LMFDB - Embedded newform 352.2.m.f.225.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [352,2,Mod(97,352)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(352, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("352.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 352 = 2^{5} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	352.m (of order $5$, degree $4$, 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:	$2.81073415115$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 11 x^{10} - 11 x^{9} + 39 x^{8} - 43 x^{7} + 99 x^{6} + 36 x^{5} + 431 x^{4} + \cdots + 25 $ x^12 - 2x^11 + 11x^10 - 11x^9 + 39x^8 - 43x^7 + 99x^6 + 36x^5 + 431x^4 - 350x^3 + 510x^2 - 175*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			225.1
Root			$0.885530 - 2.72538i$ of defining polynomial
Character	$\chi$	$=$	352.225
Dual form			352.2.m.f.97.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50933 - 1.09659i) q^{3} +(-0.686361 + 2.11240i) q^{5} +(0.787585 - 0.572214i) q^{7} +(0.148512 + 0.457073i) q^{9} +(-2.94543 + 1.52462i) q^{11} +(1.78094 + 5.48116i) q^{13} +(3.35239 - 2.43565i) q^{15} +(-1.22859 + 3.78121i) q^{17} +(2.27651 + 1.65398i) q^{19} -1.81621 q^{21} +1.20615 q^{23} +(0.0539368 + 0.0391874i) q^{25} +(-1.45247 + 4.47024i) q^{27} +(-1.68573 + 1.22475i) q^{29} +(2.11632 + 6.51337i) q^{31} +(6.11751 + 0.928786i) q^{33} +(0.668178 + 2.05644i) q^{35} +(7.61289 - 5.53109i) q^{37} +(3.32258 - 10.2258i) q^{39} +(-3.56050 - 2.58685i) q^{41} -8.84372 q^{43} -1.06745 q^{45} +(-1.16955 - 0.849729i) q^{47} +(-1.87026 + 5.75606i) q^{49} +(6.00079 - 4.35983i) q^{51} +(-3.16432 - 9.73877i) q^{53} +(-1.19897 - 7.26836i) q^{55} +(-1.62226 - 4.99281i) q^{57} +(-2.85539 + 2.07456i) q^{59} +(1.27790 - 3.93298i) q^{61} +(0.378510 + 0.275003i) q^{63} -12.8008 q^{65} -12.2596 q^{67} +(-1.82048 - 1.32266i) q^{69} +(-2.91871 + 8.98287i) q^{71} +(5.35678 - 3.89193i) q^{73} +(-0.0384358 - 0.118293i) q^{75} +(-1.44737 + 2.88618i) q^{77} +(2.39931 + 7.38431i) q^{79} +(8.26072 - 6.00177i) q^{81} +(5.33355 - 16.4150i) q^{83} +(-7.14417 - 5.19055i) q^{85} +3.88737 q^{87} -0.470432 q^{89} +(4.53903 + 3.29780i) q^{91} +(3.94828 - 12.1516i) q^{93} +(-5.05638 + 3.67368i) q^{95} +(-2.79977 - 8.61681i) q^{97} +(-1.13429 - 1.11985i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{7} - q^{9} - 11 q^{11} - 2 q^{13} + 4 q^{15} + 12 q^{17} + 5 q^{19} + 24 q^{21} - 12 q^{23} + 13 q^{25} + 3 q^{27} + 16 q^{31} - 7 q^{33} - 28 q^{35} - 4 q^{37} + 46 q^{39} - 4 q^{41} - 22 q^{43}+ \cdots - 65 q^{99}+O(q^{100}) $ 12 * q + 6 * q^7 - q^9 - 11 * q^11 - 2 * q^13 + 4 * q^15 + 12 * q^17 + 5 * q^19 + 24 * q^21 - 12 * q^23 + 13 * q^25 + 3 * q^27 + 16 * q^31 - 7 * q^33 - 28 * q^35 - 4 * q^37 + 46 * q^39 - 4 * q^41 - 22 * q^43 + 28 * q^45 - 24 * q^47 - 5 * q^49 + 17 * q^51 - 14 * q^53 - 46 * q^55 - 37 * q^57 + 31 * q^59 - 14 * q^61 + 58 * q^63 - 52 * q^65 - 62 * q^67 - 18 * q^69 + 6 * q^71 - 8 * q^73 + 53 * q^75 - 46 * q^77 - 4 * q^79 - 22 * q^81 + 41 * q^83 - 36 * q^85 - 76 * q^87 - 2 * q^89 - 22 * q^91 + 8 * q^93 + 16 * q^95 + 3 * q^97 - 65 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/352\mathbb{Z}\right)^\times$.

$n$	$133$	$287$	$321$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

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
$3$	−1.50933	−	1.09659i	−0.871412	−	0.633118i	0.0595531	−	0.998225i	$-0.481032\pi$
$3$	−1.50933	−	1.09659i	−0.871412	−	0.633118i	−0.930966	+	0.365107i	$0.881032\pi$
$4$		0			0
$5$	−0.686361	+	2.11240i	−0.306950	+	0.944695i	0.671993	+	0.740558i	$0.265439\pi$
$5$	−0.686361	+	2.11240i	−0.306950	+	0.944695i	−0.978942	+	0.204137i	$0.934561\pi$
$6$		0			0
$7$	0.787585	−	0.572214i	0.297679	−	0.216277i	−0.428913	−	0.903346i	$-0.641103\pi$
$7$	0.787585	−	0.572214i	0.297679	−	0.216277i	0.726592	+	0.687069i	$0.241103\pi$
$8$		0			0
$9$	0.148512	+	0.457073i	0.0495040	+	0.152358i
$10$		0			0
$11$	−2.94543	+	1.52462i	−0.888080	+	0.459689i
$11$	−2.94543	+	1.52462i	−0.888080	+	0.459689i
$12$		0			0
$13$	1.78094	+	5.48116i	0.493943	+	1.52020i	0.818598	+	0.574367i	$0.194752\pi$
$13$	1.78094	+	5.48116i	0.493943	+	1.52020i	−0.324655	+	0.945832i	$0.605248\pi$
$14$		0			0
$15$	3.35239	−	2.43565i	0.865583	−	0.628883i
$16$		0			0
$17$	−1.22859	+	3.78121i	−0.297977	+	0.917078i	0.684229	+	0.729267i	$0.260139\pi$
$17$	−1.22859	+	3.78121i	−0.297977	+	0.917078i	−0.982205	+	0.187810i	$0.939861\pi$
$18$		0			0
$19$	2.27651	+	1.65398i	0.522268	+	0.379450i	0.817457	−	0.575989i	$-0.195383\pi$
$19$	2.27651	+	1.65398i	0.522268	+	0.379450i	−0.295190	+	0.955439i	$0.595383\pi$
$20$		0			0
$21$	−1.81621			−0.396330
$22$		0			0
$23$	1.20615			0.251500			0.125750	−	0.992062i	$-0.459866\pi$
$23$	1.20615			0.251500			0.125750	+	0.992062i	$0.459866\pi$
$24$		0			0
$25$	0.0539368	+	0.0391874i	0.0107874	+	0.00783747i
$26$		0			0
$27$	−1.45247	+	4.47024i	−0.279528	+	0.860298i
$28$		0			0
$29$	−1.68573	+	1.22475i	−0.313031	+	0.227431i	−0.733196	−	0.680017i	$-0.761972\pi$
$29$	−1.68573	+	1.22475i	−0.313031	+	0.227431i	0.420165	+	0.907448i	$0.361972\pi$
$30$		0			0
$31$	2.11632	+	6.51337i	0.380103	+	1.16984i	0.939971	+	0.341254i	$0.110852\pi$
$31$	2.11632	+	6.51337i	0.380103	+	1.16984i	−0.559868	+	0.828581i	$0.689148\pi$
$32$		0			0
$33$	6.11751	+	0.928786i	1.06492	+	0.161681i
$34$		0			0
$35$	0.668178	+	2.05644i	0.112943	+	0.347602i
$36$		0			0
$37$	7.61289	−	5.53109i	1.25155	−	0.909305i	0.253240	−	0.967404i	$-0.418504\pi$
$37$	7.61289	−	5.53109i	1.25155	−	0.909305i	0.998311	+	0.0580987i	$0.0185038\pi$
$38$		0			0
$39$	3.32258	−	10.2258i	0.532038	−	1.63745i
$40$		0			0
$41$	−3.56050	−	2.58685i	−0.556056	−	0.403998i	0.273957	−	0.961742i	$-0.411667\pi$
$41$	−3.56050	−	2.58685i	−0.556056	−	0.403998i	−0.830013	+	0.557743i	$0.811667\pi$
$42$		0			0
$43$	−8.84372			−1.34865			−0.674327	−	0.738432i	$-0.735566\pi$
$43$	−8.84372			−1.34865			−0.674327	+	0.738432i	$0.735566\pi$
$44$		0			0
$45$	−1.06745			−0.159127
$46$		0			0
$47$	−1.16955	−	0.849729i	−0.170597	−	0.123946i	0.499211	−	0.866481i	$-0.333623\pi$
$47$	−1.16955	−	0.849729i	−0.170597	−	0.123946i	−0.669807	+	0.742535i	$0.733623\pi$
$48$		0			0
$49$	−1.87026	+	5.75606i	−0.267180	+	0.822294i
$50$		0			0
$51$	6.00079	−	4.35983i	0.840279	−	0.610499i
$52$		0			0
$53$	−3.16432	−	9.73877i	−0.434652	−	1.33772i	−0.893442	−	0.449178i	$-0.851717\pi$
$53$	−3.16432	−	9.73877i	−0.434652	−	1.33772i	0.458790	−	0.888545i	$-0.348283\pi$
$54$		0			0
$55$	−1.19897	−	7.26836i	−0.161670	−	0.980066i
$56$		0			0
$57$	−1.62226	−	4.99281i	−0.214874	−	0.661314i
$58$		0			0
$59$	−2.85539	+	2.07456i	−0.371740	+	0.270085i	−0.757932	−	0.652334i	$-0.773790\pi$
$59$	−2.85539	+	2.07456i	−0.371740	+	0.270085i	0.386192	+	0.922418i	$0.373790\pi$
$60$		0			0
$61$	1.27790	−	3.93298i	0.163619	−	0.503567i	−0.835313	−	0.549775i	$-0.814714\pi$
$61$	1.27790	−	3.93298i	0.163619	−	0.503567i	0.998932	+	0.0462077i	$0.0147136\pi$
$62$		0			0
$63$	0.378510	+	0.275003i	0.0476877	+	0.0346472i
$64$		0			0
$65$	−12.8008			−1.58774
$66$		0			0
$67$	−12.2596			−1.49774			−0.748872	−	0.662714i	$-0.769404\pi$
$67$	−12.2596			−1.49774			−0.748872	+	0.662714i	$0.769404\pi$
$68$		0			0
$69$	−1.82048	−	1.32266i	−0.219160	−	0.159229i
$70$		0			0
$71$	−2.91871	+	8.98287i	−0.346387	+	1.06607i	0.614449	+	0.788956i	$0.289378\pi$
$71$	−2.91871	+	8.98287i	−0.346387	+	1.06607i	−0.960837	+	0.277115i	$0.910622\pi$
$72$		0			0
$73$	5.35678	−	3.89193i	0.626963	−	0.455516i	−0.228383	−	0.973571i	$-0.573344\pi$
$73$	5.35678	−	3.89193i	0.626963	−	0.455516i	0.855347	+	0.518056i	$0.173344\pi$
$74$		0			0
$75$	−0.0384358	−	0.118293i	−0.00443819	−	0.0136593i
$76$		0			0
$77$	−1.44737	+	2.88618i	−0.164943	+	0.328911i
$78$		0			0
$79$	2.39931	+	7.38431i	0.269943	+	0.830800i	0.990513	+	0.137417i	$0.0438802\pi$
$79$	2.39931	+	7.38431i	0.269943	+	0.830800i	−0.720570	+	0.693382i	$0.756120\pi$
$80$		0			0
$81$	8.26072	−	6.00177i	0.917858	−	0.666863i
$82$		0			0
$83$	5.33355	−	16.4150i	0.585434	−	1.80178i	−0.0120889	−	0.999927i	$-0.503848\pi$
$83$	5.33355	−	16.4150i	0.585434	−	1.80178i	0.597522	−	0.801852i	$-0.296152\pi$
$84$		0			0
$85$	−7.14417	−	5.19055i	−0.774894	−	0.562994i
$86$		0			0
$87$	3.88737			0.416770
$88$		0			0
$89$	−0.470432			−0.0498657			−0.0249328	−	0.999689i	$-0.507937\pi$
$89$	−0.470432			−0.0498657			−0.0249328	+	0.999689i	$0.507937\pi$
$90$		0			0
$91$	4.53903	+	3.29780i	0.475820	+	0.345704i
$92$		0			0
$93$	3.94828	−	12.1516i	0.409418	−	1.26006i
$94$		0			0
$95$	−5.05638	+	3.67368i	−0.518774	+	0.376911i
$96$		0			0
$97$	−2.79977	−	8.61681i	−0.284274	−	0.874905i	−0.986615	−	0.163065i	$-0.947862\pi$
$97$	−2.79977	−	8.61681i	−0.284274	−	0.874905i	0.702342	−	0.711840i	$-0.252138\pi$
$98$		0			0
$99$	−1.13429	−	1.11985i	−0.114001	−	0.112549i
$100$		0			0
$101$	4.09183	+	12.5933i	0.407152	+	1.25309i	0.919085	+	0.394060i	$0.128930\pi$
$101$	4.09183	+	12.5933i	0.407152	+	1.25309i	−0.511933	+	0.859025i	$0.671070\pi$
$102$		0			0
$103$	12.2970	−	8.93433i	1.21166	−	0.880325i	0.216283	−	0.976331i	$-0.430607\pi$
$103$	12.2970	−	8.93433i	1.21166	−	0.880325i	0.995381	+	0.0960055i	$0.0306066\pi$
$104$		0			0
$105$	1.24658	−	3.83657i	0.121653	−	0.374411i
$106$		0			0
$107$	16.5940	+	12.0562i	1.60420	+	1.16552i	0.878801	+	0.477189i	$0.158344\pi$
$107$	16.5940	+	12.0562i	1.60420	+	1.16552i	0.725398	+	0.688330i	$0.241656\pi$
$108$		0			0
$109$	4.79668			0.459438			0.229719	−	0.973257i	$-0.426219\pi$
$109$	4.79668			0.459438			0.229719	+	0.973257i	$0.426219\pi$
$110$		0			0
$111$	−17.5557			−1.66631
$112$		0			0
$113$	−5.27699	−	3.83395i	−0.496417	−	0.360668i	0.311230	−	0.950335i	$-0.399259\pi$
$113$	−5.27699	−	3.83395i	−0.496417	−	0.360668i	−0.807647	+	0.589667i	$0.799259\pi$
$114$		0			0
$115$	−0.827856	+	2.54788i	−0.0771979	+	0.237591i
$116$		0			0
$117$	−2.24080	+	1.62804i	−0.207162	+	0.150512i
$118$		0			0
$119$	1.19604	+	3.68104i	0.109641	+	0.337440i
$120$		0			0
$121$	6.35109	−	8.98129i	0.577372	−	0.816481i
$122$		0			0
$123$	2.53724	+	7.80883i	0.228776	+	0.704099i
$124$		0			0
$125$	−9.10438	+	6.61472i	−0.814320	+	0.591638i
$126$		0			0
$127$	−4.18229	+	12.8718i	−0.371118	+	1.14218i	0.574942	+	0.818194i	$0.305025\pi$
$127$	−4.18229	+	12.8718i	−0.371118	+	1.14218i	−0.946060	+	0.323990i	$0.894975\pi$
$128$		0			0
$129$	13.3481	+	9.69796i	1.17523	+	0.853858i
$130$		0			0
$131$	11.8240			1.03306			0.516532	−	0.856268i	$-0.327223\pi$
$131$	11.8240			1.03306			0.516532	+	0.856268i	$0.327223\pi$
$132$		0			0
$133$	2.73938			0.237534
$134$		0			0
$135$	−8.44603	−	6.13640i	−0.726918	−	0.528137i
$136$		0			0
$137$	−5.17162	+	15.9166i	−0.441841	+	1.35985i	0.444070	+	0.895992i	$0.353534\pi$
$137$	−5.17162	+	15.9166i	−0.441841	+	1.35985i	−0.885911	+	0.463855i	$0.846466\pi$
$138$		0			0
$139$	9.34431	−	6.78904i	0.792574	−	0.575839i	−0.116152	−	0.993231i	$-0.537056\pi$
$139$	9.34431	−	6.78904i	0.792574	−	0.575839i	0.908726	+	0.417393i	$0.137056\pi$
$140$		0			0
$141$	0.833433	+	2.56504i	0.0701877	+	0.216016i
$142$		0			0
$143$	−13.6023	−	13.4291i	−1.13748	−	1.12300i
$144$		0			0
$145$	−1.43015	−	4.40155i	−0.118768	−	0.365529i
$146$		0			0
$147$	9.13489	−	6.63689i	0.753433	−	0.547401i
$148$		0			0
$149$	−4.79081	+	14.7446i	−0.392478	+	1.20792i	0.538430	+	0.842671i	$0.319018\pi$
$149$	−4.79081	+	14.7446i	−0.392478	+	1.20792i	−0.930908	+	0.365254i	$0.880982\pi$
$150$		0			0
$151$	7.76046	+	5.63831i	0.631538	+	0.458839i	0.856933	−	0.515429i	$-0.172367\pi$
$151$	7.76046	+	5.63831i	0.631538	+	0.458839i	−0.225395	+	0.974267i	$0.572367\pi$
$152$		0			0
$153$	−1.91075			−0.154475
$154$		0			0
$155$	−15.2114			−1.22181
$156$		0			0
$157$	2.58988	+	1.88166i	0.206695	+	0.150173i	0.686317	−	0.727302i	$-0.259226\pi$
$157$	2.58988	+	1.88166i	0.206695	+	0.150173i	−0.479622	+	0.877475i	$0.659226\pi$
$158$		0			0
$159$	−5.90346	+	18.1690i	−0.468175	+	1.44089i
$160$		0			0
$161$	0.949948	−	0.690177i	0.0748664	−	0.0543936i
$162$		0			0
$163$	−7.30643	−	22.4869i	−0.572284	−	1.76131i	−0.645248	−	0.763973i	$-0.723246\pi$
$163$	−7.30643	−	22.4869i	−0.572284	−	1.76131i	0.0729645	−	0.997335i	$-0.476754\pi$
$164$		0			0
$165$	−6.16079	+	12.2851i	−0.479617	+	0.956398i
$166$		0			0
$167$	−2.42488	−	7.46301i	−0.187643	−	0.577505i	0.812341	−	0.583183i	$-0.198193\pi$
$167$	−2.42488	−	7.46301i	−0.187643	−	0.577505i	−0.999984	+	0.00567748i	$0.998193\pi$
$168$		0			0
$169$	−16.3541	+	11.8820i	−1.25801	+	0.913998i
$170$		0			0
$171$	−0.417902	+	1.28617i	−0.0319577	+	0.0983558i
$172$		0			0
$173$	−1.52614	−	1.10881i	−0.116030	−	0.0843009i	0.528257	−	0.849085i	$-0.322846\pi$
$173$	−1.52614	−	1.10881i	−0.116030	−	0.0843009i	−0.644287	+	0.764784i	$0.722846\pi$
$174$		0			0
$175$	0.0649034			0.00490623
$176$		0			0
$177$	6.58467			0.494934
$178$		0			0
$179$	−2.48023	−	1.80199i	−0.185381	−	0.134687i	0.491224	−	0.871033i	$-0.336550\pi$
$179$	−2.48023	−	1.80199i	−0.185381	−	0.134687i	−0.676605	+	0.736346i	$0.736550\pi$
$180$		0			0
$181$	2.07757	−	6.39411i	0.154425	−	0.475270i	−0.843677	−	0.536850i	$-0.819614\pi$
$181$	2.07757	−	6.39411i	0.154425	−	0.475270i	0.998102	+	0.0615801i	$0.0196140\pi$
$182$		0			0
$183$	−6.24166	+	4.53483i	−0.461397	+	0.335224i
$184$		0			0
$185$	6.45869	+	19.8778i	0.474852	+	1.46144i
$186$		0			0
$187$	−2.14617	−	13.0104i	−0.156944	−	0.951415i
$188$		0			0
$189$	1.41399	+	4.35182i	0.102853	+	0.316548i
$190$		0			0
$191$	1.46066	−	1.06123i	0.105689	−	0.0767879i	−0.533685	−	0.845683i	$-0.679193\pi$
$191$	1.46066	−	1.06123i	0.105689	−	0.0767879i	0.639375	+	0.768895i	$0.279193\pi$
$192$		0			0
$193$	−0.250567	+	0.771165i	−0.0180362	+	0.0555097i	−0.959670	−	0.281131i	$-0.909291\pi$
$193$	−0.250567	+	0.771165i	−0.0180362	+	0.0555097i	0.941633	+	0.336640i	$0.109291\pi$
$194$		0			0
$195$	19.3206	+	14.0372i	1.38358	+	1.00523i
$196$		0			0
$197$	18.6154			1.32629			0.663147	−	0.748489i	$-0.269220\pi$
$197$	18.6154			1.32629			0.663147	+	0.748489i	$0.269220\pi$
$198$		0			0
$199$	−16.8109			−1.19170			−0.595848	−	0.803097i	$-0.703184\pi$
$199$	−16.8109			−1.19170			−0.595848	+	0.803097i	$0.703184\pi$
$200$		0			0
$201$	18.5037	+	13.4438i	1.30515	+	0.948249i
$202$		0			0
$203$	−0.626832	+	1.92919i	−0.0439950	+	0.135403i
$204$		0			0
$205$	7.90826	−	5.74568i	0.552337	−	0.401296i
$206$		0			0
$207$	0.179128	+	0.551300i	0.0124503	+	0.0383180i
$208$		0			0
$209$	−9.22699	−	1.40088i	−0.638244	−	0.0969009i
$210$		0			0
$211$	0.118697	+	0.365311i	0.00817142	+	0.0251491i	0.955059	−	0.296415i	$-0.0957913\pi$
$211$	0.118697	+	0.365311i	0.00817142	+	0.0251491i	−0.946888	+	0.321565i	$0.895791\pi$
$212$		0			0
$213$	14.2559	−	10.3575i	0.976795	−	0.709683i
$214$		0			0
$215$	6.06998	−	18.6815i	0.413969	−	1.27407i
$216$		0			0
$217$	5.39383	+	3.91884i	0.366157	+	0.266028i
$218$		0			0
$219$	−12.3530			−0.834739
$220$		0			0
$221$	−22.9134			−1.54132
$222$		0			0
$223$	18.8617	+	13.7038i	1.26307	+	0.917676i	0.998904	−	0.0468004i	$-0.0149025\pi$
$223$	18.8617	+	13.7038i	1.26307	+	0.917676i	0.264169	+	0.964477i	$0.414902\pi$
$224$		0			0
$225$	−0.00990123	+	0.0304728i	−0.000660082	+	0.00203152i
$226$		0			0
$227$	2.20487	−	1.60193i	0.146342	−	0.106324i	−0.512205	−	0.858863i	$-0.671171\pi$
$227$	2.20487	−	1.60193i	0.146342	−	0.106324i	0.658547	+	0.752539i	$0.271171\pi$
$228$		0			0
$229$	7.71049	+	23.7305i	0.509524	+	1.56815i	0.793030	+	0.609182i	$0.208502\pi$
$229$	7.71049	+	23.7305i	0.509524	+	1.56815i	−0.283507	+	0.958970i	$0.591498\pi$
$230$		0			0
$231$	5.34952	−	2.76903i	0.351973	−	0.182189i
$232$		0			0
$233$	−6.53229	−	20.1043i	−0.427944	−	1.31708i	−0.900147	−	0.435587i	$-0.856541\pi$
$233$	−6.53229	−	20.1043i	−0.427944	−	1.31708i	0.472202	−	0.881490i	$-0.343459\pi$
$234$		0			0
$235$	2.59770	−	1.88734i	0.169455	−	0.123117i
$236$		0			0
$237$	4.47623	−	13.7764i	0.290763	−	0.894875i
$238$		0			0
$239$	−0.168281	−	0.122263i	−0.0108852	−	0.00790854i	0.582329	−	0.812953i	$-0.302141\pi$
$239$	−0.168281	−	0.122263i	−0.0108852	−	0.00790854i	−0.593215	+	0.805044i	$0.702141\pi$
$240$		0			0
$241$	1.25123			0.0805990			0.0402995	−	0.999188i	$-0.487169\pi$
$241$	1.25123			0.0805990			0.0402995	+	0.999188i	$0.487169\pi$
$242$		0			0
$243$	−4.94878			−0.317465
$244$		0			0
$245$	−10.8754	−	7.90147i	−0.694806	−	0.504806i
$246$		0			0
$247$	−5.01142	+	15.4236i	−0.318869	+	0.981378i
$248$		0			0
$249$	−26.0507	+	18.9269i	−1.65089	+	1.19944i
$250$		0			0
$251$	6.90297	+	21.2452i	0.435712	+	1.34098i	0.892356	+	0.451333i	$0.149051\pi$
$251$	6.90297	+	21.2452i	0.435712	+	1.34098i	−0.456644	+	0.889649i	$0.650949\pi$
$252$		0			0
$253$	−3.55264	+	1.83892i	−0.223352	+	0.115612i
$254$		0			0
$255$	5.09100	+	15.6685i	0.318811	+	0.981200i
$256$		0			0
$257$	−17.5229	+	12.7312i	−1.09305	+	0.794148i	−0.979912	−	0.199431i	$-0.936091\pi$
$257$	−17.5229	+	12.7312i	−1.09305	+	0.794148i	−0.113139	+	0.993579i	$0.536091\pi$
$258$		0			0
$259$	2.83083	−	8.71240i	0.175899	−	0.541362i
$260$		0			0
$261$	−0.810151	−	0.588610i	−0.0501471	−	0.0364340i
$262$		0			0
$263$	11.3447			0.699545			0.349773	−	0.936835i	$-0.386259\pi$
$263$	11.3447			0.699545			0.349773	+	0.936835i	$0.386259\pi$
$264$		0			0
$265$	22.7440			1.39716
$266$		0			0
$267$	0.710037	+	0.515872i	0.0434536	+	0.0315709i
$268$		0			0
$269$	4.44338	−	13.6753i	0.270918	−	0.833799i	−0.719353	−	0.694645i	$-0.755562\pi$
$269$	4.44338	−	13.6753i	0.270918	−	0.833799i	0.990271	−	0.139154i	$-0.0444384\pi$
$270$		0			0
$271$	8.90858	−	6.47246i	0.541158	−	0.393174i	−0.283357	−	0.959014i	$-0.591448\pi$
$271$	8.90858	−	6.47246i	0.541158	−	0.393174i	0.824515	+	0.565840i	$0.191448\pi$
$272$		0			0
$273$	−3.23456	−	9.95495i	−0.195764	−	0.602501i
$274$		0			0
$275$	−0.218613	−	0.0331907i	−0.0131828	−	0.00200147i
$276$		0			0
$277$	−1.82394	−	5.61352i	−0.109590	−	0.337284i	0.881190	−	0.472762i	$-0.156743\pi$
$277$	−1.82394	−	5.61352i	−0.109590	−	0.337284i	−0.990780	+	0.135478i	$0.956743\pi$
$278$		0			0
$279$	−2.66279	+	1.93463i	−0.159417	+	0.115823i
$280$		0			0
$281$	4.07866	−	12.5528i	0.243312	−	0.748839i	−0.752597	−	0.658481i	$-0.771199\pi$
$281$	4.07866	−	12.5528i	0.243312	−	0.748839i	0.995909	−	0.0903572i	$-0.0288009\pi$
$282$		0			0
$283$	−7.07353	−	5.13922i	−0.420478	−	0.305495i	0.357352	−	0.933970i	$-0.383680\pi$
$283$	−7.07353	−	5.13922i	−0.420478	−	0.305495i	−0.777830	+	0.628475i	$0.783680\pi$
$284$		0			0
$285$	11.6603			0.690696
$286$		0			0
$287$	−4.28443			−0.252902
$288$		0			0
$289$	0.965183	+	0.701247i	0.0567755	+	0.0412498i
$290$		0			0
$291$	−5.22335	+	16.0758i	−0.306198	+	0.942382i
$292$		0			0
$293$	1.22671	−	0.891257i	0.0716652	−	0.0520678i	−0.551376	−	0.834257i	$-0.685897\pi$
$293$	1.22671	−	0.891257i	0.0716652	−	0.0520678i	0.623041	+	0.782189i	$0.285897\pi$
$294$		0			0
$295$	−2.42248	−	7.45562i	−0.141042	−	0.434083i
$296$		0			0
$297$	−2.53726	−	15.3812i	−0.147227	−	0.892510i
$298$		0			0
$299$	2.14808	+	6.61111i	0.124227	+	0.382330i
$300$		0			0
$301$	−6.96518	+	5.06050i	−0.401467	+	0.291683i
$302$		0			0
$303$	7.63386	−	23.4946i	0.438554	−	1.34973i
$304$		0			0
$305$	7.43094	+	5.39889i	0.425494	+	0.309140i
$306$		0			0
$307$	5.53572			0.315940			0.157970	−	0.987444i	$-0.449505\pi$
$307$	5.53572			0.315940			0.157970	+	0.987444i	$0.449505\pi$
$308$		0			0
$309$	−28.3576			−1.61321
$310$		0			0
$311$	−7.41098	−	5.38439i	−0.420238	−	0.305321i	0.357495	−	0.933915i	$-0.383631\pi$
$311$	−7.41098	−	5.38439i	−0.420238	−	0.305321i	−0.777734	+	0.628594i	$0.783631\pi$
$312$		0			0
$313$	5.02906	−	15.4779i	0.284259	−	0.874860i	−0.702361	−	0.711821i	$-0.747871\pi$
$313$	5.02906	−	15.4779i	0.284259	−	0.874860i	0.986620	−	0.163038i	$-0.0521295\pi$
$314$		0			0
$315$	−0.840712	+	0.610813i	−0.0473687	+	0.0344154i
$316$		0			0
$317$	−1.09591	−	3.37286i	−0.0615524	−	0.189439i	0.915552	−	0.402200i	$-0.131754\pi$
$317$	−1.09591	−	3.37286i	−0.0615524	−	0.189439i	−0.977104	+	0.212761i	$0.931754\pi$
$318$		0			0
$319$	3.09791	−	6.17750i	0.173450	−	0.345874i
$320$		0			0
$321$	−11.8250	−	36.3936i	−0.660008	−	2.03129i
$322$		0			0
$323$	−9.05095	+	6.57590i	−0.503608	+	0.365893i
$324$		0			0
$325$	−0.118734	+	0.365426i	−0.00658619	+	0.0202702i
$326$		0			0
$327$	−7.23977	−	5.26000i	−0.400360	−	0.290879i
$328$		0			0
$329$	−1.40735			−0.0775896
$330$		0			0
$331$	−16.2332			−0.892257			−0.446128	−	0.894969i	$-0.647198\pi$
$331$	−16.2332			−0.892257			−0.446128	+	0.894969i	$0.647198\pi$
$332$		0			0
$333$	3.65872	+	2.65821i	0.200496	+	0.145669i
$334$		0			0
$335$	8.41449	−	25.8971i	0.459733	−	1.41491i
$336$		0			0
$337$	6.84497	−	4.97316i	0.372869	−	0.270905i	−0.385531	−	0.922695i	$-0.625982\pi$
$337$	6.84497	−	4.97316i	0.372869	−	0.270905i	0.758400	+	0.651790i	$0.225982\pi$
$338$		0			0
$339$	3.76043	+	11.5734i	0.204238	+	0.628581i
$340$		0			0
$341$	−16.1639	−	15.9581i	−0.875322	−	0.864178i
$342$		0			0
$343$	3.92653	+	12.0846i	0.212013	+	0.652508i
$344$		0			0
$345$	4.04349	−	2.93777i	0.217694	−	0.158164i
$346$		0			0
$347$	1.66589	−	5.12710i	0.0894299	−	0.275237i	−0.896332	−	0.443383i	$-0.853778\pi$
$347$	1.66589	−	5.12710i	0.0894299	−	0.275237i	0.985762	+	0.168146i	$0.0537781\pi$
$348$		0			0
$349$	−10.4565	−	7.59712i	−0.559725	−	0.406664i	0.271633	−	0.962401i	$-0.412436\pi$
$349$	−10.4565	−	7.59712i	−0.559725	−	0.406664i	−0.831358	+	0.555737i	$0.812436\pi$
$350$		0			0
$351$	−27.0889			−1.44590
$352$		0			0
$353$	34.5770			1.84035			0.920173	−	0.391511i	$-0.128047\pi$
$353$	34.5770			1.84035			0.920173	+	0.391511i	$0.128047\pi$
$354$		0			0
$355$	−16.9721	−	12.3310i	−0.900788	−	0.654461i
$356$		0			0
$357$	2.23138	−	6.86748i	0.118097	−	0.363465i
$358$		0			0
$359$	18.7680	−	13.6358i	0.990539	−	0.719669i	0.0305003	−	0.999535i	$-0.490290\pi$
$359$	18.7680	−	13.6358i	0.990539	−	0.719669i	0.960039	+	0.279866i	$0.0902899\pi$
$360$		0			0
$361$	−3.42448	−	10.5395i	−0.180236	−	0.554708i
$362$		0			0
$363$	−19.4347	+	6.59118i	−1.02006	+	0.345947i
$364$		0			0
$365$	4.54463	+	13.9869i	0.237877	+	0.732109i
$366$		0			0
$367$	12.5161	−	9.09348i	0.653335	−	0.474676i	−0.211071	−	0.977471i	$-0.567695\pi$
$367$	12.5161	−	9.09348i	0.653335	−	0.474676i	0.864406	+	0.502795i	$0.167695\pi$
$368$		0			0
$369$	0.653604	−	2.01159i	0.0340253	−	0.104719i
$370$		0			0
$371$	−8.06483	−	5.85944i	−0.418705	−	0.304207i
$372$		0			0
$373$	30.5787			1.58331			0.791653	−	0.610970i	$-0.209221\pi$
$373$	30.5787			1.58331			0.791653	+	0.610970i	$0.209221\pi$
$374$		0			0
$375$	20.9952			1.08419
$376$		0			0
$377$	−9.71522	−	7.05852i	−0.500360	−	0.363532i
$378$		0			0
$379$	0.840099	−	2.58556i	0.0431530	−	0.132811i	−0.927159	−	0.374668i	$-0.877757\pi$
$379$	0.840099	−	2.58556i	0.0431530	−	0.132811i	0.970312	+	0.241857i	$0.0777565\pi$
$380$		0			0
$381$	20.4275	−	14.8415i	1.04653	−	0.760352i
$382$		0			0
$383$	5.68665	+	17.5017i	0.290574	+	0.894296i	0.984672	+	0.174415i	$0.0558035\pi$
$383$	5.68665	+	17.5017i	0.290574	+	0.894296i	−0.694098	+	0.719881i	$0.744196\pi$
$384$		0			0
$385$	−5.10335	−	5.03838i	−0.260091	−	0.256780i
$386$		0			0
$387$	−1.31340	−	4.04223i	−0.0667638	−	0.205478i
$388$		0			0
$389$	−0.514886	+	0.374087i	−0.0261058	+	0.0189669i	−0.600762	−	0.799428i	$-0.705136\pi$
$389$	−0.514886	+	0.374087i	−0.0261058	+	0.0189669i	0.574656	+	0.818395i	$0.305136\pi$
$390$		0			0
$391$	−1.48187	+	4.56071i	−0.0749412	+	0.230645i
$392$		0			0
$393$	−17.8463	−	12.9661i	−0.900225	−	0.654052i
$394$		0			0
$395$	−17.2454			−0.867711
$396$		0			0
$397$	−19.6411			−0.985760			−0.492880	−	0.870097i	$-0.664056\pi$
$397$	−19.6411			−0.985760			−0.492880	+	0.870097i	$0.664056\pi$
$398$		0			0
$399$	−4.13463	−	3.00398i	−0.206990	−	0.150387i
$400$		0			0
$401$	−1.77896	+	5.47507i	−0.0888369	+	0.273412i	−0.985599	−	0.169102i	$-0.945913\pi$
$401$	−1.77896	+	5.47507i	−0.0888369	+	0.273412i	0.896762	+	0.442514i	$0.145913\pi$
$402$		0			0
$403$	−31.9318	+	23.1998i	−1.59063	+	1.15566i
$404$		0			0
$405$	7.00830	+	21.5693i	0.348245	+	1.07179i
$406$		0			0
$407$	−13.9904	+	27.8981i	−0.693480	+	1.38286i
$408$		0			0
$409$	7.14831	+	22.0002i	0.353461	+	1.08784i	0.956896	+	0.290429i	$0.0937981\pi$
$409$	7.14831	+	22.0002i	0.353461	+	1.08784i	−0.603436	+	0.797412i	$0.706202\pi$
$410$		0			0
$411$	25.2597	−	18.3523i	1.24597	−	0.905250i
$412$		0			0
$413$	−1.06177	+	3.26778i	−0.0522462	+	0.160797i
$414$		0			0
$415$	31.0143	+	22.5332i	1.52243	+	1.10611i
$416$		0			0
$417$	−21.5485			−1.05523
$418$		0			0
$419$	20.6359			1.00813			0.504065	−	0.863666i	$-0.331837\pi$
$419$	20.6359			1.00813			0.504065	+	0.863666i	$0.331837\pi$
$420$		0			0
$421$	−24.3859	−	17.7174i	−1.18850	−	0.863494i	−0.195392	−	0.980725i	$-0.562598\pi$
$421$	−24.3859	−	17.7174i	−1.18850	−	0.863494i	−0.993105	+	0.117231i	$0.962598\pi$
$422$		0			0
$423$	0.214696	−	0.660765i	0.0104389	−	0.0321275i
$424$		0			0
$425$	−0.214442	+	0.155801i	−0.0104020	+	0.00755746i
$426$		0			0
$427$	−1.24405	−	3.82879i	−0.0602038	−	0.185288i
$428$		0			0
$429$	5.80407	+	35.1851i	0.280223	+	1.69875i
$430$		0			0
$431$	−10.0976	−	31.0772i	−0.486384	−	1.49694i	−0.829967	−	0.557813i	$-0.811641\pi$
$431$	−10.0976	−	31.0772i	−0.486384	−	1.49694i	0.343583	−	0.939122i	$-0.388359\pi$
$432$		0			0
$433$	−22.6740	+	16.4736i	−1.08964	+	0.791672i	−0.979339	−	0.202226i	$-0.935182\pi$
$433$	−22.6740	+	16.4736i	−1.08964	+	0.791672i	−0.110304	+	0.993898i	$0.535182\pi$
$434$		0			0
$435$	−2.66814	+	8.21169i	−0.127927	+	0.393720i
$436$		0			0
$437$	2.74582	+	1.99496i	0.131350	+	0.0954317i
$438$		0			0
$439$	19.4940			0.930399			0.465200	−	0.885206i	$-0.345983\pi$
$439$	19.4940			0.930399			0.465200	+	0.885206i	$0.345983\pi$
$440$		0			0
$441$	−2.90870			−0.138509
$442$		0			0
$443$	7.21362	+	5.24100i	0.342729	+	0.249007i	0.745812	−	0.666156i	$-0.232061\pi$
$443$	7.21362	+	5.24100i	0.342729	+	0.249007i	−0.403083	+	0.915163i	$0.632061\pi$
$444$		0			0
$445$	0.322886	−	0.993741i	0.0153063	−	0.0471078i
$446$		0			0
$447$	23.3997	−	17.0009i	1.10677	−	0.804115i
$448$		0			0
$449$	0.225866	+	0.695145i	0.0106593	+	0.0328059i	0.956245	−	0.292568i	$-0.0945098\pi$
$449$	0.225866	+	0.695145i	0.0106593	+	0.0328059i	−0.945585	+	0.325374i	$0.894510\pi$
$450$		0			0
$451$	14.4311	+	2.19100i	0.679536	+	0.103170i
$452$		0			0
$453$	−5.53018	−	17.0201i	−0.259830	−	0.799676i
$454$		0			0
$455$	−10.0817	+	7.32478i	−0.472637	+	0.343391i
$456$		0			0
$457$	0.504920	−	1.55398i	0.0236192	−	0.0726923i	−0.938552	−	0.345137i	$-0.887832\pi$
$457$	0.504920	−	1.55398i	0.0236192	−	0.0726923i	0.962171	+	0.272445i	$0.0878323\pi$
$458$		0			0
$459$	−15.1184	−	10.9842i	−0.705668	−	0.512698i
$460$		0			0
$461$	−2.38755			−0.111199			−0.0555996	−	0.998453i	$-0.517707\pi$
$461$	−2.38755			−0.111199			−0.0555996	+	0.998453i	$0.517707\pi$
$462$		0			0
$463$	16.3739			0.760961			0.380480	−	0.924789i	$-0.375759\pi$
$463$	16.3739			0.760961			0.380480	+	0.924789i	$0.375759\pi$
$464$		0			0
$465$	22.9590	+	16.6807i	1.06470	+	0.773550i
$466$		0			0
$467$	−6.80913	+	20.9564i	−0.315089	+	0.969745i	0.660629	+	0.750713i	$0.270290\pi$
$467$	−6.80913	+	20.9564i	−0.315089	+	0.969745i	−0.975718	+	0.219032i	$0.929710\pi$
$468$		0			0
$469$	−9.65545	+	7.01510i	−0.445847	+	0.323927i
$470$		0			0
$471$	−1.84557	−	5.68009i	−0.0850395	−	0.261725i
$472$		0			0
$473$	26.0485	−	13.4833i	1.19771	−	0.619962i
$474$		0			0
$475$	0.0579725	+	0.178421i	0.00265996	+	0.00818652i
$476$		0			0
$477$	3.98139	−	2.89265i	0.182295	−	0.132445i
$478$		0			0
$479$	−7.62945	+	23.4810i	−0.348598	+	1.07288i	0.611031	+	0.791607i	$0.290755\pi$
$479$	−7.62945	+	23.4810i	−0.348598	+	1.07288i	−0.959629	+	0.281268i	$0.909245\pi$
$480$		0			0
$481$	43.8748	+	31.8769i	2.00052	+	1.45346i
$482$		0			0
$483$	−2.19063			−0.0996771
$484$		0			0
$485$	20.1238			0.913776
$486$		0			0
$487$	−15.7904	−	11.4724i	−0.715532	−	0.519864i	0.169422	−	0.985544i	$-0.445810\pi$
$487$	−15.7904	−	11.4724i	−0.715532	−	0.519864i	−0.884953	+	0.465679i	$0.845810\pi$
$488$		0			0
$489$	−13.6311	+	41.9523i	−0.616421	+	1.89715i
$490$		0			0
$491$	11.9467	−	8.67982i	0.539149	−	0.391715i	−0.284620	−	0.958641i	$-0.591867\pi$
$491$	11.9467	−	8.67982i	0.539149	−	0.391715i	0.823769	+	0.566926i	$0.191867\pi$
$492$		0			0
$493$	−2.55998	−	7.87880i	−0.115296	−	0.354843i
$494$		0			0
$495$	3.14411	−	1.62746i	0.141317	−	0.0731488i
$496$		0			0
$497$	2.84139	+	8.74491i	0.127454	+	0.392263i
$498$		0			0
$499$	−14.3683	+	10.4392i	−0.643212	+	0.467321i	−0.860952	−	0.508686i	$-0.830131\pi$
$499$	−14.3683	+	10.4392i	−0.643212	+	0.467321i	0.217740	+	0.976007i	$0.430131\pi$
$500$		0			0
$501$	−4.52394	+	13.9233i	−0.202115	+	0.622045i
$502$		0			0
$503$	13.2819	+	9.64987i	0.592211	+	0.430266i	0.843106	−	0.537748i	$-0.180725\pi$
$503$	13.2819	+	9.64987i	0.592211	+	0.430266i	−0.250895	+	0.968014i	$0.580725\pi$
$504$		0			0
$505$	−29.4107			−1.30876
$506$		0			0
$507$	37.7135			1.67491
$508$		0			0
$509$	10.8901	+	7.91213i	0.482696	+	0.350699i	0.802368	−	0.596829i	$-0.203573\pi$
$509$	10.8901	+	7.91213i	0.482696	+	0.350699i	−0.319673	+	0.947528i	$0.603573\pi$
$510$		0			0
$511$	1.99190	−	6.13045i	0.0881166	−	0.271195i
$512$		0			0
$513$	−10.7003	+	7.77420i	−0.472428	+	0.343239i
$514$		0			0
$515$	10.4327	+	32.1085i	0.459718	+	1.41487i
$516$		0			0
$517$	4.74034	+	0.719698i	0.208480	+	0.0316523i
$518$		0			0
$519$	1.08754	+	3.34711i	0.0477378	+	0.146922i
$520$		0			0
$521$	29.4858	−	21.4227i	1.29179	−	0.938544i	0.291954	−	0.956432i	$-0.405694\pi$
$521$	29.4858	−	21.4227i	1.29179	−	0.938544i	0.999840	+	0.0178887i	$0.00569445\pi$
$522$		0			0
$523$	−3.50372	+	10.7833i	−0.153207	+	0.471523i	−0.997975	−	0.0636104i	$-0.979739\pi$
$523$	−3.50372	+	10.7833i	−0.153207	+	0.471523i	0.844768	+	0.535133i	$0.179739\pi$
$524$		0			0
$525$	−0.0979606	−	0.0711726i	−0.00427535	−	0.00310623i
$526$		0			0
$527$	−27.2285			−1.18609
$528$		0			0
$529$	−21.5452			−0.936748
$530$		0			0
$531$	−1.37228	−	0.997023i	−0.0595521	−	0.0432671i
$532$		0			0
$533$	7.83793	−	24.1227i	0.339498	−	1.04487i
$534$		0			0
$535$	−36.8570	+	26.7782i	−1.59347	+	1.15772i
$536$		0			0
$537$	1.76744	+	5.43961i	0.0762705	+	0.234736i
$538$		0			0
$539$	−3.26707	−	19.8055i	−0.140723	−	0.853083i
$540$		0			0
$541$	12.6257	+	38.8579i	0.542821	+	1.67063i	0.726116	+	0.687572i	$0.241323\pi$
$541$	12.6257	+	38.8579i	0.542821	+	1.67063i	−0.183296	+	0.983058i	$0.558677\pi$
$542$		0			0
$543$	−10.1475	+	7.37257i	−0.435470	+	0.316387i
$544$		0			0
$545$	−3.29225	+	10.1325i	−0.141025	+	0.434029i
$546$		0			0
$547$	−26.5326	−	19.2770i	−1.13445	−	0.824227i	−0.148115	−	0.988970i	$-0.547320\pi$
$547$	−26.5326	−	19.2770i	−1.13445	−	0.824227i	−0.986336	+	0.164743i	$0.947320\pi$
$548$		0			0
$549$	1.98744			0.0848221
$550$		0			0
$551$	−5.86329			−0.249785
$552$		0			0
$553$	6.11506	+	4.44285i	0.260039	+	0.188929i
$554$		0			0
$555$	12.0496	−	37.0847i	0.511475	−	1.57416i
$556$		0			0
$557$	6.06808	−	4.40872i	0.257113	−	0.186803i	−0.451760	−	0.892139i	$-0.649204\pi$
$557$	6.06808	−	4.40872i	0.257113	−	0.186803i	0.708873	+	0.705336i	$0.249204\pi$
$558$		0			0
$559$	−15.7501	−	48.4738i	−0.666158	−	2.05022i
$560$		0			0
$561$	−11.0278	+	21.9905i	−0.465596	+	0.928439i
$562$		0			0
$563$	−3.62177	−	11.1467i	−0.152639	−	0.469775i	0.845275	−	0.534332i	$-0.179437\pi$
$563$	−3.62177	−	11.1467i	−0.152639	−	0.469775i	−0.997914	+	0.0645565i	$0.979437\pi$
$564$		0			0
$565$	11.7208	−	8.51563i	0.493096	−	0.358255i
$566$		0			0
$567$	3.07173	−	9.45380i	0.129000	−	0.397022i
$568$		0			0
$569$	−6.00794	−	4.36502i	−0.251866	−	0.182991i	0.454687	−	0.890651i	$-0.349751\pi$
$569$	−6.00794	−	4.36502i	−0.251866	−	0.182991i	−0.706553	+	0.707660i	$0.749751\pi$
$570$		0			0
$571$	37.7892			1.58143			0.790714	−	0.612185i	$-0.209709\pi$
$571$	37.7892			1.58143			0.790714	+	0.612185i	$0.209709\pi$
$572$		0			0
$573$	−3.36835			−0.140715
$574$		0			0
$575$	0.0650560	+	0.0472659i	0.00271302	+	0.00197113i
$576$		0			0
$577$	−6.63455	+	20.4190i	−0.276200	+	0.850056i	0.712699	+	0.701470i	$0.247472\pi$
$577$	−6.63455	+	20.4190i	−0.276200	+	0.850056i	−0.988899	+	0.148587i	$0.952528\pi$
$578$		0			0
$579$	1.22384	−	0.889173i	0.0508611	−	0.0369528i
$580$		0			0
$581$	−5.19226	−	15.9801i	−0.215411	−	0.662968i
$582$		0			0
$583$	24.1681	+	23.8605i	1.00094	+	0.988199i
$584$		0			0
$585$	−1.90107	−	5.85089i	−0.0785995	−	0.241904i
$586$		0			0
$587$	1.59529	−	1.15904i	0.0658445	−	0.0478388i	−0.554376	−	0.832266i	$-0.687043\pi$
$587$	1.59529	−	1.15904i	0.0658445	−	0.0478388i	0.620221	+	0.784427i	$0.287043\pi$
$588$		0			0
$589$	−5.95517	+	18.3281i	−0.245378	+	0.755197i
$590$		0			0
$591$	−28.0968	−	20.4135i	−1.15575	−	0.839701i
$592$		0			0
$593$	7.57118			0.310911			0.155456	−	0.987843i	$-0.450315\pi$
$593$	7.57118			0.310911			0.155456	+	0.987843i	$0.450315\pi$
$594$		0			0
$595$	−8.59675			−0.352432
$596$		0			0
$597$	25.3733	+	18.4348i	1.03846	+	0.754484i
$598$		0			0
$599$	3.16675	−	9.74625i	0.129390	−	0.398221i	−0.865286	−	0.501279i	$-0.832863\pi$
$599$	3.16675	−	9.74625i	0.129390	−	0.398221i	0.994675	+	0.103059i	$0.0328629\pi$
$600$		0			0
$601$	−2.79241	+	2.02880i	−0.113905	+	0.0827567i	−0.643279	−	0.765632i	$-0.722427\pi$
$601$	−2.79241	+	2.02880i	−0.113905	+	0.0827567i	0.529375	+	0.848388i	$0.322427\pi$
$602$		0			0
$603$	−1.82069	−	5.60352i	−0.0741444	−	0.228193i
$604$		0			0
$605$	14.6130	+	19.5805i	0.594101	+	0.796059i
$606$		0			0
$607$	−0.972368	−	2.99264i	−0.0394672	−	0.121468i	0.929382	−	0.369120i	$-0.120341\pi$
$607$	−0.972368	−	2.99264i	−0.0394672	−	0.121468i	−0.968849	+	0.247652i	$0.920341\pi$
$608$		0			0
$609$	3.06164	−	2.22441i	0.124064	−	0.0901376i
$610$		0			0
$611$	2.57460	−	7.92381i	0.104157	−	0.320563i
$612$		0			0
$613$	−37.0732	−	26.9353i	−1.49737	−	1.08791i	−0.971413	−	0.237397i	$-0.923706\pi$
$613$	−37.0732	−	26.9353i	−1.49737	−	1.08791i	−0.525961	−	0.850508i	$-0.676294\pi$
$614$		0			0
$615$	−18.2369			−0.735381
$616$		0			0
$617$	6.41440			0.258234			0.129117	−	0.991629i	$-0.458786\pi$
$617$	6.41440			0.258234			0.129117	+	0.991629i	$0.458786\pi$
$618$		0			0
$619$	24.0778	+	17.4936i	0.967770	+	0.703126i	0.954942	−	0.296792i	$-0.0959168\pi$
$619$	24.0778	+	17.4936i	0.967770	+	0.703126i	0.0128275	+	0.999918i	$0.495917\pi$
$620$		0			0
$621$	−1.75190	+	5.39179i	−0.0703013	+	0.216365i
$622$		0			0
$623$	−0.370505	+	0.269188i	−0.0148440	+	0.0107848i
$624$		0			0
$625$	−7.62104	−	23.4552i	−0.304842	−	0.938206i
$626$		0			0
$627$	12.3904	+	12.2326i	0.494824	+	0.488525i
$628$		0			0
$629$	11.5611	+	35.5813i	0.460970	+	1.41872i
$630$		0			0
$631$	−39.4007	+	28.6263i	−1.56852	+	1.13959i	−0.639959	+	0.768409i	$0.721049\pi$
$631$	−39.4007	+	28.6263i	−1.56852	+	1.13959i	−0.928559	+	0.371186i	$0.878951\pi$
$632$		0			0
$633$	0.221445	−	0.681537i	0.00880164	−	0.0270887i
$634$		0			0
$635$	−24.3198	−	17.6693i	−0.965101	−	0.701187i
$636$		0			0
$637$	−34.8807			−1.38202
$638$		0			0
$639$	−4.53929			−0.179572
$640$		0			0
$641$	−13.6347	−	9.90618i	−0.538538	−	0.391270i	0.285004	−	0.958526i	$-0.408005\pi$
$641$	−13.6347	−	9.90618i	−0.538538	−	0.391270i	−0.823542	+	0.567256i	$0.808005\pi$
$642$		0			0
$643$	−2.02874	+	6.24381i	−0.0800056	+	0.246232i	−0.983057	−	0.183301i	$-0.941322\pi$
$643$	−2.02874	+	6.24381i	−0.0800056	+	0.246232i	0.903051	+	0.429533i	$0.141322\pi$
$644$		0			0
$645$	−29.6476	+	21.5402i	−1.16737	+	0.848146i
$646$		0			0
$647$	1.09099	+	3.35774i	0.0428914	+	0.132006i	0.970209	−	0.242269i	$-0.0778916\pi$
$647$	1.09099	+	3.35774i	0.0428914	+	0.132006i	−0.927318	+	0.374275i	$0.877892\pi$
$648$		0			0
$649$	5.24743	−	10.4638i	0.205980	−	0.410741i
$650$		0			0
$651$	−3.84369	−	11.8297i	−0.150646	−	0.463641i
$652$		0			0
$653$	4.96362	−	3.60628i	0.194241	−	0.141125i	−0.486414	−	0.873729i	$-0.661695\pi$
$653$	4.96362	−	3.60628i	0.194241	−	0.141125i	0.680655	+	0.732604i	$0.261695\pi$
$654$		0			0
$655$	−8.11550	+	24.9770i	−0.317099	+	0.975930i
$656$		0			0
$657$	2.57444	+	1.87044i	0.100439	+	0.0729729i
$658$		0			0
$659$	27.9511			1.08882			0.544410	−	0.838819i	$-0.316754\pi$
$659$	27.9511			1.08882			0.544410	+	0.838819i	$0.316754\pi$
$660$		0			0
$661$	11.5665			0.449886			0.224943	−	0.974372i	$-0.427780\pi$
$661$	11.5665			0.449886			0.224943	+	0.974372i	$0.427780\pi$
$662$		0			0
$663$	34.5840	+	25.1267i	1.34313	+	0.975841i
$664$		0			0
$665$	−1.88020	+	5.78667i	−0.0729111	+	0.224397i
$666$		0			0
$667$	−2.03324	+	1.47724i	−0.0787274	+	0.0571988i
$668$		0			0
$669$	−13.4410	−	41.3672i	−0.519660	−	1.59935i
$670$		0			0
$671$	2.23232	+	13.5326i	0.0861776	+	0.522421i
$672$		0			0
$673$	−4.37705	−	13.4712i	−0.168723	−	0.519276i	0.830568	−	0.556917i	$-0.188016\pi$
$673$	−4.37705	−	13.4712i	−0.168723	−	0.519276i	−0.999291	+	0.0376407i	$0.988016\pi$
$674$		0			0
$675$	−0.253519	+	0.184192i	−0.00975793	+	0.00708955i
$676$		0			0
$677$	7.84568	−	24.1465i	0.301534	−	0.928026i	−0.679414	−	0.733755i	$-0.737766\pi$
$677$	7.84568	−	24.1465i	0.301534	−	0.928026i	0.980948	−	0.194271i	$-0.0622341\pi$
$678$		0			0
$679$	−7.13572	−	5.18441i	−0.273844	−	0.198959i
$680$		0			0
$681$	−5.08454			−0.194840
$682$		0			0
$683$	14.6841			0.561870			0.280935	−	0.959727i	$-0.409355\pi$
$683$	14.6841			0.561870			0.280935	+	0.959727i	$0.409355\pi$
$684$		0			0
$685$	−30.0727	−	21.8491i	−1.14902	−	0.834810i
$686$		0			0
$687$	14.3850	−	44.2724i	0.548821	−	1.68910i
$688$		0			0
$689$	47.7443	−	34.6882i	1.81891	−	1.32152i
$690$		0			0
$691$	−9.85170	−	30.3204i	−0.374776	−	1.15344i	−0.943629	−	0.331004i	$-0.892613\pi$
$691$	−9.85170	−	30.3204i	−0.374776	−	1.15344i	0.568853	−	0.822439i	$-0.307387\pi$
$692$		0			0
$693$	−1.53415	−	0.232921i	−0.0582774	−	0.00884792i
$694$		0			0
$695$	7.92761	+	24.3987i	0.300711	+	0.925494i
$696$		0			0
$697$	14.1558	−	10.2848i	0.536190	−	0.389565i
$698$		0			0
$699$	−12.1869	+	37.5073i	−0.460949	+	1.41866i
$700$		0			0
$701$	13.5108	+	9.81615i	0.510295	+	0.370751i	0.812935	−	0.582354i	$-0.197868\pi$
$701$	13.5108	+	9.81615i	0.510295	+	0.370751i	−0.302641	+	0.953105i	$0.597868\pi$
$702$		0			0
$703$	26.4791			0.998680
$704$		0			0
$705$	−5.99044			−0.225613
$706$		0			0
$707$	10.4288	+	7.57693i	0.392214	+	0.284960i
$708$		0			0
$709$	−8.24276	+	25.3686i	−0.309564	+	0.952739i	0.668371	+	0.743828i	$0.266992\pi$
$709$	−8.24276	+	25.3686i	−0.309564	+	0.952739i	−0.977935	+	0.208911i	$0.933008\pi$
$710$		0			0
$711$	−3.01884	+	2.19332i	−0.113215	+	0.0822558i
$712$		0			0
$713$	2.55261	+	7.85612i	0.0955959	+	0.294214i
$714$		0			0
$715$	37.7037	−	19.5163i	1.41004	−	0.729867i
$716$		0			0
$717$	0.119918	+	0.369071i	0.00447843	+	0.0137832i
$718$		0			0
$719$	−15.8748	+	11.5337i	−0.592032	+	0.430136i	−0.843042	−	0.537848i	$-0.819237\pi$
$719$	−15.8748	+	11.5337i	−0.592032	+	0.430136i	0.251010	+	0.967984i	$0.419237\pi$
$720$		0			0
$721$	4.57262	−	14.0731i	0.170293	−	0.524109i
$722$		0			0
$723$	−1.88852	−	1.37209i	−0.0702349	−	0.0510287i
$724$		0			0
$725$	−0.138917			−0.00515926
$726$		0			0
$727$	−23.9815			−0.889424			−0.444712	−	0.895674i	$-0.646694\pi$
$727$	−23.9815			−0.889424			−0.444712	+	0.895674i	$0.646694\pi$
$728$		0			0
$729$	−17.3128	−	12.5785i	−0.641215	−	0.465870i
$730$		0			0
$731$	10.8653	−	33.4400i	0.401868	−	1.23682i
$732$		0			0
$733$	12.4119	−	9.01779i	0.458445	−	0.333080i	−0.334476	−	0.942404i	$-0.608559\pi$
$733$	12.4119	−	9.01779i	0.458445	−	0.333080i	0.792921	+	0.609325i	$0.208559\pi$
$734$		0			0
$735$	7.74994	+	23.8519i	0.285861	+	0.879789i
$736$		0			0
$737$	36.1097	−	18.6911i	1.33012	−	0.688497i
$738$		0			0
$739$	0.987413	+	3.03894i	0.0363226	+	0.111789i	0.967574	−	0.252588i	$-0.0812818\pi$
$739$	0.987413	+	3.03894i	0.0363226	+	0.111789i	−0.931251	+	0.364378i	$0.881282\pi$
$740$		0			0
$741$	24.4773	−	17.7838i	0.899194	−	0.653303i
$742$		0			0
$743$	−9.56687	+	29.4438i	−0.350974	+	1.08019i	0.607333	+	0.794448i	$0.292239\pi$
$743$	−9.56687	+	29.4438i	−0.350974	+	1.08019i	−0.958307	+	0.285740i	$0.907761\pi$
$744$		0			0
$745$	−27.8583	−	20.2402i	−1.02065	−	0.741545i
$746$		0			0
$747$	8.29495			0.303496
$748$		0			0
$749$	19.9679			0.729611
$750$		0			0
$751$	14.5388	+	10.5630i	0.530528	+	0.385451i	0.820555	−	0.571567i	$-0.193664\pi$
$751$	14.5388	+	10.5630i	0.530528	+	0.385451i	−0.290027	+	0.957018i	$0.593664\pi$
$752$		0			0
$753$	12.8784	−	39.6357i	0.469316	−	1.44441i
$754$		0			0
$755$	−17.2368	+	12.5233i	−0.627313	+	0.455770i
$756$		0			0
$757$	4.53896	+	13.9695i	0.164971	+	0.507729i	0.999034	−	0.0439400i	$-0.0139910\pi$
$757$	4.53896	+	13.9695i	0.164971	+	0.507729i	−0.834063	+	0.551669i	$0.813991\pi$
$758$		0			0
$759$	7.37865	+	1.12026i	0.267828	+	0.0406628i
$760$		0			0
$761$	−4.09898	−	12.6154i	−0.148588	−	0.457307i	0.848867	−	0.528606i	$-0.177285\pi$
$761$	−4.09898	−	12.6154i	−0.148588	−	0.457307i	−0.997455	+	0.0712999i	$0.977285\pi$
$762$		0			0
$763$	3.77779	−	2.74473i	0.136765	−	0.0993658i
$764$		0			0
$765$	1.31146	−	4.03627i	0.0474161	−	0.145932i
$766$		0			0
$767$	−16.4562	−	11.9562i	−0.594201	−	0.431712i
$768$		0			0
$769$	−30.0680			−1.08428			−0.542139	−	0.840289i	$-0.682385\pi$
$769$	−30.0680			−1.08428			−0.542139	+	0.840289i	$0.682385\pi$
$770$		0			0
$771$	40.4088			1.45529
$772$		0			0
$773$	−8.52718	−	6.19536i	−0.306701	−	0.222832i	0.423778	−	0.905766i	$-0.360703\pi$
$773$	−8.52718	−	6.19536i	−0.306701	−	0.222832i	−0.730480	+	0.682934i	$0.760703\pi$
$774$		0			0
$775$	−0.141094	+	0.434243i	−0.00506825	+	0.0155985i
$776$		0			0
$777$	−13.8266	+	10.0456i	−0.496027	+	0.360385i
$778$		0			0
$779$	−3.82690	−	11.7780i	−0.137113	−	0.421991i
$780$		0			0
$781$	−5.09857	−	30.9083i	−0.182441	−	1.10599i
$782$		0			0
$783$	−3.02647	−	9.31452i	−0.108157	−	0.332874i
$784$		0			0
$785$	−5.75241	+	4.17937i	−0.205312	+	0.149168i
$786$		0			0
$787$	−11.6052	+	35.7171i	−0.413680	+	1.27318i	0.499746	+	0.866172i	$0.333427\pi$
$787$	−11.6052	+	35.7171i	−0.413680	+	1.27318i	−0.913426	+	0.407004i	$0.866573\pi$
$788$		0			0
$789$	−17.1229	−	12.4405i	−0.609592	−	0.442895i
$790$		0			0
$791$	−6.34992			−0.225777
$792$		0			0
$793$	23.8332			0.846340
$794$		0			0
$795$	−34.3283	−	24.9410i	−1.21750	−	0.884565i
$796$		0			0
$797$	4.86857	−	14.9839i	0.172454	−	0.530758i	−0.827054	−	0.562122i	$-0.809985\pi$
$797$	4.86857	−	14.9839i	0.172454	−	0.530758i	0.999508	+	0.0313641i	$0.00998515\pi$
$798$		0			0
$799$	4.64990	−	3.37835i	0.164502	−	0.119517i
$800$		0			0
$801$	−0.0698648	−	0.215022i	−0.00246855	−	0.00759742i
$802$		0			0
$803$	−9.84431	+	19.6304i	−0.347398	+	0.692742i
$804$		0			0
$805$	0.805925	+	2.48038i	0.0284051	+	0.0874220i
$806$		0			0
$807$	−21.7028	+	15.7680i	−0.763975	+	0.555060i
$808$		0			0
$809$	−10.9888	+	33.8200i	−0.386345	+	1.18905i	0.549154	+	0.835721i	$0.314950\pi$
$809$	−10.9888	+	33.8200i	−0.386345	+	1.18905i	−0.935500	+	0.353328i	$0.885050\pi$
$810$		0			0
$811$	6.30228	+	4.57888i	0.221303	+	0.160786i	0.692913	−	0.721021i	$-0.256327\pi$
$811$	6.30228	+	4.57888i	0.221303	+	0.160786i	−0.471610	+	0.881807i	$0.656327\pi$
$812$		0			0
$813$	−20.5436			−0.720497
$814$		0			0
$815$	52.5161			1.83956
$816$		0			0
$817$	−20.1328	−	14.6274i	−0.704359	−	0.511747i
$818$		0			0
$819$	−0.833235	+	2.56443i	−0.0291156	+	0.0896086i
$820$		0			0
$821$	4.87943	−	3.54511i	0.170293	−	0.123725i	−0.499374	−	0.866386i	$-0.666437\pi$
$821$	4.87943	−	3.54511i	0.170293	−	0.123725i	0.669667	+	0.742661i	$0.266437\pi$
$822$		0			0
$823$	−15.4682	−	47.6063i	−0.539188	−	1.65945i	−0.734422	−	0.678694i	$-0.762546\pi$
$823$	−15.4682	−	47.6063i	−0.539188	−	1.65945i	0.195234	−	0.980757i	$-0.437454\pi$
$824$		0			0
$825$	0.293562	+	0.289825i	0.0102205	+	0.0100904i
$826$		0			0
$827$	−8.75315	−	26.9394i	−0.304377	−	0.936776i	−0.979909	−	0.199445i	$-0.936086\pi$
$827$	−8.75315	−	26.9394i	−0.304377	−	0.936776i	0.675532	−	0.737331i	$-0.263914\pi$
$828$		0			0
$829$	4.38986	−	3.18942i	0.152466	−	0.110773i	−0.508937	−	0.860804i	$-0.669961\pi$
$829$	4.38986	−	3.18942i	0.152466	−	0.110773i	0.661403	+	0.750031i	$0.269961\pi$
$830$		0			0
$831$	−3.40281	+	10.4728i	−0.118042	+	0.363297i
$832$		0			0
$833$	−19.4671	−	14.1437i	−0.674495	−	0.490049i
$834$		0			0
$835$	17.4292			0.603163
$836$		0			0
$837$	−32.1902			−1.11266
$838$		0			0
$839$	−32.6943	−	23.7538i	−1.12873	−	0.820071i	−0.143222	−	0.989691i	$-0.545746\pi$
$839$	−32.6943	−	23.7538i	−1.12873	−	0.820071i	−0.985510	+	0.169619i	$0.945746\pi$
$840$		0			0
$841$	−7.61984	+	23.4514i	−0.262753	+	0.808671i
$842$		0			0
$843$	−19.9214	+	14.4737i	−0.686129	+	0.498502i
$844$		0			0
$845$	−13.8747	−	42.7018i	−0.477303	−	1.46899i
$846$		0			0
$847$	−0.137197	−	10.7077i	−0.00471416	−	0.367922i
$848$		0			0
$849$	5.04066	+	15.5136i	0.172995	+	0.532424i
$850$		0			0
$851$	9.18230	−	6.67133i	0.314765	−	0.228690i
$852$		0			0
$853$	−7.42894	+	22.8639i	−0.254362	+	0.782846i	0.739593	+	0.673055i	$0.235018\pi$
$853$	−7.42894	+	22.8639i	−0.254362	+	0.782846i	−0.993955	+	0.109791i	$0.964982\pi$
$854$		0			0
$855$	−2.43007	−	1.76555i	−0.0831068	−	0.0603806i
$856$		0			0
$857$	42.9442			1.46695			0.733474	−	0.679718i	$-0.237898\pi$
$857$	42.9442			1.46695			0.733474	+	0.679718i	$0.237898\pi$
$858$		0			0
$859$	12.9486			0.441800			0.220900	−	0.975296i	$-0.429101\pi$
$859$	12.9486			0.441800			0.220900	+	0.975296i	$0.429101\pi$
$860$		0			0
$861$	6.46662	+	4.69827i	0.220382	+	0.160117i
$862$		0			0
$863$	3.63584	−	11.1900i	0.123765	−	0.380910i	−0.869909	−	0.493213i	$-0.835822\pi$
$863$	3.63584	−	11.1900i	0.123765	−	0.380910i	0.993674	+	0.112302i	$0.0358225\pi$
$864$		0			0
$865$	3.38973	−	2.46278i	0.115254	−	0.0837370i
$866$		0			0
$867$	−0.687798	−	2.11683i	−0.0233589	−	0.0718912i
$868$		0			0
$869$	−18.3252	−	18.0919i	−0.621641	−	0.613727i
$870$		0			0
$871$	−21.8335	−	67.1966i	−0.739800	−	2.27687i
$872$		0			0
$873$	3.52271	−	2.55940i	0.119226	−	0.0866226i
$874$		0			0
$875$	−3.38544	+	10.4193i	−0.114449	+	0.352237i
$876$		0			0
$877$	33.5126	+	24.3483i	1.13164	+	0.822185i	0.985933	−	0.167142i	$-0.0534539\pi$
$877$	33.5126	+	24.3483i	1.13164	+	0.822185i	0.145708	+	0.989328i	$0.453454\pi$
$878$		0			0
$879$	−2.82886			−0.0954150
$880$		0			0
$881$	−44.7091			−1.50629			−0.753143	−	0.657857i	$-0.771463\pi$
$881$	−44.7091			−1.50629			−0.753143	+	0.657857i	$0.771463\pi$
$882$		0			0
$883$	17.7445	+	12.8922i	0.597151	+	0.433856i	0.844867	−	0.534977i	$-0.179680\pi$
$883$	17.7445	+	12.8922i	0.597151	+	0.433856i	−0.247715	+	0.968833i	$0.579680\pi$
$884$		0			0
$885$	−4.51946	+	13.9095i	−0.151920	+	0.467561i
$886$		0			0
$887$	−14.1400	+	10.2733i	−0.474776	+	0.344945i	−0.799300	−	0.600933i	$-0.794796\pi$
$887$	−14.1400	+	10.2733i	−0.474776	+	0.344945i	0.324524	+	0.945877i	$0.394796\pi$
$888$		0			0
$889$	4.07150	+	12.5308i	0.136554	+	0.420269i
$890$		0			0
$891$	−15.1810	+	30.2722i	−0.508582	+	1.01416i
$892$		0			0
$893$	−1.25706	−	3.86884i	−0.0420659	−	0.129466i
$894$		0			0
$895$	5.50887	−	4.00243i	0.184141	−	0.133786i
$896$		0			0
$897$	4.00753	−	12.3339i	0.133808	−	0.411818i
$898$		0			0
$899$	−11.5448	−	8.38778i	−0.385040	−	0.279748i
$900$		0			0
$901$	40.7119			1.35631
$902$		0			0
$903$	16.0621			0.534513
$904$		0			0
$905$	12.0810	+	8.77733i	0.401585	+	0.291768i
$906$		0			0
$907$	5.08397	−	15.6469i	0.168810	−	0.519545i	−0.830486	−	0.557039i	$-0.811937\pi$
$907$	5.08397	−	15.6469i	0.168810	−	0.519545i	0.999297	+	0.0374937i	$0.0119374\pi$
$908$		0			0
$909$	−5.14840	+	3.74053i	−0.170762	+	0.124066i
$910$		0			0
$911$	−4.69348	−	14.4450i	−0.155502	−	0.478585i	0.842710	−	0.538368i	$-0.180959\pi$
$911$	−4.69348	−	14.4450i	−0.155502	−	0.478585i	−0.998211	+	0.0597831i	$0.980959\pi$
$912$		0			0
$913$	9.31696	+	56.4808i	0.308346	+	1.86924i
$914$		0			0
$915$	−5.29535	−	16.2974i	−0.175059	−	0.538776i
$916$		0			0
$917$	9.31238	−	6.76584i	0.307522	−	0.223428i
$918$		0			0
$919$	−12.9316	+	39.7994i	−0.426575	+	1.31286i	0.474904	+	0.880038i	$0.342483\pi$
$919$	−12.9316	+	39.7994i	−0.426575	+	1.31286i	−0.901478	+	0.432824i	$0.857517\pi$
$920$		0			0
$921$	−8.35523	−	6.07043i	−0.275314	−	0.200027i
$922$		0			0
$923$	−54.4346			−1.79174
$924$		0			0
$925$	0.627363			0.0206276
$926$		0			0
$927$	5.90990	+	4.29379i	0.194107	+	0.141027i
$928$		0			0
$929$	0.0970194	−	0.298595i	0.00318310	−	0.00979659i	−0.949452	−	0.313911i	$-0.898361\pi$
$929$	0.0970194	−	0.298595i	0.00318310	−	0.00979659i	0.952635	+	0.304115i	$0.0983606\pi$
$930$		0			0
$931$	−13.7781	+	10.0104i	−0.451559	+	0.328077i
$932$		0			0
$933$	5.28113	+	16.2537i	0.172897	+	0.532121i
$934$		0			0
$935$	28.9562	+	4.39626i	0.946970	+	0.143773i
$936$		0			0
$937$	−3.27217	−	10.0707i	−0.106897	−	0.328996i	0.883274	−	0.468857i	$-0.155334\pi$
$937$	−3.27217	−	10.0707i	−0.106897	−	0.328996i	−0.990171	+	0.139862i	$0.955334\pi$
$938$		0			0
$939$	−24.5634	+	17.8464i	−0.801597	+	0.582394i
$940$		0			0
$941$	18.1868	−	55.9733i	0.592874	−	1.82468i	0.0278375	−	0.999612i	$-0.491138\pi$
$941$	18.1868	−	55.9733i	0.592874	−	1.82468i	0.565036	−	0.825066i	$-0.308862\pi$
$942$		0			0
$943$	−4.29450	−	3.12014i	−0.139848	−	0.101606i
$944$		0			0
$945$	−10.1633			−0.330612
$946$		0			0
$947$	15.0139			0.487887			0.243943	−	0.969789i	$-0.421559\pi$
$947$	15.0139			0.487887			0.243943	+	0.969789i	$0.421559\pi$
$948$		0			0
$949$	30.8723	+	22.4301i	1.00216	+	0.728111i
$950$		0			0
$951$	−2.04457	+	6.29253i	−0.0662996	+	0.204049i
$952$		0			0
$953$	−8.67162	+	6.30030i	−0.280901	+	0.204087i	−0.719310	−	0.694689i	$-0.755542\pi$
$953$	−8.67162	+	6.30030i	−0.280901	+	0.204087i	0.438409	+	0.898775i	$0.355542\pi$
$954$		0			0
$955$	1.23920	+	3.81388i	0.0400997	+	0.123414i
$956$		0			0
$957$	−11.4500	+	5.92675i	−0.370125	+	0.191585i
$958$		0			0
$959$	5.03462	+	15.4950i	0.162576	+	0.500358i
$960$		0			0
$961$	−12.8656	+	9.34743i	−0.415020	+	0.301530i
$962$		0			0
$963$	−3.04617	+	9.37515i	−0.0981615	+	0.302110i
$964$		0			0
$965$	−1.45703	−	1.05859i	−0.0469035	−	0.0340774i
$966$		0			0
$967$	43.1296			1.38695			0.693477	−	0.720479i	$-0.256078\pi$
$967$	43.1296			1.38695			0.693477	+	0.720479i	$0.256078\pi$
$968$		0			0
$969$	20.8720			0.670504
$970$		0			0
$971$	13.3942	+	9.73143i	0.429839	+	0.312296i	0.781585	−	0.623799i	$-0.214412\pi$
$971$	13.3942	+	9.73143i	0.429839	+	0.312296i	−0.351745	+	0.936096i	$0.614412\pi$
$972$		0			0
$973$	3.47466	−	10.6939i	0.111392	−	0.342831i
$974$		0			0
$975$	0.579933	−	0.421346i	0.0185727	−	0.0134939i
$976$		0			0
$977$	0.482558	+	1.48516i	0.0154384	+	0.0475145i	0.958479	−	0.285163i	$-0.0920478\pi$
$977$	0.482558	+	1.48516i	0.0154384	+	0.0475145i	−0.943041	+	0.332678i	$0.892048\pi$
$978$		0			0
$979$	1.38562	−	0.717228i	0.0442847	−	0.0229227i
$980$		0			0
$981$	0.712364	+	2.19243i	0.0227440	+	0.0699990i
$982$		0			0
$983$	39.3187	−	28.5667i	1.25407	−	0.911136i	0.255621	−	0.966777i	$-0.417720\pi$
$983$	39.3187	−	28.5667i	1.25407	−	0.911136i	0.998451	+	0.0556406i	$0.0177201\pi$
$984$		0			0
$985$	−12.7769	+	39.3232i	−0.407106	+	1.25294i
$986$		0			0
$987$	2.12415	+	1.54329i	0.0676126	+	0.0491234i
$988$		0			0
$989$	−10.6669			−0.339187
$990$		0			0
$991$	13.0806			0.415518			0.207759	−	0.978180i	$-0.433383\pi$
$991$	13.0806			0.415518			0.207759	+	0.978180i	$0.433383\pi$
$992$		0			0
$993$	24.5012	+	17.8012i	0.777524	+	0.564904i
$994$		0			0
$995$	11.5384	−	35.5114i	0.365791	−	1.12579i
$996$		0			0
$997$	−24.7329	+	17.9695i	−0.783299	+	0.569100i	−0.905967	−	0.423348i	$-0.860855\pi$
$997$	−24.7329	+	17.9695i	−0.783299	+	0.569100i	0.122668	+	0.992448i	$0.460855\pi$
$998$		0			0
$999$	13.6678	+	42.0652i	0.432430	+	1.33088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	352.2.m.f.225.1	yes	12
4.3	odd	2		352.2.m.e.225.3	yes	12
8.3	odd	2		704.2.m.m.577.1		12
8.5	even	2		704.2.m.n.577.3		12
11.3	even	5		3872.2.a.bn.1.6		6
11.8	odd	10		3872.2.a.bo.1.6		6
11.9	even	5	inner	352.2.m.f.97.1	yes	12
44.3	odd	10		3872.2.a.bq.1.1		6
44.19	even	10		3872.2.a.bp.1.1		6
44.31	odd	10		352.2.m.e.97.3	✓	12
88.3	odd	10		7744.2.a.du.1.6		6
88.19	even	10		7744.2.a.dt.1.6		6
88.53	even	10		704.2.m.n.449.3		12
88.69	even	10		7744.2.a.dv.1.1		6
88.75	odd	10		704.2.m.m.449.1		12
88.85	odd	10		7744.2.a.dw.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
352.2.m.e.97.3	✓	12	44.31	odd	10
352.2.m.e.225.3	yes	12	4.3	odd	2
352.2.m.f.97.1	yes	12	11.9	even	5	inner
352.2.m.f.225.1	yes	12	1.1	even	1	trivial
704.2.m.m.449.1		12	88.75	odd	10
704.2.m.m.577.1		12	8.3	odd	2
704.2.m.n.449.3		12	88.53	even	10
704.2.m.n.577.3		12	8.5	even	2
3872.2.a.bn.1.6		6	11.3	even	5
3872.2.a.bo.1.6		6	11.8	odd	10
3872.2.a.bp.1.1		6	44.19	even	10
3872.2.a.bq.1.1		6	44.3	odd	10
7744.2.a.dt.1.6		6	88.19	even	10
7744.2.a.du.1.6		6	88.3	odd	10
7744.2.a.dv.1.1		6	88.69	even	10
7744.2.a.dw.1.1		6	88.85	odd	10

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:	\( N \)	\(=\)	\( 352 = 2^{5} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	352.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50933 - 1.09659i) q^{3} +(-0.686361 + 2.11240i) q^{5} +(0.787585 - 0.572214i) q^{7} +(0.148512 + 0.457073i) q^{9} +(-2.94543 + 1.52462i) q^{11} +(1.78094 + 5.48116i) q^{13} +(3.35239 - 2.43565i) q^{15} +(-1.22859 + 3.78121i) q^{17} +(2.27651 + 1.65398i) q^{19} -1.81621 q^{21} +1.20615 q^{23} +(0.0539368 + 0.0391874i) q^{25} +(-1.45247 + 4.47024i) q^{27} +(-1.68573 + 1.22475i) q^{29} +(2.11632 + 6.51337i) q^{31} +(6.11751 + 0.928786i) q^{33} +(0.668178 + 2.05644i) q^{35} +(7.61289 - 5.53109i) q^{37} +(3.32258 - 10.2258i) q^{39} +(-3.56050 - 2.58685i) q^{41} -8.84372 q^{43} -1.06745 q^{45} +(-1.16955 - 0.849729i) q^{47} +(-1.87026 + 5.75606i) q^{49} +(6.00079 - 4.35983i) q^{51} +(-3.16432 - 9.73877i) q^{53} +(-1.19897 - 7.26836i) q^{55} +(-1.62226 - 4.99281i) q^{57} +(-2.85539 + 2.07456i) q^{59} +(1.27790 - 3.93298i) q^{61} +(0.378510 + 0.275003i) q^{63} -12.8008 q^{65} -12.2596 q^{67} +(-1.82048 - 1.32266i) q^{69} +(-2.91871 + 8.98287i) q^{71} +(5.35678 - 3.89193i) q^{73} +(-0.0384358 - 0.118293i) q^{75} +(-1.44737 + 2.88618i) q^{77} +(2.39931 + 7.38431i) q^{79} +(8.26072 - 6.00177i) q^{81} +(5.33355 - 16.4150i) q^{83} +(-7.14417 - 5.19055i) q^{85} +3.88737 q^{87} -0.470432 q^{89} +(4.53903 + 3.29780i) q^{91} +(3.94828 - 12.1516i) q^{93} +(-5.05638 + 3.67368i) q^{95} +(-2.79977 - 8.61681i) q^{97} +(-1.13429 - 1.11985i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{7} - q^{9} - 11 q^{11} - 2 q^{13} + 4 q^{15} + 12 q^{17} + 5 q^{19} + 24 q^{21} - 12 q^{23} + 13 q^{25} + 3 q^{27} + 16 q^{31} - 7 q^{33} - 28 q^{35} - 4 q^{37} + 46 q^{39} - 4 q^{41} - 22 q^{43}+ \cdots - 65 q^{99}+O(q^{100}) \) 12 * q + 6 * q^7 - q^9 - 11 * q^11 - 2 * q^13 + 4 * q^15 + 12 * q^17 + 5 * q^19 + 24 * q^21 - 12 * q^23 + 13 * q^25 + 3 * q^27 + 16 * q^31 - 7 * q^33 - 28 * q^35 - 4 * q^37 + 46 * q^39 - 4 * q^41 - 22 * q^43 + 28 * q^45 - 24 * q^47 - 5 * q^49 + 17 * q^51 - 14 * q^53 - 46 * q^55 - 37 * q^57 + 31 * q^59 - 14 * q^61 + 58 * q^63 - 52 * q^65 - 62 * q^67 - 18 * q^69 + 6 * q^71 - 8 * q^73 + 53 * q^75 - 46 * q^77 - 4 * q^79 - 22 * q^81 + 41 * q^83 - 36 * q^85 - 76 * q^87 - 2 * q^89 - 22 * q^91 + 8 * q^93 + 16 * q^95 + 3 * q^97 - 65 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more