LMFDB - Embedded newform 1800.2.k.s.901.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1800,2,Mod(901,1800)]

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, 0]))

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

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

chi := DirichletCharacter("1800.901");

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.k (of order $2$, degree $1$, 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:	$8$
Coefficient field:	8.0.212336640000.29
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 2x^{4} + 16 $ x^8 + 2*x^4 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			901.6
Root			$-0.622597 + 1.26979i$ of defining polynomial
Character	$\chi$	$=$	1800.901
Dual form			1800.2.k.s.901.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.622597 + 1.26979i) q^{2} +(-1.22474 + 1.58114i) q^{4} -1.44949 q^{7} +(-2.77024 - 0.570759i) q^{8} +O(q^{10})$	\(q+(0.622597 + 1.26979i) q^{2} +(-1.22474 + 1.58114i) q^{4} -1.44949 q^{7} +(-2.77024 - 0.570759i) q^{8} -1.14152i q^{11} -3.87298i q^{13} +(-0.902449 - 1.84055i) q^{14} +(-1.00000 - 3.87298i) q^{16} +3.05009 q^{17} +0.710706i q^{19} +(1.44949 - 0.710706i) q^{22} -5.54048 q^{23} +(4.91788 - 2.41131i) q^{26} +(1.77526 - 2.29184i) q^{28} -6.22069i q^{29} +3.44949 q^{31} +(4.29529 - 3.68110i) q^{32} +(1.89898 + 3.87298i) q^{34} -6.32456i q^{37} +(-0.902449 + 0.442484i) q^{38} +8.03087 q^{41} -7.03526i q^{43} +(1.80490 + 1.39807i) q^{44} +(-3.44949 - 7.03526i) q^{46} +4.98078 q^{47} -4.89898 q^{49} +(6.12372 + 4.74342i) q^{52} -3.93765i q^{53} +(4.01544 + 0.827309i) q^{56} +(7.89898 - 3.87298i) q^{58} +10.1583i q^{59} +2.45157i q^{61} +(2.14764 + 4.38014i) q^{62} +(7.34847 + 3.16228i) q^{64} -13.3598i q^{67} +(-3.73558 + 4.82262i) q^{68} +11.6407 q^{71} -2.89898 q^{73} +(8.03087 - 3.93765i) q^{74} +(-1.12372 - 0.870433i) q^{76} +1.65462i q^{77} -6.89898 q^{79} +(5.00000 + 10.1975i) q^{82} +12.4414i q^{83} +(8.93332 - 4.38014i) q^{86} +(-0.651531 + 3.16228i) q^{88} +16.0617 q^{89} +5.61385i q^{91} +(6.78568 - 8.76027i) q^{92} +(3.10102 + 6.32456i) q^{94} -13.6969 q^{97} +(-3.05009 - 6.22069i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{7}+O(q^{10}) $ 8 * q + 8 * q^7	$ 8 q + 8 q^{7} - 8 q^{16} - 8 q^{22} + 24 q^{28} + 8 q^{31} - 24 q^{34} - 8 q^{46} + 24 q^{58} + 16 q^{73} + 40 q^{76} - 16 q^{79} + 40 q^{82} - 64 q^{88} + 64 q^{94} + 8 q^{97}+O(q^{100}) $ 8 * q + 8 * q^7 - 8 * q^16 - 8 * q^22 + 24 * q^28 + 8 * q^31 - 24 * q^34 - 8 * q^46 + 24 * q^58 + 16 * q^73 + 40 * q^76 - 16 * q^79 + 40 * q^82 - 64 * q^88 + 64 * q^94 + 8 * q^97

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
$7$	−1.44949			−0.547856			−0.273928	−	0.961750i	$-0.588323\pi$
$7$	−1.44949			−0.547856			−0.273928	+	0.961750i	$0.588323\pi$
$8$	−2.77024	−	0.570759i	−0.979428	−	0.201794i
$9$		0			0
$10$		0			0
$11$		−	1.14152i		−	0.344180i	−0.985081	−	0.172090i	$-0.944948\pi$
$11$		−	1.14152i		−	0.344180i	0.985081	−	0.172090i	$-0.0550521\pi$
$12$		0			0
$13$		−	3.87298i		−	1.07417i	−0.843527	−	0.537086i	$-0.819525\pi$
$13$		−	3.87298i		−	1.07417i	0.843527	−	0.537086i	$-0.180475\pi$
$14$	−0.902449	−	1.84055i	−0.241190	−	0.491908i
$15$		0			0
$16$	−1.00000	−	3.87298i	−0.250000	−	0.968246i
$17$	3.05009			0.739756			0.369878	−	0.929080i	$-0.379399\pi$
$17$	3.05009			0.739756			0.369878	+	0.929080i	$0.379399\pi$
$18$		0			0
$19$			0.710706i			0.163047i	0.996671	+	0.0815235i	$0.0259786\pi$
$19$			0.710706i			0.163047i	−0.996671	+	0.0815235i	$0.974021\pi$
$20$		0			0
$21$		0			0
$22$	1.44949	−	0.710706i	0.309032	−	0.151523i
$23$	−5.54048			−1.15527			−0.577635	−	0.816295i	$-0.696024\pi$
$23$	−5.54048			−1.15527			−0.577635	+	0.816295i	$0.696024\pi$
$24$		0			0
$25$		0			0
$26$	4.91788	−	2.41131i	0.964476	−	0.472897i
$27$		0			0
$28$	1.77526	−	2.29184i	0.335492	−	0.433118i
$29$		−	6.22069i		−	1.15515i	−0.816337	−	0.577576i	$-0.803999\pi$
$29$		−	6.22069i		−	1.15515i	0.816337	−	0.577576i	$-0.196001\pi$
$30$		0			0
$31$	3.44949			0.619547			0.309773	−	0.950810i	$-0.399747\pi$
$31$	3.44949			0.619547			0.309773	+	0.950810i	$0.399747\pi$
$32$	4.29529	−	3.68110i	0.759307	−	0.650733i
$33$		0			0
$34$	1.89898	+	3.87298i	0.325672	+	0.664211i
$35$		0			0
$36$		0			0
$37$		−	6.32456i		−	1.03975i	−0.854242	−	0.519875i	$-0.825978\pi$
$37$		−	6.32456i		−	1.03975i	0.854242	−	0.519875i	$-0.174022\pi$
$38$	−0.902449	+	0.442484i	−0.146396	+	0.0717803i
$39$		0			0
$40$		0			0
$41$	8.03087			1.25421			0.627106	−	0.778934i	$-0.284239\pi$
$41$	8.03087			1.25421			0.627106	+	0.778934i	$0.284239\pi$
$42$		0			0
$43$		−	7.03526i		−	1.07287i	−0.843943	−	0.536434i	$-0.819771\pi$
$43$		−	7.03526i		−	1.07287i	0.843943	−	0.536434i	$-0.180229\pi$
$44$	1.80490	+	1.39807i	0.272098	+	0.210767i
$45$		0			0
$46$	−3.44949	−	7.03526i	−0.508600	−	1.03729i
$47$	4.98078			0.726521			0.363261	−	0.931688i	$-0.381663\pi$
$47$	4.98078			0.726521			0.363261	+	0.931688i	$0.381663\pi$
$48$		0			0
$49$	−4.89898			−0.699854
$50$		0			0
$51$		0			0
$52$	6.12372	+	4.74342i	0.849208	+	0.657794i
$53$		−	3.93765i		−	0.540878i	−0.962737	−	0.270439i	$-0.912831\pi$
$53$		−	3.93765i		−	0.540878i	0.962737	−	0.270439i	$-0.0871689\pi$
$54$		0			0
$55$		0			0
$56$	4.01544	+	0.827309i	0.536585	+	0.110554i
$57$		0			0
$58$	7.89898	−	3.87298i	1.03719	−	0.508548i
$59$			10.1583i			1.32250i	0.750164	+	0.661251i	$0.229974\pi$
$59$			10.1583i			1.32250i	−0.750164	+	0.661251i	$0.770026\pi$
$60$		0			0
$61$			2.45157i			0.313892i	0.987607	+	0.156946i	$0.0501648\pi$
$61$			2.45157i			0.313892i	−0.987607	+	0.156946i	$0.949835\pi$
$62$	2.14764	+	4.38014i	0.272751	+	0.556278i
$63$		0			0
$64$	7.34847	+	3.16228i	0.918559	+	0.395285i
$65$		0			0
$66$		0			0
$67$		−	13.3598i		−	1.63216i	−0.577938	−	0.816081i	$-0.696142\pi$
$67$		−	13.3598i		−	1.63216i	0.577938	−	0.816081i	$-0.303858\pi$
$68$	−3.73558	+	4.82262i	−0.453006	+	0.584828i
$69$		0			0
$70$		0			0
$71$	11.6407			1.38149			0.690746	−	0.723097i	$-0.257282\pi$
$71$	11.6407			1.38149			0.690746	+	0.723097i	$0.257282\pi$
$72$		0			0
$73$	−2.89898			−0.339300			−0.169650	−	0.985504i	$-0.554264\pi$
$73$	−2.89898			−0.339300			−0.169650	+	0.985504i	$0.554264\pi$
$74$	8.03087	−	3.93765i	0.933570	−	0.457743i
$75$		0			0
$76$	−1.12372	−	0.870433i	−0.128900	−	0.0998455i
$77$			1.65462i			0.188561i
$78$		0			0
$79$	−6.89898			−0.776196			−0.388098	−	0.921618i	$-0.626868\pi$
$79$	−6.89898			−0.776196			−0.388098	+	0.921618i	$0.626868\pi$
$80$		0			0
$81$		0			0
$82$	5.00000	+	10.1975i	0.552158	+	1.12613i
$83$			12.4414i			1.36562i	0.730597	+	0.682809i	$0.239242\pi$
$83$			12.4414i			1.36562i	−0.730597	+	0.682809i	$0.760758\pi$
$84$		0			0
$85$		0			0
$86$	8.93332	−	4.38014i	0.963305	−	0.472322i
$87$		0			0
$88$	−0.651531	+	3.16228i	−0.0694534	+	0.337100i
$89$	16.0617			1.70254			0.851271	−	0.524727i	$-0.175833\pi$
$89$	16.0617			1.70254			0.851271	+	0.524727i	$0.175833\pi$
$90$		0			0
$91$			5.61385i			0.588491i
$92$	6.78568	−	8.76027i	0.707456	−	0.913321i
$93$		0			0
$94$	3.10102	+	6.32456i	0.319846	+	0.652328i
$95$		0			0
$96$		0			0
$97$	−13.6969			−1.39071			−0.695357	−	0.718665i	$-0.744754\pi$
$97$	−13.6969			−1.39071			−0.695357	+	0.718665i	$0.744754\pi$
$98$	−3.05009	−	6.22069i	−0.308106	−	0.628384i
$99$		0			0
$100$		0			0
$101$		−	8.50372i		−	0.846152i	−0.906094	−	0.423076i	$-0.860950\pi$
$101$		−	8.50372i		−	0.846152i	0.906094	−	0.423076i	$-0.139050\pi$
$102$		0			0
$103$	−2.89898			−0.285645			−0.142822	−	0.989748i	$-0.545618\pi$
$103$	−2.89898			−0.285645			−0.142822	+	0.989748i	$0.545618\pi$
$104$	−2.21054	+	10.7291i	−0.216761	+	1.05207i
$105$		0			0
$106$	5.00000	−	2.45157i	0.485643	−	0.238118i
$107$		−	11.2999i		−	1.09240i	−0.837655	−	0.546199i	$-0.816074\pi$
$107$		−	11.2999i		−	1.09240i	0.837655	−	0.546199i	$-0.183926\pi$
$108$		0			0
$109$		−	8.77613i		−	0.840601i	−0.907385	−	0.420300i	$-0.861925\pi$
$109$		−	8.77613i		−	0.840601i	0.907385	−	0.420300i	$-0.138075\pi$
$110$		0			0
$111$		0			0
$112$	1.44949	+	5.61385i	0.136964	+	0.530459i
$113$	−6.10018			−0.573857			−0.286929	−	0.957952i	$-0.592634\pi$
$113$	−6.10018			−0.573857			−0.286929	+	0.957952i	$0.592634\pi$
$114$		0			0
$115$		0			0
$116$	9.83577	+	7.61875i	0.913228	+	0.707384i
$117$		0			0
$118$	−12.8990	+	6.32456i	−1.18745	+	0.582223i
$119$	−4.42108			−0.405279
$120$		0			0
$121$	9.69694			0.881540
$122$	−3.11299	+	1.52634i	−0.281837	+	0.138189i
$123$		0			0
$124$	−4.22474	+	5.45412i	−0.379393	+	0.489795i
$125$		0			0
$126$		0			0
$127$	−15.7980			−1.40184			−0.700921	−	0.713239i	$-0.747227\pi$
$127$	−15.7980			−1.40184			−0.700921	+	0.713239i	$0.747227\pi$
$128$	0.559702	+	11.2999i	0.0494712	+	0.998776i
$129$		0			0
$130$		0			0
$131$			9.01682i			0.787803i	0.919153	+	0.393902i	$0.128875\pi$
$131$			9.01682i			0.787803i	−0.919153	+	0.393902i	$0.871125\pi$
$132$		0			0
$133$		−	1.03016i		−	0.0893263i
$134$	16.9642	−	8.31779i	1.46548	−	0.718547i
$135$		0			0
$136$	−8.44949	−	1.74087i	−0.724538	−	0.149278i
$137$	−4.98078			−0.425537			−0.212768	−	0.977103i	$-0.568248\pi$
$137$	−4.98078			−0.425537			−0.212768	+	0.977103i	$0.568248\pi$
$138$		0			0
$139$		−	21.8165i		−	1.85045i	−0.379418	−	0.925225i	$-0.623876\pi$
$139$		−	21.8165i		−	1.85045i	0.379418	−	0.925225i	$-0.376124\pi$
$140$		0			0
$141$		0			0
$142$	7.24745	+	14.7812i	0.608192	+	1.24041i
$143$	−4.42108			−0.369709
$144$		0			0
$145$		0			0
$146$	−1.80490	−	3.68110i	−0.149374	−	0.304650i
$147$		0			0
$148$	10.0000	+	7.74597i	0.821995	+	0.636715i
$149$		−	18.0336i		−	1.47737i	−0.674049	−	0.738687i	$-0.735446\pi$
$149$		−	18.0336i		−	1.47737i	0.674049	−	0.738687i	$-0.264554\pi$
$150$		0			0
$151$	2.34847			0.191116			0.0955579	−	0.995424i	$-0.469537\pi$
$151$	2.34847			0.191116			0.0955579	+	0.995424i	$0.469537\pi$
$152$	0.405641	−	1.96883i	0.0329019	−	0.159693i
$153$		0			0
$154$	−2.10102	+	1.03016i	−0.169305	+	0.0830127i
$155$		0			0
$156$		0			0
$157$		−	16.5221i		−	1.31861i	−0.751877	−	0.659303i	$-0.770851\pi$
$157$		−	16.5221i		−	1.31861i	0.751877	−	0.659303i	$-0.229149\pi$
$158$	−4.29529	−	8.76027i	−0.341715	−	0.696930i
$159$		0			0
$160$		0			0
$161$	8.03087			0.632921
$162$		0			0
$163$			8.45667i			0.662378i	0.943564	+	0.331189i	$0.107450\pi$
$163$			8.45667i			0.662378i	−0.943564	+	0.331189i	$0.892550\pi$
$164$	−9.83577	+	12.6979i	−0.768045	+	0.991541i
$165$		0			0
$166$	−15.7980	+	7.74597i	−1.22616	+	0.601204i
$167$	16.6214			1.28621			0.643103	−	0.765780i	$-0.277647\pi$
$167$	16.6214			1.28621			0.643103	+	0.765780i	$0.277647\pi$
$168$		0			0
$169$	−2.00000			−0.153846
$170$		0			0
$171$		0			0
$172$	11.1237	+	8.61640i	0.848176	+	0.656994i
$173$		−	16.3790i		−	1.24527i	−0.782511	−	0.622637i	$-0.786061\pi$
$173$		−	16.3790i		−	1.24527i	0.782511	−	0.622637i	$-0.213939\pi$
$174$		0			0
$175$		0			0
$176$	−4.42108	+	1.14152i	−0.333251	+	0.0860451i
$177$		0			0
$178$	10.0000	+	20.3951i	0.749532	+	1.52868i
$179$			18.0336i			1.34790i	0.738778	+	0.673949i	$0.235403\pi$
$179$			18.0336i			1.34790i	−0.738778	+	0.673949i	$0.764597\pi$
$180$		0			0
$181$			17.9435i			1.33373i	0.745178	+	0.666865i	$0.232364\pi$
$181$			17.9435i			1.33373i	−0.745178	+	0.666865i	$0.767636\pi$
$182$	−7.12842	+	3.49517i	−0.528394	+	0.259079i
$183$		0			0
$184$	15.3485	+	3.16228i	1.13150	+	0.233126i
$185$		0			0
$186$		0			0
$187$		−	3.48173i		−	0.254610i
$188$	−6.10018	+	7.87530i	−0.444902	+	0.574366i
$189$		0			0
$190$		0			0
$191$	−11.6407			−0.842289			−0.421145	−	0.906994i	$-0.638371\pi$
$191$	−11.6407			−0.842289			−0.421145	+	0.906994i	$0.638371\pi$
$192$		0			0
$193$	−2.10102			−0.151235			−0.0756174	−	0.997137i	$-0.524093\pi$
$193$	−2.10102			−0.151235			−0.0756174	+	0.997137i	$0.524093\pi$
$194$	−8.52768	−	17.3923i	−0.612252	−	1.24869i
$195$		0			0
$196$	6.00000	−	7.74597i	0.428571	−	0.553283i
$197$			27.1658i			1.93548i	0.251948	+	0.967741i	$0.418929\pi$
$197$			27.1658i			1.93548i	−0.251948	+	0.967741i	$0.581071\pi$
$198$		0			0
$199$	−3.24745			−0.230206			−0.115103	−	0.993354i	$-0.536720\pi$
$199$	−3.24745			−0.230206			−0.115103	+	0.993354i	$0.536720\pi$
$200$		0			0
$201$		0			0
$202$	10.7980	−	5.29439i	0.759742	−	0.372512i
$203$			9.01682i			0.632857i
$204$		0			0
$205$		0			0
$206$	−1.80490	−	3.68110i	−0.125753	−	0.256475i
$207$		0			0
$208$	−15.0000	+	3.87298i	−1.04006	+	0.268543i
$209$	0.811283			0.0561176
$210$		0			0
$211$			21.1058i			1.45298i	0.687176	+	0.726491i	$0.258850\pi$
$211$			21.1058i			1.45298i	−0.687176	+	0.726491i	$0.741150\pi$
$212$	6.22597	+	4.82262i	0.427602	+	0.331219i
$213$		0			0
$214$	14.3485	−	7.03526i	0.980841	−	0.480921i
$215$		0			0
$216$		0			0
$217$	−5.00000			−0.339422
$218$	11.1439	−	5.46399i	0.754757	−	0.370068i
$219$		0			0
$220$		0			0
$221$		−	11.8130i		−	0.794625i
$222$		0			0
$223$	−14.3485			−0.960845			−0.480422	−	0.877037i	$-0.659517\pi$
$223$	−14.3485			−0.960845			−0.480422	+	0.877037i	$0.659517\pi$
$224$	−6.22597	+	5.33572i	−0.415990	+	0.356508i
$225$		0			0
$226$	−3.79796	−	7.74597i	−0.252636	−	0.515254i
$227$		−	21.4582i		−	1.42423i	−0.702063	−	0.712115i	$-0.747737\pi$
$227$		−	21.4582i		−	1.42423i	0.702063	−	0.712115i	$-0.252263\pi$
$228$		0			0
$229$		−	17.9435i		−	1.18574i	−0.805298	−	0.592870i	$-0.797995\pi$
$229$		−	17.9435i		−	1.18574i	0.805298	−	0.592870i	$-0.202005\pi$
$230$		0			0
$231$		0			0
$232$	−3.55051	+	17.2328i	−0.233102	+	1.13139i
$233$	17.9924			1.17872			0.589362	−	0.807869i	$-0.299379\pi$
$233$	17.9924			1.17872			0.589362	+	0.807869i	$0.299379\pi$
$234$		0			0
$235$		0			0
$236$	−16.0617	−	12.4414i	−1.04553	−	0.809864i
$237$		0			0
$238$	−2.75255	−	5.61385i	−0.178421	−	0.363892i
$239$	−20.4828			−1.32492			−0.662462	−	0.749096i	$-0.730488\pi$
$239$	−20.4828			−1.32492			−0.662462	+	0.749096i	$0.730488\pi$
$240$		0			0
$241$	−5.69694			−0.366972			−0.183486	−	0.983022i	$-0.558738\pi$
$241$	−5.69694			−0.366972			−0.183486	+	0.983022i	$0.558738\pi$
$242$	6.03729	+	12.3131i	0.388092	+	0.791516i
$243$		0			0
$244$	−3.87628	−	3.00255i	−0.248153	−	0.192219i
$245$		0			0
$246$		0			0
$247$	2.75255			0.175141
$248$	−9.55592	−	1.96883i	−0.606801	−	0.125021i
$249$		0			0
$250$		0			0
$251$			12.4414i			0.785292i	0.919690	+	0.392646i	$0.128440\pi$
$251$			12.4414i			0.785292i	−0.919690	+	0.392646i	$0.871560\pi$
$252$		0			0
$253$			6.32456i			0.397621i
$254$	−9.83577	−	20.0601i	−0.617151	−	1.25868i
$255$		0			0
$256$	−14.0000	+	7.74597i	−0.875000	+	0.484123i
$257$	−11.0810			−0.691212			−0.345606	−	0.938380i	$-0.612327\pi$
$257$	−11.0810			−0.691212			−0.345606	+	0.938380i	$0.612327\pi$
$258$		0			0
$259$			9.16738i			0.569633i
$260$		0			0
$261$		0			0
$262$	−11.4495	+	5.61385i	−0.707352	+	0.346825i
$263$	−10.5213			−0.648769			−0.324384	−	0.945925i	$-0.605157\pi$
$263$	−10.5213			−0.648769			−0.324384	+	0.945925i	$0.605157\pi$
$264$		0			0
$265$		0			0
$266$	1.30809	−	0.641375i	0.0802041	−	0.0393252i
$267$		0			0
$268$	21.1237	+	16.3624i	1.29034	+	0.999491i
$269$		−	28.8204i		−	1.75721i	−0.477549	−	0.878605i	$-0.658475\pi$
$269$		−	28.8204i		−	1.75721i	0.477549	−	0.878605i	$-0.341525\pi$
$270$		0			0
$271$	14.8990			0.905049			0.452524	−	0.891752i	$-0.350524\pi$
$271$	14.8990			0.905049			0.452524	+	0.891752i	$0.350524\pi$
$272$	−3.05009	−	11.8130i	−0.184939	−	0.716266i
$273$		0			0
$274$	−3.10102	−	6.32456i	−0.187340	−	0.382080i
$275$		0			0
$276$		0			0
$277$		−	1.03016i		−	0.0618964i	−0.999521	−	0.0309482i	$-0.990147\pi$
$277$		−	1.03016i		−	0.0618964i	0.999521	−	0.0309482i	$-0.00985268\pi$
$278$	27.7024	−	13.5829i	1.66148	−	0.814648i
$279$		0			0
$280$		0			0
$281$	−8.03087			−0.479082			−0.239541	−	0.970886i	$-0.576997\pi$
$281$	−8.03087			−0.479082			−0.239541	+	0.970886i	$0.576997\pi$
$282$		0			0
$283$		−	7.03526i		−	0.418203i	−0.977894	−	0.209101i	$-0.932946\pi$
$283$		−	7.03526i		−	0.418203i	0.977894	−	0.209101i	$-0.0670539\pi$
$284$	−14.2568	+	18.4055i	−0.845988	+	1.09217i
$285$		0			0
$286$	−2.75255	−	5.61385i	−0.162762	−	0.331954i
$287$	−11.6407			−0.687127
$288$		0			0
$289$	−7.69694			−0.452761
$290$		0			0
$291$		0			0
$292$	3.55051	−	4.58369i	0.207778	−	0.268240i
$293$		−	7.87530i		−	0.460080i	−0.973181	−	0.230040i	$-0.926114\pi$
$293$		−	7.87530i		−	0.460080i	0.973181	−	0.230040i	$-0.0738857\pi$
$294$		0			0
$295$		0			0
$296$	−3.60979	+	17.5205i	−0.209815	+	1.01836i
$297$		0			0
$298$	22.8990	−	11.2277i	1.32650	−	0.650403i
$299$			21.4582i			1.24096i
$300$		0			0
$301$			10.1975i			0.587776i
$302$	1.46215	+	2.98207i	0.0841373	+	0.171599i
$303$		0			0
$304$	2.75255	−	0.710706i	0.157870	−	0.0407618i
$305$		0			0
$306$		0			0
$307$		−	8.45667i		−	0.482648i	−0.970445	−	0.241324i	$-0.922418\pi$
$307$		−	8.45667i		−	0.482648i	0.970445	−	0.241324i	$-0.0775816\pi$
$308$	−2.61618	−	2.02648i	−0.149071	−	0.115470i
$309$		0			0
$310$		0			0
$311$	−32.1235			−1.82156			−0.910778	−	0.412897i	$-0.864517\pi$
$311$	−32.1235			−1.82156			−0.910778	+	0.412897i	$0.864517\pi$
$312$		0			0
$313$	−16.5959			−0.938057			−0.469028	−	0.883183i	$-0.655396\pi$
$313$	−16.5959			−0.938057			−0.469028	+	0.883183i	$0.655396\pi$
$314$	20.9796	−	10.2866i	1.18395	−	0.580507i
$315$		0			0
$316$	8.44949	−	10.9082i	0.475321	−	0.613637i
$317$			18.0336i			1.01287i	0.862278	+	0.506435i	$0.169037\pi$
$317$			18.0336i			1.01287i	−0.862278	+	0.506435i	$0.830963\pi$
$318$		0			0
$319$	−7.10102			−0.397581
$320$		0			0
$321$		0			0
$322$	5.00000	+	10.1975i	0.278639	+	0.568287i
$323$			2.16772i			0.120615i
$324$		0			0
$325$		0			0
$326$	−10.7382	+	5.26510i	−0.594735	+	0.291607i
$327$		0			0
$328$	−22.2474	−	4.58369i	−1.22841	−	0.253092i
$329$	−7.21959			−0.398029
$330$		0			0
$331$		−	12.6491i		−	0.695258i	−0.937632	−	0.347629i	$-0.886987\pi$
$331$		−	12.6491i		−	0.695258i	0.937632	−	0.347629i	$-0.113013\pi$
$332$	−19.6715	−	15.2375i	−1.07962	−	0.836267i
$333$		0			0
$334$	10.3485	+	21.1058i	0.566243	+	1.15486i
$335$		0			0
$336$		0			0
$337$	−0.797959			−0.0434676			−0.0217338	−	0.999764i	$-0.506919\pi$
$337$	−0.797959			−0.0434676			−0.0217338	+	0.999764i	$0.506919\pi$
$338$	−1.24519	−	2.53958i	−0.0677297	−	0.138135i
$339$		0			0
$340$		0			0
$341$		−	3.93765i		−	0.213236i
$342$		0			0
$343$	17.2474			0.931275
$344$	−4.01544	+	19.4894i	−0.216498	+	1.05080i
$345$		0			0
$346$	20.7980	−	10.1975i	1.11811	−	0.548223i
$347$		−	7.87530i		−	0.422768i	−0.977403	−	0.211384i	$-0.932203\pi$
$347$		−	7.87530i		−	0.422768i	0.977403	−	0.211384i	$-0.0677971\pi$
$348$		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
$352$	−4.20204	−	4.90314i	−0.223970	−	0.261338i
$353$	30.1928			1.60700			0.803500	−	0.595304i	$-0.202969\pi$
$353$	30.1928			1.60700			0.803500	+	0.595304i	$0.202969\pi$
$354$		0			0
$355$		0			0
$356$	−19.6715	+	25.3958i	−1.04259	+	1.34598i
$357$		0			0
$358$	−22.8990	+	11.2277i	−1.21025	+	0.593402i
$359$	−4.42108			−0.233336			−0.116668	−	0.993171i	$-0.537221\pi$
$359$	−4.42108			−0.233336			−0.116668	+	0.993171i	$0.537221\pi$
$360$		0			0
$361$	18.4949			0.973416
$362$	−22.7845	+	11.1716i	−1.19753	+	0.587165i
$363$		0			0
$364$	−8.87628	−	6.87553i	−0.465243	−	0.360376i
$365$		0			0
$366$		0			0
$367$	−18.5505			−0.968329			−0.484164	−	0.874977i	$-0.660876\pi$
$367$	−18.5505			−0.968329			−0.484164	+	0.874977i	$0.660876\pi$
$368$	5.54048	+	21.4582i	0.288818	+	1.11859i
$369$		0			0
$370$		0			0
$371$			5.70759i			0.296323i
$372$		0			0
$373$		−	13.0404i		−	0.675204i	−0.941289	−	0.337602i	$-0.890384\pi$
$373$		−	13.0404i		−	0.675204i	0.941289	−	0.337602i	$-0.109616\pi$
$374$	4.42108	−	2.16772i	0.228608	−	0.112090i
$375$		0			0
$376$	−13.7980	−	2.84282i	−0.711575	−	0.146607i
$377$	−24.0926			−1.24083
$378$		0			0
$379$		−	5.61385i		−	0.288364i	−0.989551	−	0.144182i	$-0.953945\pi$
$379$		−	5.61385i		−	0.288364i	0.989551	−	0.144182i	$-0.0460551\pi$
$380$		0			0
$381$		0			0
$382$	−7.24745	−	14.7812i	−0.370812	−	0.756273i
$383$	6.10018			0.311705			0.155852	−	0.987780i	$-0.450188\pi$
$383$	6.10018			0.311705			0.155852	+	0.987780i	$0.450188\pi$
$384$		0			0
$385$		0			0
$386$	−1.30809	−	2.66786i	−0.0665800	−	0.135790i
$387$		0			0
$388$	16.7753	−	21.6568i	0.851635	−	1.09946i
$389$		−	9.52992i		−	0.483186i	−0.970378	−	0.241593i	$-0.922330\pi$
$389$		−	9.52992i		−	0.483186i	0.970378	−	0.241593i	$-0.0776699\pi$
$390$		0			0
$391$	−16.8990			−0.854618
$392$	13.5714	+	2.79613i	0.685457	+	0.141226i
$393$		0			0
$394$	−34.4949	+	16.9133i	−1.73783	+	0.852082i
$395$		0			0
$396$		0			0
$397$			10.1975i			0.511800i	0.966703	+	0.255900i	$0.0823717\pi$
$397$			10.1975i			0.511800i	−0.966703	+	0.255900i	$0.917628\pi$
$398$	−2.02185	−	4.12359i	−0.101346	−	0.206697i
$399$		0			0
$400$		0			0
$401$	−15.2505			−0.761572			−0.380786	−	0.924663i	$-0.624346\pi$
$401$	−15.2505			−0.761572			−0.380786	+	0.924663i	$0.624346\pi$
$402$		0			0
$403$		−	13.3598i		−	0.665500i
$404$	13.4456	+	10.4149i	0.668942	+	0.518160i
$405$		0			0
$406$	−11.4495	+	5.61385i	−0.568229	+	0.278611i
$407$	−7.21959			−0.357862
$408$		0			0
$409$	1.89898			0.0938985			0.0469492	−	0.998897i	$-0.485050\pi$
$409$	1.89898			0.0938985			0.0469492	+	0.998897i	$0.485050\pi$
$410$		0			0
$411$		0			0
$412$	3.55051	−	4.58369i	0.174921	−	0.225822i
$413$		−	14.7244i		−	0.724541i
$414$		0			0
$415$		0			0
$416$	−14.2568	−	16.6356i	−0.698999	−	0.815626i
$417$		0			0
$418$	0.505103	+	1.03016i	0.0247054	+	0.0503868i
$419$			38.4656i			1.87917i	0.342317	+	0.939585i	$0.388788\pi$
$419$			38.4656i			1.87917i	−0.342317	+	0.939585i	$0.611212\pi$
$420$		0			0
$421$		−	37.3084i		−	1.81830i	−0.416467	−	0.909151i	$-0.636732\pi$
$421$		−	37.3084i		−	1.81830i	0.416467	−	0.909151i	$-0.363268\pi$
$422$	−26.8000	+	13.1404i	−1.30460	+	0.639665i
$423$		0			0
$424$	−2.24745	+	10.9082i	−0.109146	+	0.529751i
$425$		0			0
$426$		0			0
$427$		−	3.55353i		−	0.171967i
$428$	17.8666	+	13.8394i	0.863617	+	0.668955i
$429$		0			0
$430$		0			0
$431$	−4.42108			−0.212956			−0.106478	−	0.994315i	$-0.533957\pi$
$431$	−4.42108			−0.212956			−0.106478	+	0.994315i	$0.533957\pi$
$432$		0			0
$433$	26.5959			1.27812			0.639059	−	0.769158i	$-0.279324\pi$
$433$	26.5959			1.27812			0.639059	+	0.769158i	$0.279324\pi$
$434$	−3.11299	−	6.34896i	−0.149428	−	0.304760i
$435$		0			0
$436$	13.8763	+	10.7485i	0.664553	+	0.514761i
$437$		−	3.93765i		−	0.188363i
$438$		0			0
$439$	27.0454			1.29081			0.645403	−	0.763842i	$-0.276689\pi$
$439$	27.0454			1.29081			0.645403	+	0.763842i	$0.276689\pi$
$440$		0			0
$441$		0			0
$442$	15.0000	−	7.35472i	0.713477	−	0.349828i
$443$			35.0411i			1.66485i	0.554136	+	0.832426i	$0.313049\pi$
$443$			35.0411i			1.66485i	−0.554136	+	0.832426i	$0.686951\pi$
$444$		0			0
$445$		0			0
$446$	−8.93332	−	18.2196i	−0.423005	−	0.862722i
$447$		0			0
$448$	−10.6515	−	4.58369i	−0.503238	−	0.216559i
$449$	39.3431			1.85671			0.928357	−	0.371689i	$-0.121221\pi$
$449$	39.3431			1.85671			0.928357	+	0.371689i	$0.121221\pi$
$450$		0			0
$451$		−	9.16738i		−	0.431675i
$452$	7.47117	−	9.64524i	0.351414	−	0.453674i
$453$		0			0
$454$	27.2474	−	13.3598i	1.27879	−	0.627007i
$455$		0			0
$456$		0			0
$457$	8.69694			0.406826			0.203413	−	0.979093i	$-0.434797\pi$
$457$	8.69694			0.406826			0.203413	+	0.979093i	$0.434797\pi$
$458$	22.7845	−	11.1716i	1.06465	−	0.522014i
$459$		0			0
$460$		0			0
$461$			10.7868i			0.502389i	0.967937	+	0.251195i	$0.0808234\pi$
$461$			10.7868i			0.502389i	−0.967937	+	0.251195i	$0.919177\pi$
$462$		0			0
$463$	2.89898			0.134727			0.0673635	−	0.997728i	$-0.478541\pi$
$463$	2.89898			0.134727			0.0673635	+	0.997728i	$0.478541\pi$
$464$	−24.0926	+	6.22069i	−1.11847	+	0.288788i
$465$		0			0
$466$	11.2020	+	22.8466i	0.518925	+	1.05835i
$467$		−	4.45075i		−	0.205956i	−0.994684	−	0.102978i	$-0.967163\pi$
$467$		−	4.45075i		−	0.205956i	0.994684	−	0.102978i	$-0.0328372\pi$
$468$		0			0
$469$			19.3649i			0.894189i
$470$		0			0
$471$		0			0
$472$	5.79796	−	28.1410i	0.266873	−	1.29530i
$473$	−8.03087			−0.369260
$474$		0			0
$475$		0			0
$476$	5.41469	−	6.99034i	0.248182	−	0.320402i
$477$		0			0
$478$	−12.7526	−	26.0089i	−0.583288	−	1.18962i
$479$	−16.0617			−0.733880			−0.366940	−	0.930245i	$-0.619595\pi$
$479$	−16.0617			−0.733880			−0.366940	+	0.930245i	$0.619595\pi$
$480$		0			0
$481$	−24.4949			−1.11687
$482$	−3.54690	−	7.23393i	−0.161557	−	0.329496i
$483$		0			0
$484$	−11.8763	+	15.3322i	−0.539831	+	0.696918i
$485$		0			0
$486$		0			0
$487$	43.0454			1.95057			0.975287	−	0.220943i	$-0.0709134\pi$
$487$	43.0454			1.95057			0.975287	+	0.220943i	$0.0709134\pi$
$488$	1.39926	−	6.79144i	0.0633413	−	0.307434i
$489$		0			0
$490$		0			0
$491$			22.5997i			1.01991i	0.860201	+	0.509955i	$0.170338\pi$
$491$			22.5997i			1.01991i	−0.860201	+	0.509955i	$0.829662\pi$
$492$		0			0
$493$		−	18.9737i		−	0.854531i
$494$	1.71373	+	3.49517i	0.0771044	+	0.157255i
$495$		0			0
$496$	−3.44949	−	13.3598i	−0.154887	−	0.599873i
$497$	−16.8730			−0.756859
$498$		0			0
$499$			11.9384i			0.534436i	0.963636	+	0.267218i	$0.0861044\pi$
$499$			11.9384i			0.534436i	−0.963636	+	0.267218i	$0.913896\pi$
$500$		0			0
$501$		0			0
$502$	−15.7980	+	7.74597i	−0.705097	+	0.345719i
$503$	28.8218			1.28510			0.642551	−	0.766243i	$-0.277876\pi$
$503$	28.8218			1.28510			0.642551	+	0.766243i	$0.277876\pi$
$504$		0			0
$505$		0			0
$506$	−8.03087	+	3.93765i	−0.357016	+	0.175050i
$507$		0			0
$508$	19.3485	−	24.9788i	0.858450	−	1.10825i
$509$		−	18.0336i		−	0.799327i	−0.916662	−	0.399664i	$-0.869127\pi$
$509$		−	18.0336i		−	0.799327i	0.916662	−	0.399664i	$-0.130873\pi$
$510$		0			0
$511$	4.20204			0.185887
$512$	−18.5521	−	12.9545i	−0.819896	−	0.572512i
$513$		0			0
$514$	−6.89898	−	14.0705i	−0.304301	−	0.620624i
$515$		0			0
$516$		0			0
$517$		−	5.68565i		−	0.250054i
$518$	−11.6407	+	5.70759i	−0.511461	+	0.250777i
$519$		0			0
$520$		0			0
$521$	−15.2505			−0.668135			−0.334067	−	0.942549i	$-0.608421\pi$
$521$	−15.2505			−0.668135			−0.334067	+	0.942549i	$0.608421\pi$
$522$		0			0
$523$			10.5170i			0.459876i	0.973205	+	0.229938i	$0.0738523\pi$
$523$			10.5170i			0.459876i	−0.973205	+	0.229938i	$0.926148\pi$
$524$	−14.2568	−	11.0433i	−0.622813	−	0.482429i
$525$		0			0
$526$	−6.55051	−	13.3598i	−0.285616	−	0.582516i
$527$	10.5213			0.458313
$528$		0			0
$529$	7.69694			0.334649
$530$		0			0
$531$		0			0
$532$	1.62883	+	1.26168i	0.0706186	+	0.0547009i
$533$		−	31.1034i		−	1.34724i
$534$		0			0
$535$		0			0
$536$	−7.62523	+	37.0099i	−0.329360	+	1.59858i
$537$		0			0
$538$	36.5959	−	17.9435i	1.57776	−	0.773599i
$539$			5.59227i			0.240876i
$540$		0			0
$541$		−	16.5221i		−	0.710340i	−0.934802	−	0.355170i	$-0.884423\pi$
$541$		−	16.5221i		−	0.710340i	0.934802	−	0.355170i	$-0.115577\pi$
$542$	9.27607	+	18.9186i	0.398441	+	0.812624i
$543$		0			0
$544$	13.1010	−	11.2277i	0.561702	−	0.481384i
$545$		0			0
$546$		0			0
$547$			21.8165i			0.932806i	0.884572	+	0.466403i	$0.154450\pi$
$547$			21.8165i			0.932806i	−0.884572	+	0.466403i	$0.845550\pi$
$548$	6.10018	−	7.87530i	0.260587	−	0.336416i
$549$		0			0
$550$		0			0
$551$	4.42108			0.188344
$552$		0			0
$553$	10.0000			0.425243
$554$	1.30809	−	0.641375i	0.0555754	−	0.0272494i
$555$		0			0
$556$	34.4949	+	26.7196i	1.46291	+	1.13316i
$557$		0			0		1.00000			$0$
$557$		0			0		−1.00000			$\pi$
$558$		0			0
$559$	−27.2474			−1.15244
$560$		0			0
$561$		0			0
$562$	−5.00000	−	10.1975i	−0.210912	−	0.430157i
$563$		−	2.16772i		−	0.0913584i	−0.998956	−	0.0456792i	$-0.985455\pi$
$563$		−	2.16772i		−	0.0913584i	0.998956	−	0.0456792i	$-0.0145452\pi$
$564$		0			0
$565$		0			0
$566$	8.93332	−	4.38014i	0.375495	−	0.184111i
$567$		0			0
$568$	−32.2474	−	6.64401i	−1.35307	−	0.278776i
$569$	−8.03087			−0.336672			−0.168336	−	0.985730i	$-0.553839\pi$
$569$	−8.03087			−0.336672			−0.168336	+	0.985730i	$0.553839\pi$
$570$		0			0
$571$		−	14.7812i		−	0.618575i	−0.950969	−	0.309288i	$-0.899909\pi$
$571$		−	14.7812i		−	0.618575i	0.950969	−	0.309288i	$-0.100091\pi$
$572$	5.41469	−	6.99034i	0.226400	−	0.292281i
$573$		0			0
$574$	−7.24745	−	14.7812i	−0.302503	−	0.616957i
$575$		0			0
$576$		0			0
$577$	13.6969			0.570211			0.285106	−	0.958496i	$-0.407971\pi$
$577$	13.6969			0.570211			0.285106	+	0.958496i	$0.407971\pi$
$578$	−4.79209	−	9.77351i	−0.199325	−	0.406525i
$579$		0			0
$580$		0			0
$581$		−	18.0336i		−	0.748162i
$582$		0			0
$583$	−4.49490			−0.186160
$584$	8.03087	+	1.65462i	0.332320	+	0.0684686i
$585$		0			0
$586$	10.0000	−	4.90314i	0.413096	−	0.202547i
$587$			3.42455i			0.141346i	0.997500	+	0.0706732i	$0.0225147\pi$
$587$			3.42455i			0.141346i	−0.997500	+	0.0706732i	$0.977485\pi$
$588$		0			0
$589$			2.45157i			0.101015i
$590$		0			0
$591$		0			0
$592$	−24.4949	+	6.32456i	−1.00673	+	0.259938i
$593$	6.91147			0.283820			0.141910	−	0.989880i	$-0.454676\pi$
$593$	6.91147			0.283820			0.141910	+	0.989880i	$0.454676\pi$
$594$		0			0
$595$		0			0
$596$	28.5137	+	22.0866i	1.16797	+	0.904703i
$597$		0			0
$598$	−27.2474	+	13.3598i	−1.11423	+	0.546324i
$599$	−39.3431			−1.60751			−0.803757	−	0.594957i	$-0.797169\pi$
$599$	−39.3431			−1.60751			−0.803757	+	0.594957i	$0.797169\pi$
$600$		0			0
$601$	−9.89898			−0.403788			−0.201894	−	0.979407i	$-0.564710\pi$
$601$	−9.89898			−0.403788			−0.201894	+	0.979407i	$0.564710\pi$
$602$	−12.9488	+	6.34896i	−0.527752	+	0.258764i
$603$		0			0
$604$	−2.87628	+	3.71326i	−0.117034	+	0.151090i
$605$		0			0
$606$		0			0
$607$	−11.3031			−0.458777			−0.229389	−	0.973335i	$-0.573673\pi$
$607$	−11.3031			−0.458777			−0.229389	+	0.973335i	$0.573673\pi$
$608$	2.61618	+	3.05268i	0.106100	+	0.123803i
$609$		0			0
$610$		0			0
$611$		−	19.2905i		−	0.780409i
$612$		0			0
$613$			31.6228i			1.27723i	0.769526	+	0.638616i	$0.220493\pi$
$613$			31.6228i			1.27723i	−0.769526	+	0.638616i	$0.779507\pi$
$614$	10.7382	−	5.26510i	0.433359	−	0.212482i
$615$		0			0
$616$	0.944387	−	4.58369i	0.0380504	−	0.184682i
$617$	36.2930			1.46110			0.730550	−	0.682859i	$-0.239264\pi$
$617$	36.2930			1.46110			0.730550	+	0.682859i	$0.239264\pi$
$618$		0			0
$619$			44.9826i			1.80800i	0.427529	+	0.904002i	$0.359384\pi$
$619$			44.9826i			1.80800i	−0.427529	+	0.904002i	$0.640616\pi$
$620$		0			0
$621$		0			0
$622$	−20.0000	−	40.7902i	−0.801927	−	1.63554i
$623$	−23.2813			−0.932747
$624$		0			0
$625$		0			0
$626$	−10.3326	−	21.0734i	−0.412973	−	0.842261i
$627$		0			0
$628$	26.1237	+	20.2353i	1.04245	+	0.807478i
$629$		−	19.2905i		−	0.769162i
$630$		0			0
$631$	−23.4495			−0.933509			−0.466755	−	0.884387i	$-0.654577\pi$
$631$	−23.4495			−0.933509			−0.466755	+	0.884387i	$0.654577\pi$
$632$	19.1118	+	3.93765i	0.760228	+	0.156631i
$633$		0			0
$634$	−22.8990	+	11.2277i	−0.909435	+	0.445909i
$635$		0			0
$636$		0			0
$637$			18.9737i			0.751764i
$638$	−4.42108	−	9.01682i	−0.175032	−	0.356979i
$639$		0			0
$640$		0			0
$641$	7.21959			0.285157			0.142578	−	0.989784i	$-0.454461\pi$
$641$	7.21959			0.285157			0.142578	+	0.989784i	$0.454461\pi$
$642$		0			0
$643$			3.48173i			0.137306i	0.997641	+	0.0686531i	$0.0218702\pi$
$643$			3.48173i			0.137306i	−0.997641	+	0.0686531i	$0.978130\pi$
$644$	−9.83577	+	12.6979i	−0.387584	+	0.500368i
$645$		0			0
$646$	−2.75255	+	1.34962i	−0.108298	+	0.0530999i
$647$	−12.2004			−0.479646			−0.239823	−	0.970817i	$-0.577089\pi$
$647$	−12.2004			−0.479646			−0.239823	+	0.970817i	$0.577089\pi$
$648$		0			0
$649$	11.5959			0.455180
$650$		0			0
$651$		0			0
$652$	−13.3712	−	10.3573i	−0.523656	−	0.405622i
$653$			12.4414i			0.486869i	0.969917	+	0.243434i	$0.0782740\pi$
$653$			12.4414i			0.486869i	−0.969917	+	0.243434i	$0.921726\pi$
$654$		0			0
$655$		0			0
$656$	−8.03087	−	31.1034i	−0.313553	−	1.21438i
$657$		0			0
$658$	−4.49490	−	9.16738i	−0.175229	−	0.357382i
$659$		−	15.8659i		−	0.618049i	−0.951054	−	0.309024i	$-0.899998\pi$
$659$		−	15.8659i		−	0.618049i	0.951054	−	0.309024i	$-0.100002\pi$
$660$		0			0
$661$			24.6593i			0.959136i	0.877505	+	0.479568i	$0.159207\pi$
$661$			24.6593i			0.959136i	−0.877505	+	0.479568i	$0.840793\pi$
$662$	16.0617	−	7.87530i	0.624257	−	0.306082i
$663$		0			0
$664$	7.10102	−	34.4656i	0.275573	−	1.33752i
$665$		0			0
$666$		0			0
$667$			34.4656i			1.33451i
$668$	−20.3570	+	26.2808i	−0.787637	+	1.01684i
$669$		0			0
$670$		0			0
$671$	2.79851			0.108035
$672$		0			0
$673$	−17.1010			−0.659196			−0.329598	−	0.944121i	$-0.606913\pi$
$673$	−17.1010			−0.659196			−0.329598	+	0.944121i	$0.606913\pi$
$674$	−0.496807	−	1.01324i	−0.0191363	−	0.0390286i
$675$		0			0
$676$	2.44949	−	3.16228i	0.0942111	−	0.121626i
$677$			9.52992i			0.366265i	0.983088	+	0.183132i	$0.0586237\pi$
$677$			9.52992i			0.366265i	−0.983088	+	0.183132i	$0.941376\pi$
$678$		0			0
$679$	19.8536			0.761910
$680$		0			0
$681$		0			0
$682$	5.00000	−	2.45157i	0.191460	−	0.0938755i
$683$		−	6.84910i		−	0.262074i	−0.991378	−	0.131037i	$-0.958169\pi$
$683$		−	6.84910i		−	0.262074i	0.991378	−	0.131037i	$-0.0418306\pi$
$684$		0			0
$685$		0			0
$686$	10.7382	+	21.9007i	0.409987	+	0.836172i
$687$		0			0
$688$	−27.2474	+	7.03526i	−1.03880	+	0.268217i
$689$	−15.2505			−0.580996
$690$		0			0
$691$		−	37.9473i		−	1.44358i	−0.692110	−	0.721792i	$-0.743319\pi$
$691$		−	37.9473i		−	1.44358i	0.692110	−	0.721792i	$-0.256681\pi$
$692$	25.8975	+	20.0601i	0.984476	+	0.762572i
$693$		0			0
$694$	10.0000	−	4.90314i	0.379595	−	0.186121i
$695$		0			0
$696$		0			0
$697$	24.4949			0.927810
$698$	−16.0617	+	7.87530i	−0.607946	+	0.298085i
$699$		0			0
$700$		0			0
$701$		−	2.91145i		−	0.109964i	−0.998487	−	0.0549820i	$-0.982490\pi$
$701$		−	2.91145i		−	0.109964i	0.998487	−	0.0549820i	$-0.0175101\pi$
$702$		0			0
$703$	4.49490			0.169528
$704$	3.60979	−	8.38840i	0.136049	−	0.316150i
$705$		0			0
$706$	18.7980	+	38.3386i	0.707471	+	1.44289i
$707$			12.3261i			0.463569i
$708$		0			0
$709$			24.2681i			0.911406i	0.890132	+	0.455703i	$0.150612\pi$
$709$			24.2681i			0.911406i	−0.890132	+	0.455703i	$0.849388\pi$
$710$		0			0
$711$		0			0
$712$	−44.4949	−	9.16738i	−1.66752	−	0.343562i
$713$	−19.1118			−0.715744
$714$		0			0
$715$		0			0
$716$	−28.5137	−	22.0866i	−1.06561	−	0.825415i
$717$		0			0
$718$	−2.75255	−	5.61385i	−0.102724	−	0.209507i
$719$	43.7642			1.63213			0.816064	−	0.577962i	$-0.196152\pi$
$719$	43.7642			1.63213			0.816064	+	0.577962i	$0.196152\pi$
$720$		0			0
$721$	4.20204			0.156492
$722$	11.5149	+	23.4847i	0.428539	+	0.874009i
$723$		0			0
$724$	−28.3712	−	21.9762i	−1.05441	−	0.816740i
$725$		0			0
$726$		0			0
$727$	38.5505			1.42976			0.714880	−	0.699248i	$-0.246481\pi$
$727$	38.5505			1.42976			0.714880	+	0.699248i	$0.246481\pi$
$728$	3.20415	−	15.5517i	0.118754	−	0.576385i
$729$		0			0
$730$		0			0
$731$		−	21.4582i		−	0.793660i
$732$		0			0
$733$			30.9839i			1.14442i	0.820109	+	0.572208i	$0.193913\pi$
$733$			30.9839i			1.14442i	−0.820109	+	0.572208i	$0.806087\pi$
$734$	−11.5495	−	23.5553i	−0.426300	−	0.869442i
$735$		0			0
$736$	−23.7980	+	20.3951i	−0.877204	+	0.751773i
$737$	−15.2505			−0.561758
$738$		0			0
$739$		−	30.9839i		−	1.13976i	−0.821728	−	0.569880i	$-0.806990\pi$
$739$		−	30.9839i		−	1.13976i	0.821728	−	0.569880i	$-0.193010\pi$
$740$		0			0
$741$		0			0
$742$	−7.24745	+	3.55353i	−0.266062	+	0.130454i
$743$	−33.2429			−1.21956			−0.609782	−	0.792569i	$-0.708743\pi$
$743$	−33.2429			−1.21956			−0.609782	+	0.792569i	$0.708743\pi$
$744$		0			0
$745$		0			0
$746$	16.5586	−	8.11890i	0.606252	−	0.297254i
$747$		0			0
$748$	5.50510	+	4.26423i	0.201286	+	0.155916i
$749$			16.3790i			0.598477i
$750$		0			0
$751$	16.2020			0.591221			0.295610	−	0.955309i	$-0.404477\pi$
$751$	16.2020			0.591221			0.295610	+	0.955309i	$0.404477\pi$
$752$	−4.98078	−	19.2905i	−0.181630	−	0.703451i
$753$		0			0
$754$	−15.0000	−	30.5926i	−0.546268	−	1.11412i
$755$		0			0
$756$		0			0
$757$			50.9877i			1.85318i	0.376074	+	0.926590i	$0.377274\pi$
$757$			50.9877i			1.85318i	−0.376074	+	0.926590i	$0.622726\pi$
$758$	7.12842	−	3.49517i	0.258916	−	0.126950i
$759$		0			0
$760$		0			0
$761$	32.1235			1.16448			0.582238	−	0.813019i	$-0.302177\pi$
$761$	32.1235			1.16448			0.582238	+	0.813019i	$0.302177\pi$
$762$		0			0
$763$			12.7209i			0.460528i
$764$	14.2568	−	18.4055i	0.515795	−	0.665888i
$765$		0			0
$766$	3.79796	+	7.74597i	0.137226	+	0.279873i
$767$	39.3431			1.42060
$768$		0			0
$769$	24.7980			0.894237			0.447119	−	0.894475i	$-0.352450\pi$
$769$	24.7980			0.894237			0.447119	+	0.894475i	$0.352450\pi$
$770$		0			0
$771$		0			0
$772$	2.57321	−	3.32201i	0.0926120	−	0.119562i
$773$			18.6621i			0.671228i	0.942000	+	0.335614i	$0.108944\pi$
$773$			18.6621i			0.671228i	−0.942000	+	0.335614i	$0.891056\pi$
$774$		0			0
$775$		0			0
$776$	37.9438	+	7.81765i	1.36210	+	0.280637i
$777$		0			0
$778$	12.1010	−	5.93330i	0.433843	−	0.212719i
$779$			5.70759i			0.204495i
$780$		0			0
$781$		−	13.2880i		−	0.475483i
$782$	−10.5213	−	21.4582i	−0.376240	−	0.767343i
$783$		0			0
$784$	4.89898	+	18.9737i	0.174964	+	0.677631i
$785$		0			0
$786$		0			0
$787$			33.7549i			1.20323i	0.798785	+	0.601616i	$0.205476\pi$
$787$			33.7549i			1.20323i	−0.798785	+	0.601616i	$0.794524\pi$
$788$	−42.9529	−	33.2711i	−1.53013	−	1.18524i
$789$		0			0
$790$		0			0
$791$	8.84215			0.314391
$792$		0			0
$793$	9.49490			0.337174
$794$	−12.9488	+	6.34896i	−0.459534	+	0.225316i
$795$		0			0
$796$	3.97730	−	5.13467i	0.140972	−	0.181993i
$797$		−	5.59227i		−	0.198088i	−0.995083	−	0.0990442i	$-0.968421\pi$
$797$		−	5.59227i		−	0.198088i	0.995083	−	0.0990442i	$-0.0315785\pi$
$798$		0			0
$799$	15.1918			0.537449
$800$		0			0
$801$		0			0
$802$	−9.49490	−	19.3649i	−0.335276	−	0.683799i
$803$			3.30923i			0.116780i
$804$		0			0
$805$		0			0
$806$	16.9642	−	8.31779i	0.597538	−	0.292982i
$807$		0			0
$808$	−4.85357	+	23.5574i	−0.170748	+	0.828745i
$809$	8.03087			0.282350			0.141175	−	0.989985i	$-0.454912\pi$
$809$	8.03087			0.282350			0.141175	+	0.989985i	$0.454912\pi$
$810$		0			0
$811$			45.7651i			1.60703i	0.595285	+	0.803515i	$0.297039\pi$
$811$			45.7651i			1.60703i	−0.595285	+	0.803515i	$0.702961\pi$
$812$	−14.2568	−	11.0433i	−0.500317	−	0.387544i
$813$		0			0
$814$	−4.49490	−	9.16738i	−0.157546	−	0.321316i
$815$		0			0
$816$		0			0
$817$	5.00000			0.174928
$818$	1.18230	+	2.41131i	0.0413381	+	0.0843095i
$819$		0			0
$820$		0			0
$821$			28.1920i			0.983907i	0.870622	+	0.491953i	$0.163717\pi$
$821$			28.1920i			0.983907i	−0.870622	+	0.491953i	$0.836283\pi$
$822$		0			0
$823$	28.8434			1.00542			0.502708	−	0.864456i	$-0.332337\pi$
$823$	28.8434			1.00542			0.502708	+	0.864456i	$0.332337\pi$
$824$	8.03087	+	1.65462i	0.279769	+	0.0576413i
$825$		0			0
$826$	18.6969	−	9.16738i	0.650550	−	0.318974i
$827$		−	13.5829i		−	0.472323i	−0.971714	−	0.236162i	$-0.924111\pi$
$827$		−	13.5829i		−	0.472323i	0.971714	−	0.236162i	$-0.0758895\pi$
$828$		0			0
$829$		−	24.6593i		−	0.856453i	−0.903671	−	0.428227i	$-0.859138\pi$
$829$		−	24.6593i		−	0.856453i	0.903671	−	0.428227i	$-0.140862\pi$
$830$		0			0
$831$		0			0
$832$	12.2474	−	28.4605i	0.424604	−	0.986690i
$833$	−14.9423			−0.517721
$834$		0			0
$835$		0			0
$836$	−0.993614	+	1.28275i	−0.0343649	+	0.0443649i
$837$		0			0
$838$	−48.8434	+	23.9486i	−1.68727	+	0.827291i
$839$	27.7024			0.956393			0.478197	−	0.878253i	$-0.341291\pi$
$839$	27.7024			0.956393			0.478197	+	0.878253i	$0.341291\pi$
$840$		0			0
$841$	−9.69694			−0.334377
$842$	47.3739	−	23.2281i	1.63261	−	0.800494i
$843$		0			0
$844$	−33.3712	−	25.8492i	−1.14868	−	0.889766i
$845$		0			0
$846$		0			0
$847$	−14.0556			−0.482957
$848$	−15.2505	+	3.93765i	−0.523703	+	0.135220i
$849$		0			0
$850$		0			0
$851$			35.0411i			1.20119i
$852$		0			0
$853$		−	17.9435i		−	0.614374i	−0.951649	−	0.307187i	$-0.900612\pi$
$853$		−	17.9435i		−	0.614374i	0.951649	−	0.307187i	$-0.0993877\pi$
$854$	4.51224	−	2.21242i	0.154406	−	0.0757074i
$855$		0			0
$856$	−6.44949	+	31.3033i	−0.220439	+	1.06993i
$857$	21.0425			0.718799			0.359399	−	0.933184i	$-0.382982\pi$
$857$	21.0425			0.718799			0.359399	+	0.933184i	$0.382982\pi$
$858$		0			0
$859$			18.3348i			0.625574i	0.949823	+	0.312787i	$0.101263\pi$
$859$			18.3348i			0.625574i	−0.949823	+	0.312787i	$0.898737\pi$
$860$		0			0
$861$		0			0
$862$	−2.75255	−	5.61385i	−0.0937523	−	0.191208i
$863$	−6.10018			−0.207653			−0.103826	−	0.994595i	$-0.533109\pi$
$863$	−6.10018			−0.207653			−0.103826	+	0.994595i	$0.533109\pi$
$864$		0			0
$865$		0			0
$866$	16.5586	+	33.7713i	0.562682	+	1.14760i
$867$		0			0
$868$	6.12372	−	7.90569i	0.207853	−	0.268337i
$869$			7.87530i			0.267151i
$870$		0			0
$871$	−51.7423			−1.75322
$872$	−5.00905	+	24.3120i	−0.169628	+	0.823308i
$873$		0			0
$874$	5.00000	−	2.45157i	0.169128	−	0.0829257i
$875$		0			0
$876$		0			0
$877$			33.4354i			1.12903i	0.825421	+	0.564517i	$0.190938\pi$
$877$			33.4354i			1.12903i	−0.825421	+	0.564517i	$0.809062\pi$
$878$	16.8384	+	34.3420i	0.568269	+	1.15899i
$879$		0			0
$880$		0			0
$881$	39.3431			1.32550			0.662751	−	0.748840i	$-0.269389\pi$
$881$	39.3431			1.32550			0.662751	+	0.748840i	$0.269389\pi$
$882$		0			0
$883$			38.6580i			1.30095i	0.759529	+	0.650473i	$0.225429\pi$
$883$			38.6580i			1.30095i	−0.759529	+	0.650473i	$0.774571\pi$
$884$	18.6779	+	14.4679i	0.628207	+	0.486607i
$885$		0			0
$886$	−44.4949	+	21.8165i	−1.49484	+	0.732939i
$887$	−13.8229			−0.464129			−0.232064	−	0.972700i	$-0.574548\pi$
$887$	−13.8229			−0.464129			−0.232064	+	0.972700i	$0.574548\pi$
$888$		0			0
$889$	22.8990			0.768007
$890$		0			0
$891$		0			0
$892$	17.5732	−	22.6869i	0.588395	−	0.759614i
$893$			3.53987i			0.118457i
$894$		0			0
$895$		0			0
$896$	−0.811283	−	16.3790i	−0.0271031	−	0.547185i
$897$		0			0
$898$	24.4949	+	49.9575i	0.817405	+	1.66710i
$899$		−	21.4582i		−	0.715671i
$900$		0			0
$901$		−	12.0102i		−	0.400118i
$902$	11.6407	−	5.70759i	0.387592	−	0.190042i
$903$		0			0
$904$	16.8990	+	3.48173i	0.562052	+	0.115801i
$905$		0			0
$906$		0			0
$907$		−	5.68565i		−	0.188789i	−0.995535	−	0.0943944i	$-0.969909\pi$
$907$		−	5.68565i		−	0.188789i	0.995535	−	0.0943944i	$-0.0300915\pi$
$908$	33.9284	+	26.2808i	1.12595	+	0.872159i
$909$		0			0
$910$		0			0
$911$	48.1852			1.59645			0.798224	−	0.602361i	$-0.205773\pi$
$911$	48.1852			1.59645			0.798224	+	0.602361i	$0.205773\pi$
$912$		0			0
$913$	14.2020			0.470019
$914$	5.41469	+	11.0433i	0.179102	+	0.365280i
$915$		0			0
$916$	28.3712	+	21.9762i	0.937410	+	0.726115i
$917$		−	13.0698i		−	0.431602i
$918$		0			0
$919$	48.6413			1.60453			0.802265	−	0.596969i	$-0.203628\pi$
$919$	48.6413			1.60453			0.802265	+	0.596969i	$0.203628\pi$
$920$		0			0
$921$		0			0
$922$	−13.6969	+	6.71581i	−0.451085	+	0.221173i
$923$		−	45.0841i		−	1.48396i
$924$		0			0
$925$		0			0
$926$	1.80490	+	3.68110i	0.0593126	+	0.120969i
$927$		0			0
$928$	−22.8990	−	26.7196i	−0.751696	−	0.877115i
$929$	−0.811283			−0.0266173			−0.0133087	−	0.999911i	$-0.504236\pi$
$929$	−0.811283			−0.0266173			−0.0133087	+	0.999911i	$0.504236\pi$
$930$		0			0
$931$		−	3.48173i		−	0.114109i
$932$	−22.0361	+	28.4485i	−0.721818	+	0.931863i
$933$		0			0
$934$	5.65153	−	2.77103i	0.184924	−	0.0906708i
$935$		0			0
$936$		0			0
$937$	20.7980			0.679440			0.339720	−	0.940527i	$-0.389668\pi$
$937$	20.7980			0.679440			0.339720	+	0.940527i	$0.389668\pi$
$938$	−24.5894	+	12.0565i	−0.802873	+	0.393660i
$939$		0			0
$940$		0			0
$941$		−	41.8902i		−	1.36558i	−0.730614	−	0.682791i	$-0.760766\pi$
$941$		−	41.8902i		−	1.36558i	0.730614	−	0.682791i	$-0.239234\pi$
$942$		0			0
$943$	−44.4949			−1.44895
$944$	39.3431	−	10.1583i	1.28051	−	0.330626i
$945$		0			0
$946$	−5.00000	−	10.1975i	−0.162564	−	0.331551i
$947$		−	21.4582i		−	0.697298i	−0.937253	−	0.348649i	$-0.886641\pi$
$947$		−	21.4582i		−	0.697298i	0.937253	−	0.348649i	$-0.113359\pi$
$948$		0			0
$949$			11.2277i			0.364467i
$950$		0			0
$951$		0			0
$952$	12.2474	+	2.52337i	0.396942	+	0.0817828i
$953$	22.1619			0.717895			0.358948	−	0.933358i	$-0.383136\pi$
$953$	22.1619			0.717895			0.358948	+	0.933358i	$0.383136\pi$
$954$		0			0
$955$		0			0
$956$	25.0862	−	32.3862i	0.811347	−	1.04744i
$957$		0			0
$958$	−10.0000	−	20.3951i	−0.323085	−	0.658935i
$959$	7.21959			0.233133
$960$		0			0
$961$	−19.1010			−0.616162
$962$	−15.2505	−	31.1034i	−0.491695	−	1.00281i
$963$		0			0
$964$	6.97730	−	9.00765i	0.224724	−	0.290117i
$965$		0			0
$966$		0			0
$967$	60.2929			1.93889			0.969444	−	0.245314i	$-0.0788909\pi$
$967$	60.2929			1.93889			0.969444	+	0.245314i	$0.0788909\pi$
$968$	−26.8629	−	5.53461i	−0.863405	−	0.177889i
$969$		0			0
$970$		0			0
$971$		−	31.7318i		−	1.01832i	−0.860671	−	0.509162i	$-0.829956\pi$
$971$		−	31.7318i		−	1.01832i	0.860671	−	0.509162i	$-0.170044\pi$
$972$		0			0
$973$			31.6228i			1.01378i
$974$	26.8000	+	54.6587i	0.858726	+	1.75138i
$975$		0			0
$976$	9.49490	−	2.45157i	0.303924	−	0.0784729i
$977$	53.1660			1.70093			0.850466	−	0.526031i	$-0.176320\pi$
$977$	53.1660			1.70093			0.850466	+	0.526031i	$0.176320\pi$
$978$		0			0
$979$		−	18.3348i		−	0.585981i
$980$		0			0
$981$		0			0
$982$	−28.6969	+	14.0705i	−0.915756	+	0.449008i
$983$	1.11940			0.0357035			0.0178517	−	0.999841i	$-0.494317\pi$
$983$	1.11940			0.0357035			0.0178517	+	0.999841i	$0.494317\pi$
$984$		0			0
$985$		0			0
$986$	24.0926	−	11.8130i	0.767265	−	0.376201i
$987$		0			0
$988$	−3.37117	+	4.35217i	−0.107251	+	0.138461i
$989$			38.9787i			1.23945i
$990$		0			0
$991$	29.2474			0.929076			0.464538	−	0.885553i	$-0.346220\pi$
$991$	29.2474			0.929076			0.464538	+	0.885553i	$0.346220\pi$
$992$	14.8165	−	12.6979i	0.470426	−	0.403159i
$993$		0			0
$994$	−10.5051	−	21.4252i	−0.333202	−	0.679567i
$995$		0			0
$996$		0			0
$997$		−	12.6491i		−	0.400601i	−0.979734	−	0.200301i	$-0.935808\pi$
$997$		−	12.6491i		−	0.400601i	0.979734	−	0.200301i	$-0.0641919\pi$
$998$	−15.1593	+	7.43282i	−0.479859	+	0.235282i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1800.2.k.s.901.6	yes	8
3.2	odd	2	inner	1800.2.k.s.901.3	yes	8
4.3	odd	2		7200.2.k.q.3601.7		8
5.2	odd	4		1800.2.d.u.1549.3		16
5.3	odd	4		1800.2.d.u.1549.14		16
5.4	even	2		1800.2.k.r.901.3	✓	8
8.3	odd	2		7200.2.k.q.3601.6		8
8.5	even	2	inner	1800.2.k.s.901.5	yes	8
12.11	even	2		7200.2.k.q.3601.5		8
15.2	even	4		1800.2.d.u.1549.13		16
15.8	even	4		1800.2.d.u.1549.4		16
15.14	odd	2		1800.2.k.r.901.6	yes	8
20.3	even	4		7200.2.d.u.2449.8		16
20.7	even	4		7200.2.d.u.2449.11		16
20.19	odd	2		7200.2.k.t.3601.4		8
24.5	odd	2	inner	1800.2.k.s.901.4	yes	8
24.11	even	2		7200.2.k.q.3601.8		8
40.3	even	4		7200.2.d.u.2449.5		16
40.13	odd	4		1800.2.d.u.1549.2		16
40.19	odd	2		7200.2.k.t.3601.1		8
40.27	even	4		7200.2.d.u.2449.10		16
40.29	even	2		1800.2.k.r.901.4	yes	8
40.37	odd	4		1800.2.d.u.1549.15		16
60.23	odd	4		7200.2.d.u.2449.6		16
60.47	odd	4		7200.2.d.u.2449.9		16
60.59	even	2		7200.2.k.t.3601.2		8
120.29	odd	2		1800.2.k.r.901.5	yes	8
120.53	even	4		1800.2.d.u.1549.16		16
120.59	even	2		7200.2.k.t.3601.3		8
120.77	even	4		1800.2.d.u.1549.1		16
120.83	odd	4		7200.2.d.u.2449.7		16
120.107	odd	4		7200.2.d.u.2449.12		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1800.2.d.u.1549.1		16	120.77	even	4
1800.2.d.u.1549.2		16	40.13	odd	4
1800.2.d.u.1549.3		16	5.2	odd	4
1800.2.d.u.1549.4		16	15.8	even	4
1800.2.d.u.1549.13		16	15.2	even	4
1800.2.d.u.1549.14		16	5.3	odd	4
1800.2.d.u.1549.15		16	40.37	odd	4
1800.2.d.u.1549.16		16	120.53	even	4
1800.2.k.r.901.3	✓	8	5.4	even	2
1800.2.k.r.901.4	yes	8	40.29	even	2
1800.2.k.r.901.5	yes	8	120.29	odd	2
1800.2.k.r.901.6	yes	8	15.14	odd	2
1800.2.k.s.901.3	yes	8	3.2	odd	2	inner
1800.2.k.s.901.4	yes	8	24.5	odd	2	inner
1800.2.k.s.901.5	yes	8	8.5	even	2	inner
1800.2.k.s.901.6	yes	8	1.1	even	1	trivial
7200.2.d.u.2449.5		16	40.3	even	4
7200.2.d.u.2449.6		16	60.23	odd	4
7200.2.d.u.2449.7		16	120.83	odd	4
7200.2.d.u.2449.8		16	20.3	even	4
7200.2.d.u.2449.9		16	60.47	odd	4
7200.2.d.u.2449.10		16	40.27	even	4
7200.2.d.u.2449.11		16	20.7	even	4
7200.2.d.u.2449.12		16	120.107	odd	4
7200.2.k.q.3601.5		8	12.11	even	2
7200.2.k.q.3601.6		8	8.3	odd	2
7200.2.k.q.3601.7		8	4.3	odd	2
7200.2.k.q.3601.8		8	24.11	even	2
7200.2.k.t.3601.1		8	40.19	odd	2
7200.2.k.t.3601.2		8	60.59	even	2
7200.2.k.t.3601.3		8	120.59	even	2
7200.2.k.t.3601.4		8	20.19	odd	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.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.622597 + 1.26979i) q^{2} +(-1.22474 + 1.58114i) q^{4} -1.44949 q^{7} +(-2.77024 - 0.570759i) q^{8} +O(q^{10})\)	\(q+(0.622597 + 1.26979i) q^{2} +(-1.22474 + 1.58114i) q^{4} -1.44949 q^{7} +(-2.77024 - 0.570759i) q^{8} -1.14152i q^{11} -3.87298i q^{13} +(-0.902449 - 1.84055i) q^{14} +(-1.00000 - 3.87298i) q^{16} +3.05009 q^{17} +0.710706i q^{19} +(1.44949 - 0.710706i) q^{22} -5.54048 q^{23} +(4.91788 - 2.41131i) q^{26} +(1.77526 - 2.29184i) q^{28} -6.22069i q^{29} +3.44949 q^{31} +(4.29529 - 3.68110i) q^{32} +(1.89898 + 3.87298i) q^{34} -6.32456i q^{37} +(-0.902449 + 0.442484i) q^{38} +8.03087 q^{41} -7.03526i q^{43} +(1.80490 + 1.39807i) q^{44} +(-3.44949 - 7.03526i) q^{46} +4.98078 q^{47} -4.89898 q^{49} +(6.12372 + 4.74342i) q^{52} -3.93765i q^{53} +(4.01544 + 0.827309i) q^{56} +(7.89898 - 3.87298i) q^{58} +10.1583i q^{59} +2.45157i q^{61} +(2.14764 + 4.38014i) q^{62} +(7.34847 + 3.16228i) q^{64} -13.3598i q^{67} +(-3.73558 + 4.82262i) q^{68} +11.6407 q^{71} -2.89898 q^{73} +(8.03087 - 3.93765i) q^{74} +(-1.12372 - 0.870433i) q^{76} +1.65462i q^{77} -6.89898 q^{79} +(5.00000 + 10.1975i) q^{82} +12.4414i q^{83} +(8.93332 - 4.38014i) q^{86} +(-0.651531 + 3.16228i) q^{88} +16.0617 q^{89} +5.61385i q^{91} +(6.78568 - 8.76027i) q^{92} +(3.10102 + 6.32456i) q^{94} -13.6969 q^{97} +(-3.05009 - 6.22069i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{7}+O(q^{10}) \) 8 * q + 8 * q^7	\( 8 q + 8 q^{7} - 8 q^{16} - 8 q^{22} + 24 q^{28} + 8 q^{31} - 24 q^{34} - 8 q^{46} + 24 q^{58} + 16 q^{73} + 40 q^{76} - 16 q^{79} + 40 q^{82} - 64 q^{88} + 64 q^{94} + 8 q^{97}+O(q^{100}) \) 8 * q + 8 * q^7 - 8 * q^16 - 8 * q^22 + 24 * q^28 + 8 * q^31 - 24 * q^34 - 8 * q^46 + 24 * q^58 + 16 * q^73 + 40 * q^76 - 16 * q^79 + 40 * q^82 - 64 * q^88 + 64 * q^94 + 8 * q^97

Introduction

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