LMFDB - Embedded newform 960.3.i.a.929.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,3,Mod(929,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("960.929");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	960.i (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$26.1581053786$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			929.7
Character	$\chi$	$=$	960.929
Dual form			960.3.i.a.929.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.81345 + 1.04140i) q^{3} +(4.33946 - 2.48376i) q^{5} -10.8770i q^{7} +(6.83095 - 5.85987i) q^{9} +O(q^{10})$	\(q+(-2.81345 + 1.04140i) q^{3} +(4.33946 - 2.48376i) q^{5} -10.8770i q^{7} +(6.83095 - 5.85987i) q^{9} +15.2961 q^{11} -1.83874 q^{13} +(-9.62225 + 11.5071i) q^{15} +20.4760 q^{17} -13.6619i q^{19} +(11.3274 + 30.6019i) q^{21} -19.4502 q^{23} +(12.6619 - 21.5563i) q^{25} +(-13.1160 + 23.6002i) q^{27} +24.5696 q^{29} -50.8574 q^{31} +(-43.0348 + 15.9295i) q^{33} +(-27.0159 - 47.2004i) q^{35} +16.2378 q^{37} +(5.17319 - 1.91487i) q^{39} +42.3120i q^{41} +26.2320 q^{43} +(15.0882 - 42.3951i) q^{45} -58.3505 q^{47} -69.3095 q^{49} +(-57.6081 + 21.3238i) q^{51} -63.7379i q^{53} +(66.3770 - 37.9919i) q^{55} +(14.2276 + 38.4370i) q^{57} +31.5828 q^{59} +81.8966i q^{61} +(-63.7379 - 74.3004i) q^{63} +(-7.97914 + 4.56698i) q^{65} +50.6420 q^{67} +(54.7220 - 20.2555i) q^{69} -135.929i q^{71} -33.7613i q^{73} +(-13.1747 + 73.8338i) q^{75} -166.376i q^{77} +81.8966 q^{79} +(12.3238 - 80.0570i) q^{81} +75.6556i q^{83} +(88.8549 - 50.8574i) q^{85} +(-69.1253 + 25.5869i) q^{87} -124.350i q^{89} +20.0000i q^{91} +(143.085 - 52.9632i) q^{93} +(-33.9328 - 59.2853i) q^{95} +58.1713i q^{97} +(104.487 - 89.6333i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{9}+O(q^{10}) $ 32 * q + 32 * q^9	$ 32 q + 32 q^{9} + 32 q^{25} - 352 q^{49} - 352 q^{81}+O(q^{100}) $ 32 * q + 32 * q^9 + 32 * q^25 - 352 * q^49 - 352 * q^81

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$1$	$-1$	$-1$	$-1$

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
$3$	−2.81345	+	1.04140i	−0.937815	+	0.347135i
$3$	−2.81345	+	1.04140i	−0.937815	+	0.347135i
$4$		0			0
$5$	4.33946	−	2.48376i	0.867893	−	0.496751i
$5$	4.33946	−	2.48376i	0.867893	−	0.496751i
$6$		0			0
$7$		−	10.8770i		−	1.55386i	−0.629587	−	0.776930i	$-0.716776\pi$
$7$		−	10.8770i		−	1.55386i	0.629587	−	0.776930i	$-0.283224\pi$
$8$		0			0
$9$	6.83095	−	5.85987i	0.758995	−	0.651097i
$10$		0			0
$11$	15.2961			1.39056			0.695278	−	0.718741i	$-0.255281\pi$
$11$	15.2961			1.39056			0.695278	+	0.718741i	$0.255281\pi$
$12$		0			0
$13$	−1.83874			−0.141441			−0.0707207	−	0.997496i	$-0.522530\pi$
$13$	−1.83874			−0.141441			−0.0707207	+	0.997496i	$0.522530\pi$
$14$		0			0
$15$	−9.62225	+	11.5071i	−0.641483	+	0.767137i
$16$		0			0
$17$	20.4760			1.20447			0.602235	−	0.798319i	$-0.294277\pi$
$17$	20.4760			1.20447			0.602235	+	0.798319i	$0.294277\pi$
$18$		0			0
$19$		−	13.6619i		−	0.719048i	−0.933136	−	0.359524i	$-0.882939\pi$
$19$		−	13.6619i		−	0.719048i	0.933136	−	0.359524i	$-0.117061\pi$
$20$		0			0
$21$	11.3274	+	30.6019i	0.539399	+	1.45723i
$22$		0			0
$23$	−19.4502			−0.845660			−0.422830	−	0.906209i	$-0.638963\pi$
$23$	−19.4502			−0.845660			−0.422830	+	0.906209i	$0.638963\pi$
$24$		0			0
$25$	12.6619	−	21.5563i	0.506476	−	0.862254i
$26$		0			0
$27$	−13.1160	+	23.6002i	−0.485778	+	0.874082i
$28$		0			0
$29$	24.5696			0.847229			0.423614	−	0.905843i	$-0.360761\pi$
$29$	24.5696			0.847229			0.423614	+	0.905843i	$0.360761\pi$
$30$		0			0
$31$	−50.8574			−1.64056			−0.820281	−	0.571961i	$-0.806183\pi$
$31$	−50.8574			−1.64056			−0.820281	+	0.571961i	$0.806183\pi$
$32$		0			0
$33$	−43.0348	+	15.9295i	−1.30409	+	0.482711i
$34$		0			0
$35$	−27.0159	−	47.2004i	−0.771882	−	1.34858i
$36$		0			0
$37$	16.2378			0.438860			0.219430	−	0.975628i	$-0.429580\pi$
$37$	16.2378			0.438860			0.219430	+	0.975628i	$0.429580\pi$
$38$		0			0
$39$	5.17319	−	1.91487i	0.132646	−	0.0490993i
$40$		0			0
$41$			42.3120i			1.03200i	0.856589	+	0.516000i	$0.172580\pi$
$41$			42.3120i			1.03200i	−0.856589	+	0.516000i	$0.827420\pi$
$42$		0			0
$43$	26.2320			0.610047			0.305024	−	0.952345i	$-0.401336\pi$
$43$	26.2320			0.610047			0.305024	+	0.952345i	$0.401336\pi$
$44$		0			0
$45$	15.0882	−	42.3951i	0.335293	−	0.942114i
$46$		0			0
$47$	−58.3505			−1.24150			−0.620750	−	0.784008i	$-0.713172\pi$
$47$	−58.3505			−1.24150			−0.620750	+	0.784008i	$0.713172\pi$
$48$		0			0
$49$	−69.3095			−1.41448
$50$		0			0
$51$	−57.6081	+	21.3238i	−1.12957	+	0.418114i
$52$		0			0
$53$		−	63.7379i		−	1.20260i	−0.799022	−	0.601301i	$-0.794649\pi$
$53$		−	63.7379i		−	1.20260i	0.799022	−	0.601301i	$-0.205351\pi$
$54$		0			0
$55$	66.3770	−	37.9919i	1.20685	−	0.690761i
$56$		0			0
$57$	14.2276	+	38.4370i	0.249607	+	0.674334i
$58$		0			0
$59$	31.5828			0.535303			0.267651	−	0.963516i	$-0.413752\pi$
$59$	31.5828			0.535303			0.267651	+	0.963516i	$0.413752\pi$
$60$		0			0
$61$			81.8966i			1.34257i	0.741201	+	0.671283i	$0.234257\pi$
$61$			81.8966i			1.34257i	−0.741201	+	0.671283i	$0.765743\pi$
$62$		0			0
$63$	−63.7379	−	74.3004i	−1.01171	−	1.17937i
$64$		0			0
$65$	−7.97914	+	4.56698i	−0.122756	+	0.0702613i
$66$		0			0
$67$	50.6420			0.755851			0.377926	−	0.925836i	$-0.376638\pi$
$67$	50.6420			0.755851			0.377926	+	0.925836i	$0.376638\pi$
$68$		0			0
$69$	54.7220	−	20.2555i	0.793073	−	0.293558i
$70$		0			0
$71$		−	135.929i		−	1.91449i	−0.289284	−	0.957243i	$-0.593417\pi$
$71$		−	135.929i		−	1.91449i	0.289284	−	0.957243i	$-0.406583\pi$
$72$		0			0
$73$		−	33.7613i		−	0.462484i	−0.972896	−	0.231242i	$-0.925721\pi$
$73$		−	33.7613i		−	0.462484i	0.972896	−	0.231242i	$-0.0742789\pi$
$74$		0			0
$75$	−13.1747	+	73.8338i	−0.175663	+	0.984450i
$76$		0			0
$77$		−	166.376i		−	2.16073i
$78$		0			0
$79$	81.8966			1.03667			0.518333	−	0.855179i	$-0.326553\pi$
$79$	81.8966			1.03667			0.518333	+	0.855179i	$0.326553\pi$
$80$		0			0
$81$	12.3238	−	80.0570i	0.152146	−	0.988358i
$82$		0			0
$83$			75.6556i			0.911513i	0.890104	+	0.455756i	$0.150631\pi$
$83$			75.6556i			0.911513i	−0.890104	+	0.455756i	$0.849369\pi$
$84$		0			0
$85$	88.8549	−	50.8574i	1.04535	−	0.598322i
$86$		0			0
$87$	−69.1253	+	25.5869i	−0.794544	+	0.294103i
$88$		0			0
$89$		−	124.350i		−	1.39719i	−0.715516	−	0.698597i	$-0.753808\pi$
$89$		−	124.350i		−	1.39719i	0.715516	−	0.698597i	$-0.246192\pi$
$90$		0			0
$91$			20.0000i			0.219780i
$92$		0			0
$93$	143.085	−	52.9632i	1.53854	−	0.569496i
$94$		0			0
$95$	−33.9328	−	59.2853i	−0.357188	−	0.624056i
$96$		0			0
$97$			58.1713i			0.599705i	0.953986	+	0.299852i	$0.0969374\pi$
$97$			58.1713i			0.599705i	−0.953986	+	0.299852i	$0.903063\pi$
$98$		0			0
$99$	104.487	−	89.6333i	1.05543	−	0.905387i
$100$		0			0
$101$	−62.2197			−0.616036			−0.308018	−	0.951380i	$-0.599666\pi$
$101$	−62.2197			−0.616036			−0.308018	+	0.951380i	$0.599666\pi$
$102$		0			0
$103$			94.5265i			0.917733i	0.888505	+	0.458867i	$0.151744\pi$
$103$			94.5265i			0.917733i	−0.888505	+	0.458867i	$0.848256\pi$
$104$		0			0
$105$	125.162	+	104.661i	1.19202	+	0.996775i
$106$		0			0
$107$			2.78700i			0.0260467i	0.999915	+	0.0130234i	$0.00414558\pi$
$107$			2.78700i			0.0260467i	−0.999915	+	0.0130234i	$0.995854\pi$
$108$		0			0
$109$		−	19.8183i		−	0.181819i	−0.995859	−	0.0909094i	$-0.971023\pi$
$109$		−	19.8183i		−	0.181819i	0.995859	−	0.0909094i	$-0.0289774\pi$
$110$		0			0
$111$	−45.6842	+	16.9101i	−0.411570	+	0.152344i
$112$		0			0
$113$	73.9249			0.654202			0.327101	−	0.944989i	$-0.393928\pi$
$113$	73.9249			0.654202			0.327101	+	0.944989i	$0.393928\pi$
$114$		0			0
$115$	−84.4034	+	48.3095i	−0.733942	+	0.420083i
$116$		0			0
$117$	−12.5603	+	10.7748i	−0.107353	+	0.0920921i
$118$		0			0
$119$		−	222.718i		−	1.87158i
$120$		0			0
$121$	112.971			0.933648
$122$		0			0
$123$	−44.0639	−	119.042i	−0.358243	−	0.967825i
$124$		0			0
$125$	1.40515	−	124.992i	0.0112412	−	0.999937i
$126$		0			0
$127$		−	119.647i		−	0.942104i	−0.882105	−	0.471052i	$-0.843874\pi$
$127$		−	119.647i		−	0.942104i	0.882105	−	0.471052i	$-0.156126\pi$
$128$		0			0
$129$	−73.8024	+	27.3182i	−0.572111	+	0.211769i
$130$		0			0
$131$	13.3149			0.101641			0.0508203	−	0.998708i	$-0.483816\pi$
$131$	13.3149			0.101641			0.0508203	+	0.998708i	$0.483816\pi$
$132$		0			0
$133$	−148.601			−1.11730
$134$		0			0
$135$	1.70073	+	134.989i	0.0125980	+	0.999921i
$136$		0			0
$137$	−271.762			−1.98366			−0.991832	−	0.127550i	$-0.959289\pi$
$137$	−271.762			−1.98366			−0.991832	+	0.127550i	$0.959289\pi$
$138$		0			0
$139$		−	170.281i		−	1.22504i	−0.790454	−	0.612521i	$-0.790155\pi$
$139$		−	170.281i		−	1.22504i	0.790454	−	0.612521i	$-0.209845\pi$
$140$		0			0
$141$	164.166	−	60.7665i	1.16430	−	0.430968i
$142$		0			0
$143$	−28.1256			−0.196682
$144$		0			0
$145$	106.619	−	61.0250i	0.735304	−	0.420862i
$146$		0			0
$147$	194.999	−	72.1793i	1.32652	−	0.491015i
$148$		0			0
$149$	−179.323			−1.20351			−0.601756	−	0.798680i	$-0.705532\pi$
$149$	−179.323			−1.20351			−0.601756	+	0.798680i	$0.705532\pi$
$150$		0			0
$151$	183.611			1.21597			0.607985	−	0.793949i	$-0.291978\pi$
$151$	183.611			1.21597			0.607985	+	0.793949i	$0.291978\pi$
$152$		0			0
$153$	139.871	−	119.987i	0.914187	−	0.784227i
$154$		0			0
$155$	−220.694	+	126.317i	−1.42383	+	0.814951i
$156$		0			0
$157$	175.560			1.11822			0.559109	−	0.829094i	$-0.311143\pi$
$157$	175.560			1.11822			0.559109	+	0.829094i	$0.311143\pi$
$158$		0			0
$159$	66.3770	+	179.323i	0.417465	+	1.12782i
$160$		0			0
$161$			211.560i			1.31404i
$162$		0			0
$163$	−266.206			−1.63316			−0.816581	−	0.577230i	$-0.804133\pi$
$163$	−266.206			−1.63316			−0.816581	+	0.577230i	$0.804133\pi$
$164$		0			0
$165$	−147.183	+	176.013i	−0.892019	+	1.06675i
$166$		0			0
$167$	118.800			0.711380			0.355690	−	0.934604i	$-0.384246\pi$
$167$	118.800			0.711380			0.355690	+	0.934604i	$0.384246\pi$
$168$		0			0
$169$	−165.619			−0.979994
$170$		0			0
$171$	−80.0570	−	93.3238i	−0.468170	−	0.545753i
$172$		0			0
$173$		−	201.989i		−	1.16756i	−0.811910	−	0.583782i	$-0.801572\pi$
$173$		−	201.989i		−	1.16756i	0.811910	−	0.583782i	$-0.198428\pi$
$174$		0			0
$175$	−234.469	−	137.724i	−1.33982	−	0.786993i
$176$		0			0
$177$	−88.8566	+	32.8905i	−0.502015	+	0.185822i
$178$		0			0
$179$	87.5958			0.489362			0.244681	−	0.969604i	$-0.421317\pi$
$179$	87.5958			0.489362			0.244681	+	0.969604i	$0.421317\pi$
$180$		0			0
$181$		−	163.793i		−	0.904934i	−0.891781	−	0.452467i	$-0.850544\pi$
$181$		−	163.793i		−	0.904934i	0.891781	−	0.452467i	$-0.149456\pi$
$182$		0			0
$183$	−85.2875	−	230.412i	−0.466052	−	1.25908i
$184$		0			0
$185$	70.4634	−	40.3308i	0.380883	−	0.218004i
$186$		0			0
$187$	313.203			1.67488
$188$		0			0
$189$	256.700	+	142.663i	1.35820	+	0.754831i
$190$		0			0
$191$			11.4892i			0.0601530i	0.999548	+	0.0300765i	$0.00957510\pi$
$191$			11.4892i			0.0601530i	−0.999548	+	0.0300765i	$0.990425\pi$
$192$		0			0
$193$		−	33.7613i		−	0.174929i	−0.996168	−	0.0874646i	$-0.972124\pi$
$193$		−	33.7613i		−	0.174929i	0.996168	−	0.0874646i	$-0.0278765\pi$
$194$		0			0
$195$	17.6928	−	21.1585i	0.0907324	−	0.108505i
$196$		0			0
$197$			197.790i			1.00401i	0.864865	+	0.502005i	$0.167404\pi$
$197$			197.790i			1.00401i	−0.864865	+	0.502005i	$0.832596\pi$
$198$		0			0
$199$	−316.365			−1.58978			−0.794888	−	0.606756i	$-0.792470\pi$
$199$	−316.365			−1.58978			−0.794888	+	0.606756i	$0.792470\pi$
$200$		0			0
$201$	−142.479	+	52.7388i	−0.708849	+	0.262382i
$202$		0			0
$203$		−	267.244i		−	1.31647i
$204$		0			0
$205$	105.093	+	183.611i	0.512647	+	0.895665i
$206$		0			0
$207$	−132.863	+	113.976i	−0.641851	+	0.550607i
$208$		0			0
$209$		−	208.974i		−	0.999876i
$210$		0			0
$211$			366.900i			1.73886i	0.494054	+	0.869431i	$0.335515\pi$
$211$			366.900i			1.73886i	−0.494054	+	0.869431i	$0.664485\pi$
$212$		0			0
$213$	141.557	+	382.428i	0.664585	+	1.79543i
$214$		0			0
$215$	113.833	−	65.1540i	0.529456	−	0.303042i
$216$		0			0
$217$			553.177i			2.54920i
$218$		0			0
$219$	35.1592	+	94.9857i	0.160544	+	0.433725i
$220$		0			0
$221$	−37.6500			−0.170362
$222$		0			0
$223$			256.905i			1.15204i	0.817436	+	0.576020i	$0.195395\pi$
$223$			256.905i			1.15204i	−0.817436	+	0.576020i	$0.804605\pi$
$224$		0			0
$225$	−39.8246	−	221.448i	−0.176998	−	0.984211i
$226$		0			0
$227$			266.570i			1.17432i	0.809472	+	0.587158i	$0.199753\pi$
$227$			266.570i			1.17432i	−0.809472	+	0.587158i	$0.800247\pi$
$228$		0			0
$229$			141.351i			0.617255i	0.951183	+	0.308627i	$0.0998696\pi$
$229$			141.351i			0.617255i	−0.951183	+	0.308627i	$0.900130\pi$
$230$		0			0
$231$	173.265	+	468.090i	0.750065	+	2.02637i
$232$		0			0
$233$	38.5469			0.165437			0.0827186	−	0.996573i	$-0.473640\pi$
$233$	38.5469			0.165437			0.0827186	+	0.996573i	$0.473640\pi$
$234$		0			0
$235$	−253.210	+	144.929i	−1.07749	+	0.616717i
$236$		0			0
$237$	−230.412	+	85.2875i	−0.972201	+	0.359863i
$238$		0			0
$239$			49.1393i			0.205604i	0.994702	+	0.102802i	$0.0327807\pi$
$239$			49.1393i			0.205604i	−0.994702	+	0.102802i	$0.967219\pi$
$240$		0			0
$241$	106.338			0.441237			0.220618	−	0.975360i	$-0.429192\pi$
$241$	106.338			0.441237			0.220618	+	0.975360i	$0.429192\pi$
$242$		0			0
$243$	48.6994	+	238.070i	0.200409	+	0.979712i
$244$		0			0
$245$	−300.766	+	172.148i	−1.22762	+	0.702645i
$246$		0			0
$247$			25.1207i			0.101703i
$248$		0			0
$249$	−78.7881	−	212.853i	−0.316418	−	0.854831i
$250$		0			0
$251$	155.933			0.621247			0.310624	−	0.950533i	$-0.399462\pi$
$251$	155.933			0.621247			0.310624	+	0.950533i	$0.399462\pi$
$252$		0			0
$253$	−297.512			−1.17594
$254$		0			0
$255$	−197.025	+	235.618i	−0.772648	+	0.923994i
$256$		0			0
$257$	276.572			1.07616			0.538078	−	0.842895i	$-0.319150\pi$
$257$	276.572			1.07616			0.538078	+	0.842895i	$0.319150\pi$
$258$		0			0
$259$		−	176.619i		−	0.681927i
$260$		0			0
$261$	167.834	−	143.975i	0.643042	−	0.551628i
$262$		0			0
$263$	423.427			1.60999			0.804995	−	0.593282i	$-0.202168\pi$
$263$	423.427			1.60999			0.804995	+	0.593282i	$0.202168\pi$
$264$		0			0
$265$	−158.310	−	276.588i	−0.597394	−	1.04373i
$266$		0			0
$267$	129.499	+	349.853i	0.485015	+	1.31031i
$268$		0			0
$269$	−254.623			−0.946555			−0.473277	−	0.880913i	$-0.656929\pi$
$269$	−254.623			−0.946555			−0.473277	+	0.880913i	$0.656929\pi$
$270$		0			0
$271$	19.8183			0.0731301			0.0365650	−	0.999331i	$-0.488358\pi$
$271$	19.8183			0.0731301			0.0365650	+	0.999331i	$0.488358\pi$
$272$		0			0
$273$	−20.8281	−	56.2689i	−0.0762934	−	0.206113i
$274$		0			0
$275$	193.678	−	329.729i	0.704284	−	1.19901i
$276$		0			0
$277$	−388.801			−1.40362			−0.701808	−	0.712367i	$-0.747623\pi$
$277$	−388.801			−1.40362			−0.701808	+	0.712367i	$0.747623\pi$
$278$		0			0
$279$	−347.405	+	298.018i	−1.24518	+	1.06816i
$280$		0			0
$281$		−	256.458i		−	0.912661i	−0.889810	−	0.456330i	$-0.849163\pi$
$281$		−	256.458i		−	0.912661i	0.889810	−	0.456330i	$-0.150837\pi$
$282$		0			0
$283$	−3.88526			−0.0137288			−0.00686442	−	0.999976i	$-0.502185\pi$
$283$	−3.88526			−0.0137288			−0.00686442	+	0.999976i	$0.502185\pi$
$284$		0			0
$285$	157.208	+	131.458i	0.551608	+	0.461257i
$286$		0			0
$287$	460.228			1.60358
$288$		0			0
$289$	130.267			0.450750
$290$		0			0
$291$	−60.5799	−	163.662i	−0.208178	−	0.562412i
$292$		0			0
$293$			491.642i			1.67796i	0.544163	+	0.838979i	$0.316847\pi$
$293$			491.642i			1.67796i	−0.544163	+	0.838979i	$0.683153\pi$
$294$		0			0
$295$	137.053	−	78.4441i	0.464585	−	0.265912i
$296$		0			0
$297$	−200.624	+	360.992i	−0.675502	+	1.21546i
$298$		0			0
$299$	35.7638			0.119611
$300$		0			0
$301$		−	285.326i		−	0.947928i
$302$		0			0
$303$	175.052	−	64.7959i	0.577728	−	0.213848i
$304$		0			0
$305$	203.411	+	355.387i	0.666922	+	1.16520i
$306$		0			0
$307$	341.499			1.11237			0.556187	−	0.831057i	$-0.312264\pi$
$307$	341.499			1.11237			0.556187	+	0.831057i	$0.312264\pi$
$308$		0			0
$309$	−98.4404	−	265.945i	−0.318577	−	0.860664i
$310$		0			0
$311$		−	75.3001i		−	0.242122i	−0.992645	−	0.121061i	$-0.961370\pi$
$311$		−	75.3001i		−	0.242122i	0.992645	−	0.121061i	$-0.0386297\pi$
$312$		0			0
$313$		−	448.249i		−	1.43210i	−0.698046	−	0.716052i	$-0.745947\pi$
$313$		−	448.249i		−	1.43210i	0.698046	−	0.716052i	$-0.254053\pi$
$314$		0			0
$315$	−461.133	−	164.114i	−1.46391	−	0.520998i
$316$		0			0
$317$		−	163.088i		−	0.514474i	−0.966348	−	0.257237i	$-0.917188\pi$
$317$		−	163.088i		−	0.514474i	0.966348	−	0.257237i	$-0.0828121\pi$
$318$		0			0
$319$	375.820			1.17812
$320$		0			0
$321$	−2.90240	−	7.84107i	−0.00904173	−	0.0244270i
$322$		0			0
$323$		−	279.741i		−	0.866072i
$324$		0			0
$325$	−23.2819	+	39.6365i	−0.0716367	+	0.121958i
$326$		0			0
$327$	20.6388	+	55.7576i	0.0631157	+	0.170512i
$328$		0			0
$329$			634.680i			1.92912i
$330$		0			0
$331$		−	320.138i		−	0.967184i	−0.875293	−	0.483592i	$-0.839332\pi$
$331$		−	320.138i		−	0.967184i	0.875293	−	0.483592i	$-0.160668\pi$
$332$		0			0
$333$	110.920	−	95.1515i	0.333092	−	0.285740i
$334$		0			0
$335$	219.759	−	125.782i	0.655998	−	0.375470i
$336$		0			0
$337$			324.618i			0.963258i	0.876375	+	0.481629i	$0.159955\pi$
$337$			324.618i			0.963258i	−0.876375	+	0.481629i	$0.840045\pi$
$338$		0			0
$339$	−207.984	+	76.9857i	−0.613521	+	0.227096i
$340$		0			0
$341$	−777.921			−2.28129
$342$		0			0
$343$			220.907i			0.644044i
$344$		0			0
$345$	187.155	−	223.814i	0.542477	−	0.648737i
$346$		0			0
$347$			152.749i			0.440200i	0.975477	+	0.220100i	$0.0706383\pi$
$347$			152.749i			0.440200i	−0.975477	+	0.220100i	$0.929362\pi$
$348$		0			0
$349$		−	101.715i		−	0.291446i	−0.989325	−	0.145723i	$-0.953449\pi$
$349$		−	101.715i		−	0.291446i	0.989325	−	0.145723i	$-0.0465509\pi$
$350$		0			0
$351$	24.1169	−	43.3946i	0.0687092	−	0.123631i
$352$		0			0
$353$	−385.583			−1.09230			−0.546151	−	0.837687i	$-0.683908\pi$
$353$	−385.583			−1.09230			−0.546151	+	0.837687i	$0.683908\pi$
$354$		0			0
$355$	−337.613	−	589.857i	−0.951024	−	1.66157i
$356$		0			0
$357$	231.939	+	626.605i	0.649690	+	1.75519i
$358$		0			0
$359$		−	237.389i		−	0.661252i	−0.943762	−	0.330626i	$-0.892740\pi$
$359$		−	237.389i		−	0.661252i	0.943762	−	0.330626i	$-0.107260\pi$
$360$		0			0
$361$	174.352			0.482971
$362$		0			0
$363$	−317.839	+	117.649i	−0.875589	+	0.324102i
$364$		0			0
$365$	−83.8550	−	146.506i	−0.229740	−	0.401387i
$366$		0			0
$367$			286.946i			0.781870i	0.920418	+	0.390935i	$0.127848\pi$
$367$			286.946i			0.781870i	−0.920418	+	0.390935i	$0.872152\pi$
$368$		0			0
$369$	247.943	+	289.031i	0.671932	+	0.783282i
$370$		0			0
$371$	−693.279			−1.86868
$372$		0			0
$373$	2.77125			0.00742961			0.00371481	−	0.999993i	$-0.498818\pi$
$373$	2.77125			0.00742961			0.00371481	+	0.999993i	$0.498818\pi$
$374$		0			0
$375$	126.214	+	353.122i	0.336571	+	0.941658i
$376$		0			0
$377$	−45.1771			−0.119833
$378$		0			0
$379$			283.519i			0.748071i	0.927414	+	0.374036i	$0.122026\pi$
$379$			283.519i			0.748071i	−0.927414	+	0.374036i	$0.877974\pi$
$380$		0			0
$381$	124.601	+	336.621i	0.327037	+	0.883519i
$382$		0			0
$383$	397.679			1.03833			0.519163	−	0.854675i	$-0.326244\pi$
$383$	397.679			1.03833			0.519163	+	0.854675i	$0.326244\pi$
$384$		0			0
$385$	−413.238	−	721.984i	−1.07335	−	1.87528i
$386$		0			0
$387$	179.190	−	153.716i	0.463022	−	0.397200i
$388$		0			0
$389$	−500.320			−1.28617			−0.643084	−	0.765795i	$-0.722346\pi$
$389$	−500.320			−1.28617			−0.643084	+	0.765795i	$0.722346\pi$
$390$		0			0
$391$	−398.262			−1.01857
$392$		0			0
$393$	−37.4608	+	13.8662i	−0.0953201	+	0.0352830i
$394$		0			0
$395$	355.387	−	203.411i	0.899715	−	0.514965i
$396$		0			0
$397$	672.847			1.69483			0.847415	−	0.530932i	$-0.178158\pi$
$397$	672.847			1.69483			0.847415	+	0.530932i	$0.178158\pi$
$398$		0			0
$399$	418.080	−	154.754i	1.04782	−	0.387854i
$400$		0			0
$401$		−	307.904i		−	0.767840i	−0.923366	−	0.383920i	$-0.874574\pi$
$401$		−	307.904i		−	0.767840i	0.923366	−	0.383920i	$-0.125426\pi$
$402$		0			0
$403$	93.5135			0.232043
$404$		0			0
$405$	−145.363	−	378.014i	−0.358922	−	0.933368i
$406$		0			0
$407$	248.376			0.610260
$408$		0			0
$409$	42.9571			0.105030			0.0525148	−	0.998620i	$-0.483276\pi$
$409$	42.9571			0.105030			0.0525148	+	0.998620i	$0.483276\pi$
$410$		0			0
$411$	764.588	−	283.014i	1.86031	−	0.688599i
$412$		0			0
$413$		−	343.527i		−	0.831785i
$414$		0			0
$415$	187.910	+	328.305i	0.452795	+	0.791096i
$416$		0			0
$417$	177.331	+	479.076i	0.425255	+	1.14886i
$418$		0			0
$419$	11.3337			0.0270495			0.0135247	−	0.999909i	$-0.495695\pi$
$419$	11.3337			0.0270495			0.0135247	+	0.999909i	$0.495695\pi$
$420$		0			0
$421$			324.963i			0.771883i	0.922523	+	0.385941i	$0.126123\pi$
$421$			324.963i			0.771883i	−0.922523	+	0.385941i	$0.873877\pi$
$422$		0			0
$423$	−398.590	+	341.927i	−0.942293	+	0.808337i
$424$		0			0
$425$	259.265	−	441.388i	0.610036	−	1.03856i
$426$		0			0
$427$	890.790			2.08616
$428$		0			0
$429$	79.1298	−	29.2901i	0.184452	−	0.0682753i
$430$		0			0
$431$		−	332.486i		−	0.771428i	−0.922618	−	0.385714i	$-0.873955\pi$
$431$		−	332.486i		−	0.771428i	0.922618	−	0.385714i	$-0.126045\pi$
$432$		0			0
$433$			249.325i			0.575808i	0.957659	+	0.287904i	$0.0929584\pi$
$433$			249.325i			0.575808i	−0.957659	+	0.287904i	$0.907042\pi$
$434$		0			0
$435$	−236.415	+	282.724i	−0.543483	+	0.649940i
$436$		0			0
$437$			265.726i			0.608070i
$438$		0			0
$439$	−152.572			−0.347545			−0.173772	−	0.984786i	$-0.555596\pi$
$439$	−152.572			−0.347545			−0.173772	+	0.984786i	$0.555596\pi$
$440$		0			0
$441$	−473.450	+	406.145i	−1.07358	+	0.920963i
$442$		0			0
$443$			759.343i			1.71409i	0.515240	+	0.857046i	$0.327703\pi$
$443$			759.343i			1.71409i	−0.515240	+	0.857046i	$0.672297\pi$
$444$		0			0
$445$	−308.856	−	539.613i	−0.694058	−	1.21261i
$446$		0			0
$447$	504.516	−	186.748i	1.12867	−	0.417781i
$448$		0			0
$449$		−	356.596i		−	0.794201i	−0.917775	−	0.397101i	$-0.870016\pi$
$449$		−	356.596i		−	0.794201i	0.917775	−	0.397101i	$-0.129984\pi$
$450$		0			0
$451$			647.209i			1.43505i
$452$		0			0
$453$	−516.581	+	191.214i	−1.14035	+	0.422105i
$454$		0			0
$455$	49.6751	+	86.7893i	0.109176	+	0.190746i
$456$		0			0
$457$			379.145i			0.829640i	0.909904	+	0.414820i	$0.136155\pi$
$457$			379.145i			0.829640i	−0.909904	+	0.414820i	$0.863845\pi$
$458$		0			0
$459$	−268.563	+	483.238i	−0.585106	+	1.05281i
$460$		0			0
$461$	47.5481			0.103141			0.0515706	−	0.998669i	$-0.483577\pi$
$461$	47.5481			0.103141			0.0515706	+	0.998669i	$0.483577\pi$
$462$		0			0
$463$		−	478.123i		−	1.03266i	−0.856389	−	0.516331i	$-0.827297\pi$
$463$		−	478.123i		−	1.03266i	0.856389	−	0.516331i	$-0.172703\pi$
$464$		0			0
$465$	489.363	−	585.219i	1.05239	−	1.25854i
$466$		0			0
$467$			313.096i			0.670441i	0.942140	+	0.335220i	$0.108811\pi$
$467$			313.096i			0.670441i	−0.942140	+	0.335220i	$0.891189\pi$
$468$		0			0
$469$		−	550.834i		−	1.17449i
$470$		0			0
$471$	−493.929	+	182.829i	−1.04868	+	0.388172i
$472$		0			0
$473$	401.248			0.848305
$474$		0			0
$475$	−294.501	−	172.986i	−0.620002	−	0.364180i
$476$		0			0
$477$	−373.496	−	435.391i	−0.783011	−	0.912769i
$478$		0			0
$479$			260.368i			0.543565i	0.962359	+	0.271783i	$0.0876132\pi$
$479$			260.368i			0.543565i	−0.962359	+	0.271783i	$0.912387\pi$
$480$		0			0
$481$	−29.8571			−0.0620730
$482$		0			0
$483$	−220.320	−	595.212i	−0.456148	−	1.23232i
$484$		0			0
$485$	144.483	+	252.432i	0.297904	+	0.520479i
$486$		0			0
$487$		−	286.325i		−	0.587935i	−0.955815	−	0.293968i	$-0.905024\pi$
$487$		−	286.325i		−	0.587935i	0.955815	−	0.293968i	$-0.0949758\pi$
$488$		0			0
$489$	748.955	−	277.228i	1.53160	−	0.566928i
$490$		0			0
$491$	302.514			0.616117			0.308059	−	0.951367i	$-0.400321\pi$
$491$	302.514			0.616117			0.308059	+	0.951367i	$0.400321\pi$
$492$		0			0
$493$	503.088			1.02046
$494$		0			0
$495$	230.791	−	648.481i	0.466244	−	1.31006i
$496$		0			0
$497$	−1478.50			−2.97484
$498$		0			0
$499$			192.929i			0.386630i	0.981137	+	0.193315i	$0.0619240\pi$
$499$			192.929i			0.386630i	−0.981137	+	0.193315i	$0.938076\pi$
$500$		0			0
$501$	−334.239	+	123.719i	−0.667143	+	0.246945i
$502$		0			0
$503$	−248.654			−0.494341			−0.247171	−	0.968972i	$-0.579501\pi$
$503$	−248.654			−0.494341			−0.247171	+	0.968972i	$0.579501\pi$
$504$		0			0
$505$	−270.000	+	154.539i	−0.534653	+	0.306017i
$506$		0			0
$507$	465.960	−	172.476i	0.919054	−	0.340190i
$508$		0			0
$509$	730.373			1.43492			0.717459	−	0.696601i	$-0.245305\pi$
$509$	730.373			1.43492			0.717459	+	0.696601i	$0.245305\pi$
$510$		0			0
$511$	−367.223			−0.718636
$512$		0			0
$513$	322.424	+	179.190i	0.628507	+	0.349298i
$514$		0			0
$515$	234.781	+	410.194i	0.455885	+	0.796494i
$516$		0			0
$517$	−892.537			−1.72638
$518$		0			0
$519$	210.352	+	568.284i	0.405302	+	1.09496i
$520$		0			0
$521$		−	263.006i		−	0.504810i	−0.967622	−	0.252405i	$-0.918779\pi$
$521$		−	263.006i		−	0.504810i	0.967622	−	0.252405i	$-0.0812215\pi$
$522$		0			0
$523$	−764.855			−1.46244			−0.731219	−	0.682143i	$-0.761048\pi$
$523$	−764.855			−1.46244			−0.731219	+	0.682143i	$0.761048\pi$
$524$		0			0
$525$	803.091	+	143.301i	1.52970	+	0.272955i
$526$		0			0
$527$	−1041.36			−1.97601
$528$		0			0
$529$	−150.690			−0.284859
$530$		0			0
$531$	215.741	−	185.071i	0.406292	−	0.348534i
$532$		0			0
$533$		−	77.8007i		−	0.145968i
$534$		0			0
$535$	6.92223	+	12.0941i	0.0129387	+	0.0226058i
$536$		0			0
$537$	−246.446	+	91.2227i	−0.458931	+	0.169875i
$538$		0			0
$539$	−1060.17			−1.96691
$540$		0			0
$541$			1062.03i			1.96309i	0.191231	+	0.981545i	$0.438752\pi$
$541$			1062.03i			1.96309i	−0.191231	+	0.981545i	$0.561248\pi$
$542$		0			0
$543$	170.575	+	460.823i	0.314134	+	0.848661i
$544$		0			0
$545$	−49.2237	−	86.0006i	−0.0903188	−	0.157799i
$546$		0			0
$547$	886.905			1.62140			0.810699	−	0.585463i	$-0.199087\pi$
$547$	886.905			1.62140			0.810699	+	0.585463i	$0.199087\pi$
$548$		0			0
$549$	479.903	+	559.432i	0.874141	+	1.01900i
$550$		0			0
$551$		−	335.668i		−	0.609198i
$552$		0			0
$553$		−	890.790i		−	1.61083i
$554$		0			0
$555$	−156.244	+	186.849i	−0.281521	+	0.336666i
$556$		0			0
$557$		−	690.342i		−	1.23939i	−0.784841	−	0.619697i	$-0.787255\pi$
$557$		−	690.342i		−	1.23939i	0.784841	−	0.619697i	$-0.212745\pi$
$558$		0			0
$559$	−48.2339			−0.0862860
$560$		0			0
$561$	−881.181	+	326.172i	−1.57073	+	0.581411i
$562$		0			0
$563$		−	282.528i		−	0.501826i	−0.968010	−	0.250913i	$-0.919269\pi$
$563$		−	282.528i		−	0.501826i	0.968010	−	0.250913i	$-0.0807308\pi$
$564$		0			0
$565$	320.794	−	183.611i	0.567778	−	0.324976i
$566$		0			0
$567$	−870.781	−	134.046i	−1.53577	−	0.236413i
$568$		0			0
$569$			987.481i			1.73547i	0.497029	+	0.867734i	$0.334424\pi$
$569$			987.481i			1.73547i	−0.497029	+	0.867734i	$0.665576\pi$
$570$		0			0
$571$			13.8334i			0.0242266i	0.999927	+	0.0121133i	$0.00385587\pi$
$571$			13.8334i			0.0242266i	−0.999927	+	0.0121133i	$0.996144\pi$
$572$		0			0
$573$	−11.9649	−	32.3243i	−0.0208812	−	0.0564124i
$574$		0			0
$575$	−246.276	+	419.275i	−0.428307	+	0.729174i
$576$		0			0
$577$			849.259i			1.47185i	0.677062	+	0.735926i	$0.263253\pi$
$577$			849.259i			1.47185i	−0.677062	+	0.735926i	$0.736747\pi$
$578$		0			0
$579$	35.1592	+	94.9857i	0.0607241	+	0.164051i
$580$		0			0
$581$	822.907			1.41636
$582$		0			0
$583$		−	974.943i		−	1.67229i
$584$		0			0
$585$	−27.7432	+	77.9536i	−0.0474243	+	0.133254i
$586$		0			0
$587$		−	493.447i		−	0.840626i	−0.907379	−	0.420313i	$-0.861920\pi$
$587$		−	493.447i		−	0.840626i	0.907379	−	0.420313i	$-0.138080\pi$
$588$		0			0
$589$			694.809i			1.17964i
$590$		0			0
$591$	−205.979	−	556.471i	−0.348527	−	0.941575i
$592$		0			0
$593$	604.188			1.01887			0.509434	−	0.860510i	$-0.329855\pi$
$593$	604.188			1.01887			0.509434	+	0.860510i	$0.329855\pi$
$594$		0			0
$595$	−553.177	−	966.476i	−0.929709	−	1.62433i
$596$		0			0
$597$	890.077	−	329.464i	1.49092	−	0.551867i
$598$		0			0
$599$		−	268.675i		−	0.448539i	−0.974527	−	0.224269i	$-0.928000\pi$
$599$		−	268.675i		−	0.448539i	0.974527	−	0.224269i	$-0.0719996\pi$
$600$		0			0
$601$	799.576			1.33041			0.665205	−	0.746661i	$-0.268344\pi$
$601$	799.576			1.33041			0.665205	+	0.746661i	$0.268344\pi$
$602$		0			0
$603$	345.933	−	296.756i	0.573687	−	0.492132i
$604$		0			0
$605$	490.235	−	280.594i	0.810307	−	0.463791i
$606$		0			0
$607$			253.227i			0.417178i	0.978003	+	0.208589i	$0.0668871\pi$
$607$			253.227i			0.417178i	−0.978003	+	0.208589i	$0.933113\pi$
$608$		0			0
$609$	278.310	+	751.877i	0.456994	+	1.23461i
$610$		0			0
$611$	107.291			0.175600
$612$		0			0
$613$	620.741			1.01263			0.506314	−	0.862349i	$-0.331008\pi$
$613$	620.741			1.01263			0.506314	+	0.862349i	$0.331008\pi$
$614$		0			0
$615$	−486.886	−	407.137i	−0.791685	−	0.662011i
$616$		0			0
$617$	230.046			0.372847			0.186423	−	0.982470i	$-0.440310\pi$
$617$	230.046			0.372847			0.186423	+	0.982470i	$0.440310\pi$
$618$		0			0
$619$			303.405i			0.490153i	0.969504	+	0.245077i	$0.0788131\pi$
$619$			303.405i			0.490153i	−0.969504	+	0.245077i	$0.921187\pi$
$620$		0			0
$621$	255.109	−	459.028i	0.410803	−	0.739176i
$622$		0			0
$623$	−1352.56			−2.17104
$624$		0			0
$625$	−304.352	−	545.889i	−0.486964	−	0.873422i
$626$		0			0
$627$	217.627	+	587.937i	0.347092	+	0.937699i
$628$		0			0
$629$	332.486			0.528594
$630$		0			0
$631$	440.522			0.698133			0.349067	−	0.937098i	$-0.386499\pi$
$631$	440.522			0.698133			0.349067	+	0.937098i	$0.386499\pi$
$632$		0			0
$633$	−382.091	−	1032.25i	−0.603620	−	1.63073i
$634$		0			0
$635$	−297.175	−	519.205i	−0.467991	−	0.817645i
$636$		0			0
$637$	127.442			0.200066
$638$		0			0
$639$	−796.524	−	928.521i	−1.24652	−	1.45309i
$640$		0			0
$641$		−	283.860i		−	0.442839i	−0.975179	−	0.221419i	$-0.928931\pi$
$641$		−	283.860i		−	0.442839i	0.975179	−	0.221419i	$-0.0710690\pi$
$642$		0			0
$643$	−241.796			−0.376043			−0.188021	−	0.982165i	$-0.560207\pi$
$643$	−241.796			−0.376043			−0.188021	+	0.982165i	$0.560207\pi$
$644$		0			0
$645$	−252.411	+	301.853i	−0.391335	+	0.467990i
$646$		0			0
$647$	−142.727			−0.220599			−0.110299	−	0.993898i	$-0.535181\pi$
$647$	−142.727			−0.220599			−0.110299	+	0.993898i	$0.535181\pi$
$648$		0			0
$649$	483.095			0.744369
$650$		0			0
$651$	−576.081	−	1556.33i	−0.884917	−	2.39068i
$652$		0			0
$653$		−	282.167i		−	0.432108i	−0.976381	−	0.216054i	$-0.930681\pi$
$653$		−	282.167i		−	0.432108i	0.976381	−	0.216054i	$-0.0693187\pi$
$654$		0			0
$655$	57.7796	−	33.0710i	0.0882132	−	0.0504901i
$656$		0			0
$657$	−197.837	−	230.622i	−0.301122	−	0.351023i
$658$		0			0
$659$	497.619			0.755113			0.377556	−	0.925987i	$-0.376764\pi$
$659$	497.619			0.755113			0.377556	+	0.925987i	$0.376764\pi$
$660$		0			0
$661$		−	59.4548i		−	0.0899467i	−0.998988	−	0.0449733i	$-0.985680\pi$
$661$		−	59.4548i		−	0.0899467i	0.998988	−	0.0449733i	$-0.0143203\pi$
$662$		0			0
$663$	105.926	−	39.2089i	0.159768	−	0.0591386i
$664$		0			0
$665$	−644.848	+	369.088i	−0.969696	+	0.555020i
$666$		0			0
$667$	−477.884			−0.716467
$668$		0			0
$669$	−267.542	−	722.787i	−0.399913	−	1.08040i
$670$		0			0
$671$			1252.70i			1.86692i
$672$		0			0
$673$			302.271i			0.449140i	0.974458	+	0.224570i	$0.0720978\pi$
$673$			302.271i			0.449140i	−0.974458	+	0.224570i	$0.927902\pi$
$674$		0			0
$675$	342.661	+	581.557i	0.507646	+	0.861566i
$676$		0			0
$677$		−	219.339i		−	0.323987i	−0.986792	−	0.161994i	$-0.948208\pi$
$677$		−	219.339i		−	0.323987i	0.986792	−	0.161994i	$-0.0517924\pi$
$678$		0			0
$679$	632.731			0.931857
$680$		0			0
$681$	−277.607	−	749.980i	−0.407646	−	1.10129i
$682$		0			0
$683$		−	442.875i		−	0.648426i	−0.945984	−	0.324213i	$-0.894901\pi$
$683$		−	442.875i		−	0.648426i	0.945984	−	0.324213i	$-0.105099\pi$
$684$		0			0
$685$	−1179.30	+	674.991i	−1.72161	+	0.985388i
$686$		0			0
$687$	−147.204	−	397.684i	−0.214271	−	0.578871i
$688$		0			0
$689$			117.197i			0.170098i
$690$		0			0
$691$			586.338i			0.848536i	0.905537	+	0.424268i	$0.139468\pi$
$691$			586.338i			0.848536i	−0.905537	+	0.424268i	$0.860532\pi$
$692$		0			0
$693$	−974.943	−	1136.51i	−1.40684	−	1.63998i
$694$		0			0
$695$	−422.936	−	738.928i	−0.608542	−	1.06321i
$696$		0			0
$697$			866.380i			1.24301i
$698$		0			0
$699$	−108.449	+	40.1429i	−0.155149	+	0.0574290i
$700$		0			0
$701$	488.830			0.697333			0.348666	−	0.937247i	$-0.386635\pi$
$701$	488.830			0.697333			0.348666	+	0.937247i	$0.386635\pi$
$702$		0			0
$703$		−	221.840i		−	0.315561i
$704$		0			0
$705$	561.464	−	671.443i	0.796402	−	0.952401i
$706$		0			0
$707$			676.764i			0.957234i
$708$		0			0
$709$			22.4418i			0.0316528i	0.999875	+	0.0158264i	$0.00503790\pi$
$709$			22.4418i			0.0316528i	−0.999875	+	0.0158264i	$0.994962\pi$
$710$		0			0
$711$	559.432	−	479.903i	0.786824	−	0.674970i
$712$		0			0
$713$	989.186			1.38736
$714$		0			0
$715$	−122.050	+	69.8571i	−0.170699	+	0.0977023i
$716$		0			0
$717$	−51.1739	−	138.251i	−0.0713722	−	0.192818i
$718$		0			0
$719$		−	83.6070i		−	0.116282i	−0.998308	−	0.0581411i	$-0.981483\pi$
$719$		−	83.6070i		−	0.116282i	0.998308	−	0.0581411i	$-0.0185173\pi$
$720$		0			0
$721$	1028.17			1.42603
$722$		0			0
$723$	−299.176	+	110.741i	−0.413799	+	0.153169i
$724$		0			0
$725$	311.098	−	529.632i	0.429101	−	0.730526i
$726$		0			0
$727$			359.563i			0.494585i	0.968941	+	0.247292i	$0.0795408\pi$
$727$			359.563i			0.494585i	−0.968941	+	0.247292i	$0.920459\pi$
$728$		0			0
$729$	−384.940	−	619.081i	−0.528039	−	0.849220i
$730$		0			0
$731$	537.127			0.734784
$732$		0			0
$733$	626.594			0.854835			0.427418	−	0.904054i	$-0.359423\pi$
$733$	626.594			0.854835			0.427418	+	0.904054i	$0.359423\pi$
$734$		0			0
$735$	666.914	−	797.548i	0.907365	−	1.08510i
$736$		0			0
$737$	774.627			1.05105
$738$		0			0
$739$		−	80.3095i		−	0.108673i	−0.998523	−	0.0543366i	$-0.982696\pi$
$739$		−	80.3095i		−	0.108673i	0.998523	−	0.0543366i	$-0.0173044\pi$
$740$		0			0
$741$	−26.1608	−	70.6757i	−0.0353047	−	0.0953788i
$742$		0			0
$743$	−133.774			−0.180046			−0.0900229	−	0.995940i	$-0.528694\pi$
$743$	−133.774			−0.180046			−0.0900229	+	0.995940i	$0.528694\pi$
$744$		0			0
$745$	−778.167	+	445.395i	−1.04452	+	0.597846i
$746$		0			0
$747$	443.332	+	516.800i	0.593483	+	0.691833i
$748$		0			0
$749$	30.3142			0.0404730
$750$		0			0
$751$	1237.05			1.64720			0.823599	−	0.567172i	$-0.191963\pi$
$751$	1237.05			1.64720			0.823599	+	0.567172i	$0.191963\pi$
$752$		0			0
$753$	−438.709	+	162.389i	−0.582615	+	0.215657i
$754$		0			0
$755$	796.775	−	456.046i	1.05533	−	0.604034i
$756$		0			0
$757$	436.609			0.576762			0.288381	−	0.957516i	$-0.406883\pi$
$757$	436.609			0.576762			0.288381	+	0.957516i	$0.406883\pi$
$758$		0			0
$759$	837.035	−	309.831i	1.10281	−	0.408209i
$760$		0			0
$761$			610.636i			0.802412i	0.915988	+	0.401206i	$0.131409\pi$
$761$			610.636i			0.802412i	−0.915988	+	0.401206i	$0.868591\pi$
$762$		0			0
$763$	−215.563			−0.282521
$764$		0			0
$765$	308.946	−	868.083i	0.403850	−	1.13475i
$766$		0			0
$767$	−58.0726			−0.0757140
$768$		0			0
$769$	41.2667			0.0536627			0.0268314	−	0.999640i	$-0.491458\pi$
$769$	41.2667			0.0536627			0.0268314	+	0.999640i	$0.491458\pi$
$770$		0			0
$771$	−778.121	+	288.024i	−1.00924	+	0.373572i
$772$		0			0
$773$		−	502.417i		−	0.649957i	−0.945721	−	0.324978i	$-0.894643\pi$
$773$		−	502.417i		−	0.649957i	0.945721	−	0.324978i	$-0.105357\pi$
$774$		0			0
$775$	−643.952	+	1096.30i	−0.830905	+	1.41458i
$776$		0			0
$777$	183.932	+	496.908i	0.236721	+	0.639521i
$778$		0			0
$779$	578.062			0.742057
$780$		0			0
$781$		−	2079.18i		−	2.66220i
$782$		0			0
$783$	−322.256	+	579.849i	−0.411565	+	0.740547i
$784$		0			0
$785$	761.837	−	436.049i	0.970493	−	0.555476i
$786$		0			0
$787$	95.8180			0.121751			0.0608754	−	0.998145i	$-0.480611\pi$
$787$	95.8180			0.121751			0.0608754	+	0.998145i	$0.480611\pi$
$788$		0			0
$789$	−1191.29	+	440.959i	−1.50987	+	0.558884i
$790$		0			0
$791$		−	804.082i		−	1.01654i
$792$		0			0
$793$		−	150.586i		−	0.189895i
$794$		0			0
$795$	733.436	+	613.302i	0.922561	+	0.771449i
$796$		0			0
$797$			808.865i			1.01489i	0.861685	+	0.507444i	$0.169409\pi$
$797$			808.865i			1.01489i	−0.861685	+	0.507444i	$0.830591\pi$
$798$		0			0
$799$	−1194.79			−1.49535
$800$		0			0
$801$	−728.676	−	849.430i	−0.909708	−	1.06046i
$802$		0			0
$803$		−	516.418i		−	0.643111i
$804$		0			0
$805$	525.464	+	918.057i	0.652750	+	1.14044i
$806$		0			0
$807$	716.369	−	265.166i	0.887694	−	0.328582i
$808$		0			0
$809$		−	1115.63i		−	1.37902i	−0.724277	−	0.689510i	$-0.757826\pi$
$809$		−	1115.63i		−	1.37902i	0.724277	−	0.689510i	$-0.242174\pi$
$810$		0			0
$811$			1266.17i			1.56124i	0.625005	+	0.780621i	$0.285097\pi$
$811$			1266.17i			1.56124i	−0.625005	+	0.780621i	$0.714903\pi$
$812$		0			0
$813$	−55.7576	+	20.6388i	−0.0685825	+	0.0253860i
$814$		0			0
$815$	−1155.19	+	661.190i	−1.41741	+	0.811276i
$816$		0			0
$817$		−	358.379i		−	0.438653i
$818$		0			0
$819$	117.197	+	136.619i	0.143098	+	0.166812i
$820$		0			0
$821$	537.970			0.655261			0.327631	−	0.944806i	$-0.393750\pi$
$821$	537.970			0.655261			0.327631	+	0.944806i	$0.393750\pi$
$822$		0			0
$823$			74.9483i			0.0910672i	0.998963	+	0.0455336i	$0.0144988\pi$
$823$			74.9483i			0.0910672i	−0.998963	+	0.0455336i	$0.985501\pi$
$824$		0			0
$825$	−201.522	+	1129.37i	−0.244269	+	1.36893i
$826$		0			0
$827$			848.170i			1.02560i	0.858509	+	0.512799i	$0.171391\pi$
$827$			848.170i			1.02560i	−0.858509	+	0.512799i	$0.828609\pi$
$828$		0			0
$829$			223.248i			0.269298i	0.990893	+	0.134649i	$0.0429907\pi$
$829$			223.248i			0.269298i	−0.990893	+	0.134649i	$0.957009\pi$
$830$		0			0
$831$	1093.87	−	404.900i	1.31633	−	0.487244i
$832$		0			0
$833$	−1419.18			−1.70370
$834$		0			0
$835$	515.530	−	295.071i	0.617402	−	0.353379i
$836$		0			0
$837$	667.046	−	1200.25i	0.796949	−	1.43399i
$838$		0			0
$839$		−	139.111i		−	0.165806i	−0.996558	−	0.0829028i	$-0.973581\pi$
$839$		−	139.111i		−	0.165806i	0.996558	−	0.0829028i	$-0.0264191\pi$
$840$		0			0
$841$	−237.333			−0.282204
$842$		0			0
$843$	267.076	+	721.530i	0.316817	+	0.855907i
$844$		0			0
$845$	−718.698	+	411.357i	−0.850530	+	0.486814i
$846$		0			0
$847$		−	1228.79i		−	1.45076i
$848$		0			0
$849$	10.9310	−	4.04613i	0.0128751	−	0.00476576i
$850$		0			0
$851$	−315.828			−0.371126
$852$		0			0
$853$	1056.44			1.23850			0.619252	−	0.785193i	$-0.287436\pi$
$853$	1056.44			1.23850			0.619252	+	0.785193i	$0.287436\pi$
$854$		0			0
$855$	−579.198	−	206.133i	−0.677425	−	0.241091i
$856$		0			0
$857$	508.439			0.593277			0.296639	−	0.954990i	$-0.404134\pi$
$857$	508.439			0.593277			0.296639	+	0.954990i	$0.404134\pi$
$858$		0			0
$859$		−	972.814i		−	1.13250i	−0.824235	−	0.566248i	$-0.808394\pi$
$859$		−	972.814i		−	1.13250i	0.824235	−	0.566248i	$-0.191606\pi$
$860$		0			0
$861$	−1294.83	+	479.284i	−1.50386	+	0.556660i
$862$		0			0
$863$	287.554			0.333203			0.166601	−	0.986024i	$-0.446721\pi$
$863$	287.554			0.333203			0.166601	+	0.986024i	$0.446721\pi$
$864$		0			0
$865$	−501.690	−	876.522i	−0.579989	−	1.01332i
$866$		0			0
$867$	−366.498	+	135.660i	−0.422720	+	0.156471i
$868$		0			0
$869$	1252.70			1.44154
$870$		0			0
$871$	−93.1175			−0.106909
$872$		0			0
$873$	340.877	+	397.366i	0.390466	+	0.455173i
$874$		0			0
$875$	−1359.54	−	15.2839i	−1.55376	−	0.0174673i
$876$		0			0
$877$	−34.0035			−0.0387726			−0.0193863	−	0.999812i	$-0.506171\pi$
$877$	−34.0035			−0.0387726			−0.0193863	+	0.999812i	$0.506171\pi$
$878$		0			0
$879$	−511.998	−	1383.21i	−0.582478	−	1.57362i
$880$		0			0
$881$			1453.52i			1.64985i	0.565242	+	0.824925i	$0.308783\pi$
$881$			1453.52i			1.64985i	−0.565242	+	0.824925i	$0.691217\pi$
$882$		0			0
$883$	689.562			0.780931			0.390465	−	0.920618i	$-0.372314\pi$
$883$	689.562			0.780931			0.390465	+	0.920618i	$0.372314\pi$
$884$		0			0
$885$	−303.898	+	363.426i	−0.343388	+	0.410650i
$886$		0			0
$887$	−116.423			−0.131255			−0.0656275	−	0.997844i	$-0.520905\pi$
$887$	−116.423			−0.131255			−0.0656275	+	0.997844i	$0.520905\pi$
$888$		0			0
$889$	−1301.40			−1.46390
$890$		0			0
$891$	188.506	−	1224.56i	0.211567	−	1.37437i
$892$		0			0
$893$			797.179i			0.892698i
$894$		0			0
$895$	380.119	−	217.567i	0.424714	−	0.243091i
$896$		0			0
$897$	−100.620	+	37.2446i	−0.112173	+	0.0415213i
$898$		0			0
$899$	−1249.55			−1.38993
$900$		0			0
$901$		−	1305.10i		−	1.44850i
$902$		0			0
$903$	297.140	+	802.750i	0.329059	+	0.888981i
$904$		0			0
$905$	−406.822	−	710.774i	−0.449527	−	0.785386i
$906$		0			0
$907$	−189.331			−0.208745			−0.104372	−	0.994538i	$-0.533283\pi$
$907$	−189.331			−0.208745			−0.104372	+	0.994538i	$0.533283\pi$
$908$		0			0
$909$	−425.019	+	364.599i	−0.467568	+	0.401099i
$910$		0			0
$911$			1079.12i			1.18455i	0.805737	+	0.592273i	$0.201769\pi$
$911$			1079.12i			1.18455i	−0.805737	+	0.592273i	$0.798231\pi$
$912$		0			0
$913$			1157.24i			1.26751i
$914$		0			0
$915$	−942.388	−	788.029i	−1.02993	−	0.861234i
$916$		0			0
$917$		−	144.827i		−	0.157935i
$918$		0			0
$919$	1223.20			1.33101			0.665507	−	0.746392i	$-0.268215\pi$
$919$	1223.20			1.33101			0.665507	+	0.746392i	$0.268215\pi$
$920$		0			0
$921$	−960.788	+	355.638i	−1.04320	+	0.386144i
$922$		0			0
$923$			249.937i			0.270788i
$924$		0			0
$925$	205.602	−	350.028i	0.222272	−	0.378409i
$926$		0			0
$927$	553.913	+	645.706i	0.597533	+	0.696555i
$928$		0			0
$929$			291.450i			0.313724i	0.987621	+	0.156862i	$0.0501378\pi$
$929$			291.450i			0.313724i	−0.987621	+	0.156862i	$0.949862\pi$
$930$		0			0
$931$			946.900i			1.01708i
$932$		0			0
$933$	78.4178	+	211.853i	0.0840491	+	0.227066i
$934$		0			0
$935$	1359.14	−	777.921i	1.45362	−	0.832001i
$936$		0			0
$937$		−	706.443i		−	0.753941i	−0.926225	−	0.376970i	$-0.876966\pi$
$937$		−	706.443i		−	0.753941i	0.926225	−	0.376970i	$-0.123034\pi$
$938$		0			0
$939$	466.809	+	1261.12i	0.497134	+	1.34305i
$940$		0			0
$941$	661.438			0.702909			0.351455	−	0.936205i	$-0.385687\pi$
$941$	661.438			0.702909			0.351455	+	0.936205i	$0.385687\pi$
$942$		0			0
$943$		−	822.976i		−	0.872721i
$944$		0			0
$945$	1468.28	−	18.4989i	1.55374	−	0.0195755i
$946$		0			0
$947$		−	1699.89i		−	1.79503i	−0.440988	−	0.897513i	$-0.645372\pi$
$947$		−	1699.89i		−	1.79503i	0.440988	−	0.897513i	$-0.354628\pi$
$948$		0			0
$949$			62.0783i			0.0654145i
$950$		0			0
$951$	169.841	+	458.840i	0.178592	+	0.482481i
$952$		0			0
$953$	−1691.82			−1.77526			−0.887629	−	0.460558i	$-0.847649\pi$
$953$	−1691.82			−1.77526			−0.887629	+	0.460558i	$0.847649\pi$
$954$		0			0
$955$	28.5365	+	49.8571i	0.0298811	+	0.0522064i
$956$		0			0
$957$	−1057.35	+	391.381i	−1.10486	+	0.408966i
$958$		0			0
$959$			2955.96i			3.08234i
$960$		0			0
$961$	1625.48			1.69144
$962$		0			0
$963$	16.3315	+	19.0379i	0.0169589	+	0.0197693i
$964$		0			0
$965$	−83.8550	−	146.506i	−0.0868963	−	0.151820i
$966$		0			0
$967$			1252.98i			1.29574i	0.761751	+	0.647870i	$0.224340\pi$
$967$			1252.98i			1.29574i	−0.761751	+	0.647870i	$0.775660\pi$
$968$		0			0
$969$	291.324	+	787.037i	0.300644	+	0.812215i
$970$		0			0
$971$	1013.73			1.04400			0.522001	−	0.852945i	$-0.325186\pi$
$971$	1013.73			1.04400			0.522001	+	0.852945i	$0.325186\pi$
$972$		0			0
$973$	−1852.15			−1.90354
$974$		0			0
$975$	24.2248	−	135.761i	0.0248460	−	0.139242i
$976$		0			0
$977$	−7.21543			−0.00738529			−0.00369265	−	0.999993i	$-0.501175\pi$
$977$	−7.21543			−0.00738529			−0.00369265	+	0.999993i	$0.501175\pi$
$978$		0			0
$979$		−	1902.08i		−	1.94288i
$980$		0			0
$981$	−116.132	−	135.378i	−0.118382	−	0.138000i
$982$		0			0
$983$	483.877			0.492245			0.246123	−	0.969239i	$-0.420843\pi$
$983$	483.877			0.492245			0.246123	+	0.969239i	$0.420843\pi$
$984$		0			0
$985$	491.262	+	858.302i	0.498743	+	0.871372i
$986$		0			0
$987$	−660.959	−	1785.64i	−0.669664	−	1.80916i
$988$		0			0
$989$	−510.218			−0.515892
$990$		0			0
$991$	−799.147			−0.806405			−0.403203	−	0.915111i	$-0.632103\pi$
$991$	−799.147			−0.806405			−0.403203	+	0.915111i	$0.632103\pi$
$992$		0			0
$993$	333.393	+	900.691i	0.335744	+	0.907040i
$994$		0			0
$995$	−1372.86	+	785.775i	−1.37976	+	0.789723i
$996$		0			0
$997$	−1692.54			−1.69763			−0.848817	−	0.528686i	$-0.822685\pi$
$997$	−1692.54			−1.69763			−0.848817	+	0.528686i	$0.822685\pi$
$998$		0			0
$999$	−212.975	+	383.216i	−0.213189	+	0.383600i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.3.i.a.929.7	yes	32
3.2	odd	2	inner	960.3.i.a.929.2	yes	32
4.3	odd	2	inner	960.3.i.a.929.27	yes	32
5.4	even	2	inner	960.3.i.a.929.28	yes	32
8.3	odd	2	inner	960.3.i.a.929.6	yes	32
8.5	even	2	inner	960.3.i.a.929.26	yes	32
12.11	even	2	inner	960.3.i.a.929.30	yes	32
15.14	odd	2	inner	960.3.i.a.929.29	yes	32
20.19	odd	2	inner	960.3.i.a.929.8	yes	32
24.5	odd	2	inner	960.3.i.a.929.31	yes	32
24.11	even	2	inner	960.3.i.a.929.3	yes	32
40.19	odd	2	inner	960.3.i.a.929.25	yes	32
40.29	even	2	inner	960.3.i.a.929.5	yes	32
60.59	even	2	inner	960.3.i.a.929.1	✓	32
120.29	odd	2	inner	960.3.i.a.929.4	yes	32
120.59	even	2	inner	960.3.i.a.929.32	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
960.3.i.a.929.1	✓	32	60.59	even	2	inner
960.3.i.a.929.2	yes	32	3.2	odd	2	inner
960.3.i.a.929.3	yes	32	24.11	even	2	inner
960.3.i.a.929.4	yes	32	120.29	odd	2	inner
960.3.i.a.929.5	yes	32	40.29	even	2	inner
960.3.i.a.929.6	yes	32	8.3	odd	2	inner
960.3.i.a.929.7	yes	32	1.1	even	1	trivial
960.3.i.a.929.8	yes	32	20.19	odd	2	inner
960.3.i.a.929.25	yes	32	40.19	odd	2	inner
960.3.i.a.929.26	yes	32	8.5	even	2	inner
960.3.i.a.929.27	yes	32	4.3	odd	2	inner
960.3.i.a.929.28	yes	32	5.4	even	2	inner
960.3.i.a.929.29	yes	32	15.14	odd	2	inner
960.3.i.a.929.30	yes	32	12.11	even	2	inner
960.3.i.a.929.31	yes	32	24.5	odd	2	inner
960.3.i.a.929.32	yes	32	120.59	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	960.i (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.81345 + 1.04140i) q^{3} +(4.33946 - 2.48376i) q^{5} -10.8770i q^{7} +(6.83095 - 5.85987i) q^{9} +O(q^{10})\)	\(q+(-2.81345 + 1.04140i) q^{3} +(4.33946 - 2.48376i) q^{5} -10.8770i q^{7} +(6.83095 - 5.85987i) q^{9} +15.2961 q^{11} -1.83874 q^{13} +(-9.62225 + 11.5071i) q^{15} +20.4760 q^{17} -13.6619i q^{19} +(11.3274 + 30.6019i) q^{21} -19.4502 q^{23} +(12.6619 - 21.5563i) q^{25} +(-13.1160 + 23.6002i) q^{27} +24.5696 q^{29} -50.8574 q^{31} +(-43.0348 + 15.9295i) q^{33} +(-27.0159 - 47.2004i) q^{35} +16.2378 q^{37} +(5.17319 - 1.91487i) q^{39} +42.3120i q^{41} +26.2320 q^{43} +(15.0882 - 42.3951i) q^{45} -58.3505 q^{47} -69.3095 q^{49} +(-57.6081 + 21.3238i) q^{51} -63.7379i q^{53} +(66.3770 - 37.9919i) q^{55} +(14.2276 + 38.4370i) q^{57} +31.5828 q^{59} +81.8966i q^{61} +(-63.7379 - 74.3004i) q^{63} +(-7.97914 + 4.56698i) q^{65} +50.6420 q^{67} +(54.7220 - 20.2555i) q^{69} -135.929i q^{71} -33.7613i q^{73} +(-13.1747 + 73.8338i) q^{75} -166.376i q^{77} +81.8966 q^{79} +(12.3238 - 80.0570i) q^{81} +75.6556i q^{83} +(88.8549 - 50.8574i) q^{85} +(-69.1253 + 25.5869i) q^{87} -124.350i q^{89} +20.0000i q^{91} +(143.085 - 52.9632i) q^{93} +(-33.9328 - 59.2853i) q^{95} +58.1713i q^{97} +(104.487 - 89.6333i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{9}+O(q^{10}) \) 32 * q + 32 * q^9	\( 32 q + 32 q^{9} + 32 q^{25} - 352 q^{49} - 352 q^{81}+O(q^{100}) \) 32 * q + 32 * q^9 + 32 * q^25 - 352 * q^49 - 352 * q^81

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