LMFDB - Embedded newform 931.2.c.f.930.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(930,931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("931.930");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.c (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:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			930.13
Character	$\chi$	$=$	931.930
Dual form			931.2.c.f.930.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.894152i q^{2} -1.05130 q^{3} +1.20049 q^{4} +0.287796i q^{5} +0.940021i q^{6} -2.86173i q^{8} -1.89477 q^{9} +O(q^{10})$	\(q-0.894152i q^{2} -1.05130 q^{3} +1.20049 q^{4} +0.287796i q^{5} +0.940021i q^{6} -2.86173i q^{8} -1.89477 q^{9} +0.257333 q^{10} -0.476646 q^{11} -1.26208 q^{12} -6.36831 q^{13} -0.302559i q^{15} -0.157837 q^{16} +5.78081i q^{17} +1.69421i q^{18} +(-2.59409 - 3.50296i) q^{19} +0.345496i q^{20} +0.426194i q^{22} -6.52995 q^{23} +3.00853i q^{24} +4.91717 q^{25} +5.69424i q^{26} +5.14587 q^{27} -5.71402i q^{29} -0.270534 q^{30} -4.33215 q^{31} -5.58232i q^{32} +0.501097 q^{33} +5.16892 q^{34} -2.27466 q^{36} -1.40774i q^{37} +(-3.13218 + 2.31951i) q^{38} +6.69500 q^{39} +0.823593 q^{40} -7.44541 q^{41} -7.20284 q^{43} -0.572209 q^{44} -0.545307i q^{45} +5.83877i q^{46} -4.13942i q^{47} +0.165934 q^{48} -4.39670i q^{50} -6.07736i q^{51} -7.64511 q^{52} +8.33078i q^{53} -4.60119i q^{54} -0.137177i q^{55} +(2.72716 + 3.68266i) q^{57} -5.10921 q^{58} +1.92408 q^{59} -0.363220i q^{60} -2.62306i q^{61} +3.87361i q^{62} -5.30712 q^{64} -1.83277i q^{65} -0.448057i q^{66} +6.60473i q^{67} +6.93981i q^{68} +6.86493 q^{69} +12.2159i q^{71} +5.42232i q^{72} +1.31567i q^{73} -1.25873 q^{74} -5.16942 q^{75} +(-3.11418 - 4.20527i) q^{76} -5.98635i q^{78} -11.9972i q^{79} -0.0454249i q^{80} +0.274467 q^{81} +6.65733i q^{82} -0.627610i q^{83} -1.66369 q^{85} +6.44044i q^{86} +6.00715i q^{87} +1.36403i q^{88} -1.54857 q^{89} -0.487588 q^{90} -7.83915 q^{92} +4.55439 q^{93} -3.70127 q^{94} +(1.00814 - 0.746567i) q^{95} +5.86869i q^{96} -1.36169 q^{97} +0.903134 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 40 q^{4} + 40 q^{9}+O(q^{10}) $ 40 * q - 40 * q^4 + 40 * q^9	$ 40 q - 40 q^{4} + 40 q^{9} + 40 q^{16} + 48 q^{23} - 56 q^{25} - 64 q^{30} - 40 q^{36} + 32 q^{39} - 16 q^{43} - 48 q^{57} - 96 q^{58} + 56 q^{64} + 144 q^{74} - 88 q^{81} - 160 q^{85} - 48 q^{92} + 72 q^{95} - 48 q^{99}+O(q^{100}) $ 40 * q - 40 * q^4 + 40 * q^9 + 40 * q^16 + 48 * q^23 - 56 * q^25 - 64 * q^30 - 40 * q^36 + 32 * q^39 - 16 * q^43 - 48 * q^57 - 96 * q^58 + 56 * q^64 + 144 * q^74 - 88 * q^81 - 160 * q^85 - 48 * q^92 + 72 * q^95 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/931\mathbb{Z}\right)^\times$.

$n$	$248$	$344$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	0.894152i		−	0.632261i	−0.948716	−	0.316131i	$-0.897616\pi$
$2$		−	0.894152i		−	0.632261i	0.948716	−	0.316131i	$-0.102384\pi$
$3$	−1.05130			−0.606968			−0.303484	−	0.952837i	$-0.598150\pi$
$3$	−1.05130			−0.606968			−0.303484	+	0.952837i	$0.598150\pi$
$4$	1.20049			0.600246
$5$			0.287796i			0.128706i	0.997927	+	0.0643531i	$0.0204984\pi$
$5$			0.287796i			0.128706i	−0.997927	+	0.0643531i	$0.979502\pi$
$6$			0.940021i			0.383762i
$7$		0			0
$7$		0			0
$8$		−	2.86173i		−	1.01177i
$9$	−1.89477			−0.631590
$10$	0.257333			0.0813759
$11$	−0.476646			−0.143714			−0.0718570	−	0.997415i	$-0.522893\pi$
$11$	−0.476646			−0.143714			−0.0718570	+	0.997415i	$0.522893\pi$
$12$	−1.26208			−0.364330
$13$	−6.36831			−1.76625			−0.883126	−	0.469135i	$-0.844566\pi$
$13$	−6.36831			−1.76625			−0.883126	+	0.469135i	$0.844566\pi$
$14$		0			0
$15$		−	0.302559i		−	0.0781205i
$16$	−0.157837			−0.0394593
$17$			5.78081i			1.40205i	0.713136	+	0.701026i	$0.247274\pi$
$17$			5.78081i			1.40205i	−0.713136	+	0.701026i	$0.752726\pi$
$18$			1.69421i			0.399330i
$19$	−2.59409	−	3.50296i	−0.595124	−	0.803634i
$19$	−2.59409	−	3.50296i	−0.595124	−	0.803634i
$20$			0.345496i			0.0772553i
$21$		0			0
$22$			0.426194i			0.0908648i
$23$	−6.52995			−1.36159			−0.680794	−	0.732475i	$-0.738365\pi$
$23$	−6.52995			−1.36159			−0.680794	+	0.732475i	$0.738365\pi$
$24$			3.00853i			0.614114i
$25$	4.91717			0.983435
$26$			5.69424i			1.11673i
$27$	5.14587			0.990323
$28$		0			0
$29$		−	5.71402i		−	1.06107i	−0.847664	−	0.530534i	$-0.821992\pi$
$29$		−	5.71402i		−	1.06107i	0.847664	−	0.530534i	$-0.178008\pi$
$30$	−0.270534			−0.0493926
$31$	−4.33215			−0.778078			−0.389039	−	0.921221i	$-0.627193\pi$
$31$	−4.33215			−0.778078			−0.389039	+	0.921221i	$0.627193\pi$
$32$		−	5.58232i		−	0.986825i
$33$	0.501097			0.0872298
$34$	5.16892			0.886463
$35$		0			0
$36$	−2.27466			−0.379109
$37$		−	1.40774i		−	0.231430i	−0.993282	−	0.115715i	$-0.963084\pi$
$37$		−	1.40774i		−	0.231430i	0.993282	−	0.115715i	$-0.0369160\pi$
$38$	−3.13218	+	2.31951i	−0.508106	+	0.376274i
$39$	6.69500			1.07206
$40$	0.823593			0.130222
$41$	−7.44541			−1.16278			−0.581389	−	0.813626i	$-0.697490\pi$
$41$	−7.44541			−1.16278			−0.581389	+	0.813626i	$0.697490\pi$
$42$		0			0
$43$	−7.20284			−1.09842			−0.549212	−	0.835683i	$-0.685072\pi$
$43$	−7.20284			−1.09842			−0.549212	+	0.835683i	$0.685072\pi$
$44$	−0.572209			−0.0862638
$45$		−	0.545307i		−	0.0812896i
$46$			5.83877i			0.860879i
$47$		−	4.13942i		−	0.603797i	−0.953340	−	0.301898i	$-0.902380\pi$
$47$		−	4.13942i		−	0.603797i	0.953340	−	0.301898i	$-0.0976203\pi$
$48$	0.165934			0.0239505
$49$		0			0
$50$		−	4.39670i		−	0.621788i
$51$		−	6.07736i		−	0.851000i
$52$	−7.64511			−1.06019
$53$			8.33078i			1.14432i	0.820142	+	0.572161i	$0.193895\pi$
$53$			8.33078i			1.14432i	−0.820142	+	0.572161i	$0.806105\pi$
$54$		−	4.60119i		−	0.626143i
$55$		−	0.137177i		−	0.0184969i
$56$		0			0
$57$	2.72716	+	3.68266i	0.361221	+	0.487780i
$58$	−5.10921			−0.670872
$59$	1.92408			0.250494			0.125247	−	0.992126i	$-0.460028\pi$
$59$	1.92408			0.250494			0.125247	+	0.992126i	$0.460028\pi$
$60$		−	0.363220i		−	0.0468915i
$61$		−	2.62306i		−	0.335848i	−0.985800	−	0.167924i	$-0.946294\pi$
$61$		−	2.62306i		−	0.335848i	0.985800	−	0.167924i	$-0.0537064\pi$
$62$			3.87361i			0.491948i
$63$		0			0
$64$	−5.30712			−0.663390
$65$		−	1.83277i		−	0.227328i
$66$		−	0.448057i		−	0.0551520i
$67$			6.60473i			0.806896i	0.915003	+	0.403448i	$0.132188\pi$
$67$			6.60473i			0.806896i	−0.915003	+	0.403448i	$0.867812\pi$
$68$			6.93981i			0.841575i
$69$	6.86493			0.826440
$70$		0			0
$71$			12.2159i			1.44976i	0.688875	+	0.724880i	$0.258105\pi$
$71$			12.2159i			1.44976i	−0.688875	+	0.724880i	$0.741895\pi$
$72$			5.42232i			0.639026i
$73$			1.31567i			0.153987i	0.997032	+	0.0769937i	$0.0245321\pi$
$73$			1.31567i			0.153987i	−0.997032	+	0.0769937i	$0.975468\pi$
$74$	−1.25873			−0.146324
$75$	−5.16942			−0.596913
$76$	−3.11418	−	4.20527i	−0.357221	−	0.482378i
$77$		0			0
$78$		−	5.98635i		−	0.677821i
$79$		−	11.9972i		−	1.34979i	−0.737914	−	0.674895i	$-0.764189\pi$
$79$		−	11.9972i		−	1.34979i	0.737914	−	0.674895i	$-0.235811\pi$
$80$		−	0.0454249i		−	0.00507866i
$81$	0.274467			0.0304963
$82$			6.65733i			0.735179i
$83$		−	0.627610i		−	0.0688892i	−0.999407	−	0.0344446i	$-0.989034\pi$
$83$		−	0.627610i		−	0.0688892i	0.999407	−	0.0344446i	$-0.0109662\pi$
$84$		0			0
$85$	−1.66369			−0.180453
$86$			6.44044i			0.694490i
$87$			6.00715i			0.644034i
$88$			1.36403i			0.145406i
$89$	−1.54857			−0.164148			−0.0820739	−	0.996626i	$-0.526154\pi$
$89$	−1.54857			−0.164148			−0.0820739	+	0.996626i	$0.526154\pi$
$90$	−0.487588			−0.0513962
$91$		0			0
$92$	−7.83915			−0.817287
$93$	4.55439			0.472268
$94$	−3.70127			−0.381757
$95$	1.00814	−	0.746567i	0.103433	−	0.0765962i
$96$			5.86869i			0.598971i
$97$	−1.36169			−0.138258			−0.0691291	−	0.997608i	$-0.522022\pi$
$97$	−1.36169			−0.138258			−0.0691291	+	0.997608i	$0.522022\pi$
$98$		0			0
$99$	0.903134			0.0907684
$100$	5.90302			0.590302
$101$		−	3.33778i		−	0.332122i	−0.986116	−	0.166061i	$-0.946895\pi$
$101$		−	3.33778i		−	0.332122i	0.986116	−	0.166061i	$-0.0531048\pi$
$102$	−5.43408			−0.538054
$103$	13.7191			1.35178			0.675891	−	0.737002i	$-0.263759\pi$
$103$	13.7191			1.35178			0.675891	+	0.737002i	$0.263759\pi$
$104$			18.2244i			1.78705i
$105$		0			0
$106$	7.44899			0.723510
$107$			6.16644i			0.596132i	0.954545	+	0.298066i	$0.0963416\pi$
$107$			6.16644i			0.596132i	−0.954545	+	0.298066i	$0.903658\pi$
$108$	6.17757			0.594437
$109$		−	12.9643i		−	1.24176i	−0.783906	−	0.620879i	$-0.786776\pi$
$109$		−	12.9643i		−	1.24176i	0.783906	−	0.620879i	$-0.213224\pi$
$110$	−0.122657			−0.0116949
$111$			1.47995i			0.140471i
$112$		0			0
$113$			18.6883i			1.75804i	0.476781	+	0.879022i	$0.341803\pi$
$113$			18.6883i			1.75804i	−0.476781	+	0.879022i	$0.658197\pi$
$114$	3.29286	−	2.43850i	0.308404	−	0.228386i
$115$		−	1.87929i		−	0.175245i
$116$		−	6.85964i		−	0.636901i
$117$	12.0665			1.11555
$118$		−	1.72042i		−	0.158378i
$119$		0			0
$120$	−0.865843			−0.0790403
$121$	−10.7728			−0.979346
$122$	−2.34542			−0.212344
$123$	7.82735			0.705768
$124$	−5.20071			−0.467038
$125$			2.85412i			0.255280i
$126$		0			0
$127$		−	11.3013i		−	1.00282i	−0.865209	−	0.501412i	$-0.832814\pi$
$127$		−	11.3013i		−	1.00282i	0.865209	−	0.501412i	$-0.167186\pi$
$128$		−	6.41927i		−	0.567389i
$129$	7.57234			0.666707
$130$	−1.63878			−0.143730
$131$		−	0.132799i		−	0.0116027i	−0.999983	−	0.00580136i	$-0.998153\pi$
$131$		−	0.132799i		−	0.0116027i	0.999983	−	0.00580136i	$-0.00184664\pi$
$132$	0.601563			0.0523593
$133$		0			0
$134$	5.90564			0.510169
$135$			1.48096i			0.127461i
$136$	16.5431			1.41856
$137$	−19.1020			−1.63200			−0.815999	−	0.578053i	$-0.803813\pi$
$137$	−19.1020			−1.63200			−0.815999	+	0.578053i	$0.803813\pi$
$138$		−	6.13829i		−	0.522526i
$139$		−	17.9635i		−	1.52365i	−0.647786	−	0.761823i	$-0.724305\pi$
$139$		−	17.9635i		−	1.52365i	0.647786	−	0.761823i	$-0.275695\pi$
$140$		0			0
$141$			4.35177i			0.366485i
$142$	10.9229			0.916627
$143$	3.03543			0.253835
$144$	0.299065			0.0249221
$145$	1.64447			0.136566
$146$	1.17641			0.0973603
$147$		0			0
$148$		−	1.68998i		−	0.138915i
$149$	−5.56021			−0.455510			−0.227755	−	0.973718i	$-0.573139\pi$
$149$	−5.56021			−0.455510			−0.227755	+	0.973718i	$0.573139\pi$
$150$			4.62225i			0.377405i
$151$			9.74426i			0.792977i	0.918040	+	0.396488i	$0.129771\pi$
$151$			9.74426i			0.792977i	−0.918040	+	0.396488i	$0.870229\pi$
$152$	−10.0245	+	7.42357i	−0.813095	+	0.602131i
$153$		−	10.9533i		−	0.885522i
$154$		0			0
$155$		−	1.24678i		−	0.100143i
$156$	8.03729			0.643499
$157$		−	22.9325i		−	1.83021i	−0.403214	−	0.915106i	$-0.632107\pi$
$157$		−	22.9325i		−	1.83021i	0.403214	−	0.915106i	$-0.367893\pi$
$158$	−10.7273			−0.853419
$159$		−	8.75814i		−	0.694566i
$160$	1.60657			0.127010
$161$		0			0
$162$		−	0.245415i		−	0.0192816i
$163$	10.7711			0.843658			0.421829	−	0.906675i	$-0.361388\pi$
$163$	10.7711			0.843658			0.421829	+	0.906675i	$0.361388\pi$
$164$	−8.93815			−0.697952
$165$			0.144214i			0.0112270i
$166$	−0.561179			−0.0435560
$167$	−11.0372			−0.854081			−0.427041	−	0.904232i	$-0.640444\pi$
$167$	−11.0372			−0.854081			−0.427041	+	0.904232i	$0.640444\pi$
$168$		0			0
$169$	27.5554			2.11965
$170$			1.48759i			0.114093i
$171$	4.91520	+	6.63730i	0.375875	+	0.507567i
$172$	−8.64695			−0.659324
$173$	8.14801			0.619482			0.309741	−	0.950821i	$-0.399758\pi$
$173$	8.14801			0.619482			0.309741	+	0.950821i	$0.399758\pi$
$174$	5.37131			0.407198
$175$		0			0
$176$	0.0752324			0.00567086
$177$	−2.02279			−0.152042
$178$			1.38466i			0.103784i
$179$		−	9.84400i		−	0.735775i	−0.929870	−	0.367888i	$-0.880081\pi$
$179$		−	9.84400i		−	0.735775i	0.929870	−	0.367888i	$-0.119919\pi$
$180$		−	0.654636i		−	0.0487937i
$181$	−3.29904			−0.245216			−0.122608	−	0.992455i	$-0.539126\pi$
$181$	−3.29904			−0.245216			−0.122608	+	0.992455i	$0.539126\pi$
$182$		0			0
$183$			2.75762i			0.203849i
$184$			18.6869i			1.37762i
$185$	0.405141			0.0297865
$186$		−	4.07232i		−	0.298597i
$187$		−	2.75540i		−	0.201495i
$188$		−	4.96934i		−	0.362426i
$189$		0			0
$190$	−0.667545	−	0.901428i	−0.0484288	−	0.0653965i
$191$	11.3135			0.818615			0.409308	−	0.912396i	$-0.365770\pi$
$191$	11.3135			0.818615			0.409308	+	0.912396i	$0.365770\pi$
$192$	5.57937			0.402657
$193$			15.1882i			1.09327i	0.837370	+	0.546636i	$0.184092\pi$
$193$			15.1882i			1.09327i	−0.837370	+	0.546636i	$0.815908\pi$
$194$			1.21755i			0.0874153i
$195$			1.92679i			0.137981i
$196$		0			0
$197$	10.6450			0.758428			0.379214	−	0.925309i	$-0.376195\pi$
$197$	10.6450			0.758428			0.379214	+	0.925309i	$0.376195\pi$
$198$		−	0.807540i		−	0.0573893i
$199$		−	18.5233i		−	1.31308i	−0.754290	−	0.656541i	$-0.772019\pi$
$199$		−	18.5233i		−	1.31308i	0.754290	−	0.656541i	$-0.227981\pi$
$200$		−	14.0716i		−	0.995013i
$201$		−	6.94355i		−	0.489760i
$202$	−2.98448			−0.209988
$203$		0			0
$204$		−	7.29581i		−	0.510809i
$205$		−	2.14276i		−	0.149657i
$206$		−	12.2670i		−	0.854679i
$207$	12.3727			0.859966
$208$	1.00516			0.0696951
$209$	1.23646	+	1.66967i	0.0855277	+	0.115494i
$210$		0			0
$211$		−	6.64234i		−	0.457277i	−0.973511	−	0.228639i	$-0.926573\pi$
$211$		−	6.64234i		−	0.457277i	0.973511	−	0.228639i	$-0.0734274\pi$
$212$			10.0010i			0.686874i
$213$		−	12.8426i		−	0.879958i
$214$	5.51374			0.376911
$215$		−	2.07295i		−	0.141374i
$216$		−	14.7261i		−	1.00198i
$217$		0			0
$218$	−11.5921			−0.785115
$219$		−	1.38316i		−	0.0934654i
$220$		−	0.164679i		−	0.0111027i
$221$		−	36.8140i		−	2.47638i
$222$	1.32330			0.0888142
$223$	26.9969			1.80785			0.903924	−	0.427692i	$-0.140673\pi$
$223$	26.9969			1.80785			0.903924	+	0.427692i	$0.140673\pi$
$224$		0			0
$225$	−9.31692			−0.621128
$226$	16.7102			1.11154
$227$	21.9842			1.45914			0.729570	−	0.683907i	$-0.239720\pi$
$227$	21.9842			1.45914			0.729570	+	0.683907i	$0.239720\pi$
$228$	3.27393	+	4.42100i	0.216821	+	0.292788i
$229$			9.65067i			0.637734i	0.947799	+	0.318867i	$0.103302\pi$
$229$			9.65067i			0.637734i	−0.947799	+	0.318867i	$0.896698\pi$
$230$	−1.68037			−0.110801
$231$		0			0
$232$	−16.3520			−1.07356
$233$	−10.1216			−0.663090			−0.331545	−	0.943439i	$-0.607570\pi$
$233$	−10.1216			−0.663090			−0.331545	+	0.943439i	$0.607570\pi$
$234$		−	10.7893i		−	0.705318i
$235$	1.19131			0.0777124
$236$	2.30984			0.150358
$237$			12.6126i			0.819279i
$238$		0			0
$239$	26.4382			1.71014			0.855072	−	0.518509i	$-0.173513\pi$
$239$	26.4382			1.71014			0.855072	+	0.518509i	$0.173513\pi$
$240$			0.0477551i			0.00308258i
$241$	−5.74582			−0.370121			−0.185060	−	0.982727i	$-0.559248\pi$
$241$	−5.74582			−0.370121			−0.185060	+	0.982727i	$0.559248\pi$
$242$			9.63253i			0.619203i
$243$	−15.7261			−1.00883
$244$		−	3.14896i		−	0.201592i
$245$		0			0
$246$		−	6.99884i		−	0.446230i
$247$	16.5200	+	22.3079i	1.05114	+	1.41942i
$248$			12.3974i			0.787238i
$249$			0.659806i			0.0418135i
$250$	2.55202			0.161404
$251$			5.77064i			0.364240i	0.983276	+	0.182120i	$0.0582959\pi$
$251$			5.77064i			0.364240i	−0.983276	+	0.182120i	$0.941704\pi$
$252$		0			0
$253$	3.11247			0.195679
$254$	−10.1050			−0.634047
$255$	1.74904			0.109529
$256$	−16.3541			−1.02213
$257$	−22.9519			−1.43170			−0.715851	−	0.698254i	$-0.753961\pi$
$257$	−22.9519			−1.43170			−0.715851	+	0.698254i	$0.753961\pi$
$258$		−	6.77083i		−	0.421533i
$259$		0			0
$260$		−	2.20023i		−	0.136452i
$261$			10.8268i			0.670160i
$262$	−0.118743			−0.00733595
$263$	−4.35688			−0.268657			−0.134328	−	0.990937i	$-0.542888\pi$
$263$	−4.35688			−0.268657			−0.134328	+	0.990937i	$0.542888\pi$
$264$		−	1.43400i		−	0.0882568i
$265$	−2.39756			−0.147281
$266$		0			0
$267$	1.62801			0.0996325
$268$			7.92892i			0.484336i
$269$	−4.17211			−0.254378			−0.127189	−	0.991878i	$-0.540595\pi$
$269$	−4.17211			−0.254378			−0.127189	+	0.991878i	$0.540595\pi$
$270$	1.32420			0.0805884
$271$		−	27.4210i		−	1.66571i	−0.553494	−	0.832853i	$-0.686706\pi$
$271$		−	27.4210i		−	1.66571i	0.553494	−	0.832853i	$-0.313294\pi$
$272$		−	0.912427i		−	0.0553240i
$273$		0			0
$274$			17.0801i			1.03185i
$275$	−2.34375			−0.141333
$276$	8.24129			0.496067
$277$	1.59051			0.0955647			0.0477823	−	0.998858i	$-0.484785\pi$
$277$	1.59051			0.0955647			0.0477823	+	0.998858i	$0.484785\pi$
$278$	−16.0621			−0.963342
$279$	8.20844			0.491426
$280$		0			0
$281$			29.2240i			1.74336i	0.490079	+	0.871678i	$0.336968\pi$
$281$			29.2240i			1.74336i	−0.490079	+	0.871678i	$0.663032\pi$
$282$	3.89114			0.231714
$283$			14.1516i			0.841223i	0.907241	+	0.420612i	$0.138185\pi$
$283$			14.1516i			0.841223i	−0.907241	+	0.420612i	$0.861815\pi$
$284$			14.6651i			0.870212i
$285$	−1.05985	+	0.784865i	−0.0627803	+	0.0464914i
$286$		−	2.71414i		−	0.160490i
$287$		0			0
$288$			10.5772i			0.623269i
$289$	−16.4177			−0.965749
$290$		−	1.47041i		−	0.0863454i
$291$	1.43154			0.0839183
$292$			1.57945i			0.0924303i
$293$	−8.00946			−0.467918			−0.233959	−	0.972246i	$-0.575168\pi$
$293$	−8.00946			−0.467918			−0.233959	+	0.972246i	$0.575168\pi$
$294$		0			0
$295$			0.553743i			0.0322402i
$296$	−4.02856			−0.234155
$297$	−2.45276			−0.142323
$298$			4.97167i			0.288001i
$299$	41.5848			2.40491
$300$	−6.20584			−0.358295
$301$		0			0
$302$	8.71286			0.501369
$303$			3.50900i			0.201587i
$304$	0.409443	+	0.552897i	0.0234832	+	0.0317108i
$305$	0.754906			0.0432258
$306$	−9.79392			−0.559881
$307$	13.3461			0.761701			0.380850	−	0.924637i	$-0.375631\pi$
$307$	13.3461			0.761701			0.380850	+	0.924637i	$0.375631\pi$
$308$		0			0
$309$	−14.4229			−0.820488
$310$	−1.11481			−0.0633168
$311$		−	23.3680i		−	1.32508i	−0.749028	−	0.662538i	$-0.769479\pi$
$311$		−	23.3680i		−	1.32508i	0.749028	−	0.662538i	$-0.230521\pi$
$312$		−	19.1593i		−	1.08468i
$313$		−	22.3409i		−	1.26278i	−0.775465	−	0.631391i	$-0.782484\pi$
$313$		−	22.3409i		−	1.26278i	0.775465	−	0.631391i	$-0.217516\pi$
$314$	−20.5051			−1.15717
$315$		0			0
$316$		−	14.4025i		−	0.810205i
$317$		−	5.65624i		−	0.317686i	−0.987304	−	0.158843i	$-0.949224\pi$
$317$		−	5.65624i		−	0.317686i	0.987304	−	0.158843i	$-0.0507764\pi$
$318$	−7.83112			−0.439147
$319$			2.72356i			0.152490i
$320$		−	1.52737i		−	0.0853824i
$321$		−	6.48277i		−	0.361833i
$322$		0			0
$323$	20.2499	−	14.9959i	1.12674	−	0.834395i
$324$	0.329495			0.0183053
$325$	−31.3141			−1.73699
$326$		−	9.63101i		−	0.533412i
$327$			13.6294i			0.753707i
$328$			21.3067i			1.17647i
$329$		0			0
$330$	0.128949			0.00709841
$331$		−	26.3130i		−	1.44630i	−0.690693	−	0.723148i	$-0.742695\pi$
$331$		−	26.3130i		−	1.44630i	0.690693	−	0.723148i	$-0.257305\pi$
$332$		−	0.753441i		−	0.0413504i
$333$			2.66734i			0.146169i
$334$			9.86891i			0.540003i
$335$	−1.90081			−0.103853
$336$		0			0
$337$		−	23.8906i		−	1.30141i	−0.759333	−	0.650703i	$-0.774474\pi$
$337$		−	23.8906i		−	1.30141i	0.759333	−	0.650703i	$-0.225526\pi$
$338$		−	24.6388i		−	1.34017i
$339$		−	19.6470i		−	1.06708i
$340$	−1.99725			−0.108316
$341$	2.06490			0.111821
$342$	5.93476	−	4.39494i	0.320915	−	0.237651i
$343$		0			0
$344$			20.6126i			1.11136i
$345$			1.97570i			0.106368i
$346$		−	7.28556i		−	0.391674i
$347$	−6.91563			−0.371250			−0.185625	−	0.982621i	$-0.559431\pi$
$347$	−6.91563			−0.371250			−0.185625	+	0.982621i	$0.559431\pi$
$348$			7.21153i			0.386579i
$349$			13.1300i			0.702831i	0.936220	+	0.351416i	$0.114300\pi$
$349$			13.1300i			0.702831i	−0.936220	+	0.351416i	$0.885700\pi$
$350$		0			0
$351$	−32.7705			−1.74916
$352$			2.66079i			0.141821i
$353$			21.3978i			1.13889i	0.822030	+	0.569445i	$0.192842\pi$
$353$			21.3978i			1.13889i	−0.822030	+	0.569445i	$0.807158\pi$
$354$			1.80868i			0.0961302i
$355$	−3.51568			−0.186593
$356$	−1.85904			−0.0985291
$357$		0			0
$358$	−8.80204			−0.465202
$359$	−11.0195			−0.581589			−0.290795	−	0.956786i	$-0.593920\pi$
$359$	−11.0195			−0.581589			−0.290795	+	0.956786i	$0.593920\pi$
$360$	−1.56052			−0.0822466
$361$	−5.54144	+	18.1740i	−0.291655	+	0.956524i
$362$			2.94985i			0.155041i
$363$	11.3254			0.594432
$364$		0			0
$365$	−0.378644			−0.0198191
$366$	2.46573			0.128886
$367$			24.8826i			1.29886i	0.760420	+	0.649432i	$0.224993\pi$
$367$			24.8826i			1.29886i	−0.760420	+	0.649432i	$0.775007\pi$
$368$	1.03067			0.0537273
$369$	14.1073			0.734399
$370$		−	0.362257i		−	0.0188329i
$371$		0			0
$372$	5.46750			0.283477
$373$			5.98108i			0.309689i	0.987939	+	0.154844i	$0.0494876\pi$
$373$			5.98108i			0.309689i	−0.987939	+	0.154844i	$0.950512\pi$
$374$	−2.46374			−0.127397
$375$		−	3.00053i		−	0.154947i
$376$	−11.8459			−0.610905
$377$			36.3887i			1.87411i
$378$		0			0
$379$		−	3.98456i		−	0.204673i	−0.994750	−	0.102336i	$-0.967368\pi$
$379$		−	3.98456i		−	0.204673i	0.994750	−	0.102336i	$-0.0326318\pi$
$380$	1.21026	−	0.896247i	0.0620850	−	0.0459765i
$381$			11.8810i			0.608682i
$382$		−	10.1160i		−	0.517579i
$383$	−10.1843			−0.520394			−0.260197	−	0.965556i	$-0.583787\pi$
$383$	−10.1843			−0.520394			−0.260197	+	0.965556i	$0.583787\pi$
$384$			6.74857i			0.344387i
$385$		0			0
$386$	13.5806			0.691234
$387$	13.6477			0.693753
$388$	−1.63469			−0.0829889
$389$	−11.1175			−0.563679			−0.281840	−	0.959462i	$-0.590945\pi$
$389$	−11.1175			−0.563679			−0.281840	+	0.959462i	$0.590945\pi$
$390$	1.72285			0.0872398
$391$		−	37.7484i		−	1.90902i
$392$		0			0
$393$			0.139612i			0.00704248i
$394$		−	9.51829i		−	0.479524i
$395$	3.45274			0.173726
$396$	1.08420			0.0544833
$397$			31.6326i			1.58759i	0.608182	+	0.793797i	$0.291899\pi$
$397$			31.6326i			1.58759i	−0.608182	+	0.793797i	$0.708101\pi$
$398$	−16.5627			−0.830211
$399$		0			0
$400$	−0.776113			−0.0388057
$401$		−	18.2180i		−	0.909763i	−0.890552	−	0.454881i	$-0.849682\pi$
$401$		−	18.2180i		−	0.909763i	0.890552	−	0.454881i	$-0.150318\pi$
$402$	−6.20859			−0.309656
$403$	27.5885			1.37428
$404$		−	4.00698i		−	0.199355i
$405$			0.0789903i			0.00392506i
$406$		0			0
$407$			0.670991i			0.0332598i
$408$	−17.3917			−0.861019
$409$	−5.32484			−0.263296			−0.131648	−	0.991297i	$-0.542027\pi$
$409$	−5.32484			−0.263296			−0.131648	+	0.991297i	$0.542027\pi$
$410$	−1.91595			−0.0946221
$411$	20.0820			0.990570
$412$	16.4696			0.811401
$413$		0			0
$414$		−	11.0631i		−	0.543723i
$415$	0.180624			0.00886647
$416$			35.5500i			1.74298i
$417$			18.8850i			0.924803i
$418$	1.49294	−	1.10558i	0.0730221	−	0.0540759i
$419$		−	8.09389i		−	0.395412i	−0.980261	−	0.197706i	$-0.936651\pi$
$419$		−	8.09389i		−	0.395412i	0.980261	−	0.197706i	$-0.0633492\pi$
$420$		0			0
$421$			25.4935i			1.24248i	0.783621	+	0.621239i	$0.213371\pi$
$421$			25.4935i			1.24248i	−0.783621	+	0.621239i	$0.786629\pi$
$422$	−5.93926			−0.289119
$423$			7.84325i			0.381352i
$424$	23.8404			1.15779
$425$			28.4252i			1.37883i
$426$	−11.4832			−0.556363
$427$		0			0
$428$			7.40276i			0.357826i
$429$	−3.19114			−0.154070
$430$	−1.85353			−0.0893852
$431$			6.42429i			0.309447i	0.987958	+	0.154724i	$0.0494487\pi$
$431$			6.42429i			0.309447i	−0.987958	+	0.154724i	$0.950551\pi$
$432$	−0.812209			−0.0390774
$433$	−24.2261			−1.16423			−0.582115	−	0.813106i	$-0.697775\pi$
$433$	−24.2261			−1.16423			−0.582115	+	0.813106i	$0.697775\pi$
$434$		0			0
$435$	−1.72883			−0.0828911
$436$		−	15.5636i		−	0.745360i
$437$	16.9392	+	22.8741i	0.810314	+	1.09422i
$438$	−1.23676			−0.0590946
$439$	−1.83390			−0.0875272			−0.0437636	−	0.999042i	$-0.513935\pi$
$439$	−1.83390			−0.0875272			−0.0437636	+	0.999042i	$0.513935\pi$
$440$	−0.392562			−0.0187147
$441$		0			0
$442$	−32.9173			−1.56572
$443$	−10.7024			−0.508486			−0.254243	−	0.967140i	$-0.581826\pi$
$443$	−10.7024			−0.508486			−0.254243	+	0.967140i	$0.581826\pi$
$444$			1.77667i			0.0843170i
$445$		−	0.445671i		−	0.0211268i
$446$		−	24.1394i		−	1.14303i
$447$	5.84544			0.276480
$448$		0			0
$449$		−	19.6699i		−	0.928278i	−0.885762	−	0.464139i	$-0.846364\pi$
$449$		−	19.6699i		−	0.928278i	0.885762	−	0.464139i	$-0.153636\pi$
$450$			8.33074i			0.392715i
$451$	3.54882			0.167107
$452$			22.4351i			1.05526i
$453$		−	10.2441i		−	0.481311i
$454$		−	19.6572i		−	0.922557i
$455$		0			0
$456$	10.5388	−	7.80439i	0.493523	−	0.365474i
$457$	−9.41737			−0.440526			−0.220263	−	0.975440i	$-0.570692\pi$
$457$	−9.41737			−0.440526			−0.220263	+	0.975440i	$0.570692\pi$
$458$	8.62917			0.403215
$459$			29.7473i			1.38848i
$460$		−	2.25607i		−	0.105190i
$461$			28.3908i			1.32229i	0.750258	+	0.661145i	$0.229929\pi$
$461$			28.3908i			1.32229i	−0.750258	+	0.661145i	$0.770071\pi$
$462$		0			0
$463$	−25.1625			−1.16940			−0.584700	−	0.811250i	$-0.698788\pi$
$463$	−25.1625			−1.16940			−0.584700	+	0.811250i	$0.698788\pi$
$464$			0.901886i			0.0418690i
$465$			1.31073i			0.0607838i
$466$			9.05028i			0.419246i
$467$			16.5448i			0.765603i	0.923831	+	0.382801i	$0.125041\pi$
$467$			16.5448i			0.765603i	−0.923831	+	0.382801i	$0.874959\pi$
$468$	14.4857			0.669603
$469$		0			0
$470$		−	1.06521i		−	0.0491345i
$471$			24.1089i			1.11088i
$472$		−	5.50620i		−	0.253443i
$473$	3.43320			0.157859
$474$	11.2776			0.517998
$475$	−12.7556	−	17.2247i	−0.585266	−	0.790321i
$476$		0			0
$477$		−	15.7849i		−	0.722742i
$478$		−	23.6398i		−	1.08126i
$479$		−	6.50563i		−	0.297250i	−0.988894	−	0.148625i	$-0.952515\pi$
$479$		−	6.50563i		−	0.297250i	0.988894	−	0.148625i	$-0.0474847\pi$
$480$	−1.68898			−0.0770913
$481$			8.96491i			0.408765i
$482$			5.13764i			0.234013i
$483$		0			0
$484$	−12.9327			−0.587848
$485$		−	0.391888i		−	0.0177947i
$486$			14.0616i			0.637846i
$487$		−	5.66098i		−	0.256524i	−0.991740	−	0.128262i	$-0.959060\pi$
$487$		−	5.66098i		−	0.256524i	0.991740	−	0.128262i	$-0.0409398\pi$
$488$	−7.50648			−0.339802
$489$	−11.3237			−0.512073
$490$		0			0
$491$	−19.0570			−0.860031			−0.430015	−	0.902822i	$-0.641492\pi$
$491$	−19.0570			−0.860031			−0.430015	+	0.902822i	$0.641492\pi$
$492$	9.39666			0.423634
$493$	33.0317			1.48767
$494$	19.9467	−	14.7714i	0.897444	−	0.664595i
$495$			0.259918i			0.0116825i
$496$	0.683775			0.0307024
$497$		0			0
$498$	0.589967			0.0264371
$499$	1.04094			0.0465990			0.0232995	−	0.999729i	$-0.492583\pi$
$499$	1.04094			0.0465990			0.0232995	+	0.999729i	$0.492583\pi$
$500$			3.42635i			0.153231i
$501$	11.6034			0.518400
$502$	5.15983			0.230295
$503$			23.5048i			1.04803i	0.851710	+	0.524013i	$0.175566\pi$
$503$			23.5048i			1.04803i	−0.851710	+	0.524013i	$0.824434\pi$
$504$		0			0
$505$	0.960599			0.0427461
$506$		−	2.78302i		−	0.123720i
$507$	−28.9690			−1.28656
$508$		−	13.5671i		−	0.601941i
$509$	18.8500			0.835511			0.417755	−	0.908560i	$-0.362817\pi$
$509$	18.8500			0.835511			0.417755	+	0.908560i	$0.362817\pi$
$510$		−	1.56391i		−	0.0692509i
$511$		0			0
$512$			1.78447i			0.0788633i
$513$	−13.3488	−	18.0258i	−0.589365	−	0.795857i
$514$			20.5225i			0.905209i
$515$			3.94830i			0.173983i
$516$	9.09053			0.400188
$517$			1.97304i			0.0867741i
$518$		0			0
$519$	−8.56599			−0.376005
$520$	−5.24490			−0.230004
$521$	−28.9707			−1.26923			−0.634614	−	0.772829i	$-0.718841\pi$
$521$	−28.9707			−1.26923			−0.634614	+	0.772829i	$0.718841\pi$
$522$	9.68078			0.423716
$523$	−9.96451			−0.435718			−0.217859	−	0.975980i	$-0.569907\pi$
$523$	−9.96451			−0.435718			−0.217859	+	0.975980i	$0.569907\pi$
$524$		−	0.159424i		−	0.00696449i
$525$		0			0
$526$			3.89571i			0.169861i
$527$		−	25.0433i		−	1.09091i
$528$	−0.0790918			−0.00344203
$529$	19.6402			0.853922
$530$			2.14379i			0.0931202i
$531$	−3.64570			−0.158210
$532$		0			0
$533$	47.4147			2.05376
$534$		−	1.45569i		−	0.0629937i
$535$	−1.77468			−0.0767259
$536$	18.9009			0.816396
$537$			10.3490i			0.446592i
$538$			3.73050i			0.160833i
$539$		0			0
$540$			1.77788i			0.0765077i
$541$	−9.24358			−0.397412			−0.198706	−	0.980059i	$-0.563674\pi$
$541$	−9.24358			−0.397412			−0.198706	+	0.980059i	$0.563674\pi$
$542$	−24.5185			−1.05316
$543$	3.46828			0.148838
$544$	32.2703			1.38358
$545$	3.73108			0.159822
$546$		0			0
$547$		−	34.8556i		−	1.49032i	−0.666887	−	0.745158i	$-0.732374\pi$
$547$		−	34.8556i		−	1.49032i	0.666887	−	0.745158i	$-0.267626\pi$
$548$	−22.9318			−0.979600
$549$			4.97010i			0.212119i
$550$			2.09567i			0.0893596i
$551$	−20.0160	+	14.8227i	−0.852710	+	0.631467i
$552$		−	19.6455i		−	0.836170i
$553$		0			0
$554$		−	1.42216i		−	0.0604218i
$555$	−0.425924			−0.0180795
$556$		−	21.5650i		−	0.914562i
$557$	−37.0565			−1.57014			−0.785068	−	0.619409i	$-0.787372\pi$
$557$	−37.0565			−1.57014			−0.785068	+	0.619409i	$0.787372\pi$
$558$		−	7.33959i		−	0.310710i
$559$	45.8700			1.94009
$560$		0			0
$561$			2.89675i			0.122301i
$562$	26.1307			1.10226
$563$	−14.6009			−0.615355			−0.307678	−	0.951491i	$-0.599552\pi$
$563$	−14.6009			−0.615355			−0.307678	+	0.951491i	$0.599552\pi$
$564$			5.22426i			0.219981i
$565$	−5.37840			−0.226271
$566$	12.6537			0.531873
$567$		0			0
$568$	34.9586			1.46683
$569$		−	16.2923i		−	0.683008i	−0.939880	−	0.341504i	$-0.889064\pi$
$569$		−	16.2923i		−	0.683008i	0.939880	−	0.341504i	$-0.110936\pi$
$570$	0.701789	+	0.947670i	0.0293947	+	0.0396935i
$571$	13.5537			0.567207			0.283603	−	0.958942i	$-0.408470\pi$
$571$	13.5537			0.567207			0.283603	+	0.958942i	$0.408470\pi$
$572$	3.64401			0.152364
$573$	−11.8939			−0.496873
$574$		0			0
$575$	−32.1089			−1.33903
$576$	10.0558			0.418991
$577$			33.5046i			1.39481i	0.716675	+	0.697407i	$0.245663\pi$
$577$			33.5046i			1.39481i	−0.716675	+	0.697407i	$0.754337\pi$
$578$			14.6799i			0.610605i
$579$		−	15.9674i		−	0.663581i
$580$	1.97417			0.0819731
$581$		0			0
$582$		−	1.28001i		−	0.0530583i
$583$		−	3.97083i		−	0.164455i
$584$	3.76509			0.155800
$585$			3.47269i			0.143578i
$586$			7.16168i			0.295846i
$587$		−	23.4332i		−	0.967190i	−0.875292	−	0.483595i	$-0.839331\pi$
$587$		−	23.4332i		−	0.967190i	0.875292	−	0.483595i	$-0.160669\pi$
$588$		0			0
$589$	11.2380	+	15.1754i	0.463053	+	0.625290i
$590$	0.495131			0.0203842
$591$	−11.1911			−0.460341
$592$			0.222193i			0.00913208i
$593$		−	41.2003i		−	1.69189i	−0.533266	−	0.845947i	$-0.679036\pi$
$593$		−	41.2003i		−	1.69189i	0.533266	−	0.845947i	$-0.320964\pi$
$594$			2.19314i			0.0899855i
$595$		0			0
$596$	−6.67498			−0.273418
$597$			19.4735i			0.796998i
$598$		−	37.1831i		−	1.52053i
$599$			24.4612i			0.999458i	0.866182	+	0.499729i	$0.166567\pi$
$599$			24.4612i			0.999458i	−0.866182	+	0.499729i	$0.833433\pi$
$600$			14.7935i			0.603941i
$601$	−24.4746			−0.998340			−0.499170	−	0.866504i	$-0.666362\pi$
$601$	−24.4746			−0.998340			−0.499170	+	0.866504i	$0.666362\pi$
$602$		0			0
$603$		−	12.5144i		−	0.509628i
$604$			11.6979i			0.475981i
$605$		−	3.10037i		−	0.126048i
$606$	3.13759			0.127456
$607$	−36.5191			−1.48226			−0.741132	−	0.671359i	$-0.765711\pi$
$607$	−36.5191			−1.48226			−0.741132	+	0.671359i	$0.765711\pi$
$608$	−19.5546	+	14.4810i	−0.793046	+	0.587283i
$609$		0			0
$610$		−	0.675001i		−	0.0273300i
$611$			26.3611i			1.06646i
$612$		−	13.1493i		−	0.531531i
$613$	−32.2097			−1.30094			−0.650468	−	0.759534i	$-0.725427\pi$
$613$	−32.2097			−1.30094			−0.650468	+	0.759534i	$0.725427\pi$
$614$		−	11.9334i		−	0.481594i
$615$			2.25268i			0.0908367i
$616$		0			0
$617$	−34.7646			−1.39957			−0.699785	−	0.714354i	$-0.746721\pi$
$617$	−34.7646			−1.39957			−0.699785	+	0.714354i	$0.746721\pi$
$618$			12.8962i			0.518763i
$619$			39.0342i			1.56892i	0.620183	+	0.784458i	$0.287059\pi$
$619$			39.0342i			1.56892i	−0.620183	+	0.784458i	$0.712941\pi$
$620$		−	1.49674i		−	0.0601107i
$621$	−33.6022			−1.34841
$622$	−20.8945			−0.837795
$623$		0			0
$624$	−1.05672			−0.0423027
$625$	23.7645			0.950579
$626$	−19.9762			−0.798408
$627$	−1.29989	−	1.75532i	−0.0519126	−	0.0701008i
$628$		−	27.5303i		−	1.09858i
$629$	8.13785			0.324477
$630$		0			0
$631$	−28.8349			−1.14790			−0.573950	−	0.818890i	$-0.694590\pi$
$631$	−28.8349			−1.14790			−0.573950	+	0.818890i	$0.694590\pi$
$632$	−34.3327			−1.36568
$633$			6.98308i			0.277553i
$634$	−5.05754			−0.200861
$635$	3.25245			0.129070
$636$		−	10.5141i		−	0.416910i
$637$		0			0
$638$	2.43528			0.0964137
$639$		−	23.1463i		−	0.915654i
$640$	1.84744			0.0730265
$641$		−	39.8990i		−	1.57591i	−0.615730	−	0.787957i	$-0.711139\pi$
$641$		−	39.8990i		−	1.57591i	0.615730	−	0.787957i	$-0.288861\pi$
$642$	−5.79658			−0.228773
$643$			20.5969i			0.812263i	0.913815	+	0.406132i	$0.133123\pi$
$643$			20.5969i			0.812263i	−0.913815	+	0.406132i	$0.866877\pi$
$644$		0			0
$645$			2.17929i			0.0858094i
$646$	−13.4086	−	18.1065i	−0.527555	−	0.712392i
$647$			2.14499i			0.0843284i	0.999111	+	0.0421642i	$0.0134253\pi$
$647$			2.14499i			0.0843284i	−0.999111	+	0.0421642i	$0.986575\pi$
$648$		−	0.785448i		−	0.0308553i
$649$	−0.917106			−0.0359996
$650$			27.9996i			1.09823i
$651$		0			0
$652$	12.9306			0.506402
$653$	16.7636			0.656012			0.328006	−	0.944676i	$-0.393623\pi$
$653$	16.7636			0.656012			0.328006	+	0.944676i	$0.393623\pi$
$654$	12.1868			0.476540
$655$	0.0382191			0.00149334
$656$	1.17516			0.0458824
$657$		−	2.49289i		−	0.0972570i
$658$		0			0
$659$			41.1006i			1.60105i	0.599297	+	0.800527i	$0.295447\pi$
$659$			41.1006i			1.60105i	−0.599297	+	0.800527i	$0.704553\pi$
$660$			0.173127i			0.00673897i
$661$	18.2152			0.708488			0.354244	−	0.935153i	$-0.384738\pi$
$661$	18.2152			0.708488			0.354244	+	0.935153i	$0.384738\pi$
$662$	−23.5279			−0.914437
$663$			38.7025i			1.50308i
$664$	−1.79605			−0.0697003
$665$		0			0
$666$	2.38501			0.0924171
$667$			37.3123i			1.44474i
$668$	−13.2500			−0.512659
$669$	−28.3819			−1.09731
$670$			1.69962i			0.0656619i
$671$			1.25027i			0.0482661i
$672$		0			0
$673$		−	35.7582i		−	1.37838i	−0.724581	−	0.689189i	$-0.757967\pi$
$673$		−	35.7582i		−	1.37838i	0.724581	−	0.689189i	$-0.242033\pi$
$674$	−21.3619			−0.822828
$675$	25.3031			0.973918
$676$	33.0801			1.27231
$677$	−32.5080			−1.24938			−0.624691	−	0.780872i	$-0.714775\pi$
$677$	−32.5080			−1.24938			−0.624691	+	0.780872i	$0.714775\pi$
$678$	−17.5674			−0.674671
$679$		0			0
$680$			4.76103i			0.182577i
$681$	−23.1119			−0.885650
$682$		−	1.84634i		−	0.0706999i
$683$		−	17.0666i		−	0.653036i	−0.945191	−	0.326518i	$-0.894125\pi$
$683$		−	17.0666i		−	0.653036i	0.945191	−	0.326518i	$-0.105875\pi$
$684$	5.90065	+	7.96803i	0.225617	+	0.304665i
$685$		−	5.49749i		−	0.210048i
$686$		0			0
$687$		−	10.1457i		−	0.387084i
$688$	1.13688			0.0433430
$689$		−	53.0531i		−	2.02116i
$690$	1.76657			0.0672523
$691$		−	21.2596i		−	0.808755i	−0.914592	−	0.404378i	$-0.867488\pi$
$691$		−	21.2596i		−	0.808755i	0.914592	−	0.404378i	$-0.132512\pi$
$692$	9.78161			0.371841
$693$		0			0
$694$			6.18362i			0.234727i
$695$	5.16982			0.196103
$696$	17.1908			0.651616
$697$		−	43.0405i		−	1.63027i
$698$	11.7402			0.444373
$699$	10.6409			0.402474
$700$		0			0
$701$	47.7171			1.80225			0.901126	−	0.433558i	$-0.142742\pi$
$701$	47.7171			1.80225			0.901126	+	0.433558i	$0.142742\pi$
$702$			29.3018i			1.10593i
$703$	−4.93124	+	3.65179i	−0.185985	+	0.137730i
$704$	2.52962			0.0953385
$705$	−1.25242			−0.0471689
$706$	19.1329			0.720076
$707$		0			0
$708$	−2.42834			−0.0912625
$709$	−4.80626			−0.180503			−0.0902514	−	0.995919i	$-0.528767\pi$
$709$	−4.80626			−0.180503			−0.0902514	+	0.995919i	$0.528767\pi$
$710$			3.14356i			0.117976i
$711$			22.7319i			0.852514i
$712$			4.43158i			0.166080i
$713$	28.2887			1.05942
$714$		0			0
$715$			0.873584i			0.0326702i
$716$		−	11.8176i		−	0.441646i
$717$	−27.7945			−1.03800
$718$			9.85315i			0.367716i
$719$		−	28.0706i		−	1.04686i	−0.852070	−	0.523428i	$-0.824653\pi$
$719$		−	28.0706i		−	1.04686i	0.852070	−	0.523428i	$-0.175347\pi$
$720$			0.0860697i			0.00320763i
$721$		0			0
$722$	16.2503	+	4.95489i	0.604773	+	0.184402i
$723$	6.04057			0.224651
$724$	−3.96047			−0.147190
$725$		−	28.0968i		−	1.04349i
$726$		−	10.1267i		−	0.375836i
$727$			11.6510i			0.432111i	0.976381	+	0.216055i	$0.0693192\pi$
$727$			11.6510i			0.432111i	−0.976381	+	0.216055i	$0.930681\pi$
$728$		0			0
$729$	15.7095			0.581833
$730$			0.338566i			0.0125309i
$731$		−	41.6382i		−	1.54005i
$732$			3.31050i			0.122360i
$733$			0.852572i			0.0314905i	0.999876	+	0.0157452i	$0.00501207\pi$
$733$			0.852572i			0.0314905i	−0.999876	+	0.0157452i	$0.994988\pi$
$734$	22.2489			0.821221
$735$		0			0
$736$			36.4523i			1.34365i
$737$		−	3.14812i		−	0.115962i
$738$		−	12.6141i		−	0.464332i
$739$	24.9187			0.916648			0.458324	−	0.888785i	$-0.348450\pi$
$739$	24.9187			0.916648			0.458324	+	0.888785i	$0.348450\pi$
$740$	0.486368			0.0178792
$741$	−17.3674	−	23.4523i	−0.638008	−	0.861542i
$742$		0			0
$743$			13.5921i			0.498646i	0.968420	+	0.249323i	$0.0802080\pi$
$743$			13.5921i			0.498646i	−0.968420	+	0.249323i	$0.919792\pi$
$744$		−	13.0334i		−	0.477828i
$745$		−	1.60020i		−	0.0586269i
$746$	5.34800			0.195804
$747$			1.18918i			0.0435097i
$748$		−	3.30783i		−	0.120946i
$749$		0			0
$750$	−2.68294			−0.0979669
$751$			30.6873i			1.11980i	0.828561	+	0.559898i	$0.189160\pi$
$751$			30.6873i			1.11980i	−0.828561	+	0.559898i	$0.810840\pi$
$752$			0.653355i			0.0238254i
$753$		−	6.06667i		−	0.221082i
$754$	32.5370			1.18493
$755$	−2.80436			−0.102061
$756$		0			0
$757$	−33.7950			−1.22830			−0.614150	−	0.789189i	$-0.710501\pi$
$757$	−33.7950			−1.22830			−0.614150	+	0.789189i	$0.710501\pi$
$758$	−3.56280			−0.129407
$759$	−3.27214			−0.118771
$760$	−2.13647	−	2.88501i	−0.0774980	−	0.104650i
$761$			32.9743i			1.19532i	0.801751	+	0.597658i	$0.203902\pi$
$761$			32.9743i			1.19532i	−0.801751	+	0.597658i	$0.796098\pi$
$762$	10.6234			0.384846
$763$		0			0
$764$	13.5817			0.491370
$765$	3.15231			0.113972
$766$			9.10632i			0.329025i
$767$	−12.2532			−0.442436
$768$	17.1930			0.620399
$769$			39.5435i			1.42598i	0.701176	+	0.712988i	$0.252659\pi$
$769$			39.5435i			1.42598i	−0.701176	+	0.712988i	$0.747341\pi$
$770$		0			0
$771$	24.1293			0.868996
$772$			18.2333i			0.656232i
$773$	19.7882			0.711733			0.355866	−	0.934537i	$-0.384186\pi$
$773$	19.7882			0.711733			0.355866	+	0.934537i	$0.384186\pi$
$774$		−	12.2032i		−	0.438633i
$775$	−21.3020			−0.765189
$776$			3.89677i			0.139886i
$777$		0			0
$778$			9.94073i			0.356393i
$779$	19.3140	+	26.0809i	0.691997	+	0.934447i
$780$			2.31310i			0.0828222i
$781$		−	5.82265i		−	0.208351i
$782$	−33.7528			−1.20700
$783$		−	29.4036i		−	1.05080i
$784$		0			0
$785$	6.59987			0.235560
$786$	0.124834			0.00445269
$787$	17.4422			0.621748			0.310874	−	0.950451i	$-0.399378\pi$
$787$	17.4422			0.621748			0.310874	+	0.950451i	$0.399378\pi$
$788$	12.7793			0.455243
$789$	4.58038			0.163066
$790$		−	3.08728i		−	0.109840i
$791$		0			0
$792$		−	2.58452i		−	0.0918371i
$793$			16.7045i			0.593193i
$794$	28.2844			1.00377
$795$	2.52056			0.0893950
$796$		−	22.2371i		−	0.788172i
$797$	−23.8795			−0.845854			−0.422927	−	0.906164i	$-0.638997\pi$
$797$	−23.8795			−0.845854			−0.422927	+	0.906164i	$0.638997\pi$
$798$		0			0
$799$	23.9292			0.846554
$800$		−	27.4493i		−	0.970478i
$801$	2.93418			0.103674
$802$	−16.2897			−0.575208
$803$		−	0.627108i		−	0.0221302i
$804$		−	8.33567i		−	0.293976i
$805$		0			0
$806$		−	24.6683i		−	0.868905i
$807$	4.38613			0.154399
$808$	−9.55182			−0.336032
$809$	−16.5380			−0.581446			−0.290723	−	0.956807i	$-0.593896\pi$
$809$	−16.5380			−0.581446			−0.290723	+	0.956807i	$0.593896\pi$
$810$	0.0706294			0.00248166
$811$	−35.1379			−1.23386			−0.616930	−	0.787018i	$-0.711624\pi$
$811$	−35.1379			−1.23386			−0.616930	+	0.787018i	$0.711624\pi$
$812$		0			0
$813$			28.8277i			1.01103i
$814$	0.599969			0.0210289
$815$			3.09988i			0.108584i
$816$			0.959233i			0.0335799i
$817$	18.6848	+	25.2313i	0.653698	+	0.882730i
$818$			4.76122i			0.166472i
$819$		0			0
$820$		−	2.57236i		−	0.0898307i
$821$	50.1320			1.74962			0.874809	−	0.484468i	$-0.160987\pi$
$821$	50.1320			1.74962			0.874809	+	0.484468i	$0.160987\pi$
$822$		−	17.9563i		−	0.626299i
$823$	−6.18009			−0.215424			−0.107712	−	0.994182i	$-0.534353\pi$
$823$	−6.18009			−0.215424			−0.107712	+	0.994182i	$0.534353\pi$
$824$		−	39.2603i		−	1.36770i
$825$	2.46398			0.0857848
$826$		0			0
$827$		−	39.4829i		−	1.37296i	−0.727151	−	0.686478i	$-0.759156\pi$
$827$		−	39.4829i		−	1.37296i	0.727151	−	0.686478i	$-0.240844\pi$
$828$	14.8534			0.516191
$829$	−14.3404			−0.498063			−0.249031	−	0.968495i	$-0.580112\pi$
$829$	−14.3404			−0.498063			−0.249031	+	0.968495i	$0.580112\pi$
$830$		−	0.161505i		−	0.00560592i
$831$	−1.67210			−0.0580047
$832$	33.7974			1.17171
$833$		0			0
$834$	16.8861			0.584717
$835$		−	3.17645i		−	0.109926i
$836$	1.48436	+	2.00442i	0.0513376	+	0.0693245i
$837$	−22.2927			−0.770548
$838$	−7.23717			−0.250004
$839$	−38.1902			−1.31847			−0.659237	−	0.751935i	$-0.729121\pi$
$839$	−38.1902			−1.31847			−0.659237	+	0.751935i	$0.729121\pi$
$840$		0			0
$841$	−3.65007			−0.125864
$842$	22.7951			0.785571
$843$		−	30.7231i		−	1.05816i
$844$		−	7.97407i		−	0.274479i
$845$			7.93034i			0.272812i
$846$	7.01306			0.241114
$847$		0			0
$848$		−	1.31491i		−	0.0451541i
$849$		−	14.8775i		−	0.510595i
$850$	25.4165			0.871778
$851$			9.19244i			0.315113i
$852$		−	15.4174i		−	0.528191i
$853$		−	42.6408i		−	1.45999i	−0.683450	−	0.729997i	$-0.739521\pi$
$853$		−	42.6408i		−	1.45999i	0.683450	−	0.729997i	$-0.260479\pi$
$854$		0			0
$855$	−1.91019	+	1.41457i	−0.0653270	+	0.0483774i
$856$	17.6467			0.603151
$857$	31.4764			1.07521			0.537607	−	0.843196i	$-0.319329\pi$
$857$	31.4764			1.07521			0.537607	+	0.843196i	$0.319329\pi$
$858$			2.85337i			0.0974124i
$859$		−	11.2260i		−	0.383025i	−0.981490	−	0.191512i	$-0.938661\pi$
$859$		−	11.2260i		−	0.383025i	0.981490	−	0.191512i	$-0.0613392\pi$
$860$		−	2.48856i		−	0.0848591i
$861$		0			0
$862$	5.74430			0.195652
$863$			23.3451i			0.794677i	0.917672	+	0.397338i	$0.130066\pi$
$863$			23.3451i			0.794677i	−0.917672	+	0.397338i	$0.869934\pi$
$864$		−	28.7259i		−	0.977275i
$865$			2.34496i			0.0797311i
$866$			21.6618i			0.736097i
$867$	17.2599			0.586178
$868$		0			0
$869$			5.71841i			0.193984i
$870$			1.54584i			0.0524089i
$871$		−	42.0610i		−	1.42518i
$872$	−37.1004			−1.25638
$873$	2.58008			0.0873226
$874$	20.4530	−	15.1463i	0.691832	−	0.512330i
$875$		0			0
$876$		−	1.66047i		−	0.0561022i
$877$		−	0.0818845i		−	0.00276504i	−0.999999	−	0.00138252i	$-0.999560\pi$
$877$		−	0.0818845i		−	0.00276504i	0.999999	−	0.00138252i	$-0.000440071\pi$
$878$			1.63979i			0.0553401i
$879$	8.42034			0.284011
$880$			0.0216516i			0.000729875i
$881$		−	4.56861i		−	0.153920i	−0.997034	−	0.0769602i	$-0.975479\pi$
$881$		−	4.56861i		−	0.153920i	0.997034	−	0.0769602i	$-0.0245215\pi$
$882$		0			0
$883$	−38.5387			−1.29693			−0.648466	−	0.761244i	$-0.724589\pi$
$883$	−38.5387			−1.29693			−0.648466	+	0.761244i	$0.724589\pi$
$884$		−	44.1949i		−	1.48643i
$885$		−	0.582149i		−	0.0195687i
$886$			9.56956i			0.321496i
$887$	18.6266			0.625421			0.312710	−	0.949849i	$-0.398763\pi$
$887$	18.6266			0.625421			0.312710	+	0.949849i	$0.398763\pi$
$888$	4.23522			0.142125
$889$		0			0
$890$	−0.398498			−0.0133577
$891$	−0.130823			−0.00438275
$892$	32.4096			1.08515
$893$	−14.5002	+	10.7380i	−0.485231	+	0.359334i
$894$		−	5.22671i		−	0.174807i
$895$	2.83306			0.0946989
$896$		0			0
$897$	−43.7180			−1.45970
$898$	−17.5878			−0.586914
$899$			24.7540i			0.825593i
$900$	−11.1849			−0.372829
$901$	−48.1587			−1.60440
$902$		−	3.17319i		−	0.105656i
$903$		0			0
$904$	53.4807			1.77874
$905$		−	0.949451i		−	0.0315608i
$906$	−9.15982			−0.304315
$907$			25.4288i			0.844348i	0.906515	+	0.422174i	$0.138733\pi$
$907$			25.4288i			0.844348i	−0.906515	+	0.422174i	$0.861267\pi$
$908$	26.3918			0.875842
$909$			6.32433i			0.209765i
$910$		0			0
$911$		−	20.7634i		−	0.687921i	−0.938984	−	0.343961i	$-0.888231\pi$
$911$		−	20.7634i		−	0.687921i	0.938984	−	0.343961i	$-0.111769\pi$
$912$	−0.430447	−	0.581260i	−0.0142535	−	0.0192475i
$913$			0.299148i			0.00990035i
$914$			8.42057i			0.278528i
$915$	−0.793631			−0.0262366
$916$			11.5855i			0.382797i
$917$		0			0
$918$	26.5986			0.877884
$919$	22.9121			0.755802			0.377901	−	0.925846i	$-0.376646\pi$
$919$	22.9121			0.755802			0.377901	+	0.925846i	$0.376646\pi$
$920$	−5.37802			−0.177308
$921$	−14.0307			−0.462328
$922$	25.3857			0.836033
$923$		−	77.7947i		−	2.56064i
$924$		0			0
$925$		−	6.92208i		−	0.227597i
$926$			22.4991i			0.739366i
$927$	−25.9945			−0.853772
$928$	−31.8975			−1.04709
$929$			34.4030i			1.12872i	0.825527	+	0.564362i	$0.190878\pi$
$929$			34.4030i			1.12872i	−0.825527	+	0.564362i	$0.809122\pi$
$930$	1.17200			0.0384313
$931$		0			0
$932$	−12.1509			−0.398017
$933$			24.5667i			0.804279i
$934$	14.7936			0.484061
$935$	0.792992			0.0259336
$936$		−	34.5310i		−	1.12868i
$937$			27.7349i			0.906058i	0.891496	+	0.453029i	$0.149657\pi$
$937$			27.7349i			0.906058i	−0.891496	+	0.453029i	$0.850343\pi$
$938$		0			0
$939$			23.4870i			0.766468i
$940$	1.43016			0.0466465
$941$	55.0846			1.79571			0.897853	−	0.440296i	$-0.145126\pi$
$941$	55.0846			1.79571			0.897853	+	0.440296i	$0.145126\pi$
$942$	21.5570			0.702366
$943$	48.6181			1.58322
$944$	−0.303692			−0.00988433
$945$		0			0
$946$		−	3.06981i		−	0.0998081i
$947$	58.8166			1.91128			0.955641	−	0.294533i	$-0.0951642\pi$
$947$	58.8166			1.91128			0.955641	+	0.294533i	$0.0951642\pi$
$948$			15.1414i			0.491768i
$949$		−	8.37860i		−	0.271981i
$950$	−15.4015	+	11.4054i	−0.499690	+	0.370041i
$951$			5.94640i			0.192825i
$952$		0			0
$953$		−	3.64330i		−	0.118018i	−0.998257	−	0.0590090i	$-0.981206\pi$
$953$		−	3.64330i		−	0.118018i	0.998257	−	0.0590090i	$-0.0187941\pi$
$954$	−14.1141			−0.456962
$955$			3.25597i			0.105361i
$956$	31.7388			1.02651
$957$		−	2.86328i		−	0.0925567i
$958$	−5.81702			−0.187940
$959$		0			0
$960$			1.60572i			0.0518244i
$961$	−12.2324			−0.394595
$962$	8.01599			0.258446
$963$		−	11.6840i		−	0.376511i
$964$	−6.89781			−0.222163
$965$	−4.37111			−0.140711
$966$		0			0
$967$	0.538006			0.0173011			0.00865055	−	0.999963i	$-0.497246\pi$
$967$	0.538006			0.0173011			0.00865055	+	0.999963i	$0.497246\pi$
$968$			30.8288i			0.990876i
$969$	−21.2887	+	15.7652i	−0.683892	+	0.506451i
$970$	−0.350407			−0.0112509
$971$	54.0781			1.73545			0.867725	−	0.497045i	$-0.165582\pi$
$971$	54.0781			1.73545			0.867725	+	0.497045i	$0.165582\pi$
$972$	−18.8791			−0.605548
$973$		0			0
$974$	−5.06178			−0.162190
$975$	32.9205			1.05430
$976$			0.414016i			0.0132523i
$977$		−	45.9604i		−	1.47040i	−0.677848	−	0.735202i	$-0.737087\pi$
$977$		−	45.9604i		−	1.47040i	0.677848	−	0.735202i	$-0.262913\pi$
$978$			10.1251i			0.323764i
$979$	0.738118			0.0235904
$980$		0			0
$981$			24.5644i			0.784282i
$982$			17.0399i			0.543764i
$983$	−8.52319			−0.271848			−0.135924	−	0.990719i	$-0.543400\pi$
$983$	−8.52319			−0.271848			−0.135924	+	0.990719i	$0.543400\pi$
$984$		−	22.3997i		−	0.714077i
$985$			3.06360i			0.0976143i
$986$		−	29.5353i		−	0.940597i
$987$		0			0
$988$	19.8321	+	26.7805i	0.630942	+	0.852001i
$989$	47.0342			1.49560
$990$	0.232407			0.00738636
$991$		−	46.2815i		−	1.47018i	−0.677969	−	0.735091i	$-0.737139\pi$
$991$		−	46.2815i		−	1.47018i	0.677969	−	0.735091i	$-0.262861\pi$
$992$			24.1835i			0.767826i
$993$			27.6629i			0.877855i
$994$		0			0
$995$	5.33093			0.169002
$996$			0.792092i			0.0250984i
$997$		−	26.6116i		−	0.842797i	−0.906876	−	0.421398i	$-0.861539\pi$
$997$		−	26.6116i		−	0.842797i	0.906876	−	0.421398i	$-0.138461\pi$
$998$		−	0.930762i		−	0.0294627i
$999$		−	7.24402i		−	0.229191i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.c.f.930.13	✓	40
7.2	even	3		931.2.o.i.227.14		80
7.3	odd	6		931.2.o.i.607.27		80
7.4	even	3		931.2.o.i.607.28		80
7.5	odd	6		931.2.o.i.227.13		80
7.6	odd	2	inner	931.2.c.f.930.14	yes	40
19.18	odd	2	inner	931.2.c.f.930.28	yes	40
133.18	odd	6		931.2.o.i.607.13		80
133.37	odd	6		931.2.o.i.227.27		80
133.75	even	6		931.2.o.i.227.28		80
133.94	even	6		931.2.o.i.607.14		80
133.132	even	2	inner	931.2.c.f.930.27	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
931.2.c.f.930.13	✓	40	1.1	even	1	trivial
931.2.c.f.930.14	yes	40	7.6	odd	2	inner
931.2.c.f.930.27	yes	40	133.132	even	2	inner
931.2.c.f.930.28	yes	40	19.18	odd	2	inner
931.2.o.i.227.13		80	7.5	odd	6
931.2.o.i.227.14		80	7.2	even	3
931.2.o.i.227.27		80	133.37	odd	6
931.2.o.i.227.28		80	133.75	even	6
931.2.o.i.607.13		80	133.18	odd	6
931.2.o.i.607.14		80	133.94	even	6
931.2.o.i.607.27		80	7.3	odd	6
931.2.o.i.607.28		80	7.4	even	3

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:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.894152i q^{2} -1.05130 q^{3} +1.20049 q^{4} +0.287796i q^{5} +0.940021i q^{6} -2.86173i q^{8} -1.89477 q^{9} +O(q^{10})\)	\(q-0.894152i q^{2} -1.05130 q^{3} +1.20049 q^{4} +0.287796i q^{5} +0.940021i q^{6} -2.86173i q^{8} -1.89477 q^{9} +0.257333 q^{10} -0.476646 q^{11} -1.26208 q^{12} -6.36831 q^{13} -0.302559i q^{15} -0.157837 q^{16} +5.78081i q^{17} +1.69421i q^{18} +(-2.59409 - 3.50296i) q^{19} +0.345496i q^{20} +0.426194i q^{22} -6.52995 q^{23} +3.00853i q^{24} +4.91717 q^{25} +5.69424i q^{26} +5.14587 q^{27} -5.71402i q^{29} -0.270534 q^{30} -4.33215 q^{31} -5.58232i q^{32} +0.501097 q^{33} +5.16892 q^{34} -2.27466 q^{36} -1.40774i q^{37} +(-3.13218 + 2.31951i) q^{38} +6.69500 q^{39} +0.823593 q^{40} -7.44541 q^{41} -7.20284 q^{43} -0.572209 q^{44} -0.545307i q^{45} +5.83877i q^{46} -4.13942i q^{47} +0.165934 q^{48} -4.39670i q^{50} -6.07736i q^{51} -7.64511 q^{52} +8.33078i q^{53} -4.60119i q^{54} -0.137177i q^{55} +(2.72716 + 3.68266i) q^{57} -5.10921 q^{58} +1.92408 q^{59} -0.363220i q^{60} -2.62306i q^{61} +3.87361i q^{62} -5.30712 q^{64} -1.83277i q^{65} -0.448057i q^{66} +6.60473i q^{67} +6.93981i q^{68} +6.86493 q^{69} +12.2159i q^{71} +5.42232i q^{72} +1.31567i q^{73} -1.25873 q^{74} -5.16942 q^{75} +(-3.11418 - 4.20527i) q^{76} -5.98635i q^{78} -11.9972i q^{79} -0.0454249i q^{80} +0.274467 q^{81} +6.65733i q^{82} -0.627610i q^{83} -1.66369 q^{85} +6.44044i q^{86} +6.00715i q^{87} +1.36403i q^{88} -1.54857 q^{89} -0.487588 q^{90} -7.83915 q^{92} +4.55439 q^{93} -3.70127 q^{94} +(1.00814 - 0.746567i) q^{95} +5.86869i q^{96} -1.36169 q^{97} +0.903134 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{4} + 40 q^{9}+O(q^{10}) \) 40 * q - 40 * q^4 + 40 * q^9	\( 40 q - 40 q^{4} + 40 q^{9} + 40 q^{16} + 48 q^{23} - 56 q^{25} - 64 q^{30} - 40 q^{36} + 32 q^{39} - 16 q^{43} - 48 q^{57} - 96 q^{58} + 56 q^{64} + 144 q^{74} - 88 q^{81} - 160 q^{85} - 48 q^{92} + 72 q^{95} - 48 q^{99}+O(q^{100}) \) 40 * q - 40 * q^4 + 40 * q^9 + 40 * q^16 + 48 * q^23 - 56 * q^25 - 64 * q^30 - 40 * q^36 + 32 * q^39 - 16 * q^43 - 48 * q^57 - 96 * q^58 + 56 * q^64 + 144 * q^74 - 88 * q^81 - 160 * q^85 - 48 * q^92 + 72 * q^95 - 48 * q^99

Introduction

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Modular forms

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