LMFDB - Embedded newform 1716.3.s.a.265.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1716,3,Mod(265,1716)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1716, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1716.265");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1716 = 2^{2} \cdot 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1716.s (of order $4$, 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:	$46.7576133642$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			265.5
Character	$\chi$	$=$	1716.265
Dual form			1716.3.s.a.1321.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73205 q^{3} +(-4.83880 + 4.83880i) q^{5} +(7.59021 + 7.59021i) q^{7} +3.00000 q^{9} +O(q^{10})$	\(q-1.73205 q^{3} +(-4.83880 + 4.83880i) q^{5} +(7.59021 + 7.59021i) q^{7} +3.00000 q^{9} +(-2.34521 - 2.34521i) q^{11} +(-0.217155 - 12.9982i) q^{13} +(8.38105 - 8.38105i) q^{15} +17.7190i q^{17} +(22.9736 - 22.9736i) q^{19} +(-13.1466 - 13.1466i) q^{21} -40.9663i q^{23} -21.8280i q^{25} -5.19615 q^{27} -55.3976 q^{29} +(-25.5028 + 25.5028i) q^{31} +(4.06202 + 4.06202i) q^{33} -73.4550 q^{35} +(12.3403 + 12.3403i) q^{37} +(0.376124 + 22.5135i) q^{39} +(17.9709 - 17.9709i) q^{41} -45.1571i q^{43} +(-14.5164 + 14.5164i) q^{45} +(-60.1062 - 60.1062i) q^{47} +66.2225i q^{49} -30.6902i q^{51} +105.074 q^{53} +22.6960 q^{55} +(-39.7914 + 39.7914i) q^{57} +(19.4544 + 19.4544i) q^{59} +73.8107 q^{61} +(22.7706 + 22.7706i) q^{63} +(63.9464 + 61.8449i) q^{65} +(55.0456 - 55.0456i) q^{67} +70.9557i q^{69} +(-57.1233 + 57.1233i) q^{71} +(-36.3760 - 36.3760i) q^{73} +37.8072i q^{75} -35.6012i q^{77} +56.7149 q^{79} +9.00000 q^{81} +(-12.8488 + 12.8488i) q^{83} +(-85.7387 - 85.7387i) q^{85} +95.9515 q^{87} +(-86.3700 - 86.3700i) q^{89} +(97.0107 - 100.307i) q^{91} +(44.1722 - 44.1722i) q^{93} +222.329i q^{95} +(-68.5542 + 68.5542i) q^{97} +(-7.03562 - 7.03562i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 24 q^{5} + 16 q^{7} + 288 q^{9}+O(q^{10}) $ 96 * q - 24 * q^5 + 16 * q^7 + 288 * q^9	$ 96 q - 24 q^{5} + 16 q^{7} + 288 q^{9} - 16 q^{13} - 40 q^{19} + 80 q^{29} + 88 q^{31} + 112 q^{35} + 8 q^{37} - 144 q^{39} + 120 q^{41} - 72 q^{45} + 80 q^{47} + 64 q^{53} - 48 q^{57} - 16 q^{59} + 176 q^{61} + 48 q^{63} + 120 q^{65} + 24 q^{67} - 176 q^{73} - 208 q^{79} + 864 q^{81} - 64 q^{83} - 200 q^{85} + 240 q^{87} + 120 q^{89} + 168 q^{91} - 192 q^{93} - 120 q^{97}+O(q^{100}) $ 96 * q - 24 * q^5 + 16 * q^7 + 288 * q^9 - 16 * q^13 - 40 * q^19 + 80 * q^29 + 88 * q^31 + 112 * q^35 + 8 * q^37 - 144 * q^39 + 120 * q^41 - 72 * q^45 + 80 * q^47 + 64 * q^53 - 48 * q^57 - 16 * q^59 + 176 * q^61 + 48 * q^63 + 120 * q^65 + 24 * q^67 - 176 * q^73 - 208 * q^79 + 864 * q^81 - 64 * q^83 - 200 * q^85 + 240 * q^87 + 120 * q^89 + 168 * q^91 - 192 * q^93 - 120 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1716\mathbb{Z}\right)^\times$.

$n$	$859$	$925$	$937$	$1145$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$		0			0
$5$	−4.83880	+	4.83880i	−0.967760	+	0.967760i	−0.999496	−	0.0317359i	$-0.989896\pi$
$5$	−4.83880	+	4.83880i	−0.967760	+	0.967760i	0.0317359	+	0.999496i	$0.489896\pi$
$6$		0			0
$7$	7.59021	+	7.59021i	1.08432	+	1.08432i	0.996102	+	0.0882137i	$0.0281158\pi$
$7$	7.59021	+	7.59021i	1.08432	+	1.08432i	0.0882137	+	0.996102i	$0.471884\pi$
$8$		0			0
$9$	3.00000			0.333333
$10$		0			0
$11$	−2.34521	−	2.34521i	−0.213201	−	0.213201i
$11$	−2.34521	−	2.34521i	−0.213201	−	0.213201i
$12$		0			0
$13$	−0.217155	−	12.9982i	−0.0167042	−	0.999860i
$13$	−0.217155	−	12.9982i	−0.0167042	−	0.999860i
$14$		0			0
$15$	8.38105	−	8.38105i	0.558737	−	0.558737i
$16$		0			0
$17$			17.7190i			1.04229i	0.853467	+	0.521147i	$0.174496\pi$
$17$			17.7190i			1.04229i	−0.853467	+	0.521147i	$0.825504\pi$
$18$		0			0
$19$	22.9736	−	22.9736i	1.20913	−	1.20913i	0.237827	−	0.971308i	$-0.423565\pi$
$19$	22.9736	−	22.9736i	1.20913	−	1.20913i	0.971308	−	0.237827i	$-0.0764351\pi$
$20$		0			0
$21$	−13.1466	−	13.1466i	−0.626030	−	0.626030i
$22$		0			0
$23$		−	40.9663i		−	1.78114i	−0.454843	−	0.890572i	$-0.650305\pi$
$23$		−	40.9663i		−	1.78114i	0.454843	−	0.890572i	$-0.349695\pi$
$24$		0			0
$25$		−	21.8280i		−	0.873120i
$26$		0			0
$27$	−5.19615			−0.192450
$28$		0			0
$29$	−55.3976			−1.91026			−0.955131	−	0.296183i	$-0.904286\pi$
$29$	−55.3976			−1.91026			−0.955131	+	0.296183i	$0.904286\pi$
$30$		0			0
$31$	−25.5028	+	25.5028i	−0.822671	+	0.822671i	−0.986490	−	0.163819i	$-0.947619\pi$
$31$	−25.5028	+	25.5028i	−0.822671	+	0.822671i	0.163819	+	0.986490i	$0.447619\pi$
$32$		0			0
$33$	4.06202	+	4.06202i	0.123091	+	0.123091i
$34$		0			0
$35$	−73.4550			−2.09871
$36$		0			0
$37$	12.3403	+	12.3403i	0.333522	+	0.333522i	0.853922	−	0.520400i	$-0.174217\pi$
$37$	12.3403	+	12.3403i	0.333522	+	0.333522i	−0.520400	+	0.853922i	$0.674217\pi$
$38$		0			0
$39$	0.376124	+	22.5135i	0.00964420	+	0.577270i
$40$		0			0
$41$	17.9709	−	17.9709i	0.438314	−	0.438314i	−0.453130	−	0.891444i	$-0.649693\pi$
$41$	17.9709	−	17.9709i	0.438314	−	0.438314i	0.891444	+	0.453130i	$0.149693\pi$
$42$		0			0
$43$		−	45.1571i		−	1.05016i	−0.851051	−	0.525082i	$-0.824034\pi$
$43$		−	45.1571i		−	1.05016i	0.851051	−	0.525082i	$-0.175966\pi$
$44$		0			0
$45$	−14.5164	+	14.5164i	−0.322587	+	0.322587i
$46$		0			0
$47$	−60.1062	−	60.1062i	−1.27886	−	1.27886i	−0.941309	−	0.337547i	$-0.890403\pi$
$47$	−60.1062	−	60.1062i	−1.27886	−	1.27886i	−0.337547	−	0.941309i	$-0.609597\pi$
$48$		0			0
$49$			66.2225i			1.35148i
$50$		0			0
$51$		−	30.6902i		−	0.601768i
$52$		0			0
$53$	105.074			1.98252			0.991260	−	0.131925i	$-0.0421157\pi$
$53$	105.074			1.98252			0.991260	+	0.131925i	$0.0421157\pi$
$54$		0			0
$55$	22.6960			0.412654
$56$		0			0
$57$	−39.7914	+	39.7914i	−0.698094	+	0.698094i
$58$		0			0
$59$	19.4544	+	19.4544i	0.329736	+	0.329736i	0.852486	−	0.522750i	$-0.175094\pi$
$59$	19.4544	+	19.4544i	0.329736	+	0.329736i	−0.522750	+	0.852486i	$0.675094\pi$
$60$		0			0
$61$	73.8107			1.21001			0.605006	−	0.796221i	$-0.293171\pi$
$61$	73.8107			1.21001			0.605006	+	0.796221i	$0.293171\pi$
$62$		0			0
$63$	22.7706	+	22.7706i	0.361438	+	0.361438i
$64$		0			0
$65$	63.9464	+	61.8449i	0.983791	+	0.951460i
$66$		0			0
$67$	55.0456	−	55.0456i	0.821577	−	0.821577i	−0.164757	−	0.986334i	$-0.552684\pi$
$67$	55.0456	−	55.0456i	0.821577	−	0.821577i	0.986334	+	0.164757i	$0.0526841\pi$
$68$		0			0
$69$			70.9557i			1.02834i
$70$		0			0
$71$	−57.1233	+	57.1233i	−0.804554	+	0.804554i	−0.983804	−	0.179249i	$-0.942633\pi$
$71$	−57.1233	+	57.1233i	−0.804554	+	0.804554i	0.179249	+	0.983804i	$0.442633\pi$
$72$		0			0
$73$	−36.3760	−	36.3760i	−0.498301	−	0.498301i	0.412608	−	0.910909i	$-0.364618\pi$
$73$	−36.3760	−	36.3760i	−0.498301	−	0.498301i	−0.910909	+	0.412608i	$0.864618\pi$
$74$		0			0
$75$			37.8072i			0.504096i
$76$		0			0
$77$		−	35.6012i		−	0.462354i
$78$		0			0
$79$	56.7149			0.717911			0.358955	−	0.933355i	$-0.383133\pi$
$79$	56.7149			0.717911			0.358955	+	0.933355i	$0.383133\pi$
$80$		0			0
$81$	9.00000			0.111111
$82$		0			0
$83$	−12.8488	+	12.8488i	−0.154805	+	0.154805i	−0.780260	−	0.625455i	$-0.784913\pi$
$83$	−12.8488	+	12.8488i	−0.154805	+	0.154805i	0.625455	+	0.780260i	$0.284913\pi$
$84$		0			0
$85$	−85.7387	−	85.7387i	−1.00869	−	1.00869i
$86$		0			0
$87$	95.9515			1.10289
$88$		0			0
$89$	−86.3700	−	86.3700i	−0.970449	−	0.970449i	0.0291264	−	0.999576i	$-0.490727\pi$
$89$	−86.3700	−	86.3700i	−0.970449	−	0.970449i	−0.999576	+	0.0291264i	$0.990727\pi$
$90$		0			0
$91$	97.0107	−	100.307i	1.06605	−	1.10228i
$92$		0			0
$93$	44.1722	−	44.1722i	0.474969	−	0.474969i
$94$		0			0
$95$			222.329i			2.34030i
$96$		0			0
$97$	−68.5542	+	68.5542i	−0.706744	+	0.706744i	−0.965849	−	0.259105i	$-0.916572\pi$
$97$	−68.5542	+	68.5542i	−0.706744	+	0.706744i	0.259105	+	0.965849i	$0.416572\pi$
$98$		0			0
$99$	−7.03562	−	7.03562i	−0.0710669	−	0.0710669i
$100$		0			0
$101$		−	19.0765i		−	0.188876i	−0.995531	−	0.0944381i	$-0.969895\pi$
$101$		−	19.0765i		−	0.188876i	0.995531	−	0.0944381i	$-0.0301055\pi$
$102$		0			0
$103$		−	100.271i		−	0.973503i	−0.873540	−	0.486752i	$-0.838182\pi$
$103$		−	100.271i		−	0.973503i	0.873540	−	0.486752i	$-0.161818\pi$
$104$		0			0
$105$	127.228			1.21169
$106$		0			0
$107$	35.4772			0.331563			0.165781	−	0.986163i	$-0.446985\pi$
$107$	35.4772			0.331563			0.165781	+	0.986163i	$0.446985\pi$
$108$		0			0
$109$	0.873920	−	0.873920i	0.00801761	−	0.00801761i	−0.703087	−	0.711104i	$-0.748195\pi$
$109$	0.873920	−	0.873920i	0.00801761	−	0.00801761i	0.711104	+	0.703087i	$0.248195\pi$
$110$		0			0
$111$	−21.3740	−	21.3740i	−0.192559	−	0.192559i
$112$		0			0
$113$	64.1810			0.567973			0.283987	−	0.958828i	$-0.408343\pi$
$113$	64.1810			0.567973			0.283987	+	0.958828i	$0.408343\pi$
$114$		0			0
$115$	198.228	+	198.228i	1.72372	+	1.72372i
$116$		0			0
$117$	−0.651465	−	38.9946i	−0.00556808	−	0.333287i
$118$		0			0
$119$	−134.491	+	134.491i	−1.13017	+	1.13017i
$120$		0			0
$121$			11.0000i			0.0909091i
$122$		0			0
$123$	−31.1265	+	31.1265i	−0.253061	+	0.253061i
$124$		0			0
$125$	−15.3486	−	15.3486i	−0.122789	−	0.122789i
$126$		0			0
$127$		−	103.011i		−	0.811107i	−0.914071	−	0.405553i	$-0.867079\pi$
$127$		−	103.011i		−	0.811107i	0.914071	−	0.405553i	$-0.132921\pi$
$128$		0			0
$129$			78.2144i			0.606313i
$130$		0			0
$131$	121.958			0.930980			0.465490	−	0.885053i	$-0.345878\pi$
$131$	121.958			0.930980			0.465490	+	0.885053i	$0.345878\pi$
$132$		0			0
$133$	348.748			2.62217
$134$		0			0
$135$	25.1432	−	25.1432i	0.186246	−	0.186246i
$136$		0			0
$137$	−8.08429	−	8.08429i	−0.0590094	−	0.0590094i	0.676986	−	0.735996i	$-0.263286\pi$
$137$	−8.08429	−	8.08429i	−0.0590094	−	0.0590094i	−0.735996	+	0.676986i	$0.763286\pi$
$138$		0			0
$139$	127.380			0.916399			0.458200	−	0.888849i	$-0.348494\pi$
$139$	127.380			0.916399			0.458200	+	0.888849i	$0.348494\pi$
$140$		0			0
$141$	104.107	+	104.107i	0.738348	+	0.738348i
$142$		0			0
$143$	−29.9742	+	30.9927i	−0.209610	+	0.216732i
$144$		0			0
$145$	268.058	−	268.058i	1.84868	−	1.84868i
$146$		0			0
$147$		−	114.701i		−	0.780277i
$148$		0			0
$149$	119.585	−	119.585i	0.802585	−	0.802585i	−0.180914	−	0.983499i	$-0.557906\pi$
$149$	119.585	−	119.585i	0.802585	−	0.802585i	0.983499	+	0.180914i	$0.0579056\pi$
$150$		0			0
$151$	−77.9475	−	77.9475i	−0.516209	−	0.516209i	0.400213	−	0.916422i	$-0.368936\pi$
$151$	−77.9475	−	77.9475i	−0.516209	−	0.516209i	−0.916422	+	0.400213i	$0.868936\pi$
$152$		0			0
$153$			53.1570i			0.347431i
$154$		0			0
$155$		−	246.806i		−	1.59230i
$156$		0			0
$157$	−160.593			−1.02288			−0.511441	−	0.859318i	$-0.670888\pi$
$157$	−160.593			−1.02288			−0.511441	+	0.859318i	$0.670888\pi$
$158$		0			0
$159$	−181.993			−1.14461
$160$		0			0
$161$	310.943	−	310.943i	1.93132	−	1.93132i
$162$		0			0
$163$	147.224	+	147.224i	0.903217	+	0.903217i	0.995713	−	0.0924957i	$-0.0294844\pi$
$163$	147.224	+	147.224i	0.903217	+	0.903217i	−0.0924957	+	0.995713i	$0.529484\pi$
$164$		0			0
$165$	−39.3106			−0.238246
$166$		0			0
$167$	164.659	+	164.659i	0.985984	+	0.985984i	0.999903	−	0.0139192i	$-0.00443078\pi$
$167$	164.659	+	164.659i	0.985984	+	0.985984i	−0.0139192	+	0.999903i	$0.504431\pi$
$168$		0			0
$169$	−168.906	+	5.64524i	−0.999442	+	0.0334038i
$170$		0			0
$171$	68.9207	−	68.9207i	0.403045	−	0.403045i
$172$		0			0
$173$		−	33.6697i		−	0.194623i	−0.995254	−	0.0973114i	$-0.968976\pi$
$173$		−	33.6697i		−	0.194623i	0.995254	−	0.0973114i	$-0.0310243\pi$
$174$		0			0
$175$	165.679	−	165.679i	0.946738	−	0.946738i
$176$		0			0
$177$	−33.6960	−	33.6960i	−0.190373	−	0.190373i
$178$		0			0
$179$		−	279.218i		−	1.55988i	−0.625857	−	0.779938i	$-0.715251\pi$
$179$		−	279.218i		−	1.55988i	0.625857	−	0.779938i	$-0.284749\pi$
$180$		0			0
$181$		−	289.287i		−	1.59827i	−0.601152	−	0.799134i	$-0.705292\pi$
$181$		−	289.287i		−	1.59827i	0.601152	−	0.799134i	$-0.294708\pi$
$182$		0			0
$183$	−127.844			−0.698601
$184$		0			0
$185$	−119.425			−0.645538
$186$		0			0
$187$	41.5547	−	41.5547i	0.222218	−	0.222218i
$188$		0			0
$189$	−39.4399	−	39.4399i	−0.208677	−	0.208677i
$190$		0			0
$191$	140.707			0.736688			0.368344	−	0.929690i	$-0.379925\pi$
$191$	140.707			0.736688			0.368344	+	0.929690i	$0.379925\pi$
$192$		0			0
$193$	−17.8535	−	17.8535i	−0.0925049	−	0.0925049i	0.659340	−	0.751845i	$-0.270836\pi$
$193$	−17.8535	−	17.8535i	−0.0925049	−	0.0925049i	−0.751845	+	0.659340i	$0.770836\pi$
$194$		0			0
$195$	−110.758	−	107.118i	−0.567992	−	0.549325i
$196$		0			0
$197$	−36.1935	+	36.1935i	−0.183724	+	0.183724i	−0.792976	−	0.609253i	$-0.791470\pi$
$197$	−36.1935	+	36.1935i	−0.183724	+	0.183724i	0.609253	+	0.792976i	$0.291470\pi$
$198$		0			0
$199$			226.684i			1.13912i	0.821951	+	0.569558i	$0.192886\pi$
$199$			226.684i			1.13912i	−0.821951	+	0.569558i	$0.807114\pi$
$200$		0			0
$201$	−95.3418	+	95.3418i	−0.474337	+	0.474337i
$202$		0			0
$203$	−420.479	−	420.479i	−2.07133	−	2.07133i
$204$		0			0
$205$			173.915i			0.848366i
$206$		0			0
$207$		−	122.899i		−	0.593715i
$208$		0			0
$209$	−107.756			−0.515577
$210$		0			0
$211$	298.542			1.41489			0.707447	−	0.706767i	$-0.249847\pi$
$211$	298.542			1.41489			0.707447	+	0.706767i	$0.249847\pi$
$212$		0			0
$213$	98.9405	−	98.9405i	0.464510	−	0.464510i
$214$		0			0
$215$	218.506	+	218.506i	1.01631	+	1.01631i
$216$		0			0
$217$	−387.143			−1.78407
$218$		0			0
$219$	63.0051	+	63.0051i	0.287694	+	0.287694i
$220$		0			0
$221$	230.315	−	3.84777i	1.04215	−	0.0174107i
$222$		0			0
$223$	81.4932	−	81.4932i	0.365440	−	0.365440i	−0.500371	−	0.865811i	$-0.666803\pi$
$223$	81.4932	−	81.4932i	0.365440	−	0.365440i	0.865811	+	0.500371i	$0.166803\pi$
$224$		0			0
$225$		−	65.4840i		−	0.291040i
$226$		0			0
$227$	−105.813	+	105.813i	−0.466137	+	0.466137i	−0.900660	−	0.434524i	$-0.856917\pi$
$227$	−105.813	+	105.813i	−0.466137	+	0.466137i	0.434524	+	0.900660i	$0.356917\pi$
$228$		0			0
$229$	134.962	+	134.962i	0.589353	+	0.589353i	0.937456	−	0.348103i	$-0.113174\pi$
$229$	134.962	+	134.962i	0.589353	+	0.589353i	−0.348103	+	0.937456i	$0.613174\pi$
$230$		0			0
$231$			61.6631i			0.266940i
$232$		0			0
$233$			351.130i			1.50700i	0.657450	+	0.753498i	$0.271635\pi$
$233$			351.130i			1.50700i	−0.657450	+	0.753498i	$0.728365\pi$
$234$		0			0
$235$	581.684			2.47525
$236$		0			0
$237$	−98.2331			−0.414486
$238$		0			0
$239$	138.094	−	138.094i	0.577797	−	0.577797i	−0.356498	−	0.934296i	$-0.616029\pi$
$239$	138.094	−	138.094i	0.577797	−	0.577797i	0.934296	+	0.356498i	$0.116029\pi$
$240$		0			0
$241$	311.036	+	311.036i	1.29061	+	1.29061i	0.934411	+	0.356196i	$0.115927\pi$
$241$	311.036	+	311.036i	1.29061	+	1.29061i	0.356196	+	0.934411i	$0.384073\pi$
$242$		0			0
$243$	−15.5885			−0.0641500
$244$		0			0
$245$	−320.437	−	320.437i	−1.30791	−	1.30791i
$246$		0			0
$247$	−303.603	−	293.626i	−1.22916	−	1.18877i
$248$		0			0
$249$	22.2548	−	22.2548i	0.0893767	−	0.0893767i
$250$		0			0
$251$			116.680i			0.464860i	0.972613	+	0.232430i	$0.0746676\pi$
$251$			116.680i			0.464860i	−0.972613	+	0.232430i	$0.925332\pi$
$252$		0			0
$253$	−96.0745	+	96.0745i	−0.379741	+	0.379741i
$254$		0			0
$255$	148.504	+	148.504i	0.582368	+	0.582368i
$256$		0			0
$257$		−	144.152i		−	0.560903i	−0.959868	−	0.280452i	$-0.909516\pi$
$257$		−	144.152i		−	0.560903i	0.959868	−	0.280452i	$-0.0904842\pi$
$258$		0			0
$259$			187.331i			0.723286i
$260$		0			0
$261$	−166.193			−0.636754
$262$		0			0
$263$	86.1428			0.327539			0.163770	−	0.986499i	$-0.447635\pi$
$263$	86.1428			0.327539			0.163770	+	0.986499i	$0.447635\pi$
$264$		0			0
$265$	−508.430	+	508.430i	−1.91860	+	1.91860i
$266$		0			0
$267$	149.597	+	149.597i	0.560289	+	0.560289i
$268$		0			0
$269$	−263.374			−0.979085			−0.489543	−	0.871979i	$-0.662836\pi$
$269$	−263.374			−0.979085			−0.489543	+	0.871979i	$0.662836\pi$
$270$		0			0
$271$	43.8766	+	43.8766i	0.161906	+	0.161906i	0.783411	−	0.621504i	$-0.213478\pi$
$271$	43.8766	+	43.8766i	0.161906	+	0.161906i	−0.621504	+	0.783411i	$0.713478\pi$
$272$		0			0
$273$	−168.027	+	173.737i	−0.615485	+	0.636400i
$274$		0			0
$275$	−51.1912	+	51.1912i	−0.186150	+	0.186150i
$276$		0			0
$277$		−	414.418i		−	1.49609i	−0.663646	−	0.748047i	$-0.730992\pi$
$277$		−	414.418i		−	1.49609i	0.663646	−	0.748047i	$-0.269008\pi$
$278$		0			0
$279$	−76.5084	+	76.5084i	−0.274224	+	0.274224i
$280$		0			0
$281$	154.424	+	154.424i	0.549550	+	0.549550i	0.926311	−	0.376760i	$-0.122962\pi$
$281$	154.424	+	154.424i	0.549550	+	0.549550i	−0.376760	+	0.926311i	$0.622962\pi$
$282$		0			0
$283$			336.944i			1.19061i	0.803498	+	0.595307i	$0.202970\pi$
$283$			336.944i			1.19061i	−0.803498	+	0.595307i	$0.797030\pi$
$284$		0			0
$285$		−	385.085i		−	1.35118i
$286$		0			0
$287$	272.805			0.950542
$288$		0			0
$289$	−24.9626			−0.0863758
$290$		0			0
$291$	118.739	−	118.739i	0.408039	−	0.408039i
$292$		0			0
$293$	88.4403	+	88.4403i	0.301844	+	0.301844i	0.841735	−	0.539891i	$-0.181535\pi$
$293$	88.4403	+	88.4403i	0.301844	+	0.301844i	−0.539891	+	0.841735i	$0.681535\pi$
$294$		0			0
$295$	−188.272			−0.638210
$296$		0			0
$297$	12.1861	+	12.1861i	0.0410305	+	0.0410305i
$298$		0			0
$299$	−532.488	+	8.89604i	−1.78090	+	0.0297526i
$300$		0			0
$301$	342.752	−	342.752i	1.13871	−	1.13871i
$302$		0			0
$303$			33.0415i			0.109048i
$304$		0			0
$305$	−357.156	+	357.156i	−1.17100	+	1.17100i
$306$		0			0
$307$	−12.8036	−	12.8036i	−0.0417055	−	0.0417055i	0.685946	−	0.727652i	$-0.259388\pi$
$307$	−12.8036	−	12.8036i	−0.0417055	−	0.0417055i	−0.727652	+	0.685946i	$0.759388\pi$
$308$		0			0
$309$			173.674i			0.562052i
$310$		0			0
$311$		−	227.843i		−	0.732615i	−0.930494	−	0.366308i	$-0.880622\pi$
$311$		−	227.843i		−	0.732615i	0.930494	−	0.366308i	$-0.119378\pi$
$312$		0			0
$313$	75.5095			0.241244			0.120622	−	0.992698i	$-0.461511\pi$
$313$	75.5095			0.241244			0.120622	+	0.992698i	$0.461511\pi$
$314$		0			0
$315$	−220.365			−0.699572
$316$		0			0
$317$	−197.359	+	197.359i	−0.622584	+	0.622584i	−0.946191	−	0.323607i	$-0.895104\pi$
$317$	−197.359	+	197.359i	−0.622584	+	0.622584i	0.323607	+	0.946191i	$0.395104\pi$
$318$		0			0
$319$	129.919	+	129.919i	0.407269	+	0.407269i
$320$		0			0
$321$	−61.4483			−0.191428
$322$		0			0
$323$	407.068	+	407.068i	1.26027	+	1.26027i
$324$		0			0
$325$	−283.724	+	4.74006i	−0.872998	+	0.0145848i
$326$		0			0
$327$	−1.51367	+	1.51367i	−0.00462897	+	0.00462897i
$328$		0			0
$329$		−	912.437i		−	2.77337i
$330$		0			0
$331$	3.56863	−	3.56863i	0.0107814	−	0.0107814i	−0.701696	−	0.712477i	$-0.747573\pi$
$331$	3.56863	−	3.56863i	0.0107814	−	0.0107814i	0.712477	+	0.701696i	$0.247573\pi$
$332$		0			0
$333$	37.0209	+	37.0209i	0.111174	+	0.111174i
$334$		0			0
$335$			532.710i			1.59018i
$336$		0			0
$337$		−	147.705i		−	0.438293i	−0.975692	−	0.219146i	$-0.929673\pi$
$337$		−	147.705i		−	0.438293i	0.975692	−	0.219146i	$-0.0703272\pi$
$338$		0			0
$339$	−111.165			−0.327919
$340$		0			0
$341$	119.619			0.350788
$342$		0			0
$343$	−130.722	+	130.722i	−0.381114	+	0.381114i
$344$		0			0
$345$	−343.341	−	343.341i	−0.995190	−	0.995190i
$346$		0			0
$347$	8.35278			0.0240714			0.0120357	−	0.999928i	$-0.496169\pi$
$347$	8.35278			0.0240714			0.0120357	+	0.999928i	$0.496169\pi$
$348$		0			0
$349$	−455.927	−	455.927i	−1.30638	−	1.30638i	−0.924009	−	0.382372i	$-0.875107\pi$
$349$	−455.927	−	455.927i	−1.30638	−	1.30638i	−0.382372	−	0.924009i	$-0.624893\pi$
$350$		0			0
$351$	1.12837	+	67.5406i	0.00321473	+	0.192423i
$352$		0			0
$353$	303.886	−	303.886i	0.860867	−	0.860867i	−0.130571	−	0.991439i	$-0.541681\pi$
$353$	303.886	−	303.886i	0.860867	−	0.860867i	0.991439	+	0.130571i	$0.0416812\pi$
$354$		0			0
$355$		−	552.817i		−	1.55723i
$356$		0			0
$357$	232.945	−	232.945i	0.652507	−	0.652507i
$358$		0			0
$359$	266.517	+	266.517i	0.742388	+	0.742388i	0.973037	−	0.230649i	$-0.0740848\pi$
$359$	266.517	+	266.517i	0.742388	+	0.742388i	−0.230649	+	0.973037i	$0.574085\pi$
$360$		0			0
$361$		−	694.568i		−	1.92401i
$362$		0			0
$363$		−	19.0526i		−	0.0524864i
$364$		0			0
$365$	352.032			0.964472
$366$		0			0
$367$	−234.340			−0.638529			−0.319265	−	0.947666i	$-0.603436\pi$
$367$	−234.340			−0.638529			−0.319265	+	0.947666i	$0.603436\pi$
$368$		0			0
$369$	53.9127	−	53.9127i	0.146105	−	0.146105i
$370$		0			0
$371$	797.530	+	797.530i	2.14968	+	2.14968i
$372$		0			0
$373$	335.953			0.900678			0.450339	−	0.892858i	$-0.351303\pi$
$373$	335.953			0.900678			0.450339	+	0.892858i	$0.351303\pi$
$374$		0			0
$375$	26.5846	+	26.5846i	0.0708924	+	0.0708924i
$376$		0			0
$377$	12.0299	+	720.068i	0.0319095	+	1.91000i
$378$		0			0
$379$	−368.522	+	368.522i	−0.972354	+	0.972354i	−0.999628	−	0.0272741i	$-0.991317\pi$
$379$	−368.522	+	368.522i	−0.972354	+	0.972354i	0.0272741	+	0.999628i	$0.491317\pi$
$380$		0			0
$381$			178.419i			0.468293i
$382$		0			0
$383$	−212.301	+	212.301i	−0.554310	+	0.554310i	−0.927682	−	0.373372i	$-0.878201\pi$
$383$	−212.301	+	212.301i	−0.554310	+	0.554310i	0.373372	+	0.927682i	$0.378201\pi$
$384$		0			0
$385$	172.267	+	172.267i	0.447447	+	0.447447i
$386$		0			0
$387$		−	135.471i		−	0.350055i
$388$		0			0
$389$		−	243.902i		−	0.626998i	−0.949588	−	0.313499i	$-0.898499\pi$
$389$		−	243.902i		−	0.626998i	0.949588	−	0.313499i	$-0.101501\pi$
$390$		0			0
$391$	725.881			1.85647
$392$		0			0
$393$	−211.238			−0.537502
$394$		0			0
$395$	−274.432	+	274.432i	−0.694765	+	0.694765i
$396$		0			0
$397$	−236.347	−	236.347i	−0.595333	−	0.595333i	0.343734	−	0.939067i	$-0.388308\pi$
$397$	−236.347	−	236.347i	−0.595333	−	0.595333i	−0.939067	+	0.343734i	$0.888308\pi$
$398$		0			0
$399$	−604.049			−1.51391
$400$		0			0
$401$	−370.977	−	370.977i	−0.925131	−	0.925131i	0.0722555	−	0.997386i	$-0.476980\pi$
$401$	−370.977	−	370.977i	−0.925131	−	0.925131i	−0.997386	+	0.0722555i	$0.976980\pi$
$402$		0			0
$403$	337.028	+	325.952i	0.836299	+	0.808814i
$404$		0			0
$405$	−43.5492	+	43.5492i	−0.107529	+	0.107529i
$406$		0			0
$407$		−	57.8812i		−	0.142214i
$408$		0			0
$409$	387.297	−	387.297i	0.946937	−	0.946937i	−0.0517244	−	0.998661i	$-0.516472\pi$
$409$	387.297	−	387.297i	0.946937	−	0.946937i	0.998661	+	0.0517244i	$0.0164717\pi$
$410$		0			0
$411$	14.0024	+	14.0024i	0.0340691	+	0.0340691i
$412$		0			0
$413$			295.326i			0.715075i
$414$		0			0
$415$		−	124.346i		−	0.299628i
$416$		0			0
$417$	−220.628			−0.529083
$418$		0			0
$419$	−291.152			−0.694874			−0.347437	−	0.937703i	$-0.612948\pi$
$419$	−291.152			−0.694874			−0.347437	+	0.937703i	$0.612948\pi$
$420$		0			0
$421$	−154.602	+	154.602i	−0.367227	+	0.367227i	−0.866465	−	0.499238i	$-0.833613\pi$
$421$	−154.602	+	154.602i	−0.367227	+	0.367227i	0.499238	+	0.866465i	$0.333613\pi$
$422$		0			0
$423$	−180.319	−	180.319i	−0.426285	−	0.426285i
$424$		0			0
$425$	386.770			0.910048
$426$		0			0
$427$	560.239	+	560.239i	1.31203	+	1.31203i
$428$		0			0
$429$	51.9168	−	53.6810i	0.121018	−	0.125130i
$430$		0			0
$431$	−43.8093	+	43.8093i	−0.101646	+	0.101646i	−0.756101	−	0.654455i	$-0.772898\pi$
$431$	−43.8093	+	43.8093i	−0.101646	+	0.101646i	0.654455	+	0.756101i	$0.272898\pi$
$432$		0			0
$433$			302.643i			0.698946i	0.936947	+	0.349473i	$0.113639\pi$
$433$			302.643i			0.698946i	−0.936947	+	0.349473i	$0.886361\pi$
$434$		0			0
$435$	−464.290	+	464.290i	−1.06733	+	1.06733i
$436$		0			0
$437$	−941.142	−	941.142i	−2.15364	−	2.15364i
$438$		0			0
$439$		−	168.472i		−	0.383763i	−0.981418	−	0.191882i	$-0.938541\pi$
$439$		−	168.472i		−	0.383763i	0.981418	−	0.191882i	$-0.0614590\pi$
$440$		0			0
$441$			198.667i			0.450493i
$442$		0			0
$443$	147.793			0.333620			0.166810	−	0.985989i	$-0.446653\pi$
$443$	147.793			0.333620			0.166810	+	0.985989i	$0.446653\pi$
$444$		0			0
$445$	835.855			1.87832
$446$		0			0
$447$	−207.127	+	207.127i	−0.463372	+	0.463372i
$448$		0			0
$449$	376.493	+	376.493i	0.838514	+	0.838514i	0.988663	−	0.150150i	$-0.0479755\pi$
$449$	376.493	+	376.493i	0.838514	+	0.838514i	−0.150150	+	0.988663i	$0.547976\pi$
$450$		0			0
$451$	−84.2909			−0.186898
$452$		0			0
$453$	135.009	+	135.009i	0.298033	+	0.298033i
$454$		0			0
$455$	15.9511	+	954.782i	0.0350574	+	2.09842i
$456$		0			0
$457$	−381.131	+	381.131i	−0.833984	+	0.833984i	−0.988059	−	0.154075i	$-0.950760\pi$
$457$	−381.131	+	381.131i	−0.833984	+	0.833984i	0.154075	+	0.988059i	$0.450760\pi$
$458$		0			0
$459$		−	92.0706i		−	0.200589i
$460$		0			0
$461$	−24.6421	+	24.6421i	−0.0534536	+	0.0534536i	−0.733328	−	0.679875i	$-0.762034\pi$
$461$	−24.6421	+	24.6421i	−0.0534536	+	0.0534536i	0.679875	+	0.733328i	$0.262034\pi$
$462$		0			0
$463$	−534.806	−	534.806i	−1.15509	−	1.15509i	−0.985518	−	0.169570i	$-0.945762\pi$
$463$	−534.806	−	534.806i	−1.15509	−	1.15509i	−0.169570	−	0.985518i	$-0.554238\pi$
$464$		0			0
$465$			427.481i			0.919313i
$466$		0			0
$467$			148.890i			0.318821i	0.987212	+	0.159411i	$0.0509594\pi$
$467$			148.890i			0.318821i	−0.987212	+	0.159411i	$0.949041\pi$
$468$		0			0
$469$	835.615			1.78170
$470$		0			0
$471$	278.154			0.590561
$472$		0			0
$473$	−105.903	+	105.903i	−0.223896	+	0.223896i
$474$		0			0
$475$	−501.467	−	501.467i	−1.05572	−	1.05572i
$476$		0			0
$477$	315.221			0.660840
$478$		0			0
$479$	−39.0514	−	39.0514i	−0.0815269	−	0.0815269i	0.665167	−	0.746694i	$-0.268360\pi$
$479$	−39.0514	−	39.0514i	−0.0815269	−	0.0815269i	−0.746694	+	0.665167i	$0.768360\pi$
$480$		0			0
$481$	157.722	−	163.081i	0.327904	−	0.339047i
$482$		0			0
$483$	−538.569	+	538.569i	−1.11505	+	1.11505i
$484$		0			0
$485$		−	663.440i		−	1.36792i
$486$		0			0
$487$	−139.878	+	139.878i	−0.287223	+	0.287223i	−0.835981	−	0.548758i	$-0.815101\pi$
$487$	−139.878	+	139.878i	−0.287223	+	0.287223i	0.548758	+	0.835981i	$0.315101\pi$
$488$		0			0
$489$	−255.000	−	255.000i	−0.521473	−	0.521473i
$490$		0			0
$491$			359.641i			0.732467i	0.930523	+	0.366234i	$0.119353\pi$
$491$			359.641i			0.732467i	−0.930523	+	0.366234i	$0.880647\pi$
$492$		0			0
$493$		−	981.590i		−	1.99105i
$494$		0			0
$495$	68.0880			0.137551
$496$		0			0
$497$	−867.156			−1.74478
$498$		0			0
$499$	507.347	−	507.347i	1.01673	−	1.01673i	0.0168688	−	0.999858i	$-0.494630\pi$
$499$	507.347	−	507.347i	1.01673	−	1.01673i	0.999858	−	0.0168688i	$-0.00536975\pi$
$500$		0			0
$501$	−285.198	−	285.198i	−0.569258	−	0.569258i
$502$		0			0
$503$	−509.067			−1.01206			−0.506030	−	0.862516i	$-0.668888\pi$
$503$	−509.067			−1.01206			−0.506030	+	0.862516i	$0.668888\pi$
$504$		0			0
$505$	92.3074	+	92.3074i	0.182787	+	0.182787i
$506$		0			0
$507$	292.553	−	9.77785i	0.577028	−	0.0192857i
$508$		0			0
$509$	394.378	−	394.378i	0.774810	−	0.774810i	−0.204133	−	0.978943i	$-0.565438\pi$
$509$	394.378	−	394.378i	0.774810	−	0.774810i	0.978943	+	0.204133i	$0.0654376\pi$
$510$		0			0
$511$		−	552.203i		−	1.08063i
$512$		0			0
$513$	−119.374	+	119.374i	−0.232698	+	0.232698i
$514$		0			0
$515$	485.191	+	485.191i	0.942118	+	0.942118i
$516$		0			0
$517$			281.923i			0.545306i
$518$		0			0
$519$			58.3177i			0.112366i
$520$		0			0
$521$	−928.341			−1.78185			−0.890923	−	0.454155i	$-0.849941\pi$
$521$	−928.341			−1.78185			−0.890923	+	0.454155i	$0.849941\pi$
$522$		0			0
$523$	852.176			1.62940			0.814700	−	0.579882i	$-0.196902\pi$
$523$	852.176			1.62940			0.814700	+	0.579882i	$0.196902\pi$
$524$		0			0
$525$	−286.965	+	286.965i	−0.546599	+	0.546599i
$526$		0			0
$527$	−451.884	−	451.884i	−0.857465	−	0.857465i
$528$		0			0
$529$	−1149.24			−2.17247
$530$		0			0
$531$	58.3632	+	58.3632i	0.109912	+	0.109912i
$532$		0			0
$533$	−237.491	−	229.686i	−0.445575	−	0.430931i
$534$		0			0
$535$	−171.667	+	171.667i	−0.320873	+	0.320873i
$536$		0			0
$537$			483.619i			0.900595i
$538$		0			0
$539$	155.305	−	155.305i	0.288136	−	0.288136i
$540$		0			0
$541$	−608.414	−	608.414i	−1.12461	−	1.12461i	−0.991039	−	0.133570i	$-0.957356\pi$
$541$	−608.414	−	608.414i	−1.12461	−	1.12461i	−0.133570	−	0.991039i	$-0.542644\pi$
$542$		0			0
$543$			501.059i			0.922761i
$544$		0			0
$545$			8.45745i			0.0155183i
$546$		0			0
$547$	658.415			1.20368			0.601842	−	0.798615i	$-0.294434\pi$
$547$	658.415			1.20368			0.601842	+	0.798615i	$0.294434\pi$
$548$		0			0
$549$	221.432			0.403337
$550$		0			0
$551$	−1272.68	+	1272.68i	−2.30976	+	2.30976i
$552$		0			0
$553$	430.478	+	430.478i	0.778441	+	0.778441i
$554$		0			0
$555$	206.849			0.372702
$556$		0			0
$557$	−128.057	−	128.057i	−0.229905	−	0.229905i	0.582748	−	0.812653i	$-0.301977\pi$
$557$	−128.057	−	128.057i	−0.229905	−	0.229905i	−0.812653	+	0.582748i	$0.801977\pi$
$558$		0			0
$559$	−586.960	+	9.80609i	−1.05002	+	0.0175422i
$560$		0			0
$561$	−71.9749	+	71.9749i	−0.128297	+	0.128297i
$562$		0			0
$563$			49.0065i			0.0870453i	0.999052	+	0.0435227i	$0.0138581\pi$
$563$			49.0065i			0.0870453i	−0.999052	+	0.0435227i	$0.986142\pi$
$564$		0			0
$565$	−310.559	+	310.559i	−0.549662	+	0.549662i
$566$		0			0
$567$	68.3119	+	68.3119i	0.120479	+	0.120479i
$568$		0			0
$569$		−	747.338i		−	1.31342i	−0.754142	−	0.656712i	$-0.771947\pi$
$569$		−	747.338i		−	1.31342i	0.754142	−	0.656712i	$-0.228053\pi$
$570$		0			0
$571$			70.8779i			0.124129i	0.998072	+	0.0620647i	$0.0197685\pi$
$571$			70.8779i			0.124129i	−0.998072	+	0.0620647i	$0.980231\pi$
$572$		0			0
$573$	−243.712			−0.425327
$574$		0			0
$575$	−894.213			−1.55515
$576$		0			0
$577$	−117.026	+	117.026i	−0.202818	+	0.202818i	−0.801206	−	0.598388i	$-0.795808\pi$
$577$	−117.026	+	117.026i	−0.202818	+	0.202818i	0.598388	+	0.801206i	$0.295808\pi$
$578$		0			0
$579$	30.9231	+	30.9231i	0.0534077	+	0.0534077i
$580$		0			0
$581$	−195.050			−0.335715
$582$		0			0
$583$	−246.419	−	246.419i	−0.422675	−	0.422675i
$584$		0			0
$585$	191.839	+	185.535i	0.327930	+	0.317153i
$586$		0			0
$587$	−164.713	+	164.713i	−0.280602	+	0.280602i	−0.833349	−	0.552747i	$-0.813580\pi$
$587$	−164.713	+	164.713i	−0.280602	+	0.280602i	0.552747	+	0.833349i	$0.313580\pi$
$588$		0			0
$589$			1171.78i			1.98944i
$590$		0			0
$591$	62.6890	−	62.6890i	0.106073	−	0.106073i
$592$		0			0
$593$	286.598	+	286.598i	0.483302	+	0.483302i	0.906184	−	0.422883i	$-0.138982\pi$
$593$	286.598	+	286.598i	0.483302	+	0.483302i	−0.422883	+	0.906184i	$0.638982\pi$
$594$		0			0
$595$		−	1301.55i		−	2.18748i
$596$		0			0
$597$		−	392.628i		−	0.657669i
$598$		0			0
$599$	−470.036			−0.784701			−0.392350	−	0.919816i	$-0.628338\pi$
$599$	−470.036			−0.784701			−0.392350	+	0.919816i	$0.628338\pi$
$600$		0			0
$601$	−899.620			−1.49687			−0.748436	−	0.663208i	$-0.769195\pi$
$601$	−899.620			−1.49687			−0.748436	+	0.663208i	$0.769195\pi$
$602$		0			0
$603$	165.137	−	165.137i	0.273859	−	0.273859i
$604$		0			0
$605$	−53.2268	−	53.2268i	−0.0879782	−	0.0879782i
$606$		0			0
$607$	269.379			0.443788			0.221894	−	0.975071i	$-0.428776\pi$
$607$	269.379			0.443788			0.221894	+	0.975071i	$0.428776\pi$
$608$		0			0
$609$	728.292	+	728.292i	1.19588	+	1.19588i
$610$		0			0
$611$	−768.219	+	794.324i	−1.25732	+	1.30004i
$612$		0			0
$613$	544.378	−	544.378i	0.888056	−	0.888056i	−0.106280	−	0.994336i	$-0.533894\pi$
$613$	544.378	−	544.378i	0.888056	−	0.888056i	0.994336	+	0.106280i	$0.0338941\pi$
$614$		0			0
$615$		−	301.230i		−	0.489805i
$616$		0			0
$617$	164.882	−	164.882i	0.267232	−	0.267232i	−0.560752	−	0.827984i	$-0.689488\pi$
$617$	164.882	−	164.882i	0.267232	−	0.267232i	0.827984	+	0.560752i	$0.189488\pi$
$618$		0			0
$619$	512.468	+	512.468i	0.827897	+	0.827897i	0.987226	−	0.159329i	$-0.0509330\pi$
$619$	512.468	+	512.468i	0.827897	+	0.827897i	−0.159329	+	0.987226i	$0.550933\pi$
$620$		0			0
$621$			212.867i			0.342781i
$622$		0			0
$623$		−	1311.13i		−	2.10455i
$624$		0			0
$625$	694.238			1.11078
$626$		0			0
$627$	186.638			0.297668
$628$		0			0
$629$	−218.658	+	218.658i	−0.347628	+	0.347628i
$630$		0			0
$631$	−502.876	−	502.876i	−0.796951	−	0.796951i	0.185662	−	0.982614i	$-0.440557\pi$
$631$	−502.876	−	502.876i	−0.796951	−	0.796951i	−0.982614	+	0.185662i	$0.940557\pi$
$632$		0			0
$633$	−517.091			−0.816889
$634$		0			0
$635$	498.448	+	498.448i	0.784957	+	0.784957i
$636$		0			0
$637$	860.772	−	14.3805i	1.35129	−	0.0225754i
$638$		0			0
$639$	−171.370	+	171.370i	−0.268185	+	0.268185i
$640$		0			0
$641$		−	864.862i		−	1.34924i	−0.738166	−	0.674620i	$-0.764308\pi$
$641$		−	864.862i		−	1.34924i	0.738166	−	0.674620i	$-0.235692\pi$
$642$		0			0
$643$	−101.853	+	101.853i	−0.158402	+	0.158402i	−0.781858	−	0.623456i	$-0.785728\pi$
$643$	−101.853	+	101.853i	−0.158402	+	0.158402i	0.623456	+	0.781858i	$0.285728\pi$
$644$		0			0
$645$	−378.464	−	378.464i	−0.586766	−	0.586766i
$646$		0			0
$647$		−	30.2280i		−	0.0467202i	−0.999727	−	0.0233601i	$-0.992564\pi$
$647$		−	30.2280i		−	0.0467202i	0.999727	−	0.0233601i	$-0.00743643\pi$
$648$		0			0
$649$		−	91.2492i		−	0.140600i
$650$		0			0
$651$	670.552			1.03003
$652$		0			0
$653$	−101.806			−0.155905			−0.0779527	−	0.996957i	$-0.524838\pi$
$653$	−101.806			−0.155905			−0.0779527	+	0.996957i	$0.524838\pi$
$654$		0			0
$655$	−590.132	+	590.132i	−0.900966	+	0.900966i
$656$		0			0
$657$	−109.128	−	109.128i	−0.166100	−	0.166100i
$658$		0			0
$659$	4.83033			0.00732979			0.00366490	−	0.999993i	$-0.498833\pi$
$659$	4.83033			0.00732979			0.00366490	+	0.999993i	$0.498833\pi$
$660$		0			0
$661$	550.790	+	550.790i	0.833268	+	0.833268i	0.987962	−	0.154694i	$-0.0494392\pi$
$661$	550.790	+	550.790i	0.833268	+	0.833268i	−0.154694	+	0.987962i	$0.549439\pi$
$662$		0			0
$663$	−398.917	+	6.66453i	−0.601684	+	0.0100521i
$664$		0			0
$665$	−1687.52	+	1687.52i	−2.53763	+	2.53763i
$666$		0			0
$667$			2269.44i			3.40245i
$668$		0			0
$669$	−141.150	+	141.150i	−0.210987	+	0.210987i
$670$		0			0
$671$	−173.102	−	173.102i	−0.257975	−	0.257975i
$672$		0			0
$673$		−	169.145i		−	0.251330i	−0.992073	−	0.125665i	$-0.959893\pi$
$673$		−	169.145i		−	0.251330i	0.992073	−	0.125665i	$-0.0401065\pi$
$674$		0			0
$675$			113.422i			0.168032i
$676$		0			0
$677$	−493.637			−0.729154			−0.364577	−	0.931173i	$-0.618786\pi$
$677$	−493.637			−0.729154			−0.364577	+	0.931173i	$0.618786\pi$
$678$		0			0
$679$	−1040.68			−1.53267
$680$		0			0
$681$	183.274	−	183.274i	0.269124	−	0.269124i
$682$		0			0
$683$	68.8097	+	68.8097i	0.100746	+	0.100746i	0.755683	−	0.654937i	$-0.227305\pi$
$683$	68.8097	+	68.8097i	0.100746	+	0.100746i	−0.654937	+	0.755683i	$0.727305\pi$
$684$		0			0
$685$	78.2366			0.114214
$686$		0			0
$687$	−233.761	−	233.761i	−0.340263	−	0.340263i
$688$		0			0
$689$	−22.8173	−	1365.77i	−0.0331165	−	1.98224i
$690$		0			0
$691$	−159.768	+	159.768i	−0.231213	+	0.231213i	−0.813199	−	0.581986i	$-0.802276\pi$
$691$	−159.768	+	159.768i	−0.231213	+	0.231213i	0.581986	+	0.813199i	$0.302276\pi$
$692$		0			0
$693$		−	106.804i		−	0.154118i
$694$		0			0
$695$	−616.364	+	616.364i	−0.886855	+	0.886855i
$696$		0			0
$697$	318.426	+	318.426i	0.456852	+	0.456852i
$698$		0			0
$699$		−	608.175i		−	0.870064i
$700$		0			0
$701$		−	498.904i		−	0.711703i	−0.934543	−	0.355851i	$-0.884191\pi$
$701$		−	498.904i		−	0.711703i	0.934543	−	0.355851i	$-0.115809\pi$
$702$		0			0
$703$	567.001			0.806545
$704$		0			0
$705$	−1007.51			−1.42909
$706$		0			0
$707$	144.795	−	144.795i	0.204801	−	0.204801i
$708$		0			0
$709$	−484.929	−	484.929i	−0.683963	−	0.683963i	0.276928	−	0.960891i	$-0.410684\pi$
$709$	−484.929	−	484.929i	−0.683963	−	0.683963i	−0.960891	+	0.276928i	$0.910684\pi$
$710$		0			0
$711$	170.145			0.239304
$712$		0			0
$713$	1044.76	+	1044.76i	1.46530	+	1.46530i
$714$		0			0
$715$	−4.92855	−	295.007i	−0.00689308	−	0.412597i
$716$		0			0
$717$	−239.185	+	239.185i	−0.333592	+	0.333592i
$718$		0			0
$719$		−	427.711i		−	0.594870i	−0.954742	−	0.297435i	$-0.903869\pi$
$719$		−	427.711i		−	0.594870i	0.954742	−	0.297435i	$-0.0961311\pi$
$720$		0			0
$721$	761.077	−	761.077i	1.05558	−	1.05558i
$722$		0			0
$723$	−538.731	−	538.731i	−0.745133	−	0.745133i
$724$		0			0
$725$			1209.22i			1.66789i
$726$		0			0
$727$		−	839.600i		−	1.15488i	−0.816432	−	0.577441i	$-0.804051\pi$
$727$		−	839.600i		−	1.15488i	0.816432	−	0.577441i	$-0.195949\pi$
$728$		0			0
$729$	27.0000			0.0370370
$730$		0			0
$731$	800.138			1.09458
$732$		0			0
$733$	46.5739	−	46.5739i	0.0635388	−	0.0635388i	−0.674623	−	0.738162i	$-0.735694\pi$
$733$	46.5739	−	46.5739i	0.0635388	−	0.0635388i	0.738162	+	0.674623i	$0.235694\pi$
$734$		0			0
$735$	555.014	+	555.014i	0.755121	+	0.755121i
$736$		0			0
$737$	−258.187			−0.350321
$738$		0			0
$739$	82.1909	+	82.1909i	0.111219	+	0.111219i	0.760526	−	0.649307i	$-0.224941\pi$
$739$	82.1909	+	82.1909i	0.111219	+	0.111219i	−0.649307	+	0.760526i	$0.724941\pi$
$740$		0			0
$741$	525.856	+	508.575i	0.709658	+	0.686336i
$742$		0			0
$743$	662.739	−	662.739i	0.891977	−	0.891977i	−0.102732	−	0.994709i	$-0.532758\pi$
$743$	662.739	−	662.739i	0.891977	−	0.891977i	0.994709	+	0.102732i	$0.0327583\pi$
$744$		0			0
$745$			1157.30i			1.55342i
$746$		0			0
$747$	−38.5464	+	38.5464i	−0.0516017	+	0.0516017i
$748$		0			0
$749$	269.279	+	269.279i	0.359518	+	0.359518i
$750$		0			0
$751$			605.065i			0.805679i	0.915271	+	0.402839i	$0.131977\pi$
$751$			605.065i			0.805679i	−0.915271	+	0.402839i	$0.868023\pi$
$752$		0			0
$753$		−	202.095i		−	0.268387i
$754$		0			0
$755$	754.345			0.999133
$756$		0			0
$757$	−232.237			−0.306786			−0.153393	−	0.988165i	$-0.549020\pi$
$757$	−232.237			−0.306786			−0.153393	+	0.988165i	$0.549020\pi$
$758$		0			0
$759$	166.406	−	166.406i	0.219244	−	0.219244i
$760$		0			0
$761$	287.341	+	287.341i	0.377583	+	0.377583i	0.870230	−	0.492646i	$-0.163970\pi$
$761$	287.341	+	287.341i	0.377583	+	0.377583i	−0.492646	+	0.870230i	$0.663970\pi$
$762$		0			0
$763$	13.2665			0.0173872
$764$		0			0
$765$	−257.216	−	257.216i	−0.336230	−	0.336230i
$766$		0			0
$767$	248.647	−	257.097i	0.324182	−	0.335198i
$768$		0			0
$769$	514.795	−	514.795i	0.669435	−	0.669435i	−0.288150	−	0.957585i	$-0.593040\pi$
$769$	514.795	−	514.795i	0.669435	−	0.669435i	0.957585	+	0.288150i	$0.0930403\pi$
$770$		0			0
$771$			249.679i			0.323838i
$772$		0			0
$773$	1022.18	−	1022.18i	1.32235	−	1.32235i	0.410487	−	0.911866i	$-0.365359\pi$
$773$	1022.18	−	1022.18i	1.32235	−	1.32235i	0.911866	−	0.410487i	$-0.134641\pi$
$774$		0			0
$775$	556.675	+	556.675i	0.718291	+	0.718291i
$776$		0			0
$777$		−	324.467i		−	0.417589i
$778$		0			0
$779$		−	825.710i		−	1.05996i
$780$		0			0
$781$	267.932			0.343063
$782$		0			0
$783$	287.854			0.367630
$784$		0			0
$785$	777.075	−	777.075i	0.989905	−	0.989905i
$786$		0			0
$787$	−75.2097	−	75.2097i	−0.0955651	−	0.0955651i	0.657708	−	0.753273i	$-0.271526\pi$
$787$	−75.2097	−	75.2097i	−0.0955651	−	0.0955651i	−0.753273	+	0.657708i	$0.771526\pi$
$788$		0			0
$789$	−149.204			−0.189105
$790$		0			0
$791$	487.147	+	487.147i	0.615862	+	0.615862i
$792$		0			0
$793$	−16.0284	−	959.406i	−0.0202123	−	1.20984i
$794$		0			0
$795$	880.627	−	880.627i	1.10771	−	1.10771i
$796$		0			0
$797$			616.204i			0.773154i	0.922257	+	0.386577i	$0.126343\pi$
$797$			616.204i			0.773154i	−0.922257	+	0.386577i	$0.873657\pi$
$798$		0			0
$799$	1065.02	−	1065.02i	1.33294	−	1.33294i
$800$		0			0
$801$	−259.110	−	259.110i	−0.323483	−	0.323483i
$802$		0			0
$803$			170.619i			0.212476i
$804$		0			0
$805$			3009.18i			3.73811i
$806$		0			0
$807$	456.177			0.565275
$808$		0			0
$809$	−1248.92			−1.54379			−0.771894	−	0.635751i	$-0.780690\pi$
$809$	−1248.92			−1.54379			−0.771894	+	0.635751i	$0.780690\pi$
$810$		0			0
$811$	−207.228	+	207.228i	−0.255521	+	0.255521i	−0.823230	−	0.567708i	$-0.807830\pi$
$811$	−207.228	+	207.228i	−0.255521	+	0.255521i	0.567708	+	0.823230i	$0.307830\pi$
$812$		0			0
$813$	−75.9965	−	75.9965i	−0.0934767	−	0.0934767i
$814$		0			0
$815$	−1424.78			−1.74820
$816$		0			0
$817$	−1037.42	−	1037.42i	−1.26979	−	1.26979i
$818$		0			0
$819$	291.032	−	300.922i	0.355350	−	0.367426i
$820$		0			0
$821$	−394.145	+	394.145i	−0.480079	+	0.480079i	−0.905157	−	0.425078i	$-0.860247\pi$
$821$	−394.145	+	394.145i	−0.480079	+	0.480079i	0.425078	+	0.905157i	$0.360247\pi$
$822$		0			0
$823$		−	1513.18i		−	1.83861i	−0.393545	−	0.919305i	$-0.628752\pi$
$823$		−	1513.18i		−	1.83861i	0.393545	−	0.919305i	$-0.371248\pi$
$824$		0			0
$825$	88.6658	−	88.6658i	0.107474	−	0.107474i
$826$		0			0
$827$	−732.981	−	732.981i	−0.886313	−	0.886313i	0.107854	−	0.994167i	$-0.465602\pi$
$827$	−732.981	−	732.981i	−0.886313	−	0.886313i	−0.994167	+	0.107854i	$0.965602\pi$
$828$		0			0
$829$			11.4516i			0.0138138i	0.999976	+	0.00690690i	$0.00219855\pi$
$829$			11.4516i			0.0138138i	−0.999976	+	0.00690690i	$0.997801\pi$
$830$		0			0
$831$			717.793i			0.863770i
$832$		0			0
$833$	−1173.40			−1.40864
$834$		0			0
$835$	−1593.51			−1.90839
$836$		0			0
$837$	132.516	−	132.516i	0.158323	−	0.158323i
$838$		0			0
$839$	−50.2827	−	50.2827i	−0.0599318	−	0.0599318i	0.676506	−	0.736437i	$-0.263493\pi$
$839$	−50.2827	−	50.2827i	−0.0599318	−	0.0599318i	−0.736437	+	0.676506i	$0.763493\pi$
$840$		0			0
$841$	2227.90			2.64910
$842$		0			0
$843$	−267.470	−	267.470i	−0.317283	−	0.317283i
$844$		0			0
$845$	789.985	−	844.617i	0.934893	−	0.999547i
$846$		0			0
$847$	−83.4923	+	83.4923i	−0.0985741	+	0.0985741i
$848$		0			0
$849$		−	583.604i		−	0.687401i
$850$		0			0
$851$	505.537	−	505.537i	0.594050	−	0.594050i
$852$		0			0
$853$	−128.625	−	128.625i	−0.150791	−	0.150791i	0.627680	−	0.778471i	$-0.284005\pi$
$853$	−128.625	−	128.625i	−0.150791	−	0.150791i	−0.778471	+	0.627680i	$0.784005\pi$
$854$		0			0
$855$			666.987i			0.780102i
$856$		0			0
$857$			706.522i			0.824413i	0.911091	+	0.412206i	$0.135242\pi$
$857$			706.522i			0.824413i	−0.911091	+	0.412206i	$0.864758\pi$
$858$		0			0
$859$	−843.485			−0.981938			−0.490969	−	0.871177i	$-0.663357\pi$
$859$	−843.485			−0.981938			−0.490969	+	0.871177i	$0.663357\pi$
$860$		0			0
$861$	−472.513			−0.548795
$862$		0			0
$863$	−908.334	+	908.334i	−1.05253	+	1.05253i	−0.0539888	+	0.998542i	$0.517194\pi$
$863$	−908.334	+	908.334i	−1.05253	+	1.05253i	−0.998542	+	0.0539888i	$0.982806\pi$
$864$		0			0
$865$	162.921	+	162.921i	0.188348	+	0.188348i
$866$		0			0
$867$	43.2365			0.0498691
$868$		0			0
$869$	−133.008	−	133.008i	−0.153059	−	0.153059i
$870$		0			0
$871$	−727.447	−	703.540i	−0.835186	−	0.807738i
$872$		0			0
$873$	−205.663	+	205.663i	−0.235581	+	0.235581i
$874$		0			0
$875$		−	232.999i		−	0.266284i
$876$		0			0
$877$	709.911	−	709.911i	0.809477	−	0.809477i	−0.175078	−	0.984555i	$-0.556018\pi$
$877$	709.911	−	709.911i	0.809477	−	0.809477i	0.984555	+	0.175078i	$0.0560176\pi$
$878$		0			0
$879$	−153.183	−	153.183i	−0.174270	−	0.174270i
$880$		0			0
$881$			688.880i			0.781930i	0.920406	+	0.390965i	$0.127859\pi$
$881$			688.880i			0.781930i	−0.920406	+	0.390965i	$0.872141\pi$
$882$		0			0
$883$		−	550.082i		−	0.622970i	−0.950251	−	0.311485i	$-0.899174\pi$
$883$		−	550.082i		−	0.622970i	0.950251	−	0.311485i	$-0.100826\pi$
$884$		0			0
$885$	326.097			0.368471
$886$		0			0
$887$	−172.821			−0.194837			−0.0974187	−	0.995243i	$-0.531059\pi$
$887$	−172.821			−0.194837			−0.0974187	+	0.995243i	$0.531059\pi$
$888$		0			0
$889$	781.871	−	781.871i	0.879495	−	0.879495i
$890$		0			0
$891$	−21.1069	−	21.1069i	−0.0236890	−	0.0236890i
$892$		0			0
$893$	−2761.71			−3.09262
$894$		0			0
$895$	1351.08	+	1351.08i	1.50959	+	1.50959i
$896$		0			0
$897$	922.296	−	15.4084i	1.02820	−	0.0171777i
$898$		0			0
$899$	1412.79	−	1412.79i	1.57152	−	1.57152i
$900$		0			0
$901$			1861.80i			2.06637i
$902$		0			0
$903$	−593.663	+	593.663i	−0.657434	+	0.657434i
$904$		0			0
$905$	1399.80	+	1399.80i	1.54674	+	1.54674i
$906$		0			0
$907$		−	836.402i		−	0.922163i	−0.887358	−	0.461082i	$-0.847462\pi$
$907$		−	836.402i		−	0.922163i	0.887358	−	0.461082i	$-0.152538\pi$
$908$		0			0
$909$		−	57.2295i		−	0.0629587i
$910$		0			0
$911$	−576.799			−0.633150			−0.316575	−	0.948568i	$-0.602533\pi$
$911$	−576.799			−0.633150			−0.316575	+	0.948568i	$0.602533\pi$
$912$		0			0
$913$	60.2663			0.0660091
$914$		0			0
$915$	618.612	−	618.612i	0.676078	−	0.676078i
$916$		0			0
$917$	925.689	+	925.689i	1.00948	+	1.00948i
$918$		0			0
$919$	−512.447			−0.557614			−0.278807	−	0.960347i	$-0.589939\pi$
$919$	−512.447			−0.557614			−0.278807	+	0.960347i	$0.589939\pi$
$920$		0			0
$921$	22.1765	+	22.1765i	0.0240787	+	0.0240787i
$922$		0			0
$923$	754.905	+	730.095i	0.817881	+	0.791002i
$924$		0			0
$925$	269.364	−	269.364i	0.291205	−	0.291205i
$926$		0			0
$927$		−	300.813i		−	0.324501i
$928$		0			0
$929$	1053.90	−	1053.90i	1.13445	−	1.13445i	0.145017	−	0.989429i	$-0.453676\pi$
$929$	1053.90	−	1053.90i	1.13445	−	1.13445i	0.989429	−	0.145017i	$-0.0463238\pi$
$930$		0			0
$931$	1521.37	+	1521.37i	1.63412	+	1.63412i
$932$		0			0
$933$			394.636i			0.422976i
$934$		0			0
$935$			402.150i			0.430107i
$936$		0			0
$937$	−960.298			−1.02486			−0.512432	−	0.858728i	$-0.671255\pi$
$937$	−960.298			−1.02486			−0.512432	+	0.858728i	$0.671255\pi$
$938$		0			0
$939$	−130.786			−0.139282
$940$		0			0
$941$	905.803	−	905.803i	0.962596	−	0.962596i	−0.0367295	−	0.999325i	$-0.511694\pi$
$941$	905.803	−	905.803i	0.962596	−	0.962596i	0.999325	+	0.0367295i	$0.0116940\pi$
$942$		0			0
$943$	−736.201	−	736.201i	−0.780701	−	0.780701i
$944$		0			0
$945$	381.683			0.403898
$946$		0			0
$947$	−26.8322	−	26.8322i	−0.0283339	−	0.0283339i	0.692798	−	0.721132i	$-0.256378\pi$
$947$	−26.8322	−	26.8322i	−0.0283339	−	0.0283339i	−0.721132	+	0.692798i	$0.756378\pi$
$948$		0			0
$949$	−464.923	+	480.721i	−0.489908	+	0.506556i
$950$		0			0
$951$	341.836	−	341.836i	0.359449	−	0.359449i
$952$		0			0
$953$		−	863.412i		−	0.905994i	−0.891512	−	0.452997i	$-0.850355\pi$
$953$		−	863.412i		−	0.905994i	0.891512	−	0.452997i	$-0.149645\pi$
$954$		0			0
$955$	−680.855	+	680.855i	−0.712937	+	0.712937i
$956$		0			0
$957$	−225.026	−	225.026i	−0.235137	−	0.235137i
$958$		0			0
$959$		−	122.723i		−	0.127970i
$960$		0			0
$961$		−	339.787i		−	0.353576i
$962$		0			0
$963$	106.432			0.110521
$964$		0			0
$965$	172.779			0.179045
$966$		0			0
$967$	−1072.33	+	1072.33i	−1.10893	+	1.10893i	−0.115638	+	0.993291i	$0.536891\pi$
$967$	−1072.33	+	1072.33i	−1.10893	+	1.10893i	−0.993291	+	0.115638i	$0.963109\pi$
$968$		0			0
$969$	−705.063	−	705.063i	−0.727619	−	0.727619i
$970$		0			0
$971$	339.135			0.349264			0.174632	−	0.984634i	$-0.444126\pi$
$971$	339.135			0.349264			0.174632	+	0.984634i	$0.444126\pi$
$972$		0			0
$973$	966.837	+	966.837i	0.993666	+	0.993666i
$974$		0			0
$975$	491.425	−	8.21003i	0.504026	−	0.00842054i
$976$		0			0
$977$	690.746	−	690.746i	0.707007	−	0.707007i	−0.258897	−	0.965905i	$-0.583359\pi$
$977$	690.746	−	690.746i	0.707007	−	0.707007i	0.965905	+	0.258897i	$0.0833592\pi$
$978$		0			0
$979$			405.111i			0.413801i
$980$		0			0
$981$	2.62176	−	2.62176i	0.00267254	−	0.00267254i
$982$		0			0
$983$	418.621	+	418.621i	0.425861	+	0.425861i	0.887216	−	0.461355i	$-0.152636\pi$
$983$	418.621	+	418.621i	0.425861	+	0.425861i	−0.461355	+	0.887216i	$0.652636\pi$
$984$		0			0
$985$		−	350.267i		−	0.355601i
$986$		0			0
$987$			1580.39i			1.60120i
$988$		0			0
$989$	−1849.92			−1.87049
$990$		0			0
$991$	44.3312			0.0447338			0.0223669	−	0.999750i	$-0.492880\pi$
$991$	44.3312			0.0447338			0.0223669	+	0.999750i	$0.492880\pi$
$992$		0			0
$993$	−6.18105	+	6.18105i	−0.00622462	+	0.00622462i
$994$		0			0
$995$	−1096.88	−	1096.88i	−1.10239	−	1.10239i
$996$		0			0
$997$	891.053			0.893734			0.446867	−	0.894600i	$-0.352540\pi$
$997$	891.053			0.893734			0.446867	+	0.894600i	$0.352540\pi$
$998$		0			0
$999$	−64.1221	−	64.1221i	−0.0641863	−	0.0641863i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1716.3.s.a.265.5	✓	96
13.8	odd	4	inner	1716.3.s.a.1321.5	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1716.3.s.a.265.5	✓	96	1.1	even	1	trivial
1716.3.s.a.1321.5	yes	96	13.8	odd	4	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:	\( N \)	\(=\)	\( 1716 = 2^{2} \cdot 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1716.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.73205 q^{3} +(-4.83880 + 4.83880i) q^{5} +(7.59021 + 7.59021i) q^{7} +3.00000 q^{9} +O(q^{10})\)	\(q-1.73205 q^{3} +(-4.83880 + 4.83880i) q^{5} +(7.59021 + 7.59021i) q^{7} +3.00000 q^{9} +(-2.34521 - 2.34521i) q^{11} +(-0.217155 - 12.9982i) q^{13} +(8.38105 - 8.38105i) q^{15} +17.7190i q^{17} +(22.9736 - 22.9736i) q^{19} +(-13.1466 - 13.1466i) q^{21} -40.9663i q^{23} -21.8280i q^{25} -5.19615 q^{27} -55.3976 q^{29} +(-25.5028 + 25.5028i) q^{31} +(4.06202 + 4.06202i) q^{33} -73.4550 q^{35} +(12.3403 + 12.3403i) q^{37} +(0.376124 + 22.5135i) q^{39} +(17.9709 - 17.9709i) q^{41} -45.1571i q^{43} +(-14.5164 + 14.5164i) q^{45} +(-60.1062 - 60.1062i) q^{47} +66.2225i q^{49} -30.6902i q^{51} +105.074 q^{53} +22.6960 q^{55} +(-39.7914 + 39.7914i) q^{57} +(19.4544 + 19.4544i) q^{59} +73.8107 q^{61} +(22.7706 + 22.7706i) q^{63} +(63.9464 + 61.8449i) q^{65} +(55.0456 - 55.0456i) q^{67} +70.9557i q^{69} +(-57.1233 + 57.1233i) q^{71} +(-36.3760 - 36.3760i) q^{73} +37.8072i q^{75} -35.6012i q^{77} +56.7149 q^{79} +9.00000 q^{81} +(-12.8488 + 12.8488i) q^{83} +(-85.7387 - 85.7387i) q^{85} +95.9515 q^{87} +(-86.3700 - 86.3700i) q^{89} +(97.0107 - 100.307i) q^{91} +(44.1722 - 44.1722i) q^{93} +222.329i q^{95} +(-68.5542 + 68.5542i) q^{97} +(-7.03562 - 7.03562i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 24 q^{5} + 16 q^{7} + 288 q^{9}+O(q^{10}) \) 96 * q - 24 * q^5 + 16 * q^7 + 288 * q^9	\( 96 q - 24 q^{5} + 16 q^{7} + 288 q^{9} - 16 q^{13} - 40 q^{19} + 80 q^{29} + 88 q^{31} + 112 q^{35} + 8 q^{37} - 144 q^{39} + 120 q^{41} - 72 q^{45} + 80 q^{47} + 64 q^{53} - 48 q^{57} - 16 q^{59} + 176 q^{61} + 48 q^{63} + 120 q^{65} + 24 q^{67} - 176 q^{73} - 208 q^{79} + 864 q^{81} - 64 q^{83} - 200 q^{85} + 240 q^{87} + 120 q^{89} + 168 q^{91} - 192 q^{93} - 120 q^{97}+O(q^{100}) \) 96 * q - 24 * q^5 + 16 * q^7 + 288 * q^9 - 16 * q^13 - 40 * q^19 + 80 * q^29 + 88 * q^31 + 112 * q^35 + 8 * q^37 - 144 * q^39 + 120 * q^41 - 72 * q^45 + 80 * q^47 + 64 * q^53 - 48 * q^57 - 16 * q^59 + 176 * q^61 + 48 * q^63 + 120 * q^65 + 24 * q^67 - 176 * q^73 - 208 * q^79 + 864 * q^81 - 64 * q^83 - 200 * q^85 + 240 * q^87 + 120 * q^89 + 168 * q^91 - 192 * q^93 - 120 * q^97

Introduction

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