LMFDB - Embedded newform 370.2.r.d.23.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(23,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 5]))

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

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

chi := DirichletCharacter("370.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.r (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} - 4x^{10} + 6x^{8} + 44x^{7} + 56x^{6} + 32x^{5} + 92x^{4} - 16x^{3} + 36x^{2} - 24x + 4 $ x^12 - 2x^11 - 4x^10 + 6x^8 + 44x^7 + 56x^6 + 32x^5 + 92x^4 - 16x^3 + 36x^2 - 24x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.2
Root			$2.78638 - 0.746609i$ of defining polynomial
Character	$\chi$	$=$	370.23
Dual form			370.2.r.d.177.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(1.62090 + 0.434319i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.05890 + 0.872317i) q^{5} +(1.18658 + 1.18658i) q^{6} +(2.36181 + 0.632846i) q^{7} +1.00000i q^{8} +(-0.159392 - 0.0920251i) q^{9} +(-2.21922 - 0.274000i) q^{10} +3.49322i q^{11} +(0.434319 + 1.62090i) q^{12} +(2.56752 - 1.48236i) q^{13} +(1.72897 + 1.72897i) q^{14} +(-3.71613 + 0.519721i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.10658 - 1.91666i) q^{17} +(-0.0920251 - 0.159392i) q^{18} +(-1.37008 - 0.367111i) q^{19} +(-1.78490 - 1.34690i) q^{20} +(3.55340 + 2.05156i) q^{21} +(-1.74661 + 3.02521i) q^{22} +2.35663i q^{23} +(-0.434319 + 1.62090i) q^{24} +(3.47813 - 3.59203i) q^{25} +2.96472 q^{26} +(-3.77813 - 3.77813i) q^{27} +(0.632846 + 2.36181i) q^{28} +(-2.69380 - 2.69380i) q^{29} +(-3.47813 - 1.40797i) q^{30} +(1.18350 - 1.18350i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.51717 + 5.66216i) q^{33} +(1.91666 - 1.10658i) q^{34} +(-5.41477 + 0.757284i) q^{35} -0.184050i q^{36} +(1.25090 - 5.95275i) q^{37} +(-1.00297 - 1.00297i) q^{38} +(4.80551 - 1.28763i) q^{39} +(-0.872317 - 2.05890i) q^{40} +(2.80211 - 1.61780i) q^{41} +(2.05156 + 3.55340i) q^{42} -9.95193i q^{43} +(-3.02521 + 1.74661i) q^{44} +(0.408447 + 0.0504298i) q^{45} +(-1.17832 + 2.04090i) q^{46} +(-7.46221 + 7.46221i) q^{47} +(-1.18658 + 1.18658i) q^{48} +(-0.884516 - 0.510676i) q^{49} +(4.80816 - 1.37172i) q^{50} +(2.62610 - 2.62610i) q^{51} +(2.56752 + 1.48236i) q^{52} +(8.34541 - 2.23615i) q^{53} +(-1.38289 - 5.16103i) q^{54} +(-3.04719 - 7.19218i) q^{55} +(-0.632846 + 2.36181i) q^{56} +(-2.06132 - 1.19010i) q^{57} +(-0.985999 - 3.67980i) q^{58} +(-0.795776 - 2.96988i) q^{59} +(-2.30816 - 2.95840i) q^{60} +(-3.62907 - 0.972406i) q^{61} +(1.61669 - 0.433190i) q^{62} +(-0.318216 - 0.318216i) q^{63} -1.00000 q^{64} +(-3.99317 + 5.29171i) q^{65} +(-4.14499 + 4.14499i) q^{66} +(-2.04187 + 7.62035i) q^{67} +2.21317 q^{68} +(-1.02353 + 3.81986i) q^{69} +(-5.06797 - 2.05156i) q^{70} +(2.78149 + 4.81768i) q^{71} +(0.0920251 - 0.159392i) q^{72} +(-6.28228 + 6.28228i) q^{73} +(4.05969 - 4.52978i) q^{74} +(7.19778 - 4.31170i) q^{75} +(-0.367111 - 1.37008i) q^{76} +(-2.21067 + 8.25032i) q^{77} +(4.80551 + 1.28763i) q^{78} +(14.7958 + 3.96452i) q^{79} +(0.274000 - 2.21922i) q^{80} +(-4.20699 - 7.28672i) q^{81} +3.23559 q^{82} +(10.0566 - 2.69465i) q^{83} +4.10312i q^{84} +(-0.606408 + 4.91150i) q^{85} +(4.97597 - 8.61863i) q^{86} +(-3.19641 - 5.53635i) q^{87} -3.49322 q^{88} +(-7.87485 + 2.11006i) q^{89} +(0.328511 + 0.247897i) q^{90} +(7.00210 - 1.87621i) q^{91} +(-2.04090 + 1.17832i) q^{92} +(2.43234 - 1.40431i) q^{93} +(-10.1936 + 2.73136i) q^{94} +(3.14109 - 0.439298i) q^{95} +(-1.62090 + 0.434319i) q^{96} -10.8299 q^{97} +(-0.510676 - 0.884516i) q^{98} +(0.321464 - 0.556791i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} + 6 q^{4} - 8 q^{5} + 6 q^{6} - 4 q^{7} - 18 q^{9} - 4 q^{10} - 6 q^{13} - 8 q^{14} - 14 q^{15} - 6 q^{16} + 12 q^{17} + 10 q^{18} + 8 q^{19} - 4 q^{20} + 54 q^{21} - 10 q^{22} - 10 q^{25}+ \cdots - 28 q^{99}+O(q^{100}) $ 12 * q + 6 * q^3 + 6 * q^4 - 8 * q^5 + 6 * q^6 - 4 * q^7 - 18 * q^9 - 4 * q^10 - 6 * q^13 - 8 * q^14 - 14 * q^15 - 6 * q^16 + 12 * q^17 + 10 * q^18 + 8 * q^19 - 4 * q^20 + 54 * q^21 - 10 * q^22 - 10 * q^25 - 18 * q^27 + 4 * q^28 - 4 * q^29 + 10 * q^30 - 2 * q^31 - 28 * q^33 - 12 * q^34 + 14 * q^35 + 12 * q^37 + 16 * q^38 + 30 * q^39 - 2 * q^40 + 12 * q^41 - 22 * q^42 - 6 * q^44 + 24 * q^45 + 2 * q^46 - 28 * q^47 - 6 * q^48 - 24 * q^49 + 16 * q^50 - 8 * q^51 - 6 * q^52 + 14 * q^53 + 18 * q^54 - 32 * q^55 - 4 * q^56 - 72 * q^57 - 10 * q^58 + 14 * q^60 + 24 * q^61 - 16 * q^62 + 8 * q^63 - 12 * q^64 - 26 * q^65 + 8 * q^66 + 18 * q^67 + 24 * q^68 + 40 * q^69 + 6 * q^70 - 10 * q^72 + 28 * q^73 - 38 * q^74 - 30 * q^75 - 8 * q^76 + 26 * q^77 + 30 * q^78 + 56 * q^79 + 4 * q^80 + 4 * q^81 - 28 * q^82 + 14 * q^83 + 28 * q^85 - 22 * q^86 - 10 * q^87 - 20 * q^88 + 2 * q^89 + 42 * q^90 + 38 * q^91 - 18 * q^92 + 18 * q^93 + 16 * q^94 - 56 * q^95 - 6 * q^96 - 44 * q^97 + 22 * q^98 - 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	1.62090	+	0.434319i	0.935827	+	0.250754i	0.694338	−	0.719649i	$-0.255697\pi$
$3$	1.62090	+	0.434319i	0.935827	+	0.250754i	0.241489	+	0.970403i	$0.422364\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−2.05890	+	0.872317i	−0.920767	+	0.390112i
$5$	−2.05890	+	0.872317i	−0.920767	+	0.390112i
$6$	1.18658	+	1.18658i	0.484420	+	0.484420i
$7$	2.36181	+	0.632846i	0.892681	+	0.239193i	0.675870	−	0.737021i	$-0.263768\pi$
$7$	2.36181	+	0.632846i	0.892681	+	0.239193i	0.216811	+	0.976214i	$0.430435\pi$
$8$			1.00000i			0.353553i
$9$	−0.159392	−	0.0920251i	−0.0531307	−	0.0306750i
$10$	−2.21922	−	0.274000i	−0.701778	−	0.0866465i
$11$			3.49322i			1.05324i	0.850099	+	0.526622i	$0.176542\pi$
$11$			3.49322i			1.05324i	−0.850099	+	0.526622i	$0.823458\pi$
$12$	0.434319	+	1.62090i	0.125377	+	0.467914i
$13$	2.56752	−	1.48236i	0.712102	−	0.411132i	−0.0997371	−	0.995014i	$-0.531800\pi$
$13$	2.56752	−	1.48236i	0.712102	−	0.411132i	0.811839	+	0.583882i	$0.198467\pi$
$14$	1.72897	+	1.72897i	0.462086	+	0.462086i
$15$	−3.71613	+	0.519721i	−0.959501	+	0.134191i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.10658	−	1.91666i	0.268386	−	0.464858i	−0.700059	−	0.714085i	$-0.746843\pi$
$17$	1.10658	−	1.91666i	0.268386	−	0.464858i	0.968445	+	0.249227i	$0.0801765\pi$
$18$	−0.0920251	−	0.159392i	−0.0216905	−	0.0375691i
$19$	−1.37008	−	0.367111i	−0.314317	−	0.0842211i	0.0982116	−	0.995166i	$-0.468688\pi$
$19$	−1.37008	−	0.367111i	−0.314317	−	0.0842211i	−0.412529	+	0.910944i	$0.635354\pi$
$20$	−1.78490	−	1.34690i	−0.399115	−	0.301176i
$21$	3.55340	+	2.05156i	0.775416	+	0.447687i
$22$	−1.74661	+	3.02521i	−0.372378	+	0.644978i
$23$			2.35663i			0.491391i	0.969347	+	0.245696i	$0.0790164\pi$
$23$			2.35663i			0.491391i	−0.969347	+	0.245696i	$0.920984\pi$
$24$	−0.434319	+	1.62090i	−0.0886550	+	0.330865i
$25$	3.47813	−	3.59203i	0.695625	−	0.718405i
$26$	2.96472			0.581428
$27$	−3.77813	−	3.77813i	−0.727102	−	0.727102i
$28$	0.632846	+	2.36181i	0.119597	+	0.446340i
$29$	−2.69380	−	2.69380i	−0.500226	−	0.500226i	0.411282	−	0.911508i	$-0.365081\pi$
$29$	−2.69380	−	2.69380i	−0.500226	−	0.500226i	−0.911508	+	0.411282i	$0.865081\pi$
$30$	−3.47813	−	1.40797i	−0.635016	−	0.257060i
$31$	1.18350	−	1.18350i	0.212562	−	0.212562i	−0.592793	−	0.805355i	$-0.701975\pi$
$31$	1.18350	−	1.18350i	0.212562	−	0.212562i	0.805355	+	0.592793i	$0.201975\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−1.51717	+	5.66216i	−0.264105	+	0.985655i
$34$	1.91666	−	1.10658i	0.328704	−	0.189777i
$35$	−5.41477	+	0.757284i	−0.915264	+	0.128004i
$36$		−	0.184050i		−	0.0306750i
$37$	1.25090	−	5.95275i	0.205647	−	0.978626i
$37$	1.25090	−	5.95275i	0.205647	−	0.978626i
$38$	−1.00297	−	1.00297i	−0.162703	−	0.162703i
$39$	4.80551	−	1.28763i	0.769497	−	0.206186i
$40$	−0.872317	−	2.05890i	−0.137925	−	0.325540i
$41$	2.80211	−	1.61780i	0.437615	−	0.252657i	−0.264970	−	0.964257i	$-0.585362\pi$
$41$	2.80211	−	1.61780i	0.437615	−	0.252657i	0.702586	+	0.711599i	$0.252029\pi$
$42$	2.05156	+	3.55340i	0.316562	+	0.548302i
$43$		−	9.95193i		−	1.51766i	−0.651291	−	0.758828i	$-0.725772\pi$
$43$		−	9.95193i		−	1.51766i	0.651291	−	0.758828i	$-0.274228\pi$
$44$	−3.02521	+	1.74661i	−0.456068	+	0.263311i
$45$	0.408447	+	0.0504298i	0.0608877	+	0.00751763i
$46$	−1.17832	+	2.04090i	−0.173733	+	0.300915i
$47$	−7.46221	+	7.46221i	−1.08847	+	1.08847i	−0.0927889	+	0.995686i	$0.529578\pi$
$47$	−7.46221	+	7.46221i	−1.08847	+	1.08847i	−0.995686	+	0.0927889i	$0.970422\pi$
$48$	−1.18658	+	1.18658i	−0.171268	+	0.171268i
$49$	−0.884516	−	0.510676i	−0.126359	−	0.0729537i
$50$	4.80816	−	1.37172i	0.679976	−	0.193991i
$51$	2.62610	−	2.62610i	0.367728	−	0.367728i
$52$	2.56752	+	1.48236i	0.356051	+	0.205566i
$53$	8.34541	−	2.23615i	1.14633	−	0.307158i	0.364837	−	0.931071i	$-0.381125\pi$
$53$	8.34541	−	2.23615i	1.14633	−	0.307158i	0.781494	+	0.623913i	$0.214458\pi$
$54$	−1.38289	−	5.16103i	−0.188188	−	0.702327i
$55$	−3.04719	−	7.19218i	−0.410883	−	0.969793i
$56$	−0.632846	+	2.36181i	−0.0845675	+	0.315610i
$57$	−2.06132	−	1.19010i	−0.273028	−	0.157633i
$58$	−0.985999	−	3.67980i	−0.129468	−	0.483181i
$59$	−0.795776	−	2.96988i	−0.103601	−	0.386645i	0.894581	−	0.446905i	$-0.147474\pi$
$59$	−0.795776	−	2.96988i	−0.103601	−	0.386645i	−0.998183	+	0.0602597i	$0.980807\pi$
$60$	−2.30816	−	2.95840i	−0.297982	−	0.381928i
$61$	−3.62907	−	0.972406i	−0.464654	−	0.124504i	0.0188938	−	0.999821i	$-0.493986\pi$
$61$	−3.62907	−	0.972406i	−0.464654	−	0.124504i	−0.483548	+	0.875318i	$0.660652\pi$
$62$	1.61669	−	0.433190i	0.205319	−	0.0550152i
$63$	−0.318216	−	0.318216i	−0.0400915	−	0.0400915i
$64$	−1.00000			−0.125000
$65$	−3.99317	+	5.29171i	−0.495292	+	0.656356i
$66$	−4.14499	+	4.14499i	−0.510212	+	0.510212i
$67$	−2.04187	+	7.62035i	−0.249454	+	0.930974i	0.721639	+	0.692270i	$0.243389\pi$
$67$	−2.04187	+	7.62035i	−0.249454	+	0.930974i	−0.971092	+	0.238704i	$0.923277\pi$
$68$	2.21317			0.268386
$69$	−1.02353	+	3.81986i	−0.123218	+	0.459857i
$70$	−5.06797	−	2.05156i	−0.605739	−	0.245208i
$71$	2.78149	+	4.81768i	0.330102	+	0.571754i	0.982532	−	0.186096i	$-0.0595834\pi$
$71$	2.78149	+	4.81768i	0.330102	+	0.571754i	−0.652429	+	0.757850i	$0.726250\pi$
$72$	0.0920251	−	0.159392i	0.0108453	−	0.0187845i
$73$	−6.28228	+	6.28228i	−0.735285	+	0.735285i	−0.971662	−	0.236376i	$-0.924040\pi$
$73$	−6.28228	+	6.28228i	−0.735285	+	0.735285i	0.236376	+	0.971662i	$0.424040\pi$
$74$	4.05969	−	4.52978i	0.471929	−	0.526577i
$75$	7.19778	−	4.31170i	0.831128	−	0.497872i
$76$	−0.367111	−	1.37008i	−0.0421105	−	0.157159i
$77$	−2.21067	+	8.25032i	−0.251929	+	0.940211i
$78$	4.80551	+	1.28763i	0.544117	+	0.145796i
$79$	14.7958	+	3.96452i	1.66466	+	0.446043i	0.963662	−	0.267123i	$-0.0860732\pi$
$79$	14.7958	+	3.96452i	1.66466	+	0.446043i	0.700994	+	0.713167i	$0.252740\pi$
$80$	0.274000	−	2.21922i	0.0306342	−	0.248116i
$81$	−4.20699	−	7.28672i	−0.467443	−	0.809635i
$82$	3.23559			0.357312
$83$	10.0566	−	2.69465i	1.10385	−	0.295777i	0.339521	−	0.940599i	$-0.389735\pi$
$83$	10.0566	−	2.69465i	1.10385	−	0.295777i	0.764333	+	0.644822i	$0.223068\pi$
$84$			4.10312i			0.447687i
$85$	−0.606408	+	4.91150i	−0.0657742	+	0.532726i
$86$	4.97597	−	8.61863i	0.536572	−	0.929371i
$87$	−3.19641	−	5.53635i	−0.342691	−	0.593559i
$88$	−3.49322			−0.372378
$89$	−7.87485	+	2.11006i	−0.834732	+	0.223666i	−0.650777	−	0.759269i	$-0.725557\pi$
$89$	−7.87485	+	2.11006i	−0.834732	+	0.223666i	−0.183955	+	0.982935i	$0.558890\pi$
$90$	0.328511	+	0.247897i	0.0346281	+	0.0261306i
$91$	7.00210	−	1.87621i	0.734019	−	0.196680i
$92$	−2.04090	+	1.17832i	−0.212779	+	0.122848i
$93$	2.43234	−	1.40431i	0.252222	−	0.145621i
$94$	−10.1936	+	2.73136i	−1.05139	+	0.281718i
$95$	3.14109	−	0.439298i	0.322269	−	0.0450710i
$96$	−1.62090	+	0.434319i	−0.165432	+	0.0443275i
$97$	−10.8299			−1.09961			−0.549803	−	0.835294i	$-0.685297\pi$
$97$	−10.8299			−1.09961			−0.549803	+	0.835294i	$0.685297\pi$
$98$	−0.510676	−	0.884516i	−0.0515860	−	0.0893496i
$99$	0.321464	−	0.556791i	0.0323083	−	0.0559596i
$100$	4.84985	+	1.21613i	0.484985	+	0.121613i
$101$		−	5.97730i		−	0.594763i	−0.954759	−	0.297382i	$-0.903887\pi$
$101$		−	5.97730i		−	0.594763i	0.954759	−	0.297382i	$-0.0961134\pi$
$102$	3.58732	−	0.961220i	0.355198	−	0.0951749i
$103$	4.06301			0.400341			0.200170	−	0.979761i	$-0.435850\pi$
$103$	4.06301			0.400341			0.200170	+	0.979761i	$0.435850\pi$
$104$	1.48236	+	2.56752i	0.145357	+	0.251766i
$105$	−9.10571	−	1.12426i	−0.888626	−	0.109716i
$106$	8.34541	+	2.23615i	0.810578	+	0.217194i
$107$	−18.9567	−	5.07945i	−1.83262	−	0.491049i	−0.834424	−	0.551123i	$-0.814200\pi$
$107$	−18.9567	−	5.07945i	−1.83262	−	0.491049i	−0.998194	+	0.0600742i	$0.980866\pi$
$108$	1.38289	−	5.16103i	0.133069	−	0.496620i
$109$	−3.99357	−	14.9042i	−0.382515	−	1.42756i	−0.842047	−	0.539404i	$-0.818650\pi$
$109$	−3.99357	−	14.9042i	−0.382515	−	1.42756i	0.459533	−	0.888161i	$-0.348017\pi$
$110$	0.957143	−	7.75221i	0.0912600	−	0.739144i
$111$	4.61298	−	9.10552i	0.437845	−	0.864258i
$112$	−1.72897	+	1.72897i	−0.163372	+	0.163372i
$113$	−2.01671	+	3.49304i	−0.189716	+	0.328598i	−0.945156	−	0.326621i	$-0.894090\pi$
$113$	−2.01671	+	3.49304i	−0.189716	+	0.328598i	0.755440	+	0.655218i	$0.227423\pi$
$114$	−1.19010	−	2.06132i	−0.111463	−	0.193060i
$115$	−2.05573	−	4.85206i	−0.191698	−	0.452457i
$116$	0.985999	−	3.67980i	0.0915477	−	0.341661i
$117$	−0.545656			−0.0504459
$118$	0.795776	−	2.96988i	0.0732572	−	0.273399i
$119$	3.82649	−	3.82649i	0.350774	−	0.350774i
$120$	−0.519721	−	3.71613i	−0.0474438	−	0.339235i
$121$	−1.20257			−0.109324
$122$	−2.65666	−	2.65666i	−0.240523	−	0.240523i
$123$	5.24457	−	1.40528i	0.472887	−	0.126710i
$124$	1.61669	+	0.433190i	0.145183	+	0.0389016i
$125$	−4.02772	+	10.4296i	−0.360250	+	0.932856i
$126$	−0.116475	−	0.434692i	−0.0103764	−	0.0387254i
$127$	4.70345	+	17.5535i	0.417363	+	1.55762i	0.780054	+	0.625712i	$0.215191\pi$
$127$	4.70345	+	17.5535i	0.417363	+	1.55762i	−0.362691	+	0.931910i	$0.618142\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	4.32231	−	16.1311i	0.380558	−	1.42026i
$130$	−6.10405	+	2.58617i	−0.535360	+	0.226822i
$131$	−0.340371	−	1.27028i	−0.0297384	−	0.110985i	0.949461	−	0.313884i	$-0.101630\pi$
$131$	−0.340371	−	1.27028i	−0.0297384	−	0.110985i	−0.979200	+	0.202899i	$0.934964\pi$
$132$	−5.66216	+	1.51717i	−0.492827	+	0.132053i
$133$	−3.00354	−	1.73410i	−0.260440	−	0.150365i
$134$	−5.57848	+	5.57848i	−0.481907	+	0.481907i
$135$	11.0745	+	4.48306i	0.953143	+	0.385841i
$136$	1.91666	+	1.10658i	0.164352	+	0.0948887i
$137$	−1.14123	+	1.14123i	−0.0975023	+	0.0975023i	−0.754175	−	0.656673i	$-0.771963\pi$
$137$	−1.14123	+	1.14123i	−0.0975023	+	0.0975023i	0.656673	+	0.754175i	$0.271963\pi$
$138$	−2.79633	+	2.79633i	−0.238040	+	0.238040i
$139$	6.46760	−	11.2022i	0.548574	−	0.950159i	−0.449798	−	0.893130i	$-0.648504\pi$
$139$	6.46760	−	11.2022i	0.548574	−	0.950159i	0.998373	−	0.0570285i	$-0.0181626\pi$
$140$	−3.36321	−	4.31069i	−0.284243	−	0.364320i
$141$	−15.3365	+	8.85451i	−1.29156	+	0.745685i
$142$			5.56298i			0.466835i
$143$	5.17820	+	8.96890i	0.433023	+	0.750017i
$144$	0.159392	−	0.0920251i	0.0132827	−	0.00766876i
$145$	7.89611	+	3.19641i	0.655736	+	0.265448i
$146$	−8.58176	+	2.29947i	−0.710231	+	0.190306i
$147$	−1.21192	−	1.21192i	−0.0999572	−	0.0999572i
$148$	5.78068	−	1.89306i	0.475169	−	0.155609i
$149$			12.7009i			1.04050i	0.854014	+	0.520250i	$0.174161\pi$
$149$			12.7009i			1.04050i	−0.854014	+	0.520250i	$0.825839\pi$
$150$	8.38931	−	0.135151i	0.684984	−	0.0110351i
$151$	1.78346	−	1.02968i	0.145136	−	0.0837943i	−0.425674	−	0.904877i	$-0.639963\pi$
$151$	1.78346	−	1.02968i	0.145136	−	0.0837943i	0.570810	+	0.821082i	$0.306629\pi$
$152$	0.367111	−	1.37008i	0.0297767	−	0.111128i
$153$	−0.352761	+	0.203667i	−0.0285190	+	0.0164655i
$154$	−6.03965	+	6.03965i	−0.486689	+	0.486689i
$155$	−1.40431	+	3.46908i	−0.112797	+	0.278644i
$156$	3.51788	+	3.51788i	0.281655	+	0.281655i
$157$	4.81173	+	17.9576i	0.384018	+	1.43318i	0.839709	+	0.543037i	$0.182726\pi$
$157$	4.81173	+	17.9576i	0.384018	+	1.43318i	−0.455690	+	0.890138i	$0.650608\pi$
$158$	10.8313	+	10.8313i	0.861690	+	0.861690i
$159$	14.4983			1.14979
$160$	1.34690	−	1.78490i	0.106482	−	0.141109i
$161$	−1.49138	+	5.56592i	−0.117537	+	0.438656i
$162$		−	8.41398i		−	0.661064i
$163$	−11.2446	+	19.4762i	−0.880743	+	1.52549i	−0.0302266	+	0.999543i	$0.509623\pi$
$163$	−11.2446	+	19.4762i	−0.880743	+	1.52549i	−0.850516	+	0.525949i	$0.823710\pi$
$164$	2.80211	+	1.61780i	0.218808	+	0.126329i
$165$	−1.81550	−	12.9813i	−0.141336	−	1.01059i
$166$	10.0566	+	2.69465i	0.780542	+	0.209146i
$167$	0.321723	+	0.557240i	0.0248957	+	0.0431206i	0.878205	−	0.478285i	$-0.158741\pi$
$167$	0.321723	+	0.557240i	0.0248957	+	0.0431206i	−0.853309	+	0.521405i	$0.825408\pi$
$168$	−2.05156	+	3.55340i	−0.158281	+	0.274151i
$169$	−2.10523	+	3.64637i	−0.161941	+	0.280490i
$170$	−2.98091	+	3.95028i	−0.228626	+	0.302972i
$171$	0.184596	+	0.184596i	0.0141164	+	0.0141164i
$172$	8.61863	−	4.97597i	0.657164	−	0.379414i
$173$	−0.741863	−	2.76867i	−0.0564028	−	0.210498i	0.931973	−	0.362527i	$-0.118086\pi$
$173$	−0.741863	−	2.76867i	−0.0564028	−	0.210498i	−0.988376	+	0.152029i	$0.951419\pi$
$174$		−	6.39282i		−	0.484639i
$175$	10.4879	−	6.28257i	0.792809	−	0.474918i
$176$	−3.02521	−	1.74661i	−0.228034	−	0.131656i
$177$		−	5.15950i		−	0.387811i
$178$	−7.87485	−	2.11006i	−0.590245	−	0.158156i
$179$	0.470627	+	0.470627i	0.0351763	+	0.0351763i	0.724476	−	0.689300i	$-0.242082\pi$
$179$	0.470627	+	0.470627i	0.0351763	+	0.0351763i	−0.689300	+	0.724476i	$0.742082\pi$
$180$	0.160550	+	0.378941i	0.0119667	+	0.0282446i
$181$	−3.15781	−	5.46948i	−0.234718	−	0.406543i	0.724473	−	0.689303i	$-0.242083\pi$
$181$	−3.15781	−	5.46948i	−0.234718	−	0.406543i	−0.959191	+	0.282760i	$0.908750\pi$
$182$	7.00210	+	1.87621i	0.519030	+	0.139074i
$183$	−5.46002	−	3.15234i	−0.403616	−	0.233028i
$184$	−2.35663			−0.173733
$185$	2.61721	+	13.3473i	0.192421	+	0.981312i
$186$	2.80863			0.205939
$187$	6.69530	+	3.86553i	0.489609	+	0.282676i
$188$	−10.1936	−	2.73136i	−0.743442	−	0.199205i
$189$	−6.53227	−	11.3142i	−0.475152	−	0.822988i
$190$	2.93991	+	1.19010i	0.213284	+	0.0863390i
$191$	4.70925	+	4.70925i	0.340749	+	0.340749i	0.856649	−	0.515900i	$-0.172542\pi$
$191$	4.70925	+	4.70925i	0.340749	+	0.340749i	−0.515900	+	0.856649i	$0.672542\pi$
$192$	−1.62090	−	0.434319i	−0.116978	−	0.0313443i
$193$			15.2352i			1.09665i	0.836264	+	0.548326i	$0.184735\pi$
$193$			15.2352i			1.09665i	−0.836264	+	0.548326i	$0.815265\pi$
$194$	−9.37894	−	5.41493i	−0.673369	−	0.388770i
$195$	−8.77083	+	6.84303i	−0.628092	+	0.490040i
$196$		−	1.02135i		−	0.0729537i
$197$	4.74662	+	17.7146i	0.338183	+	1.26212i	0.900377	+	0.435110i	$0.143291\pi$
$197$	4.74662	+	17.7146i	0.338183	+	1.26212i	−0.562194	+	0.827005i	$0.690043\pi$
$198$	0.556791	−	0.321464i	0.0395694	−	0.0228454i
$199$	−1.80868	−	1.80868i	−0.128214	−	0.128214i	0.640088	−	0.768302i	$-0.278898\pi$
$199$	−1.80868	−	1.80868i	−0.128214	−	0.128214i	−0.768302	+	0.640088i	$0.778898\pi$
$200$	3.59203	+	3.47813i	0.253995	+	0.245941i
$201$	−6.61932	+	11.4650i	−0.466891	+	0.808679i
$202$	2.98865	−	5.17649i	0.210281	−	0.364217i
$203$	−4.65749	−	8.06701i	−0.326892	−	0.566193i
$204$	3.58732	+	0.961220i	0.251163	+	0.0672988i
$205$	−4.35802	+	5.77520i	−0.304377	+	0.403358i
$206$	3.51867	+	2.03151i	0.245158	+	0.141542i
$207$	0.216869	−	0.375628i	0.0150734	−	0.0261080i
$208$			2.96472i			0.205566i
$209$	1.28240	−	4.78598i	0.0887054	−	0.331053i
$210$	−7.32365	−	5.52649i	−0.505380	−	0.381364i
$211$	−0.988606			−0.0680585			−0.0340292	−	0.999421i	$-0.510834\pi$
$211$	−0.988606			−0.0680585			−0.0340292	+	0.999421i	$0.510834\pi$
$212$	6.10927	+	6.10927i	0.419586	+	0.419586i
$213$	2.41611	+	9.01704i	0.165549	+	0.617837i
$214$	−13.8773	−	13.8773i	−0.948633	−	0.948633i
$215$	8.68124	+	20.4900i	0.592056	+	1.39741i
$216$	3.77813	−	3.77813i	0.257069	−	0.257069i
$217$	3.54417	−	2.04623i	0.240594	−	0.138907i
$218$	3.99357	−	14.9042i	0.270479	−	1.00944i
$219$	−12.9115	+	7.45444i	−0.872476	+	0.503724i
$220$	4.70501	−	6.23504i	0.317212	−	0.420366i
$221$		−	6.56141i		−	0.441368i
$222$	8.54772	−	5.57913i	0.573685	−	0.374446i
$223$	9.31830	+	9.31830i	0.624000	+	0.624000i	0.946552	−	0.322552i	$-0.104541\pi$
$223$	9.31830	+	9.31830i	0.624000	+	0.624000i	−0.322552	+	0.946552i	$0.604541\pi$
$224$	−2.36181	+	0.632846i	−0.157805	+	0.0422838i
$225$	−0.884942	+	0.252466i	−0.0589961	+	0.0168310i
$226$	−3.49304	+	2.01671i	−0.232354	+	0.134149i
$227$	−8.21358	−	14.2263i	−0.545154	−	0.944235i	−0.998597	−	0.0529497i	$-0.983138\pi$
$227$	−8.21358	−	14.2263i	−0.545154	−	0.944235i	0.453443	−	0.891285i	$-0.350196\pi$
$228$		−	2.38020i		−	0.157633i
$229$	−7.10267	+	4.10073i	−0.469357	+	0.270984i	−0.715971	−	0.698130i	$-0.754016\pi$
$229$	−7.10267	+	4.10073i	−0.469357	+	0.270984i	0.246613	+	0.969114i	$0.420682\pi$
$230$	0.645718	−	5.22987i	0.0425774	−	0.344848i
$231$	−7.16654	+	12.4128i	−0.471524	+	0.816703i
$232$	2.69380	−	2.69380i	0.176857	−	0.176857i
$233$	−20.0962	+	20.0962i	−1.31654	+	1.31654i	−0.400052	+	0.916493i	$0.631008\pi$
$233$	−20.0962	+	20.0962i	−1.31654	+	1.31654i	−0.916493	+	0.400052i	$0.868992\pi$
$234$	−0.472552	−	0.272828i	−0.0308917	−	0.0178353i
$235$	8.85451	−	21.8733i	0.577605	−	1.42686i
$236$	2.17410	−	2.17410i	0.141522	−	0.141522i
$237$	22.2606	+	12.8522i	1.44598	+	0.834839i
$238$	5.22708	−	1.40059i	0.338821	−	0.0907869i
$239$	2.33098	+	8.69934i	0.150779	+	0.562714i	0.999430	+	0.0337608i	$0.0107485\pi$
$239$	2.33098	+	8.69934i	0.150779	+	0.562714i	−0.848651	+	0.528953i	$0.822585\pi$
$240$	1.40797	−	3.47813i	0.0908844	−	0.224512i
$241$	6.50247	−	24.2676i	0.418861	−	1.56321i	−0.358113	−	0.933678i	$-0.616580\pi$
$241$	6.50247	−	24.2676i	0.418861	−	1.56321i	0.776974	−	0.629532i	$-0.216753\pi$
$242$	−1.04145	−	0.601283i	−0.0669472	−	0.0386520i
$243$	0.494331	+	1.84487i	0.0317113	+	0.118348i
$244$	−0.972406	−	3.62907i	−0.0622519	−	0.232327i
$245$	2.26660	+	0.279851i	0.144808	+	0.0178790i
$246$	5.24457	+	1.40528i	0.334382	+	0.0895973i
$247$	−4.06189	+	1.08838i	−0.258452	+	0.0692520i
$248$	1.18350	+	1.18350i	0.0751521	+	0.0751521i
$249$	17.4711			1.10718
$250$	−8.70293	+	7.01848i	−0.550422	+	0.443887i
$251$	14.1633	−	14.1633i	0.893979	−	0.893979i	−0.100916	−	0.994895i	$-0.532177\pi$
$251$	14.1633	−	14.1633i	0.893979	−	0.893979i	0.994895	+	0.100916i	$0.0321772\pi$
$252$	0.116475	−	0.434692i	0.00733726	−	0.0273830i
$253$	−8.23222			−0.517555
$254$	−4.70345	+	17.5535i	−0.295121	+	1.10140i
$255$	−3.11608	+	7.69767i	−0.195137	+	0.482047i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	12.3172	−	21.3340i	0.768327	−	1.33078i	−0.170143	−	0.985419i	$-0.554423\pi$
$257$	12.3172	−	21.3340i	0.768327	−	1.33078i	0.938470	−	0.345362i	$-0.112244\pi$
$258$	11.8088	−	11.8088i	0.735182	−	0.735182i
$259$	6.72157	−	13.2677i	0.417658	−	0.824412i
$260$	−6.57935	−	0.812333i	−0.408034	−	0.0503788i
$261$	0.181473	+	0.677267i	0.0112329	+	0.0419218i
$262$	0.340371	−	1.27028i	0.0210282	−	0.0784784i
$263$	−12.2296	−	3.27692i	−0.754112	−	0.202064i	−0.138771	−	0.990325i	$-0.544315\pi$
$263$	−12.2296	−	3.27692i	−0.754112	−	0.202064i	−0.615341	+	0.788261i	$0.710982\pi$
$264$	−5.66216	−	1.51717i	−0.348482	−	0.0933754i
$265$	−15.2317	+	11.8838i	−0.935678	+	0.730019i
$266$	−1.73410	−	3.00354i	−0.106324	−	0.184159i
$267$	−13.6808			−0.837250
$268$	−7.62035	+	2.04187i	−0.465487	+	0.124727i
$269$			30.2272i			1.84299i	0.388394	+	0.921493i	$0.373030\pi$
$269$			30.2272i			1.84299i	−0.388394	+	0.921493i	$0.626970\pi$
$270$	7.34929	+	9.41971i	0.447263	+	0.573265i
$271$	7.93046	−	13.7360i	0.481741	−	0.834400i	−0.518039	−	0.855357i	$-0.673338\pi$
$271$	7.93046	−	13.7360i	0.481741	−	0.834400i	0.999780	+	0.0209568i	$0.00667123\pi$
$272$	1.10658	+	1.91666i	0.0670964	+	0.116214i
$273$	12.1646			0.736234
$274$	−1.55896	+	0.417721i	−0.0941800	+	0.0252354i
$275$	12.5477	+	12.1498i	0.756656	+	0.732663i
$276$	−3.81986	+	1.02353i	−0.229929	+	0.0616092i
$277$	−3.66810	+	2.11778i	−0.220395	+	0.127245i	−0.606133	−	0.795363i	$-0.707280\pi$
$277$	−3.66810	+	2.11778i	−0.220395	+	0.127245i	0.385738	+	0.922608i	$0.373947\pi$
$278$	11.2022	−	6.46760i	0.671864	−	0.387901i
$279$	−0.297551	+	0.0797286i	−0.0178139	+	0.00477323i
$280$	−0.757284	−	5.41477i	−0.0452564	−	0.323595i
$281$	−15.6022	+	4.18061i	−0.930751	+	0.249394i	−0.692175	−	0.721730i	$-0.743347\pi$
$281$	−15.6022	+	4.18061i	−0.930751	+	0.249394i	−0.238576	+	0.971124i	$0.576681\pi$
$282$	−17.7090			−1.05456
$283$	−8.25105	−	14.2912i	−0.490474	−	0.849526i	0.509466	−	0.860491i	$-0.329843\pi$
$283$	−8.25105	−	14.2912i	−0.490474	−	0.849526i	−0.999940	+	0.0109650i	$0.996510\pi$
$284$	−2.78149	+	4.81768i	−0.165051	+	0.285877i
$285$	5.28219	+	0.652176i	0.312890	+	0.0386316i
$286$			10.3564i			0.612386i
$287$	7.64186	−	2.04763i	0.451085	−	0.120868i
$288$	0.184050			0.0108453
$289$	6.05095	+	10.4806i	0.355938	+	0.616503i
$290$	5.24002	+	6.71623i	0.307705	+	0.394390i
$291$	−17.5541	−	4.70362i	−1.02904	−	0.275731i
$292$	−8.58176	−	2.29947i	−0.502209	−	0.134567i
$293$	3.55993	−	13.2858i	0.207973	−	0.776167i	−0.780549	−	0.625094i	$-0.785061\pi$
$293$	3.55993	−	13.2858i	0.207973	−	0.776167i	0.988523	−	0.151073i	$-0.0482727\pi$
$294$	−0.443592	−	1.65551i	−0.0258708	−	0.0965512i
$295$	4.22910	+	5.42051i	0.246228	+	0.315594i
$296$	5.95275	+	1.25090i	0.345997	+	0.0727072i
$297$	13.1978	−	13.1978i	0.765817	−	0.765817i
$298$	−6.35046	+	10.9993i	−0.367872	+	0.637174i
$299$	3.49337	+	6.05069i	0.202027	+	0.349921i
$300$	7.33293	+	4.07761i	0.423367	+	0.235421i
$301$	6.29804	−	23.5046i	0.363013	−	1.35478i
$302$	2.05936			0.118503
$303$	2.59605	−	9.68860i	0.149139	−	0.556596i
$304$	1.00297	−	1.00297i	0.0575241	−	0.0575241i
$305$	8.32013	−	1.16361i	0.476409	−	0.0666283i
$306$	−0.407333			−0.0232857
$307$	−5.60560	−	5.60560i	−0.319928	−	0.319928i	0.528811	−	0.848740i	$-0.322638\pi$
$307$	−5.60560	−	5.60560i	−0.319928	−	0.319928i	−0.848740	+	0.528811i	$0.822638\pi$
$308$	−8.25032	+	2.21067i	−0.470106	+	0.125964i
$309$	6.58574	+	1.76464i	0.374650	+	0.100387i
$310$	−2.95071	+	2.30216i	−0.167589	+	0.130754i
$311$	6.86912	+	25.6359i	0.389512	+	1.45368i	0.830930	+	0.556377i	$0.187809\pi$
$311$	6.86912	+	25.6359i	0.389512	+	1.45368i	−0.441417	+	0.897302i	$0.645524\pi$
$312$	1.28763	+	4.80551i	0.0728978	+	0.272058i
$313$	−19.1806	−	11.0739i	−1.08415	−	0.625934i	−0.152137	−	0.988359i	$-0.548615\pi$
$313$	−19.1806	−	11.0739i	−1.08415	−	0.625934i	−0.932013	+	0.362425i	$0.881949\pi$
$314$	−4.81173	+	17.9576i	−0.271542	+	1.01341i
$315$	0.932761	+	0.377590i	0.0525551	+	0.0212748i
$316$	3.96452	+	14.7958i	0.223022	+	0.832328i
$317$	4.97383	−	1.33273i	0.279358	−	0.0748537i	−0.116420	−	0.993200i	$-0.537142\pi$
$317$	4.97383	−	1.33273i	0.279358	−	0.0748537i	0.395778	+	0.918346i	$0.370475\pi$
$318$	12.5559	+	7.24914i	0.704099	+	0.406512i
$319$	9.41003	−	9.41003i	0.526860	−	0.526860i
$320$	2.05890	−	0.872317i	0.115096	−	0.0487640i
$321$	−28.5209	−	16.4665i	−1.59188	−	0.919073i
$322$	−4.07453	+	4.07453i	−0.227065	+	0.227065i
$323$	−2.21973	+	2.21973i	−0.123509	+	0.123509i
$324$	4.20699	−	7.28672i	0.233722	−	0.404818i
$325$	3.60549	−	14.3784i	0.199996	−	0.797571i
$326$	−19.4762	+	11.2446i	−1.07869	+	0.622779i
$327$		−	25.8927i		−	1.43187i
$328$	1.61780	+	2.80211i	0.0893279	+	0.154720i
$329$	−22.3468	+	12.9019i	−1.23202	+	0.711305i
$330$	4.91836	−	12.1498i	0.270747	−	0.668827i
$331$	11.0330	−	2.95628i	0.606428	−	0.162492i	0.0574777	−	0.998347i	$-0.481694\pi$
$331$	11.0330	−	2.95628i	0.606428	−	0.162492i	0.548951	+	0.835855i	$0.315028\pi$
$332$	7.36193	+	7.36193i	0.404038	+	0.404038i
$333$	−0.747186	+	0.833707i	−0.0409455	+	0.0456869i
$334$			0.643446i			0.0352078i
$335$	−2.44337	−	17.4707i	−0.133495	−	0.954525i
$336$	−3.55340	+	2.05156i	−0.193854	+	0.111922i
$337$	6.43147	−	24.0026i	0.350344	−	1.30750i	−0.535898	−	0.844283i	$-0.680027\pi$
$337$	6.43147	−	24.0026i	0.350344	−	1.30750i	0.886243	−	0.463221i	$-0.153306\pi$
$338$	−3.64637	+	2.10523i	−0.198336	+	0.114510i
$339$	−4.78598	+	4.78598i	−0.259939	+	0.259939i
$340$	−4.55668	+	1.93058i	−0.247121	+	0.104701i
$341$	4.13421	+	4.13421i	0.223880	+	0.223880i
$342$	0.0675669	+	0.252163i	0.00365360	+	0.0136354i
$343$	−13.8686	−	13.8686i	−0.748836	−	0.748836i
$344$	9.95193			0.536572
$345$	−1.22479	−	8.75755i	−0.0659404	−	0.471491i
$346$	0.741863	−	2.76867i	0.0398828	−	0.148845i
$347$		−	22.1398i		−	1.18853i	−0.804270	−	0.594264i	$-0.797443\pi$
$347$		−	22.1398i		−	1.18853i	0.804270	−	0.594264i	$-0.202557\pi$
$348$	3.19641	−	5.53635i	0.171346	−	0.296779i
$349$	8.85764	+	5.11396i	0.474139	+	0.273744i	0.717971	−	0.696073i	$-0.245071\pi$
$349$	8.85764	+	5.11396i	0.474139	+	0.273744i	−0.243832	+	0.969818i	$0.578405\pi$
$350$	12.2241	−	0.196929i	0.653403	−	0.0105263i
$351$	−15.3010	−	4.09988i	−0.816706	−	0.218836i
$352$	−1.74661	−	3.02521i	−0.0930946	−	0.161244i
$353$	5.91121	−	10.2385i	0.314622	−	0.544941i	−0.664735	−	0.747079i	$-0.731456\pi$
$353$	5.91121	−	10.2385i	0.314622	−	0.544941i	0.979357	+	0.202138i	$0.0647889\pi$
$354$	2.57975	−	4.46825i	0.137112	−	0.237485i
$355$	−9.92936	−	7.49278i	−0.526996	−	0.397675i
$356$	−5.76479	−	5.76479i	−0.305533	−	0.305533i
$357$	7.86427	−	4.54044i	0.416221	−	0.240306i
$358$	0.172261	+	0.642888i	0.00910430	+	0.0339777i
$359$		−	10.0299i		−	0.529357i	−0.964337	−	0.264678i	$-0.914734\pi$
$359$		−	10.0299i		−	0.529357i	0.964337	−	0.264678i	$-0.0852658\pi$
$360$	−0.0504298	+	0.408447i	−0.00265788	+	0.0215271i
$361$	−14.7121	−	8.49406i	−0.774323	−	0.447056i
$362$		−	6.31561i		−	0.331941i
$363$	−1.94924	−	0.522297i	−0.102309	−	0.0274135i
$364$	5.12589	+	5.12589i	0.268670	+	0.268670i
$365$	7.45444	−	18.4147i	0.390183	−	0.963871i
$366$	−3.15234	−	5.46002i	−0.164776	−	0.285400i
$367$	1.28022	+	0.343035i	0.0668271	+	0.0179063i	0.292078	−	0.956395i	$-0.405653\pi$
$367$	1.28022	+	0.343035i	0.0668271	+	0.0179063i	−0.225251	+	0.974301i	$0.572320\pi$
$368$	−2.04090	−	1.17832i	−0.106389	−	0.0614239i
$369$	−0.595511			−0.0310011
$370$	−4.40708	+	12.8677i	−0.229113	+	0.668960i
$371$	21.1254			1.09678
$372$	2.43234	+	1.40431i	0.126111	+	0.0728103i
$373$	10.4548	+	2.80135i	0.541329	+	0.145049i	0.519115	−	0.854705i	$-0.326262\pi$
$373$	10.4548	+	2.80135i	0.541329	+	0.145049i	0.0222142	+	0.999753i	$0.492928\pi$
$374$	3.86553	+	6.69530i	0.199882	+	0.346206i
$375$	−11.0583	+	15.1561i	−0.571049	+	0.782657i
$376$	−7.46221	−	7.46221i	−0.384834	−	0.384834i
$377$	−10.9096	−	2.92321i	−0.561871	−	0.150553i
$378$		−	13.0645i		−	0.671967i
$379$	23.6555	+	13.6575i	1.21510	+	0.701540i	0.963867	−	0.266386i	$-0.0858294\pi$
$379$	23.6555	+	13.6575i	1.21510	+	0.701540i	0.251237	+	0.967926i	$0.419163\pi$
$380$	1.95099	+	2.50061i	0.100084	+	0.128279i
$381$			30.4953i			1.56232i
$382$	1.72370	+	6.43295i	0.0881923	+	0.329138i
$383$	−18.9456	+	10.9382i	−0.968075	+	0.558918i	−0.898649	−	0.438669i	$-0.855450\pi$
$383$	−18.9456	+	10.9382i	−0.968075	+	0.558918i	−0.0694263	+	0.997587i	$0.522117\pi$
$384$	−1.18658	−	1.18658i	−0.0605525	−	0.0605525i
$385$	−2.64536	−	18.9150i	−0.134820	−	0.963997i
$386$	−7.61759	+	13.1941i	−0.387725	+	0.671560i
$387$	−0.915827	+	1.58626i	−0.0465541	+	0.0806341i
$388$	−5.41493	−	9.37894i	−0.274902	−	0.476144i
$389$	−15.2282	−	4.08038i	−0.772100	−	0.206884i	−0.148801	−	0.988867i	$-0.547541\pi$
$389$	−15.2282	−	4.08038i	−0.772100	−	0.206884i	−0.623299	+	0.781984i	$0.714208\pi$
$390$	−11.0173	+	1.54082i	−0.557881	+	0.0780226i
$391$	4.51685	+	2.60781i	0.228427	+	0.131882i
$392$	0.510676	−	0.884516i	0.0257930	−	0.0446748i
$393$		−	2.20683i		−	0.111320i
$394$	−4.74662	+	17.7146i	−0.239131	+	0.892450i
$395$	−33.9214	+	4.74408i	−1.70677	+	0.238701i
$396$	0.642927			0.0323083
$397$	−20.1070	−	20.1070i	−1.00914	−	1.00914i	−0.999958	−	0.00918282i	$-0.997077\pi$
$397$	−20.1070	−	20.1070i	−1.00914	−	1.00914i	−0.00918282	−	0.999958i	$-0.502923\pi$
$398$	−0.662025	−	2.47071i	−0.0331843	−	0.123845i
$399$	−4.11529	−	4.11529i	−0.206022	−	0.206022i
$400$	1.37172	+	4.80816i	0.0685861	+	0.240408i
$401$	−12.4652	+	12.4652i	−0.622484	+	0.622484i	−0.946166	−	0.323682i	$-0.895079\pi$
$401$	−12.4652	+	12.4652i	−0.622484	+	0.622484i	0.323682	+	0.946166i	$0.395079\pi$
$402$	−11.4650	+	6.61932i	−0.571822	+	0.330142i
$403$	1.28428	−	4.79301i	0.0639748	−	0.238757i
$404$	5.17649	−	2.98865i	0.257540	−	0.148691i
$405$	15.0181	+	11.3328i	0.746255	+	0.563130i
$406$		−	9.31498i		−	0.462295i
$407$	20.7943	+	4.36967i	1.03073	+	0.216597i
$408$	2.62610	+	2.62610i	0.130011	+	0.130011i
$409$	34.1278	−	9.14453i	1.68751	−	0.452168i	0.717767	−	0.696283i	$-0.245164\pi$
$409$	34.1278	−	9.14453i	1.68751	−	0.452168i	0.969746	+	0.244116i	$0.0784976\pi$
$410$	−6.66176	+	2.82246i	−0.329001	+	0.139392i
$411$	−2.34549	+	1.35417i	−0.115694	+	0.0667962i
$412$	2.03151	+	3.51867i	0.100085	+	0.173353i
$413$		−	7.51790i		−	0.369932i
$414$	0.375628	−	0.216869i	0.0184611	−	0.0106585i
$415$	−18.3549	+	14.3206i	−0.901006	+	0.702968i
$416$	−1.48236	+	2.56752i	−0.0726786	+	0.125883i
$417$	15.3487	−	15.3487i	0.751627	−	0.751627i
$418$	3.50358	−	3.50358i	0.171366	−	0.171366i
$419$	−20.5291	−	11.8525i	−1.00291	−	0.579032i	−0.0938034	−	0.995591i	$-0.529903\pi$
$419$	−20.5291	−	11.8525i	−1.00291	−	0.579032i	−0.909109	+	0.416559i	$0.863236\pi$
$420$	−3.57922	−	8.44790i	−0.174648	−	0.412215i
$421$	−7.38381	+	7.38381i	−0.359865	+	0.359865i	−0.863763	−	0.503898i	$-0.831899\pi$
$421$	−7.38381	+	7.38381i	−0.359865	+	0.359865i	0.503898	+	0.863763i	$0.331899\pi$
$422$	−0.856158	−	0.494303i	−0.0416771	−	0.0240623i
$423$	1.87613	−	0.502707i	0.0912204	−	0.0244424i
$424$	2.23615	+	8.34541i	0.108597	+	0.405289i
$425$	−3.03585	−	10.6412i	−0.147260	−	0.516176i
$426$	−2.41611	+	9.01704i	−0.117061	+	0.436877i
$427$	−7.95579	−	4.59328i	−0.385008	−	0.222284i
$428$	−5.07945	−	18.9567i	−0.245524	−	0.916309i
$429$	4.49798	+	16.7867i	0.217164	+	0.810469i
$430$	−2.72683	+	22.0855i	−0.131500	+	1.06506i
$431$	6.79675	+	1.82118i	0.327388	+	0.0877234i	0.418769	−	0.908093i	$-0.362462\pi$
$431$	6.79675	+	1.82118i	0.327388	+	0.0877234i	−0.0913813	+	0.995816i	$0.529128\pi$
$432$	5.16103	−	1.38289i	0.248310	−	0.0665345i
$433$	−13.5027	−	13.5027i	−0.648898	−	0.648898i	0.303829	−	0.952727i	$-0.401735\pi$
$433$	−13.5027	−	13.5027i	−0.648898	−	0.648898i	−0.952727	+	0.303829i	$0.901735\pi$
$434$	4.09245			0.196444
$435$	11.4105	+	8.61049i	0.547093	+	0.412842i
$436$	10.9106	−	10.9106i	0.522525	−	0.522525i
$437$	0.865146	−	3.22877i	0.0413855	−	0.154453i
$438$	−14.9089			−0.712374
$439$	8.08839	−	30.1863i	0.386038	−	1.44071i	−0.450487	−	0.892783i	$-0.648750\pi$
$439$	8.08839	−	30.1863i	0.386038	−	1.44071i	0.836525	−	0.547929i	$-0.184584\pi$
$440$	7.19218	−	3.04719i	0.342874	−	0.145269i
$441$	0.0939899	+	0.162795i	0.00447571	+	0.00775216i
$442$	3.28070	−	5.68234i	0.156047	−	0.270282i
$443$	19.8158	−	19.8158i	0.941475	−	0.941475i	−0.0569049	−	0.998380i	$-0.518123\pi$
$443$	19.8158	−	19.8158i	0.941475	−	0.941475i	0.998380	+	0.0569049i	$0.0181232\pi$
$444$	10.1921	−	0.557805i	0.483696	−	0.0264723i
$445$	14.3729	−	11.2138i	0.681340	−	0.531584i
$446$	3.41073	+	12.7290i	0.161503	+	0.602737i
$447$	−5.51625	+	20.5869i	−0.260910	+	0.973728i
$448$	−2.36181	−	0.632846i	−0.111585	−	0.0298991i
$449$	−18.4205	−	4.93575i	−0.869315	−	0.232932i	−0.203523	−	0.979070i	$-0.565239\pi$
$449$	−18.4205	−	4.93575i	−0.869315	−	0.232932i	−0.665791	+	0.746138i	$0.731906\pi$
$450$	−0.892615	−	0.223829i	−0.0420783	−	0.0105514i
$451$	5.65132	+	9.78837i	0.266110	+	0.460916i
$452$	−4.03342			−0.189716
$453$	3.33802	−	0.894421i	0.156834	−	0.0420236i
$454$		−	16.4272i		−	0.770965i
$455$	−12.7800	+	9.97097i	−0.599134	+	0.467446i
$456$	1.19010	−	2.06132i	0.0557316	−	0.0965300i
$457$	16.4482	+	28.4891i	0.769414	+	1.33266i	0.937881	+	0.346956i	$0.112785\pi$
$457$	16.4482	+	28.4891i	0.769414	+	1.33266i	−0.168468	+	0.985707i	$0.553882\pi$
$458$	−8.20145			−0.383229
$459$	−11.4222	+	3.06057i	−0.533143	+	0.142855i
$460$	3.17414	−	4.20634i	0.147995	−	0.196122i
$461$	35.0617	−	9.39475i	1.63299	−	0.437557i	0.678206	−	0.734872i	$-0.262758\pi$
$461$	35.0617	−	9.39475i	1.63299	−	0.437557i	0.954780	+	0.297314i	$0.0960909\pi$
$462$	−12.4128	+	7.16654i	−0.577496	+	0.333418i
$463$	20.7278	−	11.9672i	0.963303	−	0.556163i	0.0661149	−	0.997812i	$-0.478940\pi$
$463$	20.7278	−	11.9672i	0.963303	−	0.556163i	0.897188	+	0.441649i	$0.145606\pi$
$464$	3.67980	−	0.985999i	0.170830	−	0.0457739i
$465$	−3.78294	+	5.01312i	−0.175430	+	0.232478i
$466$	−27.4519	+	7.35571i	−1.27168	+	0.340747i
$467$	−27.3563			−1.26590			−0.632948	−	0.774194i	$-0.718155\pi$
$467$	−27.3563			−1.26590			−0.632948	+	0.774194i	$0.718155\pi$
$468$	−0.272828	−	0.472552i	−0.0126115	−	0.0218437i
$469$	−9.64501	+	16.7056i	−0.445365	+	0.771395i
$470$	18.6049	−	14.5156i	0.858180	−	0.669555i
$471$			31.1974i			1.43750i
$472$	2.96988	−	0.795776i	0.136700	−	0.0366286i
$473$	34.7643			1.59846
$474$	12.8522	+	22.2606i	0.590320	+	1.02246i
$475$	−6.08398	+	3.64449i	−0.279152	+	0.167221i
$476$	5.22708	+	1.40059i	0.239583	+	0.0641960i
$477$	−1.53597	−	0.411563i	−0.0703274	−	0.0188442i
$478$	−2.33098	+	8.69934i	−0.106617	+	0.397899i
$479$	−5.57077	−	20.7904i	−0.254535	−	0.949938i	−0.968349	−	0.249602i	$-0.919700\pi$
$479$	−5.57077	−	20.7904i	−0.254535	−	0.949938i	0.713814	−	0.700336i	$-0.246966\pi$
$480$	2.95840	−	2.30816i	0.135032	−	0.105352i
$481$	−5.61239	−	17.1381i	−0.255903	−	0.781429i
$482$	17.7651	−	17.7651i	0.809177	−	0.809177i
$483$	−4.83477	+	8.37406i	−0.219989	+	0.381033i
$484$	−0.601283	−	1.04145i	−0.0273311	−	0.0473388i
$485$	22.2976	−	9.44708i	1.01248	−	0.428970i
$486$	−0.494331	+	1.84487i	−0.0224233	+	0.0836849i
$487$	18.4473			0.835928			0.417964	−	0.908464i	$-0.362744\pi$
$487$	18.4473			0.835928			0.417964	+	0.908464i	$0.362744\pi$
$488$	0.972406	−	3.62907i	0.0440187	−	0.164280i
$489$	−26.6852	+	26.6852i	−1.20675	+	1.20675i
$490$	1.82301	+	1.37566i	0.0823551	+	0.0621459i
$491$	−11.6850			−0.527338			−0.263669	−	0.964613i	$-0.584933\pi$
$491$	−11.6850			−0.527338			−0.263669	+	0.964613i	$0.584933\pi$
$492$	3.83929	+	3.83929i	0.173089	+	0.173089i
$493$	−8.14400	+	2.18218i	−0.366787	+	0.0982804i
$494$	−4.06189	−	1.08838i	−0.182753	−	0.0489685i
$495$	−0.176162	+	1.42679i	−0.00791790	+	0.0641297i
$496$	0.433190	+	1.61669i	0.0194508	+	0.0725914i
$497$	3.52051	+	13.1387i	0.157916	+	0.589352i
$498$	15.1304	+	8.73553i	0.678009	+	0.391448i
$499$	−9.24703	+	34.5104i	−0.413954	+	1.54490i	0.372968	+	0.927844i	$0.378340\pi$
$499$	−9.24703	+	34.5104i	−0.413954	+	1.54490i	−0.786922	+	0.617053i	$0.788327\pi$
$500$	−11.0462	+	1.72671i	−0.494001	+	0.0772209i
$501$	0.279461	+	1.04296i	0.0124854	+	0.0465961i
$502$	19.3474	−	5.18413i	0.863518	−	0.231379i
$503$	−8.21204	−	4.74122i	−0.366157	−	0.211401i	0.305621	−	0.952153i	$-0.401136\pi$
$503$	−8.21204	−	4.74122i	−0.366157	−	0.211401i	−0.671778	+	0.740752i	$0.734469\pi$
$504$	0.318216	−	0.318216i	0.0141745	−	0.0141745i
$505$	5.21410	+	12.3067i	0.232024	+	0.547639i
$506$	−7.12931	−	4.11611i	−0.316937	−	0.182983i
$507$	−4.99606	+	4.99606i	−0.221883	+	0.221883i
$508$	−12.8501	+	12.8501i	−0.570129	+	0.570129i
$509$	6.92535	−	11.9951i	0.306961	−	0.531672i	−0.670735	−	0.741697i	$-0.734021\pi$
$509$	6.92535	−	11.9951i	0.306961	−	0.531672i	0.977696	+	0.210025i	$0.0673547\pi$
$510$	−6.54744	+	5.10834i	−0.289926	+	0.226201i
$511$	−18.8133	+	10.8619i	−0.832251	+	0.480500i
$512$		−	1.00000i		−	0.0441942i
$513$	3.78934	+	6.56333i	0.167304	+	0.289778i
$514$	21.3340	−	12.3172i	0.941004	−	0.543289i
$515$	−8.36533	+	3.54424i	−0.368621	+	0.156178i
$516$	16.1311	−	4.32231i	0.710132	−	0.190279i
$517$	−26.0671	−	26.0671i	−1.14643	−	1.14643i
$518$	12.4549	−	8.12934i	0.547236	−	0.357183i
$519$		−	4.80994i		−	0.211133i
$520$	−5.29171	−	3.99317i	−0.232057	−	0.175112i
$521$	1.49191	−	0.861352i	0.0653615	−	0.0377365i	−0.466963	−	0.884277i	$-0.654652\pi$
$521$	1.49191	−	0.861352i	0.0653615	−	0.0377365i	0.532325	+	0.846540i	$0.321319\pi$
$522$	−0.181473	+	0.677267i	−0.00794287	+	0.0296432i
$523$	−29.0447	+	16.7690i	−1.27004	+	0.733256i	−0.974995	−	0.222228i	$-0.928667\pi$
$523$	−29.0447	+	16.7690i	−1.27004	+	0.733256i	−0.295042	+	0.955484i	$0.595334\pi$
$524$	0.929912	−	0.929912i	0.0406234	−	0.0406234i
$525$	19.7284	−	5.62834i	0.861020	−	0.245641i
$526$	−8.95272	−	8.95272i	−0.390357	−	0.390357i
$527$	−0.958721	−	3.57800i	−0.0417625	−	0.155860i
$528$	−4.14499	−	4.14499i	−0.180387	−	0.180387i
$529$	17.4463			0.758534
$530$	−19.1330	+	2.67585i	−0.831084	+	0.116231i
$531$	−0.146463	+	0.546606i	−0.00635594	+	0.0237207i
$532$		−	3.46819i		−	0.150365i
$533$	4.79631	−	8.30745i	0.207751	−	0.359835i
$534$	−11.8479	−	6.84039i	−0.512709	−	0.296013i
$535$	43.4609	−	6.07824i	1.87898	−	0.262785i
$536$	−7.62035	−	2.04187i	−0.329149	−	0.0881952i
$537$	0.558437	+	0.967241i	0.0240983	+	0.0417395i
$538$	−15.1136	+	26.1775i	−0.651594	+	1.12859i
$539$	1.78390	−	3.08981i	0.0768381	−	0.133087i
$540$	1.65482	+	11.8324i	0.0712120	+	0.509183i
$541$	−31.7923	−	31.7923i	−1.36686	−	1.36686i	−0.864881	−	0.501976i	$-0.832606\pi$
$541$	−31.7923	−	31.7923i	−1.36686	−	1.36686i	−0.501976	−	0.864881i	$-0.667394\pi$
$542$	13.7360	−	7.93046i	0.590010	−	0.340642i
$543$	−2.74299	−	10.2370i	−0.117713	−	0.439311i
$544$			2.21317i			0.0948887i
$545$	21.2236	+	27.2026i	0.909117	+	1.16523i
$546$	10.5348	+	6.08229i	0.450849	+	0.260298i
$547$			16.9250i			0.723662i	0.932244	+	0.361831i	$0.117848\pi$
$547$			16.9250i			0.723662i	−0.932244	+	0.361831i	$0.882152\pi$
$548$	−1.55896	−	0.417721i	−0.0665953	−	0.0178442i
$549$	0.488959	+	0.488959i	0.0208683	+	0.0208683i
$550$	4.79172	+	16.7959i	0.204320	+	0.716181i
$551$	2.70179	+	4.67964i	0.115100	+	0.199359i
$552$	−3.81986	−	1.02353i	−0.162584	−	0.0435643i
$553$	32.4359	+	18.7269i	1.37932	+	0.796349i
$554$	−4.23555			−0.179951
$555$	−1.55475	+	22.7713i	−0.0659954	+	0.966589i
$556$	12.9352			0.548574
$557$	13.9527	+	8.05558i	0.591194	+	0.341326i	0.765569	−	0.643353i	$-0.222457\pi$
$557$	13.9527	+	8.05558i	0.591194	+	0.341326i	−0.174376	+	0.984679i	$0.555791\pi$
$558$	−0.297551	−	0.0797286i	−0.0125964	−	0.00337518i
$559$	−14.7523	−	25.5518i	−0.623957	−	1.08073i
$560$	2.05156	−	5.06797i	0.0866942	−	0.214161i
$561$	9.17354	+	9.17354i	0.387307	+	0.387307i
$562$	−15.6022	−	4.18061i	−0.658141	−	0.176348i
$563$			9.61453i			0.405204i	0.979261	+	0.202602i	$0.0649398\pi$
$563$			9.61453i			0.405204i	−0.979261	+	0.202602i	$0.935060\pi$
$564$	−15.3365	−	8.85451i	−0.645782	−	0.372842i
$565$	1.10516	−	8.95103i	0.0464943	−	0.376572i
$566$		−	16.5021i		−	0.693635i
$567$	−5.32475	−	19.8722i	−0.223618	−	0.834555i
$568$	−4.81768	+	2.78149i	−0.202146	+	0.116709i
$569$	11.8059	+	11.8059i	0.494930	+	0.494930i	0.909855	−	0.414926i	$-0.136192\pi$
$569$	11.8059	+	11.8059i	0.494930	+	0.494930i	−0.414926	+	0.909855i	$0.636192\pi$
$570$	4.24842	+	3.20589i	0.177947	+	0.134280i
$571$	−2.04047	+	3.53420i	−0.0853911	+	0.147902i	−0.905558	−	0.424223i	$-0.860547\pi$
$571$	−2.04047	+	3.53420i	−0.0853911	+	0.147902i	0.820167	+	0.572125i	$0.193881\pi$
$572$	−5.17820	+	8.96890i	−0.216511	+	0.375009i
$573$	5.58790	+	9.67853i	0.233438	+	0.404326i
$574$	7.64186	+	2.04763i	0.318965	+	0.0854665i
$575$	8.46508	+	8.19666i	0.353018	+	0.341824i
$576$	0.159392	+	0.0920251i	0.00664134	+	0.00383438i
$577$	−18.0820	+	31.3189i	−0.752762	+	1.30382i	0.193718	+	0.981057i	$0.437945\pi$
$577$	−18.0820	+	31.3189i	−0.752762	+	1.30382i	−0.946479	+	0.322764i	$0.895388\pi$
$578$			12.1019i			0.503373i
$579$	−6.61693	+	24.6947i	−0.274990	+	1.02628i
$580$	1.17988	+	8.43644i	0.0489918	+	0.350304i
$581$	25.4571			1.05614
$582$	−12.8505	−	12.8505i	−0.532671	−	0.532671i
$583$	7.81135	+	29.1523i	0.323513	+	1.20737i
$584$	−6.28228	−	6.28228i	−0.259963	−	0.259963i
$585$	1.12345	−	0.475985i	0.0464490	−	0.0196796i
$586$	9.72590	−	9.72590i	0.401773	−	0.401773i
$587$	30.4198	−	17.5629i	1.25556	−	0.724897i	0.283350	−	0.959017i	$-0.408554\pi$
$587$	30.4198	−	17.5629i	1.25556	−	0.724897i	0.972208	+	0.234120i	$0.0752208\pi$
$588$	0.443592	−	1.65551i	0.0182934	−	0.0682720i
$589$	−2.05596	+	1.18701i	−0.0847142	+	0.0489098i
$590$	0.952253	+	6.80885i	0.0392036	+	0.280316i
$591$			30.7752i			1.26592i
$592$	4.52978	+	4.05969i	0.186173	+	0.166852i
$593$	−6.62602	−	6.62602i	−0.272098	−	0.272098i	0.557846	−	0.829944i	$-0.311628\pi$
$593$	−6.62602	−	6.62602i	−0.272098	−	0.272098i	−0.829944	+	0.557846i	$0.811628\pi$
$594$	18.0286	−	4.83075i	0.739722	−	0.198208i
$595$	−4.54044	+	11.2163i	−0.186140	+	0.459822i
$596$	−10.9993	+	6.35046i	−0.450550	+	0.260125i
$597$	−2.14615	−	3.71724i	−0.0878361	−	0.152137i
$598$			6.98674i			0.285709i
$599$	35.4303	−	20.4557i	1.44764	−	0.835797i	0.449302	−	0.893380i	$-0.351673\pi$
$599$	35.4303	−	20.4557i	1.44764	−	0.835797i	0.998341	+	0.0575829i	$0.0183393\pi$
$600$	4.31170	+	7.19778i	0.176024	+	0.293848i
$601$	−13.4363	+	23.2723i	−0.548078	+	0.949299i	0.450328	+	0.892863i	$0.351307\pi$
$601$	−13.4363	+	23.2723i	−0.548078	+	0.949299i	−0.998406	+	0.0564357i	$0.982026\pi$
$602$	17.2066	−	17.2066i	0.701287	−	0.701287i
$603$	1.02672	−	1.02672i	0.0418113	−	0.0418113i
$604$	1.78346	+	1.02968i	0.0725680	+	0.0418972i
$605$	2.47596	−	1.04902i	0.100662	−	0.0426487i
$606$	7.09255	−	7.09255i	0.288115	−	0.288115i
$607$	33.6155	+	19.4079i	1.36441	+	0.787743i	0.990207	−	0.139604i	$-0.0445828\pi$
$607$	33.6155	+	19.4079i	1.36441	+	0.787743i	0.374203	+	0.927347i	$0.377916\pi$
$608$	1.37008	−	0.367111i	0.0555640	−	0.0148883i
$609$	−4.04567	−	15.0986i	−0.163939	−	0.611828i
$610$	7.78725	+	3.15234i	0.315296	+	0.127635i
$611$	−8.09770	+	30.2210i	−0.327598	+	1.22261i
$612$	−0.352761	−	0.203667i	−0.0142595	−	0.00823274i
$613$	−0.798609	−	2.98045i	−0.0322555	−	0.120379i	0.947921	−	0.318506i	$-0.103181\pi$
$613$	−0.798609	−	2.98045i	−0.0322555	−	0.120379i	−0.980176	+	0.198126i	$0.936514\pi$
$614$	−2.05179	−	7.65739i	−0.0828036	−	0.309027i
$615$	−9.57220	+	7.46826i	−0.385988	+	0.301149i
$616$	−8.25032	−	2.21067i	−0.332415	−	0.0890703i
$617$	3.24389	−	0.869197i	0.130594	−	0.0349926i	−0.192930	−	0.981213i	$-0.561799\pi$
$617$	3.24389	−	0.869197i	0.130594	−	0.0349926i	0.323524	+	0.946220i	$0.395132\pi$
$618$	4.82110	+	4.82110i	0.193933	+	0.193933i
$619$	12.8047			0.514665			0.257332	−	0.966323i	$-0.417156\pi$
$619$	12.8047			0.514665			0.257332	+	0.966323i	$0.417156\pi$
$620$	−3.70647	+	0.518370i	−0.148856	+	0.0208182i
$621$	8.90367	−	8.90367i	0.357292	−	0.357292i
$622$	−6.86912	+	25.6359i	−0.275427	+	1.02791i
$623$	−19.9343			−0.798649
$624$	−1.28763	+	4.80551i	−0.0515465	+	0.192374i
$625$	−0.805288	−	24.9870i	−0.0322115	−	0.999481i
$626$	−11.0739	−	19.1806i	−0.442602	−	0.766610i
$627$	4.15728	−	7.20062i	0.166026	−	0.287565i
$628$	−13.1459	+	13.1459i	−0.524579	+	0.524579i
$629$	−10.0252	−	8.98476i	−0.399729	−	0.358246i
$630$	0.619000	+	0.793383i	0.0246615	+	0.0316091i
$631$	12.1780	+	45.4491i	0.484800	+	1.80930i	0.580959	+	0.813933i	$0.302678\pi$
$631$	12.1780	+	45.4491i	0.484800	+	1.80930i	−0.0961584	+	0.995366i	$0.530656\pi$
$632$	−3.96452	+	14.7958i	−0.157700	+	0.588545i
$633$	−1.60243	−	0.429370i	−0.0636909	−	0.0170659i
$634$	4.97383	+	1.33273i	0.197536	+	0.0529296i
$635$	−24.9961	−	32.0380i	−0.991942	−	1.27139i
$636$	7.24914	+	12.5559i	0.287447	+	0.497873i
$637$	−3.02802			−0.119974
$638$	12.8543	−	3.44431i	0.508908	−	0.136361i
$639$		−	1.02387i		−	0.0405036i
$640$	2.21922	+	0.274000i	0.0877223	+	0.0108308i
$641$	3.89777	−	6.75113i	0.153953	−	0.266654i	−0.778725	−	0.627366i	$-0.784133\pi$
$641$	3.89777	−	6.75113i	0.153953	−	0.266654i	0.932677	+	0.360712i	$0.117466\pi$
$642$	−16.4665	−	28.5209i	−0.649883	−	1.12563i
$643$	11.1150			0.438333			0.219167	−	0.975687i	$-0.429666\pi$
$643$	11.1150			0.438333			0.219167	+	0.975687i	$0.429666\pi$
$644$	−5.56592	+	1.49138i	−0.219328	+	0.0587687i
$645$	5.17223	+	36.9827i	0.203656	+	1.45619i
$646$	−3.03221	+	0.812478i	−0.119301	+	0.0319665i
$647$	−32.6007	+	18.8220i	−1.28167	+	0.739970i	−0.977153	−	0.212538i	$-0.931827\pi$
$647$	−32.6007	+	18.8220i	−1.28167	+	0.739970i	−0.304513	+	0.952508i	$0.598494\pi$
$648$	7.28672	−	4.20699i	0.286249	−	0.165266i
$649$	10.3744	−	2.77982i	0.407232	−	0.109117i
$650$	10.3117	−	10.6493i	0.404456	−	0.417701i
$651$	6.63345	−	1.77743i	0.259986	−	0.0696629i
$652$	−22.4891			−0.880743
$653$	−11.2471	−	19.4806i	−0.440135	−	0.762335i	0.557564	−	0.830134i	$-0.311736\pi$
$653$	−11.2471	−	19.4806i	−0.440135	−	0.762335i	−0.997699	+	0.0677982i	$0.978403\pi$
$654$	12.9464	−	22.4238i	0.506243	−	0.876838i
$655$	1.80888	+	2.31847i	0.0706788	+	0.0905902i
$656$			3.23559i			0.126329i
$657$	1.57947	−	0.423219i	0.0616211	−	0.0165113i
$658$	−25.8038			−1.00594
$659$	5.01498	+	8.68620i	0.195356	+	0.338366i	0.947017	−	0.321183i	$-0.104080\pi$
$659$	5.01498	+	8.68620i	0.195356	+	0.338366i	−0.751661	+	0.659549i	$0.770747\pi$
$660$	10.3344	−	8.06290i	0.402264	−	0.313848i
$661$	−2.00913	−	0.538344i	−0.0781459	−	0.0209391i	0.219534	−	0.975605i	$-0.429546\pi$
$661$	−2.00913	−	0.538344i	−0.0781459	−	0.0209391i	−0.297680	+	0.954666i	$0.596213\pi$
$662$	11.0330	+	2.95628i	0.428810	+	0.114899i
$663$	2.84974	−	10.6354i	0.110675	−	0.413044i
$664$	2.69465	+	10.0566i	0.104573	+	0.390271i
$665$	7.69667	+	0.950285i	0.298464	+	0.0368505i
$666$	−1.06394	+	0.348418i	−0.0412267	+	0.0135009i
$667$	6.34829	−	6.34829i	0.245807	−	0.245807i
$668$	−0.321723	+	0.557240i	−0.0124478	+	0.0215603i
$669$	11.0569	+	19.1511i	0.427485	+	0.740426i
$670$	6.61932	−	16.3517i	0.255727	−	0.631723i
$671$	3.39682	−	12.6771i	0.131133	−	0.489395i
$672$	−4.10312			−0.158281
$673$	−10.6266	+	39.6590i	−0.409625	+	1.52874i	0.385738	+	0.922609i	$0.373947\pi$
$673$	−10.6266	+	39.6590i	−0.409625	+	1.52874i	−0.795363	+	0.606134i	$0.792720\pi$
$674$	17.5711	−	17.5711i	0.676814	−	0.676814i
$675$	−26.7120	+	0.430328i	−1.02814	+	0.0165633i
$676$	−4.21046			−0.161941
$677$	31.0400	+	31.0400i	1.19296	+	1.19296i	0.976231	+	0.216732i	$0.0695397\pi$
$677$	31.0400	+	31.0400i	1.19296	+	1.19296i	0.216732	+	0.976231i	$0.430460\pi$
$678$	−6.53776	+	1.75179i	−0.251081	+	0.0672770i
$679$	−25.5781	−	6.85363i	−0.981598	−	0.263018i
$680$	−4.91150	−	0.606408i	−0.188347	−	0.0232547i
$681$	−7.13462	−	26.6268i	−0.273399	−	1.02034i
$682$	1.51323	+	5.64744i	0.0579444	+	0.216252i
$683$	−6.22979	−	3.59677i	−0.238376	−	0.137627i	0.376054	−	0.926598i	$-0.377281\pi$
$683$	−6.22979	−	3.59677i	−0.238376	−	0.137627i	−0.614430	+	0.788971i	$0.710614\pi$
$684$	−0.0675669	+	0.252163i	−0.00258348	+	0.00964169i
$685$	1.35417	−	3.34520i	0.0517401	−	0.127814i
$686$	−5.07628	−	18.9449i	−0.193813	−	0.723321i
$687$	−13.2937	+	3.56205i	−0.507188	+	0.135901i
$688$	8.61863	+	4.97597i	0.328582	+	0.189707i
$689$	18.1122	−	18.1122i	0.690021	−	0.690021i
$690$	3.31808	−	8.19666i	0.126317	−	0.312041i
$691$	−6.86509	−	3.96356i	−0.261160	−	0.150781i	0.363703	−	0.931515i	$-0.381512\pi$
$691$	−6.86509	−	3.96356i	−0.261160	−	0.150781i	−0.624864	+	0.780734i	$0.714846\pi$
$692$	2.02681	−	2.02681i	0.0770476	−	0.0770476i
$693$	1.11160	−	1.11160i	0.0422262	−	0.0422262i
$694$	11.0699	−	19.1736i	0.420208	−	0.727822i
$695$	−3.54425	+	28.7060i	−0.134441	+	1.08888i
$696$	5.53635	−	3.19641i	0.209855	−	0.121160i
$697$		−	7.16091i		−	0.271239i
$698$	5.11396	+	8.85764i	0.193566	+	0.335267i
$699$	−41.3020	+	23.8457i	−1.56219	+	0.901929i
$700$	10.6848	+	5.94148i	0.403848	+	0.224567i
$701$	−34.5973	+	9.27031i	−1.30672	+	0.350135i	−0.843987	−	0.536363i	$-0.819798\pi$
$701$	−34.5973	+	9.27031i	−1.30672	+	0.350135i	−0.462733	+	0.886498i	$0.653131\pi$
$702$	−11.2011	−	11.2011i	−0.422758	−	0.422758i
$703$	−3.89915	+	7.69651i	−0.147059	+	0.290279i
$704$		−	3.49322i		−	0.131656i
$705$	23.8523	−	31.6088i	0.898329	−	1.19046i
$706$	10.2385	−	5.91121i	0.385332	−	0.222471i
$707$	3.78271	−	14.1173i	0.142263	−	0.530934i
$708$	4.46825	−	2.57975i	0.167927	−	0.0969529i
$709$	−3.06214	+	3.06214i	−0.115001	+	0.115001i	−0.762266	−	0.647264i	$-0.775913\pi$
$709$	−3.06214	+	3.06214i	−0.115001	+	0.115001i	0.647264	+	0.762266i	$0.275913\pi$
$710$	−4.85269	−	11.4536i	−0.182118	−	0.429847i
$711$	−1.99350	−	1.99350i	−0.0747620	−	0.0747620i
$712$	−2.11006	−	7.87485i	−0.0790778	−	0.295122i
$713$	2.78906	+	2.78906i	0.104451	+	0.104451i
$714$	9.08088			0.339843
$715$	−18.4851	−	13.9490i	−0.691304	−	0.521664i
$716$	−0.172261	+	0.642888i	−0.00643771	+	0.0240259i
$717$			15.1132i			0.564411i
$718$	5.01494	−	8.68613i	0.187156	−	0.324163i
$719$	−23.9560	−	13.8310i	−0.893409	−	0.515810i	−0.0183527	−	0.999832i	$-0.505842\pi$
$719$	−23.9560	−	13.8310i	−0.893409	−	0.515810i	−0.875056	+	0.484022i	$0.839175\pi$
$720$	−0.247897	+	0.328511i	−0.00923858	+	0.0122429i
$721$	9.59607	+	2.57126i	0.357376	+	0.0957587i
$722$	−8.49406	−	14.7121i	−0.316116	−	0.547529i
$723$	21.0797	−	36.5111i	0.783963	−	1.35786i
$724$	3.15781	−	5.46948i	0.117359	−	0.203272i
$725$	−19.0456	+	0.306823i	−0.707335	+	0.0113951i
$726$	−1.42694	−	1.42694i	−0.0529588	−	0.0529588i
$727$	−19.6374	+	11.3377i	−0.728312	+	0.420491i	−0.817804	−	0.575496i	$-0.804809\pi$
$727$	−19.6374	+	11.3377i	−0.728312	+	0.420491i	0.0894923	+	0.995988i	$0.471476\pi$
$728$	1.87621	+	7.00210i	0.0695369	+	0.259515i
$729$			28.4470i			1.05359i
$730$	15.6631	−	12.2204i	0.579717	−	0.452297i
$731$	−19.0745	−	11.0126i	−0.705494	−	0.407317i
$732$		−	6.30469i		−	0.233028i
$733$	−13.3187	−	3.56873i	−0.491937	−	0.131814i	0.00431824	−	0.999991i	$-0.498625\pi$
$733$	−13.3187	−	3.56873i	−0.491937	−	0.131814i	−0.496256	+	0.868176i	$0.665292\pi$
$734$	0.937188	+	0.937188i	0.0345922	+	0.0345922i
$735$	3.55239	+	1.43804i	0.131032	+	0.0530428i
$736$	−1.17832	−	2.04090i	−0.0434333	−	0.0752286i
$737$	−26.6195	−	7.13268i	−0.980543	−	0.262736i
$738$	−0.515728	−	0.297756i	−0.0189842	−	0.0109605i
$739$	−0.943189			−0.0346958			−0.0173479	−	0.999850i	$-0.505522\pi$
$739$	−0.943189			−0.0346958			−0.0173479	+	0.999850i	$0.505522\pi$
$740$	−10.2505	+	8.94021i	−0.376816	+	0.328649i
$741$	−7.05662			−0.259232
$742$	18.2952	+	10.5627i	0.671636	+	0.387769i
$743$	5.08817	+	1.36337i	0.186667	+	0.0500172i	0.350941	−	0.936397i	$-0.385862\pi$
$743$	5.08817	+	1.36337i	0.186667	+	0.0500172i	−0.164275	+	0.986415i	$0.552528\pi$
$744$	1.40431	+	2.43234i	0.0514847	+	0.0891741i
$745$	−11.0792	−	26.1499i	−0.405912	−	0.958059i
$746$	7.65344	+	7.65344i	0.280212	+	0.280212i
$747$	−1.85092	−	0.495951i	−0.0677215	−	0.0181459i
$748$			7.73107i			0.282676i
$749$	−41.5578	−	23.9934i	−1.51849	−	0.876699i
$750$	−17.1548	+	7.59640i	−0.626406	+	0.277381i
$751$		−	31.9929i		−	1.16744i	−0.811956	−	0.583718i	$-0.801597\pi$
$751$		−	31.9929i		−	1.16744i	0.811956	−	0.583718i	$-0.198403\pi$
$752$	−2.73136	−	10.1936i	−0.0996024	−	0.371721i
$753$	29.1087	−	16.8059i	1.06078	−	0.612441i
$754$	−7.98635	−	7.98635i	−0.290846	−	0.290846i
$755$	−2.77376	+	3.67576i	−0.100947	+	0.133774i
$756$	6.53227	−	11.3142i	0.237576	−	0.411494i
$757$	17.6478	−	30.5668i	0.641419	−	1.11097i	−0.343697	−	0.939081i	$-0.611679\pi$
$757$	17.6478	−	30.5668i	0.641419	−	1.11097i	0.985116	−	0.171890i	$-0.0549873\pi$
$758$	13.6575	+	23.6555i	0.496064	+	0.859208i
$759$	−13.3436	−	3.57541i	−0.484342	−	0.129779i
$760$	0.439298	+	3.14109i	0.0159350	+	0.113939i
$761$	37.6582	+	21.7420i	1.36511	+	0.788147i	0.990299	−	0.138954i	$-0.0443741\pi$
$761$	37.6582	+	21.7420i	1.36511	+	0.788147i	0.374811	+	0.927101i	$0.377707\pi$
$762$	−15.2476	+	26.4097i	−0.552364	+	0.956722i
$763$		−	37.7283i		−	1.36585i
$764$	−1.72370	+	6.43295i	−0.0623614	+	0.232736i
$765$	0.548637	−	0.727049i	0.0198360	−	0.0262865i
$766$	−21.8765			−0.790430
$767$	−6.44559	−	6.44559i	−0.232737	−	0.232737i
$768$	−0.434319	−	1.62090i	−0.0156721	−	0.0584892i
$769$	33.4001	+	33.4001i	1.20444	+	1.20444i	0.972803	+	0.231635i	$0.0744075\pi$
$769$	33.4001	+	33.4001i	1.20444	+	1.20444i	0.231635	+	0.972803i	$0.425593\pi$
$770$	7.16654	−	17.7035i	0.258264	−	0.637991i
$771$	29.2308	−	29.2308i	1.05272	−	1.05272i
$772$	−13.1941	+	7.61759i	−0.474865	+	0.274163i
$773$	4.91951	−	18.3598i	0.176942	−	0.660358i	−0.819270	−	0.573407i	$-0.805621\pi$
$773$	4.91951	−	18.3598i	0.176942	−	0.660358i	0.996213	−	0.0869502i	$-0.0277121\pi$
$774$	−1.58626	+	0.915827i	−0.0570169	+	0.0329187i
$775$	−0.134800	−	8.36750i	−0.00484216	−	0.300569i
$776$		−	10.8299i		−	0.388770i
$777$	16.6574	−	18.5862i	0.597580	−	0.666777i
$778$	−11.1478	−	11.1478i	−0.399668	−	0.399668i
$779$	−4.43302	+	1.18782i	−0.158829	+	0.0425582i
$780$	−10.3117	−	4.17424i	−0.369216	−	0.149462i
$781$	−16.8292	+	9.71635i	−0.602197	+	0.347678i
$782$	2.60781	+	4.51685i	0.0932550	+	0.161522i
$783$			20.3551i			0.727431i
$784$	0.884516	−	0.510676i	0.0315899	−	0.0182384i
$785$	−25.5716	−	32.7756i	−0.912691	−	1.16981i
$786$	1.10342	−	1.91117i	0.0393575	−	0.0681693i
$787$	20.7014	−	20.7014i	0.737927	−	0.737927i	−0.234250	−	0.972176i	$-0.575263\pi$
$787$	20.7014	−	20.7014i	0.737927	−	0.737927i	0.972176	+	0.234250i	$0.0752634\pi$
$788$	−12.9680	+	12.9680i	−0.461966	+	0.461966i
$789$	−18.3998	−	10.6231i	−0.655050	−	0.378194i
$790$	−31.7488	−	12.8522i	−1.12957	−	0.457260i
$791$	−6.97364	+	6.97364i	−0.247954	+	0.247954i
$792$	0.556791	+	0.321464i	0.0197847	+	0.0114227i
$793$	−10.7592	+	2.88291i	−0.382069	+	0.102375i
$794$	−7.35967	−	27.4667i	−0.261185	−	0.974755i
$795$	−29.8505	+	12.6471i	−1.05869	+	0.448546i
$796$	0.662025	−	2.47071i	0.0234648	−	0.0875720i
$797$	−32.5161	−	18.7732i	−1.15178	−	0.664980i	−0.202459	−	0.979291i	$-0.564893\pi$
$797$	−32.5161	−	18.7732i	−1.15178	−	0.664980i	−0.949320	+	0.314310i	$0.898227\pi$
$798$	−1.50630	−	5.62159i	−0.0533225	−	0.199002i
$799$	6.04495	+	22.5600i	0.213855	+	0.798117i
$800$	−1.21613	+	4.84985i	−0.0429968	+	0.171468i
$801$	1.44937	+	0.388357i	0.0512109	+	0.0137219i
$802$	−17.0278	+	4.56259i	−0.601273	+	0.161111i
$803$	−21.9454	−	21.9454i	−0.774435	−	0.774435i
$804$	−13.2386			−0.466891
$805$	−1.78464	−	12.7606i	−0.0629003	−	0.449753i
$806$	3.50873	−	3.50873i	0.123590	−	0.123590i
$807$	−13.1283	+	48.9953i	−0.462136	+	1.72472i
$808$	5.97730			0.210281
$809$	11.3061	−	42.1949i	0.397501	−	1.48350i	−0.419976	−	0.907535i	$-0.637962\pi$
$809$	11.3061	−	42.1949i	0.397501	−	1.48350i	0.817478	−	0.575960i	$-0.195372\pi$
$810$	7.33966	+	17.3235i	0.257889	+	0.608686i
$811$	7.61395	+	13.1877i	0.267362	+	0.463084i	0.968180	−	0.250256i	$-0.0805148\pi$
$811$	7.61395	+	13.1877i	0.267362	+	0.463084i	−0.700818	+	0.713340i	$0.747181\pi$
$812$	4.65749	−	8.06701i	0.163446	−	0.283096i
$813$	18.8203	−	18.8203i	0.660056	−	0.660056i
$814$	15.8235	+	14.1814i	0.554614	+	0.497057i
$815$	6.16203	−	49.9083i	0.215847	−	1.74821i
$816$	0.961220	+	3.58732i	0.0336494	+	0.125581i
$817$	−3.65347	+	13.6349i	−0.127819	+	0.477026i
$818$	34.1278	+	9.14453i	1.19325	+	0.319731i
$819$	−1.28874	−	0.345316i	−0.0450321	−	0.0120663i
$820$	−7.18048	−	0.886554i	−0.250753	−	0.0309598i
$821$	−24.1313	−	41.7967i	−0.842189	−	1.45871i	−0.888040	−	0.459766i	$-0.847933\pi$
$821$	−24.1313	−	41.7967i	−0.842189	−	1.45871i	0.0458512	−	0.998948i	$-0.485400\pi$
$822$	−2.70834			−0.0944640
$823$	38.1099	−	10.2115i	1.32843	−	0.355951i	0.476298	−	0.879284i	$-0.341978\pi$
$823$	38.1099	−	10.2115i	1.32843	−	0.355951i	0.852128	+	0.523333i	$0.175312\pi$
$824$			4.06301i			0.141542i
$825$	15.0617	+	25.1434i	0.524381	+	0.875381i
$826$	3.75895	−	6.51069i	0.130791	−	0.226536i
$827$	−9.08828	−	15.7414i	−0.316030	−	0.547381i	0.663626	−	0.748065i	$-0.269017\pi$
$827$	−9.08828	−	15.7414i	−0.316030	−	0.547381i	−0.979656	+	0.200684i	$0.935683\pi$
$828$	0.433738			0.0150734
$829$	7.66475	−	2.05376i	0.266208	−	0.0713302i	−0.123246	−	0.992376i	$-0.539330\pi$
$829$	7.66475	−	2.05376i	0.266208	−	0.0713302i	0.389454	+	0.921046i	$0.372664\pi$
$830$	−23.0561	+	3.22451i	−0.800288	+	0.111925i
$831$	−6.86541	+	1.83958i	−0.238158	+	0.0638144i
$832$	−2.56752	+	1.48236i	−0.0890127	+	0.0513915i
$833$	−1.95758	+	1.13021i	−0.0678262	+	0.0391595i
$834$	20.9667	−	5.61800i	0.726016	−	0.194535i
$835$	−1.14849	−	0.866657i	−0.0397450	−	0.0299919i
$836$	4.78598	−	1.28240i	0.165527	−	0.0443527i
$837$	−8.94282			−0.309109
$838$	−11.8525	−	20.5291i	−0.409437	−	0.709166i
$839$	−13.3280	+	23.0848i	−0.460135	+	0.796977i	−0.998967	−	0.0454359i	$-0.985532\pi$
$839$	−13.3280	+	23.0848i	−0.460135	+	0.796977i	0.538832	+	0.842413i	$0.318866\pi$
$840$	1.12426	−	9.10571i	0.0387905	−	0.314177i
$841$		−	14.4869i		−	0.499548i
$842$	−10.0865	+	2.70266i	−0.347603	+	0.0931398i
$843$	−27.1054			−0.933559
$844$	−0.494303	−	0.856158i	−0.0170146	−	0.0294702i
$845$	1.15367	−	9.34393i	0.0396874	−	0.321441i
$846$	1.87613	+	0.502707i	0.0645026	+	0.0172834i
$847$	−2.84024	−	0.761039i	−0.0975917	−	0.0261496i
$848$	−2.23615	+	8.34541i	−0.0767896	+	0.286583i
$849$	−7.16717	−	26.7483i	−0.245977	−	0.917998i
$850$	2.69150	−	10.7335i	0.0923178	−	0.368157i
$851$	14.0284	+	2.94791i	0.480889	+	0.101053i
$852$	−6.60093	+	6.60093i	−0.226144	+	0.226144i
$853$	−23.7600	+	41.1535i	−0.813526	+	1.40907i	0.0968561	+	0.995298i	$0.469121\pi$
$853$	−23.7600	+	41.1535i	−0.813526	+	1.40907i	−0.910382	+	0.413769i	$0.864212\pi$
$854$	−4.59328	−	7.95579i	−0.157179	−	0.272242i
$855$	−0.541091	−	0.219038i	−0.0185049	−	0.00749095i
$856$	5.07945	−	18.9567i	0.173612	−	0.647928i
$857$	50.7542			1.73373			0.866865	−	0.498543i	$-0.166131\pi$
$857$	50.7542			1.73373			0.866865	+	0.498543i	$0.166131\pi$
$858$	−4.49798	+	16.7867i	−0.153558	+	0.573088i
$859$	0.540804	−	0.540804i	0.0184520	−	0.0184520i	−0.697821	−	0.716273i	$-0.745847\pi$
$859$	0.540804	−	0.540804i	0.0184520	−	0.0184520i	0.716273	+	0.697821i	$0.245847\pi$
$860$	−13.4043	+	17.7632i	−0.457081	+	0.605720i
$861$	13.2760			0.452446
$862$	4.97557	+	4.97557i	0.169469	+	0.169469i
$863$	12.6429	−	3.38764i	0.430368	−	0.115317i	−0.0371310	−	0.999310i	$-0.511822\pi$
$863$	12.6429	−	3.38764i	0.430368	−	0.115317i	0.467499	+	0.883994i	$0.345155\pi$
$864$	5.16103	+	1.38289i	0.175582	+	0.0470470i
$865$	3.94258	+	5.05327i	0.134052	+	0.171816i
$866$	−4.94233	−	18.4450i	−0.167947	−	0.626787i
$867$	5.25608	+	19.6160i	0.178506	+	0.666193i
$868$	3.54417	+	2.04623i	0.120297	+	0.0694534i
$869$	−13.8489	+	51.6849i	−0.469793	+	1.75329i
$870$	5.57657	+	13.1622i	0.189063	+	0.446239i
$871$	6.05355	+	22.5922i	0.205117	+	0.765506i
$872$	14.9042	−	3.99357i	0.504720	−	0.135239i
$873$	1.72620	+	0.996619i	0.0584229	+	0.0337305i
$874$	2.36362	−	2.36362i	0.0799507	−	0.0799507i
$875$	−16.1131	+	22.0839i	−0.544721	+	0.746573i
$876$	−12.9115	−	7.45444i	−0.436238	−	0.251862i
$877$	−35.1143	+	35.1143i	−1.18573	+	1.18573i	−0.207488	+	0.978238i	$0.566529\pi$
$877$	−35.1143	+	35.1143i	−1.18573	+	1.18573i	−0.978238	+	0.207488i	$0.933471\pi$
$878$	22.0979	−	22.0979i	0.745768	−	0.745768i
$879$	11.5406	−	19.9889i	0.389254	−	0.674208i
$880$	7.75221	+	0.957143i	0.261327	+	0.0322653i
$881$	17.6111	−	10.1678i	0.593333	−	0.342561i	−0.173081	−	0.984908i	$-0.555372\pi$
$881$	17.6111	−	10.1678i	0.593333	−	0.342561i	0.766414	+	0.642346i	$0.222039\pi$
$882$			0.187980i			0.00632961i
$883$	−2.35326	−	4.07596i	−0.0791935	−	0.137167i	0.823709	−	0.567013i	$-0.191901\pi$
$883$	−2.35326	−	4.07596i	−0.0791935	−	0.137167i	−0.902902	+	0.429846i	$0.858568\pi$
$884$	5.68234	−	3.28070i	0.191118	−	0.110342i
$885$	4.50072	+	10.6229i	0.151290	+	0.357084i
$886$	27.0688	−	7.25307i	0.909395	−	0.243672i
$887$	30.0936	+	30.0936i	1.01044	+	1.01044i	0.999945	+	0.0104992i	$0.00334207\pi$
$887$	30.0936	+	30.0936i	1.01044	+	1.01044i	0.0104992	+	0.999945i	$0.496658\pi$
$888$	9.10552	+	4.61298i	0.305561	+	0.154801i
$889$			44.4346i			1.49029i
$890$	18.0542	−	2.52497i	0.605177	−	0.0846371i
$891$	25.4541	−	14.6959i	0.852744	−	0.492332i
$892$	−3.41073	+	12.7290i	−0.114200	+	0.426200i
$893$	12.9633	−	7.48434i	0.433799	−	0.250454i
$894$	−15.0707	+	15.0707i	−0.504039	+	0.504039i
$895$	−1.37951	−	0.558437i	−0.0461119	−	0.0186665i
$896$	−1.72897	−	1.72897i	−0.0577607	−	0.0577607i
$897$	3.03447	+	11.3248i	0.101318	+	0.378124i
$898$	−13.4847	−	13.4847i	−0.449990	−	0.449990i
$899$	−6.37621			−0.212658
$900$	−0.661113	−	0.640149i	−0.0220371	−	0.0213383i
$901$	4.94896	−	18.4698i	0.164874	−	0.615318i
$902$			11.3026i			0.376336i
$903$	20.4170	−	35.3632i	0.679435	−	1.17682i
$904$	−3.49304	−	2.01671i	−0.116177	−	0.0670747i
$905$	11.2727	+	8.50650i	0.374718	+	0.282766i
$906$	3.33802	+	0.894421i	0.110898	+	0.0297151i
$907$	21.4996	+	37.2384i	0.713883	+	1.23648i	0.963389	+	0.268108i	$0.0863983\pi$
$907$	21.4996	+	37.2384i	0.713883	+	1.23648i	−0.249506	+	0.968373i	$0.580268\pi$
$908$	8.21358	−	14.2263i	0.272577	−	0.472118i
$909$	−0.550061	+	0.952734i	−0.0182444	+	0.0316002i
$910$	−16.0533	+	2.24513i	−0.532160	+	0.0744254i
$911$	8.75535	+	8.75535i	0.290078	+	0.290078i	0.837111	−	0.547033i	$-0.184243\pi$
$911$	8.75535	+	8.75535i	0.290078	+	0.290078i	−0.547033	+	0.837111i	$0.684243\pi$
$912$	2.06132	−	1.19010i	0.0682570	−	0.0394082i
$913$	9.41301	+	35.1298i	0.311525	+	1.16263i
$914$			32.8964i			1.08812i
$915$	13.9915	+	1.72749i	0.462544	+	0.0571090i
$916$	−7.10267	−	4.10073i	−0.234679	−	0.135492i
$917$		−	3.21557i		−	0.106188i
$918$	−11.4222	−	3.06057i	−0.376989	−	0.101014i
$919$	23.4173	+	23.4173i	0.772465	+	0.772465i	0.978537	−	0.206072i	$-0.0660680\pi$
$919$	23.4173	+	23.4173i	0.772465	+	0.772465i	−0.206072	+	0.978537i	$0.566068\pi$
$920$	4.85206	−	2.05573i	0.159968	−	0.0677754i
$921$	−6.65150	−	11.5207i	−0.219174	−	0.379621i
$922$	35.0617	+	9.39475i	1.15470	+	0.309400i
$923$	14.2831	+	8.24633i	0.470133	+	0.271431i
$924$	−14.3331			−0.471524
$925$	−17.0316	−	25.1977i	−0.559997	−	0.828495i
$926$	23.9344			0.786533
$927$	−0.647612	−	0.373899i	−0.0212704	−	0.0122805i
$928$	3.67980	+	0.985999i	0.120795	+	0.0323670i
$929$	−21.0299	−	36.4248i	−0.689967	−	1.19506i	−0.971848	−	0.235609i	$-0.924292\pi$
$929$	−21.0299	−	36.4248i	−0.689967	−	1.19506i	0.281881	−	0.959449i	$-0.409042\pi$
$930$	−5.78268	+	2.45002i	−0.189622	+	0.0803392i
$931$	1.02438	+	1.02438i	0.0335727	+	0.0335727i
$932$	−27.4519	−	7.35571i	−0.899216	−	0.240944i
$933$			44.5366i			1.45806i
$934$	−23.6912	−	13.6781i	−0.775200	−	0.447562i
$935$	−17.1569	−	2.11832i	−0.561091	−	0.0692763i
$936$		−	0.545656i		−	0.0178353i
$937$	12.5616	+	46.8805i	0.410370	+	1.53152i	0.793933	+	0.608005i	$0.208030\pi$
$937$	12.5616	+	46.8805i	0.410370	+	1.53152i	−0.383563	+	0.923515i	$0.625303\pi$
$938$	−16.7056	+	9.64501i	−0.545459	+	0.314921i
$939$	−26.2802	−	26.2802i	−0.857621	−	0.857621i
$940$	23.3701	−	3.26843i	0.762249	−	0.106605i
$941$	−5.95047	+	10.3065i	−0.193980	+	0.335983i	−0.946566	−	0.322512i	$-0.895473\pi$
$941$	−5.95047	+	10.3065i	−0.193980	+	0.335983i	0.752586	+	0.658494i	$0.228806\pi$
$942$	−15.5987	+	27.0177i	−0.508232	+	0.880284i
$943$	3.81255	+	6.60353i	0.124154	+	0.215040i
$944$	2.96988	+	0.795776i	0.0966613	+	0.0259003i
$945$	23.3189	+	17.5966i	0.758563	+	0.572418i
$946$	30.1067	+	17.3821i	0.978855	+	0.565142i
$947$	2.61458	−	4.52858i	0.0849623	−	0.147159i	−0.820413	−	0.571772i	$-0.806256\pi$
$947$	2.61458	−	4.52858i	0.0849623	−	0.147159i	0.905375	+	0.424613i	$0.139590\pi$
$948$			25.7044i			0.834839i
$949$	−6.81729	+	25.4425i	−0.221299	+	0.825897i
$950$	−7.09112	+	0.114238i	−0.230066	+	0.00370636i
$951$	8.64091			0.280201
$952$	3.82649	+	3.82649i	0.124017	+	0.124017i
$953$	7.57331	+	28.2640i	0.245324	+	0.915560i	0.973220	+	0.229874i	$0.0738313\pi$
$953$	7.57331	+	28.2640i	0.245324	+	0.915560i	−0.727897	+	0.685687i	$0.759502\pi$
$954$	−1.12441	−	1.12441i	−0.0364042	−	0.0364042i
$955$	−13.8038	−	5.58790i	−0.446681	−	0.180820i
$956$	−6.36836	+	6.36836i	−0.205967	+	0.205967i
$957$	19.3397	−	11.1658i	0.625163	−	0.360938i
$958$	5.57077	−	20.7904i	0.179983	−	0.671707i
$959$	−3.41761	+	1.97316i	−0.110360	+	0.0637165i
$960$	3.71613	−	0.519721i	0.119938	−	0.0167739i
$961$			28.1987i			0.909635i
$962$	3.70857	−	17.6482i	0.119569	−	0.569001i
$963$	2.55412	+	2.55412i	0.0823054	+	0.0823054i
$964$	24.2676	−	6.50247i	0.781605	−	0.209430i
$965$	−13.2899	−	31.3677i	−0.427818	−	1.00976i
$966$	−8.37406	+	4.83477i	−0.269431	+	0.155556i
$967$	−0.562044	−	0.973490i	−0.0180741	−	0.0313053i	0.856847	−	0.515571i	$-0.172420\pi$
$967$	−0.562044	−	0.973490i	−0.0180741	−	0.0313053i	−0.874921	+	0.484266i	$0.839087\pi$
$968$		−	1.20257i		−	0.0386520i
$969$	−4.56203	+	2.63389i	−0.146554	+	0.0846128i
$970$	24.0338	+	2.96739i	0.771680	+	0.0952771i
$971$	18.2601	−	31.6274i	0.585994	−	1.01497i	−0.408757	−	0.912643i	$-0.634038\pi$
$971$	18.2601	−	31.6274i	0.585994	−	1.01497i	0.994751	−	0.102328i	$-0.0326291\pi$
$972$	−1.35054	+	1.35054i	−0.0433185	+	0.0433185i
$973$	22.3645	−	22.3645i	0.716973	−	0.716973i
$974$	15.9758	+	9.22366i	0.511899	+	0.295545i
$975$	12.0890	−	21.7400i	0.387156	−	0.696239i
$976$	2.65666	−	2.65666i	0.0850377	−	0.0850377i
$977$	−0.299965	−	0.173185i	−0.00959672	−	0.00554067i	0.495194	−	0.868782i	$-0.335097\pi$
$977$	−0.299965	−	0.173185i	−0.00959672	−	0.00554067i	−0.504791	+	0.863242i	$0.668430\pi$
$978$	−36.4527	+	9.76746i	−1.16563	+	0.312329i
$979$	−7.37090	−	27.5086i	−0.235575	−	0.879177i
$980$	0.890942	+	2.10286i	0.0284601	+	0.0671734i
$981$	−0.735017	+	2.74312i	−0.0234673	+	0.0875812i
$982$	−10.1195	−	5.84251i	−0.322927	−	0.186442i
$983$	−6.35616	−	23.7215i	−0.202730	−	0.756599i	−0.990129	−	0.140156i	$-0.955240\pi$
$983$	−6.35616	−	23.7215i	−0.202730	−	0.756599i	0.787399	−	0.616443i	$-0.211427\pi$
$984$	1.40528	+	5.24457i	0.0447987	+	0.167191i
$985$	−25.2256	−	32.3321i	−0.803754	−	1.03019i
$986$	−8.14400	−	2.18218i	−0.259358	−	0.0694947i
$987$	−41.8254	+	11.2071i	−1.33132	+	0.356725i
$988$	−2.97351	−	2.97351i	−0.0946000	−	0.0946000i
$989$	23.4530			0.745763
$990$	−0.865958	+	1.14756i	−0.0275220	+	0.0364718i
$991$	13.9031	−	13.9031i	0.441647	−	0.441647i	−0.450918	−	0.892565i	$-0.648903\pi$
$991$	13.9031	−	13.9031i	0.441647	−	0.441647i	0.892565	+	0.450918i	$0.148903\pi$
$992$	−0.433190	+	1.61669i	−0.0137538	+	0.0513298i
$993$	19.1674			0.608258
$994$	−3.52051	+	13.1387i	−0.111664	+	0.416735i
$995$	5.30164	+	2.14615i	0.168073	+	0.0680376i
$996$	8.73553	+	15.1304i	0.276796	+	0.479424i
$997$	−12.0943	+	20.9480i	−0.383031	+	0.663429i	−0.991494	−	0.130153i	$-0.958453\pi$
$997$	−12.0943	+	20.9480i	−0.383031	+	0.663429i	0.608463	+	0.793582i	$0.291786\pi$
$998$	−25.2634	+	25.2634i	−0.799697	+	0.799697i
$999$	−27.2164	+	17.7642i	−0.861088	+	0.562035i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.r.d.23.2	yes	12
5.2	odd	4		370.2.q.d.97.2	✓	12
37.29	odd	12		370.2.q.d.103.2	yes	12
185.177	even	12	inner	370.2.r.d.177.2	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.q.d.97.2	✓	12	5.2	odd	4
370.2.q.d.103.2	yes	12	37.29	odd	12
370.2.r.d.23.2	yes	12	1.1	even	1	trivial
370.2.r.d.177.2	yes	12	185.177	even	12	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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.r (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.62090 + 0.434319i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.05890 + 0.872317i) q^{5} +(1.18658 + 1.18658i) q^{6} +(2.36181 + 0.632846i) q^{7} +1.00000i q^{8} +(-0.159392 - 0.0920251i) q^{9} +(-2.21922 - 0.274000i) q^{10} +3.49322i q^{11} +(0.434319 + 1.62090i) q^{12} +(2.56752 - 1.48236i) q^{13} +(1.72897 + 1.72897i) q^{14} +(-3.71613 + 0.519721i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.10658 - 1.91666i) q^{17} +(-0.0920251 - 0.159392i) q^{18} +(-1.37008 - 0.367111i) q^{19} +(-1.78490 - 1.34690i) q^{20} +(3.55340 + 2.05156i) q^{21} +(-1.74661 + 3.02521i) q^{22} +2.35663i q^{23} +(-0.434319 + 1.62090i) q^{24} +(3.47813 - 3.59203i) q^{25} +2.96472 q^{26} +(-3.77813 - 3.77813i) q^{27} +(0.632846 + 2.36181i) q^{28} +(-2.69380 - 2.69380i) q^{29} +(-3.47813 - 1.40797i) q^{30} +(1.18350 - 1.18350i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.51717 + 5.66216i) q^{33} +(1.91666 - 1.10658i) q^{34} +(-5.41477 + 0.757284i) q^{35} -0.184050i q^{36} +(1.25090 - 5.95275i) q^{37} +(-1.00297 - 1.00297i) q^{38} +(4.80551 - 1.28763i) q^{39} +(-0.872317 - 2.05890i) q^{40} +(2.80211 - 1.61780i) q^{41} +(2.05156 + 3.55340i) q^{42} -9.95193i q^{43} +(-3.02521 + 1.74661i) q^{44} +(0.408447 + 0.0504298i) q^{45} +(-1.17832 + 2.04090i) q^{46} +(-7.46221 + 7.46221i) q^{47} +(-1.18658 + 1.18658i) q^{48} +(-0.884516 - 0.510676i) q^{49} +(4.80816 - 1.37172i) q^{50} +(2.62610 - 2.62610i) q^{51} +(2.56752 + 1.48236i) q^{52} +(8.34541 - 2.23615i) q^{53} +(-1.38289 - 5.16103i) q^{54} +(-3.04719 - 7.19218i) q^{55} +(-0.632846 + 2.36181i) q^{56} +(-2.06132 - 1.19010i) q^{57} +(-0.985999 - 3.67980i) q^{58} +(-0.795776 - 2.96988i) q^{59} +(-2.30816 - 2.95840i) q^{60} +(-3.62907 - 0.972406i) q^{61} +(1.61669 - 0.433190i) q^{62} +(-0.318216 - 0.318216i) q^{63} -1.00000 q^{64} +(-3.99317 + 5.29171i) q^{65} +(-4.14499 + 4.14499i) q^{66} +(-2.04187 + 7.62035i) q^{67} +2.21317 q^{68} +(-1.02353 + 3.81986i) q^{69} +(-5.06797 - 2.05156i) q^{70} +(2.78149 + 4.81768i) q^{71} +(0.0920251 - 0.159392i) q^{72} +(-6.28228 + 6.28228i) q^{73} +(4.05969 - 4.52978i) q^{74} +(7.19778 - 4.31170i) q^{75} +(-0.367111 - 1.37008i) q^{76} +(-2.21067 + 8.25032i) q^{77} +(4.80551 + 1.28763i) q^{78} +(14.7958 + 3.96452i) q^{79} +(0.274000 - 2.21922i) q^{80} +(-4.20699 - 7.28672i) q^{81} +3.23559 q^{82} +(10.0566 - 2.69465i) q^{83} +4.10312i q^{84} +(-0.606408 + 4.91150i) q^{85} +(4.97597 - 8.61863i) q^{86} +(-3.19641 - 5.53635i) q^{87} -3.49322 q^{88} +(-7.87485 + 2.11006i) q^{89} +(0.328511 + 0.247897i) q^{90} +(7.00210 - 1.87621i) q^{91} +(-2.04090 + 1.17832i) q^{92} +(2.43234 - 1.40431i) q^{93} +(-10.1936 + 2.73136i) q^{94} +(3.14109 - 0.439298i) q^{95} +(-1.62090 + 0.434319i) q^{96} -10.8299 q^{97} +(-0.510676 - 0.884516i) q^{98} +(0.321464 - 0.556791i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} + 6 q^{4} - 8 q^{5} + 6 q^{6} - 4 q^{7} - 18 q^{9} - 4 q^{10} - 6 q^{13} - 8 q^{14} - 14 q^{15} - 6 q^{16} + 12 q^{17} + 10 q^{18} + 8 q^{19} - 4 q^{20} + 54 q^{21} - 10 q^{22} - 10 q^{25}+ \cdots - 28 q^{99}+O(q^{100}) \) 12 * q + 6 * q^3 + 6 * q^4 - 8 * q^5 + 6 * q^6 - 4 * q^7 - 18 * q^9 - 4 * q^10 - 6 * q^13 - 8 * q^14 - 14 * q^15 - 6 * q^16 + 12 * q^17 + 10 * q^18 + 8 * q^19 - 4 * q^20 + 54 * q^21 - 10 * q^22 - 10 * q^25 - 18 * q^27 + 4 * q^28 - 4 * q^29 + 10 * q^30 - 2 * q^31 - 28 * q^33 - 12 * q^34 + 14 * q^35 + 12 * q^37 + 16 * q^38 + 30 * q^39 - 2 * q^40 + 12 * q^41 - 22 * q^42 - 6 * q^44 + 24 * q^45 + 2 * q^46 - 28 * q^47 - 6 * q^48 - 24 * q^49 + 16 * q^50 - 8 * q^51 - 6 * q^52 + 14 * q^53 + 18 * q^54 - 32 * q^55 - 4 * q^56 - 72 * q^57 - 10 * q^58 + 14 * q^60 + 24 * q^61 - 16 * q^62 + 8 * q^63 - 12 * q^64 - 26 * q^65 + 8 * q^66 + 18 * q^67 + 24 * q^68 + 40 * q^69 + 6 * q^70 - 10 * q^72 + 28 * q^73 - 38 * q^74 - 30 * q^75 - 8 * q^76 + 26 * q^77 + 30 * q^78 + 56 * q^79 + 4 * q^80 + 4 * q^81 - 28 * q^82 + 14 * q^83 + 28 * q^85 - 22 * q^86 - 10 * q^87 - 20 * q^88 + 2 * q^89 + 42 * q^90 + 38 * q^91 - 18 * q^92 + 18 * q^93 + 16 * q^94 - 56 * q^95 - 6 * q^96 - 44 * q^97 + 22 * q^98 - 28 * q^99

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