LMFDB - Embedded newform 3234.2.e.d.2155.4

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			2155.4
Character	$\chi$	$=$	3234.2155
Dual form			3234.2.e.d.2155.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -0.516505i q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -0.516505i q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} -0.516505 q^{10} +(-3.09541 + 1.19099i) q^{11} -1.00000i q^{12} +2.41249 q^{13} +0.516505 q^{15} +1.00000 q^{16} -7.29986 q^{17} +1.00000i q^{18} +2.57557 q^{19} +0.516505i q^{20} +(1.19099 + 3.09541i) q^{22} -1.88937 q^{23} -1.00000 q^{24} +4.73322 q^{25} -2.41249i q^{26} -1.00000i q^{27} -1.33100i q^{29} -0.516505i q^{30} -4.58708i q^{31} -1.00000i q^{32} +(-1.19099 - 3.09541i) q^{33} +7.29986i q^{34} +1.00000 q^{36} +6.34068 q^{37} -2.57557i q^{38} +2.41249i q^{39} +0.516505 q^{40} +2.14721 q^{41} -2.68147i q^{43} +(3.09541 - 1.19099i) q^{44} +0.516505i q^{45} +1.88937i q^{46} -1.14068i q^{47} +1.00000i q^{48} -4.73322i q^{50} -7.29986i q^{51} -2.41249 q^{52} +7.15143 q^{53} -1.00000 q^{54} +(0.615152 + 1.59879i) q^{55} +2.57557i q^{57} -1.33100 q^{58} +1.00336i q^{59} -0.516505 q^{60} +4.50704 q^{61} -4.58708 q^{62} -1.00000 q^{64} -1.24606i q^{65} +(-3.09541 + 1.19099i) q^{66} +8.00023 q^{67} +7.29986 q^{68} -1.88937i q^{69} +9.05635 q^{71} -1.00000i q^{72} -5.82214 q^{73} -6.34068i q^{74} +4.73322i q^{75} -2.57557 q^{76} +2.41249 q^{78} -17.5335i q^{79} -0.516505i q^{80} +1.00000 q^{81} -2.14721i q^{82} +3.86307 q^{83} +3.77041i q^{85} -2.68147 q^{86} +1.33100 q^{87} +(-1.19099 - 3.09541i) q^{88} +14.3064i q^{89} +0.516505 q^{90} +1.88937 q^{92} +4.58708 q^{93} -1.14068 q^{94} -1.33029i q^{95} +1.00000 q^{96} +3.02541i q^{97} +(3.09541 - 1.19099i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$		−	0.516505i		−	0.230988i	−0.993308	−	0.115494i	$-0.963155\pi$
$5$		−	0.516505i		−	0.230988i	0.993308	−	0.115494i	$-0.0368451\pi$
$6$	1.00000			0.408248
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	−1.00000			−0.333333
$10$	−0.516505			−0.163333
$11$	−3.09541	+	1.19099i	−0.933300	+	0.359097i
$11$	−3.09541	+	1.19099i	−0.933300	+	0.359097i
$12$		−	1.00000i		−	0.288675i
$13$	2.41249			0.669103			0.334552	−	0.942377i	$-0.391415\pi$
$13$	2.41249			0.669103			0.334552	+	0.942377i	$0.391415\pi$
$14$		0			0
$15$	0.516505			0.133361
$16$	1.00000			0.250000
$17$	−7.29986			−1.77048			−0.885238	−	0.465139i	$-0.846004\pi$
$17$	−7.29986			−1.77048			−0.885238	+	0.465139i	$0.846004\pi$
$18$			1.00000i			0.235702i
$19$	2.57557			0.590877			0.295438	−	0.955362i	$-0.404534\pi$
$19$	2.57557			0.590877			0.295438	+	0.955362i	$0.404534\pi$
$20$			0.516505i			0.115494i
$21$		0			0
$22$	1.19099	+	3.09541i	0.253920	+	0.659943i
$23$	−1.88937			−0.393960			−0.196980	−	0.980407i	$-0.563113\pi$
$23$	−1.88937			−0.393960			−0.196980	+	0.980407i	$0.563113\pi$
$24$	−1.00000			−0.204124
$25$	4.73322			0.946645
$26$		−	2.41249i		−	0.473127i
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$		−	1.33100i		−	0.247160i	−0.992335	−	0.123580i	$-0.960562\pi$
$29$		−	1.33100i		−	0.247160i	0.992335	−	0.123580i	$-0.0394376\pi$
$30$		−	0.516505i		−	0.0943004i
$31$		−	4.58708i		−	0.823864i	−0.911215	−	0.411932i	$-0.864854\pi$
$31$		−	4.58708i		−	0.823864i	0.911215	−	0.411932i	$-0.135146\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−1.19099	−	3.09541i	−0.207325	−	0.538841i
$34$			7.29986i			1.25191i
$35$		0			0
$36$	1.00000			0.166667
$37$	6.34068			1.04240			0.521200	−	0.853434i	$-0.325484\pi$
$37$	6.34068			1.04240			0.521200	+	0.853434i	$0.325484\pi$
$38$		−	2.57557i		−	0.417813i
$39$			2.41249i			0.386307i
$40$	0.516505			0.0816665
$41$	2.14721			0.335338			0.167669	−	0.985843i	$-0.446376\pi$
$41$	2.14721			0.335338			0.167669	+	0.985843i	$0.446376\pi$
$42$		0			0
$43$		−	2.68147i		−	0.408920i	−0.978875	−	0.204460i	$-0.934456\pi$
$43$		−	2.68147i		−	0.408920i	0.978875	−	0.204460i	$-0.0655438\pi$
$44$	3.09541	−	1.19099i	0.466650	−	0.179548i
$45$			0.516505i			0.0769959i
$46$			1.88937i			0.278572i
$47$		−	1.14068i		−	0.166385i	−0.996533	−	0.0831926i	$-0.973488\pi$
$47$		−	1.14068i		−	0.166385i	0.996533	−	0.0831926i	$-0.0265117\pi$
$48$			1.00000i			0.144338i
$49$		0			0
$50$		−	4.73322i		−	0.669379i
$51$		−	7.29986i		−	1.02218i
$52$	−2.41249			−0.334552
$53$	7.15143			0.982325			0.491162	−	0.871068i	$-0.336572\pi$
$53$	7.15143			0.982325			0.491162	+	0.871068i	$0.336572\pi$
$54$	−1.00000			−0.136083
$55$	0.615152	+	1.59879i	0.0829470	+	0.215581i
$56$		0			0
$57$			2.57557i			0.341143i
$58$	−1.33100			−0.174769
$59$			1.00336i			0.130627i	0.997865	+	0.0653134i	$0.0208047\pi$
$59$			1.00336i			0.130627i	−0.997865	+	0.0653134i	$0.979195\pi$
$60$	−0.516505			−0.0666804
$61$	4.50704			0.577068			0.288534	−	0.957470i	$-0.406832\pi$
$61$	4.50704			0.577068			0.288534	+	0.957470i	$0.406832\pi$
$62$	−4.58708			−0.582560
$63$		0			0
$64$	−1.00000			−0.125000
$65$		−	1.24606i		−	0.154555i
$66$	−3.09541	+	1.19099i	−0.381018	+	0.146601i
$67$	8.00023			0.977384			0.488692	−	0.872456i	$-0.337474\pi$
$67$	8.00023			0.977384			0.488692	+	0.872456i	$0.337474\pi$
$68$	7.29986			0.885238
$69$		−	1.88937i		−	0.227453i
$70$		0			0
$71$	9.05635			1.07479			0.537396	−	0.843330i	$-0.319408\pi$
$71$	9.05635			1.07479			0.537396	+	0.843330i	$0.319408\pi$
$72$		−	1.00000i		−	0.117851i
$73$	−5.82214			−0.681430			−0.340715	−	0.940167i	$-0.610669\pi$
$73$	−5.82214			−0.681430			−0.340715	+	0.940167i	$0.610669\pi$
$74$		−	6.34068i		−	0.737089i
$75$			4.73322i			0.546546i
$76$	−2.57557			−0.295438
$77$		0			0
$78$	2.41249			0.273160
$79$		−	17.5335i		−	1.97268i	−0.164733	−	0.986338i	$-0.552676\pi$
$79$		−	17.5335i		−	1.97268i	0.164733	−	0.986338i	$-0.447324\pi$
$80$		−	0.516505i		−	0.0577470i
$81$	1.00000			0.111111
$82$		−	2.14721i		−	0.237119i
$83$	3.86307			0.424027			0.212014	−	0.977267i	$-0.431998\pi$
$83$	3.86307			0.424027			0.212014	+	0.977267i	$0.431998\pi$
$84$		0			0
$85$			3.77041i			0.408958i
$86$	−2.68147			−0.289150
$87$	1.33100			0.142698
$88$	−1.19099	−	3.09541i	−0.126960	−	0.329971i
$89$			14.3064i			1.51648i	0.651976	+	0.758240i	$0.273940\pi$
$89$			14.3064i			1.51648i	−0.651976	+	0.758240i	$0.726060\pi$
$90$	0.516505			0.0544444
$91$		0			0
$92$	1.88937			0.196980
$93$	4.58708			0.475658
$94$	−1.14068			−0.117652
$95$		−	1.33029i		−	0.136485i
$96$	1.00000			0.102062
$97$			3.02541i			0.307184i	0.988134	+	0.153592i	$0.0490841\pi$
$97$			3.02541i			0.307184i	−0.988134	+	0.153592i	$0.950916\pi$
$98$		0			0
$99$	3.09541	−	1.19099i	0.311100	−	0.119699i
$100$	−4.73322			−0.473322
$101$	−17.0462			−1.69616			−0.848078	−	0.529872i	$-0.822240\pi$
$101$	−17.0462			−1.69616			−0.848078	+	0.529872i	$0.822240\pi$
$102$	−7.29986			−0.722793
$103$		−	13.4342i		−	1.32371i	−0.749633	−	0.661854i	$-0.769770\pi$
$103$		−	13.4342i		−	1.32371i	0.749633	−	0.661854i	$-0.230230\pi$
$104$			2.41249i			0.236564i
$105$		0			0
$106$		−	7.15143i		−	0.694608i
$107$			4.74835i			0.459040i	0.973304	+	0.229520i	$0.0737156\pi$
$107$			4.74835i			0.459040i	−0.973304	+	0.229520i	$0.926284\pi$
$108$			1.00000i			0.0962250i
$109$			1.61490i			0.154680i	0.997005	+	0.0773398i	$0.0246426\pi$
$109$			1.61490i			0.154680i	−0.997005	+	0.0773398i	$0.975357\pi$
$110$	1.59879	−	0.615152i	0.152439	−	0.0586524i
$111$			6.34068i			0.601830i
$112$		0			0
$113$	18.4489			1.73553			0.867763	−	0.496978i	$-0.165557\pi$
$113$	18.4489			1.73553			0.867763	+	0.496978i	$0.165557\pi$
$114$	2.57557			0.241224
$115$			0.975866i			0.0910000i
$116$			1.33100i			0.123580i
$117$	−2.41249			−0.223034
$118$	1.00336			0.0923671
$119$		0			0
$120$			0.516505i			0.0471502i
$121$	8.16309	−	7.37320i	0.742099	−	0.670291i
$122$		−	4.50704i		−	0.408048i
$123$			2.14721i			0.193607i
$124$			4.58708i			0.411932i
$125$		−	5.02725i		−	0.449651i
$126$		0			0
$127$		−	12.7652i		−	1.13273i	−0.824155	−	0.566365i	$-0.808349\pi$
$127$		−	12.7652i		−	1.13273i	0.824155	−	0.566365i	$-0.191651\pi$
$128$			1.00000i			0.0883883i
$129$	2.68147			0.236090
$130$	−1.24606			−0.109287
$131$	13.1155			1.14590			0.572952	−	0.819589i	$-0.305798\pi$
$131$	13.1155			1.14590			0.572952	+	0.819589i	$0.305798\pi$
$132$	1.19099	+	3.09541i	0.103662	+	0.269421i
$133$		0			0
$134$		−	8.00023i		−	0.691115i
$135$	−0.516505			−0.0444536
$136$		−	7.29986i		−	0.625957i
$137$	6.94935			0.593723			0.296861	−	0.954921i	$-0.404060\pi$
$137$	6.94935			0.593723			0.296861	+	0.954921i	$0.404060\pi$
$138$	−1.88937			−0.160834
$139$	8.43815			0.715714			0.357857	−	0.933776i	$-0.383507\pi$
$139$	8.43815			0.715714			0.357857	+	0.933776i	$0.383507\pi$
$140$		0			0
$141$	1.14068			0.0960626
$142$		−	9.05635i		−	0.759992i
$143$	−7.46762	+	2.87325i	−0.624474	+	0.240273i
$144$	−1.00000			−0.0833333
$145$	−0.687466			−0.0570910
$146$			5.82214i			0.481844i
$147$		0			0
$148$	−6.34068			−0.521200
$149$		−	5.18030i		−	0.424387i	−0.977228	−	0.212193i	$-0.931939\pi$
$149$		−	5.18030i		−	0.424387i	0.977228	−	0.212193i	$-0.0680607\pi$
$150$	4.73322			0.386466
$151$			14.8174i			1.20582i	0.797808	+	0.602911i	$0.205993\pi$
$151$			14.8174i			1.20582i	−0.797808	+	0.602911i	$0.794007\pi$
$152$			2.57557i			0.208906i
$153$	7.29986			0.590158
$154$		0			0
$155$	−2.36925			−0.190303
$156$		−	2.41249i		−	0.193153i
$157$			0.378604i			0.0302159i	0.999886	+	0.0151079i	$0.00480919\pi$
$157$			0.378604i			0.0302159i	−0.999886	+	0.0151079i	$0.995191\pi$
$158$	−17.5335			−1.39489
$159$			7.15143i			0.567145i
$160$	−0.516505			−0.0408333
$161$		0			0
$162$		−	1.00000i		−	0.0785674i
$163$	4.69605			0.367823			0.183912	−	0.982943i	$-0.441124\pi$
$163$	4.69605			0.367823			0.183912	+	0.982943i	$0.441124\pi$
$164$	−2.14721			−0.167669
$165$	−1.59879	+	0.615152i	−0.124466	+	0.0478895i
$166$		−	3.86307i		−	0.299833i
$167$	−20.6417			−1.59730			−0.798652	−	0.601793i	$-0.794453\pi$
$167$	−20.6417			−1.59730			−0.798652	+	0.601793i	$0.794453\pi$
$168$		0			0
$169$	−7.17991			−0.552301
$170$	3.77041			0.289177
$171$	−2.57557			−0.196959
$172$			2.68147i			0.204460i
$173$	12.9992			0.988310			0.494155	−	0.869374i	$-0.335477\pi$
$173$	12.9992			0.988310			0.494155	+	0.869374i	$0.335477\pi$
$174$		−	1.33100i		−	0.100903i
$175$		0			0
$176$	−3.09541	+	1.19099i	−0.233325	+	0.0897742i
$177$	−1.00336			−0.0754175
$178$	14.3064			1.07231
$179$	25.6730			1.91889			0.959444	−	0.281900i	$-0.0909645\pi$
$179$	25.6730			1.91889			0.959444	+	0.281900i	$0.0909645\pi$
$180$		−	0.516505i		−	0.0384980i
$181$		−	10.7864i		−	0.801750i	−0.916133	−	0.400875i	$-0.868706\pi$
$181$		−	10.7864i		−	0.801750i	0.916133	−	0.400875i	$-0.131294\pi$
$182$		0			0
$183$			4.50704i			0.333170i
$184$		−	1.88937i		−	0.139286i
$185$		−	3.27499i		−	0.240782i
$186$		−	4.58708i		−	0.336341i
$187$	22.5960	−	8.69405i	1.65238	−	0.635772i
$188$			1.14068i			0.0831926i
$189$		0			0
$190$	−1.33029			−0.0965097
$191$	5.40879			0.391367			0.195683	−	0.980667i	$-0.437308\pi$
$191$	5.40879			0.391367			0.195683	+	0.980667i	$0.437308\pi$
$192$		−	1.00000i		−	0.0721688i
$193$		−	6.80675i		−	0.489960i	−0.969528	−	0.244980i	$-0.921219\pi$
$193$		−	6.80675i		−	0.489960i	0.969528	−	0.244980i	$-0.0787814\pi$
$194$	3.02541			0.217212
$195$	1.24606			0.0892322
$196$		0			0
$197$		−	19.3261i		−	1.37693i	−0.725269	−	0.688465i	$-0.758285\pi$
$197$		−	19.3261i		−	1.37693i	0.725269	−	0.688465i	$-0.241715\pi$
$198$	−1.19099	−	3.09541i	−0.0846400	−	0.219981i
$199$		−	7.03030i		−	0.498364i	−0.968457	−	0.249182i	$-0.919838\pi$
$199$		−	7.03030i		−	0.498364i	0.968457	−	0.249182i	$-0.0801618\pi$
$200$			4.73322i			0.334689i
$201$			8.00023i			0.564293i
$202$			17.0462i			1.19936i
$203$		0			0
$204$			7.29986i			0.511092i
$205$		−	1.10904i		−	0.0774589i
$206$	−13.4342			−0.936003
$207$	1.88937			0.131320
$208$	2.41249			0.167276
$209$	−7.97244	+	3.06748i	−0.551465	+	0.212182i
$210$		0			0
$211$			0.276202i			0.0190145i	0.999955	+	0.00950725i	$0.00302630\pi$
$211$			0.276202i			0.0190145i	−0.999955	+	0.00950725i	$0.996974\pi$
$212$	−7.15143			−0.491162
$213$			9.05635i			0.620531i
$214$	4.74835			0.324590
$215$	−1.38499			−0.0944555
$216$	1.00000			0.0680414
$217$		0			0
$218$	1.61490			0.109375
$219$		−	5.82214i		−	0.393424i
$220$	−0.615152	−	1.59879i	−0.0414735	−	0.107791i
$221$	−17.6108			−1.18463
$222$	6.34068			0.425558
$223$		−	22.9482i		−	1.53673i	−0.640014	−	0.768363i	$-0.721071\pi$
$223$		−	22.9482i		−	1.53673i	0.640014	−	0.768363i	$-0.278929\pi$
$224$		0			0
$225$	−4.73322			−0.315548
$226$		−	18.4489i		−	1.22720i
$227$	−4.78439			−0.317551			−0.158775	−	0.987315i	$-0.550755\pi$
$227$	−4.78439			−0.317551			−0.158775	+	0.987315i	$0.550755\pi$
$228$		−	2.57557i		−	0.170571i
$229$			12.8296i			0.847803i	0.905708	+	0.423901i	$0.139340\pi$
$229$			12.8296i			0.847803i	−0.905708	+	0.423901i	$0.860660\pi$
$230$	0.975866			0.0643467
$231$		0			0
$232$	1.33100			0.0873843
$233$			0.0966329i			0.00633063i	0.999995	+	0.00316532i	$0.00100755\pi$
$233$			0.0966329i			0.00633063i	−0.999995	+	0.00316532i	$0.998992\pi$
$234$			2.41249i			0.157709i
$235$	−0.589166			−0.0384330
$236$		−	1.00336i		−	0.0653134i
$237$	17.5335			1.13893
$238$		0			0
$239$		−	15.8209i		−	1.02337i	−0.859173	−	0.511686i	$-0.829021\pi$
$239$		−	15.8209i		−	1.02337i	0.859173	−	0.511686i	$-0.170979\pi$
$240$	0.516505			0.0333402
$241$	14.5518			0.937363			0.468682	−	0.883367i	$-0.344729\pi$
$241$	14.5518			0.937363			0.468682	+	0.883367i	$0.344729\pi$
$242$	−7.37320	−	8.16309i	−0.473967	−	0.524743i
$243$			1.00000i			0.0641500i
$244$	−4.50704			−0.288534
$245$		0			0
$246$	2.14721			0.136901
$247$	6.21353			0.395357
$248$	4.58708			0.291280
$249$			3.86307i			0.244812i
$250$	−5.02725			−0.317951
$251$		−	20.9000i		−	1.31919i	−0.751619	−	0.659597i	$-0.770727\pi$
$251$		−	20.9000i		−	1.31919i	0.751619	−	0.659597i	$-0.229273\pi$
$252$		0			0
$253$	5.84836	−	2.25022i	0.367683	−	0.141470i
$254$	−12.7652			−0.800960
$255$	−3.77041			−0.236112
$256$	1.00000			0.0625000
$257$			18.2140i			1.13616i	0.822973	+	0.568080i	$0.192314\pi$
$257$			18.2140i			1.13616i	−0.822973	+	0.568080i	$0.807686\pi$
$258$		−	2.68147i		−	0.166941i
$259$		0			0
$260$			1.24606i			0.0772773i
$261$			1.33100i			0.0823867i
$262$		−	13.1155i		−	0.810276i
$263$		−	15.6132i		−	0.962751i	−0.876514	−	0.481376i	$-0.840137\pi$
$263$		−	15.6132i		−	0.962751i	0.876514	−	0.481376i	$-0.159863\pi$
$264$	3.09541	−	1.19099i	0.190509	−	0.0733004i
$265$		−	3.69375i		−	0.226905i
$266$		0			0
$267$	−14.3064			−0.875540
$268$	−8.00023			−0.488692
$269$			19.8599i			1.21088i	0.795890	+	0.605441i	$0.207003\pi$
$269$			19.8599i			1.21088i	−0.795890	+	0.605441i	$0.792997\pi$
$270$			0.516505i			0.0314335i
$271$	−15.7584			−0.957256			−0.478628	−	0.878018i	$-0.658866\pi$
$271$	−15.7584			−0.957256			−0.478628	+	0.878018i	$0.658866\pi$
$272$	−7.29986			−0.442619
$273$		0			0
$274$		−	6.94935i		−	0.419826i
$275$	−14.6513	+	5.63722i	−0.883504	+	0.339937i
$276$			1.88937i			0.113727i
$277$			20.1002i			1.20770i	0.797097	+	0.603852i	$0.206368\pi$
$277$			20.1002i			1.20770i	−0.797097	+	0.603852i	$0.793632\pi$
$278$		−	8.43815i		−	0.506087i
$279$			4.58708i			0.274621i
$280$		0			0
$281$		−	24.3187i		−	1.45073i	−0.688364	−	0.725365i	$-0.741671\pi$
$281$		−	24.3187i		−	1.45073i	0.688364	−	0.725365i	$-0.258329\pi$
$282$		−	1.14068i		−	0.0679265i
$283$	−2.29408			−0.136369			−0.0681845	−	0.997673i	$-0.521721\pi$
$283$	−2.29408			−0.136369			−0.0681845	+	0.997673i	$0.521721\pi$
$284$	−9.05635			−0.537396
$285$	1.33029			0.0787998
$286$	2.87325	+	7.46762i	0.169899	+	0.441570i
$287$		0			0
$288$			1.00000i			0.0589256i
$289$	36.2879			2.13458
$290$			0.687466i			0.0403694i
$291$	−3.02541			−0.177353
$292$	5.82214			0.340715
$293$	−10.4490			−0.610438			−0.305219	−	0.952282i	$-0.598730\pi$
$293$	−10.4490			−0.610438			−0.305219	+	0.952282i	$0.598730\pi$
$294$		0			0
$295$	0.518242			0.0301732
$296$			6.34068i			0.368544i
$297$	1.19099	+	3.09541i	0.0691082	+	0.179614i
$298$	−5.18030			−0.300087
$299$	−4.55807			−0.263600
$300$		−	4.73322i		−	0.273273i
$301$		0			0
$302$	14.8174			0.852645
$303$		−	17.0462i		−	0.979276i
$304$	2.57557			0.147719
$305$		−	2.32791i		−	0.133296i
$306$		−	7.29986i		−	0.417305i
$307$	24.2172			1.38215			0.691073	−	0.722785i	$-0.257138\pi$
$307$	24.2172			1.38215			0.691073	+	0.722785i	$0.257138\pi$
$308$		0			0
$309$	13.4342			0.764243
$310$			2.36925i			0.134564i
$311$			7.98705i			0.452904i	0.974022	+	0.226452i	$0.0727126\pi$
$311$			7.98705i			0.452904i	−0.974022	+	0.226452i	$0.927287\pi$
$312$	−2.41249			−0.136580
$313$			6.10743i			0.345213i	0.984991	+	0.172606i	$0.0552188\pi$
$313$			6.10743i			0.345213i	−0.984991	+	0.172606i	$0.944781\pi$
$314$	0.378604			0.0213659
$315$		0			0
$316$			17.5335i			0.986338i
$317$	15.0861			0.847321			0.423661	−	0.905821i	$-0.360745\pi$
$317$	15.0861			0.847321			0.423661	+	0.905821i	$0.360745\pi$
$318$	7.15143			0.401032
$319$	1.58521	+	4.11998i	0.0887544	+	0.230675i
$320$			0.516505i			0.0288735i
$321$	−4.74835			−0.265027
$322$		0			0
$323$	−18.8013			−1.04613
$324$	−1.00000			−0.0555556
$325$	11.4188			0.633403
$326$		−	4.69605i		−	0.260090i
$327$	−1.61490			−0.0893043
$328$			2.14721i			0.118560i
$329$		0			0
$330$	0.615152	+	1.59879i	0.0338630	+	0.0880106i
$331$	7.60617			0.418073			0.209036	−	0.977908i	$-0.432967\pi$
$331$	7.60617			0.418073			0.209036	+	0.977908i	$0.432967\pi$
$332$	−3.86307			−0.212014
$333$	−6.34068			−0.347467
$334$			20.6417i			1.12946i
$335$		−	4.13216i		−	0.225764i
$336$		0			0
$337$			16.7783i			0.913973i	0.889474	+	0.456987i	$0.151071\pi$
$337$			16.7783i			0.913973i	−0.889474	+	0.456987i	$0.848929\pi$
$338$			7.17991i			0.390536i
$339$			18.4489i			1.00201i
$340$		−	3.77041i		−	0.204479i
$341$	5.46317	+	14.1989i	0.295847	+	0.768912i
$342$			2.57557i			0.139271i
$343$		0			0
$344$	2.68147			0.144575
$345$	−0.975866			−0.0525389
$346$		−	12.9992i		−	0.698841i
$347$		−	7.26500i		−	0.390005i	−0.980803	−	0.195003i	$-0.937528\pi$
$347$		−	7.26500i		−	0.390005i	0.980803	−	0.195003i	$-0.0624716\pi$
$348$	−1.33100			−0.0713490
$349$	19.0310			1.01871			0.509354	−	0.860557i	$-0.329884\pi$
$349$	19.0310			1.01871			0.509354	+	0.860557i	$0.329884\pi$
$350$		0			0
$351$		−	2.41249i		−	0.128769i
$352$	1.19099	+	3.09541i	0.0634800	+	0.164986i
$353$		−	20.1289i		−	1.07136i	−0.844422	−	0.535678i	$-0.820056\pi$
$353$		−	20.1289i		−	1.07136i	0.844422	−	0.535678i	$-0.179944\pi$
$354$			1.00336i			0.0533282i
$355$		−	4.67765i		−	0.248264i
$356$		−	14.3064i		−	0.758240i
$357$		0			0
$358$		−	25.6730i		−	1.35686i
$359$			17.1576i			0.905544i	0.891626	+	0.452772i	$0.149565\pi$
$359$			17.1576i			0.905544i	−0.891626	+	0.452772i	$0.850435\pi$
$360$	−0.516505			−0.0272222
$361$	−12.3664			−0.650865
$362$	−10.7864			−0.566923
$363$	7.37320	+	8.16309i	0.386992	+	0.428451i
$364$		0			0
$365$			3.00716i			0.157402i
$366$	4.50704			0.235587
$367$		−	1.86109i		−	0.0971479i	−0.998820	−	0.0485739i	$-0.984532\pi$
$367$		−	1.86109i		−	0.0971479i	0.998820	−	0.0485739i	$-0.0154677\pi$
$368$	−1.88937			−0.0984901
$369$	−2.14721			−0.111779
$370$	−3.27499			−0.170258
$371$		0			0
$372$	−4.58708			−0.237829
$373$			14.5431i			0.753013i	0.926414	+	0.376507i	$0.122875\pi$
$373$			14.5431i			0.753013i	−0.926414	+	0.376507i	$0.877125\pi$
$374$	−8.69405	−	22.5960i	−0.449559	−	1.16841i
$375$	5.02725			0.259606
$376$	1.14068			0.0588261
$377$		−	3.21101i		−	0.165376i
$378$		0			0
$379$	−31.0016			−1.59244			−0.796222	−	0.605004i	$-0.793171\pi$
$379$	−31.0016			−1.59244			−0.796222	+	0.605004i	$0.793171\pi$
$380$			1.33029i			0.0682427i
$381$	12.7652			0.653981
$382$		−	5.40879i		−	0.276738i
$383$		−	18.2949i		−	0.934826i	−0.884039	−	0.467413i	$-0.845186\pi$
$383$		−	18.2949i		−	0.934826i	0.884039	−	0.467413i	$-0.154814\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−6.80675			−0.346454
$387$			2.68147i			0.136307i
$388$		−	3.02541i		−	0.153592i
$389$	4.49563			0.227938			0.113969	−	0.993484i	$-0.463644\pi$
$389$	4.49563			0.227938			0.113969	+	0.993484i	$0.463644\pi$
$390$		−	1.24606i		−	0.0630967i
$391$	13.7921			0.697497
$392$		0			0
$393$			13.1155i			0.661587i
$394$	−19.3261			−0.973637
$395$	−9.05615			−0.455664
$396$	−3.09541	+	1.19099i	−0.155550	+	0.0598495i
$397$		−	29.5441i		−	1.48277i	−0.671077	−	0.741387i	$-0.734168\pi$
$397$		−	29.5441i		−	1.48277i	0.671077	−	0.741387i	$-0.265832\pi$
$398$	−7.03030			−0.352397
$399$		0			0
$400$	4.73322			0.236661
$401$	−1.94172			−0.0969648			−0.0484824	−	0.998824i	$-0.515438\pi$
$401$	−1.94172			−0.0969648			−0.0484824	+	0.998824i	$0.515438\pi$
$402$	8.00023			0.399015
$403$		−	11.0663i		−	0.551250i
$404$	17.0462			0.848078
$405$		−	0.516505i		−	0.0256653i
$406$		0			0
$407$	−19.6270	+	7.55168i	−0.972873	+	0.374323i
$408$	7.29986			0.361397
$409$	−3.22431			−0.159432			−0.0797160	−	0.996818i	$-0.525401\pi$
$409$	−3.22431			−0.159432			−0.0797160	+	0.996818i	$0.525401\pi$
$410$	−1.10904			−0.0547717
$411$			6.94935i			0.342786i
$412$			13.4342i			0.661854i
$413$		0			0
$414$		−	1.88937i		−	0.0928573i
$415$		−	1.99529i		−	0.0979451i
$416$		−	2.41249i		−	0.118282i
$417$			8.43815i			0.413218i
$418$	3.06748	+	7.97244i	0.150035	+	0.389945i
$419$		−	20.1284i		−	0.983338i	−0.870782	−	0.491669i	$-0.836387\pi$
$419$		−	20.1284i		−	0.983338i	0.870782	−	0.491669i	$-0.163613\pi$
$420$		0			0
$421$	−16.0464			−0.782054			−0.391027	−	0.920379i	$-0.627880\pi$
$421$	−16.0464			−0.782054			−0.391027	+	0.920379i	$0.627880\pi$
$422$	0.276202			0.0134453
$423$			1.14068i			0.0554617i
$424$			7.15143i			0.347304i
$425$	−34.5518			−1.67601
$426$	9.05635			0.438782
$427$		0			0
$428$		−	4.74835i		−	0.229520i
$429$	−2.87325	−	7.46762i	−0.138722	−	0.360540i
$430$			1.38499i			0.0667902i
$431$			28.4344i			1.36963i	0.728715	+	0.684817i	$0.240118\pi$
$431$			28.4344i			1.36963i	−0.728715	+	0.684817i	$0.759882\pi$
$432$		−	1.00000i		−	0.0481125i
$433$			15.4748i			0.743672i	0.928298	+	0.371836i	$0.121272\pi$
$433$			15.4748i			0.743672i	−0.928298	+	0.371836i	$0.878728\pi$
$434$		0			0
$435$		−	0.687466i		−	0.0329615i
$436$		−	1.61490i		−	0.0773398i
$437$	−4.86620			−0.232782
$438$	−5.82214			−0.278193
$439$	2.87850			0.137384			0.0686918	−	0.997638i	$-0.478118\pi$
$439$	2.87850			0.137384			0.0686918	+	0.997638i	$0.478118\pi$
$440$	−1.59879	+	0.615152i	−0.0762194	+	0.0293262i
$441$		0			0
$442$			17.6108i			0.837660i
$443$	−5.55756			−0.264048			−0.132024	−	0.991247i	$-0.542148\pi$
$443$	−5.55756			−0.264048			−0.132024	+	0.991247i	$0.542148\pi$
$444$		−	6.34068i		−	0.300915i
$445$	7.38934			0.350288
$446$	−22.9482			−1.08663
$447$	5.18030			0.245020
$448$		0			0
$449$	14.7075			0.694091			0.347046	−	0.937848i	$-0.387185\pi$
$449$	14.7075			0.694091			0.347046	+	0.937848i	$0.387185\pi$
$450$			4.73322i			0.223126i
$451$	−6.64648	+	2.55730i	−0.312971	+	0.120419i
$452$	−18.4489			−0.867763
$453$	−14.8174			−0.696182
$454$			4.78439i			0.224542i
$455$		0			0
$456$	−2.57557			−0.120612
$457$			31.4706i			1.47213i	0.676910	+	0.736066i	$0.263319\pi$
$457$			31.4706i			1.47213i	−0.676910	+	0.736066i	$0.736681\pi$
$458$	12.8296			0.599487
$459$			7.29986i			0.340728i
$460$		−	0.975866i		−	0.0455000i
$461$	−18.8445			−0.877678			−0.438839	−	0.898566i	$-0.644610\pi$
$461$	−18.8445			−0.877678			−0.438839	+	0.898566i	$0.644610\pi$
$462$		0			0
$463$	5.15933			0.239774			0.119887	−	0.992788i	$-0.461747\pi$
$463$	5.15933			0.239774			0.119887	+	0.992788i	$0.461747\pi$
$464$		−	1.33100i		−	0.0617900i
$465$		−	2.36925i		−	0.109871i
$466$	0.0966329			0.00447643
$467$			14.6712i			0.678900i	0.940624	+	0.339450i	$0.110241\pi$
$467$			14.6712i			0.678900i	−0.940624	+	0.339450i	$0.889759\pi$
$468$	2.41249			0.111517
$469$		0			0
$470$			0.589166i			0.0271762i
$471$	−0.378604			−0.0174452
$472$	−1.00336			−0.0461836
$473$	3.19360	+	8.30023i	0.146842	+	0.381645i
$474$		−	17.5335i		−	0.805342i
$475$	12.1908			0.559350
$476$		0			0
$477$	−7.15143			−0.327442
$478$	−15.8209			−0.723633
$479$	−26.7570			−1.22256			−0.611279	−	0.791415i	$-0.709345\pi$
$479$	−26.7570			−1.22256			−0.611279	+	0.791415i	$0.709345\pi$
$480$		−	0.516505i		−	0.0235751i
$481$	15.2968			0.697473
$482$		−	14.5518i		−	0.662816i
$483$		0			0
$484$	−8.16309	+	7.37320i	−0.371049	+	0.335145i
$485$	1.56264			0.0709557
$486$	1.00000			0.0453609
$487$	18.4972			0.838189			0.419094	−	0.907943i	$-0.362348\pi$
$487$	18.4972			0.838189			0.419094	+	0.907943i	$0.362348\pi$
$488$			4.50704i			0.204024i
$489$			4.69605i			0.212363i
$490$		0			0
$491$		−	11.5475i		−	0.521133i	−0.965456	−	0.260567i	$-0.916091\pi$
$491$		−	11.5475i		−	0.521133i	0.965456	−	0.260567i	$-0.0839094\pi$
$492$		−	2.14721i		−	0.0968036i
$493$			9.71609i			0.437591i
$494$		−	6.21353i		−	0.279560i
$495$	−0.615152	−	1.59879i	−0.0276490	−	0.0718603i
$496$		−	4.58708i		−	0.205966i
$497$		0			0
$498$	3.86307			0.173108
$499$	−26.7968			−1.19959			−0.599796	−	0.800153i	$-0.704752\pi$
$499$	−26.7968			−1.19959			−0.599796	+	0.800153i	$0.704752\pi$
$500$			5.02725i			0.224826i
$501$		−	20.6417i		−	0.922204i
$502$	−20.9000			−0.932811
$503$	−29.5306			−1.31670			−0.658352	−	0.752710i	$-0.728746\pi$
$503$	−29.5306			−1.31670			−0.658352	+	0.752710i	$0.728746\pi$
$504$		0			0
$505$			8.80441i			0.391791i
$506$	−2.25022	−	5.84836i	−0.100034	−	0.259991i
$507$		−	7.17991i		−	0.318871i
$508$			12.7652i			0.566365i
$509$			10.4707i			0.464107i	0.972703	+	0.232053i	$0.0745444\pi$
$509$			10.4707i			0.464107i	−0.972703	+	0.232053i	$0.925456\pi$
$510$			3.77041i			0.166956i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$		−	2.57557i		−	0.113714i
$514$	18.2140			0.803387
$515$	−6.93881			−0.305761
$516$	−2.68147			−0.118045
$517$	1.35854	+	3.53087i	0.0597484	+	0.155287i
$518$		0			0
$519$			12.9992i			0.570601i
$520$	1.24606			0.0546433
$521$		−	16.0333i		−	0.702433i	−0.936294	−	0.351217i	$-0.885768\pi$
$521$		−	16.0333i		−	0.702433i	0.936294	−	0.351217i	$-0.114232\pi$
$522$	1.33100			0.0582562
$523$	−39.0430			−1.70723			−0.853616	−	0.520903i	$-0.825595\pi$
$523$	−39.0430			−1.70723			−0.853616	+	0.520903i	$0.825595\pi$
$524$	−13.1155			−0.572952
$525$		0			0
$526$	−15.6132			−0.680768
$527$			33.4850i			1.45863i
$528$	−1.19099	−	3.09541i	−0.0518312	−	0.134710i
$529$	−19.4303			−0.844795
$530$	−3.69375			−0.160446
$531$		−	1.00336i		−	0.0435423i
$532$		0			0
$533$	5.18011			0.224375
$534$			14.3064i			0.619100i
$535$	2.45254			0.106033
$536$			8.00023i			0.345557i
$537$			25.6730i			1.10787i
$538$	19.8599			0.856223
$539$		0			0
$540$	0.516505			0.0222268
$541$		−	10.2056i		−	0.438775i	−0.975638	−	0.219387i	$-0.929594\pi$
$541$		−	10.2056i		−	0.438775i	0.975638	−	0.219387i	$-0.0704059\pi$
$542$			15.7584i			0.676882i
$543$	10.7864			0.462890
$544$			7.29986i			0.312979i
$545$	0.834104			0.0357291
$546$		0			0
$547$			34.4836i			1.47441i	0.675668	+	0.737206i	$0.263855\pi$
$547$			34.4836i			1.47441i	−0.675668	+	0.737206i	$0.736145\pi$
$548$	−6.94935			−0.296861
$549$	−4.50704			−0.192356
$550$	5.63722	+	14.6513i	0.240372	+	0.624731i
$551$		−	3.42808i		−	0.146041i
$552$	1.88937			0.0804168
$553$		0			0
$554$	20.1002			0.853975
$555$	3.27499			0.139015
$556$	−8.43815			−0.357857
$557$			5.85427i			0.248053i	0.992279	+	0.124027i	$0.0395808\pi$
$557$			5.85427i			0.248053i	−0.992279	+	0.124027i	$0.960419\pi$
$558$	4.58708			0.194187
$559$		−	6.46900i		−	0.273610i
$560$		0			0
$561$	8.69405	+	22.5960i	0.367063	+	0.954005i
$562$	−24.3187			−1.02582
$563$	7.49773			0.315992			0.157996	−	0.987440i	$-0.449497\pi$
$563$	7.49773			0.315992			0.157996	+	0.987440i	$0.449497\pi$
$564$	−1.14068			−0.0480313
$565$		−	9.52894i		−	0.400885i
$566$			2.29408i			0.0964274i
$567$		0			0
$568$			9.05635i			0.379996i
$569$			43.0163i			1.80334i	0.432426	+	0.901670i	$0.357658\pi$
$569$			43.0163i			1.80334i	−0.432426	+	0.901670i	$0.642342\pi$
$570$		−	1.33029i		−	0.0557199i
$571$		−	24.2550i		−	1.01504i	−0.861640	−	0.507521i	$-0.830562\pi$
$571$		−	24.2550i		−	1.01504i	0.861640	−	0.507521i	$-0.169438\pi$
$572$	7.46762	−	2.87325i	0.312237	−	0.120136i
$573$			5.40879i			0.225956i
$574$		0			0
$575$	−8.94279			−0.372940
$576$	1.00000			0.0416667
$577$			33.9166i			1.41197i	0.708228	+	0.705984i	$0.249495\pi$
$577$			33.9166i			1.41197i	−0.708228	+	0.705984i	$0.750505\pi$
$578$		−	36.2879i		−	1.50938i
$579$	6.80675			0.282879
$580$	0.687466			0.0285455
$581$		0			0
$582$			3.02541i			0.125407i
$583$	−22.1366	+	8.51728i	−0.916804	+	0.352750i
$584$		−	5.82214i		−	0.240922i
$585$			1.24606i			0.0515182i
$586$			10.4490i			0.431645i
$587$			13.6010i			0.561372i	0.959800	+	0.280686i	$0.0905619\pi$
$587$			13.6010i			0.561372i	−0.959800	+	0.280686i	$0.909438\pi$
$588$		0			0
$589$		−	11.8144i		−	0.486802i
$590$		−	0.518242i		−	0.0213357i
$591$	19.3261			0.794971
$592$	6.34068			0.260600
$593$	−47.4393			−1.94810			−0.974050	−	0.226334i	$-0.927326\pi$
$593$	−47.4393			−1.94810			−0.974050	+	0.226334i	$0.927326\pi$
$594$	3.09541	−	1.19099i	0.127006	−	0.0488669i
$595$		0			0
$596$			5.18030i			0.212193i
$597$	7.03030			0.287731
$598$			4.55807i			0.186393i
$599$	30.2176			1.23466			0.617329	−	0.786705i	$-0.288215\pi$
$599$	30.2176			1.23466			0.617329	+	0.786705i	$0.288215\pi$
$600$	−4.73322			−0.193233
$601$	−40.6902			−1.65979			−0.829893	−	0.557922i	$-0.811599\pi$
$601$	−40.6902			−1.65979			−0.829893	+	0.557922i	$0.811599\pi$
$602$		0			0
$603$	−8.00023			−0.325795
$604$		−	14.8174i		−	0.602911i
$605$	−3.80829	−	4.21627i	−0.154829	−	0.171416i
$606$	−17.0462			−0.692453
$607$	30.4472			1.23581			0.617907	−	0.786251i	$-0.287981\pi$
$607$	30.4472			1.23581			0.617907	+	0.786251i	$0.287981\pi$
$608$		−	2.57557i		−	0.104453i
$609$		0			0
$610$	−2.32791			−0.0942542
$611$		−	2.75187i		−	0.111329i
$612$	−7.29986			−0.295079
$613$		−	39.9547i		−	1.61375i	−0.590719	−	0.806877i	$-0.701156\pi$
$613$		−	39.9547i		−	1.61375i	0.590719	−	0.806877i	$-0.298844\pi$
$614$		−	24.2172i		−	0.977325i
$615$	1.10904			0.0447209
$616$		0			0
$617$	13.0978			0.527299			0.263649	−	0.964619i	$-0.415074\pi$
$617$	13.0978			0.527299			0.263649	+	0.964619i	$0.415074\pi$
$618$		−	13.4342i		−	0.540402i
$619$			38.3268i			1.54048i	0.637753	+	0.770241i	$0.279864\pi$
$619$			38.3268i			1.54048i	−0.637753	+	0.770241i	$0.720136\pi$
$620$	2.36925			0.0951513
$621$			1.88937i			0.0758177i
$622$	7.98705			0.320251
$623$		0			0
$624$			2.41249i			0.0965767i
$625$	21.0695			0.842781
$626$	6.10743			0.244102
$627$	−3.06748	−	7.97244i	−0.122503	−	0.318389i
$628$		−	0.378604i		−	0.0151079i
$629$	−46.2860			−1.84554
$630$		0			0
$631$	−2.88637			−0.114905			−0.0574523	−	0.998348i	$-0.518298\pi$
$631$	−2.88637			−0.114905			−0.0574523	+	0.998348i	$0.518298\pi$
$632$	17.5335			0.697446
$633$	−0.276202			−0.0109780
$634$		−	15.0861i		−	0.599147i
$635$	−6.59329			−0.261647
$636$		−	7.15143i		−	0.283573i
$637$		0			0
$638$	4.11998	−	1.58521i	0.163112	−	0.0627589i
$639$	−9.05635			−0.358264
$640$	0.516505			0.0204166
$641$	29.2123			1.15382			0.576908	−	0.816809i	$-0.304259\pi$
$641$	29.2123			1.15382			0.576908	+	0.816809i	$0.304259\pi$
$642$			4.74835i			0.187402i
$643$		−	18.8359i		−	0.742816i	−0.928470	−	0.371408i	$-0.878875\pi$
$643$		−	18.8359i		−	0.742816i	0.928470	−	0.371408i	$-0.121125\pi$
$644$		0			0
$645$		−	1.38499i		−	0.0545339i
$646$			18.8013i			0.739727i
$647$			15.1888i			0.597134i	0.954389	+	0.298567i	$0.0965086\pi$
$647$			15.1888i			0.597134i	−0.954389	+	0.298567i	$0.903491\pi$
$648$			1.00000i			0.0392837i
$649$	−1.19500	−	3.10582i	−0.0469077	−	0.121914i
$650$		−	11.4188i		−	0.447883i
$651$		0			0
$652$	−4.69605			−0.183912
$653$	−21.0264			−0.822825			−0.411413	−	0.911449i	$-0.634964\pi$
$653$	−21.0264			−0.822825			−0.411413	+	0.911449i	$0.634964\pi$
$654$			1.61490i			0.0631477i
$655$		−	6.77419i		−	0.264690i
$656$	2.14721			0.0838344
$657$	5.82214			0.227143
$658$		0			0
$659$		−	25.9809i		−	1.01207i	−0.862513	−	0.506036i	$-0.831110\pi$
$659$		−	25.9809i		−	1.01207i	0.862513	−	0.506036i	$-0.168890\pi$
$660$	1.59879	−	0.615152i	0.0622329	−	0.0239447i
$661$		−	18.2876i		−	0.711307i	−0.934618	−	0.355653i	$-0.884258\pi$
$661$		−	18.2876i		−	0.711307i	0.934618	−	0.355653i	$-0.115742\pi$
$662$		−	7.60617i		−	0.295622i
$663$		−	17.6108i		−	0.683947i
$664$			3.86307i			0.149916i
$665$		0			0
$666$			6.34068i			0.245696i
$667$			2.51474i			0.0973713i
$668$	20.6417			0.798652
$669$	22.9482			0.887230
$670$	−4.13216			−0.159639
$671$	−13.9511	+	5.36784i	−0.538577	+	0.207223i
$672$		0			0
$673$			31.0446i			1.19668i	0.801242	+	0.598340i	$0.204173\pi$
$673$			31.0446i			1.19668i	−0.801242	+	0.598340i	$0.795827\pi$
$674$	16.7783			0.646277
$675$		−	4.73322i		−	0.182182i
$676$	7.17991			0.276151
$677$	−7.98432			−0.306862			−0.153431	−	0.988159i	$-0.549032\pi$
$677$	−7.98432			−0.306862			−0.153431	+	0.988159i	$0.549032\pi$
$678$	18.4489			0.708526
$679$		0			0
$680$	−3.77041			−0.144589
$681$		−	4.78439i		−	0.183338i
$682$	14.1989	−	5.46317i	0.543703	−	0.209195i
$683$	−9.95220			−0.380810			−0.190405	−	0.981706i	$-0.560980\pi$
$683$	−9.95220			−0.380810			−0.190405	+	0.981706i	$0.560980\pi$
$684$	2.57557			0.0984795
$685$		−	3.58937i		−	0.137143i
$686$		0			0
$687$	−12.8296			−0.489479
$688$		−	2.68147i		−	0.102230i
$689$	17.2527			0.657276
$690$			0.975866i			0.0371506i
$691$		−	22.8178i		−	0.868030i	−0.900906	−	0.434015i	$-0.857096\pi$
$691$		−	22.8178i		−	0.868030i	0.900906	−	0.434015i	$-0.142904\pi$
$692$	−12.9992			−0.494155
$693$		0			0
$694$	−7.26500			−0.275776
$695$		−	4.35834i		−	0.165321i
$696$			1.33100i			0.0504513i
$697$	−15.6743			−0.593707
$698$		−	19.0310i		−	0.720335i
$699$	−0.0966329			−0.00365499
$700$		0			0
$701$			50.0953i			1.89207i	0.324059	+	0.946037i	$0.394952\pi$
$701$			50.0953i			1.89207i	−0.324059	+	0.946037i	$0.605048\pi$
$702$	−2.41249			−0.0910534
$703$	16.3309			0.615930
$704$	3.09541	−	1.19099i	0.116663	−	0.0448871i
$705$		−	0.589166i		−	0.0221893i
$706$	−20.1289			−0.757563
$707$		0			0
$708$	1.00336			0.0377087
$709$	39.4466			1.48145			0.740725	−	0.671808i	$-0.234482\pi$
$709$	39.4466			1.48145			0.740725	+	0.671808i	$0.234482\pi$
$710$	−4.67765			−0.175549
$711$			17.5335i			0.657559i
$712$	−14.3064			−0.536156
$713$			8.66668i			0.324570i
$714$		0			0
$715$	1.48404	+	3.85706i	0.0555001	+	0.144246i
$716$	−25.6730			−0.959444
$717$	15.8209			0.590844
$718$	17.1576			0.640316
$719$		−	49.2461i		−	1.83657i	−0.395922	−	0.918284i	$-0.629575\pi$
$719$		−	49.2461i		−	1.83657i	0.395922	−	0.918284i	$-0.370425\pi$
$720$			0.516505i			0.0192490i
$721$		0			0
$722$			12.3664i			0.460231i
$723$			14.5518i			0.541187i
$724$			10.7864i			0.400875i
$725$		−	6.29991i		−	0.233973i
$726$	8.16309	−	7.37320i	0.302961	−	0.273645i
$727$			12.9593i			0.480633i	0.970695	+	0.240316i	$0.0772512\pi$
$727$			12.9593i			0.480633i	−0.970695	+	0.240316i	$0.922749\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	3.00716			0.111300
$731$			19.5743i			0.723983i
$732$		−	4.50704i		−	0.166585i
$733$	−15.2932			−0.564869			−0.282434	−	0.959287i	$-0.591142\pi$
$733$	−15.2932			−0.564869			−0.282434	+	0.959287i	$0.591142\pi$
$734$	−1.86109			−0.0686939
$735$		0			0
$736$			1.88937i			0.0696430i
$737$	−24.7640	+	9.52820i	−0.912193	+	0.350976i
$738$			2.14721i			0.0790398i
$739$			43.9489i			1.61669i	0.588711	+	0.808344i	$0.299636\pi$
$739$			43.9489i			1.61669i	−0.588711	+	0.808344i	$0.700364\pi$
$740$			3.27499i			0.120391i
$741$			6.21353i			0.228260i
$742$		0			0
$743$		−	28.8447i		−	1.05821i	−0.848557	−	0.529104i	$-0.822528\pi$
$743$		−	28.8447i		−	1.05821i	0.848557	−	0.529104i	$-0.177472\pi$
$744$			4.58708i			0.168171i
$745$	−2.67565			−0.0980282
$746$	14.5431			0.532461
$747$	−3.86307			−0.141342
$748$	−22.5960	+	8.69405i	−0.826192	+	0.317886i
$749$		0			0
$750$		−	5.02725i		−	0.183569i
$751$	1.64654			0.0600832			0.0300416	−	0.999549i	$-0.490436\pi$
$751$	1.64654			0.0600832			0.0300416	+	0.999549i	$0.490436\pi$
$752$		−	1.14068i		−	0.0415963i
$753$	20.9000			0.761637
$754$	−3.21101			−0.116938
$755$	7.65325			0.278530
$756$		0			0
$757$	29.2401			1.06275			0.531375	−	0.847137i	$-0.321676\pi$
$757$	29.2401			1.06275			0.531375	+	0.847137i	$0.321676\pi$
$758$			31.0016i			1.12603i
$759$	2.25022	+	5.84836i	0.0816777	+	0.212282i
$760$	1.33029			0.0482549
$761$	7.95411			0.288336			0.144168	−	0.989553i	$-0.453949\pi$
$761$	7.95411			0.288336			0.144168	+	0.989553i	$0.453949\pi$
$762$		−	12.7652i		−	0.462435i
$763$		0			0
$764$	−5.40879			−0.195683
$765$		−	3.77041i		−	0.136319i
$766$	−18.2949			−0.661022
$767$			2.42060i			0.0874028i
$768$			1.00000i			0.0360844i
$769$	48.7306			1.75727			0.878635	−	0.477494i	$-0.158455\pi$
$769$	48.7306			1.75727			0.878635	+	0.477494i	$0.158455\pi$
$770$		0			0
$771$	−18.2140			−0.655963
$772$			6.80675i			0.244980i
$773$		−	28.0705i		−	1.00963i	−0.863229	−	0.504813i	$-0.831561\pi$
$773$		−	28.0705i		−	1.00963i	0.863229	−	0.504813i	$-0.168439\pi$
$774$	2.68147			0.0963834
$775$		−	21.7117i		−	0.779906i
$776$	−3.02541			−0.108606
$777$		0			0
$778$		−	4.49563i		−	0.161176i
$779$	5.53029			0.198143
$780$	−1.24606			−0.0446161
$781$	−28.0331	+	10.7860i	−1.00310	+	0.385954i
$782$		−	13.7921i		−	0.493205i
$783$	−1.33100			−0.0475660
$784$		0			0
$785$	0.195551			0.00697950
$786$	13.1155			0.467813
$787$	52.3968			1.86774			0.933872	−	0.357608i	$-0.116408\pi$
$787$	52.3968			1.86774			0.933872	+	0.357608i	$0.116408\pi$
$788$			19.3261i			0.688465i
$789$	15.6132			0.555845
$790$			9.05615i			0.322203i
$791$		0			0
$792$	1.19099	+	3.09541i	0.0423200	+	0.109990i
$793$	10.8732			0.386118
$794$	−29.5441			−1.04848
$795$	3.69375			0.131004
$796$			7.03030i			0.249182i
$797$		−	30.1448i		−	1.06778i	−0.845553	−	0.533891i	$-0.820729\pi$
$797$		−	30.1448i		−	1.06778i	0.845553	−	0.533891i	$-0.179271\pi$
$798$		0			0
$799$			8.32680i			0.294581i
$800$		−	4.73322i		−	0.167345i
$801$		−	14.3064i		−	0.505493i
$802$			1.94172i			0.0685645i
$803$	18.0219	−	6.93411i	0.635979	−	0.244700i
$804$		−	8.00023i		−	0.282146i
$805$		0			0
$806$	−11.0663			−0.389793
$807$	−19.8599			−0.699103
$808$		−	17.0462i		−	0.599682i
$809$		−	31.6620i		−	1.11318i	−0.830788	−	0.556589i	$-0.812110\pi$
$809$		−	31.6620i		−	1.11318i	0.830788	−	0.556589i	$-0.187890\pi$
$810$	−0.516505			−0.0181481
$811$	−32.9219			−1.15605			−0.578023	−	0.816021i	$-0.696176\pi$
$811$	−32.9219			−1.15605			−0.578023	+	0.816021i	$0.696176\pi$
$812$		0			0
$813$		−	15.7584i		−	0.552672i
$814$	7.55168	+	19.6270i	0.264686	+	0.687925i
$815$		−	2.42553i		−	0.0849627i
$816$		−	7.29986i		−	0.255546i
$817$		−	6.90631i		−	0.241621i
$818$			3.22431i			0.112735i
$819$		0			0
$820$			1.10904i			0.0387294i
$821$			22.4729i			0.784308i	0.919900	+	0.392154i	$0.128270\pi$
$821$			22.4729i			0.784308i	−0.919900	+	0.392154i	$0.871730\pi$
$822$	6.94935			0.242386
$823$	−1.90917			−0.0665495			−0.0332748	−	0.999446i	$-0.510594\pi$
$823$	−1.90917			−0.0665495			−0.0332748	+	0.999446i	$0.510594\pi$
$824$	13.4342			0.468002
$825$	−5.63722	−	14.6513i	−0.196263	−	0.510091i
$826$		0			0
$827$			26.2948i			0.914359i	0.889374	+	0.457179i	$0.151140\pi$
$827$			26.2948i			0.914359i	−0.889374	+	0.457179i	$0.848860\pi$
$828$	−1.88937			−0.0656600
$829$		−	0.890046i		−	0.0309126i	−0.999881	−	0.0154563i	$-0.995080\pi$
$829$		−	0.890046i		−	0.0309126i	0.999881	−	0.0154563i	$-0.00492008\pi$
$830$	−1.99529			−0.0692577
$831$	−20.1002			−0.697268
$832$	−2.41249			−0.0836379
$833$		0			0
$834$	8.43815			0.292189
$835$			10.6615i			0.368958i
$836$	7.97244	−	3.06748i	0.275733	−	0.106091i
$837$	−4.58708			−0.158553
$838$	−20.1284			−0.695325
$839$			6.18078i			0.213384i	0.994292	+	0.106692i	$0.0340259\pi$
$839$			6.18078i			0.213384i	−0.994292	+	0.106692i	$0.965974\pi$
$840$		0			0
$841$	27.2284			0.938912
$842$			16.0464i			0.552996i
$843$	24.3187			0.837580
$844$		−	0.276202i		−	0.00950725i
$845$			3.70846i			0.127575i
$846$	1.14068			0.0392174
$847$		0			0
$848$	7.15143			0.245581
$849$		−	2.29408i		−	0.0787327i
$850$			34.5518i			1.18512i
$851$	−11.9799			−0.410664
$852$		−	9.05635i		−	0.310266i
$853$	37.4345			1.28173			0.640867	−	0.767652i	$-0.278575\pi$
$853$	37.4345			1.28173			0.640867	+	0.767652i	$0.278575\pi$
$854$		0			0
$855$			1.33029i			0.0454951i
$856$	−4.74835			−0.162295
$857$	25.3397			0.865587			0.432793	−	0.901493i	$-0.357528\pi$
$857$	25.3397			0.865587			0.432793	+	0.901493i	$0.357528\pi$
$858$	−7.46762	+	2.87325i	−0.254940	+	0.0980910i
$859$			20.6952i			0.706109i	0.935603	+	0.353055i	$0.114857\pi$
$859$			20.6952i			0.706109i	−0.935603	+	0.353055i	$0.885143\pi$
$860$	1.38499			0.0472278
$861$		0			0
$862$	28.4344			0.968478
$863$	−37.7053			−1.28350			−0.641752	−	0.766913i	$-0.721792\pi$
$863$	−37.7053			−1.28350			−0.641752	+	0.766913i	$0.721792\pi$
$864$	−1.00000			−0.0340207
$865$		−	6.71414i		−	0.228288i
$866$	15.4748			0.525855
$867$			36.2879i			1.23240i
$868$		0			0
$869$	20.8823	+	54.2734i	0.708382	+	1.84110i
$870$	−0.687466			−0.0233073
$871$	19.3004			0.653971
$872$	−1.61490			−0.0546875
$873$		−	3.02541i		−	0.102395i
$874$			4.86620i			0.164602i
$875$		0			0
$876$			5.82214i			0.196712i
$877$			18.8756i			0.637384i	0.947858	+	0.318692i	$0.103244\pi$
$877$			18.8756i			0.637384i	−0.947858	+	0.318692i	$0.896756\pi$
$878$		−	2.87850i		−	0.0971448i
$879$		−	10.4490i		−	0.352436i
$880$	0.615152	+	1.59879i	0.0207368	+	0.0538953i
$881$			53.5511i			1.80418i	0.431545	+	0.902092i	$0.357969\pi$
$881$			53.5511i			1.80418i	−0.431545	+	0.902092i	$0.642031\pi$
$882$		0			0
$883$	26.7180			0.899131			0.449566	−	0.893247i	$-0.351579\pi$
$883$	26.7180			0.899131			0.449566	+	0.893247i	$0.351579\pi$
$884$	17.6108			0.592315
$885$			0.518242i			0.0174205i
$886$			5.55756i			0.186710i
$887$	9.98396			0.335229			0.167614	−	0.985853i	$-0.446394\pi$
$887$	9.98396			0.335229			0.167614	+	0.985853i	$0.446394\pi$
$888$	−6.34068			−0.212779
$889$		0			0
$890$		−	7.38934i		−	0.247691i
$891$	−3.09541	+	1.19099i	−0.103700	+	0.0398997i
$892$			22.9482i			0.768363i
$893$		−	2.93790i		−	0.0983132i
$894$		−	5.18030i		−	0.173255i
$895$		−	13.2602i		−	0.443240i
$896$		0			0
$897$		−	4.55807i		−	0.152190i
$898$		−	14.7075i		−	0.490797i
$899$	−6.10540			−0.203626
$900$	4.73322			0.157774
$901$	−52.2044			−1.73918
$902$	2.55730	+	6.64648i	0.0851489	+	0.221304i
$903$		0			0
$904$			18.4489i			0.613601i
$905$	−5.57124			−0.185194
$906$			14.8174i			0.492275i
$907$	−17.8142			−0.591510			−0.295755	−	0.955264i	$-0.595571\pi$
$907$	−17.8142			−0.591510			−0.295755	+	0.955264i	$0.595571\pi$
$908$	4.78439			0.158775
$909$	17.0462			0.565385
$910$		0			0
$911$	−11.9803			−0.396925			−0.198463	−	0.980108i	$-0.563595\pi$
$911$	−11.9803			−0.396925			−0.198463	+	0.980108i	$0.563595\pi$
$912$			2.57557i			0.0852857i
$913$	−11.9578	+	4.60088i	−0.395745	+	0.152267i
$914$	31.4706			1.04095
$915$	2.32791			0.0769582
$916$		−	12.8296i		−	0.423901i
$917$		0			0
$918$	7.29986			0.240931
$919$		−	18.5312i		−	0.611287i	−0.952146	−	0.305644i	$-0.901128\pi$
$919$		−	18.5312i		−	0.611287i	0.952146	−	0.305644i	$-0.0988716\pi$
$920$	−0.975866			−0.0321734
$921$			24.2172i			0.797982i
$922$			18.8445i			0.620612i
$923$	21.8483			0.719146
$924$		0			0
$925$	30.0118			0.986783
$926$		−	5.15933i		−	0.169546i
$927$			13.4342i			0.441236i
$928$	−1.33100			−0.0436922
$929$			1.15853i			0.0380101i	0.999819	+	0.0190050i	$0.00604986\pi$
$929$			1.15853i			0.0380101i	−0.999819	+	0.0190050i	$0.993950\pi$
$930$	−2.36925			−0.0776907
$931$		0			0
$932$		−	0.0966329i		−	0.00316532i
$933$	−7.98705			−0.261484
$934$	14.6712			0.480055
$935$	−4.49052	−	11.6709i	−0.146856	−	0.381681i
$936$		−	2.41249i		−	0.0788546i
$937$	−54.5037			−1.78056			−0.890280	−	0.455414i	$-0.849491\pi$
$937$	−54.5037			−1.78056			−0.890280	+	0.455414i	$0.849491\pi$
$938$		0			0
$939$	−6.10743			−0.199309
$940$	0.589166			0.0192165
$941$	19.3839			0.631896			0.315948	−	0.948776i	$-0.397677\pi$
$941$	19.3839			0.631896			0.315948	+	0.948776i	$0.397677\pi$
$942$			0.378604i			0.0123356i
$943$	−4.05686			−0.132110
$944$			1.00336i			0.0326567i
$945$		0			0
$946$	8.30023	−	3.19360i	0.269864	−	0.103833i
$947$	−20.0226			−0.650647			−0.325324	−	0.945603i	$-0.605473\pi$
$947$	−20.0226			−0.650647			−0.325324	+	0.945603i	$0.605473\pi$
$948$	−17.5335			−0.569463
$949$	−14.0458			−0.455947
$950$		−	12.1908i		−	0.395520i
$951$			15.0861i			0.489201i
$952$		0			0
$953$		−	46.5508i		−	1.50793i	−0.656915	−	0.753964i	$-0.728139\pi$
$953$		−	46.5508i		−	1.50793i	0.656915	−	0.753964i	$-0.271861\pi$
$954$			7.15143i			0.231536i
$955$		−	2.79367i		−	0.0904009i
$956$			15.8209i			0.511686i
$957$	−4.11998	+	1.58521i	−0.133180	+	0.0512424i
$958$			26.7570i			0.864480i
$959$		0			0
$960$	−0.516505			−0.0166701
$961$	9.95869			0.321248
$962$		−	15.2968i		−	0.493188i
$963$		−	4.74835i		−	0.153013i
$964$	−14.5518			−0.468682
$965$	−3.51571			−0.113175
$966$		0			0
$967$			26.0366i			0.837280i	0.908152	+	0.418640i	$0.137493\pi$
$967$			26.0366i			0.837280i	−0.908152	+	0.418640i	$0.862507\pi$
$968$	7.37320	+	8.16309i	0.236983	+	0.262372i
$969$		−	18.8013i		−	0.603985i
$970$		−	1.56264i		−	0.0501732i
$971$			39.1267i			1.25564i	0.778360	+	0.627818i	$0.216052\pi$
$971$			39.1267i			1.25564i	−0.778360	+	0.627818i	$0.783948\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		0			0
$974$		−	18.4972i		−	0.592689i
$975$			11.4188i			0.365695i
$976$	4.50704			0.144267
$977$	19.8640			0.635507			0.317753	−	0.948173i	$-0.397072\pi$
$977$	19.8640			0.635507			0.317753	+	0.948173i	$0.397072\pi$
$978$	4.69605			0.150163
$979$	−17.0388	−	44.2842i	−0.544563	−	1.41533i
$980$		0			0
$981$		−	1.61490i		−	0.0515598i
$982$	−11.5475			−0.368497
$983$			22.4112i			0.714805i	0.933950	+	0.357402i	$0.116338\pi$
$983$			22.4112i			0.714805i	−0.933950	+	0.357402i	$0.883662\pi$
$984$	−2.14721			−0.0684505
$985$	−9.98204			−0.318054
$986$	9.71609			0.309423
$987$		0			0
$988$	−6.21353			−0.197679
$989$			5.06628i			0.161098i
$990$	−1.59879	+	0.615152i	−0.0508129	+	0.0195508i
$991$	−26.7246			−0.848935			−0.424467	−	0.905443i	$-0.639539\pi$
$991$	−26.7246			−0.848935			−0.424467	+	0.905443i	$0.639539\pi$
$992$	−4.58708			−0.145640
$993$			7.60617i			0.241375i
$994$		0			0
$995$	−3.63118			−0.115116
$996$		−	3.86307i		−	0.122406i
$997$	−21.2635			−0.673421			−0.336711	−	0.941608i	$-0.609314\pi$
$997$	−21.2635			−0.673421			−0.336711	+	0.941608i	$0.609314\pi$
$998$			26.7968i			0.848239i
$999$		−	6.34068i		−	0.200610i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3234.2.e.c.2155.9	✓	24	7.6	odd	2
3234.2.e.c.2155.16	yes	24	11.10	odd	2
3234.2.e.d.2155.4	yes	24	1.1	even	1	trivial
3234.2.e.d.2155.21	yes	24	77.76	even	2	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:	\( N \)	\(=\)	\( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3234.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -0.516505i q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -0.516505i q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} -0.516505 q^{10} +(-3.09541 + 1.19099i) q^{11} -1.00000i q^{12} +2.41249 q^{13} +0.516505 q^{15} +1.00000 q^{16} -7.29986 q^{17} +1.00000i q^{18} +2.57557 q^{19} +0.516505i q^{20} +(1.19099 + 3.09541i) q^{22} -1.88937 q^{23} -1.00000 q^{24} +4.73322 q^{25} -2.41249i q^{26} -1.00000i q^{27} -1.33100i q^{29} -0.516505i q^{30} -4.58708i q^{31} -1.00000i q^{32} +(-1.19099 - 3.09541i) q^{33} +7.29986i q^{34} +1.00000 q^{36} +6.34068 q^{37} -2.57557i q^{38} +2.41249i q^{39} +0.516505 q^{40} +2.14721 q^{41} -2.68147i q^{43} +(3.09541 - 1.19099i) q^{44} +0.516505i q^{45} +1.88937i q^{46} -1.14068i q^{47} +1.00000i q^{48} -4.73322i q^{50} -7.29986i q^{51} -2.41249 q^{52} +7.15143 q^{53} -1.00000 q^{54} +(0.615152 + 1.59879i) q^{55} +2.57557i q^{57} -1.33100 q^{58} +1.00336i q^{59} -0.516505 q^{60} +4.50704 q^{61} -4.58708 q^{62} -1.00000 q^{64} -1.24606i q^{65} +(-3.09541 + 1.19099i) q^{66} +8.00023 q^{67} +7.29986 q^{68} -1.88937i q^{69} +9.05635 q^{71} -1.00000i q^{72} -5.82214 q^{73} -6.34068i q^{74} +4.73322i q^{75} -2.57557 q^{76} +2.41249 q^{78} -17.5335i q^{79} -0.516505i q^{80} +1.00000 q^{81} -2.14721i q^{82} +3.86307 q^{83} +3.77041i q^{85} -2.68147 q^{86} +1.33100 q^{87} +(-1.19099 - 3.09541i) q^{88} +14.3064i q^{89} +0.516505 q^{90} +1.88937 q^{92} +4.58708 q^{93} -1.14068 q^{94} -1.33029i q^{95} +1.00000 q^{96} +3.02541i q^{97} +(3.09541 - 1.19099i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{4} + 24 q^{6} - 24 q^{9}+O(q^{10}) \) 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

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