LMFDB - Embedded newform 2100.2.s.c.1457.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2100,2,Mod(1457,2100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2100, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1, 0]))

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

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

chi := DirichletCharacter("2100.1457");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2100.s (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$16.7685844245$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1457.5
Character	$\chi$	$=$	2100.1457
Dual form			2100.2.s.c.1793.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15804 - 1.28800i) q^{3} +(0.707107 + 0.707107i) q^{7} +(-0.317883 + 2.98311i) q^{9} +O(q^{10})$	$q+(-1.15804 - 1.28800i) q^{3} +(0.707107 + 0.707107i) q^{7} +(-0.317883 + 2.98311i) q^{9} -1.81675i q^{11} +(-2.28690 + 2.28690i) q^{13} +(-0.614103 + 0.614103i) q^{17} -0.915840i q^{19} +(0.0918944 - 1.72961i) q^{21} +(-3.11658 - 3.11658i) q^{23} +(4.21037 - 3.04513i) q^{27} +6.83864 q^{29} +8.15001 q^{31} +(-2.33998 + 2.10387i) q^{33} +(-1.57980 - 1.57980i) q^{37} +(5.59386 + 0.297202i) q^{39} -0.926896i q^{41} +(-3.34906 + 3.34906i) q^{43} +(7.74636 - 7.74636i) q^{47} +1.00000i q^{49} +(1.50212 + 0.0798077i) q^{51} +(-3.13170 - 3.13170i) q^{53} +(-1.17960 + 1.06058i) q^{57} +9.50920 q^{59} +0.778193 q^{61} +(-2.33416 + 1.88460i) q^{63} +(3.95804 + 3.95804i) q^{67} +(-0.405025 + 7.62327i) q^{69} +10.0067i q^{71} +(3.51085 - 3.51085i) q^{73} +(1.28464 - 1.28464i) q^{77} -8.66336i q^{79} +(-8.79790 - 1.89656i) q^{81} +(-9.57830 - 9.57830i) q^{83} +(-7.91942 - 8.80816i) q^{87} +8.12082 q^{89} -3.23417 q^{91} +(-9.43804 - 10.4972i) q^{93} +(3.33732 + 3.33732i) q^{97} +(5.41958 + 0.577515i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{21} + 48 q^{31} - 32 q^{51} + 16 q^{61} + 64 q^{81} + 32 q^{91}+O(q^{100}) $ 32 * q - 8 * q^21 + 48 * q^31 - 32 * q^51 + 16 * q^61 + 64 * q^81 + 32 * q^91

Display 100 coefficients 10 coefficients

Character values

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

$n$	$701$	$1051$	$1177$	$1501$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	−1.15804	−	1.28800i	−0.668595	−	0.743627i
$3$	−1.15804	−	1.28800i	−0.668595	−	0.743627i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$		0			0
$9$	−0.317883	+	2.98311i	−0.105961	+	0.994370i
$10$		0			0
$11$		−	1.81675i		−	0.547772i	−0.961762	−	0.273886i	$-0.911691\pi$
$11$		−	1.81675i		−	0.547772i	0.961762	−	0.273886i	$-0.0883090\pi$
$12$		0			0
$13$	−2.28690	+	2.28690i	−0.634273	+	0.634273i	−0.949137	−	0.314864i	$-0.898041\pi$
$13$	−2.28690	+	2.28690i	−0.634273	+	0.634273i	0.314864	+	0.949137i	$0.398041\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.614103	+	0.614103i	−0.148942	+	0.148942i	−0.777645	−	0.628703i	$-0.783586\pi$
$17$	−0.614103	+	0.614103i	−0.148942	+	0.148942i	0.628703	+	0.777645i	$0.283586\pi$
$18$		0			0
$19$		−	0.915840i		−	0.210108i	−0.994467	−	0.105054i	$-0.966498\pi$
$19$		−	0.915840i		−	0.210108i	0.994467	−	0.105054i	$-0.0335015\pi$
$20$		0			0
$21$	0.0918944	−	1.72961i	0.0200530	−	0.377432i
$22$		0			0
$23$	−3.11658	−	3.11658i	−0.649851	−	0.649851i	0.303106	−	0.952957i	$-0.401976\pi$
$23$	−3.11658	−	3.11658i	−0.649851	−	0.649851i	−0.952957	+	0.303106i	$0.901976\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	4.21037	−	3.04513i	0.810285	−	0.586036i
$28$		0			0
$29$	6.83864			1.26990			0.634952	−	0.772552i	$-0.281020\pi$
$29$	6.83864			1.26990			0.634952	+	0.772552i	$0.281020\pi$
$30$		0			0
$31$	8.15001			1.46379			0.731893	−	0.681420i	$-0.238637\pi$
$31$	8.15001			1.46379			0.731893	+	0.681420i	$0.238637\pi$
$32$		0			0
$33$	−2.33998	+	2.10387i	−0.407338	+	0.366237i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.57980	−	1.57980i	−0.259717	−	0.259717i	0.565222	−	0.824939i	$-0.308791\pi$
$37$	−1.57980	−	1.57980i	−0.259717	−	0.259717i	−0.824939	+	0.565222i	$0.808791\pi$
$38$		0			0
$39$	5.59386	+	0.297202i	0.895734	+	0.0475904i
$40$		0			0
$41$		−	0.926896i		−	0.144757i	−0.997377	−	0.0723784i	$-0.976941\pi$
$41$		−	0.926896i		−	0.144757i	0.997377	−	0.0723784i	$-0.0230589\pi$
$42$		0			0
$43$	−3.34906	+	3.34906i	−0.510727	+	0.510727i	−0.914749	−	0.404022i	$-0.867612\pi$
$43$	−3.34906	+	3.34906i	−0.510727	+	0.510727i	0.404022	+	0.914749i	$0.367612\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	7.74636	−	7.74636i	1.12992	−	1.12992i	0.139734	−	0.990189i	$-0.455375\pi$
$47$	7.74636	−	7.74636i	1.12992	−	1.12992i	0.990189	−	0.139734i	$-0.0446248\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$	1.50212	+	0.0798077i	0.210339	+	0.0111753i
$52$		0			0
$53$	−3.13170	−	3.13170i	−0.430172	−	0.430172i	0.458515	−	0.888687i	$-0.348382\pi$
$53$	−3.13170	−	3.13170i	−0.430172	−	0.430172i	−0.888687	+	0.458515i	$0.848382\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−1.17960	+	1.06058i	−0.156242	+	0.140477i
$58$		0			0
$59$	9.50920			1.23799			0.618996	−	0.785394i	$-0.287540\pi$
$59$	9.50920			1.23799			0.618996	+	0.785394i	$0.287540\pi$
$60$		0			0
$61$	0.778193			0.0996374			0.0498187	−	0.998758i	$-0.484136\pi$
$61$	0.778193			0.0996374			0.0498187	+	0.998758i	$0.484136\pi$
$62$		0			0
$63$	−2.33416	+	1.88460i	−0.294076	+	0.237437i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	3.95804	+	3.95804i	0.483551	+	0.483551i	0.906264	−	0.422713i	$-0.138922\pi$
$67$	3.95804	+	3.95804i	0.483551	+	0.483551i	−0.422713	+	0.906264i	$0.638922\pi$
$68$		0			0
$69$	−0.405025	+	7.62327i	−0.0487592	+	0.917734i
$70$		0			0
$71$			10.0067i			1.18758i	0.804620	+	0.593790i	$0.202369\pi$
$71$			10.0067i			1.18758i	−0.804620	+	0.593790i	$0.797631\pi$
$72$		0			0
$73$	3.51085	−	3.51085i	0.410913	−	0.410913i	−0.471143	−	0.882057i	$-0.656159\pi$
$73$	3.51085	−	3.51085i	0.410913	−	0.410913i	0.882057	+	0.471143i	$0.156159\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.28464	−	1.28464i	0.146398	−	0.146398i
$78$		0			0
$79$		−	8.66336i		−	0.974704i	−0.873206	−	0.487352i	$-0.837963\pi$
$79$		−	8.66336i		−	0.974704i	0.873206	−	0.487352i	$-0.162037\pi$
$80$		0			0
$81$	−8.79790	−	1.89656i	−0.977545	−	0.210729i
$82$		0			0
$83$	−9.57830	−	9.57830i	−1.05135	−	1.05135i	−0.998608	−	0.0527470i	$-0.983202\pi$
$83$	−9.57830	−	9.57830i	−1.05135	−	1.05135i	−0.0527470	−	0.998608i	$-0.516798\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−7.91942	−	8.80816i	−0.849051	−	0.944334i
$88$		0			0
$89$	8.12082			0.860805			0.430402	−	0.902637i	$-0.358372\pi$
$89$	8.12082			0.860805			0.430402	+	0.902637i	$0.358372\pi$
$90$		0			0
$91$	−3.23417			−0.339033
$92$		0			0
$93$	−9.43804	−	10.4972i	−0.978680	−	1.08851i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	3.33732	+	3.33732i	0.338854	+	0.338854i	0.855936	−	0.517082i	$-0.172982\pi$
$97$	3.33732	+	3.33732i	0.338854	+	0.338854i	−0.517082	+	0.855936i	$0.672982\pi$
$98$		0			0
$99$	5.41958	+	0.577515i	0.544688	+	0.0580424i
$100$		0			0
$101$		−	13.9488i		−	1.38796i	−0.719995	−	0.693980i	$-0.755856\pi$
$101$		−	13.9488i		−	1.38796i	0.719995	−	0.693980i	$-0.244144\pi$
$102$		0			0
$103$	9.36891	−	9.36891i	0.923146	−	0.923146i	−0.0741044	−	0.997250i	$-0.523610\pi$
$103$	9.36891	−	9.36891i	0.923146	−	0.923146i	0.997250	+	0.0741044i	$0.0236098\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.35305	−	2.35305i	0.227477	−	0.227477i	−0.584161	−	0.811638i	$-0.698576\pi$
$107$	2.35305	−	2.35305i	0.227477	−	0.227477i	0.811638	+	0.584161i	$0.198576\pi$
$108$		0			0
$109$		−	4.83168i		−	0.462791i	−0.972860	−	0.231395i	$-0.925671\pi$
$109$		−	4.83168i		−	0.462791i	0.972860	−	0.231395i	$-0.0743291\pi$
$110$		0			0
$111$	−0.205308	+	3.86425i	−0.0194869	+	0.366778i
$112$		0			0
$113$	−7.67956	−	7.67956i	−0.722432	−	0.722432i	0.246668	−	0.969100i	$-0.420664\pi$
$113$	−7.67956	−	7.67956i	−0.722432	−	0.722432i	−0.969100	+	0.246668i	$0.920664\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−6.09512	−	7.54906i	−0.563494	−	0.697911i
$118$		0			0
$119$	−0.868473			−0.0796128
$120$		0			0
$121$	7.69941			0.699946
$122$		0			0
$123$	−1.19384	+	1.07338i	−0.107645	+	0.0967837i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	15.4839	+	15.4839i	1.37397	+	1.37397i	0.854466	+	0.519507i	$0.173884\pi$
$127$	15.4839	+	15.4839i	1.37397	+	1.37397i	0.519507	+	0.854466i	$0.326116\pi$
$128$		0			0
$129$	8.19194	+	0.435238i	0.721260	+	0.0383206i
$130$		0			0
$131$		−	13.4873i		−	1.17839i	−0.807989	−	0.589197i	$-0.799444\pi$
$131$		−	13.4873i		−	1.17839i	0.807989	−	0.589197i	$-0.200556\pi$
$132$		0			0
$133$	0.647596	−	0.647596i	0.0561537	−	0.0561537i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.329097	−	0.329097i	0.0281166	−	0.0281166i	−0.692909	−	0.721025i	$-0.743671\pi$
$137$	0.329097	−	0.329097i	0.0281166	−	0.0281166i	0.721025	+	0.692909i	$0.243671\pi$
$138$		0			0
$139$		−	13.8933i		−	1.17841i	−0.807982	−	0.589207i	$-0.799440\pi$
$139$		−	13.8933i		−	1.17841i	0.807982	−	0.589207i	$-0.200560\pi$
$140$		0			0
$141$	−18.9479	−	1.00670i	−1.59570	−	0.0847797i
$142$		0			0
$143$	4.15474	+	4.15474i	0.347437	+	0.347437i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	1.28800	−	1.15804i	0.106232	−	0.0955136i
$148$		0			0
$149$	−6.24564			−0.511663			−0.255831	−	0.966721i	$-0.582349\pi$
$149$	−6.24564			−0.511663			−0.255831	+	0.966721i	$0.582349\pi$
$150$		0			0
$151$	−8.13878			−0.662325			−0.331162	−	0.943574i	$-0.607441\pi$
$151$	−8.13878			−0.662325			−0.331162	+	0.943574i	$0.607441\pi$
$152$		0			0
$153$	−1.63672	−	2.02715i	−0.132321	−	0.163885i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−9.08730	−	9.08730i	−0.725246	−	0.725246i	0.244423	−	0.969669i	$-0.421401\pi$
$157$	−9.08730	−	9.08730i	−0.725246	−	0.725246i	−0.969669	+	0.244423i	$0.921401\pi$
$158$		0			0
$159$	−0.406990	+	7.66025i	−0.0322764	+	0.607498i
$160$		0			0
$161$		−	4.40750i		−	0.347360i
$162$		0			0
$163$	8.62179	−	8.62179i	0.675310	−	0.675310i	−0.283625	−	0.958935i	$-0.591537\pi$
$163$	8.62179	−	8.62179i	0.675310	−	0.675310i	0.958935	+	0.283625i	$0.0915370\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	4.40121	−	4.40121i	0.340576	−	0.340576i	−0.516008	−	0.856584i	$-0.672582\pi$
$167$	4.40121	−	4.40121i	0.340576	−	0.340576i	0.856584	+	0.516008i	$0.172582\pi$
$168$		0			0
$169$			2.54014i			0.195395i
$170$		0			0
$171$	2.73205	+	0.291130i	0.208925	+	0.0222633i
$172$		0			0
$173$	−3.75339	−	3.75339i	−0.285365	−	0.285365i	0.549879	−	0.835244i	$-0.314674\pi$
$173$	−3.75339	−	3.75339i	−0.285365	−	0.285365i	−0.835244	+	0.549879i	$0.814674\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−11.0120	−	12.2478i	−0.827715	−	0.920604i
$178$		0			0
$179$	12.7357			0.951912			0.475956	−	0.879469i	$-0.342102\pi$
$179$	12.7357			0.951912			0.475956	+	0.879469i	$0.342102\pi$
$180$		0			0
$181$	−12.3369			−0.916995			−0.458497	−	0.888696i	$-0.651612\pi$
$181$	−12.3369			−0.916995			−0.458497	+	0.888696i	$0.651612\pi$
$182$		0			0
$183$	−0.901179	−	1.00231i	−0.0666171	−	0.0740930i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.11567	+	1.11567i	0.0815861	+	0.0815861i
$188$		0			0
$189$	5.13041	+	0.823945i	0.373182	+	0.0599332i
$190$		0			0
$191$			26.9639i			1.95104i	0.219906	+	0.975521i	$0.429425\pi$
$191$			26.9639i			1.95104i	−0.219906	+	0.975521i	$0.570575\pi$
$192$		0			0
$193$	−6.57391	+	6.57391i	−0.473201	+	0.473201i	−0.902949	−	0.429748i	$-0.858602\pi$
$193$	−6.57391	+	6.57391i	−0.473201	+	0.473201i	0.429748	+	0.902949i	$0.358602\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	2.55416	−	2.55416i	0.181976	−	0.181976i	−0.610240	−	0.792216i	$-0.708927\pi$
$197$	2.55416	−	2.55416i	0.181976	−	0.181976i	0.792216	+	0.610240i	$0.208927\pi$
$198$		0			0
$199$		−	19.1790i		−	1.35956i	−0.733415	−	0.679781i	$-0.762075\pi$
$199$		−	19.1790i		−	1.35956i	0.733415	−	0.679781i	$-0.237925\pi$
$200$		0			0
$201$	0.514379	−	9.68151i	0.0362815	−	0.682881i
$202$		0			0
$203$	4.83565	+	4.83565i	0.339396	+	0.339396i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	10.2878	−	8.30638i	0.715051	−	0.577334i
$208$		0			0
$209$	−1.66385			−0.115091
$210$		0			0
$211$	−2.59440			−0.178606			−0.0893031	−	0.996004i	$-0.528464\pi$
$211$	−2.59440			−0.178606			−0.0893031	+	0.996004i	$0.528464\pi$
$212$		0			0
$213$	12.8887	−	11.5882i	0.883116	−	0.794011i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	5.76293	+	5.76293i	0.391213	+	0.391213i
$218$		0			0
$219$	−8.58767	−	0.456263i	−0.580301	−	0.0308314i
$220$		0			0
$221$		−	2.80879i		−	0.188940i
$222$		0			0
$223$	−1.00759	+	1.00759i	−0.0674732	+	0.0674732i	−0.740038	−	0.672565i	$-0.765193\pi$
$223$	−1.00759	+	1.00759i	−0.0674732	+	0.0674732i	0.672565	+	0.740038i	$0.265193\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	6.18906	−	6.18906i	0.410782	−	0.410782i	−0.471229	−	0.882011i	$-0.656189\pi$
$227$	6.18906	−	6.18906i	0.410782	−	0.410782i	0.882011	+	0.471229i	$0.156189\pi$
$228$		0			0
$229$		−	17.8649i		−	1.18054i	−0.807204	−	0.590272i	$-0.799020\pi$
$229$		−	17.8649i		−	1.18054i	0.807204	−	0.590272i	$-0.200980\pi$
$230$		0			0
$231$	−3.14228	−	0.166949i	−0.206747	−	0.0109845i
$232$		0			0
$233$	−18.5715	−	18.5715i	−1.21666	−	1.21666i	−0.968795	−	0.247862i	$-0.920272\pi$
$233$	−18.5715	−	18.5715i	−1.21666	−	1.21666i	−0.247862	−	0.968795i	$-0.579728\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−11.1584	+	10.0325i	−0.724816	+	0.651682i
$238$		0			0
$239$	−9.40800			−0.608553			−0.304277	−	0.952584i	$-0.598415\pi$
$239$	−9.40800			−0.608553			−0.304277	+	0.952584i	$0.598415\pi$
$240$		0			0
$241$	25.7004			1.65551			0.827756	−	0.561089i	$-0.189617\pi$
$241$	25.7004			1.65551			0.827756	+	0.561089i	$0.189617\pi$
$242$		0			0
$243$	7.74556	+	13.5280i	0.496878	+	0.867820i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	2.09444	+	2.09444i	0.133266	+	0.133266i
$248$		0			0
$249$	−1.24478	+	23.4289i	−0.0788847	+	1.48475i
$250$		0			0
$251$			21.7942i			1.37564i	0.725884	+	0.687818i	$0.241431\pi$
$251$			21.7942i			1.37564i	−0.725884	+	0.687818i	$0.758569\pi$
$252$		0			0
$253$	−5.66205	+	5.66205i	−0.355970	+	0.355970i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−14.7169	+	14.7169i	−0.918012	+	0.918012i	−0.996885	−	0.0788726i	$-0.974868\pi$
$257$	−14.7169	+	14.7169i	−0.918012	+	0.918012i	0.0788726	+	0.996885i	$0.474868\pi$
$258$		0			0
$259$		−	2.23417i		−	0.138825i
$260$		0			0
$261$	−2.17389	+	20.4004i	−0.134560	+	1.26275i
$262$		0			0
$263$	22.0701	+	22.0701i	1.36090	+	1.36090i	0.872772	+	0.488128i	$0.162320\pi$
$263$	22.0701	+	22.0701i	1.36090	+	1.36090i	0.488128	+	0.872772i	$0.337680\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−9.40424	−	10.4596i	−0.575530	−	0.640117i
$268$		0			0
$269$	−5.94878			−0.362704			−0.181352	−	0.983418i	$-0.558047\pi$
$269$	−5.94878			−0.362704			−0.181352	+	0.983418i	$0.558047\pi$
$270$		0			0
$271$	10.7968			0.655857			0.327928	−	0.944703i	$-0.393650\pi$
$271$	10.7968			0.655857			0.327928	+	0.944703i	$0.393650\pi$
$272$		0			0
$273$	3.74530	+	4.16561i	0.226676	+	0.252114i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	16.9527	+	16.9527i	1.01859	+	1.01859i	0.999824	+	0.0187635i	$0.00597297\pi$
$277$	16.9527	+	16.9527i	1.01859	+	1.01859i	0.0187635	+	0.999824i	$0.494027\pi$
$278$		0			0
$279$	−2.59075	+	24.3124i	−0.155104	+	1.45554i
$280$		0			0
$281$		−	18.4918i		−	1.10313i	−0.834133	−	0.551563i	$-0.814032\pi$
$281$		−	18.4918i		−	1.10313i	0.834133	−	0.551563i	$-0.185968\pi$
$282$		0			0
$283$	7.26573	−	7.26573i	0.431903	−	0.431903i	−0.457372	−	0.889275i	$-0.651209\pi$
$283$	7.26573	−	7.26573i	0.431903	−	0.431903i	0.889275	+	0.457372i	$0.151209\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.655414	−	0.655414i	0.0386879	−	0.0386879i
$288$		0			0
$289$			16.2458i			0.955633i
$290$		0			0
$291$	0.433713	−	8.16322i	0.0254247	−	0.478537i
$292$		0			0
$293$	1.63645	+	1.63645i	0.0956024	+	0.0956024i	0.753290	−	0.657688i	$-0.228465\pi$
$293$	1.63645	+	1.63645i	0.0956024	+	0.0956024i	−0.657688	+	0.753290i	$0.728465\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−5.53225	−	7.64919i	−0.321014	−	0.443851i
$298$		0			0
$299$	14.2546			0.824366
$300$		0			0
$301$	−4.73629			−0.272995
$302$		0			0
$303$	−17.9661	+	16.1533i	−1.03212	+	0.927983i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	9.74785	+	9.74785i	0.556339	+	0.556339i	0.928263	−	0.371924i	$-0.121302\pi$
$307$	9.74785	+	9.74785i	0.556339	+	0.556339i	−0.371924	+	0.928263i	$0.621302\pi$
$308$		0			0
$309$	−22.9167	−	1.21757i	−1.30369	−	0.0692650i
$310$		0			0
$311$		−	6.45205i		−	0.365862i	−0.983126	−	0.182931i	$-0.941442\pi$
$311$		−	6.45205i		−	0.365862i	0.983126	−	0.182931i	$-0.0585585\pi$
$312$		0			0
$313$	−10.3823	+	10.3823i	−0.586843	+	0.586843i	−0.936775	−	0.349932i	$-0.886205\pi$
$313$	−10.3823	+	10.3823i	−0.586843	+	0.586843i	0.349932	+	0.936775i	$0.386205\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−21.2914	+	21.2914i	−1.19585	+	1.19585i	−0.220448	+	0.975399i	$0.570752\pi$
$317$	−21.2914	+	21.2914i	−1.19585	+	1.19585i	−0.975399	+	0.220448i	$0.929248\pi$
$318$		0			0
$319$		−	12.4241i		−	0.695617i
$320$		0			0
$321$	−5.75564	−	0.305798i	−0.321249	−	0.0170680i
$322$		0			0
$323$	0.562420	+	0.562420i	0.0312939	+	0.0312939i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−6.22320	+	5.59528i	−0.344144	+	0.309420i
$328$		0			0
$329$	10.9550			0.603969
$330$		0			0
$331$	22.5396			1.23889			0.619443	−	0.785041i	$-0.287358\pi$
$331$	22.5396			1.23889			0.619443	+	0.785041i	$0.287358\pi$
$332$		0			0
$333$	5.21490	−	4.21052i	0.285775	−	0.230735i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	7.64028	+	7.64028i	0.416192	+	0.416192i	0.883889	−	0.467697i	$-0.154916\pi$
$337$	7.64028	+	7.64028i	0.416192	+	0.416192i	−0.467697	+	0.883889i	$0.654916\pi$
$338$		0			0
$339$	−0.998022	+	18.7845i	−0.0542051	+	1.02023i
$340$		0			0
$341$		−	14.8066i		−	0.801820i
$342$		0			0
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	7.92603	−	7.92603i	0.425492	−	0.425492i	−0.461598	−	0.887089i	$-0.652724\pi$
$347$	7.92603	−	7.92603i	0.425492	−	0.425492i	0.887089	+	0.461598i	$0.152724\pi$
$348$		0			0
$349$		−	14.7166i		−	0.787761i	−0.919162	−	0.393880i	$-0.871132\pi$
$349$		−	14.7166i		−	0.787761i	0.919162	−	0.393880i	$-0.128868\pi$
$350$		0			0
$351$	−2.66478	+	16.5926i	−0.142235	+	0.885649i
$352$		0			0
$353$	21.1607	+	21.1607i	1.12627	+	1.12627i	0.990779	+	0.135491i	$0.0432610\pi$
$353$	21.1607	+	21.1607i	1.12627	+	1.12627i	0.135491	+	0.990779i	$0.456739\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	1.00573	+	1.11859i	0.0532287	+	0.0592022i
$358$		0			0
$359$	−32.2360			−1.70135			−0.850675	−	0.525692i	$-0.823806\pi$
$359$	−32.2360			−1.70135			−0.850675	+	0.525692i	$0.823806\pi$
$360$		0			0
$361$	18.1612			0.955855
$362$		0			0
$363$	−8.91623	−	9.91683i	−0.467981	−	0.520499i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−13.7264	−	13.7264i	−0.716510	−	0.716510i	0.251378	−	0.967889i	$-0.419116\pi$
$367$	−13.7264	−	13.7264i	−0.716510	−	0.716510i	−0.967889	+	0.251378i	$0.919116\pi$
$368$		0			0
$369$	2.76503	+	0.294644i	0.143942	+	0.0153386i
$370$		0			0
$371$		−	4.42889i		−	0.229936i
$372$		0			0
$373$	14.2556	−	14.2556i	0.738125	−	0.738125i	−0.234090	−	0.972215i	$-0.575211\pi$
$373$	14.2556	−	14.2556i	0.738125	−	0.738125i	0.972215	+	0.234090i	$0.0752110\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−15.6393	+	15.6393i	−0.805465	+	0.805465i
$378$		0			0
$379$			7.10982i			0.365207i	0.983187	+	0.182603i	$0.0584524\pi$
$379$			7.10982i			0.365207i	−0.983187	+	0.182603i	$0.941548\pi$
$380$		0			0
$381$	2.01226	−	37.8742i	0.103091	−	1.94035i
$382$		0			0
$383$	25.9109	+	25.9109i	1.32398	+	1.32398i	0.910522	+	0.413461i	$0.135680\pi$
$383$	25.9109	+	25.9109i	1.32398	+	1.32398i	0.413461	+	0.910522i	$0.364320\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−8.92602	−	11.0552i	−0.453735	−	0.561969i
$388$		0			0
$389$	−19.4040			−0.983822			−0.491911	−	0.870646i	$-0.663701\pi$
$389$	−19.4040			−0.983822			−0.491911	+	0.870646i	$0.663701\pi$
$390$		0			0
$391$	3.82780			0.193580
$392$		0			0
$393$	−17.3717	+	15.6189i	−0.876285	+	0.787869i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	7.21357	+	7.21357i	0.362039	+	0.362039i	0.864563	−	0.502524i	$-0.167595\pi$
$397$	7.21357	+	7.21357i	0.362039	+	0.362039i	−0.502524	+	0.864563i	$0.667595\pi$
$398$		0			0
$399$	−1.58405	−	0.0841605i	−0.0793015	−	0.00421329i
$400$		0			0
$401$			32.3956i			1.61776i	0.587974	+	0.808879i	$0.299926\pi$
$401$			32.3956i			1.61776i	−0.587974	+	0.808879i	$0.700074\pi$
$402$		0			0
$403$	−18.6383	+	18.6383i	−0.928439	+	0.928439i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.87010	+	2.87010i	−0.142266	+	0.142266i
$408$		0			0
$409$		−	5.27721i		−	0.260941i	−0.991452	−	0.130471i	$-0.958351\pi$
$409$		−	5.27721i		−	0.260941i	0.991452	−	0.130471i	$-0.0416488\pi$
$410$		0			0
$411$	−0.804984	−	0.0427688i	−0.0397069	−	0.00210963i
$412$		0			0
$413$	6.72402	+	6.72402i	0.330867	+	0.330867i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−17.8945	+	16.0890i	−0.876300	+	0.787881i
$418$		0			0
$419$	−19.9881			−0.976480			−0.488240	−	0.872709i	$-0.662361\pi$
$419$	−19.9881			−0.976480			−0.488240	+	0.872709i	$0.662361\pi$
$420$		0			0
$421$	9.48459			0.462251			0.231125	−	0.972924i	$-0.425759\pi$
$421$	9.48459			0.462251			0.231125	+	0.972924i	$0.425759\pi$
$422$		0			0
$423$	20.6458	+	25.5707i	1.00383	+	1.24329i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	0.550265	+	0.550265i	0.0266292	+	0.0266292i
$428$		0			0
$429$	0.539943	−	10.1627i	0.0260687	−	0.490658i
$430$		0			0
$431$		−	13.7200i		−	0.660871i	−0.943829	−	0.330436i	$-0.892804\pi$
$431$		−	13.7200i		−	0.660871i	0.943829	−	0.330436i	$-0.107196\pi$
$432$		0			0
$433$	−18.5650	+	18.5650i	−0.892178	+	0.892178i	−0.994728	−	0.102549i	$-0.967300\pi$
$433$	−18.5650	+	18.5650i	−0.892178	+	0.892178i	0.102549	+	0.994728i	$0.467300\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.85428	+	2.85428i	−0.136539	+	0.136539i
$438$		0			0
$439$			23.0045i			1.09794i	0.835840	+	0.548972i	$0.184981\pi$
$439$			23.0045i			1.09794i	−0.835840	+	0.548972i	$0.815019\pi$
$440$		0			0
$441$	−2.98311	−	0.317883i	−0.142053	−	0.0151373i
$442$		0			0
$443$	−14.3093	−	14.3093i	−0.679856	−	0.679856i	0.280112	−	0.959967i	$-0.409628\pi$
$443$	−14.3093	−	14.3093i	−0.679856	−	0.679856i	−0.959967	+	0.280112i	$0.909628\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	7.23271	+	8.04438i	0.342095	+	0.380486i
$448$		0			0
$449$	−38.3590			−1.81028			−0.905138	−	0.425119i	$-0.860232\pi$
$449$	−38.3590			−1.81028			−0.905138	+	0.425119i	$0.860232\pi$
$450$		0			0
$451$	−1.68394			−0.0792937
$452$		0			0
$453$	9.42504	+	10.4827i	0.442827	+	0.492522i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	22.2772	+	22.2772i	1.04208	+	1.04208i	0.999075	+	0.0430065i	$0.0136936\pi$
$457$	22.2772	+	22.2772i	1.04208	+	1.04208i	0.0430065	+	0.999075i	$0.486306\pi$
$458$		0			0
$459$	−0.715574	+	4.45562i	−0.0334001	+	0.207971i
$460$		0			0
$461$			23.1124i			1.07645i	0.842801	+	0.538226i	$0.180905\pi$
$461$			23.1124i			1.07645i	−0.842801	+	0.538226i	$0.819095\pi$
$462$		0			0
$463$	23.1962	−	23.1962i	1.07802	−	1.07802i	0.0813329	−	0.996687i	$-0.474082\pi$
$463$	23.1962	−	23.1962i	1.07802	−	1.07802i	0.996687	−	0.0813329i	$-0.0259177\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	12.4361	−	12.4361i	0.575472	−	0.575472i	−0.358180	−	0.933652i	$-0.616603\pi$
$467$	12.4361	−	12.4361i	0.575472	−	0.575472i	0.933652	+	0.358180i	$0.116603\pi$
$468$		0			0
$469$			5.59751i			0.258469i
$470$		0			0
$471$	−1.18097	+	22.2279i	−0.0544162	+	1.02421i
$472$		0			0
$473$	6.08442	+	6.08442i	0.279762	+	0.279762i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	10.3377	−	8.34668i	0.473331	−	0.382168i
$478$		0			0
$479$	6.26702			0.286348			0.143174	−	0.989698i	$-0.454269\pi$
$479$	6.26702			0.286348			0.143174	+	0.989698i	$0.454269\pi$
$480$		0			0
$481$	7.22569			0.329463
$482$		0			0
$483$	−5.67686	+	5.10407i	−0.258306	+	0.232243i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−16.4714	−	16.4714i	−0.746390	−	0.746390i	0.227409	−	0.973799i	$-0.426975\pi$
$487$	−16.4714	−	16.4714i	−0.746390	−	0.746390i	−0.973799	+	0.227409i	$0.926975\pi$
$488$		0			0
$489$	−21.0892	−	1.12047i	−0.953688	−	0.0506695i
$490$		0			0
$491$			30.5176i			1.37724i	0.725122	+	0.688621i	$0.241784\pi$
$491$			30.5176i			1.37724i	−0.725122	+	0.688621i	$0.758216\pi$
$492$		0			0
$493$	−4.19963	+	4.19963i	−0.189142	+	0.189142i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−7.07583	+	7.07583i	−0.317394	+	0.317394i
$498$		0			0
$499$		−	10.9169i		−	0.488707i	−0.969686	−	0.244353i	$-0.921424\pi$
$499$		−	10.9169i		−	0.488707i	0.969686	−	0.244353i	$-0.0785757\pi$
$500$		0			0
$501$	−10.7655	−	0.571974i	−0.480969	−	0.0255539i
$502$		0			0
$503$	2.38329	+	2.38329i	0.106266	+	0.106266i	0.758240	−	0.651975i	$-0.226059\pi$
$503$	2.38329	+	2.38329i	0.106266	+	0.106266i	−0.651975	+	0.758240i	$0.726059\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	3.27170	−	2.94158i	0.145301	−	0.130640i
$508$		0			0
$509$	2.79313			0.123804			0.0619018	−	0.998082i	$-0.480283\pi$
$509$	2.79313			0.123804			0.0619018	+	0.998082i	$0.480283\pi$
$510$		0			0
$511$	4.96509			0.219642
$512$		0			0
$513$	−2.78885	−	3.85602i	−0.123131	−	0.170247i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−14.0732	−	14.0732i	−0.618940	−	0.618940i
$518$		0			0
$519$	−0.487784	+	9.18095i	−0.0214114	+	0.402999i
$520$		0			0
$521$		−	27.7166i		−	1.21428i	−0.794593	−	0.607142i	$-0.792316\pi$
$521$		−	27.7166i		−	1.21428i	0.794593	−	0.607142i	$-0.207684\pi$
$522$		0			0
$523$	28.9685	−	28.9685i	1.26670	−	1.26670i	0.318922	−	0.947781i	$-0.396679\pi$
$523$	28.9685	−	28.9685i	1.26670	−	1.26670i	0.947781	−	0.318922i	$-0.103321\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−5.00494	+	5.00494i	−0.218019	+	0.218019i
$528$		0			0
$529$		−	3.57392i		−	0.155388i
$530$		0			0
$531$	−3.02281	+	28.3670i	−0.131179	+	1.23102i
$532$		0			0
$533$	2.11972	+	2.11972i	0.0918154	+	0.0918154i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−14.7485	−	16.4036i	−0.636444	−	0.707867i
$538$		0			0
$539$	1.81675			0.0782531
$540$		0			0
$541$	4.67695			0.201078			0.100539	−	0.994933i	$-0.467943\pi$
$541$	4.67695			0.201078			0.100539	+	0.994933i	$0.467943\pi$
$542$		0			0
$543$	14.2866	+	15.8899i	0.613098	+	0.681902i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	7.58370	+	7.58370i	0.324255	+	0.324255i	0.850397	−	0.526142i	$-0.176362\pi$
$547$	7.58370	+	7.58370i	0.324255	+	0.324255i	−0.526142	+	0.850397i	$0.676362\pi$
$548$		0			0
$549$	−0.247374	+	2.32144i	−0.0105577	+	0.0990764i
$550$		0			0
$551$		−	6.26309i		−	0.266817i
$552$		0			0
$553$	6.12592	−	6.12592i	0.260501	−	0.260501i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−2.69726	+	2.69726i	−0.114287	+	0.114287i	−0.761937	−	0.647651i	$-0.775752\pi$
$557$	−2.69726	+	2.69726i	−0.114287	+	0.114287i	0.647651	+	0.761937i	$0.275752\pi$
$558$		0			0
$559$		−	15.3180i		−	0.647881i
$560$		0			0
$561$	0.144991	−	2.72898i	0.00612152	−	0.115218i
$562$		0			0
$563$	10.5552	+	10.5552i	0.444849	+	0.444849i	0.893638	−	0.448789i	$-0.148144\pi$
$563$	10.5552	+	10.5552i	0.444849	+	0.444849i	−0.448789	+	0.893638i	$0.648144\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−4.87998	−	7.56213i	−0.204940	−	0.317579i
$568$		0			0
$569$	−41.9498			−1.75863			−0.879313	−	0.476244i	$-0.841998\pi$
$569$	−41.9498			−1.75863			−0.879313	+	0.476244i	$0.841998\pi$
$570$		0			0
$571$	−40.1607			−1.68067			−0.840336	−	0.542066i	$-0.817642\pi$
$571$	−40.1607			−1.68067			−0.840336	+	0.542066i	$0.817642\pi$
$572$		0			0
$573$	34.7295	−	31.2253i	1.45085	−	1.30446i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	21.8604	+	21.8604i	0.910060	+	0.910060i	0.996276	−	0.0862162i	$-0.0274776\pi$
$577$	21.8604	+	21.8604i	0.910060	+	0.910060i	−0.0862162	+	0.996276i	$0.527478\pi$
$578$		0			0
$579$	16.0801	+	0.854334i	0.668264	+	0.0355049i
$580$		0			0
$581$		−	13.5458i		−	0.561973i
$582$		0			0
$583$	−5.68952	+	5.68952i	−0.235636	+	0.235636i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	3.94407	−	3.94407i	0.162789	−	0.162789i	−0.621012	−	0.783801i	$-0.713278\pi$
$587$	3.94407	−	3.94407i	0.162789	−	0.162789i	0.783801	+	0.621012i	$0.213278\pi$
$588$		0			0
$589$		−	7.46410i		−	0.307553i
$590$		0			0
$591$	−6.24757	−	0.331934i	−0.256991	−	0.0136539i
$592$		0			0
$593$	29.0441	+	29.0441i	1.19270	+	1.19270i	0.976306	+	0.216393i	$0.0694292\pi$
$593$	29.0441	+	29.0441i	1.19270	+	1.19270i	0.216393	+	0.976306i	$0.430571\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−24.7025	+	22.2100i	−1.01101	+	0.908996i
$598$		0			0
$599$	9.24338			0.377674			0.188837	−	0.982008i	$-0.439528\pi$
$599$	9.24338			0.377674			0.188837	+	0.982008i	$0.439528\pi$
$600$		0			0
$601$	30.7255			1.25332			0.626660	−	0.779293i	$-0.284421\pi$
$601$	30.7255			1.25332			0.626660	+	0.779293i	$0.284421\pi$
$602$		0			0
$603$	−13.0655	+	10.5491i	−0.532066	+	0.429591i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	5.82544	+	5.82544i	0.236447	+	0.236447i	0.815377	−	0.578930i	$-0.196530\pi$
$607$	5.82544	+	5.82544i	0.236447	+	0.236447i	−0.578930	+	0.815377i	$0.696530\pi$
$608$		0			0
$609$	0.628432	−	11.8282i	0.0254654	−	0.479302i
$610$		0			0
$611$			35.4304i			1.43336i
$612$		0			0
$613$	22.7731	−	22.7731i	0.919797	−	0.919797i	−0.0772173	−	0.997014i	$-0.524604\pi$
$613$	22.7731	−	22.7731i	0.919797	−	0.919797i	0.997014	+	0.0772173i	$0.0246035\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.793772	+	0.793772i	−0.0319561	+	0.0319561i	−0.722904	−	0.690948i	$-0.757193\pi$
$617$	−0.793772	+	0.793772i	−0.0319561	+	0.0319561i	0.690948	+	0.722904i	$0.257193\pi$
$618$		0			0
$619$		−	9.04339i		−	0.363485i	−0.983346	−	0.181742i	$-0.941826\pi$
$619$		−	9.04339i		−	0.363485i	0.983346	−	0.181742i	$-0.0581737\pi$
$620$		0			0
$621$	−22.6123	−	3.63154i	−0.907400	−	0.145729i
$622$		0			0
$623$	5.74228	+	5.74228i	0.230060	+	0.230060i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	1.92681	+	2.14304i	0.0769494	+	0.0855849i
$628$		0			0
$629$	1.94032			0.0773655
$630$		0			0
$631$	−23.3225			−0.928453			−0.464227	−	0.885716i	$-0.653668\pi$
$631$	−23.3225			−0.928453			−0.464227	+	0.885716i	$0.653668\pi$
$632$		0			0
$633$	3.00443	+	3.34159i	0.119415	+	0.132816i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−2.28690	−	2.28690i	−0.0906104	−	0.0906104i
$638$		0			0
$639$	−29.8512	−	3.18097i	−1.18089	−	0.125837i
$640$		0			0
$641$		−	37.4896i		−	1.48075i	−0.672194	−	0.740375i	$-0.734648\pi$
$641$		−	37.4896i		−	1.48075i	0.672194	−	0.740375i	$-0.265352\pi$
$642$		0			0
$643$	−13.0507	+	13.0507i	−0.514669	+	0.514669i	−0.915953	−	0.401285i	$-0.868564\pi$
$643$	−13.0507	+	13.0507i	−0.514669	+	0.514669i	0.401285	+	0.915953i	$0.368564\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−12.9234	+	12.9234i	−0.508073	+	0.508073i	−0.913935	−	0.405861i	$-0.866972\pi$
$647$	−12.9234	+	12.9234i	−0.508073	+	0.508073i	0.405861	+	0.913935i	$0.366972\pi$
$648$		0			0
$649$		−	17.2759i		−	0.678137i
$650$		0			0
$651$	0.748940	−	14.0964i	0.0293533	−	0.552480i
$652$		0			0
$653$	−31.8165	−	31.8165i	−1.24508	−	1.24508i	−0.957869	−	0.287206i	$-0.907273\pi$
$653$	−31.8165	−	31.8165i	−1.24508	−	1.24508i	−0.287206	−	0.957869i	$-0.592727\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	9.35720	+	11.5893i	0.365059	+	0.452141i
$658$		0			0
$659$	34.7626			1.35416			0.677079	−	0.735910i	$-0.263246\pi$
$659$	34.7626			1.35416			0.677079	+	0.735910i	$0.263246\pi$
$660$		0			0
$661$	−32.2224			−1.25331			−0.626653	−	0.779299i	$-0.715575\pi$
$661$	−32.2224			−1.25331			−0.626653	+	0.779299i	$0.715575\pi$
$662$		0			0
$663$	−3.61772	+	3.25269i	−0.140500	+	0.126324i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−21.3131	−	21.3131i	−0.825248	−	0.825248i
$668$		0			0
$669$	2.46460	+	0.130945i	0.0952871	+	0.00506261i
$670$		0			0
$671$		−	1.41378i		−	0.0545785i
$672$		0			0
$673$	3.83342	−	3.83342i	0.147767	−	0.147767i	−0.629353	−	0.777120i	$-0.716680\pi$
$673$	3.83342	−	3.83342i	0.147767	−	0.147767i	0.777120	+	0.629353i	$0.216680\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−2.73452	+	2.73452i	−0.105096	+	0.105096i	−0.757700	−	0.652603i	$-0.773677\pi$
$677$	−2.73452	+	2.73452i	−0.105096	+	0.105096i	0.652603	+	0.757700i	$0.273677\pi$
$678$		0			0
$679$			4.71969i			0.181125i
$680$		0			0
$681$	−15.1387	−	0.804319i	−0.580116	−	0.0308216i
$682$		0			0
$683$	6.43426	+	6.43426i	0.246200	+	0.246200i	0.819409	−	0.573209i	$-0.194302\pi$
$683$	6.43426	+	6.43426i	0.246200	+	0.246200i	−0.573209	+	0.819409i	$0.694302\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−23.0100	+	20.6883i	−0.877885	+	0.789307i
$688$		0			0
$689$	14.3238			0.545693
$690$		0			0
$691$	−11.3311			−0.431054			−0.215527	−	0.976498i	$-0.569147\pi$
$691$	−11.3311			−0.431054			−0.215527	+	0.976498i	$0.569147\pi$
$692$		0			0
$693$	3.42385	+	4.24058i	0.130061	+	0.161086i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	0.569209	+	0.569209i	0.0215603	+	0.0215603i
$698$		0			0
$699$	−2.41352	+	45.4265i	−0.0912875	+	1.71819i
$700$		0			0
$701$			6.58848i			0.248843i	0.992229	+	0.124422i	$0.0397076\pi$
$701$			6.58848i			0.248843i	−0.992229	+	0.124422i	$0.960292\pi$
$702$		0			0
$703$	−1.44684	+	1.44684i	−0.0545686	+	0.0545686i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	9.86331	−	9.86331i	0.370948	−	0.370948i
$708$		0			0
$709$			21.3143i			0.800475i	0.916411	+	0.400238i	$0.131072\pi$
$709$			21.3143i			0.800475i	−0.916411	+	0.400238i	$0.868928\pi$
$710$		0			0
$711$	25.8438	+	2.75393i	0.969217	+	0.103281i
$712$		0			0
$713$	−25.4001	−	25.4001i	−0.951242	−	0.951242i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	10.8949	+	12.1175i	0.406876	+	0.452536i
$718$		0			0
$719$	−24.6692			−0.920007			−0.460004	−	0.887917i	$-0.652152\pi$
$719$	−24.6692			−0.920007			−0.460004	+	0.887917i	$0.652152\pi$
$720$		0			0
$721$	13.2496			0.493442
$722$		0			0
$723$	−29.7622	−	33.1022i	−1.10687	−	1.23108i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−20.8410	−	20.8410i	−0.772950	−	0.772950i	0.205671	−	0.978621i	$-0.434062\pi$
$727$	−20.8410	−	20.8410i	−0.772950	−	0.772950i	−0.978621	+	0.205671i	$0.934062\pi$
$728$		0			0
$729$	8.45435	−	25.6422i	0.313124	−	0.949712i
$730$		0			0
$731$		−	4.11334i		−	0.152137i
$732$		0			0
$733$	−11.1136	+	11.1136i	−0.410489	+	0.410489i	−0.881909	−	0.471420i	$-0.843742\pi$
$733$	−11.1136	+	11.1136i	−0.410489	+	0.410489i	0.471420	+	0.881909i	$0.343742\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	7.19077	−	7.19077i	0.264876	−	0.264876i
$738$		0			0
$739$		−	32.2705i		−	1.18709i	−0.804801	−	0.593544i	$-0.797728\pi$
$739$		−	32.2705i		−	1.18709i	0.804801	−	0.593544i	$-0.202272\pi$
$740$		0			0
$741$	0.272189	−	5.12308i	0.00999913	−	0.188201i
$742$		0			0
$743$	8.15183	+	8.15183i	0.299062	+	0.299062i	0.840646	−	0.541585i	$-0.182175\pi$
$743$	8.15183	+	8.15183i	0.299062	+	0.299062i	−0.541585	+	0.840646i	$0.682175\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	31.6179	−	25.5284i	1.15684	−	0.934033i
$748$		0			0
$749$	3.32771			0.121592
$750$		0			0
$751$	−42.8741			−1.56450			−0.782248	−	0.622967i	$-0.785927\pi$
$751$	−42.8741			−1.56450			−0.782248	+	0.622967i	$0.785927\pi$
$752$		0			0
$753$	28.0709	−	25.2385i	1.02296	−	0.919743i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−20.3539	−	20.3539i	−0.739775	−	0.739775i	0.232759	−	0.972534i	$-0.425225\pi$
$757$	−20.3539	−	20.3539i	−0.739775	−	0.739775i	−0.972534	+	0.232759i	$0.925225\pi$
$758$		0			0
$759$	13.8496	+	0.735830i	0.502708	+	0.0267089i
$760$		0			0
$761$		−	6.31471i		−	0.228908i	−0.993429	−	0.114454i	$-0.963488\pi$
$761$		−	6.31471i		−	0.228908i	0.993429	−	0.114454i	$-0.0365119\pi$
$762$		0			0
$763$	3.41651	−	3.41651i	0.123686	−	0.123686i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−21.7466	+	21.7466i	−0.785225	+	0.785225i
$768$		0			0
$769$		−	22.2423i		−	0.802078i	−0.916061	−	0.401039i	$-0.868649\pi$
$769$		−	22.2423i		−	0.802078i	0.916061	−	0.401039i	$-0.131351\pi$
$770$		0			0
$771$	35.9980	+	1.91258i	1.29644	+	0.0688798i
$772$		0			0
$773$	5.98186	+	5.98186i	0.215153	+	0.215153i	0.806452	−	0.591299i	$-0.201385\pi$
$773$	5.98186	+	5.98186i	0.215153	+	0.215153i	−0.591299	+	0.806452i	$0.701385\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−2.87761	+	2.58726i	−0.103234	+	0.0928175i
$778$		0			0
$779$	−0.848888			−0.0304146
$780$		0			0
$781$	18.1798			0.650523
$782$		0			0
$783$	28.7932	−	20.8245i	1.02898	−	0.744209i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	7.56921	+	7.56921i	0.269813	+	0.269813i	0.829025	−	0.559212i	$-0.188896\pi$
$787$	7.56921	+	7.56921i	0.269813	+	0.269813i	−0.559212	+	0.829025i	$0.688896\pi$
$788$		0			0
$789$	2.86819	−	53.9843i	0.102110	−	1.92189i
$790$		0			0
$791$		−	10.8605i		−	0.386156i
$792$		0			0
$793$	−1.77965	+	1.77965i	−0.0631973	+	0.0631973i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−3.62534	+	3.62534i	−0.128416	+	0.128416i	−0.768394	−	0.639977i	$-0.778944\pi$
$797$	−3.62534	+	3.62534i	−0.128416	+	0.128416i	0.639977	+	0.768394i	$0.278944\pi$
$798$		0			0
$799$			9.51413i			0.336586i
$800$		0			0
$801$	−2.58147	+	24.2253i	−0.0912118	+	0.855959i
$802$		0			0
$803$	−6.37834	−	6.37834i	−0.225087	−	0.225087i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	6.88893	+	7.66202i	0.242502	+	0.269716i
$808$		0			0
$809$	43.5699			1.53184			0.765918	−	0.642939i	$-0.222285\pi$
$809$	43.5699			1.53184			0.765918	+	0.642939i	$0.222285\pi$
$810$		0			0
$811$	−33.3205			−1.17004			−0.585021	−	0.811018i	$-0.698914\pi$
$811$	−33.3205			−1.17004			−0.585021	+	0.811018i	$0.698914\pi$
$812$		0			0
$813$	−12.5031	−	13.9062i	−0.438503	−	0.487713i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	3.06720	+	3.06720i	0.107308	+	0.107308i
$818$		0			0
$819$	1.02809	−	9.64789i	0.0359243	−	0.337125i
$820$		0			0
$821$			41.4901i			1.44801i	0.689792	+	0.724007i	$0.257702\pi$
$821$			41.4901i			1.44801i	−0.689792	+	0.724007i	$0.742298\pi$
$822$		0			0
$823$	3.05418	−	3.05418i	0.106462	−	0.106462i	−0.651869	−	0.758331i	$-0.726015\pi$
$823$	3.05418	−	3.05418i	0.106462	−	0.106462i	0.758331	+	0.651869i	$0.226015\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−12.0224	+	12.0224i	−0.418059	+	0.418059i	−0.884534	−	0.466475i	$-0.845524\pi$
$827$	−12.0224	+	12.0224i	−0.418059	+	0.418059i	0.466475	+	0.884534i	$0.345524\pi$
$828$		0			0
$829$			16.7660i			0.582309i	0.956676	+	0.291154i	$0.0940393\pi$
$829$			16.7660i			0.582309i	−0.956676	+	0.291154i	$0.905961\pi$
$830$		0			0
$831$	2.20314	−	41.4669i	0.0764261	−	1.43847i
$832$		0			0
$833$	−0.614103	−	0.614103i	−0.0212774	−	0.0212774i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	34.3145	−	24.8178i	1.18608	−	0.857830i
$838$		0			0
$839$	−53.8374			−1.85867			−0.929337	−	0.369232i	$-0.879621\pi$
$839$	−53.8374			−1.85867			−0.929337	+	0.369232i	$0.879621\pi$
$840$		0			0
$841$	17.7670			0.612654
$842$		0			0
$843$	−23.8174	+	21.4142i	−0.820314	+	0.737545i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	5.44430	+	5.44430i	0.187069	+	0.187069i
$848$		0			0
$849$	−17.7723	−	0.944241i	−0.609943	−	0.0324063i
$850$		0			0
$851$			9.84712i			0.337555i
$852$		0			0
$853$	−39.8451	+	39.8451i	−1.36427	+	1.36427i	−0.495878	+	0.868392i	$0.665154\pi$
$853$	−39.8451	+	39.8451i	−1.36427	+	1.36427i	−0.868392	+	0.495878i	$0.834846\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	25.2268	−	25.2268i	0.861730	−	0.861730i	−0.129809	−	0.991539i	$-0.541436\pi$
$857$	25.2268	−	25.2268i	0.861730	−	0.861730i	0.991539	+	0.129809i	$0.0414364\pi$
$858$		0			0
$859$			40.9390i			1.39682i	0.715698	+	0.698410i	$0.246109\pi$
$859$			40.9390i			1.39682i	−0.715698	+	0.698410i	$0.753891\pi$
$860$		0			0
$861$	−1.60317	−	0.0851765i	−0.0546359	−	0.00290281i
$862$		0			0
$863$	−19.4574	−	19.4574i	−0.662338	−	0.662338i	0.293592	−	0.955931i	$-0.405149\pi$
$863$	−19.4574	−	19.4574i	−0.662338	−	0.662338i	−0.955931	+	0.293592i	$0.905149\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	20.9245	−	18.8132i	0.710634	−	0.638931i
$868$		0			0
$869$	−15.7392			−0.533915
$870$		0			0
$871$	−18.1033			−0.613407
$872$		0			0
$873$	−11.0165	+	8.89473i	−0.372851	+	0.301041i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	30.0431	+	30.0431i	1.01448	+	1.01448i	0.999894	+	0.0145904i	$0.00464444\pi$
$877$	30.0431	+	30.0431i	1.01448	+	1.01448i	0.0145904	+	0.999894i	$0.495356\pi$
$878$		0			0
$879$	0.212670	−	4.00282i	0.00717318	−	0.135012i
$880$		0			0
$881$			16.6290i			0.560247i	0.959964	+	0.280123i	$0.0903753\pi$
$881$			16.6290i			0.560247i	−0.959964	+	0.280123i	$0.909625\pi$
$882$		0			0
$883$	28.0848	−	28.0848i	0.945128	−	0.945128i	−0.0534426	−	0.998571i	$-0.517019\pi$
$883$	28.0848	−	28.0848i	0.945128	−	0.945128i	0.998571	+	0.0534426i	$0.0170194\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	20.3800	−	20.3800i	0.684293	−	0.684293i	−0.276671	−	0.960965i	$-0.589231\pi$
$887$	20.3800	−	20.3800i	0.684293	−	0.684293i	0.960965	+	0.276671i	$0.0892314\pi$
$888$		0			0
$889$			21.8975i			0.734420i
$890$		0			0
$891$	−3.44558	+	15.9836i	−0.115431	+	0.535471i
$892$		0			0
$893$	−7.09442	−	7.09442i	−0.237406	−	0.237406i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−16.5074	−	18.3599i	−0.551167	−	0.613020i
$898$		0			0
$899$	55.7350			1.85887
$900$		0			0
$901$	3.84637			0.128141
$902$		0			0
$903$	5.48482	+	6.10034i	0.182523	+	0.203007i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−25.1542	−	25.1542i	−0.835230	−	0.835230i	0.152997	−	0.988227i	$-0.451108\pi$
$907$	−25.1542	−	25.1542i	−0.835230	−	0.835230i	−0.988227	+	0.152997i	$0.951108\pi$
$908$		0			0
$909$	41.6109	+	4.43409i	1.38015	+	0.147070i
$910$		0			0
$911$			33.1054i			1.09683i	0.836206	+	0.548416i	$0.184769\pi$
$911$			33.1054i			1.09683i	−0.836206	+	0.548416i	$0.815231\pi$
$912$		0			0
$913$	−17.4014	+	17.4014i	−0.575902	+	0.575902i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	9.53699	−	9.53699i	0.314939	−	0.314939i
$918$		0			0
$919$			34.1197i			1.12550i	0.826626	+	0.562752i	$0.190258\pi$
$919$			34.1197i			1.12550i	−0.826626	+	0.562752i	$0.809742\pi$
$920$		0			0
$921$	1.26681	−	23.8436i	0.0417429	−	0.785674i
$922$		0			0
$923$	−22.8844	−	22.8844i	−0.753250	−	0.753250i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	24.9703	+	30.9267i	0.820132	+	1.01577i
$928$		0			0
$929$	51.1795			1.67914			0.839572	−	0.543248i	$-0.182806\pi$
$929$	51.1795			1.67914			0.839572	+	0.543248i	$0.182806\pi$
$930$		0			0
$931$	0.915840			0.0300154
$932$		0			0
$933$	−8.31023	+	7.47173i	−0.272065	+	0.244614i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−26.5430	−	26.5430i	−0.867123	−	0.867123i	0.125030	−	0.992153i	$-0.460097\pi$
$937$	−26.5430	−	26.5430i	−0.867123	−	0.867123i	−0.992153	+	0.125030i	$0.960097\pi$
$938$		0			0
$939$	25.3955	+	1.34927i	0.828752	+	0.0440317i
$940$		0			0
$941$		−	55.1606i		−	1.79818i	−0.437761	−	0.899092i	$-0.644228\pi$
$941$		−	55.1606i		−	1.79818i	0.437761	−	0.899092i	$-0.355772\pi$
$942$		0			0
$943$	−2.88874	+	2.88874i	−0.0940703	+	0.0940703i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	27.9440	−	27.9440i	0.908057	−	0.908057i	−0.0880583	−	0.996115i	$-0.528066\pi$
$947$	27.9440	−	27.9440i	0.908057	−	0.908057i	0.996115	+	0.0880583i	$0.0280662\pi$
$948$		0			0
$949$			16.0579i			0.521263i
$950$		0			0
$951$	52.0797	+	2.76700i	1.68880	+	0.0897261i
$952$		0			0
$953$	−27.2403	−	27.2403i	−0.882399	−	0.882399i	0.111379	−	0.993778i	$-0.464473\pi$
$953$	−27.2403	−	27.2403i	−0.882399	−	0.882399i	−0.993778	+	0.111379i	$0.964473\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−16.0022	+	14.3876i	−0.517279	+	0.465086i
$958$		0			0
$959$	0.465413			0.0150290
$960$		0			0
$961$	35.4227			1.14267
$962$		0			0
$963$	6.27140	+	7.76739i	0.202093	+	0.250301i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−8.88371	−	8.88371i	−0.285681	−	0.285681i	0.549689	−	0.835370i	$-0.314746\pi$
$967$	−8.88371	−	8.88371i	−0.285681	−	0.285681i	−0.835370	+	0.549689i	$0.814746\pi$
$968$		0			0
$969$	0.0730911	−	1.37570i	0.00234802	−	0.0441939i
$970$		0			0
$971$		−	47.3377i		−	1.51914i	−0.650426	−	0.759569i	$-0.725410\pi$
$971$		−	47.3377i		−	1.51914i	0.650426	−	0.759569i	$-0.274590\pi$
$972$		0			0
$973$	9.82404	−	9.82404i	0.314944	−	0.314944i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	21.5847	−	21.5847i	0.690557	−	0.690557i	−0.271798	−	0.962354i	$-0.587618\pi$
$977$	21.5847	−	21.5847i	0.690557	−	0.690557i	0.962354	+	0.271798i	$0.0876181\pi$
$978$		0			0
$979$		−	14.7535i		−	0.471524i
$980$		0			0
$981$	14.4134	+	1.53591i	0.460186	+	0.0490378i
$982$		0			0
$983$	27.9392	+	27.9392i	0.891121	+	0.891121i	0.994629	−	0.103508i	$-0.0330067\pi$
$983$	27.9392	+	27.9392i	0.891121	+	0.891121i	−0.103508	+	0.994629i	$0.533007\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−12.6863	−	14.1100i	−0.403811	−	0.449128i
$988$		0			0
$989$	20.8752			0.663793
$990$		0			0
$991$	24.2120			0.769119			0.384559	−	0.923100i	$-0.374353\pi$
$991$	24.2120			0.769119			0.384559	+	0.923100i	$0.374353\pi$
$992$		0			0
$993$	−26.1017	−	29.0309i	−0.828314	−	0.921269i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	12.0723	+	12.0723i	0.382334	+	0.382334i	0.871942	−	0.489608i	$-0.162860\pi$
$997$	12.0723	+	12.0723i	0.382334	+	0.382334i	−0.489608	+	0.871942i	$0.662860\pi$
$998$		0			0
$999$	−11.4622	−	1.84083i	−0.362648	−	0.0582414i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.s.c.1457.5	yes	32
3.2	odd	2	inner	2100.2.s.c.1457.13	yes	32
5.2	odd	4	inner	2100.2.s.c.1793.4	yes	32
5.3	odd	4	inner	2100.2.s.c.1793.13	yes	32
5.4	even	2	inner	2100.2.s.c.1457.12	yes	32
15.2	even	4	inner	2100.2.s.c.1793.12	yes	32
15.8	even	4	inner	2100.2.s.c.1793.5	yes	32
15.14	odd	2	inner	2100.2.s.c.1457.4	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.s.c.1457.4	✓	32	15.14	odd	2	inner
2100.2.s.c.1457.5	yes	32	1.1	even	1	trivial
2100.2.s.c.1457.12	yes	32	5.4	even	2	inner
2100.2.s.c.1457.13	yes	32	3.2	odd	2	inner
2100.2.s.c.1793.4	yes	32	5.2	odd	4	inner
2100.2.s.c.1793.5	yes	32	15.8	even	4	inner
2100.2.s.c.1793.12	yes	32	15.2	even	4	inner
2100.2.s.c.1793.13	yes	32	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2100.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.15804 - 1.28800i) q^{3} +(0.707107 + 0.707107i) q^{7} +(-0.317883 + 2.98311i) q^{9} +O(q^{10})\)	\(q+(-1.15804 - 1.28800i) q^{3} +(0.707107 + 0.707107i) q^{7} +(-0.317883 + 2.98311i) q^{9} -1.81675i q^{11} +(-2.28690 + 2.28690i) q^{13} +(-0.614103 + 0.614103i) q^{17} -0.915840i q^{19} +(0.0918944 - 1.72961i) q^{21} +(-3.11658 - 3.11658i) q^{23} +(4.21037 - 3.04513i) q^{27} +6.83864 q^{29} +8.15001 q^{31} +(-2.33998 + 2.10387i) q^{33} +(-1.57980 - 1.57980i) q^{37} +(5.59386 + 0.297202i) q^{39} -0.926896i q^{41} +(-3.34906 + 3.34906i) q^{43} +(7.74636 - 7.74636i) q^{47} +1.00000i q^{49} +(1.50212 + 0.0798077i) q^{51} +(-3.13170 - 3.13170i) q^{53} +(-1.17960 + 1.06058i) q^{57} +9.50920 q^{59} +0.778193 q^{61} +(-2.33416 + 1.88460i) q^{63} +(3.95804 + 3.95804i) q^{67} +(-0.405025 + 7.62327i) q^{69} +10.0067i q^{71} +(3.51085 - 3.51085i) q^{73} +(1.28464 - 1.28464i) q^{77} -8.66336i q^{79} +(-8.79790 - 1.89656i) q^{81} +(-9.57830 - 9.57830i) q^{83} +(-7.91942 - 8.80816i) q^{87} +8.12082 q^{89} -3.23417 q^{91} +(-9.43804 - 10.4972i) q^{93} +(3.33732 + 3.33732i) q^{97} +(5.41958 + 0.577515i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{21} + 48 q^{31} - 32 q^{51} + 16 q^{61} + 64 q^{81} + 32 q^{91}+O(q^{100}) \) 32 * q - 8 * q^21 + 48 * q^31 - 32 * q^51 + 16 * q^61 + 64 * q^81 + 32 * q^91

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