LMFDB - Embedded newform 3420.2.bj.c.2629.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3420,2,Mod(1189,3420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3420, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))

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

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

chi := DirichletCharacter("3420.1189");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3420.bj (of order $6$, degree $2$, 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:	$27.3088374913$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 20 x^{18} + 261 x^{16} - 1994 x^{14} + 11074 x^{12} - 39211 x^{10} + 99376 x^{8} - 134299 x^{6} + \cdots + 4096 $ x^20 - 20x^18 + 261x^16 - 1994x^14 + 11074x^12 - 39211x^10 + 99376x^8 - 134299x^6 + 124617x^4 - 24768*x^2 + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 380)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2629.5
Root			$0.392182 - 0.226426i$ of defining polynomial
Character	$\chi$	$=$	3420.2629
Dual form			3420.2.bj.c.1189.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.207009 - 2.22647i) q^{5} -2.54366i q^{7} -2.22377 q^{11} +(6.08116 + 3.51096i) q^{13} +(-2.21492 + 1.27878i) q^{17} +(2.70498 + 3.41805i) q^{19} +(6.95328 + 4.01448i) q^{23} +(-4.91429 + 0.921799i) q^{25} +(0.941734 - 1.63113i) q^{29} +5.98111 q^{31} +(-5.66338 + 0.526562i) q^{35} +2.86105i q^{37} +(3.67524 + 6.36571i) q^{41} +(3.19919 - 1.84706i) q^{43} +(-4.09540 - 2.36448i) q^{47} +0.529782 q^{49} +(8.91226 + 5.14549i) q^{53} +(0.460341 + 4.95114i) q^{55} +(3.73666 + 6.47208i) q^{59} +(4.17839 - 7.23719i) q^{61} +(6.55817 - 14.2663i) q^{65} +(-10.7040 - 6.17997i) q^{67} +(4.13931 + 7.16950i) q^{71} +(-10.9489 + 6.32134i) q^{73} +5.65651i q^{77} +(-2.13067 - 3.69043i) q^{79} -14.7613i q^{83} +(3.30568 + 4.66672i) q^{85} +(7.19403 - 12.4604i) q^{89} +(8.93069 - 15.4684i) q^{91} +(7.05022 - 6.73011i) q^{95} +(5.04871 - 2.91488i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - q^{5} + 14 q^{19} + 9 q^{25} + 16 q^{29} + 8 q^{31} + 2 q^{35} - 26 q^{41} - 44 q^{49} - 12 q^{55} - 4 q^{59} + 2 q^{61} + 18 q^{65} + 2 q^{71} - 16 q^{79} - 39 q^{85} + 40 q^{89} - 4 q^{91} + 43 q^{95}+O(q^{100}) $ 20 * q - q^5 + 14 * q^19 + 9 * q^25 + 16 * q^29 + 8 * q^31 + 2 * q^35 - 26 * q^41 - 44 * q^49 - 12 * q^55 - 4 * q^59 + 2 * q^61 + 18 * q^65 + 2 * q^71 - 16 * q^79 - 39 * q^85 + 40 * q^89 - 4 * q^91 + 43 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3420\mathbb{Z}\right)^\times$.

$n$	$1711$	$1901$	$2737$	$3061$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.207009	−	2.22647i	−0.0925774	−	0.995705i
$5$	−0.207009	−	2.22647i	−0.0925774	−	0.995705i
$6$		0			0
$7$		−	2.54366i		−	0.961414i	−0.876881	−	0.480707i	$-0.840380\pi$
$7$		−	2.54366i		−	0.961414i	0.876881	−	0.480707i	$-0.159620\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.22377			−0.670491			−0.335246	−	0.942131i	$-0.608819\pi$
$11$	−2.22377			−0.670491			−0.335246	+	0.942131i	$0.608819\pi$
$12$		0			0
$13$	6.08116	+	3.51096i	1.68661	+	0.973765i	0.957084	+	0.289812i	$0.0935927\pi$
$13$	6.08116	+	3.51096i	1.68661	+	0.973765i	0.729526	+	0.683953i	$0.239741\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.21492	+	1.27878i	−0.537197	+	0.310151i	−0.743942	−	0.668244i	$-0.767046\pi$
$17$	−2.21492	+	1.27878i	−0.537197	+	0.310151i	0.206745	+	0.978395i	$0.433713\pi$
$18$		0			0
$19$	2.70498	+	3.41805i	0.620565	+	0.784155i
$19$	2.70498	+	3.41805i	0.620565	+	0.784155i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	6.95328	+	4.01448i	1.44986	+	0.837076i	0.998472	−	0.0552521i	$-0.0175962\pi$
$23$	6.95328	+	4.01448i	1.44986	+	0.837076i	0.451387	+	0.892329i	$0.350930\pi$
$24$		0			0
$25$	−4.91429	+	0.921799i	−0.982859	+	0.184360i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.941734	−	1.63113i	0.174876	−	0.302893i	−0.765243	−	0.643742i	$-0.777381\pi$
$29$	0.941734	−	1.63113i	0.174876	−	0.302893i	0.940118	+	0.340849i	$0.110714\pi$
$30$		0			0
$31$	5.98111			1.07424			0.537120	−	0.843506i	$-0.319512\pi$
$31$	5.98111			1.07424			0.537120	+	0.843506i	$0.319512\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−5.66338	+	0.526562i	−0.957285	+	0.0890052i
$36$		0			0
$37$			2.86105i			0.470353i	0.971953	+	0.235177i	$0.0755669\pi$
$37$			2.86105i			0.470353i	−0.971953	+	0.235177i	$0.924433\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.67524	+	6.36571i	0.573977	+	0.994157i	0.996152	+	0.0876426i	$0.0279333\pi$
$41$	3.67524	+	6.36571i	0.573977	+	0.994157i	−0.422175	+	0.906514i	$0.638733\pi$
$42$		0			0
$43$	3.19919	−	1.84706i	0.487873	−	0.281673i	−0.235819	−	0.971797i	$-0.575777\pi$
$43$	3.19919	−	1.84706i	0.487873	−	0.281673i	0.723691	+	0.690124i	$0.242444\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.09540	−	2.36448i	−0.597376	−	0.344895i	0.170633	−	0.985335i	$-0.445419\pi$
$47$	−4.09540	−	2.36448i	−0.597376	−	0.344895i	−0.768008	+	0.640440i	$0.778752\pi$
$48$		0			0
$49$	0.529782			0.0756832
$50$		0			0
$51$		0			0
$52$		0			0
$53$	8.91226	+	5.14549i	1.22419	+	0.706788i	0.965809	−	0.259255i	$-0.0834769\pi$
$53$	8.91226	+	5.14549i	1.22419	+	0.706788i	0.258383	+	0.966042i	$0.416810\pi$
$54$		0			0
$55$	0.460341	+	4.95114i	0.0620724	+	0.667612i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.73666	+	6.47208i	0.486472	+	0.842593i	0.999879	−	0.0155515i	$-0.00495040\pi$
$59$	3.73666	+	6.47208i	0.486472	+	0.842593i	−0.513408	+	0.858145i	$0.671617\pi$
$60$		0			0
$61$	4.17839	−	7.23719i	0.534988	−	0.926627i	−0.464176	−	0.885743i	$-0.653649\pi$
$61$	4.17839	−	7.23719i	0.534988	−	0.926627i	0.999164	−	0.0408838i	$-0.0130174\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	6.55817	−	14.2663i	0.813441	−	1.76952i
$66$		0			0
$67$	−10.7040	−	6.17997i	−1.30771	−	0.755004i	−0.325993	−	0.945372i	$-0.605698\pi$
$67$	−10.7040	−	6.17997i	−1.30771	−	0.755004i	−0.981713	+	0.190368i	$0.939032\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	4.13931	+	7.16950i	0.491246	+	0.850863i	0.999949	−	0.0100790i	$-0.00320829\pi$
$71$	4.13931	+	7.16950i	0.491246	+	0.850863i	−0.508703	+	0.860942i	$0.669875\pi$
$72$		0			0
$73$	−10.9489	+	6.32134i	−1.28147	+	0.739857i	−0.977117	−	0.212703i	$-0.931773\pi$
$73$	−10.9489	+	6.32134i	−1.28147	+	0.739857i	−0.304352	+	0.952559i	$0.598440\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			5.65651i			0.644620i
$78$		0			0
$79$	−2.13067	−	3.69043i	−0.239719	−	0.415206i	0.720914	−	0.693024i	$-0.243722\pi$
$79$	−2.13067	−	3.69043i	−0.239719	−	0.415206i	−0.960634	+	0.277818i	$0.910389\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	14.7613i		−	1.62026i	−0.586248	−	0.810132i	$-0.699396\pi$
$83$		−	14.7613i		−	1.62026i	0.586248	−	0.810132i	$-0.300604\pi$
$84$		0			0
$85$	3.30568	+	4.66672i	0.358551	+	0.506177i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	7.19403	−	12.4604i	0.762566	−	1.32080i	−0.178958	−	0.983857i	$-0.557273\pi$
$89$	7.19403	−	12.4604i	0.762566	−	1.32080i	0.941524	−	0.336946i	$-0.109394\pi$
$90$		0			0
$91$	8.93069	−	15.4684i	0.936191	−	1.62153i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	7.05022	−	6.73011i	0.723337	−	0.690495i
$96$		0			0
$97$	5.04871	−	2.91488i	0.512619	−	0.295961i	−0.221291	−	0.975208i	$-0.571027\pi$
$97$	5.04871	−	2.91488i	0.512619	−	0.295961i	0.733910	+	0.679247i	$0.237694\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.47686	+	11.2183i	−0.644472	+	1.11626i	0.339951	+	0.940443i	$0.389589\pi$
$101$	−6.47686	+	11.2183i	−0.644472	+	1.11626i	−0.984423	+	0.175815i	$0.943744\pi$
$102$		0			0
$103$		−	16.6116i		−	1.63679i	−0.574658	−	0.818394i	$-0.694865\pi$
$103$		−	16.6116i		−	1.63679i	0.574658	−	0.818394i	$-0.305135\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	4.59275i		−	0.443998i	−0.975047	−	0.221999i	$-0.928742\pi$
$107$		−	4.59275i		−	0.443998i	0.975047	−	0.221999i	$-0.0712582\pi$
$108$		0			0
$109$	−1.30902	−	2.26728i	−0.125381	−	0.217166i	0.796501	−	0.604637i	$-0.206682\pi$
$109$	−1.30902	−	2.26728i	−0.125381	−	0.217166i	−0.921882	+	0.387471i	$0.873349\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			0.509357i			0.0479163i	0.999713	+	0.0239581i	$0.00762684\pi$
$113$			0.509357i			0.0479163i	−0.999713	+	0.0239581i	$0.992373\pi$
$114$		0			0
$115$	7.49870	−	16.3123i	0.699257	−	1.52113i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	3.25279	+	5.63401i	0.298183	+	0.516468i
$120$		0			0
$121$	−6.05486			−0.550441
$122$		0			0
$123$		0			0
$124$		0			0
$125$	3.06966	+	10.7507i	0.274559	+	0.961570i
$126$		0			0
$127$	−0.636081	−	0.367242i	−0.0564431	−	0.0325874i	0.471513	−	0.881859i	$-0.343708\pi$
$127$	−0.636081	−	0.367242i	−0.0564431	−	0.0325874i	−0.527956	+	0.849272i	$0.677041\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.84274	−	4.92377i	−0.248371	−	0.430192i	0.714703	−	0.699428i	$-0.246562\pi$
$131$	−2.84274	−	4.92377i	−0.248371	−	0.430192i	−0.963074	+	0.269236i	$0.913229\pi$
$132$		0			0
$133$	8.69437	−	6.88055i	0.753898	−	0.596620i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−16.2812	−	9.39993i	−1.39099	−	0.803091i	−0.397568	−	0.917573i	$-0.630146\pi$
$137$	−16.2812	−	9.39993i	−1.39099	−	0.803091i	−0.993425	+	0.114482i	$0.963479\pi$
$138$		0			0
$139$	2.05362	−	3.55697i	0.174186	−	0.301698i	−0.765694	−	0.643206i	$-0.777604\pi$
$139$	2.05362	−	3.55697i	0.174186	−	0.301698i	0.939879	+	0.341507i	$0.110937\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−13.5231	−	7.80756i	−1.13086	−	0.652901i
$144$		0			0
$145$	−3.82660	−	1.75908i	−0.317782	−	0.146084i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	2.08175	+	3.60570i	0.170544	+	0.295391i	0.938610	−	0.344980i	$-0.112114\pi$
$149$	2.08175	+	3.60570i	0.170544	+	0.295391i	−0.768066	+	0.640370i	$0.778781\pi$
$150$		0			0
$151$	17.7955			1.44818			0.724090	−	0.689706i	$-0.242260\pi$
$151$	17.7955			1.44818			0.724090	+	0.689706i	$0.242260\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−1.23815	−	13.3167i	−0.0994504	−	1.06963i
$156$		0			0
$157$	−8.09693	+	4.67476i	−0.646205	+	0.373087i	−0.787001	−	0.616952i	$-0.788367\pi$
$157$	−8.09693	+	4.67476i	−0.646205	+	0.373087i	0.140796	+	0.990039i	$0.455034\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	10.2115	−	17.6868i	0.804777	−	1.39391i
$162$		0			0
$163$			1.55215i			0.121574i	0.998151	+	0.0607869i	$0.0193610\pi$
$163$			1.55215i			0.121574i	−0.998151	+	0.0607869i	$0.980639\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	7.03177	+	4.05980i	0.544135	+	0.314157i	0.746753	−	0.665101i	$-0.231612\pi$
$167$	7.03177	+	4.05980i	0.544135	+	0.314157i	−0.202618	+	0.979258i	$0.564945\pi$
$168$		0			0
$169$	18.1537	+	31.4431i	1.39644	+	2.41870i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	0.633386	−	0.365686i	0.0481555	−	0.0278026i	−0.475729	−	0.879592i	$-0.657816\pi$
$173$	0.633386	−	0.365686i	0.0481555	−	0.0278026i	0.523884	+	0.851789i	$0.324482\pi$
$174$		0			0
$175$	2.34474	+	12.5003i	0.177246	+	0.944934i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	2.68858			0.200954			0.100477	−	0.994939i	$-0.467963\pi$
$179$	2.68858			0.200954			0.100477	+	0.994939i	$0.467963\pi$
$180$		0			0
$181$	2.75090	−	4.76469i	0.204473	−	0.354157i	−0.745492	−	0.666515i	$-0.767785\pi$
$181$	2.75090	−	4.76469i	0.204473	−	0.354157i	0.949965	+	0.312358i	$0.101119\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	6.37002	−	0.592264i	0.468333	−	0.0435441i
$186$		0			0
$187$	4.92547	−	2.84372i	0.360186	−	0.207953i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−9.39845			−0.680048			−0.340024	−	0.940417i	$-0.610435\pi$
$191$	−9.39845			−0.680048			−0.340024	+	0.940417i	$0.610435\pi$
$192$		0			0
$193$	10.0089	−	5.77864i	0.720457	−	0.415956i	−0.0944641	−	0.995528i	$-0.530114\pi$
$193$	10.0089	−	5.77864i	0.720457	−	0.415956i	0.814921	+	0.579572i	$0.196780\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			5.11825i			0.364660i	0.983237	+	0.182330i	$0.0583639\pi$
$197$			5.11825i			0.364660i	−0.983237	+	0.182330i	$0.941636\pi$
$198$		0			0
$199$	6.71897	−	11.6376i	0.476295	−	0.824968i	−0.523336	−	0.852127i	$-0.675313\pi$
$199$	6.71897	−	11.6376i	0.476295	−	0.824968i	0.999631	+	0.0271588i	$0.00864598\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−4.14905	−	2.39545i	−0.291206	−	0.168128i
$204$		0			0
$205$	13.4122	−	9.50056i	0.936750	−	0.663548i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−6.01524	−	7.60096i	−0.416083	−	0.525769i
$210$		0			0
$211$	2.54063	+	4.40050i	0.174904	+	0.302943i	0.940128	−	0.340821i	$-0.110705\pi$
$211$	2.54063	+	4.40050i	0.174904	+	0.302943i	−0.765224	+	0.643764i	$0.777372\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−4.77467	−	6.74054i	−0.325630	−	0.459701i
$216$		0			0
$217$		−	15.2139i		−	1.03279i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−17.9590			−1.20806
$222$		0			0
$223$	−20.5186	+	11.8464i	−1.37403	+	0.793295i	−0.991432	−	0.130621i	$-0.958303\pi$
$223$	−20.5186	+	11.8464i	−1.37403	+	0.793295i	−0.382595	+	0.923916i	$0.624970\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$			19.0306i			1.26310i	0.775334	+	0.631551i	$0.217582\pi$
$227$			19.0306i			1.26310i	−0.775334	+	0.631551i	$0.782418\pi$
$228$		0			0
$229$	27.9233			1.84523			0.922613	−	0.385727i	$-0.126049\pi$
$229$	27.9233			1.84523			0.922613	+	0.385727i	$0.126049\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−12.2680	+	7.08296i	−0.803706	+	0.464020i	−0.844765	−	0.535137i	$-0.820260\pi$
$233$	−12.2680	+	7.08296i	−0.803706	+	0.464020i	0.0410592	+	0.999157i	$0.486927\pi$
$234$		0			0
$235$	−4.41665	+	9.60774i	−0.288110	+	0.626740i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	17.0237			1.10117			0.550585	−	0.834779i	$-0.314405\pi$
$239$	17.0237			1.10117			0.550585	+	0.834779i	$0.314405\pi$
$240$		0			0
$241$	−8.59549	+	14.8878i	−0.553684	+	0.959009i	0.444321	+	0.895868i	$0.353445\pi$
$241$	−8.59549	+	14.8878i	−0.553684	+	0.959009i	−0.998005	+	0.0631409i	$0.979888\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−0.109670	−	1.17954i	−0.00700655	−	0.0753581i
$246$		0			0
$247$	4.44876	+	30.2828i	0.283068	+	1.92685i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	11.8853	−	20.5860i	0.750195	−	1.29938i	−0.197534	−	0.980296i	$-0.563293\pi$
$251$	11.8853	−	20.5860i	0.750195	−	1.29938i	0.947728	−	0.319079i	$-0.103374\pi$
$252$		0			0
$253$	−15.4625	−	8.92727i	−0.972118	−	0.561252i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−1.24086	−	0.716409i	−0.0774026	−	0.0446884i	0.460799	−	0.887504i	$-0.347563\pi$
$257$	−1.24086	−	0.716409i	−0.0774026	−	0.0446884i	−0.538202	+	0.842816i	$0.680896\pi$
$258$		0			0
$259$	7.27754			0.452204
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−6.17484	+	3.56505i	−0.380757	+	0.219830i	−0.678148	−	0.734926i	$-0.737217\pi$
$263$	−6.17484	+	3.56505i	−0.380757	+	0.219830i	0.297390	+	0.954756i	$0.403884\pi$
$264$		0			0
$265$	9.61134	−	20.9080i	0.590420	−	1.28437i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	9.13452	+	15.8214i	0.556941	+	0.964651i	0.997750	+	0.0670494i	$0.0213585\pi$
$269$	9.13452	+	15.8214i	0.556941	+	0.964651i	−0.440808	+	0.897601i	$0.645308\pi$
$270$		0			0
$271$	2.90265	+	5.02754i	0.176324	+	0.305401i	0.940619	−	0.339465i	$-0.110246\pi$
$271$	2.90265	+	5.02754i	0.176324	+	0.305401i	−0.764295	+	0.644867i	$0.776913\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	10.9282	−	2.04987i	0.658998	−	0.123612i
$276$		0			0
$277$			5.72209i			0.343807i	0.985114	+	0.171904i	$0.0549918\pi$
$277$			5.72209i			0.343807i	−0.985114	+	0.171904i	$0.945008\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−3.07155	+	5.32009i	−0.183233	+	0.317370i	−0.942980	−	0.332850i	$-0.891990\pi$
$281$	−3.07155	+	5.32009i	−0.183233	+	0.317370i	0.759746	+	0.650220i	$0.225323\pi$
$282$		0			0
$283$	−14.2484	+	8.22632i	−0.846980	+	0.489004i	−0.859631	−	0.510916i	$-0.829306\pi$
$283$	−14.2484	+	8.22632i	−0.846980	+	0.489004i	0.0126510	+	0.999920i	$0.495973\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	16.1922	−	9.34858i	0.955796	−	0.551829i
$288$		0			0
$289$	−5.22942	+	9.05763i	−0.307613	+	0.532801i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	19.5684i		−	1.14320i	−0.820533	−	0.571599i	$-0.806323\pi$
$293$		−	19.5684i		−	1.14320i	0.820533	−	0.571599i	$-0.193677\pi$
$294$		0			0
$295$	13.6363	−	9.65932i	0.793939	−	0.562388i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	28.1893	+	48.8253i	1.63023	+	2.82364i
$300$		0			0
$301$	−4.69829	−	8.13767i	−0.270805	−	0.469047i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−16.9783	−	7.80488i	−0.972175	−	0.446906i
$306$		0			0
$307$	24.9405	−	14.3994i	1.42343	−	0.821817i	0.426839	−	0.904327i	$-0.359627\pi$
$307$	24.9405	−	14.3994i	1.42343	−	0.821817i	0.996590	+	0.0825100i	$0.0262937\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	19.4309			1.10182			0.550911	−	0.834564i	$-0.314280\pi$
$311$	19.4309			1.10182			0.550911	+	0.834564i	$0.314280\pi$
$312$		0			0
$313$	8.34649	+	4.81885i	0.471772	+	0.272377i	0.716981	−	0.697093i	$-0.245523\pi$
$313$	8.34649	+	4.81885i	0.471772	+	0.272377i	−0.245209	+	0.969470i	$0.578857\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.199789	−	0.115348i	−0.0112213	−	0.00647860i	0.494379	−	0.869247i	$-0.335396\pi$
$317$	−0.199789	−	0.115348i	−0.0112213	−	0.00647860i	−0.505600	+	0.862768i	$0.668729\pi$
$318$		0			0
$319$	−2.09420	+	3.62726i	−0.117253	+	0.203087i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−10.3623	−	4.11163i	−0.576572	−	0.228777i
$324$		0			0
$325$	−33.1210	−	11.6483i	−1.83722	−	0.646130i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−6.01444	+	10.4173i	−0.331587	+	0.574325i
$330$		0			0
$331$	−12.1135			−0.665820			−0.332910	−	0.942959i	$-0.608031\pi$
$331$	−12.1135			−0.665820			−0.332910	+	0.942959i	$0.608031\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−11.5437	+	25.1115i	−0.630698	+	1.37199i
$336$		0			0
$337$	−9.64909	+	5.57090i	−0.525619	+	0.303466i	−0.739231	−	0.673452i	$-0.764811\pi$
$337$	−9.64909	+	5.57090i	−0.525619	+	0.303466i	0.213611	+	0.976919i	$0.431477\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−13.3006			−0.720268
$342$		0			0
$343$		−	19.1532i		−	1.03418i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.92730	−	2.84478i	0.264511	−	0.152716i	−0.361880	−	0.932225i	$-0.617865\pi$
$347$	4.92730	−	2.84478i	0.264511	−	0.152716i	0.626391	+	0.779509i	$0.284532\pi$
$348$		0			0
$349$	−0.369374			−0.0197722			−0.00988608	−	0.999951i	$-0.503147\pi$
$349$	−0.369374			−0.0197722			−0.00988608	+	0.999951i	$0.503147\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$			1.87124i			0.0995962i	0.998759	+	0.0497981i	$0.0158578\pi$
$353$			1.87124i			0.0995962i	−0.998759	+	0.0497981i	$0.984142\pi$
$354$		0			0
$355$	15.1058	−	10.7002i	0.801731	−	0.567907i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	8.47802	+	14.6844i	0.447453	+	0.775011i	0.998219	−	0.0596485i	$-0.0189980\pi$
$359$	8.47802	+	14.6844i	0.447453	+	0.775011i	−0.550767	+	0.834659i	$0.685665\pi$
$360$		0			0
$361$	−4.36618	+	18.4915i	−0.229799	+	0.973238i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	16.3408	+	23.0687i	0.855315	+	1.20747i
$366$		0			0
$367$	−3.27769	−	1.89237i	−0.171094	−	0.0987812i	0.412008	−	0.911180i	$-0.364828\pi$
$367$	−3.27769	−	1.89237i	−0.171094	−	0.0987812i	−0.583102	+	0.812399i	$0.698161\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	13.0884	−	22.6698i	0.679516	−	1.17696i
$372$		0			0
$373$			4.51203i			0.233624i	0.993154	+	0.116812i	$0.0372675\pi$
$373$			4.51203i			0.233624i	−0.993154	+	0.116812i	$0.962732\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	11.4537	−	6.61278i	0.589894	−	0.340575i
$378$		0			0
$379$	−4.64242			−0.238465			−0.119233	−	0.992866i	$-0.538043\pi$
$379$	−4.64242			−0.238465			−0.119233	+	0.992866i	$0.538043\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	12.1086	−	6.99088i	0.618719	−	0.357218i	−0.157651	−	0.987495i	$-0.550392\pi$
$383$	12.1086	−	6.99088i	0.618719	−	0.357218i	0.776370	+	0.630277i	$0.217059\pi$
$384$		0			0
$385$	12.5940	−	1.17095i	0.641851	−	0.0596772i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−3.93460	+	6.81492i	−0.199492	+	0.345530i	−0.948364	−	0.317185i	$-0.897263\pi$
$389$	−3.93460	+	6.81492i	−0.199492	+	0.345530i	0.748872	+	0.662715i	$0.230596\pi$
$390$		0			0
$391$	−20.5346			−1.03848
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−7.77555	+	5.50782i	−0.391231	+	0.277129i
$396$		0			0
$397$	14.6969	−	8.48528i	0.737618	−	0.425864i	−0.0835846	−	0.996501i	$-0.526637\pi$
$397$	14.6969	−	8.48528i	0.737618	−	0.425864i	0.821203	+	0.570637i	$0.193304\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	7.16651	+	12.4128i	0.357878	+	0.619864i	0.987606	−	0.156952i	$-0.0501669\pi$
$401$	7.16651	+	12.4128i	0.357878	+	0.619864i	−0.629728	+	0.776816i	$0.716834\pi$
$402$		0			0
$403$	36.3721	+	20.9994i	1.81182	+	1.04606i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	6.36231i		−	0.315368i
$408$		0			0
$409$	−0.122530	+	0.212228i	−0.00605872	+	0.0104940i	−0.869039	−	0.494744i	$-0.835262\pi$
$409$	−0.122530	+	0.212228i	−0.00605872	+	0.0104940i	0.862980	+	0.505238i	$0.168595\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	16.4628	−	9.50480i	0.810081	−	0.467701i
$414$		0			0
$415$	−32.8655	+	3.05573i	−1.61330	+	0.150000i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−25.4690			−1.24424			−0.622122	−	0.782920i	$-0.713729\pi$
$419$	−25.4690			−1.24424			−0.622122	+	0.782920i	$0.713729\pi$
$420$		0			0
$421$	−3.02703	−	5.24297i	−0.147529	−	0.255527i	0.782785	−	0.622292i	$-0.213798\pi$
$421$	−3.02703	−	5.24297i	−0.147529	−	0.255527i	−0.930313	+	0.366765i	$0.880465\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	9.70598	−	8.32603i	0.470809	−	0.403872i
$426$		0			0
$427$	−18.4090	−	10.6284i	−0.890872	−	0.514345i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	11.1005	−	19.2267i	0.534694	−	0.926117i	−0.464484	−	0.885581i	$-0.653760\pi$
$431$	11.1005	−	19.2267i	0.534694	−	0.926117i	0.999178	−	0.0405356i	$-0.0129064\pi$
$432$		0			0
$433$	21.0094	+	12.1298i	1.00965	+	0.582920i	0.911089	−	0.412211i	$-0.135243\pi$
$433$	21.0094	+	12.1298i	1.00965	+	0.582920i	0.0985593	+	0.995131i	$0.468577\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	5.08677	+	34.6258i	0.243333	+	1.65637i
$438$		0			0
$439$	−11.9487	−	20.6957i	−0.570279	−	0.987753i	−0.996537	−	0.0831509i	$-0.973502\pi$
$439$	−11.9487	−	20.6957i	−0.570279	−	0.987753i	0.426258	−	0.904602i	$-0.359832\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	17.9017	+	10.3356i	0.850536	+	0.491057i	0.860832	−	0.508890i	$-0.169944\pi$
$443$	17.9017	+	10.3356i	0.850536	+	0.491057i	−0.0102958	+	0.999947i	$0.503277\pi$
$444$		0			0
$445$	−29.2319	−	13.4378i	−1.38573	−	0.637015i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−6.64143			−0.313429			−0.156714	−	0.987644i	$-0.550090\pi$
$449$	−6.64143			−0.313429			−0.156714	+	0.987644i	$0.550090\pi$
$450$		0			0
$451$	−8.17289	−	14.1559i	−0.384846	−	0.666573i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−36.2886	−	16.6818i	−1.70124	−	0.782053i
$456$		0			0
$457$		−	14.3433i		−	0.670952i	−0.942049	−	0.335476i	$-0.891103\pi$
$457$		−	14.3433i		−	0.670952i	0.942049	−	0.335476i	$-0.108897\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−13.3682	−	23.1544i	−0.622618	−	1.07841i	−0.988996	−	0.147940i	$-0.952736\pi$
$461$	−13.3682	−	23.1544i	−0.622618	−	1.07841i	0.366378	−	0.930466i	$-0.380598\pi$
$462$		0			0
$463$		−	12.0950i		−	0.562101i	−0.959693	−	0.281051i	$-0.909317\pi$
$463$		−	12.0950i		−	0.562101i	0.959693	−	0.281051i	$-0.0906829\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	27.3169i		−	1.26408i	−0.774938	−	0.632038i	$-0.782219\pi$
$467$		−	27.3169i		−	1.26408i	0.774938	−	0.632038i	$-0.217781\pi$
$468$		0			0
$469$	−15.7198	+	27.2274i	−0.725871	+	1.25725i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−7.11427	+	4.10742i	−0.327114	+	0.188860i
$474$		0			0
$475$	−16.4438	−	14.3039i	−0.754494	−	0.656307i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−3.69624	+	6.40208i	−0.168886	+	0.292519i	−0.938028	−	0.346559i	$-0.887350\pi$
$479$	−3.69624	+	6.40208i	−0.168886	+	0.292519i	0.769143	+	0.639077i	$0.220684\pi$
$480$		0			0
$481$	−10.0450	+	17.3985i	−0.458013	+	0.793302i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−7.53500	−	10.6374i	−0.342147	−	0.483018i
$486$		0			0
$487$		−	12.9424i		−	0.586477i	−0.956039	−	0.293239i	$-0.905267\pi$
$487$		−	12.9424i		−	0.586477i	0.956039	−	0.293239i	$-0.0947330\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−5.59974	−	9.69903i	−0.252713	−	0.437711i	0.711559	−	0.702626i	$-0.247989\pi$
$491$	−5.59974	−	9.69903i	−0.252713	−	0.437711i	−0.964272	+	0.264915i	$0.914656\pi$
$492$		0			0
$493$			4.81710i			0.216951i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	18.2368	−	10.5290i	0.818032	−	0.472291i
$498$		0			0
$499$	−12.9699	−	22.4645i	−0.580611	−	1.00565i	−0.995407	−	0.0957335i	$-0.969480\pi$
$499$	−12.9699	−	22.4645i	−0.580611	−	1.00565i	0.414796	−	0.909914i	$-0.363853\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−23.6079	−	13.6300i	−1.05262	−	0.607733i	−0.129241	−	0.991613i	$-0.541254\pi$
$503$	−23.6079	−	13.6300i	−1.05262	−	0.607733i	−0.923383	+	0.383881i	$0.874587\pi$
$504$		0			0
$505$	26.3178	+	12.0982i	1.17113	+	0.538364i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−12.6203	+	21.8591i	−0.559386	+	0.968885i	0.438161	+	0.898896i	$0.355630\pi$
$509$	−12.6203	+	21.8591i	−0.559386	+	0.968885i	−0.997548	+	0.0699892i	$0.977704\pi$
$510$		0			0
$511$	16.0794	+	27.8503i	0.711309	+	1.23202i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−36.9851	+	3.43875i	−1.62976	+	0.151530i
$516$		0			0
$517$	9.10722	+	5.25806i	0.400535	+	0.231249i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	24.8142			1.08713			0.543565	−	0.839367i	$-0.317074\pi$
$521$	24.8142			1.08713			0.543565	+	0.839367i	$0.317074\pi$
$522$		0			0
$523$	−5.33581	−	3.08063i	−0.233318	−	0.134706i	0.378784	−	0.925485i	$-0.376342\pi$
$523$	−5.33581	−	3.08063i	−0.233318	−	0.134706i	−0.612102	+	0.790779i	$0.709676\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−13.2477	+	7.64855i	−0.577078	+	0.333176i
$528$		0			0
$529$	20.7321	+	35.9090i	0.901394	+	1.56126i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			51.6145i			2.23567i
$534$		0			0
$535$	−10.2256	+	0.950743i	−0.442092	+	0.0411042i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−1.17811			−0.0507449
$540$		0			0
$541$	−3.27394	+	5.67063i	−0.140758	+	0.243799i	−0.927782	−	0.373122i	$-0.878287\pi$
$541$	−3.27394	+	5.67063i	−0.140758	+	0.243799i	0.787025	+	0.616922i	$0.211620\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−4.77704	+	3.38383i	−0.204626	+	0.144947i
$546$		0			0
$547$	−19.5323	−	11.2770i	−0.835141	−	0.482169i	0.0204683	−	0.999791i	$-0.493484\pi$
$547$	−19.5323	−	11.2770i	−0.835141	−	0.482169i	−0.855610	+	0.517621i	$0.826818\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	8.12266	−	1.19328i	0.346037	−	0.0508353i
$552$		0			0
$553$	−9.38722	+	5.41971i	−0.399185	+	0.230470i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−14.0691	−	8.12281i	−0.596128	−	0.344175i	0.171389	−	0.985203i	$-0.445175\pi$
$557$	−14.0691	−	8.12281i	−0.596128	−	0.344175i	−0.767517	+	0.641029i	$0.778508\pi$
$558$		0			0
$559$	25.9397			1.09713
$560$		0			0
$561$		0			0
$562$		0			0
$563$			32.4581i			1.36795i	0.729506	+	0.683974i	$0.239750\pi$
$563$			32.4581i			1.36795i	−0.729506	+	0.683974i	$0.760250\pi$
$564$		0			0
$565$	1.13407	−	0.105442i	0.0477105	−	0.00443597i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	25.5422			1.07078			0.535392	−	0.844604i	$-0.320164\pi$
$569$	25.5422			1.07078			0.535392	+	0.844604i	$0.320164\pi$
$570$		0			0
$571$	25.9974			1.08796			0.543979	−	0.839099i	$-0.316917\pi$
$571$	25.9974			1.08796			0.543979	+	0.839099i	$0.316917\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−37.8710	−	13.3188i	−1.57933	−	0.555432i
$576$		0			0
$577$			44.5844i			1.85607i	0.372489	+	0.928037i	$0.378504\pi$
$577$			44.5844i			1.85607i	−0.372489	+	0.928037i	$0.621496\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−37.5478			−1.55774
$582$		0			0
$583$	−19.8188	−	11.4424i	−0.820810	−	0.473895i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	12.6246	−	7.28884i	0.521074	−	0.300842i	−0.216300	−	0.976327i	$-0.569399\pi$
$587$	12.6246	−	7.28884i	0.521074	−	0.300842i	0.737374	+	0.675485i	$0.236065\pi$
$588$		0			0
$589$	16.1788	+	20.4438i	0.666635	+	0.842371i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	20.5520	+	11.8657i	0.843968	+	0.487265i	0.858611	−	0.512628i	$-0.171328\pi$
$593$	20.5520	+	11.8657i	0.843968	+	0.487265i	−0.0146433	+	0.999893i	$0.504661\pi$
$594$		0			0
$595$	11.8706	−	8.40853i	0.486645	−	0.344716i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	9.86173	−	17.0810i	0.402939	−	0.697911i	−0.591140	−	0.806569i	$-0.701322\pi$
$599$	9.86173	−	17.0810i	0.402939	−	0.697911i	0.994079	+	0.108658i	$0.0346552\pi$
$600$		0			0
$601$	−45.0351			−1.83702			−0.918509	−	0.395400i	$-0.870606\pi$
$601$	−45.0351			−1.83702			−0.918509	+	0.395400i	$0.870606\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.25341	+	13.4809i	0.0509585	+	0.548078i
$606$		0			0
$607$			7.24160i			0.293928i	0.989142	+	0.146964i	$0.0469501\pi$
$607$			7.24160i			0.293928i	−0.989142	+	0.146964i	$0.953050\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−16.6032	−	28.7576i	−0.671693	−	1.16341i
$612$		0			0
$613$	−31.8788	+	18.4052i	−1.28757	+	0.743381i	−0.978221	−	0.207567i	$-0.933446\pi$
$613$	−31.8788	+	18.4052i	−1.28757	+	0.743381i	−0.309352	+	0.950947i	$0.600112\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−31.7741	−	18.3448i	−1.27918	−	0.738533i	−0.302479	−	0.953156i	$-0.597814\pi$
$617$	−31.7741	−	18.3448i	−1.27918	−	0.738533i	−0.976697	+	0.214623i	$0.931148\pi$
$618$		0			0
$619$	−24.1569			−0.970948			−0.485474	−	0.874251i	$-0.661353\pi$
$619$	−24.1569			−0.970948			−0.485474	+	0.874251i	$0.661353\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−31.6951	−	18.2992i	−1.26984	−	0.733142i
$624$		0			0
$625$	23.3006	−	9.05998i	0.932023	−	0.362399i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−3.65866	−	6.33699i	−0.145880	−	0.252672i
$630$		0			0
$631$	−7.11258	+	12.3193i	−0.283147	+	0.490426i	−0.972158	−	0.234325i	$-0.924712\pi$
$631$	−7.11258	+	12.3193i	−0.283147	+	0.490426i	0.689011	+	0.724751i	$0.258045\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.685976	+	1.49223i	−0.0272221	+	0.0592175i
$636$		0			0
$637$	3.22169	+	1.86004i	0.127648	+	0.0736976i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−10.1834	−	17.6382i	−0.402222	−	0.696668i	0.591772	−	0.806105i	$-0.298429\pi$
$641$	−10.1834	−	17.6382i	−0.402222	−	0.696668i	−0.993994	+	0.109437i	$0.965095\pi$
$642$		0			0
$643$	10.0041	−	5.77586i	0.394523	−	0.227778i	−0.289595	−	0.957149i	$-0.593521\pi$
$643$	10.0041	−	5.77586i	0.394523	−	0.227778i	0.684118	+	0.729371i	$0.260187\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	13.1233i		−	0.515932i	−0.966154	−	0.257966i	$-0.916948\pi$
$647$		−	13.1233i		−	0.515932i	0.966154	−	0.257966i	$-0.0830522\pi$
$648$		0			0
$649$	−8.30946	−	14.3924i	−0.326175	−	0.564952i
$650$		0			0
$651$		0			0
$652$		0			0
$653$		−	19.4406i		−	0.760769i	−0.924828	−	0.380385i	$-0.875792\pi$
$653$		−	19.4406i		−	0.760769i	0.924828	−	0.380385i	$-0.124208\pi$
$654$		0			0
$655$	−10.3741	+	7.34853i	−0.405351	+	0.287131i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	13.7848	−	23.8759i	0.536979	−	0.930074i	−0.462086	−	0.886835i	$-0.652899\pi$
$659$	13.7848	−	23.8759i	0.536979	−	0.930074i	0.999065	−	0.0432391i	$-0.0137677\pi$
$660$		0			0
$661$	3.88006	−	6.72046i	0.150917	−	0.261396i	−0.780648	−	0.624971i	$-0.785111\pi$
$661$	3.88006	−	6.72046i	0.150917	−	0.261396i	0.931565	+	0.363575i	$0.118444\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−17.1191	−	17.9334i	−0.663851	−	0.695427i
$666$		0			0
$667$	13.0963	−	7.56114i	0.507090	−	0.292769i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−9.29178	+	16.0938i	−0.358705	+	0.621295i
$672$		0			0
$673$			24.2617i			0.935220i	0.883935	+	0.467610i	$0.154885\pi$
$673$			24.2617i			0.935220i	−0.883935	+	0.467610i	$0.845115\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		−	4.88851i		−	0.187881i	−0.995578	−	0.0939403i	$-0.970054\pi$
$677$		−	4.88851i		−	0.187881i	0.995578	−	0.0939403i	$-0.0299463\pi$
$678$		0			0
$679$	−7.41446	−	12.8422i	−0.284541	−	0.492839i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			0.560031i			0.0214290i	0.999943	+	0.0107145i	$0.00341060\pi$
$683$			0.560031i			0.0214290i	−0.999943	+	0.0107145i	$0.996589\pi$
$684$		0			0
$685$	−17.5583	+	38.1953i	−0.670867	+	1.45937i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	36.1312	+	62.5811i	1.37649	+	2.38415i
$690$		0			0
$691$	−14.5255			−0.552576			−0.276288	−	0.961075i	$-0.589104\pi$
$691$	−14.5255			−0.552576			−0.276288	+	0.961075i	$0.589104\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−8.34459	−	3.83598i	−0.316528	−	0.145507i
$696$		0			0
$697$	−16.2807	−	9.39969i	−0.616677	−	0.356039i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−1.23926	−	2.14647i	−0.0468064	−	0.0810710i	0.841673	−	0.539987i	$-0.181571\pi$
$701$	−1.23926	−	2.14647i	−0.0468064	−	0.0810710i	−0.888479	+	0.458916i	$0.848238\pi$
$702$		0			0
$703$	−9.77921	+	7.73907i	−0.368830	+	0.291885i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	28.5354	+	16.4749i	1.07319	+	0.619604i
$708$		0			0
$709$	−16.1966	+	28.0533i	−0.608276	+	1.05356i	0.383249	+	0.923645i	$0.374805\pi$
$709$	−16.1966	+	28.0533i	−0.608276	+	1.05356i	−0.991525	+	0.129919i	$0.958528\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	41.5884	+	24.0110i	1.55750	+	0.899221i
$714$		0			0
$715$	−14.5838	+	31.7249i	−0.545405	+	1.18644i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−8.64373	−	14.9714i	−0.322357	−	0.558338i	0.658617	−	0.752478i	$-0.271142\pi$
$719$	−8.64373	−	14.9714i	−0.322357	−	0.558338i	−0.980974	+	0.194140i	$0.937808\pi$
$720$		0			0
$721$	−42.2542			−1.57363
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−3.12438	+	8.88395i	−0.116037	+	0.329942i
$726$		0			0
$727$	16.4031	−	9.47034i	0.608358	−	0.351236i	−0.163965	−	0.986466i	$-0.552428\pi$
$727$	16.4031	−	9.47034i	0.608358	−	0.351236i	0.772323	+	0.635231i	$0.219095\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−4.72397	+	8.18216i	−0.174722	+	0.302628i
$732$		0			0
$733$		−	0.542118i		−	0.0200236i	−0.999950	−	0.0100118i	$-0.996813\pi$
$733$		−	0.542118i		−	0.0200236i	0.999950	−	0.0100118i	$-0.00318690\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	23.8033	+	13.7428i	0.876805	+	0.506224i
$738$		0			0
$739$	−2.87033	−	4.97156i	−0.105587	−	0.182882i	0.808391	−	0.588646i	$-0.200339\pi$
$739$	−2.87033	−	4.97156i	−0.105587	−	0.182882i	−0.913978	+	0.405764i	$0.867005\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	19.9290	−	11.5060i	0.731125	−	0.422115i	−0.0877087	−	0.996146i	$-0.527954\pi$
$743$	19.9290	−	11.5060i	0.731125	−	0.422115i	0.818834	+	0.574031i	$0.194621\pi$
$744$		0			0
$745$	7.59703	−	5.38137i	0.278334	−	0.197158i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−11.6824			−0.426866
$750$		0			0
$751$	25.9704	−	44.9821i	0.947674	−	1.64142i	0.197368	−	0.980330i	$-0.436761\pi$
$751$	25.9704	−	44.9821i	0.947674	−	1.64142i	0.750306	−	0.661090i	$-0.229906\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−3.68384	−	39.6211i	−0.134069	−	1.44196i
$756$		0			0
$757$	11.0229	−	6.36406i	0.400633	−	0.231306i	−0.286124	−	0.958193i	$-0.592367\pi$
$757$	11.0229	−	6.36406i	0.400633	−	0.231306i	0.686757	+	0.726887i	$0.259034\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	10.6089			0.384573			0.192287	−	0.981339i	$-0.438410\pi$
$761$	10.6089			0.384573			0.192287	+	0.981339i	$0.438410\pi$
$762$		0			0
$763$	−5.76720	+	3.32969i	−0.208787	+	0.120543i
$764$		0			0
$765$		0			0
$766$		0			0
$767$			52.4770i			1.89484i
$768$		0			0
$769$	10.8089	−	18.7215i	0.389777	−	0.675114i	−0.602642	−	0.798012i	$-0.705885\pi$
$769$	10.8089	−	18.7215i	0.389777	−	0.675114i	0.992419	+	0.122898i	$0.0392187\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−37.5227	−	21.6637i	−1.34960	−	0.779190i	−0.361404	−	0.932409i	$-0.617702\pi$
$773$	−37.5227	−	21.6637i	−1.34960	−	0.779190i	−0.988192	+	0.153220i	$0.951036\pi$
$774$		0			0
$775$	−29.3930	+	5.51338i	−1.05583	+	0.198047i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−11.8169	+	29.7813i	−0.423384	+	1.06703i
$780$		0			0
$781$	−9.20487	−	15.9433i	−0.329376	−	0.570496i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	12.0843	+	17.0598i	0.431309	+	0.608891i
$786$		0			0
$787$			29.0046i			1.03390i	0.856015	+	0.516950i	$0.172933\pi$
$787$			29.0046i			1.03390i	−0.856015	+	0.516950i	$0.827067\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	1.29563			0.0460674
$792$		0			0
$793$	50.8189	−	29.3403i	1.80463	−	1.04191i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	14.2045i		−	0.503150i	−0.967838	−	0.251575i	$-0.919051\pi$
$797$		−	14.2045i		−	0.503150i	0.967838	−	0.251575i	$-0.0809485\pi$
$798$		0			0
$799$	12.0946			0.427878
$800$		0			0
$801$		0			0
$802$		0			0
$803$	24.3478	−	14.0572i	0.859214	−	0.496067i
$804$		0			0
$805$	−41.4929	−	19.0742i	−1.46243	−	0.672276i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	14.9781			0.526603			0.263301	−	0.964714i	$-0.415189\pi$
$809$	14.9781			0.526603			0.263301	+	0.964714i	$0.415189\pi$
$810$		0			0
$811$	20.5388	−	35.5742i	0.721214	−	1.24918i	−0.239300	−	0.970946i	$-0.576918\pi$
$811$	20.5388	−	35.5742i	0.721214	−	1.24918i	0.960513	−	0.278233i	$-0.0897489\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	3.45581	−	0.321310i	0.121052	−	0.0112550i
$816$		0			0
$817$	14.9671	+	5.93877i	0.523632	+	0.207771i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−21.5219	+	37.2771i	−0.751120	+	1.30098i	0.196160	+	0.980572i	$0.437153\pi$
$821$	−21.5219	+	37.2771i	−0.751120	+	1.30098i	−0.947280	+	0.320407i	$0.896180\pi$
$822$		0			0
$823$	12.4379	+	7.18105i	0.433559	+	0.250316i	0.700862	−	0.713297i	$-0.252799\pi$
$823$	12.4379	+	7.18105i	0.433559	+	0.250316i	−0.267302	+	0.963613i	$0.586132\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−38.4326	−	22.1891i	−1.33643	−	0.771590i	−0.350157	−	0.936691i	$-0.613872\pi$
$827$	−38.4326	−	22.1891i	−1.33643	−	0.771590i	−0.986277	+	0.165101i	$0.947205\pi$
$828$		0			0
$829$	−35.6112			−1.23683			−0.618413	−	0.785853i	$-0.712224\pi$
$829$	−35.6112			−1.23683			−0.618413	+	0.785853i	$0.712224\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1.17342	+	0.677477i	−0.0406567	+	0.0234732i
$834$		0			0
$835$	7.58335	−	16.4964i	0.262433	−	0.570882i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	21.1147	+	36.5718i	0.728962	+	1.26260i	0.957322	+	0.289022i	$0.0933301\pi$
$839$	21.1147	+	36.5718i	0.728962	+	1.26260i	−0.228361	+	0.973577i	$0.573337\pi$
$840$		0			0
$841$	12.7263	+	22.0426i	0.438837	+	0.760088i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	66.2489	−	46.9275i	2.27903	−	1.61435i
$846$		0			0
$847$			15.4015i			0.529202i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−11.4856	+	19.8937i	−0.393722	+	0.681946i
$852$		0			0
$853$	17.1632	−	9.90917i	0.587656	−	0.339284i	−0.176514	−	0.984298i	$-0.556482\pi$
$853$	17.1632	−	9.90917i	0.587656	−	0.339284i	0.764170	+	0.645015i	$0.223149\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	44.5279	−	25.7082i	1.52104	−	0.878175i	0.521352	−	0.853342i	$-0.325428\pi$
$857$	44.5279	−	25.7082i	1.52104	−	0.878175i	0.999692	−	0.0248328i	$-0.00790535\pi$
$858$		0			0
$859$	−10.5243	+	18.2286i	−0.359084	+	0.621951i	−0.987808	−	0.155677i	$-0.950244\pi$
$859$	−10.5243	+	18.2286i	−0.359084	+	0.621951i	0.628724	+	0.777628i	$0.283577\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			38.8358i			1.32199i	0.750391	+	0.660994i	$0.229865\pi$
$863$			38.8358i			1.32199i	−0.750391	+	0.660994i	$0.770135\pi$
$864$		0			0
$865$	−0.945303	−	1.33451i	−0.0321413	−	0.0453748i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	4.73812	+	8.20667i	0.160730	+	0.278392i
$870$		0			0
$871$	−43.3953	−	75.1628i	−1.47039	−	2.54679i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	27.3461	−	7.80817i	0.924467	−	0.263964i
$876$		0			0
$877$	−22.5823	+	13.0379i	−0.762551	+	0.440259i	−0.830211	−	0.557450i	$-0.811780\pi$
$877$	−22.5823	+	13.0379i	−0.762551	+	0.440259i	0.0676600	+	0.997708i	$0.478447\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−8.23096			−0.277308			−0.138654	−	0.990341i	$-0.544278\pi$
$881$	−8.23096			−0.277308			−0.138654	+	0.990341i	$0.544278\pi$
$882$		0			0
$883$	−28.4622	−	16.4326i	−0.957828	−	0.553003i	−0.0623244	−	0.998056i	$-0.519851\pi$
$883$	−28.4622	−	16.4326i	−0.957828	−	0.553003i	−0.895504	+	0.445053i	$0.853185\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−12.3177	−	7.11165i	−0.413589	−	0.238786i	0.278741	−	0.960366i	$-0.410083\pi$
$887$	−12.3177	−	7.11165i	−0.413589	−	0.238786i	−0.692331	+	0.721580i	$0.743416\pi$
$888$		0			0
$889$	−0.934139	+	1.61798i	−0.0313300	+	0.0542652i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−2.99605	−	20.3942i	−0.100259	−	0.682465i
$894$		0			0
$895$	−0.556562	−	5.98603i	−0.0186038	−	0.200091i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	5.63262	−	9.75598i	0.187858	−	0.325380i
$900$		0			0
$901$	−26.3199			−0.876843
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−11.1779	−	5.13844i	−0.371565	−	0.170808i
$906$		0			0
$907$	−38.9008	+	22.4594i	−1.29168	+	0.745752i	−0.978952	−	0.204090i	$-0.934576\pi$
$907$	−38.9008	+	22.4594i	−1.29168	+	0.745752i	−0.312729	+	0.949842i	$0.601243\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−38.3516			−1.27064			−0.635322	−	0.772247i	$-0.719133\pi$
$911$	−38.3516			−1.27064			−0.635322	+	0.772247i	$0.719133\pi$
$912$		0			0
$913$			32.8257i			1.08637i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−12.5244	+	7.23097i	−0.413593	+	0.238788i
$918$		0			0
$919$	36.3727			1.19983			0.599913	−	0.800065i	$-0.295202\pi$
$919$	36.3727			1.19983			0.599913	+	0.800065i	$0.295202\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			58.1318i			1.91343i
$924$		0			0
$925$	−2.63731	−	14.0600i	−0.0867142	−	0.462291i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.96542	−	3.40421i	−0.0644834	−	0.111689i	0.831981	−	0.554804i	$-0.187207\pi$
$929$	−1.96542	−	3.40421i	−0.0644834	−	0.111689i	−0.896465	+	0.443115i	$0.853873\pi$
$930$		0			0
$931$	1.43305	+	1.81082i	0.0469663	+	0.0593473i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−7.35106	−	10.3777i	−0.240405	−	0.339387i
$936$		0			0
$937$	46.8937	+	27.0741i	1.53195	+	0.884473i	0.999272	+	0.0381558i	$0.0121483\pi$
$937$	46.8937	+	27.0741i	1.53195	+	0.884473i	0.532680	+	0.846317i	$0.321185\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−14.9969	+	25.9755i	−0.488886	+	0.846776i	−0.999918	−	0.0127858i	$-0.995930\pi$
$941$	−14.9969	+	25.9755i	−0.488886	+	0.846776i	0.511032	+	0.859562i	$0.329263\pi$
$942$		0			0
$943$			59.0167i			1.92185i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−34.1378	+	19.7095i	−1.10933	+	0.640472i	−0.938656	−	0.344856i	$-0.887928\pi$
$947$	−34.1378	+	19.7095i	−1.10933	+	0.640472i	−0.170674	+	0.985328i	$0.554594\pi$
$948$		0			0
$949$	−88.7758			−2.88179
$950$		0			0
$951$		0			0
$952$		0			0
$953$	1.14860	−	0.663142i	0.0372067	−	0.0214813i	−0.481281	−	0.876566i	$-0.659828\pi$
$953$	1.14860	−	0.663142i	0.0372067	−	0.0214813i	0.518488	+	0.855085i	$0.326495\pi$
$954$		0			0
$955$	1.94557	+	20.9253i	0.0629571	+	0.677127i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−23.9103	+	41.4138i	−0.772102	+	1.33732i
$960$		0			0
$961$	4.77372			0.153991
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−14.9379	−	21.0882i	−0.480867	−	0.678854i
$966$		0			0
$967$	−6.18431	+	3.57052i	−0.198874	+	0.114820i	−0.596130	−	0.802888i	$-0.703296\pi$
$967$	−6.18431	+	3.57052i	−0.198874	+	0.114820i	0.397256	+	0.917708i	$0.369962\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	12.5252	+	21.6943i	0.401953	+	0.696202i	0.993962	−	0.109729i	$-0.0349983\pi$
$971$	12.5252	+	21.6943i	0.401953	+	0.696202i	−0.592009	+	0.805931i	$0.701665\pi$
$972$		0			0
$973$	−9.04773	−	5.22371i	−0.290057	−	0.167464i
$974$		0			0
$975$		0			0
$976$		0			0
$977$			0.00409135i			0.000130894i	1.00000		6.54469e-5i	$2.08324e-5\pi$
$977$			0.00409135i			0.000130894i	−1.00000		6.54469e-5i	$0.999979\pi$
$978$		0			0
$979$	−15.9979	+	27.7091i	−0.511294	+	0.885587i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	38.4495	−	22.1988i	1.22635	−	0.708033i	0.260084	−	0.965586i	$-0.416250\pi$
$983$	38.4495	−	22.1988i	1.22635	−	0.708033i	0.966264	+	0.257553i	$0.0829163\pi$
$984$		0			0
$985$	11.3956	−	1.05953i	0.363094	−	0.0337593i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	29.6599			0.943128
$990$		0			0
$991$	23.7636	+	41.1598i	0.754877	+	1.30749i	0.945435	+	0.325810i	$0.105637\pi$
$991$	23.7636	+	41.1598i	0.754877	+	1.30749i	−0.190558	+	0.981676i	$0.561030\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−27.3016	−	12.5505i	−0.865519	−	0.397877i
$996$		0			0
$997$	−25.6381	−	14.8021i	−0.811965	−	0.468788i	0.0356725	−	0.999364i	$-0.488643\pi$
$997$	−25.6381	−	14.8021i	−0.811965	−	0.468788i	−0.847638	+	0.530575i	$0.821976\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3420.2.bj.c.2629.5		20
3.2	odd	2		380.2.r.a.349.6	yes	20
5.4	even	2	inner	3420.2.bj.c.2629.3		20
15.2	even	4		1900.2.i.g.501.5		20
15.8	even	4		1900.2.i.g.501.6		20
15.14	odd	2		380.2.r.a.349.5	yes	20
19.11	even	3	inner	3420.2.bj.c.1189.3		20
57.11	odd	6		380.2.r.a.49.5	✓	20
95.49	even	6	inner	3420.2.bj.c.1189.5		20
285.68	even	12		1900.2.i.g.201.6		20
285.182	even	12		1900.2.i.g.201.5		20
285.239	odd	6		380.2.r.a.49.6	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.r.a.49.5	✓	20	57.11	odd	6
380.2.r.a.49.6	yes	20	285.239	odd	6
380.2.r.a.349.5	yes	20	15.14	odd	2
380.2.r.a.349.6	yes	20	3.2	odd	2
1900.2.i.g.201.5		20	285.182	even	12
1900.2.i.g.201.6		20	285.68	even	12
1900.2.i.g.501.5		20	15.2	even	4
1900.2.i.g.501.6		20	15.8	even	4
3420.2.bj.c.1189.3		20	19.11	even	3	inner
3420.2.bj.c.1189.5		20	95.49	even	6	inner
3420.2.bj.c.2629.3		20	5.4	even	2	inner
3420.2.bj.c.2629.5		20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3420.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.207009 - 2.22647i) q^{5} -2.54366i q^{7} -2.22377 q^{11} +(6.08116 + 3.51096i) q^{13} +(-2.21492 + 1.27878i) q^{17} +(2.70498 + 3.41805i) q^{19} +(6.95328 + 4.01448i) q^{23} +(-4.91429 + 0.921799i) q^{25} +(0.941734 - 1.63113i) q^{29} +5.98111 q^{31} +(-5.66338 + 0.526562i) q^{35} +2.86105i q^{37} +(3.67524 + 6.36571i) q^{41} +(3.19919 - 1.84706i) q^{43} +(-4.09540 - 2.36448i) q^{47} +0.529782 q^{49} +(8.91226 + 5.14549i) q^{53} +(0.460341 + 4.95114i) q^{55} +(3.73666 + 6.47208i) q^{59} +(4.17839 - 7.23719i) q^{61} +(6.55817 - 14.2663i) q^{65} +(-10.7040 - 6.17997i) q^{67} +(4.13931 + 7.16950i) q^{71} +(-10.9489 + 6.32134i) q^{73} +5.65651i q^{77} +(-2.13067 - 3.69043i) q^{79} -14.7613i q^{83} +(3.30568 + 4.66672i) q^{85} +(7.19403 - 12.4604i) q^{89} +(8.93069 - 15.4684i) q^{91} +(7.05022 - 6.73011i) q^{95} +(5.04871 - 2.91488i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{5} + 14 q^{19} + 9 q^{25} + 16 q^{29} + 8 q^{31} + 2 q^{35} - 26 q^{41} - 44 q^{49} - 12 q^{55} - 4 q^{59} + 2 q^{61} + 18 q^{65} + 2 q^{71} - 16 q^{79} - 39 q^{85} + 40 q^{89} - 4 q^{91} + 43 q^{95}+O(q^{100}) \) 20 * q - q^5 + 14 * q^19 + 9 * q^25 + 16 * q^29 + 8 * q^31 + 2 * q^35 - 26 * q^41 - 44 * q^49 - 12 * q^55 - 4 * q^59 + 2 * q^61 + 18 * q^65 + 2 * q^71 - 16 * q^79 - 39 * q^85 + 40 * q^89 - 4 * q^91 + 43 * q^95

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