LMFDB - Embedded newform 1800.2.d.u.1549.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1800,2,Mod(1549,1800)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1800, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))

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

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

chi := DirichletCharacter("1800.1549");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1800.d (of order $2$, degree $1$, 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:	$14.3730723638$
Analytic rank:	$0$
Dimension:	$16$
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} - 4x^{14} - 4x^{12} + 12x^{10} + 389x^{8} + 816x^{6} + 2924x^{4} + 1040x^{2} + 100 $ x^16 - 4x^14 - 4x^12 + 12x^10 + 389x^8 + 816x^6 + 2924x^4 + 1040*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{10}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1549.11
Root			$-2.33132 - 0.608977i$ of defining polynomial
Character	$\chi$	$=$	1800.1549
Dual form			1800.2.d.u.1549.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.622597 + 1.26979i) q^{2} +(-1.22474 + 1.58114i) q^{4} -3.44949i q^{7} +(-2.77024 - 0.570759i) q^{8} +O(q^{10})$	\(q+(0.622597 + 1.26979i) q^{2} +(-1.22474 + 1.58114i) q^{4} -3.44949i q^{7} +(-2.77024 - 0.570759i) q^{8} +5.54048i q^{11} +3.87298 q^{13} +(4.38014 - 2.14764i) q^{14} +(-1.00000 - 3.87298i) q^{16} -6.22069i q^{17} -7.03526i q^{19} +(-7.03526 + 3.44949i) q^{22} -1.14152i q^{23} +(2.41131 + 4.91788i) q^{26} +(5.45412 + 4.22474i) q^{28} -3.05009i q^{29} -1.44949 q^{31} +(4.29529 - 3.68110i) q^{32} +(7.89898 - 3.87298i) q^{34} +6.32456 q^{37} +(8.93332 - 4.38014i) q^{38} -3.93765 q^{41} +0.710706 q^{43} +(-8.76027 - 6.78568i) q^{44} +(1.44949 - 0.710706i) q^{46} +10.1583i q^{47} -4.89898 q^{49} +(-4.74342 + 6.12372i) q^{52} +8.03087 q^{53} +(-1.96883 + 9.55592i) q^{56} +(3.87298 - 1.89898i) q^{58} -4.98078i q^{59} -10.1975i q^{61} +(-0.902449 - 1.84055i) q^{62} +(7.34847 + 3.16228i) q^{64} +5.61385 q^{67} +(9.83577 + 7.61875i) q^{68} +13.5829 q^{71} +6.89898i q^{73} +(3.93765 + 8.03087i) q^{74} +(11.1237 + 8.61640i) q^{76} +19.1118 q^{77} -2.89898 q^{79} +(-2.45157 - 5.00000i) q^{82} +6.10018 q^{83} +(0.442484 + 0.902449i) q^{86} +(3.16228 - 15.3485i) q^{88} +7.87530 q^{89} -13.3598i q^{91} +(1.80490 + 1.39807i) q^{92} +(-12.8990 + 6.32456i) q^{94} -15.6969i q^{97} +(-3.05009 - 6.22069i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 16 q^{16} + 16 q^{31} + 48 q^{34} - 16 q^{46} + 80 q^{76} + 32 q^{79} - 128 q^{94}+O(q^{100}) $ 16 * q - 16 * q^16 + 16 * q^31 + 48 * q^34 - 16 * q^46 + 80 * q^76 + 32 * q^79 - 128 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1001$	$1351$
$\chi(n)$	$-1$	$-1$	$1$	$1$

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 $

$2$	0.622597	+	1.26979i	0.440243	+	0.897879i
$2$	0.622597	+	1.26979i	0.440243	+	0.897879i
$3$		0			0
$3$		0			0
$4$	−1.22474	+	1.58114i	−0.612372	+	0.790569i
$5$		0			0
$5$		0			0
$6$		0			0
$7$		−	3.44949i		−	1.30378i	−0.758312	−	0.651892i	$-0.773975\pi$
$7$		−	3.44949i		−	1.30378i	0.758312	−	0.651892i	$-0.226025\pi$
$8$	−2.77024	−	0.570759i	−0.979428	−	0.201794i
$9$		0			0
$10$		0			0
$11$			5.54048i			1.67052i	0.549857	+	0.835259i	$0.314682\pi$
$11$			5.54048i			1.67052i	−0.549857	+	0.835259i	$0.685318\pi$
$12$		0			0
$13$	3.87298			1.07417			0.537086	−	0.843527i	$-0.319525\pi$
$13$	3.87298			1.07417			0.537086	+	0.843527i	$0.319525\pi$
$14$	4.38014	−	2.14764i	1.17064	−	0.573982i
$15$		0			0
$16$	−1.00000	−	3.87298i	−0.250000	−	0.968246i
$17$		−	6.22069i		−	1.50874i	−0.656451	−	0.754369i	$-0.727943\pi$
$17$		−	6.22069i		−	1.50874i	0.656451	−	0.754369i	$-0.272057\pi$
$18$		0			0
$19$		−	7.03526i		−	1.61400i	−0.590552	−	0.807000i	$-0.701090\pi$
$19$		−	7.03526i		−	1.61400i	0.590552	−	0.807000i	$-0.298910\pi$
$20$		0			0
$21$		0			0
$22$	−7.03526	+	3.44949i	−1.49992	+	0.735434i
$23$		−	1.14152i		−	0.238023i	−0.992893	−	0.119011i	$-0.962027\pi$
$23$		−	1.14152i		−	0.238023i	0.992893	−	0.119011i	$-0.0379725\pi$
$24$		0			0
$25$		0			0
$26$	2.41131	+	4.91788i	0.472897	+	0.964476i
$27$		0			0
$28$	5.45412	+	4.22474i	1.03073	+	0.798402i
$29$		−	3.05009i		−	0.566388i	−0.959063	−	0.283194i	$-0.908606\pi$
$29$		−	3.05009i		−	0.566388i	0.959063	−	0.283194i	$-0.0913940\pi$
$30$		0			0
$31$	−1.44949			−0.260336			−0.130168	−	0.991492i	$-0.541552\pi$
$31$	−1.44949			−0.260336			−0.130168	+	0.991492i	$0.541552\pi$
$32$	4.29529	−	3.68110i	0.759307	−	0.650733i
$33$		0			0
$34$	7.89898	−	3.87298i	1.35466	−	0.664211i
$35$		0			0
$36$		0			0
$37$	6.32456			1.03975			0.519875	−	0.854242i	$-0.325978\pi$
$37$	6.32456			1.03975			0.519875	+	0.854242i	$0.325978\pi$
$38$	8.93332	−	4.38014i	1.44918	−	0.710552i
$39$		0			0
$40$		0			0
$41$	−3.93765			−0.614958			−0.307479	−	0.951555i	$-0.599485\pi$
$41$	−3.93765			−0.614958			−0.307479	+	0.951555i	$0.599485\pi$
$42$		0			0
$43$	0.710706			0.108382			0.0541908	−	0.998531i	$-0.482742\pi$
$43$	0.710706			0.108382			0.0541908	+	0.998531i	$0.482742\pi$
$44$	−8.76027	−	6.78568i	−1.32066	−	1.02298i
$45$		0			0
$46$	1.44949	−	0.710706i	0.213716	−	0.104788i
$47$			10.1583i			1.48175i	0.671645	+	0.740873i	$0.265588\pi$
$47$			10.1583i			1.48175i	−0.671645	+	0.740873i	$0.734412\pi$
$48$		0			0
$49$	−4.89898			−0.699854
$50$		0			0
$51$		0			0
$52$	−4.74342	+	6.12372i	−0.657794	+	0.849208i
$53$	8.03087			1.10313			0.551563	−	0.834134i	$-0.314032\pi$
$53$	8.03087			1.10313			0.551563	+	0.834134i	$0.314032\pi$
$54$		0			0
$55$		0			0
$56$	−1.96883	+	9.55592i	−0.263095	+	1.27696i
$57$		0			0
$58$	3.87298	−	1.89898i	0.508548	−	0.249348i
$59$		−	4.98078i		−	0.648442i	−0.945981	−	0.324221i	$-0.894898\pi$
$59$		−	4.98078i		−	0.648442i	0.945981	−	0.324221i	$-0.105102\pi$
$60$		0			0
$61$		−	10.1975i		−	1.30566i	−0.757504	−	0.652831i	$-0.773581\pi$
$61$		−	10.1975i		−	1.30566i	0.757504	−	0.652831i	$-0.226419\pi$
$62$	−0.902449	−	1.84055i	−0.114611	−	0.233750i
$63$		0			0
$64$	7.34847	+	3.16228i	0.918559	+	0.395285i
$65$		0			0
$66$		0			0
$67$	5.61385			0.685841			0.342920	−	0.939364i	$-0.388584\pi$
$67$	5.61385			0.685841			0.342920	+	0.939364i	$0.388584\pi$
$68$	9.83577	+	7.61875i	1.19276	+	0.923910i
$69$		0			0
$70$		0			0
$71$	13.5829			1.61199			0.805996	−	0.591921i	$-0.201630\pi$
$71$	13.5829			1.61199			0.805996	+	0.591921i	$0.201630\pi$
$72$		0			0
$73$			6.89898i			0.807464i	0.914877	+	0.403732i	$0.132287\pi$
$73$			6.89898i			0.807464i	−0.914877	+	0.403732i	$0.867713\pi$
$74$	3.93765	+	8.03087i	0.457743	+	0.933570i
$75$		0			0
$76$	11.1237	+	8.61640i	1.27598	+	0.988369i
$77$	19.1118			2.17800
$78$		0			0
$79$	−2.89898			−0.326161			−0.163080	−	0.986613i	$-0.552143\pi$
$79$	−2.89898			−0.326161			−0.163080	+	0.986613i	$0.552143\pi$
$80$		0			0
$81$		0			0
$82$	−2.45157	−	5.00000i	−0.270731	−	0.552158i
$83$	6.10018			0.669582			0.334791	−	0.942292i	$-0.391334\pi$
$83$	6.10018			0.669582			0.334791	+	0.942292i	$0.391334\pi$
$84$		0			0
$85$		0			0
$86$	0.442484	+	0.902449i	0.0477142	+	0.0973135i
$87$		0			0
$88$	3.16228	−	15.3485i	0.337100	−	1.63615i
$89$	7.87530			0.834781			0.417390	−	0.908727i	$-0.362945\pi$
$89$	7.87530			0.834781			0.417390	+	0.908727i	$0.362945\pi$
$90$		0			0
$91$		−	13.3598i		−	1.40049i
$92$	1.80490	+	1.39807i	0.188174	+	0.145759i
$93$		0			0
$94$	−12.8990	+	6.32456i	−1.33043	+	0.652328i
$95$		0			0
$96$		0			0
$97$		−	15.6969i		−	1.59378i	−0.604123	−	0.796891i	$-0.706476\pi$
$97$		−	15.6969i		−	1.59378i	0.604123	−	0.796891i	$-0.293524\pi$
$98$	−3.05009	−	6.22069i	−0.308106	−	0.628384i
$99$		0			0
$100$		0			0
$101$			14.1311i			1.40609i	0.711144	+	0.703046i	$0.248177\pi$
$101$			14.1311i			1.40609i	−0.711144	+	0.703046i	$0.751823\pi$
$102$		0			0
$103$			6.89898i			0.679777i	0.940466	+	0.339888i	$0.110389\pi$
$103$			6.89898i			0.679777i	−0.940466	+	0.339888i	$0.889611\pi$
$104$	−10.7291	−	2.21054i	−1.05207	−	0.216761i
$105$		0			0
$106$	5.00000	+	10.1975i	0.485643	+	0.990473i
$107$	0.559702			0.0541085			0.0270542	−	0.999634i	$-0.491387\pi$
$107$	0.559702			0.0541085			0.0270542	+	0.999634i	$0.491387\pi$
$108$		0			0
$109$		−	16.5221i		−	1.58253i	−0.611474	−	0.791265i	$-0.709423\pi$
$109$		−	16.5221i		−	1.58253i	0.611474	−	0.791265i	$-0.290577\pi$
$110$		0			0
$111$		0			0
$112$	−13.3598	+	3.44949i	−1.26238	+	0.325946i
$113$		−	12.4414i		−	1.17039i	−0.810894	−	0.585193i	$-0.801019\pi$
$113$		−	12.4414i		−	1.17039i	0.810894	−	0.585193i	$-0.198981\pi$
$114$		0			0
$115$		0			0
$116$	4.82262	+	3.73558i	0.447769	+	0.346840i
$117$		0			0
$118$	6.32456	−	3.10102i	0.582223	−	0.285472i
$119$	−21.4582			−1.96707
$120$		0			0
$121$	−19.6969			−1.79063
$122$	12.9488	−	6.34896i	1.17233	−	0.574808i
$123$		0			0
$124$	1.77526	−	2.29184i	0.159423	−	0.205814i
$125$		0			0
$126$		0			0
$127$		−	3.79796i		−	0.337014i	−0.985700	−	0.168507i	$-0.946105\pi$
$127$		−	3.79796i		−	0.337014i	0.985700	−	0.168507i	$-0.0538946\pi$
$128$	0.559702	+	11.2999i	0.0494712	+	0.998776i
$129$		0			0
$130$		0			0
$131$			10.5213i			0.919247i	0.888114	+	0.459623i	$0.152016\pi$
$131$			10.5213i			0.919247i	−0.888114	+	0.459623i	$0.847984\pi$
$132$		0			0
$133$	−24.2681			−2.10431
$134$	3.49517	+	7.12842i	0.301937	+	0.615802i
$135$		0			0
$136$	−3.55051	+	17.2328i	−0.304454	+	1.47770i
$137$		−	10.1583i		−	0.867885i	−0.900940	−	0.433943i	$-0.857122\pi$
$137$		−	10.1583i		−	0.867885i	0.900940	−	0.433943i	$-0.142878\pi$
$138$		0			0
$139$			9.16738i			0.777567i	0.921329	+	0.388783i	$0.127105\pi$
$139$			9.16738i			0.777567i	−0.921329	+	0.388783i	$0.872895\pi$
$140$		0			0
$141$		0			0
$142$	8.45667	+	17.2474i	0.709668	+	1.44737i
$143$			21.4582i			1.79442i
$144$		0			0
$145$		0			0
$146$	−8.76027	+	4.29529i	−0.725005	+	0.355480i
$147$		0			0
$148$	−7.74597	+	10.0000i	−0.636715	+	0.821995i
$149$			21.0425i			1.72387i	0.507018	+	0.861935i	$0.330748\pi$
$149$			21.0425i			1.72387i	−0.507018	+	0.861935i	$0.669252\pi$
$150$		0			0
$151$	−12.3485			−1.00490			−0.502452	−	0.864605i	$-0.667569\pi$
$151$	−12.3485			−1.00490			−0.502452	+	0.864605i	$0.667569\pi$
$152$	−4.01544	+	19.4894i	−0.325695	+	1.58080i
$153$		0			0
$154$	11.8990	+	24.2681i	0.958847	+	1.95558i
$155$		0			0
$156$		0			0
$157$	8.77613			0.700411			0.350206	−	0.936673i	$-0.386112\pi$
$157$	8.77613			0.700411			0.350206	+	0.936673i	$0.386112\pi$
$158$	−1.80490	−	3.68110i	−0.143590	−	0.292853i
$159$		0			0
$160$		0			0
$161$	−3.93765			−0.310330
$162$		0			0
$163$	−14.7812			−1.15776			−0.578878	−	0.815414i	$-0.696509\pi$
$163$	−14.7812			−1.15776			−0.578878	+	0.815414i	$0.696509\pi$
$164$	4.82262	−	6.22597i	0.376583	−	0.486167i
$165$		0			0
$166$	3.79796	+	7.74597i	0.294779	+	0.601204i
$167$		−	3.42455i		−	0.265000i	−0.991183	−	0.132500i	$-0.957700\pi$
$167$		−	3.42455i		−	0.265000i	0.991183	−	0.132500i	$-0.0423004\pi$
$168$		0			0
$169$	2.00000			0.153846
$170$		0			0
$171$		0			0
$172$	−0.870433	+	1.12372i	−0.0663699	+	0.0856832i
$173$	1.93069			0.146787			0.0733937	−	0.997303i	$-0.476617\pi$
$173$	1.93069			0.146787			0.0733937	+	0.997303i	$0.476617\pi$
$174$		0			0
$175$		0			0
$176$	21.4582	−	5.54048i	1.61747	−	0.417630i
$177$		0			0
$178$	4.90314	+	10.0000i	0.367506	+	0.749532i
$179$		−	21.0425i		−	1.57279i	−0.617723	−	0.786396i	$-0.711945\pi$
$179$		−	21.0425i		−	1.57279i	0.617723	−	0.786396i	$-0.288055\pi$
$180$		0			0
$181$			5.29439i			0.393529i	0.980451	+	0.196765i	$0.0630435\pi$
$181$			5.29439i			0.393529i	−0.980451	+	0.196765i	$0.936957\pi$
$182$	16.9642	−	8.31779i	1.25747	−	0.616555i
$183$		0			0
$184$	−0.651531	+	3.16228i	−0.0480315	+	0.233126i
$185$		0			0
$186$		0			0
$187$	34.4656			2.52037
$188$	−16.0617	−	12.4414i	−1.17142	−	0.907380i
$189$		0			0
$190$		0			0
$191$	−13.5829			−0.982823			−0.491412	−	0.870927i	$-0.663519\pi$
$191$	−13.5829			−0.982823			−0.491412	+	0.870927i	$0.663519\pi$
$192$		0			0
$193$		−	11.8990i		−	0.856507i	−0.903659	−	0.428254i	$-0.859129\pi$
$193$		−	11.8990i		−	0.856507i	0.903659	−	0.428254i	$-0.140871\pi$
$194$	19.9319	−	9.77287i	1.43102	−	0.701651i
$195$		0			0
$196$	6.00000	−	7.74597i	0.428571	−	0.553283i
$197$	−23.2813			−1.65873			−0.829363	−	0.558710i	$-0.811296\pi$
$197$	−23.2813			−1.65873			−0.829363	+	0.558710i	$0.811296\pi$
$198$		0			0
$199$	−21.2474			−1.50619			−0.753096	−	0.657911i	$-0.771440\pi$
$199$	−21.2474			−1.50619			−0.753096	+	0.657911i	$0.771440\pi$
$200$		0			0
$201$		0			0
$202$	−17.9435	+	8.79796i	−1.26250	+	0.619022i
$203$	−10.5213			−0.738448
$204$		0			0
$205$		0			0
$206$	−8.76027	+	4.29529i	−0.610357	+	0.299267i
$207$		0			0
$208$	−3.87298	−	15.0000i	−0.268543	−	1.04006i
$209$	38.9787			2.69622
$210$		0			0
$211$			2.13212i			0.146781i	0.997303	+	0.0733905i	$0.0233819\pi$
$211$			2.13212i			0.146781i	−0.997303	+	0.0733905i	$0.976618\pi$
$212$	−9.83577	+	12.6979i	−0.675523	+	0.872097i
$213$		0			0
$214$	0.348469	+	0.710706i	0.0238209	+	0.0485828i
$215$		0			0
$216$		0			0
$217$			5.00000i			0.339422i
$218$	20.9796	−	10.2866i	1.42092	−	0.696697i
$219$		0			0
$220$		0			0
$221$		−	24.0926i		−	1.62064i
$222$		0			0
$223$			0.348469i			0.0233352i	0.999932	+	0.0116676i	$0.00371400\pi$
$223$			0.348469i			0.0233352i	−0.999932	+	0.0116676i	$0.996286\pi$
$224$	−12.6979	−	14.8165i	−0.848416	−	0.989972i
$225$		0			0
$226$	15.7980	−	7.74597i	1.05086	−	0.515254i
$227$	−4.42108			−0.293437			−0.146719	−	0.989178i	$-0.546871\pi$
$227$	−4.42108			−0.293437			−0.146719	+	0.989178i	$0.546871\pi$
$228$		0			0
$229$			5.29439i			0.349863i	0.984581	+	0.174932i	$0.0559705\pi$
$229$			5.29439i			0.349863i	−0.984581	+	0.174932i	$0.944030\pi$
$230$		0			0
$231$		0			0
$232$	−1.74087	+	8.44949i	−0.114293	+	0.554736i
$233$		−	24.2543i		−	1.58895i	−0.607294	−	0.794477i	$-0.707745\pi$
$233$		−	24.2543i		−	1.58895i	0.607294	−	0.794477i	$-0.292255\pi$
$234$		0			0
$235$		0			0
$236$	7.87530	+	6.10018i	0.512639	+	0.397088i
$237$		0			0
$238$	−13.3598	−	27.2474i	−0.865988	−	1.76619i
$239$	−29.3335			−1.89743			−0.948713	−	0.316138i	$-0.897614\pi$
$239$	−29.3335			−1.89743			−0.948713	+	0.316138i	$0.897614\pi$
$240$		0			0
$241$	23.6969			1.52645			0.763227	−	0.646130i	$-0.223614\pi$
$241$	23.6969			1.52645			0.763227	+	0.646130i	$0.223614\pi$
$242$	−12.2633	−	25.0110i	−0.788312	−	1.60777i
$243$		0			0
$244$	16.1237	+	12.4894i	1.03222	+	0.799551i
$245$		0			0
$246$		0			0
$247$		−	27.2474i		−	1.73371i
$248$	4.01544	+	0.827309i	0.254980	+	0.0525342i
$249$		0			0
$250$		0			0
$251$		−	6.10018i		−	0.385040i	−0.981293	−	0.192520i	$-0.938334\pi$
$251$		−	6.10018i		−	0.385040i	0.981293	−	0.192520i	$-0.0616661\pi$
$252$		0			0
$253$	6.32456			0.397621
$254$	4.82262	−	2.36460i	0.302598	−	0.148368i
$255$		0			0
$256$	−14.0000	+	7.74597i	−0.875000	+	0.484123i
$257$			2.28303i			0.142412i	0.997462	+	0.0712059i	$0.0226847\pi$
$257$			2.28303i			0.142412i	−0.997462	+	0.0712059i	$0.977315\pi$
$258$		0			0
$259$		−	21.8165i		−	1.35561i
$260$		0			0
$261$		0			0
$262$	−13.3598	+	6.55051i	−0.825372	+	0.404692i
$263$			9.01682i			0.556001i	0.960581	+	0.278001i	$0.0896717\pi$
$263$			9.01682i			0.556001i	−0.960581	+	0.278001i	$0.910328\pi$
$264$		0			0
$265$		0			0
$266$	−15.1092	−	30.8154i	−0.926406	−	1.88941i
$267$		0			0
$268$	−6.87553	+	8.87628i	−0.419990	+	0.542205i
$269$		−	4.16950i		−	0.254219i	−0.991889	−	0.127109i	$-0.959430\pi$
$269$		−	4.16950i		−	0.254219i	0.991889	−	0.127109i	$-0.0405699\pi$
$270$		0			0
$271$	5.10102			0.309865			0.154932	−	0.987925i	$-0.450484\pi$
$271$	5.10102			0.309865			0.154932	+	0.987925i	$0.450484\pi$
$272$	−24.0926	+	6.22069i	−1.46083	+	0.377185i
$273$		0			0
$274$	12.8990	−	6.32456i	0.779256	−	0.382080i
$275$		0			0
$276$		0			0
$277$	24.2681			1.45813			0.729063	−	0.684446i	$-0.239956\pi$
$277$	24.2681			1.45813			0.729063	+	0.684446i	$0.239956\pi$
$278$	−11.6407	+	5.70759i	−0.698161	+	0.342318i
$279$		0			0
$280$		0			0
$281$	3.93765			0.234901			0.117450	−	0.993079i	$-0.462528\pi$
$281$	3.93765			0.234901			0.117450	+	0.993079i	$0.462528\pi$
$282$		0			0
$283$	0.710706			0.0422471			0.0211235	−	0.999777i	$-0.493276\pi$
$283$	0.710706			0.0422471			0.0211235	+	0.999777i	$0.493276\pi$
$284$	−16.6356	+	21.4764i	−0.987140	+	1.27439i
$285$		0			0
$286$	−27.2474	+	13.3598i	−1.61118	+	0.789983i
$287$			13.5829i			0.801773i
$288$		0			0
$289$	−21.6969			−1.27629
$290$		0			0
$291$		0			0
$292$	−10.9082	−	8.44949i	−0.638357	−	0.494469i
$293$	16.0617			0.938337			0.469169	−	0.883109i	$-0.344554\pi$
$293$	16.0617			0.938337			0.469169	+	0.883109i	$0.344554\pi$
$294$		0			0
$295$		0			0
$296$	−17.5205	−	3.60979i	−1.01836	−	0.209815i
$297$		0			0
$298$	−26.7196	+	13.1010i	−1.54783	+	0.758922i
$299$		−	4.42108i		−	0.255677i
$300$		0			0
$301$		−	2.45157i		−	0.141306i
$302$	−7.68813	−	15.6800i	−0.442402	−	0.902282i
$303$		0			0
$304$	−27.2474	+	7.03526i	−1.56275	+	0.403500i
$305$		0			0
$306$		0			0
$307$	−14.7812			−0.843609			−0.421805	−	0.906687i	$-0.638603\pi$
$307$	−14.7812			−0.843609			−0.421805	+	0.906687i	$0.638603\pi$
$308$	−23.4071	+	30.2185i	−1.33374	+	1.72186i
$309$		0			0
$310$		0			0
$311$	15.7506			0.893135			0.446568	−	0.894750i	$-0.352646\pi$
$311$	15.7506			0.893135			0.446568	+	0.894750i	$0.352646\pi$
$312$		0			0
$313$			22.5959i			1.27720i	0.769540	+	0.638598i	$0.220485\pi$
$313$			22.5959i			1.27720i	−0.769540	+	0.638598i	$0.779515\pi$
$314$	5.46399	+	11.1439i	0.308351	+	0.628884i
$315$		0			0
$316$	3.55051	−	4.58369i	0.199732	−	0.257853i
$317$	21.0425			1.18187			0.590933	−	0.806721i	$-0.298760\pi$
$317$	21.0425			1.18187			0.590933	+	0.806721i	$0.298760\pi$
$318$		0			0
$319$	16.8990			0.946161
$320$		0			0
$321$		0			0
$322$	−2.45157	−	5.00000i	−0.136621	−	0.278639i
$323$	−43.7642			−2.43510
$324$		0			0
$325$		0			0
$326$	−9.20275	−	18.7691i	−0.509693	−	1.03952i
$327$		0			0
$328$	10.9082	+	2.24745i	0.602307	+	0.124095i
$329$	35.0411			1.93188
$330$		0			0
$331$			12.6491i			0.695258i	0.937632	+	0.347629i	$0.113013\pi$
$331$			12.6491i			0.695258i	−0.937632	+	0.347629i	$0.886987\pi$
$332$	−7.47117	+	9.64524i	−0.410034	+	0.529351i
$333$		0			0
$334$	4.34847	−	2.13212i	0.237938	−	0.116664i
$335$		0			0
$336$		0			0
$337$		−	18.7980i		−	1.02399i	−0.858988	−	0.511995i	$-0.828907\pi$
$337$		−	18.7980i		−	1.02399i	0.858988	−	0.511995i	$-0.171093\pi$
$338$	1.24519	+	2.53958i	0.0677297	+	0.138135i
$339$		0			0
$340$		0			0
$341$		−	8.03087i		−	0.434896i
$342$		0			0
$343$		−	7.24745i		−	0.391325i
$344$	−1.96883	−	0.405641i	−0.106152	−	0.0218707i
$345$		0			0
$346$	1.20204	+	2.45157i	0.0646221	+	0.131797i
$347$	−16.0617			−0.862240			−0.431120	−	0.902295i	$-0.641881\pi$
$347$	−16.0617			−0.862240			−0.431120	+	0.902295i	$0.641881\pi$
$348$		0			0
$349$			12.6491i			0.677091i	0.940950	+	0.338546i	$0.109935\pi$
$349$			12.6491i			0.677091i	−0.940950	+	0.338546i	$0.890065\pi$
$350$		0			0
$351$		0			0
$352$	20.3951	+	23.7980i	1.08706	+	1.26844i
$353$			0.628417i			0.0334473i	0.999860	+	0.0167236i	$0.00532354\pi$
$353$			0.628417i			0.0334473i	−0.999860	+	0.0167236i	$0.994676\pi$
$354$		0			0
$355$		0			0
$356$	−9.64524	+	12.4519i	−0.511197	+	0.659952i
$357$		0			0
$358$	26.7196	−	13.1010i	1.41218	−	0.692410i
$359$	−21.4582			−1.13252			−0.566260	−	0.824227i	$-0.691610\pi$
$359$	−21.4582			−1.13252			−0.566260	+	0.824227i	$0.691610\pi$
$360$		0			0
$361$	−30.4949			−1.60499
$362$	−6.72278	+	3.29628i	−0.353342	+	0.173248i
$363$		0			0
$364$	21.1237	+	16.3624i	1.10718	+	0.857621i
$365$		0			0
$366$		0			0
$367$			23.4495i			1.22405i	0.790837	+	0.612027i	$0.209646\pi$
$367$			23.4495i			1.22405i	−0.790837	+	0.612027i	$0.790354\pi$
$368$	−4.42108	+	1.14152i	−0.230465	+	0.0595057i
$369$		0			0
$370$		0			0
$371$		−	27.7024i		−	1.43824i
$372$		0			0
$373$	25.6895			1.33015			0.665075	−	0.746776i	$-0.268399\pi$
$373$	25.6895			1.33015			0.665075	+	0.746776i	$0.268399\pi$
$374$	21.4582	+	43.7642i	1.10958	+	2.26299i
$375$		0			0
$376$	5.79796	−	28.1410i	0.299007	−	1.45126i
$377$		−	11.8130i		−	0.608398i
$378$		0			0
$379$		−	13.3598i		−	0.686248i	−0.939290	−	0.343124i	$-0.888515\pi$
$379$		−	13.3598i		−	0.686248i	0.939290	−	0.343124i	$-0.111485\pi$
$380$		0			0
$381$		0			0
$382$	−8.45667	−	17.2474i	−0.432681	−	0.882456i
$383$			12.4414i			0.635724i	0.948137	+	0.317862i	$0.102965\pi$
$383$			12.4414i			0.635724i	−0.948137	+	0.317862i	$0.897035\pi$
$384$		0			0
$385$		0			0
$386$	15.1092	−	7.40827i	0.769040	−	0.377071i
$387$		0			0
$388$	24.8190	+	19.2247i	1.26000	+	0.975989i
$389$			35.1736i			1.78337i	0.452655	+	0.891686i	$0.350477\pi$
$389$			35.1736i			1.78337i	−0.452655	+	0.891686i	$0.649523\pi$
$390$		0			0
$391$	−7.10102			−0.359114
$392$	13.5714	+	2.79613i	0.685457	+	0.141226i
$393$		0			0
$394$	−14.4949	−	29.5625i	−0.730242	−	1.48933i
$395$		0			0
$396$		0			0
$397$	−2.45157			−0.123041			−0.0615204	−	0.998106i	$-0.519595\pi$
$397$	−2.45157			−0.123041			−0.0615204	+	0.998106i	$0.519595\pi$
$398$	−13.2286	−	26.9798i	−0.663090	−	1.35238i
$399$		0			0
$400$		0			0
$401$	−31.1034			−1.55323			−0.776616	−	0.629975i	$-0.783065\pi$
$401$	−31.1034			−1.55323			−0.776616	+	0.629975i	$0.783065\pi$
$402$		0			0
$403$	−5.61385			−0.279646
$404$	−22.3432	−	17.3069i	−1.11161	−	0.861052i
$405$		0			0
$406$	−6.55051	−	13.3598i	−0.325096	−	0.663037i
$407$			35.0411i			1.73692i
$408$		0			0
$409$	7.89898			0.390579			0.195290	−	0.980746i	$-0.437435\pi$
$409$	7.89898			0.390579			0.195290	+	0.980746i	$0.437435\pi$
$410$		0			0
$411$		0			0
$412$	−10.9082	−	8.44949i	−0.537411	−	0.416276i
$413$	−17.1811			−0.845429
$414$		0			0
$415$		0			0
$416$	16.6356	−	14.2568i	0.815626	−	0.698999i
$417$		0			0
$418$	24.2681	+	49.4949i	1.18699	+	2.42087i
$419$			23.8410i			1.16471i	0.812934	+	0.582355i	$0.197869\pi$
$419$			23.8410i			1.16471i	−0.812934	+	0.582355i	$0.802131\pi$
$420$		0			0
$421$		−	24.6593i		−	1.20182i	−0.799316	−	0.600911i	$-0.794805\pi$
$421$		−	24.6593i		−	1.20182i	0.799316	−	0.600911i	$-0.205195\pi$
$422$	−2.70735	+	1.32745i	−0.131792	+	0.0646193i
$423$		0			0
$424$	−22.2474	−	4.58369i	−1.08043	−	0.222604i
$425$		0			0
$426$		0			0
$427$	−35.1763			−1.70230
$428$	−0.685493	+	0.884967i	−0.0331345	+	0.0427765i
$429$		0			0
$430$		0			0
$431$	21.4582			1.03360			0.516802	−	0.856105i	$-0.327122\pi$
$431$	21.4582			1.03360			0.516802	+	0.856105i	$0.327122\pi$
$432$		0			0
$433$		−	12.5959i		−	0.605321i	−0.953098	−	0.302661i	$-0.902125\pi$
$433$		−	12.5959i		−	0.605321i	0.953098	−	0.302661i	$-0.0978749\pi$
$434$	−6.34896	+	3.11299i	−0.304760	+	0.149428i
$435$		0			0
$436$	26.1237	+	20.2353i	1.25110	+	0.969098i
$437$	−8.03087			−0.384169
$438$		0			0
$439$	17.0454			0.813533			0.406766	−	0.913532i	$-0.366656\pi$
$439$	17.0454			0.813533			0.406766	+	0.913532i	$0.366656\pi$
$440$		0			0
$441$		0			0
$442$	30.5926	−	15.0000i	1.45514	−	0.713477i
$443$	7.21959			0.343013			0.171507	−	0.985183i	$-0.445137\pi$
$443$	7.21959			0.343013			0.171507	+	0.985183i	$0.445137\pi$
$444$		0			0
$445$		0			0
$446$	−0.442484	+	0.216956i	−0.0209522	+	0.0102732i
$447$		0			0
$448$	10.9082	−	25.3485i	0.515366	−	1.19760i
$449$	−19.2905			−0.910374			−0.455187	−	0.890396i	$-0.650428\pi$
$449$	−19.2905			−0.910374			−0.455187	+	0.890396i	$0.650428\pi$
$450$		0			0
$451$		−	21.8165i		−	1.02730i
$452$	19.6715	+	15.2375i	0.925271	+	0.716712i
$453$		0			0
$454$	−2.75255	−	5.61385i	−0.129184	−	0.263471i
$455$		0			0
$456$		0			0
$457$			20.6969i			0.968162i	0.875023	+	0.484081i	$0.160846\pi$
$457$			20.6969i			0.968162i	−0.875023	+	0.484081i	$0.839154\pi$
$458$	−6.72278	+	3.29628i	−0.314135	+	0.154025i
$459$		0			0
$460$		0			0
$461$		−	25.2120i		−	1.17424i	−0.809500	−	0.587120i	$-0.800262\pi$
$461$		−	25.2120i		−	1.17424i	0.809500	−	0.587120i	$-0.199738\pi$
$462$		0			0
$463$		−	6.89898i		−	0.320623i	−0.987066	−	0.160311i	$-0.948750\pi$
$463$		−	6.89898i		−	0.320623i	0.987066	−	0.160311i	$-0.0512498\pi$
$464$	−11.8130	+	3.05009i	−0.548403	+	0.141597i
$465$		0			0
$466$	30.7980	−	15.1007i	1.42669	−	0.699526i
$467$	−32.6832			−1.51240			−0.756199	−	0.654342i	$-0.772946\pi$
$467$	−32.6832			−1.51240			−0.756199	+	0.654342i	$0.772946\pi$
$468$		0			0
$469$		−	19.3649i		−	0.894189i
$470$		0			0
$471$		0			0
$472$	−2.84282	+	13.7980i	−0.130852	+	0.635103i
$473$			3.93765i			0.181053i
$474$		0			0
$475$		0			0
$476$	26.2808	−	33.9284i	1.20458	−	1.55510i
$477$		0			0
$478$	−18.2630	−	37.2474i	−0.835328	−	1.70366i
$479$	−7.87530			−0.359832			−0.179916	−	0.983682i	$-0.557583\pi$
$479$	−7.87530			−0.359832			−0.179916	+	0.983682i	$0.557583\pi$
$480$		0			0
$481$	24.4949			1.11687
$482$	14.7537	+	30.0902i	0.672010	+	1.37057i
$483$		0			0
$484$	24.1237	−	31.1436i	1.09653	−	1.41562i
$485$		0			0
$486$		0			0
$487$			1.04541i			0.0473719i	0.999719	+	0.0236860i	$0.00754018\pi$
$487$			1.04541i			0.0473719i	−0.999719	+	0.0236860i	$0.992460\pi$
$488$	−5.82033	+	28.2496i	−0.263474	+	1.27880i
$489$		0			0
$490$		0			0
$491$		−	1.11940i		−	0.0505180i	−0.999681	−	0.0252590i	$-0.991959\pi$
$491$		−	1.11940i		−	0.0505180i	0.999681	−	0.0252590i	$-0.00804105\pi$
$492$		0			0
$493$	−18.9737			−0.854531
$494$	34.5986	−	16.9642i	1.55666	−	0.763255i
$495$		0			0
$496$	1.44949	+	5.61385i	0.0650840	+	0.252069i
$497$		−	46.8540i		−	2.10169i
$498$		0			0
$499$			19.6844i			0.881193i	0.897705	+	0.440597i	$0.145233\pi$
$499$			19.6844i			0.881193i	−0.897705	+	0.440597i	$0.854767\pi$
$500$		0			0
$501$		0			0
$502$	7.74597	−	3.79796i	0.345719	−	0.169511i
$503$			28.3073i			1.26216i	0.775718	+	0.631080i	$0.217388\pi$
$503$			28.3073i			1.26216i	−0.775718	+	0.631080i	$0.782612\pi$
$504$		0			0
$505$		0			0
$506$	3.93765	+	8.03087i	0.175050	+	0.357016i
$507$		0			0
$508$	6.00510	+	4.65153i	0.266433	+	0.206378i
$509$			21.0425i			0.932693i	0.884602	+	0.466347i	$0.154430\pi$
$509$			21.0425i			0.932693i	−0.884602	+	0.466347i	$0.845570\pi$
$510$		0			0
$511$	23.7980			1.05276
$512$	−18.5521	−	12.9545i	−0.819896	−	0.572512i
$513$		0			0
$514$	−2.89898	+	1.42141i	−0.127869	+	0.0626958i
$515$		0			0
$516$		0			0
$517$	−56.2821			−2.47528
$518$	27.7024	−	13.5829i	1.21717	−	0.596798i
$519$		0			0
$520$		0			0
$521$	−31.1034			−1.36267			−0.681333	−	0.731974i	$-0.738599\pi$
$521$	−31.1034			−1.36267			−0.681333	+	0.731974i	$0.738599\pi$
$522$		0			0
$523$	33.7549			1.47600			0.737999	−	0.674802i	$-0.235771\pi$
$523$	33.7549			1.47600			0.737999	+	0.674802i	$0.235771\pi$
$524$	−16.6356	−	12.8859i	−0.726728	−	0.562921i
$525$		0			0
$526$	−11.4495	+	5.61385i	−0.499221	+	0.244775i
$527$			9.01682i			0.392779i
$528$		0			0
$529$	21.6969			0.943345
$530$		0			0
$531$		0			0
$532$	29.7222	−	38.3712i	1.28862	−	1.66360i
$533$	−15.2505			−0.660571
$534$		0			0
$535$		0			0
$536$	−15.5517	−	3.20415i	−0.671732	−	0.138398i
$537$		0			0
$538$	5.29439	−	2.59592i	0.228258	−	0.111918i
$539$		−	27.1427i		−	1.16912i
$540$		0			0
$541$			8.77613i			0.377315i	0.982043	+	0.188658i	$0.0604136\pi$
$541$			8.77613i			0.377315i	−0.982043	+	0.188658i	$0.939586\pi$
$542$	3.17588	+	6.47724i	0.136416	+	0.278221i
$543$		0			0
$544$	−22.8990	−	26.7196i	−0.981786	−	1.14559i
$545$		0			0
$546$		0			0
$547$	9.16738			0.391969			0.195984	−	0.980607i	$-0.437210\pi$
$547$	9.16738			0.391969			0.195984	+	0.980607i	$0.437210\pi$
$548$	16.0617	+	12.4414i	0.686124	+	0.531469i
$549$		0			0
$550$		0			0
$551$	−21.4582			−0.914150
$552$		0			0
$553$			10.0000i			0.425243i
$554$	15.1092	+	30.8154i	0.641930	+	1.30922i
$555$		0			0
$556$	−14.4949	−	11.2277i	−0.614721	−	0.476161i
$557$		0			0			−	1.00000i	$-0.5\pi$
$557$		0			0				1.00000i	$0.5\pi$
$558$		0			0
$559$	2.75255			0.116421
$560$		0			0
$561$		0			0
$562$	2.45157	+	5.00000i	0.103413	+	0.210912i
$563$	43.7642			1.84444			0.922220	−	0.386667i	$-0.126374\pi$
$563$	43.7642			1.84444			0.922220	+	0.386667i	$0.126374\pi$
$564$		0			0
$565$		0			0
$566$	0.442484	+	0.902449i	0.0185990	+	0.0379327i
$567$		0			0
$568$	−37.6279	−	7.75255i	−1.57883	−	0.325290i
$569$	−3.93765			−0.165075			−0.0825375	−	0.996588i	$-0.526302\pi$
$569$	−3.93765			−0.165075			−0.0825375	+	0.996588i	$0.526302\pi$
$570$		0			0
$571$		−	8.45667i		−	0.353901i	−0.984220	−	0.176950i	$-0.943377\pi$
$571$		−	8.45667i		−	0.353901i	0.984220	−	0.176950i	$-0.0566232\pi$
$572$	−33.9284	−	26.2808i	−1.41862	−	1.09886i
$573$		0			0
$574$	−17.2474	+	8.45667i	−0.719895	+	0.352975i
$575$		0			0
$576$		0			0
$577$			15.6969i			0.653472i	0.945116	+	0.326736i	$0.105949\pi$
$577$			15.6969i			0.653472i	−0.945116	+	0.326736i	$0.894051\pi$
$578$	−13.5085	−	27.5506i	−0.561878	−	1.14595i
$579$		0			0
$580$		0			0
$581$		−	21.0425i		−	0.872991i
$582$		0			0
$583$			44.4949i			1.84279i
$584$	3.93765	−	19.1118i	0.162941	−	0.790853i
$585$		0			0
$586$	10.0000	+	20.3951i	0.413096	+	0.842513i
$587$	−16.6214			−0.686040			−0.343020	−	0.939328i	$-0.611450\pi$
$587$	−16.6214			−0.686040			−0.343020	+	0.939328i	$0.611450\pi$
$588$		0			0
$589$			10.1975i			0.420182i
$590$		0			0
$591$		0			0
$592$	−6.32456	−	24.4949i	−0.259938	−	1.00673i
$593$		−	26.5374i		−	1.08976i	−0.838514	−	0.544879i	$-0.816575\pi$
$593$		−	26.5374i		−	1.08976i	0.838514	−	0.544879i	$-0.183425\pi$
$594$		0			0
$595$		0			0
$596$	−33.2711	−	25.7717i	−1.36284	−	1.05565i
$597$		0			0
$598$	5.61385	−	2.75255i	0.229567	−	0.112560i
$599$	19.2905			0.788187			0.394094	−	0.919070i	$-0.371059\pi$
$599$	19.2905			0.788187			0.394094	+	0.919070i	$0.371059\pi$
$600$		0			0
$601$	−0.101021			−0.00412071			−0.00206036	−	0.999998i	$-0.500656\pi$
$601$	−0.101021			−0.00412071			−0.00206036	+	0.999998i	$0.500656\pi$
$602$	3.11299	−	1.52634i	0.126876	−	0.0622091i
$603$		0			0
$604$	15.1237	−	19.5246i	0.615376	−	0.794447i
$605$		0			0
$606$		0			0
$607$			40.6969i			1.65184i	0.563789	+	0.825919i	$0.309343\pi$
$607$			40.6969i			1.65184i	−0.563789	+	0.825919i	$0.690657\pi$
$608$	−25.8975	−	30.2185i	−1.05028	−	1.22552i
$609$		0			0
$610$		0			0
$611$			39.3431i			1.59165i
$612$		0			0
$613$	31.6228			1.27723			0.638616	−	0.769526i	$-0.279507\pi$
$613$	31.6228			1.27723			0.638616	+	0.769526i	$0.279507\pi$
$614$	−9.20275	−	18.7691i	−0.371393	−	0.757459i
$615$		0			0
$616$	−52.9444	−	10.9082i	−2.13319	−	0.439506i
$617$		−	13.0698i		−	0.526170i	−0.964773	−	0.263085i	$-0.915260\pi$
$617$		−	13.0698i		−	0.526170i	0.964773	−	0.263085i	$-0.0847400\pi$
$618$		0			0
$619$			37.2366i			1.49667i	0.663323	+	0.748333i	$0.269146\pi$
$619$			37.2366i			1.49667i	−0.663323	+	0.748333i	$0.730854\pi$
$620$		0			0
$621$		0			0
$622$	9.80629	+	20.0000i	0.393196	+	0.801927i
$623$		−	27.1658i		−	1.08837i
$624$		0			0
$625$		0			0
$626$	−28.6921	+	14.0682i	−1.14677	+	0.562277i
$627$		0			0
$628$	−10.7485	+	13.8763i	−0.428913	+	0.553724i
$629$		−	39.3431i		−	1.56871i
$630$		0			0
$631$	−18.5505			−0.738484			−0.369242	−	0.929333i	$-0.620383\pi$
$631$	−18.5505			−0.738484			−0.369242	+	0.929333i	$0.620383\pi$
$632$	8.03087	+	1.65462i	0.319451	+	0.0658171i
$633$		0			0
$634$	13.1010	+	26.7196i	0.520308	+	1.06117i
$635$		0			0
$636$		0			0
$637$	−18.9737			−0.751764
$638$	10.5213	+	21.4582i	0.416541	+	0.849538i
$639$		0			0
$640$		0			0
$641$	35.0411			1.38404			0.692020	−	0.721879i	$-0.256721\pi$
$641$	35.0411			1.38404			0.692020	+	0.721879i	$0.256721\pi$
$642$		0			0
$643$	34.4656			1.35919			0.679595	−	0.733587i	$-0.262155\pi$
$643$	34.4656			1.35919			0.679595	+	0.733587i	$0.262155\pi$
$644$	4.82262	−	6.22597i	0.190038	−	0.245338i
$645$		0			0
$646$	−27.2474	−	55.5714i	−1.07204	−	2.18643i
$647$			24.8827i			0.978242i	0.872216	+	0.489121i	$0.162682\pi$
$647$			24.8827i			0.978242i	−0.872216	+	0.489121i	$0.837318\pi$
$648$		0			0
$649$	27.5959			1.08323
$650$		0			0
$651$		0			0
$652$	18.1032	−	23.3712i	0.708977	−	0.915286i
$653$	6.10018			0.238719			0.119359	−	0.992851i	$-0.461916\pi$
$653$	6.10018			0.238719			0.119359	+	0.992851i	$0.461916\pi$
$654$		0			0
$655$		0			0
$656$	3.93765	+	15.2505i	0.153739	+	0.595430i
$657$		0			0
$658$	21.8165	+	44.4949i	0.850495	+	1.73459i
$659$		−	22.7216i		−	0.885109i	−0.896742	−	0.442555i	$-0.854072\pi$
$659$		−	22.7216i		−	0.885109i	0.896742	−	0.442555i	$-0.145928\pi$
$660$		0			0
$661$			37.3084i			1.45113i	0.688154	+	0.725565i	$0.258421\pi$
$661$			37.3084i			1.45113i	−0.688154	+	0.725565i	$0.741579\pi$
$662$	−16.0617	+	7.87530i	−0.624257	+	0.306082i
$663$		0			0
$664$	−16.8990	−	3.48173i	−0.655808	−	0.135117i
$665$		0			0
$666$		0			0
$667$	−3.48173			−0.134813
$668$	5.41469	+	4.19420i	0.209501	+	0.162279i
$669$		0			0
$670$		0			0
$671$	56.4993			2.18113
$672$		0			0
$673$		−	26.8990i		−	1.03688i	−0.855114	−	0.518440i	$-0.826513\pi$
$673$		−	26.8990i		−	1.03688i	0.855114	−	0.518440i	$-0.173487\pi$
$674$	23.8695	−	11.7036i	0.919419	−	0.450804i
$675$		0			0
$676$	−2.44949	+	3.16228i	−0.0942111	+	0.121626i
$677$	35.1736			1.35183			0.675915	−	0.736979i	$-0.263749\pi$
$677$	35.1736			1.35183			0.675915	+	0.736979i	$0.263749\pi$
$678$		0			0
$679$	−54.1464			−2.07795
$680$		0			0
$681$		0			0
$682$	10.1975	−	5.00000i	0.390484	−	0.191460i
$683$	−33.2429			−1.27200			−0.636002	−	0.771687i	$-0.719413\pi$
$683$	−33.2429			−1.27200			−0.636002	+	0.771687i	$0.719413\pi$
$684$		0			0
$685$		0			0
$686$	9.20275	−	4.51224i	0.351363	−	0.172278i
$687$		0			0
$688$	−0.710706	−	2.75255i	−0.0270954	−	0.104940i
$689$	31.1034			1.18495
$690$		0			0
$691$			37.9473i			1.44358i	0.692110	+	0.721792i	$0.256681\pi$
$691$			37.9473i			1.44358i	−0.692110	+	0.721792i	$0.743319\pi$
$692$	−2.36460	+	3.05268i	−0.0898886	+	0.116046i
$693$		0			0
$694$	−10.0000	−	20.3951i	−0.379595	−	0.774187i
$695$		0			0
$696$		0			0
$697$			24.4949i			0.927810i
$698$	−16.0617	+	7.87530i	−0.607946	+	0.298085i
$699$		0			0
$700$		0			0
$701$			41.2738i			1.55889i	0.626472	+	0.779444i	$0.284498\pi$
$701$			41.2738i			1.55889i	−0.626472	+	0.779444i	$0.715502\pi$
$702$		0			0
$703$		−	44.4949i		−	1.67816i
$704$	−17.5205	+	40.7141i	−0.660330	+	1.53447i
$705$		0			0
$706$	−0.797959	+	0.391251i	−0.0300316	+	0.0147249i
$707$	48.7449			1.83324
$708$		0			0
$709$			1.03016i			0.0386885i	0.999813	+	0.0193442i	$0.00615785\pi$
$709$			1.03016i			0.0386885i	−0.999813	+	0.0193442i	$0.993842\pi$
$710$		0			0
$711$		0			0
$712$	−21.8165	−	4.49490i	−0.817607	−	0.168453i
$713$			1.65462i			0.0619659i
$714$		0			0
$715$		0			0
$716$	33.2711	+	25.7717i	1.24340	+	0.963134i
$717$		0			0
$718$	−13.3598	−	27.2474i	−0.498584	−	1.01687i
$719$	2.16772			0.0808422			0.0404211	−	0.999183i	$-0.487130\pi$
$719$	2.16772			0.0808422			0.0404211	+	0.999183i	$0.487130\pi$
$720$		0			0
$721$	23.7980			0.886282
$722$	−18.9860	−	38.7222i	−0.706587	−	1.44109i
$723$		0			0
$724$	−8.37117	−	6.48428i	−0.311112	−	0.240986i
$725$		0			0
$726$		0			0
$727$		−	43.4495i		−	1.61145i	−0.592288	−	0.805726i	$-0.701775\pi$
$727$		−	43.4495i		−	1.61145i	0.592288	−	0.805726i	$-0.298225\pi$
$728$	−7.62523	+	37.0099i	−0.282610	+	1.37168i
$729$		0			0
$730$		0			0
$731$		−	4.42108i		−	0.163519i
$732$		0			0
$733$	−30.9839			−1.14442			−0.572208	−	0.820109i	$-0.693913\pi$
$733$	−30.9839			−1.14442			−0.572208	+	0.820109i	$0.693913\pi$
$734$	−29.7760	+	14.5996i	−1.09905	+	0.538881i
$735$		0			0
$736$	−4.20204	−	4.90314i	−0.154889	−	0.180732i
$737$			31.1034i			1.14571i
$738$		0			0
$739$			30.9839i			1.13976i	0.821728	+	0.569880i	$0.193010\pi$
$739$			30.9839i			1.13976i	−0.821728	+	0.569880i	$0.806990\pi$
$740$		0			0
$741$		0			0
$742$	35.1763	−	17.2474i	1.29136	−	0.633174i
$743$		−	6.84910i		−	0.251269i	−0.992077	−	0.125635i	$-0.959903\pi$
$743$		−	6.84910i		−	0.251269i	0.992077	−	0.125635i	$-0.0400967\pi$
$744$		0			0
$745$		0			0
$746$	15.9942	+	32.6203i	0.585589	+	1.19431i
$747$		0			0
$748$	−42.2116	+	54.4949i	−1.54341	+	1.99253i
$749$		−	1.93069i		−	0.0705458i
$750$		0			0
$751$	35.7980			1.30629			0.653143	−	0.757235i	$-0.273450\pi$
$751$	35.7980			1.30629			0.653143	+	0.757235i	$0.273450\pi$
$752$	39.3431	−	10.1583i	1.43469	−	0.370436i
$753$		0			0
$754$	15.0000	−	7.35472i	0.546268	−	0.267843i
$755$		0			0
$756$		0			0
$757$	−12.2579			−0.445519			−0.222760	−	0.974873i	$-0.571507\pi$
$757$	−12.2579			−0.445519			−0.222760	+	0.974873i	$0.571507\pi$
$758$	16.9642	−	8.31779i	0.616167	−	0.302116i
$759$		0			0
$760$		0			0
$761$	−15.7506			−0.570959			−0.285480	−	0.958385i	$-0.592153\pi$
$761$	−15.7506			−0.570959			−0.285480	+	0.958385i	$0.592153\pi$
$762$		0			0
$763$	−56.9928			−2.06328
$764$	16.6356	−	21.4764i	0.601854	−	0.776990i
$765$		0			0
$766$	−15.7980	+	7.74597i	−0.570803	+	0.279873i
$767$		−	19.2905i		−	0.696539i
$768$		0			0
$769$	−5.20204			−0.187590			−0.0937952	−	0.995592i	$-0.529900\pi$
$769$	−5.20204			−0.187590			−0.0937952	+	0.995592i	$0.529900\pi$
$770$		0			0
$771$		0			0
$772$	18.8139	+	14.5732i	0.677128	+	0.524501i
$773$	9.15028			0.329113			0.164556	−	0.986368i	$-0.447381\pi$
$773$	9.15028			0.329113			0.164556	+	0.986368i	$0.447381\pi$
$774$		0			0
$775$		0			0
$776$	−8.95916	+	43.4843i	−0.321615	+	1.56100i
$777$		0			0
$778$	−44.6631	+	21.8990i	−1.60125	+	0.785116i
$779$			27.7024i			0.992542i
$780$		0			0
$781$			75.2558i			2.69286i
$782$	−4.42108	−	9.01682i	−0.158097	−	0.322441i
$783$		0			0
$784$	4.89898	+	18.9737i	0.174964	+	0.677631i
$785$		0			0
$786$		0			0
$787$	−10.5170			−0.374890			−0.187445	−	0.982275i	$-0.560021\pi$
$787$	−10.5170			−0.374890			−0.187445	+	0.982275i	$0.560021\pi$
$788$	28.5137	−	36.8110i	1.01576	−	1.31134i
$789$		0			0
$790$		0			0
$791$	−42.9164			−1.52593
$792$		0			0
$793$		−	39.4949i		−	1.40250i
$794$	−1.52634	−	3.11299i	−0.0541679	−	0.110476i
$795$		0			0
$796$	26.0227	−	33.5952i	0.922350	−	1.19075i
$797$	−27.1427			−0.961444			−0.480722	−	0.876873i	$-0.659625\pi$
$797$	−27.1427			−0.961444			−0.480722	+	0.876873i	$0.659625\pi$
$798$		0			0
$799$	63.1918			2.23557
$800$		0			0
$801$		0			0
$802$	−19.3649	−	39.4949i	−0.683799	−	1.39461i
$803$	−38.2237			−1.34888
$804$		0			0
$805$		0			0
$806$	−3.49517	−	7.12842i	−0.123112	−	0.251088i
$807$		0			0
$808$	8.06542	−	39.1464i	0.283741	−	1.37717i
$809$	3.93765			0.138440			0.0692202	−	0.997601i	$-0.477949\pi$
$809$	3.93765			0.138440			0.0692202	+	0.997601i	$0.477949\pi$
$810$		0			0
$811$			39.4405i			1.38494i	0.721444	+	0.692472i	$0.243479\pi$
$811$			39.4405i			1.38494i	−0.721444	+	0.692472i	$0.756521\pi$
$812$	12.8859	−	16.6356i	0.452205	−	0.583794i
$813$		0			0
$814$	−44.4949	+	21.8165i	−1.55955	+	0.764668i
$815$		0			0
$816$		0			0
$817$		−	5.00000i		−	0.174928i
$818$	4.91788	+	10.0301i	0.171950	+	0.350693i
$819$		0			0
$820$		0			0
$821$			26.0233i			0.908220i	0.890946	+	0.454110i	$0.150043\pi$
$821$			26.0233i			0.908220i	−0.890946	+	0.454110i	$0.849957\pi$
$822$		0			0
$823$		−	34.8434i		−	1.21456i	−0.794487	−	0.607282i	$-0.792260\pi$
$823$		−	34.8434i		−	1.21456i	0.794487	−	0.607282i	$-0.207740\pi$
$824$	3.93765	−	19.1118i	0.137175	−	0.665792i
$825$		0			0
$826$	−10.6969	−	21.8165i	−0.372194	−	0.759093i
$827$	11.6407			0.404786			0.202393	−	0.979304i	$-0.435128\pi$
$827$	11.6407			0.404786			0.202393	+	0.979304i	$0.435128\pi$
$828$		0			0
$829$			37.3084i			1.29578i	0.761736	+	0.647888i	$0.224347\pi$
$829$			37.3084i			1.29578i	−0.761736	+	0.647888i	$0.775653\pi$
$830$		0			0
$831$		0			0
$832$	28.4605	+	12.2474i	0.986690	+	0.424604i
$833$			30.4750i			1.05590i
$834$		0			0
$835$		0			0
$836$	−47.7390	+	61.6308i	−1.65109	+	2.13155i
$837$		0			0
$838$	−30.2732	+	14.8434i	−1.04577	+	0.512756i
$839$	−5.70759			−0.197048			−0.0985239	−	0.995135i	$-0.531412\pi$
$839$	−5.70759			−0.197048			−0.0985239	+	0.995135i	$0.531412\pi$
$840$		0			0
$841$	19.6969			0.679205
$842$	31.3122	−	15.3528i	1.07909	−	0.529093i
$843$		0			0
$844$	−3.37117	−	2.61130i	−0.116041	−	0.0898846i
$845$		0			0
$846$		0			0
$847$			67.9444i			2.33460i
$848$	−8.03087	−	31.1034i	−0.275781	−	1.06810i
$849$		0			0
$850$		0			0
$851$		−	7.21959i		−	0.247484i
$852$		0			0
$853$	5.29439			0.181277			0.0906383	−	0.995884i	$-0.471109\pi$
$853$	5.29439			0.181277			0.0906383	+	0.995884i	$0.471109\pi$
$854$	−21.9007	−	44.6666i	−0.749426	−	1.52846i
$855$		0			0
$856$	−1.55051	−	0.319455i	−0.0529953	−	0.0109187i
$857$			18.0336i			0.616017i	0.951384	+	0.308009i	$0.0996626\pi$
$857$			18.0336i			0.616017i	−0.951384	+	0.308009i	$0.900337\pi$
$858$		0			0
$859$		−	43.6330i		−	1.48874i	−0.667769	−	0.744369i	$-0.732750\pi$
$859$		−	43.6330i		−	1.48874i	0.667769	−	0.744369i	$-0.267250\pi$
$860$		0			0
$861$		0			0
$862$	13.3598	+	27.2474i	0.455037	+	0.928052i
$863$		−	12.4414i		−	0.423509i	−0.977323	−	0.211755i	$-0.932082\pi$
$863$		−	12.4414i		−	0.423509i	0.977323	−	0.211755i	$-0.0679178\pi$
$864$		0			0
$865$		0			0
$866$	15.9942	−	7.84219i	0.543505	−	0.266488i
$867$		0			0
$868$	−7.90569	−	6.12372i	−0.268337	−	0.207853i
$869$		−	16.0617i		−	0.544857i
$870$		0			0
$871$	21.7423			0.736711
$872$	−9.43013	+	45.7702i	−0.319344	+	1.54997i
$873$		0			0
$874$	−5.00000	−	10.1975i	−0.169128	−	0.344937i
$875$		0			0
$876$		0			0
$877$	20.7863			0.701904			0.350952	−	0.936393i	$-0.385858\pi$
$877$	20.7863			0.701904			0.350952	+	0.936393i	$0.385858\pi$
$878$	10.6124	+	21.6441i	0.358152	+	0.730454i
$879$		0			0
$880$		0			0
$881$	19.2905			0.649913			0.324956	−	0.945729i	$-0.394650\pi$
$881$	19.2905			0.649913			0.324956	+	0.945729i	$0.394650\pi$
$882$		0			0
$883$	30.9121			1.04027			0.520137	−	0.854083i	$-0.325881\pi$
$883$	30.9121			1.04027			0.520137	+	0.854083i	$0.325881\pi$
$884$	38.0938	+	29.5073i	1.28123	+	0.992438i
$885$		0			0
$886$	4.49490	+	9.16738i	0.151009	+	0.307984i
$887$		−	53.0747i		−	1.78207i	−0.453930	−	0.891037i	$-0.649978\pi$
$887$		−	53.0747i		−	1.78207i	0.453930	−	0.891037i	$-0.350022\pi$
$888$		0			0
$889$	−13.1010			−0.439394
$890$		0			0
$891$		0			0
$892$	−0.550978	−	0.426786i	−0.0184481	−	0.0142898i
$893$	71.4666			2.39154
$894$		0			0
$895$		0			0
$896$	38.9787	−	1.93069i	1.30219	−	0.0644997i
$897$		0			0
$898$	−12.0102	−	24.4949i	−0.400786	−	0.817405i
$899$			4.42108i			0.147451i
$900$		0			0
$901$		−	49.9575i		−	1.66433i
$902$	27.7024	−	13.5829i	0.922389	−	0.452261i
$903$		0			0
$904$	−7.10102	+	34.4656i	−0.236176	+	1.14631i
$905$		0			0
$906$		0			0
$907$	−56.2821			−1.86882			−0.934408	−	0.356204i	$-0.884071\pi$
$907$	−56.2821			−1.86882			−0.934408	+	0.356204i	$0.884071\pi$
$908$	5.41469	−	6.99034i	0.179693	−	0.231982i
$909$		0			0
$910$		0			0
$911$	−23.6259			−0.782761			−0.391381	−	0.920229i	$-0.628002\pi$
$911$	−23.6259			−0.782761			−0.391381	+	0.920229i	$0.628002\pi$
$912$		0			0
$913$			33.7980i			1.11855i
$914$	−26.2808	+	12.8859i	−0.869292	+	0.426226i
$915$		0			0
$916$	−8.37117	−	6.48428i	−0.276591	−	0.214247i
$917$	36.2930			1.19850
$918$		0			0
$919$	34.6413			1.14271			0.571356	−	0.820702i	$-0.306418\pi$
$919$	34.6413			1.14271			0.571356	+	0.820702i	$0.306418\pi$
$920$		0			0
$921$		0			0
$922$	32.0140	−	15.6969i	1.05433	−	0.516951i
$923$	52.6063			1.73156
$924$		0			0
$925$		0			0
$926$	8.76027	−	4.29529i	0.287880	−	0.141152i
$927$		0			0
$928$	−11.2277	−	13.1010i	−0.368567	−	0.430062i
$929$	−38.9787			−1.27885			−0.639425	−	0.768853i	$-0.720828\pi$
$929$	−38.9787			−1.27885			−0.639425	+	0.768853i	$0.720828\pi$
$930$		0			0
$931$			34.4656i			1.12956i
$932$	38.3495	+	29.7054i	1.25618	+	0.973032i
$933$		0			0
$934$	−20.3485	−	41.5009i	−0.665822	−	1.35795i
$935$		0			0
$936$		0			0
$937$		−	1.20204i		−	0.0392690i	−0.999807	−	0.0196345i	$-0.993750\pi$
$937$		−	1.20204i		−	0.0392690i	0.999807	−	0.0196345i	$-0.00625025\pi$
$938$	24.5894	−	12.0565i	0.802873	−	0.393660i
$939$		0			0
$940$		0			0
$941$			40.4625i			1.31904i	0.751687	+	0.659520i	$0.229240\pi$
$941$			40.4625i			1.31904i	−0.751687	+	0.659520i	$0.770760\pi$
$942$		0			0
$943$			4.49490i			0.146374i
$944$	−19.2905	+	4.98078i	−0.627852	+	0.162111i
$945$		0			0
$946$	−5.00000	+	2.45157i	−0.162564	+	0.0797075i
$947$	−4.42108			−0.143666			−0.0718329	−	0.997417i	$-0.522885\pi$
$947$	−4.42108			−0.143666			−0.0718329	+	0.997417i	$0.522885\pi$
$948$		0			0
$949$			26.7196i			0.867356i
$950$		0			0
$951$		0			0
$952$	59.4444	+	12.2474i	1.92660	+	0.396942i
$953$			4.56607i			0.147909i	0.997262	+	0.0739547i	$0.0235620\pi$
$953$			4.56607i			0.147909i	−0.997262	+	0.0739547i	$0.976438\pi$
$954$		0			0
$955$		0			0
$956$	35.9261	−	46.3803i	1.16193	−	1.50005i
$957$		0			0
$958$	−4.90314	−	10.0000i	−0.158413	−	0.323085i
$959$	−35.0411			−1.13154
$960$		0			0
$961$	−28.8990			−0.932225
$962$	15.2505	+	31.1034i	0.491695	+	1.00281i
$963$		0			0
$964$	−29.0227	+	37.4681i	−0.934758	+	1.20677i
$965$		0			0
$966$		0			0
$967$			8.29286i			0.266680i	0.991070	+	0.133340i	$0.0425703\pi$
$967$			8.29286i			0.266680i	−0.991070	+	0.133340i	$0.957430\pi$
$968$	54.5653	+	11.2422i	1.75379	+	0.361338i
$969$		0			0
$970$		0			0
$971$			45.4433i			1.45834i	0.684331	+	0.729172i	$0.260094\pi$
$971$			45.4433i			1.45834i	−0.684331	+	0.729172i	$0.739906\pi$
$972$		0			0
$973$	31.6228			1.01378
$974$	−1.32745	+	0.650868i	−0.0425343	+	0.0208552i
$975$		0			0
$976$	−39.4949	+	10.1975i	−1.26420	+	0.326415i
$977$			33.7842i			1.08085i	0.841391	+	0.540427i	$0.181737\pi$
$977$			33.7842i			1.08085i	−0.841391	+	0.540427i	$0.818263\pi$
$978$		0			0
$979$			43.6330i			1.39452i
$980$		0			0
$981$		0			0
$982$	1.42141	−	0.696938i	0.0453591	−	0.0222402i
$983$			22.5997i			0.720819i	0.932794	+	0.360409i	$0.117363\pi$
$983$			22.5997i			0.720819i	−0.932794	+	0.360409i	$0.882637\pi$
$984$		0			0
$985$		0			0
$986$	−11.8130	−	24.0926i	−0.376201	−	0.767265i
$987$		0			0
$988$	43.0820	+	33.3712i	1.37062	+	1.06168i
$989$		−	0.811283i		−	0.0257973i
$990$		0			0
$991$	4.75255			0.150970			0.0754849	−	0.997147i	$-0.475950\pi$
$991$	4.75255			0.150970			0.0754849	+	0.997147i	$0.475950\pi$
$992$	−6.22597	+	5.33572i	−0.197675	+	0.169409i
$993$		0			0
$994$	59.4949	−	29.1712i	1.88706	−	0.925254i
$995$		0			0
$996$		0			0
$997$	12.6491			0.400601			0.200301	−	0.979734i	$-0.435808\pi$
$997$	12.6491			0.400601			0.200301	+	0.979734i	$0.435808\pi$
$998$	−24.9951	+	12.2554i	−0.791205	+	0.387939i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1800.2.d.u.1549.11		16
3.2	odd	2	inner	1800.2.d.u.1549.5		16
4.3	odd	2		7200.2.d.u.2449.14		16
5.2	odd	4		1800.2.k.s.901.2	yes	8
5.3	odd	4		1800.2.k.r.901.7	yes	8
5.4	even	2	inner	1800.2.d.u.1549.6		16
8.3	odd	2		7200.2.d.u.2449.15		16
8.5	even	2	inner	1800.2.d.u.1549.7		16
12.11	even	2		7200.2.d.u.2449.16		16
15.2	even	4		1800.2.k.s.901.7	yes	8
15.8	even	4		1800.2.k.r.901.2	yes	8
15.14	odd	2	inner	1800.2.d.u.1549.12		16
20.3	even	4		7200.2.k.t.3601.6		8
20.7	even	4		7200.2.k.q.3601.1		8
20.19	odd	2		7200.2.d.u.2449.1		16
24.5	odd	2	inner	1800.2.d.u.1549.9		16
24.11	even	2		7200.2.d.u.2449.13		16
40.3	even	4		7200.2.k.t.3601.7		8
40.13	odd	4		1800.2.k.r.901.8	yes	8
40.19	odd	2		7200.2.d.u.2449.4		16
40.27	even	4		7200.2.k.q.3601.4		8
40.29	even	2	inner	1800.2.d.u.1549.10		16
40.37	odd	4		1800.2.k.s.901.1	yes	8
60.23	odd	4		7200.2.k.t.3601.8		8
60.47	odd	4		7200.2.k.q.3601.3		8
60.59	even	2		7200.2.d.u.2449.3		16
120.29	odd	2	inner	1800.2.d.u.1549.8		16
120.53	even	4		1800.2.k.r.901.1	✓	8
120.59	even	2		7200.2.d.u.2449.2		16
120.77	even	4		1800.2.k.s.901.8	yes	8
120.83	odd	4		7200.2.k.t.3601.5		8
120.107	odd	4		7200.2.k.q.3601.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1800.2.d.u.1549.5		16	3.2	odd	2	inner
1800.2.d.u.1549.6		16	5.4	even	2	inner
1800.2.d.u.1549.7		16	8.5	even	2	inner
1800.2.d.u.1549.8		16	120.29	odd	2	inner
1800.2.d.u.1549.9		16	24.5	odd	2	inner
1800.2.d.u.1549.10		16	40.29	even	2	inner
1800.2.d.u.1549.11		16	1.1	even	1	trivial
1800.2.d.u.1549.12		16	15.14	odd	2	inner
1800.2.k.r.901.1	✓	8	120.53	even	4
1800.2.k.r.901.2	yes	8	15.8	even	4
1800.2.k.r.901.7	yes	8	5.3	odd	4
1800.2.k.r.901.8	yes	8	40.13	odd	4
1800.2.k.s.901.1	yes	8	40.37	odd	4
1800.2.k.s.901.2	yes	8	5.2	odd	4
1800.2.k.s.901.7	yes	8	15.2	even	4
1800.2.k.s.901.8	yes	8	120.77	even	4
7200.2.d.u.2449.1		16	20.19	odd	2
7200.2.d.u.2449.2		16	120.59	even	2
7200.2.d.u.2449.3		16	60.59	even	2
7200.2.d.u.2449.4		16	40.19	odd	2
7200.2.d.u.2449.13		16	24.11	even	2
7200.2.d.u.2449.14		16	4.3	odd	2
7200.2.d.u.2449.15		16	8.3	odd	2
7200.2.d.u.2449.16		16	12.11	even	2
7200.2.k.q.3601.1		8	20.7	even	4
7200.2.k.q.3601.2		8	120.107	odd	4
7200.2.k.q.3601.3		8	60.47	odd	4
7200.2.k.q.3601.4		8	40.27	even	4
7200.2.k.t.3601.5		8	120.83	odd	4
7200.2.k.t.3601.6		8	20.3	even	4
7200.2.k.t.3601.7		8	40.3	even	4
7200.2.k.t.3601.8		8	60.23	odd	4

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:	\( N \)	\(=\)	\( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1800.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.622597 + 1.26979i) q^{2} +(-1.22474 + 1.58114i) q^{4} -3.44949i q^{7} +(-2.77024 - 0.570759i) q^{8} +O(q^{10})\)	\(q+(0.622597 + 1.26979i) q^{2} +(-1.22474 + 1.58114i) q^{4} -3.44949i q^{7} +(-2.77024 - 0.570759i) q^{8} +5.54048i q^{11} +3.87298 q^{13} +(4.38014 - 2.14764i) q^{14} +(-1.00000 - 3.87298i) q^{16} -6.22069i q^{17} -7.03526i q^{19} +(-7.03526 + 3.44949i) q^{22} -1.14152i q^{23} +(2.41131 + 4.91788i) q^{26} +(5.45412 + 4.22474i) q^{28} -3.05009i q^{29} -1.44949 q^{31} +(4.29529 - 3.68110i) q^{32} +(7.89898 - 3.87298i) q^{34} +6.32456 q^{37} +(8.93332 - 4.38014i) q^{38} -3.93765 q^{41} +0.710706 q^{43} +(-8.76027 - 6.78568i) q^{44} +(1.44949 - 0.710706i) q^{46} +10.1583i q^{47} -4.89898 q^{49} +(-4.74342 + 6.12372i) q^{52} +8.03087 q^{53} +(-1.96883 + 9.55592i) q^{56} +(3.87298 - 1.89898i) q^{58} -4.98078i q^{59} -10.1975i q^{61} +(-0.902449 - 1.84055i) q^{62} +(7.34847 + 3.16228i) q^{64} +5.61385 q^{67} +(9.83577 + 7.61875i) q^{68} +13.5829 q^{71} +6.89898i q^{73} +(3.93765 + 8.03087i) q^{74} +(11.1237 + 8.61640i) q^{76} +19.1118 q^{77} -2.89898 q^{79} +(-2.45157 - 5.00000i) q^{82} +6.10018 q^{83} +(0.442484 + 0.902449i) q^{86} +(3.16228 - 15.3485i) q^{88} +7.87530 q^{89} -13.3598i q^{91} +(1.80490 + 1.39807i) q^{92} +(-12.8990 + 6.32456i) q^{94} -15.6969i q^{97} +(-3.05009 - 6.22069i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 16 q^{16} + 16 q^{31} + 48 q^{34} - 16 q^{46} + 80 q^{76} + 32 q^{79} - 128 q^{94}+O(q^{100}) \) 16 * q - 16 * q^16 + 16 * q^31 + 48 * q^34 - 16 * q^46 + 80 * q^76 + 32 * q^79 - 128 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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