LMFDB - Embedded newform 2100.2.bc.h.949.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(949,2100)]

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, 3, 4]))

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

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

chi := DirichletCharacter("2100.949");

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.bc (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.49787136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			949.3
Root			$-1.09445 - 0.895644i$ of defining polynomial
Character	$\chi$	$=$	2100.949
Dual form			2100.2.bc.h.1549.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{3} +(-2.29129 - 1.32288i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	$q+(0.866025 + 0.500000i) q^{3} +(-2.29129 - 1.32288i) q^{7} +(0.500000 + 0.866025i) q^{9} +(2.82288 - 4.88936i) q^{11} +1.00000i q^{13} +(-1.42526 - 0.822876i) q^{17} +(-2.32288 - 4.02334i) q^{19} +(-1.32288 - 2.29129i) q^{21} +(-1.73205 + 1.00000i) q^{23} +1.00000i q^{27} -7.29150 q^{29} +(-2.00000 + 3.46410i) q^{31} +(4.88936 - 2.82288i) q^{33} +(-7.18065 + 4.14575i) q^{37} +(-0.500000 + 0.866025i) q^{39} -0.354249 q^{41} -7.29150i q^{43} +(-2.54374 + 1.46863i) q^{47} +(3.50000 + 6.06218i) q^{49} +(-0.822876 - 1.42526i) q^{51} +(-2.03884 - 1.17712i) q^{53} -4.64575i q^{57} +(7.46863 - 12.9360i) q^{59} +(-4.79150 - 8.29913i) q^{61} -2.64575i q^{63} +(-6.87386 - 3.96863i) q^{67} -2.00000 q^{69} +3.29150 q^{71} +(5.44860 + 3.14575i) q^{73} +(-12.9360 + 7.46863i) q^{77} +(-3.32288 - 5.75539i) q^{79} +(-0.500000 + 0.866025i) q^{81} +3.64575i q^{83} +(-6.31463 - 3.64575i) q^{87} +(-4.46863 - 7.73989i) q^{89} +(1.32288 - 2.29129i) q^{91} +(-3.46410 + 2.00000i) q^{93} -14.2915i q^{97} +5.64575 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^9	$ 8 q + 4 q^{9} + 12 q^{11} - 8 q^{19} - 16 q^{29} - 16 q^{31} - 4 q^{39} - 24 q^{41} + 28 q^{49} + 4 q^{51} + 28 q^{59} + 4 q^{61} - 16 q^{69} - 16 q^{71} - 16 q^{79} - 4 q^{81} - 4 q^{89} + 24 q^{99}+O(q^{100}) $ 8 * q + 4 * q^9 + 12 * q^11 - 8 * q^19 - 16 * q^29 - 16 * q^31 - 4 * q^39 - 24 * q^41 + 28 * q^49 + 4 * q^51 + 28 * q^59 + 4 * q^61 - 16 * q^69 - 16 * q^71 - 16 * q^79 - 4 * q^81 - 4 * q^89 + 24 * 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
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.29129	−	1.32288i	−0.866025	−	0.500000i
$7$	−2.29129	−	1.32288i	−0.866025	−	0.500000i
$8$		0			0
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	2.82288	−	4.88936i	0.851129	−	1.47420i	−0.0290612	−	0.999578i	$-0.509252\pi$
$11$	2.82288	−	4.88936i	0.851129	−	1.47420i	0.880190	−	0.474621i	$-0.157415\pi$
$12$		0			0
$13$			1.00000i			0.277350i	0.990338	+	0.138675i	$0.0442844\pi$
$13$			1.00000i			0.277350i	−0.990338	+	0.138675i	$0.955716\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.42526	−	0.822876i	−0.345677	−	0.199577i	0.317103	−	0.948391i	$-0.397290\pi$
$17$	−1.42526	−	0.822876i	−0.345677	−	0.199577i	−0.662780	+	0.748815i	$0.730623\pi$
$18$		0			0
$19$	−2.32288	−	4.02334i	−0.532904	−	0.923017i	−0.999262	−	0.0384208i	$-0.987767\pi$
$19$	−2.32288	−	4.02334i	−0.532904	−	0.923017i	0.466357	−	0.884596i	$-0.345566\pi$
$20$		0			0
$21$	−1.32288	−	2.29129i	−0.288675	−	0.500000i
$22$		0			0
$23$	−1.73205	+	1.00000i	−0.361158	+	0.208514i	−0.669588	−	0.742732i	$-0.733529\pi$
$23$	−1.73205	+	1.00000i	−0.361158	+	0.208514i	0.308431	+	0.951247i	$0.400196\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$			1.00000i			0.192450i
$28$		0			0
$29$	−7.29150			−1.35400			−0.676999	−	0.735984i	$-0.736720\pi$
$29$	−7.29150			−1.35400			−0.676999	+	0.735984i	$0.736720\pi$
$30$		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
$33$	4.88936	−	2.82288i	0.851129	−	0.491400i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−7.18065	+	4.14575i	−1.18049	+	0.681557i	−0.956128	−	0.292948i	$-0.905364\pi$
$37$	−7.18065	+	4.14575i	−1.18049	+	0.681557i	−0.224364	+	0.974506i	$0.572030\pi$
$38$		0			0
$39$	−0.500000	+	0.866025i	−0.0800641	+	0.138675i
$40$		0			0
$41$	−0.354249			−0.0553244			−0.0276622	−	0.999617i	$-0.508806\pi$
$41$	−0.354249			−0.0553244			−0.0276622	+	0.999617i	$0.508806\pi$
$42$		0			0
$43$		−	7.29150i		−	1.11194i	−0.831201	−	0.555972i	$-0.812346\pi$
$43$		−	7.29150i		−	1.11194i	0.831201	−	0.555972i	$-0.187654\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.54374	+	1.46863i	−0.371042	+	0.214221i	−0.673914	−	0.738810i	$-0.735388\pi$
$47$	−2.54374	+	1.46863i	−0.371042	+	0.214221i	0.302872	+	0.953031i	$0.402055\pi$
$48$		0			0
$49$	3.50000	+	6.06218i	0.500000	+	0.866025i
$50$		0			0
$51$	−0.822876	−	1.42526i	−0.115226	−	0.199577i
$52$		0			0
$53$	−2.03884	−	1.17712i	−0.280056	−	0.161690i	0.353393	−	0.935475i	$-0.385028\pi$
$53$	−2.03884	−	1.17712i	−0.280056	−	0.161690i	−0.633449	+	0.773785i	$0.718361\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		−	4.64575i		−	0.615345i
$58$		0			0
$59$	7.46863	−	12.9360i	0.972332	−	1.68413i	0.283861	−	0.958865i	$-0.408384\pi$
$59$	7.46863	−	12.9360i	0.972332	−	1.68413i	0.688471	−	0.725264i	$-0.258282\pi$
$60$		0			0
$61$	−4.79150	−	8.29913i	−0.613489	−	1.06259i	−0.990648	−	0.136445i	$-0.956432\pi$
$61$	−4.79150	−	8.29913i	−0.613489	−	1.06259i	0.377159	−	0.926149i	$-0.376901\pi$
$62$		0			0
$63$		−	2.64575i		−	0.333333i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−6.87386	−	3.96863i	−0.839776	−	0.484845i	0.0174120	−	0.999848i	$-0.494457\pi$
$67$	−6.87386	−	3.96863i	−0.839776	−	0.484845i	−0.857188	+	0.515003i	$0.827791\pi$
$68$		0			0
$69$	−2.00000			−0.240772
$70$		0			0
$71$	3.29150			0.390629			0.195315	−	0.980741i	$-0.437427\pi$
$71$	3.29150			0.390629			0.195315	+	0.980741i	$0.437427\pi$
$72$		0			0
$73$	5.44860	+	3.14575i	0.637711	+	0.368182i	0.783732	−	0.621099i	$-0.213314\pi$
$73$	5.44860	+	3.14575i	0.637711	+	0.368182i	−0.146022	+	0.989281i	$0.546647\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−12.9360	+	7.46863i	−1.47420	+	0.851129i
$78$		0			0
$79$	−3.32288	−	5.75539i	−0.373853	−	0.647532i	0.616302	−	0.787510i	$-0.288630\pi$
$79$	−3.32288	−	5.75539i	−0.373853	−	0.647532i	−0.990155	+	0.139978i	$0.955297\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$			3.64575i			0.400173i	0.979778	+	0.200087i	$0.0641224\pi$
$83$			3.64575i			0.400173i	−0.979778	+	0.200087i	$0.935878\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−6.31463	−	3.64575i	−0.676999	−	0.390866i
$88$		0			0
$89$	−4.46863	−	7.73989i	−0.473674	−	0.820427i	0.525872	−	0.850564i	$-0.323739\pi$
$89$	−4.46863	−	7.73989i	−0.473674	−	0.820427i	−0.999546	+	0.0301370i	$0.990406\pi$
$90$		0			0
$91$	1.32288	−	2.29129i	0.138675	−	0.240192i
$92$		0			0
$93$	−3.46410	+	2.00000i	−0.359211	+	0.207390i
$94$		0			0
$95$		0			0
$96$		0			0
$97$		−	14.2915i		−	1.45108i	−0.688179	−	0.725541i	$-0.741590\pi$
$97$		−	14.2915i		−	1.45108i	0.688179	−	0.725541i	$-0.258410\pi$
$98$		0			0
$99$	5.64575			0.567419
$100$		0			0
$101$	5.46863	−	9.47194i	0.544149	−	0.942493i	−0.454511	−	0.890741i	$-0.650186\pi$
$101$	5.46863	−	9.47194i	0.544149	−	0.942493i	0.998660	−	0.0517522i	$-0.0164806\pi$
$102$		0			0
$103$	13.8021	−	7.96863i	1.35996	−	0.785172i	0.370340	−	0.928896i	$-0.379241\pi$
$103$	13.8021	−	7.96863i	1.35996	−	0.785172i	0.989618	+	0.143724i	$0.0459078\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.85836	+	5.11438i	−0.856370	+	0.494426i	−0.862795	−	0.505554i	$-0.831288\pi$
$107$	−8.85836	+	5.11438i	−0.856370	+	0.494426i	0.00642483	+	0.999979i	$0.497955\pi$
$108$		0			0
$109$	4.79150	−	8.29913i	0.458943	−	0.794912i	−0.539963	−	0.841689i	$-0.681562\pi$
$109$	4.79150	−	8.29913i	0.458943	−	0.794912i	0.998905	+	0.0467769i	$0.0148950\pi$
$110$		0			0
$111$	−8.29150			−0.786995
$112$		0			0
$113$			12.5830i			1.18371i	0.806045	+	0.591855i	$0.201604\pi$
$113$			12.5830i			1.18371i	−0.806045	+	0.591855i	$0.798396\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.866025	+	0.500000i	−0.0800641	+	0.0462250i
$118$		0			0
$119$	2.17712	+	3.77089i	0.199577	+	0.345677i
$120$		0			0
$121$	−10.4373	−	18.0779i	−0.948841	−	1.64344i
$122$		0			0
$123$	−0.306788	−	0.177124i	−0.0276622	−	0.0159708i
$124$		0			0
$125$		0			0
$126$		0			0
$127$			6.64575i			0.589715i	0.955541	+	0.294858i	$0.0952722\pi$
$127$			6.64575i			0.589715i	−0.955541	+	0.294858i	$0.904728\pi$
$128$		0			0
$129$	3.64575	−	6.31463i	0.320991	−	0.555972i
$130$		0			0
$131$	10.2915	+	17.8254i	0.899173	+	1.55741i	0.828554	+	0.559910i	$0.189164\pi$
$131$	10.2915	+	17.8254i	0.899173	+	1.55741i	0.0706190	+	0.997503i	$0.477503\pi$
$132$		0			0
$133$			12.2915i			1.06581i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−8.04668	−	4.64575i	−0.687474	−	0.396913i	0.115191	−	0.993343i	$-0.463252\pi$
$137$	−8.04668	−	4.64575i	−0.687474	−	0.396913i	−0.802665	+	0.596430i	$0.796585\pi$
$138$		0			0
$139$	−0.0627461			−0.00532205			−0.00266103	−	0.999996i	$-0.500847\pi$
$139$	−0.0627461			−0.00532205			−0.00266103	+	0.999996i	$0.500847\pi$
$140$		0			0
$141$	−2.93725			−0.247361
$142$		0			0
$143$	4.88936	+	2.82288i	0.408869	+	0.236061i
$144$		0			0
$145$		0			0
$146$		0			0
$147$			7.00000i			0.577350i
$148$		0			0
$149$	−5.46863	−	9.47194i	−0.448007	−	0.775972i	0.550249	−	0.835001i	$-0.314533\pi$
$149$	−5.46863	−	9.47194i	−0.448007	−	0.775972i	−0.998256	+	0.0590292i	$0.981200\pi$
$150$		0			0
$151$	8.32288	−	14.4156i	0.677306	−	1.17313i	−0.298483	−	0.954415i	$-0.596481\pi$
$151$	8.32288	−	14.4156i	0.677306	−	1.17313i	0.975789	−	0.218714i	$-0.0701860\pi$
$152$		0			0
$153$		−	1.64575i		−	0.133051i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	14.7224	+	8.50000i	1.17498	+	0.678374i	0.954847	−	0.297097i	$-0.0960183\pi$
$157$	14.7224	+	8.50000i	1.17498	+	0.678374i	0.220131	+	0.975470i	$0.429352\pi$
$158$		0			0
$159$	−1.17712	−	2.03884i	−0.0933520	−	0.161690i
$160$		0			0
$161$	5.29150			0.417029
$162$		0			0
$163$	7.99234	−	4.61438i	0.626008	−	0.361426i	−0.153196	−	0.988196i	$-0.548957\pi$
$163$	7.99234	−	4.61438i	0.626008	−	0.361426i	0.779204	+	0.626770i	$0.215623\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			17.5203i			1.35576i	0.735173	+	0.677879i	$0.237101\pi$
$167$			17.5203i			1.35576i	−0.735173	+	0.677879i	$0.762899\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$		0			0
$171$	2.32288	−	4.02334i	0.177635	−	0.307672i
$172$		0			0
$173$	−0.504897	+	0.291503i	−0.0383866	+	0.0221625i	−0.519071	−	0.854731i	$-0.673722\pi$
$173$	−0.504897	+	0.291503i	−0.0383866	+	0.0221625i	0.480684	+	0.876894i	$0.340388\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	12.9360	−	7.46863i	0.972332	−	0.561376i
$178$		0			0
$179$	−6.35425	+	11.0059i	−0.474939	+	0.822618i	−0.999588	−	0.0287003i	$-0.990863\pi$
$179$	−6.35425	+	11.0059i	−0.474939	+	0.822618i	0.524649	+	0.851319i	$0.324196\pi$
$180$		0			0
$181$	−6.58301			−0.489311			−0.244655	−	0.969610i	$-0.578675\pi$
$181$	−6.58301			−0.489311			−0.244655	+	0.969610i	$0.578675\pi$
$182$		0			0
$183$		−	9.58301i		−	0.708396i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−8.04668	+	4.64575i	−0.588431	+	0.339731i
$188$		0			0
$189$	1.32288	−	2.29129i	0.0962250	−	0.166667i
$190$		0			0
$191$	11.7601	+	20.3691i	0.850933	+	1.47386i	0.880367	+	0.474293i	$0.157296\pi$
$191$	11.7601	+	20.3691i	0.850933	+	1.47386i	−0.0294341	+	0.999567i	$0.509371\pi$
$192$		0			0
$193$	−13.8564	−	8.00000i	−0.997406	−	0.575853i	−0.0899262	−	0.995948i	$-0.528663\pi$
$193$	−13.8564	−	8.00000i	−0.997406	−	0.575853i	−0.907480	+	0.420096i	$0.861996\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			19.2915i			1.37446i	0.726439	+	0.687231i	$0.241174\pi$
$197$			19.2915i			1.37446i	−0.726439	+	0.687231i	$0.758826\pi$
$198$		0			0
$199$	−2.32288	+	4.02334i	−0.164664	+	0.285207i	−0.936536	−	0.350571i	$-0.885987\pi$
$199$	−2.32288	+	4.02334i	−0.164664	+	0.285207i	0.771872	+	0.635778i	$0.219321\pi$
$200$		0			0
$201$	−3.96863	−	6.87386i	−0.279925	−	0.484845i
$202$		0			0
$203$	16.7069	+	9.64575i	1.17260	+	0.676999i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.73205	−	1.00000i	−0.120386	−	0.0695048i
$208$		0			0
$209$	−26.2288			−1.81428
$210$		0			0
$211$	−17.9373			−1.23485			−0.617426	−	0.786629i	$-0.711824\pi$
$211$	−17.9373			−1.23485			−0.617426	+	0.786629i	$0.711824\pi$
$212$		0			0
$213$	2.85052	+	1.64575i	0.195315	+	0.112765i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	9.16515	−	5.29150i	0.622171	−	0.359211i
$218$		0			0
$219$	3.14575	+	5.44860i	0.212570	+	0.368182i
$220$		0			0
$221$	0.822876	−	1.42526i	0.0553526	−	0.0958735i
$222$		0			0
$223$		−	1.93725i		−	0.129728i	−0.997894	−	0.0648641i	$-0.979339\pi$
$223$		−	1.93725i		−	0.129728i	0.997894	−	0.0648641i	$-0.0206614\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−16.7069	−	9.64575i	−1.10888	−	0.640211i	−0.170339	−	0.985385i	$-0.554486\pi$
$227$	−16.7069	−	9.64575i	−1.10888	−	0.640211i	−0.938539	+	0.345174i	$0.887820\pi$
$228$		0			0
$229$	−4.85425	−	8.40781i	−0.320778	−	0.555603i	0.659871	−	0.751379i	$-0.270611\pi$
$229$	−4.85425	−	8.40781i	−0.320778	−	0.555603i	−0.980649	+	0.195776i	$0.937278\pi$
$230$		0			0
$231$	−14.9373			−0.982799
$232$		0			0
$233$	−1.93016	+	1.11438i	−0.126449	+	0.0730053i	−0.561890	−	0.827212i	$-0.689926\pi$
$233$	−1.93016	+	1.11438i	−0.126449	+	0.0730053i	0.435441	+	0.900217i	$0.356592\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		−	6.64575i		−	0.431688i
$238$		0			0
$239$	30.5830			1.97825			0.989125	−	0.147077i	$-0.0469864\pi$
$239$	30.5830			1.97825			0.989125	+	0.147077i	$0.0469864\pi$
$240$		0			0
$241$	−5.14575	+	8.91270i	−0.331467	+	0.574118i	−0.982800	−	0.184675i	$-0.940877\pi$
$241$	−5.14575	+	8.91270i	−0.331467	+	0.574118i	0.651333	+	0.758792i	$0.274210\pi$
$242$		0			0
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	4.02334	−	2.32288i	0.255999	−	0.147801i
$248$		0			0
$249$	−1.82288	+	3.15731i	−0.115520	+	0.200087i
$250$		0			0
$251$	18.8118			1.18739			0.593694	−	0.804691i	$-0.297669\pi$
$251$	18.8118			1.18739			0.593694	+	0.804691i	$0.297669\pi$
$252$		0			0
$253$			11.2915i			0.709891i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	10.6991	−	6.17712i	0.667391	−	0.385318i	−0.127696	−	0.991813i	$-0.540758\pi$
$257$	10.6991	−	6.17712i	0.667391	−	0.385318i	0.795087	+	0.606495i	$0.207425\pi$
$258$		0			0
$259$	21.9373			1.36311
$260$		0			0
$261$	−3.64575	−	6.31463i	−0.225666	−	0.390866i
$262$		0			0
$263$	−20.7846	−	12.0000i	−1.28163	−	0.739952i	−0.304487	−	0.952517i	$-0.598485\pi$
$263$	−20.7846	−	12.0000i	−1.28163	−	0.739952i	−0.977147	+	0.212565i	$0.931818\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	8.93725i		−	0.546951i
$268$		0			0
$269$	−3.11438	+	5.39426i	−0.189887	+	0.328894i	−0.945212	−	0.326456i	$-0.894145\pi$
$269$	−3.11438	+	5.39426i	−0.189887	+	0.328894i	0.755325	+	0.655350i	$0.227479\pi$
$270$		0			0
$271$	6.64575	+	11.5108i	0.403701	+	0.699230i	0.994169	−	0.107831i	$-0.0343904\pi$
$271$	6.64575	+	11.5108i	0.403701	+	0.699230i	−0.590469	+	0.807061i	$0.701057\pi$
$272$		0			0
$273$	2.29129	−	1.32288i	0.138675	−	0.0800641i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−21.6506	−	12.5000i	−1.30086	−	0.751052i	−0.320309	−	0.947313i	$-0.603787\pi$
$277$	−21.6506	−	12.5000i	−1.30086	−	0.751052i	−0.980552	+	0.196261i	$0.937120\pi$
$278$		0			0
$279$	−4.00000			−0.239474
$280$		0			0
$281$	4.22876			0.252266			0.126133	−	0.992013i	$-0.459743\pi$
$281$	4.22876			0.252266			0.126133	+	0.992013i	$0.459743\pi$
$282$		0			0
$283$	−26.4313	−	15.2601i	−1.57118	−	0.907121i	−0.996025	−	0.0890754i	$-0.971609\pi$
$283$	−26.4313	−	15.2601i	−1.57118	−	0.907121i	−0.575154	−	0.818045i	$-0.695058\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.811686	+	0.468627i	0.0479123	+	0.0276622i
$288$		0			0
$289$	−7.14575	−	12.3768i	−0.420338	−	0.728047i
$290$		0			0
$291$	7.14575	−	12.3768i	0.418891	−	0.725541i
$292$		0			0
$293$			21.8745i			1.27792i	0.769239	+	0.638961i	$0.220636\pi$
$293$			21.8745i			1.27792i	−0.769239	+	0.638961i	$0.779364\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	4.88936	+	2.82288i	0.283710	+	0.163800i
$298$		0			0
$299$	−1.00000	−	1.73205i	−0.0578315	−	0.100167i
$300$		0			0
$301$	−9.64575	+	16.7069i	−0.555972	+	0.962972i
$302$		0			0
$303$	9.47194	−	5.46863i	0.544149	−	0.314164i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	29.8745i		−	1.70503i	−0.522704	−	0.852514i	$-0.675077\pi$
$307$		−	29.8745i		−	1.70503i	0.522704	−	0.852514i	$-0.324923\pi$
$308$		0			0
$309$	15.9373			0.906639
$310$		0			0
$311$	1.35425	−	2.34563i	0.0767924	−	0.133008i	−0.825072	−	0.565028i	$-0.808865\pi$
$311$	1.35425	−	2.34563i	0.0767924	−	0.133008i	0.901864	+	0.432019i	$0.142199\pi$
$312$		0			0
$313$	7.54178	−	4.35425i	0.426287	−	0.246117i	−0.271477	−	0.962445i	$-0.587512\pi$
$313$	7.54178	−	4.35425i	0.426287	−	0.246117i	0.697763	+	0.716328i	$0.254179\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	10.8972	−	6.29150i	0.612048	−	0.353366i	−0.161719	−	0.986837i	$-0.551704\pi$
$317$	10.8972	−	6.29150i	0.612048	−	0.353366i	0.773767	+	0.633471i	$0.218370\pi$
$318$		0			0
$319$	−20.5830	+	35.6508i	−1.15243	+	1.99606i
$320$		0			0
$321$	−10.2288			−0.570914
$322$		0			0
$323$			7.64575i			0.425421i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	8.29913	−	4.79150i	0.458943	−	0.264971i
$328$		0			0
$329$	7.77124			0.428443
$330$		0			0
$331$	4.32288	+	7.48744i	0.237607	+	0.411547i	0.960027	−	0.279907i	$-0.0903037\pi$
$331$	4.32288	+	7.48744i	0.237607	+	0.411547i	−0.722420	+	0.691454i	$0.756970\pi$
$332$		0			0
$333$	−7.18065	−	4.14575i	−0.393497	−	0.227186i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			8.70850i			0.474382i	0.971463	+	0.237191i	$0.0762267\pi$
$337$			8.70850i			0.474382i	−0.971463	+	0.237191i	$0.923773\pi$
$338$		0			0
$339$	−6.29150	+	10.8972i	−0.341708	+	0.591855i
$340$		0			0
$341$	11.2915	+	19.5575i	0.611469	+	1.05910i
$342$		0			0
$343$		−	18.5203i		−	1.00000i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	22.1012	+	12.7601i	1.18645	+	0.685000i	0.957499	−	0.288437i	$-0.0931357\pi$
$347$	22.1012	+	12.7601i	1.18645	+	0.685000i	0.228955	+	0.973437i	$0.426469\pi$
$348$		0			0
$349$	−15.2915			−0.818535			−0.409268	−	0.912414i	$-0.634216\pi$
$349$	−15.2915			−0.818535			−0.409268	+	0.912414i	$0.634216\pi$
$350$		0			0
$351$	−1.00000			−0.0533761
$352$		0			0
$353$	0.920365	+	0.531373i	0.0489861	+	0.0282821i	0.524293	−	0.851538i	$-0.324330\pi$
$353$	0.920365	+	0.531373i	0.0489861	+	0.0282821i	−0.475307	+	0.879820i	$0.657663\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$			4.35425i			0.230451i
$358$		0			0
$359$	−4.53137	−	7.84857i	−0.239157	−	0.414232i	0.721316	−	0.692606i	$-0.243538\pi$
$359$	−4.53137	−	7.84857i	−0.239157	−	0.414232i	−0.960473	+	0.278375i	$0.910204\pi$
$360$		0			0
$361$	−1.29150	+	2.23695i	−0.0679738	+	0.117734i
$362$		0			0
$363$		−	20.8745i		−	1.09563i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	17.2118	+	9.93725i	0.898450	+	0.518720i	0.876697	−	0.481043i	$-0.159742\pi$
$367$	17.2118	+	9.93725i	0.898450	+	0.518720i	0.0217531	+	0.999763i	$0.493075\pi$
$368$		0			0
$369$	−0.177124	−	0.306788i	−0.00922073	−	0.0159708i
$370$		0			0
$371$	3.11438	+	5.39426i	0.161690	+	0.280056i
$372$		0			0
$373$	2.09318	−	1.20850i	0.108381	−	0.0625736i	−0.444830	−	0.895615i	$-0.646736\pi$
$373$	2.09318	−	1.20850i	0.108381	−	0.0625736i	0.553211	+	0.833041i	$0.313403\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	7.29150i		−	0.375531i
$378$		0			0
$379$	20.6458			1.06050			0.530251	−	0.847841i	$-0.322098\pi$
$379$	20.6458			1.06050			0.530251	+	0.847841i	$0.322098\pi$
$380$		0			0
$381$	−3.32288	+	5.75539i	−0.170236	+	0.294858i
$382$		0			0
$383$	−1.11847	+	0.645751i	−0.0571514	+	0.0329964i	−0.528303	−	0.849056i	$-0.677172\pi$
$383$	−1.11847	+	0.645751i	−0.0571514	+	0.0329964i	0.471152	+	0.882052i	$0.343838\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	6.31463	−	3.64575i	0.320991	−	0.185324i
$388$		0			0
$389$	−18.7601	+	32.4935i	−0.951176	+	1.64749i	−0.208291	+	0.978067i	$0.566790\pi$
$389$	−18.7601	+	32.4935i	−0.951176	+	1.64749i	−0.742885	+	0.669419i	$0.766543\pi$
$390$		0			0
$391$	3.29150			0.166458
$392$		0			0
$393$			20.5830i			1.03828i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	28.1090	−	16.2288i	1.41075	−	0.814498i	0.415293	−	0.909688i	$-0.363679\pi$
$397$	28.1090	−	16.2288i	1.41075	−	0.814498i	0.995459	+	0.0951899i	$0.0303458\pi$
$398$		0			0
$399$	−6.14575	+	10.6448i	−0.307672	+	0.532904i
$400$		0			0
$401$	0.760130	+	1.31658i	0.0379591	+	0.0657470i	0.884381	−	0.466766i	$-0.154581\pi$
$401$	0.760130	+	1.31658i	0.0379591	+	0.0657470i	−0.846422	+	0.532513i	$0.821248\pi$
$402$		0			0
$403$	−3.46410	−	2.00000i	−0.172559	−	0.0996271i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			46.8118i			2.32037i
$408$		0			0
$409$	−6.79150	+	11.7632i	−0.335818	+	0.581654i	−0.983642	−	0.180136i	$-0.942346\pi$
$409$	−6.79150	+	11.7632i	−0.335818	+	0.581654i	0.647823	+	0.761790i	$0.275679\pi$
$410$		0			0
$411$	−4.64575	−	8.04668i	−0.229158	−	0.396913i
$412$		0			0
$413$	−34.2255	+	19.7601i	−1.68413	+	0.972332i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.0543397	−	0.0313730i	−0.00266103	−	0.00153634i
$418$		0			0
$419$	−26.3542			−1.28749			−0.643745	−	0.765240i	$-0.722620\pi$
$419$	−26.3542			−1.28749			−0.643745	+	0.765240i	$0.722620\pi$
$420$		0			0
$421$	−2.87451			−0.140095			−0.0700475	−	0.997544i	$-0.522315\pi$
$421$	−2.87451			−0.140095			−0.0700475	+	0.997544i	$0.522315\pi$
$422$		0			0
$423$	−2.54374	−	1.46863i	−0.123681	−	0.0714071i
$424$		0			0
$425$		0			0
$426$		0			0
$427$			25.3542i			1.22698i
$428$		0			0
$429$	2.82288	+	4.88936i	0.136290	+	0.236061i
$430$		0			0
$431$	−1.93725	+	3.35542i	−0.0933142	+	0.161625i	−0.908904	−	0.417006i	$-0.863079\pi$
$431$	−1.93725	+	3.35542i	−0.0933142	+	0.161625i	0.815590	+	0.578631i	$0.196413\pi$
$432$		0			0
$433$			7.29150i			0.350407i	0.984532	+	0.175204i	$0.0560584\pi$
$433$			7.29150i			0.350407i	−0.984532	+	0.175204i	$0.943942\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	8.04668	+	4.64575i	0.384925	+	0.222236i
$438$		0			0
$439$	3.90588	+	6.76518i	0.186418	+	0.322885i	0.944053	−	0.329793i	$-0.106979\pi$
$439$	3.90588	+	6.76518i	0.186418	+	0.322885i	−0.757636	+	0.652678i	$0.773646\pi$
$440$		0			0
$441$	−3.50000	+	6.06218i	−0.166667	+	0.288675i
$442$		0			0
$443$	−14.9749	+	8.64575i	−0.711478	+	0.410772i	−0.811608	−	0.584202i	$-0.801407\pi$
$443$	−14.9749	+	8.64575i	−0.711478	+	0.410772i	0.100130	+	0.994974i	$0.468074\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		−	10.9373i		−	0.517314i
$448$		0			0
$449$	−26.1033			−1.23189			−0.615945	−	0.787789i	$-0.711225\pi$
$449$	−26.1033			−1.23189			−0.615945	+	0.787789i	$0.711225\pi$
$450$		0			0
$451$	−1.00000	+	1.73205i	−0.0470882	+	0.0815591i
$452$		0			0
$453$	14.4156	−	8.32288i	0.677306	−	0.391043i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	29.5886	−	17.0830i	1.38410	−	0.799109i	0.391456	−	0.920197i	$-0.371972\pi$
$457$	29.5886	−	17.0830i	1.38410	−	0.799109i	0.992642	+	0.121088i	$0.0386382\pi$
$458$		0			0
$459$	0.822876	−	1.42526i	0.0384085	−	0.0665256i
$460$		0			0
$461$	21.2915			0.991644			0.495822	−	0.868424i	$-0.334867\pi$
$461$	21.2915			0.991644			0.495822	+	0.868424i	$0.334867\pi$
$462$		0			0
$463$			18.0627i			0.839447i	0.907652	+	0.419723i	$0.137873\pi$
$463$			18.0627i			0.839447i	−0.907652	+	0.419723i	$0.862127\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	28.8313	−	16.6458i	1.33415	−	0.770274i	0.348220	−	0.937413i	$-0.386786\pi$
$467$	28.8313	−	16.6458i	1.33415	−	0.770274i	0.985933	+	0.167139i	$0.0534530\pi$
$468$		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
$473$	−35.6508	−	20.5830i	−1.63923	−	0.946408i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		−	2.35425i		−	0.107794i
$478$		0			0
$479$	10.1771	−	17.6273i	0.465005	−	0.805412i	−0.534197	−	0.845360i	$-0.679386\pi$
$479$	10.1771	−	17.6273i	0.465005	−	0.805412i	0.999202	+	0.0399482i	$0.0127193\pi$
$480$		0			0
$481$	−4.14575	−	7.18065i	−0.189030	−	0.327410i
$482$		0			0
$483$	4.58258	+	2.64575i	0.208514	+	0.120386i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	10.7885	+	6.22876i	0.488875	+	0.282252i	0.724107	−	0.689687i	$-0.242252\pi$
$487$	10.7885	+	6.22876i	0.488875	+	0.282252i	−0.235233	+	0.971939i	$0.575585\pi$
$488$		0			0
$489$	9.22876			0.417339
$490$		0			0
$491$	18.4575			0.832976			0.416488	−	0.909141i	$-0.363261\pi$
$491$	18.4575			0.832976			0.416488	+	0.909141i	$0.363261\pi$
$492$		0			0
$493$	10.3923	+	6.00000i	0.468046	+	0.270226i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−7.54178	−	4.35425i	−0.338295	−	0.195315i
$498$		0			0
$499$	13.9059	+	24.0857i	0.622513	+	1.07822i	0.989016	+	0.147807i	$0.0472214\pi$
$499$	13.9059	+	24.0857i	0.622513	+	1.07822i	−0.366504	+	0.930417i	$0.619445\pi$
$500$		0			0
$501$	−8.76013	+	15.1730i	−0.391374	+	0.677879i
$502$		0			0
$503$		−	27.2915i		−	1.21687i	−0.793604	−	0.608434i	$-0.791798\pi$
$503$		−	27.2915i		−	1.21687i	0.793604	−	0.608434i	$-0.208202\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	10.3923	+	6.00000i	0.461538	+	0.266469i
$508$		0			0
$509$	2.93725	+	5.08747i	0.130191	+	0.225498i	0.923750	−	0.382995i	$-0.125107\pi$
$509$	2.93725	+	5.08747i	0.130191	+	0.225498i	−0.793559	+	0.608494i	$0.791774\pi$
$510$		0			0
$511$	−8.32288	−	14.4156i	−0.368182	−	0.637711i
$512$		0			0
$513$	4.02334	−	2.32288i	0.177635	−	0.102557i
$514$		0			0
$515$		0			0
$516$		0			0
$517$			16.5830i			0.729320i
$518$		0			0
$519$	−0.583005			−0.0255911
$520$		0			0
$521$	−7.93725	+	13.7477i	−0.347737	+	0.602299i	−0.985847	−	0.167647i	$-0.946383\pi$
$521$	−7.93725	+	13.7477i	−0.347737	+	0.602299i	0.638110	+	0.769945i	$0.279717\pi$
$522$		0			0
$523$	36.2644	−	20.9373i	1.58573	−	0.915522i	0.591732	−	0.806135i	$-0.298444\pi$
$523$	36.2644	−	20.9373i	1.58573	−	0.915522i	0.993999	−	0.109387i	$-0.0348889\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	5.70105	−	3.29150i	0.248342	−	0.143380i
$528$		0			0
$529$	−9.50000	+	16.4545i	−0.413043	+	0.715412i
$530$		0			0
$531$	14.9373			0.648222
$532$		0			0
$533$		−	0.354249i		−	0.0153442i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−11.0059	+	6.35425i	−0.474939	+	0.274206i
$538$		0			0
$539$	39.5203			1.70226
$540$		0			0
$541$	2.43725	+	4.22145i	0.104786	+	0.181494i	0.913651	−	0.406500i	$-0.133251\pi$
$541$	2.43725	+	4.22145i	0.104786	+	0.181494i	−0.808865	+	0.587995i	$0.799918\pi$
$542$		0			0
$543$	−5.70105	−	3.29150i	−0.244655	−	0.141252i
$544$		0			0
$545$		0			0
$546$		0			0
$547$		−	31.8745i		−	1.36286i	−0.731885	−	0.681428i	$-0.761359\pi$
$547$		−	31.8745i		−	1.36286i	0.731885	−	0.681428i	$-0.238641\pi$
$548$		0			0
$549$	4.79150	−	8.29913i	0.204496	−	0.354198i
$550$		0			0
$551$	16.9373	+	29.3362i	0.721551	+	1.24976i
$552$		0			0
$553$			17.5830i			0.747705i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−23.6351	−	13.6458i	−1.00145	−	0.578189i	−0.0927750	−	0.995687i	$-0.529574\pi$
$557$	−23.6351	−	13.6458i	−1.00145	−	0.578189i	−0.908678	+	0.417498i	$0.862907\pi$
$558$		0			0
$559$	7.29150			0.308398
$560$		0			0
$561$	−9.29150			−0.392288
$562$		0			0
$563$	27.2973	+	15.7601i	1.15045	+	0.664210i	0.948996	−	0.315289i	$-0.102101\pi$
$563$	27.2973	+	15.7601i	1.15045	+	0.664210i	0.201450	+	0.979499i	$0.435435\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	2.29129	−	1.32288i	0.0962250	−	0.0555556i
$568$		0			0
$569$	−5.46863	−	9.47194i	−0.229257	−	0.397084i	0.728331	−	0.685225i	$-0.240296\pi$
$569$	−5.46863	−	9.47194i	−0.229257	−	0.397084i	−0.957588	+	0.288141i	$0.906963\pi$
$570$		0			0
$571$	4.96863	−	8.60591i	0.207931	−	0.360146i	−0.743132	−	0.669145i	$-0.766661\pi$
$571$	4.96863	−	8.60591i	0.207931	−	0.360146i	0.951062	+	0.308999i	$0.0999939\pi$
$572$		0			0
$573$			23.5203i			0.982573i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	14.3613	+	8.29150i	0.597869	+	0.345180i	0.768203	−	0.640207i	$-0.221151\pi$
$577$	14.3613	+	8.29150i	0.597869	+	0.345180i	−0.170334	+	0.985386i	$0.554485\pi$
$578$		0			0
$579$	−8.00000	−	13.8564i	−0.332469	−	0.575853i
$580$		0			0
$581$	4.82288	−	8.35347i	0.200087	−	0.346560i
$582$		0			0
$583$	−11.5108	+	6.64575i	−0.476728	+	0.275239i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	6.00000i		−	0.247647i	−0.992304	−	0.123823i	$-0.960484\pi$
$587$		−	6.00000i		−	0.247647i	0.992304	−	0.123823i	$-0.0395156\pi$
$588$		0			0
$589$	18.5830			0.765699
$590$		0			0
$591$	−9.64575	+	16.7069i	−0.396773	+	0.687231i
$592$		0			0
$593$	−17.8254	+	10.2915i	−0.732002	+	0.422621i	−0.819154	−	0.573574i	$-0.805557\pi$
$593$	−17.8254	+	10.2915i	−0.732002	+	0.422621i	0.0871523	+	0.996195i	$0.472223\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−4.02334	+	2.32288i	−0.164664	+	0.0950690i
$598$		0			0
$599$	−8.53137	+	14.7768i	−0.348582	+	0.603763i	−0.985998	−	0.166758i	$-0.946670\pi$
$599$	−8.53137	+	14.7768i	−0.348582	+	0.603763i	0.637415	+	0.770520i	$0.280004\pi$
$600$		0			0
$601$	3.70850			0.151273			0.0756364	−	0.997135i	$-0.475901\pi$
$601$	3.70850			0.151273			0.0756364	+	0.997135i	$0.475901\pi$
$602$		0			0
$603$		−	7.93725i		−	0.323230i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	9.83307	−	5.67712i	0.399112	−	0.230427i	−0.286989	−	0.957934i	$-0.592654\pi$
$607$	9.83307	−	5.67712i	0.399112	−	0.230427i	0.686101	+	0.727507i	$0.259321\pi$
$608$		0			0
$609$	9.64575	+	16.7069i	0.390866	+	0.676999i
$610$		0			0
$611$	−1.46863	−	2.54374i	−0.0594143	−	0.102909i
$612$		0			0
$613$	−21.3982	−	12.3542i	−0.864265	−	0.498983i	0.00117347	−	0.999999i	$-0.499626\pi$
$613$	−21.3982	−	12.3542i	−0.864265	−	0.498983i	−0.865438	+	0.501016i	$0.832960\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			10.1255i			0.407637i	0.979009	+	0.203818i	$0.0653352\pi$
$617$			10.1255i			0.407637i	−0.979009	+	0.203818i	$0.934665\pi$
$618$		0			0
$619$	17.6458	−	30.5633i	0.709243	−	1.22844i	−0.255896	−	0.966704i	$-0.582370\pi$
$619$	17.6458	−	30.5633i	0.709243	−	1.22844i	0.965138	−	0.261740i	$-0.0842963\pi$
$620$		0			0
$621$	−1.00000	−	1.73205i	−0.0401286	−	0.0695048i
$622$		0			0
$623$			23.6458i			0.947347i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−22.7148	−	13.1144i	−0.907141	−	0.523738i
$628$		0			0
$629$	13.6458			0.544092
$630$		0			0
$631$	−6.64575			−0.264563			−0.132282	−	0.991212i	$-0.542230\pi$
$631$	−6.64575			−0.264563			−0.132282	+	0.991212i	$0.542230\pi$
$632$		0			0
$633$	−15.5341	−	8.96863i	−0.617426	−	0.356471i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−6.06218	+	3.50000i	−0.240192	+	0.138675i
$638$		0			0
$639$	1.64575	+	2.85052i	0.0651049	+	0.112765i
$640$		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
$643$		−	32.6458i		−	1.28742i	−0.765268	−	0.643711i	$-0.777394\pi$
$643$		−	32.6458i		−	1.28742i	0.765268	−	0.643711i	$-0.222606\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	24.8430	+	14.3431i	0.976681	+	0.563887i	0.901266	−	0.433265i	$-0.142639\pi$
$647$	24.8430	+	14.3431i	0.976681	+	0.563887i	0.0754143	+	0.997152i	$0.475972\pi$
$648$		0			0
$649$	−42.1660	−	73.0337i	−1.65516	−	2.86682i
$650$		0			0
$651$	10.5830			0.414781
$652$		0			0
$653$	−8.85836	+	5.11438i	−0.346655	+	0.200141i	−0.663211	−	0.748433i	$-0.730807\pi$
$653$	−8.85836	+	5.11438i	−0.346655	+	0.200141i	0.316556	+	0.948574i	$0.397473\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			6.29150i			0.245455i
$658$		0			0
$659$	18.1033			0.705203			0.352602	−	0.935774i	$-0.385297\pi$
$659$	18.1033			0.705203			0.352602	+	0.935774i	$0.385297\pi$
$660$		0			0
$661$	−6.14575	+	10.6448i	−0.239042	+	0.414033i	−0.960440	−	0.278488i	$-0.910167\pi$
$661$	−6.14575	+	10.6448i	−0.239042	+	0.414033i	0.721398	+	0.692521i	$0.243500\pi$
$662$		0			0
$663$	1.42526	−	0.822876i	0.0553526	−	0.0319578i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	12.6293	−	7.29150i	0.489007	−	0.282328i
$668$		0			0
$669$	0.968627	−	1.67771i	0.0374493	−	0.0648641i
$670$		0			0
$671$	−54.1033			−2.08863
$672$		0			0
$673$		−	8.29150i		−	0.319614i	−0.987148	−	0.159807i	$-0.948913\pi$
$673$		−	8.29150i		−	0.319614i	0.987148	−	0.159807i	$-0.0510872\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	42.6877	−	24.6458i	1.64062	−	0.947213i	0.660008	−	0.751258i	$-0.270553\pi$
$677$	42.6877	−	24.6458i	1.64062	−	0.947213i	0.980613	−	0.195955i	$-0.0627806\pi$
$678$		0			0
$679$	−18.9059	+	32.7459i	−0.725541	+	1.25667i
$680$		0			0
$681$	−9.64575	−	16.7069i	−0.369626	−	0.640211i
$682$		0			0
$683$	32.9984	+	19.0516i	1.26265	+	0.728990i	0.973586	−	0.228320i	$-0.0733232\pi$
$683$	32.9984	+	19.0516i	1.26265	+	0.728990i	0.289062	+	0.957310i	$0.406657\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		−	9.70850i		−	0.370402i
$688$		0			0
$689$	1.17712	−	2.03884i	0.0448449	−	0.0776736i
$690$		0			0
$691$	5.61438	+	9.72439i	0.213581	+	0.369933i	0.952833	−	0.303496i	$-0.0981539\pi$
$691$	5.61438	+	9.72439i	0.213581	+	0.369933i	−0.739252	+	0.673429i	$0.764821\pi$
$692$		0			0
$693$	−12.9360	−	7.46863i	−0.491400	−	0.283710i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	0.504897	+	0.291503i	0.0191244	+	0.0110414i
$698$		0			0
$699$	−2.22876			−0.0842993
$700$		0			0
$701$	−40.9373			−1.54618			−0.773089	−	0.634297i	$-0.781290\pi$
$701$	−40.9373			−1.54618			−0.773089	+	0.634297i	$0.781290\pi$
$702$		0			0
$703$	33.3595	+	19.2601i	1.25818	+	0.726410i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−25.0604	+	14.4686i	−0.942493	+	0.544149i
$708$		0			0
$709$	18.0830	+	31.3207i	0.679122	+	1.17627i	0.975246	+	0.221124i	$0.0709724\pi$
$709$	18.0830	+	31.3207i	0.679122	+	1.17627i	−0.296124	+	0.955149i	$0.595694\pi$
$710$		0			0
$711$	3.32288	−	5.75539i	0.124618	−	0.215844i
$712$		0			0
$713$		−	8.00000i		−	0.299602i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	26.4857	+	15.2915i	0.989125	+	0.571072i
$718$		0			0
$719$	−12.1144	−	20.9827i	−0.451790	−	0.782523i	0.546707	−	0.837324i	$-0.315881\pi$
$719$	−12.1144	−	20.9827i	−0.451790	−	0.782523i	−0.998497	+	0.0548005i	$0.982548\pi$
$720$		0			0
$721$	−42.1660			−1.57034
$722$		0			0
$723$	−8.91270	+	5.14575i	−0.331467	+	0.191373i
$724$		0			0
$725$		0			0
$726$		0			0
$727$			31.1033i			1.15356i	0.816901	+	0.576778i	$0.195690\pi$
$727$			31.1033i			1.15356i	−0.816901	+	0.576778i	$0.804310\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−6.00000	+	10.3923i	−0.221918	+	0.384373i
$732$		0			0
$733$	−36.4082	+	21.0203i	−1.34477	+	0.776401i	−0.987503	−	0.157603i	$-0.949623\pi$
$733$	−36.4082	+	21.0203i	−1.34477	+	0.776401i	−0.357263	+	0.934004i	$0.616290\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−38.8081	+	22.4059i	−1.42952	+	0.825331i
$738$		0			0
$739$	−6.73987	+	11.6738i	−0.247930	+	0.429428i	−0.962951	−	0.269675i	$-0.913084\pi$
$739$	−6.73987	+	11.6738i	−0.247930	+	0.429428i	0.715021	+	0.699103i	$0.246417\pi$
$740$		0			0
$741$	4.64575			0.170666
$742$		0			0
$743$		−	32.5830i		−	1.19535i	−0.801737	−	0.597677i	$-0.796090\pi$
$743$		−	32.5830i		−	1.19535i	0.801737	−	0.597677i	$-0.203910\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−3.15731	+	1.82288i	−0.115520	+	0.0666955i
$748$		0			0
$749$	27.0627			0.988851
$750$		0			0
$751$	19.3229	+	33.4682i	0.705102	+	1.22127i	0.966655	+	0.256083i	$0.0824320\pi$
$751$	19.3229	+	33.4682i	0.705102	+	1.22127i	−0.261553	+	0.965189i	$0.584235\pi$
$752$		0			0
$753$	16.2915	+	9.40588i	0.593694	+	0.342769i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	11.0000i		−	0.399802i	−0.979816	−	0.199901i	$-0.935938\pi$
$757$		−	11.0000i		−	0.399802i	0.979816	−	0.199901i	$-0.0640620\pi$
$758$		0			0
$759$	−5.64575	+	9.77873i	−0.204928	+	0.354945i
$760$		0			0
$761$	24.8229	+	42.9945i	0.899829	+	1.55855i	0.827712	+	0.561153i	$0.189642\pi$
$761$	24.8229	+	42.9945i	0.899829	+	1.55855i	0.0721161	+	0.997396i	$0.477025\pi$
$762$		0			0
$763$	−21.9574	+	12.6771i	−0.794912	+	0.458943i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	12.9360	+	7.46863i	0.467093	+	0.269676i
$768$		0			0
$769$	−4.00000			−0.144244			−0.0721218	−	0.997396i	$-0.522977\pi$
$769$	−4.00000			−0.144244			−0.0721218	+	0.997396i	$0.522977\pi$
$770$		0			0
$771$	12.3542			0.444927
$772$		0			0
$773$	4.69126	+	2.70850i	0.168733	+	0.0974179i	0.581988	−	0.813197i	$-0.302275\pi$
$773$	4.69126	+	2.70850i	0.168733	+	0.0974179i	−0.413255	+	0.910615i	$0.635608\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	18.9982	+	10.9686i	0.681557	+	0.393497i
$778$		0			0
$779$	0.822876	+	1.42526i	0.0294826	+	0.0510653i
$780$		0			0
$781$	9.29150	−	16.0934i	0.332476	−	0.575866i
$782$		0			0
$783$		−	7.29150i		−	0.260577i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−38.9519	−	22.4889i	−1.38849	−	0.801642i	−0.395340	−	0.918535i	$-0.629373\pi$
$787$	−38.9519	−	22.4889i	−1.38849	−	0.801642i	−0.993145	+	0.116892i	$0.962707\pi$
$788$		0			0
$789$	−12.0000	−	20.7846i	−0.427211	−	0.739952i
$790$		0			0
$791$	16.6458	−	28.8313i	0.591855	−	1.02512i
$792$		0			0
$793$	8.29913	−	4.79150i	0.294711	−	0.170151i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	27.8745i		−	0.987366i	−0.869642	−	0.493683i	$-0.835650\pi$
$797$		−	27.8745i		−	0.987366i	0.869642	−	0.493683i	$-0.164350\pi$
$798$		0			0
$799$	4.83399			0.171014
$800$		0			0
$801$	4.46863	−	7.73989i	0.157891	−	0.273476i
$802$		0			0
$803$	30.7614	−	17.7601i	1.08555	−	0.626741i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−5.39426	+	3.11438i	−0.189887	+	0.109631i
$808$		0			0
$809$	−22.6458	+	39.2236i	−0.796182	+	1.37903i	0.125904	+	0.992042i	$0.459817\pi$
$809$	−22.6458	+	39.2236i	−0.796182	+	1.37903i	−0.922086	+	0.386986i	$0.873516\pi$
$810$		0			0
$811$	7.93725			0.278715			0.139357	−	0.990242i	$-0.455496\pi$
$811$	7.93725			0.278715			0.139357	+	0.990242i	$0.455496\pi$
$812$		0			0
$813$			13.2915i			0.466153i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−29.3362	+	16.9373i	−1.02634	+	0.592560i
$818$		0			0
$819$	2.64575			0.0924500
$820$		0			0
$821$	−25.6974	−	44.5092i	−0.896845	−	1.55338i	−0.831505	−	0.555518i	$-0.812520\pi$
$821$	−25.6974	−	44.5092i	−0.896845	−	1.55338i	−0.0653402	−	0.997863i	$-0.520813\pi$
$822$		0			0
$823$	−17.7711	−	10.2601i	−0.619460	−	0.357646i	0.157198	−	0.987567i	$-0.449754\pi$
$823$	−17.7711	−	10.2601i	−0.619460	−	0.357646i	−0.776659	+	0.629921i	$0.783087\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			21.4170i			0.744742i	0.928084	+	0.372371i	$0.121455\pi$
$827$			21.4170i			0.744742i	−0.928084	+	0.372371i	$0.878545\pi$
$828$		0			0
$829$	22.6660	−	39.2587i	0.787223	−	1.36351i	−0.140439	−	0.990089i	$-0.544851\pi$
$829$	22.6660	−	39.2587i	0.787223	−	1.36351i	0.927662	−	0.373421i	$-0.121815\pi$
$830$		0			0
$831$	−12.5000	−	21.6506i	−0.433620	−	0.751052i
$832$		0			0
$833$		−	11.5203i		−	0.399153i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−3.46410	−	2.00000i	−0.119737	−	0.0691301i
$838$		0			0
$839$	23.1660			0.799780			0.399890	−	0.916563i	$-0.369048\pi$
$839$	23.1660			0.799780			0.399890	+	0.916563i	$0.369048\pi$
$840$		0			0
$841$	24.1660			0.833311
$842$		0			0
$843$	3.66221	+	2.11438i	0.126133	+	0.0728231i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			55.2288i			1.89768i
$848$		0			0
$849$	−15.2601	−	26.4313i	−0.523726	−	0.907121i
$850$		0			0
$851$	8.29150	−	14.3613i	0.284229	−	0.492299i
$852$		0			0
$853$		−	2.00000i		−	0.0684787i	−0.999414	−	0.0342393i	$-0.989099\pi$
$853$		−	2.00000i		−	0.0684787i	0.999414	−	0.0342393i	$-0.0109009\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−13.1342	−	7.58301i	−0.448654	−	0.259031i	0.258608	−	0.965982i	$-0.416736\pi$
$857$	−13.1342	−	7.58301i	−0.448654	−	0.259031i	−0.707262	+	0.706952i	$0.750070\pi$
$858$		0			0
$859$	0.583005	+	1.00979i	0.0198919	+	0.0344538i	0.875800	−	0.482674i	$-0.160334\pi$
$859$	0.583005	+	1.00979i	0.0198919	+	0.0344538i	−0.855908	+	0.517128i	$0.827001\pi$
$860$		0			0
$861$	0.468627	+	0.811686i	0.0159708	+	0.0276622i
$862$		0			0
$863$	45.1228	−	26.0516i	1.53600	−	0.886808i	0.536929	−	0.843627i	$-0.319584\pi$
$863$	45.1228	−	26.0516i	1.53600	−	0.886808i	0.999067	−	0.0431804i	$-0.0137490\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		−	14.2915i		−	0.485365i
$868$		0			0
$869$	−37.5203			−1.27279
$870$		0			0
$871$	3.96863	−	6.87386i	0.134472	−	0.232912i
$872$		0			0
$873$	12.3768	−	7.14575i	0.418891	−	0.241847i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−16.2371	+	9.37451i	−0.548289	+	0.316555i	−0.748431	−	0.663212i	$-0.769193\pi$
$877$	−16.2371	+	9.37451i	−0.548289	+	0.316555i	0.200143	+	0.979767i	$0.435859\pi$
$878$		0			0
$879$	−10.9373	+	18.9439i	−0.368904	+	0.638961i
$880$		0			0
$881$	55.2915			1.86282			0.931409	−	0.363974i	$-0.118580\pi$
$881$	55.2915			1.86282			0.931409	+	0.363974i	$0.118580\pi$
$882$		0			0
$883$			28.6458i			0.964006i	0.876169	+	0.482003i	$0.160091\pi$
$883$			28.6458i			0.964006i	−0.876169	+	0.482003i	$0.839909\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	26.5943	−	15.3542i	0.892951	−	0.515545i	0.0180441	−	0.999837i	$-0.494256\pi$
$887$	26.5943	−	15.3542i	0.892951	−	0.515545i	0.874906	+	0.484292i	$0.160923\pi$
$888$		0			0
$889$	8.79150	−	15.2273i	0.294858	−	0.510708i
$890$		0			0
$891$	2.82288	+	4.88936i	0.0945699	+	0.163800i
$892$		0			0
$893$	11.8176	+	6.82288i	0.395460	+	0.228319i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	2.00000i		−	0.0667781i
$898$		0			0
$899$	14.5830	−	25.2585i	0.486370	−	0.842418i
$900$		0			0
$901$	1.93725	+	3.35542i	0.0645393	+	0.111785i
$902$		0			0
$903$	−16.7069	+	9.64575i	−0.555972	+	0.320991i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−51.0762	−	29.4889i	−1.69596	−	0.979162i	−0.949519	−	0.313710i	$-0.898428\pi$
$907$	−51.0762	−	29.4889i	−1.69596	−	0.979162i	−0.746440	−	0.665453i	$-0.768239\pi$
$908$		0			0
$909$	10.9373			0.362766
$910$		0			0
$911$	−52.3320			−1.73384			−0.866919	−	0.498450i	$-0.833903\pi$
$911$	−52.3320			−1.73384			−0.866919	+	0.498450i	$0.833903\pi$
$912$		0			0
$913$	17.8254	+	10.2915i	0.589935	+	0.340599i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	54.4575i		−	1.79835i
$918$		0			0
$919$	−28.4575	−	49.2899i	−0.938727	−	1.62592i	−0.767850	−	0.640630i	$-0.778673\pi$
$919$	−28.4575	−	49.2899i	−0.938727	−	1.62592i	−0.170877	−	0.985292i	$-0.554660\pi$
$920$		0			0
$921$	14.9373	−	25.8721i	0.492199	−	0.852514i
$922$		0			0
$923$			3.29150i			0.108341i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	13.8021	+	7.96863i	0.453319	+	0.261724i
$928$		0			0
$929$	3.82288	+	6.62141i	0.125424	+	0.217242i	0.921899	−	0.387431i	$-0.126637\pi$
$929$	3.82288	+	6.62141i	0.125424	+	0.217242i	−0.796474	+	0.604672i	$0.793304\pi$
$930$		0			0
$931$	16.2601	−	28.1634i	0.532904	−	0.923017i
$932$		0			0
$933$	2.34563	−	1.35425i	0.0767924	−	0.0443361i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		1.00000			$0$
$937$		0			0		−1.00000			$\pi$
$938$		0			0
$939$	8.70850			0.284191
$940$		0			0
$941$	24.8745	−	43.0839i	0.810886	−	1.40450i	−0.101359	−	0.994850i	$-0.532319\pi$
$941$	24.8745	−	43.0839i	0.810886	−	1.40450i	0.912245	−	0.409645i	$-0.134348\pi$
$942$		0			0
$943$	0.613577	−	0.354249i	0.0199808	−	0.0115359i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−32.2954	+	18.6458i	−1.04946	+	0.605906i	−0.922498	−	0.386002i	$-0.873856\pi$
$947$	−32.2954	+	18.6458i	−1.04946	+	0.605906i	−0.126961	+	0.991908i	$0.540522\pi$
$948$		0			0
$949$	−3.14575	+	5.44860i	−0.102115	+	0.176869i
$950$		0			0
$951$	12.5830			0.408032
$952$		0			0
$953$			10.4797i			0.339472i	0.985490	+	0.169736i	$0.0542915\pi$
$953$			10.4797i			0.339472i	−0.985490	+	0.169736i	$0.945708\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−35.6508	+	20.5830i	−1.15243	+	0.665354i
$958$		0			0
$959$	12.2915	+	21.2895i	0.396913	+	0.687474i
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$		0			0
$963$	−8.85836	−	5.11438i	−0.285457	−	0.164809i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		−	14.0627i		−	0.452227i	−0.974101	−	0.226114i	$-0.927398\pi$
$967$		−	14.0627i		−	0.452227i	0.974101	−	0.226114i	$-0.0726021\pi$
$968$		0			0
$969$	−3.82288	+	6.62141i	−0.122808	+	0.212710i
$970$		0			0
$971$	−29.2804	−	50.7151i	−0.939652	−	1.62753i	−0.766120	−	0.642698i	$-0.777815\pi$
$971$	−29.2804	−	50.7151i	−0.939652	−	1.62753i	−0.173532	−	0.984828i	$-0.555518\pi$
$972$		0			0
$973$	0.143769	+	0.0830052i	0.00460903	+	0.00266103i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−47.3597	−	27.3431i	−1.51517	−	0.874784i	−0.999842	−	0.0177921i	$-0.994336\pi$
$977$	−47.3597	−	27.3431i	−1.51517	−	0.874784i	−0.515329	−	0.856992i	$-0.672330\pi$
$978$		0			0
$979$	−50.4575			−1.61263
$980$		0			0
$981$	9.58301			0.305962
$982$		0			0
$983$	0.306788	+	0.177124i	0.00978503	+	0.00564939i	0.504885	−	0.863187i	$-0.331535\pi$
$983$	0.306788	+	0.177124i	0.00978503	+	0.00564939i	−0.495100	+	0.868836i	$0.664868\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	6.73009	+	3.88562i	0.214221	+	0.123681i
$988$		0			0
$989$	7.29150	+	12.6293i	0.231856	+	0.401587i
$990$		0			0
$991$	−3.93725	+	6.81952i	−0.125071	+	0.216629i	−0.921761	−	0.387759i	$-0.873249\pi$
$991$	−3.93725	+	6.81952i	−0.125071	+	0.216629i	0.796690	+	0.604389i	$0.206583\pi$
$992$		0			0
$993$			8.64575i			0.274365i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−12.7730	−	7.37451i	−0.404526	−	0.233553i	0.283909	−	0.958851i	$-0.408369\pi$
$997$	−12.7730	−	7.37451i	−0.404526	−	0.233553i	−0.688435	+	0.725298i	$0.741702\pi$
$998$		0			0
$999$	−4.14575	−	7.18065i	−0.131166	−	0.227186i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.bc.h.949.3		8
5.2	odd	4		2100.2.q.i.1201.2	yes	4
5.3	odd	4		2100.2.q.g.1201.1	✓	4
5.4	even	2	inner	2100.2.bc.h.949.2		8
7.2	even	3	inner	2100.2.bc.h.1549.2		8
35.2	odd	12		2100.2.q.i.1801.2	yes	4
35.9	even	6	inner	2100.2.bc.h.1549.3		8
35.23	odd	12		2100.2.q.g.1801.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.q.g.1201.1	✓	4	5.3	odd	4
2100.2.q.g.1801.1	yes	4	35.23	odd	12
2100.2.q.i.1201.2	yes	4	5.2	odd	4
2100.2.q.i.1801.2	yes	4	35.2	odd	12
2100.2.bc.h.949.2		8	5.4	even	2	inner
2100.2.bc.h.949.3		8	1.1	even	1	trivial
2100.2.bc.h.1549.2		8	7.2	even	3	inner
2100.2.bc.h.1549.3		8	35.9	even	6	inner

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.bc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{3} +(-2.29129 - 1.32288i) q^{7} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{3} +(-2.29129 - 1.32288i) q^{7} +(0.500000 + 0.866025i) q^{9} +(2.82288 - 4.88936i) q^{11} +1.00000i q^{13} +(-1.42526 - 0.822876i) q^{17} +(-2.32288 - 4.02334i) q^{19} +(-1.32288 - 2.29129i) q^{21} +(-1.73205 + 1.00000i) q^{23} +1.00000i q^{27} -7.29150 q^{29} +(-2.00000 + 3.46410i) q^{31} +(4.88936 - 2.82288i) q^{33} +(-7.18065 + 4.14575i) q^{37} +(-0.500000 + 0.866025i) q^{39} -0.354249 q^{41} -7.29150i q^{43} +(-2.54374 + 1.46863i) q^{47} +(3.50000 + 6.06218i) q^{49} +(-0.822876 - 1.42526i) q^{51} +(-2.03884 - 1.17712i) q^{53} -4.64575i q^{57} +(7.46863 - 12.9360i) q^{59} +(-4.79150 - 8.29913i) q^{61} -2.64575i q^{63} +(-6.87386 - 3.96863i) q^{67} -2.00000 q^{69} +3.29150 q^{71} +(5.44860 + 3.14575i) q^{73} +(-12.9360 + 7.46863i) q^{77} +(-3.32288 - 5.75539i) q^{79} +(-0.500000 + 0.866025i) q^{81} +3.64575i q^{83} +(-6.31463 - 3.64575i) q^{87} +(-4.46863 - 7.73989i) q^{89} +(1.32288 - 2.29129i) q^{91} +(-3.46410 + 2.00000i) q^{93} -14.2915i q^{97} +5.64575 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^9	\( 8 q + 4 q^{9} + 12 q^{11} - 8 q^{19} - 16 q^{29} - 16 q^{31} - 4 q^{39} - 24 q^{41} + 28 q^{49} + 4 q^{51} + 28 q^{59} + 4 q^{61} - 16 q^{69} - 16 q^{71} - 16 q^{79} - 4 q^{81} - 4 q^{89} + 24 q^{99}+O(q^{100}) \) 8 * q + 4 * q^9 + 12 * q^11 - 8 * q^19 - 16 * q^29 - 16 * q^31 - 4 * q^39 - 24 * q^41 + 28 * q^49 + 4 * q^51 + 28 * q^59 + 4 * q^61 - 16 * q^69 - 16 * q^71 - 16 * q^79 - 4 * q^81 - 4 * q^89 + 24 * q^99

Introduction

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