LMFDB - Embedded newform 3420.2.bj.c.2629.4

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			2629.4
Root			$-2.48777 + 1.43632i$ of defining polynomial
Character	$\chi$	$=$	3420.2629
Dual form			3420.2.bj.c.1189.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38776 + 1.75332i) q^{5} +3.54568i q^{7} +1.81575 q^{11} +(2.78308 + 1.60681i) q^{13} +(6.92193 - 3.99638i) q^{17} +(0.863760 + 4.27246i) q^{19} +(7.30026 + 4.21480i) q^{23} +(-1.14823 - 4.86637i) q^{25} +(4.29124 - 7.43265i) q^{29} -1.70874 q^{31} +(-6.21669 - 4.92056i) q^{35} +5.50608i q^{37} +(-4.05694 - 7.02683i) q^{41} +(4.35373 - 2.51363i) q^{43} +(-1.16834 - 0.674543i) q^{47} -5.57183 q^{49} +(1.92201 + 1.10967i) q^{53} +(-2.51983 + 3.18359i) q^{55} +(-0.960774 - 1.66411i) q^{59} +(2.83047 - 4.90251i) q^{61} +(-6.67950 + 2.64974i) q^{65} +(8.04360 + 4.64397i) q^{67} +(2.94365 + 5.09854i) q^{71} +(-2.82716 + 1.63226i) q^{73} +6.43807i q^{77} +(2.08739 + 3.61546i) q^{79} +6.30268i q^{83} +(-2.59909 + 17.6824i) q^{85} +(-2.73646 + 4.73968i) q^{89} +(-5.69723 + 9.86789i) q^{91} +(-8.68966 - 4.41472i) q^{95} +(6.91255 - 3.99096i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.38776	+	1.75332i	−0.620626	+	0.784106i
$5$	−1.38776	+	1.75332i	−0.620626	+	0.784106i
$6$		0			0
$7$			3.54568i			1.34014i	0.742298	+	0.670070i	$0.233736\pi$
$7$			3.54568i			1.34014i	−0.742298	+	0.670070i	$0.766264\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.81575			0.547470			0.273735	−	0.961805i	$-0.411741\pi$
$11$	1.81575			0.547470			0.273735	+	0.961805i	$0.411741\pi$
$12$		0			0
$13$	2.78308	+	1.60681i	0.771887	+	0.445649i	0.833547	−	0.552448i	$-0.186306\pi$
$13$	2.78308	+	1.60681i	0.771887	+	0.445649i	−0.0616606	+	0.998097i	$0.519640\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	6.92193	−	3.99638i	1.67881	−	0.969264i	0.716396	−	0.697694i	$-0.245790\pi$
$17$	6.92193	−	3.99638i	1.67881	−	0.969264i	0.962419	−	0.271570i	$-0.0875429\pi$
$18$		0			0
$19$	0.863760	+	4.27246i	0.198160	+	0.980170i
$19$	0.863760	+	4.27246i	0.198160	+	0.980170i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	7.30026	+	4.21480i	1.52221	+	0.878848i	0.999656	+	0.0262406i	$0.00835362\pi$
$23$	7.30026	+	4.21480i	1.52221	+	0.878848i	0.522553	+	0.852607i	$0.324980\pi$
$24$		0			0
$25$	−1.14823	−	4.86637i	−0.229646	−	0.973274i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.29124	−	7.43265i	0.796863	−	1.38021i	−0.124786	−	0.992184i	$-0.539824\pi$
$29$	4.29124	−	7.43265i	0.796863	−	1.38021i	0.921649	−	0.388024i	$-0.126842\pi$
$30$		0			0
$31$	−1.70874			−0.306899			−0.153450	−	0.988156i	$-0.549038\pi$
$31$	−1.70874			−0.306899			−0.153450	+	0.988156i	$0.549038\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−6.21669	−	4.92056i	−1.05081	−	0.831726i
$36$		0			0
$37$			5.50608i			0.905193i	0.891715	+	0.452597i	$0.149502\pi$
$37$			5.50608i			0.905193i	−0.891715	+	0.452597i	$0.850498\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.05694	−	7.02683i	−0.633588	−	1.09741i	−0.986812	−	0.161868i	$-0.948248\pi$
$41$	−4.05694	−	7.02683i	−0.633588	−	1.09741i	0.353224	−	0.935539i	$-0.385085\pi$
$42$		0			0
$43$	4.35373	−	2.51363i	0.663938	−	0.383325i	−0.129838	−	0.991535i	$-0.541446\pi$
$43$	4.35373	−	2.51363i	0.663938	−	0.383325i	0.793776	+	0.608211i	$0.208112\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.16834	−	0.674543i	−0.170420	−	0.0983922i	0.412364	−	0.911019i	$-0.364703\pi$
$47$	−1.16834	−	0.674543i	−0.170420	−	0.0983922i	−0.582784	+	0.812627i	$0.698037\pi$
$48$		0			0
$49$	−5.57183			−0.795976
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.92201	+	1.10967i	0.264009	+	0.152426i	0.626162	−	0.779693i	$-0.284625\pi$
$53$	1.92201	+	1.10967i	0.264009	+	0.152426i	−0.362153	+	0.932119i	$0.617958\pi$
$54$		0			0
$55$	−2.51983	+	3.18359i	−0.339774	+	0.429275i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.960774	−	1.66411i	−0.125082	−	0.216649i	0.796683	−	0.604398i	$-0.206586\pi$
$59$	−0.960774	−	1.66411i	−0.125082	−	0.216649i	−0.921765	+	0.387749i	$0.873253\pi$
$60$		0			0
$61$	2.83047	−	4.90251i	0.362404	−	0.627702i	−0.625952	−	0.779862i	$-0.715289\pi$
$61$	2.83047	−	4.90251i	0.362404	−	0.627702i	0.988356	+	0.152159i	$0.0486227\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−6.67950	+	2.64974i	−0.828489	+	0.328660i
$66$		0			0
$67$	8.04360	+	4.64397i	0.982682	+	0.567352i	0.903079	−	0.429475i	$-0.141301\pi$
$67$	8.04360	+	4.64397i	0.982682	+	0.567352i	0.0796032	+	0.996827i	$0.474635\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	2.94365	+	5.09854i	0.349346	+	0.605086i	0.986134	−	0.165954i	$-0.0530703\pi$
$71$	2.94365	+	5.09854i	0.349346	+	0.605086i	−0.636787	+	0.771040i	$0.719737\pi$
$72$		0			0
$73$	−2.82716	+	1.63226i	−0.330894	+	0.191042i	−0.656238	−	0.754554i	$-0.727853\pi$
$73$	−2.82716	+	1.63226i	−0.330894	+	0.191042i	0.325344	+	0.945596i	$0.394520\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$			6.43807i			0.733687i
$78$		0			0
$79$	2.08739	+	3.61546i	0.234850	+	0.406771i	0.959229	−	0.282630i	$-0.0912069\pi$
$79$	2.08739	+	3.61546i	0.234850	+	0.406771i	−0.724379	+	0.689402i	$0.757874\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$			6.30268i			0.691809i	0.938270	+	0.345905i	$0.112428\pi$
$83$			6.30268i			0.691809i	−0.938270	+	0.345905i	$0.887572\pi$
$84$		0			0
$85$	−2.59909	+	17.6824i	−0.281910	+	1.91792i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−2.73646	+	4.73968i	−0.290064	+	0.502405i	−0.973825	−	0.227301i	$-0.927010\pi$
$89$	−2.73646	+	4.73968i	−0.290064	+	0.502405i	0.683761	+	0.729706i	$0.260343\pi$
$90$		0			0
$91$	−5.69723	+	9.86789i	−0.597232	+	1.03444i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−8.68966	−	4.41472i	−0.891541	−	0.452941i
$96$		0			0
$97$	6.91255	−	3.99096i	0.701863	−	0.405221i	−0.106178	−	0.994347i	$-0.533861\pi$
$97$	6.91255	−	3.99096i	0.701863	−	0.405221i	0.808041	+	0.589126i	$0.200528\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−2.46731	+	4.27351i	−0.245507	+	0.425230i	−0.962274	−	0.272082i	$-0.912288\pi$
$101$	−2.46731	+	4.27351i	−0.245507	+	0.425230i	0.716767	+	0.697313i	$0.245621\pi$
$102$		0			0
$103$		−	5.56291i		−	0.548130i	−0.961711	−	0.274065i	$-0.911632\pi$
$103$		−	5.56291i		−	0.548130i	0.961711	−	0.274065i	$-0.0883684\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	9.12251i		−	0.881907i	−0.897530	−	0.440953i	$-0.854640\pi$
$107$		−	9.12251i		−	0.881907i	0.897530	−	0.440953i	$-0.145360\pi$
$108$		0			0
$109$	7.57225	+	13.1155i	0.725290	+	1.25624i	0.958855	+	0.283898i	$0.0916276\pi$
$109$	7.57225	+	13.1155i	0.725290	+	1.25624i	−0.233565	+	0.972341i	$0.575039\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			4.46091i			0.419647i	0.977739	+	0.209823i	$0.0672889\pi$
$113$			4.46091i			0.419647i	−0.977739	+	0.209823i	$0.932711\pi$
$114$		0			0
$115$	−17.5209	+	6.95050i	−1.63383	+	0.648138i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	14.1699	+	24.5429i	1.29895	+	2.24985i
$120$		0			0
$121$	−7.70304			−0.700277
$122$		0			0
$123$		0			0
$124$		0			0
$125$	10.1258	+	4.74016i	0.905675	+	0.423973i
$126$		0			0
$127$	0.180177	+	0.104025i	0.0159881	+	0.00923073i	0.507973	−	0.861373i	$-0.330395\pi$
$127$	0.180177	+	0.104025i	0.0159881	+	0.00923073i	−0.491985	+	0.870604i	$0.663728\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−7.55409	−	13.0841i	−0.660004	−	1.14316i	−0.980614	−	0.195950i	$-0.937221\pi$
$131$	−7.55409	−	13.0841i	−0.660004	−	1.14316i	0.320610	−	0.947211i	$-0.396112\pi$
$132$		0			0
$133$	−15.1488	+	3.06261i	−1.31356	+	0.265562i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.56291	+	2.63439i	0.389835	+	0.225072i	0.682089	−	0.731269i	$-0.261072\pi$
$137$	4.56291	+	2.63439i	0.389835	+	0.225072i	−0.292253	+	0.956341i	$0.594405\pi$
$138$		0			0
$139$	3.38336	−	5.86016i	0.286973	−	0.497052i	−0.686113	−	0.727495i	$-0.740684\pi$
$139$	3.38336	−	5.86016i	0.286973	−	0.497052i	0.973086	+	0.230443i	$0.0740176\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	5.05338	+	2.91757i	0.422585	+	0.243979i
$144$		0			0
$145$	7.07655	+	17.8386i	0.587675	+	1.48142i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−4.83003	−	8.36586i	−0.395692	−	0.685358i	0.597498	−	0.801871i	$-0.296162\pi$
$149$	−4.83003	−	8.36586i	−0.395692	−	0.685358i	−0.993189	+	0.116513i	$0.962828\pi$
$150$		0			0
$151$	−12.0256			−0.978631			−0.489316	−	0.872107i	$-0.662753\pi$
$151$	−12.0256			−0.978631			−0.489316	+	0.872107i	$0.662753\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.37133	−	2.99597i	0.190470	−	0.240642i
$156$		0			0
$157$	−1.36610	+	0.788721i	−0.109027	+	0.0629468i	−0.553522	−	0.832835i	$-0.686716\pi$
$157$	−1.36610	+	0.788721i	−0.109027	+	0.0629468i	0.444495	+	0.895781i	$0.353383\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−14.9443	+	25.8844i	−1.17778	+	2.03997i
$162$		0			0
$163$			16.0641i			1.25823i	0.777310	+	0.629117i	$0.216584\pi$
$163$			16.0641i			1.25823i	−0.777310	+	0.629117i	$0.783416\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.16826	−	3.56125i	−0.477314	−	0.275578i	0.241982	−	0.970281i	$-0.422202\pi$
$167$	−6.16826	−	3.56125i	−0.477314	−	0.275578i	−0.719297	+	0.694703i	$0.755536\pi$
$168$		0			0
$169$	−1.33632	−	2.31458i	−0.102794	−	0.178044i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−14.8757	+	8.58850i	−1.13098	+	0.652972i	−0.944181	−	0.329427i	$-0.893145\pi$
$173$	−14.8757	+	8.58850i	−1.13098	+	0.652972i	−0.186799	+	0.982398i	$0.559811\pi$
$174$		0			0
$175$	17.2546	−	4.07125i	1.30432	−	0.307758i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−3.38519			−0.253021			−0.126510	−	0.991965i	$-0.540378\pi$
$179$	−3.38519			−0.253021			−0.126510	+	0.991965i	$0.540378\pi$
$180$		0			0
$181$	10.4226	−	18.0524i	0.774704	−	1.34183i	−0.160257	−	0.987075i	$-0.551232\pi$
$181$	10.4226	−	18.0524i	0.774704	−	1.34183i	0.934961	−	0.354751i	$-0.115434\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−9.65389	−	7.64113i	−0.709768	−	0.561787i
$186$		0			0
$187$	12.5685	−	7.25643i	0.919101	−	0.530643i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−4.58794			−0.331972			−0.165986	−	0.986128i	$-0.553081\pi$
$191$	−4.58794			−0.331972			−0.165986	+	0.986128i	$0.553081\pi$
$192$		0			0
$193$	−17.4238	+	10.0596i	−1.25419	+	0.724108i	−0.971939	−	0.235232i	$-0.924415\pi$
$193$	−17.4238	+	10.0596i	−1.25419	+	0.724108i	−0.282252	+	0.959340i	$0.591082\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			0.983439i			0.0700671i	0.999386	+	0.0350336i	$0.0111538\pi$
$197$			0.983439i			0.0700671i	−0.999386	+	0.0350336i	$0.988846\pi$
$198$		0			0
$199$	−5.84473	+	10.1234i	−0.414322	+	0.717626i	−0.995357	−	0.0962520i	$-0.969315\pi$
$199$	−5.84473	+	10.1234i	−0.414322	+	0.717626i	0.581035	+	0.813878i	$0.302648\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	26.3538	+	15.2154i	1.84967	+	1.06791i
$204$		0			0
$205$	17.9503	+	2.63848i	1.25371	+	0.184279i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.56837	+	7.75773i	0.108487	+	0.536613i
$210$		0			0
$211$	−5.35987	−	9.28357i	−0.368989	−	0.639107i	0.620419	−	0.784270i	$-0.286963\pi$
$211$	−5.35987	−	9.28357i	−0.368989	−	0.639107i	−0.989408	+	0.145163i	$0.953629\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.63476	+	11.1218i	−0.111490	+	0.758499i
$216$		0			0
$217$		−	6.05865i		−	0.411288i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	25.6857			1.72781
$222$		0			0
$223$	17.8291	−	10.2936i	1.19393	−	0.689313i	0.234731	−	0.972060i	$-0.424579\pi$
$223$	17.8291	−	10.2936i	1.19393	−	0.689313i	0.959195	+	0.282747i	$0.0912456\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		−	7.47441i		−	0.496094i	−0.968748	−	0.248047i	$-0.920211\pi$
$227$		−	7.47441i		−	0.496094i	0.968748	−	0.248047i	$-0.0797887\pi$
$228$		0			0
$229$	11.0863			0.732604			0.366302	−	0.930496i	$-0.380624\pi$
$229$	11.0863			0.732604			0.366302	+	0.930496i	$0.380624\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−15.8785	+	9.16743i	−1.04023	+	0.600578i	−0.919899	−	0.392155i	$-0.871730\pi$
$233$	−15.8785	+	9.16743i	−1.04023	+	0.600578i	−0.120333	+	0.992734i	$0.538396\pi$
$234$		0			0
$235$	2.80407	−	1.11237i	0.182917	−	0.0725628i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	11.8518			0.766630			0.383315	−	0.923618i	$-0.374782\pi$
$239$	11.8518			0.766630			0.383315	+	0.923618i	$0.374782\pi$
$240$		0			0
$241$	−2.34317	+	4.05850i	−0.150937	+	0.261431i	−0.931572	−	0.363556i	$-0.881562\pi$
$241$	−2.34317	+	4.05850i	−0.150937	+	0.261431i	0.780635	+	0.624987i	$0.214896\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	7.73238	−	9.76918i	0.494004	−	0.624130i
$246$		0			0
$247$	−4.46112	+	13.2785i	−0.283854	+	0.844890i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−0.0510129	+	0.0883569i	−0.00321990	+	0.00557704i	−0.867631	−	0.497209i	$-0.834358\pi$
$251$	−0.0510129	+	0.0883569i	−0.00321990	+	0.00557704i	0.864411	+	0.502786i	$0.167692\pi$
$252$		0			0
$253$	13.2555	+	7.65304i	0.833363	+	0.481143i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−13.3268	−	7.69424i	−0.831303	−	0.479953i	0.0229953	−	0.999736i	$-0.492680\pi$
$257$	−13.3268	−	7.69424i	−0.831303	−	0.479953i	−0.854299	+	0.519782i	$0.826013\pi$
$258$		0			0
$259$	−19.5228			−1.21309
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−16.9467	+	9.78416i	−1.04498	+	0.603317i	−0.921239	−	0.388998i	$-0.872821\pi$
$263$	−16.9467	+	9.78416i	−1.04498	+	0.603317i	−0.123737	+	0.992315i	$0.539488\pi$
$264$		0			0
$265$	−4.61291	+	1.82993i	−0.283369	+	0.112412i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−0.585331	−	1.01382i	−0.0356883	−	0.0618139i	0.847630	−	0.530588i	$-0.178029\pi$
$269$	−0.585331	−	1.01382i	−0.0356883	−	0.0618139i	−0.883318	+	0.468775i	$0.844696\pi$
$270$		0			0
$271$	6.40442	+	11.0928i	0.389041	+	0.673838i	0.992321	−	0.123691i	$-0.0394732\pi$
$271$	6.40442	+	11.0928i	0.389041	+	0.673838i	−0.603280	+	0.797529i	$0.706140\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.08490	−	8.83613i	−0.125724	−	0.532838i
$276$		0			0
$277$			11.0122i			0.661656i	0.943691	+	0.330828i	$0.107328\pi$
$277$			11.0122i			0.661656i	−0.943691	+	0.330828i	$0.892672\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.93481	−	3.35119i	0.115421	−	0.199915i	−0.802527	−	0.596616i	$-0.796512\pi$
$281$	1.93481	−	3.35119i	0.115421	−	0.199915i	0.917948	+	0.396701i	$0.129845\pi$
$282$		0			0
$283$	19.5893	−	11.3099i	1.16446	−	0.672303i	0.212093	−	0.977249i	$-0.431972\pi$
$283$	19.5893	−	11.3099i	1.16446	−	0.672303i	0.952369	+	0.304947i	$0.0986387\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	24.9149	−	14.3846i	1.47068	−	0.849097i
$288$		0			0
$289$	23.4421	−	40.6029i	1.37895	−	2.38840i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	28.4482i		−	1.66196i	−0.556303	−	0.830980i	$-0.687781\pi$
$293$		−	28.4482i		−	1.66196i	0.556303	−	0.830980i	$-0.312219\pi$
$294$		0			0
$295$	4.25104	+	0.624850i	0.247505	+	0.0363801i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	13.5448	+	23.4603i	0.783315	+	1.35674i
$300$		0			0
$301$	8.91251	+	15.4369i	0.513709	+	0.889770i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	4.66763	+	11.7662i	0.267268	+	0.673732i
$306$		0			0
$307$	12.2248	−	7.05802i	0.697709	−	0.402822i	−0.108785	−	0.994065i	$-0.534696\pi$
$307$	12.2248	−	7.05802i	0.697709	−	0.402822i	0.806494	+	0.591243i	$0.201363\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−16.4672			−0.933768			−0.466884	−	0.884319i	$-0.654623\pi$
$311$	−16.4672			−0.933768			−0.466884	+	0.884319i	$0.654623\pi$
$312$		0			0
$313$	−21.6363	−	12.4917i	−1.22295	−	0.706073i	−0.257408	−	0.966303i	$-0.582868\pi$
$313$	−21.6363	−	12.4917i	−1.22295	−	0.706073i	−0.965547	+	0.260229i	$0.916202\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.91012	+	1.10281i	0.107283	+	0.0619399i	0.552681	−	0.833393i	$-0.313605\pi$
$317$	1.91012	+	1.10281i	0.107283	+	0.0619399i	−0.445398	+	0.895332i	$0.646938\pi$
$318$		0			0
$319$	7.79183	−	13.4958i	0.436259	−	0.755622i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	23.0533	+	26.1218i	1.28272	+	1.45345i
$324$		0			0
$325$	4.62373	−	15.3885i	0.256478	−	0.853599i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	2.39171	−	4.14257i	0.131859	−	0.228387i
$330$		0			0
$331$	−27.5415			−1.51382			−0.756910	−	0.653519i	$-0.773292\pi$
$331$	−27.5415			−1.51382			−0.756910	+	0.653519i	$0.773292\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−19.3050	+	7.65823i	−1.05474	+	0.418414i
$336$		0			0
$337$	−15.9464	+	9.20668i	−0.868658	+	0.501520i	−0.866902	−	0.498479i	$-0.833892\pi$
$337$	−15.9464	+	9.20668i	−0.868658	+	0.501520i	−0.00175582	+	0.999998i	$0.500559\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−3.10265			−0.168018
$342$		0			0
$343$			5.06383i			0.273421i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−22.8072	+	13.1677i	−1.22435	+	0.706881i	−0.965843	−	0.259128i	$-0.916565\pi$
$347$	−22.8072	+	13.1677i	−1.22435	+	0.706881i	−0.258510	+	0.966009i	$0.583232\pi$
$348$		0			0
$349$	7.40515			0.396388			0.198194	−	0.980163i	$-0.436492\pi$
$349$	7.40515			0.396388			0.198194	+	0.980163i	$0.436492\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		−	2.42201i		−	0.128910i	−0.997921	−	0.0644552i	$-0.979469\pi$
$353$		−	2.42201i		−	0.128910i	0.997921	−	0.0644552i	$-0.0205309\pi$
$354$		0			0
$355$	−13.0244	−	1.91443i	−0.691265	−	0.101607i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−2.28083	−	3.95051i	−0.120377	−	0.208500i	0.799539	−	0.600614i	$-0.205077\pi$
$359$	−2.28083	−	3.95051i	−0.120377	−	0.208500i	−0.919917	+	0.392114i	$0.871744\pi$
$360$		0			0
$361$	−17.5078	+	7.38076i	−0.921465	+	0.388461i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.06156	−	7.22209i	0.0555645	−	0.378021i
$366$		0			0
$367$	9.11478	+	5.26242i	0.475788	+	0.274696i	0.718659	−	0.695362i	$-0.244756\pi$
$367$	9.11478	+	5.26242i	0.475788	+	0.274696i	−0.242872	+	0.970058i	$0.578089\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−3.93455	+	6.81484i	−0.204272	+	0.353809i
$372$		0			0
$373$		−	21.8633i		−	1.13204i	−0.824392	−	0.566019i	$-0.808483\pi$
$373$		−	21.8633i		−	1.13204i	0.824392	−	0.566019i	$-0.191517\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	23.8857	−	13.7904i	1.23018	−	0.710243i
$378$		0			0
$379$	−9.33617			−0.479567			−0.239783	−	0.970826i	$-0.577076\pi$
$379$	−9.33617			−0.479567			−0.239783	+	0.970826i	$0.577076\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	4.77320	−	2.75581i	0.243899	−	0.140815i	−0.373068	−	0.927804i	$-0.621694\pi$
$383$	4.77320	−	2.75581i	0.243899	−	0.140815i	0.616968	+	0.786989i	$0.288361\pi$
$384$		0			0
$385$	−11.2880	−	8.93452i	−0.575288	−	0.455345i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−8.50605	+	14.7329i	−0.431274	+	0.746988i	−0.996983	−	0.0776163i	$-0.975269\pi$
$389$	−8.50605	+	14.7329i	−0.431274	+	0.746988i	0.565709	+	0.824605i	$0.308602\pi$
$390$		0			0
$391$	67.3758			3.40734
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−9.23585	−	1.35755i	−0.464706	−	0.0683060i
$396$		0			0
$397$	−27.2122	+	15.7110i	−1.36574	+	0.788512i	−0.990381	−	0.138366i	$-0.955815\pi$
$397$	−27.2122	+	15.7110i	−1.36574	+	0.788512i	−0.375362	+	0.926878i	$0.622482\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−13.4762	−	23.3415i	−0.672971	−	1.16562i	−0.977058	−	0.212976i	$-0.931685\pi$
$401$	−13.4762	−	23.3415i	−0.672971	−	1.16562i	0.304087	−	0.952644i	$-0.401649\pi$
$402$		0			0
$403$	−4.75556	−	2.74563i	−0.236891	−	0.136769i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			9.99767i			0.495566i
$408$		0			0
$409$	−17.0791	+	29.5819i	−0.844509	+	1.46273i	0.0415373	+	0.999137i	$0.486774\pi$
$409$	−17.0791	+	29.5819i	−0.844509	+	1.46273i	−0.886047	+	0.463596i	$0.846559\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	5.90040	−	3.40660i	0.290340	−	0.167628i
$414$		0			0
$415$	−11.0506	−	8.74663i	−0.542452	−	0.429355i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	36.5998			1.78802			0.894009	−	0.448049i	$-0.147881\pi$
$419$	36.5998			1.78802			0.894009	+	0.448049i	$0.147881\pi$
$420$		0			0
$421$	−4.85007	−	8.40057i	−0.236378	−	0.409419i	0.723294	−	0.690540i	$-0.242627\pi$
$421$	−4.85007	−	8.40057i	−0.236378	−	0.409419i	−0.959672	+	0.281121i	$0.909294\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−27.3958	−	29.0959i	−1.32889	−	1.41136i
$426$		0			0
$427$	17.3827	+	10.0359i	0.841209	+	0.485672i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	14.4779	−	25.0764i	0.697375	−	1.20789i	−0.271999	−	0.962298i	$-0.587685\pi$
$431$	14.4779	−	25.0764i	0.697375	−	1.20789i	0.969373	−	0.245591i	$-0.0789821\pi$
$432$		0			0
$433$	6.44994	+	3.72388i	0.309965	+	0.178958i	0.646911	−	0.762566i	$-0.276061\pi$
$433$	6.44994	+	3.72388i	0.309965	+	0.178958i	−0.336946	+	0.941524i	$0.609394\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−11.7019	+	34.8306i	−0.559779	+	1.66618i
$438$		0			0
$439$	5.70008	+	9.87283i	0.272050	+	0.471204i	0.969387	−	0.245539i	$-0.0789650\pi$
$439$	5.70008	+	9.87283i	0.272050	+	0.471204i	−0.697337	+	0.716744i	$0.745632\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−6.66042	−	3.84540i	−0.316446	−	0.182700i	0.333361	−	0.942799i	$-0.391817\pi$
$443$	−6.66042	−	3.84540i	−0.316446	−	0.182700i	−0.649807	+	0.760099i	$0.725150\pi$
$444$		0			0
$445$	−4.51260	−	11.3754i	−0.213918	−	0.539247i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	37.0590			1.74892			0.874460	−	0.485097i	$-0.161216\pi$
$449$	37.0590			1.74892			0.874460	+	0.485097i	$0.161216\pi$
$450$		0			0
$451$	−7.36641	−	12.7590i	−0.346871	−	0.600797i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−9.39512	−	23.6833i	−0.440450	−	1.11029i
$456$		0			0
$457$			22.1647i			1.03682i	0.855131	+	0.518411i	$0.173476\pi$
$457$			22.1647i			1.03682i	−0.855131	+	0.518411i	$0.826524\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−21.0779	−	36.5080i	−0.981697	−	1.70035i	−0.655783	−	0.754949i	$-0.727661\pi$
$461$	−21.0779	−	36.5080i	−0.981697	−	1.70035i	−0.325914	−	0.945400i	$-0.605672\pi$
$462$		0			0
$463$			5.16758i			0.240158i	0.992764	+	0.120079i	$0.0383148\pi$
$463$			5.16758i			0.240158i	−0.992764	+	0.120079i	$0.961685\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			12.7096i			0.588129i	0.955786	+	0.294064i	$0.0950080\pi$
$467$			12.7096i			0.588129i	−0.955786	+	0.294064i	$0.904992\pi$
$468$		0			0
$469$	−16.4660	+	28.5200i	−0.760331	+	1.31693i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	7.90530	−	4.56413i	0.363486	−	0.209859i
$474$		0			0
$475$	19.7996	−	9.10914i	0.908467	−	0.417956i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	11.0555	−	19.1487i	0.505140	−	0.874928i	−0.494842	−	0.868983i	$-0.664774\pi$
$479$	11.0555	−	19.1487i	0.505140	−	0.874928i	0.999982	−	0.00594539i	$-0.00189249\pi$
$480$		0			0
$481$	−8.84722	+	15.3238i	−0.403399	+	0.698707i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.59556	+	17.6584i	−0.117858	+	0.801826i
$486$		0			0
$487$		−	28.3389i		−	1.28416i	−0.766639	−	0.642078i	$-0.778072\pi$
$487$		−	28.3389i		−	1.28416i	0.766639	−	0.642078i	$-0.221928\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	4.33288	+	7.50477i	0.195540	+	0.338686i	0.947077	−	0.321005i	$-0.104021\pi$
$491$	4.33288	+	7.50477i	0.195540	+	0.338686i	−0.751537	+	0.659691i	$0.770687\pi$
$492$		0			0
$493$		−	68.5977i		−	3.08948i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−18.0778	+	10.4372i	−0.810900	+	0.468173i
$498$		0			0
$499$	−8.07784	−	13.9912i	−0.361614	−	0.626334i	0.626613	−	0.779331i	$-0.284441\pi$
$499$	−8.07784	−	13.9912i	−0.361614	−	0.626334i	−0.988227	+	0.152997i	$0.951107\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	22.3262	+	12.8900i	0.995474	+	0.574737i	0.906906	−	0.421333i	$-0.138438\pi$
$503$	22.3262	+	12.8900i	0.995474	+	0.574737i	0.0885682	+	0.996070i	$0.471771\pi$
$504$		0			0
$505$	−4.06877	−	10.2566i	−0.181058	−	0.456413i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	6.15335	−	10.6579i	0.272743	−	0.472404i	−0.696821	−	0.717246i	$-0.745403\pi$
$509$	6.15335	−	10.6579i	0.272743	−	0.472404i	0.969563	+	0.244842i	$0.0787359\pi$
$510$		0			0
$511$	−5.78747	−	10.0242i	−0.256023	−	0.443444i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	9.75354	+	7.72000i	0.429792	+	0.340184i
$516$		0			0
$517$	−2.12142	−	1.22480i	−0.0933000	−	0.0538668i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−17.0934			−0.748875			−0.374438	−	0.927252i	$-0.622164\pi$
$521$	−17.0934			−0.748875			−0.374438	+	0.927252i	$0.622164\pi$
$522$		0			0
$523$	2.29269	+	1.32368i	0.100252	+	0.0578806i	0.549288	−	0.835633i	$-0.314899\pi$
$523$	2.29269	+	1.32368i	0.100252	+	0.0578806i	−0.449036	+	0.893514i	$0.648232\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−11.8278	+	6.82878i	−0.515227	+	0.297466i
$528$		0			0
$529$	24.0292	+	41.6197i	1.04475	+	1.80955i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		−	26.0750i		−	1.12943i
$534$		0			0
$535$	15.9946	+	12.6599i	0.691509	+	0.547335i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−10.1171			−0.435773
$540$		0			0
$541$	−5.06701	+	8.77631i	−0.217848	+	0.377323i	−0.954150	−	0.299330i	$-0.903237\pi$
$541$	−5.06701	+	8.77631i	−0.217848	+	0.377323i	0.736302	+	0.676653i	$0.236570\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−33.5041	−	4.92469i	−1.43516	−	0.210951i
$546$		0			0
$547$	−19.4639	−	11.2375i	−0.832217	−	0.480480i	0.0223944	−	0.999749i	$-0.492871\pi$
$547$	−19.4639	−	11.2375i	−0.832217	−	0.480480i	−0.854611	+	0.519269i	$0.826204\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	35.4623	+	11.9141i	1.51074	+	0.507559i
$552$		0			0
$553$	−12.8193	+	7.40121i	−0.545131	+	0.314731i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−3.86157	−	2.22948i	−0.163620	−	0.0944659i	0.415954	−	0.909386i	$-0.363448\pi$
$557$	−3.86157	−	2.22948i	−0.163620	−	0.0944659i	−0.579574	+	0.814920i	$0.696781\pi$
$558$		0			0
$559$	16.1557			0.683313
$560$		0			0
$561$		0			0
$562$		0			0
$563$		−	10.0514i		−	0.423616i	−0.977311	−	0.211808i	$-0.932065\pi$
$563$		−	10.0514i		−	0.423616i	0.977311	−	0.211808i	$-0.0679352\pi$
$564$		0			0
$565$	−7.82137	−	6.19068i	−0.329048	−	0.260444i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−5.41442			−0.226984			−0.113492	−	0.993539i	$-0.536204\pi$
$569$	−5.41442			−0.226984			−0.113492	+	0.993539i	$0.536204\pi$
$570$		0			0
$571$	−24.0418			−1.00612			−0.503059	−	0.864252i	$-0.667792\pi$
$571$	−24.0418			−1.00612			−0.503059	+	0.864252i	$0.667792\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	12.1284	−	40.3653i	0.505791	−	1.68335i
$576$		0			0
$577$		−	1.40727i		−	0.0585855i	−0.999571	−	0.0292928i	$-0.990674\pi$
$577$		−	1.40727i		−	0.0585855i	0.999571	−	0.0292928i	$-0.00932551\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−22.3473			−0.927121
$582$		0			0
$583$	3.48990	+	2.01489i	0.144537	+	0.0834484i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.224303	−	0.129501i	0.00925798	−	0.00534510i	−0.495364	−	0.868686i	$-0.664965\pi$
$587$	0.224303	−	0.129501i	0.00925798	−	0.00534510i	0.504622	+	0.863340i	$0.331632\pi$
$588$		0			0
$589$	−1.47594	−	7.30054i	−0.0608152	−	0.300813i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−2.57044	−	1.48405i	−0.105555	−	0.0609425i	0.446293	−	0.894887i	$-0.352744\pi$
$593$	−2.57044	−	1.48405i	−0.105555	−	0.0609425i	−0.551848	+	0.833944i	$0.686077\pi$
$594$		0			0
$595$	−62.6959	−	9.21552i	−2.57028	−	0.377800i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−23.7083	+	41.0640i	−0.968696	+	1.67783i	−0.269359	+	0.963040i	$0.586812\pi$
$599$	−23.7083	+	41.0640i	−0.968696	+	1.67783i	−0.699338	+	0.714791i	$0.746522\pi$
$600$		0			0
$601$	−22.2047			−0.905747			−0.452874	−	0.891575i	$-0.649601\pi$
$601$	−22.2047			−0.905747			−0.452874	+	0.891575i	$0.649601\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	10.6900	−	13.5059i	0.434610	−	0.549091i
$606$		0			0
$607$			37.6580i			1.52849i	0.644925	+	0.764246i	$0.276888\pi$
$607$			37.6580i			1.52849i	−0.644925	+	0.764246i	$0.723112\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−2.16772	−	3.75461i	−0.0876968	−	0.151895i
$612$		0			0
$613$	−38.3694	+	22.1526i	−1.54973	+	0.894734i	−0.551563	+	0.834133i	$0.685969\pi$
$613$	−38.3694	+	22.1526i	−1.54973	+	0.894734i	−0.998162	+	0.0606013i	$0.980698\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−20.1247	−	11.6190i	−0.810190	−	0.467764i	0.0368317	−	0.999321i	$-0.488273\pi$
$617$	−20.1247	−	11.6190i	−0.810190	−	0.467764i	−0.847022	+	0.531558i	$0.821607\pi$
$618$		0			0
$619$	28.8420			1.15926			0.579630	−	0.814880i	$-0.303197\pi$
$619$	28.8420			1.15926			0.579630	+	0.814880i	$0.303197\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−16.8054	−	9.70259i	−0.673294	−	0.388726i
$624$		0			0
$625$	−22.3631	+	11.1754i	−0.894526	+	0.447017i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	22.0044	+	38.1127i	0.877371	+	1.51965i
$630$		0			0
$631$	6.79323	−	11.7662i	0.270434	−	0.468406i	−0.698539	−	0.715572i	$-0.746166\pi$
$631$	6.79323	−	11.7662i	0.270434	−	0.468406i	0.968973	+	0.247166i	$0.0794994\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.432431	+	0.171544i	−0.0171605	+	0.00680753i
$636$		0			0
$637$	−15.5068	−	8.95287i	−0.614403	−	0.354726i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−3.15731	−	5.46863i	−0.124706	−	0.215998i	0.796912	−	0.604096i	$-0.206466\pi$
$641$	−3.15731	−	5.46863i	−0.124706	−	0.215998i	−0.921618	+	0.388098i	$0.873132\pi$
$642$		0			0
$643$	−11.8657	+	6.85067i	−0.467938	+	0.270164i	−0.715376	−	0.698740i	$-0.753745\pi$
$643$	−11.8657	+	6.85067i	−0.467938	+	0.270164i	0.247438	+	0.968904i	$0.420411\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			8.50227i			0.334259i	0.985935	+	0.167129i	$0.0534497\pi$
$647$			8.50227i			0.334259i	−0.985935	+	0.167129i	$0.946550\pi$
$648$		0			0
$649$	−1.74453	−	3.02161i	−0.0684787	−	0.118609i
$650$		0			0
$651$		0			0
$652$		0			0
$653$			6.89369i			0.269771i	0.990861	+	0.134885i	$0.0430667\pi$
$653$			6.89369i			0.269771i	−0.990861	+	0.134885i	$0.956933\pi$
$654$		0			0
$655$	33.4238	+	4.91288i	1.30598	+	0.191962i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	10.9585	−	18.9807i	0.426884	−	0.739384i	−0.569711	−	0.821845i	$-0.692945\pi$
$659$	10.9585	−	18.9807i	0.426884	−	0.739384i	0.996594	+	0.0824611i	$0.0262780\pi$
$660$		0			0
$661$	15.5768	−	26.9797i	0.605866	−	1.04939i	−0.386048	−	0.922479i	$-0.626160\pi$
$661$	15.5768	−	26.9797i	0.605866	−	1.04939i	0.991914	−	0.126912i	$-0.0405065\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	15.6532	−	30.8107i	0.607004	−	1.19479i
$666$		0			0
$667$	62.6543	−	36.1735i	2.42598	−	1.40064i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	5.13943	−	8.90175i	0.198405	−	0.343648i
$672$		0			0
$673$		−	24.5193i		−	0.945150i	−0.881290	−	0.472575i	$-0.843325\pi$
$673$		−	24.5193i		−	0.945150i	0.881290	−	0.472575i	$-0.156675\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$			7.89395i			0.303389i	0.988427	+	0.151695i	$0.0484730\pi$
$677$			7.89395i			0.303389i	−0.988427	+	0.151695i	$0.951527\pi$
$678$		0			0
$679$	14.1507	+	24.5097i	0.543053	+	0.940595i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	44.3352i		−	1.69644i	−0.529644	−	0.848220i	$-0.677675\pi$
$683$		−	44.3352i		−	1.69644i	0.529644	−	0.848220i	$-0.322325\pi$
$684$		0			0
$685$	−10.9512	+	4.34430i	−0.418422	+	0.165987i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	3.56607	+	6.17662i	0.135857	+	0.235311i
$690$		0			0
$691$	44.2501			1.68335			0.841676	−	0.539982i	$-0.181569\pi$
$691$	44.2501			1.68335			0.841676	+	0.539982i	$0.181569\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	5.57940	+	14.0646i	0.211639	+	0.533501i
$696$		0			0
$697$	−56.1638	−	32.4262i	−2.12735	−	1.22823i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	9.27840	+	16.0707i	0.350440	+	0.606980i	0.986327	−	0.164802i	$-0.0526987\pi$
$701$	9.27840	+	16.0707i	0.350440	+	0.606980i	−0.635886	+	0.771783i	$0.719365\pi$
$702$		0			0
$703$	−23.5245	+	4.75593i	−0.887243	+	0.179373i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−15.1525	−	8.74830i	−0.569868	−	0.329014i
$708$		0			0
$709$	21.4349	−	37.1263i	0.805003	−	1.39431i	−0.111285	−	0.993788i	$-0.535497\pi$
$709$	21.4349	−	37.1263i	0.805003	−	1.39431i	0.916289	−	0.400518i	$-0.131170\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−12.4743	−	7.20202i	−0.467165	−	0.269718i
$714$		0			0
$715$	−12.1283	+	4.81127i	−0.453573	+	0.179931i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	17.5024	+	30.3150i	0.652728	+	1.13056i	0.982458	+	0.186483i	$0.0597088\pi$
$719$	17.5024	+	30.3150i	0.652728	+	1.13056i	−0.329730	+	0.944075i	$0.606958\pi$
$720$		0			0
$721$	19.7243			0.734571
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−41.0973	−	12.3484i	−1.52632	−	0.458608i
$726$		0			0
$727$	0.436587	−	0.252064i	0.0161921	−	0.00934852i	−0.491882	−	0.870662i	$-0.663691\pi$
$727$	0.436587	−	0.252064i	0.0161921	−	0.00934852i	0.508074	+	0.861313i	$0.330358\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	20.0908	−	34.7983i	0.743086	−	1.28706i
$732$		0			0
$733$		−	26.5745i		−	0.981553i	−0.871285	−	0.490777i	$-0.836713\pi$
$733$		−	26.5745i		−	0.981553i	0.871285	−	0.490777i	$-0.163287\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	14.6052	+	8.43231i	0.537989	+	0.310608i
$738$		0			0
$739$	12.8643	+	22.2817i	0.473222	+	0.819645i	0.999530	−	0.0306492i	$-0.00975746\pi$
$739$	12.8643	+	22.2817i	0.473222	+	0.819645i	−0.526308	+	0.850294i	$0.676424\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−3.70400	+	2.13851i	−0.135887	+	0.0784542i	−0.566402	−	0.824129i	$-0.691665\pi$
$743$	−3.70400	+	2.13851i	−0.135887	+	0.0784542i	0.430516	+	0.902583i	$0.358332\pi$
$744$		0			0
$745$	21.3709	+	3.14126i	0.782970	+	0.115087i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	32.3455			1.18188
$750$		0			0
$751$	−7.26869	+	12.5897i	−0.265238	+	0.459406i	−0.967626	−	0.252388i	$-0.918784\pi$
$751$	−7.26869	+	12.5897i	−0.265238	+	0.459406i	0.702388	+	0.711795i	$0.252117\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	16.6887	−	21.0847i	0.607364	−	0.767351i
$756$		0			0
$757$	−14.1482	+	8.16844i	−0.514224	+	0.296887i	−0.734568	−	0.678535i	$-0.762615\pi$
$757$	−14.1482	+	8.16844i	−0.514224	+	0.296887i	0.220345	+	0.975422i	$0.429282\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	21.9812			0.796819			0.398409	−	0.917208i	$-0.369562\pi$
$761$	21.9812			0.796819			0.398409	+	0.917208i	$0.369562\pi$
$762$		0			0
$763$	−46.5034	+	26.8488i	−1.68354	+	0.971990i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	6.17513i		−	0.222971i
$768$		0			0
$769$	23.1977	−	40.1796i	0.836530	−	1.44891i	−0.0562477	−	0.998417i	$-0.517914\pi$
$769$	23.1977	−	40.1796i	0.836530	−	1.44891i	0.892778	−	0.450496i	$-0.148753\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	21.6426	+	12.4954i	0.778431	+	0.449428i	0.835874	−	0.548921i	$-0.184961\pi$
$773$	21.6426	+	12.4954i	0.778431	+	0.449428i	−0.0574426	+	0.998349i	$0.518295\pi$
$774$		0			0
$775$	1.96203	+	8.31538i	0.0704781	+	0.298697i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	26.5176	−	23.4026i	0.950093	−	0.838486i
$780$		0			0
$781$	5.34493	+	9.25769i	0.191257	+	0.331266i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.512953	−	3.48977i	0.0183081	−	0.124555i
$786$		0			0
$787$		−	36.4986i		−	1.30103i	−0.759492	−	0.650517i	$-0.774552\pi$
$787$		−	36.4986i		−	1.30103i	0.759492	−	0.650517i	$-0.225448\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−15.8169			−0.562385
$792$		0			0
$793$	15.7548	−	9.09604i	0.559470	−	0.323010i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			11.9753i			0.424188i	0.977249	+	0.212094i	$0.0680283\pi$
$797$			11.9753i			0.424188i	−0.977249	+	0.212094i	$0.931972\pi$
$798$		0			0
$799$	−10.7829			−0.381472
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−5.13342	+	2.96378i	−0.181154	+	0.104590i
$804$		0			0
$805$	−24.6442	−	62.1235i	−0.868595	−	2.18956i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	29.4153			1.03419			0.517093	−	0.855929i	$-0.327014\pi$
$809$	29.4153			1.03419			0.517093	+	0.855929i	$0.327014\pi$
$810$		0			0
$811$	−27.4062	+	47.4690i	−0.962363	+	1.66686i	−0.245825	+	0.969314i	$0.579059\pi$
$811$	−27.4062	+	47.4690i	−0.962363	+	1.66686i	−0.716538	+	0.697548i	$0.754274\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−28.1654	−	22.2931i	−0.986590	−	0.780894i
$816$		0			0
$817$	14.5000	+	16.4300i	0.507289	+	0.574812i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−4.32200	+	7.48592i	−0.150839	+	0.261260i	−0.931536	−	0.363649i	$-0.881531\pi$
$821$	−4.32200	+	7.48592i	−0.150839	+	0.261260i	0.780697	+	0.624909i	$0.214864\pi$
$822$		0			0
$823$	35.1614	+	20.3004i	1.22565	+	0.707628i	0.966117	−	0.258106i	$-0.0830985\pi$
$823$	35.1614	+	20.3004i	1.22565	+	0.707628i	0.259532	+	0.965735i	$0.416432\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.64002	−	0.946864i	−0.0570290	−	0.0329257i	0.471214	−	0.882019i	$-0.343816\pi$
$827$	−1.64002	−	0.946864i	−0.0570290	−	0.0329257i	−0.528243	+	0.849093i	$0.677149\pi$
$828$		0			0
$829$	54.2488			1.88414			0.942070	−	0.335416i	$-0.108877\pi$
$829$	54.2488			1.88414			0.942070	+	0.335416i	$0.108877\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−38.5678	+	22.2671i	−1.33630	+	0.771511i
$834$		0			0
$835$	14.8041	−	5.87274i	0.512316	−	0.203235i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−19.4931	−	33.7630i	−0.672976	−	1.16563i	−0.977056	−	0.212982i	$-0.931682\pi$
$839$	−19.4931	−	33.7630i	−0.672976	−	1.16563i	0.304080	−	0.952647i	$-0.401651\pi$
$840$		0			0
$841$	−22.3295	−	38.6758i	−0.769982	−	1.33365i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	5.91268	+	0.869090i	0.203402	+	0.0298976i
$846$		0			0
$847$		−	27.3125i		−	0.938469i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−23.2070	+	40.1958i	−0.795527	+	1.37789i
$852$		0			0
$853$	26.5103	−	15.3058i	0.907697	−	0.524059i	0.0280076	−	0.999608i	$-0.491084\pi$
$853$	26.5103	−	15.3058i	0.907697	−	0.524059i	0.879689	+	0.475549i	$0.157750\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	11.6725	−	6.73913i	0.398726	−	0.230204i	−0.287208	−	0.957868i	$-0.592727\pi$
$857$	11.6725	−	6.73913i	0.398726	−	0.230204i	0.685934	+	0.727664i	$0.259394\pi$
$858$		0			0
$859$	−4.96411	+	8.59809i	−0.169373	+	0.293363i	−0.938200	−	0.346094i	$-0.887508\pi$
$859$	−4.96411	+	8.59809i	−0.169373	+	0.293363i	0.768826	+	0.639458i	$0.220841\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	36.8000i		−	1.25269i	−0.779547	−	0.626344i	$-0.784551\pi$
$863$		−	36.8000i		−	1.25269i	0.779547	−	0.626344i	$-0.215449\pi$
$864$		0			0
$865$	5.58562	−	38.0006i	0.189917	−	1.29206i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	3.79018	+	6.56479i	0.128573	+	0.222695i
$870$		0			0
$871$	14.9240	+	25.8491i	0.505679	+	0.875862i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−16.8071	+	35.9027i	−0.568183	+	1.21373i
$876$		0			0
$877$	4.96267	−	2.86520i	0.167577	−	0.0967509i	−0.413866	−	0.910338i	$-0.635822\pi$
$877$	4.96267	−	2.86520i	0.167577	−	0.0967509i	0.581443	+	0.813587i	$0.302488\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−21.5926			−0.727474			−0.363737	−	0.931502i	$-0.618499\pi$
$881$	−21.5926			−0.727474			−0.363737	+	0.931502i	$0.618499\pi$
$882$		0			0
$883$	36.0904	+	20.8368i	1.21454	+	0.701214i	0.963745	−	0.266826i	$-0.0859749\pi$
$883$	36.0904	+	20.8368i	1.21454	+	0.701214i	0.250794	+	0.968040i	$0.419308\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−43.9856	−	25.3951i	−1.47689	−	0.852685i	−0.477234	−	0.878776i	$-0.658361\pi$
$887$	−43.9856	−	25.3951i	−1.47689	−	0.852685i	−0.999660	+	0.0260915i	$0.991694\pi$
$888$		0			0
$889$	−0.368839	+	0.638849i	−0.0123705	+	0.0214263i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.87279	−	5.57434i	0.0626705	−	0.186538i
$894$		0			0
$895$	4.69784	−	5.93531i	0.157031	−	0.198395i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−7.33263	+	12.7005i	−0.244557	+	0.423585i
$900$		0			0
$901$	17.7387			0.590962
$902$		0			0
$903$		0			0
$904$		0			0
$905$	17.1875	+	43.3265i	0.571333	+	1.44022i
$906$		0			0
$907$	−17.4646	+	10.0832i	−0.579902	+	0.334806i	−0.761094	−	0.648641i	$-0.775338\pi$
$907$	−17.4646	+	10.0832i	−0.579902	+	0.334806i	0.181193	+	0.983448i	$0.442004\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−47.2962			−1.56699			−0.783496	−	0.621397i	$-0.786566\pi$
$911$	−47.2962			−1.56699			−0.783496	+	0.621397i	$0.786566\pi$
$912$		0			0
$913$			11.4441i			0.378745i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	46.3919	−	26.7844i	1.53200	−	0.884498i
$918$		0			0
$919$	33.8678			1.11719			0.558597	−	0.829439i	$-0.311340\pi$
$919$	33.8678			1.11719			0.558597	+	0.829439i	$0.311340\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			18.9195i			0.622744i
$924$		0			0
$925$	26.7946	−	6.32224i	0.881001	−	0.207874i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.457146	+	0.791800i	0.0149985	+	0.0259781i	0.873427	−	0.486955i	$-0.161892\pi$
$929$	0.457146	+	0.791800i	0.0149985	+	0.0259781i	−0.858429	+	0.512933i	$0.828559\pi$
$930$		0			0
$931$	−4.81272	−	23.8054i	−0.157731	−	0.780191i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−4.71930	+	32.1068i	−0.154337	+	1.05000i
$936$		0			0
$937$	−45.0186	−	25.9915i	−1.47069	−	0.849106i	−0.471236	−	0.882007i	$-0.656192\pi$
$937$	−45.0186	−	25.9915i	−1.47069	−	0.849106i	−0.999459	+	0.0329014i	$0.989525\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−12.4228	+	21.5169i	−0.404972	+	0.701432i	−0.994318	−	0.106449i	$-0.966052\pi$
$941$	−12.4228	+	21.5169i	−0.404972	+	0.701432i	0.589346	+	0.807880i	$0.299385\pi$
$942$		0			0
$943$		−	68.3969i		−	2.22731i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	24.0042	−	13.8588i	0.780032	−	0.450352i	−0.0564097	−	0.998408i	$-0.517965\pi$
$947$	24.0042	−	13.8588i	0.780032	−	0.450352i	0.836442	+	0.548056i	$0.184632\pi$
$948$		0			0
$949$	−10.4909			−0.340550
$950$		0			0
$951$		0			0
$952$		0			0
$953$	14.3605	−	8.29103i	0.465182	−	0.268573i	−0.249039	−	0.968494i	$-0.580115\pi$
$953$	14.3605	−	8.29103i	0.465182	−	0.268573i	0.714221	+	0.699921i	$0.246781\pi$
$954$		0			0
$955$	6.36697	−	8.04411i	0.206030	−	0.260301i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−9.34072	+	16.1786i	−0.301627	+	0.522434i
$960$		0			0
$961$	−28.0802			−0.905813
$962$		0			0
$963$		0			0
$964$		0			0
$965$	6.54238	−	44.5098i	0.210607	−	1.43282i
$966$		0			0
$967$	−16.5612	+	9.56159i	−0.532571	+	0.307480i	−0.742063	−	0.670330i	$-0.766152\pi$
$967$	−16.5612	+	9.56159i	−0.532571	+	0.307480i	0.209492	+	0.977810i	$0.432819\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−7.56801	−	13.1082i	−0.242869	−	0.420661i	0.718661	−	0.695360i	$-0.244755\pi$
$971$	−7.56801	−	13.1082i	−0.242869	−	0.420661i	−0.961530	+	0.274699i	$0.911422\pi$
$972$		0			0
$973$	20.7782	+	11.9963i	0.666120	+	0.384584i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	5.83858i		−	0.186793i	−0.995629	−	0.0933964i	$-0.970228\pi$
$977$		−	5.83858i		−	0.186793i	0.995629	−	0.0933964i	$-0.0297724\pi$
$978$		0			0
$979$	−4.96873	+	8.60609i	−0.158801	+	0.275052i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−17.9231	+	10.3479i	−0.571657	+	0.330047i	−0.757811	−	0.652474i	$-0.773731\pi$
$983$	−17.9231	+	10.3479i	−0.571657	+	0.330047i	0.186154	+	0.982521i	$0.440398\pi$
$984$		0			0
$985$	−1.72428	−	1.36478i	−0.0549401	−	0.0434855i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	42.3778			1.34754
$990$		0			0
$991$	−22.9776	−	39.7984i	−0.729907	−	1.26424i	−0.956922	−	0.290345i	$-0.906230\pi$
$991$	−22.9776	−	39.7984i	−0.729907	−	1.26424i	0.227014	−	0.973891i	$-0.427104\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−9.63836	−	24.2965i	−0.305556	−	0.770250i
$996$		0			0
$997$	−6.31974	−	3.64870i	−0.200148	−	0.115556i	0.396576	−	0.918002i	$-0.370198\pi$
$997$	−6.31974	−	3.64870i	−0.200148	−	0.115556i	−0.596725	+	0.802446i	$0.703532\pi$
$998$		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.2629.4		20
3.2	odd	2		380.2.r.a.349.1	yes	20
5.4	even	2	inner	3420.2.bj.c.2629.10		20
15.2	even	4		1900.2.i.g.501.10		20
15.8	even	4		1900.2.i.g.501.1		20
15.14	odd	2		380.2.r.a.349.10	yes	20
19.11	even	3	inner	3420.2.bj.c.1189.10		20
57.11	odd	6		380.2.r.a.49.10	yes	20
95.49	even	6	inner	3420.2.bj.c.1189.4		20
285.68	even	12		1900.2.i.g.201.1		20
285.182	even	12		1900.2.i.g.201.10		20
285.239	odd	6		380.2.r.a.49.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.r.a.49.1	✓	20	285.239	odd	6
380.2.r.a.49.10	yes	20	57.11	odd	6
380.2.r.a.349.1	yes	20	3.2	odd	2
380.2.r.a.349.10	yes	20	15.14	odd	2
1900.2.i.g.201.1		20	285.68	even	12
1900.2.i.g.201.10		20	285.182	even	12
1900.2.i.g.501.1		20	15.8	even	4
1900.2.i.g.501.10		20	15.2	even	4
3420.2.bj.c.1189.4		20	95.49	even	6	inner
3420.2.bj.c.1189.10		20	19.11	even	3	inner
3420.2.bj.c.2629.4		20	1.1	even	1	trivial
3420.2.bj.c.2629.10		20	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.38776 + 1.75332i) q^{5} +3.54568i q^{7} +1.81575 q^{11} +(2.78308 + 1.60681i) q^{13} +(6.92193 - 3.99638i) q^{17} +(0.863760 + 4.27246i) q^{19} +(7.30026 + 4.21480i) q^{23} +(-1.14823 - 4.86637i) q^{25} +(4.29124 - 7.43265i) q^{29} -1.70874 q^{31} +(-6.21669 - 4.92056i) q^{35} +5.50608i q^{37} +(-4.05694 - 7.02683i) q^{41} +(4.35373 - 2.51363i) q^{43} +(-1.16834 - 0.674543i) q^{47} -5.57183 q^{49} +(1.92201 + 1.10967i) q^{53} +(-2.51983 + 3.18359i) q^{55} +(-0.960774 - 1.66411i) q^{59} +(2.83047 - 4.90251i) q^{61} +(-6.67950 + 2.64974i) q^{65} +(8.04360 + 4.64397i) q^{67} +(2.94365 + 5.09854i) q^{71} +(-2.82716 + 1.63226i) q^{73} +6.43807i q^{77} +(2.08739 + 3.61546i) q^{79} +6.30268i q^{83} +(-2.59909 + 17.6824i) q^{85} +(-2.73646 + 4.73968i) q^{89} +(-5.69723 + 9.86789i) q^{91} +(-8.68966 - 4.41472i) q^{95} +(6.91255 - 3.99096i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - q^{5} + 14 q^{19} + 9 q^{25} + 16 q^{29} + 8 q^{31} + 2 q^{35} - 26 q^{41} - 44 q^{49} - 12 q^{55} - 4 q^{59} + 2 q^{61} + 18 q^{65} + 2 q^{71} - 16 q^{79} - 39 q^{85} + 40 q^{89} - 4 q^{91} + 43 q^{95}+O(q^{100}) \) 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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