LMFDB - Embedded newform 704.2.s.d.607.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [704,2,Mod(95,704)]

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([5, 5, 7]))

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

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

chi := DirichletCharacter("704.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 704 = 2^{6} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	704.s (of order $10$, 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:	$5.62146830230$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			607.1
Root			$-0.951057 - 0.309017i$ of defining polynomial
Character	$\chi$	$=$	704.607
Dual form			704.2.s.d.479.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.11803 - 1.53884i) q^{3} +(-1.17557 + 0.381966i) q^{5} +(-3.07768 - 2.23607i) q^{7} +(1.19098 - 3.66547i) q^{9} +(-2.80902 - 1.76336i) q^{11} +(-1.90211 + 2.61803i) q^{15} +(3.35410 - 1.08981i) q^{17} +(-2.07295 - 2.85317i) q^{19} -9.95959 q^{21} -6.00000i q^{23} +(-2.80902 + 2.04087i) q^{25} +(-0.690983 - 2.12663i) q^{27} +(-4.25325 - 3.09017i) q^{29} +(6.88191 + 2.23607i) q^{31} +(-8.66312 + 0.587785i) q^{33} +(4.47214 + 1.45309i) q^{35} +(2.17963 - 3.00000i) q^{37} +(3.35410 + 4.61653i) q^{41} -12.7598i q^{43} +4.76393i q^{45} +(5.70634 + 7.85410i) q^{47} +(2.30902 + 7.10642i) q^{49} +(5.42705 - 7.46969i) q^{51} +(-3.07768 - 1.00000i) q^{53} +(3.97574 + 1.00000i) q^{55} +(-8.78115 - 2.85317i) q^{57} +(8.39919 + 6.10237i) q^{59} +(3.52671 + 10.8541i) q^{61} +(-11.8617 + 8.61803i) q^{63} -14.5623 q^{67} +(-9.23305 - 12.7082i) q^{69} +(11.4127 - 3.70820i) q^{71} +(-0.590170 + 0.812299i) q^{73} +(-2.80902 + 8.64527i) q^{75} +(4.70228 + 11.7082i) q^{77} +(1.45309 - 4.47214i) q^{79} +(4.61803 + 3.35520i) q^{81} +(-0.427051 + 0.138757i) q^{83} +(-3.52671 + 2.56231i) q^{85} -13.7638 q^{87} +1.85410 q^{89} +(18.0171 - 5.85410i) q^{93} +(3.52671 + 2.56231i) q^{95} +(2.57295 - 7.91872i) q^{97} +(-9.80902 + 8.19624i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{3} + 14 q^{9} - 18 q^{11} - 30 q^{19} - 18 q^{25} - 10 q^{27} - 38 q^{33} + 14 q^{49} + 30 q^{51} - 30 q^{57} + 18 q^{59} - 36 q^{67} + 40 q^{73} - 18 q^{75} + 28 q^{81} + 10 q^{83} - 12 q^{89}+ \cdots - 74 q^{99}+O(q^{100}) $ 8 * q + 8 * q^3 + 14 * q^9 - 18 * q^11 - 30 * q^19 - 18 * q^25 - 10 * q^27 - 38 * q^33 + 14 * q^49 + 30 * q^51 - 30 * q^57 + 18 * q^59 - 36 * q^67 + 40 * q^73 - 18 * q^75 + 28 * q^81 + 10 * q^83 - 12 * q^89 + 34 * q^97 - 74 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/704\mathbb{Z}\right)^\times$.

$n$	$133$	$321$	$639$
$\chi(n)$	$-1$	$e\left(\frac{1}{10}\right)$	$-1$

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
$3$	2.11803	−	1.53884i	1.22285	−	0.888451i	0.226514	−	0.974008i	$-0.427267\pi$
$3$	2.11803	−	1.53884i	1.22285	−	0.888451i	0.996333	+	0.0855571i	$0.0272670\pi$
$4$		0			0
$5$	−1.17557	+	0.381966i	−0.525731	+	0.170820i	−0.559845	−	0.828598i	$-0.689139\pi$
$5$	−1.17557	+	0.381966i	−0.525731	+	0.170820i	0.0341136	+	0.999418i	$0.489139\pi$
$6$		0			0
$7$	−3.07768	−	2.23607i	−1.16326	−	0.845154i	−0.173069	−	0.984910i	$-0.555368\pi$
$7$	−3.07768	−	2.23607i	−1.16326	−	0.845154i	−0.990186	+	0.139755i	$0.955368\pi$
$8$		0			0
$9$	1.19098	−	3.66547i	0.396994	−	1.22182i
$10$		0			0
$11$	−2.80902	−	1.76336i	−0.846950	−	0.531672i
$11$	−2.80902	−	1.76336i	−0.846950	−	0.531672i
$12$		0			0
$13$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$13$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$14$		0			0
$15$	−1.90211	+	2.61803i	−0.491123	+	0.675973i
$16$		0			0
$17$	3.35410	−	1.08981i	0.813489	−	0.264319i	0.127414	−	0.991850i	$-0.459332\pi$
$17$	3.35410	−	1.08981i	0.813489	−	0.264319i	0.686075	+	0.727531i	$0.259332\pi$
$18$		0			0
$19$	−2.07295	−	2.85317i	−0.475567	−	0.654562i	0.502078	−	0.864822i	$-0.332569\pi$
$19$	−2.07295	−	2.85317i	−0.475567	−	0.654562i	−0.977645	+	0.210260i	$0.932569\pi$
$20$		0			0
$21$	−9.95959			−2.17336
$22$		0			0
$23$		−	6.00000i		−	1.25109i	−0.780189	−	0.625543i	$-0.784877\pi$
$23$		−	6.00000i		−	1.25109i	0.780189	−	0.625543i	$-0.215123\pi$
$24$		0			0
$25$	−2.80902	+	2.04087i	−0.561803	+	0.408174i
$26$		0			0
$27$	−0.690983	−	2.12663i	−0.132980	−	0.409270i
$28$		0			0
$29$	−4.25325	−	3.09017i	−0.789809	−	0.573830i	0.118097	−	0.993002i	$-0.462320\pi$
$29$	−4.25325	−	3.09017i	−0.789809	−	0.573830i	−0.907907	+	0.419172i	$0.862320\pi$
$30$		0			0
$31$	6.88191	+	2.23607i	1.23603	+	0.401610i	0.852894	−	0.522083i	$-0.174845\pi$
$31$	6.88191	+	2.23607i	1.23603	+	0.401610i	0.383133	+	0.923693i	$0.374845\pi$
$32$		0			0
$33$	−8.66312	+	0.587785i	−1.50806	+	0.102320i
$34$		0			0
$35$	4.47214	+	1.45309i	0.755929	+	0.245616i
$36$		0			0
$37$	2.17963	−	3.00000i	0.358329	−	0.493197i	−0.591354	−	0.806412i	$-0.701406\pi$
$37$	2.17963	−	3.00000i	0.358329	−	0.493197i	0.949682	+	0.313215i	$0.101406\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.35410	+	4.61653i	0.523823	+	0.720980i	0.986173	−	0.165717i	$-0.0529938\pi$
$41$	3.35410	+	4.61653i	0.523823	+	0.720980i	−0.462351	+	0.886697i	$0.652994\pi$
$42$		0			0
$43$		−	12.7598i		−	1.94585i	−0.231131	−	0.972923i	$-0.574242\pi$
$43$		−	12.7598i		−	1.94585i	0.231131	−	0.972923i	$-0.425758\pi$
$44$		0			0
$45$			4.76393i			0.710165i
$46$		0			0
$47$	5.70634	+	7.85410i	0.832355	+	1.14564i	0.987480	+	0.157744i	$0.0504220\pi$
$47$	5.70634	+	7.85410i	0.832355	+	1.14564i	−0.155125	+	0.987895i	$0.549578\pi$
$48$		0			0
$49$	2.30902	+	7.10642i	0.329860	+	1.01520i
$50$		0			0
$51$	5.42705	−	7.46969i	0.759939	−	1.04597i
$52$		0			0
$53$	−3.07768	−	1.00000i	−0.422752	−	0.137361i	0.0899119	−	0.995950i	$-0.471341\pi$
$53$	−3.07768	−	1.00000i	−0.422752	−	0.137361i	−0.512664	+	0.858589i	$0.671341\pi$
$54$		0			0
$55$	3.97574	+	1.00000i	0.536089	+	0.134840i
$56$		0			0
$57$	−8.78115	−	2.85317i	−1.16309	−	0.377912i
$58$		0			0
$59$	8.39919	+	6.10237i	1.09348	+	0.794460i	0.979984	−	0.199078i	$-0.0637947\pi$
$59$	8.39919	+	6.10237i	1.09348	+	0.794460i	0.113497	+	0.993538i	$0.463795\pi$
$60$		0			0
$61$	3.52671	+	10.8541i	0.451549	+	1.38973i	0.875139	+	0.483871i	$0.160770\pi$
$61$	3.52671	+	10.8541i	0.451549	+	1.38973i	−0.423590	+	0.905854i	$0.639230\pi$
$62$		0			0
$63$	−11.8617	+	8.61803i	−1.49443	+	1.08577i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−14.5623			−1.77907			−0.889534	−	0.456868i	$-0.848971\pi$
$67$	−14.5623			−1.77907			−0.889534	+	0.456868i	$0.848971\pi$
$68$		0			0
$69$	−9.23305	−	12.7082i	−1.11153	−	1.52989i
$70$		0			0
$71$	11.4127	−	3.70820i	1.35444	−	0.440083i	0.460254	−	0.887787i	$-0.347758\pi$
$71$	11.4127	−	3.70820i	1.35444	−	0.440083i	0.894182	+	0.447704i	$0.147758\pi$
$72$		0			0
$73$	−0.590170	+	0.812299i	−0.0690742	+	0.0950724i	−0.842156	−	0.539233i	$-0.818714\pi$
$73$	−0.590170	+	0.812299i	−0.0690742	+	0.0950724i	0.773082	+	0.634306i	$0.218714\pi$
$74$		0			0
$75$	−2.80902	+	8.64527i	−0.324357	+	0.998269i
$76$		0			0
$77$	4.70228	+	11.7082i	0.535875	+	1.33427i
$78$		0			0
$79$	1.45309	−	4.47214i	0.163485	−	0.503155i	−0.835437	−	0.549587i	$-0.814785\pi$
$79$	1.45309	−	4.47214i	0.163485	−	0.503155i	0.998921	+	0.0464322i	$0.0147852\pi$
$80$		0			0
$81$	4.61803	+	3.35520i	0.513115	+	0.372800i
$82$		0			0
$83$	−0.427051	+	0.138757i	−0.0468749	+	0.0152306i	−0.332361	−	0.943152i	$-0.607845\pi$
$83$	−0.427051	+	0.138757i	−0.0468749	+	0.0152306i	0.285486	+	0.958383i	$0.407845\pi$
$84$		0			0
$85$	−3.52671	+	2.56231i	−0.382526	+	0.277921i
$86$		0			0
$87$	−13.7638			−1.47564
$88$		0			0
$89$	1.85410			0.196534			0.0982672	−	0.995160i	$-0.468670\pi$
$89$	1.85410			0.196534			0.0982672	+	0.995160i	$0.468670\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	18.0171	−	5.85410i	1.86828	−	0.607042i
$94$		0			0
$95$	3.52671	+	2.56231i	0.361833	+	0.262887i
$96$		0			0
$97$	2.57295	−	7.91872i	0.261243	−	0.804024i	−0.731292	−	0.682065i	$-0.761082\pi$
$97$	2.57295	−	7.91872i	0.261243	−	0.804024i	0.992535	−	0.121960i	$-0.0389178\pi$
$98$		0			0
$99$	−9.80902	+	8.19624i	−0.985843	+	0.823753i
$100$		0			0
$101$	5.42882	−	16.7082i	0.540188	−	1.66253i	−0.191975	−	0.981400i	$-0.561489\pi$
$101$	5.42882	−	16.7082i	0.540188	−	1.66253i	0.732164	−	0.681129i	$-0.238511\pi$
$102$		0			0
$103$	0.726543	−	1.00000i	0.0715884	−	0.0985329i	−0.771721	−	0.635961i	$-0.780604\pi$
$103$	0.726543	−	1.00000i	0.0715884	−	0.0985329i	0.843310	+	0.537428i	$0.180604\pi$
$104$		0			0
$105$	11.7082	−	3.80423i	1.14260	−	0.371254i
$106$		0			0
$107$	2.50000	+	3.44095i	0.241684	+	0.332650i	0.912577	−	0.408904i	$-0.134089\pi$
$107$	2.50000	+	3.44095i	0.241684	+	0.332650i	−0.670893	+	0.741554i	$0.734089\pi$
$108$		0			0
$109$	−11.4127			−1.09314			−0.546568	−	0.837415i	$-0.684066\pi$
$109$	−11.4127			−1.09314			−0.546568	+	0.837415i	$0.684066\pi$
$110$		0			0
$111$		−	9.70820i		−	0.921462i
$112$		0			0
$113$	3.92705	−	2.85317i	0.369426	−	0.268404i	−0.387547	−	0.921850i	$-0.626677\pi$
$113$	3.92705	−	2.85317i	0.369426	−	0.268404i	0.756973	+	0.653446i	$0.226677\pi$
$114$		0			0
$115$	2.29180	+	7.05342i	0.213711	+	0.657735i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−12.7598	−	4.14590i	−1.16969	−	0.380054i
$120$		0			0
$121$	4.78115	+	9.90659i	0.434650	+	0.900599i
$122$		0			0
$123$	14.2082	+	4.61653i	1.28111	+	0.416258i
$124$		0			0
$125$	6.15537	−	8.47214i	0.550553	−	0.757771i
$126$		0			0
$127$	−5.70634	−	17.5623i	−0.506356	−	1.55840i	−0.798479	−	0.602022i	$-0.794362\pi$
$127$	−5.70634	−	17.5623i	−0.506356	−	1.55840i	0.292124	−	0.956381i	$-0.405638\pi$
$128$		0			0
$129$	−19.6353	−	27.0256i	−1.72879	−	2.37947i
$130$		0			0
$131$		−	6.43288i		−	0.562043i	−0.959701	−	0.281022i	$-0.909327\pi$
$131$		−	6.43288i		−	0.562043i	0.959701	−	0.281022i	$-0.0906733\pi$
$132$		0			0
$133$			13.4164i			1.16335i
$134$		0			0
$135$	1.62460	+	2.23607i	0.139823	+	0.192450i
$136$		0			0
$137$	−1.71885	−	5.29007i	−0.146851	−	0.451961i	0.850393	−	0.526147i	$-0.176364\pi$
$137$	−1.71885	−	5.29007i	−0.146851	−	0.451961i	−0.997244	+	0.0741865i	$0.976364\pi$
$138$		0			0
$139$	−2.56231	+	3.52671i	−0.217332	+	0.299132i	−0.903737	−	0.428087i	$-0.859188\pi$
$139$	−2.56231	+	3.52671i	−0.217332	+	0.299132i	0.686405	+	0.727219i	$0.259188\pi$
$140$		0			0
$141$	24.1724	+	7.85410i	2.03569	+	0.661435i
$142$		0			0
$143$		0			0
$144$		0			0
$145$	6.18034	+	2.00811i	0.513249	+	0.166765i
$146$		0			0
$147$	15.8262	+	11.4984i	1.30533	+	0.948375i
$148$		0			0
$149$	2.62866	+	8.09017i	0.215348	+	0.662773i	0.999129	+	0.0417351i	$0.0132885\pi$
$149$	2.62866	+	8.09017i	0.215348	+	0.662773i	−0.783781	+	0.621037i	$0.786711\pi$
$150$		0			0
$151$	−7.33094	+	5.32624i	−0.596583	+	0.433443i	−0.844664	−	0.535296i	$-0.820200\pi$
$151$	−7.33094	+	5.32624i	−0.596583	+	0.433443i	0.248081	+	0.968739i	$0.420200\pi$
$152$		0			0
$153$		−	13.5923i		−	1.09887i
$154$		0			0
$155$	−8.94427			−0.718421
$156$		0			0
$157$	10.5801	+	14.5623i	0.844387	+	1.16220i	0.985072	+	0.172144i	$0.0550695\pi$
$157$	10.5801	+	14.5623i	0.844387	+	1.16220i	−0.140685	+	0.990054i	$0.544931\pi$
$158$		0			0
$159$	−8.05748	+	2.61803i	−0.639000	+	0.207624i
$160$		0			0
$161$	−13.4164	+	18.4661i	−1.05736	+	1.45533i
$162$		0			0
$163$	−5.20820	+	16.0292i	−0.407938	+	1.25550i	0.510479	+	0.859890i	$0.329468\pi$
$163$	−5.20820	+	16.0292i	−0.407938	+	1.25550i	−0.918417	+	0.395614i	$0.870532\pi$
$164$		0			0
$165$	9.95959	−	4.00000i	0.775353	−	0.311400i
$166$		0			0
$167$	−1.34708	+	4.14590i	−0.104240	+	0.320819i	−0.989551	−	0.144180i	$-0.953945\pi$
$167$	−1.34708	+	4.14590i	−0.104240	+	0.320819i	0.885311	+	0.464999i	$0.153945\pi$
$168$		0			0
$169$	10.5172	+	7.64121i	0.809017	+	0.587785i
$170$		0			0
$171$	−12.9271	+	4.20025i	−0.988556	+	0.321201i
$172$		0			0
$173$	17.2905	−	12.5623i	1.31457	−	0.955094i	0.314592	−	0.949227i	$-0.398132\pi$
$173$	17.2905	−	12.5623i	1.31457	−	0.955094i	0.999983	−	0.00586742i	$-0.00186767\pi$
$174$		0			0
$175$	13.2088			0.998491
$176$		0			0
$177$	27.1803			2.04300
$178$		0			0
$179$	7.92705	−	5.75934i	0.592496	−	0.430473i	−0.250712	−	0.968062i	$-0.580665\pi$
$179$	7.92705	−	5.75934i	0.592496	−	0.430473i	0.843207	+	0.537589i	$0.180665\pi$
$180$		0			0
$181$	−11.4127	+	3.70820i	−0.848298	+	0.275629i	−0.700733	−	0.713424i	$-0.747144\pi$
$181$	−11.4127	+	3.70820i	−0.848298	+	0.275629i	−0.147565	+	0.989052i	$0.547144\pi$
$182$		0			0
$183$	24.1724	+	17.5623i	1.78688	+	1.29824i
$184$		0			0
$185$	−1.41641	+	4.35926i	−0.104136	+	0.320499i
$186$		0			0
$187$	−11.3435	−	2.85317i	−0.829516	−	0.208644i
$188$		0			0
$189$	−2.62866	+	8.09017i	−0.191207	+	0.588473i
$190$		0			0
$191$	12.7598	−	17.5623i	0.923264	−	1.27076i	−0.0391657	−	0.999233i	$-0.512470\pi$
$191$	12.7598	−	17.5623i	0.923264	−	1.27076i	0.962430	−	0.271531i	$-0.0875300\pi$
$192$		0			0
$193$	−7.23607	+	2.35114i	−0.520864	+	0.169239i	−0.557637	−	0.830085i	$-0.688292\pi$
$193$	−7.23607	+	2.35114i	−0.520864	+	0.169239i	0.0367736	+	0.999324i	$0.488292\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−12.3107			−0.877103			−0.438552	−	0.898706i	$-0.644508\pi$
$197$	−12.3107			−0.877103			−0.438552	+	0.898706i	$0.644508\pi$
$198$		0			0
$199$			5.52786i			0.391860i	0.980618	+	0.195930i	$0.0627725\pi$
$199$			5.52786i			0.391860i	−0.980618	+	0.195930i	$0.937227\pi$
$200$		0			0
$201$	−30.8435	+	22.4091i	−2.17553	+	1.58061i
$202$		0			0
$203$	6.18034	+	19.0211i	0.433775	+	1.33502i
$204$		0			0
$205$	−5.70634	−	4.14590i	−0.398548	−	0.289562i
$206$		0			0
$207$	−21.9928	−	7.14590i	−1.52861	−	0.496674i
$208$		0			0
$209$	0.791796	+	11.6699i	0.0547697	+	0.807227i
$210$		0			0
$211$	−1.28115	−	0.416272i	−0.0881982	−	0.0286573i	0.264586	−	0.964362i	$-0.414765\pi$
$211$	−1.28115	−	0.416272i	−0.0881982	−	0.0286573i	−0.352784	+	0.935705i	$0.614765\pi$
$212$		0			0
$213$	18.4661	−	25.4164i	1.26528	−	1.74150i
$214$		0			0
$215$	4.87380	+	15.0000i	0.332390	+	1.02299i
$216$		0			0
$217$	−16.1803	−	22.2703i	−1.09839	−	1.51181i
$218$		0			0
$219$			2.62866i			0.177628i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	2.73466	+	3.76393i	0.183126	+	0.252052i	0.890704	−	0.454584i	$-0.150212\pi$
$223$	2.73466	+	3.76393i	0.183126	+	0.252052i	−0.707578	+	0.706636i	$0.750212\pi$
$224$		0			0
$225$	4.13525	+	12.7270i	0.275684	+	0.848467i
$226$		0			0
$227$	−3.12868	+	4.30625i	−0.207658	+	0.285816i	−0.900124	−	0.435634i	$-0.856524\pi$
$227$	−3.12868	+	4.30625i	−0.207658	+	0.285816i	0.692466	+	0.721450i	$0.256524\pi$
$228$		0			0
$229$	−7.05342	−	2.29180i	−0.466103	−	0.151446i	0.0665439	−	0.997783i	$-0.478803\pi$
$229$	−7.05342	−	2.29180i	−0.466103	−	0.151446i	−0.532647	+	0.846337i	$0.678803\pi$
$230$		0			0
$231$	27.9767	+	17.5623i	1.84073	+	1.15551i
$232$		0			0
$233$	18.8435	+	6.12261i	1.23448	+	0.401106i	0.852334	−	0.522998i	$-0.175186\pi$
$233$	18.8435	+	6.12261i	1.23448	+	0.401106i	0.382142	+	0.924104i	$0.375186\pi$
$234$		0			0
$235$	−9.70820	−	7.05342i	−0.633293	−	0.460115i
$236$		0			0
$237$	−3.80423	−	11.7082i	−0.247111	−	0.760530i
$238$		0			0
$239$	−11.4127	+	8.29180i	−0.738225	+	0.536352i	−0.892155	−	0.451730i	$-0.850807\pi$
$239$	−11.4127	+	8.29180i	−0.738225	+	0.536352i	0.153930	+	0.988082i	$0.450807\pi$
$240$		0			0
$241$			2.97168i			0.191423i	0.995409	+	0.0957114i	$0.0305126\pi$
$241$			2.97168i			0.191423i	−0.995409	+	0.0957114i	$0.969487\pi$
$242$		0			0
$243$	21.6525			1.38901
$244$		0			0
$245$	−5.42882	−	7.47214i	−0.346835	−	0.477377i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−0.690983	+	0.951057i	−0.0437893	+	0.0602708i
$250$		0			0
$251$	4.47214	−	13.7638i	0.282279	−	0.868765i	−0.704922	−	0.709284i	$-0.749018\pi$
$251$	4.47214	−	13.7638i	0.282279	−	0.868765i	0.987201	−	0.159480i	$-0.0509818\pi$
$252$		0			0
$253$	−10.5801	+	16.8541i	−0.665167	+	1.05961i
$254$		0			0
$255$	−3.52671	+	10.8541i	−0.220851	+	0.679710i
$256$		0			0
$257$	−17.2082	−	12.5025i	−1.07342	−	0.779884i	−0.0968947	−	0.995295i	$-0.530891\pi$
$257$	−17.2082	−	12.5025i	−1.07342	−	0.779884i	−0.976524	+	0.215411i	$0.930891\pi$
$258$		0			0
$259$	−13.4164	+	4.35926i	−0.833655	+	0.270871i
$260$		0			0
$261$	−16.3925	+	11.9098i	−1.01467	+	0.737200i
$262$		0			0
$263$	−15.7719			−0.972539			−0.486270	−	0.873809i	$-0.661643\pi$
$263$	−15.7719			−0.972539			−0.486270	+	0.873809i	$0.661643\pi$
$264$		0			0
$265$	4.00000			0.245718
$266$		0			0
$267$	3.92705	−	2.85317i	0.240332	−	0.174611i
$268$		0			0
$269$	10.6861	−	3.47214i	0.651545	−	0.211700i	0.0354499	−	0.999371i	$-0.488714\pi$
$269$	10.6861	−	3.47214i	0.651545	−	0.211700i	0.616095	+	0.787672i	$0.288714\pi$
$270$		0			0
$271$	12.7598	+	9.27051i	0.775100	+	0.563143i	0.903505	−	0.428579i	$-0.140985\pi$
$271$	12.7598	+	9.27051i	0.775100	+	0.563143i	−0.128404	+	0.991722i	$0.540985\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	11.4894	−	0.779543i	0.692834	−	0.0470082i
$276$		0			0
$277$	2.17963	−	6.70820i	0.130961	−	0.403057i	−0.863979	−	0.503528i	$-0.832035\pi$
$277$	2.17963	−	6.70820i	0.130961	−	0.403057i	0.994940	+	0.100471i	$0.0320350\pi$
$278$		0			0
$279$	16.3925	−	22.5623i	0.981392	−	1.35077i
$280$		0			0
$281$	5.42705	−	1.76336i	0.323751	−	0.105193i	−0.142633	−	0.989776i	$-0.545557\pi$
$281$	5.42705	−	1.76336i	0.323751	−	0.105193i	0.466383	+	0.884583i	$0.345557\pi$
$282$		0			0
$283$	−2.56231	−	3.52671i	−0.152313	−	0.209641i	0.726041	−	0.687651i	$-0.241358\pi$
$283$	−2.56231	−	3.52671i	−0.152313	−	0.209641i	−0.878354	+	0.478010i	$0.841358\pi$
$284$		0			0
$285$	11.4127			0.676029
$286$		0			0
$287$		−	21.7082i		−	1.28139i
$288$		0			0
$289$	−3.69098	+	2.68166i	−0.217117	+	0.157744i
$290$		0			0
$291$	−6.73607	−	20.7315i	−0.394875	−	1.21530i
$292$		0			0
$293$	17.2905	+	12.5623i	1.01012	+	0.733898i	0.964235	−	0.265049i	$-0.0853881\pi$
$293$	17.2905	+	12.5623i	1.01012	+	0.733898i	0.0458886	+	0.998947i	$0.485388\pi$
$294$		0			0
$295$	−12.2047	−	3.96556i	−0.710587	−	0.230884i
$296$		0			0
$297$	−1.80902	+	7.19218i	−0.104970	+	0.417333i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−28.5317	+	39.2705i	−1.64454	+	2.26351i
$302$		0			0
$303$	−14.2128	−	43.7426i	−0.816507	−	2.51295i
$304$		0			0
$305$	−8.29180	−	11.4127i	−0.474787	−	0.653488i
$306$		0			0
$307$		−	21.4783i		−	1.22583i	−0.790149	−	0.612915i	$-0.789997\pi$
$307$		−	21.4783i		−	1.22583i	0.790149	−	0.612915i	$-0.210003\pi$
$308$		0			0
$309$		−	3.23607i		−	0.184093i
$310$		0			0
$311$	2.17963	+	3.00000i	0.123595	+	0.170114i	0.866331	−	0.499470i	$-0.166472\pi$
$311$	2.17963	+	3.00000i	0.123595	+	0.170114i	−0.742736	+	0.669585i	$0.766472\pi$
$312$		0			0
$313$	0.208204	+	0.640786i	0.0117684	+	0.0362194i	0.956768	−	0.290851i	$-0.0939385\pi$
$313$	0.208204	+	0.640786i	0.0117684	+	0.0362194i	−0.945000	+	0.327071i	$0.893938\pi$
$314$		0			0
$315$	10.6525	−	14.6619i	0.600199	−	0.826103i
$316$		0			0
$317$	−8.61251	−	2.79837i	−0.483727	−	0.157172i	0.0569940	−	0.998375i	$-0.481848\pi$
$317$	−8.61251	−	2.79837i	−0.483727	−	0.157172i	−0.540721	+	0.841202i	$0.681848\pi$
$318$		0			0
$319$	6.49839	+	16.1803i	0.363840	+	0.905925i
$320$		0			0
$321$	10.5902	+	3.44095i	0.591086	+	0.192055i
$322$		0			0
$323$	−10.0623	−	7.31069i	−0.559882	−	0.406778i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−24.1724	+	17.5623i	−1.33674	+	0.971198i
$328$		0			0
$329$		−	36.9322i		−	2.03614i
$330$		0			0
$331$	−16.1459			−0.887459			−0.443729	−	0.896161i	$-0.646345\pi$
$331$	−16.1459			−0.887459			−0.443729	+	0.896161i	$0.646345\pi$
$332$		0			0
$333$	−8.40051	−	11.5623i	−0.460345	−	0.633610i
$334$		0			0
$335$	17.1190	−	5.56231i	0.935312	−	0.303901i
$336$		0			0
$337$	6.21885	−	8.55951i	0.338762	−	0.466266i	−0.605317	−	0.795984i	$-0.706954\pi$
$337$	6.21885	−	8.55951i	0.338762	−	0.466266i	0.944079	+	0.329718i	$0.106954\pi$
$338$		0			0
$339$	3.92705	−	12.0862i	0.213288	−	0.656433i
$340$		0			0
$341$	−15.3884	−	18.4164i	−0.833330	−	0.997304i
$342$		0			0
$343$	0.555029	−	1.70820i	0.0299688	−	0.0922343i
$344$		0			0
$345$	15.7082	+	11.4127i	0.845701	+	0.614438i
$346$		0			0
$347$	26.2426	−	8.52675i	1.40878	−	0.457740i	0.496760	−	0.867888i	$-0.334523\pi$
$347$	26.2426	−	8.52675i	1.40878	−	0.457740i	0.912019	+	0.410148i	$0.134523\pi$
$348$		0			0
$349$	−9.23305	+	6.70820i	−0.494234	+	0.359082i	−0.806810	−	0.590811i	$-0.798808\pi$
$349$	−9.23305	+	6.70820i	−0.494234	+	0.359082i	0.312576	+	0.949893i	$0.398808\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	16.8541			0.897053			0.448527	−	0.893769i	$-0.351949\pi$
$353$	16.8541			0.897053			0.448527	+	0.893769i	$0.351949\pi$
$354$		0			0
$355$	−12.0000	+	8.71851i	−0.636894	+	0.462730i
$356$		0			0
$357$	−33.4055	+	10.8541i	−1.76801	+	0.574460i
$358$		0			0
$359$	−26.3521	−	19.1459i	−1.39081	−	1.01048i	−0.995776	−	0.0918149i	$-0.970733\pi$
$359$	−26.3521	−	19.1459i	−1.39081	−	1.01048i	−0.395033	−	0.918667i	$-0.629267\pi$
$360$		0			0
$361$	2.02786	−	6.24112i	0.106730	−	0.328480i
$362$		0			0
$363$	25.3713	+	13.6251i	1.33165	+	0.715130i
$364$		0			0
$365$	0.383516	−	1.18034i	0.0200741	−	0.0617818i
$366$		0			0
$367$	−16.5640	+	22.7984i	−0.864633	+	1.19007i	0.115812	+	0.993271i	$0.463053\pi$
$367$	−16.5640	+	22.7984i	−0.864633	+	1.19007i	−0.980445	+	0.196794i	$0.936947\pi$
$368$		0			0
$369$	20.9164	−	6.79615i	1.08886	−	0.353794i
$370$		0			0
$371$	7.23607	+	9.95959i	0.375678	+	0.517076i
$372$		0			0
$373$	27.1846			1.40757			0.703783	−	0.710415i	$-0.251493\pi$
$373$	27.1846			1.40757			0.703783	+	0.710415i	$0.251493\pi$
$374$		0			0
$375$		−	27.4164i		−	1.41578i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−4.71885	−	14.5231i	−0.242391	−	0.746002i	−0.996055	−	0.0887422i	$-0.971715\pi$
$379$	−4.71885	−	14.5231i	−0.242391	−	0.746002i	0.753664	−	0.657260i	$-0.228285\pi$
$380$		0			0
$381$	−39.1118	−	28.4164i	−2.00376	−	1.45582i
$382$		0			0
$383$	−14.9394	−	4.85410i	−0.763367	−	0.248033i	−0.0986440	−	0.995123i	$-0.531451\pi$
$383$	−14.9394	−	4.85410i	−0.763367	−	0.248033i	−0.664723	+	0.747090i	$0.731451\pi$
$384$		0			0
$385$	−10.0000	−	11.9677i	−0.509647	−	0.609931i
$386$		0			0
$387$	−46.7705	−	15.1967i	−2.37748	−	0.772490i
$388$		0			0
$389$	−1.28157	+	1.76393i	−0.0649783	+	0.0894349i	−0.840269	−	0.542169i	$-0.817603\pi$
$389$	−1.28157	+	1.76393i	−0.0649783	+	0.0894349i	0.775291	+	0.631604i	$0.217603\pi$
$390$		0			0
$391$	−6.53888	−	20.1246i	−0.330686	−	1.01775i
$392$		0			0
$393$	−9.89919	−	13.6251i	−0.499348	−	0.687293i
$394$		0			0
$395$			5.81234i			0.292451i
$396$		0			0
$397$		−	18.0000i		−	0.903394i	−0.892171	−	0.451697i	$-0.850819\pi$
$397$		−	18.0000i		−	0.903394i	0.892171	−	0.451697i	$-0.149181\pi$
$398$		0			0
$399$	20.6457	+	28.4164i	1.03358	+	1.42260i
$400$		0			0
$401$	5.42705	+	16.7027i	0.271014	+	0.834095i	0.990247	+	0.139326i	$0.0444936\pi$
$401$	5.42705	+	16.7027i	0.271014	+	0.834095i	−0.719233	+	0.694769i	$0.755506\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−6.71040	−	2.18034i	−0.333442	−	0.108342i
$406$		0			0
$407$	−11.4127	+	4.58359i	−0.565705	+	0.227200i
$408$		0			0
$409$	−30.6525	−	9.95959i	−1.51567	−	0.492470i	−0.571126	−	0.820862i	$-0.693493\pi$
$409$	−30.6525	−	9.95959i	−1.51567	−	0.492470i	−0.944541	+	0.328392i	$0.893493\pi$
$410$		0			0
$411$	−11.7812	−	8.55951i	−0.581121	−	0.422209i
$412$		0			0
$413$	−12.2047	−	37.5623i	−0.600556	−	1.84832i
$414$		0			0
$415$	0.449028	−	0.326238i	0.0220419	−	0.0160144i
$416$		0			0
$417$			11.4127i			0.558881i
$418$		0			0
$419$	16.5066			0.806399			0.403200	−	0.915112i	$-0.367898\pi$
$419$	16.5066			0.806399			0.403200	+	0.915112i	$0.367898\pi$
$420$		0			0
$421$	7.05342	+	9.70820i	0.343763	+	0.473149i	0.945536	−	0.325518i	$-0.105539\pi$
$421$	7.05342	+	9.70820i	0.343763	+	0.473149i	−0.601773	+	0.798667i	$0.705539\pi$
$422$		0			0
$423$	35.5851	−	11.5623i	1.73021	−	0.562179i
$424$		0			0
$425$	−7.19756	+	9.90659i	−0.349133	+	0.480540i
$426$		0			0
$427$	13.4164	−	41.2915i	0.649265	−	1.99823i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−9.23305	+	28.4164i	−0.444740	+	1.36877i	0.438028	+	0.898961i	$0.355677\pi$
$431$	−9.23305	+	28.4164i	−0.444740	+	1.36877i	−0.882768	+	0.469809i	$0.844323\pi$
$432$		0			0
$433$	6.07295	+	4.41226i	0.291847	+	0.212039i	0.724068	−	0.689728i	$-0.242270\pi$
$433$	6.07295	+	4.41226i	0.291847	+	0.212039i	−0.432221	+	0.901768i	$0.642270\pi$
$434$		0			0
$435$	16.1803	−	5.25731i	0.775788	−	0.252069i
$436$		0			0
$437$	−17.1190	+	12.4377i	−0.818914	+	0.594976i
$438$		0			0
$439$	−36.3772			−1.73619			−0.868094	−	0.496400i	$-0.834655\pi$
$439$	−36.3772			−1.73619			−0.868094	+	0.496400i	$0.834655\pi$
$440$		0			0
$441$	28.7984			1.37135
$442$		0			0
$443$	−16.8262	+	12.2250i	−0.799439	+	0.580826i	−0.910749	−	0.412959i	$-0.864495\pi$
$443$	−16.8262	+	12.2250i	−0.799439	+	0.580826i	0.111311	+	0.993786i	$0.464495\pi$
$444$		0			0
$445$	−2.17963	+	0.708204i	−0.103324	+	0.0335721i
$446$		0			0
$447$	18.0171	+	13.0902i	0.852178	+	0.619144i
$448$		0			0
$449$	3.08359	−	9.49032i	0.145524	−	0.447876i	−0.851554	−	0.524266i	$-0.824340\pi$
$449$	3.08359	−	9.49032i	0.145524	−	0.447876i	0.997078	+	0.0763905i	$0.0243396\pi$
$450$		0			0
$451$	−1.28115	−	18.8824i	−0.0603271	−	0.889136i
$452$		0			0
$453$	−7.33094	+	22.5623i	−0.344437	+	1.06007i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	27.7877	−	9.02878i	1.29986	−	0.422349i	0.424324	−	0.905510i	$-0.360512\pi$
$457$	27.7877	−	9.02878i	1.29986	−	0.422349i	0.875531	+	0.483162i	$0.160512\pi$
$458$		0			0
$459$	−4.63525	−	6.37988i	−0.216355	−	0.297787i
$460$		0			0
$461$	7.05342			0.328511			0.164255	−	0.986418i	$-0.447478\pi$
$461$	7.05342			0.328511			0.164255	+	0.986418i	$0.447478\pi$
$462$		0			0
$463$		−	13.2361i		−	0.615132i	−0.951527	−	0.307566i	$-0.900485\pi$
$463$		−	13.2361i		−	0.615132i	0.951527	−	0.307566i	$-0.0995145\pi$
$464$		0			0
$465$	−18.9443	+	13.7638i	−0.878520	+	0.638282i
$466$		0			0
$467$	0.291796	+	0.898056i	0.0135027	+	0.0415571i	0.957581	−	0.288165i	$-0.0930451\pi$
$467$	0.291796	+	0.898056i	0.0135027	+	0.0415571i	−0.944078	+	0.329722i	$0.893045\pi$
$468$		0			0
$469$	44.8182	+	32.5623i	2.06951	+	1.50359i
$470$		0			0
$471$	44.8182	+	14.5623i	2.06511	+	0.670996i
$472$		0			0
$473$	−22.5000	+	35.8424i	−1.03455	+	1.64803i
$474$		0			0
$475$	11.6459	+	3.78398i	0.534350	+	0.173621i
$476$		0			0
$477$	−7.33094	+	10.0902i	−0.335661	+	0.461997i
$478$		0			0
$479$	10.0656	+	30.9787i	0.459909	+	1.41545i	0.865274	+	0.501299i	$0.167144\pi$
$479$	10.0656	+	30.9787i	0.459909	+	1.41545i	−0.405365	+	0.914155i	$0.632856\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$			59.7576i			2.71906i
$484$		0			0
$485$			10.2918i			0.467326i
$486$		0			0
$487$	7.67396	+	10.5623i	0.347741	+	0.478624i	0.946682	−	0.322169i	$-0.104412\pi$
$487$	7.67396	+	10.5623i	0.347741	+	0.478624i	−0.598942	+	0.800793i	$0.704412\pi$
$488$		0			0
$489$	13.6353	+	41.9650i	0.616608	+	1.89772i
$490$		0			0
$491$	−14.2082	+	19.5559i	−0.641207	+	0.882546i	−0.998679	−	0.0513778i	$-0.983639\pi$
$491$	−14.2082	+	19.5559i	−0.641207	+	0.882546i	0.357472	+	0.933924i	$0.383639\pi$
$492$		0			0
$493$	−17.6336	−	5.72949i	−0.794175	−	0.258043i
$494$		0			0
$495$	8.40051	−	13.3820i	0.377575	−	0.601475i
$496$		0			0
$497$	−43.4164	−	14.1068i	−1.94749	−	0.632779i
$498$		0			0
$499$	−19.0623	−	13.8496i	−0.853346	−	0.619992i	0.0727206	−	0.997352i	$-0.476832\pi$
$499$	−19.0623	−	13.8496i	−0.853346	−	0.619992i	−0.926067	+	0.377360i	$0.876832\pi$
$500$		0			0
$501$	3.52671	+	10.8541i	0.157562	+	0.484926i
$502$		0			0
$503$	−9.23305	+	6.70820i	−0.411681	+	0.299104i	−0.774282	−	0.632841i	$-0.781889\pi$
$503$	−9.23305	+	6.70820i	−0.411681	+	0.299104i	0.362601	+	0.931945i	$0.381889\pi$
$504$		0			0
$505$			21.7153i			0.966318i
$506$		0			0
$507$	34.0344			1.51152
$508$		0			0
$509$	20.9232	+	28.7984i	0.927406	+	1.27647i	0.960863	+	0.277025i	$0.0893486\pi$
$509$	20.9232	+	28.7984i	0.927406	+	1.27647i	−0.0334562	+	0.999440i	$0.510651\pi$
$510$		0			0
$511$	3.63271	−	1.18034i	0.160702	−	0.0522152i
$512$		0			0
$513$	−4.63525	+	6.37988i	−0.204652	+	0.281679i
$514$		0			0
$515$	−0.472136	+	1.45309i	−0.0208048	+	0.0640306i
$516$		0			0
$517$	−2.17963	−	32.1246i	−0.0958599	−	1.41284i
$518$		0			0
$519$	17.2905	−	53.2148i	0.758970	−	2.33587i
$520$		0			0
$521$	−19.6353	−	14.2658i	−0.860236	−	0.624998i	0.0677131	−	0.997705i	$-0.478430\pi$
$521$	−19.6353	−	14.2658i	−0.860236	−	0.624998i	−0.927949	+	0.372707i	$0.878430\pi$
$522$		0			0
$523$	−23.4787	+	7.62870i	−1.02665	+	0.333580i	−0.773466	−	0.633838i	$-0.781479\pi$
$523$	−23.4787	+	7.62870i	−1.02665	+	0.333580i	−0.253187	+	0.967417i	$0.581479\pi$
$524$		0			0
$525$	27.9767	−	20.3262i	1.22100	−	0.887110i
$526$		0			0
$527$	25.5195			1.11165
$528$		0			0
$529$	−13.0000			−0.565217
$530$		0			0
$531$	32.3713	−	23.5191i	1.40480	−	1.02064i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−4.25325	−	3.09017i	−0.183884	−	0.133600i
$536$		0			0
$537$	7.92705	−	24.3970i	0.342077	−	1.05281i
$538$		0			0
$539$	6.04508	−	24.0337i	0.260380	−	1.03520i
$540$		0			0
$541$	−10.0656	+	30.9787i	−0.432754	+	1.33188i	0.462617	+	0.886558i	$0.346910\pi$
$541$	−10.0656	+	30.9787i	−0.432754	+	1.33188i	−0.895371	+	0.445321i	$0.853090\pi$
$542$		0			0
$543$	−18.4661	+	25.4164i	−0.792456	+	1.09072i
$544$		0			0
$545$	13.4164	−	4.35926i	0.574696	−	0.186730i
$546$		0			0
$547$	−10.3647	−	14.2658i	−0.443164	−	0.609964i	0.527747	−	0.849402i	$-0.323037\pi$
$547$	−10.3647	−	14.2658i	−0.443164	−	0.609964i	−0.970912	+	0.239438i	$0.923037\pi$
$548$		0			0
$549$	43.9856			1.87726
$550$		0			0
$551$			18.5410i			0.789874i
$552$		0			0
$553$	−14.4721	+	10.5146i	−0.615418	+	0.447127i
$554$		0			0
$555$	3.70820	+	11.4127i	0.157404	+	0.484441i
$556$		0			0
$557$	−10.2371	−	7.43769i	−0.433760	−	0.315145i	0.349390	−	0.936977i	$-0.386389\pi$
$557$	−10.2371	−	7.43769i	−0.433760	−	0.315145i	−0.783151	+	0.621832i	$0.786389\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−28.4164	+	11.4127i	−1.19974	+	0.481844i
$562$		0			0
$563$	22.9894	+	7.46969i	0.968886	+	0.314810i	0.750366	−	0.661022i	$-0.229877\pi$
$563$	22.9894	+	7.46969i	0.968886	+	0.314810i	0.218520	+	0.975833i	$0.429877\pi$
$564$		0			0
$565$	−3.52671	+	4.85410i	−0.148370	+	0.204214i
$566$		0			0
$567$	−6.71040	−	20.6525i	−0.281810	−	0.867322i
$568$		0			0
$569$	3.05166	+	4.20025i	0.127932	+	0.176084i	0.868178	−	0.496252i	$-0.165291\pi$
$569$	3.05166	+	4.20025i	0.127932	+	0.176084i	−0.740246	+	0.672336i	$0.765291\pi$
$570$		0			0
$571$			32.5729i			1.36314i	0.731755	+	0.681568i	$0.238702\pi$
$571$			32.5729i			1.36314i	−0.731755	+	0.681568i	$0.761298\pi$
$572$		0			0
$573$		−	56.8328i		−	2.37422i
$574$		0			0
$575$	12.2452	+	16.8541i	0.510661	+	0.702865i
$576$		0			0
$577$	−6.02786	−	18.5519i	−0.250943	−	0.772324i	−0.994602	−	0.103764i	$-0.966911\pi$
$577$	−6.02786	−	18.5519i	−0.250943	−	0.772324i	0.743659	−	0.668560i	$-0.233089\pi$
$578$		0			0
$579$	−11.7082	+	16.1150i	−0.486576	+	0.669715i
$580$		0			0
$581$	1.62460	+	0.527864i	0.0673997	+	0.0218995i
$582$		0			0
$583$	6.88191	+	8.23607i	0.285020	+	0.341103i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−21.6353	−	15.7189i	−0.892983	−	0.648790i	0.0436714	−	0.999046i	$-0.486095\pi$
$587$	−21.6353	−	15.7189i	−0.892983	−	0.648790i	−0.936654	+	0.350256i	$0.886095\pi$
$588$		0			0
$589$	−7.88597	−	24.2705i	−0.324936	−	1.00005i
$590$		0			0
$591$	−26.0746	+	18.9443i	−1.07256	+	0.779263i
$592$		0			0
$593$		−	26.3521i		−	1.08215i	−0.840974	−	0.541075i	$-0.818018\pi$
$593$		−	26.3521i		−	1.08215i	0.840974	−	0.541075i	$-0.181982\pi$
$594$		0			0
$595$	16.5836			0.679861
$596$		0			0
$597$	8.50651	+	11.7082i	0.348148	+	0.479185i
$598$		0			0
$599$	−5.70634	+	1.85410i	−0.233155	+	0.0757566i	−0.423264	−	0.906006i	$-0.639116\pi$
$599$	−5.70634	+	1.85410i	−0.233155	+	0.0757566i	0.190109	+	0.981763i	$0.439116\pi$
$600$		0			0
$601$	−1.11803	+	1.53884i	−0.0456056	+	0.0627707i	−0.831211	−	0.555957i	$-0.812352\pi$
$601$	−1.11803	+	1.53884i	−0.0456056	+	0.0627707i	0.785605	+	0.618728i	$0.212352\pi$
$602$		0			0
$603$	−17.3435	+	53.3777i	−0.706280	+	2.17371i
$604$		0			0
$605$	−9.40456	−	9.81966i	−0.382350	−	0.399226i
$606$		0			0
$607$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$607$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$608$		0			0
$609$	42.3607	+	30.7768i	1.71654	+	1.24714i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	26.3521	−	19.1459i	1.06435	−	0.773296i	0.0894618	−	0.995990i	$-0.471485\pi$
$613$	26.3521	−	19.1459i	1.06435	−	0.773296i	0.974888	+	0.222695i	$0.0714853\pi$
$614$		0			0
$615$	−18.4661			−0.744625
$616$		0			0
$617$	14.5623			0.586256			0.293128	−	0.956073i	$-0.405304\pi$
$617$	14.5623			0.586256			0.293128	+	0.956073i	$0.405304\pi$
$618$		0			0
$619$	−19.6353	+	14.2658i	−0.789208	+	0.573393i	−0.907728	−	0.419559i	$-0.862185\pi$
$619$	−19.6353	+	14.2658i	−0.789208	+	0.573393i	0.118521	+	0.992952i	$0.462185\pi$
$620$		0			0
$621$	−12.7598	+	4.14590i	−0.512032	+	0.166369i
$622$		0			0
$623$	−5.70634	−	4.14590i	−0.228620	−	0.166102i
$624$		0			0
$625$	1.36475	−	4.20025i	0.0545898	−	0.168010i
$626$		0			0
$627$	19.6353	+	23.4989i	0.784157	+	0.938456i
$628$		0			0
$629$	4.04125	−	12.4377i	0.161135	−	0.495923i
$630$		0			0
$631$	13.8293	−	19.0344i	0.550537	−	0.757749i	−0.439548	−	0.898219i	$-0.644861\pi$
$631$	13.8293	−	19.0344i	0.550537	−	0.757749i	0.990085	+	0.140470i	$0.0448613\pi$
$632$		0			0
$633$	−3.35410	+	1.08981i	−0.133314	+	0.0433162i
$634$		0			0
$635$	13.4164	+	18.4661i	0.532414	+	0.732805i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		−	46.2492i		−	1.82959i
$640$		0			0
$641$	20.9164	−	15.1967i	0.826148	−	0.600232i	−0.0923186	−	0.995730i	$-0.529428\pi$
$641$	20.9164	−	15.1967i	0.826148	−	0.600232i	0.918467	+	0.395498i	$0.129428\pi$
$642$		0			0
$643$	3.57295	+	10.9964i	0.140903	+	0.433656i	0.996461	−	0.0840509i	$-0.0267858\pi$
$643$	3.57295	+	10.9964i	0.140903	+	0.433656i	−0.855558	+	0.517707i	$0.826786\pi$
$644$		0			0
$645$	33.4055	+	24.2705i	1.31534	+	0.955650i
$646$		0			0
$647$	−1.34708	−	0.437694i	−0.0529593	−	0.0172075i	0.282418	−	0.959292i	$-0.408864\pi$
$647$	−1.34708	−	0.437694i	−0.0529593	−	0.0172075i	−0.335377	+	0.942084i	$0.608864\pi$
$648$		0			0
$649$	−12.8328	−	31.9524i	−0.503732	−	1.25424i
$650$		0			0
$651$	−68.5410	−	22.2703i	−2.68633	−	0.872843i
$652$		0			0
$653$	−9.02105	+	12.4164i	−0.353021	+	0.485892i	−0.948188	−	0.317711i	$-0.897086\pi$
$653$	−9.02105	+	12.4164i	−0.353021	+	0.485892i	0.595167	+	0.803602i	$0.297086\pi$
$654$		0			0
$655$	2.45714	+	7.56231i	0.0960085	+	0.295484i
$656$		0			0
$657$	2.27458	+	3.13068i	0.0887396	+	0.122140i
$658$		0			0
$659$			28.1482i			1.09650i	0.836315	+	0.548249i	$0.184705\pi$
$659$			28.1482i			1.09650i	−0.836315	+	0.548249i	$0.815295\pi$
$660$		0			0
$661$			13.4164i			0.521838i	0.965361	+	0.260919i	$0.0840255\pi$
$661$			13.4164i			0.521838i	−0.965361	+	0.260919i	$0.915974\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−5.12461	−	15.7719i	−0.198724	−	0.611609i
$666$		0			0
$667$	−18.5410	+	25.5195i	−0.717911	+	0.988120i
$668$		0			0
$669$	11.5842	+	3.76393i	0.447871	+	0.145522i
$670$		0			0
$671$	9.23305	−	36.7082i	0.356438	−	1.41710i
$672$		0			0
$673$	42.2984	+	13.7436i	1.63048	+	0.529776i	0.974382	−	0.224898i	$-0.0722049\pi$
$673$	42.2984	+	13.7436i	1.63048	+	0.529776i	0.656100	+	0.754674i	$0.272205\pi$
$674$		0			0
$675$	6.28115	+	4.56352i	0.241762	+	0.175650i
$676$		0			0
$677$	7.95148	+	24.4721i	0.305600	+	0.940541i	0.979453	+	0.201675i	$0.0646384\pi$
$677$	7.95148	+	24.4721i	0.305600	+	0.940541i	−0.673852	+	0.738866i	$0.735362\pi$
$678$		0			0
$679$	−25.6255	+	18.6180i	−0.983417	+	0.714495i
$680$		0			0
$681$			13.9353i			0.534003i
$682$		0			0
$683$	30.4721			1.16598			0.582992	−	0.812478i	$-0.301882\pi$
$683$	30.4721			1.16598			0.582992	+	0.812478i	$0.301882\pi$
$684$		0			0
$685$	4.04125	+	5.56231i	0.154408	+	0.212525i
$686$		0			0
$687$	−18.4661	+	6.00000i	−0.704526	+	0.228914i
$688$		0			0
$689$		0			0
$690$		0			0
$691$	5.91641	−	18.2088i	0.225071	−	0.692697i	−0.773214	−	0.634146i	$-0.781352\pi$
$691$	5.91641	−	18.2088i	0.225071	−	0.692697i	0.998284	−	0.0585510i	$-0.0186480\pi$
$692$		0			0
$693$	48.5164	−	3.29180i	1.84299	−	0.125045i
$694$		0			0
$695$	1.66509	−	5.12461i	0.0631604	−	0.194388i
$696$		0			0
$697$	16.2812	+	11.8290i	0.616693	+	0.448053i
$698$		0			0
$699$	49.3328	−	16.0292i	1.86594	−	0.606280i
$700$		0			0
$701$	11.4127	−	8.29180i	0.431051	−	0.313177i	−0.351018	−	0.936369i	$-0.614164\pi$
$701$	11.4127	−	8.29180i	0.431051	−	0.313177i	0.782069	+	0.623192i	$0.214164\pi$
$702$		0			0
$703$	−13.0778			−0.493237
$704$		0			0
$705$	−31.4164			−1.18321
$706$		0			0
$707$	−54.0689	+	39.2833i	−2.03347	+	1.47740i
$708$		0			0
$709$	20.6457	−	6.70820i	0.775367	−	0.251932i	0.105506	−	0.994419i	$-0.466354\pi$
$709$	20.6457	−	6.70820i	0.775367	−	0.251932i	0.669861	+	0.742487i	$0.266354\pi$
$710$		0			0
$711$	−14.6619	−	10.6525i	−0.549863	−	0.399499i
$712$		0			0
$713$	13.4164	−	41.2915i	0.502448	−	1.54638i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−11.4127	+	35.1246i	−0.426214	+	1.31175i
$718$		0			0
$719$	3.52671	−	4.85410i	0.131524	−	0.181027i	−0.738176	−	0.674609i	$-0.764312\pi$
$719$	3.52671	−	4.85410i	0.131524	−	0.181027i	0.869700	+	0.493581i	$0.164312\pi$
$720$		0			0
$721$	−4.47214	+	1.45309i	−0.166551	+	0.0541157i
$722$		0			0
$723$	4.57295	+	6.29412i	0.170070	+	0.234081i
$724$		0			0
$725$	18.2541			0.677940
$726$		0			0
$727$		−	8.00000i		−	0.296704i	−0.988935	−	0.148352i	$-0.952603\pi$
$727$		−	8.00000i		−	0.296704i	0.988935	−	0.148352i	$-0.0473968\pi$
$728$		0			0
$729$	32.0066	−	23.2541i	1.18543	−	0.861264i
$730$		0			0
$731$	−13.9058	−	42.7975i	−0.514323	−	1.58292i
$732$		0			0
$733$	7.88597	+	5.72949i	0.291275	+	0.211624i	0.723820	−	0.689989i	$-0.242384\pi$
$733$	7.88597	+	5.72949i	0.291275	+	0.211624i	−0.432545	+	0.901612i	$0.642384\pi$
$734$		0			0
$735$	−22.9969	−	7.47214i	−0.848252	−	0.275614i
$736$		0			0
$737$	40.9058	+	25.6785i	1.50678	+	0.945881i
$738$		0			0
$739$	25.0623	+	8.14324i	0.921932	+	0.299554i	0.731259	−	0.682100i	$-0.238933\pi$
$739$	25.0623	+	8.14324i	0.921932	+	0.299554i	0.190673	+	0.981654i	$0.438933\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	5.70634	+	17.5623i	0.209345	+	0.644299i	0.999507	+	0.0314000i	$0.00999657\pi$
$743$	5.70634	+	17.5623i	0.209345	+	0.644299i	−0.790162	+	0.612899i	$0.790003\pi$
$744$		0			0
$745$	−6.18034	−	8.50651i	−0.226430	−	0.311654i
$746$		0			0
$747$			1.73060i			0.0633193i
$748$		0			0
$749$		−	16.1803i		−	0.591217i
$750$		0			0
$751$	−12.9313	−	17.7984i	−0.471869	−	0.649472i	0.505048	−	0.863091i	$-0.331475\pi$
$751$	−12.9313	−	17.7984i	−0.471869	−	0.649472i	−0.976917	+	0.213619i	$0.931475\pi$
$752$		0			0
$753$	−11.7082	−	36.0341i	−0.426671	−	1.31316i
$754$		0			0
$755$	6.58359	−	9.06154i	0.239601	−	0.329783i
$756$		0			0
$757$	−11.4127	−	3.70820i	−0.414801	−	0.134777i	0.0941792	−	0.995555i	$-0.469977\pi$
$757$	−11.4127	−	3.70820i	−0.414801	−	0.134777i	−0.508980	+	0.860778i	$0.669977\pi$
$758$		0			0
$759$	3.52671	+	51.9787i	0.128012	+	1.88671i
$760$		0			0
$761$	16.7705	+	5.44907i	0.607931	+	0.197529i	0.596774	−	0.802409i	$-0.296449\pi$
$761$	16.7705	+	5.44907i	0.607931	+	0.197529i	0.0111562	+	0.999938i	$0.496449\pi$
$762$		0			0
$763$	35.1246	+	25.5195i	1.27160	+	0.923869i
$764$		0			0
$765$	5.19180	+	15.9787i	0.187710	+	0.577712i
$766$		0			0
$767$		0			0
$768$		0			0
$769$		−	27.5276i		−	0.992672i	−0.868130	−	0.496336i	$-0.834678\pi$
$769$		−	27.5276i		−	0.992672i	0.868130	−	0.496336i	$-0.165322\pi$
$770$		0			0
$771$	−55.6869			−2.00552
$772$		0			0
$773$	−1.96763	−	2.70820i	−0.0707706	−	0.0974073i	0.772164	−	0.635423i	$-0.219174\pi$
$773$	−1.96763	−	2.70820i	−0.0707706	−	0.0974073i	−0.842935	+	0.538016i	$0.819174\pi$
$774$		0			0
$775$	−23.8949	+	7.76393i	−0.858331	+	0.278889i
$776$		0			0
$777$	−21.7082	+	29.8788i	−0.778777	+	1.07190i
$778$		0			0
$779$	6.21885	−	19.1396i	0.222813	−	0.685749i
$780$		0			0
$781$	−38.5973	−	9.70820i	−1.38112	−	0.347387i
$782$		0			0
$783$	−3.63271	+	11.1803i	−0.129823	+	0.399553i
$784$		0			0
$785$	−18.0000	−	13.0778i	−0.642448	−	0.466765i
$786$		0			0
$787$	25.0623	−	8.14324i	0.893375	−	0.290275i	0.173875	−	0.984768i	$-0.444371\pi$
$787$	25.0623	−	8.14324i	0.893375	−	0.290275i	0.719500	+	0.694493i	$0.244371\pi$
$788$		0			0
$789$	−33.4055	+	24.2705i	−1.18927	+	0.864053i
$790$		0			0
$791$	−18.4661			−0.656579
$792$		0			0
$793$		0			0
$794$		0			0
$795$	8.47214	−	6.15537i	0.300476	−	0.218308i
$796$		0			0
$797$	47.0633	−	15.2918i	1.66707	−	0.541663i	0.684733	−	0.728794i	$-0.259919\pi$
$797$	47.0633	−	15.2918i	1.66707	−	0.541663i	0.982335	+	0.187131i	$0.0599188\pi$
$798$		0			0
$799$	27.6992	+	20.1246i	0.979926	+	0.711958i
$800$		0			0
$801$	2.20820	−	6.79615i	0.0780230	−	0.240130i
$802$		0			0
$803$	3.09017	−	1.24108i	0.109050	−	0.0437969i
$804$		0			0
$805$	8.71851	−	26.8328i	0.307287	−	0.945732i
$806$		0			0
$807$	17.2905	−	23.7984i	0.608656	−	0.837742i
$808$		0			0
$809$	−38.4787	+	12.5025i	−1.35284	+	0.439564i	−0.893646	−	0.448772i	$-0.851861\pi$
$809$	−38.4787	+	12.5025i	−1.35284	+	0.439564i	−0.459193	+	0.888336i	$0.651861\pi$
$810$		0			0
$811$	26.0410	+	35.8424i	0.914424	+	1.25860i	0.965633	+	0.259909i	$0.0836924\pi$
$811$	26.0410	+	35.8424i	0.914424	+	1.25860i	−0.0512094	+	0.998688i	$0.516308\pi$
$812$		0			0
$813$	41.2915			1.44815
$814$		0			0
$815$		−	20.8328i		−	0.729742i
$816$		0			0
$817$	−36.4058	+	26.4503i	−1.27368	+	0.925380i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	10.2371	+	7.43769i	0.357278	+	0.259577i	0.751916	−	0.659259i	$-0.229130\pi$
$821$	10.2371	+	7.43769i	0.357278	+	0.259577i	−0.394638	+	0.918837i	$0.629130\pi$
$822$		0			0
$823$	38.2138	+	12.4164i	1.33205	+	0.432809i	0.886616	−	0.462507i	$-0.153050\pi$
$823$	38.2138	+	12.4164i	1.33205	+	0.432809i	0.445433	+	0.895315i	$0.353050\pi$
$824$		0			0
$825$	23.1353	−	19.3314i	0.805466	−	0.673033i
$826$		0			0
$827$	26.2426	+	8.52675i	0.912546	+	0.296504i	0.727406	−	0.686208i	$-0.240726\pi$
$827$	26.2426	+	8.52675i	0.912546	+	0.296504i	0.185141	+	0.982712i	$0.440726\pi$
$828$		0			0
$829$	−12.7598	+	17.5623i	−0.443165	+	0.609964i	−0.970912	−	0.239438i	$-0.923037\pi$
$829$	−12.7598	+	17.5623i	−0.443165	+	0.609964i	0.527747	+	0.849402i	$0.323037\pi$
$830$		0			0
$831$	−5.70634	−	17.5623i	−0.197951	−	0.609230i
$832$		0			0
$833$	15.4894	+	21.3193i	0.536674	+	0.738669i
$834$		0			0
$835$		−	5.38834i		−	0.186471i
$836$		0			0
$837$		−	16.1803i		−	0.559274i
$838$		0			0
$839$	−10.8981	−	15.0000i	−0.376246	−	0.517858i	0.578340	−	0.815796i	$-0.303701\pi$
$839$	−10.8981	−	15.0000i	−0.376246	−	0.517858i	−0.954585	+	0.297939i	$0.903701\pi$
$840$		0			0
$841$	−0.420473	−	1.29408i	−0.0144991	−	0.0446236i
$842$		0			0
$843$	8.78115	−	12.0862i	0.302439	−	0.416272i
$844$		0			0
$845$	−15.2824	−	4.96556i	−0.525731	−	0.170820i
$846$		0			0
$847$	7.43694	−	41.1803i	0.255536	−	1.41497i
$848$		0			0
$849$	−10.8541	−	3.52671i	−0.372512	−	0.121036i
$850$		0			0
$851$	−18.0000	−	13.0778i	−0.617032	−	0.448300i
$852$		0			0
$853$	−2.17963	−	6.70820i	−0.0746290	−	0.229685i	0.906783	−	0.421598i	$-0.138531\pi$
$853$	−2.17963	−	6.70820i	−0.0746290	−	0.229685i	−0.981412	+	0.191914i	$0.938531\pi$
$854$		0			0
$855$	13.5923	−	9.87539i	0.464847	−	0.337731i
$856$		0			0
$857$			39.9444i			1.36447i	0.731131	+	0.682237i	$0.238993\pi$
$857$			39.9444i			1.36447i	−0.731131	+	0.682237i	$0.761007\pi$
$858$		0			0
$859$	−19.1459			−0.653250			−0.326625	−	0.945154i	$-0.605911\pi$
$859$	−19.1459			−0.653250			−0.326625	+	0.945154i	$0.605911\pi$
$860$		0			0
$861$	−33.4055	−	45.9787i	−1.13846	−	1.56695i
$862$		0			0
$863$	23.3399	−	7.58359i	0.794499	−	0.258148i	0.116480	−	0.993193i	$-0.462839\pi$
$863$	23.3399	−	7.58359i	0.794499	−	0.258148i	0.678019	+	0.735045i	$0.262839\pi$
$864$		0			0
$865$	−15.5279	+	21.3723i	−0.527963	+	0.726679i
$866$		0			0
$867$	−3.69098	+	11.3597i	−0.125352	+	0.385795i
$868$		0			0
$869$	−11.9677	+	10.0000i	−0.405977	+	0.339227i
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−25.9615	−	18.8621i	−0.878663	−	0.638386i
$874$		0			0
$875$	−37.8885	+	12.3107i	−1.28087	+	0.416179i
$876$		0			0
$877$	−18.4661	+	13.4164i	−0.623556	+	0.453040i	−0.854162	−	0.520007i	$-0.825929\pi$
$877$	−18.4661	+	13.4164i	−0.623556	+	0.453040i	0.230606	+	0.973047i	$0.425929\pi$
$878$		0			0
$879$	55.9533			1.88726
$880$		0			0
$881$	5.56231			0.187399			0.0936994	−	0.995601i	$-0.470131\pi$
$881$	5.56231			0.187399			0.0936994	+	0.995601i	$0.470131\pi$
$882$		0			0
$883$	−5.64590	+	4.10199i	−0.190000	+	0.138043i	−0.678719	−	0.734399i	$-0.737464\pi$
$883$	−5.64590	+	4.10199i	−0.190000	+	0.138043i	0.488719	+	0.872441i	$0.337464\pi$
$884$		0			0
$885$	−31.9524	+	10.3820i	−1.07407	+	0.348986i
$886$		0			0
$887$	33.4055	+	24.2705i	1.12165	+	0.814924i	0.984458	−	0.175621i	$-0.0561933\pi$
$887$	33.4055	+	24.2705i	1.12165	+	0.814924i	0.137189	+	0.990545i	$0.456193\pi$
$888$		0			0
$889$	−21.7082	+	66.8110i	−0.728070	+	2.24077i
$890$		0			0
$891$	−7.05573	−	17.5680i	−0.236376	−	0.588552i
$892$		0			0
$893$	10.5801	−	32.5623i	0.354051	−	1.08966i
$894$		0			0
$895$	−7.11894	+	9.79837i	−0.237960	+	0.327524i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−22.3607	−	30.7768i	−0.745770	−	1.02646i
$900$		0			0
$901$	−11.4127			−0.380211
$902$		0			0
$903$			127.082i			4.22903i
$904$		0			0
$905$	12.0000	−	8.71851i	0.398893	−	0.289813i
$906$		0			0
$907$	3.79180	+	11.6699i	0.125905	+	0.387494i	0.994065	−	0.108790i	$-0.0346975\pi$
$907$	3.79180	+	11.6699i	0.125905	+	0.387494i	−0.868160	+	0.496284i	$0.834697\pi$
$908$		0			0
$909$	−54.7778	−	39.7984i	−1.81686	−	1.32003i
$910$		0			0
$911$	−49.1774	−	15.9787i	−1.62932	−	0.529398i	−0.655206	−	0.755451i	$-0.727418\pi$
$911$	−49.1774	−	15.9787i	−1.62932	−	0.529398i	−0.974115	+	0.226052i	$0.927418\pi$
$912$		0			0
$913$	1.44427	+	0.363271i	0.0477984	+	0.0120225i
$914$		0			0
$915$	−35.1246	−	11.4127i	−1.16118	−	0.377292i
$916$		0			0
$917$	−14.3844	+	19.7984i	−0.475013	+	0.653800i
$918$		0			0
$919$	4.97980	+	15.3262i	0.164268	+	0.505566i	0.998982	−	0.0451188i	$-0.0143666\pi$
$919$	4.97980	+	15.3262i	0.164268	+	0.505566i	−0.834713	+	0.550685i	$0.814367\pi$
$920$		0			0
$921$	−33.0517	−	45.4917i	−1.08909	−	1.49900i
$922$		0			0
$923$		0			0
$924$		0			0
$925$			12.8754i			0.423340i
$926$		0			0
$927$	−2.80017	−	3.85410i	−0.0919696	−	0.126585i
$928$		0			0
$929$	14.2082	+	43.7284i	0.466156	+	1.43468i	0.857523	+	0.514446i	$0.172002\pi$
$929$	14.2082	+	43.7284i	0.466156	+	1.43468i	−0.391367	+	0.920235i	$0.627998\pi$
$930$		0			0
$931$	15.4894	−	21.3193i	0.507643	−	0.698711i
$932$		0			0
$933$	9.23305	+	3.00000i	0.302277	+	0.0982156i
$934$		0			0
$935$	14.4248	−	0.978714i	0.471743	−	0.0320074i
$936$		0			0
$937$	17.2984	+	5.62058i	0.565113	+	0.183616i	0.577621	−	0.816305i	$-0.303981\pi$
$937$	17.2984	+	5.62058i	0.565113	+	0.183616i	−0.0125074	+	0.999922i	$0.503981\pi$
$938$		0			0
$939$	1.42705	+	1.03681i	0.0465700	+	0.0338351i
$940$		0			0
$941$	8.40051	+	25.8541i	0.273849	+	0.842820i	0.989522	+	0.144384i	$0.0461201\pi$
$941$	8.40051	+	25.8541i	0.273849	+	0.842820i	−0.715673	+	0.698435i	$0.753880\pi$
$942$		0			0
$943$	27.6992	−	20.1246i	0.902008	−	0.655348i
$944$		0			0
$945$		−	10.5146i		−	0.342041i
$946$		0			0
$947$	−3.90983			−0.127052			−0.0635262	−	0.997980i	$-0.520235\pi$
$947$	−3.90983			−0.127052			−0.0635262	+	0.997980i	$0.520235\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−22.5478	+	7.32624i	−0.731164	+	0.237570i
$952$		0			0
$953$	4.93769	−	6.79615i	0.159948	−	0.220149i	−0.721520	−	0.692394i	$-0.756556\pi$
$953$	4.93769	−	6.79615i	0.159948	−	0.220149i	0.881467	+	0.472245i	$0.156556\pi$
$954$		0			0
$955$	−8.29180	+	25.5195i	−0.268316	+	0.825792i
$956$		0			0
$957$	38.6628	+	24.2705i	1.24979	+	0.784554i
$958$		0			0
$959$	−6.53888	+	20.1246i	−0.211152	+	0.649858i
$960$		0			0
$961$	17.2812	+	12.5555i	0.557457	+	0.405016i
$962$		0			0
$963$	15.5902	−	5.06555i	0.502386	−	0.163235i
$964$		0			0
$965$	7.60845	−	5.52786i	0.244925	−	0.177948i
$966$		0			0
$967$	40.9484			1.31681			0.658406	−	0.752663i	$-0.271231\pi$
$967$	40.9484			1.31681			0.658406	+	0.752663i	$0.271231\pi$
$968$		0			0
$969$	−32.5623			−1.04605
$970$		0			0
$971$	32.6525	−	23.7234i	1.04787	−	0.761321i	0.0760620	−	0.997103i	$-0.475765\pi$
$971$	32.6525	−	23.7234i	1.04787	−	0.761321i	0.971806	+	0.235783i	$0.0757653\pi$
$972$		0			0
$973$	15.7719	−	5.12461i	0.505625	−	0.164288i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−7.85410	+	24.1724i	−0.251275	+	0.773345i	0.743266	+	0.668996i	$0.233276\pi$
$977$	−7.85410	+	24.1724i	−0.251275	+	0.773345i	−0.994541	+	0.104349i	$0.966724\pi$
$978$		0			0
$979$	−5.20820	−	3.26944i	−0.166455	−	0.104492i
$980$		0			0
$981$	−13.5923	+	41.8328i	−0.433969	+	1.33562i
$982$		0			0
$983$	21.1603	−	29.1246i	0.674908	−	0.928931i	−0.324951	−	0.945731i	$-0.605348\pi$
$983$	21.1603	−	29.1246i	0.674908	−	0.928931i	0.999859	+	0.0168000i	$0.00534785\pi$
$984$		0			0
$985$	14.4721	−	4.70228i	0.461121	−	0.149827i
$986$		0			0
$987$	−56.8328	−	78.2237i	−1.80901	−	2.48989i
$988$		0			0
$989$	−76.5586			−2.43442
$990$		0			0
$991$		−	2.36068i		−	0.0749895i	−0.999297	−	0.0374947i	$-0.988062\pi$
$991$		−	2.36068i		−	0.0749895i	0.999297	−	0.0374947i	$-0.0119377\pi$
$992$		0			0
$993$	−34.1976	+	24.8460i	−1.08523	+	0.788463i
$994$		0			0
$995$	−2.11146	−	6.49839i	−0.0669377	−	0.206013i
$996$		0			0
$997$	−12.7598	−	9.27051i	−0.404106	−	0.293600i	0.367106	−	0.930179i	$-0.380349\pi$
$997$	−12.7598	−	9.27051i	−0.404106	−	0.293600i	−0.771211	+	0.636579i	$0.780349\pi$
$998$		0			0
$999$	−7.88597	−	2.56231i	−0.249501	−	0.0810678i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	704.2.s.d.607.1	yes	8
4.3	odd	2		704.2.s.a.607.1	yes	8
8.3	odd	2	inner	704.2.s.d.607.2	yes	8
8.5	even	2		704.2.s.a.607.2	yes	8
11.6	odd	10	inner	704.2.s.d.479.2	yes	8
44.39	even	10		704.2.s.a.479.2	yes	8
88.61	odd	10		704.2.s.a.479.1	✓	8
88.83	even	10	inner	704.2.s.d.479.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
704.2.s.a.479.1	✓	8	88.61	odd	10
704.2.s.a.479.2	yes	8	44.39	even	10
704.2.s.a.607.1	yes	8	4.3	odd	2
704.2.s.a.607.2	yes	8	8.5	even	2
704.2.s.d.479.1	yes	8	88.83	even	10	inner
704.2.s.d.479.2	yes	8	11.6	odd	10	inner
704.2.s.d.607.1	yes	8	1.1	even	1	trivial
704.2.s.d.607.2	yes	8	8.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 704 = 2^{6} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	704.s (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.11803 - 1.53884i) q^{3} +(-1.17557 + 0.381966i) q^{5} +(-3.07768 - 2.23607i) q^{7} +(1.19098 - 3.66547i) q^{9} +(-2.80902 - 1.76336i) q^{11} +(-1.90211 + 2.61803i) q^{15} +(3.35410 - 1.08981i) q^{17} +(-2.07295 - 2.85317i) q^{19} -9.95959 q^{21} -6.00000i q^{23} +(-2.80902 + 2.04087i) q^{25} +(-0.690983 - 2.12663i) q^{27} +(-4.25325 - 3.09017i) q^{29} +(6.88191 + 2.23607i) q^{31} +(-8.66312 + 0.587785i) q^{33} +(4.47214 + 1.45309i) q^{35} +(2.17963 - 3.00000i) q^{37} +(3.35410 + 4.61653i) q^{41} -12.7598i q^{43} +4.76393i q^{45} +(5.70634 + 7.85410i) q^{47} +(2.30902 + 7.10642i) q^{49} +(5.42705 - 7.46969i) q^{51} +(-3.07768 - 1.00000i) q^{53} +(3.97574 + 1.00000i) q^{55} +(-8.78115 - 2.85317i) q^{57} +(8.39919 + 6.10237i) q^{59} +(3.52671 + 10.8541i) q^{61} +(-11.8617 + 8.61803i) q^{63} -14.5623 q^{67} +(-9.23305 - 12.7082i) q^{69} +(11.4127 - 3.70820i) q^{71} +(-0.590170 + 0.812299i) q^{73} +(-2.80902 + 8.64527i) q^{75} +(4.70228 + 11.7082i) q^{77} +(1.45309 - 4.47214i) q^{79} +(4.61803 + 3.35520i) q^{81} +(-0.427051 + 0.138757i) q^{83} +(-3.52671 + 2.56231i) q^{85} -13.7638 q^{87} +1.85410 q^{89} +(18.0171 - 5.85410i) q^{93} +(3.52671 + 2.56231i) q^{95} +(2.57295 - 7.91872i) q^{97} +(-9.80902 + 8.19624i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{3} + 14 q^{9} - 18 q^{11} - 30 q^{19} - 18 q^{25} - 10 q^{27} - 38 q^{33} + 14 q^{49} + 30 q^{51} - 30 q^{57} + 18 q^{59} - 36 q^{67} + 40 q^{73} - 18 q^{75} + 28 q^{81} + 10 q^{83} - 12 q^{89}+ \cdots - 74 q^{99}+O(q^{100}) \) 8 * q + 8 * q^3 + 14 * q^9 - 18 * q^11 - 30 * q^19 - 18 * q^25 - 10 * q^27 - 38 * q^33 + 14 * q^49 + 30 * q^51 - 30 * q^57 + 18 * q^59 - 36 * q^67 + 40 * q^73 - 18 * q^75 + 28 * q^81 + 10 * q^83 - 12 * q^89 + 34 * q^97 - 74 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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