LMFDB - Embedded newform 960.2.bb.a.497.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(497,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2, 1]))

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

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

chi := DirichletCharacter("960.497");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.bb (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			497.13
Character	$\chi$	$=$	960.497
Dual form			960.2.bb.a.593.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.09486 - 1.34211i) q^{3} +(-1.71343 - 1.43671i) q^{5} +(-3.11495 + 3.11495i) q^{7} +(-0.602544 + 2.93887i) q^{9} +O(q^{10})$	\(q+(-1.09486 - 1.34211i) q^{3} +(-1.71343 - 1.43671i) q^{5} +(-3.11495 + 3.11495i) q^{7} +(-0.602544 + 2.93887i) q^{9} +(3.15836 - 3.15836i) q^{11} +4.72071i q^{13} +(-0.0522594 + 3.87263i) q^{15} +(1.27146 - 1.27146i) q^{17} +(-1.33059 - 1.33059i) q^{19} +(7.59106 + 0.770172i) q^{21} +(1.09034 - 1.09034i) q^{23} +(0.871703 + 4.92343i) q^{25} +(4.60400 - 2.40898i) q^{27} +(1.67641 - 1.67641i) q^{29} +3.42372 q^{31} +(-7.69687 - 0.780907i) q^{33} +(9.81254 - 0.861963i) q^{35} -1.11057i q^{37} +(6.33574 - 5.16854i) q^{39} -0.0298672 q^{41} +5.45244 q^{43} +(5.25473 - 4.16987i) q^{45} +(0.608051 - 0.608051i) q^{47} -12.4058i q^{49} +(-3.09853 - 0.314370i) q^{51} +3.62613i q^{53} +(-9.94931 + 0.873977i) q^{55} +(-0.328990 + 3.24263i) q^{57} +(5.30621 + 5.30621i) q^{59} +(8.39022 - 8.39022i) q^{61} +(-7.27752 - 11.0313i) q^{63} +(6.78232 - 8.08863i) q^{65} +7.23224 q^{67} +(-2.65714 - 0.269587i) q^{69} -1.80640 q^{71} +(3.82128 + 3.82128i) q^{73} +(5.65341 - 6.56041i) q^{75} +19.6763i q^{77} +3.05546i q^{79} +(-8.27388 - 3.54160i) q^{81} -14.3316 q^{83} +(-4.00530 + 0.351838i) q^{85} +(-4.08538 - 0.414493i) q^{87} -7.83926i q^{89} +(-14.7048 - 14.7048i) q^{91} +(-3.74851 - 4.59503i) q^{93} +(0.368200 + 4.19157i) q^{95} +(6.89142 + 6.89142i) q^{97} +(7.37896 + 11.1851i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q+O(q^{10}) $ 88 * q	$ 88 q + 4 q^{15} + 8 q^{19} - 4 q^{21} + 16 q^{31} - 4 q^{33} - 24 q^{39} + 40 q^{43} + 8 q^{45} + 4 q^{51} + 12 q^{57} - 24 q^{61} + 32 q^{63} + 8 q^{67} - 12 q^{69} + 24 q^{75} - 8 q^{81} - 24 q^{85} + 12 q^{87} + 8 q^{91} - 8 q^{97} + 32 q^{99}+O(q^{100}) $ 88 * q + 4 * q^15 + 8 * q^19 - 4 * q^21 + 16 * q^31 - 4 * q^33 - 24 * q^39 + 40 * q^43 + 8 * q^45 + 4 * q^51 + 12 * q^57 - 24 * q^61 + 32 * q^63 + 8 * q^67 - 12 * q^69 + 24 * q^75 - 8 * q^81 - 24 * q^85 + 12 * q^87 + 8 * q^91 - 8 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.09486	−	1.34211i	−0.632120	−	0.774870i
$3$	−1.09486	−	1.34211i	−0.632120	−	0.774870i
$4$		0			0
$5$	−1.71343	−	1.43671i	−0.766270	−	0.642518i
$5$	−1.71343	−	1.43671i	−0.766270	−	0.642518i
$6$		0			0
$7$	−3.11495	+	3.11495i	−1.17734	+	1.17734i	−0.196919	+	0.980420i	$0.563094\pi$
$7$	−3.11495	+	3.11495i	−1.17734	+	1.17734i	−0.980420	+	0.196919i	$0.936906\pi$
$8$		0			0
$9$	−0.602544	+	2.93887i	−0.200848	+	0.979622i
$10$		0			0
$11$	3.15836	−	3.15836i	0.952283	−	0.952283i	−0.0466296	−	0.998912i	$-0.514848\pi$
$11$	3.15836	−	3.15836i	0.952283	−	0.952283i	0.998912	+	0.0466296i	$0.0148480\pi$
$12$		0			0
$13$			4.72071i			1.30929i	0.755936	+	0.654645i	$0.227182\pi$
$13$			4.72071i			1.30929i	−0.755936	+	0.654645i	$0.772818\pi$
$14$		0			0
$15$	−0.0522594	+	3.87263i	−0.0134933	+	0.999909i
$16$		0			0
$17$	1.27146	−	1.27146i	0.308376	−	0.308376i	−0.535904	−	0.844279i	$-0.680029\pi$
$17$	1.27146	−	1.27146i	0.308376	−	0.308376i	0.844279	+	0.535904i	$0.180029\pi$
$18$		0			0
$19$	−1.33059	−	1.33059i	−0.305259	−	0.305259i	0.537808	−	0.843067i	$-0.319253\pi$
$19$	−1.33059	−	1.33059i	−0.305259	−	0.305259i	−0.843067	+	0.537808i	$0.819253\pi$
$20$		0			0
$21$	7.59106	+	0.770172i	1.65651	+	0.168065i
$22$		0			0
$23$	1.09034	−	1.09034i	0.227352	−	0.227352i	−0.584234	−	0.811585i	$-0.698605\pi$
$23$	1.09034	−	1.09034i	0.227352	−	0.227352i	0.811585	+	0.584234i	$0.198605\pi$
$24$		0			0
$25$	0.871703	+	4.92343i	0.174341	+	0.984685i
$26$		0			0
$27$	4.60400	−	2.40898i	0.886040	−	0.463608i
$28$		0			0
$29$	1.67641	−	1.67641i	0.311302	−	0.311302i	−0.534112	−	0.845414i	$-0.679354\pi$
$29$	1.67641	−	1.67641i	0.311302	−	0.311302i	0.845414	+	0.534112i	$0.179354\pi$
$30$		0			0
$31$	3.42372			0.614918			0.307459	−	0.951561i	$-0.400521\pi$
$31$	3.42372			0.614918			0.307459	+	0.951561i	$0.400521\pi$
$32$		0			0
$33$	−7.69687	−	0.780907i	−1.33985	−	0.135938i
$34$		0			0
$35$	9.81254	−	0.861963i	1.65862	−	0.145698i
$36$		0			0
$37$		−	1.11057i		−	0.182576i	−0.995825	−	0.0912880i	$-0.970902\pi$
$37$		−	1.11057i		−	0.182576i	0.995825	−	0.0912880i	$-0.0290984\pi$
$38$		0			0
$39$	6.33574	−	5.16854i	1.01453	−	0.827629i
$40$		0			0
$41$	−0.0298672			−0.00466447			−0.00233223	−	0.999997i	$-0.500742\pi$
$41$	−0.0298672			−0.00466447			−0.00233223	+	0.999997i	$0.500742\pi$
$42$		0			0
$43$	5.45244			0.831490			0.415745	−	0.909481i	$-0.363521\pi$
$43$	5.45244			0.831490			0.415745	+	0.909481i	$0.363521\pi$
$44$		0			0
$45$	5.25473	−	4.16987i	0.783329	−	0.621607i
$46$		0			0
$47$	0.608051	−	0.608051i	0.0886933	−	0.0886933i	−0.661368	−	0.750061i	$-0.730024\pi$
$47$	0.608051	−	0.608051i	0.0886933	−	0.0886933i	0.750061	+	0.661368i	$0.230024\pi$
$48$		0			0
$49$		−	12.4058i		−	1.77225i
$50$		0			0
$51$	−3.09853	−	0.314370i	−0.433881	−	0.0440207i
$52$		0			0
$53$			3.62613i			0.498088i	0.968492	+	0.249044i	$0.0801163\pi$
$53$			3.62613i			0.498088i	−0.968492	+	0.249044i	$0.919884\pi$
$54$		0			0
$55$	−9.94931	+	0.873977i	−1.34156	+	0.117847i
$56$		0			0
$57$	−0.328990	+	3.24263i	−0.0435758	+	0.429497i
$58$		0			0
$59$	5.30621	+	5.30621i	0.690809	+	0.690809i	0.962410	−	0.271601i	$-0.0875530\pi$
$59$	5.30621	+	5.30621i	0.690809	+	0.690809i	−0.271601	+	0.962410i	$0.587553\pi$
$60$		0			0
$61$	8.39022	−	8.39022i	1.07426	−	1.07426i	0.0772461	−	0.997012i	$-0.475387\pi$
$61$	8.39022	−	8.39022i	1.07426	−	1.07426i	0.997012	−	0.0772461i	$-0.0246127\pi$
$62$		0			0
$63$	−7.27752	−	11.0313i	−0.916881	−	1.38981i
$64$		0			0
$65$	6.78232	−	8.08863i	0.841243	−	1.00327i
$66$		0			0
$67$	7.23224			0.883559			0.441780	−	0.897124i	$-0.354347\pi$
$67$	7.23224			0.883559			0.441780	+	0.897124i	$0.354347\pi$
$68$		0			0
$69$	−2.65714	−	0.269587i	−0.319882	−	0.0324545i
$70$		0			0
$71$	−1.80640			−0.214380			−0.107190	−	0.994239i	$-0.534185\pi$
$71$	−1.80640			−0.214380			−0.107190	+	0.994239i	$0.534185\pi$
$72$		0			0
$73$	3.82128	+	3.82128i	0.447247	+	0.447247i	0.894438	−	0.447191i	$-0.147576\pi$
$73$	3.82128	+	3.82128i	0.447247	+	0.447247i	−0.447191	+	0.894438i	$0.647576\pi$
$74$		0			0
$75$	5.65341	−	6.56041i	0.652799	−	0.757531i
$76$		0			0
$77$			19.6763i			2.24232i
$78$		0			0
$79$			3.05546i			0.343766i	0.985117	+	0.171883i	$0.0549851\pi$
$79$			3.05546i			0.343766i	−0.985117	+	0.171883i	$0.945015\pi$
$80$		0			0
$81$	−8.27388	−	3.54160i	−0.919320	−	0.393511i
$82$		0			0
$83$	−14.3316			−1.57309			−0.786546	−	0.617532i	$-0.788133\pi$
$83$	−14.3316			−1.57309			−0.786546	+	0.617532i	$0.788133\pi$
$84$		0			0
$85$	−4.00530	+	0.351838i	−0.434436	+	0.0381621i
$86$		0			0
$87$	−4.08538	−	0.414493i	−0.437999	−	0.0444384i
$88$		0			0
$89$		−	7.83926i		−	0.830960i	−0.909602	−	0.415480i	$-0.863614\pi$
$89$		−	7.83926i		−	0.830960i	0.909602	−	0.415480i	$-0.136386\pi$
$90$		0			0
$91$	−14.7048	−	14.7048i	−1.54148	−	1.54148i
$92$		0			0
$93$	−3.74851	−	4.59503i	−0.388702	−	0.476482i
$94$		0			0
$95$	0.368200	+	4.19157i	0.0377765	+	0.430046i
$96$		0			0
$97$	6.89142	+	6.89142i	0.699718	+	0.699718i	0.964350	−	0.264632i	$-0.0852504\pi$
$97$	6.89142	+	6.89142i	0.699718	+	0.699718i	−0.264632	+	0.964350i	$0.585250\pi$
$98$		0			0
$99$	7.37896	+	11.1851i	0.741613	+	1.12414i
$100$		0			0
$101$	3.80284	−	3.80284i	0.378397	−	0.378397i	−0.492127	−	0.870524i	$-0.663780\pi$
$101$	3.80284	−	3.80284i	0.378397	−	0.378397i	0.870524	+	0.492127i	$0.163780\pi$
$102$		0			0
$103$	11.5064	+	11.5064i	1.13376	+	1.13376i	0.989546	+	0.144216i	$0.0460661\pi$
$103$	11.5064	+	11.5064i	1.13376	+	1.13376i	0.144216	+	0.989546i	$0.453934\pi$
$104$		0			0
$105$	−11.9003	−	12.2258i	−1.16135	−	1.19312i
$106$		0			0
$107$	1.42591			0.137848			0.0689241	−	0.997622i	$-0.478043\pi$
$107$	1.42591			0.137848			0.0689241	+	0.997622i	$0.478043\pi$
$108$		0			0
$109$	10.0313	+	10.0313i	0.960828	+	0.960828i	0.999261	−	0.0384331i	$-0.0122366\pi$
$109$	10.0313	+	10.0313i	0.960828	+	0.960828i	−0.0384331	+	0.999261i	$0.512237\pi$
$110$		0			0
$111$	−1.49051	+	1.21592i	−0.141473	+	0.115410i
$112$		0			0
$113$	12.0556	+	12.0556i	1.13410	+	1.13410i	0.989489	+	0.144606i	$0.0461914\pi$
$113$	12.0556	+	12.0556i	1.13410	+	1.13410i	0.144606	+	0.989489i	$0.453809\pi$
$114$		0			0
$115$	−3.43473	+	0.301717i	−0.320290	+	0.0281353i
$116$		0			0
$117$	−13.8736	−	2.84444i	−1.28261	−	0.262969i
$118$		0			0
$119$			7.92109i			0.726125i
$120$		0			0
$121$		−	8.95053i		−	0.813685i
$122$		0			0
$123$	0.0327005	+	0.0400852i	0.00294850	+	0.00361436i
$124$		0			0
$125$	5.57995	−	9.68835i	0.499086	−	0.866552i
$126$		0			0
$127$	10.9747	+	10.9747i	0.973848	+	0.973848i	0.999667	−	0.0258185i	$-0.00821921\pi$
$127$	10.9747	+	10.9747i	0.973848	+	0.973848i	−0.0258185	+	0.999667i	$0.508219\pi$
$128$		0			0
$129$	−5.96969	−	7.31780i	−0.525601	−	0.644297i
$130$		0			0
$131$	7.39123	+	7.39123i	0.645774	+	0.645774i	0.951969	−	0.306195i	$-0.0990558\pi$
$131$	7.39123	+	7.39123i	0.645774	+	0.645774i	−0.306195	+	0.951969i	$0.599056\pi$
$132$		0			0
$133$	8.28946			0.718788
$134$		0			0
$135$	−11.3497	−	2.48702i	−0.976823	−	0.214048i
$136$		0			0
$137$	−3.38743	−	3.38743i	−0.289407	−	0.289407i	0.547439	−	0.836846i	$-0.315603\pi$
$137$	−3.38743	−	3.38743i	−0.289407	−	0.289407i	−0.836846	+	0.547439i	$0.815603\pi$
$138$		0			0
$139$	−6.27845	+	6.27845i	−0.532531	+	0.532531i	−0.921325	−	0.388794i	$-0.872892\pi$
$139$	−6.27845	+	6.27845i	−0.532531	+	0.532531i	0.388794	+	0.921325i	$0.372892\pi$
$140$		0			0
$141$	−1.48181	−	0.150341i	−0.124791	−	0.0126610i
$142$		0			0
$143$	14.9097	+	14.9097i	1.24681	+	1.24681i
$144$		0			0
$145$	−5.28094	+	0.463894i	−0.438558	+	0.0385243i
$146$		0			0
$147$	−16.6500	+	13.5827i	−1.37327	+	1.12028i
$148$		0			0
$149$	12.3212	+	12.3212i	1.00939	+	1.00939i	0.999955	+	0.00943461i	$0.00300317\pi$
$149$	12.3212	+	12.3212i	1.00939	+	1.00939i	0.00943461	+	0.999955i	$0.496997\pi$
$150$		0			0
$151$			17.5352i			1.42699i	0.700660	+	0.713495i	$0.252889\pi$
$151$			17.5352i			1.42699i	−0.700660	+	0.713495i	$0.747111\pi$
$152$		0			0
$153$	2.97055	+	4.50278i	0.240155	+	0.364028i
$154$		0			0
$155$	−5.86632	−	4.91891i	−0.471194	−	0.395096i
$156$		0			0
$157$	−16.4449			−1.31245			−0.656223	−	0.754567i	$-0.727847\pi$
$157$	−16.4449			−1.31245			−0.656223	+	0.754567i	$0.727847\pi$
$158$		0			0
$159$	4.86669	−	3.97012i	0.385953	−	0.314851i
$160$		0			0
$161$			6.79270i			0.535340i
$162$		0			0
$163$		−	11.3954i		−	0.892553i	−0.894895	−	0.446277i	$-0.852750\pi$
$163$		−	11.3954i		−	0.892553i	0.894895	−	0.446277i	$-0.147250\pi$
$164$		0			0
$165$	12.0661	+	12.3962i	0.939347	+	0.965045i
$166$		0			0
$167$	−12.3593	−	12.3593i	−0.956391	−	0.956391i	0.0426968	−	0.999088i	$-0.486405\pi$
$167$	−12.3593	−	12.3593i	−0.956391	−	0.956391i	−0.999088	+	0.0426968i	$0.986405\pi$
$168$		0			0
$169$	−9.28514			−0.714242
$170$		0			0
$171$	4.71218	−	3.10870i	0.360350	−	0.237728i
$172$		0			0
$173$	0.692222			0.0526287			0.0263143	−	0.999654i	$-0.491623\pi$
$173$	0.692222			0.0526287			0.0263143	+	0.999654i	$0.491623\pi$
$174$		0			0
$175$	−18.0515	−	12.6209i	−1.36457	−	0.954051i
$176$		0			0
$177$	1.31196	−	12.9311i	0.0986131	−	0.971962i
$178$		0			0
$179$	5.03213	−	5.03213i	0.376119	−	0.376119i	−0.493581	−	0.869700i	$-0.664312\pi$
$179$	5.03213	−	5.03213i	0.376119	−	0.376119i	0.869700	+	0.493581i	$0.164312\pi$
$180$		0			0
$181$	−17.7560	−	17.7560i	−1.31980	−	1.31980i	−0.913935	−	0.405862i	$-0.866972\pi$
$181$	−17.7560	−	17.7560i	−1.31980	−	1.31980i	−0.405862	−	0.913935i	$-0.633028\pi$
$182$		0			0
$183$	−20.4468	−	2.07449i	−1.51147	−	0.153351i
$184$		0			0
$185$	−1.59557	+	1.90288i	−0.117308	+	0.139903i
$186$		0			0
$187$		−	8.03150i		−	0.587321i
$188$		0			0
$189$	−6.83738	+	21.8451i	−0.497346	+	1.58899i
$190$		0			0
$191$			1.12803i			0.0816210i	0.999167	+	0.0408105i	$0.0129940\pi$
$191$			1.12803i			0.0816210i	−0.999167	+	0.0408105i	$0.987006\pi$
$192$		0			0
$193$	−0.138692	+	0.138692i	−0.00998326	+	0.00998326i	−0.712081	−	0.702098i	$-0.752247\pi$
$193$	−0.138692	+	0.138692i	−0.00998326	+	0.00998326i	0.702098	+	0.712081i	$0.252247\pi$
$194$		0			0
$195$	−18.2816	−	0.246702i	−1.30917	−	0.0176667i
$196$		0			0
$197$	−11.2854			−0.804050			−0.402025	−	0.915629i	$-0.631694\pi$
$197$	−11.2854			−0.804050			−0.402025	+	0.915629i	$0.631694\pi$
$198$		0			0
$199$	0.0336089			0.00238248			0.00119124	−	0.999999i	$-0.499621\pi$
$199$	0.0336089			0.00238248			0.00119124	+	0.999999i	$0.499621\pi$
$200$		0			0
$201$	−7.91832	−	9.70650i	−0.558516	−	0.684644i
$202$		0			0
$203$			10.4439i			0.733015i
$204$		0			0
$205$	0.0511754	+	0.0429106i	0.00357424	+	0.00299701i
$206$		0			0
$207$	2.54739	+	3.86134i	0.177056	+	0.268382i
$208$		0			0
$209$	−8.40501			−0.581386
$210$		0			0
$211$	19.7280	−	19.7280i	1.35813	−	1.35813i	0.481912	−	0.876219i	$-0.339942\pi$
$211$	19.7280	−	19.7280i	1.35813	−	1.35813i	0.876219	−	0.481912i	$-0.160058\pi$
$212$		0			0
$213$	1.97776	+	2.42439i	0.135514	+	0.166117i
$214$		0			0
$215$	−9.34239	−	7.83360i	−0.637146	−	0.534247i
$216$		0			0
$217$	−10.6647	+	10.6647i	−0.723968	+	0.723968i
$218$		0			0
$219$	0.944814	−	9.31238i	0.0638446	−	0.629273i
$220$		0			0
$221$	6.00222	+	6.00222i	0.403753	+	0.403753i
$222$		0			0
$223$	−3.36405	+	3.36405i	−0.225274	+	0.225274i	−0.810715	−	0.585441i	$-0.800921\pi$
$223$	−3.36405	+	3.36405i	−0.225274	+	0.225274i	0.585441	+	0.810715i	$0.300921\pi$
$224$		0			0
$225$	−14.9945	−	0.404763i	−0.999636	−	0.0269842i
$226$		0			0
$227$		−	11.8014i		−	0.783288i	−0.920117	−	0.391644i	$-0.871906\pi$
$227$		−	11.8014i		−	0.783288i	0.920117	−	0.391644i	$-0.128094\pi$
$228$		0			0
$229$	−1.86279	+	1.86279i	−0.123096	+	0.123096i	−0.765971	−	0.642875i	$-0.777742\pi$
$229$	−1.86279	+	1.86279i	−0.123096	+	0.123096i	0.642875	+	0.765971i	$0.277742\pi$
$230$		0			0
$231$	26.4078	−	21.5428i	1.73751	−	1.41742i
$232$		0			0
$233$	−16.3518	+	16.3518i	−1.07124	+	1.07124i	−0.0739815	+	0.997260i	$0.523571\pi$
$233$	−16.3518	+	16.3518i	−1.07124	+	1.07124i	−0.997260	+	0.0739815i	$0.976429\pi$
$234$		0			0
$235$	−1.91545	+	0.168259i	−0.124950	+	0.0109760i
$236$		0			0
$237$	4.10077	−	3.34531i	0.266374	−	0.217301i
$238$		0			0
$239$	−5.31961			−0.344097			−0.172048	−	0.985089i	$-0.555039\pi$
$239$	−5.31961			−0.344097			−0.172048	+	0.985089i	$0.555039\pi$
$240$		0			0
$241$	6.89117			0.443899			0.221950	−	0.975058i	$-0.428758\pi$
$241$	6.89117			0.443899			0.221950	+	0.975058i	$0.428758\pi$
$242$		0			0
$243$	4.30555	+	14.9821i	0.276201	+	0.961100i
$244$		0			0
$245$	−17.8236	+	21.2565i	−1.13871	+	1.35803i
$246$		0			0
$247$	6.28136	−	6.28136i	0.399673	−	0.399673i
$248$		0			0
$249$	15.6911	+	19.2346i	0.994383	+	1.21894i
$250$		0			0
$251$	−17.1806	+	17.1806i	−1.08443	+	1.08443i	−0.0883399	+	0.996090i	$0.528156\pi$
$251$	−17.1806	+	17.1806i	−1.08443	+	1.08443i	−0.996090	+	0.0883399i	$0.971844\pi$
$252$		0			0
$253$		−	6.88738i		−	0.433006i
$254$		0			0
$255$	4.85747	+	4.99036i	0.304186	+	0.312508i
$256$		0			0
$257$	6.90145	−	6.90145i	0.430501	−	0.430501i	−0.458298	−	0.888799i	$-0.651541\pi$
$257$	6.90145	−	6.90145i	0.430501	−	0.430501i	0.888799	+	0.458298i	$0.151541\pi$
$258$		0			0
$259$	3.45935	+	3.45935i	0.214954	+	0.214954i
$260$		0			0
$261$	3.91664	+	5.93686i	0.242434	+	0.367482i
$262$		0			0
$263$	5.59948	−	5.59948i	0.345279	−	0.345279i	−0.513069	−	0.858347i	$-0.671491\pi$
$263$	5.59948	−	5.59948i	0.345279	−	0.345279i	0.858347	+	0.513069i	$0.171491\pi$
$264$		0			0
$265$	5.20972	−	6.21314i	0.320030	−	0.381670i
$266$		0			0
$267$	−10.5212	+	8.58293i	−0.643886	+	0.525267i
$268$		0			0
$269$	5.86954	−	5.86954i	0.357872	−	0.357872i	−0.505156	−	0.863028i	$-0.668565\pi$
$269$	5.86954	−	5.86954i	0.357872	−	0.357872i	0.863028	+	0.505156i	$0.168565\pi$
$270$		0			0
$271$	−9.88099			−0.600228			−0.300114	−	0.953903i	$-0.597025\pi$
$271$	−9.88099			−0.600228			−0.300114	+	0.953903i	$0.597025\pi$
$272$		0			0
$273$	−3.63576	+	35.8352i	−0.220046	+	2.16885i
$274$		0			0
$275$	18.3031	+	12.7968i	1.10372	+	0.771677i
$276$		0			0
$277$		−	5.90526i		−	0.354813i	−0.984138	−	0.177406i	$-0.943229\pi$
$277$		−	5.90526i		−	0.354813i	0.984138	−	0.177406i	$-0.0567707\pi$
$278$		0			0
$279$	−2.06294	+	10.0619i	−0.123505	+	0.602388i
$280$		0			0
$281$	19.7902			1.18058			0.590292	−	0.807190i	$-0.299013\pi$
$281$	19.7902			1.18058			0.590292	+	0.807190i	$0.299013\pi$
$282$		0			0
$283$	1.73444			0.103102			0.0515509	−	0.998670i	$-0.483584\pi$
$283$	1.73444			0.103102			0.0515509	+	0.998670i	$0.483584\pi$
$284$		0			0
$285$	5.22244	−	5.08337i	0.309351	−	0.301113i
$286$		0			0
$287$	0.0930346	−	0.0930346i	0.00549166	−	0.00549166i
$288$		0			0
$289$			13.7668i			0.809809i
$290$		0			0
$291$	1.70391	−	16.7942i	0.0998848	−	0.984496i
$292$		0			0
$293$		−	14.2607i		−	0.833116i	−0.909109	−	0.416558i	$-0.863236\pi$
$293$		−	14.2607i		−	0.833116i	0.909109	−	0.416558i	$-0.136764\pi$
$294$		0			0
$295$	−1.46832	−	16.7153i	−0.0854892	−	0.973204i
$296$		0			0
$297$	6.93269	−	22.1495i	0.402275	−	1.28525i
$298$		0			0
$299$	5.14718	+	5.14718i	0.297669	+	0.297669i
$300$		0			0
$301$	−16.9841	+	16.9841i	−0.978945	+	0.978945i
$302$		0			0
$303$	−9.26745	−	0.940255i	−0.532401	−	0.0540162i
$304$		0			0
$305$	−26.4304	+	2.32173i	−1.51340	+	0.132942i
$306$		0			0
$307$	−15.6287			−0.891978			−0.445989	−	0.895038i	$-0.647148\pi$
$307$	−15.6287			−0.891978			−0.445989	+	0.895038i	$0.647148\pi$
$308$		0			0
$309$	2.84497	−	28.0409i	0.161845	−	1.59519i
$310$		0			0
$311$	25.4793			1.44480			0.722401	−	0.691475i	$-0.243039\pi$
$311$	25.4793			1.44480			0.722401	+	0.691475i	$0.243039\pi$
$312$		0			0
$313$	8.20084	+	8.20084i	0.463539	+	0.463539i	0.899814	−	0.436275i	$-0.143702\pi$
$313$	8.20084	+	8.20084i	0.463539	+	0.463539i	−0.436275	+	0.899814i	$0.643702\pi$
$314$		0			0
$315$	−3.37930	+	29.3571i	−0.190402	+	1.65409i
$316$		0			0
$317$		−	33.1755i		−	1.86332i	−0.363332	−	0.931660i	$-0.618361\pi$
$317$		−	33.1755i		−	1.86332i	0.363332	−	0.931660i	$-0.381639\pi$
$318$		0			0
$319$		−	10.5894i		−	0.592894i
$320$		0			0
$321$	−1.56118	−	1.91374i	−0.0871366	−	0.106814i
$322$		0			0
$323$	−3.38361			−0.188269
$324$		0			0
$325$	−23.2421	+	4.11506i	−1.28924	+	0.228263i
$326$		0			0
$327$	2.48025	−	24.4462i	0.137158	−	1.35188i
$328$		0			0
$329$			3.78809i			0.208844i
$330$		0			0
$331$	−9.73926	−	9.73926i	−0.535318	−	0.535318i	0.386832	−	0.922150i	$-0.373569\pi$
$331$	−9.73926	−	9.73926i	−0.535318	−	0.535318i	−0.922150	+	0.386832i	$0.873569\pi$
$332$		0			0
$333$	3.26381	+	0.669165i	0.178855	+	0.0366700i
$334$		0			0
$335$	−12.3920	−	10.3907i	−0.677045	−	0.567703i
$336$		0			0
$337$	17.8205	+	17.8205i	0.970743	+	0.970743i	0.999584	−	0.0288408i	$-0.00918159\pi$
$337$	17.8205	+	17.8205i	0.970743	+	0.970743i	−0.0288408	+	0.999584i	$0.509182\pi$
$338$		0			0
$339$	2.98075	−	29.3792i	0.161892	−	1.59566i
$340$		0			0
$341$	10.8134	−	10.8134i	0.585576	−	0.585576i
$342$		0			0
$343$	16.8387	+	16.8387i	0.909206	+	0.909206i
$344$		0			0
$345$	4.16550	+	4.27947i	0.224263	+	0.230399i
$346$		0			0
$347$	19.7879			1.06227			0.531135	−	0.847287i	$-0.321766\pi$
$347$	19.7879			1.06227			0.531135	+	0.847287i	$0.321766\pi$
$348$		0			0
$349$	0.721226	+	0.721226i	0.0386063	+	0.0386063i	0.726146	−	0.687540i	$-0.241309\pi$
$349$	0.721226	+	0.721226i	0.0386063	+	0.0386063i	−0.687540	+	0.726146i	$0.741309\pi$
$350$		0			0
$351$	11.3721	+	21.7342i	0.606997	+	1.16008i
$352$		0			0
$353$	−4.16096	−	4.16096i	−0.221466	−	0.221466i	0.587650	−	0.809115i	$-0.300053\pi$
$353$	−4.16096	−	4.16096i	−0.221466	−	0.221466i	−0.809115	+	0.587650i	$0.800053\pi$
$354$		0			0
$355$	3.09514	+	2.59528i	0.164273	+	0.137743i
$356$		0			0
$357$	10.6310	−	8.67252i	0.562653	−	0.458998i
$358$		0			0
$359$			23.0311i			1.21553i	0.794115	+	0.607767i	$0.207935\pi$
$359$			23.0311i			1.21553i	−0.794115	+	0.607767i	$0.792065\pi$
$360$		0			0
$361$		−	15.4590i		−	0.813633i
$362$		0			0
$363$	−12.0126	+	9.79962i	−0.630500	+	0.514346i
$364$		0			0
$365$	−1.05742	−	12.0376i	−0.0553478	−	0.630077i
$366$		0			0
$367$	−12.9741	−	12.9741i	−0.677244	−	0.677244i	0.282132	−	0.959376i	$-0.408958\pi$
$367$	−12.9741	−	12.9741i	−0.677244	−	0.677244i	−0.959376	+	0.282132i	$0.908958\pi$
$368$		0			0
$369$	0.0179963	−	0.0877756i	0.000936849	−	0.00456942i
$370$		0			0
$371$	−11.2952	−	11.2952i	−0.586418	−	0.586418i
$372$		0			0
$373$	0.388790			0.0201308			0.0100654	−	0.999949i	$-0.496796\pi$
$373$	0.388790			0.0201308			0.0100654	+	0.999949i	$0.496796\pi$
$374$		0			0
$375$	−19.1122	+	3.11849i	−0.986948	+	0.161038i
$376$		0			0
$377$	7.91386	+	7.91386i	0.407584	+	0.407584i
$378$		0			0
$379$	12.4274	−	12.4274i	0.638354	−	0.638354i	−0.311795	−	0.950149i	$-0.600930\pi$
$379$	12.4274	−	12.4274i	0.638354	−	0.638354i	0.950149	+	0.311795i	$0.100930\pi$
$380$		0			0
$381$	2.71350	−	26.7451i	0.139017	−	1.37020i
$382$		0			0
$383$	−10.1538	−	10.1538i	−0.518837	−	0.518837i	0.398383	−	0.917219i	$-0.369572\pi$
$383$	−10.1538	−	10.1538i	−0.518837	−	0.518837i	−0.917219	+	0.398383i	$0.869572\pi$
$384$		0			0
$385$	28.2692	−	33.7140i	1.44073	−	1.71822i
$386$		0			0
$387$	−3.28534	+	16.0240i	−0.167003	+	0.814546i
$388$		0			0
$389$	4.85022	+	4.85022i	0.245916	+	0.245916i	0.819292	−	0.573376i	$-0.194367\pi$
$389$	4.85022	+	4.85022i	0.245916	+	0.245916i	−0.573376	+	0.819292i	$0.694367\pi$
$390$		0			0
$391$		−	2.77266i		−	0.140219i
$392$		0			0
$393$	1.82748	−	18.0123i	0.0921844	−	0.908598i
$394$		0			0
$395$	4.38982	−	5.23532i	0.220876	−	0.263417i
$396$		0			0
$397$	−35.3658			−1.77496			−0.887478	−	0.460849i	$-0.847545\pi$
$397$	−35.3658			−1.77496			−0.887478	+	0.460849i	$0.847545\pi$
$398$		0			0
$399$	−9.07584	−	11.1254i	−0.454360	−	0.556967i
$400$		0			0
$401$			32.4540i			1.62068i	0.585962	+	0.810338i	$0.300717\pi$
$401$			32.4540i			1.62068i	−0.585962	+	0.810338i	$0.699283\pi$
$402$		0			0
$403$			16.1624i			0.805107i
$404$		0			0
$405$	9.08848	+	17.9555i	0.451610	+	0.892215i
$406$		0			0
$407$	−3.50757	−	3.50757i	−0.173864	−	0.173864i
$408$		0			0
$409$	15.8193			0.782215			0.391107	−	0.920345i	$-0.372092\pi$
$409$	15.8193			0.782215			0.391107	+	0.920345i	$0.372092\pi$
$410$		0			0
$411$	−0.837543	+	8.25509i	−0.0413129	+	0.407193i
$412$		0			0
$413$	−33.0571			−1.62663
$414$		0			0
$415$	24.5561	+	20.5903i	1.20541	+	1.01074i
$416$		0			0
$417$	15.3005	+	1.55235i	0.749266	+	0.0760189i
$418$		0			0
$419$	−17.1289	+	17.1289i	−0.836799	+	0.836799i	−0.988436	−	0.151637i	$-0.951545\pi$
$419$	−17.1289	+	17.1289i	−0.836799	+	0.836799i	0.151637	+	0.988436i	$0.451545\pi$
$420$		0			0
$421$	9.54269	+	9.54269i	0.465082	+	0.465082i	0.900317	−	0.435235i	$-0.143335\pi$
$421$	9.54269	+	9.54269i	0.465082	+	0.465082i	−0.435235	+	0.900317i	$0.643335\pi$
$422$		0			0
$423$	1.42060	+	2.15336i	0.0690721	+	0.104700i
$424$		0			0
$425$	7.36831	+	5.15162i	0.357415	+	0.249891i
$426$		0			0
$427$			52.2702i			2.52953i
$428$		0			0
$429$	3.68644	−	36.3347i	0.177983	−	1.75426i
$430$		0			0
$431$		−	22.5898i		−	1.08811i	−0.839049	−	0.544056i	$-0.816888\pi$
$431$		−	22.5898i		−	1.08811i	0.839049	−	0.544056i	$-0.183112\pi$
$432$		0			0
$433$	16.4212	−	16.4212i	0.789151	−	0.789151i	−0.192204	−	0.981355i	$-0.561563\pi$
$433$	16.4212	−	16.4212i	0.789151	−	0.789151i	0.981355	+	0.192204i	$0.0615635\pi$
$434$		0			0
$435$	6.40451	+	6.57973i	0.307073	+	0.315474i
$436$		0			0
$437$	−2.90160			−0.138802
$438$		0			0
$439$	8.90863			0.425186			0.212593	−	0.977141i	$-0.431809\pi$
$439$	8.90863			0.425186			0.212593	+	0.977141i	$0.431809\pi$
$440$		0			0
$441$	36.4590	+	7.47504i	1.73614	+	0.355954i
$442$		0			0
$443$		−	15.3417i		−	0.728904i	−0.931222	−	0.364452i	$-0.881256\pi$
$443$		−	15.3417i		−	0.728904i	0.931222	−	0.364452i	$-0.118744\pi$
$444$		0			0
$445$	−11.2628	+	13.4320i	−0.533907	+	0.636740i
$446$		0			0
$447$	3.04642	−	30.0264i	0.144091	−	1.42020i
$448$		0			0
$449$	1.24427			0.0587206			0.0293603	−	0.999569i	$-0.490653\pi$
$449$	1.24427			0.0587206			0.0293603	+	0.999569i	$0.490653\pi$
$450$		0			0
$451$	−0.0943314	+	0.0943314i	−0.00444189	+	0.00444189i
$452$		0			0
$453$	23.5342	−	19.1986i	1.10573	−	0.902030i
$454$		0			0
$455$	4.06908	+	46.3222i	0.190761	+	2.17162i
$456$		0			0
$457$	−6.22962	+	6.22962i	−0.291409	+	0.291409i	−0.837637	−	0.546228i	$-0.816063\pi$
$457$	−6.22962	+	6.22962i	−0.291409	+	0.291409i	0.546228	+	0.837637i	$0.316063\pi$
$458$		0			0
$459$	2.79090	−	8.91676i	0.130268	−	0.416199i
$460$		0			0
$461$	11.4194	+	11.4194i	0.531856	+	0.531856i	0.921124	−	0.389268i	$-0.127272\pi$
$461$	11.4194	+	11.4194i	0.531856	+	0.531856i	−0.389268	+	0.921124i	$0.627272\pi$
$462$		0			0
$463$	17.6243	−	17.6243i	0.819072	−	0.819072i	−0.166902	−	0.985974i	$-0.553376\pi$
$463$	17.6243	−	17.6243i	0.819072	−	0.819072i	0.985974	+	0.166902i	$0.0533763\pi$
$464$		0			0
$465$	−0.178922	+	13.2588i	−0.00829729	+	0.614862i
$466$		0			0
$467$			6.28155i			0.290675i	0.989382	+	0.145338i	$0.0464269\pi$
$467$			6.28155i			0.290675i	−0.989382	+	0.145338i	$0.953573\pi$
$468$		0			0
$469$	−22.5281	+	22.5281i	−1.04025	+	1.04025i
$470$		0			0
$471$	18.0049	+	22.0710i	0.829624	+	1.01698i
$472$		0			0
$473$	17.2208	−	17.2208i	0.791813	−	0.791813i
$474$		0			0
$475$	5.39120	−	7.71097i	0.247365	−	0.353804i
$476$		0			0
$477$	−10.6567	−	2.18491i	−0.487938	−	0.100040i
$478$		0			0
$479$	5.47225			0.250034			0.125017	−	0.992155i	$-0.460102\pi$
$479$	5.47225			0.250034			0.125017	+	0.992155i	$0.460102\pi$
$480$		0			0
$481$	5.24267			0.239045
$482$		0			0
$483$	9.11659	−	7.43709i	0.414819	−	0.338399i
$484$		0			0
$485$	−1.90698	−	21.7090i	−0.0865916	−	0.985754i
$486$		0			0
$487$	−5.21331	+	5.21331i	−0.236238	+	0.236238i	−0.815290	−	0.579053i	$-0.803423\pi$
$487$	−5.21331	+	5.21331i	−0.236238	+	0.236238i	0.579053	+	0.815290i	$0.303423\pi$
$488$		0			0
$489$	−15.2939	+	12.4764i	−0.691613	+	0.564201i
$490$		0			0
$491$	5.74012	−	5.74012i	0.259048	−	0.259048i	−0.565619	−	0.824667i	$-0.691363\pi$
$491$	5.74012	−	5.74012i	0.259048	−	0.259048i	0.824667	+	0.565619i	$0.191363\pi$
$492$		0			0
$493$		−	4.26300i		−	0.191996i
$494$		0			0
$495$	3.42640	−	29.7663i	0.154005	−	1.33790i
$496$		0			0
$497$	5.62683	−	5.62683i	0.252398	−	0.252398i
$498$		0			0
$499$	18.9929	+	18.9929i	0.850238	+	0.850238i	0.990162	−	0.139924i	$-0.0446859\pi$
$499$	18.9929	+	18.9929i	0.850238	+	0.850238i	−0.139924	+	0.990162i	$0.544686\pi$
$500$		0			0
$501$	−3.05584	+	30.1194i	−0.136525	+	1.34563i
$502$		0			0
$503$	29.4820	−	29.4820i	1.31454	−	1.31454i	0.396502	−	0.918034i	$-0.370224\pi$
$503$	29.4820	−	29.4820i	1.31454	−	1.31454i	0.918034	−	0.396502i	$-0.129776\pi$
$504$		0			0
$505$	−11.9795	+	1.05232i	−0.533081	+	0.0468275i
$506$		0			0
$507$	10.1660	+	12.4617i	0.451487	+	0.553445i
$508$		0			0
$509$	2.63203	−	2.63203i	0.116663	−	0.116663i	−0.646365	−	0.763028i	$-0.723712\pi$
$509$	2.63203	−	2.63203i	0.116663	−	0.116663i	0.763028	+	0.646365i	$0.223712\pi$
$510$		0			0
$511$	−23.8062			−1.05312
$512$		0			0
$513$	−9.33143	−	2.92069i	−0.411993	−	0.128952i
$514$		0			0
$515$	−3.18404	−	36.2470i	−0.140306	−	1.59723i
$516$		0			0
$517$		−	3.84089i		−	0.168922i
$518$		0			0
$519$	−0.757889	−	0.929041i	−0.0332676	−	0.0407804i
$520$		0			0
$521$	−27.6785			−1.21262			−0.606308	−	0.795230i	$-0.707350\pi$
$521$	−27.6785			−1.21262			−0.606308	+	0.795230i	$0.707350\pi$
$522$		0			0
$523$	23.2284			1.01571			0.507853	−	0.861444i	$-0.330439\pi$
$523$	23.2284			1.01571			0.507853	+	0.861444i	$0.330439\pi$
$524$		0			0
$525$	2.82527	+	38.0454i	0.123305	+	1.66044i
$526$		0			0
$527$	4.35314	−	4.35314i	0.189626	−	0.189626i
$528$		0			0
$529$			20.6223i			0.896622i
$530$		0			0
$531$	−18.7915	+	12.3970i	−0.815480	+	0.537984i
$532$		0			0
$533$		−	0.140994i		−	0.00610714i
$534$		0			0
$535$	−2.44321	−	2.04863i	−0.105629	−	0.0885700i
$536$		0			0
$537$	−12.2632	−	1.24420i	−0.529196	−	0.0536911i
$538$		0			0
$539$	−39.1820	−	39.1820i	−1.68769	−	1.68769i
$540$		0			0
$541$	9.29813	−	9.29813i	0.399758	−	0.399758i	−0.478390	−	0.878148i	$-0.658779\pi$
$541$	9.29813	−	9.29813i	0.399758	−	0.399758i	0.878148	+	0.478390i	$0.158779\pi$
$542$		0			0
$543$	−4.39019	+	43.2711i	−0.188401	+	1.85694i
$544$		0			0
$545$	−2.77586	−	31.6002i	−0.118905	−	1.35360i
$546$		0			0
$547$	−16.8418			−0.720105			−0.360053	−	0.932932i	$-0.617241\pi$
$547$	−16.8418			−0.720105			−0.360053	+	0.932932i	$0.617241\pi$
$548$		0			0
$549$	19.6023	+	29.7132i	0.836605	+	1.26813i
$550$		0			0
$551$	−4.46125			−0.190055
$552$		0			0
$553$	−9.51758	−	9.51758i	−0.404729	−	0.404729i
$554$		0			0
$555$	4.30081	+	0.0580375i	0.182559	+	0.00246356i
$556$		0			0
$557$			25.3128i			1.07254i	0.844047	+	0.536269i	$0.180167\pi$
$557$			25.3128i			1.07254i	−0.844047	+	0.536269i	$0.819833\pi$
$558$		0			0
$559$			25.7394i			1.08866i
$560$		0			0
$561$	−10.7792	+	8.79340i	−0.455098	+	0.371258i
$562$		0			0
$563$	−14.3570			−0.605075			−0.302537	−	0.953138i	$-0.597834\pi$
$563$	−14.3570			−0.605075			−0.302537	+	0.953138i	$0.597834\pi$
$564$		0			0
$565$	−3.33600	−	37.9769i	−0.140347	−	1.59770i
$566$		0			0
$567$	36.8046	−	14.7408i	1.54565	−	0.619056i
$568$		0			0
$569$		−	27.5445i		−	1.15472i	−0.816488	−	0.577362i	$-0.804082\pi$
$569$		−	27.5445i		−	1.15472i	0.816488	−	0.577362i	$-0.195918\pi$
$570$		0			0
$571$	22.9584	+	22.9584i	0.960778	+	0.960778i	0.999259	−	0.0384814i	$-0.0122520\pi$
$571$	22.9584	+	22.9584i	0.960778	+	0.960778i	−0.0384814	+	0.999259i	$0.512252\pi$
$572$		0			0
$573$	1.51394	−	1.23503i	0.0632457	−	0.0515943i
$574$		0			0
$575$	6.31866	+	4.41776i	0.263506	+	0.184233i
$576$		0			0
$577$	18.5107	+	18.5107i	0.770611	+	0.770611i	0.978213	−	0.207602i	$-0.0665660\pi$
$577$	18.5107	+	18.5107i	0.770611	+	0.770611i	−0.207602	+	0.978213i	$0.566566\pi$
$578$		0			0
$579$	0.337989	+	0.0342916i	0.0140464	+	0.00142511i
$580$		0			0
$581$	44.6420	−	44.6420i	1.85206	−	1.85206i
$582$		0			0
$583$	11.4527	+	11.4527i	0.474320	+	0.474320i
$584$		0			0
$585$	19.6848	+	24.8061i	0.813864	+	1.02561i
$586$		0			0
$587$	−39.3173			−1.62280			−0.811400	−	0.584492i	$-0.801294\pi$
$587$	−39.3173			−1.62280			−0.811400	+	0.584492i	$0.801294\pi$
$588$		0			0
$589$	−4.55558	−	4.55558i	−0.187710	−	0.187710i
$590$		0			0
$591$	12.3560	+	15.1463i	0.508257	+	0.623035i
$592$		0			0
$593$	−17.6375	−	17.6375i	−0.724284	−	0.724284i	0.245190	−	0.969475i	$-0.421149\pi$
$593$	−17.6375	−	17.6375i	−0.724284	−	0.724284i	−0.969475	+	0.245190i	$0.921149\pi$
$594$		0			0
$595$	11.3803	−	13.5723i	0.466549	−	0.556408i
$596$		0			0
$597$	−0.0367972	−	0.0451071i	−0.00150601	−	0.00184611i
$598$		0			0
$599$			2.28629i			0.0934153i	0.998909	+	0.0467077i	$0.0148729\pi$
$599$			2.28629i			0.0934153i	−0.998909	+	0.0467077i	$0.985127\pi$
$600$		0			0
$601$			7.98198i			0.325592i	0.986660	+	0.162796i	$0.0520512\pi$
$601$			7.98198i			0.325592i	−0.986660	+	0.162796i	$0.947949\pi$
$602$		0			0
$603$	−4.35775	+	21.2546i	−0.177461	+	0.865554i
$604$		0			0
$605$	−12.8594	+	15.3361i	−0.522807	+	0.623502i
$606$		0			0
$607$	−5.09956	−	5.09956i	−0.206985	−	0.206985i	0.596000	−	0.802985i	$-0.296756\pi$
$607$	−5.09956	−	5.09956i	−0.206985	−	0.206985i	−0.802985	+	0.596000i	$0.796756\pi$
$608$		0			0
$609$	14.0169	−	11.4346i	0.567992	−	0.463354i
$610$		0			0
$611$	2.87043	+	2.87043i	0.116125	+	0.116125i
$612$		0			0
$613$	44.3177			1.78998			0.894988	−	0.446090i	$-0.147184\pi$
$613$	44.3177			1.78998			0.894988	+	0.446090i	$0.147184\pi$
$614$		0			0
$615$	0.00156084	−	0.115664i	6.29391e−5	−	0.00466404i
$616$		0			0
$617$	21.2051	+	21.2051i	0.853685	+	0.853685i	0.990585	−	0.136900i	$-0.0437139\pi$
$617$	21.2051	+	21.2051i	0.853685	+	0.853685i	−0.136900	+	0.990585i	$0.543714\pi$
$618$		0			0
$619$	−25.1795	+	25.1795i	−1.01205	+	1.01205i	−0.0121214	+	0.999927i	$0.503858\pi$
$619$	−25.1795	+	25.1795i	−1.01205	+	1.01205i	−0.999927	+	0.0121214i	$0.996142\pi$
$620$		0			0
$621$	2.39332	−	7.64653i	0.0960408	−	0.306845i
$622$		0			0
$623$	24.4189	+	24.4189i	0.978322	+	0.978322i
$624$		0			0
$625$	−23.4803	+	8.58354i	−0.939211	+	0.343341i
$626$		0			0
$627$	9.20234	+	11.2805i	0.367506	+	0.450499i
$628$		0			0
$629$	−1.41205	−	1.41205i	−0.0563020	−	0.0563020i
$630$		0			0
$631$		−	28.3651i		−	1.12920i	−0.825366	−	0.564599i	$-0.809031\pi$
$631$		−	28.3651i		−	1.12920i	0.825366	−	0.564599i	$-0.190969\pi$
$632$		0			0
$633$	−48.0767	−	4.87776i	−1.91088	−	0.193874i
$634$		0			0
$635$	−3.03690	−	34.5720i	−0.120516	−	1.37195i
$636$		0			0
$637$	58.5642			2.32040
$638$		0			0
$639$	1.08843	−	5.30876i	0.0430578	−	0.210011i
$640$		0			0
$641$			2.09968i			0.0829322i	0.999140	+	0.0414661i	$0.0132029\pi$
$641$			2.09968i			0.0829322i	−0.999140	+	0.0414661i	$0.986797\pi$
$642$		0			0
$643$		−	42.5323i		−	1.67731i	−0.544663	−	0.838655i	$-0.683343\pi$
$643$		−	42.5323i		−	1.67731i	0.544663	−	0.838655i	$-0.316657\pi$
$644$		0			0
$645$	−0.284941	+	21.1153i	−0.0112196	+	0.831414i
$646$		0			0
$647$	−12.2012	−	12.2012i	−0.479680	−	0.479680i	0.425349	−	0.905029i	$-0.360151\pi$
$647$	−12.2012	−	12.2012i	−0.479680	−	0.479680i	−0.905029	+	0.425349i	$0.860151\pi$
$648$		0			0
$649$	33.5179			1.31569
$650$		0			0
$651$	25.9897	+	2.63685i	1.01862	+	0.103346i
$652$		0			0
$653$	−4.49231			−0.175798			−0.0878989	−	0.996129i	$-0.528015\pi$
$653$	−4.49231			−0.175798			−0.0878989	+	0.996129i	$0.528015\pi$
$654$		0			0
$655$	−2.04529	−	23.2834i	−0.0799160	−	0.909760i
$656$		0			0
$657$	−13.5327	+	8.92775i	−0.527962	+	0.348305i
$658$		0			0
$659$	−24.6295	+	24.6295i	−0.959430	+	0.959430i	−0.999209	−	0.0397785i	$-0.987335\pi$
$659$	−24.6295	+	24.6295i	−0.959430	+	0.959430i	0.0397785	+	0.999209i	$0.487335\pi$
$660$		0			0
$661$	8.98193	+	8.98193i	0.349356	+	0.349356i	0.859870	−	0.510513i	$-0.170545\pi$
$661$	8.98193	+	8.98193i	0.349356	+	0.349356i	−0.510513	+	0.859870i	$0.670545\pi$
$662$		0			0
$663$	1.48405	−	14.6273i	0.0576358	−	0.568077i
$664$		0			0
$665$	−14.2034	−	11.9096i	−0.550786	−	0.461834i
$666$		0			0
$667$		−	3.65572i		−	0.141550i
$668$		0			0
$669$	8.19812	+	0.831763i	0.316958	+	0.0321578i
$670$		0			0
$671$		−	52.9988i		−	2.04599i
$672$		0			0
$673$	18.8473	−	18.8473i	0.726509	−	0.726509i	−0.243414	−	0.969923i	$-0.578267\pi$
$673$	18.8473	−	18.8473i	0.726509	−	0.726509i	0.969923	+	0.243414i	$0.0782673\pi$
$674$		0			0
$675$	15.8737	+	20.5676i	0.610981	+	0.791645i
$676$		0			0
$677$	−32.2800			−1.24062			−0.620311	−	0.784356i	$-0.712993\pi$
$677$	−32.2800			−1.24062			−0.620311	+	0.784356i	$0.712993\pi$
$678$		0			0
$679$	−42.9328			−1.64761
$680$		0			0
$681$	−15.8389	+	12.9210i	−0.606947	+	0.495132i
$682$		0			0
$683$			29.6935i			1.13619i	0.822963	+	0.568095i	$0.192319\pi$
$683$			29.6935i			1.13619i	−0.822963	+	0.568095i	$0.807681\pi$
$684$		0			0
$685$	0.937363	+	10.6709i	0.0358148	+	0.407714i
$686$		0			0
$687$	4.53957	+	0.460575i	0.173195	+	0.0175720i
$688$		0			0
$689$	−17.1179			−0.652142
$690$		0			0
$691$	0.523086	−	0.523086i	0.0198991	−	0.0198991i	−0.697087	−	0.716986i	$-0.745521\pi$
$691$	0.523086	−	0.523086i	0.0198991	−	0.0198991i	0.716986	+	0.697087i	$0.245521\pi$
$692$		0			0
$693$	−57.8260	−	11.8558i	−2.19663	−	0.450366i
$694$		0			0
$695$	19.7780	−	1.73736i	0.750224	−	0.0659019i
$696$		0			0
$697$	−0.0379751	+	0.0379751i	−0.00143841	+	0.00143841i
$698$		0			0
$699$	39.8490	+	4.04299i	1.50723	+	0.152920i
$700$		0			0
$701$	−35.8181	−	35.8181i	−1.35283	−	1.35283i	−0.882480	−	0.470349i	$-0.844128\pi$
$701$	−35.8181	−	35.8181i	−1.35283	−	1.35283i	−0.470349	−	0.882480i	$-0.655872\pi$
$702$		0			0
$703$	−1.47771	+	1.47771i	−0.0557330	+	0.0557330i
$704$		0			0
$705$	2.32298	+	2.38653i	0.0874885	+	0.0898820i
$706$		0			0
$707$			23.6913i			0.891003i
$708$		0			0
$709$	9.01504	−	9.01504i	0.338567	−	0.338567i	−0.517261	−	0.855828i	$-0.673048\pi$
$709$	9.01504	−	9.01504i	0.338567	−	0.338567i	0.855828	+	0.517261i	$0.173048\pi$
$710$		0			0
$711$	−8.97958	−	1.84105i	−0.336761	−	0.0690447i
$712$		0			0
$713$	3.73302	−	3.73302i	0.139803	−	0.139803i
$714$		0			0
$715$	−4.12580	−	46.9679i	−0.154296	−	1.75650i
$716$		0			0
$717$	5.82425	+	7.13952i	0.217510	+	0.266630i
$718$		0			0
$719$	−8.72666			−0.325449			−0.162725	−	0.986672i	$-0.552028\pi$
$719$	−8.72666			−0.325449			−0.162725	+	0.986672i	$0.552028\pi$
$720$		0			0
$721$	−71.6838			−2.66965
$722$		0			0
$723$	−7.54490	−	9.24874i	−0.280598	−	0.343964i
$724$		0			0
$725$	9.71502	+	6.79235i	0.360807	+	0.252262i
$726$		0			0
$727$	7.46236	−	7.46236i	0.276763	−	0.276763i	−0.555052	−	0.831816i	$-0.687302\pi$
$727$	7.46236	−	7.46236i	0.276763	−	0.276763i	0.831816	+	0.555052i	$0.187302\pi$
$728$		0			0
$729$	15.3937	−	22.1819i	0.570136	−	0.821551i
$730$		0			0
$731$	6.93259	−	6.93259i	0.256411	−	0.256411i
$732$		0			0
$733$			17.5123i			0.646831i	0.946257	+	0.323416i	$0.104831\pi$
$733$			17.5123i			0.646831i	−0.946257	+	0.323416i	$0.895169\pi$
$734$		0			0
$735$	48.0430	+	0.648319i	1.77209	+	0.0239136i
$736$		0			0
$737$	22.8421	−	22.8421i	0.841398	−	0.841398i
$738$		0			0
$739$	−8.86712	−	8.86712i	−0.326182	−	0.326182i	0.524950	−	0.851133i	$-0.324084\pi$
$739$	−8.86712	−	8.86712i	−0.326182	−	0.326182i	−0.851133	+	0.524950i	$0.824084\pi$
$740$		0			0
$741$	−15.3075	−	1.55307i	−0.562336	−	0.0570534i
$742$		0			0
$743$	−5.34319	+	5.34319i	−0.196023	+	0.196023i	−0.798292	−	0.602270i	$-0.794263\pi$
$743$	−5.34319	+	5.34319i	−0.196023	+	0.196023i	0.602270	+	0.798292i	$0.294263\pi$
$744$		0			0
$745$	−3.40949	−	38.8135i	−0.124914	−	1.42202i
$746$		0			0
$747$	8.63539	−	42.1185i	0.315953	−	1.54104i
$748$		0			0
$749$	−4.44164	+	4.44164i	−0.162294	+	0.162294i
$750$		0			0
$751$	7.05238			0.257345			0.128672	−	0.991687i	$-0.458928\pi$
$751$	7.05238			0.257345			0.128672	+	0.991687i	$0.458928\pi$
$752$		0			0
$753$	41.8688	+	4.24791i	1.52578	+	0.154803i
$754$		0			0
$755$	25.1930	−	30.0453i	0.916867	−	1.09346i
$756$		0			0
$757$		−	5.33633i		−	0.193952i	−0.995287	−	0.0969760i	$-0.969083\pi$
$757$		−	5.33633i		−	0.193952i	0.995287	−	0.0969760i	$-0.0309170\pi$
$758$		0			0
$759$	−9.24366	+	7.54075i	−0.335524	+	0.273712i
$760$		0			0
$761$	−17.7227			−0.642446			−0.321223	−	0.947004i	$-0.604094\pi$
$761$	−17.7227			−0.642446			−0.321223	+	0.947004i	$0.604094\pi$
$762$		0			0
$763$	−62.4942			−2.26244
$764$		0			0
$765$	1.37937	−	11.9830i	0.0498712	−	0.433248i
$766$		0			0
$767$	−25.0491	+	25.0491i	−0.904470	+	0.904470i
$768$		0			0
$769$		−	0.628276i		−	0.0226562i	−0.999936	−	0.0113281i	$-0.996394\pi$
$769$		−	0.628276i		−	0.0226562i	0.999936	−	0.0113281i	$-0.00360593\pi$
$770$		0			0
$771$	−16.8187	−	1.70639i	−0.605710	−	0.0614540i
$772$		0			0
$773$			38.6782i			1.39116i	0.718450	+	0.695579i	$0.244852\pi$
$773$			38.6782i			1.39116i	−0.718450	+	0.695579i	$0.755148\pi$
$774$		0			0
$775$	2.98447	+	16.8564i	0.107205	+	0.605501i
$776$		0			0
$777$	0.855327	−	8.43037i	0.0306847	−	0.302438i
$778$		0			0
$779$	0.0397411	+	0.0397411i	0.00142387	+	0.00142387i
$780$		0			0
$781$	−5.70526	+	5.70526i	−0.204150	+	0.204150i
$782$		0			0
$783$	3.67976	−	11.7566i	0.131504	−	0.420148i
$784$		0			0
$785$	28.1772	+	23.6266i	1.00569	+	0.843271i
$786$		0			0
$787$	−17.6339			−0.628582			−0.314291	−	0.949327i	$-0.601767\pi$
$787$	−17.6339			−0.628582			−0.314291	+	0.949327i	$0.601767\pi$
$788$		0			0
$789$	−13.6458	−	1.38447i	−0.485804	−	0.0492886i
$790$		0			0
$791$	−75.1051			−2.67043
$792$		0			0
$793$	39.6079	+	39.6079i	1.40652	+	1.40652i
$794$		0			0
$795$	−14.0427	−	0.189500i	−0.498042	−	0.00672086i
$796$		0			0
$797$			38.4460i			1.36183i	0.732364	+	0.680913i	$0.238417\pi$
$797$			38.4460i			1.36183i	−0.732364	+	0.680913i	$0.761583\pi$
$798$		0			0
$799$		−	1.54623i		−	0.0547017i
$800$		0			0
$801$	23.0385	+	4.72350i	0.814027	+	0.166897i
$802$		0			0
$803$	24.1380			0.851811
$804$		0			0
$805$	9.75917	−	11.6388i	0.343966	−	0.410215i
$806$		0			0
$807$	−14.3040	−	1.45125i	−0.503523	−	0.0510863i
$808$		0			0
$809$		−	30.1296i		−	1.05930i	−0.848217	−	0.529649i	$-0.822323\pi$
$809$		−	30.1296i		−	1.05930i	0.848217	−	0.529649i	$-0.177677\pi$
$810$		0			0
$811$	−8.43839	−	8.43839i	−0.296312	−	0.296312i	0.543256	−	0.839567i	$-0.317191\pi$
$811$	−8.43839	−	8.43839i	−0.296312	−	0.296312i	−0.839567	+	0.543256i	$0.817191\pi$
$812$		0			0
$813$	10.8183	+	13.2614i	0.379416	+	0.465099i
$814$		0			0
$815$	−16.3719	+	19.5252i	−0.573482	+	0.683937i
$816$		0			0
$817$	−7.25499	−	7.25499i	−0.253820	−	0.253820i
$818$		0			0
$819$	52.0757	−	34.3551i	1.81967	−	1.20046i
$820$		0			0
$821$	−22.0276	+	22.0276i	−0.768770	+	0.768770i	−0.977890	−	0.209120i	$-0.932940\pi$
$821$	−22.0276	+	22.0276i	−0.768770	+	0.768770i	0.209120	+	0.977890i	$0.432940\pi$
$822$		0			0
$823$	−4.27792	−	4.27792i	−0.149119	−	0.149119i	0.628605	−	0.777724i	$-0.283626\pi$
$823$	−4.27792	−	4.27792i	−0.149119	−	0.149119i	−0.777724	+	0.628605i	$0.783626\pi$
$824$		0			0
$825$	−2.86465	−	38.5757i	−0.0997342	−	1.34303i
$826$		0			0
$827$	46.9732			1.63342			0.816709	−	0.577050i	$-0.195796\pi$
$827$	46.9732			1.63342			0.816709	+	0.577050i	$0.195796\pi$
$828$		0			0
$829$	−30.1655	−	30.1655i	−1.04769	−	1.04769i	−0.998804	−	0.0488871i	$-0.984433\pi$
$829$	−30.1655	−	30.1655i	−1.04769	−	1.04769i	−0.0488871	−	0.998804i	$-0.515567\pi$
$830$		0			0
$831$	−7.92554	+	6.46546i	−0.274934	+	0.224284i
$832$		0			0
$833$	−15.7735	−	15.7735i	−0.546520	−	0.546520i
$834$		0			0
$835$	3.42004	+	38.9336i	0.118356	+	1.34735i
$836$		0			0
$837$	15.7628	−	8.24767i	0.544843	−	0.285081i
$838$		0			0
$839$		−	33.8782i		−	1.16961i	−0.811175	−	0.584803i	$-0.801172\pi$
$839$		−	33.8782i		−	1.16961i	0.811175	−	0.584803i	$-0.198828\pi$
$840$		0			0
$841$			23.3793i			0.806183i
$842$		0			0
$843$	−21.6676	−	26.5607i	−0.746271	−	0.914800i
$844$		0			0
$845$	15.9095	+	13.3401i	0.547302	+	0.458913i
$846$		0			0
$847$	27.8804	+	27.8804i	0.957983	+	0.957983i
$848$		0			0
$849$	−1.89898	−	2.32782i	−0.0651728	−	0.0798906i
$850$		0			0
$851$	−1.21089	−	1.21089i	−0.0415089	−	0.0415089i
$852$		0			0
$853$	−3.57891			−0.122540			−0.0612698	−	0.998121i	$-0.519515\pi$
$853$	−3.57891			−0.122540			−0.0612698	+	0.998121i	$0.519515\pi$
$854$		0			0
$855$	−12.5403	−	1.44352i	−0.428870	−	0.0493672i
$856$		0			0
$857$	27.5013	+	27.5013i	0.939426	+	0.939426i	0.998267	−	0.0588410i	$-0.0187405\pi$
$857$	27.5013	+	27.5013i	0.939426	+	0.939426i	−0.0588410	+	0.998267i	$0.518741\pi$
$858$		0			0
$859$	0.936601	−	0.936601i	0.0319564	−	0.0319564i	−0.690948	−	0.722904i	$-0.742807\pi$
$859$	0.936601	−	0.936601i	0.0319564	−	0.0319564i	0.722904	+	0.690948i	$0.242807\pi$
$860$		0			0
$861$	−0.226723	−	0.0230029i	−0.00772671	−	0.000783935i
$862$		0			0
$863$	−36.3053	−	36.3053i	−1.23585	−	1.23585i	−0.961682	−	0.274166i	$-0.911598\pi$
$863$	−36.3053	−	36.3053i	−1.23585	−	1.23585i	−0.274166	−	0.961682i	$-0.588402\pi$
$864$		0			0
$865$	−1.18608	−	0.994525i	−0.0403278	−	0.0338149i
$866$		0			0
$867$	18.4766	−	15.0727i	0.627497	−	0.511897i
$868$		0			0
$869$	9.65024	+	9.65024i	0.327362	+	0.327362i
$870$		0			0
$871$			34.1414i			1.15684i
$872$		0			0
$873$	−24.4054	+	16.1006i	−0.825996	+	0.544922i
$874$		0			0
$875$	12.7974	+	47.5599i	0.432632	+	1.60782i
$876$		0			0
$877$	25.0257			0.845058			0.422529	−	0.906349i	$-0.361142\pi$
$877$	25.0257			0.845058			0.422529	+	0.906349i	$0.361142\pi$
$878$		0			0
$879$	−19.1394	+	15.6135i	−0.645557	+	0.526630i
$880$		0			0
$881$			23.8527i			0.803619i	0.915723	+	0.401810i	$0.131619\pi$
$881$			23.8527i			0.803619i	−0.915723	+	0.401810i	$0.868381\pi$
$882$		0			0
$883$		−	4.08020i		−	0.137310i	−0.997640	−	0.0686548i	$-0.978129\pi$
$883$		−	4.08020i		−	0.137310i	0.997640	−	0.0686548i	$-0.0218707\pi$
$884$		0			0
$885$	−20.8263	+	20.2717i	−0.700068	+	0.681425i
$886$		0			0
$887$	18.8794	+	18.8794i	0.633908	+	0.633908i	0.949046	−	0.315138i	$-0.102051\pi$
$887$	18.8794	+	18.8794i	0.633908	+	0.633908i	−0.315138	+	0.949046i	$0.602051\pi$
$888$		0			0
$889$	−68.3713			−2.29310
$890$		0			0
$891$	−37.3176	+	14.9463i	−1.25019	+	0.500719i
$892$		0			0
$893$	−1.61814			−0.0541489
$894$		0			0
$895$	−15.8520	+	1.39248i	−0.529872	+	0.0465456i
$896$		0			0
$897$	1.27264	−	12.5436i	0.0424923	−	0.418818i
$898$		0			0
$899$	5.73956	−	5.73956i	0.191425	−	0.191425i
$900$		0			0
$901$	4.61050	+	4.61050i	0.153598	+	0.153598i
$902$		0			0
$903$	41.3898	+	4.19932i	1.37737	+	0.139745i
$904$		0			0
$905$	4.91342	+	55.9341i	0.163328	+	1.85931i
$906$		0			0
$907$		−	6.14856i		−	0.204160i	−0.994776	−	0.102080i	$-0.967450\pi$
$907$		−	6.14856i		−	0.204160i	0.994776	−	0.102080i	$-0.0325497\pi$
$908$		0			0
$909$	8.88467	+	13.4674i	0.294686	+	0.446686i
$910$		0			0
$911$			45.1469i			1.49579i	0.663820	+	0.747893i	$0.268934\pi$
$911$			45.1469i			1.49579i	−0.663820	+	0.747893i	$0.731066\pi$
$912$		0			0
$913$	−45.2643	+	45.2643i	−1.49803	+	1.49803i
$914$		0			0
$915$	32.0538	+	32.9307i	1.05967	+	1.08866i
$916$		0			0
$917$	−46.0465			−1.52059
$918$		0			0
$919$	−24.1800			−0.797625			−0.398813	−	0.917032i	$-0.630578\pi$
$919$	−24.1800			−0.797625			−0.398813	+	0.917032i	$0.630578\pi$
$920$		0			0
$921$	17.1113	+	20.9755i	0.563838	+	0.691168i
$922$		0			0
$923$		−	8.52749i		−	0.280686i
$924$		0			0
$925$	5.46779	−	0.968084i	0.179780	−	0.0318304i
$926$		0			0
$927$	−40.7490	+	26.8827i	−1.33837	+	0.882945i
$928$		0			0
$929$	−27.0953			−0.888968			−0.444484	−	0.895787i	$-0.646613\pi$
$929$	−27.0953			−0.888968			−0.444484	+	0.895787i	$0.646613\pi$
$930$		0			0
$931$	−16.5071	+	16.5071i	−0.540997	+	0.540997i
$932$		0			0
$933$	−27.8964	−	34.1962i	−0.913288	−	1.11953i
$934$		0			0
$935$	−11.5390	+	13.7614i	−0.377365	+	0.450047i
$936$		0			0
$937$	21.2311	−	21.2311i	0.693591	−	0.693591i	−0.269429	−	0.963020i	$-0.586835\pi$
$937$	21.2311	−	21.2311i	0.693591	−	0.693591i	0.963020	+	0.269429i	$0.0868350\pi$
$938$		0			0
$939$	2.02766	−	19.9853i	0.0661702	−	0.652195i
$940$		0			0
$941$	1.04685	+	1.04685i	0.0341263	+	0.0341263i	0.723964	−	0.689838i	$-0.242318\pi$
$941$	1.04685	+	1.04685i	0.0341263	+	0.0341263i	−0.689838	+	0.723964i	$0.742318\pi$
$942$		0			0
$943$	−0.0325654	+	0.0325654i	−0.00106047	+	0.00106047i
$944$		0			0
$945$	43.1005	−	27.6067i	1.40206	−	0.898045i
$946$		0			0
$947$			18.5933i			0.604202i	0.953276	+	0.302101i	$0.0976880\pi$
$947$			18.5933i			0.604202i	−0.953276	+	0.302101i	$0.902312\pi$
$948$		0			0
$949$	−18.0392	+	18.0392i	−0.585576	+	0.585576i
$950$		0			0
$951$	−44.5253	+	36.3226i	−1.44383	+	1.17784i
$952$		0			0
$953$	22.0491	−	22.0491i	0.714239	−	0.714239i	−0.253180	−	0.967419i	$-0.581477\pi$
$953$	22.0491	−	22.0491i	0.714239	−	0.714239i	0.967419	+	0.253180i	$0.0814765\pi$
$954$		0			0
$955$	1.62065	−	1.93280i	0.0524430	−	0.0625438i
$956$		0			0
$957$	−14.2122	+	11.5940i	−0.459416	+	0.374781i
$958$		0			0
$959$	21.1033			0.681461
$960$		0			0
$961$	−19.2781			−0.621875
$962$		0			0
$963$	−0.859176	+	4.19057i	−0.0276866	+	0.135039i
$964$		0			0
$965$	0.436900	−	0.0383786i	0.0140643	−	0.00123545i
$966$		0			0
$967$	6.84457	−	6.84457i	0.220107	−	0.220107i	−0.588437	−	0.808543i	$-0.700256\pi$
$967$	6.84457	−	6.84457i	0.220107	−	0.220107i	0.808543	+	0.588437i	$0.200256\pi$
$968$		0			0
$969$	3.70459	+	4.54119i	0.119009	+	0.145884i
$970$		0			0
$971$	−16.5996	+	16.5996i	−0.532708	+	0.532708i	−0.921377	−	0.388669i	$-0.872935\pi$
$971$	−16.5996	+	16.5996i	−0.532708	+	0.532708i	0.388669	+	0.921377i	$0.372935\pi$
$972$		0			0
$973$		−	39.1141i		−	1.25394i
$974$		0			0
$975$	30.9698	+	26.6881i	0.991828	+	0.854704i
$976$		0			0
$977$	3.19411	−	3.19411i	0.102189	−	0.102189i	−0.654164	−	0.756353i	$-0.726979\pi$
$977$	3.19411	−	3.19411i	0.102189	−	0.102189i	0.756353	+	0.654164i	$0.226979\pi$
$978$		0			0
$979$	−24.7592	−	24.7592i	−0.791309	−	0.791309i
$980$		0			0
$981$	−35.5251	+	23.4364i	−1.13423	+	0.748268i
$982$		0			0
$983$	−22.7323	+	22.7323i	−0.725049	+	0.725049i	−0.969629	−	0.244580i	$-0.921350\pi$
$983$	−22.7323	+	22.7323i	−0.725049	+	0.725049i	0.244580	+	0.969629i	$0.421350\pi$
$984$		0			0
$985$	19.3368	+	16.2139i	0.616120	+	0.516617i
$986$		0			0
$987$	5.08405	−	4.14745i	0.161827	−	0.132015i
$988$		0			0
$989$	5.94502	−	5.94502i	0.189041	−	0.189041i
$990$		0			0
$991$	4.91828			0.156234			0.0781171	−	0.996944i	$-0.475109\pi$
$991$	4.91828			0.156234			0.0781171	+	0.996944i	$0.475109\pi$
$992$		0			0
$993$	−2.40804	+	23.7344i	−0.0764167	+	0.753187i
$994$		0			0
$995$	−0.0575867	−	0.0482865i	−0.00182562	−	0.00153078i
$996$		0			0
$997$			35.6569i			1.12927i	0.825342	+	0.564633i	$0.190982\pi$
$997$			35.6569i			1.12927i	−0.825342	+	0.564633i	$0.809018\pi$
$998$		0			0
$999$	−2.67533	−	5.11305i	−0.0846436	−	0.161770i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.bb.a.497.13		88
3.2	odd	2	inner	960.2.bb.a.497.32		88
4.3	odd	2		240.2.bb.a.197.36	yes	88
5.3	odd	4		960.2.bf.a.113.33		88
12.11	even	2		240.2.bb.a.197.9	yes	88
15.8	even	4		960.2.bf.a.113.34		88
16.3	odd	4		240.2.bf.a.77.31	yes	88
16.13	even	4		960.2.bf.a.17.33		88
20.3	even	4		240.2.bf.a.53.14	yes	88
48.29	odd	4		960.2.bf.a.17.34		88
48.35	even	4		240.2.bf.a.77.14	yes	88
60.23	odd	4		240.2.bf.a.53.31	yes	88
80.3	even	4		240.2.bb.a.173.9	✓	88
80.13	odd	4	inner	960.2.bb.a.593.32		88
240.83	odd	4		240.2.bb.a.173.36	yes	88
240.173	even	4	inner	960.2.bb.a.593.13		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bb.a.173.9	✓	88	80.3	even	4
240.2.bb.a.173.36	yes	88	240.83	odd	4
240.2.bb.a.197.9	yes	88	12.11	even	2
240.2.bb.a.197.36	yes	88	4.3	odd	2
240.2.bf.a.53.14	yes	88	20.3	even	4
240.2.bf.a.53.31	yes	88	60.23	odd	4
240.2.bf.a.77.14	yes	88	48.35	even	4
240.2.bf.a.77.31	yes	88	16.3	odd	4
960.2.bb.a.497.13		88	1.1	even	1	trivial
960.2.bb.a.497.32		88	3.2	odd	2	inner
960.2.bb.a.593.13		88	240.173	even	4	inner
960.2.bb.a.593.32		88	80.13	odd	4	inner
960.2.bf.a.17.33		88	16.13	even	4
960.2.bf.a.17.34		88	48.29	odd	4
960.2.bf.a.113.33		88	5.3	odd	4
960.2.bf.a.113.34		88	15.8	even	4

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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.bb (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.09486 - 1.34211i) q^{3} +(-1.71343 - 1.43671i) q^{5} +(-3.11495 + 3.11495i) q^{7} +(-0.602544 + 2.93887i) q^{9} +O(q^{10})\)	\(q+(-1.09486 - 1.34211i) q^{3} +(-1.71343 - 1.43671i) q^{5} +(-3.11495 + 3.11495i) q^{7} +(-0.602544 + 2.93887i) q^{9} +(3.15836 - 3.15836i) q^{11} +4.72071i q^{13} +(-0.0522594 + 3.87263i) q^{15} +(1.27146 - 1.27146i) q^{17} +(-1.33059 - 1.33059i) q^{19} +(7.59106 + 0.770172i) q^{21} +(1.09034 - 1.09034i) q^{23} +(0.871703 + 4.92343i) q^{25} +(4.60400 - 2.40898i) q^{27} +(1.67641 - 1.67641i) q^{29} +3.42372 q^{31} +(-7.69687 - 0.780907i) q^{33} +(9.81254 - 0.861963i) q^{35} -1.11057i q^{37} +(6.33574 - 5.16854i) q^{39} -0.0298672 q^{41} +5.45244 q^{43} +(5.25473 - 4.16987i) q^{45} +(0.608051 - 0.608051i) q^{47} -12.4058i q^{49} +(-3.09853 - 0.314370i) q^{51} +3.62613i q^{53} +(-9.94931 + 0.873977i) q^{55} +(-0.328990 + 3.24263i) q^{57} +(5.30621 + 5.30621i) q^{59} +(8.39022 - 8.39022i) q^{61} +(-7.27752 - 11.0313i) q^{63} +(6.78232 - 8.08863i) q^{65} +7.23224 q^{67} +(-2.65714 - 0.269587i) q^{69} -1.80640 q^{71} +(3.82128 + 3.82128i) q^{73} +(5.65341 - 6.56041i) q^{75} +19.6763i q^{77} +3.05546i q^{79} +(-8.27388 - 3.54160i) q^{81} -14.3316 q^{83} +(-4.00530 + 0.351838i) q^{85} +(-4.08538 - 0.414493i) q^{87} -7.83926i q^{89} +(-14.7048 - 14.7048i) q^{91} +(-3.74851 - 4.59503i) q^{93} +(0.368200 + 4.19157i) q^{95} +(6.89142 + 6.89142i) q^{97} +(7.37896 + 11.1851i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q+O(q^{10}) \) 88 * q	\( 88 q + 4 q^{15} + 8 q^{19} - 4 q^{21} + 16 q^{31} - 4 q^{33} - 24 q^{39} + 40 q^{43} + 8 q^{45} + 4 q^{51} + 12 q^{57} - 24 q^{61} + 32 q^{63} + 8 q^{67} - 12 q^{69} + 24 q^{75} - 8 q^{81} - 24 q^{85} + 12 q^{87} + 8 q^{91} - 8 q^{97} + 32 q^{99}+O(q^{100}) \) 88 * q + 4 * q^15 + 8 * q^19 - 4 * q^21 + 16 * q^31 - 4 * q^33 - 24 * q^39 + 40 * q^43 + 8 * q^45 + 4 * q^51 + 12 * q^57 - 24 * q^61 + 32 * q^63 + 8 * q^67 - 12 * q^69 + 24 * q^75 - 8 * q^81 - 24 * q^85 + 12 * q^87 + 8 * q^91 - 8 * q^97 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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