LMFDB - Embedded newform 1305.2.c.k.784.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1305,2,Mod(784,1305)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1305, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1305.784");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1305 = 3^{2} \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1305.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:	$10.4204774638$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 20x^{10} + 148x^{8} + 502x^{6} + 792x^{4} + 496x^{2} + 45 $ x^12 + 20x^10 + 148x^8 + 502x^6 + 792x^4 + 496*x^2 + 45
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			784.5
Root			$-1.27263i$ of defining polynomial
Character	$\chi$	$=$	1305.784
Dual form			1305.2.c.k.784.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.27263i q^{2} +0.380419 q^{4} +(1.10723 + 1.94269i) q^{5} +0.255813i q^{7} -3.02939i q^{8} +(2.47232 - 1.40909i) q^{10} +4.63446 q^{11} -5.02700i q^{13} +0.325555 q^{14} -3.09444 q^{16} +0.336444i q^{17} +2.91437 q^{19} +(0.421212 + 0.739035i) q^{20} -5.89795i q^{22} +8.65656i q^{23} +(-2.54807 + 4.30201i) q^{25} -6.39750 q^{26} +0.0973162i q^{28} -1.00000 q^{29} -3.26943 q^{31} -2.12070i q^{32} +0.428167 q^{34} +(-0.496966 + 0.283245i) q^{35} -3.86954i q^{37} -3.70891i q^{38} +(5.88515 - 3.35424i) q^{40} +5.71649 q^{41} -6.98619i q^{43} +1.76304 q^{44} +11.0166 q^{46} +0.336444i q^{47} +6.93456 q^{49} +(5.47486 + 3.24275i) q^{50} -1.91237i q^{52} +6.01484i q^{53} +(5.13143 + 9.00332i) q^{55} +0.774958 q^{56} +1.27263i q^{58} +13.2799 q^{59} -7.77792 q^{61} +4.16077i q^{62} -8.88775 q^{64} +(9.76589 - 5.56606i) q^{65} -11.2605i q^{67} +0.127989i q^{68} +(0.360465 + 0.632452i) q^{70} -13.9668 q^{71} -8.46426i q^{73} -4.92448 q^{74} +1.10868 q^{76} +1.18556i q^{77} +15.3102 q^{79} +(-3.42627 - 6.01154i) q^{80} -7.27496i q^{82} +7.60521i q^{83} +(-0.653605 + 0.372521i) q^{85} -8.89082 q^{86} -14.0396i q^{88} +13.0383 q^{89} +1.28597 q^{91} +3.29312i q^{92} +0.428167 q^{94} +(3.22689 + 5.66171i) q^{95} +11.5445i q^{97} -8.82511i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 16 q^{4} - 10 q^{10} - 12 q^{11} + 16 q^{14} + 16 q^{16} + 20 q^{19} + 14 q^{20} + 8 q^{25} - 56 q^{26} - 12 q^{29} - 16 q^{31} - 4 q^{34} - 16 q^{35} + 16 q^{40} - 32 q^{41} + 68 q^{44} + 20 q^{46}+ \cdots - 8 q^{95}+O(q^{100}) $ 12 * q - 16 * q^4 - 10 * q^10 - 12 * q^11 + 16 * q^14 + 16 * q^16 + 20 * q^19 + 14 * q^20 + 8 * q^25 - 56 * q^26 - 12 * q^29 - 16 * q^31 - 4 * q^34 - 16 * q^35 + 16 * q^40 - 32 * q^41 + 68 * q^44 + 20 * q^46 + 4 * q^49 - 8 * q^50 + 4 * q^55 - 76 * q^56 + 44 * q^59 - 52 * q^61 - 36 * q^64 - 8 * q^65 - 30 * q^70 - 20 * q^71 + 20 * q^74 - 28 * q^76 + 4 * q^79 + 34 * q^80 + 20 * q^85 - 36 * q^86 + 68 * q^89 + 48 * q^91 - 4 * q^94 - 8 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1305\mathbb{Z}\right)^\times$.

$n$	$146$	$262$	$901$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	1.27263i		−	0.899884i	−0.893058	−	0.449942i	$-0.851445\pi$
$2$		−	1.27263i		−	0.899884i	0.893058	−	0.449942i	$-0.148555\pi$
$3$		0			0
$3$		0			0
$4$	0.380419			0.190209
$5$	1.10723	+	1.94269i	0.495169	+	0.868796i
$5$	1.10723	+	1.94269i	0.495169	+	0.868796i
$6$		0			0
$7$			0.255813i			0.0966884i	0.998831	+	0.0483442i	$0.0153944\pi$
$7$			0.255813i			0.0966884i	−0.998831	+	0.0483442i	$0.984606\pi$
$8$		−	3.02939i		−	1.07105i
$9$		0			0
$10$	2.47232	−	1.40909i	0.781816	−	0.445595i
$11$	4.63446			1.39734			0.698672	−	0.715442i	$-0.253775\pi$
$11$	4.63446			1.39734			0.698672	+	0.715442i	$0.253775\pi$
$12$		0			0
$13$		−	5.02700i		−	1.39424i	−0.716955	−	0.697120i	$-0.754465\pi$
$13$		−	5.02700i		−	1.39424i	0.716955	−	0.697120i	$-0.245535\pi$
$14$	0.325555			0.0870083
$15$		0			0
$16$	−3.09444			−0.773611
$17$			0.336444i			0.0815995i	0.999167	+	0.0407998i	$0.0129906\pi$
$17$			0.336444i			0.0815995i	−0.999167	+	0.0407998i	$0.987009\pi$
$18$		0			0
$19$	2.91437			0.668602			0.334301	−	0.942466i	$-0.391500\pi$
$19$	2.91437			0.668602			0.334301	+	0.942466i	$0.391500\pi$
$20$	0.421212	+	0.739035i	0.0941859	+	0.165253i
$21$		0			0
$22$		−	5.89795i		−	1.25745i
$23$			8.65656i			1.80502i	0.430671	+	0.902509i	$0.358277\pi$
$23$			8.65656i			1.80502i	−0.430671	+	0.902509i	$0.641723\pi$
$24$		0			0
$25$	−2.54807	+	4.30201i	−0.509614	+	0.860403i
$26$	−6.39750			−1.25465
$27$		0			0
$28$			0.0973162i			0.0183910i
$29$	−1.00000			−0.185695
$29$	−1.00000			−0.185695
$30$		0			0
$31$	−3.26943			−0.587207			−0.293603	−	0.955927i	$-0.594854\pi$
$31$	−3.26943			−0.587207			−0.293603	+	0.955927i	$0.594854\pi$
$32$		−	2.12070i		−	0.374890i
$33$		0			0
$34$	0.428167			0.0734301
$35$	−0.496966	+	0.283245i	−0.0840025	+	0.0478771i
$36$		0			0
$37$		−	3.86954i		−	0.636148i	−0.948066	−	0.318074i	$-0.896964\pi$
$37$		−	3.86954i		−	0.636148i	0.948066	−	0.318074i	$-0.103036\pi$
$38$		−	3.70891i		−	0.601664i
$39$		0			0
$40$	5.88515	−	3.35424i	0.930524	−	0.530351i
$41$	5.71649			0.892765			0.446383	−	0.894842i	$-0.352712\pi$
$41$	5.71649			0.892765			0.446383	+	0.894842i	$0.352712\pi$
$42$		0			0
$43$		−	6.98619i		−	1.06538i	−0.846309	−	0.532692i	$-0.821180\pi$
$43$		−	6.98619i		−	1.06538i	0.846309	−	0.532692i	$-0.178820\pi$
$44$	1.76304			0.265788
$45$		0			0
$46$	11.0166			1.62431
$47$			0.336444i			0.0490753i	0.999699	+	0.0245377i	$0.00781137\pi$
$47$			0.336444i			0.0490753i	−0.999699	+	0.0245377i	$0.992189\pi$
$48$		0			0
$49$	6.93456			0.990651
$50$	5.47486	+	3.24275i	0.774263	+	0.458594i
$51$		0			0
$52$		−	1.91237i		−	0.265197i
$53$			6.01484i			0.826202i	0.910685	+	0.413101i	$0.135554\pi$
$53$			6.01484i			0.826202i	−0.910685	+	0.413101i	$0.864446\pi$
$54$		0			0
$55$	5.13143	+	9.00332i	0.691922	+	1.21401i
$56$	0.774958			0.103558
$57$		0			0
$58$			1.27263i			0.167104i
$59$	13.2799			1.72890			0.864451	−	0.502718i	$-0.167666\pi$
$59$	13.2799			1.72890			0.864451	+	0.502718i	$0.167666\pi$
$60$		0			0
$61$	−7.77792			−0.995861			−0.497930	−	0.867217i	$-0.665906\pi$
$61$	−7.77792			−0.995861			−0.497930	+	0.867217i	$0.665906\pi$
$62$			4.16077i			0.528418i
$63$		0			0
$64$	−8.88775			−1.11097
$65$	9.76589	−	5.56606i	1.21131	−	0.690385i
$66$		0			0
$67$		−	11.2605i		−	1.37569i	−0.725856	−	0.687847i	$-0.758556\pi$
$67$		−	11.2605i		−	1.37569i	0.725856	−	0.687847i	$-0.241444\pi$
$68$			0.127989i			0.0155210i
$69$		0			0
$70$	0.360465	+	0.632452i	0.0430839	+	0.0755925i
$71$	−13.9668			−1.65756			−0.828778	−	0.559578i	$-0.810963\pi$
$71$	−13.9668			−1.65756			−0.828778	+	0.559578i	$0.810963\pi$
$72$		0			0
$73$		−	8.46426i		−	0.990667i	−0.868703	−	0.495333i	$-0.835046\pi$
$73$		−	8.46426i		−	0.990667i	0.868703	−	0.495333i	$-0.164954\pi$
$74$	−4.92448			−0.572459
$75$		0			0
$76$	1.10868			0.127174
$77$			1.18556i			0.135107i
$78$		0			0
$79$	15.3102			1.72253			0.861267	−	0.508153i	$-0.169672\pi$
$79$	15.3102			1.72253			0.861267	+	0.508153i	$0.169672\pi$
$80$	−3.42627	−	6.01154i	−0.383069	−	0.672111i
$81$		0			0
$82$		−	7.27496i		−	0.803385i
$83$			7.60521i			0.834781i	0.908727	+	0.417390i	$0.137055\pi$
$83$			7.60521i			0.834781i	−0.908727	+	0.417390i	$0.862945\pi$
$84$		0			0
$85$	−0.653605	+	0.372521i	−0.0708934	+	0.0404056i
$86$	−8.89082			−0.958722
$87$		0			0
$88$		−	14.0396i		−	1.49662i
$89$	13.0383			1.38206			0.691029	−	0.722827i	$-0.257157\pi$
$89$	13.0383			1.38206			0.691029	+	0.722827i	$0.257157\pi$
$90$		0			0
$91$	1.28597			0.134807
$92$			3.29312i			0.343331i
$93$		0			0
$94$	0.428167			0.0441621
$95$	3.22689	+	5.66171i	0.331071	+	0.580879i
$96$		0			0
$97$			11.5445i			1.17216i	0.810253	+	0.586081i	$0.199330\pi$
$97$			11.5445i			1.17216i	−0.810253	+	0.586081i	$0.800670\pi$
$98$		−	8.82511i		−	0.891471i
$99$		0			0
$100$	−0.969334	+	1.63657i	−0.0969334	+	0.163657i
$101$	−8.19832			−0.815763			−0.407882	−	0.913035i	$-0.633732\pi$
$101$	−8.19832			−0.815763			−0.407882	+	0.913035i	$0.633732\pi$
$102$		0			0
$103$			1.73014i			0.170476i	0.996361	+	0.0852380i	$0.0271651\pi$
$103$			1.73014i			0.170476i	−0.996361	+	0.0852380i	$0.972835\pi$
$104$	−15.2287			−1.49330
$105$		0			0
$106$	7.65465			0.743486
$107$		−	5.38921i		−	0.520995i	−0.965475	−	0.260497i	$-0.916113\pi$
$107$		−	5.38921i		−	0.520995i	0.965475	−	0.260497i	$-0.0838865\pi$
$108$		0			0
$109$	−14.2391			−1.36386			−0.681929	−	0.731418i	$-0.738859\pi$
$109$	−14.2391			−1.36386			−0.681929	+	0.731418i	$0.738859\pi$
$110$	11.4579	−	6.53040i	1.09247	−	0.622649i
$111$		0			0
$112$		−	0.791600i		−	0.0747992i
$113$		−	9.89466i		−	0.930811i	−0.885098	−	0.465406i	$-0.845909\pi$
$113$		−	9.89466i		−	0.930811i	0.885098	−	0.465406i	$-0.154091\pi$
$114$		0			0
$115$	−16.8170	+	9.58483i	−1.56819	+	0.893790i
$116$	−0.380419			−0.0353210
$117$		0			0
$118$		−	16.9004i		−	1.55581i
$119$	−0.0860668			−0.00788973
$120$		0			0
$121$	10.4783			0.952569
$122$			9.89840i			0.896159i
$123$		0			0
$124$	−1.24375			−0.111692
$125$	−11.1788	−	0.186778i	−0.999860	−	0.0167059i
$126$		0			0
$127$			12.2226i			1.08458i	0.840191	+	0.542291i	$0.182443\pi$
$127$			12.2226i			1.08458i	−0.840191	+	0.542291i	$0.817557\pi$
$128$			7.06940i			0.624852i
$129$		0			0
$130$	−7.08352	−	12.4283i	−0.621266	−	1.09004i
$131$	−12.0464			−1.05250			−0.526250	−	0.850330i	$-0.676402\pi$
$131$	−12.0464			−1.05250			−0.526250	+	0.850330i	$0.676402\pi$
$132$		0			0
$133$			0.745535i			0.0646461i
$134$	−14.3305			−1.23796
$135$		0			0
$136$	1.01922			0.0873972
$137$			5.47512i			0.467771i	0.972264	+	0.233886i	$0.0751441\pi$
$137$			5.47512i			0.467771i	−0.972264	+	0.233886i	$0.924856\pi$
$138$		0			0
$139$	−2.71403			−0.230201			−0.115100	−	0.993354i	$-0.536719\pi$
$139$	−2.71403			−0.230201			−0.115100	+	0.993354i	$0.536719\pi$
$140$	−0.189055	+	0.107752i	−0.0159781	+	0.00910668i
$141$		0			0
$142$			17.7745i			1.49161i
$143$		−	23.2975i		−	1.94823i
$144$		0			0
$145$	−1.10723	−	1.94269i	−0.0919507	−	0.161331i
$146$	−10.7719			−0.891485
$147$		0			0
$148$		−	1.47204i		−	0.121001i
$149$	3.70395			0.303439			0.151720	−	0.988424i	$-0.451519\pi$
$149$	3.70395			0.303439			0.151720	+	0.988424i	$0.451519\pi$
$150$		0			0
$151$	15.3481			1.24901			0.624505	−	0.781021i	$-0.285301\pi$
$151$	15.3481			1.24901			0.624505	+	0.781021i	$0.285301\pi$
$152$		−	8.82875i		−	0.716107i
$153$		0			0
$154$	1.50877			0.121580
$155$	−3.62002	−	6.35148i	−0.290767	−	0.510163i
$156$		0			0
$157$			21.8231i			1.74168i	0.491571	+	0.870838i	$0.336423\pi$
$157$			21.8231i			1.74168i	−0.491571	+	0.870838i	$0.663577\pi$
$158$		−	19.4842i		−	1.55008i
$159$		0			0
$160$	4.11985	−	2.34811i	0.325703	−	0.185634i
$161$	−2.21447			−0.174524
$162$		0			0
$163$			3.08019i			0.241259i	0.992698	+	0.120630i	$0.0384914\pi$
$163$			3.08019i			0.241259i	−0.992698	+	0.120630i	$0.961509\pi$
$164$	2.17466			0.169812
$165$		0			0
$166$	9.67861			0.751206
$167$		−	8.55017i		−	0.661632i	−0.943695	−	0.330816i	$-0.892676\pi$
$167$		−	8.55017i		−	0.661632i	0.943695	−	0.330816i	$-0.107324\pi$
$168$		0			0
$169$	−12.2707			−0.943903
$170$	0.474081	+	0.831796i	0.0363603	+	0.0637958i
$171$		0			0
$172$		−	2.65768i		−	0.202646i
$173$			5.76340i			0.438183i	0.975704	+	0.219092i	$0.0703093\pi$
$173$			5.76340i			0.438183i	−0.975704	+	0.219092i	$0.929691\pi$
$174$		0			0
$175$	−1.10051	−	0.651831i	−0.0831910	−	0.0492738i
$176$	−14.3411			−1.08100
$177$		0			0
$178$		−	16.5929i		−	1.24369i
$179$	−14.1430			−1.05710			−0.528548	−	0.848903i	$-0.677264\pi$
$179$	−14.1430			−1.05710			−0.528548	+	0.848903i	$0.677264\pi$
$180$		0			0
$181$	−15.0322			−1.11734			−0.558668	−	0.829391i	$-0.688688\pi$
$181$	−15.0322			−1.11734			−0.558668	+	0.829391i	$0.688688\pi$
$182$		−	1.63657i		−	0.121310i
$183$		0			0
$184$	26.2241			1.93326
$185$	7.51731	−	4.28448i	0.552683	−	0.315001i
$186$		0			0
$187$			1.55924i			0.114023i
$188$			0.127989i			0.00933459i
$189$		0			0
$190$	7.20525	−	4.10662i	0.522724	−	0.297926i
$191$	−12.2634			−0.887346			−0.443673	−	0.896189i	$-0.646325\pi$
$191$	−12.2634			−0.887346			−0.443673	+	0.896189i	$0.646325\pi$
$192$		0			0
$193$		−	8.34203i		−	0.600472i	−0.953865	−	0.300236i	$-0.902935\pi$
$193$		−	8.34203i		−	0.600472i	0.953865	−	0.300236i	$-0.0970655\pi$
$194$	14.6918			1.05481
$195$		0			0
$196$	2.63804			0.188431
$197$		−	6.69263i		−	0.476830i	−0.971163	−	0.238415i	$-0.923372\pi$
$197$		−	6.69263i		−	0.476830i	0.971163	−	0.238415i	$-0.0766279\pi$
$198$		0			0
$199$	−12.5583			−0.890235			−0.445117	−	0.895472i	$-0.646838\pi$
$199$	−12.5583			−0.890235			−0.445117	+	0.895472i	$0.646838\pi$
$200$	13.0325	+	7.71910i	0.921535	+	0.545822i
$201$		0			0
$202$			10.4334i			0.734092i
$203$		−	0.255813i		−	0.0179546i
$204$		0			0
$205$	6.32948	+	11.1054i	0.442070	+	0.775631i
$206$	2.20183			0.153409
$207$		0			0
$208$			15.5558i			1.07860i
$209$	13.5065			0.934267
$210$		0			0
$211$	−13.6479			−0.939563			−0.469782	−	0.882783i	$-0.655667\pi$
$211$	−13.6479			−0.939563			−0.469782	+	0.882783i	$0.655667\pi$
$212$			2.28816i			0.157151i
$213$		0			0
$214$	−6.85846			−0.468835
$215$	13.5720	−	7.73534i	0.925602	−	0.527546i
$216$		0			0
$217$		−	0.836364i		−	0.0567761i
$218$			18.1211i			1.22731i
$219$		0			0
$220$	1.95209	+	3.42503i	0.131610	+	0.230916i
$221$	1.69130			0.113769
$222$		0			0
$223$		−	13.4721i		−	0.902158i	−0.892484	−	0.451079i	$-0.851039\pi$
$223$		−	13.4721i		−	0.902158i	0.892484	−	0.451079i	$-0.148961\pi$
$224$	0.542503			0.0362475
$225$		0			0
$226$	−12.5922			−0.837622
$227$			1.54298i			0.102411i	0.998688	+	0.0512057i	$0.0163064\pi$
$227$			1.54298i			0.102411i	−0.998688	+	0.0512057i	$0.983694\pi$
$228$		0			0
$229$	−7.89526			−0.521734			−0.260867	−	0.965375i	$-0.584008\pi$
$229$	−7.89526			−0.521734			−0.260867	+	0.965375i	$0.584008\pi$
$230$	12.1979	+	21.4018i	0.804307	+	1.41119i
$231$		0			0
$232$			3.02939i			0.198889i
$233$			28.4782i			1.86567i	0.360301	+	0.932836i	$0.382674\pi$
$233$			28.4782i			1.86567i	−0.360301	+	0.932836i	$0.617326\pi$
$234$		0			0
$235$	−0.653605	+	0.372521i	−0.0426365	+	0.0243006i
$236$	5.05194			0.328853
$237$		0			0
$238$			0.109531i			0.00709984i
$239$	−8.88508			−0.574728			−0.287364	−	0.957821i	$-0.592779\pi$
$239$	−8.88508			−0.574728			−0.287364	+	0.957821i	$0.592779\pi$
$240$		0			0
$241$	−29.8901			−1.92539			−0.962695	−	0.270589i	$-0.912782\pi$
$241$	−29.8901			−1.92539			−0.962695	+	0.270589i	$0.912782\pi$
$242$		−	13.3349i		−	0.857202i
$243$		0			0
$244$	−2.95887			−0.189422
$245$	7.67817	+	13.4717i	0.490540	+	0.860674i
$246$		0			0
$247$		−	14.6505i		−	0.932192i
$248$			9.90437i			0.628928i
$249$		0			0
$250$	−0.237699	+	14.2264i	−0.0150334	+	0.899758i
$251$	−15.9551			−1.00708			−0.503539	−	0.863973i	$-0.667969\pi$
$251$	−15.9551			−1.00708			−0.503539	+	0.863973i	$0.667969\pi$
$252$		0			0
$253$			40.1185i			2.52223i
$254$	15.5548			0.975998
$255$		0			0
$256$	−8.77878			−0.548674
$257$			17.1593i			1.07037i	0.844735	+	0.535185i	$0.179758\pi$
$257$			17.1593i			1.07037i	−0.844735	+	0.535185i	$0.820242\pi$
$258$		0			0
$259$	0.989880			0.0615081
$260$	3.71513	−	2.11743i	0.230403	−	0.131318i
$261$		0			0
$262$			15.3306i			0.947128i
$263$			1.72781i			0.106542i	0.998580	+	0.0532708i	$0.0169647\pi$
$263$			1.72781i			0.106542i	−0.998580	+	0.0532708i	$0.983035\pi$
$264$		0			0
$265$	−11.6850	+	6.65983i	−0.717801	+	0.409110i
$266$	0.948789			0.0581740
$267$		0			0
$268$		−	4.28372i		−	0.261670i
$269$	4.97931			0.303594			0.151797	−	0.988412i	$-0.451494\pi$
$269$	4.97931			0.303594			0.151797	+	0.988412i	$0.451494\pi$
$270$		0			0
$271$	13.0881			0.795047			0.397524	−	0.917592i	$-0.369870\pi$
$271$	13.0881			0.795047			0.397524	+	0.917592i	$0.369870\pi$
$272$		−	1.04111i		−	0.0631263i
$273$		0			0
$274$	6.96779			0.420939
$275$	−11.8089	+	19.9375i	−0.712106	+	1.20228i
$276$		0			0
$277$			20.8147i			1.25063i	0.780371	+	0.625316i	$0.215030\pi$
$277$			20.8147i			1.25063i	−0.780371	+	0.625316i	$0.784970\pi$
$278$			3.45394i			0.207154i
$279$		0			0
$280$	0.858059	+	1.50550i	0.0512788	+	0.0899709i
$281$	3.93338			0.234646			0.117323	−	0.993094i	$-0.462569\pi$
$281$	3.93338			0.234646			0.117323	+	0.993094i	$0.462569\pi$
$282$		0			0
$283$			5.47745i			0.325600i	0.986659	+	0.162800i	$0.0520526\pi$
$283$			5.47745i			0.325600i	−0.986659	+	0.162800i	$0.947947\pi$
$284$	−5.31324			−0.315282
$285$		0			0
$286$	−29.6490			−1.75318
$287$			1.46235i			0.0863201i
$288$		0			0
$289$	16.8868			0.993342
$290$	−2.47232	+	1.40909i	−0.145180	+	0.0827449i
$291$		0			0
$292$		−	3.21996i		−	0.188434i
$293$		−	11.9974i		−	0.700893i	−0.936583	−	0.350446i	$-0.886030\pi$
$293$		−	11.9974i		−	0.700893i	0.936583	−	0.350446i	$-0.113970\pi$
$294$		0			0
$295$	14.7040	+	25.7988i	0.856099	+	1.50206i
$296$	−11.7223			−0.681347
$297$		0			0
$298$		−	4.71375i		−	0.273060i
$299$	43.5166			2.51663
$300$		0			0
$301$	1.78716			0.103010
$302$		−	19.5324i		−	1.12396i
$303$		0			0
$304$	−9.01836			−0.517238
$305$	−8.61197	−	15.1101i	−0.493120	−	0.865200i
$306$		0			0
$307$		−	26.4807i		−	1.51133i	−0.654957	−	0.755666i	$-0.727313\pi$
$307$		−	26.4807i		−	1.51133i	0.654957	−	0.755666i	$-0.272687\pi$
$308$			0.451009i			0.0256986i
$309$		0			0
$310$	−8.08307	+	4.60694i	−0.459088	+	0.261656i
$311$	−1.71530			−0.0972660			−0.0486330	−	0.998817i	$-0.515486\pi$
$311$	−1.71530			−0.0972660			−0.0486330	+	0.998817i	$0.515486\pi$
$312$		0			0
$313$			33.3782i			1.88665i	0.331871	+	0.943325i	$0.392320\pi$
$313$			33.3782i			1.88665i	−0.331871	+	0.943325i	$0.607680\pi$
$314$	27.7727			1.56731
$315$		0			0
$316$	5.82429			0.327642
$317$			17.9712i			1.00936i	0.863305	+	0.504682i	$0.168390\pi$
$317$			17.9712i			1.00936i	−0.863305	+	0.504682i	$0.831610\pi$
$318$		0			0
$319$	−4.63446			−0.259480
$320$	−9.84080	−	17.2661i	−0.550118	−	0.965205i
$321$		0			0
$322$			2.81819i			0.157052i
$323$			0.980521i			0.0545577i
$324$		0			0
$325$	21.6262	+	12.8092i	1.19961	+	0.710524i
$326$	3.91994			0.217105
$327$		0			0
$328$		−	17.3175i		−	0.956196i
$329$	−0.0860668			−0.00474501
$330$		0			0
$331$	6.49393			0.356939			0.178469	−	0.983945i	$-0.442885\pi$
$331$	6.49393			0.356939			0.178469	+	0.983945i	$0.442885\pi$
$332$			2.89317i			0.158783i
$333$		0			0
$334$	−10.8812			−0.595392
$335$	21.8757	−	12.4680i	1.19520	−	0.681202i
$336$		0			0
$337$			6.36156i			0.346536i	0.984875	+	0.173268i	$0.0554327\pi$
$337$			6.36156i			0.346536i	−0.984875	+	0.173268i	$0.944567\pi$
$338$			15.6161i			0.849403i
$339$		0			0
$340$	−0.248643	+	0.141714i	−0.0134846	+	0.00768552i
$341$	−15.1521			−0.820530
$342$		0			0
$343$			3.56465i			0.192473i
$344$	−21.1639			−1.14108
$345$		0			0
$346$	7.33466			0.394314
$347$		−	21.6036i		−	1.15974i	−0.814708	−	0.579871i	$-0.803103\pi$
$347$		−	21.6036i		−	1.15974i	0.814708	−	0.579871i	$-0.196897\pi$
$348$		0			0
$349$	4.12603			0.220861			0.110431	−	0.993884i	$-0.464777\pi$
$349$	4.12603			0.220861			0.110431	+	0.993884i	$0.464777\pi$
$350$	−0.829538	+	1.40054i	−0.0443407	+	0.0748622i
$351$		0			0
$352$		−	9.82830i		−	0.523850i
$353$			7.07724i			0.376684i	0.982104	+	0.188342i	$0.0603113\pi$
$353$			7.07724i			0.376684i	−0.982104	+	0.188342i	$0.939689\pi$
$354$		0			0
$355$	−15.4645	−	27.1331i	−0.820771	−	1.44008i
$356$	4.96002			0.262881
$357$		0			0
$358$			17.9988i			0.951264i
$359$	14.4359			0.761900			0.380950	−	0.924596i	$-0.375597\pi$
$359$	14.4359			0.761900			0.380950	+	0.924596i	$0.375597\pi$
$360$		0			0
$361$	−10.5064			−0.552971
$362$			19.1304i			1.00547i
$363$		0			0
$364$	0.489209			0.0256415
$365$	16.4434	−	9.37190i	0.860688	−	0.490548i
$366$		0			0
$367$			15.4145i			0.804630i	0.915501	+	0.402315i	$0.131794\pi$
$367$			15.4145i			0.804630i	−0.915501	+	0.402315i	$0.868206\pi$
$368$		−	26.7873i		−	1.39638i
$369$		0			0
$370$	−5.45255	−	9.56673i	−0.283464	−	0.497351i
$371$	−1.53868			−0.0798841
$372$		0			0
$373$		−	29.8574i		−	1.54596i	−0.634432	−	0.772979i	$-0.718766\pi$
$373$		−	29.8574i		−	1.54596i	0.634432	−	0.772979i	$-0.281234\pi$
$374$	1.98433			0.102607
$375$		0			0
$376$	1.01922			0.0525621
$377$			5.02700i			0.258904i
$378$		0			0
$379$	−37.3451			−1.91829			−0.959144	−	0.282920i	$-0.908697\pi$
$379$	−37.3451			−1.91829			−0.959144	+	0.282920i	$0.908697\pi$
$380$	1.22757	+	2.15382i	0.0629729	+	0.110489i
$381$		0			0
$382$			15.6067i			0.798508i
$383$		−	25.8159i		−	1.31913i	−0.751647	−	0.659566i	$-0.770740\pi$
$383$		−	25.8159i		−	1.31913i	0.751647	−	0.659566i	$-0.229260\pi$
$384$		0			0
$385$	−2.30317	+	1.31269i	−0.117380	+	0.0669008i
$386$	−10.6163			−0.540355
$387$		0			0
$388$			4.39173i			0.222956i
$389$	−20.6935			−1.04920			−0.524600	−	0.851349i	$-0.675785\pi$
$389$	−20.6935			−1.04920			−0.524600	+	0.851349i	$0.675785\pi$
$390$		0			0
$391$	−2.91245			−0.147289
$392$		−	21.0075i		−	1.06104i
$393$		0			0
$394$	−8.51723			−0.429092
$395$	16.9520	+	29.7430i	0.852946	+	1.49653i
$396$		0			0
$397$			2.38045i			0.119471i	0.998214	+	0.0597357i	$0.0190258\pi$
$397$			2.38045i			0.119471i	−0.998214	+	0.0597357i	$0.980974\pi$
$398$			15.9820i			0.801108i
$399$		0			0
$400$	7.88487	−	13.3123i	0.394243	−	0.665617i
$401$	−32.0936			−1.60268			−0.801339	−	0.598211i	$-0.795879\pi$
$401$	−32.0936			−1.60268			−0.801339	+	0.598211i	$0.795879\pi$
$402$		0			0
$403$			16.4354i			0.818707i
$404$	−3.11879			−0.155166
$405$		0			0
$406$	−0.325555			−0.0161570
$407$		−	17.9332i		−	0.888918i
$408$		0			0
$409$	31.5011			1.55763			0.778815	−	0.627253i	$-0.215821\pi$
$409$	31.5011			1.55763			0.778815	+	0.627253i	$0.215821\pi$
$410$	14.1330	−	8.05507i	0.697978	−	0.397812i
$411$		0			0
$412$			0.658179i			0.0324261i
$413$			3.39719i			0.167165i
$414$		0			0
$415$	−14.7746	+	8.42074i	−0.725255	+	0.413358i
$416$	−10.6608			−0.522686
$417$		0			0
$418$		−	17.1888i		−	0.840732i
$419$	3.15481			0.154123			0.0770613	−	0.997026i	$-0.475446\pi$
$419$	3.15481			0.154123			0.0770613	+	0.997026i	$0.475446\pi$
$420$		0			0
$421$	−11.9631			−0.583048			−0.291524	−	0.956564i	$-0.594162\pi$
$421$	−11.9631			−0.583048			−0.291524	+	0.956564i	$0.594162\pi$
$422$			17.3687i			0.845497i
$423$		0			0
$424$	18.2213			0.884904
$425$	−1.44739	−	0.857282i	−0.0702085	−	0.0415843i
$426$		0			0
$427$		−	1.98970i		−	0.0962882i
$428$		−	2.05016i		−	0.0990981i
$429$		0			0
$430$	−9.84420	−	17.2721i	−0.474730	−	0.832934i
$431$	−31.2658			−1.50602			−0.753011	−	0.658008i	$-0.771399\pi$
$431$	−31.2658			−1.50602			−0.753011	+	0.658008i	$0.771399\pi$
$432$		0			0
$433$			30.6459i			1.47275i	0.676575	+	0.736373i	$0.263463\pi$
$433$			30.6459i			1.47275i	−0.676575	+	0.736373i	$0.736537\pi$
$434$	−1.06438			−0.0510919
$435$		0			0
$436$	−5.41682			−0.259419
$437$			25.2284i			1.20684i
$438$		0			0
$439$	−0.717425			−0.0342408			−0.0171204	−	0.999853i	$-0.505450\pi$
$439$	−0.717425			−0.0342408			−0.0171204	+	0.999853i	$0.505450\pi$
$440$	27.2745	−	15.5451i	1.30026	−	0.741083i
$441$		0			0
$442$		−	2.15240i		−	0.102379i
$443$		−	27.0649i		−	1.28589i	−0.765911	−	0.642947i	$-0.777712\pi$
$443$		−	27.0649i		−	1.28589i	0.765911	−	0.642947i	$-0.222288\pi$
$444$		0			0
$445$	14.4365	+	25.3294i	0.684353	+	1.20073i
$446$	−17.1450			−0.811838
$447$		0			0
$448$		−	2.27361i		−	0.107418i
$449$	30.3663			1.43307			0.716536	−	0.697550i	$-0.245727\pi$
$449$	30.3663			1.43307			0.716536	+	0.697550i	$0.245727\pi$
$450$		0			0
$451$	26.4929			1.24750
$452$		−	3.76411i		−	0.177049i
$453$		0			0
$454$	1.96364			0.0921584
$455$	1.42387	+	2.49825i	0.0667522	+	0.117120i
$456$		0			0
$457$		−	2.43167i		−	0.113749i	−0.998381	−	0.0568743i	$-0.981887\pi$
$457$		−	2.43167i		−	0.113749i	0.998381	−	0.0568743i	$-0.0181134\pi$
$458$			10.0477i			0.469500i
$459$		0			0
$460$	−6.39750	+	3.64625i	−0.298285	+	0.170007i
$461$	8.28439			0.385842			0.192921	−	0.981214i	$-0.438204\pi$
$461$	8.28439			0.385842			0.192921	+	0.981214i	$0.438204\pi$
$462$		0			0
$463$			7.05654i			0.327945i	0.986465	+	0.163973i	$0.0524309\pi$
$463$			7.05654i			0.327945i	−0.986465	+	0.163973i	$0.947569\pi$
$464$	3.09444			0.143656
$465$		0			0
$466$	36.2422			1.67889
$467$			6.07165i			0.280963i	0.990083	+	0.140481i	$0.0448650\pi$
$467$			6.07165i			0.280963i	−0.990083	+	0.140481i	$0.955135\pi$
$468$		0			0
$469$	2.88060			0.133014
$470$	0.474081	+	0.831796i	0.0218677	+	0.0383679i
$471$		0			0
$472$		−	40.2301i		−	1.85174i
$473$		−	32.3773i		−	1.48871i
$474$		0			0
$475$	−7.42603	+	12.5377i	−0.340729	+	0.575267i
$476$	−0.0327414			−0.00150070
$477$		0			0
$478$			11.3074i			0.517188i
$479$	29.7675			1.36011			0.680055	−	0.733161i	$-0.261956\pi$
$479$	29.7675			1.36011			0.680055	+	0.733161i	$0.261956\pi$
$480$		0			0
$481$	−19.4522			−0.886943
$482$			38.0390i			1.73263i
$483$		0			0
$484$	3.98613			0.181188
$485$	−22.4273	+	12.7824i	−1.01837	+	0.580419i
$486$		0			0
$487$		−	41.9050i		−	1.89890i	−0.313923	−	0.949448i	$-0.601643\pi$
$487$		−	41.9050i		−	1.89890i	0.313923	−	0.949448i	$-0.398357\pi$
$488$			23.5623i			1.06662i
$489$		0			0
$490$	17.1444	−	9.77145i	0.774507	−	0.441429i
$491$	−7.22435			−0.326030			−0.163015	−	0.986624i	$-0.552122\pi$
$491$	−7.22435			−0.326030			−0.163015	+	0.986624i	$0.552122\pi$
$492$		0			0
$493$		−	0.336444i		−	0.0151527i
$494$	−18.6447			−0.838864
$495$		0			0
$496$	10.1171			0.454270
$497$		−	3.57290i		−	0.160266i
$498$		0			0
$499$	15.5607			0.696593			0.348296	−	0.937384i	$-0.386760\pi$
$499$	15.5607			0.696593			0.348296	+	0.937384i	$0.386760\pi$
$500$	−4.25262	−	0.0710538i	−0.190183	−	0.00317762i
$501$		0			0
$502$			20.3049i			0.906253i
$503$			38.5096i			1.71706i	0.512765	+	0.858529i	$0.328621\pi$
$503$			38.5096i			1.71706i	−0.512765	+	0.858529i	$0.671379\pi$
$504$		0			0
$505$	−9.07745	−	15.9268i	−0.403941	−	0.708732i
$506$	51.0560			2.26971
$507$		0			0
$508$			4.64971i			0.206298i
$509$	−31.6646			−1.40351			−0.701754	−	0.712419i	$-0.747600\pi$
$509$	−31.6646			−1.40351			−0.701754	+	0.712419i	$0.747600\pi$
$510$		0			0
$511$	2.16527			0.0957860
$512$			25.3109i			1.11860i
$513$		0			0
$514$	21.8375			0.963209
$515$	−3.36113	+	1.91567i	−0.148109	+	0.0844145i
$516$		0			0
$517$			1.55924i			0.0685751i
$518$		−	1.25975i		−	0.0553502i
$519$		0			0
$520$	−16.8617	−	29.5847i	−0.739437	−	1.29737i
$521$	20.2023			0.885079			0.442539	−	0.896749i	$-0.354078\pi$
$521$	20.2023			0.885079			0.442539	+	0.896749i	$0.354078\pi$
$522$		0			0
$523$		−	12.1052i		−	0.529325i	−0.964341	−	0.264663i	$-0.914739\pi$
$523$		−	12.1052i		−	0.529325i	0.964341	−	0.264663i	$-0.0852606\pi$
$524$	−4.58268			−0.200195
$525$		0			0
$526$	2.19886			0.0958751
$527$		−	1.09998i		−	0.0479158i
$528$		0			0
$529$	−51.9361			−2.25809
$530$	8.47548	+	14.8706i	0.368151	+	0.645938i
$531$		0			0
$532$			0.283615i			0.0122963i
$533$		−	28.7368i		−	1.24473i
$534$		0			0
$535$	10.4696	−	5.96711i	0.452638	−	0.257981i
$536$	−34.1125			−1.47344
$537$		0			0
$538$		−	6.33681i		−	0.273199i
$539$	32.1380			1.38428
$540$		0			0
$541$	−14.4279			−0.620304			−0.310152	−	0.950687i	$-0.600380\pi$
$541$	−14.4279			−0.620304			−0.310152	+	0.950687i	$0.600380\pi$
$542$		−	16.6563i		−	0.715450i
$543$		0			0
$544$	0.713495			0.0305909
$545$	−15.7660	−	27.6621i	−0.675341	−	1.18492i
$546$		0			0
$547$		−	41.9178i		−	1.79228i	−0.443774	−	0.896139i	$-0.646361\pi$
$547$		−	41.9178i		−	1.79228i	0.443774	−	0.896139i	$-0.353639\pi$
$548$			2.08284i			0.0889744i
$549$		0			0
$550$	25.3731	+	15.0284i	1.08191	+	0.640813i
$551$	−2.91437			−0.124156
$552$		0			0
$553$			3.91656i			0.166549i
$554$	26.4893			1.12542
$555$		0			0
$556$	−1.03247			−0.0437863
$557$		−	3.60324i		−	0.152674i	−0.997082	−	0.0763372i	$-0.975677\pi$
$557$		−	3.60324i		−	0.152674i	0.997082	−	0.0763372i	$-0.0243225\pi$
$558$		0			0
$559$	−35.1196			−1.48540
$560$	1.53783	−	0.876486i	0.0649853	−	0.0370383i
$561$		0			0
$562$		−	5.00573i		−	0.211154i
$563$			15.5829i			0.656741i	0.944549	+	0.328370i	$0.106499\pi$
$563$			15.5829i			0.656741i	−0.944549	+	0.328370i	$0.893501\pi$
$564$		0			0
$565$	19.2222	−	10.9557i	0.808685	−	0.460909i
$566$	6.97075			0.293003
$567$		0			0
$568$			42.3109i			1.77532i
$569$	−36.9718			−1.54994			−0.774970	−	0.631998i	$-0.782235\pi$
$569$	−36.9718			−1.54994			−0.774970	+	0.631998i	$0.782235\pi$
$570$		0			0
$571$	29.9692			1.25417			0.627086	−	0.778950i	$-0.284248\pi$
$571$	29.9692			1.25417			0.627086	+	0.778950i	$0.284248\pi$
$572$		−	8.86279i		−	0.370572i
$573$		0			0
$574$	1.86103			0.0776780
$575$	−37.2407	−	22.0575i	−1.55304	−	0.919863i
$576$		0			0
$577$		−	7.12327i		−	0.296546i	−0.988946	−	0.148273i	$-0.952629\pi$
$577$		−	7.12327i		−	0.296546i	0.988946	−	0.148273i	$-0.0473714\pi$
$578$		−	21.4906i		−	0.893892i
$579$		0			0
$580$	−0.421212	−	0.739035i	−0.0174899	−	0.0306867i
$581$	−1.94552			−0.0807136
$582$		0			0
$583$			27.8756i			1.15449i
$584$	−25.6415			−1.06105
$585$		0			0
$586$	−15.2682			−0.630722
$587$			7.87237i			0.324928i	0.986715	+	0.162464i	$0.0519441\pi$
$587$			7.87237i			0.324928i	−0.986715	+	0.162464i	$0.948056\pi$
$588$		0			0
$589$	−9.52833			−0.392608
$590$	32.8322	−	18.7127i	1.35168	−	0.770390i
$591$		0			0
$592$			11.9741i			0.492131i
$593$		−	17.9188i		−	0.735836i	−0.929858	−	0.367918i	$-0.880071\pi$
$593$		−	17.9188i		−	0.735836i	0.929858	−	0.367918i	$-0.119929\pi$
$594$		0			0
$595$	−0.0952959	−	0.167201i	−0.00390675	−	0.00685457i
$596$	1.40905			0.0577170
$597$		0			0
$598$		−	55.3804i		−	2.26467i
$599$	−20.1934			−0.825078			−0.412539	−	0.910940i	$-0.635358\pi$
$599$	−20.1934			−0.825078			−0.412539	+	0.910940i	$0.635358\pi$
$600$		0			0
$601$	23.2527			0.948496			0.474248	−	0.880391i	$-0.342720\pi$
$601$	23.2527			0.948496			0.474248	+	0.880391i	$0.342720\pi$
$602$		−	2.27439i		−	0.0926973i
$603$		0			0
$604$	5.83870			0.237573
$605$	11.6019	+	20.3560i	0.471683	+	0.827589i
$606$		0			0
$607$		−	17.6177i		−	0.715082i	−0.933897	−	0.357541i	$-0.883615\pi$
$607$		−	17.6177i		−	0.715082i	0.933897	−	0.357541i	$-0.116385\pi$
$608$		−	6.18050i		−	0.250652i
$609$		0			0
$610$	−19.2295	+	10.9598i	−0.778580	+	0.443750i
$611$	1.69130			0.0684228
$612$		0			0
$613$		−	13.4161i		−	0.541873i	−0.962597	−	0.270937i	$-0.912667\pi$
$613$		−	13.4161i		−	0.541873i	0.962597	−	0.270937i	$-0.0873334\pi$
$614$	−33.7001			−1.36002
$615$		0			0
$616$	3.59151			0.144706
$617$		−	7.99166i		−	0.321732i	−0.986976	−	0.160866i	$-0.948571\pi$
$617$		−	7.99166i		−	0.321732i	0.986976	−	0.160866i	$-0.0514287\pi$
$618$		0			0
$619$	15.0770			0.605996			0.302998	−	0.952991i	$-0.402012\pi$
$619$	15.0770			0.605996			0.302998	+	0.952991i	$0.402012\pi$
$620$	−1.37712	−	2.41622i	−0.0553066	−	0.0970378i
$621$		0			0
$622$			2.18294i			0.0875281i
$623$			3.33538i			0.133629i
$624$		0			0
$625$	−12.0147	−	21.9237i	−0.480586	−	0.876947i
$626$	42.4781			1.69776
$627$		0			0
$628$			8.30193i			0.331283i
$629$	1.30188			0.0519094
$630$		0			0
$631$	10.5154			0.418611			0.209306	−	0.977850i	$-0.432880\pi$
$631$	10.5154			0.418611			0.209306	+	0.977850i	$0.432880\pi$
$632$		−	46.3805i		−	1.84492i
$633$		0			0
$634$	22.8707			0.908311
$635$	−23.7447	+	13.5333i	−0.942281	+	0.537052i
$636$		0			0
$637$		−	34.8600i		−	1.38121i
$638$			5.89795i			0.233502i
$639$		0			0
$640$	−13.7336	+	7.82747i	−0.542870	+	0.309408i
$641$	−27.2479			−1.07623			−0.538113	−	0.842873i	$-0.680863\pi$
$641$	−27.2479			−1.07623			−0.538113	+	0.842873i	$0.680863\pi$
$642$		0			0
$643$		−	36.3023i		−	1.43162i	−0.698293	−	0.715812i	$-0.746057\pi$
$643$		−	36.3023i		−	1.43162i	0.698293	−	0.715812i	$-0.253943\pi$
$644$	−0.842424			−0.0331962
$645$		0			0
$646$	1.24784			0.0490955
$647$		−	8.77892i		−	0.345135i	−0.984998	−	0.172567i	$-0.944794\pi$
$647$		−	8.77892i		−	0.345135i	0.984998	−	0.172567i	$-0.0552063\pi$
$648$		0			0
$649$	61.5454			2.41587
$650$	16.3013	−	27.5221i	0.639389	−	1.07951i
$651$		0			0
$652$			1.17176i			0.0458898i
$653$			44.1466i			1.72759i	0.503845	+	0.863794i	$0.331918\pi$
$653$			44.1466i			1.72759i	−0.503845	+	0.863794i	$0.668082\pi$
$654$		0			0
$655$	−13.3382	−	23.4024i	−0.521166	−	0.914408i
$656$	−17.6894			−0.690653
$657$		0			0
$658$			0.109531i			0.00426996i
$659$	−22.7653			−0.886810			−0.443405	−	0.896321i	$-0.646230\pi$
$659$	−22.7653			−0.886810			−0.443405	+	0.896321i	$0.646230\pi$
$660$		0			0
$661$	29.3474			1.14148			0.570740	−	0.821131i	$-0.306656\pi$
$661$	29.3474			1.14148			0.570740	+	0.821131i	$0.306656\pi$
$662$		−	8.26435i		−	0.321203i
$663$		0			0
$664$	23.0391			0.894092
$665$	−1.44834	+	0.825481i	−0.0561643	+	0.0320108i
$666$		0			0
$667$		−	8.65656i		−	0.335183i
$668$		−	3.25264i		−	0.125849i
$669$		0			0
$670$	−15.8672	−	27.8397i	−0.613002	−	1.07554i
$671$	−36.0465			−1.39156
$672$		0			0
$673$			42.2267i			1.62772i	0.581060	+	0.813860i	$0.302638\pi$
$673$			42.2267i			1.62772i	−0.581060	+	0.813860i	$0.697362\pi$
$674$	8.09590			0.311842
$675$		0			0
$676$	−4.66802			−0.179539
$677$			19.9803i			0.767907i	0.923353	+	0.383953i	$0.125438\pi$
$677$			19.9803i			0.767907i	−0.923353	+	0.383953i	$0.874562\pi$
$678$		0			0
$679$	−2.95323			−0.113334
$680$	1.12851	+	1.98002i	0.0432764	+	0.0759304i
$681$		0			0
$682$			19.2829i			0.738381i
$683$			23.0491i			0.881950i	0.897519	+	0.440975i	$0.145367\pi$
$683$			23.0491i			0.881950i	−0.897519	+	0.440975i	$0.854633\pi$
$684$		0			0
$685$	−10.6364	+	6.06223i	−0.406398	+	0.231626i
$686$	4.53647			0.173203
$687$		0			0
$688$			21.6184i			0.824193i
$689$	30.2366			1.15192
$690$		0			0
$691$	4.01208			0.152627			0.0763134	−	0.997084i	$-0.475685\pi$
$691$	4.01208			0.152627			0.0763134	+	0.997084i	$0.475685\pi$
$692$			2.19250i			0.0833465i
$693$		0			0
$694$	−27.4933			−1.04363
$695$	−3.00506	−	5.27250i	−0.113988	−	0.199997i
$696$		0			0
$697$			1.92328i			0.0728493i
$698$		−	5.25090i		−	0.198750i
$699$		0			0
$700$	−0.418656	−	0.247969i	−0.0158237	−	0.00937234i
$701$	4.49887			0.169920			0.0849599	−	0.996384i	$-0.472924\pi$
$701$	4.49887			0.169920			0.0849599	+	0.996384i	$0.472924\pi$
$702$		0			0
$703$		−	11.2773i		−	0.425330i
$704$	−41.1900			−1.55240
$705$		0			0
$706$	9.00670			0.338971
$707$		−	2.09724i		−	0.0788748i
$708$		0			0
$709$	−36.7777			−1.38121			−0.690607	−	0.723230i	$-0.742657\pi$
$709$	−36.7777			−1.38121			−0.690607	+	0.723230i	$0.742657\pi$
$710$	−34.5304	+	19.6806i	−1.29590	+	0.738598i
$711$		0			0
$712$		−	39.4981i		−	1.48025i
$713$		−	28.3020i		−	1.05992i
$714$		0			0
$715$	45.2597	−	25.7957i	1.69262	−	0.964705i
$716$	−5.38026			−0.201070
$717$		0			0
$718$		−	18.3716i		−	0.685621i
$719$	25.4279			0.948300			0.474150	−	0.880444i	$-0.342755\pi$
$719$	25.4279			0.948300			0.474150	+	0.880444i	$0.342755\pi$
$720$		0			0
$721$	−0.442594			−0.0164831
$722$			13.3708i			0.497609i
$723$		0			0
$724$	−5.71854			−0.212528
$725$	2.54807	−	4.30201i	0.0946330	−	0.159773i
$726$		0			0
$727$			11.6265i			0.431205i	0.976481	+	0.215602i	$0.0691715\pi$
$727$			11.6265i			0.431205i	−0.976481	+	0.215602i	$0.930829\pi$
$728$		−	3.89571i		−	0.144385i
$729$		0			0
$730$	−11.9269	−	20.9263i	−0.441436	−	0.774519i
$731$	2.35046			0.0869349
$732$		0			0
$733$		−	25.6926i		−	0.948978i	−0.880261	−	0.474489i	$-0.842633\pi$
$733$		−	25.6926i		−	0.948978i	0.880261	−	0.474489i	$-0.157367\pi$
$734$	19.6169			0.724073
$735$		0			0
$736$	18.3580			0.676683
$737$		−	52.1866i		−	1.92232i
$738$		0			0
$739$	33.3612			1.22721			0.613606	−	0.789612i	$-0.289718\pi$
$739$	33.3612			1.22721			0.613606	+	0.789612i	$0.289718\pi$
$740$	2.85972	−	1.62990i	0.105126	−	0.0599162i
$741$		0			0
$742$			1.95816i			0.0718864i
$743$			25.6430i			0.940750i	0.882467	+	0.470375i	$0.155881\pi$
$743$			25.6430i			0.940750i	−0.882467	+	0.470375i	$0.844119\pi$
$744$		0			0
$745$	4.10113	+	7.19562i	0.150254	+	0.263627i
$746$	−37.9973			−1.39118
$747$		0			0
$748$			0.593162i			0.0216882i
$749$	1.37863			0.0503741
$750$		0			0
$751$	46.6411			1.70196			0.850979	−	0.525200i	$-0.176009\pi$
$751$	46.6411			1.70196			0.850979	+	0.525200i	$0.176009\pi$
$752$		−	1.04111i		−	0.0379652i
$753$		0			0
$754$	6.39750			0.232983
$755$	16.9939	+	29.8165i	0.618472	+	1.08514i
$756$		0			0
$757$			2.69262i			0.0978650i	0.998802	+	0.0489325i	$0.0155819\pi$
$757$			2.69262i			0.0978650i	−0.998802	+	0.0489325i	$0.984418\pi$
$758$			47.5264i			1.72624i
$759$		0			0
$760$	17.1515	−	9.77549i	0.622151	−	0.354594i
$761$	−0.471501			−0.0170919			−0.00854595	−	0.999963i	$-0.502720\pi$
$761$	−0.471501			−0.0170919			−0.00854595	+	0.999963i	$0.502720\pi$
$762$		0			0
$763$		−	3.64255i		−	0.131869i
$764$	−4.66521			−0.168781
$765$		0			0
$766$	−32.8540			−1.18706
$767$		−	66.7583i		−	2.41050i
$768$		0			0
$769$	−9.04380			−0.326128			−0.163064	−	0.986616i	$-0.552138\pi$
$769$	−9.04380			−0.326128			−0.163064	+	0.986616i	$0.552138\pi$
$770$	1.67056	+	2.93108i	0.0602029	+	0.105629i
$771$		0			0
$772$		−	3.17346i		−	0.114215i
$773$		−	9.91726i		−	0.356699i	−0.983967	−	0.178350i	$-0.942924\pi$
$773$		−	9.91726i		−	0.356699i	0.983967	−	0.178350i	$-0.0570758\pi$
$774$		0			0
$775$	8.33074	−	14.0651i	0.299249	−	0.505234i
$776$	34.9726			1.25544
$777$		0			0
$778$			26.3351i			0.944159i
$779$	16.6600			0.596905
$780$		0			0
$781$	−64.7287			−2.31617
$782$			3.70646i			0.132543i
$783$		0			0
$784$	−21.4586			−0.766379
$785$	−42.3955	+	24.1633i	−1.51316	+	0.862425i
$786$		0			0
$787$			8.53609i			0.304279i	0.988359	+	0.152139i	$0.0486162\pi$
$787$			8.53609i			0.304279i	−0.988359	+	0.152139i	$0.951384\pi$
$788$		−	2.54600i		−	0.0906976i
$789$		0			0
$790$	37.8517	−	21.5735i	1.34670	−	0.767552i
$791$	2.53119			0.0899986
$792$		0			0
$793$			39.0996i			1.38847i
$794$	3.02943			0.107510
$795$		0			0
$796$	−4.77741			−0.169331
$797$			12.5563i			0.444768i	0.974959	+	0.222384i	$0.0713838\pi$
$797$			12.5563i			0.444768i	−0.974959	+	0.222384i	$0.928616\pi$
$798$		0			0
$799$	−0.113194			−0.00400453
$800$	9.12327	+	5.40369i	0.322556	+	0.191049i
$801$		0			0
$802$			40.8432i			1.44222i
$803$		−	39.2273i		−	1.38430i
$804$		0			0
$805$	−2.45193	−	4.30201i	−0.0864191	−	0.151626i
$806$	20.9162			0.736741
$807$		0			0
$808$			24.8359i			0.873723i
$809$	−16.4082			−0.576883			−0.288441	−	0.957498i	$-0.593137\pi$
$809$	−16.4082			−0.576883			−0.288441	+	0.957498i	$0.593137\pi$
$810$		0			0
$811$	29.4688			1.03479			0.517394	−	0.855747i	$-0.326902\pi$
$811$	29.4688			1.03479			0.517394	+	0.855747i	$0.326902\pi$
$812$		−	0.0973162i		−	0.00341513i
$813$		0			0
$814$	−22.8223			−0.799923
$815$	−5.98385	+	3.41049i	−0.209605	+	0.119464i
$816$		0			0
$817$		−	20.3603i		−	0.712318i
$818$		−	40.0892i		−	1.40169i
$819$		0			0
$820$	2.40785	+	4.22468i	0.0840859	+	0.147532i
$821$	−28.5209			−0.995385			−0.497693	−	0.867353i	$-0.665819\pi$
$821$	−28.5209			−0.995385			−0.497693	+	0.867353i	$0.665819\pi$
$822$		0			0
$823$		−	16.7546i		−	0.584028i	−0.956414	−	0.292014i	$-0.905675\pi$
$823$		−	16.7546i		−	0.584028i	0.956414	−	0.292014i	$-0.0943253\pi$
$824$	5.24127			0.182588
$825$		0			0
$826$	4.32336			0.150429
$827$		−	3.38369i		−	0.117662i	−0.998268	−	0.0588312i	$-0.981263\pi$
$827$		−	3.38369i		−	0.117662i	0.998268	−	0.0588312i	$-0.0187374\pi$
$828$		0			0
$829$	14.4434			0.501639			0.250819	−	0.968034i	$-0.419300\pi$
$829$	14.4434			0.501639			0.250819	+	0.968034i	$0.419300\pi$
$830$	10.7165	+	18.8025i	0.371974	+	0.652645i
$831$		0			0
$832$			44.6787i			1.54896i
$833$			2.33309i			0.0808367i
$834$		0			0
$835$	16.6103	−	9.46702i	0.574823	−	0.327620i
$836$	5.13814			0.177706
$837$		0			0
$838$		−	4.01490i		−	0.138692i
$839$	−27.6642			−0.955075			−0.477538	−	0.878611i	$-0.658471\pi$
$839$	−27.6642			−0.955075			−0.477538	+	0.878611i	$0.658471\pi$
$840$		0			0
$841$	1.00000			0.0344828
$842$			15.2246i			0.524675i
$843$		0			0
$844$	−5.19193			−0.178714
$845$	−13.5866	−	23.8382i	−0.467392	−	0.820060i
$846$		0			0
$847$			2.68048i			0.0921024i
$848$		−	18.6126i		−	0.639159i
$849$		0			0
$850$	−1.09100	+	1.84198i	−0.0374210	+	0.0631795i
$851$	33.4969			1.14826
$852$		0			0
$853$		−	4.26068i		−	0.145883i	−0.997336	−	0.0729415i	$-0.976761\pi$
$853$		−	4.26068i		−	0.145883i	0.997336	−	0.0729415i	$-0.0232386\pi$
$854$	−2.53214			−0.0866481
$855$		0			0
$856$	−16.3260			−0.558011
$857$			28.7104i			0.980729i	0.871518	+	0.490364i	$0.163136\pi$
$857$			28.7104i			0.980729i	−0.871518	+	0.490364i	$0.836864\pi$
$858$		0			0
$859$	39.3734			1.34340			0.671701	−	0.740822i	$-0.265564\pi$
$859$	39.3734			1.34340			0.671701	+	0.740822i	$0.265564\pi$
$860$	5.16304	−	2.94267i	0.176058	−	0.100344i
$861$		0			0
$862$			39.7898i			1.35525i
$863$		−	22.1235i		−	0.753094i	−0.926398	−	0.376547i	$-0.877111\pi$
$863$		−	22.1235i		−	0.753094i	0.926398	−	0.376547i	$-0.122889\pi$
$864$		0			0
$865$	−11.1965	+	6.38142i	−0.380692	+	0.216975i
$866$	39.0008			1.32530
$867$		0			0
$868$		−	0.318168i		−	0.0107993i
$869$	70.9546			2.40697
$870$		0			0
$871$	−56.6068			−1.91805
$872$			43.1357i			1.46076i
$873$		0			0
$874$	32.1064			1.08602
$875$	0.0477803	−	2.85968i	0.00161527	−	0.0966749i
$876$		0			0
$877$		−	32.3439i		−	1.09217i	−0.837728	−	0.546087i	$-0.816117\pi$
$877$		−	32.3439i		−	1.09217i	0.837728	−	0.546087i	$-0.183883\pi$
$878$			0.913015i			0.0308128i
$879$		0			0
$880$	−15.8789	−	27.8603i	−0.535278	−	0.939169i
$881$	54.6109			1.83989			0.919944	−	0.392051i	$-0.128234\pi$
$881$	54.6109			1.83989			0.919944	+	0.392051i	$0.128234\pi$
$882$		0			0
$883$		−	47.5511i		−	1.60022i	−0.599852	−	0.800111i	$-0.704774\pi$
$883$		−	47.5511i		−	1.60022i	0.599852	−	0.800111i	$-0.295226\pi$
$884$	0.643403			0.0216400
$885$		0			0
$886$	−34.4436			−1.15715
$887$			10.4630i			0.351312i	0.984452	+	0.175656i	$0.0562047\pi$
$887$			10.4630i			0.351312i	−0.984452	+	0.175656i	$0.943795\pi$
$888$		0			0
$889$	−3.12671			−0.104866
$890$	32.2349	−	18.3722i	1.08052	−	0.615838i
$891$		0			0
$892$		−	5.12504i		−	0.171599i
$893$			0.980521i			0.0328119i
$894$		0			0
$895$	−15.6596	−	27.4754i	−0.523442	−	0.918402i
$896$	−1.80845			−0.0604160
$897$		0			0
$898$		−	38.6449i		−	1.28960i
$899$	3.26943			0.109042
$900$		0			0
$901$	−2.02365			−0.0674177
$902$		−	33.7156i		−	1.12261i
$903$		0			0
$904$	−29.9747			−0.996945
$905$	−16.6442	−	29.2029i	−0.553271	−	0.970738i
$906$		0			0
$907$			10.7211i			0.355989i	0.984032	+	0.177994i	$0.0569609\pi$
$907$			10.7211i			0.355989i	−0.984032	+	0.177994i	$0.943039\pi$
$908$			0.586980i			0.0194796i
$909$		0			0
$910$	3.17934	−	1.81206i	0.105394	−	0.0600692i
$911$	3.57634			0.118489			0.0592447	−	0.998243i	$-0.481131\pi$
$911$	3.57634			0.118489			0.0592447	+	0.998243i	$0.481131\pi$
$912$		0			0
$913$			35.2461i			1.16648i
$914$	−3.09461			−0.102361
$915$		0			0
$916$	−3.00351			−0.0992386
$917$		−	3.08163i		−	0.101765i
$918$		0			0
$919$	22.2776			0.734870			0.367435	−	0.930049i	$-0.380236\pi$
$919$	22.2776			0.734870			0.367435	+	0.930049i	$0.380236\pi$
$920$	29.0362	+	50.9452i	0.957294	+	1.67961i
$921$		0			0
$922$		−	10.5429i		−	0.347213i
$923$			70.2112i			2.31103i
$924$		0			0
$925$	16.6468	+	9.85986i	0.547344	+	0.324190i
$926$	8.98035			0.295113
$927$		0			0
$928$			2.12070i			0.0696153i
$929$	−21.1779			−0.694826			−0.347413	−	0.937712i	$-0.612940\pi$
$929$	−21.1779			−0.694826			−0.347413	+	0.937712i	$0.612940\pi$
$930$		0			0
$931$	20.2099			0.662352
$932$			10.8337i			0.354868i
$933$		0			0
$934$	7.72695			0.252834
$935$	−3.02911	+	1.72644i	−0.0990624	+	0.0564605i
$936$		0			0
$937$		−	34.4462i		−	1.12531i	−0.826693	−	0.562654i	$-0.809780\pi$
$937$		−	34.4462i		−	1.12531i	0.826693	−	0.562654i	$-0.190220\pi$
$938$		−	3.66593i		−	0.119697i
$939$		0			0
$940$	−0.248643	+	0.141714i	−0.00810986	+	0.00462220i
$941$	−0.296167			−0.00965477			−0.00482738	−	0.999988i	$-0.501537\pi$
$941$	−0.296167			−0.00965477			−0.00482738	+	0.999988i	$0.501537\pi$
$942$		0			0
$943$			49.4851i			1.61146i
$944$	−41.0940			−1.33750
$945$		0			0
$946$	−41.2042			−1.33966
$947$			46.9467i			1.52556i	0.646656	+	0.762782i	$0.276167\pi$
$947$			46.9467i			1.52556i	−0.646656	+	0.762782i	$0.723833\pi$
$948$		0			0
$949$	−42.5498			−1.38123
$950$	15.9558	+	9.45057i	0.517674	+	0.306617i
$951$		0			0
$952$			0.260730i			0.00845029i
$953$			1.91375i			0.0619926i	0.999519	+	0.0309963i	$0.00986801\pi$
$953$			1.91375i			0.0619926i	−0.999519	+	0.0309963i	$0.990132\pi$
$954$		0			0
$955$	−13.5784	−	23.8239i	−0.439386	−	0.770923i
$956$	−3.38005			−0.109319
$957$		0			0
$958$		−	37.8829i		−	1.22394i
$959$	−1.40061			−0.0452280
$960$		0			0
$961$	−20.3108			−0.655188
$962$			24.7554i			0.798145i
$963$		0			0
$964$	−11.3707			−0.366227
$965$	16.2060	−	9.23656i	0.521688	−	0.297335i
$966$		0			0
$967$			4.01326i			0.129058i	0.997916	+	0.0645288i	$0.0205544\pi$
$967$			4.01326i			0.129058i	−0.997916	+	0.0645288i	$0.979446\pi$
$968$		−	31.7427i		−	1.02025i
$969$		0			0
$970$	16.2672	+	28.5416i	0.522309	+	0.916414i
$971$	4.54751			0.145937			0.0729683	−	0.997334i	$-0.476753\pi$
$971$	4.54751			0.145937			0.0729683	+	0.997334i	$0.476753\pi$
$972$		0			0
$973$		−	0.694284i		−	0.0222577i
$974$	−53.3295			−1.70879
$975$		0			0
$976$	24.0683			0.770409
$977$		−	44.2333i		−	1.41515i	−0.706639	−	0.707574i	$-0.749789\pi$
$977$		−	44.2333i		−	1.41515i	0.706639	−	0.707574i	$-0.250211\pi$
$978$		0			0
$979$	60.4256			1.93121
$980$	2.92092	+	5.12488i	0.0933053	+	0.163708i
$981$		0			0
$982$			9.19391i			0.293389i
$983$			34.2083i			1.09107i	0.838087	+	0.545537i	$0.183674\pi$
$983$			34.2083i			1.09107i	−0.838087	+	0.545537i	$0.816326\pi$
$984$		0			0
$985$	13.0017	−	7.41030i	0.414269	−	0.236112i
$986$	−0.428167			−0.0136356
$987$		0			0
$988$		−	5.57334i		−	0.177312i
$989$	60.4764			1.92304
$990$		0			0
$991$	−1.76770			−0.0561528			−0.0280764	−	0.999606i	$-0.508938\pi$
$991$	−1.76770			−0.0561528			−0.0280764	+	0.999606i	$0.508938\pi$
$992$			6.93347i			0.220138i
$993$		0			0
$994$	−4.54697			−0.144221
$995$	−13.9050	−	24.3969i	−0.440817	−	0.773433i
$996$		0			0
$997$			23.7398i			0.751848i	0.926650	+	0.375924i	$0.122675\pi$
$997$			23.7398i			0.751848i	−0.926650	+	0.375924i	$0.877325\pi$
$998$		−	19.8030i		−	0.626853i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1305.2.c.k.784.5	✓	12
3.2	odd	2		1305.2.c.l.784.8	yes	12
5.2	odd	4		6525.2.a.ce.1.8		12
5.3	odd	4		6525.2.a.ce.1.5		12
5.4	even	2	inner	1305.2.c.k.784.8	yes	12
15.2	even	4		6525.2.a.cf.1.5		12
15.8	even	4		6525.2.a.cf.1.8		12
15.14	odd	2		1305.2.c.l.784.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1305.2.c.k.784.5	✓	12	1.1	even	1	trivial
1305.2.c.k.784.8	yes	12	5.4	even	2	inner
1305.2.c.l.784.5	yes	12	15.14	odd	2
1305.2.c.l.784.8	yes	12	3.2	odd	2
6525.2.a.ce.1.5		12	5.3	odd	4
6525.2.a.ce.1.8		12	5.2	odd	4
6525.2.a.cf.1.5		12	15.2	even	4
6525.2.a.cf.1.8		12	15.8	even	4

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:	\( N \)	\(=\)	\( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1305.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.27263i q^{2} +0.380419 q^{4} +(1.10723 + 1.94269i) q^{5} +0.255813i q^{7} -3.02939i q^{8} +(2.47232 - 1.40909i) q^{10} +4.63446 q^{11} -5.02700i q^{13} +0.325555 q^{14} -3.09444 q^{16} +0.336444i q^{17} +2.91437 q^{19} +(0.421212 + 0.739035i) q^{20} -5.89795i q^{22} +8.65656i q^{23} +(-2.54807 + 4.30201i) q^{25} -6.39750 q^{26} +0.0973162i q^{28} -1.00000 q^{29} -3.26943 q^{31} -2.12070i q^{32} +0.428167 q^{34} +(-0.496966 + 0.283245i) q^{35} -3.86954i q^{37} -3.70891i q^{38} +(5.88515 - 3.35424i) q^{40} +5.71649 q^{41} -6.98619i q^{43} +1.76304 q^{44} +11.0166 q^{46} +0.336444i q^{47} +6.93456 q^{49} +(5.47486 + 3.24275i) q^{50} -1.91237i q^{52} +6.01484i q^{53} +(5.13143 + 9.00332i) q^{55} +0.774958 q^{56} +1.27263i q^{58} +13.2799 q^{59} -7.77792 q^{61} +4.16077i q^{62} -8.88775 q^{64} +(9.76589 - 5.56606i) q^{65} -11.2605i q^{67} +0.127989i q^{68} +(0.360465 + 0.632452i) q^{70} -13.9668 q^{71} -8.46426i q^{73} -4.92448 q^{74} +1.10868 q^{76} +1.18556i q^{77} +15.3102 q^{79} +(-3.42627 - 6.01154i) q^{80} -7.27496i q^{82} +7.60521i q^{83} +(-0.653605 + 0.372521i) q^{85} -8.89082 q^{86} -14.0396i q^{88} +13.0383 q^{89} +1.28597 q^{91} +3.29312i q^{92} +0.428167 q^{94} +(3.22689 + 5.66171i) q^{95} +11.5445i q^{97} -8.82511i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 16 q^{4} - 10 q^{10} - 12 q^{11} + 16 q^{14} + 16 q^{16} + 20 q^{19} + 14 q^{20} + 8 q^{25} - 56 q^{26} - 12 q^{29} - 16 q^{31} - 4 q^{34} - 16 q^{35} + 16 q^{40} - 32 q^{41} + 68 q^{44} + 20 q^{46}+ \cdots - 8 q^{95}+O(q^{100}) \) 12 * q - 16 * q^4 - 10 * q^10 - 12 * q^11 + 16 * q^14 + 16 * q^16 + 20 * q^19 + 14 * q^20 + 8 * q^25 - 56 * q^26 - 12 * q^29 - 16 * q^31 - 4 * q^34 - 16 * q^35 + 16 * q^40 - 32 * q^41 + 68 * q^44 + 20 * q^46 + 4 * q^49 - 8 * q^50 + 4 * q^55 - 76 * q^56 + 44 * q^59 - 52 * q^61 - 36 * q^64 - 8 * q^65 - 30 * q^70 - 20 * q^71 + 20 * q^74 - 28 * q^76 + 4 * q^79 + 34 * q^80 + 20 * q^85 - 36 * q^86 + 68 * q^89 + 48 * q^91 - 4 * q^94 - 8 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more