LMFDB - Embedded newform 930.2.be.b.553.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(37,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("930.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.be (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			553.1
Character	$\chi$	$=$	930.553
Dual form			930.2.be.b.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.258819 + 0.965926i) q^{3} -1.00000i q^{4} +(-2.15172 - 0.608374i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(0.345988 + 1.29125i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.258819 + 0.965926i) q^{3} -1.00000i q^{4} +(-2.15172 - 0.608374i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(0.345988 + 1.29125i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(1.95168 - 1.09131i) q^{10} +(0.967795 - 0.558756i) q^{11} +(0.965926 - 0.258819i) q^{12} +(0.196733 + 0.0527145i) q^{13} +(-1.15770 - 0.668398i) q^{14} +(0.0307391 - 2.23586i) q^{15} -1.00000 q^{16} +(-5.67060 + 1.51943i) q^{17} +(0.258819 - 0.965926i) q^{18} +(-1.93983 - 1.11996i) q^{19} +(-0.608374 + 2.15172i) q^{20} +(-1.15770 + 0.668398i) q^{21} +(-0.289234 + 1.07943i) q^{22} +(0.950791 - 0.950791i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(4.25976 + 2.61810i) q^{25} +(-0.176386 + 0.101837i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(1.29125 - 0.345988i) q^{28} -5.82226 q^{29} +(1.55925 + 1.60273i) q^{30} +(-1.78006 - 5.27555i) q^{31} +(0.707107 - 0.707107i) q^{32} +(0.790201 + 0.790201i) q^{33} +(2.93532 - 5.08412i) q^{34} +(0.0410919 - 2.98888i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-0.592219 + 0.158685i) q^{37} +(2.16360 - 0.579735i) q^{38} +0.203673i q^{39} +(-1.09131 - 1.95168i) q^{40} +(-4.94695 - 8.56837i) q^{41} +(0.345988 - 1.29125i) q^{42} +(-0.988872 - 3.69052i) q^{43} +(-0.558756 - 0.967795i) q^{44} +(2.16763 - 0.548991i) q^{45} +1.34462i q^{46} +(-0.238845 + 0.238845i) q^{47} +(-0.258819 - 0.965926i) q^{48} +(4.51457 - 2.60649i) q^{49} +(-4.86338 + 1.16083i) q^{50} +(-2.93532 - 5.08412i) q^{51} +(0.0527145 - 0.196733i) q^{52} +(-2.79320 - 0.748436i) q^{53} +1.00000 q^{54} +(-2.42235 + 0.613504i) q^{55} +(-0.668398 + 1.15770i) q^{56} +(0.579735 - 2.16360i) q^{57} +(4.11696 - 4.11696i) q^{58} +(-12.2868 - 7.09379i) q^{59} +(-2.23586 - 0.0307391i) q^{60} -1.48870i q^{61} +(4.98907 + 2.47168i) q^{62} +(-0.945257 - 0.945257i) q^{63} +1.00000i q^{64} +(-0.391244 - 0.233114i) q^{65} -1.11751 q^{66} +(-2.89574 - 0.775910i) q^{67} +(1.51943 + 5.67060i) q^{68} +(1.16448 + 0.672311i) q^{69} +(2.08440 + 2.14252i) q^{70} +(0.224061 + 0.388085i) q^{71} +(-0.965926 - 0.258819i) q^{72} +(9.35629 + 2.50701i) q^{73} +(0.306555 - 0.530969i) q^{74} +(-1.42638 + 4.79223i) q^{75} +(-1.11996 + 1.93983i) q^{76} +(1.05634 + 1.05634i) q^{77} +(-0.144019 - 0.144019i) q^{78} +(-0.494348 + 0.856236i) q^{79} +(2.15172 + 0.608374i) q^{80} +(0.500000 - 0.866025i) q^{81} +(9.55678 + 2.56073i) q^{82} +(1.22264 + 0.327604i) q^{83} +(0.668398 + 1.15770i) q^{84} +(13.1259 + 0.180458i) q^{85} +(3.30883 + 1.91035i) q^{86} +(-1.50691 - 5.62387i) q^{87} +(1.07943 + 0.289234i) q^{88} -7.32708 q^{89} +(-1.14455 + 1.92094i) q^{90} +0.272269i q^{91} +(-0.950791 - 0.950791i) q^{92} +(4.63507 - 3.08482i) q^{93} -0.337778i q^{94} +(3.49261 + 3.58999i) q^{95} +(0.866025 + 0.500000i) q^{96} +(-9.91783 + 9.91783i) q^{97} +(-1.34922 + 5.03535i) q^{98} +(-0.558756 + 0.967795i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 4 q^{7}+O(q^{10}) $ 64 * q + 4 * q^7	$ 64 q + 4 q^{7} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 64 q^{16} - 4 q^{17} + 12 q^{20} - 24 q^{21} - 4 q^{22} - 32 q^{24} + 28 q^{25} + 8 q^{28} - 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 16 q^{37} - 28 q^{38} - 8 q^{41} + 4 q^{42} - 40 q^{43} + 4 q^{44} - 12 q^{45} + 8 q^{47} + 60 q^{49} - 8 q^{50} - 24 q^{53} + 64 q^{54} + 44 q^{55} + 4 q^{57} - 52 q^{58} - 24 q^{59} + 20 q^{62} - 4 q^{63} + 44 q^{65} + 8 q^{66} - 44 q^{67} - 4 q^{68} + 12 q^{69} - 44 q^{70} + 8 q^{71} + 4 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{76} + 104 q^{77} - 56 q^{79} + 32 q^{81} - 16 q^{82} - 48 q^{83} - 32 q^{85} - 24 q^{86} - 32 q^{87} + 8 q^{88} + 176 q^{89} + 16 q^{93} + 64 q^{95} - 68 q^{97} + 32 q^{98} + 4 q^{99}+O(q^{100}) $ 64 * q + 4 * q^7 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 64 * q^16 - 4 * q^17 + 12 * q^20 - 24 * q^21 - 4 * q^22 - 32 * q^24 + 28 * q^25 + 8 * q^28 - 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 16 * q^37 - 28 * q^38 - 8 * q^41 + 4 * q^42 - 40 * q^43 + 4 * q^44 - 12 * q^45 + 8 * q^47 + 60 * q^49 - 8 * q^50 - 24 * q^53 + 64 * q^54 + 44 * q^55 + 4 * q^57 - 52 * q^58 - 24 * q^59 + 20 * q^62 - 4 * q^63 + 44 * q^65 + 8 * q^66 - 44 * q^67 - 4 * q^68 + 12 * q^69 - 44 * q^70 + 8 * q^71 + 4 * q^73 - 12 * q^74 + 8 * q^75 - 8 * q^76 + 104 * q^77 - 56 * q^79 + 32 * q^81 - 16 * q^82 - 48 * q^83 - 32 * q^85 - 24 * q^86 - 32 * q^87 + 8 * q^88 + 176 * q^89 + 16 * q^93 + 64 * q^95 - 68 * q^97 + 32 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$4$		−	1.00000i		−	0.500000i
$5$	−2.15172	−	0.608374i	−0.962277	−	0.272073i
$5$	−2.15172	−	0.608374i	−0.962277	−	0.272073i
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	0.345988	+	1.29125i	0.130771	+	0.488045i	0.999980	−	0.00640123i	$-0.00203759\pi$
$7$	0.345988	+	1.29125i	0.130771	+	0.488045i	−0.869208	+	0.494446i	$0.835371\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$	1.95168	−	1.09131i	0.617175	−	0.345102i
$11$	0.967795	−	0.558756i	0.291801	−	0.168471i	−0.346953	−	0.937883i	$-0.612784\pi$
$11$	0.967795	−	0.558756i	0.291801	−	0.168471i	0.638754	+	0.769411i	$0.279450\pi$
$12$	0.965926	−	0.258819i	0.278839	−	0.0747146i
$13$	0.196733	+	0.0527145i	0.0545640	+	0.0146204i	0.285998	−	0.958230i	$-0.407675\pi$
$13$	0.196733	+	0.0527145i	0.0545640	+	0.0146204i	−0.231434	+	0.972851i	$0.574342\pi$
$14$	−1.15770	−	0.668398i	−0.309408	−	0.178637i
$15$	0.0307391	−	2.23586i	0.00793680	−	0.577296i
$16$	−1.00000			−0.250000
$17$	−5.67060	+	1.51943i	−1.37532	+	0.368517i	−0.869420	−	0.494074i	$-0.835507\pi$
$17$	−5.67060	+	1.51943i	−1.37532	+	0.368517i	−0.505903	+	0.862591i	$0.668841\pi$
$18$	0.258819	−	0.965926i	0.0610042	−	0.227671i
$19$	−1.93983	−	1.11996i	−0.445028	−	0.256937i	0.260700	−	0.965420i	$-0.416047\pi$
$19$	−1.93983	−	1.11996i	−0.445028	−	0.256937i	−0.705728	+	0.708483i	$0.749380\pi$
$20$	−0.608374	+	2.15172i	−0.136037	+	0.481138i
$21$	−1.15770	+	0.668398i	−0.252631	+	0.145856i
$22$	−0.289234	+	1.07943i	−0.0616648	+	0.230136i
$23$	0.950791	−	0.950791i	0.198254	−	0.198254i	−0.600997	−	0.799251i	$-0.705230\pi$
$23$	0.950791	−	0.950791i	0.198254	−	0.198254i	0.799251	+	0.600997i	$0.205230\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	4.25976	+	2.61810i	0.851952	+	0.523619i
$26$	−0.176386	+	0.101837i	−0.0345922	+	0.0199718i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	1.29125	−	0.345988i	0.244022	−	0.0653856i
$29$	−5.82226			−1.08117			−0.540583	−	0.841290i	$-0.681796\pi$
$29$	−5.82226			−1.08117			−0.540583	+	0.841290i	$0.681796\pi$
$30$	1.55925	+	1.60273i	0.284679	+	0.292616i
$31$	−1.78006	−	5.27555i	−0.319708	−	0.947516i
$31$	−1.78006	−	5.27555i	−0.319708	−	0.947516i
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	0.790201	+	0.790201i	0.137556	+	0.137556i
$34$	2.93532	−	5.08412i	0.503403	−	0.871920i
$35$	0.0410919	−	2.98888i	0.00694579	−	0.505214i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−0.592219	+	0.158685i	−0.0973602	+	0.0260876i	−0.307170	−	0.951655i	$-0.599382\pi$
$37$	−0.592219	+	0.158685i	−0.0973602	+	0.0260876i	0.209810	+	0.977742i	$0.432715\pi$
$38$	2.16360	−	0.579735i	0.350983	−	0.0940455i
$39$			0.203673i			0.0326138i
$40$	−1.09131	−	1.95168i	−0.172551	−	0.308587i
$41$	−4.94695	−	8.56837i	−0.772584	−	1.33815i	−0.936142	−	0.351621i	$-0.885631\pi$
$41$	−4.94695	−	8.56837i	−0.772584	−	1.33815i	0.163558	−	0.986534i	$-0.447703\pi$
$42$	0.345988	−	1.29125i	0.0533871	−	0.199243i
$43$	−0.988872	−	3.69052i	−0.150802	−	0.562799i	−0.999428	−	0.0338072i	$-0.989237\pi$
$43$	−0.988872	−	3.69052i	−0.150802	−	0.562799i	0.848627	−	0.528992i	$-0.177430\pi$
$44$	−0.558756	−	0.967795i	−0.0842357	−	0.145901i
$45$	2.16763	−	0.548991i	0.323131	−	0.0818387i
$46$			1.34462i			0.198254i
$47$	−0.238845	+	0.238845i	−0.0348391	+	0.0348391i	−0.724312	−	0.689473i	$-0.757842\pi$
$47$	−0.238845	+	0.238845i	−0.0348391	+	0.0348391i	0.689473	+	0.724312i	$0.257842\pi$
$48$	−0.258819	−	0.965926i	−0.0373573	−	0.139419i
$49$	4.51457	−	2.60649i	0.644939	−	0.372356i
$50$	−4.86338	+	1.16083i	−0.687786	+	0.164167i
$51$	−2.93532	−	5.08412i	−0.411027	−	0.711919i
$52$	0.0527145	−	0.196733i	0.00731018	−	0.0272820i
$53$	−2.79320	−	0.748436i	−0.383676	−	0.102806i	0.0618254	−	0.998087i	$-0.480308\pi$
$53$	−2.79320	−	0.748436i	−0.383676	−	0.102806i	−0.445501	+	0.895281i	$0.646974\pi$
$54$	1.00000			0.136083
$55$	−2.42235	+	0.613504i	−0.326630	+	0.0827249i
$56$	−0.668398	+	1.15770i	−0.0893184	+	0.154704i
$57$	0.579735	−	2.16360i	0.0767878	−	0.286576i
$58$	4.11696	−	4.11696i	0.540583	−	0.540583i
$59$	−12.2868	−	7.09379i	−1.59961	−	0.923532i	−0.991563	−	0.129628i	$-0.958622\pi$
$59$	−12.2868	−	7.09379i	−1.59961	−	0.923532i	−0.608042	−	0.793905i	$-0.708045\pi$
$60$	−2.23586	−	0.0307391i	−0.288648	−	0.00396840i
$61$		−	1.48870i		−	0.190609i	−0.995448	−	0.0953043i	$-0.969618\pi$
$61$		−	1.48870i		−	0.190609i	0.995448	−	0.0953043i	$-0.0303824\pi$
$62$	4.98907	+	2.47168i	0.633612	+	0.313904i
$63$	−0.945257	−	0.945257i	−0.119091	−	0.119091i
$64$			1.00000i			0.125000i
$65$	−0.391244	−	0.233114i	−0.0485278	−	0.0289142i
$66$	−1.11751			−0.137556
$67$	−2.89574	−	0.775910i	−0.353770	−	0.0947925i	0.0775571	−	0.996988i	$-0.475288\pi$
$67$	−2.89574	−	0.775910i	−0.353770	−	0.0947925i	−0.431328	+	0.902195i	$0.641955\pi$
$68$	1.51943	+	5.67060i	0.184258	+	0.687661i
$69$	1.16448	+	0.672311i	0.140186	+	0.0809367i
$70$	2.08440	+	2.14252i	0.249134	+	0.256080i
$71$	0.224061	+	0.388085i	0.0265911	+	0.0460572i	0.879015	−	0.476795i	$-0.158201\pi$
$71$	0.224061	+	0.388085i	0.0265911	+	0.0460572i	−0.852424	+	0.522852i	$0.824868\pi$
$72$	−0.965926	−	0.258819i	−0.113835	−	0.0305021i
$73$	9.35629	+	2.50701i	1.09507	+	0.293423i	0.760756	−	0.649038i	$-0.224828\pi$
$73$	9.35629	+	2.50701i	1.09507	+	0.293423i	0.334315	+	0.942461i	$0.391495\pi$
$74$	0.306555	−	0.530969i	0.0356363	−	0.0617239i
$75$	−1.42638	+	4.79223i	−0.164704	+	0.553359i
$76$	−1.11996	+	1.93983i	−0.128469	+	0.222514i
$77$	1.05634	+	1.05634i	0.120381	+	0.120381i
$78$	−0.144019	−	0.144019i	−0.0163069	−	0.0163069i
$79$	−0.494348	+	0.856236i	−0.0556185	+	0.0963341i	−0.892494	−	0.451059i	$-0.851046\pi$
$79$	−0.494348	+	0.856236i	−0.0556185	+	0.0963341i	0.836876	+	0.547393i	$0.184380\pi$
$80$	2.15172	+	0.608374i	0.240569	+	0.0680183i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	9.55678	+	2.56073i	1.05537	+	0.282785i
$83$	1.22264	+	0.327604i	0.134202	+	0.0359592i	0.325295	−	0.945613i	$-0.394537\pi$
$83$	1.22264	+	0.327604i	0.134202	+	0.0359592i	−0.191093	+	0.981572i	$0.561203\pi$
$84$	0.668398	+	1.15770i	0.0729282	+	0.126315i
$85$	13.1259	+	0.180458i	1.42370	+	0.0195734i
$86$	3.30883	+	1.91035i	0.356800	+	0.205999i
$87$	−1.50691	−	5.62387i	−0.161558	−	0.602942i
$88$	1.07943	+	0.289234i	0.115068	+	0.0308324i
$89$	−7.32708			−0.776669			−0.388334	−	0.921519i	$-0.626949\pi$
$89$	−7.32708			−0.776669			−0.388334	+	0.921519i	$0.626949\pi$
$90$	−1.14455	+	1.92094i	−0.120646	+	0.202485i
$91$			0.272269i			0.0285416i
$92$	−0.950791	−	0.950791i	−0.0991268	−	0.0991268i
$93$	4.63507	−	3.08482i	0.480635	−	0.319880i
$94$		−	0.337778i		−	0.0348391i
$95$	3.49261	+	3.58999i	0.358334	+	0.368325i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	−9.91783	+	9.91783i	−1.00700	+	1.00700i	−0.00702771	+	0.999975i	$0.502237\pi$
$97$	−9.91783	+	9.91783i	−1.00700	+	1.00700i	−0.999975	+	0.00702771i	$0.997763\pi$
$98$	−1.34922	+	5.03535i	−0.136292	+	0.508647i
$99$	−0.558756	+	0.967795i	−0.0561571	+	0.0972670i
$100$	2.61810	−	4.25976i	0.261810	−	0.425976i
$101$	6.39218			0.636045			0.318023	−	0.948083i	$-0.396981\pi$
$101$	6.39218			0.636045			0.318023	+	0.948083i	$0.396981\pi$
$102$	5.67060	+	1.51943i	0.561473	+	0.150446i
$103$	1.63850	−	6.11498i	0.161447	−	0.602527i	−0.837020	−	0.547172i	$-0.815704\pi$
$103$	1.63850	−	6.11498i	0.161447	−	0.602527i	0.998467	−	0.0553547i	$-0.0176290\pi$
$104$	0.101837	+	0.176386i	0.00998590	+	0.0172961i
$105$	2.89768	−	0.733888i	0.282784	−	0.0716202i
$106$	2.50432	−	1.44587i	0.243241	−	0.140435i
$107$	−0.488367	−	1.82261i	−0.0472123	−	0.176199i	0.938294	−	0.345840i	$-0.112406\pi$
$107$	−0.488367	−	1.82261i	−0.0472123	−	0.176199i	−0.985506	+	0.169641i	$0.945739\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$		−	6.39294i		−	0.612332i	−0.951978	−	0.306166i	$-0.900954\pi$
$109$		−	6.39294i		−	0.612332i	0.951978	−	0.306166i	$-0.0990463\pi$
$110$	1.27905	−	2.14667i	0.121952	−	0.204677i
$111$	−0.306555	−	0.530969i	−0.0290969	−	0.0503974i
$112$	−0.345988	−	1.29125i	−0.0326928	−	0.122011i
$113$	1.87629	−	7.00242i	0.176507	−	0.658732i	−0.819783	−	0.572674i	$-0.805906\pi$
$113$	1.87629	−	7.00242i	0.176507	−	0.658732i	0.996290	−	0.0860585i	$-0.0274272\pi$
$114$	1.11996	+	1.93983i	0.104894	+	0.181682i
$115$	−2.62427	+	1.46740i	−0.244714	+	0.136835i
$116$			5.82226i			0.540583i
$117$	−0.196733	+	0.0527145i	−0.0181880	+	0.00487346i
$118$	13.7041	−	3.67201i	1.26157	−	0.338036i
$119$	−3.92392	−	6.79643i	−0.359705	−	0.623028i
$120$	1.60273	−	1.55925i	0.146308	−	0.142340i
$121$	−4.87558	+	8.44476i	−0.443235	+	0.767705i
$122$	1.05267	+	1.05267i	0.0953043	+	0.0953043i
$123$	6.99605	−	6.99605i	0.630812	−	0.630812i
$124$	−5.27555	+	1.78006i	−0.473758	+	0.159854i
$125$	−7.57302	−	8.22493i	−0.677351	−	0.735660i
$126$	1.33680			0.119091
$127$	4.35089	−	1.16582i	0.386079	−	0.103450i	−0.0605581	−	0.998165i	$-0.519288\pi$
$127$	4.35089	−	1.16582i	0.386079	−	0.103450i	0.446637	+	0.894715i	$0.352621\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	3.30883	−	1.91035i	0.291326	−	0.168197i
$130$	0.441488	−	0.111815i	0.0387210	−	0.00980679i
$131$	−5.24382	+	9.08256i	−0.458155	+	0.793547i	−0.998863	−	0.0476627i	$-0.984823\pi$
$131$	−5.24382	+	9.08256i	−0.458155	+	0.793547i	0.540709	+	0.841210i	$0.318156\pi$
$132$	0.790201	−	0.790201i	0.0687782	−	0.0687782i
$133$	0.774988	−	2.89229i	0.0672000	−	0.250794i
$134$	2.59625	−	1.49894i	0.224281	−	0.129489i
$135$	1.09131	+	1.95168i	0.0939248	+	0.167974i
$136$	−5.08412	−	2.93532i	−0.435960	−	0.251702i
$137$	−0.174035	+	0.649508i	−0.0148688	+	0.0554912i	−0.972962	−	0.230967i	$-0.925811\pi$
$137$	−0.174035	+	0.649508i	−0.0148688	+	0.0554912i	0.958093	+	0.286458i	$0.0924778\pi$
$138$	−1.29880	+	0.348014i	−0.110562	+	0.0296249i
$139$	−18.0841			−1.53387			−0.766936	−	0.641723i	$-0.778220\pi$
$139$	−18.0841			−1.53387			−0.766936	+	0.641723i	$0.778220\pi$
$140$	−2.98888	−	0.0410919i	−0.252607	−	0.00347290i
$141$	−0.292524	−	0.168889i	−0.0246350	−	0.0142230i
$142$	−0.432852	−	0.115982i	−0.0363242	−	0.00973303i
$143$	0.219852	−	0.0589091i	0.0183849	−	0.00492623i
$144$	0.866025	−	0.500000i	0.0721688	−	0.0416667i
$145$	12.5279	+	3.54211i	1.04038	+	0.294156i
$146$	−8.38862	+	4.84317i	−0.694247	+	0.400824i
$147$	3.68613	+	3.68613i	0.304027	+	0.304027i
$148$	0.158685	+	0.592219i	0.0130438	+	0.0486801i
$149$	5.71728	+	3.30087i	0.468378	+	0.270418i	0.715560	−	0.698551i	$-0.246171\pi$
$149$	5.71728	+	3.30087i	0.468378	+	0.270418i	−0.247183	+	0.968969i	$0.579505\pi$
$150$	−2.38001	−	4.39722i	−0.194327	−	0.359031i
$151$			9.53215i			0.775716i	0.921719	+	0.387858i	$0.126785\pi$
$151$			9.53215i			0.775716i	−0.921719	+	0.387858i	$0.873215\pi$
$152$	−0.579735	−	2.16360i	−0.0470228	−	0.175491i
$153$	4.15117	−	4.15117i	0.335602	−	0.335602i
$154$	−1.49389			−0.120381
$155$	0.620671	+	12.4344i	0.0498535	+	0.998757i
$156$	0.203673			0.0163069
$157$	4.99867	−	4.99867i	0.398937	−	0.398937i	−0.478921	−	0.877858i	$-0.658972\pi$
$157$	4.99867	−	4.99867i	0.398937	−	0.398937i	0.877858	+	0.478921i	$0.158972\pi$
$158$	−0.255893	−	0.955007i	−0.0203578	−	0.0759763i
$159$		−	2.89173i		−	0.229329i
$160$	−1.95168	+	1.09131i	−0.154294	+	0.0862754i
$161$	1.55667	+	0.898742i	0.122683	+	0.0708308i
$162$	0.258819	+	0.965926i	0.0203347	+	0.0758903i
$163$	9.29071	+	9.29071i	0.727704	+	0.727704i	0.970162	−	0.242458i	$-0.0779535\pi$
$163$	9.29071	+	9.29071i	0.727704	+	0.727704i	−0.242458	+	0.970162i	$0.577954\pi$
$164$	−8.56837	+	4.94695i	−0.669077	+	0.386292i
$165$	−1.21955	−	2.18103i	−0.0949419	−	0.169793i
$166$	−1.09619	+	0.632883i	−0.0850805	+	0.0491212i
$167$	−1.07834	+	0.288940i	−0.0834443	+	0.0223588i	−0.300300	−	0.953845i	$-0.597087\pi$
$167$	−1.07834	+	0.288940i	−0.0834443	+	0.0223588i	0.216855	+	0.976204i	$0.430420\pi$
$168$	−1.29125	−	0.345988i	−0.0996217	−	0.0266936i
$169$	−11.2224	−	6.47926i	−0.863262	−	0.498405i
$170$	−9.40902	+	9.15381i	−0.721639	+	0.702065i
$171$	2.23993			0.171291
$172$	−3.69052	+	0.988872i	−0.281400	+	0.0754008i
$173$	−4.16505	+	15.5442i	−0.316663	+	1.18180i	0.605769	+	0.795641i	$0.292866\pi$
$173$	−4.16505	+	15.5442i	−0.316663	+	1.18180i	−0.922432	+	0.386161i	$0.873801\pi$
$174$	5.04223	+	2.91113i	0.382250	+	0.220692i
$175$	−1.90678	+	6.40623i	−0.144139	+	0.484265i
$176$	−0.967795	+	0.558756i	−0.0729503	+	0.0421179i
$177$	3.67201	−	13.7041i	0.276006	−	1.03007i
$178$	5.18103	−	5.18103i	0.388334	−	0.388334i
$179$	−10.3139	+	17.8641i	−0.770895	+	1.33523i	0.166178	+	0.986096i	$0.446857\pi$
$179$	−10.3139	+	17.8641i	−0.770895	+	1.33523i	−0.937073	+	0.349133i	$0.886476\pi$
$180$	−0.548991	−	2.16763i	−0.0409193	−	0.161565i
$181$	−3.66497	+	2.11597i	−0.272415	+	0.157279i	−0.629985	−	0.776608i	$-0.716939\pi$
$181$	−3.66497	+	2.11597i	−0.272415	+	0.157279i	0.357569	+	0.933887i	$0.383606\pi$
$182$	−0.192524	−	0.192524i	−0.0142708	−	0.0142708i
$183$	1.43797	−	0.385304i	0.106298	−	0.0284825i
$184$	1.34462			0.0991268
$185$	1.37083	+	0.0188465i	0.100785	+	0.00138562i
$186$	−1.09620	+	5.45879i	−0.0803772	+	0.400258i
$187$	−4.63898	+	4.63898i	−0.339236	+	0.339236i
$188$	0.238845	+	0.238845i	0.0174196	+	0.0174196i
$189$	0.668398	−	1.15770i	0.0486188	−	0.0842102i
$190$	−5.00815	−	0.0688533i	−0.363330	−	0.00499514i
$191$	7.38558	+	12.7922i	0.534402	+	0.925612i	0.999192	+	0.0401907i	$0.0127965\pi$
$191$	7.38558	+	12.7922i	0.534402	+	0.925612i	−0.464790	+	0.885421i	$0.653870\pi$
$192$	−0.965926	+	0.258819i	−0.0697097	+	0.0186787i
$193$	−18.4936	+	4.95533i	−1.33120	+	0.356693i	−0.853161	−	0.521648i	$-0.825317\pi$
$193$	−18.4936	+	4.95533i	−1.33120	+	0.356693i	−0.478035	+	0.878341i	$0.658651\pi$
$194$		−	14.0259i		−	1.00700i
$195$	0.123909	−	0.438247i	0.00887334	−	0.0313835i
$196$	−2.60649	−	4.51457i	−0.186178	−	0.322469i
$197$	4.87345	−	18.1880i	0.347219	−	1.29584i	−0.542779	−	0.839876i	$-0.682628\pi$
$197$	4.87345	−	18.1880i	0.347219	−	1.29584i	0.889998	−	0.455964i	$-0.150706\pi$
$198$	−0.289234	−	1.07943i	−0.0205549	−	0.0767121i
$199$	−12.1960	−	21.1240i	−0.864548	−	1.49744i	−0.867495	−	0.497446i	$-0.834271\pi$
$199$	−12.1960	−	21.1240i	−0.864548	−	1.49744i	0.00294709	−	0.999996i	$-0.499062\pi$
$200$	1.16083	+	4.86338i	0.0820833	+	0.343893i
$201$		−	2.99789i		−	0.211455i
$202$	−4.51995	+	4.51995i	−0.318023	+	0.318023i
$203$	−2.01443	−	7.51797i	−0.141386	−	0.527658i
$204$	−5.08412	+	2.93532i	−0.355960	+	0.205513i
$205$	5.43166	+	21.4463i	0.379364	+	1.49787i
$206$	3.16535	+	5.48254i	0.220540	+	0.381987i
$207$	−0.348014	+	1.29880i	−0.0241886	+	0.0902732i
$208$	−0.196733	−	0.0527145i	−0.0136410	−	0.00365509i
$209$	−2.50315			−0.173146
$210$	−1.53003	+	2.56790i	−0.105582	+	0.177202i
$211$	−0.510067	+	0.883462i	−0.0351144	+	0.0608200i	−0.883049	−	0.469282i	$-0.844513\pi$
$211$	−0.510067	+	0.883462i	−0.0351144	+	0.0608200i	0.847934	+	0.530102i	$0.177846\pi$
$212$	−0.748436	+	2.79320i	−0.0514028	+	0.191838i
$213$	−0.316870	+	0.316870i	−0.0217116	+	0.0217116i
$214$	1.63411	+	0.943453i	0.111705	+	0.0644932i
$215$	−0.117445	+	8.54256i	−0.00800969	+	0.582598i
$216$		−	1.00000i		−	0.0680414i
$217$	6.19615	−	4.12377i	0.420622	−	0.279940i
$218$	4.52049	+	4.52049i	0.306166	+	0.306166i
$219$			9.68634i			0.654542i
$220$	0.613504	+	2.42235i	0.0413624	+	0.163315i
$221$	−1.19569			−0.0804309
$222$	0.592219	+	0.158685i	0.0397472	+	0.0106502i
$223$	5.01305	+	18.7089i	0.335698	+	1.25284i	0.903110	+	0.429409i	$0.141278\pi$
$223$	5.01305	+	18.7089i	0.335698	+	1.25284i	−0.567412	+	0.823434i	$0.692055\pi$
$224$	1.15770	+	0.668398i	0.0773520	+	0.0446592i
$225$	−4.99811	−	0.137456i	−0.333207	−	0.00916376i
$226$	3.62472	+	6.27820i	0.241113	+	0.417620i
$227$	−3.87721	−	1.03890i	−0.257340	−	0.0689539i	0.127843	−	0.991794i	$-0.459195\pi$
$227$	−3.87721	−	1.03890i	−0.257340	−	0.0689539i	−0.385182	+	0.922841i	$0.625861\pi$
$228$	−2.16360	−	0.579735i	−0.143288	−	0.0383939i
$229$	4.89693	−	8.48173i	0.323598	−	0.560488i	−0.657630	−	0.753342i	$-0.728441\pi$
$229$	4.89693	−	8.48173i	0.323598	−	0.560488i	0.981228	+	0.192853i	$0.0617741\pi$
$230$	0.818033	−	2.89324i	0.0539395	−	0.190775i
$231$	−0.746943	+	1.29374i	−0.0491453	+	0.0851221i
$232$	−4.11696	−	4.11696i	−0.270292	−	0.270292i
$233$	20.1337	+	20.1337i	1.31900	+	1.31900i	0.914568	+	0.404432i	$0.132531\pi$
$233$	20.1337	+	20.1337i	1.31900	+	1.31900i	0.404432	+	0.914568i	$0.367469\pi$
$234$	0.101837	−	0.176386i	0.00665727	−	0.0115307i
$235$	0.659234	−	0.368619i	0.0430037	−	0.0240461i
$236$	−7.09379	+	12.2868i	−0.461766	+	0.799803i
$237$	−0.955007	−	0.255893i	−0.0620344	−	0.0166221i
$238$	7.58043	+	2.03117i	0.491367	+	0.131661i
$239$	3.23978	+	5.61146i	0.209564	+	0.362975i	0.951577	−	0.307410i	$-0.0994622\pi$
$239$	3.23978	+	5.61146i	0.209564	+	0.362975i	−0.742013	+	0.670385i	$0.766129\pi$
$240$	−0.0307391	+	2.23586i	−0.00198420	+	0.144324i
$241$	6.00837	+	3.46894i	0.387033	+	0.223454i	0.680874	−	0.732401i	$-0.261600\pi$
$241$	6.00837	+	3.46894i	0.387033	+	0.223454i	−0.293841	+	0.955854i	$0.594933\pi$
$242$	−2.52379	−	9.41890i	−0.162235	−	0.605470i
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$	−1.48870			−0.0953043
$245$	−11.2998	+	2.86188i	−0.721917	+	0.182839i
$246$			9.89390i			0.630812i
$247$	−0.322591	−	0.322591i	−0.0205260	−	0.0205260i
$248$	2.47168	−	4.98907i	0.156952	−	0.316806i
$249$			1.26577i			0.0802146i
$250$	11.1708	+	0.460970i	0.706506	+	0.0291543i
$251$	5.04751	+	2.91418i	0.318596	+	0.183942i	0.650767	−	0.759278i	$-0.274448\pi$
$251$	5.04751	+	2.91418i	0.318596	+	0.183942i	−0.332170	+	0.943219i	$0.607781\pi$
$252$	−0.945257	+	0.945257i	−0.0595456	+	0.0595456i
$253$	0.388910	−	1.45143i	0.0244505	−	0.0912507i
$254$	−2.25219	+	3.90090i	−0.141315	+	0.244764i
$255$	3.22292	+	12.7254i	0.201827	+	0.796893i
$256$	1.00000			0.0625000
$257$	−8.40670	−	2.25257i	−0.524396	−	0.140511i	−0.0130966	−	0.999914i	$-0.504169\pi$
$257$	−8.40670	−	2.25257i	−0.524396	−	0.140511i	−0.511299	+	0.859403i	$0.670836\pi$
$258$	−0.988872	+	3.69052i	−0.0615645	+	0.229762i
$259$	−0.409802	−	0.709797i	−0.0254638	−	0.0441047i
$260$	−0.233114	+	0.391244i	−0.0144571	+	0.0242639i
$261$	5.04223	−	2.91113i	0.312106	−	0.180194i
$262$	−2.71440	−	10.1303i	−0.167696	−	0.625851i
$263$	−18.2607	+	18.2607i	−1.12600	+	1.12600i	−0.135179	+	0.990821i	$0.543161\pi$
$263$	−18.2607	+	18.2607i	−1.12600	+	1.12600i	−0.990821	+	0.135179i	$0.956839\pi$
$264$			1.11751i			0.0687782i
$265$	5.55485	+	3.30973i	0.341232	+	0.203315i
$266$	1.49716	+	2.59316i	0.0917969	+	0.158997i
$267$	−1.89639	−	7.07741i	−0.116057	−	0.433131i
$268$	−0.775910	+	2.89574i	−0.0473963	+	0.176885i
$269$	0.273279	+	0.473332i	0.0166621	+	0.0288596i	0.874236	−	0.485501i	$-0.161363\pi$
$269$	0.273279	+	0.473332i	0.0166621	+	0.0288596i	−0.857574	+	0.514360i	$0.828029\pi$
$270$	−2.15172	−	0.608374i	−0.130949	−	0.0370245i
$271$			16.1815i			0.982957i	0.870890	+	0.491478i	$0.163543\pi$
$271$			16.1815i			0.982957i	−0.870890	+	0.491478i	$0.836457\pi$
$272$	5.67060	−	1.51943i	0.343831	−	0.0921291i
$273$	−0.262992	+	0.0704685i	−0.0159170	+	0.00426495i
$274$	−0.336210	−	0.582333i	−0.0203112	−	0.0351800i
$275$	5.58545	+	0.153609i	0.336815	+	0.00926299i
$276$	0.672311	−	1.16448i	0.0404684	−	0.0700932i
$277$	0.900681	+	0.900681i	0.0541167	+	0.0541167i	0.733647	−	0.679531i	$-0.237816\pi$
$277$	0.900681	+	0.900681i	0.0541167	+	0.0541167i	−0.679531	+	0.733647i	$0.737816\pi$
$278$	12.7874	−	12.7874i	0.766936	−	0.766936i
$279$	4.17935	+	3.67873i	0.250211	+	0.220240i
$280$	2.14252	−	2.08440i	0.128040	−	0.124567i
$281$	13.8284			0.824934			0.412467	−	0.910972i	$-0.364667\pi$
$281$	13.8284			0.824934			0.412467	+	0.910972i	$0.364667\pi$
$282$	0.326268	−	0.0874233i	0.0194290	−	0.00520598i
$283$	0.884063	+	0.884063i	0.0525521	+	0.0525521i	0.732894	−	0.680342i	$-0.238169\pi$
$283$	0.884063	+	0.884063i	0.0525521	+	0.0525521i	−0.680342	+	0.732894i	$0.738169\pi$
$284$	0.388085	−	0.224061i	0.0230286	−	0.0132956i
$285$	−2.56371	+	4.30276i	−0.151861	+	0.254874i
$286$	−0.113804	+	0.197114i	−0.00672935	+	0.0116556i
$287$	9.35228	−	9.35228i	0.552048	−	0.552048i
$288$	−0.258819	+	0.965926i	−0.0152511	+	0.0569177i
$289$	15.1246	−	8.73219i	0.889682	−	0.513658i
$290$	−11.3632	+	6.35388i	−0.667269	+	0.373113i
$291$	−12.1468	−	7.01296i	−0.712059	−	0.411107i
$292$	2.50701	−	9.35629i	0.146712	−	0.547535i
$293$	−0.153464	+	0.0411206i	−0.00896548	+	0.00240229i	−0.263299	−	0.964714i	$-0.584811\pi$
$293$	−0.153464	+	0.0411206i	−0.00896548	+	0.00240229i	0.254334	+	0.967117i	$0.418144\pi$
$294$	−5.21298			−0.304027
$295$	22.1220	+	22.7388i	1.28799	+	1.32390i
$296$	−0.530969	−	0.306555i	−0.0308620	−	0.0178182i
$297$	−1.07943	−	0.289234i	−0.0626351	−	0.0167830i
$298$	−6.37680	+	1.70866i	−0.369398	+	0.0989799i
$299$	0.237173	−	0.136932i	0.0137160	−	0.00791896i
$300$	4.79223	+	1.42638i	0.276679	+	0.0823520i
$301$	4.42323	−	2.55375i	0.254951	−	0.147196i
$302$	−6.74025	−	6.74025i	−0.387858	−	0.387858i
$303$	1.65442	+	6.17437i	0.0950438	+	0.354708i
$304$	1.93983	+	1.11996i	0.111257	+	0.0642343i
$305$	−0.905687	+	3.20326i	−0.0518595	+	0.183418i
$306$			5.87064i			0.335602i
$307$	−4.54171	−	16.9499i	−0.259209	−	0.967381i	−0.965700	−	0.259659i	$-0.916390\pi$
$307$	−4.54171	−	16.9499i	−0.259209	−	0.967381i	0.706491	−	0.707722i	$-0.250277\pi$
$308$	1.05634	−	1.05634i	0.0601904	−	0.0601904i
$309$	6.33069			0.360140
$310$	−9.23134	−	8.35358i	−0.524305	−	0.474452i
$311$	19.8867			1.12767			0.563835	−	0.825888i	$-0.309325\pi$
$311$	19.8867			1.12767			0.563835	+	0.825888i	$0.309325\pi$
$312$	−0.144019	+	0.144019i	−0.00815345	+	0.00815345i
$313$	−3.78272	−	14.1173i	−0.213812	−	0.797958i	−0.986581	−	0.163271i	$-0.947796\pi$
$313$	−3.78272	−	14.1173i	−0.213812	−	0.797958i	0.772769	−	0.634687i	$-0.218871\pi$
$314$			7.06918i			0.398937i
$315$	1.45886	+	2.60899i	0.0821972	+	0.147000i
$316$	0.856236	+	0.494348i	0.0481670	+	0.0278093i
$317$	8.08234	+	30.1637i	0.453950	+	1.69416i	0.691157	+	0.722704i	$0.257101\pi$
$317$	8.08234	+	30.1637i	0.453950	+	1.69416i	−0.237208	+	0.971459i	$0.576232\pi$
$318$	2.04477	+	2.04477i	0.114665	+	0.114665i
$319$	−5.63475	+	3.25323i	−0.315486	+	0.182146i
$320$	0.608374	−	2.15172i	0.0340091	−	0.120285i
$321$	1.63411	−	0.943453i	0.0912071	−	0.0526584i
$322$	−1.73624	+	0.465223i	−0.0967567	+	0.0259259i
$323$	12.7017	+	3.40342i	0.706743	+	0.189371i
$324$	−0.866025	−	0.500000i	−0.0481125	−	0.0277778i
$325$	0.700025	+	0.739617i	0.0388304	+	0.0410266i
$326$	−13.1390			−0.727704
$327$	6.17510	−	1.65461i	0.341484	−	0.0915004i
$328$	2.56073	−	9.55678i	0.141393	−	0.527685i
$329$	−0.391045	−	0.225770i	−0.0215590	−	0.0124471i
$330$	2.40457	+	0.679866i	0.132367	+	0.0374254i
$331$	−30.9212	+	17.8523i	−1.69958	+	0.981254i	−0.753430	+	0.657528i	$0.771602\pi$
$331$	−30.9212	+	17.8523i	−1.69958	+	0.981254i	−0.946151	+	0.323726i	$0.895064\pi$
$332$	0.327604	−	1.22264i	0.0179796	−	0.0671008i
$333$	0.433535	−	0.433535i	0.0237575	−	0.0237575i
$334$	0.558189	−	0.966812i	0.0305427	−	0.0529016i
$335$	5.75876	+	3.43123i	0.314635	+	0.187468i
$336$	1.15770	−	0.668398i	0.0631577	−	0.0364641i
$337$	5.50504	+	5.50504i	0.299878	+	0.299878i	0.840966	−	0.541088i	$-0.181987\pi$
$337$	5.50504	+	5.50504i	0.299878	+	0.299878i	−0.541088	+	0.840966i	$0.681987\pi$
$338$	12.5170	−	3.35391i	0.680833	−	0.182429i
$339$	7.24944			0.393736
$340$	0.180458	−	13.1259i	0.00978671	−	0.711852i
$341$	−4.67048	−	4.11103i	−0.252920	−	0.222625i
$342$	−1.58387	+	1.58387i	−0.0856457	+	0.0856457i
$343$	11.5444	+	11.5444i	0.623339	+	0.623339i
$344$	1.91035	−	3.30883i	0.102999	−	0.178400i
$345$	−2.09661	−	2.15506i	−0.112877	−	0.116024i
$346$	−8.04625	−	13.9365i	−0.432569	−	0.749232i
$347$	−15.1255	+	4.05287i	−0.811980	+	0.217569i	−0.640837	−	0.767677i	$-0.721413\pi$
$347$	−15.1255	+	4.05287i	−0.811980	+	0.217569i	−0.171143	+	0.985246i	$0.554746\pi$
$348$	−5.62387	+	1.50691i	−0.301471	+	0.0807790i
$349$		−	13.0895i		−	0.700664i	−0.936626	−	0.350332i	$-0.886069\pi$
$349$		−	13.0895i		−	0.700664i	0.936626	−	0.350332i	$-0.113931\pi$
$350$	−3.18159	−	5.87818i	−0.170063	−	0.314202i
$351$	−0.101837	−	0.176386i	−0.00543563	−	0.00941479i
$352$	0.289234	−	1.07943i	0.0154162	−	0.0575341i
$353$	−7.89126	−	29.4506i	−0.420010	−	1.56750i	−0.774585	−	0.632470i	$-0.782041\pi$
$353$	−7.89126	−	29.4506i	−0.420010	−	1.56750i	0.354575	−	0.935027i	$-0.384625\pi$
$354$	7.09379	+	12.2868i	0.377031	+	0.653036i
$355$	−0.246015	−	0.971361i	−0.0130571	−	0.0515545i
$356$			7.32708i			0.388334i
$357$	5.54926	−	5.54926i	0.293698	−	0.293698i
$358$	−5.33885	−	19.9249i	−0.282167	−	1.05306i
$359$	4.83099	−	2.78917i	0.254970	−	0.147207i	−0.367068	−	0.930194i	$-0.619638\pi$
$359$	4.83099	−	2.78917i	0.254970	−	0.147207i	0.622038	+	0.782987i	$0.286305\pi$
$360$	1.92094	+	1.14455i	0.101242	+	0.0603230i
$361$	−6.99137	−	12.1094i	−0.367967	−	0.637337i
$362$	1.09531	−	4.08774i	0.0575681	−	0.214847i
$363$	−9.41890	−	2.52379i	−0.494364	−	0.132464i
$364$	0.272269			0.0142708
$365$	−18.6069	−	11.0865i	−0.973928	−	0.580294i
$366$	−0.744351	+	1.28925i	−0.0389078	+	0.0673903i
$367$	−4.87889	+	18.2083i	−0.254676	+	0.950464i	0.713595	+	0.700559i	$0.247066\pi$
$367$	−4.87889	+	18.2083i	−0.254676	+	0.950464i	−0.968270	+	0.249905i	$0.919601\pi$
$368$	−0.950791	+	0.950791i	−0.0495634	+	0.0495634i
$369$	8.56837	+	4.94695i	0.446052	+	0.257528i
$370$	−0.982648	+	0.955995i	−0.0510854	+	0.0496998i
$371$		−	3.86566i		−	0.200695i
$372$	−3.08482	−	4.63507i	−0.159940	−	0.240317i
$373$	−10.6084	−	10.6084i	−0.549284	−	0.549284i	0.376950	−	0.926234i	$-0.376973\pi$
$373$	−10.6084	−	10.6084i	−0.549284	−	0.549284i	−0.926234	+	0.376950i	$0.876973\pi$
$374$		−	6.56051i		−	0.339236i
$375$	5.98463	−	9.44374i	0.309045	−	0.487673i
$376$	−0.337778			−0.0174196
$377$	−1.14543	−	0.306918i	−0.0589927	−	0.0158071i
$378$	0.345988	+	1.29125i	0.0177957	+	0.0664145i
$379$	−32.1700	−	18.5734i	−1.65246	−	0.954049i	−0.976056	−	0.217521i	$-0.930203\pi$
$379$	−32.1700	−	18.5734i	−1.65246	−	0.954049i	−0.676406	−	0.736529i	$-0.736464\pi$
$380$	3.58999	−	3.49261i	0.184162	−	0.179167i
$381$	2.25219	+	3.90090i	0.115383	+	0.199849i
$382$	−14.2679	−	3.82306i	−0.730007	−	0.195605i
$383$	−3.57248	−	0.957242i	−0.182545	−	0.0489128i	0.166388	−	0.986060i	$-0.446789\pi$
$383$	−3.57248	−	0.957242i	−0.182545	−	0.0489128i	−0.348933	+	0.937147i	$0.613456\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	−1.63029	−	2.91559i	−0.0830872	−	0.148592i
$386$	9.57297	−	16.5809i	0.487251	−	0.843944i
$387$	2.70165	+	2.70165i	0.137333	+	0.137333i
$388$	9.91783	+	9.91783i	0.503502	+	0.503502i
$389$	15.5167	−	26.8757i	0.786727	−	1.36265i	−0.141236	−	0.989976i	$-0.545108\pi$
$389$	15.5167	−	26.8757i	0.786727	−	1.36265i	0.927962	−	0.372674i	$-0.121559\pi$
$390$	0.222270	+	0.397504i	0.0112551	+	0.0201284i
$391$	−3.94689	+	6.83622i	−0.199603	+	0.345722i
$392$	5.03535	+	1.34922i	0.254324	+	0.0681458i
$393$	−10.1303	−	2.71440i	−0.511005	−	0.136923i
$394$	9.41479	+	16.3069i	0.474310	+	0.821530i
$395$	1.58461	−	1.54163i	0.0797303	−	0.0775677i
$396$	0.967795	+	0.558756i	0.0486335	+	0.0280786i
$397$	−0.175149	−	0.653667i	−0.00879050	−	0.0328066i	0.961391	−	0.275185i	$-0.0887391\pi$
$397$	−0.175149	−	0.653667i	−0.00879050	−	0.0328066i	−0.970182	+	0.242378i	$0.922072\pi$
$398$	23.5608	+	6.31309i	1.18099	+	0.316447i
$399$	2.99432			0.149904
$400$	−4.25976	−	2.61810i	−0.212988	−	0.130905i
$401$		−	13.4600i		−	0.672159i	−0.941834	−	0.336080i	$-0.890899\pi$
$401$		−	13.4600i		−	0.672159i	0.941834	−	0.336080i	$-0.109101\pi$
$402$	2.11983	+	2.11983i	0.105727	+	0.105727i
$403$	−0.0720985	−	1.13171i	−0.00359148	−	0.0563745i
$404$		−	6.39218i		−	0.318023i
$405$	−1.60273	+	1.55925i	−0.0796401	+	0.0774799i
$406$	6.74043	+	3.89159i	0.334522	+	0.193136i
$407$	−0.484481	+	0.484481i	−0.0240148	+	0.0240148i
$408$	1.51943	−	5.67060i	0.0752231	−	0.280737i
$409$	4.09874	−	7.09922i	0.202670	−	0.351034i	−0.746718	−	0.665141i	$-0.768372\pi$
$409$	4.09874	−	7.09922i	0.202670	−	0.351034i	0.949388	+	0.314107i	$0.101705\pi$
$410$	−19.0056	−	11.3241i	−0.938619	−	0.559255i
$411$	−0.672420			−0.0331680
$412$	−6.11498	−	1.63850i	−0.301263	−	0.0807233i
$413$	4.90873	−	18.3196i	0.241543	−	0.901451i
$414$	−0.672311	−	1.16448i	−0.0330423	−	0.0572309i
$415$	−2.43146	−	1.44873i	−0.119356	−	0.0711154i
$416$	0.176386	−	0.101837i	0.00864804	−	0.00499295i
$417$	−4.68051	−	17.4679i	−0.229205	−	0.855406i
$418$	1.76999	−	1.76999i	0.0865731	−	0.0865731i
$419$			14.8400i			0.724981i	0.931987	+	0.362490i	$0.118073\pi$
$419$			14.8400i			0.724981i	−0.931987	+	0.362490i	$0.881927\pi$
$420$	−0.733888	−	2.89768i	−0.0358101	−	0.141392i
$421$	5.50696	+	9.53833i	0.268393	+	0.464870i	0.968447	−	0.249220i	$-0.0801742\pi$
$421$	5.50696	+	9.53833i	0.268393	+	0.464870i	−0.700054	+	0.714090i	$0.746841\pi$
$422$	−0.264030	−	0.985373i	−0.0128528	−	0.0479672i
$423$	0.0874233	−	0.326268i	0.00425067	−	0.0158637i
$424$	−1.44587	−	2.50432i	−0.0702175	−	0.121620i
$425$	−28.1334	−	8.37375i	−1.36467	−	0.406187i
$426$		−	0.448122i		−	0.0217116i
$427$	1.92228	−	0.515073i	0.0930256	−	0.0249261i
$428$	−1.82261	+	0.488367i	−0.0880993	+	0.0236061i
$429$	0.113804	+	0.197114i	0.00549449	+	0.00951674i
$430$	−5.95746	−	6.12355i	−0.287294	−	0.295304i
$431$	15.4828	−	26.8170i	0.745782	−	1.29173i	−0.204047	−	0.978961i	$-0.565410\pi$
$431$	15.4828	−	26.8170i	0.745782	−	1.29173i	0.949829	−	0.312771i	$-0.101257\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$	6.75028	−	6.75028i	0.324398	−	0.324398i	−0.526054	−	0.850451i	$-0.676329\pi$
$433$	6.75028	−	6.75028i	0.324398	−	0.324398i	0.850451	+	0.526054i	$0.176329\pi$
$434$	−1.46539	+	7.29728i	−0.0703412	+	0.350281i
$435$	−0.178971	+	13.0177i	−0.00858100	+	0.624153i
$436$	−6.39294			−0.306166
$437$	−2.90923	+	0.779525i	−0.139167	+	0.0372897i
$438$	−6.84928	−	6.84928i	−0.327271	−	0.327271i
$439$	−12.8958	+	7.44539i	−0.615483	+	0.355349i	−0.775108	−	0.631828i	$-0.782305\pi$
$439$	−12.8958	+	7.44539i	−0.615483	+	0.355349i	0.159625	+	0.987178i	$0.448971\pi$
$440$	−2.14667	−	1.27905i	−0.102339	−	0.0609762i
$441$	−2.60649	+	4.51457i	−0.124119	+	0.214980i
$442$	0.845481	−	0.845481i	0.0402154	−	0.0402154i
$443$	7.56641	−	28.2382i	0.359491	−	1.34164i	−0.515247	−	0.857042i	$-0.672300\pi$
$443$	7.56641	−	28.2382i	0.359491	−	1.34164i	0.874738	−	0.484596i	$-0.161033\pi$
$444$	−0.530969	+	0.306555i	−0.0251987	+	0.0145485i
$445$	15.7658	+	4.45760i	0.747370	+	0.211311i
$446$	−16.7740	−	9.68446i	−0.794271	−	0.458573i
$447$	−1.70866	+	6.37680i	−0.0808167	+	0.301612i
$448$	−1.29125	+	0.345988i	−0.0610056	+	0.0163464i
$449$	21.8672			1.03198			0.515989	−	0.856595i	$-0.327424\pi$
$449$	21.8672			1.03198			0.515989	+	0.856595i	$0.327424\pi$
$450$	3.63139	−	3.43700i	0.171186	−	0.162022i
$451$	−9.57527	−	5.52828i	−0.450882	−	0.260317i
$452$	−7.00242	−	1.87629i	−0.329366	−	0.0882534i
$453$	−9.20735	+	2.46710i	−0.432599	+	0.115915i
$454$	3.47621	−	2.00699i	0.163147	−	0.0941928i
$455$	0.165642	−	0.585846i	0.00776540	−	0.0274649i
$456$	1.93983	−	1.11996i	0.0908410	−	0.0524471i
$457$	25.8187	+	25.8187i	1.20775	+	1.20775i	0.971754	+	0.235995i	$0.0758347\pi$
$457$	25.8187	+	25.8187i	1.20775	+	1.20775i	0.235995	+	0.971754i	$0.424165\pi$
$458$	2.53484	+	9.46014i	0.118445	+	0.442043i
$459$	5.08412	+	2.93532i	0.237306	+	0.137009i
$460$	1.46740	+	2.62427i	0.0684177	+	0.122357i
$461$		−	41.8932i		−	1.95116i	−0.219638	−	0.975582i	$-0.570488\pi$
$461$		−	41.8932i		−	1.95116i	0.219638	−	0.975582i	$-0.429512\pi$
$462$	−0.386646	−	1.44298i	−0.0179884	−	0.0671337i
$463$	−10.7357	+	10.7357i	−0.498930	+	0.498930i	−0.911105	−	0.412175i	$-0.864769\pi$
$463$	−10.7357	+	10.7357i	−0.498930	+	0.498930i	0.412175	+	0.911105i	$0.364769\pi$
$464$	5.82226			0.270292
$465$	−11.8501	+	3.81779i	−0.549535	+	0.177046i
$466$	−28.4733			−1.31900
$467$	0.612599	−	0.612599i	0.0283477	−	0.0283477i	−0.692791	−	0.721139i	$-0.743619\pi$
$467$	0.612599	−	0.612599i	0.0283477	−	0.0283477i	0.721139	+	0.692791i	$0.243619\pi$
$468$	0.0527145	+	0.196733i	0.00243673	+	0.00909399i
$469$		−	4.00756i		−	0.185052i
$470$	−0.205495	+	0.726802i	−0.00947879	+	0.0335249i
$471$	6.12209	+	3.53459i	0.282091	+	0.162865i
$472$	−3.67201	−	13.7041i	−0.169018	−	0.630784i
$473$	−3.01913	−	3.01913i	−0.138820	−	0.138820i
$474$	0.856236	−	0.494348i	0.0393282	−	0.0227062i
$475$	−5.33106	−	9.84944i	−0.244606	−	0.451923i
$476$	−6.79643	+	3.92392i	−0.311514	+	0.179853i
$477$	2.79320	−	0.748436i	0.127892	−	0.0342685i
$478$	−6.25877	−	1.67703i	−0.286270	−	0.0767057i
$479$	−5.70923	−	3.29622i	−0.260861	−	0.150608i	0.363866	−	0.931451i	$-0.381457\pi$
$479$	−5.70923	−	3.29622i	−0.260861	−	0.150608i	−0.624727	+	0.780843i	$0.714790\pi$
$480$	−1.55925	−	1.60273i	−0.0711699	−	0.0731541i
$481$	−0.124874			−0.00569377
$482$	−6.70147	+	1.79565i	−0.305244	+	0.0817898i
$483$	−0.465223	+	1.73624i	−0.0211684	+	0.0790015i
$484$	8.44476	+	4.87558i	0.383853	+	0.221617i
$485$	27.3741	−	15.3066i	1.24299	−	0.695037i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	2.76640	−	10.3244i	0.125358	−	0.467841i	−0.874494	−	0.485036i	$-0.838807\pi$
$487$	2.76640	−	10.3244i	0.125358	−	0.467841i	0.999852	+	0.0171941i	$0.00547334\pi$
$488$	1.05267	−	1.05267i	0.0476522	−	0.0476522i
$489$	−6.56952	+	11.3787i	−0.297084	+	0.514565i
$490$	5.96651	−	10.0138i	0.269539	−	0.452378i
$491$	3.07095	−	1.77302i	0.138590	−	0.0800151i	−0.429102	−	0.903256i	$-0.641170\pi$
$491$	3.07095	−	1.77302i	0.138590	−	0.0800151i	0.567692	+	0.823241i	$0.307836\pi$
$492$	−6.99605	−	6.99605i	−0.315406	−	0.315406i
$493$	33.0157	−	8.84653i	1.48695	−	0.398428i
$494$	0.456213			0.0205260
$495$	1.79107	−	1.74249i	0.0805024	−	0.0783189i
$496$	1.78006	+	5.27555i	0.0799269	+	0.236879i
$497$	−0.423590	+	0.423590i	−0.0190006	+	0.0190006i
$498$	−0.895031	−	0.895031i	−0.0401073	−	0.0401073i
$499$	5.62259	−	9.73862i	0.251702	−	0.435960i	−0.712293	−	0.701883i	$-0.752343\pi$
$499$	5.62259	−	9.73862i	0.251702	−	0.435960i	0.963994	+	0.265922i	$0.0856764\pi$
$500$	−8.22493	+	7.57302i	−0.367830	+	0.338676i
$501$	−0.558189	−	0.966812i	−0.0249380	−	0.0431940i
$502$	−5.62977	+	1.50849i	−0.251269	+	0.0673273i
$503$	14.6888	−	3.93585i	0.654941	−	0.175491i	0.0839791	−	0.996468i	$-0.473237\pi$
$503$	14.6888	−	3.93585i	0.654941	−	0.175491i	0.570962	+	0.820977i	$0.306570\pi$
$504$		−	1.33680i		−	0.0595456i
$505$	−13.7541	−	3.88883i	−0.612051	−	0.173051i
$506$	0.751316	+	1.30132i	0.0334001	+	0.0578506i
$507$	3.35391	−	12.5170i	0.148952	−	0.555898i
$508$	−1.16582	−	4.35089i	−0.0517248	−	0.193040i
$509$	13.3879	+	23.1886i	0.593409	+	1.02782i	0.993769	+	0.111457i	$0.0355518\pi$
$509$	13.3879	+	23.1886i	0.593409	+	1.02782i	−0.400360	+	0.916358i	$0.631115\pi$
$510$	−11.2771	−	6.71923i	−0.499360	−	0.297533i
$511$			12.9487i			0.572815i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	0.579735	+	2.16360i	0.0255959	+	0.0955254i
$514$	7.53724	−	4.35163i	0.332454	−	0.191942i
$515$	−7.24579	+	12.1609i	−0.319288	+	0.535872i
$516$	−1.91035	−	3.30883i	−0.0840987	−	0.145663i
$517$	−0.0976967	+	0.364609i	−0.00429670	+	0.0160355i
$518$	0.791676	+	0.212129i	0.0347843	+	0.00932041i
$519$	−16.0925			−0.706383
$520$	−0.111815	−	0.441488i	−0.00490340	−	0.0193605i
$521$	16.8776	−	29.2329i	0.739421	−	1.28072i	−0.213335	−	0.976979i	$-0.568433\pi$
$521$	16.8776	−	29.2329i	0.739421	−	1.28072i	0.952756	−	0.303736i	$-0.0982341\pi$
$522$	−1.50691	+	5.62387i	−0.0659557	+	0.246150i
$523$	−13.4167	+	13.4167i	−0.586671	+	0.586671i	−0.936728	−	0.350057i	$-0.886162\pi$
$523$	−13.4167	+	13.4167i	−0.586671	+	0.586671i	0.350057	+	0.936728i	$0.386162\pi$
$524$	9.08256	+	5.24382i	0.396774	+	0.229077i
$525$	−6.68145	−	0.183751i	−0.291602	−	0.00801955i
$526$		−	25.8245i		−	1.12600i
$527$	18.1098	+	27.2108i	0.788877	+	1.18532i
$528$	−0.790201	−	0.790201i	−0.0343891	−	0.0343891i
$529$			21.1920i			0.921391i
$530$	−6.26820	+	1.58754i	−0.272273	+	0.0689581i
$531$	14.1876			0.615688
$532$	−2.89229	−	0.774988i	−0.125397	−	0.0336000i
$533$	−0.521552	−	1.94646i	−0.0225909	−	0.0843105i
$534$	6.34543	+	3.66354i	0.274594	+	0.158537i
$535$	−0.0580018	+	4.21885i	−0.00250764	+	0.182397i
$536$	−1.49894	−	2.59625i	−0.0647445	−	0.112141i
$537$	−19.9249	−	5.33885i	−0.859822	−	0.230388i
$538$	−0.527934	−	0.141459i	−0.0227608	−	0.00609875i
$539$	2.91278	−	5.04509i	0.125463	−	0.217307i
$540$	1.95168	−	1.09131i	0.0839869	−	0.0469624i
$541$	8.08640	−	14.0060i	0.347661	−	0.602167i	−0.638172	−	0.769894i	$-0.720309\pi$
$541$	8.08640	−	14.0060i	0.347661	−	0.602167i	0.985834	+	0.167727i	$0.0536426\pi$
$542$	−11.4421	−	11.4421i	−0.491478	−	0.491478i
$543$	−2.99244	−	2.99244i	−0.128418	−	0.128418i
$544$	−2.93532	+	5.08412i	−0.125851	+	0.217980i
$545$	−3.88930	+	13.7558i	−0.166599	+	0.589233i
$546$	0.136135	−	0.235792i	0.00582603	−	0.0100910i
$547$	−39.8034	−	10.6653i	−1.70187	−	0.456015i	−0.728462	−	0.685086i	$-0.759765\pi$
$547$	−39.8034	−	10.6653i	−1.70187	−	0.456015i	−0.973410	+	0.229070i	$0.926431\pi$
$548$	0.649508	+	0.174035i	0.0277456	+	0.00743441i
$549$	0.744351	+	1.28925i	0.0317681	+	0.0550240i
$550$	−4.05813	+	3.84089i	−0.173039	+	0.163776i
$551$	11.2942	+	6.52072i	0.481150	+	0.277792i
$552$	0.348014	+	1.29880i	0.0148124	+	0.0552808i
$553$	−1.27665	−	0.342077i	−0.0542887	−	0.0145466i
$554$	−1.27376			−0.0541167
$555$	0.336592	+	1.32900i	0.0142875	+	0.0564127i
$556$			18.0841i			0.766936i
$557$	−6.05111	−	6.05111i	−0.256394	−	0.256394i	0.567192	−	0.823586i	$-0.308030\pi$
$557$	−6.05111	−	6.05111i	−0.256394	−	0.256394i	−0.823586	+	0.567192i	$0.808030\pi$
$558$	−5.55650	+	0.353991i	−0.235225	+	0.0149856i
$559$		−	0.778176i		−	0.0329133i
$560$	−0.0410919	+	2.98888i	−0.00173645	+	0.126303i
$561$	−5.68157	−	3.28026i	−0.239876	−	0.138493i
$562$	−9.77817	+	9.77817i	−0.412467	+	0.412467i
$563$	2.09282	−	7.81050i	0.0882017	−	0.329173i	−0.907700	−	0.419621i	$-0.862163\pi$
$563$	2.09282	−	7.81050i	0.0882017	−	0.329173i	0.995901	+	0.0904476i	$0.0288298\pi$
$564$	−0.168889	+	0.292524i	−0.00711151	+	0.0123175i
$565$	−8.29734	+	13.9257i	−0.349072	+	0.585860i
$566$	−1.25025			−0.0525521
$567$	1.29125	+	0.345988i	0.0542272	+	0.0145301i
$568$	−0.115982	+	0.432852i	−0.00486651	+	0.0181621i
$569$	16.6570	+	28.8508i	0.698297	+	1.20949i	0.969056	+	0.246839i	$0.0793920\pi$
$569$	16.6570	+	28.8508i	0.698297	+	1.20949i	−0.270759	+	0.962647i	$0.587275\pi$
$570$	−1.22970	−	4.85532i	−0.0515064	−	0.203367i
$571$	−3.53897	+	2.04323i	−0.148101	+	0.0855063i	−0.572219	−	0.820101i	$-0.693917\pi$
$571$	−3.53897	+	2.04323i	−0.148101	+	0.0855063i	0.424118	+	0.905607i	$0.360584\pi$
$572$	−0.0589091	−	0.219852i	−0.00246311	−	0.00919247i
$573$	−10.4448	+	10.4448i	−0.436338	+	0.436338i
$574$			13.2261i			0.552048i
$575$	6.53941	−	1.56088i	0.272712	−	0.0650933i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−2.43148	−	9.07440i	−0.101224	−	0.377772i	0.896666	−	0.442708i	$-0.145982\pi$
$577$	−2.43148	−	9.07440i	−0.101224	−	0.377772i	−0.997889	+	0.0649362i	$0.979316\pi$
$578$	−4.52012	+	16.8693i	−0.188012	+	0.701670i
$579$	−9.57297	−	16.5809i	−0.397839	−	0.689077i
$580$	3.54211	−	12.5279i	0.147078	−	0.520191i
$581$			1.69207i			0.0701989i
$582$	13.5480	−	3.63018i	0.561583	−	0.150476i
$583$	−3.12144	+	0.836387i	−0.129277	+	0.0346396i
$584$	4.84317	+	8.38862i	0.200412	+	0.347124i
$585$	0.455384	+	0.00626073i	0.0188278	+	0.000258849i
$586$	0.0794389	−	0.137592i	0.00328159	−	0.00568388i
$587$	−19.4785	−	19.4785i	−0.803965	−	0.803965i	0.179748	−	0.983713i	$-0.442472\pi$
$587$	−19.4785	−	19.4785i	−0.803965	−	0.803965i	−0.983713	+	0.179748i	$0.942472\pi$
$588$	3.68613	−	3.68613i	0.152014	−	0.152014i
$589$	−2.45540	+	12.2273i	−0.101173	+	0.503816i
$590$	−31.7214	−	0.436113i	−1.30595	−	0.0179545i
$591$	18.8296			0.774546
$592$	0.592219	−	0.158685i	0.0243401	−	0.00652190i
$593$	9.83476	+	9.83476i	0.403865	+	0.403865i	0.879593	−	0.475727i	$-0.157815\pi$
$593$	9.83476	+	9.83476i	0.403865	+	0.403865i	−0.475727	+	0.879593i	$0.657815\pi$
$594$	0.967795	−	0.558756i	0.0397091	−	0.0229261i
$595$	4.30839	+	17.0112i	0.176627	+	0.697391i
$596$	3.30087	−	5.71728i	0.135209	−	0.234189i
$597$	17.2477	−	17.2477i	0.705901	−	0.705901i
$598$	−0.0708810	+	0.264532i	−0.00289854	+	0.0108175i
$599$	34.9582	−	20.1831i	1.42835	−	0.824659i	0.431361	−	0.902179i	$-0.358033\pi$
$599$	34.9582	−	20.1831i	1.42835	−	0.824659i	0.996991	+	0.0775199i	$0.0247001\pi$
$600$	−4.39722	+	2.38001i	−0.179516	+	0.0971637i
$601$	−31.8196	−	18.3711i	−1.29795	−	0.749372i	−0.317900	−	0.948124i	$-0.602978\pi$
$601$	−31.8196	−	18.3711i	−1.29795	−	0.749372i	−0.980050	+	0.198752i	$0.936311\pi$
$602$	−1.32192	+	4.93347i	−0.0538775	+	0.201073i
$603$	2.89574	−	0.775910i	0.117923	−	0.0315975i
$604$	9.53215			0.387858
$605$	15.6284	−	15.2045i	0.635386	−	0.618152i
$606$	−5.53579	−	3.19609i	−0.224876	−	0.129832i
$607$	28.6403	+	7.67415i	1.16248	+	0.311484i	0.787954	−	0.615734i	$-0.211140\pi$
$607$	28.6403	+	7.67415i	1.16248	+	0.311484i	0.374521	+	0.927218i	$0.377807\pi$
$608$	−2.16360	+	0.579735i	−0.0877457	+	0.0235114i
$609$	6.74043	−	3.89159i	0.273136	−	0.157695i
$610$	−1.62463	−	2.90547i	−0.0657794	−	0.117639i
$611$	−0.0595793	+	0.0343981i	−0.00241032	+	0.00139160i
$612$	−4.15117	−	4.15117i	−0.167801	−	0.167801i
$613$	4.51865	+	16.8638i	0.182507	+	0.681124i	0.995151	+	0.0983636i	$0.0313608\pi$
$613$	4.51865	+	16.8638i	0.182507	+	0.681124i	−0.812644	+	0.582761i	$0.801973\pi$
$614$	15.1968	+	8.77390i	0.613295	+	0.354086i
$615$	−19.3097	+	10.7973i	−0.778643	+	0.435389i
$616$			1.49389i			0.0601904i
$617$	3.42401	+	12.7786i	0.137845	+	0.514446i	0.999970	+	0.00774951i	$0.00246677\pi$
$617$	3.42401	+	12.7786i	0.137845	+	0.514446i	−0.862125	+	0.506696i	$0.830867\pi$
$618$	−4.47647	+	4.47647i	−0.180070	+	0.180070i
$619$	−11.7804			−0.473496			−0.236748	−	0.971571i	$-0.576082\pi$
$619$	−11.7804			−0.473496			−0.236748	+	0.971571i	$0.576082\pi$
$620$	12.4344	−	0.620671i	0.499378	−	0.0249268i
$621$	−1.34462			−0.0539578
$622$	−14.0620	+	14.0620i	−0.563835	+	0.563835i
$623$	−2.53508	−	9.46105i	−0.101566	−	0.379049i
$624$		−	0.203673i		−	0.00815345i
$625$	11.2911	+	22.3049i	0.451646	+	0.892197i
$626$	12.6572	+	7.30766i	0.505885	+	0.292073i
$627$	−0.647862	−	2.41785i	−0.0258731	−	0.0965598i
$628$	−4.99867	−	4.99867i	−0.199468	−	0.199468i
$629$	3.11713	−	1.79967i	0.124288	−	0.0717577i
$630$	−2.87640	−	0.813272i	−0.114599	−	0.0324015i
$631$	33.7838	−	19.5051i	1.34491	−	0.776485i	0.357387	−	0.933956i	$-0.383668\pi$
$631$	33.7838	−	19.5051i	1.34491	−	0.776485i	0.987523	+	0.157472i	$0.0503343\pi$
$632$	−0.955007	+	0.255893i	−0.0379882	+	0.0101789i
$633$	−0.985373	−	0.264030i	−0.0391651	−	0.0104943i
$634$	−27.0441	−	15.6139i	−1.07406	−	0.620107i
$635$	−10.0711	−	0.138460i	−0.399661	−	0.00549463i
$636$	−2.89173			−0.114665
$637$	1.02557	−	0.274799i	0.0406344	−	0.0108880i
$638$	1.68399	−	6.28475i	0.0666699	−	0.248816i
$639$	−0.388085	−	0.224061i	−0.0153524	−	0.00886371i
$640$	1.09131	+	1.95168i	0.0431377	+	0.0771469i
$641$	16.9938	−	9.81138i	0.671215	−	0.387526i	−0.125322	−	0.992116i	$-0.539996\pi$
$641$	16.9938	−	9.81138i	0.671215	−	0.387526i	0.796537	+	0.604590i	$0.206663\pi$
$642$	−0.488367	+	1.82261i	−0.0192743	+	0.0719328i
$643$	−2.66286	+	2.66286i	−0.105013	+	0.105013i	−0.757661	−	0.652648i	$-0.773658\pi$
$643$	−2.66286	+	2.66286i	−0.105013	+	0.105013i	0.652648	+	0.757661i	$0.273658\pi$
$644$	0.898742	−	1.55667i	0.0354154	−	0.0613413i
$645$	−8.28188	+	2.09753i	−0.326099	+	0.0825903i
$646$	−11.3881	+	6.57490i	−0.448057	+	0.258686i
$647$	26.7080	+	26.7080i	1.05000	+	1.05000i	0.998682	+	0.0513163i	$0.0163417\pi$
$647$	26.7080	+	26.7080i	1.05000	+	1.05000i	0.0513163	+	0.998682i	$0.483658\pi$
$648$	0.965926	−	0.258819i	0.0379452	−	0.0101674i
$649$	−15.8548			−0.622355
$650$	−1.01798	−	0.0279962i	−0.0399285	−	0.00109810i
$651$	5.58693	+	4.91771i	0.218969	+	0.192740i
$652$	9.29071	−	9.29071i	0.363852	−	0.363852i
$653$	−24.2483	−	24.2483i	−0.948909	−	0.948909i	0.0498477	−	0.998757i	$-0.484126\pi$
$653$	−24.2483	−	24.2483i	−0.948909	−	0.948909i	−0.998757	+	0.0498477i	$0.984126\pi$
$654$	−3.19647	+	5.53645i	−0.124992	+	0.216492i
$655$	16.8088	−	16.3529i	0.656774	−	0.638960i
$656$	4.94695	+	8.56837i	0.193146	+	0.334539i
$657$	−9.35629	+	2.50701i	−0.365024	+	0.0978078i
$658$	0.436154	−	0.116867i	0.0170031	−	0.00455595i
$659$		−	17.2560i		−	0.672198i	−0.941827	−	0.336099i	$-0.890892\pi$
$659$		−	17.2560i		−	0.672198i	0.941827	−	0.336099i	$-0.109108\pi$
$660$	−2.18103	+	1.21955i	−0.0848963	+	0.0474709i
$661$	−17.5435	−	30.3863i	−0.682364	−	1.18189i	−0.974258	−	0.225438i	$-0.927619\pi$
$661$	−17.5435	−	30.3863i	−0.682364	−	1.18189i	0.291894	−	0.956451i	$-0.405715\pi$
$662$	9.24105	−	34.4881i	0.359164	−	1.34042i
$663$	−0.309468	−	1.15495i	−0.0120187	−	0.0448545i
$664$	0.632883	+	1.09619i	0.0245606	+	0.0425402i
$665$	−3.42715	+	5.75191i	−0.132899	+	0.223050i
$666$			0.613110i			0.0237575i
$667$	−5.53575	+	5.53575i	−0.214345	+	0.214345i
$668$	0.288940	+	1.07834i	0.0111794	+	0.0417222i
$669$	−16.7740	+	9.68446i	−0.648520	+	0.374423i
$670$	−6.49830	+	1.64581i	−0.251051	+	0.0635832i
$671$	−0.831821	−	1.44076i	−0.0321121	−	0.0556198i
$672$	−0.345988	+	1.29125i	−0.0133468	+	0.0498109i
$673$	−13.0165	−	3.48775i	−0.501748	−	0.134443i	−0.000936676	−	1.00000i	$-0.500298\pi$
$673$	−13.0165	−	3.48775i	−0.501748	−	0.134443i	−0.500811	+	0.865557i	$0.666965\pi$
$674$	−7.78530			−0.299878
$675$	−1.16083	−	4.86338i	−0.0446805	−	0.187192i
$676$	−6.47926	+	11.2224i	−0.249202	+	0.431631i
$677$	4.59584	−	17.1519i	0.176632	−	0.659201i	−0.819635	−	0.572886i	$-0.805824\pi$
$677$	4.59584	−	17.1519i	0.176632	−	0.659201i	0.996268	−	0.0863157i	$-0.0275094\pi$
$678$	−5.12613	+	5.12613i	−0.196868	+	0.196868i
$679$	−16.2378	−	9.37490i	−0.623150	−	0.359776i
$680$	9.15381	+	9.40902i	0.351033	+	0.360819i
$681$		−	4.01399i		−	0.153816i
$682$	6.20946	−	0.395589i	0.237773	−	0.0151479i
$683$	−21.7325	−	21.7325i	−0.831569	−	0.831569i	0.156162	−	0.987731i	$-0.450088\pi$
$683$	−21.7325	−	21.7325i	−0.831569	−	0.831569i	−0.987731	+	0.156162i	$0.950088\pi$
$684$		−	2.23993i		−	0.0856457i
$685$	0.769618	−	1.29168i	0.0294056	−	0.0493525i
$686$	−16.3263			−0.623339
$687$	9.46014	+	2.53484i	0.360927	+	0.0967100i
$688$	0.988872	+	3.69052i	0.0377004	+	0.140700i
$689$	−0.510062	−	0.294484i	−0.0194318	−	0.0112190i
$690$	3.00638	+	0.0413324i	0.114451	+	0.00157350i
$691$	−2.84374	−	4.92550i	−0.108181	−	0.187375i	0.806852	−	0.590753i	$-0.201169\pi$
$691$	−2.84374	−	4.92550i	−0.108181	−	0.187375i	−0.915033	+	0.403378i	$0.867836\pi$
$692$	15.5442	+	4.16505i	0.590901	+	0.158331i
$693$	−1.44298	−	0.386646i	−0.0548144	−	0.0146875i
$694$	7.82954	−	13.5612i	0.297205	−	0.514775i
$695$	38.9118	+	11.0019i	1.47601	+	0.417326i
$696$	2.91113	−	5.04223i	0.110346	−	0.191125i
$697$	41.0713	+	41.0713i	1.55568	+	1.55568i
$698$	9.25566	+	9.25566i	0.350332	+	0.350332i
$699$	−14.2366	+	24.6586i	−0.538479	+	0.932674i
$700$	6.40623	+	1.90678i	0.242133	+	0.0720694i
$701$	−8.36391	+	14.4867i	−0.315901	+	0.547156i	−0.979629	−	0.200818i	$-0.935640\pi$
$701$	−8.36391	+	14.4867i	−0.315901	+	0.547156i	0.663728	+	0.747974i	$0.268973\pi$
$702$	0.196733	+	0.0527145i	0.00742521	+	0.00198958i
$703$	1.32653	+	0.355442i	0.0500309	+	0.0134057i
$704$	0.558756	+	0.967795i	0.0210589	+	0.0364751i
$705$	0.526681	+	0.541365i	0.0198360	+	0.0203890i
$706$	26.4047	+	15.2448i	0.993753	+	0.573744i
$707$	2.21162	+	8.25387i	0.0831764	+	0.310419i
$708$	−13.7041	−	3.67201i	−0.515033	−	0.138003i
$709$	51.3406			1.92814			0.964069	−	0.265653i	$-0.0855875\pi$
$709$	51.3406			1.92814			0.964069	+	0.265653i	$0.0855875\pi$
$710$	0.860814	+	0.512897i	0.0323058	+	0.0192487i
$711$		−	0.988696i		−	0.0370790i
$712$	−5.18103	−	5.18103i	−0.194167	−	0.194167i
$713$	−6.70841	−	3.32348i	−0.251232	−	0.124465i
$714$			7.84784i			0.293698i
$715$	−0.508897	−	0.00699644i	−0.0190317	−	0.000261652i
$716$	17.8641	+	10.3139i	0.667615	+	0.385447i
$717$	−4.58174	+	4.58174i	−0.171108	+	0.171108i
$718$	−1.44378	+	5.38827i	−0.0538814	+	0.201088i
$719$	−17.1728	+	29.7441i	−0.640437	+	1.10927i	0.344898	+	0.938640i	$0.387913\pi$
$719$	−17.1728	+	29.7441i	−0.640437	+	1.10927i	−0.985335	+	0.170629i	$0.945420\pi$
$720$	−2.16763	+	0.548991i	−0.0807827	+	0.0204597i
$721$	8.46284			0.315173
$722$	13.5063	+	3.61900i	0.502652	+	0.134685i
$723$	−1.79565	+	6.70147i	−0.0667811	+	0.249230i
$724$	2.11597	+	3.66497i	0.0786395	+	0.136208i
$725$	−24.8014	−	15.2432i	−0.921103	−	0.566120i
$726$	8.44476	−	4.87558i	0.313414	−	0.180950i
$727$	4.20102	+	15.6784i	0.155807	+	0.581480i	0.999035	+	0.0439235i	$0.0139858\pi$
$727$	4.20102	+	15.6784i	0.155807	+	0.581480i	−0.843228	+	0.537556i	$0.819348\pi$
$728$	−0.192524	+	0.192524i	−0.00713540	+	0.00713540i
$729$			1.00000i			0.0370370i
$730$	20.9964	−	5.31771i	0.777111	−	0.196817i
$731$	11.2150	+	19.4250i	0.414802	+	0.718458i
$732$	−0.385304	−	1.43797i	−0.0142413	−	0.0531491i
$733$	−7.75773	+	28.9522i	−0.286538	+	1.06938i	0.661170	+	0.750236i	$0.270060\pi$
$733$	−7.75773	+	28.9522i	−0.286538	+	1.06938i	−0.947708	+	0.319139i	$0.896606\pi$
$734$	−9.42529	−	16.3251i	−0.347894	−	0.602570i
$735$	−5.68896	−	10.1741i	−0.209841	−	0.375276i
$736$		−	1.34462i		−	0.0495634i
$737$	−3.23602	+	0.867090i	−0.119200	+	0.0319397i
$738$	−9.55678	+	2.56073i	−0.351790	+	0.0942618i
$739$	−16.1818	−	28.0276i	−0.595256	−	1.03101i	−0.993511	−	0.113738i	$-0.963717\pi$
$739$	−16.1818	−	28.0276i	−0.595256	−	1.03101i	0.398255	−	0.917275i	$-0.369616\pi$
$740$	0.0188465	−	1.37083i	0.000692809	−	0.0503926i
$741$	0.228106	−	0.395092i	0.00837970	−	0.0145141i
$742$	2.73343	+	2.73343i	0.100347	+	0.100347i
$743$	−28.0346	+	28.0346i	−1.02849	+	1.02849i	−0.0289060	+	0.999582i	$0.509202\pi$
$743$	−28.0346	+	28.0346i	−1.02849	+	1.02849i	−0.999582	+	0.0289060i	$0.990798\pi$
$744$	5.45879	+	1.09620i	0.200129	+	0.0401886i
$745$	−10.2938	−	10.5808i	−0.377136	−	0.387650i
$746$	15.0026			0.549284
$747$	−1.22264	+	0.327604i	−0.0447339	+	0.0119864i
$748$	4.63898	+	4.63898i	0.169618	+	0.169618i
$749$	2.18447	−	1.26120i	0.0798188	−	0.0460834i
$750$	2.44596	+	10.9095i	0.0893139	+	0.398359i
$751$	−13.5808	+	23.5226i	−0.495569	+	0.858351i	−0.999987	−	0.00510876i	$-0.998374\pi$
$751$	−13.5808	+	23.5226i	−0.495569	+	0.858351i	0.504418	+	0.863460i	$0.331707\pi$
$752$	0.238845	−	0.238845i	0.00870978	−	0.00870978i
$753$	−1.50849	+	5.62977i	−0.0549725	+	0.205160i
$754$	1.02697	−	0.592919i	0.0373999	−	0.0215928i
$755$	5.79911	−	20.5105i	0.211051	−	0.746453i
$756$	−1.15770	−	0.668398i	−0.0421051	−	0.0243094i
$757$	3.49950	−	13.0603i	0.127192	−	0.474685i	−0.872717	−	0.488227i	$-0.837644\pi$
$757$	3.49950	−	13.0603i	0.127192	−	0.474685i	0.999908	+	0.0135415i	$0.00431052\pi$
$758$	35.8810	−	9.61428i	1.30326	−	0.349206i
$759$	1.50263			0.0545421
$760$	−0.0688533	+	5.00815i	−0.00249757	+	0.181665i
$761$	9.17229	+	5.29562i	0.332495	+	0.191966i	0.656948	−	0.753936i	$-0.271847\pi$
$761$	9.17229	+	5.29562i	0.332495	+	0.191966i	−0.324453	+	0.945902i	$0.605180\pi$
$762$	−4.35089	−	1.16582i	−0.157616	−	0.0422331i
$763$	8.25485	−	2.21188i	0.298846	−	0.0800755i
$764$	12.7922	−	7.38558i	0.462806	−	0.267201i
$765$	−11.4576	+	6.40667i	−0.414250	+	0.231634i
$766$	3.20299	−	1.84925i	0.115729	−	0.0668161i
$767$	−2.04328	−	2.04328i	−0.0737784	−	0.0737784i
$768$	0.258819	+	0.965926i	0.00933933	+	0.0348548i
$769$	1.41244	+	0.815474i	0.0509340	+	0.0294067i	0.525251	−	0.850948i	$-0.323972\pi$
$769$	1.41244	+	0.815474i	0.0509340	+	0.0294067i	−0.474317	+	0.880354i	$0.657305\pi$
$770$	3.21442	+	0.908842i	0.115840	+	0.0327524i
$771$		−	8.70326i		−	0.313440i
$772$	4.95533	+	18.4936i	0.178346	+	0.665598i
$773$	−31.1276	+	31.1276i	−1.11958	+	1.11958i	−0.127779	+	0.991803i	$0.540785\pi$
$773$	−31.1276	+	31.1276i	−1.11958	+	1.11958i	−0.991803	+	0.127779i	$0.959215\pi$
$774$	−3.82071			−0.137333
$775$	6.22927	−	27.1329i	0.223762	−	0.974644i
$776$	−14.0259			−0.503502
$777$	0.579547	−	0.579547i	0.0207911	−	0.0207911i
$778$	8.03202	+	29.9759i	0.287962	+	1.07469i
$779$			22.1616i			0.794022i
$780$	−0.438247	−	0.123909i	−0.0156918	−	0.00443667i
$781$	0.433690	+	0.250391i	0.0155186	+	0.00895969i
$782$	−2.04306	−	7.62481i	−0.0730598	−	0.272663i
$783$	4.11696	+	4.11696i	0.147128	+	0.147128i
$784$	−4.51457	+	2.60649i	−0.161235	+	0.0930889i
$785$	−13.7968	+	7.71465i	−0.492428	+	0.275348i
$786$	9.08256	−	5.24382i	0.323964	−	0.187041i
$787$	−16.8541	+	4.51605i	−0.600784	+	0.160980i	−0.546377	−	0.837539i	$-0.683994\pi$
$787$	−16.8541	+	4.51605i	−0.600784	+	0.160980i	−0.0544071	+	0.998519i	$0.517327\pi$
$788$	−18.1880	−	4.87345i	−0.647920	−	0.173610i
$789$	−22.3646	−	12.9122i	−0.796202	−	0.459688i
$790$	−0.0303916	+	2.21058i	−0.00108129	+	0.0786490i
$791$	9.69102			0.344573
$792$	−1.07943	+	0.289234i	−0.0383560	+	0.0102775i
$793$	0.0784761	−	0.292877i	0.00278677	−	0.0104004i
$794$	0.586061	+	0.338363i	0.0207985	+	0.0120080i
$795$	−1.75926	+	6.22219i	−0.0623944	+	0.220678i
$796$	−21.1240	+	12.1960i	−0.748721	+	0.432274i
$797$	−6.98464	+	26.0670i	−0.247408	+	0.923341i	0.724749	+	0.689013i	$0.241956\pi$
$797$	−6.98464	+	26.0670i	−0.247408	+	0.923341i	−0.972158	+	0.234328i	$0.924711\pi$
$798$	−2.11731	+	2.11731i	−0.0749518	+	0.0749518i
$799$	0.991486	−	1.71730i	0.0350762	−	0.0607538i
$800$	4.86338	−	1.16083i	0.171946	−	0.0410417i
$801$	6.34543	−	3.66354i	0.224205	−	0.129445i
$802$	9.51764	+	9.51764i	0.336080	+	0.336080i
$803$	10.4558	−	2.80162i	0.368976	−	0.0988669i
$804$	−2.99789			−0.105727
$805$	−2.80273	−	2.88087i	−0.0987834	−	0.101537i
$806$	0.851221	+	0.749258i	0.0299830	+	0.0263915i
$807$	−0.386474	+	0.386474i	−0.0136045	+	0.0136045i
$808$	4.51995	+	4.51995i	0.159011	+	0.159011i
$809$	−23.1826	+	40.1535i	−0.815057	+	1.41172i	0.0942296	+	0.995550i	$0.469961\pi$
$809$	−23.1826	+	40.1535i	−0.815057	+	1.41172i	−0.909287	+	0.416170i	$0.863372\pi$
$810$	0.0307391	−	2.23586i	0.00108006	−	0.0785600i
$811$	3.59969	+	6.23484i	0.126402	+	0.218935i	0.922280	−	0.386522i	$-0.126324\pi$
$811$	3.59969	+	6.23484i	0.126402	+	0.218935i	−0.795878	+	0.605457i	$0.792990\pi$
$812$	−7.51797	+	2.01443i	−0.263829	+	0.0706928i
$813$	−15.6301	+	4.18808i	−0.548173	+	0.146882i
$814$		−	0.685159i		−	0.0240148i
$815$	−14.3387	−	25.6432i	−0.502264	−	0.898242i
$816$	2.93532	+	5.08412i	0.102757	+	0.177980i
$817$	−2.21500	+	8.26650i	−0.0774931	+	0.289208i
$818$	2.12166	+	7.91815i	0.0741822	+	0.276852i
$819$	−0.136135	−	0.235792i	−0.00475693	−	0.00823925i
$820$	21.4463	−	5.43166i	0.748937	−	0.189682i
$821$		−	11.4595i		−	0.399940i	−0.979802	−	0.199970i	$-0.935916\pi$
$821$		−	11.4595i		−	0.399940i	0.979802	−	0.199970i	$-0.0640845\pi$
$822$	0.475473	−	0.475473i	0.0165840	−	0.0165840i
$823$	2.74268	+	10.2358i	0.0956038	+	0.356798i	0.997110	−	0.0759673i	$-0.0242045\pi$
$823$	2.74268	+	10.2358i	0.0956038	+	0.356798i	−0.901507	+	0.432766i	$0.857538\pi$
$824$	5.48254	−	3.16535i	0.190993	−	0.110270i
$825$	1.29725	+	5.43489i	0.0451643	+	0.189219i
$826$	9.48294	+	16.4249i	0.329954	+	0.571497i
$827$	1.02881	−	3.83959i	0.0357754	−	0.133516i	−0.945728	−	0.324958i	$-0.894650\pi$
$827$	1.02881	−	3.83959i	0.0357754	−	0.133516i	0.981504	+	0.191442i	$0.0613165\pi$
$828$	1.29880	+	0.348014i	0.0451366	+	0.0120943i
$829$	28.9467			1.00536			0.502681	−	0.864472i	$-0.332347\pi$
$829$	28.9467			1.00536			0.502681	+	0.864472i	$0.332347\pi$
$830$	2.74371	−	0.694893i	0.0952355	−	0.0241201i
$831$	−0.636878	+	1.10310i	−0.0220930	+	0.0382663i
$832$	−0.0527145	+	0.196733i	−0.00182755	+	0.00682049i
$833$	−21.6399	+	21.6399i	−0.749780	+	0.749780i
$834$	15.6613	+	9.04205i	0.542306	+	0.313100i
$835$	2.49606	+	0.0343164i	0.0863797	+	0.00118757i
$836$			2.50315i			0.0865731i
$837$	−2.47168	+	4.98907i	−0.0854339	+	0.172447i
$838$	−10.4935	−	10.4935i	−0.362490	−	0.362490i
$839$		−	15.6026i		−	0.538661i	−0.963048	−	0.269331i	$-0.913198\pi$
$839$		−	15.6026i		−	0.538661i	0.963048	−	0.269331i	$-0.0868024\pi$
$840$	2.56790	+	1.53003i	0.0886011	+	0.0527910i
$841$	4.89872			0.168921
$842$	−10.6386	−	2.85061i	−0.366631	−	0.0982385i
$843$	3.57906	+	13.3572i	0.123269	+	0.460047i
$844$	0.883462	+	0.510067i	0.0304100	+	0.0175572i
$845$	20.2056	+	20.7689i	0.695094	+	0.714473i
$846$	0.168889	+	0.292524i	0.00580652	+	0.0100572i
$847$	−12.5911	−	3.37379i	−0.432637	−	0.115925i
$848$	2.79320	+	0.748436i	0.0959189	+	0.0257014i
$849$	−0.625127	+	1.08275i	−0.0214543	+	0.0371599i
$850$	25.8145	−	13.9722i	0.885429	−	0.479243i
$851$	−0.412201	+	0.713953i	−0.0141301	+	0.0244740i
$852$	0.316870	+	0.316870i	0.0108558	+	0.0108558i
$853$	−15.5790	−	15.5790i	−0.533416	−	0.533416i	0.388171	−	0.921587i	$-0.373107\pi$
$853$	−15.5790	−	15.5790i	−0.533416	−	0.533416i	−0.921587	+	0.388171i	$0.873107\pi$
$854$	−0.995045	+	1.72347i	−0.0340497	+	0.0589759i
$855$	−4.81968	−	1.36271i	−0.164830	−	0.0466038i
$856$	0.943453	−	1.63411i	0.0322466	−	0.0558527i
$857$	−33.7088	−	9.03225i	−1.15147	−	0.308536i	−0.367917	−	0.929859i	$-0.619929\pi$
$857$	−33.7088	−	9.03225i	−1.15147	−	0.308536i	−0.783555	+	0.621323i	$0.786596\pi$
$858$	−0.219852	−	0.0589091i	−0.00750562	−	0.00201112i
$859$	−11.2299	−	19.4507i	−0.383158	−	0.663649i	0.608354	−	0.793666i	$-0.291830\pi$
$859$	−11.2299	−	19.4507i	−0.383158	−	0.663649i	−0.991512	+	0.130017i	$0.958497\pi$
$860$	8.54256	+	0.117445i	0.291299	+	0.00400484i
$861$	11.4542	+	6.61306i	0.390357	+	0.225373i
$862$	8.01450	+	29.9105i	0.272975	+	1.01876i
$863$	−19.7832	−	5.30090i	−0.673428	−	0.180445i	−0.0941297	−	0.995560i	$-0.530007\pi$
$863$	−19.7832	−	5.30090i	−0.673428	−	0.180445i	−0.579299	+	0.815115i	$0.696674\pi$
$864$	−1.00000			−0.0340207
$865$	18.4187	−	30.9127i	0.626253	−	1.05106i
$866$			9.54634i			0.324398i
$867$	12.3492	+	12.3492i	0.419400	+	0.419400i
$868$	−4.12377	−	6.19615i	−0.139970	−	0.210311i
$869$			1.10488i			0.0374805i
$870$	−9.07838	−	9.33148i	−0.307786	−	0.316367i
$871$	−0.528786	−	0.305294i	−0.0179172	−	0.0103445i
$872$	4.52049	−	4.52049i	0.153083	−	0.153083i
$873$	3.63018	−	13.5480i	0.122863	−	0.458531i
$874$	1.50593	−	2.60834i	0.0509387	−	0.0882285i
$875$	8.00022	−	12.6244i	0.270457	−	0.426781i
$876$	9.68634			0.327271
$877$	−9.90995	−	2.65536i	−0.334635	−	0.0896652i	0.0875890	−	0.996157i	$-0.472084\pi$
$877$	−9.90995	−	2.65536i	−0.334635	−	0.0896652i	−0.422224	+	0.906491i	$0.638750\pi$
$878$	3.85402	−	14.3834i	0.130067	−	0.485416i
$879$	−0.0794389	−	0.137592i	−0.00267941	−	0.00464087i
$880$	2.42235	−	0.613504i	0.0816575	−	0.0206812i
$881$	9.70920	−	5.60561i	0.327111	−	0.188858i	−0.327447	−	0.944870i	$-0.606188\pi$
$881$	9.70920	−	5.60561i	0.327111	−	0.188858i	0.654558	+	0.756012i	$0.272855\pi$
$882$	−1.34922	−	5.03535i	−0.0454305	−	0.169549i
$883$	−1.01155	+	1.01155i	−0.0340414	+	0.0340414i	−0.723923	−	0.689881i	$-0.757663\pi$
$883$	−1.01155	+	1.01155i	−0.0340414	+	0.0340414i	0.689881	+	0.723923i	$0.257663\pi$
$884$			1.19569i			0.0402154i
$885$	−16.2384	+	27.2535i	−0.545847	+	0.916115i
$886$	14.6172	+	25.3177i	0.491074	+	0.850564i
$887$	11.5743	+	43.1960i	0.388628	+	1.45038i	0.832368	+	0.554223i	$0.186984\pi$
$887$	11.5743	+	43.1960i	0.388628	+	1.45038i	−0.443741	+	0.896155i	$0.646349\pi$
$888$	0.158685	−	0.592219i	0.00532511	−	0.0198736i
$889$	3.01072	+	5.21471i	0.100976	+	0.174896i
$890$	−14.3001	+	7.99609i	−0.479340	+	0.268030i
$891$		−	1.11751i		−	0.0374381i
$892$	18.7089	−	5.01305i	0.626422	−	0.167849i
$893$	0.730817	−	0.195822i	0.0244559	−	0.00655293i
$894$	−3.30087	−	5.71728i	−0.110398	−	0.191214i
$895$	33.0606	−	32.1639i	1.10509	−	1.07512i
$896$	0.668398	−	1.15770i	0.0223296	−	0.0386760i
$897$	0.193651	+	0.193651i	0.00646581	+	0.00646581i
$898$	−15.4625	+	15.4625i	−0.515989	+	0.515989i
$899$	10.3640	+	30.7156i	0.345657	+	1.02442i
$900$	−0.137456	+	4.99811i	−0.00458188	+	0.166604i
$901$	16.9763			0.565563
$902$	10.6798	−	2.86165i	0.355599	−	0.0952825i
$903$	3.61155	+	3.61155i	0.120185	+	0.120185i
$904$	6.27820	−	3.62472i	0.208810	−	0.120556i
$905$	9.17328	−	2.32330i	0.304930	−	0.0772290i
$906$	4.76608	−	8.25509i	0.158342	−	0.274257i
$907$	−16.9747	+	16.9747i	−0.563637	+	0.563637i	−0.930339	−	0.366702i	$-0.880487\pi$
$907$	−16.9747	+	16.9747i	−0.563637	+	0.563637i	0.366702	+	0.930339i	$0.380487\pi$
$908$	−1.03890	+	3.87721i	−0.0344770	+	0.128670i
$909$	−5.53579	+	3.19609i	−0.183610	+	0.106008i
$910$	0.297130	+	0.531382i	0.00984975	+	0.0176151i
$911$	−46.7050	−	26.9651i	−1.54741	−	0.893395i	−0.998339	−	0.0576163i	$-0.981650\pi$
$911$	−46.7050	−	26.9651i	−1.54741	−	0.893395i	−0.549067	−	0.835779i	$-0.685017\pi$
$912$	−0.579735	+	2.16360i	−0.0191970	+	0.0716440i
$913$	1.36631	−	0.366102i	0.0452183	−	0.0121162i
$914$	−36.5132			−1.20775
$915$	−3.32852	−	0.0457613i	−0.110038	−	0.00151282i
$916$	−8.48173	−	4.89693i	−0.280244	−	0.161799i
$917$	−13.5421	−	3.62860i	−0.447200	−	0.119827i
$918$	−5.67060	+	1.51943i	−0.187158	+	0.0501488i
$919$	−52.4734	+	30.2955i	−1.73094	+	0.999357i	−0.847546	+	0.530722i	$0.821921\pi$
$919$	−52.4734	+	30.2955i	−1.73094	+	0.999357i	−0.883392	+	0.468636i	$0.844746\pi$
$920$	−2.89324	−	0.818033i	−0.0953874	−	0.0269697i
$921$	15.1968	−	8.77390i	0.500753	−	0.289110i
$922$	29.6230	+	29.6230i	0.975582	+	0.975582i
$923$	0.0236225	+	0.0881604i	0.000777544	+	0.00290183i
$924$	1.29374	+	0.746943i	0.0425610	+	0.0245726i
$925$	−2.93816	−	0.874528i	−0.0966063	−	0.0287543i
$926$		−	15.1826i		−	0.498930i
$927$	1.63850	+	6.11498i	0.0538155	+	0.200842i
$928$	−4.11696	+	4.11696i	−0.135146	+	0.135146i
$929$	2.15324			0.0706456			0.0353228	−	0.999376i	$-0.488754\pi$
$929$	2.15324			0.0706456			0.0353228	+	0.999376i	$0.488754\pi$
$930$	5.67969	−	11.0789i	0.186244	−	0.363290i
$931$	−11.6767			−0.382688
$932$	20.1337	−	20.1337i	0.659500	−	0.659500i
$933$	5.14705	+	19.2090i	0.168507	+	0.628876i
$934$			0.866346i			0.0283477i
$935$	12.8040	−	7.15954i	0.418736	−	0.234142i
$936$	−0.176386	−	0.101837i	−0.00576536	−	0.00332863i
$937$	4.83258	+	18.0354i	0.157874	+	0.589192i	0.998842	+	0.0481082i	$0.0153192\pi$
$937$	4.83258	+	18.0354i	0.157874	+	0.589192i	−0.840969	+	0.541084i	$0.818014\pi$
$938$	2.83377	+	2.83377i	0.0925260	+	0.0925260i
$939$	12.6572	−	7.30766i	0.413053	−	0.238476i
$940$	−0.368619	−	0.659234i	−0.0120230	−	0.0215018i
$941$	38.5202	−	22.2397i	1.25572	−	0.724992i	0.283483	−	0.958977i	$-0.408510\pi$
$941$	38.5202	−	22.2397i	1.25572	−	0.724992i	0.972240	+	0.233985i	$0.0751766\pi$
$942$	−6.82830	+	1.82964i	−0.222478	+	0.0596128i
$943$	−12.8502	−	3.44321i	−0.418462	−	0.112126i
$944$	12.2868	+	7.09379i	0.399901	+	0.230883i
$945$	−2.14252	+	2.08440i	−0.0696961	+	0.0678056i
$946$	4.26969			0.138820
$947$	16.3526	−	4.38167i	0.531389	−	0.142385i	0.0168592	−	0.999858i	$-0.494633\pi$
$947$	16.3526	−	4.38167i	0.531389	−	0.142385i	0.514529	+	0.857473i	$0.327967\pi$
$948$	−0.255893	+	0.955007i	−0.00831103	+	0.0310172i
$949$	1.70854	+	0.986424i	0.0554614	+	0.0320207i
$950$	10.7342	+	3.19498i	0.348265	+	0.103659i
$951$	−27.0441	+	15.6139i	−0.876963	+	0.506315i
$952$	2.03117	−	7.58043i	0.0658306	−	0.245683i
$953$	−25.1359	+	25.1359i	−0.814232	+	0.814232i	−0.985265	−	0.171033i	$-0.945289\pi$
$953$	−25.1359	+	25.1359i	−0.814232	+	0.814232i	0.171033	+	0.985265i	$0.445289\pi$
$954$	−1.44587	+	2.50432i	−0.0468117	+	0.0810802i
$955$	−8.10923	−	32.0184i	−0.262409	−	1.03609i
$956$	5.61146	−	3.23978i	0.181488	−	0.104782i
$957$	−4.60076	−	4.60076i	−0.148721	−	0.148721i
$958$	6.36782	−	1.70625i	0.205735	−	0.0551265i
$959$	−0.898888			−0.0290266
$960$	2.23586	+	0.0307391i	0.0721620	+	0.000992100i
$961$	−24.6628	+	18.7815i	−0.795574	+	0.605856i
$962$	0.0882994	−	0.0882994i	0.00284689	−	0.00284689i
$963$	1.33424	+	1.33424i	0.0429954	+	0.0429954i
$964$	3.46894	−	6.00837i	0.111727	−	0.193517i
$965$	42.8076	+	0.588529i	1.37802	+	0.0189454i
$966$	−0.898742	−	1.55667i	−0.0289166	−	0.0500849i
$967$	18.5312	−	4.96542i	0.595923	−	0.159677i	0.0517644	−	0.998659i	$-0.483516\pi$
$967$	18.5312	−	4.96542i	0.595923	−	0.159677i	0.544159	+	0.838982i	$0.316849\pi$
$968$	−9.41890	+	2.52379i	−0.302735	+	0.0811176i
$969$			13.1498i			0.422432i
$970$	−8.53301	+	30.1798i	−0.273978	+	0.969015i
$971$	−23.4128	−	40.5522i	−0.751354	−	1.30138i	−0.947167	−	0.320741i	$-0.896068\pi$
$971$	−23.4128	−	40.5522i	−0.751354	−	1.30138i	0.195813	−	0.980641i	$-0.437265\pi$
$972$	0.258819	−	0.965926i	0.00830162	−	0.0309821i
$973$	−6.25688	−	23.3510i	−0.200586	−	0.748599i
$974$	5.34428	+	9.25657i	0.171242	+	0.296600i
$975$	−0.533236	+	0.867599i	−0.0170772	+	0.0277854i
$976$			1.48870i			0.0476522i
$977$	21.0166	−	21.0166i	0.672380	−	0.672380i	−0.285884	−	0.958264i	$-0.592287\pi$
$977$	21.0166	−	21.0166i	0.672380	−	0.672380i	0.958264	+	0.285884i	$0.0922872\pi$
$978$	−3.40064	−	12.6913i	−0.108740	−	0.405824i
$979$	−7.09110	+	4.09405i	−0.226633	+	0.130846i
$980$	2.86188	+	11.2998i	0.0914193	+	0.360959i
$981$	3.19647	+	5.53645i	0.102055	+	0.176765i
$982$	−0.917780	+	3.42520i	−0.0292875	+	0.109303i
$983$	−48.8997	−	13.1026i	−1.55966	−	0.417909i	−0.627103	−	0.778936i	$-0.715760\pi$
$983$	−48.8997	−	13.1026i	−1.55966	−	0.417909i	−0.932555	+	0.361027i	$0.882426\pi$
$984$	9.89390			0.315406
$985$	−21.5514	+	36.1705i	−0.686684	+	1.15249i
$986$	−17.0902	+	29.6011i	−0.544263	+	0.942690i
$987$	0.116867	−	0.436154i	0.00371992	−	0.0138829i
$988$	−0.322591	+	0.322591i	−0.0102630	+	0.0102630i
$989$	−4.44913	−	2.56870i	−0.141474	−	0.0816800i
$990$	−0.0343513	+	2.49860i	−0.00109176	+	0.0794107i
$991$		−	3.70350i		−	0.117646i	−0.998268	−	0.0588228i	$-0.981265\pi$
$991$		−	3.70350i		−	0.117646i	0.998268	−	0.0588228i	$-0.0187347\pi$
$992$	−4.98907	−	2.47168i	−0.158403	−	0.0784761i
$993$	−25.2470	−	25.2470i	−0.801190	−	0.801190i
$994$		−	0.599047i		−	0.0190006i
$995$	13.3909	+	52.8726i	0.424521	+	1.67617i
$996$	1.26577			0.0401073
$997$	−42.2913	−	11.3319i	−1.33938	−	0.358885i	−0.483174	−	0.875524i	$-0.660516\pi$
$997$	−42.2913	−	11.3319i	−1.33938	−	0.358885i	−0.856203	+	0.516639i	$0.827183\pi$
$998$	2.91047	+	10.8620i	0.0921293	+	0.343831i
$999$	0.530969	+	0.306555i	0.0167991	+	0.00969898i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.be.b.553.1	yes	64
5.2	odd	4		930.2.be.a.367.5	yes	64
31.6	odd	6		930.2.be.a.223.5	✓	64
155.37	even	12	inner	930.2.be.b.37.1	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.be.a.223.5	✓	64	31.6	odd	6
930.2.be.a.367.5	yes	64	5.2	odd	4
930.2.be.b.37.1	yes	64	155.37	even	12	inner
930.2.be.b.553.1	yes	64	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.258819 + 0.965926i) q^{3} -1.00000i q^{4} +(-2.15172 - 0.608374i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(0.345988 + 1.29125i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.258819 + 0.965926i) q^{3} -1.00000i q^{4} +(-2.15172 - 0.608374i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(0.345988 + 1.29125i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(1.95168 - 1.09131i) q^{10} +(0.967795 - 0.558756i) q^{11} +(0.965926 - 0.258819i) q^{12} +(0.196733 + 0.0527145i) q^{13} +(-1.15770 - 0.668398i) q^{14} +(0.0307391 - 2.23586i) q^{15} -1.00000 q^{16} +(-5.67060 + 1.51943i) q^{17} +(0.258819 - 0.965926i) q^{18} +(-1.93983 - 1.11996i) q^{19} +(-0.608374 + 2.15172i) q^{20} +(-1.15770 + 0.668398i) q^{21} +(-0.289234 + 1.07943i) q^{22} +(0.950791 - 0.950791i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(4.25976 + 2.61810i) q^{25} +(-0.176386 + 0.101837i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(1.29125 - 0.345988i) q^{28} -5.82226 q^{29} +(1.55925 + 1.60273i) q^{30} +(-1.78006 - 5.27555i) q^{31} +(0.707107 - 0.707107i) q^{32} +(0.790201 + 0.790201i) q^{33} +(2.93532 - 5.08412i) q^{34} +(0.0410919 - 2.98888i) q^{35} +(0.500000 + 0.866025i) q^{36} +(-0.592219 + 0.158685i) q^{37} +(2.16360 - 0.579735i) q^{38} +0.203673i q^{39} +(-1.09131 - 1.95168i) q^{40} +(-4.94695 - 8.56837i) q^{41} +(0.345988 - 1.29125i) q^{42} +(-0.988872 - 3.69052i) q^{43} +(-0.558756 - 0.967795i) q^{44} +(2.16763 - 0.548991i) q^{45} +1.34462i q^{46} +(-0.238845 + 0.238845i) q^{47} +(-0.258819 - 0.965926i) q^{48} +(4.51457 - 2.60649i) q^{49} +(-4.86338 + 1.16083i) q^{50} +(-2.93532 - 5.08412i) q^{51} +(0.0527145 - 0.196733i) q^{52} +(-2.79320 - 0.748436i) q^{53} +1.00000 q^{54} +(-2.42235 + 0.613504i) q^{55} +(-0.668398 + 1.15770i) q^{56} +(0.579735 - 2.16360i) q^{57} +(4.11696 - 4.11696i) q^{58} +(-12.2868 - 7.09379i) q^{59} +(-2.23586 - 0.0307391i) q^{60} -1.48870i q^{61} +(4.98907 + 2.47168i) q^{62} +(-0.945257 - 0.945257i) q^{63} +1.00000i q^{64} +(-0.391244 - 0.233114i) q^{65} -1.11751 q^{66} +(-2.89574 - 0.775910i) q^{67} +(1.51943 + 5.67060i) q^{68} +(1.16448 + 0.672311i) q^{69} +(2.08440 + 2.14252i) q^{70} +(0.224061 + 0.388085i) q^{71} +(-0.965926 - 0.258819i) q^{72} +(9.35629 + 2.50701i) q^{73} +(0.306555 - 0.530969i) q^{74} +(-1.42638 + 4.79223i) q^{75} +(-1.11996 + 1.93983i) q^{76} +(1.05634 + 1.05634i) q^{77} +(-0.144019 - 0.144019i) q^{78} +(-0.494348 + 0.856236i) q^{79} +(2.15172 + 0.608374i) q^{80} +(0.500000 - 0.866025i) q^{81} +(9.55678 + 2.56073i) q^{82} +(1.22264 + 0.327604i) q^{83} +(0.668398 + 1.15770i) q^{84} +(13.1259 + 0.180458i) q^{85} +(3.30883 + 1.91035i) q^{86} +(-1.50691 - 5.62387i) q^{87} +(1.07943 + 0.289234i) q^{88} -7.32708 q^{89} +(-1.14455 + 1.92094i) q^{90} +0.272269i q^{91} +(-0.950791 - 0.950791i) q^{92} +(4.63507 - 3.08482i) q^{93} -0.337778i q^{94} +(3.49261 + 3.58999i) q^{95} +(0.866025 + 0.500000i) q^{96} +(-9.91783 + 9.91783i) q^{97} +(-1.34922 + 5.03535i) q^{98} +(-0.558756 + 0.967795i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 4 q^{7}+O(q^{10}) \) 64 * q + 4 * q^7	\( 64 q + 4 q^{7} - 4 q^{10} - 24 q^{14} - 8 q^{15} - 64 q^{16} - 4 q^{17} + 12 q^{20} - 24 q^{21} - 4 q^{22} - 32 q^{24} + 28 q^{25} + 8 q^{28} - 16 q^{29} + 8 q^{31} + 4 q^{33} + 24 q^{35} + 32 q^{36} + 16 q^{37} - 28 q^{38} - 8 q^{41} + 4 q^{42} - 40 q^{43} + 4 q^{44} - 12 q^{45} + 8 q^{47} + 60 q^{49} - 8 q^{50} - 24 q^{53} + 64 q^{54} + 44 q^{55} + 4 q^{57} - 52 q^{58} - 24 q^{59} + 20 q^{62} - 4 q^{63} + 44 q^{65} + 8 q^{66} - 44 q^{67} - 4 q^{68} + 12 q^{69} - 44 q^{70} + 8 q^{71} + 4 q^{73} - 12 q^{74} + 8 q^{75} - 8 q^{76} + 104 q^{77} - 56 q^{79} + 32 q^{81} - 16 q^{82} - 48 q^{83} - 32 q^{85} - 24 q^{86} - 32 q^{87} + 8 q^{88} + 176 q^{89} + 16 q^{93} + 64 q^{95} - 68 q^{97} + 32 q^{98} + 4 q^{99}+O(q^{100}) \) 64 * q + 4 * q^7 - 4 * q^10 - 24 * q^14 - 8 * q^15 - 64 * q^16 - 4 * q^17 + 12 * q^20 - 24 * q^21 - 4 * q^22 - 32 * q^24 + 28 * q^25 + 8 * q^28 - 16 * q^29 + 8 * q^31 + 4 * q^33 + 24 * q^35 + 32 * q^36 + 16 * q^37 - 28 * q^38 - 8 * q^41 + 4 * q^42 - 40 * q^43 + 4 * q^44 - 12 * q^45 + 8 * q^47 + 60 * q^49 - 8 * q^50 - 24 * q^53 + 64 * q^54 + 44 * q^55 + 4 * q^57 - 52 * q^58 - 24 * q^59 + 20 * q^62 - 4 * q^63 + 44 * q^65 + 8 * q^66 - 44 * q^67 - 4 * q^68 + 12 * q^69 - 44 * q^70 + 8 * q^71 + 4 * q^73 - 12 * q^74 + 8 * q^75 - 8 * q^76 + 104 * q^77 - 56 * q^79 + 32 * q^81 - 16 * q^82 - 48 * q^83 - 32 * q^85 - 24 * q^86 - 32 * q^87 + 8 * q^88 + 176 * q^89 + 16 * q^93 + 64 * q^95 - 68 * q^97 + 32 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

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