LMFDB - Embedded newform 2254.2.c.c.2253.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2254,2,Mod(2253,2254)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2254, 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("2254.2253");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2254 = 2 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2254.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:	$17.9982806156$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 18x^{14} + 226x^{12} + 1434x^{10} + 6585x^{8} + 14406x^{6} + 22423x^{4} + 8085x^{2} + 2401 $ x^16 + 18x^14 + 226x^12 + 1434x^10 + 6585x^8 + 14406x^6 + 22423x^4 + 8085*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{8}\cdot 7^{2} $
Twist minimal:	no (minimal twist has level 322)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2253.3
Root			$1.52769 - 2.64604i$ of defining polynomial
Character	$\chi$	$=$	2254.2253
Dual form			2254.2.c.c.2253.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.14817i q^{3} +1.00000 q^{4} -0.528453 q^{5} -2.14817i q^{6} +1.00000 q^{8} -1.61463 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.14817i q^{3} +1.00000 q^{4} -0.528453 q^{5} -2.14817i q^{6} +1.00000 q^{8} -1.61463 q^{9} -0.528453 q^{10} +2.05052i q^{11} -2.14817i q^{12} -3.70082i q^{13} +1.13521i q^{15} +1.00000 q^{16} -6.89954 q^{17} -1.61463 q^{18} -0.528453 q^{19} -0.528453 q^{20} +2.05052i q^{22} +(-4.33536 - 2.05052i) q^{23} -2.14817i q^{24} -4.72074 q^{25} -3.70082i q^{26} -2.97601i q^{27} +3.68928 q^{29} +1.13521i q^{30} -4.94479i q^{31} +1.00000 q^{32} +4.40485 q^{33} -6.89954 q^{34} -1.61463 q^{36} -8.66983i q^{37} -0.528453 q^{38} -7.94999 q^{39} -0.528453 q^{40} -3.70082i q^{41} -8.98453i q^{43} +2.05052i q^{44} +0.853256 q^{45} +(-4.33536 - 2.05052i) q^{46} +1.96877i q^{47} -2.14817i q^{48} -4.72074 q^{50} +14.8214i q^{51} -3.70082i q^{52} +13.6862i q^{53} -2.97601i q^{54} -1.08360i q^{55} +1.13521i q^{57} +3.68928 q^{58} -5.77702i q^{59} +1.13521i q^{60} -5.84264 q^{61} -4.94479i q^{62} +1.00000 q^{64} +1.95571i q^{65} +4.40485 q^{66} -0.820506i q^{67} -6.89954 q^{68} +(-4.40485 + 9.31309i) q^{69} +1.03146 q^{71} -1.61463 q^{72} -4.94479i q^{73} -8.66983i q^{74} +10.1409i q^{75} -0.528453 q^{76} -7.94999 q^{78} +11.9504i q^{79} -0.528453 q^{80} -11.2369 q^{81} -3.70082i q^{82} +16.4544 q^{83} +3.64609 q^{85} -8.98453i q^{86} -7.92519i q^{87} +2.05052i q^{88} +7.63165 q^{89} +0.853256 q^{90} +(-4.33536 - 2.05052i) q^{92} -10.6222 q^{93} +1.96877i q^{94} +0.279263 q^{95} -2.14817i q^{96} -11.1402 q^{97} -3.31082i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 16 q^{4} + 16 q^{8} - 20 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 + 16 * q^4 + 16 * q^8 - 20 * q^9	$ 16 q + 16 q^{2} + 16 q^{4} + 16 q^{8} - 20 q^{9} + 16 q^{16} - 20 q^{18} + 8 q^{23} - 4 q^{25} + 16 q^{29} + 16 q^{32} - 20 q^{36} - 44 q^{39} + 8 q^{46} - 4 q^{50} + 16 q^{58} + 16 q^{64} - 12 q^{71} - 20 q^{72} - 44 q^{78} + 72 q^{81} + 24 q^{85} + 8 q^{92} + 76 q^{93} + 76 q^{95}+O(q^{100}) $ 16 * q + 16 * q^2 + 16 * q^4 + 16 * q^8 - 20 * q^9 + 16 * q^16 - 20 * q^18 + 8 * q^23 - 4 * q^25 + 16 * q^29 + 16 * q^32 - 20 * q^36 - 44 * q^39 + 8 * q^46 - 4 * q^50 + 16 * q^58 + 16 * q^64 - 12 * q^71 - 20 * q^72 - 44 * q^78 + 72 * q^81 + 24 * q^85 + 8 * q^92 + 76 * q^93 + 76 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2254\mathbb{Z}\right)^\times$.

$n$	$1473$	$1569$
$\chi(n)$	$-1$	$-1$

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		−	2.14817i		−	1.24025i	−0.784505	−	0.620123i	$-0.787083\pi$
$3$		−	2.14817i		−	1.24025i	0.784505	−	0.620123i	$-0.212917\pi$
$4$	1.00000			0.500000
$5$	−0.528453			−0.236332			−0.118166	−	0.992994i	$-0.537701\pi$
$5$	−0.528453			−0.236332			−0.118166	+	0.992994i	$0.537701\pi$
$6$		−	2.14817i		−	0.876986i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−1.61463			−0.538209
$10$	−0.528453			−0.167112
$11$			2.05052i			0.618254i	0.951021	+	0.309127i	$0.100037\pi$
$11$			2.05052i			0.618254i	−0.951021	+	0.309127i	$0.899963\pi$
$12$		−	2.14817i		−	0.620123i
$13$		−	3.70082i		−	1.02642i	−0.858262	−	0.513212i	$-0.828456\pi$
$13$		−	3.70082i		−	1.02642i	0.858262	−	0.513212i	$-0.171544\pi$
$14$		0			0
$15$			1.13521i			0.293109i
$16$	1.00000			0.250000
$17$	−6.89954			−1.67338			−0.836692	−	0.547673i	$-0.815514\pi$
$17$	−6.89954			−1.67338			−0.836692	+	0.547673i	$0.815514\pi$
$18$	−1.61463			−0.380571
$19$	−0.528453			−0.121236			−0.0606178	−	0.998161i	$-0.519307\pi$
$19$	−0.528453			−0.121236			−0.0606178	+	0.998161i	$0.519307\pi$
$20$	−0.528453			−0.118166
$21$		0			0
$22$			2.05052i			0.437171i
$23$	−4.33536	−	2.05052i	−0.903986	−	0.427562i
$23$	−4.33536	−	2.05052i	−0.903986	−	0.427562i
$24$		−	2.14817i		−	0.438493i
$25$	−4.72074			−0.944147
$26$		−	3.70082i		−	0.725791i
$27$		−	2.97601i		−	0.572734i
$28$		0			0
$29$	3.68928			0.685082			0.342541	−	0.939503i	$-0.388713\pi$
$29$	3.68928			0.685082			0.342541	+	0.939503i	$0.388713\pi$
$30$			1.13521i			0.207260i
$31$		−	4.94479i		−	0.888110i	−0.896000	−	0.444055i	$-0.853540\pi$
$31$		−	4.94479i		−	0.888110i	0.896000	−	0.444055i	$-0.146460\pi$
$32$	1.00000			0.176777
$33$	4.40485			0.766786
$34$	−6.89954			−1.18326
$35$		0			0
$36$	−1.61463			−0.269105
$37$		−	8.66983i		−	1.42531i	−0.701514	−	0.712656i	$-0.747492\pi$
$37$		−	8.66983i		−	1.42531i	0.701514	−	0.712656i	$-0.252508\pi$
$38$	−0.528453			−0.0857265
$39$	−7.94999			−1.27302
$40$	−0.528453			−0.0835558
$41$		−	3.70082i		−	0.577972i	−0.957333	−	0.288986i	$-0.906682\pi$
$41$		−	3.70082i		−	0.577972i	0.957333	−	0.288986i	$-0.0933180\pi$
$42$		0			0
$43$		−	8.98453i		−	1.37013i	−0.728483	−	0.685064i	$-0.759774\pi$
$43$		−	8.98453i		−	1.37013i	0.728483	−	0.685064i	$-0.240226\pi$
$44$			2.05052i			0.309127i
$45$	0.853256			0.127196
$46$	−4.33536	−	2.05052i	−0.639215	−	0.302332i
$47$			1.96877i			0.287175i	0.989638	+	0.143588i	$0.0458639\pi$
$47$			1.96877i			0.287175i	−0.989638	+	0.143588i	$0.954136\pi$
$48$		−	2.14817i		−	0.310061i
$49$		0			0
$50$	−4.72074			−0.667613
$51$			14.8214i			2.07541i
$52$		−	3.70082i		−	0.513212i
$53$			13.6862i			1.87994i	0.341257	+	0.939970i	$0.389147\pi$
$53$			13.6862i			1.87994i	−0.341257	+	0.939970i	$0.610853\pi$
$54$		−	2.97601i		−	0.404984i
$55$		−	1.08360i		−	0.146113i
$56$		0			0
$57$			1.13521i			0.150362i
$58$	3.68928			0.484426
$59$		−	5.77702i		−	0.752104i	−0.926599	−	0.376052i	$-0.877281\pi$
$59$		−	5.77702i		−	0.752104i	0.926599	−	0.376052i	$-0.122719\pi$
$60$			1.13521i			0.146555i
$61$	−5.84264			−0.748073			−0.374036	−	0.927414i	$-0.622026\pi$
$61$	−5.84264			−0.748073			−0.374036	+	0.927414i	$0.622026\pi$
$62$		−	4.94479i		−	0.627988i
$63$		0			0
$64$	1.00000			0.125000
$65$			1.95571i			0.242576i
$66$	4.40485			0.542200
$67$		−	0.820506i		−	0.100241i	−0.998743	−	0.0501204i	$-0.984040\pi$
$67$		−	0.820506i		−	0.100241i	0.998743	−	0.0501204i	$-0.0159605\pi$
$68$	−6.89954			−0.836692
$69$	−4.40485	+	9.31309i	−0.530282	+	1.12116i
$70$		0			0
$71$	1.03146			0.122412			0.0612059	−	0.998125i	$-0.480505\pi$
$71$	1.03146			0.122412			0.0612059	+	0.998125i	$0.480505\pi$
$72$	−1.61463			−0.190286
$73$		−	4.94479i		−	0.578743i	−0.957217	−	0.289372i	$-0.906554\pi$
$73$		−	4.94479i		−	0.578743i	0.957217	−	0.289372i	$-0.0934464\pi$
$74$		−	8.66983i		−	1.00785i
$75$			10.1409i			1.17097i
$76$	−0.528453			−0.0606178
$77$		0			0
$78$	−7.94999			−0.900159
$79$			11.9504i			1.34452i	0.740315	+	0.672260i	$0.234676\pi$
$79$			11.9504i			1.34452i	−0.740315	+	0.672260i	$0.765324\pi$
$80$	−0.528453			−0.0590829
$81$	−11.2369			−1.24854
$82$		−	3.70082i		−	0.408688i
$83$	16.4544			1.80610			0.903051	−	0.429533i	$-0.141322\pi$
$83$	16.4544			1.80610			0.903051	+	0.429533i	$0.141322\pi$
$84$		0			0
$85$	3.64609			0.395474
$86$		−	8.98453i		−	0.968827i
$87$		−	7.92519i		−	0.849669i
$88$			2.05052i			0.218586i
$89$	7.63165			0.808953			0.404476	−	0.914548i	$-0.367454\pi$
$89$	7.63165			0.808953			0.404476	+	0.914548i	$0.367454\pi$
$90$	0.853256			0.0899410
$91$		0			0
$92$	−4.33536	−	2.05052i	−0.451993	−	0.213781i
$93$	−10.6222			−1.10147
$94$			1.96877i			0.203063i
$95$	0.279263			0.0286518
$96$		−	2.14817i		−	0.219247i
$97$	−11.1402			−1.13112			−0.565558	−	0.824709i	$-0.691339\pi$
$97$	−11.1402			−1.13112			−0.565558	+	0.824709i	$0.691339\pi$
$98$		0			0
$99$		−	3.31082i		−	0.332750i
$100$	−4.72074			−0.472074
$101$		−	2.98040i		−	0.296561i	−0.988945	−	0.148281i	$-0.952626\pi$
$101$		−	2.98040i		−	0.296561i	0.988945	−	0.148281i	$-0.0473739\pi$
$102$			14.8214i			1.46754i
$103$	−1.76259			−0.173673			−0.0868363	−	0.996223i	$-0.527676\pi$
$103$	−1.76259			−0.173673			−0.0868363	+	0.996223i	$0.527676\pi$
$104$		−	3.70082i		−	0.362896i
$105$		0			0
$106$			13.6862i			1.32932i
$107$		−	8.88973i		−	0.859403i	−0.902971	−	0.429701i	$-0.858619\pi$
$107$		−	8.88973i		−	0.859403i	0.902971	−	0.429701i	$-0.141381\pi$
$108$		−	2.97601i		−	0.286367i
$109$		−	6.93402i		−	0.664159i	−0.943251	−	0.332079i	$-0.892250\pi$
$109$		−	6.93402i		−	0.664159i	0.943251	−	0.332079i	$-0.107750\pi$
$110$		−	1.08360i		−	0.103317i
$111$	−18.6243			−1.76774
$112$		0			0
$113$			5.00860i			0.471169i	0.971854	+	0.235585i	$0.0757005\pi$
$113$			5.00860i			0.471169i	−0.971854	+	0.235585i	$0.924299\pi$
$114$			1.13521i			0.106322i
$115$	2.29104	+	1.08360i	0.213640	+	0.101046i
$116$	3.68928			0.342541
$117$			5.97545i			0.552431i
$118$		−	5.77702i		−	0.531818i
$119$		0			0
$120$			1.13521i			0.103630i
$121$	6.79539			0.617762
$122$	−5.84264			−0.528967
$123$	−7.94999			−0.716827
$124$		−	4.94479i		−	0.444055i
$125$	5.13696			0.459463
$126$		0			0
$127$	−3.31072			−0.293779			−0.146890	−	0.989153i	$-0.546926\pi$
$127$	−3.31072			−0.293779			−0.146890	+	0.989153i	$0.546926\pi$
$128$	1.00000			0.0883883
$129$	−19.3003			−1.69930
$130$			1.95571i			0.171527i
$131$			16.3341i			1.42711i	0.700597	+	0.713557i	$0.252917\pi$
$131$			16.3341i			1.42711i	−0.700597	+	0.713557i	$0.747083\pi$
$132$	4.40485			0.383393
$133$		0			0
$134$		−	0.820506i		−	0.0708809i
$135$			1.57268i			0.135355i
$136$	−6.89954			−0.591631
$137$		−	9.80504i		−	0.837701i	−0.908055	−	0.418851i	$-0.862433\pi$
$137$		−	9.80504i		−	0.837701i	0.908055	−	0.418851i	$-0.137567\pi$
$138$	−4.40485	+	9.31309i	−0.374966	+	0.792783i
$139$			18.4468i			1.56464i	0.622879	+	0.782318i	$0.285963\pi$
$139$			18.4468i			1.56464i	−0.622879	+	0.782318i	$0.714037\pi$
$140$		0			0
$141$	4.22926			0.356168
$142$	1.03146			0.0865582
$143$	7.58860			0.634590
$144$	−1.61463			−0.134552
$145$	−1.94961			−0.161906
$146$		−	4.94479i		−	0.409233i
$147$		0			0
$148$		−	8.66983i		−	0.712656i
$149$		−	4.10103i		−	0.335970i	−0.985790	−	0.167985i	$-0.946274\pi$
$149$		−	4.10103i		−	0.335970i	0.985790	−	0.167985i	$-0.0537259\pi$
$150$			10.1409i			0.828004i
$151$	1.77074			0.144101			0.0720506	−	0.997401i	$-0.477046\pi$
$151$	1.77074			0.144101			0.0720506	+	0.997401i	$0.477046\pi$
$152$	−0.528453			−0.0428632
$153$	11.1402			0.900631
$154$		0			0
$155$			2.61309i			0.209888i
$156$	−7.94999			−0.636509
$157$	7.46744			0.595967			0.297983	−	0.954571i	$-0.403686\pi$
$157$	7.46744			0.595967			0.297983	+	0.954571i	$0.403686\pi$
$158$			11.9504i			0.950719i
$159$	29.4002			2.33159
$160$	−0.528453			−0.0417779
$161$		0			0
$162$	−11.2369			−0.882851
$163$	−5.61463			−0.439772			−0.219886	−	0.975526i	$-0.570568\pi$
$163$	−5.61463			−0.439772			−0.219886	+	0.975526i	$0.570568\pi$
$164$		−	3.70082i		−	0.288986i
$165$	−2.32776			−0.181216
$166$	16.4544			1.27711
$167$			4.65513i			0.360225i	0.983646	+	0.180112i	$0.0576461\pi$
$167$			4.65513i			0.360225i	−0.983646	+	0.180112i	$0.942354\pi$
$168$		0			0
$169$	−0.696095			−0.0535458
$170$	3.64609			0.279642
$171$	0.853256			0.0652501
$172$		−	8.98453i		−	0.685064i
$173$			14.7858i			1.12414i	0.827088	+	0.562072i	$0.189996\pi$
$173$			14.7858i			1.12414i	−0.827088	+	0.562072i	$0.810004\pi$
$174$		−	7.92519i		−	0.600807i
$175$		0			0
$176$			2.05052i			0.154563i
$177$	−12.4100			−0.932794
$178$	7.63165			0.572016
$179$	3.38537			0.253035			0.126517	−	0.991964i	$-0.459620\pi$
$179$	3.38537			0.253035			0.126517	+	0.991964i	$0.459620\pi$
$180$	0.853256			0.0635979
$181$	10.2869			0.764622			0.382311	−	0.924034i	$-0.375128\pi$
$181$	10.2869			0.764622			0.382311	+	0.924034i	$0.375128\pi$
$182$		0			0
$183$			12.5510i			0.927794i
$184$	−4.33536	−	2.05052i	−0.319607	−	0.151166i
$185$			4.58160i			0.336846i
$186$	−10.6222			−0.778860
$187$		−	14.1476i		−	1.03458i
$188$			1.96877i			0.143588i
$189$		0			0
$190$	0.279263			0.0202599
$191$		−	3.88113i		−	0.280829i	−0.990093	−	0.140414i	$-0.955157\pi$
$191$		−	3.88113i		−	0.280829i	0.990093	−	0.140414i	$-0.0448435\pi$
$192$		−	2.14817i		−	0.155031i
$193$	13.6954			0.985814			0.492907	−	0.870082i	$-0.335934\pi$
$193$	13.6954			0.985814			0.492907	+	0.870082i	$0.335934\pi$
$194$	−11.1402			−0.799819
$195$	4.20120			0.300854
$196$		0			0
$197$	20.4976			1.46039			0.730196	−	0.683238i	$-0.239429\pi$
$197$	20.4976			1.46039			0.730196	+	0.683238i	$0.239429\pi$
$198$		−	3.31082i		−	0.235290i
$199$	−20.8857			−1.48054			−0.740272	−	0.672307i	$-0.765303\pi$
$199$	−20.8857			−1.48054			−0.740272	+	0.672307i	$0.765303\pi$
$200$	−4.72074			−0.333807
$201$	−1.76259			−0.124323
$202$		−	2.98040i		−	0.209700i
$203$		0			0
$204$			14.8214i			1.03770i
$205$			1.95571i			0.136593i
$206$	−1.76259			−0.122805
$207$	7.00000	+	3.31082i	0.486534	+	0.230118i
$208$		−	3.70082i		−	0.256606i
$209$		−	1.08360i		−	0.0749543i
$210$		0			0
$211$	−26.0807			−1.79547			−0.897736	−	0.440533i	$-0.854789\pi$
$211$	−26.0807			−1.79547			−0.897736	+	0.440533i	$0.854789\pi$
$212$			13.6862i			0.939970i
$213$		−	2.21575i		−	0.151821i
$214$		−	8.88973i		−	0.607690i
$215$			4.74791i			0.323805i
$216$		−	2.97601i		−	0.202492i
$217$		0			0
$218$		−	6.93402i		−	0.469631i
$219$	−10.6222			−0.717784
$220$		−	1.08360i		−	0.0730564i
$221$			25.5340i			1.71760i
$222$	−18.6243			−1.24998
$223$		−	3.15541i		−	0.211302i	−0.994403	−	0.105651i	$-0.966307\pi$
$223$		−	3.15541i		−	0.211302i	0.994403	−	0.105651i	$-0.0336926\pi$
$224$		0			0
$225$	7.62223			0.508149
$226$			5.00860i			0.333167i
$227$	−7.79225			−0.517190			−0.258595	−	0.965986i	$-0.583259\pi$
$227$	−7.79225			−0.517190			−0.258595	+	0.965986i	$0.583259\pi$
$228$			1.13521i			0.0751809i
$229$	5.67843			0.375241			0.187621	−	0.982242i	$-0.439922\pi$
$229$	5.67843			0.375241			0.187621	+	0.982242i	$0.439922\pi$
$230$	2.29104	+	1.08360i	0.151067	+	0.0714506i
$231$		0			0
$232$	3.68928			0.242213
$233$	28.5037			1.86734			0.933669	−	0.358138i	$-0.116588\pi$
$233$	28.5037			1.86734			0.933669	+	0.358138i	$0.116588\pi$
$234$			5.97545i			0.390628i
$235$		−	1.04040i		−	0.0678685i
$236$		−	5.77702i		−	0.376052i
$237$	25.6714			1.66754
$238$		0			0
$239$	2.10460			0.136135			0.0680676	−	0.997681i	$-0.478317\pi$
$239$	2.10460			0.136135			0.0680676	+	0.997681i	$0.478317\pi$
$240$			1.13521i			0.0732773i
$241$	15.2072			0.979583			0.489792	−	0.871840i	$-0.337073\pi$
$241$	15.2072			0.979583			0.489792	+	0.871840i	$0.337073\pi$
$242$	6.79539			0.436824
$243$			15.2106i			0.975762i
$244$	−5.84264			−0.374036
$245$		0			0
$246$	−7.94999			−0.506873
$247$			1.95571i			0.124439i
$248$		−	4.94479i		−	0.313994i
$249$		−	35.3468i		−	2.24001i
$250$	5.13696			0.324890
$251$	−21.0463			−1.32843			−0.664214	−	0.747543i	$-0.731234\pi$
$251$	−21.0463			−1.32843			−0.664214	+	0.747543i	$0.731234\pi$
$252$		0			0
$253$	4.20461	−	8.88973i	0.264342	−	0.558893i
$254$	−3.31072			−0.207733
$255$		−	7.83241i		−	0.490485i
$256$	1.00000			0.0625000
$257$		−	22.3961i		−	1.39703i	−0.715594	−	0.698517i	$-0.753844\pi$
$257$		−	22.3961i		−	1.39703i	0.715594	−	0.698517i	$-0.246156\pi$
$258$	−19.3003			−1.20158
$259$		0			0
$260$			1.95571i			0.121288i
$261$	−5.95681			−0.368717
$262$			16.3341i			1.00912i
$263$		−	9.58514i		−	0.591045i	−0.955336	−	0.295523i	$-0.904506\pi$
$263$		−	9.58514i		−	0.591045i	0.955336	−	0.295523i	$-0.0954938\pi$
$264$	4.40485			0.271100
$265$		−	7.23251i		−	0.444289i
$266$		0			0
$267$		−	16.3941i		−	1.00330i
$268$		−	0.820506i		−	0.0501204i
$269$		−	17.0691i		−	1.04072i	−0.853946	−	0.520362i	$-0.825797\pi$
$269$		−	17.0691i		−	1.04072i	0.853946	−	0.520362i	$-0.174203\pi$
$270$			1.57268i			0.0957105i
$271$		−	14.9063i		−	0.905495i	−0.891639	−	0.452747i	$-0.850444\pi$
$271$		−	14.9063i		−	0.905495i	0.891639	−	0.452747i	$-0.149556\pi$
$272$	−6.89954			−0.418346
$273$		0			0
$274$		−	9.80504i		−	0.592344i
$275$		−	9.67994i		−	0.583723i
$276$	−4.40485	+	9.31309i	−0.265141	+	0.560582i
$277$	29.8814			1.79540			0.897701	−	0.440606i	$-0.145236\pi$
$277$	29.8814			1.79540			0.897701	+	0.440606i	$0.145236\pi$
$278$			18.4468i			1.10637i
$279$			7.98399i			0.477989i
$280$		0			0
$281$		−	21.7934i		−	1.30009i	−0.759897	−	0.650044i	$-0.774751\pi$
$281$		−	21.7934i		−	1.30009i	0.759897	−	0.650044i	$-0.225249\pi$
$282$	4.22926			0.251848
$283$	26.7283			1.58883			0.794416	−	0.607374i	$-0.207777\pi$
$283$	26.7283			1.58883			0.794416	+	0.607374i	$0.207777\pi$
$284$	1.03146			0.0612059
$285$		−	0.599904i		−	0.0355353i
$286$	7.58860			0.448723
$287$		0			0
$288$	−1.61463			−0.0951429
$289$	30.6037			1.80022
$290$	−1.94961			−0.114485
$291$			23.9310i			1.40286i
$292$		−	4.94479i		−	0.289372i
$293$	−21.3877			−1.24948			−0.624741	−	0.780832i	$-0.714795\pi$
$293$	−21.3877			−1.24948			−0.624741	+	0.780832i	$0.714795\pi$
$294$		0			0
$295$			3.05289i			0.177746i
$296$		−	8.66983i		−	0.503924i
$297$	6.10236			0.354095
$298$		−	4.10103i		−	0.237566i
$299$	−7.58860	+	16.0444i	−0.438860	+	0.927873i
$300$			10.1409i			0.585487i
$301$		0			0
$302$	1.77074			0.101895
$303$	−6.40241			−0.367809
$304$	−0.528453			−0.0303089
$305$	3.08756			0.176793
$306$	11.1402			0.636842
$307$		−	2.16565i		−	0.123600i	−0.998089	−	0.0618001i	$-0.980316\pi$
$307$		−	2.16565i		−	0.123600i	0.998089	−	0.0618001i	$-0.0196841\pi$
$308$		0			0
$309$			3.78633i			0.215397i
$310$			2.61309i			0.148413i
$311$			18.7483i			1.06312i	0.847022	+	0.531558i	$0.178393\pi$
$311$			18.7483i			1.06312i	−0.847022	+	0.531558i	$0.821607\pi$
$312$	−7.94999			−0.450080
$313$	−31.3104			−1.76977			−0.884883	−	0.465813i	$-0.845762\pi$
$313$	−31.3104			−1.76977			−0.884883	+	0.465813i	$0.845762\pi$
$314$	7.46744			0.421412
$315$		0			0
$316$			11.9504i			0.672260i
$317$	28.6469			1.60897			0.804484	−	0.593974i	$-0.202442\pi$
$317$	28.6469			1.60897			0.804484	+	0.593974i	$0.202442\pi$
$318$	29.4002			1.64868
$319$			7.56492i			0.423554i
$320$	−0.528453			−0.0295414
$321$	−19.0966			−1.06587
$322$		0			0
$323$	3.64609			0.202874
$324$	−11.2369			−0.624270
$325$			17.4706i			0.969095i
$326$	−5.61463			−0.310965
$327$	−14.8954			−0.823720
$328$		−	3.70082i		−	0.204344i
$329$		0			0
$330$	−2.32776			−0.128139
$331$	27.3100			1.50109			0.750547	−	0.660817i	$-0.229790\pi$
$331$	27.3100			1.50109			0.750547	+	0.660817i	$0.229790\pi$
$332$	16.4544			0.903051
$333$			13.9986i			0.767116i
$334$			4.65513i			0.254717i
$335$			0.433599i			0.0236901i
$336$		0			0
$337$			3.09092i			0.168373i	0.996450	+	0.0841866i	$0.0268292\pi$
$337$			3.09092i			0.168373i	−0.996450	+	0.0841866i	$0.973171\pi$
$338$	−0.696095			−0.0378626
$339$	10.7593			0.584366
$340$	3.64609			0.197737
$341$	10.1394			0.549077
$342$	0.853256			0.0461388
$343$		0			0
$344$		−	8.98453i		−	0.484414i
$345$	2.32776	−	4.92154i	0.125322	−	0.264967i
$346$			14.7858i			0.794890i
$347$	−5.44829			−0.292480			−0.146240	−	0.989249i	$-0.546717\pi$
$347$	−5.44829			−0.292480			−0.146240	+	0.989249i	$0.546717\pi$
$348$		−	7.92519i		−	0.424835i
$349$		−	7.05311i		−	0.377544i	−0.982021	−	0.188772i	$-0.939549\pi$
$349$		−	7.05311i		−	0.377544i	0.982021	−	0.188772i	$-0.0604508\pi$
$350$		0			0
$351$	−11.0137			−0.587868
$352$			2.05052i			0.109293i
$353$			8.86485i			0.471828i	0.971774	+	0.235914i	$0.0758084\pi$
$353$			8.86485i			0.471828i	−0.971774	+	0.235914i	$0.924192\pi$
$354$	−12.4100			−0.659585
$355$	−0.545078			−0.0289298
$356$	7.63165			0.404476
$357$		0			0
$358$	3.38537			0.178922
$359$		−	9.62317i		−	0.507892i	−0.967218	−	0.253946i	$-0.918271\pi$
$359$		−	9.62317i		−	0.507892i	0.967218	−	0.253946i	$-0.0817285\pi$
$360$	0.853256			0.0449705
$361$	−18.7207			−0.985302
$362$	10.2869			0.540669
$363$		−	14.5976i		−	0.766177i
$364$		0			0
$365$			2.61309i			0.136775i
$366$			12.5510i			0.656049i
$367$	−24.2072			−1.26360			−0.631802	−	0.775130i	$-0.717684\pi$
$367$	−24.2072			−1.26360			−0.631802	+	0.775130i	$0.717684\pi$
$368$	−4.33536	−	2.05052i	−0.225997	−	0.106891i
$369$			5.97545i			0.311070i
$370$			4.58160i			0.238186i
$371$		0			0
$372$	−10.6222			−0.550737
$373$		−	0.0567690i		−	0.00293939i	−0.999999	−	0.00146969i	$-0.999532\pi$
$373$		−	0.0567690i		−	0.00293939i	0.999999	−	0.00146969i	$-0.000467818\pi$
$374$		−	14.1476i		−	0.731556i
$375$		−	11.0350i		−	0.569848i
$376$			1.96877i			0.101532i
$377$		−	13.6534i		−	0.703184i
$378$		0			0
$379$			20.4003i			1.04789i	0.851751	+	0.523946i	$0.175541\pi$
$379$			20.4003i			1.04789i	−0.851751	+	0.523946i	$0.824459\pi$
$380$	0.279263			0.0143259
$381$			7.11199i			0.364358i
$382$		−	3.88113i		−	0.198576i
$383$	12.9458			0.661501			0.330750	−	0.943718i	$-0.392698\pi$
$383$	12.9458			0.661501			0.330750	+	0.943718i	$0.392698\pi$
$384$		−	2.14817i		−	0.109623i
$385$		0			0
$386$	13.6954			0.697076
$387$			14.5067i			0.737416i
$388$	−11.1402			−0.565558
$389$		−	35.7943i		−	1.81484i	−0.420221	−	0.907422i	$-0.638048\pi$
$389$		−	35.7943i		−	1.81484i	0.420221	−	0.907422i	$-0.361952\pi$
$390$	4.20120			0.212736
$391$	29.9120	+	14.1476i	1.51272	+	0.715476i
$392$		0			0
$393$	35.0883			1.76997
$394$	20.4976			1.03265
$395$		−	6.31521i		−	0.317753i
$396$		−	3.31082i		−	0.166375i
$397$		−	21.8641i		−	1.09733i	−0.836043	−	0.548664i	$-0.815136\pi$
$397$		−	21.8641i		−	1.09733i	0.836043	−	0.548664i	$-0.184864\pi$
$398$	−20.8857			−1.04690
$399$		0			0
$400$	−4.72074			−0.236037
$401$		−	17.4345i		−	0.870636i	−0.900277	−	0.435318i	$-0.856636\pi$
$401$		−	17.4345i		−	0.870636i	0.900277	−	0.435318i	$-0.143364\pi$
$402$	−1.76259			−0.0879098
$403$	−18.2998			−0.911577
$404$		−	2.98040i		−	0.148281i
$405$	5.93816			0.295069
$406$		0			0
$407$	17.7776			0.881204
$408$			14.8214i			0.733768i
$409$			33.1136i			1.63736i	0.574250	+	0.818680i	$0.305294\pi$
$409$			33.1136i			1.63736i	−0.574250	+	0.818680i	$0.694706\pi$
$410$			1.95571i			0.0965858i
$411$	−21.0629			−1.03896
$412$	−1.76259			−0.0868363
$413$		0			0
$414$	7.00000	+	3.31082i	0.344031	+	0.162718i
$415$	−8.69537			−0.426839
$416$		−	3.70082i		−	0.181448i
$417$	39.6268			1.94053
$418$		−	1.08360i		−	0.0530007i
$419$	22.9995			1.12360			0.561799	−	0.827274i	$-0.310110\pi$
$419$	22.9995			1.12360			0.561799	+	0.827274i	$0.310110\pi$
$420$		0			0
$421$		−	13.9931i		−	0.681984i	−0.940066	−	0.340992i	$-0.889237\pi$
$421$		−	13.9931i		−	0.681984i	0.940066	−	0.340992i	$-0.110763\pi$
$422$	−26.0807			−1.26959
$423$		−	3.17884i		−	0.154560i
$424$			13.6862i			0.664659i
$425$	32.5709			1.57992
$426$		−	2.21575i		−	0.107353i
$427$		0			0
$428$		−	8.88973i		−	0.429701i
$429$		−	16.3016i		−	0.787048i
$430$			4.74791i			0.228964i
$431$		−	15.0335i		−	0.724140i	−0.932151	−	0.362070i	$-0.882070\pi$
$431$		−	15.0335i		−	0.724140i	0.932151	−	0.362070i	$-0.117930\pi$
$432$		−	2.97601i		−	0.143183i
$433$	8.50153			0.408557			0.204279	−	0.978913i	$-0.434515\pi$
$433$	8.50153			0.408557			0.204279	+	0.978913i	$0.434515\pi$
$434$		0			0
$435$			4.18809i			0.200804i
$436$		−	6.93402i		−	0.332079i
$437$	2.29104	+	1.08360i	0.109595	+	0.0518357i
$438$	−10.6222			−0.507550
$439$		−	1.78938i		−	0.0854023i	−0.999088	−	0.0427012i	$-0.986404\pi$
$439$		−	1.78938i		−	0.0854023i	0.999088	−	0.0427012i	$-0.0135963\pi$
$440$		−	1.08360i		−	0.0516587i
$441$		0			0
$442$			25.5340i			1.21453i
$443$	14.4229			0.685254			0.342627	−	0.939472i	$-0.388683\pi$
$443$	14.4229			0.685254			0.342627	+	0.939472i	$0.388683\pi$
$444$	−18.6243			−0.883868
$445$	−4.03297			−0.191181
$446$		−	3.15541i		−	0.149413i
$447$	−8.80970			−0.416685
$448$		0			0
$449$	9.65218			0.455515			0.227757	−	0.973718i	$-0.426861\pi$
$449$	9.65218			0.455515			0.227757	+	0.973718i	$0.426861\pi$
$450$	7.62223			0.359315
$451$	7.58860			0.357333
$452$			5.00860i			0.235585i
$453$		−	3.80386i		−	0.178721i
$454$	−7.79225			−0.365708
$455$		0			0
$456$			1.13521i			0.0531609i
$457$		−	36.1370i		−	1.69042i	−0.534437	−	0.845208i	$-0.679476\pi$
$457$		−	36.1370i		−	1.69042i	0.534437	−	0.845208i	$-0.320524\pi$
$458$	5.67843			0.265336
$459$			20.5331i			0.958404i
$460$	2.29104	+	1.08360i	0.106820	+	0.0505232i
$461$			27.5367i			1.28251i	0.767326	+	0.641257i	$0.221587\pi$
$461$			27.5367i			1.28251i	−0.767326	+	0.641257i	$0.778413\pi$
$462$		0			0
$463$	−0.186065			−0.00864718			−0.00432359	−	0.999991i	$-0.501376\pi$
$463$	−0.186065			−0.00864718			−0.00432359	+	0.999991i	$0.501376\pi$
$464$	3.68928			0.171270
$465$	5.61336			0.260313
$466$	28.5037			1.32041
$467$	−17.3243			−0.801671			−0.400835	−	0.916150i	$-0.631280\pi$
$467$	−17.3243			−0.801671			−0.400835	+	0.916150i	$0.631280\pi$
$468$			5.97545i			0.276215i
$469$		0			0
$470$		−	1.04040i		−	0.0479903i
$471$		−	16.0413i		−	0.739145i
$472$		−	5.77702i		−	0.265909i
$473$	18.4229			0.847087
$474$	25.6714			1.17913
$475$	2.49469			0.114464
$476$		0			0
$477$		−	22.0981i		−	1.01180i
$478$	2.10460			0.0962621
$479$	−32.3673			−1.47890			−0.739449	−	0.673212i	$-0.764914\pi$
$479$	−32.3673			−1.47890			−0.739449	+	0.673212i	$0.764914\pi$
$480$			1.13521i			0.0518149i
$481$	−32.0855			−1.46297
$482$	15.2072			0.692670
$483$		0			0
$484$	6.79539			0.308881
$485$	5.88707			0.267318
$486$			15.2106i			0.689968i
$487$	30.0020			1.35952			0.679759	−	0.733435i	$-0.262084\pi$
$487$	30.0020			1.35952			0.679759	+	0.733435i	$0.262084\pi$
$488$	−5.84264			−0.264484
$489$			12.0612i			0.545425i
$490$		0			0
$491$	−11.9761			−0.540476			−0.270238	−	0.962794i	$-0.587102\pi$
$491$	−11.9761			−0.540476			−0.270238	+	0.962794i	$0.587102\pi$
$492$	−7.94999			−0.358413
$493$	−25.4543			−1.14641
$494$			1.95571i			0.0879917i
$495$			1.74961i			0.0786393i
$496$		−	4.94479i		−	0.222027i
$497$		0			0
$498$		−	35.3468i		−	1.58393i
$499$	−40.2744			−1.80293			−0.901465	−	0.432852i	$-0.857507\pi$
$499$	−40.2744			−1.80293			−0.901465	+	0.432852i	$0.857507\pi$
$500$	5.13696			0.229732
$501$	10.0000			0.446767
$502$	−21.0463			−0.939340
$503$	19.6812			0.877540			0.438770	−	0.898599i	$-0.355414\pi$
$503$	19.6812			0.877540			0.438770	+	0.898599i	$0.355414\pi$
$504$		0			0
$505$			1.57500i			0.0700868i
$506$	4.20461	−	8.88973i	0.186918	−	0.395197i
$507$			1.49533i			0.0664099i
$508$	−3.31072			−0.146890
$509$		−	28.9509i		−	1.28323i	−0.767028	−	0.641613i	$-0.778265\pi$
$509$		−	28.9509i		−	1.28323i	0.767028	−	0.641613i	$-0.221735\pi$
$510$		−	7.83241i		−	0.346825i
$511$		0			0
$512$	1.00000			0.0441942
$513$			1.57268i			0.0694357i
$514$		−	22.3961i		−	0.987852i
$515$	0.931444			0.0410443
$516$	−19.3003			−0.849648
$517$	−4.03700			−0.177547
$518$		0			0
$519$	31.7624			1.39422
$520$			1.95571i			0.0857637i
$521$	29.1571			1.27740			0.638698	−	0.769458i	$-0.279473\pi$
$521$	29.1571			1.27740			0.638698	+	0.769458i	$0.279473\pi$
$522$	−5.95681			−0.260722
$523$	16.7397			0.731977			0.365989	−	0.930619i	$-0.380731\pi$
$523$	16.7397			0.731977			0.365989	+	0.930619i	$0.380731\pi$
$524$			16.3341i			0.713557i
$525$		0			0
$526$		−	9.58514i		−	0.417932i
$527$			34.1168i			1.48615i
$528$	4.40485			0.191697
$529$	14.5908	+	17.7795i	0.634381	+	0.773020i
$530$		−	7.23251i		−	0.314160i
$531$			9.32774i			0.404789i
$532$		0			0
$533$	−13.6961			−0.593244
$534$		−	16.3941i		−	0.709441i
$535$			4.69781i			0.203104i
$536$		−	0.820506i		−	0.0354405i
$537$		−	7.27235i		−	0.313825i
$538$		−	17.0691i		−	0.735903i
$539$		0			0
$540$			1.57268i			0.0676776i
$541$	−27.8890			−1.19904			−0.599522	−	0.800358i	$-0.704643\pi$
$541$	−27.8890			−1.19904			−0.599522	+	0.800358i	$0.704643\pi$
$542$		−	14.9063i		−	0.640282i
$543$		−	22.0981i		−	0.948319i
$544$	−6.89954			−0.295815
$545$			3.66431i			0.156962i
$546$		0			0
$547$	−29.2861			−1.25219			−0.626093	−	0.779749i	$-0.715347\pi$
$547$	−29.2861			−1.25219			−0.626093	+	0.779749i	$0.715347\pi$
$548$		−	9.80504i		−	0.418851i
$549$	9.43368			0.402620
$550$		−	9.67994i		−	0.412754i
$551$	−1.94961			−0.0830562
$552$	−4.40485	+	9.31309i	−0.187483	+	0.396392i
$553$		0			0
$554$	29.8814			1.26954
$555$	9.84206			0.417772
$556$			18.4468i			0.782318i
$557$		−	26.5215i		−	1.12375i	−0.827221	−	0.561877i	$-0.810079\pi$
$557$		−	26.5215i		−	1.12375i	0.827221	−	0.561877i	$-0.189921\pi$
$558$			7.98399i			0.337989i
$559$	−33.2502			−1.40633
$560$		0			0
$561$	−30.3915			−1.28313
$562$		−	21.7934i		−	0.919300i
$563$	−22.5007			−0.948290			−0.474145	−	0.880447i	$-0.657243\pi$
$563$	−22.5007			−0.948290			−0.474145	+	0.880447i	$0.657243\pi$
$564$	4.22926			0.178084
$565$		−	2.64681i		−	0.111352i
$566$	26.7283			1.12347
$567$		0			0
$568$	1.03146			0.0432791
$569$			46.1239i			1.93361i	0.255508	+	0.966807i	$0.417757\pi$
$569$			46.1239i			1.93361i	−0.255508	+	0.966807i	$0.582243\pi$
$570$		−	0.599904i		−	0.0251272i
$571$			9.64191i			0.403501i	0.979437	+	0.201751i	$0.0646631\pi$
$571$			9.64191i			0.403501i	−0.979437	+	0.201751i	$0.935337\pi$
$572$	7.58860			0.317295
$573$	−8.33733			−0.348297
$574$		0			0
$575$	20.4661	+	9.67994i	0.853496	+	0.403682i
$576$	−1.61463			−0.0672762
$577$		−	6.43834i		−	0.268032i	−0.990979	−	0.134016i	$-0.957213\pi$
$577$		−	6.43834i		−	0.268032i	0.990979	−	0.134016i	$-0.0427873\pi$
$578$	30.6037			1.27295
$579$		−	29.4200i		−	1.22265i
$580$	−1.94961			−0.0809532
$581$		0			0
$582$			23.9310i			0.991972i
$583$	−28.0637			−1.16228
$584$		−	4.94479i		−	0.204617i
$585$		−	3.15775i		−	0.130557i
$586$	−21.3877			−0.883517
$587$			23.4844i			0.969303i	0.874707	+	0.484652i	$0.161054\pi$
$587$			23.4844i			0.969303i	−0.874707	+	0.484652i	$0.838946\pi$
$588$		0			0
$589$			2.61309i			0.107670i
$590$			3.05289i			0.125685i
$591$		−	44.0322i		−	1.81124i
$592$		−	8.66983i		−	0.356328i
$593$			5.34187i			0.219364i	0.993967	+	0.109682i	$0.0349833\pi$
$593$			5.34187i			0.219364i	−0.993967	+	0.109682i	$0.965017\pi$
$594$	6.10236			0.250383
$595$		0			0
$596$		−	4.10103i		−	0.167985i
$597$			44.8659i			1.83624i
$598$	−7.58860	+	16.0444i	−0.310321	+	0.656105i
$599$	14.0576			0.574378			0.287189	−	0.957874i	$-0.407279\pi$
$599$	14.0576			0.574378			0.287189	+	0.957874i	$0.407279\pi$
$600$			10.1409i			0.414002i
$601$			13.0270i			0.531383i	0.964058	+	0.265691i	$0.0856002\pi$
$601$			13.0270i			0.531383i	−0.964058	+	0.265691i	$0.914400\pi$
$602$		0			0
$603$			1.32481i			0.0539505i
$604$	1.77074			0.0720506
$605$	−3.59105			−0.145997
$606$	−6.40241			−0.260080
$607$		−	39.6771i		−	1.61044i	−0.592973	−	0.805222i	$-0.702046\pi$
$607$		−	39.6771i		−	1.61044i	0.592973	−	0.805222i	$-0.297954\pi$
$608$	−0.528453			−0.0214316
$609$		0			0
$610$	3.08756			0.125012
$611$	7.28608			0.294763
$612$	11.1402			0.450316
$613$		−	26.3700i		−	1.06507i	−0.846407	−	0.532537i	$-0.821239\pi$
$613$		−	26.3700i		−	1.06507i	0.846407	−	0.532537i	$-0.178761\pi$
$614$		−	2.16565i		−	0.0873985i
$615$	4.20120			0.169409
$616$		0			0
$617$		−	10.7491i		−	0.432744i	−0.976311	−	0.216372i	$-0.930578\pi$
$617$		−	10.7491i		−	0.432744i	0.976311	−	0.216372i	$-0.0694224\pi$
$618$			3.78633i			0.152309i
$619$	35.8758			1.44197			0.720985	−	0.692950i	$-0.243689\pi$
$619$	35.8758			1.44197			0.720985	+	0.692950i	$0.243689\pi$
$620$			2.61309i			0.104944i
$621$	−6.10236	+	12.9021i	−0.244879	+	0.517744i
$622$			18.7483i			0.751737i
$623$		0			0
$624$	−7.94999			−0.318254
$625$	20.8890			0.835562
$626$	−31.3104			−1.25141
$627$	−2.32776			−0.0929618
$628$	7.46744			0.297983
$629$			59.8179i			2.38510i
$630$		0			0
$631$			33.2092i			1.32204i	0.750370	+	0.661018i	$0.229876\pi$
$631$			33.2092i			1.32204i	−0.750370	+	0.661018i	$0.770124\pi$
$632$			11.9504i			0.475360i
$633$			56.0258i			2.22683i
$634$	28.6469			1.13771
$635$	1.74956			0.0694293
$636$	29.4002			1.16579
$637$		0			0
$638$			7.56492i			0.299498i
$639$	−1.66542			−0.0658831
$640$	−0.528453			−0.0208890
$641$		−	5.45614i		−	0.215504i	−0.994178	−	0.107752i	$-0.965635\pi$
$641$		−	5.45614i		−	0.215504i	0.994178	−	0.107752i	$-0.0343653\pi$
$642$	−19.0966			−0.753684
$643$	19.3950			0.764865			0.382432	−	0.923983i	$-0.375086\pi$
$643$	19.3950			0.764865			0.382432	+	0.923983i	$0.375086\pi$
$644$		0			0
$645$	10.1993			0.401597
$646$	3.64609			0.143453
$647$		−	37.9892i		−	1.49351i	−0.665099	−	0.746755i	$-0.731611\pi$
$647$		−	37.9892i		−	1.49351i	0.665099	−	0.746755i	$-0.268389\pi$
$648$	−11.2369			−0.441426
$649$	11.8459			0.464991
$650$			17.4706i			0.685254i
$651$		0			0
$652$	−5.61463			−0.219886
$653$	−6.65782			−0.260541			−0.130270	−	0.991479i	$-0.541585\pi$
$653$	−6.65782			−0.260541			−0.130270	+	0.991479i	$0.541585\pi$
$654$	−14.8954			−0.582458
$655$		−	8.63180i		−	0.337272i
$656$		−	3.70082i		−	0.144493i
$657$			7.98399i			0.311485i
$658$		0			0
$659$			7.65972i			0.298380i	0.988809	+	0.149190i	$0.0476667\pi$
$659$			7.65972i			0.298380i	−0.988809	+	0.149190i	$0.952333\pi$
$660$	−2.32776			−0.0906079
$661$	23.3705			0.909009			0.454504	−	0.890745i	$-0.349816\pi$
$661$	23.3705			0.909009			0.454504	+	0.890745i	$0.349816\pi$
$662$	27.3100			1.06143
$663$	54.8513			2.13025
$664$	16.4544			0.638554
$665$		0			0
$666$			13.9986i			0.542433i
$667$	−15.9944	−	7.56492i	−0.619304	−	0.292915i
$668$			4.65513i			0.180112i
$669$	−6.77835			−0.262066
$670$			0.433599i			0.0167514i
$671$		−	11.9804i		−	0.462499i
$672$		0			0
$673$	−32.0944			−1.23715			−0.618575	−	0.785726i	$-0.712290\pi$
$673$	−32.0944			−1.23715			−0.618575	+	0.785726i	$0.712290\pi$
$674$			3.09092i			0.119058i
$675$			14.0490i			0.540745i
$676$	−0.696095			−0.0267729
$677$	10.6117			0.407842			0.203921	−	0.978987i	$-0.434631\pi$
$677$	10.6117			0.407842			0.203921	+	0.978987i	$0.434631\pi$
$678$	10.7593			0.413209
$679$		0			0
$680$	3.64609			0.139821
$681$			16.7391i			0.641442i
$682$	10.1394			0.388256
$683$	−41.4737			−1.58695			−0.793474	−	0.608604i	$-0.791730\pi$
$683$	−41.4737			−1.58695			−0.793474	+	0.608604i	$0.791730\pi$
$684$	0.853256			0.0326250
$685$			5.18151i			0.197975i
$686$		0			0
$687$		−	12.1982i		−	0.465392i
$688$		−	8.98453i		−	0.342532i
$689$	50.6501			1.92962
$690$	2.32776	−	4.92154i	0.0886163	−	0.187360i
$691$			4.32846i			0.164663i	0.996605	+	0.0823313i	$0.0262365\pi$
$691$			4.32846i			0.164663i	−0.996605	+	0.0823313i	$0.973763\pi$
$692$			14.7858i			0.562072i
$693$		0			0
$694$	−5.44829			−0.206814
$695$		−	9.74827i		−	0.369773i
$696$		−	7.92519i		−	0.300404i
$697$			25.5340i			0.967169i
$698$		−	7.05311i		−	0.266964i
$699$		−	61.2307i		−	2.31596i
$700$		0			0
$701$		−	4.85553i		−	0.183391i	−0.995787	−	0.0916954i	$-0.970771\pi$
$701$		−	4.85553i		−	0.183391i	0.995787	−	0.0916954i	$-0.0292286\pi$
$702$	−11.0137			−0.415685
$703$			4.58160i			0.172798i
$704$			2.05052i			0.0772817i
$705$	−2.23496			−0.0841736
$706$			8.86485i			0.333633i
$707$		0			0
$708$	−12.4100			−0.466397
$709$			14.0086i			0.526104i	0.964782	+	0.263052i	$0.0847292\pi$
$709$			14.0086i			0.526104i	−0.964782	+	0.263052i	$0.915271\pi$
$710$	−0.545078			−0.0204564
$711$		−	19.2954i		−	0.723633i
$712$	7.63165			0.286008
$713$	−10.1394	+	21.4374i	−0.379722	+	0.802839i
$714$		0			0
$715$	−4.01022			−0.149974
$716$	3.38537			0.126517
$717$		−	4.52103i		−	0.168841i
$718$		−	9.62317i		−	0.359134i
$719$			34.5763i			1.28948i	0.764403	+	0.644739i	$0.223034\pi$
$719$			34.5763i			1.28948i	−0.764403	+	0.644739i	$0.776966\pi$
$720$	0.853256			0.0317990
$721$		0			0
$722$	−18.7207			−0.696714
$723$		−	32.6677i		−	1.21492i
$724$	10.2869			0.382311
$725$	−17.4161			−0.646818
$726$		−	14.5976i		−	0.541769i
$727$	−29.9681			−1.11146			−0.555728	−	0.831364i	$-0.687560\pi$
$727$	−29.9681			−1.11146			−0.555728	+	0.831364i	$0.687560\pi$
$728$		0			0
$729$	−1.03559			−0.0383550
$730$			2.61309i			0.0967148i
$731$			61.9892i			2.29275i
$732$			12.5510i			0.463897i
$733$	−47.6700			−1.76073			−0.880366	−	0.474295i	$-0.842703\pi$
$733$	−47.6700			−1.76073			−0.880366	+	0.474295i	$0.842703\pi$
$734$	−24.2072			−0.893503
$735$		0			0
$736$	−4.33536	−	2.05052i	−0.159804	−	0.0755830i
$737$	1.68246			0.0619742
$738$			5.97545i			0.219959i
$739$	−0.345584			−0.0127125			−0.00635626	−	0.999980i	$-0.502023\pi$
$739$	−0.345584			−0.0127125			−0.00635626	+	0.999980i	$0.502023\pi$
$740$			4.58160i			0.168423i
$741$	4.20120			0.154335
$742$		0			0
$743$			14.5735i			0.534650i	0.963606	+	0.267325i	$0.0861397\pi$
$743$			14.5735i			0.534650i	−0.963606	+	0.267325i	$0.913860\pi$
$744$	−10.6222			−0.389430
$745$			2.16720i			0.0794002i
$746$		−	0.0567690i		−	0.00207846i
$747$	−26.5677			−0.972061
$748$		−	14.1476i		−	0.517288i
$749$		0			0
$750$		−	11.0350i		−	0.402943i
$751$			46.2645i			1.68821i	0.536175	+	0.844107i	$0.319869\pi$
$751$			46.2645i			1.68821i	−0.536175	+	0.844107i	$0.680131\pi$
$752$			1.96877i			0.0717938i
$753$			45.2109i			1.64758i
$754$		−	13.6534i		−	0.497226i
$755$	−0.935756			−0.0340557
$756$		0			0
$757$			5.74054i			0.208644i	0.994544	+	0.104322i	$0.0332672\pi$
$757$			5.74054i			0.208644i	−0.994544	+	0.104322i	$0.966733\pi$
$758$			20.4003i			0.740972i
$759$	−19.0966	−	9.03222i	−0.693164	−	0.327849i
$760$	0.279263			0.0101299
$761$			44.7232i			1.62121i	0.585591	+	0.810607i	$0.300862\pi$
$761$			44.7232i			1.62121i	−0.585591	+	0.810607i	$0.699138\pi$
$762$			7.11199i			0.257640i
$763$		0			0
$764$		−	3.88113i		−	0.140414i
$765$	−5.88707			−0.212848
$766$	12.9458			0.467752
$767$	−21.3797			−0.771978
$768$		−	2.14817i		−	0.0775154i
$769$	30.7425			1.10860			0.554301	−	0.832316i	$-0.312986\pi$
$769$	30.7425			1.10860			0.554301	+	0.832316i	$0.312986\pi$
$770$		0			0
$771$	−48.1107			−1.73266
$772$	13.6954			0.492907
$773$	28.3038			1.01802			0.509009	−	0.860761i	$-0.330012\pi$
$773$	28.3038			1.01802			0.509009	+	0.860761i	$0.330012\pi$
$774$			14.5067i			0.521432i
$775$			23.3430i			0.838506i
$776$	−11.1402			−0.399910
$777$		0			0
$778$		−	35.7943i		−	1.28329i
$779$			1.95571i			0.0700707i
$780$	4.20120			0.150427
$781$			2.11502i			0.0756815i
$782$	29.9120	+	14.1476i	1.06965	+	0.505918i
$783$		−	10.9793i		−	0.392370i
$784$		0			0
$785$	−3.94620			−0.140846
$786$	35.0883			1.25156
$787$	−3.75165			−0.133732			−0.0668659	−	0.997762i	$-0.521300\pi$
$787$	−3.75165			−0.133732			−0.0668659	+	0.997762i	$0.521300\pi$
$788$	20.4976			0.730196
$789$	−20.5905			−0.733041
$790$		−	6.31521i		−	0.224685i
$791$		0			0
$792$		−	3.31082i		−	0.117645i
$793$			21.6226i			0.767840i
$794$		−	21.8641i		−	0.775929i
$795$	−15.5366			−0.551028
$796$	−20.8857			−0.740272
$797$	−14.8394			−0.525637			−0.262819	−	0.964845i	$-0.584652\pi$
$797$	−14.8394			−0.525637			−0.262819	+	0.964845i	$0.584652\pi$
$798$		0			0
$799$		−	13.5836i		−	0.480554i
$800$	−4.72074			−0.166903
$801$	−12.3223			−0.435386
$802$		−	17.4345i		−	0.615632i
$803$	10.1394			0.357810
$804$	−1.76259			−0.0621616
$805$		0			0
$806$	−18.2998			−0.644582
$807$	−36.6674			−1.29075
$808$		−	2.98040i		−	0.104850i
$809$	46.6720			1.64090			0.820450	−	0.571719i	$-0.193723\pi$
$809$	46.6720			1.64090			0.820450	+	0.571719i	$0.193723\pi$
$810$	5.93816			0.208646
$811$			10.5200i			0.369409i	0.982794	+	0.184704i	$0.0591328\pi$
$811$			10.5200i			0.369409i	−0.982794	+	0.184704i	$0.940867\pi$
$812$		0			0
$813$	−32.0213			−1.12304
$814$	17.7776			0.623105
$815$	2.96707			0.103932
$816$			14.8214i			0.518852i
$817$			4.74791i			0.166108i
$818$			33.1136i			1.15779i
$819$		0			0
$820$			1.95571i			0.0682965i
$821$	−14.0561			−0.490561			−0.245281	−	0.969452i	$-0.578880\pi$
$821$	−14.0561			−0.490561			−0.245281	+	0.969452i	$0.578880\pi$
$822$	−21.0629			−0.734652
$823$	−6.99436			−0.243808			−0.121904	−	0.992542i	$-0.538900\pi$
$823$	−6.99436			−0.243808			−0.121904	+	0.992542i	$0.538900\pi$
$824$	−1.76259			−0.0614026
$825$	−20.7941			−0.723959
$826$		0			0
$827$		−	36.9598i		−	1.28522i	−0.766194	−	0.642609i	$-0.777852\pi$
$827$		−	36.9598i		−	1.28522i	0.766194	−	0.642609i	$-0.222148\pi$
$828$	7.00000	+	3.31082i	0.243267	+	0.115059i
$829$			3.55072i			0.123322i	0.998097	+	0.0616608i	$0.0196397\pi$
$829$			3.55072i			0.123322i	−0.998097	+	0.0616608i	$0.980360\pi$
$830$	−8.69537			−0.301821
$831$		−	64.1904i		−	2.22674i
$832$		−	3.70082i		−	0.128303i
$833$		0			0
$834$	39.6268			1.37216
$835$		−	2.46002i		−	0.0851325i
$836$		−	1.08360i		−	0.0374772i
$837$	−14.7157			−0.508651
$838$	22.9995			0.794503
$839$	−4.89386			−0.168955			−0.0844774	−	0.996425i	$-0.526922\pi$
$839$	−4.89386			−0.168955			−0.0844774	+	0.996425i	$0.526922\pi$
$840$		0			0
$841$	−15.3892			−0.530663
$842$		−	13.9931i		−	0.482235i
$843$	−46.8160			−1.61243
$844$	−26.0807			−0.897736
$845$	0.367854			0.0126546
$846$		−	3.17884i		−	0.109291i
$847$		0			0
$848$			13.6862i			0.469985i
$849$		−	57.4169i		−	1.97054i
$850$	32.5709			1.11717
$851$	−17.7776	+	37.5869i	−0.609409	+	1.28846i
$852$		−	2.21575i		−	0.0759103i
$853$		−	15.0374i		−	0.514871i	−0.966296	−	0.257435i	$-0.917123\pi$
$853$		−	15.0374i		−	0.514871i	0.966296	−	0.257435i	$-0.0828774\pi$
$854$		0			0
$855$	−0.450906			−0.0154207
$856$		−	8.88973i		−	0.303845i
$857$		−	24.4456i		−	0.835045i	−0.908666	−	0.417523i	$-0.862898\pi$
$857$		−	24.4456i		−	0.835045i	0.908666	−	0.417523i	$-0.137102\pi$
$858$		−	16.3016i		−	0.556527i
$859$			45.4187i			1.54967i	0.632166	+	0.774833i	$0.282166\pi$
$859$			45.4187i			1.54967i	−0.632166	+	0.774833i	$0.717834\pi$
$860$			4.74791i			0.161902i
$861$		0			0
$862$		−	15.0335i		−	0.512044i
$863$	−31.0376			−1.05653			−0.528265	−	0.849079i	$-0.677157\pi$
$863$	−31.0376			−1.05653			−0.528265	+	0.849079i	$0.677157\pi$
$864$		−	2.97601i		−	0.101246i
$865$		−	7.81361i		−	0.265671i
$866$	8.50153			0.288894
$867$		−	65.7419i		−	2.23271i
$868$		0			0
$869$	−24.5044			−0.831255
$870$			4.18809i			0.141990i
$871$	−3.03655			−0.102889
$872$		−	6.93402i		−	0.234816i
$873$	17.9873			0.608777
$874$	2.29104	+	1.08360i	0.0774955	+	0.0366534i
$875$		0			0
$876$	−10.6222			−0.358892
$877$	−26.9940			−0.911522			−0.455761	−	0.890102i	$-0.650633\pi$
$877$	−26.9940			−0.911522			−0.455761	+	0.890102i	$0.650633\pi$
$878$		−	1.78938i		−	0.0603885i
$879$			45.9443i			1.54966i
$880$		−	1.08360i		−	0.0365282i
$881$	41.9616			1.41372			0.706860	−	0.707353i	$-0.250111\pi$
$881$	41.9616			1.41372			0.706860	+	0.707353i	$0.250111\pi$
$882$		0			0
$883$	−10.3346			−0.347786			−0.173893	−	0.984765i	$-0.555635\pi$
$883$	−10.3346			−0.347786			−0.173893	+	0.984765i	$0.555635\pi$
$884$			25.5340i			0.858801i
$885$	6.55812			0.220449
$886$	14.4229			0.484548
$887$			34.6999i			1.16511i	0.812792	+	0.582554i	$0.197947\pi$
$887$			34.6999i			1.16511i	−0.812792	+	0.582554i	$0.802053\pi$
$888$	−18.6243			−0.624989
$889$		0			0
$890$	−4.03297			−0.135185
$891$		−	23.0414i		−	0.771914i
$892$		−	3.15541i		−	0.105651i
$893$		−	1.04040i		−	0.0348158i
$894$	−8.80970			−0.294641
$895$	−1.78901			−0.0598001
$896$		0			0
$897$	34.4661	+	16.3016i	1.15079	+	0.544294i
$898$	9.65218			0.322097
$899$		−	18.2427i		−	0.608428i
$900$	7.62223			0.254074
$901$		−	94.4283i		−	3.14586i
$902$	7.58860			0.252673
$903$		0			0
$904$			5.00860i			0.166584i
$905$	−5.43617			−0.180704
$906$		−	3.80386i		−	0.126375i
$907$		−	31.8184i		−	1.05651i	−0.849085	−	0.528256i	$-0.822846\pi$
$907$		−	31.8184i		−	1.05651i	0.849085	−	0.528256i	$-0.177154\pi$
$908$	−7.79225			−0.258595
$909$			4.81224i			0.159612i
$910$		0			0
$911$			3.68229i			0.122000i	0.998138	+	0.0609998i	$0.0194289\pi$
$911$			3.68229i			0.122000i	−0.998138	+	0.0609998i	$0.980571\pi$
$912$			1.13521i			0.0375905i
$913$			33.7399i			1.11663i
$914$		−	36.1370i		−	1.19531i
$915$		−	6.63260i		−	0.219267i
$916$	5.67843			0.187621
$917$		0			0
$918$			20.5331i			0.677694i
$919$		−	52.4083i		−	1.72879i	−0.502814	−	0.864395i	$-0.667702\pi$
$919$		−	52.4083i		−	1.72879i	0.502814	−	0.864395i	$-0.332298\pi$
$920$	2.29104	+	1.08360i	0.0755333	+	0.0357253i
$921$	−4.65218			−0.153295
$922$			27.5367i			0.906874i
$923$		−	3.81725i		−	0.125646i
$924$		0			0
$925$			40.9280i			1.34570i
$926$	−0.186065			−0.00611448
$927$	2.84592			0.0934722
$928$	3.68928			0.121106
$929$			1.70276i			0.0558658i	0.999610	+	0.0279329i	$0.00889247\pi$
$929$			1.70276i			0.0558658i	−0.999610	+	0.0279329i	$0.991108\pi$
$930$	5.61336			0.184069
$931$		0			0
$932$	28.5037			0.933669
$933$	40.2744			1.31853
$934$	−17.3243			−0.566867
$935$			7.47636i			0.244503i
$936$			5.97545i			0.195314i
$937$	17.8589			0.583425			0.291713	−	0.956506i	$-0.405775\pi$
$937$	17.8589			0.583425			0.291713	+	0.956506i	$0.405775\pi$
$938$		0			0
$939$			67.2599i			2.19495i
$940$		−	1.04040i		−	0.0339343i
$941$	−57.3232			−1.86868			−0.934341	−	0.356380i	$-0.884011\pi$
$941$	−57.3232			−1.86868			−0.934341	+	0.356380i	$0.884011\pi$
$942$		−	16.0413i		−	0.522655i
$943$	−7.58860	+	16.0444i	−0.247119	+	0.522478i
$944$		−	5.77702i		−	0.188026i
$945$		0			0
$946$	18.4229			0.598981
$947$	2.45851			0.0798909			0.0399454	−	0.999202i	$-0.487282\pi$
$947$	2.45851			0.0798909			0.0399454	+	0.999202i	$0.487282\pi$
$948$	25.6714			0.833768
$949$	−18.2998			−0.594036
$950$	2.49469			0.0809384
$951$		−	61.5383i		−	1.99552i
$952$		0			0
$953$			22.3180i			0.722950i	0.932382	+	0.361475i	$0.117727\pi$
$953$			22.3180i			0.722950i	−0.932382	+	0.361475i	$0.882273\pi$
$954$		−	22.0981i		−	0.715452i
$955$			2.05100i			0.0663687i
$956$	2.10460			0.0680676
$957$	16.2507			0.525311
$958$	−32.3673			−1.04574
$959$		0			0
$960$			1.13521i			0.0366387i
$961$	6.54909			0.211261
$962$	−32.0855			−1.03448
$963$			14.3536i			0.462539i
$964$	15.2072			0.489792
$965$	−7.23737			−0.232979
$966$		0			0
$967$	52.7700			1.69697			0.848485	−	0.529220i	$-0.177515\pi$
$967$	52.7700			1.69697			0.848485	+	0.529220i	$0.177515\pi$
$968$	6.79539			0.218412
$969$		−	7.83241i		−	0.251613i
$970$	5.88707			0.189023
$971$	3.50893			0.112607			0.0563034	−	0.998414i	$-0.482069\pi$
$971$	3.50893			0.112607			0.0563034	+	0.998414i	$0.482069\pi$
$972$			15.2106i			0.487881i
$973$		0			0
$974$	30.0020			0.961325
$975$	37.5298			1.20192
$976$	−5.84264			−0.187018
$977$		−	30.2053i		−	0.966354i	−0.875523	−	0.483177i	$-0.839483\pi$
$977$		−	30.2053i		−	0.966354i	0.875523	−	0.483177i	$-0.160517\pi$
$978$			12.0612i			0.385674i
$979$			15.6488i			0.500138i
$980$		0			0
$981$			11.1959i			0.357456i
$982$	−11.9761			−0.382174
$983$	−21.1876			−0.675780			−0.337890	−	0.941186i	$-0.609713\pi$
$983$	−21.1876			−0.675780			−0.337890	+	0.941186i	$0.609713\pi$
$984$	−7.94999			−0.253437
$985$	−10.8320			−0.345137
$986$	−25.4543			−0.810631
$987$		0			0
$988$			1.95571i			0.0622195i
$989$	−18.4229	+	38.9512i	−0.585815	+	1.23858i
$990$			1.74961i			0.0556064i
$991$	−55.6132			−1.76661			−0.883305	−	0.468798i	$-0.844687\pi$
$991$	−55.6132			−1.76661			−0.883305	+	0.468798i	$0.844687\pi$
$992$		−	4.94479i		−	0.156997i
$993$		−	58.6665i		−	1.86172i
$994$		0			0
$995$	11.0371			0.349899
$996$		−	35.3468i		−	1.12001i
$997$			6.48719i			0.205451i	0.994710	+	0.102726i	$0.0327564\pi$
$997$			6.48719i			0.205451i	−0.994710	+	0.102726i	$0.967244\pi$
$998$	−40.2744			−1.27486
$999$	−25.8015			−0.816324

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2254.2.c.c.2253.3		16
7.4	even	3		322.2.g.a.229.2	yes	16
7.5	odd	6		322.2.g.a.45.1	✓	16
7.6	odd	2	inner	2254.2.c.c.2253.14		16
23.22	odd	2	inner	2254.2.c.c.2253.4		16
161.68	even	6		322.2.g.a.45.2	yes	16
161.137	odd	6		322.2.g.a.229.1	yes	16
161.160	even	2	inner	2254.2.c.c.2253.13		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.g.a.45.1	✓	16	7.5	odd	6
322.2.g.a.45.2	yes	16	161.68	even	6
322.2.g.a.229.1	yes	16	161.137	odd	6
322.2.g.a.229.2	yes	16	7.4	even	3
2254.2.c.c.2253.3		16	1.1	even	1	trivial
2254.2.c.c.2253.4		16	23.22	odd	2	inner
2254.2.c.c.2253.13		16	161.160	even	2	inner
2254.2.c.c.2253.14		16	7.6	odd	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:	\( N \)	\(=\)	\( 2254 = 2 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2254.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.14817i q^{3} +1.00000 q^{4} -0.528453 q^{5} -2.14817i q^{6} +1.00000 q^{8} -1.61463 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.14817i q^{3} +1.00000 q^{4} -0.528453 q^{5} -2.14817i q^{6} +1.00000 q^{8} -1.61463 q^{9} -0.528453 q^{10} +2.05052i q^{11} -2.14817i q^{12} -3.70082i q^{13} +1.13521i q^{15} +1.00000 q^{16} -6.89954 q^{17} -1.61463 q^{18} -0.528453 q^{19} -0.528453 q^{20} +2.05052i q^{22} +(-4.33536 - 2.05052i) q^{23} -2.14817i q^{24} -4.72074 q^{25} -3.70082i q^{26} -2.97601i q^{27} +3.68928 q^{29} +1.13521i q^{30} -4.94479i q^{31} +1.00000 q^{32} +4.40485 q^{33} -6.89954 q^{34} -1.61463 q^{36} -8.66983i q^{37} -0.528453 q^{38} -7.94999 q^{39} -0.528453 q^{40} -3.70082i q^{41} -8.98453i q^{43} +2.05052i q^{44} +0.853256 q^{45} +(-4.33536 - 2.05052i) q^{46} +1.96877i q^{47} -2.14817i q^{48} -4.72074 q^{50} +14.8214i q^{51} -3.70082i q^{52} +13.6862i q^{53} -2.97601i q^{54} -1.08360i q^{55} +1.13521i q^{57} +3.68928 q^{58} -5.77702i q^{59} +1.13521i q^{60} -5.84264 q^{61} -4.94479i q^{62} +1.00000 q^{64} +1.95571i q^{65} +4.40485 q^{66} -0.820506i q^{67} -6.89954 q^{68} +(-4.40485 + 9.31309i) q^{69} +1.03146 q^{71} -1.61463 q^{72} -4.94479i q^{73} -8.66983i q^{74} +10.1409i q^{75} -0.528453 q^{76} -7.94999 q^{78} +11.9504i q^{79} -0.528453 q^{80} -11.2369 q^{81} -3.70082i q^{82} +16.4544 q^{83} +3.64609 q^{85} -8.98453i q^{86} -7.92519i q^{87} +2.05052i q^{88} +7.63165 q^{89} +0.853256 q^{90} +(-4.33536 - 2.05052i) q^{92} -10.6222 q^{93} +1.96877i q^{94} +0.279263 q^{95} -2.14817i q^{96} -11.1402 q^{97} -3.31082i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{4} + 16 q^{8} - 20 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 + 16 * q^4 + 16 * q^8 - 20 * q^9	\( 16 q + 16 q^{2} + 16 q^{4} + 16 q^{8} - 20 q^{9} + 16 q^{16} - 20 q^{18} + 8 q^{23} - 4 q^{25} + 16 q^{29} + 16 q^{32} - 20 q^{36} - 44 q^{39} + 8 q^{46} - 4 q^{50} + 16 q^{58} + 16 q^{64} - 12 q^{71} - 20 q^{72} - 44 q^{78} + 72 q^{81} + 24 q^{85} + 8 q^{92} + 76 q^{93} + 76 q^{95}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^4 + 16 * q^8 - 20 * q^9 + 16 * q^16 - 20 * q^18 + 8 * q^23 - 4 * q^25 + 16 * q^29 + 16 * q^32 - 20 * q^36 - 44 * q^39 + 8 * q^46 - 4 * q^50 + 16 * q^58 + 16 * q^64 - 12 * q^71 - 20 * q^72 - 44 * q^78 + 72 * q^81 + 24 * q^85 + 8 * q^92 + 76 * q^93 + 76 * q^95

Introduction

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