	0.991632	−	0.129097i	$-0.0412079\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	14.0194	+	8.09412i	0.741987	+	0.428386i
$358$		0			0
$359$	−3.67376	−	6.36314i	−0.193894	−	0.335834i	0.752644	−	0.658428i	$-0.228778\pi$
$359$	−3.67376	−	6.36314i	−0.193894	−	0.335834i	−0.946537	+	0.322594i	$0.895445\pi$
$360$		0			0
$361$	0.405741	+	18.9957i	0.0213548	+	0.999772i
$362$		0			0
$363$	0.0349186	−	0.0201603i	0.00183275	−	0.00105814i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	11.2892	+	6.51784i	0.589293	+	0.340228i	0.764818	−	0.644247i	$-0.222829\pi$
$367$	11.2892	+	6.51784i	0.589293	+	0.340228i	−0.175525	+	0.984475i	$0.556162\pi$
$368$		0			0
$369$	2.44018			0.127031
$370$		0			0
$371$	12.2502	−	21.2179i	0.635998	−	1.10158i
$372$		0			0
$373$		−	28.5514i		−	1.47833i	−0.673522	−	0.739167i	$-0.735219\pi$
$373$		−	28.5514i		−	1.47833i	0.673522	−	0.739167i	$-0.264781\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	11.0667	−	6.38936i	0.569964	−	0.329069i
$378$		0			0
$379$	−13.2128			−0.678698			−0.339349	−	0.940661i	$-0.610207\pi$
$379$	−13.2128			−0.678698			−0.339349	+	0.940661i	$0.610207\pi$
$380$		0			0
$381$	22.9956			1.17810
$382$		0			0
$383$	−32.6160	+	18.8309i	−1.66660	+	0.962212i	−0.697150	+	0.716925i	$0.745549\pi$
$383$	−32.6160	+	18.8309i	−1.66660	+	0.962212i	−0.969450	+	0.245287i	$0.921118\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$			7.95995i			0.404627i
$388$		0			0
$389$	−12.8223	+	22.2090i	−0.650119	+	1.12604i	0.332975	+	0.942936i	$0.391948\pi$
$389$	−12.8223	+	22.2090i	−0.650119	+	1.12604i	−0.983094	+	0.183103i	$0.941386\pi$
$390$		0			0
$391$	−5.05736			−0.255762
$392$		0			0
$393$	48.6078	+	28.0637i	2.45194	+	1.41563i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	28.8154	−	16.6366i	1.44620	−	0.834965i	0.447949	−	0.894059i	$-0.352155\pi$
$397$	28.8154	−	16.6366i	1.44620	−	0.834965i	0.998252	+	0.0590940i	$0.0188212\pi$
$398$		0			0
$399$	−7.44699	+	29.0290i	−0.372816	+	1.45327i
$400$		0			0
$401$	−4.70674	−	8.15232i	−0.235044	−	0.407107i	0.724242	−	0.689546i	$-0.242190\pi$
$401$	−4.70674	−	8.15232i	−0.235044	−	0.407107i	−0.959285	+	0.282439i	$0.908857\pi$
$402$		0			0
$403$	28.6639	+	16.5491i	1.42785	+	0.824370i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			12.2155i			0.605499i
$408$		0			0
$409$	−1.25545	+	2.17450i	−0.0620779	+	0.107522i	−0.895394	−	0.445275i	$-0.853106\pi$
$409$	−1.25545	+	2.17450i	−0.0620779	+	0.107522i	0.833316	+	0.552797i	$0.186439\pi$
$410$		0			0
$411$	19.2266			0.948376
$412$		0			0
$413$	−25.9248	+	14.9677i	−1.27567	+	0.736511i
$414$		0			0
$415$		0			0
$416$		0			0
$417$			42.6480i			2.08848i
$418$		0			0
$419$	39.5638			1.93282			0.966409	−	0.257011i	$-0.0827376\pi$
$419$	39.5638			1.93282			0.966409	+	0.257011i	$0.0827376\pi$
$420$		0			0
$421$	7.07892	+	12.2611i	0.345006	+	0.597567i	0.985355	−	0.170517i	$-0.0545437\pi$
$421$	7.07892	+	12.2611i	0.345006	+	0.597567i	−0.640349	+	0.768084i	$0.721210\pi$
$422$		0			0
$423$	−32.0238	+	18.4890i	−1.55705	+	0.898965i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−19.9705	−	11.5300i	−0.966442	−	0.557976i
$428$		0			0
$429$	27.1376			1.31022
$430$		0			0
$431$	3.26287	−	5.65145i	0.157167	−	0.272221i	−0.776679	−	0.629897i	$-0.783097\pi$
$431$	3.26287	−	5.65145i	0.157167	−	0.272221i	0.933846	+	0.357676i	$0.116431\pi$
$432$		0			0
$433$	7.44908	+	4.30073i	0.357980	+	0.206680i	0.668194	−	0.743987i	$-0.267067\pi$
$433$	7.44908	+	4.30073i	0.357980	+	0.206680i	−0.310214	+	0.950667i	$0.600401\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.51965	−	9.01718i	−0.120531	−	0.431350i
$438$		0			0
$439$	−5.77939	−	10.0102i	−0.275835	−	0.477760i	0.694510	−	0.719483i	$-0.255621\pi$
$439$	−5.77939	−	10.0102i	−0.275835	−	0.477760i	−0.970345	+	0.241722i	$0.922288\pi$
$440$		0			0
$441$	−0.736084	+	1.27494i	−0.0350516	+	0.0607112i
$442$		0			0
$443$	9.86626	+	5.69629i	0.468760	+	0.270639i	0.715721	−	0.698387i	$-0.246098\pi$
$443$	9.86626	+	5.69629i	0.468760	+	0.270639i	−0.246960	+	0.969026i	$0.579432\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	27.0620	+	15.6243i	1.27999	+	0.739002i
$448$		0			0
$449$	−17.2252			−0.812909			−0.406455	−	0.913671i	$-0.633235\pi$
$449$	−17.2252			−0.812909			−0.406455	+	0.913671i	$0.633235\pi$
$450$		0			0
$451$	1.20542	+	2.08786i	0.0567612	+	0.0983133i
$452$		0			0
$453$	31.5563	−	18.2190i	1.48264	−	0.856005i
$454$		0			0
$455$		0			0
$456$		0			0
$457$			26.1885i			1.22505i	0.790452	+	0.612524i	$0.209846\pi$
$457$			26.1885i			1.22505i	−0.790452	+	0.612524i	$0.790154\pi$
$458$		0			0
$459$	1.05214	+	1.82236i	0.0491097	+	0.0850605i
$460$		0			0
$461$	−20.2166	−	35.0162i	−0.941580	−	1.63086i	−0.762458	−	0.647038i	$-0.776008\pi$
$461$	−20.2166	−	35.0162i	−0.941580	−	1.63086i	−0.179122	−	0.983827i	$-0.557326\pi$
$462$		0			0
$463$			9.48542i			0.440825i	0.975407	+	0.220412i	$0.0707403\pi$
$463$			9.48542i			0.440825i	−0.975407	+	0.220412i	$0.929260\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			39.2462i			1.81610i	0.418867	+	0.908048i	$0.362427\pi$
$467$			39.2462i			1.81610i	−0.418867	+	0.908048i	$0.637573\pi$
$468$		0			0
$469$	−13.2972	+	23.0314i	−0.614006	+	1.06349i
$470$		0			0
$471$	−22.9557	+	39.7604i	−1.05774	+	1.83206i
$472$		0			0
$473$	−6.81066	+	3.93214i	−0.313155	+	0.180800i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	26.0965	−	15.0668i	1.19488	−	0.689862i
$478$		0			0
$479$	2.72677	−	4.72290i	0.124589	−	0.215795i	−0.796983	−	0.604002i	$-0.793572\pi$
$479$	2.72677	−	4.72290i	0.124589	−	0.215795i	0.921572	+	0.388207i	$0.126905\pi$
$480$		0			0
$481$	5.98617	−	10.3684i	0.272946	−	0.472756i
$482$		0			0
$483$		−	14.7677i		−	0.671956i
$484$		0			0
$485$		0			0
$486$		0			0
$487$		−	25.0662i		−	1.13586i	−0.823077	−	0.567930i	$-0.807744\pi$
$487$		−	25.0662i		−	1.13586i	0.823077	−	0.567930i	$-0.192256\pi$
$488$		0			0
$489$	−24.2808	−	42.0557i	−1.09802	−	1.90182i
$490$		0			0
$491$	−14.8412	−	25.7057i	−0.669773	−	1.16008i	−0.977967	−	0.208758i	$-0.933058\pi$
$491$	−14.8412	−	25.7057i	−0.669773	−	1.16008i	0.308194	−	0.951324i	$-0.400275\pi$
$492$		0			0
$493$			9.26281i			0.417176i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−16.3381	+	9.43280i	−0.732863	+	0.423119i
$498$		0			0
$499$	−6.85519	−	11.8735i	−0.306881	−	0.531533i	0.670798	−	0.741640i	$-0.265952\pi$
$499$	−6.85519	−	11.8735i	−0.306881	−	0.531533i	−0.977678	+	0.210108i	$0.932619\pi$
$500$		0			0
$501$	−14.3328			−0.640344
$502$		0			0
$503$	−31.7404	−	18.3253i	−1.41523	−	0.817086i	−0.419359	−	0.907820i	$-0.637745\pi$
$503$	−31.7404	−	18.3253i	−1.41523	−	0.817086i	−0.995875	+	0.0907343i	$0.971079\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	5.34616	+	3.08661i	0.237431	+	0.137081i
$508$		0			0
$509$	−6.32519	+	10.9556i	−0.280359	+	0.485596i	−0.971473	−	0.237149i	$-0.923787\pi$
$509$	−6.32519	+	10.9556i	−0.280359	+	0.485596i	0.691114	+	0.722746i	$0.257120\pi$
$510$		0			0
$511$	3.38269	+	5.85899i	0.149641	+	0.259187i
$512$		0			0
$513$	−2.72504	+	2.78387i	−0.120314	+	0.122911i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−31.6389	−	18.2667i	−1.39148	−	0.803371i
$518$		0			0
$519$	11.5393	−	19.9867i	0.506520	−	0.877318i
$520$		0			0
$521$	16.3339			0.715601			0.357800	−	0.933798i	$-0.383527\pi$
$521$	16.3339			0.715601			0.357800	+	0.933798i	$0.383527\pi$
$522$		0			0
$523$	7.91086	+	4.56734i	0.345918	+	0.199716i	0.662886	−	0.748720i	$-0.269331\pi$
$523$	7.91086	+	4.56734i	0.345918	+	0.199716i	−0.316968	+	0.948436i	$0.602665\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−20.7774	+	11.9958i	−0.905078	+	0.522547i
$528$		0			0
$529$	−9.19321	−	15.9231i	−0.399705	−	0.692309i
$530$		0			0
$531$	−36.8183			−1.59778
$532$		0			0
$533$		−	2.36286i		−	0.102347i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	26.5922	−	15.3530i	1.14754	−	0.662531i
$538$		0			0
$539$	−1.45447			−0.0626486
$540$		0			0
$541$	1.45954	−	2.52800i	0.0627507	−	0.108687i	−0.832943	−	0.553358i	$-0.813346\pi$
$541$	1.45954	−	2.52800i	0.0627507	−	0.108687i	0.895694	+	0.444671i	$0.146679\pi$
$542$		0			0
$543$		−	38.8513i		−	1.66727i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−3.01329	−	1.73973i	−0.128839	−	0.0743853i	0.434195	−	0.900819i	$-0.357033\pi$
$547$	−3.01329	−	1.73973i	−0.128839	−	0.0743853i	−0.563034	+	0.826433i	$0.690366\pi$
$548$		0			0
$549$	−14.1810	−	24.5623i	−0.605232	−	1.04829i
$550$		0			0
$551$	−16.5154	+	4.61486i	−0.703580	+	0.196600i
$552$		0			0
$553$	28.3418	−	16.3631i	1.20522	−	0.695831i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	13.7920	+	7.96280i	0.584385	+	0.337395i	0.762874	−	0.646547i	$-0.223788\pi$
$557$	13.7920	+	7.96280i	0.584385	+	0.337395i	−0.178489	+	0.983942i	$0.557121\pi$
$558$		0			0
$559$	7.70775			0.326003
$560$		0			0
$561$	−9.83551	+	17.0356i	−0.415256	+	0.719244i
$562$		0			0
$563$			19.6274i			0.827195i	0.910460	+	0.413598i	$0.135728\pi$
$563$			19.6274i			0.827195i	−0.910460	+	0.413598i	$0.864272\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	18.4491	−	10.6516i	0.774788	−	0.447324i
$568$		0			0
$569$	11.7544			0.492770			0.246385	−	0.969172i	$-0.420757\pi$
$569$	11.7544			0.492770			0.246385	+	0.969172i	$0.420757\pi$
$570$		0			0
$571$	32.4868			1.35953			0.679766	−	0.733429i	$-0.262081\pi$
$571$	32.4868			1.35953			0.679766	+	0.733429i	$0.262081\pi$
$572$		0			0
$573$	35.4715	−	20.4795i	1.48184	−	0.855541i
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	25.7287i		−	1.07110i	−0.844503	−	0.535551i	$-0.820104\pi$
$577$		−	25.7287i		−	1.07110i	0.844503	−	0.535551i	$-0.179896\pi$
$578$		0			0
$579$	−1.07264	+	1.85787i	−0.0445775	+	0.0772106i
$580$		0			0
$581$	12.7837			0.530359
$582$		0			0
$583$	25.7828	+	14.8857i	1.06782	+	0.616503i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	36.0750	−	20.8279i	1.48897	−	0.859659i	0.489052	−	0.872255i	$-0.337343\pi$
$587$	36.0750	−	20.8279i	1.48897	−	0.859659i	0.999921	+	0.0125958i	$0.00400947\pi$
$588$		0			0
$589$	−31.7399	−	31.0692i	−1.30782	−	1.28018i
$590$		0			0
$591$	25.1884	+	43.6276i	1.03611	+	1.79460i
$592$		0			0
$593$	−15.2986	−	8.83267i	−0.628239	−	0.362714i	0.151831	−	0.988407i	$-0.451483\pi$
$593$	−15.2986	−	8.83267i	−0.628239	−	0.362714i	−0.780070	+	0.625692i	$0.784817\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		−	16.2775i		−	0.666193i
$598$		0			0
$599$	−13.1925	+	22.8502i	−0.539033	+	0.933632i	0.459924	+	0.887959i	$0.347877\pi$
$599$	−13.1925	+	22.8502i	−0.539033	+	0.933632i	−0.998956	+	0.0456738i	$0.985457\pi$
$600$		0			0
$601$	9.46838			0.386223			0.193112	−	0.981177i	$-0.438142\pi$
$601$	9.46838			0.386223			0.193112	+	0.981177i	$0.438142\pi$
$602$		0			0
$603$	−28.3269	+	16.3545i	−1.15356	+	0.666008i
$604$		0			0
$605$		0			0
$606$		0			0
$607$			8.26529i			0.335478i	0.985831	+	0.167739i	$0.0536465\pi$
$607$			8.26529i			0.335478i	−0.985831	+	0.167739i	$0.946353\pi$
$608$		0			0
$609$	−27.0479			−1.09604
$610$		0			0
$611$	17.9032	+	31.0092i	0.724285	+	1.25450i
$612$		0			0
$613$	5.89620	−	3.40417i	0.238145	−	0.137493i	−0.376179	−	0.926547i	$-0.622762\pi$
$613$	5.89620	−	3.40417i	0.238145	−	0.137493i	0.614324	+	0.789054i	$0.289429\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	5.20772	+	3.00668i	0.209655	+	0.121044i	0.601151	−	0.799135i	$-0.294709\pi$
$617$	5.20772	+	3.00668i	0.209655	+	0.121044i	−0.391496	+	0.920180i	$0.628042\pi$
$618$		0			0
$619$	−13.2299			−0.531754			−0.265877	−	0.964007i	$-0.585662\pi$
$619$	−13.2299			−0.531754			−0.265877	+	0.964007i	$0.585662\pi$
$620$		0			0
$621$	0.959816	−	1.66245i	0.0385161	−	0.0667118i
$622$		0			0
$623$	−20.1813	−	11.6517i	−0.808548	−	0.466816i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−35.2743	−	9.04916i	−1.40872	−	0.361389i
$628$		0			0
$629$	4.33915	+	7.51564i	0.173013	+	0.299668i
$630$		0			0
$631$	11.8932	−	20.5996i	0.473460	−	0.820058i	−0.526078	−	0.850436i	$-0.676338\pi$
$631$	11.8932	−	20.5996i	0.473460	−	0.820058i	0.999538	+	0.0303788i	$0.00967135\pi$
$632$		0			0
$633$	23.0188	+	13.2899i	0.914914	+	0.528226i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	1.23454	+	0.712762i	0.0489143	+	0.0282407i
$638$		0			0
$639$	−23.2033			−0.917908
$640$		0			0
$641$	−6.14239	−	10.6389i	−0.242610	−	0.420212i	0.718847	−	0.695168i	$-0.244670\pi$
$641$	−6.14239	−	10.6389i	−0.242610	−	0.420212i	−0.961457	+	0.274956i	$0.911337\pi$
$642$		0			0
$643$	25.2492	−	14.5776i	0.995729	−	0.574885i	0.0887474	−	0.996054i	$-0.471714\pi$
$643$	25.2492	−	14.5776i	0.995729	−	0.574885i	0.906982	+	0.421170i	$0.138380\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			36.7499i			1.44479i	0.691481	+	0.722394i	$0.256958\pi$
$647$			36.7499i			1.44479i	−0.691481	+	0.722394i	$0.743042\pi$
$648$		0			0
$649$	−18.1879	−	31.5023i	−0.713936	−	1.23657i
$650$		0			0
$651$	−35.0284	−	60.6710i	−1.37287	−	2.37788i
$652$		0			0
$653$			24.7707i			0.969351i	0.874694	+	0.484675i	$0.161062\pi$
$653$			24.7707i			0.969351i	−0.874694	+	0.484675i	$0.838938\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			8.32092i			0.324630i
$658$		0			0
$659$	11.1156	−	19.2528i	0.433002	−	0.749982i	−0.564128	−	0.825687i	$-0.690787\pi$
$659$	11.1156	−	19.2528i	0.433002	−	0.749982i	0.997130	+	0.0757053i	$0.0241208\pi$
$660$		0			0
$661$	−20.4684	+	35.4524i	−0.796130	+	1.37894i	0.125990	+	0.992032i	$0.459789\pi$
$661$	−20.4684	+	35.4524i	−0.796130	+	1.37894i	−0.922119	+	0.386905i	$0.873544\pi$
$662$		0			0
$663$	16.6965	−	9.63975i	0.648440	−	0.374377i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	7.31793	−	4.22501i	0.283351	−	0.163593i
$668$		0			0
$669$	−12.2592	+	21.2336i	−0.473969	+	0.820939i
$670$		0			0
$671$	14.0106	−	24.2671i	0.540873	−	0.936819i
$672$		0			0
$673$		−	33.5992i		−	1.29515i	−0.762000	−	0.647577i	$-0.775783\pi$
$673$		−	33.5992i		−	1.29515i	0.762000	−	0.647577i	$-0.224217\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		−	29.5883i		−	1.13717i	−0.822624	−	0.568585i	$-0.807491\pi$
$677$		−	29.5883i		−	1.13717i	0.822624	−	0.568585i	$-0.192509\pi$
$678$		0			0
$679$	9.85949	+	17.0771i	0.378373	+	0.655361i
$680$		0			0
$681$	28.4598	+	49.2938i	1.09058	+	1.88894i
$682$		0			0
$683$			41.0567i			1.57099i	0.618868	+	0.785495i	$0.287592\pi$
$683$			41.0567i			1.57099i	−0.618868	+	0.785495i	$0.712408\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−35.4183	+	20.4488i	−1.35129	+	0.780170i
$688$		0			0
$689$	−14.5894	−	25.2696i	−0.555813	−	0.962697i
$690$		0			0
$691$	1.22497			0.0466000			0.0233000	−	0.999729i	$-0.492583\pi$
$691$	1.22497			0.0466000			0.0233000	+	0.999729i	$0.492583\pi$
$692$		0			0
$693$	−26.2601	−	15.1613i	−0.997538	−	0.575929i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	1.48329	+	0.856376i	0.0561835	+	0.0324375i
$698$		0			0
$699$	23.5228	−	40.7426i	0.889712	−	1.54103i
$700$		0			0
$701$	−22.0101	−	38.1226i	−0.831309	−	1.43987i	−0.897001	−	0.442029i	$-0.854259\pi$
$701$	−22.0101	−	38.1226i	−0.831309	−	1.43987i	0.0656918	−	0.997840i	$-0.479075\pi$
$702$		0			0
$703$	−11.2384	+	11.4810i	−0.423865	+	0.433015i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−13.6439	−	7.87729i	−0.513130	−	0.296256i
$708$		0			0
$709$	8.16255	−	14.1379i	0.306551	−	0.530962i	−0.671055	−	0.741408i	$-0.734158\pi$
$709$	8.16255	−	14.1379i	0.306551	−	0.530962i	0.977605	+	0.210446i	$0.0674917\pi$
$710$		0			0
$711$	40.2509			1.50953
$712$		0			0
$713$	18.9542	+	10.9432i	0.709841	+	0.409827i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	1.31593	−	0.759750i	0.0491442	−	0.0283734i
$718$		0			0
$719$	5.08574	+	8.80876i	0.189666	+	0.328511i	0.945139	−	0.326669i	$-0.105926\pi$
$719$	5.08574	+	8.80876i	0.189666	+	0.328511i	−0.755473	+	0.655180i	$0.772593\pi$
$720$		0			0
$721$	−41.0686			−1.52947
$722$		0			0
$723$		−	55.1595i		−	2.05141i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−6.96541	+	4.02148i	−0.258333	+	0.149148i	−0.623574	−	0.781765i	$-0.714320\pi$
$727$	−6.96541	+	4.02148i	−0.258333	+	0.149148i	0.365241	+	0.930913i	$0.380987\pi$
$728$		0			0
$729$	32.9600			1.22074
$730$		0			0
$731$	−2.79353	+	4.83853i	−0.103322	+	0.178960i
$732$		0			0
$733$			41.2325i			1.52296i	0.648190	+	0.761479i	$0.275526\pi$
$733$			41.2325i			1.52296i	−0.648190	+	0.761479i	$0.724474\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−27.9864	−	16.1580i	−1.03089	−	0.595186i
$738$		0			0
$739$	16.5253	+	28.6227i	0.607893	+	1.05290i	0.991587	+	0.129442i	$0.0413186\pi$
$739$	16.5253	+	28.6227i	0.607893	+	1.05290i	−0.383694	+	0.923460i	$0.625348\pi$
$740$		0			0
$741$	25.5059	+	24.9669i	0.936983	+	0.917184i
$742$		0			0
$743$	30.1261	−	17.3933i	1.10522	−	0.638099i	0.167633	−	0.985849i	$-0.446388\pi$
$743$	30.1261	−	17.3933i	1.10522	−	0.638099i	0.937587	+	0.347750i	$0.113054\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	13.6166	+	7.86153i	0.498204	+	0.287638i
$748$		0			0
$749$	41.4284			1.51376
$750$		0			0
$751$	21.7350	−	37.6462i	0.793123	−	1.37373i	−0.130902	−	0.991395i	$-0.541787\pi$
$751$	21.7350	−	37.6462i	0.793123	−	1.37373i	0.924024	−	0.382334i	$-0.124879\pi$
$752$		0			0
$753$		−	20.8537i		−	0.759950i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	5.34328	−	3.08494i	0.194205	−	0.112124i	−0.399745	−	0.916626i	$-0.630901\pi$
$757$	5.34328	−	3.08494i	0.194205	−	0.112124i	0.593949	+	0.804502i	$0.297568\pi$
$758$		0			0
$759$	17.9449			0.651359
$760$		0			0
$761$	−9.81318			−0.355728			−0.177864	−	0.984055i	$-0.556919\pi$
$761$	−9.81318			−0.355728			−0.177864	+	0.984055i	$0.556919\pi$
$762$		0			0
$763$	−29.8114	+	17.2116i	−1.07925	+	0.623103i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			35.6517i			1.28731i
$768$		0			0
$769$	−20.7452	+	35.9317i	−0.748090	+	1.29573i	0.200647	+	0.979664i	$0.435695\pi$
$769$	−20.7452	+	35.9317i	−0.748090	+	1.29573i	−0.948737	+	0.316066i	$0.897638\pi$
$770$		0			0
$771$	−35.7727			−1.28832
$772$		0			0
$773$	−36.1279	−	20.8584i	−1.29943	−	0.750226i	−0.319124	−	0.947713i	$-0.603389\pi$
$773$	−36.1279	−	20.8584i	−1.29943	−	0.750226i	−0.980306	+	0.197487i	$0.936722\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−21.9460	+	12.6705i	−0.787309	+	0.454553i
$778$		0			0
$779$	−0.787908	+	3.07133i	−0.0282297	+	0.110042i
$780$		0			0
$781$	−11.4622	−	19.8531i	−0.410149	−	0.710400i
$782$		0			0
$783$	−3.04486	−	1.75795i	−0.108814	−	0.0628240i
$784$		0			0
$785$		0			0
$786$		0			0
$787$			13.0342i			0.464621i	0.972642	+	0.232310i	$0.0746285\pi$
$787$			13.0342i			0.464621i	−0.972642	+	0.232310i	$0.925371\pi$
$788$		0			0
$789$	23.3718	−	40.4812i	0.832060	−	1.44117i
$790$		0			0
$791$	−16.6580			−0.592292
$792$		0			0
$793$	−23.7841	+	13.7317i	−0.844596	+	0.487628i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	33.1911i		−	1.17569i	−0.808974	−	0.587844i	$-0.799977\pi$
$797$		−	33.1911i		−	1.17569i	0.808974	−	0.587844i	$-0.200023\pi$
$798$		0			0
$799$	−25.9547			−0.918210
$800$		0			0
$801$	−14.3307	−	24.8216i	−0.506351	−	0.877026i
$802$		0			0
$803$	−7.11951	+	4.11045i	−0.251242	+	0.145055i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−14.5556	−	8.40369i	−0.512382	−	0.295824i
$808$		0			0
$809$	29.5271			1.03812			0.519058	−	0.854739i	$-0.326283\pi$
$809$	29.5271			1.03812			0.519058	+	0.854739i	$0.326283\pi$
$810$		0			0
$811$	−14.4097	+	24.9583i	−0.505993	+	0.876406i	0.493983	+	0.869472i	$0.335541\pi$
$811$	−14.4097	+	24.9583i	−0.505993	+	0.876406i	−0.999976	+	0.00693438i	$0.997793\pi$
$812$		0			0
$813$	48.1727	+	27.8125i	1.68949	+	0.975427i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−10.0188	−	2.57018i	−0.350513	−	0.0899194i
$818$		0			0
$819$	14.8595	+	25.7374i	0.519233	+	0.899338i
$820$		0			0
$821$	9.40280	−	16.2861i	0.328160	−	0.568390i	−0.653987	−	0.756506i	$-0.726905\pi$
$821$	9.40280	−	16.2861i	0.328160	−	0.568390i	0.982147	+	0.188116i	$0.0602382\pi$
$822$		0			0
$823$	−6.55545	−	3.78479i	−0.228509	−	0.131929i	0.381375	−	0.924420i	$-0.375451\pi$
$823$	−6.55545	−	3.78479i	−0.228509	−	0.131929i	−0.609884	+	0.792491i	$0.708784\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	30.2560	+	17.4683i	1.05211	+	0.607434i	0.923238	−	0.384228i	$-0.125532\pi$
$827$	30.2560	+	17.4683i	1.05211	+	0.607434i	0.128868	+	0.991662i	$0.458866\pi$
$828$		0			0
$829$	45.8376			1.59201			0.796003	−	0.605293i	$-0.206944\pi$
$829$	45.8376			1.59201			0.796003	+	0.605293i	$0.206944\pi$
$830$		0			0
$831$	−30.8327	−	53.4037i	−1.06957	−	1.85256i
$832$		0			0
$833$	−0.894872	+	0.516655i	−0.0310055	+	0.0179010i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		−	9.10656i		−	0.314769i
$838$		0			0
$839$	7.00502	+	12.1330i	0.241840	+	0.418879i	0.961238	−	0.275719i	$-0.0889158\pi$
$839$	7.00502	+	12.1330i	0.241840	+	0.418879i	−0.719398	+	0.694598i	$0.755582\pi$
$840$		0			0
$841$	6.76169	+	11.7116i	0.233162	+	0.403848i
$842$		0			0
$843$		−	47.0455i		−	1.62033i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			0.0436252i			0.00149898i
$848$		0			0
$849$	−5.66708	+	9.81568i	−0.194494	+	0.336873i
$850$		0			0
$851$	3.95840	−	6.85615i	0.135692	−	0.235026i
$852$		0			0
$853$	−32.5205	+	18.7757i	−1.11348	+	0.642869i	−0.939729	−	0.341920i	$-0.888923\pi$
$853$	−32.5205	+	18.7757i	−1.11348	+	0.642869i	−0.173753	+	0.984789i	$0.555589\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−3.52261	+	2.03378i	−0.120330	+	0.0694726i	−0.558957	−	0.829197i	$-0.688798\pi$
$857$	−3.52261	+	2.03378i	−0.120330	+	0.0694726i	0.438627	+	0.898669i	$0.355465\pi$
$858$		0			0
$859$	6.31785	−	10.9428i	0.215562	−	0.373365i	−0.737884	−	0.674928i	$-0.764175\pi$
$859$	6.31785	−	10.9428i	0.215562	−	0.373365i	0.953446	+	0.301563i	$0.0975082\pi$
$860$		0			0
$861$	−2.50066	+	4.33127i	−0.0852223	+	0.147609i
$862$		0			0
$863$		−	14.5147i		−	0.494085i	−0.969005	−	0.247042i	$-0.920541\pi$
$863$		−	14.5147i		−	0.494085i	0.969005	−	0.247042i	$-0.0794587\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		−	28.8790i		−	0.980781i
$868$		0			0
$869$	19.8835	+	34.4393i	0.674503	+	1.16827i
$870$		0			0
$871$	15.8364	+	27.4294i	0.536594	+	0.929409i
$872$		0			0
$873$			24.2529i			0.820836i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.67583	+	0.967541i	−0.0565887	+	0.0326715i	−0.528027	−	0.849227i	$-0.677068\pi$
$877$	−1.67583	+	0.967541i	−0.0565887	+	0.0326715i	0.471439	+	0.881899i	$0.343735\pi$
$878$		0			0
$879$	−1.60098	−	2.77298i	−0.0539998	−	0.0935303i
$880$		0			0
$881$	15.9037			0.535811			0.267905	−	0.963445i	$-0.413669\pi$
$881$	15.9037			0.535811			0.267905	+	0.963445i	$0.413669\pi$
$882$		0			0
$883$	30.3483	+	17.5216i	1.02130	+	0.589648i	0.914480	−	0.404631i	$-0.132600\pi$
$883$	30.3483	+	17.5216i	1.02130	+	0.589648i	0.106820	+	0.994278i	$0.465933\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−14.0089	−	8.08806i	−0.470374	−	0.271571i	0.246022	−	0.969264i	$-0.420876\pi$
$887$	−14.0089	−	8.08806i	−0.470374	−	0.271571i	−0.716396	+	0.697694i	$0.754210\pi$
$888$		0			0
$889$	−12.4402	+	21.5470i	−0.417230	+	0.722664i
$890$		0			0
$891$	12.9432	+	22.4182i	0.433613	+	0.751039i
$892$		0			0
$893$	−12.9310	−	46.2767i	−0.432718	−	1.54859i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−15.2314	−	8.79387i	−0.508563	−	0.293619i
$898$		0			0
$899$	20.0431	−	34.7156i	0.668473	−	1.15783i
$900$		0			0
$901$	21.1507			0.704631
$902$		0			0
$903$	−14.1288	−	8.15724i	−0.470176	−	0.271456i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−19.9143	+	11.4975i	−0.661244	+	0.381770i	−0.792751	−	0.609546i	$-0.791352\pi$
$907$	−19.9143	+	11.4975i	−0.661244	+	0.381770i	0.131507	+	0.991315i	$0.458019\pi$
$908$		0			0
$909$	−9.68848	−	16.7809i	−0.321347	−	0.556589i
$910$		0			0
$911$	−23.0833			−0.764783			−0.382392	−	0.924000i	$-0.624899\pi$
$911$	−23.0833			−0.764783			−0.382392	+	0.924000i	$0.624899\pi$
$912$		0			0
$913$			15.5341i			0.514103i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−52.5917	+	30.3638i	−1.73673	+	1.00270i
$918$		0			0
$919$	−12.5454			−0.413835			−0.206918	−	0.978358i	$-0.566343\pi$
$919$	−12.5454			−0.413835			−0.206918	+	0.978358i	$0.566343\pi$
$920$		0			0
$921$	−10.9060	+	18.8898i	−0.359365	+	0.622439i
$922$		0			0
$923$			22.4681i			0.739547i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−43.7441	−	25.2557i	−1.43674	−	0.829505i
$928$		0			0
$929$	−26.6494	−	46.1581i	−0.874338	−	1.51440i	−0.857466	−	0.514540i	$-0.827963\pi$
$929$	−26.6494	−	46.1581i	−0.874338	−	1.51440i	−0.0168714	−	0.999858i	$-0.505371\pi$
$930$		0			0
$931$	−1.36702	−	1.33814i	−0.0448024	−	0.0438556i
$932$		0			0
$933$	−52.0662	+	30.0604i	−1.70457	+	0.984134i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−30.4152	−	17.5602i	−0.993622	−	0.573668i	−0.0872667	−	0.996185i	$-0.527813\pi$
$937$	−30.4152	−	17.5602i	−0.993622	−	0.573668i	−0.906355	+	0.422517i	$0.861147\pi$
$938$		0			0
$939$	−1.95704			−0.0638656
$940$		0			0
$941$	−6.57898	+	11.3951i	−0.214469	+	0.371470i	−0.953108	−	0.302630i	$-0.902135\pi$
$941$	−6.57898	+	11.3951i	−0.214469	+	0.371470i	0.738639	+	0.674101i	$0.235469\pi$
$942$		0			0
$943$		−	1.56246i		−	0.0508807i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	9.05015	−	5.22510i	0.294090	−	0.169793i	−0.345695	−	0.938347i	$-0.612357\pi$
$947$	9.05015	−	5.22510i	0.294090	−	0.169793i	0.639785	+	0.768554i	$0.279023\pi$
$948$		0			0
$949$	8.05728			0.261550
$950$		0			0
$951$	34.8940			1.13152
$952$		0			0
$953$	3.76057	−	2.17117i	0.121817	−	0.0703310i	−0.437853	−	0.899046i	$-0.644261\pi$
$953$	3.76057	−	2.17117i	0.121817	−	0.0703310i	0.559670	+	0.828715i	$0.310928\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		−	32.8670i		−	1.06244i
$958$		0			0
$959$	−10.4012	+	18.0154i	−0.335872	+	0.581747i
$960$		0			0
$961$	72.8272			2.34927
$962$		0			0
$963$	44.1274	+	25.4770i	1.42198	+	0.820983i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	13.5810	−	7.84100i	0.436736	−	0.252149i	−0.265476	−	0.964117i	$-0.585529\pi$
$967$	13.5810	−	7.84100i	0.436736	−	0.252149i	0.702212	+	0.711968i	$0.252196\pi$
$968$		0			0
$969$	−24.9171	+	6.96253i	−0.800454	+	0.223669i
$970$		0			0
$971$	−1.33867	−	2.31865i	−0.0429601	−	0.0744091i	0.843746	−	0.536743i	$-0.180346\pi$
$971$	−1.33867	−	2.31865i	−0.0429601	−	0.0744091i	−0.886706	+	0.462334i	$0.847012\pi$
$972$		0			0
$973$	−39.9614	−	23.0717i	−1.28110	−	0.739646i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	2.87156i		−	0.0918693i	−0.998944	−	0.0459347i	$-0.985373\pi$
$977$		−	2.87156i		−	0.0918693i	0.998944	−	0.0459347i	$-0.0146266\pi$
$978$		0			0
$979$	14.1585	−	24.5232i	0.452507	−	0.783765i
$980$		0			0
$981$	−42.3380			−1.35175
$982$		0			0
$983$	−29.3660	+	16.9545i	−0.936630	+	0.540764i	−0.888902	−	0.458097i	$-0.848531\pi$
$983$	−29.3660	+	16.9545i	−0.936630	+	0.540764i	−0.0477276	+	0.998860i	$0.515198\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		−	75.7889i		−	2.41239i
$988$		0			0
$989$	5.09680			0.162069
$990$		0			0
$991$	20.0649	+	34.7535i	0.637383	+	1.10398i	0.986005	+	0.166716i	$0.0533165\pi$
$991$	20.0649	+	34.7535i	0.637383	+	1.10398i	−0.348622	+	0.937264i	$0.613350\pi$
$992$		0			0
$993$	−62.6533	+	36.1729i	−1.98824	+	1.14791i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	3.03748	+	1.75369i	0.0961979	+	0.0555399i	0.547327	−	0.836919i	$-0.315645\pi$
$997$	3.03748	+	1.75369i	0.0961979	+	0.0555399i	−0.451129	+	0.892459i	$0.648979\pi$
$998$		0			0
$999$	−3.29404			−0.104219

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1900.2.s.d.349.2		16
5.2	odd	4		380.2.i.c.121.4	✓	8
5.3	odd	4		1900.2.i.d.501.1		8
5.4	even	2	inner	1900.2.s.d.349.7		16
15.2	even	4		3420.2.t.w.1261.3		8
19.11	even	3	inner	1900.2.s.d.49.7		16
20.7	even	4		1520.2.q.m.881.1		8
95.7	odd	12		7220.2.a.r.1.1		4
95.12	even	12		7220.2.a.p.1.4		4
95.49	even	6	inner	1900.2.s.d.49.2		16
95.68	odd	12		1900.2.i.d.201.1		8
95.87	odd	12		380.2.i.c.201.4	yes	8
285.182	even	12		3420.2.t.w.3241.3		8
380.87	even	12		1520.2.q.m.961.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.i.c.121.4	✓	8	5.2	odd	4
380.2.i.c.201.4	yes	8	95.87	odd	12
1520.2.q.m.881.1		8	20.7	even	4
1520.2.q.m.961.1		8	380.87	even	12
1900.2.i.d.201.1		8	95.68	odd	12
1900.2.i.d.501.1		8	5.3	odd	4
1900.2.s.d.49.2		16	95.49	even	6	inner
1900.2.s.d.49.7		16	19.11	even	3	inner
1900.2.s.d.349.2		16	1.1	even	1	trivial
1900.2.s.d.349.7		16	5.4	even	2	inner
3420.2.t.w.1261.3		8	15.2	even	4
3420.2.t.w.3241.3		8	285.182	even	12
7220.2.a.p.1.4		4	95.12	even	12
7220.2.a.r.1.1		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)

\(f(q)\)	\(=\)	\(q+(-2.18309 + 1.26041i) q^{3} -2.72743i q^{7} +(1.67727 - 2.90511i) q^{9} +O(q^{10})\)	\(q+(-2.18309 + 1.26041i) q^{3} -2.72743i q^{7} +(1.67727 - 2.90511i) q^{9} +3.31421 q^{11} +(-2.81306 - 1.62412i) q^{13} +(2.03909 - 1.17727i) q^{17} +(3.11494 + 3.04912i) q^{19} +(3.43768 + 5.95423i) q^{21} +(-1.86016 - 1.07396i) q^{23} +0.893714i q^{27} +(-1.96702 + 3.40697i) q^{29} -10.1896 q^{31} +(-7.23524 + 4.17727i) q^{33} +3.68579i q^{37} +8.18825 q^{39} +(0.363714 + 0.629971i) q^{41} +(-2.05499 + 1.18645i) q^{43} +(-9.54644 - 5.51164i) q^{47} -0.438860 q^{49} +(-2.96768 + 5.14017i) q^{51} +(7.77947 + 4.49148i) q^{53} +(-10.6434 - 2.73041i) q^{57} +(-5.48784 - 9.50521i) q^{59} +(4.22743 - 7.32212i) q^{61} +(-7.92348 - 4.57462i) q^{63} +(-8.44436 - 4.87535i) q^{67} +5.41453 q^{69} +(-3.45850 - 5.99029i) q^{71} +(-2.14818 + 1.24025i) q^{73} -9.03927i q^{77} +(5.99948 + 10.3914i) q^{79} +(3.90535 + 6.76427i) q^{81} +4.68711i q^{83} -9.91699i q^{87} +(4.27205 - 7.39941i) q^{89} +(-4.42968 + 7.67243i) q^{91} +(22.2448 - 12.8430i) q^{93} +(-6.26127 + 3.61494i) q^{97} +(5.55882 - 9.62816i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 10 q^{9}+O(q^{10}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more