LMFDB - Embedded newform 1800.2.m.f.899.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1800,2,Mod(899,1800)]

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([1, 1, 1, 1]))

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

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

chi := DirichletCharacter("1800.899");

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.m (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:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			899.24
Character	$\chi$	$=$	1800.899
Dual form			1800.2.m.f.899.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.980435 + 1.01919i) q^{2} +(-0.0774950 + 1.99850i) q^{4} +4.53014 q^{7} +(-2.11283 + 1.88042i) q^{8} +O(q^{10})$	\(q+(0.980435 + 1.01919i) q^{2} +(-0.0774950 + 1.99850i) q^{4} +4.53014 q^{7} +(-2.11283 + 1.88042i) q^{8} +5.63987i q^{11} -2.34956 q^{13} +(4.44151 + 4.61707i) q^{14} +(-3.98799 - 0.309747i) q^{16} +5.85906 q^{17} -3.92808 q^{19} +(-5.74810 + 5.52952i) q^{22} +0.438049i q^{23} +(-2.30359 - 2.39465i) q^{26} +(-0.351063 + 9.05347i) q^{28} +6.09065 q^{29} -9.84876i q^{31} +(-3.59427 - 4.36820i) q^{32} +(5.74442 + 5.97149i) q^{34} -6.38490 q^{37} +(-3.85123 - 4.00346i) q^{38} +4.00647i q^{41} +9.90406i q^{43} +(-11.2713 - 0.437062i) q^{44} +(-0.446455 + 0.429478i) q^{46} +4.89863i q^{47} +13.5222 q^{49} +(0.182079 - 4.69559i) q^{52} -1.89178i q^{53} +(-9.57140 + 8.51854i) q^{56} +(5.97149 + 6.20753i) q^{58} +5.11676i q^{59} -1.90277i q^{61} +(10.0377 - 9.65606i) q^{62} +(0.928079 - 7.94598i) q^{64} -0.691882i q^{67} +(-0.454048 + 11.7093i) q^{68} -2.18498 q^{71} +0.429801i q^{73} +(-6.25998 - 6.50743i) q^{74} +(0.304406 - 7.85026i) q^{76} +25.5494i q^{77} +2.47054i q^{79} +(-4.08335 + 3.92808i) q^{82} +2.28834 q^{83} +(-10.0941 + 9.71028i) q^{86} +(-10.6053 - 11.9161i) q^{88} -8.28186i q^{89} -10.6438 q^{91} +(-0.875440 - 0.0339466i) q^{92} +(-4.99263 + 4.80279i) q^{94} +9.09580i q^{97} +(13.2576 + 13.7816i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4}+O(q^{10}) $ 32 * q + 8 * q^4	$ 32 q + 8 q^{4} - 16 q^{16} - 32 q^{19} - 24 q^{34} + 40 q^{46} + 64 q^{49} - 64 q^{64} + 72 q^{76} + 96 q^{91} + 40 q^{94}+O(q^{100}) $ 32 * q + 8 * q^4 - 16 * q^16 - 32 * q^19 - 24 * q^34 + 40 * q^46 + 64 * q^49 - 64 * q^64 + 72 * q^76 + 96 * q^91 + 40 * 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 $

$2$	0.980435	+	1.01919i	0.693272	+	0.720676i
$2$	0.980435	+	1.01919i	0.693272	+	0.720676i
$3$		0			0
$3$		0			0
$4$	−0.0774950	+	1.99850i	−0.0387475	+	0.999249i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	4.53014			1.71223			0.856116	−	0.516784i	$-0.172871\pi$
$7$	4.53014			1.71223			0.856116	+	0.516784i	$0.172871\pi$
$8$	−2.11283	+	1.88042i	−0.746997	+	0.664827i
$9$		0			0
$10$		0			0
$11$			5.63987i			1.70048i	0.526392	+	0.850242i	$0.323545\pi$
$11$			5.63987i			1.70048i	−0.526392	+	0.850242i	$0.676455\pi$
$12$		0			0
$13$	−2.34956			−0.651651			−0.325826	−	0.945430i	$-0.605642\pi$
$13$	−2.34956			−0.651651			−0.325826	+	0.945430i	$0.605642\pi$
$14$	4.44151	+	4.61707i	1.18704	+	1.23396i
$15$		0			0
$16$	−3.98799	−	0.309747i	−0.996997	−	0.0774368i
$17$	5.85906			1.42103			0.710515	−	0.703682i	$-0.248462\pi$
$17$	5.85906			1.42103			0.710515	+	0.703682i	$0.248462\pi$
$18$		0			0
$19$	−3.92808			−0.901163			−0.450582	−	0.892735i	$-0.648783\pi$
$19$	−3.92808			−0.901163			−0.450582	+	0.892735i	$0.648783\pi$
$20$		0			0
$21$		0			0
$22$	−5.74810	+	5.52952i	−1.22550	+	1.17890i
$23$			0.438049i			0.0913395i	0.998957	+	0.0456697i	$0.0145422\pi$
$23$			0.438049i			0.0913395i	−0.998957	+	0.0456697i	$0.985458\pi$
$24$		0			0
$25$		0			0
$26$	−2.30359	−	2.39465i	−0.451771	−	0.469629i
$27$		0			0
$28$	−0.351063	+	9.05347i	−0.0663447	+	1.71095i
$29$	6.09065			1.13101			0.565503	−	0.824746i	$-0.308682\pi$
$29$	6.09065			1.13101			0.565503	+	0.824746i	$0.308682\pi$
$30$		0			0
$31$		−	9.84876i		−	1.76889i	−0.466646	−	0.884444i	$-0.654538\pi$
$31$		−	9.84876i		−	1.76889i	0.466646	−	0.884444i	$-0.345462\pi$
$32$	−3.59427	−	4.36820i	−0.635384	−	0.772197i
$33$		0			0
$34$	5.74442	+	5.97149i	0.985161	+	1.02410i
$35$		0			0
$36$		0			0
$37$	−6.38490			−1.04967			−0.524836	−	0.851204i	$-0.675873\pi$
$37$	−6.38490			−1.04967			−0.524836	+	0.851204i	$0.675873\pi$
$38$	−3.85123	−	4.00346i	−0.624751	−	0.649446i
$39$		0			0
$40$		0			0
$41$			4.00647i			0.625705i	0.949802	+	0.312852i	$0.101285\pi$
$41$			4.00647i			0.625705i	−0.949802	+	0.312852i	$0.898715\pi$
$42$		0			0
$43$			9.90406i			1.51035i	0.655521	+	0.755177i	$0.272449\pi$
$43$			9.90406i			1.51035i	−0.655521	+	0.755177i	$0.727551\pi$
$44$	−11.2713	−	0.437062i	−1.69921	−	0.0658895i
$45$		0			0
$46$	−0.446455	+	0.429478i	−0.0658262	+	0.0633231i
$47$			4.89863i			0.714538i	0.934001	+	0.357269i	$0.116292\pi$
$47$			4.89863i			0.714538i	−0.934001	+	0.357269i	$0.883708\pi$
$48$		0			0
$49$	13.5222			1.93174
$50$		0			0
$51$		0			0
$52$	0.182079	−	4.69559i	0.0252499	−	0.651162i
$53$		−	1.89178i		−	0.259855i	−0.991523	−	0.129928i	$-0.958525\pi$
$53$		−	1.89178i		−	0.259855i	0.991523	−	0.129928i	$-0.0414745\pi$
$54$		0			0
$55$		0			0
$56$	−9.57140	+	8.51854i	−1.27903	+	1.13834i
$57$		0			0
$58$	5.97149	+	6.20753i	0.784095	+	0.815089i
$59$			5.11676i			0.666146i	0.942901	+	0.333073i	$0.108086\pi$
$59$			5.11676i			0.666146i	−0.942901	+	0.333073i	$0.891914\pi$
$60$		0			0
$61$		−	1.90277i		−	0.243625i	−0.992553	−	0.121812i	$-0.961129\pi$
$61$		−	1.90277i		−	0.243625i	0.992553	−	0.121812i	$-0.0388706\pi$
$62$	10.0377	−	9.65606i	1.27480	−	1.22632i
$63$		0			0
$64$	0.928079	−	7.94598i	0.116010	−	0.993248i
$65$		0			0
$66$		0			0
$67$		−	0.691882i		−	0.0845268i	−0.999107	−	0.0422634i	$-0.986543\pi$
$67$		−	0.691882i		−	0.0845268i	0.999107	−	0.0422634i	$-0.0134569\pi$
$68$	−0.454048	+	11.7093i	−0.0550614	+	1.41996i
$69$		0			0
$70$		0			0
$71$	−2.18498			−0.259310			−0.129655	−	0.991559i	$-0.541387\pi$
$71$	−2.18498			−0.259310			−0.129655	+	0.991559i	$0.541387\pi$
$72$		0			0
$73$			0.429801i			0.0503044i	0.999684	+	0.0251522i	$0.00800704\pi$
$73$			0.429801i			0.0503044i	−0.999684	+	0.0251522i	$0.991993\pi$
$74$	−6.25998	−	6.50743i	−0.727708	−	0.756473i
$75$		0			0
$76$	0.304406	−	7.85026i	0.0349178	−	0.900486i
$77$			25.5494i			2.91162i
$78$		0			0
$79$			2.47054i			0.277957i	0.990295	+	0.138979i	$0.0443819\pi$
$79$			2.47054i			0.277957i	−0.990295	+	0.138979i	$0.955618\pi$
$80$		0			0
$81$		0			0
$82$	−4.08335	+	3.92808i	−0.450930	+	0.433784i
$83$	2.28834			0.251178			0.125589	−	0.992082i	$-0.459918\pi$
$83$	2.28834			0.251178			0.125589	+	0.992082i	$0.459918\pi$
$84$		0			0
$85$		0			0
$86$	−10.0941	+	9.71028i	−1.08848	+	1.04709i
$87$		0			0
$88$	−10.6053	−	11.9161i	−1.13053	−	1.27026i
$89$		−	8.28186i		−	0.877875i	−0.898518	−	0.438938i	$-0.855355\pi$
$89$		−	8.28186i		−	0.877875i	0.898518	−	0.438938i	$-0.144645\pi$
$90$		0			0
$91$	−10.6438			−1.11578
$92$	−0.875440	−	0.0339466i	−0.0912709	−	0.00353918i
$93$		0			0
$94$	−4.99263	+	4.80279i	−0.514951	+	0.495370i
$95$		0			0
$96$		0			0
$97$			9.09580i			0.923538i	0.887000	+	0.461769i	$0.152785\pi$
$97$			9.09580i			0.923538i	−0.887000	+	0.461769i	$0.847215\pi$
$98$	13.2576	+	13.7816i	1.33922	+	1.39216i
$99$		0			0
$100$		0			0
$101$	14.7049			1.46320			0.731598	−	0.681736i	$-0.238775\pi$
$101$	14.7049			1.46320			0.731598	+	0.681736i	$0.238775\pi$
$102$		0			0
$103$	−7.54720			−0.743648			−0.371824	−	0.928303i	$-0.621267\pi$
$103$	−7.54720			−0.743648			−0.371824	+	0.928303i	$0.621267\pi$
$104$	4.96422	−	4.41815i	0.486782	−	0.433235i
$105$		0			0
$106$	1.92808	−	1.85476i	0.187272	−	0.180151i
$107$	5.97653			0.577773			0.288887	−	0.957363i	$-0.406715\pi$
$107$	5.97653			0.577773			0.288887	+	0.957363i	$0.406715\pi$
$108$		0			0
$109$		−	16.5558i		−	1.58575i	−0.609382	−	0.792877i	$-0.708582\pi$
$109$		−	16.5558i		−	1.58575i	0.609382	−	0.792877i	$-0.291418\pi$
$110$		0			0
$111$		0			0
$112$	−18.0661	−	1.40320i	−1.70709	−	0.132590i
$113$	−11.1103			−1.04517			−0.522584	−	0.852588i	$-0.675032\pi$
$113$	−11.1103			−1.04517			−0.522584	+	0.852588i	$0.675032\pi$
$114$		0			0
$115$		0			0
$116$	−0.471995	+	12.1722i	−0.0438237	+	1.13016i
$117$		0			0
$118$	−5.21495	+	5.01665i	−0.480075	+	0.461820i
$119$	26.5423			2.43313
$120$		0			0
$121$	−20.8081			−1.89165
$122$	1.93928	−	1.86554i	0.175575	−	0.168898i
$123$		0			0
$124$	19.6827	+	0.763229i	1.76756	+	0.0685400i
$125$		0			0
$126$		0			0
$127$	13.1399			1.16598			0.582989	−	0.812480i	$-0.301883\pi$
$127$	13.1399			1.16598			0.582989	+	0.812480i	$0.301883\pi$
$128$	9.00839	−	6.84463i	0.796236	−	0.604986i
$129$		0			0
$130$		0			0
$131$		−	14.4618i		−	1.26353i	−0.775158	−	0.631767i	$-0.782330\pi$
$131$		−	14.4618i		−	1.26353i	0.775158	−	0.631767i	$-0.217670\pi$
$132$		0			0
$133$	−17.7947			−1.54300
$134$	0.705158	−	0.678345i	0.0609164	−	0.0586001i
$135$		0			0
$136$	−12.3792	+	11.0175i	−1.06151	+	0.944739i
$137$	−20.0991			−1.71718			−0.858589	−	0.512665i	$-0.828658\pi$
$137$	−20.0991			−1.71718			−0.858589	+	0.512665i	$0.828658\pi$
$138$		0			0
$139$	−1.11638			−0.0946898			−0.0473449	−	0.998879i	$-0.515076\pi$
$139$	−1.11638			−0.0946898			−0.0473449	+	0.998879i	$0.515076\pi$
$140$		0			0
$141$		0			0
$142$	−2.14223	−	2.22691i	−0.179772	−	0.186878i
$143$		−	13.2512i		−	1.10812i
$144$		0			0
$145$		0			0
$146$	−0.438049	+	0.421392i	−0.0362532	+	0.0348746i
$147$		0			0
$148$	0.494798	−	12.7602i	0.0406721	−	1.04888i
$149$	−13.8604			−1.13548			−0.567742	−	0.823206i	$-0.692183\pi$
$149$	−13.8604			−1.13548			−0.567742	+	0.823206i	$0.692183\pi$
$150$		0			0
$151$		−	9.22926i		−	0.751067i	−0.926809	−	0.375533i	$-0.877460\pi$
$151$		−	9.22926i		−	0.751067i	0.926809	−	0.375533i	$-0.122540\pi$
$152$	8.29935	−	7.38642i	0.673166	−	0.599118i
$153$		0			0
$154$	−26.0397	+	25.0495i	−2.09834	+	2.01855i
$155$		0			0
$156$		0			0
$157$	17.5528			1.40086			0.700432	−	0.713719i	$-0.252990\pi$
$157$	17.5528			1.40086			0.700432	+	0.713719i	$0.252990\pi$
$158$	−2.51795	+	2.42220i	−0.200317	+	0.192700i
$159$		0			0
$160$		0			0
$161$			1.98442i			0.156394i
$162$		0			0
$163$			1.18830i			0.0930746i	0.998917	+	0.0465373i	$0.0148186\pi$
$163$			1.18830i			0.0930746i	−0.998917	+	0.0465373i	$0.985181\pi$
$164$	−8.00691	−	0.310481i	−0.625235	−	0.0242445i
$165$		0			0
$166$	2.24357	+	2.33225i	0.174134	+	0.181018i
$167$			9.99633i			0.773539i	0.922176	+	0.386770i	$0.126409\pi$
$167$			9.99633i			0.773539i	−0.922176	+	0.386770i	$0.873591\pi$
$168$		0			0
$169$	−7.47956			−0.575351
$170$		0			0
$171$		0			0
$172$	−19.7932	−	0.767515i	−1.50922	−	0.0585225i
$173$			14.8760i			1.13100i	0.824747	+	0.565502i	$0.191317\pi$
$173$			14.8760i			1.13100i	−0.824747	+	0.565502i	$0.808683\pi$
$174$		0			0
$175$		0			0
$176$	1.74693	−	22.4917i	0.131680	−	1.69538i
$177$		0			0
$178$	8.44078	−	8.11982i	0.632663	−	0.608606i
$179$			7.30339i			0.545881i	0.962031	+	0.272940i	$0.0879962\pi$
$179$			7.30339i			0.545881i	−0.962031	+	0.272940i	$0.912004\pi$
$180$		0			0
$181$		−	22.6987i		−	1.68718i	−0.536987	−	0.843591i	$-0.680438\pi$
$181$		−	22.6987i		−	1.68718i	0.536987	−	0.843591i	$-0.319562\pi$
$182$	−10.4356	−	10.8481i	−0.773537	−	0.804114i
$183$		0			0
$184$	−0.823713	−	0.925521i	−0.0607250	−	0.0682303i
$185$		0			0
$186$		0			0
$187$			33.0443i			2.41644i
$188$	−9.78990	−	0.379619i	−0.714002	−	0.0276866i
$189$		0			0
$190$		0			0
$191$	10.8672			0.786320			0.393160	−	0.919470i	$-0.371382\pi$
$191$	10.8672			0.786320			0.393160	+	0.919470i	$0.371382\pi$
$192$		0			0
$193$		−	11.9022i		−	0.856739i	−0.903604	−	0.428369i	$-0.859088\pi$
$193$		−	11.9022i		−	0.856739i	0.903604	−	0.428369i	$-0.140912\pi$
$194$	−9.27034	+	8.91784i	−0.665572	+	0.640263i
$195$		0			0
$196$	−1.04790	+	27.0240i	−0.0748500	+	1.93029i
$197$			1.81483i			0.129301i	0.997908	+	0.0646505i	$0.0205933\pi$
$197$			1.81483i			0.129301i	−0.997908	+	0.0646505i	$0.979407\pi$
$198$		0			0
$199$			9.75274i			0.691353i	0.938354	+	0.345677i	$0.112351\pi$
$199$			9.75274i			0.691353i	−0.938354	+	0.345677i	$0.887649\pi$
$200$		0			0
$201$		0			0
$202$	14.4172	+	14.9871i	1.01439	+	1.05449i
$203$	27.5915			1.93654
$204$		0			0
$205$		0			0
$206$	−7.39954	−	7.69203i	−0.515550	−	0.535929i
$207$		0			0
$208$	9.37002	+	0.727770i	0.649694	+	0.0504618i
$209$		−	22.1538i		−	1.53241i
$210$		0			0
$211$	21.7362			1.49638			0.748191	−	0.663484i	$-0.230923\pi$
$211$	21.7362			1.49638			0.748191	+	0.663484i	$0.230923\pi$
$212$	3.78071	+	0.146603i	0.259660	+	0.0100687i
$213$		0			0
$214$	5.85960	+	6.09122i	0.400554	+	0.416387i
$215$		0			0
$216$		0			0
$217$		−	44.6162i		−	3.02875i
$218$	16.8734	−	16.2318i	1.14281	−	1.09936i
$219$		0			0
$220$		0			0
$221$	−13.7662			−0.926016
$222$		0			0
$223$	20.7601			1.39020			0.695099	−	0.718914i	$-0.255361\pi$
$223$	20.7601			1.39020			0.695099	+	0.718914i	$0.255361\pi$
$224$	−16.2826	−	19.7886i	−1.08792	−	1.32218i
$225$		0			0
$226$	−10.8929	−	11.3235i	−0.724586	−	0.753227i
$227$	19.5108			1.29498			0.647490	−	0.762074i	$-0.275819\pi$
$227$	19.5108			1.29498			0.647490	+	0.762074i	$0.275819\pi$
$228$		0			0
$229$		−	20.2653i		−	1.33917i	−0.742737	−	0.669584i	$-0.766473\pi$
$229$		−	20.2653i		−	1.33917i	0.742737	−	0.669584i	$-0.233527\pi$
$230$		0			0
$231$		0			0
$232$	−12.8685	+	11.4530i	−0.844859	+	0.751924i
$233$	21.3814			1.40074			0.700372	−	0.713778i	$-0.253017\pi$
$233$	21.3814			1.40074			0.700372	+	0.713778i	$0.253017\pi$
$234$		0			0
$235$		0			0
$236$	−10.2258	−	0.396524i	−0.665646	−	0.0258115i
$237$		0			0
$238$	26.0230	+	27.0517i	1.68682	+	1.75350i
$239$	20.2897			1.31243			0.656214	−	0.754575i	$-0.272157\pi$
$239$	20.2897			1.31243			0.656214	+	0.754575i	$0.272157\pi$
$240$		0			0
$241$	9.09580			0.585912			0.292956	−	0.956126i	$-0.405361\pi$
$241$	9.09580			0.585912			0.292956	+	0.956126i	$0.405361\pi$
$242$	−20.4010	−	21.2074i	−1.31143	−	1.36326i
$243$		0			0
$244$	3.80268	+	0.147455i	0.243442	+	0.00943986i
$245$		0			0
$246$		0			0
$247$	9.22926			0.587244
$248$	18.5197	+	20.8087i	1.17601	+	1.32136i
$249$		0			0
$250$		0			0
$251$			0.641803i			0.0405102i	0.999795	+	0.0202551i	$0.00644784\pi$
$251$			0.641803i			0.0405102i	−0.999795	+	0.0202551i	$0.993552\pi$
$252$		0			0
$253$	−2.47054			−0.155321
$254$	12.8828	+	13.3921i	0.808340	+	0.840292i
$255$		0			0
$256$	15.8081	+	2.47054i	0.988007	+	0.154409i
$257$	3.87464			0.241693			0.120847	−	0.992671i	$-0.461439\pi$
$257$	3.87464			0.241693			0.120847	+	0.992671i	$0.461439\pi$
$258$		0			0
$259$	−28.9245			−1.79728
$260$		0			0
$261$		0			0
$262$	14.7393	−	14.1789i	0.910599	−	0.875973i
$263$		−	29.1654i		−	1.79841i	−0.437524	−	0.899207i	$-0.644144\pi$
$263$		−	29.1654i		−	1.79841i	0.437524	−	0.899207i	$-0.355856\pi$
$264$		0			0
$265$		0			0
$266$	−17.4466	−	18.1362i	−1.06972	−	1.11200i
$267$		0			0
$268$	1.38272	+	0.0536174i	0.0844633	+	0.00327520i
$269$	1.72069			0.104912			0.0524562	−	0.998623i	$-0.483295\pi$
$269$	1.72069			0.104912			0.0524562	+	0.998623i	$0.483295\pi$
$270$		0			0
$271$			1.85848i			0.112895i	0.998406	+	0.0564474i	$0.0179773\pi$
$271$			1.85848i			0.112895i	−0.998406	+	0.0564474i	$0.982023\pi$
$272$	−23.3659	−	1.81483i	−1.41676	−	0.110040i
$273$		0			0
$274$	−19.7058	−	20.4847i	−1.19047	−	1.23753i
$275$		0			0
$276$		0			0
$277$	−3.24314			−0.194862			−0.0974308	−	0.995242i	$-0.531062\pi$
$277$	−3.24314			−0.194862			−0.0974308	+	0.995242i	$0.531062\pi$
$278$	−1.09453	−	1.13780i	−0.0656458	−	0.0682406i
$279$		0			0
$280$		0			0
$281$			8.24911i			0.492100i	0.969257	+	0.246050i	$0.0791328\pi$
$281$			8.24911i			0.492100i	−0.969257	+	0.246050i	$0.920867\pi$
$282$		0			0
$283$		−	10.1677i		−	0.604408i	−0.953243	−	0.302204i	$-0.902278\pi$
$283$		−	10.1677i		−	0.604408i	0.953243	−	0.302204i	$-0.0977224\pi$
$284$	0.169325	−	4.36668i	0.0100476	−	0.259115i
$285$		0			0
$286$	13.5055	−	12.9920i	0.798597	−	0.768230i
$287$			18.1498i			1.07135i
$288$		0			0
$289$	17.3286			1.01933
$290$		0			0
$291$		0			0
$292$	−0.858957	−	0.0333074i	−0.0502666	−	0.00194917i
$293$		−	21.6717i		−	1.26607i	−0.774122	−	0.633037i	$-0.781808\pi$
$293$		−	21.6717i		−	1.26607i	0.774122	−	0.633037i	$-0.218192\pi$
$294$		0			0
$295$		0			0
$296$	13.4902	−	12.0063i	0.784102	−	0.697850i
$297$		0			0
$298$	−13.5892	−	14.1263i	−0.787200	−	0.818316i
$299$		−	1.02922i		−	0.0595215i
$300$		0			0
$301$			44.8667i			2.58608i
$302$	9.40637	−	9.04869i	0.541276	−	0.520694i
$303$		0			0
$304$	15.6651	+	1.21671i	0.898457	+	0.0697832i
$305$		0			0
$306$		0			0
$307$		−	6.93152i		−	0.395603i	−0.980242	−	0.197801i	$-0.936620\pi$
$307$		−	6.93152i		−	0.395603i	0.980242	−	0.197801i	$-0.0633801\pi$
$308$	−51.0604	−	1.97995i	−2.90944	−	0.112818i
$309$		0			0
$310$		0			0
$311$	14.8043			0.839477			0.419739	−	0.907645i	$-0.362122\pi$
$311$	14.8043			0.839477			0.419739	+	0.907645i	$0.362122\pi$
$312$		0			0
$313$		−	14.3783i		−	0.812710i	−0.913715	−	0.406355i	$-0.866800\pi$
$313$		−	14.3783i		−	0.812710i	0.913715	−	0.406355i	$-0.133200\pi$
$314$	17.2094	+	17.8896i	0.971181	+	1.00957i
$315$		0			0
$316$	−4.93736	−	0.191454i	−0.277748	−	0.0107701i
$317$			5.92336i			0.332689i	0.986068	+	0.166345i	$0.0531964\pi$
$317$			5.92336i			0.332689i	−0.986068	+	0.166345i	$0.946804\pi$
$318$		0			0
$319$			34.3505i			1.92326i
$320$		0			0
$321$		0			0
$322$	−2.02250	+	1.94560i	−0.112710	+	0.108424i
$323$	−23.0148			−1.28058
$324$		0			0
$325$		0			0
$326$	−1.21110	+	1.16505i	−0.0670766	+	0.0645261i
$327$		0			0
$328$	−7.53382	−	8.46497i	−0.415986	−	0.467400i
$329$			22.1915i			1.22346i
$330$		0			0
$331$	31.1641			1.71294			0.856468	−	0.516200i	$-0.172654\pi$
$331$	31.1641			1.71294			0.856468	+	0.516200i	$0.172654\pi$
$332$	−0.177335	+	4.57324i	−0.00973251	+	0.250989i
$333$		0			0
$334$	−10.1882	+	9.80075i	−0.557471	+	0.536273i
$335$		0			0
$336$		0			0
$337$		−	2.42636i		−	0.132172i	−0.997814	−	0.0660860i	$-0.978949\pi$
$337$		−	2.42636i		−	0.132172i	0.997814	−	0.0660860i	$-0.0210512\pi$
$338$	−7.33322	−	7.62309i	−0.398875	−	0.414642i
$339$		0			0
$340$		0			0
$341$	55.5457			3.00797
$342$		0			0
$343$	29.5463			1.59535
$344$	−18.6237	−	20.9256i	−1.00412	−	1.12823i
$345$		0			0
$346$	−15.1615	+	14.5850i	−0.815087	+	0.784093i
$347$	−11.8538			−0.636345			−0.318173	−	0.948033i	$-0.603069\pi$
$347$	−11.8538			−0.636345			−0.318173	+	0.948033i	$0.603069\pi$
$348$		0			0
$349$		−	35.5895i		−	1.90506i	−0.304443	−	0.952531i	$-0.598470\pi$
$349$		−	35.5895i		−	1.90506i	0.304443	−	0.952531i	$-0.401530\pi$
$350$		0			0
$351$		0			0
$352$	24.6361	−	20.2712i	1.31311	−	1.08046i
$353$	−18.8870			−1.00526			−0.502628	−	0.864503i	$-0.667633\pi$
$353$	−18.8870			−1.00526			−0.502628	+	0.864503i	$0.667633\pi$
$354$		0			0
$355$		0			0
$356$	16.5513	+	0.641803i	0.877216	+	0.0340155i
$357$		0			0
$358$	−7.44354	+	7.16050i	−0.393403	+	0.378444i
$359$	−10.8724			−0.573825			−0.286912	−	0.957957i	$-0.592629\pi$
$359$	−10.8724			−0.573825			−0.286912	+	0.957957i	$0.592629\pi$
$360$		0			0
$361$	−3.57020			−0.187905
$362$	23.1343	−	22.2546i	1.21591	−	1.16968i
$363$		0			0
$364$	0.824844	−	21.2717i	0.0432336	−	1.11494i
$365$		0			0
$366$		0			0
$367$	18.2574			0.953029			0.476514	−	0.879167i	$-0.341900\pi$
$367$	18.2574			0.953029			0.476514	+	0.879167i	$0.341900\pi$
$368$	0.135684	−	1.74693i	0.00707304	−	0.0910652i
$369$		0			0
$370$		0			0
$371$		−	8.57001i		−	0.444933i
$372$		0			0
$373$	−28.2914			−1.46487			−0.732437	−	0.680835i	$-0.761617\pi$
$373$	−28.2914			−1.46487			−0.732437	+	0.680835i	$0.761617\pi$
$374$	−33.6784	+	32.3978i	−1.74147	+	1.67525i
$375$		0			0
$376$	−9.21146	−	10.3500i	−0.475045	−	0.533758i
$377$	−14.3104			−0.737021
$378$		0			0
$379$	−20.9724			−1.07728			−0.538640	−	0.842536i	$-0.681062\pi$
$379$	−20.9724			−1.07728			−0.538640	+	0.842536i	$0.681062\pi$
$380$		0			0
$381$		0			0
$382$	10.6545	+	11.0757i	0.545134	+	0.566682i
$383$			25.8706i			1.32192i	0.750419	+	0.660962i	$0.229852\pi$
$383$			25.8706i			1.32192i	−0.750419	+	0.660962i	$0.770148\pi$
$384$		0			0
$385$		0			0
$386$	12.1306	−	11.6693i	0.617431	−	0.593953i
$387$		0			0
$388$	−18.1779	−	0.704879i	−0.922845	−	0.0357848i
$389$	−1.64754			−0.0835334			−0.0417667	−	0.999127i	$-0.513299\pi$
$389$	−1.64754			−0.0835334			−0.0417667	+	0.999127i	$0.513299\pi$
$390$		0			0
$391$			2.56655i			0.129796i
$392$	−28.5700	+	25.4273i	−1.44300	+	1.28427i
$393$		0			0
$394$	−1.84965	+	1.77932i	−0.0931842	+	0.0896408i
$395$		0			0
$396$		0			0
$397$	−12.6488			−0.634826			−0.317413	−	0.948287i	$-0.602814\pi$
$397$	−12.6488			−0.634826			−0.317413	+	0.948287i	$0.602814\pi$
$398$	−9.93989	+	9.56193i	−0.498242	+	0.479296i
$399$		0			0
$400$		0			0
$401$		−	12.4578i		−	0.622112i	−0.950392	−	0.311056i	$-0.899317\pi$
$401$		−	12.4578i		−	0.622112i	0.950392	−	0.311056i	$-0.100683\pi$
$402$		0			0
$403$			23.1403i			1.15270i
$404$	−1.13956	+	29.3878i	−0.0566952	+	1.46210i
$405$		0			0
$406$	27.0517	+	28.1210i	1.34255	+	1.39562i
$407$		−	36.0100i		−	1.78495i
$408$		0			0
$409$	30.8544			1.52565			0.762827	−	0.646603i	$-0.223811\pi$
$409$	30.8544			1.52565			0.762827	+	0.646603i	$0.223811\pi$
$410$		0			0
$411$		0			0
$412$	0.584870	−	15.0831i	0.0288145	−	0.743089i
$413$			23.1796i			1.14060i
$414$		0			0
$415$		0			0
$416$	8.44496	+	10.2634i	0.414048	+	0.503203i
$417$		0			0
$418$	22.5790	−	21.7204i	1.10437	−	1.06238i
$419$			5.06581i			0.247481i	0.992315	+	0.123740i	$0.0394890\pi$
$419$			5.06581i			0.247481i	−0.992315	+	0.123740i	$0.960511\pi$
$420$		0			0
$421$		−	2.33741i		−	0.113918i	−0.998377	−	0.0569591i	$-0.981860\pi$
$421$		−	2.33741i		−	0.113918i	0.998377	−	0.0569591i	$-0.0181405\pi$
$422$	21.3109	+	22.1533i	1.03740	+	1.07841i
$423$		0			0
$424$	3.55732	+	3.99700i	0.172759	+	0.194111i
$425$		0			0
$426$		0			0
$427$		−	8.61982i		−	0.417142i
$428$	−0.463152	+	11.9441i	−0.0223873	+	0.577339i
$429$		0			0
$430$		0			0
$431$	−21.1605			−1.01927			−0.509633	−	0.860392i	$-0.670219\pi$
$431$	−21.1605			−1.01927			−0.509633	+	0.860392i	$0.670219\pi$
$432$		0			0
$433$		−	18.9983i		−	0.912999i	−0.889724	−	0.456499i	$-0.849103\pi$
$433$		−	18.9983i		−	0.912999i	0.889724	−	0.456499i	$-0.150897\pi$
$434$	45.4724	−	43.7433i	2.18274	−	2.09975i
$435$		0			0
$436$	33.0866	+	1.28299i	1.58456	+	0.0614440i
$437$		−	1.72069i		−	0.0823118i
$438$		0			0
$439$		−	8.61721i		−	0.411277i	−0.978628	−	0.205638i	$-0.934073\pi$
$439$		−	8.61721i		−	0.411277i	0.978628	−	0.205638i	$-0.0659271\pi$
$440$		0			0
$441$		0			0
$442$	−13.4969	−	14.0304i	−0.641981	−	0.667357i
$443$	−25.9618			−1.23348			−0.616740	−	0.787167i	$-0.711547\pi$
$443$	−25.9618			−1.23348			−0.616740	+	0.787167i	$0.711547\pi$
$444$		0			0
$445$		0			0
$446$	20.3539	+	21.1585i	0.963785	+	1.00188i
$447$		0			0
$448$	4.20432	−	35.9964i	0.198636	−	1.70067i
$449$		−	10.0641i		−	0.474953i	−0.971393	−	0.237477i	$-0.923680\pi$
$449$		−	10.0641i		−	0.474953i	0.971393	−	0.237477i	$-0.0763203\pi$
$450$		0			0
$451$	−22.5959			−1.06400
$452$	0.860992	−	22.2039i	0.0404976	−	1.04438i
$453$		0			0
$454$	19.1291	+	19.8852i	0.897773	+	0.933261i
$455$		0			0
$456$		0			0
$457$			1.38376i			0.0647297i	0.999476	+	0.0323649i	$0.0103039\pi$
$457$			1.38376i			0.0647297i	−0.999476	+	0.0323649i	$0.989696\pi$
$458$	20.6542	−	19.8688i	0.965106	−	0.928407i
$459$		0			0
$460$		0			0
$461$	−39.9331			−1.85987			−0.929936	−	0.367722i	$-0.880138\pi$
$461$	−39.9331			−1.85987			−0.929936	+	0.367722i	$0.880138\pi$
$462$		0			0
$463$	−21.9582			−1.02049			−0.510243	−	0.860030i	$-0.670444\pi$
$463$	−21.9582			−1.02049			−0.510243	+	0.860030i	$0.670444\pi$
$464$	−24.2895	−	1.88656i	−1.12761	−	0.0875815i
$465$		0			0
$466$	20.9631	+	21.7917i	0.971097	+	1.00948i
$467$	2.61046			0.120798			0.0603988	−	0.998174i	$-0.480763\pi$
$467$	2.61046			0.120798			0.0603988	+	0.998174i	$0.480763\pi$
$468$		0			0
$469$		−	3.13432i		−	0.144729i
$470$		0			0
$471$		0			0
$472$	−9.62164	−	10.8108i	−0.442872	−	0.497609i
$473$	−55.8576			−2.56833
$474$		0			0
$475$		0			0
$476$	−2.05690	+	53.0448i	−0.0942778	+	2.43131i
$477$		0			0
$478$	19.8927	+	20.6790i	0.909870	+	0.945836i
$479$	−15.4816			−0.707374			−0.353687	−	0.935364i	$-0.615072\pi$
$479$	−15.4816			−0.707374			−0.353687	+	0.935364i	$0.615072\pi$
$480$		0			0
$481$	15.0017			0.684019
$482$	8.91784	+	9.27034i	0.406196	+	0.422253i
$483$		0			0
$484$	1.61252	−	41.5850i	0.0732966	−	1.89023i
$485$		0			0
$486$		0			0
$487$	13.8324			0.626804			0.313402	−	0.949620i	$-0.398531\pi$
$487$	13.8324			0.626804			0.313402	+	0.949620i	$0.398531\pi$
$488$	3.57800	+	4.02023i	0.161968	+	0.181987i
$489$		0			0
$490$		0			0
$491$		−	8.41734i		−	0.379869i	−0.981797	−	0.189935i	$-0.939172\pi$
$491$		−	8.41734i		−	0.379869i	0.981797	−	0.189935i	$-0.0608276\pi$
$492$		0			0
$493$	35.6855			1.60719
$494$	9.04869	+	9.40637i	0.407120	+	0.423212i
$495$		0			0
$496$	−3.05062	+	39.2767i	−0.136977	+	1.76358i
$497$	−9.89827			−0.443998
$498$		0			0
$499$	−6.56834			−0.294039			−0.147020	−	0.989134i	$-0.546968\pi$
$499$	−6.56834			−0.294039			−0.147020	+	0.989134i	$0.546968\pi$
$500$		0			0
$501$		0			0
$502$	−0.654119	+	0.629246i	−0.0291947	+	0.0280846i
$503$			0.677028i			0.0301872i	0.999886	+	0.0150936i	$0.00480462\pi$
$503$			0.677028i			0.0301872i	−0.999886	+	0.0150936i	$0.995195\pi$
$504$		0			0
$505$		0			0
$506$	−2.42220	−	2.51795i	−0.107680	−	0.111936i
$507$		0			0
$508$	−1.01828	+	26.2601i	−0.0451787	+	1.16510i
$509$	−29.6713			−1.31516			−0.657579	−	0.753386i	$-0.728419\pi$
$509$	−29.6713			−1.31516			−0.657579	+	0.753386i	$0.728419\pi$
$510$		0			0
$511$			1.94706i			0.0861328i
$512$	12.9809	+	18.5337i	0.573679	+	0.819080i
$513$		0			0
$514$	3.79883	+	3.94899i	0.167559	+	0.174182i
$515$		0			0
$516$		0			0
$517$	−27.6276			−1.21506
$518$	−28.3586	−	29.4795i	−1.24600	−	1.29526i
$519$		0			0
$520$		0			0
$521$		−	3.84189i		−	0.168316i	−0.996452	−	0.0841580i	$-0.973180\pi$
$521$		−	3.84189i		−	0.168316i	0.996452	−	0.0841580i	$-0.0268201\pi$
$522$		0			0
$523$			30.4722i			1.33246i	0.745747	+	0.666229i	$0.232093\pi$
$523$			30.4722i			1.33246i	−0.745747	+	0.666229i	$0.767907\pi$
$524$	28.9019	+	1.12072i	1.26259	+	0.0489588i
$525$		0			0
$526$	29.7250	−	28.5947i	1.29607	−	1.24679i
$527$		−	57.7044i		−	2.51364i
$528$		0			0
$529$	22.8081			0.991657
$530$		0			0
$531$		0			0
$532$	1.37900	−	35.5628i	0.0597874	−	1.54184i
$533$		−	9.41344i		−	0.407741i
$534$		0			0
$535$		0			0
$536$	1.30102	+	1.46183i	0.0561957	+	0.0631413i
$537$		0			0
$538$	1.68702	+	1.75371i	0.0727328	+	0.0756078i
$539$			76.2632i			3.28489i
$540$		0			0
$541$			23.8417i			1.02503i	0.858677	+	0.512517i	$0.171287\pi$
$541$			23.8417i			1.02503i	−0.858677	+	0.512517i	$0.828713\pi$
$542$	−1.89415	+	1.82212i	−0.0813606	+	0.0782668i
$543$		0			0
$544$	−21.0590	−	25.5936i	−0.902899	−	1.09731i
$545$		0			0
$546$		0			0
$547$		−	17.2602i		−	0.737994i	−0.929431	−	0.368997i	$-0.879701\pi$
$547$		−	17.2602i		−	0.737994i	0.929431	−	0.368997i	$-0.120299\pi$
$548$	1.55758	−	40.1679i	0.0665364	−	1.71589i
$549$		0			0
$550$		0			0
$551$	−23.9246			−1.01922
$552$		0			0
$553$			11.1919i			0.475927i
$554$	−3.17969	−	3.30538i	−0.135092	−	0.140432i
$555$		0			0
$556$	0.0865136	−	2.23108i	0.00366899	−	0.0946187i
$557$			5.70683i			0.241806i	0.992664	+	0.120903i	$0.0385790\pi$
$557$			5.70683i			0.241806i	−0.992664	+	0.120903i	$0.961421\pi$
$558$		0			0
$559$		−	23.2702i		−	0.984224i
$560$		0			0
$561$		0			0
$562$	−8.40740	+	8.08771i	−0.354645	+	0.341160i
$563$	39.5446			1.66661			0.833303	−	0.552817i	$-0.186447\pi$
$563$	39.5446			1.66661			0.833303	+	0.552817i	$0.186447\pi$
$564$		0			0
$565$		0			0
$566$	10.3628	−	9.96879i	0.435582	−	0.419019i
$567$		0			0
$568$	4.61649	−	4.10867i	0.193704	−	0.172396i
$569$		−	28.3846i		−	1.18994i	−0.803747	−	0.594971i	$-0.797163\pi$
$569$		−	28.3846i		−	1.18994i	0.803747	−	0.594971i	$-0.202837\pi$
$570$		0			0
$571$	13.1680			0.551064			0.275532	−	0.961292i	$-0.411146\pi$
$571$	13.1680			0.551064			0.275532	+	0.961292i	$0.411146\pi$
$572$	26.4825	+	1.02690i	1.10729	+	0.0429370i
$573$		0			0
$574$	−18.4981	+	17.7947i	−0.772097	+	0.742738i
$575$		0			0
$576$		0			0
$577$			12.0961i			0.503566i	0.967784	+	0.251783i	$0.0810170\pi$
$577$			12.0961i			0.503566i	−0.967784	+	0.251783i	$0.918983\pi$
$578$	16.9895	+	17.6611i	0.706671	+	0.734604i
$579$		0			0
$580$		0			0
$581$	10.3665			0.430074
$582$		0			0
$583$	10.6694			0.441880
$584$	−0.808204	−	0.908095i	−0.0334437	−	0.0375773i
$585$		0			0
$586$	22.0876	−	21.2477i	0.912429	−	0.877734i
$587$	−38.7433			−1.59911			−0.799553	−	0.600596i	$-0.794930\pi$
$587$	−38.7433			−1.59911			−0.799553	+	0.600596i	$0.794930\pi$
$588$		0			0
$589$			38.6867i			1.59406i
$590$		0			0
$591$		0			0
$592$	25.4629	+	1.97771i	1.04652	+	0.0812832i
$593$	9.29044			0.381513			0.190756	−	0.981637i	$-0.438906\pi$
$593$	9.29044			0.381513			0.190756	+	0.981637i	$0.438906\pi$
$594$		0			0
$595$		0			0
$596$	1.07411	−	27.6999i	0.0439972	−	1.13463i
$597$		0			0
$598$	1.04897	−	1.00909i	0.0428957	−	0.0412646i
$599$	7.67556			0.313615			0.156807	−	0.987629i	$-0.449880\pi$
$599$	7.67556			0.313615			0.156807	+	0.987629i	$0.449880\pi$
$600$		0			0
$601$	21.1421			0.862405			0.431202	−	0.902255i	$-0.358089\pi$
$601$	21.1421			0.862405			0.431202	+	0.902255i	$0.358089\pi$
$602$	−45.7277	+	43.9889i	−1.86372	+	1.79285i
$603$		0			0
$604$	18.4447	+	0.715222i	0.750503	+	0.0291020i
$605$		0			0
$606$		0			0
$607$	11.1928			0.454304			0.227152	−	0.973859i	$-0.427059\pi$
$607$	11.1928			0.454304			0.227152	+	0.973859i	$0.427059\pi$
$608$	14.1186	+	17.1586i	0.572584	+	0.695875i
$609$		0			0
$610$		0			0
$611$		−	11.5096i		−	0.465630i
$612$		0			0
$613$	24.1547			0.975598			0.487799	−	0.872956i	$-0.337800\pi$
$613$	24.1547			0.975598			0.487799	+	0.872956i	$0.337800\pi$
$614$	7.06454	−	6.79591i	0.285102	−	0.274260i
$615$		0			0
$616$	−48.0434	−	53.9814i	−1.93573	−	2.17497i
$617$	26.5659			1.06950			0.534752	−	0.845009i	$-0.320405\pi$
$617$	26.5659			1.06950			0.534752	+	0.845009i	$0.320405\pi$
$618$		0			0
$619$	22.0239			0.885214			0.442607	−	0.896716i	$-0.354054\pi$
$619$	22.0239			0.885214			0.442607	+	0.896716i	$0.354054\pi$
$620$		0			0
$621$		0			0
$622$	14.5147	+	15.0884i	0.581986	+	0.604991i
$623$		−	37.5180i		−	1.50313i
$624$		0			0
$625$		0			0
$626$	14.6542	−	14.0970i	0.585701	−	0.563429i
$627$		0			0
$628$	−1.36025	+	35.0792i	−0.0542800	+	1.39981i
$629$	−37.4095			−1.49161
$630$		0			0
$631$		−	9.22926i		−	0.367411i	−0.982981	−	0.183706i	$-0.941191\pi$
$631$		−	9.22926i		−	0.367411i	0.982981	−	0.183706i	$-0.0588093\pi$
$632$	−4.64564	−	5.21982i	−0.184793	−	0.207633i
$633$		0			0
$634$	−6.03703	+	5.80747i	−0.239761	+	0.230644i
$635$		0			0
$636$		0			0
$637$	−31.7711			−1.25882
$638$	−35.0097	+	33.6784i	−1.38605	+	1.33334i
$639$		0			0
$640$		0			0
$641$		−	12.8925i		−	0.509223i	−0.967043	−	0.254612i	$-0.918052\pi$
$641$		−	12.8925i		−	0.509223i	0.967043	−	0.254612i	$-0.0819476\pi$
$642$		0			0
$643$			3.26394i			0.128717i	0.997927	+	0.0643587i	$0.0205002\pi$
$643$			3.26394i			0.128717i	−0.997927	+	0.0643587i	$0.979500\pi$
$644$	−3.96586	−	0.153783i	−0.156277	−	0.00605989i
$645$		0			0
$646$	−22.5645	−	23.4565i	−0.887790	−	0.922883i
$647$			1.21827i			0.0478951i	0.999713	+	0.0239476i	$0.00762347\pi$
$647$			1.21827i			0.0478951i	−0.999713	+	0.0239476i	$0.992377\pi$
$648$		0			0
$649$	−28.8579			−1.13277
$650$		0			0
$651$		0			0
$652$	−2.37481	−	0.0920871i	−0.0930047	−	0.00360641i
$653$			28.7952i			1.12684i	0.826169	+	0.563422i	$0.190515\pi$
$653$			28.7952i			1.12684i	−0.826169	+	0.563422i	$0.809485\pi$
$654$		0			0
$655$		0			0
$656$	1.24099	−	15.9777i	0.0484526	−	0.623826i
$657$		0			0
$658$	−22.6173	+	21.7573i	−0.881715	+	0.848187i
$659$		−	29.8143i		−	1.16140i	−0.814117	−	0.580701i	$-0.802779\pi$
$659$		−	29.8143i		−	1.16140i	0.814117	−	0.580701i	$-0.197221\pi$
$660$		0			0
$661$			12.2785i			0.477577i	0.971072	+	0.238788i	$0.0767502\pi$
$661$			12.2785i			0.477577i	−0.971072	+	0.238788i	$0.923250\pi$
$662$	30.5544	+	31.7622i	1.18753	+	1.23447i
$663$		0			0
$664$	−4.83486	+	4.30302i	−0.187629	+	0.166990i
$665$		0			0
$666$		0			0
$667$			2.66800i			0.103306i
$668$	−19.9776	−	0.774665i	−0.772958	−	0.0299727i
$669$		0			0
$670$		0			0
$671$	10.7314			0.414280
$672$		0			0
$673$		−	4.19016i		−	0.161519i	−0.996734	−	0.0807594i	$-0.974265\pi$
$673$		−	4.19016i		−	0.161519i	0.996734	−	0.0807594i	$-0.0257345\pi$
$674$	2.47292	−	2.37888i	0.0952532	−	0.0916312i
$675$		0			0
$676$	0.579629	−	14.9479i	0.0222934	−	0.574919i
$677$		−	28.7011i		−	1.10307i	−0.834151	−	0.551536i	$-0.814042\pi$
$677$		−	28.7011i		−	1.10307i	0.834151	−	0.551536i	$-0.185958\pi$
$678$		0			0
$679$			41.2052i			1.58131i
$680$		0			0
$681$		0			0
$682$	54.4589	+	56.6116i	2.08534	+	2.16777i
$683$	23.8091			0.911030			0.455515	−	0.890228i	$-0.349455\pi$
$683$	23.8091			0.911030			0.455515	+	0.890228i	$0.349455\pi$
$684$		0			0
$685$		0			0
$686$	28.9682	+	30.1132i	1.10601	+	1.14973i
$687$		0			0
$688$	3.06775	−	39.4973i	0.116957	−	1.50582i
$689$			4.44484i			0.169335i
$690$		0			0
$691$	−32.5479			−1.23818			−0.619090	−	0.785320i	$-0.712498\pi$
$691$	−32.5479			−1.23818			−0.619090	+	0.785320i	$0.712498\pi$
$692$	−29.7297	−	1.15282i	−1.13015	−	0.0438236i
$693$		0			0
$694$	−11.6219	−	12.0813i	−0.441160	−	0.458599i
$695$		0			0
$696$		0			0
$697$			23.4741i			0.889145i
$698$	36.2724	−	34.8932i	1.37293	−	1.32073i
$699$		0			0
$700$		0			0
$701$	0.897080			0.0338822			0.0169411	−	0.999856i	$-0.494607\pi$
$701$	0.897080			0.0338822			0.0169411	+	0.999856i	$0.494607\pi$
$702$		0			0
$703$	25.0804			0.945925
$704$	44.8143	+	5.23424i	1.68900	+	0.197273i
$705$		0			0
$706$	−18.5175	−	19.2495i	−0.696916	−	0.724464i
$707$	66.6154			2.50533
$708$		0			0
$709$			35.0217i			1.31527i	0.753338	+	0.657634i	$0.228443\pi$
$709$			35.0217i			1.31527i	−0.753338	+	0.657634i	$0.771557\pi$
$710$		0			0
$711$		0			0
$712$	15.5733	+	17.4981i	0.583635	+	0.655770i
$713$	4.31424			0.161569
$714$		0			0
$715$		0			0
$716$	−14.5958	−	0.565976i	−0.545471	−	0.0211515i
$717$		0			0
$718$	−10.6597	−	11.0811i	−0.397817	−	0.413542i
$719$	32.4657			1.21077			0.605383	−	0.795934i	$-0.293020\pi$
$719$	32.4657			1.21077			0.605383	+	0.795934i	$0.293020\pi$
$720$		0			0
$721$	−34.1899			−1.27330
$722$	−3.50035	−	3.63871i	−0.130269	−	0.135419i
$723$		0			0
$724$	45.3633	+	1.75904i	1.68591	+	0.0653741i
$725$		0			0
$726$		0			0
$727$	−38.9766			−1.44556			−0.722782	−	0.691076i	$-0.757137\pi$
$727$	−38.9766			−1.44556			−0.722782	+	0.691076i	$0.757137\pi$
$728$	22.4886	−	20.0148i	0.833483	−	0.741799i
$729$		0			0
$730$		0			0
$731$			58.0284i			2.14626i
$732$		0			0
$733$	−30.4308			−1.12399			−0.561993	−	0.827142i	$-0.689965\pi$
$733$	−30.4308			−1.12399			−0.561993	+	0.827142i	$0.689965\pi$
$734$	17.9002	+	18.6078i	0.660708	+	0.686825i
$735$		0			0
$736$	1.91349	−	1.57447i	0.0705320	−	0.0580356i
$737$	3.90212			0.143736
$738$		0			0
$739$	−20.0000			−0.735712			−0.367856	−	0.929883i	$-0.619908\pi$
$739$	−20.0000			−0.735712			−0.367856	+	0.929883i	$0.619908\pi$
$740$		0			0
$741$		0			0
$742$	8.73446	−	8.40233i	0.320652	−	0.308459i
$743$			39.7936i			1.45988i	0.683509	+	0.729942i	$0.260453\pi$
$743$			39.7936i			1.45988i	−0.683509	+	0.729942i	$0.739547\pi$
$744$		0			0
$745$		0			0
$746$	−27.7379	−	28.8343i	−1.01556	−	1.05570i
$747$		0			0
$748$	−66.0390	−	2.56077i	−2.41462	−	0.0936310i
$749$	27.0745			0.989282
$750$		0			0
$751$			26.3194i			0.960408i	0.877157	+	0.480204i	$0.159437\pi$
$751$			26.3194i			0.960408i	−0.877157	+	0.480204i	$0.840563\pi$
$752$	1.51734	−	19.5357i	0.0553316	−	0.712393i
$753$		0			0
$754$	−14.0304	−	14.5850i	−0.510956	−	0.531154i
$755$		0			0
$756$		0			0
$757$	−22.5899			−0.821043			−0.410522	−	0.911851i	$-0.634653\pi$
$757$	−22.5899			−0.821043			−0.410522	+	0.911851i	$0.634653\pi$
$758$	−20.5621	−	21.3748i	−0.746848	−	0.776369i
$759$		0			0
$760$		0			0
$761$			35.6267i			1.29147i	0.763563	+	0.645733i	$0.223448\pi$
$761$			35.6267i			1.29147i	−0.763563	+	0.645733i	$0.776552\pi$
$762$		0			0
$763$		−	74.9998i		−	2.71518i
$764$	−0.842151	+	21.7180i	−0.0304680	+	0.785730i
$765$		0			0
$766$	−26.3670	+	25.3644i	−0.952679	+	0.916453i
$767$		−	12.0222i		−	0.434095i
$768$		0			0
$769$	−41.7103			−1.50411			−0.752056	−	0.659099i	$-0.770938\pi$
$769$	−41.7103			−1.50411			−0.752056	+	0.659099i	$0.770938\pi$
$770$		0			0
$771$		0			0
$772$	23.7865	+	0.922361i	0.856095	+	0.0331965i
$773$			19.2107i			0.690961i	0.938426	+	0.345480i	$0.112284\pi$
$773$			19.2107i			0.690961i	−0.938426	+	0.345480i	$0.887716\pi$
$774$		0			0
$775$		0			0
$776$	−17.1039	−	19.2179i	−0.613993	−	0.689881i
$777$		0			0
$778$	−1.61530	−	1.67915i	−0.0579114	−	0.0602005i
$779$		−	15.7377i		−	0.563862i
$780$		0			0
$781$		−	12.3230i		−	0.440952i
$782$	−2.61580	+	2.51634i	−0.0935410	+	0.0899841i
$783$		0			0
$784$	−53.9262	−	4.18845i	−1.92594	−	0.149588i
$785$		0			0
$786$		0			0
$787$			26.2841i			0.936926i	0.883483	+	0.468463i	$0.155192\pi$
$787$			26.2841i			0.936926i	−0.883483	+	0.468463i	$0.844808\pi$
$788$	−3.62693	−	0.140640i	−0.129204	−	0.00501009i
$789$		0			0
$790$		0			0
$791$	−50.3311			−1.78957
$792$		0			0
$793$			4.47068i			0.158758i
$794$	−12.4014	−	12.8916i	−0.440107	−	0.457504i
$795$		0			0
$796$	−19.4908	−	0.755789i	−0.690834	−	0.0267882i
$797$		−	13.3366i		−	0.472406i	−0.971704	−	0.236203i	$-0.924097\pi$
$797$		−	13.3366i		−	0.472406i	0.971704	−	0.236203i	$-0.0759030\pi$
$798$		0			0
$799$			28.7013i			1.01538i
$800$		0			0
$801$		0			0
$802$	12.6968	−	12.2140i	0.448341	−	0.431293i
$803$	−2.42402			−0.0855419
$804$		0			0
$805$		0			0
$806$	−23.5843	+	22.6875i	−0.830722	+	0.799133i
$807$		0			0
$808$	−31.0690	+	27.6514i	−1.09300	+	0.972773i
$809$		−	25.2848i		−	0.888965i	−0.895787	−	0.444483i	$-0.853388\pi$
$809$		−	25.2848i		−	0.888965i	0.895787	−	0.444483i	$-0.146612\pi$
$810$		0			0
$811$	45.2398			1.58858			0.794292	−	0.607537i	$-0.207842\pi$
$811$	45.2398			1.58858			0.794292	+	0.607537i	$0.207842\pi$
$812$	−2.13820	+	55.1416i	−0.0750363	+	1.93509i
$813$		0			0
$814$	36.7010	−	35.3055i	1.28637	−	1.23746i
$815$		0			0
$816$		0			0
$817$		−	38.9039i		−	1.36108i
$818$	30.2508	+	31.4465i	1.05769	+	1.09950i
$819$		0			0
$820$		0			0
$821$	−54.7742			−1.91163			−0.955817	−	0.293962i	$-0.905026\pi$
$821$	−54.7742			−1.91163			−0.955817	+	0.293962i	$0.905026\pi$
$822$		0			0
$823$	−33.0460			−1.15191			−0.575955	−	0.817481i	$-0.695370\pi$
$823$	−33.0460			−1.15191			−0.575955	+	0.817481i	$0.695370\pi$
$824$	15.9459	−	14.1919i	0.555503	−	0.494397i
$825$		0			0
$826$	−23.6245	+	22.7261i	−0.822000	+	0.790743i
$827$	−24.5938			−0.855211			−0.427606	−	0.903965i	$-0.640643\pi$
$827$	−24.5938			−0.855211			−0.427606	+	0.903965i	$0.640643\pi$
$828$		0			0
$829$		−	10.9509i		−	0.380340i	−0.981751	−	0.190170i	$-0.939096\pi$
$829$		−	10.9509i		−	0.380340i	0.981751	−	0.190170i	$-0.0609040\pi$
$830$		0			0
$831$		0			0
$832$	−2.18058	+	18.6696i	−0.0755979	+	0.647251i
$833$	79.2271			2.74506
$834$		0			0
$835$		0			0
$836$	44.2744	+	1.71681i	1.53126	+	0.0593772i
$837$		0			0
$838$	−5.16302	+	4.96669i	−0.178353	+	0.171572i
$839$	−42.8948			−1.48089			−0.740447	−	0.672115i	$-0.765386\pi$
$839$	−42.8948			−1.48089			−0.740447	+	0.672115i	$0.765386\pi$
$840$		0			0
$841$	8.09608			0.279175
$842$	2.38226	−	2.29168i	0.0820982	−	0.0789764i
$843$		0			0
$844$	−1.68445	+	43.4397i	−0.0579810	+	1.49526i
$845$		0			0
$846$		0			0
$847$	−94.2636			−3.23894
$848$	−0.585972	+	7.54438i	−0.0201224	+	0.259075i
$849$		0			0
$850$		0			0
$851$		−	2.79690i		−	0.0958764i
$852$		0			0
$853$	−2.49013			−0.0852605			−0.0426302	−	0.999091i	$-0.513574\pi$
$853$	−2.49013			−0.0852605			−0.0426302	+	0.999091i	$0.513574\pi$
$854$	8.78523	−	8.45117i	0.300624	−	0.289193i
$855$		0			0
$856$	−12.6274	+	11.2384i	−0.431595	+	0.384119i
$857$	−11.9531			−0.408309			−0.204155	−	0.978939i	$-0.565444\pi$
$857$	−11.9531			−0.408309			−0.204155	+	0.978939i	$0.565444\pi$
$858$		0			0
$859$	−15.5476			−0.530478			−0.265239	−	0.964183i	$-0.585451\pi$
$859$	−15.5476			−0.530478			−0.265239	+	0.964183i	$0.585451\pi$
$860$		0			0
$861$		0			0
$862$	−20.7465	−	21.5666i	−0.706628	−	0.734560i
$863$			32.9038i			1.12006i	0.828473	+	0.560028i	$0.189210\pi$
$863$			32.9038i			1.12006i	−0.828473	+	0.560028i	$0.810790\pi$
$864$		0			0
$865$		0			0
$866$	19.3628	−	18.6266i	0.657976	−	0.632957i
$867$		0			0
$868$	89.1654	+	3.45753i	3.02647	+	0.117356i
$869$	−13.9335			−0.472662
$870$		0			0
$871$			1.62562i			0.0550820i
$872$	31.1317	+	34.9794i	1.05425	+	1.18455i
$873$		0			0
$874$	1.75371	−	1.68702i	0.0593201	−	0.0570645i
$875$		0			0
$876$		0			0
$877$	38.3858			1.29620			0.648099	−	0.761556i	$-0.275564\pi$
$877$	38.3858			1.29620			0.648099	+	0.761556i	$0.275564\pi$
$878$	8.78257	−	8.44861i	0.296397	−	0.285127i
$879$		0			0
$880$		0			0
$881$			49.5262i			1.66858i	0.551327	+	0.834289i	$0.314122\pi$
$881$			49.5262i			1.66858i	−0.551327	+	0.834289i	$0.685878\pi$
$882$		0			0
$883$			20.2395i			0.681113i	0.940224	+	0.340557i	$0.110616\pi$
$883$			20.2395i			0.681113i	−0.940224	+	0.340557i	$0.889384\pi$
$884$	1.06681	−	27.5118i	0.0358808	−	0.925320i
$885$		0			0
$886$	−25.4538	−	26.4600i	−0.855138	−	0.888940i
$887$			12.3748i			0.415507i	0.978181	+	0.207753i	$0.0666151\pi$
$887$			12.3748i			0.415507i	−0.978181	+	0.207753i	$0.933385\pi$
$888$		0			0
$889$	59.5256			1.99642
$890$		0			0
$891$		0			0
$892$	−1.60880	+	41.4890i	−0.0538667	+	1.38915i
$893$		−	19.2422i		−	0.643916i
$894$		0			0
$895$		0			0
$896$	40.8092	−	31.0071i	1.36334	−	1.03588i
$897$		0			0
$898$	10.2572	−	9.86717i	0.342287	−	0.329272i
$899$		−	59.9854i		−	2.00062i
$900$		0			0
$901$		−	11.0840i		−	0.369262i
$902$	−22.1538	−	23.0295i	−0.737642	−	0.766800i
$903$		0			0
$904$	23.4741	−	20.8919i	0.780737	−	0.694856i
$905$		0			0
$906$		0			0
$907$			24.6200i			0.817492i	0.912648	+	0.408746i	$0.134034\pi$
$907$			24.6200i			0.817492i	−0.912648	+	0.408746i	$0.865966\pi$
$908$	−1.51199	+	38.9924i	−0.0501772	+	1.29401i
$909$		0			0
$910$		0			0
$911$	−25.3692			−0.840520			−0.420260	−	0.907404i	$-0.638061\pi$
$911$	−25.3692			−0.840520			−0.420260	+	0.907404i	$0.638061\pi$
$912$		0			0
$913$			12.9059i			0.427124i
$914$	−1.41032	+	1.35669i	−0.0466491	+	0.0448753i
$915$		0			0
$916$	40.5001	+	1.57046i	1.33816	+	0.0518894i
$917$		−	65.5140i		−	2.16346i
$918$		0			0
$919$		−	1.09470i		−	0.0361108i	−0.999837	−	0.0180554i	$-0.994252\pi$
$919$		−	1.09470i		−	0.0361108i	0.999837	−	0.0180554i	$-0.00574752\pi$
$920$		0			0
$921$		0			0
$922$	−39.1518	−	40.6994i	−1.28940	−	1.34036i
$923$	5.13375			0.168979
$924$		0			0
$925$		0			0
$926$	−21.5286	−	22.3796i	−0.707474	−	0.735439i
$927$		0			0
$928$	−21.8915	−	26.6052i	−0.718623	−	0.873359i
$929$			25.2512i			0.828465i	0.910171	+	0.414232i	$0.135950\pi$
$929$			25.2512i			0.828465i	−0.910171	+	0.414232i	$0.864050\pi$
$930$		0			0
$931$	−53.1161			−1.74081
$932$	−1.65695	+	42.7308i	−0.0542753	+	1.39969i
$933$		0			0
$934$	2.55939	+	2.66055i	0.0837457	+	0.0870560i
$935$		0			0
$936$		0			0
$937$			38.0495i			1.24302i	0.783405	+	0.621511i	$0.213481\pi$
$937$			38.0495i			1.24302i	−0.783405	+	0.621511i	$0.786519\pi$
$938$	3.19447	−	3.07300i	0.104303	−	0.100337i
$939$		0			0
$940$		0			0
$941$	−21.8600			−0.712615			−0.356307	−	0.934369i	$-0.615964\pi$
$941$	−21.8600			−0.712615			−0.356307	+	0.934369i	$0.615964\pi$
$942$		0			0
$943$	−1.75503			−0.0571516
$944$	1.58490	−	20.4056i	0.0515842	−	0.664146i
$945$		0			0
$946$	−54.7647	−	56.9295i	−1.78055	−	1.85094i
$947$	28.4707			0.925174			0.462587	−	0.886574i	$-0.346921\pi$
$947$	28.4707			0.925174			0.462587	+	0.886574i	$0.346921\pi$
$948$		0			0
$949$		−	1.00984i		−	0.0327809i
$950$		0			0
$951$		0			0
$952$	−56.0794	+	49.9106i	−1.81754	+	1.61761i
$953$	34.7422			1.12541			0.562706	−	0.826657i	$-0.309760\pi$
$953$	34.7422			1.12541			0.562706	+	0.826657i	$0.309760\pi$
$954$		0			0
$955$		0			0
$956$	−1.57235	+	40.5488i	−0.0508533	+	1.31144i
$957$		0			0
$958$	−15.1787	−	15.7787i	−0.490403	−	0.509788i
$959$	−91.0515			−2.94021
$960$		0			0
$961$	−65.9980			−2.12897
$962$	14.7082	+	15.2896i	0.474212	+	0.492956i
$963$		0			0
$964$	−0.704879	+	18.1779i	−0.0227026	+	0.585472i
$965$		0			0
$966$		0			0
$967$	4.79514			0.154201			0.0771006	−	0.997023i	$-0.475434\pi$
$967$	4.79514			0.154201			0.0771006	+	0.997023i	$0.475434\pi$
$968$	43.9640	−	39.1279i	1.41305	−	1.25762i
$969$		0			0
$970$		0			0
$971$		−	57.6723i		−	1.85079i	−0.379000	−	0.925397i	$-0.623732\pi$
$971$		−	57.6723i		−	1.85079i	0.379000	−	0.925397i	$-0.376268\pi$
$972$		0			0
$973$	−5.05734			−0.162131
$974$	13.5617	+	14.0978i	0.434546	+	0.451723i
$975$		0			0
$976$	−0.589378	+	7.58823i	−0.0188655	+	0.242893i
$977$	−38.9586			−1.24640			−0.623198	−	0.782064i	$-0.714167\pi$
$977$	−38.9586			−1.24640			−0.623198	+	0.782064i	$0.714167\pi$
$978$		0			0
$979$	46.7086			1.49281
$980$		0			0
$981$		0			0
$982$	8.57886	−	8.25265i	0.273763	−	0.263353i
$983$			16.4428i			0.524445i	0.965008	+	0.262222i	$0.0844554\pi$
$983$			16.4428i			0.524445i	−0.965008	+	0.262222i	$0.915545\pi$
$984$		0			0
$985$		0			0
$986$	34.9873	+	36.3703i	1.11422	+	1.15827i
$987$		0			0
$988$	−0.715222	+	18.4447i	−0.0227542	+	0.586803i
$989$	−4.33846			−0.137955
$990$		0			0
$991$		−	43.6832i		−	1.38764i	−0.720147	−	0.693821i	$-0.755926\pi$
$991$		−	43.6832i		−	1.38764i	0.720147	−	0.693821i	$-0.244074\pi$
$992$	−43.0214	+	35.3991i	−1.36593	+	1.12392i
$993$		0			0
$994$	−9.70461	−	10.0882i	−0.307812	−	0.319979i
$995$		0			0
$996$		0			0
$997$	9.85784			0.312201			0.156100	−	0.987741i	$-0.450108\pi$
$997$	9.85784			0.312201			0.156100	+	0.987741i	$0.450108\pi$
$998$	−6.43983	−	6.69438i	−0.203849	−	0.211907i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1800.2.m.f.899.24		32
3.2	odd	2	inner	1800.2.m.f.899.10		32
4.3	odd	2		7200.2.m.f.3599.2		32
5.2	odd	4		1800.2.b.h.251.4	yes	16
5.3	odd	4		1800.2.b.i.251.13	yes	16
5.4	even	2	inner	1800.2.m.f.899.9		32
8.3	odd	2	inner	1800.2.m.f.899.21		32
8.5	even	2		7200.2.m.f.3599.32		32
12.11	even	2		7200.2.m.f.3599.1		32
15.2	even	4		1800.2.b.h.251.13	yes	16
15.8	even	4		1800.2.b.i.251.4	yes	16
15.14	odd	2	inner	1800.2.m.f.899.23		32
20.3	even	4		7200.2.b.h.4751.15		16
20.7	even	4		7200.2.b.g.4751.1		16
20.19	odd	2		7200.2.m.f.3599.30		32
24.5	odd	2		7200.2.m.f.3599.31		32
24.11	even	2	inner	1800.2.m.f.899.11		32
40.3	even	4		1800.2.b.i.251.3	yes	16
40.13	odd	4		7200.2.b.h.4751.1		16
40.19	odd	2	inner	1800.2.m.f.899.12		32
40.27	even	4		1800.2.b.h.251.14	yes	16
40.29	even	2		7200.2.m.f.3599.4		32
40.37	odd	4		7200.2.b.g.4751.15		16
60.23	odd	4		7200.2.b.h.4751.16		16
60.47	odd	4		7200.2.b.g.4751.2		16
60.59	even	2		7200.2.m.f.3599.29		32
120.29	odd	2		7200.2.m.f.3599.3		32
120.53	even	4		7200.2.b.h.4751.2		16
120.59	even	2	inner	1800.2.m.f.899.22		32
120.77	even	4		7200.2.b.g.4751.16		16
120.83	odd	4		1800.2.b.i.251.14	yes	16
120.107	odd	4		1800.2.b.h.251.3	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1800.2.b.h.251.3	✓	16	120.107	odd	4
1800.2.b.h.251.4	yes	16	5.2	odd	4
1800.2.b.h.251.13	yes	16	15.2	even	4
1800.2.b.h.251.14	yes	16	40.27	even	4
1800.2.b.i.251.3	yes	16	40.3	even	4
1800.2.b.i.251.4	yes	16	15.8	even	4
1800.2.b.i.251.13	yes	16	5.3	odd	4
1800.2.b.i.251.14	yes	16	120.83	odd	4
1800.2.m.f.899.9		32	5.4	even	2	inner
1800.2.m.f.899.10		32	3.2	odd	2	inner
1800.2.m.f.899.11		32	24.11	even	2	inner
1800.2.m.f.899.12		32	40.19	odd	2	inner
1800.2.m.f.899.21		32	8.3	odd	2	inner
1800.2.m.f.899.22		32	120.59	even	2	inner
1800.2.m.f.899.23		32	15.14	odd	2	inner
1800.2.m.f.899.24		32	1.1	even	1	trivial
7200.2.b.g.4751.1		16	20.7	even	4
7200.2.b.g.4751.2		16	60.47	odd	4
7200.2.b.g.4751.15		16	40.37	odd	4
7200.2.b.g.4751.16		16	120.77	even	4
7200.2.b.h.4751.1		16	40.13	odd	4
7200.2.b.h.4751.2		16	120.53	even	4
7200.2.b.h.4751.15		16	20.3	even	4
7200.2.b.h.4751.16		16	60.23	odd	4
7200.2.m.f.3599.1		32	12.11	even	2
7200.2.m.f.3599.2		32	4.3	odd	2
7200.2.m.f.3599.3		32	120.29	odd	2
7200.2.m.f.3599.4		32	40.29	even	2
7200.2.m.f.3599.29		32	60.59	even	2
7200.2.m.f.3599.30		32	20.19	odd	2
7200.2.m.f.3599.31		32	24.5	odd	2
7200.2.m.f.3599.32		32	8.5	even	2

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.m (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.980435 + 1.01919i) q^{2} +(-0.0774950 + 1.99850i) q^{4} +4.53014 q^{7} +(-2.11283 + 1.88042i) q^{8} +O(q^{10})\)	\(q+(0.980435 + 1.01919i) q^{2} +(-0.0774950 + 1.99850i) q^{4} +4.53014 q^{7} +(-2.11283 + 1.88042i) q^{8} +5.63987i q^{11} -2.34956 q^{13} +(4.44151 + 4.61707i) q^{14} +(-3.98799 - 0.309747i) q^{16} +5.85906 q^{17} -3.92808 q^{19} +(-5.74810 + 5.52952i) q^{22} +0.438049i q^{23} +(-2.30359 - 2.39465i) q^{26} +(-0.351063 + 9.05347i) q^{28} +6.09065 q^{29} -9.84876i q^{31} +(-3.59427 - 4.36820i) q^{32} +(5.74442 + 5.97149i) q^{34} -6.38490 q^{37} +(-3.85123 - 4.00346i) q^{38} +4.00647i q^{41} +9.90406i q^{43} +(-11.2713 - 0.437062i) q^{44} +(-0.446455 + 0.429478i) q^{46} +4.89863i q^{47} +13.5222 q^{49} +(0.182079 - 4.69559i) q^{52} -1.89178i q^{53} +(-9.57140 + 8.51854i) q^{56} +(5.97149 + 6.20753i) q^{58} +5.11676i q^{59} -1.90277i q^{61} +(10.0377 - 9.65606i) q^{62} +(0.928079 - 7.94598i) q^{64} -0.691882i q^{67} +(-0.454048 + 11.7093i) q^{68} -2.18498 q^{71} +0.429801i q^{73} +(-6.25998 - 6.50743i) q^{74} +(0.304406 - 7.85026i) q^{76} +25.5494i q^{77} +2.47054i q^{79} +(-4.08335 + 3.92808i) q^{82} +2.28834 q^{83} +(-10.0941 + 9.71028i) q^{86} +(-10.6053 - 11.9161i) q^{88} -8.28186i q^{89} -10.6438 q^{91} +(-0.875440 - 0.0339466i) q^{92} +(-4.99263 + 4.80279i) q^{94} +9.09580i q^{97} +(13.2576 + 13.7816i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4}+O(q^{10}) \) 32 * q + 8 * q^4	\( 32 q + 8 q^{4} - 16 q^{16} - 32 q^{19} - 24 q^{34} + 40 q^{46} + 64 q^{49} - 64 q^{64} + 72 q^{76} + 96 q^{91} + 40 q^{94}+O(q^{100}) \) 32 * q + 8 * q^4 - 16 * q^16 - 32 * q^19 - 24 * q^34 + 40 * q^46 + 64 * q^49 - 64 * q^64 + 72 * q^76 + 96 * q^91 + 40 * q^94

Introduction

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