LMFDB - Embedded newform 2520.2.bi.l.1801.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2520,2,Mod(361,2520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2520, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("2520.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2520.bi (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:	$20.1223013094$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 840)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1801.2
Root			$0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	2520.1801
Dual form			2520.2.bi.l.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{5} +(1.62132 + 2.09077i) q^{7} +O(q^{10})$	$q+(0.500000 - 0.866025i) q^{5} +(1.62132 + 2.09077i) q^{7} +(0.707107 + 1.22474i) q^{11} -5.24264 q^{13} +(-2.70711 - 4.68885i) q^{17} +(0.0857864 - 0.148586i) q^{19} +(3.53553 - 6.12372i) q^{23} +(-0.500000 - 0.866025i) q^{25} +9.07107 q^{29} +(2.50000 + 4.33013i) q^{31} +(2.62132 - 0.358719i) q^{35} +(3.79289 - 6.56948i) q^{37} +8.24264 q^{41} +8.89949 q^{43} +(1.82843 - 3.16693i) q^{47} +(-1.74264 + 6.77962i) q^{49} +(-0.585786 - 1.01461i) q^{53} +1.41421 q^{55} +(-7.12132 - 12.3345i) q^{59} +(-7.41421 + 12.8418i) q^{61} +(-2.62132 + 4.54026i) q^{65} +(5.44975 + 9.43924i) q^{67} +3.07107 q^{71} +(3.62132 + 6.27231i) q^{73} +(-1.41421 + 3.46410i) q^{77} +(3.08579 - 5.34474i) q^{79} +2.24264 q^{83} -5.41421 q^{85} +(-3.12132 + 5.40629i) q^{89} +(-8.50000 - 10.9612i) q^{91} +(-0.0857864 - 0.148586i) q^{95} +8.48528 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{5} - 2 q^{7}+O(q^{10}) $ 4 * q + 2 * q^5 - 2 * q^7	$ 4 q + 2 q^{5} - 2 q^{7} - 4 q^{13} - 8 q^{17} + 6 q^{19} - 2 q^{25} + 8 q^{29} + 10 q^{31} + 2 q^{35} + 18 q^{37} + 16 q^{41} - 4 q^{43} - 4 q^{47} + 10 q^{49} - 8 q^{53} - 20 q^{59} - 24 q^{61} - 2 q^{65} + 2 q^{67} - 16 q^{71} + 6 q^{73} + 18 q^{79} - 8 q^{83} - 16 q^{85} - 4 q^{89} - 34 q^{91} - 6 q^{95}+O(q^{100}) $ 4 * q + 2 * q^5 - 2 * q^7 - 4 * q^13 - 8 * q^17 + 6 * q^19 - 2 * q^25 + 8 * q^29 + 10 * q^31 + 2 * q^35 + 18 * q^37 + 16 * q^41 - 4 * q^43 - 4 * q^47 + 10 * q^49 - 8 * q^53 - 20 * q^59 - 24 * q^61 - 2 * q^65 + 2 * q^67 - 16 * q^71 + 6 * q^73 + 18 * q^79 - 8 * q^83 - 16 * q^85 - 4 * q^89 - 34 * q^91 - 6 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$1081$	$1261$	$2017$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	1.62132	+	2.09077i	0.612801	+	0.790237i
$7$	1.62132	+	2.09077i	0.612801	+	0.790237i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.707107	+	1.22474i	0.213201	+	0.369274i	0.952714	−	0.303867i	$-0.0982778\pi$
$11$	0.707107	+	1.22474i	0.213201	+	0.369274i	−0.739514	+	0.673141i	$0.764945\pi$
$12$		0			0
$13$	−5.24264			−1.45405			−0.727023	−	0.686613i	$-0.759097\pi$
$13$	−5.24264			−1.45405			−0.727023	+	0.686613i	$0.759097\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.70711	−	4.68885i	−0.656570	−	1.13721i	−0.981498	−	0.191474i	$-0.938673\pi$
$17$	−2.70711	−	4.68885i	−0.656570	−	1.13721i	0.324928	−	0.945739i	$-0.394660\pi$
$18$		0			0
$19$	0.0857864	−	0.148586i	0.0196808	−	0.0340881i	−0.856017	−	0.516947i	$-0.827068\pi$
$19$	0.0857864	−	0.148586i	0.0196808	−	0.0340881i	0.875698	+	0.482859i	$0.160402\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.53553	−	6.12372i	0.737210	−	1.27688i	−0.216537	−	0.976274i	$-0.569476\pi$
$23$	3.53553	−	6.12372i	0.737210	−	1.27688i	0.953747	−	0.300610i	$-0.0971904\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	9.07107			1.68446			0.842228	−	0.539122i	$-0.181244\pi$
$29$	9.07107			1.68446			0.842228	+	0.539122i	$0.181244\pi$
$30$		0			0
$31$	2.50000	+	4.33013i	0.449013	+	0.777714i	0.998322	−	0.0579057i	$-0.0184423\pi$
$31$	2.50000	+	4.33013i	0.449013	+	0.777714i	−0.549309	+	0.835619i	$0.685109\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.62132	−	0.358719i	0.443084	−	0.0606347i
$36$		0			0
$37$	3.79289	−	6.56948i	0.623548	−	1.08002i	−0.365272	−	0.930901i	$-0.619024\pi$
$37$	3.79289	−	6.56948i	0.623548	−	1.08002i	0.988820	−	0.149116i	$-0.0476427\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	8.24264			1.28728			0.643642	−	0.765327i	$-0.277423\pi$
$41$	8.24264			1.28728			0.643642	+	0.765327i	$0.277423\pi$
$42$		0			0
$43$	8.89949			1.35716			0.678580	−	0.734526i	$-0.262596\pi$
$43$	8.89949			1.35716			0.678580	+	0.734526i	$0.262596\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.82843	−	3.16693i	0.266704	−	0.461944i	−0.701305	−	0.712861i	$-0.747399\pi$
$47$	1.82843	−	3.16693i	0.266704	−	0.461944i	0.968009	+	0.250917i	$0.0807322\pi$
$48$		0			0
$49$	−1.74264	+	6.77962i	−0.248949	+	0.968517i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.585786	−	1.01461i	−0.0804640	−	0.139368i	0.822985	−	0.568063i	$-0.192307\pi$
$53$	−0.585786	−	1.01461i	−0.0804640	−	0.139368i	−0.903449	+	0.428695i	$0.858974\pi$
$54$		0			0
$55$	1.41421			0.190693
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−7.12132	−	12.3345i	−0.927117	−	1.60581i	−0.788121	−	0.615521i	$-0.788946\pi$
$59$	−7.12132	−	12.3345i	−0.927117	−	1.60581i	−0.138996	−	0.990293i	$-0.544388\pi$
$60$		0			0
$61$	−7.41421	+	12.8418i	−0.949293	+	1.64422i	−0.202374	+	0.979308i	$0.564866\pi$
$61$	−7.41421	+	12.8418i	−0.949293	+	1.64422i	−0.746919	+	0.664915i	$0.768468\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.62132	+	4.54026i	−0.325135	+	0.563150i
$66$		0			0
$67$	5.44975	+	9.43924i	0.665793	+	1.15319i	0.979070	+	0.203525i	$0.0652398\pi$
$67$	5.44975	+	9.43924i	0.665793	+	1.15319i	−0.313277	+	0.949662i	$0.601427\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	3.07107			0.364469			0.182234	−	0.983255i	$-0.441667\pi$
$71$	3.07107			0.364469			0.182234	+	0.983255i	$0.441667\pi$
$72$		0			0
$73$	3.62132	+	6.27231i	0.423843	+	0.734118i	0.996312	−	0.0858085i	$-0.0273473\pi$
$73$	3.62132	+	6.27231i	0.423843	+	0.734118i	−0.572468	+	0.819927i	$0.694014\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.41421	+	3.46410i	−0.161165	+	0.394771i
$78$		0			0
$79$	3.08579	−	5.34474i	0.347178	−	0.601330i	−0.638569	−	0.769565i	$-0.720473\pi$
$79$	3.08579	−	5.34474i	0.347178	−	0.601330i	0.985747	+	0.168235i	$0.0538066\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.24264			0.246162			0.123081	−	0.992397i	$-0.460723\pi$
$83$	2.24264			0.246162			0.123081	+	0.992397i	$0.460723\pi$
$84$		0			0
$85$	−5.41421			−0.587254
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.12132	+	5.40629i	−0.330859	+	0.573065i	−0.982681	−	0.185307i	$-0.940672\pi$
$89$	−3.12132	+	5.40629i	−0.330859	+	0.573065i	0.651821	+	0.758373i	$0.274005\pi$
$90$		0			0
$91$	−8.50000	−	10.9612i	−0.891042	−	1.14904i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.0857864	−	0.148586i	−0.00880150	−	0.0152447i
$96$		0			0
$97$	8.48528			0.861550			0.430775	−	0.902459i	$-0.358240\pi$
$97$	8.48528			0.861550			0.430775	+	0.902459i	$0.358240\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.77817	+	13.4722i	0.773957	+	1.34053i	0.935379	+	0.353648i	$0.115059\pi$
$101$	7.77817	+	13.4722i	0.773957	+	1.34053i	−0.161421	+	0.986886i	$0.551608\pi$
$102$		0			0
$103$	4.62132	−	8.00436i	0.455352	−	0.788693i	−0.543356	−	0.839502i	$-0.682847\pi$
$103$	4.62132	−	8.00436i	0.455352	−	0.788693i	0.998708	+	0.0508091i	$0.0161800\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.707107	−	1.22474i	0.0683586	−	0.118401i	−0.829820	−	0.558031i	$-0.811557\pi$
$107$	0.707107	−	1.22474i	0.0683586	−	0.118401i	0.898179	+	0.439630i	$0.144890\pi$
$108$		0			0
$109$	−7.74264	−	13.4106i	−0.741610	−	1.28451i	−0.951762	−	0.306838i	$-0.900729\pi$
$109$	−7.74264	−	13.4106i	−0.741610	−	1.28451i	0.210151	−	0.977669i	$-0.432604\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	9.31371			0.876160			0.438080	−	0.898936i	$-0.355659\pi$
$113$	9.31371			0.876160			0.438080	+	0.898936i	$0.355659\pi$
$114$		0			0
$115$	−3.53553	−	6.12372i	−0.329690	−	0.571040i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	5.41421	−	13.2621i	0.496320	−	1.21573i
$120$		0			0
$121$	4.50000	−	7.79423i	0.409091	−	0.708566i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−6.07107			−0.538720			−0.269360	−	0.963040i	$-0.586812\pi$
$127$	−6.07107			−0.538720			−0.269360	+	0.963040i	$0.586812\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.24264	+	9.08052i	−0.458052	+	0.793369i	−0.998858	−	0.0477784i	$-0.984786\pi$
$131$	−5.24264	+	9.08052i	−0.458052	+	0.793369i	0.540806	+	0.841147i	$0.318119\pi$
$132$		0			0
$133$	0.449747	−	0.0615465i	0.0389981	−	0.00533676i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.464466	+	0.804479i	0.0396820	+	0.0687313i	0.885184	−	0.465241i	$-0.154032\pi$
$137$	0.464466	+	0.804479i	0.0396820	+	0.0687313i	−0.845502	+	0.533972i	$0.820699\pi$
$138$		0			0
$139$	0.313708			0.0266084			0.0133042	−	0.999911i	$-0.495765\pi$
$139$	0.313708			0.0266084			0.0133042	+	0.999911i	$0.495765\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−3.70711	−	6.42090i	−0.310004	−	0.536942i
$144$		0			0
$145$	4.53553	−	7.85578i	0.376656	−	0.652387i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	2.00000	−	3.46410i	0.163846	−	0.283790i	−0.772399	−	0.635138i	$-0.780943\pi$
$149$	2.00000	−	3.46410i	0.163846	−	0.283790i	0.936245	+	0.351348i	$0.114277\pi$
$150$		0			0
$151$	−3.24264	−	5.61642i	−0.263882	−	0.457058i	0.703388	−	0.710806i	$-0.251670\pi$
$151$	−3.24264	−	5.61642i	−0.263882	−	0.457058i	−0.967270	+	0.253749i	$0.918336\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	5.00000			0.401610
$156$		0			0
$157$	11.2426	+	19.4728i	0.897260	+	1.55410i	0.830982	+	0.556299i	$0.187779\pi$
$157$	11.2426	+	19.4728i	0.897260	+	1.55410i	0.0662785	+	0.997801i	$0.478887\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	18.5355	−	2.53653i	1.46080	−	0.199907i
$162$		0			0
$163$	11.3137	−	19.5959i	0.886158	−	1.53487i	0.0417775	−	0.999127i	$-0.486698\pi$
$163$	11.3137	−	19.5959i	0.886158	−	1.53487i	0.844381	−	0.535744i	$-0.179969\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	11.8995			0.920811			0.460405	−	0.887709i	$-0.347704\pi$
$167$	11.8995			0.920811			0.460405	+	0.887709i	$0.347704\pi$
$168$		0			0
$169$	14.4853			1.11425
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.58579	−	4.47871i	0.196594	−	0.340510i	−0.750828	−	0.660498i	$-0.770345\pi$
$173$	2.58579	−	4.47871i	0.196594	−	0.340510i	0.947422	+	0.319987i	$0.103679\pi$
$174$		0			0
$175$	1.00000	−	2.44949i	0.0755929	−	0.185164i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	9.82843	+	17.0233i	0.734611	+	1.27238i	0.954894	+	0.296948i	$0.0959687\pi$
$179$	9.82843	+	17.0233i	0.734611	+	1.27238i	−0.220283	+	0.975436i	$0.570698\pi$
$180$		0			0
$181$	−8.31371			−0.617953			−0.308977	−	0.951070i	$-0.599986\pi$
$181$	−8.31371			−0.617953			−0.308977	+	0.951070i	$0.599986\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−3.79289	−	6.56948i	−0.278859	−	0.482998i
$186$		0			0
$187$	3.82843	−	6.63103i	0.279962	−	0.484909i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2.17157	−	3.76127i	0.157129	−	0.272156i	−0.776703	−	0.629867i	$-0.783109\pi$
$191$	2.17157	−	3.76127i	0.157129	−	0.272156i	0.933832	+	0.357711i	$0.116443\pi$
$192$		0			0
$193$	−4.79289	−	8.30153i	−0.345000	−	0.597558i	0.640354	−	0.768080i	$-0.278788\pi$
$193$	−4.79289	−	8.30153i	−0.345000	−	0.597558i	−0.985354	+	0.170523i	$0.945454\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−24.0416			−1.71290			−0.856448	−	0.516234i	$-0.827334\pi$
$197$	−24.0416			−1.71290			−0.856448	+	0.516234i	$0.827334\pi$
$198$		0			0
$199$	3.24264	+	5.61642i	0.229865	+	0.398137i	0.957768	−	0.287543i	$-0.0928383\pi$
$199$	3.24264	+	5.61642i	0.229865	+	0.398137i	−0.727903	+	0.685680i	$0.759505\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	14.7071	+	18.9655i	1.03224	+	1.33112i
$204$		0			0
$205$	4.12132	−	7.13834i	0.287845	−	0.498563i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.242641			0.0167838
$210$		0			0
$211$	−4.82843			−0.332403			−0.166201	−	0.986092i	$-0.553150\pi$
$211$	−4.82843			−0.332403			−0.166201	+	0.986092i	$0.553150\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	4.44975	−	7.70719i	0.303470	−	0.525626i
$216$		0			0
$217$	−5.00000	+	12.2474i	−0.339422	+	0.831411i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	14.1924	+	24.5819i	0.954683	+	1.65356i
$222$		0			0
$223$	6.14214			0.411308			0.205654	−	0.978625i	$-0.434068\pi$
$223$	6.14214			0.411308			0.205654	+	0.978625i	$0.434068\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−7.46447	−	12.9288i	−0.495434	−	0.858117i	0.504552	−	0.863381i	$-0.331658\pi$
$227$	−7.46447	−	12.9288i	−0.495434	−	0.858117i	−0.999986	+	0.00526434i	$0.998324\pi$
$228$		0			0
$229$	−8.98528	+	15.5630i	−0.593764	+	1.02843i	0.399956	+	0.916534i	$0.369025\pi$
$229$	−8.98528	+	15.5630i	−0.593764	+	1.02843i	−0.993720	+	0.111895i	$0.964308\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−2.75736	+	4.77589i	−0.180641	+	0.312879i	−0.942099	−	0.335335i	$-0.891150\pi$
$233$	−2.75736	+	4.77589i	−0.180641	+	0.312879i	0.761458	+	0.648214i	$0.224484\pi$
$234$		0			0
$235$	−1.82843	−	3.16693i	−0.119273	−	0.206588i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−29.3137			−1.89615			−0.948073	−	0.318053i	$-0.896971\pi$
$239$	−29.3137			−1.89615			−0.948073	+	0.318053i	$0.896971\pi$
$240$		0			0
$241$	−4.82843	−	8.36308i	−0.311026	−	0.538713i	0.667558	−	0.744557i	$-0.267339\pi$
$241$	−4.82843	−	8.36308i	−0.311026	−	0.538713i	−0.978585	+	0.205844i	$0.934006\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	5.00000	+	4.89898i	0.319438	+	0.312984i
$246$		0			0
$247$	−0.449747	+	0.778985i	−0.0286167	+	0.0495657i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	0.100505			0.00634382			0.00317191	−	0.999995i	$-0.498990\pi$
$251$	0.100505			0.00634382			0.00317191	+	0.999995i	$0.498990\pi$
$252$		0			0
$253$	10.0000			0.628695
$254$		0			0
$255$		0			0
$256$		0			0
$257$	8.77817	−	15.2042i	0.547567	−	0.948415i	−0.450873	−	0.892588i	$-0.648887\pi$
$257$	8.77817	−	15.2042i	0.547567	−	0.948415i	0.998440	−	0.0558266i	$-0.0177794\pi$
$258$		0			0
$259$	19.8848	−	2.72117i	1.23558	−	0.169085i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−9.89949	−	17.1464i	−0.610429	−	1.05729i	−0.991168	−	0.132612i	$-0.957664\pi$
$263$	−9.89949	−	17.1464i	−0.610429	−	1.05729i	0.380739	−	0.924683i	$-0.375670\pi$
$264$		0			0
$265$	−1.17157			−0.0719691
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−5.24264	−	9.08052i	−0.319649	−	0.553649i	0.660765	−	0.750592i	$-0.270232\pi$
$269$	−5.24264	−	9.08052i	−0.319649	−	0.553649i	−0.980415	+	0.196943i	$0.936898\pi$
$270$		0			0
$271$	7.24264	−	12.5446i	0.439959	−	0.762031i	−0.557727	−	0.830025i	$-0.688326\pi$
$271$	7.24264	−	12.5446i	0.439959	−	0.762031i	0.997686	+	0.0679932i	$0.0216596\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.707107	−	1.22474i	0.0426401	−	0.0738549i
$276$		0			0
$277$	6.69239	+	11.5916i	0.402107	+	0.696469i	0.993980	−	0.109562i	$-0.0349448\pi$
$277$	6.69239	+	11.5916i	0.402107	+	0.696469i	−0.591873	+	0.806031i	$0.701611\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−13.6569			−0.814700			−0.407350	−	0.913272i	$-0.633547\pi$
$281$	−13.6569			−0.814700			−0.407350	+	0.913272i	$0.633547\pi$
$282$		0			0
$283$	−11.8640	−	20.5490i	−0.705239	−	1.22151i	−0.966605	−	0.256270i	$-0.917506\pi$
$283$	−11.8640	−	20.5490i	−0.705239	−	1.22151i	0.261366	−	0.965240i	$-0.415827\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	13.3640	+	17.2335i	0.788850	+	1.01726i
$288$		0			0
$289$	−6.15685	+	10.6640i	−0.362168	+	0.627293i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−9.65685			−0.564159			−0.282080	−	0.959391i	$-0.591024\pi$
$293$	−9.65685			−0.564159			−0.282080	+	0.959391i	$0.591024\pi$
$294$		0			0
$295$	−14.2426			−0.829239
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−18.5355	+	32.1045i	−1.07194	+	1.85665i
$300$		0			0
$301$	14.4289	+	18.6068i	0.831670	+	1.07248i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	7.41421	+	12.8418i	0.424537	+	0.735319i
$306$		0			0
$307$	−8.07107			−0.460640			−0.230320	−	0.973115i	$-0.573977\pi$
$307$	−8.07107			−0.460640			−0.230320	+	0.973115i	$0.573977\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−5.87868	−	10.1822i	−0.333349	−	0.577378i	0.649817	−	0.760091i	$-0.274846\pi$
$311$	−5.87868	−	10.1822i	−0.333349	−	0.577378i	−0.983166	+	0.182713i	$0.941512\pi$
$312$		0			0
$313$	2.03553	−	3.52565i	0.115055	−	0.199281i	−0.802747	−	0.596320i	$-0.796629\pi$
$313$	2.03553	−	3.52565i	0.115055	−	0.199281i	0.917802	+	0.397039i	$0.129962\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−6.70711	+	11.6170i	−0.376709	+	0.652479i	−0.990581	−	0.136927i	$-0.956278\pi$
$317$	−6.70711	+	11.6170i	−0.376709	+	0.652479i	0.613873	+	0.789405i	$0.289611\pi$
$318$		0			0
$319$	6.41421	+	11.1097i	0.359127	+	0.622026i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−0.928932			−0.0516872
$324$		0			0
$325$	2.62132	+	4.54026i	0.145405	+	0.251848i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	9.58579	−	1.31178i	0.528482	−	0.0723210i
$330$		0			0
$331$	−3.91421	+	6.77962i	−0.215145	+	0.372641i	−0.953317	−	0.301970i	$-0.902356\pi$
$331$	−3.91421	+	6.77962i	−0.215145	+	0.372641i	0.738173	+	0.674612i	$0.235689\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	10.8995			0.595503
$336$		0			0
$337$	−10.8995			−0.593733			−0.296867	−	0.954919i	$-0.595942\pi$
$337$	−10.8995			−0.593733			−0.296867	+	0.954919i	$0.595942\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−3.53553	+	6.12372i	−0.191460	+	0.331618i
$342$		0			0
$343$	−17.0000	+	7.34847i	−0.917914	+	0.396780i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	0.828427	+	1.43488i	0.0444723	+	0.0770283i	0.887405	−	0.460991i	$-0.152506\pi$
$347$	0.828427	+	1.43488i	0.0444723	+	0.0770283i	−0.842932	+	0.538019i	$0.819173\pi$
$348$		0			0
$349$	−13.3137			−0.712666			−0.356333	−	0.934359i	$-0.615973\pi$
$349$	−13.3137			−0.712666			−0.356333	+	0.934359i	$0.615973\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−11.1213	−	19.2627i	−0.591928	−	1.02525i	−0.993973	−	0.109629i	$-0.965034\pi$
$353$	−11.1213	−	19.2627i	−0.591928	−	1.02525i	0.402044	−	0.915620i	$-0.368300\pi$
$354$		0			0
$355$	1.53553	−	2.65962i	0.0814977	−	0.141158i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	8.87868	−	15.3783i	0.468599	−	0.811637i	−0.530757	−	0.847524i	$-0.678092\pi$
$359$	8.87868	−	15.3783i	0.468599	−	0.811637i	0.999356	+	0.0358871i	$0.0114257\pi$
$360$		0			0
$361$	9.48528	+	16.4290i	0.499225	+	0.864684i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	7.24264			0.379097
$366$		0			0
$367$	7.79289	+	13.4977i	0.406786	+	0.704574i	0.994528	−	0.104475i	$-0.0333162\pi$
$367$	7.79289	+	13.4977i	0.406786	+	0.704574i	−0.587742	+	0.809049i	$0.699983\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.17157	−	2.86976i	0.0608250	−	0.148990i
$372$		0			0
$373$	4.55025	−	7.88127i	0.235603	−	0.408077i	−0.723845	−	0.689963i	$-0.757627\pi$
$373$	4.55025	−	7.88127i	0.235603	−	0.408077i	0.959448	+	0.281886i	$0.0909601\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−47.5563			−2.44928
$378$		0			0
$379$	20.3137			1.04345			0.521723	−	0.853115i	$-0.325290\pi$
$379$	20.3137			1.04345			0.521723	+	0.853115i	$0.325290\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	3.89949	−	6.75412i	0.199255	−	0.345120i	−0.749032	−	0.662534i	$-0.769481\pi$
$383$	3.89949	−	6.75412i	0.199255	−	0.345120i	0.948287	+	0.317414i	$0.102814\pi$
$384$		0			0
$385$	2.29289	+	2.95680i	0.116857	+	0.150692i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−6.60660	−	11.4430i	−0.334968	−	0.580182i	0.648511	−	0.761206i	$-0.275392\pi$
$389$	−6.60660	−	11.4430i	−0.334968	−	0.580182i	−0.983479	+	0.181024i	$0.942059\pi$
$390$		0			0
$391$	−38.2843			−1.93612
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−3.08579	−	5.34474i	−0.155263	−	0.268923i
$396$		0			0
$397$	−6.20711	+	10.7510i	−0.311526	+	0.539578i	−0.978693	−	0.205330i	$-0.934173\pi$
$397$	−6.20711	+	10.7510i	−0.311526	+	0.539578i	0.667167	+	0.744908i	$0.267507\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−3.07107	+	5.31925i	−0.153362	+	0.265630i	−0.932461	−	0.361270i	$-0.882343\pi$
$401$	−3.07107	+	5.31925i	−0.153362	+	0.265630i	0.779100	+	0.626900i	$0.215677\pi$
$402$		0			0
$403$	−13.1066	−	22.7013i	−0.652886	−	1.13083i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	10.7279			0.531763
$408$		0			0
$409$	14.3284	+	24.8176i	0.708495	+	1.22715i	0.965415	+	0.260717i	$0.0839589\pi$
$409$	14.3284	+	24.8176i	0.708495	+	1.22715i	−0.256920	+	0.966433i	$0.582708\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	14.2426	−	34.8872i	0.700835	−	1.71669i
$414$		0			0
$415$	1.12132	−	1.94218i	0.0550435	−	0.0953381i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	24.8284			1.21295			0.606474	−	0.795103i	$-0.292583\pi$
$419$	24.8284			1.21295			0.606474	+	0.795103i	$0.292583\pi$
$420$		0			0
$421$	−26.4558			−1.28938			−0.644689	−	0.764445i	$-0.723013\pi$
$421$	−26.4558			−1.28938			−0.644689	+	0.764445i	$0.723013\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−2.70711	+	4.68885i	−0.131314	+	0.227442i
$426$		0			0
$427$	−38.8701	+	5.31925i	−1.88105	+	0.257416i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	9.58579	+	16.6031i	0.461731	+	0.799742i	0.999047	−	0.0436391i	$-0.0138952\pi$
$431$	9.58579	+	16.6031i	0.461731	+	0.799742i	−0.537316	+	0.843381i	$0.680562\pi$
$432$		0			0
$433$	−17.5858			−0.845119			−0.422559	−	0.906335i	$-0.638868\pi$
$433$	−17.5858			−0.845119			−0.422559	+	0.906335i	$0.638868\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−0.606602	−	1.05066i	−0.0290177	−	0.0502601i
$438$		0			0
$439$	11.8284	−	20.4874i	0.564540	−	0.977812i	−0.432552	−	0.901609i	$-0.642387\pi$
$439$	11.8284	−	20.4874i	0.564540	−	0.977812i	0.997092	−	0.0762032i	$-0.0242798\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	7.75736	−	13.4361i	0.368563	−	0.638370i	−0.620778	−	0.783986i	$-0.713183\pi$
$443$	7.75736	−	13.4361i	0.368563	−	0.638370i	0.989341	+	0.145616i	$0.0465165\pi$
$444$		0			0
$445$	3.12132	+	5.40629i	0.147965	+	0.256283i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−2.68629			−0.126774			−0.0633870	−	0.997989i	$-0.520190\pi$
$449$	−2.68629			−0.126774			−0.0633870	+	0.997989i	$0.520190\pi$
$450$		0			0
$451$	5.82843	+	10.0951i	0.274450	+	0.475361i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−13.7426	+	1.88064i	−0.644265	+	0.0881656i
$456$		0			0
$457$	16.6213	−	28.7890i	0.777513	−	1.34669i	−0.155859	−	0.987779i	$-0.549815\pi$
$457$	16.6213	−	28.7890i	0.777513	−	1.34669i	0.933371	−	0.358912i	$-0.116852\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−22.7279			−1.05854			−0.529272	−	0.848452i	$-0.677535\pi$
$461$	−22.7279			−1.05854			−0.529272	+	0.848452i	$0.677535\pi$
$462$		0			0
$463$	35.2426			1.63786			0.818932	−	0.573890i	$-0.194566\pi$
$463$	35.2426			1.63786			0.818932	+	0.573890i	$0.194566\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−0.656854	+	1.13770i	−0.0303956	+	0.0526467i	−0.880823	−	0.473446i	$-0.843010\pi$
$467$	−0.656854	+	1.13770i	−0.0303956	+	0.0526467i	0.850427	+	0.526092i	$0.176343\pi$
$468$		0			0
$469$	−10.8995	+	26.6982i	−0.503292	+	1.23281i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	6.29289	+	10.8996i	0.289348	+	0.501165i
$474$		0			0
$475$	−0.171573			−0.00787230
$476$		0			0
$477$		0			0
$478$		0			0
$479$	17.6569	+	30.5826i	0.806762	+	1.39735i	0.915095	+	0.403239i	$0.132116\pi$
$479$	17.6569	+	30.5826i	0.806762	+	1.39735i	−0.108333	+	0.994115i	$0.534551\pi$
$480$		0			0
$481$	−19.8848	+	34.4414i	−0.906668	+	1.57039i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4.24264	−	7.34847i	0.192648	−	0.333677i
$486$		0			0
$487$	11.5503	+	20.0056i	0.523392	+	0.906541i	0.999629	+	0.0272246i	$0.00866694\pi$
$487$	11.5503	+	20.0056i	0.523392	+	0.906541i	−0.476237	+	0.879317i	$0.658000\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−38.1421			−1.72133			−0.860665	−	0.509171i	$-0.829952\pi$
$491$	−38.1421			−1.72133			−0.860665	+	0.509171i	$0.829952\pi$
$492$		0			0
$493$	−24.5563	−	42.5328i	−1.10596	−	1.91558i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4.97918	+	6.42090i	0.223347	+	0.288017i
$498$		0			0
$499$	1.67157	−	2.89525i	0.0748299	−	0.129609i	−0.826182	−	0.563403i	$-0.809492\pi$
$499$	1.67157	−	2.89525i	0.0748299	−	0.129609i	0.901012	+	0.433794i	$0.142825\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−28.1421			−1.25480			−0.627398	−	0.778699i	$-0.715880\pi$
$503$	−28.1421			−1.25480			−0.627398	+	0.778699i	$0.715880\pi$
$504$		0			0
$505$	15.5563			0.692248
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−6.75736	+	11.7041i	−0.299515	+	0.518775i	−0.976025	−	0.217659i	$-0.930158\pi$
$509$	−6.75736	+	11.7041i	−0.299515	+	0.518775i	0.676510	+	0.736433i	$0.263491\pi$
$510$		0			0
$511$	−7.24264	+	17.7408i	−0.320396	+	0.784806i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−4.62132	−	8.00436i	−0.203640	−	0.352714i
$516$		0			0
$517$	5.17157			0.227446
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.07107	−	1.85514i	−0.0469243	−	0.0812753i	0.841609	−	0.540087i	$-0.181609\pi$
$521$	−1.07107	−	1.85514i	−0.0469243	−	0.0812753i	−0.888534	+	0.458812i	$0.848275\pi$
$522$		0			0
$523$	4.27817	−	7.41002i	0.187072	−	0.324017i	−0.757201	−	0.653182i	$-0.773434\pi$
$523$	4.27817	−	7.41002i	0.187072	−	0.324017i	0.944273	+	0.329164i	$0.106767\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	13.5355	−	23.4442i	0.589617	−	1.02125i
$528$		0			0
$529$	−13.5000	−	23.3827i	−0.586957	−	1.01664i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−43.2132			−1.87177
$534$		0			0
$535$	−0.707107	−	1.22474i	−0.0305709	−	0.0529503i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−9.53553	+	2.65962i	−0.410725	+	0.114558i
$540$		0			0
$541$	−18.6421	+	32.2891i	−0.801488	+	1.38822i	0.117149	+	0.993114i	$0.462625\pi$
$541$	−18.6421	+	32.2891i	−0.801488	+	1.38822i	−0.918637	+	0.395104i	$0.870709\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−15.4853			−0.663317
$546$		0			0
$547$	−18.8284			−0.805045			−0.402523	−	0.915410i	$-0.631867\pi$
$547$	−18.8284			−0.805045			−0.402523	+	0.915410i	$0.631867\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	0.778175	−	1.34784i	0.0331514	−	0.0574198i
$552$		0			0
$553$	16.1777	−	2.21386i	0.687944	−	0.0941430i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−7.48528	−	12.9649i	−0.317162	−	0.549340i	0.662733	−	0.748856i	$-0.269396\pi$
$557$	−7.48528	−	12.9649i	−0.317162	−	0.549340i	−0.979895	+	0.199516i	$0.936063\pi$
$558$		0			0
$559$	−46.6569			−1.97337
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−9.48528	−	16.4290i	−0.399757	−	0.692399i	0.593939	−	0.804510i	$-0.297572\pi$
$563$	−9.48528	−	16.4290i	−0.399757	−	0.692399i	−0.993696	+	0.112111i	$0.964239\pi$
$564$		0			0
$565$	4.65685	−	8.06591i	0.195915	−	0.339335i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	14.1213	−	24.4588i	0.591997	−	1.02537i	−0.401967	−	0.915654i	$-0.631673\pi$
$569$	14.1213	−	24.4588i	0.591997	−	1.02537i	0.993963	−	0.109714i	$-0.0349934\pi$
$570$		0			0
$571$	15.7426	+	27.2671i	0.658809	+	1.14109i	0.980924	+	0.194390i	$0.0622728\pi$
$571$	15.7426	+	27.2671i	0.658809	+	1.14109i	−0.322115	+	0.946700i	$0.604394\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−7.07107			−0.294884
$576$		0			0
$577$	12.2071	+	21.1433i	0.508189	+	0.880208i	0.999955	+	0.00948122i	$0.00301801\pi$
$577$	12.2071	+	21.1433i	0.508189	+	0.880208i	−0.491767	+	0.870727i	$0.663649\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	3.63604	+	4.68885i	0.150848	+	0.194526i
$582$		0			0
$583$	0.828427	−	1.43488i	0.0343099	−	0.0594266i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	15.7574			0.650376			0.325188	−	0.945649i	$-0.394572\pi$
$587$	15.7574			0.650376			0.325188	+	0.945649i	$0.394572\pi$
$588$		0			0
$589$	0.857864			0.0353477
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.12132	−	1.94218i	0.0460471	−	0.0797559i	−0.842083	−	0.539348i	$-0.818671\pi$
$593$	1.12132	−	1.94218i	0.0460471	−	0.0797559i	0.888130	+	0.459592i	$0.152004\pi$
$594$		0			0
$595$	−8.77817	−	11.3199i	−0.359870	−	0.464070i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−9.89949	−	17.1464i	−0.404482	−	0.700584i	0.589779	−	0.807565i	$-0.299215\pi$
$599$	−9.89949	−	17.1464i	−0.404482	−	0.700584i	−0.994261	+	0.106981i	$0.965882\pi$
$600$		0			0
$601$	36.1127			1.47307			0.736534	−	0.676401i	$-0.236461\pi$
$601$	36.1127			1.47307			0.736534	+	0.676401i	$0.236461\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−4.50000	−	7.79423i	−0.182951	−	0.316880i
$606$		0			0
$607$	−14.3492	+	24.8536i	−0.582418	+	1.00878i	0.412774	+	0.910833i	$0.364560\pi$
$607$	−14.3492	+	24.8536i	−0.582418	+	1.00878i	−0.995192	+	0.0979438i	$0.968773\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−9.58579	+	16.6031i	−0.387799	+	0.671688i
$612$		0			0
$613$	−10.7279	−	18.5813i	−0.433297	−	0.750492i	0.563858	−	0.825872i	$-0.309316\pi$
$613$	−10.7279	−	18.5813i	−0.433297	−	0.750492i	−0.997155	+	0.0753797i	$0.975983\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	25.5147			1.02718			0.513592	−	0.858035i	$-0.328315\pi$
$617$	25.5147			1.02718			0.513592	+	0.858035i	$0.328315\pi$
$618$		0			0
$619$	−8.74264	−	15.1427i	−0.351396	−	0.608636i	0.635098	−	0.772432i	$-0.280960\pi$
$619$	−8.74264	−	15.1427i	−0.351396	−	0.608636i	−0.986494	+	0.163795i	$0.947626\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−16.3640	+	2.23936i	−0.655608	+	0.0897179i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−41.0711			−1.63761
$630$		0			0
$631$	2.34315			0.0932792			0.0466396	−	0.998912i	$-0.485149\pi$
$631$	2.34315			0.0932792			0.0466396	+	0.998912i	$0.485149\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−3.03553	+	5.25770i	−0.120461	+	0.208645i
$636$		0			0
$637$	9.13604	−	35.5431i	0.361983	−	1.40827i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	12.4350	+	21.5381i	0.491154	+	0.850704i	0.999948	−	0.0101844i	$-0.00324185\pi$
$641$	12.4350	+	21.5381i	0.491154	+	0.850704i	−0.508794	+	0.860888i	$0.669909\pi$
$642$		0			0
$643$	−8.41421			−0.331824			−0.165912	−	0.986141i	$-0.553057\pi$
$643$	−8.41421			−0.331824			−0.165912	+	0.986141i	$0.553057\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−6.05025	−	10.4793i	−0.237860	−	0.411986i	0.722240	−	0.691643i	$-0.243113\pi$
$647$	−6.05025	−	10.4793i	−0.237860	−	0.411986i	−0.960100	+	0.279657i	$0.909779\pi$
$648$		0			0
$649$	10.0711	−	17.4436i	0.395324	−	0.684721i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	0.636039	−	1.10165i	0.0248901	−	0.0431110i	−0.853312	−	0.521401i	$-0.825410\pi$
$653$	0.636039	−	1.10165i	0.0248901	−	0.0431110i	0.878202	+	0.478290i	$0.158743\pi$
$654$		0			0
$655$	5.24264	+	9.08052i	0.204847	+	0.354805i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−4.97056			−0.193626			−0.0968128	−	0.995303i	$-0.530865\pi$
$659$	−4.97056			−0.193626			−0.0968128	+	0.995303i	$0.530865\pi$
$660$		0			0
$661$	3.64214	+	6.30836i	0.141663	+	0.245367i	0.928123	−	0.372274i	$-0.121422\pi$
$661$	3.64214	+	6.30836i	0.141663	+	0.245367i	−0.786460	+	0.617641i	$0.788089\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	0.171573	−	0.420266i	0.00665331	−	0.0162972i
$666$		0			0
$667$	32.0711	−	55.5487i	1.24180	−	2.15085i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−20.9706			−0.809560
$672$		0			0
$673$	10.8995			0.420145			0.210072	−	0.977686i	$-0.432630\pi$
$673$	10.8995			0.420145			0.210072	+	0.977686i	$0.432630\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−21.9203	+	37.9671i	−0.842466	+	1.45919i	0.0453378	+	0.998972i	$0.485564\pi$
$677$	−21.9203	+	37.9671i	−0.842466	+	1.45919i	−0.887804	+	0.460222i	$0.847770\pi$
$678$		0			0
$679$	13.7574	+	17.7408i	0.527959	+	0.680828i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	18.2635	+	31.6332i	0.698832	+	1.21041i	0.968872	+	0.247563i	$0.0796297\pi$
$683$	18.2635	+	31.6332i	0.698832	+	1.21041i	−0.270040	+	0.962849i	$0.587037\pi$
$684$		0			0
$685$	0.928932			0.0354927
$686$		0			0
$687$		0			0
$688$		0			0
$689$	3.07107	+	5.31925i	0.116998	+	0.202647i
$690$		0			0
$691$	−3.22792	+	5.59093i	−0.122796	+	0.212689i	−0.920869	−	0.389872i	$-0.872519\pi$
$691$	−3.22792	+	5.59093i	−0.122796	+	0.212689i	0.798073	+	0.602560i	$0.205853\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.156854	−	0.271680i	0.00594982	−	0.0103054i
$696$		0			0
$697$	−22.3137	−	38.6485i	−0.845192	−	1.46392i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	24.5858			0.928592			0.464296	−	0.885680i	$-0.346307\pi$
$701$	24.5858			0.928592			0.464296	+	0.885680i	$0.346307\pi$
$702$		0			0
$703$	−0.650758	−	1.12715i	−0.0245438	−	0.0425111i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−15.5563	+	38.1051i	−0.585057	+	1.43309i
$708$		0			0
$709$	−10.9289	+	18.9295i	−0.410445	+	0.710911i	−0.994938	−	0.100487i	$-0.967960\pi$
$709$	−10.9289	+	18.9295i	−0.410445	+	0.710911i	0.584494	+	0.811398i	$0.301293\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	35.3553			1.32407
$714$		0			0
$715$	−7.41421			−0.277276
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−6.55635	+	11.3559i	−0.244511	+	0.423505i	−0.961994	−	0.273071i	$-0.911961\pi$
$719$	−6.55635	+	11.3559i	−0.244511	+	0.423505i	0.717483	+	0.696576i	$0.245294\pi$
$720$		0			0
$721$	24.2279	−	3.31552i	0.902295	−	0.123476i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−4.53553	−	7.85578i	−0.168446	−	0.291756i
$726$		0			0
$727$	−39.2426			−1.45543			−0.727714	−	0.685880i	$-0.759417\pi$
$727$	−39.2426			−1.45543			−0.727714	+	0.685880i	$0.759417\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−24.0919	−	41.7284i	−0.891070	−	1.54338i
$732$		0			0
$733$	−25.6213	+	44.3774i	−0.946345	+	1.63912i	−0.193310	+	0.981138i	$0.561922\pi$
$733$	−25.6213	+	44.3774i	−0.946345	+	1.63912i	−0.753035	+	0.657980i	$0.771411\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−7.70711	+	13.3491i	−0.283895	+	0.491720i
$738$		0			0
$739$	16.3284	+	28.2817i	0.600651	+	1.04036i	0.992723	+	0.120423i	$0.0384252\pi$
$739$	16.3284	+	28.2817i	0.600651	+	1.04036i	−0.392072	+	0.919935i	$0.628242\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−6.92893			−0.254198			−0.127099	−	0.991890i	$-0.540567\pi$
$743$	−6.92893			−0.254198			−0.127099	+	0.991890i	$0.540567\pi$
$744$		0			0
$745$	−2.00000	−	3.46410i	−0.0732743	−	0.126915i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	3.70711	−	0.507306i	0.135455	−	0.0185366i
$750$		0			0
$751$	−17.3995	+	30.1368i	−0.634917	+	1.09971i	0.351616	+	0.936144i	$0.385632\pi$
$751$	−17.3995	+	30.1368i	−0.634917	+	1.09971i	−0.986533	+	0.163564i	$0.947701\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−6.48528			−0.236024
$756$		0			0
$757$	−38.0000			−1.38113			−0.690567	−	0.723269i	$-0.742639\pi$
$757$	−38.0000			−1.38113			−0.690567	+	0.723269i	$0.742639\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−13.8492	+	23.9876i	−0.502035	+	0.869550i	0.497963	+	0.867199i	$0.334082\pi$
$761$	−13.8492	+	23.9876i	−0.502035	+	0.869550i	−0.999997	+	0.00235100i	$0.999252\pi$
$762$		0			0
$763$	15.4853	−	37.9310i	0.560605	−	1.37320i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	37.3345	+	64.6653i	1.34807	+	2.33493i
$768$		0			0
$769$	−36.9411			−1.33213			−0.666066	−	0.745893i	$-0.732023\pi$
$769$	−36.9411			−1.33213			−0.666066	+	0.745893i	$0.732023\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	25.3640	+	43.9317i	0.912278	+	1.58011i	0.810838	+	0.585271i	$0.199012\pi$
$773$	25.3640	+	43.9317i	0.912278	+	1.58011i	0.101440	+	0.994842i	$0.467655\pi$
$774$		0			0
$775$	2.50000	−	4.33013i	0.0898027	−	0.155543i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	0.707107	−	1.22474i	0.0253347	−	0.0438810i
$780$		0			0
$781$	2.17157	+	3.76127i	0.0777050	+	0.134589i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	22.4853			0.802534
$786$		0			0
$787$	23.4142	+	40.5546i	0.834627	+	1.44562i	0.894334	+	0.447400i	$0.147650\pi$
$787$	23.4142	+	40.5546i	0.834627	+	1.44562i	−0.0597075	+	0.998216i	$0.519017\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	15.1005	+	19.4728i	0.536912	+	0.692374i
$792$		0			0
$793$	38.8701	−	67.3249i	1.38032	−	2.39078i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−46.5858			−1.65015			−0.825077	−	0.565021i	$-0.808868\pi$
$797$	−46.5858			−1.65015			−0.825077	+	0.565021i	$0.808868\pi$
$798$		0			0
$799$	−19.7990			−0.700438
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−5.12132	+	8.87039i	−0.180727	+	0.313029i
$804$		0			0
$805$	7.07107	−	17.3205i	0.249222	−	0.610468i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	20.6569	+	35.7787i	0.726256	+	1.25791i	0.958455	+	0.285244i	$0.0920748\pi$
$809$	20.6569	+	35.7787i	0.726256	+	1.25791i	−0.232198	+	0.972668i	$0.574592\pi$
$810$		0			0
$811$	45.3137			1.59118			0.795590	−	0.605836i	$-0.207161\pi$
$811$	45.3137			1.59118			0.795590	+	0.605836i	$0.207161\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−11.3137	−	19.5959i	−0.396302	−	0.686415i
$816$		0			0
$817$	0.763456	−	1.32234i	0.0267099	−	0.0462630i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−3.77817	+	6.54399i	−0.131859	+	0.228387i	−0.924393	−	0.381441i	$-0.875428\pi$
$821$	−3.77817	+	6.54399i	−0.131859	+	0.228387i	0.792534	+	0.609828i	$0.208761\pi$
$822$		0			0
$823$	23.4853	+	40.6777i	0.818645	+	1.41794i	0.906680	+	0.421818i	$0.138608\pi$
$823$	23.4853	+	40.6777i	0.818645	+	1.41794i	−0.0880350	+	0.996117i	$0.528059\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	32.1421			1.11769			0.558846	−	0.829272i	$-0.311244\pi$
$827$	32.1421			1.11769			0.558846	+	0.829272i	$0.311244\pi$
$828$		0			0
$829$	−27.6421	−	47.8776i	−0.960051	−	1.66286i	−0.722361	−	0.691516i	$-0.756943\pi$
$829$	−27.6421	−	47.8776i	−0.960051	−	1.66286i	−0.237690	−	0.971341i	$-0.576390\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	36.5061	−	10.1822i	1.26486	−	0.352791i
$834$		0			0
$835$	5.94975	−	10.3053i	0.205900	−	0.356628i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−32.3848			−1.11805			−0.559023	−	0.829152i	$-0.688824\pi$
$839$	−32.3848			−1.11805			−0.559023	+	0.829152i	$0.688824\pi$
$840$		0			0
$841$	53.2843			1.83739
$842$		0			0
$843$		0			0
$844$		0			0
$845$	7.24264	−	12.5446i	0.249154	−	0.431548i
$846$		0			0
$847$	23.5919	−	3.22848i	0.810627	−	0.110932i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−26.8198	−	46.4533i	−0.919371	−	1.59240i
$852$		0			0
$853$	8.69848			0.297830			0.148915	−	0.988850i	$-0.452422\pi$
$853$	8.69848			0.297830			0.148915	+	0.988850i	$0.452422\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−12.2218	−	21.1688i	−0.417490	−	0.723113i	0.578197	−	0.815897i	$-0.303757\pi$
$857$	−12.2218	−	21.1688i	−0.417490	−	0.723113i	−0.995686	+	0.0927842i	$0.970423\pi$
$858$		0			0
$859$	2.51472	−	4.35562i	0.0858011	−	0.148612i	−0.819931	−	0.572462i	$-0.805988\pi$
$859$	2.51472	−	4.35562i	0.0858011	−	0.148612i	0.905732	+	0.423850i	$0.139322\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	19.5858	−	33.9236i	0.666708	−	1.15477i	−0.312111	−	0.950046i	$-0.601036\pi$
$863$	19.5858	−	33.9236i	0.666708	−	1.15477i	0.978819	−	0.204726i	$-0.0656305\pi$
$864$		0			0
$865$	−2.58579	−	4.47871i	−0.0879194	−	0.152281i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	8.72792			0.296074
$870$		0			0
$871$	−28.5711	−	49.4865i	−0.968094	−	1.67679i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.62132	−	2.09077i	−0.0548106	−	0.0706809i
$876$		0			0
$877$	−23.4853	+	40.6777i	−0.793042	+	1.37359i	0.131034	+	0.991378i	$0.458170\pi$
$877$	−23.4853	+	40.6777i	−0.793042	+	1.37359i	−0.924075	+	0.382210i	$0.875163\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	8.28427			0.279104			0.139552	−	0.990215i	$-0.455434\pi$
$881$	8.28427			0.279104			0.139552	+	0.990215i	$0.455434\pi$
$882$		0			0
$883$	−45.5858			−1.53408			−0.767042	−	0.641597i	$-0.778272\pi$
$883$	−45.5858			−1.53408			−0.767042	+	0.641597i	$0.778272\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−25.5061	+	44.1779i	−0.856411	+	1.48335i	0.0189190	+	0.999821i	$0.493978\pi$
$887$	−25.5061	+	44.1779i	−0.856411	+	1.48335i	−0.875330	+	0.483526i	$0.839356\pi$
$888$		0			0
$889$	−9.84315	−	12.6932i	−0.330129	−	0.425717i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.313708	−	0.543359i	−0.0104979	−	0.0181828i
$894$		0			0
$895$	19.6569			0.657056
$896$		0			0
$897$		0			0
$898$		0			0
$899$	22.6777	+	39.2789i	0.756343	+	1.31002i
$900$		0			0
$901$	−3.17157	+	5.49333i	−0.105660	+	0.183009i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−4.15685	+	7.19988i	−0.138179	+	0.239332i
$906$		0			0
$907$	24.1066	+	41.7539i	0.800447	+	1.38641i	0.919322	+	0.393505i	$0.128738\pi$
$907$	24.1066	+	41.7539i	0.800447	+	1.38641i	−0.118876	+	0.992909i	$0.537929\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−31.2132			−1.03414			−0.517070	−	0.855943i	$-0.672977\pi$
$911$	−31.2132			−1.03414			−0.517070	+	0.855943i	$0.672977\pi$
$912$		0			0
$913$	1.58579	+	2.74666i	0.0524819	+	0.0909013i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−27.4853	+	3.76127i	−0.907644	+	0.124208i
$918$		0			0
$919$	18.2279	−	31.5717i	0.601284	−	1.04145i	−0.391343	−	0.920245i	$-0.627990\pi$
$919$	18.2279	−	31.5717i	0.601284	−	1.04145i	0.992627	−	0.121209i	$-0.0386772\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−16.1005			−0.529955
$924$		0			0
$925$	−7.58579			−0.249419
$926$		0			0
$927$		0			0
$928$		0			0
$929$	4.02082	−	6.96426i	0.131919	−	0.228490i	−0.792497	−	0.609875i	$-0.791220\pi$
$929$	4.02082	−	6.96426i	0.131919	−	0.228490i	0.924416	+	0.381385i	$0.124553\pi$
$930$		0			0
$931$	0.857864	+	0.840532i	0.0281154	+	0.0275473i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−3.82843	−	6.63103i	−0.125203	−	0.216858i
$936$		0			0
$937$	5.38478			0.175913			0.0879565	−	0.996124i	$-0.471966\pi$
$937$	5.38478			0.175913			0.0879565	+	0.996124i	$0.471966\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	14.0919	+	24.4079i	0.459382	+	0.795673i	0.998928	−	0.0462826i	$-0.0147375\pi$
$941$	14.0919	+	24.4079i	0.459382	+	0.795673i	−0.539546	+	0.841956i	$0.681404\pi$
$942$		0			0
$943$	29.1421	−	50.4757i	0.948999	−	1.64371i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.56497	−	2.71061i	0.0508547	−	0.0880830i	−0.839477	−	0.543395i	$-0.817139\pi$
$947$	1.56497	−	2.71061i	0.0508547	−	0.0880830i	0.890332	+	0.455312i	$0.150472\pi$
$948$		0			0
$949$	−18.9853	−	32.8835i	−0.616288	−	1.06744i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−30.1421			−0.976400			−0.488200	−	0.872732i	$-0.662346\pi$
$953$	−30.1421			−0.976400			−0.488200	+	0.872732i	$0.662346\pi$
$954$		0			0
$955$	−2.17157	−	3.76127i	−0.0702704	−	0.121712i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−0.928932	+	2.27541i	−0.0299968	+	0.0734768i
$960$		0			0
$961$	3.00000	−	5.19615i	0.0967742	−	0.167618i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−9.58579			−0.308577
$966$		0			0
$967$	−18.2721			−0.587590			−0.293795	−	0.955868i	$-0.594918\pi$
$967$	−18.2721			−0.587590			−0.293795	+	0.955868i	$0.594918\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	14.1421	−	24.4949i	0.453843	−	0.786079i	−0.544778	−	0.838580i	$-0.683386\pi$
$971$	14.1421	−	24.4949i	0.453843	−	0.786079i	0.998621	+	0.0525016i	$0.0167195\pi$
$972$		0			0
$973$	0.508622	+	0.655892i	0.0163057	+	0.0210269i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	4.77817	+	8.27604i	0.152867	+	0.264774i	0.932280	−	0.361736i	$-0.117816\pi$
$977$	4.77817	+	8.27604i	0.152867	+	0.264774i	−0.779413	+	0.626510i	$0.784483\pi$
$978$		0			0
$979$	−8.82843			−0.282158
$980$		0			0
$981$		0			0
$982$		0			0
$983$	0.807612	+	1.39882i	0.0257588	+	0.0446156i	0.878617	−	0.477526i	$-0.158466\pi$
$983$	0.807612	+	1.39882i	0.0257588	+	0.0446156i	−0.852859	+	0.522142i	$0.825133\pi$
$984$		0			0
$985$	−12.0208	+	20.8207i	−0.383015	+	0.663401i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	31.4645	−	54.4981i	1.00051	−	1.73294i
$990$		0			0
$991$	26.5711	+	46.0224i	0.844058	+	1.46195i	0.886437	+	0.462849i	$0.153173\pi$
$991$	26.5711	+	46.0224i	0.844058	+	1.46195i	−0.0423792	+	0.999102i	$0.513494\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	6.48528			0.205597
$996$		0			0
$997$	−27.6630	−	47.9136i	−0.876094	−	1.51744i	−0.855592	−	0.517650i	$-0.826807\pi$
$997$	−27.6630	−	47.9136i	−0.876094	−	1.51744i	−0.0205021	−	0.999790i	$-0.506526\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2520.2.bi.l.1801.2		4
3.2	odd	2		840.2.bg.g.121.2	✓	4
7.4	even	3	inner	2520.2.bi.l.361.2		4
12.11	even	2		1680.2.bg.r.961.1		4
21.2	odd	6		5880.2.a.bs.1.2		2
21.5	even	6		5880.2.a.bm.1.2		2
21.11	odd	6		840.2.bg.g.361.2	yes	4
84.11	even	6		1680.2.bg.r.1201.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bg.g.121.2	✓	4	3.2	odd	2
840.2.bg.g.361.2	yes	4	21.11	odd	6
1680.2.bg.r.961.1		4	12.11	even	2
1680.2.bg.r.1201.1		4	84.11	even	6
2520.2.bi.l.361.2		4	7.4	even	3	inner
2520.2.bi.l.1801.2		4	1.1	even	1	trivial
5880.2.a.bm.1.2		2	21.5	even	6
5880.2.a.bs.1.2		2	21.2	odd	6

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:	\( N \)	\(=\)	\( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2520.bi (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{5} +(1.62132 + 2.09077i) q^{7} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{5} +(1.62132 + 2.09077i) q^{7} +(0.707107 + 1.22474i) q^{11} -5.24264 q^{13} +(-2.70711 - 4.68885i) q^{17} +(0.0857864 - 0.148586i) q^{19} +(3.53553 - 6.12372i) q^{23} +(-0.500000 - 0.866025i) q^{25} +9.07107 q^{29} +(2.50000 + 4.33013i) q^{31} +(2.62132 - 0.358719i) q^{35} +(3.79289 - 6.56948i) q^{37} +8.24264 q^{41} +8.89949 q^{43} +(1.82843 - 3.16693i) q^{47} +(-1.74264 + 6.77962i) q^{49} +(-0.585786 - 1.01461i) q^{53} +1.41421 q^{55} +(-7.12132 - 12.3345i) q^{59} +(-7.41421 + 12.8418i) q^{61} +(-2.62132 + 4.54026i) q^{65} +(5.44975 + 9.43924i) q^{67} +3.07107 q^{71} +(3.62132 + 6.27231i) q^{73} +(-1.41421 + 3.46410i) q^{77} +(3.08579 - 5.34474i) q^{79} +2.24264 q^{83} -5.41421 q^{85} +(-3.12132 + 5.40629i) q^{89} +(-8.50000 - 10.9612i) q^{91} +(-0.0857864 - 0.148586i) q^{95} +8.48528 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{5} - 2 q^{7}+O(q^{10}) \) 4 * q + 2 * q^5 - 2 * q^7	\( 4 q + 2 q^{5} - 2 q^{7} - 4 q^{13} - 8 q^{17} + 6 q^{19} - 2 q^{25} + 8 q^{29} + 10 q^{31} + 2 q^{35} + 18 q^{37} + 16 q^{41} - 4 q^{43} - 4 q^{47} + 10 q^{49} - 8 q^{53} - 20 q^{59} - 24 q^{61} - 2 q^{65} + 2 q^{67} - 16 q^{71} + 6 q^{73} + 18 q^{79} - 8 q^{83} - 16 q^{85} - 4 q^{89} - 34 q^{91} - 6 q^{95}+O(q^{100}) \) 4 * q + 2 * q^5 - 2 * q^7 - 4 * q^13 - 8 * q^17 + 6 * q^19 - 2 * q^25 + 8 * q^29 + 10 * q^31 + 2 * q^35 + 18 * q^37 + 16 * q^41 - 4 * q^43 - 4 * q^47 + 10 * q^49 - 8 * q^53 - 20 * q^59 - 24 * q^61 - 2 * q^65 + 2 * q^67 - 16 * q^71 + 6 * q^73 + 18 * q^79 - 8 * q^83 - 16 * q^85 - 4 * q^89 - 34 * q^91 - 6 * q^95

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