LMFDB - Embedded newform 1148.2.ba.a.701.1

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			701.1
Character	$\chi$	$=$	1148.701
Dual form			1148.2.ba.a.113.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.97070i q^{3} +(-1.19128 + 3.66638i) q^{5} +(0.587785 - 0.809017i) q^{7} -5.82504 q^{9} +O(q^{10})$	\(q-2.97070i q^{3} +(-1.19128 + 3.66638i) q^{5} +(0.587785 - 0.809017i) q^{7} -5.82504 q^{9} +(4.98041 - 1.61823i) q^{11} +(-2.38697 - 3.28538i) q^{13} +(10.8917 + 3.53893i) q^{15} +(2.97903 - 0.967945i) q^{17} +(-3.36727 + 4.63465i) q^{19} +(-2.40334 - 1.74613i) q^{21} +(5.39996 - 3.92330i) q^{23} +(-7.97814 - 5.79646i) q^{25} +8.39233i q^{27} +(-1.02744 - 0.333834i) q^{29} +(-3.02483 - 9.30948i) q^{31} +(-4.80728 - 14.7953i) q^{33} +(2.26595 + 3.11881i) q^{35} +(2.04499 - 6.29382i) q^{37} +(-9.75986 + 7.09095i) q^{39} +(5.80494 + 2.70234i) q^{41} +(4.17317 - 3.03199i) q^{43} +(6.93925 - 21.3568i) q^{45} +(-6.87656 - 9.46477i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(-2.87547 - 8.84979i) q^{51} +(-7.78264 - 2.52873i) q^{53} +20.1879i q^{55} +(13.7682 + 10.0031i) q^{57} +(-6.32287 + 4.59383i) q^{59} +(2.36896 + 1.72115i) q^{61} +(-3.42387 + 4.71255i) q^{63} +(14.8890 - 4.83773i) q^{65} +(5.27199 + 1.71297i) q^{67} +(-11.6549 - 16.0417i) q^{69} +(-1.52552 + 0.495673i) q^{71} -0.262695 q^{73} +(-17.2195 + 23.7006i) q^{75} +(1.61823 - 4.98041i) q^{77} -7.95510i q^{79} +7.45595 q^{81} +14.9661 q^{83} +12.0754i q^{85} +(-0.991720 + 3.05220i) q^{87} +(-8.00164 + 11.0133i) q^{89} -4.06095 q^{91} +(-27.6556 + 8.98586i) q^{93} +(-12.9811 - 17.8669i) q^{95} +(-3.97545 - 1.29170i) q^{97} +(-29.0111 + 9.42627i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{10}\right)$

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
$3$		−	2.97070i		−	1.71513i	−0.514374	−	0.857566i	$-0.671976\pi$
$3$		−	2.97070i		−	1.71513i	0.514374	−	0.857566i	$-0.328024\pi$
$4$		0			0
$5$	−1.19128	+	3.66638i	−0.532757	+	1.63966i	0.215690	+	0.976462i	$0.430800\pi$
$5$	−1.19128	+	3.66638i	−0.532757	+	1.63966i	−0.748447	+	0.663195i	$0.769200\pi$
$6$		0			0
$7$	0.587785	−	0.809017i	0.222162	−	0.305780i
$7$	0.587785	−	0.809017i	0.222162	−	0.305780i
$8$		0			0
$9$	−5.82504			−1.94168
$10$		0			0
$11$	4.98041	−	1.61823i	1.50165	−	0.487916i	0.561151	−	0.827713i	$-0.310359\pi$
$11$	4.98041	−	1.61823i	1.50165	−	0.487916i	0.940499	+	0.339798i	$0.110359\pi$
$12$		0			0
$13$	−2.38697	−	3.28538i	−0.662025	−	0.911199i	0.337521	−	0.941318i	$-0.390412\pi$
$13$	−2.38697	−	3.28538i	−0.662025	−	0.911199i	−0.999546	+	0.0301185i	$0.990412\pi$
$14$		0			0
$15$	10.8917	+	3.53893i	2.81223	+	0.913749i
$16$		0			0
$17$	2.97903	−	0.967945i	0.722520	−	0.234761i	0.0754047	−	0.997153i	$-0.475975\pi$
$17$	2.97903	−	0.967945i	0.722520	−	0.234761i	0.647116	+	0.762392i	$0.275975\pi$
$18$		0			0
$19$	−3.36727	+	4.63465i	−0.772505	+	1.06326i	0.223564	+	0.974689i	$0.428231\pi$
$19$	−3.36727	+	4.63465i	−0.772505	+	1.06326i	−0.996070	+	0.0885733i	$0.971769\pi$
$20$		0			0
$21$	−2.40334	−	1.74613i	−0.524453	−	0.381037i
$22$		0			0
$23$	5.39996	−	3.92330i	1.12597	−	0.818065i	0.140867	−	0.990029i	$-0.455011\pi$
$23$	5.39996	−	3.92330i	1.12597	−	0.818065i	0.985103	+	0.171963i	$0.0550110\pi$
$24$		0			0
$25$	−7.97814	−	5.79646i	−1.59563	−	1.15929i
$26$		0			0
$27$			8.39233i			1.61510i
$28$		0			0
$29$	−1.02744	−	0.333834i	−0.190790	−	0.0619915i	0.212064	−	0.977256i	$-0.431982\pi$
$29$	−1.02744	−	0.333834i	−0.190790	−	0.0619915i	−0.402854	+	0.915264i	$0.631982\pi$
$30$		0			0
$31$	−3.02483	−	9.30948i	−0.543276	−	1.67203i	−0.725053	−	0.688693i	$-0.758185\pi$
$31$	−3.02483	−	9.30948i	−0.543276	−	1.67203i	0.181777	−	0.983340i	$-0.441815\pi$
$32$		0			0
$33$	−4.80728	−	14.7953i	−0.836840	−	2.57553i
$34$		0			0
$35$	2.26595	+	3.11881i	0.383016	+	0.527176i
$36$		0			0
$37$	2.04499	−	6.29382i	0.336193	−	1.03470i	−0.629938	−	0.776646i	$-0.716920\pi$
$37$	2.04499	−	6.29382i	0.336193	−	1.03470i	0.966131	−	0.258051i	$-0.0830804\pi$
$38$		0			0
$39$	−9.75986	+	7.09095i	−1.56283	+	1.13546i
$40$		0			0
$41$	5.80494	+	2.70234i	0.906580	+	0.422034i
$41$	5.80494	+	2.70234i	0.906580	+	0.422034i
$42$		0			0
$43$	4.17317	−	3.03199i	0.636403	−	0.462374i	−0.222210	−	0.974999i	$-0.571327\pi$
$43$	4.17317	−	3.03199i	0.636403	−	0.462374i	0.858613	+	0.512625i	$0.171327\pi$
$44$		0			0
$45$	6.93925	−	21.3568i	1.03444	−	3.18369i
$46$		0			0
$47$	−6.87656	−	9.46477i	−1.00305	−	1.38058i	−0.923436	−	0.383753i	$-0.874631\pi$
$47$	−6.87656	−	9.46477i	−1.00305	−	1.38058i	−0.0796134	−	0.996826i	$-0.525369\pi$
$48$		0			0
$49$	−0.309017	−	0.951057i	−0.0441453	−	0.135865i
$50$		0			0
$51$	−2.87547	−	8.84979i	−0.402646	−	1.23922i
$52$		0			0
$53$	−7.78264	−	2.52873i	−1.06903	−	0.347348i	−0.278919	−	0.960315i	$-0.589976\pi$
$53$	−7.78264	−	2.52873i	−1.06903	−	0.347348i	−0.790109	+	0.612967i	$0.789976\pi$
$54$		0			0
$55$			20.1879i			2.72213i
$56$		0			0
$57$	13.7682	+	10.0031i	1.82364	+	1.32495i
$58$		0			0
$59$	−6.32287	+	4.59383i	−0.823167	+	0.598066i	−0.917618	−	0.397464i	$-0.869890\pi$
$59$	−6.32287	+	4.59383i	−0.823167	+	0.598066i	0.0944509	+	0.995530i	$0.469890\pi$
$60$		0			0
$61$	2.36896	+	1.72115i	0.303315	+	0.220371i	0.729023	−	0.684490i	$-0.239975\pi$
$61$	2.36896	+	1.72115i	0.303315	+	0.220371i	−0.425708	+	0.904861i	$0.639975\pi$
$62$		0			0
$63$	−3.42387	+	4.71255i	−0.431367	+	0.593726i
$64$		0			0
$65$	14.8890	−	4.83773i	1.84675	−	0.600046i
$66$		0			0
$67$	5.27199	+	1.71297i	0.644077	+	0.209273i	0.612801	−	0.790238i	$-0.290043\pi$
$67$	5.27199	+	1.71297i	0.644077	+	0.209273i	0.0312761	+	0.999511i	$0.490043\pi$
$68$		0			0
$69$	−11.6549	−	16.0417i	−1.40309	−	1.93119i
$70$		0			0
$71$	−1.52552	+	0.495673i	−0.181046	+	0.0588255i	−0.398137	−	0.917326i	$-0.630343\pi$
$71$	−1.52552	+	0.495673i	−0.181046	+	0.0588255i	0.217091	+	0.976151i	$0.430343\pi$
$72$		0			0
$73$	−0.262695			−0.0307461			−0.0153730	−	0.999882i	$-0.504894\pi$
$73$	−0.262695			−0.0307461			−0.0153730	+	0.999882i	$0.504894\pi$
$74$		0			0
$75$	−17.2195	+	23.7006i	−1.98834	+	2.73671i
$76$		0			0
$77$	1.61823	−	4.98041i	0.184415	−	0.567570i
$78$		0			0
$79$		−	7.95510i		−	0.895018i	−0.894279	−	0.447509i	$-0.852311\pi$
$79$		−	7.95510i		−	0.895018i	0.894279	−	0.447509i	$-0.147689\pi$
$80$		0			0
$81$	7.45595			0.828439
$82$		0			0
$83$	14.9661			1.64275			0.821373	−	0.570392i	$-0.193209\pi$
$83$	14.9661			1.64275			0.821373	+	0.570392i	$0.193209\pi$
$84$		0			0
$85$			12.0754i			1.30976i
$86$		0			0
$87$	−0.991720	+	3.05220i	−0.106324	+	0.327230i
$88$		0			0
$89$	−8.00164	+	11.0133i	−0.848172	+	1.16741i	0.136090	+	0.990696i	$0.456546\pi$
$89$	−8.00164	+	11.0133i	−0.848172	+	1.16741i	−0.984262	+	0.176713i	$0.943454\pi$
$90$		0			0
$91$	−4.06095			−0.425703
$92$		0			0
$93$	−27.6556	+	8.98586i	−2.86776	+	0.931791i
$94$		0			0
$95$	−12.9811	−	17.8669i	−1.33183	−	1.83310i
$96$		0			0
$97$	−3.97545	−	1.29170i	−0.403646	−	0.131153i	0.100156	−	0.994972i	$-0.468066\pi$
$97$	−3.97545	−	1.29170i	−0.403646	−	0.131153i	−0.503802	+	0.863819i	$0.668066\pi$
$98$		0			0
$99$	−29.0111	+	9.42627i	−2.91572	+	0.947376i
$100$		0			0
$101$	4.58989	−	6.31745i	0.456711	−	0.628609i	−0.517111	−	0.855918i	$-0.672993\pi$
$101$	4.58989	−	6.31745i	0.456711	−	0.628609i	0.973823	+	0.227309i	$0.0729927\pi$
$102$		0			0
$103$	6.61588	+	4.80672i	0.651882	+	0.473620i	0.863912	−	0.503643i	$-0.168007\pi$
$103$	6.61588	+	4.80672i	0.651882	+	0.473620i	−0.212030	+	0.977263i	$0.568007\pi$
$104$		0			0
$105$	9.26505	−	6.73145i	0.904176	−	0.656922i
$106$		0			0
$107$	−10.1340	−	7.36280i	−0.979693	−	0.711788i	−0.0220528	−	0.999757i	$-0.507020\pi$
$107$	−10.1340	−	7.36280i	−0.979693	−	0.711788i	−0.957640	+	0.287968i	$0.907020\pi$
$108$		0			0
$109$			6.60432i			0.632579i	0.948663	+	0.316290i	$0.102437\pi$
$109$			6.60432i			0.632579i	−0.948663	+	0.316290i	$0.897563\pi$
$110$		0			0
$111$	−18.6970	−	6.07503i	−1.77464	−	0.576616i
$112$		0			0
$113$	−3.43262	−	10.5645i	−0.322913	−	0.993825i	−0.972374	−	0.233430i	$-0.925005\pi$
$113$	−3.43262	−	10.5645i	−0.322913	−	0.993825i	0.649460	−	0.760396i	$-0.274995\pi$
$114$		0			0
$115$	7.95147	+	24.4721i	0.741478	+	2.28204i
$116$		0			0
$117$	13.9042	+	19.1374i	1.28544	+	1.76926i
$118$		0			0
$119$	0.967945	−	2.97903i	0.0887313	−	0.273087i
$120$		0			0
$121$	13.2866	−	9.65328i	1.20787	−	0.877571i
$122$		0			0
$123$	8.02782	−	17.2447i	0.723844	−	1.55490i
$124$		0			0
$125$	15.1622	−	11.0160i	1.35615	−	0.985299i
$126$		0			0
$127$	−2.96625	+	9.12918i	−0.263212	+	0.810083i	0.728888	+	0.684633i	$0.240038\pi$
$127$	−2.96625	+	9.12918i	−0.263212	+	0.810083i	−0.992100	+	0.125450i	$0.959962\pi$
$128$		0			0
$129$	−9.00712	−	12.3972i	−0.793032	−	1.09152i
$130$		0			0
$131$	−2.24859	−	6.92044i	−0.196460	−	0.604641i	−0.999956	−	0.00933190i	$-0.997030\pi$
$131$	−2.24859	−	6.92044i	−0.196460	−	0.604641i	0.803497	−	0.595309i	$-0.202970\pi$
$132$		0			0
$133$	1.77028	+	5.44836i	0.153503	+	0.472433i
$134$		0			0
$135$	−30.7695	−	9.99762i	−2.64822	−	0.860458i
$136$		0			0
$137$		−	3.23696i		−	0.276552i	−0.990394	−	0.138276i	$-0.955844\pi$
$137$		−	3.23696i		−	0.276552i	0.990394	−	0.138276i	$-0.0441561\pi$
$138$		0			0
$139$	11.7339	+	8.52515i	0.995254	+	0.723094i	0.961065	−	0.276321i	$-0.0891154\pi$
$139$	11.7339	+	8.52515i	0.995254	+	0.723094i	0.0341884	+	0.999415i	$0.489115\pi$
$140$		0			0
$141$	−28.1170	+	20.4282i	−2.36788	+	1.72036i
$142$		0			0
$143$	−17.2046	−	12.4999i	−1.43872	−	1.04529i
$144$		0			0
$145$	2.44793	−	3.36929i	0.203289	−	0.279804i
$146$		0			0
$147$	−2.82530	+	0.917996i	−0.233027	+	0.0757150i
$148$		0			0
$149$	19.8381	+	6.44581i	1.62520	+	0.528061i	0.973162	−	0.230121i	$-0.0739123\pi$
$149$	19.8381	+	6.44581i	1.62520	+	0.528061i	0.652043	+	0.758182i	$0.273912\pi$
$150$		0			0
$151$	8.57436	+	11.8016i	0.697772	+	0.960401i	0.999974	+	0.00715685i	$0.00227812\pi$
$151$	8.57436	+	11.8016i	0.697772	+	0.960401i	−0.302203	+	0.953244i	$0.597722\pi$
$152$		0			0
$153$	−17.3529	+	5.63831i	−1.40290	+	0.455831i
$154$		0			0
$155$	37.7356			3.03099
$156$		0			0
$157$	−0.780720	+	1.07457i	−0.0623083	+	0.0857600i	−0.839034	−	0.544079i	$-0.816879\pi$
$157$	−0.780720	+	1.07457i	−0.0623083	+	0.0857600i	0.776726	+	0.629839i	$0.216879\pi$
$158$		0			0
$159$	−7.51210	+	23.1199i	−0.595748	+	1.83352i
$160$		0			0
$161$		−	6.67472i		−	0.526042i
$162$		0			0
$163$	4.29344			0.336288			0.168144	−	0.985762i	$-0.446223\pi$
$163$	4.29344			0.336288			0.168144	+	0.985762i	$0.446223\pi$
$164$		0			0
$165$	59.9720			4.66882
$166$		0			0
$167$			6.99195i			0.541053i	0.962713	+	0.270526i	$0.0871978\pi$
$167$			6.99195i			0.541053i	−0.962713	+	0.270526i	$0.912802\pi$
$168$		0			0
$169$	−1.07887	+	3.32042i	−0.0829901	+	0.255417i
$170$		0			0
$171$	19.6145	−	26.9970i	1.49996	−	2.06451i
$172$		0			0
$173$	9.14472			0.695260			0.347630	−	0.937632i	$-0.386987\pi$
$173$	9.14472			0.695260			0.347630	+	0.937632i	$0.386987\pi$
$174$		0			0
$175$	−9.37887	+	3.04738i	−0.708976	+	0.230360i
$176$		0			0
$177$	13.6469	+	18.7833i	1.02576	+	1.41184i
$178$		0			0
$179$	16.4623	+	5.34893i	1.23045	+	0.399798i	0.850878	−	0.525364i	$-0.176071\pi$
$179$	16.4623	+	5.34893i	1.23045	+	0.399798i	0.379573	+	0.925162i	$0.376071\pi$
$180$		0			0
$181$	−19.6633	+	6.38900i	−1.46156	+	0.474891i	−0.928547	−	0.371214i	$-0.878942\pi$
$181$	−19.6633	+	6.38900i	−1.46156	+	0.474891i	−0.533016	+	0.846105i	$0.678942\pi$
$182$		0			0
$183$	5.11302	−	7.03747i	0.377965	−	0.520225i
$184$		0			0
$185$	20.6394	+	14.9954i	1.51744	+	1.10248i
$186$		0			0
$187$	13.2704	−	9.64152i	0.970429	−	0.705058i
$188$		0			0
$189$	6.78954	+	4.93289i	0.493866	+	0.358815i
$190$		0			0
$191$		−	16.7182i		−	1.20969i	−0.796343	−	0.604845i	$-0.793235\pi$
$191$		−	16.7182i		−	1.20969i	0.796343	−	0.604845i	$-0.206765\pi$
$192$		0			0
$193$	13.9528	+	4.53353i	1.00434	+	0.326331i	0.764600	−	0.644505i	$-0.222937\pi$
$193$	13.9528	+	4.53353i	1.00434	+	0.326331i	0.239743	+	0.970836i	$0.422937\pi$
$194$		0			0
$195$	−14.3714	−	44.2307i	−1.02916	−	3.16743i
$196$		0			0
$197$	−3.11701	−	9.59316i	−0.222077	−	0.683484i	−0.998575	−	0.0533639i	$-0.983006\pi$
$197$	−3.11701	−	9.59316i	−0.222077	−	0.683484i	0.776498	−	0.630120i	$-0.216994\pi$
$198$		0			0
$199$	−1.51152	−	2.08043i	−0.107149	−	0.147477i	0.752075	−	0.659077i	$-0.229053\pi$
$199$	−1.51152	−	2.08043i	−0.107149	−	0.147477i	−0.859224	+	0.511600i	$0.829053\pi$
$200$		0			0
$201$	5.08873	−	15.6615i	0.358931	−	1.10468i
$202$		0			0
$203$	−0.873989	+	0.634990i	−0.0613420	+	0.0445676i
$204$		0			0
$205$	−16.8231	+	18.0639i	−1.17498	+	1.26164i
$206$		0			0
$207$	−31.4550	+	22.8534i	−2.18627	+	1.58842i
$208$		0			0
$209$	−9.27045	+	28.5315i	−0.641250	+	1.97357i
$210$		0			0
$211$	3.88236	+	5.34360i	0.267272	+	0.367869i	0.921467	−	0.388458i	$-0.126992\pi$
$211$	3.88236	+	5.34360i	0.267272	+	0.367869i	−0.654194	+	0.756327i	$0.726992\pi$
$212$		0			0
$213$	1.47249	+	4.53187i	0.100894	+	0.310518i
$214$		0			0
$215$	6.14501	+	18.9124i	0.419086	+	1.28982i
$216$		0			0
$217$	−9.30948	−	3.02483i	−0.631969	−	0.205339i
$218$		0			0
$219$			0.780386i			0.0527336i
$220$		0			0
$221$	−10.2909	−	7.47677i	−0.692241	−	0.502942i
$222$		0			0
$223$	1.50009	−	1.08988i	0.100454	−	0.0729839i	−0.536425	−	0.843948i	$-0.680225\pi$
$223$	1.50009	−	1.08988i	0.100454	−	0.0729839i	0.636878	+	0.770964i	$0.280225\pi$
$224$		0			0
$225$	46.4730	+	33.7646i	3.09820	+	2.25097i
$226$		0			0
$227$	5.44266	−	7.49118i	0.361242	−	0.497207i	−0.589252	−	0.807949i	$-0.700578\pi$
$227$	5.44266	−	7.49118i	0.361242	−	0.497207i	0.950494	+	0.310742i	$0.100578\pi$
$228$		0			0
$229$	4.53439	−	1.47331i	0.299641	−	0.0973592i	−0.155338	−	0.987861i	$-0.549647\pi$
$229$	4.53439	−	1.47331i	0.299641	−	0.0973592i	0.454979	+	0.890502i	$0.349647\pi$
$230$		0			0
$231$	−14.7953	−	4.80728i	−0.973458	−	0.316296i
$232$		0			0
$233$	−6.95886	−	9.57804i	−0.455890	−	0.627479i	0.517760	−	0.855526i	$-0.326766\pi$
$233$	−6.95886	−	9.57804i	−0.455890	−	0.627479i	−0.973650	+	0.228047i	$0.926766\pi$
$234$		0			0
$235$	42.8934	−	13.9369i	2.79806	−	0.909144i
$236$		0			0
$237$	−23.6322			−1.53508
$238$		0			0
$239$	14.2989	−	19.6808i	0.924919	−	1.27304i	−0.0368895	−	0.999319i	$-0.511745\pi$
$239$	14.2989	−	19.6808i	0.924919	−	1.27304i	0.961809	−	0.273723i	$-0.0882550\pi$
$240$		0			0
$241$	1.22228	−	3.76179i	0.0787339	−	0.242318i	−0.903941	−	0.427658i	$-0.859339\pi$
$241$	1.22228	−	3.76179i	0.0787339	−	0.242318i	0.982674	+	0.185340i	$0.0593387\pi$
$242$		0			0
$243$			3.02761i			0.194222i
$244$		0			0
$245$	3.85506			0.246291
$246$		0			0
$247$	23.2641			1.48026
$248$		0			0
$249$		−	44.4598i		−	2.81753i
$250$		0			0
$251$	1.77278	−	5.45604i	0.111897	−	0.344382i	−0.879390	−	0.476101i	$-0.842050\pi$
$251$	1.77278	−	5.45604i	0.111897	−	0.344382i	0.991287	+	0.131719i	$0.0420496\pi$
$252$		0			0
$253$	20.5452	−	28.2781i	1.29167	−	1.77783i
$254$		0			0
$255$	35.8722			2.24640
$256$		0			0
$257$	−9.51315	+	3.09101i	−0.593414	+	0.192812i	−0.590301	−	0.807183i	$-0.700991\pi$
$257$	−9.51315	+	3.09101i	−0.593414	+	0.192812i	−0.00311306	+	0.999995i	$0.500991\pi$
$258$		0			0
$259$	−3.88979	−	5.35384i	−0.241700	−	0.332671i
$260$		0			0
$261$	5.98485	+	1.94460i	0.370453	+	0.120368i
$262$		0			0
$263$	−14.1985	+	4.61338i	−0.875518	+	0.284473i	−0.712095	−	0.702083i	$-0.752253\pi$
$263$	−14.1985	+	4.61338i	−0.875518	+	0.284473i	−0.163423	+	0.986556i	$0.552253\pi$
$264$		0			0
$265$	18.5426	−	25.5217i	1.13906	−	1.56779i
$266$		0			0
$267$	32.7172	+	23.7704i	2.00226	+	1.45473i
$268$		0			0
$269$	−4.23806	+	3.07913i	−0.258399	+	0.187738i	−0.709441	−	0.704765i	$-0.751052\pi$
$269$	−4.23806	+	3.07913i	−0.258399	+	0.187738i	0.451042	+	0.892503i	$0.351052\pi$
$270$		0			0
$271$	1.71026	+	1.24258i	0.103891	+	0.0754811i	0.638518	−	0.769607i	$-0.279548\pi$
$271$	1.71026	+	1.24258i	0.103891	+	0.0754811i	−0.534627	+	0.845088i	$0.679548\pi$
$272$		0			0
$273$			12.0638i			0.730137i
$274$		0			0
$275$	−49.1144	−	15.9582i	−2.96171	−	0.962318i
$276$		0			0
$277$	3.63707	+	11.1938i	0.218530	+	0.672568i	0.998884	+	0.0472291i	$0.0150391\pi$
$277$	3.63707	+	11.1938i	0.218530	+	0.672568i	−0.780354	+	0.625338i	$0.784961\pi$
$278$		0			0
$279$	17.6198	+	54.2281i	1.05487	+	3.24655i
$280$		0			0
$281$	1.80727	+	2.48749i	0.107813	+	0.148391i	0.859514	−	0.511113i	$-0.170766\pi$
$281$	1.80727	+	2.48749i	0.107813	+	0.148391i	−0.751701	+	0.659504i	$0.770766\pi$
$282$		0			0
$283$	−2.24964	+	6.92369i	−0.133727	+	0.411570i	−0.995390	−	0.0959112i	$-0.969424\pi$
$283$	−2.24964	+	6.92369i	−0.133727	+	0.411570i	0.861663	+	0.507482i	$0.169424\pi$
$284$		0			0
$285$	−53.0771	+	38.5628i	−3.14402	+	2.28426i
$286$		0			0
$287$	5.59830	−	3.10791i	0.330457	−	0.183454i
$288$		0			0
$289$	−5.81560	+	4.22528i	−0.342094	+	0.248546i
$290$		0			0
$291$	−3.83726	+	11.8099i	−0.224944	+	0.692307i
$292$		0			0
$293$	2.72283	+	3.74766i	0.159070	+	0.218941i	0.881111	−	0.472909i	$-0.156796\pi$
$293$	2.72283	+	3.74766i	0.159070	+	0.218941i	−0.722042	+	0.691850i	$0.756796\pi$
$294$		0			0
$295$	−9.31044	−	28.6546i	−0.542075	−	1.66834i
$296$		0			0
$297$	13.5807	+	41.7972i	0.788035	+	2.42532i
$298$		0			0
$299$	−25.7791	−	8.37612i	−1.49084	−	0.484404i
$300$		0			0
$301$		−	5.15833i		−	0.297321i
$302$		0			0
$303$	−18.7672	−	13.6352i	−1.07815	−	0.783321i
$304$		0			0
$305$	−9.13251	+	6.63515i	−0.522926	+	0.379928i
$306$		0			0
$307$	−8.91405	−	6.47644i	−0.508752	−	0.369630i	0.303598	−	0.952800i	$-0.401812\pi$
$307$	−8.91405	−	6.47644i	−0.508752	−	0.369630i	−0.812350	+	0.583170i	$0.801812\pi$
$308$		0			0
$309$	14.2793	−	19.6538i	0.812321	−	1.11806i
$310$		0			0
$311$	−32.2878	+	10.4909i	−1.83087	+	0.594887i	−0.831658	+	0.555289i	$0.812608\pi$
$311$	−32.2878	+	10.4909i	−1.83087	+	0.594887i	−0.999216	+	0.0395980i	$0.987392\pi$
$312$		0			0
$313$	8.62551	+	2.80260i	0.487543	+	0.158412i	0.542465	−	0.840078i	$-0.317491\pi$
$313$	8.62551	+	2.80260i	0.487543	+	0.158412i	−0.0549222	+	0.998491i	$0.517491\pi$
$314$		0			0
$315$	−13.1992	−	18.1672i	−0.743693	−	1.02361i
$316$		0			0
$317$	14.8460	−	4.82376i	0.833834	−	0.270929i	0.139175	−	0.990268i	$-0.455555\pi$
$317$	14.8460	−	4.82376i	0.833834	−	0.270929i	0.694660	+	0.719339i	$0.255555\pi$
$318$		0			0
$319$	−5.65727			−0.316747
$320$		0			0
$321$	−21.8726	+	30.1051i	−1.22081	+	1.68030i
$322$		0			0
$323$	−5.54511	+	17.0661i	−0.308538	+	0.949583i
$324$		0			0
$325$			40.0471i			2.22142i
$326$		0			0
$327$	19.6194			1.08496
$328$		0			0
$329$	−11.6991			−0.644992
$330$		0			0
$331$			31.7320i			1.74415i	0.489373	+	0.872075i	$0.337226\pi$
$331$			31.7320i			1.74415i	−0.489373	+	0.872075i	$0.662774\pi$
$332$		0			0
$333$	−11.9121	+	36.6617i	−0.652780	+	2.00905i
$334$		0			0
$335$	−12.5608	+	17.2885i	−0.686272	+	0.944573i
$336$		0			0
$337$	17.2822			0.941420			0.470710	−	0.882288i	$-0.343998\pi$
$337$	17.2822			0.941420			0.470710	+	0.882288i	$0.343998\pi$
$338$		0			0
$339$	−31.3839	+	10.1973i	−1.70454	+	0.553839i
$340$		0			0
$341$	−30.1298	−	41.4701i	−1.63162	−	2.24573i
$342$		0			0
$343$	−0.951057	−	0.309017i	−0.0513522	−	0.0166853i
$344$		0			0
$345$	72.6992	−	23.6214i	3.91399	−	1.27173i
$346$		0			0
$347$	−10.5340	+	14.4988i	−0.565493	+	0.778335i	−0.992012	−	0.126144i	$-0.959740\pi$
$347$	−10.5340	+	14.4988i	−0.565493	+	0.778335i	0.426519	+	0.904479i	$0.359740\pi$
$348$		0			0
$349$	−19.6771	−	14.2962i	−1.05329	−	0.765259i	−0.0804541	−	0.996758i	$-0.525637\pi$
$349$	−19.6771	−	14.2962i	−1.05329	−	0.765259i	−0.972835	+	0.231499i	$0.925637\pi$
$350$		0			0
$351$	27.5720	−	20.0322i	1.47168	−	1.06924i
$352$		0			0
$353$	14.1620	+	10.2893i	0.753765	+	0.547643i	0.896992	−	0.442047i	$-0.145748\pi$
$353$	14.1620	+	10.2893i	0.753765	+	0.547643i	−0.143226	+	0.989690i	$0.545748\pi$
$354$		0			0
$355$		−	6.18364i		−	0.328194i
$356$		0			0
$357$	−8.84979	−	2.87547i	−0.468380	−	0.152186i
$358$		0			0
$359$	9.06232	+	27.8910i	0.478291	+	1.47203i	0.841467	+	0.540308i	$0.181692\pi$
$359$	9.06232	+	27.8910i	0.478291	+	1.47203i	−0.363176	+	0.931720i	$0.618308\pi$
$360$		0			0
$361$	−4.27017	−	13.1422i	−0.224746	−	0.691696i
$362$		0			0
$363$	−28.6770	−	39.4705i	−1.50515	−	2.07166i
$364$		0			0
$365$	0.312943	−	0.963140i	0.0163802	−	0.0504130i
$366$		0			0
$367$	−18.2612	+	13.2676i	−0.953229	+	0.692562i	−0.951568	−	0.307437i	$-0.900529\pi$
$367$	−18.2612	+	13.2676i	−0.953229	+	0.692562i	−0.00166078	+	0.999999i	$0.500529\pi$
$368$		0			0
$369$	−33.8140	−	15.7412i	−1.76029	−	0.819454i
$370$		0			0
$371$	−6.62031	+	4.80993i	−0.343709	+	0.249719i
$372$		0			0
$373$	−5.16355	+	15.8918i	−0.267359	+	0.822845i	0.723782	+	0.690029i	$0.242402\pi$
$373$	−5.16355	+	15.8918i	−0.267359	+	0.822845i	−0.991141	+	0.132817i	$0.957598\pi$
$374$		0			0
$375$	−32.7251	−	45.0423i	−1.68992	−	2.32597i
$376$		0			0
$377$	1.35568	+	4.17237i	0.0698213	+	0.214888i
$378$		0			0
$379$	0.0691676	+	0.212876i	0.00355290	+	0.0109347i	0.952817	−	0.303545i	$-0.0981701\pi$
$379$	0.0691676	+	0.212876i	0.00355290	+	0.0109347i	−0.949264	+	0.314479i	$0.898170\pi$
$380$		0			0
$381$	27.1200	+	8.81183i	1.38940	+	0.451444i
$382$		0			0
$383$			21.7968i			1.11376i	0.830592	+	0.556882i	$0.188002\pi$
$383$			21.7968i			1.11376i	−0.830592	+	0.556882i	$0.811998\pi$
$384$		0			0
$385$	16.3323	+	11.8661i	0.832372	+	0.604754i
$386$		0			0
$387$	−24.3089	+	17.6614i	−1.23569	+	0.897782i
$388$		0			0
$389$	8.00647	+	5.81704i	0.405944	+	0.294936i	0.771958	−	0.635674i	$-0.219278\pi$
$389$	8.00647	+	5.81704i	0.405944	+	0.294936i	−0.366014	+	0.930610i	$0.619278\pi$
$390$		0			0
$391$	12.2891	−	16.9145i	0.621486	−	0.855403i
$392$		0			0
$393$	−20.5585	+	6.67987i	−1.03704	+	0.336955i
$394$		0			0
$395$	29.1664	+	9.47675i	1.46752	+	0.476827i
$396$		0			0
$397$	5.19042	+	7.14399i	0.260499	+	0.358547i	0.919154	−	0.393899i	$-0.128874\pi$
$397$	5.19042	+	7.14399i	0.260499	+	0.358547i	−0.658654	+	0.752446i	$0.728874\pi$
$398$		0			0
$399$	16.1854	−	5.25897i	0.810285	−	0.263278i
$400$		0			0
$401$	22.1463			1.10593			0.552966	−	0.833204i	$-0.313496\pi$
$401$	22.1463			1.10593			0.552966	+	0.833204i	$0.313496\pi$
$402$		0			0
$403$	−23.3650	+	32.1591i	−1.16389	+	1.60196i
$404$		0			0
$405$	−8.88213	+	27.3364i	−0.441357	+	1.35836i
$406$		0			0
$407$		−	34.6550i		−	1.71779i
$408$		0			0
$409$	−15.5384			−0.768324			−0.384162	−	0.923266i	$-0.625510\pi$
$409$	−15.5384			−0.768324			−0.384162	+	0.923266i	$0.625510\pi$
$410$		0			0
$411$	−9.61602			−0.474323
$412$		0			0
$413$			7.81549i			0.384575i
$414$		0			0
$415$	−17.8288	+	54.8716i	−0.875184	+	2.69354i
$416$		0			0
$417$	25.3256	−	34.8578i	1.24020	−	1.70699i
$418$		0			0
$419$	0.834711			0.0407783			0.0203892	−	0.999792i	$-0.493509\pi$
$419$	0.834711			0.0407783			0.0203892	+	0.999792i	$0.493509\pi$
$420$		0			0
$421$	−5.83545	+	1.89605i	−0.284402	+	0.0924080i	−0.447745	−	0.894162i	$-0.647773\pi$
$421$	−5.83545	+	1.89605i	−0.284402	+	0.0924080i	0.163342	+	0.986570i	$0.447773\pi$
$422$		0			0
$423$	40.0562	+	55.1327i	1.94760	+	2.68064i
$424$		0			0
$425$	−29.3777	−	9.54541i	−1.42503	−	0.463020i
$426$		0			0
$427$	2.78488	−	0.904863i	0.134770	−	0.0437894i
$428$		0			0
$429$	−37.1333	+	51.1096i	−1.79281	+	2.46759i
$430$		0			0
$431$	−23.1608	−	16.8273i	−1.11562	−	0.810542i	−0.132077	−	0.991239i	$-0.542165\pi$
$431$	−23.1608	−	16.8273i	−1.11562	−	0.810542i	−0.983539	+	0.180697i	$0.942165\pi$
$432$		0			0
$433$	24.9993	−	18.1630i	1.20139	−	0.872859i	0.206967	−	0.978348i	$-0.433641\pi$
$433$	24.9993	−	18.1630i	1.20139	−	0.872859i	0.994420	+	0.105489i	$0.0336407\pi$
$434$		0			0
$435$	−10.0091	−	7.27206i	−0.479901	−	0.348668i
$436$		0			0
$437$			38.2378i			1.82916i
$438$		0			0
$439$	−17.4652	−	5.67480i	−0.833570	−	0.270843i	−0.139022	−	0.990289i	$-0.544396\pi$
$439$	−17.4652	−	5.67480i	−0.833570	−	0.270843i	−0.694548	+	0.719446i	$0.744396\pi$
$440$		0			0
$441$	1.80004	+	5.53994i	0.0857160	+	0.263807i
$442$		0			0
$443$	2.24539	+	6.91059i	0.106681	+	0.328332i	0.990121	−	0.140213i	$-0.0447786\pi$
$443$	2.24539	+	6.91059i	0.106681	+	0.328332i	−0.883440	+	0.468544i	$0.844779\pi$
$444$		0			0
$445$	−30.8468	−	42.4570i	−1.46228	−	2.01266i
$446$		0			0
$447$	19.1485	−	58.9331i	0.905695	−	2.78744i
$448$		0			0
$449$	−9.33107	+	6.77942i	−0.440361	+	0.319941i	−0.785778	−	0.618508i	$-0.787737\pi$
$449$	−9.33107	+	6.77942i	−0.440361	+	0.319941i	0.345418	+	0.938449i	$0.387737\pi$
$450$		0			0
$451$	33.2840	+	4.06498i	1.56728	+	0.191412i
$452$		0			0
$453$	35.0590	−	25.4718i	1.64721	−	1.19677i
$454$		0			0
$455$	4.83773	−	14.8890i	0.226796	−	0.698007i
$456$		0			0
$457$	15.1886	+	20.9053i	0.710493	+	0.977910i	0.999786	+	0.0206697i	$0.00657985\pi$
$457$	15.1886	+	20.9053i	0.710493	+	0.977910i	−0.289293	+	0.957241i	$0.593420\pi$
$458$		0			0
$459$	8.12331	+	25.0010i	0.379164	+	1.16695i
$460$		0			0
$461$	11.6166	+	35.7521i	0.541037	+	1.66514i	0.730230	+	0.683202i	$0.239413\pi$
$461$	11.6166	+	35.7521i	0.541037	+	1.66514i	−0.189192	+	0.981940i	$0.560587\pi$
$462$		0			0
$463$	−34.6062	−	11.2442i	−1.60829	−	0.522564i	−0.639149	−	0.769083i	$-0.720713\pi$
$463$	−34.6062	−	11.2442i	−1.60829	−	0.522564i	−0.969138	+	0.246519i	$0.920713\pi$
$464$		0			0
$465$		−	112.101i		−	5.19856i
$466$		0			0
$467$	17.5964	+	12.7846i	0.814266	+	0.591599i	0.915064	−	0.403308i	$-0.132140\pi$
$467$	17.5964	+	12.7846i	0.814266	+	0.591599i	−0.100798	+	0.994907i	$0.532140\pi$
$468$		0			0
$469$	4.48463	−	3.25827i	0.207081	−	0.150453i
$470$		0			0
$471$	3.19222	+	2.31928i	0.147090	+	0.106867i
$472$		0			0
$473$	15.8776	−	21.8537i	0.730055	−	1.00483i
$474$		0			0
$475$	53.7292	−	17.4577i	2.46526	−	0.801013i
$476$		0			0
$477$	45.3342	+	14.7300i	2.07571	+	0.674439i
$478$		0			0
$479$	−18.1217	−	24.9423i	−0.828001	−	1.13965i	−0.988292	−	0.152575i	$-0.951243\pi$
$479$	−18.1217	−	24.9423i	−0.828001	−	1.13965i	0.160291	−	0.987070i	$-0.448757\pi$
$480$		0			0
$481$	−25.5589	+	8.30458i	−1.16538	+	0.378656i
$482$		0			0
$483$	−19.8286			−0.902231
$484$		0			0
$485$	9.47176	−	13.0368i	0.430091	−	0.591969i
$486$		0			0
$487$	−5.44184	+	16.7483i	−0.246593	+	0.758936i	0.748777	+	0.662822i	$0.230641\pi$
$487$	−5.44184	+	16.7483i	−0.246593	+	0.758936i	−0.995370	+	0.0961140i	$0.969359\pi$
$488$		0			0
$489$		−	12.7545i		−	0.576779i
$490$		0			0
$491$	18.7779			0.847435			0.423717	−	0.905795i	$-0.360725\pi$
$491$	18.7779			0.847435			0.423717	+	0.905795i	$0.360725\pi$
$492$		0			0
$493$	−3.38389			−0.152403
$494$		0			0
$495$		−	117.595i		−	5.28551i
$496$		0			0
$497$	−0.495673	+	1.52552i	−0.0222340	+	0.0684291i
$498$		0			0
$499$	5.70625	−	7.85398i	0.255447	−	0.351593i	−0.661963	−	0.749537i	$-0.730276\pi$
$499$	5.70625	−	7.85398i	0.255447	−	0.351593i	0.917410	+	0.397944i	$0.130276\pi$
$500$		0			0
$501$	20.7709			0.927977
$502$		0			0
$503$	27.6016	−	8.96830i	1.23069	−	0.399877i	0.379729	−	0.925098i	$-0.376017\pi$
$503$	27.6016	−	8.96830i	1.23069	−	0.399877i	0.850966	+	0.525221i	$0.176017\pi$
$504$		0			0
$505$	17.6943	+	24.3542i	0.787388	+	1.08375i
$506$		0			0
$507$	9.86397	+	3.20500i	0.438074	+	0.142339i
$508$		0			0
$509$	9.05328	−	2.94159i	0.401280	−	0.130384i	−0.101422	−	0.994843i	$-0.532339\pi$
$509$	9.05328	−	2.94159i	0.401280	−	0.130384i	0.502702	+	0.864460i	$0.332339\pi$
$510$		0			0
$511$	−0.154408	+	0.212524i	−0.00683061	+	0.00940153i
$512$		0			0
$513$	−38.8956	−	28.2593i	−1.71728	−	1.24768i
$514$		0			0
$515$	−25.5046	+	18.5302i	−1.12387	+	0.816538i
$516$		0			0
$517$	−49.5643	−	36.0106i	−2.17983	−	1.58374i
$518$		0			0
$519$		−	27.1662i		−	1.19246i
$520$		0			0
$521$	−36.8958	−	11.9882i	−1.61644	−	0.525212i	−0.645339	−	0.763897i	$-0.723284\pi$
$521$	−36.8958	−	11.9882i	−1.61644	−	0.525212i	−0.971097	+	0.238685i	$0.923284\pi$
$522$		0			0
$523$	9.19704	+	28.3056i	0.402158	+	1.23772i	0.923245	+	0.384213i	$0.125527\pi$
$523$	9.19704	+	28.3056i	0.402158	+	1.23772i	−0.521086	+	0.853504i	$0.674473\pi$
$524$		0			0
$525$	9.05284	+	27.8618i	0.395098	+	1.21599i
$526$		0			0
$527$	−18.0221	−	24.8053i	−0.785056	−	1.08054i
$528$		0			0
$529$	6.65991	−	20.4971i	0.289561	−	0.891178i
$530$		0			0
$531$	36.8309	−	26.7592i	1.59833	−	1.16125i
$532$		0			0
$533$	−4.97802	−	25.5218i	−0.215622	−	1.10547i
$534$		0			0
$535$	39.0673	−	28.3841i	1.68903	−	1.22715i
$536$		0			0
$537$	15.8900	−	48.9045i	0.685706	−	2.11039i
$538$		0			0
$539$	−3.07806	−	4.23659i	−0.132582	−	0.182483i
$540$		0			0
$541$	−8.07530	−	24.8532i	−0.347184	−	1.06852i	−0.960404	−	0.278611i	$-0.910126\pi$
$541$	−8.07530	−	24.8532i	−0.347184	−	1.06852i	0.613220	−	0.789912i	$-0.289874\pi$
$542$		0			0
$543$	18.9798	+	58.4138i	0.814501	+	2.50678i
$544$		0			0
$545$	−24.2140	−	7.86760i	−1.03721	−	0.337011i
$546$		0			0
$547$			36.3465i			1.55406i	0.629461	+	0.777032i	$0.283276\pi$
$547$			36.3465i			1.55406i	−0.629461	+	0.777032i	$0.716724\pi$
$548$		0			0
$549$	−13.7993	−	10.0258i	−0.588940	−	0.427890i
$550$		0			0
$551$	5.00686	−	3.63770i	0.213300	−	0.154971i
$552$		0			0
$553$	−6.43581	−	4.67589i	−0.273678	−	0.198839i
$554$		0			0
$555$	44.5468	−	61.3134i	1.89091	−	2.60261i
$556$		0			0
$557$	12.9322	−	4.20192i	0.547955	−	0.178041i	−0.0219396	−	0.999759i	$-0.506984\pi$
$557$	12.9322	−	4.20192i	0.547955	−	0.178041i	0.569894	+	0.821718i	$0.306984\pi$
$558$		0			0
$559$	−19.9224	−	6.47319i	−0.842630	−	0.273787i
$560$		0			0
$561$	−28.6420	−	39.4224i	−1.20927	−	1.66441i
$562$		0			0
$563$	−20.1820	+	6.55751i	−0.850568	+	0.276366i	−0.701684	−	0.712488i	$-0.747568\pi$
$563$	−20.1820	+	6.55751i	−0.850568	+	0.276366i	−0.148884	+	0.988855i	$0.547568\pi$
$564$		0			0
$565$	42.8228			1.80157
$566$		0			0
$567$	4.38250	−	6.03199i	0.184048	−	0.253320i
$568$		0			0
$569$	6.08577	−	18.7301i	0.255129	−	0.785206i	−0.738675	−	0.674061i	$-0.764548\pi$
$569$	6.08577	−	18.7301i	0.255129	−	0.785206i	0.993804	−	0.111145i	$-0.0354517\pi$
$570$		0			0
$571$			2.76007i			0.115505i	0.998331	+	0.0577526i	$0.0183935\pi$
$571$			2.76007i			0.115505i	−0.998331	+	0.0577526i	$0.981607\pi$
$572$		0			0
$573$	−49.6648			−2.07478
$574$		0			0
$575$	−65.8229			−2.74501
$576$		0			0
$577$		−	3.43113i		−	0.142840i	−0.997446	−	0.0714199i	$-0.977247\pi$
$577$		−	3.43113i		−	0.142840i	0.997446	−	0.0714199i	$-0.0227530\pi$
$578$		0			0
$579$	13.4678	−	41.4495i	0.559701	−	1.72258i
$580$		0			0
$581$	8.79687	−	12.1078i	0.364955	−	0.502318i
$582$		0			0
$583$	−42.8528			−1.77478
$584$		0			0
$585$	−86.7290	+	28.1800i	−3.58580	+	1.16510i
$586$		0			0
$587$	24.1938	+	33.2999i	0.998584	+	1.37443i	0.926190	+	0.377057i	$0.123064\pi$
$587$	24.1938	+	33.2999i	0.998584	+	1.37443i	0.0723938	+	0.997376i	$0.476936\pi$
$588$		0			0
$589$	53.3317	+	17.3285i	2.19749	+	0.714009i
$590$		0			0
$591$	−28.4984	+	9.25968i	−1.17227	+	0.380892i
$592$		0			0
$593$	7.50753	−	10.3332i	0.308297	−	0.424335i	−0.626552	−	0.779380i	$-0.715534\pi$
$593$	7.50753	−	10.3332i	0.308297	−	0.424335i	0.934849	+	0.355045i	$0.115534\pi$
$594$		0			0
$595$	9.76917	+	7.09771i	0.400497	+	0.290978i
$596$		0			0
$597$	−6.18031	+	4.49026i	−0.252943	+	0.183774i
$598$		0			0
$599$	17.0935	+	12.4192i	0.698423	+	0.507434i	0.879418	−	0.476050i	$-0.157932\pi$
$599$	17.0935	+	12.4192i	0.698423	+	0.507434i	−0.180995	+	0.983484i	$0.557932\pi$
$600$		0			0
$601$			12.7699i			0.520894i	0.965488	+	0.260447i	$0.0838700\pi$
$601$			12.7699i			0.520894i	−0.965488	+	0.260447i	$0.916130\pi$
$602$		0			0
$603$	−30.7096	−	9.97814i	−1.25059	−	0.406341i
$604$		0			0
$605$	19.5646	+	60.2136i	0.795413	+	2.44803i
$606$		0			0
$607$	−6.51703	−	20.0574i	−0.264518	−	0.814103i	−0.991804	−	0.127768i	$-0.959219\pi$
$607$	−6.51703	−	20.0574i	−0.264518	−	0.814103i	0.727286	−	0.686334i	$-0.240781\pi$
$608$		0			0
$609$	1.88636	+	2.59636i	0.0764393	+	0.105210i
$610$		0			0
$611$	−14.6812	+	45.1842i	−0.593939	+	1.82796i
$612$		0			0
$613$	−8.14323	+	5.91640i	−0.328902	+	0.238961i	−0.739965	−	0.672646i	$-0.765158\pi$
$613$	−8.14323	+	5.91640i	−0.328902	+	0.238961i	0.411063	+	0.911607i	$0.365158\pi$
$614$		0			0
$615$	53.6624	+	49.9764i	2.16388	+	2.01524i
$616$		0			0
$617$	10.0985	−	7.33697i	0.406549	−	0.295375i	−0.365654	−	0.930751i	$-0.619155\pi$
$617$	10.0985	−	7.33697i	0.406549	−	0.295375i	0.772203	+	0.635375i	$0.219155\pi$
$618$		0			0
$619$	2.01315	−	6.19583i	0.0809152	−	0.249031i	−0.902413	−	0.430873i	$-0.858206\pi$
$619$	2.01315	−	6.19583i	0.0809152	−	0.249031i	0.983328	+	0.181841i	$0.0582058\pi$
$620$		0			0
$621$	32.9257	+	45.3183i	1.32126	+	1.81856i
$622$		0			0
$623$	4.20671	+	12.9469i	0.168538	+	0.518708i
$624$		0			0
$625$	7.08948	+	21.8192i	0.283579	+	0.872767i
$626$		0			0
$627$	84.7584	+	27.5397i	3.38493	+	1.09983i
$628$		0			0
$629$		−	20.7289i		−	0.826515i
$630$		0			0
$631$	6.63173	+	4.81823i	0.264005	+	0.191811i	0.711911	−	0.702270i	$-0.247830\pi$
$631$	6.63173	+	4.81823i	0.264005	+	0.191811i	−0.447906	+	0.894081i	$0.647830\pi$
$632$		0			0
$633$	15.8742	−	11.5333i	0.630944	−	0.458408i
$634$		0			0
$635$	−29.9374	−	21.7508i	−1.18803	−	0.863155i
$636$		0			0
$637$	−2.38697	+	3.28538i	−0.0945750	+	0.130171i
$638$		0			0
$639$	8.88623	−	2.88731i	0.351534	−	0.114220i
$640$		0			0
$641$	−11.2746	−	3.66334i	−0.445321	−	0.144693i	0.0777685	−	0.996971i	$-0.475220\pi$
$641$	−11.2746	−	3.66334i	−0.445321	−	0.144693i	−0.523089	+	0.852278i	$0.675220\pi$
$642$		0			0
$643$	−11.2237	−	15.4480i	−0.442618	−	0.609211i	0.528173	−	0.849137i	$-0.322877\pi$
$643$	−11.2237	−	15.4480i	−0.442618	−	0.609211i	−0.970791	+	0.239925i	$0.922877\pi$
$644$		0			0
$645$	56.1830	−	18.2550i	2.21220	−	0.718789i
$646$		0			0
$647$	17.3516			0.682161			0.341081	−	0.940034i	$-0.389207\pi$
$647$	17.3516			0.682161			0.341081	+	0.940034i	$0.389207\pi$
$648$		0			0
$649$	−24.0566	+	33.1110i	−0.944303	+	1.29972i
$650$		0			0
$651$	−8.98586	+	27.6556i	−0.352184	+	1.08391i
$652$		0			0
$653$			1.75123i			0.0685311i	0.999413	+	0.0342656i	$0.0109092\pi$
$653$			1.75123i			0.0685311i	−0.999413	+	0.0342656i	$0.989091\pi$
$654$		0			0
$655$	28.0517			1.09607
$656$		0			0
$657$	1.53021			0.0596990
$658$		0			0
$659$			17.0302i			0.663404i	0.943384	+	0.331702i	$0.107623\pi$
$659$			17.0302i			0.663404i	−0.943384	+	0.331702i	$0.892377\pi$
$660$		0			0
$661$	−6.80064	+	20.9302i	−0.264514	+	0.814091i	0.727291	+	0.686330i	$0.240779\pi$
$661$	−6.80064	+	20.9302i	−0.264514	+	0.814091i	−0.991805	+	0.127762i	$0.959221\pi$
$662$		0			0
$663$	−22.2112	+	30.5711i	−0.862613	+	1.18728i
$664$		0			0
$665$	−22.0847			−0.856408
$666$		0			0
$667$	−6.85785	+	2.22825i	−0.265537	+	0.0862782i
$668$		0			0
$669$	−3.23771	−	4.45632i	−0.125177	−	0.172291i
$670$		0			0
$671$	14.5836	+	4.73851i	0.562995	+	0.182928i
$672$		0			0
$673$	−11.1012	+	3.60699i	−0.427919	+	0.139039i	−0.515055	−	0.857157i	$-0.672228\pi$
$673$	−11.1012	+	3.60699i	−0.427919	+	0.139039i	0.0871361	+	0.996196i	$0.472228\pi$
$674$		0			0
$675$	48.6458	−	66.9552i	1.87238	−	2.57711i
$676$		0			0
$677$	0.239096	+	0.173713i	0.00918920	+	0.00667635i	0.592370	−	0.805666i	$-0.298192\pi$
$677$	0.239096	+	0.173713i	0.00918920	+	0.00667635i	−0.583181	+	0.812342i	$0.698192\pi$
$678$		0			0
$679$	−3.38172	+	2.45697i	−0.129779	+	0.0942897i
$680$		0			0
$681$	−22.2540	−	16.1685i	−0.852776	−	0.619578i
$682$		0			0
$683$			19.9422i			0.763069i	0.924355	+	0.381534i	$0.124604\pi$
$683$			19.9422i			0.763069i	−0.924355	+	0.381534i	$0.875396\pi$
$684$		0			0
$685$	11.8679	+	3.85613i	0.453451	+	0.147335i
$686$		0			0
$687$	−4.37676	−	13.4703i	−0.166984	−	0.513924i
$688$		0			0
$689$	10.2691	+	31.6049i	0.391220	+	1.20405i
$690$		0			0
$691$	6.94995	+	9.56579i	0.264389	+	0.363900i	0.920485	−	0.390777i	$-0.127794\pi$
$691$	6.94995	+	9.56579i	0.264389	+	0.363900i	−0.656097	+	0.754677i	$0.727794\pi$
$692$		0			0
$693$	−9.42627	+	29.0111i	−0.358074	+	1.10204i
$694$		0			0
$695$	−45.2348	+	32.8650i	−1.71585	+	1.24664i
$696$		0			0
$697$	19.9088	+	2.43147i	0.754100	+	0.0920983i
$698$		0			0
$699$	−28.4535	+	20.6727i	−1.07621	+	0.781911i
$700$		0			0
$701$	−9.12472	+	28.0830i	−0.344636	+	1.06068i	0.617143	+	0.786851i	$0.288290\pi$
$701$	−9.12472	+	28.0830i	−0.344636	+	1.06068i	−0.961779	+	0.273829i	$0.911710\pi$
$702$		0			0
$703$	22.2836	+	30.6708i	0.840443	+	1.15677i
$704$		0			0
$705$	−41.4023	−	127.423i	−1.55930	−	4.79904i
$706$		0			0
$707$	−2.41305	−	7.42660i	−0.0907521	−	0.279306i
$708$		0			0
$709$	−20.9216	−	6.79783i	−0.785726	−	0.255298i	−0.111443	−	0.993771i	$-0.535547\pi$
$709$	−20.9216	−	6.79783i	−0.785726	−	0.255298i	−0.674283	+	0.738473i	$0.735547\pi$
$710$		0			0
$711$			46.3388i			1.73784i
$712$		0			0
$713$	−52.8579	−	38.4035i	−1.97954	−	1.43822i
$714$		0			0
$715$	66.3247	−	48.1877i	2.48040	−	1.80212i
$716$		0			0
$717$	−58.4655	−	42.4777i	−2.18344	−	1.58636i
$718$		0			0
$719$	23.3074	−	32.0800i	0.869221	−	1.19638i	−0.110070	−	0.993924i	$-0.535108\pi$
$719$	23.3074	−	32.0800i	0.869221	−	1.19638i	0.979291	−	0.202456i	$-0.0648925\pi$
$720$		0			0
$721$	7.77743	−	2.52704i	0.289647	−	0.0941119i
$722$		0			0
$723$	−11.1751	−	3.63102i	−0.415607	−	0.135039i
$724$		0			0
$725$	6.26197	+	8.61887i	0.232564	+	0.320097i
$726$		0			0
$727$	−30.0540	+	9.76513i	−1.11464	+	0.362169i	−0.807720	−	0.589566i	$-0.799299\pi$
$727$	−30.0540	+	9.76513i	−1.11464	+	0.362169i	−0.306921	+	0.951735i	$0.599299\pi$
$728$		0			0
$729$	31.3620			1.16156
$730$		0			0
$731$	9.49720	−	13.0718i	0.351267	−	0.483477i
$732$		0			0
$733$	2.62554	−	8.08058i	0.0969765	−	0.298463i	−0.890787	−	0.454421i	$-0.849846\pi$
$733$	2.62554	−	8.08058i	0.0969765	−	0.298463i	0.987764	+	0.155958i	$0.0498463\pi$
$734$		0			0
$735$		−	11.4522i		−	0.422422i
$736$		0			0
$737$	29.0287			1.06929
$738$		0			0
$739$	12.7252			0.468105			0.234052	−	0.972224i	$-0.424801\pi$
$739$	12.7252			0.468105			0.234052	+	0.972224i	$0.424801\pi$
$740$		0			0
$741$		−	69.1107i		−	2.53885i
$742$		0			0
$743$	9.98294	−	30.7243i	0.366239	−	1.12717i	−0.582963	−	0.812498i	$-0.698107\pi$
$743$	9.98294	−	30.7243i	0.366239	−	1.12717i	0.949202	−	0.314668i	$-0.101893\pi$
$744$		0			0
$745$	−47.2656	+	65.0555i	−1.73168	+	2.38345i
$746$		0			0
$747$	−87.1782			−3.18968
$748$		0			0
$749$	−11.9133	+	3.87085i	−0.435301	+	0.141438i
$750$		0			0
$751$	9.71540	+	13.3721i	0.354520	+	0.487955i	0.948612	−	0.316442i	$-0.102488\pi$
$751$	9.71540	+	13.3721i	0.354520	+	0.487955i	−0.594092	+	0.804397i	$0.702488\pi$
$752$		0			0
$753$	−16.2083	−	5.26638i	−0.590662	−	0.191918i
$754$		0			0
$755$	−53.4837	+	17.3779i	−1.94647	+	0.632447i
$756$		0			0
$757$	−23.4310	+	32.2500i	−0.851614	+	1.17215i	0.131891	+	0.991264i	$0.457895\pi$
$757$	−23.4310	+	32.2500i	−0.851614	+	1.17215i	−0.983505	+	0.180882i	$0.942105\pi$
$758$		0			0
$759$	−84.0055	−	61.0336i	−3.04921	−	2.21538i
$760$		0			0
$761$	22.7363	−	16.5189i	0.824190	−	0.598809i	−0.0937198	−	0.995599i	$-0.529876\pi$
$761$	22.7363	−	16.5189i	0.824190	−	0.598809i	0.917910	+	0.396790i	$0.129876\pi$
$762$		0			0
$763$	5.34301	+	3.88192i	0.193430	+	0.140535i
$764$		0			0
$765$		−	70.3394i		−	2.54313i
$766$		0			0
$767$	30.1849	+	9.80768i	1.08991	+	0.354135i
$768$		0			0
$769$	−9.07695	−	27.9360i	−0.327323	−	1.00740i	−0.970381	−	0.241580i	$-0.922335\pi$
$769$	−9.07695	−	27.9360i	−0.327323	−	1.00740i	0.643058	−	0.765818i	$-0.277665\pi$
$770$		0			0
$771$	9.18245	+	28.2607i	0.330698	+	1.01778i
$772$		0			0
$773$	14.4361	+	19.8695i	0.519229	+	0.714658i	0.985441	−	0.170015i	$-0.0543817\pi$
$773$	14.4361	+	19.8695i	0.519229	+	0.714658i	−0.466212	+	0.884673i	$0.654382\pi$
$774$		0			0
$775$	−29.8295	+	91.8057i	−1.07151	+	3.29776i
$776$		0			0
$777$	−15.9046	+	11.5554i	−0.570576	+	0.414547i
$778$		0			0
$779$	−32.0712	+	17.8044i	−1.14907	+	0.637909i
$780$		0			0
$781$	−6.79562	+	4.93730i	−0.243166	+	0.176671i
$782$		0			0
$783$	2.80165	−	8.62258i	0.100123	−	0.308146i
$784$		0			0
$785$	−3.00973	−	4.14253i	−0.107422	−	0.147853i
$786$		0			0
$787$	−6.70583	−	20.6384i	−0.239037	−	0.735680i	−0.996560	−	0.0828721i	$-0.973591\pi$
$787$	−6.70583	−	20.6384i	−0.239037	−	0.735680i	0.757523	−	0.652808i	$-0.226409\pi$
$788$		0			0
$789$	13.7049	+	42.1795i	0.487909	+	1.50163i
$790$		0			0
$791$	−10.5645	−	3.43262i	−0.375631	−	0.122050i
$792$		0			0
$793$		−	11.8913i		−	0.422271i
$794$		0			0
$795$	−75.8173	−	55.0845i	−2.68896	−	1.95364i
$796$		0			0
$797$	9.18455	−	6.67297i	0.325333	−	0.236369i	−0.413114	−	0.910679i	$-0.635559\pi$
$797$	9.18455	−	6.67297i	0.325333	−	0.236369i	0.738448	+	0.674311i	$0.235559\pi$
$798$		0			0
$799$	−29.6468	−	21.5397i	−1.04883	−	0.762019i
$800$		0			0
$801$	46.6099	−	64.1530i	1.64688	−	2.26673i
$802$		0			0
$803$	−1.30833	+	0.425101i	−0.0461698	+	0.0150015i
$804$		0			0
$805$	24.4721	+	7.95147i	0.862528	+	0.280252i
$806$		0			0
$807$	9.14716	+	12.5900i	0.321995	+	0.443188i
$808$		0			0
$809$	−24.1467	+	7.84572i	−0.848951	+	0.275841i	−0.701007	−	0.713155i	$-0.747266\pi$
$809$	−24.1467	+	7.84572i	−0.848951	+	0.275841i	−0.147944	+	0.988996i	$0.547266\pi$
$810$		0			0
$811$	40.1308			1.40918			0.704591	−	0.709614i	$-0.251131\pi$
$811$	40.1308			1.40918			0.704591	+	0.709614i	$0.251131\pi$
$812$		0			0
$813$	3.69132	−	5.08066i	0.129460	−	0.178187i
$814$		0			0
$815$	−5.11469	+	15.7414i	−0.179160	+	0.551397i
$816$		0			0
$817$			29.5507i			1.03385i
$818$		0			0
$819$	23.6552			0.826579
$820$		0			0
$821$	−29.9852			−1.04649			−0.523246	−	0.852182i	$-0.675279\pi$
$821$	−29.9852			−1.04649			−0.523246	+	0.852182i	$0.675279\pi$
$822$		0			0
$823$		−	32.1063i		−	1.11916i	−0.828778	−	0.559578i	$-0.810963\pi$
$823$		−	32.1063i		−	1.11916i	0.828778	−	0.559578i	$-0.189037\pi$
$824$		0			0
$825$	−47.4071	+	145.904i	−1.65050	+	5.07973i
$826$		0			0
$827$	5.69802	−	7.84265i	0.198140	−	0.272716i	−0.698373	−	0.715734i	$-0.746092\pi$
$827$	5.69802	−	7.84265i	0.198140	−	0.272716i	0.896513	+	0.443018i	$0.146092\pi$
$828$		0			0
$829$	−3.26322			−0.113336			−0.0566681	−	0.998393i	$-0.518048\pi$
$829$	−3.26322			−0.113336			−0.0566681	+	0.998393i	$0.518048\pi$
$830$		0			0
$831$	33.2532	−	10.8046i	1.15354	−	0.374809i
$832$		0			0
$833$	−1.84114	−	2.53411i	−0.0637917	−	0.0878018i
$834$		0			0
$835$	−25.6352	−	8.32937i	−0.887141	−	0.288250i
$836$		0			0
$837$	78.1283	−	25.3854i	2.70051	−	0.877448i
$838$		0			0
$839$	9.77891	−	13.4595i	0.337605	−	0.464674i	−0.606135	−	0.795362i	$-0.707281\pi$
$839$	9.77891	−	13.4595i	0.337605	−	0.464674i	0.943740	+	0.330688i	$0.107281\pi$
$840$		0			0
$841$	−22.5173	−	16.3598i	−0.776459	−	0.564131i
$842$		0			0
$843$	7.38958	−	5.36884i	0.254511	−	0.184913i
$844$		0			0
$845$	−10.8887	−	7.91111i	−0.374583	−	0.272151i
$846$		0			0
$847$		−	16.4231i		−	0.564306i
$848$		0			0
$849$	20.5682	+	6.68300i	0.705898	+	0.229360i
$850$		0			0
$851$	−13.6497	−	42.0095i	−0.467906	−	1.44007i
$852$		0			0
$853$	−4.64958	−	14.3099i	−0.159199	−	0.489963i	0.839363	−	0.543571i	$-0.182928\pi$
$853$	−4.64958	−	14.3099i	−0.159199	−	0.489963i	−0.998562	+	0.0536074i	$0.982928\pi$
$854$		0			0
$855$	75.6152	+	104.075i	2.58598	+	3.55930i
$856$		0			0
$857$	4.48326	−	13.7981i	0.153145	−	0.471333i	−0.844823	−	0.535046i	$-0.820294\pi$
$857$	4.48326	−	13.7981i	0.153145	−	0.471333i	0.997968	+	0.0637132i	$0.0202943\pi$
$858$		0			0
$859$	43.1630	−	31.3598i	1.47270	−	1.06998i	0.492884	−	0.870095i	$-0.335943\pi$
$859$	43.1630	−	31.3598i	1.47270	−	1.06998i	0.979819	−	0.199887i	$-0.0640575\pi$
$860$		0			0
$861$	−9.23265	−	16.6308i	−0.314648	−	0.566777i
$862$		0			0
$863$	23.3771	−	16.9845i	0.795767	−	0.578159i	−0.113902	−	0.993492i	$-0.536335\pi$
$863$	23.3771	−	16.9845i	0.795767	−	0.578159i	0.909669	+	0.415333i	$0.136335\pi$
$864$		0			0
$865$	−10.8939	+	33.5281i	−0.370405	+	1.13999i
$866$		0			0
$867$	12.5520	+	17.2764i	0.426289	+	0.586737i
$868$		0			0
$869$	−12.8732	−	39.6196i	−0.436693	−	1.34400i
$870$		0			0
$871$	−6.95630	−	21.4093i	−0.235705	−	0.725426i
$872$		0			0
$873$	23.1572	+	7.52422i	0.783751	+	0.254656i
$874$		0			0
$875$		−	18.7415i		−	0.633578i
$876$		0			0
$877$	12.9325	+	9.39600i	0.436699	+	0.317281i	0.784322	−	0.620354i	$-0.213011\pi$
$877$	12.9325	+	9.39600i	0.436699	+	0.317281i	−0.347623	+	0.937634i	$0.613011\pi$
$878$		0			0
$879$	11.1332	−	8.08871i	0.375512	−	0.272825i
$880$		0			0
$881$	10.3556	+	7.52379i	0.348889	+	0.253483i	0.748403	−	0.663244i	$-0.230821\pi$
$881$	10.3556	+	7.52379i	0.348889	+	0.253483i	−0.399514	+	0.916727i	$0.630821\pi$
$882$		0			0
$883$	−7.42679	+	10.2221i	−0.249931	+	0.344001i	−0.915487	−	0.402347i	$-0.868195\pi$
$883$	−7.42679	+	10.2221i	−0.249931	+	0.344001i	0.665556	+	0.746348i	$0.268195\pi$
$884$		0			0
$885$	−85.1241	+	27.6585i	−2.86142	+	0.929730i
$886$		0			0
$887$	−6.59062	−	2.14142i	−0.221291	−	0.0719019i	0.196273	−	0.980549i	$-0.437116\pi$
$887$	−6.59062	−	2.14142i	−0.221291	−	0.0719019i	−0.417564	+	0.908647i	$0.637116\pi$
$888$		0			0
$889$	5.64214	+	7.76574i	0.189231	+	0.260455i
$890$		0			0
$891$	37.1337	−	12.0655i	1.24403	−	0.404208i
$892$		0			0
$893$	67.0212			2.24278
$894$		0			0
$895$	−39.2225	+	53.9851i	−1.31106	+	1.80452i
$896$		0			0
$897$	−24.8829	+	76.5818i	−0.830816	+	2.55699i
$898$		0			0
$899$			10.5747i			0.352686i
$900$		0			0
$901$	−25.6324			−0.853938
$902$		0			0
$903$	−15.3238			−0.509945
$904$		0			0
$905$		−	79.7044i		−	2.64946i
$906$		0			0
$907$	−7.10807	+	21.8764i	−0.236019	+	0.726393i	0.760965	+	0.648793i	$0.224726\pi$
$907$	−7.10807	+	21.8764i	−0.236019	+	0.726393i	−0.996985	+	0.0776004i	$0.975274\pi$
$908$		0			0
$909$	−26.7363	+	36.7994i	−0.886787	+	1.22056i
$910$		0			0
$911$	32.7387			1.08468			0.542340	−	0.840159i	$-0.317538\pi$
$911$	32.7387			1.08468			0.542340	+	0.840159i	$0.317538\pi$
$912$		0			0
$913$	74.5374	−	24.2187i	2.46683	−	0.801521i
$914$		0			0
$915$	19.7110	+	27.1299i	0.651627	+	0.896887i
$916$		0			0
$917$	−6.92044	−	2.24859i	−0.228533	−	0.0742548i
$918$		0			0
$919$	−6.20163	+	2.01503i	−0.204573	+	0.0664697i	−0.409511	−	0.912305i	$-0.634301\pi$
$919$	−6.20163	+	2.01503i	−0.204573	+	0.0664697i	0.204938	+	0.978775i	$0.434301\pi$
$920$		0			0
$921$	−19.2395	+	26.4809i	−0.633964	+	0.872576i
$922$		0			0
$923$	5.26984	+	3.82876i	0.173459	+	0.126025i
$924$		0			0
$925$	−52.7970	+	38.3593i	−1.73596	+	1.26125i
$926$		0			0
$927$	−38.5377	−	27.9993i	−1.26575	−	0.919618i
$928$		0			0
$929$		−	38.3509i		−	1.25825i	−0.777303	−	0.629126i	$-0.783413\pi$
$929$		−	38.3509i		−	1.25825i	0.777303	−	0.629126i	$-0.216587\pi$
$930$		0			0
$931$	5.44836	+	1.77028i	0.178563	+	0.0580186i
$932$		0			0
$933$	31.1654	+	95.9173i	1.02031	+	3.14019i
$934$		0			0
$935$	19.5407	+	60.1402i	0.639050	+	1.96679i
$936$		0			0
$937$	−25.6228	−	35.2667i	−0.837059	−	1.15211i	−0.986568	−	0.163353i	$-0.947769\pi$
$937$	−25.6228	−	35.2667i	−0.837059	−	1.15211i	0.149509	−	0.988760i	$-0.452231\pi$
$938$		0			0
$939$	8.32567	−	25.6238i	0.271698	−	0.836201i
$940$		0			0
$941$	−26.2526	+	19.0736i	−0.855810	+	0.621782i	−0.926742	−	0.375699i	$-0.877403\pi$
$941$	−26.2526	+	19.0736i	−0.855810	+	0.621782i	0.0709320	+	0.997481i	$0.477403\pi$
$942$		0			0
$943$	41.9486	−	8.18205i	1.36603	−	0.266444i
$944$		0			0
$945$	−26.1741	+	19.0166i	−0.851444	+	0.618610i
$946$		0			0
$947$	−0.768548	+	2.36535i	−0.0249745	+	0.0768635i	−0.962767	−	0.270333i	$-0.912866\pi$
$947$	−0.768548	+	2.36535i	−0.0249745	+	0.0768635i	0.937792	+	0.347196i	$0.112866\pi$
$948$		0			0
$949$	0.627043	+	0.863051i	0.0203547	+	0.0280158i
$950$		0			0
$951$	−14.3299	−	44.1030i	−0.464679	−	1.43014i
$952$		0			0
$953$	−0.460130	−	1.41613i	−0.0149051	−	0.0458731i	0.943327	−	0.331864i	$-0.107677\pi$
$953$	−0.460130	−	1.41613i	−0.0149051	−	0.0458731i	−0.958232	+	0.285991i	$0.907677\pi$
$954$		0			0
$955$	61.2955	+	19.9161i	1.98348	+	0.644470i
$956$		0			0
$957$			16.8060i			0.543262i
$958$		0			0
$959$	−2.61875	−	1.90264i	−0.0845640	−	0.0614393i
$960$		0			0
$961$	−52.4373	+	38.0979i	−1.69153	+	1.22897i
$962$		0			0
$963$	59.0311	+	42.8886i	1.90225	+	1.38206i
$964$		0			0
$965$	−33.2434	+	45.7555i	−1.07014	+	1.47292i
$966$		0			0
$967$	55.1208	−	17.9098i	1.77257	−	0.575942i	0.774193	−	0.632950i	$-0.218156\pi$
$967$	55.1208	−	17.9098i	1.77257	−	0.575942i	0.998374	+	0.0570079i	$0.0181560\pi$
$968$		0			0
$969$	50.6982	+	16.4728i	1.62866	+	0.529184i
$970$		0			0
$971$	−18.7576	−	25.8176i	−0.601960	−	0.828527i	0.393926	−	0.919142i	$-0.371117\pi$
$971$	−18.7576	−	25.8176i	−0.601960	−	0.828527i	−0.995886	+	0.0906154i	$0.971117\pi$
$972$		0			0
$973$	13.7940	−	4.48194i	0.442215	−	0.143684i
$974$		0			0
$975$	118.968			3.81002
$976$		0			0
$977$	−14.3170	+	19.7057i	−0.458041	+	0.630440i	−0.974101	−	0.226113i	$-0.927398\pi$
$977$	−14.3170	+	19.7057i	−0.458041	+	0.630440i	0.516060	+	0.856553i	$0.327398\pi$
$978$		0			0
$979$	−22.0293	+	67.7993i	−0.704061	+	2.16688i
$980$		0			0
$981$		−	38.4704i		−	1.22827i
$982$		0			0
$983$	49.9198			1.59220			0.796098	−	0.605168i	$-0.206894\pi$
$983$	49.9198			1.59220			0.796098	+	0.605168i	$0.206894\pi$
$984$		0			0
$985$	38.8854			1.23899
$986$		0			0
$987$			34.7545i			1.10625i
$988$		0			0
$989$	10.6396	−	32.7453i	0.338319	−	1.04124i
$990$		0			0
$991$	29.5159	−	40.6251i	0.937603	−	1.29050i	−0.0192163	−	0.999815i	$-0.506117\pi$
$991$	29.5159	−	40.6251i	0.937603	−	1.29050i	0.956819	−	0.290684i	$-0.0938829\pi$
$992$		0			0
$993$	94.2662			2.99145
$994$		0			0
$995$	9.42828	−	3.06343i	0.298897	−	0.0971174i
$996$		0			0
$997$	12.6812	+	17.4541i	0.401617	+	0.552778i	0.961149	−	0.276031i	$-0.0890192\pi$
$997$	12.6812	+	17.4541i	0.401617	+	0.552778i	−0.559532	+	0.828809i	$0.689019\pi$
$998$		0			0
$999$	52.8198	+	17.1622i	1.67114	+	0.542988i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.ba.a.701.1	yes	80
41.31	even	10	inner	1148.2.ba.a.113.20	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.ba.a.113.20	✓	80	41.31	even	10	inner
1148.2.ba.a.701.1	yes	80	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.97070i q^{3} +(-1.19128 + 3.66638i) q^{5} +(0.587785 - 0.809017i) q^{7} -5.82504 q^{9} +O(q^{10})\)	\(q-2.97070i q^{3} +(-1.19128 + 3.66638i) q^{5} +(0.587785 - 0.809017i) q^{7} -5.82504 q^{9} +(4.98041 - 1.61823i) q^{11} +(-2.38697 - 3.28538i) q^{13} +(10.8917 + 3.53893i) q^{15} +(2.97903 - 0.967945i) q^{17} +(-3.36727 + 4.63465i) q^{19} +(-2.40334 - 1.74613i) q^{21} +(5.39996 - 3.92330i) q^{23} +(-7.97814 - 5.79646i) q^{25} +8.39233i q^{27} +(-1.02744 - 0.333834i) q^{29} +(-3.02483 - 9.30948i) q^{31} +(-4.80728 - 14.7953i) q^{33} +(2.26595 + 3.11881i) q^{35} +(2.04499 - 6.29382i) q^{37} +(-9.75986 + 7.09095i) q^{39} +(5.80494 + 2.70234i) q^{41} +(4.17317 - 3.03199i) q^{43} +(6.93925 - 21.3568i) q^{45} +(-6.87656 - 9.46477i) q^{47} +(-0.309017 - 0.951057i) q^{49} +(-2.87547 - 8.84979i) q^{51} +(-7.78264 - 2.52873i) q^{53} +20.1879i q^{55} +(13.7682 + 10.0031i) q^{57} +(-6.32287 + 4.59383i) q^{59} +(2.36896 + 1.72115i) q^{61} +(-3.42387 + 4.71255i) q^{63} +(14.8890 - 4.83773i) q^{65} +(5.27199 + 1.71297i) q^{67} +(-11.6549 - 16.0417i) q^{69} +(-1.52552 + 0.495673i) q^{71} -0.262695 q^{73} +(-17.2195 + 23.7006i) q^{75} +(1.61823 - 4.98041i) q^{77} -7.95510i q^{79} +7.45595 q^{81} +14.9661 q^{83} +12.0754i q^{85} +(-0.991720 + 3.05220i) q^{87} +(-8.00164 + 11.0133i) q^{89} -4.06095 q^{91} +(-27.6556 + 8.98586i) q^{93} +(-12.9811 - 17.8669i) q^{95} +(-3.97545 - 1.29170i) q^{97} +(-29.0111 + 9.42627i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 4 q^{5} - 60 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more