LMFDB - Embedded newform 360.2.bm.b.11.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(11,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))

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

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

chi := DirichletCharacter("360.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bm (of order $6$, degree $2$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.20
Character	$\chi$	$=$	360.11
Dual form			360.2.bm.b.131.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02877 - 0.970379i) q^{2} +(1.62132 - 0.609351i) q^{3} +(0.116731 - 1.99659i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.07667 - 2.20018i) q^{6} +(-0.518944 - 0.299612i) q^{7} +(-1.81736 - 2.16730i) q^{8} +(2.25738 - 1.97591i) q^{9} +O(q^{10})$	\(q+(1.02877 - 0.970379i) q^{2} +(1.62132 - 0.609351i) q^{3} +(0.116731 - 1.99659i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.07667 - 2.20018i) q^{6} +(-0.518944 - 0.299612i) q^{7} +(-1.81736 - 2.16730i) q^{8} +(2.25738 - 1.97591i) q^{9} +(1.35476 + 0.405751i) q^{10} +(0.700444 + 0.404402i) q^{11} +(-1.02737 - 3.30825i) q^{12} +(-3.52330 + 2.03418i) q^{13} +(-0.824611 + 0.195340i) q^{14} +(1.33838 + 1.09943i) q^{15} +(-3.97275 - 0.466128i) q^{16} +1.87026i q^{17} +(0.404943 - 4.22327i) q^{18} +3.32144 q^{19} +(1.78746 - 0.897203i) q^{20} +(-1.02395 - 0.169550i) q^{21} +(1.11302 - 0.263660i) q^{22} +(1.00356 + 1.73822i) q^{23} +(-4.26718 - 2.40649i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.65074 + 5.51163i) q^{26} +(2.45592 - 4.57913i) q^{27} +(-0.658780 + 1.00114i) q^{28} +(1.38869 - 2.40528i) q^{29} +(2.44374 - 0.167669i) q^{30} +(-4.04078 + 2.33294i) q^{31} +(-4.53936 + 3.37553i) q^{32} +(1.38207 + 0.228850i) q^{33} +(1.81486 + 1.92406i) q^{34} -0.599225i q^{35} +(-3.68158 - 4.73772i) q^{36} +7.30473i q^{37} +(3.41700 - 3.22306i) q^{38} +(-4.47288 + 5.44499i) q^{39} +(0.968260 - 2.65753i) q^{40} +(-7.32564 + 4.22946i) q^{41} +(-1.21793 + 0.819187i) q^{42} +(-4.19270 + 7.26197i) q^{43} +(0.889188 - 1.35129i) q^{44} +(2.83988 + 0.966995i) q^{45} +(2.71917 + 0.814392i) q^{46} +(6.76075 - 11.7100i) q^{47} +(-6.72515 + 1.66505i) q^{48} +(-3.32046 - 5.75121i) q^{49} +(0.325988 + 1.37613i) q^{50} +(1.13964 + 3.03229i) q^{51} +(3.65014 + 7.27204i) q^{52} +5.27329 q^{53} +(-1.91691 - 7.09404i) q^{54} +0.808804i q^{55} +(0.293757 + 1.66921i) q^{56} +(5.38514 - 2.02393i) q^{57} +(-0.905391 - 3.82203i) q^{58} +(6.41997 - 3.70657i) q^{59} +(2.35135 - 2.54385i) q^{60} +(-4.38245 - 2.53021i) q^{61} +(-1.89319 + 6.32115i) q^{62} +(-1.76346 + 0.349047i) q^{63} +(-1.39441 + 7.87754i) q^{64} +(-3.52330 - 2.03418i) q^{65} +(1.64390 - 1.10570i) q^{66} +(6.68152 + 11.5727i) q^{67} +(3.73414 + 0.218317i) q^{68} +(2.68629 + 2.20670i) q^{69} +(-0.581475 - 0.616464i) q^{70} +3.24261 q^{71} +(-8.38487 - 1.30149i) q^{72} -16.0211 q^{73} +(7.08835 + 7.51488i) q^{74} +(-0.282948 + 1.70878i) q^{75} +(0.387715 - 6.63157i) q^{76} +(-0.242328 - 0.419724i) q^{77} +(0.682138 + 9.94202i) q^{78} +(3.85168 + 2.22377i) q^{79} +(-1.58270 - 3.67356i) q^{80} +(1.19155 - 8.92077i) q^{81} +(-3.43221 + 11.4598i) q^{82} +(4.04472 + 2.33522i) q^{83} +(-0.458047 + 2.02461i) q^{84} +(-1.61969 + 0.935129i) q^{85} +(2.73354 + 11.5394i) q^{86} +(0.785854 - 4.74593i) q^{87} +(-0.396498 - 2.25302i) q^{88} -9.41789i q^{89} +(3.85993 - 1.76094i) q^{90} +2.43786 q^{91} +(3.58766 - 1.80080i) q^{92} +(-5.12983 + 6.24471i) q^{93} +(-4.40785 - 18.6073i) q^{94} +(1.66072 + 2.87646i) q^{95} +(-5.30289 + 8.23889i) q^{96} +(1.95567 - 3.38732i) q^{97} +(-8.99685 - 2.69456i) q^{98} +(2.38023 - 0.471126i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{5} - q^{6} + 6 q^{8}+O(q^{10}) $ 48 * q + 24 * q^5 - q^6 + 6 * q^8	$ 48 q + 24 q^{5} - q^{6} + 6 q^{8} + 13 q^{12} + 15 q^{14} - 12 q^{16} + 7 q^{18} + 4 q^{21} - 21 q^{22} - 4 q^{24} - 24 q^{25} + 12 q^{27} - 2 q^{30} - 8 q^{33} - 27 q^{34} - 31 q^{36} - 27 q^{38} - 16 q^{39} + 12 q^{40} + 12 q^{41} - 9 q^{42} + 24 q^{44} - 6 q^{46} - 12 q^{47} + 7 q^{48} + 24 q^{49} - 20 q^{51} + 54 q^{52} - 32 q^{54} + 21 q^{56} + 4 q^{57} + 33 q^{58} - 36 q^{59} - q^{60} - 12 q^{61} - 42 q^{62} - 56 q^{63} - 12 q^{64} - 32 q^{66} + 51 q^{68} + 40 q^{69} + 15 q^{70} + 6 q^{72} + 54 q^{74} - 51 q^{76} - 24 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} + 41 q^{84} + 27 q^{86} - 36 q^{87} - 57 q^{88} - 22 q^{90} - 9 q^{92} - 75 q^{94} + 13 q^{96} - 42 q^{98} - 16 q^{99}+O(q^{100}) $ 48 * q + 24 * q^5 - q^6 + 6 * q^8 + 13 * q^12 + 15 * q^14 - 12 * q^16 + 7 * q^18 + 4 * q^21 - 21 * q^22 - 4 * q^24 - 24 * q^25 + 12 * q^27 - 2 * q^30 - 8 * q^33 - 27 * q^34 - 31 * q^36 - 27 * q^38 - 16 * q^39 + 12 * q^40 + 12 * q^41 - 9 * q^42 + 24 * q^44 - 6 * q^46 - 12 * q^47 + 7 * q^48 + 24 * q^49 - 20 * q^51 + 54 * q^52 - 32 * q^54 + 21 * q^56 + 4 * q^57 + 33 * q^58 - 36 * q^59 - q^60 - 12 * q^61 - 42 * q^62 - 56 * q^63 - 12 * q^64 - 32 * q^66 + 51 * q^68 + 40 * q^69 + 15 * q^70 + 6 * q^72 + 54 * q^74 - 51 * q^76 - 24 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 + 41 * q^84 + 27 * q^86 - 36 * q^87 - 57 * q^88 - 22 * q^90 - 9 * q^92 - 75 * q^94 + 13 * q^96 - 42 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.02877	−	0.970379i	0.727449	−	0.686161i
$2$	1.02877	−	0.970379i	0.727449	−	0.686161i
$3$	1.62132	−	0.609351i	0.936072	−	0.351809i
$3$	1.62132	−	0.609351i	0.936072	−	0.351809i
$4$	0.116731	−	1.99659i	0.0583655	−	0.998295i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	1.07667	−	2.20018i	0.439547	−	0.898219i
$7$	−0.518944	−	0.299612i	−0.196142	−	0.113243i	0.398713	−	0.917076i	$-0.369457\pi$
$7$	−0.518944	−	0.299612i	−0.196142	−	0.113243i	−0.594855	+	0.803833i	$0.702790\pi$
$8$	−1.81736	−	2.16730i	−0.642534	−	0.766258i
$9$	2.25738	−	1.97591i	0.752461	−	0.658637i
$10$	1.35476	+	0.405751i	0.428412	+	0.128310i
$11$	0.700444	+	0.404402i	0.211192	+	0.121932i	0.601865	−	0.798598i	$-0.294424\pi$
$11$	0.700444	+	0.404402i	0.211192	+	0.121932i	−0.390673	+	0.920529i	$0.627758\pi$
$12$	−1.02737	−	3.30825i	−0.296575	−	0.955010i
$13$	−3.52330	+	2.03418i	−0.977187	+	0.564179i	−0.901420	−	0.432946i	$-0.857474\pi$
$13$	−3.52330	+	2.03418i	−0.977187	+	0.564179i	−0.0757674	+	0.997126i	$0.524141\pi$
$14$	−0.824611	+	0.195340i	−0.220386	+	0.0522068i
$15$	1.33838	+	1.09943i	0.345567	+	0.283872i
$16$	−3.97275	−	0.466128i	−0.993187	−	0.116532i
$17$			1.87026i			0.453604i	0.973941	+	0.226802i	$0.0728270\pi$
$17$			1.87026i			0.453604i	−0.973941	+	0.226802i	$0.927173\pi$
$18$	0.404943	−	4.22327i	0.0954460	−	0.995435i
$19$	3.32144			0.761992			0.380996	−	0.924577i	$-0.375581\pi$
$19$	3.32144			0.761992			0.380996	+	0.924577i	$0.375581\pi$
$20$	1.78746	−	0.897203i	0.399689	−	0.200621i
$21$	−1.02395	−	0.169550i	−0.223443	−	0.0369988i
$22$	1.11302	−	0.263660i	0.237296	−	0.0562126i
$23$	1.00356	+	1.73822i	0.209257	+	0.362444i	0.951481	−	0.307708i	$-0.0995621\pi$
$23$	1.00356	+	1.73822i	0.209257	+	0.362444i	−0.742224	+	0.670152i	$0.766229\pi$
$24$	−4.26718	−	2.40649i	−0.871034	−	0.491223i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.65074	+	5.51163i	−0.323736	+	1.08092i
$27$	2.45592	−	4.57913i	0.472643	−	0.881254i
$28$	−0.658780	+	1.00114i	−0.124498	+	0.189198i
$29$	1.38869	−	2.40528i	0.257873	−	0.446649i	−0.707799	−	0.706414i	$-0.750312\pi$
$29$	1.38869	−	2.40528i	0.257873	−	0.446649i	0.965672	+	0.259765i	$0.0836451\pi$
$30$	2.44374	−	0.167669i	0.446165	−	0.0306121i
$31$	−4.04078	+	2.33294i	−0.725745	+	0.419009i	−0.816864	−	0.576831i	$-0.804289\pi$
$31$	−4.04078	+	2.33294i	−0.725745	+	0.419009i	0.0911183	+	0.995840i	$0.470956\pi$
$32$	−4.53936	+	3.37553i	−0.802453	+	0.596715i
$33$	1.38207	+	0.228850i	0.240588	+	0.0398376i
$34$	1.81486	+	1.92406i	0.311245	+	0.329974i
$35$		−	0.599225i		−	0.101287i
$36$	−3.68158	−	4.73772i	−0.613596	−	0.789620i
$37$			7.30473i			1.20089i	0.799666	+	0.600445i	$0.205010\pi$
$37$			7.30473i			1.20089i	−0.799666	+	0.600445i	$0.794990\pi$
$38$	3.41700	−	3.22306i	0.554310	−	0.522849i
$39$	−4.47288	+	5.44499i	−0.716234	+	0.871896i
$40$	0.968260	−	2.65753i	0.153095	−	0.420193i
$41$	−7.32564	+	4.22946i	−1.14407	+	0.660531i	−0.947436	−	0.319945i	$-0.896335\pi$
$41$	−7.32564	+	4.22946i	−1.14407	+	0.660531i	−0.196637	+	0.980476i	$0.563002\pi$
$42$	−1.21793	+	0.819187i	−0.187931	+	0.126403i
$43$	−4.19270	+	7.26197i	−0.639381	+	1.10744i	0.346188	+	0.938165i	$0.387476\pi$
$43$	−4.19270	+	7.26197i	−0.639381	+	1.10744i	−0.985569	+	0.169275i	$0.945857\pi$
$44$	0.889188	−	1.35129i	0.134050	−	0.203715i
$45$	2.83988	+	0.966995i	0.423344	+	0.144151i
$46$	2.71917	+	0.814392i	0.400919	+	0.120076i
$47$	6.76075	−	11.7100i	0.986157	−	1.70807i	0.349479	−	0.936944i	$-0.386359\pi$
$47$	6.76075	−	11.7100i	0.986157	−	1.70807i	0.636678	−	0.771130i	$-0.280308\pi$
$48$	−6.72515	+	1.66505i	−0.970691	+	0.240330i
$49$	−3.32046	−	5.75121i	−0.474352	−	0.821602i
$50$	0.325988	+	1.37613i	0.0461017	+	0.194614i
$51$	1.13964	+	3.03229i	0.159582	+	0.424606i
$52$	3.65014	+	7.27204i	0.506184	+	1.00845i
$53$	5.27329			0.724343			0.362171	−	0.932112i	$-0.382036\pi$
$53$	5.27329			0.724343			0.362171	+	0.932112i	$0.382036\pi$
$54$	−1.91691	−	7.09404i	−0.260859	−	0.965377i
$55$			0.808804i			0.109059i
$56$	0.293757	+	1.66921i	0.0392549	+	0.223058i
$57$	5.38514	−	2.02393i	0.713279	−	0.268076i
$58$	−0.905391	−	3.82203i	−0.118884	−	0.501857i
$59$	6.41997	−	3.70657i	0.835809	−	0.482554i	−0.0200287	−	0.999799i	$-0.506376\pi$
$59$	6.41997	−	3.70657i	0.835809	−	0.482554i	0.855837	+	0.517245i	$0.173042\pi$
$60$	2.35135	−	2.54385i	0.303557	−	0.328410i
$61$	−4.38245	−	2.53021i	−0.561115	−	0.323960i	0.192478	−	0.981301i	$-0.438348\pi$
$61$	−4.38245	−	2.53021i	−0.561115	−	0.323960i	−0.753593	+	0.657341i	$0.771681\pi$
$62$	−1.89319	+	6.32115i	−0.240435	+	0.802786i
$63$	−1.76346	+	0.349047i	−0.222175	+	0.0439758i
$64$	−1.39441	+	7.87754i	−0.174301	+	0.984692i
$65$	−3.52330	−	2.03418i	−0.437011	−	0.252309i
$66$	1.64390	−	1.10570i	0.202350	−	0.136102i
$67$	6.68152	+	11.5727i	0.816278	+	1.41383i	0.908407	+	0.418088i	$0.137300\pi$
$67$	6.68152	+	11.5727i	0.816278	+	1.41383i	−0.0921287	+	0.995747i	$0.529367\pi$
$68$	3.73414	+	0.218317i	0.452831	+	0.0264748i
$69$	2.68629	+	2.20670i	0.323391	+	0.265655i
$70$	−0.581475	−	0.616464i	−0.0694995	−	0.0736815i
$71$	3.24261			0.384827			0.192414	−	0.981314i	$-0.438368\pi$
$71$	3.24261			0.384827			0.192414	+	0.981314i	$0.438368\pi$
$72$	−8.38487	−	1.30149i	−0.988167	−	0.153382i
$73$	−16.0211			−1.87513			−0.937563	−	0.347815i	$-0.886924\pi$
$73$	−16.0211			−1.87513			−0.937563	+	0.347815i	$0.886924\pi$
$74$	7.08835	+	7.51488i	0.824004	+	0.873587i
$75$	−0.282948	+	1.70878i	−0.0326721	+	0.197313i
$76$	0.387715	−	6.63157i	0.0444740	−	0.760693i
$77$	−0.242328	−	0.419724i	−0.0276158	−	0.0478319i
$78$	0.682138	+	9.94202i	0.0772369	+	1.12571i
$79$	3.85168	+	2.22377i	0.433348	+	0.250193i	0.700772	−	0.713385i	$-0.252839\pi$
$79$	3.85168	+	2.22377i	0.433348	+	0.250193i	−0.267424	+	0.963579i	$0.586172\pi$
$80$	−1.58270	−	3.67356i	−0.176951	−	0.410717i
$81$	1.19155	−	8.92077i	0.132395	−	0.991197i
$82$	−3.43221	+	11.4598i	−0.379025	+	1.26552i
$83$	4.04472	+	2.33522i	0.443966	+	0.256324i	0.705278	−	0.708930i	$-0.250822\pi$
$83$	4.04472	+	2.33522i	0.443966	+	0.256324i	−0.261313	+	0.965254i	$0.584155\pi$
$84$	−0.458047	+	2.02461i	−0.0499771	+	0.220903i
$85$	−1.61969	+	0.935129i	−0.175680	+	0.101429i
$86$	2.73354	+	11.5394i	0.294765	+	1.24433i
$87$	0.785854	−	4.74593i	0.0842524	−	0.508818i
$88$	−0.396498	−	2.25302i	−0.0422668	−	0.240173i
$89$		−	9.41789i		−	0.998294i	−0.866517	−	0.499147i	$-0.833647\pi$
$89$		−	9.41789i		−	0.998294i	0.866517	−	0.499147i	$-0.166353\pi$
$90$	3.85993	−	1.76094i	0.406873	−	0.185620i
$91$	2.43786			0.255557
$92$	3.58766	−	1.80080i	0.374040	−	0.187746i
$93$	−5.12983	+	6.24471i	−0.531938	+	0.647547i
$94$	−4.40785	−	18.6073i	−0.454635	−	1.91920i
$95$	1.66072	+	2.87646i	0.170387	+	0.295118i
$96$	−5.30289	+	8.23889i	−0.541224	+	0.840879i
$97$	1.95567	−	3.38732i	0.198568	−	0.343930i	−0.749496	−	0.662009i	$-0.769704\pi$
$97$	1.95567	−	3.38732i	0.198568	−	0.343930i	0.948064	+	0.318078i	$0.103038\pi$
$98$	−8.99685	−	2.69456i	−0.908819	−	0.272192i
$99$	2.38023	−	0.471126i	0.239222	−	0.0473500i
$100$	1.67073	+	1.09939i	0.167073	+	0.109939i
$101$	0.225380	−	0.390370i	0.0224262	−	0.0388433i	−0.854595	−	0.519296i	$-0.826194\pi$
$101$	0.225380	−	0.390370i	0.0224262	−	0.0388433i	0.877021	+	0.480453i	$0.159528\pi$
$102$	4.11490	+	2.01364i	0.407436	+	0.199380i
$103$	−0.427706	+	0.246936i	−0.0421431	+	0.0243313i	−0.520924	−	0.853603i	$-0.674412\pi$
$103$	−0.427706	+	0.246936i	−0.0421431	+	0.0243313i	0.478780	+	0.877935i	$0.341079\pi$
$104$	10.8118	+	3.93923i	1.06018	+	0.386273i
$105$	−0.365138	−	0.971537i	−0.0356338	−	0.0948123i
$106$	5.42500	−	5.11709i	0.526923	−	0.497016i
$107$			0.151516i			0.0146476i	0.999973	+	0.00732378i	$0.00233125\pi$
$107$			0.151516i			0.0146476i	−0.999973	+	0.00732378i	$0.997669\pi$
$108$	−8.85597	−	5.43800i	−0.852166	−	0.523272i
$109$		−	4.45180i		−	0.426405i	−0.977008	−	0.213202i	$-0.931611\pi$
$109$		−	4.45180i		−	0.426405i	0.977008	−	0.213202i	$-0.0683894\pi$
$110$	0.784846	+	0.832072i	0.0748321	+	0.0793349i
$111$	4.45115	+	11.8433i	0.422484	+	1.12412i
$112$	1.92198	+	1.43218i	0.181610	+	0.135328i
$113$	−14.2998	+	8.25601i	−1.34522	+	0.776660i	−0.987567	−	0.157196i	$-0.949755\pi$
$113$	−14.2998	+	8.25601i	−1.34522	+	0.776660i	−0.357648	+	0.933857i	$0.616421\pi$
$114$	3.57609	−	7.30777i	0.334931	−	0.684436i
$115$	−1.00356	+	1.73822i	−0.0935827	+	0.162090i
$116$	−4.64025	−	3.05341i	−0.430837	−	0.283502i
$117$	−3.93408	+	11.5536i	−0.363706	+	1.06813i
$118$	3.00789	−	10.0430i	0.276898	−	0.924533i
$119$	0.560352	−	0.970558i	0.0513674	−	0.0889709i
$120$	−0.0495062	−	4.89873i	−0.00451928	−	0.447191i
$121$	−5.17292	−	8.95976i	−0.470265	−	0.814523i
$122$	−6.96379	+	1.64964i	−0.630472	+	0.149351i
$123$	−9.30001	+	11.3212i	−0.838554	+	1.02080i
$124$	4.18625	+	8.34011i	0.375936	+	0.748964i
$125$	−1.00000			−0.0894427
$126$	−1.47549	+	2.07031i	−0.131447	+	0.184438i
$127$		−	11.4614i		−	1.01704i	−0.861051	−	0.508519i	$-0.830193\pi$
$127$		−	11.4614i		−	1.01704i	0.861051	−	0.508519i	$-0.169807\pi$
$128$	6.20967	+	9.45727i	0.548863	+	0.835913i
$129$	−2.37264	+	14.3288i	−0.208899	+	1.26158i
$130$	−5.59858	+	1.32623i	−0.491028	+	0.116318i
$131$	12.3778	−	7.14631i	1.08145	−	0.624376i	0.150164	−	0.988661i	$-0.452020\pi$
$131$	12.3778	−	7.14631i	1.08145	−	0.624376i	0.931288	+	0.364285i	$0.118687\pi$
$132$	0.618249	−	2.73271i	0.0538117	−	0.237852i
$133$	−1.72364	−	0.995146i	−0.149459	−	0.0862901i
$134$	18.1037	+	5.42207i	1.56392	+	0.468395i
$135$	5.19361	−	0.162672i	0.446994	−	0.0140006i
$136$	4.05342	−	3.39893i	0.347577	−	0.291456i
$137$	1.59539	+	0.921101i	0.136304	+	0.0786950i	0.566601	−	0.823992i	$-0.308258\pi$
$137$	1.59539	+	0.921101i	0.136304	+	0.0786950i	−0.430298	+	0.902687i	$0.641591\pi$
$138$	4.90490	−	0.336533i	0.417533	−	0.0286476i
$139$	4.92786	+	8.53531i	0.417976	+	0.723956i	0.995736	−	0.0922512i	$-0.0294063\pi$
$139$	4.92786	+	8.53531i	0.417976	+	0.723956i	−0.577760	+	0.816207i	$0.696073\pi$
$140$	−1.19641	−	0.0699481i	−0.101115	−	0.00591169i
$141$	3.82589	−	23.1053i	0.322198	−	1.94582i
$142$	3.33590	−	3.14656i	0.279942	−	0.264054i
$143$	−3.29050			−0.275165
$144$	−9.88904	+	6.79757i	−0.824087	+	0.566464i
$145$	2.77738			0.230649
$146$	−16.4820	+	15.5465i	−1.36406	+	1.28664i
$147$	−8.88806	−	7.30125i	−0.733075	−	0.602197i
$148$	14.5846	+	0.852688i	1.19884	+	0.0700905i
$149$	5.68180	+	9.84116i	0.465471	+	0.806219i	0.999223	−	0.0394219i	$-0.0125516\pi$
$149$	5.68180	+	9.84116i	0.465471	+	0.806219i	−0.533752	+	0.845641i	$0.679218\pi$
$150$	1.36708	+	2.03251i	0.111621	+	0.165954i
$151$	−10.9144	−	6.30145i	−0.888204	−	0.512805i	−0.0148491	−	0.999890i	$-0.504727\pi$
$151$	−10.9144	−	6.30145i	−0.888204	−	0.512805i	−0.873354	+	0.487085i	$0.838060\pi$
$152$	−6.03626	−	7.19858i	−0.489605	−	0.583882i
$153$	3.69546	+	4.22189i	0.298760	+	0.341319i
$154$	−0.656590	−	0.196649i	−0.0529095	−	0.0158464i
$155$	−4.04078	−	2.33294i	−0.324563	−	0.187387i
$156$	10.3493	+	9.56611i	0.828606	+	0.765902i
$157$	−15.4516	+	8.92099i	−1.23317	+	0.711972i	−0.967690	−	0.252144i	$-0.918864\pi$
$157$	−15.4516	+	8.92099i	−1.23317	+	0.711972i	−0.265482	+	0.964116i	$0.585531\pi$
$158$	6.12039	−	1.44984i	0.486912	−	0.115343i
$159$	8.54972	−	3.21329i	0.678037	−	0.254830i
$160$	−5.19298	−	2.24344i	−0.410541	−	0.177359i
$161$		−	1.20272i		−	0.0947875i
$162$	−7.43070	−	10.3337i	−0.583811	−	0.811890i
$163$	−12.4417			−0.974507			−0.487253	−	0.873261i	$-0.662001\pi$
$163$	−12.4417			−0.974507			−0.487253	+	0.873261i	$0.662001\pi$
$164$	7.58938	+	15.1200i	0.592631	+	1.18068i
$165$	0.492845	+	1.31133i	0.0383680	+	0.102087i
$166$	6.42713	−	1.52251i	0.498842	−	0.118170i
$167$	−12.1610	−	21.0634i	−0.941044	−	1.62994i	−0.763484	−	0.645827i	$-0.776513\pi$
$167$	−12.1610	−	21.0634i	−0.941044	−	1.62994i	−0.177561	−	0.984110i	$-0.556821\pi$
$168$	1.49341	+	2.52733i	0.115219	+	0.194988i
$169$	1.77576	−	3.07570i	0.136597	−	0.236592i
$170$	−0.758858	+	2.53374i	−0.0582018	+	0.194329i
$171$	7.49777	−	6.56288i	0.573369	−	0.501876i
$172$	14.0098	+	9.21881i	1.06824	+	0.702928i
$173$	10.3034	−	17.8460i	0.783352	−	1.35681i	−0.146627	−	0.989192i	$-0.546842\pi$
$173$	10.3034	−	17.8460i	0.783352	−	1.35681i	0.929979	−	0.367613i	$-0.119825\pi$
$174$	−3.79689	−	5.64505i	−0.287842	−	0.427950i
$175$	0.518944	−	0.299612i	0.0392285	−	0.0226486i
$176$	−2.59419	−	1.93308i	−0.195544	−	0.145712i
$177$	8.15025	−	9.92157i	0.612610	−	0.745751i
$178$	−9.13892	−	9.68883i	−0.684991	−	0.726209i
$179$		−	16.9909i		−	1.26996i	−0.772528	−	0.634981i	$-0.781008\pi$
$179$		−	16.9909i		−	1.26996i	0.772528	−	0.634981i	$-0.218992\pi$
$180$	2.26220	−	5.55720i	0.168614	−	0.414209i
$181$		−	22.5201i		−	1.67390i	−0.547278	−	0.836951i	$-0.684336\pi$
$181$		−	22.5201i		−	1.67390i	0.547278	−	0.836951i	$-0.315664\pi$
$182$	2.50799	−	2.36565i	0.185905	−	0.175353i
$183$	−8.64716	−	1.43184i	−0.639216	−	0.105844i
$184$	1.94342	−	5.33400i	0.143271	−	0.393227i
$185$	−6.32608	+	3.65236i	−0.465103	+	0.268527i
$186$	0.782326	+	11.4022i	0.0573629	+	0.836053i
$187$	−0.756335	+	1.31001i	−0.0553087	+	0.0957975i
$188$	−22.5908	−	14.8654i	−1.64760	−	1.08417i
$189$	−2.64645	+	1.64049i	−0.192501	+	0.119328i
$190$	4.49975	+	1.34768i	0.326446	+	0.0977709i
$191$	−3.66201	+	6.34278i	−0.264973	+	0.458947i	−0.967557	−	0.252654i	$-0.918697\pi$
$191$	−3.66201	+	6.34278i	−0.264973	+	0.458947i	0.702583	+	0.711602i	$0.252030\pi$
$192$	2.53940	+	13.6217i	0.183265	+	0.983063i
$193$	0.361899	+	0.626828i	0.0260501	+	0.0451200i	0.878757	−	0.477270i	$-0.158374\pi$
$193$	0.361899	+	0.626828i	0.0260501	+	0.0451200i	−0.852706	+	0.522390i	$0.825040\pi$
$194$	−1.27505	−	5.38251i	−0.0915433	−	0.386442i
$195$	−6.95194	−	1.15113i	−0.497839	−	0.0824345i
$196$	−11.8704	+	5.95826i	−0.847887	+	0.425590i
$197$	−2.66910			−0.190165			−0.0950826	−	0.995469i	$-0.530312\pi$
$197$	−2.66910			−0.190165			−0.0950826	+	0.995469i	$0.530312\pi$
$198$	1.99154	−	2.79441i	0.141532	−	0.198590i
$199$		−	25.4805i		−	1.80626i	−0.429366	−	0.903131i	$-0.641263\pi$
$199$		−	25.4805i		−	1.80626i	0.429366	−	0.903131i	$-0.358737\pi$
$200$	2.78562	−	0.490228i	0.196973	−	0.0346643i
$201$	17.8848	+	14.6918i	1.26149	+	1.03628i
$202$	−0.146943	−	0.620305i	−0.0103388	−	0.0436445i
$203$	−1.44130	+	0.832136i	−0.101160	+	0.0584045i
$204$	6.18728	−	1.92144i	0.433196	−	0.134528i
$205$	−7.32564	−	4.22946i	−0.511645	−	0.295398i
$206$	−0.200389	+	0.669077i	−0.0139618	+	0.0466168i
$207$	5.69999	+	1.94088i	0.396177	+	0.134900i
$208$	14.9454	−	6.43897i	1.03627	−	0.446462i
$209$	2.32649	+	1.34320i	0.160926	+	0.0929110i
$210$	−1.31840	−	0.645165i	−0.0909784	−	0.0445206i
$211$	7.09060	+	12.2813i	0.488137	+	0.845479i	0.999907	−	0.0136441i	$-0.00434319\pi$
$211$	7.09060	+	12.2813i	0.488137	+	0.845479i	−0.511770	+	0.859123i	$0.671010\pi$
$212$	0.615557	−	10.5286i	0.0422766	−	0.723108i
$213$	5.25732	−	1.97589i	0.360226	−	0.135386i
$214$	0.147027	+	0.155875i	0.0100506	+	0.0106554i
$215$	−8.38541			−0.571880
$216$	−14.3877	+	2.99919i	−0.978956	+	0.204069i
$217$	2.79592			0.189799
$218$	−4.31993	−	4.57987i	−0.292582	−	0.310188i
$219$	−25.9754	+	9.76247i	−1.75525	+	0.659686i
$220$	1.61485	+	0.0944124i	0.108873	+	0.00636528i
$221$	−3.80443	−	6.58947i	−0.255914	−	0.443256i
$222$	16.0717	+	7.86476i	1.07866	+	0.527848i
$223$	23.3748	+	13.4954i	1.56529	+	0.903722i	0.996706	+	0.0810987i	$0.0258429\pi$
$223$	23.3748	+	13.4954i	1.56529	+	0.903722i	0.568587	+	0.822623i	$0.307490\pi$
$224$	3.36702	−	0.391663i	0.224969	−	0.0261691i
$225$	0.582498	+	2.94291i	0.0388332	+	0.196194i
$226$	−6.69977	+	22.3698i	−0.445662	+	1.48802i
$227$	−17.7458	−	10.2455i	−1.17783	−	0.680020i	−0.222318	−	0.974974i	$-0.571362\pi$
$227$	−17.7458	−	10.2455i	−1.17783	−	0.680020i	−0.955512	+	0.294954i	$0.904696\pi$
$228$	−3.41234	−	10.9882i	−0.225988	−	0.727709i
$229$	10.4781	−	6.04952i	0.692410	−	0.399763i	−0.112104	−	0.993696i	$-0.535759\pi$
$229$	10.4781	−	6.04952i	0.692410	−	0.399763i	0.804514	+	0.593933i	$0.202426\pi$
$230$	0.654299	+	2.76206i	0.0431432	+	0.182125i
$231$	−0.648650	−	0.532845i	−0.0426781	−	0.0350587i
$232$	−7.73671	+	1.36155i	−0.507940	+	0.0893899i
$233$			7.05758i			0.462358i	0.972911	+	0.231179i	$0.0742582\pi$
$233$			7.05758i			0.462358i	−0.972911	+	0.231179i	$0.925742\pi$
$234$	7.16415	+	15.7036i	0.468335	+	1.02657i
$235$	13.5215			0.882046
$236$	−6.65109	−	13.2507i	−0.432949	−	0.862548i
$237$	7.59988	+	1.25842i	0.493665	+	0.0817434i
$238$	−0.365336	−	1.54223i	−0.0236812	−	0.0999682i
$239$	1.45168	+	2.51438i	0.0939013	+	0.162642i	0.909150	−	0.416470i	$-0.136733\pi$
$239$	1.45168	+	2.51438i	0.0939013	+	0.162642i	−0.815248	+	0.579112i	$0.803400\pi$
$240$	−4.80455	−	4.99162i	−0.310133	−	0.322208i
$241$	4.85247	−	8.40472i	0.312575	−	0.541396i	−0.666344	−	0.745644i	$-0.732142\pi$
$241$	4.85247	−	8.40472i	0.312575	−	0.541396i	0.978919	+	0.204249i	$0.0654751\pi$
$242$	−14.0161	−	4.19783i	−0.900989	−	0.269847i
$243$	−3.50399	−	15.1895i	−0.224781	−	0.974409i
$244$	−5.56336	+	8.45461i	−0.356158	+	0.541251i
$245$	3.32046	−	5.75121i	0.212137	−	0.367432i
$246$	1.41830	+	20.6715i	0.0904276	+	1.31796i
$247$	−11.7024	+	6.75641i	−0.744608	+	0.429900i
$248$	12.3997	+	4.51780i	0.787385	+	0.286880i
$249$	7.98077	+	1.32149i	0.505761	+	0.0837463i
$250$	−1.02877	+	0.970379i	−0.0650651	+	0.0613721i
$251$		−	7.28459i		−	0.459800i	−0.973214	−	0.229900i	$-0.926160\pi$
$251$		−	7.28459i		−	0.459800i	0.973214	−	0.229900i	$-0.0738398\pi$
$252$	0.491054	+	3.56166i	0.0309335	+	0.224363i
$253$			1.62337i			0.102060i
$254$	−11.1219	−	11.7912i	−0.697851	−	0.739843i
$255$	−2.05622	+	2.50311i	−0.128766	+	0.156751i
$256$	15.5654	+	3.70362i	0.972841	+	0.231476i
$257$	−14.6491	+	8.45768i	−0.913788	+	0.527576i	−0.881648	−	0.471908i	$-0.843566\pi$
$257$	−14.6491	+	8.45768i	−0.913788	+	0.527576i	−0.0321398	+	0.999483i	$0.510232\pi$
$258$	11.4635	+	17.0434i	0.713687	+	1.06108i
$259$	2.18859	−	3.79074i	0.135992	−	0.235545i
$260$	−4.47270	+	6.79713i	−0.277385	+	0.421540i
$261$	−1.61782	−	8.17356i	−0.100140	−	0.505931i
$262$	5.79924	−	19.3630i	0.358279	−	1.19625i
$263$	−3.28261	+	5.68564i	−0.202414	+	0.350592i	−0.949306	−	0.314354i	$-0.898212\pi$
$263$	−3.28261	+	5.68564i	−0.202414	+	0.350592i	0.746892	+	0.664946i	$0.231545\pi$
$264$	−2.01573	−	3.41127i	−0.124060	−	0.209949i
$265$	2.63665	+	4.56681i	0.161968	+	0.280537i
$266$	−2.73890	+	0.648811i	−0.167933	+	0.0397812i
$267$	−5.73880	−	15.2694i	−0.351209	−	0.934475i
$268$	23.8860	−	11.9894i	1.45907	−	0.732367i
$269$	−14.9125			−0.909232			−0.454616	−	0.890688i	$-0.650223\pi$
$269$	−14.9125			−0.909232			−0.454616	+	0.890688i	$0.650223\pi$
$270$	5.18517	−	5.20712i	0.315559	−	0.316895i
$271$			16.6853i			1.01356i	0.862075	+	0.506781i	$0.169165\pi$
$271$			16.6853i			1.01356i	−0.862075	+	0.506781i	$0.830835\pi$
$272$	0.871779	−	7.43006i	0.0528594	−	0.450514i
$273$	3.95256	−	1.48551i	0.239220	−	0.0899073i
$274$	2.53511	−	0.600536i	0.153151	−	0.0362797i
$275$	−0.700444	+	0.404402i	−0.0422384	+	0.0243863i
$276$	4.71944	−	5.10582i	0.284077	−	0.307334i
$277$	17.1138	+	9.88066i	1.02827	+	0.593671i	0.916488	−	0.400061i	$-0.131011\pi$
$277$	17.1138	+	9.88066i	1.02827	+	0.593671i	0.111781	+	0.993733i	$0.464345\pi$
$278$	13.3521	+	3.99897i	0.800807	+	0.239842i
$279$	−4.51189	+	13.2506i	−0.270120	+	0.793291i
$280$	−1.29870	+	1.08901i	−0.0776123	+	0.0650806i
$281$	15.0261	+	8.67532i	0.896382	+	0.517526i	0.876024	−	0.482267i	$-0.160186\pi$
$281$	15.0261	+	8.67532i	0.896382	+	0.517526i	0.0203571	+	0.999793i	$0.493520\pi$
$282$	−18.4849	−	27.4826i	−1.10076	−	1.63656i
$283$	−2.43180	−	4.21200i	−0.144556	−	0.250378i	0.784651	−	0.619937i	$-0.212842\pi$
$283$	−2.43180	−	4.21200i	−0.144556	−	0.250378i	−0.929207	+	0.369560i	$0.879509\pi$
$284$	0.378513	−	6.47417i	0.0224606	−	0.384171i
$285$	4.44534	+	3.65170i	0.263319	+	0.216308i
$286$	−3.38516	+	3.19303i	−0.200169	+	0.188808i
$287$	5.06880			0.299202
$288$	−3.57732	+	16.5892i	−0.210796	+	0.977530i
$289$	13.5021			0.794243
$290$	2.85728	−	2.69511i	0.167785	−	0.158262i
$291$	1.10671	−	6.68363i	0.0648764	−	0.391802i
$292$	−1.87016	+	31.9876i	−0.109443	+	1.87193i
$293$	16.0019	+	27.7161i	0.934841	+	1.61919i	0.774918	+	0.632062i	$0.217791\pi$
$293$	16.0019	+	27.7161i	0.934841	+	1.61919i	0.159923	+	0.987129i	$0.448875\pi$
$294$	−16.2287	+	1.11348i	−0.946479	+	0.0649395i
$295$	6.41997	+	3.70657i	0.373785	+	0.215805i
$296$	15.8316	−	13.2753i	0.920191	−	0.771612i
$297$	3.57205	−	2.21425i	0.207271	−	0.128484i
$298$	15.3949	+	4.61079i	0.891803	+	0.267096i
$299$	−7.07170	−	4.08285i	−0.408967	−	0.236117i
$300$	3.37871	+	0.764400i	0.195070	+	0.0441327i
$301$	4.35155	−	2.51237i	0.250819	−	0.144811i
$302$	−17.3432	+	4.10839i	−0.997990	+	0.236411i
$303$	0.127542	−	0.770252i	0.00732710	−	0.0442498i
$304$	−13.1953	−	1.54822i	−0.756800	−	0.0887964i
$305$		−	5.06042i		−	0.289759i
$306$	7.89860	+	0.757348i	0.451533	+	0.0432947i
$307$	−10.7917			−0.615913			−0.307956	−	0.951400i	$-0.599645\pi$
$307$	−10.7917			−0.615913			−0.307956	+	0.951400i	$0.599645\pi$
$308$	−0.866303	+	0.434834i	−0.0493622	+	0.0247770i
$309$	−0.542979	+	0.660986i	−0.0308890	+	0.0376022i
$310$	−6.42087	+	1.52102i	−0.364681	+	0.0863884i
$311$	−1.21973	−	2.11263i	−0.0691644	−	0.119796i	0.829369	−	0.558701i	$-0.188700\pi$
$311$	−1.21973	−	2.11263i	−0.0691644	−	0.119796i	−0.898534	+	0.438905i	$0.855367\pi$
$312$	19.9298	−	0.201409i	1.12830	−	0.0114025i
$313$	6.88538	−	11.9258i	0.389185	−	0.674088i	−0.603155	−	0.797624i	$-0.706090\pi$
$313$	6.88538	−	11.9258i	0.389185	−	0.674088i	0.992340	+	0.123536i	$0.0394234\pi$
$314$	−7.23939	+	24.1715i	−0.408543	+	1.36408i
$315$	−1.18401	−	1.35268i	−0.0667117	−	0.0762148i
$316$	4.88957	−	7.43064i	0.275060	−	0.418006i
$317$	−7.83931	+	13.5781i	−0.440300	+	0.762621i	−0.997712	−	0.0676148i	$-0.978461\pi$
$317$	−7.83931	+	13.5781i	−0.440300	+	0.762621i	0.557412	+	0.830236i	$0.311794\pi$
$318$	5.67758	−	11.6022i	0.318383	−	0.650619i
$319$	1.94540	−	1.12318i	0.108921	−	0.0628858i
$320$	−7.51935	+	2.73118i	−0.420345	+	0.152677i
$321$	0.0923262	+	0.245656i	0.00515314	+	0.0137112i
$322$	−1.16709	−	1.23732i	−0.0650395	−	0.0689531i
$323$			6.21196i			0.345642i
$324$	−17.6720	−	3.42037i	−0.981780	−	0.190021i
$325$		−	4.06835i		−	0.225672i
$326$	−12.7996	+	12.0731i	−0.708904	+	0.668669i
$327$	−2.71271	−	7.21781i	−0.150013	−	0.399146i
$328$	22.4799	+	8.19044i	1.24124	+	0.452241i
$329$	−7.01690	+	4.05121i	−0.386854	+	0.223350i
$330$	1.77951	+	0.870812i	0.0979590	+	0.0479366i
$331$	1.07345	−	1.85927i	0.0590021	−	0.102195i	−0.835016	−	0.550226i	$-0.814541\pi$
$331$	1.07345	−	1.85927i	0.0590021	−	0.102195i	0.894018	+	0.448032i	$0.147875\pi$
$332$	5.13462	−	7.80306i	0.281799	−	0.428249i
$333$	14.4335	+	16.4896i	0.790951	+	0.903623i
$334$	−32.9503	−	9.86865i	−1.80296	−	0.539988i
$335$	−6.68152	+	11.5727i	−0.365051	+	0.632286i
$336$	3.98884	+	1.15087i	0.217609	+	0.0627850i
$337$	10.7535	+	18.6257i	0.585783	+	1.01461i	0.994777	+	0.102069i	$0.0325462\pi$
$337$	10.7535	+	18.6257i	0.585783	+	1.01461i	−0.408995	+	0.912537i	$0.634120\pi$
$338$	−1.15775	−	4.88734i	−0.0629733	−	0.265836i
$339$	−18.1539	+	22.0993i	−0.985982	+	1.20027i
$340$	1.67800	+	3.34302i	0.0910024	+	0.181301i
$341$	−3.77379			−0.204362
$342$	1.34500	−	14.0274i	0.0727291	−	0.758513i
$343$			8.17398i			0.441354i
$344$	23.3586	−	4.11076i	1.25941	−	0.221637i
$345$	−0.567913	+	3.42974i	−0.0305754	+	0.184651i
$346$	−6.71756	−	28.3576i	−0.361138	−	1.52451i
$347$	17.3931	−	10.0419i	0.933709	−	0.539077i	0.0457265	−	0.998954i	$-0.485440\pi$
$347$	17.3931	−	10.0419i	0.933709	−	0.539077i	0.887983	+	0.459877i	$0.152106\pi$
$348$	−9.38395	−	2.12303i	−0.503033	−	0.113806i
$349$	3.44434	+	1.98859i	0.184371	+	0.106447i	0.589345	−	0.807882i	$-0.299386\pi$
$349$	3.44434	+	1.98859i	0.184371	+	0.106447i	−0.404973	+	0.914328i	$0.632719\pi$
$350$	0.243136	−	0.811804i	0.0129962	−	0.0433927i
$351$	0.661807	+	21.1294i	0.0353247	+	1.12781i
$352$	−4.54464	+	0.528647i	−0.242230	+	0.0281770i
$353$	27.3846	+	15.8105i	1.45754	+	0.841508i	0.998890	−	0.0471110i	$-0.0150014\pi$
$353$	27.3846	+	15.8105i	1.45754	+	0.841508i	0.458646	+	0.888619i	$0.348335\pi$
$354$	−1.24296	−	18.1158i	−0.0660624	−	0.962845i
$355$	1.62131	+	2.80818i	0.0860500	+	0.149043i
$356$	−18.8037	−	1.09936i	−0.996592	−	0.0582659i
$357$	0.317102	−	1.91504i	0.0167828	−	0.101355i
$358$	−16.4876	−	17.4797i	−0.871399	−	0.923833i
$359$	−24.5943			−1.29804			−0.649019	−	0.760772i	$-0.724821\pi$
$359$	−24.5943			−1.29804			−0.649019	+	0.760772i	$0.724821\pi$
$360$	−3.06531	−	7.91226i	−0.161556	−	0.417013i
$361$	−7.96801			−0.419369
$362$	−21.8530	−	23.1679i	−1.14857	−	1.21768i
$363$	−13.8466	−	11.3745i	−0.726759	−	0.597009i
$364$	0.284574	−	4.86741i	0.0149157	−	0.255121i
$365$	−8.01054	−	13.8747i	−0.419291	−	0.726233i
$366$	−10.2854	+	6.91799i	−0.537624	+	0.361609i
$367$	6.34516	+	3.66338i	0.331214	+	0.191227i	0.656380	−	0.754430i	$-0.272087\pi$
$367$	6.34516	+	3.66338i	0.331214	+	0.191227i	−0.325166	+	0.945657i	$0.605420\pi$
$368$	−3.17667	−	7.37330i	−0.165595	−	0.384360i
$369$	−8.17974	+	24.0223i	−0.425820	+	1.25055i
$370$	−2.96390	+	9.89613i	−0.154086	+	0.514475i
$371$	−2.73654	−	1.57994i	−0.142074	−	0.0820266i
$372$	11.8693	+	10.9711i	0.615396	+	0.568826i
$373$	−27.9329	+	16.1271i	−1.44631	+	0.835027i	−0.998259	−	0.0589810i	$-0.981215\pi$
$373$	−27.9329	+	16.1271i	−1.44631	+	0.835027i	−0.448051	+	0.894008i	$0.647882\pi$
$374$	0.493113	+	2.08163i	0.0254982	+	0.107639i
$375$	−1.62132	+	0.609351i	−0.0837248	+	0.0314668i
$376$	−37.6658	+	6.62862i	−1.94246	+	0.341845i
$377$			11.2994i			0.581946i
$378$	−1.13069	+	4.25574i	−0.0581566	+	0.218892i
$379$	−6.95220			−0.357110			−0.178555	−	0.983930i	$-0.557142\pi$
$379$	−6.95220			−0.357110			−0.178555	+	0.983930i	$0.557142\pi$
$380$	5.93696	−	2.98001i	0.304560	−	0.152871i
$381$	−6.98403	−	18.5827i	−0.357803	−	0.952020i
$382$	2.38754	+	10.0788i	0.122157	+	0.515676i
$383$	13.7399	+	23.7982i	0.702075	+	1.21603i	0.967737	+	0.251963i	$0.0810762\pi$
$383$	13.7399	+	23.7982i	0.702075	+	1.21603i	−0.265662	+	0.964066i	$0.585590\pi$
$384$	15.8307	+	11.5494i	0.807856	+	0.589379i
$385$	0.242328	−	0.419724i	0.0123502	−	0.0213911i
$386$	0.980571	+	0.293682i	0.0499097	+	0.0149480i
$387$	4.88448	+	24.6775i	0.248292	+	1.25443i
$388$	−6.53481	−	4.30008i	−0.331755	−	0.218303i
$389$	−15.8542	+	27.4603i	−0.803842	+	1.39230i	0.113228	+	0.993569i	$0.463881\pi$
$389$	−15.8542	+	27.4603i	−0.803842	+	1.39230i	−0.917070	+	0.398726i	$0.869452\pi$
$390$	−8.26897	+	5.56176i	−0.418716	+	0.281631i
$391$	−3.25092	+	1.87692i	−0.164406	+	0.0949199i
$392$	−6.43015	+	17.6485i	−0.324772	+	0.891383i
$393$	15.7138	−	19.1289i	0.792655	−	0.964926i
$394$	−2.74588	+	2.59003i	−0.138336	+	0.130484i
$395$			4.44754i			0.223780i
$396$	−0.662800	−	4.80735i	−0.0333069	−	0.241578i
$397$			2.72557i			0.136792i	0.997658	+	0.0683961i	$0.0217882\pi$
$397$			2.72557i			0.136792i	−0.997658	+	0.0683961i	$0.978212\pi$
$398$	−24.7257	−	26.2135i	−1.23939	−	1.31396i
$399$	−3.40098	−	0.563150i	−0.170262	−	0.0281928i
$400$	2.39005	−	3.20744i	0.119503	−	0.160372i
$401$	9.65586	−	5.57482i	0.482191	−	0.278393i	−0.239138	−	0.970986i	$-0.576865\pi$
$401$	9.65586	−	5.57482i	0.482191	−	0.278393i	0.721329	+	0.692593i	$0.243532\pi$
$402$	32.6559	−	2.24057i	1.62873	−	0.111750i
$403$	9.49125	−	16.4393i	0.472793	−	0.818901i
$404$	−0.753100	−	0.495560i	−0.0374681	−	0.0246551i
$405$	8.32139	−	3.42847i	0.413493	−	0.170362i
$406$	−0.675280	+	2.25468i	−0.0335136	+	0.111898i
$407$	−2.95405	+	5.11656i	−0.146427	+	0.253618i
$408$	4.50076	−	7.98072i	0.222821	−	0.395104i
$409$	5.29072	+	9.16380i	0.261609	+	0.453121i	0.966670	−	0.256027i	$-0.0824135\pi$
$409$	5.29072	+	9.16380i	0.261609	+	0.453121i	−0.705060	+	0.709147i	$0.749080\pi$
$410$	−11.6406	+	2.75751i	−0.574887	+	0.136184i
$411$	3.14792	+	0.521248i	0.155276	+	0.0257113i
$412$	0.443104	+	0.882778i	0.0218301	+	0.0434914i
$413$	−4.44214			−0.218583
$414$	7.74736	−	3.53443i	0.380762	−	0.173708i
$415$			4.67044i			0.229263i
$416$	9.12709	−	21.1269i	0.447492	−	1.03583i
$417$	13.1907	+	10.8357i	0.645950	+	0.530627i
$418$	3.69683	−	0.875733i	0.180818	−	0.0428335i
$419$	10.6537	−	6.15093i	0.520468	−	0.300492i	−0.216658	−	0.976248i	$-0.569516\pi$
$419$	10.6537	−	6.15093i	0.520468	−	0.300492i	0.737126	+	0.675755i	$0.236182\pi$
$420$	−1.98239	+	0.615623i	−0.0967305	+	0.0300393i
$421$	31.8320	+	18.3782i	1.55140	+	0.895701i	0.998028	+	0.0627653i	$0.0199920\pi$
$421$	31.8320	+	18.3782i	1.55140	+	0.895701i	0.553370	+	0.832935i	$0.313341\pi$
$422$	19.2121	+	5.75404i	0.935230	+	0.280102i
$423$	−7.87625	−	39.7925i	−0.382956	−	1.93478i
$424$	−9.58347	−	11.4288i	−0.465414	−	0.555033i
$425$	−1.61969	−	0.935129i	−0.0785665	−	0.0453604i
$426$	3.49121	−	7.13433i	0.169150	−	0.345659i
$427$	1.51616	+	2.62607i	0.0733723	+	0.127085i
$428$	0.302515	+	0.0176866i	0.0146226	+	0.000854912i
$429$	−5.33497	+	2.00507i	−0.257575	+	0.0968057i
$430$	−8.62665	+	8.13702i	−0.416014	+	0.392402i
$431$	31.5455			1.51949			0.759746	−	0.650220i	$-0.225323\pi$
$431$	31.5455			1.51949			0.759746	+	0.650220i	$0.225323\pi$
$432$	−11.8912	+	17.0470i	−0.572117	+	0.820172i
$433$	−21.6927			−1.04248			−0.521241	−	0.853409i	$-0.674531\pi$
$433$	−21.6927			−1.04248			−0.521241	+	0.853409i	$0.674531\pi$
$434$	2.87635	−	2.71310i	0.138069	−	0.130233i
$435$	4.50303	−	1.69240i	0.215904	−	0.0811442i
$436$	−8.88842	−	0.519663i	−0.425678	−	0.0248873i
$437$	3.33328	+	5.77340i	0.159452	+	0.276179i
$438$	−17.2494	+	35.2493i	−0.824207	+	1.68428i
$439$	−1.34898	−	0.778832i	−0.0643832	−	0.0371716i	0.467463	−	0.884013i	$-0.345168\pi$
$439$	−1.34898	−	0.778832i	−0.0643832	−	0.0371716i	−0.531846	+	0.846841i	$0.678501\pi$
$440$	1.75292	−	1.46989i	0.0835673	−	0.0700741i
$441$	−18.8594	−	6.42175i	−0.898069	−	0.305797i
$442$	−10.3082	−	3.08730i	−0.490310	−	0.146848i
$443$	20.8779	+	12.0539i	0.991941	+	0.572697i	0.905854	−	0.423590i	$-0.139230\pi$
$443$	20.8779	+	12.0539i	0.991941	+	0.572697i	0.0860869	+	0.996288i	$0.472564\pi$
$444$	24.1659	−	7.50463i	1.14686	−	0.356154i
$445$	8.15613	−	4.70894i	0.386638	−	0.223225i
$446$	37.1430	−	8.79871i	1.75877	−	0.416631i
$447$	15.2088	+	12.4935i	0.719349	+	0.590922i
$448$	3.08383	−	3.67022i	0.145697	−	0.173401i
$449$		−	22.7101i		−	1.07176i	−0.844295	−	0.535879i	$-0.819980\pi$
$449$		−	22.7101i		−	1.07176i	0.844295	−	0.535879i	$-0.180020\pi$
$450$	3.45499	+	2.46233i	0.162870	+	0.116075i
$451$	−6.84161			−0.322159
$452$	14.8146	+	29.5146i	0.696822	+	1.38825i
$453$	−21.5356	−	3.56597i	−1.01183	−	0.167544i
$454$	−28.1984	+	6.67985i	−1.32342	+	0.313501i
$455$	1.21893	+	2.11125i	0.0571443	+	0.0989768i
$456$	−14.1732	−	7.99303i	−0.663721	−	0.374308i
$457$	15.8352	−	27.4274i	0.740739	−	1.28300i	−0.211420	−	0.977395i	$-0.567809\pi$
$457$	15.8352	−	27.4274i	0.740739	−	1.28300i	0.952159	−	0.305603i	$-0.0988580\pi$
$458$	4.90919	−	16.3912i	0.229391	−	0.765913i
$459$	8.56415	+	4.59321i	0.399740	+	0.214393i
$460$	3.35337	+	2.20661i	0.156352	+	0.102884i
$461$	−0.934556	+	1.61870i	−0.0435266	+	0.0753903i	−0.886968	−	0.461831i	$-0.847193\pi$
$461$	−0.934556	+	1.61870i	−0.0435266	+	0.0753903i	0.843441	+	0.537221i	$0.180526\pi$
$462$	−1.18437	+	0.0812617i	−0.0551020	+	0.00378064i
$463$	23.8604	−	13.7758i	1.10889	−	0.640217i	0.170347	−	0.985384i	$-0.445511\pi$
$463$	23.8604	−	13.7758i	1.10889	−	0.640217i	0.938541	+	0.345168i	$0.112178\pi$
$464$	−6.63807	+	8.90826i	−0.308165	+	0.413556i
$465$	−7.97299	−	1.32021i	−0.369739	−	0.0612231i
$466$	6.84853	+	7.26062i	0.317252	+	0.336342i
$467$			34.5674i			1.59959i	0.600273	+	0.799795i	$0.295059\pi$
$467$			34.5674i			1.59959i	−0.600273	+	0.799795i	$0.704941\pi$
$468$	22.6087	+	9.20341i	1.04509	+	0.425428i
$469$		−	8.00747i		−	0.369750i
$470$	13.9105	−	13.1210i	0.641644	−	0.605226i
$471$	−19.6160	+	23.8793i	−0.903859	+	1.10030i
$472$	−19.7007	−	7.17785i	−0.906796	−	0.330387i
$473$	−5.87351	+	3.39107i	−0.270064	+	0.155922i
$474$	9.03966	−	6.08013i	0.415205	−	0.279270i
$475$	−1.66072	+	2.87646i	−0.0761992	+	0.131981i
$476$	−1.87240	−	1.23209i	−0.0858212	−	0.0564727i
$477$	11.9038	−	10.4196i	0.545039	−	0.477079i
$478$	3.93334	+	1.17804i	0.179907	+	0.0538823i
$479$	−3.19775	+	5.53866i	−0.146109	+	0.253068i	−0.929786	−	0.368100i	$-0.880008\pi$
$479$	−3.19775	+	5.53866i	−0.146109	+	0.253068i	0.783677	+	0.621168i	$0.213342\pi$
$480$	−9.78654	−	0.472990i	−0.446692	−	0.0215889i
$481$	−14.8591	−	25.7367i	−0.677517	−	1.17349i
$482$	−3.16369	−	13.3553i	−0.144102	−	0.608315i
$483$	−0.732878	−	1.95000i	−0.0333471	−	0.0887279i
$484$	−18.4928	+	9.28232i	−0.840582	+	0.421924i
$485$	3.91134			0.177605
$486$	−18.3444	−	12.2263i	−0.832119	−	0.554597i
$487$		−	9.60635i		−	0.435305i	−0.976026	−	0.217653i	$-0.930160\pi$
$487$		−	9.60635i		−	0.435305i	0.976026	−	0.217653i	$-0.0698400\pi$
$488$	2.48076	+	14.0964i	0.112299	+	0.638114i
$489$	−20.1720	+	7.58135i	−0.912208	+	0.342840i
$490$	−2.16486	−	9.13878i	−0.0977986	−	0.412848i
$491$	1.42930	−	0.825208i	0.0645035	−	0.0372411i	−0.467401	−	0.884045i	$-0.654810\pi$
$491$	1.42930	−	0.825208i	0.0645035	−	0.0372411i	0.531905	+	0.846804i	$0.321476\pi$
$492$	21.5182	+	19.8899i	0.970117	+	0.896704i
$493$	4.49849	+	2.59720i	0.202602	+	0.116972i
$494$	−5.48283	+	18.3066i	−0.246684	+	0.823652i
$495$	1.59812	+	1.82578i	0.0718303	+	0.0820627i
$496$	17.1404	−	7.38468i	0.769629	−	0.331582i
$497$	−1.68273	−	0.971526i	−0.0754809	−	0.0435789i
$498$	9.49272	−	6.38486i	0.425379	−	0.286112i
$499$	4.96576	+	8.60094i	0.222298	+	0.385031i	0.955505	−	0.294974i	$-0.0953109\pi$
$499$	4.96576	+	8.60094i	0.222298	+	0.385031i	−0.733208	+	0.680005i	$0.761978\pi$
$500$	−0.116731	+	1.99659i	−0.00522037	+	0.0892902i
$501$	−32.5519	−	26.7403i	−1.45431	−	1.19467i
$502$	−7.06881	−	7.49416i	−0.315497	−	0.334481i
$503$	−16.1641			−0.720722			−0.360361	−	0.932813i	$-0.617346\pi$
$503$	−16.1641			−0.720722			−0.360361	+	0.932813i	$0.617346\pi$
$504$	3.96134	+	3.18761i	0.176452	+	0.141988i
$505$	0.450761			0.0200586
$506$	1.57528	+	1.67007i	0.0700299	+	0.0742438i
$507$	1.00489	−	6.06876i	0.0446289	−	0.269523i
$508$	−22.8838	−	1.33790i	−1.01530	−	0.0593598i
$509$	3.56528	+	6.17525i	0.158028	+	0.273713i	0.934158	−	0.356861i	$-0.116153\pi$
$509$	3.56528	+	6.17525i	0.158028	+	0.273713i	−0.776129	+	0.630574i	$0.782820\pi$
$510$	0.313585	+	4.57043i	0.0138858	+	0.202382i
$511$	8.31405	+	4.80012i	0.367792	+	0.212345i
$512$	19.6072	−	11.2942i	0.866522	−	0.499138i
$513$	8.15722	−	15.2093i	0.360150	−	0.671508i
$514$	−6.86342	+	22.9162i	−0.302732	+	1.01079i
$515$	−0.427706	−	0.246936i	−0.0188470	−	0.0108813i
$516$	28.3319	+	6.40981i	1.24724	+	0.282176i
$517$	9.47106	−	5.46812i	0.416537	−	0.240488i
$518$	−1.42691	−	6.02356i	−0.0626947	−	0.264660i
$519$	5.83065	−	35.2125i	0.255937	−	1.54566i
$520$	1.99442	+	11.3329i	0.0874611	+	0.496980i
$521$			18.3498i			0.803921i	0.915657	+	0.401960i	$0.131671\pi$
$521$			18.3498i			0.803921i	−0.915657	+	0.401960i	$0.868329\pi$
$522$	−9.59580	−	6.83881i	−0.419997	−	0.299327i
$523$	−13.4690			−0.588957			−0.294478	−	0.955658i	$-0.595146\pi$
$523$	−13.4690			−0.588957			−0.294478	+	0.955658i	$0.595146\pi$
$524$	−12.8234	−	25.5476i	−0.560193	−	1.11605i
$525$	0.658807	−	0.801988i	0.0287527	−	0.0350016i
$526$	2.14018	+	9.03458i	0.0933163	+	0.393927i
$527$	−4.36321	−	7.55730i	−0.190064	−	0.329201i
$528$	−5.38394	−	1.55338i	−0.234306	−	0.0676023i
$529$	9.48573	−	16.4298i	0.412423	−	0.714337i
$530$	7.14403	+	2.13964i	0.310317	+	0.0929401i
$531$	7.16847	−	21.0524i	0.311085	−	0.913598i
$532$	−2.18810	+	3.32525i	−0.0948662	+	0.144168i
$533$	17.2070	−	29.8033i	0.745316	−	1.29092i
$534$	−20.7210	−	10.1399i	−0.896687	−	0.438797i
$535$	−0.131216	+	0.0757578i	−0.00567298	+	0.00327529i
$536$	12.9389	−	35.5127i	0.558876	−	1.53392i
$537$	−10.3534	−	27.5478i	−0.446784	−	1.18878i
$538$	−15.3415	+	14.4708i	−0.661420	+	0.623880i
$539$		−	5.37121i		−	0.231354i
$540$	0.281465	−	10.3885i	0.0121123	−	0.447050i
$541$			37.2583i			1.60186i	0.598758	+	0.800930i	$0.295661\pi$
$541$			37.2583i			1.60186i	−0.598758	+	0.800930i	$0.704339\pi$
$542$	16.1911	+	17.1653i	0.695466	+	0.737315i
$543$	−13.7226	−	36.5123i	−0.588894	−	1.56689i
$544$	−6.31311	−	8.48977i	−0.270672	−	0.363996i
$545$	3.85537	−	2.22590i	0.165146	−	0.0953470i
$546$	2.62476	−	5.36373i	0.112329	−	0.229546i
$547$	5.57601	−	9.65793i	0.238413	−	0.412943i	−0.721846	−	0.692054i	$-0.756706\pi$
$547$	5.57601	−	9.65793i	0.238413	−	0.412943i	0.960259	+	0.279110i	$0.0900395\pi$
$548$	2.02529	−	3.07783i	0.0865162	−	0.131478i
$549$	−14.8923	+	2.94768i	−0.635589	+	0.125804i
$550$	−0.328173	+	1.09573i	−0.0139933	+	0.0467222i
$551$	4.61245	−	7.98900i	0.196497	−	0.340343i
$552$	−0.0993651	−	9.83236i	−0.00422926	−	0.418493i
$553$	−1.33254	−	2.30802i	−0.0566652	−	0.0981471i
$554$	27.1941	−	6.44195i	1.15537	−	0.273692i
$555$	−8.03105	+	9.77647i	−0.340899	+	0.414988i
$556$	17.6168	−	8.84259i	0.747117	−	0.375009i
$557$	11.3629			0.481464			0.240732	−	0.970592i	$-0.422613\pi$
$557$	11.3629			0.481464			0.240732	+	0.970592i	$0.422613\pi$
$558$	8.21637	+	18.0100i	0.347827	+	0.762425i
$559$		−	34.1148i		−	1.44290i
$560$	−0.279315	+	2.38057i	−0.0118032	+	0.100597i
$561$	−0.428008	+	2.58483i	−0.0180705	+	0.109131i
$562$	23.8767	−	5.65610i	1.00718	−	0.238588i
$563$	21.2512	−	12.2694i	0.895630	−	0.517092i	0.0198504	−	0.999803i	$-0.493681\pi$
$563$	21.2512	−	12.2694i	0.895630	−	0.517092i	0.875780	+	0.482711i	$0.160348\pi$
$564$	−45.6853	−	10.3358i	−1.92370	−	0.435217i
$565$	−14.2998	−	8.25601i	−0.601599	−	0.347333i
$566$	−6.58900	−	1.97341i	−0.276956	−	0.0829486i
$567$	−3.29112	+	4.27238i	−0.138214	+	0.179423i
$568$	−5.89299	−	7.02772i	−0.247264	−	0.294877i
$569$	22.0405	+	12.7251i	0.923986	+	0.533464i	0.884905	−	0.465772i	$-0.154223\pi$
$569$	22.0405	+	12.7251i	0.923986	+	0.533464i	0.0390818	+	0.999236i	$0.487557\pi$
$570$	8.11676	−	0.556904i	0.339974	−	0.0233261i
$571$	−14.0201	−	24.2836i	−0.586725	−	1.01624i	−0.994658	−	0.103225i	$-0.967084\pi$
$571$	−14.0201	−	24.2836i	−0.586725	−	1.01624i	0.407933	−	0.913012i	$-0.366250\pi$
$572$	−0.384103	+	6.56978i	−0.0160602	+	0.274696i
$573$	−2.07232	+	12.5151i	−0.0865723	+	0.522828i
$574$	5.21462	−	4.91865i	0.217654	−	0.205301i
$575$	−2.00712			−0.0837029
$576$	12.4176	+	20.5378i	0.517400	+	0.855744i
$577$	−18.6560			−0.776659			−0.388329	−	0.921521i	$-0.626948\pi$
$577$	−18.6560			−0.776659			−0.388329	+	0.921521i	$0.626948\pi$
$578$	13.8906	−	13.1022i	0.577772	−	0.544979i
$579$	0.968714	+	0.795767i	0.0402584	+	0.0330710i
$580$	0.324206	−	5.54528i	0.0134619	−	0.230255i
$581$	−1.39932	−	2.42370i	−0.0580537	−	0.100552i
$582$	−5.34711	−	7.94984i	−0.221645	−	0.329532i
$583$	3.69365	+	2.13253i	0.152975	+	0.0883203i
$584$	29.1161	+	34.7226i	1.20483	+	1.43683i
$585$	−11.9728	+	2.36981i	−0.495014	+	0.0979795i
$586$	43.3574	+	12.9856i	1.79108	+	0.536429i
$587$	−17.4680	−	10.0851i	−0.720980	−	0.416258i	0.0941335	−	0.995560i	$-0.469992\pi$
$587$	−17.4680	−	10.0851i	−0.720980	−	0.416258i	−0.815113	+	0.579302i	$0.803325\pi$
$588$	−15.6151	+	16.8935i	−0.643957	+	0.696677i
$589$	−13.4212	+	7.74875i	−0.553012	+	0.319282i
$590$	10.2014	−	2.41660i	0.419987	−	0.0994896i
$591$	−4.32747	+	1.62642i	−0.178008	+	0.0669018i
$592$	3.40494	−	29.0198i	0.139942	−	1.19271i
$593$		−	27.7648i		−	1.14016i	−0.821589	−	0.570081i	$-0.806912\pi$
$593$		−	27.7648i		−	1.14016i	0.821589	−	0.570081i	$-0.193088\pi$
$594$	1.52615	−	5.74419i	0.0626189	−	0.235687i
$595$	1.12070			0.0459444
$596$	20.3120	−	10.1955i	0.832012	−	0.417622i
$597$	−15.5265	−	41.3121i	−0.635459	−	1.69079i
$598$	−11.2371	+	2.66192i	−0.459517	+	0.108854i
$599$	−7.44295	−	12.8916i	−0.304111	−	0.526735i	0.672952	−	0.739686i	$-0.265026\pi$
$599$	−7.44295	−	12.8916i	−0.304111	−	0.526735i	−0.977063	+	0.212951i	$0.931693\pi$
$600$	4.21767	−	2.49224i	0.172186	−	0.101745i
$601$	−17.1527	+	29.7093i	−0.699671	+	1.21187i	0.268909	+	0.963166i	$0.413337\pi$
$601$	−17.1527	+	29.7093i	−0.699671	+	1.21187i	−0.968580	+	0.248701i	$0.919996\pi$
$602$	2.03879	−	6.80730i	0.0830950	−	0.277445i
$603$	37.9495	+	12.9220i	1.54542	+	0.526225i
$604$	−13.8555	+	21.0561i	−0.563771	+	0.856759i
$605$	5.17292	−	8.95976i	0.210309	−	0.364266i
$606$	−0.616225	−	0.916175i	−0.0250324	−	0.0372171i
$607$	−15.5493	+	8.97738i	−0.631126	+	0.364381i	−0.781188	−	0.624296i	$-0.785386\pi$
$607$	−15.5493	+	8.97738i	−0.631126	+	0.364381i	0.150062	+	0.988677i	$0.452053\pi$
$608$	−15.0772	+	11.2116i	−0.611463	+	0.454692i
$609$	−1.82975	+	2.22742i	−0.0741454	+	0.0902597i
$610$	−4.91052	−	5.20600i	−0.198821	−	0.210785i
$611$			55.0103i			2.22548i
$612$	8.86075	−	6.88550i	0.358175	−	0.278330i
$613$		−	21.2137i		−	0.856814i	−0.903586	−	0.428407i	$-0.859075\pi$
$613$		−	21.2137i		−	0.856814i	0.903586	−	0.428407i	$-0.140925\pi$
$614$	−11.1021	+	10.4720i	−0.448045	+	0.422616i
$615$	−14.4545	−	2.39344i	−0.582860	−	0.0965128i
$616$	−0.469272	+	1.28799i	−0.0189075	+	0.0518944i
$617$	21.3493	−	12.3260i	0.859491	−	0.496227i	−0.00435075	−	0.999991i	$-0.501385\pi$
$617$	21.3493	−	12.3260i	0.859491	−	0.496227i	0.863842	+	0.503763i	$0.168052\pi$
$618$	0.0828071	+	1.20690i	0.00333099	+	0.0485485i
$619$	13.3766	−	23.1689i	0.537650	−	0.931237i	−0.461380	−	0.887203i	$-0.652645\pi$
$619$	13.3766	−	23.1689i	0.537650	−	0.931237i	0.999030	−	0.0440347i	$-0.0140212\pi$
$620$	−5.12962	+	7.79545i	−0.206010	+	0.313073i
$621$	10.4242	−	0.326503i	0.418309	−	0.0131021i
$622$	−3.30487	−	0.989810i	−0.132513	−	0.0396878i
$623$	−2.82172	+	4.88735i	−0.113050	+	0.195808i
$624$	20.3077	−	19.5466i	0.812958	−	0.782491i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−4.48910	−	18.9504i	−0.179421	−	0.757408i
$627$	4.59047	+	0.760112i	0.183326	+	0.0303559i
$628$	16.0079	+	31.8919i	0.638784	+	1.27262i
$629$	−13.6617			−0.544729
$630$	−2.53069	−	0.242652i	−0.100825	−	0.00966749i
$631$			31.8679i			1.26864i	0.773069	+	0.634322i	$0.218720\pi$
$631$			31.8679i			1.26864i	−0.773069	+	0.634322i	$0.781280\pi$
$632$	−2.18031	−	12.3891i	−0.0867279	−	0.492814i
$633$	18.9798	+	15.5913i	0.754379	+	0.619698i
$634$	5.11104	+	21.5758i	0.202985	+	0.856885i
$635$	9.92589	−	5.73071i	0.393897	−	0.227416i
$636$	−5.41760	−	17.4454i	−0.214822	−	0.691754i
$637$	23.3980	+	13.5088i	0.927062	+	0.535239i
$638$	0.911459	−	3.04326i	0.0360850	−	0.120484i
$639$	7.31981	−	6.40711i	0.289567	−	0.253461i
$640$	−5.08540	+	10.1064i	−0.201018	+	0.399489i
$641$	2.74659	+	1.58575i	0.108484	+	0.0626332i	0.553260	−	0.833008i	$-0.313384\pi$
$641$	2.74659	+	1.58575i	0.108484	+	0.0626332i	−0.444776	+	0.895642i	$0.646717\pi$
$642$	0.333361	+	0.163132i	0.0131567	+	0.00643830i
$643$	−18.4793	−	32.0071i	−0.728752	−	1.26223i	−0.957411	−	0.288728i	$-0.906768\pi$
$643$	−18.4793	−	32.0071i	−0.728752	−	1.26223i	0.228659	−	0.973507i	$-0.426566\pi$
$644$	−2.40134	−	0.140394i	−0.0946259	−	0.00553232i
$645$	−13.5955	+	5.10966i	−0.535321	+	0.201193i
$646$	6.02795	+	6.39067i	0.237166	+	0.251437i
$647$	35.4240			1.39266			0.696331	−	0.717720i	$-0.254814\pi$
$647$	35.4240			1.39266			0.696331	+	0.717720i	$0.254814\pi$
$648$	−21.4995	+	13.6298i	−0.844580	+	0.535429i
$649$	5.99577			0.235355
$650$	−3.94784	−	4.18540i	−0.154847	−	0.164165i
$651$	4.53309	−	1.70369i	0.177666	−	0.0667731i
$652$	−1.45233	+	24.8409i	−0.0568775	+	0.972846i
$653$	−16.5954	−	28.7441i	−0.649428	−	1.12484i	−0.983260	−	0.182209i	$-0.941675\pi$
$653$	−16.5954	−	28.7441i	−0.649428	−	1.12484i	0.333832	−	0.942633i	$-0.391658\pi$
$654$	−9.79475	−	4.79310i	−0.383005	−	0.187425i
$655$	12.3778	+	7.14631i	0.483640	+	0.279230i
$656$	31.0744	−	13.3879i	1.21325	−	0.522710i
$657$	−36.1657	+	31.6562i	−1.41096	+	1.23503i
$658$	−3.28756	+	10.9768i	−0.128163	+	0.427921i
$659$	−19.4711	−	11.2416i	−0.758487	−	0.437912i	0.0702655	−	0.997528i	$-0.477615\pi$
$659$	−19.4711	−	11.2416i	−0.758487	−	0.437912i	−0.828752	+	0.559616i	$0.810949\pi$
$660$	2.67572	−	0.830937i	0.104152	−	0.0323442i
$661$	43.5920	−	25.1678i	1.69553	−	0.978916i	0.745634	−	0.666356i	$-0.232147\pi$
$661$	43.5920	−	25.1678i	1.69553	−	0.978916i	0.949898	−	0.312559i	$-0.101186\pi$
$662$	−0.699863	−	2.95441i	−0.0272009	−	0.114826i
$663$	−10.1835	−	8.36544i	−0.395495	−	0.324887i
$664$	−2.28958	−	13.0101i	−0.0888529	−	0.504889i
$665$		−	1.99029i		−	0.0771802i
$666$	30.8499	+	2.95800i	1.19541	+	0.114620i
$667$	5.57454			0.215847
$668$	−43.4746	+	21.8217i	−1.68208	+	0.844308i
$669$	46.1216	+	7.63703i	1.78316	+	0.295265i
$670$	4.35619	+	18.3893i	0.168294	+	0.710440i
$671$	−2.04644	−	3.54454i	−0.0790020	−	0.136836i
$672$	5.22038	−	2.68671i	0.201380	−	0.103642i
$673$	−14.4128	+	24.9638i	−0.555574	+	0.962282i	0.442285	+	0.896875i	$0.354168\pi$
$673$	−14.4128	+	24.9638i	−0.555574	+	0.962282i	−0.997859	+	0.0654077i	$0.979165\pi$
$674$	29.1369	+	8.72652i	1.12231	+	0.336133i
$675$	2.73768	+	4.41646i	0.105373	+	0.169990i
$676$	−5.93362	−	3.90448i	−0.228216	−	0.150172i
$677$	−19.2116	+	33.2754i	−0.738361	+	1.27888i	0.214873	+	0.976642i	$0.431066\pi$
$677$	−19.2116	+	33.2754i	−0.738361	+	1.27888i	−0.953233	+	0.302236i	$0.902267\pi$
$678$	2.76856	+	40.3512i	0.106326	+	1.54968i
$679$	−2.02977	+	1.17189i	−0.0778953	+	0.0449729i
$680$	4.97027	+	1.81090i	0.190601	+	0.0694447i
$681$	−35.0148	−	5.79792i	−1.34177	−	0.222177i
$682$	−3.88236	+	3.66200i	−0.148663	+	0.140225i
$683$			49.7921i			1.90524i	0.304160	+	0.952621i	$0.401624\pi$
$683$			49.7921i			1.90524i	−0.304160	+	0.952621i	$0.598376\pi$
$684$	−12.2282	−	15.7361i	−0.467555	−	0.601684i
$685$			1.84220i			0.0703869i
$686$	7.93186	+	8.40914i	0.302840	+	0.321062i
$687$	13.3021	−	16.1930i	0.507505	−	0.617803i
$688$	20.0416	−	26.8957i	0.764077	−	1.02539i
$689$	−18.5794	+	10.7268i	−0.707818	+	0.408659i
$690$	2.74390	+	4.07950i	0.104458	+	0.155304i
$691$	−22.6143	+	39.1691i	−0.860289	+	1.49006i	0.0113615	+	0.999935i	$0.496383\pi$
$691$	−22.6143	+	39.1691i	−0.860289	+	1.49006i	−0.871650	+	0.490128i	$0.836950\pi$
$692$	−34.4284	−	22.6548i	−1.30877	−	0.861207i
$693$	−1.37636	−	0.468659i	−0.0522837	−	0.0178029i
$694$	8.14902	−	27.2087i	0.309332	−	1.03283i
$695$	−4.92786	+	8.53531i	−0.186925	+	0.323763i
$696$	−11.7141	+	6.92188i	−0.444020	+	0.262373i
$697$	−7.91018	−	13.7008i	−0.299620	−	0.518956i
$698$	5.47312	−	1.29651i	0.207161	−	0.0490738i
$699$	4.30055	+	11.4426i	0.162662	+	0.432800i
$700$	−0.537626	−	1.07109i	−0.0203204	−	0.0404835i
$701$	−3.69419			−0.139528			−0.0697638	−	0.997564i	$-0.522225\pi$
$701$	−3.69419			−0.139528			−0.0697638	+	0.997564i	$0.522225\pi$
$702$	21.1844	+	21.0951i	0.799553	+	0.796183i
$703$			24.2623i			0.915068i
$704$	−4.16240	+	4.95388i	−0.156876	+	0.186706i
$705$	21.9227	−	8.23934i	0.825658	−	0.310312i
$706$	43.5146	−	10.3081i	1.63769	−	0.387949i
$707$	−0.233919	+	0.135053i	−0.00879744	+	0.00507921i
$708$	−18.8579	−	17.4309i	−0.708724	−	0.655092i
$709$	−8.06684	−	4.65739i	−0.302956	−	0.174912i	0.340814	−	0.940131i	$-0.389297\pi$
$709$	−8.06684	−	4.65739i	−0.302956	−	0.174912i	−0.643770	+	0.765219i	$0.722631\pi$
$710$	4.39295	+	1.31569i	0.164864	+	0.0493770i
$711$	13.0887	−	2.59068i	0.490864	−	0.0971581i
$712$	−20.4114	+	17.1157i	−0.764950	+	0.641438i
$713$	−8.11035	−	4.68251i	−0.303735	−	0.175361i
$714$	−1.53209	−	2.27784i	−0.0573370	−	0.0852461i
$715$	−1.64525	−	2.84966i	−0.0615289	−	0.106571i
$716$	−33.9239	−	1.98337i	−1.26780	−	0.0741219i
$717$	3.88578	+	3.19205i	0.145117	+	0.119209i
$718$	−25.3019	+	23.8658i	−0.944257	+	0.890664i
$719$	28.6898			1.06995			0.534975	−	0.844868i	$-0.320321\pi$
$719$	28.6898			1.06995			0.534975	+	0.844868i	$0.320321\pi$
$720$	−10.8314	−	5.16537i	−0.403662	−	0.192502i
$721$	0.295940			0.0110214
$722$	−8.19724	+	7.73198i	−0.305070	+	0.287755i
$723$	2.74600	−	16.5836i	0.102125	−	0.616752i
$724$	−44.9633	−	2.62879i	−1.67105	−	0.0976981i
$725$	1.38869	+	2.40528i	0.0515746	+	0.0893298i
$726$	−25.2826	+	1.73468i	−0.938325	+	0.0643800i
$727$	−37.1076	−	21.4241i	−1.37624	−	0.794575i	−0.384539	−	0.923109i	$-0.625640\pi$
$727$	−37.1076	−	21.4241i	−1.37624	−	0.794575i	−0.991705	+	0.128534i	$0.958973\pi$
$728$	−4.43047	−	5.28358i	−0.164204	−	0.195822i
$729$	−14.9369	−	22.4920i	−0.553217	−	0.833037i
$730$	−21.7047	−	6.50057i	−0.803326	−	0.240597i
$731$	−13.5818	−	7.84143i	−0.502340	−	0.290026i
$732$	−3.86818	+	17.0977i	−0.142972	+	0.631949i
$733$	−32.8767	+	18.9813i	−1.21433	+	0.701092i	−0.963699	−	0.266991i	$-0.913970\pi$
$733$	−32.8767	+	18.9813i	−1.21433	+	0.701092i	−0.250628	+	0.968083i	$0.580637\pi$
$734$	10.0826	−	2.38843i	0.372154	−	0.0881587i
$735$	1.87904	−	11.3479i	0.0693095	−	0.418574i
$736$	−10.4229	−	4.50285i	−0.384195	−	0.165977i
$737$			10.8081i			0.398121i
$738$	14.8957	+	32.6509i	0.548318	+	1.20190i
$739$	10.5865			0.389432			0.194716	−	0.980860i	$-0.437622\pi$
$739$	10.5865			0.389432			0.194716	+	0.980860i	$0.437622\pi$
$740$	6.55383	+	13.0569i	0.240924	+	0.479983i
$741$	−14.8564	+	18.0852i	−0.545764	+	0.664377i
$742$	−4.34841	+	1.03009i	−0.159635	+	0.0378156i
$743$	−9.31534	−	16.1346i	−0.341747	−	0.591922i	0.643011	−	0.765857i	$-0.277685\pi$
$743$	−9.31534	−	16.1346i	−0.341747	−	0.591922i	−0.984757	+	0.173935i	$0.944352\pi$
$744$	22.8569	−	0.230991i	0.837976	−	0.00846852i
$745$	−5.68180	+	9.84116i	−0.208165	+	0.360552i
$746$	−13.0871	+	43.6965i	−0.479154	+	1.59984i
$747$	13.7447	−	2.72052i	0.502891	−	0.0995387i
$748$	2.52727	+	1.66301i	0.0924061	+	0.0608057i
$749$	0.0453959	−	0.0786281i	0.00165873	−	0.00287301i
$750$	−1.07667	+	2.20018i	−0.0393143	+	0.0803392i
$751$	−19.5847	+	11.3073i	−0.714657	+	0.412608i	−0.812783	−	0.582566i	$-0.802049\pi$
$751$	−19.5847	+	11.3073i	−0.714657	+	0.412608i	0.0981257	+	0.995174i	$0.468715\pi$
$752$	−32.3171	+	43.3694i	−1.17848	+	1.58152i
$753$	−4.43888	−	11.8107i	−0.161762	−	0.430405i
$754$	10.9646	+	11.6244i	0.399309	+	0.423336i
$755$		−	12.6029i		−	0.458666i
$756$	2.96646	+	5.47537i	0.107889	+	0.199137i
$757$		−	35.8025i		−	1.30126i	−0.759394	−	0.650631i	$-0.774504\pi$
$757$		−	35.8025i		−	1.30126i	0.759394	−	0.650631i	$-0.225496\pi$
$758$	−7.15220	+	6.74626i	−0.259780	+	0.245035i
$759$	0.989202	+	2.63201i	0.0359058	+	0.0955358i
$760$	3.21602	−	8.82684i	0.116657	−	0.320183i
$761$	−31.6012	+	18.2449i	−1.14554	+	0.661379i	−0.947797	−	0.318875i	$-0.896695\pi$
$761$	−31.6012	+	18.2449i	−1.14554	+	0.661379i	−0.197745	+	0.980254i	$0.563362\pi$
$762$	−25.2172	−	12.3401i	−0.913522	−	0.447036i
$763$	−1.33381	+	2.31023i	−0.0482873	+	0.0836360i
$764$	12.2365	+	8.05192i	0.442700	+	0.291308i
$765$	−1.80853	+	5.31131i	−0.0653875	+	0.192031i
$766$	37.2284	+	11.1499i	1.34512	+	0.402863i
$767$	−15.0796	+	26.1187i	−0.544494	+	0.943092i
$768$	27.4934	−	3.48006i	0.992084	−	0.125576i
$769$	15.6746	+	27.1492i	0.565241	+	0.979026i	0.997027	+	0.0770499i	$0.0245501\pi$
$769$	15.6746	+	27.1492i	0.565241	+	0.979026i	−0.431786	+	0.901976i	$0.642117\pi$
$770$	−0.157992	−	0.666948i	−0.00569363	−	0.0240351i
$771$	−18.5973	+	22.6391i	−0.669765	+	0.815327i
$772$	1.29376	−	0.649394i	0.0465636	−	0.0233722i
$773$	35.5512			1.27869			0.639344	−	0.768921i	$-0.279206\pi$
$773$	35.5512			1.27869			0.639344	+	0.768921i	$0.279206\pi$
$774$	28.9715	+	20.6476i	1.04136	+	0.742163i
$775$		−	4.66589i		−	0.167604i
$776$	−10.8955	+	1.91745i	−0.391126	+	0.0688324i
$777$	1.23851	−	7.47964i	0.0444315	−	0.268331i
$778$	10.3366	+	43.6350i	0.370585	+	1.56439i
$779$	−24.3317	+	14.0479i	−0.871774	+	0.503319i
$780$	−3.10985	+	13.7458i	−0.111351	+	0.492179i
$781$	2.27127	+	1.31132i	0.0812724	+	0.0469226i
$782$	−1.52312	+	5.08554i	−0.0544668	+	0.181859i
$783$	−7.60357	−	12.2662i	−0.271729	−	0.438357i
$784$	10.5106	+	24.3959i	0.375377	+	0.871282i
$785$	−15.4516	−	8.92099i	−0.551491	−	0.318404i
$786$	−2.39643	−	34.9275i	−0.0854780	−	1.24582i
$787$	−2.50484	−	4.33851i	−0.0892879	−	0.154651i	0.817922	−	0.575329i	$-0.195126\pi$
$787$	−2.50484	−	4.33851i	−0.0892879	−	0.154651i	−0.907210	+	0.420677i	$0.861792\pi$
$788$	−0.311566	+	5.32909i	−0.0110991	+	0.189841i
$789$	−1.85762	+	11.2185i	−0.0661329	+	0.399390i
$790$	4.31579	+	4.57549i	0.153549	+	0.162789i
$791$	9.89441			0.351805
$792$	−5.34681	−	4.30248i	−0.189991	−	0.152882i
$793$	20.5876			0.731086
$794$	2.64483	+	2.80398i	0.0938615	+	0.0995094i
$795$	7.05765	+	5.79763i	0.250309	+	0.205621i
$796$	−50.8740	−	2.97436i	−1.80318	−	0.105423i
$797$	−8.82804	−	15.2906i	−0.312705	−	0.541621i	0.666242	−	0.745736i	$-0.267902\pi$
$797$	−8.82804	−	15.2906i	−0.312705	−	0.541621i	−0.978947	+	0.204114i	$0.934569\pi$
$798$	−4.04529	+	2.72088i	−0.143202	+	0.0963182i
$799$	21.9006	+	12.6443i	0.774789	+	0.447325i
$800$	−0.653616	−	5.61897i	−0.0231088	−	0.198660i
$801$	−18.6089	−	21.2598i	−0.657513	−	0.751177i
$802$	4.52397	−	15.1050i	0.159747	−	0.533378i
$803$	−11.2219	−	6.47896i	−0.396012	−	0.228637i
$804$	31.4211	−	33.9936i	1.10814	−	1.19886i
$805$	1.04158	−	0.601359i	0.0367110	−	0.0211951i
$806$	−6.18807	−	26.1224i	−0.217965	−	0.920121i
$807$	−24.1780	+	9.08696i	−0.851106	+	0.319876i
$808$	−1.25565	+	0.220975i	−0.0441735	+	0.00777388i
$809$		−	52.1748i		−	1.83437i	−0.398463	−	0.917184i	$-0.630456\pi$
$809$		−	52.1748i		−	1.83437i	0.398463	−	0.917184i	$-0.369544\pi$
$810$	5.23387	−	11.6020i	0.183900	−	0.407653i
$811$	13.3347			0.468244			0.234122	−	0.972207i	$-0.424778\pi$
$811$	13.3347			0.468244			0.234122	+	0.972207i	$0.424778\pi$
$812$	1.49319	+	2.97483i	0.0524007	+	0.104396i
$813$	10.1672	+	27.0523i	0.356580	+	0.948766i
$814$	1.92597	+	8.13030i	0.0675051	+	0.284967i
$815$	−6.22083	−	10.7748i	−0.217906	−	0.377425i
$816$	−3.11408	−	12.5778i	−0.109015	−	0.440309i
$817$	−13.9258	+	24.1202i	−0.487203	+	0.843861i
$818$	14.3353	+	4.29343i	0.501221	+	0.150116i
$819$	5.50318	−	4.81699i	0.192297	−	0.168319i
$820$	−9.29963	+	14.1326i	−0.324757	+	0.493532i
$821$	−18.4884	+	32.0228i	−0.645249	+	1.11760i	0.338995	+	0.940788i	$0.389913\pi$
$821$	−18.4884	+	32.0228i	−0.645249	+	1.11760i	−0.984244	+	0.176816i	$0.943420\pi$
$822$	3.74429	−	2.51843i	0.130597	−	0.0878405i
$823$	29.4402	−	16.9973i	1.02622	−	0.592488i	0.110320	−	0.993896i	$-0.464812\pi$
$823$	29.4402	−	16.9973i	1.02622	−	0.592488i	0.915899	+	0.401408i	$0.131479\pi$
$824$	1.31248	+	0.478197i	0.0457224	+	0.0166588i
$825$	−0.889225	+	1.08248i	−0.0309588	+	0.0376872i
$826$	−4.56993	+	4.31055i	−0.159008	+	0.149983i
$827$			19.2929i			0.670881i	0.942061	+	0.335441i	$0.108885\pi$
$827$			19.2929i			0.670881i	−0.942061	+	0.335441i	$0.891115\pi$
$828$	4.54051	−	11.1540i	0.157794	−	0.387628i
$829$			18.2468i			0.633737i	0.948469	+	0.316869i	$0.102631\pi$
$829$			18.2468i			0.633737i	−0.948469	+	0.316869i	$0.897369\pi$
$830$	4.53210	+	4.80481i	0.157311	+	0.166777i
$831$	33.7678	+	5.59144i	1.17139	+	0.193965i
$832$	−11.1114	−	30.5914i	−0.385218	−	1.06057i
$833$	10.7562	−	6.21012i	0.372682	−	0.215168i
$834$	24.0849	−	1.65250i	0.833991	−	0.0572215i
$835$	12.1610	−	21.0634i	0.420848	−	0.728930i
$836$	2.95339	−	4.48825i	0.102145	−	0.155229i
$837$	0.759009	+	24.2328i	0.0262352	+	0.837608i
$838$	4.99149	−	16.6660i	0.172428	−	0.575718i
$839$	1.62551	−	2.81546i	0.0561187	−	0.0972005i	−0.836601	−	0.547812i	$-0.815461\pi$
$839$	1.62551	−	2.81546i	0.0561187	−	0.0972005i	0.892720	+	0.450612i	$0.148794\pi$
$840$	−1.44203	+	2.55700i	−0.0497547	+	0.0882248i
$841$	10.6431	+	18.4344i	0.367003	+	0.635668i
$842$	50.5817	−	11.9822i	1.74316	−	0.412933i
$843$	29.6485	+	4.90934i	1.02115	+	0.169087i
$844$	25.3484	−	12.7234i	0.872528	−	0.437958i
$845$	3.55151			0.122176
$846$	−46.7166	−	33.2944i	−1.60615	−	1.14468i
$847$			6.19948i			0.213017i
$848$	−20.9495	−	2.45803i	−0.719408	−	0.0844091i
$849$	−6.50933	−	5.34720i	−0.223399	−	0.183515i
$850$	−2.57372	+	0.609681i	−0.0882777	+	0.0209119i
$851$	−12.6972	+	7.33075i	−0.435256	+	0.251295i
$852$	−3.33135	−	10.7274i	−0.114130	−	0.367514i
$853$	−30.7596	−	17.7590i	−1.05319	−	0.608058i	−0.129648	−	0.991560i	$-0.541385\pi$
$853$	−30.7596	−	17.7590i	−1.05319	−	0.608058i	−0.923540	+	0.383502i	$0.874718\pi$
$854$	4.10807	+	1.23037i	0.140575	+	0.0421024i
$855$	9.43251	+	3.21182i	0.322585	+	0.109842i
$856$	0.328380	−	0.275358i	0.0112238	−	0.00941155i
$857$	−8.43191	−	4.86817i	−0.288029	−	0.166293i	0.349024	−	0.937114i	$-0.386513\pi$
$857$	−8.43191	−	4.86817i	−0.288029	−	0.166293i	−0.637052	+	0.770820i	$0.719847\pi$
$858$	−3.54277	+	7.23969i	−0.120948	+	0.247159i
$859$	10.2239	+	17.7083i	0.348835	+	0.604200i	0.986043	−	0.166492i	$-0.0532439\pi$
$859$	10.2239	+	17.7083i	0.348835	+	0.604200i	−0.637208	+	0.770692i	$0.719911\pi$
$860$	−0.978836	+	16.7422i	−0.0333780	+	0.570905i
$861$	8.21816	−	3.08868i	0.280074	−	0.105262i
$862$	32.4530	−	30.6111i	1.10535	−	1.04262i
$863$	−15.1892			−0.517047			−0.258523	−	0.966005i	$-0.583236\pi$
$863$	−15.1892			−0.517047			−0.258523	+	0.966005i	$0.583236\pi$
$864$	4.30867	+	29.0764i	0.146584	+	0.989198i
$865$	20.6068			0.700651
$866$	−22.3167	+	21.0501i	−0.758353	+	0.715311i
$867$	21.8913	−	8.22754i	0.743469	−	0.279422i
$868$	0.326370	−	5.58230i	0.0110777	−	0.189476i
$869$	1.79859	+	3.11525i	0.0610130	+	0.105678i
$870$	2.99031	−	6.11073i	0.101381	−	0.207173i
$871$	−47.0820	−	27.1828i	−1.59531	−	0.921054i
$872$	−9.64840	+	8.09052i	−0.326736	+	0.273979i
$873$	−2.27835	−	11.5107i	−0.0771104	−	0.389579i
$874$	9.03156	+	2.70496i	0.305497	+	0.0914966i
$875$	0.518944	+	0.299612i	0.0175435	+	0.0101287i
$876$	16.4595	+	53.0018i	0.556116	+	1.79076i
$877$	−17.8435	+	10.3020i	−0.602533	+	0.347873i	−0.770037	−	0.637999i	$-0.779762\pi$
$877$	−17.8435	+	10.3020i	−0.602533	+	0.347873i	0.167504	+	0.985871i	$0.446429\pi$
$878$	−2.14355	+	0.507780i	−0.0723412	+	0.0171367i
$879$	42.8331	+	35.1860i	1.44472	+	1.18679i
$880$	0.377006	−	3.21317i	0.0127089	−	0.108316i
$881$		−	13.0624i		−	0.440083i	−0.975490	−	0.220042i	$-0.929381\pi$
$881$		−	13.0624i		−	0.440083i	0.975490	−	0.220042i	$-0.0706193\pi$
$882$	−25.6335	+	11.6943i	−0.863126	+	0.393768i
$883$	38.3841			1.29173			0.645864	−	0.763452i	$-0.276497\pi$
$883$	38.3841			1.29173			0.645864	+	0.763452i	$0.276497\pi$
$884$	−13.6006	+	6.82670i	−0.457437	+	0.229607i
$885$	12.6675	+	2.09754i	0.425812	+	0.0705079i
$886$	33.1754	−	7.85884i	1.11455	−	0.264023i
$887$	−0.0432052	−	0.0748336i	−0.00145069	−	0.00251267i	0.865299	−	0.501256i	$-0.167128\pi$
$887$	−0.0432052	−	0.0748336i	−0.00145069	−	0.00251267i	−0.866750	+	0.498743i	$0.833795\pi$
$888$	17.5788	−	31.1706i	0.589905	−	1.04602i
$889$	−3.43398	+	5.94784i	−0.115172	+	0.199484i
$890$	3.82132	−	12.7589i	0.128091	−	0.427681i
$891$	4.44219	−	5.76664i	0.148819	−	0.193190i
$892$	29.6734	−	45.0946i	0.993541	−	1.50988i
$893$	22.4555	−	38.8940i	0.751443	−	1.30154i
$894$	27.7697	−	1.90533i	0.928758	−	0.0637236i
$895$	14.7146	−	8.49547i	0.491854	−	0.283972i
$896$	−0.388955	−	6.76829i	−0.0129941	−	0.226113i
$897$	−13.9534	−	2.31047i	−0.465891	−	0.0771444i
$898$	−22.0374	−	23.3635i	−0.735399	−	0.779650i
$899$			12.9589i			0.432205i
$900$	5.94377	−	0.819482i	0.198126	−	0.0273161i
$901$			9.86242i			0.328565i
$902$	−7.03843	+	6.63895i	−0.234354	+	0.221053i
$903$	5.52436	−	6.72499i	0.183839	−	0.223794i
$904$	43.8812	+	15.9879i	1.45947	+	0.531751i
$905$	19.5029	−	11.2600i	0.648300	−	0.374296i
$906$	−25.6155	+	17.2291i	−0.851018	+	0.572400i
$907$	−1.90025	+	3.29134i	−0.0630969	+	0.109287i	−0.895848	−	0.444360i	$-0.853431\pi$
$907$	−1.90025	+	3.29134i	−0.0630969	+	0.109287i	0.832751	+	0.553647i	$0.186764\pi$
$908$	−22.5276	+	34.2351i	−0.747606	+	1.13613i
$909$	−0.262567	−	1.32655i	−0.00870880	−	0.0439988i
$910$	3.30271	+	0.989163i	0.109484	+	0.0327904i
$911$	24.8293	−	43.0056i	0.822630	−	1.42484i	−0.0810866	−	0.996707i	$-0.525839\pi$
$911$	24.8293	−	43.0056i	0.822630	−	1.42484i	0.903717	−	0.428130i	$-0.140828\pi$
$912$	−22.3372	+	5.53038i	−0.739659	+	0.183129i
$913$	1.88873	+	3.27138i	0.0625080	+	0.108267i
$914$	−10.3242	−	43.5826i	−0.341493	−	1.44158i
$915$	−3.08357	−	8.20458i	−0.101940	−	0.271235i
$916$	−10.8553	−	21.6266i	−0.358669	−	0.714562i
$917$	−8.56450			−0.282825
$918$	13.2677	−	3.58512i	0.437899	−	0.118326i
$919$			6.89894i			0.227575i	0.993505	+	0.113787i	$0.0362983\pi$
$919$			6.89894i			0.227575i	−0.993505	+	0.113787i	$0.963702\pi$
$920$	5.59109	−	0.983948i	0.184333	−	0.0324398i
$921$	−17.4968	+	6.57591i	−0.576539	+	0.216684i
$922$	0.609308	+	2.57214i	0.0200665	+	0.0847089i
$923$	−11.4247	+	6.59605i	−0.376048	+	0.217112i
$924$	−1.13959	+	1.23289i	−0.0374898	+	0.0405591i
$925$	−6.32608	−	3.65236i	−0.208000	−	0.120089i
$926$	11.1791	−	37.3258i	0.367368	−	1.22660i
$927$	−0.477572	+	1.40254i	−0.0156855	+	0.0460654i
$928$	1.81534	+	15.6060i	0.0595914	+	0.512292i
$929$	−24.6040	−	14.2051i	−0.807231	−	0.466055i	0.0387624	−	0.999248i	$-0.487658\pi$
$929$	−24.6040	−	14.2051i	−0.807231	−	0.466055i	−0.845993	+	0.533193i	$0.820992\pi$
$930$	−9.48347	+	6.37864i	−0.310975	+	0.209164i
$931$	−11.0287	−	19.1023i	−0.361452	−	0.626054i
$932$	14.0911	+	0.823838i	0.461569	+	0.0269857i
$933$	−3.26491	−	2.68201i	−0.106888	−	0.0878052i
$934$	33.5435	+	35.5619i	1.09758	+	1.16362i
$935$	−1.51267			−0.0494696
$936$	32.1899	−	12.4708i	1.05216	−	0.407620i
$937$	−12.4845			−0.407852			−0.203926	−	0.978986i	$-0.565370\pi$
$937$	−12.4845			−0.407852			−0.203926	+	0.978986i	$0.565370\pi$
$938$	−7.77027	−	8.23783i	−0.253708	−	0.268975i
$939$	3.89642	−	23.5313i	0.127155	−	0.767913i
$940$	1.57838	−	26.9969i	0.0514810	−	0.880542i
$941$	10.2303	+	17.7194i	0.333498	+	0.577636i	0.983195	−	0.182558i	$-0.0584376\pi$
$941$	10.2303	+	17.7194i	0.333498	+	0.577636i	−0.649697	+	0.760193i	$0.725104\pi$
$942$	2.99155	+	43.6012i	0.0974700	+	1.42060i
$943$	−14.7035	−	8.48906i	−0.478811	−	0.276442i
$944$	−27.2327	+	11.7327i	−0.886347	+	0.381868i
$945$	−2.74393	−	1.47165i	−0.0892600	−	0.0478728i
$946$	−2.75186	+	9.18816i	−0.0894707	+	0.298733i
$947$	−6.24338	−	3.60462i	−0.202883	−	0.117134i	0.395117	−	0.918631i	$-0.370704\pi$
$947$	−6.24338	−	3.60462i	−0.202883	−	0.117134i	−0.597999	+	0.801497i	$0.704037\pi$
$948$	3.39970	−	15.0269i	0.110417	−	0.488052i
$949$	56.4471	−	32.5897i	1.83235	−	1.05791i
$950$	1.08275	+	4.57074i	0.0351291	+	0.148294i
$951$	−4.43624	+	26.7914i	−0.143855	+	0.868770i
$952$	−3.12186	+	0.549400i	−0.101180	+	0.0178062i
$953$		−	22.0465i		−	0.714157i	−0.934074	−	0.357079i	$-0.883773\pi$
$953$		−	22.0465i		−	0.714157i	0.934074	−	0.357079i	$-0.116227\pi$
$954$	2.13538	−	22.2706i	0.0691356	−	0.721036i
$955$	−7.32401			−0.236999
$956$	5.18965	−	2.60490i	0.167845	−	0.0842486i
$957$	2.46971	−	3.00646i	0.0798344	−	0.0971851i
$958$	2.08485	+	8.80103i	0.0673586	+	0.284348i
$959$	−0.551946	−	0.955999i	−0.0178233	−	0.0308708i
$960$	−10.5271	+	9.01005i	−0.339759	+	0.290798i
$961$	−4.61474	+	7.99296i	−0.148862	+	0.257837i
$962$	−40.2610	−	12.0582i	−1.29807	−	0.388772i
$963$	0.299381	+	0.342029i	0.00964743	+	0.0110217i
$964$	−16.2144	−	10.6695i	−0.522229	−	0.343641i
$965$	−0.361899	+	0.626828i	−0.0116499	+	0.0201783i
$966$	−2.64620	−	1.29493i	−0.0851400	−	0.0416636i
$967$	17.7473	−	10.2464i	0.570714	−	0.329502i	−0.186720	−	0.982413i	$-0.559786\pi$
$967$	17.7473	−	10.2464i	0.570714	−	0.329502i	0.757434	+	0.652911i	$0.226453\pi$
$968$	−10.0175	+	27.4944i	−0.321973	+	0.883703i
$969$	3.78526	+	10.0716i	0.121600	+	0.323546i
$970$	4.02387	−	3.79548i	0.129199	−	0.121866i
$971$		−	22.1348i		−	0.710341i	−0.934802	−	0.355170i	$-0.884423\pi$
$971$		−	22.1348i		−	0.710341i	0.934802	−	0.355170i	$-0.115577\pi$
$972$	−30.7363	+	5.22295i	−0.985868	+	0.167526i
$973$		−	5.90580i		−	0.189331i
$974$	−9.32179	−	9.88271i	−0.298690	−	0.316663i
$975$	−2.47906	−	6.59612i	−0.0793933	−	0.211245i
$976$	16.2310	+	12.0947i	0.519541	+	0.387141i
$977$	37.3001	−	21.5352i	1.19334	−	0.688974i	0.234275	−	0.972170i	$-0.424728\pi$
$977$	37.3001	−	21.5352i	1.19334	−	0.688974i	0.959062	+	0.283197i	$0.0913949\pi$
$978$	−13.3955	+	27.3739i	−0.428342	+	0.875321i
$979$	3.80861	−	6.59671i	0.121724	−	0.210832i
$980$	−11.0952	−	7.30095i	−0.354424	−	0.233220i
$981$	−8.79636	−	10.0494i	−0.280846	−	0.320853i
$982$	0.669657	−	2.23591i	0.0213696	−	0.0713508i
$983$	−18.6912	+	32.3741i	−0.596157	+	1.03257i	0.397226	+	0.917721i	$0.369973\pi$
$983$	−18.6912	+	32.3741i	−0.596157	+	1.03257i	−0.993383	+	0.114853i	$0.963360\pi$
$984$	41.4380	−	0.418769i	1.32099	−	0.0133499i
$985$	−1.33455	−	2.31150i	−0.0425222	−	0.0736506i
$986$	7.14818	−	1.69331i	0.227644	−	0.0539261i
$987$	−8.90806	+	10.8441i	−0.283547	+	0.345171i
$988$	12.1237	+	24.1537i	0.385708	+	0.768430i
$989$	−16.8306			−0.535180
$990$	3.41580	+	0.327520i	0.108561	+	0.0104093i
$991$		−	25.8741i		−	0.821917i	−0.911654	−	0.410959i	$-0.865194\pi$
$991$		−	25.8741i		−	0.821917i	0.911654	−	0.410959i	$-0.134806\pi$
$992$	10.4676	−	24.2299i	0.332347	−	0.769299i
$993$	0.607461	−	3.66858i	0.0192772	−	0.116419i
$994$	−2.67389	+	0.633412i	−0.0848107	+	0.0200906i
$995$	22.0667	−	12.7402i	0.699562	−	0.403892i
$996$	3.57009	−	15.7801i	0.113122	−	0.500011i
$997$	−9.32829	−	5.38569i	−0.295430	−	0.170566i	0.344958	−	0.938618i	$-0.387893\pi$
$997$	−9.32829	−	5.38569i	−0.295430	−	0.170566i	−0.640388	+	0.768052i	$0.721226\pi$
$998$	13.4548	+	4.02972i	0.425904	+	0.127559i
$999$	33.4493	+	17.9399i	1.05829	+	0.567592i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bm.b.11.20	yes	48
3.2	odd	2		1080.2.bm.a.251.5		48
4.3	odd	2		1440.2.cc.b.911.3		48
8.3	odd	2		360.2.bm.a.11.11	✓	48
8.5	even	2		1440.2.cc.a.911.3		48
9.4	even	3		1080.2.bm.b.611.14		48
9.5	odd	6		360.2.bm.a.131.11	yes	48
12.11	even	2		4320.2.cc.a.1871.12		48
24.5	odd	2		4320.2.cc.b.1871.13		48
24.11	even	2		1080.2.bm.b.251.14		48
36.23	even	6		1440.2.cc.a.1391.3		48
36.31	odd	6		4320.2.cc.b.3311.13		48
72.5	odd	6		1440.2.cc.b.1391.3		48
72.13	even	6		4320.2.cc.a.3311.12		48
72.59	even	6	inner	360.2.bm.b.131.20	yes	48
72.67	odd	6		1080.2.bm.a.611.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bm.a.11.11	✓	48	8.3	odd	2
360.2.bm.a.131.11	yes	48	9.5	odd	6
360.2.bm.b.11.20	yes	48	1.1	even	1	trivial
360.2.bm.b.131.20	yes	48	72.59	even	6	inner
1080.2.bm.a.251.5		48	3.2	odd	2
1080.2.bm.a.611.5		48	72.67	odd	6
1080.2.bm.b.251.14		48	24.11	even	2
1080.2.bm.b.611.14		48	9.4	even	3
1440.2.cc.a.911.3		48	8.5	even	2
1440.2.cc.a.1391.3		48	36.23	even	6
1440.2.cc.b.911.3		48	4.3	odd	2
1440.2.cc.b.1391.3		48	72.5	odd	6
4320.2.cc.a.1871.12		48	12.11	even	2
4320.2.cc.a.3311.12		48	72.13	even	6
4320.2.cc.b.1871.13		48	24.5	odd	2
4320.2.cc.b.3311.13		48	36.31	odd	6

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.02877 - 0.970379i) q^{2} +(1.62132 - 0.609351i) q^{3} +(0.116731 - 1.99659i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.07667 - 2.20018i) q^{6} +(-0.518944 - 0.299612i) q^{7} +(-1.81736 - 2.16730i) q^{8} +(2.25738 - 1.97591i) q^{9} +O(q^{10})\)	\(q+(1.02877 - 0.970379i) q^{2} +(1.62132 - 0.609351i) q^{3} +(0.116731 - 1.99659i) q^{4} +(0.500000 + 0.866025i) q^{5} +(1.07667 - 2.20018i) q^{6} +(-0.518944 - 0.299612i) q^{7} +(-1.81736 - 2.16730i) q^{8} +(2.25738 - 1.97591i) q^{9} +(1.35476 + 0.405751i) q^{10} +(0.700444 + 0.404402i) q^{11} +(-1.02737 - 3.30825i) q^{12} +(-3.52330 + 2.03418i) q^{13} +(-0.824611 + 0.195340i) q^{14} +(1.33838 + 1.09943i) q^{15} +(-3.97275 - 0.466128i) q^{16} +1.87026i q^{17} +(0.404943 - 4.22327i) q^{18} +3.32144 q^{19} +(1.78746 - 0.897203i) q^{20} +(-1.02395 - 0.169550i) q^{21} +(1.11302 - 0.263660i) q^{22} +(1.00356 + 1.73822i) q^{23} +(-4.26718 - 2.40649i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.65074 + 5.51163i) q^{26} +(2.45592 - 4.57913i) q^{27} +(-0.658780 + 1.00114i) q^{28} +(1.38869 - 2.40528i) q^{29} +(2.44374 - 0.167669i) q^{30} +(-4.04078 + 2.33294i) q^{31} +(-4.53936 + 3.37553i) q^{32} +(1.38207 + 0.228850i) q^{33} +(1.81486 + 1.92406i) q^{34} -0.599225i q^{35} +(-3.68158 - 4.73772i) q^{36} +7.30473i q^{37} +(3.41700 - 3.22306i) q^{38} +(-4.47288 + 5.44499i) q^{39} +(0.968260 - 2.65753i) q^{40} +(-7.32564 + 4.22946i) q^{41} +(-1.21793 + 0.819187i) q^{42} +(-4.19270 + 7.26197i) q^{43} +(0.889188 - 1.35129i) q^{44} +(2.83988 + 0.966995i) q^{45} +(2.71917 + 0.814392i) q^{46} +(6.76075 - 11.7100i) q^{47} +(-6.72515 + 1.66505i) q^{48} +(-3.32046 - 5.75121i) q^{49} +(0.325988 + 1.37613i) q^{50} +(1.13964 + 3.03229i) q^{51} +(3.65014 + 7.27204i) q^{52} +5.27329 q^{53} +(-1.91691 - 7.09404i) q^{54} +0.808804i q^{55} +(0.293757 + 1.66921i) q^{56} +(5.38514 - 2.02393i) q^{57} +(-0.905391 - 3.82203i) q^{58} +(6.41997 - 3.70657i) q^{59} +(2.35135 - 2.54385i) q^{60} +(-4.38245 - 2.53021i) q^{61} +(-1.89319 + 6.32115i) q^{62} +(-1.76346 + 0.349047i) q^{63} +(-1.39441 + 7.87754i) q^{64} +(-3.52330 - 2.03418i) q^{65} +(1.64390 - 1.10570i) q^{66} +(6.68152 + 11.5727i) q^{67} +(3.73414 + 0.218317i) q^{68} +(2.68629 + 2.20670i) q^{69} +(-0.581475 - 0.616464i) q^{70} +3.24261 q^{71} +(-8.38487 - 1.30149i) q^{72} -16.0211 q^{73} +(7.08835 + 7.51488i) q^{74} +(-0.282948 + 1.70878i) q^{75} +(0.387715 - 6.63157i) q^{76} +(-0.242328 - 0.419724i) q^{77} +(0.682138 + 9.94202i) q^{78} +(3.85168 + 2.22377i) q^{79} +(-1.58270 - 3.67356i) q^{80} +(1.19155 - 8.92077i) q^{81} +(-3.43221 + 11.4598i) q^{82} +(4.04472 + 2.33522i) q^{83} +(-0.458047 + 2.02461i) q^{84} +(-1.61969 + 0.935129i) q^{85} +(2.73354 + 11.5394i) q^{86} +(0.785854 - 4.74593i) q^{87} +(-0.396498 - 2.25302i) q^{88} -9.41789i q^{89} +(3.85993 - 1.76094i) q^{90} +2.43786 q^{91} +(3.58766 - 1.80080i) q^{92} +(-5.12983 + 6.24471i) q^{93} +(-4.40785 - 18.6073i) q^{94} +(1.66072 + 2.87646i) q^{95} +(-5.30289 + 8.23889i) q^{96} +(1.95567 - 3.38732i) q^{97} +(-8.99685 - 2.69456i) q^{98} +(2.38023 - 0.471126i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{5} - q^{6} + 6 q^{8}+O(q^{10}) \) 48 * q + 24 * q^5 - q^6 + 6 * q^8	\( 48 q + 24 q^{5} - q^{6} + 6 q^{8} + 13 q^{12} + 15 q^{14} - 12 q^{16} + 7 q^{18} + 4 q^{21} - 21 q^{22} - 4 q^{24} - 24 q^{25} + 12 q^{27} - 2 q^{30} - 8 q^{33} - 27 q^{34} - 31 q^{36} - 27 q^{38} - 16 q^{39} + 12 q^{40} + 12 q^{41} - 9 q^{42} + 24 q^{44} - 6 q^{46} - 12 q^{47} + 7 q^{48} + 24 q^{49} - 20 q^{51} + 54 q^{52} - 32 q^{54} + 21 q^{56} + 4 q^{57} + 33 q^{58} - 36 q^{59} - q^{60} - 12 q^{61} - 42 q^{62} - 56 q^{63} - 12 q^{64} - 32 q^{66} + 51 q^{68} + 40 q^{69} + 15 q^{70} + 6 q^{72} + 54 q^{74} - 51 q^{76} - 24 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} + 41 q^{84} + 27 q^{86} - 36 q^{87} - 57 q^{88} - 22 q^{90} - 9 q^{92} - 75 q^{94} + 13 q^{96} - 42 q^{98} - 16 q^{99}+O(q^{100}) \) 48 * q + 24 * q^5 - q^6 + 6 * q^8 + 13 * q^12 + 15 * q^14 - 12 * q^16 + 7 * q^18 + 4 * q^21 - 21 * q^22 - 4 * q^24 - 24 * q^25 + 12 * q^27 - 2 * q^30 - 8 * q^33 - 27 * q^34 - 31 * q^36 - 27 * q^38 - 16 * q^39 + 12 * q^40 + 12 * q^41 - 9 * q^42 + 24 * q^44 - 6 * q^46 - 12 * q^47 + 7 * q^48 + 24 * q^49 - 20 * q^51 + 54 * q^52 - 32 * q^54 + 21 * q^56 + 4 * q^57 + 33 * q^58 - 36 * q^59 - q^60 - 12 * q^61 - 42 * q^62 - 56 * q^63 - 12 * q^64 - 32 * q^66 + 51 * q^68 + 40 * q^69 + 15 * q^70 + 6 * q^72 + 54 * q^74 - 51 * q^76 - 24 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 + 41 * q^84 + 27 * q^86 - 36 * q^87 - 57 * q^88 - 22 * q^90 - 9 * q^92 - 75 * q^94 + 13 * q^96 - 42 * q^98 - 16 * q^99

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