LMFDB - Embedded newform 1148.2.ba.a.113.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(113,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

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

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

chi := DirichletCharacter("1148.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.ba (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			113.12
Character	$\chi$	$=$	1148.113
Dual form			1148.2.ba.a.701.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.927936i q^{3} +(0.718305 + 2.21072i) q^{5} +(-0.587785 - 0.809017i) q^{7} +2.13894 q^{9} +O(q^{10})$	\(q+0.927936i q^{3} +(0.718305 + 2.21072i) q^{5} +(-0.587785 - 0.809017i) q^{7} +2.13894 q^{9} +(-2.17752 - 0.707518i) q^{11} +(2.09337 - 2.88128i) q^{13} +(-2.05140 + 0.666541i) q^{15} +(4.08898 + 1.32859i) q^{17} +(3.47829 + 4.78745i) q^{19} +(0.750716 - 0.545427i) q^{21} +(1.51889 + 1.10354i) q^{23} +(-0.326219 + 0.237012i) q^{25} +4.76860i q^{27} +(4.40009 - 1.42968i) q^{29} +(-2.17082 + 6.68111i) q^{31} +(0.656531 - 2.02060i) q^{33} +(1.36630 - 1.88055i) q^{35} +(-0.715941 - 2.20344i) q^{37} +(2.67364 + 1.94251i) q^{39} +(-6.06374 - 2.05695i) q^{41} +(0.206092 + 0.149735i) q^{43} +(1.53641 + 4.72858i) q^{45} +(-6.91235 + 9.51404i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(-1.23285 + 3.79431i) q^{51} +(-13.4073 + 4.35631i) q^{53} -5.32209i q^{55} +(-4.44245 + 3.22763i) q^{57} +(-0.491392 - 0.357017i) q^{59} +(5.39061 - 3.91651i) q^{61} +(-1.25723 - 1.73044i) q^{63} +(7.87337 + 2.55821i) q^{65} +(2.80488 - 0.911362i) q^{67} +(-1.02401 + 1.40944i) q^{69} +(-2.31494 - 0.752169i) q^{71} -0.789290 q^{73} +(-0.219932 - 0.302710i) q^{75} +(0.707518 + 2.17752i) q^{77} +2.86187i q^{79} +1.99185 q^{81} -0.0274158 q^{83} +9.99390i q^{85} +(1.32665 + 4.08300i) q^{87} +(4.94716 + 6.80918i) q^{89} -3.56146 q^{91} +(-6.19964 - 2.01438i) q^{93} +(-8.08523 + 11.1284i) q^{95} +(13.0991 - 4.25615i) q^{97} +(-4.65757 - 1.51334i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) $ 80 * q - 4 * q^5 - 60 * q^9	$ 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) $ 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$			0.927936i			0.535744i	0.963455	+	0.267872i	$0.0863204\pi$
$3$			0.927936i			0.535744i	−0.963455	+	0.267872i	$0.913680\pi$
$4$		0			0
$5$	0.718305	+	2.21072i	0.321236	+	0.988662i	0.973111	+	0.230336i	$0.0739826\pi$
$5$	0.718305	+	2.21072i	0.321236	+	0.988662i	−0.651875	+	0.758326i	$0.726017\pi$
$6$		0			0
$7$	−0.587785	−	0.809017i	−0.222162	−	0.305780i
$7$	−0.587785	−	0.809017i	−0.222162	−	0.305780i
$8$		0			0
$9$	2.13894			0.712978
$10$		0			0
$11$	−2.17752	−	0.707518i	−0.656546	−	0.213325i	−0.0382478	−	0.999268i	$-0.512178\pi$
$11$	−2.17752	−	0.707518i	−0.656546	−	0.213325i	−0.618298	+	0.785944i	$0.712178\pi$
$12$		0			0
$13$	2.09337	−	2.88128i	0.580597	−	0.799123i	−0.413164	−	0.910657i	$-0.635576\pi$
$13$	2.09337	−	2.88128i	0.580597	−	0.799123i	0.993761	+	0.111534i	$0.0355763\pi$
$14$		0			0
$15$	−2.05140	+	0.666541i	−0.529670	+	0.172100i
$16$		0			0
$17$	4.08898	+	1.32859i	0.991723	+	0.322230i	0.759553	−	0.650445i	$-0.225418\pi$
$17$	4.08898	+	1.32859i	0.991723	+	0.322230i	0.232170	+	0.972675i	$0.425418\pi$
$18$		0			0
$19$	3.47829	+	4.78745i	0.797974	+	1.09832i	0.993069	+	0.117533i	$0.0374986\pi$
$19$	3.47829	+	4.78745i	0.797974	+	1.09832i	−0.195095	+	0.980784i	$0.562501\pi$
$20$		0			0
$21$	0.750716	−	0.545427i	0.163820	−	0.119022i
$22$		0			0
$23$	1.51889	+	1.10354i	0.316711	+	0.230104i	0.734771	−	0.678315i	$-0.237290\pi$
$23$	1.51889	+	1.10354i	0.316711	+	0.230104i	−0.418060	+	0.908420i	$0.637290\pi$
$24$		0			0
$25$	−0.326219	+	0.237012i	−0.0652438	+	0.0474024i
$26$		0			0
$27$			4.76860i			0.917718i
$28$		0			0
$29$	4.40009	−	1.42968i	0.817077	−	0.265484i	0.129485	−	0.991581i	$-0.458668\pi$
$29$	4.40009	−	1.42968i	0.817077	−	0.265484i	0.687592	+	0.726097i	$0.258668\pi$
$30$		0			0
$31$	−2.17082	+	6.68111i	−0.389891	+	1.19996i	0.542978	+	0.839747i	$0.317297\pi$
$31$	−2.17082	+	6.68111i	−0.389891	+	1.19996i	−0.932869	+	0.360215i	$0.882703\pi$
$32$		0			0
$33$	0.656531	−	2.02060i	0.114287	−	0.351741i
$34$		0			0
$35$	1.36630	−	1.88055i	0.230946	−	0.317871i
$36$		0			0
$37$	−0.715941	−	2.20344i	−0.117700	−	0.362243i	0.874801	−	0.484483i	$-0.160992\pi$
$37$	−0.715941	−	2.20344i	−0.117700	−	0.362243i	−0.992501	+	0.122240i	$0.960992\pi$
$38$		0			0
$39$	2.67364	+	1.94251i	0.428125	+	0.311051i
$40$		0			0
$41$	−6.06374	−	2.05695i	−0.946997	−	0.321242i
$41$	−6.06374	−	2.05695i	−0.946997	−	0.321242i
$42$		0			0
$43$	0.206092	+	0.149735i	0.0314288	+	0.0228343i	0.603389	−	0.797447i	$-0.293817\pi$
$43$	0.206092	+	0.149735i	0.0314288	+	0.0228343i	−0.571960	+	0.820282i	$0.693817\pi$
$44$		0			0
$45$	1.53641	+	4.72858i	0.229034	+	0.704895i
$46$		0			0
$47$	−6.91235	+	9.51404i	−1.00827	+	1.38777i	−0.0881600	+	0.996106i	$0.528099\pi$
$47$	−6.91235	+	9.51404i	−1.00827	+	1.38777i	−0.920110	+	0.391659i	$0.871901\pi$
$48$		0			0
$49$	−0.309017	+	0.951057i	−0.0441453	+	0.135865i
$50$		0			0
$51$	−1.23285	+	3.79431i	−0.172633	+	0.531310i
$52$		0			0
$53$	−13.4073	+	4.35631i	−1.84164	+	0.598385i	−0.843520	+	0.537098i	$0.819521\pi$
$53$	−13.4073	+	4.35631i	−1.84164	+	0.598385i	−0.998120	+	0.0612872i	$0.980479\pi$
$54$		0			0
$55$		−	5.32209i		−	0.717630i
$56$		0			0
$57$	−4.44245	+	3.22763i	−0.588417	+	0.427510i
$58$		0			0
$59$	−0.491392	−	0.357017i	−0.0639738	−	0.0464797i	0.555339	−	0.831624i	$-0.312589\pi$
$59$	−0.491392	−	0.357017i	−0.0639738	−	0.0464797i	−0.619313	+	0.785145i	$0.712589\pi$
$60$		0			0
$61$	5.39061	−	3.91651i	0.690197	−	0.501457i	−0.186528	−	0.982450i	$-0.559723\pi$
$61$	5.39061	−	3.91651i	0.690197	−	0.501457i	0.876725	+	0.480992i	$0.159723\pi$
$62$		0			0
$63$	−1.25723	−	1.73044i	−0.158397	−	0.218014i
$64$		0			0
$65$	7.87337	+	2.55821i	0.976571	+	0.317307i
$66$		0			0
$67$	2.80488	−	0.911362i	0.342671	−	0.111341i	−0.132626	−	0.991166i	$-0.542341\pi$
$67$	2.80488	−	0.911362i	0.342671	−	0.111341i	0.475297	+	0.879826i	$0.342341\pi$
$68$		0			0
$69$	−1.02401	+	1.40944i	−0.123277	+	0.169676i
$70$		0			0
$71$	−2.31494	−	0.752169i	−0.274733	−	0.0892661i	0.168410	−	0.985717i	$-0.446137\pi$
$71$	−2.31494	−	0.752169i	−0.274733	−	0.0892661i	−0.443143	+	0.896451i	$0.646137\pi$
$72$		0			0
$73$	−0.789290			−0.0923794			−0.0461897	−	0.998933i	$-0.514708\pi$
$73$	−0.789290			−0.0923794			−0.0461897	+	0.998933i	$0.514708\pi$
$74$		0			0
$75$	−0.219932	−	0.302710i	−0.0253956	−	0.0349540i
$76$		0			0
$77$	0.707518	+	2.17752i	0.0806292	+	0.248151i
$78$		0			0
$79$			2.86187i			0.321986i	0.986956	+	0.160993i	$0.0514696\pi$
$79$			2.86187i			0.321986i	−0.986956	+	0.160993i	$0.948530\pi$
$80$		0			0
$81$	1.99185			0.221317
$82$		0			0
$83$	−0.0274158			−0.00300927			−0.00150464	−	0.999999i	$-0.500479\pi$
$83$	−0.0274158			−0.00300927			−0.00150464	+	0.999999i	$0.500479\pi$
$84$		0			0
$85$			9.99390i			1.08399i
$86$		0			0
$87$	1.32665	+	4.08300i	0.142232	+	0.437744i
$88$		0			0
$89$	4.94716	+	6.80918i	0.524398	+	0.721772i	0.986264	−	0.165178i	$-0.0528199\pi$
$89$	4.94716	+	6.80918i	0.524398	+	0.721772i	−0.461866	+	0.886950i	$0.652820\pi$
$90$		0			0
$91$	−3.56146			−0.373342
$92$		0			0
$93$	−6.19964	−	2.01438i	−0.642873	−	0.208882i
$94$		0			0
$95$	−8.08523	+	11.1284i	−0.829527	+	1.14175i
$96$		0			0
$97$	13.0991	−	4.25615i	1.33001	−	0.432146i	0.444089	−	0.895983i	$-0.353528\pi$
$97$	13.0991	−	4.25615i	1.33001	−	0.432146i	0.885921	+	0.463837i	$0.153528\pi$
$98$		0			0
$99$	−4.65757	−	1.51334i	−0.468103	−	0.152096i
$100$		0			0
$101$	−0.0657389	−	0.0904818i	−0.00654126	−	0.00900327i	0.805734	−	0.592278i	$-0.201771\pi$
$101$	−0.0657389	−	0.0904818i	−0.00654126	−	0.00900327i	−0.812275	+	0.583275i	$0.801771\pi$
$102$		0			0
$103$	12.0420	−	8.74903i	1.18653	−	0.862068i	0.193641	−	0.981072i	$-0.437970\pi$
$103$	12.0420	−	8.74903i	1.18653	−	0.862068i	0.992894	+	0.119005i	$0.0379703\pi$
$104$		0			0
$105$	1.74503	+	1.26784i	0.170297	+	0.123728i
$106$		0			0
$107$	5.10145	−	3.70642i	0.493175	−	0.358313i	−0.313229	−	0.949678i	$-0.601411\pi$
$107$	5.10145	−	3.70642i	0.493175	−	0.358313i	0.806404	+	0.591365i	$0.201411\pi$
$108$		0			0
$109$		−	14.0228i		−	1.34314i	−0.740942	−	0.671569i	$-0.765621\pi$
$109$		−	14.0228i		−	1.34314i	0.740942	−	0.671569i	$-0.234379\pi$
$110$		0			0
$111$	2.04465	−	0.664347i	0.194070	−	0.0630570i
$112$		0			0
$113$	−5.71578	+	17.5914i	−0.537695	+	1.65486i	0.200057	+	0.979784i	$0.435887\pi$
$113$	−5.71578	+	17.5914i	−0.537695	+	1.65486i	−0.737752	+	0.675072i	$0.764113\pi$
$114$		0			0
$115$	−1.34859	+	4.15052i	−0.125756	+	0.387038i
$116$		0			0
$117$	4.47759	−	6.16287i	0.413953	−	0.569757i
$118$		0			0
$119$	−1.32859	−	4.08898i	−0.121792	−	0.374836i
$120$		0			0
$121$	−4.65819	−	3.38437i	−0.423472	−	0.307670i
$122$		0			0
$123$	1.90872	−	5.62676i	0.172103	−	0.507348i
$124$		0			0
$125$	8.64445	+	6.28056i	0.773183	+	0.561750i
$126$		0			0
$127$	1.85636	+	5.71329i	0.164725	+	0.506973i	0.999016	−	0.0443523i	$-0.0141224\pi$
$127$	1.85636	+	5.71329i	0.164725	+	0.506973i	−0.834291	+	0.551325i	$0.814122\pi$
$128$		0			0
$129$	−0.138944	+	0.191240i	−0.0122334	+	0.0168378i
$130$		0			0
$131$	4.81926	−	14.8322i	0.421060	−	1.29589i	−0.485656	−	0.874150i	$-0.661419\pi$
$131$	4.81926	−	14.8322i	0.421060	−	1.29589i	0.906716	−	0.421741i	$-0.138581\pi$
$132$		0			0
$133$	1.82865	−	5.62799i	0.158564	−	0.488009i
$134$		0			0
$135$	−10.5420	+	3.42531i	−0.907313	+	0.294804i
$136$		0			0
$137$		−	1.91000i		−	0.163183i	−0.996666	−	0.0815913i	$-0.974000\pi$
$137$		−	1.91000i		−	0.163183i	0.996666	−	0.0815913i	$-0.0260002\pi$
$138$		0			0
$139$	1.08709	−	0.789815i	0.0922055	−	0.0669912i	−0.540727	−	0.841198i	$-0.681851\pi$
$139$	1.08709	−	0.789815i	0.0922055	−	0.0669912i	0.632933	+	0.774207i	$0.281851\pi$
$140$		0			0
$141$	−8.82842	−	6.41422i	−0.743487	−	0.540175i
$142$		0			0
$143$	−6.59691	+	4.79294i	−0.551661	+	0.400805i
$144$		0			0
$145$	6.32122	+	8.70041i	0.524949	+	0.722530i
$146$		0			0
$147$	−0.882519	−	0.286748i	−0.0727890	−	0.0236506i
$148$		0			0
$149$	2.80250	−	0.910588i	0.229590	−	0.0745983i	−0.191963	−	0.981402i	$-0.561485\pi$
$149$	2.80250	−	0.910588i	0.229590	−	0.0745983i	0.421553	+	0.906804i	$0.361485\pi$
$150$		0			0
$151$	−3.90234	+	5.37111i	−0.317568	+	0.437094i	−0.937723	−	0.347385i	$-0.887070\pi$
$151$	−3.90234	+	5.37111i	−0.317568	+	0.437094i	0.620155	+	0.784479i	$0.287070\pi$
$152$		0			0
$153$	8.74606	+	2.84177i	0.707077	+	0.229743i
$154$		0			0
$155$	−16.3294			−1.31161
$156$		0			0
$157$	−10.2781	−	14.1466i	−0.820280	−	1.12902i	−0.989655	−	0.143467i	$-0.954175\pi$
$157$	−10.2781	−	14.1466i	−0.820280	−	1.12902i	0.169375	−	0.985552i	$-0.445825\pi$
$158$		0			0
$159$	−4.04237	−	12.4412i	−0.320581	−	0.986647i
$160$		0			0
$161$		−	1.87746i		−	0.147964i
$162$		0			0
$163$	−4.04965			−0.317193			−0.158596	−	0.987343i	$-0.550697\pi$
$163$	−4.04965			−0.317193			−0.158596	+	0.987343i	$0.550697\pi$
$164$		0			0
$165$	4.93855			0.384466
$166$		0			0
$167$		−	14.3600i		−	1.11121i	−0.831446	−	0.555606i	$-0.812486\pi$
$167$		−	14.3600i		−	1.11121i	0.831446	−	0.555606i	$-0.187514\pi$
$168$		0			0
$169$	0.0976583	+	0.300561i	0.00751218	+	0.0231201i
$170$		0			0
$171$	7.43984	+	10.2401i	0.568939	+	0.783077i
$172$		0			0
$173$	17.0283			1.29464			0.647321	−	0.762218i	$-0.275889\pi$
$173$	17.0283			1.29464			0.647321	+	0.762218i	$0.275889\pi$
$174$		0			0
$175$	0.383494	+	0.124605i	0.0289894	+	0.00941923i
$176$		0			0
$177$	0.331289	−	0.455980i	0.0249012	−	0.0342736i
$178$		0			0
$179$	13.4952	−	4.38486i	1.00868	−	0.327740i	0.242351	−	0.970189i	$-0.422081\pi$
$179$	13.4952	−	4.38486i	1.00868	−	0.327740i	0.766329	+	0.642449i	$0.222081\pi$
$180$		0			0
$181$	13.6189	+	4.42504i	1.01228	+	0.328911i	0.767763	−	0.640734i	$-0.221370\pi$
$181$	13.6189	+	4.42504i	1.01228	+	0.328911i	0.244519	+	0.969644i	$0.421370\pi$
$182$		0			0
$183$	3.63427	+	5.00214i	0.268653	+	0.369769i
$184$		0			0
$185$	4.35692	−	3.16548i	0.320327	−	0.232731i
$186$		0			0
$187$	−7.96382	−	5.78605i	−0.582372	−	0.423118i
$188$		0			0
$189$	3.85788	−	2.80291i	0.280619	−	0.203882i
$190$		0			0
$191$		−	6.38731i		−	0.462170i	−0.972934	−	0.231085i	$-0.925773\pi$
$191$		−	6.38731i		−	0.462170i	0.972934	−	0.231085i	$-0.0742275\pi$
$192$		0			0
$193$	−5.97950	+	1.94286i	−0.430414	+	0.139850i	−0.516209	−	0.856463i	$-0.672657\pi$
$193$	−5.97950	+	1.94286i	−0.430414	+	0.139850i	0.0857946	+	0.996313i	$0.472657\pi$
$194$		0			0
$195$	−2.37386	+	7.30598i	−0.169995	+	0.523192i
$196$		0			0
$197$	−0.604573	+	1.86068i	−0.0430740	+	0.132568i	−0.970281	−	0.241981i	$-0.922203\pi$
$197$	−0.604573	+	1.86068i	−0.0430740	+	0.132568i	0.927207	+	0.374550i	$0.122203\pi$
$198$		0			0
$199$	−9.80973	+	13.5019i	−0.695393	+	0.957127i	0.304596	+	0.952482i	$0.401479\pi$
$199$	−9.80973	+	13.5019i	−0.695393	+	0.957127i	−0.999989	+	0.00464515i	$0.998521\pi$
$200$		0			0
$201$	0.845685	+	2.60275i	0.0596500	+	0.183584i
$202$		0			0
$203$	−3.74294	−	2.71941i	−0.262703	−	0.190865i
$204$		0			0
$205$	0.191720	−	14.8827i	0.0133903	−	1.03945i
$206$		0			0
$207$	3.24881	+	2.36040i	0.225808	+	0.164059i
$208$		0			0
$209$	−4.18682	−	12.8857i	−0.289609	−	0.891324i
$210$		0			0
$211$	−2.00836	+	2.76428i	−0.138262	+	0.190301i	−0.872533	−	0.488555i	$-0.837524\pi$
$211$	−2.00836	+	2.76428i	−0.138262	+	0.190301i	0.734271	+	0.678856i	$0.237524\pi$
$212$		0			0
$213$	0.697965	−	2.14811i	0.0478237	−	0.147186i
$214$		0			0
$215$	−0.182984	+	0.563167i	−0.0124794	+	0.0384077i
$216$		0			0
$217$	6.68111	−	2.17082i	0.453543	−	0.147365i
$218$		0			0
$219$		−	0.732410i		−	0.0494917i
$220$		0			0
$221$	12.3878	−	9.00025i	0.833293	−	0.605423i
$222$		0			0
$223$	−20.4162	−	14.8332i	−1.36717	−	0.993307i	−0.997952	−	0.0639641i	$-0.979626\pi$
$223$	−20.4162	−	14.8332i	−1.36717	−	0.993307i	−0.369218	−	0.929343i	$-0.620374\pi$
$224$		0			0
$225$	−0.697762	+	0.506954i	−0.0465175	+	0.0337969i
$226$		0			0
$227$	−13.2752	−	18.2717i	−0.881103	−	1.21273i	−0.976114	−	0.217258i	$-0.930289\pi$
$227$	−13.2752	−	18.2717i	−0.881103	−	1.21273i	0.0950113	−	0.995476i	$-0.469711\pi$
$228$		0			0
$229$	−14.9109	−	4.84486i	−0.985342	−	0.320157i	−0.228349	−	0.973579i	$-0.573333\pi$
$229$	−14.9109	−	4.84486i	−0.985342	−	0.320157i	−0.756994	+	0.653422i	$0.773333\pi$
$230$		0			0
$231$	−2.02060	+	0.656531i	−0.132945	+	0.0431966i
$232$		0			0
$233$	7.23281	−	9.95511i	0.473837	−	0.652181i	−0.503469	−	0.864014i	$-0.667943\pi$
$233$	7.23281	−	9.95511i	0.473837	−	0.652181i	0.977306	+	0.211832i	$0.0679431\pi$
$234$		0			0
$235$	−25.9980	−	8.44727i	−1.69592	−	0.551039i
$236$		0			0
$237$	−2.65563			−0.172502
$238$		0			0
$239$	−2.08097	−	2.86421i	−0.134607	−	0.185270i	0.736393	−	0.676555i	$-0.236528\pi$
$239$	−2.08097	−	2.86421i	−0.134607	−	0.185270i	−0.870999	+	0.491284i	$0.836528\pi$
$240$		0			0
$241$	4.95810	+	15.2594i	0.319379	+	0.982947i	0.973914	+	0.226916i	$0.0728643\pi$
$241$	4.95810	+	15.2594i	0.319379	+	0.982947i	−0.654535	+	0.756031i	$0.727136\pi$
$242$		0			0
$243$			16.1541i			1.03629i
$244$		0			0
$245$	−2.32448			−0.148506
$246$		0			0
$247$	21.0753			1.34099
$248$		0			0
$249$		−	0.0254401i		−	0.00161220i
$250$		0			0
$251$	2.43021	+	7.47941i	0.153393	+	0.472096i	0.997995	−	0.0632996i	$-0.0201624\pi$
$251$	2.43021	+	7.47941i	0.153393	+	0.472096i	−0.844601	+	0.535396i	$0.820162\pi$
$252$		0			0
$253$	−2.52664	−	3.47762i	−0.158849	−	0.218636i
$254$		0			0
$255$	−9.27370			−0.580742
$256$		0			0
$257$	−11.5894	−	3.76563i	−0.722927	−	0.234893i	−0.0756353	−	0.997136i	$-0.524098\pi$
$257$	−11.5894	−	3.76563i	−0.722927	−	0.234893i	−0.647292	+	0.762242i	$0.724098\pi$
$258$		0			0
$259$	−1.36180	+	1.87436i	−0.0846182	+	0.116467i
$260$		0			0
$261$	9.41152	−	3.05799i	0.582558	−	0.189285i
$262$		0			0
$263$	−17.1700	−	5.57888i	−1.05875	−	0.344009i	−0.272653	−	0.962112i	$-0.587901\pi$
$263$	−17.1700	−	5.57888i	−1.05875	−	0.344009i	−0.786097	+	0.618104i	$0.787901\pi$
$264$		0			0
$265$	−19.2611	−	26.5107i	−1.18320	−	1.62854i
$266$		0			0
$267$	−6.31848	+	4.59065i	−0.386685	+	0.280943i
$268$		0			0
$269$	7.39565	+	5.37325i	0.450921	+	0.327613i	0.789959	−	0.613160i	$-0.210102\pi$
$269$	7.39565	+	5.37325i	0.450921	+	0.327613i	−0.339039	+	0.940772i	$0.610102\pi$
$270$		0			0
$271$	23.7229	−	17.2357i	1.44107	−	1.04700i	0.453248	−	0.891384i	$-0.350265\pi$
$271$	23.7229	−	17.2357i	1.44107	−	1.04700i	0.987818	−	0.155611i	$-0.0497348\pi$
$272$		0			0
$273$		−	3.30480i		−	0.200016i
$274$		0			0
$275$	0.878038	−	0.285292i	0.0529477	−	0.0172038i
$276$		0			0
$277$	9.43052	−	29.0242i	0.566625	−	1.74389i	−0.0964473	−	0.995338i	$-0.530748\pi$
$277$	9.43052	−	29.0242i	0.566625	−	1.74389i	0.663073	−	0.748555i	$-0.269252\pi$
$278$		0			0
$279$	−4.64325	+	14.2905i	−0.277984	+	0.855548i
$280$		0			0
$281$	−15.2131	+	20.9390i	−0.907538	+	1.24912i	0.0604624	+	0.998170i	$0.480742\pi$
$281$	−15.2131	+	20.9390i	−0.907538	+	1.24912i	−0.968000	+	0.250948i	$0.919258\pi$
$282$		0			0
$283$	−6.86559	−	21.1301i	−0.408117	−	1.25606i	−0.918264	−	0.395968i	$-0.870409\pi$
$283$	−6.86559	−	21.1301i	−0.408117	−	1.25606i	0.510147	−	0.860087i	$-0.329591\pi$
$284$		0			0
$285$	−10.3264	−	7.50257i	−0.611684	−	0.444414i
$286$		0			0
$287$	1.90007	+	6.11472i	0.112157	+	0.360940i
$288$		0			0
$289$	1.20130	+	0.872799i	0.0706650	+	0.0513411i
$290$		0			0
$291$	3.94943	+	12.1551i	0.231520	+	0.712544i
$292$		0			0
$293$	1.22909	−	1.69170i	0.0718044	−	0.0988303i	−0.771604	−	0.636103i	$-0.780545\pi$
$293$	1.22909	−	1.69170i	0.0718044	−	0.0988303i	0.843409	+	0.537273i	$0.180545\pi$
$294$		0			0
$295$	0.436294	−	1.34278i	0.0254020	−	0.0781794i
$296$		0			0
$297$	3.37387	−	10.3837i	0.195772	−	0.602524i
$298$		0			0
$299$	6.35922	−	2.06623i	0.367763	−	0.119493i
$300$		0			0
$301$		−	0.254744i		−	0.0146832i
$302$		0			0
$303$	0.0839613	−	0.0610014i	0.00482345	−	0.00350444i
$304$		0			0
$305$	12.5304	+	9.10386i	0.717488	+	0.521286i
$306$		0			0
$307$	14.6282	−	10.6280i	0.834876	−	0.606573i	−0.0860589	−	0.996290i	$-0.527427\pi$
$307$	14.6282	−	10.6280i	0.834876	−	0.606573i	0.920934	+	0.389717i	$0.127427\pi$
$308$		0			0
$309$	8.11854	+	11.1742i	0.461848	+	0.635679i
$310$		0			0
$311$	1.54919	+	0.503363i	0.0878467	+	0.0285431i	0.352611	−	0.935770i	$-0.385294\pi$
$311$	1.54919	+	0.503363i	0.0878467	+	0.0285431i	−0.264764	+	0.964313i	$0.585294\pi$
$312$		0			0
$313$	1.37897	−	0.448054i	0.0779439	−	0.0253255i	−0.269785	−	0.962920i	$-0.586953\pi$
$313$	1.37897	−	0.448054i	0.0779439	−	0.0253255i	0.347729	+	0.937595i	$0.386953\pi$
$314$		0			0
$315$	2.92242	−	4.02237i	0.164660	−	0.226635i
$316$		0			0
$317$	−23.8274	−	7.74198i	−1.33828	−	0.434833i	−0.449545	−	0.893258i	$-0.648414\pi$
$317$	−23.8274	−	7.74198i	−1.33828	−	0.434833i	−0.888733	+	0.458425i	$0.848414\pi$
$318$		0			0
$319$	−10.5928			−0.593083
$320$		0			0
$321$	3.43932	+	4.73381i	0.191964	+	0.264216i
$322$		0			0
$323$	7.86209	+	24.1970i	0.437458	+	1.34636i
$324$		0			0
$325$			1.43608i			0.0796596i
$326$		0			0
$327$	13.0122			0.719578
$328$		0			0
$329$	11.7600			0.648350
$330$		0			0
$331$		−	29.0787i		−	1.59831i	−0.601124	−	0.799156i	$-0.705280\pi$
$331$		−	29.0787i		−	1.59831i	0.601124	−	0.799156i	$-0.294720\pi$
$332$		0			0
$333$	−1.53135	−	4.71302i	−0.0839176	−	0.258272i
$334$		0			0
$335$	4.02952	+	5.54616i	0.220156	+	0.303019i
$336$		0			0
$337$	−8.95467			−0.487792			−0.243896	−	0.969801i	$-0.578426\pi$
$337$	−8.95467			−0.487792			−0.243896	+	0.969801i	$0.578426\pi$
$338$		0			0
$339$	−16.3236	−	5.30388i	−0.886579	−	0.288067i
$340$		0			0
$341$	9.45401	−	13.0123i	0.511964	−	0.704657i
$342$		0			0
$343$	0.951057	−	0.309017i	0.0513522	−	0.0166853i
$344$		0			0
$345$	−3.85142	−	1.25140i	−0.207353	−	0.0673732i
$346$		0			0
$347$	16.8230	+	23.1549i	0.903106	+	1.24302i	0.969467	+	0.245222i	$0.0788610\pi$
$347$	16.8230	+	23.1549i	0.903106	+	1.24302i	−0.0663613	+	0.997796i	$0.521139\pi$
$348$		0			0
$349$	5.96806	−	4.33605i	0.319463	−	0.232103i	−0.416483	−	0.909143i	$-0.636738\pi$
$349$	5.96806	−	4.33605i	0.319463	−	0.232103i	0.735946	+	0.677040i	$0.236738\pi$
$350$		0			0
$351$	13.7397	+	9.98245i	0.733369	+	0.532824i
$352$		0			0
$353$	6.18363	−	4.49267i	0.329121	−	0.239121i	−0.410936	−	0.911664i	$-0.634798\pi$
$353$	6.18363	−	4.49267i	0.329121	−	0.239121i	0.740058	+	0.672543i	$0.234798\pi$
$354$		0			0
$355$		−	5.65796i		−	0.300293i
$356$		0			0
$357$	3.79431	−	1.23285i	0.200816	−	0.0652491i
$358$		0			0
$359$	−7.19235	+	22.1358i	−0.379598	+	1.16828i	0.560726	+	0.828001i	$0.310522\pi$
$359$	−7.19235	+	22.1358i	−0.379598	+	1.16828i	−0.940324	+	0.340281i	$0.889478\pi$
$360$		0			0
$361$	−4.94990	+	15.2342i	−0.260521	+	0.801802i
$362$		0			0
$363$	3.14048	−	4.32250i	0.164832	−	0.226872i
$364$		0			0
$365$	−0.566951	−	1.74490i	−0.0296756	−	0.0913320i
$366$		0			0
$367$	−18.8964	−	13.7291i	−0.986385	−	0.716651i	−0.0272588	−	0.999628i	$-0.508678\pi$
$367$	−18.8964	−	13.7291i	−0.986385	−	0.716651i	−0.959127	+	0.282977i	$0.908678\pi$
$368$		0			0
$369$	−12.9699	−	4.39969i	−0.675189	−	0.229039i
$370$		0			0
$371$	11.4050	+	8.28619i	0.592116	+	0.430198i
$372$		0			0
$373$	−5.72887	−	17.6317i	−0.296630	−	0.912933i	−0.982669	−	0.185368i	$-0.940652\pi$
$373$	−5.72887	−	17.6317i	−0.296630	−	0.912933i	0.686039	−	0.727564i	$-0.259348\pi$
$374$		0			0
$375$	−5.82795	+	8.02149i	−0.300954	+	0.414228i
$376$		0			0
$377$	5.09173	−	15.6707i	0.262238	−	0.807084i
$378$		0			0
$379$	1.09937	−	3.38350i	0.0564707	−	0.173799i	−0.918843	−	0.394624i	$-0.870875\pi$
$379$	1.09937	−	3.38350i	0.0564707	−	0.173799i	0.975313	+	0.220825i	$0.0708749\pi$
$380$		0			0
$381$	−5.30157	+	1.72258i	−0.271608	+	0.0882506i
$382$		0			0
$383$		−	16.6699i		−	0.851793i	−0.904772	−	0.425897i	$-0.859959\pi$
$383$		−	16.6699i		−	0.851793i	0.904772	−	0.425897i	$-0.140041\pi$
$384$		0			0
$385$	−4.30566	+	3.12824i	−0.219437	+	0.159430i
$386$		0			0
$387$	0.440818	+	0.320273i	0.0224080	+	0.0162804i
$388$		0			0
$389$	−17.5979	+	12.7856i	−0.892249	+	0.648257i	−0.936463	−	0.350765i	$-0.885921\pi$
$389$	−17.5979	+	12.7856i	−0.892249	+	0.648257i	0.0442145	+	0.999022i	$0.485921\pi$
$390$		0			0
$391$	4.74457	+	6.53034i	0.239943	+	0.330253i
$392$		0			0
$393$	13.7633	+	4.47196i	0.694266	+	0.225581i
$394$		0			0
$395$	−6.32678	+	2.05570i	−0.318335	+	0.103433i
$396$		0			0
$397$	−1.93140	+	2.65834i	−0.0969341	+	0.133418i	−0.854729	−	0.519074i	$-0.826277\pi$
$397$	−1.93140	+	2.65834i	−0.0969341	+	0.133418i	0.757795	+	0.652493i	$0.226277\pi$
$398$		0			0
$399$	5.22241	+	1.69686i	0.261448	+	0.0849495i
$400$		0			0
$401$	31.0618			1.55115			0.775577	−	0.631253i	$-0.217459\pi$
$401$	31.0618			1.55115			0.775577	+	0.631253i	$0.217459\pi$
$402$		0			0
$403$	14.7058	+	20.2408i	0.732548	+	1.00827i
$404$		0			0
$405$	1.43076	+	4.40342i	0.0710949	+	0.218808i
$406$		0			0
$407$			5.30457i			0.262938i
$408$		0			0
$409$	−31.6976			−1.56734			−0.783672	−	0.621175i	$-0.786656\pi$
$409$	−31.6976			−1.56734			−0.783672	+	0.621175i	$0.786656\pi$
$410$		0			0
$411$	1.77236			0.0874241
$412$		0			0
$413$			0.607394i			0.0298879i
$414$		0			0
$415$	−0.0196929	−	0.0606085i	−0.000966687	−	0.00297516i
$416$		0			0
$417$	0.732898	+	1.00875i	0.0358901	+	0.0493985i
$418$		0			0
$419$	11.9740			0.584967			0.292484	−	0.956271i	$-0.405518\pi$
$419$	11.9740			0.584967			0.292484	+	0.956271i	$0.405518\pi$
$420$		0			0
$421$	−16.4889	−	5.35757i	−0.803620	−	0.261112i	−0.121727	−	0.992564i	$-0.538843\pi$
$421$	−16.4889	−	5.35757i	−0.803620	−	0.261112i	−0.681893	+	0.731452i	$0.738843\pi$
$422$		0			0
$423$	−14.7851	+	20.3499i	−0.718875	+	0.989447i
$424$		0			0
$425$	−1.64880	+	0.535726i	−0.0799783	+	0.0259865i
$426$		0			0
$427$	−6.33704	−	2.05903i	−0.306671	−	0.0996434i
$428$		0			0
$429$	−4.44754	−	6.12151i	−0.214729	−	0.295549i
$430$		0			0
$431$	−12.2261	+	8.88281i	−0.588913	+	0.427870i	−0.841926	−	0.539593i	$-0.818578\pi$
$431$	−12.2261	+	8.88281i	−0.588913	+	0.427870i	0.253014	+	0.967463i	$0.418578\pi$
$432$		0			0
$433$	16.7707	+	12.1846i	0.805950	+	0.585557i	0.912653	−	0.408734i	$-0.134030\pi$
$433$	16.7707	+	12.1846i	0.805950	+	0.585557i	−0.106704	+	0.994291i	$0.534030\pi$
$434$		0			0
$435$	−8.07342	+	5.86569i	−0.387091	+	0.281238i
$436$		0			0
$437$			11.1101i			0.531467i
$438$		0			0
$439$	14.4008	−	4.67911i	0.687313	−	0.223322i	0.0555187	−	0.998458i	$-0.482319\pi$
$439$	14.4008	−	4.67911i	0.687313	−	0.223322i	0.631794	+	0.775136i	$0.282319\pi$
$440$		0			0
$441$	−0.660967	+	2.03425i	−0.0314746	+	0.0968690i
$442$		0			0
$443$	3.92888	−	12.0919i	0.186667	−	0.574502i	−0.813306	−	0.581836i	$-0.802335\pi$
$443$	3.92888	−	12.0919i	0.186667	−	0.574502i	0.999973	+	0.00733416i	$0.00233456\pi$
$444$		0			0
$445$	−11.4996	+	15.8278i	−0.545133	+	0.750311i
$446$		0			0
$447$	0.844967	+	2.60054i	0.0399656	+	0.123001i
$448$		0			0
$449$	20.6976	+	15.0377i	0.976779	+	0.709672i	0.956987	−	0.290132i	$-0.0936994\pi$
$449$	20.6976	+	15.0377i	0.976779	+	0.709672i	0.0197928	+	0.999804i	$0.493699\pi$
$450$		0			0
$451$	11.7486	+	8.76926i	0.553218	+	0.412928i
$452$		0			0
$453$	−4.98404	−	3.62112i	−0.234171	−	0.170135i
$454$		0			0
$455$	−2.55821	−	7.87337i	−0.119931	−	0.369109i
$456$		0			0
$457$	13.0151	−	17.9138i	0.608821	−	0.837970i	−0.387659	−	0.921803i	$-0.626716\pi$
$457$	13.0151	−	17.9138i	0.608821	−	0.837970i	0.996480	+	0.0838328i	$0.0267162\pi$
$458$		0			0
$459$	−6.33551	+	19.4987i	−0.295716	+	0.910122i
$460$		0			0
$461$	4.85336	−	14.9371i	0.226044	−	0.695691i	−0.772140	−	0.635452i	$-0.780814\pi$
$461$	4.85336	−	14.9371i	0.226044	−	0.695691i	0.998184	−	0.0602387i	$-0.0191862\pi$
$462$		0			0
$463$	−36.0497	+	11.7132i	−1.67537	+	0.544361i	−0.984004	−	0.178145i	$-0.942990\pi$
$463$	−36.0497	+	11.7132i	−1.67537	+	0.544361i	−0.691365	+	0.722505i	$0.742990\pi$
$464$		0			0
$465$		−	15.1526i		−	0.702684i
$466$		0			0
$467$	2.88590	−	2.09673i	0.133544	−	0.0970251i	−0.519008	−	0.854769i	$-0.673699\pi$
$467$	2.88590	−	2.09673i	0.133544	−	0.0970251i	0.652552	+	0.757744i	$0.273699\pi$
$468$		0			0
$469$	−2.38598	−	1.73351i	−0.110174	−	0.0800462i
$470$		0			0
$471$	13.1271	−	9.53740i	0.604865	−	0.439460i
$472$		0			0
$473$	−0.342829	−	0.471864i	−0.0157633	−	0.0216963i
$474$		0			0
$475$	−2.26937	−	0.737363i	−0.104126	−	0.0338325i
$476$		0			0
$477$	−28.6774	+	9.31786i	−1.31305	+	0.426636i
$478$		0			0
$479$	−12.0651	+	16.6062i	−0.551268	+	0.758755i	−0.990184	−	0.139773i	$-0.955363\pi$
$479$	−12.0651	+	16.6062i	−0.551268	+	0.758755i	0.438915	+	0.898528i	$0.355363\pi$
$480$		0			0
$481$	−7.84745	−	2.54979i	−0.357813	−	0.116261i
$482$		0			0
$483$	1.74216			0.0792709
$484$		0			0
$485$	18.8183	+	25.9011i	0.854494	+	1.17611i
$486$		0			0
$487$	1.87756	+	5.77853i	0.0850803	+	0.261850i	0.984542	−	0.175150i	$-0.0560410\pi$
$487$	1.87756	+	5.77853i	0.0850803	+	0.261850i	−0.899461	+	0.437000i	$0.856041\pi$
$488$		0			0
$489$		−	3.75781i		−	0.169934i
$490$		0			0
$491$	−11.2978			−0.509863			−0.254931	−	0.966959i	$-0.582053\pi$
$491$	−11.2978			−0.509863			−0.254931	+	0.966959i	$0.582053\pi$
$492$		0			0
$493$	19.8913			0.895861
$494$		0			0
$495$		−	11.3836i		−	0.511655i
$496$		0			0
$497$	0.752169	+	2.31494i	0.0337394	+	0.103839i
$498$		0			0
$499$	−16.4072	−	22.5826i	−0.734488	−	1.01094i	−0.998917	−	0.0465313i	$-0.985183\pi$
$499$	−16.4072	−	22.5826i	−0.734488	−	1.01094i	0.264428	−	0.964405i	$-0.414817\pi$
$500$		0			0
$501$	13.3252			0.595325
$502$		0			0
$503$	−32.5023	−	10.5606i	−1.44920	−	0.470875i	−0.524450	−	0.851441i	$-0.675729\pi$
$503$	−32.5023	−	10.5606i	−1.44920	−	0.470875i	−0.924754	+	0.380566i	$0.875729\pi$
$504$		0			0
$505$	0.152809	−	0.210323i	0.00679991	−	0.00935927i
$506$		0			0
$507$	−0.278902	+	0.0906206i	−0.0123865	+	0.00402460i
$508$		0			0
$509$	−16.4263	−	5.33722i	−0.728082	−	0.236568i	−0.0785584	−	0.996910i	$-0.525032\pi$
$509$	−16.4263	−	5.33722i	−0.728082	−	0.236568i	−0.649524	+	0.760341i	$0.725032\pi$
$510$		0			0
$511$	0.463933	+	0.638549i	0.0205232	+	0.0282477i
$512$		0			0
$513$	−22.8295	+	16.5866i	−1.00795	+	0.732315i
$514$		0			0
$515$	27.9915	+	20.3370i	1.23345	+	0.896155i
$516$		0			0
$517$	21.7831	−	15.8264i	0.958021	−	0.696043i
$518$		0			0
$519$			15.8012i			0.693596i
$520$		0			0
$521$	28.7877	−	9.35370i	1.26121	−	0.409793i	0.399287	−	0.916826i	$-0.369258\pi$
$521$	28.7877	−	9.35370i	1.26121	−	0.409793i	0.861927	+	0.507033i	$0.169258\pi$
$522$		0			0
$523$	6.69725	−	20.6120i	0.292850	−	0.901301i	−0.691085	−	0.722774i	$-0.742867\pi$
$523$	6.69725	−	20.6120i	0.292850	−	0.901301i	0.983935	−	0.178527i	$-0.0571332\pi$
$524$		0			0
$525$	−0.115625	+	0.355857i	−0.00504629	+	0.0155309i
$526$		0			0
$527$	−17.7529	+	24.4348i	−0.773329	+	1.06440i
$528$		0			0
$529$	−6.01816	−	18.5220i	−0.261659	−	0.805303i
$530$		0			0
$531$	−1.05106	−	0.763636i	−0.0456119	−	0.0331390i
$532$		0			0
$533$	−18.6203	+	13.1654i	−0.806535	+	0.570255i
$534$		0			0
$535$	11.8582	+	8.61551i	0.512676	+	0.372481i
$536$		0			0
$537$	4.06887	+	12.5227i	0.175585	+	0.540394i
$538$		0			0
$539$	1.34578	−	1.85231i	0.0579668	−	0.0797845i
$540$		0			0
$541$	−0.737024	+	2.26833i	−0.0316871	+	0.0975230i	−0.965649	−	0.259849i	$-0.916327\pi$
$541$	−0.737024	+	2.26833i	−0.0316871	+	0.0975230i	0.933962	+	0.357372i	$0.116327\pi$
$542$		0			0
$543$	−4.10615	+	12.6374i	−0.176212	+	0.542324i
$544$		0			0
$545$	31.0004	−	10.0726i	1.32791	−	0.431464i
$546$		0			0
$547$		−	37.0731i		−	1.58513i	−0.609787	−	0.792565i	$-0.708745\pi$
$547$		−	37.0731i		−	1.58513i	0.609787	−	0.792565i	$-0.291255\pi$
$548$		0			0
$549$	11.5302	−	8.37716i	0.492096	−	0.357528i
$550$		0			0
$551$	22.1493	+	16.0924i	0.943593	+	0.685560i
$552$		0			0
$553$	2.31530	−	1.68217i	0.0984567	−	0.0715330i
$554$		0			0
$555$	2.93737	+	4.04294i	0.124684	+	0.171613i
$556$		0			0
$557$	−39.4647	−	12.8228i	−1.67217	−	0.543321i	−0.688804	−	0.724948i	$-0.741864\pi$
$557$	−39.4647	−	12.8228i	−1.67217	−	0.543321i	−0.983368	+	0.181626i	$0.941864\pi$
$558$		0			0
$559$	0.862855	−	0.280359i	0.0364949	−	0.0118579i
$560$		0			0
$561$	5.36909	−	7.38991i	0.226683	−	0.312002i
$562$		0			0
$563$	9.92782	+	3.22574i	0.418408	+	0.135949i	0.510652	−	0.859788i	$-0.329404\pi$
$563$	9.92782	+	3.22574i	0.418408	+	0.135949i	−0.0922444	+	0.995736i	$0.529404\pi$
$564$		0			0
$565$	−42.9952			−1.80882
$566$		0			0
$567$	−1.17078	−	1.61144i	−0.0491682	−	0.0676742i
$568$		0			0
$569$	6.24267	+	19.2130i	0.261706	+	0.805450i	0.992434	+	0.122780i	$0.0391811\pi$
$569$	6.24267	+	19.2130i	0.261706	+	0.805450i	−0.730727	+	0.682669i	$0.760819\pi$
$570$		0			0
$571$			18.2960i			0.765662i	0.923818	+	0.382831i	$0.125051\pi$
$571$			18.2960i			0.765662i	−0.923818	+	0.382831i	$0.874949\pi$
$572$		0			0
$573$	5.92701			0.247604
$574$		0			0
$575$	−0.757045			−0.0315709
$576$		0			0
$577$			32.5111i			1.35346i	0.736233	+	0.676728i	$0.236603\pi$
$577$			32.5111i			1.35346i	−0.736233	+	0.676728i	$0.763397\pi$
$578$		0			0
$579$	−1.80285	−	5.54859i	−0.0749238	−	0.230592i
$580$		0			0
$581$	0.0161146	+	0.0221798i	0.000668546	+	0.000920175i
$582$		0			0
$583$	32.2769			1.33677
$584$		0			0
$585$	16.8406	+	5.47185i	0.696274	+	0.226233i
$586$		0			0
$587$	−0.320688	+	0.441389i	−0.0132362	+	0.0182181i	−0.815584	−	0.578639i	$-0.803584\pi$
$587$	−0.320688	+	0.441389i	−0.0132362	+	0.0182181i	0.802348	+	0.596857i	$0.203584\pi$
$588$		0			0
$589$	−39.5363	+	12.8461i	−1.62906	+	0.529315i
$590$		0			0
$591$	−1.72660	−	0.561005i	−0.0710226	−	0.0230767i
$592$		0			0
$593$	18.4403	+	25.3810i	0.757254	+	1.04227i	0.997437	+	0.0715436i	$0.0227925\pi$
$593$	18.4403	+	25.3810i	0.757254	+	1.04227i	−0.240183	+	0.970728i	$0.577207\pi$
$594$		0			0
$595$	8.08524	−	5.87427i	0.331462	−	0.240822i
$596$		0			0
$597$	−12.5289	−	9.10280i	−0.512775	−	0.372553i
$598$		0			0
$599$	31.3307	−	22.7631i	1.28014	−	0.930074i	0.280580	−	0.959831i	$-0.409473\pi$
$599$	31.3307	−	22.7631i	1.28014	−	0.930074i	0.999557	+	0.0297565i	$0.00947318\pi$
$600$		0			0
$601$			36.7746i			1.50007i	0.661400	+	0.750033i	$0.269962\pi$
$601$			36.7746i			1.50007i	−0.661400	+	0.750033i	$0.730038\pi$
$602$		0			0
$603$	5.99946	−	1.94934i	0.244317	−	0.0793834i
$604$		0			0
$605$	4.13588	−	12.7289i	0.168148	−	0.517505i
$606$		0			0
$607$	9.02060	−	27.7626i	0.366135	−	1.12685i	−0.583132	−	0.812377i	$-0.698173\pi$
$607$	9.02060	−	27.7626i	0.366135	−	1.12685i	0.949267	−	0.314470i	$-0.101827\pi$
$608$		0			0
$609$	2.52344	−	3.47321i	0.102255	−	0.140742i
$610$		0			0
$611$	12.9425	+	39.8328i	0.523596	+	1.61146i
$612$		0			0
$613$	−7.07340	−	5.13912i	−0.285692	−	0.207567i	0.435704	−	0.900090i	$-0.356499\pi$
$613$	−7.07340	−	5.13912i	−0.285692	−	0.207567i	−0.721396	+	0.692523i	$0.756499\pi$
$614$		0			0
$615$	13.8102	+	0.177904i	0.556882	+	0.00717379i
$616$		0			0
$617$	6.41150	+	4.65823i	0.258117	+	0.187533i	0.709317	−	0.704890i	$-0.249004\pi$
$617$	6.41150	+	4.65823i	0.258117	+	0.187533i	−0.451199	+	0.892423i	$0.649004\pi$
$618$		0			0
$619$	6.74574	+	20.7613i	0.271134	+	0.834465i	0.990216	+	0.139540i	$0.0445625\pi$
$619$	6.74574	+	20.7613i	0.271134	+	0.834465i	−0.719082	+	0.694925i	$0.755438\pi$
$620$		0			0
$621$	−5.26235	+	7.24300i	−0.211171	+	0.290651i
$622$		0			0
$623$	2.60088	−	8.00467i	0.104202	−	0.320700i
$624$		0			0
$625$	−8.29820	+	25.5392i	−0.331928	+	1.02157i
$626$		0			0
$627$	11.9571	−	3.88510i	0.477521	−	0.155156i
$628$		0			0
$629$		−	9.96101i		−	0.397171i
$630$		0			0
$631$	9.07496	−	6.59335i	0.361269	−	0.262477i	−0.392312	−	0.919832i	$-0.628325\pi$
$631$	9.07496	−	6.59335i	0.361269	−	0.262477i	0.753581	+	0.657355i	$0.228325\pi$
$632$		0			0
$633$	−2.56507	−	1.86363i	−0.101952	−	0.0740728i
$634$		0			0
$635$	−11.2970	+	8.20778i	−0.448309	+	0.325716i
$636$		0			0
$637$	2.09337	+	2.88128i	0.0829424	+	0.114160i
$638$		0			0
$639$	−4.95150	−	1.60884i	−0.195878	−	0.0636448i
$640$		0			0
$641$	−0.0931082	+	0.0302527i	−0.00367755	+	0.00119491i	−0.310855	−	0.950457i	$-0.600615\pi$
$641$	−0.0931082	+	0.0302527i	−0.00367755	+	0.00119491i	0.307178	+	0.951652i	$0.400615\pi$
$642$		0			0
$643$	2.25548	−	3.10440i	0.0889475	−	0.122426i	−0.762224	−	0.647313i	$-0.775893\pi$
$643$	2.25548	−	3.10440i	0.0889475	−	0.122426i	0.851172	+	0.524887i	$0.175893\pi$
$644$		0			0
$645$	−0.522582	−	0.169797i	−0.0205767	−	0.00668576i
$646$		0			0
$647$	−0.487361			−0.0191602			−0.00958008	−	0.999954i	$-0.503049\pi$
$647$	−0.487361			−0.0191602			−0.00958008	+	0.999954i	$0.503049\pi$
$648$		0			0
$649$	0.817418	+	1.12508i	0.0320865	+	0.0441632i
$650$		0			0
$651$	2.01438	+	6.19964i	0.0789500	+	0.242983i
$652$		0			0
$653$			32.0771i			1.25528i	0.778506	+	0.627638i	$0.215978\pi$
$653$			32.0771i			1.25528i	−0.778506	+	0.627638i	$0.784022\pi$
$654$		0			0
$655$	36.2514			1.41646
$656$		0			0
$657$	−1.68824			−0.0658645
$658$		0			0
$659$			29.8372i			1.16229i	0.813800	+	0.581146i	$0.197395\pi$
$659$			29.8372i			1.16229i	−0.813800	+	0.581146i	$0.802605\pi$
$660$		0			0
$661$	12.5364	+	38.5830i	0.487608	+	1.50070i	0.828168	+	0.560480i	$0.189383\pi$
$661$	12.5364	+	38.5830i	0.487608	+	1.50070i	−0.340560	+	0.940223i	$0.610617\pi$
$662$		0			0
$663$	8.35166	+	11.4951i	0.324351	+	0.446432i
$664$		0			0
$665$	13.7554			0.533412
$666$		0			0
$667$	8.26098	+	2.68415i	0.319866	+	0.103931i
$668$		0			0
$669$	13.7643	−	18.9449i	0.532158	−	0.732453i
$670$		0			0
$671$	−14.5091	+	4.71431i	−0.560119	+	0.181994i
$672$		0			0
$673$	43.2222	+	14.0437i	1.66609	+	0.541347i	0.982136	−	0.188175i	$-0.0602571\pi$
$673$	43.2222	+	14.0437i	1.66609	+	0.541347i	0.683958	+	0.729521i	$0.260257\pi$
$674$		0			0
$675$	−1.13022	−	1.55561i	−0.0435021	−	0.0598754i
$676$		0			0
$677$	4.47672	−	3.25253i	0.172054	−	0.125005i	−0.498426	−	0.866933i	$-0.666088\pi$
$677$	4.47672	−	3.25253i	0.172054	−	0.125005i	0.670480	+	0.741928i	$0.266088\pi$
$678$		0			0
$679$	−11.1427	−	8.09567i	−0.427619	−	0.310683i
$680$		0			0
$681$	16.9549	−	12.3185i	0.649715	−	0.472046i
$682$		0			0
$683$		−	8.33546i		−	0.318948i	−0.987202	−	0.159474i	$-0.949020\pi$
$683$		−	8.33546i		−	0.318948i	0.987202	−	0.159474i	$-0.0509798\pi$
$684$		0			0
$685$	4.22248	−	1.37197i	0.161333	−	0.0524201i
$686$		0			0
$687$	4.49571	−	13.8364i	0.171522	−	0.527891i
$688$		0			0
$689$	−15.5148	+	47.7497i	−0.591067	+	1.81912i
$690$		0			0
$691$	−19.4249	+	26.7361i	−0.738959	+	1.01709i	0.259719	+	0.965684i	$0.416370\pi$
$691$	−19.4249	+	26.7361i	−0.738959	+	1.01709i	−0.998678	+	0.0514058i	$0.983630\pi$
$692$		0			0
$693$	1.51334	+	4.65757i	0.0574869	+	0.176926i
$694$		0			0
$695$	2.52692	+	1.83591i	0.0958514	+	0.0696401i
$696$		0			0
$697$	−22.0617	−	16.4671i	−0.835645	−	0.623734i
$698$		0			0
$699$	9.23771	+	6.71159i	0.349402	+	0.253856i
$700$		0			0
$701$	13.7945	+	42.4552i	0.521013	+	1.60351i	0.772068	+	0.635540i	$0.219222\pi$
$701$	13.7945	+	42.4552i	0.521013	+	1.60351i	−0.251056	+	0.967973i	$0.580778\pi$
$702$		0			0
$703$	8.05862	−	11.0917i	0.303937	−	0.418333i
$704$		0			0
$705$	7.83852	−	24.1245i	0.295216	−	0.908581i
$706$		0			0
$707$	−0.0345610	+	0.106368i	−0.00129980	+	0.00400037i
$708$		0			0
$709$	11.7843	−	3.82894i	0.442567	−	0.143799i	−0.0792525	−	0.996855i	$-0.525253\pi$
$709$	11.7843	−	3.82894i	0.442567	−	0.143799i	0.521820	+	0.853056i	$0.325253\pi$
$710$		0			0
$711$			6.12136i			0.229569i
$712$		0			0
$713$	−10.6701	+	7.75230i	−0.399599	+	0.290326i
$714$		0			0
$715$	−15.3344	−	11.1411i	−0.573475	−	0.416654i
$716$		0			0
$717$	2.65780	−	1.93101i	0.0992575	−	0.0721148i
$718$		0			0
$719$	−2.18707	−	3.01025i	−0.0815640	−	0.112263i	0.766285	−	0.642500i	$-0.222103\pi$
$719$	−2.18707	−	3.01025i	−0.0815640	−	0.112263i	−0.847849	+	0.530237i	$0.822103\pi$
$720$		0			0
$721$	−14.1562	−	4.59964i	−0.527206	−	0.171300i
$722$		0			0
$723$	−14.1598	+	4.60079i	−0.526608	+	0.171105i
$724$		0			0
$725$	−1.09654	+	1.50926i	−0.0407246	+	0.0560527i
$726$		0			0
$727$	−23.1431	−	7.51967i	−0.858332	−	0.278889i	−0.153400	−	0.988164i	$-0.549022\pi$
$727$	−23.1431	−	7.51967i	−0.858332	−	0.278889i	−0.704932	+	0.709275i	$0.749022\pi$
$728$		0			0
$729$	−9.01443			−0.333868
$730$		0			0
$731$	0.643771	+	0.886074i	0.0238107	+	0.0327726i
$732$		0			0
$733$	4.18628	+	12.8841i	0.154624	+	0.475883i	0.998123	−	0.0612478i	$-0.0195080\pi$
$733$	4.18628	+	12.8841i	0.154624	+	0.475883i	−0.843499	+	0.537131i	$0.819508\pi$
$734$		0			0
$735$		−	2.15697i		−	0.0795611i
$736$		0			0
$737$	−6.75248			−0.248731
$738$		0			0
$739$	−21.6946			−0.798049			−0.399025	−	0.916940i	$-0.630651\pi$
$739$	−21.6946			−0.798049			−0.399025	+	0.916940i	$0.630651\pi$
$740$		0			0
$741$			19.5566i			0.718428i
$742$		0			0
$743$	−6.73798	−	20.7374i	−0.247192	−	0.760780i	−0.995268	−	0.0971666i	$-0.969022\pi$
$743$	−6.73798	−	20.7374i	−0.247192	−	0.760780i	0.748076	−	0.663613i	$-0.230978\pi$
$744$		0			0
$745$	4.02610	+	5.54146i	0.147505	+	0.203023i
$746$		0			0
$747$	−0.0586406			−0.00214555
$748$		0			0
$749$	−5.99711	−	1.94858i	−0.219130	−	0.0711995i
$750$		0			0
$751$	21.9400	−	30.1978i	0.800602	−	1.10193i	−0.192104	−	0.981375i	$-0.561531\pi$
$751$	21.9400	−	30.1978i	0.800602	−	1.10193i	0.992706	−	0.120560i	$-0.0384690\pi$
$752$		0			0
$753$	−6.94042	+	2.25508i	−0.252923	+	0.0821796i
$754$		0			0
$755$	−14.6771	−	4.76887i	−0.534153	−	0.173557i
$756$		0			0
$757$	−18.7888	−	25.8606i	−0.682891	−	0.939919i	0.317073	−	0.948401i	$-0.397300\pi$
$757$	−18.7888	−	25.8606i	−0.682891	−	0.939919i	−0.999964	+	0.00848196i	$0.997300\pi$
$758$		0			0
$759$	3.22701	−	2.34456i	0.117133	−	0.0851022i
$760$		0			0
$761$	−0.424665	−	0.308537i	−0.0153941	−	0.0111845i	0.580062	−	0.814573i	$-0.303028\pi$
$761$	−0.424665	−	0.308537i	−0.0153941	−	0.0111845i	−0.595456	+	0.803388i	$0.703028\pi$
$762$		0			0
$763$	−11.3447	+	8.24238i	−0.410704	+	0.298394i
$764$		0			0
$765$			21.3763i			0.772862i
$766$		0			0
$767$	−2.05733	+	0.668467i	−0.0742859	+	0.0241370i
$768$		0			0
$769$	9.45426	−	29.0972i	0.340929	−	1.04927i	−0.622798	−	0.782383i	$-0.714004\pi$
$769$	9.45426	−	29.0972i	0.340929	−	1.04927i	0.963727	−	0.266889i	$-0.0859959\pi$
$770$		0			0
$771$	3.49426	−	10.7542i	0.125843	−	0.387304i
$772$		0			0
$773$	4.19030	−	5.76746i	0.150715	−	0.207441i	−0.726983	−	0.686655i	$-0.759078\pi$
$773$	4.19030	−	5.76746i	0.150715	−	0.207441i	0.877698	+	0.479214i	$0.159078\pi$
$774$		0			0
$775$	−0.875340	−	2.69402i	−0.0314431	−	0.0967720i
$776$		0			0
$777$	−1.73928	−	1.26366i	−0.0623964	−	0.0453337i
$778$		0			0
$779$	−11.2439	−	36.1846i	−0.402854	−	1.29645i
$780$		0			0
$781$	4.50865	+	3.27572i	0.161332	+	0.117215i
$782$		0			0
$783$	6.81756	+	20.9823i	0.243640	+	0.749846i
$784$		0			0
$785$	23.8912	−	32.8835i	0.852715	−	1.17366i
$786$		0			0
$787$	0.633760	−	1.95051i	0.0225911	−	0.0695283i	−0.939125	−	0.343575i	$-0.888362\pi$
$787$	0.633760	−	1.95051i	0.0225911	−	0.0695283i	0.961716	+	0.274046i	$0.0883622\pi$
$788$		0			0
$789$	5.17685	−	15.9327i	0.184301	−	0.567219i
$790$		0			0
$791$	17.5914	−	5.71578i	0.625477	−	0.203230i
$792$		0			0
$793$		−	23.7306i		−	0.842697i
$794$		0			0
$795$	24.6002	−	17.8731i	0.872479	−	0.633893i
$796$		0			0
$797$	−28.7439	−	20.8836i	−1.01816	−	0.739736i	−0.0522549	−	0.998634i	$-0.516641\pi$
$797$	−28.7439	−	20.8836i	−1.01816	−	0.739736i	−0.965905	+	0.258897i	$0.916641\pi$
$798$		0			0
$799$	−40.9047	+	29.7190i	−1.44710	+	1.05138i
$800$		0			0
$801$	10.5817	+	14.5644i	0.373884	+	0.514608i
$802$		0			0
$803$	1.71869	+	0.558437i	0.0606513	+	0.0197068i
$804$		0			0
$805$	4.15052	−	1.34859i	0.146287	−	0.0475314i
$806$		0			0
$807$	−4.98603	+	6.86268i	−0.175517	+	0.241578i
$808$		0			0
$809$	−6.37688	−	2.07197i	−0.224199	−	0.0728467i	0.194763	−	0.980850i	$-0.437606\pi$
$809$	−6.37688	−	2.07197i	−0.224199	−	0.0728467i	−0.418962	+	0.908004i	$0.637606\pi$
$810$		0			0
$811$	−0.700800			−0.0246084			−0.0123042	−	0.999924i	$-0.503917\pi$
$811$	−0.700800			−0.0246084			−0.0123042	+	0.999924i	$0.503917\pi$
$812$		0			0
$813$	15.9936	+	22.0134i	0.560922	+	0.772042i
$814$		0			0
$815$	−2.90888	−	8.95262i	−0.101894	−	0.313597i
$816$		0			0
$817$			1.50748i			0.0527400i
$818$		0			0
$819$	−7.61773			−0.266185
$820$		0			0
$821$	−28.2970			−0.987573			−0.493787	−	0.869583i	$-0.664388\pi$
$821$	−28.2970			−0.987573			−0.493787	+	0.869583i	$0.664388\pi$
$822$		0			0
$823$		−	54.3429i		−	1.89427i	−0.320830	−	0.947137i	$-0.603962\pi$
$823$		−	54.3429i		−	1.89427i	0.320830	−	0.947137i	$-0.396038\pi$
$824$		0			0
$825$	0.264733	+	0.814763i	0.00921681	+	0.0283664i
$826$		0			0
$827$	−26.0067	−	35.7952i	−0.904343	−	1.24472i	−0.969062	−	0.246818i	$-0.920615\pi$
$827$	−26.0067	−	35.7952i	−0.904343	−	1.24472i	0.0647188	−	0.997904i	$-0.479385\pi$
$828$		0			0
$829$	−25.4091			−0.882494			−0.441247	−	0.897386i	$-0.645464\pi$
$829$	−25.4091			−0.882494			−0.441247	+	0.897386i	$0.645464\pi$
$830$		0			0
$831$	26.9326	+	8.75092i	0.934280	+	0.303566i
$832$		0			0
$833$	−2.52713	+	3.47829i	−0.0875598	+	0.120516i
$834$		0			0
$835$	31.7459	−	10.3149i	1.09861	−	0.356961i
$836$		0			0
$837$	−31.8595	−	10.3518i	−1.10123	−	0.357810i
$838$		0			0
$839$	−16.5176	−	22.7345i	−0.570250	−	0.784881i	0.422335	−	0.906440i	$-0.361211\pi$
$839$	−16.5176	−	22.7345i	−0.570250	−	0.784881i	−0.992584	+	0.121559i	$0.961211\pi$
$840$		0			0
$841$	−6.14464	+	4.46435i	−0.211884	+	0.153943i
$842$		0			0
$843$	−19.4301	−	14.1168i	−0.669208	−	0.486208i
$844$		0			0
$845$	−0.594307	+	0.431790i	−0.0204448	+	0.0148540i
$846$		0			0
$847$			5.75784i			0.197842i
$848$		0			0
$849$	19.6074	−	6.37083i	0.672924	−	0.218646i
$850$		0			0
$851$	1.34415	−	4.13686i	0.0460768	−	0.141810i
$852$		0			0
$853$	−15.7703	+	48.5359i	−0.539963	+	1.66184i	0.192710	+	0.981256i	$0.438272\pi$
$853$	−15.7703	+	48.5359i	−0.539963	+	1.66184i	−0.732673	+	0.680581i	$0.761728\pi$
$854$		0			0
$855$	−17.2938	+	23.8029i	−0.591435	+	0.814040i
$856$		0			0
$857$	−3.08182	−	9.48486i	−0.105273	−	0.323997i	0.884522	−	0.466499i	$-0.154485\pi$
$857$	−3.08182	−	9.48486i	−0.105273	−	0.323997i	−0.989794	+	0.142503i	$0.954485\pi$
$858$		0			0
$859$	8.31953	+	6.04449i	0.283859	+	0.206235i	0.720599	−	0.693352i	$-0.243867\pi$
$859$	8.31953	+	6.04449i	0.283859	+	0.206235i	−0.436740	+	0.899588i	$0.643867\pi$
$860$		0			0
$861$	−5.67406	+	1.76314i	−0.193372	+	0.0600877i
$862$		0			0
$863$	28.0011	+	20.3440i	0.953169	+	0.692518i	0.951554	−	0.307481i	$-0.0994861\pi$
$863$	28.0011	+	20.3440i	0.953169	+	0.692518i	0.00161461	+	0.999999i	$0.499486\pi$
$864$		0			0
$865$	12.2316	+	37.6448i	0.415885	+	1.27996i
$866$		0			0
$867$	−0.809901	+	1.11473i	−0.0275057	+	0.0378583i
$868$		0			0
$869$	2.02483	−	6.23177i	0.0686875	−	0.211398i
$870$		0			0
$871$	3.24577	−	9.98947i	0.109979	−	0.338480i
$872$		0			0
$873$	28.0181	−	9.10362i	0.948268	−	0.308111i
$874$		0			0
$875$		−	10.6851i		−	0.361223i
$876$		0			0
$877$	−15.1109	+	10.9787i	−0.510258	+	0.370724i	−0.812921	−	0.582373i	$-0.802124\pi$
$877$	−15.1109	+	10.9787i	−0.510258	+	0.370724i	0.302664	+	0.953097i	$0.402124\pi$
$878$		0			0
$879$	1.56979	+	1.14052i	0.0529477	+	0.0384688i
$880$		0			0
$881$	−16.1798	+	11.7553i	−0.545110	+	0.396046i	−0.825979	−	0.563700i	$-0.809377\pi$
$881$	−16.1798	+	11.7553i	−0.545110	+	0.396046i	0.280869	+	0.959746i	$0.409377\pi$
$882$		0			0
$883$	−22.0073	−	30.2905i	−0.740605	−	1.01935i	−0.998584	−	0.0532044i	$-0.983057\pi$
$883$	−22.0073	−	30.2905i	−0.740605	−	1.01935i	0.257979	−	0.966151i	$-0.416943\pi$
$884$		0			0
$885$	1.24601	+	0.404853i	0.0418841	+	0.0136090i
$886$		0			0
$887$	7.05716	−	2.29301i	0.236956	−	0.0769918i	−0.188132	−	0.982144i	$-0.560243\pi$
$887$	7.05716	−	2.29301i	0.236956	−	0.0769918i	0.425088	+	0.905152i	$0.360243\pi$
$888$		0			0
$889$	3.53101	−	4.86002i	0.118426	−	0.163000i
$890$		0			0
$891$	−4.33729	−	1.40927i	−0.145305	−	0.0472123i
$892$		0			0
$893$	−69.5912			−2.32878
$894$		0			0
$895$	19.3874	+	26.6844i	0.648048	+	0.891962i
$896$		0			0
$897$	1.91733	+	5.90094i	0.0640179	+	0.197027i
$898$		0			0
$899$			32.5011i			1.08397i
$900$		0			0
$901$	−60.6101			−2.01921
$902$		0			0
$903$	0.236386			0.00786643
$904$		0			0
$905$			33.2860i			1.10646i
$906$		0			0
$907$	9.27979	+	28.5603i	0.308131	+	0.948328i	0.978490	+	0.206292i	$0.0661397\pi$
$907$	9.27979	+	28.5603i	0.308131	+	0.948328i	−0.670360	+	0.742036i	$0.733860\pi$
$908$		0			0
$909$	−0.140611	−	0.193535i	−0.00466378	−	0.00641914i
$910$		0			0
$911$	5.36919			0.177889			0.0889447	−	0.996037i	$-0.471651\pi$
$911$	5.36919			0.177889			0.0889447	+	0.996037i	$0.471651\pi$
$912$		0			0
$913$	0.0596984	+	0.0193972i	0.00197573	+	0.000641953i
$914$		0			0
$915$	−8.44780	+	11.6274i	−0.279276	+	0.384390i
$916$		0			0
$917$	−14.8322	+	4.81926i	−0.489801	+	0.159146i
$918$		0			0
$919$	−30.3814	−	9.87152i	−1.00219	−	0.325632i	−0.238450	−	0.971155i	$-0.576639\pi$
$919$	−30.3814	−	9.87152i	−1.00219	−	0.325632i	−0.763741	+	0.645523i	$0.776639\pi$
$920$		0			0
$921$	9.86211	+	13.5740i	0.324968	+	0.447279i
$922$		0			0
$923$	−7.01324	+	5.09541i	−0.230843	+	0.167718i
$924$		0			0
$925$	0.755796	+	0.549118i	0.0248504	+	0.0180549i
$926$		0			0
$927$	25.7571	−	18.7136i	0.845974	−	0.614636i
$928$		0			0
$929$		−	28.8823i		−	0.947599i	−0.880633	−	0.473800i	$-0.842882\pi$
$929$		−	28.8823i		−	0.947599i	0.880633	−	0.473800i	$-0.157118\pi$
$930$		0			0
$931$	−5.62799	+	1.82865i	−0.184450	+	0.0599314i
$932$		0			0
$933$	−0.467089	+	1.43755i	−0.0152918	+	0.0470633i
$934$		0			0
$935$	7.07087	−	21.7619i	0.231242	−	0.711690i
$936$		0			0
$937$	−7.56024	+	10.4058i	−0.246982	+	0.339942i	−0.914451	−	0.404696i	$-0.867378\pi$
$937$	−7.56024	+	10.4058i	−0.246982	+	0.339942i	0.667469	+	0.744637i	$0.267378\pi$
$938$		0			0
$939$	0.415765	+	1.27959i	0.0135680	+	0.0417580i
$940$		0			0
$941$	16.7994	+	12.2054i	0.547643	+	0.397886i	0.826916	−	0.562326i	$-0.190093\pi$
$941$	16.7994	+	12.2054i	0.547643	+	0.397886i	−0.279273	+	0.960212i	$0.590093\pi$
$942$		0			0
$943$	−6.94024	−	9.81587i	−0.226005	−	0.319649i
$944$		0			0
$945$	8.96758	+	6.51533i	0.291715	+	0.211944i
$946$		0			0
$947$	−7.09398	−	21.8330i	−0.230523	−	0.709478i	−0.997684	−	0.0680224i	$-0.978331\pi$
$947$	−7.09398	−	21.8330i	−0.230523	−	0.709478i	0.767161	−	0.641455i	$-0.221669\pi$
$948$		0			0
$949$	−1.65228	+	2.27416i	−0.0536352	+	0.0738225i
$950$		0			0
$951$	7.18406	−	22.1103i	0.232959	−	0.716975i
$952$		0			0
$953$	−3.48669	+	10.7309i	−0.112945	+	0.347609i	−0.991513	−	0.130009i	$-0.958499\pi$
$953$	−3.48669	+	10.7309i	−0.112945	+	0.347609i	0.878568	+	0.477617i	$0.158499\pi$
$954$		0			0
$955$	14.1205	−	4.58804i	0.456930	−	0.148465i
$956$		0			0
$957$		−	9.82944i		−	0.317741i
$958$		0			0
$959$	−1.54523	+	1.12267i	−0.0498979	+	0.0362530i
$960$		0			0
$961$	−14.8452	−	10.7857i	−0.478878	−	0.347925i
$962$		0			0
$963$	10.9117	−	7.92779i	0.351623	−	0.255469i
$964$		0			0
$965$	−8.59022	−	11.8234i	−0.276529	−	0.380609i
$966$		0			0
$967$	46.2085	+	15.0140i	1.48596	+	0.482819i	0.935889	−	0.352296i	$-0.114599\pi$
$967$	46.2085	+	15.0140i	1.48596	+	0.482819i	0.550076	+	0.835115i	$0.314599\pi$
$968$		0			0
$969$	−22.4533	+	7.29551i	−0.721303	+	0.234366i
$970$		0			0
$971$	−13.4581	+	18.5235i	−0.431892	+	0.594448i	−0.968386	−	0.249456i	$-0.919748\pi$
$971$	−13.4581	+	18.5235i	−0.431892	+	0.594448i	0.536494	+	0.843904i	$0.319748\pi$
$972$		0			0
$973$	−1.27795	−	0.415230i	−0.0409691	−	0.0133117i
$974$		0			0
$975$	−1.33259			−0.0426771
$976$		0			0
$977$	−13.3144	−	18.3258i	−0.425967	−	0.586293i	0.541055	−	0.840987i	$-0.318025\pi$
$977$	−13.3144	−	18.3258i	−0.425967	−	0.586293i	−0.967022	+	0.254695i	$0.918025\pi$
$978$		0			0
$979$	−5.95491	−	18.3273i	−0.190320	−	0.585743i
$980$		0			0
$981$		−	29.9938i		−	0.957629i
$982$		0			0
$983$	20.6056			0.657215			0.328608	−	0.944467i	$-0.393421\pi$
$983$	20.6056			0.657215			0.328608	+	0.944467i	$0.393421\pi$
$984$		0			0
$985$	−4.54771			−0.144902
$986$		0			0
$987$			10.9125i			0.347349i
$988$		0			0
$989$	0.147794	+	0.454862i	0.00469957	+	0.0144638i
$990$		0			0
$991$	19.1552	+	26.3649i	0.608486	+	0.837510i	0.996452	−	0.0841642i	$-0.0268220\pi$
$991$	19.1552	+	26.3649i	0.608486	+	0.837510i	−0.387965	+	0.921674i	$0.626822\pi$
$992$		0			0
$993$	26.9832			0.856286
$994$		0			0
$995$	−36.8953	−	11.9880i	−1.16966	−	0.380046i
$996$		0			0
$997$	−5.10498	+	7.02641i	−0.161676	+	0.222529i	−0.882168	−	0.470936i	$-0.843916\pi$
$997$	−5.10498	+	7.02641i	−0.161676	+	0.222529i	0.720491	+	0.693464i	$0.243916\pi$
$998$		0			0
$999$	10.5073	−	3.41404i	0.332437	−	0.108015i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.ba.a.113.12	✓	80
41.4	even	10	inner	1148.2.ba.a.701.9	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.ba.a.113.12	✓	80	1.1	even	1	trivial
1148.2.ba.a.701.9	yes	80	41.4	even	10	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:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.ba (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+0.927936i q^{3} +(0.718305 + 2.21072i) q^{5} +(-0.587785 - 0.809017i) q^{7} +2.13894 q^{9} +O(q^{10})\)	\(q+0.927936i q^{3} +(0.718305 + 2.21072i) q^{5} +(-0.587785 - 0.809017i) q^{7} +2.13894 q^{9} +(-2.17752 - 0.707518i) q^{11} +(2.09337 - 2.88128i) q^{13} +(-2.05140 + 0.666541i) q^{15} +(4.08898 + 1.32859i) q^{17} +(3.47829 + 4.78745i) q^{19} +(0.750716 - 0.545427i) q^{21} +(1.51889 + 1.10354i) q^{23} +(-0.326219 + 0.237012i) q^{25} +4.76860i q^{27} +(4.40009 - 1.42968i) q^{29} +(-2.17082 + 6.68111i) q^{31} +(0.656531 - 2.02060i) q^{33} +(1.36630 - 1.88055i) q^{35} +(-0.715941 - 2.20344i) q^{37} +(2.67364 + 1.94251i) q^{39} +(-6.06374 - 2.05695i) q^{41} +(0.206092 + 0.149735i) q^{43} +(1.53641 + 4.72858i) q^{45} +(-6.91235 + 9.51404i) q^{47} +(-0.309017 + 0.951057i) q^{49} +(-1.23285 + 3.79431i) q^{51} +(-13.4073 + 4.35631i) q^{53} -5.32209i q^{55} +(-4.44245 + 3.22763i) q^{57} +(-0.491392 - 0.357017i) q^{59} +(5.39061 - 3.91651i) q^{61} +(-1.25723 - 1.73044i) q^{63} +(7.87337 + 2.55821i) q^{65} +(2.80488 - 0.911362i) q^{67} +(-1.02401 + 1.40944i) q^{69} +(-2.31494 - 0.752169i) q^{71} -0.789290 q^{73} +(-0.219932 - 0.302710i) q^{75} +(0.707518 + 2.17752i) q^{77} +2.86187i q^{79} +1.99185 q^{81} -0.0274158 q^{83} +9.99390i q^{85} +(1.32665 + 4.08300i) q^{87} +(4.94716 + 6.80918i) q^{89} -3.56146 q^{91} +(-6.19964 - 2.01438i) q^{93} +(-8.08523 + 11.1284i) q^{95} +(13.0991 - 4.25615i) q^{97} +(-4.65757 - 1.51334i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) \) 80 * q - 4 * q^5 - 60 * q^9	\( 80 q - 4 q^{5} - 60 q^{9} + 10 q^{11} + 20 q^{15} - 10 q^{17} - 30 q^{19} - 4 q^{21} - 20 q^{25} + 2 q^{31} + 10 q^{33} + 10 q^{37} + 36 q^{39} - 14 q^{41} + 30 q^{43} + 44 q^{45} - 60 q^{47} + 20 q^{49} - 32 q^{51} + 16 q^{57} - 60 q^{59} + 44 q^{61} - 10 q^{65} - 10 q^{67} - 40 q^{71} - 88 q^{73} - 70 q^{75} - 8 q^{77} - 40 q^{81} + 28 q^{83} - 24 q^{87} + 24 q^{91} - 100 q^{93} + 120 q^{97} - 100 q^{99}+O(q^{100}) \) 80 * q - 4 * q^5 - 60 * q^9 + 10 * q^11 + 20 * q^15 - 10 * q^17 - 30 * q^19 - 4 * q^21 - 20 * q^25 + 2 * q^31 + 10 * q^33 + 10 * q^37 + 36 * q^39 - 14 * q^41 + 30 * q^43 + 44 * q^45 - 60 * q^47 + 20 * q^49 - 32 * q^51 + 16 * q^57 - 60 * q^59 + 44 * q^61 - 10 * q^65 - 10 * q^67 - 40 * q^71 - 88 * q^73 - 70 * q^75 - 8 * q^77 - 40 * q^81 + 28 * q^83 - 24 * q^87 + 24 * q^91 - 100 * q^93 + 120 * q^97 - 100 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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