LMFDB - Embedded newform 931.2.c.f.930.20

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			930.20
Character	$\chi$	$=$	931.930
Dual form			931.2.c.f.930.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.196456i q^{2} +2.78973 q^{3} +1.96140 q^{4} -2.75005i q^{5} -0.548060i q^{6} -0.778243i q^{8} +4.78260 q^{9} +O(q^{10})$	\(q-0.196456i q^{2} +2.78973 q^{3} +1.96140 q^{4} -2.75005i q^{5} -0.548060i q^{6} -0.778243i q^{8} +4.78260 q^{9} -0.540264 q^{10} -2.07934 q^{11} +5.47179 q^{12} -5.35598 q^{13} -7.67190i q^{15} +3.76992 q^{16} -3.70809i q^{17} -0.939572i q^{18} +(1.06311 + 4.22727i) q^{19} -5.39396i q^{20} +0.408499i q^{22} +1.06003 q^{23} -2.17109i q^{24} -2.56277 q^{25} +1.05222i q^{26} +4.97298 q^{27} +7.59133i q^{29} -1.50719 q^{30} +9.90698 q^{31} -2.29711i q^{32} -5.80079 q^{33} -0.728477 q^{34} +9.38062 q^{36} +2.85770i q^{37} +(0.830473 - 0.208855i) q^{38} -14.9417 q^{39} -2.14020 q^{40} -4.10043 q^{41} -2.06533 q^{43} -4.07842 q^{44} -13.1524i q^{45} -0.208250i q^{46} -8.20058i q^{47} +10.5171 q^{48} +0.503471i q^{50} -10.3446i q^{51} -10.5052 q^{52} +7.36306i q^{53} -0.976973i q^{54} +5.71828i q^{55} +(2.96579 + 11.7929i) q^{57} +1.49136 q^{58} -10.0289 q^{59} -15.0477i q^{60} +11.2309i q^{61} -1.94629i q^{62} +7.08856 q^{64} +14.7292i q^{65} +1.13960i q^{66} +8.91380i q^{67} -7.27307i q^{68} +2.95721 q^{69} +3.64198i q^{71} -3.72203i q^{72} -12.9420i q^{73} +0.561412 q^{74} -7.14943 q^{75} +(2.08519 + 8.29138i) q^{76} +2.93540i q^{78} +13.1850i q^{79} -10.3675i q^{80} -0.474522 q^{81} +0.805554i q^{82} -10.4730i q^{83} -10.1974 q^{85} +0.405746i q^{86} +21.1778i q^{87} +1.61823i q^{88} +12.8270 q^{89} -2.58387 q^{90} +2.07916 q^{92} +27.6378 q^{93} -1.61105 q^{94} +(11.6252 - 2.92361i) q^{95} -6.40832i q^{96} +1.90757 q^{97} -9.94464 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$		−	0.196456i		−	0.138916i	−0.997585	−	0.0694578i	$-0.977873\pi$
$2$		−	0.196456i		−	0.138916i	0.997585	−	0.0694578i	$-0.0221269\pi$
$3$	2.78973			1.61065			0.805326	−	0.592832i	$-0.201990\pi$
$3$	2.78973			1.61065			0.805326	+	0.592832i	$0.201990\pi$
$4$	1.96140			0.980702
$5$		−	2.75005i		−	1.22986i	−0.788582	−	0.614929i	$-0.789184\pi$
$5$		−	2.75005i		−	1.22986i	0.788582	−	0.614929i	$-0.210816\pi$
$6$		−	0.548060i		−	0.223745i
$7$		0			0
$7$		0			0
$8$		−	0.778243i		−	0.275150i
$9$	4.78260			1.59420
$10$	−0.540264			−0.170847
$11$	−2.07934			−0.626944			−0.313472	−	0.949597i	$-0.601492\pi$
$11$	−2.07934			−0.626944			−0.313472	+	0.949597i	$0.601492\pi$
$12$	5.47179			1.57957
$13$	−5.35598			−1.48548			−0.742741	−	0.669579i	$-0.766475\pi$
$13$	−5.35598			−1.48548			−0.742741	+	0.669579i	$0.766475\pi$
$14$		0			0
$15$		−	7.67190i		−	1.98088i
$16$	3.76992			0.942480
$17$		−	3.70809i		−	0.899344i	−0.893194	−	0.449672i	$-0.851541\pi$
$17$		−	3.70809i		−	0.899344i	0.893194	−	0.449672i	$-0.148459\pi$
$18$		−	0.939572i		−	0.221459i
$19$	1.06311	+	4.22727i	0.243894	+	0.969802i
$19$	1.06311	+	4.22727i	0.243894	+	0.969802i
$20$		−	5.39396i		−	1.20613i
$21$		0			0
$22$			0.408499i			0.0870922i
$23$	1.06003			0.221033			0.110516	−	0.993874i	$-0.464750\pi$
$23$	1.06003			0.221033			0.110516	+	0.993874i	$0.464750\pi$
$24$		−	2.17109i		−	0.443172i
$25$	−2.56277			−0.512553
$26$			1.05222i			0.206356i
$27$	4.97298			0.957051
$28$		0			0
$29$			7.59133i			1.40967i	0.709369	+	0.704837i	$0.248980\pi$
$29$			7.59133i			1.40967i	−0.709369	+	0.704837i	$0.751020\pi$
$30$	−1.50719			−0.275174
$31$	9.90698			1.77935			0.889673	−	0.456598i	$-0.150932\pi$
$31$	9.90698			1.77935			0.889673	+	0.456598i	$0.150932\pi$
$32$		−	2.29711i		−	0.406075i
$33$	−5.80079			−1.00979
$34$	−0.728477			−0.124933
$35$		0			0
$36$	9.38062			1.56344
$37$			2.85770i			0.469802i	0.972019	+	0.234901i	$0.0754767\pi$
$37$			2.85770i			0.469802i	−0.972019	+	0.234901i	$0.924523\pi$
$38$	0.830473	−	0.208855i	0.134721	−	0.0338807i
$39$	−14.9417			−2.39259
$40$	−2.14020			−0.338396
$41$	−4.10043			−0.640379			−0.320190	−	0.947353i	$-0.603747\pi$
$41$	−4.10043			−0.640379			−0.320190	+	0.947353i	$0.603747\pi$
$42$		0			0
$43$	−2.06533			−0.314959			−0.157480	−	0.987522i	$-0.550337\pi$
$43$	−2.06533			−0.314959			−0.157480	+	0.987522i	$0.550337\pi$
$44$	−4.07842			−0.614845
$45$		−	13.1524i		−	1.96064i
$46$		−	0.208250i		−	0.0307049i
$47$		−	8.20058i		−	1.19618i	−0.801430	−	0.598089i	$-0.795927\pi$
$47$		−	8.20058i		−	1.19618i	0.801430	−	0.598089i	$-0.204073\pi$
$48$	10.5171			1.51801
$49$		0			0
$50$			0.503471i			0.0712016i
$51$		−	10.3446i		−	1.44853i
$52$	−10.5052			−1.45682
$53$			7.36306i			1.01139i	0.862711	+	0.505697i	$0.168765\pi$
$53$			7.36306i			1.01139i	−0.862711	+	0.505697i	$0.831235\pi$
$54$		−	0.976973i		−	0.132949i
$55$			5.71828i			0.771052i
$56$		0			0
$57$	2.96579	+	11.7929i	0.392829	+	1.56201i
$58$	1.49136			0.195826
$59$	−10.0289			−1.30565			−0.652823	−	0.757511i	$-0.726415\pi$
$59$	−10.0289			−1.30565			−0.652823	+	0.757511i	$0.726415\pi$
$60$		−	15.0477i		−	1.94265i
$61$			11.2309i			1.43797i	0.695028	+	0.718983i	$0.255392\pi$
$61$			11.2309i			1.43797i	−0.695028	+	0.718983i	$0.744608\pi$
$62$		−	1.94629i		−	0.247179i
$63$		0			0
$64$	7.08856			0.886070
$65$			14.7292i			1.82693i
$66$			1.13960i			0.140275i
$67$			8.91380i			1.08899i	0.838763	+	0.544497i	$0.183279\pi$
$67$			8.91380i			1.08899i	−0.838763	+	0.544497i	$0.816721\pi$
$68$		−	7.27307i		−	0.881989i
$69$	2.95721			0.356007
$70$		0			0
$71$			3.64198i			0.432223i	0.976369	+	0.216112i	$0.0693376\pi$
$71$			3.64198i			0.432223i	−0.976369	+	0.216112i	$0.930662\pi$
$72$		−	3.72203i		−	0.438645i
$73$		−	12.9420i		−	1.51475i	−0.652983	−	0.757373i	$-0.726483\pi$
$73$		−	12.9420i		−	1.51475i	0.652983	−	0.757373i	$-0.273517\pi$
$74$	0.561412			0.0652628
$75$	−7.14943			−0.825545
$76$	2.08519	+	8.29138i	0.239188	+	0.951087i
$77$		0			0
$78$			2.93540i			0.332369i
$79$			13.1850i			1.48343i	0.670713	+	0.741717i	$0.265988\pi$
$79$			13.1850i			1.48343i	−0.670713	+	0.741717i	$0.734012\pi$
$80$		−	10.3675i		−	1.15912i
$81$	−0.474522			−0.0527246
$82$			0.805554i			0.0889586i
$83$		−	10.4730i		−	1.14956i	−0.818307	−	0.574781i	$-0.805087\pi$
$83$		−	10.4730i		−	1.14956i	0.818307	−	0.574781i	$-0.194913\pi$
$84$		0			0
$85$	−10.1974			−1.10607
$86$			0.405746i			0.0437527i
$87$			21.1778i			2.27050i
$88$			1.61823i			0.172504i
$89$	12.8270			1.35966			0.679828	−	0.733372i	$-0.262055\pi$
$89$	12.8270			1.35966			0.679828	+	0.733372i	$0.262055\pi$
$90$	−2.58387			−0.272364
$91$		0			0
$92$	2.07916			0.216767
$93$	27.6378			2.86591
$94$	−1.61105			−0.166168
$95$	11.6252	−	2.92361i	1.19272	−	0.299956i
$96$		−	6.40832i		−	0.654046i
$97$	1.90757			0.193684			0.0968421	−	0.995300i	$-0.469126\pi$
$97$	1.90757			0.193684			0.0968421	+	0.995300i	$0.469126\pi$
$98$		0			0
$99$	−9.94464			−0.999474
$100$	−5.02662			−0.502662
$101$			14.3622i			1.42910i	0.699586	+	0.714549i	$0.253368\pi$
$101$			14.3622i			1.42910i	−0.699586	+	0.714549i	$0.746632\pi$
$102$	−2.03226			−0.201223
$103$	−12.2416			−1.20620			−0.603100	−	0.797665i	$-0.706068\pi$
$103$	−12.2416			−1.20620			−0.603100	+	0.797665i	$0.706068\pi$
$104$			4.16825i			0.408731i
$105$		0			0
$106$	1.44652			0.140498
$107$		−	4.59799i		−	0.444504i	−0.974989	−	0.222252i	$-0.928659\pi$
$107$		−	4.59799i		−	0.444504i	0.974989	−	0.222252i	$-0.0713408\pi$
$108$	9.75403			0.938582
$109$		−	6.85569i		−	0.656656i	−0.944564	−	0.328328i	$-0.893515\pi$
$109$		−	6.85569i		−	0.656656i	0.944564	−	0.328328i	$-0.106485\pi$
$110$	1.12339			0.107111
$111$			7.97221i			0.756688i
$112$		0			0
$113$		−	11.9637i		−	1.12545i	−0.826644	−	0.562726i	$-0.809753\pi$
$113$		−	11.9637i		−	1.12545i	0.826644	−	0.562726i	$-0.190247\pi$
$114$	2.31680	−	0.582648i	0.216988	−	0.0545700i
$115$		−	2.91515i		−	0.271839i
$116$			14.8897i			1.38247i
$117$	−25.6155			−2.36816
$118$			1.97023i			0.181374i
$119$		0			0
$120$	−5.97060			−0.545038
$121$	−6.67636			−0.606942
$122$	2.20637			0.199756
$123$	−11.4391			−1.03143
$124$	19.4316			1.74501
$125$		−	6.70251i		−	0.599491i
$126$		0			0
$127$			2.67572i			0.237432i	0.992928	+	0.118716i	$0.0378777\pi$
$127$			2.67572i			0.237432i	−0.992928	+	0.118716i	$0.962122\pi$
$128$		−	5.98681i		−	0.529164i
$129$	−5.76171			−0.507290
$130$	2.89364			0.253789
$131$		−	1.47290i		−	0.128688i	−0.997928	−	0.0643439i	$-0.979505\pi$
$131$		−	1.47290i		−	0.128688i	0.997928	−	0.0643439i	$-0.0204955\pi$
$132$	−11.3777			−0.990302
$133$		0			0
$134$	1.75117			0.151278
$135$		−	13.6759i		−	1.17704i
$136$	−2.88579			−0.247455
$137$	15.7373			1.34453			0.672263	−	0.740312i	$-0.265322\pi$
$137$	15.7373			1.34453			0.672263	+	0.740312i	$0.265322\pi$
$138$		−	0.580963i		−	0.0494548i
$139$		−	5.58936i		−	0.474084i	−0.971499	−	0.237042i	$-0.923822\pi$
$139$		−	5.58936i		−	0.474084i	0.971499	−	0.237042i	$-0.0761778\pi$
$140$		0			0
$141$		−	22.8774i		−	1.92663i
$142$	0.715490			0.0600426
$143$	11.1369			0.931313
$144$	18.0300			1.50250
$145$	20.8765			1.73370
$146$	−2.54254			−0.210422
$147$		0			0
$148$			5.60510i			0.460736i
$149$	−2.30629			−0.188939			−0.0944693	−	0.995528i	$-0.530115\pi$
$149$	−2.30629			−0.188939			−0.0944693	+	0.995528i	$0.530115\pi$
$150$			1.40455i			0.114681i
$151$		−	9.50156i		−	0.773226i	−0.922242	−	0.386613i	$-0.873645\pi$
$151$		−	9.50156i		−	0.773226i	0.922242	−	0.386613i	$-0.126355\pi$
$152$	3.28984	−	0.827358i	0.266841	−	0.0671076i
$153$		−	17.7343i		−	1.43373i
$154$		0			0
$155$		−	27.2447i		−	2.18835i
$156$	−29.3068			−2.34642
$157$			5.80517i			0.463303i	0.972799	+	0.231652i	$0.0744129\pi$
$157$			5.80517i			0.463303i	−0.972799	+	0.231652i	$0.925587\pi$
$158$	2.59029			0.206072
$159$			20.5410i			1.62900i
$160$	−6.31716			−0.499415
$161$		0			0
$162$			0.0932227i			0.00732427i
$163$	−5.94087			−0.465325			−0.232663	−	0.972558i	$-0.574744\pi$
$163$	−5.94087			−0.465325			−0.232663	+	0.972558i	$0.574744\pi$
$164$	−8.04260			−0.628021
$165$			15.9525i			1.24190i
$166$	−2.05749			−0.159692
$167$	4.66951			0.361337			0.180669	−	0.983544i	$-0.442174\pi$
$167$	4.66951			0.361337			0.180669	+	0.983544i	$0.442174\pi$
$168$		0			0
$169$	15.6865			1.20666
$170$			2.00335i			0.153650i
$171$	5.08443	+	20.2173i	0.388816	+	1.54606i
$172$	−4.05094			−0.308881
$173$	17.4249			1.32479			0.662395	−	0.749155i	$-0.269540\pi$
$173$	17.4249			1.32479			0.662395	+	0.749155i	$0.269540\pi$
$174$	4.16051			0.315407
$175$		0			0
$176$	−7.83893			−0.590882
$177$	−27.9778			−2.10294
$178$		−	2.51994i		−	0.188877i
$179$		−	25.5846i		−	1.91228i	−0.292903	−	0.956142i	$-0.594621\pi$
$179$		−	25.5846i		−	1.91228i	0.292903	−	0.956142i	$-0.405379\pi$
$180$		−	25.7972i		−	1.92281i
$181$	−19.1000			−1.41970			−0.709848	−	0.704355i	$-0.751236\pi$
$181$	−19.1000			−1.41970			−0.709848	+	0.704355i	$0.751236\pi$
$182$		0			0
$183$			31.3311i			2.31606i
$184$		−	0.824964i		−	0.0608172i
$185$	7.85880			0.577791
$186$		−	5.42962i		−	0.398119i
$187$			7.71037i			0.563838i
$188$		−	16.0847i		−	1.17309i
$189$		0			0
$190$	−0.574360	−	2.28384i	−0.0416685	−	0.165687i
$191$	4.47316			0.323667			0.161833	−	0.986818i	$-0.448259\pi$
$191$	4.47316			0.323667			0.161833	+	0.986818i	$0.448259\pi$
$192$	19.7752			1.42715
$193$			5.17767i			0.372697i	0.982484	+	0.186348i	$0.0596653\pi$
$193$			5.17767i			0.372697i	−0.982484	+	0.186348i	$0.940335\pi$
$194$		−	0.374753i		−	0.0269057i
$195$			41.0905i			2.94255i
$196$		0			0
$197$	−17.0268			−1.21311			−0.606555	−	0.795042i	$-0.707449\pi$
$197$	−17.0268			−1.21311			−0.606555	+	0.795042i	$0.707449\pi$
$198$			1.95369i			0.138842i
$199$			6.92090i			0.490609i	0.969446	+	0.245305i	$0.0788880\pi$
$199$			6.92090i			0.490609i	−0.969446	+	0.245305i	$0.921112\pi$
$200$			1.99445i			0.141029i
$201$			24.8671i			1.75399i
$202$	2.82155			0.198524
$203$		0			0
$204$		−	20.2899i		−	1.42058i
$205$			11.2764i			0.787576i
$206$			2.40494i			0.167560i
$207$	5.06973			0.352370
$208$	−20.1916			−1.40004
$209$	−2.21057	−	8.78992i	−0.152908	−	0.608011i
$210$		0			0
$211$		−	4.72533i		−	0.325305i	−0.986683	−	0.162652i	$-0.947995\pi$
$211$		−	4.72533i		−	0.325305i	0.986683	−	0.162652i	$-0.0520049\pi$
$212$			14.4419i			0.991877i
$213$			10.1601i			0.696162i
$214$	−0.903303			−0.0617485
$215$			5.67975i			0.387356i
$216$		−	3.87019i		−	0.263333i
$217$		0			0
$218$	−1.34684			−0.0912197
$219$		−	36.1047i		−	2.43973i
$220$			11.2159i			0.756173i
$221$			19.8605i			1.33596i
$222$	1.56619			0.105116
$223$	−2.41092			−0.161447			−0.0807235	−	0.996737i	$-0.525723\pi$
$223$	−2.41092			−0.161447			−0.0807235	+	0.996737i	$0.525723\pi$
$224$		0			0
$225$	−12.2567			−0.817112
$226$	−2.35035			−0.156343
$227$	−7.44424			−0.494092			−0.247046	−	0.969004i	$-0.579460\pi$
$227$	−7.44424			−0.494092			−0.247046	+	0.969004i	$0.579460\pi$
$228$	5.81712	+	23.1307i	0.385248	+	1.53187i
$229$			17.7639i			1.17387i	0.809634	+	0.586936i	$0.199666\pi$
$229$			17.7639i			1.17387i	−0.809634	+	0.586936i	$0.800334\pi$
$230$	−0.572699			−0.0377626
$231$		0			0
$232$	5.90790			0.387872
$233$	5.73857			0.375946			0.187973	−	0.982174i	$-0.439808\pi$
$233$	5.73857			0.375946			0.187973	+	0.982174i	$0.439808\pi$
$234$			5.03233i			0.328974i
$235$	−22.5520			−1.47113
$236$	−19.6706			−1.28045
$237$			36.7828i			2.38930i
$238$		0			0
$239$	−16.5222			−1.06874			−0.534368	−	0.845252i	$-0.679450\pi$
$239$	−16.5222			−1.06874			−0.534368	+	0.845252i	$0.679450\pi$
$240$		−	28.9224i		−	1.86693i
$241$	−15.0902			−0.972046			−0.486023	−	0.873946i	$-0.661553\pi$
$241$	−15.0902			−0.972046			−0.486023	+	0.873946i	$0.661553\pi$
$242$			1.31161i			0.0843136i
$243$	−16.2427			−1.04197
$244$			22.0283i			1.41022i
$245$		0			0
$246$			2.24728i			0.143281i
$247$	−5.69400	−	22.6412i	−0.362300	−	1.44062i
$248$		−	7.71004i		−	0.489588i
$249$		−	29.2169i		−	1.85155i
$250$	−1.31675			−0.0832786
$251$			1.76593i			0.111464i	0.998446	+	0.0557321i	$0.0177493\pi$
$251$			1.76593i			0.111464i	−0.998446	+	0.0557321i	$0.982251\pi$
$252$		0			0
$253$	−2.20417			−0.138575
$254$	0.525661			0.0329829
$255$	−28.4481			−1.78149
$256$	13.0010			0.812561
$257$	13.6381			0.850719			0.425360	−	0.905024i	$-0.360148\pi$
$257$	13.6381			0.850719			0.425360	+	0.905024i	$0.360148\pi$
$258$			1.13192i			0.0704705i
$259$		0			0
$260$			28.8899i			1.79168i
$261$			36.3063i			2.24730i
$262$	−0.289360			−0.0178767
$263$	−4.94649			−0.305014			−0.152507	−	0.988302i	$-0.548735\pi$
$263$	−4.94649			−0.305014			−0.152507	+	0.988302i	$0.548735\pi$
$264$			4.51442i			0.277844i
$265$	20.2488			1.24387
$266$		0			0
$267$	35.7838			2.18993
$268$			17.4836i			1.06798i
$269$	−26.0652			−1.58922			−0.794612	−	0.607117i	$-0.792326\pi$
$269$	−26.0652			−1.58922			−0.794612	+	0.607117i	$0.792326\pi$
$270$	−2.68672			−0.163509
$271$		−	27.0886i		−	1.64552i	−0.568392	−	0.822758i	$-0.692434\pi$
$271$		−	27.0886i		−	1.64552i	0.568392	−	0.822758i	$-0.307566\pi$
$272$		−	13.9792i		−	0.847614i
$273$		0			0
$274$		−	3.09169i		−	0.186776i
$275$	5.32885			0.321342
$276$	5.80029			0.349137
$277$	13.8820			0.834089			0.417045	−	0.908886i	$-0.363066\pi$
$277$	13.8820			0.834089			0.417045	+	0.908886i	$0.363066\pi$
$278$	−1.09806			−0.0658576
$279$	47.3812			2.83664
$280$		0			0
$281$			20.1211i			1.20032i	0.799879	+	0.600161i	$0.204897\pi$
$281$			20.1211i			1.20032i	−0.799879	+	0.600161i	$0.795103\pi$
$282$	−4.49441			−0.267638
$283$			20.4888i			1.21793i	0.793197	+	0.608965i	$0.208415\pi$
$283$			20.4888i			1.21793i	−0.793197	+	0.608965i	$0.791585\pi$
$284$			7.14340i			0.423883i
$285$	32.4312	−	8.15607i	1.92106	−	0.483124i
$286$		−	2.18791i		−	0.129374i
$287$		0			0
$288$		−	10.9862i		−	0.647366i
$289$	3.25007			0.191180
$290$		−	4.10132i		−	0.240838i
$291$	5.32160			0.311958
$292$		−	25.3845i		−	1.48551i
$293$	−21.3544			−1.24754			−0.623769	−	0.781608i	$-0.714400\pi$
$293$	−21.3544			−1.24754			−0.623769	+	0.781608i	$0.714400\pi$
$294$		0			0
$295$			27.5798i			1.60576i
$296$	2.22398			0.129266
$297$	−10.3405			−0.600017
$298$			0.453085i			0.0262465i
$299$	−5.67753			−0.328340
$300$	−14.0229			−0.809614
$301$		0			0
$302$	−1.86664			−0.107413
$303$			40.0668i			2.30178i
$304$	4.00784	+	15.9365i	0.229865	+	0.914019i
$305$	30.8854			1.76850
$306$	−3.48402			−0.199168
$307$	−14.7170			−0.839943			−0.419972	−	0.907537i	$-0.637960\pi$
$307$	−14.7170			−0.839943			−0.419972	+	0.907537i	$0.637960\pi$
$308$		0			0
$309$	−34.1508			−1.94277
$310$	−5.35239			−0.303995
$311$		−	10.3591i		−	0.587409i	−0.955896	−	0.293704i	$-0.905112\pi$
$311$		−	10.3591i		−	0.587409i	0.955896	−	0.293704i	$-0.0948882\pi$
$312$			11.6283i			0.658323i
$313$			3.32150i			0.187742i	0.995584	+	0.0938710i	$0.0299241\pi$
$313$			3.32150i			0.187742i	−0.995584	+	0.0938710i	$0.970076\pi$
$314$	1.14046			0.0643600
$315$		0			0
$316$			25.8612i			1.45481i
$317$			6.35683i			0.357035i	0.983937	+	0.178518i	$0.0571301\pi$
$317$			6.35683i			0.357035i	−0.983937	+	0.178518i	$0.942870\pi$
$318$	4.03540			0.226294
$319$		−	15.7849i		−	0.883787i
$320$		−	19.4939i		−	1.08974i
$321$		−	12.8271i		−	0.715941i
$322$		0			0
$323$	15.6751	−	3.94211i	0.872185	−	0.219345i
$324$	−0.930729			−0.0517072
$325$	13.7261			0.761388
$326$			1.16712i			0.0646409i
$327$		−	19.1255i		−	1.05764i
$328$			3.19113i			0.176201i
$329$		0			0
$330$	3.13396			0.172519
$331$		−	12.7311i		−	0.699766i	−0.936793	−	0.349883i	$-0.886221\pi$
$331$		−	12.7311i		−	0.699766i	0.936793	−	0.349883i	$-0.113779\pi$
$332$		−	20.5418i		−	1.12738i
$333$			13.6672i			0.748959i
$334$		−	0.917354i		−	0.0501954i
$335$	24.5134			1.33931
$336$		0			0
$337$		−	19.0069i		−	1.03537i	−0.855571	−	0.517685i	$-0.826794\pi$
$337$		−	19.0069i		−	1.03537i	0.855571	−	0.517685i	$-0.173206\pi$
$338$		−	3.08172i		−	0.167623i
$339$		−	33.3756i		−	1.81271i
$340$	−20.0013			−1.08472
$341$	−20.6000			−1.11555
$342$	3.97182	−	0.998869i	0.214772	−	0.0540126i
$343$		0			0
$344$			1.60733i			0.0866612i
$345$		−	8.13248i		−	0.437838i
$346$		−	3.42323i		−	0.184034i
$347$	11.1271			0.597334			0.298667	−	0.954357i	$-0.403458\pi$
$347$	11.1271			0.597334			0.298667	+	0.954357i	$0.403458\pi$
$348$			41.5382i			2.22668i
$349$		−	10.0729i		−	0.539190i	−0.962974	−	0.269595i	$-0.913110\pi$
$349$		−	10.0729i		−	0.539190i	0.962974	−	0.269595i	$-0.0868899\pi$
$350$		0			0
$351$	−26.6352			−1.42168
$352$			4.77646i			0.254586i
$353$			10.7713i			0.573299i	0.958036	+	0.286649i	$0.0925415\pi$
$353$			10.7713i			0.573299i	−0.958036	+	0.286649i	$0.907459\pi$
$354$			5.49641i			0.292131i
$355$	10.0156			0.531574
$356$	25.1589			1.33342
$357$		0			0
$358$	−5.02626			−0.265646
$359$	28.0647			1.48120			0.740599	−	0.671947i	$-0.234542\pi$
$359$	28.0647			1.48120			0.740599	+	0.671947i	$0.234542\pi$
$360$	−10.2357			−0.539471
$361$	−16.7396	+	8.98811i	−0.881031	+	0.473058i
$362$			3.75232i			0.197218i
$363$	−18.6252			−0.977572
$364$		0			0
$365$	−35.5911			−1.86292
$366$	6.15519			0.321737
$367$		−	19.4906i		−	1.01740i	−0.860944	−	0.508700i	$-0.830126\pi$
$367$		−	19.4906i		−	1.01740i	0.860944	−	0.508700i	$-0.169874\pi$
$368$	3.99625			0.208319
$369$	−19.6107			−1.02089
$370$		−	1.54391i		−	0.0802641i
$371$		0			0
$372$	54.2090			2.81060
$373$		−	15.8353i		−	0.819921i	−0.912103	−	0.409960i	$-0.865543\pi$
$373$		−	15.8353i		−	0.819921i	0.912103	−	0.409960i	$-0.134457\pi$
$374$	1.51475			0.0783259
$375$		−	18.6982i		−	0.965572i
$376$	−6.38204			−0.329129
$377$		−	40.6590i		−	2.09405i
$378$		0			0
$379$		−	20.7777i		−	1.06728i	−0.845712	−	0.533640i	$-0.820824\pi$
$379$		−	20.7777i		−	1.06728i	0.845712	−	0.533640i	$-0.179176\pi$
$380$	22.8017	−	5.73437i	1.16970	−	0.294167i
$381$			7.46454i			0.382420i
$382$		−	0.878781i		−	0.0449623i
$383$	−32.2659			−1.64871			−0.824355	−	0.566074i	$-0.808462\pi$
$383$	−32.2659			−1.64871			−0.824355	+	0.566074i	$0.808462\pi$
$384$		−	16.7016i		−	0.852300i
$385$		0			0
$386$	1.01719			0.0517734
$387$	−9.87764			−0.502108
$388$	3.74151			0.189947
$389$	9.58397			0.485926			0.242963	−	0.970036i	$-0.421881\pi$
$389$	9.58397			0.485926			0.242963	+	0.970036i	$0.421881\pi$
$390$	8.07249			0.408766
$391$		−	3.93071i		−	0.198784i
$392$		0			0
$393$		−	4.10899i		−	0.207271i
$394$			3.34502i			0.168520i
$395$	36.2595			1.82441
$396$	−19.5055			−0.980187
$397$			3.53192i			0.177262i	0.996065	+	0.0886311i	$0.0282492\pi$
$397$			3.53192i			0.177262i	−0.996065	+	0.0886311i	$0.971751\pi$
$398$	1.35965			0.0681532
$399$		0			0
$400$	−9.66142			−0.483071
$401$		−	7.17572i		−	0.358338i	−0.983818	−	0.179169i	$-0.942659\pi$
$401$		−	7.17572i		−	0.358338i	0.983818	−	0.179169i	$-0.0573410\pi$
$402$	4.88530			0.243656
$403$	−53.0616			−2.64319
$404$			28.1702i			1.40152i
$405$			1.30496i			0.0648439i
$406$		0			0
$407$		−	5.94211i		−	0.294540i
$408$	−8.05059			−0.398564
$409$	−1.14934			−0.0568314			−0.0284157	−	0.999596i	$-0.509046\pi$
$409$	−1.14934			−0.0568314			−0.0284157	+	0.999596i	$0.509046\pi$
$410$	2.21531			0.109407
$411$	43.9028			2.16556
$412$	−24.0107			−1.18292
$413$		0			0
$414$		−	0.995979i		−	0.0489497i
$415$	−28.8013			−1.41380
$416$			12.3033i			0.603218i
$417$		−	15.5928i		−	0.763584i
$418$	−1.72683	+	0.434279i	−0.0844622	+	0.0212413i
$419$			23.2054i			1.13366i	0.823836	+	0.566828i	$0.191830\pi$
$419$			23.2054i			1.13366i	−0.823836	+	0.566828i	$0.808170\pi$
$420$		0			0
$421$		−	17.4983i		−	0.852816i	−0.904531	−	0.426408i	$-0.859779\pi$
$421$		−	17.4983i		−	0.852816i	0.904531	−	0.426408i	$-0.140221\pi$
$422$	−0.928320			−0.0451899
$423$		−	39.2201i		−	1.90695i
$424$	5.73025			0.278285
$425$			9.50297i			0.460962i
$426$	1.99602			0.0967077
$427$		0			0
$428$		−	9.01851i		−	0.435926i
$429$	31.0689			1.50002
$430$	1.11582			0.0538097
$431$			21.1941i			1.02088i	0.859913	+	0.510441i	$0.170518\pi$
$431$			21.1941i			1.02088i	−0.859913	+	0.510441i	$0.829482\pi$
$432$	18.7477			0.902001
$433$	3.12283			0.150074			0.0750368	−	0.997181i	$-0.476093\pi$
$433$	3.12283			0.150074			0.0750368	+	0.997181i	$0.476093\pi$
$434$		0			0
$435$	58.2399			2.79239
$436$		−	13.4468i		−	0.643984i
$437$	1.12693	+	4.48105i	0.0539086	+	0.214358i
$438$	−7.09299			−0.338916
$439$	6.40242			0.305571			0.152785	−	0.988259i	$-0.451176\pi$
$439$	6.40242			0.305571			0.152785	+	0.988259i	$0.451176\pi$
$440$	4.45021			0.212155
$441$		0			0
$442$	3.90171			0.185585
$443$	12.2454			0.581794			0.290897	−	0.956754i	$-0.406046\pi$
$443$	12.2454			0.581794			0.290897	+	0.956754i	$0.406046\pi$
$444$			15.6367i			0.742086i
$445$		−	35.2748i		−	1.67218i
$446$			0.473640i			0.0224275i
$447$	−6.43393			−0.304314
$448$		0			0
$449$		−	32.1137i		−	1.51554i	−0.652523	−	0.757769i	$-0.726289\pi$
$449$		−	32.1137i		−	1.51554i	0.652523	−	0.757769i	$-0.273711\pi$
$450$			2.40790i			0.113510i
$451$	8.52617			0.401482
$452$		−	23.4657i		−	1.10373i
$453$		−	26.5068i		−	1.24540i
$454$			1.46247i			0.0686370i
$455$		0			0
$456$	9.17777	−	2.30811i	0.429789	−	0.108087i
$457$	21.8426			1.02175			0.510877	−	0.859654i	$-0.329321\pi$
$457$	21.8426			1.02175			0.510877	+	0.859654i	$0.329321\pi$
$458$	3.48983			0.163069
$459$		−	18.4403i		−	0.860718i
$460$		−	5.71778i		−	0.266593i
$461$		−	10.1233i		−	0.471490i	−0.971815	−	0.235745i	$-0.924247\pi$
$461$		−	10.1233i		−	0.471490i	0.971815	−	0.235745i	$-0.0757531\pi$
$462$		0			0
$463$	18.9728			0.881742			0.440871	−	0.897571i	$-0.354670\pi$
$463$	18.9728			0.881742			0.440871	+	0.897571i	$0.354670\pi$
$464$			28.6187i			1.32859i
$465$		−	76.0053i		−	3.52466i
$466$		−	1.12738i		−	0.0522248i
$467$			14.0902i			0.652018i	0.945367	+	0.326009i	$0.105704\pi$
$467$			14.0902i			0.652018i	−0.945367	+	0.326009i	$0.894296\pi$
$468$	−50.2424			−2.32246
$469$		0			0
$470$			4.43048i			0.204363i
$471$			16.1949i			0.746220i
$472$			7.80488i			0.359249i
$473$	4.29451			0.197462
$474$	7.22620			0.331910
$475$	−2.72450	−	10.8335i	−0.125009	−	0.497075i
$476$		0			0
$477$			35.2146i			1.61237i
$478$			3.24590i			0.148464i
$479$		−	2.16428i		−	0.0988883i	−0.998777	−	0.0494441i	$-0.984255\pi$
$479$		−	2.16428i		−	0.0988883i	0.998777	−	0.0494441i	$-0.0157450\pi$
$480$	−17.6232			−0.804385
$481$		−	15.3058i		−	0.697883i
$482$			2.96457i			0.135032i
$483$		0			0
$484$	−13.0950			−0.595229
$485$		−	5.24590i		−	0.238204i
$486$			3.19099i			0.144746i
$487$			18.0514i			0.817985i	0.912538	+	0.408992i	$0.134120\pi$
$487$			18.0514i			0.817985i	−0.912538	+	0.408992i	$0.865880\pi$
$488$	8.74034			0.395657
$489$	−16.5734			−0.749477
$490$		0			0
$491$	−36.4068			−1.64302			−0.821508	−	0.570196i	$-0.806867\pi$
$491$	−36.4068			−1.64302			−0.821508	+	0.570196i	$0.806867\pi$
$492$	−22.4367			−1.01152
$493$	28.1493			1.26778
$494$	−4.44800	+	1.11862i	−0.200125	+	0.0503292i
$495$			27.3482i			1.22921i
$496$	37.3485			1.67700
$497$		0			0
$498$	−5.73984			−0.257208
$499$	−12.8482			−0.575163			−0.287581	−	0.957756i	$-0.592851\pi$
$499$	−12.8482			−0.575163			−0.287581	+	0.957756i	$0.592851\pi$
$500$		−	13.1463i		−	0.587922i
$501$	13.0267			0.581989
$502$	0.346927			0.0154841
$503$			16.0405i			0.715209i	0.933873	+	0.357604i	$0.116406\pi$
$503$			16.0405i			0.715209i	−0.933873	+	0.357604i	$0.883594\pi$
$504$		0			0
$505$	39.4969			1.75759
$506$			0.433023i			0.0192502i
$507$	43.7612			1.94350
$508$			5.24817i			0.232850i
$509$	35.6010			1.57798			0.788992	−	0.614403i	$-0.210603\pi$
$509$	35.6010			1.57798			0.788992	+	0.614403i	$0.210603\pi$
$510$			5.58880i			0.247476i
$511$		0			0
$512$		−	14.5277i		−	0.642042i
$513$	5.28683	+	21.0221i	0.233419	+	0.928150i
$514$		−	2.67928i		−	0.118178i
$515$			33.6650i			1.48346i
$516$	−11.3010			−0.497501
$517$			17.0518i			0.749936i
$518$		0			0
$519$	48.6108			2.13378
$520$	11.4629			0.502681
$521$	−0.667003			−0.0292220			−0.0146110	−	0.999893i	$-0.504651\pi$
$521$	−0.667003			−0.0292220			−0.0146110	+	0.999893i	$0.504651\pi$
$522$	7.13260			0.312185
$523$	−5.33821			−0.233424			−0.116712	−	0.993166i	$-0.537235\pi$
$523$	−5.33821			−0.233424			−0.116712	+	0.993166i	$0.537235\pi$
$524$		−	2.88895i		−	0.126204i
$525$		0			0
$526$			0.971769i			0.0423711i
$527$		−	36.7360i		−	1.60024i
$528$	−21.8685			−0.951705
$529$	−21.8763			−0.951145
$530$		−	3.97800i		−	0.172793i
$531$	−47.9640			−2.08146
$532$		0			0
$533$	21.9618			0.951272
$534$		−	7.02995i		−	0.304216i
$535$	−12.6447			−0.546677
$536$	6.93710			0.299637
$537$		−	71.3742i		−	3.08002i
$538$			5.12068i			0.220768i
$539$		0			0
$540$		−	26.8241i		−	1.15432i
$541$	3.88163			0.166884			0.0834421	−	0.996513i	$-0.473409\pi$
$541$	3.88163			0.166884			0.0834421	+	0.996513i	$0.473409\pi$
$542$	−5.32173			−0.228588
$543$	−53.2840			−2.28664
$544$	−8.51789			−0.365201
$545$	−18.8535			−0.807594
$546$		0			0
$547$		−	20.3483i		−	0.870033i	−0.900423	−	0.435016i	$-0.856743\pi$
$547$		−	20.3483i		−	0.870033i	0.900423	−	0.435016i	$-0.143257\pi$
$548$	30.8672			1.31858
$549$			53.7128i			2.29241i
$550$		−	1.04689i		−	0.0446394i
$551$	−32.0906	+	8.07042i	−1.36710	+	0.343812i
$552$		−	2.30143i		−	0.0979553i
$553$		0			0
$554$		−	2.72721i		−	0.115868i
$555$	21.9239			0.930620
$556$		−	10.9630i		−	0.464935i
$557$	−2.52447			−0.106965			−0.0534826	−	0.998569i	$-0.517032\pi$
$557$	−2.52447			−0.106965			−0.0534826	+	0.998569i	$0.517032\pi$
$558$		−	9.30832i		−	0.394053i
$559$	11.0618			0.467866
$560$		0			0
$561$			21.5099i			0.908147i
$562$	3.95291			0.166743
$563$	29.5811			1.24670			0.623348	−	0.781945i	$-0.285772\pi$
$563$	29.5811			1.24670			0.623348	+	0.781945i	$0.285772\pi$
$564$		−	44.8719i		−	1.88945i
$565$	−32.9008			−1.38415
$566$	4.02514			0.169189
$567$		0			0
$568$	2.83434			0.118926
$569$		−	19.1030i		−	0.800839i	−0.916332	−	0.400419i	$-0.868864\pi$
$569$		−	19.1030i		−	0.800839i	0.916332	−	0.400419i	$-0.131136\pi$
$570$	−1.60231	−	6.37130i	−0.0671134	−	0.266865i
$571$	20.1308			0.842448			0.421224	−	0.906957i	$-0.361601\pi$
$571$	20.1308			0.842448			0.421224	+	0.906957i	$0.361601\pi$
$572$	21.8439			0.913341
$573$	12.4789			0.521315
$574$		0			0
$575$	−2.71662			−0.113291
$576$	33.9018			1.41257
$577$		−	4.80662i		−	0.200102i	−0.994982	−	0.100051i	$-0.968099\pi$
$577$		−	4.80662i		−	0.200102i	0.994982	−	0.100051i	$-0.0319007\pi$
$578$		−	0.638496i		−	0.0265579i
$579$			14.4443i			0.600285i
$580$	40.9473			1.70024
$581$		0			0
$582$		−	1.04546i		−	0.0433358i
$583$		−	15.3103i		−	0.634087i
$584$	−10.0720			−0.416783
$585$			70.4439i			2.91250i
$586$			4.19521i			0.173303i
$587$		−	27.5950i		−	1.13897i	−0.822002	−	0.569485i	$-0.807143\pi$
$587$		−	27.5950i		−	1.13897i	0.822002	−	0.569485i	$-0.192857\pi$
$588$		0			0
$589$	10.5322	+	41.8795i	0.433972	+	1.72561i
$590$	5.41823			0.223065
$591$	−47.5002			−1.95390
$592$			10.7733i			0.442779i
$593$		−	29.2795i		−	1.20237i	−0.799111	−	0.601183i	$-0.794696\pi$
$593$		−	29.2795i		−	1.20237i	0.799111	−	0.601183i	$-0.205304\pi$
$594$			2.03146i			0.0833517i
$595$		0			0
$596$	−4.52357			−0.185293
$597$			19.3074i			0.790201i
$598$			1.11539i			0.0456115i
$599$		−	16.1966i		−	0.661776i	−0.943670	−	0.330888i	$-0.892652\pi$
$599$		−	16.1966i		−	0.661776i	0.943670	−	0.330888i	$-0.107348\pi$
$600$			5.56399i			0.227149i
$601$	28.5965			1.16648			0.583238	−	0.812301i	$-0.301785\pi$
$601$	28.5965			1.16648			0.583238	+	0.812301i	$0.301785\pi$
$602$		0			0
$603$			42.6311i			1.73607i
$604$		−	18.6364i		−	0.758304i
$605$			18.3603i			0.746453i
$606$	7.87138			0.319753
$607$	4.99513			0.202746			0.101373	−	0.994848i	$-0.467676\pi$
$607$	4.99513			0.202746			0.101373	+	0.994848i	$0.467676\pi$
$608$	9.71050	−	2.44208i	0.393813	−	0.0990395i
$609$		0			0
$610$		−	6.06764i		−	0.245671i
$611$			43.9221i			1.77690i
$612$		−	34.7842i		−	1.40607i
$613$	8.31650			0.335900			0.167950	−	0.985796i	$-0.446285\pi$
$613$	8.31650			0.335900			0.167950	+	0.985796i	$0.446285\pi$
$614$			2.89125i			0.116681i
$615$			31.4581i			1.26851i
$616$		0			0
$617$	−34.7548			−1.39918			−0.699588	−	0.714546i	$-0.746633\pi$
$617$	−34.7548			−1.39918			−0.699588	+	0.714546i	$0.746633\pi$
$618$			6.70913i			0.269881i
$619$		−	11.9308i		−	0.479539i	−0.970830	−	0.239769i	$-0.922928\pi$
$619$		−	11.9308i		−	0.479539i	0.970830	−	0.239769i	$-0.0770718\pi$
$620$		−	53.4378i		−	2.14612i
$621$	5.27154			0.211539
$622$	−2.03510			−0.0816002
$623$		0			0
$624$	−56.3292			−2.25497
$625$	−31.2461			−1.24984
$626$	0.652528			0.0260803
$627$	−6.16688	−	24.5215i	−0.246282	−	0.979295i
$628$			11.3863i			0.454363i
$629$	10.5966			0.422514
$630$		0			0
$631$	16.2305			0.646124			0.323062	−	0.946378i	$-0.395288\pi$
$631$	16.2305			0.646124			0.323062	+	0.946378i	$0.395288\pi$
$632$	10.2612			0.408167
$633$		−	13.1824i		−	0.523953i
$634$	1.24884			0.0495977
$635$	7.35835			0.292007
$636$			40.2891i			1.59757i
$637$		0			0
$638$	−3.10105			−0.122772
$639$			17.4181i			0.689051i
$640$	−16.4640			−0.650797
$641$		−	7.09776i		−	0.280345i	−0.990127	−	0.140172i	$-0.955234\pi$
$641$		−	7.09776i		−	0.280345i	0.990127	−	0.140172i	$-0.0447657\pi$
$642$	−2.51997			−0.0994554
$643$			50.2116i			1.98015i	0.140537	+	0.990075i	$0.455117\pi$
$643$			50.2116i			1.98015i	−0.140537	+	0.990075i	$0.544883\pi$
$644$		0			0
$645$			15.8450i			0.623895i
$646$	−0.774452	−	3.07947i	−0.0304704	−	0.121160i
$647$			36.2059i			1.42340i	0.702483	+	0.711701i	$0.252075\pi$
$647$			36.2059i			1.42340i	−0.702483	+	0.711701i	$0.747925\pi$
$648$			0.369293i			0.0145072i
$649$	20.8534			0.818566
$650$		−	2.69658i		−	0.105769i
$651$		0			0
$652$	−11.6525			−0.456345
$653$	−11.4195			−0.446878			−0.223439	−	0.974718i	$-0.571728\pi$
$653$	−11.4195			−0.446878			−0.223439	+	0.974718i	$0.571728\pi$
$654$	−3.75733			−0.146923
$655$	−4.05054			−0.158268
$656$	−15.4583			−0.603544
$657$		−	61.8964i		−	2.41481i
$658$		0			0
$659$		−	29.3341i		−	1.14269i	−0.820709	−	0.571347i	$-0.806421\pi$
$659$		−	29.3341i		−	1.14269i	0.820709	−	0.571347i	$-0.193579\pi$
$660$			31.2892i			1.21793i
$661$	1.55131			0.0603390			0.0301695	−	0.999545i	$-0.490395\pi$
$661$	1.55131			0.0603390			0.0301695	+	0.999545i	$0.490395\pi$
$662$	−2.50111			−0.0972083
$663$			55.4054i			2.15177i
$664$	−8.15054			−0.316302
$665$		0			0
$666$	2.68501			0.104042
$667$			8.04708i			0.311584i
$668$	9.15880			0.354364
$669$	−6.72582			−0.260035
$670$		−	4.81580i		−	0.186051i
$671$		−	23.3528i		−	0.901524i
$672$		0			0
$673$			30.2992i			1.16795i	0.811773	+	0.583973i	$0.198503\pi$
$673$			30.2992i			1.16795i	−0.811773	+	0.583973i	$0.801497\pi$
$674$	−3.73402			−0.143829
$675$	−12.7446			−0.490539
$676$	30.7676			1.18337
$677$	−12.7610			−0.490445			−0.245223	−	0.969467i	$-0.578861\pi$
$677$	−12.7610			−0.490445			−0.245223	+	0.969467i	$0.578861\pi$
$678$	−6.55684			−0.251814
$679$		0			0
$680$			7.93607i			0.304335i
$681$	−20.7674			−0.795810
$682$			4.04699i			0.154967i
$683$			20.0794i			0.768319i	0.923267	+	0.384159i	$0.125509\pi$
$683$			20.0794i			0.768319i	−0.923267	+	0.384159i	$0.874491\pi$
$684$	9.97264	+	39.6544i	0.381313	+	1.51622i
$685$		−	43.2783i		−	1.65358i
$686$		0			0
$687$			49.5565i			1.89070i
$688$	−7.78611			−0.296843
$689$		−	39.4364i		−	1.50241i
$690$	−1.59768			−0.0608225
$691$			2.53536i			0.0964495i	0.998837	+	0.0482248i	$0.0153564\pi$
$691$			2.53536i			0.0964495i	−0.998837	+	0.0482248i	$0.984644\pi$
$692$	34.1773			1.29923
$693$		0			0
$694$		−	2.18599i		−	0.0829789i
$695$	−15.3710			−0.583056
$696$	16.4814			0.624728
$697$			15.2048i			0.575921i
$698$	−1.97888			−0.0749019
$699$	16.0091			0.605519
$700$		0			0
$701$	−12.3718			−0.467278			−0.233639	−	0.972323i	$-0.575063\pi$
$701$	−12.3718			−0.467278			−0.233639	+	0.972323i	$0.575063\pi$
$702$			5.23265i			0.197494i
$703$	−12.0802	+	3.03805i	−0.455615	+	0.114582i
$704$	−14.7395			−0.555516
$705$	−62.9140			−2.36948
$706$	2.11609			0.0796401
$707$		0			0
$708$	−54.8758			−2.06236
$709$	42.0172			1.57799			0.788995	−	0.614399i	$-0.210602\pi$
$709$	42.0172			1.57799			0.788995	+	0.614399i	$0.210602\pi$
$710$		−	1.96763i		−	0.0738439i
$711$			63.0589i			2.36489i
$712$		−	9.98249i		−	0.374110i
$713$	10.5017			0.393294
$714$		0			0
$715$		−	30.6270i		−	1.14538i
$716$		−	50.1818i		−	1.87538i
$717$	−46.0926			−1.72136
$718$		−	5.51349i		−	0.205762i
$719$		−	43.4739i		−	1.62130i	−0.585529	−	0.810652i	$-0.699113\pi$
$719$		−	43.4739i		−	1.62130i	0.585529	−	0.810652i	$-0.300887\pi$
$720$		−	49.5834i		−	1.84787i
$721$		0			0
$722$	1.76577	+	3.28860i	0.0657151	+	0.122389i
$723$	−42.0976			−1.56563
$724$	−37.4629			−1.39230
$725$		−	19.4548i		−	0.722533i
$726$			3.65905i			0.135800i
$727$			40.2084i			1.49125i	0.666368	+	0.745623i	$0.267848\pi$
$727$			40.2084i			1.49125i	−0.666368	+	0.745623i	$0.732152\pi$
$728$		0			0
$729$	−43.8893			−1.62553
$730$			6.99209i			0.258789i
$731$			7.65842i			0.283257i
$732$			61.4530i			2.27137i
$733$			3.74230i			0.138225i	0.997609	+	0.0691126i	$0.0220168\pi$
$733$			3.74230i			0.138225i	−0.997609	+	0.0691126i	$0.977983\pi$
$734$	−3.82905			−0.141333
$735$		0			0
$736$		−	2.43502i		−	0.0897559i
$737$		−	18.5348i		−	0.682738i
$738$			3.85265i			0.141818i
$739$	44.8303			1.64911			0.824555	−	0.565782i	$-0.191426\pi$
$739$	44.8303			1.64911			0.824555	+	0.565782i	$0.191426\pi$
$740$	15.4143			0.566641
$741$	−15.8847	−	63.1628i	−0.583540	−	2.32034i
$742$		0			0
$743$			9.87990i			0.362458i	0.983441	+	0.181229i	$0.0580076\pi$
$743$			9.87990i			0.362458i	−0.983441	+	0.181229i	$0.941992\pi$
$744$		−	21.5089i		−	0.788556i
$745$			6.34241i			0.232368i
$746$	−3.11094			−0.113900
$747$		−	50.0882i		−	1.83263i
$748$			15.1232i			0.552957i
$749$		0			0
$750$	−3.67338			−0.134133
$751$			36.2222i			1.32177i	0.750489	+	0.660883i	$0.229818\pi$
$751$			36.2222i			1.32177i	−0.750489	+	0.660883i	$0.770182\pi$
$752$		−	30.9155i		−	1.12737i
$753$			4.92646i			0.179530i
$754$	−7.98772			−0.290895
$755$	−26.1297			−0.950958
$756$		0			0
$757$	45.8007			1.66465			0.832327	−	0.554285i	$-0.187008\pi$
$757$	45.8007			1.66465			0.832327	+	0.554285i	$0.187008\pi$
$758$	−4.08191			−0.148262
$759$	−6.14904			−0.223196
$760$	−2.27527	−	9.04722i	−0.0825329	−	0.328177i
$761$		−	0.124409i		−	0.00450982i	−0.999997	−	0.00225491i	$-0.999282\pi$
$761$		−	0.124409i		−	0.00450982i	0.999997	−	0.00225491i	$-0.000717761\pi$
$762$	1.46645			0.0531240
$763$		0			0
$764$	8.77369			0.317421
$765$	−48.7702			−1.76329
$766$			6.33883i			0.229031i
$767$	53.7143			1.93951
$768$	36.2692			1.30875
$769$		−	6.78020i		−	0.244500i	−0.992499	−	0.122250i	$-0.960989\pi$
$769$		−	6.78020i		−	0.244500i	0.992499	−	0.122250i	$-0.0390110\pi$
$770$		0			0
$771$	38.0465			1.37021
$772$			10.1555i			0.365505i
$773$	−34.9022			−1.25535			−0.627673	−	0.778477i	$-0.715992\pi$
$773$	−34.9022			−1.25535			−0.627673	+	0.778477i	$0.715992\pi$
$774$			1.94052i			0.0697507i
$775$	−25.3893			−0.912009
$776$		−	1.48455i		−	0.0532923i
$777$		0			0
$778$		−	1.88283i		−	0.0675027i
$779$	−4.35921	−	17.3336i	−0.156185	−	0.621041i
$780$			80.5952i			2.88577i
$781$		−	7.57290i		−	0.270980i
$782$	−0.772212			−0.0276142
$783$			37.7515i			1.34913i
$784$		0			0
$785$	15.9645			0.569798
$786$	−0.807237			−0.0287932
$787$	40.5398			1.44509			0.722543	−	0.691325i	$-0.242973\pi$
$787$	40.5398			1.44509			0.722543	+	0.691325i	$0.242973\pi$
$788$	−33.3964			−1.18970
$789$	−13.7994			−0.491271
$790$		−	7.12341i		−	0.253440i
$791$		0			0
$792$			7.73934i			0.275006i
$793$		−	60.1523i		−	2.13607i
$794$	0.693869			0.0246245
$795$	56.4886			2.00345
$796$			13.5747i			0.481142i
$797$	52.3080			1.85284			0.926422	−	0.376486i	$-0.122868\pi$
$797$	52.3080			1.85284			0.926422	+	0.376486i	$0.122868\pi$
$798$		0			0
$799$	−30.4085			−1.07578
$800$			5.88695i			0.208135i
$801$	61.3463			2.16756
$802$	−1.40972			−0.0497788
$803$			26.9108i			0.949660i
$804$			48.7745i			1.72014i
$805$		0			0
$806$			10.4243i			0.367180i
$807$	−72.7150			−2.55969
$808$	11.1773			0.393217
$809$	−27.0365			−0.950554			−0.475277	−	0.879836i	$-0.657652\pi$
$809$	−27.0365			−0.950554			−0.475277	+	0.879836i	$0.657652\pi$
$810$	0.256367			0.00900782
$811$	−13.9380			−0.489430			−0.244715	−	0.969595i	$-0.578694\pi$
$811$	−13.9380			−0.489430			−0.244715	+	0.969595i	$0.578694\pi$
$812$		0			0
$813$		−	75.5700i		−	2.65035i
$814$	−1.16737			−0.0409161
$815$			16.3377i			0.572284i
$816$		−	38.9982i		−	1.36521i
$817$	−2.19567	−	8.73069i	−0.0768168	−	0.305448i
$818$			0.225796i			0.00789476i
$819$		0			0
$820$			22.1175i			0.772378i
$821$	28.2386			0.985534			0.492767	−	0.870161i	$-0.335985\pi$
$821$	28.2386			0.985534			0.492767	+	0.870161i	$0.335985\pi$
$822$		−	8.62497i		−	0.300830i
$823$	18.0346			0.628648			0.314324	−	0.949316i	$-0.398222\pi$
$823$	18.0346			0.628648			0.314324	+	0.949316i	$0.398222\pi$
$824$			9.52693i			0.331886i
$825$	14.8661			0.517570
$826$		0			0
$827$		−	4.26694i		−	0.148376i	−0.997244	−	0.0741879i	$-0.976364\pi$
$827$		−	4.26694i		−	0.148376i	0.997244	−	0.0741879i	$-0.0236365\pi$
$828$	9.94379			0.345570
$829$	7.32976			0.254573			0.127287	−	0.991866i	$-0.459373\pi$
$829$	7.32976			0.254573			0.127287	+	0.991866i	$0.459373\pi$
$830$			5.65819i			0.196399i
$831$	38.7271			1.34343
$832$	−37.9662			−1.31624
$833$		0			0
$834$	−3.06331			−0.106074
$835$		−	12.8414i		−	0.444394i
$836$	−4.33581	−	17.2406i	−0.149957	−	0.596278i
$837$	49.2672			1.70292
$838$	4.55884			0.157482
$839$	−16.0686			−0.554749			−0.277374	−	0.960762i	$-0.589464\pi$
$839$	−16.0686			−0.554749			−0.277374	+	0.960762i	$0.589464\pi$
$840$		0			0
$841$	−28.6283			−0.987182
$842$	−3.43765			−0.118469
$843$			56.1324i			1.93330i
$844$		−	9.26828i		−	0.319027i
$845$		−	43.1387i		−	1.48402i
$846$	−7.70503			−0.264905
$847$		0			0
$848$			27.7581i			0.953218i
$849$			57.1581i			1.96166i
$850$	1.86692			0.0640347
$851$			3.02926i			0.103842i
$852$			19.9282i			0.682728i
$853$			26.9689i			0.923399i	0.887037	+	0.461699i	$0.152760\pi$
$853$			26.9689i			0.923399i	−0.887037	+	0.461699i	$0.847240\pi$
$854$		0			0
$855$	55.5987	−	13.9824i	1.90143	−	0.478189i
$856$	−3.57835			−0.122305
$857$	42.2905			1.44462			0.722308	−	0.691571i	$-0.243081\pi$
$857$	42.2905			1.44462			0.722308	+	0.691571i	$0.243081\pi$
$858$		−	6.10368i		−	0.208376i
$859$			33.9539i			1.15849i	0.815153	+	0.579246i	$0.196653\pi$
$859$			33.9539i			1.15849i	−0.815153	+	0.579246i	$0.803347\pi$
$860$			11.1403i			0.379881i
$861$		0			0
$862$	4.16370			0.141816
$863$		−	47.6988i		−	1.62368i	−0.583877	−	0.811842i	$-0.698465\pi$
$863$		−	47.6988i		−	1.62368i	0.583877	−	0.811842i	$-0.301535\pi$
$864$		−	11.4235i		−	0.388635i
$865$		−	47.9193i		−	1.62931i
$866$		−	0.613499i		−	0.0208475i
$867$	9.06681			0.307925
$868$		0			0
$869$		−	27.4162i		−	0.930030i
$870$		−	11.4416i		−	0.387906i
$871$		−	47.7421i		−	1.61768i
$872$	−5.33539			−0.180679
$873$	9.12314			0.308771
$874$	0.880331	−	0.221393i	0.0297776	−	0.00748874i
$875$		0			0
$876$		−	70.8159i		−	2.39265i
$877$		−	55.9115i		−	1.88800i	−0.329949	−	0.943999i	$-0.607032\pi$
$877$		−	55.9115i		−	1.88800i	0.329949	−	0.943999i	$-0.392968\pi$
$878$		−	1.25780i		−	0.0424485i
$879$	−59.5731			−2.00935
$880$			21.5574i			0.726701i
$881$			26.2554i			0.884567i	0.896875	+	0.442283i	$0.145831\pi$
$881$			26.2554i			0.884567i	−0.896875	+	0.442283i	$0.854169\pi$
$882$		0			0
$883$	−44.0477			−1.48232			−0.741161	−	0.671327i	$-0.765725\pi$
$883$	−44.0477			−1.48232			−0.741161	+	0.671327i	$0.765725\pi$
$884$			38.9544i			1.31018i
$885$			76.9403i			2.58632i
$886$		−	2.40568i		−	0.0808203i
$887$	−26.1341			−0.877497			−0.438748	−	0.898610i	$-0.644578\pi$
$887$	−26.1341			−0.877497			−0.438748	+	0.898610i	$0.644578\pi$
$888$	6.20431			0.208203
$889$		0			0
$890$	−6.92995			−0.232292
$891$	0.986691			0.0330554
$892$	−4.72879			−0.158332
$893$	34.6660	−	8.71812i	1.16006	−	0.291741i
$894$			1.26399i			0.0422740i
$895$	−70.3589			−2.35184
$896$		0			0
$897$	−15.8388			−0.528841
$898$	−6.30893			−0.210532
$899$			75.2072i			2.50830i
$900$	−24.0403			−0.801344
$901$	27.3029			0.909591
$902$		−	1.67502i		−	0.0557720i
$903$		0			0
$904$	−9.31067			−0.309668
$905$			52.5260i			1.74602i
$906$	−5.20742			−0.173005
$907$			3.00450i			0.0997629i	0.998755	+	0.0498814i	$0.0158843\pi$
$907$			3.00450i			0.0997629i	−0.998755	+	0.0498814i	$0.984116\pi$
$908$	−14.6012			−0.484557
$909$			68.6889i			2.27827i
$910$		0			0
$911$			20.6988i			0.685781i	0.939375	+	0.342890i	$0.111406\pi$
$911$			20.6988i			0.685781i	−0.939375	+	0.342890i	$0.888594\pi$
$912$	11.1808	+	44.4584i	0.370233	+	1.47217i
$913$			21.7769i			0.720711i
$914$		−	4.29111i		−	0.141937i
$915$	86.1621			2.84843
$916$			34.8422i			1.15122i
$917$		0			0
$918$	−3.62271			−0.119567
$919$	−3.88300			−0.128088			−0.0640442	−	0.997947i	$-0.520400\pi$
$919$	−3.88300			−0.128088			−0.0640442	+	0.997947i	$0.520400\pi$
$920$	−2.26869			−0.0747966
$921$	−41.0565			−1.35286
$922$	−1.98879			−0.0654973
$923$		−	19.5064i		−	0.642060i
$924$		0			0
$925$		−	7.32360i		−	0.240799i
$926$		−	3.72733i		−	0.122488i
$927$	−58.5467			−1.92293
$928$	17.4381			0.572434
$929$			32.7416i			1.07422i	0.843513	+	0.537108i	$0.180483\pi$
$929$			32.7416i			1.07422i	−0.843513	+	0.537108i	$0.819517\pi$
$930$	−14.9317			−0.489630
$931$		0			0
$932$	11.2557			0.368691
$933$		−	28.8990i		−	0.946112i
$934$	2.76811			0.0905754
$935$	21.2039			0.693441
$936$			19.9351i			0.651599i
$937$		−	30.5156i		−	0.996901i	−0.866918	−	0.498451i	$-0.833903\pi$
$937$		−	30.5156i		−	0.996901i	0.866918	−	0.498451i	$-0.166097\pi$
$938$		0			0
$939$			9.26608i			0.302387i
$940$	−44.2336			−1.44274
$941$	−2.48267			−0.0809329			−0.0404664	−	0.999181i	$-0.512884\pi$
$941$	−2.48267			−0.0809329			−0.0404664	+	0.999181i	$0.512884\pi$
$942$	3.18158			0.103662
$943$	−4.34660			−0.141545
$944$	−37.8080			−1.23054
$945$		0			0
$946$		−	0.843683i		−	0.0274305i
$947$	−30.9716			−1.00644			−0.503222	−	0.864157i	$-0.667852\pi$
$947$	−30.9716			−1.00644			−0.503222	+	0.864157i	$0.667852\pi$
$948$			72.1459i			2.34319i
$949$			69.3171i			2.25013i
$950$	−2.12831	+	0.535246i	−0.0690514	+	0.0173657i
$951$			17.7338i			0.575059i
$952$		0			0
$953$			12.9585i			0.419768i	0.977726	+	0.209884i	$0.0673086\pi$
$953$			12.9585i			0.419768i	−0.977726	+	0.209884i	$0.932691\pi$
$954$	6.91812			0.223983
$955$		−	12.3014i		−	0.398064i
$956$	−32.4068			−1.04811
$957$		−	44.0357i		−	1.42347i
$958$	−0.425185			−0.0137371
$959$		0			0
$960$		−	54.3827i		−	1.75519i
$961$	67.1483			2.16607
$962$	−3.00691			−0.0969468
$963$		−	21.9903i		−	0.708629i
$964$	−29.5980			−0.953288
$965$	14.2388			0.458364
$966$		0			0
$967$	22.3430			0.718504			0.359252	−	0.933241i	$-0.383032\pi$
$967$	22.3430			0.718504			0.359252	+	0.933241i	$0.383032\pi$
$968$			5.19583i			0.167000i
$969$	43.7293	−	10.9974i	1.40479	−	0.353288i
$970$	−1.03059			−0.0330903
$971$	17.0976			0.548689			0.274345	−	0.961631i	$-0.411539\pi$
$971$	17.0976			0.548689			0.274345	+	0.961631i	$0.411539\pi$
$972$	−31.8586			−1.02186
$973$		0			0
$974$	3.54630			0.113631
$975$	38.2922			1.22633
$976$			42.3395i			1.35525i
$977$		−	3.24881i		−	0.103939i	−0.998649	−	0.0519693i	$-0.983450\pi$
$977$		−	3.24881i		−	0.103939i	0.998649	−	0.0519693i	$-0.0165498\pi$
$978$			3.25596i			0.104114i
$979$	−26.6716			−0.852427
$980$		0			0
$981$		−	32.7880i		−	1.04684i
$982$			7.15235i			0.228241i
$983$	−1.99031			−0.0634809			−0.0317404	−	0.999496i	$-0.510105\pi$
$983$	−1.99031			−0.0634809			−0.0317404	+	0.999496i	$0.510105\pi$
$984$			8.90239i			0.283798i
$985$			46.8245i			1.49195i
$986$		−	5.53011i		−	0.176115i
$987$		0			0
$988$	−11.1682	−	44.4085i	−0.355309	−	1.41282i
$989$	−2.18932			−0.0696163
$990$	5.37273			0.170757
$991$			18.6276i			0.591724i	0.955231	+	0.295862i	$0.0956069\pi$
$991$			18.6276i			0.591724i	−0.955231	+	0.295862i	$0.904393\pi$
$992$		−	22.7574i		−	0.722549i
$993$		−	35.5164i		−	1.12708i
$994$		0			0
$995$	19.0328			0.603380
$996$		−	57.3062i		−	1.81581i
$997$		−	18.6460i		−	0.590525i	−0.955416	−	0.295262i	$-0.904593\pi$
$997$		−	18.6460i		−	0.590525i	0.955416	−	0.295262i	$-0.0954071\pi$
$998$			2.52410i			0.0798990i
$999$			14.2113i			0.449625i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.c.f.930.20	yes	40
7.2	even	3		931.2.o.i.227.19		80
7.3	odd	6		931.2.o.i.607.22		80
7.4	even	3		931.2.o.i.607.21		80
7.5	odd	6		931.2.o.i.227.20		80
7.6	odd	2	inner	931.2.c.f.930.19	✓	40
19.18	odd	2	inner	931.2.c.f.930.21	yes	40
133.18	odd	6		931.2.o.i.607.20		80
133.37	odd	6		931.2.o.i.227.22		80
133.75	even	6		931.2.o.i.227.21		80
133.94	even	6		931.2.o.i.607.19		80
133.132	even	2	inner	931.2.c.f.930.22	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
931.2.c.f.930.19	✓	40	7.6	odd	2	inner
931.2.c.f.930.20	yes	40	1.1	even	1	trivial
931.2.c.f.930.21	yes	40	19.18	odd	2	inner
931.2.c.f.930.22	yes	40	133.132	even	2	inner
931.2.o.i.227.19		80	7.2	even	3
931.2.o.i.227.20		80	7.5	odd	6
931.2.o.i.227.21		80	133.75	even	6
931.2.o.i.227.22		80	133.37	odd	6
931.2.o.i.607.19		80	133.94	even	6
931.2.o.i.607.20		80	133.18	odd	6
931.2.o.i.607.21		80	7.4	even	3
931.2.o.i.607.22		80	7.3	odd	6

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)

\(f(q)\)	\(=\)	\(q-0.196456i q^{2} +2.78973 q^{3} +1.96140 q^{4} -2.75005i q^{5} -0.548060i q^{6} -0.778243i q^{8} +4.78260 q^{9} +O(q^{10})\)	\(q-0.196456i q^{2} +2.78973 q^{3} +1.96140 q^{4} -2.75005i q^{5} -0.548060i q^{6} -0.778243i q^{8} +4.78260 q^{9} -0.540264 q^{10} -2.07934 q^{11} +5.47179 q^{12} -5.35598 q^{13} -7.67190i q^{15} +3.76992 q^{16} -3.70809i q^{17} -0.939572i q^{18} +(1.06311 + 4.22727i) q^{19} -5.39396i q^{20} +0.408499i q^{22} +1.06003 q^{23} -2.17109i q^{24} -2.56277 q^{25} +1.05222i q^{26} +4.97298 q^{27} +7.59133i q^{29} -1.50719 q^{30} +9.90698 q^{31} -2.29711i q^{32} -5.80079 q^{33} -0.728477 q^{34} +9.38062 q^{36} +2.85770i q^{37} +(0.830473 - 0.208855i) q^{38} -14.9417 q^{39} -2.14020 q^{40} -4.10043 q^{41} -2.06533 q^{43} -4.07842 q^{44} -13.1524i q^{45} -0.208250i q^{46} -8.20058i q^{47} +10.5171 q^{48} +0.503471i q^{50} -10.3446i q^{51} -10.5052 q^{52} +7.36306i q^{53} -0.976973i q^{54} +5.71828i q^{55} +(2.96579 + 11.7929i) q^{57} +1.49136 q^{58} -10.0289 q^{59} -15.0477i q^{60} +11.2309i q^{61} -1.94629i q^{62} +7.08856 q^{64} +14.7292i q^{65} +1.13960i q^{66} +8.91380i q^{67} -7.27307i q^{68} +2.95721 q^{69} +3.64198i q^{71} -3.72203i q^{72} -12.9420i q^{73} +0.561412 q^{74} -7.14943 q^{75} +(2.08519 + 8.29138i) q^{76} +2.93540i q^{78} +13.1850i q^{79} -10.3675i q^{80} -0.474522 q^{81} +0.805554i q^{82} -10.4730i q^{83} -10.1974 q^{85} +0.405746i q^{86} +21.1778i q^{87} +1.61823i q^{88} +12.8270 q^{89} -2.58387 q^{90} +2.07916 q^{92} +27.6378 q^{93} -1.61105 q^{94} +(11.6252 - 2.92361i) q^{95} -6.40832i q^{96} +1.90757 q^{97} -9.94464 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{4} + 40 q^{9}+O(q^{10}) \) 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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