LMFDB - Embedded newform 2100.2.s.c.1457.3

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			1457.3
Character	$\chi$	$=$	2100.1457
Dual form			2100.2.s.c.1793.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.63431 + 0.573626i) q^{3} +(-0.707107 - 0.707107i) q^{7} +(2.34191 - 1.87496i) q^{9} +O(q^{10})$	$q+(-1.63431 + 0.573626i) q^{3} +(-0.707107 - 0.707107i) q^{7} +(2.34191 - 1.87496i) q^{9} -6.10537i q^{11} +(-2.13396 + 2.13396i) q^{13} +(1.21226 - 1.21226i) q^{17} -0.390435i q^{19} +(1.56124 + 0.750013i) q^{21} +(2.04421 + 2.04421i) q^{23} +(-2.75186 + 4.40764i) q^{27} -5.67664 q^{29} +1.37257 q^{31} +(3.50220 + 9.97805i) q^{33} +(-2.84106 - 2.84106i) q^{37} +(2.26344 - 4.71163i) q^{39} +5.59818i q^{41} +(-3.04317 + 3.04317i) q^{43} +(1.32322 - 1.32322i) q^{47} +1.00000i q^{49} +(-1.28582 + 2.67659i) q^{51} +(9.10761 + 9.10761i) q^{53} +(0.223964 + 0.638091i) q^{57} -6.21447 q^{59} -6.30077 q^{61} +(-2.98177 - 0.330181i) q^{63} +(-7.63586 - 7.63586i) q^{67} +(-4.51348 - 2.16825i) q^{69} -6.26230i q^{71} +(-11.3446 + 11.3446i) q^{73} +(-4.31715 + 4.31715i) q^{77} -6.56174i q^{79} +(1.96905 - 8.78196i) q^{81} +(-3.59616 - 3.59616i) q^{83} +(9.27736 - 3.25627i) q^{87} +17.7783 q^{89} +3.01787 q^{91} +(-2.24319 + 0.787340i) q^{93} +(-10.3143 - 10.3143i) q^{97} +(-11.4473 - 14.2982i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.63431	+	0.573626i	−0.943566	+	0.331183i
$3$	−1.63431	+	0.573626i	−0.943566	+	0.331183i
$4$		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
$9$	2.34191	−	1.87496i	0.780635	−	0.624987i
$10$		0			0
$11$		−	6.10537i		−	1.84084i	−0.390931	−	0.920420i	$-0.627847\pi$
$11$		−	6.10537i		−	1.84084i	0.390931	−	0.920420i	$-0.372153\pi$
$12$		0			0
$13$	−2.13396	+	2.13396i	−0.591853	+	0.591853i	−0.938132	−	0.346279i	$-0.887445\pi$
$13$	−2.13396	+	2.13396i	−0.591853	+	0.591853i	0.346279	+	0.938132i	$0.387445\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.21226	−	1.21226i	0.294016	−	0.294016i	−0.544648	−	0.838665i	$-0.683337\pi$
$17$	1.21226	−	1.21226i	0.294016	−	0.294016i	0.838665	+	0.544648i	$0.183337\pi$
$18$		0			0
$19$		−	0.390435i		−	0.0895720i	−0.998997	−	0.0447860i	$-0.985739\pi$
$19$		−	0.390435i		−	0.0895720i	0.998997	−	0.0447860i	$-0.0142606\pi$
$20$		0			0
$21$	1.56124	+	0.750013i	0.340691	+	0.163666i
$22$		0			0
$23$	2.04421	+	2.04421i	0.426248	+	0.426248i	0.887348	−	0.461100i	$-0.152545\pi$
$23$	2.04421	+	2.04421i	0.426248	+	0.426248i	−0.461100	+	0.887348i	$0.652545\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−2.75186	+	4.40764i	−0.529596	+	0.848250i
$28$		0			0
$29$	−5.67664			−1.05413			−0.527063	−	0.849826i	$-0.676707\pi$
$29$	−5.67664			−1.05413			−0.527063	+	0.849826i	$0.676707\pi$
$30$		0			0
$31$	1.37257			0.246520			0.123260	−	0.992374i	$-0.460665\pi$
$31$	1.37257			0.246520			0.123260	+	0.992374i	$0.460665\pi$
$32$		0			0
$33$	3.50220	+	9.97805i	0.609655	+	1.73695i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.84106	−	2.84106i	−0.467068	−	0.467068i	0.433895	−	0.900963i	$-0.357139\pi$
$37$	−2.84106	−	2.84106i	−0.467068	−	0.467068i	−0.900963	+	0.433895i	$0.857139\pi$
$38$		0			0
$39$	2.26344	−	4.71163i	0.362441	−	0.754464i
$40$		0			0
$41$			5.59818i			0.874288i	0.899391	+	0.437144i	$0.144010\pi$
$41$			5.59818i			0.874288i	−0.899391	+	0.437144i	$0.855990\pi$
$42$		0			0
$43$	−3.04317	+	3.04317i	−0.464079	+	0.464079i	−0.899990	−	0.435911i	$-0.856426\pi$
$43$	−3.04317	+	3.04317i	−0.464079	+	0.464079i	0.435911	+	0.899990i	$0.356426\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.32322	−	1.32322i	0.193012	−	0.193012i	−0.603984	−	0.796996i	$-0.706421\pi$
$47$	1.32322	−	1.32322i	0.193012	−	0.193012i	0.796996	+	0.603984i	$0.206421\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$	−1.28582	+	2.67659i	−0.180051	+	0.374797i
$52$		0			0
$53$	9.10761	+	9.10761i	1.25103	+	1.25103i	0.955260	+	0.295767i	$0.0955751\pi$
$53$	9.10761	+	9.10761i	1.25103	+	1.25103i	0.295767	+	0.955260i	$0.404425\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	0.223964	+	0.638091i	0.0296647	+	0.0845172i
$58$		0			0
$59$	−6.21447			−0.809056			−0.404528	−	0.914526i	$-0.632564\pi$
$59$	−6.21447			−0.809056			−0.404528	+	0.914526i	$0.632564\pi$
$60$		0			0
$61$	−6.30077			−0.806731			−0.403365	−	0.915039i	$-0.632160\pi$
$61$	−6.30077			−0.806731			−0.403365	+	0.915039i	$0.632160\pi$
$62$		0			0
$63$	−2.98177	−	0.330181i	−0.375668	−	0.0415989i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−7.63586	−	7.63586i	−0.932869	−	0.932869i	0.0650152	−	0.997884i	$-0.479290\pi$
$67$	−7.63586	−	7.63586i	−0.932869	−	0.932869i	−0.997884	+	0.0650152i	$0.979290\pi$
$68$		0			0
$69$	−4.51348	−	2.16825i	−0.543359	−	0.261027i
$70$		0			0
$71$		−	6.26230i		−	0.743199i	−0.928393	−	0.371599i	$-0.878810\pi$
$71$		−	6.26230i		−	0.743199i	0.928393	−	0.371599i	$-0.121190\pi$
$72$		0			0
$73$	−11.3446	+	11.3446i	−1.32779	+	1.32779i	−0.420490	+	0.907297i	$0.638142\pi$
$73$	−11.3446	+	11.3446i	−1.32779	+	1.32779i	−0.907297	+	0.420490i	$0.861858\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−4.31715	+	4.31715i	−0.491985	+	0.491985i
$78$		0			0
$79$		−	6.56174i		−	0.738254i	−0.929379	−	0.369127i	$-0.879657\pi$
$79$		−	6.56174i		−	0.738254i	0.929379	−	0.369127i	$-0.120343\pi$
$80$		0			0
$81$	1.96905	−	8.78196i	0.218783	−	0.975773i
$82$		0			0
$83$	−3.59616	−	3.59616i	−0.394730	−	0.394730i	0.481639	−	0.876370i	$-0.340042\pi$
$83$	−3.59616	−	3.59616i	−0.394730	−	0.394730i	−0.876370	+	0.481639i	$0.840042\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	9.27736	−	3.25627i	0.994637	−	0.349109i
$88$		0			0
$89$	17.7783			1.88450			0.942248	−	0.334917i	$-0.108708\pi$
$89$	17.7783			1.88450			0.942248	+	0.334917i	$0.108708\pi$
$90$		0			0
$91$	3.01787			0.316359
$92$		0			0
$93$	−2.24319	+	0.787340i	−0.232608	+	0.0816433i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−10.3143	−	10.3143i	−1.04726	−	1.04726i	−0.998827	−	0.0484294i	$-0.984578\pi$
$97$	−10.3143	−	10.3143i	−1.04726	−	1.04726i	−0.0484294	−	0.998827i	$-0.515422\pi$
$98$		0			0
$99$	−11.4473	−	14.2982i	−1.15050	−	1.43702i
$100$		0			0
$101$			16.1678i			1.60875i	0.594120	+	0.804376i	$0.297500\pi$
$101$			16.1678i			1.60875i	−0.594120	+	0.804376i	$0.702500\pi$
$102$		0			0
$103$	−6.28299	+	6.28299i	−0.619081	+	0.619081i	−0.945296	−	0.326215i	$-0.894227\pi$
$103$	−6.28299	+	6.28299i	−0.619081	+	0.619081i	0.326215	+	0.945296i	$0.394227\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.37114	+	3.37114i	−0.325900	+	0.325900i	−0.851025	−	0.525125i	$-0.824019\pi$
$107$	−3.37114	+	3.37114i	−0.325900	+	0.325900i	0.525125	+	0.851025i	$0.324019\pi$
$108$		0			0
$109$		−	3.78087i		−	0.362142i	−0.983470	−	0.181071i	$-0.942044\pi$
$109$		−	3.78087i		−	0.362142i	0.983470	−	0.181071i	$-0.0579563\pi$
$110$		0			0
$111$	6.27287	+	3.01346i	0.595395	+	0.286025i
$112$		0			0
$113$	−9.12558	−	9.12558i	−0.858462	−	0.858462i	0.132695	−	0.991157i	$-0.457637\pi$
$113$	−9.12558	−	9.12558i	−0.858462	−	0.858462i	−0.991157	+	0.132695i	$0.957637\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.996442	+	8.99861i	−0.0921211	+	0.831921i
$118$		0			0
$119$	−1.71439			−0.157158
$120$		0			0
$121$	−26.2756			−2.38869
$122$		0			0
$123$	−3.21126	−	9.14913i	−0.289550	−	0.824949i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−9.57696	−	9.57696i	−0.849818	−	0.849818i	0.140292	−	0.990110i	$-0.455196\pi$
$127$	−9.57696	−	9.57696i	−0.849818	−	0.849818i	−0.990110	+	0.140292i	$0.955196\pi$
$128$		0			0
$129$	3.22782	−	6.71910i	0.284194	−	0.591584i
$130$		0			0
$131$		−	2.22683i		−	0.194559i	−0.995257	−	0.0972794i	$-0.968986\pi$
$131$		−	2.22683i		−	0.194559i	0.995257	−	0.0972794i	$-0.0310140\pi$
$132$		0			0
$133$	−0.276080	+	0.276080i	−0.0239391	+	0.0239391i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−9.04843	+	9.04843i	−0.773060	+	0.773060i	−0.978640	−	0.205581i	$-0.934092\pi$
$137$	−9.04843	+	9.04843i	−0.773060	+	0.773060i	0.205581	+	0.978640i	$0.434092\pi$
$138$		0			0
$139$		−	11.1155i		−	0.942805i	−0.881918	−	0.471403i	$-0.843748\pi$
$139$		−	11.1155i		−	0.942805i	0.881918	−	0.471403i	$-0.156252\pi$
$140$		0			0
$141$	−1.40352	+	2.92159i	−0.118197	+	0.246042i
$142$		0			0
$143$	13.0286	+	13.0286i	1.08951	+	1.08951i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−0.573626	−	1.63431i	−0.0473119	−	0.134795i
$148$		0			0
$149$	−18.9855			−1.55535			−0.777676	−	0.628666i	$-0.783601\pi$
$149$	−18.9855			−1.55535			−0.777676	+	0.628666i	$0.783601\pi$
$150$		0			0
$151$	6.10243			0.496609			0.248304	−	0.968682i	$-0.420127\pi$
$151$	6.10243			0.496609			0.248304	+	0.968682i	$0.420127\pi$
$152$		0			0
$153$	0.566060	−	5.11194i	0.0457632	−	0.413276i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	5.73647	+	5.73647i	0.457820	+	0.457820i	0.897939	−	0.440119i	$-0.145064\pi$
$157$	5.73647	+	5.73647i	0.457820	+	0.457820i	−0.440119	+	0.897939i	$0.645064\pi$
$158$		0			0
$159$	−20.1090	−	9.66025i	−1.59475	−	0.766108i
$160$		0			0
$161$		−	2.89095i		−	0.227839i
$162$		0			0
$163$	9.48806	−	9.48806i	0.743162	−	0.743162i	−0.230023	−	0.973185i	$-0.573880\pi$
$163$	9.48806	−	9.48806i	0.743162	−	0.743162i	0.973185	+	0.230023i	$0.0738801\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.36137	+	6.36137i	−0.492257	+	0.492257i	−0.909017	−	0.416760i	$-0.863166\pi$
$167$	−6.36137	+	6.36137i	−0.492257	+	0.492257i	0.416760	+	0.909017i	$0.363166\pi$
$168$		0			0
$169$			3.89246i			0.299420i
$170$		0			0
$171$	−0.732051	−	0.914363i	−0.0559813	−	0.0699231i
$172$		0			0
$173$	−5.82578	−	5.82578i	−0.442926	−	0.442926i	0.450068	−	0.892994i	$-0.351400\pi$
$173$	−5.82578	−	5.82578i	−0.442926	−	0.442926i	−0.892994	+	0.450068i	$0.851400\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	10.1563	−	3.56478i	0.763398	−	0.267946i
$178$		0			0
$179$	−14.1127			−1.05483			−0.527417	−	0.849607i	$-0.676839\pi$
$179$	−14.1127			−1.05483			−0.527417	+	0.849607i	$0.676839\pi$
$180$		0			0
$181$	−23.7170			−1.76287			−0.881437	−	0.472301i	$-0.843423\pi$
$181$	−23.7170			−1.76287			−0.881437	+	0.472301i	$0.843423\pi$
$182$		0			0
$183$	10.2974	−	3.61429i	0.761204	−	0.267176i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−7.40130	−	7.40130i	−0.541237	−	0.541237i
$188$		0			0
$189$	5.06253	−	1.17081i	0.368245	−	0.0851637i
$190$		0			0
$191$			27.2871i			1.97442i	0.159420	+	0.987211i	$0.449038\pi$
$191$			27.2871i			1.97442i	−0.159420	+	0.987211i	$0.550962\pi$
$192$		0			0
$193$	−13.7722	+	13.7722i	−0.991346	+	0.991346i	−0.999963	−	0.00861662i	$-0.997257\pi$
$193$	−13.7722	+	13.7722i	−0.991346	+	0.991346i	0.00861662	+	0.999963i	$0.497257\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1.57090	+	1.57090i	−0.111922	+	0.111922i	−0.760850	−	0.648928i	$-0.775218\pi$
$197$	−1.57090	+	1.57090i	−0.111922	+	0.111922i	0.648928	+	0.760850i	$0.275218\pi$
$198$		0			0
$199$			19.8363i			1.40616i	0.711110	+	0.703081i	$0.248193\pi$
$199$			19.8363i			1.40616i	−0.711110	+	0.703081i	$0.751807\pi$
$200$		0			0
$201$	16.8595	+	8.09920i	1.18917	+	0.571273i
$202$		0			0
$203$	4.01399	+	4.01399i	0.281727	+	0.281727i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	8.62017	+	0.954537i	0.599143	+	0.0663449i
$208$		0			0
$209$	−2.38375			−0.164888
$210$		0			0
$211$	7.42326			0.511038			0.255519	−	0.966804i	$-0.417754\pi$
$211$	7.42326			0.511038			0.255519	+	0.966804i	$0.417754\pi$
$212$		0			0
$213$	3.59222	+	10.2345i	0.246135	+	0.701257i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−0.970551	−	0.970551i	−0.0658853	−	0.0658853i
$218$		0			0
$219$	12.0330	−	25.0481i	0.813115	−	1.69260i
$220$		0			0
$221$			5.17382i			0.348029i
$222$		0			0
$223$	7.88512	−	7.88512i	0.528027	−	0.528027i	−0.391957	−	0.919984i	$-0.628202\pi$
$223$	7.88512	−	7.88512i	0.528027	−	0.528027i	0.919984	+	0.391957i	$0.128202\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	12.7962	−	12.7962i	0.849312	−	0.849312i	−0.140735	−	0.990047i	$-0.544947\pi$
$227$	12.7962	−	12.7962i	0.849312	−	0.849312i	0.990047	+	0.140735i	$0.0449466\pi$
$228$		0			0
$229$			20.9997i			1.38770i	0.720121	+	0.693849i	$0.244086\pi$
$229$			20.9997i			1.38770i	−0.720121	+	0.693849i	$0.755914\pi$
$230$		0			0
$231$	4.57911	−	9.53197i	0.301283	−	0.627158i
$232$		0			0
$233$	1.41661	+	1.41661i	0.0928055	+	0.0928055i	0.751985	−	0.659180i	$-0.229096\pi$
$233$	1.41661	+	1.41661i	0.0928055	+	0.0928055i	−0.659180	+	0.751985i	$0.729096\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	3.76399	+	10.7239i	0.244497	+	0.696591i
$238$		0			0
$239$	18.8802			1.22126			0.610630	−	0.791916i	$-0.290916\pi$
$239$	18.8802			1.22126			0.610630	+	0.791916i	$0.290916\pi$
$240$		0			0
$241$	−16.3942			−1.05604			−0.528021	−	0.849231i	$-0.677066\pi$
$241$	−16.3942			−1.05604			−0.528021	+	0.849231i	$0.677066\pi$
$242$		0			0
$243$	1.81953	+	15.4819i	0.116723	+	0.993164i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	0.833172	+	0.833172i	0.0530135	+	0.0530135i
$248$		0			0
$249$	7.94008	+	3.81438i	0.503182	+	0.241726i
$250$		0			0
$251$		−	24.7660i		−	1.56322i	−0.623770	−	0.781608i	$-0.714400\pi$
$251$		−	24.7660i		−	1.56322i	0.623770	−	0.781608i	$-0.285600\pi$
$252$		0			0
$253$	12.4807	−	12.4807i	0.784654	−	0.784654i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	13.6724	−	13.6724i	0.852864	−	0.852864i	−0.137621	−	0.990485i	$-0.543946\pi$
$257$	13.6724	−	13.6724i	0.852864	−	0.852864i	0.990485	+	0.137621i	$0.0439457\pi$
$258$		0			0
$259$			4.01787i			0.249658i
$260$		0			0
$261$	−13.2942	+	10.6435i	−0.822888	+	0.658814i
$262$		0			0
$263$	−17.5538	−	17.5538i	−1.08241	−	1.08241i	−0.996284	−	0.0861303i	$-0.972550\pi$
$263$	−17.5538	−	17.5538i	−1.08241	−	1.08241i	−0.0861303	−	0.996284i	$-0.527450\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−29.0552	+	10.1981i	−1.77815	+	0.624113i
$268$		0			0
$269$	17.3802			1.05969			0.529844	−	0.848095i	$-0.322250\pi$
$269$	17.3802			1.05969			0.529844	+	0.848095i	$0.322250\pi$
$270$		0			0
$271$	20.8246			1.26500			0.632502	−	0.774559i	$-0.282028\pi$
$271$	20.8246			1.26500			0.632502	+	0.774559i	$0.282028\pi$
$272$		0			0
$273$	−4.93212	+	1.73113i	−0.298505	+	0.104773i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−2.19684	−	2.19684i	−0.131996	−	0.131996i	0.638022	−	0.770018i	$-0.279753\pi$
$277$	−2.19684	−	2.19684i	−0.131996	−	0.131996i	−0.770018	+	0.638022i	$0.779753\pi$
$278$		0			0
$279$	3.21442	−	2.57351i	0.192442	−	0.154072i
$280$		0			0
$281$		−	11.6467i		−	0.694781i	−0.937720	−	0.347391i	$-0.887068\pi$
$281$		−	11.6467i		−	0.694781i	0.937720	−	0.347391i	$-0.112932\pi$
$282$		0			0
$283$	−16.5339	+	16.5339i	−0.982836	+	0.982836i	−0.999855	−	0.0170192i	$-0.994582\pi$
$283$	−16.5339	+	16.5339i	−0.982836	+	0.982836i	0.0170192	+	0.999855i	$0.494582\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	3.95851	−	3.95851i	0.233663	−	0.233663i
$288$		0			0
$289$			14.0609i			0.827109i
$290$		0			0
$291$	22.7732	+	10.9401i	1.33499	+	0.641322i
$292$		0			0
$293$	−4.28333	−	4.28333i	−0.250235	−	0.250235i	0.570832	−	0.821067i	$-0.306621\pi$
$293$	−4.28333	−	4.28333i	−0.250235	−	0.250235i	−0.821067	+	0.570832i	$0.806621\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	26.9103	+	16.8012i	1.56149	+	0.974902i
$298$		0			0
$299$	−8.72452			−0.504552
$300$		0			0
$301$	4.30369			0.248060
$302$		0			0
$303$	−9.27425	−	26.4231i	−0.532792	−	1.51796i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−11.5609	−	11.5609i	−0.659816	−	0.659816i	0.295521	−	0.955336i	$-0.404507\pi$
$307$	−11.5609	−	11.5609i	−0.659816	−	0.659816i	−0.955336	+	0.295521i	$0.904507\pi$
$308$		0			0
$309$	6.66423	−	13.8724i	0.379115	−	0.789174i
$310$		0			0
$311$		−	19.8520i		−	1.12570i	−0.826557	−	0.562852i	$-0.809704\pi$
$311$		−	19.8520i		−	1.12570i	0.826557	−	0.562852i	$-0.190296\pi$
$312$		0			0
$313$	−0.272468	+	0.272468i	−0.0154008	+	0.0154008i	−0.714765	−	0.699364i	$-0.753466\pi$
$313$	−0.272468	+	0.272468i	−0.0154008	+	0.0154008i	0.699364	+	0.714765i	$0.253466\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	11.8173	−	11.8173i	0.663728	−	0.663728i	−0.292529	−	0.956257i	$-0.594497\pi$
$317$	11.8173	−	11.8173i	0.663728	−	0.663728i	0.956257	+	0.292529i	$0.0944968\pi$
$318$		0			0
$319$			34.6580i			1.94048i
$320$		0			0
$321$	3.57570	−	7.44324i	0.199576	−	0.415441i
$322$		0			0
$323$	−0.473309	−	0.473309i	−0.0263356	−	0.0263356i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	2.16881	+	6.17910i	0.119935	+	0.341705i
$328$		0			0
$329$	−1.87132			−0.103169
$330$		0			0
$331$	−23.6380			−1.29926			−0.649631	−	0.760250i	$-0.725077\pi$
$331$	−23.6380			−1.29926			−0.649631	+	0.760250i	$0.725077\pi$
$332$		0			0
$333$	−11.9804	−	1.32662i	−0.656521	−	0.0726985i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.284624	−	0.284624i	−0.0155045	−	0.0155045i	0.699312	−	0.714817i	$-0.253490\pi$
$337$	−0.284624	−	0.284624i	−0.0155045	−	0.0155045i	−0.714817	+	0.699312i	$0.753490\pi$
$338$		0			0
$339$	20.1486	+	9.67931i	1.09432	+	0.525708i
$340$		0			0
$341$		−	8.38003i		−	0.453804i
$342$		0			0
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−10.2644	+	10.2644i	−0.551021	+	0.551021i	−0.926736	−	0.375714i	$-0.877397\pi$
$347$	−10.2644	+	10.2644i	−0.551021	+	0.551021i	0.375714	+	0.926736i	$0.377397\pi$
$348$		0			0
$349$		−	9.36459i		−	0.501275i	−0.968081	−	0.250638i	$-0.919360\pi$
$349$		−	9.36459i		−	0.501275i	0.968081	−	0.250638i	$-0.0806402\pi$
$350$		0			0
$351$	−3.53334	−	15.2781i	−0.188596	−	0.815482i
$352$		0			0
$353$	21.0867	+	21.0867i	1.12233	+	1.12233i	0.991390	+	0.130942i	$0.0418001\pi$
$353$	21.0867	+	21.0867i	1.12233	+	1.12233i	0.130942	+	0.991390i	$0.458200\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	2.80184	−	0.983421i	0.148289	−	0.0520482i
$358$		0			0
$359$	−0.701397			−0.0370183			−0.0185092	−	0.999829i	$-0.505892\pi$
$359$	−0.701397			−0.0370183			−0.0185092	+	0.999829i	$0.505892\pi$
$360$		0			0
$361$	18.8476			0.991977
$362$		0			0
$363$	42.9424	−	15.0724i	2.25389	−	0.791094i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−3.57837	−	3.57837i	−0.186790	−	0.186790i	0.607517	−	0.794307i	$-0.292166\pi$
$367$	−3.57837	−	3.57837i	−0.186790	−	0.186790i	−0.794307	+	0.607517i	$0.792166\pi$
$368$		0			0
$369$	10.4964	+	13.1104i	0.546418	+	0.682500i
$370$		0			0
$371$		−	12.8801i		−	0.668702i
$372$		0			0
$373$	25.4288	−	25.4288i	1.31665	−	1.31665i	0.400242	−	0.916410i	$-0.368926\pi$
$373$	25.4288	−	25.4288i	1.31665	−	1.31665i	0.916410	−	0.400242i	$-0.131074\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	12.1137	−	12.1137i	0.623887	−	0.623887i
$378$		0			0
$379$			25.1065i			1.28963i	0.764337	+	0.644817i	$0.223066\pi$
$379$			25.1065i			1.28963i	−0.764337	+	0.644817i	$0.776934\pi$
$380$		0			0
$381$	21.1453	+	10.1581i	1.08331	+	0.520414i
$382$		0			0
$383$	−2.54018	−	2.54018i	−0.129797	−	0.129797i	0.639224	−	0.769021i	$-0.279256\pi$
$383$	−2.54018	−	2.54018i	−0.129797	−	0.129797i	−0.769021	+	0.639224i	$0.779256\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.42099	+	12.8326i	−0.0722332	+	0.652319i
$388$		0			0
$389$	2.30912			0.117077			0.0585385	−	0.998285i	$-0.481356\pi$
$389$	2.30912			0.117077			0.0585385	+	0.998285i	$0.481356\pi$
$390$		0			0
$391$	4.95624			0.250648
$392$		0			0
$393$	1.27737	+	3.63931i	0.0644346	+	0.183579i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	18.7818	+	18.7818i	0.942630	+	0.942630i	0.998441	−	0.0558117i	$-0.0177747\pi$
$397$	18.7818	+	18.7818i	0.942630	+	0.942630i	−0.0558117	+	0.998441i	$0.517775\pi$
$398$		0			0
$399$	0.292832	−	0.609565i	0.0146599	−	0.0305164i
$400$		0			0
$401$			6.05457i			0.302351i	0.988507	+	0.151175i	$0.0483058\pi$
$401$			6.05457i			0.302351i	−0.988507	+	0.151175i	$0.951694\pi$
$402$		0			0
$403$	−2.92900	+	2.92900i	−0.145904	+	0.145904i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−17.3458	+	17.3458i	−0.859797	+	0.859797i
$408$		0			0
$409$			19.8086i			0.979471i	0.871871	+	0.489736i	$0.162907\pi$
$409$			19.8086i			0.979471i	−0.871871	+	0.489736i	$0.837093\pi$
$410$		0			0
$411$	9.59748	−	19.9783i	0.473409	−	0.985457i
$412$		0			0
$413$	4.39430	+	4.39430i	0.216229	+	0.216229i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	6.37615	+	18.1661i	0.312241	+	0.889599i
$418$		0			0
$419$	−1.95119			−0.0953218			−0.0476609	−	0.998864i	$-0.515177\pi$
$419$	−1.95119			−0.0953218			−0.0476609	+	0.998864i	$0.515177\pi$
$420$		0			0
$421$	−18.5297			−0.903084			−0.451542	−	0.892250i	$-0.649126\pi$
$421$	−18.5297			−0.903084			−0.451542	+	0.892250i	$0.649126\pi$
$422$		0			0
$423$	0.617875	−	5.57986i	0.0300421	−	0.271302i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	4.45532	+	4.45532i	0.215608	+	0.215608i
$428$		0			0
$429$	−28.7663	−	13.8192i	−1.38885	−	0.667195i
$430$		0			0
$431$		−	8.62503i		−	0.415453i	−0.978187	−	0.207727i	$-0.933394\pi$
$431$		−	8.62503i		−	0.415453i	0.978187	−	0.207727i	$-0.0666064\pi$
$432$		0			0
$433$	5.79494	−	5.79494i	0.278487	−	0.278487i	−0.554018	−	0.832505i	$-0.686906\pi$
$433$	5.79494	−	5.79494i	0.278487	−	0.278487i	0.832505	+	0.554018i	$0.186906\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.798133	−	0.798133i	0.0381799	−	0.0381799i
$438$		0			0
$439$			26.7072i			1.27466i	0.770590	+	0.637331i	$0.219962\pi$
$439$			26.7072i			1.27466i	−0.770590	+	0.637331i	$0.780038\pi$
$440$		0			0
$441$	1.87496	+	2.34191i	0.0892838	+	0.111519i
$442$		0			0
$443$	−13.3937	−	13.3937i	−0.636352	−	0.636352i	0.313302	−	0.949654i	$-0.398565\pi$
$443$	−13.3937	−	13.3937i	−0.636352	−	0.636352i	−0.949654	+	0.313302i	$0.898565\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	31.0281	−	10.8906i	1.46758	−	0.515106i
$448$		0			0
$449$	2.96802			0.140069			0.0700347	−	0.997545i	$-0.477689\pi$
$449$	2.96802			0.140069			0.0700347	+	0.997545i	$0.477689\pi$
$450$		0			0
$451$	34.1790			1.60942
$452$		0			0
$453$	−9.97323	+	3.50051i	−0.468583	+	0.164468i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	2.54155	+	2.54155i	0.118889	+	0.118889i	0.764048	−	0.645159i	$-0.223209\pi$
$457$	2.54155	+	2.54155i	0.118889	+	0.118889i	−0.645159	+	0.764048i	$0.723209\pi$
$458$		0			0
$459$	2.00723	+	8.67917i	0.0936893	+	0.405109i
$460$		0			0
$461$			17.0357i			0.793432i	0.917941	+	0.396716i	$0.129850\pi$
$461$			17.0357i			0.793432i	−0.917941	+	0.396716i	$0.870150\pi$
$462$		0			0
$463$	17.7681	−	17.7681i	0.825756	−	0.825756i	−0.161171	−	0.986927i	$-0.551527\pi$
$463$	17.7681	−	17.7681i	0.825756	−	0.825756i	0.986927	+	0.161171i	$0.0515270\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	5.94995	−	5.94995i	0.275331	−	0.275331i	−0.555911	−	0.831242i	$-0.687630\pi$
$467$	5.94995	−	5.94995i	0.275331	−	0.275331i	0.831242	+	0.555911i	$0.187630\pi$
$468$		0			0
$469$			10.7987i			0.498639i
$470$		0			0
$471$	−12.6657	−	6.08455i	−0.583606	−	0.280361i
$472$		0			0
$473$	18.5797	+	18.5797i	0.854294	+	0.854294i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	38.4056	+	4.25276i	1.75847	+	0.194721i
$478$		0			0
$479$	28.9746			1.32389			0.661943	−	0.749555i	$-0.269732\pi$
$479$	28.9746			1.32389			0.661943	+	0.749555i	$0.269732\pi$
$480$		0			0
$481$	12.1254			0.552871
$482$		0			0
$483$	1.65833	+	4.72470i	0.0754565	+	0.214981i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−8.07521	−	8.07521i	−0.365923	−	0.365923i	0.500065	−	0.865988i	$-0.333309\pi$
$487$	−8.07521	−	8.07521i	−0.365923	−	0.365923i	−0.865988	+	0.500065i	$0.833309\pi$
$488$		0			0
$489$	−10.0638	+	20.9490i	−0.455100	+	0.947346i
$490$		0			0
$491$			36.8212i			1.66172i	0.556483	+	0.830859i	$0.312150\pi$
$491$			36.8212i			1.66172i	−0.556483	+	0.830859i	$0.687850\pi$
$492$		0			0
$493$	−6.88156	+	6.88156i	−0.309930	+	0.309930i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.42812	+	4.42812i	−0.198628	+	0.198628i
$498$		0			0
$499$		−	2.27186i		−	0.101703i	−0.998706	−	0.0508513i	$-0.983807\pi$
$499$		−	2.27186i		−	0.101703i	0.998706	−	0.0508513i	$-0.0161935\pi$
$500$		0			0
$501$	6.74737	−	14.0455i	0.301450	−	0.627505i
$502$		0			0
$503$	−17.4979	−	17.4979i	−0.780195	−	0.780195i	0.199669	−	0.979863i	$-0.436013\pi$
$503$	−17.4979	−	17.4979i	−0.780195	−	0.780195i	−0.979863	+	0.199669i	$0.936013\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−2.23282	−	6.36147i	−0.0991630	−	0.282523i
$508$		0			0
$509$	22.1171			0.980322			0.490161	−	0.871632i	$-0.336938\pi$
$509$	22.1171			0.980322			0.490161	+	0.871632i	$0.336938\pi$
$510$		0			0
$511$	16.0437			0.709732
$512$		0			0
$513$	1.72090	+	1.07442i	0.0759795	+	0.0474370i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−8.07878	−	8.07878i	−0.355304	−	0.355304i
$518$		0			0
$519$	12.8629	+	6.17928i	0.564619	+	0.271240i
$520$		0			0
$521$		−	7.97810i		−	0.349527i	−0.984610	−	0.174763i	$-0.944084\pi$
$521$		−	7.97810i		−	0.349527i	0.984610	−	0.174763i	$-0.0559161\pi$
$522$		0			0
$523$	−13.9549	+	13.9549i	−0.610206	+	0.610206i	−0.943000	−	0.332794i	$-0.892009\pi$
$523$	−13.9549	+	13.9549i	−0.610206	+	0.610206i	0.332794	+	0.943000i	$0.392009\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.66391	−	1.66391i	0.0724809	−	0.0724809i
$528$		0			0
$529$		−	14.6424i		−	0.636625i
$530$		0			0
$531$	−14.5537	+	11.6519i	−0.631577	+	0.505649i
$532$		0			0
$533$	−11.9463	−	11.9463i	−0.517450	−	0.517450i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	23.0645	−	8.09542i	0.995305	−	0.349343i
$538$		0			0
$539$	6.10537			0.262977
$540$		0			0
$541$	−44.2256			−1.90141			−0.950703	−	0.310102i	$-0.899637\pi$
$541$	−44.2256			−1.90141			−0.950703	+	0.310102i	$0.899637\pi$
$542$		0			0
$543$	38.7609	−	13.6047i	1.66339	−	0.583834i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−4.87648	−	4.87648i	−0.208503	−	0.208503i	0.595128	−	0.803631i	$-0.297101\pi$
$547$	−4.87648	−	4.87648i	−0.208503	−	0.208503i	−0.803631	+	0.595128i	$0.797101\pi$
$548$		0			0
$549$	−14.7558	+	11.8137i	−0.629763	+	0.504196i
$550$		0			0
$551$			2.21636i			0.0944202i
$552$		0			0
$553$	−4.63985	+	4.63985i	−0.197307	+	0.197307i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	19.4830	−	19.4830i	0.825520	−	0.825520i	−0.161374	−	0.986893i	$-0.551592\pi$
$557$	19.4830	−	19.4830i	0.825520	−	0.825520i	0.986893	+	0.161374i	$0.0515924\pi$
$558$		0			0
$559$		−	12.9880i		−	0.549333i
$560$		0			0
$561$	16.3416	+	7.85040i	0.689941	+	0.331444i
$562$		0			0
$563$	−17.6394	−	17.6394i	−0.743413	−	0.743413i	0.229821	−	0.973233i	$-0.426186\pi$
$563$	−17.6394	−	17.6394i	−0.743413	−	0.743413i	−0.973233	+	0.229821i	$0.926186\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−7.60211	+	4.81746i	−0.319259	+	0.202314i
$568$		0			0
$569$	10.7356			0.450059			0.225029	−	0.974352i	$-0.427752\pi$
$569$	10.7356			0.450059			0.225029	+	0.974352i	$0.427752\pi$
$570$		0			0
$571$	6.68291			0.279671			0.139836	−	0.990175i	$-0.455343\pi$
$571$	6.68291			0.279671			0.139836	+	0.990175i	$0.455343\pi$
$572$		0			0
$573$	−15.6526	−	44.5954i	−0.653895	−	1.86300i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	12.1198	+	12.1198i	0.504555	+	0.504555i	0.912850	−	0.408295i	$-0.133876\pi$
$577$	12.1198	+	12.1198i	0.504555	+	0.504555i	−0.408295	+	0.912850i	$0.633876\pi$
$578$		0			0
$579$	14.6079	−	30.4081i	0.607084	−	1.26372i
$580$		0			0
$581$			5.08574i			0.210992i
$582$		0			0
$583$	55.6054	−	55.6054i	2.30294	−	2.30294i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−25.8190	+	25.8190i	−1.06566	+	1.06566i	−0.0679761	+	0.997687i	$0.521654\pi$
$587$	−25.8190	+	25.8190i	−1.06566	+	1.06566i	−0.997687	+	0.0679761i	$0.978346\pi$
$588$		0			0
$589$		−	0.535898i		−	0.0220813i
$590$		0			0
$591$	1.66622	−	3.46845i	0.0685393	−	0.142673i
$592$		0			0
$593$	9.95714	+	9.95714i	0.408891	+	0.408891i	0.881352	−	0.472461i	$-0.156634\pi$
$593$	9.95714	+	9.95714i	0.408891	+	0.408891i	−0.472461	+	0.881352i	$0.656634\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−11.3786	−	32.4186i	−0.465697	−	1.32681i
$598$		0			0
$599$	35.8800			1.46602			0.733010	−	0.680218i	$-0.238115\pi$
$599$	35.8800			1.46602			0.733010	+	0.680218i	$0.238115\pi$
$600$		0			0
$601$	−41.4277			−1.68987			−0.844936	−	0.534867i	$-0.820362\pi$
$601$	−41.4277			−1.68987			−0.844936	+	0.534867i	$0.820362\pi$
$602$		0			0
$603$	−32.1994	−	3.56554i	−1.31126	−	0.145200i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	2.53816	+	2.53816i	0.103021	+	0.103021i	0.756739	−	0.653718i	$-0.226792\pi$
$607$	2.53816	+	2.53816i	0.103021	+	0.103021i	−0.653718	+	0.756739i	$0.726792\pi$
$608$		0			0
$609$	−8.86261	−	4.25756i	−0.359131	−	0.172525i
$610$		0			0
$611$			5.64741i			0.228470i
$612$		0			0
$613$	0.604060	−	0.604060i	0.0243978	−	0.0243978i	−0.694803	−	0.719200i	$-0.744508\pi$
$613$	0.604060	−	0.604060i	0.0243978	−	0.0243978i	0.719200	+	0.694803i	$0.244508\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	12.7999	−	12.7999i	0.515304	−	0.515304i	−0.400843	−	0.916147i	$-0.631283\pi$
$617$	12.7999	−	12.7999i	0.515304	−	0.515304i	0.916147	+	0.400843i	$0.131283\pi$
$618$		0			0
$619$			13.1870i			0.530030i	0.964244	+	0.265015i	$0.0853769\pi$
$619$			13.1870i			0.530030i	−0.964244	+	0.265015i	$0.914623\pi$
$620$		0			0
$621$	−14.6355	+	3.38475i	−0.587304	+	0.135825i
$622$		0			0
$623$	−12.5711	−	12.5711i	−0.503652	−	0.503652i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	3.89578	−	1.36738i	0.155583	−	0.0546081i
$628$		0			0
$629$	−6.88821			−0.274651
$630$		0			0
$631$	−24.6951			−0.983097			−0.491549	−	0.870850i	$-0.663569\pi$
$631$	−24.6951			−0.983097			−0.491549	+	0.870850i	$0.663569\pi$
$632$		0			0
$633$	−12.1319	+	4.25817i	−0.482198	+	0.169247i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−2.13396	−	2.13396i	−0.0845504	−	0.0845504i
$638$		0			0
$639$	−11.7416	−	14.6657i	−0.464489	−	0.580167i
$640$		0			0
$641$		−	30.9661i		−	1.22309i	−0.791211	−	0.611543i	$-0.790549\pi$
$641$		−	30.9661i		−	1.22309i	0.791211	−	0.611543i	$-0.209451\pi$
$642$		0			0
$643$	−25.7147	+	25.7147i	−1.01409	+	1.01409i	−0.0141913	+	0.999899i	$0.504517\pi$
$643$	−25.7147	+	25.7147i	−1.01409	+	1.01409i	−0.999899	+	0.0141913i	$0.995483\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−11.2808	+	11.2808i	−0.443492	+	0.443492i	−0.893184	−	0.449692i	$-0.851534\pi$
$647$	−11.2808	+	11.2808i	−0.443492	+	0.443492i	0.449692	+	0.893184i	$0.351534\pi$
$648$		0			0
$649$			37.9417i			1.48934i
$650$		0			0
$651$	2.14291	+	1.02944i	0.0839872	+	0.0403470i
$652$		0			0
$653$	−24.0248	−	24.0248i	−0.940161	−	0.940161i	0.0581466	−	0.998308i	$-0.481481\pi$
$653$	−24.0248	−	24.0248i	−0.940161	−	0.940161i	−0.998308	+	0.0581466i	$0.981481\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−5.29733	+	47.8387i	−0.206668	+	1.86637i
$658$		0			0
$659$	−32.4805			−1.26526			−0.632630	−	0.774454i	$-0.718025\pi$
$659$	−32.4805			−1.26526			−0.632630	+	0.774454i	$0.718025\pi$
$660$		0			0
$661$	29.0233			1.12888			0.564438	−	0.825475i	$-0.309093\pi$
$661$	29.0233			1.12888			0.564438	+	0.825475i	$0.309093\pi$
$662$		0			0
$663$	−2.96784	−	8.45560i	−0.115261	−	0.328388i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−11.6043	−	11.6043i	−0.449319	−	0.449319i
$668$		0			0
$669$	−8.36358	+	17.4098i	−0.323355	+	0.673102i
$670$		0			0
$671$			38.4686i			1.48506i
$672$		0			0
$673$	33.6591	−	33.6591i	1.29746	−	1.29746i	0.367403	−	0.930062i	$-0.380247\pi$
$673$	33.6591	−	33.6591i	1.29746	−	1.29746i	0.930062	−	0.367403i	$-0.119753\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−12.0488	+	12.0488i	−0.463072	+	0.463072i	−0.899661	−	0.436589i	$-0.856186\pi$
$677$	−12.0488	+	12.0488i	−0.463072	+	0.463072i	0.436589	+	0.899661i	$0.356186\pi$
$678$		0			0
$679$			14.5866i			0.559782i
$680$		0			0
$681$	−13.5726	+	28.2531i	−0.520104	+	1.08266i
$682$		0			0
$683$	−2.28819	−	2.28819i	−0.0875552	−	0.0875552i	0.661973	−	0.749528i	$-0.269719\pi$
$683$	−2.28819	−	2.28819i	−0.0875552	−	0.0875552i	−0.749528	+	0.661973i	$0.769719\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−12.0460	−	34.3199i	−0.459582	−	1.30939i
$688$		0			0
$689$	−38.8705			−1.48085
$690$		0			0
$691$	11.1232			0.423147			0.211574	−	0.977362i	$-0.432141\pi$
$691$	11.1232			0.423147			0.211574	+	0.977362i	$0.432141\pi$
$692$		0			0
$693$	−2.01588	+	18.2049i	−0.0765769	+	0.691545i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	6.78644	+	6.78644i	0.257055	+	0.257055i
$698$		0			0
$699$	−3.12779	−	1.50257i	−0.118304	−	0.0568325i
$700$		0			0
$701$			9.12700i			0.344722i	0.985034	+	0.172361i	$0.0551396\pi$
$701$			9.12700i			0.344722i	−0.985034	+	0.172361i	$0.944860\pi$
$702$		0			0
$703$	−1.10925	+	1.10925i	−0.0418362	+	0.0418362i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	11.4323	−	11.4323i	0.429957	−	0.429957i
$708$		0			0
$709$		−	43.7645i		−	1.64361i	−0.569769	−	0.821805i	$-0.692967\pi$
$709$		−	43.7645i		−	1.64361i	0.569769	−	0.821805i	$-0.307033\pi$
$710$		0			0
$711$	−12.3030	−	15.3670i	−0.461399	−	0.576307i
$712$		0			0
$713$	2.80582	+	2.80582i	0.105079	+	0.105079i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−30.8560	+	10.8302i	−1.15234	+	0.404461i
$718$		0			0
$719$	−25.1296			−0.937177			−0.468588	−	0.883417i	$-0.655237\pi$
$719$	−25.1296			−0.937177			−0.468588	+	0.883417i	$0.655237\pi$
$720$		0			0
$721$	8.88549			0.330913
$722$		0			0
$723$	26.7931	−	9.40413i	0.996445	−	0.349743i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	2.31511	+	2.31511i	0.0858625	+	0.0858625i	0.748734	−	0.662871i	$-0.230662\pi$
$727$	2.31511	+	2.31511i	0.0858625	+	0.0858625i	−0.662871	+	0.748734i	$0.730662\pi$
$728$		0			0
$729$	−11.8545	−	24.2584i	−0.439055	−	0.898460i
$730$		0			0
$731$			7.37822i			0.272893i
$732$		0			0
$733$	4.92735	−	4.92735i	0.181996	−	0.181996i	−0.610229	−	0.792225i	$-0.708923\pi$
$733$	4.92735	−	4.92735i	0.181996	−	0.181996i	0.792225	+	0.610229i	$0.208923\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−46.6198	+	46.6198i	−1.71726	+	1.71726i
$738$		0			0
$739$		−	3.42357i		−	0.125938i	−0.998015	−	0.0629691i	$-0.979943\pi$
$739$		−	3.42357i		−	0.125938i	0.998015	−	0.0629691i	$-0.0200570\pi$
$740$		0			0
$741$	−1.83959	−	0.883728i	−0.0675789	−	0.0324646i
$742$		0			0
$743$	21.5198	+	21.5198i	0.789484	+	0.789484i	0.981410	−	0.191925i	$-0.0614731\pi$
$743$	21.5198	+	21.5198i	0.789484	+	0.789484i	−0.191925	+	0.981410i	$0.561473\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−15.1645	−	1.67921i	−0.554842	−	0.0614393i
$748$		0			0
$749$	4.76751			0.174201
$750$		0			0
$751$	11.8653			0.432969			0.216485	−	0.976286i	$-0.430541\pi$
$751$	11.8653			0.432969			0.216485	+	0.976286i	$0.430541\pi$
$752$		0			0
$753$	14.2064	+	40.4752i	0.517711	+	1.47500i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	34.4693	+	34.4693i	1.25281	+	1.25281i	0.954456	+	0.298352i	$0.0964370\pi$
$757$	34.4693	+	34.4693i	1.25281	+	1.25281i	0.298352	+	0.954456i	$0.403563\pi$
$758$		0			0
$759$	−13.2380	+	27.5565i	−0.480509	+	1.00024i
$760$		0			0
$761$		−	44.4955i		−	1.61296i	−0.591262	−	0.806480i	$-0.701370\pi$
$761$		−	44.4955i		−	1.61296i	0.591262	−	0.806480i	$-0.298630\pi$
$762$		0			0
$763$	−2.67348	+	2.67348i	−0.0967865	+	0.0967865i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	13.2614	−	13.2614i	0.478842	−	0.478842i
$768$		0			0
$769$		−	8.23513i		−	0.296966i	−0.988915	−	0.148483i	$-0.952561\pi$
$769$		−	8.23513i		−	0.296966i	0.988915	−	0.148483i	$-0.0474391\pi$
$770$		0			0
$771$	−14.5021	+	30.1878i	−0.522279	+	1.08719i
$772$		0			0
$773$	−22.8995	−	22.8995i	−0.823637	−	0.823637i	0.162991	−	0.986628i	$-0.447886\pi$
$773$	−22.8995	−	22.8995i	−0.823637	−	0.823637i	−0.986628	+	0.162991i	$0.947886\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−2.30475	−	6.56642i	−0.0826826	−	0.235569i
$778$		0			0
$779$	2.18573			0.0783118
$780$		0			0
$781$	−38.2337			−1.36811
$782$		0			0
$783$	15.6213	−	25.0206i	0.558261	−	0.894162i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−19.7721	−	19.7721i	−0.704800	−	0.704800i	0.260637	−	0.965437i	$-0.416068\pi$
$787$	−19.7721	−	19.7721i	−0.704800	−	0.704800i	−0.965437	+	0.260637i	$0.916068\pi$
$788$		0			0
$789$	38.7576	+	18.6190i	1.37981	+	0.662852i
$790$		0			0
$791$			12.9055i			0.458867i
$792$		0			0
$793$	13.4456	−	13.4456i	0.477466	−	0.477466i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	22.6803	−	22.6803i	0.803376	−	0.803376i	−0.180246	−	0.983622i	$-0.557689\pi$
$797$	22.6803	−	22.6803i	0.803376	−	0.803376i	0.983622	+	0.180246i	$0.0576893\pi$
$798$		0			0
$799$		−	3.20818i		−	0.113497i
$800$		0			0
$801$	41.6351	−	33.3336i	1.47110	−	1.17778i
$802$		0			0
$803$	69.2631	+	69.2631i	2.44424	+	2.44424i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−28.4045	+	9.96973i	−0.999887	+	0.350951i
$808$		0			0
$809$	7.31835			0.257299			0.128650	−	0.991690i	$-0.458936\pi$
$809$	7.31835			0.257299			0.128650	+	0.991690i	$0.458936\pi$
$810$		0			0
$811$	1.32051			0.0463693			0.0231847	−	0.999731i	$-0.492619\pi$
$811$	1.32051			0.0463693			0.0231847	+	0.999731i	$0.492619\pi$
$812$		0			0
$813$	−34.0337	+	11.9455i	−1.19361	+	0.418948i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	1.18816	+	1.18816i	0.0415685	+	0.0415685i
$818$		0			0
$819$	7.06757	−	5.65838i	0.246961	−	0.197720i
$820$		0			0
$821$			13.7480i			0.479810i	0.970796	+	0.239905i	$0.0771163\pi$
$821$			13.7480i			0.479810i	−0.970796	+	0.239905i	$0.922884\pi$
$822$		0			0
$823$	−30.2118	+	30.2118i	−1.05312	+	1.05312i	−0.0546082	+	0.998508i	$0.517391\pi$
$823$	−30.2118	+	30.2118i	−1.05312	+	1.05312i	−0.998508	+	0.0546082i	$0.982609\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	16.2448	−	16.2448i	0.564889	−	0.564889i	−0.365803	−	0.930692i	$-0.619206\pi$
$827$	16.2448	−	16.2448i	0.564889	−	0.564889i	0.930692	+	0.365803i	$0.119206\pi$
$828$		0			0
$829$		−	41.9100i		−	1.45559i	−0.685793	−	0.727797i	$-0.740544\pi$
$829$		−	41.9100i		−	1.45559i	0.685793	−	0.727797i	$-0.259456\pi$
$830$		0			0
$831$	4.85048	+	2.33015i	0.168261	+	0.0808319i
$832$		0			0
$833$	1.21226	+	1.21226i	0.0420023	+	0.0420023i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−3.77711	+	6.04977i	−0.130556	+	0.209111i
$838$		0			0
$839$	−19.0750			−0.658541			−0.329270	−	0.944236i	$-0.606803\pi$
$839$	−19.0750			−0.658541			−0.329270	+	0.944236i	$0.606803\pi$
$840$		0			0
$841$	3.22424			0.111181
$842$		0			0
$843$	6.68083	+	19.0342i	0.230100	+	0.655572i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	18.5797	+	18.5797i	0.638405	+	0.638405i
$848$		0			0
$849$	17.5371	−	36.5056i	0.601872	−	1.25287i
$850$		0			0
$851$		−	11.6155i		−	0.398173i
$852$		0			0
$853$	−7.44543	+	7.44543i	−0.254927	+	0.254927i	−0.822987	−	0.568060i	$-0.807694\pi$
$853$	−7.44543	+	7.44543i	−0.254927	+	0.254927i	0.568060	+	0.822987i	$0.307694\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	29.2330	−	29.2330i	0.998582	−	0.998582i	−0.00141712	−	0.999999i	$-0.500451\pi$
$857$	29.2330	−	29.2330i	0.998582	−	0.998582i	0.999999	+	0.00141712i	$0.000451084\pi$
$858$		0			0
$859$		−	25.6587i		−	0.875465i	−0.899105	−	0.437733i	$-0.855782\pi$
$859$		−	25.6587i		−	0.875465i	0.899105	−	0.437733i	$-0.144218\pi$
$860$		0			0
$861$	−4.19871	+	8.74011i	−0.143092	+	0.297862i
$862$		0			0
$863$	−33.1724	−	33.1724i	−1.12920	−	1.12920i	−0.990307	−	0.138894i	$-0.955645\pi$
$863$	−33.1724	−	33.1724i	−1.12920	−	1.12920i	−0.138894	−	0.990307i	$-0.544355\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−8.06567	−	22.9797i	−0.273925	−	0.780432i
$868$		0			0
$869$	−40.0619			−1.35901
$870$		0			0
$871$	32.5892			1.10424
$872$		0			0
$873$	−43.4939	−	4.81621i	−1.47205	−	0.163004i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	6.05243	+	6.05243i	0.204376	+	0.204376i	0.801872	−	0.597496i	$-0.203838\pi$
$877$	6.05243	+	6.05243i	0.204376	+	0.204376i	−0.597496	+	0.801872i	$0.703838\pi$
$878$		0			0
$879$	9.45730	+	4.54324i	0.318987	+	0.153240i
$880$		0			0
$881$			51.7654i			1.74402i	0.489486	+	0.872011i	$0.337184\pi$
$881$			51.7654i			1.74402i	−0.489486	+	0.872011i	$0.662816\pi$
$882$		0			0
$883$	−25.1198	+	25.1198i	−0.845350	+	0.845350i	−0.989549	−	0.144199i	$-0.953939\pi$
$883$	−25.1198	+	25.1198i	−0.845350	+	0.845350i	0.144199	+	0.989549i	$0.453939\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−33.4332	+	33.4332i	−1.12258	+	1.12258i	−0.131225	+	0.991353i	$0.541891\pi$
$887$	−33.4332	+	33.4332i	−1.12258	+	1.12258i	−0.991353	+	0.131225i	$0.958109\pi$
$888$		0			0
$889$			13.5439i			0.454247i
$890$		0			0
$891$	−53.6172	−	12.0218i	−1.79624	−	0.402745i
$892$		0			0
$893$	−0.516634	−	0.516634i	−0.0172885	−	0.0172885i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	14.2585	−	5.00461i	0.476078	−	0.167099i
$898$		0			0
$899$	−7.79156			−0.259863
$900$		0			0
$901$	22.0816			0.735644
$902$		0			0
$903$	−7.03354	+	2.46871i	−0.234062	+	0.0821534i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−0.627972	−	0.627972i	−0.0208515	−	0.0208515i	0.696604	−	0.717456i	$-0.254693\pi$
$907$	−0.627972	−	0.627972i	−0.0208515	−	0.0208515i	−0.717456	+	0.696604i	$0.754693\pi$
$908$		0			0
$909$	30.3139	+	37.8634i	1.00545	+	1.25585i
$910$		0			0
$911$		−	33.2327i		−	1.10105i	−0.834819	−	0.550524i	$-0.814428\pi$
$911$		−	33.2327i		−	1.10105i	0.834819	−	0.550524i	$-0.185572\pi$
$912$		0			0
$913$	−21.9559	+	21.9559i	−0.726635	+	0.726635i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.57460	+	1.57460i	−0.0519980	+	0.0519980i
$918$		0			0
$919$			29.4484i			0.971412i	0.874122	+	0.485706i	$0.161437\pi$
$919$			29.4484i			0.971412i	−0.874122	+	0.485706i	$0.838563\pi$
$920$		0			0
$921$	25.5257	+	12.2624i	0.841100	+	0.404060i
$922$		0			0
$923$	13.3635	+	13.3635i	0.439864	+	0.439864i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−2.93382	+	26.4945i	−0.0963592	+	0.870194i
$928$		0			0
$929$	−18.8616			−0.618830			−0.309415	−	0.950927i	$-0.600133\pi$
$929$	−18.8616			−0.618830			−0.309415	+	0.950927i	$0.600133\pi$
$930$		0			0
$931$	0.390435			0.0127960
$932$		0			0
$933$	11.3876	+	32.4443i	0.372814	+	1.06218i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−22.6123	−	22.6123i	−0.738711	−	0.738711i	0.233618	−	0.972328i	$-0.424944\pi$
$937$	−22.6123	−	22.6123i	−0.738711	−	0.738711i	−0.972328	+	0.233618i	$0.924944\pi$
$938$		0			0
$939$	0.289001	−	0.601591i	0.00943120	−	0.0196322i
$940$		0			0
$941$		−	56.4192i		−	1.83921i	−0.392842	−	0.919606i	$-0.628508\pi$
$941$		−	56.4192i		−	1.83921i	0.392842	−	0.919606i	$-0.371492\pi$
$942$		0			0
$943$	−11.4439	+	11.4439i	−0.372663	+	0.372663i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	40.8877	−	40.8877i	1.32867	−	1.32867i	0.422142	−	0.906530i	$-0.361278\pi$
$947$	40.8877	−	40.8877i	1.32867	−	1.32867i	0.906530	−	0.422142i	$-0.138722\pi$
$948$		0			0
$949$		−	48.4178i		−	1.57171i
$950$		0			0
$951$	−12.5344	+	26.0919i	−0.406456	+	0.846086i
$952$		0			0
$953$	−1.46536	−	1.46536i	−0.0474676	−	0.0474676i	0.682975	−	0.730442i	$-0.260686\pi$
$953$	−1.46536	−	1.46536i	−0.0474676	−	0.0474676i	−0.730442	+	0.682975i	$0.760686\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−19.8807	−	56.6418i	−0.642653	−	1.83097i
$958$		0			0
$959$	12.7964			0.413218
$960$		0			0
$961$	−29.1161			−0.939228
$962$		0			0
$963$	−1.57414	+	14.2156i	−0.0507259	+	0.458093i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−0.869720	−	0.869720i	−0.0279683	−	0.0279683i	0.692984	−	0.720953i	$-0.256295\pi$
$967$	−0.869720	−	0.869720i	−0.0279683	−	0.0279683i	−0.720953	+	0.692984i	$0.756295\pi$
$968$		0			0
$969$	1.04503	+	0.502029i	0.0335713	+	0.0161275i
$970$		0			0
$971$			16.2979i			0.523024i	0.965200	+	0.261512i	$0.0842211\pi$
$971$			16.2979i			0.523024i	−0.965200	+	0.261512i	$0.915779\pi$
$972$		0			0
$973$	−7.85985	+	7.85985i	−0.251975	+	0.251975i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	37.3718	−	37.3718i	1.19563	−	1.19563i	0.220167	−	0.975462i	$-0.429340\pi$
$977$	37.3718	−	37.3718i	1.19563	−	1.19563i	0.975462	−	0.220167i	$-0.0706602\pi$
$978$		0			0
$979$		−	108.543i		−	3.46905i
$980$		0			0
$981$	−7.08898	−	8.85444i	−0.226334	−	0.282701i
$982$		0			0
$983$	2.68668	+	2.68668i	0.0856917	+	0.0856917i	0.748653	−	0.662962i	$-0.230701\pi$
$983$	2.68668	+	2.68668i	0.0856917	+	0.0856917i	−0.662962	+	0.748653i	$0.730701\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	3.05831	−	1.07344i	0.0973471	−	0.0341680i
$988$		0			0
$989$	−12.4418			−0.395625
$990$		0			0
$991$	12.3109			0.391070			0.195535	−	0.980697i	$-0.437356\pi$
$991$	12.3109			0.391070			0.195535	+	0.980697i	$0.437356\pi$
$992$		0			0
$993$	38.6317	−	13.5594i	1.22594	−	0.430294i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−16.1288	−	16.1288i	−0.510806	−	0.510806i	0.403968	−	0.914773i	$-0.367631\pi$
$997$	−16.1288	−	16.1288i	−0.510806	−	0.510806i	−0.914773	+	0.403968i	$0.867631\pi$
$998$		0			0
$999$	20.3406	−	4.70415i	0.643548	−	0.148833i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2100.2.s.c.1457.3	✓	32
3.2	odd	2	inner	2100.2.s.c.1457.6	yes	32
5.2	odd	4	inner	2100.2.s.c.1793.11	yes	32
5.3	odd	4	inner	2100.2.s.c.1793.6	yes	32
5.4	even	2	inner	2100.2.s.c.1457.14	yes	32
15.2	even	4	inner	2100.2.s.c.1793.14	yes	32
15.8	even	4	inner	2100.2.s.c.1793.3	yes	32
15.14	odd	2	inner	2100.2.s.c.1457.11	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2100.2.s.c.1457.3	✓	32	1.1	even	1	trivial
2100.2.s.c.1457.6	yes	32	3.2	odd	2	inner
2100.2.s.c.1457.11	yes	32	15.14	odd	2	inner
2100.2.s.c.1457.14	yes	32	5.4	even	2	inner
2100.2.s.c.1793.3	yes	32	15.8	even	4	inner
2100.2.s.c.1793.6	yes	32	5.3	odd	4	inner
2100.2.s.c.1793.11	yes	32	5.2	odd	4	inner
2100.2.s.c.1793.14	yes	32	15.2	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)

\(f(q)\)	\(=\)	\(q+(-1.63431 + 0.573626i) q^{3} +(-0.707107 - 0.707107i) q^{7} +(2.34191 - 1.87496i) q^{9} +O(q^{10})\)	\(q+(-1.63431 + 0.573626i) q^{3} +(-0.707107 - 0.707107i) q^{7} +(2.34191 - 1.87496i) q^{9} -6.10537i q^{11} +(-2.13396 + 2.13396i) q^{13} +(1.21226 - 1.21226i) q^{17} -0.390435i q^{19} +(1.56124 + 0.750013i) q^{21} +(2.04421 + 2.04421i) q^{23} +(-2.75186 + 4.40764i) q^{27} -5.67664 q^{29} +1.37257 q^{31} +(3.50220 + 9.97805i) q^{33} +(-2.84106 - 2.84106i) q^{37} +(2.26344 - 4.71163i) q^{39} +5.59818i q^{41} +(-3.04317 + 3.04317i) q^{43} +(1.32322 - 1.32322i) q^{47} +1.00000i q^{49} +(-1.28582 + 2.67659i) q^{51} +(9.10761 + 9.10761i) q^{53} +(0.223964 + 0.638091i) q^{57} -6.21447 q^{59} -6.30077 q^{61} +(-2.98177 - 0.330181i) q^{63} +(-7.63586 - 7.63586i) q^{67} +(-4.51348 - 2.16825i) q^{69} -6.26230i q^{71} +(-11.3446 + 11.3446i) q^{73} +(-4.31715 + 4.31715i) q^{77} -6.56174i q^{79} +(1.96905 - 8.78196i) q^{81} +(-3.59616 - 3.59616i) q^{83} +(9.27736 - 3.25627i) q^{87} +17.7783 q^{89} +3.01787 q^{91} +(-2.24319 + 0.787340i) q^{93} +(-10.3143 - 10.3143i) q^{97} +(-11.4473 - 14.2982i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 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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