LMFDB - Embedded newform 704.2.m.m.577.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [704,2,Mod(257,704)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(704, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("704.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 704 = 2^{6} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	704.m (of order $5$, degree $4$, 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:	$5.62146830230$
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:	no (minimal twist has level 352)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			577.1
Root			$0.885530 - 2.72538i$ of defining polynomial
Character	$\chi$	$=$	704.577
Dual form			704.2.m.m.449.1

$q$-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 $\left(\mathbb{Z}/704\mathbb{Z}\right)^\times$.

$n$	$133$	$321$	$639$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.50933	−	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	$-0.734561\pi$
$5$	0.686361	−	2.11240i	0.306950	−	0.944695i	0.978942	−	0.204137i	$-0.0654387\pi$
$6$		0			0
$7$	−0.787585	+	0.572214i	−0.297679	+	0.216277i	−0.726592	−	0.687069i	$-0.758897\pi$
$7$	−0.787585	+	0.572214i	−0.297679	+	0.216277i	0.428913	+	0.903346i	$0.358897\pi$
$8$		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	$-0.805248\pi$
$13$	−1.78094	−	5.48116i	−0.493943	−	1.52020i	0.324655	−	0.945832i	$-0.394752\pi$
$14$		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	$-0.540134\pi$
$23$	−1.20615			−0.251500			−0.125750	+	0.992062i	$0.540134\pi$
$24$		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	−0.420165	−	0.907448i	$-0.638028\pi$
$29$	1.68573	−	1.22475i	0.313031	−	0.227431i	0.733196	+	0.680017i	$0.238028\pi$
$30$		0			0
$31$	−2.11632	−	6.51337i	−0.380103	−	1.16984i	−0.939971	−	0.341254i	$-0.889148\pi$
$31$	−2.11632	−	6.51337i	−0.380103	−	1.16984i	0.559868	−	0.828581i	$-0.310852\pi$
$32$		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	−0.998311	−	0.0580987i	$-0.981496\pi$
$37$	−7.61289	+	5.53109i	−1.25155	+	0.909305i	−0.253240	+	0.967404i	$0.581496\pi$
$38$		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	0.669807	−	0.742535i	$-0.266377\pi$
$47$	1.16955	+	0.849729i	0.170597	+	0.123946i	−0.499211	+	0.866481i	$0.666377\pi$
$48$		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	$0.148283\pi$
$53$	3.16432	+	9.73877i	0.434652	+	1.33772i	−0.458790	+	0.888545i	$0.651717\pi$
$54$		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	−0.998932	−	0.0462077i	$-0.985286\pi$
$61$	−1.27790	+	3.93298i	−0.163619	+	0.503567i	0.835313	+	0.549775i	$0.185286\pi$
$62$		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	$-0.710622\pi$
$71$	2.91871	−	8.98287i	0.346387	−	1.06607i	0.960837	−	0.277115i	$-0.0893782\pi$
$72$		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	$-0.956120\pi$
$79$	−2.39931	−	7.38431i	−0.269943	−	0.830800i	0.720570	−	0.693382i	$-0.243880\pi$
$80$		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	$-0.871070\pi$
$101$	−4.09183	−	12.5933i	−0.407152	−	1.25309i	0.511933	−	0.859025i	$-0.328930\pi$
$102$		0			0
$103$	−12.2970	+	8.93433i	−1.21166	+	0.880325i	−0.995381	−	0.0960055i	$-0.969393\pi$
$103$	−12.2970	+	8.93433i	−1.21166	+	0.880325i	−0.216283	+	0.976331i	$0.569393\pi$
$104$		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	$-0.573781\pi$
$109$	−4.79668			−0.459438			−0.229719	+	0.973257i	$0.573781\pi$
$110$		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	$-0.694975\pi$
$127$	4.18229	−	12.8718i	0.371118	−	1.14218i	0.946060	−	0.323990i	$-0.105025\pi$
$128$		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	$-0.680982\pi$
$149$	4.79081	−	14.7446i	0.392478	−	1.20792i	0.930908	−	0.365254i	$-0.119018\pi$
$150$		0			0
$151$	−7.76046	−	5.63831i	−0.631538	−	0.458839i	0.225395	−	0.974267i	$-0.427633\pi$
$151$	−7.76046	−	5.63831i	−0.631538	−	0.458839i	−0.856933	+	0.515429i	$0.827633\pi$
$152$		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	0.479622	−	0.877475i	$-0.340774\pi$
$157$	−2.58988	−	1.88166i	−0.206695	−	0.150173i	−0.686317	+	0.727302i	$0.740774\pi$
$158$		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	0.999984	−	0.00567748i	$-0.00180721\pi$
$167$	2.42488	+	7.46301i	0.187643	+	0.577505i	−0.812341	+	0.583183i	$0.801807\pi$
$168$		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	0.644287	−	0.764784i	$-0.277154\pi$
$173$	1.52614	+	1.10881i	0.116030	+	0.0843009i	−0.528257	+	0.849085i	$0.677154\pi$
$174$		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	−0.998102	−	0.0615801i	$-0.980386\pi$
$181$	−2.07757	+	6.39411i	−0.154425	+	0.475270i	0.843677	+	0.536850i	$0.180386\pi$
$182$		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	−0.639375	−	0.768895i	$-0.720807\pi$
$191$	−1.46066	+	1.06123i	−0.105689	+	0.0767879i	0.533685	+	0.845683i	$0.320807\pi$
$192$		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	$-0.730780\pi$
$197$	−18.6154			−1.32629			−0.663147	+	0.748489i	$0.730780\pi$
$198$		0			0
$199$	16.8109			1.19170			0.595848	−	0.803097i	$-0.296816\pi$
$199$	16.8109			1.19170			0.595848	+	0.803097i	$0.296816\pi$
$200$		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	−0.264169	−	0.964477i	$-0.585098\pi$
$223$	−18.8617	−	13.7038i	−1.26307	−	0.917676i	−0.998904	+	0.0468004i	$0.985098\pi$
$224$		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	$-0.791498\pi$
$229$	−7.71049	−	23.7305i	−0.509524	−	1.56815i	0.283507	−	0.958970i	$-0.408502\pi$
$230$		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	0.593215	−	0.805044i	$-0.297859\pi$
$239$	0.168281	+	0.122263i	0.0108852	+	0.00790854i	−0.582329	+	0.812953i	$0.697859\pi$
$240$		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	$-0.613741\pi$
$263$	−11.3447			−0.699545			−0.349773	+	0.936835i	$0.613741\pi$
$264$		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	$0.244438\pi$
$269$	−4.44338	+	13.6753i	−0.270918	+	0.833799i	−0.990271	+	0.139154i	$0.955562\pi$
$270$		0			0
$271$	−8.90858	+	6.47246i	−0.541158	+	0.393174i	−0.824515	−	0.565840i	$-0.808552\pi$
$271$	−8.90858	+	6.47246i	−0.541158	+	0.393174i	0.283357	+	0.959014i	$0.408552\pi$
$272$		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	0.990780	−	0.135478i	$-0.0432570\pi$
$277$	1.82394	+	5.61352i	0.109590	+	0.337284i	−0.881190	+	0.472762i	$0.843257\pi$
$278$		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	−0.623041	−	0.782189i	$-0.714103\pi$
$293$	−1.22671	+	0.891257i	−0.0716652	+	0.0520678i	0.551376	+	0.834257i	$0.314103\pi$
$294$		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	0.777734	−	0.628594i	$-0.216369\pi$
$311$	7.41098	+	5.38439i	0.420238	+	0.305321i	−0.357495	+	0.933915i	$0.616369\pi$
$312$		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	0.977104	−	0.212761i	$-0.0682457\pi$
$317$	1.09591	+	3.37286i	0.0615524	+	0.189439i	−0.915552	+	0.402200i	$0.868246\pi$
$318$		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	0.831358	−	0.555737i	$-0.187564\pi$
$349$	10.4565	+	7.59712i	0.559725	+	0.406664i	−0.271633	+	0.962401i	$0.587564\pi$
$350$		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	−0.960039	−	0.279866i	$-0.909710\pi$
$359$	−18.7680	+	13.6358i	−0.990539	+	0.719669i	−0.0305003	+	0.999535i	$0.509710\pi$
$360$		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	−0.864406	−	0.502795i	$-0.832305\pi$
$367$	−12.5161	+	9.09348i	−0.653335	+	0.474676i	0.211071	+	0.977471i	$0.432305\pi$
$368$		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	$-0.790779\pi$
$373$	−30.5787			−1.58331			−0.791653	+	0.610970i	$0.790779\pi$
$374$		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	$-0.944196\pi$
$383$	−5.68665	−	17.5017i	−0.290574	−	0.894296i	0.694098	−	0.719881i	$-0.255804\pi$
$384$		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	−0.574656	−	0.818395i	$-0.694864\pi$
$389$	0.514886	−	0.374087i	0.0261058	−	0.0189669i	0.600762	+	0.799428i	$0.294864\pi$
$390$		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	$-0.335944\pi$
$397$	19.6411			0.985760			0.492880	+	0.870097i	$0.335944\pi$
$398$		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	0.993105	−	0.117231i	$-0.0374019\pi$
$421$	24.3859	+	17.7174i	1.18850	+	0.863494i	0.195392	+	0.980725i	$0.437402\pi$
$422$		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	$0.188359\pi$
$431$	10.0976	+	31.0772i	0.486384	+	1.49694i	−0.343583	+	0.939122i	$0.611641\pi$
$432$		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	$-0.654017\pi$
$439$	−19.4940			−0.930399			−0.465200	+	0.885206i	$0.654017\pi$
$440$		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	$-0.482293\pi$
$461$	2.38755			0.111199			0.0555996	+	0.998453i	$0.482293\pi$
$462$		0			0
$463$	−16.3739			−0.760961			−0.380480	−	0.924789i	$-0.624241\pi$
$463$	−16.3739			−0.760961			−0.380480	+	0.924789i	$0.624241\pi$
$464$		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	$-0.709245\pi$
$479$	7.62945	−	23.4810i	0.348598	−	1.07288i	0.959629	−	0.281268i	$-0.0907551\pi$
$480$		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	0.884953	−	0.465679i	$-0.154190\pi$
$487$	15.7904	+	11.4724i	0.715532	+	0.519864i	−0.169422	+	0.985544i	$0.554190\pi$
$488$		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	0.250895	−	0.968014i	$-0.419275\pi$
$503$	−13.2819	−	9.64987i	−0.592211	−	0.430266i	−0.843106	+	0.537748i	$0.819275\pi$
$504$		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	0.319673	−	0.947528i	$-0.396427\pi$
$509$	−10.8901	−	7.91213i	−0.482696	−	0.350699i	−0.802368	+	0.596829i	$0.796427\pi$
$510$		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	$-0.758677\pi$
$541$	−12.6257	−	38.8579i	−0.542821	−	1.67063i	0.183296	−	0.983058i	$-0.441323\pi$
$542$		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	−0.708873	−	0.705336i	$-0.750796\pi$
$557$	−6.06808	+	4.40872i	−0.257113	+	0.186803i	0.451760	+	0.892139i	$0.350796\pi$
$558$		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	−0.994675	−	0.103059i	$-0.967137\pi$
$599$	−3.16675	+	9.74625i	−0.129390	+	0.398221i	0.865286	+	0.501279i	$0.167137\pi$
$600$		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	0.968849	−	0.247652i	$-0.0796591\pi$
$607$	0.972368	+	2.99264i	0.0394672	+	0.121468i	−0.929382	+	0.369120i	$0.879659\pi$
$608$		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	$0.0762944\pi$
$613$	37.0732	+	26.9353i	1.49737	+	1.08791i	0.525961	+	0.850508i	$0.323706\pi$
$614$		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	$-0.278951\pi$
$631$	39.4007	−	28.6263i	1.56852	−	1.13959i	0.928559	−	0.371186i	$-0.121049\pi$
$632$		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	0.927318	−	0.374275i	$-0.122108\pi$
$647$	−1.09099	−	3.35774i	−0.0428914	−	0.132006i	−0.970209	+	0.242269i	$0.922108\pi$
$648$		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	−0.680655	−	0.732604i	$-0.738305\pi$
$653$	−4.96362	+	3.60628i	−0.194241	+	0.141125i	0.486414	+	0.873729i	$0.338305\pi$
$654$		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	$-0.572220\pi$
$661$	−11.5665			−0.449886			−0.224943	+	0.974372i	$0.572220\pi$
$662$		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	$0.262234\pi$
$677$	−7.84568	+	24.1465i	−0.301534	+	0.928026i	−0.980948	+	0.194271i	$0.937766\pi$
$678$		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	0.302641	−	0.953105i	$-0.402132\pi$
$701$	−13.5108	−	9.81615i	−0.510295	−	0.370751i	−0.812935	+	0.582354i	$0.802132\pi$
$702$		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	$-0.733008\pi$
$709$	8.24276	−	25.3686i	0.309564	−	0.952739i	0.977935	−	0.208911i	$-0.0669918\pi$
$710$		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	−0.251010	−	0.967984i	$-0.580763\pi$
$719$	15.8748	−	11.5337i	0.592032	−	0.430136i	0.843042	+	0.537848i	$0.180763\pi$
$720$		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	$-0.353306\pi$
$727$	23.9815			0.889424			0.444712	+	0.895674i	$0.353306\pi$
$728$		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	−0.792921	−	0.609325i	$-0.791441\pi$
$733$	−12.4119	+	9.01779i	−0.458445	+	0.333080i	0.334476	+	0.942404i	$0.391441\pi$
$734$		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	$-0.707761\pi$
$743$	9.56687	−	29.4438i	0.350974	−	1.08019i	0.958307	−	0.285740i	$-0.0922395\pi$
$744$		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	0.290027	−	0.957018i	$-0.406336\pi$
$751$	−14.5388	−	10.5630i	−0.530528	−	0.385451i	−0.820555	+	0.571567i	$0.806336\pi$
$752$		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	0.834063	−	0.551669i	$-0.186009\pi$
$757$	−4.53896	−	13.9695i	−0.164971	−	0.507729i	−0.999034	+	0.0439400i	$0.986009\pi$
$758$		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	0.730480	−	0.682934i	$-0.239297\pi$
$773$	8.52718	+	6.19536i	0.306701	+	0.222832i	−0.423778	+	0.905766i	$0.639297\pi$
$774$		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	−0.999508	−	0.0313641i	$-0.990015\pi$
$797$	−4.86857	+	14.9839i	−0.172454	+	0.530758i	0.827054	+	0.562122i	$0.190015\pi$
$798$		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	−0.669667	−	0.742661i	$-0.733563\pi$
$821$	−4.87943	+	3.54511i	−0.170293	+	0.123725i	0.499374	+	0.866386i	$0.333563\pi$
$822$		0			0
$823$	15.4682	+	47.6063i	0.539188	+	1.65945i	0.734422	+	0.678694i	$0.237454\pi$
$823$	15.4682	+	47.6063i	0.539188	+	1.65945i	−0.195234	+	0.980757i	$0.562546\pi$
$824$		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	−0.661403	−	0.750031i	$-0.730039\pi$
$829$	−4.38986	+	3.18942i	−0.152466	+	0.110773i	0.508937	+	0.860804i	$0.330039\pi$
$830$		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	0.985510	−	0.169619i	$-0.0542538\pi$
$839$	32.6943	+	23.7538i	1.12873	+	0.820071i	0.143222	+	0.989691i	$0.454254\pi$
$840$		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	$-0.764982\pi$
$853$	7.42894	−	22.8639i	0.254362	−	0.782846i	0.993955	−	0.109791i	$-0.0350182\pi$
$854$		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	−0.993674	−	0.112302i	$-0.964178\pi$
$863$	−3.63584	+	11.1900i	−0.123765	+	0.380910i	0.869909	+	0.493213i	$0.164178\pi$
$864$		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	−0.145708	−	0.989328i	$-0.546546\pi$
$877$	−33.5126	−	24.3483i	−1.13164	−	0.822185i	−0.985933	+	0.167142i	$0.946546\pi$
$878$		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	−0.324524	−	0.945877i	$-0.605204\pi$
$887$	14.1400	−	10.2733i	0.474776	−	0.344945i	0.799300	+	0.600933i	$0.205204\pi$
$888$		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	0.998211	−	0.0597831i	$-0.0190409\pi$
$911$	4.69348	+	14.4450i	0.155502	+	0.478585i	−0.842710	+	0.538368i	$0.819041\pi$
$912$		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	$-0.657517\pi$
$919$	12.9316	−	39.7994i	0.426575	−	1.31286i	0.901478	−	0.432824i	$-0.142483\pi$
$920$		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	$0.508862\pi$
$941$	−18.1868	+	55.9733i	−0.592874	+	1.82468i	−0.565036	+	0.825066i	$0.691138\pi$
$942$		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	$-0.743922\pi$
$967$	−43.1296			−1.38695			−0.693477	+	0.720479i	$0.743922\pi$
$968$		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	−0.998451	−	0.0556406i	$-0.982280\pi$
$983$	−39.3187	+	28.5667i	−1.25407	+	0.911136i	−0.255621	+	0.966777i	$0.582280\pi$
$984$		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	$-0.566617\pi$
$991$	−13.0806			−0.415518			−0.207759	+	0.978180i	$0.566617\pi$
$992$		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	−0.122668	−	0.992448i	$-0.539145\pi$
$997$	24.7329	−	17.9695i	0.783299	−	0.569100i	0.905967	+	0.423348i	$0.139145\pi$
$998$		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	704.2.m.m.577.1		12
4.3	odd	2		704.2.m.n.577.3		12
8.3	odd	2		352.2.m.f.225.1	yes	12
8.5	even	2		352.2.m.e.225.3	yes	12
11.3	even	5		7744.2.a.du.1.6		6
11.8	odd	10		7744.2.a.dt.1.6		6
11.9	even	5	inner	704.2.m.m.449.1		12
44.3	odd	10		7744.2.a.dv.1.1		6
44.19	even	10		7744.2.a.dw.1.1		6
44.31	odd	10		704.2.m.n.449.3		12
88.3	odd	10		3872.2.a.bn.1.6		6
88.19	even	10		3872.2.a.bo.1.6		6
88.53	even	10		352.2.m.e.97.3	✓	12
88.69	even	10		3872.2.a.bq.1.1		6
88.75	odd	10		352.2.m.f.97.1	yes	12
88.85	odd	10		3872.2.a.bp.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
352.2.m.e.97.3	✓	12	88.53	even	10
352.2.m.e.225.3	yes	12	8.5	even	2
352.2.m.f.97.1	yes	12	88.75	odd	10
352.2.m.f.225.1	yes	12	8.3	odd	2
704.2.m.m.449.1		12	11.9	even	5	inner
704.2.m.m.577.1		12	1.1	even	1	trivial
704.2.m.n.449.3		12	44.31	odd	10
704.2.m.n.577.3		12	4.3	odd	2
3872.2.a.bn.1.6		6	88.3	odd	10
3872.2.a.bo.1.6		6	88.19	even	10
3872.2.a.bp.1.1		6	88.85	odd	10
3872.2.a.bq.1.1		6	88.69	even	10
7744.2.a.dt.1.6		6	11.8	odd	10
7744.2.a.du.1.6		6	11.3	even	5
7744.2.a.dv.1.1		6	44.3	odd	10
7744.2.a.dw.1.1		6	44.19	even	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:	\( N \)	\(=\)	\( 704 = 2^{6} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	704.m (of order \(5\), degree \(4\), not 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

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