LMFDB - Embedded newform 2100.2.q.i.1201.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(1201,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("2100.1201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1201.1
Root			$-1.32288 + 2.29129i$ of defining polynomial
Character	$\chi$	$=$	2100.1201
Dual form			2100.2.q.i.1801.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +(-1.32288 + 2.29129i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	$q+(0.500000 - 0.866025i) q^{3} +(-1.32288 + 2.29129i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(0.177124 - 0.306788i) q^{11} +1.00000 q^{13} +(-1.82288 + 3.15731i) q^{17} +(-0.322876 - 0.559237i) q^{19} +(1.32288 + 2.29129i) q^{21} +(1.00000 + 1.73205i) q^{23} -1.00000 q^{27} -3.29150 q^{29} +(-2.00000 + 3.46410i) q^{31} +(-0.177124 - 0.306788i) q^{33} +(1.14575 + 1.98450i) q^{37} +(0.500000 - 0.866025i) q^{39} -5.64575 q^{41} +3.29150 q^{43} +(6.46863 + 11.2040i) q^{47} +(-3.50000 - 6.06218i) q^{49} +(1.82288 + 3.15731i) q^{51} +(-3.82288 + 6.62141i) q^{53} -0.645751 q^{57} +(0.468627 - 0.811686i) q^{59} +(5.79150 + 10.0312i) q^{61} +2.64575 q^{63} +(-3.96863 + 6.87386i) q^{67} +2.00000 q^{69} -7.29150 q^{71} +(-2.14575 + 3.71655i) q^{73} +(0.468627 + 0.811686i) q^{77} +(0.677124 + 1.17281i) q^{79} +(-0.500000 + 0.866025i) q^{81} -1.64575 q^{83} +(-1.64575 + 2.85052i) q^{87} +(-3.46863 - 6.00784i) q^{89} +(-1.32288 + 2.29129i) q^{91} +(2.00000 + 3.46410i) q^{93} +3.70850 q^{97} -0.354249 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 - 2 * q^9	$ 4 q + 2 q^{3} - 2 q^{9} + 6 q^{11} + 4 q^{13} - 2 q^{17} + 4 q^{19} + 4 q^{23} - 4 q^{27} + 8 q^{29} - 8 q^{31} - 6 q^{33} - 6 q^{37} + 2 q^{39} - 12 q^{41} - 8 q^{43} + 10 q^{47} - 14 q^{49} + 2 q^{51} - 10 q^{53} + 8 q^{57} - 14 q^{59} + 2 q^{61} + 8 q^{69} - 8 q^{71} + 2 q^{73} - 14 q^{77} + 8 q^{79} - 2 q^{81} + 4 q^{83} + 4 q^{87} + 2 q^{89} + 8 q^{93} + 36 q^{97} - 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 - 2 * q^9 + 6 * q^11 + 4 * q^13 - 2 * q^17 + 4 * q^19 + 4 * q^23 - 4 * q^27 + 8 * q^29 - 8 * q^31 - 6 * q^33 - 6 * q^37 + 2 * q^39 - 12 * q^41 - 8 * q^43 + 10 * q^47 - 14 * q^49 + 2 * q^51 - 10 * q^53 + 8 * q^57 - 14 * q^59 + 2 * q^61 + 8 * q^69 - 8 * q^71 + 2 * q^73 - 14 * q^77 + 8 * q^79 - 2 * q^81 + 4 * q^83 + 4 * q^87 + 2 * q^89 + 8 * q^93 + 36 * q^97 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.32288	+	2.29129i	−0.500000	+	0.866025i
$7$	−1.32288	+	2.29129i	−0.500000	+	0.866025i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	0.177124	−	0.306788i	0.0534050	−	0.0925002i	−0.838087	−	0.545537i	$-0.816326\pi$
$11$	0.177124	−	0.306788i	0.0534050	−	0.0925002i	0.891492	+	0.453036i	$0.149659\pi$
$12$		0			0
$13$	1.00000			0.277350			0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000			0.277350			0.138675	+	0.990338i	$0.455716\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.82288	+	3.15731i	−0.442112	+	0.765761i	−0.997846	−	0.0655994i	$-0.979104\pi$
$17$	−1.82288	+	3.15731i	−0.442112	+	0.765761i	0.555734	+	0.831360i	$0.312437\pi$
$18$		0			0
$19$	−0.322876	−	0.559237i	−0.0740728	−	0.128298i	0.826610	−	0.562775i	$-0.190266\pi$
$19$	−0.322876	−	0.559237i	−0.0740728	−	0.128298i	−0.900683	+	0.434478i	$0.856933\pi$
$20$		0			0
$21$	1.32288	+	2.29129i	0.288675	+	0.500000i
$22$		0			0
$23$	1.00000	+	1.73205i	0.208514	+	0.361158i	0.951247	−	0.308431i	$-0.0998038\pi$
$23$	1.00000	+	1.73205i	0.208514	+	0.361158i	−0.742732	+	0.669588i	$0.766471\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−3.29150			−0.611217			−0.305608	−	0.952157i	$-0.598860\pi$
$29$	−3.29150			−0.611217			−0.305608	+	0.952157i	$0.598860\pi$
$30$		0			0
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	0.628619	+	0.777714i	$0.283621\pi$
$32$		0			0
$33$	−0.177124	−	0.306788i	−0.0308334	−	0.0534050i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	1.14575	+	1.98450i	0.188360	+	0.326250i	0.944704	−	0.327925i	$-0.106349\pi$
$37$	1.14575	+	1.98450i	0.188360	+	0.326250i	−0.756343	+	0.654175i	$0.773016\pi$
$38$		0			0
$39$	0.500000	−	0.866025i	0.0800641	−	0.138675i
$40$		0			0
$41$	−5.64575			−0.881718			−0.440859	−	0.897576i	$-0.645326\pi$
$41$	−5.64575			−0.881718			−0.440859	+	0.897576i	$0.645326\pi$
$42$		0			0
$43$	3.29150			0.501949			0.250975	−	0.967994i	$-0.419249\pi$
$43$	3.29150			0.501949			0.250975	+	0.967994i	$0.419249\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	6.46863	+	11.2040i	0.943546	+	1.63427i	0.758636	+	0.651515i	$0.225866\pi$
$47$	6.46863	+	11.2040i	0.943546	+	1.63427i	0.184910	+	0.982755i	$0.440801\pi$
$48$		0			0
$49$	−3.50000	−	6.06218i	−0.500000	−	0.866025i
$50$		0			0
$51$	1.82288	+	3.15731i	0.255254	+	0.442112i
$52$		0			0
$53$	−3.82288	+	6.62141i	−0.525112	+	0.909521i	0.474460	+	0.880277i	$0.342643\pi$
$53$	−3.82288	+	6.62141i	−0.525112	+	0.909521i	−0.999572	+	0.0292442i	$0.990690\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−0.645751			−0.0855319
$58$		0			0
$59$	0.468627	−	0.811686i	0.0610100	−	0.105672i	−0.833907	−	0.551905i	$-0.813901\pi$
$59$	0.468627	−	0.811686i	0.0610100	−	0.105672i	0.894917	+	0.446232i	$0.147235\pi$
$60$		0			0
$61$	5.79150	+	10.0312i	0.741526	+	1.28436i	0.951800	+	0.306718i	$0.0992309\pi$
$61$	5.79150	+	10.0312i	0.741526	+	1.28436i	−0.210274	+	0.977642i	$0.567436\pi$
$62$		0			0
$63$	2.64575			0.333333
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−3.96863	+	6.87386i	−0.484845	+	0.839776i	−0.999848	−	0.0174120i	$-0.994457\pi$
$67$	−3.96863	+	6.87386i	−0.484845	+	0.839776i	0.515003	+	0.857188i	$0.327791\pi$
$68$		0			0
$69$	2.00000			0.240772
$70$		0			0
$71$	−7.29150			−0.865342			−0.432671	−	0.901552i	$-0.642429\pi$
$71$	−7.29150			−0.865342			−0.432671	+	0.901552i	$0.642429\pi$
$72$		0			0
$73$	−2.14575	+	3.71655i	−0.251141	+	0.434989i	−0.963840	−	0.266481i	$-0.914139\pi$
$73$	−2.14575	+	3.71655i	−0.251141	+	0.434989i	0.712699	+	0.701470i	$0.247473\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.468627	+	0.811686i	0.0534050	+	0.0925002i
$78$		0			0
$79$	0.677124	+	1.17281i	0.0761824	+	0.131952i	0.901600	−	0.432571i	$-0.142394\pi$
$79$	0.677124	+	1.17281i	0.0761824	+	0.131952i	−0.825417	+	0.564523i	$0.809060\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−1.64575			−0.180645			−0.0903223	−	0.995913i	$-0.528790\pi$
$83$	−1.64575			−0.180645			−0.0903223	+	0.995913i	$0.528790\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−1.64575	+	2.85052i	−0.176443	+	0.305608i
$88$		0			0
$89$	−3.46863	−	6.00784i	−0.367674	−	0.636830i	0.621528	−	0.783392i	$-0.286512\pi$
$89$	−3.46863	−	6.00784i	−0.367674	−	0.636830i	−0.989201	+	0.146563i	$0.953179\pi$
$90$		0			0
$91$	−1.32288	+	2.29129i	−0.138675	+	0.240192i
$92$		0			0
$93$	2.00000	+	3.46410i	0.207390	+	0.359211i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	3.70850			0.376541			0.188270	−	0.982117i	$-0.439712\pi$
$97$	3.70850			0.376541			0.188270	+	0.982117i	$0.439712\pi$
$98$		0			0
$99$	−0.354249			−0.0356033
$100$		0			0
$101$	−2.46863	+	4.27579i	−0.245638	+	0.425457i	−0.962311	−	0.271953i	$-0.912331\pi$
$101$	−2.46863	+	4.27579i	−0.245638	+	0.425457i	0.716673	+	0.697409i	$0.245664\pi$
$102$		0			0
$103$	−0.0313730	−	0.0543397i	−0.00309128	−	0.00535425i	0.864476	−	0.502675i	$-0.167651\pi$
$103$	−0.0313730	−	0.0543397i	−0.00309128	−	0.00535425i	−0.867567	+	0.497320i	$0.834317\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.11438	+	14.0545i	0.784447	+	1.35870i	0.929329	+	0.369252i	$0.120386\pi$
$107$	8.11438	+	14.0545i	0.784447	+	1.35870i	−0.144883	+	0.989449i	$0.546280\pi$
$108$		0			0
$109$	5.79150	−	10.0312i	0.554725	−	0.960812i	−0.443200	−	0.896423i	$-0.646157\pi$
$109$	5.79150	−	10.0312i	0.554725	−	0.960812i	0.997925	−	0.0643895i	$-0.0205100\pi$
$110$		0			0
$111$	2.29150			0.217500
$112$		0			0
$113$	−8.58301			−0.807421			−0.403711	−	0.914887i	$-0.632280\pi$
$113$	−8.58301			−0.807421			−0.403711	+	0.914887i	$0.632280\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.500000	−	0.866025i	−0.0462250	−	0.0800641i
$118$		0			0
$119$	−4.82288	−	8.35347i	−0.442112	−	0.765761i
$120$		0			0
$121$	5.43725	+	9.41760i	0.494296	+	0.856145i
$122$		0			0
$123$	−2.82288	+	4.88936i	−0.254530	+	0.440859i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−1.35425			−0.120170			−0.0600851	−	0.998193i	$-0.519137\pi$
$127$	−1.35425			−0.120170			−0.0600851	+	0.998193i	$0.519137\pi$
$128$		0			0
$129$	1.64575	−	2.85052i	0.144900	−	0.250975i
$130$		0			0
$131$	−0.291503	−	0.504897i	−0.0254687	−	0.0441131i	0.853010	−	0.521894i	$-0.174774\pi$
$131$	−0.291503	−	0.504897i	−0.0254687	−	0.0441131i	−0.878479	+	0.477781i	$0.841441\pi$
$132$		0			0
$133$	1.70850			0.148146
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−0.645751	+	1.11847i	−0.0551703	+	0.0955577i	−0.892292	−	0.451460i	$-0.850903\pi$
$137$	−0.645751	+	1.11847i	−0.0551703	+	0.0955577i	0.837121	+	0.547017i	$0.184237\pi$
$138$		0			0
$139$	15.9373			1.35178			0.675890	−	0.737002i	$-0.263759\pi$
$139$	15.9373			1.35178			0.675890	+	0.737002i	$0.263759\pi$
$140$		0			0
$141$	12.9373			1.08951
$142$		0			0
$143$	0.177124	−	0.306788i	0.0148119	−	0.0256549i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−7.00000			−0.577350
$148$		0			0
$149$	−2.46863	−	4.27579i	−0.202238	−	0.350286i	0.747011	−	0.664811i	$-0.231488\pi$
$149$	−2.46863	−	4.27579i	−0.202238	−	0.350286i	−0.949249	+	0.314525i	$0.898155\pi$
$150$		0			0
$151$	5.67712	−	9.83307i	0.461998	−	0.800204i	−0.537063	−	0.843542i	$-0.680466\pi$
$151$	5.67712	−	9.83307i	0.461998	−	0.800204i	0.999060	+	0.0433387i	$0.0137995\pi$
$152$		0			0
$153$	3.64575			0.294742
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−8.50000	+	14.7224i	−0.678374	+	1.17498i	0.297097	+	0.954847i	$0.403982\pi$
$157$	−8.50000	+	14.7224i	−0.678374	+	1.17498i	−0.975470	+	0.220131i	$0.929352\pi$
$158$		0			0
$159$	3.82288	+	6.62141i	0.303174	+	0.525112i
$160$		0			0
$161$	−5.29150			−0.417029
$162$		0			0
$163$	8.61438	+	14.9205i	0.674730	+	1.16867i	0.976548	+	0.215301i	$0.0690733\pi$
$163$	8.61438	+	14.9205i	0.674730	+	1.16867i	−0.301818	+	0.953366i	$0.597593\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	19.5203			1.51052			0.755262	−	0.655424i	$-0.227510\pi$
$167$	19.5203			1.51052			0.755262	+	0.655424i	$0.227510\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$		0			0
$171$	−0.322876	+	0.559237i	−0.0246909	+	0.0427659i
$172$		0			0
$173$	−10.2915	−	17.8254i	−0.782448	−	1.35524i	−0.930512	−	0.366263i	$-0.880637\pi$
$173$	−10.2915	−	17.8254i	−0.782448	−	1.35524i	0.148063	−	0.988978i	$-0.452696\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−0.468627	−	0.811686i	−0.0352242	−	0.0610100i
$178$		0			0
$179$	11.6458	−	20.1710i	0.870444	−	1.50765i	0.00890653	−	0.999960i	$-0.497165\pi$
$179$	11.6458	−	20.1710i	0.870444	−	1.50765i	0.861538	−	0.507693i	$-0.169502\pi$
$180$		0			0
$181$	14.5830			1.08395			0.541973	−	0.840396i	$-0.317677\pi$
$181$	14.5830			1.08395			0.541973	+	0.840396i	$0.317677\pi$
$182$		0			0
$183$	11.5830			0.856240
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.645751	+	1.11847i	0.0472220	+	0.0817909i
$188$		0			0
$189$	1.32288	−	2.29129i	0.0962250	−	0.166667i
$190$		0			0
$191$	−6.76013	−	11.7089i	−0.489146	−	0.847225i	0.510776	−	0.859714i	$-0.329358\pi$
$191$	−6.76013	−	11.7089i	−0.489146	−	0.847225i	−0.999922	+	0.0124883i	$0.996025\pi$
$192$		0			0
$193$	−8.00000	+	13.8564i	−0.575853	+	0.997406i	0.420096	+	0.907480i	$0.361996\pi$
$193$	−8.00000	+	13.8564i	−0.575853	+	0.997406i	−0.995948	+	0.0899262i	$0.971337\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−8.70850			−0.620455			−0.310227	−	0.950662i	$-0.600405\pi$
$197$	−8.70850			−0.620455			−0.310227	+	0.950662i	$0.600405\pi$
$198$		0			0
$199$	−0.322876	+	0.559237i	−0.0228880	+	0.0396433i	−0.877243	−	0.480047i	$-0.840619\pi$
$199$	−0.322876	+	0.559237i	−0.0228880	+	0.0396433i	0.854355	+	0.519691i	$0.173953\pi$
$200$		0			0
$201$	3.96863	+	6.87386i	0.279925	+	0.484845i
$202$		0			0
$203$	4.35425	−	7.54178i	0.305608	−	0.529329i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.00000	−	1.73205i	0.0695048	−	0.120386i
$208$		0			0
$209$	−0.228757			−0.0158234
$210$		0			0
$211$	−2.06275			−0.142005			−0.0710026	−	0.997476i	$-0.522620\pi$
$211$	−2.06275			−0.142005			−0.0710026	+	0.997476i	$0.522620\pi$
$212$		0			0
$213$	−3.64575	+	6.31463i	−0.249803	+	0.432671i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−5.29150	−	9.16515i	−0.359211	−	0.622171i
$218$		0			0
$219$	2.14575	+	3.71655i	0.144996	+	0.251141i
$220$		0			0
$221$	−1.82288	+	3.15731i	−0.122620	+	0.212384i
$222$		0			0
$223$	13.9373			0.933308			0.466654	−	0.884440i	$-0.345459\pi$
$223$	13.9373			0.933308			0.466654	+	0.884440i	$0.345459\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.35425	−	7.54178i	0.289002	−	0.500566i	−0.684570	−	0.728947i	$-0.740010\pi$
$227$	4.35425	−	7.54178i	0.289002	−	0.500566i	0.973572	+	0.228382i	$0.0733434\pi$
$228$		0			0
$229$	10.1458	+	17.5730i	0.670450	+	1.16125i	0.977777	+	0.209650i	$0.0672323\pi$
$229$	10.1458	+	17.5730i	0.670450	+	1.16125i	−0.307326	+	0.951604i	$0.599434\pi$
$230$		0			0
$231$	0.937254			0.0616668
$232$		0			0
$233$	−12.1144	−	20.9827i	−0.793639	−	1.37462i	−0.923700	−	0.383118i	$-0.874850\pi$
$233$	−12.1144	−	20.9827i	−0.793639	−	1.37462i	0.130060	−	0.991506i	$-0.458483\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	1.35425			0.0879679
$238$		0			0
$239$	−9.41699			−0.609135			−0.304567	−	0.952491i	$-0.598512\pi$
$239$	−9.41699			−0.609135			−0.304567	+	0.952491i	$0.598512\pi$
$240$		0			0
$241$	0.145751	−	0.252449i	0.00938867	−	0.0162616i	−0.861293	−	0.508109i	$-0.830345\pi$
$241$	0.145751	−	0.252449i	0.00938867	−	0.0162616i	0.870682	+	0.491847i	$0.163678\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−0.322876	−	0.559237i	−0.0205441	−	0.0355834i
$248$		0			0
$249$	−0.822876	+	1.42526i	−0.0521476	+	0.0903223i
$250$		0			0
$251$	−28.8118			−1.81858			−0.909291	−	0.416161i	$-0.863375\pi$
$251$	−28.8118			−1.81858			−0.909291	+	0.416161i	$0.863375\pi$
$252$		0			0
$253$	0.708497			0.0445428
$254$		0			0
$255$		0			0
$256$		0			0
$257$	8.82288	+	15.2817i	0.550356	+	0.953244i	0.998249	+	0.0591571i	$0.0188413\pi$
$257$	8.82288	+	15.2817i	0.550356	+	0.953244i	−0.447893	+	0.894087i	$0.647825\pi$
$258$		0			0
$259$	−6.06275			−0.376721
$260$		0			0
$261$	1.64575	+	2.85052i	0.101869	+	0.176443i
$262$		0			0
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	0.212565	+	0.977147i	$0.431818\pi$
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	−0.952517	+	0.304487i	$0.901515\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−6.93725			−0.424553
$268$		0			0
$269$	−10.1144	+	17.5186i	−0.616685	+	1.06813i	0.373402	+	0.927670i	$0.378191\pi$
$269$	−10.1144	+	17.5186i	−0.616685	+	1.06813i	−0.990086	+	0.140459i	$0.955142\pi$
$270$		0			0
$271$	1.35425	+	2.34563i	0.0822647	+	0.142487i	0.904222	−	0.427062i	$-0.140451\pi$
$271$	1.35425	+	2.34563i	0.0822647	+	0.142487i	−0.821958	+	0.569549i	$0.807118\pi$
$272$		0			0
$273$	1.32288	+	2.29129i	0.0800641	+	0.138675i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	12.5000	−	21.6506i	0.751052	−	1.30086i	−0.196261	−	0.980552i	$-0.562880\pi$
$277$	12.5000	−	21.6506i	0.751052	−	1.30086i	0.947313	−	0.320309i	$-0.103787\pi$
$278$		0			0
$279$	4.00000			0.239474
$280$		0			0
$281$	−22.2288			−1.32606			−0.663028	−	0.748594i	$-0.730729\pi$
$281$	−22.2288			−1.32606			−0.663028	+	0.748594i	$0.730729\pi$
$282$		0			0
$283$	3.26013	−	5.64671i	0.193795	−	0.335662i	−0.752710	−	0.658352i	$-0.771254\pi$
$283$	3.26013	−	5.64671i	0.193795	−	0.335662i	0.946505	+	0.322690i	$0.104587\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	7.46863	−	12.9360i	0.440859	−	0.763590i
$288$		0			0
$289$	1.85425	+	3.21165i	0.109073	+	0.188921i
$290$		0			0
$291$	1.85425	−	3.21165i	0.108698	−	0.188270i
$292$		0			0
$293$	−9.87451			−0.576875			−0.288437	−	0.957499i	$-0.593136\pi$
$293$	−9.87451			−0.576875			−0.288437	+	0.957499i	$0.593136\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−0.177124	+	0.306788i	−0.0102778	+	0.0178017i
$298$		0			0
$299$	1.00000	+	1.73205i	0.0578315	+	0.100167i
$300$		0			0
$301$	−4.35425	+	7.54178i	−0.250975	+	0.434701i
$302$		0			0
$303$	2.46863	+	4.27579i	0.141819	+	0.245638i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−1.87451			−0.106984			−0.0534919	−	0.998568i	$-0.517035\pi$
$307$	−1.87451			−0.106984			−0.0534919	+	0.998568i	$0.517035\pi$
$308$		0			0
$309$	−0.0627461			−0.00356950
$310$		0			0
$311$	6.64575	−	11.5108i	0.376846	−	0.652716i	−0.613755	−	0.789496i	$-0.710342\pi$
$311$	6.64575	−	11.5108i	0.376846	−	0.652716i	0.990601	+	0.136780i	$0.0436753\pi$
$312$		0			0
$313$	−9.64575	−	16.7069i	−0.545210	−	0.944332i	−0.998594	−	0.0530161i	$-0.983117\pi$
$313$	−9.64575	−	16.7069i	−0.545210	−	0.944332i	0.453384	−	0.891316i	$-0.350217\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.29150	−	7.43310i	−0.241035	−	0.417485i	0.719975	−	0.694000i	$-0.244153\pi$
$317$	−4.29150	−	7.43310i	−0.241035	−	0.417485i	−0.961009	+	0.276516i	$0.910820\pi$
$318$		0			0
$319$	−0.583005	+	1.00979i	−0.0326420	+	0.0565376i
$320$		0			0
$321$	16.2288			0.905801
$322$		0			0
$323$	2.35425			0.130994
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−5.79150	−	10.0312i	−0.320271	−	0.554725i
$328$		0			0
$329$	−34.2288			−1.88709
$330$		0			0
$331$	1.67712	+	2.90486i	0.0921831	+	0.159666i	0.908429	−	0.418038i	$-0.137282\pi$
$331$	1.67712	+	2.90486i	0.0921831	+	0.159666i	−0.816246	+	0.577704i	$0.803949\pi$
$332$		0			0
$333$	1.14575	−	1.98450i	0.0627868	−	0.108750i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−19.2915			−1.05088			−0.525438	−	0.850832i	$-0.676098\pi$
$337$	−19.2915			−1.05088			−0.525438	+	0.850832i	$0.676098\pi$
$338$		0			0
$339$	−4.29150	+	7.43310i	−0.233082	+	0.403711i
$340$		0			0
$341$	0.708497	+	1.22715i	0.0383673	+	0.0664541i
$342$		0			0
$343$	18.5203			1.00000
$344$		0			0
$345$		0			0
$346$		0			0
$347$	5.76013	−	9.97684i	0.309220	−	0.535585i	−0.668972	−	0.743288i	$-0.733265\pi$
$347$	5.76013	−	9.97684i	0.309220	−	0.535585i	0.978192	+	0.207703i	$0.0665987\pi$
$348$		0			0
$349$	4.70850			0.252040			0.126020	−	0.992028i	$-0.459780\pi$
$349$	4.70850			0.252040			0.126020	+	0.992028i	$0.459780\pi$
$350$		0			0
$351$	−1.00000			−0.0533761
$352$		0			0
$353$	8.46863	−	14.6681i	0.450740	−	0.780704i	−0.547693	−	0.836680i	$-0.684494\pi$
$353$	8.46863	−	14.6681i	0.450740	−	0.780704i	0.998432	+	0.0559759i	$0.0178270\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−9.64575			−0.510507
$358$		0			0
$359$	12.4686	+	21.5963i	0.658069	+	1.13981i	0.981115	+	0.193426i	$0.0619598\pi$
$359$	12.4686	+	21.5963i	0.658069	+	1.13981i	−0.323046	+	0.946383i	$0.604707\pi$
$360$		0			0
$361$	9.29150	−	16.0934i	0.489026	−	0.847019i
$362$		0			0
$363$	10.8745			0.570764
$364$		0			0
$365$		0			0
$366$		0			0
$367$	5.93725	−	10.2836i	0.309922	−	0.536801i	−0.668423	−	0.743781i	$-0.733030\pi$
$367$	5.93725	−	10.2836i	0.309922	−	0.536801i	0.978345	+	0.206981i	$0.0663637\pi$
$368$		0			0
$369$	2.82288	+	4.88936i	0.146953	+	0.254530i
$370$		0			0
$371$	−10.1144	−	17.5186i	−0.525112	−	0.909521i
$372$		0			0
$373$	−11.7915	−	20.4235i	−0.610541	−	1.05749i	−0.991149	−	0.132752i	$-0.957619\pi$
$373$	−11.7915	−	20.4235i	−0.610541	−	1.05749i	0.380608	−	0.924736i	$-0.375715\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−3.29150			−0.169521
$378$		0			0
$379$	−15.3542			−0.788695			−0.394347	−	0.918961i	$-0.629029\pi$
$379$	−15.3542			−0.788695			−0.394347	+	0.918961i	$0.629029\pi$
$380$		0			0
$381$	−0.677124	+	1.17281i	−0.0346901	+	0.0600851i
$382$		0			0
$383$	−4.64575	−	8.04668i	−0.237387	−	0.411166i	0.722577	−	0.691291i	$-0.242958\pi$
$383$	−4.64575	−	8.04668i	−0.237387	−	0.411166i	−0.959964	+	0.280125i	$0.909624\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.64575	−	2.85052i	−0.0836582	−	0.144900i
$388$		0			0
$389$	0.239870	−	0.415468i	0.0121619	−	0.0210651i	−0.859880	−	0.510496i	$-0.829462\pi$
$389$	0.239870	−	0.415468i	0.0121619	−	0.0210651i	0.872042	+	0.489430i	$0.162795\pi$
$390$		0			0
$391$	−7.29150			−0.368747
$392$		0			0
$393$	−0.583005			−0.0294087
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−10.2288	−	17.7167i	−0.513367	−	0.889177i	−0.999880	−	0.0155038i	$-0.995065\pi$
$397$	−10.2288	−	17.7167i	−0.513367	−	0.889177i	0.486513	−	0.873673i	$-0.338269\pi$
$398$		0			0
$399$	0.854249	−	1.47960i	0.0427659	−	0.0740728i
$400$		0			0
$401$	−17.7601	−	30.7614i	−0.886899	−	1.53615i	−0.843522	−	0.537095i	$-0.819522\pi$
$401$	−17.7601	−	30.7614i	−0.886899	−	1.53615i	−0.0433765	−	0.999059i	$-0.513812\pi$
$402$		0			0
$403$	−2.00000	+	3.46410i	−0.0996271	+	0.172559i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	0.811762			0.0402375
$408$		0			0
$409$	−3.79150	+	6.56708i	−0.187478	+	0.324721i	−0.944409	−	0.328774i	$-0.893365\pi$
$409$	−3.79150	+	6.56708i	−0.187478	+	0.324721i	0.756931	+	0.653495i	$0.226698\pi$
$410$		0			0
$411$	0.645751	+	1.11847i	0.0318526	+	0.0551703i
$412$		0			0
$413$	1.23987	+	2.14752i	0.0610100	+	0.105672i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	7.96863	−	13.8021i	0.390225	−	0.675890i
$418$		0			0
$419$	31.6458			1.54600			0.772998	−	0.634408i	$-0.218756\pi$
$419$	31.6458			1.54600			0.772998	+	0.634408i	$0.218756\pi$
$420$		0			0
$421$	28.8745			1.40726			0.703629	−	0.710568i	$-0.251562\pi$
$421$	28.8745			1.40726			0.703629	+	0.710568i	$0.251562\pi$
$422$		0			0
$423$	6.46863	−	11.2040i	0.314515	−	0.544757i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−30.6458			−1.48305
$428$		0			0
$429$	−0.177124	−	0.306788i	−0.00855164	−	0.0148119i
$430$		0			0
$431$	13.9373	−	24.1400i	0.671334	−	1.16278i	−0.306192	−	0.951970i	$-0.599055\pi$
$431$	13.9373	−	24.1400i	0.671334	−	1.16278i	0.977526	−	0.210815i	$-0.0676117\pi$
$432$		0			0
$433$	−3.29150			−0.158180			−0.0790898	−	0.996867i	$-0.525201\pi$
$433$	−3.29150			−0.158180			−0.0790898	+	0.996867i	$0.525201\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.645751	−	1.11847i	0.0308905	−	0.0535039i
$438$		0			0
$439$	19.9059	+	34.4780i	0.950056	+	1.64555i	0.745297	+	0.666733i	$0.232308\pi$
$439$	19.9059	+	34.4780i	0.950056	+	1.64555i	0.204759	+	0.978812i	$0.434359\pi$
$440$		0			0
$441$	−3.50000	+	6.06218i	−0.166667	+	0.288675i
$442$		0			0
$443$	3.35425	+	5.80973i	0.159365	+	0.276029i	0.934640	−	0.355596i	$-0.115722\pi$
$443$	3.35425	+	5.80973i	0.159365	+	0.276029i	−0.775275	+	0.631624i	$0.782389\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−4.93725			−0.233524
$448$		0			0
$449$	−32.1033			−1.51505			−0.757523	−	0.652808i	$-0.773591\pi$
$449$	−32.1033			−1.51505			−0.757523	+	0.652808i	$0.773591\pi$
$450$		0			0
$451$	−1.00000	+	1.73205i	−0.0470882	+	0.0815591i
$452$		0			0
$453$	−5.67712	−	9.83307i	−0.266735	−	0.461998i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−4.08301	−	7.07197i	−0.190995	−	0.330813i	0.754585	−	0.656202i	$-0.227838\pi$
$457$	−4.08301	−	7.07197i	−0.190995	−	0.330813i	−0.945580	+	0.325389i	$0.894505\pi$
$458$		0			0
$459$	1.82288	−	3.15731i	0.0850845	−	0.147371i
$460$		0			0
$461$	10.7085			0.498744			0.249372	−	0.968408i	$-0.419776\pi$
$461$	10.7085			0.498744			0.249372	+	0.968408i	$0.419776\pi$
$462$		0			0
$463$	33.9373			1.57720			0.788599	−	0.614908i	$-0.210807\pi$
$463$	33.9373			1.57720			0.788599	+	0.614908i	$0.210807\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	11.3542	+	19.6661i	0.525412	+	0.910040i	0.999562	+	0.0295961i	$0.00942212\pi$
$467$	11.3542	+	19.6661i	0.525412	+	0.910040i	−0.474150	+	0.880444i	$0.657245\pi$
$468$		0			0
$469$	−10.5000	−	18.1865i	−0.484845	−	0.839776i
$470$		0			0
$471$	8.50000	+	14.7224i	0.391659	+	0.678374i
$472$		0			0
$473$	0.583005	−	1.00979i	0.0268066	−	0.0464304i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	7.64575			0.350075
$478$		0			0
$479$	−12.8229	+	22.2099i	−0.585892	+	1.01479i	0.408871	+	0.912592i	$0.365922\pi$
$479$	−12.8229	+	22.2099i	−0.585892	+	1.01479i	−0.994764	+	0.102203i	$0.967411\pi$
$480$		0			0
$481$	1.14575	+	1.98450i	0.0522418	+	0.0904854i
$482$		0			0
$483$	−2.64575	+	4.58258i	−0.120386	+	0.208514i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	20.2288	−	35.0372i	0.916652	−	1.58769i	0.112189	−	0.993687i	$-0.464214\pi$
$487$	20.2288	−	35.0372i	0.916652	−	1.58769i	0.804464	−	0.594002i	$-0.202453\pi$
$488$		0			0
$489$	17.2288			0.779111
$490$		0			0
$491$	−34.4575			−1.55505			−0.777523	−	0.628855i	$-0.783524\pi$
$491$	−34.4575			−1.55505			−0.777523	+	0.628855i	$0.783524\pi$
$492$		0			0
$493$	6.00000	−	10.3923i	0.270226	−	0.468046i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	9.64575	−	16.7069i	0.432671	−	0.749408i
$498$		0			0
$499$	9.90588	+	17.1575i	0.443448	+	0.768075i	0.997943	−	0.0641127i	$-0.0204217\pi$
$499$	9.90588	+	17.1575i	0.443448	+	0.768075i	−0.554495	+	0.832187i	$0.687088\pi$
$500$		0			0
$501$	9.76013	−	16.9050i	0.436050	−	0.755262i
$502$		0			0
$503$	−16.7085			−0.744995			−0.372498	−	0.928033i	$-0.621498\pi$
$503$	−16.7085			−0.744995			−0.372498	+	0.928033i	$0.621498\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−6.00000	+	10.3923i	−0.266469	+	0.461538i
$508$		0			0
$509$	12.9373	+	22.4080i	0.573434	+	0.993216i	0.996210	+	0.0869822i	$0.0277223\pi$
$509$	12.9373	+	22.4080i	0.573434	+	0.993216i	−0.422776	+	0.906234i	$0.638944\pi$
$510$		0			0
$511$	−5.67712	−	9.83307i	−0.251141	−	0.434989i
$512$		0			0
$513$	0.322876	+	0.559237i	0.0142553	+	0.0246909i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	4.58301			0.201560
$518$		0			0
$519$	−20.5830			−0.903494
$520$		0			0
$521$	7.93725	−	13.7477i	0.347737	−	0.602299i	−0.638110	−	0.769945i	$-0.720283\pi$
$521$	7.93725	−	13.7477i	0.347737	−	0.602299i	0.985847	+	0.167647i	$0.0536167\pi$
$522$		0			0
$523$	−5.06275	−	8.76893i	−0.221378	−	0.383439i	0.733848	−	0.679313i	$-0.237722\pi$
$523$	−5.06275	−	8.76893i	−0.221378	−	0.383439i	−0.955227	+	0.295875i	$0.904389\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−7.29150	−	12.6293i	−0.317623	−	0.550139i
$528$		0			0
$529$	9.50000	−	16.4545i	0.413043	−	0.715412i
$530$		0			0
$531$	−0.937254			−0.0406734
$532$		0			0
$533$	−5.64575			−0.244545
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−11.6458	−	20.1710i	−0.502551	−	0.870444i
$538$		0			0
$539$	−2.47974			−0.106810
$540$		0			0
$541$	−13.4373	−	23.2740i	−0.577713	−	1.00063i	−0.995741	−	0.0921937i	$-0.970612\pi$
$541$	−13.4373	−	23.2740i	−0.577713	−	1.00063i	0.418028	−	0.908434i	$-0.362721\pi$
$542$		0			0
$543$	7.29150	−	12.6293i	0.312908	−	0.541973i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	0.125492			0.00536566			0.00268283	−	0.999996i	$-0.499146\pi$
$547$	0.125492			0.00536566			0.00268283	+	0.999996i	$0.499146\pi$
$548$		0			0
$549$	5.79150	−	10.0312i	0.247175	−	0.428120i
$550$		0			0
$551$	1.06275	+	1.84073i	0.0452745	+	0.0784177i
$552$		0			0
$553$	−3.58301			−0.152365
$554$		0			0
$555$		0			0
$556$		0			0
$557$	8.35425	−	14.4700i	0.353981	−	0.613113i	−0.632962	−	0.774183i	$-0.718161\pi$
$557$	8.35425	−	14.4700i	0.353981	−	0.613113i	0.986943	+	0.161070i	$0.0514945\pi$
$558$		0			0
$559$	3.29150			0.139216
$560$		0			0
$561$	1.29150			0.0545273
$562$		0			0
$563$	−2.76013	+	4.78068i	−0.116326	+	0.201482i	−0.918309	−	0.395865i	$-0.870445\pi$
$563$	−2.76013	+	4.78068i	−0.116326	+	0.201482i	0.801983	+	0.597346i	$0.203778\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−1.32288	−	2.29129i	−0.0555556	−	0.0962250i
$568$		0			0
$569$	−2.46863	−	4.27579i	−0.103490	−	0.179250i	0.809630	−	0.586940i	$-0.199668\pi$
$569$	−2.46863	−	4.27579i	−0.103490	−	0.179250i	−0.913120	+	0.407690i	$0.866334\pi$
$570$		0			0
$571$	−2.96863	+	5.14181i	−0.124233	+	0.215178i	−0.921433	−	0.388537i	$-0.872980\pi$
$571$	−2.96863	+	5.14181i	−0.124233	+	0.215178i	0.797200	+	0.603716i	$0.206314\pi$
$572$		0			0
$573$	−13.5203			−0.564817
$574$		0			0
$575$		0			0
$576$		0			0
$577$	2.29150	−	3.96900i	0.0953965	−	0.165232i	−0.814378	−	0.580335i	$-0.802921\pi$
$577$	2.29150	−	3.96900i	0.0953965	−	0.165232i	0.909774	+	0.415104i	$0.136255\pi$
$578$		0			0
$579$	8.00000	+	13.8564i	0.332469	+	0.575853i
$580$		0			0
$581$	2.17712	−	3.77089i	0.0903223	−	0.156443i
$582$		0			0
$583$	1.35425	+	2.34563i	0.0560872	+	0.0971460i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	6.00000			0.247647			0.123823	−	0.992304i	$-0.460484\pi$
$587$	6.00000			0.247647			0.123823	+	0.992304i	$0.460484\pi$
$588$		0			0
$589$	2.58301			0.106431
$590$		0			0
$591$	−4.35425	+	7.54178i	−0.179110	+	0.310227i
$592$		0			0
$593$	−0.291503	−	0.504897i	−0.0119706	−	0.0207336i	0.859978	−	0.510331i	$-0.170477\pi$
$593$	−0.291503	−	0.504897i	−0.0119706	−	0.0207336i	−0.871949	+	0.489597i	$0.837144\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	0.322876	+	0.559237i	0.0132144	+	0.0228880i
$598$		0			0
$599$	16.4686	−	28.5245i	0.672890	−	1.16548i	−0.304191	−	0.952611i	$-0.598386\pi$
$599$	16.4686	−	28.5245i	0.672890	−	1.16548i	0.977081	−	0.212868i	$-0.0682806\pi$
$600$		0			0
$601$	14.2915			0.582963			0.291481	−	0.956577i	$-0.405852\pi$
$601$	14.2915			0.582963			0.291481	+	0.956577i	$0.405852\pi$
$602$		0			0
$603$	7.93725			0.323230
$604$		0			0
$605$		0			0
$606$		0			0
$607$	8.32288	+	14.4156i	0.337815	+	0.585113i	0.984021	−	0.178050i	$-0.0569788\pi$
$607$	8.32288	+	14.4156i	0.337815	+	0.585113i	−0.646206	+	0.763163i	$0.723645\pi$
$608$		0			0
$609$	−4.35425	−	7.54178i	−0.176443	−	0.305608i
$610$		0			0
$611$	6.46863	+	11.2040i	0.261693	+	0.453265i
$612$		0			0
$613$	−17.6458	+	30.5633i	−0.712705	+	1.23444i	0.251133	+	0.967953i	$0.419197\pi$
$613$	−17.6458	+	30.5633i	−0.712705	+	1.23444i	−0.963838	+	0.266489i	$0.914136\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−41.8745			−1.68580			−0.842902	−	0.538067i	$-0.819155\pi$
$617$	−41.8745			−1.68580			−0.842902	+	0.538067i	$0.819155\pi$
$618$		0			0
$619$	−12.3542	+	21.3982i	−0.496559	+	0.860066i	−0.999992	−	0.00396857i	$-0.998737\pi$
$619$	−12.3542	+	21.3982i	−0.496559	+	0.860066i	0.503433	+	0.864034i	$0.332070\pi$
$620$		0			0
$621$	−1.00000	−	1.73205i	−0.0401286	−	0.0695048i
$622$		0			0
$623$	18.3542			0.735347
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−0.114378	+	0.198109i	−0.00456783	+	0.00791171i
$628$		0			0
$629$	−8.35425			−0.333106
$630$		0			0
$631$	−1.35425			−0.0539118			−0.0269559	−	0.999637i	$-0.508581\pi$
$631$	−1.35425			−0.0539118			−0.0269559	+	0.999637i	$0.508581\pi$
$632$		0			0
$633$	−1.03137	+	1.78639i	−0.0409934	+	0.0710026i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−3.50000	−	6.06218i	−0.138675	−	0.240192i
$638$		0			0
$639$	3.64575	+	6.31463i	0.144224	+	0.249803i
$640$		0			0
$641$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$641$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$642$		0			0
$643$	−27.3542			−1.07875			−0.539373	−	0.842067i	$-0.681339\pi$
$643$	−27.3542			−1.07875			−0.539373	+	0.842067i	$0.681339\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	25.3431	−	43.8956i	0.996341	−	1.72571i	0.424159	−	0.905588i	$-0.360570\pi$
$647$	25.3431	−	43.8956i	0.996341	−	1.72571i	0.572183	−	0.820126i	$-0.306097\pi$
$648$		0			0
$649$	−0.166010	−	0.287539i	−0.00651648	−	0.0112869i
$650$		0			0
$651$	−10.5830			−0.414781
$652$		0			0
$653$	−8.11438	−	14.0545i	−0.317540	−	0.549996i	0.662434	−	0.749120i	$-0.269523\pi$
$653$	−8.11438	−	14.0545i	−0.317540	−	0.549996i	−0.979974	+	0.199125i	$0.936190\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	4.29150			0.167427
$658$		0			0
$659$	40.1033			1.56220			0.781101	−	0.624405i	$-0.214659\pi$
$659$	40.1033			1.56220			0.781101	+	0.624405i	$0.214659\pi$
$660$		0			0
$661$	−0.854249	+	1.47960i	−0.0332264	+	0.0575499i	−0.882160	−	0.470949i	$-0.843912\pi$
$661$	−0.854249	+	1.47960i	−0.0332264	+	0.0575499i	0.848934	+	0.528499i	$0.177245\pi$
$662$		0			0
$663$	1.82288	+	3.15731i	0.0707946	+	0.122620i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−3.29150	−	5.70105i	−0.127447	−	0.220746i
$668$		0			0
$669$	6.96863	−	12.0700i	0.269423	−	0.466654i
$670$		0			0
$671$	4.10326			0.158405
$672$		0			0
$673$	2.29150			0.0883309			0.0441655	−	0.999024i	$-0.485937\pi$
$673$	2.29150			0.0883309			0.0441655	+	0.999024i	$0.485937\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	19.3542	+	33.5225i	0.743844	+	1.28838i	0.950733	+	0.310011i	$0.100333\pi$
$677$	19.3542	+	33.5225i	0.743844	+	1.28838i	−0.206889	+	0.978365i	$0.566334\pi$
$678$		0			0
$679$	−4.90588	+	8.49723i	−0.188270	+	0.326094i
$680$		0			0
$681$	−4.35425	−	7.54178i	−0.166855	−	0.289002i
$682$		0			0
$683$	−10.0516	+	17.4099i	−0.384615	+	0.666173i	−0.991716	−	0.128452i	$-0.958999\pi$
$683$	−10.0516	+	17.4099i	−0.384615	+	0.666173i	0.607101	+	0.794625i	$0.292332\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	20.2915			0.774169
$688$		0			0
$689$	−3.82288	+	6.62141i	−0.145640	+	0.252256i
$690$		0			0
$691$	−7.61438	−	13.1885i	−0.289665	−	0.501714i	0.684065	−	0.729421i	$-0.260210\pi$
$691$	−7.61438	−	13.1885i	−0.289665	−	0.501714i	−0.973730	+	0.227707i	$0.926877\pi$
$692$		0			0
$693$	0.468627	−	0.811686i	0.0178017	−	0.0308334i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	10.2915	−	17.8254i	0.389818	−	0.675185i
$698$		0			0
$699$	−24.2288			−0.916416
$700$		0			0
$701$	−25.0627			−0.946607			−0.473303	−	0.880899i	$-0.656939\pi$
$701$	−25.0627			−0.946607			−0.473303	+	0.880899i	$0.656939\pi$
$702$		0			0
$703$	0.739870	−	1.28149i	0.0279047	−	0.0483324i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−6.53137	−	11.3127i	−0.245638	−	0.425457i
$708$		0			0
$709$	3.08301	+	5.33992i	0.115785	+	0.200545i	0.918093	−	0.396365i	$-0.129728\pi$
$709$	3.08301	+	5.33992i	0.115785	+	0.200545i	−0.802308	+	0.596910i	$0.796395\pi$
$710$		0			0
$711$	0.677124	−	1.17281i	0.0253941	−	0.0439840i
$712$		0			0
$713$	−8.00000			−0.299602
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−4.70850	+	8.15536i	−0.175842	+	0.304567i
$718$		0			0
$719$	−1.11438	−	1.93016i	−0.0415593	−	0.0719828i	0.844498	−	0.535559i	$-0.179899\pi$
$719$	−1.11438	−	1.93016i	−0.0415593	−	0.0719828i	−0.886057	+	0.463577i	$0.846566\pi$
$720$		0			0
$721$	0.166010			0.00618255
$722$		0			0
$723$	−0.145751	−	0.252449i	−0.00542055	−	0.00938867i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	27.1033			1.00520			0.502602	−	0.864518i	$-0.332376\pi$
$727$	27.1033			1.00520			0.502602	+	0.864518i	$0.332376\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−6.00000	+	10.3923i	−0.221918	+	0.384373i
$732$		0			0
$733$	−16.0203	−	27.7479i	−0.591722	−	1.02489i	−0.994001	−	0.109375i	$-0.965115\pi$
$733$	−16.0203	−	27.7479i	−0.591722	−	1.02489i	0.402279	−	0.915517i	$-0.368218\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.40588	+	2.43506i	0.0517863	+	0.0896965i
$738$		0			0
$739$	25.2601	−	43.7518i	0.929209	−	1.60944i	0.144560	−	0.989496i	$-0.453823\pi$
$739$	25.2601	−	43.7518i	0.929209	−	1.60944i	0.784648	−	0.619941i	$-0.212843\pi$
$740$		0			0
$741$	−0.645751			−0.0237223
$742$		0			0
$743$	−11.4170			−0.418849			−0.209424	−	0.977825i	$-0.567159\pi$
$743$	−11.4170			−0.418849			−0.209424	+	0.977825i	$0.567159\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.822876	+	1.42526i	0.0301074	+	0.0521476i
$748$		0			0
$749$	−42.9373			−1.56889
$750$		0			0
$751$	16.6771	+	28.8856i	0.608557	+	1.05405i	0.991478	+	0.130271i	$0.0415846\pi$
$751$	16.6771	+	28.8856i	0.608557	+	1.05405i	−0.382922	+	0.923781i	$0.625082\pi$
$752$		0			0
$753$	−14.4059	+	24.9517i	−0.524979	+	0.909291i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	11.0000			0.399802			0.199901	−	0.979816i	$-0.435938\pi$
$757$	11.0000			0.399802			0.199901	+	0.979816i	$0.435938\pi$
$758$		0			0
$759$	0.354249	−	0.613577i	0.0128584	−	0.0222714i
$760$		0			0
$761$	22.1771	+	38.4119i	0.803920	+	1.39243i	0.917018	+	0.398847i	$0.130589\pi$
$761$	22.1771	+	38.4119i	0.803920	+	1.39243i	−0.113098	+	0.993584i	$0.536077\pi$
$762$		0			0
$763$	15.3229	+	26.5400i	0.554725	+	0.960812i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.468627	−	0.811686i	0.0169211	−	0.0293083i
$768$		0			0
$769$	4.00000			0.144244			0.0721218	−	0.997396i	$-0.477023\pi$
$769$	4.00000			0.144244			0.0721218	+	0.997396i	$0.477023\pi$
$770$		0			0
$771$	17.6458			0.635496
$772$		0			0
$773$	13.2915	−	23.0216i	0.478062	−	0.828028i	−0.521622	−	0.853177i	$-0.674673\pi$
$773$	13.2915	−	23.0216i	0.478062	−	0.828028i	0.999684	+	0.0251491i	$0.00800604\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−3.03137	+	5.25049i	−0.108750	+	0.188360i
$778$		0			0
$779$	1.82288	+	3.15731i	0.0653113	+	0.113122i
$780$		0			0
$781$	−1.29150	+	2.23695i	−0.0462136	+	0.0800443i
$782$		0			0
$783$	3.29150			0.117629
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−22.4889	+	38.9519i	−0.801642	+	1.38849i	0.116892	+	0.993145i	$0.462707\pi$
$787$	−22.4889	+	38.9519i	−0.801642	+	1.38849i	−0.918535	+	0.395340i	$0.870627\pi$
$788$		0			0
$789$	12.0000	+	20.7846i	0.427211	+	0.739952i
$790$		0			0
$791$	11.3542	−	19.6661i	0.403711	−	0.699247i
$792$		0			0
$793$	5.79150	+	10.0312i	0.205662	+	0.356218i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−3.87451			−0.137242			−0.0686211	−	0.997643i	$-0.521860\pi$
$797$	−3.87451			−0.137242			−0.0686211	+	0.997643i	$0.521860\pi$
$798$		0			0
$799$	−47.1660			−1.66861
$800$		0			0
$801$	−3.46863	+	6.00784i	−0.122558	+	0.212277i
$802$		0			0
$803$	0.760130	+	1.31658i	0.0268244	+	0.0464612i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	10.1144	+	17.5186i	0.356043	+	0.616685i
$808$		0			0
$809$	17.3542	−	30.0584i	0.610143	−	1.05680i	−0.381073	−	0.924545i	$-0.624445\pi$
$809$	17.3542	−	30.0584i	0.610143	−	1.05680i	0.991216	−	0.132254i	$-0.0422213\pi$
$810$		0			0
$811$	−7.93725			−0.278715			−0.139357	−	0.990242i	$-0.544504\pi$
$811$	−7.93725			−0.278715			−0.139357	+	0.990242i	$0.544504\pi$
$812$		0			0
$813$	2.70850			0.0949912
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−1.06275	−	1.84073i	−0.0371808	−	0.0643990i
$818$		0			0
$819$	2.64575			0.0924500
$820$		0			0
$821$	8.69738	+	15.0643i	0.303541	+	0.525748i	0.976935	−	0.213535i	$-0.0684978\pi$
$821$	8.69738	+	15.0643i	0.303541	+	0.525748i	−0.673395	+	0.739283i	$0.735164\pi$
$822$		0			0
$823$	8.26013	−	14.3070i	0.287930	−	0.498709i	−0.685385	−	0.728180i	$-0.740366\pi$
$823$	8.26013	−	14.3070i	0.287930	−	0.498709i	0.973315	+	0.229471i	$0.0736996\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−42.5830			−1.48076			−0.740378	−	0.672191i	$-0.765354\pi$
$827$	−42.5830			−1.48076			−0.740378	+	0.672191i	$0.765354\pi$
$828$		0			0
$829$	19.6660	−	34.0625i	0.683029	−	1.18304i	−0.291023	−	0.956716i	$-0.593996\pi$
$829$	19.6660	−	34.0625i	0.683029	−	1.18304i	0.974052	−	0.226325i	$-0.0726710\pi$
$830$		0			0
$831$	−12.5000	−	21.6506i	−0.433620	−	0.751052i
$832$		0			0
$833$	25.5203			0.884225
$834$		0			0
$835$		0			0
$836$		0			0
$837$	2.00000	−	3.46410i	0.0691301	−	0.119737i
$838$		0			0
$839$	19.1660			0.661684			0.330842	−	0.943686i	$-0.392667\pi$
$839$	19.1660			0.661684			0.330842	+	0.943686i	$0.392667\pi$
$840$		0			0
$841$	−18.1660			−0.626414
$842$		0			0
$843$	−11.1144	+	19.2507i	−0.382800	+	0.663028i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−28.7712			−0.988592
$848$		0			0
$849$	−3.26013	−	5.64671i	−0.111887	−	0.193795i
$850$		0			0
$851$	−2.29150	+	3.96900i	−0.0785517	+	0.136056i
$852$		0			0
$853$	−2.00000			−0.0684787			−0.0342393	−	0.999414i	$-0.510901\pi$
$853$	−2.00000			−0.0684787			−0.0342393	+	0.999414i	$0.510901\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−13.5830	+	23.5265i	−0.463987	+	0.803648i	−0.999155	−	0.0410969i	$-0.986915\pi$
$857$	−13.5830	+	23.5265i	−0.463987	+	0.803648i	0.535169	+	0.844745i	$0.320248\pi$
$858$		0			0
$859$	20.5830	+	35.6508i	0.702283	+	1.21639i	0.967663	+	0.252246i	$0.0811692\pi$
$859$	20.5830	+	35.6508i	0.702283	+	1.21639i	−0.265380	+	0.964144i	$0.585497\pi$
$860$		0			0
$861$	−7.46863	−	12.9360i	−0.254530	−	0.440859i
$862$		0			0
$863$	3.05163	+	5.28558i	0.103879	+	0.179923i	0.913280	−	0.407333i	$-0.133541\pi$
$863$	3.05163	+	5.28558i	0.103879	+	0.179923i	−0.809401	+	0.587257i	$0.800208\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	3.70850			0.125947
$868$		0			0
$869$	0.479741			0.0162741
$870$		0			0
$871$	−3.96863	+	6.87386i	−0.134472	+	0.232912i
$872$		0			0
$873$	−1.85425	−	3.21165i	−0.0627568	−	0.108698i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	22.3745	+	38.7538i	0.755533	+	1.30862i	0.945109	+	0.326756i	$0.105956\pi$
$877$	22.3745	+	38.7538i	0.755533	+	1.30862i	−0.189575	+	0.981866i	$0.560711\pi$
$878$		0			0
$879$	−4.93725	+	8.55157i	−0.166529	+	0.288437i
$880$		0			0
$881$	44.7085			1.50627			0.753134	−	0.657867i	$-0.228541\pi$
$881$	44.7085			1.50627			0.753134	+	0.657867i	$0.228541\pi$
$882$		0			0
$883$	23.3542			0.785933			0.392967	−	0.919553i	$-0.371449\pi$
$883$	23.3542			0.785933			0.392967	+	0.919553i	$0.371449\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	20.6458	+	35.7595i	0.693216	+	1.20069i	0.970778	+	0.239978i	$0.0771404\pi$
$887$	20.6458	+	35.7595i	0.693216	+	1.20069i	−0.277562	+	0.960708i	$0.589526\pi$
$888$		0			0
$889$	1.79150	−	3.10297i	0.0600851	−	0.104070i
$890$		0			0
$891$	0.177124	+	0.306788i	0.00593389	+	0.0102778i
$892$		0			0
$893$	4.17712	−	7.23499i	0.139782	−	0.242110i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	2.00000			0.0667781
$898$		0			0
$899$	6.58301	−	11.4021i	0.219556	−	0.380281i
$900$		0			0
$901$	−13.9373	−	24.1400i	−0.464317	−	0.804221i
$902$		0			0
$903$	4.35425	+	7.54178i	0.144900	+	0.250975i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−15.4889	+	26.8275i	−0.514300	+	0.890794i	0.485562	+	0.874202i	$0.338615\pi$
$907$	−15.4889	+	26.8275i	−0.514300	+	0.890794i	−0.999862	+	0.0165917i	$0.994718\pi$
$908$		0			0
$909$	4.93725			0.163758
$910$		0			0
$911$	32.3320			1.07121			0.535604	−	0.844469i	$-0.320084\pi$
$911$	32.3320			1.07121			0.535604	+	0.844469i	$0.320084\pi$
$912$		0			0
$913$	−0.291503	+	0.504897i	−0.00964733	+	0.0167097i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.54249			0.0509374
$918$		0			0
$919$	−24.4575	−	42.3617i	−0.806779	−	1.39738i	−0.915084	−	0.403264i	$-0.867876\pi$
$919$	−24.4575	−	42.3617i	−0.806779	−	1.39738i	0.108305	−	0.994118i	$-0.465458\pi$
$920$		0			0
$921$	−0.937254	+	1.62337i	−0.0308836	+	0.0534919i
$922$		0			0
$923$	−7.29150			−0.240003
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−0.0313730	+	0.0543397i	−0.00103043	+	0.00178475i
$928$		0			0
$929$	−1.17712	−	2.03884i	−0.0386202	−	0.0668921i	0.846069	−	0.533073i	$-0.178963\pi$
$929$	−1.17712	−	2.03884i	−0.0386202	−	0.0668921i	−0.884689	+	0.466181i	$0.845630\pi$
$930$		0			0
$931$	−2.26013	+	3.91466i	−0.0740728	+	0.128298i
$932$		0			0
$933$	−6.64575	−	11.5108i	−0.217572	−	0.376846i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$		0			0
$939$	−19.2915			−0.629554
$940$		0			0
$941$	−6.87451	+	11.9070i	−0.224103	+	0.388157i	−0.956050	−	0.293204i	$-0.905278\pi$
$941$	−6.87451	+	11.9070i	−0.224103	+	0.388157i	0.731947	+	0.681361i	$0.238612\pi$
$942$		0			0
$943$	−5.64575	−	9.77873i	−0.183851	−	0.318439i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−13.3542	−	23.1302i	−0.433955	−	0.751632i	0.563255	−	0.826283i	$-0.309549\pi$
$947$	−13.3542	−	23.1302i	−0.433955	−	0.751632i	−0.997210	+	0.0746515i	$0.976216\pi$
$948$		0			0
$949$	−2.14575	+	3.71655i	−0.0696540	+	0.120644i
$950$		0			0
$951$	−8.58301			−0.278323
$952$		0			0
$953$	47.5203			1.53933			0.769666	−	0.638447i	$-0.220423\pi$
$953$	47.5203			1.53933			0.769666	+	0.638447i	$0.220423\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	0.583005	+	1.00979i	0.0188459	+	0.0326420i
$958$		0			0
$959$	−1.70850	−	2.95920i	−0.0551703	−	0.0955577i
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$		0			0
$963$	8.11438	−	14.0545i	0.261482	−	0.452900i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	29.9373			0.962717			0.481359	−	0.876524i	$-0.340143\pi$
$967$	29.9373			0.962717			0.481359	+	0.876524i	$0.340143\pi$
$968$		0			0
$969$	1.17712	−	2.03884i	0.0378147	−	0.0654970i
$970$		0			0
$971$	26.2804	+	45.5190i	0.843378	+	1.46077i	0.887023	+	0.461726i	$0.152770\pi$
$971$	26.2804	+	45.5190i	0.843378	+	1.46077i	−0.0436447	+	0.999047i	$0.513897\pi$
$972$		0			0
$973$	−21.0830	+	36.5168i	−0.675890	+	1.17068i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−12.3431	+	21.3789i	−0.394892	+	0.683973i	−0.993087	−	0.117377i	$-0.962551\pi$
$977$	−12.3431	+	21.3789i	−0.394892	+	0.683973i	0.598196	+	0.801350i	$0.295885\pi$
$978$		0			0
$979$	−2.45751			−0.0785425
$980$		0			0
$981$	−11.5830			−0.369817
$982$		0			0
$983$	2.82288	−	4.88936i	0.0900358	−	0.155946i	−0.817490	−	0.575943i	$-0.804635\pi$
$983$	2.82288	−	4.88936i	0.0900358	−	0.155946i	0.907526	+	0.419996i	$0.137969\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−17.1144	+	29.6430i	−0.544757	+	0.943546i
$988$		0			0
$989$	3.29150	+	5.70105i	0.104664	+	0.181283i
$990$		0			0
$991$	11.9373	−	20.6759i	0.379199	−	0.656793i	−0.611747	−	0.791054i	$-0.709533\pi$
$991$	11.9373	−	20.6759i	0.379199	−	0.656793i	0.990946	+	0.134261i	$0.0428661\pi$
$992$		0			0
$993$	3.35425			0.106444
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−24.3745	+	42.2179i	−0.771948	+	1.33705i	0.164545	+	0.986370i	$0.447384\pi$
$997$	−24.3745	+	42.2179i	−0.771948	+	1.33705i	−0.936494	+	0.350684i	$0.885949\pi$
$998$		0			0
$999$	−1.14575	−	1.98450i	−0.0362500	−	0.0627868i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.q.i.1201.1	yes	4
5.2	odd	4		2100.2.bc.h.949.1		8
5.3	odd	4		2100.2.bc.h.949.4		8
5.4	even	2		2100.2.q.g.1201.2	✓	4
7.2	even	3	inner	2100.2.q.i.1801.1	yes	4
35.2	odd	12		2100.2.bc.h.1549.4		8
35.9	even	6		2100.2.q.g.1801.2	yes	4
35.23	odd	12		2100.2.bc.h.1549.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.q.g.1201.2	✓	4	5.4	even	2
2100.2.q.g.1801.2	yes	4	35.9	even	6
2100.2.q.i.1201.1	yes	4	1.1	even	1	trivial
2100.2.q.i.1801.1	yes	4	7.2	even	3	inner
2100.2.bc.h.949.1		8	5.2	odd	4
2100.2.bc.h.949.4		8	5.3	odd	4
2100.2.bc.h.1549.1		8	35.23	odd	12
2100.2.bc.h.1549.4		8	35.2	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(-1.32288 + 2.29129i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +(-1.32288 + 2.29129i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(0.177124 - 0.306788i) q^{11} +1.00000 q^{13} +(-1.82288 + 3.15731i) q^{17} +(-0.322876 - 0.559237i) q^{19} +(1.32288 + 2.29129i) q^{21} +(1.00000 + 1.73205i) q^{23} -1.00000 q^{27} -3.29150 q^{29} +(-2.00000 + 3.46410i) q^{31} +(-0.177124 - 0.306788i) q^{33} +(1.14575 + 1.98450i) q^{37} +(0.500000 - 0.866025i) q^{39} -5.64575 q^{41} +3.29150 q^{43} +(6.46863 + 11.2040i) q^{47} +(-3.50000 - 6.06218i) q^{49} +(1.82288 + 3.15731i) q^{51} +(-3.82288 + 6.62141i) q^{53} -0.645751 q^{57} +(0.468627 - 0.811686i) q^{59} +(5.79150 + 10.0312i) q^{61} +2.64575 q^{63} +(-3.96863 + 6.87386i) q^{67} +2.00000 q^{69} -7.29150 q^{71} +(-2.14575 + 3.71655i) q^{73} +(0.468627 + 0.811686i) q^{77} +(0.677124 + 1.17281i) q^{79} +(-0.500000 + 0.866025i) q^{81} -1.64575 q^{83} +(-1.64575 + 2.85052i) q^{87} +(-3.46863 - 6.00784i) q^{89} +(-1.32288 + 2.29129i) q^{91} +(2.00000 + 3.46410i) q^{93} +3.70850 q^{97} -0.354249 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 - 2 * q^9	\( 4 q + 2 q^{3} - 2 q^{9} + 6 q^{11} + 4 q^{13} - 2 q^{17} + 4 q^{19} + 4 q^{23} - 4 q^{27} + 8 q^{29} - 8 q^{31} - 6 q^{33} - 6 q^{37} + 2 q^{39} - 12 q^{41} - 8 q^{43} + 10 q^{47} - 14 q^{49} + 2 q^{51} - 10 q^{53} + 8 q^{57} - 14 q^{59} + 2 q^{61} + 8 q^{69} - 8 q^{71} + 2 q^{73} - 14 q^{77} + 8 q^{79} - 2 q^{81} + 4 q^{83} + 4 q^{87} + 2 q^{89} + 8 q^{93} + 36 q^{97} - 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 - 2 * q^9 + 6 * q^11 + 4 * q^13 - 2 * q^17 + 4 * q^19 + 4 * q^23 - 4 * q^27 + 8 * q^29 - 8 * q^31 - 6 * q^33 - 6 * q^37 + 2 * q^39 - 12 * q^41 - 8 * q^43 + 10 * q^47 - 14 * q^49 + 2 * q^51 - 10 * q^53 + 8 * q^57 - 14 * q^59 + 2 * q^61 + 8 * q^69 - 8 * q^71 + 2 * q^73 - 14 * q^77 + 8 * q^79 - 2 * q^81 + 4 * q^83 + 4 * q^87 + 2 * q^89 + 8 * q^93 + 36 * q^97 - 12 * q^99

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