LMFDB - Embedded newform 2100.2.q.g.1801.1

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			1801.1
Root			$1.32288 + 2.29129i$ of defining polynomial
Character	$\chi$	$=$	2100.1801
Dual form			2100.2.q.g.1201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{3} +(-1.32288 - 2.29129i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	$q+(-0.500000 - 0.866025i) q^{3} +(-1.32288 - 2.29129i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(2.82288 + 4.88936i) q^{11} -1.00000 q^{13} +(-0.822876 - 1.42526i) q^{17} +(2.32288 - 4.02334i) q^{19} +(-1.32288 + 2.29129i) q^{21} +(-1.00000 + 1.73205i) q^{23} +1.00000 q^{27} +7.29150 q^{29} +(-2.00000 - 3.46410i) q^{31} +(2.82288 - 4.88936i) q^{33} +(4.14575 - 7.18065i) q^{37} +(0.500000 + 0.866025i) q^{39} -0.354249 q^{41} +7.29150 q^{43} +(1.46863 - 2.54374i) q^{47} +(-3.50000 + 6.06218i) q^{49} +(-0.822876 + 1.42526i) q^{51} +(1.17712 + 2.03884i) q^{53} -4.64575 q^{57} +(-7.46863 - 12.9360i) q^{59} +(-4.79150 + 8.29913i) q^{61} +2.64575 q^{63} +(-3.96863 - 6.87386i) q^{67} +2.00000 q^{69} +3.29150 q^{71} +(-3.14575 - 5.44860i) q^{73} +(7.46863 - 12.9360i) q^{77} +(3.32288 - 5.75539i) q^{79} +(-0.500000 - 0.866025i) q^{81} -3.64575 q^{83} +(-3.64575 - 6.31463i) q^{87} +(4.46863 - 7.73989i) q^{89} +(1.32288 + 2.29129i) q^{91} +(-2.00000 + 3.46410i) q^{93} -14.2915 q^{97} -5.64575 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times$.

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

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
$11$	2.82288	+	4.88936i	0.851129	+	1.47420i	0.880190	+	0.474621i	$0.157415\pi$
$11$	2.82288	+	4.88936i	0.851129	+	1.47420i	−0.0290612	+	0.999578i	$0.509252\pi$
$12$		0			0
$13$	−1.00000			−0.277350			−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000			−0.277350			−0.138675	+	0.990338i	$0.544284\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.822876	−	1.42526i	−0.199577	−	0.345677i	0.748815	−	0.662780i	$-0.230623\pi$
$17$	−0.822876	−	1.42526i	−0.199577	−	0.345677i	−0.948391	+	0.317103i	$0.897290\pi$
$18$		0			0
$19$	2.32288	−	4.02334i	0.532904	−	0.923017i	−0.466357	−	0.884596i	$-0.654434\pi$
$19$	2.32288	−	4.02334i	0.532904	−	0.923017i	0.999262	−	0.0384208i	$-0.0122327\pi$
$20$		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	$-0.900196\pi$
$23$	−1.00000	+	1.73205i	−0.208514	+	0.361158i	0.742732	+	0.669588i	$0.233529\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	7.29150			1.35400			0.676999	−	0.735984i	$-0.263280\pi$
$29$	7.29150			1.35400			0.676999	+	0.735984i	$0.263280\pi$
$30$		0			0
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$		0			0
$33$	2.82288	−	4.88936i	0.491400	−	0.851129i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	4.14575	−	7.18065i	0.681557	−	1.18049i	−0.292948	−	0.956128i	$-0.594636\pi$
$37$	4.14575	−	7.18065i	0.681557	−	1.18049i	0.974506	−	0.224364i	$-0.0720303\pi$
$38$		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
$43$	7.29150			1.11194			0.555972	−	0.831201i	$-0.312346\pi$
$43$	7.29150			1.11194			0.555972	+	0.831201i	$0.312346\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.46863	−	2.54374i	0.214221	−	0.371042i	−0.738810	−	0.673914i	$-0.764612\pi$
$47$	1.46863	−	2.54374i	0.214221	−	0.371042i	0.953031	+	0.302872i	$0.0979453\pi$
$48$		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
$53$	1.17712	+	2.03884i	0.161690	+	0.280056i	0.935475	−	0.353393i	$-0.114972\pi$
$53$	1.17712	+	2.03884i	0.161690	+	0.280056i	−0.773785	+	0.633449i	$0.781639\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−4.64575			−0.615345
$58$		0			0
$59$	−7.46863	−	12.9360i	−0.972332	−	1.68413i	−0.688471	−	0.725264i	$-0.741718\pi$
$59$	−7.46863	−	12.9360i	−0.972332	−	1.68413i	−0.283861	−	0.958865i	$-0.591616\pi$
$60$		0			0
$61$	−4.79150	+	8.29913i	−0.613489	+	1.06259i	0.377159	+	0.926149i	$0.376901\pi$
$61$	−4.79150	+	8.29913i	−0.613489	+	1.06259i	−0.990648	+	0.136445i	$0.956432\pi$
$62$		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	0.515003	−	0.857188i	$-0.327791\pi$
$67$	−3.96863	−	6.87386i	−0.484845	−	0.839776i	−0.999848	+	0.0174120i	$0.994457\pi$
$68$		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
$73$	−3.14575	−	5.44860i	−0.368182	−	0.637711i	0.621099	−	0.783732i	$-0.286686\pi$
$73$	−3.14575	−	5.44860i	−0.368182	−	0.637711i	−0.989281	+	0.146022i	$0.953353\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	7.46863	−	12.9360i	0.851129	−	1.47420i
$78$		0			0
$79$	3.32288	−	5.75539i	0.373853	−	0.647532i	−0.616302	−	0.787510i	$-0.711370\pi$
$79$	3.32288	−	5.75539i	0.373853	−	0.647532i	0.990155	+	0.139978i	$0.0447032\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−3.64575			−0.400173			−0.200087	−	0.979778i	$-0.564122\pi$
$83$	−3.64575			−0.400173			−0.200087	+	0.979778i	$0.564122\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−3.64575	−	6.31463i	−0.390866	−	0.676999i
$88$		0			0
$89$	4.46863	−	7.73989i	0.473674	−	0.820427i	−0.525872	−	0.850564i	$-0.676261\pi$
$89$	4.46863	−	7.73989i	0.473674	−	0.820427i	0.999546	+	0.0301370i	$0.00959435\pi$
$90$		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
$97$	−14.2915			−1.45108			−0.725541	−	0.688179i	$-0.758410\pi$
$97$	−14.2915			−1.45108			−0.725541	+	0.688179i	$0.758410\pi$
$98$		0			0
$99$	−5.64575			−0.567419
$100$		0			0
$101$	5.46863	+	9.47194i	0.544149	+	0.942493i	0.998660	+	0.0517522i	$0.0164806\pi$
$101$	5.46863	+	9.47194i	0.544149	+	0.942493i	−0.454511	+	0.890741i	$0.650186\pi$
$102$		0			0
$103$	7.96863	−	13.8021i	0.785172	−	1.35996i	−0.143724	−	0.989618i	$-0.545908\pi$
$103$	7.96863	−	13.8021i	0.785172	−	1.35996i	0.928896	−	0.370340i	$-0.120759\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.11438	−	8.85836i	0.494426	−	0.856370i	−0.505554	−	0.862795i	$-0.668712\pi$
$107$	5.11438	−	8.85836i	0.494426	−	0.856370i	0.999979	+	0.00642483i	$0.00204510\pi$
$108$		0			0
$109$	−4.79150	−	8.29913i	−0.458943	−	0.794912i	0.539963	−	0.841689i	$-0.318438\pi$
$109$	−4.79150	−	8.29913i	−0.458943	−	0.794912i	−0.998905	+	0.0467769i	$0.985105\pi$
$110$		0			0
$111$	−8.29150			−0.786995
$112$		0			0
$113$	−12.5830			−1.18371			−0.591855	−	0.806045i	$-0.701604\pi$
$113$	−12.5830			−1.18371			−0.591855	+	0.806045i	$0.701604\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.500000	−	0.866025i	0.0462250	−	0.0800641i
$118$		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
$123$	0.177124	+	0.306788i	0.0159708	+	0.0276622i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	6.64575			0.589715			0.294858	−	0.955541i	$-0.404728\pi$
$127$	6.64575			0.589715			0.294858	+	0.955541i	$0.404728\pi$
$128$		0			0
$129$	−3.64575	−	6.31463i	−0.320991	−	0.555972i
$130$		0			0
$131$	10.2915	−	17.8254i	0.899173	−	1.55741i	0.0706190	−	0.997503i	$-0.477503\pi$
$131$	10.2915	−	17.8254i	0.899173	−	1.55741i	0.828554	−	0.559910i	$-0.189164\pi$
$132$		0			0
$133$	−12.2915			−1.06581
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.64575	−	8.04668i	−0.396913	−	0.687474i	0.596430	−	0.802665i	$-0.296585\pi$
$137$	−4.64575	−	8.04668i	−0.396913	−	0.687474i	−0.993343	+	0.115191i	$0.963252\pi$
$138$		0			0
$139$	0.0627461			0.00532205			0.00266103	−	0.999996i	$-0.499153\pi$
$139$	0.0627461			0.00532205			0.00266103	+	0.999996i	$0.499153\pi$
$140$		0			0
$141$	−2.93725			−0.247361
$142$		0			0
$143$	−2.82288	−	4.88936i	−0.236061	−	0.408869i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	7.00000			0.577350
$148$		0			0
$149$	5.46863	−	9.47194i	0.448007	−	0.775972i	−0.550249	−	0.835001i	$-0.685467\pi$
$149$	5.46863	−	9.47194i	0.448007	−	0.775972i	0.998256	+	0.0590292i	$0.0188005\pi$
$150$		0			0
$151$	8.32288	+	14.4156i	0.677306	+	1.17313i	0.975789	+	0.218714i	$0.0701860\pi$
$151$	8.32288	+	14.4156i	0.677306	+	1.17313i	−0.298483	+	0.954415i	$0.596481\pi$
$152$		0			0
$153$	1.64575			0.133051
$154$		0			0
$155$		0			0
$156$		0			0
$157$	8.50000	+	14.7224i	0.678374	+	1.17498i	0.975470	+	0.220131i	$0.0706483\pi$
$157$	8.50000	+	14.7224i	0.678374	+	1.17498i	−0.297097	+	0.954847i	$0.596018\pi$
$158$		0			0
$159$	1.17712	−	2.03884i	0.0933520	−	0.161690i
$160$		0			0
$161$	5.29150			0.417029
$162$		0			0
$163$	4.61438	−	7.99234i	0.361426	−	0.626008i	−0.626770	−	0.779204i	$-0.715623\pi$
$163$	4.61438	−	7.99234i	0.361426	−	0.626008i	0.988196	+	0.153196i	$0.0489567\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	17.5203			1.35576			0.677879	−	0.735173i	$-0.262899\pi$
$167$	17.5203			1.35576			0.677879	+	0.735173i	$0.262899\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$		0			0
$171$	2.32288	+	4.02334i	0.177635	+	0.307672i
$172$		0			0
$173$	−0.291503	+	0.504897i	−0.0221625	+	0.0383866i	−0.876894	−	0.480684i	$-0.840388\pi$
$173$	−0.291503	+	0.504897i	−0.0221625	+	0.0383866i	0.854731	+	0.519071i	$0.173722\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−7.46863	+	12.9360i	−0.561376	+	0.972332i
$178$		0			0
$179$	6.35425	+	11.0059i	0.474939	+	0.822618i	0.999588	−	0.0287003i	$-0.00913684\pi$
$179$	6.35425	+	11.0059i	0.474939	+	0.822618i	−0.524649	+	0.851319i	$0.675804\pi$
$180$		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
$183$	9.58301			0.708396
$184$		0			0
$185$		0			0
$186$		0			0
$187$	4.64575	−	8.04668i	0.339731	−	0.588431i
$188$		0			0
$189$	−1.32288	−	2.29129i	−0.0962250	−	0.166667i
$190$		0			0
$191$	11.7601	−	20.3691i	0.850933	−	1.47386i	−0.0294341	−	0.999567i	$-0.509371\pi$
$191$	11.7601	−	20.3691i	0.850933	−	1.47386i	0.880367	−	0.474293i	$-0.157296\pi$
$192$		0			0
$193$	8.00000	+	13.8564i	0.575853	+	0.997406i	0.995948	+	0.0899262i	$0.0286631\pi$
$193$	8.00000	+	13.8564i	0.575853	+	0.997406i	−0.420096	+	0.907480i	$0.638004\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	19.2915			1.37446			0.687231	−	0.726439i	$-0.258826\pi$
$197$	19.2915			1.37446			0.687231	+	0.726439i	$0.258826\pi$
$198$		0			0
$199$	2.32288	+	4.02334i	0.164664	+	0.285207i	0.936536	−	0.350571i	$-0.114013\pi$
$199$	2.32288	+	4.02334i	0.164664	+	0.285207i	−0.771872	+	0.635778i	$0.780679\pi$
$200$		0			0
$201$	−3.96863	+	6.87386i	−0.279925	+	0.484845i
$202$		0			0
$203$	−9.64575	−	16.7069i	−0.676999	−	1.17260i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−1.00000	−	1.73205i	−0.0695048	−	0.120386i
$208$		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
$213$	−1.64575	−	2.85052i	−0.112765	−	0.195315i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−5.29150	+	9.16515i	−0.359211	+	0.622171i
$218$		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
$223$	1.93725			0.129728			0.0648641	−	0.997894i	$-0.479339\pi$
$223$	1.93725			0.129728			0.0648641	+	0.997894i	$0.479339\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−9.64575	−	16.7069i	−0.640211	−	1.10888i	−0.985385	−	0.170339i	$-0.945514\pi$
$227$	−9.64575	−	16.7069i	−0.640211	−	1.10888i	0.345174	−	0.938539i	$-0.387820\pi$
$228$		0			0
$229$	4.85425	−	8.40781i	0.320778	−	0.555603i	−0.659871	−	0.751379i	$-0.729389\pi$
$229$	4.85425	−	8.40781i	0.320778	−	0.555603i	0.980649	+	0.195776i	$0.0627224\pi$
$230$		0			0
$231$	−14.9373			−0.982799
$232$		0			0
$233$	−1.11438	+	1.93016i	−0.0730053	+	0.126449i	−0.900217	−	0.435441i	$-0.856592\pi$
$233$	−1.11438	+	1.93016i	−0.0730053	+	0.126449i	0.827212	+	0.561890i	$0.189926\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−6.64575			−0.431688
$238$		0			0
$239$	−30.5830			−1.97825			−0.989125	−	0.147077i	$-0.953014\pi$
$239$	−30.5830			−1.97825			−0.989125	+	0.147077i	$0.953014\pi$
$240$		0			0
$241$	−5.14575	−	8.91270i	−0.331467	−	0.574118i	0.651333	−	0.758792i	$-0.274210\pi$
$241$	−5.14575	−	8.91270i	−0.331467	−	0.574118i	−0.982800	+	0.184675i	$0.940877\pi$
$242$		0			0
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−2.32288	+	4.02334i	−0.147801	+	0.255999i
$248$		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
$253$	−11.2915			−0.709891
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.17712	+	10.6991i	−0.385318	+	0.667391i	−0.991813	−	0.127696i	$-0.959242\pi$
$257$	−6.17712	+	10.6991i	−0.385318	+	0.667391i	0.606495	+	0.795087i	$0.292575\pi$
$258$		0			0
$259$	−21.9373			−1.36311
$260$		0			0
$261$	−3.64575	+	6.31463i	−0.225666	+	0.390866i
$262$		0			0
$263$	12.0000	+	20.7846i	0.739952	+	1.28163i	0.952517	+	0.304487i	$0.0984850\pi$
$263$	12.0000	+	20.7846i	0.739952	+	1.28163i	−0.212565	+	0.977147i	$0.568182\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−8.93725			−0.546951
$268$		0			0
$269$	3.11438	+	5.39426i	0.189887	+	0.328894i	0.945212	−	0.326456i	$-0.105855\pi$
$269$	3.11438	+	5.39426i	0.189887	+	0.328894i	−0.755325	+	0.655350i	$0.772521\pi$
$270$		0			0
$271$	6.64575	−	11.5108i	0.403701	−	0.699230i	−0.590469	−	0.807061i	$-0.701057\pi$
$271$	6.64575	−	11.5108i	0.403701	−	0.699230i	0.994169	+	0.107831i	$0.0343904\pi$
$272$		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	−0.947313	−	0.320309i	$-0.896213\pi$
$277$	−12.5000	−	21.6506i	−0.751052	−	1.30086i	0.196261	−	0.980552i	$-0.437120\pi$
$278$		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
$283$	15.2601	+	26.4313i	0.907121	+	1.57118i	0.818045	+	0.575154i	$0.195058\pi$
$283$	15.2601	+	26.4313i	0.907121	+	1.57118i	0.0890754	+	0.996025i	$0.471609\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.468627	+	0.811686i	0.0276622	+	0.0479123i
$288$		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
$293$	−21.8745			−1.27792			−0.638961	−	0.769239i	$-0.720636\pi$
$293$	−21.8745			−1.27792			−0.638961	+	0.769239i	$0.720636\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	2.82288	+	4.88936i	0.163800	+	0.283710i
$298$		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
$303$	5.46863	−	9.47194i	0.314164	−	0.544149i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−29.8745			−1.70503			−0.852514	−	0.522704i	$-0.824923\pi$
$307$	−29.8745			−1.70503			−0.852514	+	0.522704i	$0.824923\pi$
$308$		0			0
$309$	−15.9373			−0.906639
$310$		0			0
$311$	1.35425	+	2.34563i	0.0767924	+	0.133008i	0.901864	−	0.432019i	$-0.142199\pi$
$311$	1.35425	+	2.34563i	0.0767924	+	0.133008i	−0.825072	+	0.565028i	$0.808865\pi$
$312$		0			0
$313$	4.35425	−	7.54178i	0.246117	−	0.426287i	−0.716328	−	0.697763i	$-0.754179\pi$
$313$	4.35425	−	7.54178i	0.246117	−	0.426287i	0.962445	+	0.271477i	$0.0875120\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−6.29150	+	10.8972i	−0.353366	+	0.612048i	−0.986837	−	0.161719i	$-0.948296\pi$
$317$	−6.29150	+	10.8972i	−0.353366	+	0.612048i	0.633471	+	0.773767i	$0.281630\pi$
$318$		0			0
$319$	20.5830	+	35.6508i	1.15243	+	1.99606i
$320$		0			0
$321$	−10.2288			−0.570914
$322$		0			0
$323$	−7.64575			−0.425421
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−4.79150	+	8.29913i	−0.264971	+	0.458943i
$328$		0			0
$329$	−7.77124			−0.428443
$330$		0			0
$331$	4.32288	−	7.48744i	0.237607	−	0.411547i	−0.722420	−	0.691454i	$-0.756970\pi$
$331$	4.32288	−	7.48744i	0.237607	−	0.411547i	0.960027	+	0.279907i	$0.0903037\pi$
$332$		0			0
$333$	4.14575	+	7.18065i	0.227186	+	0.393497i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	8.70850			0.474382			0.237191	−	0.971463i	$-0.423773\pi$
$337$	8.70850			0.474382			0.237191	+	0.971463i	$0.423773\pi$
$338$		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
$343$	18.5203			1.00000
$344$		0			0
$345$		0			0
$346$		0			0
$347$	12.7601	+	22.1012i	0.685000	+	1.18645i	0.973437	+	0.228955i	$0.0735310\pi$
$347$	12.7601	+	22.1012i	0.685000	+	1.18645i	−0.288437	+	0.957499i	$0.593136\pi$
$348$		0			0
$349$	15.2915			0.818535			0.409268	−	0.912414i	$-0.365784\pi$
$349$	15.2915			0.818535			0.409268	+	0.912414i	$0.365784\pi$
$350$		0			0
$351$	−1.00000			−0.0533761
$352$		0			0
$353$	−0.531373	−	0.920365i	−0.0282821	−	0.0489861i	0.851538	−	0.524293i	$-0.175670\pi$
$353$	−0.531373	−	0.920365i	−0.0282821	−	0.0489861i	−0.879820	+	0.475307i	$0.842337\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	4.35425			0.230451
$358$		0			0
$359$	4.53137	−	7.84857i	0.239157	−	0.414232i	−0.721316	−	0.692606i	$-0.756462\pi$
$359$	4.53137	−	7.84857i	0.239157	−	0.414232i	0.960473	+	0.278375i	$0.0897957\pi$
$360$		0			0
$361$	−1.29150	−	2.23695i	−0.0679738	−	0.117734i
$362$		0			0
$363$	20.8745			1.09563
$364$		0			0
$365$		0			0
$366$		0			0
$367$	9.93725	+	17.2118i	0.518720	+	0.898450i	0.999763	+	0.0217531i	$0.00692478\pi$
$367$	9.93725	+	17.2118i	0.518720	+	0.898450i	−0.481043	+	0.876697i	$0.659742\pi$
$368$		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
$373$	1.20850	−	2.09318i	0.0625736	−	0.108381i	−0.833041	−	0.553211i	$-0.813403\pi$
$373$	1.20850	−	2.09318i	0.0625736	−	0.108381i	0.895615	+	0.444830i	$0.146736\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−7.29150			−0.375531
$378$		0			0
$379$	−20.6458			−1.06050			−0.530251	−	0.847841i	$-0.677902\pi$
$379$	−20.6458			−1.06050			−0.530251	+	0.847841i	$0.677902\pi$
$380$		0			0
$381$	−3.32288	−	5.75539i	−0.170236	−	0.294858i
$382$		0			0
$383$	−0.645751	+	1.11847i	−0.0329964	+	0.0571514i	−0.882052	−	0.471152i	$-0.843838\pi$
$383$	−0.645751	+	1.11847i	−0.0329964	+	0.0571514i	0.849056	+	0.528303i	$0.177172\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−3.64575	+	6.31463i	−0.185324	+	0.320991i
$388$		0			0
$389$	18.7601	+	32.4935i	0.951176	+	1.64749i	0.742885	+	0.669419i	$0.233457\pi$
$389$	18.7601	+	32.4935i	0.951176	+	1.64749i	0.208291	+	0.978067i	$0.433210\pi$
$390$		0			0
$391$	3.29150			0.166458
$392$		0			0
$393$	−20.5830			−1.03828
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−16.2288	+	28.1090i	−0.814498	+	1.41075i	0.0951899	+	0.995459i	$0.469654\pi$
$397$	−16.2288	+	28.1090i	−0.814498	+	1.41075i	−0.909688	+	0.415293i	$0.863679\pi$
$398$		0			0
$399$	6.14575	+	10.6448i	0.307672	+	0.532904i
$400$		0			0
$401$	0.760130	−	1.31658i	0.0379591	−	0.0657470i	−0.846422	−	0.532513i	$-0.821248\pi$
$401$	0.760130	−	1.31658i	0.0379591	−	0.0657470i	0.884381	+	0.466766i	$0.154581\pi$
$402$		0			0
$403$	2.00000	+	3.46410i	0.0996271	+	0.172559i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	46.8118			2.32037
$408$		0			0
$409$	6.79150	+	11.7632i	0.335818	+	0.581654i	0.983642	−	0.180136i	$-0.0576539\pi$
$409$	6.79150	+	11.7632i	0.335818	+	0.581654i	−0.647823	+	0.761790i	$0.724321\pi$
$410$		0			0
$411$	−4.64575	+	8.04668i	−0.229158	+	0.396913i
$412$		0			0
$413$	−19.7601	+	34.2255i	−0.972332	+	1.68413i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.0313730	−	0.0543397i	−0.00153634	−	0.00266103i
$418$		0			0
$419$	26.3542			1.28749			0.643745	−	0.765240i	$-0.277380\pi$
$419$	26.3542			1.28749			0.643745	+	0.765240i	$0.277380\pi$
$420$		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
$423$	1.46863	+	2.54374i	0.0714071	+	0.123681i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	25.3542			1.22698
$428$		0			0
$429$	−2.82288	+	4.88936i	−0.136290	+	0.236061i
$430$		0			0
$431$	−1.93725	−	3.35542i	−0.0933142	−	0.161625i	0.815590	−	0.578631i	$-0.196413\pi$
$431$	−1.93725	−	3.35542i	−0.0933142	−	0.161625i	−0.908904	+	0.417006i	$0.863079\pi$
$432$		0			0
$433$	−7.29150			−0.350407			−0.175204	−	0.984532i	$-0.556058\pi$
$433$	−7.29150			−0.350407			−0.175204	+	0.984532i	$0.556058\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	4.64575	+	8.04668i	0.222236	+	0.384925i
$438$		0			0
$439$	−3.90588	+	6.76518i	−0.186418	+	0.322885i	−0.944053	−	0.329793i	$-0.893021\pi$
$439$	−3.90588	+	6.76518i	−0.186418	+	0.322885i	0.757636	+	0.652678i	$0.226354\pi$
$440$		0			0
$441$	−3.50000	−	6.06218i	−0.166667	−	0.288675i
$442$		0			0
$443$	−8.64575	+	14.9749i	−0.410772	+	0.711478i	−0.994974	−	0.100130i	$-0.968074\pi$
$443$	−8.64575	+	14.9749i	−0.410772	+	0.711478i	0.584202	+	0.811608i	$0.301407\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−10.9373			−0.517314
$448$		0			0
$449$	26.1033			1.23189			0.615945	−	0.787789i	$-0.288775\pi$
$449$	26.1033			1.23189			0.615945	+	0.787789i	$0.288775\pi$
$450$		0			0
$451$	−1.00000	−	1.73205i	−0.0470882	−	0.0815591i
$452$		0			0
$453$	8.32288	−	14.4156i	0.391043	−	0.677306i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−17.0830	+	29.5886i	−0.799109	+	1.38410i	0.121088	+	0.992642i	$0.461362\pi$
$457$	−17.0830	+	29.5886i	−0.799109	+	1.38410i	−0.920197	+	0.391456i	$0.871972\pi$
$458$		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
$463$	−18.0627			−0.839447			−0.419723	−	0.907652i	$-0.637873\pi$
$463$	−18.0627			−0.839447			−0.419723	+	0.907652i	$0.637873\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−16.6458	+	28.8313i	−0.770274	+	1.33415i	0.167139	+	0.985933i	$0.446547\pi$
$467$	−16.6458	+	28.8313i	−0.770274	+	1.33415i	−0.937413	+	0.348220i	$0.886786\pi$
$468$		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
$473$	20.5830	+	35.6508i	0.946408	+	1.63923i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−2.35425			−0.107794
$478$		0			0
$479$	−10.1771	−	17.6273i	−0.465005	−	0.805412i	0.534197	−	0.845360i	$-0.320614\pi$
$479$	−10.1771	−	17.6273i	−0.465005	−	0.805412i	−0.999202	+	0.0399482i	$0.987281\pi$
$480$		0			0
$481$	−4.14575	+	7.18065i	−0.189030	+	0.327410i
$482$		0			0
$483$	−2.64575	−	4.58258i	−0.120386	−	0.208514i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	6.22876	+	10.7885i	0.282252	+	0.488875i	0.971939	−	0.235233i	$-0.0755853\pi$
$487$	6.22876	+	10.7885i	0.282252	+	0.488875i	−0.689687	+	0.724107i	$0.742252\pi$
$488$		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
$493$	−6.00000	−	10.3923i	−0.270226	−	0.468046i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.35425	−	7.54178i	−0.195315	−	0.338295i
$498$		0			0
$499$	−13.9059	+	24.0857i	−0.622513	+	1.07822i	0.366504	+	0.930417i	$0.380555\pi$
$499$	−13.9059	+	24.0857i	−0.622513	+	1.07822i	−0.989016	+	0.147807i	$0.952779\pi$
$500$		0			0
$501$	−8.76013	−	15.1730i	−0.391374	−	0.677879i
$502$		0			0
$503$	27.2915			1.21687			0.608434	−	0.793604i	$-0.291798\pi$
$503$	27.2915			1.21687			0.608434	+	0.793604i	$0.291798\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	6.00000	+	10.3923i	0.266469	+	0.461538i
$508$		0			0
$509$	−2.93725	+	5.08747i	−0.130191	+	0.225498i	−0.923750	−	0.382995i	$-0.874893\pi$
$509$	−2.93725	+	5.08747i	−0.130191	+	0.225498i	0.793559	+	0.608494i	$0.208226\pi$
$510$		0			0
$511$	−8.32288	+	14.4156i	−0.368182	+	0.637711i
$512$		0			0
$513$	2.32288	−	4.02334i	0.102557	−	0.177635i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	16.5830			0.729320
$518$		0			0
$519$	0.583005			0.0255911
$520$		0			0
$521$	−7.93725	−	13.7477i	−0.347737	−	0.602299i	0.638110	−	0.769945i	$-0.279717\pi$
$521$	−7.93725	−	13.7477i	−0.347737	−	0.602299i	−0.985847	+	0.167647i	$0.946383\pi$
$522$		0			0
$523$	20.9373	−	36.2644i	0.915522	−	1.58573i	0.109387	−	0.993999i	$-0.465111\pi$
$523$	20.9373	−	36.2644i	0.915522	−	1.58573i	0.806135	−	0.591732i	$-0.201556\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.29150	+	5.70105i	−0.143380	+	0.248342i
$528$		0			0
$529$	9.50000	+	16.4545i	0.413043	+	0.715412i
$530$		0			0
$531$	14.9373			0.648222
$532$		0			0
$533$	0.354249			0.0153442
$534$		0			0
$535$		0			0
$536$		0			0
$537$	6.35425	−	11.0059i	0.274206	−	0.474939i
$538$		0			0
$539$	−39.5203			−1.70226
$540$		0			0
$541$	2.43725	−	4.22145i	0.104786	−	0.181494i	−0.808865	−	0.587995i	$-0.799918\pi$
$541$	2.43725	−	4.22145i	0.104786	−	0.181494i	0.913651	+	0.406500i	$0.133251\pi$
$542$		0			0
$543$	3.29150	+	5.70105i	0.141252	+	0.244655i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−31.8745			−1.36286			−0.681428	−	0.731885i	$-0.738641\pi$
$547$	−31.8745			−1.36286			−0.681428	+	0.731885i	$0.738641\pi$
$548$		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
$553$	−17.5830			−0.747705
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−13.6458	−	23.6351i	−0.578189	−	1.00145i	−0.995687	−	0.0927750i	$-0.970426\pi$
$557$	−13.6458	−	23.6351i	−0.578189	−	1.00145i	0.417498	−	0.908678i	$-0.362907\pi$
$558$		0			0
$559$	−7.29150			−0.308398
$560$		0			0
$561$	−9.29150			−0.392288
$562$		0			0
$563$	−15.7601	−	27.2973i	−0.664210	−	1.15045i	−0.979499	−	0.201450i	$-0.935435\pi$
$563$	−15.7601	−	27.2973i	−0.664210	−	1.15045i	0.315289	−	0.948996i	$-0.397899\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−1.32288	+	2.29129i	−0.0555556	+	0.0962250i
$568$		0			0
$569$	5.46863	−	9.47194i	0.229257	−	0.397084i	−0.728331	−	0.685225i	$-0.759704\pi$
$569$	5.46863	−	9.47194i	0.229257	−	0.397084i	0.957588	+	0.288141i	$0.0930371\pi$
$570$		0			0
$571$	4.96863	+	8.60591i	0.207931	+	0.360146i	0.951062	−	0.308999i	$-0.0999939\pi$
$571$	4.96863	+	8.60591i	0.207931	+	0.360146i	−0.743132	+	0.669145i	$0.766661\pi$
$572$		0			0
$573$	−23.5203			−0.982573
$574$		0			0
$575$		0			0
$576$		0			0
$577$	8.29150	+	14.3613i	0.345180	+	0.597869i	0.985386	−	0.170334i	$-0.0544846\pi$
$577$	8.29150	+	14.3613i	0.345180	+	0.597869i	−0.640207	+	0.768203i	$0.721151\pi$
$578$		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
$583$	−6.64575	+	11.5108i	−0.275239	+	0.476728i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−6.00000			−0.247647			−0.123823	−	0.992304i	$-0.539516\pi$
$587$	−6.00000			−0.247647			−0.123823	+	0.992304i	$0.539516\pi$
$588$		0			0
$589$	−18.5830			−0.765699
$590$		0			0
$591$	−9.64575	−	16.7069i	−0.396773	−	0.687231i
$592$		0			0
$593$	−10.2915	+	17.8254i	−0.422621	+	0.732002i	−0.996195	−	0.0871523i	$-0.972223\pi$
$593$	−10.2915	+	17.8254i	−0.422621	+	0.732002i	0.573574	+	0.819154i	$0.305557\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	2.32288	−	4.02334i	0.0950690	−	0.164664i
$598$		0			0
$599$	8.53137	+	14.7768i	0.348582	+	0.603763i	0.985998	−	0.166758i	$-0.0533298\pi$
$599$	8.53137	+	14.7768i	0.348582	+	0.603763i	−0.637415	+	0.770520i	$0.719996\pi$
$600$		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
$603$	7.93725			0.323230
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−5.67712	+	9.83307i	−0.230427	+	0.399112i	−0.957934	−	0.286989i	$-0.907346\pi$
$607$	−5.67712	+	9.83307i	−0.230427	+	0.399112i	0.727507	+	0.686101i	$0.240679\pi$
$608$		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
$613$	12.3542	+	21.3982i	0.498983	+	0.864265i	0.999999	−	0.00117347i	$-0.000373526\pi$
$613$	12.3542	+	21.3982i	0.498983	+	0.864265i	−0.501016	+	0.865438i	$0.667040\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	10.1255			0.407637			0.203818	−	0.979009i	$-0.434665\pi$
$617$	10.1255			0.407637			0.203818	+	0.979009i	$0.434665\pi$
$618$		0			0
$619$	−17.6458	−	30.5633i	−0.709243	−	1.22844i	−0.965138	−	0.261740i	$-0.915704\pi$
$619$	−17.6458	−	30.5633i	−0.709243	−	1.22844i	0.255896	−	0.966704i	$-0.417630\pi$
$620$		0			0
$621$	−1.00000	+	1.73205i	−0.0401286	+	0.0695048i
$622$		0			0
$623$	−23.6458			−0.947347
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−13.1144	−	22.7148i	−0.523738	−	0.907141i
$628$		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
$633$	8.96863	+	15.5341i	0.356471	+	0.617426i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	3.50000	−	6.06218i	0.138675	−	0.240192i
$638$		0			0
$639$	−1.64575	+	2.85052i	−0.0651049	+	0.112765i
$640$		0			0
$641$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$641$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$642$		0			0
$643$	32.6458			1.28742			0.643711	−	0.765268i	$-0.277394\pi$
$643$	32.6458			1.28742			0.643711	+	0.765268i	$0.277394\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	14.3431	+	24.8430i	0.563887	+	0.976681i	0.997152	+	0.0754143i	$0.0240279\pi$
$647$	14.3431	+	24.8430i	0.563887	+	0.976681i	−0.433265	+	0.901266i	$0.642639\pi$
$648$		0			0
$649$	42.1660	−	73.0337i	1.65516	−	2.86682i
$650$		0			0
$651$	10.5830			0.414781
$652$		0			0
$653$	−5.11438	+	8.85836i	−0.200141	+	0.346655i	−0.948574	−	0.316556i	$-0.897473\pi$
$653$	−5.11438	+	8.85836i	−0.200141	+	0.346655i	0.748433	+	0.663211i	$0.230807\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	6.29150			0.245455
$658$		0			0
$659$	−18.1033			−0.705203			−0.352602	−	0.935774i	$-0.614703\pi$
$659$	−18.1033			−0.705203			−0.352602	+	0.935774i	$0.614703\pi$
$660$		0			0
$661$	−6.14575	−	10.6448i	−0.239042	−	0.414033i	0.721398	−	0.692521i	$-0.243500\pi$
$661$	−6.14575	−	10.6448i	−0.239042	−	0.414033i	−0.960440	+	0.278488i	$0.910167\pi$
$662$		0			0
$663$	0.822876	−	1.42526i	0.0319578	−	0.0553526i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−7.29150	+	12.6293i	−0.282328	+	0.489007i
$668$		0			0
$669$	−0.968627	−	1.67771i	−0.0374493	−	0.0648641i
$670$		0			0
$671$	−54.1033			−2.08863
$672$		0			0
$673$	8.29150			0.319614			0.159807	−	0.987148i	$-0.448913\pi$
$673$	8.29150			0.319614			0.159807	+	0.987148i	$0.448913\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−24.6458	+	42.6877i	−0.947213	+	1.64062i	−0.195955	+	0.980613i	$0.562781\pi$
$677$	−24.6458	+	42.6877i	−0.947213	+	1.64062i	−0.751258	+	0.660008i	$0.770553\pi$
$678$		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
$683$	−19.0516	−	32.9984i	−0.728990	−	1.26265i	−0.957310	−	0.289062i	$-0.906657\pi$
$683$	−19.0516	−	32.9984i	−0.728990	−	1.26265i	0.228320	−	0.973586i	$-0.426677\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−9.70850			−0.370402
$688$		0			0
$689$	−1.17712	−	2.03884i	−0.0448449	−	0.0776736i
$690$		0			0
$691$	5.61438	−	9.72439i	0.213581	−	0.369933i	−0.739252	−	0.673429i	$-0.764821\pi$
$691$	5.61438	−	9.72439i	0.213581	−	0.369933i	0.952833	+	0.303496i	$0.0981539\pi$
$692$		0			0
$693$	7.46863	+	12.9360i	0.283710	+	0.491400i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	0.291503	+	0.504897i	0.0110414	+	0.0191244i
$698$		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
$703$	−19.2601	−	33.3595i	−0.726410	−	1.25818i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	14.4686	−	25.0604i	0.544149	−	0.942493i
$708$		0			0
$709$	−18.0830	+	31.3207i	−0.679122	+	1.17627i	0.296124	+	0.955149i	$0.404306\pi$
$709$	−18.0830	+	31.3207i	−0.679122	+	1.17627i	−0.975246	+	0.221124i	$0.929028\pi$
$710$		0			0
$711$	3.32288	+	5.75539i	0.124618	+	0.215844i
$712$		0			0
$713$	8.00000			0.299602
$714$		0			0
$715$		0			0
$716$		0			0
$717$	15.2915	+	26.4857i	0.571072	+	0.989125i
$718$		0			0
$719$	12.1144	−	20.9827i	0.451790	−	0.782523i	−0.546707	−	0.837324i	$-0.684119\pi$
$719$	12.1144	−	20.9827i	0.451790	−	0.782523i	0.998497	+	0.0548005i	$0.0174523\pi$
$720$		0			0
$721$	−42.1660			−1.57034
$722$		0			0
$723$	−5.14575	+	8.91270i	−0.191373	+	0.331467i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	31.1033			1.15356			0.576778	−	0.816901i	$-0.304310\pi$
$727$	31.1033			1.15356			0.576778	+	0.816901i	$0.304310\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−6.00000	−	10.3923i	−0.221918	−	0.384373i
$732$		0			0
$733$	−21.0203	+	36.4082i	−0.776401	+	1.34477i	0.157603	+	0.987503i	$0.449623\pi$
$733$	−21.0203	+	36.4082i	−0.776401	+	1.34477i	−0.934004	+	0.357263i	$0.883710\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	22.4059	−	38.8081i	0.825331	−	1.42952i
$738$		0			0
$739$	6.73987	+	11.6738i	0.247930	+	0.429428i	0.962951	−	0.269675i	$-0.0869163\pi$
$739$	6.73987	+	11.6738i	0.247930	+	0.429428i	−0.715021	+	0.699103i	$0.753583\pi$
$740$		0			0
$741$	4.64575			0.170666
$742$		0			0
$743$	32.5830			1.19535			0.597677	−	0.801737i	$-0.296090\pi$
$743$	32.5830			1.19535			0.597677	+	0.801737i	$0.296090\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.82288	−	3.15731i	0.0666955	−	0.115520i
$748$		0			0
$749$	−27.0627			−0.988851
$750$		0			0
$751$	19.3229	−	33.4682i	0.705102	−	1.22127i	−0.261553	−	0.965189i	$-0.584235\pi$
$751$	19.3229	−	33.4682i	0.705102	−	1.22127i	0.966655	−	0.256083i	$-0.0824320\pi$
$752$		0			0
$753$	−9.40588	−	16.2915i	−0.342769	−	0.593694i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−11.0000			−0.399802			−0.199901	−	0.979816i	$-0.564062\pi$
$757$	−11.0000			−0.399802			−0.199901	+	0.979816i	$0.564062\pi$
$758$		0			0
$759$	5.64575	+	9.77873i	0.204928	+	0.354945i
$760$		0			0
$761$	24.8229	−	42.9945i	0.899829	−	1.55855i	0.0721161	−	0.997396i	$-0.477025\pi$
$761$	24.8229	−	42.9945i	0.899829	−	1.55855i	0.827712	−	0.561153i	$-0.189642\pi$
$762$		0			0
$763$	−12.6771	+	21.9574i	−0.458943	+	0.794912i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	7.46863	+	12.9360i	0.269676	+	0.467093i
$768$		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
$771$	12.3542			0.444927
$772$		0			0
$773$	−2.70850	−	4.69126i	−0.0974179	−	0.168733i	0.813197	−	0.581988i	$-0.197725\pi$
$773$	−2.70850	−	4.69126i	−0.0974179	−	0.168733i	−0.910615	+	0.413255i	$0.864392\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	10.9686	+	18.9982i	0.393497	+	0.681557i
$778$		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
$783$	7.29150			0.260577
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−22.4889	−	38.9519i	−0.801642	−	1.38849i	−0.918535	−	0.395340i	$-0.870627\pi$
$787$	−22.4889	−	38.9519i	−0.801642	−	1.38849i	0.116892	−	0.993145i	$-0.462707\pi$
$788$		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
$793$	4.79150	−	8.29913i	0.170151	−	0.294711i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−27.8745			−0.987366			−0.493683	−	0.869642i	$-0.664350\pi$
$797$	−27.8745			−0.987366			−0.493683	+	0.869642i	$0.664350\pi$
$798$		0			0
$799$	−4.83399			−0.171014
$800$		0			0
$801$	4.46863	+	7.73989i	0.157891	+	0.273476i
$802$		0			0
$803$	17.7601	−	30.7614i	0.626741	−	1.08555i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	3.11438	−	5.39426i	0.109631	−	0.189887i
$808$		0			0
$809$	22.6458	+	39.2236i	0.796182	+	1.37903i	0.922086	+	0.386986i	$0.126484\pi$
$809$	22.6458	+	39.2236i	0.796182	+	1.37903i	−0.125904	+	0.992042i	$0.540183\pi$
$810$		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
$813$	−13.2915			−0.466153
$814$		0			0
$815$		0			0
$816$		0			0
$817$	16.9373	−	29.3362i	0.592560	−	1.02634i
$818$		0			0
$819$	−2.64575			−0.0924500
$820$		0			0
$821$	−25.6974	+	44.5092i	−0.896845	+	1.55338i	−0.0653402	+	0.997863i	$0.520813\pi$
$821$	−25.6974	+	44.5092i	−0.896845	+	1.55338i	−0.831505	+	0.555518i	$0.812520\pi$
$822$		0			0
$823$	10.2601	+	17.7711i	0.357646	+	0.619460i	0.987567	−	0.157198i	$-0.0502462\pi$
$823$	10.2601	+	17.7711i	0.357646	+	0.619460i	−0.629921	+	0.776659i	$0.716913\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	21.4170			0.744742			0.372371	−	0.928084i	$-0.378545\pi$
$827$	21.4170			0.744742			0.372371	+	0.928084i	$0.378545\pi$
$828$		0			0
$829$	−22.6660	−	39.2587i	−0.787223	−	1.36351i	−0.927662	−	0.373421i	$-0.878185\pi$
$829$	−22.6660	−	39.2587i	−0.787223	−	1.36351i	0.140439	−	0.990089i	$-0.455149\pi$
$830$		0			0
$831$	−12.5000	+	21.6506i	−0.433620	+	0.751052i
$832$		0			0
$833$	11.5203			0.399153
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−2.00000	−	3.46410i	−0.0691301	−	0.119737i
$838$		0			0
$839$	−23.1660			−0.799780			−0.399890	−	0.916563i	$-0.630952\pi$
$839$	−23.1660			−0.799780			−0.399890	+	0.916563i	$0.630952\pi$
$840$		0			0
$841$	24.1660			0.833311
$842$		0			0
$843$	−2.11438	−	3.66221i	−0.0728231	−	0.126133i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	55.2288			1.89768
$848$		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
$853$	2.00000			0.0684787			0.0342393	−	0.999414i	$-0.489099\pi$
$853$	2.00000			0.0684787			0.0342393	+	0.999414i	$0.489099\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−7.58301	−	13.1342i	−0.259031	−	0.448654i	0.706952	−	0.707262i	$-0.250070\pi$
$857$	−7.58301	−	13.1342i	−0.259031	−	0.448654i	−0.965982	+	0.258608i	$0.916736\pi$
$858$		0			0
$859$	−0.583005	+	1.00979i	−0.0198919	+	0.0344538i	−0.875800	−	0.482674i	$-0.839666\pi$
$859$	−0.583005	+	1.00979i	−0.0198919	+	0.0344538i	0.855908	+	0.517128i	$0.172999\pi$
$860$		0			0
$861$	0.468627	−	0.811686i	0.0159708	−	0.0276622i
$862$		0			0
$863$	26.0516	−	45.1228i	0.886808	−	1.53600i	0.0431804	−	0.999067i	$-0.486251\pi$
$863$	26.0516	−	45.1228i	0.886808	−	1.53600i	0.843627	−	0.536929i	$-0.180416\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−14.2915			−0.485365
$868$		0			0
$869$	37.5203			1.27279
$870$		0			0
$871$	3.96863	+	6.87386i	0.134472	+	0.232912i
$872$		0			0
$873$	7.14575	−	12.3768i	0.241847	−	0.418891i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	9.37451	−	16.2371i	0.316555	−	0.548289i	−0.663212	−	0.748431i	$-0.730807\pi$
$877$	9.37451	−	16.2371i	0.316555	−	0.548289i	0.979767	+	0.200143i	$0.0641406\pi$
$878$		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
$883$	−28.6458			−0.964006			−0.482003	−	0.876169i	$-0.660091\pi$
$883$	−28.6458			−0.964006			−0.482003	+	0.876169i	$0.660091\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−15.3542	+	26.5943i	−0.515545	+	0.892951i	0.484292	+	0.874906i	$0.339077\pi$
$887$	−15.3542	+	26.5943i	−0.515545	+	0.892951i	−0.999837	+	0.0180441i	$0.994256\pi$
$888$		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
$893$	−6.82288	−	11.8176i	−0.228319	−	0.395460i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−2.00000			−0.0667781
$898$		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
$903$	−9.64575	+	16.7069i	−0.320991	+	0.555972i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−29.4889	−	51.0762i	−0.979162	−	1.69596i	−0.665453	−	0.746440i	$-0.731761\pi$
$907$	−29.4889	−	51.0762i	−0.979162	−	1.69596i	−0.313710	−	0.949519i	$-0.601572\pi$
$908$		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
$913$	−10.2915	−	17.8254i	−0.340599	−	0.589935i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−54.4575			−1.79835
$918$		0			0
$919$	28.4575	−	49.2899i	0.938727	−	1.62592i	0.170877	−	0.985292i	$-0.445340\pi$
$919$	28.4575	−	49.2899i	0.938727	−	1.62592i	0.767850	−	0.640630i	$-0.221327\pi$
$920$		0			0
$921$	14.9373	+	25.8721i	0.492199	+	0.852514i
$922$		0			0
$923$	−3.29150			−0.108341
$924$		0			0
$925$		0			0
$926$		0			0
$927$	7.96863	+	13.8021i	0.261724	+	0.453319i
$928$		0			0
$929$	−3.82288	+	6.62141i	−0.125424	+	0.217242i	−0.921899	−	0.387431i	$-0.873363\pi$
$929$	−3.82288	+	6.62141i	−0.125424	+	0.217242i	0.796474	+	0.604672i	$0.206696\pi$
$930$		0			0
$931$	16.2601	+	28.1634i	0.532904	+	0.923017i
$932$		0			0
$933$	1.35425	−	2.34563i	0.0443361	−	0.0767924i
$934$		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
$939$	−8.70850			−0.284191
$940$		0			0
$941$	24.8745	+	43.0839i	0.810886	+	1.40450i	0.912245	+	0.409645i	$0.134348\pi$
$941$	24.8745	+	43.0839i	0.810886	+	1.40450i	−0.101359	+	0.994850i	$0.532319\pi$
$942$		0			0
$943$	0.354249	−	0.613577i	0.0115359	−	0.0199808i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	18.6458	−	32.2954i	0.605906	−	1.04946i	−0.386002	−	0.922498i	$-0.626144\pi$
$947$	18.6458	−	32.2954i	0.605906	−	1.04946i	0.991908	−	0.126961i	$-0.0405224\pi$
$948$		0			0
$949$	3.14575	+	5.44860i	0.102115	+	0.176869i
$950$		0			0
$951$	12.5830			0.408032
$952$		0			0
$953$	−10.4797			−0.339472			−0.169736	−	0.985490i	$-0.554292\pi$
$953$	−10.4797			−0.339472			−0.169736	+	0.985490i	$0.554292\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	20.5830	−	35.6508i	0.665354	−	1.15243i
$958$		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
$963$	5.11438	+	8.85836i	0.164809	+	0.285457i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−14.0627			−0.452227			−0.226114	−	0.974101i	$-0.572602\pi$
$967$	−14.0627			−0.452227			−0.226114	+	0.974101i	$0.572602\pi$
$968$		0			0
$969$	3.82288	+	6.62141i	0.122808	+	0.212710i
$970$		0			0
$971$	−29.2804	+	50.7151i	−0.939652	+	1.62753i	−0.173532	+	0.984828i	$0.555518\pi$
$971$	−29.2804	+	50.7151i	−0.939652	+	1.62753i	−0.766120	+	0.642698i	$0.777815\pi$
$972$		0			0
$973$	−0.0830052	−	0.143769i	−0.00266103	−	0.00460903i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−27.3431	−	47.3597i	−0.874784	−	1.51517i	−0.856992	−	0.515329i	$-0.827670\pi$
$977$	−27.3431	−	47.3597i	−0.874784	−	1.51517i	−0.0177921	−	0.999842i	$-0.505664\pi$
$978$		0			0
$979$	50.4575			1.61263
$980$		0			0
$981$	9.58301			0.305962
$982$		0			0
$983$	−0.177124	−	0.306788i	−0.00564939	−	0.00978503i	0.863187	−	0.504885i	$-0.168465\pi$
$983$	−0.177124	−	0.306788i	−0.00564939	−	0.00978503i	−0.868836	+	0.495100i	$0.835132\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	3.88562	+	6.73009i	0.123681	+	0.214221i
$988$		0			0
$989$	−7.29150	+	12.6293i	−0.231856	+	0.401587i
$990$		0			0
$991$	−3.93725	−	6.81952i	−0.125071	−	0.216629i	0.796690	−	0.604389i	$-0.206583\pi$
$991$	−3.93725	−	6.81952i	−0.125071	−	0.216629i	−0.921761	+	0.387759i	$0.873249\pi$
$992$		0			0
$993$	−8.64575			−0.274365
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−7.37451	−	12.7730i	−0.233553	−	0.404526i	0.725298	−	0.688435i	$-0.241702\pi$
$997$	−7.37451	−	12.7730i	−0.233553	−	0.404526i	−0.958851	+	0.283909i	$0.908369\pi$
$998$		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.q.g.1801.1	yes	4
5.2	odd	4		2100.2.bc.h.1549.2		8
5.3	odd	4		2100.2.bc.h.1549.3		8
5.4	even	2		2100.2.q.i.1801.2	yes	4
7.4	even	3	inner	2100.2.q.g.1201.1	✓	4
35.4	even	6		2100.2.q.i.1201.2	yes	4
35.18	odd	12		2100.2.bc.h.949.2		8
35.32	odd	12		2100.2.bc.h.949.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.q.g.1201.1	✓	4	7.4	even	3	inner
2100.2.q.g.1801.1	yes	4	1.1	even	1	trivial
2100.2.q.i.1201.2	yes	4	35.4	even	6
2100.2.q.i.1801.2	yes	4	5.4	even	2
2100.2.bc.h.949.2		8	35.18	odd	12
2100.2.bc.h.949.3		8	35.32	odd	12
2100.2.bc.h.1549.2		8	5.2	odd	4
2100.2.bc.h.1549.3		8	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} +(-1.32288 - 2.29129i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{3} +(-1.32288 - 2.29129i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(2.82288 + 4.88936i) q^{11} -1.00000 q^{13} +(-0.822876 - 1.42526i) q^{17} +(2.32288 - 4.02334i) q^{19} +(-1.32288 + 2.29129i) q^{21} +(-1.00000 + 1.73205i) q^{23} +1.00000 q^{27} +7.29150 q^{29} +(-2.00000 - 3.46410i) q^{31} +(2.82288 - 4.88936i) q^{33} +(4.14575 - 7.18065i) q^{37} +(0.500000 + 0.866025i) q^{39} -0.354249 q^{41} +7.29150 q^{43} +(1.46863 - 2.54374i) q^{47} +(-3.50000 + 6.06218i) q^{49} +(-0.822876 + 1.42526i) q^{51} +(1.17712 + 2.03884i) q^{53} -4.64575 q^{57} +(-7.46863 - 12.9360i) q^{59} +(-4.79150 + 8.29913i) q^{61} +2.64575 q^{63} +(-3.96863 - 6.87386i) q^{67} +2.00000 q^{69} +3.29150 q^{71} +(-3.14575 - 5.44860i) q^{73} +(7.46863 - 12.9360i) q^{77} +(3.32288 - 5.75539i) q^{79} +(-0.500000 - 0.866025i) q^{81} -3.64575 q^{83} +(-3.64575 - 6.31463i) q^{87} +(4.46863 - 7.73989i) q^{89} +(1.32288 + 2.29129i) q^{91} +(-2.00000 + 3.46410i) q^{93} -14.2915 q^{97} -5.64575 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 2 q^{9}+O(q^{10}) \) 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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