LMFDB - Embedded newform 1900.2.i.d.501.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1900.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.1715763840$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 9x^{6} + 2x^{5} + 65x^{4} - 20x^{3} + 25x^{2} + 6x + 4 $ x^8 - x^7 + 9x^6 + 2x^5 + 65x^4 - 20x^3 + 25x^2 + 6x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 380)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			501.1
Root			$-1.26041 - 2.18309i$ of defining polynomial
Character	$\chi$	$=$	1900.501
Dual form			1900.2.i.d.201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26041 - 2.18309i) q^{3} -2.72743 q^{7} +(-1.67727 + 2.90511i) q^{9} +O(q^{10})$	$q+(-1.26041 - 2.18309i) q^{3} -2.72743 q^{7} +(-1.67727 + 2.90511i) q^{9} +3.31421 q^{11} +(1.62412 - 2.81306i) q^{13} +(-1.17727 - 2.03909i) q^{17} +(-3.11494 - 3.04912i) q^{19} +(3.43768 + 5.95423i) q^{21} +(1.07396 - 1.86016i) q^{23} +0.893714 q^{27} +(1.96702 - 3.40697i) q^{29} -10.1896 q^{31} +(-4.17727 - 7.23524i) q^{33} +3.68579 q^{37} -8.18825 q^{39} +(0.363714 + 0.629971i) q^{41} +(-1.18645 - 2.05499i) q^{43} +(-5.51164 + 9.54644i) q^{47} +0.438860 q^{49} +(-2.96768 + 5.14017i) q^{51} +(-4.49148 + 7.77947i) q^{53} +(-2.73041 + 10.6434i) q^{57} +(5.48784 + 9.50521i) q^{59} +(4.22743 - 7.32212i) q^{61} +(4.57462 - 7.92348i) q^{63} +(-4.87535 + 8.44436i) q^{67} -5.41453 q^{69} +(-3.45850 - 5.99029i) q^{71} +(-1.24025 - 2.14818i) q^{73} -9.03927 q^{77} +(-5.99948 - 10.3914i) q^{79} +(3.90535 + 6.76427i) q^{81} -4.68711 q^{83} -9.91699 q^{87} +(-4.27205 + 7.39941i) q^{89} +(-4.42968 + 7.67243i) q^{91} +(12.8430 + 22.2448i) q^{93} +(3.61494 + 6.26127i) q^{97} +(-5.55882 + 9.62816i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{3} - 5 q^{9}+O(q^{10}) $ 8 * q + q^3 - 5 * q^9	$ 8 q + q^{3} - 5 q^{9} + 4 q^{11} - 9 q^{13} - q^{17} + 3 q^{19} + 8 q^{21} - 20 q^{27} + 5 q^{29} - 20 q^{31} - 25 q^{33} + 52 q^{37} - 54 q^{39} - 8 q^{41} - 7 q^{43} - 16 q^{47} + 20 q^{49} + 12 q^{51} - 5 q^{53} - 27 q^{57} + 11 q^{59} + 12 q^{61} + 3 q^{63} + 6 q^{69} + 14 q^{71} + 4 q^{73} + 44 q^{77} + 13 q^{79} - 24 q^{81} - 10 q^{83} + 4 q^{87} + 5 q^{89} - 46 q^{91} + 28 q^{93} + q^{97} + 24 q^{99}+O(q^{100}) $ 8 * q + q^3 - 5 * q^9 + 4 * q^11 - 9 * q^13 - q^17 + 3 * q^19 + 8 * q^21 - 20 * q^27 + 5 * q^29 - 20 * q^31 - 25 * q^33 + 52 * q^37 - 54 * q^39 - 8 * q^41 - 7 * q^43 - 16 * q^47 + 20 * q^49 + 12 * q^51 - 5 * q^53 - 27 * q^57 + 11 * q^59 + 12 * q^61 + 3 * q^63 + 6 * q^69 + 14 * q^71 + 4 * q^73 + 44 * q^77 + 13 * q^79 - 24 * q^81 - 10 * q^83 + 4 * q^87 + 5 * q^89 - 46 * q^91 + 28 * q^93 + q^97 + 24 * 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
$3$	−1.26041	−	2.18309i	−0.727698	−	1.26041i	−0.957854	−	0.287256i	$-0.907257\pi$
$3$	−1.26041	−	2.18309i	−0.727698	−	1.26041i	0.230156	−	0.973154i	$-0.426076\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.72743			−1.03087			−0.515435	−	0.856928i	$-0.672370\pi$
$7$	−2.72743			−1.03087			−0.515435	+	0.856928i	$0.672370\pi$
$8$		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
$13$	1.62412	−	2.81306i	0.450451	−	0.780204i	−0.547963	−	0.836502i	$-0.684597\pi$
$13$	1.62412	−	2.81306i	0.450451	−	0.780204i	0.998414	+	0.0562987i	$0.0179299\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.17727	−	2.03909i	−0.285529	−	0.494551i	0.687208	−	0.726460i	$-0.258836\pi$
$17$	−1.17727	−	2.03909i	−0.285529	−	0.494551i	−0.972737	+	0.231910i	$0.925503\pi$
$18$		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
$23$	1.07396	−	1.86016i	0.223937	−	0.387870i	−0.732063	−	0.681237i	$-0.761442\pi$
$23$	1.07396	−	1.86016i	0.223937	−	0.387870i	0.956000	+	0.293367i	$0.0947758\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.893714			0.171995
$28$		0			0
$29$	1.96702	−	3.40697i	0.365266	−	0.632659i	−0.623553	−	0.781781i	$-0.714311\pi$
$29$	1.96702	−	3.40697i	0.365266	−	0.632659i	0.988819	+	0.149122i	$0.0476447\pi$
$30$		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
$33$	−4.17727	−	7.23524i	−0.727169	−	1.25949i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	3.68579			0.605940			0.302970	−	0.953000i	$-0.402022\pi$
$37$	3.68579			0.605940			0.302970	+	0.953000i	$0.402022\pi$
$38$		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
$43$	−1.18645	−	2.05499i	−0.180931	−	0.313383i	0.761267	−	0.648439i	$-0.224578\pi$
$43$	−1.18645	−	2.05499i	−0.180931	−	0.313383i	−0.942198	+	0.335057i	$0.891245\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.51164	+	9.54644i	−0.803955	+	1.39249i	0.113039	+	0.993591i	$0.463942\pi$
$47$	−5.51164	+	9.54644i	−0.803955	+	1.39249i	−0.916994	+	0.398901i	$0.869392\pi$
$48$		0			0
$49$	0.438860			0.0626942
$50$		0			0
$51$	−2.96768	+	5.14017i	−0.415558	+	0.719767i
$52$		0			0
$53$	−4.49148	+	7.77947i	−0.616952	+	1.06859i	0.373087	+	0.927797i	$0.378299\pi$
$53$	−4.49148	+	7.77947i	−0.616952	+	1.06859i	−0.990039	+	0.140796i	$0.955034\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−2.73041	+	10.6434i	−0.361652	+	1.40975i
$58$		0			0
$59$	5.48784	+	9.50521i	0.714456	+	1.23747i	0.963169	+	0.268896i	$0.0866589\pi$
$59$	5.48784	+	9.50521i	0.714456	+	1.23747i	−0.248714	+	0.968577i	$0.580008\pi$
$60$		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
$63$	4.57462	−	7.92348i	0.576348	−	0.998264i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−4.87535	+	8.44436i	−0.595619	+	1.03164i	0.397840	+	0.917455i	$0.369760\pi$
$67$	−4.87535	+	8.44436i	−0.595619	+	1.03164i	−0.993459	+	0.114188i	$0.963573\pi$
$68$		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
$73$	−1.24025	−	2.14818i	−0.145160	−	0.251425i	0.784272	−	0.620417i	$-0.213036\pi$
$73$	−1.24025	−	2.14818i	−0.145160	−	0.251425i	−0.929433	+	0.368992i	$0.879703\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−9.03927			−1.03012
$78$		0			0
$79$	−5.99948	−	10.3914i	−0.674994	−	1.16912i	−0.976471	−	0.215650i	$-0.930813\pi$
$79$	−5.99948	−	10.3914i	−0.674994	−	1.16912i	0.301477	−	0.953474i	$-0.402520\pi$
$80$		0			0
$81$	3.90535	+	6.76427i	0.433928	+	0.751586i
$82$		0			0
$83$	−4.68711			−0.514477			−0.257238	−	0.966348i	$-0.582813\pi$
$83$	−4.68711			−0.514477			−0.257238	+	0.966348i	$0.582813\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−9.91699			−1.06321
$88$		0			0
$89$	−4.27205	+	7.39941i	−0.452836	+	0.784336i	−0.998561	−	0.0536291i	$-0.982921\pi$
$89$	−4.27205	+	7.39941i	−0.452836	+	0.784336i	0.545725	+	0.837965i	$0.316254\pi$
$90$		0			0
$91$	−4.42968	+	7.67243i	−0.464357	+	0.804289i
$92$		0			0
$93$	12.8430	+	22.2448i	1.33176	+	2.30668i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	3.61494	+	6.26127i	0.367042	+	0.635735i	0.989102	−	0.147235i	$-0.0470372\pi$
$97$	3.61494	+	6.26127i	0.367042	+	0.635735i	−0.622060	+	0.782970i	$0.713704\pi$
$98$		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
$103$	15.0576			1.48367			0.741836	−	0.670581i	$-0.233955\pi$
$103$	15.0576			1.48367			0.741836	+	0.670581i	$0.233955\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	15.1896			1.46843			0.734215	−	0.678917i	$-0.237550\pi$
$107$	15.1896			1.46843			0.734215	+	0.678917i	$0.237550\pi$
$108$		0			0
$109$	6.31057	+	10.9302i	0.604443	+	1.04693i	0.992139	+	0.125139i	$0.0399376\pi$
$109$	6.31057	+	10.9302i	0.604443	+	1.04693i	−0.387696	+	0.921787i	$0.626729\pi$
$110$		0			0
$111$	−4.64560	−	8.04642i	−0.440941	−	0.763732i
$112$		0			0
$113$	6.10761			0.574555			0.287278	−	0.957847i	$-0.407250\pi$
$113$	6.10761			0.574555			0.287278	+	0.957847i	$0.407250\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	5.44818	+	9.43652i	0.503684	+	0.872406i
$118$		0			0
$119$	3.21091	+	5.56146i	0.294344	+	0.509818i
$120$		0			0
$121$	−0.0159950			−0.00145409
$122$		0			0
$123$	0.916857	−	1.58804i	0.0826702	−	0.143189i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−4.56114	+	7.90013i	−0.404736	+	0.701023i	−0.994291	−	0.106705i	$-0.965970\pi$
$127$	−4.56114	+	7.90013i	−0.404736	+	0.701023i	0.589555	+	0.807728i	$0.299303\pi$
$128$		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
$133$	8.49578	+	8.31625i	0.736678	+	0.721110i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.81355	+	6.60527i	−0.325814	+	0.564326i	−0.981677	−	0.190554i	$-0.938972\pi$
$137$	−3.81355	+	6.60527i	−0.325814	+	0.564326i	0.655863	+	0.754880i	$0.272305\pi$
$138$		0			0
$139$	−8.45916	+	14.6517i	−0.717496	+	1.24274i	0.244493	+	0.969651i	$0.421379\pi$
$139$	−8.45916	+	14.6517i	−0.717496	+	1.24274i	−0.961989	+	0.273089i	$0.911955\pi$
$140$		0			0
$141$	27.7877			2.34015
$142$		0			0
$143$	5.38269	−	9.32309i	0.450123	−	0.779636i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−0.553143	−	0.958072i	−0.0456225	−	0.0790204i
$148$		0			0
$149$	6.19809	+	10.7354i	0.507767	+	0.879478i	0.999960	+	0.00899193i	$0.00286226\pi$
$149$	6.19809	+	10.7354i	0.507767	+	0.879478i	−0.492193	+	0.870486i	$0.663804\pi$
$150$		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
$153$	7.89836			0.638544
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−9.10642	−	15.7728i	−0.726772	−	1.25881i	−0.958241	−	0.285963i	$-0.907687\pi$
$157$	−9.10642	−	15.7728i	−0.726772	−	1.25881i	0.231469	−	0.972842i	$-0.425647\pi$
$158$		0			0
$159$	22.6444			1.79582
$160$		0			0
$161$	−2.92916	+	5.07345i	−0.230850	+	0.399844i
$162$		0			0
$163$	−19.2642			−1.50889			−0.754446	−	0.656362i	$-0.772094\pi$
$163$	−19.2642			−1.50889			−0.754446	+	0.656362i	$0.772094\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.84289	−	4.92404i	0.219990	−	0.381033i	−0.734815	−	0.678268i	$-0.762731\pi$
$167$	2.84289	−	4.92404i	0.219990	−	0.381033i	0.954805	+	0.297234i	$0.0960643\pi$
$168$		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
$173$	−4.57760	−	7.92864i	−0.348029	−	0.602804i	0.637870	−	0.770144i	$-0.279816\pi$
$173$	−4.57760	−	7.92864i	−0.348029	−	0.602804i	−0.985899	+	0.167340i	$0.946482\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	13.8338	−	23.9609i	1.03982	−	1.80101i
$178$		0			0
$179$	12.1810			0.910448			0.455224	−	0.890377i	$-0.349559\pi$
$179$	12.1810			0.910448			0.455224	+	0.890377i	$0.349559\pi$
$180$		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
$183$	−21.3132			−1.57551
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−3.90171	−	6.75796i	−0.285321	−	0.494191i
$188$		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
$193$	0.425514	+	0.737011i	0.0306292	+	0.0530512i	0.880934	−	0.473240i	$-0.156916\pi$
$193$	0.425514	+	0.737011i	0.0306292	+	0.0530512i	−0.850305	+	0.526291i	$0.823582\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−19.9843			−1.42382			−0.711910	−	0.702270i	$-0.752170\pi$
$197$	−19.9843			−1.42382			−0.711910	+	0.702270i	$0.752170\pi$
$198$		0			0
$199$	3.22861	−	5.59212i	0.228870	−	0.396415i	−0.728603	−	0.684936i	$-0.759830\pi$
$199$	3.22861	−	5.59212i	0.228870	−	0.396415i	0.957474	+	0.288521i	$0.0931636\pi$
$200$		0			0
$201$	24.5798			1.73372
$202$		0			0
$203$	−5.36490	+	9.29227i	−0.376542	+	0.652190i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	3.60264	+	6.23996i	0.250401	+	0.433707i
$208$		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
$213$	−8.71825	+	15.1004i	−0.597364	+	1.03467i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	27.7913			1.88660
$218$		0			0
$219$	−3.12645	+	5.41516i	−0.211266	+	0.365923i
$220$		0			0
$221$	−7.64811			−0.514467
$222$		0			0
$223$	4.86319	+	8.42329i	0.325663	+	0.564065i	0.981646	−	0.190710i	$-0.0610791\pi$
$223$	4.86319	+	8.42329i	0.325663	+	0.564065i	−0.655983	+	0.754776i	$0.727746\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−22.5798			−1.49867			−0.749336	−	0.662190i	$-0.769627\pi$
$227$	−22.5798			−1.49867			−0.749336	+	0.662190i	$0.769627\pi$
$228$		0			0
$229$	−16.2239			−1.07211			−0.536053	−	0.844184i	$-0.680085\pi$
$229$	−16.2239			−1.07211			−0.536053	+	0.844184i	$0.680085\pi$
$230$		0			0
$231$	11.3932	+	19.7336i	0.749617	+	1.29837i
$232$		0			0
$233$	−9.33139	−	16.1624i	−0.611320	−	1.05884i	−0.991018	−	0.133727i	$-0.957306\pi$
$233$	−9.33139	−	16.1624i	−0.611320	−	1.05884i	0.379699	−	0.925110i	$-0.376028\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−15.1236	+	26.1948i	−0.982383	+	1.70154i
$238$		0			0
$239$	0.602780			0.0389906			0.0194953	−	0.999810i	$-0.493794\pi$
$239$	0.602780			0.0389906			0.0194953	+	0.999810i	$0.493794\pi$
$240$		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
$243$	11.1853	−	19.3734i	0.717535	−	1.24281i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−13.6364	+	3.81039i	−0.867665	+	0.242449i
$248$		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
$253$	3.55934	−	6.16496i	0.223774	−	0.387588i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	7.09544	−	12.2897i	0.442602	−	0.766608i	−0.555280	−	0.831663i	$-0.687389\pi$
$257$	7.09544	−	12.2897i	0.442602	−	0.766608i	0.997882	+	0.0650550i	$0.0207223\pi$
$258$		0			0
$259$	−10.0527			−0.624645
$260$		0			0
$261$	6.59842	+	11.4288i	0.408432	+	0.707425i
$262$		0			0
$263$	−9.27153	−	16.0588i	−0.571707	−	0.990225i	−0.996391	−	0.0848836i	$-0.972948\pi$
$263$	−9.27153	−	16.0588i	−0.571707	−	0.990225i	0.424684	−	0.905342i	$-0.360385\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	21.5381			1.31811
$268$		0			0
$269$	−3.33371	−	5.77416i	−0.203260	−	0.352057i	0.746317	−	0.665591i	$-0.231820\pi$
$269$	−3.33371	−	5.77416i	−0.203260	−	0.352057i	−0.949577	+	0.313534i	$0.898487\pi$
$270$		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
$273$	22.3328			1.35165
$274$		0			0
$275$		0			0
$276$		0			0
$277$	24.4624			1.46980			0.734902	−	0.678173i	$-0.237228\pi$
$277$	24.4624			1.46980			0.734902	+	0.678173i	$0.237228\pi$
$278$		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
$283$	2.24811	+	3.89384i	0.133636	+	0.231465i	0.925076	−	0.379783i	$-0.124001\pi$
$283$	2.24811	+	3.89384i	0.133636	+	0.231465i	−0.791439	+	0.611248i	$0.790668\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.992002	−	1.71820i	−0.0585561	−	0.101422i
$288$		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
$293$	−1.27021			−0.0742063			−0.0371031	−	0.999311i	$-0.511813\pi$
$293$	−1.27021			−0.0742063			−0.0371031	+	0.999311i	$0.511813\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	2.96196			0.171870
$298$		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
$303$	−14.5611			−0.836516
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−4.32638	−	7.49350i	−0.246919	−	0.427677i	0.715750	−	0.698356i	$-0.246085\pi$
$307$	−4.32638	−	7.49350i	−0.246919	−	0.427677i	−0.962669	+	0.270680i	$0.912752\pi$
$308$		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
$313$	−0.388175	+	0.672340i	−0.0219410	+	0.0380029i	−0.876787	−	0.480878i	$-0.840318\pi$
$313$	−0.388175	+	0.672340i	−0.0219410	+	0.0380029i	0.854846	+	0.518881i	$0.173651\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−6.92116	+	11.9878i	−0.388731	+	0.673302i	−0.992279	−	0.124025i	$-0.960420\pi$
$317$	−6.92116	+	11.9878i	−0.388731	+	0.673302i	0.603548	+	0.797327i	$0.293753\pi$
$318$		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
$323$	−2.55030	+	9.94126i	−0.141902	+	0.553147i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	15.9078	−	27.5531i	0.879704	−	1.52369i
$328$		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
$333$	−6.18205	+	10.7076i	−0.338774	+	0.586774i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−17.6628	−	30.5928i	−0.962153	−	1.66650i	−0.717077	−	0.696994i	$-0.754520\pi$
$337$	−17.6628	−	30.5928i	−0.962153	−	1.66650i	−0.245076	−	0.969504i	$-0.578813\pi$
$338$		0			0
$339$	−7.69809	−	13.3335i	−0.418103	−	0.724175i
$340$		0			0
$341$	−33.7704			−1.82877
$342$		0			0
$343$	17.8950			0.966241
$344$		0			0
$345$		0			0
$346$		0			0
$347$	13.0031	+	22.5221i	0.698044	+	1.20905i	0.969144	+	0.246496i	$0.0792793\pi$
$347$	13.0031	+	22.5221i	0.698044	+	1.20905i	−0.271100	+	0.962551i	$0.587387\pi$
$348$		0			0
$349$	2.44757			0.131015			0.0655077	−	0.997852i	$-0.479133\pi$
$349$	2.44757			0.131015			0.0655077	+	0.997852i	$0.479133\pi$
$350$		0			0
$351$	1.45150	−	2.51408i	0.0774755	−	0.134191i
$352$		0			0
$353$	4.85103			0.258194			0.129097	−	0.991632i	$-0.458792\pi$
$353$	4.85103			0.258194			0.129097	+	0.991632i	$0.458792\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	8.09412	−	14.0194i	0.428386	−	0.741987i
$358$		0			0
$359$	3.67376	+	6.36314i	0.193894	+	0.335834i	0.946537	−	0.322594i	$-0.104555\pi$
$359$	3.67376	+	6.36314i	0.193894	+	0.335834i	−0.752644	+	0.658428i	$0.771222\pi$
$360$		0			0
$361$	0.405741	+	18.9957i	0.0213548	+	0.999772i
$362$		0			0
$363$	0.0201603	+	0.0349186i	0.00105814	+	0.00183275i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	6.51784	−	11.2892i	0.340228	−	0.589293i	−0.644247	−	0.764818i	$-0.722829\pi$
$367$	6.51784	−	11.2892i	0.340228	−	0.589293i	0.984475	+	0.175525i	$0.0561623\pi$
$368$		0			0
$369$	−2.44018			−0.127031
$370$		0			0
$371$	12.2502	−	21.2179i	0.635998	−	1.10158i
$372$		0			0
$373$	28.5514			1.47833			0.739167	−	0.673522i	$-0.235219\pi$
$373$	28.5514			1.47833			0.739167	+	0.673522i	$0.235219\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−6.38936	−	11.0667i	−0.329069	−	0.569964i
$378$		0			0
$379$	13.2128			0.678698			0.339349	−	0.940661i	$-0.389793\pi$
$379$	13.2128			0.678698			0.339349	+	0.940661i	$0.389793\pi$
$380$		0			0
$381$	22.9956			1.17810
$382$		0			0
$383$	−18.8309	−	32.6160i	−0.962212	−	1.66660i	−0.716925	−	0.697150i	$-0.754451\pi$
$383$	−18.8309	−	32.6160i	−0.962212	−	1.66660i	−0.245287	−	0.969450i	$-0.578882\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	7.95995			0.404627
$388$		0			0
$389$	12.8223	−	22.2090i	0.650119	−	1.12604i	−0.332975	−	0.942936i	$-0.608052\pi$
$389$	12.8223	−	22.2090i	0.650119	−	1.12604i	0.983094	−	0.183103i	$-0.0586142\pi$
$390$		0			0
$391$	−5.05736			−0.255762
$392$		0			0
$393$	−28.0637	+	48.6078i	−1.41563	+	2.45194i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−16.6366	−	28.8154i	−0.834965	−	1.44620i	−0.894059	−	0.447949i	$-0.852155\pi$
$397$	−16.6366	−	28.8154i	−0.834965	−	1.44620i	0.0590940	−	0.998252i	$-0.481179\pi$
$398$		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
$403$	−16.5491	+	28.6639i	−0.824370	+	1.42785i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	12.2155			0.605499
$408$		0			0
$409$	1.25545	−	2.17450i	0.0620779	−	0.107522i	−0.833316	−	0.552797i	$-0.813561\pi$
$409$	1.25545	−	2.17450i	0.0620779	−	0.107522i	0.895394	+	0.445275i	$0.146894\pi$
$410$		0			0
$411$	19.2266			0.948376
$412$		0			0
$413$	−14.9677	−	25.9248i	−0.736511	−	1.27567i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	42.6480			2.08848
$418$		0			0
$419$	−39.5638			−1.93282			−0.966409	−	0.257011i	$-0.917262\pi$
$419$	−39.5638			−1.93282			−0.966409	+	0.257011i	$0.917262\pi$
$420$		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
$423$	−18.4890	−	32.0238i	−0.898965	−	1.55705i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−11.5300	+	19.9705i	−0.557976	+	0.966442i
$428$		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
$433$	−4.30073	+	7.44908i	−0.206680	+	0.357980i	−0.950667	−	0.310214i	$-0.899599\pi$
$433$	−4.30073	+	7.44908i	−0.206680	+	0.357980i	0.743987	+	0.668194i	$0.232933\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−9.01718	+	2.51965i	−0.431350	+	0.120531i
$438$		0			0
$439$	5.77939	+	10.0102i	0.275835	+	0.477760i	0.970345	−	0.241722i	$-0.0777123\pi$
$439$	5.77939	+	10.0102i	0.275835	+	0.477760i	−0.694510	+	0.719483i	$0.744379\pi$
$440$		0			0
$441$	−0.736084	+	1.27494i	−0.0350516	+	0.0607112i
$442$		0			0
$443$	−5.69629	+	9.86626i	−0.270639	+	0.468760i	−0.969026	−	0.246960i	$-0.920568\pi$
$443$	−5.69629	+	9.86626i	−0.270639	+	0.468760i	0.698387	+	0.715721i	$0.253902\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	15.6243	−	27.0620i	0.739002	−	1.27999i
$448$		0			0
$449$	17.2252			0.812909			0.406455	−	0.913671i	$-0.366765\pi$
$449$	17.2252			0.812909			0.406455	+	0.913671i	$0.366765\pi$
$450$		0			0
$451$	1.20542	+	2.08786i	0.0567612	+	0.0983133i
$452$		0			0
$453$	18.2190	+	31.5563i	0.856005	+	1.48264i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	26.1885			1.22505			0.612524	−	0.790452i	$-0.290154\pi$
$457$	26.1885			1.22505			0.612524	+	0.790452i	$0.290154\pi$
$458$		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
$463$	−9.48542			−0.440825			−0.220412	−	0.975407i	$-0.570740\pi$
$463$	−9.48542			−0.440825			−0.220412	+	0.975407i	$0.570740\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	39.2462			1.81610			0.908048	−	0.418867i	$-0.137573\pi$
$467$	39.2462			1.81610			0.908048	+	0.418867i	$0.137573\pi$
$468$		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
$473$	−3.93214	−	6.81066i	−0.180800	−	0.313155i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−15.0668	−	26.0965i	−0.689862	−	1.19488i
$478$		0			0
$479$	−2.72677	+	4.72290i	−0.124589	+	0.215795i	−0.921572	−	0.388207i	$-0.873095\pi$
$479$	−2.72677	+	4.72290i	−0.124589	+	0.215795i	0.796983	+	0.604002i	$0.206428\pi$
$480$		0			0
$481$	5.98617	−	10.3684i	0.272946	−	0.472756i
$482$		0			0
$483$	14.7677			0.671956
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−25.0662			−1.13586			−0.567930	−	0.823077i	$-0.692256\pi$
$487$	−25.0662			−1.13586			−0.567930	+	0.823077i	$0.692256\pi$
$488$		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
$493$	−9.26281			−0.417176
$494$		0			0
$495$		0			0
$496$		0			0
$497$	9.43280	+	16.3381i	0.423119	+	0.732863i
$498$		0			0
$499$	6.85519	+	11.8735i	0.306881	+	0.531533i	0.977678	−	0.210108i	$-0.0673814\pi$
$499$	6.85519	+	11.8735i	0.306881	+	0.531533i	−0.670798	+	0.741640i	$0.734048\pi$
$500$		0			0
$501$	−14.3328			−0.640344
$502$		0			0
$503$	18.3253	−	31.7404i	0.817086	−	1.41523i	−0.0907343	−	0.995875i	$-0.528921\pi$
$503$	18.3253	−	31.7404i	0.817086	−	1.41523i	0.907820	−	0.419359i	$-0.137745\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	3.08661	−	5.34616i	0.137081	−	0.237431i
$508$		0			0
$509$	6.32519	−	10.9556i	0.280359	−	0.485596i	−0.691114	−	0.722746i	$-0.742880\pi$
$509$	6.32519	−	10.9556i	0.280359	−	0.485596i	0.971473	+	0.237149i	$0.0762131\pi$
$510$		0			0
$511$	3.38269	+	5.85899i	0.149641	+	0.259187i
$512$		0			0
$513$	−2.78387	−	2.72504i	−0.122911	−	0.120314i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−18.2667	+	31.6389i	−0.803371	+	1.39148i
$518$		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
$523$	−4.56734	+	7.91086i	−0.199716	+	0.345918i	−0.948436	−	0.316968i	$-0.897335\pi$
$523$	−4.56734	+	7.91086i	−0.199716	+	0.345918i	0.748720	+	0.662886i	$0.230669\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	11.9958	+	20.7774i	0.522547	+	0.905078i
$528$		0			0
$529$	9.19321	+	15.9231i	0.399705	+	0.692309i
$530$		0			0
$531$	−36.8183			−1.59778
$532$		0			0
$533$	2.36286			0.102347
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−15.3530	−	26.5922i	−0.662531	−	1.14754i
$538$		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
$543$	38.8513			1.66727
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.73973	+	3.01329i	−0.0743853	+	0.128839i	−0.900819	−	0.434195i	$-0.857033\pi$
$547$	−1.73973	+	3.01329i	−0.0743853	+	0.128839i	0.826433	+	0.563034i	$0.190366\pi$
$548$		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
$553$	16.3631	+	28.3418i	0.695831	+	1.20522i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	7.96280	−	13.7920i	0.337395	−	0.584385i	−0.646547	−	0.762874i	$-0.723788\pi$
$557$	7.96280	−	13.7920i	0.337395	−	0.584385i	0.983942	+	0.178489i	$0.0571210\pi$
$558$		0			0
$559$	−7.70775			−0.326003
$560$		0			0
$561$	−9.83551	+	17.0356i	−0.415256	+	0.719244i
$562$		0			0
$563$	−19.6274			−0.827195			−0.413598	−	0.910460i	$-0.635728\pi$
$563$	−19.6274			−0.827195			−0.413598	+	0.910460i	$0.635728\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−10.6516	−	18.4491i	−0.447324	−	0.774788i
$568$		0			0
$569$	−11.7544			−0.492770			−0.246385	−	0.969172i	$-0.579243\pi$
$569$	−11.7544			−0.492770			−0.246385	+	0.969172i	$0.579243\pi$
$570$		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
$573$	20.4795	+	35.4715i	0.855541	+	1.48184i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−25.7287			−1.07110			−0.535551	−	0.844503i	$-0.679896\pi$
$577$	−25.7287			−1.07110			−0.535551	+	0.844503i	$0.679896\pi$
$578$		0			0
$579$	1.07264	−	1.85787i	0.0445775	−	0.0772106i
$580$		0			0
$581$	12.7837			0.530359
$582$		0			0
$583$	−14.8857	+	25.7828i	−0.616503	+	1.06782i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−20.8279	−	36.0750i	−0.859659	−	1.48897i	−0.872255	−	0.489052i	$-0.837343\pi$
$587$	−20.8279	−	36.0750i	−0.859659	−	1.48897i	0.0125958	−	0.999921i	$-0.495991\pi$
$588$		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
$593$	8.83267	−	15.2986i	0.362714	−	0.628239i	−0.625692	−	0.780070i	$-0.715183\pi$
$593$	8.83267	−	15.2986i	0.362714	−	0.628239i	0.988407	+	0.151831i	$0.0485168\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−16.2775			−0.666193
$598$		0			0
$599$	13.1925	−	22.8502i	0.539033	−	0.933632i	−0.459924	−	0.887959i	$-0.652123\pi$
$599$	13.1925	−	22.8502i	0.539033	−	0.933632i	0.998956	−	0.0456738i	$-0.0145435\pi$
$600$		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
$603$	−16.3545	−	28.3269i	−0.666008	−	1.15356i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	8.26529			0.335478			0.167739	−	0.985831i	$-0.446353\pi$
$607$	8.26529			0.335478			0.167739	+	0.985831i	$0.446353\pi$
$608$		0			0
$609$	27.0479			1.09604
$610$		0			0
$611$	17.9032	+	31.0092i	0.724285	+	1.25450i
$612$		0			0
$613$	3.40417	+	5.89620i	0.137493	+	0.238145i	0.926547	−	0.376179i	$-0.122762\pi$
$613$	3.40417	+	5.89620i	0.137493	+	0.238145i	−0.789054	+	0.614324i	$0.789429\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	3.00668	−	5.20772i	0.121044	−	0.209655i	−0.799135	−	0.601151i	$-0.794709\pi$
$617$	3.00668	−	5.20772i	0.121044	−	0.209655i	0.920180	+	0.391496i	$0.128042\pi$
$618$		0			0
$619$	13.2299			0.531754			0.265877	−	0.964007i	$-0.414338\pi$
$619$	13.2299			0.531754			0.265877	+	0.964007i	$0.414338\pi$
$620$		0			0
$621$	0.959816	−	1.66245i	0.0385161	−	0.0667118i
$622$		0			0
$623$	11.6517	−	20.1813i	0.466816	−	0.808548i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−9.04916	+	35.2743i	−0.361389	+	1.40872i
$628$		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
$633$	−13.2899	+	23.0188i	−0.528226	+	0.914914i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	0.712762	−	1.23454i	0.0282407	−	0.0489143i
$638$		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
$643$	14.5776	+	25.2492i	0.574885	+	0.995729i	0.996054	+	0.0887474i	$0.0282864\pi$
$643$	14.5776	+	25.2492i	0.574885	+	0.995729i	−0.421170	+	0.906982i	$0.638380\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	36.7499			1.44479			0.722394	−	0.691481i	$-0.243042\pi$
$647$	36.7499			1.44479			0.722394	+	0.691481i	$0.243042\pi$
$648$		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
$653$	−24.7707			−0.969351			−0.484675	−	0.874694i	$-0.661062\pi$
$653$	−24.7707			−0.969351			−0.484675	+	0.874694i	$0.661062\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	8.32092			0.324630
$658$		0			0
$659$	−11.1156	+	19.2528i	−0.433002	+	0.749982i	−0.997130	−	0.0757053i	$-0.975879\pi$
$659$	−11.1156	+	19.2528i	−0.433002	+	0.749982i	0.564128	+	0.825687i	$0.309213\pi$
$660$		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
$663$	9.63975	+	16.6965i	0.374377	+	0.648440i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−4.22501	−	7.31793i	−0.163593	−	0.283351i
$668$		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
$673$	33.5992			1.29515			0.647577	−	0.762000i	$-0.275783\pi$
$673$	33.5992			1.29515			0.647577	+	0.762000i	$0.275783\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−29.5883			−1.13717			−0.568585	−	0.822624i	$-0.692509\pi$
$677$	−29.5883			−1.13717			−0.568585	+	0.822624i	$0.692509\pi$
$678$		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
$683$	−41.0567			−1.57099			−0.785495	−	0.618868i	$-0.787592\pi$
$683$	−41.0567			−1.57099			−0.785495	+	0.618868i	$0.787592\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	20.4488	+	35.4183i	0.780170	+	1.35129i
$688$		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
$693$	15.1613	−	26.2601i	0.575929	−	0.997538i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	0.856376	−	1.48329i	0.0324375	−	0.0561835i
$698$		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
$703$	−11.4810	−	11.2384i	−0.433015	−	0.423865i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−7.87729	+	13.6439i	−0.296256	+	0.513130i
$708$		0			0
$709$	−8.16255	+	14.1379i	−0.306551	+	0.530962i	−0.977605	−	0.210446i	$-0.932508\pi$
$709$	−8.16255	+	14.1379i	−0.306551	+	0.530962i	0.671055	+	0.741408i	$0.265842\pi$
$710$		0			0
$711$	40.2509			1.50953
$712$		0			0
$713$	−10.9432	+	18.9542i	−0.409827	+	0.709841i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−0.759750	−	1.31593i	−0.0283734	−	0.0491442i
$718$		0			0
$719$	−5.08574	−	8.80876i	−0.189666	−	0.328511i	0.755473	−	0.655180i	$-0.227407\pi$
$719$	−5.08574	−	8.80876i	−0.189666	−	0.328511i	−0.945139	+	0.326669i	$0.894074\pi$
$720$		0			0
$721$	−41.0686			−1.52947
$722$		0			0
$723$	55.1595			2.05141
$724$		0			0
$725$		0			0
$726$		0			0
$727$	4.02148	+	6.96541i	0.149148	+	0.258333i	0.930913	−	0.365241i	$-0.119013\pi$
$727$	4.02148	+	6.96541i	0.149148	+	0.258333i	−0.781765	+	0.623574i	$0.785680\pi$
$728$		0			0
$729$	−32.9600			−1.22074
$730$		0			0
$731$	−2.79353	+	4.83853i	−0.103322	+	0.178960i
$732$		0			0
$733$	−41.2325			−1.52296			−0.761479	−	0.648190i	$-0.775526\pi$
$733$	−41.2325			−1.52296			−0.761479	+	0.648190i	$0.775526\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−16.1580	+	27.9864i	−0.595186	+	1.03089i
$738$		0			0
$739$	−16.5253	−	28.6227i	−0.607893	−	1.05290i	−0.991587	−	0.129442i	$-0.958681\pi$
$739$	−16.5253	−	28.6227i	−0.607893	−	1.05290i	0.383694	−	0.923460i	$-0.374652\pi$
$740$		0			0
$741$	25.5059	+	24.9669i	0.936983	+	0.917184i
$742$		0			0
$743$	17.3933	+	30.1261i	0.638099	+	1.10522i	0.985849	+	0.167633i	$0.0536124\pi$
$743$	17.3933	+	30.1261i	0.638099	+	1.10522i	−0.347750	+	0.937587i	$0.613054\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	7.86153	−	13.6166i	0.287638	−	0.498204i
$748$		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
$753$	20.8537			0.759950
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−3.08494	−	5.34328i	−0.112124	−	0.194205i	0.804502	−	0.593949i	$-0.202432\pi$
$757$	−3.08494	−	5.34328i	−0.112124	−	0.194205i	−0.916626	+	0.399745i	$0.869099\pi$
$758$		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
$763$	−17.2116	−	29.8114i	−0.623103	−	1.07925i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	35.6517			1.28731
$768$		0			0
$769$	20.7452	−	35.9317i	0.748090	−	1.29573i	−0.200647	−	0.979664i	$-0.564305\pi$
$769$	20.7452	−	35.9317i	0.748090	−	1.29573i	0.948737	−	0.316066i	$-0.102362\pi$
$770$		0			0
$771$	−35.7727			−1.28832
$772$		0			0
$773$	20.8584	−	36.1279i	0.750226	−	1.29943i	−0.197487	−	0.980306i	$-0.563278\pi$
$773$	20.8584	−	36.1279i	0.750226	−	1.29943i	0.947713	−	0.319124i	$-0.103389\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	12.6705	+	21.9460i	0.454553	+	0.787309i
$778$		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
$783$	1.75795	−	3.04486i	0.0628240	−	0.108814i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	13.0342			0.464621			0.232310	−	0.972642i	$-0.425371\pi$
$787$	13.0342			0.464621			0.232310	+	0.972642i	$0.425371\pi$
$788$		0			0
$789$	−23.3718	+	40.4812i	−0.832060	+	1.44117i
$790$		0			0
$791$	−16.6580			−0.592292
$792$		0			0
$793$	−13.7317	−	23.7841i	−0.487628	−	0.844596i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−33.1911			−1.17569			−0.587844	−	0.808974i	$-0.700023\pi$
$797$	−33.1911			−1.17569			−0.587844	+	0.808974i	$0.700023\pi$
$798$		0			0
$799$	25.9547			0.918210
$800$		0			0
$801$	−14.3307	−	24.8216i	−0.506351	−	0.877026i
$802$		0			0
$803$	−4.11045	−	7.11951i	−0.145055	−	0.251242i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−8.40369	+	14.5556i	−0.295824	+	0.512382i
$808$		0			0
$809$	−29.5271			−1.03812			−0.519058	−	0.854739i	$-0.673717\pi$
$809$	−29.5271			−1.03812			−0.519058	+	0.854739i	$0.673717\pi$
$810$		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
$813$	−27.8125	+	48.1727i	−0.975427	+	1.68949i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−2.57018	+	10.0188i	−0.0899194	+	0.350513i
$818$		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
$823$	3.78479	−	6.55545i	0.131929	−	0.228509i	−0.792491	−	0.609884i	$-0.791216\pi$
$823$	3.78479	−	6.55545i	0.131929	−	0.228509i	0.924420	+	0.381375i	$0.124549\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	17.4683	−	30.2560i	0.607434	−	1.05211i	−0.384228	−	0.923238i	$-0.625532\pi$
$827$	17.4683	−	30.2560i	0.607434	−	1.05211i	0.991662	−	0.128868i	$-0.0411342\pi$
$828$		0			0
$829$	−45.8376			−1.59201			−0.796003	−	0.605293i	$-0.793056\pi$
$829$	−45.8376			−1.59201			−0.796003	+	0.605293i	$0.793056\pi$
$830$		0			0
$831$	−30.8327	−	53.4037i	−1.06957	−	1.85256i
$832$		0			0
$833$	−0.516655	−	0.894872i	−0.0179010	−	0.0310055i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−9.10656			−0.314769
$838$		0			0
$839$	−7.00502	−	12.1330i	−0.241840	−	0.418879i	0.719398	−	0.694598i	$-0.244418\pi$
$839$	−7.00502	−	12.1330i	−0.241840	−	0.418879i	−0.961238	+	0.275719i	$0.911084\pi$
$840$		0			0
$841$	6.76169	+	11.7116i	0.233162	+	0.403848i
$842$		0			0
$843$	47.0455			1.62033
$844$		0			0
$845$		0			0
$846$		0			0
$847$	0.0436252			0.00149898
$848$		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
$853$	−18.7757	−	32.5205i	−0.642869	−	1.11348i	−0.984789	−	0.173753i	$-0.944411\pi$
$853$	−18.7757	−	32.5205i	−0.642869	−	1.11348i	0.341920	−	0.939729i	$-0.388923\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	2.03378	+	3.52261i	0.0694726	+	0.120330i	0.898669	−	0.438627i	$-0.144535\pi$
$857$	2.03378	+	3.52261i	0.0694726	+	0.120330i	−0.829197	+	0.558957i	$0.811202\pi$
$858$		0			0
$859$	−6.31785	+	10.9428i	−0.215562	+	0.373365i	−0.953446	−	0.301563i	$-0.902492\pi$
$859$	−6.31785	+	10.9428i	−0.215562	+	0.373365i	0.737884	+	0.674928i	$0.235825\pi$
$860$		0			0
$861$	−2.50066	+	4.33127i	−0.0852223	+	0.147609i
$862$		0			0
$863$	14.5147			0.494085			0.247042	−	0.969005i	$-0.420541\pi$
$863$	14.5147			0.494085			0.247042	+	0.969005i	$0.420541\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−28.8790			−0.980781
$868$		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
$873$	−24.2529			−0.820836
$874$		0			0
$875$		0			0
$876$		0			0
$877$	0.967541	+	1.67583i	0.0326715	+	0.0565887i	0.881899	−	0.471439i	$-0.156265\pi$
$877$	0.967541	+	1.67583i	0.0326715	+	0.0565887i	−0.849227	+	0.528027i	$0.822932\pi$
$878$		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
$883$	−17.5216	+	30.3483i	−0.589648	+	1.02130i	0.404631	+	0.914480i	$0.367400\pi$
$883$	−17.5216	+	30.3483i	−0.589648	+	1.02130i	−0.994278	+	0.106820i	$0.965933\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−8.08806	+	14.0089i	−0.271571	+	0.470374i	−0.969264	−	0.246022i	$-0.920876\pi$
$887$	−8.08806	+	14.0089i	−0.271571	+	0.470374i	0.697694	+	0.716396i	$0.254210\pi$
$888$		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
$893$	46.2767	−	12.9310i	1.54859	−	0.432718i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−8.79387	+	15.2314i	−0.293619	+	0.508563i
$898$		0			0
$899$	−20.0431	+	34.7156i	−0.668473	+	1.15783i
$900$		0			0
$901$	21.1507			0.704631
$902$		0			0
$903$	8.15724	−	14.1288i	0.271456	−	0.470176i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	11.4975	+	19.9143i	0.381770	+	0.661244i	0.991315	−	0.131507i	$-0.0419815\pi$
$907$	11.4975	+	19.9143i	0.381770	+	0.661244i	−0.609546	+	0.792751i	$0.708648\pi$
$908$		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
$913$	−15.5341			−0.514103
$914$		0			0
$915$		0			0
$916$		0			0
$917$	30.3638	+	52.5917i	1.00270	+	1.73673i
$918$		0			0
$919$	12.5454			0.413835			0.206918	−	0.978358i	$-0.433657\pi$
$919$	12.5454			0.413835			0.206918	+	0.978358i	$0.433657\pi$
$920$		0			0
$921$	−10.9060	+	18.8898i	−0.359365	+	0.622439i
$922$		0			0
$923$	−22.4681			−0.739547
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−25.2557	+	43.7441i	−0.829505	+	1.43674i
$928$		0			0
$929$	26.6494	+	46.1581i	0.874338	+	1.51440i	0.857466	+	0.514540i	$0.172037\pi$
$929$	26.6494	+	46.1581i	0.874338	+	1.51440i	0.0168714	+	0.999858i	$0.494629\pi$
$930$		0			0
$931$	−1.36702	−	1.33814i	−0.0448024	−	0.0438556i
$932$		0			0
$933$	−30.0604	−	52.0662i	−0.984134	−	1.70457i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−17.5602	+	30.4152i	−0.573668	+	0.993622i	0.422517	+	0.906355i	$0.361147\pi$
$937$	−17.5602	+	30.4152i	−0.573668	+	0.993622i	−0.996185	+	0.0872667i	$0.972187\pi$
$938$		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
$943$	1.56246			0.0508807
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−5.22510	−	9.05015i	−0.169793	−	0.294090i	0.768554	−	0.639785i	$-0.220977\pi$
$947$	−5.22510	−	9.05015i	−0.169793	−	0.294090i	−0.938347	+	0.345695i	$0.887643\pi$
$948$		0			0
$949$	−8.05728			−0.261550
$950$		0			0
$951$	34.8940			1.13152
$952$		0			0
$953$	2.17117	+	3.76057i	0.0703310	+	0.121817i	0.899046	−	0.437853i	$-0.144261\pi$
$953$	2.17117	+	3.76057i	0.0703310	+	0.121817i	−0.828715	+	0.559670i	$0.810928\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−32.8670			−1.06244
$958$		0			0
$959$	10.4012	−	18.0154i	0.335872	−	0.581747i
$960$		0			0
$961$	72.8272			2.34927
$962$		0			0
$963$	−25.4770	+	44.1274i	−0.820983	+	1.42198i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−7.84100	−	13.5810i	−0.252149	−	0.436736i	0.711968	−	0.702212i	$-0.247804\pi$
$967$	−7.84100	−	13.5810i	−0.252149	−	0.436736i	−0.964117	+	0.265476i	$0.914471\pi$
$968$		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
$973$	23.0717	−	39.9614i	0.739646	−	1.28110i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−2.87156			−0.0918693			−0.0459347	−	0.998944i	$-0.514627\pi$
$977$	−2.87156			−0.0918693			−0.0459347	+	0.998944i	$0.514627\pi$
$978$		0			0
$979$	−14.1585	+	24.5232i	−0.452507	+	0.783765i
$980$		0			0
$981$	−42.3380			−1.35175
$982$		0			0
$983$	−16.9545	−	29.3660i	−0.540764	−	0.936630i	−0.998860	−	0.0477276i	$-0.984802\pi$
$983$	−16.9545	−	29.3660i	−0.540764	−	0.936630i	0.458097	−	0.888902i	$-0.348531\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−75.7889			−2.41239
$988$		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
$993$	−36.1729	−	62.6533i	−1.14791	−	1.98824i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	1.75369	−	3.03748i	0.0555399	−	0.0961979i	−0.836919	−	0.547327i	$-0.815645\pi$
$997$	1.75369	−	3.03748i	0.0555399	−	0.0961979i	0.892459	+	0.451129i	$0.148979\pi$
$998$		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.i.d.501.1		8
5.2	odd	4		1900.2.s.d.349.2		16
5.3	odd	4		1900.2.s.d.349.7		16
5.4	even	2		380.2.i.c.121.4	✓	8
15.14	odd	2		3420.2.t.w.1261.3		8
19.11	even	3	inner	1900.2.i.d.201.1		8
20.19	odd	2		1520.2.q.m.881.1		8
95.49	even	6		380.2.i.c.201.4	yes	8
95.64	even	6		7220.2.a.r.1.1		4
95.68	odd	12		1900.2.s.d.49.2		16
95.69	odd	6		7220.2.a.p.1.4		4
95.87	odd	12		1900.2.s.d.49.7		16
285.239	odd	6		3420.2.t.w.3241.3		8
380.239	odd	6		1520.2.q.m.961.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.i.c.121.4	✓	8	5.4	even	2
380.2.i.c.201.4	yes	8	95.49	even	6
1520.2.q.m.881.1		8	20.19	odd	2
1520.2.q.m.961.1		8	380.239	odd	6
1900.2.i.d.201.1		8	19.11	even	3	inner
1900.2.i.d.501.1		8	1.1	even	1	trivial
1900.2.s.d.49.2		16	95.68	odd	12
1900.2.s.d.49.7		16	95.87	odd	12
1900.2.s.d.349.2		16	5.2	odd	4
1900.2.s.d.349.7		16	5.3	odd	4
3420.2.t.w.1261.3		8	15.14	odd	2
3420.2.t.w.3241.3		8	285.239	odd	6
7220.2.a.p.1.4		4	95.69	odd	6
7220.2.a.r.1.1		4	95.64	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.26041 - 2.18309i) q^{3} -2.72743 q^{7} +(-1.67727 + 2.90511i) q^{9} +O(q^{10})\)	\(q+(-1.26041 - 2.18309i) q^{3} -2.72743 q^{7} +(-1.67727 + 2.90511i) q^{9} +3.31421 q^{11} +(1.62412 - 2.81306i) q^{13} +(-1.17727 - 2.03909i) q^{17} +(-3.11494 - 3.04912i) q^{19} +(3.43768 + 5.95423i) q^{21} +(1.07396 - 1.86016i) q^{23} +0.893714 q^{27} +(1.96702 - 3.40697i) q^{29} -10.1896 q^{31} +(-4.17727 - 7.23524i) q^{33} +3.68579 q^{37} -8.18825 q^{39} +(0.363714 + 0.629971i) q^{41} +(-1.18645 - 2.05499i) q^{43} +(-5.51164 + 9.54644i) q^{47} +0.438860 q^{49} +(-2.96768 + 5.14017i) q^{51} +(-4.49148 + 7.77947i) q^{53} +(-2.73041 + 10.6434i) q^{57} +(5.48784 + 9.50521i) q^{59} +(4.22743 - 7.32212i) q^{61} +(4.57462 - 7.92348i) q^{63} +(-4.87535 + 8.44436i) q^{67} -5.41453 q^{69} +(-3.45850 - 5.99029i) q^{71} +(-1.24025 - 2.14818i) q^{73} -9.03927 q^{77} +(-5.99948 - 10.3914i) q^{79} +(3.90535 + 6.76427i) q^{81} -4.68711 q^{83} -9.91699 q^{87} +(-4.27205 + 7.39941i) q^{89} +(-4.42968 + 7.67243i) q^{91} +(12.8430 + 22.2448i) q^{93} +(3.61494 + 6.26127i) q^{97} +(-5.55882 + 9.62816i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{3} - 5 q^{9}+O(q^{10}) \) 8 * q + q^3 - 5 * q^9	\( 8 q + q^{3} - 5 q^{9} + 4 q^{11} - 9 q^{13} - q^{17} + 3 q^{19} + 8 q^{21} - 20 q^{27} + 5 q^{29} - 20 q^{31} - 25 q^{33} + 52 q^{37} - 54 q^{39} - 8 q^{41} - 7 q^{43} - 16 q^{47} + 20 q^{49} + 12 q^{51} - 5 q^{53} - 27 q^{57} + 11 q^{59} + 12 q^{61} + 3 q^{63} + 6 q^{69} + 14 q^{71} + 4 q^{73} + 44 q^{77} + 13 q^{79} - 24 q^{81} - 10 q^{83} + 4 q^{87} + 5 q^{89} - 46 q^{91} + 28 q^{93} + q^{97} + 24 q^{99}+O(q^{100}) \) 8 * q + q^3 - 5 * q^9 + 4 * q^11 - 9 * q^13 - q^17 + 3 * q^19 + 8 * q^21 - 20 * q^27 + 5 * q^29 - 20 * q^31 - 25 * q^33 + 52 * q^37 - 54 * q^39 - 8 * q^41 - 7 * q^43 - 16 * q^47 + 20 * q^49 + 12 * q^51 - 5 * q^53 - 27 * q^57 + 11 * q^59 + 12 * q^61 + 3 * q^63 + 6 * q^69 + 14 * q^71 + 4 * q^73 + 44 * q^77 + 13 * q^79 - 24 * q^81 - 10 * q^83 + 4 * q^87 + 5 * q^89 - 46 * q^91 + 28 * q^93 + q^97 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more