LMFDB - Embedded newform 2100.2.s.b.1457.6

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:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 420)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1457.6
Character	$\chi$	$=$	2100.1457
Dual form			2100.2.s.b.1793.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.210923 + 1.71916i) q^{3} +(0.707107 + 0.707107i) q^{7} +(-2.91102 + 0.725222i) q^{9} +O(q^{10})$	$q+(0.210923 + 1.71916i) q^{3} +(0.707107 + 0.707107i) q^{7} +(-2.91102 + 0.725222i) q^{9} -6.43376i q^{11} +(-4.23809 + 4.23809i) q^{13} +(1.00413 - 1.00413i) q^{17} -6.08104i q^{19} +(-1.06648 + 1.36478i) q^{21} +(-0.649352 - 0.649352i) q^{23} +(-1.86078 - 4.85155i) q^{27} +0.486067 q^{29} -2.38204 q^{31} +(11.0607 - 1.35703i) q^{33} +(-4.10080 - 4.10080i) q^{37} +(-8.17987 - 6.39205i) q^{39} -5.91916i q^{41} +(6.74855 - 6.74855i) q^{43} +(-4.70030 + 4.70030i) q^{47} +1.00000i q^{49} +(1.93806 + 1.51447i) q^{51} +(-4.00778 - 4.00778i) q^{53} +(10.4543 - 1.28263i) q^{57} +8.86958 q^{59} -7.72565 q^{61} +(-2.57121 - 1.54559i) q^{63} +(-8.66039 - 8.66039i) q^{67} +(0.979376 - 1.25330i) q^{69} +0.938289i q^{71} +(0.399054 - 0.399054i) q^{73} +(4.54936 - 4.54936i) q^{77} +6.65496i q^{79} +(7.94811 - 4.22228i) q^{81} +(8.35674 + 8.35674i) q^{83} +(0.102523 + 0.835627i) q^{87} +8.32068 q^{89} -5.99357 q^{91} +(-0.502428 - 4.09511i) q^{93} +(1.26743 + 1.26743i) q^{97} +(4.66591 + 18.7288i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3}+O(q^{10}) $ 24 * q + 4 * q^3	$ 24 q + 4 q^{3} - 24 q^{13} + 4 q^{21} - 8 q^{27} - 16 q^{31} + 20 q^{33} - 32 q^{37} + 8 q^{43} + 52 q^{51} + 28 q^{57} - 8 q^{63} + 24 q^{67} - 12 q^{81} + 20 q^{87} - 24 q^{91} - 20 q^{93} + 104 q^{97}+O(q^{100}) $ 24 * q + 4 * q^3 - 24 * q^13 + 4 * q^21 - 8 * q^27 - 16 * q^31 + 20 * q^33 - 32 * q^37 + 8 * q^43 + 52 * q^51 + 28 * q^57 - 8 * q^63 + 24 * q^67 - 12 * q^81 + 20 * q^87 - 24 * q^91 - 20 * q^93 + 104 * q^97

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
$3$	0.210923	+	1.71916i	0.121777	+	0.992558i
$3$	0.210923	+	1.71916i	0.121777	+	0.992558i
$4$		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
$9$	−2.91102	+	0.725222i	−0.970341	+	0.241741i
$10$		0			0
$11$		−	6.43376i		−	1.93985i	−0.243398	−	0.969926i	$-0.578262\pi$
$11$		−	6.43376i		−	1.93985i	0.243398	−	0.969926i	$-0.421738\pi$
$12$		0			0
$13$	−4.23809	+	4.23809i	−1.17544	+	1.17544i	−0.194541	+	0.980894i	$0.562322\pi$
$13$	−4.23809	+	4.23809i	−1.17544	+	1.17544i	−0.980894	+	0.194541i	$0.937678\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.00413	−	1.00413i	0.243538	−	0.243538i	−0.574774	−	0.818312i	$-0.694910\pi$
$17$	1.00413	−	1.00413i	0.243538	−	0.243538i	0.818312	+	0.574774i	$0.194910\pi$
$18$		0			0
$19$		−	6.08104i		−	1.39509i	−0.716543	−	0.697543i	$-0.754277\pi$
$19$		−	6.08104i		−	1.39509i	0.716543	−	0.697543i	$-0.245723\pi$
$20$		0			0
$21$	−1.06648	+	1.36478i	−0.232726	+	0.297818i
$22$		0			0
$23$	−0.649352	−	0.649352i	−0.135399	−	0.135399i	0.636159	−	0.771558i	$-0.280522\pi$
$23$	−0.649352	−	0.649352i	−0.135399	−	0.135399i	−0.771558	+	0.636159i	$0.780522\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−1.86078	−	4.85155i	−0.358107	−	0.933681i
$28$		0			0
$29$	0.486067			0.0902604			0.0451302	−	0.998981i	$-0.485630\pi$
$29$	0.486067			0.0902604			0.0451302	+	0.998981i	$0.485630\pi$
$30$		0			0
$31$	−2.38204			−0.427827			−0.213914	−	0.976853i	$-0.568621\pi$
$31$	−2.38204			−0.427827			−0.213914	+	0.976853i	$0.568621\pi$
$32$		0			0
$33$	11.0607	−	1.35703i	1.92542	−	0.236229i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−4.10080	−	4.10080i	−0.674167	−	0.674167i	0.284507	−	0.958674i	$-0.408170\pi$
$37$	−4.10080	−	4.10080i	−0.674167	−	0.674167i	−0.958674	+	0.284507i	$0.908170\pi$
$38$		0			0
$39$	−8.17987	−	6.39205i	−1.30983	−	1.02355i
$40$		0			0
$41$		−	5.91916i		−	0.924418i	−0.886771	−	0.462209i	$-0.847057\pi$
$41$		−	5.91916i		−	0.924418i	0.886771	−	0.462209i	$-0.152943\pi$
$42$		0			0
$43$	6.74855	−	6.74855i	1.02914	−	1.02914i	0.0295826	−	0.999562i	$-0.490582\pi$
$43$	6.74855	−	6.74855i	1.02914	−	1.02914i	0.999562	−	0.0295826i	$-0.00941781\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.70030	+	4.70030i	−0.685610	+	0.685610i	−0.961258	−	0.275649i	$-0.911107\pi$
$47$	−4.70030	+	4.70030i	−0.685610	+	0.685610i	0.275649	+	0.961258i	$0.411107\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$	1.93806	+	1.51447i	0.271383	+	0.212069i
$52$		0			0
$53$	−4.00778	−	4.00778i	−0.550511	−	0.550511i	0.376077	−	0.926588i	$-0.377273\pi$
$53$	−4.00778	−	4.00778i	−0.550511	−	0.550511i	−0.926588	+	0.376077i	$0.877273\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	10.4543	−	1.28263i	1.38470	−	0.169889i
$58$		0			0
$59$	8.86958			1.15472			0.577360	−	0.816490i	$-0.304083\pi$
$59$	8.86958			1.15472			0.577360	+	0.816490i	$0.304083\pi$
$60$		0			0
$61$	−7.72565			−0.989168			−0.494584	−	0.869130i	$-0.664680\pi$
$61$	−7.72565			−0.989168			−0.494584	+	0.869130i	$0.664680\pi$
$62$		0			0
$63$	−2.57121	−	1.54559i	−0.323942	−	0.194727i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−8.66039	−	8.66039i	−1.05804	−	1.05804i	−0.998209	−	0.0598266i	$-0.980945\pi$
$67$	−8.66039	−	8.66039i	−1.05804	−	1.05804i	−0.0598266	−	0.998209i	$-0.519055\pi$
$68$		0			0
$69$	0.979376	−	1.25330i	0.117903	−	0.150880i
$70$		0			0
$71$			0.938289i			0.111354i	0.998449	+	0.0556772i	$0.0177318\pi$
$71$			0.938289i			0.111354i	−0.998449	+	0.0556772i	$0.982268\pi$
$72$		0			0
$73$	0.399054	−	0.399054i	0.0467057	−	0.0467057i	−0.683368	−	0.730074i	$-0.739486\pi$
$73$	0.399054	−	0.399054i	0.0467057	−	0.0467057i	0.730074	+	0.683368i	$0.239486\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.54936	−	4.54936i	0.518447	−	0.518447i
$78$		0			0
$79$			6.65496i			0.748742i	0.927279	+	0.374371i	$0.122141\pi$
$79$			6.65496i			0.748742i	−0.927279	+	0.374371i	$0.877859\pi$
$80$		0			0
$81$	7.94811	−	4.22228i	0.883123	−	0.469142i
$82$		0			0
$83$	8.35674	+	8.35674i	0.917271	+	0.917271i	0.996830	−	0.0795590i	$-0.0253512\pi$
$83$	8.35674	+	8.35674i	0.917271	+	0.917271i	−0.0795590	+	0.996830i	$0.525351\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	0.102523	+	0.835627i	0.0109916	+	0.0895886i
$88$		0			0
$89$	8.32068			0.881990			0.440995	−	0.897510i	$-0.354626\pi$
$89$	8.32068			0.881990			0.440995	+	0.897510i	$0.354626\pi$
$90$		0			0
$91$	−5.99357			−0.628297
$92$		0			0
$93$	−0.502428	−	4.09511i	−0.0520994	−	0.424643i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	1.26743	+	1.26743i	0.128688	+	0.128688i	0.768517	−	0.639829i	$-0.220995\pi$
$97$	1.26743	+	1.26743i	0.128688	+	0.128688i	−0.639829	+	0.768517i	$0.720995\pi$
$98$		0			0
$99$	4.66591	+	18.7288i	0.468942	+	1.88232i
$100$		0			0
$101$		−	5.03940i		−	0.501439i	−0.968060	−	0.250719i	$-0.919333\pi$
$101$		−	5.03940i		−	0.501439i	0.968060	−	0.250719i	$-0.0806671\pi$
$102$		0			0
$103$	−3.13529	+	3.13529i	−0.308929	+	0.308929i	−0.844494	−	0.535565i	$-0.820099\pi$
$103$	−3.13529	+	3.13529i	−0.308929	+	0.308929i	0.535565	+	0.844494i	$0.320099\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.21798	−	2.21798i	0.214421	−	0.214421i	−0.591722	−	0.806142i	$-0.701552\pi$
$107$	2.21798	−	2.21798i	0.214421	−	0.214421i	0.806142	+	0.591722i	$0.201552\pi$
$108$		0			0
$109$		−	7.24411i		−	0.693860i	−0.937891	−	0.346930i	$-0.887224\pi$
$109$		−	7.24411i		−	0.693860i	0.937891	−	0.346930i	$-0.112776\pi$
$110$		0			0
$111$	6.18497	−	7.91488i	0.587051	−	0.751247i
$112$		0			0
$113$	−8.12238	−	8.12238i	−0.764089	−	0.764089i	0.212970	−	0.977059i	$-0.431686\pi$
$113$	−8.12238	−	8.12238i	−0.764089	−	0.764089i	−0.977059	+	0.212970i	$0.931686\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	9.26362	−	15.4107i	0.856422	−	1.42472i
$118$		0			0
$119$	1.42006			0.130177
$120$		0			0
$121$	−30.3933			−2.76303
$122$		0			0
$123$	10.1760	−	1.24849i	0.917538	−	0.112573i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−1.46614	−	1.46614i	−0.130099	−	0.130099i	0.639059	−	0.769158i	$-0.279324\pi$
$127$	−1.46614	−	1.46614i	−0.130099	−	0.130099i	−0.769158	+	0.639059i	$0.779324\pi$
$128$		0			0
$129$	13.0253	+	10.1784i	1.14681	+	0.896160i
$130$		0			0
$131$			18.8577i			1.64760i	0.566880	+	0.823801i	$0.308150\pi$
$131$			18.8577i			1.64760i	−0.566880	+	0.823801i	$0.691850\pi$
$132$		0			0
$133$	4.29994	−	4.29994i	0.372852	−	0.372852i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	9.48610	−	9.48610i	0.810452	−	0.810452i	−0.174250	−	0.984702i	$-0.555750\pi$
$137$	9.48610	−	9.48610i	0.810452	−	0.810452i	0.984702	+	0.174250i	$0.0557500\pi$
$138$		0			0
$139$		−	0.875540i		−	0.0742623i	−0.999310	−	0.0371312i	$-0.988178\pi$
$139$		−	0.875540i		−	0.0742623i	0.999310	−	0.0371312i	$-0.0118219\pi$
$140$		0			0
$141$	−9.07198	−	7.08917i	−0.763998	−	0.597016i
$142$		0			0
$143$	27.2669	+	27.2669i	2.28017	+	2.28017i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−1.71916	+	0.210923i	−0.141794	+	0.0173967i
$148$		0			0
$149$	3.41699			0.279931			0.139965	−	0.990156i	$-0.455301\pi$
$149$	3.41699			0.279931			0.139965	+	0.990156i	$0.455301\pi$
$150$		0			0
$151$	7.91753			0.644320			0.322160	−	0.946685i	$-0.395591\pi$
$151$	7.91753			0.644320			0.322160	+	0.946685i	$0.395591\pi$
$152$		0			0
$153$	−2.19484	+	3.65128i	−0.177442	+	0.295188i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−11.3595	−	11.3595i	−0.906590	−	0.906590i	0.0894052	−	0.995995i	$-0.471503\pi$
$157$	−11.3595	−	11.3595i	−0.906590	−	0.906590i	−0.995995	+	0.0894052i	$0.971503\pi$
$158$		0			0
$159$	6.04468	−	7.73535i	0.479374	−	0.613453i
$160$		0			0
$161$		−	0.918322i		−	0.0723739i
$162$		0			0
$163$	1.45321	−	1.45321i	0.113824	−	0.113824i	−0.647901	−	0.761725i	$-0.724353\pi$
$163$	1.45321	−	1.45321i	0.113824	−	0.113824i	0.761725	+	0.647901i	$0.224353\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−3.38874	+	3.38874i	−0.262228	+	0.262228i	−0.825959	−	0.563731i	$-0.809366\pi$
$167$	−3.38874	+	3.38874i	−0.262228	+	0.262228i	0.563731	+	0.825959i	$0.309366\pi$
$168$		0			0
$169$		−	22.9229i		−	1.76330i
$170$		0			0
$171$	4.41010	+	17.7020i	0.337249	+	1.35371i
$172$		0			0
$173$	−9.14032	−	9.14032i	−0.694926	−	0.694926i	0.268386	−	0.963312i	$-0.413510\pi$
$173$	−9.14032	−	9.14032i	−0.694926	−	0.694926i	−0.963312	+	0.268386i	$0.913510\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	1.87080	+	15.2482i	0.140618	+	1.14613i
$178$		0			0
$179$	20.5105			1.53303			0.766514	−	0.642227i	$-0.221989\pi$
$179$	20.5105			1.53303			0.766514	+	0.642227i	$0.221989\pi$
$180$		0			0
$181$	6.27904			0.466718			0.233359	−	0.972391i	$-0.425028\pi$
$181$	6.27904			0.466718			0.233359	+	0.972391i	$0.425028\pi$
$182$		0			0
$183$	−1.62952	−	13.2816i	−0.120458	−	0.981806i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−6.46036	−	6.46036i	−0.472429	−	0.472429i
$188$		0			0
$189$	2.11479	−	4.74633i	0.153829	−	0.345245i
$190$		0			0
$191$		−	5.62633i		−	0.407107i	−0.979064	−	0.203553i	$-0.934751\pi$
$191$		−	5.62633i		−	0.407107i	0.979064	−	0.203553i	$-0.0652490\pi$
$192$		0			0
$193$	−10.5045	+	10.5045i	−0.756132	+	0.756132i	−0.975616	−	0.219484i	$-0.929563\pi$
$193$	−10.5045	+	10.5045i	−0.756132	+	0.756132i	0.219484	+	0.975616i	$0.429563\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	10.2492	−	10.2492i	0.730226	−	0.730226i	−0.240438	−	0.970664i	$-0.577291\pi$
$197$	10.2492	−	10.2492i	0.730226	−	0.730226i	0.970664	+	0.240438i	$0.0772911\pi$
$198$		0			0
$199$		−	22.1655i		−	1.57127i	−0.618691	−	0.785634i	$-0.712337\pi$
$199$		−	22.1655i		−	1.57127i	0.618691	−	0.785634i	$-0.287663\pi$
$200$		0			0
$201$	13.0619	−	16.7153i	0.921317	−	1.17901i
$202$		0			0
$203$	0.343701	+	0.343701i	0.0241231	+	0.0241231i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	2.36120	+	1.41935i	0.164115	+	0.0986519i
$208$		0			0
$209$	−39.1240			−2.70626
$210$		0			0
$211$	−16.1292			−1.11038			−0.555190	−	0.831724i	$-0.687354\pi$
$211$	−16.1292			−1.11038			−0.555190	+	0.831724i	$0.687354\pi$
$212$		0			0
$213$	−1.61307	+	0.197907i	−0.110526	+	0.0135604i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−1.68436	−	1.68436i	−0.114342	−	0.114342i
$218$		0			0
$219$	0.770207	+	0.601868i	0.0520458	+	0.0406705i
$220$		0			0
$221$			8.51123i			0.572527i
$222$		0			0
$223$	−11.9844	+	11.9844i	−0.802536	+	0.802536i	−0.983491	−	0.180955i	$-0.942081\pi$
$223$	−11.9844	+	11.9844i	−0.802536	+	0.802536i	0.180955	+	0.983491i	$0.442081\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.32769	−	5.32769i	0.353611	−	0.353611i	−0.507840	−	0.861451i	$-0.669556\pi$
$227$	5.32769	−	5.32769i	0.353611	−	0.353611i	0.861451	+	0.507840i	$0.169556\pi$
$228$		0			0
$229$			18.1153i			1.19709i	0.801088	+	0.598546i	$0.204255\pi$
$229$			18.1153i			1.19709i	−0.801088	+	0.598546i	$0.795745\pi$
$230$		0			0
$231$	8.78064	+	6.86151i	0.577724	+	0.451454i
$232$		0			0
$233$	3.44811	+	3.44811i	0.225893	+	0.225893i	0.810975	−	0.585081i	$-0.198937\pi$
$233$	3.44811	+	3.44811i	0.225893	+	0.225893i	−0.585081	+	0.810975i	$0.698937\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−11.4409	+	1.40369i	−0.743169	+	0.0911793i
$238$		0			0
$239$	−29.1223			−1.88377			−0.941883	−	0.335941i	$-0.890946\pi$
$239$	−29.1223			−1.88377			−0.941883	+	0.335941i	$0.890946\pi$
$240$		0			0
$241$	23.9979			1.54584			0.772920	−	0.634504i	$-0.218796\pi$
$241$	23.9979			1.54584			0.772920	+	0.634504i	$0.218796\pi$
$242$		0			0
$243$	8.93521	+	12.7735i	0.573194	+	0.819420i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	25.7720	+	25.7720i	1.63983	+	1.63983i
$248$		0			0
$249$	−12.6039	+	16.1292i	−0.798742	+	1.02215i
$250$		0			0
$251$		−	23.6036i		−	1.48985i	−0.667150	−	0.744924i	$-0.732486\pi$
$251$		−	23.6036i		−	1.48985i	0.667150	−	0.744924i	$-0.267514\pi$
$252$		0			0
$253$	−4.17778	+	4.17778i	−0.262655	+	0.262655i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.67798	−	5.67798i	0.354183	−	0.354183i	−0.507481	−	0.861663i	$-0.669423\pi$
$257$	5.67798	−	5.67798i	0.354183	−	0.354183i	0.861663	+	0.507481i	$0.169423\pi$
$258$		0			0
$259$		−	5.79940i		−	0.360357i
$260$		0			0
$261$	−1.41495	+	0.352507i	−0.0875833	+	0.0218196i
$262$		0			0
$263$	2.34025	+	2.34025i	0.144306	+	0.144306i	0.775569	−	0.631263i	$-0.217463\pi$
$263$	2.34025	+	2.34025i	0.144306	+	0.144306i	−0.631263	+	0.775569i	$0.717463\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	1.75503	+	14.3046i	0.107406	+	0.875426i
$268$		0			0
$269$	11.0751			0.675260			0.337630	−	0.941279i	$-0.390375\pi$
$269$	11.0751			0.675260			0.337630	+	0.941279i	$0.390375\pi$
$270$		0			0
$271$	−16.4463			−0.999041			−0.499520	−	0.866302i	$-0.666490\pi$
$271$	−16.4463			−0.999041			−0.499520	+	0.866302i	$0.666490\pi$
$272$		0			0
$273$	−1.26418	−	10.3039i	−0.0765119	−	0.623621i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	8.97137	+	8.97137i	0.539037	+	0.539037i	0.923246	−	0.384209i	$-0.125526\pi$
$277$	8.97137	+	8.97137i	0.539037	+	0.539037i	−0.384209	+	0.923246i	$0.625526\pi$
$278$		0			0
$279$	6.93417	−	1.72751i	0.415138	−	0.103423i
$280$		0			0
$281$		−	9.92244i		−	0.591923i	−0.955200	−	0.295962i	$-0.904360\pi$
$281$		−	9.92244i		−	0.591923i	0.955200	−	0.295962i	$-0.0956400\pi$
$282$		0			0
$283$	−6.92581	+	6.92581i	−0.411696	+	0.411696i	−0.882329	−	0.470633i	$-0.844026\pi$
$283$	−6.92581	+	6.92581i	−0.411696	+	0.411696i	0.470633	+	0.882329i	$0.344026\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4.18548	−	4.18548i	0.247061	−	0.247061i
$288$		0			0
$289$			14.9834i			0.881378i
$290$		0			0
$291$	−1.91158	+	2.44624i	−0.112059	+	0.143401i
$292$		0			0
$293$	−10.9365	−	10.9365i	−0.638916	−	0.638916i	0.311372	−	0.950288i	$-0.399211\pi$
$293$	−10.9365	−	10.9365i	−0.638916	−	0.638916i	−0.950288	+	0.311372i	$0.899211\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−31.2137	+	11.9718i	−1.81120	+	0.694674i
$298$		0			0
$299$	5.50403			0.318306
$300$		0			0
$301$	9.54390			0.550101
$302$		0			0
$303$	8.66353	−	1.06293i	0.497707	−	0.0610636i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	5.69314	+	5.69314i	0.324924	+	0.324924i	0.850653	−	0.525728i	$-0.176207\pi$
$307$	5.69314	+	5.69314i	0.324924	+	0.324924i	−0.525728	+	0.850653i	$0.676207\pi$
$308$		0			0
$309$	−6.05137	−	4.72876i	−0.344251	−	0.269010i
$310$		0			0
$311$			16.4991i			0.935581i	0.883839	+	0.467790i	$0.154950\pi$
$311$			16.4991i			0.935581i	−0.883839	+	0.467790i	$0.845050\pi$
$312$		0			0
$313$	1.45645	−	1.45645i	0.0823236	−	0.0823236i	−0.664746	−	0.747070i	$-0.731460\pi$
$313$	1.45645	−	1.45645i	0.0823236	−	0.0823236i	0.747070	+	0.664746i	$0.231460\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−21.8297	+	21.8297i	−1.22608	+	1.22608i	−0.260644	+	0.965435i	$0.583935\pi$
$317$	−21.8297	+	21.8297i	−1.22608	+	1.22608i	−0.965435	+	0.260644i	$0.916065\pi$
$318$		0			0
$319$		−	3.12724i		−	0.175092i
$320$		0			0
$321$	4.28089	+	3.34524i	0.238936	+	0.186713i
$322$		0			0
$323$	−6.10618	−	6.10618i	−0.339757	−	0.339757i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	12.4538	−	1.52795i	0.688696	−	0.0844959i
$328$		0			0
$329$	−6.64723			−0.366474
$330$		0			0
$331$	−2.46631			−0.135560			−0.0677802	−	0.997700i	$-0.521592\pi$
$331$	−2.46631			−0.135560			−0.0677802	+	0.997700i	$0.521592\pi$
$332$		0			0
$333$	14.9115	+	8.96352i	0.817145	+	0.491198i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−14.9566	−	14.9566i	−0.814740	−	0.814740i	0.170600	−	0.985340i	$-0.445429\pi$
$337$	−14.9566	−	14.9566i	−0.814740	−	0.814740i	−0.985340	+	0.170600i	$0.945429\pi$
$338$		0			0
$339$	12.2505	−	15.6769i	0.665354	−	0.851450i
$340$		0			0
$341$			15.3255i			0.829922i
$342$		0			0
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	2.11616	−	2.11616i	0.113601	−	0.113601i	−0.648021	−	0.761622i	$-0.724403\pi$
$347$	2.11616	−	2.11616i	0.113601	−	0.113601i	0.761622	+	0.648021i	$0.224403\pi$
$348$		0			0
$349$			2.91173i			0.155862i	0.996959	+	0.0779308i	$0.0248313\pi$
$349$			2.91173i			0.155862i	−0.996959	+	0.0779308i	$0.975169\pi$
$350$		0			0
$351$	28.4475	+	12.6752i	1.51841	+	0.676550i
$352$		0			0
$353$	−0.701527	−	0.701527i	−0.0373385	−	0.0373385i	0.688191	−	0.725530i	$-0.258405\pi$
$353$	−0.701527	−	0.701527i	−0.0373385	−	0.0373385i	−0.725530	+	0.688191i	$0.758405\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	0.299524	+	2.44131i	0.0158525	+	0.129208i
$358$		0			0
$359$	−18.7184			−0.987919			−0.493959	−	0.869485i	$-0.664451\pi$
$359$	−18.7184			−0.987919			−0.493959	+	0.869485i	$0.664451\pi$
$360$		0			0
$361$	−17.9790			−0.946264
$362$		0			0
$363$	−6.41066	−	52.2510i	−0.336473	−	2.74247i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−3.06964	−	3.06964i	−0.160234	−	0.160234i	0.622436	−	0.782670i	$-0.286143\pi$
$367$	−3.06964	−	3.06964i	−0.160234	−	0.160234i	−0.782670	+	0.622436i	$0.786143\pi$
$368$		0			0
$369$	4.29271	+	17.2308i	0.223469	+	0.897000i
$370$		0			0
$371$		−	5.66786i		−	0.294260i
$372$		0			0
$373$	−13.5778	+	13.5778i	−0.703030	+	0.703030i	−0.965060	−	0.262030i	$-0.915608\pi$
$373$	−13.5778	+	13.5778i	−0.703030	+	0.703030i	0.262030	+	0.965060i	$0.415608\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.06000	+	2.06000i	−0.106095	+	0.106095i
$378$		0			0
$379$			17.9162i			0.920295i	0.887843	+	0.460147i	$0.152203\pi$
$379$			17.9162i			0.920295i	−0.887843	+	0.460147i	$0.847797\pi$
$380$		0			0
$381$	2.21129	−	2.82978i	0.113288	−	0.144974i
$382$		0			0
$383$	−8.60482	−	8.60482i	−0.439686	−	0.439686i	0.452221	−	0.891906i	$-0.350632\pi$
$383$	−8.60482	−	8.60482i	−0.439686	−	0.439686i	−0.891906	+	0.452221i	$0.850632\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−14.7510	+	24.5394i	−0.749835	+	1.24741i
$388$		0			0
$389$	19.7974			1.00377			0.501884	−	0.864935i	$-0.332640\pi$
$389$	19.7974			1.00377			0.501884	+	0.864935i	$0.332640\pi$
$390$		0			0
$391$	−1.30407			−0.0659498
$392$		0			0
$393$	−32.4193	+	3.97752i	−1.63534	+	0.200639i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−5.67115	−	5.67115i	−0.284627	−	0.284627i	0.550324	−	0.834951i	$-0.314504\pi$
$397$	−5.67115	−	5.67115i	−0.284627	−	0.284627i	−0.834951	+	0.550324i	$0.814504\pi$
$398$		0			0
$399$	8.29925	+	6.48533i	0.415482	+	0.324673i
$400$		0			0
$401$			0.0667155i			0.00333161i	0.999999	+	0.00166581i	$0.000530243\pi$
$401$			0.0667155i			0.00333161i	−0.999999	+	0.00166581i	$0.999470\pi$
$402$		0			0
$403$	10.0953	−	10.0953i	0.502883	−	0.502883i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−26.3836	+	26.3836i	−1.30778	+	1.30778i
$408$		0			0
$409$		−	3.11817i		−	0.154183i	−0.997024	−	0.0770917i	$-0.975437\pi$
$409$		−	3.11817i		−	0.154183i	0.997024	−	0.0770917i	$-0.0245634\pi$
$410$		0			0
$411$	18.3090	+	14.3073i	0.903114	+	0.705726i
$412$		0			0
$413$	6.27174	+	6.27174i	0.308612	+	0.308612i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.50519	−	0.184672i	0.0737096	−	0.00904342i
$418$		0			0
$419$	−5.96945			−0.291627			−0.145813	−	0.989312i	$-0.546580\pi$
$419$	−5.96945			−0.291627			−0.145813	+	0.989312i	$0.546580\pi$
$420$		0			0
$421$	−17.7870			−0.866886			−0.433443	−	0.901181i	$-0.642702\pi$
$421$	−17.7870			−0.866886			−0.433443	+	0.901181i	$0.642702\pi$
$422$		0			0
$423$	10.2739	−	17.0915i	0.499535	−	0.831015i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−5.46286	−	5.46286i	−0.264366	−	0.264366i
$428$		0			0
$429$	−41.1249	+	52.6274i	−1.98553	+	2.54087i
$430$		0			0
$431$			17.4845i			0.842199i	0.907014	+	0.421100i	$0.138356\pi$
$431$			17.4845i			0.842199i	−0.907014	+	0.421100i	$0.861644\pi$
$432$		0			0
$433$	−3.51538	+	3.51538i	−0.168938	+	0.168938i	−0.786513	−	0.617574i	$-0.788115\pi$
$433$	−3.51538	+	3.51538i	−0.168938	+	0.168938i	0.617574	+	0.786513i	$0.288115\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3.94873	+	3.94873i	−0.188893	+	0.188893i
$438$		0			0
$439$		−	30.0909i		−	1.43616i	−0.695959	−	0.718081i	$-0.745021\pi$
$439$		−	30.0909i		−	1.43616i	0.695959	−	0.718081i	$-0.254979\pi$
$440$		0			0
$441$	−0.725222	−	2.91102i	−0.0345344	−	0.138620i
$442$		0			0
$443$	−15.9976	−	15.9976i	−0.760070	−	0.760070i	0.216265	−	0.976335i	$-0.430612\pi$
$443$	−15.9976	−	15.9976i	−0.760070	−	0.760070i	−0.976335	+	0.216265i	$0.930612\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	0.720724	+	5.87436i	0.0340891	+	0.277848i
$448$		0			0
$449$	−28.5257			−1.34621			−0.673104	−	0.739547i	$-0.735040\pi$
$449$	−28.5257			−1.34621			−0.673104	+	0.739547i	$0.735040\pi$
$450$		0			0
$451$	−38.0825			−1.79323
$452$		0			0
$453$	1.66999	+	13.6115i	0.0784632	+	0.639525i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−29.2200	−	29.2200i	−1.36686	−	1.36686i	−0.864885	−	0.501970i	$-0.832609\pi$
$457$	−29.2200	−	29.2200i	−1.36686	−	1.36686i	−0.501970	−	0.864885i	$-0.667391\pi$
$458$		0			0
$459$	−6.74008	−	3.00314i	−0.314600	−	0.140174i
$460$		0			0
$461$			2.62137i			0.122089i	0.998135	+	0.0610447i	$0.0194432\pi$
$461$			2.62137i			0.122089i	−0.998135	+	0.0610447i	$0.980557\pi$
$462$		0			0
$463$	−3.05883	+	3.05883i	−0.142156	+	0.142156i	−0.774603	−	0.632448i	$-0.782050\pi$
$463$	−3.05883	+	3.05883i	−0.142156	+	0.142156i	0.632448	+	0.774603i	$0.282050\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−19.2354	+	19.2354i	−0.890107	+	0.890107i	−0.994533	−	0.104426i	$-0.966699\pi$
$467$	−19.2354	+	19.2354i	−0.890107	+	0.890107i	0.104426	+	0.994533i	$0.466699\pi$
$468$		0			0
$469$		−	12.2476i		−	0.565544i
$470$		0			0
$471$	17.1329	−	21.9249i	0.789441	−	1.01024i
$472$		0			0
$473$	−43.4186	−	43.4186i	−1.99639	−	1.99639i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	14.5733	+	8.76021i	0.667264	+	0.401102i
$478$		0			0
$479$	−14.5708			−0.665758			−0.332879	−	0.942970i	$-0.608020\pi$
$479$	−14.5708			−0.665758			−0.332879	+	0.942970i	$0.608020\pi$
$480$		0			0
$481$	34.7591			1.58488
$482$		0			0
$483$	1.57874	−	0.193696i	0.0718353	−	0.00881346i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	14.1401	+	14.1401i	0.640748	+	0.640748i	0.950739	−	0.309991i	$-0.100326\pi$
$487$	14.1401	+	14.1401i	0.640748	+	0.640748i	−0.309991	+	0.950739i	$0.600326\pi$
$488$		0			0
$489$	2.80482	+	2.19178i	0.126838	+	0.0991159i
$490$		0			0
$491$			5.39052i			0.243271i	0.992575	+	0.121635i	$0.0388139\pi$
$491$			5.39052i			0.243271i	−0.992575	+	0.121635i	$0.961186\pi$
$492$		0			0
$493$	0.488077	−	0.488077i	0.0219819	−	0.0219819i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.663470	+	0.663470i	−0.0297607	+	0.0297607i
$498$		0			0
$499$			4.11696i			0.184300i	0.995745	+	0.0921502i	$0.0293740\pi$
$499$			4.11696i			0.184300i	−0.995745	+	0.0921502i	$0.970626\pi$
$500$		0			0
$501$	−6.54054	−	5.11102i	−0.292210	−	0.228343i
$502$		0			0
$503$	−0.763683	−	0.763683i	−0.0340509	−	0.0340509i	0.689876	−	0.723927i	$-0.257665\pi$
$503$	−0.763683	−	0.763683i	−0.0340509	−	0.0340509i	−0.723927	+	0.689876i	$0.757665\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	39.4081	−	4.83497i	1.75017	−	0.214729i
$508$		0			0
$509$	32.9289			1.45955			0.729774	−	0.683689i	$-0.239625\pi$
$509$	32.9289			1.45955			0.729774	+	0.683689i	$0.239625\pi$
$510$		0			0
$511$	0.564347			0.0249653
$512$		0			0
$513$	−29.5024	+	11.3155i	−1.30256	+	0.499589i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	30.2406	+	30.2406i	1.32998	+	1.32998i
$518$		0			0
$519$	13.7858	−	17.6416i	0.605128	−	0.774380i
$520$		0			0
$521$			21.0256i			0.921147i	0.887621	+	0.460574i	$0.152356\pi$
$521$			21.0256i			0.921147i	−0.887621	+	0.460574i	$0.847644\pi$
$522$		0			0
$523$	20.2858	−	20.2858i	0.887035	−	0.887035i	−0.107202	−	0.994237i	$-0.534189\pi$
$523$	20.2858	−	20.2858i	0.887035	−	0.887035i	0.994237	+	0.107202i	$0.0341892\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.39189	+	2.39189i	−0.104192	+	0.104192i
$528$		0			0
$529$		−	22.1567i		−	0.963334i
$530$		0			0
$531$	−25.8195	+	6.43241i	−1.12047	+	0.279143i
$532$		0			0
$533$	25.0860	+	25.0860i	1.08659	+	1.08659i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	4.32615	+	35.2609i	0.186687	+	1.52162i
$538$		0			0
$539$	6.43376			0.277122
$540$		0			0
$541$	24.7139			1.06254			0.531268	−	0.847204i	$-0.321716\pi$
$541$	24.7139			1.06254			0.531268	+	0.847204i	$0.321716\pi$
$542$		0			0
$543$	1.32440	+	10.7947i	0.0568353	+	0.463244i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	8.13542	+	8.13542i	0.347846	+	0.347846i	0.859307	−	0.511461i	$-0.170896\pi$
$547$	8.13542	+	8.13542i	0.347846	+	0.347846i	−0.511461	+	0.859307i	$0.670896\pi$
$548$		0			0
$549$	22.4895	−	5.60281i	0.959830	−	0.239122i
$550$		0			0
$551$		−	2.95579i		−	0.125921i
$552$		0			0
$553$	−4.70577	+	4.70577i	−0.200110	+	0.200110i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−4.00130	+	4.00130i	−0.169541	+	0.169541i	−0.786777	−	0.617237i	$-0.788252\pi$
$557$	−4.00130	+	4.00130i	−0.169541	+	0.169541i	0.617237	+	0.786777i	$0.288252\pi$
$558$		0			0
$559$			57.2020i			2.41939i
$560$		0			0
$561$	9.74376	−	12.4690i	0.411382	−	0.526443i
$562$		0			0
$563$	18.0800	+	18.0800i	0.761982	+	0.761982i	0.976680	−	0.214698i	$-0.0688767\pi$
$563$	18.0800	+	18.0800i	0.761982	+	0.761982i	−0.214698	+	0.976680i	$0.568877\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	8.60576	+	2.63456i	0.361408	+	0.110641i
$568$		0			0
$569$	−32.5102			−1.36290			−0.681449	−	0.731866i	$-0.738650\pi$
$569$	−32.5102			−1.36290			−0.681449	+	0.731866i	$0.738650\pi$
$570$		0			0
$571$	28.6106			1.19732			0.598659	−	0.801004i	$-0.295701\pi$
$571$	28.6106			1.19732			0.598659	+	0.801004i	$0.295701\pi$
$572$		0			0
$573$	9.67256	−	1.18672i	0.404077	−	0.0495761i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	5.13605	+	5.13605i	0.213817	+	0.213817i	0.805887	−	0.592070i	$-0.201689\pi$
$577$	5.13605	+	5.13605i	0.213817	+	0.213817i	−0.592070	+	0.805887i	$0.701689\pi$
$578$		0			0
$579$	−20.2746	−	15.8433i	−0.842584	−	0.658425i
$580$		0			0
$581$			11.8182i			0.490302i
$582$		0			0
$583$	−25.7851	+	25.7851i	−1.06791	+	1.06791i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−5.21017	+	5.21017i	−0.215047	+	0.215047i	−0.806407	−	0.591361i	$-0.798591\pi$
$587$	−5.21017	+	5.21017i	−0.215047	+	0.215047i	0.591361	+	0.806407i	$0.298591\pi$
$588$		0			0
$589$			14.4853i			0.596856i
$590$		0			0
$591$	19.7818	+	15.4582i	0.813716	+	0.635867i
$592$		0			0
$593$	33.7500	+	33.7500i	1.38594	+	1.38594i	0.833647	+	0.552298i	$0.186249\pi$
$593$	33.7500	+	33.7500i	1.38594	+	1.38594i	0.552298	+	0.833647i	$0.313751\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	38.1060	−	4.67522i	1.55957	−	0.191344i
$598$		0			0
$599$	20.6389			0.843284			0.421642	−	0.906762i	$-0.361454\pi$
$599$	20.6389			0.843284			0.421642	+	0.906762i	$0.361454\pi$
$600$		0			0
$601$	−24.7049			−1.00774			−0.503868	−	0.863781i	$-0.668090\pi$
$601$	−24.7049			−1.00774			−0.503868	+	0.863781i	$0.668090\pi$
$602$		0			0
$603$	31.4913	+	18.9299i	1.28243	+	0.770885i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	1.23907	+	1.23907i	0.0502924	+	0.0502924i	0.731806	−	0.681513i	$-0.238678\pi$
$607$	1.23907	+	1.23907i	0.0502924	+	0.0502924i	−0.681513	+	0.731806i	$0.738678\pi$
$608$		0			0
$609$	−0.518383	+	0.663372i	−0.0210059	+	0.0268812i
$610$		0			0
$611$		−	39.8406i		−	1.61178i
$612$		0			0
$613$	−9.96157	+	9.96157i	−0.402344	+	0.402344i	−0.879058	−	0.476714i	$-0.841828\pi$
$613$	−9.96157	+	9.96157i	−0.402344	+	0.402344i	0.476714	+	0.879058i	$0.341828\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	3.05795	−	3.05795i	0.123108	−	0.123108i	−0.642868	−	0.765977i	$-0.722256\pi$
$617$	3.05795	−	3.05795i	0.123108	−	0.123108i	0.765977	+	0.642868i	$0.222256\pi$
$618$		0			0
$619$			11.8289i			0.475445i	0.971333	+	0.237723i	$0.0764009\pi$
$619$			11.8289i			0.475445i	−0.971333	+	0.237723i	$0.923599\pi$
$620$		0			0
$621$	−1.94206	+	4.35866i	−0.0779323	+	0.174907i
$622$		0			0
$623$	5.88361	+	5.88361i	0.235722	+	0.235722i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−8.25216	−	67.2604i	−0.329560	−	2.68612i
$628$		0			0
$629$	−8.23550			−0.328371
$630$		0			0
$631$	27.1167			1.07950			0.539750	−	0.841826i	$-0.318519\pi$
$631$	27.1167			1.07950			0.539750	+	0.841826i	$0.318519\pi$
$632$		0			0
$633$	−3.40203	−	27.7287i	−0.135218	−	1.10212i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−4.23809	−	4.23809i	−0.167919	−	0.167919i
$638$		0			0
$639$	−0.680468	−	2.73138i	−0.0269189	−	0.108052i
$640$		0			0
$641$			36.0112i			1.42236i	0.703011	+	0.711179i	$0.251838\pi$
$641$			36.0112i			1.42236i	−0.703011	+	0.711179i	$0.748162\pi$
$642$		0			0
$643$	−2.33145	+	2.33145i	−0.0919434	+	0.0919434i	−0.751583	−	0.659639i	$-0.770709\pi$
$643$	−2.33145	+	2.33145i	−0.0919434	+	0.0919434i	0.659639	+	0.751583i	$0.270709\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	5.49581	−	5.49581i	0.216063	−	0.216063i	−0.590774	−	0.806837i	$-0.701178\pi$
$647$	5.49581	−	5.49581i	0.216063	−	0.216063i	0.806837	+	0.590774i	$0.201178\pi$
$648$		0			0
$649$		−	57.0648i		−	2.23999i
$650$		0			0
$651$	2.54041	−	3.25095i	0.0995665	−	0.127415i
$652$		0			0
$653$	−18.4945	−	18.4945i	−0.723745	−	0.723745i	0.245621	−	0.969366i	$-0.421008\pi$
$653$	−18.4945	−	18.4945i	−0.723745	−	0.723745i	−0.969366	+	0.245621i	$0.921008\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−0.872252	+	1.45106i	−0.0340298	+	0.0566112i
$658$		0			0
$659$	36.7240			1.43056			0.715281	−	0.698836i	$-0.246298\pi$
$659$	36.7240			1.43056			0.715281	+	0.698836i	$0.246298\pi$
$660$		0			0
$661$	−3.93060			−0.152883			−0.0764414	−	0.997074i	$-0.524356\pi$
$661$	−3.93060			−0.152883			−0.0764414	+	0.997074i	$0.524356\pi$
$662$		0			0
$663$	−14.6322	+	1.79522i	−0.568266	+	0.0697205i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−0.315628	−	0.315628i	−0.0122212	−	0.0122212i
$668$		0			0
$669$	−23.1309	−	18.0753i	−0.894294	−	0.698833i
$670$		0			0
$671$			49.7050i			1.91884i
$672$		0			0
$673$	−22.2394	+	22.2394i	−0.857266	+	0.857266i	−0.991015	−	0.133750i	$-0.957298\pi$
$673$	−22.2394	+	22.2394i	−0.857266	+	0.857266i	0.133750	+	0.991015i	$0.457298\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	28.3639	−	28.3639i	1.09011	−	1.09011i	0.0945965	−	0.995516i	$-0.469844\pi$
$677$	28.3639	−	28.3639i	1.09011	−	1.09011i	0.995516	−	0.0945965i	$-0.0301561\pi$
$678$		0			0
$679$			1.79242i			0.0687866i
$680$		0			0
$681$	10.2829	+	8.03542i	0.394041	+	0.307918i
$682$		0			0
$683$	−7.62062	−	7.62062i	−0.291595	−	0.291595i	0.546115	−	0.837710i	$-0.316106\pi$
$683$	−7.62062	−	7.62062i	−0.291595	−	0.291595i	−0.837710	+	0.546115i	$0.816106\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−31.1431	+	3.82094i	−1.18818	+	0.145778i
$688$		0			0
$689$	33.9707			1.29418
$690$		0			0
$691$	19.5969			0.745500			0.372750	−	0.927932i	$-0.378415\pi$
$691$	19.5969			0.745500			0.372750	+	0.927932i	$0.378415\pi$
$692$		0			0
$693$	−9.94399	+	16.5426i	−0.377741	+	0.628401i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−5.94363	−	5.94363i	−0.225131	−	0.225131i
$698$		0			0
$699$	−5.20056	+	6.65514i	−0.196703	+	0.251720i
$700$		0			0
$701$		−	25.9234i		−	0.979113i	−0.871972	−	0.489556i	$-0.837159\pi$
$701$		−	25.9234i		−	0.979113i	0.871972	−	0.489556i	$-0.162841\pi$
$702$		0			0
$703$	−24.9371	+	24.9371i	−0.940520	+	0.940520i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	3.56339	−	3.56339i	0.134015	−	0.134015i
$708$		0			0
$709$		−	15.7297i		−	0.590740i	−0.955383	−	0.295370i	$-0.904557\pi$
$709$		−	15.7297i		−	0.590740i	0.955383	−	0.295370i	$-0.0954429\pi$
$710$		0			0
$711$	−4.82633	−	19.3728i	−0.181001	−	0.726535i
$712$		0			0
$713$	1.54678	+	1.54678i	0.0579275	+	0.0579275i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−6.14258	−	50.0659i	−0.229399	−	1.86975i
$718$		0			0
$719$	35.0380			1.30670			0.653349	−	0.757057i	$-0.273364\pi$
$719$	35.0380			1.30670			0.653349	+	0.757057i	$0.273364\pi$
$720$		0			0
$721$	−4.43397			−0.165130
$722$		0			0
$723$	5.06172	+	41.2562i	0.188247	+	1.53433i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	18.0598	+	18.0598i	0.669801	+	0.669801i	0.957670	−	0.287869i	$-0.0929466\pi$
$727$	18.0598	+	18.0598i	0.669801	+	0.669801i	−0.287869	+	0.957670i	$0.592947\pi$
$728$		0			0
$729$	−20.0750	+	18.0553i	−0.743519	+	0.668714i
$730$		0			0
$731$		−	13.5529i		−	0.501273i
$732$		0			0
$733$	−2.19204	+	2.19204i	−0.0809648	+	0.0809648i	−0.746429	−	0.665465i	$-0.768233\pi$
$733$	−2.19204	+	2.19204i	−0.0809648	+	0.0809648i	0.665465	+	0.746429i	$0.268233\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−55.7189	+	55.7189i	−2.05243	+	2.05243i
$738$		0			0
$739$			18.6617i			0.686481i	0.939248	+	0.343240i	$0.111525\pi$
$739$			18.6617i			0.686481i	−0.939248	+	0.343240i	$0.888475\pi$
$740$		0			0
$741$	−38.8703	+	49.7421i	−1.42794	+	1.82732i
$742$		0			0
$743$	−1.75928	−	1.75928i	−0.0645419	−	0.0645419i	0.674099	−	0.738641i	$-0.264532\pi$
$743$	−1.75928	−	1.75928i	−0.0645419	−	0.0645419i	−0.738641	+	0.674099i	$0.764532\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−30.3871	−	18.2662i	−1.11181	−	0.668324i
$748$		0			0
$749$	3.13670			0.114613
$750$		0			0
$751$	−46.5068			−1.69706			−0.848529	−	0.529148i	$-0.822512\pi$
$751$	−46.5068			−1.69706			−0.848529	+	0.529148i	$0.822512\pi$
$752$		0			0
$753$	40.5784	−	4.97856i	1.47876	−	0.181429i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	16.5393	+	16.5393i	0.601132	+	0.601132i	0.940613	−	0.339481i	$-0.110251\pi$
$757$	16.5393	+	16.5393i	0.601132	+	0.601132i	−0.339481	+	0.940613i	$0.610251\pi$
$758$		0			0
$759$	−8.06346	−	6.30107i	−0.292685	−	0.228715i
$760$		0			0
$761$		−	5.10549i		−	0.185074i	−0.995709	−	0.0925370i	$-0.970502\pi$
$761$		−	5.10549i		−	0.185074i	0.995709	−	0.0925370i	$-0.0294976\pi$
$762$		0			0
$763$	5.12236	−	5.12236i	0.185442	−	0.185442i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−37.5901	+	37.5901i	−1.35730	+	1.35730i
$768$		0			0
$769$			17.9917i			0.648796i	0.945921	+	0.324398i	$0.105162\pi$
$769$			17.9917i			0.648796i	−0.945921	+	0.324398i	$0.894838\pi$
$770$		0			0
$771$	10.9590	+	8.56374i	0.394678	+	0.308415i
$772$		0			0
$773$	−25.0325	−	25.0325i	−0.900357	−	0.900357i	0.0951098	−	0.995467i	$-0.469680\pi$
$773$	−25.0325	−	25.0325i	−0.900357	−	0.900357i	−0.995467	+	0.0951098i	$0.969680\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	9.97010	−	1.22323i	0.357675	−	0.0438831i
$778$		0			0
$779$	−35.9946			−1.28964
$780$		0			0
$781$	6.03673			0.216011
$782$		0			0
$783$	−0.904462	−	2.35818i	−0.0323228	−	0.0842743i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	30.3373	+	30.3373i	1.08141	+	1.08141i	0.996378	+	0.0850305i	$0.0270988\pi$
$787$	30.3373	+	30.3373i	1.08141	+	1.08141i	0.0850305	+	0.996378i	$0.472901\pi$
$788$		0			0
$789$	−3.52964	+	4.51687i	−0.125659	+	0.160805i
$790$		0			0
$791$		−	11.4868i		−	0.408423i
$792$		0			0
$793$	32.7420	−	32.7420i	1.16270	−	1.16270i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	23.0440	−	23.0440i	0.816260	−	0.816260i	−0.169304	−	0.985564i	$-0.554152\pi$
$797$	23.0440	−	23.0440i	0.816260	−	0.816260i	0.985564	+	0.169304i	$0.0541520\pi$
$798$		0			0
$799$			9.43947i			0.333945i
$800$		0			0
$801$	−24.2217	+	6.03434i	−0.855831	+	0.213213i
$802$		0			0
$803$	−2.56742	−	2.56742i	−0.0906022	−	0.0906022i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	2.33600	+	19.0399i	0.0822310	+	0.670235i
$808$		0			0
$809$	−25.3191			−0.890172			−0.445086	−	0.895488i	$-0.646827\pi$
$809$	−25.3191			−0.890172			−0.445086	+	0.895488i	$0.646827\pi$
$810$		0			0
$811$	−14.1521			−0.496946			−0.248473	−	0.968639i	$-0.579929\pi$
$811$	−14.1521			−0.496946			−0.248473	+	0.968639i	$0.579929\pi$
$812$		0			0
$813$	−3.46891	−	28.2738i	−0.121660	−	0.991605i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−41.0382	−	41.0382i	−1.43575	−	1.43575i
$818$		0			0
$819$	17.4474	−	4.34667i	0.609662	−	0.151885i
$820$		0			0
$821$		−	39.8059i		−	1.38924i	−0.719379	−	0.694618i	$-0.755573\pi$
$821$		−	39.8059i		−	1.38924i	0.719379	−	0.694618i	$-0.244427\pi$
$822$		0			0
$823$	33.6402	−	33.6402i	1.17262	−	1.17262i	0.191041	−	0.981582i	$-0.438814\pi$
$823$	33.6402	−	33.6402i	1.17262	−	1.17262i	0.981582	−	0.191041i	$-0.0611864\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	18.6457	−	18.6457i	0.648374	−	0.648374i	−0.304226	−	0.952600i	$-0.598398\pi$
$827$	18.6457	−	18.6457i	0.648374	−	0.648374i	0.952600	+	0.304226i	$0.0983978\pi$
$828$		0			0
$829$			15.5263i			0.539249i	0.962965	+	0.269625i	$0.0868996\pi$
$829$			15.5263i			0.539249i	−0.962965	+	0.269625i	$0.913100\pi$
$830$		0			0
$831$	−13.5309	+	17.3155i	−0.469383	+	0.600668i
$832$		0			0
$833$	1.00413	+	1.00413i	0.0347912	+	0.0347912i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	4.43244	+	11.5566i	0.153208	+	0.399454i
$838$		0			0
$839$	39.2471			1.35496			0.677481	−	0.735540i	$-0.263072\pi$
$839$	39.2471			1.35496			0.677481	+	0.735540i	$0.263072\pi$
$840$		0			0
$841$	−28.7637			−0.991853
$842$		0			0
$843$	17.0583	−	2.09287i	0.587518	−	0.0720824i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−21.4913	−	21.4913i	−0.738451	−	0.738451i
$848$		0			0
$849$	−13.3674	−	10.4458i	−0.458767	−	0.358497i
$850$		0			0
$851$			5.32572i			0.182563i
$852$		0			0
$853$	16.5786	−	16.5786i	0.567640	−	0.567640i	−0.363827	−	0.931467i	$-0.618530\pi$
$853$	16.5786	−	16.5786i	0.567640	−	0.567640i	0.931467	+	0.363827i	$0.118530\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	37.2269	−	37.2269i	1.27165	−	1.27165i	0.326425	−	0.945223i	$-0.394156\pi$
$857$	37.2269	−	37.2269i	1.27165	−	1.27165i	0.945223	−	0.326425i	$-0.105844\pi$
$858$		0			0
$859$			0.571240i			0.0194905i	0.999953	+	0.00974523i	$0.00310205\pi$
$859$			0.571240i			0.0194905i	−0.999953	+	0.00974523i	$0.996898\pi$
$860$		0			0
$861$	8.07832	+	6.31269i	0.275309	+	0.215136i
$862$		0			0
$863$	−11.9209	−	11.9209i	−0.405792	−	0.405792i	0.474476	−	0.880268i	$-0.342637\pi$
$863$	−11.9209	−	11.9209i	−0.405792	−	0.405792i	−0.880268	+	0.474476i	$0.842637\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−25.7589	+	3.16036i	−0.874818	+	0.107331i
$868$		0			0
$869$	42.8165			1.45245
$870$		0			0
$871$	73.4071			2.48730
$872$		0			0
$873$	−4.60868	−	2.77035i	−0.155980	−	0.0937620i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	10.7959	+	10.7959i	0.364553	+	0.364553i	0.865486	−	0.500933i	$-0.167010\pi$
$877$	10.7959	+	10.7959i	0.364553	+	0.364553i	−0.500933	+	0.865486i	$0.667010\pi$
$878$		0			0
$879$	16.4948	−	21.1083i	0.556356	−	0.711966i
$880$		0			0
$881$		−	46.2409i		−	1.55789i	−0.627089	−	0.778947i	$-0.715754\pi$
$881$		−	46.2409i		−	1.55789i	0.627089	−	0.778947i	$-0.284246\pi$
$882$		0			0
$883$	1.53325	−	1.53325i	0.0515981	−	0.0515981i	−0.680837	−	0.732435i	$-0.738384\pi$
$883$	1.53325	−	1.53325i	0.0515981	−	0.0515981i	0.732435	+	0.680837i	$0.238384\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	26.1717	−	26.1717i	0.878761	−	0.878761i	−0.114645	−	0.993406i	$-0.536573\pi$
$887$	26.1717	−	26.1717i	0.878761	−	0.878761i	0.993406	+	0.114645i	$0.0365731\pi$
$888$		0			0
$889$		−	2.07344i		−	0.0695410i
$890$		0			0
$891$	−27.1651	−	51.1362i	−0.910066	−	1.71313i
$892$		0			0
$893$	28.5827	+	28.5827i	0.956484	+	0.956484i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	1.16093	+	9.46230i	0.0387623	+	0.315937i
$898$		0			0
$899$	−1.15783			−0.0386158
$900$		0			0
$901$	−8.04870			−0.268141
$902$		0			0
$903$	2.01303	+	16.4075i	0.0669895	+	0.546007i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	9.37737	+	9.37737i	0.311370	+	0.311370i	0.845440	−	0.534070i	$-0.179338\pi$
$907$	9.37737	+	9.37737i	0.311370	+	0.311370i	−0.534070	+	0.845440i	$0.679338\pi$
$908$		0			0
$909$	3.65468	+	14.6698i	0.121218	+	0.486566i
$910$		0			0
$911$		−	15.2153i		−	0.504106i	−0.967713	−	0.252053i	$-0.918894\pi$
$911$		−	15.2153i		−	0.504106i	0.967713	−	0.252053i	$-0.0811058\pi$
$912$		0			0
$913$	53.7653	−	53.7653i	1.77937	−	1.77937i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−13.3344	+	13.3344i	−0.440340	+	0.440340i
$918$		0			0
$919$			28.1023i			0.927008i	0.886095	+	0.463504i	$0.153408\pi$
$919$			28.1023i			0.927008i	−0.886095	+	0.463504i	$0.846592\pi$
$920$		0			0
$921$	−8.58660	+	10.9882i	−0.282938	+	0.362074i
$922$		0			0
$923$	−3.97655	−	3.97655i	−0.130890	−	0.130890i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	6.85312	−	11.4007i	0.225086	−	0.374448i
$928$		0			0
$929$	−22.0987			−0.725034			−0.362517	−	0.931977i	$-0.618083\pi$
$929$	−22.0987			−0.725034			−0.362517	+	0.931977i	$0.618083\pi$
$930$		0			0
$931$	6.08104			0.199298
$932$		0			0
$933$	−28.3647	+	3.48006i	−0.928618	+	0.113932i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	10.6715	+	10.6715i	0.348621	+	0.348621i	0.859596	−	0.510975i	$-0.170715\pi$
$937$	10.6715	+	10.6715i	0.348621	+	0.348621i	−0.510975	+	0.859596i	$0.670715\pi$
$938$		0			0
$939$	2.81108	+	2.19668i	0.0917361	+	0.0716859i
$940$		0			0
$941$			13.7394i			0.447892i	0.974602	+	0.223946i	$0.0718940\pi$
$941$			13.7394i			0.447892i	−0.974602	+	0.223946i	$0.928106\pi$
$942$		0			0
$943$	−3.84362	+	3.84362i	−0.125165	+	0.125165i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	39.4345	−	39.4345i	1.28145	−	1.28145i	0.341604	−	0.939844i	$-0.389030\pi$
$947$	39.4345	−	39.4345i	1.28145	−	1.28145i	0.939844	−	0.341604i	$-0.110970\pi$
$948$		0			0
$949$			3.38246i			0.109799i
$950$		0			0
$951$	−42.1332	−	32.9244i	−1.36626	−	1.06765i
$952$		0			0
$953$	8.24554	+	8.24554i	0.267099	+	0.267099i	0.827930	−	0.560831i	$-0.189518\pi$
$953$	8.24554	+	8.24554i	0.267099	+	0.267099i	−0.560831	+	0.827930i	$0.689518\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	5.37623	−	0.659608i	0.173789	−	0.0213221i
$958$		0			0
$959$	13.4154			0.433205
$960$		0			0
$961$	−25.3259			−0.816964
$962$		0			0
$963$	−4.84807	+	8.06513i	−0.156227	+	0.259895i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−18.1306	−	18.1306i	−0.583041	−	0.583041i	0.352697	−	0.935738i	$-0.385265\pi$
$967$	−18.1306	−	18.1306i	−0.583041	−	0.583041i	−0.935738	+	0.352697i	$0.885265\pi$
$968$		0			0
$969$	9.20956	−	11.7854i	0.295854	−	0.378603i
$970$		0			0
$971$		−	57.0729i		−	1.83156i	−0.401686	−	0.915778i	$-0.631576\pi$
$971$		−	57.0729i		−	1.83156i	0.401686	−	0.915778i	$-0.368424\pi$
$972$		0			0
$973$	0.619100	−	0.619100i	0.0198474	−	0.0198474i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	11.5308	−	11.5308i	0.368902	−	0.368902i	−0.498175	−	0.867077i	$-0.665996\pi$
$977$	11.5308	−	11.5308i	0.368902	−	0.368902i	0.867077	+	0.498175i	$0.165996\pi$
$978$		0			0
$979$		−	53.5333i		−	1.71093i
$980$		0			0
$981$	5.25359	+	21.0878i	0.167734	+	0.673280i
$982$		0			0
$983$	−41.1083	−	41.1083i	−1.31115	−	1.31115i	−0.920567	−	0.390585i	$-0.872273\pi$
$983$	−41.1083	−	41.1083i	−1.31115	−	1.31115i	−0.390585	−	0.920567i	$-0.627727\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−1.40206	−	11.4277i	−0.0446280	−	0.363746i
$988$		0			0
$989$	−8.76437			−0.278691
$990$		0			0
$991$	15.5429			0.493737			0.246869	−	0.969049i	$-0.420598\pi$
$991$	15.5429			0.493737			0.246869	+	0.969049i	$0.420598\pi$
$992$		0			0
$993$	−0.520202	−	4.23998i	−0.0165081	−	0.134552i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−33.4971	−	33.4971i	−1.06086	−	1.06086i	−0.998024	−	0.0628388i	$-0.979985\pi$
$997$	−33.4971	−	33.4971i	−1.06086	−	1.06086i	−0.0628388	−	0.998024i	$-0.520015\pi$
$998$		0			0
$999$	−12.2645	+	27.5259i	−0.388033	+	0.870880i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.s.b.1457.6		24
3.2	odd	2	inner	2100.2.s.b.1457.1		24
5.2	odd	4		420.2.s.a.113.12	yes	24
5.3	odd	4	inner	2100.2.s.b.1793.1		24
5.4	even	2		420.2.s.a.197.7	yes	24
15.2	even	4		420.2.s.a.113.7	✓	24
15.8	even	4	inner	2100.2.s.b.1793.6		24
15.14	odd	2		420.2.s.a.197.12	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.s.a.113.7	✓	24	15.2	even	4
420.2.s.a.113.12	yes	24	5.2	odd	4
420.2.s.a.197.7	yes	24	5.4	even	2
420.2.s.a.197.12	yes	24	15.14	odd	2
2100.2.s.b.1457.1		24	3.2	odd	2	inner
2100.2.s.b.1457.6		24	1.1	even	1	trivial
2100.2.s.b.1793.1		24	5.3	odd	4	inner
2100.2.s.b.1793.6		24	15.8	even	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)

\(f(q)\)	\(=\)	\(q+(0.210923 + 1.71916i) q^{3} +(0.707107 + 0.707107i) q^{7} +(-2.91102 + 0.725222i) q^{9} +O(q^{10})\)	\(q+(0.210923 + 1.71916i) q^{3} +(0.707107 + 0.707107i) q^{7} +(-2.91102 + 0.725222i) q^{9} -6.43376i q^{11} +(-4.23809 + 4.23809i) q^{13} +(1.00413 - 1.00413i) q^{17} -6.08104i q^{19} +(-1.06648 + 1.36478i) q^{21} +(-0.649352 - 0.649352i) q^{23} +(-1.86078 - 4.85155i) q^{27} +0.486067 q^{29} -2.38204 q^{31} +(11.0607 - 1.35703i) q^{33} +(-4.10080 - 4.10080i) q^{37} +(-8.17987 - 6.39205i) q^{39} -5.91916i q^{41} +(6.74855 - 6.74855i) q^{43} +(-4.70030 + 4.70030i) q^{47} +1.00000i q^{49} +(1.93806 + 1.51447i) q^{51} +(-4.00778 - 4.00778i) q^{53} +(10.4543 - 1.28263i) q^{57} +8.86958 q^{59} -7.72565 q^{61} +(-2.57121 - 1.54559i) q^{63} +(-8.66039 - 8.66039i) q^{67} +(0.979376 - 1.25330i) q^{69} +0.938289i q^{71} +(0.399054 - 0.399054i) q^{73} +(4.54936 - 4.54936i) q^{77} +6.65496i q^{79} +(7.94811 - 4.22228i) q^{81} +(8.35674 + 8.35674i) q^{83} +(0.102523 + 0.835627i) q^{87} +8.32068 q^{89} -5.99357 q^{91} +(-0.502428 - 4.09511i) q^{93} +(1.26743 + 1.26743i) q^{97} +(4.66591 + 18.7288i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3}+O(q^{10}) \) 24 * q + 4 * q^3	\( 24 q + 4 q^{3} - 24 q^{13} + 4 q^{21} - 8 q^{27} - 16 q^{31} + 20 q^{33} - 32 q^{37} + 8 q^{43} + 52 q^{51} + 28 q^{57} - 8 q^{63} + 24 q^{67} - 12 q^{81} + 20 q^{87} - 24 q^{91} - 20 q^{93} + 104 q^{97}+O(q^{100}) \) 24 * q + 4 * q^3 - 24 * q^13 + 4 * q^21 - 8 * q^27 - 16 * q^31 + 20 * q^33 - 32 * q^37 + 8 * q^43 + 52 * q^51 + 28 * q^57 - 8 * q^63 + 24 * q^67 - 12 * q^81 + 20 * q^87 - 24 * q^91 - 20 * q^93 + 104 * q^97

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