LMFDB - Embedded newform 930.2.bn.a.19.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(19,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 15, 4]))

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

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

chi := DirichletCharacter("930.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bn (of order $30$, degree $8$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.11
Character	$\chi$	$=$	930.19
Dual form			930.2.bn.a.49.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 - 0.809017i) q^{2} +(-0.406737 + 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-1.39519 - 1.74741i) q^{5} +(0.500000 + 0.866025i) q^{6} +(0.274259 + 0.246944i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +O(q^{10})$	\(q+(0.587785 - 0.809017i) q^{2} +(-0.406737 + 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-1.39519 - 1.74741i) q^{5} +(0.500000 + 0.866025i) q^{6} +(0.274259 + 0.246944i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +(-2.23376 + 0.101626i) q^{10} +(-0.624761 - 0.132797i) q^{11} +(0.994522 + 0.104528i) q^{12} +(-5.51543 + 0.579695i) q^{13} +(0.360988 - 0.0767303i) q^{14} +(2.16382 - 0.563829i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.840896 + 3.95611i) q^{17} +(-0.994522 + 0.104528i) q^{18} +(-0.197463 + 1.87873i) q^{19} +(-1.23075 + 1.86688i) q^{20} +(-0.337146 + 0.150107i) q^{21} +(-0.474660 + 0.427386i) q^{22} +(-0.917222 - 0.298023i) q^{23} +(0.669131 - 0.743145i) q^{24} +(-1.10691 + 4.87594i) q^{25} +(-2.77291 + 4.80281i) q^{26} +(0.951057 - 0.309017i) q^{27} +(0.150107 - 0.337146i) q^{28} +(2.93911 + 2.13539i) q^{29} +(0.815711 - 2.08197i) q^{30} +(-5.14964 - 2.11690i) q^{31} +1.00000i q^{32} +(0.375429 - 0.516734i) q^{33} +(3.69482 + 1.64504i) q^{34} +(0.0488707 - 0.823778i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-4.46700 + 2.57902i) q^{37} +(1.40386 + 1.26404i) q^{38} +(1.71375 - 5.27438i) q^{39} +(0.786921 + 2.09303i) q^{40} +(-3.87300 + 1.72437i) q^{41} +(-0.0767303 + 0.360988i) q^{42} +(-10.0214 - 1.05329i) q^{43} +(0.0667642 + 0.635219i) q^{44} +(-0.365019 + 2.20607i) q^{45} +(-0.780235 + 0.566874i) q^{46} +(3.95690 + 5.44621i) q^{47} +(-0.207912 - 0.978148i) q^{48} +(-0.717462 - 6.82620i) q^{49} +(3.29409 + 3.76151i) q^{50} +(-3.95611 - 0.840896i) q^{51} +(2.25569 + 5.06635i) q^{52} +(-0.374618 + 0.337307i) q^{53} +(0.309017 - 0.951057i) q^{54} +(0.639606 + 1.27699i) q^{55} +(-0.184526 - 0.319609i) q^{56} +(-1.63599 - 0.944540i) q^{57} +(3.45513 - 1.12264i) q^{58} +(-2.97847 - 1.32610i) q^{59} +(-1.20489 - 1.88368i) q^{60} +3.58422 q^{61} +(-4.73948 + 2.92186i) q^{62} -0.369052i q^{63} +(0.809017 + 0.587785i) q^{64} +(8.70802 + 8.82896i) q^{65} +(-0.197375 - 0.607457i) q^{66} +(-5.47923 - 3.16343i) q^{67} +(3.50263 - 2.02224i) q^{68} +(0.645325 - 0.716707i) q^{69} +(-0.637725 - 0.523742i) q^{70} +(1.87509 + 2.08249i) q^{71} +(0.406737 + 0.913545i) q^{72} +(-1.76347 + 8.29649i) q^{73} +(-0.539163 + 5.12979i) q^{74} +(-4.00417 - 2.99443i) q^{75} +(1.84780 - 0.392762i) q^{76} +(-0.138553 - 0.190702i) q^{77} +(-3.25975 - 4.48666i) q^{78} +(-3.64435 + 0.774630i) q^{79} +(2.15583 + 0.593617i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(-0.881446 + 4.14688i) q^{82} +(-4.74056 - 10.6475i) q^{83} +(0.246944 + 0.274259i) q^{84} +(5.73975 - 6.98890i) q^{85} +(-6.74256 + 7.48837i) q^{86} +(-3.14621 + 1.81647i) q^{87} +(0.553146 + 0.319359i) q^{88} +(1.95518 + 6.01741i) q^{89} +(1.57020 + 1.59200i) q^{90} +(-1.65581 - 1.20302i) q^{91} +0.964424i q^{92} +(4.02843 - 3.84341i) q^{93} +6.73188 q^{94} +(3.55842 - 2.27613i) q^{95} +(-0.913545 - 0.406737i) q^{96} +(-7.70670 + 2.50406i) q^{97} +(-5.94423 - 3.43190i) q^{98} +(0.319359 + 0.553146i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 28 q^{4} - 2 q^{5} + 56 q^{6} - 14 q^{9}+O(q^{10}) $ 112 * q + 28 * q^4 - 2 * q^5 + 56 * q^6 - 14 * q^9	$ 112 q + 28 q^{4} - 2 q^{5} + 56 q^{6} - 14 q^{9} - 4 q^{10} + 18 q^{11} + 8 q^{14} + 8 q^{15} - 28 q^{16} + 16 q^{19} + 2 q^{20} + 28 q^{21} + 14 q^{24} + 14 q^{25} + 12 q^{26} + 16 q^{29} - 4 q^{30} + 10 q^{34} - 38 q^{35} - 56 q^{36} + 16 q^{39} - 6 q^{40} + 20 q^{41} + 2 q^{44} + 2 q^{45} - 2 q^{46} + 38 q^{49} + 8 q^{50} - 10 q^{51} - 28 q^{54} - 46 q^{55} + 12 q^{56} + 60 q^{59} - 8 q^{60} + 88 q^{61} + 28 q^{64} - 28 q^{65} + 6 q^{66} + 46 q^{69} + 26 q^{70} + 116 q^{71} - 34 q^{74} + 8 q^{75} + 24 q^{76} - 40 q^{79} - 12 q^{80} + 14 q^{81} - 8 q^{84} + 18 q^{85} - 38 q^{86} - 60 q^{89} + 4 q^{90} - 92 q^{91} + 132 q^{94} + 132 q^{95} - 14 q^{96} + 2 q^{99}+O(q^{100}) $ 112 * q + 28 * q^4 - 2 * q^5 + 56 * q^6 - 14 * q^9 - 4 * q^10 + 18 * q^11 + 8 * q^14 + 8 * q^15 - 28 * q^16 + 16 * q^19 + 2 * q^20 + 28 * q^21 + 14 * q^24 + 14 * q^25 + 12 * q^26 + 16 * q^29 - 4 * q^30 + 10 * q^34 - 38 * q^35 - 56 * q^36 + 16 * q^39 - 6 * q^40 + 20 * q^41 + 2 * q^44 + 2 * q^45 - 2 * q^46 + 38 * q^49 + 8 * q^50 - 10 * q^51 - 28 * q^54 - 46 * q^55 + 12 * q^56 + 60 * q^59 - 8 * q^60 + 88 * q^61 + 28 * q^64 - 28 * q^65 + 6 * q^66 + 46 * q^69 + 26 * q^70 + 116 * q^71 - 34 * q^74 + 8 * q^75 + 24 * q^76 - 40 * q^79 - 12 * q^80 + 14 * q^81 - 8 * q^84 + 18 * q^85 - 38 * q^86 - 60 * q^89 + 4 * q^90 - 92 * q^91 + 132 * q^94 + 132 * q^95 - 14 * q^96 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{15}\right)$

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 $

$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$3$	−0.406737	+	0.913545i	−0.234830	+	0.527436i
$3$	−0.406737	+	0.913545i	−0.234830	+	0.527436i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	−1.39519	−	1.74741i	−0.623946	−	0.781467i
$5$	−1.39519	−	1.74741i	−0.623946	−	0.781467i
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	0.274259	+	0.246944i	0.103660	+	0.0933362i	0.719331	−	0.694667i	$-0.244448\pi$
$7$	0.274259	+	0.246944i	0.103660	+	0.0933362i	−0.615671	+	0.788003i	$0.711115\pi$
$8$	−0.951057	−	0.309017i	−0.336249	−	0.109254i
$9$	−0.669131	−	0.743145i	−0.223044	−	0.247715i
$10$	−2.23376	+	0.101626i	−0.706376	+	0.0321369i
$11$	−0.624761	−	0.132797i	−0.188372	−	0.0400398i	0.112759	−	0.993622i	$-0.464031\pi$
$11$	−0.624761	−	0.132797i	−0.188372	−	0.0400398i	−0.301132	+	0.953583i	$0.597364\pi$
$12$	0.994522	+	0.104528i	0.287094	+	0.0301748i
$13$	−5.51543	+	0.579695i	−1.52971	+	0.160779i	−0.831664	−	0.555279i	$-0.812612\pi$
$13$	−5.51543	+	0.579695i	−1.52971	+	0.160779i	−0.698041	+	0.716057i	$0.745945\pi$
$14$	0.360988	−	0.0767303i	0.0964781	−	0.0205070i
$15$	2.16382	−	0.563829i	0.558695	−	0.145580i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	0.840896	+	3.95611i	0.203947	+	0.959497i	0.954390	+	0.298562i	$0.0965068\pi$
$17$	0.840896	+	3.95611i	0.203947	+	0.959497i	−0.750443	+	0.660935i	$0.770160\pi$
$18$	−0.994522	+	0.104528i	−0.234411	+	0.0246376i
$19$	−0.197463	+	1.87873i	−0.0453010	+	0.431011i	0.948241	+	0.317550i	$0.102860\pi$
$19$	−0.197463	+	1.87873i	−0.0453010	+	0.431011i	−0.993543	+	0.113460i	$0.963806\pi$
$20$	−1.23075	+	1.86688i	−0.275205	+	0.417447i
$21$	−0.337146	+	0.150107i	−0.0735713	+	0.0327561i
$22$	−0.474660	+	0.427386i	−0.101198	+	0.0911190i
$23$	−0.917222	−	0.298023i	−0.191254	−	0.0621422i	0.211824	−	0.977308i	$-0.432060\pi$
$23$	−0.917222	−	0.298023i	−0.191254	−	0.0621422i	−0.403078	+	0.915166i	$0.632060\pi$
$24$	0.669131	−	0.743145i	0.136586	−	0.151694i
$25$	−1.10691	+	4.87594i	−0.221382	+	0.975187i
$26$	−2.77291	+	4.80281i	−0.543812	+	0.941909i
$27$	0.951057	−	0.309017i	0.183031	−	0.0594703i
$28$	0.150107	−	0.337146i	0.0283676	−	0.0637146i
$29$	2.93911	+	2.13539i	0.545778	+	0.396531i	0.826227	−	0.563338i	$-0.190483\pi$
$29$	2.93911	+	2.13539i	0.545778	+	0.396531i	−0.280448	+	0.959869i	$0.590483\pi$
$30$	0.815711	−	2.08197i	0.148928	−	0.380115i
$31$	−5.14964	−	2.11690i	−0.924902	−	0.380206i
$31$	−5.14964	−	2.11690i	−0.924902	−	0.380206i
$32$			1.00000i			0.176777i
$33$	0.375429	−	0.516734i	0.0653538	−	0.0899518i
$34$	3.69482	+	1.64504i	0.633657	+	0.282122i
$35$	0.0488707	−	0.823778i	0.00826066	−	0.139244i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−4.46700	+	2.57902i	−0.734371	+	0.423989i	−0.820019	−	0.572336i	$-0.806037\pi$
$37$	−4.46700	+	2.57902i	−0.734371	+	0.423989i	0.0856483	+	0.996325i	$0.472704\pi$
$38$	1.40386	+	1.26404i	0.227736	+	0.205055i
$39$	1.71375	−	5.27438i	0.274420	−	0.844577i
$40$	0.786921	+	2.09303i	0.124423	+	0.330936i
$41$	−3.87300	+	1.72437i	−0.604860	+	0.269301i	−0.686232	−	0.727383i	$-0.740737\pi$
$41$	−3.87300	+	1.72437i	−0.604860	+	0.269301i	0.0813717	+	0.996684i	$0.474070\pi$
$42$	−0.0767303	+	0.360988i	−0.0118397	+	0.0557016i
$43$	−10.0214	−	1.05329i	−1.52825	−	0.160625i	−0.697221	−	0.716857i	$-0.745580\pi$
$43$	−10.0214	−	1.05329i	−1.52825	−	0.160625i	−0.831028	+	0.556231i	$0.812247\pi$
$44$	0.0667642	+	0.635219i	0.0100651	+	0.0957629i
$45$	−0.365019	+	2.20607i	−0.0544138	+	0.328862i
$46$	−0.780235	+	0.566874i	−0.115039	+	0.0835810i
$47$	3.95690	+	5.44621i	0.577174	+	0.794411i	0.993382	−	0.114858i	$-0.0366413\pi$
$47$	3.95690	+	5.44621i	0.577174	+	0.794411i	−0.416208	+	0.909269i	$0.636641\pi$
$48$	−0.207912	−	0.978148i	−0.0300095	−	0.141183i
$49$	−0.717462	−	6.82620i	−0.102495	−	0.975171i
$50$	3.29409	+	3.76151i	0.465855	+	0.531958i
$51$	−3.95611	−	0.840896i	−0.553966	−	0.117749i
$52$	2.25569	+	5.06635i	0.312807	+	0.702577i
$53$	−0.374618	+	0.337307i	−0.0514577	+	0.0463327i	−0.694458	−	0.719533i	$-0.744356\pi$
$53$	−0.374618	+	0.337307i	−0.0514577	+	0.0463327i	0.643001	+	0.765866i	$0.277689\pi$
$54$	0.309017	−	0.951057i	0.0420519	−	0.129422i
$55$	0.639606	+	1.27699i	0.0862445	+	0.172190i
$56$	−0.184526	−	0.319609i	−0.0246584	−	0.0427095i
$57$	−1.63599	−	0.944540i	−0.216692	−	0.125107i
$58$	3.45513	−	1.12264i	0.453680	−	0.147410i
$59$	−2.97847	−	1.32610i	−0.387764	−	0.172644i	0.203589	−	0.979056i	$-0.434739\pi$
$59$	−2.97847	−	1.32610i	−0.387764	−	0.172644i	−0.591353	+	0.806413i	$0.701406\pi$
$60$	−1.20489	−	1.88368i	−0.155551	−	0.243182i
$61$	3.58422			0.458912			0.229456	−	0.973319i	$-0.426305\pi$
$61$	3.58422			0.458912			0.229456	+	0.973319i	$0.426305\pi$
$62$	−4.73948	+	2.92186i	−0.601915	+	0.371077i
$63$		−	0.369052i		−	0.0464962i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	8.70802	+	8.82896i	1.08010	+	1.09510i
$66$	−0.197375	−	0.607457i	−0.0242952	−	0.0747728i
$67$	−5.47923	−	3.16343i	−0.669394	−	0.386475i	0.126453	−	0.991973i	$-0.459641\pi$
$67$	−5.47923	−	3.16343i	−0.669394	−	0.386475i	−0.795847	+	0.605498i	$0.792974\pi$
$68$	3.50263	−	2.02224i	0.424756	−	0.245233i
$69$	0.645325	−	0.716707i	0.0776881	−	0.0862813i
$70$	−0.637725	−	0.523742i	−0.0762227	−	0.0625991i
$71$	1.87509	+	2.08249i	0.222532	+	0.247147i	0.844065	−	0.536242i	$-0.180156\pi$
$71$	1.87509	+	2.08249i	0.222532	+	0.247147i	−0.621533	+	0.783388i	$0.713490\pi$
$72$	0.406737	+	0.913545i	0.0479344	+	0.107662i
$73$	−1.76347	+	8.29649i	−0.206399	+	0.971031i	0.745946	+	0.666007i	$0.231998\pi$
$73$	−1.76347	+	8.29649i	−0.206399	+	0.971031i	−0.952345	+	0.305024i	$0.901336\pi$
$74$	−0.539163	+	5.12979i	−0.0626764	+	0.596326i
$75$	−4.00417	−	2.99443i	−0.462362	−	0.345767i
$76$	1.84780	−	0.392762i	0.211957	−	0.0450529i
$77$	−0.138553	−	0.190702i	−0.0157896	−	0.0217325i
$78$	−3.25975	−	4.48666i	−0.369094	−	0.508014i
$79$	−3.64435	+	0.774630i	−0.410021	+	0.0871526i	−0.408304	−	0.912846i	$-0.633880\pi$
$79$	−3.64435	+	0.774630i	−0.410021	+	0.0871526i	−0.00171666	+	0.999999i	$0.500546\pi$
$80$	2.15583	+	0.593617i	0.241030	+	0.0663684i
$81$	−0.104528	+	0.994522i	−0.0116143	+	0.110502i
$82$	−0.881446	+	4.14688i	−0.0973395	+	0.457946i
$83$	−4.74056	−	10.6475i	−0.520344	−	1.16871i	−0.962378	−	0.271713i	$-0.912410\pi$
$83$	−4.74056	−	10.6475i	−0.520344	−	1.16871i	0.442035	−	0.896998i	$-0.354257\pi$
$84$	0.246944	+	0.274259i	0.0269438	+	0.0299242i
$85$	5.73975	−	6.98890i	0.622563	−	0.758053i
$86$	−6.74256	+	7.48837i	−0.727069	+	0.807492i
$87$	−3.14621	+	1.81647i	−0.337310	+	0.194746i
$88$	0.553146	+	0.319359i	0.0589656	+	0.0340438i
$89$	1.95518	+	6.01741i	0.207248	+	0.637845i	0.999614	+	0.0277976i	$0.00884940\pi$
$89$	1.95518	+	6.01741i	0.207248	+	0.637845i	−0.792365	+	0.610047i	$0.791151\pi$
$90$	1.57020	+	1.59200i	0.165513	+	0.167812i
$91$	−1.65581	−	1.20302i	−0.173576	−	0.126111i
$92$			0.964424i			0.100548i
$93$	4.02843	−	3.84341i	0.417728	−	0.398543i
$94$	6.73188			0.694341
$95$	3.55842	−	2.27613i	0.365086	−	0.233526i
$96$	−0.913545	−	0.406737i	−0.0932383	−	0.0415124i
$97$	−7.70670	+	2.50406i	−0.782496	+	0.254249i	−0.672906	−	0.739728i	$-0.734954\pi$
$97$	−7.70670	+	2.50406i	−0.782496	+	0.254249i	−0.109591	+	0.993977i	$0.534954\pi$
$98$	−5.94423	−	3.43190i	−0.600457	−	0.346674i
$99$	0.319359	+	0.553146i	0.0320968	+	0.0555933i
$100$	4.97934	−	0.454015i	0.497934	−	0.0454015i
$101$	1.21772	−	3.74777i	0.121168	−	0.372917i	−0.872015	−	0.489478i	$-0.837187\pi$
$101$	1.21772	−	3.74777i	0.121168	−	0.372917i	0.993183	+	0.116561i	$0.0371872\pi$
$102$	−3.00564	+	2.70629i	−0.297603	+	0.267963i
$103$	2.66541	+	5.98661i	0.262631	+	0.589878i	0.995940	−	0.0900169i	$-0.0286921\pi$
$103$	2.66541	+	5.98661i	0.262631	+	0.589878i	−0.733310	+	0.679895i	$0.762025\pi$
$104$	5.42462	+	1.15304i	0.531928	+	0.113065i
$105$	0.732681	+	0.379706i	0.0715024	+	0.0370555i
$106$	0.0526926	+	0.501336i	0.00511795	+	0.0486941i
$107$	−1.69142	−	7.95749i	−0.163516	−	0.769280i	−0.981105	−	0.193478i	$-0.938023\pi$
$107$	−1.69142	−	7.95749i	−0.163516	−	0.769280i	0.817589	−	0.575802i	$-0.195310\pi$
$108$	−0.587785	−	0.809017i	−0.0565597	−	0.0778477i
$109$	13.0853	−	9.50704i	1.25335	−	0.910609i	0.254935	−	0.966958i	$-0.417946\pi$
$109$	13.0853	−	9.50704i	1.25335	−	0.910609i	0.998411	+	0.0563492i	$0.0179460\pi$
$110$	1.40906	+	0.233144i	0.134349	+	0.0222294i
$111$	−0.539163	−	5.12979i	−0.0511751	−	0.486898i
$112$	−0.367031	−	0.0385765i	−0.0346811	−	0.00364514i
$113$	3.01334	−	14.1766i	0.283471	−	1.33363i	−0.573899	−	0.818926i	$-0.694570\pi$
$113$	3.01334	−	14.1766i	0.283471	−	1.33363i	0.857370	−	0.514701i	$-0.172097\pi$
$114$	−1.72576	+	0.768358i	−0.161632	+	0.0719633i
$115$	0.758925	+	2.01856i	0.0707701	+	0.188232i
$116$	1.12264	−	3.45513i	0.104234	−	0.320801i
$117$	4.12134	+	3.71087i	0.381018	+	0.343070i
$118$	−2.82354	+	1.63017i	−0.259928	+	0.150070i
$119$	−0.746314	+	1.29265i	−0.0684145	+	0.118497i
$120$	−2.23214	−	0.132422i	−0.203766	−	0.0120884i
$121$	−9.67631	−	4.30817i	−0.879664	−	0.391652i
$122$	2.10675	−	2.89969i	0.190736	−	0.262526i
$123$		−	4.23952i		−	0.382265i
$124$	−0.421963	+	5.55175i	−0.0378934	+	0.498562i
$125$	10.0646	−	4.86862i	0.900207	−	0.435462i
$126$	−0.298570	−	0.216924i	−0.0265987	−	0.0193251i
$127$	3.48906	−	7.83655i	0.309604	−	0.695382i	−0.689992	−	0.723817i	$-0.742386\pi$
$127$	3.48906	−	7.83655i	0.309604	−	0.695382i	0.999596	+	0.0284355i	$0.00905254\pi$
$128$	0.951057	−	0.309017i	0.0840623	−	0.0273135i
$129$	5.03830	−	8.72659i	0.443597	−	0.768333i
$130$	12.2612	−	1.85541i	1.07538	−	0.162730i
$131$	−7.46288	+	8.28837i	−0.652035	+	0.724158i	−0.974988	−	0.222257i	$-0.928658\pi$
$131$	−7.46288	+	8.28837i	−0.652035	+	0.724158i	0.322953	+	0.946415i	$0.395324\pi$
$132$	−0.607457	−	0.197375i	−0.0528723	−	0.0171793i
$133$	−0.518098	+	0.466498i	−0.0449248	+	0.0404505i
$134$	−5.77988	+	2.57337i	−0.499306	+	0.222305i
$135$	−1.86688	−	1.23075i	−0.160676	−	0.105926i
$136$	0.422764	−	4.02233i	0.0362517	−	0.344912i
$137$	12.8773	−	1.35345i	1.10018	−	0.115633i	0.463006	−	0.886355i	$-0.346771\pi$
$137$	12.8773	−	1.35345i	1.10018	−	0.115633i	0.637172	+	0.770722i	$0.280104\pi$
$138$	−0.200515	−	0.943349i	−0.0170690	−	0.0803032i
$139$	−7.29039	+	5.29678i	−0.618363	+	0.449267i	−0.852349	−	0.522973i	$-0.824823\pi$
$139$	−7.29039	+	5.29678i	−0.618363	+	0.449267i	0.233986	+	0.972240i	$0.424823\pi$
$140$	−0.798561	+	0.208083i	−0.0674908	+	0.0175862i
$141$	−6.58478	+	1.39964i	−0.554538	+	0.117871i
$142$	2.78692	−	0.292917i	0.233873	−	0.0245811i
$143$	3.52281	+	0.370262i	0.294592	+	0.0309629i
$144$	0.978148	+	0.207912i	0.0815123	+	0.0173260i
$145$	−0.369200	−	8.11510i	−0.0306604	−	0.673922i
$146$	5.67546	+	6.30324i	0.469704	+	0.521659i
$147$	6.52786	+	2.12103i	0.538409	+	0.174940i
$148$	3.83318	+	3.45141i	0.315085	+	0.283704i
$149$	−1.96462	−	3.40282i	−0.160948	−	0.278770i	0.774261	−	0.632866i	$-0.218122\pi$
$149$	−1.96462	−	3.40282i	−0.160948	−	0.278770i	−0.935209	+	0.354097i	$0.884788\pi$
$150$	−4.77614	+	1.47936i	−0.389970	+	0.120789i
$151$	−1.85856	−	5.72004i	−0.151247	−	0.465491i	0.846514	−	0.532366i	$-0.178697\pi$
$151$	−1.85856	−	5.72004i	−0.151247	−	0.465491i	−0.997761	+	0.0668754i	$0.978697\pi$
$152$	0.768358	−	1.72576i	0.0623221	−	0.139978i
$153$	2.37729	−	3.27206i	0.192193	−	0.264530i
$154$	−0.235721			−0.0189949
$155$	3.48561	+	11.9520i	0.279971	+	0.960008i
$156$	−5.54581			−0.444020
$157$	10.6070	−	14.5993i	0.846534	−	1.16515i	−0.138082	−	0.990421i	$-0.544094\pi$
$157$	10.6070	−	14.5993i	0.846534	−	1.16515i	0.984616	−	0.174733i	$-0.0559064\pi$
$158$	−1.51540	+	3.40365i	−0.120559	+	0.270780i
$159$	−0.155775	−	0.479425i	−0.0123537	−	0.0380209i
$160$	1.74741	−	1.39519i	0.138145	−	0.110299i
$161$	−0.177962	−	0.308238i	−0.0140253	−	0.0242926i
$162$	0.743145	+	0.669131i	0.0583870	+	0.0525719i
$163$	−10.7351	−	3.48803i	−0.840835	−	0.273204i	−0.143233	−	0.989689i	$-0.545750\pi$
$163$	−10.7351	−	3.48803i	−0.840835	−	0.273204i	−0.697602	+	0.716485i	$0.745750\pi$
$164$	2.83679	+	3.15058i	0.221516	+	0.246019i
$165$	−1.42674	+	0.0649103i	−0.111072	+	0.00505326i
$166$	−11.4004	−	2.42323i	−0.884843	−	0.188079i
$167$	20.6234	+	2.16761i	1.59589	+	0.167735i	0.860334	−	0.509731i	$-0.170255\pi$
$167$	20.6234	+	2.16761i	1.59589	+	0.167735i	0.735554	+	0.677466i	$0.236922\pi$
$168$	0.367031	−	0.0385765i	0.0283170	−	0.00297624i
$169$	17.3680	−	3.69169i	1.33600	−	0.283976i
$170$	−2.28040	−	8.75152i	−0.174899	−	0.671211i
$171$	1.52830	−	1.11037i	0.116872	−	0.0849124i
$172$	2.09504	+	9.85640i	0.159745	+	0.751543i
$173$	4.15655	−	0.436871i	0.316016	−	0.0332147i	0.0548074	−	0.998497i	$-0.482546\pi$
$173$	4.15655	−	0.436871i	0.316016	−	0.0332147i	0.261209	+	0.965282i	$0.415879\pi$
$174$	−0.379745	+	3.61303i	−0.0287884	+	0.273903i
$175$	−1.50766	+	1.06393i	−0.113969	+	0.0804253i
$176$	0.583498	−	0.259790i	0.0439828	−	0.0195824i
$177$	2.42291	−	2.18160i	0.182117	−	0.163979i
$178$	6.01741	+	1.95518i	0.451024	+	0.146547i
$179$	−9.64503	+	10.7119i	−0.720903	+	0.800644i	−0.986556	−	0.163425i	$-0.947746\pi$
$179$	−9.64503	+	10.7119i	−0.720903	+	0.800644i	0.265653	+	0.964069i	$0.414413\pi$
$180$	2.21090	−	0.334560i	0.164791	−	0.0249367i
$181$	−4.99143	+	8.64540i	−0.371010	+	0.642608i	−0.989721	−	0.143011i	$-0.954322\pi$
$181$	−4.99143	+	8.64540i	−0.371010	+	0.642608i	0.618711	+	0.785618i	$0.287655\pi$
$182$	−1.94652	+	0.632464i	−0.144286	+	0.0468813i
$183$	−1.45783	+	3.27434i	−0.107766	+	0.242046i
$184$	0.780235	+	0.566874i	0.0575197	+	0.0417905i
$185$	10.7389	+	4.20748i	0.789541	+	0.309340i
$186$	−0.741532	−	5.51816i	−0.0543718	−	0.404611i
$187$		−	2.58329i		−	0.188909i
$188$	3.95690	−	5.44621i	0.288587	−	0.397206i
$189$	0.337146	+	0.150107i	0.0245238	+	0.0109187i
$190$	0.250156	−	4.21670i	0.0181482	−	0.305911i
$191$	−1.06654	+	1.84730i	−0.0771721	+	0.133666i	−0.902029	−	0.431676i	$-0.857922\pi$
$191$	−1.06654	+	1.84730i	−0.0771721	+	0.133666i	0.824857	+	0.565342i	$0.191256\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	−1.58936	−	1.43107i	−0.114405	−	0.103011i	0.609943	−	0.792445i	$-0.291192\pi$
$193$	−1.58936	−	1.43107i	−0.114405	−	0.103011i	−0.724348	+	0.689435i	$0.757859\pi$
$194$	−2.50406	+	7.70670i	−0.179781	+	0.553309i
$195$	−11.6075	+	4.36412i	−0.831232	+	0.312521i
$196$	−6.27039	+	2.79176i	−0.447885	+	0.199411i
$197$	−1.73659	+	8.17001i	−0.123727	+	0.582089i	0.871981	+	0.489539i	$0.162835\pi$
$197$	−1.73659	+	8.17001i	−0.123727	+	0.582089i	−0.995708	+	0.0925496i	$0.970498\pi$
$198$	0.635219	+	0.0667642i	0.0451431	+	0.00474473i
$199$	−0.976176	−	9.28769i	−0.0691993	−	0.658387i	−0.973059	−	0.230558i	$-0.925945\pi$
$199$	−0.976176	−	9.28769i	−0.0691993	−	0.658387i	0.903859	−	0.427830i	$-0.140722\pi$
$200$	2.55948	−	4.29524i	0.180983	−	0.303719i
$201$	5.11854	−	3.71884i	0.361034	−	0.262307i
$202$	−2.31625	−	3.18804i	−0.162971	−	0.224310i
$203$	0.278756	+	1.31145i	0.0195649	+	0.0920454i
$204$	0.422764	+	4.02233i	0.0295994	+	0.281620i
$205$	8.41674	+	4.36191i	0.587851	+	0.304649i
$206$	6.40995	+	1.36248i	0.446603	+	0.0949283i
$207$	0.392266	+	0.881045i	0.0272644	+	0.0612369i
$208$	4.12134	−	3.71087i	0.285764	−	0.257303i
$209$	0.372857	−	1.14753i	0.0257910	−	0.0793767i
$210$	0.737848	−	0.369566i	0.0509164	−	0.0255025i
$211$	−6.59390	−	11.4210i	−0.453942	−	0.786251i	0.544684	−	0.838641i	$-0.316650\pi$
$211$	−6.59390	−	11.4210i	−0.453942	−	0.786251i	−0.998627	+	0.0523898i	$0.983316\pi$
$212$	0.436561	+	0.252049i	0.0299832	+	0.0173108i
$213$	−2.66512	+	0.865950i	−0.182611	+	0.0593339i
$214$	−7.43194	−	3.30891i	−0.508037	−	0.226193i
$215$	12.1412	+	18.9811i	0.828022	+	1.29450i
$216$	−1.00000			−0.0680414
$217$	−0.889581	−	1.85225i	−0.0603887	−	0.125739i
$218$		−	16.1743i		−	1.09546i
$219$	−6.86195	−	4.98550i	−0.463688	−	0.336889i
$220$	1.01684	−	1.00291i	0.0685555	−	0.0676165i
$221$	−6.93124	−	21.3322i	−0.466246	−	1.43496i
$222$	−4.46700	−	2.57902i	−0.299806	−	0.173093i
$223$	8.79002	−	5.07492i	0.588623	−	0.339842i	−0.175930	−	0.984403i	$-0.556293\pi$
$223$	8.79002	−	5.07492i	0.588623	−	0.339842i	0.764553	+	0.644561i	$0.222960\pi$
$224$	−0.246944	+	0.274259i	−0.0164997	+	0.0183247i
$225$	4.36419	−	2.44005i	0.290946	−	0.162670i
$226$	−9.69795	−	10.7707i	−0.645098	−	0.716454i
$227$	5.61618	+	12.6141i	0.372759	+	0.837230i	0.998369	+	0.0570940i	$0.0181835\pi$
$227$	5.61618	+	12.6141i	0.372759	+	0.837230i	−0.625610	+	0.780136i	$0.715150\pi$
$228$	−0.392762	+	1.84780i	−0.0260113	+	0.122373i
$229$	−0.469169	+	4.46385i	−0.0310036	+	0.294979i	0.968023	+	0.250862i	$0.0807141\pi$
$229$	−0.469169	+	4.46385i	−0.0310036	+	0.294979i	−0.999026	+	0.0441171i	$0.985953\pi$
$230$	2.07914	+	0.572498i	0.137094	+	0.0377494i
$231$	0.230569	−	0.0490091i	0.0151704	−	0.00322456i
$232$	−2.13539	−	2.93911i	−0.140195	−	0.192962i
$233$	10.0614	+	13.8483i	0.659144	+	0.907234i	0.999453	−	0.0330798i	$-0.0105315\pi$
$233$	10.0614	+	13.8483i	0.659144	+	0.907234i	−0.340309	+	0.940314i	$0.610532\pi$
$234$	5.42462	−	1.15304i	0.354619	−	0.0753765i
$235$	3.99616	−	14.5128i	0.260681	−	0.946712i
$236$	−0.340799	+	3.24249i	−0.0221841	+	0.211068i
$237$	0.774630	−	3.64435i	0.0503176	−	0.236726i
$238$	0.607107	+	1.36358i	0.0393529	+	0.0883880i
$239$	−2.47726	−	2.75127i	−0.160240	−	0.177965i	0.657678	−	0.753299i	$-0.271539\pi$
$239$	−2.47726	−	2.75127i	−0.160240	−	0.177965i	−0.817918	+	0.575334i	$0.804872\pi$
$240$	−1.41915	+	1.72801i	−0.0916059	+	0.111542i
$241$	−12.8557	+	14.2776i	−0.828105	+	0.919704i	−0.997834	−	0.0657868i	$-0.979044\pi$
$241$	−12.8557	+	14.2776i	−0.828105	+	0.919704i	0.169728	+	0.985491i	$0.445711\pi$
$242$	−9.17297	+	5.29602i	−0.589661	+	0.340441i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−1.10758	−	3.40879i	−0.0709058	−	0.218226i
$245$	−10.9272	+	10.7775i	−0.698113	+	0.688551i
$246$	−3.42985	−	2.49193i	−0.218679	−	0.158880i
$247$		−	10.4765i		−	0.666603i
$248$	4.24344	+	3.60461i	0.269459	+	0.228893i
$249$	11.6551			0.738612
$250$	1.97704	−	11.0041i	0.125039	−	0.695964i
$251$	5.05190	+	2.24925i	0.318873	+	0.141972i	0.559931	−	0.828539i	$-0.310828\pi$
$251$	5.05190	+	2.24925i	0.318873	+	0.141972i	−0.241058	+	0.970511i	$0.577494\pi$
$252$	−0.350990	+	0.114043i	−0.0221103	+	0.00718406i
$253$	0.533467	+	0.307997i	0.0335388	+	0.0193636i
$254$	−4.28909	−	7.42892i	−0.269121	−	0.466132i
$255$	4.05011	+	8.08616i	0.253628	+	0.506375i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	6.85710	−	6.17416i	0.427734	−	0.385134i	−0.426956	−	0.904273i	$-0.640414\pi$
$257$	6.85710	−	6.17416i	0.427734	−	0.385134i	0.854690	+	0.519139i	$0.173747\pi$
$258$	−4.09852	−	9.20543i	−0.255163	−	0.573105i
$259$	−1.86199	−	0.395779i	−0.115699	−	0.0245925i
$260$	5.70591	−	11.0101i	0.353865	−	0.682819i
$261$	−0.379745	−	3.61303i	−0.0235056	−	0.223641i
$262$	2.31886	+	10.9094i	0.143260	+	0.673983i
$263$	7.08901	+	9.75719i	0.437127	+	0.601654i	0.969571	−	0.244812i	$-0.0787261\pi$
$263$	7.08901	+	9.75719i	0.437127	+	0.601654i	−0.532444	+	0.846466i	$0.678726\pi$
$264$	−0.516734	+	0.375429i	−0.0318028	+	0.0231061i
$265$	1.11208	+	0.184005i	0.0683143	+	0.0113034i
$266$	0.0728741	+	0.693351i	0.00446820	+	0.0425120i
$267$	−6.29242	−	0.661360i	−0.385090	−	0.0404746i
$268$	−1.31543	+	6.18861i	−0.0803526	+	0.378029i
$269$	−17.3926	+	7.74369i	−1.06045	+	0.472141i	−0.861441	−	0.507857i	$-0.830438\pi$
$269$	−17.3926	+	7.74369i	−1.06045	+	0.472141i	−0.199005	+	0.979998i	$0.563771\pi$
$270$	−2.09303	+	0.786921i	−0.127377	+	0.0478905i
$271$	−5.74094	+	17.6688i	−0.348737	+	1.07330i	0.610815	+	0.791773i	$0.290842\pi$
$271$	−5.74094	+	17.6688i	−0.348737	+	1.07330i	−0.959552	+	0.281530i	$0.909158\pi$
$272$	−3.00564	−	2.70629i	−0.182244	−	0.164093i
$273$	1.77249	−	1.02335i	0.107276	−	0.0619358i
$274$	6.47410	−	11.2135i	0.391114	−	0.677430i
$275$	1.33906	−	2.89930i	0.0807485	−	0.174834i
$276$	−0.881045	−	0.392266i	−0.0530327	−	0.0236117i
$277$	15.6123	−	21.4885i	0.938052	−	1.29112i	−0.0185820	−	0.999827i	$-0.505915\pi$
$277$	15.6123	−	21.4885i	0.938052	−	1.29112i	0.956634	−	0.291291i	$-0.0940848\pi$
$278$			9.01142i			0.540469i
$279$	1.87262	+	5.24341i	0.112111	+	0.313914i
$280$	−0.301040	+	0.768358i	−0.0179906	+	0.0459182i
$281$	−17.3025	−	12.5710i	−1.03218	−	0.749925i	−0.0634382	−	0.997986i	$-0.520207\pi$
$281$	−17.3025	−	12.5710i	−1.03218	−	0.749925i	−0.968744	+	0.248061i	$0.920207\pi$
$282$	−2.73810	+	6.14988i	−0.163052	+	0.366220i
$283$	−25.0115	+	8.12674i	−1.48678	+	0.483085i	−0.936131	−	0.351651i	$-0.885620\pi$
$283$	−25.0115	+	8.12674i	−1.48678	+	0.483085i	−0.550650	+	0.834736i	$0.685620\pi$
$284$	1.40114	−	2.42684i	0.0831421	−	0.144006i
$285$	0.632011	+	4.17656i	0.0374371	+	0.247398i
$286$	2.37020	−	2.63238i	0.140153	−	0.155656i
$287$	−1.48803	−	0.483490i	−0.0878356	−	0.0285395i
$288$	0.743145	−	0.669131i	0.0437902	−	0.0394289i
$289$	0.586605	−	0.261173i	0.0345062	−	0.0153631i
$290$	−6.78226	−	4.47125i	−0.398268	−	0.262561i
$291$	0.847025	−	8.05891i	0.0496535	−	0.472422i
$292$	8.43538	−	0.886594i	0.493643	−	0.0518840i
$293$	−4.29695	−	20.2155i	−0.251030	−	1.18100i	−0.905310	−	0.424752i	$-0.860361\pi$
$293$	−4.29695	−	20.2155i	−0.251030	−	1.18100i	0.654280	−	0.756253i	$-0.272972\pi$
$294$	5.55293	−	4.03444i	0.323854	−	0.235293i
$295$	1.83828	+	7.05479i	0.107029	+	0.410746i
$296$	5.04533	−	1.07242i	0.293254	−	0.0623331i
$297$	−0.635219	+	0.0667642i	−0.0368592	+	0.00387405i
$298$	−3.90771	−	0.410717i	−0.226368	−	0.0237922i
$299$	5.23164	+	1.11202i	0.302553	+	0.0643097i
$300$	−1.61052	+	4.73352i	−0.0929833	+	0.273290i
$301$	−2.48836	−	2.76360i	−0.143427	−	0.159291i
$302$	−5.72004	−	1.85856i	−0.329152	−	0.106948i
$303$	2.92846	+	2.63680i	0.168236	+	0.151480i
$304$	−0.944540	−	1.63599i	−0.0541731	−	0.0938305i
$305$	−5.00065	−	6.26311i	−0.286336	−	0.358625i
$306$	−1.24982	−	3.84654i	−0.0714472	−	0.219892i
$307$	10.5096	−	23.6051i	0.599817	−	1.34721i	−0.317198	−	0.948359i	$-0.602742\pi$
$307$	10.5096	−	23.6051i	0.599817	−	1.34721i	0.917015	−	0.398852i	$-0.130591\pi$
$308$	−0.138553	+	0.190702i	−0.00789479	+	0.0108662i
$309$	−6.55316			−0.372796
$310$	11.7182	+	4.20530i	0.665547	+	0.238845i
$311$	−23.9613			−1.35872			−0.679360	−	0.733805i	$-0.737742\pi$
$311$	−23.9613			−1.35872			−0.679360	+	0.733805i	$0.737742\pi$
$312$	−3.25975	+	4.48666i	−0.184547	+	0.254007i
$313$	−1.44931	+	3.25521i	−0.0819199	+	0.183995i	−0.949861	−	0.312671i	$-0.898776\pi$
$313$	−1.44931	+	3.25521i	−0.0819199	+	0.183995i	0.867941	+	0.496667i	$0.165443\pi$
$314$	−5.57645	−	17.1626i	−0.314697	−	0.968539i
$315$	−0.644887	+	0.514897i	−0.0363353	+	0.0290112i
$316$	1.86288	+	3.22661i	0.104795	+	0.181511i
$317$	−25.1924	−	22.6834i	−1.41495	−	1.27403i	−0.912293	−	0.409539i	$-0.865690\pi$
$317$	−25.1924	−	22.6834i	−1.41495	−	1.27403i	−0.502656	−	0.864487i	$-0.667644\pi$
$318$	−0.479425	−	0.155775i	−0.0268848	−	0.00873541i
$319$	−1.55267	−	1.72441i	−0.0869326	−	0.0965484i
$320$	−0.101626	−	2.23376i	−0.00568106	−	0.124871i
$321$	7.95749	+	1.69142i	0.444144	+	0.0944057i
$322$	−0.353973	−	0.0372041i	−0.0197262	−	0.00207330i
$323$	−7.59851	+	0.798635i	−0.422792	+	0.0444373i
$324$	0.978148	−	0.207912i	0.0543415	−	0.0115506i
$325$	3.27852	−	27.5346i	0.181859	−	1.52734i
$326$	−9.13179	+	6.63463i	−0.505763	+	0.367458i
$327$	3.36283	+	15.8209i	0.185965	+	0.874897i
$328$	4.21630	−	0.443151i	0.232806	−	0.0244689i
$329$	−0.259692	+	2.47081i	−0.0143173	+	0.136220i
$330$	−0.786104	+	1.19241i	−0.0432736	+	0.0656401i
$331$	−29.6626	+	13.2066i	−1.63040	+	0.725902i	−0.998780	−	0.0493742i	$-0.984277\pi$
$331$	−29.6626	+	13.2066i	−1.63040	+	0.725902i	−0.631622	+	0.775276i	$0.717611\pi$
$332$	−8.66143	+	7.79878i	−0.475358	+	0.428014i
$333$	4.90560	+	1.59392i	0.268825	+	0.0873466i
$334$	13.8758	−	15.4106i	0.759248	−	0.843231i
$335$	2.11672	+	13.9881i	0.115649	+	0.764249i
$336$	0.184526	−	0.319609i	0.0100667	−	0.0174361i
$337$	−31.0857	+	10.1004i	−1.69335	+	0.550201i	−0.987425	−	0.158090i	$-0.949466\pi$
$337$	−31.0857	+	10.1004i	−1.69335	+	0.550201i	−0.705921	+	0.708291i	$0.749466\pi$
$338$	7.22203	−	16.2209i	0.392827	−	0.882303i
$339$	11.7254	+	8.51899i	0.636835	+	0.462688i
$340$	−8.42052	−	3.29913i	−0.456667	−	0.178921i
$341$	2.93617	+	2.00641i	0.159003	+	0.108653i
$342$		−	1.88908i		−	0.102150i
$343$	3.00739	−	4.13931i	0.162384	−	0.223502i
$344$	9.20543	+	4.09852i	0.496323	+	0.220977i
$345$	−2.15273	−	0.127711i	−0.115899	−	0.00687573i
$346$	2.08972	−	3.61950i	0.112344	−	0.194586i
$347$	15.0693	−	8.70025i	0.808961	−	0.467054i	−0.0376340	−	0.999292i	$-0.511982\pi$
$347$	15.0693	−	8.70025i	0.808961	−	0.467054i	0.846595	+	0.532238i	$0.178649\pi$
$348$	2.69980	+	2.43091i	0.144724	+	0.130310i
$349$	−5.96388	+	18.3549i	−0.319239	+	0.982518i	0.654735	+	0.755859i	$0.272780\pi$
$349$	−5.96388	+	18.3549i	−0.319239	+	0.982518i	−0.973974	+	0.226659i	$0.927220\pi$
$350$	−0.0254481	+	1.84509i	−0.00136026	+	0.0986240i
$351$	−5.06635	+	2.25569i	−0.270422	+	0.120400i
$352$	0.132797	−	0.624761i	0.00707810	−	0.0332999i
$353$	16.8516	+	1.77118i	0.896921	+	0.0942702i	0.541758	−	0.840534i	$-0.317759\pi$
$353$	16.8516	+	1.77118i	0.896921	+	0.0942702i	0.355163	+	0.934804i	$0.384425\pi$
$354$	−0.340799	−	3.24249i	−0.0181133	−	0.172336i
$355$	1.02288	−	6.18202i	0.0542890	−	0.328108i
$356$	5.11872	−	3.71897i	0.271291	−	0.197105i
$357$	−0.877345	−	1.20756i	−0.0464340	−	0.0639109i
$358$	2.99690	+	14.0993i	0.158391	+	0.745170i
$359$	1.10655	+	10.5282i	0.0584017	+	0.555655i	0.984128	+	0.177461i	$0.0567882\pi$
$359$	1.10655	+	10.5282i	0.0584017	+	0.555655i	−0.925726	+	0.378194i	$0.876545\pi$
$360$	1.02887	−	1.98530i	0.0542261	−	0.104635i
$361$	15.0942	+	3.20836i	0.794430	+	0.168861i
$362$	4.06039	+	9.11979i	0.213409	+	0.479325i
$363$	7.87142	−	7.08746i	0.413142	−	0.371995i
$364$	−0.632464	+	1.94652i	−0.0331501	+	0.102026i
$365$	16.9578	−	8.49364i	0.887611	−	0.444577i
$366$	1.79211	+	3.10402i	0.0936750	+	0.162250i
$367$	−26.5945	−	15.3543i	−1.38822	−	0.801489i	−0.395106	−	0.918636i	$-0.629292\pi$
$367$	−26.5945	−	15.3543i	−1.38822	−	0.801489i	−0.993115	+	0.117146i	$0.962625\pi$
$368$	0.917222	−	0.298023i	0.0478135	−	0.0155355i
$369$	3.87300	+	1.72437i	0.201620	+	0.0897671i
$370$	9.71610	−	6.21488i	0.505116	−	0.323096i
$371$	−0.186038			−0.00965864
$372$	−4.90015	−	2.64358i	−0.254061	−	0.137063i
$373$			27.7128i			1.43491i	0.696604	+	0.717456i	$0.254694\pi$
$373$			27.7128i			1.43491i	−0.696604	+	0.717456i	$0.745306\pi$
$374$	−2.08992	−	1.51842i	−0.108067	−	0.0785155i
$375$	0.354052	+	11.1747i	0.0182832	+	0.577061i
$376$	−2.08027	−	6.40240i	−0.107282	−	0.330179i
$377$	−17.4483	−	10.0738i	−0.898634	−	0.518827i
$378$	0.319609	−	0.184526i	0.0164389	−	0.00949101i
$379$	−5.12436	+	5.69118i	−0.263221	+	0.292336i	−0.860239	−	0.509892i	$-0.829685\pi$
$379$	−5.12436	+	5.69118i	−0.263221	+	0.292336i	0.597018	+	0.802228i	$0.296352\pi$
$380$	−3.26434	−	2.68089i	−0.167457	−	0.137527i
$381$	5.73992	+	6.37483i	0.294065	+	0.326592i
$382$	0.867602	+	1.94867i	0.0443904	+	0.0997024i
$383$	−6.18965	+	29.1200i	−0.316276	+	1.48796i	0.476892	+	0.878962i	$0.341763\pi$
$383$	−6.18965	+	29.1200i	−0.316276	+	1.48796i	−0.793169	+	0.609002i	$0.791570\pi$
$384$	−0.104528	+	0.994522i	−0.00533420	+	0.0507515i
$385$	−0.139928	+	0.508174i	−0.00713138	+	0.0258990i
$386$	−2.09196	+	0.444660i	−0.106478	+	0.0226326i
$387$	5.92287	+	8.15214i	0.301077	+	0.414396i
$388$	4.76300	+	6.55571i	0.241805	+	0.332816i
$389$	20.3124	−	4.31753i	1.02988	−	0.218908i	0.338171	−	0.941085i	$-0.390192\pi$
$389$	20.3124	−	4.31753i	1.02988	−	0.218908i	0.691708	+	0.722177i	$0.256858\pi$
$390$	−3.29209	+	11.9558i	−0.166701	+	0.605408i
$391$	0.407724	−	3.87923i	0.0206195	−	0.196181i
$392$	−1.42706	+	6.71381i	−0.0720776	+	0.339099i
$393$	−4.53637	−	10.1889i	−0.228830	−	0.513960i
$394$	5.58893	+	6.20714i	0.281566	+	0.312711i
$395$	6.43814	+	5.28743i	0.323938	+	0.266039i
$396$	0.427386	−	0.474660i	0.0214769	−	0.0238526i
$397$	7.74447	−	4.47127i	0.388684	−	0.224407i	−0.292906	−	0.956141i	$-0.594622\pi$
$397$	7.74447	−	4.47127i	0.388684	−	0.224407i	0.681590	+	0.731735i	$0.261289\pi$
$398$	−8.08768	−	4.66943i	−0.405399	−	0.234057i
$399$	−0.215437	−	0.663048i	−0.0107854	−	0.0331939i
$400$	−1.97050	−	4.59534i	−0.0985248	−	0.229767i
$401$	15.1599	+	11.0143i	0.757049	+	0.550028i	0.898004	−	0.439988i	$-0.145017\pi$
$401$	15.1599	+	11.0143i	0.757049	+	0.550028i	−0.140955	+	0.990016i	$0.545017\pi$
$402$		−	6.32687i		−	0.315555i
$403$	29.6296	+	8.69038i	1.47596	+	0.432898i
$404$	−3.94064			−0.196054
$405$	1.88368	−	1.20489i	0.0936007	−	0.0598714i
$406$	1.22483	+	0.545330i	0.0607873	+	0.0270643i
$407$	3.13329	−	1.01807i	0.155312	−	0.0504638i
$408$	3.50263	+	2.02224i	0.173406	+	0.100116i
$409$	11.3517	+	19.6618i	0.561307	+	0.972213i	0.997383	+	0.0723028i	$0.0230348\pi$
$409$	11.3517	+	19.6618i	0.561307	+	0.972213i	−0.436075	+	0.899910i	$0.643632\pi$
$410$	8.47609	−	4.24542i	0.418604	−	0.209666i
$411$	−4.00121	+	12.3145i	−0.197365	+	0.607428i
$412$	4.86994	−	4.38492i	0.239925	−	0.216029i
$413$	−0.489401	−	1.09921i	−0.0240819	−	0.0540888i
$414$	0.943349	+	0.200515i	0.0463631	+	0.00985477i
$415$	−11.9916	+	23.1389i	−0.588643	+	1.13584i
$416$	−0.579695	−	5.51543i	−0.0284219	−	0.270416i
$417$	−1.87358	−	8.81450i	−0.0917496	−	0.431648i
$418$	−0.709216	−	0.976152i	−0.0346889	−	0.0477451i
$419$	−18.5079	+	13.4467i	−0.904168	+	0.656916i	−0.939533	−	0.342458i	$-0.888741\pi$
$419$	−18.5079	+	13.4467i	−0.904168	+	0.656916i	0.0353654	+	0.999374i	$0.488741\pi$
$420$	0.134711	−	0.814157i	0.00657324	−	0.0397268i
$421$	2.82446	+	26.8730i	0.137656	+	1.30971i	0.817319	+	0.576185i	$0.195459\pi$
$421$	2.82446	+	26.8730i	0.137656	+	1.30971i	−0.679663	+	0.733524i	$0.737874\pi$
$422$	−13.1155	−	1.37850i	−0.638455	−	0.0671043i
$423$	1.39964	−	6.58478i	0.0680527	−	0.320163i
$424$	0.460516	−	0.205035i	0.0223646	−	0.00995738i
$425$	−20.2205	−	0.278889i	−0.980839	−	0.0135281i
$426$	−0.865950	+	2.66512i	−0.0419554	+	0.129125i
$427$	0.983005	+	0.885102i	0.0475710	+	0.0428331i
$428$	−7.04535	+	4.06763i	−0.340550	+	0.196617i
$429$	−1.77111	+	3.06764i	−0.0855098	+	0.148107i
$430$	22.4924	+	1.33436i	1.08468	+	0.0643487i
$431$	−10.3992	−	4.63004i	−0.500914	−	0.223021i	0.140695	−	0.990053i	$-0.455066\pi$
$431$	−10.3992	−	4.63004i	−0.500914	−	0.223021i	−0.641609	+	0.767032i	$0.721733\pi$
$432$	−0.587785	+	0.809017i	−0.0282798	+	0.0389238i
$433$			16.6354i			0.799448i	0.916636	+	0.399724i	$0.130894\pi$
$433$			16.6354i			0.799448i	−0.916636	+	0.399724i	$0.869106\pi$
$434$	−2.02139	−	0.369040i	−0.0970296	−	0.0177145i
$435$	7.56368	+	2.96343i	0.362651	+	0.142085i
$436$	−13.0853	−	9.50704i	−0.626673	−	0.455305i
$437$	0.741023	−	1.66436i	0.0354479	−	0.0796173i
$438$	−8.06671	+	2.62103i	−0.385442	+	0.125238i
$439$	−1.43154	+	2.47949i	−0.0683235	+	0.118340i	−0.898163	−	0.439662i	$-0.855098\pi$
$439$	−1.43154	+	2.47949i	−0.0683235	+	0.118340i	0.829840	+	0.558001i	$0.188432\pi$
$440$	−0.213690	−	1.41214i	−0.0101873	−	0.0673212i
$441$	−4.59278	+	5.10080i	−0.218704	+	0.242895i
$442$	−21.3322	−	6.93124i	−1.01467	−	0.329686i
$443$	−20.1095	+	18.1067i	−0.955433	+	0.860275i	−0.990276	−	0.139117i	$-0.955573\pi$
$443$	−20.1095	+	18.1067i	−0.955433	+	0.860275i	0.0348433	+	0.999393i	$0.488907\pi$
$444$	−4.71211	+	2.09797i	−0.223627	+	0.0995651i
$445$	7.78707	−	11.8119i	0.369143	−	0.559939i
$446$	1.06095	−	10.0942i	0.0502373	−	0.477976i
$447$	3.90771	−	0.410717i	0.184828	−	0.0194262i
$448$	0.0767303	+	0.360988i	0.00362517	+	0.0170551i
$449$	−6.73846	+	4.89577i	−0.318007	+	0.231046i	−0.735325	−	0.677715i	$-0.762970\pi$
$449$	−6.73846	+	4.89577i	−0.318007	+	0.231046i	0.417317	+	0.908761i	$0.362970\pi$
$450$	0.591170	−	4.96493i	0.0278680	−	0.234049i
$451$	2.64869	−	0.562996i	0.124722	−	0.0265104i
$452$	−14.4140	+	1.51497i	−0.677976	+	0.0712581i
$453$	5.98146	+	0.628677i	0.281034	+	0.0295378i
$454$	13.5062	+	2.87082i	0.633876	+	0.134734i
$455$	0.207997	+	4.57182i	0.00975106	+	0.214330i
$456$	1.26404	+	1.40386i	0.0591942	+	0.0657418i
$457$	37.5782	+	12.2099i	1.75783	+	0.571155i	0.996972	−	0.0777597i	$-0.0247767\pi$
$457$	37.5782	+	12.2099i	1.75783	+	0.571155i	0.760861	+	0.648914i	$0.224777\pi$
$458$	3.33556	+	3.00335i	0.155860	+	0.140337i
$459$	2.02224	+	3.50263i	0.0943903	+	0.163489i
$460$	1.68525	−	1.34555i	0.0785751	−	0.0627367i
$461$	6.95067	+	21.3920i	0.323725	+	0.996323i	0.972013	+	0.234928i	$0.0754853\pi$
$461$	6.95067	+	21.3920i	0.323725	+	0.996323i	−0.648288	+	0.761395i	$0.724515\pi$
$462$	0.0958762	−	0.215341i	0.00446056	−	0.0100186i
$463$	−15.4775	+	21.3030i	−0.719301	+	0.990033i	0.280246	+	0.959928i	$0.409584\pi$
$463$	−15.4775	+	21.3030i	−0.719301	+	0.990033i	−0.999547	+	0.0301045i	$0.990416\pi$
$464$	−3.63294			−0.168655
$465$	−12.3364	−	1.67706i	−0.572088	−	0.0777716i
$466$	17.1175			0.792952
$467$	−18.4693	+	25.4209i	−0.854660	+	1.17634i	0.128157	+	0.991754i	$0.459094\pi$
$467$	−18.4693	+	25.4209i	−0.854660	+	1.17634i	−0.982817	+	0.184584i	$0.940906\pi$
$468$	2.25569	−	5.06635i	0.104269	−	0.234192i
$469$	−0.721538	−	2.22067i	−0.0333175	−	0.102541i
$470$	−9.39224	−	11.7634i	−0.433232	−	0.542605i
$471$	9.02289	+	15.6281i	0.415753	+	0.720105i
$472$	2.42291	+	2.18160i	0.111523	+	0.100416i
$473$	6.12110	+	1.98887i	0.281448	+	0.0914481i
$474$	−2.49302	−	2.76878i	−0.114508	−	0.127174i
$475$	−8.94200	−	3.04240i	−0.410287	−	0.139595i
$476$	1.46001	+	0.310335i	0.0669195	+	0.0142242i
$477$	0.501336	+	0.0526926i	0.0229546	+	0.00241263i
$478$	−3.68192	+	0.386985i	−0.168407	+	0.0177003i
$479$	37.6429	−	8.00125i	1.71995	−	0.365587i	0.760910	−	0.648858i	$-0.224753\pi$
$479$	37.6429	−	8.00125i	1.71995	−	0.365587i	0.959040	+	0.283271i	$0.0914197\pi$
$480$	0.563829	+	2.16382i	0.0257352	+	0.0987642i
$481$	23.1424	−	16.8139i	1.05520	−	0.766649i
$482$	3.99450	+	18.7926i	0.181944	+	0.855981i
$483$	0.353973	−	0.0372041i	0.0161063	−	0.00169284i
$484$	−1.10717	+	10.5340i	−0.0503259	+	0.478819i
$485$	15.1279	+	9.97316i	0.686923	+	0.452858i
$486$	−0.913545	+	0.406737i	−0.0414393	+	0.0184499i
$487$	19.9394	−	17.9535i	0.903540	−	0.813551i	−0.0795201	−	0.996833i	$-0.525339\pi$
$487$	19.9394	−	17.9535i	0.903540	−	0.813551i	0.983060	+	0.183282i	$0.0586721\pi$
$488$	−3.40879	−	1.10758i	−0.154309	−	0.0501380i
$489$	7.55282	−	8.38826i	0.341550	−	0.379330i
$490$	2.29636	+	15.1752i	0.103739	+	0.685544i
$491$	14.0793	−	24.3861i	0.635391	−	1.10053i	−0.351041	−	0.936360i	$-0.614172\pi$
$491$	14.0793	−	24.3861i	0.635391	−	1.10053i	0.986432	−	0.164169i	$-0.0524943\pi$
$492$	−4.03203	+	1.31008i	−0.181778	+	0.0590632i
$493$	−5.97633	+	13.4231i	−0.269160	+	0.604544i
$494$	−8.47565	−	6.15792i	−0.381338	−	0.277058i
$495$	0.521009	−	1.32979i	0.0234176	−	0.0597698i
$496$	5.41042	−	1.31428i	0.242935	−	0.0590127i
$497$			1.03419i			0.0463896i
$498$	6.85070	−	9.42917i	0.306987	−	0.422531i
$499$	1.21984	+	0.543109i	0.0546077	+	0.0243129i	0.433859	−	0.900981i	$-0.357152\pi$
$499$	1.21984	+	0.543109i	0.0546077	+	0.0243129i	−0.379251	+	0.925294i	$0.623818\pi$
$500$	−7.74047	−	8.06754i	−0.346164	−	0.360791i
$501$	−10.3685	+	17.9588i	−0.463231	+	0.802339i
$502$	4.78912	−	2.76500i	0.213749	−	0.123408i
$503$	−17.5012	−	15.7581i	−0.780338	−	0.702620i	0.179319	−	0.983791i	$-0.442611\pi$
$503$	−17.5012	−	15.7581i	−0.780338	−	0.702620i	−0.959658	+	0.281171i	$0.909277\pi$
$504$	−0.114043	+	0.350990i	−0.00507990	+	0.0156343i
$505$	−8.24786	+	3.10097i	−0.367025	+	0.137991i
$506$	0.562739	−	0.250548i	0.0250168	−	0.0111382i
$507$	−3.69169	+	17.3680i	−0.163954	+	0.771341i
$508$	−8.53118	−	0.896664i	−0.378510	−	0.0397830i
$509$	−1.45439	−	13.8376i	−0.0644646	−	0.613340i	−0.978291	−	0.207235i	$-0.933553\pi$
$509$	−1.45439	−	13.8376i	−0.0644646	−	0.613340i	0.913826	−	0.406105i	$-0.133113\pi$
$510$	8.92244	+	1.47632i	0.395092	+	0.0653724i
$511$	−2.53242	+	1.83991i	−0.112028	+	0.0813929i
$512$	−0.587785	−	0.809017i	−0.0259767	−	0.0357538i
$513$	0.392762	+	1.84780i	0.0173409	+	0.0815823i
$514$	−0.964499	−	9.17660i	−0.0425422	−	0.404762i
$515$	6.74233	−	13.0100i	0.297103	−	0.573289i
$516$	−9.85640	−	2.09504i	−0.433904	−	0.0922291i
$517$	−1.74888	−	3.92804i	−0.0769155	−	0.172755i
$518$	−1.41464	+	1.27375i	−0.0621559	+	0.0559654i
$519$	−1.29152	+	3.97489i	−0.0566914	+	0.174478i
$520$	−5.55353	−	11.0878i	−0.243538	−	0.486231i
$521$	6.68977	+	11.5870i	0.293084	+	0.507636i	0.974537	−	0.224225i	$-0.0719851\pi$
$521$	6.68977	+	11.5870i	0.293084	+	0.507636i	−0.681453	+	0.731862i	$0.738652\pi$
$522$	−3.14621	−	1.81647i	−0.137706	−	0.0795046i
$523$	−17.0213	+	5.53054i	−0.744288	+	0.241834i	−0.656521	−	0.754307i	$-0.727973\pi$
$523$	−17.0213	+	5.53054i	−0.744288	+	0.241834i	−0.0877662	+	0.996141i	$0.527973\pi$
$524$	10.1889	+	4.53637i	0.445102	+	0.198172i
$525$	−0.358723	−	1.81006i	−0.0156560	−	0.0789974i
$526$	12.0605			0.525865
$527$	4.04435	−	22.1526i	0.176175	−	0.964982i
$528$			0.638718i			0.0277966i
$529$	−17.8549	−	12.9724i	−0.776301	−	0.564015i
$530$	0.802526	−	0.791533i	0.0348595	−	0.0343820i
$531$	1.00750	+	3.10077i	0.0437219	+	0.134562i
$532$	0.603767	+	0.348585i	0.0261766	+	0.0151131i
$533$	20.3616	−	11.7558i	0.881960	−	0.509200i
$534$	−4.23364	+	4.70194i	−0.183208	+	0.203473i
$535$	−11.5452	+	14.0578i	−0.499142	+	0.607772i
$536$	4.23350	+	4.70178i	0.182859	+	0.203086i
$537$	−5.86281	−	13.1681i	−0.252999	−	0.568245i
$538$	−3.95835	+	18.6226i	−0.170656	+	0.802875i
$539$	−0.458256	+	4.36002i	−0.0197385	+	0.187799i
$540$	−0.593617	+	2.15583i	−0.0255452	+	0.0927723i
$541$	40.7098	−	8.65313i	1.75025	−	0.372027i	0.782248	−	0.622967i	$-0.214073\pi$
$541$	40.7098	−	8.65313i	1.75025	−	0.372027i	0.968003	+	0.250940i	$0.0807397\pi$
$542$	10.9199	+	15.0300i	0.469051	+	0.645593i
$543$	−5.86777	−	8.07630i	−0.251810	−	0.346587i
$544$	−3.95611	+	0.840896i	−0.169617	+	0.0360531i
$545$	−34.8692	−	9.60136i	−1.49363	−	0.411277i
$546$	0.213938	−	2.03548i	0.00915570	−	0.0871107i
$547$	−6.25688	+	29.4363i	−0.267525	+	1.25861i	0.615070	+	0.788472i	$0.289128\pi$
$547$	−6.25688	+	29.4363i	−0.267525	+	1.25861i	−0.882595	+	0.470134i	$0.844206\pi$
$548$	−5.26650	−	11.8288i	−0.224974	−	0.505300i
$549$	−2.39831	−	2.66359i	−0.102357	−	0.113679i
$550$	−1.55850	−	2.78749i	−0.0664547	−	0.118859i
$551$	−4.59218	+	5.10013i	−0.195633	+	0.217273i
$552$	−0.835215	+	0.482212i	−0.0355491	+	0.0205243i
$553$	−1.19079	−	0.687501i	−0.0506374	−	0.0292355i
$554$	−8.20787	−	25.2612i	−0.348719	−	1.07325i
$555$	−8.21164	+	8.09916i	−0.348565	+	0.343790i
$556$	7.29039	+	5.29678i	0.309182	+	0.224634i
$557$		−	28.4695i		−	1.20629i	−0.797631	−	0.603146i	$-0.793914\pi$
$557$		−	28.4695i		−	1.20629i	0.797631	−	0.603146i	$-0.206086\pi$
$558$	5.34270	+	1.56702i	0.226175	+	0.0663371i
$559$	55.8829			2.36359
$560$	0.444667	+	0.695176i	0.0187906	+	0.0293765i
$561$	2.35995	+	1.05072i	0.0996372	+	0.0443613i
$562$	−20.3403	+	6.60898i	−0.858006	+	0.278783i
$563$	2.95330	+	1.70509i	0.124467	+	0.0718609i	0.560941	−	0.827856i	$-0.310440\pi$
$563$	2.95330	+	1.70509i	0.124467	+	0.0718609i	−0.436474	+	0.899717i	$0.643773\pi$
$564$	3.36594	+	5.82998i	0.141732	+	0.245487i
$565$	−28.9766	+	14.5135i	−1.21906	+	0.610588i
$566$	−8.12674	+	25.0115i	−0.341592	+	1.05131i
$567$	−0.274259	+	0.246944i	−0.0115178	+	0.0103707i
$568$	−1.13979	−	2.56000i	−0.0478244	−	0.107415i
$569$	−4.34948	−	0.924511i	−0.182340	−	0.0387575i	0.115837	−	0.993268i	$-0.463045\pi$
$569$	−4.34948	−	0.924511i	−0.182340	−	0.0387575i	−0.298177	+	0.954511i	$0.596378\pi$
$570$	3.75040	+	1.94361i	0.157087	+	0.0814090i
$571$	−1.82543	−	17.3678i	−0.0763917	−	0.726818i	−0.963943	−	0.266109i	$-0.914262\pi$
$571$	−1.82543	−	17.3678i	−0.0763917	−	0.726818i	0.887551	−	0.460709i	$-0.152405\pi$
$572$	−0.736467	−	3.46481i	−0.0307932	−	0.144871i
$573$	−1.25379	−	1.72570i	−0.0523780	−	0.0720921i
$574$	−1.26579	+	0.919653i	−0.0528332	+	0.0383856i
$575$	2.46842	−	4.14243i	0.102940	−	0.172751i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	−16.9992	−	1.78669i	−0.707688	−	0.0743810i	−0.256155	−	0.966636i	$-0.582456\pi$
$577$	−16.9992	−	1.78669i	−0.707688	−	0.0743810i	−0.451533	+	0.892255i	$0.649123\pi$
$578$	0.133504	−	0.628087i	0.00555304	−	0.0261250i
$579$	1.95380	−	0.869887i	0.0811971	−	0.0361513i
$580$	−7.60383	+	2.85883i	−0.315732	+	0.118707i
$581$	1.32919	−	4.09082i	0.0551440	−	0.169716i
$582$	−6.02193	−	5.42217i	−0.249617	−	0.224756i
$583$	0.278840	−	0.160988i	0.0115484	−	0.00666745i
$584$	4.24092	−	7.34549i	0.175491	−	0.303958i
$585$	0.734388	−	12.3790i	0.0303632	−	0.511811i
$586$	−18.8804	−	8.40609i	−0.779942	−	0.347253i
$587$	−9.54853	+	13.1424i	−0.394110	+	0.542446i	−0.959253	−	0.282547i	$-0.908821\pi$
$587$	−9.54853	+	13.1424i	−0.394110	+	0.542446i	0.565144	+	0.824993i	$0.308821\pi$
$588$		−	6.86380i		−	0.283058i
$589$	4.99394	−	9.25678i	0.205772	−	0.381419i
$590$	6.78796	+	2.65950i	0.279456	+	0.109490i
$591$	−6.75734	−	4.90949i	−0.277960	−	0.201950i
$592$	2.09797	−	4.71211i	0.0862259	−	0.193667i
$593$	−10.1084	+	3.28442i	−0.415103	+	0.134875i	−0.509120	−	0.860695i	$-0.670029\pi$
$593$	−10.1084	+	3.28442i	−0.415103	+	0.134875i	0.0940172	+	0.995571i	$0.470029\pi$
$594$	−0.319359	+	0.553146i	−0.0131035	+	0.0226959i
$595$	3.30005	−	0.499374i	0.135289	−	0.0204724i
$596$	−2.62917	+	2.91999i	−0.107695	+	0.119607i
$597$	8.88178	+	2.88586i	0.363507	+	0.118111i
$598$	3.97472	−	3.57885i	0.162538	−	0.146350i
$599$	−12.1491	+	5.40913i	−0.496399	+	0.221011i	−0.639637	−	0.768677i	$-0.720915\pi$
$599$	−12.1491	+	5.40913i	−0.496399	+	0.221011i	0.143238	+	0.989688i	$0.454249\pi$
$600$	2.88286	+	4.08523i	0.117692	+	0.166779i
$601$	−3.33925	+	31.7708i	−0.136211	+	1.29596i	0.686346	+	0.727275i	$0.259214\pi$
$601$	−3.33925	+	31.7708i	−0.136211	+	1.29596i	−0.822556	+	0.568683i	$0.807453\pi$
$602$	−3.69842	+	0.388720i	−0.150736	+	0.0158430i
$603$	1.31543	+	6.18861i	0.0535684	+	0.252020i
$604$	−4.86576	+	3.53518i	−0.197985	+	0.143845i
$605$	5.97210	+	22.9192i	0.242801	+	0.931799i
$606$	3.85453	−	0.819305i	0.156579	−	0.0332820i
$607$	25.5844	−	2.68903i	1.03844	−	0.109144i	0.430067	−	0.902797i	$-0.358490\pi$
$607$	25.5844	−	2.68903i	1.03844	−	0.109144i	0.608371	+	0.793653i	$0.291823\pi$
$608$	−1.87873	−	0.197463i	−0.0761926	−	0.00800817i
$609$	−1.31145	−	0.278756i	−0.0531425	−	0.0112958i
$610$	−8.00627	+	0.364249i	−0.324164	+	0.0147480i
$611$	−24.9812	−	27.7444i	−1.01063	−	1.12242i
$612$	−3.84654	−	1.24982i	−0.155487	−	0.0505208i
$613$	18.0798	+	16.2791i	0.730235	+	0.657507i	0.947919	−	0.318513i	$-0.103183\pi$
$613$	18.0798	+	16.2791i	0.730235	+	0.657507i	−0.217684	+	0.976019i	$0.569850\pi$
$614$	−12.9195	−	22.3772i	−0.521388	−	0.903070i
$615$	−7.40820	+	5.91493i	−0.298727	+	0.238513i
$616$	0.0728416	+	0.224184i	0.00293487	+	0.00903261i
$617$	6.15647	−	13.8277i	0.247850	−	0.556681i	−0.746185	−	0.665739i	$-0.768117\pi$
$617$	6.15647	−	13.8277i	0.247850	−	0.556681i	0.994035	+	0.109058i	$0.0347833\pi$
$618$	−3.85185	+	5.30161i	−0.154944	+	0.213262i
$619$	−32.7194			−1.31510			−0.657551	−	0.753410i	$-0.728408\pi$
$619$	−32.7194			−1.31510			−0.657551	+	0.753410i	$0.728408\pi$
$620$	10.2899	−	7.00839i	0.413253	−	0.281464i
$621$	−0.964424			−0.0387010
$622$	−14.0841	+	19.3851i	−0.564720	+	0.777271i
$623$	−0.949740	+	2.13315i	−0.0380505	+	0.0854629i
$624$	1.71375	+	5.27438i	0.0686049	+	0.211144i
$625$	−22.5495	−	10.7944i	−0.901980	−	0.431777i
$626$	1.78163	+	3.08588i	0.0712084	+	0.123337i
$627$	0.896671	+	0.807366i	0.0358096	+	0.0322431i
$628$	−17.1626	−	5.57645i	−0.684861	−	0.222525i
$629$	−13.9592	−	15.5032i	−0.556589	−	0.618155i
$630$	0.0375053	+	0.824374i	0.00149425	+	0.0328438i
$631$	−3.86211	−	0.820917i	−0.153748	−	0.0326802i	0.130395	−	0.991462i	$-0.458376\pi$
$631$	−3.86211	−	0.820917i	−0.153748	−	0.0326802i	−0.284143	+	0.958782i	$0.591709\pi$
$632$	3.70535	+	0.389448i	0.147391	+	0.0154914i
$633$	13.1155	−	1.37850i	0.521296	−	0.0547904i
$634$	−33.1590	+	7.04816i	−1.31691	+	0.279918i
$635$	−18.5616	+	4.83663i	−0.736594	+	0.191936i
$636$	−0.407824	+	0.296301i	−0.0161713	+	0.0117491i
$637$	7.91423	+	37.2335i	0.313573	+	1.47525i
$638$	−2.30771	+	0.242550i	−0.0913631	+	0.00960265i
$639$	0.292917	−	2.78692i	0.0115876	−	0.110249i
$640$	−1.86688	−	1.23075i	−0.0737950	−	0.0486498i
$641$	10.6342	−	4.73466i	0.420027	−	0.187008i	−0.185830	−	0.982582i	$-0.559497\pi$
$641$	10.6342	−	4.73466i	0.420027	−	0.187008i	0.605856	+	0.795574i	$0.292831\pi$
$642$	6.04568	−	5.44356i	0.238604	−	0.214840i
$643$	3.67382	+	1.19370i	0.144881	+	0.0470747i	0.380560	−	0.924756i	$-0.375731\pi$
$643$	3.67382	+	1.19370i	0.144881	+	0.0470747i	−0.235679	+	0.971831i	$0.575731\pi$
$644$	−0.238159	+	0.264502i	−0.00938478	+	0.0104229i
$645$	−22.2783	+	3.37123i	−0.877208	+	0.132742i
$646$	−3.82018	+	6.61675i	−0.150303	+	0.260332i
$647$	−6.79226	+	2.20694i	−0.267031	+	0.0867637i	−0.439472	−	0.898256i	$-0.644835\pi$
$647$	−6.79226	+	2.20694i	−0.267031	+	0.0867637i	0.172441	+	0.985020i	$0.444835\pi$
$648$	0.406737	−	0.913545i	0.0159781	−	0.0358875i
$649$	1.68473	+	1.22403i	0.0661315	+	0.0480473i
$650$	−20.3489	−	18.8368i	−0.798148	−	0.738840i
$651$	2.05394	−	0.0592938i	0.0805003	−	0.00232391i
$652$			11.2875i			0.442053i
$653$	26.7487	−	36.8164i	1.04676	−	1.44074i	0.155169	−	0.987888i	$-0.450408\pi$
$653$	26.7487	−	36.8164i	1.04676	−	1.44074i	0.891587	−	0.452849i	$-0.149592\pi$
$654$	14.7760	+	6.57870i	0.577787	+	0.257247i
$655$	24.8953	+	1.47692i	0.972740	+	0.0577079i
$656$	2.11976	−	3.67153i	0.0827628	−	0.143349i
$657$	7.34549	−	4.24092i	0.286575	−	0.165454i
$658$	1.84628	+	1.66240i	0.0719756	+	0.0648071i
$659$	9.19457	−	28.2980i	0.358169	−	1.10233i	−0.595979	−	0.803000i	$-0.703236\pi$
$659$	9.19457	−	28.2980i	0.358169	−	1.10233i	0.954149	−	0.299333i	$-0.0967640\pi$
$660$	0.502621	+	1.33685i	0.0195645	+	0.0520369i
$661$	6.06092	−	2.69849i	0.235742	−	0.104959i	−0.285466	−	0.958389i	$-0.592148\pi$
$661$	6.06092	−	2.69849i	0.235742	−	0.104959i	0.521208	+	0.853430i	$0.325482\pi$
$662$	−6.75084	+	31.7602i	−0.262379	+	1.23439i
$663$	22.3071	+	2.34457i	0.866336	+	0.0910556i
$664$	1.21829	+	11.5913i	0.0472788	+	0.449828i
$665$	1.53801	+	0.254480i	0.0596414	+	0.00986832i
$666$	4.17295	−	3.03183i	0.161699	−	0.117481i
$667$	−2.05942	−	2.83454i	−0.0797409	−	0.109754i
$668$	−4.31147	−	20.2839i	−0.166816	−	0.784806i
$669$	1.06095	+	10.0942i	0.0410186	+	0.390266i
$670$	12.5607	+	6.50951i	0.485264	+	0.251484i
$671$	−2.23928	−	0.475973i	−0.0864463	−	0.0183747i
$672$	−0.150107	−	0.337146i	−0.00579051	−	0.0130057i
$673$	−28.3163	+	25.4961i	−1.09151	+	0.982803i	−0.999916	−	0.0129926i	$-0.995864\pi$
$673$	−28.3163	+	25.4961i	−1.09151	+	0.982803i	−0.0915982	+	0.995796i	$0.529198\pi$
$674$	−10.1004	+	31.0857i	−0.389051	+	1.19738i
$675$	0.454015	+	4.97934i	0.0174750	+	0.191655i
$676$	−8.87802	−	15.3772i	−0.341462	−	0.591430i
$677$	−17.6021	−	10.1626i	−0.676503	−	0.390579i	0.122033	−	0.992526i	$-0.461059\pi$
$677$	−17.6021	−	10.1626i	−0.676503	−	0.390579i	−0.798536	+	0.601947i	$0.794392\pi$
$678$	13.7840	−	4.47870i	0.529372	−	0.172003i
$679$	−2.73200	−	1.21636i	−0.104844	−	0.0466797i
$680$	−7.61851	+	4.87316i	−0.292157	+	0.186877i
$681$	−13.8079			−0.529120
$682$	3.34906	−	1.19608i	0.128242	−	0.0458001i
$683$			18.4465i			0.705835i	0.935654	+	0.352918i	$0.114810\pi$
$683$			18.4465i			0.705835i	−0.935654	+	0.352918i	$0.885190\pi$
$684$	−1.52830	−	1.11037i	−0.0584359	−	0.0424562i
$685$	−20.3312	−	20.6136i	−0.776816	−	0.787604i
$686$	−1.58108	−	4.86605i	−0.0603658	−	0.185787i
$687$	−3.88710	−	2.24422i	−0.148302	−	0.0856223i
$688$	8.72659	−	5.03830i	0.332698	−	0.192083i
$689$	1.87064	−	2.07756i	0.0712658	−	0.0791487i
$690$	−1.36866	+	1.66653i	−0.0521042	+	0.0634437i
$691$	1.25848	+	1.39768i	0.0478748	+	0.0531704i	0.766607	−	0.642117i	$-0.221944\pi$
$691$	1.25848	+	1.39768i	0.0478748	+	0.0531704i	−0.718732	+	0.695287i	$0.755277\pi$
$692$	−1.69993	−	3.81811i	−0.0646217	−	0.145143i
$693$	−0.0490091	+	0.230569i	−0.00186170	+	0.00875861i
$694$	1.81885	−	17.3052i	0.0690425	−	0.656895i
$695$	19.4271	+	5.34933i	0.736913	+	0.202912i
$696$	3.55355	−	0.755330i	0.134697	−	0.0286307i
$697$	−10.0786	−	13.8720i	−0.381753	−	0.525438i
$698$	11.3440	+	15.6137i	0.429376	+	0.590985i
$699$	−16.7434	+	3.55892i	−0.633294	+	0.134611i
$700$	1.47775	+	1.10510i	0.0558537	+	0.0417690i
$701$	4.66183	−	44.3544i	0.176075	−	1.67524i	−0.448121	−	0.893973i	$-0.647907\pi$
$701$	4.66183	−	44.3544i	0.176075	−	1.67524i	0.624196	−	0.781268i	$-0.285427\pi$
$702$	−1.15304	+	5.42462i	−0.0435187	+	0.204739i
$703$	−3.96323	−	8.90156i	−0.149476	−	0.335729i
$704$	−0.427386	−	0.474660i	−0.0161077	−	0.0178894i
$705$	11.6327	+	9.55357i	0.438114	+	0.359808i
$706$	11.3380	−	12.5922i	0.426713	−	0.473913i
$707$	1.25946	−	0.727151i	0.0473670	−	0.0273473i
$708$	−2.82354	−	1.63017i	−0.106115	−	0.0612657i
$709$	6.60914	+	20.3408i	0.248211	+	0.763916i	0.995092	+	0.0989576i	$0.0315508\pi$
$709$	6.60914	+	20.3408i	0.248211	+	0.763916i	−0.746880	+	0.664959i	$0.768449\pi$
$710$	−4.40012	−	4.46123i	−0.165134	−	0.167427i
$711$	3.01421	+	2.18995i	0.113042	+	0.0821295i
$712$		−	6.32708i		−	0.237117i
$713$	4.09247	+	3.47637i	0.153264	+	0.130191i
$714$	−1.49263			−0.0558602
$715$	−4.26797	−	6.67238i	−0.159613	−	0.249533i
$716$	13.1681	+	5.86281i	0.492115	+	0.219104i
$717$	3.52100	−	1.14404i	0.131494	−	0.0427251i
$718$	9.16787	+	5.29307i	0.342142	+	0.197536i
$719$	−18.9652	−	32.8487i	−0.707283	−	1.22505i	−0.965861	−	0.259060i	$-0.916587\pi$
$719$	−18.9652	−	32.8487i	−0.707283	−	1.22505i	0.258578	−	0.965990i	$-0.416746\pi$
$720$	−1.00139	−	1.99930i	−0.0373196	−	0.0745097i
$721$	−0.747345	+	2.30009i	−0.0278326	+	0.0856599i
$722$	11.4677	−	10.3256i	0.426785	−	0.384279i
$723$	−7.81442	−	17.5515i	−0.290621	−	0.652746i
$724$	9.76470	+	2.07555i	0.362902	+	0.0771373i
$725$	−13.6653	+	11.9672i	−0.507518	+	0.444451i
$726$	−1.10717	−	10.5340i	−0.0410909	−	0.390954i
$727$	−2.75878	−	12.9790i	−0.102318	−	0.481366i	−0.999233	−	0.0391637i	$-0.987531\pi$
$727$	−2.75878	−	12.9790i	−0.102318	−	0.481366i	0.896915	−	0.442202i	$-0.145803\pi$
$728$	1.20302	+	1.65581i	0.0445868	+	0.0613685i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	3.09603	−	18.7116i	0.114589	−	0.692546i
$731$	−4.26002	−	40.5314i	−0.157563	−	1.49911i
$732$	3.56458	+	0.374653i	0.131751	+	0.0138476i
$733$	−9.01770	+	42.4249i	−0.333076	+	1.56700i	0.419039	+	0.907968i	$0.362367\pi$
$733$	−9.01770	+	42.4249i	−0.333076	+	1.56700i	−0.752115	+	0.659032i	$0.770966\pi$
$734$	−28.0538	+	12.4903i	−1.03548	+	0.461027i
$735$	−5.40127	−	14.3661i	−0.199229	−	0.529902i
$736$	0.298023	−	0.917222i	0.0109853	−	0.0338092i
$737$	3.00311	+	2.70401i	0.110621	+	0.0996036i
$738$	3.67153	−	2.11976i	0.135151	−	0.0780295i
$739$	3.31105	−	5.73491i	0.121799	−	0.210962i	−0.798678	−	0.601758i	$-0.794467\pi$
$739$	3.31105	−	5.73491i	0.121799	−	0.210962i	0.920477	+	0.390796i	$0.127800\pi$
$740$	0.683040	−	11.5135i	0.0251090	−	0.423245i
$741$	9.57074	+	4.26117i	0.351590	+	0.156538i
$742$	−0.109351	+	0.150508i	−0.00401439	+	0.00552533i
$743$		−	3.40259i		−	0.124829i	−0.998050	−	0.0624145i	$-0.980120\pi$
$743$		−	3.40259i		−	0.124829i	0.998050	−	0.0624145i	$-0.0198801\pi$
$744$	−5.01894	+	2.41045i	−0.184003	+	0.0883712i
$745$	−3.20512	+	8.18056i	−0.117427	+	0.299713i
$746$	22.4201	+	16.2892i	0.820858	+	0.596388i
$747$	−4.74056	+	10.6475i	−0.173448	+	0.389570i
$748$	−2.45685	+	0.798280i	−0.0898314	+	0.0291880i
$749$	1.50117	−	2.60010i	0.0548516	−	0.0950057i
$750$	9.24865	+	6.28191i	0.337713	+	0.229383i
$751$	−31.3938	+	34.8663i	−1.14557	+	1.27229i	−0.188620	+	0.982050i	$0.560402\pi$
$751$	−31.3938	+	34.8663i	−1.14557	+	1.27229i	−0.956954	+	0.290239i	$0.906265\pi$
$752$	−6.40240	−	2.08027i	−0.233472	−	0.0758595i
$753$	−4.10959	+	3.70029i	−0.149762	+	0.134846i
$754$	−18.4057	+	8.19476i	−0.670297	+	0.298436i
$755$	−7.40225	+	11.2282i	−0.269396	+	0.408636i
$756$	0.0385765	−	0.367031i	0.00140301	−	0.0133488i
$757$	0.295196	−	0.0310263i	0.0107291	−	0.00112767i	−0.0991624	−	0.995071i	$-0.531616\pi$
$757$	0.295196	−	0.0310263i	0.0107291	−	0.00112767i	0.109891	+	0.993944i	$0.464950\pi$
$758$	1.59224	+	7.49089i	0.0578327	+	0.272081i
$759$	−0.498350	+	0.362073i	−0.0180890	+	0.0131424i
$760$	−4.08762	+	1.06512i	−0.148274	+	0.0386359i
$761$	14.8908	−	3.16513i	0.539790	−	0.114736i	0.0700543	−	0.997543i	$-0.477683\pi$
$761$	14.8908	−	3.16513i	0.539790	−	0.114736i	0.469735	+	0.882807i	$0.344349\pi$
$762$	8.53118	−	0.896664i	0.309052	−	0.0324827i
$763$	5.93648	+	0.623949i	0.214915	+	0.0225885i
$764$	2.08647	+	0.443492i	0.0754858	+	0.0160450i
$765$	−9.03440	+	0.411025i	−0.326640	+	0.0148606i
$766$	19.9204	+	22.1239i	0.719754	+	0.799367i
$767$	17.1963	+	5.58742i	0.620923	+	0.201750i
$768$	0.743145	+	0.669131i	0.0268159	+	0.0241452i
$769$	4.56835	+	7.91262i	0.164739	+	0.285336i	0.936563	−	0.350500i	$-0.113988\pi$
$769$	4.56835	+	7.91262i	0.164739	+	0.285336i	−0.771824	+	0.635837i	$0.780655\pi$
$770$	0.328874	+	0.411901i	0.0118518	+	0.0148439i
$771$	2.85134	+	8.77554i	0.102689	+	0.316043i
$772$	−0.869887	+	1.95380i	−0.0313079	+	0.0703187i
$773$	16.4875	−	22.6931i	0.593015	−	0.816216i	−0.402031	−	0.915626i	$-0.631696\pi$
$773$	16.4875	−	22.6931i	0.593015	−	0.816216i	0.995047	+	0.0994103i	$0.0316956\pi$
$774$	10.0766			0.362196
$775$	16.0220	−	22.7661i	0.575528	−	0.817782i
$776$	8.10330			0.290892
$777$	1.11890	−	1.54004i	0.0401404	−	0.0552485i
$778$	8.44637	−	18.9709i	0.302817	−	0.680138i
$779$	−2.47485	−	7.61682i	−0.0886709	−	0.272901i
$780$	7.73744	+	9.69083i	0.277045	+	0.346987i
$781$	−0.894931	−	1.55007i	−0.0320232	−	0.0554657i
$782$	−2.89871	−	2.61001i	−0.103658	−	0.0933338i
$783$	3.45513	+	1.12264i	0.123476	+	0.0401198i
$784$	4.59278	+	5.10080i	0.164028	+	0.182171i
$785$	−40.3099	+	1.83392i	−1.43872	+	0.0654553i
$786$	−10.9094	−	2.31886i	−0.389125	−	0.0827110i
$787$	44.9080	+	4.72002i	1.60080	+	0.168250i	0.862439	−	0.506160i	$-0.168936\pi$
$787$	44.9080	+	4.72002i	1.60080	+	0.168250i	0.738356	+	0.674411i	$0.235602\pi$
$788$	8.30677	−	0.873077i	0.295917	−	0.0311021i
$789$	−11.7970	+	2.50753i	−0.419984	+	0.0892704i
$790$	8.06186	−	2.10069i	0.286828	−	0.0747394i
$791$	4.32728	−	3.14395i	0.153860	−	0.111786i
$792$	−0.132797	−	0.624761i	−0.00471873	−	0.0221999i
$793$	−19.7685	+	2.07775i	−0.702000	+	0.0737832i
$794$	0.934750	−	8.89355i	0.0331730	−	0.315620i
$795$	−0.620419	+	0.941091i	−0.0220040	+	0.0333771i
$796$	−8.53147	+	3.79845i	−0.302390	+	0.134633i
$797$	−4.14124	+	3.72879i	−0.146690	+	0.132081i	−0.739209	−	0.673476i	$-0.764800\pi$
$797$	−4.14124	+	3.72879i	−0.146690	+	0.132081i	0.592518	+	0.805557i	$0.298134\pi$
$798$	−0.663048	−	0.215437i	−0.0234716	−	0.00762640i
$799$	−18.2184	+	20.2336i	−0.644522	+	0.715814i
$800$	−4.87594	−	1.10691i	−0.172390	−	0.0391351i
$801$	3.16354	−	5.47941i	0.111778	−	0.193606i
$802$	17.8215	−	5.79056i	0.629300	−	0.204472i
$803$	2.20350	−	4.94914i	0.0777597	−	0.174651i
$804$	−5.11854	−	3.71884i	−0.180517	−	0.131153i
$805$	−0.290330	+	0.741022i	−0.0102328	+	0.0261176i
$806$	24.4465	−	18.8628i	0.861092	−	0.664414i
$807$		−	19.0386i		−	0.670190i
$808$	−2.31625	+	3.18804i	−0.0814853	+	0.112155i
$809$	23.4662	+	10.4478i	0.825026	+	0.367325i	0.775422	−	0.631444i	$-0.217537\pi$
$809$	23.4662	+	10.4478i	0.825026	+	0.367325i	0.0496045	+	0.998769i	$0.484204\pi$
$810$	0.132422	−	2.23214i	0.00465284	−	0.0784295i
$811$	18.8112	−	32.5819i	0.660550	−	1.14411i	−0.319921	−	0.947444i	$-0.603656\pi$
$811$	18.8112	−	32.5819i	0.660550	−	1.14411i	0.980471	−	0.196663i	$-0.0630103\pi$
$812$	1.16112	−	0.670372i	0.0407473	−	0.0235254i
$813$	−13.8062	−	12.4312i	−0.484205	−	0.435980i
$814$	1.01807	−	3.13329i	0.0356833	−	0.109822i
$815$	8.88238	+	23.6251i	0.311136	+	0.827550i
$816$	3.69482	−	1.64504i	0.129345	−	0.0575880i
$817$	3.95770	−	18.6195i	0.138462	−	0.651415i
$818$	22.5791	+	2.37316i	0.789460	+	0.0829756i
$819$	0.213938	+	2.03548i	0.00747560	+	0.0711256i
$820$	1.54751	−	9.35270i	0.0540413	−	0.326610i
$821$	−14.4134	+	10.4719i	−0.503031	+	0.365473i	−0.810174	−	0.586190i	$-0.800627\pi$
$821$	−14.4134	+	10.4719i	−0.503031	+	0.365473i	0.307143	+	0.951664i	$0.400627\pi$
$822$	7.61076	+	10.4753i	0.265456	+	0.365368i
$823$	−2.25638	−	10.6154i	−0.0786526	−	0.370031i	0.921164	−	0.389174i	$-0.127240\pi$
$823$	−2.25638	−	10.6154i	−0.0786526	−	0.370031i	−0.999817	+	0.0191429i	$0.993906\pi$
$824$	−0.684991	−	6.51726i	−0.0238628	−	0.227039i
$825$	2.10400	+	2.40255i	0.0732517	+	0.0836459i
$826$	−1.17695	−	0.250167i	−0.0409512	−	0.00870444i
$827$	−3.23732	−	7.27114i	−0.112573	−	0.252842i	0.848469	−	0.529244i	$-0.177525\pi$
$827$	−3.23732	−	7.27114i	−0.112573	−	0.252842i	−0.961042	+	0.276402i	$0.910858\pi$
$828$	0.716707	−	0.645325i	0.0249073	−	0.0224266i
$829$	9.22763	−	28.3997i	0.320489	−	0.986363i	−0.652947	−	0.757404i	$-0.726468\pi$
$829$	9.22763	−	28.3997i	0.320489	−	0.986363i	0.973436	−	0.228960i	$-0.0735324\pi$
$830$	11.6713	+	23.3021i	0.405117	+	0.808827i
$831$	13.2806	+	23.0027i	0.460700	+	0.797955i
$832$	−4.80281	−	2.77291i	−0.166508	−	0.0961332i
$833$	26.4019	−	8.57848i	0.914770	−	0.297227i
$834$	−8.23234	−	3.66527i	−0.285063	−	0.126918i
$835$	−24.9858	−	39.0619i	−0.864669	−	1.35179i
$836$	−1.20659			−0.0417308
$837$	−5.55175	−	0.421963i	−0.191897	−	0.0145852i
$838$			22.8770i			0.790272i
$839$	11.2594	+	8.18040i	0.388716	+	0.282419i	0.764929	−	0.644114i	$-0.222774\pi$
$839$	11.2594	+	8.18040i	0.388716	+	0.282419i	−0.376213	+	0.926533i	$0.622774\pi$
$840$	−0.579486	−	0.587533i	−0.0199942	−	0.0202718i
$841$	−4.88302	−	15.0284i	−0.168380	−	0.518220i
$842$	23.4009	+	13.5105i	0.806448	+	0.465603i
$843$	18.5218	−	10.6936i	0.637924	−	0.368306i
$844$	−8.82435	+	9.80044i	−0.303747	+	0.337345i
$845$	−30.6825	−	25.1985i	−1.05551	−	0.866856i
$846$	−4.50451	−	5.00277i	−0.154868	−	0.171999i
$847$	−1.58994	−	3.57107i	−0.0546310	−	0.122703i
$848$	0.104808	−	0.493082i	0.00359911	−	0.0169325i
$849$	2.74896	−	26.1546i	0.0943441	−	0.897624i
$850$	−12.1109	+	16.1948i	−0.415402	+	0.555478i
$851$	4.86584	−	1.03427i	0.166799	−	0.0354542i
$852$	1.64713	+	2.26709i	0.0564299	+	0.0776691i
$853$	3.96355	+	5.45536i	0.135709	+	0.186788i	0.871463	−	0.490462i	$-0.163172\pi$
$853$	3.96355	+	5.45536i	0.135709	+	0.186788i	−0.735753	+	0.677249i	$0.763172\pi$
$854$	1.29386	−	0.275018i	0.0442749	−	0.00941092i
$855$	−4.07254	−	1.12139i	−0.139278	−	0.0383507i
$856$	−0.850367	+	8.09070i	−0.0290650	+	0.276535i
$857$	−7.12700	+	33.5299i	−0.243454	+	1.14536i	0.671249	+	0.741232i	$0.265758\pi$
$857$	−7.12700	+	33.5299i	−0.243454	+	1.14536i	−0.914703	+	0.404127i	$0.867575\pi$
$858$	1.44075	+	3.23597i	0.0491863	+	0.110474i
$859$	4.63812	+	5.15115i	0.158251	+	0.175755i	0.817056	−	0.576558i	$-0.195605\pi$
$859$	4.63812	+	5.15115i	0.158251	+	0.175755i	−0.658805	+	0.752313i	$0.728938\pi$
$860$	14.3002	−	17.4124i	0.487634	−	0.593759i
$861$	1.04693	−	1.16273i	0.0356791	−	0.0396257i
$862$	−9.85830	+	5.69169i	−0.335775	+	0.193860i
$863$	−39.8437	−	23.0038i	−1.35630	−	0.783058i	−0.367174	−	0.930152i	$-0.619675\pi$
$863$	−39.8437	−	23.0038i	−1.35630	−	0.783058i	−0.989123	+	0.147094i	$0.953008\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$	−6.56255	−	6.65369i	−0.223133	−	0.226232i
$866$	13.4583	+	9.77806i	0.457333	+	0.332272i
$867$			0.642119i			0.0218075i
$868$	−1.48670	+	1.41842i	−0.0504619	+	0.0481443i
$869$	2.37971			0.0807262
$870$	6.84328	−	4.37729i	0.232009	−	0.148404i
$871$	32.0541	+	14.2714i	1.08611	+	0.483569i
$872$	−15.3827	+	4.99815i	−0.520924	+	0.169259i
$873$	7.01766	+	4.05165i	0.237512	+	0.137128i
$874$	−0.910937	−	1.57779i	−0.0308129	−	0.0533695i
$875$	3.96259	+	1.15014i	0.133960	+	0.0388817i
$876$	−2.62103	+	8.06671i	−0.0885565	+	0.272549i
$877$	−2.05486	+	1.85021i	−0.0693878	+	0.0624771i	−0.703095	−	0.711096i	$-0.748199\pi$
$877$	−2.05486	+	1.85021i	−0.0693878	+	0.0624771i	0.633707	+	0.773573i	$0.281532\pi$
$878$	1.16452	+	2.61555i	0.0393005	+	0.0882704i
$879$	20.2155	+	4.29695i	0.681853	+	0.144932i
$880$	−1.26805	−	0.657157i	−0.0427459	−	0.0221527i
$881$	−2.04347	−	19.4423i	−0.0688462	−	0.655028i	−0.973470	−	0.228816i	$-0.926515\pi$
$881$	−2.04347	−	19.4423i	−0.0688462	−	0.655028i	0.904623	−	0.426212i	$-0.140152\pi$
$882$	1.42706	+	6.71381i	0.0480518	+	0.226066i
$883$	−17.9858	−	24.7553i	−0.605269	−	0.833082i	0.390909	−	0.920430i	$-0.372161\pi$
$883$	−17.9858	−	24.7553i	−0.605269	−	0.833082i	−0.996178	+	0.0873478i	$0.972161\pi$
$884$	−18.1462	+	13.1840i	−0.610324	+	0.443426i
$885$	−7.19256	−	1.19009i	−0.241775	−	0.0400044i
$886$	2.82854	+	26.9118i	0.0950268	+	0.904120i
$887$	21.9747	+	2.30963i	0.737837	+	0.0775498i	0.465989	−	0.884790i	$-0.345699\pi$
$887$	21.9747	+	2.30963i	0.737837	+	0.0775498i	0.271848	+	0.962340i	$0.412365\pi$
$888$	−1.07242	+	5.04533i	−0.0359880	+	0.169310i
$889$	2.89210	−	1.28765i	0.0969979	−	0.0431863i
$890$	−4.97891	−	13.2427i	−0.166894	−	0.443898i
$891$	0.197375	−	0.607457i	0.00661230	−	0.0203506i
$892$	−7.54280	−	6.79157i	−0.252552	−	0.227398i
$893$	−11.0133	+	6.35853i	−0.368546	+	0.212780i
$894$	1.96462	−	3.40282i	0.0657066	−	0.113807i
$895$	32.1747	+	1.90877i	1.07548	+	0.0638031i
$896$	0.337146	+	0.150107i	0.0112633	+	0.00501473i
$897$	−3.14378	+	4.32704i	−0.104968	+	0.144476i
$898$			8.32919i			0.277949i
$899$	−10.6149	−	17.2182i	−0.354028	−	0.574261i
$900$	−3.66923	−	3.39658i	−0.122308	−	0.113219i
$901$	−1.64944	−	1.19839i	−0.0549507	−	0.0399240i
$902$	1.10139	−	2.47375i	0.0366721	−	0.0823670i
$903$	3.53678	−	1.14917i	0.117697	−	0.0382420i
$904$	−7.24668	+	12.5516i	−0.241021	+	0.417461i
$905$	22.0711	−	3.33987i	0.733667	−	0.111021i
$906$	4.02443	−	4.46958i	0.133703	−	0.148492i
$907$	−16.7431	−	5.44018i	−0.555947	−	0.180638i	0.0175497	−	0.999846i	$-0.494413\pi$
$907$	−16.7431	−	5.44018i	−0.555947	−	0.180638i	−0.573497	+	0.819208i	$0.694413\pi$
$908$	10.2613	−	9.23929i	0.340532	−	0.306616i
$909$	−3.59995	+	1.60280i	−0.119403	+	0.0531616i
$910$	3.82094	+	2.51898i	0.126663	+	0.0835033i
$911$	4.03178	−	38.3598i	0.133579	−	1.27092i	−0.698237	−	0.715866i	$-0.746032\pi$
$911$	4.03178	−	38.3598i	0.133579	−	1.27092i	0.831816	−	0.555051i	$-0.187301\pi$
$912$	1.87873	−	0.197463i	0.0622110	−	0.00653864i
$913$	1.54776	+	7.28165i	0.0512234	+	0.240987i
$914$	31.9659	−	23.2246i	1.05734	−	0.768201i
$915$	7.75558	−	2.02089i	0.256392	−	0.0668084i
$916$	4.39035	−	0.933199i	0.145061	−	0.0308337i
$917$	−4.09353	+	0.430247i	−0.135180	+	0.0142080i
$918$	4.02233	+	0.422764i	0.132757	+	0.0139533i
$919$	−43.9638	−	9.34479i	−1.45023	−	0.308256i	−0.585575	−	0.810619i	$-0.699131\pi$
$919$	−43.9638	−	9.34479i	−1.45023	−	0.308256i	−0.864657	+	0.502362i	$0.832464\pi$
$920$	−0.0980104	−	2.15429i	−0.00323131	−	0.0710248i
$921$	17.2896	+	19.2021i	0.569713	+	0.632730i
$922$	21.3920	+	6.95067i	0.704507	+	0.228908i
$923$	−11.5491	−	10.3989i	−0.380144	−	0.342283i
$924$	−0.117860	−	0.204140i	−0.00387732	−	0.00671571i
$925$	−7.63060	−	24.6356i	−0.250893	−	0.810012i
$926$	8.13701	+	25.0431i	0.267399	+	0.822969i
$927$	2.66541	−	5.98661i	0.0875435	−	0.196626i
$928$	−2.13539	+	2.93911i	−0.0700975	+	0.0964809i
$929$	−24.2471			−0.795522			−0.397761	−	0.917489i	$-0.630213\pi$
$929$	−24.2471			−0.795522			−0.397761	+	0.917489i	$0.630213\pi$
$930$	−8.60794	+	8.99463i	−0.282265	+	0.294946i
$931$	12.9663			0.424952
$932$	10.0614	−	13.8483i	0.329572	−	0.453617i
$933$	9.74593	−	21.8897i	0.319067	−	0.716637i
$934$	9.70991	+	29.8840i	0.317718	+	0.977836i
$935$	−4.51407	+	3.60417i	−0.147626	+	0.117869i
$936$	−2.77291	−	4.80281i	−0.0906353	−	0.156985i
$937$	−15.7610	−	14.1912i	−0.514888	−	0.463607i	0.370252	−	0.928931i	$-0.379271\pi$
$937$	−15.7610	−	14.1912i	−0.514888	−	0.463607i	−0.885141	+	0.465324i	$0.845938\pi$
$938$	−2.22067	−	0.721538i	−0.0725073	−	0.0235590i
$939$	−2.38429	−	2.64802i	−0.0778084	−	0.0864150i
$940$	−15.0374	+	0.684134i	−0.490466	+	0.0223140i
$941$	9.51350	+	2.02216i	0.310131	+	0.0659204i	0.360348	−	0.932818i	$-0.382658\pi$
$941$	9.51350	+	2.02216i	0.310131	+	0.0659204i	−0.0502168	+	0.998738i	$0.515991\pi$
$942$	17.9469	+	1.88630i	0.584742	+	0.0614589i
$943$	4.06630	−	0.427385i	0.132417	−	0.0139176i
$944$	3.18910	−	0.677864i	0.103796	−	0.0220626i
$945$	−0.208083	−	0.798561i	−0.00676893	−	0.0259772i
$946$	5.20692	−	3.78305i	0.169291	−	0.122997i
$947$	0.00878303	+	0.0413209i	0.000285410	+	0.00134275i	0.978290	−	0.207240i	$-0.0664482\pi$
$947$	0.00878303	+	0.0413209i	0.000285410	+	0.00134275i	−0.978005	+	0.208583i	$0.933115\pi$
$948$	−3.70535	+	0.389448i	−0.120344	+	0.0126487i
$949$	4.91688	−	46.7810i	0.159609	−	1.51858i
$950$	−7.71733	+	5.44595i	−0.250383	+	0.176690i
$951$	30.9690	−	13.7883i	1.00424	−	0.447116i
$952$	1.10924	−	0.998763i	0.0359506	−	0.0323701i
$953$	12.0596	+	3.91841i	0.390649	+	0.126930i	0.497754	−	0.867318i	$-0.334158\pi$
$953$	12.0596	+	3.91841i	0.390649	+	0.126930i	−0.107105	+	0.994248i	$0.534158\pi$
$954$	0.337307	−	0.374618i	0.0109207	−	0.0121287i
$955$	4.71602	−	0.713644i	0.152607	−	0.0230930i
$956$	−1.85110	+	3.20620i	−0.0598689	+	0.103696i
$957$	2.20685	−	0.717050i	0.0713374	−	0.0231789i
$958$	15.6528	−	35.1568i	0.505719	−	1.13586i
$959$	3.86594	+	2.80877i	0.124838	+	0.0906999i
$960$	2.08197	+	0.815711i	0.0671954	+	0.0263270i
$961$	22.0375	+	21.8025i	0.710887	+	0.703306i
$962$		−	28.6056i		−	0.922281i
$963$	−4.78179	+	6.58157i	−0.154091	+	0.212088i
$964$	17.5515	+	7.81442i	0.565295	+	0.251685i
$965$	−0.283211	+	4.77388i	−0.00911688	+	0.153677i
$966$	0.177962	−	0.308238i	0.00572582	−	0.00991741i
$967$	31.9594	−	18.4517i	1.02774	−	0.593368i	0.111406	−	0.993775i	$-0.464465\pi$
$967$	31.9594	−	18.4517i	1.02774	−	0.593368i	0.916337	+	0.400407i	$0.131131\pi$
$968$	7.87142	+	7.08746i	0.252997	+	0.227800i
$969$	2.36100	−	7.26642i	0.0758463	−	0.233431i
$970$	16.9604	−	6.37666i	0.544566	−	0.204742i
$971$	20.4980	−	9.12631i	0.657813	−	0.292877i	−0.0505541	−	0.998721i	$-0.516099\pi$
$971$	20.4980	−	9.12631i	0.657813	−	0.292877i	0.708367	+	0.705844i	$0.249432\pi$
$972$	−0.207912	+	0.978148i	−0.00666877	+	0.0313741i
$973$	−3.30747	−	0.347629i	−0.106033	−	0.0111445i
$974$	−2.80461	−	26.6841i	−0.0898656	−	0.855014i
$975$	23.8206	+	14.1944i	0.762869	+	0.454584i
$976$	−2.89969	+	2.10675i	−0.0928169	+	0.0674354i
$977$	14.4040	+	19.8254i	0.460824	+	0.634270i	0.974679	−	0.223607i	$-0.0717833\pi$
$977$	14.4040	+	19.8254i	0.460824	+	0.634270i	−0.513856	+	0.857877i	$0.671783\pi$
$978$	−2.34681	−	11.0409i	−0.0750426	−	0.353048i
$979$	−0.422423	−	4.01908i	−0.0135007	−	0.128450i
$980$	13.6267	+	7.06195i	0.435290	+	0.225586i
$981$	−15.8209	−	3.36283i	−0.505122	−	0.107367i
$982$	−11.4532	−	25.7242i	−0.365485	−	0.820892i
$983$	38.3208	−	34.5042i	1.22224	−	1.10051i	0.230395	−	0.973097i	$-0.425998\pi$
$983$	38.3208	−	34.5042i	1.22224	−	1.10051i	0.991849	−	0.127416i	$-0.0406683\pi$
$984$	−1.31008	+	4.03203i	−0.0417640	+	0.128536i
$985$	16.6992	−	8.36415i	0.532082	−	0.266504i
$986$	7.34668	+	12.7248i	0.233966	+	0.405241i
$987$	−2.15157	−	1.24221i	−0.0684852	−	0.0395400i
$988$	−9.96373	+	3.23741i	−0.316988	+	0.102996i
$989$	8.87793	+	3.95271i	0.282302	+	0.125689i
$990$	−0.769585	−	1.20314i	−0.0244590	−	0.0382383i
$991$	60.7357			1.92933			0.964667	−	0.263474i	$-0.0848682\pi$
$991$	60.7357			1.92933			0.964667	+	0.263474i	$0.0848682\pi$
$992$	2.11690	−	5.14964i	0.0672115	−	0.163501i
$993$		−	32.4697i		−	1.03040i
$994$	0.836674	+	0.607879i	0.0265377	+	0.0192808i
$995$	−14.8675	+	14.6639i	−0.471331	+	0.464875i
$996$	−3.60162	−	11.0847i	−0.114122	−	0.351231i
$997$	40.4002	+	23.3251i	1.27949	+	0.738712i	0.976754	−	0.214364i	$-0.0687677\pi$
$997$	40.4002	+	23.3251i	1.27949	+	0.738712i	0.302733	+	0.953076i	$0.402101\pi$
$998$	1.15639	−	0.667642i	0.0366049	−	0.0211338i
$999$	−3.45141	+	3.83318i	−0.109198	+	0.121276i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bn.a.19.11	yes	112
5.4	even	2	inner	930.2.bn.a.19.7	✓	112
31.18	even	15	inner	930.2.bn.a.49.7	yes	112
155.49	even	30	inner	930.2.bn.a.49.11	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bn.a.19.7	✓	112	5.4	even	2	inner
930.2.bn.a.19.11	yes	112	1.1	even	1	trivial
930.2.bn.a.49.7	yes	112	31.18	even	15	inner
930.2.bn.a.49.11	yes	112	155.49	even	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bn (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 - 0.809017i) q^{2} +(-0.406737 + 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-1.39519 - 1.74741i) q^{5} +(0.500000 + 0.866025i) q^{6} +(0.274259 + 0.246944i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +O(q^{10})\)	\(q+(0.587785 - 0.809017i) q^{2} +(-0.406737 + 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-1.39519 - 1.74741i) q^{5} +(0.500000 + 0.866025i) q^{6} +(0.274259 + 0.246944i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +(-2.23376 + 0.101626i) q^{10} +(-0.624761 - 0.132797i) q^{11} +(0.994522 + 0.104528i) q^{12} +(-5.51543 + 0.579695i) q^{13} +(0.360988 - 0.0767303i) q^{14} +(2.16382 - 0.563829i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(0.840896 + 3.95611i) q^{17} +(-0.994522 + 0.104528i) q^{18} +(-0.197463 + 1.87873i) q^{19} +(-1.23075 + 1.86688i) q^{20} +(-0.337146 + 0.150107i) q^{21} +(-0.474660 + 0.427386i) q^{22} +(-0.917222 - 0.298023i) q^{23} +(0.669131 - 0.743145i) q^{24} +(-1.10691 + 4.87594i) q^{25} +(-2.77291 + 4.80281i) q^{26} +(0.951057 - 0.309017i) q^{27} +(0.150107 - 0.337146i) q^{28} +(2.93911 + 2.13539i) q^{29} +(0.815711 - 2.08197i) q^{30} +(-5.14964 - 2.11690i) q^{31} +1.00000i q^{32} +(0.375429 - 0.516734i) q^{33} +(3.69482 + 1.64504i) q^{34} +(0.0488707 - 0.823778i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-4.46700 + 2.57902i) q^{37} +(1.40386 + 1.26404i) q^{38} +(1.71375 - 5.27438i) q^{39} +(0.786921 + 2.09303i) q^{40} +(-3.87300 + 1.72437i) q^{41} +(-0.0767303 + 0.360988i) q^{42} +(-10.0214 - 1.05329i) q^{43} +(0.0667642 + 0.635219i) q^{44} +(-0.365019 + 2.20607i) q^{45} +(-0.780235 + 0.566874i) q^{46} +(3.95690 + 5.44621i) q^{47} +(-0.207912 - 0.978148i) q^{48} +(-0.717462 - 6.82620i) q^{49} +(3.29409 + 3.76151i) q^{50} +(-3.95611 - 0.840896i) q^{51} +(2.25569 + 5.06635i) q^{52} +(-0.374618 + 0.337307i) q^{53} +(0.309017 - 0.951057i) q^{54} +(0.639606 + 1.27699i) q^{55} +(-0.184526 - 0.319609i) q^{56} +(-1.63599 - 0.944540i) q^{57} +(3.45513 - 1.12264i) q^{58} +(-2.97847 - 1.32610i) q^{59} +(-1.20489 - 1.88368i) q^{60} +3.58422 q^{61} +(-4.73948 + 2.92186i) q^{62} -0.369052i q^{63} +(0.809017 + 0.587785i) q^{64} +(8.70802 + 8.82896i) q^{65} +(-0.197375 - 0.607457i) q^{66} +(-5.47923 - 3.16343i) q^{67} +(3.50263 - 2.02224i) q^{68} +(0.645325 - 0.716707i) q^{69} +(-0.637725 - 0.523742i) q^{70} +(1.87509 + 2.08249i) q^{71} +(0.406737 + 0.913545i) q^{72} +(-1.76347 + 8.29649i) q^{73} +(-0.539163 + 5.12979i) q^{74} +(-4.00417 - 2.99443i) q^{75} +(1.84780 - 0.392762i) q^{76} +(-0.138553 - 0.190702i) q^{77} +(-3.25975 - 4.48666i) q^{78} +(-3.64435 + 0.774630i) q^{79} +(2.15583 + 0.593617i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(-0.881446 + 4.14688i) q^{82} +(-4.74056 - 10.6475i) q^{83} +(0.246944 + 0.274259i) q^{84} +(5.73975 - 6.98890i) q^{85} +(-6.74256 + 7.48837i) q^{86} +(-3.14621 + 1.81647i) q^{87} +(0.553146 + 0.319359i) q^{88} +(1.95518 + 6.01741i) q^{89} +(1.57020 + 1.59200i) q^{90} +(-1.65581 - 1.20302i) q^{91} +0.964424i q^{92} +(4.02843 - 3.84341i) q^{93} +6.73188 q^{94} +(3.55842 - 2.27613i) q^{95} +(-0.913545 - 0.406737i) q^{96} +(-7.70670 + 2.50406i) q^{97} +(-5.94423 - 3.43190i) q^{98} +(0.319359 + 0.553146i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 28 q^{4} - 2 q^{5} + 56 q^{6} - 14 q^{9}+O(q^{10}) \) 112 * q + 28 * q^4 - 2 * q^5 + 56 * q^6 - 14 * q^9	\( 112 q + 28 q^{4} - 2 q^{5} + 56 q^{6} - 14 q^{9} - 4 q^{10} + 18 q^{11} + 8 q^{14} + 8 q^{15} - 28 q^{16} + 16 q^{19} + 2 q^{20} + 28 q^{21} + 14 q^{24} + 14 q^{25} + 12 q^{26} + 16 q^{29} - 4 q^{30} + 10 q^{34} - 38 q^{35} - 56 q^{36} + 16 q^{39} - 6 q^{40} + 20 q^{41} + 2 q^{44} + 2 q^{45} - 2 q^{46} + 38 q^{49} + 8 q^{50} - 10 q^{51} - 28 q^{54} - 46 q^{55} + 12 q^{56} + 60 q^{59} - 8 q^{60} + 88 q^{61} + 28 q^{64} - 28 q^{65} + 6 q^{66} + 46 q^{69} + 26 q^{70} + 116 q^{71} - 34 q^{74} + 8 q^{75} + 24 q^{76} - 40 q^{79} - 12 q^{80} + 14 q^{81} - 8 q^{84} + 18 q^{85} - 38 q^{86} - 60 q^{89} + 4 q^{90} - 92 q^{91} + 132 q^{94} + 132 q^{95} - 14 q^{96} + 2 q^{99}+O(q^{100}) \) 112 * q + 28 * q^4 - 2 * q^5 + 56 * q^6 - 14 * q^9 - 4 * q^10 + 18 * q^11 + 8 * q^14 + 8 * q^15 - 28 * q^16 + 16 * q^19 + 2 * q^20 + 28 * q^21 + 14 * q^24 + 14 * q^25 + 12 * q^26 + 16 * q^29 - 4 * q^30 + 10 * q^34 - 38 * q^35 - 56 * q^36 + 16 * q^39 - 6 * q^40 + 20 * q^41 + 2 * q^44 + 2 * q^45 - 2 * q^46 + 38 * q^49 + 8 * q^50 - 10 * q^51 - 28 * q^54 - 46 * q^55 + 12 * q^56 + 60 * q^59 - 8 * q^60 + 88 * q^61 + 28 * q^64 - 28 * q^65 + 6 * q^66 + 46 * q^69 + 26 * q^70 + 116 * q^71 - 34 * q^74 + 8 * q^75 + 24 * q^76 - 40 * q^79 - 12 * q^80 + 14 * q^81 - 8 * q^84 + 18 * q^85 - 38 * q^86 - 60 * q^89 + 4 * q^90 - 92 * q^91 + 132 * q^94 + 132 * q^95 - 14 * q^96 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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