LMFDB - Embedded newform 3234.2.e.d.2155.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3234,2,Mod(2155,3234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3234, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3234.2155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3234.e (of order $2$, degree $1$, 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:	$25.8236200137$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2155.16
Character	$\chi$	$=$	3234.2155
Dual form			3234.2.e.d.2155.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.58222i q^{5} +1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.58222i q^{5} +1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +1.58222 q^{10} +(3.29433 + 0.383929i) q^{11} +1.00000i q^{12} +2.26904 q^{13} -1.58222 q^{15} +1.00000 q^{16} -2.99510 q^{17} -1.00000i q^{18} +1.32564 q^{19} +1.58222i q^{20} +(-0.383929 + 3.29433i) q^{22} +2.32457 q^{23} -1.00000 q^{24} +2.49657 q^{25} +2.26904i q^{26} +1.00000i q^{27} +2.90437i q^{29} -1.58222i q^{30} -10.1167i q^{31} +1.00000i q^{32} +(0.383929 - 3.29433i) q^{33} -2.99510i q^{34} +1.00000 q^{36} -2.83146 q^{37} +1.32564i q^{38} -2.26904i q^{39} -1.58222 q^{40} +11.6507 q^{41} +12.0294i q^{43} +(-3.29433 - 0.383929i) q^{44} +1.58222i q^{45} +2.32457i q^{46} +0.996186i q^{47} -1.00000i q^{48} +2.49657i q^{50} +2.99510i q^{51} -2.26904 q^{52} -0.531530 q^{53} -1.00000 q^{54} +(0.607462 - 5.21236i) q^{55} -1.32564i q^{57} -2.90437 q^{58} -0.121579i q^{59} +1.58222 q^{60} -7.54642 q^{61} +10.1167 q^{62} -1.00000 q^{64} -3.59013i q^{65} +(3.29433 + 0.383929i) q^{66} +0.628819 q^{67} +2.99510 q^{68} -2.32457i q^{69} -7.26798 q^{71} +1.00000i q^{72} +9.21350 q^{73} -2.83146i q^{74} -2.49657i q^{75} -1.32564 q^{76} +2.26904 q^{78} -11.7454i q^{79} -1.58222i q^{80} +1.00000 q^{81} +11.6507i q^{82} +7.48210 q^{83} +4.73892i q^{85} -12.0294 q^{86} +2.90437 q^{87} +(0.383929 - 3.29433i) q^{88} -11.3984i q^{89} -1.58222 q^{90} -2.32457 q^{92} -10.1167 q^{93} -0.996186 q^{94} -2.09746i q^{95} +1.00000 q^{96} +1.49379i q^{97} +(-3.29433 - 0.383929i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{4} + 24 q^{6} - 24 q^{9}+O(q^{10}) $ 24 * q - 24 * q^4 + 24 * q^6 - 24 * q^9	$ 24 q - 24 q^{4} + 24 q^{6} - 24 q^{9} + 24 q^{16} - 16 q^{17} + 32 q^{19} - 8 q^{22} - 24 q^{24} - 8 q^{25} + 8 q^{33} + 24 q^{36} + 16 q^{37} + 16 q^{41} - 24 q^{54} - 16 q^{55} + 16 q^{62} - 24 q^{64} - 64 q^{67} + 16 q^{68} + 64 q^{71} - 32 q^{76} + 24 q^{81} + 16 q^{83} + 8 q^{88} - 16 q^{93} - 64 q^{94} + 24 q^{96}+O(q^{100}) $ 24 * q - 24 * q^4 + 24 * q^6 - 24 * q^9 + 24 * q^16 - 16 * q^17 + 32 * q^19 - 8 * q^22 - 24 * q^24 - 8 * q^25 + 8 * q^33 + 24 * q^36 + 16 * q^37 + 16 * q^41 - 24 * q^54 - 16 * q^55 + 16 * q^62 - 24 * q^64 - 64 * q^67 + 16 * q^68 + 64 * q^71 - 32 * q^76 + 24 * q^81 + 16 * q^83 + 8 * q^88 - 16 * q^93 - 64 * q^94 + 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3234\mathbb{Z}\right)^\times$.

$n$	$199$	$1079$	$2059$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.00000			−0.500000
$5$		−	1.58222i		−	0.707592i	−0.935323	−	0.353796i	$-0.884891\pi$
$5$		−	1.58222i		−	0.707592i	0.935323	−	0.353796i	$-0.115109\pi$
$6$	1.00000			0.408248
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−1.00000			−0.333333
$10$	1.58222			0.500343
$11$	3.29433	+	0.383929i	0.993277	+	0.115759i
$11$	3.29433	+	0.383929i	0.993277	+	0.115759i
$12$			1.00000i			0.288675i
$13$	2.26904			0.629319			0.314659	−	0.949205i	$-0.398110\pi$
$13$	2.26904			0.629319			0.314659	+	0.949205i	$0.398110\pi$
$14$		0			0
$15$	−1.58222			−0.408528
$16$	1.00000			0.250000
$17$	−2.99510			−0.726419			−0.363210	−	0.931707i	$-0.618319\pi$
$17$	−2.99510			−0.726419			−0.363210	+	0.931707i	$0.618319\pi$
$18$		−	1.00000i		−	0.235702i
$19$	1.32564			0.304123			0.152061	−	0.988371i	$-0.451409\pi$
$19$	1.32564			0.304123			0.152061	+	0.988371i	$0.451409\pi$
$20$			1.58222i			0.353796i
$21$		0			0
$22$	−0.383929	+	3.29433i	−0.0818540	+	0.702353i
$23$	2.32457			0.484706			0.242353	−	0.970188i	$-0.422081\pi$
$23$	2.32457			0.484706			0.242353	+	0.970188i	$0.422081\pi$
$24$	−1.00000			−0.204124
$25$	2.49657			0.499314
$26$			2.26904i			0.444995i
$27$			1.00000i			0.192450i
$28$		0			0
$29$			2.90437i			0.539327i	0.962955	+	0.269664i	$0.0869125\pi$
$29$			2.90437i			0.539327i	−0.962955	+	0.269664i	$0.913087\pi$
$30$		−	1.58222i		−	0.288873i
$31$		−	10.1167i		−	1.81702i	−0.417867	−	0.908508i	$-0.637222\pi$
$31$		−	10.1167i		−	1.81702i	0.417867	−	0.908508i	$-0.362778\pi$
$32$			1.00000i			0.176777i
$33$	0.383929	−	3.29433i	0.0668335	−	0.573469i
$34$		−	2.99510i		−	0.513656i
$35$		0			0
$36$	1.00000			0.166667
$37$	−2.83146			−0.465489			−0.232744	−	0.972538i	$-0.574771\pi$
$37$	−2.83146			−0.465489			−0.232744	+	0.972538i	$0.574771\pi$
$38$			1.32564i			0.215047i
$39$		−	2.26904i		−	0.363337i
$40$	−1.58222			−0.250172
$41$	11.6507			1.81954			0.909769	−	0.415114i	$-0.136258\pi$
$41$	11.6507			1.81954			0.909769	+	0.415114i	$0.136258\pi$
$42$		0			0
$43$			12.0294i			1.83447i	0.398343	+	0.917237i	$0.369585\pi$
$43$			12.0294i			1.83447i	−0.398343	+	0.917237i	$0.630415\pi$
$44$	−3.29433	−	0.383929i	−0.496639	−	0.0578795i
$45$			1.58222i			0.235864i
$46$			2.32457i			0.342739i
$47$			0.996186i			0.145309i	0.997357	+	0.0726544i	$0.0231470\pi$
$47$			0.996186i			0.145309i	−0.997357	+	0.0726544i	$0.976853\pi$
$48$		−	1.00000i		−	0.144338i
$49$		0			0
$50$			2.49657i			0.353068i
$51$			2.99510i			0.419398i
$52$	−2.26904			−0.314659
$53$	−0.531530			−0.0730112			−0.0365056	−	0.999333i	$-0.511623\pi$
$53$	−0.531530			−0.0730112			−0.0365056	+	0.999333i	$0.511623\pi$
$54$	−1.00000			−0.136083
$55$	0.607462	−	5.21236i	0.0819101	−	0.702835i
$56$		0			0
$57$		−	1.32564i		−	0.175585i
$58$	−2.90437			−0.381362
$59$		−	0.121579i		−	0.0158283i	−0.999969	−	0.00791415i	$-0.997481\pi$
$59$		−	0.121579i		−	0.0158283i	0.999969	−	0.00791415i	$-0.00251918\pi$
$60$	1.58222			0.204264
$61$	−7.54642			−0.966220			−0.483110	−	0.875560i	$-0.660493\pi$
$61$	−7.54642			−0.966220			−0.483110	+	0.875560i	$0.660493\pi$
$62$	10.1167			1.28482
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	3.59013i		−	0.445301i
$66$	3.29433	+	0.383929i	0.405504	+	0.0472584i
$67$	0.628819			0.0768225			0.0384112	−	0.999262i	$-0.487770\pi$
$67$	0.628819			0.0768225			0.0384112	+	0.999262i	$0.487770\pi$
$68$	2.99510			0.363210
$69$		−	2.32457i		−	0.279845i
$70$		0			0
$71$	−7.26798			−0.862550			−0.431275	−	0.902221i	$-0.641936\pi$
$71$	−7.26798			−0.862550			−0.431275	+	0.902221i	$0.641936\pi$
$72$			1.00000i			0.117851i
$73$	9.21350			1.07836			0.539180	−	0.842191i	$-0.318734\pi$
$73$	9.21350			1.07836			0.539180	+	0.842191i	$0.318734\pi$
$74$		−	2.83146i		−	0.329150i
$75$		−	2.49657i		−	0.288279i
$76$	−1.32564			−0.152061
$77$		0			0
$78$	2.26904			0.256918
$79$		−	11.7454i		−	1.32146i	−0.750625	−	0.660729i	$-0.770247\pi$
$79$		−	11.7454i		−	1.32146i	0.750625	−	0.660729i	$-0.229753\pi$
$80$		−	1.58222i		−	0.176898i
$81$	1.00000			0.111111
$82$			11.6507i			1.28661i
$83$	7.48210			0.821267			0.410633	−	0.911801i	$-0.365308\pi$
$83$	7.48210			0.821267			0.410633	+	0.911801i	$0.365308\pi$
$84$		0			0
$85$			4.73892i			0.514009i
$86$	−12.0294			−1.29717
$87$	2.90437			0.311381
$88$	0.383929	−	3.29433i	0.0409270	−	0.351177i
$89$		−	11.3984i		−	1.20823i	−0.796899	−	0.604113i	$-0.793528\pi$
$89$		−	11.3984i		−	1.20823i	0.796899	−	0.604113i	$-0.206472\pi$
$90$	−1.58222			−0.166781
$91$		0			0
$92$	−2.32457			−0.242353
$93$	−10.1167			−1.04905
$94$	−0.996186			−0.102749
$95$		−	2.09746i		−	0.215195i
$96$	1.00000			0.102062
$97$			1.49379i			0.151672i	0.997120	+	0.0758358i	$0.0241625\pi$
$97$			1.49379i			0.151672i	−0.997120	+	0.0758358i	$0.975838\pi$
$98$		0			0
$99$	−3.29433	−	0.383929i	−0.331092	−	0.0385863i
$100$	−2.49657			−0.249657
$101$	−8.45020			−0.840827			−0.420413	−	0.907333i	$-0.638115\pi$
$101$	−8.45020			−0.840827			−0.420413	+	0.907333i	$0.638115\pi$
$102$	−2.99510			−0.296560
$103$		−	10.8258i		−	1.06670i	−0.845895	−	0.533350i	$-0.820933\pi$
$103$		−	10.8258i		−	1.06670i	0.845895	−	0.533350i	$-0.179067\pi$
$104$		−	2.26904i		−	0.222498i
$105$		0			0
$106$		−	0.531530i		−	0.0516267i
$107$		−	5.48462i		−	0.530218i	−0.964218	−	0.265109i	$-0.914592\pi$
$107$		−	5.48462i		−	0.530218i	0.964218	−	0.265109i	$-0.0854080\pi$
$108$		−	1.00000i		−	0.0962250i
$109$		−	13.1165i		−	1.25633i	−0.778080	−	0.628165i	$-0.783806\pi$
$109$		−	13.1165i		−	1.25633i	0.778080	−	0.628165i	$-0.216194\pi$
$110$	5.21236	+	0.607462i	0.496979	+	0.0579192i
$111$			2.83146i			0.268750i
$112$		0			0
$113$	10.8139			1.01728			0.508641	−	0.860979i	$-0.330148\pi$
$113$	10.8139			1.01728			0.508641	+	0.860979i	$0.330148\pi$
$114$	1.32564			0.124158
$115$		−	3.67799i		−	0.342974i
$116$		−	2.90437i		−	0.269664i
$117$	−2.26904			−0.209773
$118$	0.121579			0.0111923
$119$		0			0
$120$			1.58222i			0.144437i
$121$	10.7052	+	2.52958i	0.973200	+	0.229962i
$122$		−	7.54642i		−	0.683221i
$123$		−	11.6507i		−	1.05051i
$124$			10.1167i			0.908508i
$125$		−	11.8612i		−	1.06090i
$126$		0			0
$127$			2.74115i			0.243237i	0.992577	+	0.121619i	$0.0388085\pi$
$127$			2.74115i			0.243237i	−0.992577	+	0.121619i	$0.961191\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	12.0294			1.05913
$130$	3.59013			0.314875
$131$	3.99038			0.348641			0.174321	−	0.984689i	$-0.444227\pi$
$131$	3.99038			0.348641			0.174321	+	0.984689i	$0.444227\pi$
$132$	−0.383929	+	3.29433i	−0.0334167	+	0.286734i
$133$		0			0
$134$			0.628819i			0.0543217i
$135$	1.58222			0.136176
$136$			2.99510i			0.256828i
$137$	−1.11219			−0.0950211			−0.0475106	−	0.998871i	$-0.515129\pi$
$137$	−1.11219			−0.0950211			−0.0475106	+	0.998871i	$0.515129\pi$
$138$	2.32457			0.197880
$139$	12.6619			1.07397			0.536984	−	0.843593i	$-0.319564\pi$
$139$	12.6619			1.07397			0.536984	+	0.843593i	$0.319564\pi$
$140$		0			0
$141$	0.996186			0.0838940
$142$		−	7.26798i		−	0.609915i
$143$	7.47496	+	0.871151i	0.625088	+	0.0728493i
$144$	−1.00000			−0.0833333
$145$	4.59536			0.381624
$146$			9.21350i			0.762515i
$147$		0			0
$148$	2.83146			0.232744
$149$			12.7201i			1.04207i	0.853536	+	0.521034i	$0.174454\pi$
$149$			12.7201i			1.04207i	−0.853536	+	0.521034i	$0.825546\pi$
$150$	2.49657			0.203844
$151$		−	12.9633i		−	1.05494i	−0.849575	−	0.527468i	$-0.823141\pi$
$151$		−	12.9633i		−	1.05494i	0.849575	−	0.527468i	$-0.176859\pi$
$152$		−	1.32564i		−	0.107524i
$153$	2.99510			0.242140
$154$		0			0
$155$	−16.0069			−1.28571
$156$			2.26904i			0.181669i
$157$		−	5.08417i		−	0.405761i	−0.979204	−	0.202880i	$-0.934970\pi$
$157$		−	5.08417i		−	0.405761i	0.979204	−	0.202880i	$-0.0650303\pi$
$158$	11.7454			0.934411
$159$			0.531530i			0.0421531i
$160$	1.58222			0.125086
$161$		0			0
$162$			1.00000i			0.0785674i
$163$	17.2229			1.34900			0.674502	−	0.738273i	$-0.264358\pi$
$163$	17.2229			1.34900			0.674502	+	0.738273i	$0.264358\pi$
$164$	−11.6507			−0.909769
$165$	−5.21236	−	0.607462i	−0.405782	−	0.0472908i
$166$			7.48210i			0.580723i
$167$	5.31157			0.411022			0.205511	−	0.978655i	$-0.434114\pi$
$167$	5.31157			0.411022			0.205511	+	0.978655i	$0.434114\pi$
$168$		0			0
$169$	−7.85145			−0.603958
$170$	−4.73892			−0.363459
$171$	−1.32564			−0.101374
$172$		−	12.0294i		−	0.917237i
$173$	20.3662			1.54842			0.774208	−	0.632932i	$-0.218149\pi$
$173$	20.3662			1.54842			0.774208	+	0.632932i	$0.218149\pi$
$174$			2.90437i			0.220179i
$175$		0			0
$176$	3.29433	+	0.383929i	0.248319	+	0.0289397i
$177$	−0.121579			−0.00913847
$178$	11.3984			0.854345
$179$	−13.6465			−1.01998			−0.509992	−	0.860179i	$-0.670352\pi$
$179$	−13.6465			−1.01998			−0.509992	+	0.860179i	$0.670352\pi$
$180$		−	1.58222i		−	0.117932i
$181$		−	14.0377i		−	1.04342i	−0.853124	−	0.521708i	$-0.825295\pi$
$181$		−	14.0377i		−	1.04342i	0.853124	−	0.521708i	$-0.174705\pi$
$182$		0			0
$183$			7.54642i			0.557848i
$184$		−	2.32457i		−	0.171369i
$185$			4.48000i			0.329376i
$186$		−	10.1167i		−	0.741794i
$187$	−9.86686	−	1.14991i	−0.721536	−	0.0840896i
$188$		−	0.996186i		−	0.0726544i
$189$		0			0
$190$	2.09746			0.152166
$191$	−1.84378			−0.133411			−0.0667057	−	0.997773i	$-0.521249\pi$
$191$	−1.84378			−0.133411			−0.0667057	+	0.997773i	$0.521249\pi$
$192$			1.00000i			0.0721688i
$193$		−	15.1029i		−	1.08713i	−0.839366	−	0.543567i	$-0.817073\pi$
$193$		−	15.1029i		−	1.08713i	0.839366	−	0.543567i	$-0.182927\pi$
$194$	−1.49379			−0.107248
$195$	−3.59013			−0.257095
$196$		0			0
$197$			0.778951i			0.0554980i	0.999615	+	0.0277490i	$0.00883391\pi$
$197$			0.778951i			0.0554980i	−0.999615	+	0.0277490i	$0.991166\pi$
$198$	0.383929	−	3.29433i	0.0272847	−	0.234118i
$199$		−	3.81257i		−	0.270266i	−0.990827	−	0.135133i	$-0.956854\pi$
$199$		−	3.81257i		−	0.270266i	0.990827	−	0.135133i	$-0.0431462\pi$
$200$		−	2.49657i		−	0.176534i
$201$		−	0.628819i		−	0.0443535i
$202$		−	8.45020i		−	0.594554i
$203$		0			0
$204$		−	2.99510i		−	0.209699i
$205$		−	18.4341i		−	1.28749i
$206$	10.8258			0.754271
$207$	−2.32457			−0.161569
$208$	2.26904			0.157330
$209$	4.36709	+	0.508952i	0.302078	+	0.0352049i
$210$		0			0
$211$		−	16.0767i		−	1.10676i	−0.832928	−	0.553381i	$-0.813337\pi$
$211$		−	16.0767i		−	1.10676i	0.832928	−	0.553381i	$-0.186663\pi$
$212$	0.531530			0.0365056
$213$			7.26798i			0.497994i
$214$	5.48462			0.374921
$215$	19.0333			1.29806
$216$	1.00000			0.0680414
$217$		0			0
$218$	13.1165			0.888360
$219$		−	9.21350i		−	0.622591i
$220$	−0.607462	+	5.21236i	−0.0409551	+	0.351418i
$221$	−6.79601			−0.457149
$222$	−2.83146			−0.190035
$223$			3.84808i			0.257686i	0.991665	+	0.128843i	$0.0411264\pi$
$223$			3.84808i			0.257686i	−0.991665	+	0.128843i	$0.958874\pi$
$224$		0			0
$225$	−2.49657			−0.166438
$226$			10.8139i			0.719327i
$227$	−20.4070			−1.35446			−0.677231	−	0.735770i	$-0.736820\pi$
$227$	−20.4070			−1.35446			−0.677231	+	0.735770i	$0.736820\pi$
$228$			1.32564i			0.0877926i
$229$			0.675126i			0.0446136i	0.999751	+	0.0223068i	$0.00710106\pi$
$229$			0.675126i			0.0446136i	−0.999751	+	0.0223068i	$0.992899\pi$
$230$	3.67799			0.242519
$231$		0			0
$232$	2.90437			0.190681
$233$		−	24.1684i		−	1.58332i	−0.610961	−	0.791661i	$-0.709217\pi$
$233$		−	24.1684i		−	1.58332i	0.610961	−	0.791661i	$-0.290783\pi$
$234$		−	2.26904i		−	0.148332i
$235$	1.57619			0.102819
$236$			0.121579i			0.00791415i
$237$	−11.7454			−0.762944
$238$		0			0
$239$			18.2701i			1.18179i	0.806747	+	0.590897i	$0.201226\pi$
$239$			18.2701i			1.18179i	−0.806747	+	0.590897i	$0.798774\pi$
$240$	−1.58222			−0.102132
$241$	−15.0265			−0.967939			−0.483970	−	0.875085i	$-0.660806\pi$
$241$	−15.0265			−0.967939			−0.483970	+	0.875085i	$0.660806\pi$
$242$	−2.52958	+	10.7052i	−0.162607	+	0.688156i
$243$		−	1.00000i		−	0.0641500i
$244$	7.54642			0.483110
$245$		0			0
$246$	11.6507			0.742824
$247$	3.00793			0.191390
$248$	−10.1167			−0.642412
$249$		−	7.48210i		−	0.474159i
$250$	11.8612			0.750171
$251$			8.42904i			0.532036i	0.963968	+	0.266018i	$0.0857081\pi$
$251$			8.42904i			0.532036i	−0.963968	+	0.266018i	$0.914292\pi$
$252$		0			0
$253$	7.65789	+	0.892469i	0.481447	+	0.0561091i
$254$	−2.74115			−0.171995
$255$	4.73892			0.296763
$256$	1.00000			0.0625000
$257$		−	12.2440i		−	0.763760i	−0.924212	−	0.381880i	$-0.875277\pi$
$257$		−	12.2440i		−	0.763760i	0.924212	−	0.381880i	$-0.124723\pi$
$258$			12.0294i			0.748921i
$259$		0			0
$260$			3.59013i			0.222650i
$261$		−	2.90437i		−	0.179776i
$262$			3.99038i			0.246527i
$263$			8.97546i			0.553451i	0.960949	+	0.276725i	$0.0892492\pi$
$263$			8.97546i			0.553451i	−0.960949	+	0.276725i	$0.910751\pi$
$264$	−3.29433	−	0.383929i	−0.202752	−	0.0236292i
$265$			0.840999i			0.0516622i
$266$		0			0
$267$	−11.3984			−0.697569
$268$	−0.628819			−0.0384112
$269$			7.72732i			0.471143i	0.971857	+	0.235571i	$0.0756962\pi$
$269$			7.72732i			0.471143i	−0.971857	+	0.235571i	$0.924304\pi$
$270$			1.58222i			0.0962911i
$271$	0.156105			0.00948272			0.00474136	−	0.999989i	$-0.498491\pi$
$271$	0.156105			0.00948272			0.00474136	+	0.999989i	$0.498491\pi$
$272$	−2.99510			−0.181605
$273$		0			0
$274$		−	1.11219i		−	0.0671901i
$275$	8.22452	+	0.958505i	0.495957	+	0.0578001i
$276$			2.32457i			0.139923i
$277$			7.57693i			0.455254i	0.973748	+	0.227627i	$0.0730966\pi$
$277$			7.57693i			0.455254i	−0.973748	+	0.227627i	$0.926903\pi$
$278$			12.6619i			0.759410i
$279$			10.1167i			0.605672i
$280$		0			0
$281$			22.5836i			1.34722i	0.739085	+	0.673612i	$0.235258\pi$
$281$			22.5836i			1.34722i	−0.739085	+	0.673612i	$0.764742\pi$
$282$			0.996186i			0.0593220i
$283$	9.06544			0.538884			0.269442	−	0.963017i	$-0.413161\pi$
$283$	9.06544			0.538884			0.269442	+	0.963017i	$0.413161\pi$
$284$	7.26798			0.431275
$285$	−2.09746			−0.124243
$286$	−0.871151	+	7.47496i	−0.0515122	+	0.442004i
$287$		0			0
$288$		−	1.00000i		−	0.0589256i
$289$	−8.02935			−0.472315
$290$			4.59536i			0.269849i
$291$	1.49379			0.0875677
$292$	−9.21350			−0.539180
$293$	33.9508			1.98343			0.991713	−	0.128471i	$-0.0410069\pi$
$293$	33.9508			1.98343			0.991713	+	0.128471i	$0.0410069\pi$
$294$		0			0
$295$	−0.192366			−0.0112000
$296$			2.83146i			0.164575i
$297$	−0.383929	+	3.29433i	−0.0222778	+	0.191156i
$298$	−12.7201			−0.736854
$299$	5.27454			0.305034
$300$			2.49657i			0.144139i
$301$		0			0
$302$	12.9633			0.745953
$303$			8.45020i			0.485452i
$304$	1.32564			0.0760306
$305$			11.9401i			0.683690i
$306$			2.99510i			0.171219i
$307$	−11.4905			−0.655800			−0.327900	−	0.944712i	$-0.606341\pi$
$307$	−11.4905			−0.655800			−0.327900	+	0.944712i	$0.606341\pi$
$308$		0			0
$309$	−10.8258			−0.615859
$310$		−	16.0069i		−	0.909131i
$311$			25.3863i			1.43952i	0.694221	+	0.719762i	$0.255749\pi$
$311$			25.3863i			1.43952i	−0.694221	+	0.719762i	$0.744251\pi$
$312$	−2.26904			−0.128459
$313$		−	5.05454i		−	0.285699i	−0.989744	−	0.142850i	$-0.954373\pi$
$313$		−	5.05454i		−	0.285699i	0.989744	−	0.142850i	$-0.0456265\pi$
$314$	5.08417			0.286916
$315$		0			0
$316$			11.7454i			0.660729i
$317$	−7.75474			−0.435550			−0.217775	−	0.975999i	$-0.569880\pi$
$317$	−7.75474			−0.435550			−0.217775	+	0.975999i	$0.569880\pi$
$318$	−0.531530			−0.0298067
$319$	−1.11507	+	9.56794i	−0.0624320	+	0.535702i
$320$			1.58222i			0.0884490i
$321$	−5.48462			−0.306122
$322$		0			0
$323$	−3.97043			−0.220921
$324$	−1.00000			−0.0555556
$325$	5.66482			0.314227
$326$			17.2229i			0.953890i
$327$	−13.1165			−0.725343
$328$		−	11.6507i		−	0.643304i
$329$		0			0
$330$	0.607462	−	5.21236i	0.0334397	−	0.286931i
$331$	33.0937			1.81899			0.909496	−	0.415712i	$-0.136467\pi$
$331$	33.0937			1.81899			0.909496	+	0.415712i	$0.136467\pi$
$332$	−7.48210			−0.410633
$333$	2.83146			0.155163
$334$			5.31157i			0.290636i
$335$		−	0.994933i		−	0.0543590i
$336$		0			0
$337$		−	5.65795i		−	0.308208i	−0.988055	−	0.154104i	$-0.950751\pi$
$337$		−	5.65795i		−	0.308208i	0.988055	−	0.154104i	$-0.0492491\pi$
$338$		−	7.85145i		−	0.427063i
$339$		−	10.8139i		−	0.587328i
$340$		−	4.73892i		−	0.257004i
$341$	3.88410	−	33.3278i	0.210336	−	1.80480i
$342$		−	1.32564i		−	0.0716824i
$343$		0			0
$344$	12.0294			0.648584
$345$	−3.67799			−0.198016
$346$			20.3662i			1.09489i
$347$			11.8453i			0.635891i	0.948109	+	0.317945i	$0.102993\pi$
$347$			11.8453i			0.635891i	−0.948109	+	0.317945i	$0.897007\pi$
$348$	−2.90437			−0.155690
$349$	−14.8773			−0.796362			−0.398181	−	0.917307i	$-0.630358\pi$
$349$	−14.8773			−0.796362			−0.398181	+	0.917307i	$0.630358\pi$
$350$		0			0
$351$			2.26904i			0.121112i
$352$	−0.383929	+	3.29433i	−0.0204635	+	0.175588i
$353$			2.13963i			0.113881i	0.998378	+	0.0569406i	$0.0181346\pi$
$353$			2.13963i			0.113881i	−0.998378	+	0.0569406i	$0.981865\pi$
$354$		−	0.121579i		−	0.00646188i
$355$			11.4996i			0.610333i
$356$			11.3984i			0.604113i
$357$		0			0
$358$		−	13.6465i		−	0.721238i
$359$			14.4213i			0.761125i	0.924755	+	0.380562i	$0.124270\pi$
$359$			14.4213i			0.761125i	−0.924755	+	0.380562i	$0.875730\pi$
$360$	1.58222			0.0833905
$361$	−17.2427			−0.907509
$362$	14.0377			0.737807
$363$	2.52958	−	10.7052i	0.132768	−	0.561877i
$364$		0			0
$365$		−	14.5778i		−	0.763038i
$366$	−7.54642			−0.394458
$367$		−	30.4236i		−	1.58810i	−0.607853	−	0.794050i	$-0.707969\pi$
$367$		−	30.4236i		−	1.58810i	0.607853	−	0.794050i	$-0.292031\pi$
$368$	2.32457			0.121176
$369$	−11.6507			−0.606513
$370$	−4.48000			−0.232904
$371$		0			0
$372$	10.1167			0.524527
$373$			2.76153i			0.142987i	0.997441	+	0.0714934i	$0.0227765\pi$
$373$			2.76153i			0.142987i	−0.997441	+	0.0714934i	$0.977224\pi$
$374$	1.14991	−	9.86686i	0.0594603	−	0.510203i
$375$	−11.8612			−0.612512
$376$	0.996186			0.0513744
$377$			6.59013i			0.339409i
$378$		0			0
$379$	17.2095			0.883992			0.441996	−	0.897017i	$-0.354271\pi$
$379$	17.2095			0.883992			0.441996	+	0.897017i	$0.354271\pi$
$380$			2.09746i			0.107597i
$381$	2.74115			0.140433
$382$		−	1.84378i		−	0.0943361i
$383$			16.5823i			0.847317i	0.905822	+	0.423659i	$0.139254\pi$
$383$			16.5823i			0.847317i	−0.905822	+	0.423659i	$0.860746\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	15.1029			0.768720
$387$		−	12.0294i		−	0.611491i
$388$		−	1.49379i		−	0.0758358i
$389$	−24.4438			−1.23935			−0.619675	−	0.784859i	$-0.712735\pi$
$389$	−24.4438			−1.23935			−0.619675	+	0.784859i	$0.712735\pi$
$390$		−	3.59013i		−	0.181793i
$391$	−6.96232			−0.352100
$392$		0			0
$393$		−	3.99038i		−	0.201288i
$394$	−0.778951			−0.0392430
$395$	−18.5838			−0.935052
$396$	3.29433	+	0.383929i	0.165546	+	0.0192932i
$397$		−	12.4085i		−	0.622766i	−0.950284	−	0.311383i	$-0.899208\pi$
$397$		−	12.4085i		−	0.622766i	0.950284	−	0.311383i	$-0.100792\pi$
$398$	3.81257			0.191107
$399$		0			0
$400$	2.49657			0.124828
$401$	18.4210			0.919903			0.459951	−	0.887944i	$-0.347867\pi$
$401$	18.4210			0.919903			0.459951	+	0.887944i	$0.347867\pi$
$402$	0.628819			0.0313627
$403$		−	22.9552i		−	1.14348i
$404$	8.45020			0.420413
$405$		−	1.58222i		−	0.0786213i
$406$		0			0
$407$	−9.32775	−	1.08708i	−0.462360	−	0.0538845i
$408$	2.99510			0.148280
$409$	−3.58825			−0.177428			−0.0887139	−	0.996057i	$-0.528276\pi$
$409$	−3.58825			−0.177428			−0.0887139	+	0.996057i	$0.528276\pi$
$410$	18.4341			0.910393
$411$			1.11219i			0.0548605i
$412$			10.8258i			0.533350i
$413$		0			0
$414$		−	2.32457i		−	0.114246i
$415$		−	11.8383i		−	0.581122i
$416$			2.26904i			0.111249i
$417$		−	12.6619i		−	0.620055i
$418$	−0.508952	+	4.36709i	−0.0248936	+	0.213601i
$419$			2.68501i			0.131172i	0.997847	+	0.0655858i	$0.0208916\pi$
$419$			2.68501i			0.131172i	−0.997847	+	0.0655858i	$0.979108\pi$
$420$		0			0
$421$	24.3315			1.18585			0.592923	−	0.805259i	$-0.297974\pi$
$421$	24.3315			1.18585			0.592923	+	0.805259i	$0.297974\pi$
$422$	16.0767			0.782599
$423$		−	0.996186i		−	0.0484362i
$424$			0.531530i			0.0258134i
$425$	−7.47748			−0.362711
$426$	−7.26798			−0.352135
$427$		0			0
$428$			5.48462i			0.265109i
$429$	0.871151	−	7.47496i	0.0420596	−	0.360895i
$430$			19.0333i			0.917866i
$431$			35.1977i			1.69541i	0.530465	+	0.847707i	$0.322018\pi$
$431$			35.1977i			1.69541i	−0.530465	+	0.847707i	$0.677982\pi$
$432$			1.00000i			0.0481125i
$433$			1.21836i			0.0585508i	0.999571	+	0.0292754i	$0.00931998\pi$
$433$			1.21836i			0.0585508i	−0.999571	+	0.0292754i	$0.990680\pi$
$434$		0			0
$435$		−	4.59536i		−	0.220331i
$436$			13.1165i			0.628165i
$437$	3.08154			0.147410
$438$	9.21350			0.440238
$439$	20.1641			0.962381			0.481191	−	0.876616i	$-0.340204\pi$
$439$	20.1641			0.962381			0.481191	+	0.876616i	$0.340204\pi$
$440$	−5.21236	−	0.607462i	−0.248490	−	0.0289596i
$441$		0			0
$442$		−	6.79601i		−	0.323253i
$443$	−1.17070			−0.0556217			−0.0278109	−	0.999613i	$-0.508854\pi$
$443$	−1.17070			−0.0556217			−0.0278109	+	0.999613i	$0.508854\pi$
$444$		−	2.83146i		−	0.134375i
$445$	−18.0348			−0.854931
$446$	−3.84808			−0.182212
$447$	12.7201			0.601638
$448$		0			0
$449$	−37.9855			−1.79265			−0.896323	−	0.443402i	$-0.853772\pi$
$449$	−37.9855			−1.79265			−0.896323	+	0.443402i	$0.853772\pi$
$450$		−	2.49657i		−	0.117689i
$451$	38.3813	+	4.47306i	1.80731	+	0.210628i
$452$	−10.8139			−0.508641
$453$	−12.9633			−0.609068
$454$		−	20.4070i		−	0.957749i
$455$		0			0
$456$	−1.32564			−0.0620788
$457$			39.0523i			1.82679i	0.407077	+	0.913394i	$0.366548\pi$
$457$			39.0523i			1.82679i	−0.407077	+	0.913394i	$0.633452\pi$
$458$	−0.675126			−0.0315466
$459$		−	2.99510i		−	0.139799i
$460$			3.67799i			0.171487i
$461$	−35.4263			−1.64997			−0.824983	−	0.565158i	$-0.808815\pi$
$461$	−35.4263			−1.64997			−0.824983	+	0.565158i	$0.808815\pi$
$462$		0			0
$463$	−26.8021			−1.24560			−0.622799	−	0.782382i	$-0.714004\pi$
$463$	−26.8021			−1.24560			−0.622799	+	0.782382i	$0.714004\pi$
$464$			2.90437i			0.134832i
$465$			16.0069i			0.742303i
$466$	24.1684			1.11958
$467$			38.3106i			1.77280i	0.462918	+	0.886401i	$0.346802\pi$
$467$			38.3106i			1.77280i	−0.462918	+	0.886401i	$0.653198\pi$
$468$	2.26904			0.104886
$469$		0			0
$470$			1.57619i			0.0727042i
$471$	−5.08417			−0.234266
$472$	−0.121579			−0.00559615
$473$	−4.61845	+	39.6289i	−0.212357	+	1.82214i
$474$		−	11.7454i		−	0.539483i
$475$	3.30955			0.151853
$476$		0			0
$477$	0.531530			0.0243371
$478$	−18.2701			−0.835655
$479$	−31.7857			−1.45232			−0.726162	−	0.687524i	$-0.758698\pi$
$479$	−31.7857			−1.45232			−0.726162	+	0.687524i	$0.758698\pi$
$480$		−	1.58222i		−	0.0722183i
$481$	−6.42469			−0.292941
$482$		−	15.0265i		−	0.684436i
$483$		0			0
$484$	−10.7052	−	2.52958i	−0.486600	−	0.114981i
$485$	2.36351			0.107322
$486$	1.00000			0.0453609
$487$	35.7648			1.62066			0.810329	−	0.585976i	$-0.199289\pi$
$487$	35.7648			1.62066			0.810329	+	0.585976i	$0.199289\pi$
$488$			7.54642i			0.341610i
$489$		−	17.2229i		−	0.778848i
$490$		0			0
$491$			10.3116i			0.465356i	0.972554	+	0.232678i	$0.0747489\pi$
$491$			10.3116i			0.465356i	−0.972554	+	0.232678i	$0.925251\pi$
$492$			11.6507i			0.525256i
$493$		−	8.69888i		−	0.391778i
$494$			3.00793i			0.135333i
$495$	−0.607462	+	5.21236i	−0.0273034	+	0.234278i
$496$		−	10.1167i		−	0.454254i
$497$		0			0
$498$	7.48210			0.335281
$499$	36.2793			1.62408			0.812042	−	0.583599i	$-0.198356\pi$
$499$	36.2793			1.62408			0.812042	+	0.583599i	$0.198356\pi$
$500$			11.8612i			0.530451i
$501$		−	5.31157i		−	0.237304i
$502$	−8.42904			−0.376206
$503$	25.3821			1.13173			0.565866	−	0.824497i	$-0.308542\pi$
$503$	25.3821			1.13173			0.565866	+	0.824497i	$0.308542\pi$
$504$		0			0
$505$			13.3701i			0.594962i
$506$	−0.892469	+	7.65789i	−0.0396751	+	0.340435i
$507$			7.85145i			0.348695i
$508$		−	2.74115i		−	0.121619i
$509$		−	25.7407i		−	1.14094i	−0.821319	−	0.570469i	$-0.806761\pi$
$509$		−	25.7407i		−	1.14094i	0.821319	−	0.570469i	$-0.193239\pi$
$510$			4.73892i			0.209843i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$			1.32564i			0.0585284i
$514$	12.2440			0.540060
$515$	−17.1289			−0.754788
$516$	−12.0294			−0.529567
$517$	−0.382465	+	3.28176i	−0.0168208	+	0.144332i
$518$		0			0
$519$		−	20.3662i		−	0.893978i
$520$	−3.59013			−0.157438
$521$			12.0805i			0.529257i	0.964350	+	0.264628i	$0.0852493\pi$
$521$			12.0805i			0.529257i	−0.964350	+	0.264628i	$0.914751\pi$
$522$	2.90437			0.127121
$523$	−34.8322			−1.52310			−0.761552	−	0.648103i	$-0.775562\pi$
$523$	−34.8322			−1.52310			−0.761552	+	0.648103i	$0.775562\pi$
$524$	−3.99038			−0.174321
$525$		0			0
$526$	−8.97546			−0.391349
$527$			30.3006i			1.31992i
$528$	0.383929	−	3.29433i	0.0167084	−	0.143367i
$529$	−17.5964			−0.765060
$530$	−0.840999			−0.0365307
$531$			0.121579i			0.00527610i
$532$		0			0
$533$	26.4360			1.14507
$534$		−	11.3984i		−	0.493256i
$535$	−8.67790			−0.375178
$536$		−	0.628819i		−	0.0271609i
$537$			13.6465i			0.588888i
$538$	−7.72732			−0.333148
$539$		0			0
$540$	−1.58222			−0.0680881
$541$			12.7516i			0.548233i	0.961696	+	0.274117i	$0.0883854\pi$
$541$			12.7516i			0.548233i	−0.961696	+	0.274117i	$0.911615\pi$
$542$			0.156105i			0.00670530i
$543$	−14.0377			−0.602417
$544$		−	2.99510i		−	0.128414i
$545$	−20.7532			−0.888969
$546$		0			0
$547$		−	33.8711i		−	1.44822i	−0.689683	−	0.724111i	$-0.742250\pi$
$547$		−	33.8711i		−	1.44822i	0.689683	−	0.724111i	$-0.257750\pi$
$548$	1.11219			0.0475106
$549$	7.54642			0.322073
$550$	−0.958505	+	8.22452i	−0.0408708	+	0.350695i
$551$			3.85014i			0.164022i
$552$	−2.32457			−0.0989402
$553$		0			0
$554$	−7.57693			−0.321913
$555$	4.48000			0.190165
$556$	−12.6619			−0.536984
$557$			19.9509i			0.845346i	0.906282	+	0.422673i	$0.138908\pi$
$557$			19.9509i			0.845346i	−0.906282	+	0.422673i	$0.861092\pi$
$558$	−10.1167			−0.428275
$559$			27.2953i			1.15447i
$560$		0			0
$561$	−1.14991	+	9.86686i	−0.0485491	+	0.416579i
$562$	−22.5836			−0.952632
$563$	20.5464			0.865928			0.432964	−	0.901411i	$-0.357468\pi$
$563$	20.5464			0.865928			0.432964	+	0.901411i	$0.357468\pi$
$564$	−0.996186			−0.0419470
$565$		−	17.1099i		−	0.719821i
$566$			9.06544i			0.381049i
$567$		0			0
$568$			7.26798i			0.304958i
$569$			10.4524i			0.438186i	0.975704	+	0.219093i	$0.0703098\pi$
$569$			10.4524i			0.438186i	−0.975704	+	0.219093i	$0.929690\pi$
$570$		−	2.09746i		−	0.0878529i
$571$		−	13.8331i		−	0.578898i	−0.957193	−	0.289449i	$-0.906528\pi$
$571$		−	13.8331i		−	0.578898i	0.957193	−	0.289449i	$-0.0934720\pi$
$572$	−7.47496	−	0.871151i	−0.312544	−	0.0364246i
$573$			1.84378i			0.0770251i
$574$		0			0
$575$	5.80344			0.242020
$576$	1.00000			0.0416667
$577$		−	10.1150i		−	0.421092i	−0.977584	−	0.210546i	$-0.932476\pi$
$577$		−	10.1150i		−	0.421092i	0.977584	−	0.210546i	$-0.0675242\pi$
$578$		−	8.02935i		−	0.333977i
$579$	−15.1029			−0.627657
$580$	−4.59536			−0.190812
$581$		0			0
$582$			1.49379i			0.0619197i
$583$	−1.75103	−	0.204070i	−0.0725204	−	0.00845171i
$584$		−	9.21350i		−	0.381258i
$585$			3.59013i			0.148434i
$586$			33.9508i			1.40249i
$587$		−	0.774875i		−	0.0319825i	−0.999872	−	0.0159913i	$-0.994910\pi$
$587$		−	0.774875i		−	0.0319825i	0.999872	−	0.0159913i	$-0.00509039\pi$
$588$		0			0
$589$		−	13.4111i		−	0.552596i
$590$		−	0.192366i		−	0.00791958i
$591$	0.778951			0.0320418
$592$	−2.83146			−0.116372
$593$	5.18240			0.212816			0.106408	−	0.994323i	$-0.466065\pi$
$593$	5.18240			0.212816			0.106408	+	0.994323i	$0.466065\pi$
$594$	−3.29433	−	0.383929i	−0.135168	−	0.0157528i
$595$		0			0
$596$		−	12.7201i		−	0.521034i
$597$	−3.81257			−0.156038
$598$			5.27454i			0.215692i
$599$	40.9217			1.67202			0.836009	−	0.548716i	$-0.184883\pi$
$599$	40.9217			1.67202			0.836009	+	0.548716i	$0.184883\pi$
$600$	−2.49657			−0.101922
$601$	−26.6524			−1.08717			−0.543586	−	0.839353i	$-0.682934\pi$
$601$	−26.6524			−1.08717			−0.543586	+	0.839353i	$0.682934\pi$
$602$		0			0
$603$	−0.628819			−0.0256075
$604$			12.9633i			0.527468i
$605$	4.00236	−	16.9380i	0.162719	−	0.688628i
$606$	−8.45020			−0.343266
$607$	−20.5436			−0.833840			−0.416920	−	0.908943i	$-0.636891\pi$
$607$	−20.5436			−0.833840			−0.416920	+	0.908943i	$0.636891\pi$
$608$			1.32564i			0.0537618i
$609$		0			0
$610$	−11.9401			−0.483442
$611$			2.26039i			0.0914455i
$612$	−2.99510			−0.121070
$613$			33.1390i			1.33847i	0.743050	+	0.669235i	$0.233378\pi$
$613$			33.1390i			1.33847i	−0.743050	+	0.669235i	$0.766622\pi$
$614$		−	11.4905i		−	0.463721i
$615$	−18.4341			−0.743333
$616$		0			0
$617$	−14.8223			−0.596725			−0.298362	−	0.954453i	$-0.596440\pi$
$617$	−14.8223			−0.596725			−0.298362	+	0.954453i	$0.596440\pi$
$618$		−	10.8258i		−	0.435478i
$619$			23.8285i			0.957747i	0.877884	+	0.478874i	$0.158955\pi$
$619$			23.8285i			0.957747i	−0.877884	+	0.478874i	$0.841045\pi$
$620$	16.0069			0.642853
$621$			2.32457i			0.0932817i
$622$	−25.3863			−1.01790
$623$		0			0
$624$		−	2.26904i		−	0.0908343i
$625$	−6.28430			−0.251372
$626$	5.05454			0.202020
$627$	0.508952	−	4.36709i	0.0203256	−	0.174405i
$628$			5.08417i			0.202880i
$629$	8.48051			0.338140
$630$		0			0
$631$	2.11115			0.0840436			0.0420218	−	0.999117i	$-0.486620\pi$
$631$	2.11115			0.0840436			0.0420218	+	0.999117i	$0.486620\pi$
$632$	−11.7454			−0.467206
$633$	−16.0767			−0.638990
$634$		−	7.75474i		−	0.307980i
$635$	4.33711			0.172113
$636$		−	0.531530i		−	0.0210765i
$637$		0			0
$638$	−9.56794	−	1.11507i	−0.378798	−	0.0441461i
$639$	7.26798			0.287517
$640$	−1.58222			−0.0625429
$641$	10.4982			0.414652			0.207326	−	0.978272i	$-0.433524\pi$
$641$	10.4982			0.414652			0.207326	+	0.978272i	$0.433524\pi$
$642$		−	5.48462i		−	0.216461i
$643$			29.6553i			1.16949i	0.811216	+	0.584746i	$0.198806\pi$
$643$			29.6553i			1.16949i	−0.811216	+	0.584746i	$0.801194\pi$
$644$		0			0
$645$		−	19.0333i		−	0.749434i
$646$		−	3.97043i		−	0.156214i
$647$			19.4760i			0.765679i	0.923815	+	0.382840i	$0.125054\pi$
$647$			19.4760i			0.765679i	−0.923815	+	0.382840i	$0.874946\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	0.0466779	−	0.400523i	0.00183227	−	0.0157219i
$650$			5.66482i			0.222192i
$651$		0			0
$652$	−17.2229			−0.674502
$653$	−27.4187			−1.07298			−0.536488	−	0.843908i	$-0.680249\pi$
$653$	−27.4187			−1.07298			−0.536488	+	0.843908i	$0.680249\pi$
$654$		−	13.1165i		−	0.512895i
$655$		−	6.31368i		−	0.246696i
$656$	11.6507			0.454885
$657$	−9.21350			−0.359453
$658$		0			0
$659$			16.4997i			0.642738i	0.946954	+	0.321369i	$0.104143\pi$
$659$			16.4997i			0.642738i	−0.946954	+	0.321369i	$0.895857\pi$
$660$	5.21236	+	0.607462i	0.202891	+	0.0236454i
$661$		−	43.2145i		−	1.68085i	−0.541929	−	0.840424i	$-0.682306\pi$
$661$		−	43.2145i		−	1.68085i	0.541929	−	0.840424i	$-0.317694\pi$
$662$			33.0937i			1.28622i
$663$			6.79601i			0.263935i
$664$		−	7.48210i		−	0.290362i
$665$		0			0
$666$			2.83146i			0.109717i
$667$			6.75140i			0.261415i
$668$	−5.31157			−0.205511
$669$	3.84808			0.148775
$670$	0.994933			0.0384376
$671$	−24.8604	−	2.89729i	−0.959725	−	0.111849i
$672$		0			0
$673$		−	44.4447i		−	1.71322i	−0.515967	−	0.856609i	$-0.672567\pi$
$673$		−	44.4447i		−	1.71322i	0.515967	−	0.856609i	$-0.327433\pi$
$674$	5.65795			0.217936
$675$			2.49657i			0.0960930i
$676$	7.85145			0.301979
$677$	−8.74648			−0.336155			−0.168077	−	0.985774i	$-0.553756\pi$
$677$	−8.74648			−0.336155			−0.168077	+	0.985774i	$0.553756\pi$
$678$	10.8139			0.415304
$679$		0			0
$680$	4.73892			0.181729
$681$			20.4070i			0.781999i
$682$	33.3278	+	3.88410i	1.27619	+	0.148730i
$683$	40.1462			1.53615			0.768076	−	0.640358i	$-0.221214\pi$
$683$	40.1462			1.53615			0.768076	+	0.640358i	$0.221214\pi$
$684$	1.32564			0.0506871
$685$			1.75974i			0.0672362i
$686$		0			0
$687$	0.675126			0.0257577
$688$			12.0294i			0.458618i
$689$	−1.20606			−0.0459473
$690$		−	3.67799i		−	0.140019i
$691$		−	5.04332i		−	0.191857i	−0.995388	−	0.0959285i	$-0.969418\pi$
$691$		−	5.04332i		−	0.191857i	0.995388	−	0.0959285i	$-0.0305820\pi$
$692$	−20.3662			−0.774208
$693$		0			0
$694$	−11.8453			−0.449642
$695$		−	20.0339i		−	0.759931i
$696$		−	2.90437i		−	0.110090i
$697$	−34.8952			−1.32175
$698$		−	14.8773i		−	0.563113i
$699$	−24.1684			−0.914131
$700$		0			0
$701$			22.7055i			0.857573i	0.903406	+	0.428787i	$0.141059\pi$
$701$			22.7055i			0.857573i	−0.903406	+	0.428787i	$0.858941\pi$
$702$	−2.26904			−0.0856394
$703$	−3.75349			−0.141566
$704$	−3.29433	−	0.383929i	−0.124160	−	0.0144699i
$705$		−	1.57619i		−	0.0593627i
$706$	−2.13963			−0.0805262
$707$		0			0
$708$	0.121579			0.00456924
$709$	−4.44396			−0.166897			−0.0834483	−	0.996512i	$-0.526593\pi$
$709$	−4.44396			−0.166897			−0.0834483	+	0.996512i	$0.526593\pi$
$710$	−11.4996			−0.431571
$711$			11.7454i			0.440486i
$712$	−11.3984			−0.427172
$713$		−	23.5170i		−	0.880719i
$714$		0			0
$715$	1.37836	−	11.8271i	0.0515476	−	0.442307i
$716$	13.6465			0.509992
$717$	18.2701			0.682309
$718$	−14.4213			−0.538196
$719$		−	8.41658i		−	0.313885i	−0.987608	−	0.156943i	$-0.949836\pi$
$719$		−	8.41658i		−	0.313885i	0.987608	−	0.156943i	$-0.0501638\pi$
$720$			1.58222i			0.0589660i
$721$		0			0
$722$		−	17.2427i		−	0.641706i
$723$			15.0265i			0.558840i
$724$			14.0377i			0.521708i
$725$			7.25095i			0.269294i
$726$	10.7052	+	2.52958i	0.397307	+	0.0938814i
$727$			26.7407i			0.991759i	0.868391	+	0.495880i	$0.165154\pi$
$727$			26.7407i			0.991759i	−0.868391	+	0.495880i	$0.834846\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	14.5778			0.539549
$731$		−	36.0294i		−	1.33260i
$732$		−	7.54642i		−	0.278924i
$733$	−28.3973			−1.04888			−0.524439	−	0.851448i	$-0.675725\pi$
$733$	−28.3973			−1.04888			−0.524439	+	0.851448i	$0.675725\pi$
$734$	30.4236			1.12296
$735$		0			0
$736$			2.32457i			0.0856847i
$737$	2.07154	+	0.241422i	0.0763060	+	0.00889290i
$738$		−	11.6507i		−	0.428869i
$739$			31.7877i			1.16933i	0.811275	+	0.584664i	$0.198774\pi$
$739$			31.7877i			1.16933i	−0.811275	+	0.584664i	$0.801226\pi$
$740$		−	4.48000i		−	0.164688i
$741$		−	3.00793i		−	0.110499i
$742$		0			0
$743$		−	13.8830i		−	0.509320i	−0.967031	−	0.254660i	$-0.918037\pi$
$743$		−	13.8830i		−	0.509320i	0.967031	−	0.254660i	$-0.0819635\pi$
$744$			10.1167i			0.370897i
$745$	20.1260			0.737359
$746$	−2.76153			−0.101107
$747$	−7.48210			−0.273756
$748$	9.86686	+	1.14991i	0.360768	+	0.0420448i
$749$		0			0
$750$		−	11.8612i		−	0.433112i
$751$	−35.4197			−1.29248			−0.646241	−	0.763133i	$-0.723660\pi$
$751$	−35.4197			−1.29248			−0.646241	+	0.763133i	$0.723660\pi$
$752$			0.996186i			0.0363272i
$753$	8.42904			0.307171
$754$	−6.59013			−0.239998
$755$	−20.5108			−0.746464
$756$		0			0
$757$	37.8069			1.37411			0.687057	−	0.726604i	$-0.258902\pi$
$757$	37.8069			1.37411			0.687057	+	0.726604i	$0.258902\pi$
$758$			17.2095i			0.625076i
$759$	0.892469	−	7.65789i	0.0323946	−	0.277964i
$760$	−2.09746			−0.0760828
$761$	17.2528			0.625412			0.312706	−	0.949850i	$-0.398765\pi$
$761$	17.2528			0.625412			0.312706	+	0.949850i	$0.398765\pi$
$762$			2.74115i			0.0993012i
$763$		0			0
$764$	1.84378			0.0667057
$765$		−	4.73892i		−	0.171336i
$766$	−16.5823			−0.599144
$767$		−	0.275869i		−	0.00996104i
$768$		−	1.00000i		−	0.0360844i
$769$	16.8690			0.608311			0.304156	−	0.952622i	$-0.401626\pi$
$769$	16.8690			0.608311			0.304156	+	0.952622i	$0.401626\pi$
$770$		0			0
$771$	−12.2440			−0.440957
$772$			15.1029i			0.543567i
$773$		−	35.3596i		−	1.27179i	−0.771774	−	0.635897i	$-0.780630\pi$
$773$		−	35.3596i		−	1.27179i	0.771774	−	0.635897i	$-0.219370\pi$
$774$	12.0294			0.432389
$775$		−	25.2571i		−	0.907261i
$776$	1.49379			0.0536240
$777$		0			0
$778$		−	24.4438i		−	0.876352i
$779$	15.4447			0.553363
$780$	3.59013			0.128547
$781$	−23.9431	−	2.79039i	−0.856751	−	0.0998479i
$782$		−	6.96232i		−	0.248972i
$783$	−2.90437			−0.103794
$784$		0			0
$785$	−8.04429			−0.287113
$786$	3.99038			0.142332
$787$	−49.8626			−1.77741			−0.888704	−	0.458481i	$-0.848394\pi$
$787$	−49.8626			−1.77741			−0.888704	+	0.458481i	$0.848394\pi$
$788$		−	0.778951i		−	0.0277490i
$789$	8.97546			0.319535
$790$		−	18.5838i		−	0.661182i
$791$		0			0
$792$	−0.383929	+	3.29433i	−0.0136423	+	0.117059i
$793$	−17.1231			−0.608060
$794$	12.4085			0.440362
$795$	0.840999			0.0298272
$796$			3.81257i			0.135133i
$797$		−	39.3786i		−	1.39486i	−0.716653	−	0.697430i	$-0.754327\pi$
$797$		−	39.3786i		−	1.39486i	0.716653	−	0.697430i	$-0.245673\pi$
$798$		0			0
$799$		−	2.98368i		−	0.105555i
$800$			2.49657i			0.0882670i
$801$			11.3984i			0.402742i
$802$			18.4210i			0.650469i
$803$	30.3523	+	3.53733i	1.07111	+	0.124830i
$804$			0.628819i			0.0221767i
$805$		0			0
$806$	22.9552			0.808564
$807$	7.72732			0.272015
$808$			8.45020i			0.297277i
$809$			0.637591i			0.0224165i	0.999937	+	0.0112082i	$0.00356777\pi$
$809$			0.637591i			0.0224165i	−0.999937	+	0.0112082i	$0.996432\pi$
$810$	1.58222			0.0555937
$811$	−33.8761			−1.18955			−0.594775	−	0.803892i	$-0.702759\pi$
$811$	−33.8761			−1.18955			−0.594775	+	0.803892i	$0.702759\pi$
$812$		0			0
$813$		−	0.156105i		−	0.00547485i
$814$	1.08708	−	9.32775i	0.0381021	−	0.326938i
$815$		−	27.2505i		−	0.954544i
$816$			2.99510i			0.104850i
$817$			15.9467i			0.557905i
$818$		−	3.58825i		−	0.125460i
$819$		0			0
$820$			18.4341i			0.643745i
$821$			55.5805i			1.93977i	0.243560	+	0.969886i	$0.421685\pi$
$821$			55.5805i			1.93977i	−0.243560	+	0.969886i	$0.578315\pi$
$822$	−1.11219			−0.0387922
$823$	45.8886			1.59958			0.799788	−	0.600282i	$-0.204945\pi$
$823$	45.8886			1.59958			0.799788	+	0.600282i	$0.204945\pi$
$824$	−10.8258			−0.377135
$825$	0.958505	−	8.22452i	0.0333709	−	0.286341i
$826$		0			0
$827$		−	33.3404i		−	1.15936i	−0.814844	−	0.579680i	$-0.803178\pi$
$827$		−	33.3404i		−	1.15936i	0.814844	−	0.579680i	$-0.196822\pi$
$828$	2.32457			0.0807843
$829$		−	18.6848i		−	0.648950i	−0.945894	−	0.324475i	$-0.894812\pi$
$829$		−	18.6848i		−	0.648950i	0.945894	−	0.324475i	$-0.105188\pi$
$830$	11.8383			0.410915
$831$	7.57693			0.262841
$832$	−2.26904			−0.0786648
$833$		0			0
$834$	12.6619			0.438445
$835$		−	8.40410i		−	0.290836i
$836$	−4.36709	−	0.508952i	−0.151039	−	0.0176025i
$837$	10.1167			0.349685
$838$	−2.68501			−0.0927523
$839$			21.1689i			0.730831i	0.930845	+	0.365415i	$0.119073\pi$
$839$			21.1689i			0.730831i	−0.930845	+	0.365415i	$0.880927\pi$
$840$		0			0
$841$	20.5647			0.709126
$842$			24.3315i			0.838520i
$843$	22.5836			0.777821
$844$			16.0767i			0.553381i
$845$			12.4228i			0.427356i
$846$	0.996186			0.0342496
$847$		0			0
$848$	−0.531530			−0.0182528
$849$		−	9.06544i		−	0.311125i
$850$		−	7.47748i		−	0.256476i
$851$	−6.58192			−0.225625
$852$		−	7.26798i		−	0.248997i
$853$	−6.03669			−0.206692			−0.103346	−	0.994645i	$-0.532955\pi$
$853$	−6.03669			−0.206692			−0.103346	+	0.994645i	$0.532955\pi$
$854$		0			0
$855$			2.09746i			0.0717316i
$856$	−5.48462			−0.187461
$857$	−44.1033			−1.50654			−0.753271	−	0.657711i	$-0.771525\pi$
$857$	−44.1033			−1.50654			−0.753271	+	0.657711i	$0.771525\pi$
$858$	7.47496	+	0.871151i	0.255191	+	0.0297406i
$859$		−	34.1469i		−	1.16508i	−0.812803	−	0.582538i	$-0.802060\pi$
$859$		−	34.1469i		−	1.16508i	0.812803	−	0.582538i	$-0.197940\pi$
$860$	−19.0333			−0.649029
$861$		0			0
$862$	−35.1977			−1.19884
$863$	−49.3156			−1.67872			−0.839361	−	0.543574i	$-0.817071\pi$
$863$	−49.3156			−1.67872			−0.839361	+	0.543574i	$0.817071\pi$
$864$	−1.00000			−0.0340207
$865$		−	32.2239i		−	1.09565i
$866$	−1.21836			−0.0414017
$867$			8.02935i			0.272691i
$868$		0			0
$869$	4.50939	−	38.6931i	0.152971	−	1.31257i
$870$	4.59536			0.155797
$871$	1.42682			0.0483458
$872$	−13.1165			−0.444180
$873$		−	1.49379i		−	0.0505572i
$874$			3.08154i			0.104235i
$875$		0			0
$876$			9.21350i			0.311295i
$877$		−	42.7988i		−	1.44521i	−0.691259	−	0.722607i	$-0.742944\pi$
$877$		−	42.7988i		−	1.44521i	0.691259	−	0.722607i	$-0.257056\pi$
$878$			20.1641i			0.680506i
$879$		−	33.9508i		−	1.14513i
$880$	0.607462	−	5.21236i	0.0204775	−	0.175709i
$881$		−	15.9264i		−	0.536573i	−0.963339	−	0.268287i	$-0.913543\pi$
$881$		−	15.9264i		−	0.536573i	0.963339	−	0.268287i	$-0.0864574\pi$
$882$		0			0
$883$	3.36737			0.113321			0.0566606	−	0.998393i	$-0.481955\pi$
$883$	3.36737			0.113321			0.0566606	+	0.998393i	$0.481955\pi$
$884$	6.79601			0.228575
$885$			0.192366i			0.00646631i
$886$		−	1.17070i		−	0.0393305i
$887$	18.1771			0.610328			0.305164	−	0.952300i	$-0.401289\pi$
$887$	18.1771			0.610328			0.305164	+	0.952300i	$0.401289\pi$
$888$	2.83146			0.0950175
$889$		0			0
$890$		−	18.0348i		−	0.604527i
$891$	3.29433	+	0.383929i	0.110364	+	0.0128621i
$892$		−	3.84808i		−	0.128843i
$893$			1.32058i			0.0441917i
$894$			12.7201i			0.425423i
$895$			21.5918i			0.721733i
$896$		0			0
$897$		−	5.27454i		−	0.176112i
$898$		−	37.9855i		−	1.26759i
$899$	29.3827			0.979966
$900$	2.49657			0.0832189
$901$	1.59199			0.0530368
$902$	−4.47306	+	38.3813i	−0.148936	+	1.27796i
$903$		0			0
$904$		−	10.8139i		−	0.359664i
$905$	−22.2108			−0.738313
$906$		−	12.9633i		−	0.430676i
$907$	32.9272			1.09333			0.546666	−	0.837351i	$-0.315897\pi$
$907$	32.9272			1.09333			0.546666	+	0.837351i	$0.315897\pi$
$908$	20.4070			0.677231
$909$	8.45020			0.280276
$910$		0			0
$911$	−40.9371			−1.35631			−0.678153	−	0.734921i	$-0.737219\pi$
$911$	−40.9371			−1.35631			−0.678153	+	0.734921i	$0.737219\pi$
$912$		−	1.32564i		−	0.0438963i
$913$	24.6485	+	2.87259i	0.815746	+	0.0950690i
$914$	−39.0523			−1.29173
$915$	11.9401			0.394728
$916$		−	0.675126i		−	0.0223068i
$917$		0			0
$918$	2.99510			0.0988532
$919$			52.2417i			1.72330i	0.507507	+	0.861648i	$0.330567\pi$
$919$			52.2417i			1.72330i	−0.507507	+	0.861648i	$0.669433\pi$
$920$	−3.67799			−0.121260
$921$			11.4905i			0.378626i
$922$		−	35.4263i		−	1.16670i
$923$	−16.4913			−0.542819
$924$		0			0
$925$	−7.06893			−0.232425
$926$		−	26.8021i		−	0.880770i
$927$			10.8258i			0.355567i
$928$	−2.90437			−0.0953405
$929$			31.7764i			1.04255i	0.853389	+	0.521275i	$0.174543\pi$
$929$			31.7764i			1.04255i	−0.853389	+	0.521275i	$0.825457\pi$
$930$	−16.0069			−0.524887
$931$		0			0
$932$			24.1684i			0.791661i
$933$	25.3863			0.831109
$934$	−38.3106			−1.25356
$935$	−1.81941	+	15.6116i	−0.0595011	+	0.510553i
$936$			2.26904i			0.0741659i
$937$	8.18236			0.267306			0.133653	−	0.991028i	$-0.457329\pi$
$937$	8.18236			0.267306			0.133653	+	0.991028i	$0.457329\pi$
$938$		0			0
$939$	−5.05454			−0.164949
$940$	−1.57619			−0.0514096
$941$	−50.2619			−1.63849			−0.819245	−	0.573443i	$-0.805607\pi$
$941$	−50.2619			−1.63849			−0.819245	+	0.573443i	$0.805607\pi$
$942$		−	5.08417i		−	0.165651i
$943$	27.0829			0.881941
$944$		−	0.121579i		−	0.00395707i
$945$		0			0
$946$	−39.6289	−	4.61845i	−1.28845	−	0.150159i
$947$	56.9689			1.85124			0.925620	−	0.378454i	$-0.123544\pi$
$947$	56.9689			1.85124			0.925620	+	0.378454i	$0.123544\pi$
$948$	11.7454			0.381472
$949$	20.9058			0.678632
$950$			3.30955i			0.107376i
$951$			7.75474i			0.251465i
$952$		0			0
$953$		−	25.4800i		−	0.825377i	−0.910872	−	0.412689i	$-0.864590\pi$
$953$		−	25.4800i		−	0.825377i	0.910872	−	0.412689i	$-0.135410\pi$
$954$			0.531530i			0.0172089i
$955$			2.91728i			0.0944009i
$956$		−	18.2701i		−	0.590897i
$957$	9.56794	+	1.11507i	0.309287	+	0.0360451i
$958$		−	31.7857i		−	1.02695i
$959$		0			0
$960$	1.58222			0.0510660
$961$	−71.3480			−2.30155
$962$		−	6.42469i		−	0.207140i
$963$			5.48462i			0.176739i
$964$	15.0265			0.483970
$965$	−23.8962			−0.769247
$966$		0			0
$967$		−	10.1244i		−	0.325578i	−0.986661	−	0.162789i	$-0.947951\pi$
$967$		−	10.1244i		−	0.325578i	0.986661	−	0.162789i	$-0.0520489\pi$
$968$	2.52958	−	10.7052i	0.0813037	−	0.344078i
$969$			3.97043i			0.127549i
$970$			2.36351i			0.0758879i
$971$			46.7134i			1.49911i	0.661944	+	0.749553i	$0.269731\pi$
$971$			46.7134i			1.49911i	−0.661944	+	0.749553i	$0.730269\pi$
$972$			1.00000i			0.0320750i
$973$		0			0
$974$			35.7648i			1.14598i
$975$		−	5.66482i		−	0.181419i
$976$	−7.54642			−0.241555
$977$	24.7059			0.790413			0.395206	−	0.918592i	$-0.370673\pi$
$977$	24.7059			0.790413			0.395206	+	0.918592i	$0.370673\pi$
$978$	17.2229			0.550729
$979$	4.37617	−	37.5500i	0.139863	−	1.20010i
$980$		0			0
$981$			13.1165i			0.418777i
$982$	−10.3116			−0.329057
$983$			24.9275i			0.795064i	0.917588	+	0.397532i	$0.130133\pi$
$983$			24.9275i			0.795064i	−0.917588	+	0.397532i	$0.869867\pi$
$984$	−11.6507			−0.371412
$985$	1.23247			0.0392699
$986$	8.69888			0.277029
$987$		0			0
$988$	−3.00793			−0.0956950
$989$			27.9633i			0.889180i
$990$	−5.21236	−	0.607462i	−0.165660	−	0.0193064i
$991$	23.2544			0.738700			0.369350	−	0.929290i	$-0.379580\pi$
$991$	23.2544			0.738700			0.369350	+	0.929290i	$0.379580\pi$
$992$	10.1167			0.321206
$993$		−	33.0937i		−	1.05020i
$994$		0			0
$995$	−6.03234			−0.191238
$996$			7.48210i			0.237079i
$997$	−40.9499			−1.29690			−0.648448	−	0.761259i	$-0.724582\pi$
$997$	−40.9499			−1.29690			−0.648448	+	0.761259i	$0.724582\pi$
$998$			36.2793i			1.14840i
$999$		−	2.83146i		−	0.0895834i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3234.2.e.d.2155.16	yes	24
7.6	odd	2		3234.2.e.c.2155.21	yes	24
11.10	odd	2		3234.2.e.c.2155.4	✓	24
77.76	even	2	inner	3234.2.e.d.2155.9	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3234.2.e.c.2155.4	✓	24	11.10	odd	2
3234.2.e.c.2155.21	yes	24	7.6	odd	2
3234.2.e.d.2155.9	yes	24	77.76	even	2	inner
3234.2.e.d.2155.16	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3234.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.58222i q^{5} +1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.58222i q^{5} +1.00000 q^{6} -1.00000i q^{8} -1.00000 q^{9} +1.58222 q^{10} +(3.29433 + 0.383929i) q^{11} +1.00000i q^{12} +2.26904 q^{13} -1.58222 q^{15} +1.00000 q^{16} -2.99510 q^{17} -1.00000i q^{18} +1.32564 q^{19} +1.58222i q^{20} +(-0.383929 + 3.29433i) q^{22} +2.32457 q^{23} -1.00000 q^{24} +2.49657 q^{25} +2.26904i q^{26} +1.00000i q^{27} +2.90437i q^{29} -1.58222i q^{30} -10.1167i q^{31} +1.00000i q^{32} +(0.383929 - 3.29433i) q^{33} -2.99510i q^{34} +1.00000 q^{36} -2.83146 q^{37} +1.32564i q^{38} -2.26904i q^{39} -1.58222 q^{40} +11.6507 q^{41} +12.0294i q^{43} +(-3.29433 - 0.383929i) q^{44} +1.58222i q^{45} +2.32457i q^{46} +0.996186i q^{47} -1.00000i q^{48} +2.49657i q^{50} +2.99510i q^{51} -2.26904 q^{52} -0.531530 q^{53} -1.00000 q^{54} +(0.607462 - 5.21236i) q^{55} -1.32564i q^{57} -2.90437 q^{58} -0.121579i q^{59} +1.58222 q^{60} -7.54642 q^{61} +10.1167 q^{62} -1.00000 q^{64} -3.59013i q^{65} +(3.29433 + 0.383929i) q^{66} +0.628819 q^{67} +2.99510 q^{68} -2.32457i q^{69} -7.26798 q^{71} +1.00000i q^{72} +9.21350 q^{73} -2.83146i q^{74} -2.49657i q^{75} -1.32564 q^{76} +2.26904 q^{78} -11.7454i q^{79} -1.58222i q^{80} +1.00000 q^{81} +11.6507i q^{82} +7.48210 q^{83} +4.73892i q^{85} -12.0294 q^{86} +2.90437 q^{87} +(0.383929 - 3.29433i) q^{88} -11.3984i q^{89} -1.58222 q^{90} -2.32457 q^{92} -10.1167 q^{93} -0.996186 q^{94} -2.09746i q^{95} +1.00000 q^{96} +1.49379i q^{97} +(-3.29433 - 0.383929i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} + 24 q^{6} - 24 q^{9}+O(q^{10}) \) 24 * q - 24 * q^4 + 24 * q^6 - 24 * q^9	\( 24 q - 24 q^{4} + 24 q^{6} - 24 q^{9} + 24 q^{16} - 16 q^{17} + 32 q^{19} - 8 q^{22} - 24 q^{24} - 8 q^{25} + 8 q^{33} + 24 q^{36} + 16 q^{37} + 16 q^{41} - 24 q^{54} - 16 q^{55} + 16 q^{62} - 24 q^{64} - 64 q^{67} + 16 q^{68} + 64 q^{71} - 32 q^{76} + 24 q^{81} + 16 q^{83} + 8 q^{88} - 16 q^{93} - 64 q^{94} + 24 q^{96}+O(q^{100}) \) 24 * q - 24 * q^4 + 24 * q^6 - 24 * q^9 + 24 * q^16 - 16 * q^17 + 32 * q^19 - 8 * q^22 - 24 * q^24 - 8 * q^25 + 8 * q^33 + 24 * q^36 + 16 * q^37 + 16 * q^41 - 24 * q^54 - 16 * q^55 + 16 * q^62 - 24 * q^64 - 64 * q^67 + 16 * q^68 + 64 * q^71 - 32 * q^76 + 24 * q^81 + 16 * q^83 + 8 * q^88 - 16 * q^93 - 64 * q^94 + 24 * q^96

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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