LMFDB - Embedded newform 572.2.bc.a.241.2

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			241.2
Character	$\chi$	$=$	572.241
Dual form			572.2.bc.a.197.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.56324 + 2.70762i) q^{3} +(0.477789 + 0.477789i) q^{5} +(1.02740 - 3.83429i) q^{7} +(-3.38745 - 5.86724i) q^{9} +O(q^{10})$	\(q+(-1.56324 + 2.70762i) q^{3} +(0.477789 + 0.477789i) q^{5} +(1.02740 - 3.83429i) q^{7} +(-3.38745 - 5.86724i) q^{9} +(1.12228 - 3.12098i) q^{11} +(3.33231 - 1.37685i) q^{13} +(-2.04057 + 0.546769i) q^{15} +(-1.99621 - 3.45753i) q^{17} +(-7.12208 - 1.90835i) q^{19} +(8.77572 + 8.77572i) q^{21} +(-2.01091 - 1.16100i) q^{23} -4.54344i q^{25} +11.8022 q^{27} +(7.62932 + 4.40479i) q^{29} +(2.95758 + 2.95758i) q^{31} +(6.69600 + 7.91755i) q^{33} +(2.32286 - 1.34110i) q^{35} +(-1.14913 - 4.28860i) q^{37} +(-1.48122 + 11.1750i) q^{39} +(0.299301 + 1.11701i) q^{41} +(0.498991 + 0.864278i) q^{43} +(1.18482 - 4.42179i) q^{45} +(-8.42186 + 8.42186i) q^{47} +(-7.58407 - 4.37866i) q^{49} +12.4822 q^{51} +7.84262 q^{53} +(2.02738 - 0.954954i) q^{55} +(16.3006 - 16.3006i) q^{57} +(-5.51724 - 1.47834i) q^{59} +(5.61754 - 3.24329i) q^{61} +(-25.9770 + 6.96051i) q^{63} +(2.24998 + 0.934296i) q^{65} +(-5.15648 + 1.38168i) q^{67} +(6.28708 - 3.62984i) q^{69} +(1.78241 - 6.65206i) q^{71} +(-3.78927 - 3.78927i) q^{73} +(12.3019 + 7.10249i) q^{75} +(-10.8137 - 7.50962i) q^{77} -15.5491i q^{79} +(-8.28734 + 14.3541i) q^{81} +(-2.95729 + 2.95729i) q^{83} +(0.698206 - 2.60574i) q^{85} +(-23.8530 + 13.7715i) q^{87} +(-0.236225 - 0.881602i) q^{89} +(-1.85565 - 14.1916i) q^{91} +(-12.6314 + 3.38457i) q^{93} +(-2.49106 - 4.31464i) q^{95} +(-3.56447 + 13.3028i) q^{97} +(-22.1132 + 3.98747i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$-1$

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	−0.0783509	+	0.996926i	$0.524965\pi$
$3$	−1.56324	+	2.70762i	−0.902539	+	1.56324i	−0.824188	+	0.566317i	$0.808368\pi$
$4$		0			0
$5$	0.477789	+	0.477789i	0.213674	+	0.213674i	0.805826	−	0.592152i	$-0.201722\pi$
$5$	0.477789	+	0.477789i	0.213674	+	0.213674i	−0.592152	+	0.805826i	$0.701722\pi$
$6$		0			0
$7$	1.02740	−	3.83429i	0.388319	−	1.44923i	−0.444549	−	0.895754i	$-0.646636\pi$
$7$	1.02740	−	3.83429i	0.388319	−	1.44923i	0.832868	−	0.553471i	$-0.186697\pi$
$8$		0			0
$9$	−3.38745	−	5.86724i	−1.12915	−	1.95575i
$10$		0			0
$11$	1.12228	−	3.12098i	0.338380	−	0.941009i
$11$	1.12228	−	3.12098i	0.338380	−	0.941009i
$12$		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	$-0.327538\pi$
$17$	−1.99621	−	3.45753i	−0.484152	−	0.838575i	−0.999834	+	0.0182044i	$0.994205\pi$
$18$		0			0
$19$	−7.12208	−	1.90835i	−1.63392	−	0.437807i	−0.678869	−	0.734260i	$-0.737530\pi$
$19$	−7.12208	−	1.90835i	−1.63392	−	0.437807i	−0.955047	+	0.296453i	$0.904196\pi$
$20$		0			0
$21$	8.77572	+	8.77572i	1.91502	+	1.91502i
$22$		0			0
$23$	−2.01091	−	1.16100i	−0.419303	−	0.242085i	0.275476	−	0.961308i	$-0.411165\pi$
$23$	−2.01091	−	1.16100i	−0.419303	−	0.242085i	−0.694779	+	0.719223i	$0.744498\pi$
$24$		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	$-0.0284444\pi$
$29$	7.62932	+	4.40479i	1.41673	+	0.817949i	0.420719	+	0.907191i	$0.361778\pi$
$30$		0			0
$31$	2.95758	+	2.95758i	0.531197	+	0.531197i	0.920928	−	0.389732i	$-0.127432\pi$
$31$	2.95758	+	2.95758i	0.531197	+	0.531197i	−0.389732	+	0.920928i	$0.627432\pi$
$32$		0			0
$33$	6.69600	+	7.91755i	1.16562	+	1.37827i
$34$		0			0
$35$	2.32286	−	1.34110i	0.392635	−	0.226688i
$36$		0			0
$37$	−1.14913	−	4.28860i	−0.188915	−	0.705042i	−0.993758	−	0.111554i	$-0.964417\pi$
$37$	−1.14913	−	4.28860i	−0.188915	−	0.705042i	0.804843	−	0.593488i	$-0.202250\pi$
$38$		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	$-0.0545506\pi$
$41$	0.299301	+	1.11701i	0.0467429	+	0.174447i	−0.938608	+	0.344985i	$0.887884\pi$
$42$		0			0
$43$	0.498991	+	0.864278i	0.0760955	+	0.131801i	0.901562	−	0.432650i	$-0.142421\pi$
$43$	0.498991	+	0.864278i	0.0760955	+	0.131801i	−0.825467	+	0.564451i	$0.809088\pi$
$44$		0			0
$45$	1.18482	−	4.42179i	0.176622	−	0.659162i
$46$		0			0
$47$	−8.42186	+	8.42186i	−1.22845	+	1.22845i	−0.263905	+	0.964549i	$0.585011\pi$
$47$	−8.42186	+	8.42186i	−1.22845	+	1.22845i	−0.964549	+	0.263905i	$0.914989\pi$
$48$		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
$55$	2.02738	−	0.954954i	0.273372	−	0.128766i
$56$		0			0
$57$	16.3006	−	16.3006i	2.15907	−	2.15907i
$58$		0			0
$59$	−5.51724	−	1.47834i	−0.718284	−	0.192464i	−0.118878	−	0.992909i	$-0.537930\pi$
$59$	−5.51724	−	1.47834i	−0.718284	−	0.192464i	−0.599406	+	0.800445i	$0.704596\pi$
$60$		0			0
$61$	5.61754	−	3.24329i	0.719252	−	0.415260i	−0.0952254	−	0.995456i	$-0.530357\pi$
$61$	5.61754	−	3.24329i	0.719252	−	0.415260i	0.814477	+	0.580195i	$0.197024\pi$
$62$		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	−0.559654	−	0.828727i	$-0.689066\pi$
$67$	−5.15648	+	1.38168i	−0.629964	+	0.168798i	−0.0703109	+	0.997525i	$0.522399\pi$
$68$		0			0
$69$	6.28708	−	3.62984i	0.756875	−	0.436982i
$70$		0			0
$71$	1.78241	−	6.65206i	0.211534	−	0.789455i	−0.775824	−	0.630949i	$-0.782666\pi$
$71$	1.78241	−	6.65206i	0.211534	−	0.789455i	0.987358	−	0.158506i	$-0.0506676\pi$
$72$		0			0
$73$	−3.78927	−	3.78927i	−0.443500	−	0.443500i	0.449686	−	0.893187i	$-0.351536\pi$
$73$	−3.78927	−	3.78927i	−0.443500	−	0.443500i	−0.893187	+	0.449686i	$0.851536\pi$
$74$		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	$-0.823719\pi$
$83$	−2.95729	+	2.95729i	−0.324605	+	0.324605i	0.525926	+	0.850530i	$0.323719\pi$
$84$		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	0.952275	−	0.305241i	$-0.0987370\pi$
$89$	−0.236225	−	0.881602i	−0.0250398	−	0.0934497i	−0.977315	+	0.211791i	$0.932070\pi$
$90$		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	0.509635	+	0.860391i	$0.329780\pi$
$97$	−3.56447	+	13.3028i	−0.361917	+	1.35069i	−0.871552	+	0.490303i	$0.836886\pi$
$98$		0			0
$99$	−22.1132	+	3.98747i	−2.22246	+	0.400756i
$100$		0			0
$101$	3.01454	−	5.22134i	0.299958	−	0.519543i	−0.676168	−	0.736748i	$-0.736361\pi$
$101$	3.01454	−	5.22134i	0.299958	−	0.519543i	0.976126	+	0.217205i	$0.0696939\pi$
$102$		0			0
$103$			10.5179i			1.03636i	0.855272	+	0.518180i	$0.173390\pi$
$103$			10.5179i			1.03636i	−0.855272	+	0.518180i	$0.826610\pi$
$104$		0			0
$105$			8.38588i			0.818378i
$106$		0			0
$107$	11.6909	+	6.74973i	1.13020	+	0.652521i	0.943985	−	0.329988i	$-0.107045\pi$
$107$	11.6909	+	6.74973i	1.13020	+	0.652521i	0.186215	+	0.982509i	$0.440378\pi$
$108$		0			0
$109$	−2.07100	+	2.07100i	−0.198366	+	0.198366i	−0.799299	−	0.600933i	$-0.794796\pi$
$109$	−2.07100	+	2.07100i	−0.198366	+	0.198366i	0.600933	+	0.799299i	$0.294796\pi$
$110$		0			0
$111$	13.4083	+	3.59273i	1.27266	+	0.341007i
$112$		0			0
$113$	4.34851	+	7.53184i	0.409073	+	0.708536i	0.994786	−	0.101983i	$-0.0325187\pi$
$113$	4.34851	+	7.53184i	0.409073	+	0.708536i	−0.585713	+	0.810519i	$0.699185\pi$
$114$		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
$121$	−8.48097	−	7.00522i	−0.770998	−	0.636838i
$122$		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	−0.483680	−	0.875245i	$-0.660700\pi$
$127$	5.81666	−	10.0747i	0.516145	−	0.893989i	0.999824	−	0.0187438i	$-0.00596668\pi$
$128$		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	0.908409	−	0.418084i	$-0.137298\pi$
$137$	17.3940	+	4.66071i	1.48607	+	0.398192i	0.577663	+	0.816275i	$0.303965\pi$
$138$		0			0
$139$	17.9003	−	10.3347i	1.51828	−	0.876582i	0.518516	−	0.855068i	$-0.326485\pi$
$139$	17.9003	−	10.3347i	1.51828	−	0.876582i	0.999769	−	0.0215139i	$-0.00684861\pi$
$140$		0			0
$141$	−9.63774	−	35.9686i	−0.811645	−	3.02910i
$142$		0			0
$143$	−0.557335	−	11.9453i	−0.0466067	−	0.998913i
$144$		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	$-0.308793\pi$
$149$	7.83951	+	2.10059i	0.642237	+	0.172087i	0.0770207	+	0.997029i	$0.475459\pi$
$150$		0			0
$151$	6.56303	+	6.56303i	0.534092	+	0.534092i	0.921788	−	0.387695i	$-0.126729\pi$
$151$	6.56303	+	6.56303i	0.534092	+	0.534092i	−0.387695	+	0.921788i	$0.626729\pi$
$152$		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	−0.236795	−	0.971560i	$-0.576097\pi$
$163$	−11.8434	−	3.17343i	−0.927646	−	0.248562i	−0.690850	+	0.722998i	$0.742764\pi$
$164$		0			0
$165$	−0.583639	+	6.98219i	−0.0454362	+	0.543563i
$166$		0			0
$167$	3.36037	−	0.900408i	0.260033	−	0.0696757i	−0.126447	−	0.991973i	$-0.540357\pi$
$167$	3.36037	−	0.900408i	0.260033	−	0.0696757i	0.386480	+	0.922298i	$0.373691\pi$
$168$		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	$-0.159281\pi$
$173$	0.305153	+	0.528541i	0.0232004	+	0.0401842i	−0.854192	+	0.519958i	$0.825948\pi$
$174$		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	0.999639	−	0.0268853i	$-0.00855888\pi$
$179$	19.7499	+	11.4026i	1.47617	+	0.852270i	0.476536	+	0.879155i	$0.341892\pi$
$180$		0			0
$181$			6.40584i			0.476142i	0.971248	+	0.238071i	$0.0765152\pi$
$181$			6.40584i			0.476142i	−0.971248	+	0.238071i	$0.923485\pi$
$182$		0			0
$183$			20.2802i			1.49915i
$184$		0			0
$185$	1.50001	−	2.59809i	0.110283	−	0.191015i
$186$		0			0
$187$	−13.0312	+	2.34979i	−0.952935	+	0.171834i
$188$		0			0
$189$	12.1255	−	45.2531i	0.882002	−	3.29168i
$190$		0			0
$191$	−4.22458	−	7.31719i	−0.305680	−	0.529453i	0.671732	−	0.740794i	$-0.265550\pi$
$191$	−4.22458	−	7.31719i	−0.305680	−	0.529453i	−0.977413	+	0.211340i	$0.932217\pi$
$192$		0			0
$193$	−19.3129	+	5.17489i	−1.39018	+	0.372497i	−0.874807	−	0.484472i	$-0.839012\pi$
$193$	−19.3129	+	5.17489i	−1.39018	+	0.372497i	−0.515369	+	0.856968i	$0.672345\pi$
$194$		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	$-0.116752\pi$
$197$	−0.761372	−	2.84148i	−0.0542455	−	0.202447i	−0.987730	+	0.156170i	$0.950085\pi$
$198$		0			0
$199$	11.8089	−	6.81790i	0.837114	−	0.483308i	−0.0191684	−	0.999816i	$-0.506102\pi$
$199$	11.8089	−	6.81790i	0.837114	−	0.483308i	0.856282	+	0.516508i	$0.172769\pi$
$200$		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	$-0.451859\pi$
$211$	−9.15337	−	5.28470i	−0.630144	−	0.363814i	−0.780808	+	0.624771i	$0.785192\pi$
$212$		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	−0.218658	−	0.975801i	$-0.570168\pi$
$223$	1.19284	−	0.319621i	0.0798785	−	0.0214034i	0.298537	+	0.954398i	$0.403501\pi$
$224$		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	$-0.0308010\pi$
$227$	27.2552	+	7.30300i	1.80899	+	0.484717i	0.813668	+	0.581330i	$0.197468\pi$
$228$		0			0
$229$	−5.79059	+	5.79059i	−0.382653	+	0.382653i	−0.872057	−	0.489404i	$-0.837214\pi$
$229$	−5.79059	+	5.79059i	−0.382653	+	0.382653i	0.489404	+	0.872057i	$0.337214\pi$
$230$		0			0
$231$	37.2376	−	17.5400i	2.45006	−	1.15405i
$232$		0			0
$233$	2.46751			0.161652			0.0808261	−	0.996728i	$-0.474244\pi$
$233$	2.46751			0.161652			0.0808261	+	0.996728i	$0.474244\pi$
$234$		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	$-0.878854\pi$
$239$	−8.61060	+	8.61060i	−0.556974	+	0.556974i	0.371471	+	0.928445i	$0.378854\pi$
$240$		0			0
$241$	−1.64691	+	6.14636i	−0.106087	+	0.395922i	−0.998466	−	0.0553645i	$-0.982368\pi$
$241$	−1.64691	+	6.14636i	−0.106087	+	0.395922i	0.892379	+	0.451286i	$0.149035\pi$
$242$		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	−0.450323	−	0.892866i	$-0.648691\pi$
$251$	1.54880	−	0.894197i	0.0977591	−	0.0564412i	0.548082	+	0.836424i	$0.315358\pi$
$252$		0			0
$253$	−5.88025	+	4.97303i	−0.369688	+	0.312652i
$254$		0			0
$255$	5.96387	+	5.96387i	0.373472	+	0.373472i
$256$		0			0
$257$	−16.3333	−	9.43002i	−1.01884	−	0.588229i	−0.105074	−	0.994464i	$-0.533508\pi$
$257$	−16.3333	−	9.43002i	−1.01884	−	0.588229i	−0.913768	+	0.406236i	$0.866841\pi$
$258$		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	$-0.295004\pi$
$263$	3.37420	+	1.94810i	0.208062	+	0.120125i	−0.392348	+	0.919817i	$0.628337\pi$
$264$		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	0.996480	+	0.0838349i	$0.0267168\pi$
$269$	9.36252	+	16.2164i	0.570843	+	0.988729i	−0.425637	+	0.904894i	$0.639950\pi$
$270$		0			0
$271$	−4.59616	+	1.23154i	−0.279197	+	0.0748106i	−0.395700	−	0.918380i	$-0.629498\pi$
$271$	−4.59616	+	1.23154i	−0.279197	+	0.0748106i	0.116503	+	0.993190i	$0.462831\pi$
$272$		0			0
$273$	41.3263	+	17.1605i	2.50118	+	1.03860i
$274$		0			0
$275$	−14.1799	−	5.09901i	−0.855083	−	0.307482i
$276$		0			0
$277$	−10.8710	−	18.8291i	−0.653173	−	1.13133i	−0.982348	−	0.187060i	$-0.940104\pi$
$277$	−10.8710	−	18.8291i	−0.653173	−	1.13133i	0.329175	−	0.944269i	$-0.393229\pi$
$278$		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	$-0.353129\pi$
$281$	−7.54703	−	7.54703i	−0.450218	−	0.450218i	−0.895427	+	0.445209i	$0.853129\pi$
$282$		0			0
$283$	1.48163	−	2.56626i	0.0880738	−	0.152548i	−0.818623	−	0.574331i	$-0.805262\pi$
$283$	1.48163	−	2.56626i	0.0880738	−	0.152548i	0.906697	+	0.421783i	$0.138596\pi$
$284$		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	0.375690	+	0.926746i	$0.377406\pi$
$293$	−7.07010	+	26.3860i	−0.413040	+	1.54149i	−0.788730	+	0.614740i	$0.789261\pi$
$294$		0			0
$295$	−1.92974	−	3.34241i	−0.112354	−	0.194603i
$296$		0			0
$297$	13.2454	−	36.8344i	0.768575	−	2.13735i
$298$		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	$-0.153331\pi$
$307$	7.41011	+	7.41011i	0.422917	+	0.422917i	−0.463290	+	0.886207i	$0.653331\pi$
$308$		0			0
$309$	−28.4784	−	16.4420i	−1.62008	−	0.935354i
$310$		0			0
$311$			11.7397i			0.665700i	0.942980	+	0.332850i	$0.108010\pi$
$311$			11.7397i			0.665700i	−0.942980	+	0.332850i	$0.891990\pi$
$312$		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	0.530885	−	0.847444i	$-0.321860\pi$
$317$	−5.63617	−	5.63617i	−0.316559	−	0.316559i	−0.847444	+	0.530885i	$0.821860\pi$
$318$		0			0
$319$	22.3095	−	18.8675i	1.24909	−	1.05638i
$320$		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	−0.873835	−	0.486223i	$-0.838374\pi$
$331$	2.29309	−	8.55794i	0.126040	−	0.470387i	0.999875	+	0.0158360i	$0.00504097\pi$
$332$		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	$-0.384786\pi$
$337$	13.0009			0.708206			0.354103	+	0.935206i	$0.384786\pi$
$338$		0			0
$339$	−27.1911			−1.47682
$340$		0			0
$341$	12.5498	−	5.91130i	0.679608	−	0.320115i
$342$		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	$-0.994832\pi$
$347$	−27.6763	+	15.9789i	−1.48574	+	0.857793i	−0.485873	+	0.874030i	$0.661498\pi$
$348$		0			0
$349$	−0.645630	+	0.172996i	−0.0345598	+	0.00926027i	−0.276058	−	0.961141i	$-0.589028\pi$
$349$	−0.645630	+	0.172996i	−0.0345598	+	0.00926027i	0.241498	+	0.970401i	$0.422361\pi$
$350$		0			0
$351$	39.3286	−	16.2499i	2.09920	−	0.867354i
$352$		0			0
$353$	17.0160	−	4.55942i	0.905670	−	0.242674i	0.224220	−	0.974538i	$-0.428016\pi$
$353$	17.0160	−	4.55942i	0.905670	−	0.242674i	0.681450	+	0.731865i	$0.261350\pi$
$354$		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	$-0.342203\pi$
$359$	−7.65365	−	7.65365i	−0.403944	−	0.403944i	−0.879620	+	0.475676i	$0.842203\pi$
$360$		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	−0.987533	−	0.157414i	$-0.949684\pi$
$367$	−6.84759	+	11.8604i	−0.357442	+	0.619107i	0.630091	+	0.776521i	$0.283018\pi$
$368$		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	$-0.738525\pi$
$373$	−7.48769	+	4.32302i	−0.387698	+	0.223837i	0.293464	+	0.955970i	$0.405192\pi$
$374$		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	−0.182139	−	0.983273i	$-0.558302\pi$
$379$	2.95447	−	0.791648i	0.151761	−	0.0406642i	0.333900	+	0.942609i	$0.391635\pi$
$380$		0			0
$381$	18.1857	+	31.4985i	0.931681	+	1.61372i
$382$		0			0
$383$	1.63995	−	6.12037i	0.0837975	−	0.312736i	−0.911286	−	0.411773i	$-0.864910\pi$
$383$	1.63995	−	6.12037i	0.0837975	−	0.312736i	0.995084	+	0.0990369i	$0.0315762\pi$
$384$		0			0
$385$	−1.57865	−	8.75468i	−0.0804556	−	0.446180i
$386$		0			0
$387$	3.38062	−	5.85541i	0.171847	−	0.297647i
$388$		0			0
$389$		−	13.9676i		−	0.708183i	−0.935211	−	0.354092i	$-0.884790\pi$
$389$		−	13.9676i		−	0.708183i	0.935211	−	0.354092i	$-0.115210\pi$
$390$		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	0.481762	−	0.876302i	$-0.339997\pi$
$397$	9.18194	+	2.46029i	0.460828	+	0.123479i	−0.0209333	+	0.999781i	$0.506664\pi$
$398$		0			0
$399$	−45.7542	−	79.2485i	−2.29057	−	3.96739i
$400$		0			0
$401$	6.28094	+	23.4408i	0.313655	+	1.17058i	0.925235	+	0.379395i	$0.123868\pi$
$401$	6.28094	+	23.4408i	0.313655	+	1.17058i	−0.611580	+	0.791183i	$0.709466\pi$
$402$		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
$407$	−14.6743	−	1.22662i	−0.727376	−	0.0608011i
$408$		0			0
$409$	−20.9059	−	5.60172i	−1.03373	−	0.276987i	−0.298218	−	0.954498i	$-0.596392\pi$
$409$	−20.9059	−	5.60172i	−1.03373	−	0.276987i	−0.735513	+	0.677510i	$0.763059\pi$
$410$		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	−0.924280	−	0.381716i	$-0.875333\pi$
$419$	−2.69305	+	4.66449i	−0.131564	+	0.227875i	0.792716	+	0.609592i	$0.208667\pi$
$420$		0			0
$421$	14.8300	+	14.8300i	0.722769	+	0.722769i	0.969168	−	0.246400i	$-0.0792476\pi$
$421$	14.8300	+	14.8300i	0.722769	+	0.722769i	−0.246400	+	0.969168i	$0.579248\pi$
$422$		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
$429$	33.2144	+	17.1643i	1.60361	+	0.828700i
$430$		0			0
$431$	1.72236	+	6.42795i	0.0829633	+	0.309623i	0.994921	−	0.100662i	$-0.0320959\pi$
$431$	1.72236	+	6.42795i	0.0829633	+	0.309623i	−0.911957	+	0.410285i	$0.865429\pi$
$432$		0			0
$433$	−8.94600	+	5.16498i	−0.429917	+	0.248213i	−0.699311	−	0.714817i	$-0.746510\pi$
$433$	−8.94600	+	5.16498i	−0.429917	+	0.248213i	0.269394	+	0.963030i	$0.413177\pi$
$434$		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	−0.287607	−	0.957749i	$-0.592860\pi$
$439$	14.3656	−	24.8819i	0.685631	−	1.18755i	0.973238	−	0.229800i	$-0.0738070\pi$
$440$		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	0.474313	−	0.880356i	$-0.342696\pi$
$449$	9.42731	+	2.52604i	0.444902	+	0.119211i	−0.0294108	+	0.999567i	$0.509363\pi$
$450$		0			0
$451$	3.82205	+	0.319483i	0.179973	+	0.0150439i
$452$		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	$-0.0811727\pi$
$457$	0.0751127	+	0.280324i	0.00351362	+	0.0131130i	−0.964147	+	0.265370i	$0.914506\pi$
$458$		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	$-0.410714\pi$
$461$	0.775606	+	0.207823i	0.0361236	+	0.00967929i	−0.240712	+	0.970597i	$0.577381\pi$
$462$		0			0
$463$	16.1917	−	16.1917i	0.752492	−	0.752492i	−0.222452	−	0.974944i	$-0.571406\pi$
$463$	16.1917	−	16.1917i	0.752492	−	0.752492i	0.974944	+	0.222452i	$0.0714060\pi$
$464$		0			0
$465$	−7.65225	−	4.41803i	−0.354865	−	0.204881i
$466$		0			0
$467$			26.1802i			1.21147i	0.795665	+	0.605737i	$0.207122\pi$
$467$			26.1802i			1.21147i	−0.795665	+	0.605737i	$0.792878\pi$
$468$		0			0
$469$			21.1910i			0.978508i
$470$		0			0
$471$	22.2439	−	38.5275i	1.02494	−	1.77525i
$472$		0			0
$473$	3.25740	−	0.587377i	0.149775	−	0.0270076i
$474$		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	$-0.556606\pi$
$479$	3.54595	−	0.950135i	0.162019	−	0.0434128i	0.338917	+	0.940816i	$0.389940\pi$
$480$		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	0.221711	+	0.975112i	$0.428836\pi$
$487$	−10.1039	+	37.7084i	−0.457853	+	1.70873i	−0.679563	+	0.733617i	$0.737831\pi$
$488$		0			0
$489$	27.1065	−	27.1065i	1.22580	−	1.22580i
$490$		0			0
$491$	−15.4238	+	26.7148i	−0.696066	+	1.20562i	0.273755	+	0.961800i	$0.411734\pi$
$491$	−15.4238	+	26.7148i	−0.696066	+	1.20562i	−0.969820	+	0.243821i	$0.921599\pi$
$492$		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	0.863049	−	0.505121i	$-0.168552\pi$
$499$	7.99551	+	7.99551i	0.357928	+	0.357928i	−0.505121	+	0.863049i	$0.668552\pi$
$500$		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	$-0.675459\pi$
$503$	−1.07284	+	0.619403i	−0.0478355	+	0.0276178i	0.475892	+	0.879504i	$0.342125\pi$
$504$		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	−0.0967916	−	0.995305i	$-0.530858\pi$
$509$	7.15268	−	1.91655i	0.317037	−	0.0849498i	0.413828	+	0.910355i	$0.364191\pi$
$510$		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
$517$	16.8327	+	35.7361i	0.740302	+	1.57167i
$518$		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	$-0.420374\pi$
$523$	−10.6969	−	6.17584i	−0.467741	−	0.270050i	−0.715294	+	0.698824i	$0.753707\pi$
$524$		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
$539$	−22.1772	+	18.7556i	−0.955238	+	0.807861i
$540$		0			0
$541$	−24.4117	−	24.4117i	−1.04954	−	1.04954i	−0.998707	−	0.0508347i	$-0.983812\pi$
$541$	−24.4117	−	24.4117i	−1.04954	−	1.04954i	−0.0508347	−	0.998707i	$-0.516188\pi$
$542$		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	$-0.525369\pi$
$557$	8.25675	−	2.21239i	0.349850	−	0.0937420i	0.429464	+	0.903084i	$0.358702\pi$
$558$		0			0
$559$	2.85278	+	2.19301i	0.120660	+	0.0927542i
$560$		0			0
$561$	14.0086	−	38.9567i	0.591442	−	1.64475i
$562$		0			0
$563$	4.69347	+	8.12933i	0.197806	+	0.342610i	0.947817	−	0.318815i	$-0.103285\pi$
$563$	4.69347	+	8.12933i	0.197806	+	0.342610i	−0.750011	+	0.661426i	$0.769952\pi$
$564$		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	−0.190732	−	0.981642i	$-0.561086\pi$
$569$	18.0039	−	31.1836i	0.754761	−	1.30728i	0.945493	−	0.325642i	$-0.105580\pi$
$570$		0			0
$571$	14.8778			0.622618			0.311309	−	0.950309i	$-0.399233\pi$
$571$	14.8778			0.622618			0.311309	+	0.950309i	$0.399233\pi$
$572$		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	0.260445	−	0.965489i	$-0.416131\pi$
$577$	−16.9357	−	16.9357i	−0.705043	−	0.705043i	−0.965489	+	0.260445i	$0.916131\pi$
$578$		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
$583$	8.80162	−	24.4766i	0.364526	−	1.01372i
$584$		0			0
$585$	−2.13998	−	16.3661i	−0.0884773	−	0.676655i
$586$		0			0
$587$	36.2901	−	9.72391i	1.49785	−	0.401349i	0.585473	−	0.810692i	$-0.300909\pi$
$587$	36.2901	−	9.72391i	1.49785	−	0.401349i	0.912380	+	0.409343i	$0.134242\pi$
$588$		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	$-0.485741\pi$
$593$	−23.2367	−	23.2367i	−0.954216	−	0.954216i	−0.998997	+	0.0447806i	$0.985741\pi$
$594$		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	$-0.363210\pi$
$601$	−3.97969	−	2.29767i	−0.162335	−	0.0937240i	−0.578966	+	0.815351i	$0.696544\pi$
$602$		0			0
$603$	25.5740	+	25.5740i	1.04145	+	1.04145i
$604$		0			0
$605$	−0.705099	−	7.39913i	−0.0286664	−	0.300818i
$606$		0			0
$607$	27.7384	−	16.0148i	1.12587	−	0.650020i	0.182976	−	0.983117i	$-0.441427\pi$
$607$	27.7384	−	16.0148i	1.12587	−	0.650020i	0.942893	+	0.333097i	$0.108094\pi$
$608$		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	0.853429	+	0.521209i	$0.174519\pi$
$613$	9.28313	+	34.6451i	0.374942	+	1.39930i	−0.478487	+	0.878095i	$0.658815\pi$
$614$		0			0
$615$	−1.22149	−	2.11568i	−0.0492551	−	0.0853124i
$616$		0			0
$617$	1.25696	−	4.69102i	0.0506031	−	0.188854i	−0.935998	−	0.352006i	$-0.885500\pi$
$617$	1.25696	−	4.69102i	0.0506031	−	0.188854i	0.986601	+	0.163153i	$0.0521663\pi$
$618$		0			0
$619$	7.70022	−	7.70022i	0.309498	−	0.309498i	−0.535217	−	0.844715i	$-0.679770\pi$
$619$	7.70022	−	7.70022i	0.309498	−	0.309498i	0.844715	+	0.535217i	$0.179770\pi$
$620$		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
$627$	−32.5800	−	69.1677i	−1.30112	−	2.76229i
$628$		0			0
$629$	−12.5341	+	12.5341i	−0.499767	+	0.499767i
$630$		0			0
$631$	2.20198	+	0.590020i	0.0876596	+	0.0234883i	0.302382	−	0.953187i	$-0.402218\pi$
$631$	2.20198	+	0.590020i	0.0876596	+	0.0234883i	−0.214723	+	0.976675i	$0.568885\pi$
$632$		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	0.560220	−	0.828344i	$-0.310716\pi$
$641$	39.4377	−	22.7694i	1.55770	−	0.899337i	0.997477	−	0.0709934i	$-0.0226169\pi$
$642$		0			0
$643$	1.89343	−	7.06639i	0.0746697	−	0.278671i	−0.918489	−	0.395448i	$-0.870589\pi$
$643$	1.89343	−	7.06639i	0.0746697	−	0.278671i	0.993158	+	0.116777i	$0.0372561\pi$
$644$		0			0
$645$	−1.49079	−	1.49079i	−0.0586997	−	0.0586997i
$646$		0			0
$647$	30.5341	+	17.6288i	1.20042	+	0.693061i	0.960648	−	0.277768i	$-0.0895948\pi$
$647$	30.5341	+	17.6288i	1.20042	+	0.693061i	0.239770	+	0.970830i	$0.422928\pi$
$648$		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	0.0676008	+	0.997712i	$0.478466\pi$
$653$	−21.2159	+	36.7471i	−0.830244	+	1.43802i	−0.897845	+	0.440312i	$0.854868\pi$
$654$		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	$-0.530403\pi$
$659$	18.4581	−	10.6568i	0.719027	−	0.415131i	0.814395	+	0.580312i	$0.197069\pi$
$660$		0			0
$661$	2.75930	+	10.2978i	0.107324	+	0.400540i	0.998598	−	0.0529250i	$-0.0168544\pi$
$661$	2.75930	+	10.2978i	0.107324	+	0.400540i	−0.891274	+	0.453465i	$0.850188\pi$
$662$		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
$671$	−3.81777	−	21.1721i	−0.147383	−	0.817339i
$672$		0			0
$673$	−20.1774	+	34.9483i	−0.777782	+	1.34716i	0.155436	+	0.987846i	$0.450322\pi$
$673$	−20.1774	+	34.9483i	−0.777782	+	1.34716i	−0.933218	+	0.359311i	$0.883012\pi$
$674$		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	−0.399981	−	0.916523i	$-0.630983\pi$
$683$	−31.4823	−	8.43566i	−1.20464	−	0.322782i	−0.804656	+	0.593742i	$0.797650\pi$
$684$		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	0.124588	−	0.992209i	$-0.460239\pi$
$691$	19.1523	−	5.13185i	0.728589	−	0.195225i	0.604001	+	0.796984i	$0.293572\pi$
$692$		0			0
$693$	−7.42987	+	88.8851i	−0.282237	+	3.37647i
$694$		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	$-0.153790\pi$
$701$	46.8917			1.77108			0.885538	+	0.464566i	$0.153790\pi$
$702$		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	0.743448	−	0.668794i	$-0.233189\pi$
$709$	28.0355	+	7.51209i	1.05290	+	0.282123i	0.309448	+	0.950916i	$0.399856\pi$
$710$		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
$715$	5.44103	−	5.97361i	0.203483	−	0.223400i
$716$		0			0
$717$	−9.85374	−	36.7747i	−0.367995	−	1.37337i
$718$		0			0
$719$	40.9746	−	23.6567i	1.52809	−	0.882245i	0.528652	−	0.848839i	$-0.322698\pi$
$719$	40.9746	−	23.6567i	1.52809	−	0.882245i	0.999442	−	0.0334064i	$-0.0106356\pi$
$720$		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	$0.137755\pi$
$727$			22.6158i			0.838775i	−0.907807	+	0.419387i	$0.862245\pi$
$728$		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	$-0.568083\pi$
$733$	20.7102	−	20.7102i	0.764949	−	0.764949i	0.977213	+	0.212263i	$0.0680834\pi$
$734$		0			0
$735$	17.8699	+	4.78823i	0.659142	+	0.176617i
$736$		0			0
$737$	−1.47484	+	17.6439i	−0.0543266	+	0.649921i
$738$		0			0
$739$	32.3783	−	8.67575i	1.19106	−	0.319143i	0.391753	−	0.920070i	$-0.371869\pi$
$739$	32.3783	−	8.67575i	1.19106	−	0.319143i	0.799303	+	0.600928i	$0.205202\pi$
$740$		0			0
$741$	31.8752	−	76.7622i	1.17096	−	2.81993i
$742$		0			0
$743$	−11.6411	−	43.4452i	−0.427070	−	1.59385i	−0.759360	−	0.650671i	$-0.774488\pi$
$743$	−11.6411	−	43.4452i	−0.427070	−	1.59385i	0.332289	−	0.943177i	$-0.392179\pi$
$744$		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	0.635015	−	0.772500i	$-0.280994\pi$
$751$	7.76965	+	4.48581i	0.283519	+	0.163690i	−0.351497	+	0.936189i	$0.614327\pi$
$752$		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	−0.998898	−	0.0469373i	$-0.985054\pi$
$757$	−12.6233	+	21.8641i	−0.458800	+	0.794665i	0.540098	+	0.841602i	$0.318387\pi$
$758$		0			0
$759$	−4.27279	−	23.6955i	−0.155093	−	0.860093i
$760$		0			0
$761$	−6.78957	+	25.3390i	−0.246122	+	0.918539i	0.726695	+	0.686961i	$0.241056\pi$
$761$	−6.78957	+	25.3390i	−0.246122	+	0.918539i	−0.972816	+	0.231578i	$0.925611\pi$
$762$		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	0.924271	+	0.381738i	$0.124674\pi$
$769$	8.72684	+	32.5690i	0.314698	+	1.17447i	−0.609573	+	0.792730i	$0.708659\pi$
$770$		0			0
$771$	51.0658	−	29.4828i	1.83909	−	1.06180i
$772$		0			0
$773$	5.71139	−	21.3152i	0.205424	−	0.766654i	−0.783895	−	0.620893i	$-0.786770\pi$
$773$	5.71139	−	21.3152i	0.205424	−	0.766654i	0.989320	−	0.145761i	$-0.0465631\pi$
$774$		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	$-0.981133\pi$
$787$	−2.92094	+	10.9011i	−0.104120	+	0.388582i	0.894124	+	0.447820i	$0.147799\pi$
$788$		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	−0.887330	−	0.461136i	$-0.847442\pi$
$797$	−26.3013	+	15.1851i	−0.931639	+	0.537882i	−0.0443097	+	0.999018i	$0.514109\pi$
$798$		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
$803$	−16.0788	+	7.57359i	−0.567410	+	0.267266i
$804$		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	$-0.456447\pi$
$809$	−18.5827	−	10.7287i	−0.653332	−	0.377201i	−0.789732	+	0.613453i	$0.789780\pi$
$810$		0			0
$811$	21.5160	−	21.5160i	0.755528	−	0.755528i	−0.219977	−	0.975505i	$-0.570598\pi$
$811$	21.5160	−	21.5160i	0.755528	−	0.755528i	0.975505	+	0.219977i	$0.0705984\pi$
$812$		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	$-0.0535564\pi$
$821$	1.38546	+	5.17061i	0.0483529	+	0.180455i	−0.937526	+	0.347915i	$0.886890\pi$
$822$		0			0
$823$	6.78358	−	3.91650i	0.236461	−	0.136521i	−0.377088	−	0.926177i	$-0.623075\pi$
$823$	6.78358	−	3.91650i	0.236461	−	0.136521i	0.613549	+	0.789657i	$0.289741\pi$
$824$		0			0
$825$	35.9729	−	30.4229i	1.25241	−	1.05919i
$826$		0			0
$827$	−26.4534	−	26.4534i	−0.919874	−	0.919874i	0.0771459	−	0.997020i	$-0.475419\pi$
$827$	−26.4534	−	26.4534i	−0.919874	−	0.919874i	−0.997020	+	0.0771459i	$0.975419\pi$
$828$		0			0
$829$	−4.76096	−	2.74874i	−0.165355	−	0.0954677i	0.415039	−	0.909804i	$-0.363768\pi$
$829$	−4.76096	−	2.74874i	−0.165355	−	0.0954677i	−0.580394	+	0.814336i	$0.697101\pi$
$830$		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	−0.0229774	−	0.999736i	$-0.507315\pi$
$839$	−15.7209	−	4.21239i	−0.542744	−	0.145428i	−0.519767	+	0.854308i	$0.673981\pi$
$840$		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
$847$	−35.5734	+	25.3214i	−1.22232	+	0.870053i
$848$		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	$-0.279718\pi$
$853$	−3.85064	−	3.85064i	−0.131843	−	0.131843i	−0.769949	+	0.638106i	$0.779718\pi$
$854$		0			0
$855$	−16.8767	+	29.2313i	−0.577171	+	0.999689i
$856$		0			0
$857$	24.3553			0.831960			0.415980	−	0.909374i	$-0.363439\pi$
$857$	24.3553			0.831960			0.415980	+	0.909374i	$0.363439\pi$
$858$		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	0.498815	−	0.866709i	$-0.333769\pi$
$863$	−10.8076	−	10.8076i	−0.367894	−	0.367894i	−0.866709	+	0.498815i	$0.833769\pi$
$864$		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
$869$	−48.5283	−	17.4504i	−1.64621	−	0.591965i
$870$		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	$-0.638805\pi$
$877$	−36.7625	−	9.85048i	−1.24138	−	0.332627i	−0.819001	+	0.573792i	$0.805472\pi$
$878$		0			0
$879$	−60.3908	−	60.3908i	−2.03693	−	2.03693i
$880$		0			0
$881$	2.69048	+	1.55335i	0.0906447	+	0.0523337i	0.544637	−	0.838672i	$-0.316667\pi$
$881$	2.69048	+	1.55335i	0.0906447	+	0.0523337i	−0.453992	+	0.891006i	$0.650001\pi$
$882$		0			0
$883$		−	26.1708i		−	0.880717i	−0.897822	−	0.440359i	$-0.854851\pi$
$883$		−	26.1708i		−	0.880717i	0.897822	−	0.440359i	$-0.145149\pi$
$884$		0			0
$885$	12.0666			0.405615
$886$		0			0
$887$	−8.37977	−	4.83806i	−0.281365	−	0.162446i	0.352676	−	0.935745i	$-0.385272\pi$
$887$	−8.37977	−	4.83806i	−0.281365	−	0.162446i	−0.634041	+	0.773299i	$0.718605\pi$
$888$		0			0
$889$	−32.6535	−	32.6535i	−1.09516	−	1.09516i
$890$		0			0
$891$	35.4980	+	41.9739i	1.18923	+	1.40618i
$892$		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	0.998916	−	0.0465497i	$-0.0148226\pi$
$907$	43.9116	+	25.3524i	1.45806	+	0.841812i	0.459145	+	0.888361i	$0.348156\pi$
$908$		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
$913$	5.91072	+	12.5485i	0.195616	+	0.415296i
$914$		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	$-0.703436\pi$
$919$	−6.05177	+	3.49399i	−0.199629	+	0.115256i	0.396853	+	0.917882i	$0.370102\pi$
$920$		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	−0.999709	−	0.0241169i	$-0.992323\pi$
$929$	−3.71476	+	13.8637i	−0.121877	+	0.454852i	0.877832	+	0.478969i	$0.158989\pi$
$930$		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	$-0.773221\pi$
$941$	−3.16199	+	3.16199i	−0.103078	+	0.103078i	0.653687	+	0.756765i	$0.273221\pi$
$942$		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	0.881905	+	0.471427i	$0.156261\pi$
$947$	10.8897	+	40.6408i	0.353866	+	1.32065i	−0.528039	+	0.849220i	$0.677072\pi$
$948$		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	0.975087	+	0.221821i	$0.0712000\pi$
$953$	20.9812	+	36.3404i	0.679646	+	1.17718i	−0.295441	+	0.955361i	$0.595467\pi$
$954$		0			0
$955$	1.47761	−	5.51453i	0.0478145	−	0.178446i
$956$		0			0
$957$	16.2108	+	89.9000i	0.524022	+	2.90605i
$958$		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	$-0.906288\pi$
$967$	−20.7354	+	20.7354i	−0.666806	+	0.666806i	0.290169	+	0.956975i	$0.406288\pi$
$968$		0			0
$969$	−88.8994	−	23.8205i	−2.85586	−	0.765226i
$970$		0			0
$971$	3.46895	+	6.00840i	0.111324	+	0.192819i	0.916304	−	0.400483i	$-0.131158\pi$
$971$	3.46895	+	6.00840i	0.111324	+	0.192819i	−0.804980	+	0.593301i	$0.797824\pi$
$972$		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	−0.483840	−	0.875156i	$-0.660758\pi$
$977$	−14.5433	+	3.89685i	−0.465280	+	0.124671i	0.0185602	+	0.999828i	$0.494092\pi$
$978$		0			0
$979$	−3.01657	−	0.252154i	−0.0964100	−	0.00805887i
$980$		0			0
$981$	19.1665	+	5.13564i	0.611939	+	0.163969i
$982$		0			0
$983$	−10.5129	+	10.5129i	−0.335310	+	0.335310i	−0.854599	−	0.519289i	$-0.826197\pi$
$983$	−10.5129	+	10.5129i	−0.335310	+	0.335310i	0.519289	+	0.854599i	$0.326197\pi$
$984$		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	−0.997398	−	0.0720944i	$-0.977032\pi$
$991$	−13.7336	+	23.7874i	−0.436263	+	0.755630i	0.561135	+	0.827725i	$0.310365\pi$
$992$		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	$-0.351526\pi$
$997$	45.7236	−	26.3985i	1.44808	−	0.836049i	0.998367	+	0.0571244i	$0.0181932\pi$
$998$		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.241.2	yes	56
11.10	odd	2	inner	572.2.bc.a.241.1	yes	56
13.2	odd	12	inner	572.2.bc.a.197.1	✓	56
143.54	even	12	inner	572.2.bc.a.197.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bc.a.197.1	✓	56	13.2	odd	12	inner
572.2.bc.a.197.2	yes	56	143.54	even	12	inner
572.2.bc.a.241.1	yes	56	11.10	odd	2	inner
572.2.bc.a.241.2	yes	56	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-1.56324 + 2.70762i) q^{3} +(0.477789 + 0.477789i) q^{5} +(1.02740 - 3.83429i) q^{7} +(-3.38745 - 5.86724i) q^{9} +O(q^{10})\)	\(q+(-1.56324 + 2.70762i) q^{3} +(0.477789 + 0.477789i) q^{5} +(1.02740 - 3.83429i) q^{7} +(-3.38745 - 5.86724i) q^{9} +(1.12228 - 3.12098i) q^{11} +(3.33231 - 1.37685i) q^{13} +(-2.04057 + 0.546769i) q^{15} +(-1.99621 - 3.45753i) q^{17} +(-7.12208 - 1.90835i) q^{19} +(8.77572 + 8.77572i) q^{21} +(-2.01091 - 1.16100i) q^{23} -4.54344i q^{25} +11.8022 q^{27} +(7.62932 + 4.40479i) q^{29} +(2.95758 + 2.95758i) q^{31} +(6.69600 + 7.91755i) q^{33} +(2.32286 - 1.34110i) q^{35} +(-1.14913 - 4.28860i) q^{37} +(-1.48122 + 11.1750i) q^{39} +(0.299301 + 1.11701i) q^{41} +(0.498991 + 0.864278i) q^{43} +(1.18482 - 4.42179i) q^{45} +(-8.42186 + 8.42186i) q^{47} +(-7.58407 - 4.37866i) q^{49} +12.4822 q^{51} +7.84262 q^{53} +(2.02738 - 0.954954i) q^{55} +(16.3006 - 16.3006i) q^{57} +(-5.51724 - 1.47834i) q^{59} +(5.61754 - 3.24329i) q^{61} +(-25.9770 + 6.96051i) q^{63} +(2.24998 + 0.934296i) q^{65} +(-5.15648 + 1.38168i) q^{67} +(6.28708 - 3.62984i) q^{69} +(1.78241 - 6.65206i) q^{71} +(-3.78927 - 3.78927i) q^{73} +(12.3019 + 7.10249i) q^{75} +(-10.8137 - 7.50962i) q^{77} -15.5491i q^{79} +(-8.28734 + 14.3541i) q^{81} +(-2.95729 + 2.95729i) q^{83} +(0.698206 - 2.60574i) q^{85} +(-23.8530 + 13.7715i) q^{87} +(-0.236225 - 0.881602i) q^{89} +(-1.85565 - 14.1916i) q^{91} +(-12.6314 + 3.38457i) q^{93} +(-2.49106 - 4.31464i) q^{95} +(-3.56447 + 13.3028i) q^{97} +(-22.1132 + 3.98747i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 28 q^{9}+O(q^{10}) \) 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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