LMFDB - Embedded newform 1120.2.bz.e.591.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1120,2,Mod(271,1120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1120, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("1120.271");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1120 = 2^{5} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1120.bz (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.94324502638$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			591.7
Character	$\chi$	$=$	1120.591
Dual form			1120.2.bz.e.271.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.725648 - 0.418953i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(2.36913 + 1.17781i) q^{7} +(-1.14896 - 1.99005i) q^{9} +O(q^{10})$	\(q+(-0.725648 - 0.418953i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(2.36913 + 1.17781i) q^{7} +(-1.14896 - 1.99005i) q^{9} +(-2.98938 + 5.17776i) q^{11} -2.87544 q^{13} +0.837906i q^{15} +(2.07668 + 1.19897i) q^{17} +(4.05564 - 2.34152i) q^{19} +(-1.22570 - 1.84723i) q^{21} +(-5.81623 + 3.35800i) q^{23} +(-0.500000 + 0.866025i) q^{25} +4.43915i q^{27} -1.31035i q^{29} +(-4.34775 + 7.53053i) q^{31} +(4.33848 - 2.50482i) q^{33} +(-0.164546 - 2.64063i) q^{35} +(-3.26889 + 1.88729i) q^{37} +(2.08656 + 1.20468i) q^{39} +1.79404i q^{41} +6.73760 q^{43} +(-1.14896 + 1.99005i) q^{45} +(-0.874599 - 1.51485i) q^{47} +(4.22551 + 5.58078i) q^{49} +(-1.00463 - 1.74007i) q^{51} +(-0.0994447 - 0.0574144i) q^{53} +5.97876 q^{55} -3.92395 q^{57} +(-2.61363 - 1.50898i) q^{59} +(4.40120 + 7.62310i) q^{61} +(-0.378112 - 6.06794i) q^{63} +(1.43772 + 2.49021i) q^{65} +(2.83761 - 4.91489i) q^{67} +5.62738 q^{69} +3.06734i q^{71} +(8.69332 + 5.01909i) q^{73} +(0.725648 - 0.418953i) q^{75} +(-13.1807 + 8.74583i) q^{77} +(-11.9852 + 6.91965i) q^{79} +(-1.58707 + 2.74889i) q^{81} +17.4215i q^{83} -2.39795i q^{85} +(-0.548973 + 0.950850i) q^{87} +(-11.0658 + 6.38886i) q^{89} +(-6.81228 - 3.38674i) q^{91} +(6.30988 - 3.64301i) q^{93} +(-4.05564 - 2.34152i) q^{95} +3.76431i q^{97} +13.7387 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{3} - 12 q^{5} - 10 q^{7} + 12 q^{9}+O(q^{10}) $ 24 * q - 12 * q^3 - 12 * q^5 - 10 * q^7 + 12 * q^9	$ 24 q - 12 q^{3} - 12 q^{5} - 10 q^{7} + 12 q^{9} - 8 q^{11} + 20 q^{13} + 6 q^{17} - 18 q^{19} - 26 q^{21} - 18 q^{23} - 12 q^{25} + 6 q^{31} + 12 q^{33} + 8 q^{35} + 18 q^{39} - 32 q^{43} + 12 q^{45} + 8 q^{49} + 22 q^{51} + 30 q^{53} + 16 q^{55} - 44 q^{57} + 18 q^{59} + 22 q^{61} + 12 q^{63} - 10 q^{65} + 8 q^{67} - 12 q^{69} + 30 q^{73} + 12 q^{75} - 32 q^{77} - 6 q^{79} - 4 q^{81} - 14 q^{87} - 60 q^{89} - 18 q^{91} - 18 q^{93} + 18 q^{95} + 56 q^{99}+O(q^{100}) $ 24 * q - 12 * q^3 - 12 * q^5 - 10 * q^7 + 12 * q^9 - 8 * q^11 + 20 * q^13 + 6 * q^17 - 18 * q^19 - 26 * q^21 - 18 * q^23 - 12 * q^25 + 6 * q^31 + 12 * q^33 + 8 * q^35 + 18 * q^39 - 32 * q^43 + 12 * q^45 + 8 * q^49 + 22 * q^51 + 30 * q^53 + 16 * q^55 - 44 * q^57 + 18 * q^59 + 22 * q^61 + 12 * q^63 - 10 * q^65 + 8 * q^67 - 12 * q^69 + 30 * q^73 + 12 * q^75 - 32 * q^77 - 6 * q^79 - 4 * q^81 - 14 * q^87 - 60 * q^89 - 18 * q^91 - 18 * q^93 + 18 * q^95 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times$.

$n$	$351$	$421$	$801$	$897$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	−0.725648	−	0.418953i	−0.418953	−	0.241883i	0.275676	−	0.961251i	$-0.411098\pi$
$3$	−0.725648	−	0.418953i	−0.418953	−	0.241883i	−0.694629	+	0.719368i	$0.744432\pi$
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	2.36913	+	1.17781i	0.895445	+	0.445172i
$7$	2.36913	+	1.17781i	0.895445	+	0.445172i
$8$		0			0
$9$	−1.14896	−	1.99005i	−0.382985	−	0.663350i
$10$		0			0
$11$	−2.98938	+	5.17776i	−0.901332	+	1.56115i	−0.0755665	+	0.997141i	$0.524077\pi$
$11$	−2.98938	+	5.17776i	−0.901332	+	1.56115i	−0.825766	+	0.564013i	$0.809257\pi$
$12$		0			0
$13$	−2.87544			−0.797504			−0.398752	−	0.917059i	$-0.630557\pi$
$13$	−2.87544			−0.797504			−0.398752	+	0.917059i	$0.630557\pi$
$14$		0			0
$15$			0.837906i			0.216346i
$16$		0			0
$17$	2.07668	+	1.19897i	0.503670	+	0.290794i	0.730228	−	0.683204i	$-0.239414\pi$
$17$	2.07668	+	1.19897i	0.503670	+	0.290794i	−0.226558	+	0.973998i	$0.572747\pi$
$18$		0			0
$19$	4.05564	−	2.34152i	0.930427	−	0.537182i	0.0434803	−	0.999054i	$-0.486155\pi$
$19$	4.05564	−	2.34152i	0.930427	−	0.537182i	0.886947	+	0.461872i	$0.152822\pi$
$20$		0			0
$21$	−1.22570	−	1.84723i	−0.267470	−	0.403099i
$22$		0			0
$23$	−5.81623	+	3.35800i	−1.21277	+	0.700191i	−0.963361	−	0.268208i	$-0.913569\pi$
$23$	−5.81623	+	3.35800i	−1.21277	+	0.700191i	−0.249406	+	0.968399i	$0.580235\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$			4.43915i			0.854316i
$28$		0			0
$29$		−	1.31035i		−	0.243325i	−0.992572	−	0.121663i	$-0.961177\pi$
$29$		−	1.31035i		−	0.243325i	0.992572	−	0.121663i	$-0.0388226\pi$
$30$		0			0
$31$	−4.34775	+	7.53053i	−0.780879	+	1.35252i	0.150551	+	0.988602i	$0.451895\pi$
$31$	−4.34775	+	7.53053i	−0.780879	+	1.35252i	−0.931430	+	0.363920i	$0.881438\pi$
$32$		0			0
$33$	4.33848	−	2.50482i	0.755232	−	0.436034i
$34$		0			0
$35$	−0.164546	−	2.64063i	−0.0278133	−	0.446348i
$36$		0			0
$37$	−3.26889	+	1.88729i	−0.537402	+	0.310269i	−0.744025	−	0.668151i	$-0.767086\pi$
$37$	−3.26889	+	1.88729i	−0.537402	+	0.310269i	0.206624	+	0.978421i	$0.433752\pi$
$38$		0			0
$39$	2.08656	+	1.20468i	0.334117	+	0.192903i
$40$		0			0
$41$			1.79404i			0.280181i	0.990139	+	0.140091i	$0.0447394\pi$
$41$			1.79404i			0.280181i	−0.990139	+	0.140091i	$0.955261\pi$
$42$		0			0
$43$	6.73760			1.02747			0.513737	−	0.857948i	$-0.328261\pi$
$43$	6.73760			1.02747			0.513737	+	0.857948i	$0.328261\pi$
$44$		0			0
$45$	−1.14896	+	1.99005i	−0.171276	+	0.296659i
$46$		0			0
$47$	−0.874599	−	1.51485i	−0.127573	−	0.220963i	0.795163	−	0.606396i	$-0.207385\pi$
$47$	−0.874599	−	1.51485i	−0.127573	−	0.220963i	−0.922736	+	0.385433i	$0.874052\pi$
$48$		0			0
$49$	4.22551	+	5.58078i	0.603644	+	0.797254i
$50$		0			0
$51$	−1.00463	−	1.74007i	−0.140676	−	0.243658i
$52$		0			0
$53$	−0.0994447	−	0.0574144i	−0.0136598	−	0.00788648i	0.493155	−	0.869942i	$-0.335844\pi$
$53$	−0.0994447	−	0.0574144i	−0.0136598	−	0.00788648i	−0.506814	+	0.862055i	$0.669177\pi$
$54$		0			0
$55$	5.97876			0.806176
$56$		0			0
$57$	−3.92395			−0.519740
$58$		0			0
$59$	−2.61363	−	1.50898i	−0.340266	−	0.196453i	0.320124	−	0.947376i	$-0.396276\pi$
$59$	−2.61363	−	1.50898i	−0.340266	−	0.196453i	−0.660390	+	0.750923i	$0.729609\pi$
$60$		0			0
$61$	4.40120	+	7.62310i	0.563516	+	0.976038i	0.997186	+	0.0749664i	$0.0238850\pi$
$61$	4.40120	+	7.62310i	0.563516	+	0.976038i	−0.433670	+	0.901072i	$0.642782\pi$
$62$		0			0
$63$	−0.378112	−	6.06794i	−0.0476376	−	0.764488i
$64$		0			0
$65$	1.43772	+	2.49021i	0.178327	+	0.308872i
$66$		0			0
$67$	2.83761	−	4.91489i	0.346670	−	0.600449i	−0.638986	−	0.769218i	$-0.720646\pi$
$67$	2.83761	−	4.91489i	0.346670	−	0.600449i	0.985656	+	0.168769i	$0.0539792\pi$
$68$		0			0
$69$	5.62738			0.677457
$70$		0			0
$71$			3.06734i			0.364026i	0.983296	+	0.182013i	$0.0582613\pi$
$71$			3.06734i			0.364026i	−0.983296	+	0.182013i	$0.941739\pi$
$72$		0			0
$73$	8.69332	+	5.01909i	1.01748	+	0.587440i	0.913372	−	0.407126i	$-0.133469\pi$
$73$	8.69332	+	5.01909i	1.01748	+	0.587440i	0.104104	+	0.994566i	$0.466802\pi$
$74$		0			0
$75$	0.725648	−	0.418953i	0.0837906	−	0.0483765i
$76$		0			0
$77$	−13.1807	+	8.74583i	−1.50208	+	0.996680i
$78$		0			0
$79$	−11.9852	+	6.91965i	−1.34844	+	0.778522i	−0.988028	−	0.154272i	$-0.950697\pi$
$79$	−11.9852	+	6.91965i	−1.34844	+	0.778522i	−0.360411	+	0.932794i	$0.617364\pi$
$80$		0			0
$81$	−1.58707	+	2.74889i	−0.176341	+	0.305432i
$82$		0			0
$83$			17.4215i			1.91226i	0.292940	+	0.956131i	$0.405366\pi$
$83$			17.4215i			1.91226i	−0.292940	+	0.956131i	$0.594634\pi$
$84$		0			0
$85$		−	2.39795i		−	0.260094i
$86$		0			0
$87$	−0.548973	+	0.950850i	−0.0588561	+	0.101942i
$88$		0			0
$89$	−11.0658	+	6.38886i	−1.17297	+	0.677217i	−0.954379	−	0.298598i	$-0.903481\pi$
$89$	−11.0658	+	6.38886i	−1.17297	+	0.677217i	−0.218596	+	0.975815i	$0.570148\pi$
$90$		0			0
$91$	−6.81228	−	3.38674i	−0.714121	−	0.355026i
$92$		0			0
$93$	6.30988	−	3.64301i	0.654304	−	0.377762i
$94$		0			0
$95$	−4.05564	−	2.34152i	−0.416100	−	0.240235i
$96$		0			0
$97$			3.76431i			0.382208i	0.981570	+	0.191104i	$0.0612067\pi$
$97$			3.76431i			0.382208i	−0.981570	+	0.191104i	$0.938793\pi$
$98$		0			0
$99$	13.7387			1.38079
$100$		0			0
$101$	−8.14097	+	14.1006i	−0.810057	+	1.40306i	0.102767	+	0.994705i	$0.467230\pi$
$101$	−8.14097	+	14.1006i	−0.810057	+	1.40306i	−0.912824	+	0.408354i	$0.866103\pi$
$102$		0			0
$103$	−1.13180	−	1.96034i	−0.111520	−	0.193158i	0.804864	−	0.593460i	$-0.202238\pi$
$103$	−1.13180	−	1.96034i	−0.111520	−	0.193158i	−0.916383	+	0.400302i	$0.868905\pi$
$104$		0			0
$105$	−0.986898	+	1.98511i	−0.0963114	+	0.193726i
$106$		0			0
$107$	−1.21095	−	2.09743i	−0.117067	−	0.202766i	0.801537	−	0.597945i	$-0.204016\pi$
$107$	−1.21095	−	2.09743i	−0.117067	−	0.202766i	−0.918604	+	0.395179i	$0.870683\pi$
$108$		0			0
$109$	−6.35090	−	3.66669i	−0.608306	−	0.351206i	0.163996	−	0.986461i	$-0.447561\pi$
$109$	−6.35090	−	3.66669i	−0.608306	−	0.351206i	−0.772302	+	0.635255i	$0.780895\pi$
$110$		0			0
$111$	3.16275			0.300195
$112$		0			0
$113$	15.0661			1.41730			0.708651	−	0.705559i	$-0.249304\pi$
$113$	15.0661			1.41730			0.708651	+	0.705559i	$0.249304\pi$
$114$		0			0
$115$	5.81623	+	3.35800i	0.542366	+	0.313135i
$116$		0			0
$117$	3.30376	+	5.72228i	0.305433	+	0.529025i
$118$		0			0
$119$	3.50775	+	5.28646i	0.321555	+	0.484609i
$120$		0			0
$121$	−12.3728	−	21.4303i	−1.12480	−	1.94821i
$122$		0			0
$123$	0.751617	−	1.30184i	0.0677710	−	0.117383i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$		−	5.22434i		−	0.463585i	−0.972765	−	0.231793i	$-0.925541\pi$
$127$		−	5.22434i		−	0.463585i	0.972765	−	0.231793i	$-0.0744591\pi$
$128$		0			0
$129$	−4.88913	−	2.82274i	−0.430464	−	0.248528i
$130$		0			0
$131$	−7.76094	+	4.48078i	−0.678076	+	0.391487i	−0.799130	−	0.601159i	$-0.794706\pi$
$131$	−7.76094	+	4.48078i	−0.678076	+	0.391487i	0.121054	+	0.992646i	$0.461373\pi$
$132$		0			0
$133$	12.3662	−	0.770575i	1.07228	−	0.0668173i
$134$		0			0
$135$	3.84442	−	2.21958i	0.330875	−	0.191031i
$136$		0			0
$137$	10.4348	−	18.0735i	0.891502	−	1.54413i	0.0534263	−	0.998572i	$-0.482986\pi$
$137$	10.4348	−	18.0735i	0.891502	−	1.54413i	0.838075	−	0.545554i	$-0.183681\pi$
$138$		0			0
$139$		−	12.8189i		−	1.08728i	−0.839318	−	0.543641i	$-0.817045\pi$
$139$		−	12.8189i		−	1.08728i	0.839318	−	0.543641i	$-0.182955\pi$
$140$		0			0
$141$			1.46566i			0.123431i
$142$		0			0
$143$	8.59580	−	14.8884i	0.718817	−	1.24503i
$144$		0			0
$145$	−1.13479	+	0.655173i	−0.0942394	+	0.0544091i
$146$		0			0
$147$	−0.728148	−	5.81997i	−0.0600566	−	0.480023i
$148$		0			0
$149$	−0.696284	+	0.402000i	−0.0570418	+	0.0329331i	−0.528250	−	0.849089i	$-0.677151\pi$
$149$	−0.696284	+	0.402000i	−0.0570418	+	0.0329331i	0.471208	+	0.882022i	$0.343818\pi$
$150$		0			0
$151$	−11.3405	−	6.54743i	−0.922875	−	0.532822i	−0.0383242	−	0.999265i	$-0.512202\pi$
$151$	−11.3405	−	6.54743i	−0.922875	−	0.532822i	−0.884551	+	0.466443i	$0.845535\pi$
$152$		0			0
$153$		−	5.51027i		−	0.445479i
$154$		0			0
$155$	8.69550			0.698440
$156$		0			0
$157$	8.58489	−	14.8695i	0.685149	−	1.18671i	−0.288241	−	0.957558i	$-0.593070\pi$
$157$	8.58489	−	14.8695i	0.685149	−	1.18671i	0.973390	−	0.229155i	$-0.0735962\pi$
$158$		0			0
$159$	0.0481079	+	0.0833254i	0.00381521	+	0.00660813i
$160$		0			0
$161$	−17.7345	+	1.10509i	−1.39767	+	0.0870932i
$162$		0			0
$163$	2.93458	+	5.08284i	0.229854	+	0.398119i	0.957765	−	0.287553i	$-0.0928418\pi$
$163$	2.93458	+	5.08284i	0.229854	+	0.398119i	−0.727911	+	0.685672i	$0.759508\pi$
$164$		0			0
$165$	−4.33848	−	2.50482i	−0.337750	−	0.195000i
$166$		0			0
$167$	−6.02260			−0.466043			−0.233022	−	0.972472i	$-0.574861\pi$
$167$	−6.02260			−0.466043			−0.233022	+	0.972472i	$0.574861\pi$
$168$		0			0
$169$	−4.73183			−0.363987
$170$		0			0
$171$	−9.31950	−	5.38062i	−0.712680	−	0.411466i
$172$		0			0
$173$	1.08168	+	1.87352i	0.0822385	+	0.142441i	0.904211	−	0.427086i	$-0.140460\pi$
$173$	1.08168	+	1.87352i	0.0822385	+	0.142441i	−0.821973	+	0.569527i	$0.807126\pi$
$174$		0			0
$175$	−2.20458	+	1.46282i	−0.166651	+	0.110578i
$176$		0			0
$177$	1.26439	+	2.18998i	0.0950371	+	0.164609i
$178$		0			0
$179$	−5.63498	+	9.76008i	−0.421178	+	0.729502i	−0.996055	−	0.0887377i	$-0.971717\pi$
$179$	−5.63498	+	9.76008i	−0.421178	+	0.729502i	0.574877	+	0.818240i	$0.305050\pi$
$180$		0			0
$181$	15.2369			1.13255			0.566274	−	0.824217i	$-0.308384\pi$
$181$	15.2369			1.13255			0.566274	+	0.824217i	$0.308384\pi$
$182$		0			0
$183$		−	7.37559i		−	0.545219i
$184$		0			0
$185$	3.26889	+	1.88729i	0.240333	+	0.138757i
$186$		0			0
$187$	−12.4160	+	7.16838i	−0.907948	+	0.524204i
$188$		0			0
$189$	−5.22850	+	10.5169i	−0.380317	+	0.764993i
$190$		0			0
$191$	5.33642	−	3.08099i	0.386130	−	0.222932i	−0.294352	−	0.955697i	$-0.595104\pi$
$191$	5.33642	−	3.08099i	0.386130	−	0.222932i	0.680482	+	0.732765i	$0.261770\pi$
$192$		0			0
$193$	5.79750	−	10.0416i	0.417313	−	0.722808i	−0.578355	−	0.815785i	$-0.696305\pi$
$193$	5.79750	−	10.0416i	0.417313	−	0.722808i	0.995668	+	0.0929776i	$0.0296385\pi$
$194$		0			0
$195$		−	2.40935i		−	0.172537i
$196$		0			0
$197$		−	13.1499i		−	0.936892i	−0.883492	−	0.468446i	$-0.844814\pi$
$197$		−	13.1499i		−	0.936892i	0.883492	−	0.468446i	$-0.155186\pi$
$198$		0			0
$199$	10.0683	−	17.4388i	0.713724	−	1.23621i	−0.249726	−	0.968317i	$-0.580341\pi$
$199$	10.0683	−	17.4388i	0.713724	−	1.23621i	0.963450	−	0.267889i	$-0.0863261\pi$
$200$		0			0
$201$	−4.11822	+	2.37765i	−0.290477	+	0.167707i
$202$		0			0
$203$	1.54334	−	3.10437i	0.108321	−	0.217884i
$204$		0			0
$205$	1.55368	−	0.897018i	0.108514	−	0.0626504i
$206$		0			0
$207$	13.3652	+	7.71639i	0.928944	+	0.536326i
$208$		0			0
$209$			27.9988i			1.93672i
$210$		0			0
$211$	−4.31289			−0.296912			−0.148456	−	0.988919i	$-0.547430\pi$
$211$	−4.31289			−0.296912			−0.148456	+	0.988919i	$0.547430\pi$
$212$		0			0
$213$	1.28507	−	2.22581i	0.0880516	−	0.152510i
$214$		0			0
$215$	−3.36880	−	5.83493i	−0.229750	−	0.397939i
$216$		0			0
$217$	−19.1699	+	12.7199i	−1.30134	+	0.863484i
$218$		0			0
$219$	−4.20553	−	7.28419i	−0.284183	−	0.492220i
$220$		0			0
$221$	−5.97138	−	3.44758i	−0.401679	−	0.231909i
$222$		0			0
$223$	11.5948			0.776447			0.388224	−	0.921565i	$-0.373089\pi$
$223$	11.5948			0.776447			0.388224	+	0.921565i	$0.373089\pi$
$224$		0			0
$225$	2.29791			0.153194
$226$		0			0
$227$	−16.7181	−	9.65222i	−1.10962	−	0.640640i	−0.170890	−	0.985290i	$-0.554664\pi$
$227$	−16.7181	−	9.65222i	−1.10962	−	0.640640i	−0.938731	+	0.344650i	$0.887998\pi$
$228$		0			0
$229$	−8.54131	−	14.7940i	−0.564425	−	0.977613i	−0.997103	−	0.0760647i	$-0.975764\pi$
$229$	−8.54131	−	14.7940i	−0.564425	−	0.977613i	0.432678	−	0.901549i	$-0.357569\pi$
$230$		0			0
$231$	13.2286	−	0.824315i	0.870379	−	0.0542360i
$232$		0			0
$233$	−6.11671	−	10.5945i	−0.400719	−	0.694066i	0.593094	−	0.805133i	$-0.297906\pi$
$233$	−6.11671	−	10.5945i	−0.400719	−	0.694066i	−0.993813	+	0.111068i	$0.964573\pi$
$234$		0			0
$235$	−0.874599	+	1.51485i	−0.0570525	+	0.0988179i
$236$		0			0
$237$	11.5960			0.753244
$238$		0			0
$239$			1.56688i			0.101353i	0.998715	+	0.0506767i	$0.0161378\pi$
$239$			1.56688i			0.101353i	−0.998715	+	0.0506767i	$0.983862\pi$
$240$		0			0
$241$	19.0828	+	11.0174i	1.22923	+	0.709695i	0.966869	−	0.255275i	$-0.0821659\pi$
$241$	19.0828	+	11.0174i	1.22923	+	0.709695i	0.262360	+	0.964970i	$0.415499\pi$
$242$		0			0
$243$	13.8366	−	7.98855i	0.887617	−	0.512466i
$244$		0			0
$245$	2.72034	−	6.44979i	0.173796	−	0.412062i
$246$		0			0
$247$	−11.6618	+	6.73291i	−0.742019	+	0.428405i
$248$		0			0
$249$	7.29881	−	12.6419i	0.462543	−	0.801148i
$250$		0			0
$251$			7.68553i			0.485106i	0.970138	+	0.242553i	$0.0779849\pi$
$251$			7.68553i			0.485106i	−0.970138	+	0.242553i	$0.922015\pi$
$252$		0			0
$253$		−	40.1534i		−	2.52442i
$254$		0			0
$255$	−1.00463	+	1.74007i	−0.0629122	+	0.108967i
$256$		0			0
$257$	1.93788	−	1.11883i	0.120881	−	0.0697909i	−0.438340	−	0.898809i	$-0.644433\pi$
$257$	1.93788	−	1.11883i	0.120881	−	0.0697909i	0.559221	+	0.829018i	$0.311100\pi$
$258$		0			0
$259$	−9.96728	+	0.621092i	−0.619337	+	0.0385928i
$260$		0			0
$261$	−2.60765	+	1.50553i	−0.161410	+	0.0931900i
$262$		0			0
$263$	−15.0365	−	8.68130i	−0.927188	−	0.535312i	−0.0412668	−	0.999148i	$-0.513139\pi$
$263$	−15.0365	−	8.68130i	−0.927188	−	0.535312i	−0.885921	+	0.463836i	$0.846473\pi$
$264$		0			0
$265$			0.114829i			0.00705388i
$266$		0			0
$267$	10.7065			0.655229
$268$		0			0
$269$	−0.374476	+	0.648612i	−0.0228322	+	0.0395466i	−0.877216	−	0.480096i	$-0.840602\pi$
$269$	−0.374476	+	0.648612i	−0.0228322	+	0.0395466i	0.854384	+	0.519643i	$0.173935\pi$
$270$		0			0
$271$	10.8572	+	18.8052i	0.659527	+	1.14233i	0.980738	+	0.195327i	$0.0625767\pi$
$271$	10.8572	+	18.8052i	0.659527	+	1.14233i	−0.321211	+	0.947008i	$0.604090\pi$
$272$		0			0
$273$	3.52444	+	5.31161i	0.213309	+	0.321473i
$274$		0			0
$275$	−2.98938	−	5.17776i	−0.180266	−	0.312231i
$276$		0			0
$277$	20.4537	+	11.8089i	1.22894	+	0.709531i	0.966809	−	0.255500i	$-0.0822402\pi$
$277$	20.4537	+	11.8089i	1.22894	+	0.709531i	0.262135	+	0.965031i	$0.415574\pi$
$278$		0			0
$279$	19.9815			1.19626
$280$		0			0
$281$	−14.4129			−0.859803			−0.429901	−	0.902876i	$-0.641452\pi$
$281$	−14.4129			−0.859803			−0.429901	+	0.902876i	$0.641452\pi$
$282$		0			0
$283$	−10.7892	−	6.22915i	−0.641351	−	0.370284i	0.143784	−	0.989609i	$-0.454073\pi$
$283$	−10.7892	−	6.22915i	−0.641351	−	0.370284i	−0.785135	+	0.619325i	$0.787406\pi$
$284$		0			0
$285$	1.96198	+	3.39824i	0.116217	+	0.201295i
$286$		0			0
$287$	−2.11304	+	4.25030i	−0.124729	+	0.250887i
$288$		0			0
$289$	−5.62493	−	9.74266i	−0.330878	−	0.573097i
$290$		0			0
$291$	1.57707	−	2.73157i	0.0924495	−	0.160127i
$292$		0			0
$293$	−8.47355			−0.495030			−0.247515	−	0.968884i	$-0.579614\pi$
$293$	−8.47355			−0.495030			−0.247515	+	0.968884i	$0.579614\pi$
$294$		0			0
$295$			3.01797i			0.175713i
$296$		0			0
$297$	−22.9849	−	13.2703i	−1.33372	−	0.770023i
$298$		0			0
$299$	16.7242	−	9.65573i	0.967187	−	0.558406i
$300$		0			0
$301$	15.9622	+	7.93564i	0.920047	+	0.457403i
$302$		0			0
$303$	11.8150	−	6.82137i	0.678752	−	0.391877i
$304$		0			0
$305$	4.40120	−	7.62310i	0.252012	−	0.436498i
$306$		0			0
$307$			11.9420i			0.681565i	0.940142	+	0.340783i	$0.110692\pi$
$307$			11.9420i			0.681565i	−0.940142	+	0.340783i	$0.889308\pi$
$308$		0			0
$309$			1.89668i			0.107899i
$310$		0			0
$311$	−7.74793	+	13.4198i	−0.439345	+	0.760967i	−0.997639	−	0.0686757i	$-0.978123\pi$
$311$	−7.74793	+	13.4198i	−0.439345	+	0.760967i	0.558294	+	0.829643i	$0.311456\pi$
$312$		0			0
$313$	14.9712	−	8.64360i	0.846220	−	0.488565i	−0.0131537	−	0.999913i	$-0.504187\pi$
$313$	14.9712	−	8.64360i	0.846220	−	0.488565i	0.859374	+	0.511348i	$0.170854\pi$
$314$		0			0
$315$	−5.06593	+	3.36142i	−0.285433	+	0.189395i
$316$		0			0
$317$	−7.20732	+	4.16115i	−0.404803	+	0.233713i	−0.688554	−	0.725185i	$-0.741754\pi$
$317$	−7.20732	+	4.16115i	−0.404803	+	0.233713i	0.283751	+	0.958898i	$0.408421\pi$
$318$		0			0
$319$	6.78466	+	3.91712i	0.379868	+	0.219317i
$320$		0			0
$321$			2.02933i			0.113266i
$322$		0			0
$323$	11.2297			0.624837
$324$		0			0
$325$	1.43772	−	2.49021i	0.0797504	−	0.138132i
$326$		0			0
$327$	3.07235	+	5.32146i	0.169901	+	0.294277i
$328$		0			0
$329$	−0.287823	−	4.61898i	−0.0158682	−	0.254653i
$330$		0			0
$331$	−12.6436	−	21.8993i	−0.694953	−	1.20369i	−0.970197	−	0.242319i	$-0.922092\pi$
$331$	−12.6436	−	21.8993i	−0.694953	−	1.20369i	0.275244	−	0.961375i	$-0.411241\pi$
$332$		0			0
$333$	7.51162	+	4.33683i	0.411634	+	0.237657i
$334$		0			0
$335$	−5.67523			−0.310071
$336$		0			0
$337$	−0.379048			−0.0206481			−0.0103240	−	0.999947i	$-0.503286\pi$
$337$	−0.379048			−0.0206481			−0.0103240	+	0.999947i	$0.503286\pi$
$338$		0			0
$339$	−10.9327	−	6.31200i	−0.593783	−	0.342821i
$340$		0			0
$341$	−25.9942	−	45.0232i	−1.40766	−	2.43815i
$342$		0			0
$343$	3.43764	+	18.1984i	0.185615	+	0.982623i
$344$		0			0
$345$	−2.81369	−	4.87345i	−0.151484	−	0.262378i
$346$		0			0
$347$	−4.89803	+	8.48364i	−0.262940	+	0.455426i	−0.967022	−	0.254693i	$-0.918026\pi$
$347$	−4.89803	+	8.48364i	−0.262940	+	0.455426i	0.704082	+	0.710119i	$0.251359\pi$
$348$		0			0
$349$	6.73905			0.360733			0.180366	−	0.983599i	$-0.442272\pi$
$349$	6.73905			0.360733			0.180366	+	0.983599i	$0.442272\pi$
$350$		0			0
$351$		−	12.7645i		−	0.681321i
$352$		0			0
$353$	18.5926	+	10.7345i	0.989587	+	0.571338i	0.905151	−	0.425091i	$-0.139758\pi$
$353$	18.5926	+	10.7345i	0.989587	+	0.571338i	0.0844361	+	0.996429i	$0.473091\pi$
$354$		0			0
$355$	2.65639	−	1.53367i	0.140987	−	0.0813986i
$356$		0			0
$357$	−0.330614	−	5.30570i	−0.0174980	−	0.280807i
$358$		0			0
$359$	−4.15852	+	2.40092i	−0.219478	+	0.126716i	−0.605709	−	0.795687i	$-0.707110\pi$
$359$	−4.15852	+	2.40092i	−0.219478	+	0.126716i	0.386231	+	0.922402i	$0.373777\pi$
$360$		0			0
$361$	1.46546	−	2.53825i	0.0771294	−	0.133592i
$362$		0			0
$363$			20.7345i			1.08828i
$364$		0			0
$365$		−	10.0382i		−	0.525423i
$366$		0			0
$367$	−5.81465	+	10.0713i	−0.303522	+	0.525716i	−0.976931	−	0.213554i	$-0.931496\pi$
$367$	−5.81465	+	10.0713i	−0.303522	+	0.525716i	0.673409	+	0.739270i	$0.264829\pi$
$368$		0			0
$369$	3.57022	−	2.06127i	0.185858	−	0.107305i
$370$		0			0
$371$	−0.167973	−	0.253149i	−0.00872075	−	0.0131429i
$372$		0			0
$373$	−25.2282	+	14.5655i	−1.30627	+	0.754174i	−0.981471	−	0.191610i	$-0.938629\pi$
$373$	−25.2282	+	14.5655i	−1.30627	+	0.754174i	−0.324797	+	0.945784i	$0.605296\pi$
$374$		0			0
$375$	−0.725648	−	0.418953i	−0.0374723	−	0.0216346i
$376$		0			0
$377$			3.76782i			0.194053i
$378$		0			0
$379$	−2.52399			−0.129649			−0.0648243	−	0.997897i	$-0.520649\pi$
$379$	−2.52399			−0.129649			−0.0648243	+	0.997897i	$0.520649\pi$
$380$		0			0
$381$	−2.18875	+	3.79103i	−0.112133	+	0.194221i
$382$		0			0
$383$	−11.6539	−	20.1851i	−0.595485	−	1.03141i	−0.993478	−	0.114022i	$-0.963627\pi$
$383$	−11.6539	−	20.1851i	−0.595485	−	1.03141i	0.397993	−	0.917388i	$-0.369707\pi$
$384$		0			0
$385$	14.1644	+	7.04187i	0.721887	+	0.358887i
$386$		0			0
$387$	−7.74121	−	13.4082i	−0.393508	−	0.681575i
$388$		0			0
$389$	0.383453	+	0.221387i	0.0194418	+	0.0112248i	0.509689	−	0.860358i	$-0.329760\pi$
$389$	0.383453	+	0.221387i	0.0194418	+	0.0112248i	−0.490248	+	0.871583i	$0.663094\pi$
$390$		0			0
$391$	−16.1046			−0.814445
$392$		0			0
$393$	7.50895			0.378776
$394$		0			0
$395$	11.9852	+	6.91965i	0.603041	+	0.348166i
$396$		0			0
$397$	4.05153	+	7.01745i	0.203340	+	0.352196i	0.949603	−	0.313456i	$-0.101487\pi$
$397$	4.05153	+	7.01745i	0.203340	+	0.352196i	−0.746262	+	0.665652i	$0.768154\pi$
$398$		0			0
$399$	−9.29634	−	4.62169i	−0.465399	−	0.231374i
$400$		0			0
$401$	−1.01905	−	1.76504i	−0.0508889	−	0.0881421i	0.839459	−	0.543423i	$-0.182872\pi$
$401$	−1.01905	−	1.76504i	−0.0508889	−	0.0881421i	−0.890348	+	0.455281i	$0.849539\pi$
$402$		0			0
$403$	12.5017	−	21.6536i	0.622755	−	1.07864i
$404$		0			0
$405$	3.17414			0.157724
$406$		0			0
$407$		−	22.5674i		−	1.11862i
$408$		0			0
$409$	−27.1993	−	15.7035i	−1.34492	−	0.776490i	−0.357395	−	0.933953i	$-0.616335\pi$
$409$	−27.1993	−	15.7035i	−1.34492	−	0.776490i	−0.987525	+	0.157463i	$0.949668\pi$
$410$		0			0
$411$	−15.1439	+	8.74335i	−0.746995	+	0.431278i
$412$		0			0
$413$	−4.41473	−	6.65334i	−0.217235	−	0.327390i
$414$		0			0
$415$	15.0875	−	8.71077i	0.740616	−	0.427595i
$416$		0			0
$417$	−5.37051	+	9.30199i	−0.262995	+	0.455521i
$418$		0			0
$419$			18.1384i			0.886117i	0.896493	+	0.443059i	$0.146107\pi$
$419$			18.1384i			0.886117i	−0.896493	+	0.443059i	$0.853893\pi$
$420$		0			0
$421$			38.6453i			1.88345i	0.336377	+	0.941727i	$0.390798\pi$
$421$			38.6453i			1.88345i	−0.336377	+	0.941727i	$0.609202\pi$
$422$		0			0
$423$	−2.00975	+	3.48099i	−0.0977175	+	0.169252i
$424$		0			0
$425$	−2.07668	+	1.19897i	−0.100734	+	0.0581588i
$426$		0			0
$427$	1.44840	+	23.2439i	0.0700928	+	1.12485i
$428$		0			0
$429$	−12.4750	+	7.20247i	−0.602301	+	0.347739i
$430$		0			0
$431$	−3.59352	−	2.07472i	−0.173094	−	0.0999358i	0.410950	−	0.911658i	$-0.365197\pi$
$431$	−3.59352	−	2.07472i	−0.173094	−	0.0999358i	−0.584044	+	0.811722i	$0.698530\pi$
$432$		0			0
$433$			21.7089i			1.04326i	0.853170	+	0.521632i	$0.174677\pi$
$433$			21.7089i			1.04326i	−0.853170	+	0.521632i	$0.825323\pi$
$434$		0			0
$435$	1.09795			0.0526425
$436$		0			0
$437$	−15.7257	+	27.2376i	−0.752260	+	1.30295i
$438$		0			0
$439$	3.86516	+	6.69465i	0.184474	+	0.319518i	0.943399	−	0.331660i	$-0.107609\pi$
$439$	3.86516	+	6.69465i	0.184474	+	0.319518i	−0.758925	+	0.651178i	$0.774275\pi$
$440$		0			0
$441$	6.25111	−	14.8210i	0.297672	−	0.705764i
$442$		0			0
$443$	8.93181	+	15.4704i	0.424363	+	0.735019i	0.996361	−	0.0852368i	$-0.0271647\pi$
$443$	8.93181	+	15.4704i	0.424363	+	0.735019i	−0.571998	+	0.820255i	$0.693831\pi$
$444$		0			0
$445$	11.0658	+	6.38886i	0.524570	+	0.302861i
$446$		0			0
$447$	0.673676			0.0318638
$448$		0			0
$449$	29.3236			1.38387			0.691933	−	0.721961i	$-0.256759\pi$
$449$	29.3236			1.38387			0.691933	+	0.721961i	$0.256759\pi$
$450$		0			0
$451$	−9.28909	−	5.36306i	−0.437406	−	0.252537i
$452$		0			0
$453$	5.48613	+	9.50226i	0.257761	+	0.446455i
$454$		0			0
$455$	0.473142	+	7.59298i	0.0221812	+	0.355964i
$456$		0			0
$457$	−4.64207	−	8.04029i	−0.217147	−	0.376109i	0.736788	−	0.676124i	$-0.236342\pi$
$457$	−4.64207	−	8.04029i	−0.217147	−	0.376109i	−0.953935	+	0.300015i	$0.903008\pi$
$458$		0			0
$459$	−5.32243	+	9.21872i	−0.248430	+	0.430293i
$460$		0			0
$461$	0.401756			0.0187116			0.00935582	−	0.999956i	$-0.497022\pi$
$461$	0.401756			0.0187116			0.00935582	+	0.999956i	$0.497022\pi$
$462$		0			0
$463$			9.04694i			0.420447i	0.977653	+	0.210223i	$0.0674191\pi$
$463$			9.04694i			0.420447i	−0.977653	+	0.210223i	$0.932581\pi$
$464$		0			0
$465$	−6.30988	−	3.64301i	−0.292614	−	0.168940i
$466$		0			0
$467$	10.4257	−	6.01931i	0.482446	−	0.278540i	−0.238989	−	0.971022i	$-0.576816\pi$
$467$	10.4257	−	6.01931i	0.482446	−	0.278540i	0.721435	+	0.692482i	$0.243483\pi$
$468$		0			0
$469$	12.5115	−	8.30181i	0.577727	−	0.383342i
$470$		0			0
$471$	−12.4592	+	7.19333i	−0.574091	+	0.331451i
$472$		0			0
$473$	−20.1413	+	34.8857i	−0.926096	+	1.60405i
$474$		0			0
$475$			4.68305i			0.214873i
$476$		0			0
$477$			0.263867i			0.0120816i
$478$		0			0
$479$	1.59624	−	2.76477i	0.0729340	−	0.126325i	−0.827252	−	0.561831i	$-0.810097\pi$
$479$	1.59624	−	2.76477i	0.0729340	−	0.126325i	0.900186	+	0.435506i	$0.143430\pi$
$480$		0			0
$481$	9.39950	−	5.42680i	0.428580	−	0.247441i
$482$		0			0
$483$	13.3320	+	6.62800i	0.606625	+	0.301585i
$484$		0			0
$485$	3.25999	−	1.88216i	0.148028	−	0.0854643i
$486$		0			0
$487$	−3.30907	−	1.91049i	−0.149948	−	0.0865727i	0.423149	−	0.906060i	$-0.360925\pi$
$487$	−3.30907	−	1.91049i	−0.149948	−	0.0865727i	−0.573097	+	0.819488i	$0.694258\pi$
$488$		0			0
$489$		−	4.91781i		−	0.222391i
$490$		0			0
$491$	42.7678			1.93008			0.965041	−	0.262097i	$-0.0844141\pi$
$491$	42.7678			1.93008			0.965041	+	0.262097i	$0.0844141\pi$
$492$		0			0
$493$	1.57107	−	2.72117i	0.0707574	−	0.122555i
$494$		0			0
$495$	−6.86934	−	11.8980i	−0.308754	−	0.534777i
$496$		0			0
$497$	−3.61275	+	7.26690i	−0.162054	+	0.325965i
$498$		0			0
$499$	3.71383	+	6.43253i	0.166254	+	0.287960i	0.937100	−	0.349062i	$-0.113500\pi$
$499$	3.71383	+	6.43253i	0.166254	+	0.287960i	−0.770846	+	0.637021i	$0.780166\pi$
$500$		0			0
$501$	4.37029	+	2.52319i	0.195250	+	0.112728i
$502$		0			0
$503$	41.0916			1.83219			0.916093	−	0.400966i	$-0.131326\pi$
$503$	41.0916			1.83219			0.916093	+	0.400966i	$0.131326\pi$
$504$		0			0
$505$	16.2819			0.724537
$506$		0			0
$507$	3.43364	+	1.98241i	0.152493	+	0.0880421i
$508$		0			0
$509$	17.7683	+	30.7755i	0.787564	+	1.36410i	0.927455	+	0.373934i	$0.121991\pi$
$509$	17.7683	+	30.7755i	0.787564	+	1.36410i	−0.139891	+	0.990167i	$0.544675\pi$
$510$		0			0
$511$	14.6840	+	22.1300i	0.649582	+	0.978972i
$512$		0			0
$513$	10.3944	+	18.0036i	0.458923	+	0.794878i
$514$		0			0
$515$	−1.13180	+	1.96034i	−0.0498731	+	0.0863827i
$516$		0			0
$517$	10.4580			0.459944
$518$		0			0
$519$		−	1.81269i		−	0.0795683i
$520$		0			0
$521$	−31.1264	−	17.9708i	−1.36367	−	0.787316i	−0.373561	−	0.927606i	$-0.621863\pi$
$521$	−31.1264	−	17.9708i	−1.36367	−	0.787316i	−0.990111	+	0.140289i	$0.955197\pi$
$522$		0			0
$523$	26.6453	−	15.3837i	1.16512	−	0.672681i	0.212592	−	0.977141i	$-0.431809\pi$
$523$	26.6453	−	15.3837i	1.16512	−	0.672681i	0.952525	+	0.304460i	$0.0984760\pi$
$524$		0			0
$525$	2.21260	−	0.137874i	0.0965658	−	0.00601731i
$526$		0			0
$527$	−18.0578	+	10.4257i	−0.786610	+	0.454150i
$528$		0			0
$529$	11.0523	−	19.1432i	0.480536	−	0.832312i
$530$		0			0
$531$			6.93502i			0.300954i
$532$		0			0
$533$		−	5.15865i		−	0.223446i
$534$		0			0
$535$	−1.21095	+	2.09743i	−0.0523540	+	0.0906798i
$536$		0			0
$537$	8.17803	−	4.72159i	0.352908	−	0.203752i
$538$		0			0
$539$	−41.5276	+	5.19560i	−1.78872	+	0.223790i
$540$		0			0
$541$	6.51224	−	3.75984i	0.279983	−	0.161648i	−0.353433	−	0.935460i	$-0.614986\pi$
$541$	6.51224	−	3.75984i	0.279983	−	0.161648i	0.633416	+	0.773812i	$0.281652\pi$
$542$		0			0
$543$	−11.0566	−	6.38354i	−0.474484	−	0.273944i
$544$		0			0
$545$			7.33339i			0.314128i
$546$		0			0
$547$	−10.8177			−0.462531			−0.231265	−	0.972891i	$-0.574287\pi$
$547$	−10.8177			−0.462531			−0.231265	+	0.972891i	$0.574287\pi$
$548$		0			0
$549$	10.1136	−	17.5172i	0.431637	−	0.747617i
$550$		0			0
$551$	−3.06820	−	5.31428i	−0.130710	−	0.226396i
$552$		0			0
$553$	−36.5445	+	2.27720i	−1.55403	+	0.0968364i
$554$		0			0
$555$	−1.58137	−	2.73902i	−0.0671256	−	0.116265i
$556$		0			0
$557$	−20.6521	−	11.9235i	−0.875057	−	0.505214i	−0.00603158	−	0.999982i	$-0.501920\pi$
$557$	−20.6521	−	11.9235i	−0.875057	−	0.505214i	−0.869025	+	0.494767i	$0.835253\pi$
$558$		0			0
$559$	−19.3736			−0.819415
$560$		0			0
$561$	12.0129			0.507183
$562$		0			0
$563$	1.24064	+	0.716284i	0.0522868	+	0.0301878i	0.525916	−	0.850537i	$-0.323723\pi$
$563$	1.24064	+	0.716284i	0.0522868	+	0.0301878i	−0.473629	+	0.880725i	$0.657056\pi$
$564$		0			0
$565$	−7.53306	−	13.0476i	−0.316918	−	0.548919i
$566$		0			0
$567$	−6.99765	+	4.64319i	−0.293874	+	0.194995i
$568$		0			0
$569$	13.6099	+	23.5731i	0.570558	+	0.988235i	0.996509	+	0.0834885i	$0.0266062\pi$
$569$	13.6099	+	23.5731i	0.570558	+	0.988235i	−0.425951	+	0.904746i	$0.640060\pi$
$570$		0			0
$571$	6.19271	−	10.7261i	0.259157	−	0.448873i	−0.706859	−	0.707354i	$-0.749889\pi$
$571$	6.19271	−	10.7261i	0.259157	−	0.448873i	0.966016	+	0.258481i	$0.0832220\pi$
$572$		0			0
$573$	−5.16316			−0.215694
$574$		0			0
$575$		−	6.71600i		−	0.280076i
$576$		0			0
$577$	20.3920	+	11.7733i	0.848929	+	0.490130i	0.860289	−	0.509806i	$-0.170283\pi$
$577$	20.3920	+	11.7733i	0.848929	+	0.490130i	−0.0113602	+	0.999935i	$0.503616\pi$
$578$		0			0
$579$	−8.41389	+	4.85776i	−0.349669	+	0.201882i
$580$		0			0
$581$	−20.5193	+	41.2738i	−0.851285	+	1.71233i
$582$		0			0
$583$	0.594557	−	0.343267i	0.0246240	−	0.0142167i
$584$		0			0
$585$	3.30376	−	5.72228i	0.136594	−	0.236587i
$586$		0			0
$587$		−	28.0077i		−	1.15600i	−0.816036	−	0.578001i	$-0.803833\pi$
$587$		−	28.0077i		−	1.15600i	0.816036	−	0.578001i	$-0.196167\pi$
$588$		0			0
$589$			40.7214i			1.67790i
$590$		0			0
$591$	−5.50920	+	9.54221i	−0.226618	+	0.392514i
$592$		0			0
$593$	−28.9741	+	16.7282i	−1.18982	+	0.686945i	−0.958266	−	0.285877i	$-0.907715\pi$
$593$	−28.9741	+	16.7282i	−1.18982	+	0.686945i	−0.231557	+	0.972821i	$0.574382\pi$
$594$		0			0
$595$	2.82434	−	5.68104i	0.115786	−	0.232900i
$596$		0			0
$597$	−14.6121	+	8.43630i	−0.598034	+	0.345275i
$598$		0			0
$599$	−37.2436	−	21.5026i	−1.52173	−	0.878571i	−0.999671	−	0.0256625i	$-0.991830\pi$
$599$	−37.2436	−	21.5026i	−1.52173	−	0.878571i	−0.522060	−	0.852909i	$-0.674836\pi$
$600$		0			0
$601$			32.3145i			1.31813i	0.752084	+	0.659067i	$0.229049\pi$
$601$			32.3145i			1.31813i	−0.752084	+	0.659067i	$0.770951\pi$
$602$		0			0
$603$	−13.0412			−0.531078
$604$		0			0
$605$	−12.3728	+	21.4303i	−0.503026	+	0.871267i
$606$		0			0
$607$	6.75765	+	11.7046i	0.274285	+	0.475075i	0.969954	−	0.243287i	$-0.0782256\pi$
$607$	6.75765	+	11.7046i	0.274285	+	0.475075i	−0.695670	+	0.718362i	$0.744892\pi$
$608$		0			0
$609$	−2.42051	+	1.60609i	−0.0980841	+	0.0650822i
$610$		0			0
$611$	2.51486	+	4.35586i	0.101740	+	0.176219i
$612$		0			0
$613$	−5.63444	−	3.25304i	−0.227573	−	0.131389i	0.381879	−	0.924212i	$-0.375277\pi$
$613$	−5.63444	−	3.25304i	−0.227573	−	0.131389i	−0.609452	+	0.792823i	$0.708610\pi$
$614$		0			0
$615$	−1.50323			−0.0606162
$616$		0			0
$617$	−1.66184			−0.0669033			−0.0334516	−	0.999440i	$-0.510650\pi$
$617$	−1.66184			−0.0669033			−0.0334516	+	0.999440i	$0.510650\pi$
$618$		0			0
$619$	24.5080	+	14.1497i	0.985061	+	0.568725i	0.903794	−	0.427967i	$-0.140770\pi$
$619$	24.5080	+	14.1497i	0.985061	+	0.568725i	0.0812670	+	0.996692i	$0.474103\pi$
$620$		0			0
$621$	−14.9067	−	25.8191i	−0.598184	−	1.03609i
$622$		0			0
$623$	−33.7412	+	2.10252i	−1.35181	+	0.0842356i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	11.7302	−	20.3173i	0.468459	−	0.811395i
$628$		0			0
$629$	−9.05126			−0.360897
$630$		0			0
$631$		−	48.7721i		−	1.94159i	−0.239918	−	0.970793i	$-0.577121\pi$
$631$		−	48.7721i		−	1.94159i	0.239918	−	0.970793i	$-0.422879\pi$
$632$		0			0
$633$	3.12964	+	1.80690i	0.124392	+	0.0718178i
$634$		0			0
$635$	−4.52441	+	2.61217i	−0.179546	+	0.103661i
$636$		0			0
$637$	−12.1502	−	16.0472i	−0.481409	−	0.635814i
$638$		0			0
$639$	6.10415	−	3.52424i	0.241477	−	0.139417i
$640$		0			0
$641$	−10.8633	+	18.8158i	−0.429074	+	0.743178i	−0.996791	−	0.0800459i	$-0.974493\pi$
$641$	−10.8633	+	18.8158i	−0.429074	+	0.743178i	0.567717	+	0.823224i	$0.307827\pi$
$642$		0			0
$643$		−	7.13929i		−	0.281546i	−0.990042	−	0.140773i	$-0.955041\pi$
$643$		−	7.13929i		−	0.281546i	0.990042	−	0.140773i	$-0.0449588\pi$
$644$		0			0
$645$			5.64548i			0.222290i
$646$		0			0
$647$	4.58700	−	7.94492i	0.180334	−	0.312347i	−0.761661	−	0.647976i	$-0.775616\pi$
$647$	4.58700	−	7.94492i	0.180334	−	0.312347i	0.941994	+	0.335629i	$0.108949\pi$
$648$		0			0
$649$	15.6263	−	9.02185i	0.613386	−	0.354139i
$650$		0			0
$651$	19.2397	−	1.19888i	0.754062	−	0.0469879i
$652$		0			0
$653$	0.710174	−	0.410019i	0.0277913	−	0.0160453i	−0.486040	−	0.873937i	$-0.661559\pi$
$653$	0.710174	−	0.410019i	0.0277913	−	0.0160453i	0.513831	+	0.857891i	$0.328226\pi$
$654$		0			0
$655$	7.76094	+	4.48078i	0.303245	+	0.175079i
$656$		0			0
$657$		−	23.0669i		−	0.899924i
$658$		0			0
$659$	10.4133			0.405645			0.202823	−	0.979216i	$-0.434989\pi$
$659$	10.4133			0.405645			0.202823	+	0.979216i	$0.434989\pi$
$660$		0			0
$661$	2.76908	−	4.79619i	0.107705	−	0.186550i	−0.807135	−	0.590367i	$-0.798983\pi$
$661$	2.76908	−	4.79619i	0.107705	−	0.186550i	0.914840	+	0.403816i	$0.132317\pi$
$662$		0			0
$663$	2.88875	+	5.00346i	0.112190	+	0.194318i
$664$		0			0
$665$	−6.85043	−	10.3241i	−0.265648	−	0.400353i
$666$		0			0
$667$	4.40014	+	7.62126i	0.170374	+	0.295097i
$668$		0			0
$669$	−8.41377	−	4.85769i	−0.325295	−	0.187809i
$670$		0			0
$671$	−52.6275			−2.03166
$672$		0			0
$673$	28.9492			1.11591			0.557956	−	0.829871i	$-0.311586\pi$
$673$	28.9492			1.11591			0.557956	+	0.829871i	$0.311586\pi$
$674$		0			0
$675$	−3.84442	−	2.21958i	−0.147972	−	0.0854316i
$676$		0			0
$677$	2.77831	+	4.81218i	0.106779	+	0.184947i	0.914464	−	0.404668i	$-0.132613\pi$
$677$	2.77831	+	4.81218i	0.106779	+	0.184947i	−0.807685	+	0.589615i	$0.799280\pi$
$678$		0			0
$679$	−4.43366	+	8.91812i	−0.170148	+	0.342246i
$680$		0			0
$681$	8.08766	+	14.0082i	0.309920	+	0.536797i
$682$		0			0
$683$	17.5473	−	30.3928i	0.671428	−	1.16295i	−0.306071	−	0.952009i	$-0.599014\pi$
$683$	17.5473	−	30.3928i	0.671428	−	1.16295i	0.977499	−	0.210939i	$-0.0676522\pi$
$684$		0			0
$685$	−20.8695			−0.797383
$686$		0			0
$687$			14.3136i			0.546099i
$688$		0			0
$689$	0.285948	+	0.165092i	0.0108937	+	0.00628950i
$690$		0			0
$691$	−6.28794	+	3.63035i	−0.239205	+	0.138105i	−0.614811	−	0.788674i	$-0.710768\pi$
$691$	−6.28794	+	3.63035i	−0.239205	+	0.138105i	0.375606	+	0.926779i	$0.377434\pi$
$692$		0			0
$693$	32.5486	+	16.1816i	1.23642	+	0.614688i
$694$		0			0
$695$	−11.1015	+	6.40944i	−0.421103	+	0.243124i
$696$		0			0
$697$	−2.15100	+	3.72564i	−0.0814750	+	0.141119i
$698$		0			0
$699$			10.2505i			0.387708i
$700$		0			0
$701$			2.84288i			0.107374i	0.998558	+	0.0536870i	$0.0170973\pi$
$701$			2.84288i			0.107374i	−0.998558	+	0.0536870i	$0.982903\pi$
$702$		0			0
$703$	−8.83828	+	15.3083i	−0.333342	+	0.577365i
$704$		0			0
$705$	1.26930	−	0.732832i	0.0478047	−	0.0276000i
$706$		0			0
$707$	−35.8948	+	23.8175i	−1.34996	+	0.895748i
$708$		0			0
$709$	14.8464	−	8.57155i	0.557567	−	0.321911i	−0.194601	−	0.980882i	$-0.562341\pi$
$709$	14.8464	−	8.57155i	0.557567	−	0.321911i	0.752168	+	0.658971i	$0.229008\pi$
$710$		0			0
$711$	27.5409	+	15.9008i	1.03287	+	0.596325i
$712$		0			0
$713$		−	58.3990i		−	2.18706i
$714$		0			0
$715$	−17.1916			−0.642929
$716$		0			0
$717$	0.656451	−	1.13701i	0.0245156	−	0.0424623i
$718$		0			0
$719$	11.0395	+	19.1210i	0.411705	+	0.713094i	0.995076	−	0.0991116i	$-0.0316001\pi$
$719$	11.0395	+	19.1210i	0.411705	+	0.713094i	−0.583371	+	0.812206i	$0.698267\pi$
$720$		0			0
$721$	−0.372466	−	5.97733i	−0.0138713	−	0.222607i
$722$		0			0
$723$	−9.23158	−	15.9896i	−0.343326	−	0.594658i
$724$		0			0
$725$	1.13479	+	0.655173i	0.0421451	+	0.0243325i
$726$		0			0
$727$	52.6712			1.95347			0.976733	−	0.214459i	$-0.0687990\pi$
$727$	52.6712			1.95347			0.976733	+	0.214459i	$0.0687990\pi$
$728$		0			0
$729$	−3.86488			−0.143144
$730$		0			0
$731$	13.9919	+	8.07820i	0.517507	+	0.298783i
$732$		0			0
$733$	0.876721	+	1.51853i	0.0323824	+	0.0560880i	0.881762	−	0.471694i	$-0.156357\pi$
$733$	0.876721	+	1.51853i	0.0323824	+	0.0560880i	−0.849380	+	0.527782i	$0.823024\pi$
$734$		0			0
$735$	−4.67617	+	3.54058i	−0.172483	+	0.130596i
$736$		0			0
$737$	16.9654	+	29.3850i	0.624929	+	1.08241i
$738$		0			0
$739$	−9.69575	+	16.7935i	−0.356664	+	0.617760i	−0.987401	−	0.158237i	$-0.949419\pi$
$739$	−9.69575	+	16.7935i	−0.356664	+	0.617760i	0.630737	+	0.775996i	$0.282752\pi$
$740$		0			0
$741$	11.2831			0.414495
$742$		0			0
$743$			44.8603i			1.64576i	0.568213	+	0.822882i	$0.307635\pi$
$743$			44.8603i			1.64576i	−0.568213	+	0.822882i	$0.692365\pi$
$744$		0			0
$745$	0.696284	+	0.402000i	0.0255099	+	0.0147281i
$746$		0			0
$747$	34.6697	−	20.0166i	1.26850	−	0.732368i
$748$		0			0
$749$	−0.398514	−	6.39535i	−0.0145614	−	0.233681i
$750$		0			0
$751$	40.9012	−	23.6143i	1.49250	−	0.861698i	0.492542	−	0.870289i	$-0.336068\pi$
$751$	40.9012	−	23.6143i	1.49250	−	0.861698i	0.999963	+	0.00859066i	$0.00273453\pi$
$752$		0			0
$753$	3.21988	−	5.57699i	0.117339	−	0.203237i
$754$		0			0
$755$			13.0949i			0.476571i
$756$		0			0
$757$			1.52456i			0.0554110i	0.999616	+	0.0277055i	$0.00882007\pi$
$757$			1.52456i			0.0554110i	−0.999616	+	0.0277055i	$0.991180\pi$
$758$		0			0
$759$	−16.8224	+	29.1372i	−0.610614	+	1.05761i
$760$		0			0
$761$	−28.6395	+	16.5350i	−1.03818	+	0.599394i	−0.919317	−	0.393517i	$-0.871258\pi$
$761$	−28.6395	+	16.5350i	−1.03818	+	0.599394i	−0.118863	+	0.992911i	$0.537925\pi$
$762$		0			0
$763$	−10.7274	−	16.1670i	−0.388358	−	0.585286i
$764$		0			0
$765$	−4.77204	+	2.75514i	−0.172533	+	0.0996122i
$766$		0			0
$767$	7.51536	+	4.33899i	0.271364	+	0.156672i
$768$		0			0
$769$		−	1.31233i		−	0.0473238i	−0.999720	−	0.0236619i	$-0.992467\pi$
$769$		−	1.31233i		−	0.0473238i	0.999720	−	0.0236619i	$-0.00753252\pi$
$770$		0			0
$771$	−1.87495			−0.0675248
$772$		0			0
$773$	−8.51479	+	14.7480i	−0.306256	+	0.530450i	−0.977540	−	0.210749i	$-0.932410\pi$
$773$	−8.51479	+	14.7480i	−0.306256	+	0.530450i	0.671284	+	0.741200i	$0.265743\pi$
$774$		0			0
$775$	−4.34775	−	7.53053i	−0.156176	−	0.270505i
$776$		0			0
$777$	7.49295	+	3.72513i	0.268808	+	0.133638i
$778$		0			0
$779$	4.20078	+	7.27596i	0.150508	+	0.260688i
$780$		0			0
$781$	−15.8819	−	9.16944i	−0.568300	−	0.328108i
$782$		0			0
$783$	5.81683			0.207876
$784$		0			0
$785$	−17.1698			−0.612816
$786$		0			0
$787$	26.0083	+	15.0159i	0.927097	+	0.535260i	0.885892	−	0.463891i	$-0.153547\pi$
$787$	26.0083	+	15.0159i	0.927097	+	0.535260i	0.0412045	+	0.999151i	$0.486880\pi$
$788$		0			0
$789$	7.27412	+	12.5991i	0.258966	+	0.448541i
$790$		0			0
$791$	35.6935	+	17.7451i	1.26912	+	0.630943i
$792$		0			0
$793$	−12.6554	−	21.9198i	−0.449406	−	0.778395i
$794$		0			0
$795$	0.0481079	−	0.0833254i	0.00170621	−	0.00295525i
$796$		0			0
$797$	34.7798			1.23196			0.615981	−	0.787761i	$-0.288760\pi$
$797$	34.7798			1.23196			0.615981	+	0.787761i	$0.288760\pi$
$798$		0			0
$799$		−	4.19448i		−	0.148390i
$800$		0			0
$801$	25.4283	+	14.6810i	0.898465	+	0.518729i
$802$		0			0
$803$	−51.9753	+	30.0080i	−1.83417	+	1.05896i
$804$		0			0
$805$	9.82427	+	14.8060i	0.346260	+	0.521841i
$806$		0			0
$807$	0.543476	−	0.313776i	0.0191313	−	0.0110454i
$808$		0			0
$809$	6.61556	−	11.4585i	0.232591	−	0.402859i	−0.725979	−	0.687717i	$-0.758613\pi$
$809$	6.61556	−	11.4585i	0.232591	−	0.402859i	0.958570	+	0.284858i	$0.0919464\pi$
$810$		0			0
$811$			17.4547i			0.612917i	0.951884	+	0.306459i	$0.0991441\pi$
$811$			17.4547i			0.612917i	−0.951884	+	0.306459i	$0.900856\pi$
$812$		0			0
$813$		−	18.1946i		−	0.638113i
$814$		0			0
$815$	2.93458	−	5.08284i	0.102794	−	0.178044i
$816$		0			0
$817$	27.3253	−	15.7762i	0.955990	−	0.551941i
$818$		0			0
$819$	1.08724	+	17.4480i	0.0379912	+	0.609683i
$820$		0			0
$821$	40.5407	−	23.4062i	1.41488	−	0.816882i	0.419039	−	0.907968i	$-0.362367\pi$
$821$	40.5407	−	23.4062i	1.41488	−	0.816882i	0.995843	+	0.0910860i	$0.0290338\pi$
$822$		0			0
$823$	13.7735	+	7.95213i	0.480114	+	0.277194i	0.720464	−	0.693492i	$-0.243929\pi$
$823$	13.7735	+	7.95213i	0.480114	+	0.277194i	−0.240350	+	0.970686i	$0.577262\pi$
$824$		0			0
$825$			5.00964i			0.174413i
$826$		0			0
$827$	−14.9258			−0.519021			−0.259511	−	0.965740i	$-0.583561\pi$
$827$	−14.9258			−0.519021			−0.259511	+	0.965740i	$0.583561\pi$
$828$		0			0
$829$	−9.10972	+	15.7785i	−0.316394	+	0.548010i	−0.979733	−	0.200309i	$-0.935805\pi$
$829$	−9.10972	+	15.7785i	−0.316394	+	0.548010i	0.663339	+	0.748319i	$0.269139\pi$
$830$		0			0
$831$	−9.89479	−	17.1383i	−0.343247	−	0.594520i
$832$		0			0
$833$	2.08384	+	16.6558i	0.0722007	+	0.577088i
$834$		0			0
$835$	3.01130	+	5.21573i	0.104210	+	0.180498i
$836$		0			0
$837$	−33.4292	−	19.3003i	−1.15548	−	0.667117i
$838$		0			0
$839$	−28.2947			−0.976843			−0.488421	−	0.872608i	$-0.662427\pi$
$839$	−28.2947			−0.976843			−0.488421	+	0.872608i	$0.662427\pi$
$840$		0			0
$841$	27.2830			0.940793
$842$		0			0
$843$	10.4587	+	6.03834i	0.360217	+	0.207971i
$844$		0			0
$845$	2.36591	+	4.09788i	0.0813899	+	0.140971i
$846$		0			0
$847$	−4.07178	−	65.3440i	−0.139908	−	2.24525i
$848$		0			0
$849$	5.21944	+	9.04034i	0.179131	+	0.310264i
$850$		0			0
$851$	12.6751	−	21.9538i	0.434495	−	0.752568i
$852$		0			0
$853$	−39.5247			−1.35330			−0.676650	−	0.736305i	$-0.736569\pi$
$853$	−39.5247			−1.35330			−0.676650	+	0.736305i	$0.736569\pi$
$854$		0			0
$855$			10.7612i			0.368026i
$856$		0			0
$857$	2.50342	+	1.44535i	0.0855151	+	0.0493722i	0.542148	−	0.840283i	$-0.317611\pi$
$857$	2.50342	+	1.44535i	0.0855151	+	0.0493722i	−0.456633	+	0.889655i	$0.650945\pi$
$858$		0			0
$859$	−12.6042	+	7.27704i	−0.430050	+	0.248290i	−0.699368	−	0.714762i	$-0.746535\pi$
$859$	−12.6042	+	7.27704i	−0.430050	+	0.248290i	0.269318	+	0.963051i	$0.413202\pi$
$860$		0			0
$861$	3.31400	−	2.19895i	0.112941	−	0.0749402i
$862$		0			0
$863$	−12.0583	+	6.96188i	−0.410470	+	0.236985i	−0.690992	−	0.722863i	$-0.742826\pi$
$863$	−12.0583	+	6.96188i	−0.410470	+	0.236985i	0.280521	+	0.959848i	$0.409493\pi$
$864$		0			0
$865$	1.08168	−	1.87352i	0.0367782	−	0.0637016i
$866$		0			0
$867$			9.42632i			0.320135i
$868$		0			0
$869$		−	82.7420i		−	2.80683i
$870$		0			0
$871$	−8.15939	+	14.1325i	−0.276471	+	0.478861i
$872$		0			0
$873$	7.49117	−	4.32503i	0.253538	−	0.146380i
$874$		0			0
$875$	2.36913	+	1.17781i	0.0800910	+	0.0398174i
$876$		0			0
$877$	−13.6311	+	7.86992i	−0.460289	+	0.265748i	−0.712166	−	0.702011i	$-0.752286\pi$
$877$	−13.6311	+	7.86992i	−0.460289	+	0.265748i	0.251877	+	0.967759i	$0.418952\pi$
$878$		0			0
$879$	6.14882	+	3.55002i	0.207394	+	0.119739i
$880$		0			0
$881$			4.77034i			0.160717i	0.996766	+	0.0803584i	$0.0256065\pi$
$881$			4.77034i			0.160717i	−0.996766	+	0.0803584i	$0.974394\pi$
$882$		0			0
$883$	−31.2410			−1.05134			−0.525672	−	0.850688i	$-0.676186\pi$
$883$	−31.2410			−1.05134			−0.525672	+	0.850688i	$0.676186\pi$
$884$		0			0
$885$	1.26439	−	2.18998i	0.0425019	−	0.0736154i
$886$		0			0
$887$	18.4386	+	31.9365i	0.619106	+	1.07232i	0.989649	+	0.143508i	$0.0458384\pi$
$887$	18.4386	+	31.9365i	0.619106	+	1.07232i	−0.370543	+	0.928815i	$0.620828\pi$
$888$		0			0
$889$	6.15330	−	12.3771i	0.206375	−	0.415115i
$890$		0			0
$891$	−9.48872	−	16.4350i	−0.317884	−	0.550592i
$892$		0			0
$893$	−7.09411	−	4.09579i	−0.237395	−	0.137060i
$894$		0			0
$895$	11.2700			0.376713
$896$		0			0
$897$	−16.1812			−0.540275
$898$		0			0
$899$	9.86759	+	5.69706i	0.329103	+	0.190007i
$900$		0			0
$901$	−0.137677	−	0.238463i	−0.00458668	−	0.00794436i
$902$		0			0
$903$	−8.25829	−	12.4459i	−0.274819	−	0.414174i
$904$		0			0
$905$	−7.61844	−	13.1955i	−0.253245	−	0.438634i
$906$		0			0
$907$	0.588928	−	1.02005i	0.0195550	−	0.0338703i	−0.856082	−	0.516840i	$-0.827108\pi$
$907$	0.588928	−	1.02005i	0.0195550	−	0.0338703i	0.875637	+	0.482969i	$0.160442\pi$
$908$		0			0
$909$	37.4145			1.24096
$910$		0			0
$911$			37.7931i			1.25214i	0.779766	+	0.626071i	$0.215338\pi$
$911$			37.7931i			1.25214i	−0.779766	+	0.626071i	$0.784662\pi$
$912$		0			0
$913$	−90.2045	−	52.0796i	−2.98533	−	1.72358i
$914$		0			0
$915$	−6.38745	+	3.68779i	−0.211162	+	0.121915i
$916$		0			0
$917$	−23.6642	+	1.47459i	−0.781459	+	0.0486951i
$918$		0			0
$919$	−37.4585	+	21.6267i	−1.23564	+	0.713398i	−0.968200	−	0.250177i	$-0.919511\pi$
$919$	−37.4585	+	21.6267i	−1.23564	+	0.713398i	−0.267441	+	0.963574i	$0.586178\pi$
$920$		0			0
$921$	5.00313	−	8.66568i	0.164859	−	0.285544i
$922$		0			0
$923$		−	8.81995i		−	0.290312i
$924$		0			0
$925$		−	3.77459i		−	0.124108i
$926$		0			0
$927$	−2.60078	+	4.50468i	−0.0854208	+	0.147953i
$928$		0			0
$929$	30.3878	−	17.5444i	0.996992	−	0.575614i	0.0896350	−	0.995975i	$-0.471430\pi$
$929$	30.3878	−	17.5444i	0.996992	−	0.575614i	0.907357	+	0.420361i	$0.138097\pi$
$930$		0			0
$931$	30.2046	+	12.7395i	0.989917	+	0.417520i
$932$		0			0
$933$	11.2445	−	6.49204i	0.368130	−	0.212540i
$934$		0			0
$935$	12.4160	+	7.16838i	0.406046	+	0.234431i
$936$		0			0
$937$			44.8914i			1.46654i	0.679938	+	0.733270i	$0.262007\pi$
$937$			44.8914i			1.46654i	−0.679938	+	0.733270i	$0.737993\pi$
$938$		0			0
$939$	−14.4851			−0.472702
$940$		0			0
$941$	28.7781	−	49.8451i	0.938138	−	1.62490i	0.169197	−	0.985582i	$-0.445882\pi$
$941$	28.7781	−	49.8451i	0.938138	−	1.62490i	0.768941	−	0.639320i	$-0.220784\pi$
$942$		0			0
$943$	−6.02437	−	10.4345i	−0.196180	−	0.339795i
$944$		0			0
$945$	11.7222	−	0.730444i	0.381322	−	0.0237613i
$946$		0			0
$947$	8.60454	+	14.9035i	0.279610	+	0.484299i	0.971288	−	0.237908i	$-0.0764615\pi$
$947$	8.60454	+	14.9035i	0.279610	+	0.484299i	−0.691678	+	0.722206i	$0.743128\pi$
$948$		0			0
$949$	−24.9972	−	14.4321i	−0.811442	−	0.468486i
$950$		0			0
$951$	6.97330			0.226125
$952$		0			0
$953$	11.6755			0.378207			0.189103	−	0.981957i	$-0.439442\pi$
$953$	11.6755			0.378207			0.189103	+	0.981957i	$0.439442\pi$
$954$		0			0
$955$	−5.33642	−	3.08099i	−0.172683	−	0.0996984i
$956$		0			0
$957$	−3.28218	−	5.68491i	−0.106098	−	0.183767i
$958$		0			0
$959$	46.0085	−	30.5283i	1.48569	−	0.985809i
$960$		0			0
$961$	−22.3059	−	38.6349i	−0.719545	−	1.24629i
$962$		0			0
$963$	−2.78266	+	4.81971i	−0.0896700	+	0.155313i
$964$		0			0
$965$	−11.5950			−0.373256
$966$		0			0
$967$		−	52.1618i		−	1.67741i	−0.544586	−	0.838705i	$-0.683313\pi$
$967$		−	52.1618i		−	1.67741i	0.544586	−	0.838705i	$-0.316687\pi$
$968$		0			0
$969$	−8.14881	−	4.70472i	−0.261777	−	0.151137i
$970$		0			0
$971$	−14.6994	+	8.48673i	−0.471728	+	0.272352i	−0.716963	−	0.697112i	$-0.754468\pi$
$971$	−14.6994	+	8.48673i	−0.471728	+	0.272352i	0.245235	+	0.969464i	$0.421135\pi$
$972$		0			0
$973$	15.0982	−	30.3695i	0.484028	−	0.973602i
$974$		0			0
$975$	−2.08656	+	1.20468i	−0.0668234	+	0.0385805i
$976$		0			0
$977$	−11.5148	+	19.9442i	−0.368390	+	0.638071i	−0.989314	−	0.145800i	$-0.953424\pi$
$977$	−11.5148	+	19.9442i	−0.368390	+	0.638071i	0.620924	+	0.783871i	$0.286758\pi$
$978$		0			0
$979$		−	76.3949i		−	2.44159i
$980$		0			0
$981$			16.8515i			0.538027i
$982$		0			0
$983$	19.4921	−	33.7613i	0.621701	−	1.07682i	−0.367468	−	0.930036i	$-0.619775\pi$
$983$	19.4921	−	33.7613i	0.621701	−	1.07682i	0.989169	−	0.146782i	$-0.0468915\pi$
$984$		0			0
$985$	−11.3882	+	6.57495i	−0.362857	+	0.209495i
$986$		0			0
$987$	−1.72628	+	3.47234i	−0.0549481	+	0.110526i
$988$		0			0
$989$	−39.1874	+	22.6249i	−1.24609	+	0.719428i
$990$		0			0
$991$	13.9773	+	8.06982i	0.444005	+	0.256346i	0.705295	−	0.708914i	$-0.250815\pi$
$991$	13.9773	+	8.06982i	0.444005	+	0.256346i	−0.261290	+	0.965260i	$0.584148\pi$
$992$		0			0
$993$			21.1882i			0.672388i
$994$		0			0
$995$	−20.1366			−0.638374
$996$		0			0
$997$	23.3556	−	40.4531i	0.739679	−	1.28116i	−0.212960	−	0.977061i	$-0.568310\pi$
$997$	23.3556	−	40.4531i	0.739679	−	1.28116i	0.952640	−	0.304102i	$-0.0983562\pi$
$998$		0			0
$999$	−8.37799	−	14.5111i	−0.265068	−	0.459111i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1120.2.bz.e.591.7		24
4.3	odd	2		280.2.bj.f.171.1	yes	24
7.5	odd	6		1120.2.bz.f.271.7		24
8.3	odd	2		1120.2.bz.f.591.7		24
8.5	even	2		280.2.bj.e.171.8	yes	24
28.19	even	6		280.2.bj.e.131.8	✓	24
56.5	odd	6		280.2.bj.f.131.1	yes	24
56.19	even	6	inner	1120.2.bz.e.271.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bj.e.131.8	✓	24	28.19	even	6
280.2.bj.e.171.8	yes	24	8.5	even	2
280.2.bj.f.131.1	yes	24	56.5	odd	6
280.2.bj.f.171.1	yes	24	4.3	odd	2
1120.2.bz.e.271.7		24	56.19	even	6	inner
1120.2.bz.e.591.7		24	1.1	even	1	trivial
1120.2.bz.f.271.7		24	7.5	odd	6
1120.2.bz.f.591.7		24	8.3	odd	2

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:	\( N \)	\(=\)	\( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1120.bz (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.725648 - 0.418953i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(2.36913 + 1.17781i) q^{7} +(-1.14896 - 1.99005i) q^{9} +O(q^{10})\)	\(q+(-0.725648 - 0.418953i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(2.36913 + 1.17781i) q^{7} +(-1.14896 - 1.99005i) q^{9} +(-2.98938 + 5.17776i) q^{11} -2.87544 q^{13} +0.837906i q^{15} +(2.07668 + 1.19897i) q^{17} +(4.05564 - 2.34152i) q^{19} +(-1.22570 - 1.84723i) q^{21} +(-5.81623 + 3.35800i) q^{23} +(-0.500000 + 0.866025i) q^{25} +4.43915i q^{27} -1.31035i q^{29} +(-4.34775 + 7.53053i) q^{31} +(4.33848 - 2.50482i) q^{33} +(-0.164546 - 2.64063i) q^{35} +(-3.26889 + 1.88729i) q^{37} +(2.08656 + 1.20468i) q^{39} +1.79404i q^{41} +6.73760 q^{43} +(-1.14896 + 1.99005i) q^{45} +(-0.874599 - 1.51485i) q^{47} +(4.22551 + 5.58078i) q^{49} +(-1.00463 - 1.74007i) q^{51} +(-0.0994447 - 0.0574144i) q^{53} +5.97876 q^{55} -3.92395 q^{57} +(-2.61363 - 1.50898i) q^{59} +(4.40120 + 7.62310i) q^{61} +(-0.378112 - 6.06794i) q^{63} +(1.43772 + 2.49021i) q^{65} +(2.83761 - 4.91489i) q^{67} +5.62738 q^{69} +3.06734i q^{71} +(8.69332 + 5.01909i) q^{73} +(0.725648 - 0.418953i) q^{75} +(-13.1807 + 8.74583i) q^{77} +(-11.9852 + 6.91965i) q^{79} +(-1.58707 + 2.74889i) q^{81} +17.4215i q^{83} -2.39795i q^{85} +(-0.548973 + 0.950850i) q^{87} +(-11.0658 + 6.38886i) q^{89} +(-6.81228 - 3.38674i) q^{91} +(6.30988 - 3.64301i) q^{93} +(-4.05564 - 2.34152i) q^{95} +3.76431i q^{97} +13.7387 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{3} - 12 q^{5} - 10 q^{7} + 12 q^{9}+O(q^{10}) \) 24 * q - 12 * q^3 - 12 * q^5 - 10 * q^7 + 12 * q^9	\( 24 q - 12 q^{3} - 12 q^{5} - 10 q^{7} + 12 q^{9} - 8 q^{11} + 20 q^{13} + 6 q^{17} - 18 q^{19} - 26 q^{21} - 18 q^{23} - 12 q^{25} + 6 q^{31} + 12 q^{33} + 8 q^{35} + 18 q^{39} - 32 q^{43} + 12 q^{45} + 8 q^{49} + 22 q^{51} + 30 q^{53} + 16 q^{55} - 44 q^{57} + 18 q^{59} + 22 q^{61} + 12 q^{63} - 10 q^{65} + 8 q^{67} - 12 q^{69} + 30 q^{73} + 12 q^{75} - 32 q^{77} - 6 q^{79} - 4 q^{81} - 14 q^{87} - 60 q^{89} - 18 q^{91} - 18 q^{93} + 18 q^{95} + 56 q^{99}+O(q^{100}) \) 24 * q - 12 * q^3 - 12 * q^5 - 10 * q^7 + 12 * q^9 - 8 * q^11 + 20 * q^13 + 6 * q^17 - 18 * q^19 - 26 * q^21 - 18 * q^23 - 12 * q^25 + 6 * q^31 + 12 * q^33 + 8 * q^35 + 18 * q^39 - 32 * q^43 + 12 * q^45 + 8 * q^49 + 22 * q^51 + 30 * q^53 + 16 * q^55 - 44 * q^57 + 18 * q^59 + 22 * q^61 + 12 * q^63 - 10 * q^65 + 8 * q^67 - 12 * q^69 + 30 * q^73 + 12 * q^75 - 32 * q^77 - 6 * q^79 - 4 * q^81 - 14 * q^87 - 60 * q^89 - 18 * q^91 - 18 * q^93 + 18 * q^95 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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