LMFDB - Embedded newform 585.2.bt.b.376.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(376,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 3]))

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

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

chi := DirichletCharacter("585.376");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bt (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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			376.20
Character	$\chi$	$=$	585.376
Dual form			585.2.bt.b.571.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.774258 - 0.447018i) q^{2} +(-0.513274 - 1.65425i) q^{3} +(-0.600350 - 1.03984i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.342074 + 1.51026i) q^{6} +(1.76954 + 1.02164i) q^{7} +2.86154i q^{8} +(-2.47310 + 1.69817i) q^{9} +O(q^{10})$	\(q+(-0.774258 - 0.447018i) q^{2} +(-0.513274 - 1.65425i) q^{3} +(-0.600350 - 1.03984i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.342074 + 1.51026i) q^{6} +(1.76954 + 1.02164i) q^{7} +2.86154i q^{8} +(-2.47310 + 1.69817i) q^{9} +0.894036 q^{10} +(0.659790 + 0.380930i) q^{11} +(-1.41201 + 1.52685i) q^{12} +(1.34463 + 3.34544i) q^{13} +(-0.913387 - 1.58203i) q^{14} +(1.27163 + 1.17599i) q^{15} +(0.0784618 - 0.135900i) q^{16} -2.67783 q^{17} +(2.67393 - 0.209302i) q^{18} +7.38079i q^{19} +(1.03984 + 0.600350i) q^{20} +(0.781798 - 3.45165i) q^{21} +(-0.340565 - 0.589876i) q^{22} +(-1.72917 - 2.99502i) q^{23} +(4.73371 - 1.46876i) q^{24} +(0.500000 - 0.866025i) q^{25} +(0.454381 - 3.19131i) q^{26} +(4.07858 + 3.21950i) q^{27} -2.45338i q^{28} +(-4.28619 + 7.42389i) q^{29} +(-0.458886 - 1.47896i) q^{30} +(7.28497 - 4.20598i) q^{31} +(4.83484 - 2.79139i) q^{32} +(0.291501 - 1.28698i) q^{33} +(2.07333 + 1.19704i) q^{34} -2.04329 q^{35} +(3.25054 + 1.55212i) q^{36} +3.24522i q^{37} +(3.29935 - 5.71463i) q^{38} +(4.84404 - 3.94149i) q^{39} +(-1.43077 - 2.47817i) q^{40} +(-5.25284 + 3.03273i) q^{41} +(-2.14826 + 2.32299i) q^{42} +(5.42269 - 9.39238i) q^{43} -0.914765i q^{44} +(1.29268 - 2.70721i) q^{45} +3.09189i q^{46} +(0.719689 + 0.415513i) q^{47} +(-0.265085 - 0.0600417i) q^{48} +(-1.41248 - 2.44650i) q^{49} +(-0.774258 + 0.447018i) q^{50} +(1.37446 + 4.42981i) q^{51} +(2.67146 - 3.40663i) q^{52} +12.9596 q^{53} +(-1.71870 - 4.31592i) q^{54} -0.761860 q^{55} +(-2.92348 + 5.06361i) q^{56} +(12.2097 - 3.78837i) q^{57} +(6.63723 - 3.83201i) q^{58} +(-8.57721 + 4.95206i) q^{59} +(0.459408 - 2.02829i) q^{60} +(1.11958 - 1.93918i) q^{61} -7.52059 q^{62} +(-6.11117 + 0.478351i) q^{63} -5.30506 q^{64} +(-2.83720 - 2.22492i) q^{65} +(-0.801001 + 0.866149i) q^{66} +(-0.874153 + 0.504693i) q^{67} +(1.60764 + 2.78451i) q^{68} +(-4.06697 + 4.39775i) q^{69} +(1.58203 + 0.913387i) q^{70} +16.2829i q^{71} +(-4.85938 - 7.07688i) q^{72} +8.99447i q^{73} +(1.45067 - 2.51264i) q^{74} +(-1.68926 - 0.382617i) q^{75} +(7.67481 - 4.43105i) q^{76} +(0.778350 + 1.34814i) q^{77} +(-5.51245 + 0.886356i) q^{78} +(-7.11738 + 12.3277i) q^{79} +0.156924i q^{80} +(3.23244 - 8.39948i) q^{81} +5.42274 q^{82} +(-7.52521 - 4.34468i) q^{83} +(-4.05850 + 1.25925i) q^{84} +(2.31907 - 1.33892i) q^{85} +(-8.39713 + 4.84808i) q^{86} +(14.4810 + 3.27994i) q^{87} +(-1.09005 + 1.88802i) q^{88} -6.84329i q^{89} +(-2.21104 + 1.51823i) q^{90} +(-1.03847 + 7.29363i) q^{91} +(-2.07622 + 3.59611i) q^{92} +(-10.6969 - 9.89235i) q^{93} +(-0.371484 - 0.643428i) q^{94} +(-3.69039 - 6.39195i) q^{95} +(-7.09926 - 6.56529i) q^{96} +(0.0788540 + 0.0455264i) q^{97} +2.52563i q^{98} +(-2.27861 + 0.178358i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	$ 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) $ 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.774258	−	0.447018i	−0.547483	−	0.316090i	0.200623	−	0.979669i	$-0.435703\pi$
$2$	−0.774258	−	0.447018i	−0.547483	−	0.316090i	−0.748106	+	0.663579i	$0.769037\pi$
$3$	−0.513274	−	1.65425i	−0.296339	−	0.955083i
$3$	−0.513274	−	1.65425i	−0.296339	−	0.955083i
$4$	−0.600350	−	1.03984i	−0.300175	−	0.519918i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$	−0.342074	+	1.51026i	−0.139651	+	0.616561i
$7$	1.76954	+	1.02164i	0.668823	+	0.386145i	0.795631	−	0.605782i	$-0.207140\pi$
$7$	1.76954	+	1.02164i	0.668823	+	0.386145i	−0.126807	+	0.991927i	$0.540473\pi$
$8$			2.86154i			1.01171i
$9$	−2.47310	+	1.69817i	−0.824366	+	0.566057i
$10$	0.894036			0.282719
$11$	0.659790	+	0.380930i	0.198934	+	0.114855i	0.596158	−	0.802867i	$-0.296693\pi$
$11$	0.659790	+	0.380930i	0.198934	+	0.114855i	−0.397224	+	0.917722i	$0.630026\pi$
$12$	−1.41201	+	1.52685i	−0.407611	+	0.440764i
$13$	1.34463	+	3.34544i	0.372934	+	0.927858i
$13$	1.34463	+	3.34544i	0.372934	+	0.927858i
$14$	−0.913387	−	1.58203i	−0.244113	−	0.422816i
$15$	1.27163	+	1.17599i	0.328335	+	0.303639i
$16$	0.0784618	−	0.135900i	0.0196155	−	0.0339750i
$17$	−2.67783			−0.649470			−0.324735	−	0.945805i	$-0.605275\pi$
$17$	−2.67783			−0.649470			−0.324735	+	0.945805i	$0.605275\pi$
$18$	2.67393	−	0.209302i	0.630251	−	0.0493328i
$19$			7.38079i			1.69327i	0.532175	+	0.846634i	$0.321375\pi$
$19$			7.38079i			1.69327i	−0.532175	+	0.846634i	$0.678625\pi$
$20$	1.03984	+	0.600350i	0.232514	+	0.134242i
$21$	0.781798	−	3.45165i	0.170602	−	0.753212i
$22$	−0.340565	−	0.589876i	−0.0726088	−	0.125762i
$23$	−1.72917	−	2.99502i	−0.360558	−	0.624504i	0.627495	−	0.778620i	$-0.284080\pi$
$23$	−1.72917	−	2.99502i	−0.360558	−	0.624504i	−0.988053	+	0.154116i	$0.950747\pi$
$24$	4.73371	−	1.46876i	0.966265	−	0.299808i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	0.454381	−	3.19131i	0.0891114	−	0.625867i
$27$	4.07858	+	3.21950i	0.784923	+	0.619594i
$28$		−	2.45338i		−	0.463644i
$29$	−4.28619	+	7.42389i	−0.795925	+	1.37858i	0.126326	+	0.991989i	$0.459682\pi$
$29$	−4.28619	+	7.42389i	−0.795925	+	1.37858i	−0.922250	+	0.386593i	$0.873652\pi$
$30$	−0.458886	−	1.47896i	−0.0837807	−	0.270020i
$31$	7.28497	−	4.20598i	1.30842	−	0.755416i	0.326586	−	0.945167i	$-0.394102\pi$
$31$	7.28497	−	4.20598i	1.30842	−	0.755416i	0.981832	+	0.189751i	$0.0607682\pi$
$32$	4.83484	−	2.79139i	0.854686	−	0.493453i
$33$	0.291501	−	1.28698i	0.0507438	−	0.224035i
$34$	2.07333	+	1.19704i	0.355574	+	0.205291i
$35$	−2.04329			−0.345379
$36$	3.25054	+	1.55212i	0.541757	+	0.258687i
$37$			3.24522i			0.533511i	0.963764	+	0.266756i	$0.0859517\pi$
$37$			3.24522i			0.533511i	−0.963764	+	0.266756i	$0.914048\pi$
$38$	3.29935	−	5.71463i	0.535224	−	0.927036i
$39$	4.84404	−	3.94149i	0.775666	−	0.631143i
$40$	−1.43077	−	2.47817i	−0.226225	−	0.391833i
$41$	−5.25284	+	3.03273i	−0.820356	+	0.473633i	−0.850539	−	0.525911i	$-0.823724\pi$
$41$	−5.25284	+	3.03273i	−0.820356	+	0.473633i	0.0301829	+	0.999544i	$0.490391\pi$
$42$	−2.14826	+	2.32299i	−0.331484	+	0.358445i
$43$	5.42269	−	9.39238i	0.826953	−	1.43232i	−0.0734653	−	0.997298i	$-0.523406\pi$
$43$	5.42269	−	9.39238i	0.826953	−	1.43232i	0.900418	−	0.435026i	$-0.143261\pi$
$44$		−	0.914765i		−	0.137906i
$45$	1.29268	−	2.70721i	0.192702	−	0.403567i
$46$			3.09189i			0.455874i
$47$	0.719689	+	0.415513i	0.104977	+	0.0606088i	0.551570	−	0.834129i	$-0.314029\pi$
$47$	0.719689	+	0.415513i	0.104977	+	0.0606088i	−0.446592	+	0.894738i	$0.647362\pi$
$48$	−0.265085	−	0.0600417i	−0.0382617	−	0.00866628i
$49$	−1.41248	−	2.44650i	−0.201784	−	0.349499i
$50$	−0.774258	+	0.447018i	−0.109497	+	0.0632179i
$51$	1.37446	+	4.42981i	0.192463	+	0.620297i
$52$	2.67146	−	3.40663i	0.370465	−	0.472414i
$53$	12.9596			1.78014			0.890072	−	0.455819i	$-0.150654\pi$
$53$	12.9596			1.78014			0.890072	+	0.455819i	$0.150654\pi$
$54$	−1.71870	−	4.31592i	−0.233885	−	0.587323i
$55$	−0.761860			−0.102729
$56$	−2.92348	+	5.06361i	−0.390666	+	0.676654i
$57$	12.2097	−	3.78837i	1.61721	−	0.501781i
$58$	6.63723	−	3.83201i	0.871511	−	0.503167i
$59$	−8.57721	+	4.95206i	−1.11666	+	0.644703i	−0.940546	−	0.339667i	$-0.889686\pi$
$59$	−8.57721	+	4.95206i	−1.11666	+	0.644703i	−0.176112	+	0.984370i	$0.556352\pi$
$60$	0.459408	−	2.02829i	0.0593094	−	0.261852i
$61$	1.11958	−	1.93918i	0.143348	−	0.248286i	−0.785407	−	0.618979i	$-0.787546\pi$
$61$	1.11958	−	1.93918i	0.143348	−	0.248286i	0.928755	+	0.370693i	$0.120880\pi$
$62$	−7.52059			−0.955116
$63$	−6.11117	+	0.478351i	−0.769936	+	0.0602666i
$64$	−5.30506			−0.663133
$65$	−2.83720	−	2.22492i	−0.351912	−	0.275967i
$66$	−0.801001	+	0.866149i	−0.0985964	+	0.106616i
$67$	−0.874153	+	0.504693i	−0.106795	+	0.0616580i	−0.552446	−	0.833549i	$-0.686305\pi$
$67$	−0.874153	+	0.504693i	−0.106795	+	0.0616580i	0.445651	+	0.895207i	$0.352972\pi$
$68$	1.60764	+	2.78451i	0.194954	+	0.337671i
$69$	−4.06697	+	4.39775i	−0.489606	+	0.529427i
$70$	1.58203	+	0.913387i	0.189089	+	0.109171i
$71$			16.2829i			1.93242i	0.257747	+	0.966212i	$0.417020\pi$
$71$			16.2829i			1.93242i	−0.257747	+	0.966212i	$0.582980\pi$
$72$	−4.85938	−	7.07688i	−0.572684	−	0.834018i
$73$			8.99447i			1.05272i	0.850261	+	0.526362i	$0.176444\pi$
$73$			8.99447i			1.05272i	−0.850261	+	0.526362i	$0.823556\pi$
$74$	1.45067	−	2.51264i	0.168637	−	0.292089i
$75$	−1.68926	−	0.382617i	−0.195059	−	0.0441809i
$76$	7.67481	−	4.43105i	0.880361	−	0.508276i
$77$	0.778350	+	1.34814i	0.0887012	+	0.153635i
$78$	−5.51245	+	0.886356i	−0.624162	+	0.100360i
$79$	−7.11738	+	12.3277i	−0.800768	+	1.38697i	0.118343	+	0.992973i	$0.462242\pi$
$79$	−7.11738	+	12.3277i	−0.800768	+	1.38697i	−0.919111	+	0.393998i	$0.871092\pi$
$80$			0.156924i			0.0175446i
$81$	3.23244	−	8.39948i	0.359160	−	0.933276i
$82$	5.42274			0.598842
$83$	−7.52521	−	4.34468i	−0.826000	−	0.476891i	0.0264814	−	0.999649i	$-0.491570\pi$
$83$	−7.52521	−	4.34468i	−0.826000	−	0.476891i	−0.852481	+	0.522758i	$0.824903\pi$
$84$	−4.05850	+	1.25925i	−0.442819	+	0.137396i
$85$	2.31907	−	1.33892i	0.251539	−	0.145226i
$86$	−8.39713	+	4.84808i	−0.905485	+	0.522782i
$87$	14.4810	+	3.27994i	1.55252	+	0.351646i
$88$	−1.09005	+	1.88802i	−0.116199	+	0.201263i
$89$		−	6.84329i		−	0.725387i	−0.931909	−	0.362693i	$-0.881857\pi$
$89$		−	6.84329i		−	0.725387i	0.931909	−	0.362693i	$-0.118143\pi$
$90$	−2.21104	+	1.51823i	−0.233064	+	0.160035i
$91$	−1.03847	+	7.29363i	−0.108861	+	0.764580i
$92$	−2.07622	+	3.59611i	−0.216461	+	0.374921i
$93$	−10.6969	−	9.89235i	−1.10922	−	1.02579i
$94$	−0.371484	−	0.643428i	−0.0383156	−	0.0663646i
$95$	−3.69039	−	6.39195i	−0.378626	−	0.655800i
$96$	−7.09926	−	6.56529i	−0.724566	−	0.670067i
$97$	0.0788540	+	0.0455264i	0.00800641	+	0.00462250i	0.503998	−	0.863705i	$-0.331862\pi$
$97$	0.0788540	+	0.0455264i	0.00800641	+	0.00462250i	−0.495991	+	0.868327i	$0.665195\pi$
$98$			2.52563i			0.255127i
$99$	−2.27861	+	0.178358i	−0.229009	+	0.0179256i
$100$	−1.20070			−0.120070
$101$	−1.01982	+	1.76639i	−0.101476	+	0.175762i	−0.912293	−	0.409538i	$-0.865690\pi$
$101$	−1.01982	+	1.76639i	−0.101476	+	0.175762i	0.810817	+	0.585300i	$0.199023\pi$
$102$	0.916017	−	4.04423i	0.0906992	−	0.400438i
$103$	3.80915	+	6.59765i	0.375327	+	0.650085i	0.990376	−	0.138404i	$-0.0441971\pi$
$103$	3.80915	+	6.59765i	0.375327	+	0.650085i	−0.615049	+	0.788489i	$0.710864\pi$
$104$	−9.57311	+	3.84772i	−0.938721	+	0.377300i
$105$	1.04877	+	3.38012i	0.102349	+	0.329865i
$106$	−10.0341	−	5.79320i	−0.974599	−	0.562685i
$107$	5.46465			0.528288			0.264144	−	0.964483i	$-0.414911\pi$
$107$	5.46465			0.528288			0.264144	+	0.964483i	$0.414911\pi$
$108$	0.899182	−	6.17388i	0.0865238	−	0.594082i
$109$			14.0618i			1.34688i	0.739244	+	0.673438i	$0.235183\pi$
$109$			14.0618i			1.34688i	−0.739244	+	0.673438i	$0.764817\pi$
$110$	0.589876	+	0.340565i	0.0562425	+	0.0324716i
$111$	5.36842	−	1.66569i	0.509548	−	0.158100i
$112$	0.277683	−	0.160320i	0.0262385	−	0.0151488i
$113$	1.56049	+	2.70286i	0.146799	+	0.254263i	0.930043	−	0.367451i	$-0.119770\pi$
$113$	1.56049	+	2.70286i	0.146799	+	0.254263i	−0.783244	+	0.621715i	$0.786436\pi$
$114$	−11.1469	−	2.52477i	−1.04400	−	0.236467i
$115$	2.99502	+	1.72917i	0.279287	+	0.161246i
$116$	10.2928			0.955666
$117$	−9.00653	−	5.99019i	−0.832654	−	0.553793i
$118$	8.85464			0.815135
$119$	−4.73853	−	2.73579i	−0.434381	−	0.250790i
$120$	−3.36514	+	3.63883i	−0.307193	+	0.332179i
$121$	−5.20978	−	9.02361i	−0.473617	−	0.820328i
$122$	−1.73369	+	1.00095i	−0.156961	+	0.0906217i
$123$	7.71305	+	7.13291i	0.695462	+	0.643152i
$124$	−8.74705	−	5.05011i	−0.785509	−	0.453514i
$125$			1.00000i			0.0894427i
$126$	4.94546	+	2.36144i	0.440576	+	0.210374i
$127$	11.1041			0.985327			0.492664	−	0.870220i	$-0.336023\pi$
$127$	11.1041			0.985327			0.492664	+	0.870220i	$0.336023\pi$
$128$	−5.56218	−	3.21133i	−0.491632	−	0.283844i
$129$	−18.3207	−	4.14963i	−1.61305	−	0.365355i
$130$	1.20215	+	2.99094i	0.105435	+	0.262323i
$131$	4.01774	+	6.95893i	0.351032	+	0.608005i	0.986431	−	0.164179i	$-0.0524976\pi$
$131$	4.01774	+	6.95893i	0.351032	+	0.608005i	−0.635399	+	0.772184i	$0.719164\pi$
$132$	−1.51325	+	0.469525i	−0.131712	+	0.0408669i
$133$	−7.54054	+	13.0606i	−0.653848	+	1.13250i
$134$	0.902427			0.0779578
$135$	−5.14190	−	0.748882i	−0.442545	−	0.0644535i
$136$		−	7.66273i		−	0.657073i
$137$	−7.61873	−	4.39868i	−0.650912	−	0.375804i	0.137894	−	0.990447i	$-0.455967\pi$
$137$	−7.61873	−	4.39868i	−0.650912	−	0.375804i	−0.788806	+	0.614643i	$0.789300\pi$
$138$	5.11476	−	1.58699i	0.435397	−	0.135093i
$139$	2.22094	+	3.84679i	0.188378	+	0.326280i	0.944710	−	0.327908i	$-0.106344\pi$
$139$	2.22094	+	3.84679i	0.188378	+	0.326280i	−0.756332	+	0.654188i	$0.773010\pi$
$140$	1.22669	+	2.12469i	0.103674	+	0.179569i
$141$	0.317965	−	1.40382i	0.0267775	−	0.118223i
$142$	7.27875	−	12.6072i	0.610819	−	1.05797i
$143$	−0.387204	+	2.71950i	−0.0323796	+	0.227416i
$144$	0.0367372	+	0.469335i	0.00306143	+	0.0391113i
$145$		−	8.57237i		−	0.711897i
$146$	4.02069	−	6.96404i	0.332755	−	0.576348i
$147$	−3.32213	+	3.59233i	−0.274004	+	0.296290i
$148$	3.37450	−	1.94827i	0.277382	−	0.160147i
$149$	8.46516	−	4.88736i	0.693493	−	0.400388i	−0.111426	−	0.993773i	$-0.535542\pi$
$149$	8.46516	−	4.88736i	0.693493	−	0.400388i	0.804919	+	0.593384i	$0.202209\pi$
$150$	1.13689	+	1.05138i	0.0928265	+	0.0858444i
$151$	7.11997	+	4.11072i	0.579415	+	0.334525i	0.760901	−	0.648868i	$-0.224757\pi$
$151$	7.11997	+	4.11072i	0.579415	+	0.334525i	−0.181486	+	0.983394i	$0.558091\pi$
$152$	−21.1204			−1.71309
$153$	6.62254	−	4.54741i	0.535401	−	0.367637i
$154$		−	1.39175i		−	0.112150i
$155$	−4.20598	+	7.28497i	−0.337832	+	0.585143i
$156$	−7.00661	−	2.67073i	−0.560978	−	0.213830i
$157$	−7.31859	−	12.6762i	−0.584087	−	1.01167i	−0.994989	−	0.0999889i	$-0.968119\pi$
$157$	−7.31859	−	12.6762i	−0.584087	−	1.01167i	0.410901	−	0.911680i	$-0.365214\pi$
$158$	11.0214	−	6.36320i	0.876814	−	0.506229i
$159$	−6.65185	−	21.4385i	−0.527526	−	1.70019i
$160$	−2.79139	+	4.83484i	−0.220679	+	0.382227i
$161$		−	7.06640i		−	0.556911i
$162$	−6.25746	+	5.05841i	−0.491633	+	0.397426i
$163$			6.10213i			0.477956i	0.971025	+	0.238978i	$0.0768123\pi$
$163$			6.10213i			0.477956i	−0.971025	+	0.238978i	$0.923188\pi$
$164$	6.30709	+	3.64140i	0.492501	+	0.284345i
$165$	0.391043	+	1.26031i	0.0304427	+	0.0981149i
$166$	3.88431	+	6.72782i	0.301481	+	0.522180i
$167$	−10.2878	+	5.93965i	−0.796092	+	0.459624i	−0.842103	−	0.539317i	$-0.818682\pi$
$167$	−10.2878	+	5.93965i	−0.796092	+	0.459624i	0.0460109	+	0.998941i	$0.485349\pi$
$168$	9.87704	+	2.23715i	0.762030	+	0.172600i
$169$	−9.38393	+	8.99677i	−0.721841	+	0.692059i
$170$	−2.39408			−0.183617
$171$	−12.5338	−	18.2534i	−0.958486	−	1.39587i
$172$	−13.0220			−0.992921
$173$	0.449299	−	0.778209i	0.0341596	−	0.0591661i	−0.848440	−	0.529291i	$-0.822458\pi$
$173$	0.449299	−	0.778209i	0.0341596	−	0.0591661i	0.882600	+	0.470125i	$0.155791\pi$
$174$	−9.74582	−	9.01278i	−0.738829	−	0.683257i
$175$	1.76954	−	1.02164i	0.133765	−	0.0772291i
$176$	0.103537	−	0.0597769i	0.00780437	−	0.00450585i
$177$	12.5944	+	11.6471i	0.946654	+	0.875450i
$178$	−3.05907	+	5.29847i	−0.229287	+	0.397137i
$179$	6.17152			0.461281			0.230641	−	0.973039i	$-0.425918\pi$
$179$	6.17152			0.461281			0.230641	+	0.973039i	$0.425918\pi$
$180$	−3.59111	+	0.281094i	−0.267666	+	0.0209515i
$181$	6.05973			0.450416			0.225208	−	0.974311i	$-0.427694\pi$
$181$	6.05973			0.450416			0.225208	+	0.974311i	$0.427694\pi$
$182$	4.06443	−	5.18293i	0.301275	−	0.384185i
$183$	−3.78254	−	0.856745i	−0.279614	−	0.0633324i
$184$	8.57036	−	4.94810i	0.631815	−	0.364779i
$185$	−1.62261	−	2.81045i	−0.119297	−	0.206628i
$186$	3.86013	+	12.4410i	0.283038	+	0.912215i
$187$	−1.76681	−	1.02007i	−0.129202	−	0.0745947i
$188$		−	0.997812i		−	0.0727729i
$189$	3.92802	+	9.86390i	0.285722	+	0.717493i
$190$			6.59869i			0.478719i
$191$	−5.00578	+	8.67026i	−0.362205	+	0.627358i	−0.988324	−	0.152370i	$-0.951309\pi$
$191$	−5.00578	+	8.67026i	−0.362205	+	0.627358i	0.626118	+	0.779728i	$0.284643\pi$
$192$	2.72295	+	8.77591i	0.196512	+	0.633347i
$193$	−8.99221	+	5.19166i	−0.647274	+	0.373704i	−0.787411	−	0.616428i	$-0.788579\pi$
$193$	−8.99221	+	5.19166i	−0.647274	+	0.373704i	0.140137	+	0.990132i	$0.455246\pi$
$194$	−0.0407022	−	0.0704983i	−0.00292225	−	0.00506148i
$195$	−2.22431	+	5.83545i	−0.159286	+	0.417885i
$196$	−1.69597	+	2.93750i	−0.121141	+	0.209822i
$197$		−	24.1432i		−	1.72013i	−0.510184	−	0.860065i	$-0.670423\pi$
$197$		−	24.1432i		−	1.72013i	0.510184	−	0.860065i	$-0.329577\pi$
$198$	1.84396	+	0.880485i	0.131045	+	0.0625733i
$199$	−23.8467			−1.69045			−0.845223	−	0.534414i	$-0.820532\pi$
$199$	−23.8467			−1.69045			−0.845223	+	0.534414i	$0.820532\pi$
$200$	2.47817	+	1.43077i	0.175233	+	0.101171i
$201$	1.28357	+	1.18702i	0.0905360	+	0.0837262i
$202$	1.57922	−	0.911760i	0.111113	−	0.0641512i
$203$	−15.1692	+	8.75792i	−1.06467	+	0.614685i
$204$	3.78112	−	4.08865i	0.264731	−	0.286263i
$205$	3.03273	−	5.25284i	0.211815	−	0.366875i
$206$		−	6.81104i		−	0.474548i
$207$	9.36246	+	4.47054i	0.650736	+	0.310724i
$208$	0.560147	+	0.0797541i	0.0388392	+	0.00552995i
$209$	−2.81156	+	4.86977i	−0.194480	+	0.336849i
$210$	0.698956	−	3.08590i	0.0482325	−	0.212947i
$211$	−7.95867	−	13.7848i	−0.547898	−	0.948987i	−0.998418	−	0.0562206i	$-0.982095\pi$
$211$	−7.95867	−	13.7848i	−0.547898	−	0.948987i	0.450521	−	0.892766i	$-0.351238\pi$
$212$	−7.78032	−	13.4759i	−0.534354	−	0.925529i
$213$	26.9360	−	8.35759i	1.84563	−	0.572653i
$214$	−4.23105	−	2.44280i	−0.289229	−	0.166986i
$215$			10.8454i			0.739649i
$216$	−9.21274	+	11.6710i	−0.626848	+	0.794112i
$217$	17.1881			1.16680
$218$	6.28588	−	10.8875i	0.425733	−	0.737392i
$219$	14.8791	−	4.61663i	1.00544	−	0.311963i
$220$	0.457382	+	0.792209i	0.0308367	+	0.0534107i
$221$	−3.60070	−	8.95853i	−0.242209	−	0.602616i
$222$	−4.90113	−	1.11011i	−0.328943	−	0.0745055i
$223$	−6.50913	−	3.75805i	−0.435883	−	0.251657i	0.265966	−	0.963982i	$-0.414309\pi$
$223$	−6.50913	−	3.75805i	−0.435883	−	0.251657i	−0.701850	+	0.712325i	$0.747642\pi$
$224$	11.4072			0.762179
$225$	0.234109	+	2.99085i	0.0156072	+	0.199390i
$226$		−	2.79028i		−	0.185607i
$227$	14.1115	+	8.14725i	0.936610	+	0.540752i	0.888896	−	0.458109i	$-0.151473\pi$
$227$	14.1115	+	8.14725i	0.936610	+	0.540752i	0.0477142	+	0.998861i	$0.484806\pi$
$228$	−11.2694	−	10.4217i	−0.746331	−	0.690195i
$229$	14.1418	−	8.16480i	0.934519	−	0.539545i	0.0462813	−	0.998928i	$-0.485263\pi$
$229$	14.1418	−	8.16480i	0.934519	−	0.539545i	0.888238	+	0.459383i	$0.151930\pi$
$230$	−1.54594	−	2.67765i	−0.101937	−	0.176559i
$231$	1.83066	−	1.97955i	0.120449	−	0.130245i
$232$	−21.2438	−	12.2651i	−1.39472	−	0.805243i
$233$	15.2265			0.997518			0.498759	−	0.866741i	$-0.333789\pi$
$233$	15.2265			0.997518			0.498759	+	0.866741i	$0.333789\pi$
$234$	4.29566	+	8.66404i	0.280816	+	0.566386i
$235$	−0.831026			−0.0542101
$236$	10.2987	+	5.94593i	0.670385	+	0.387047i
$237$	24.0462	+	5.44647i	1.56197	+	0.353786i
$238$	2.44590	+	4.23642i	0.158544	+	0.274606i
$239$	14.9885	−	8.65362i	0.969527	−	0.559756i	0.0704347	−	0.997516i	$-0.477561\pi$
$239$	14.9885	−	8.65362i	0.969527	−	0.559756i	0.899092	+	0.437760i	$0.144228\pi$
$240$	0.259591	−	0.0805448i	0.0167565	−	0.00519915i
$241$	15.8138	+	9.13011i	1.01866	+	0.588122i	0.913715	−	0.406357i	$-0.133201\pi$
$241$	15.8138	+	9.13011i	1.01866	+	0.588122i	0.104942	+	0.994478i	$0.466534\pi$
$242$			9.31547i			0.598821i
$243$	−15.5540	−	1.03603i	−0.997789	−	0.0664614i
$244$	−2.68857			−0.172118
$245$	2.44650	+	1.41248i	0.156301	+	0.0902403i
$246$	−2.78335	−	8.97058i	−0.177460	−	0.571944i
$247$	−24.6920	+	9.92444i	−1.57111	+	0.631477i
$248$	12.0356	+	20.8462i	0.764260	+	1.32374i
$249$	−3.32470	+	14.6786i	−0.210695	+	0.930219i
$250$	0.447018	−	0.774258i	0.0282719	−	0.0489684i
$251$	19.4511			1.22774			0.613870	−	0.789407i	$-0.289612\pi$
$251$	19.4511			1.22774			0.613870	+	0.789407i	$0.289612\pi$
$252$	4.16625	+	6.06744i	0.262449	+	0.382213i
$253$		−	2.63478i		−	0.165647i
$254$	−8.59742	−	4.96372i	−0.539450	−	0.311452i
$255$	−3.40522	−	3.14910i	−0.213243	−	0.197204i
$256$	8.17611	+	14.1614i	0.511007	+	0.885089i
$257$	4.11933	+	7.13489i	0.256957	+	0.445062i	0.965425	−	0.260680i	$-0.0839469\pi$
$257$	4.11933	+	7.13489i	0.256957	+	0.445062i	−0.708468	+	0.705743i	$0.750614\pi$
$258$	12.3300	+	11.4026i	0.767631	+	0.709893i
$259$	−3.31546	+	5.74255i	−0.206013	+	0.356825i
$260$	−0.610237	+	4.28596i	−0.0378453	+	0.265804i
$261$	−2.00687	−	25.6387i	−0.124222	−	1.58700i
$262$		−	7.18401i		−	0.443830i
$263$	−3.99000	+	6.91088i	−0.246034	+	0.426143i	−0.962422	−	0.271559i	$-0.912461\pi$
$263$	−3.99000	+	6.91088i	−0.246034	+	0.426143i	0.716388	+	0.697702i	$0.245794\pi$
$264$	3.68275	+	0.834142i	0.226657	+	0.0513379i
$265$	−11.2234	+	6.47982i	−0.689447	+	0.398052i
$266$	11.6766	−	6.74152i	0.715941	−	0.413349i
$267$	−11.3205	+	3.51248i	−0.692804	+	0.214960i
$268$	1.04959	+	0.605984i	0.0641142	+	0.0370164i
$269$	11.3069			0.689392			0.344696	−	0.938714i	$-0.387982\pi$
$269$	11.3069			0.689392			0.344696	+	0.938714i	$0.387982\pi$
$270$	3.64640	+	2.87835i	0.221913	+	0.175171i
$271$			28.7051i			1.74371i	0.489766	+	0.871854i	$0.337082\pi$
$271$			28.7051i			1.74371i	−0.489766	+	0.871854i	$0.662918\pi$
$272$	−0.210108	+	0.363917i	−0.0127396	+	0.0220657i
$273$	12.5985	−	2.02574i	0.762497	−	0.122603i
$274$	3.93258	+	6.81142i	0.237576	+	0.411493i
$275$	0.659790	−	0.380930i	0.0397868	−	0.0229709i
$276$	7.01455	+	1.58879i	0.422226	+	0.0956341i
$277$	7.16160	−	12.4043i	0.430299	−	0.745300i	−0.566600	−	0.823993i	$-0.691741\pi$
$277$	7.16160	−	12.4043i	0.430299	−	0.745300i	0.996899	+	0.0786934i	$0.0250748\pi$
$278$		−	3.97121i		−	0.238177i
$279$	−10.8740	+	22.7729i	−0.651008	+	1.36338i
$280$		−	5.84696i		−	0.349422i
$281$	−6.82424	−	3.93998i	−0.407100	−	0.235039i	0.282443	−	0.959284i	$-0.408855\pi$
$281$	−6.82424	−	3.93998i	−0.407100	−	0.235039i	−0.689543	+	0.724245i	$0.742189\pi$
$282$	−0.873720	+	0.944782i	−0.0520292	+	0.0562610i
$283$	3.67451	+	6.36444i	0.218427	+	0.378326i	0.954327	−	0.298763i	$-0.0965741\pi$
$283$	3.67451	+	6.36444i	0.218427	+	0.378326i	−0.735900	+	0.677090i	$0.763241\pi$
$284$	16.9315	−	9.77543i	1.00470	−	0.580065i
$285$	−8.67971	+	9.38566i	−0.514142	+	0.555959i
$286$	1.51546	−	1.93251i	0.0896111	−	0.114272i
$287$	−12.3935			−0.731565
$288$	−7.21677	+	15.1138i	−0.425252	+	0.890587i
$289$	−9.82921			−0.578189
$290$	−3.83201	+	6.63723i	−0.225023	+	0.389752i
$291$	0.0348384	−	0.153812i	0.00204226	−	0.00901661i
$292$	9.35277	−	5.39983i	0.547330	−	0.316001i
$293$	22.2137	−	12.8251i	1.29774	−	0.749251i	0.317727	−	0.948182i	$-0.397080\pi$
$293$	22.2137	−	12.8251i	1.29774	−	0.749251i	0.980013	+	0.198931i	$0.0637471\pi$
$294$	4.17802	−	1.29634i	0.243667	−	0.0756040i
$295$	4.95206	−	8.57721i	0.288320	−	0.499385i
$296$	−9.28634			−0.539758
$297$	1.46460	+	3.67785i	0.0849848	+	0.213410i
$298$	−8.73896			−0.506234
$299$	7.69454	−	9.81204i	0.444987	−	0.567445i
$300$	0.616288	+	1.98626i	0.0355814	+	0.114677i
$301$	19.1913	−	11.0801i	1.10617	−	0.638648i
$302$	−3.67513	−	6.36551i	−0.211480	−	0.366294i
$303$	3.44550	+	0.780406i	0.197939	+	0.0448331i
$304$	1.00305	+	0.579110i	0.0575287	+	0.0332142i
$305$			2.23917i			0.128214i
$306$	−7.16034	+	0.560474i	−0.409329	+	0.0320402i
$307$			25.0940i			1.43219i	0.698003	+	0.716095i	$0.254072\pi$
$307$			25.0940i			1.43219i	−0.698003	+	0.716095i	$0.745928\pi$
$308$	0.934564	−	1.61871i	0.0532517	−	0.0922347i
$309$	8.95903	−	9.68770i	0.509661	−	0.551114i
$310$	6.51302	−	3.76030i	0.369915	−	0.213570i
$311$	−13.6486	−	23.6400i	−0.773940	−	1.34050i	−0.935389	−	0.353622i	$-0.884950\pi$
$311$	−13.6486	−	23.6400i	−0.773940	−	1.34050i	0.161449	−	0.986881i	$-0.448383\pi$
$312$	11.2787	+	13.8614i	0.638532	+	0.784748i
$313$	−5.40471	+	9.36124i	−0.305492	+	0.529128i	−0.977371	−	0.211533i	$-0.932154\pi$
$313$	−5.40471	+	9.36124i	−0.305492	+	0.529128i	0.671878	+	0.740661i	$0.265488\pi$
$314$			13.0862i			0.738495i
$315$	5.05326	−	3.46985i	0.284719	−	0.195504i
$316$	17.0917			0.961481
$317$	−9.04480	−	5.22202i	−0.508007	−	0.293298i	0.224007	−	0.974587i	$-0.428086\pi$
$317$	−9.04480	−	5.22202i	−0.508007	−	0.293298i	−0.732014	+	0.681290i	$0.761419\pi$
$318$	−4.43316	+	19.5725i	−0.248599	+	1.09757i
$319$	−5.65597	+	3.26547i	−0.316673	+	0.182831i
$320$	4.59432	−	2.65253i	0.256830	−	0.148281i
$321$	−2.80486	−	9.03991i	−0.156552	−	0.504558i
$322$	−3.15881	+	5.47122i	−0.176034	+	0.304899i
$323$		−	19.7645i		−	1.09973i
$324$	−10.6747	+	1.68142i	−0.593038	+	0.0934122i
$325$	3.56955	+	0.508235i	0.198003	+	0.0281918i
$326$	2.72776	−	4.72462i	0.151077	−	0.261673i
$327$	23.2617	−	7.21755i	1.28638	−	0.399132i
$328$	−8.67829	−	15.0312i	−0.479178	−	0.829961i
$329$	0.849013	+	1.47053i	0.0468076	+	0.0810731i
$330$	0.260612	−	1.15061i	0.0143462	−	0.0633389i
$331$	−27.1815	−	15.6933i	−1.49403	−	0.862580i	−0.494056	−	0.869430i	$-0.664486\pi$
$331$	−27.1815	−	15.6933i	−1.49403	−	0.862580i	−0.999977	+	0.00684950i	$0.997820\pi$
$332$			10.4333i			0.572603i
$333$	−5.51094	−	8.02576i	−0.301998	−	0.439809i
$334$	10.6205			0.581129
$335$	0.504693	−	0.874153i	0.0275743	−	0.0477601i
$336$	−0.407737	−	0.377069i	−0.0222439	−	0.0205708i
$337$	11.6138	+	20.1156i	0.632642	+	1.09577i	0.987010	+	0.160662i	$0.0513628\pi$
$337$	11.6138	+	20.1156i	0.632642	+	1.09577i	−0.354368	+	0.935106i	$0.615304\pi$
$338$	11.2873	−	2.77103i	0.613948	−	0.150724i
$339$	3.67024	−	3.96876i	0.199340	−	0.215553i
$340$	−2.78451	−	1.60764i	−0.151011	−	0.0871863i
$341$	6.40873			0.347052
$342$	1.54481	+	19.7357i	0.0835337	+	1.06718i
$343$		−	20.0753i		−	1.08396i
$344$	26.8767	+	15.5173i	1.44909	+	0.836634i
$345$	1.32322	−	5.84205i	0.0712400	−	0.314525i
$346$	−0.695747	+	0.401690i	−0.0374036	+	0.0215950i
$347$	2.21933	+	3.84399i	0.119140	+	0.206356i	0.919427	−	0.393261i	$-0.128653\pi$
$347$	2.21933	+	3.84399i	0.119140	+	0.206356i	−0.800287	+	0.599617i	$0.795320\pi$
$348$	−5.28305	−	17.0269i	−0.283201	−	0.912740i
$349$	−10.4728	−	6.04646i	−0.560595	−	0.323660i	0.192789	−	0.981240i	$-0.438247\pi$
$349$	−10.4728	−	6.04646i	−0.560595	−	0.323660i	−0.753384	+	0.657580i	$0.771580\pi$
$350$	−1.82677			−0.0976452
$351$	−5.28647	+	17.9737i	−0.282171	+	0.959364i
$352$	4.25330			0.226702
$353$	6.26884	+	3.61931i	0.333657	+	0.192637i	0.657463	−	0.753487i	$-0.271629\pi$
$353$	6.26884	+	3.61931i	0.333657	+	0.192637i	−0.323807	+	0.946123i	$0.604963\pi$
$354$	−4.54486	−	14.6478i	−0.241556	−	0.778522i
$355$	−8.14145	−	14.1014i	−0.432103	−	0.748425i
$356$	−7.11589	+	4.10836i	−0.377142	+	0.217743i
$357$	−2.09352	+	9.24294i	−0.110801	+	0.489188i
$358$	−4.77835	−	2.75878i	−0.252544	−	0.145806i
$359$			2.86049i			0.150971i	0.997147	+	0.0754855i	$0.0240507\pi$
$359$			2.86049i			0.150971i	−0.997147	+	0.0754855i	$0.975949\pi$
$360$	7.74679	+	3.69906i	0.408291	+	0.194958i
$361$	−35.4760			−1.86716
$362$	−4.69180	−	2.70881i	−0.246595	−	0.142372i
$363$	−12.2533	+	13.2499i	−0.643130	+	0.695439i
$364$	8.20762	−	3.29889i	0.430196	−	0.172909i
$365$	−4.49724	−	7.78944i	−0.235396	−	0.407718i
$366$	2.54568	+	2.35421i	0.133065	+	0.123056i
$367$	11.5600	−	20.0225i	0.603426	−	1.04516i	−0.388872	−	0.921292i	$-0.627135\pi$
$367$	11.5600	−	20.0225i	0.603426	−	1.04516i	0.992298	−	0.123873i	$-0.0395315\pi$
$368$	−0.542696			−0.0282900
$369$	7.84071	−	16.4205i	0.408171	−	0.854815i
$370$			2.90135i			0.150834i
$371$	22.9326	+	13.2402i	1.19060	+	0.687395i
$372$	−3.86452	+	17.0619i	−0.200366	+	0.884619i
$373$	−2.60932	−	4.51947i	−0.135105	−	0.234009i	0.790532	−	0.612420i	$-0.209804\pi$
$373$	−2.60932	−	4.51947i	−0.135105	−	0.234009i	−0.925638	+	0.378411i	$0.876471\pi$
$374$	0.911977	+	1.57959i	0.0471572	+	0.0816786i
$375$	1.65425	−	0.513274i	0.0854252	−	0.0265054i
$376$	−1.18901	+	2.05942i	−0.0613184	+	0.106206i
$377$	−30.5995	−	4.35678i	−1.57596	−	0.224386i
$378$	1.36804	−	9.39310i	0.0703643	−	0.483129i
$379$		−	37.6167i		−	1.93224i	−0.258091	−	0.966121i	$-0.583094\pi$
$379$		−	37.6167i		−	1.93224i	0.258091	−	0.966121i	$-0.416906\pi$
$380$	−4.43105	+	7.67481i	−0.227308	+	0.393709i
$381$	−5.69944	−	18.3689i	−0.291991	−	0.941069i
$382$	7.75153	−	4.47535i	0.396603	−	0.228979i
$383$	−22.5495	+	13.0190i	−1.15223	+	0.665238i	−0.949429	−	0.313983i	$-0.898336\pi$
$383$	−22.5495	+	13.0190i	−1.15223	+	0.665238i	−0.202797	+	0.979221i	$0.565003\pi$
$384$	−2.45742	+	10.8495i	−0.125405	+	0.553664i
$385$	−1.34814	−	0.778350i	−0.0687077	−	0.0396684i
$386$	9.28306			0.472495
$387$	2.53900	+	32.4369i	0.129064	+	1.64886i
$388$		−	0.109327i		−	0.00555023i
$389$	−1.68107	+	2.91170i	−0.0852336	+	0.147629i	−0.905491	−	0.424366i	$-0.860497\pi$
$389$	−1.68107	+	2.91170i	−0.0852336	+	0.147629i	0.820257	+	0.571995i	$0.193830\pi$
$390$	4.33074	−	3.52383i	0.219296	−	0.178436i
$391$	4.63044	+	8.02015i	0.234171	+	0.405596i
$392$	7.00075	−	4.04188i	0.353591	−	0.204146i
$393$	9.44963	−	10.2182i	0.476671	−	0.515440i
$394$	−10.7924	+	18.6931i	−0.543715	+	0.941743i
$395$		−	14.2348i		−	0.716229i
$396$	1.55343	+	2.26230i	0.0780626	+	0.113685i
$397$		−	18.3315i		−	0.920032i	−0.887911	−	0.460016i	$-0.847844\pi$
$397$		−	18.3315i		−	0.920032i	0.887911	−	0.460016i	$-0.152156\pi$
$398$	18.4635	+	10.6599i	0.925490	+	0.534332i
$399$	25.4759	+	5.77029i	1.27539	+	0.288876i
$400$	−0.0784618	−	0.135900i	−0.00392309	−	0.00679499i
$401$	−4.10994	+	2.37287i	−0.205240	+	0.118496i	−0.599098	−	0.800676i	$-0.704474\pi$
$401$	−4.10994	+	2.37287i	−0.205240	+	0.118496i	0.393857	+	0.919172i	$0.371140\pi$
$402$	−0.463192	−	1.49284i	−0.0231019	−	0.0744562i
$403$	23.8664	+	18.7159i	1.18887	+	0.932307i
$404$	2.44901			0.121843
$405$	1.40037	+	8.89039i	0.0695848	+	0.441767i
$406$	15.6598			0.777182
$407$	−1.23620	+	2.14117i	−0.0612763	+	0.106134i
$408$	−12.6761	+	3.93308i	−0.627560	+	0.194716i
$409$	−8.37823	+	4.83717i	−0.414277	+	0.239183i	−0.692626	−	0.721297i	$-0.743546\pi$
$409$	−8.37823	+	4.83717i	−0.414277	+	0.239183i	0.278349	+	0.960480i	$0.410213\pi$
$410$	−4.69623	+	2.71137i	−0.231930	+	0.133905i
$411$	−3.36602	+	14.8610i	−0.166034	+	0.733040i
$412$	4.57365	−	7.92179i	0.225327	−	0.390278i
$413$	−20.2370			−0.995796
$414$	−5.25055	−	7.64654i	−0.258050	−	0.375807i
$415$	8.68937			0.426544
$416$	15.8395	+	12.4213i	0.776596	+	0.609002i
$417$	5.22360	−	5.64846i	0.255801	−	0.276606i
$418$	4.35375	−	2.51364i	0.212949	−	0.122946i
$419$	12.3676	+	21.4214i	0.604198	+	1.04650i	0.992178	+	0.124834i	$0.0398398\pi$
$419$	12.3676	+	21.4214i	0.604198	+	1.04650i	−0.387980	+	0.921668i	$0.626827\pi$
$420$	2.88514	−	3.11980i	0.140780	−	0.152230i
$421$	−18.5018	−	10.6820i	−0.901722	−	0.520610i	−0.0239636	−	0.999713i	$-0.507629\pi$
$421$	−18.5018	−	10.6820i	−0.901722	−	0.520610i	−0.877759	+	0.479103i	$0.840962\pi$
$422$			14.2307i			0.692739i
$423$	−2.48547	+	0.194550i	−0.120848	+	0.00945935i
$424$			37.0846i			1.80099i
$425$	−1.33892	+	2.31907i	−0.0649470	+	0.112491i
$426$	−24.5914	−	5.56996i	−1.19146	−	0.269865i
$427$	3.96230	−	2.28764i	0.191749	−	0.110706i
$428$	−3.28070	−	5.68234i	−0.158579	−	0.274666i
$429$	4.69748	−	0.755316i	0.226796	−	0.0364670i
$430$	4.84808	−	8.39713i	0.233795	−	0.404945i
$431$		−	6.07723i		−	0.292730i	−0.989231	−	0.146365i	$-0.953243\pi$
$431$		−	6.07723i		−	0.292730i	0.989231	−	0.146365i	$-0.0467574\pi$
$432$	0.757543	−	0.301670i	0.0364473	−	0.0145141i
$433$	19.0428			0.915139			0.457570	−	0.889174i	$-0.348720\pi$
$433$	19.0428			0.915139			0.457570	+	0.889174i	$0.348720\pi$
$434$	−13.3080	−	7.68337i	−0.638804	−	0.368814i
$435$	−14.1809	+	4.39998i	−0.679920	+	0.210963i
$436$	14.6220	−	8.44199i	0.700265	−	0.404298i
$437$	22.1056	−	12.7627i	1.05745	−	0.610521i
$438$	−13.5840	−	3.07677i	−0.649069	−	0.147014i
$439$	1.38512	−	2.39909i	0.0661079	−	0.114502i	−0.831077	−	0.556157i	$-0.812275\pi$
$439$	1.38512	−	2.39909i	0.0661079	−	0.114502i	0.897185	+	0.441655i	$0.145608\pi$
$440$		−	2.18009i		−	0.103932i
$441$	7.64778	+	3.65179i	0.364180	+	0.173895i
$442$	−1.21675	+	8.54579i	−0.0578751	+	0.406482i
$443$	5.14670	−	8.91434i	0.244527	−	0.423533i	−0.717471	−	0.696588i	$-0.754701\pi$
$443$	5.14670	−	8.91434i	0.244527	−	0.423533i	0.961999	+	0.273055i	$0.0880340\pi$
$444$	−4.95497	−	4.58228i	−0.235152	−	0.217465i
$445$	3.42164	+	5.92646i	0.162201	+	0.280941i
$446$	3.35983	+	5.81940i	0.159093	+	0.275556i
$447$	−12.4299	−	11.4950i	−0.587913	−	0.543693i
$448$	−9.38752	−	5.41989i	−0.443519	−	0.256066i
$449$		−	23.8978i		−	1.12781i	−0.825840	−	0.563904i	$-0.809299\pi$
$449$		−	23.8978i		−	1.12781i	0.825840	−	0.563904i	$-0.190701\pi$
$450$	1.15570	−	2.42034i	0.0544804	−	0.114096i
$451$	−4.62103			−0.217596
$452$	1.87368	−	3.24532i	0.0881307	−	0.152647i
$453$	3.14567	−	13.8882i	0.147796	−	0.652522i
$454$	−7.28394	−	12.6162i	−0.341852	−	0.592106i
$455$	−2.74747	−	6.83570i	−0.128803	−	0.320463i
$456$	10.8406	+	34.9385i	0.507656	+	1.63615i
$457$	−25.2143	−	14.5575i	−1.17948	−	0.680970i	−0.223582	−	0.974685i	$-0.571775\pi$
$457$	−25.2143	−	14.5575i	−1.17948	−	0.680970i	−0.955893	+	0.293715i	$0.905108\pi$
$458$	−14.5993			−0.682178
$459$	−10.9217	−	8.62129i	−0.509784	−	0.402407i
$460$		−	4.15243i		−	0.193608i
$461$	11.5515	+	6.66926i	0.538006	+	0.310618i	0.744271	−	0.667878i	$-0.232797\pi$
$461$	11.5515	+	6.66926i	0.538006	+	0.310618i	−0.206264	+	0.978496i	$0.566131\pi$
$462$	−2.30230	+	0.714348i	−0.107113	+	0.0332345i
$463$	−9.64572	+	5.56896i	−0.448275	+	0.258811i	−0.707101	−	0.707112i	$-0.749998\pi$
$463$	−9.64572	+	5.56896i	−0.448275	+	0.258811i	0.258827	+	0.965924i	$0.416664\pi$
$464$	0.672604	+	1.16498i	0.0312248	+	0.0540830i
$465$	14.2100	+	3.21856i	0.658973	+	0.149257i
$466$	−11.7892	−	6.80650i	−0.546125	−	0.315305i
$467$	−27.5091			−1.27297			−0.636484	−	0.771290i	$-0.719612\pi$
$467$	−27.5091			−1.27297			−0.636484	+	0.771290i	$0.719612\pi$
$468$	−0.821750	+	12.9615i	−0.0379854	+	0.599147i
$469$	−2.06247			−0.0952358
$470$	0.643428	+	0.371484i	0.0296791	+	0.0171353i
$471$	−17.2131	+	18.6131i	−0.793140	+	0.857648i
$472$	−14.1705	−	24.5440i	−0.652251	−	1.12973i
$473$	7.15568	−	4.13133i	0.329018	−	0.189959i
$474$	−16.1833	−	14.9661i	−0.743325	−	0.687415i
$475$	6.39195	+	3.69039i	0.293283	+	0.169327i
$476$			6.56973i			0.301123i
$477$	−32.0505	+	22.0077i	−1.46749	+	1.00766i
$478$	−15.4733			−0.707733
$479$	−28.0875	−	16.2163i	−1.28335	−	0.740944i	−0.305892	−	0.952066i	$-0.598955\pi$
$479$	−28.0875	−	16.2163i	−1.28335	−	0.740944i	−0.977460	+	0.211122i	$0.932288\pi$
$480$	9.43079	+	2.13607i	0.430455	+	0.0974979i
$481$	−10.8567	+	4.36363i	−0.495023	+	0.198964i
$482$	−8.16265	−	14.1381i	−0.371798	−	0.643974i
$483$	−11.6896	+	3.62700i	−0.531896	+	0.165034i
$484$	−6.25538	+	10.8346i	−0.284336	+	0.492484i
$485$	−0.0910527			−0.00413449
$486$	11.5797	+	7.75507i	0.525265	+	0.351777i
$487$		−	21.3341i		−	0.966739i	−0.875417	−	0.483369i	$-0.839413\pi$
$487$		−	21.3341i		−	0.966739i	0.875417	−	0.483369i	$-0.160587\pi$
$488$	5.54904	+	3.20374i	0.251193	+	0.145026i
$489$	10.0945	−	3.13207i	0.456487	−	0.141637i
$490$	−1.26281	−	2.18726i	−0.0570481	−	0.0988101i
$491$	7.17709	+	12.4311i	0.323898	+	0.561007i	0.981289	−	0.192543i	$-0.0616733\pi$
$491$	7.17709	+	12.4311i	0.323898	+	0.561007i	−0.657391	+	0.753550i	$0.728340\pi$
$492$	2.78652	−	12.3025i	0.125626	−	0.554642i
$493$	11.4777	−	19.8799i	0.516929	−	0.895347i
$494$	23.5544	+	3.35369i	1.05976	+	0.150889i
$495$	1.88416	−	1.29377i	0.0846865	−	0.0581505i
$496$		−	1.32003i		−	0.0592713i
$497$	−16.6353	+	28.8132i	−0.746197	+	1.29245i
$498$	9.13579	−	9.87883i	0.409384	−	0.442681i
$499$	−3.28565	+	1.89697i	−0.147086	+	0.0849200i	−0.571737	−	0.820437i	$-0.693730\pi$
$499$	−3.28565	+	1.89697i	−0.147086	+	0.0849200i	0.424651	+	0.905357i	$0.360397\pi$
$500$	1.03984	−	0.600350i	0.0465029	−	0.0268484i
$501$	15.1061	+	13.9699i	0.674892	+	0.624129i
$502$	−15.0601	−	8.69498i	−0.672167	−	0.388076i
$503$	−21.6804			−0.966680			−0.483340	−	0.875433i	$-0.660577\pi$
$503$	−21.6804			−0.966680			−0.483340	+	0.875433i	$0.660577\pi$
$504$	−1.36882	−	17.4874i	−0.0609722	−	0.778950i
$505$		−	2.03965i		−	0.0907632i
$506$	−1.17779	+	2.04000i	−0.0523593	+	0.0906889i
$507$	19.6994	+	10.9056i	0.874883	+	0.484334i
$508$	−6.66633	−	11.5464i	−0.295770	−	0.512289i
$509$	13.3737	−	7.72133i	0.592781	−	0.342242i	−0.173416	−	0.984849i	$-0.555480\pi$
$509$	13.3737	−	7.72133i	0.592781	−	0.342242i	0.766196	+	0.642607i	$0.222147\pi$
$510$	1.22882	+	3.96041i	0.0544130	+	0.175370i
$511$	−9.18915	+	15.9161i	−0.406504	+	0.704086i
$512$		−	1.77416i		−	0.0784074i
$513$	−23.7625	+	30.1031i	−1.04914	+	1.32909i
$514$		−	7.36566i		−	0.324885i
$515$	−6.59765	−	3.80915i	−0.290727	−	0.167851i
$516$	6.68388	+	21.5417i	0.294241	+	0.948322i
$517$	0.316563	+	0.548302i	0.0139224	+	0.0241143i
$518$	5.13405	−	2.96415i	0.225577	−	0.130237i
$519$	−1.51797	−	0.343820i	−0.0666314	−	0.0150920i
$520$	6.36670	−	8.11878i	0.279198	−	0.356032i
$521$	−3.87730			−0.169867			−0.0849337	−	0.996387i	$-0.527068\pi$
$521$	−3.87730			−0.169867			−0.0849337	+	0.996387i	$0.527068\pi$
$522$	−9.90713	+	20.7481i	−0.433623	+	0.908118i
$523$	−11.6603			−0.509870			−0.254935	−	0.966958i	$-0.582054\pi$
$523$	−11.6603			−0.509870			−0.254935	+	0.966958i	$0.582054\pi$
$524$	4.82410	−	8.35558i	0.210742	−	0.365015i
$525$	−2.59832	−	2.40288i	−0.113400	−	0.104870i
$526$	6.17858	−	3.56720i	0.269399	−	0.155537i
$527$	−19.5079	+	11.2629i	−0.849778	+	0.490620i
$528$	−0.152029	−	0.140594i	−0.00661620	−	0.00611856i
$529$	5.51992	−	9.56078i	0.239996	−	0.415686i
$530$	11.5864			0.503281
$531$	12.8029	−	26.8125i	0.555597	−	1.16356i
$532$	18.1078			0.785074
$533$	−17.2090	−	13.4952i	−0.745403	−	0.584541i
$534$	10.3351	+	2.34091i	0.447246	+	0.101301i
$535$	−4.73253	+	2.73232i	−0.204605	+	0.118129i
$536$	−1.44420	−	2.50143i	−0.0623799	−	0.108045i
$537$	−3.16768	−	10.2093i	−0.136696	−	0.440562i
$538$	−8.75443	−	5.05437i	−0.377430	−	0.217910i
$539$		−	2.15223i		−	0.0927032i
$540$	2.30823	+	5.79633i	0.0993302	+	0.249434i
$541$		−	8.88605i		−	0.382041i	−0.981586	−	0.191021i	$-0.938820\pi$
$541$		−	8.88605i		−	0.382041i	0.981586	−	0.191021i	$-0.0611797\pi$
$542$	12.8317	−	22.2251i	0.551168	−	0.954651i
$543$	−3.11030	−	10.0243i	−0.133476	−	0.430185i
$544$	−12.9469	+	7.47488i	−0.555093	+	0.320483i
$545$	−7.03090	−	12.1779i	−0.301170	−	0.521643i
$546$	−10.6600	−	4.06332i	−0.456208	−	0.173894i
$547$	−0.352181	+	0.609996i	−0.0150582	+	0.0260815i	−0.873456	−	0.486903i	$-0.838127\pi$
$547$	−0.352181	+	0.609996i	−0.0150582	+	0.0260815i	0.858398	+	0.512984i	$0.171460\pi$
$548$			10.5630i			0.451228i
$549$	0.524209	+	6.69702i	0.0223727	+	0.285822i
$550$	−0.681131			−0.0290435
$551$	−54.7942	−	31.6354i	−2.33431	−	1.34771i
$552$	−12.5844	−	11.6378i	−0.535626	−	0.495338i
$553$	−25.1890	+	14.5429i	−1.07114	+	0.618426i
$554$	−11.0899	+	6.40273i	−0.471163	+	0.272026i
$555$	−3.81634	+	4.12674i	−0.161995	+	0.175170i
$556$	2.66668	−	4.61883i	0.113093	−	0.195882i
$557$			5.08378i			0.215407i	0.994183	+	0.107703i	$0.0343497\pi$
$557$			5.08378i			0.215407i	−0.994183	+	0.107703i	$0.965650\pi$
$558$	18.5992	−	12.7712i	0.787366	−	0.540650i
$559$	38.7131	+	5.51200i	1.63739	+	0.233133i
$560$	−0.160320	+	0.277683i	−0.00677476	+	0.0117342i
$561$	−0.780591	+	3.44632i	−0.0329566	+	0.145504i
$562$	3.52248	+	6.10112i	0.148587	+	0.257360i
$563$	−9.47635	−	16.4135i	−0.399380	−	0.691747i	0.594269	−	0.804266i	$-0.297441\pi$
$563$	−9.47635	−	16.4135i	−0.399380	−	0.691747i	−0.993650	+	0.112519i	$0.964108\pi$
$564$	−1.65063	+	0.512151i	−0.0695041	+	0.0215654i
$565$	−2.70286	−	1.56049i	−0.113710	−	0.0656505i
$566$		−	6.57029i		−	0.276170i
$567$	14.3012	−	11.5608i	0.600595	−	0.485509i
$568$	−46.5942			−1.95505
$569$	19.6005	−	33.9491i	0.821696	−	1.42322i	−0.0827224	−	0.996573i	$-0.526361\pi$
$569$	19.6005	−	33.9491i	0.821696	−	1.42322i	0.904418	−	0.426647i	$-0.140305\pi$
$570$	10.9159	−	3.38694i	0.457217	−	0.141863i
$571$	6.30361	+	10.9182i	0.263798	+	0.456911i	0.967248	−	0.253833i	$-0.0816915\pi$
$571$	6.30361	+	10.9182i	0.263798	+	0.456911i	−0.703450	+	0.710745i	$0.748358\pi$
$572$	3.06029	−	1.23002i	0.127957	−	0.0514298i
$573$	16.9121	+	3.83060i	0.706515	+	0.160025i
$574$	9.59576	+	5.54012i	0.400519	+	0.231240i
$575$	−3.45835			−0.144223
$576$	13.1199	−	9.00889i	0.546664	−	0.375371i
$577$			30.2782i			1.26050i	0.776394	+	0.630248i	$0.217047\pi$
$577$			30.2782i			1.26050i	−0.776394	+	0.630248i	$0.782953\pi$
$578$	7.61035	+	4.39384i	0.316549	+	0.182760i
$579$	13.2038	+	12.2106i	0.548730	+	0.507457i
$580$	−8.91386	+	5.14642i	−0.370128	+	0.213693i
$581$	−8.87745	−	15.3762i	−0.368299	−	0.637912i
$582$	−0.0957306	+	0.103517i	−0.00396816	+	0.00429090i
$583$	8.55065	+	4.93672i	0.354132	+	0.204458i
$584$	−25.7380			−1.06505
$585$	10.7950	+	0.684393i	0.446318	+	0.0282962i
$586$	−22.9322			−0.947321
$587$	33.1799	+	19.1564i	1.36948	+	0.790670i	0.990862	−	0.134882i	$-0.0430657\pi$
$587$	33.1799	+	19.1564i	1.36948	+	0.790670i	0.378619	+	0.925553i	$0.376399\pi$
$588$	5.72987	+	1.29781i	0.236296	+	0.0535210i
$589$	31.0434	+	53.7688i	1.27912	+	2.21550i
$590$	−7.66834	+	4.42732i	−0.315701	+	0.182270i
$591$	−39.9389	+	12.3921i	−1.64287	+	0.509742i
$592$	0.441025	+	0.254626i	0.0181260	+	0.0104651i
$593$			11.6063i			0.476612i	0.971190	+	0.238306i	$0.0765921\pi$
$593$			11.6063i			0.476612i	−0.971190	+	0.238306i	$0.923408\pi$
$594$	0.510086	−	3.50231i	0.0209291	−	0.143701i
$595$	5.47159			0.224313
$596$	−10.1641	−	5.86825i	−0.416338	−	0.240373i
$597$	12.2399	+	39.4484i	0.500945	+	1.61452i
$598$	−10.3437	+	4.15745i	−0.422986	+	0.170011i
$599$	22.5946	+	39.1350i	0.923190	+	1.59901i	0.794447	+	0.607333i	$0.207761\pi$
$599$	22.5946	+	39.1350i	0.923190	+	1.59901i	0.128742	+	0.991678i	$0.458906\pi$
$600$	1.09488	−	4.83389i	0.0446981	−	0.197343i
$601$	−3.58234	+	6.20479i	−0.146127	+	0.253099i	−0.929793	−	0.368084i	$-0.880014\pi$
$601$	−3.58234	+	6.20479i	−0.146127	+	0.253099i	0.783666	+	0.621182i	$0.213347\pi$
$602$	−19.8121			−0.807480
$603$	1.30481	−	2.73261i	0.0531361	−	0.111281i
$604$		−	9.87147i		−	0.401664i
$605$	9.02361	+	5.20978i	0.366862	+	0.211808i
$606$	−2.31885	−	2.14444i	−0.0941969	−	0.0871118i
$607$	−4.17656	−	7.23401i	−0.169521	−	0.293619i	0.768730	−	0.639573i	$-0.220889\pi$
$607$	−4.17656	−	7.23401i	−0.169521	−	0.293619i	−0.938252	+	0.345954i	$0.887555\pi$
$608$	20.6027	+	35.6849i	0.835549	+	1.44721i
$609$	22.2737	+	20.5984i	0.902578	+	0.834689i
$610$	1.00095	−	1.73369i	0.0405273	−	0.0701953i
$611$	−0.422356	+	2.96639i	−0.0170867	+	0.120007i
$612$	−8.70441	−	4.15632i	−0.351855	−	0.168009i
$613$		−	28.0392i		−	1.13249i	−0.824236	−	0.566246i	$-0.808395\pi$
$613$		−	28.0392i		−	1.13249i	0.824236	−	0.566246i	$-0.191605\pi$
$614$	11.2175	−	19.4292i	0.452700	−	0.784100i
$615$	−10.2462	−	2.32075i	−0.413165	−	0.0935818i
$616$	−3.85776	+	2.22728i	−0.155434	+	0.0897397i
$617$	13.4342	−	7.75623i	0.540840	−	0.312254i	−0.204580	−	0.978850i	$-0.565583\pi$
$617$	13.4342	−	7.75623i	0.540840	−	0.312254i	0.745419	+	0.666596i	$0.232249\pi$
$618$	−11.2672	+	3.49593i	−0.453232	+	0.140627i
$619$	−3.36363	−	1.94199i	−0.135196	−	0.0780552i	0.430877	−	0.902411i	$-0.358204\pi$
$619$	−3.36363	−	1.94199i	−0.135196	−	0.0780552i	−0.566072	+	0.824356i	$0.691538\pi$
$620$	10.1002			0.405635
$621$	2.58989	−	17.7825i	0.103929	−	0.713587i
$622$			24.4046i			0.978537i
$623$	6.99141	−	12.1095i	0.280105	−	0.485156i
$624$	−0.155576	−	0.967560i	−0.00622801	−	0.0387334i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	8.36929	−	4.83201i	0.334504	−	0.193126i
$627$	9.49893	+	2.15151i	0.379351	+	0.0859229i
$628$	−8.78743	+	15.2203i	−0.350656	+	0.607355i
$629$		−	8.69016i		−	0.346500i
$630$	−5.46361	+	0.427663i	−0.217676	+	0.0170385i
$631$		−	27.4010i		−	1.09082i	−0.838171	−	0.545408i	$-0.816375\pi$
$631$		−	27.4010i		−	1.09082i	0.838171	−	0.545408i	$-0.183625\pi$
$632$	−35.2761	−	20.3667i	−1.40321	−	0.810143i
$633$	−18.7186	+	20.2410i	−0.743997	+	0.804509i
$634$	4.66868	+	8.08638i	0.185417	+	0.321151i
$635$	−9.61641	+	5.55204i	−0.381616	+	0.220326i
$636$	−18.2991	+	19.7874i	−0.725607	+	0.784623i
$637$	6.28533	−	8.01502i	0.249034	−	0.317567i
$638$	5.83890			0.231164
$639$	−27.6511	−	40.2692i	−1.09386	−	1.59303i
$640$	6.42266			0.253878
$641$	−7.26201	+	12.5782i	−0.286832	+	0.496808i	−0.973052	−	0.230587i	$-0.925935\pi$
$641$	−7.26201	+	12.5782i	−0.286832	+	0.496808i	0.686220	+	0.727394i	$0.259269\pi$
$642$	−1.86931	+	8.25305i	−0.0737759	+	0.325722i
$643$	22.1706	−	12.8002i	0.874325	−	0.504792i	0.00554163	−	0.999985i	$-0.498236\pi$
$643$	22.1706	−	12.8002i	0.874325	−	0.504792i	0.868783	+	0.495193i	$0.164903\pi$
$644$	−7.34790	+	4.24231i	−0.289548	+	0.167170i
$645$	17.9410	−	5.56665i	0.706426	−	0.219187i
$646$	−8.83509	+	15.3028i	−0.347612	+	0.602082i
$647$	−8.13865			−0.319963			−0.159982	−	0.987120i	$-0.551143\pi$
$647$	−8.13865			−0.319963			−0.159982	+	0.987120i	$0.551143\pi$
$648$	24.0355	+	9.24976i	0.944202	+	0.363365i
$649$	−7.54555			−0.296189
$650$	−2.53656	−	1.98916i	−0.0994922	−	0.0780212i
$651$	−8.82219	−	28.4334i	−0.345769	−	1.11439i
$652$	6.34521	−	3.66341i	0.248498	−	0.143470i
$653$	−5.31347	−	9.20321i	−0.207932	−	0.360149i	0.743131	−	0.669146i	$-0.233340\pi$
$653$	−5.31347	−	9.20321i	−0.207932	−	0.360149i	−0.951063	+	0.308997i	$0.900007\pi$
$654$	−21.2370	−	4.81017i	−0.830431	−	0.188093i
$655$	−6.95893	−	4.01774i	−0.271908	−	0.156986i
$656$			0.951814i			0.0371621i
$657$	−15.2741	−	22.2442i	−0.595901	−	0.867830i
$658$		−	1.51810i		−	0.0591816i
$659$	17.1532	−	29.7102i	0.668193	−	1.15734i	−0.310216	−	0.950666i	$-0.600401\pi$
$659$	17.1532	−	29.7102i	0.668193	−	1.15734i	0.978409	−	0.206678i	$-0.0662652\pi$
$660$	1.07575	−	1.16325i	0.0418736	−	0.0452793i
$661$	−14.2557	+	8.23055i	−0.554483	+	0.320131i	−0.750928	−	0.660384i	$-0.770394\pi$
$661$	−14.2557	+	8.23055i	−0.554483	+	0.320131i	0.196445	+	0.980515i	$0.437060\pi$
$662$	14.0304	+	24.3013i	0.545305	+	0.944496i
$663$	−12.9715	+	10.5546i	−0.503772	+	0.409908i
$664$	12.4325	−	21.5337i	0.482474	−	0.835670i
$665$		−	15.0811i		−	0.584819i
$666$	0.679230	+	8.67750i	0.0263196	+	0.336246i
$667$	29.6462			1.14791
$668$	12.3525	+	7.13173i	0.477933	+	0.275935i
$669$	−2.87579	+	12.6966i	−0.111184	+	0.490881i
$670$	−0.781525	+	0.451213i	−0.0301929	+	0.0174319i
$671$	1.47738	−	0.852967i	0.0570337	−	0.0329284i
$672$	−5.85505	−	18.8705i	−0.225863	−	0.727944i
$673$	7.25149	−	12.5599i	0.279524	−	0.484150i	−0.691742	−	0.722144i	$-0.743157\pi$
$673$	7.25149	−	12.5599i	0.279524	−	0.484150i	0.971267	+	0.237994i	$0.0764899\pi$
$674$		−	20.7662i		−	0.799886i
$675$	4.82746	−	1.92240i	0.185809	−	0.0739933i
$676$	14.9888	+	4.35655i	0.576492	+	0.167559i
$677$	16.9934	−	29.4334i	0.653108	−	1.13122i	−0.329257	−	0.944240i	$-0.606798\pi$
$677$	16.9934	−	29.4334i	0.653108	−	1.13122i	0.982365	−	0.186975i	$-0.0598685\pi$
$678$	−4.61582	+	1.43218i	−0.177270	+	0.0550025i
$679$	0.0930235	+	0.161121i	0.00356992	+	0.00618327i
$680$	3.83136	+	6.63612i	0.146926	+	0.254483i
$681$	6.23456	−	27.5257i	0.238909	−	1.05479i
$682$	−4.96201	−	2.86482i	−0.190005	−	0.109700i
$683$			24.3402i			0.931352i	0.884955	+	0.465676i	$0.154189\pi$
$683$			24.3402i			0.931352i	−0.884955	+	0.465676i	$0.845811\pi$
$684$	−11.4559	+	23.9916i	−0.438027	+	0.917340i
$685$	8.79735			0.336130
$686$	−8.97400	+	15.5434i	−0.342629	+	0.593451i
$687$	−20.7653	−	19.2034i	−0.792245	−	0.732655i
$688$	−0.850948	−	1.47389i	−0.0324421	−	0.0561914i
$689$	17.4259	+	43.3557i	0.663876	+	1.65172i
$690$	−3.63602	+	3.93175i	−0.138421	+	0.149679i
$691$	32.7729	+	18.9214i	1.24674	+	0.719805i	0.970457	−	0.241272i	$-0.0775647\pi$
$691$	32.7729	+	18.9214i	1.24674	+	0.719805i	0.276281	+	0.961077i	$0.410898\pi$
$692$	−1.07895			−0.0410154
$693$	−4.21431	−	2.01232i	−0.160088	−	0.0764416i
$694$		−	3.96832i		−	0.150635i
$695$	−3.84679	−	2.22094i	−0.145917	−	0.0842452i
$696$	−9.38568	+	41.4379i	−0.355763	+	1.57070i
$697$	14.0662	−	8.12115i	0.532797	−	0.307610i
$698$	5.40576	+	9.36305i	0.204611	+	0.354397i
$699$	−7.81535	−	25.1884i	−0.295604	−	0.952713i
$700$	−2.12469	−	1.22669i	−0.0803056	−	0.0463644i
$701$	3.61068			0.136374			0.0681868	−	0.997673i	$-0.478279\pi$
$701$	3.61068			0.136374			0.0681868	+	0.997673i	$0.478279\pi$
$702$	12.1277	−	11.5531i	0.457729	−	0.436045i
$703$	−23.9523			−0.903378
$704$	−3.50023	−	2.02086i	−0.131920	−	0.0761639i
$705$	0.426544	+	1.37473i	0.0160646	+	0.0517752i
$706$	−3.23580	−	5.60457i	−0.121781	−	0.210931i
$707$	−3.60924	+	2.08380i	−0.135740	+	0.0783693i
$708$	4.55003	−	20.0885i	0.171001	−	0.754970i
$709$	6.09225	+	3.51736i	0.228799	+	0.132097i	0.610018	−	0.792388i	$-0.291162\pi$
$709$	6.09225	+	3.51736i	0.228799	+	0.132097i	−0.381219	+	0.924485i	$0.624496\pi$
$710$			14.5575i			0.546333i
$711$	−3.33248	−	42.5741i	−0.124978	−	1.59665i
$712$	19.5823			0.733879
$713$	−25.1939	−	14.5457i	−0.943520	−	0.544742i
$714$	5.75269	−	6.22058i	0.215289	−	0.232799i
$715$	−1.02442	−	2.54876i	−0.0383112	−	0.0953181i
$716$	−3.70507	−	6.41737i	−0.138465	−	0.239828i
$717$	−22.0085	−	20.3531i	−0.821922	−	0.760101i
$718$	1.27869	−	2.21476i	0.0477204	−	0.0826541i
$719$	41.1102			1.53315			0.766575	−	0.642154i	$-0.221959\pi$
$719$	41.1102			1.53315			0.766575	+	0.642154i	$0.221959\pi$
$720$	−0.266483	−	0.388088i	−0.00993123	−	0.0144632i
$721$			15.5664i			0.579723i
$722$	27.4676	+	15.8584i	1.02224	+	0.590189i
$723$	6.98668	−	30.8463i	0.259837	−	1.14719i
$724$	−3.63796	−	6.30113i	−0.135204	−	0.234180i
$725$	4.28619	+	7.42389i	0.159185	+	0.275716i
$726$	15.4101	−	4.78139i	0.571924	−	0.177454i
$727$	−8.63490	+	14.9561i	−0.320251	+	0.554690i	−0.980540	−	0.196321i	$-0.937100\pi$
$727$	−8.63490	+	14.9561i	−0.320251	+	0.554690i	0.660289	+	0.751012i	$0.270434\pi$
$728$	−20.8710	−	2.97163i	−0.773531	−	0.110136i
$729$	6.26961	+	26.2620i	0.232208	+	0.972666i
$730$			8.04138i			0.297625i
$731$	−14.5211	+	25.1512i	−0.537081	+	0.930251i
$732$	1.37997	+	4.44757i	0.0510053	+	0.164387i
$733$	−19.4811	+	11.2474i	−0.719552	+	0.415434i	−0.814588	−	0.580040i	$-0.803037\pi$
$733$	−19.4811	+	11.2474i	−0.719552	+	0.415434i	0.0950358	+	0.995474i	$0.469703\pi$
$734$	−17.9008	+	10.3350i	−0.660731	+	0.381473i
$735$	1.08088	−	4.77211i	0.0398690	−	0.176022i
$736$	−16.7205	−	9.65361i	−0.616327	−	0.355837i
$737$	−0.769010			−0.0283269
$738$	−13.4110	+	9.20874i	−0.493665	+	0.338978i
$739$			33.9029i			1.24714i	0.781769	+	0.623569i	$0.214318\pi$
$739$			33.9029i			1.24714i	−0.781769	+	0.623569i	$0.785682\pi$
$740$	−1.94827	+	3.37450i	−0.0716198	+	0.124049i
$741$	29.0913	+	35.7528i	1.06869	+	1.31341i
$742$	−11.8372	−	20.5026i	−0.434557	−	0.752674i
$743$	15.2407	−	8.79921i	0.559126	−	0.322812i	−0.193668	−	0.981067i	$-0.562039\pi$
$743$	15.2407	−	8.79921i	0.559126	−	0.322812i	0.752795	+	0.658255i	$0.228705\pi$
$744$	28.3074	−	30.6097i	1.03780	−	1.12221i
$745$	−4.88736	+	8.46516i	−0.179059	+	0.310140i
$746$			4.66565i			0.170822i
$747$	25.9886	−	2.03426i	0.950874	−	0.0744295i
$748$			2.44959i			0.0895657i
$749$	9.66992	+	5.58293i	0.353331	+	0.203996i
$750$	−1.51026	−	0.342074i	−0.0551469	−	0.0124908i
$751$	−10.6430	−	18.4342i	−0.388368	−	0.672674i	0.603862	−	0.797089i	$-0.293628\pi$
$751$	−10.6430	−	18.4342i	−0.388368	−	0.672674i	−0.992230	+	0.124415i	$0.960294\pi$
$752$	0.112936	−	0.0652038i	0.00411836	−	0.00237774i
$753$	−9.98373	−	32.1770i	−0.363827	−	1.17259i
$754$	21.7444	+	17.0518i	0.791883	+	0.620990i
$755$	−8.22144			−0.299209
$756$	7.89865	−	10.0063i	0.287271	−	0.363925i
$757$	−19.6532			−0.714309			−0.357154	−	0.934045i	$-0.616253\pi$
$757$	−19.6532			−0.714309			−0.357154	+	0.934045i	$0.616253\pi$
$758$	−16.8154	+	29.1251i	−0.610761	+	1.05787i
$759$	−4.35858	+	1.35236i	−0.158207	+	0.0490876i
$760$	18.2908	−	10.5602i	0.663478	−	0.383059i
$761$	12.5083	−	7.22167i	0.453426	−	0.261785i	−0.255850	−	0.966716i	$-0.582355\pi$
$761$	12.5083	−	7.22167i	0.453426	−	0.261785i	0.709276	+	0.704931i	$0.249022\pi$
$762$	−3.79841	+	16.7701i	−0.137602	+	0.607515i
$763$	−14.3662	+	24.8829i	−0.520090	+	0.900822i
$764$	12.0209			0.434900
$765$	−3.46159	+	7.24945i	−0.125154	+	0.262104i
$766$	23.2788			0.841099
$767$	−28.1000	−	22.0359i	−1.01463	−	0.795669i
$768$	19.2300	−	20.7940i	0.693902	−	0.750340i
$769$	−0.210384	+	0.121465i	−0.00758665	+	0.00438016i	−0.503789	−	0.863827i	$-0.668061\pi$
$769$	−0.210384	+	0.121465i	−0.00758665	+	0.00438016i	0.496202	+	0.868207i	$0.334728\pi$
$770$	0.695873	+	1.20529i	0.0250775	+	0.0434356i
$771$	9.68856	−	10.4766i	0.348925	−	0.377304i
$772$	10.7969	+	6.23362i	0.388590	+	0.224353i
$773$			1.99165i			0.0716348i	0.999358	+	0.0358174i	$0.0114035\pi$
$773$			1.99165i			0.0716348i	−0.999358	+	0.0358174i	$0.988597\pi$
$774$	12.5341	−	26.2495i	0.450527	−	0.943520i
$775$		−	8.41195i		−	0.302166i
$776$	−0.130276	+	0.225644i	−0.00467662	+	0.00810014i
$777$	11.2014	+	2.53711i	0.401847	+	0.0910183i
$778$	2.60316	−	1.50294i	0.0933280	−	0.0538829i
$779$	−22.3839	−	38.7701i	−0.801988	−	1.38908i
$780$	7.40327	−	1.19038i	0.265080	−	0.0426226i
$781$	−6.20265	+	10.7433i	−0.221948	+	0.384425i
$782$		−	8.27956i		−	0.296076i
$783$	−41.3828	+	16.4795i	−1.47890	+	0.588931i
$784$	−0.443304			−0.0158323
$785$	12.6762	+	7.31859i	0.452432	+	0.261212i
$786$	−11.8842	+	3.68737i	−0.423894	+	0.131524i
$787$	35.5474	−	20.5233i	1.26713	−	0.731577i	0.292685	−	0.956209i	$-0.405451\pi$
$787$	35.5474	−	20.5233i	1.26713	−	0.731577i	0.974444	+	0.224631i	$0.0721178\pi$
$788$	−25.1050	+	14.4943i	−0.894327	+	0.516340i
$789$	13.4803	+	3.05329i	0.479911	+	0.108700i
$790$	−6.36320	+	11.0214i	−0.226392	+	0.392123i
$791$			6.37708i			0.226743i
$792$	−0.510378	−	6.52034i	−0.0181355	−	0.231690i
$793$	7.99283	+	1.13802i	0.283834	+	0.0404124i
$794$	−8.19452	+	14.1933i	−0.290813	+	0.503702i
$795$	16.4799	+	15.2404i	0.584483	+	0.540521i
$796$	14.3163	+	24.7966i	0.507429	+	0.878893i
$797$	−7.07762	−	12.2588i	−0.250702	−	0.434229i	0.713017	−	0.701147i	$-0.247328\pi$
$797$	−7.07762	−	12.2588i	−0.250702	−	0.434229i	−0.963719	+	0.266918i	$0.913995\pi$
$798$	−17.1455	−	15.8559i	−0.606944	−	0.561292i
$799$	−1.92721	−	1.11267i	−0.0681797	−	0.0393636i
$800$		−	5.58279i		−	0.197381i
$801$	11.6211	+	16.9241i	0.410610	+	0.597984i
$802$	4.24287			0.149821
$803$	−3.42626	+	5.93446i	−0.120910	+	0.209423i
$804$	0.463720	−	2.04733i	0.0163541	−	0.0722038i
$805$	3.53320	+	6.11968i	0.124529	+	0.215691i
$806$	−10.1124	−	25.1597i	−0.356195	−	0.886212i
$807$	−5.80352	−	18.7044i	−0.204294	−	0.658426i
$808$	−5.05459	−	2.91827i	−0.177820	−	0.102664i
$809$	14.0746			0.494837			0.247418	−	0.968909i	$-0.420418\pi$
$809$	14.0746			0.494837			0.247418	+	0.968909i	$0.420418\pi$
$810$	2.88992	−	7.50944i	0.101541	−	0.263855i
$811$			25.8062i			0.906177i	0.891466	+	0.453089i	$0.149678\pi$
$811$			25.8062i			0.906177i	−0.891466	+	0.453089i	$0.850322\pi$
$812$	18.2136	+	10.5156i	0.639172	+	0.369026i
$813$	47.4854	−	14.7336i	1.66539	−	0.516729i
$814$	1.91428	−	1.10521i	0.0670955	−	0.0387376i
$815$	−3.05106	−	5.28460i	−0.106874	−	0.185111i
$816$	0.709853	+	0.160782i	0.0248498	+	0.00562848i
$817$	69.3231	+	40.0237i	2.42531	+	1.40025i
$818$	8.64922			0.302413
$819$	−9.81757	−	19.8014i	−0.343054	−	0.691916i
$820$	−7.28280			−0.254326
$821$	1.39441	+	0.805061i	0.0486651	+	0.0280968i	0.524135	−	0.851635i	$-0.324389\pi$
$821$	1.39441	+	0.805061i	0.0486651	+	0.0280968i	−0.475470	+	0.879732i	$0.657722\pi$
$822$	9.24932	−	10.0016i	0.322607	−	0.348846i
$823$	14.7668	+	25.5768i	0.514738	+	0.891552i	0.999854	+	0.0171023i	$0.00544408\pi$
$823$	14.7668	+	25.5768i	0.514738	+	0.891552i	−0.485116	+	0.874450i	$0.661223\pi$
$824$	−18.8794	+	10.9000i	−0.657696	+	0.379721i
$825$	−0.968807	−	0.895938i	−0.0337295	−	0.0311925i
$826$	15.6686	+	9.04629i	0.545182	+	0.314761i
$827$			4.73841i			0.164771i	0.996601	+	0.0823853i	$0.0262538\pi$
$827$			4.73841i			0.164771i	−0.996601	+	0.0823853i	$0.973746\pi$
$828$	−0.972120	−	12.4193i	−0.0337835	−	0.431601i
$829$	−33.8476			−1.17558			−0.587788	−	0.809015i	$-0.700001\pi$
$829$	−33.8476			−1.17558			−0.587788	+	0.809015i	$0.700001\pi$
$830$	−6.72782	−	3.88431i	−0.233526	−	0.134826i
$831$	−24.1956	−	5.48031i	−0.839337	−	0.190110i
$832$	−7.13335	−	17.7478i	−0.247304	−	0.615293i
$833$	3.78240	+	6.55130i	0.131052	+	0.226989i
$834$	−6.56938	+	2.03832i	−0.227479	+	0.0705812i
$835$	5.93965	−	10.2878i	0.205550	−	0.356023i
$836$	6.75168			0.233512
$837$	43.2535	+	6.29956i	1.49506	+	0.217745i
$838$		−	22.1142i		−	0.763923i
$839$	31.5227	+	18.1996i	1.08828	+	0.628321i	0.933119	−	0.359567i	$-0.117076\pi$
$839$	31.5227	+	18.1996i	1.08828	+	0.628321i	0.155165	+	0.987889i	$0.450409\pi$
$840$	−9.67234	+	3.00109i	−0.333727	+	0.103548i
$841$	−22.2428	−	38.5256i	−0.766993	−	1.32847i
$842$	9.55011	+	16.5413i	0.329118	+	0.570050i
$843$	−3.01501	+	13.3113i	−0.103842	+	0.458466i
$844$	−9.55597	+	16.5514i	−0.328930	+	0.569724i
$845$	3.62834	−	12.4834i	0.124819	−	0.429442i
$846$	2.01137	+	0.960420i	0.0691522	+	0.0330199i
$847$		−	21.2902i		−	0.731540i
$848$	1.01684	−	1.76121i	0.0349183	−	0.0604803i
$849$	8.64235	−	9.34526i	0.296605	−	0.320729i
$850$	2.07333	−	1.19704i	0.0711148	−	0.0410581i
$851$	9.71950	−	5.61155i	0.333180	−	0.192362i
$852$	−24.8616	−	22.9916i	−0.851743	−	0.787678i
$853$	39.7686	+	22.9604i	1.36165	+	0.786150i	0.989844	−	0.142159i	$-0.0454045\pi$
$853$	39.7686	+	22.9604i	1.36165	+	0.786150i	0.371808	+	0.928309i	$0.378738\pi$
$854$	−4.09046			−0.139973
$855$	19.9813	+	9.54101i	0.683347	+	0.326296i
$856$			15.6373i			0.534473i
$857$	11.1477	−	19.3084i	0.380799	−	0.659563i	−0.610378	−	0.792110i	$-0.708982\pi$
$857$	11.1477	−	19.3084i	0.380799	−	0.659563i	0.991177	+	0.132547i	$0.0423157\pi$
$858$	−3.97470	−	1.51505i	−0.135694	−	0.0517229i
$859$	−5.73019	−	9.92498i	−0.195512	−	0.338636i	0.751557	−	0.659669i	$-0.229303\pi$
$859$	−5.73019	−	9.92498i	−0.195512	−	0.338636i	−0.947068	+	0.321033i	$0.895970\pi$
$860$	11.2774	−	6.51102i	0.384557	−	0.222024i
$861$	6.36126	+	20.5020i	0.216791	+	0.698705i
$862$	−2.71663	+	4.70535i	−0.0925289	+	0.160265i
$863$		−	11.2682i		−	0.383575i	−0.981437	−	0.191787i	$-0.938572\pi$
$863$		−	11.2682i		−	0.383575i	0.981437	−	0.191787i	$-0.0614284\pi$
$864$	28.7062	+	4.18085i	0.976603	+	0.142235i
$865$			0.898599i			0.0305533i
$866$	−14.7441	−	8.51248i	−0.501023	−	0.289266i
$867$	5.04508	+	16.2600i	0.171340	+	0.552218i
$868$	−10.3188	−	17.8728i	−0.350244	−	0.606641i
$869$	−9.39196	+	5.42245i	−0.318600	+	0.183944i
$870$	12.9465	+	2.93239i	0.438928	+	0.0994172i
$871$	−2.86383	−	2.24580i	−0.0970372	−	0.0760961i
$872$	−40.2384			−1.36264
$873$	−0.272325	+	0.0213162i	−0.00921681	+	0.000721445i
$874$	−22.8206			−0.771917
$875$	−1.02164	+	1.76954i	−0.0345379	+	0.0598214i
$876$	−13.7332	−	12.7003i	−0.464002	−	0.429102i
$877$	1.54963	−	0.894680i	0.0523273	−	0.0302112i	−0.473608	−	0.880736i	$-0.657049\pi$
$877$	1.54963	−	0.894680i	0.0523273	−	0.0302112i	0.525935	+	0.850524i	$0.323715\pi$
$878$	−2.14487	+	1.23834i	−0.0723860	+	0.0417921i
$879$	−32.6177	−	30.1643i	−1.10017	−	1.01742i
$880$	−0.0597769	+	0.103537i	−0.00201508	+	0.00349022i
$881$	23.2382			0.782913			0.391457	−	0.920197i	$-0.371971\pi$
$881$	23.2382			0.782913			0.391457	+	0.920197i	$0.371971\pi$
$882$	−4.28894	−	6.24612i	−0.144416	−	0.210318i
$883$	29.9725			1.00866			0.504328	−	0.863512i	$-0.331740\pi$
$883$	29.9725			1.00866			0.504328	+	0.863512i	$0.331740\pi$
$884$	−7.15372	+	9.12238i	−0.240606	+	0.306819i
$885$	−16.7306	−	3.78949i	−0.562394	−	0.127382i
$886$	−7.96975	+	4.60134i	−0.267749	+	0.154585i
$887$	28.4053	+	49.1994i	0.953756	+	1.65195i	0.737191	+	0.675685i	$0.236152\pi$
$887$	28.4053	+	49.1994i	0.953756	+	1.65195i	0.216565	+	0.976268i	$0.430515\pi$
$888$	4.76644	+	15.3619i	0.159951	+	0.515513i
$889$	19.6491	+	11.3444i	0.659010	+	0.380480i
$890$		−	6.11815i		−	0.205081i
$891$	5.33235	−	4.31056i	0.178640	−	0.144409i
$892$			9.02457i			0.302165i
$893$	−3.06681	+	5.31187i	−0.102627	+	0.177755i
$894$	4.48548	+	14.4564i	0.150017	+	0.483496i
$895$	−5.34469	+	3.08576i	−0.178653	+	0.103146i
$896$	−6.56167	−	11.3651i	−0.219210	−	0.379683i
$897$	−20.1810	−	7.69245i	−0.673824	−	0.256843i
$898$	−10.6828	+	18.5031i	−0.356488	+	0.617456i
$899$			72.1104i			2.40502i
$900$	2.96945	−	2.03899i	0.0989816	−	0.0679664i
$901$	−34.7038			−1.15615
$902$	3.57787	+	2.06569i	0.119130	+	0.0687798i
$903$	−28.1797	−	26.0602i	−0.937763	−	0.867228i
$904$	−7.73433	+	4.46542i	−0.257240	+	0.148518i
$905$	−5.24788	+	3.02987i	−0.174446	+	0.100716i
$906$	−8.64381	+	9.34685i	−0.287171	+	0.310528i
$907$	−0.588714	+	1.01968i	−0.0195479	+	0.0338580i	−0.875634	−	0.482975i	$-0.839556\pi$
$907$	−0.588714	+	1.01968i	−0.0195479	+	0.0338580i	0.856086	+	0.516833i	$0.172889\pi$
$908$		−	19.5648i		−	0.649281i
$909$	−0.477499	−	6.10029i	−0.0158377	−	0.202334i
$910$	−0.928431	+	6.52077i	−0.0307772	+	0.216161i
$911$	−10.8862	+	18.8554i	−0.360675	+	0.624707i	−0.988072	−	0.153992i	$-0.950787\pi$
$911$	−10.8862	+	18.8554i	−0.360675	+	0.624707i	0.627397	+	0.778699i	$0.284120\pi$
$912$	0.443155	−	1.95654i	0.0146743	−	0.0647874i
$913$	−3.31004	−	5.73316i	−0.109546	−	0.189740i
$914$	13.0149	+	22.5425i	0.430495	+	0.745640i
$915$	3.70415	−	1.14931i	0.122455	−	0.0379949i
$916$	−16.9801	−	9.80346i	−0.561038	−	0.323916i
$917$			16.4188i			0.542197i
$918$	4.60238	+	11.5573i	0.151901	+	0.381448i
$919$	49.2738			1.62539			0.812696	−	0.582688i	$-0.197999\pi$
$919$	49.2738			1.62539			0.812696	+	0.582688i	$0.197999\pi$
$920$	−4.94810	+	8.57036i	−0.163134	+	0.282556i
$921$	41.5118	−	12.8801i	1.36786	−	0.424414i
$922$	−5.96256	−	10.3275i	−0.196366	−	0.340116i
$923$	−54.4735	+	21.8945i	−1.79302	+	0.720666i
$924$	−3.15745	−	0.715161i	−0.103872	−	0.0235271i
$925$	2.81045	+	1.62261i	0.0924069	+	0.0533511i
$926$	9.95770			0.327230
$927$	−20.6243	−	9.84804i	−0.677392	−	0.323452i
$928$			47.8577i			1.57101i
$929$	5.07061	+	2.92752i	0.166361	+	0.0960487i	0.580869	−	0.813997i	$-0.302713\pi$
$929$	5.07061	+	2.92752i	0.166361	+	0.0960487i	−0.414508	+	0.910046i	$0.636046\pi$
$930$	−9.56345	−	8.84412i	−0.313598	−	0.290010i
$931$	18.0571	−	10.4252i	0.591796	−	0.341674i
$932$	−9.14120	−	15.8330i	−0.299430	−	0.518628i
$933$	−32.1011	+	34.7120i	−1.05094	+	1.13642i
$934$	21.2991	+	12.2970i	0.696928	+	0.402372i
$935$	2.04013			0.0667195
$936$	17.1412	−	25.7726i	0.560277	−	0.842402i
$937$	−26.0682			−0.851612			−0.425806	−	0.904814i	$-0.640009\pi$
$937$	−26.0682			−0.851612			−0.425806	+	0.904814i	$0.640009\pi$
$938$	1.59688	+	0.921960i	0.0521400	+	0.0301030i
$939$	18.2599	+	4.13588i	0.595891	+	0.134969i
$940$	0.498906	+	0.864130i	0.0162725	+	0.0281848i
$941$	−18.7970	+	10.8525i	−0.612765	+	0.353780i	−0.774047	−	0.633128i	$-0.781771\pi$
$941$	−18.7970	+	10.8525i	−0.612765	+	0.353780i	0.161282	+	0.986908i	$0.448437\pi$
$942$	21.6478	−	6.71679i	0.705324	−	0.218845i
$943$	18.1662	+	10.4882i	0.591571	+	0.341544i
$944$			1.55419i			0.0505845i
$945$	−8.33372	−	6.57837i	−0.271096	−	0.213995i
$946$	−7.38712			−0.240176
$947$	−8.45766	−	4.88303i	−0.274837	−	0.158677i	0.356247	−	0.934392i	$-0.384056\pi$
$947$	−8.45766	−	4.88303i	−0.274837	−	0.158677i	−0.631084	+	0.775715i	$0.717390\pi$
$948$	−8.77271	−	28.2739i	−0.284924	−	0.918294i
$949$	−30.0905	+	12.0942i	−0.976778	+	0.392596i
$950$	−3.29935	−	5.71463i	−0.107045	−	0.185407i
$951$	−3.99607	+	17.6427i	−0.129582	+	0.572104i
$952$	7.82858	−	13.5595i	0.253726	−	0.439466i
$953$	24.1333			0.781753			0.390877	−	0.920443i	$-0.372172\pi$
$953$	24.1333			0.781753			0.390877	+	0.920443i	$0.372172\pi$
$954$	34.6532	−	2.71247i	1.12194	−	0.0878196i
$955$		−	10.0116i		−	0.323966i
$956$	−17.9967	−	10.3904i	−0.582055	−	0.336050i
$957$	8.30498	+	7.68031i	0.268462	+	0.248269i
$958$	14.4980	+	25.1113i	0.468409	+	0.811308i
$959$	−8.98777	−	15.5673i	−0.290230	−	0.502693i
$960$	−6.74610	−	6.23868i	−0.217729	−	0.201353i
$961$	19.8805	−	34.4340i	0.641306	−	1.11077i
$962$	10.3565	+	1.47457i	0.333907	+	0.0475419i
$963$	−13.5146	+	9.27990i	−0.435503	+	0.299041i
$964$		−	21.9250i		−	0.706157i
$965$	5.19166	−	8.99221i	0.167125	−	0.289470i
$966$	10.6721	+	2.41723i	0.343370	+	0.0777732i
$967$	13.6315	−	7.87016i	0.438360	−	0.253087i	−0.264542	−	0.964374i	$-0.585221\pi$
$967$	13.6315	−	7.87016i	0.438360	−	0.253087i	0.702902	+	0.711287i	$0.251887\pi$
$968$	25.8214	−	14.9080i	0.829932	−	0.479162i
$969$	−32.6955	+	10.1446i	−1.05033	+	0.325892i
$970$	0.0704983	+	0.0407022i	0.00226356	+	0.00130687i
$971$	47.4507			1.52277			0.761383	−	0.648303i	$-0.224521\pi$
$971$	47.4507			1.52277			0.761383	+	0.648303i	$0.224521\pi$
$972$	8.26053	+	16.7956i	0.264957	+	0.538718i
$973$			9.07606i			0.290965i
$974$	−9.53671	+	16.5181i	−0.305576	+	0.529273i
$975$	−0.991410	−	6.16580i	−0.0317505	−	0.197464i
$976$	−0.175689	−	0.304303i	−0.00562368	−	0.00974049i
$977$	−47.7166	+	27.5492i	−1.52659	+	0.881376i	−0.527087	+	0.849812i	$0.676716\pi$
$977$	−47.7166	+	27.5492i	−1.52659	+	0.881376i	−0.999502	+	0.0315646i	$0.989951\pi$
$978$	−9.21581	−	2.08738i	−0.294689	−	0.0667470i
$979$	2.60681	−	4.51513i	0.0833141	−	0.144304i
$980$		−	3.39194i		−	0.108351i
$981$	−23.8793	−	34.7762i	−0.762408	−	1.11032i
$982$		−	12.8332i		−	0.409523i
$983$	24.1013	+	13.9149i	0.768711	+	0.443815i	0.832415	−	0.554153i	$-0.186958\pi$
$983$	24.1013	+	13.9149i	0.768711	+	0.443815i	−0.0637037	+	0.997969i	$0.520291\pi$
$984$	−20.4111	+	22.0712i	−0.650682	+	0.703605i
$985$	12.0716	+	20.9086i	0.384633	+	0.666204i
$986$	−17.7734	+	10.2615i	−0.566020	+	0.326792i
$987$	1.99686	−	2.15927i	0.0635606	−	0.0687303i
$988$	25.1436	+	19.7175i	0.799924	+	0.627296i
$989$	−37.5071			−1.19266
$990$	−2.03716	+	0.159458i	−0.0647452	+	0.00506792i
$991$	7.29317			0.231675			0.115838	−	0.993268i	$-0.463045\pi$
$991$	7.29317			0.231675			0.115838	+	0.993268i	$0.463045\pi$
$992$	23.4811	−	40.6704i	0.745525	−	1.29129i
$993$	−12.0090	+	53.0201i	−0.381095	+	1.68254i
$994$	25.7601	−	14.8726i	0.817060	−	0.471730i
$995$	20.6518	−	11.9233i	0.654707	−	0.377995i
$996$	17.2593	−	5.35515i	0.546883	−	0.169685i
$997$	6.11018	−	10.5831i	0.193511	−	0.335171i	−0.752900	−	0.658135i	$-0.771346\pi$
$997$	6.11018	−	10.5831i	0.193511	−	0.335171i	0.946411	+	0.322963i	$0.104679\pi$
$998$	3.39192			0.107369
$999$	−10.4480	+	13.2359i	−0.330560	+	0.418765i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bt.b.376.20	✓	108
9.4	even	3	inner	585.2.bt.b.571.35	yes	108
13.12	even	2	inner	585.2.bt.b.376.35	yes	108
117.103	even	6	inner	585.2.bt.b.571.20	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bt.b.376.20	✓	108	1.1	even	1	trivial
585.2.bt.b.376.35	yes	108	13.12	even	2	inner
585.2.bt.b.571.20	yes	108	117.103	even	6	inner
585.2.bt.b.571.35	yes	108	9.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bt (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.774258 - 0.447018i) q^{2} +(-0.513274 - 1.65425i) q^{3} +(-0.600350 - 1.03984i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.342074 + 1.51026i) q^{6} +(1.76954 + 1.02164i) q^{7} +2.86154i q^{8} +(-2.47310 + 1.69817i) q^{9} +O(q^{10})\)	\(q+(-0.774258 - 0.447018i) q^{2} +(-0.513274 - 1.65425i) q^{3} +(-0.600350 - 1.03984i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.342074 + 1.51026i) q^{6} +(1.76954 + 1.02164i) q^{7} +2.86154i q^{8} +(-2.47310 + 1.69817i) q^{9} +0.894036 q^{10} +(0.659790 + 0.380930i) q^{11} +(-1.41201 + 1.52685i) q^{12} +(1.34463 + 3.34544i) q^{13} +(-0.913387 - 1.58203i) q^{14} +(1.27163 + 1.17599i) q^{15} +(0.0784618 - 0.135900i) q^{16} -2.67783 q^{17} +(2.67393 - 0.209302i) q^{18} +7.38079i q^{19} +(1.03984 + 0.600350i) q^{20} +(0.781798 - 3.45165i) q^{21} +(-0.340565 - 0.589876i) q^{22} +(-1.72917 - 2.99502i) q^{23} +(4.73371 - 1.46876i) q^{24} +(0.500000 - 0.866025i) q^{25} +(0.454381 - 3.19131i) q^{26} +(4.07858 + 3.21950i) q^{27} -2.45338i q^{28} +(-4.28619 + 7.42389i) q^{29} +(-0.458886 - 1.47896i) q^{30} +(7.28497 - 4.20598i) q^{31} +(4.83484 - 2.79139i) q^{32} +(0.291501 - 1.28698i) q^{33} +(2.07333 + 1.19704i) q^{34} -2.04329 q^{35} +(3.25054 + 1.55212i) q^{36} +3.24522i q^{37} +(3.29935 - 5.71463i) q^{38} +(4.84404 - 3.94149i) q^{39} +(-1.43077 - 2.47817i) q^{40} +(-5.25284 + 3.03273i) q^{41} +(-2.14826 + 2.32299i) q^{42} +(5.42269 - 9.39238i) q^{43} -0.914765i q^{44} +(1.29268 - 2.70721i) q^{45} +3.09189i q^{46} +(0.719689 + 0.415513i) q^{47} +(-0.265085 - 0.0600417i) q^{48} +(-1.41248 - 2.44650i) q^{49} +(-0.774258 + 0.447018i) q^{50} +(1.37446 + 4.42981i) q^{51} +(2.67146 - 3.40663i) q^{52} +12.9596 q^{53} +(-1.71870 - 4.31592i) q^{54} -0.761860 q^{55} +(-2.92348 + 5.06361i) q^{56} +(12.2097 - 3.78837i) q^{57} +(6.63723 - 3.83201i) q^{58} +(-8.57721 + 4.95206i) q^{59} +(0.459408 - 2.02829i) q^{60} +(1.11958 - 1.93918i) q^{61} -7.52059 q^{62} +(-6.11117 + 0.478351i) q^{63} -5.30506 q^{64} +(-2.83720 - 2.22492i) q^{65} +(-0.801001 + 0.866149i) q^{66} +(-0.874153 + 0.504693i) q^{67} +(1.60764 + 2.78451i) q^{68} +(-4.06697 + 4.39775i) q^{69} +(1.58203 + 0.913387i) q^{70} +16.2829i q^{71} +(-4.85938 - 7.07688i) q^{72} +8.99447i q^{73} +(1.45067 - 2.51264i) q^{74} +(-1.68926 - 0.382617i) q^{75} +(7.67481 - 4.43105i) q^{76} +(0.778350 + 1.34814i) q^{77} +(-5.51245 + 0.886356i) q^{78} +(-7.11738 + 12.3277i) q^{79} +0.156924i q^{80} +(3.23244 - 8.39948i) q^{81} +5.42274 q^{82} +(-7.52521 - 4.34468i) q^{83} +(-4.05850 + 1.25925i) q^{84} +(2.31907 - 1.33892i) q^{85} +(-8.39713 + 4.84808i) q^{86} +(14.4810 + 3.27994i) q^{87} +(-1.09005 + 1.88802i) q^{88} -6.84329i q^{89} +(-2.21104 + 1.51823i) q^{90} +(-1.03847 + 7.29363i) q^{91} +(-2.07622 + 3.59611i) q^{92} +(-10.6969 - 9.89235i) q^{93} +(-0.371484 - 0.643428i) q^{94} +(-3.69039 - 6.39195i) q^{95} +(-7.09926 - 6.56529i) q^{96} +(0.0788540 + 0.0455264i) q^{97} +2.52563i q^{98} +(-2.27861 + 0.178358i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9}+O(q^{10}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9	\( 108 q - 6 q^{3} + 52 q^{4} - 14 q^{9} - 8 q^{10} - 36 q^{12} - 4 q^{13} - 8 q^{14} - 64 q^{16} + 36 q^{17} + 24 q^{22} - 22 q^{23} + 54 q^{25} + 40 q^{26} + 48 q^{27} - 16 q^{29} + 20 q^{30} - 40 q^{35} - 76 q^{36} - 12 q^{38} + 26 q^{39} - 52 q^{42} - 6 q^{43} - 68 q^{48} + 58 q^{49} + 34 q^{51} + 22 q^{52} - 116 q^{53} + 24 q^{55} + 40 q^{56} + 18 q^{61} + 152 q^{62} - 216 q^{64} + 2 q^{65} - 72 q^{66} - 134 q^{69} + 32 q^{74} + 40 q^{77} - 34 q^{78} + 18 q^{79} + 34 q^{81} + 88 q^{82} + 60 q^{87} + 8 q^{90} + 16 q^{91} + 176 q^{92} - 76 q^{94} - 56 q^{95}+O(q^{100}) \) 108 * q - 6 * q^3 + 52 * q^4 - 14 * q^9 - 8 * q^10 - 36 * q^12 - 4 * q^13 - 8 * q^14 - 64 * q^16 + 36 * q^17 + 24 * q^22 - 22 * q^23 + 54 * q^25 + 40 * q^26 + 48 * q^27 - 16 * q^29 + 20 * q^30 - 40 * q^35 - 76 * q^36 - 12 * q^38 + 26 * q^39 - 52 * q^42 - 6 * q^43 - 68 * q^48 + 58 * q^49 + 34 * q^51 + 22 * q^52 - 116 * q^53 + 24 * q^55 + 40 * q^56 + 18 * q^61 + 152 * q^62 - 216 * q^64 + 2 * q^65 - 72 * q^66 - 134 * q^69 + 32 * q^74 + 40 * q^77 - 34 * q^78 + 18 * q^79 + 34 * q^81 + 88 * q^82 + 60 * q^87 + 8 * q^90 + 16 * q^91 + 176 * q^92 - 76 * q^94 - 56 * q^95

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