LMFDB - Embedded newform 392.2.p.g.373.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,2,Mod(165,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("392.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.p (of order $6$, degree $2$, not 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:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.951588245534976.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 2 x^{10} - 9 x^{9} + 8 x^{8} - 13 x^{7} + 35 x^{6} - 26 x^{5} + 32 x^{4} - 72 x^{3} + \cdots + 64 $ x^12 - x^11 + 2x^10 - 9x^9 + 8x^8 - 13x^7 + 35x^6 - 26x^5 + 32x^4 - 72x^3 + 32x^2 - 32x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			373.5
Root			$-0.981777 - 1.01790i$ of defining polynomial
Character	$\chi$	$=$	392.373
Dual form			392.2.p.g.165.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.804171 + 1.16332i) q^{2} +(-0.591141 + 0.341295i) q^{3} +(-0.706619 + 1.87101i) q^{4} +(2.80486 + 1.61939i) q^{5} +(-0.872413 - 0.413225i) q^{6} +(-2.74483 + 0.682591i) q^{8} +(-1.26704 + 2.19457i) q^{9} +O(q^{10})$	\(q+(0.804171 + 1.16332i) q^{2} +(-0.591141 + 0.341295i) q^{3} +(-0.706619 + 1.87101i) q^{4} +(2.80486 + 1.61939i) q^{5} +(-0.872413 - 0.413225i) q^{6} +(-2.74483 + 0.682591i) q^{8} +(-1.26704 + 2.19457i) q^{9} +(0.371724 + 4.56521i) q^{10} +(2.08913 - 1.20616i) q^{11} +(-0.220856 - 1.34720i) q^{12} -3.09491i q^{13} -2.21076 q^{15} +(-3.00138 - 2.64419i) q^{16} +(1.97779 + 3.42563i) q^{17} +(-3.57190 + 0.290843i) q^{18} +(-2.33831 - 1.35002i) q^{19} +(-5.01186 + 4.10364i) q^{20} +(3.08317 + 1.46037i) q^{22} +(-1.37241 + 2.37709i) q^{23} +(1.38961 - 1.34030i) q^{24} +(2.74483 + 4.75418i) q^{25} +(3.60037 - 2.48884i) q^{26} -3.77750i q^{27} +2.01745i q^{29} +(-1.77782 - 2.57181i) q^{30} +(-1.10538 - 1.91457i) q^{31} +(0.662411 - 5.61794i) q^{32} +(-0.823314 + 1.42602i) q^{33} +(-2.39462 + 5.05560i) q^{34} +(-3.21076 - 3.92136i) q^{36} +(4.30285 + 2.48425i) q^{37} +(-0.309892 - 3.80584i) q^{38} +(1.05628 + 1.82953i) q^{39} +(-8.80423 - 2.53036i) q^{40} +2.11256 q^{41} -11.5899i q^{43} +(0.780522 + 4.76109i) q^{44} +(-7.10771 + 4.10364i) q^{45} +(-3.86897 + 0.315032i) q^{46} +(-3.31613 + 5.74371i) q^{47} +(2.67669 + 0.538731i) q^{48} +(-3.32331 + 7.01628i) q^{50} +(-2.33831 - 1.35002i) q^{51} +(5.79062 + 2.18693i) q^{52} +(2.23998 - 1.29325i) q^{53} +(4.39444 - 3.03776i) q^{54} +7.81297 q^{55} +1.84302 q^{57} +(-2.34694 + 1.62238i) q^{58} +(10.6283 - 6.13625i) q^{59} +(1.56216 - 4.13635i) q^{60} +(7.54801 + 4.35784i) q^{61} +(1.33834 - 2.82555i) q^{62} +(7.06814 - 3.74718i) q^{64} +(5.01186 - 8.68080i) q^{65} +(-2.32100 + 0.188989i) q^{66} +(5.01858 - 2.89748i) q^{67} +(-7.80695 + 1.27985i) q^{68} -1.87359i q^{69} +6.64663 q^{71} +(1.97980 - 6.88858i) q^{72} +(-4.77890 - 8.27729i) q^{73} +(0.570250 + 7.00335i) q^{74} +(-3.24516 - 1.87359i) q^{75} +(4.17820 - 3.42105i) q^{76} +(-1.27890 + 2.70004i) q^{78} +(-0.838343 + 1.45205i) q^{79} +(-4.13648 - 12.2770i) q^{80} +(-2.51186 - 4.35067i) q^{81} +(1.69886 + 2.45758i) q^{82} +6.47755i q^{83} +12.8112i q^{85} +(13.4828 - 9.32027i) q^{86} +(-0.688547 - 1.19260i) q^{87} +(-4.91099 + 4.73673i) q^{88} +(6.98965 - 12.1064i) q^{89} +(-10.4897 - 4.96851i) q^{90} +(-3.47779 - 4.24750i) q^{92} +(1.30687 + 0.754520i) q^{93} +(-9.34850 + 0.761205i) q^{94} +(-4.37241 - 7.57324i) q^{95} +(1.52580 + 3.54707i) q^{96} +1.37709 q^{97} +6.11300i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 8 q^{6} + 4 q^{8}+O(q^{10}) $ 12 * q - 2 * q^2 + 8 * q^6 + 4 * q^8	$ 12 q - 2 q^{2} + 8 q^{6} + 4 q^{8} + 8 q^{10} + 2 q^{12} - 20 q^{15} + 8 q^{16} + 2 q^{17} + 6 q^{18} - 8 q^{20} + 12 q^{22} + 2 q^{23} - 18 q^{24} - 4 q^{25} + 2 q^{26} + 14 q^{30} - 10 q^{31} - 12 q^{32} + 14 q^{33} - 32 q^{34} - 32 q^{36} - 18 q^{38} + 4 q^{39} - 10 q^{40} + 8 q^{41} - 30 q^{44} - 4 q^{46} - 30 q^{47} + 56 q^{48} - 16 q^{50} + 32 q^{52} - 2 q^{54} - 4 q^{55} - 4 q^{57} - 22 q^{58} + 6 q^{60} + 28 q^{62} + 24 q^{64} + 8 q^{65} + 38 q^{66} - 4 q^{68} + 32 q^{71} + 20 q^{72} + 10 q^{73} + 18 q^{74} - 52 q^{76} + 52 q^{78} - 22 q^{79} - 36 q^{80} + 22 q^{81} + 26 q^{82} + 40 q^{86} + 20 q^{87} - 14 q^{88} + 10 q^{89} - 52 q^{90} - 20 q^{92} - 42 q^{94} - 34 q^{95} - 16 q^{96} - 40 q^{97}+O(q^{100}) $ 12 * q - 2 * q^2 + 8 * q^6 + 4 * q^8 + 8 * q^10 + 2 * q^12 - 20 * q^15 + 8 * q^16 + 2 * q^17 + 6 * q^18 - 8 * q^20 + 12 * q^22 + 2 * q^23 - 18 * q^24 - 4 * q^25 + 2 * q^26 + 14 * q^30 - 10 * q^31 - 12 * q^32 + 14 * q^33 - 32 * q^34 - 32 * q^36 - 18 * q^38 + 4 * q^39 - 10 * q^40 + 8 * q^41 - 30 * q^44 - 4 * q^46 - 30 * q^47 + 56 * q^48 - 16 * q^50 + 32 * q^52 - 2 * q^54 - 4 * q^55 - 4 * q^57 - 22 * q^58 + 6 * q^60 + 28 * q^62 + 24 * q^64 + 8 * q^65 + 38 * q^66 - 4 * q^68 + 32 * q^71 + 20 * q^72 + 10 * q^73 + 18 * q^74 - 52 * q^76 + 52 * q^78 - 22 * q^79 - 36 * q^80 + 22 * q^81 + 26 * q^82 + 40 * q^86 + 20 * q^87 - 14 * q^88 + 10 * q^89 - 52 * q^90 - 20 * q^92 - 42 * q^94 - 34 * q^95 - 16 * q^96 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.804171	+	1.16332i	0.568635	+	0.822590i
$2$	0.804171	+	1.16332i	0.568635	+	0.822590i
$3$	−0.591141	+	0.341295i	−0.341295	+	0.197047i	−0.660845	−	0.750523i	$-0.729802\pi$
$3$	−0.591141	+	0.341295i	−0.341295	+	0.197047i	0.319549	+	0.947570i	$0.396468\pi$
$4$	−0.706619	+	1.87101i	−0.353310	+	0.935506i
$5$	2.80486	+	1.61939i	1.25437	+	0.724212i	0.971975	−	0.235086i	$-0.0755372\pi$
$5$	2.80486	+	1.61939i	1.25437	+	0.724212i	0.282397	+	0.959298i	$0.408870\pi$
$6$	−0.872413	−	0.413225i	−0.356161	−	0.168698i
$7$		0			0
$7$		0			0
$8$	−2.74483	+	0.682591i	−0.970443	+	0.241332i
$9$	−1.26704	+	2.19457i	−0.422345	+	0.731523i
$10$	0.371724	+	4.56521i	0.117549	+	1.44365i
$11$	2.08913	−	1.20616i	0.629897	−	0.363671i	−0.150815	−	0.988562i	$-0.548190\pi$
$11$	2.08913	−	1.20616i	0.629897	−	0.363671i	0.780712	+	0.624891i	$0.214856\pi$
$12$	−0.220856	−	1.34720i	−0.0637558	−	0.388902i
$13$		−	3.09491i		−	0.858375i	−0.903216	−	0.429187i	$-0.858800\pi$
$13$		−	3.09491i		−	0.858375i	0.903216	−	0.429187i	$-0.141200\pi$
$14$		0			0
$15$	−2.21076			−0.570815
$16$	−3.00138	−	2.64419i	−0.750345	−	0.661047i
$17$	1.97779	+	3.42563i	0.479685	+	0.830838i	0.999728	−	0.0233012i	$-0.00741769\pi$
$17$	1.97779	+	3.42563i	0.479685	+	0.830838i	−0.520044	+	0.854140i	$0.674084\pi$
$18$	−3.57190	+	0.290843i	−0.841904	+	0.0685523i
$19$	−2.33831	−	1.35002i	−0.536444	−	0.309716i	0.207192	−	0.978300i	$-0.433567\pi$
$19$	−2.33831	−	1.35002i	−0.536444	−	0.309716i	−0.743637	+	0.668584i	$0.766901\pi$
$20$	−5.01186	+	4.10364i	−1.12069	+	0.917602i
$21$		0			0
$22$	3.08317	+	1.46037i	0.657334	+	0.311351i
$23$	−1.37241	+	2.37709i	−0.286168	+	0.495657i	−0.972892	−	0.231261i	$-0.925715\pi$
$23$	−1.37241	+	2.37709i	−0.286168	+	0.495657i	0.686724	+	0.726918i	$0.259048\pi$
$24$	1.38961	−	1.34030i	0.283654	−	0.273588i
$25$	2.74483	+	4.75418i	0.548965	+	0.950836i
$26$	3.60037	−	2.48884i	0.706091	−	0.488101i
$27$		−	3.77750i		−	0.726981i
$28$		0			0
$29$			2.01745i			0.374631i	0.982300	+	0.187316i	$0.0599787\pi$
$29$			2.01745i			0.374631i	−0.982300	+	0.187316i	$0.940021\pi$
$30$	−1.77782	−	2.57181i	−0.324585	−	0.469547i
$31$	−1.10538	−	1.91457i	−0.198532	−	0.343867i	0.749521	−	0.661981i	$-0.230284\pi$
$31$	−1.10538	−	1.91457i	−0.198532	−	0.343867i	−0.948053	+	0.318114i	$0.896951\pi$
$32$	0.662411	−	5.61794i	0.117099	−	0.993120i
$33$	−0.823314	+	1.42602i	−0.143321	+	0.248239i
$34$	−2.39462	+	5.05560i	−0.410674	+	0.867027i
$35$		0			0
$36$	−3.21076	−	3.92136i	−0.535126	−	0.653561i
$37$	4.30285	+	2.48425i	0.707385	+	0.408409i	0.810092	−	0.586303i	$-0.199417\pi$
$37$	4.30285	+	2.48425i	0.707385	+	0.408409i	−0.102707	+	0.994712i	$0.532751\pi$
$38$	−0.309892	−	3.80584i	−0.0502711	−	0.617389i
$39$	1.05628	+	1.82953i	0.169140	+	0.292959i
$40$	−8.80423	−	2.53036i	−1.39207	−	0.400086i
$41$	2.11256			0.329926			0.164963	−	0.986300i	$-0.447249\pi$
$41$	2.11256			0.329926			0.164963	+	0.986300i	$0.447249\pi$
$42$		0			0
$43$		−	11.5899i		−	1.76745i	−0.468011	−	0.883723i	$-0.655029\pi$
$43$		−	11.5899i		−	1.76745i	0.468011	−	0.883723i	$-0.344971\pi$
$44$	0.780522	+	4.76109i	0.117668	+	0.717762i
$45$	−7.10771	+	4.10364i	−1.05956	+	0.611734i
$46$	−3.86897	+	0.315032i	−0.570448	+	0.0464489i
$47$	−3.31613	+	5.74371i	−0.483708	+	0.837807i	−0.999825	−	0.0187115i	$-0.994044\pi$
$47$	−3.31613	+	5.74371i	−0.483708	+	0.837807i	0.516117	+	0.856518i	$0.327377\pi$
$48$	2.67669	+	0.538731i	0.386346	+	0.0777591i
$49$		0			0
$50$	−3.32331	+	7.01628i	−0.469988	+	0.992251i
$51$	−2.33831	−	1.35002i	−0.327428	−	0.189041i
$52$	5.79062	+	2.18693i	0.803015	+	0.303272i
$53$	2.23998	−	1.29325i	0.307684	−	0.177642i	−0.338205	−	0.941072i	$-0.609820\pi$
$53$	2.23998	−	1.29325i	0.307684	−	0.177642i	0.645890	+	0.763431i	$0.276487\pi$
$54$	4.39444	−	3.03776i	0.598007	−	0.413386i
$55$	7.81297			1.05350
$56$		0			0
$57$	1.84302			0.244114
$58$	−2.34694	+	1.62238i	−0.308168	+	0.213028i
$59$	10.6283	−	6.13625i	1.38369	−	0.798872i	0.391093	−	0.920351i	$-0.372097\pi$
$59$	10.6283	−	6.13625i	1.38369	−	0.798872i	0.992594	+	0.121479i	$0.0387638\pi$
$60$	1.56216	−	4.13635i	0.201674	−	0.534001i
$61$	7.54801	+	4.35784i	0.966424	+	0.557965i	0.898144	−	0.439701i	$-0.144916\pi$
$61$	7.54801	+	4.35784i	0.966424	+	0.557965i	0.0682795	+	0.997666i	$0.478249\pi$
$62$	1.33834	−	2.82555i	0.169970	−	0.358845i
$63$		0			0
$64$	7.06814	−	3.74718i	0.883518	−	0.468398i
$65$	5.01186	−	8.68080i	0.621645	−	1.07672i
$66$	−2.32100	+	0.188989i	−0.285696	+	0.0232629i
$67$	5.01858	−	2.89748i	0.613117	−	0.353983i	−0.161067	−	0.986943i	$-0.551494\pi$
$67$	5.01858	−	2.89748i	0.613117	−	0.353983i	0.774184	+	0.632960i	$0.218160\pi$
$68$	−7.80695	+	1.27985i	−0.946732	+	0.155205i
$69$		−	1.87359i		−	0.225554i
$70$		0			0
$71$	6.64663			0.788810			0.394405	−	0.918937i	$-0.370951\pi$
$71$	6.64663			0.788810			0.394405	+	0.918937i	$0.370951\pi$
$72$	1.97980	−	6.88858i	0.233322	−	0.811827i
$73$	−4.77890	−	8.27729i	−0.559328	−	0.968784i	−0.997553	−	0.0699184i	$-0.977726\pi$
$73$	−4.77890	−	8.27729i	−0.559328	−	0.968784i	0.438225	−	0.898865i	$-0.355607\pi$
$74$	0.570250	+	7.00335i	0.0662903	+	0.814123i
$75$	−3.24516	−	1.87359i	−0.374718	−	0.216344i
$76$	4.17820	−	3.42105i	0.479272	−	0.392421i
$77$		0			0
$78$	−1.27890	+	2.70004i	−0.144806	+	0.305720i
$79$	−0.838343	+	1.45205i	−0.0943209	+	0.163369i	−0.909325	−	0.416087i	$-0.863401\pi$
$79$	−0.838343	+	1.45205i	−0.0943209	+	0.163369i	0.815004	+	0.579455i	$0.196735\pi$
$80$	−4.13648	−	12.2770i	−0.462473	−	1.37261i
$81$	−2.51186	−	4.35067i	−0.279096	−	0.483408i
$82$	1.69886	+	2.45758i	0.187607	+	0.271394i
$83$			6.47755i			0.711003i	0.934676	+	0.355502i	$0.115690\pi$
$83$			6.47755i			0.711003i	−0.934676	+	0.355502i	$0.884310\pi$
$84$		0			0
$85$			12.8112i			1.38957i
$86$	13.4828	−	9.32027i	1.45388	−	1.00503i
$87$	−0.688547	−	1.19260i	−0.0738200	−	0.127860i
$88$	−4.91099	+	4.73673i	−0.523513	+	0.504937i
$89$	6.98965	−	12.1064i	0.740902	−	1.28328i	−0.211184	−	0.977446i	$-0.567732\pi$
$89$	6.98965	−	12.1064i	0.740902	−	1.28328i	0.952085	−	0.305833i	$-0.0989349\pi$
$90$	−10.4897	−	4.96851i	−1.10571	−	0.523726i
$91$		0			0
$92$	−3.47779	−	4.24750i	−0.362585	−	0.442832i
$93$	1.30687	+	0.754520i	0.135516	+	0.0782401i
$94$	−9.34850	+	0.761205i	−0.964224	+	0.0785123i
$95$	−4.37241	−	7.57324i	−0.448600	−	0.776998i
$96$	1.52580	+	3.54707i	0.155726	+	0.362021i
$97$	1.37709			0.139823			0.0699113	−	0.997553i	$-0.477728\pi$
$97$	1.37709			0.139823			0.0699113	+	0.997553i	$0.477728\pi$
$98$		0			0
$99$			6.11300i			0.614379i
$100$	−10.8347	+	1.77621i	−1.08347	+	0.177621i
$101$	−0.689470	+	0.398066i	−0.0686048	+	0.0396090i	−0.533910	−	0.845541i	$-0.679278\pi$
$101$	−0.689470	+	0.398066i	−0.0686048	+	0.0396090i	0.465305	+	0.885150i	$0.345945\pi$
$102$	−0.309892	−	3.80584i	−0.0306839	−	0.376834i
$103$	−1.32799	+	2.30015i	−0.130851	+	0.226641i	−0.924005	−	0.382381i	$-0.875104\pi$
$103$	−1.32799	+	2.30015i	−0.130851	+	0.226641i	0.793154	+	0.609022i	$0.208438\pi$
$104$	2.11256	+	8.49500i	0.207153	+	0.833003i
$105$		0			0
$106$	3.30579	+	1.56581i	0.321086	+	0.152085i
$107$	4.70287	+	2.71520i	0.454643	+	0.262489i	0.709789	−	0.704414i	$-0.248790\pi$
$107$	4.70287	+	2.71520i	0.454643	+	0.262489i	−0.255146	+	0.966903i	$0.582123\pi$
$108$	7.06776	+	2.66926i	0.680095	+	0.256849i
$109$	−11.9614	+	6.90593i	−1.14570	+	0.661468i	−0.947835	−	0.318762i	$-0.896733\pi$
$109$	−11.9614	+	6.90593i	−1.14570	+	0.661468i	−0.197862	+	0.980230i	$0.563400\pi$
$110$	6.28296	+	9.08897i	0.599057	+	0.866599i
$111$	−3.39145			−0.321903
$112$		0			0
$113$	4.53407			0.426529			0.213265	−	0.976994i	$-0.431590\pi$
$113$	4.53407			0.426529			0.213265	+	0.976994i	$0.431590\pi$
$114$	1.48211	+	2.14402i	0.138812	+	0.200806i
$115$	−7.69885	+	4.44493i	−0.717922	+	0.414492i
$116$	−3.77468	−	1.42557i	−0.350470	−	0.132361i
$117$	6.79200	+	3.92136i	0.627921	+	0.362530i
$118$	15.6854	+	7.42950i	1.44396	+	0.683941i
$119$		0			0
$120$	6.06814	−	1.50904i	0.553943	−	0.137756i
$121$	−2.59035	+	4.48662i	−0.235486	+	0.407874i
$122$	1.00033	+	12.2852i	0.0905653	+	1.11225i
$123$	−1.24882	+	0.721006i	−0.112602	+	0.0650109i
$124$	4.36327	−	0.715304i	0.391833	−	0.0642362i
$125$			1.58587i			0.141845i
$126$		0			0
$127$	−15.4897			−1.37448			−0.687242	−	0.726428i	$-0.741179\pi$
$127$	−15.4897			−1.37448			−0.687242	+	0.726428i	$0.741179\pi$
$128$	10.0432	+	5.20912i	0.887698	+	0.460426i
$129$	3.95558	+	6.85127i	0.348270	+	0.603221i
$130$	14.1289	−	1.15045i	1.23919	−	0.100901i
$131$	−14.5574	−	8.40471i	−1.27189	−	0.734323i	−0.296543	−	0.955020i	$-0.595834\pi$
$131$	−14.5574	−	8.40471i	−1.27189	−	0.734323i	−0.975343	+	0.220696i	$0.929167\pi$
$132$	−2.08634	−	2.54809i	−0.181592	−	0.221782i
$133$		0			0
$134$	7.40648	+	3.50814i	0.639823	+	0.303057i
$135$	6.11724	−	10.5954i	0.526488	−	0.911904i
$136$	−7.76700	−	8.05275i	−0.666015	−	0.690518i
$137$	0.443721	+	0.768547i	0.0379096	+	0.0656614i	0.884358	−	0.466810i	$-0.154597\pi$
$137$	0.443721	+	0.768547i	0.0379096	+	0.0656614i	−0.846448	+	0.532471i	$0.821263\pi$
$138$	2.17958	−	1.50669i	0.185539	−	0.128258i
$139$			2.44264i			0.207182i	0.994620	+	0.103591i	$0.0330333\pi$
$139$			2.44264i			0.207182i	−0.994620	+	0.103591i	$0.966967\pi$
$140$		0			0
$141$		−	4.52712i		−	0.381253i
$142$	5.34502	+	7.73215i	0.448544	+	0.648867i
$143$	−3.73296	−	6.46568i	−0.312166	−	0.540688i
$144$	9.60570	−	3.23645i	0.800475	−	0.269705i
$145$	−3.26704	+	5.65867i	−0.271312	+	0.469927i
$146$	5.78608	−	12.2157i	0.478859	−	1.01098i
$147$		0			0
$148$	−7.68855	+	6.29527i	−0.631995	+	0.517468i
$149$	−8.16541	−	4.71430i	−0.668936	−	0.386210i	0.126737	−	0.991936i	$-0.459549\pi$
$149$	−8.16541	−	4.71430i	−0.668936	−	0.386210i	−0.795673	+	0.605726i	$0.792883\pi$
$150$	−0.430076	−	5.28184i	−0.0351155	−	0.431260i
$151$	3.52689	+	6.10875i	0.287014	+	0.497123i	0.973096	−	0.230402i	$-0.0740040\pi$
$151$	3.52689	+	6.10875i	0.287014	+	0.497123i	−0.686081	+	0.727525i	$0.740671\pi$
$152$	7.33975	+	2.10947i	0.595333	+	0.171100i
$153$	−10.0237			−0.810370
$154$		0			0
$155$		−	7.16014i		−	0.575116i
$156$	−4.16946	+	0.683532i	−0.333824	+	0.0547263i
$157$	7.54801	−	4.35784i	0.602397	−	0.347794i	−0.167587	−	0.985857i	$-0.553598\pi$
$157$	7.54801	−	4.35784i	0.602397	−	0.347794i	0.769984	+	0.638063i	$0.220264\pi$
$158$	−2.36337	+	0.192438i	−0.188020	+	0.0153096i
$159$	−0.882761	+	1.52899i	−0.0700075	+	0.121257i
$160$	10.9556	−	14.6848i	0.866115	−	1.16094i
$161$		0			0
$162$	3.04125	−	6.42078i	0.238943	−	0.504464i
$163$	−17.1711	−	9.91376i	−1.34495	−	0.776505i	−0.357418	−	0.933945i	$-0.616343\pi$
$163$	−17.1711	−	9.91376i	−1.34495	−	0.776505i	−0.987529	+	0.157439i	$0.949676\pi$
$164$	−1.49277	+	3.95262i	−0.116566	+	0.308648i
$165$	−4.61856	+	2.66653i	−0.359555	+	0.207589i
$166$	−7.53545	+	5.20905i	−0.584864	+	0.404301i
$167$	−22.1600			−1.71479			−0.857396	−	0.514657i	$-0.827919\pi$
$167$	−22.1600			−1.71479			−0.857396	+	0.514657i	$0.827919\pi$
$168$		0			0
$169$	3.42151			0.263193
$170$	−14.9035	+	10.3024i	−1.14305	+	0.790159i
$171$	5.92543	−	3.42105i	0.453129	−	0.261614i
$172$	21.6849	+	8.18965i	1.65346	+	0.624455i
$173$	−18.8200	−	10.8657i	−1.43086	−	0.826105i	−0.433669	−	0.901072i	$-0.642781\pi$
$173$	−18.8200	−	10.8657i	−1.43086	−	0.826105i	−0.997186	+	0.0749674i	$0.976115\pi$
$174$	0.833662	−	1.76005i	0.0631998	−	0.133429i
$175$		0			0
$176$	−9.45960	−	1.90391i	−0.713044	−	0.143513i
$177$	−4.18855	+	7.25478i	−0.314830	+	0.545302i
$178$	19.7045	−	1.60445i	1.47692	−	0.120258i
$179$	−3.27141	+	1.88875i	−0.244517	+	0.141172i	−0.617251	−	0.786766i	$-0.711754\pi$
$179$	−3.27141	+	1.88875i	−0.244517	+	0.141172i	0.372734	+	0.927938i	$0.378420\pi$
$180$	−2.65552	−	16.1983i	−0.197931	−	1.20735i
$181$			14.0326i			1.04303i	0.853242	+	0.521516i	$0.174633\pi$
$181$			14.0326i			1.04303i	−0.853242	+	0.521516i	$0.825367\pi$
$182$		0			0
$183$	−5.94925			−0.439781
$184$	2.14446	−	7.46149i	0.158091	−	0.550069i
$185$	8.04593	+	13.9360i	0.591549	+	1.02459i
$186$	0.173197	+	2.12707i	0.0126994	+	0.155964i
$187$	8.26374	+	4.77107i	0.604304	+	0.348895i
$188$	−8.40332	−	10.2631i	−0.612875	−	0.748517i
$189$		0			0
$190$	5.29392	−	11.1767i	0.384062	−	0.810842i
$191$	−3.63945	+	6.30371i	−0.263341	+	0.456120i	−0.967128	−	0.254291i	$-0.918158\pi$
$191$	−3.63945	+	6.30371i	−0.263341	+	0.456120i	0.703786	+	0.710412i	$0.251491\pi$
$192$	−2.89937	+	4.62744i	−0.209244	+	0.333956i
$193$	−4.76704	−	8.25675i	−0.343139	−	0.594334i	0.641875	−	0.766809i	$-0.278157\pi$
$193$	−4.76704	−	8.25675i	−0.343139	−	0.594334i	−0.985014	+	0.172476i	$0.944823\pi$
$194$	1.10742	+	1.60200i	0.0795080	+	0.115017i
$195$			6.84210i			0.489973i
$196$		0			0
$197$		−	11.6667i		−	0.831221i	−0.909543	−	0.415611i	$-0.863568\pi$
$197$		−	11.6667i		−	0.831221i	0.909543	−	0.415611i	$-0.136432\pi$
$198$	−7.11136	+	4.91589i	−0.505382	+	0.349357i
$199$	9.48247	+	16.4241i	0.672195	+	1.16428i	0.977280	+	0.211950i	$0.0679815\pi$
$199$	9.48247	+	16.4241i	0.672195	+	1.16428i	−0.305086	+	0.952325i	$0.598685\pi$
$200$	−10.7792	−	11.1758i	−0.762206	−	0.790248i
$201$	−1.97779	+	3.42563i	−0.139503	+	0.241626i
$202$	−1.01753	−	0.481960i	−0.0715930	−	0.0339106i
$203$		0			0
$204$	4.17820	−	3.42105i	0.292532	−	0.239521i
$205$	5.92543	+	3.42105i	0.413850	+	0.238936i
$206$	−3.74375	+	0.304836i	−0.260839	+	0.0212389i
$207$	−3.47779	−	6.02371i	−0.241723	−	0.418677i
$208$	−8.18353	+	9.28901i	−0.567426	+	0.644077i
$209$	−6.51337			−0.450540
$210$		0			0
$211$			16.1268i			1.11022i	0.831778	+	0.555109i	$0.187323\pi$
$211$			16.1268i			1.11022i	−0.831778	+	0.555109i	$0.812677\pi$
$212$	0.836879	+	5.10486i	0.0574771	+	0.350603i
$213$	−3.92909	+	2.26846i	−0.269217	+	0.155433i
$214$	0.623264	+	7.65442i	0.0426054	+	0.523245i
$215$	18.7685	−	32.5081i	1.28000	−	2.21703i
$216$	2.57849	+	10.3686i	0.175444	+	0.705493i
$217$		0			0
$218$	−17.6528	−	8.36140i	−1.19560	−	0.566305i
$219$	5.65000	+	3.26203i	0.381792	+	0.220428i
$220$	−5.52079	+	14.6182i	−0.372212	+	0.985556i
$221$	10.6020	−	6.12109i	0.713170	−	0.411749i
$222$	−2.72731	−	3.94534i	−0.183045	−	0.264794i
$223$	7.71477			0.516619			0.258310	−	0.966062i	$-0.416835\pi$
$223$	7.71477			0.516619			0.258310	+	0.966062i	$0.416835\pi$
$224$		0			0
$225$	−13.9112			−0.927411
$226$	3.64617	+	5.27457i	0.242539	+	0.350859i
$227$	1.83996	−	1.06230i	0.122122	−	0.0705074i	−0.437694	−	0.899124i	$-0.644205\pi$
$227$	1.83996	−	1.06230i	0.122122	−	0.0705074i	0.559817	+	0.828616i	$0.310871\pi$
$228$	−1.30232	+	3.44832i	−0.0862480	+	0.228371i
$229$	−8.11289	−	4.68398i	−0.536115	−	0.309526i	0.207388	−	0.978259i	$-0.433504\pi$
$229$	−8.11289	−	4.68398i	−0.536115	−	0.309526i	−0.743503	+	0.668733i	$0.766837\pi$
$230$	−11.3621	−	5.38173i	−0.749192	−	0.354861i
$231$		0			0
$232$	−1.37709	−	5.53756i	−0.0904106	−	0.363558i
$233$	4.41366	−	7.64469i	0.289149	−	0.500820i	−0.684458	−	0.729052i	$-0.739961\pi$
$233$	4.41366	−	7.64469i	0.289149	−	0.500820i	0.973607	+	0.228232i	$0.0732945\pi$
$234$	0.900133	+	11.0547i	0.0588436	+	0.722669i
$235$	−18.6026	+	10.7402i	−1.21350	+	0.700614i
$236$	3.97085	+	24.2217i	0.258480	+	1.57670i
$237$		−	1.14449i		−	0.0743426i
$238$		0			0
$239$	5.93489			0.383896			0.191948	−	0.981405i	$-0.438520\pi$
$239$	5.93489			0.383896			0.191948	+	0.981405i	$0.438520\pi$
$240$	6.63532	+	5.84565i	0.428308	+	0.377335i
$241$	−5.34302	−	9.25439i	−0.344174	−	0.596128i	0.641029	−	0.767517i	$-0.278508\pi$
$241$	−5.34302	−	9.25439i	−0.344174	−	0.596128i	−0.985203	+	0.171389i	$0.945174\pi$
$242$	−7.30245	+	0.594604i	−0.469419	+	0.0382226i
$243$	12.7840	+	7.38083i	0.820092	+	0.473480i
$244$	−13.4872	+	11.0431i	−0.863426	+	0.706961i
$245$		0			0
$246$	−1.84302	−	0.872962i	−0.117507	−	0.0556581i
$247$	−4.17820	+	7.23685i	−0.265852	+	0.460470i
$248$	4.34094	+	4.50064i	0.275650	+	0.285791i
$249$	−2.21076	−	3.82914i	−0.140101	−	0.242662i
$250$	−1.84487	+	1.27531i	−0.116680	+	0.0806578i
$251$			3.82402i			0.241370i	0.992691	+	0.120685i	$0.0385091\pi$
$251$			3.82402i			0.241370i	−0.992691	+	0.120685i	$0.961491\pi$
$252$		0			0
$253$			6.62141i			0.416284i
$254$	−12.4563	−	18.0194i	−0.781579	−	1.13064i
$255$	−4.37241	−	7.57324i	−0.273811	−	0.474255i
$256$	2.01655	+	15.8724i	0.126034	+	0.992026i
$257$	6.20291	−	10.7438i	0.386927	−	0.670177i	−0.605108	−	0.796144i	$-0.706870\pi$
$257$	6.20291	−	10.7438i	0.386927	−	0.670177i	0.992034	+	0.125967i	$0.0402033\pi$
$258$	−4.78924	+	10.1112i	−0.298165	+	0.629495i
$259$		0			0
$260$	12.7004	+	15.5113i	0.787646	+	0.961968i
$261$	−4.42744	−	2.55618i	−0.274052	−	0.158224i
$262$	−1.92927	−	23.6937i	−0.119191	−	1.46380i
$263$	0.672005	+	1.16395i	0.0414376	+	0.0717720i	0.886000	−	0.463685i	$-0.153473\pi$
$263$	0.672005	+	1.16395i	0.0414376	+	0.0717720i	−0.844563	+	0.535457i	$0.820140\pi$
$264$	1.28647	−	4.47617i	0.0791765	−	0.275489i
$265$	8.37709			0.514601
$266$		0			0
$267$			9.54214i			0.583970i
$268$	1.87499	+	11.4372i	0.114534	+	0.698641i
$269$	1.68912	−	0.975212i	0.102987	−	0.0594597i	−0.447622	−	0.894223i	$-0.647729\pi$
$269$	1.68912	−	0.975212i	0.102987	−	0.0594597i	0.550609	+	0.834763i	$0.314396\pi$
$270$	17.2451	−	1.40419i	1.04950	−	0.0854562i
$271$	−13.0190	+	22.5496i	−0.790850	+	1.36979i	0.134590	+	0.990901i	$0.457028\pi$
$271$	−13.0190	+	22.5496i	−0.790850	+	1.36979i	−0.925441	+	0.378892i	$0.876305\pi$
$272$	3.12192	−	15.5113i	0.189294	−	0.940509i
$273$		0			0
$274$	−0.537238	+	1.13423i	−0.0324557	+	0.0685214i
$275$	11.4686	+	6.62141i	0.691583	+	0.399286i
$276$	3.50552	+	1.32392i	0.211007	+	0.0796904i
$277$	13.9578	−	8.05852i	0.838641	−	0.484189i	−0.0181613	−	0.999835i	$-0.505781\pi$
$277$	13.9578	−	8.05852i	0.838641	−	0.484189i	0.856802	+	0.515646i	$0.172448\pi$
$278$	−2.84157	+	1.96430i	−0.170426	+	0.117811i
$279$	5.60221			0.335396
$280$		0			0
$281$	−16.1313			−0.962312			−0.481156	−	0.876635i	$-0.659783\pi$
$281$	−16.1313			−0.962312			−0.481156	+	0.876635i	$0.659783\pi$
$282$	5.26649	−	3.64058i	0.313615	−	0.216793i
$283$	−22.7949	+	13.1606i	−1.35501	+	0.782318i	−0.988947	−	0.148270i	$-0.952629\pi$
$283$	−22.7949	+	13.1606i	−1.35501	+	0.782318i	−0.366068	+	0.930588i	$0.619296\pi$
$284$	−4.69664	+	12.4359i	−0.278694	+	0.737937i
$285$	5.16942	+	2.98457i	0.306210	+	0.176791i
$286$	4.51971	−	9.54214i	0.267256	−	0.564239i
$287$		0			0
$288$	11.4897	+	8.57183i	0.677034	+	0.505100i
$289$	0.676686	−	1.17205i	0.0398050	−	0.0689444i
$290$	−9.21009	+	0.749935i	−0.540835	+	0.0440377i
$291$	−0.814056	+	0.469996i	−0.0477208	+	0.0275516i
$292$	18.8638	−	3.09248i	1.10392	−	0.180974i
$293$		−	9.64929i		−	0.563718i	−0.959456	−	0.281859i	$-0.909049\pi$
$293$		−	9.64929i		−	0.563718i	0.959456	−	0.281859i	$-0.0909510\pi$
$294$		0			0
$295$	39.7479			2.31421
$296$	−13.5063	−	3.88176i	−0.785038	−	0.225622i
$297$	−4.55628	−	7.89171i	−0.264382	−	0.457923i
$298$	−1.08215	−	13.2901i	−0.0626872	−	0.769873i
$299$	7.35688	+	4.24750i	0.425460	+	0.245639i
$300$	5.79861	−	4.74781i	0.334783	−	0.274115i
$301$		0			0
$302$	−4.27020	+	9.01537i	−0.245723	+	0.518777i
$303$	0.271716	−	0.470626i	0.0156097	−	0.0270367i
$304$	3.44843	+	10.2348i	0.197781	+	0.587009i
$305$	14.1141	+	24.4463i	0.808169	+	1.39979i
$306$	−8.06078	−	11.6608i	−0.460804	−	0.666602i
$307$		−	25.2741i		−	1.44247i	−0.692691	−	0.721235i	$-0.743575\pi$
$307$		−	25.2741i		−	1.44247i	0.692691	−	0.721235i	$-0.256425\pi$
$308$		0			0
$309$		−	1.81295i		−	0.103135i
$310$	8.32952	−	5.75797i	0.473085	−	0.327031i
$311$	11.2742	+	19.5275i	0.639302	+	1.10730i	0.985586	+	0.169174i	$0.0541100\pi$
$311$	11.2742	+	19.5275i	0.639302	+	1.10730i	−0.346284	+	0.938130i	$0.612557\pi$
$312$	−4.14812	−	4.30073i	−0.234841	−	0.243481i
$313$	−12.6901	+	21.9798i	−0.717285	+	1.24237i	0.244787	+	0.969577i	$0.421282\pi$
$313$	−12.6901	+	21.9798i	−0.717285	+	1.24237i	−0.962072	+	0.272797i	$0.912051\pi$
$314$	11.1394	+	5.27629i	0.628635	+	0.297758i
$315$		0			0
$316$	−2.12442	−	2.59460i	−0.119508	−	0.145958i
$317$	−14.8384	−	8.56693i	−0.833405	−	0.481167i	0.0216120	−	0.999766i	$-0.493120\pi$
$317$	−14.8384	−	8.56693i	−0.833405	−	0.481167i	−0.855017	+	0.518600i	$0.826453\pi$
$318$	−2.48859	+	0.202634i	−0.139553	+	0.0113632i
$319$	2.43337	+	4.21473i	0.136243	+	0.235979i
$320$	25.8933	+	0.935725i	1.44748	+	0.0523086i
$321$	−3.70674			−0.206890
$322$		0			0
$323$		−	10.6802i		−	0.594264i
$324$	9.91509	−	1.62546i	0.550838	−	0.0903032i
$325$	14.7138	−	8.49500i	0.816173	−	0.471218i
$326$	−2.27566	−	27.9478i	−0.126037	−	1.54789i
$327$	4.71392	−	8.16475i	0.260681	−	0.451512i
$328$	−5.79861	+	1.44201i	−0.320174	+	0.0796218i
$329$		0			0
$330$	−6.81613	−	3.22851i	−0.375216	−	0.177724i
$331$	7.43566	+	4.29298i	0.408701	+	0.235963i	0.690231	−	0.723589i	$-0.257509\pi$
$331$	7.43566	+	4.29298i	0.408701	+	0.235963i	−0.281531	+	0.959552i	$0.590842\pi$
$332$	−12.1196	−	4.57716i	−0.665148	−	0.251204i
$333$	−10.9037	+	6.29527i	−0.597521	+	0.344979i
$334$	−17.8204	−	25.7791i	−0.975090	−	1.41057i
$335$	18.7685			1.02544
$336$		0			0
$337$	−3.18070			−0.173264			−0.0866319	−	0.996240i	$-0.527610\pi$
$337$	−3.18070			−0.173264			−0.0866319	+	0.996240i	$0.527610\pi$
$338$	2.75148	+	3.98031i	0.149661	+	0.216500i
$339$	−2.68027	+	1.54746i	−0.145572	+	0.0840463i
$340$	−23.9700	−	9.05266i	−1.29995	−	0.490950i
$341$	−4.61856	−	2.66653i	−0.250109	−	0.144401i
$342$	8.74483	+	4.14206i	0.472866	+	0.223977i
$343$		0			0
$344$	7.91116	+	31.8123i	0.426541	+	1.71520i
$345$	3.03407	−	5.25516i	0.163349	−	0.282929i
$346$	−2.49418	−	30.6315i	−0.134088	−	1.64676i
$347$	19.0373	−	10.9912i	1.02198	−	0.590039i	0.107302	−	0.994226i	$-0.465779\pi$
$347$	19.0373	−	10.9912i	1.02198	−	0.590039i	0.914676	+	0.404187i	$0.132446\pi$
$348$	2.71791	−	0.445567i	0.145695	−	0.0238849i
$349$			15.5480i			0.832265i	0.909304	+	0.416132i	$0.136615\pi$
$349$			15.5480i			0.832265i	−0.909304	+	0.416132i	$0.863385\pi$
$350$		0			0
$351$	−11.6910			−0.624022
$352$	−5.39227	−	12.5356i	−0.287409	−	0.668149i
$353$	−13.2804	−	23.0023i	−0.706845	−	1.22429i	−0.966022	−	0.258461i	$-0.916785\pi$
$353$	−13.2804	−	23.0023i	−0.706845	−	1.22429i	0.259177	−	0.965830i	$-0.416549\pi$
$354$	−11.8079	+	0.961464i	−0.627584	+	0.0511012i
$355$	18.6429	+	10.7635i	0.989460	+	0.571265i
$356$	17.7123	+	21.6324i	0.938748	+	1.14651i
$357$		0			0
$358$	−4.82799	−	2.28682i	−0.255167	−	0.120862i
$359$	15.5062	−	26.8575i	0.818386	−	1.41749i	−0.0884855	−	0.996077i	$-0.528203\pi$
$359$	15.5062	−	26.8575i	0.818386	−	1.41749i	0.906871	−	0.421408i	$-0.138464\pi$
$360$	16.7083	−	16.1154i	0.880606	−	0.849358i
$361$	−5.85488	−	10.1410i	−0.308152	−	0.533735i
$362$	−16.3243	+	11.2846i	−0.857988	+	0.593104i
$363$		−	3.53630i		−	0.185607i
$364$		0			0
$365$		−	30.9555i		−	1.62029i
$366$	−4.78421	−	6.92087i	−0.250075	−	0.361760i
$367$	−6.38677	−	11.0622i	−0.333387	−	0.577443i	0.649787	−	0.760117i	$-0.274858\pi$
$367$	−6.38677	−	11.0622i	−0.333387	−	0.577443i	−0.983174	+	0.182674i	$0.941525\pi$
$368$	10.4046	−	3.50563i	0.542377	−	0.182743i
$369$	−2.67669	+	4.63616i	−0.139343	+	0.241349i
$370$	−9.74166	+	20.5669i	−0.506445	+	1.06922i
$371$		0			0
$372$	−2.33518	+	1.91201i	−0.121073	+	0.0991330i
$373$	5.73431	+	3.31070i	0.296911	+	0.171422i	0.641054	−	0.767495i	$-0.278497\pi$
$373$	5.73431	+	3.31070i	0.296911	+	0.171422i	−0.344143	+	0.938917i	$0.611831\pi$
$374$	1.09518	+	13.4501i	0.0566304	+	0.695489i
$375$	−0.541251	−	0.937474i	−0.0279501	−	0.0484109i
$376$	5.18161	−	18.0291i	0.267221	−	0.929777i
$377$	6.24384			0.321574
$378$		0			0
$379$			18.7804i			0.964683i	0.875983	+	0.482341i	$0.160214\pi$
$379$			18.7804i			0.964683i	−0.875983	+	0.482341i	$0.839786\pi$
$380$	17.2593	−	2.82944i	0.885382	−	0.145147i
$381$	9.15656	−	5.28654i	0.469105	−	0.270838i
$382$	−10.2600	+	0.835421i	−0.524945	+	0.0427438i
$383$	−10.2179	+	17.6980i	−0.522112	+	0.904325i	0.477557	+	0.878601i	$0.341522\pi$
$383$	−10.2179	+	17.6980i	−0.522112	+	0.904325i	−0.999669	+	0.0257240i	$0.991811\pi$
$384$	−7.71477	+	0.348359i	−0.393693	+	0.0177771i
$385$		0			0
$386$	5.77172	−	12.1854i	0.293773	−	0.620221i
$387$	25.4349	+	14.6848i	1.29293	+	0.746472i
$388$	−0.973081	+	2.57656i	−0.0494007	+	0.130805i
$389$	2.05734	−	1.18781i	0.104311	−	0.0602242i	−0.446937	−	0.894566i	$-0.647485\pi$
$389$	2.05734	−	1.18781i	0.104311	−	0.0602242i	0.551248	+	0.834341i	$0.314152\pi$
$390$	−7.95954	+	5.50221i	−0.403047	+	0.278615i
$391$	−10.8574			−0.549082
$392$		0			0
$393$	11.4740			0.578785
$394$	13.5721	−	9.38205i	0.683754	−	0.472661i
$395$	−4.70287	+	2.71520i	−0.236627	+	0.136617i
$396$	−11.4375	−	4.31956i	−0.574756	−	0.217066i
$397$	−19.1993	−	11.0847i	−0.963583	−	0.556325i	−0.0663091	−	0.997799i	$-0.521122\pi$
$397$	−19.1993	−	11.0847i	−0.963583	−	0.556325i	−0.897274	+	0.441474i	$0.854456\pi$
$398$	−11.4810	+	24.2389i	−0.575488	+	1.21499i
$399$		0			0
$400$	4.33268	−	21.5269i	0.216634	−	1.07635i
$401$	−13.1585	+	22.7912i	−0.657104	+	1.13814i	0.324258	+	0.945969i	$0.394885\pi$
$401$	−13.1585	+	22.7912i	−0.657104	+	1.13814i	−0.981362	+	0.192168i	$0.938448\pi$
$402$	−5.57558	+	0.453994i	−0.278085	+	0.0226432i
$403$	−5.92543	+	3.42105i	−0.295167	+	0.170415i
$404$	−0.257593	−	1.57129i	−0.0128157	−	0.0781745i
$405$		−	16.2707i		−	0.808497i
$406$		0			0
$407$	11.9856			0.594106
$408$	7.33975	+	2.10947i	0.363372	+	0.104434i
$409$	−0.331162	−	0.573590i	−0.0163749	−	0.0283622i	0.857722	−	0.514114i	$-0.171879\pi$
$409$	−0.331162	−	0.573590i	−0.0163749	−	0.0283622i	−0.874097	+	0.485752i	$0.838546\pi$
$410$	0.785288	+	9.64427i	0.0387826	+	0.476296i
$411$	−0.524603	−	0.302880i	−0.0258768	−	0.0149399i
$412$	−3.36523	−	4.11003i	−0.165793	−	0.202487i
$413$		0			0
$414$	4.21076	−	8.88987i	0.206947	−	0.436913i
$415$	−10.4897	+	18.1686i	−0.514917	+	0.891862i
$416$	−17.3870	−	2.05011i	−0.852469	−	0.100515i
$417$	−0.833662	−	1.44395i	−0.0408246	−	0.0707103i
$418$	−5.23786	−	7.57713i	−0.256192	−	0.370609i
$419$		−	7.55501i		−	0.369086i	−0.982824	−	0.184543i	$-0.940919\pi$
$419$		−	7.55501i		−	0.369086i	0.982824	−	0.184543i	$-0.0590805\pi$
$420$		0			0
$421$		−	12.5905i		−	0.613625i	−0.951770	−	0.306813i	$-0.900737\pi$
$421$		−	12.5905i		−	0.613625i	0.951770	−	0.306813i	$-0.0992625\pi$
$422$	−18.7606	+	12.9687i	−0.913254	+	0.631308i
$423$	−8.40332	−	14.5550i	−0.408583	−	0.707687i
$424$	−5.26559	+	5.07874i	−0.255719	+	0.246645i
$425$	−10.8574	+	18.8055i	−0.526661	+	0.912203i
$426$	−5.79861	−	2.74655i	−0.280943	−	0.133071i
$427$		0			0
$428$	−8.40332	+	6.88051i	−0.406190	+	0.332582i
$429$	4.41342	+	2.54809i	0.213082	+	0.123023i
$430$	52.9104	−	4.30825i	2.55156	−	0.207762i
$431$	6.45241	+	11.1759i	0.310802	+	0.538325i	0.978536	−	0.206075i	$-0.0660691\pi$
$431$	6.45241	+	11.1759i	0.310802	+	0.538325i	−0.667734	+	0.744400i	$0.732736\pi$
$432$	−9.98843	+	11.3377i	−0.480568	+	0.545486i
$433$	40.5815			1.95022			0.975112	−	0.221715i	$-0.0711654\pi$
$433$	40.5815			1.95022			0.975112	+	0.221715i	$0.0711654\pi$
$434$		0			0
$435$		−	4.46009i		−	0.213845i
$436$	−4.46891	−	27.2598i	−0.214022	−	1.30551i
$437$	6.41824	−	3.70557i	0.307026	−	0.177262i
$438$	0.748786	+	9.19598i	0.0357784	+	0.439401i
$439$	18.2273	−	31.5706i	0.869941	−	1.50678i	0.00788596	−	0.999969i	$-0.497490\pi$
$439$	18.2273	−	31.5706i	0.869941	−	1.50678i	0.862055	−	0.506814i	$-0.169177\pi$
$440$	−21.4452	+	5.33306i	−1.02236	+	0.254244i
$441$		0			0
$442$	15.6466	+	7.41115i	0.744234	+	0.352512i
$443$	−28.1274	−	16.2393i	−1.33637	−	0.771555i	−0.350104	−	0.936711i	$-0.613854\pi$
$443$	−28.1274	−	16.2393i	−1.33637	−	0.771555i	−0.986267	+	0.165156i	$0.947187\pi$
$444$	2.39647	−	6.34546i	0.113731	−	0.301142i
$445$	39.2100	−	22.6379i	1.85873	−	1.07314i
$446$	6.20399	+	8.97473i	0.293767	+	0.424966i
$447$	6.43587			0.304406
$448$		0			0
$449$	25.9823			1.22618			0.613091	−	0.790012i	$-0.289926\pi$
$449$	25.9823			1.22618			0.613091	+	0.790012i	$0.289926\pi$
$450$	−11.1869	−	16.1831i	−0.527358	−	0.762879i
$451$	4.41342	−	2.54809i	0.207820	−	0.119985i
$452$	−3.20386	+	8.48330i	−0.150697	+	0.399021i
$453$	−4.16978	−	2.40742i	−0.195913	−	0.113111i
$454$	2.71544	+	1.28619i	0.127442	+	0.0603638i
$455$		0			0
$456$	−5.05878	+	1.25803i	−0.236899	+	0.0589127i
$457$	5.73448	−	9.93241i	0.268248	−	0.464618i	−0.700162	−	0.713984i	$-0.746889\pi$
$457$	5.73448	−	9.93241i	0.268248	−	0.464618i	0.968409	+	0.249366i	$0.0802221\pi$
$458$	−1.07519	−	13.2046i	−0.0502403	−	0.617010i
$459$	12.9403	−	7.47111i	0.604004	−	0.348722i
$460$	−2.87637	−	17.5455i	−0.134112	−	0.818064i
$461$		−	25.1973i		−	1.17355i	−0.809749	−	0.586777i	$-0.800396\pi$
$461$		−	25.1973i		−	1.17355i	0.809749	−	0.586777i	$-0.199604\pi$
$462$		0			0
$463$	−31.8223			−1.47891			−0.739454	−	0.673207i	$-0.764916\pi$
$463$	−31.8223			−1.47891			−0.739454	+	0.673207i	$0.764916\pi$
$464$	5.33452	−	6.05514i	0.247649	−	0.281103i
$465$	2.44372	+	4.23265i	0.113325	+	0.196284i
$466$	12.4425	−	1.01314i	0.576390	−	0.0469328i
$467$	12.3089	+	7.10656i	0.569589	+	0.328852i	0.756985	−	0.653432i	$-0.226671\pi$
$467$	12.3089	+	7.10656i	0.569589	+	0.328852i	−0.187396	+	0.982284i	$0.560005\pi$
$468$	−12.1363	+	9.93701i	−0.561000	+	0.459338i
$469$		0			0
$470$	−27.4539	−	13.0038i	−1.26636	−	0.599819i
$471$	−2.97462	+	5.15220i	−0.137063	+	0.237401i
$472$	−24.9843	+	24.0977i	−1.14999	+	1.10919i
$473$	−13.9793	−	24.2129i	−0.642769	−	1.11331i
$474$	1.33141	−	0.920365i	0.0611535	−	0.0422738i
$475$		−	14.8223i		−	0.680094i
$476$		0			0
$477$			6.55438i			0.300104i
$478$	4.77266	+	6.90416i	0.218296	+	0.315789i
$479$	−5.77020	−	9.99428i	−0.263647	−	0.456650i	0.703561	−	0.710635i	$-0.251592\pi$
$479$	−5.77020	−	9.99428i	−0.263647	−	0.456650i	−0.967208	+	0.253984i	$0.918259\pi$
$480$	−1.46443	+	12.4199i	−0.0668418	+	0.566888i
$481$	7.68855	−	13.3170i	0.350568	−	0.607201i
$482$	6.46910	−	13.6577i	0.294659	−	0.622093i
$483$		0			0
$484$	−6.56413	−	8.01691i	−0.298369	−	0.364405i
$485$	3.86255	+	2.23005i	0.175390	+	0.101261i
$486$	1.69424	+	20.8073i	0.0768523	+	0.943837i
$487$	8.80829	+	15.2564i	0.399142	+	0.691333i	0.993620	−	0.112778i	$-0.0359749\pi$
$487$	8.80829	+	15.2564i	0.399142	+	0.691333i	−0.594479	+	0.804111i	$0.702642\pi$
$488$	−23.6926	−	6.80933i	−1.07251	−	0.308244i
$489$	13.5341			0.612032
$490$		0			0
$491$			26.8502i			1.21173i	0.795567	+	0.605866i	$0.207173\pi$
$491$			26.8502i			1.21173i	−0.795567	+	0.605866i	$0.792827\pi$
$492$	−0.466572	−	2.84603i	−0.0210347	−	0.128309i
$493$	−6.91105	+	3.99010i	−0.311258	+	0.179705i
$494$	−11.7787	+	0.959089i	−0.529951	+	0.0431515i
$495$	−9.89930	+	17.1461i	−0.444941	+	0.770660i
$496$	−1.74483	+	8.66918i	−0.0783450	+	0.389258i
$497$		0			0
$498$	2.67669	−	5.65110i	0.119945	−	0.253232i
$499$	−2.21925	−	1.28129i	−0.0993474	−	0.0573583i	0.449503	−	0.893279i	$-0.351601\pi$
$499$	−2.21925	−	1.28129i	−0.0993474	−	0.0573583i	−0.548851	+	0.835921i	$0.684934\pi$
$500$	−2.96719	−	1.12061i	−0.132697	−	0.0501151i
$501$	13.0997	−	7.56310i	0.585251	−	0.337895i
$502$	−4.44855	+	3.07516i	−0.198548	+	0.137251i
$503$	14.6941			0.655176			0.327588	−	0.944821i	$-0.393764\pi$
$503$	14.6941			0.655176			0.327588	+	0.944821i	$0.393764\pi$
$504$		0			0
$505$	−2.57849			−0.114741
$506$	−7.70280	+	5.32474i	−0.342431	+	0.236714i
$507$	−2.02259	+	1.16775i	−0.0898266	+	0.0518614i
$508$	10.9453	−	28.9813i	0.485619	−	1.28584i
$509$	11.0283	+	6.36720i	0.488821	+	0.282221i	0.724085	−	0.689710i	$-0.242262\pi$
$509$	11.0283	+	6.36720i	0.488821	+	0.282221i	−0.235264	+	0.971932i	$0.575595\pi$
$510$	5.29392	−	11.1767i	0.234419	−	0.494912i
$511$		0			0
$512$	−16.8430	+	15.1100i	−0.744364	+	0.667775i
$513$	−5.09971	+	8.83296i	−0.225158	+	0.389985i
$514$	17.4866	−	1.42385i	0.771301	−	0.0628035i
$515$	−7.44968	+	4.30107i	−0.328272	+	0.189528i
$516$	−15.6139	+	2.55971i	−0.687364	+	0.112685i
$517$			15.9992i			0.703643i
$518$		0			0
$519$	14.8337			0.651126
$520$	−7.83126	+	27.2483i	−0.343423	+	1.19492i
$521$	17.0134	+	29.4680i	0.745369	+	1.29102i	0.950022	+	0.312183i	$0.101060\pi$
$521$	17.0134	+	29.4680i	0.745369	+	1.29102i	−0.204652	+	0.978835i	$0.565606\pi$
$522$	−0.586762	−	7.20613i	−0.0256819	−	0.315404i
$523$	5.88515	+	3.39779i	0.257340	+	0.148575i	0.623120	−	0.782126i	$-0.285865\pi$
$523$	5.88515	+	3.39779i	0.257340	+	0.148575i	−0.365781	+	0.930701i	$0.619198\pi$
$524$	26.0119	−	21.2981i	1.13633	−	0.930413i
$525$		0			0
$526$	−0.813634	+	1.71777i	−0.0354761	+	0.0748982i
$527$	4.37241	−	7.57324i	0.190465	−	0.329896i
$528$	6.24175	−	2.10304i	0.271637	−	0.0915229i
$529$	7.73296	+	13.3939i	0.336216	+	0.582343i
$530$	6.73661	+	9.74523i	0.292620	+	0.423306i
$531$			31.0994i			1.34960i
$532$		0			0
$533$		−	6.53819i		−	0.283200i
$534$	−11.1005	+	7.67351i	−0.480368	+	0.332065i
$535$	8.79392	+	15.2315i	0.380195	+	0.658516i
$536$	−11.7973	+	11.3787i	−0.509567	+	0.491485i
$537$	1.28924	−	2.23304i	0.0556350	−	0.0963626i
$538$	2.49282	+	1.18074i	0.107473	+	0.0509055i
$539$		0			0
$540$	15.5015	+	18.9323i	0.667079	+	0.814718i
$541$	21.3952	+	12.3525i	0.919852	+	0.531077i	0.883588	−	0.468266i	$-0.155121\pi$
$541$	21.3952	+	12.3525i	0.919852	+	0.531077i	0.0362640	+	0.999342i	$0.488454\pi$
$542$	−36.7019	+	2.98847i	−1.57648	+	0.128366i
$543$	−4.78924	−	8.29521i	−0.205526	−	0.355982i
$544$	20.5551	−	8.84193i	0.881293	−	0.379094i
$545$	−44.7335			−1.91617
$546$		0			0
$547$		−	27.5793i		−	1.17920i	−0.807694	−	0.589602i	$-0.799284\pi$
$547$		−	27.5793i		−	1.17920i	0.807694	−	0.589602i	$-0.200716\pi$
$548$	−1.75150	+	0.287137i	−0.0748205	+	0.0122659i
$549$	−19.1272	+	11.0431i	−0.816328	+	0.471307i
$550$	1.51992	+	18.6664i	0.0648095	+	0.795937i
$551$	2.72360	−	4.71742i	0.116029	−	0.200969i
$552$	1.27890	+	5.14268i	0.0544334	+	0.218887i
$553$		0			0
$554$	20.5990	+	9.75690i	0.875169	+	0.414531i
$555$	−9.51256	−	5.49208i	−0.403785	−	0.233126i
$556$	−4.57021	−	1.72602i	−0.193820	−	0.0731995i
$557$	−39.1575	+	22.6076i	−1.65916	+	0.957914i	−0.686050	+	0.727555i	$0.740657\pi$
$557$	−39.1575	+	22.6076i	−1.65916	+	0.957914i	−0.973106	+	0.230359i	$0.926010\pi$
$558$	4.50513	+	6.51715i	0.190717	+	0.275893i
$559$	−35.8698			−1.51713
$560$		0			0
$561$	−6.51337			−0.274995
$562$	−12.9723	−	18.7658i	−0.547204	−	0.791588i
$563$	13.1895	−	7.61497i	0.555872	−	0.320933i	−0.195615	−	0.980681i	$-0.562670\pi$
$563$	13.1895	−	7.61497i	0.555872	−	0.320933i	0.751487	+	0.659748i	$0.229337\pi$
$564$	8.47031	+	3.19895i	0.356664	+	0.134700i
$565$	12.7174	+	7.34241i	0.535026	+	0.308898i
$566$	−33.6410	−	15.9343i	−1.41404	−	0.669769i
$567$		0			0
$568$	−18.2438	+	4.53693i	−0.765495	+	0.190365i
$569$	−7.04343	+	12.1996i	−0.295276	+	0.511433i	−0.975049	−	0.221989i	$-0.928745\pi$
$569$	−7.04343	+	12.1996i	−0.295276	+	0.511433i	0.679773	+	0.733423i	$0.262078\pi$
$570$	0.685096	+	8.41379i	0.0286955	+	0.352415i
$571$	−19.2480	+	11.1129i	−0.805505	+	0.465058i	−0.845392	−	0.534146i	$-0.820633\pi$
$571$	−19.2480	+	11.1129i	−0.805505	+	0.465058i	0.0398876	+	0.999204i	$0.487300\pi$
$572$	14.7352	−	2.41565i	0.616108	−	0.101003i
$573$		−	4.96851i		−	0.207562i
$574$		0			0
$575$	−15.0681			−0.628385
$576$	−0.732126	+	20.2593i	−0.0305053	+	0.844139i
$577$	4.68070	+	8.10721i	0.194860	+	0.337507i	0.946855	−	0.321662i	$-0.104241\pi$
$577$	4.68070	+	8.10721i	0.194860	+	0.337507i	−0.751995	+	0.659169i	$0.770908\pi$
$578$	1.90764	−	0.155331i	0.0793475	−	0.00646090i
$579$	5.63598	+	3.25393i	0.234223	+	0.135229i
$580$	−8.27890	−	10.1112i	−0.343762	−	0.419844i
$581$		0			0
$582$	−1.20139	−	0.569050i	−0.0497994	−	0.0235879i
$583$	3.11974	−	5.40355i	0.129206	−	0.223792i
$584$	18.7672	+	19.4577i	0.776594	+	0.805165i
$585$	12.7004	+	21.9978i	0.525097	+	0.909495i
$586$	11.2252	−	7.75968i	0.463709	−	0.320549i
$587$			13.0157i			0.537217i	0.963249	+	0.268608i	$0.0865637\pi$
$587$			13.0157i			0.537217i	−0.963249	+	0.268608i	$0.913436\pi$
$588$		0			0
$589$			5.96914i			0.245954i
$590$	31.9641	+	46.2394i	1.31594	+	1.90365i
$591$	3.98180	+	6.89669i	0.163790	+	0.283692i
$592$	−6.34566	−	18.8337i	−0.260805	−	0.774062i
$593$	−0.698895	+	1.21052i	−0.0287002	+	0.0497101i	−0.880019	−	0.474939i	$-0.842470\pi$
$593$	−0.698895	+	1.21052i	−0.0287002	+	0.0497101i	0.851319	+	0.524649i	$0.175803\pi$
$594$	5.51654	−	11.6467i	0.226346	−	0.477869i
$595$		0			0
$596$	14.5903	−	11.9464i	0.597644	−	0.489342i
$597$	−11.2110	−	6.47265i	−0.458834	−	0.264908i
$598$	0.974997	+	11.9741i	0.0398706	+	0.489658i
$599$	15.9302	+	27.5919i	0.650891	+	1.12738i	0.982907	+	0.184102i	$0.0589377\pi$
$599$	15.9302	+	27.5919i	0.650891	+	1.12738i	−0.332017	+	0.943274i	$0.607729\pi$
$600$	10.1863	+	2.92757i	0.415853	+	0.119518i
$601$	−34.4927			−1.40699			−0.703493	−	0.710702i	$-0.748377\pi$
$601$	−34.4927			−1.40699			−0.703493	+	0.710702i	$0.748377\pi$
$602$		0			0
$603$			14.6848i			0.598012i
$604$	−13.9217	+	2.28229i	−0.566467	+	0.0928652i
$605$	−14.5311	+	8.38955i	−0.590775	+	0.341084i
$606$	0.765993	−	0.0623713i	0.0311163	−	0.00253366i
$607$	−4.61573	+	7.99467i	−0.187347	+	0.324494i	−0.944365	−	0.328900i	$-0.893322\pi$
$607$	−4.61573	+	7.99467i	−0.187347	+	0.324494i	0.757018	+	0.653394i	$0.226655\pi$
$608$	−9.13325	+	12.2422i	−0.370402	+	0.496486i
$609$		0			0
$610$	−17.0887	+	36.0781i	−0.691901	+	1.46076i
$611$	17.7763	+	10.2631i	0.719152	+	0.415202i
$612$	7.08295	−	18.7545i	0.286311	−	0.758106i
$613$	−28.0431	+	16.1907i	−1.13265	+	0.653935i	−0.944600	−	0.328225i	$-0.893550\pi$
$613$	−28.0431	+	16.1907i	−1.13265	+	0.653935i	−0.188049	+	0.982160i	$0.560216\pi$
$614$	29.4018	−	20.3247i	1.18656	−	0.820238i
$615$	−4.67035			−0.188327
$616$		0			0
$617$	−10.1600			−0.409026			−0.204513	−	0.978864i	$-0.565561\pi$
$617$	−10.1600			−0.409026			−0.204513	+	0.978864i	$0.565561\pi$
$618$	2.10904	−	1.45792i	0.0848381	−	0.0586463i
$619$	−32.1866	+	18.5829i	−1.29369	+	0.746911i	−0.979306	−	0.202385i	$-0.935131\pi$
$619$	−32.1866	+	18.5829i	−1.29369	+	0.746911i	−0.314382	+	0.949297i	$0.601797\pi$
$620$	13.3967	+	5.05949i	0.538025	+	0.203194i
$621$	8.97946	+	5.18430i	0.360333	+	0.208039i
$622$	−13.6503	+	28.8190i	−0.547328	+	1.15553i
$623$		0			0
$624$	1.66732	−	8.28411i	0.0667464	−	0.331630i
$625$	11.1560	−	19.3227i	0.446240	−	0.772910i
$626$	−35.7745	+	2.91295i	−1.42984	+	0.116425i
$627$	3.85032	−	2.22298i	0.153767	−	0.0887774i
$628$	2.82002	+	17.2018i	0.112531	+	0.686425i
$629$			19.6533i			0.783630i
$630$		0			0
$631$	−7.31198			−0.291085			−0.145543	−	0.989352i	$-0.546493\pi$
$631$	−7.31198			−0.291085			−0.145543	+	0.989352i	$0.546493\pi$
$632$	1.30995	−	4.55788i	0.0521069	−	0.181303i
$633$	−5.50401	−	9.53323i	−0.218765	−	0.378912i
$634$	−1.96650	−	24.1510i	−0.0780999	−	0.959159i
$635$	−43.4463	−	25.0837i	−1.72411	−	0.995418i
$636$	−2.23698	−	2.73207i	−0.0887019	−	0.108334i
$637$		0			0
$638$	−2.94622	+	6.22015i	−0.116642	+	0.246258i
$639$	−8.42151	+	14.5865i	−0.333150	+	0.577032i
$640$	19.7341	+	30.8746i	0.780058	+	1.22043i
$641$	−6.85337	−	11.8704i	−0.270692	−	0.468852i	0.698347	−	0.715759i	$-0.253919\pi$
$641$	−6.85337	−	11.8704i	−0.270692	−	0.468852i	−0.969039	+	0.246907i	$0.920586\pi$
$642$	−2.98085	−	4.31212i	−0.117645	−	0.170186i
$643$		−	30.5812i		−	1.20600i	−0.797740	−	0.603002i	$-0.793971\pi$
$643$		−	30.5812i		−	1.20600i	0.797740	−	0.603002i	$-0.206029\pi$
$644$		0			0
$645$			25.6225i			1.00888i
$646$	12.4245	−	8.58874i	0.488836	−	0.337919i
$647$	21.2979	+	36.8891i	0.837308	+	1.45026i	0.892137	+	0.451765i	$0.149205\pi$
$647$	21.2979	+	36.8891i	0.837308	+	1.45026i	−0.0548287	+	0.998496i	$0.517461\pi$
$648$	9.86435	+	10.2273i	0.387508	+	0.401765i
$649$	14.8026	−	25.6389i	0.581054	−	1.00641i
$650$	21.7148	+	10.2854i	0.851723	+	0.403425i
$651$		0			0
$652$	30.6822	−	25.1222i	1.20161	−	0.983859i
$653$	−26.9273	−	15.5465i	−1.05375	−	0.608381i	−0.130051	−	0.991507i	$-0.541514\pi$
$653$	−26.9273	−	15.5465i	−1.05375	−	0.608381i	−0.923696	+	0.383126i	$0.874848\pi$
$654$	13.2890	−	1.08206i	0.519641	−	0.0423120i
$655$	−27.2210	−	47.1481i	−1.06361	−	1.84223i
$656$	−6.34059	−	5.58600i	−0.247558	−	0.218097i
$657$	24.2201			0.944917
$658$		0			0
$659$		−	35.8472i		−	1.39641i	−0.715899	−	0.698204i	$-0.753983\pi$
$659$		−	35.8472i		−	1.39641i	0.715899	−	0.698204i	$-0.246017\pi$
$660$	−1.72554	−	10.5256i	−0.0671667	−	0.409709i
$661$	23.6297	−	13.6426i	0.919087	−	0.530635i	0.0357432	−	0.999361i	$-0.488620\pi$
$661$	23.6297	−	13.6426i	0.919087	−	0.530635i	0.883344	+	0.468726i	$0.155287\pi$
$662$	0.985436	+	12.1023i	0.0383001	+	0.470370i
$663$	−4.17820	+	7.23685i	−0.162268	+	0.281056i
$664$	−4.42151	−	17.7797i	−0.171588	−	0.689988i
$665$		0			0
$666$	−16.0919	−	7.62204i	−0.623547	−	0.295348i
$667$	−4.79566	−	2.76878i	−0.185689	−	0.107208i
$668$	15.6587	−	41.4617i	0.605853	−	1.60420i
$669$	−4.56051	+	2.63301i	−0.176320	+	0.101798i
$670$	15.0931	+	21.8338i	0.583098	+	0.843513i
$671$	21.0251			0.811663
$672$		0			0
$673$	−32.2963			−1.24493			−0.622465	−	0.782648i	$-0.713869\pi$
$673$	−32.2963			−1.24493			−0.622465	+	0.782648i	$0.713869\pi$
$674$	−2.55782	−	3.70017i	−0.0985237	−	0.142525i
$675$	17.9589	−	10.3686i	0.691239	−	0.399087i
$676$	−2.41771	+	6.40169i	−0.0929887	+	0.246219i
$677$	−13.5785	−	7.83953i	−0.521863	−	0.301298i	0.215834	−	0.976430i	$-0.430753\pi$
$677$	−13.5785	−	7.83953i	−0.521863	−	0.301298i	−0.737697	+	0.675132i	$0.764086\pi$
$678$	−3.95558	−	1.87359i	−0.151913	−	0.0719549i
$679$		0			0
$680$	−8.74483	−	35.1646i	−0.335349	−	1.34850i
$681$	−0.725117	+	1.25594i	−0.0277865	+	0.0481277i
$682$	−0.612091	−	7.51720i	−0.0234382	−	0.287849i
$683$	16.5012	−	9.52698i	0.631401	−	0.364540i	−0.149893	−	0.988702i	$-0.547893\pi$
$683$	16.5012	−	9.52698i	0.631401	−	0.364540i	0.781295	+	0.624162i	$0.214560\pi$
$684$	2.21380	+	13.5039i	0.0846469	+	0.516336i
$685$			2.87422i			0.109818i
$686$		0			0
$687$	6.39448			0.243965
$688$	−30.6459	+	34.7857i	−1.16836	+	1.32619i
$689$	−4.00250	−	6.93253i	−0.152483	−	0.264108i
$690$	8.55334	−	0.696459i	0.325620	−	0.0265137i
$691$	−26.9066	−	15.5345i	−1.02358	−	0.590961i	−0.108438	−	0.994103i	$-0.534585\pi$
$691$	−26.9066	−	15.5345i	−1.02358	−	0.590961i	−0.915138	+	0.403142i	$0.867918\pi$
$692$	33.6284	−	27.5345i	1.27836	−	1.04670i
$693$		0			0
$694$	28.0956	+	13.3077i	1.06649	+	0.505153i
$695$	−3.95558	+	6.85127i	−0.150044	+	0.259883i
$696$	2.70400	+	2.80348i	0.102495	+	0.106266i
$697$	4.17820	+	7.23685i	0.158261	+	0.274115i
$698$	−18.0873	+	12.5032i	−0.684613	+	0.473254i
$699$			6.02545i			0.227903i
$700$		0			0
$701$			33.5258i			1.26625i	0.774048	+	0.633127i	$0.218229\pi$
$701$			33.5258i			1.26625i	−0.774048	+	0.633127i	$0.781771\pi$
$702$	−9.40160	−	13.6004i	−0.354840	−	0.513314i
$703$	−6.70759	−	11.6179i	−0.252981	−	0.438177i
$704$	10.2466	−	16.3537i	0.386182	−	0.616353i
$705$	7.33116	−	12.6979i	0.276108	−	0.478232i
$706$	16.0793	−	33.9472i	0.605154	−	1.27762i
$707$		0			0
$708$	−10.6141	−	12.9632i	−0.398901	−	0.487186i
$709$	7.16576	+	4.13715i	0.269116	+	0.155374i	0.628486	−	0.777821i	$-0.283675\pi$
$709$	7.16576	+	4.13715i	0.269116	+	0.155374i	−0.359370	+	0.933195i	$0.617008\pi$
$710$	2.47071	+	30.3432i	0.0927241	+	1.13876i
$711$	−2.12442	−	3.67960i	−0.0796720	−	0.137996i
$712$	−10.9216	+	38.0011i	−0.409306	+	1.42415i
$713$	6.06814			0.227254
$714$		0			0
$715$		−	24.1805i		−	0.904298i
$716$	−1.22224	−	7.45549i	−0.0456771	−	0.278625i
$717$	−3.50835	+	2.02555i	−0.131022	+	0.0756455i
$718$	43.7135	−	3.55939i	1.63137	−	0.132835i
$719$	−1.81462	+	3.14301i	−0.0676739	+	0.117215i	−0.897877	−	0.440246i	$-0.854891\pi$
$719$	−1.81462	+	3.14301i	−0.0676739	+	0.117215i	0.830203	+	0.557461i	$0.188224\pi$
$720$	32.1837	+	6.47755i	1.19942	+	0.241404i
$721$		0			0
$722$	7.08884	−	14.9662i	0.263819	−	0.556983i
$723$	6.31696	+	3.64710i	0.234930	+	0.135637i
$724$	−26.2551	−	9.91567i	−0.975763	−	0.368513i
$725$	−9.59133	+	5.53756i	−0.356213	+	0.205660i
$726$	4.11384	−	2.84379i	0.152679	−	0.105543i
$727$	−28.1550			−1.04421			−0.522106	−	0.852881i	$-0.674853\pi$
$727$	−28.1550			−1.04421			−0.522106	+	0.852881i	$0.674853\pi$
$728$		0			0
$729$	4.99500			0.185000
$730$	36.0111	−	24.8935i	1.33283	−	0.921351i
$731$	39.7028	−	22.9224i	1.46846	−	0.847816i
$732$	4.20385	−	11.1311i	0.155379	−	0.411418i
$733$	25.4264	+	14.6799i	0.939145	+	0.542215i	0.889692	−	0.456561i	$-0.150919\pi$
$733$	25.4264	+	14.6799i	0.939145	+	0.542215i	0.0494525	+	0.998776i	$0.484252\pi$
$734$	7.73282	−	16.3258i	0.285424	−	0.602595i
$735$		0			0
$736$	12.4452	+	9.28474i	0.458737	+	0.342240i
$737$	6.98965	−	12.1064i	0.257467	−	0.445946i
$738$	−7.54584	+	0.614423i	−0.277766	+	0.0226172i
$739$	11.2457	−	6.49271i	0.413680	−	0.238838i	−0.278690	−	0.960381i	$-0.589900\pi$
$739$	11.2457	−	6.49271i	0.413680	−	0.238838i	0.692370	+	0.721543i	$0.256567\pi$
$740$	−31.7598	+	5.20662i	−1.16751	+	0.191399i
$741$		−	5.70400i		−	0.209542i
$742$		0			0
$743$	21.8510			0.801637			0.400819	−	0.916157i	$-0.368726\pi$
$743$	21.8510			0.801637			0.400819	+	0.916157i	$0.368726\pi$
$744$	−4.10215	−	1.17897i	−0.150392	−	0.0432232i
$745$	−15.2685	−	26.4459i	−0.559396	−	0.968903i
$746$	0.759959	+	9.33319i	0.0278241	+	0.341713i
$747$	−14.2154	−	8.20728i	−0.520115	−	0.300289i
$748$	−14.7660	+	12.0902i	−0.539900	+	0.442062i
$749$		0			0
$750$	0.655322	−	1.38354i	0.0239290	−	0.0505196i
$751$	−6.03724	+	10.4568i	−0.220302	+	0.381574i	−0.954900	−	0.296929i	$-0.904038\pi$
$751$	−6.03724	+	10.4568i	−0.220302	+	0.381574i	0.734598	+	0.678503i	$0.237371\pi$
$752$	25.1404	−	8.47058i	0.916777	−	0.308890i
$753$	−1.30512	−	2.26053i	−0.0475612	−	0.0823783i
$754$	5.02111	+	7.26357i	0.182858	+	0.264524i
$755$			22.8456i			0.831436i
$756$		0			0
$757$			27.2309i			0.989725i	0.868971	+	0.494862i	$0.164782\pi$
$757$			27.2309i			0.989725i	−0.868971	+	0.494862i	$0.835218\pi$
$758$	−21.8475	+	15.1026i	−0.793539	+	0.548552i
$759$	−2.25985	−	3.91418i	−0.0820275	−	0.142076i
$760$	17.1709	+	17.8027i	0.622855	+	0.645770i
$761$	15.2423	−	26.4005i	0.552534	−	0.957017i	−0.445557	−	0.895254i	$-0.646994\pi$
$761$	15.2423	−	26.4005i	0.552534	−	0.957017i	0.998091	−	0.0617632i	$-0.0196724\pi$
$762$	13.5134	+	6.40072i	0.489538	+	0.231873i
$763$		0			0
$764$	−9.22262	−	11.2638i	−0.333663	−	0.407509i
$765$	−28.1151	−	16.2323i	−1.01650	−	0.586879i
$766$	−28.8054	+	2.34549i	−1.04078	+	0.0847459i
$767$	−18.9912	−	32.8937i	−0.685731	−	1.18772i
$768$	−6.60924	−	8.69459i	−0.238490	−	0.313739i
$769$	−36.6991			−1.32340			−0.661701	−	0.749768i	$-0.730165\pi$
$769$	−36.6991			−1.32340			−0.661701	+	0.749768i	$0.730165\pi$
$770$		0			0
$771$			8.46809i			0.304971i
$772$	18.8170	−	3.08481i	0.677237	−	0.111025i
$773$	−28.6220	+	16.5249i	−1.02946	+	0.594359i	−0.916830	−	0.399277i	$-0.869261\pi$
$773$	−28.6220	+	16.5249i	−1.02946	+	0.594359i	−0.112631	+	0.993637i	$0.535928\pi$
$774$	3.37084	+	41.3979i	0.121162	+	1.48802i
$775$	6.06814	−	10.5103i	0.217974	−	0.377542i
$776$	−3.77988	+	0.939991i	−0.135690	+	0.0337437i
$777$		0			0
$778$	3.03625	+	1.43814i	0.108855	+	0.0515600i
$779$	−4.93981	−	2.85200i	−0.176987	−	0.102183i
$780$	−12.8017	−	4.83476i	−0.458373	−	0.173112i
$781$	13.8857	−	8.01691i	0.496869	−	0.286867i
$782$	−8.73119	−	12.6306i	−0.312227	−	0.451669i
$783$	7.62093			0.272350
$784$		0			0
$785$	28.2281			1.00751
$786$	9.22702	+	13.3479i	0.329117	+	0.476103i
$787$	14.9922	−	8.65572i	0.534413	−	0.308543i	−0.208399	−	0.978044i	$-0.566825\pi$
$787$	14.9922	−	8.65572i	0.534413	−	0.308543i	0.742811	+	0.669501i	$0.233492\pi$
$788$	21.8286	+	8.24394i	0.777613	+	0.293678i
$789$	−0.794499	−	0.458704i	−0.0282849	−	0.0163303i
$790$	−6.94055	−	3.28745i	−0.246934	−	0.116962i
$791$		0			0
$792$	−4.17267	−	16.7791i	−0.148269	−	0.596220i
$793$	13.4872	−	23.3604i	0.478943	−	0.829553i
$794$	−2.54445	−	31.2488i	−0.0902991	−	1.10898i
$795$	−4.95204	+	2.85906i	−0.175631	+	0.101400i
$796$	−37.4302	+	6.13623i	−1.32668	+	0.217493i
$797$			41.7331i			1.47826i	0.673561	+	0.739131i	$0.264764\pi$
$797$			41.7331i			1.47826i	−0.673561	+	0.739131i	$0.735236\pi$
$798$		0			0
$799$	−26.2345			−0.928109
$800$	28.5269	−	12.2710i	1.00858	−	0.433847i
$801$	17.7123	+	30.6786i	0.625832	+	1.08397i
$802$	−37.0951	+	3.02048i	−1.30987	+	0.106657i
$803$	−19.9675	−	11.5282i	−0.704638	−	0.406823i
$804$	−5.01186	−	6.12109i	−0.176755	−	0.215874i
$805$		0			0
$806$	−8.74483	−	4.14206i	−0.308023	−	0.145898i
$807$	−0.665670	+	1.15297i	−0.0234327	+	0.0405866i
$808$	1.62076	−	1.56325i	0.0570181	−	0.0549948i
$809$	4.86273	+	8.42250i	0.170965	+	0.296119i	0.938757	−	0.344579i	$-0.111978\pi$
$809$	4.86273	+	8.42250i	0.170965	+	0.296119i	−0.767793	+	0.640698i	$0.778645\pi$
$810$	18.9280	−	13.0844i	0.665062	−	0.459740i
$811$			55.3405i			1.94327i	0.236492	+	0.971633i	$0.424002\pi$
$811$			55.3405i			1.94327i	−0.236492	+	0.971633i	$0.575998\pi$
$812$		0			0
$813$		−	17.7733i		−	0.623339i
$814$	9.63850	+	13.9431i	0.337829	+	0.488706i
$815$	−32.1084	−	55.6134i	−1.12471	−	1.94805i
$816$	3.44843	+	10.2348i	0.120719	+	0.358291i
$817$	−15.6466	+	27.1008i	−0.547406	+	0.948135i
$818$	0.400957	−	0.846511i	0.0140191	−	0.0295976i
$819$		0			0
$820$	−10.5878	+	8.66918i	−0.369744	+	0.302741i
$821$	36.5157	+	21.0823i	1.27441	+	0.735779i	0.975814	−	0.218602i	$-0.0701496\pi$
$821$	36.5157	+	21.0823i	1.27441	+	0.735779i	0.298592	+	0.954381i	$0.403483\pi$
$822$	−0.0695248	−	0.853847i	−0.00242496	−	0.0297813i
$823$	−7.60689	−	13.1755i	−0.265160	−	0.459270i	0.702446	−	0.711737i	$-0.252091\pi$
$823$	−7.60689	−	13.1755i	−0.265160	−	0.459270i	−0.967605	+	0.252467i	$0.918758\pi$
$824$	2.07505	−	7.22000i	0.0722878	−	0.251521i
$825$	−9.03942			−0.314712
$826$		0			0
$827$		−	1.24390i		−	0.0432548i	−0.999766	−	0.0216274i	$-0.993115\pi$
$827$		−	1.24390i		−	0.0432548i	0.999766	−	0.0216274i	$-0.00688475\pi$
$828$	13.7279	−	2.25052i	0.477078	−	0.0782110i
$829$	18.4517	−	10.6531i	0.640855	−	0.369998i	−0.144089	−	0.989565i	$-0.546025\pi$
$829$	18.4517	−	10.6531i	0.640855	−	0.369998i	0.784944	+	0.619567i	$0.212692\pi$
$830$	−29.5713	+	2.40786i	−1.02644	+	0.0835780i
$831$	−5.50067	+	9.52744i	−0.190816	+	0.330503i
$832$	−11.5972	−	21.8753i	−0.402061	−	0.758389i
$833$		0			0
$834$	1.00936	−	2.13099i	0.0349513	−	0.0737902i
$835$	−62.1557	−	35.8856i	−2.15099	−	1.24187i
$836$	4.60248	−	12.1866i	0.159180	−	0.421483i
$837$	−7.23230	+	4.17557i	−0.249985	+	0.144329i
$838$	8.78888	−	6.07552i	0.303607	−	0.209875i
$839$	20.9379			0.722857			0.361429	−	0.932400i	$-0.382289\pi$
$839$	20.9379			0.722857			0.361429	+	0.932400i	$0.382289\pi$
$840$		0			0
$841$	24.9299			0.859651
$842$	14.6468	−	10.1249i	0.504762	−	0.348929i
$843$	9.53586	−	5.50553i	0.328432	−	0.189621i
$844$	−30.1735	−	11.3955i	−1.03862	−	0.392250i
$845$	9.59686	+	5.54075i	0.330142	+	0.190608i
$846$	10.1744	−	21.4804i	0.349802	−	0.738512i
$847$		0			0
$848$	−10.1426	−	2.04138i	−0.348299	−	0.0701013i
$849$	8.98332	−	15.5596i	0.308307	−	0.534003i
$850$	−30.6080	+	2.49227i	−1.04985	+	0.0854841i
$851$	−11.8106	+	6.81884i	−0.404861	+	0.233747i
$852$	−1.46795	−	8.95432i	−0.0502912	−	0.306770i
$853$		−	17.4758i		−	0.598361i	−0.954197	−	0.299180i	$-0.903287\pi$
$853$		−	17.4758i		−	0.598361i	0.954197	−	0.299180i	$-0.0967133\pi$
$854$		0			0
$855$	22.1600			0.757856
$856$	−14.7619	−	4.24262i	−0.504552	−	0.145010i
$857$	1.75517	+	3.04005i	0.0599556	+	0.103846i	0.894445	−	0.447177i	$-0.147571\pi$
$857$	1.75517	+	3.04005i	0.0599556	+	0.103846i	−0.834490	+	0.551024i	$0.814237\pi$
$858$	0.584903	+	7.18330i	0.0199683	+	0.245234i
$859$	4.45370	+	2.57134i	0.151958	+	0.0877331i	0.574051	−	0.818819i	$-0.305371\pi$
$859$	4.45370	+	2.57134i	0.151958	+	0.0877331i	−0.422093	+	0.906553i	$0.638704\pi$
$860$	47.5608	+	58.0870i	1.62181	+	1.98075i
$861$		0			0
$862$	−7.81230	+	16.4936i	−0.266088	+	0.561773i
$863$	20.1410	−	34.8852i	0.685606	−	1.18750i	−0.287640	−	0.957739i	$-0.592871\pi$
$863$	20.1410	−	34.8852i	0.685606	−	1.18750i	0.973246	−	0.229766i	$-0.0737962\pi$
$864$	−21.2218	−	2.50226i	−0.721980	−	0.0851286i
$865$	−35.1916	−	60.9536i	−1.19655	−	2.07248i
$866$	32.6345	+	47.2092i	1.10896	+	1.60423i
$867$			0.923798i			0.0313738i
$868$		0			0
$869$			4.04471i			0.137207i
$870$	5.18851	−	3.58668i	0.175907	−	0.121600i
$871$	−8.96744	−	15.5321i	−0.303850	−	0.526284i
$872$	28.1181	−	27.1203i	0.952199	−	0.918410i
$873$	−1.74483	+	3.02213i	−0.0590534	+	0.102284i
$874$	9.47212	+	4.48655i	0.320399	+	0.151760i
$875$		0			0
$876$	−10.0957	+	8.26621i	−0.341102	+	0.279289i
$877$	36.3471	+	20.9850i	1.22735	+	0.708613i	0.966476	−	0.256759i	$-0.0826546\pi$
$877$	36.3471	+	20.9850i	1.22735	+	0.708613i	0.260878	+	0.965372i	$0.415988\pi$
$878$	51.3845	−	4.18400i	1.73414	−	0.141203i
$879$	3.29326	+	5.70409i	0.111079	+	0.192394i
$880$	−23.4497	−	20.6589i	−0.790488	−	0.696413i
$881$	16.5992			0.559241			0.279620	−	0.960111i	$-0.409791\pi$
$881$	16.5992			0.559241			0.279620	+	0.960111i	$0.409791\pi$
$882$		0			0
$883$		−	12.8210i		−	0.431462i	−0.976453	−	0.215731i	$-0.930787\pi$
$883$		−	12.8210i		−	0.431462i	0.976453	−	0.215731i	$-0.0692135\pi$
$884$	3.96104	+	24.1618i	0.133224	+	0.812651i
$885$	−23.4966	+	13.5658i	−0.789829	+	0.456008i
$886$	−3.72768	−	45.7803i	−0.125234	−	1.53802i
$887$	4.14980	−	7.18766i	0.139337	−	0.241338i	−0.787909	−	0.615792i	$-0.788836\pi$
$887$	4.14980	−	7.18766i	0.139337	−	0.241338i	0.927246	+	0.374454i	$0.122170\pi$
$888$	9.30895	−	2.31497i	0.312388	−	0.0776855i
$889$		0			0
$890$	57.8666	+	27.4090i	1.93969	+	0.918751i
$891$	−10.4952	−	6.05942i	−0.351603	−	0.202998i
$892$	−5.45140	+	14.4344i	−0.182527	+	0.483301i
$893$	15.5083	−	8.95370i	0.518964	−	0.299624i
$894$	5.17554	+	7.48697i	0.173096	+	0.250402i
$895$	−12.2345			−0.408954
$896$		0			0
$897$	−5.79861			−0.193610
$898$	20.8942	+	30.2257i	0.697249	+	1.00865i
$899$	3.86255	−	2.23005i	0.128823	−	0.0743762i
$900$	9.82990	−	26.0280i	0.327663	−	0.867599i
$901$	8.86041	+	5.11556i	0.295183	+	0.170424i
$902$	6.51337	+	3.08511i	0.216872	+	0.102723i
$903$		0			0
$904$	−12.4452	+	3.09491i	−0.413922	+	0.102935i
$905$	−22.7241	+	39.3593i	−0.755376	+	1.30835i
$906$	−0.552614	−	6.78675i	−0.0183594	−	0.225475i
$907$	−14.2277	+	8.21434i	−0.472422	+	0.272753i	−0.717253	−	0.696813i	$-0.754601\pi$
$907$	−14.2277	+	8.21434i	−0.472422	+	0.272753i	0.244831	+	0.969566i	$0.421267\pi$
$908$	0.687429	+	4.19323i	0.0228131	+	0.139157i
$909$		−	2.01745i		−	0.0669147i
$910$		0			0
$911$	−37.1630			−1.23127			−0.615633	−	0.788033i	$-0.711100\pi$
$911$	−37.1630			−1.23127			−0.615633	+	0.788033i	$0.711100\pi$
$912$	−5.53161	−	4.87330i	−0.183170	−	0.161371i
$913$	7.81297	+	13.5325i	0.258571	+	0.447859i
$914$	16.1661	−	1.31633i	0.534725	−	0.0435402i
$915$	−16.6868	−	9.63413i	−0.551649	−	0.318495i
$916$	14.4965	−	11.8695i	0.478978	−	0.392180i
$917$		0			0
$918$	19.0975	+	9.04569i	0.630312	+	0.298552i
$919$	18.1528	−	31.4416i	0.598806	−	1.03716i	−0.394191	−	0.919028i	$-0.628975\pi$
$919$	18.1528	−	31.4416i	0.598806	−	1.03716i	0.992998	−	0.118135i	$-0.0376914\pi$
$920$	18.0979	−	17.4557i	0.596671	−	0.575499i
$921$	8.62593	+	14.9406i	0.284234	+	0.492308i
$922$	29.3125	−	20.2629i	0.965354	−	0.667323i
$923$		−	20.5707i		−	0.677094i
$924$		0			0
$925$			27.2754i			0.896809i
$926$	−25.5906	−	37.0195i	−0.840959	−	1.21654i
$927$	−3.36523	−	5.82875i	−0.110529	−	0.191441i
$928$	11.3339	+	1.33638i	0.372054	+	0.0438689i
$929$	−10.8263	+	18.7518i	−0.355201	+	0.615226i	−0.987152	−	0.159782i	$-0.948921\pi$
$929$	−10.8263	+	18.7518i	−0.355201	+	0.615226i	0.631952	+	0.775008i	$0.282254\pi$
$930$	−2.95875	+	6.24660i	−0.0970212	+	0.204834i
$931$		0			0
$932$	11.1845	+	13.6599i	0.366362	+	0.447445i
$933$	−13.3293	−	7.69567i	−0.436382	−	0.251945i
$934$	1.63128	+	20.0341i	0.0533772	+	0.655535i
$935$	15.4524	+	26.7644i	0.505348	+	0.875288i
$936$	−21.3195	−	6.12731i	−0.696851	−	0.200277i
$937$	15.8637			0.518245			0.259123	−	0.965844i	$-0.416567\pi$
$937$	15.8637			0.518245			0.259123	+	0.965844i	$0.416567\pi$
$938$		0			0
$939$		−	17.3242i		−	0.565355i
$940$	−6.95012	−	42.3949i	−0.226688	−	1.38277i
$941$	−12.7230	+	7.34561i	−0.414757	+	0.239460i	−0.692832	−	0.721099i	$-0.743637\pi$
$941$	−12.7230	+	7.34561i	−0.414757	+	0.239460i	0.278075	+	0.960559i	$0.410304\pi$
$942$	−8.38575	+	0.682813i	−0.273223	+	0.0222473i
$943$	−2.89930	+	5.02174i	−0.0944143	+	0.163530i
$944$	−48.1249	−	9.68600i	−1.56633	−	0.315252i
$945$		0			0
$946$	16.9255	−	35.7337i	0.550296	−	1.16180i
$947$	12.0598	+	6.96270i	0.391889	+	0.226257i	0.682978	−	0.730439i	$-0.260684\pi$
$947$	12.0598	+	6.96270i	0.391889	+	0.226257i	−0.291089	+	0.956696i	$0.594018\pi$
$948$	2.14136	+	0.808718i	0.0695480	+	0.0262660i
$949$	−25.6175	+	14.7903i	−0.831579	+	0.480112i
$950$	17.2430	−	11.9197i	0.559438	−	0.386725i
$951$	11.6954			0.379250
$952$		0			0
$953$	11.2883			0.365663			0.182831	−	0.983144i	$-0.441474\pi$
$953$	11.2883			0.365663			0.182831	+	0.983144i	$0.441474\pi$
$954$	−7.62483	+	5.27084i	−0.246863	+	0.170650i
$955$	−20.4163	+	11.7873i	−0.660655	+	0.381430i
$956$	−4.19370	+	11.1042i	−0.135634	+	0.359137i
$957$	−2.87693	−	1.66100i	−0.0929980	−	0.0536924i
$958$	6.98631	−	14.7497i	0.225717	−	0.476541i
$959$		0			0
$960$	−15.6259	+	8.28411i	−0.504325	+	0.267369i
$961$	13.0563	−	22.6141i	0.421170	−	0.729488i
$962$	21.6748	−	1.76488i	0.698822	−	0.0569019i
$963$	−11.9174	+	6.88051i	−0.384033	+	0.221721i
$964$	21.0906	−	3.45754i	0.679281	−	0.111360i
$965$		−	30.8787i		−	0.994020i
$966$		0			0
$967$	−36.4276			−1.17143			−0.585716	−	0.810517i	$-0.699187\pi$
$967$	−36.4276			−1.17143			−0.585716	+	0.810517i	$0.699187\pi$
$968$	4.04754	−	14.0831i	0.130093	−	0.452649i
$969$	3.64512	+	6.31352i	0.117098	+	0.202820i
$970$	0.511898	+	6.28672i	0.0164361	+	0.201854i
$971$	5.75503	+	3.32267i	0.184688	+	0.106629i	0.589493	−	0.807773i	$-0.299327\pi$
$971$	5.75503	+	3.32267i	0.184688	+	0.106629i	−0.404806	+	0.914403i	$0.632661\pi$
$972$	−22.8430	+	18.7035i	−0.732690	+	0.599916i
$973$		0			0
$974$	−10.6647	+	22.5156i	−0.341719	+	0.721446i
$975$	−5.79861	+	10.0435i	−0.185704	+	0.321649i
$976$	−11.1315	−	33.0379i	−0.356310	−	1.05752i
$977$	22.7226	+	39.3567i	0.726961	+	1.25913i	0.958162	+	0.286227i	$0.0924012\pi$
$977$	22.7226	+	39.3567i	0.726961	+	1.25913i	−0.231201	+	0.972906i	$0.574265\pi$
$978$	10.8837	+	15.7444i	0.348022	+	0.503451i
$979$		−	33.7226i		−	1.07778i
$980$		0			0
$981$		−	35.0002i		−	1.11747i
$982$	−31.2353	+	21.5921i	−0.996759	+	0.689032i
$983$	−9.26538	−	16.0481i	−0.295520	−	0.511855i	0.679586	−	0.733596i	$-0.262159\pi$
$983$	−9.26538	−	16.0481i	−0.295520	−	0.511855i	−0.975106	+	0.221741i	$0.928826\pi$
$984$	2.93564	−	2.83147i	0.0935848	−	0.0902639i
$985$	18.8930	−	32.7236i	0.601980	−	1.04266i
$986$	−10.1994	−	4.83104i	−0.324816	−	0.153852i
$987$		0			0
$988$	−10.5878	−	12.9312i	−0.336844	−	0.411395i
$989$	27.5503	+	15.9061i	0.876047	+	0.505786i
$990$	−27.9071	+	2.27235i	−0.886946	+	0.0722199i
$991$	18.2392	+	31.5911i	0.579386	+	1.00353i	0.995550	+	0.0942363i	$0.0300409\pi$
$991$	18.2392	+	31.5911i	0.579386	+	1.00353i	−0.416164	+	0.909290i	$0.636626\pi$
$992$	−11.4882	+	4.94171i	−0.364749	+	0.156899i
$993$	−5.86069			−0.185983
$994$		0			0
$995$			61.4232i			1.94724i
$996$	8.72654	−	1.43061i	0.276511	−	0.0453305i
$997$	13.2738	−	7.66365i	0.420386	−	0.242710i	−0.274856	−	0.961485i	$-0.588630\pi$
$997$	13.2738	−	7.66365i	0.420386	−	0.242710i	0.695243	+	0.718775i	$0.255297\pi$
$998$	−0.294114	−	3.61207i	−0.00931002	−	0.114338i
$999$	9.38427	−	16.2540i	0.296905	−	0.514255i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.p.g.373.5		12
4.3	odd	2		1568.2.t.g.177.4		12
7.2	even	3		392.2.b.f.197.3		6
7.3	odd	6		56.2.p.a.53.1	yes	12
7.4	even	3	inner	392.2.p.g.165.1		12
7.5	odd	6		392.2.b.e.197.3		6
7.6	odd	2		56.2.p.a.37.5	yes	12
8.3	odd	2		1568.2.t.g.177.3		12
8.5	even	2	inner	392.2.p.g.373.1		12
21.17	even	6		504.2.cj.c.109.6		12
21.20	even	2		504.2.cj.c.37.2		12
28.3	even	6		224.2.t.a.81.4		12
28.11	odd	6		1568.2.t.g.753.3		12
28.19	even	6		1568.2.b.f.785.3		6
28.23	odd	6		1568.2.b.e.785.4		6
28.27	even	2		224.2.t.a.177.3		12
56.3	even	6		224.2.t.a.81.3		12
56.5	odd	6		392.2.b.e.197.4		6
56.11	odd	6		1568.2.t.g.753.4		12
56.13	odd	2		56.2.p.a.37.1	✓	12
56.19	even	6		1568.2.b.f.785.4		6
56.27	even	2		224.2.t.a.177.4		12
56.37	even	6		392.2.b.f.197.4		6
56.45	odd	6		56.2.p.a.53.5	yes	12
56.51	odd	6		1568.2.b.e.785.3		6
56.53	even	6	inner	392.2.p.g.165.5		12
84.59	odd	6		2016.2.cr.c.1873.1		12
84.83	odd	2		2016.2.cr.c.1297.6		12
168.59	odd	6		2016.2.cr.c.1873.6		12
168.83	odd	2		2016.2.cr.c.1297.1		12
168.101	even	6		504.2.cj.c.109.2		12
168.125	even	2		504.2.cj.c.37.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.p.a.37.1	✓	12	56.13	odd	2
56.2.p.a.37.5	yes	12	7.6	odd	2
56.2.p.a.53.1	yes	12	7.3	odd	6
56.2.p.a.53.5	yes	12	56.45	odd	6
224.2.t.a.81.3		12	56.3	even	6
224.2.t.a.81.4		12	28.3	even	6
224.2.t.a.177.3		12	28.27	even	2
224.2.t.a.177.4		12	56.27	even	2
392.2.b.e.197.3		6	7.5	odd	6
392.2.b.e.197.4		6	56.5	odd	6
392.2.b.f.197.3		6	7.2	even	3
392.2.b.f.197.4		6	56.37	even	6
392.2.p.g.165.1		12	7.4	even	3	inner
392.2.p.g.165.5		12	56.53	even	6	inner
392.2.p.g.373.1		12	8.5	even	2	inner
392.2.p.g.373.5		12	1.1	even	1	trivial
504.2.cj.c.37.2		12	21.20	even	2
504.2.cj.c.37.6		12	168.125	even	2
504.2.cj.c.109.2		12	168.101	even	6
504.2.cj.c.109.6		12	21.17	even	6
1568.2.b.e.785.3		6	56.51	odd	6
1568.2.b.e.785.4		6	28.23	odd	6
1568.2.b.f.785.3		6	28.19	even	6
1568.2.b.f.785.4		6	56.19	even	6
1568.2.t.g.177.3		12	8.3	odd	2
1568.2.t.g.177.4		12	4.3	odd	2
1568.2.t.g.753.3		12	28.11	odd	6
1568.2.t.g.753.4		12	56.11	odd	6
2016.2.cr.c.1297.1		12	168.83	odd	2
2016.2.cr.c.1297.6		12	84.83	odd	2
2016.2.cr.c.1873.1		12	84.59	odd	6
2016.2.cr.c.1873.6		12	168.59	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.804171 + 1.16332i) q^{2} +(-0.591141 + 0.341295i) q^{3} +(-0.706619 + 1.87101i) q^{4} +(2.80486 + 1.61939i) q^{5} +(-0.872413 - 0.413225i) q^{6} +(-2.74483 + 0.682591i) q^{8} +(-1.26704 + 2.19457i) q^{9} +O(q^{10})\)	\(q+(0.804171 + 1.16332i) q^{2} +(-0.591141 + 0.341295i) q^{3} +(-0.706619 + 1.87101i) q^{4} +(2.80486 + 1.61939i) q^{5} +(-0.872413 - 0.413225i) q^{6} +(-2.74483 + 0.682591i) q^{8} +(-1.26704 + 2.19457i) q^{9} +(0.371724 + 4.56521i) q^{10} +(2.08913 - 1.20616i) q^{11} +(-0.220856 - 1.34720i) q^{12} -3.09491i q^{13} -2.21076 q^{15} +(-3.00138 - 2.64419i) q^{16} +(1.97779 + 3.42563i) q^{17} +(-3.57190 + 0.290843i) q^{18} +(-2.33831 - 1.35002i) q^{19} +(-5.01186 + 4.10364i) q^{20} +(3.08317 + 1.46037i) q^{22} +(-1.37241 + 2.37709i) q^{23} +(1.38961 - 1.34030i) q^{24} +(2.74483 + 4.75418i) q^{25} +(3.60037 - 2.48884i) q^{26} -3.77750i q^{27} +2.01745i q^{29} +(-1.77782 - 2.57181i) q^{30} +(-1.10538 - 1.91457i) q^{31} +(0.662411 - 5.61794i) q^{32} +(-0.823314 + 1.42602i) q^{33} +(-2.39462 + 5.05560i) q^{34} +(-3.21076 - 3.92136i) q^{36} +(4.30285 + 2.48425i) q^{37} +(-0.309892 - 3.80584i) q^{38} +(1.05628 + 1.82953i) q^{39} +(-8.80423 - 2.53036i) q^{40} +2.11256 q^{41} -11.5899i q^{43} +(0.780522 + 4.76109i) q^{44} +(-7.10771 + 4.10364i) q^{45} +(-3.86897 + 0.315032i) q^{46} +(-3.31613 + 5.74371i) q^{47} +(2.67669 + 0.538731i) q^{48} +(-3.32331 + 7.01628i) q^{50} +(-2.33831 - 1.35002i) q^{51} +(5.79062 + 2.18693i) q^{52} +(2.23998 - 1.29325i) q^{53} +(4.39444 - 3.03776i) q^{54} +7.81297 q^{55} +1.84302 q^{57} +(-2.34694 + 1.62238i) q^{58} +(10.6283 - 6.13625i) q^{59} +(1.56216 - 4.13635i) q^{60} +(7.54801 + 4.35784i) q^{61} +(1.33834 - 2.82555i) q^{62} +(7.06814 - 3.74718i) q^{64} +(5.01186 - 8.68080i) q^{65} +(-2.32100 + 0.188989i) q^{66} +(5.01858 - 2.89748i) q^{67} +(-7.80695 + 1.27985i) q^{68} -1.87359i q^{69} +6.64663 q^{71} +(1.97980 - 6.88858i) q^{72} +(-4.77890 - 8.27729i) q^{73} +(0.570250 + 7.00335i) q^{74} +(-3.24516 - 1.87359i) q^{75} +(4.17820 - 3.42105i) q^{76} +(-1.27890 + 2.70004i) q^{78} +(-0.838343 + 1.45205i) q^{79} +(-4.13648 - 12.2770i) q^{80} +(-2.51186 - 4.35067i) q^{81} +(1.69886 + 2.45758i) q^{82} +6.47755i q^{83} +12.8112i q^{85} +(13.4828 - 9.32027i) q^{86} +(-0.688547 - 1.19260i) q^{87} +(-4.91099 + 4.73673i) q^{88} +(6.98965 - 12.1064i) q^{89} +(-10.4897 - 4.96851i) q^{90} +(-3.47779 - 4.24750i) q^{92} +(1.30687 + 0.754520i) q^{93} +(-9.34850 + 0.761205i) q^{94} +(-4.37241 - 7.57324i) q^{95} +(1.52580 + 3.54707i) q^{96} +1.37709 q^{97} +6.11300i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 8 q^{6} + 4 q^{8}+O(q^{10}) \) 12 * q - 2 * q^2 + 8 * q^6 + 4 * q^8	\( 12 q - 2 q^{2} + 8 q^{6} + 4 q^{8} + 8 q^{10} + 2 q^{12} - 20 q^{15} + 8 q^{16} + 2 q^{17} + 6 q^{18} - 8 q^{20} + 12 q^{22} + 2 q^{23} - 18 q^{24} - 4 q^{25} + 2 q^{26} + 14 q^{30} - 10 q^{31} - 12 q^{32} + 14 q^{33} - 32 q^{34} - 32 q^{36} - 18 q^{38} + 4 q^{39} - 10 q^{40} + 8 q^{41} - 30 q^{44} - 4 q^{46} - 30 q^{47} + 56 q^{48} - 16 q^{50} + 32 q^{52} - 2 q^{54} - 4 q^{55} - 4 q^{57} - 22 q^{58} + 6 q^{60} + 28 q^{62} + 24 q^{64} + 8 q^{65} + 38 q^{66} - 4 q^{68} + 32 q^{71} + 20 q^{72} + 10 q^{73} + 18 q^{74} - 52 q^{76} + 52 q^{78} - 22 q^{79} - 36 q^{80} + 22 q^{81} + 26 q^{82} + 40 q^{86} + 20 q^{87} - 14 q^{88} + 10 q^{89} - 52 q^{90} - 20 q^{92} - 42 q^{94} - 34 q^{95} - 16 q^{96} - 40 q^{97}+O(q^{100}) \) 12 * q - 2 * q^2 + 8 * q^6 + 4 * q^8 + 8 * q^10 + 2 * q^12 - 20 * q^15 + 8 * q^16 + 2 * q^17 + 6 * q^18 - 8 * q^20 + 12 * q^22 + 2 * q^23 - 18 * q^24 - 4 * q^25 + 2 * q^26 + 14 * q^30 - 10 * q^31 - 12 * q^32 + 14 * q^33 - 32 * q^34 - 32 * q^36 - 18 * q^38 + 4 * q^39 - 10 * q^40 + 8 * q^41 - 30 * q^44 - 4 * q^46 - 30 * q^47 + 56 * q^48 - 16 * q^50 + 32 * q^52 - 2 * q^54 - 4 * q^55 - 4 * q^57 - 22 * q^58 + 6 * q^60 + 28 * q^62 + 24 * q^64 + 8 * q^65 + 38 * q^66 - 4 * q^68 + 32 * q^71 + 20 * q^72 + 10 * q^73 + 18 * q^74 - 52 * q^76 + 52 * q^78 - 22 * q^79 - 36 * q^80 + 22 * q^81 + 26 * q^82 + 40 * q^86 + 20 * q^87 - 14 * q^88 + 10 * q^89 - 52 * q^90 - 20 * q^92 - 42 * q^94 - 34 * q^95 - 16 * q^96 - 40 * q^97

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