LMFDB - Embedded newform 1872.2.by.n.433.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1872,2,Mod(433,1872)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1872, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1872.433");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1872 = 2^{4} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1872.by (of order $6$, degree $2$, not 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:	$14.9479952584$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.195105024.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 4x^{5} - 20x^{4} + 12x^{3} + 45x^{2} - 108x + 81 $ x^8 - 4x^7 + 5x^6 + 4x^5 - 20x^4 + 12x^3 + 45x^2 - 108*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			433.2
Root			$0.560908 - 1.63871i$ of defining polynomial
Character	$\chi$	$=$	1872.433
Dual form			1872.2.by.n.1297.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61023i q^{5} +(0.971521 - 0.560908i) q^{7} +(0.971521 + 0.560908i) q^{11} +(-3.53796 + 0.694883i) q^{13} +(-2.77743 - 4.81064i) q^{17} +(1.45204 - 0.838335i) q^{19} +(1.63871 - 2.83834i) q^{23} -1.81333 q^{25} +(-0.167192 + 0.289586i) q^{29} +0.129717i q^{31} +(-1.46410 - 2.53590i) q^{35} +(-3.92356 - 2.26527i) q^{37} +(-4.96410 - 2.86603i) q^{41} +(2.24895 + 3.89529i) q^{43} -10.7985i q^{47} +(-2.87076 + 4.97231i) q^{49} -4.14771 q^{53} +(1.46410 - 2.53590i) q^{55} +(-0.549538 + 0.317276i) q^{59} +(-2.35387 - 4.07702i) q^{61} +(1.81381 + 9.23490i) q^{65} +(12.4372 + 7.18062i) q^{67} +(-7.45204 + 4.30244i) q^{71} -9.94462i q^{73} +1.25847 q^{77} -13.5970 q^{79} +5.75637i q^{83} +(-12.5569 + 7.24974i) q^{85} +(-12.4235 - 7.17272i) q^{89} +(-3.04743 + 2.65956i) q^{91} +(-2.18825 - 3.79016i) q^{95} +(7.80107 - 4.50395i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{7} + 6 q^{11} + 6 q^{13} + 6 q^{19} + 2 q^{23} - 20 q^{25} + 8 q^{29} + 16 q^{35} - 24 q^{37} - 12 q^{41} - 6 q^{43} + 2 q^{49} - 20 q^{53} - 16 q^{55} + 18 q^{59} - 4 q^{61} - 14 q^{65} + 42 q^{67}+ \cdots + 30 q^{97}+O(q^{100}) $ 8 * q + 6 * q^7 + 6 * q^11 + 6 * q^13 + 6 * q^19 + 2 * q^23 - 20 * q^25 + 8 * q^29 + 16 * q^35 - 24 * q^37 - 12 * q^41 - 6 * q^43 + 2 * q^49 - 20 * q^53 - 16 * q^55 + 18 * q^59 - 4 * q^61 - 14 * q^65 + 42 * q^67 - 54 * q^71 + 60 * q^77 - 16 * q^79 + 6 * q^85 + 18 * q^89 + 46 * q^91 + 16 * q^95 + 30 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1872\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$		−	2.61023i		−	1.16733i	−0.811994	−	0.583666i	$-0.801618\pi$
$5$		−	2.61023i		−	1.16733i	0.811994	−	0.583666i	$-0.198382\pi$
$6$		0			0
$7$	0.971521	−	0.560908i	0.367200	−	0.212003i	−0.305034	−	0.952341i	$-0.598668\pi$
$7$	0.971521	−	0.560908i	0.367200	−	0.212003i	0.672235	+	0.740338i	$0.265335\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.971521	+	0.560908i	0.292925	+	0.169120i	0.639260	−	0.768991i	$-0.279241\pi$
$11$	0.971521	+	0.560908i	0.292925	+	0.169120i	−0.346335	+	0.938111i	$0.612574\pi$
$12$		0			0
$13$	−3.53796	+	0.694883i	−0.981253	+	0.192726i
$13$	−3.53796	+	0.694883i	−0.981253	+	0.192726i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.77743	−	4.81064i	−0.673625	−	1.16675i	−0.976869	−	0.213840i	$-0.931403\pi$
$17$	−2.77743	−	4.81064i	−0.673625	−	1.16675i	0.303244	−	0.952913i	$-0.401930\pi$
$18$		0			0
$19$	1.45204	−	0.838335i	0.333121	−	0.192327i	−0.324105	−	0.946021i	$-0.605063\pi$
$19$	1.45204	−	0.838335i	0.333121	−	0.192327i	0.657226	+	0.753694i	$0.271730\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.63871	−	2.83834i	0.341695	−	0.591834i	−0.643052	−	0.765822i	$-0.722332\pi$
$23$	1.63871	−	2.83834i	0.341695	−	0.591834i	0.984748	+	0.173988i	$0.0556656\pi$
$24$		0			0
$25$	−1.81333			−0.362665
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.167192	+	0.289586i	−0.0310468	+	0.0537747i	−0.881131	−	0.472872i	$-0.843217\pi$
$29$	−0.167192	+	0.289586i	−0.0310468	+	0.0537747i	0.850084	+	0.526646i	$0.176551\pi$
$30$		0			0
$31$			0.129717i			0.0232978i	0.999932	+	0.0116489i	$0.00370805\pi$
$31$			0.129717i			0.0232978i	−0.999932	+	0.0116489i	$0.996292\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.46410	−	2.53590i	−0.247478	−	0.428645i
$36$		0			0
$37$	−3.92356	−	2.26527i	−0.645029	−	0.372408i	0.141520	−	0.989935i	$-0.454801\pi$
$37$	−3.92356	−	2.26527i	−0.645029	−	0.372408i	−0.786549	+	0.617528i	$0.788134\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.96410	−	2.86603i	−0.775262	−	0.447598i	0.0594862	−	0.998229i	$-0.481054\pi$
$41$	−4.96410	−	2.86603i	−0.775262	−	0.447598i	−0.834749	+	0.550631i	$0.814387\pi$
$42$		0			0
$43$	2.24895	+	3.89529i	0.342961	+	0.594027i	0.984981	−	0.172661i	$-0.0552367\pi$
$43$	2.24895	+	3.89529i	0.342961	+	0.594027i	−0.642020	+	0.766688i	$0.721903\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	10.7985i		−	1.57512i	−0.616237	−	0.787561i	$-0.711344\pi$
$47$		−	10.7985i		−	1.57512i	0.616237	−	0.787561i	$-0.288656\pi$
$48$		0			0
$49$	−2.87076	+	4.97231i	−0.410109	+	0.710330i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−4.14771			−0.569732			−0.284866	−	0.958567i	$-0.591949\pi$
$53$	−4.14771			−0.569732			−0.284866	+	0.958567i	$0.591949\pi$
$54$		0			0
$55$	1.46410	−	2.53590i	0.197419	−	0.341940i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.549538	+	0.317276i	−0.0715438	+	0.0413058i	−0.535345	−	0.844633i	$-0.679818\pi$
$59$	−0.549538	+	0.317276i	−0.0715438	+	0.0413058i	0.463801	+	0.885939i	$0.346485\pi$
$60$		0			0
$61$	−2.35387	−	4.07702i	−0.301382	−	0.522009i	0.675067	−	0.737756i	$-0.264115\pi$
$61$	−2.35387	−	4.07702i	−0.301382	−	0.522009i	−0.976449	+	0.215748i	$0.930781\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.81381	+	9.23490i	0.224975	+	1.14545i
$66$		0			0
$67$	12.4372	+	7.18062i	1.51945	+	0.877252i	0.999738	+	0.0229086i	$0.00729269\pi$
$67$	12.4372	+	7.18062i	1.51945	+	0.877252i	0.519708	+	0.854344i	$0.326041\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−7.45204	+	4.30244i	−0.884394	+	0.510605i	−0.872105	−	0.489319i	$-0.837245\pi$
$71$	−7.45204	+	4.30244i	−0.884394	+	0.510605i	−0.0122896	+	0.999924i	$0.503912\pi$
$72$		0			0
$73$		−	9.94462i		−	1.16393i	−0.813214	−	0.581965i	$-0.802284\pi$
$73$		−	9.94462i		−	1.16393i	0.813214	−	0.581965i	$-0.197716\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.25847			0.143416
$78$		0			0
$79$	−13.5970			−1.52978			−0.764889	−	0.644162i	$-0.777206\pi$
$79$	−13.5970			−1.52978			−0.764889	+	0.644162i	$0.777206\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$			5.75637i			0.631843i	0.948785	+	0.315922i	$0.102314\pi$
$83$			5.75637i			0.631843i	−0.948785	+	0.315922i	$0.897686\pi$
$84$		0			0
$85$	−12.5569	+	7.24974i	−1.36199	+	0.786344i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−12.4235	−	7.17272i	−1.31689	−	0.760307i	−0.333663	−	0.942692i	$-0.608285\pi$
$89$	−12.4235	−	7.17272i	−1.31689	−	0.760307i	−0.983227	+	0.182386i	$0.941618\pi$
$90$		0			0
$91$	−3.04743	+	2.65956i	−0.319458	+	0.278798i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.18825	−	3.79016i	−0.224510	−	0.388863i
$96$		0			0
$97$	7.80107	−	4.50395i	0.792079	−	0.457307i	−0.0486151	−	0.998818i	$-0.515481\pi$
$97$	7.80107	−	4.50395i	0.792079	−	0.457307i	0.840694	+	0.541511i	$0.182147\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.44462	−	2.50215i	0.143745	−	0.248974i	−0.785159	−	0.619294i	$-0.787419\pi$
$101$	1.44462	−	2.50215i	0.143745	−	0.248974i	0.928904	+	0.370321i	$0.120752\pi$
$102$		0			0
$103$	−5.22047			−0.514388			−0.257194	−	0.966360i	$-0.582798\pi$
$103$	−5.22047			−0.514388			−0.257194	+	0.966360i	$0.582798\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.91614	+	5.05090i	−0.281914	+	0.488289i	−0.971856	−	0.235575i	$-0.924303\pi$
$107$	−2.91614	+	5.05090i	−0.281914	+	0.488289i	0.689942	+	0.723865i	$0.257636\pi$
$108$		0			0
$109$			2.92820i			0.280471i	0.990118	+	0.140236i	$0.0447860\pi$
$109$			2.92820i			0.280471i	−0.990118	+	0.140236i	$0.955214\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	2.44304	+	4.23147i	0.229822	+	0.398064i	0.957755	−	0.287585i	$-0.0928522\pi$
$113$	2.44304	+	4.23147i	0.229822	+	0.398064i	−0.727933	+	0.685648i	$0.759519\pi$
$114$		0			0
$115$	−7.40872	−	4.27743i	−0.690867	−	0.398872i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−5.39666	−	3.11576i	−0.494711	−	0.285621i
$120$		0			0
$121$	−4.87076	−	8.43641i	−0.442797	−	0.766946i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	8.31797i		−	0.743982i
$126$		0			0
$127$	5.15977	−	8.93699i	0.457856	−	0.793030i	−0.540992	−	0.841028i	$-0.681951\pi$
$127$	5.15977	−	8.93699i	0.457856	−	0.793030i	0.998847	+	0.0479985i	$0.0152843\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−0.110761			−0.00967723			−0.00483861	−	0.999988i	$-0.501540\pi$
$131$	−0.110761			−0.00967723			−0.00483861	+	0.999988i	$0.501540\pi$
$132$		0			0
$133$	0.940458	−	1.62892i	0.0815480	−	0.141245i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.02106	+	3.47626i	−0.514414	+	0.296997i	−0.734646	−	0.678451i	$-0.762652\pi$
$137$	−6.02106	+	3.47626i	−0.514414	+	0.296997i	0.220232	+	0.975447i	$0.429318\pi$
$138$		0			0
$139$	−5.21515	−	9.03291i	−0.442344	−	0.766161i	0.555519	−	0.831504i	$-0.312519\pi$
$139$	−5.21515	−	9.03291i	−0.442344	−	0.766161i	−0.997863	+	0.0653421i	$0.979186\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−3.82697	−	1.30938i	−0.320027	−	0.109495i
$144$		0			0
$145$	0.755887	+	0.436411i	0.0627730	+	0.0362420i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	8.31587	−	4.80117i	0.681262	−	0.393327i	−0.119068	−	0.992886i	$-0.537991\pi$
$149$	8.31587	−	4.80117i	0.681262	−	0.393327i	0.800330	+	0.599559i	$0.204657\pi$
$150$		0			0
$151$		−	13.7267i		−	1.11706i	−0.829484	−	0.558531i	$-0.811365\pi$
$151$		−	13.7267i		−	1.11706i	0.829484	−	0.558531i	$-0.188635\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.338591			0.0271963
$156$		0			0
$157$	8.96200			0.715245			0.357623	−	0.933866i	$-0.383587\pi$
$157$	8.96200			0.715245			0.357623	+	0.933866i	$0.383587\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	3.67667i		−	0.289762i
$162$		0			0
$163$	1.89972	−	1.09681i	0.148798	−	0.0859085i	−0.423753	−	0.905778i	$-0.639287\pi$
$163$	1.89972	−	1.09681i	0.148798	−	0.0859085i	0.572550	+	0.819869i	$0.305954\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	12.9715	+	7.48911i	1.00377	+	0.579525i	0.909361	−	0.416009i	$-0.136572\pi$
$167$	12.9715	+	7.48911i	1.00377	+	0.579525i	0.0944059	+	0.995534i	$0.469905\pi$
$168$		0			0
$169$	12.0343	−	4.91693i	0.925714	−	0.378225i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.99742	+	3.45963i	0.151861	+	0.263030i	0.931912	−	0.362686i	$-0.118140\pi$
$173$	1.99742	+	3.45963i	0.151861	+	0.263030i	−0.780051	+	0.625716i	$0.784807\pi$
$174$		0			0
$175$	−1.76168	+	1.01711i	−0.133171	+	0.0768862i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−4.30591	+	7.45805i	−0.321839	+	0.557441i	−0.980867	−	0.194677i	$-0.937634\pi$
$179$	−4.30591	+	7.45805i	−0.321839	+	0.557441i	0.659029	+	0.752118i	$0.270967\pi$
$180$		0			0
$181$	15.6308			1.16183			0.580913	−	0.813966i	$-0.302696\pi$
$181$	15.6308			1.16183			0.580913	+	0.813966i	$0.302696\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−5.91288	+	10.2414i	−0.434724	+	0.752964i
$186$		0			0
$187$		−	6.23152i		−	0.455694i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−13.5280	−	23.4311i	−0.978848	−	1.69541i	−0.666602	−	0.745414i	$-0.732252\pi$
$191$	−13.5280	−	23.4311i	−0.978848	−	1.69541i	−0.312246	−	0.950001i	$-0.601081\pi$
$192$		0			0
$193$	20.7426	+	11.9757i	1.49308	+	0.862032i	0.999969	−	0.00793192i	$-0.00252484\pi$
$193$	20.7426	+	11.9757i	1.49308	+	0.862032i	0.493115	+	0.869964i	$0.335858\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−8.95941	−	5.17272i	−0.638332	−	0.368541i	0.145640	−	0.989338i	$-0.453476\pi$
$197$	−8.95941	−	5.17272i	−0.638332	−	0.368541i	−0.783972	+	0.620797i	$0.786809\pi$
$198$		0			0
$199$	−6.78642	−	11.7544i	−0.481077	−	0.833250i	0.518687	−	0.854964i	$-0.326421\pi$
$199$	−6.78642	−	11.7544i	−0.481077	−	0.833250i	−0.999764	+	0.0217145i	$0.993088\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$			0.375118i			0.0263281i
$204$		0			0
$205$	−7.48100	+	12.9575i	−0.522496	+	0.904989i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.88092			0.130106
$210$		0			0
$211$	−0.973098	+	1.68546i	−0.0669909	+	0.116032i	−0.897575	−	0.440861i	$-0.854673\pi$
$211$	−0.973098	+	1.68546i	−0.0669909	+	0.116032i	0.830585	+	0.556893i	$0.188006\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	10.1676	−	5.87028i	0.693427	−	0.400350i
$216$		0			0
$217$	0.0727592	+	0.126023i	0.00493922	+	0.00855498i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	13.1693	+	15.0899i	0.885860	+	1.01505i
$222$		0			0
$223$	20.7156	+	11.9602i	1.38722	+	0.800911i	0.993001	−	0.118106i	$-0.0376823\pi$
$223$	20.7156	+	11.9602i	1.38722	+	0.800911i	0.394218	+	0.919017i	$0.371016\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−15.3084	+	8.83834i	−1.01606	+	0.586621i	−0.912959	−	0.408050i	$-0.866209\pi$
$227$	−15.3084	+	8.83834i	−1.01606	+	0.586621i	−0.103098	+	0.994671i	$0.532875\pi$
$228$		0			0
$229$		−	10.9282i		−	0.722156i	−0.932536	−	0.361078i	$-0.882409\pi$
$229$		−	10.9282i		−	0.722156i	0.932536	−	0.361078i	$-0.117591\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	11.5970			0.759743			0.379871	−	0.925039i	$-0.375968\pi$
$233$	11.5970			0.759743			0.379871	+	0.925039i	$0.375968\pi$
$234$		0			0
$235$	−28.1866			−1.83869
$236$		0			0
$237$		0			0
$238$		0			0
$239$			18.0221i			1.16575i	0.812561	+	0.582877i	$0.198073\pi$
$239$			18.0221i			1.16575i	−0.812561	+	0.582877i	$0.801927\pi$
$240$		0			0
$241$	−0.709837	+	0.409825i	−0.0457246	+	0.0263991i	−0.522688	−	0.852524i	$-0.675071\pi$
$241$	−0.709837	+	0.409825i	−0.0457246	+	0.0263991i	0.476963	+	0.878923i	$0.341737\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	12.9789	+	7.49337i	0.829191	+	0.478734i
$246$		0			0
$247$	−4.55471	+	3.97499i	−0.289809	+	0.252923i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	7.17873	+	12.4339i	0.453117	+	0.784822i	0.998578	−	0.0533143i	$-0.0169785\pi$
$251$	7.17873	+	12.4339i	0.453117	+	0.784822i	−0.545460	+	0.838137i	$0.683645\pi$
$252$		0			0
$253$	3.18409	−	1.83834i	0.200182	−	0.115575i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	10.2985	−	17.8375i	0.642402	−	1.11267i	−0.342493	−	0.939520i	$-0.611271\pi$
$257$	10.2985	−	17.8375i	0.642402	−	1.11267i	0.984895	−	0.173152i	$-0.0553953\pi$
$258$		0			0
$259$	−5.08243			−0.315807
$260$		0			0
$261$		0			0
$262$		0			0
$263$	14.5115	−	25.1347i	0.894820	−	1.54987i	0.0607920	−	0.998150i	$-0.480637\pi$
$263$	14.5115	−	25.1347i	0.894820	−	1.54987i	0.834028	−	0.551723i	$-0.186029\pi$
$264$		0			0
$265$			10.8265i			0.665066i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−4.31381	−	7.47173i	−0.263017	−	0.455560i	0.704025	−	0.710175i	$-0.251384\pi$
$269$	−4.31381	−	7.47173i	−0.263017	−	0.455560i	−0.967042	+	0.254616i	$0.918051\pi$
$270$		0			0
$271$	13.8459	+	7.99395i	0.841080	+	0.485598i	0.857631	−	0.514265i	$-0.171935\pi$
$271$	13.8459	+	7.99395i	0.841080	+	0.485598i	−0.0165513	+	0.999863i	$0.505269\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.76168	−	1.01711i	−0.106234	−	0.0613340i
$276$		0			0
$277$	−14.3728	−	24.8945i	−0.863579	−	1.49576i	−0.868451	−	0.495775i	$-0.834884\pi$
$277$	−14.3728	−	24.8945i	−0.863579	−	1.49576i	0.00487180	−	0.999988i	$-0.498449\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$			5.83386i			0.348019i	0.984744	+	0.174009i	$0.0556723\pi$
$281$			5.83386i			0.348019i	−0.984744	+	0.174009i	$0.944328\pi$
$282$		0			0
$283$	−13.8459	+	23.9818i	−0.823055	+	1.42557i	0.0803425	+	0.996767i	$0.474399\pi$
$283$	−13.8459	+	23.9818i	−0.823055	+	1.42557i	−0.903397	+	0.428805i	$0.858935\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−6.43031			−0.379569
$288$		0			0
$289$	−6.92820	+	12.0000i	−0.407541	+	0.705882i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	13.7980	−	7.96626i	0.806085	−	0.465394i	−0.0395092	−	0.999219i	$-0.512579\pi$
$293$	13.7980	−	7.96626i	0.806085	−	0.465394i	0.845595	+	0.533826i	$0.179246\pi$
$294$		0			0
$295$	0.828165	+	1.43442i	0.0482176	+	0.0835154i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.82539	+	11.1806i	−0.221228	+	0.646592i
$300$		0			0
$301$	4.36980	+	2.52291i	0.251871	+	0.145418i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−10.6420	+	6.14415i	−0.609358	+	0.351813i
$306$		0			0
$307$			20.3955i			1.16403i	0.813178	+	0.582015i	$0.197736\pi$
$307$			20.3955i			1.16403i	−0.813178	+	0.582015i	$0.802264\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	12.9989			0.737103			0.368551	−	0.929607i	$-0.379854\pi$
$311$	12.9989			0.737103			0.368551	+	0.929607i	$0.379854\pi$
$312$		0			0
$313$	−9.51274			−0.537692			−0.268846	−	0.963183i	$-0.586642\pi$
$313$	−9.51274			−0.537692			−0.268846	+	0.963183i	$0.586642\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			19.1354i			1.07475i	0.843343	+	0.537376i	$0.180584\pi$
$317$			19.1354i			1.07475i	−0.843343	+	0.537376i	$0.819416\pi$
$318$		0			0
$319$	−0.324862	+	0.187559i	−0.0181888	+	0.0105013i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−8.06587	−	4.65683i	−0.448797	−	0.259113i
$324$		0			0
$325$	6.41547	−	1.26005i	0.355866	−	0.0698949i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−6.05696	−	10.4910i	−0.333931	−	0.578385i
$330$		0			0
$331$	9.78896	−	5.65166i	0.538050	−	0.310643i	−0.206238	−	0.978502i	$-0.566122\pi$
$331$	9.78896	−	5.65166i	0.538050	−	0.310643i	0.744288	+	0.667858i	$0.232789\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	18.7431	−	32.4640i	1.02405	−	1.77370i
$336$		0			0
$337$	−5.14035			−0.280013			−0.140006	−	0.990151i	$-0.544712\pi$
$337$	−5.14035			−0.280013			−0.140006	+	0.990151i	$0.544712\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−0.0727592	+	0.126023i	−0.00394013	+	0.00682451i
$342$		0			0
$343$			14.2937i			0.771785i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.36129	+	7.55397i	0.234126	+	0.405518i	0.959018	−	0.283344i	$-0.0914438\pi$
$347$	4.36129	+	7.55397i	0.234126	+	0.405518i	−0.724892	+	0.688862i	$0.758110\pi$
$348$		0			0
$349$	23.4625	+	13.5461i	1.25592	+	0.725104i	0.972278	−	0.233827i	$-0.0751248\pi$
$349$	23.4625	+	13.5461i	1.25592	+	0.725104i	0.283639	+	0.958931i	$0.408458\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	19.9524	+	11.5195i	1.06196	+	0.613123i	0.925974	−	0.377588i	$-0.123246\pi$
$353$	19.9524	+	11.5195i	1.06196	+	0.613123i	0.135986	+	0.990711i	$0.456580\pi$
$354$		0			0
$355$	11.2304	+	19.4516i	0.596046	+	1.03238i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			1.13392i			0.0598462i	0.999552	+	0.0299231i	$0.00952624\pi$
$359$			1.13392i			0.0598462i	−0.999552	+	0.0299231i	$0.990474\pi$
$360$		0			0
$361$	−8.09439	+	14.0199i	−0.426020	+	0.737889i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−25.9578			−1.35869
$366$		0			0
$367$	14.3992	−	24.9401i	0.751632	−	1.30186i	−0.195399	−	0.980724i	$-0.562600\pi$
$367$	14.3992	−	24.9401i	0.751632	−	1.30186i	0.947031	−	0.321141i	$-0.104066\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−4.02959	+	2.32648i	−0.209206	+	0.120785i
$372$		0			0
$373$	11.8939	+	20.6008i	0.615842	+	1.06667i	0.990236	+	0.139400i	$0.0445173\pi$
$373$	11.8939	+	20.6008i	0.615842	+	1.06667i	−0.374394	+	0.927270i	$0.622149\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.390291	−	1.14072i	0.0201010	−	0.0587501i
$378$		0			0
$379$	12.9434	+	7.47289i	0.664859	+	0.383856i	0.794126	−	0.607753i	$-0.207929\pi$
$379$	12.9434	+	7.47289i	0.664859	+	0.383856i	−0.129267	+	0.991610i	$0.541262\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−3.92940	+	2.26864i	−0.200783	+	0.115922i	−0.597021	−	0.802226i	$-0.703649\pi$
$383$	−3.92940	+	2.26864i	−0.200783	+	0.115922i	0.396238	+	0.918148i	$0.370316\pi$
$384$		0			0
$385$		−	3.28491i		−	0.167414i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	9.51685			0.482524			0.241262	−	0.970460i	$-0.422439\pi$
$389$	9.51685			0.482524			0.241262	+	0.970460i	$0.422439\pi$
$390$		0			0
$391$	−18.2056			−0.920698
$392$		0			0
$393$		0			0
$394$		0			0
$395$			35.4913i			1.78576i
$396$		0			0
$397$	−29.8307	+	17.2227i	−1.49716	+	0.864385i	−0.999995	−	0.00327253i	$-0.998958\pi$
$397$	−29.8307	+	17.2227i	−1.49716	+	0.864385i	−0.497163	+	0.867657i	$0.665625\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	12.2605	+	7.07859i	0.612259	+	0.353488i	0.773849	−	0.633370i	$-0.218329\pi$
$401$	12.2605	+	7.07859i	0.612259	+	0.353488i	−0.161590	+	0.986858i	$0.551662\pi$
$402$		0			0
$403$	−0.0901380	−	0.458933i	−0.00449009	−	0.0228611i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.54121	−	4.40151i	−0.125963	−	0.218175i
$408$		0			0
$409$	−0.299539	+	0.172939i	−0.0148112	+	0.00855127i	−0.507387	−	0.861718i	$-0.669389\pi$
$409$	−0.299539	+	0.172939i	−0.0148112	+	0.00855127i	0.492576	+	0.870269i	$0.336055\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−0.355925	+	0.616481i	−0.0175139	+	0.0303350i
$414$		0			0
$415$	15.0255			0.737571
$416$		0			0
$417$		0			0
$418$		0			0
$419$	6.98890	−	12.1051i	0.341430	−	0.591374i	−0.643268	−	0.765641i	$-0.722422\pi$
$419$	6.98890	−	12.1051i	0.341430	−	0.591374i	0.984699	+	0.174266i	$0.0557554\pi$
$420$		0			0
$421$		−	22.1609i		−	1.08006i	−0.841647	−	0.540028i	$-0.818414\pi$
$421$		−	22.1609i		−	1.08006i	0.841647	−	0.540028i	$-0.181586\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	5.03638	+	8.72327i	0.244300	+	0.423141i
$426$		0			0
$427$	−4.57366	−	2.64061i	−0.221335	−	0.127788i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	22.2109	+	12.8235i	1.06986	+	0.617686i	0.928144	−	0.372221i	$-0.121404\pi$
$431$	22.2109	+	12.8235i	1.06986	+	0.617686i	0.141719	+	0.989907i	$0.454737\pi$
$432$		0			0
$433$	−5.07802	−	8.79538i	−0.244034	−	0.422679i	0.717826	−	0.696223i	$-0.245137\pi$
$433$	−5.07802	−	8.79538i	−0.244034	−	0.422679i	−0.961860	+	0.273544i	$0.911804\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		−	5.49516i		−	0.262869i
$438$		0			0
$439$	10.6982	−	18.5298i	0.510598	−	0.884381i	−0.489327	−	0.872100i	$-0.662757\pi$
$439$	10.6982	−	18.5298i	0.510598	−	0.884381i	0.999925	−	0.0122808i	$-0.00390919\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	10.6688			0.506889			0.253444	−	0.967350i	$-0.418437\pi$
$443$	10.6688			0.506889			0.253444	+	0.967350i	$0.418437\pi$
$444$		0			0
$445$	−18.7225	+	32.4283i	−0.887531	+	1.53725i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	8.62407	−	4.97911i	0.406995	−	0.234979i	−0.282503	−	0.959266i	$-0.591165\pi$
$449$	8.62407	−	4.97911i	0.406995	−	0.234979i	0.689498	+	0.724288i	$0.257831\pi$
$450$		0			0
$451$	−3.21515	−	5.56881i	−0.151396	−	0.262225i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	6.94208	+	7.95452i	0.325450	+	0.372914i
$456$		0			0
$457$	−23.2035	−	13.3966i	−1.08542	−	0.626665i	−0.153063	−	0.988216i	$-0.548914\pi$
$457$	−23.2035	−	13.3966i	−1.08542	−	0.626665i	−0.932352	+	0.361552i	$0.882247\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−27.7410	+	16.0163i	−1.29203	+	0.745952i	−0.979013	−	0.203796i	$-0.934672\pi$
$461$	−27.7410	+	16.0163i	−1.29203	+	0.745952i	−0.313014	+	0.949749i	$0.601339\pi$
$462$		0			0
$463$			21.7564i			1.01110i	0.862796	+	0.505552i	$0.168711\pi$
$463$			21.7564i			1.01110i	−0.862796	+	0.505552i	$0.831289\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	33.7322			1.56094			0.780469	−	0.625195i	$-0.214980\pi$
$467$	33.7322			1.56094			0.780469	+	0.625195i	$0.214980\pi$
$468$		0			0
$469$	16.1107			0.743922
$470$		0			0
$471$		0			0
$472$		0			0
$473$			5.04581i			0.232007i
$474$		0			0
$475$	−2.63302	+	1.52017i	−0.120811	+	0.0697504i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−9.17041	−	5.29454i	−0.419007	−	0.241914i	0.275646	−	0.961259i	$-0.411108\pi$
$479$	−9.17041	−	5.29454i	−0.419007	−	0.241914i	−0.694652	+	0.719346i	$0.744442\pi$
$480$		0			0
$481$	15.4555	+	5.28801i	0.704709	+	0.241112i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−11.7564	−	20.3626i	−0.533829	−	0.924619i
$486$		0			0
$487$	19.0612	−	11.0050i	0.863746	−	0.498684i	−0.00151867	−	0.999999i	$-0.500483\pi$
$487$	19.0612	−	11.0050i	0.863746	−	0.498684i	0.865265	+	0.501315i	$0.167150\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−8.25727	+	14.3020i	−0.372645	+	0.645441i	−0.989972	−	0.141266i	$-0.954883\pi$
$491$	−8.25727	+	14.3020i	−0.372645	+	0.645441i	0.617326	+	0.786707i	$0.288216\pi$
$492$		0			0
$493$	1.85746			0.0836557
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.82654	+	8.35982i	−0.216500	+	0.374989i
$498$		0			0
$499$			11.1236i			0.497960i	0.968509	+	0.248980i	$0.0800954\pi$
$499$			11.1236i			0.497960i	−0.968509	+	0.248980i	$0.919905\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	14.6361	+	25.3504i	0.652591	+	1.13032i	0.982492	+	0.186305i	$0.0596512\pi$
$503$	14.6361	+	25.3504i	0.652591	+	1.13032i	−0.329901	+	0.944015i	$0.607015\pi$
$504$		0			0
$505$	−6.53121	−	3.77080i	−0.290635	−	0.167798i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−24.4571	−	14.1203i	−1.08404	−	0.625871i	−0.152057	−	0.988372i	$-0.548590\pi$
$509$	−24.4571	−	14.1203i	−1.08404	−	0.625871i	−0.931983	+	0.362501i	$0.881923\pi$
$510$		0			0
$511$	−5.57802	−	9.66141i	−0.246757	−	0.427396i
$512$		0			0
$513$		0			0
$514$		0			0
$515$			13.6267i			0.600462i
$516$		0			0
$517$	6.05696	−	10.4910i	0.266385	−	0.461392i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	18.6401			0.816636			0.408318	−	0.912840i	$-0.366116\pi$
$521$	18.6401			0.816636			0.408318	+	0.912840i	$0.366116\pi$
$522$		0			0
$523$	17.6561	−	30.5812i	0.772047	−	1.33722i	−0.164392	−	0.986395i	$-0.552566\pi$
$523$	17.6561	−	30.5812i	0.772047	−	1.33722i	0.936439	−	0.350830i	$-0.114100\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.624022	−	0.360279i	0.0271828	−	0.0156940i
$528$		0			0
$529$	6.12924	+	10.6161i	0.266489	+	0.461572i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	19.5543	+	6.69041i	0.846992	+	0.289794i
$534$		0			0
$535$	13.1840	+	7.61181i	0.569996	+	0.329087i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−5.57802	+	3.22047i	−0.240262	+	0.138715i
$540$		0			0
$541$		−	45.2196i		−	1.94414i	−0.234682	−	0.972072i	$-0.575405\pi$
$541$		−	45.2196i		−	1.94414i	0.234682	−	0.972072i	$-0.424595\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	7.64330			0.327403
$546$		0			0
$547$	37.8808			1.61967			0.809834	−	0.586660i	$-0.199557\pi$
$547$	37.8808			1.61967			0.809834	+	0.586660i	$0.199557\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$			0.560653i			0.0238846i
$552$		0			0
$553$	−13.2097	+	7.62665i	−0.561736	+	0.324318i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	17.8759	+	10.3206i	0.757426	+	0.437300i	0.828371	−	0.560180i	$-0.189268\pi$
$557$	17.8759	+	10.3206i	0.757426	+	0.437300i	−0.0709450	+	0.997480i	$0.522601\pi$
$558$		0			0
$559$	−10.6635	−	12.2186i	−0.451016	−	0.516793i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−10.2300	−	17.7189i	−0.431143	−	0.746761i	0.565829	−	0.824522i	$-0.308556\pi$
$563$	−10.2300	−	17.7189i	−0.431143	−	0.746761i	−0.996972	+	0.0777613i	$0.975223\pi$
$564$		0			0
$565$	11.0451	−	6.37691i	0.464673	−	0.268279i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	10.5681	−	18.3044i	0.443037	−	0.767362i	−0.554877	−	0.831933i	$-0.687235\pi$
$569$	10.5681	−	18.3044i	0.443037	−	0.767362i	0.997913	+	0.0645708i	$0.0205678\pi$
$570$		0			0
$571$	13.9221			0.582621			0.291310	−	0.956629i	$-0.405909\pi$
$571$	13.9221			0.582621			0.291310	+	0.956629i	$0.405909\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−2.97152	+	5.14683i	−0.123921	+	0.214637i
$576$		0			0
$577$		−	26.2420i		−	1.09247i	−0.837633	−	0.546234i	$-0.816061\pi$
$577$		−	26.2420i		−	1.09247i	0.837633	−	0.546234i	$-0.183939\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	3.22879	+	5.59243i	0.133953	+	0.232013i
$582$		0			0
$583$	−4.02959	−	2.32648i	−0.166889	−	0.0963531i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	21.3670	+	12.3362i	0.881910	+	0.509171i	0.871288	−	0.490773i	$-0.163285\pi$
$587$	21.3670	+	12.3362i	0.881910	+	0.509171i	0.0106221	+	0.999944i	$0.496619\pi$
$588$		0			0
$589$	0.108746	+	0.188354i	0.00448081	+	0.00776099i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	40.3506i		−	1.65700i	−0.559988	−	0.828501i	$-0.689194\pi$
$593$		−	40.3506i		−	1.65700i	0.559988	−	0.828501i	$-0.310806\pi$
$594$		0			0
$595$	−8.13287	+	14.0865i	−0.333415	+	0.577492i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−4.96104			−0.202702			−0.101351	−	0.994851i	$-0.532317\pi$
$599$	−4.96104			−0.202702			−0.101351	+	0.994851i	$0.532317\pi$
$600$		0			0
$601$	7.73846	−	13.4034i	0.315658	−	0.546737i	−0.663919	−	0.747805i	$-0.731108\pi$
$601$	7.73846	−	13.4034i	0.315658	−	0.546737i	0.979577	+	0.201068i	$0.0644413\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−22.0210	+	12.7138i	−0.895282	+	0.516891i
$606$		0			0
$607$	11.2167	+	19.4279i	0.455273	+	0.788556i	0.998704	−	0.0508979i	$-0.0162083\pi$
$607$	11.2167	+	19.4279i	0.455273	+	0.788556i	−0.543431	+	0.839454i	$0.682875\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	7.50368	+	38.2046i	0.303566	+	1.54559i
$612$		0			0
$613$	14.3634	+	8.29274i	0.580134	+	0.334941i	0.761187	−	0.648533i	$-0.224617\pi$
$613$	14.3634	+	8.29274i	0.580134	+	0.334941i	−0.181053	+	0.983473i	$0.557950\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−28.6107	+	16.5184i	−1.15182	+	0.665005i	−0.949331	−	0.314279i	$-0.898237\pi$
$617$	−28.6107	+	16.5184i	−1.15182	+	0.665005i	−0.202492	+	0.979284i	$0.564904\pi$
$618$		0			0
$619$		−	35.3913i		−	1.42249i	−0.702942	−	0.711247i	$-0.748131\pi$
$619$		−	35.3913i		−	1.42249i	0.702942	−	0.711247i	$-0.251869\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−16.0929			−0.644750
$624$		0			0
$625$	−30.7785			−1.23114
$626$		0			0
$627$		0			0
$628$		0			0
$629$			25.1665i			1.00345i
$630$		0			0
$631$	5.58850	−	3.22652i	0.222475	−	0.128446i	−0.384621	−	0.923075i	$-0.625668\pi$
$631$	5.58850	−	3.22652i	0.222475	−	0.128446i	0.607096	+	0.794629i	$0.292334\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−23.3276	−	13.4682i	−0.925729	−	0.534470i
$636$		0			0
$637$	6.70147	−	19.5867i	0.265522	−	0.776052i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	10.8871	+	18.8571i	0.430016	+	0.744810i	0.996874	−	0.0790058i	$-0.0251746\pi$
$641$	10.8871	+	18.8571i	0.430016	+	0.744810i	−0.566858	+	0.823815i	$0.691841\pi$
$642$		0			0
$643$	−34.8552	+	20.1237i	−1.37456	+	0.793600i	−0.991498	−	0.130125i	$-0.958462\pi$
$643$	−34.8552	+	20.1237i	−1.37456	+	0.793600i	−0.383058	+	0.923724i	$0.625129\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	18.8105	−	32.5808i	0.739519	−	1.28088i	−0.213193	−	0.977010i	$-0.568386\pi$
$647$	18.8105	−	32.5808i	0.739519	−	1.28088i	0.952712	−	0.303874i	$-0.0982803\pi$
$648$		0			0
$649$	−0.711850			−0.0279426
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−15.3559	+	26.5972i	−0.600924	+	1.04083i	0.391758	+	0.920068i	$0.371867\pi$
$653$	−15.3559	+	26.5972i	−0.600924	+	1.04083i	−0.992681	+	0.120762i	$0.961466\pi$
$654$		0			0
$655$			0.289112i			0.0112965i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−6.88489	−	11.9250i	−0.268197	−	0.464531i	0.700199	−	0.713947i	$-0.253094\pi$
$659$	−6.88489	−	11.9250i	−0.268197	−	0.464531i	−0.968396	+	0.249417i	$0.919761\pi$
$660$		0			0
$661$	−8.85492	−	5.11239i	−0.344416	−	0.198849i	0.317807	−	0.948155i	$-0.397054\pi$
$661$	−8.85492	−	5.11239i	−0.344416	−	0.198849i	−0.662223	+	0.749307i	$0.730387\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−4.25187	−	2.45482i	−0.164880	−	0.0951937i
$666$		0			0
$667$	0.547961	+	0.949096i	0.0212171	+	0.0367491i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		−	5.28121i		−	0.203879i
$672$		0			0
$673$	2.13077	−	3.69060i	0.0821351	−	0.142262i	−0.822032	−	0.569442i	$-0.807159\pi$
$673$	2.13077	−	3.69060i	0.0821351	−	0.142262i	0.904167	+	0.427180i	$0.140493\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	4.47885			0.172136			0.0860681	−	0.996289i	$-0.472570\pi$
$677$	4.47885			0.172136			0.0860681	+	0.996289i	$0.472570\pi$
$678$		0			0
$679$	5.05260	−	8.75137i	0.193901	−	0.335847i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	17.4014	−	10.0467i	0.665846	−	0.384426i	−0.128655	−	0.991689i	$-0.541066\pi$
$683$	17.4014	−	10.0467i	0.665846	−	0.384426i	0.794501	+	0.607263i	$0.207733\pi$
$684$		0			0
$685$	9.07386	+	15.7164i	0.346694	+	0.600492i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	14.6744	−	2.88217i	0.559051	−	0.109802i
$690$		0			0
$691$	32.6571	+	18.8546i	1.24233	+	0.717261i	0.969569	−	0.244820i	$-0.0787288\pi$
$691$	32.6571	+	18.8546i	1.24233	+	0.717261i	0.272764	+	0.962081i	$0.412062\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−23.5780	+	13.6128i	−0.894365	+	0.516362i
$696$		0			0
$697$			31.8407i			1.20605i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	17.2849			0.652842			0.326421	−	0.945225i	$-0.394157\pi$
$701$	17.2849			0.652842			0.326421	+	0.945225i	$0.394157\pi$
$702$		0			0
$703$	−7.59622			−0.286497
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	3.24119i		−	0.121898i
$708$		0			0
$709$	15.7410	−	9.08807i	0.591166	−	0.341310i	−0.174393	−	0.984676i	$-0.555796\pi$
$709$	15.7410	−	9.08807i	0.591166	−	0.341310i	0.765558	+	0.643366i	$0.222463\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	0.368180	+	0.212569i	0.0137884	+	0.00796076i
$714$		0			0
$715$	−3.41778	+	9.98928i	−0.127818	+	0.373578i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−9.95668	−	17.2455i	−0.371322	−	0.643148i	0.618448	−	0.785826i	$-0.287762\pi$
$719$	−9.95668	−	17.2455i	−0.371322	−	0.643148i	−0.989769	+	0.142678i	$0.954429\pi$
$720$		0			0
$721$	−5.07180	+	2.92820i	−0.188884	+	0.109052i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	0.303174	−	0.525113i	0.0112596	−	0.0195022i
$726$		0			0
$727$	−38.7446			−1.43696			−0.718479	−	0.695549i	$-0.755161\pi$
$727$	−38.7446			−1.43696			−0.718479	+	0.695549i	$0.755161\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	12.4926	−	21.6378i	0.462055	−	0.800302i
$732$		0			0
$733$			3.19477i			0.118001i	0.998258	+	0.0590007i	$0.0187914\pi$
$733$			3.19477i			0.118001i	−0.998258	+	0.0590007i	$0.981209\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	8.05534	+	13.9523i	0.296722	+	0.513938i
$738$		0			0
$739$	−35.2234	−	20.3362i	−1.29571	−	0.748080i	−0.316053	−	0.948742i	$-0.602358\pi$
$739$	−35.2234	−	20.3362i	−1.29571	−	0.748080i	−0.979661	+	0.200661i	$0.935691\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−12.0464	−	6.95498i	−0.441939	−	0.255154i	0.262481	−	0.964937i	$-0.415459\pi$
$743$	−12.0464	−	6.95498i	−0.441939	−	0.255154i	−0.704420	+	0.709784i	$0.748793\pi$
$744$		0			0
$745$	−12.5322	−	21.7064i	−0.459143	−	0.795260i
$746$		0			0
$747$		0			0
$748$		0			0
$749$			6.54275i			0.239067i
$750$		0			0
$751$	8.79317	−	15.2302i	0.320867	−	0.555759i	−0.659800	−	0.751441i	$-0.729359\pi$
$751$	8.79317	−	15.2302i	0.320867	−	0.555759i	0.980667	+	0.195683i	$0.0626923\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−35.8299			−1.30398
$756$		0			0
$757$	−11.0553	+	19.1484i	−0.401813	+	0.695961i	−0.993945	−	0.109881i	$-0.964953\pi$
$757$	−11.0553	+	19.1484i	−0.401813	+	0.695961i	0.592132	+	0.805841i	$0.298286\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−21.0765	+	12.1685i	−0.764022	+	0.441108i	−0.830738	−	0.556664i	$-0.812081\pi$
$761$	−21.0765	+	12.1685i	−0.764022	+	0.441108i	0.0667160	+	0.997772i	$0.478748\pi$
$762$		0			0
$763$	1.64245	+	2.84481i	0.0594608	+	0.102989i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.72377	−	1.50437i	0.0622418	−	0.0543198i
$768$		0			0
$769$	6.14197	+	3.54607i	0.221485	+	0.127875i	0.606638	−	0.794978i	$-0.292518\pi$
$769$	6.14197	+	3.54607i	0.221485	+	0.127875i	−0.385153	+	0.922853i	$0.625851\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−0.840035	+	0.484994i	−0.0302140	+	0.0174440i	−0.515031	−	0.857172i	$-0.672220\pi$
$773$	−0.840035	+	0.484994i	−0.0302140	+	0.0174440i	0.484817	+	0.874616i	$0.338886\pi$
$774$		0			0
$775$		−	0.235219i		−	0.00844931i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−9.61076			−0.344341
$780$		0			0
$781$	−9.65309			−0.345415
$782$		0			0
$783$		0			0
$784$		0			0
$785$		−	23.3929i		−	0.834929i
$786$		0			0
$787$	0.0361875	−	0.0208929i	0.00128994	−	0.000744750i	−0.499355	−	0.866398i	$-0.666430\pi$
$787$	0.0361875	−	0.0208929i	0.00128994	−	0.000744750i	0.500645	+	0.865653i	$0.333096\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	4.74693	+	2.74064i	0.168782	+	0.0974461i
$792$		0			0
$793$	11.1609	+	12.7886i	0.396336	+	0.454138i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−19.6671	−	34.0645i	−0.696646	−	1.20663i	−0.969623	−	0.244606i	$-0.921341\pi$
$797$	−19.6671	−	34.0645i	−0.696646	−	1.20663i	0.272977	−	0.962021i	$-0.411992\pi$
$798$		0			0
$799$	−51.9477	+	29.9920i	−1.83778	+	1.06104i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	5.57802	−	9.66141i	0.196844	−	0.340944i
$804$		0			0
$805$	−9.59697			−0.338249
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.404078	+	0.699884i	−0.0142066	+	0.0246066i	−0.873041	−	0.487646i	$-0.837856\pi$
$809$	−0.404078	+	0.699884i	−0.0142066	+	0.0246066i	0.858835	+	0.512253i	$0.171189\pi$
$810$		0			0
$811$			24.3955i			0.856640i	0.903627	+	0.428320i	$0.140894\pi$
$811$			24.3955i			0.856640i	−0.903627	+	0.428320i	$0.859106\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−2.86292	−	4.95873i	−0.100284	−	0.173697i
$816$		0			0
$817$	6.53112	+	3.77075i	0.228495	+	0.131922i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	15.0406	+	8.68369i	0.524920	+	0.303063i	0.738945	−	0.673765i	$-0.235324\pi$
$821$	15.0406	+	8.68369i	0.524920	+	0.303063i	−0.214025	+	0.976828i	$0.568657\pi$
$822$		0			0
$823$	−2.83865	−	4.91669i	−0.0989491	−	0.171385i	0.812301	−	0.583239i	$-0.198215\pi$
$823$	−2.83865	−	4.91669i	−0.0989491	−	0.171385i	−0.911250	+	0.411854i	$0.864881\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			14.5094i			0.504540i	0.967657	+	0.252270i	$0.0811772\pi$
$827$			14.5094i			0.504540i	−0.967657	+	0.252270i	$0.918823\pi$
$828$		0			0
$829$	23.7516	−	41.1390i	0.824928	−	1.42882i	−0.0770456	−	0.997028i	$-0.524549\pi$
$829$	23.7516	−	41.1390i	0.824928	−	1.42882i	0.901974	−	0.431790i	$-0.142118\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	31.8934			1.10504
$834$		0			0
$835$	19.5483	−	33.8587i	0.676498	−	1.17173i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	1.78192	−	1.02879i	0.0615188	−	0.0355179i	−0.468925	−	0.883238i	$-0.655359\pi$
$839$	1.78192	−	1.02879i	0.0615188	−	0.0355179i	0.530444	+	0.847720i	$0.322025\pi$
$840$		0			0
$841$	14.4441	+	25.0179i	0.498072	+	0.862686i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−12.8343	−	31.4123i	−0.441515	−	1.08062i
$846$		0			0
$847$	−9.46410	−	5.46410i	−0.325190	−	0.187749i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−12.8592	+	7.42425i	−0.440807	+	0.254500i
$852$		0			0
$853$			4.10363i			0.140506i	0.997529	+	0.0702528i	$0.0223806\pi$
$853$			4.10363i			0.140506i	−0.997529	+	0.0702528i	$0.977619\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−35.9776			−1.22897			−0.614486	−	0.788928i	$-0.710636\pi$
$857$	−35.9776			−1.22897			−0.614486	+	0.788928i	$0.710636\pi$
$858$		0			0
$859$	−12.7711			−0.435745			−0.217872	−	0.975977i	$-0.569912\pi$
$859$	−12.7711			−0.435745			−0.217872	+	0.975977i	$0.569912\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	34.2815i		−	1.16696i	−0.812128	−	0.583479i	$-0.801691\pi$
$863$		−	34.2815i		−	1.16696i	0.812128	−	0.583479i	$-0.198309\pi$
$864$		0			0
$865$	9.03043	−	5.21372i	0.307044	−	0.177272i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−13.2097	−	7.62665i	−0.448110	−	0.258716i
$870$		0			0
$871$	−48.9920	−	16.7623i	−1.66003	−	0.567970i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−4.66562	−	8.08108i	−0.157727	−	0.273190i
$876$		0			0
$877$	−39.4625	+	22.7837i	−1.33255	+	0.769351i	−0.985691	−	0.168565i	$-0.946087\pi$
$877$	−39.4625	+	22.7837i	−1.33255	+	0.769351i	−0.346864	+	0.937915i	$0.612753\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	6.88302	−	11.9217i	0.231895	−	0.401654i	−0.726471	−	0.687197i	$-0.758841\pi$
$881$	6.88302	−	11.9217i	0.231895	−	0.401654i	0.958366	+	0.285544i	$0.0921742\pi$
$882$		0			0
$883$	1.44199			0.0485269			0.0242634	−	0.999706i	$-0.492276\pi$
$883$	1.44199			0.0485269			0.0242634	+	0.999706i	$0.492276\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−13.2859	+	23.0118i	−0.446097	+	0.772662i	−0.998128	−	0.0611612i	$-0.980520\pi$
$887$	−13.2859	+	23.0118i	−0.446097	+	0.772662i	0.552031	+	0.833824i	$0.313853\pi$
$888$		0			0
$889$		−	11.5766i		−	0.388268i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−9.05275	−	15.6798i	−0.302939	−	0.524705i
$894$		0			0
$895$	19.4673	+	11.2394i	0.650719	+	0.375693i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−0.0375641	−	0.0216877i	−0.00125283	−	0.000723324i
$900$		0			0
$901$	11.5200	+	19.9532i	0.383786	+	0.664736i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	40.8000i		−	1.35624i
$906$		0			0
$907$	5.03911	−	8.72800i	0.167321	−	0.289808i	−0.770156	−	0.637855i	$-0.779822\pi$
$907$	5.03911	−	8.72800i	0.167321	−	0.289808i	0.937477	+	0.348047i	$0.113155\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−44.5252			−1.47518			−0.737592	−	0.675246i	$-0.764037\pi$
$911$	−44.5252			−1.47518			−0.737592	+	0.675246i	$0.764037\pi$
$912$		0			0
$913$	−3.22879	+	5.59243i	−0.106857	+	0.185083i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−0.107607	+	0.0621267i	−0.00355348	+	0.00205160i
$918$		0			0
$919$	−16.7591	−	29.0275i	−0.552830	−	0.957530i	−0.998069	−	0.0621180i	$-0.980214\pi$
$919$	−16.7591	−	29.0275i	−0.552830	−	0.957530i	0.445239	−	0.895412i	$-0.353119\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	23.3753	−	20.4001i	0.769407	−	0.671478i
$924$		0			0
$925$	7.11469	+	4.10767i	0.233930	+	0.135059i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−15.1077	+	8.72243i	−0.495667	+	0.286174i	−0.726923	−	0.686719i	$-0.759050\pi$
$929$	−15.1077	+	8.72243i	−0.495667	+	0.286174i	0.231255	+	0.972893i	$0.425717\pi$
$930$		0			0
$931$			9.62665i			0.315501i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−16.2657			−0.531947
$936$		0			0
$937$	17.0052			0.555535			0.277767	−	0.960648i	$-0.410406\pi$
$937$	17.0052			0.555535			0.277767	+	0.960648i	$0.410406\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		−	15.7406i		−	0.513128i	−0.966527	−	0.256564i	$-0.917410\pi$
$941$		−	15.7406i		−	0.513128i	0.966527	−	0.256564i	$-0.0825904\pi$
$942$		0			0
$943$	−16.2695	+	9.39319i	−0.529807	+	0.305884i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−28.2102	−	16.2872i	−0.916709	−	0.529262i	−0.0341252	−	0.999418i	$-0.510864\pi$
$947$	−28.2102	−	16.2872i	−0.916709	−	0.529262i	−0.882584	+	0.470155i	$0.844198\pi$
$948$		0			0
$949$	6.91034	+	35.1836i	0.224319	+	1.14211i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−15.6154	−	27.0466i	−0.505831	−	0.876125i	−0.999977	−	0.00674630i	$-0.997853\pi$
$953$	−15.6154	−	27.0466i	−0.505831	−	0.876125i	0.494146	−	0.869379i	$-0.335481\pi$
$954$		0			0
$955$	−61.1607	+	35.3111i	−1.97911	+	1.14264i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−3.89972	+	6.75452i	−0.125929	+	0.218115i
$960$		0			0
$961$	30.9832			0.999457
$962$		0			0
$963$		0			0
$964$		0			0
$965$	31.2595	−	54.1430i	1.00628	−	1.74292i
$966$		0			0
$967$			37.8998i			1.21877i	0.792873	+	0.609387i	$0.208585\pi$
$967$			37.8998i			1.21877i	−0.792873	+	0.609387i	$0.791415\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	13.6628	+	23.6647i	0.438461	+	0.759437i	0.997571	−	0.0696563i	$-0.0221903\pi$
$971$	13.6628	+	23.6647i	0.438461	+	0.759437i	−0.559110	+	0.829094i	$0.688857\pi$
$972$		0			0
$973$	−10.1333	−	5.85044i	−0.324858	−	0.187557i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−25.8089	−	14.9008i	−0.825700	−	0.476718i	0.0266779	−	0.999644i	$-0.491507\pi$
$977$	−25.8089	−	14.9008i	−0.825700	−	0.476718i	−0.852378	+	0.522926i	$0.824840\pi$
$978$		0			0
$979$	−8.04647	−	13.9369i	−0.257166	−	0.445425i
$980$		0			0
$981$		0			0
$982$		0			0
$983$		−	16.0704i		−	0.512565i	−0.966602	−	0.256282i	$-0.917502\pi$
$983$		−	16.0704i		−	0.512565i	0.966602	−	0.256282i	$-0.0824977\pi$
$984$		0			0
$985$	−13.5020	+	23.3862i	−0.430210	+	0.745145i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	14.7415			0.468753
$990$		0			0
$991$	15.9772	−	27.6733i	0.507533	−	0.879073i	−0.492429	−	0.870353i	$-0.663891\pi$
$991$	15.9772	−	27.6733i	0.507533	−	0.879073i	0.999962	−	0.00872027i	$-0.00277578\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−30.6818	+	17.7142i	−0.972679	+	0.561577i
$996$		0			0
$997$	4.39599	+	7.61407i	0.139222	+	0.241140i	0.927202	−	0.374561i	$-0.122206\pi$
$997$	4.39599	+	7.61407i	0.139222	+	0.241140i	−0.787980	+	0.615701i	$0.788873\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1872.2.by.n.433.2		8
3.2	odd	2		208.2.w.c.17.1		8
4.3	odd	2		936.2.bi.b.433.2		8
12.11	even	2		104.2.o.a.17.4	✓	8
13.10	even	6	inner	1872.2.by.n.1297.3		8
24.5	odd	2		832.2.w.i.641.4		8
24.11	even	2		832.2.w.g.641.1		8
39.17	odd	6		2704.2.f.q.337.7		8
39.20	even	12		2704.2.a.bd.1.4		4
39.23	odd	6		208.2.w.c.49.1		8
39.32	even	12		2704.2.a.be.1.4		4
39.35	odd	6		2704.2.f.q.337.8		8
52.23	odd	6		936.2.bi.b.361.3		8
156.11	odd	12		1352.2.i.k.1329.4		8
156.23	even	6		104.2.o.a.49.4	yes	8
156.35	even	6		1352.2.f.f.337.2		8
156.47	odd	4		1352.2.i.k.529.4		8
156.59	odd	12		1352.2.a.k.1.1		4
156.71	odd	12		1352.2.a.l.1.1		4
156.83	odd	4		1352.2.i.l.529.4		8
156.95	even	6		1352.2.f.f.337.1		8
156.107	even	6		1352.2.o.f.361.4		8
156.119	odd	12		1352.2.i.l.1329.4		8
156.155	even	2		1352.2.o.f.1161.4		8
312.101	odd	6		832.2.w.i.257.4		8
312.179	even	6		832.2.w.g.257.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.o.a.17.4	✓	8	12.11	even	2
104.2.o.a.49.4	yes	8	156.23	even	6
208.2.w.c.17.1		8	3.2	odd	2
208.2.w.c.49.1		8	39.23	odd	6
832.2.w.g.257.1		8	312.179	even	6
832.2.w.g.641.1		8	24.11	even	2
832.2.w.i.257.4		8	312.101	odd	6
832.2.w.i.641.4		8	24.5	odd	2
936.2.bi.b.361.3		8	52.23	odd	6
936.2.bi.b.433.2		8	4.3	odd	2
1352.2.a.k.1.1		4	156.59	odd	12
1352.2.a.l.1.1		4	156.71	odd	12
1352.2.f.f.337.1		8	156.95	even	6
1352.2.f.f.337.2		8	156.35	even	6
1352.2.i.k.529.4		8	156.47	odd	4
1352.2.i.k.1329.4		8	156.11	odd	12
1352.2.i.l.529.4		8	156.83	odd	4
1352.2.i.l.1329.4		8	156.119	odd	12
1352.2.o.f.361.4		8	156.107	even	6
1352.2.o.f.1161.4		8	156.155	even	2
1872.2.by.n.433.2		8	1.1	even	1	trivial
1872.2.by.n.1297.3		8	13.10	even	6	inner
2704.2.a.bd.1.4		4	39.20	even	12
2704.2.a.be.1.4		4	39.32	even	12
2704.2.f.q.337.7		8	39.17	odd	6
2704.2.f.q.337.8		8	39.35	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1872.by (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.61023i q^{5} +(0.971521 - 0.560908i) q^{7} +(0.971521 + 0.560908i) q^{11} +(-3.53796 + 0.694883i) q^{13} +(-2.77743 - 4.81064i) q^{17} +(1.45204 - 0.838335i) q^{19} +(1.63871 - 2.83834i) q^{23} -1.81333 q^{25} +(-0.167192 + 0.289586i) q^{29} +0.129717i q^{31} +(-1.46410 - 2.53590i) q^{35} +(-3.92356 - 2.26527i) q^{37} +(-4.96410 - 2.86603i) q^{41} +(2.24895 + 3.89529i) q^{43} -10.7985i q^{47} +(-2.87076 + 4.97231i) q^{49} -4.14771 q^{53} +(1.46410 - 2.53590i) q^{55} +(-0.549538 + 0.317276i) q^{59} +(-2.35387 - 4.07702i) q^{61} +(1.81381 + 9.23490i) q^{65} +(12.4372 + 7.18062i) q^{67} +(-7.45204 + 4.30244i) q^{71} -9.94462i q^{73} +1.25847 q^{77} -13.5970 q^{79} +5.75637i q^{83} +(-12.5569 + 7.24974i) q^{85} +(-12.4235 - 7.17272i) q^{89} +(-3.04743 + 2.65956i) q^{91} +(-2.18825 - 3.79016i) q^{95} +(7.80107 - 4.50395i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{7} + 6 q^{11} + 6 q^{13} + 6 q^{19} + 2 q^{23} - 20 q^{25} + 8 q^{29} + 16 q^{35} - 24 q^{37} - 12 q^{41} - 6 q^{43} + 2 q^{49} - 20 q^{53} - 16 q^{55} + 18 q^{59} - 4 q^{61} - 14 q^{65} + 42 q^{67}+ \cdots + 30 q^{97}+O(q^{100}) \) 8 * q + 6 * q^7 + 6 * q^11 + 6 * q^13 + 6 * q^19 + 2 * q^23 - 20 * q^25 + 8 * q^29 + 16 * q^35 - 24 * q^37 - 12 * q^41 - 6 * q^43 + 2 * q^49 - 20 * q^53 - 16 * q^55 + 18 * q^59 - 4 * q^61 - 14 * q^65 + 42 * q^67 - 54 * q^71 + 60 * q^77 - 16 * q^79 + 6 * q^85 + 18 * q^89 + 46 * q^91 + 16 * q^95 + 30 * q^97

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