LMFDB - Embedded newform 572.2.bc.a.197.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(197,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 1]))

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

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

chi := DirichletCharacter("572.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bc (of order $12$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			197.1
Character	$\chi$	$=$	572.197
Dual form			572.2.bc.a.241.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.56324 - 2.70762i) q^{3} +(0.477789 - 0.477789i) q^{5} +(-1.02740 - 3.83429i) q^{7} +(-3.38745 + 5.86724i) q^{9} +O(q^{10})$	\(q+(-1.56324 - 2.70762i) q^{3} +(0.477789 - 0.477789i) q^{5} +(-1.02740 - 3.83429i) q^{7} +(-3.38745 + 5.86724i) q^{9} +(-2.53241 + 2.14170i) q^{11} +(-3.33231 - 1.37685i) q^{13} +(-2.04057 - 0.546769i) q^{15} +(1.99621 - 3.45753i) q^{17} +(7.12208 - 1.90835i) q^{19} +(-8.77572 + 8.77572i) q^{21} +(-2.01091 + 1.16100i) q^{23} +4.54344i q^{25} +11.8022 q^{27} +(-7.62932 + 4.40479i) q^{29} +(2.95758 - 2.95758i) q^{31} +(9.75768 + 3.50879i) q^{33} +(-2.32286 - 1.34110i) q^{35} +(-1.14913 + 4.28860i) q^{37} +(1.48122 + 11.1750i) q^{39} +(-0.299301 + 1.11701i) q^{41} +(-0.498991 + 0.864278i) q^{43} +(1.18482 + 4.42179i) q^{45} +(-8.42186 - 8.42186i) q^{47} +(-7.58407 + 4.37866i) q^{49} -12.4822 q^{51} +7.84262 q^{53} +(-0.186676 + 2.23324i) q^{55} +(-16.3006 - 16.3006i) q^{57} +(-5.51724 + 1.47834i) q^{59} +(-5.61754 - 3.24329i) q^{61} +(25.9770 + 6.96051i) q^{63} +(-2.24998 + 0.934296i) q^{65} +(-5.15648 - 1.38168i) q^{67} +(6.28708 + 3.62984i) q^{69} +(1.78241 + 6.65206i) q^{71} +(3.78927 - 3.78927i) q^{73} +(12.3019 - 7.10249i) q^{75} +(10.8137 + 7.50962i) q^{77} -15.5491i q^{79} +(-8.28734 - 14.3541i) q^{81} +(2.95729 + 2.95729i) q^{83} +(-0.698206 - 2.60574i) q^{85} +(23.8530 + 13.7715i) q^{87} +(-0.236225 + 0.881602i) q^{89} +(-1.85565 + 14.1916i) q^{91} +(-12.6314 - 3.38457i) q^{93} +(2.49106 - 4.31464i) q^{95} +(-3.56447 - 13.3028i) q^{97} +(-3.98747 - 22.1132i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 28 q^{9}+O(q^{10}) $ 56 * q - 28 * q^9	$ 56 q - 28 q^{9} + 4 q^{11} + 8 q^{15} - 12 q^{23} - 24 q^{27} - 4 q^{31} - 10 q^{33} - 12 q^{37} - 64 q^{45} - 8 q^{47} + 40 q^{53} + 22 q^{55} + 48 q^{59} - 36 q^{67} - 48 q^{71} + 120 q^{75} + 28 q^{81} + 28 q^{89} + 36 q^{91} + 20 q^{93} - 68 q^{97} - 44 q^{99}+O(q^{100}) $ 56 * q - 28 * q^9 + 4 * q^11 + 8 * q^15 - 12 * q^23 - 24 * q^27 - 4 * q^31 - 10 * q^33 - 12 * q^37 - 64 * q^45 - 8 * q^47 + 40 * q^53 + 22 * q^55 + 48 * q^59 - 36 * q^67 - 48 * q^71 + 120 * q^75 + 28 * q^81 + 28 * q^89 + 36 * q^91 + 20 * q^93 - 68 * q^97 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$-1$

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
$3$	−1.56324	−	2.70762i	−0.902539	−	1.56324i	−0.824188	−	0.566317i	$-0.808368\pi$
$3$	−1.56324	−	2.70762i	−0.902539	−	1.56324i	−0.0783509	−	0.996926i	$-0.524965\pi$
$4$		0			0
$5$	0.477789	−	0.477789i	0.213674	−	0.213674i	−0.592152	−	0.805826i	$-0.701722\pi$
$5$	0.477789	−	0.477789i	0.213674	−	0.213674i	0.805826	+	0.592152i	$0.201722\pi$
$6$		0			0
$7$	−1.02740	−	3.83429i	−0.388319	−	1.44923i	−0.832868	−	0.553471i	$-0.813303\pi$
$7$	−1.02740	−	3.83429i	−0.388319	−	1.44923i	0.444549	−	0.895754i	$-0.353364\pi$
$8$		0			0
$9$	−3.38745	+	5.86724i	−1.12915	+	1.95575i
$10$		0			0
$11$	−2.53241	+	2.14170i	−0.763551	+	0.645748i
$11$	−2.53241	+	2.14170i	−0.763551	+	0.645748i
$12$		0			0
$13$	−3.33231	−	1.37685i	−0.924216	−	0.381870i
$13$	−3.33231	−	1.37685i	−0.924216	−	0.381870i
$14$		0			0
$15$	−2.04057	−	0.546769i	−0.526873	−	0.141175i
$16$		0			0
$17$	1.99621	−	3.45753i	0.484152	−	0.838575i	−0.515683	−	0.856780i	$-0.672462\pi$
$17$	1.99621	−	3.45753i	0.484152	−	0.838575i	0.999834	+	0.0182044i	$0.00579495\pi$
$18$		0			0
$19$	7.12208	−	1.90835i	1.63392	−	0.437807i	0.678869	−	0.734260i	$-0.262470\pi$
$19$	7.12208	−	1.90835i	1.63392	−	0.437807i	0.955047	+	0.296453i	$0.0958038\pi$
$20$		0			0
$21$	−8.77572	+	8.77572i	−1.91502	+	1.91502i
$22$		0			0
$23$	−2.01091	+	1.16100i	−0.419303	+	0.242085i	−0.694779	−	0.719223i	$-0.744498\pi$
$23$	−2.01091	+	1.16100i	−0.419303	+	0.242085i	0.275476	+	0.961308i	$0.411165\pi$
$24$		0			0
$25$			4.54344i			0.908687i
$26$		0			0
$27$	11.8022			2.27133
$28$		0			0
$29$	−7.62932	+	4.40479i	−1.41673	+	0.817949i	−0.996010	−	0.0892417i	$-0.971556\pi$
$29$	−7.62932	+	4.40479i	−1.41673	+	0.817949i	−0.420719	+	0.907191i	$0.638222\pi$
$30$		0			0
$31$	2.95758	−	2.95758i	0.531197	−	0.531197i	−0.389732	−	0.920928i	$-0.627432\pi$
$31$	2.95758	−	2.95758i	0.531197	−	0.531197i	0.920928	+	0.389732i	$0.127432\pi$
$32$		0			0
$33$	9.75768	+	3.50879i	1.69859	+	0.610802i
$34$		0			0
$35$	−2.32286	−	1.34110i	−0.392635	−	0.226688i
$36$		0			0
$37$	−1.14913	+	4.28860i	−0.188915	+	0.705042i	0.804843	+	0.593488i	$0.202250\pi$
$37$	−1.14913	+	4.28860i	−0.188915	+	0.705042i	−0.993758	+	0.111554i	$0.964417\pi$
$38$		0			0
$39$	1.48122	+	11.1750i	0.237185	+	1.78943i
$40$		0			0
$41$	−0.299301	+	1.11701i	−0.0467429	+	0.174447i	−0.985351	−	0.170538i	$-0.945449\pi$
$41$	−0.299301	+	1.11701i	−0.0467429	+	0.174447i	0.938608	+	0.344985i	$0.112116\pi$
$42$		0			0
$43$	−0.498991	+	0.864278i	−0.0760955	+	0.131801i	−0.901562	−	0.432650i	$-0.857579\pi$
$43$	−0.498991	+	0.864278i	−0.0760955	+	0.131801i	0.825467	+	0.564451i	$0.190912\pi$
$44$		0			0
$45$	1.18482	+	4.42179i	0.176622	+	0.659162i
$46$		0			0
$47$	−8.42186	−	8.42186i	−1.22845	−	1.22845i	−0.964549	−	0.263905i	$-0.914989\pi$
$47$	−8.42186	−	8.42186i	−1.22845	−	1.22845i	−0.263905	−	0.964549i	$-0.585011\pi$
$48$		0			0
$49$	−7.58407	+	4.37866i	−1.08344	+	0.625523i
$50$		0			0
$51$	−12.4822			−1.74786
$52$		0			0
$53$	7.84262			1.07727			0.538633	−	0.842540i	$-0.318941\pi$
$53$	7.84262			1.07727			0.538633	+	0.842540i	$0.318941\pi$
$54$		0			0
$55$	−0.186676	+	2.23324i	−0.0251713	+	0.301130i
$56$		0			0
$57$	−16.3006	−	16.3006i	−2.15907	−	2.15907i
$58$		0			0
$59$	−5.51724	+	1.47834i	−0.718284	+	0.192464i	−0.599406	−	0.800445i	$-0.704596\pi$
$59$	−5.51724	+	1.47834i	−0.718284	+	0.192464i	−0.118878	+	0.992909i	$0.537930\pi$
$60$		0			0
$61$	−5.61754	−	3.24329i	−0.719252	−	0.415260i	0.0952254	−	0.995456i	$-0.469643\pi$
$61$	−5.61754	−	3.24329i	−0.719252	−	0.415260i	−0.814477	+	0.580195i	$0.802976\pi$
$62$		0			0
$63$	25.9770	+	6.96051i	3.27279	+	0.876942i
$64$		0			0
$65$	−2.24998	+	0.934296i	−0.279076	+	0.115885i
$66$		0			0
$67$	−5.15648	−	1.38168i	−0.629964	−	0.168798i	−0.0703109	−	0.997525i	$-0.522399\pi$
$67$	−5.15648	−	1.38168i	−0.629964	−	0.168798i	−0.559654	+	0.828727i	$0.689066\pi$
$68$		0			0
$69$	6.28708	+	3.62984i	0.756875	+	0.436982i
$70$		0			0
$71$	1.78241	+	6.65206i	0.211534	+	0.789455i	0.987358	+	0.158506i	$0.0506676\pi$
$71$	1.78241	+	6.65206i	0.211534	+	0.789455i	−0.775824	+	0.630949i	$0.782666\pi$
$72$		0			0
$73$	3.78927	−	3.78927i	0.443500	−	0.443500i	−0.449686	−	0.893187i	$-0.648464\pi$
$73$	3.78927	−	3.78927i	0.443500	−	0.443500i	0.893187	+	0.449686i	$0.148464\pi$
$74$		0			0
$75$	12.3019	−	7.10249i	1.42050	−	0.820125i
$76$		0			0
$77$	10.8137	+	7.50962i	1.23234	+	0.855801i
$78$		0			0
$79$		−	15.5491i		−	1.74941i	−0.484658	−	0.874704i	$-0.661056\pi$
$79$		−	15.5491i		−	1.74941i	0.484658	−	0.874704i	$-0.338944\pi$
$80$		0			0
$81$	−8.28734	−	14.3541i	−0.920815	−	1.59490i
$82$		0			0
$83$	2.95729	+	2.95729i	0.324605	+	0.324605i	0.850530	−	0.525926i	$-0.176281\pi$
$83$	2.95729	+	2.95729i	0.324605	+	0.324605i	−0.525926	+	0.850530i	$0.676281\pi$
$84$		0			0
$85$	−0.698206	−	2.60574i	−0.0757310	−	0.282632i
$86$		0			0
$87$	23.8530	+	13.7715i	2.55731	+	1.47646i
$88$		0			0
$89$	−0.236225	+	0.881602i	−0.0250398	+	0.0934497i	−0.977315	−	0.211791i	$-0.932070\pi$
$89$	−0.236225	+	0.881602i	−0.0250398	+	0.0934497i	0.952275	+	0.305241i	$0.0987370\pi$
$90$		0			0
$91$	−1.85565	+	14.1916i	−0.194525	+	1.48769i
$92$		0			0
$93$	−12.6314	−	3.38457i	−1.30981	−	0.350964i
$94$		0			0
$95$	2.49106	−	4.31464i	0.255577	−	0.442673i
$96$		0			0
$97$	−3.56447	−	13.3028i	−0.361917	−	1.35069i	−0.871552	−	0.490303i	$-0.836886\pi$
$97$	−3.56447	−	13.3028i	−0.361917	−	1.35069i	0.509635	−	0.860391i	$-0.329780\pi$
$98$		0			0
$99$	−3.98747	−	22.1132i	−0.400756	−	2.22246i
$100$		0			0
$101$	−3.01454	−	5.22134i	−0.299958	−	0.519543i	0.676168	−	0.736748i	$-0.263639\pi$
$101$	−3.01454	−	5.22134i	−0.299958	−	0.519543i	−0.976126	+	0.217205i	$0.930306\pi$
$102$		0			0
$103$		−	10.5179i		−	1.03636i	−0.855272	−	0.518180i	$-0.826610\pi$
$103$		−	10.5179i		−	1.03636i	0.855272	−	0.518180i	$-0.173390\pi$
$104$		0			0
$105$			8.38588i			0.818378i
$106$		0			0
$107$	−11.6909	+	6.74973i	−1.13020	+	0.652521i	−0.943985	−	0.329988i	$-0.892955\pi$
$107$	−11.6909	+	6.74973i	−1.13020	+	0.652521i	−0.186215	+	0.982509i	$0.559622\pi$
$108$		0			0
$109$	2.07100	+	2.07100i	0.198366	+	0.198366i	0.799299	−	0.600933i	$-0.205204\pi$
$109$	2.07100	+	2.07100i	0.198366	+	0.198366i	−0.600933	+	0.799299i	$0.705204\pi$
$110$		0			0
$111$	13.4083	−	3.59273i	1.27266	−	0.341007i
$112$		0			0
$113$	4.34851	−	7.53184i	0.409073	−	0.708536i	−0.585713	−	0.810519i	$-0.699185\pi$
$113$	4.34851	−	7.53184i	0.409073	−	0.708536i	0.994786	+	0.101983i	$0.0325187\pi$
$114$		0			0
$115$	−0.406078	+	1.51550i	−0.0378669	+	0.141321i
$116$		0			0
$117$	19.3664	−	14.8874i	1.79042	−	1.37634i
$118$		0			0
$119$	−15.3081	−	4.10179i	−1.40329	−	0.376010i
$120$		0			0
$121$	1.82621	−	10.8473i	0.166019	−	0.986123i
$122$		0			0
$123$	3.49230	−	0.935759i	0.314890	−	0.0843746i
$124$		0			0
$125$	4.55975	+	4.55975i	0.407836	+	0.407836i
$126$		0			0
$127$	−5.81666	−	10.0747i	−0.516145	−	0.893989i	−0.999824	−	0.0187438i	$-0.994033\pi$
$127$	−5.81666	−	10.0747i	−0.516145	−	0.893989i	0.483680	−	0.875245i	$-0.339300\pi$
$128$		0			0
$129$	3.12018			0.274716
$130$		0			0
$131$		−	6.54354i		−	0.571712i	−0.958273	−	0.285856i	$-0.907722\pi$
$131$		−	6.54354i		−	0.571712i	0.958273	−	0.285856i	$-0.0922779\pi$
$132$		0			0
$133$	−14.6344	−	25.3475i	−1.26896	−	2.19791i
$134$		0			0
$135$	5.63896	−	5.63896i	0.485325	−	0.485325i
$136$		0			0
$137$	17.3940	−	4.66071i	1.48607	−	0.398192i	0.577663	−	0.816275i	$-0.303965\pi$
$137$	17.3940	−	4.66071i	1.48607	−	0.398192i	0.908409	+	0.418084i	$0.137298\pi$
$138$		0			0
$139$	−17.9003	−	10.3347i	−1.51828	−	0.876582i	−0.999769	−	0.0215139i	$-0.993151\pi$
$139$	−17.9003	−	10.3347i	−1.51828	−	0.876582i	−0.518516	−	0.855068i	$-0.673515\pi$
$140$		0			0
$141$	−9.63774	+	35.9686i	−0.811645	+	3.02910i
$142$		0			0
$143$	11.3876	−	3.65006i	0.952277	−	0.305234i
$144$		0			0
$145$	−1.54065	+	5.74977i	−0.127944	+	0.477492i
$146$		0			0
$147$	23.7115	+	13.6898i	1.95569	+	1.12912i
$148$		0			0
$149$	−7.83951	+	2.10059i	−0.642237	+	0.172087i	−0.565217	−	0.824943i	$-0.691207\pi$
$149$	−7.83951	+	2.10059i	−0.642237	+	0.172087i	−0.0770207	+	0.997029i	$0.524541\pi$
$150$		0			0
$151$	−6.56303	+	6.56303i	−0.534092	+	0.534092i	−0.921788	−	0.387695i	$-0.873271\pi$
$151$	−6.56303	+	6.56303i	−0.534092	+	0.534092i	0.387695	+	0.921788i	$0.373271\pi$
$152$		0			0
$153$	13.5241	+	23.4245i	1.09336	+	1.89376i
$154$		0			0
$155$		−	2.82620i		−	0.227006i
$156$		0			0
$157$	−14.2293			−1.13562			−0.567811	−	0.823159i	$-0.692210\pi$
$157$	−14.2293			−1.13562			−0.567811	+	0.823159i	$0.692210\pi$
$158$		0			0
$159$	−12.2599	−	21.2348i	−0.972275	−	1.68403i
$160$		0			0
$161$	6.51760	+	6.51760i	0.513659	+	0.513659i
$162$		0			0
$163$	−11.8434	+	3.17343i	−0.927646	+	0.248562i	−0.690850	−	0.722998i	$-0.742764\pi$
$163$	−11.8434	+	3.17343i	−0.927646	+	0.248562i	−0.236795	+	0.971560i	$0.576097\pi$
$164$		0			0
$165$	6.33858	−	2.98565i	0.493458	−	0.232433i
$166$		0			0
$167$	−3.36037	−	0.900408i	−0.260033	−	0.0696757i	0.126447	−	0.991973i	$-0.459643\pi$
$167$	−3.36037	−	0.900408i	−0.260033	−	0.0696757i	−0.386480	+	0.922298i	$0.626309\pi$
$168$		0			0
$169$	9.20856	+	9.17619i	0.708351	+	0.705861i
$170$		0			0
$171$	−12.9289	+	48.2514i	−0.988700	+	3.68988i
$172$		0			0
$173$	−0.305153	+	0.528541i	−0.0232004	+	0.0401842i	−0.877392	−	0.479773i	$-0.840719\pi$
$173$	−0.305153	+	0.528541i	−0.0232004	+	0.0401842i	0.854192	+	0.519958i	$0.174052\pi$
$174$		0			0
$175$	17.4209	−	4.66790i	1.31689	−	0.352860i
$176$		0			0
$177$	12.6276	+	12.6276i	0.949146	+	0.949146i
$178$		0			0
$179$	19.7499	−	11.4026i	1.47617	−	0.852270i	0.476536	−	0.879155i	$-0.341892\pi$
$179$	19.7499	−	11.4026i	1.47617	−	0.852270i	0.999639	+	0.0268853i	$0.00855888\pi$
$180$		0			0
$181$		−	6.40584i		−	0.476142i	−0.971248	−	0.238071i	$-0.923485\pi$
$181$		−	6.40584i		−	0.476142i	0.971248	−	0.238071i	$-0.0765152\pi$
$182$		0			0
$183$			20.2802i			1.49915i
$184$		0			0
$185$	1.50001	+	2.59809i	0.110283	+	0.191015i
$186$		0			0
$187$	2.34979	+	13.0312i	0.171834	+	0.952935i
$188$		0			0
$189$	−12.1255	−	45.2531i	−0.882002	−	3.29168i
$190$		0			0
$191$	−4.22458	+	7.31719i	−0.305680	+	0.529453i	−0.977413	−	0.211340i	$-0.932217\pi$
$191$	−4.22458	+	7.31719i	−0.305680	+	0.529453i	0.671732	+	0.740794i	$0.265550\pi$
$192$		0			0
$193$	19.3129	+	5.17489i	1.39018	+	0.372497i	0.874807	−	0.484472i	$-0.160988\pi$
$193$	19.3129	+	5.17489i	1.39018	+	0.372497i	0.515369	+	0.856968i	$0.327655\pi$
$194$		0			0
$195$	6.04699	+	4.63156i	0.433034	+	0.331673i
$196$		0			0
$197$	0.761372	−	2.84148i	0.0542455	−	0.202447i	−0.933485	−	0.358617i	$-0.883248\pi$
$197$	0.761372	−	2.84148i	0.0542455	−	0.202447i	0.987730	+	0.156170i	$0.0499149\pi$
$198$		0			0
$199$	11.8089	+	6.81790i	0.837114	+	0.483308i	0.856282	−	0.516508i	$-0.172769\pi$
$199$	11.8089	+	6.81790i	0.837114	+	0.483308i	−0.0191684	+	0.999816i	$0.506102\pi$
$200$		0			0
$201$	4.31979	+	16.1217i	0.304694	+	1.13713i
$202$		0			0
$203$	24.7276	+	24.7276i	1.73554	+	1.73554i
$204$		0			0
$205$	0.390690	+	0.676696i	0.0272870	+	0.0472625i
$206$		0			0
$207$		−	15.7313i		−	1.09340i
$208$		0			0
$209$	−13.9489	+	20.0861i	−0.964865	+	1.38939i
$210$		0			0
$211$	9.15337	−	5.28470i	0.630144	−	0.363814i	−0.150664	−	0.988585i	$-0.548141\pi$
$211$	9.15337	−	5.28470i	0.630144	−	0.363814i	0.780808	+	0.624771i	$0.214808\pi$
$212$		0			0
$213$	15.2249	−	15.2249i	1.04319	−	1.04319i
$214$		0			0
$215$	0.174530	+	0.651355i	0.0119029	+	0.0444221i
$216$		0			0
$217$	−14.3788	−	8.30161i	−0.976098	−	0.563550i
$218$		0			0
$219$	−16.1834	−	4.33634i	−1.09357	−	0.293022i
$220$		0			0
$221$	−11.4125	+	8.77309i	−0.767687	+	0.590142i
$222$		0			0
$223$	1.19284	+	0.319621i	0.0798785	+	0.0214034i	0.298537	−	0.954398i	$-0.403501\pi$
$223$	1.19284	+	0.319621i	0.0798785	+	0.0214034i	−0.218658	+	0.975801i	$0.570168\pi$
$224$		0			0
$225$	−26.6574	−	15.3907i	−1.77716	−	1.02605i
$226$		0			0
$227$	−27.2552	+	7.30300i	−1.80899	+	0.484717i	−0.995322	−	0.0966131i	$-0.969199\pi$
$227$	−27.2552	+	7.30300i	−1.80899	+	0.484717i	−0.813668	+	0.581330i	$0.802532\pi$
$228$		0			0
$229$	−5.79059	−	5.79059i	−0.382653	−	0.382653i	0.489404	−	0.872057i	$-0.337214\pi$
$229$	−5.79059	−	5.79059i	−0.382653	−	0.382653i	−0.872057	+	0.489404i	$0.837214\pi$
$230$		0			0
$231$	3.42874	−	41.0187i	0.225594	−	2.69883i
$232$		0			0
$233$	−2.46751			−0.161652			−0.0808261	−	0.996728i	$-0.525756\pi$
$233$	−2.46751			−0.161652			−0.0808261	+	0.996728i	$0.525756\pi$
$234$		0			0
$235$	−8.04774			−0.524977
$236$		0			0
$237$	−42.1009	+	24.3070i	−2.73475	+	1.57891i
$238$		0			0
$239$	8.61060	+	8.61060i	0.556974	+	0.556974i	0.928445	−	0.371471i	$-0.121146\pi$
$239$	8.61060	+	8.61060i	0.556974	+	0.556974i	−0.371471	+	0.928445i	$0.621146\pi$
$240$		0			0
$241$	1.64691	+	6.14636i	0.106087	+	0.395922i	0.998466	−	0.0553645i	$-0.0176321\pi$
$241$	1.64691	+	6.14636i	0.106087	+	0.395922i	−0.892379	+	0.451286i	$0.850965\pi$
$242$		0			0
$243$	−8.20694	+	14.2148i	−0.526475	+	0.911882i
$244$		0			0
$245$	−1.53151	+	5.71566i	−0.0978444	+	0.365160i
$246$		0			0
$247$	−26.3605	−	3.44682i	−1.67728	−	0.219316i
$248$		0			0
$249$	3.38424	−	12.6302i	0.214468	−	0.800404i
$250$		0			0
$251$	1.54880	+	0.894197i	0.0977591	+	0.0564412i	0.548082	−	0.836424i	$-0.315358\pi$
$251$	1.54880	+	0.894197i	0.0977591	+	0.0564412i	−0.450323	+	0.892866i	$0.648691\pi$
$252$		0			0
$253$	2.60593	−	7.24690i	0.163834	−	0.455608i
$254$		0			0
$255$	−5.96387	+	5.96387i	−0.373472	+	0.373472i
$256$		0			0
$257$	−16.3333	+	9.43002i	−1.01884	+	0.588229i	−0.913768	−	0.406236i	$-0.866841\pi$
$257$	−16.3333	+	9.43002i	−1.01884	+	0.588229i	−0.105074	+	0.994464i	$0.533508\pi$
$258$		0			0
$259$	17.6244			1.09512
$260$		0			0
$261$		−	59.6841i		−	3.69435i
$262$		0			0
$263$	−3.37420	+	1.94810i	−0.208062	+	0.120125i	−0.600411	−	0.799692i	$-0.704996\pi$
$263$	−3.37420	+	1.94810i	−0.208062	+	0.120125i	0.392348	+	0.919817i	$0.371663\pi$
$264$		0			0
$265$	3.74712	−	3.74712i	0.230184	−	0.230184i
$266$		0			0
$267$	2.75632	−	0.738553i	0.168684	−	0.0451987i
$268$		0			0
$269$	9.36252	−	16.2164i	0.570843	−	0.988729i	−0.425637	−	0.904894i	$-0.639950\pi$
$269$	9.36252	−	16.2164i	0.570843	−	0.988729i	0.996480	−	0.0838349i	$-0.0267168\pi$
$270$		0			0
$271$	4.59616	+	1.23154i	0.279197	+	0.0748106i	0.395700	−	0.918380i	$-0.370502\pi$
$271$	4.59616	+	1.23154i	0.279197	+	0.0748106i	−0.116503	+	0.993190i	$0.537169\pi$
$272$		0			0
$273$	41.3263	−	17.1605i	2.50118	−	1.03860i
$274$		0			0
$275$	−9.73069	−	11.5058i	−0.586783	−	0.693829i
$276$		0			0
$277$	10.8710	−	18.8291i	0.653173	−	1.13133i	−0.329175	−	0.944269i	$-0.606771\pi$
$277$	10.8710	−	18.8291i	0.653173	−	1.13133i	0.982348	−	0.187060i	$-0.0598960\pi$
$278$		0			0
$279$	7.33417	+	27.3715i	0.439085	+	1.63869i
$280$		0			0
$281$	7.54703	−	7.54703i	0.450218	−	0.450218i	−0.445209	−	0.895427i	$-0.646871\pi$
$281$	7.54703	−	7.54703i	0.450218	−	0.450218i	0.895427	+	0.445209i	$0.146871\pi$
$282$		0			0
$283$	−1.48163	−	2.56626i	−0.0880738	−	0.152548i	0.818623	−	0.574331i	$-0.194738\pi$
$283$	−1.48163	−	2.56626i	−0.0880738	−	0.152548i	−0.906697	+	0.421783i	$0.861404\pi$
$284$		0			0
$285$	−15.5765			−0.922673
$286$		0			0
$287$	4.59042			0.270964
$288$		0			0
$289$	0.530302	+	0.918510i	0.0311942	+	0.0540300i
$290$		0			0
$291$	−30.4467	+	30.4467i	−1.78482	+	1.78482i
$292$		0			0
$293$	7.07010	+	26.3860i	0.413040	+	1.54149i	0.788730	+	0.614740i	$0.210739\pi$
$293$	7.07010	+	26.3860i	0.413040	+	1.54149i	−0.375690	+	0.926746i	$0.622594\pi$
$294$		0			0
$295$	−1.92974	+	3.34241i	−0.112354	+	0.194603i
$296$		0			0
$297$	−29.8880	+	25.2768i	−1.73428	+	1.46671i
$298$		0			0
$299$	8.29949	−	1.10008i	0.479972	−	0.0636194i
$300$		0			0
$301$	3.82656	+	1.02532i	0.220559	+	0.0590986i
$302$		0			0
$303$	−9.42492	+	16.3244i	−0.541448	+	0.937815i
$304$		0			0
$305$	−4.23360	+	1.13439i	−0.242415	+	0.0649550i
$306$		0			0
$307$	−7.41011	+	7.41011i	−0.422917	+	0.422917i	−0.886207	−	0.463290i	$-0.846669\pi$
$307$	−7.41011	+	7.41011i	−0.422917	+	0.422917i	0.463290	+	0.886207i	$0.346669\pi$
$308$		0			0
$309$	−28.4784	+	16.4420i	−1.62008	+	0.935354i
$310$		0			0
$311$		−	11.7397i		−	0.665700i	−0.942980	−	0.332850i	$-0.891990\pi$
$311$		−	11.7397i		−	0.665700i	0.942980	−	0.332850i	$-0.108010\pi$
$312$		0			0
$313$	6.34977			0.358910			0.179455	−	0.983766i	$-0.442567\pi$
$313$	6.34977			0.358910			0.179455	+	0.983766i	$0.442567\pi$
$314$		0			0
$315$	15.7372	−	9.08586i	0.886689	−	0.511930i
$316$		0			0
$317$	−5.63617	+	5.63617i	−0.316559	+	0.316559i	−0.847444	−	0.530885i	$-0.821860\pi$
$317$	−5.63617	+	5.63617i	−0.316559	+	0.316559i	0.530885	+	0.847444i	$0.321860\pi$
$318$		0			0
$319$	9.88682	−	27.4945i	0.553556	−	1.53940i
$320$		0			0
$321$	36.5514	+	21.1029i	2.04010	+	1.17785i
$322$		0			0
$323$	7.61895	−	28.4343i	0.423930	−	1.58213i
$324$		0			0
$325$	6.25564	−	15.1401i	0.347000	−	0.839823i
$326$		0			0
$327$	2.37000	−	8.84495i	0.131061	−	0.489127i
$328$		0			0
$329$	−23.6393	+	40.9444i	−1.30328	+	2.25734i
$330$		0			0
$331$	2.29309	+	8.55794i	0.126040	+	0.470387i	0.999875	−	0.0158360i	$-0.00504097\pi$
$331$	2.29309	+	8.55794i	0.126040	+	0.470387i	−0.873835	+	0.486223i	$0.838374\pi$
$332$		0			0
$333$	−21.2697	−	21.2697i	−1.16557	−	1.16557i
$334$		0			0
$335$	−3.12386	+	1.80356i	−0.170675	+	0.0985391i
$336$		0			0
$337$	−13.0009			−0.708206			−0.354103	−	0.935206i	$-0.615214\pi$
$337$	−13.0009			−0.708206			−0.354103	+	0.935206i	$0.615214\pi$
$338$		0			0
$339$	−27.1911			−1.47682
$340$		0			0
$341$	−1.15555	+	13.8241i	−0.0625764	+	0.748615i
$342$		0			0
$343$	4.93263	+	4.93263i	0.266337	+	0.266337i
$344$		0			0
$345$	4.73820	−	1.26960i	0.255096	−	0.0683527i
$346$		0			0
$347$	27.6763	+	15.9789i	1.48574	+	0.857793i	0.999868	−	0.0162365i	$-0.00516848\pi$
$347$	27.6763	+	15.9789i	1.48574	+	0.857793i	0.485873	+	0.874030i	$0.338502\pi$
$348$		0			0
$349$	0.645630	+	0.172996i	0.0345598	+	0.00926027i	0.276058	−	0.961141i	$-0.410972\pi$
$349$	0.645630	+	0.172996i	0.0345598	+	0.00926027i	−0.241498	+	0.970401i	$0.577639\pi$
$350$		0			0
$351$	−39.3286	−	16.2499i	−2.09920	−	0.867354i
$352$		0			0
$353$	17.0160	+	4.55942i	0.905670	+	0.242674i	0.681450	−	0.731865i	$-0.261350\pi$
$353$	17.0160	+	4.55942i	0.905670	+	0.242674i	0.224220	+	0.974538i	$0.428016\pi$
$354$		0			0
$355$	4.02990	+	2.32666i	0.213885	+	0.123487i
$356$		0			0
$357$	12.8242	+	47.8605i	0.678728	+	2.53305i
$358$		0			0
$359$	7.65365	−	7.65365i	0.403944	−	0.403944i	−0.475676	−	0.879620i	$-0.657797\pi$
$359$	7.65365	−	7.65365i	0.403944	−	0.403944i	0.879620	+	0.475676i	$0.157797\pi$
$360$		0			0
$361$	30.6277	−	17.6829i	1.61198	−	0.930679i
$362$		0			0
$363$	−32.2253	+	12.0124i	−1.69139	+	0.630485i
$364$		0			0
$365$		−	3.62094i		−	0.189529i
$366$		0			0
$367$	−6.84759	−	11.8604i	−0.357442	−	0.619107i	0.630091	−	0.776521i	$-0.283018\pi$
$367$	−6.84759	−	11.8604i	−0.357442	−	0.619107i	−0.987533	+	0.157414i	$0.949684\pi$
$368$		0			0
$369$	−5.53988	−	5.53988i	−0.288394	−	0.288394i
$370$		0			0
$371$	−8.05747	−	30.0709i	−0.418323	−	1.56120i
$372$		0			0
$373$	7.48769	+	4.32302i	0.387698	+	0.223837i	0.681162	−	0.732133i	$-0.261475\pi$
$373$	7.48769	+	4.32302i	0.387698	+	0.223837i	−0.293464	+	0.955970i	$0.594808\pi$
$374$		0			0
$375$	5.21805	−	19.4740i	0.269459	−	1.00564i
$376$		0			0
$377$	31.4880	−	4.17368i	1.62171	−	0.214955i
$378$		0			0
$379$	2.95447	+	0.791648i	0.151761	+	0.0406642i	0.333900	−	0.942609i	$-0.391635\pi$
$379$	2.95447	+	0.791648i	0.151761	+	0.0406642i	−0.182139	+	0.983273i	$0.558302\pi$
$380$		0			0
$381$	−18.1857	+	31.4985i	−0.931681	+	1.61372i
$382$		0			0
$383$	1.63995	+	6.12037i	0.0837975	+	0.312736i	0.995084	−	0.0990369i	$-0.0315762\pi$
$383$	1.63995	+	6.12037i	0.0837975	+	0.312736i	−0.911286	+	0.411773i	$0.864910\pi$
$384$		0			0
$385$	8.75468	−	1.57865i	0.446180	−	0.0804556i
$386$		0			0
$387$	−3.38062	−	5.85541i	−0.171847	−	0.297647i
$388$		0			0
$389$			13.9676i			0.708183i	0.935211	+	0.354092i	$0.115210\pi$
$389$			13.9676i			0.708183i	−0.935211	+	0.354092i	$0.884790\pi$
$390$		0			0
$391$			9.27038i			0.468823i
$392$		0			0
$393$	−17.7174	+	10.2291i	−0.893724	+	0.515992i
$394$		0			0
$395$	−7.42918	−	7.42918i	−0.373802	−	0.373802i
$396$		0			0
$397$	9.18194	−	2.46029i	0.460828	−	0.123479i	−0.0209333	−	0.999781i	$-0.506664\pi$
$397$	9.18194	−	2.46029i	0.460828	−	0.123479i	0.481762	+	0.876302i	$0.339997\pi$
$398$		0			0
$399$	−45.7542	+	79.2485i	−2.29057	+	3.96739i
$400$		0			0
$401$	6.28094	−	23.4408i	0.313655	−	1.17058i	−0.611580	−	0.791183i	$-0.709466\pi$
$401$	6.28094	−	23.4408i	0.313655	−	1.17058i	0.925235	−	0.379395i	$-0.123868\pi$
$402$		0			0
$403$	−13.9277	+	5.78342i	−0.693789	+	0.288093i
$404$		0			0
$405$	−10.8178	−	2.89863i	−0.537542	−	0.144034i
$406$		0			0
$407$	−6.27485	−	13.3216i	−0.311033	−	0.660327i
$408$		0			0
$409$	20.9059	−	5.60172i	1.03373	−	0.276987i	0.298218	−	0.954498i	$-0.403608\pi$
$409$	20.9059	−	5.60172i	1.03373	−	0.276987i	0.735513	+	0.677510i	$0.236941\pi$
$410$		0			0
$411$	−39.8105	−	39.8105i	−1.96371	−	1.96371i
$412$		0			0
$413$	11.3368	+	19.6359i	0.557846	+	0.966218i
$414$		0			0
$415$	2.82592			0.138719
$416$		0			0
$417$			64.6229i			3.16460i
$418$		0			0
$419$	−2.69305	−	4.66449i	−0.131564	−	0.227875i	0.792716	−	0.609592i	$-0.208667\pi$
$419$	−2.69305	−	4.66449i	−0.131564	−	0.227875i	−0.924280	+	0.381716i	$0.875333\pi$
$420$		0			0
$421$	14.8300	−	14.8300i	0.722769	−	0.722769i	−0.246400	−	0.969168i	$-0.579248\pi$
$421$	14.8300	−	14.8300i	0.722769	−	0.722769i	0.969168	+	0.246400i	$0.0792476\pi$
$422$		0			0
$423$	77.9417	−	20.8844i	3.78966	−	1.01544i
$424$		0			0
$425$	15.7091	+	9.06964i	0.762003	+	0.439942i
$426$		0			0
$427$	−6.66427	+	24.8714i	−0.322507	+	1.20361i
$428$		0			0
$429$	−27.6845	−	25.1273i	−1.33662	−	1.21316i
$430$		0			0
$431$	−1.72236	+	6.42795i	−0.0829633	+	0.309623i	−0.994921	−	0.100662i	$-0.967904\pi$
$431$	−1.72236	+	6.42795i	−0.0829633	+	0.309623i	0.911957	+	0.410285i	$0.134571\pi$
$432$		0			0
$433$	−8.94600	−	5.16498i	−0.429917	−	0.248213i	0.269394	−	0.963030i	$-0.413177\pi$
$433$	−8.94600	−	5.16498i	−0.429917	−	0.248213i	−0.699311	+	0.714817i	$0.746510\pi$
$434$		0			0
$435$	17.9766	−	4.81680i	0.861910	−	0.230948i
$436$		0			0
$437$	−12.1062	+	12.1062i	−0.579120	+	0.579120i
$438$		0			0
$439$	−14.3656	−	24.8819i	−0.685631	−	1.18755i	−0.973238	−	0.229800i	$-0.926193\pi$
$439$	−14.3656	−	24.8819i	−0.685631	−	1.18755i	0.287607	−	0.957749i	$-0.407140\pi$
$440$		0			0
$441$		−	59.3301i		−	2.82524i
$442$		0			0
$443$	−2.79772			−0.132924			−0.0664618	−	0.997789i	$-0.521171\pi$
$443$	−2.79772			−0.132924			−0.0664618	+	0.997789i	$0.521171\pi$
$444$		0			0
$445$	0.308354	+	0.534086i	0.0146174	+	0.0253181i
$446$		0			0
$447$	17.9426	+	17.9426i	0.848658	+	0.848658i
$448$		0			0
$449$	9.42731	−	2.52604i	0.444902	−	0.119211i	−0.0294108	−	0.999567i	$-0.509363\pi$
$449$	9.42731	−	2.52604i	0.444902	−	0.119211i	0.474313	+	0.880356i	$0.342696\pi$
$450$		0			0
$451$	−1.63434	−	3.46973i	−0.0769582	−	0.163383i
$452$		0			0
$453$	28.0298	+	7.51056i	1.31695	+	0.352877i
$454$		0			0
$455$	5.89399	+	7.66721i	0.276314	+	0.359444i
$456$		0			0
$457$	−0.0751127	+	0.280324i	−0.00351362	+	0.0131130i	−0.967660	−	0.252257i	$-0.918827\pi$
$457$	−0.0751127	+	0.280324i	−0.00351362	+	0.0131130i	0.964147	+	0.265370i	$0.0854940\pi$
$458$		0			0
$459$	23.5597	−	40.8065i	1.09967	−	1.90469i
$460$		0			0
$461$	−0.775606	+	0.207823i	−0.0361236	+	0.00967929i	−0.276836	−	0.960917i	$-0.589286\pi$
$461$	−0.775606	+	0.207823i	−0.0361236	+	0.00967929i	0.240712	+	0.970597i	$0.422619\pi$
$462$		0			0
$463$	16.1917	+	16.1917i	0.752492	+	0.752492i	0.974944	−	0.222452i	$-0.0714060\pi$
$463$	16.1917	+	16.1917i	0.752492	+	0.752492i	−0.222452	+	0.974944i	$0.571406\pi$
$464$		0			0
$465$	−7.65225	+	4.41803i	−0.354865	+	0.204881i
$466$		0			0
$467$		−	26.1802i		−	1.21147i	−0.795665	−	0.605737i	$-0.792878\pi$
$467$		−	26.1802i		−	1.21147i	0.795665	−	0.605737i	$-0.207122\pi$
$468$		0			0
$469$			21.1910i			0.978508i
$470$		0			0
$471$	22.2439	+	38.5275i	1.02494	+	1.77525i
$472$		0			0
$473$	−0.587377	−	3.25740i	−0.0270076	−	0.149775i
$474$		0			0
$475$	8.67049	+	32.3587i	0.397829	+	1.48472i
$476$		0			0
$477$	−26.5665	+	46.0146i	−1.21640	+	2.10686i
$478$		0			0
$479$	−3.54595	−	0.950135i	−0.162019	−	0.0434128i	0.176898	−	0.984229i	$-0.443394\pi$
$479$	−3.54595	−	0.950135i	−0.162019	−	0.0434128i	−0.338917	+	0.940816i	$0.610060\pi$
$480$		0			0
$481$	9.73402	−	12.7088i	0.443833	−	0.579470i
$482$		0			0
$483$	7.45857	−	27.8358i	0.339377	−	1.26657i
$484$		0			0
$485$	−8.05899	−	4.65286i	−0.365940	−	0.211275i
$486$		0			0
$487$	−10.1039	−	37.7084i	−0.457853	−	1.70873i	−0.679563	−	0.733617i	$-0.737831\pi$
$487$	−10.1039	−	37.7084i	−0.457853	−	1.70873i	0.221711	−	0.975112i	$-0.428836\pi$
$488$		0			0
$489$	27.1065	+	27.1065i	1.22580	+	1.22580i
$490$		0			0
$491$	15.4238	+	26.7148i	0.696066	+	1.20562i	0.969820	+	0.243821i	$0.0784011\pi$
$491$	15.4238	+	26.7148i	0.696066	+	1.20562i	−0.273755	+	0.961800i	$0.588266\pi$
$492$		0			0
$493$			35.1715i			1.58405i
$494$		0			0
$495$	−12.4706	−	8.66027i	−0.560512	−	0.389250i
$496$		0			0
$497$	23.6747	−	13.6686i	1.06196	−	0.613120i
$498$		0			0
$499$	7.99551	−	7.99551i	0.357928	−	0.357928i	−0.505121	−	0.863049i	$-0.668552\pi$
$499$	7.99551	−	7.99551i	0.357928	−	0.357928i	0.863049	+	0.505121i	$0.168552\pi$
$500$		0			0
$501$	2.81511	+	10.5061i	0.125770	+	0.469380i
$502$		0			0
$503$	1.07284	+	0.619403i	0.0478355	+	0.0276178i	0.523727	−	0.851886i	$-0.324541\pi$
$503$	1.07284	+	0.619403i	0.0478355	+	0.0276178i	−0.475892	+	0.879504i	$0.657875\pi$
$504$		0			0
$505$	−3.93501	−	1.05438i	−0.175106	−	0.0469195i
$506$		0			0
$507$	10.4504	−	39.2778i	0.464118	−	1.74439i
$508$		0			0
$509$	7.15268	+	1.91655i	0.317037	+	0.0849498i	0.413828	−	0.910355i	$-0.364191\pi$
$509$	7.15268	+	1.91655i	0.317037	+	0.0849498i	−0.0967916	+	0.995305i	$0.530858\pi$
$510$		0			0
$511$	−18.4222	−	10.6361i	−0.814952	−	0.470513i
$512$		0			0
$513$	84.0562	−	22.5228i	3.71117	−	0.994405i
$514$		0			0
$515$	−5.02534	−	5.02534i	−0.221443	−	0.221443i
$516$		0			0
$517$	39.3647	+	3.29048i	1.73126	+	0.144715i
$518$		0			0
$519$	1.90812			0.0837570
$520$		0			0
$521$	−21.0187			−0.920847			−0.460424	−	0.887699i	$-0.652302\pi$
$521$	−21.0187			−0.920847			−0.460424	+	0.887699i	$0.652302\pi$
$522$		0			0
$523$	10.6969	−	6.17584i	0.467741	−	0.270050i	−0.247553	−	0.968874i	$-0.579626\pi$
$523$	10.6969	−	6.17584i	0.467741	−	0.270050i	0.715294	+	0.698824i	$0.246293\pi$
$524$		0			0
$525$	−39.8719	−	39.8719i	−1.74015	−	1.74015i
$526$		0			0
$527$	−4.32199	−	16.1299i	−0.188269	−	0.702628i
$528$		0			0
$529$	−8.80417	+	15.2493i	−0.382790	+	0.663011i
$530$		0			0
$531$	10.0156	−	37.3788i	0.434641	−	1.62210i
$532$		0			0
$533$	2.53531	−	3.31011i	0.109817	−	0.143377i
$534$		0			0
$535$	−2.36083	+	8.81072i	−0.102067	+	0.380921i
$536$		0			0
$537$	−61.7477	−	35.6500i	−2.66461	−	1.53841i
$538$		0			0
$539$	9.82818	−	27.3314i	0.423330	−	1.17725i
$540$		0			0
$541$	24.4117	−	24.4117i	1.04954	−	1.04954i	0.0508347	−	0.998707i	$-0.483812\pi$
$541$	24.4117	−	24.4117i	1.04954	−	1.04954i	0.998707	−	0.0508347i	$-0.0161882\pi$
$542$		0			0
$543$	−17.3446	+	10.0139i	−0.744326	+	0.429737i
$544$		0			0
$545$	1.97900			0.0847712
$546$		0			0
$547$			19.0377i			0.813992i	0.913430	+	0.406996i	$0.133424\pi$
$547$			19.0377i			0.813992i	−0.913430	+	0.406996i	$0.866576\pi$
$548$		0			0
$549$	38.0583	−	21.9730i	1.62429	−	0.937784i
$550$		0			0
$551$	−45.9307	+	45.9307i	−1.95671	+	1.95671i
$552$		0			0
$553$	−59.6197	+	15.9750i	−2.53529	+	0.679328i
$554$		0			0
$555$	4.68975	−	8.12288i	0.199069	−	0.344797i
$556$		0			0
$557$	−8.25675	−	2.21239i	−0.349850	−	0.0937420i	0.0796147	−	0.996826i	$-0.474631\pi$
$557$	−8.25675	−	2.21239i	−0.349850	−	0.0937420i	−0.429464	+	0.903084i	$0.641298\pi$
$558$		0			0
$559$	2.85278	−	2.19301i	0.120660	−	0.0927542i
$560$		0			0
$561$	31.6101	−	26.7332i	1.33458	−	1.12868i
$562$		0			0
$563$	−4.69347	+	8.12933i	−0.197806	+	0.342610i	−0.947817	−	0.318815i	$-0.896715\pi$
$563$	−4.69347	+	8.12933i	−0.197806	+	0.342610i	0.750011	+	0.661426i	$0.230048\pi$
$564$		0			0
$565$	−1.52096	−	5.67630i	−0.0639872	−	0.238804i
$566$		0			0
$567$	−46.5234	+	46.5234i	−1.95380	+	1.95380i
$568$		0			0
$569$	−18.0039	−	31.1836i	−0.754761	−	1.30728i	−0.945493	−	0.325642i	$-0.894420\pi$
$569$	−18.0039	−	31.1836i	−0.754761	−	1.30728i	0.190732	−	0.981642i	$-0.438914\pi$
$570$		0			0
$571$	−14.8778			−0.622618			−0.311309	−	0.950309i	$-0.600767\pi$
$571$	−14.8778			−0.622618			−0.311309	+	0.950309i	$0.600767\pi$
$572$		0			0
$573$	26.4162			1.10355
$574$		0			0
$575$	−5.27492	−	9.13643i	−0.219979	−	0.381016i
$576$		0			0
$577$	−16.9357	+	16.9357i	−0.705043	+	0.705043i	−0.965489	−	0.260445i	$-0.916131\pi$
$577$	−16.9357	+	16.9357i	−0.705043	+	0.705043i	0.260445	+	0.965489i	$0.416131\pi$
$578$		0			0
$579$	−16.1792	−	60.3816i	−0.672385	−	2.50938i
$580$		0			0
$581$	8.30080	−	14.3774i	0.344375	−	0.596475i
$582$		0			0
$583$	−19.8607	+	16.7966i	−0.822548	+	0.695643i
$584$		0			0
$585$	2.13998	−	16.3661i	0.0884773	−	0.676655i
$586$		0			0
$587$	36.2901	+	9.72391i	1.49785	+	0.401349i	0.912380	−	0.409343i	$-0.134242\pi$
$587$	36.2901	+	9.72391i	1.49785	+	0.401349i	0.585473	+	0.810692i	$0.300909\pi$
$588$		0			0
$589$	15.4200	−	26.7082i	0.635370	−	1.10049i
$590$		0			0
$591$	−8.88384	+	2.38042i	−0.365432	+	0.0979173i
$592$		0			0
$593$	23.2367	−	23.2367i	0.954216	−	0.954216i	−0.0447806	−	0.998997i	$-0.514259\pi$
$593$	23.2367	−	23.2367i	0.954216	−	0.954216i	0.998997	+	0.0447806i	$0.0142589\pi$
$594$		0			0
$595$	−9.27383	+	5.35425i	−0.380190	+	0.219503i
$596$		0			0
$597$		−	42.6321i		−	1.74482i
$598$		0			0
$599$	−29.5864			−1.20887			−0.604434	−	0.796656i	$-0.706600\pi$
$599$	−29.5864			−1.20887			−0.604434	+	0.796656i	$0.706600\pi$
$600$		0			0
$601$	3.97969	−	2.29767i	0.162335	−	0.0937240i	−0.416632	−	0.909075i	$-0.636790\pi$
$601$	3.97969	−	2.29767i	0.162335	−	0.0937240i	0.578966	+	0.815351i	$0.303456\pi$
$602$		0			0
$603$	25.5740	−	25.5740i	1.04145	−	1.04145i
$604$		0			0
$605$	−4.31020	−	6.05529i	−0.175235	−	0.246182i
$606$		0			0
$607$	−27.7384	−	16.0148i	−1.12587	−	0.650020i	−0.182976	−	0.983117i	$-0.558573\pi$
$607$	−27.7384	−	16.0148i	−1.12587	−	0.650020i	−0.942893	+	0.333097i	$0.891906\pi$
$608$		0			0
$609$	28.2976	−	105.608i	1.14668	−	4.27945i
$610$		0			0
$611$	16.4686	+	39.6599i	0.666247	+	1.60447i
$612$		0			0
$613$	−9.28313	+	34.6451i	−0.374942	+	1.39930i	0.478487	+	0.878095i	$0.341185\pi$
$613$	−9.28313	+	34.6451i	−0.374942	+	1.39930i	−0.853429	+	0.521209i	$0.825481\pi$
$614$		0			0
$615$	1.22149	−	2.11568i	0.0492551	−	0.0853124i
$616$		0			0
$617$	1.25696	+	4.69102i	0.0506031	+	0.188854i	0.986601	−	0.163153i	$-0.0521663\pi$
$617$	1.25696	+	4.69102i	0.0506031	+	0.188854i	−0.935998	+	0.352006i	$0.885500\pi$
$618$		0			0
$619$	7.70022	+	7.70022i	0.309498	+	0.309498i	0.844715	−	0.535217i	$-0.179770\pi$
$619$	7.70022	+	7.70022i	0.309498	+	0.309498i	−0.535217	+	0.844715i	$0.679770\pi$
$620$		0			0
$621$	−23.7331	+	13.7023i	−0.952378	+	0.549856i
$622$		0			0
$623$	3.62302			0.145153
$624$		0			0
$625$	−18.3600			−0.734399
$626$		0			0
$627$	76.1910	+	6.36877i	3.04277	+	0.254344i
$628$		0			0
$629$	12.5341	+	12.5341i	0.499767	+	0.499767i
$630$		0			0
$631$	2.20198	−	0.590020i	0.0876596	−	0.0234883i	−0.214723	−	0.976675i	$-0.568885\pi$
$631$	2.20198	−	0.590020i	0.0876596	−	0.0234883i	0.302382	+	0.953187i	$0.402218\pi$
$632$		0			0
$633$	−28.6179	−	16.5225i	−1.13746	−	0.656712i
$634$		0			0
$635$	−7.59274	−	2.03447i	−0.301309	−	0.0807354i
$636$		0			0
$637$	31.3012	−	4.14892i	1.24020	−	0.164386i
$638$		0			0
$639$	−45.0671	−	12.0757i	−1.78283	−	0.477707i
$640$		0			0
$641$	39.4377	+	22.7694i	1.55770	+	0.899337i	0.997477	+	0.0709934i	$0.0226169\pi$
$641$	39.4377	+	22.7694i	1.55770	+	0.899337i	0.560220	+	0.828344i	$0.310716\pi$
$642$		0			0
$643$	1.89343	+	7.06639i	0.0746697	+	0.278671i	0.993158	−	0.116777i	$-0.0372561\pi$
$643$	1.89343	+	7.06639i	0.0746697	+	0.278671i	−0.918489	+	0.395448i	$0.870589\pi$
$644$		0			0
$645$	1.49079	−	1.49079i	0.0586997	−	0.0586997i
$646$		0			0
$647$	30.5341	−	17.6288i	1.20042	−	0.693061i	0.239770	−	0.970830i	$-0.422928\pi$
$647$	30.5341	−	17.6288i	1.20042	−	0.693061i	0.960648	+	0.277768i	$0.0895948\pi$
$648$		0			0
$649$	10.8058	−	15.5601i	0.424163	−	0.610786i
$650$		0			0
$651$			51.9097i			2.03450i
$652$		0			0
$653$	−21.2159	−	36.7471i	−0.830244	−	1.43802i	−0.897845	−	0.440312i	$-0.854868\pi$
$653$	−21.2159	−	36.7471i	−0.830244	−	1.43802i	0.0676008	−	0.997712i	$-0.478466\pi$
$654$		0			0
$655$	−3.12643	−	3.12643i	−0.122160	−	0.122160i
$656$		0			0
$657$	9.39659	+	35.0685i	0.366596	+	1.36815i
$658$		0			0
$659$	−18.4581	−	10.6568i	−0.719027	−	0.415131i	0.0953673	−	0.995442i	$-0.469597\pi$
$659$	−18.4581	−	10.6568i	−0.719027	−	0.415131i	−0.814395	+	0.580312i	$0.802931\pi$
$660$		0			0
$661$	2.75930	−	10.2978i	0.107324	−	0.400540i	−0.891274	−	0.453465i	$-0.850188\pi$
$661$	2.75930	−	10.2978i	0.107324	−	0.400540i	0.998598	+	0.0529250i	$0.0168544\pi$
$662$		0			0
$663$	41.5947	+	17.1862i	1.61540	+	0.667456i
$664$		0			0
$665$	−19.1029	−	5.11860i	−0.740778	−	0.198491i
$666$		0			0
$667$	10.2279	−	17.7153i	0.396026	−	0.685938i
$668$		0			0
$669$	−0.999289	−	3.72940i	−0.0386347	−	0.144187i
$670$		0			0
$671$	21.1721	−	3.81777i	0.817339	−	0.147383i
$672$		0			0
$673$	20.1774	+	34.9483i	0.777782	+	1.34716i	0.933218	+	0.359311i	$0.116988\pi$
$673$	20.1774	+	34.9483i	0.777782	+	1.34716i	−0.155436	+	0.987846i	$0.549678\pi$
$674$		0			0
$675$			53.6225i			2.06393i
$676$		0			0
$677$		−	15.8030i		−	0.607360i	−0.952774	−	0.303680i	$-0.901785\pi$
$677$		−	15.8030i		−	0.607360i	0.952774	−	0.303680i	$-0.0982154\pi$
$678$		0			0
$679$	−47.3446	+	27.3344i	−1.81692	+	1.04900i
$680$		0			0
$681$	62.3802	+	62.3802i	2.39041	+	2.39041i
$682$		0			0
$683$	−31.4823	+	8.43566i	−1.20464	+	0.322782i	−0.804656	−	0.593742i	$-0.797650\pi$
$683$	−31.4823	+	8.43566i	−1.20464	+	0.322782i	−0.399981	+	0.916523i	$0.630983\pi$
$684$		0			0
$685$	6.08383	−	10.5375i	0.232451	−	0.402618i
$686$		0			0
$687$	−6.62659	+	24.7308i	−0.252820	+	0.943538i
$688$		0			0
$689$	−26.1340	−	10.7981i	−0.995627	−	0.411376i
$690$		0			0
$691$	19.1523	+	5.13185i	0.728589	+	0.195225i	0.604001	−	0.796984i	$-0.293572\pi$
$691$	19.1523	+	5.13185i	0.728589	+	0.195225i	0.124588	+	0.992209i	$0.460239\pi$
$692$		0			0
$693$	−80.6917	+	38.0081i	−3.06523	+	1.44381i
$694$		0			0
$695$	−13.4904	+	3.61474i	−0.511720	+	0.137115i
$696$		0			0
$697$	3.26462	+	3.26462i	0.123656	+	0.123656i
$698$		0			0
$699$	3.85732	+	6.68108i	0.145897	+	0.252702i
$700$		0			0
$701$	−46.8917			−1.77108			−0.885538	−	0.464566i	$-0.846210\pi$
$701$	−46.8917			−1.77108			−0.885538	+	0.464566i	$0.846210\pi$
$702$		0			0
$703$			32.7367i			1.23469i
$704$		0			0
$705$	12.5806	+	21.7902i	0.473812	+	0.820666i
$706$		0			0
$707$	−16.9230	+	16.9230i	−0.636455	+	0.636455i
$708$		0			0
$709$	28.0355	−	7.51209i	1.05290	−	0.282123i	0.309448	−	0.950916i	$-0.399856\pi$
$709$	28.0355	−	7.51209i	1.05290	−	0.282123i	0.743448	+	0.668794i	$0.233189\pi$
$710$		0			0
$711$	91.2302	+	52.6718i	3.42140	+	1.97535i
$712$		0			0
$713$	−2.51367	+	9.38116i	−0.0941379	+	0.351327i
$714$		0			0
$715$	3.69690	−	7.18482i	0.138256	−	0.268697i
$716$		0			0
$717$	9.85374	−	36.7747i	0.367995	−	1.37337i
$718$		0			0
$719$	40.9746	+	23.6567i	1.52809	+	0.882245i	0.999442	+	0.0334064i	$0.0106356\pi$
$719$	40.9746	+	23.6567i	1.52809	+	0.882245i	0.528652	+	0.848839i	$0.322698\pi$
$720$		0			0
$721$	−40.3287	+	10.8060i	−1.50192	+	0.402438i
$722$		0			0
$723$	14.0674	−	14.0674i	0.523174	−	0.523174i
$724$		0			0
$725$	−20.0129	−	34.6633i	−0.743260	−	1.28736i
$726$		0			0
$727$		−	22.6158i		−	0.838775i	−0.907807	−	0.419387i	$-0.862245\pi$
$727$		−	22.6158i		−	0.838775i	0.907807	−	0.419387i	$-0.137755\pi$
$728$		0			0
$729$	1.59371			0.0590262
$730$		0			0
$731$	1.99218	+	3.45056i	0.0736835	+	0.127624i
$732$		0			0
$733$	−20.7102	−	20.7102i	−0.764949	−	0.764949i	0.212263	−	0.977213i	$-0.431917\pi$
$733$	−20.7102	−	20.7102i	−0.764949	−	0.764949i	−0.977213	+	0.212263i	$0.931917\pi$
$734$		0			0
$735$	17.8699	−	4.78823i	0.659142	−	0.176617i
$736$		0			0
$737$	16.0175	−	7.54469i	0.590011	−	0.277912i
$738$		0			0
$739$	−32.3783	−	8.67575i	−1.19106	−	0.319143i	−0.391753	−	0.920070i	$-0.628131\pi$
$739$	−32.3783	−	8.67575i	−1.19106	−	0.319143i	−0.799303	+	0.600928i	$0.794798\pi$
$740$		0			0
$741$	31.8752	+	76.7622i	1.17096	+	2.81993i
$742$		0			0
$743$	11.6411	−	43.4452i	0.427070	−	1.59385i	−0.332289	−	0.943177i	$-0.607821\pi$
$743$	11.6411	−	43.4452i	0.427070	−	1.59385i	0.759360	−	0.650671i	$-0.225512\pi$
$744$		0			0
$745$	−2.74199	+	4.74927i	−0.100459	+	0.174000i
$746$		0			0
$747$	−27.3688	+	7.33345i	−1.00137	+	0.268317i
$748$		0			0
$749$	37.8916	+	37.8916i	1.38453	+	1.38453i
$750$		0			0
$751$	7.76965	−	4.48581i	0.283519	−	0.163690i	−0.351497	−	0.936189i	$-0.614327\pi$
$751$	7.76965	−	4.48581i	0.283519	−	0.163690i	0.635015	+	0.772500i	$0.280994\pi$
$752$		0			0
$753$		−	5.59139i		−	0.203762i
$754$		0			0
$755$			6.27149i			0.228243i
$756$		0			0
$757$	−12.6233	−	21.8641i	−0.458800	−	0.794665i	0.540098	−	0.841602i	$-0.318387\pi$
$757$	−12.6233	−	21.8641i	−0.458800	−	0.794665i	−0.998898	+	0.0469373i	$0.985054\pi$
$758$		0			0
$759$	−23.6955	+	4.27279i	−0.860093	+	0.155093i
$760$		0			0
$761$	6.78957	+	25.3390i	0.246122	+	0.918539i	0.972816	+	0.231578i	$0.0743889\pi$
$761$	6.78957	+	25.3390i	0.246122	+	0.918539i	−0.726695	+	0.686961i	$0.758944\pi$
$762$		0			0
$763$	5.81308	−	10.0686i	0.210448	−	0.364506i
$764$		0			0
$765$	17.6536	+	4.73028i	0.638269	+	0.171024i
$766$		0			0
$767$	20.4206	+	2.67014i	0.737345	+	0.0964130i
$768$		0			0
$769$	−8.72684	+	32.5690i	−0.314698	+	1.17447i	0.609573	+	0.792730i	$0.291341\pi$
$769$	−8.72684	+	32.5690i	−0.314698	+	1.17447i	−0.924271	+	0.381738i	$0.875326\pi$
$770$		0			0
$771$	51.0658	+	29.4828i	1.83909	+	1.06180i
$772$		0			0
$773$	5.71139	+	21.3152i	0.205424	+	0.766654i	0.989320	+	0.145761i	$0.0465631\pi$
$773$	5.71139	+	21.3152i	0.205424	+	0.766654i	−0.783895	+	0.620893i	$0.786770\pi$
$774$		0			0
$775$	13.4376	+	13.4376i	0.482692	+	0.482692i
$776$		0			0
$777$	−27.5511	−	47.7200i	−0.988392	−	1.71195i
$778$		0			0
$779$			8.52657i			0.305496i
$780$		0			0
$781$	−18.7606	−	13.0284i	−0.671305	−	0.466191i
$782$		0			0
$783$	−90.0428	+	51.9862i	−3.21787	+	1.85784i
$784$		0			0
$785$	−6.79860	+	6.79860i	−0.242653	+	0.242653i
$786$		0			0
$787$	2.92094	+	10.9011i	0.104120	+	0.388582i	0.998244	−	0.0592383i	$-0.0188672\pi$
$787$	2.92094	+	10.9011i	0.104120	+	0.388582i	−0.894124	+	0.447820i	$0.852201\pi$
$788$		0			0
$789$	10.5494	+	6.09070i	0.375568	+	0.216835i
$790$		0			0
$791$	−33.3469	−	8.93527i	−1.18568	−	0.317702i
$792$		0			0
$793$	14.2538	+	18.5421i	0.506169	+	0.658451i
$794$		0			0
$795$	−16.0034	−	4.28810i	−0.567583	−	0.152083i
$796$		0			0
$797$	−26.3013	−	15.1851i	−0.931639	−	0.537882i	−0.0443097	−	0.999018i	$-0.514109\pi$
$797$	−26.3013	−	15.1851i	−0.931639	−	0.537882i	−0.887330	+	0.461136i	$0.847442\pi$
$798$		0			0
$799$	−45.9306	+	12.3071i	−1.62491	+	0.435393i
$800$		0			0
$801$	−4.37238	−	4.37238i	−0.154490	−	0.154490i
$802$		0			0
$803$	−1.48049	+	17.7115i	−0.0522455	+	0.625024i
$804$		0			0
$805$	6.22808			0.219511
$806$		0			0
$807$	−58.5436			−2.06083
$808$		0			0
$809$	18.5827	−	10.7287i	0.653332	−	0.377201i	−0.136400	−	0.990654i	$-0.543553\pi$
$809$	18.5827	−	10.7287i	0.653332	−	0.377201i	0.789732	+	0.613453i	$0.210220\pi$
$810$		0			0
$811$	−21.5160	−	21.5160i	−0.755528	−	0.755528i	0.219977	−	0.975505i	$-0.429402\pi$
$811$	−21.5160	−	21.5160i	−0.755528	−	0.755528i	−0.975505	+	0.219977i	$0.929402\pi$
$812$		0			0
$813$	−3.85039	−	14.3698i	−0.135039	−	0.503972i
$814$		0			0
$815$	−4.14241	+	7.17487i	−0.145102	+	0.251325i
$816$		0			0
$817$	−1.90451	+	7.10771i	−0.0666302	+	0.248667i
$818$		0			0
$819$	−76.9797	−	58.9610i	−2.68989	−	2.06026i
$820$		0			0
$821$	−1.38546	+	5.17061i	−0.0483529	+	0.180455i	−0.985879	−	0.167460i	$-0.946444\pi$
$821$	−1.38546	+	5.17061i	−0.0483529	+	0.180455i	0.937526	+	0.347915i	$0.113110\pi$
$822$		0			0
$823$	6.78358	+	3.91650i	0.236461	+	0.136521i	0.613549	−	0.789657i	$-0.289741\pi$
$823$	6.78358	+	3.91650i	0.236461	+	0.136521i	−0.377088	+	0.926177i	$0.623075\pi$
$824$		0			0
$825$	−15.9420	+	44.3334i	−0.555028	+	1.54349i
$826$		0			0
$827$	26.4534	−	26.4534i	0.919874	−	0.919874i	−0.0771459	−	0.997020i	$-0.524581\pi$
$827$	26.4534	−	26.4534i	0.919874	−	0.919874i	0.997020	+	0.0771459i	$0.0245807\pi$
$828$		0			0
$829$	−4.76096	+	2.74874i	−0.165355	+	0.0954677i	−0.580394	−	0.814336i	$-0.697101\pi$
$829$	−4.76096	+	2.74874i	−0.165355	+	0.0954677i	0.415039	+	0.909804i	$0.363768\pi$
$830$		0			0
$831$	−67.9758			−2.35806
$832$		0			0
$833$			34.9629i			1.21139i
$834$		0			0
$835$	−2.03575	+	1.17534i	−0.0704501	+	0.0406744i
$836$		0			0
$837$	34.9059	−	34.9059i	1.20653	−	1.20653i
$838$		0			0
$839$	−15.7209	+	4.21239i	−0.542744	+	0.145428i	−0.519767	−	0.854308i	$-0.673981\pi$
$839$	−15.7209	+	4.21239i	−0.542744	+	0.145428i	−0.0229774	+	0.999736i	$0.507315\pi$
$840$		0			0
$841$	24.3044	−	42.0964i	0.838082	−	1.45160i
$842$		0			0
$843$	−32.2323	−	8.63662i	−1.11014	−	0.297461i
$844$		0			0
$845$	8.78403	−	0.0154668i	0.302180	−	0.000532075i
$846$		0			0
$847$	−43.4681	+	4.14229i	−1.49358	+	0.142331i
$848$		0			0
$849$	−4.63230	+	8.02337i	−0.158980	+	0.275361i
$850$		0			0
$851$	−2.66827	−	9.95812i	−0.0914672	−	0.341360i
$852$		0			0
$853$	3.85064	−	3.85064i	0.131843	−	0.131843i	−0.638106	−	0.769949i	$-0.720282\pi$
$853$	3.85064	−	3.85064i	0.131843	−	0.131843i	0.769949	+	0.638106i	$0.220282\pi$
$854$		0			0
$855$	16.8767	+	29.2313i	0.577171	+	0.999689i
$856$		0			0
$857$	−24.3553			−0.831960			−0.415980	−	0.909374i	$-0.636561\pi$
$857$	−24.3553			−0.831960			−0.415980	+	0.909374i	$0.636561\pi$
$858$		0			0
$859$	25.5586			0.872049			0.436024	−	0.899935i	$-0.356386\pi$
$859$	25.5586			0.872049			0.436024	+	0.899935i	$0.356386\pi$
$860$		0			0
$861$	−7.17595	−	12.4291i	−0.244556	−	0.423583i
$862$		0			0
$863$	−10.8076	+	10.8076i	−0.367894	+	0.367894i	−0.866709	−	0.498815i	$-0.833769\pi$
$863$	−10.8076	+	10.8076i	−0.367894	+	0.367894i	0.498815	+	0.866709i	$0.333769\pi$
$864$		0			0
$865$	0.106732	+	0.398330i	0.00362901	+	0.0135436i
$866$		0			0
$867$	1.65798	−	2.87171i	0.0563080	−	0.0975284i
$868$		0			0
$869$	33.3015	+	39.3766i	1.12968	+	1.33576i
$870$		0			0
$871$	15.2806	+	11.7039i	0.517764	+	0.396571i
$872$		0			0
$873$	90.1252	+	24.1490i	3.05027	+	0.817319i
$874$		0			0
$875$	12.7987	−	22.1681i	0.432676	−	0.749417i
$876$		0			0
$877$	36.7625	−	9.85048i	1.24138	−	0.332627i	0.422380	−	0.906419i	$-0.361195\pi$
$877$	36.7625	−	9.85048i	1.24138	−	0.332627i	0.819001	+	0.573792i	$0.194528\pi$
$878$		0			0
$879$	60.3908	−	60.3908i	2.03693	−	2.03693i
$880$		0			0
$881$	2.69048	−	1.55335i	0.0906447	−	0.0523337i	−0.453992	−	0.891006i	$-0.650001\pi$
$881$	2.69048	−	1.55335i	0.0906447	−	0.0523337i	0.544637	+	0.838672i	$0.316667\pi$
$882$		0			0
$883$			26.1708i			0.880717i	0.897822	+	0.440359i	$0.145149\pi$
$883$			26.1708i			0.880717i	−0.897822	+	0.440359i	$0.854851\pi$
$884$		0			0
$885$	12.0666			0.405615
$886$		0			0
$887$	8.37977	−	4.83806i	0.281365	−	0.162446i	−0.352676	−	0.935745i	$-0.614728\pi$
$887$	8.37977	−	4.83806i	0.281365	−	0.162446i	0.634041	+	0.773299i	$0.281395\pi$
$888$		0			0
$889$	−32.6535	+	32.6535i	−1.09516	+	1.09516i
$890$		0			0
$891$	51.7291	+	18.6014i	1.73299	+	0.623171i
$892$		0			0
$893$	−76.0530	−	43.9092i	−2.54502	−	1.46937i
$894$		0			0
$895$	3.98824	−	14.8843i	0.133312	−	0.497527i
$896$		0			0
$897$	−15.9527	−	20.7521i	−0.532646	−	0.692893i
$898$		0			0
$899$	−9.53680	+	35.5918i	−0.318070	+	1.18705i
$900$		0			0
$901$	15.6555	−	27.1161i	0.521561	−	0.903369i
$902$		0			0
$903$	−3.20566	−	11.9637i	−0.106678	−	0.398126i
$904$		0			0
$905$	−3.06064	−	3.06064i	−0.101739	−	0.101739i
$906$		0			0
$907$	43.9116	−	25.3524i	1.45806	−	0.841812i	0.459145	−	0.888361i	$-0.348156\pi$
$907$	43.9116	−	25.3524i	1.45806	−	0.841812i	0.998916	+	0.0465497i	$0.0148226\pi$
$908$		0			0
$909$	40.8465			1.35479
$910$		0			0
$911$	−51.0275			−1.69062			−0.845309	−	0.534278i	$-0.820584\pi$
$911$	−51.0275			−1.69062			−0.845309	+	0.534278i	$0.820584\pi$
$912$		0			0
$913$	−13.8227	−	1.15543i	−0.457465	−	0.0382393i
$914$		0			0
$915$	9.68964	+	9.68964i	0.320330	+	0.320330i
$916$		0			0
$917$	−25.0898	+	6.72280i	−0.828539	+	0.222006i
$918$		0			0
$919$	6.05177	+	3.49399i	0.199629	+	0.115256i	0.596483	−	0.802626i	$-0.296564\pi$
$919$	6.05177	+	3.49399i	0.199629	+	0.115256i	−0.396853	+	0.917882i	$0.629898\pi$
$920$		0			0
$921$	31.6475	+	8.47993i	1.04282	+	0.279423i
$922$		0			0
$923$	3.21935	−	24.6208i	0.105966	−	0.810405i
$924$		0			0
$925$	−19.4850	−	5.22099i	−0.640663	−	0.171665i
$926$		0			0
$927$	61.7111	+	35.6289i	2.02686	+	1.17021i
$928$		0			0
$929$	−3.71476	−	13.8637i	−0.121877	−	0.454852i	0.877832	−	0.478969i	$-0.158989\pi$
$929$	−3.71476	−	13.8637i	−0.121877	−	0.454852i	−0.999709	+	0.0241169i	$0.992323\pi$
$930$		0			0
$931$	−45.6583	+	45.6583i	−1.49639	+	1.49639i
$932$		0			0
$933$	−31.7867	+	18.3521i	−1.04065	+	0.600820i
$934$		0			0
$935$	7.34886	+	5.10345i	0.240334	+	0.166901i
$936$		0			0
$937$		−	55.1866i		−	1.80287i	−0.432916	−	0.901434i	$-0.642515\pi$
$937$		−	55.1866i		−	1.80287i	0.432916	−	0.901434i	$-0.357485\pi$
$938$		0			0
$939$	−9.92623	−	17.1927i	−0.323930	−	0.561064i
$940$		0			0
$941$	3.16199	+	3.16199i	0.103078	+	0.103078i	0.756765	−	0.653687i	$-0.226779\pi$
$941$	3.16199	+	3.16199i	0.103078	+	0.103078i	−0.653687	+	0.756765i	$0.726779\pi$
$942$		0			0
$943$	−0.694975	−	2.59368i	−0.0226315	−	0.0844620i
$944$		0			0
$945$	−27.4149	−	15.8280i	−0.891805	−	0.514884i
$946$		0			0
$947$	10.8897	−	40.6408i	0.353866	−	1.32065i	−0.528039	−	0.849220i	$-0.677072\pi$
$947$	10.8897	−	40.6408i	0.353866	−	1.32065i	0.881905	−	0.471427i	$-0.156261\pi$
$948$		0			0
$949$	−17.8443	+	7.40975i	−0.579250	+	0.240531i
$950$		0			0
$951$	24.0713	+	6.44988i	0.780564	+	0.209152i
$952$		0			0
$953$	−20.9812	+	36.3404i	−0.679646	+	1.17718i	0.295441	+	0.955361i	$0.404533\pi$
$953$	−20.9812	+	36.3404i	−0.679646	+	1.17718i	−0.975087	+	0.221821i	$0.928800\pi$
$954$		0			0
$955$	1.47761	+	5.51453i	0.0478145	+	0.178446i
$956$		0			0
$957$	−89.9000	+	16.2108i	−2.90605	+	0.524022i
$958$		0			0
$959$	−35.7411	−	61.9053i	−1.15414	−	1.99903i
$960$		0			0
$961$			13.5055i			0.435660i
$962$		0			0
$963$		−	91.4577i		−	2.94718i
$964$		0			0
$965$	11.7000	−	6.75501i	0.376637	−	0.217451i
$966$		0			0
$967$	20.7354	+	20.7354i	0.666806	+	0.666806i	0.956975	−	0.290169i	$-0.0937116\pi$
$967$	20.7354	+	20.7354i	0.666806	+	0.666806i	−0.290169	+	0.956975i	$0.593712\pi$
$968$		0			0
$969$	−88.8994	+	23.8205i	−2.85586	+	0.765226i
$970$		0			0
$971$	3.46895	−	6.00840i	0.111324	−	0.192819i	−0.804980	−	0.593301i	$-0.797824\pi$
$971$	3.46895	−	6.00840i	0.111324	−	0.192819i	0.916304	+	0.400483i	$0.131158\pi$
$972$		0			0
$973$	−21.2357	+	79.2529i	−0.680787	+	2.54073i
$974$		0			0
$975$	−50.7727	+	6.72984i	−1.62603	+	0.215527i
$976$		0			0
$977$	−14.5433	−	3.89685i	−0.465280	−	0.124671i	0.0185602	−	0.999828i	$-0.494092\pi$
$977$	−14.5433	−	3.89685i	−0.465280	−	0.124671i	−0.483840	+	0.875156i	$0.660758\pi$
$978$		0			0
$979$	−1.28991	−	2.73850i	−0.0412258	−	0.0875229i
$980$		0			0
$981$	−19.1665	+	5.13564i	−0.611939	+	0.163969i
$982$		0			0
$983$	−10.5129	−	10.5129i	−0.335310	−	0.335310i	0.519289	−	0.854599i	$-0.326197\pi$
$983$	−10.5129	−	10.5129i	−0.335310	−	0.335310i	−0.854599	+	0.519289i	$0.826197\pi$
$984$		0			0
$985$	−0.993852	−	1.72140i	−0.0316668	−	0.0548484i
$986$		0			0
$987$	147.816			4.70502
$988$		0			0
$989$		−	2.31731i		−	0.0736863i
$990$		0			0
$991$	−13.7336	−	23.7874i	−0.436263	−	0.755630i	0.561135	−	0.827725i	$-0.310365\pi$
$991$	−13.7336	−	23.7874i	−0.436263	−	0.755630i	−0.997398	+	0.0720944i	$0.977032\pi$
$992$		0			0
$993$	19.5869	−	19.5869i	0.621573	−	0.621573i
$994$		0			0
$995$	8.89970	−	2.38467i	0.282139	−	0.0755990i
$996$		0			0
$997$	−45.7236	−	26.3985i	−1.44808	−	0.836049i	−0.449712	−	0.893173i	$-0.648474\pi$
$997$	−45.7236	−	26.3985i	−1.44808	−	0.836049i	−0.998367	+	0.0571244i	$0.981807\pi$
$998$		0			0
$999$	−13.5622	+	50.6149i	−0.429090	+	1.60139i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bc.a.197.1	✓	56
11.10	odd	2	inner	572.2.bc.a.197.2	yes	56
13.7	odd	12	inner	572.2.bc.a.241.2	yes	56
143.98	even	12	inner	572.2.bc.a.241.1	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bc.a.197.1	✓	56	1.1	even	1	trivial
572.2.bc.a.197.2	yes	56	11.10	odd	2	inner
572.2.bc.a.241.1	yes	56	143.98	even	12	inner
572.2.bc.a.241.2	yes	56	13.7	odd	12	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.56324 - 2.70762i) q^{3} +(0.477789 - 0.477789i) q^{5} +(-1.02740 - 3.83429i) q^{7} +(-3.38745 + 5.86724i) q^{9} +O(q^{10})\)	\(q+(-1.56324 - 2.70762i) q^{3} +(0.477789 - 0.477789i) q^{5} +(-1.02740 - 3.83429i) q^{7} +(-3.38745 + 5.86724i) q^{9} +(-2.53241 + 2.14170i) q^{11} +(-3.33231 - 1.37685i) q^{13} +(-2.04057 - 0.546769i) q^{15} +(1.99621 - 3.45753i) q^{17} +(7.12208 - 1.90835i) q^{19} +(-8.77572 + 8.77572i) q^{21} +(-2.01091 + 1.16100i) q^{23} +4.54344i q^{25} +11.8022 q^{27} +(-7.62932 + 4.40479i) q^{29} +(2.95758 - 2.95758i) q^{31} +(9.75768 + 3.50879i) q^{33} +(-2.32286 - 1.34110i) q^{35} +(-1.14913 + 4.28860i) q^{37} +(1.48122 + 11.1750i) q^{39} +(-0.299301 + 1.11701i) q^{41} +(-0.498991 + 0.864278i) q^{43} +(1.18482 + 4.42179i) q^{45} +(-8.42186 - 8.42186i) q^{47} +(-7.58407 + 4.37866i) q^{49} -12.4822 q^{51} +7.84262 q^{53} +(-0.186676 + 2.23324i) q^{55} +(-16.3006 - 16.3006i) q^{57} +(-5.51724 + 1.47834i) q^{59} +(-5.61754 - 3.24329i) q^{61} +(25.9770 + 6.96051i) q^{63} +(-2.24998 + 0.934296i) q^{65} +(-5.15648 - 1.38168i) q^{67} +(6.28708 + 3.62984i) q^{69} +(1.78241 + 6.65206i) q^{71} +(3.78927 - 3.78927i) q^{73} +(12.3019 - 7.10249i) q^{75} +(10.8137 + 7.50962i) q^{77} -15.5491i q^{79} +(-8.28734 - 14.3541i) q^{81} +(2.95729 + 2.95729i) q^{83} +(-0.698206 - 2.60574i) q^{85} +(23.8530 + 13.7715i) q^{87} +(-0.236225 + 0.881602i) q^{89} +(-1.85565 + 14.1916i) q^{91} +(-12.6314 - 3.38457i) q^{93} +(2.49106 - 4.31464i) q^{95} +(-3.56447 - 13.3028i) q^{97} +(-3.98747 - 22.1132i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 28 q^{9}+O(q^{10}) \) 56 * q - 28 * q^9	\( 56 q - 28 q^{9} + 4 q^{11} + 8 q^{15} - 12 q^{23} - 24 q^{27} - 4 q^{31} - 10 q^{33} - 12 q^{37} - 64 q^{45} - 8 q^{47} + 40 q^{53} + 22 q^{55} + 48 q^{59} - 36 q^{67} - 48 q^{71} + 120 q^{75} + 28 q^{81} + 28 q^{89} + 36 q^{91} + 20 q^{93} - 68 q^{97} - 44 q^{99}+O(q^{100}) \) 56 * q - 28 * q^9 + 4 * q^11 + 8 * q^15 - 12 * q^23 - 24 * q^27 - 4 * q^31 - 10 * q^33 - 12 * q^37 - 64 * q^45 - 8 * q^47 + 40 * q^53 + 22 * q^55 + 48 * q^59 - 36 * q^67 - 48 * q^71 + 120 * q^75 + 28 * q^81 + 28 * q^89 + 36 * q^91 + 20 * q^93 - 68 * q^97 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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