LMFDB - Embedded newform 2520.2.bi.l.1801.1

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			1801.1
Root			$-0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	2520.1801
Dual form			2520.2.bi.l.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{5} +(-2.62132 - 0.358719i) q^{7} +O(q^{10})$	$q+(0.500000 - 0.866025i) q^{5} +(-2.62132 - 0.358719i) q^{7} +(-0.707107 - 1.22474i) q^{11} +3.24264 q^{13} +(-1.29289 - 2.23936i) q^{17} +(2.91421 - 5.04757i) q^{19} +(-3.53553 + 6.12372i) q^{23} +(-0.500000 - 0.866025i) q^{25} -5.07107 q^{29} +(2.50000 + 4.33013i) q^{31} +(-1.62132 + 2.09077i) q^{35} +(5.20711 - 9.01897i) q^{37} -0.242641 q^{41} -10.8995 q^{43} +(-3.82843 + 6.63103i) q^{47} +(6.74264 + 1.88064i) q^{49} +(-3.41421 - 5.91359i) q^{53} -1.41421 q^{55} +(-2.87868 - 4.98602i) q^{59} +(-4.58579 + 7.94282i) q^{61} +(1.62132 - 2.80821i) q^{65} +(-4.44975 - 7.70719i) q^{67} -11.0711 q^{71} +(-0.621320 - 1.07616i) q^{73} +(1.41421 + 3.46410i) q^{77} +(5.91421 - 10.2437i) q^{79} -6.24264 q^{83} -2.58579 q^{85} +(1.12132 - 1.94218i) q^{89} +(-8.50000 - 1.16320i) q^{91} +(-2.91421 - 5.04757i) q^{95} -8.48528 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	−2.62132	−	0.358719i	−0.990766	−	0.135583i
$7$	−2.62132	−	0.358719i	−0.990766	−	0.135583i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.707107	−	1.22474i	−0.213201	−	0.369274i	0.739514	−	0.673141i	$-0.235055\pi$
$11$	−0.707107	−	1.22474i	−0.213201	−	0.369274i	−0.952714	+	0.303867i	$0.901722\pi$
$12$		0			0
$13$	3.24264			0.899347			0.449673	−	0.893193i	$-0.351540\pi$
$13$	3.24264			0.899347			0.449673	+	0.893193i	$0.351540\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.29289	−	2.23936i	−0.313573	−	0.543124i	0.665560	−	0.746344i	$-0.268193\pi$
$17$	−1.29289	−	2.23936i	−0.313573	−	0.543124i	−0.979133	+	0.203220i	$0.934859\pi$
$18$		0			0
$19$	2.91421	−	5.04757i	0.668566	−	1.15799i	−0.309739	−	0.950822i	$-0.600242\pi$
$19$	2.91421	−	5.04757i	0.668566	−	1.15799i	0.978305	−	0.207169i	$-0.0664251\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.53553	+	6.12372i	−0.737210	+	1.27688i	0.216537	+	0.976274i	$0.430524\pi$
$23$	−3.53553	+	6.12372i	−0.737210	+	1.27688i	−0.953747	+	0.300610i	$0.902810\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−5.07107			−0.941674			−0.470837	−	0.882220i	$-0.656048\pi$
$29$	−5.07107			−0.941674			−0.470837	+	0.882220i	$0.656048\pi$
$30$		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
$35$	−1.62132	+	2.09077i	−0.274053	+	0.353405i
$36$		0			0
$37$	5.20711	−	9.01897i	0.856043	−	1.48271i	−0.0196309	−	0.999807i	$-0.506249\pi$
$37$	5.20711	−	9.01897i	0.856043	−	1.48271i	0.875674	−	0.482903i	$-0.160418\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−0.242641			−0.0378941			−0.0189471	−	0.999820i	$-0.506031\pi$
$41$	−0.242641			−0.0378941			−0.0189471	+	0.999820i	$0.506031\pi$
$42$		0			0
$43$	−10.8995			−1.66216			−0.831079	−	0.556155i	$-0.812276\pi$
$43$	−10.8995			−1.66216			−0.831079	+	0.556155i	$0.812276\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.82843	+	6.63103i	−0.558433	+	0.967235i	0.439194	+	0.898392i	$0.355264\pi$
$47$	−3.82843	+	6.63103i	−0.558433	+	0.967235i	−0.997628	+	0.0688429i	$0.978069\pi$
$48$		0			0
$49$	6.74264	+	1.88064i	0.963234	+	0.268662i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3.41421	−	5.91359i	−0.468978	−	0.812294i	0.530393	−	0.847752i	$-0.322044\pi$
$53$	−3.41421	−	5.91359i	−0.468978	−	0.812294i	−0.999371	+	0.0354577i	$0.988711\pi$
$54$		0			0
$55$	−1.41421			−0.190693
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.87868	−	4.98602i	−0.374772	−	0.649124i	0.615521	−	0.788121i	$-0.288946\pi$
$59$	−2.87868	−	4.98602i	−0.374772	−	0.649124i	−0.990293	+	0.138996i	$0.955612\pi$
$60$		0			0
$61$	−4.58579	+	7.94282i	−0.587150	+	1.01697i	0.407454	+	0.913226i	$0.366417\pi$
$61$	−4.58579	+	7.94282i	−0.587150	+	1.01697i	−0.994604	+	0.103747i	$0.966917\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.62132	−	2.80821i	0.201100	−	0.348315i
$66$		0			0
$67$	−4.44975	−	7.70719i	−0.543623	−	0.941583i	−0.998692	−	0.0511268i	$-0.983719\pi$
$67$	−4.44975	−	7.70719i	−0.543623	−	0.941583i	0.455069	−	0.890456i	$-0.349615\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−11.0711			−1.31389			−0.656947	−	0.753937i	$-0.728152\pi$
$71$	−11.0711			−1.31389			−0.656947	+	0.753937i	$0.728152\pi$
$72$		0			0
$73$	−0.621320	−	1.07616i	−0.0727200	−	0.125955i	0.827372	−	0.561654i	$-0.189835\pi$
$73$	−0.621320	−	1.07616i	−0.0727200	−	0.125955i	−0.900093	+	0.435699i	$0.856501\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.41421	+	3.46410i	0.161165	+	0.394771i
$78$		0			0
$79$	5.91421	−	10.2437i	0.665401	−	1.15251i	−0.313775	−	0.949497i	$-0.601594\pi$
$79$	5.91421	−	10.2437i	0.665401	−	1.15251i	0.979176	−	0.203011i	$-0.0650728\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−6.24264			−0.685219			−0.342609	−	0.939478i	$-0.611311\pi$
$83$	−6.24264			−0.685219			−0.342609	+	0.939478i	$0.611311\pi$
$84$		0			0
$85$	−2.58579			−0.280468
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.12132	−	1.94218i	0.118860	−	0.205871i	−0.800456	−	0.599391i	$-0.795409\pi$
$89$	1.12132	−	1.94218i	0.118860	−	0.205871i	0.919316	+	0.393520i	$0.128743\pi$
$90$		0			0
$91$	−8.50000	−	1.16320i	−0.891042	−	0.121936i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.91421	−	5.04757i	−0.298992	−	0.517869i
$96$		0			0
$97$	−8.48528			−0.861550			−0.430775	−	0.902459i	$-0.641760\pi$
$97$	−8.48528			−0.861550			−0.430775	+	0.902459i	$0.641760\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−7.77817	−	13.4722i	−0.773957	−	1.34053i	−0.935379	−	0.353648i	$-0.884941\pi$
$101$	−7.77817	−	13.4722i	−0.773957	−	1.34053i	0.161421	−	0.986886i	$-0.448392\pi$
$102$		0			0
$103$	0.378680	−	0.655892i	0.0373124	−	0.0646270i	−0.846766	−	0.531965i	$-0.821454\pi$
$103$	0.378680	−	0.655892i	0.0373124	−	0.0646270i	0.884079	+	0.467338i	$0.154787\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.707107	+	1.22474i	−0.0683586	+	0.118401i	−0.898179	−	0.439630i	$-0.855110\pi$
$107$	−0.707107	+	1.22474i	−0.0683586	+	0.118401i	0.829820	+	0.558031i	$0.188443\pi$
$108$		0			0
$109$	0.742641	+	1.28629i	0.0711321	+	0.123204i	0.899398	−	0.437131i	$-0.144005\pi$
$109$	0.742641	+	1.28629i	0.0711321	+	0.123204i	−0.828266	+	0.560336i	$0.810672\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−13.3137			−1.25245			−0.626224	−	0.779643i	$-0.715401\pi$
$113$	−13.3137			−1.25245			−0.626224	+	0.779643i	$0.715401\pi$
$114$		0			0
$115$	3.53553	+	6.12372i	0.329690	+	0.571040i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.58579	+	6.33386i	0.237039	+	0.580624i
$120$		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
$127$	8.07107			0.716191			0.358096	−	0.933685i	$-0.383426\pi$
$127$	8.07107			0.716191			0.358096	+	0.933685i	$0.383426\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	3.24264	−	5.61642i	0.283311	−	0.490709i	−0.688887	−	0.724868i	$-0.741901\pi$
$131$	3.24264	−	5.61642i	0.283311	−	0.490709i	0.972198	+	0.234160i	$0.0752339\pi$
$132$		0			0
$133$	−9.44975	+	12.1859i	−0.819397	+	1.05665i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	7.53553	+	13.0519i	0.643804	+	1.11510i	0.984576	+	0.174956i	$0.0559782\pi$
$137$	7.53553	+	13.0519i	0.643804	+	1.11510i	−0.340772	+	0.940146i	$0.610688\pi$
$138$		0			0
$139$	−22.3137			−1.89262			−0.946312	−	0.323255i	$-0.895223\pi$
$139$	−22.3137			−1.89262			−0.946312	+	0.323255i	$0.895223\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−2.29289	−	3.97141i	−0.191741	−	0.332106i
$144$		0			0
$145$	−2.53553	+	4.39167i	−0.210565	+	0.364709i
$146$		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
$151$	5.24264	+	9.08052i	0.426640	+	0.738962i	0.996572	−	0.0827296i	$-0.0263638\pi$
$151$	5.24264	+	9.08052i	0.426640	+	0.738962i	−0.569932	+	0.821692i	$0.693030\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	5.00000			0.401610
$156$		0			0
$157$	2.75736	+	4.77589i	0.220061	+	0.381157i	0.954826	−	0.297164i	$-0.0960409\pi$
$157$	2.75736	+	4.77589i	0.220061	+	0.381157i	−0.734765	+	0.678322i	$0.762708\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	11.4645	−	14.7840i	0.903527	−	1.16514i
$162$		0			0
$163$	−11.3137	+	19.5959i	−0.886158	+	1.53487i	−0.0417775	+	0.999127i	$0.513302\pi$
$163$	−11.3137	+	19.5959i	−0.886158	+	1.53487i	−0.844381	+	0.535744i	$0.820031\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−7.89949			−0.611281			−0.305641	−	0.952147i	$-0.598871\pi$
$167$	−7.89949			−0.611281			−0.305641	+	0.952147i	$0.598871\pi$
$168$		0			0
$169$	−2.48528			−0.191175
$170$		0			0
$171$		0			0
$172$		0			0
$173$	5.41421	−	9.37769i	0.411635	−	0.712973i	−0.583434	−	0.812161i	$-0.698291\pi$
$173$	5.41421	−	9.37769i	0.411635	−	0.712973i	0.995069	+	0.0991880i	$0.0316245\pi$
$174$		0			0
$175$	1.00000	+	2.44949i	0.0755929	+	0.185164i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	4.17157	+	7.22538i	0.311798	+	0.540050i	0.978752	−	0.205049i	$-0.0657354\pi$
$179$	4.17157	+	7.22538i	0.311798	+	0.540050i	−0.666954	+	0.745099i	$0.732402\pi$
$180$		0			0
$181$	14.3137			1.06393			0.531965	−	0.846766i	$-0.321454\pi$
$181$	14.3137			1.06393			0.531965	+	0.846766i	$0.321454\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−5.20711	−	9.01897i	−0.382834	−	0.663088i
$186$		0			0
$187$	−1.82843	+	3.16693i	−0.133708	+	0.231589i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	7.82843	−	13.5592i	0.566445	−	0.981112i	−0.430469	−	0.902606i	$-0.641652\pi$
$191$	7.82843	−	13.5592i	0.566445	−	0.981112i	0.996914	−	0.0785061i	$-0.0250150\pi$
$192$		0			0
$193$	−6.20711	−	10.7510i	−0.446797	−	0.773876i	0.551378	−	0.834255i	$-0.314102\pi$
$193$	−6.20711	−	10.7510i	−0.446797	−	0.773876i	−0.998175	+	0.0603798i	$0.980769\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	24.0416			1.71290			0.856448	−	0.516234i	$-0.172666\pi$
$197$	24.0416			1.71290			0.856448	+	0.516234i	$0.172666\pi$
$198$		0			0
$199$	−5.24264	−	9.08052i	−0.371641	−	0.643701i	0.618177	−	0.786039i	$-0.287871\pi$
$199$	−5.24264	−	9.08052i	−0.371641	−	0.643701i	−0.989818	+	0.142338i	$0.954538\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	13.2929	+	1.81909i	0.932978	+	0.127675i
$204$		0			0
$205$	−0.121320	+	0.210133i	−0.00847338	+	0.0146763i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−8.24264			−0.570155
$210$		0			0
$211$	0.828427			0.0570313			0.0285156	−	0.999593i	$-0.490922\pi$
$211$	0.828427			0.0570313			0.0285156	+	0.999593i	$0.490922\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−5.44975	+	9.43924i	−0.371670	+	0.643751i
$216$		0			0
$217$	−5.00000	−	12.2474i	−0.339422	−	0.831411i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−4.19239	−	7.26143i	−0.282011	−	0.488457i
$222$		0			0
$223$	−22.1421			−1.48275			−0.741374	−	0.671093i	$-0.765825\pi$
$223$	−22.1421			−1.48275			−0.741374	+	0.671093i	$0.765825\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−14.5355	−	25.1763i	−0.964757	−	1.67101i	−0.710266	−	0.703934i	$-0.751425\pi$
$227$	−14.5355	−	25.1763i	−0.964757	−	1.67101i	−0.254491	−	0.967075i	$-0.581908\pi$
$228$		0			0
$229$	7.98528	−	13.8309i	0.527682	−	0.913972i	−0.471797	−	0.881707i	$-0.656395\pi$
$229$	7.98528	−	13.8309i	0.527682	−	0.913972i	0.999479	−	0.0322653i	$-0.0102721\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−11.2426	+	19.4728i	−0.736530	+	1.27571i	0.217519	+	0.976056i	$0.430204\pi$
$233$	−11.2426	+	19.4728i	−0.736530	+	1.27571i	−0.954049	+	0.299651i	$0.903130\pi$
$234$		0			0
$235$	3.82843	+	6.63103i	0.249739	+	0.432561i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−6.68629			−0.432500			−0.216250	−	0.976338i	$-0.569383\pi$
$239$	−6.68629			−0.432500			−0.216250	+	0.976338i	$0.569383\pi$
$240$		0			0
$241$	0.828427	+	1.43488i	0.0533637	+	0.0924286i	0.891473	−	0.453073i	$-0.149672\pi$
$241$	0.828427	+	1.43488i	0.0533637	+	0.0924286i	−0.838110	+	0.545502i	$0.816339\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	5.00000	−	4.89898i	0.319438	−	0.312984i
$246$		0			0
$247$	9.44975	−	16.3674i	0.601273	−	1.04144i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	19.8995			1.25604			0.628022	−	0.778195i	$-0.283865\pi$
$251$	19.8995			1.25604			0.628022	+	0.778195i	$0.283865\pi$
$252$		0			0
$253$	10.0000			0.628695
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.77817	+	11.7401i	−0.422811	+	0.732330i	−0.996213	−	0.0869440i	$-0.972290\pi$
$257$	−6.77817	+	11.7401i	−0.422811	+	0.732330i	0.573402	+	0.819274i	$0.305623\pi$
$258$		0			0
$259$	−16.8848	+	21.7737i	−1.04917	+	1.35295i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	9.89949	+	17.1464i	0.610429	+	1.05729i	0.991168	+	0.132612i	$0.0423363\pi$
$263$	9.89949	+	17.1464i	0.610429	+	1.05729i	−0.380739	+	0.924683i	$0.624330\pi$
$264$		0			0
$265$	−6.82843			−0.419467
$266$		0			0
$267$		0			0
$268$		0			0
$269$	3.24264	+	5.61642i	0.197707	+	0.342439i	0.947785	−	0.318911i	$-0.103317\pi$
$269$	3.24264	+	5.61642i	0.197707	+	0.342439i	−0.750077	+	0.661350i	$0.769984\pi$
$270$		0			0
$271$	−1.24264	+	2.15232i	−0.0754850	+	0.130744i	−0.901297	−	0.433201i	$-0.857384\pi$
$271$	−1.24264	+	2.15232i	−0.0754850	+	0.130744i	0.825812	+	0.563945i	$0.190717\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.707107	+	1.22474i	−0.0426401	+	0.0738549i
$276$		0			0
$277$	−11.6924	−	20.2518i	−0.702528	−	1.21681i	−0.967576	−	0.252578i	$-0.918721\pi$
$277$	−11.6924	−	20.2518i	−0.702528	−	1.21681i	0.265049	−	0.964235i	$-0.414612\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−2.34315			−0.139780			−0.0698902	−	0.997555i	$-0.522265\pi$
$281$	−2.34315			−0.139780			−0.0698902	+	0.997555i	$0.522265\pi$
$282$		0			0
$283$	0.863961	+	1.49642i	0.0513572	+	0.0889532i	0.890561	−	0.454864i	$-0.150312\pi$
$283$	0.863961	+	1.49642i	0.0513572	+	0.0889532i	−0.839204	+	0.543817i	$0.816979\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.636039	+	0.0870399i	0.0375442	+	0.00513781i
$288$		0			0
$289$	5.15685	−	8.93193i	0.303344	−	0.525408i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.65685			0.0967945			0.0483972	−	0.998828i	$-0.484589\pi$
$293$	1.65685			0.0967945			0.0483972	+	0.998828i	$0.484589\pi$
$294$		0			0
$295$	−5.75736			−0.335206
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−11.4645	+	19.8570i	−0.663007	+	1.14836i
$300$		0			0
$301$	28.5711	+	3.90986i	1.64681	+	0.225361i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	4.58579	+	7.94282i	0.262581	+	0.454804i
$306$		0			0
$307$	6.07107			0.346494			0.173247	−	0.984878i	$-0.444574\pi$
$307$	6.07107			0.346494			0.173247	+	0.984878i	$0.444574\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−10.1213	−	17.5306i	−0.573927	−	0.994071i	−0.996157	−	0.0875826i	$-0.972086\pi$
$311$	−10.1213	−	17.5306i	−0.573927	−	0.994071i	0.422230	−	0.906489i	$-0.361248\pi$
$312$		0			0
$313$	−5.03553	+	8.72180i	−0.284625	+	0.492985i	−0.972518	−	0.232827i	$-0.925202\pi$
$313$	−5.03553	+	8.72180i	−0.284625	+	0.492985i	0.687893	+	0.725812i	$0.258536\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−5.29289	+	9.16756i	−0.297279	+	0.514901i	−0.975512	−	0.219945i	$-0.929412\pi$
$317$	−5.29289	+	9.16756i	−0.297279	+	0.514901i	0.678234	+	0.734846i	$0.262746\pi$
$318$		0			0
$319$	3.58579	+	6.21076i	0.200765	+	0.347736i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−15.0711			−0.838577
$324$		0			0
$325$	−1.62132	−	2.80821i	−0.0899347	−	0.155771i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	12.4142	−	16.0087i	0.684418	−	0.882589i
$330$		0			0
$331$	−1.08579	+	1.88064i	−0.0596802	+	0.103369i	−0.894322	−	0.447424i	$-0.852341\pi$
$331$	−1.08579	+	1.88064i	−0.0596802	+	0.103369i	0.834642	+	0.550793i	$0.185675\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−8.89949			−0.486231
$336$		0			0
$337$	8.89949			0.484786			0.242393	−	0.970178i	$-0.422068\pi$
$337$	8.89949			0.484786			0.242393	+	0.970178i	$0.422068\pi$
$338$		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
$347$	−4.82843	−	8.36308i	−0.259204	−	0.448954i	0.706825	−	0.707388i	$-0.250127\pi$
$347$	−4.82843	−	8.36308i	−0.259204	−	0.448954i	−0.966029	+	0.258435i	$0.916793\pi$
$348$		0			0
$349$	9.31371			0.498551			0.249276	−	0.968433i	$-0.419807\pi$
$349$	9.31371			0.498551			0.249276	+	0.968433i	$0.419807\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−6.87868	−	11.9142i	−0.366115	−	0.634130i	0.622839	−	0.782350i	$-0.285979\pi$
$353$	−6.87868	−	11.9142i	−0.366115	−	0.634130i	−0.988954	+	0.148220i	$0.952646\pi$
$354$		0			0
$355$	−5.53553	+	9.58783i	−0.293796	+	0.508869i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	13.1213	−	22.7268i	0.692517	−	1.19947i	−0.278494	−	0.960438i	$-0.589835\pi$
$359$	13.1213	−	22.7268i	0.692517	−	1.19947i	0.971011	−	0.239036i	$-0.0768315\pi$
$360$		0			0
$361$	−7.48528	−	12.9649i	−0.393962	−	0.682363i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1.24264			−0.0650428
$366$		0			0
$367$	9.20711	+	15.9472i	0.480607	+	0.832436i	0.999752	−	0.0222501i	$-0.00708301\pi$
$367$	9.20711	+	15.9472i	0.480607	+	0.832436i	−0.519145	+	0.854686i	$0.673750\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	6.82843	+	16.7262i	0.354514	+	0.868379i
$372$		0			0
$373$	14.4497	−	25.0277i	0.748180	−	1.29589i	−0.200515	−	0.979691i	$-0.564261\pi$
$373$	14.4497	−	25.0277i	0.748180	−	1.29589i	0.948694	−	0.316194i	$-0.102405\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−16.4437			−0.846891
$378$		0			0
$379$	−2.31371			−0.118847			−0.0594236	−	0.998233i	$-0.518926\pi$
$379$	−2.31371			−0.118847			−0.0594236	+	0.998233i	$0.518926\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−15.8995	+	27.5387i	−0.812426	+	1.40716i	0.0987351	+	0.995114i	$0.468520\pi$
$383$	−15.8995	+	27.5387i	−0.812426	+	1.40716i	−0.911161	+	0.412050i	$0.864813\pi$
$384$		0			0
$385$	3.70711	+	0.507306i	0.188932	+	0.0258547i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	14.6066	+	25.2994i	0.740584	+	1.28273i	0.952230	+	0.305383i	$0.0987844\pi$
$389$	14.6066	+	25.2994i	0.740584	+	1.28273i	−0.211646	+	0.977346i	$0.567882\pi$
$390$		0			0
$391$	18.2843			0.924675
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−5.91421	−	10.2437i	−0.297576	−	0.515417i
$396$		0			0
$397$	−4.79289	+	8.30153i	−0.240548	+	0.416642i	−0.960871	−	0.276998i	$-0.910661\pi$
$397$	−4.79289	+	8.30153i	−0.240548	+	0.416642i	0.720322	+	0.693640i	$0.243994\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	11.0711	−	19.1757i	0.552863	−	0.957586i	−0.445204	−	0.895429i	$-0.646869\pi$
$401$	11.0711	−	19.1757i	0.552863	−	0.957586i	0.998066	−	0.0621570i	$-0.0197980\pi$
$402$		0			0
$403$	8.10660	+	14.0410i	0.403819	+	0.699434i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−14.7279			−0.730036
$408$		0			0
$409$	8.67157	+	15.0196i	0.428782	+	0.742672i	0.996765	−	0.0803682i	$-0.0256096\pi$
$409$	8.67157	+	15.0196i	0.428782	+	0.742672i	−0.567984	+	0.823040i	$0.692276\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	5.75736	+	14.1026i	0.283301	+	0.693943i
$414$		0			0
$415$	−3.12132	+	5.40629i	−0.153220	+	0.265384i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	19.1716			0.936593			0.468296	−	0.883571i	$-0.344868\pi$
$419$	19.1716			0.936593			0.468296	+	0.883571i	$0.344868\pi$
$420$		0			0
$421$	24.4558			1.19190			0.595952	−	0.803020i	$-0.296775\pi$
$421$	24.4558			1.19190			0.595952	+	0.803020i	$0.296775\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.29289	+	2.23936i	−0.0627145	+	0.108625i
$426$		0			0
$427$	14.8701	−	19.1757i	0.719613	−	0.927975i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	12.4142	+	21.5020i	0.597972	+	1.03572i	0.993120	+	0.117100i	$0.0373598\pi$
$431$	12.4142	+	21.5020i	0.597972	+	1.03572i	−0.395149	+	0.918617i	$0.629307\pi$
$432$		0			0
$433$	−20.4142			−0.981044			−0.490522	−	0.871429i	$-0.663194\pi$
$433$	−20.4142			−0.981044			−0.490522	+	0.871429i	$0.663194\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	20.6066	+	35.6917i	0.985747	+	1.70736i
$438$		0			0
$439$	6.17157	−	10.6895i	0.294553	−	0.510181i	−0.680328	−	0.732908i	$-0.738163\pi$
$439$	6.17157	−	10.6895i	0.294553	−	0.510181i	0.974881	+	0.222727i	$0.0714959\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	16.2426	−	28.1331i	0.771711	−	1.33664i	−0.164913	−	0.986308i	$-0.552734\pi$
$443$	16.2426	−	28.1331i	0.771711	−	1.33664i	0.936625	−	0.350335i	$-0.113932\pi$
$444$		0			0
$445$	−1.12132	−	1.94218i	−0.0531557	−	0.0920683i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−25.3137			−1.19463			−0.597314	−	0.802008i	$-0.703765\pi$
$449$	−25.3137			−1.19463			−0.597314	+	0.802008i	$0.703765\pi$
$450$		0			0
$451$	0.171573	+	0.297173i	0.00807905	+	0.0139933i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−5.25736	+	6.77962i	−0.246469	+	0.317833i
$456$		0			0
$457$	12.3787	−	21.4405i	0.579050	−	1.00294i	−0.416538	−	0.909118i	$-0.636757\pi$
$457$	12.3787	−	21.4405i	0.579050	−	1.00294i	0.995589	−	0.0938263i	$-0.0299098\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	2.72792			0.127052			0.0635260	−	0.997980i	$-0.479765\pi$
$461$	2.72792			0.127052			0.0635260	+	0.997980i	$0.479765\pi$
$462$		0			0
$463$	26.7574			1.24352			0.621760	−	0.783208i	$-0.286418\pi$
$463$	26.7574			1.24352			0.621760	+	0.783208i	$0.286418\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	10.6569	−	18.4582i	0.493140	−	0.854144i	−0.506828	−	0.862047i	$-0.669182\pi$
$467$	10.6569	−	18.4582i	0.493140	−	0.854144i	0.999969	+	0.00790275i	$0.00251555\pi$
$468$		0			0
$469$	8.89949	+	21.7992i	0.410940	+	1.00659i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	7.70711	+	13.3491i	0.354373	+	0.613792i
$474$		0			0
$475$	−5.82843			−0.267427
$476$		0			0
$477$		0			0
$478$		0			0
$479$	6.34315	+	10.9867i	0.289826	+	0.501993i	0.973768	−	0.227543i	$-0.0730693\pi$
$479$	6.34315	+	10.9867i	0.289826	+	0.501993i	−0.683942	+	0.729536i	$0.739736\pi$
$480$		0			0
$481$	16.8848	−	29.2453i	0.769880	−	1.33347i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.24264	+	7.34847i	−0.192648	+	0.333677i
$486$		0			0
$487$	21.4497	+	37.1521i	0.971981	+	1.68352i	0.689558	+	0.724230i	$0.257805\pi$
$487$	21.4497	+	37.1521i	0.971981	+	1.68352i	0.282422	+	0.959290i	$0.408862\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−9.85786			−0.444879			−0.222440	−	0.974946i	$-0.571402\pi$
$491$	−9.85786			−0.444879			−0.222440	+	0.974946i	$0.571402\pi$
$492$		0			0
$493$	6.55635	+	11.3559i	0.295283	+	0.511445i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	29.0208	+	3.97141i	1.30176	+	0.178142i
$498$		0			0
$499$	7.32843	−	12.6932i	0.328065	−	0.568226i	−0.654062	−	0.756441i	$-0.726937\pi$
$499$	7.32843	−	12.6932i	0.328065	−	0.568226i	0.982128	+	0.188214i	$0.0602700\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	0.142136			0.00633751			0.00316876	−	0.999995i	$-0.498991\pi$
$503$	0.142136			0.00633751			0.00316876	+	0.999995i	$0.498991\pi$
$504$		0			0
$505$	−15.5563			−0.692248
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−15.2426	+	26.4010i	−0.675618	+	1.17020i	0.300670	+	0.953728i	$0.402790\pi$
$509$	−15.2426	+	26.4010i	−0.675618	+	1.17020i	−0.976288	+	0.216477i	$0.930543\pi$
$510$		0			0
$511$	1.24264	+	3.04384i	0.0549712	+	0.134651i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−0.378680	−	0.655892i	−0.0166866	−	0.0289021i
$516$		0			0
$517$	10.8284			0.476234
$518$		0			0
$519$		0			0
$520$		0			0
$521$	13.0711	+	22.6398i	0.572654	+	0.991866i	0.996292	+	0.0860342i	$0.0274194\pi$
$521$	13.0711	+	22.6398i	0.572654	+	0.991866i	−0.423638	+	0.905831i	$0.639247\pi$
$522$		0			0
$523$	−11.2782	+	19.5344i	−0.493160	+	0.854178i	−0.999969	−	0.00788006i	$-0.997492\pi$
$523$	−11.2782	+	19.5344i	−0.493160	+	0.854178i	0.506809	+	0.862058i	$0.330825\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.46447	−	11.1968i	0.281597	−	0.487740i
$528$		0			0
$529$	−13.5000	−	23.3827i	−0.586957	−	1.01664i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−0.786797			−0.0340799
$534$		0			0
$535$	0.707107	+	1.22474i	0.0305709	+	0.0529503i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−2.46447	−	9.58783i	−0.106152	−	0.412977i
$540$		0			0
$541$	9.64214	−	16.7007i	0.414548	−	0.718018i	−0.580833	−	0.814023i	$-0.697273\pi$
$541$	9.64214	−	16.7007i	0.414548	−	0.718018i	0.995381	+	0.0960049i	$0.0306064\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1.48528			0.0636225
$546$		0			0
$547$	−13.1716			−0.563176			−0.281588	−	0.959535i	$-0.590861\pi$
$547$	−13.1716			−0.563176			−0.281588	+	0.959535i	$0.590861\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−14.7782	+	25.5965i	−0.629571	+	1.09045i
$552$		0			0
$553$	−19.1777	+	24.7305i	−0.815517	+	1.05165i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	9.48528	+	16.4290i	0.401904	+	0.696119i	0.993956	−	0.109782i	$-0.0350151\pi$
$557$	9.48528	+	16.4290i	0.401904	+	0.696119i	−0.592051	+	0.805900i	$0.701682\pi$
$558$		0			0
$559$	−35.3431			−1.49486
$560$		0			0
$561$		0			0
$562$		0			0
$563$	7.48528	+	12.9649i	0.315467	+	0.546405i	0.979537	−	0.201266i	$-0.0645055\pi$
$563$	7.48528	+	12.9649i	0.315467	+	0.546405i	−0.664070	+	0.747671i	$0.731172\pi$
$564$		0			0
$565$	−6.65685	+	11.5300i	−0.280056	+	0.485071i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	9.87868	−	17.1104i	0.414136	−	0.717304i	−0.581202	−	0.813760i	$-0.697417\pi$
$569$	9.87868	−	17.1104i	0.414136	−	0.717304i	0.995337	+	0.0964554i	$0.0307505\pi$
$570$		0			0
$571$	7.25736	+	12.5701i	0.303711	+	0.526043i	0.976974	−	0.213361i	$-0.0684409\pi$
$571$	7.25736	+	12.5701i	0.303711	+	0.526043i	−0.673262	+	0.739404i	$0.735108\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	7.07107			0.294884
$576$		0			0
$577$	10.7929	+	18.6938i	0.449314	+	0.778235i	0.998341	−	0.0575696i	$-0.0183351\pi$
$577$	10.7929	+	18.6938i	0.449314	+	0.778235i	−0.549027	+	0.835804i	$0.685002\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	16.3640	+	2.23936i	0.678891	+	0.0929042i
$582$		0			0
$583$	−4.82843	+	8.36308i	−0.199973	+	0.346363i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	24.2426			1.00060			0.500300	−	0.865852i	$-0.333223\pi$
$587$	24.2426			1.00060			0.500300	+	0.865852i	$0.333223\pi$
$588$		0			0
$589$	29.1421			1.20078
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−3.12132	+	5.40629i	−0.128177	+	0.222010i	−0.922970	−	0.384871i	$-0.874246\pi$
$593$	−3.12132	+	5.40629i	−0.128177	+	0.222010i	0.794793	+	0.606880i	$0.207579\pi$
$594$		0			0
$595$	6.77817	+	0.927572i	0.277878	+	0.0380267i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	9.89949	+	17.1464i	0.404482	+	0.700584i	0.994261	−	0.106981i	$-0.0341184\pi$
$599$	9.89949	+	17.1464i	0.404482	+	0.700584i	−0.589779	+	0.807565i	$0.700785\pi$
$600$		0			0
$601$	−26.1127			−1.06516			−0.532580	−	0.846380i	$-0.678777\pi$
$601$	−26.1127			−1.06516			−0.532580	+	0.846380i	$0.678777\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−4.50000	−	7.79423i	−0.182951	−	0.316880i
$606$		0			0
$607$	15.3492	−	26.5857i	0.623007	−	1.07908i	−0.365916	−	0.930648i	$-0.619244\pi$
$607$	15.3492	−	26.5857i	0.623007	−	1.07908i	0.988923	−	0.148431i	$-0.0474223\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−12.4142	+	21.5020i	−0.502225	+	0.869880i
$612$		0			0
$613$	14.7279	+	25.5095i	0.594855	+	1.03032i	0.993567	+	0.113243i	$0.0361239\pi$
$613$	14.7279	+	25.5095i	0.594855	+	1.03032i	−0.398712	+	0.917076i	$0.630543\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	42.4853			1.71039			0.855197	−	0.518304i	$-0.173436\pi$
$617$	42.4853			1.71039			0.855197	+	0.518304i	$0.173436\pi$
$618$		0			0
$619$	−0.257359	−	0.445759i	−0.0103441	−	0.0179166i	0.860807	−	0.508932i	$-0.169959\pi$
$619$	−0.257359	−	0.445759i	−0.0103441	−	0.0179166i	−0.871151	+	0.491015i	$0.836626\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−3.63604	+	4.68885i	−0.145675	+	0.187855i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−26.9289			−1.07373
$630$		0			0
$631$	13.6569			0.543671			0.271835	−	0.962344i	$-0.412369\pi$
$631$	13.6569			0.543671			0.271835	+	0.962344i	$0.412369\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	4.03553	−	6.98975i	0.160145	−	0.277380i
$636$		0			0
$637$	21.8640	+	6.09823i	0.866282	+	0.241621i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−14.4350	−	25.0022i	−0.570149	−	0.987528i	−0.996550	−	0.0829933i	$-0.973552\pi$
$641$	−14.4350	−	25.0022i	−0.570149	−	0.987528i	0.426401	−	0.904534i	$-0.359781\pi$
$642$		0			0
$643$	−5.58579			−0.220282			−0.110141	−	0.993916i	$-0.535130\pi$
$643$	−5.58579			−0.220282			−0.110141	+	0.993916i	$0.535130\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−15.9497	−	27.6258i	−0.627049	−	1.08608i	−0.988141	−	0.153551i	$-0.950929\pi$
$647$	−15.9497	−	27.6258i	−0.627049	−	1.08608i	0.361091	−	0.932530i	$-0.382404\pi$
$648$		0			0
$649$	−4.07107	+	7.05130i	−0.159803	+	0.276788i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	13.3640	−	23.1471i	0.522972	−	0.905814i	−0.476670	−	0.879082i	$-0.658156\pi$
$653$	13.3640	−	23.1471i	0.522972	−	0.905814i	0.999643	−	0.0267324i	$-0.00851019\pi$
$654$		0			0
$655$	−3.24264	−	5.61642i	−0.126700	−	0.219452i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	28.9706			1.12853			0.564266	−	0.825593i	$-0.309159\pi$
$659$	28.9706			1.12853			0.564266	+	0.825593i	$0.309159\pi$
$660$		0			0
$661$	−24.6421	−	42.6814i	−0.958468	−	1.66012i	−0.726225	−	0.687458i	$-0.758727\pi$
$661$	−24.6421	−	42.6814i	−0.958468	−	1.66012i	−0.232243	−	0.972658i	$-0.574607\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	5.82843	+	14.2767i	0.226017	+	0.553626i
$666$		0			0
$667$	17.9289	−	31.0538i	0.694211	−	1.20241i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	12.9706			0.500723
$672$		0			0
$673$	−8.89949			−0.343050			−0.171525	−	0.985180i	$-0.554869\pi$
$673$	−8.89949			−0.343050			−0.171525	+	0.985180i	$0.554869\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	21.9203	−	37.9671i	0.842466	−	1.45919i	−0.0453378	−	0.998972i	$-0.514436\pi$
$677$	21.9203	−	37.9671i	0.842466	−	1.45919i	0.887804	−	0.460222i	$-0.152230\pi$
$678$		0			0
$679$	22.2426	+	3.04384i	0.853594	+	0.116812i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−14.2635	−	24.7050i	−0.545776	−	0.945312i	−0.998558	−	0.0536903i	$-0.982902\pi$
$683$	−14.2635	−	24.7050i	−0.545776	−	0.945312i	0.452782	−	0.891621i	$-0.350432\pi$
$684$		0			0
$685$	15.0711			0.575836
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−11.0711	−	19.1757i	−0.421774	−	0.730534i
$690$		0			0
$691$	22.2279	−	38.4999i	0.845590	−	1.46460i	−0.0395178	−	0.999219i	$-0.512582\pi$
$691$	22.2279	−	38.4999i	0.845590	−	1.46460i	0.885108	−	0.465386i	$-0.154084\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−11.1569	+	19.3242i	−0.423204	+	0.733010i
$696$		0			0
$697$	0.313708	+	0.543359i	0.0118826	+	0.0205812i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	27.4142			1.03542			0.517710	−	0.855556i	$-0.326785\pi$
$701$	27.4142			1.03542			0.517710	+	0.855556i	$0.326785\pi$
$702$		0			0
$703$	−30.3492	−	52.5664i	−1.14464	−	1.98258i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	15.5563	+	38.1051i	0.585057	+	1.43309i
$708$		0			0
$709$	−25.0711	+	43.4244i	−0.941564	+	1.63084i	−0.179074	+	0.983836i	$0.557310\pi$
$709$	−25.0711	+	43.4244i	−0.941564	+	1.63084i	−0.762489	+	0.647001i	$0.776023\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−35.3553			−1.32407
$714$		0			0
$715$	−4.58579			−0.171499
$716$		0			0
$717$		0			0
$718$		0			0
$719$	24.5563	−	42.5328i	0.915797	−	1.58621i	0.110068	−	0.993924i	$-0.464893\pi$
$719$	24.5563	−	42.5328i	0.915797	−	1.58621i	0.805730	−	0.592283i	$-0.201773\pi$
$720$		0			0
$721$	−1.22792	+	1.58346i	−0.0457302	+	0.0589713i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	2.53553	+	4.39167i	0.0941674	+	0.163103i
$726$		0			0
$727$	−30.7574			−1.14073			−0.570364	−	0.821392i	$-0.693198\pi$
$727$	−30.7574			−1.14073			−0.570364	+	0.821392i	$0.693198\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	14.0919	+	24.4079i	0.521207	+	0.902757i
$732$		0			0
$733$	−21.3787	+	37.0290i	−0.789640	+	1.36770i	0.136548	+	0.990633i	$0.456399\pi$
$733$	−21.3787	+	37.0290i	−0.789640	+	1.36770i	−0.926188	+	0.377062i	$0.876934\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−6.29289	+	10.8996i	−0.231802	+	0.401492i
$738$		0			0
$739$	10.6716	+	18.4837i	0.392560	+	0.679934i	0.992786	−	0.119896i	$-0.0382561\pi$
$739$	10.6716	+	18.4837i	0.392560	+	0.679934i	−0.600226	+	0.799830i	$0.704923\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−21.0711			−0.773023			−0.386511	−	0.922285i	$-0.626320\pi$
$743$	−21.0711			−0.773023			−0.386511	+	0.922285i	$0.626320\pi$
$744$		0			0
$745$	−2.00000	−	3.46410i	−0.0732743	−	0.126915i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	2.29289	−	2.95680i	0.0837805	−	0.108039i
$750$		0			0
$751$	2.39949	−	4.15605i	0.0875588	−	0.151656i	−0.818920	−	0.573908i	$-0.805427\pi$
$751$	2.39949	−	4.15605i	0.0875588	−	0.151656i	0.906479	+	0.422252i	$0.138760\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	10.4853			0.381598
$756$		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
$761$	15.8492	−	27.4517i	0.574535	−	0.995123i	−0.421557	−	0.906802i	$-0.638516\pi$
$761$	15.8492	−	27.4517i	0.574535	−	0.995123i	0.996092	−	0.0883214i	$-0.0281503\pi$
$762$		0			0
$763$	−1.48528	−	3.63818i	−0.0537708	−	0.131711i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−9.33452	−	16.1679i	−0.337050	−	0.583788i
$768$		0			0
$769$	30.9411			1.11577			0.557883	−	0.829920i	$-0.311614\pi$
$769$	30.9411			1.11577			0.557883	+	0.829920i	$0.311614\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	12.6360	+	21.8863i	0.454487	+	0.787194i	0.998659	−	0.0517797i	$-0.0164894\pi$
$773$	12.6360	+	21.8863i	0.454487	+	0.787194i	−0.544172	+	0.838974i	$0.683156\pi$
$774$		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
$781$	7.82843	+	13.5592i	0.280123	+	0.485188i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	5.51472			0.196829
$786$		0			0
$787$	20.5858	+	35.6556i	0.733804	+	1.27099i	0.955246	+	0.295812i	$0.0955903\pi$
$787$	20.5858	+	35.6556i	0.733804	+	1.27099i	−0.221442	+	0.975174i	$0.571076\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	34.8995	+	4.77589i	1.24088	+	0.169811i
$792$		0			0
$793$	−14.8701	+	25.7557i	−0.528051	+	0.914612i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−49.4142			−1.75034			−0.875171	−	0.483814i	$-0.839251\pi$
$797$	−49.4142			−1.75034			−0.875171	+	0.483814i	$0.839251\pi$
$798$		0			0
$799$	19.7990			0.700438
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−0.878680	+	1.52192i	−0.0310079	+	0.0537073i
$804$		0			0
$805$	−7.07107	−	17.3205i	−0.249222	−	0.610468i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	9.34315	+	16.1828i	0.328488	+	0.568957i	0.982212	−	0.187776i	$-0.0601278\pi$
$809$	9.34315	+	16.1828i	0.328488	+	0.568957i	−0.653724	+	0.756733i	$0.726794\pi$
$810$		0			0
$811$	22.6863			0.796623			0.398312	−	0.917250i	$-0.369596\pi$
$811$	22.6863			0.796623			0.398312	+	0.917250i	$0.369596\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	11.3137	+	19.5959i	0.396302	+	0.686415i
$816$		0			0
$817$	−31.7635	+	55.0159i	−1.11126	+	1.92476i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	11.7782	−	20.4004i	0.411061	−	0.711979i	−0.583945	−	0.811793i	$-0.698492\pi$
$821$	11.7782	−	20.4004i	0.411061	−	0.711979i	0.995006	+	0.0998145i	$0.0318249\pi$
$822$		0			0
$823$	6.51472	+	11.2838i	0.227089	+	0.393329i	0.956944	−	0.290272i	$-0.0937459\pi$
$823$	6.51472	+	11.2838i	0.227089	+	0.393329i	−0.729855	+	0.683602i	$0.760413\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	3.85786			0.134151			0.0670755	−	0.997748i	$-0.478633\pi$
$827$	3.85786			0.134151			0.0670755	+	0.997748i	$0.478633\pi$
$828$		0			0
$829$	0.642136	+	1.11221i	0.0223023	+	0.0386287i	0.876961	−	0.480561i	$-0.159567\pi$
$829$	0.642136	+	1.11221i	0.0223023	+	0.0386287i	−0.854659	+	0.519190i	$0.826234\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−4.50610	−	17.5306i	−0.156127	−	0.607401i
$834$		0			0
$835$	−3.94975	+	6.84116i	−0.136687	+	0.236748i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	4.38478			0.151379			0.0756896	−	0.997131i	$-0.475884\pi$
$839$	4.38478			0.151379			0.0756896	+	0.997131i	$0.475884\pi$
$840$		0			0
$841$	−3.28427			−0.113251
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−1.24264	+	2.15232i	−0.0427481	+	0.0740419i
$846$		0			0
$847$	−14.5919	+	18.8169i	−0.501383	+	0.646557i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	36.8198	+	63.7738i	1.26217	+	2.18614i
$852$		0			0
$853$	−50.6985			−1.73588			−0.867942	−	0.496666i	$-0.834557\pi$
$853$	−50.6985			−1.73588			−0.867942	+	0.496666i	$0.834557\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−27.7782	−	48.1132i	−0.948884	−	1.64352i	−0.747781	−	0.663946i	$-0.768880\pi$
$857$	−27.7782	−	48.1132i	−0.948884	−	1.64352i	−0.201104	−	0.979570i	$-0.564453\pi$
$858$		0			0
$859$	19.4853	−	33.7495i	0.664829	−	1.15152i	−0.314502	−	0.949257i	$-0.601838\pi$
$859$	19.4853	−	33.7495i	0.664829	−	1.15152i	0.979332	−	0.202261i	$-0.0648290\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	22.4142	−	38.8226i	0.762989	−	1.32154i	−0.178315	−	0.983974i	$-0.557065\pi$
$863$	22.4142	−	38.8226i	0.762989	−	1.32154i	0.941303	−	0.337562i	$-0.109602\pi$
$864$		0			0
$865$	−5.41421	−	9.37769i	−0.184089	−	0.318851i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−16.7279			−0.567456
$870$		0			0
$871$	−14.4289	−	24.9916i	−0.488906	−	0.846810i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	2.62132	+	0.358719i	0.0886168	+	0.0121269i
$876$		0			0
$877$	−6.51472	+	11.2838i	−0.219986	+	0.381028i	−0.954804	−	0.297238i	$-0.903935\pi$
$877$	−6.51472	+	11.2838i	−0.219986	+	0.381028i	0.734817	+	0.678265i	$0.237268\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−48.2843			−1.62674			−0.813369	−	0.581748i	$-0.802369\pi$
$881$	−48.2843			−1.62674			−0.813369	+	0.581748i	$0.802369\pi$
$882$		0			0
$883$	−48.4142			−1.62927			−0.814634	−	0.579975i	$-0.803062\pi$
$883$	−48.4142			−1.62927			−0.814634	+	0.579975i	$0.803062\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	15.5061	−	26.8573i	0.520644	−	0.901781i	−0.479068	−	0.877778i	$-0.659025\pi$
$887$	15.5061	−	26.8573i	0.520644	−	0.901781i	0.999712	−	0.0240037i	$-0.00764136\pi$
$888$		0			0
$889$	−21.1569	−	2.89525i	−0.709578	−	0.0971035i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	22.3137	+	38.6485i	0.746700	+	1.29332i
$894$		0			0
$895$	8.34315			0.278881
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−12.6777	−	21.9584i	−0.422824	−	0.732353i
$900$		0			0
$901$	−8.82843	+	15.2913i	−0.294118	+	0.509427i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	7.15685	−	12.3960i	0.237902	−	0.412058i
$906$		0			0
$907$	2.89340	+	5.01151i	0.0960737	+	0.166405i	0.910056	−	0.414485i	$-0.136038\pi$
$907$	2.89340	+	5.01151i	0.0960737	+	0.166405i	−0.813983	+	0.580889i	$0.802705\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	11.2132			0.371510			0.185755	−	0.982596i	$-0.440527\pi$
$911$	11.2132			0.371510			0.185755	+	0.982596i	$0.440527\pi$
$912$		0			0
$913$	4.41421	+	7.64564i	0.146089	+	0.253034i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−10.5147	+	13.5592i	−0.347227	+	0.447765i
$918$		0			0
$919$	−7.22792	+	12.5191i	−0.238427	+	0.412968i	−0.960263	−	0.279096i	$-0.909965\pi$
$919$	−7.22792	+	12.5191i	−0.238427	+	0.412968i	0.721836	+	0.692064i	$0.243298\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−35.8995			−1.18165
$924$		0			0
$925$	−10.4142			−0.342417
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−20.0208	+	34.6771i	−0.656862	+	1.13772i	0.324562	+	0.945864i	$0.394783\pi$
$929$	−20.0208	+	34.6771i	−0.656862	+	1.13772i	−0.981424	+	0.191853i	$0.938550\pi$
$930$		0			0
$931$	29.1421	−	28.5533i	0.955095	−	0.935798i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.82843	+	3.16693i	0.0597960	+	0.103570i
$936$		0			0
$937$	−31.3848			−1.02530			−0.512648	−	0.858599i	$-0.671335\pi$
$937$	−31.3848			−1.02530			−0.512648	+	0.858599i	$0.671335\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−24.0919	−	41.7284i	−0.785373	−	1.36031i	−0.928776	−	0.370641i	$-0.879138\pi$
$941$	−24.0919	−	41.7284i	−0.785373	−	1.36031i	0.143403	−	0.989664i	$-0.454195\pi$
$942$		0			0
$943$	0.857864	−	1.48586i	0.0279359	−	0.0483864i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	28.4350	−	49.2509i	0.924014	−	1.60044i	0.130875	−	0.991399i	$-0.458221\pi$
$947$	28.4350	−	49.2509i	0.924014	−	1.60044i	0.793139	−	0.609041i	$-0.208445\pi$
$948$		0			0
$949$	−2.01472	−	3.48960i	−0.0654005	−	0.113277i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−1.85786			−0.0601821			−0.0300911	−	0.999547i	$-0.509580\pi$
$953$	−1.85786			−0.0601821			−0.0300911	+	0.999547i	$0.509580\pi$
$954$		0			0
$955$	−7.82843	−	13.5592i	−0.253322	−	0.438766i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−15.0711	−	36.9164i	−0.486670	−	1.19209i
$960$		0			0
$961$	3.00000	−	5.19615i	0.0967742	−	0.167618i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−12.4142			−0.399628
$966$		0			0
$967$	−43.7279			−1.40620			−0.703098	−	0.711093i	$-0.748200\pi$
$967$	−43.7279			−1.40620			−0.703098	+	0.711093i	$0.748200\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−14.1421	+	24.4949i	−0.453843	+	0.786079i	−0.998621	−	0.0525016i	$-0.983281\pi$
$971$	−14.1421	+	24.4949i	−0.453843	+	0.786079i	0.544778	+	0.838580i	$0.316614\pi$
$972$		0			0
$973$	58.4914	+	8.00436i	1.87515	+	0.256608i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−10.7782	−	18.6683i	−0.344824	−	0.597253i	0.640497	−	0.767960i	$-0.278728\pi$
$977$	−10.7782	−	18.6683i	−0.344824	−	0.597253i	−0.985322	+	0.170707i	$0.945395\pi$
$978$		0			0
$979$	−3.17157			−0.101364
$980$		0			0
$981$		0			0
$982$		0			0
$983$	19.1924	+	33.2422i	0.612142	+	1.06026i	0.990879	+	0.134757i	$0.0430253\pi$
$983$	19.1924	+	33.2422i	0.612142	+	1.06026i	−0.378737	+	0.925505i	$0.623641\pi$
$984$		0			0
$985$	12.0208	−	20.8207i	0.383015	−	0.663401i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	38.5355	−	66.7455i	1.22536	−	2.12238i
$990$		0			0
$991$	12.4289	+	21.5275i	0.394818	+	0.683845i	0.993078	−	0.117457i	$-0.0374743\pi$
$991$	12.4289	+	21.5275i	0.394818	+	0.683845i	−0.598260	+	0.801302i	$0.704141\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−10.4853			−0.332406
$996$		0			0
$997$	24.6630	+	42.7175i	0.781083	+	1.35288i	0.931311	+	0.364225i	$0.118666\pi$
$997$	24.6630	+	42.7175i	0.781083	+	1.35288i	−0.150228	+	0.988651i	$0.548001\pi$
$998$		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.1801.1		4
3.2	odd	2		840.2.bg.g.121.1	✓	4
7.4	even	3	inner	2520.2.bi.l.361.1		4
12.11	even	2		1680.2.bg.r.961.2		4
21.2	odd	6		5880.2.a.bs.1.1		2
21.5	even	6		5880.2.a.bm.1.1		2
21.11	odd	6		840.2.bg.g.361.1	yes	4
84.11	even	6		1680.2.bg.r.1201.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bg.g.121.1	✓	4	3.2	odd	2
840.2.bg.g.361.1	yes	4	21.11	odd	6
1680.2.bg.r.961.2		4	12.11	even	2
1680.2.bg.r.1201.2		4	84.11	even	6
2520.2.bi.l.361.1		4	7.4	even	3	inner
2520.2.bi.l.1801.1		4	1.1	even	1	trivial
5880.2.a.bm.1.1		2	21.5	even	6
5880.2.a.bs.1.1		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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{5} +(-2.62132 - 0.358719i) q^{7} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{5} +(-2.62132 - 0.358719i) q^{7} +(-0.707107 - 1.22474i) q^{11} +3.24264 q^{13} +(-1.29289 - 2.23936i) q^{17} +(2.91421 - 5.04757i) q^{19} +(-3.53553 + 6.12372i) q^{23} +(-0.500000 - 0.866025i) q^{25} -5.07107 q^{29} +(2.50000 + 4.33013i) q^{31} +(-1.62132 + 2.09077i) q^{35} +(5.20711 - 9.01897i) q^{37} -0.242641 q^{41} -10.8995 q^{43} +(-3.82843 + 6.63103i) q^{47} +(6.74264 + 1.88064i) q^{49} +(-3.41421 - 5.91359i) q^{53} -1.41421 q^{55} +(-2.87868 - 4.98602i) q^{59} +(-4.58579 + 7.94282i) q^{61} +(1.62132 - 2.80821i) q^{65} +(-4.44975 - 7.70719i) q^{67} -11.0711 q^{71} +(-0.621320 - 1.07616i) q^{73} +(1.41421 + 3.46410i) q^{77} +(5.91421 - 10.2437i) q^{79} -6.24264 q^{83} -2.58579 q^{85} +(1.12132 - 1.94218i) q^{89} +(-8.50000 - 1.16320i) q^{91} +(-2.91421 - 5.04757i) q^{95} -8.48528 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{5} - 2 q^{7}+O(q^{10}) \) 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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