LMFDB - Embedded newform 392.2.p.g.165.5

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			165.5
Root			$-0.981777 + 1.01790i$ of defining polynomial
Character	$\chi$	$=$	392.165
Dual form			392.2.p.g.373.5

$q$-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 $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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	0.319549	−	0.947570i	$-0.396468\pi$
$3$	−0.591141	−	0.341295i	−0.341295	−	0.197047i	−0.660845	+	0.750523i	$0.729802\pi$
$4$	−0.706619	−	1.87101i	−0.353310	−	0.935506i
$5$	2.80486	−	1.61939i	1.25437	−	0.724212i	0.282397	−	0.959298i	$-0.408870\pi$
$5$	2.80486	−	1.61939i	1.25437	−	0.724212i	0.971975	+	0.235086i	$0.0755372\pi$
$6$	−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	0.780712	−	0.624891i	$-0.214856\pi$
$11$	2.08913	+	1.20616i	0.629897	+	0.363671i	−0.150815	+	0.988562i	$0.548190\pi$
$12$	−0.220856	+	1.34720i	−0.0637558	+	0.388902i
$13$			3.09491i			0.858375i	0.903216	+	0.429187i	$0.141200\pi$
$13$			3.09491i			0.858375i	−0.903216	+	0.429187i	$0.858800\pi$
$14$		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	−0.520044	−	0.854140i	$-0.674084\pi$
$17$	1.97779	−	3.42563i	0.479685	−	0.830838i	0.999728	+	0.0233012i	$0.00741769\pi$
$18$	−3.57190	−	0.290843i	−0.841904	−	0.0685523i
$19$	−2.33831	+	1.35002i	−0.536444	+	0.309716i	−0.743637	−	0.668584i	$-0.766901\pi$
$19$	−2.33831	+	1.35002i	−0.536444	+	0.309716i	0.207192	+	0.978300i	$0.433567\pi$
$20$	−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	0.686724	−	0.726918i	$-0.259048\pi$
$23$	−1.37241	−	2.37709i	−0.286168	−	0.495657i	−0.972892	+	0.231261i	$0.925715\pi$
$24$	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	$-0.940021\pi$
$29$		−	2.01745i		−	0.374631i	0.982300	−	0.187316i	$-0.0599787\pi$
$30$	−1.77782	+	2.57181i	−0.324585	+	0.469547i
$31$	−1.10538	+	1.91457i	−0.198532	+	0.343867i	−0.948053	−	0.318114i	$-0.896951\pi$
$31$	−1.10538	+	1.91457i	−0.198532	+	0.343867i	0.749521	+	0.661981i	$0.230284\pi$
$32$	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	−0.102707	−	0.994712i	$-0.532751\pi$
$37$	4.30285	−	2.48425i	0.707385	−	0.408409i	0.810092	+	0.586303i	$0.199417\pi$
$38$	−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	$0.344971\pi$
$43$			11.5899i			1.76745i	−0.468011	+	0.883723i	$0.655029\pi$
$44$	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	0.516117	−	0.856518i	$-0.327377\pi$
$47$	−3.31613	−	5.74371i	−0.483708	−	0.837807i	−0.999825	+	0.0187115i	$0.994044\pi$
$48$	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	0.645890	−	0.763431i	$-0.276487\pi$
$53$	2.23998	+	1.29325i	0.307684	+	0.177642i	−0.338205	+	0.941072i	$0.609820\pi$
$54$	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	0.992594	−	0.121479i	$-0.0387638\pi$
$59$	10.6283	+	6.13625i	1.38369	+	0.798872i	0.391093	+	0.920351i	$0.372097\pi$
$60$	1.56216	+	4.13635i	0.201674	+	0.534001i
$61$	7.54801	−	4.35784i	0.966424	−	0.557965i	0.0682795	−	0.997666i	$-0.478249\pi$
$61$	7.54801	−	4.35784i	0.966424	−	0.557965i	0.898144	+	0.439701i	$0.144916\pi$
$62$	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	0.774184	−	0.632960i	$-0.218160\pi$
$67$	5.01858	+	2.89748i	0.613117	+	0.353983i	−0.161067	+	0.986943i	$0.551494\pi$
$68$	−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	0.438225	+	0.898865i	$0.355607\pi$
$73$	−4.77890	+	8.27729i	−0.559328	+	0.968784i	−0.997553	+	0.0699184i	$0.977726\pi$
$74$	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	0.815004	−	0.579455i	$-0.196735\pi$
$79$	−0.838343	−	1.45205i	−0.0943209	−	0.163369i	−0.909325	+	0.416087i	$0.863401\pi$
$80$	−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	$-0.884310\pi$
$83$		−	6.47755i		−	0.711003i	0.934676	−	0.355502i	$-0.115690\pi$
$84$		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	0.952085	+	0.305833i	$0.0989349\pi$
$89$	6.98965	+	12.1064i	0.740902	+	1.28328i	−0.211184	+	0.977446i	$0.567732\pi$
$90$	−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	0.465305	−	0.885150i	$-0.345945\pi$
$101$	−0.689470	−	0.398066i	−0.0686048	−	0.0396090i	−0.533910	+	0.845541i	$0.679278\pi$
$102$	−0.309892	+	3.80584i	−0.0306839	+	0.376834i
$103$	−1.32799	−	2.30015i	−0.130851	−	0.226641i	0.793154	−	0.609022i	$-0.208438\pi$
$103$	−1.32799	−	2.30015i	−0.130851	−	0.226641i	−0.924005	+	0.382381i	$0.875104\pi$
$104$	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	−0.255146	−	0.966903i	$-0.582123\pi$
$107$	4.70287	−	2.71520i	0.454643	−	0.262489i	0.709789	+	0.704414i	$0.248790\pi$
$108$	7.06776	−	2.66926i	0.680095	−	0.256849i
$109$	−11.9614	−	6.90593i	−1.14570	−	0.661468i	−0.197862	−	0.980230i	$-0.563400\pi$
$109$	−11.9614	−	6.90593i	−1.14570	−	0.661468i	−0.947835	+	0.318762i	$0.896733\pi$
$110$	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	−0.975343	−	0.220696i	$-0.929167\pi$
$131$	−14.5574	+	8.40471i	−1.27189	+	0.734323i	−0.296543	+	0.955020i	$0.595834\pi$
$132$	−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	−0.846448	−	0.532471i	$-0.821263\pi$
$137$	0.443721	−	0.768547i	0.0379096	−	0.0656614i	0.884358	+	0.466810i	$0.154597\pi$
$138$	2.17958	+	1.50669i	0.185539	+	0.128258i
$139$		−	2.44264i		−	0.207182i	−0.994620	−	0.103591i	$-0.966967\pi$
$139$		−	2.44264i		−	0.207182i	0.994620	−	0.103591i	$-0.0330333\pi$
$140$		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	−0.795673	−	0.605726i	$-0.792883\pi$
$149$	−8.16541	+	4.71430i	−0.668936	+	0.386210i	0.126737	+	0.991936i	$0.459549\pi$
$150$	−0.430076	+	5.28184i	−0.0351155	+	0.431260i
$151$	3.52689	−	6.10875i	0.287014	−	0.497123i	−0.686081	−	0.727525i	$-0.740671\pi$
$151$	3.52689	−	6.10875i	0.287014	−	0.497123i	0.973096	+	0.230402i	$0.0740040\pi$
$152$	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	0.769984	−	0.638063i	$-0.220264\pi$
$157$	7.54801	+	4.35784i	0.602397	+	0.347794i	−0.167587	+	0.985857i	$0.553598\pi$
$158$	−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	−0.987529	−	0.157439i	$-0.949676\pi$
$163$	−17.1711	+	9.91376i	−1.34495	+	0.776505i	−0.357418	+	0.933945i	$0.616343\pi$
$164$	−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	−0.997186	−	0.0749674i	$-0.976115\pi$
$173$	−18.8200	+	10.8657i	−1.43086	+	0.826105i	−0.433669	+	0.901072i	$0.642781\pi$
$174$	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	0.372734	−	0.927938i	$-0.378420\pi$
$179$	−3.27141	−	1.88875i	−0.244517	−	0.141172i	−0.617251	+	0.786766i	$0.711754\pi$
$180$	−2.65552	+	16.1983i	−0.197931	+	1.20735i
$181$		−	14.0326i		−	1.04303i	−0.853242	−	0.521516i	$-0.825367\pi$
$181$		−	14.0326i		−	1.04303i	0.853242	−	0.521516i	$-0.174633\pi$
$182$		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	0.703786	−	0.710412i	$-0.251491\pi$
$191$	−3.63945	−	6.30371i	−0.263341	−	0.456120i	−0.967128	+	0.254291i	$0.918158\pi$
$192$	−2.89937	−	4.62744i	−0.209244	−	0.333956i
$193$	−4.76704	+	8.25675i	−0.343139	+	0.594334i	−0.985014	−	0.172476i	$-0.944823\pi$
$193$	−4.76704	+	8.25675i	−0.343139	+	0.594334i	0.641875	+	0.766809i	$0.278157\pi$
$194$	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	$0.136432\pi$
$197$			11.6667i			0.831221i	−0.909543	+	0.415611i	$0.863568\pi$
$198$	−7.11136	−	4.91589i	−0.505382	−	0.349357i
$199$	9.48247	−	16.4241i	0.672195	−	1.16428i	−0.305086	−	0.952325i	$-0.598685\pi$
$199$	9.48247	−	16.4241i	0.672195	−	1.16428i	0.977280	−	0.211950i	$-0.0679815\pi$
$200$	−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	$-0.812677\pi$
$211$		−	16.1268i		−	1.11022i	0.831778	−	0.555109i	$-0.187323\pi$
$212$	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	0.559817	−	0.828616i	$-0.310871\pi$
$227$	1.83996	+	1.06230i	0.122122	+	0.0705074i	−0.437694	+	0.899124i	$0.644205\pi$
$228$	−1.30232	−	3.44832i	−0.0862480	−	0.228371i
$229$	−8.11289	+	4.68398i	−0.536115	+	0.309526i	−0.743503	−	0.668733i	$-0.766837\pi$
$229$	−8.11289	+	4.68398i	−0.536115	+	0.309526i	0.207388	+	0.978259i	$0.433504\pi$
$230$	−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	0.973607	−	0.228232i	$-0.0732945\pi$
$233$	4.41366	+	7.64469i	0.289149	+	0.500820i	−0.684458	+	0.729052i	$0.739961\pi$
$234$	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	−0.985203	−	0.171389i	$-0.945174\pi$
$241$	−5.34302	+	9.25439i	−0.344174	+	0.596128i	0.641029	+	0.767517i	$0.278508\pi$
$242$	−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	$-0.961491\pi$
$251$		−	3.82402i		−	0.241370i	0.992691	−	0.120685i	$-0.0385091\pi$
$252$		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	0.992034	−	0.125967i	$-0.0402033\pi$
$257$	6.20291	+	10.7438i	0.386927	+	0.670177i	−0.605108	+	0.796144i	$0.706870\pi$
$258$	−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	−0.844563	−	0.535457i	$-0.820140\pi$
$263$	0.672005	−	1.16395i	0.0414376	−	0.0717720i	0.886000	+	0.463685i	$0.153473\pi$
$264$	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	0.550609	−	0.834763i	$-0.314396\pi$
$269$	1.68912	+	0.975212i	0.102987	+	0.0594597i	−0.447622	+	0.894223i	$0.647729\pi$
$270$	17.2451	+	1.40419i	1.04950	+	0.0854562i
$271$	−13.0190	−	22.5496i	−0.790850	−	1.36979i	−0.925441	−	0.378892i	$-0.876305\pi$
$271$	−13.0190	−	22.5496i	−0.790850	−	1.36979i	0.134590	−	0.990901i	$-0.457028\pi$
$272$	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	0.856802	−	0.515646i	$-0.172448\pi$
$277$	13.9578	+	8.05852i	0.838641	+	0.484189i	−0.0181613	+	0.999835i	$0.505781\pi$
$278$	−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	−0.366068	−	0.930588i	$-0.619296\pi$
$283$	−22.7949	−	13.1606i	−1.35501	−	0.782318i	−0.988947	+	0.148270i	$0.952629\pi$
$284$	−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	$0.0909510\pi$
$293$			9.64929i			0.563718i	−0.959456	+	0.281859i	$0.909049\pi$
$294$		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	$0.256425\pi$
$307$			25.2741i			1.44247i	−0.692691	+	0.721235i	$0.743575\pi$
$308$		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	−0.346284	−	0.938130i	$-0.612557\pi$
$311$	11.2742	−	19.5275i	0.639302	−	1.10730i	0.985586	−	0.169174i	$-0.0541100\pi$
$312$	−4.14812	+	4.30073i	−0.234841	+	0.243481i
$313$	−12.6901	−	21.9798i	−0.717285	−	1.24237i	−0.962072	−	0.272797i	$-0.912051\pi$
$313$	−12.6901	−	21.9798i	−0.717285	−	1.24237i	0.244787	−	0.969577i	$-0.421282\pi$
$314$	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	−0.855017	−	0.518600i	$-0.826453\pi$
$317$	−14.8384	+	8.56693i	−0.833405	+	0.481167i	0.0216120	+	0.999766i	$0.493120\pi$
$318$	−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	−0.281531	−	0.959552i	$-0.590842\pi$
$331$	7.43566	−	4.29298i	0.408701	−	0.235963i	0.690231	+	0.723589i	$0.257509\pi$
$332$	−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	0.914676	−	0.404187i	$-0.132446\pi$
$347$	19.0373	+	10.9912i	1.02198	+	0.590039i	0.107302	+	0.994226i	$0.465779\pi$
$348$	2.71791	+	0.445567i	0.145695	+	0.0238849i
$349$		−	15.5480i		−	0.832265i	−0.909304	−	0.416132i	$-0.863385\pi$
$349$		−	15.5480i		−	0.832265i	0.909304	−	0.416132i	$-0.136615\pi$
$350$		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	0.259177	+	0.965830i	$0.416549\pi$
$353$	−13.2804	+	23.0023i	−0.706845	+	1.22429i	−0.966022	+	0.258461i	$0.916785\pi$
$354$	−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	0.906871	+	0.421408i	$0.138464\pi$
$359$	15.5062	+	26.8575i	0.818386	+	1.41749i	−0.0884855	+	0.996077i	$0.528203\pi$
$360$	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	−0.983174	−	0.182674i	$-0.941525\pi$
$367$	−6.38677	+	11.0622i	−0.333387	+	0.577443i	0.649787	+	0.760117i	$0.274858\pi$
$368$	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	−0.344143	−	0.938917i	$-0.611831\pi$
$373$	5.73431	−	3.31070i	0.296911	−	0.171422i	0.641054	+	0.767495i	$0.278497\pi$
$374$	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	$-0.839786\pi$
$379$		−	18.7804i		−	0.964683i	0.875983	−	0.482341i	$-0.160214\pi$
$380$	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	−0.999669	−	0.0257240i	$-0.991811\pi$
$383$	−10.2179	−	17.6980i	−0.522112	−	0.904325i	0.477557	−	0.878601i	$-0.341522\pi$
$384$	−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	0.551248	−	0.834341i	$-0.314152\pi$
$389$	2.05734	+	1.18781i	0.104311	+	0.0602242i	−0.446937	+	0.894566i	$0.647485\pi$
$390$	−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	−0.897274	−	0.441474i	$-0.854456\pi$
$397$	−19.1993	+	11.0847i	−0.963583	+	0.556325i	−0.0663091	+	0.997799i	$0.521122\pi$
$398$	−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	−0.981362	−	0.192168i	$-0.938448\pi$
$401$	−13.1585	−	22.7912i	−0.657104	−	1.13814i	0.324258	−	0.945969i	$-0.394885\pi$
$402$	−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	−0.874097	−	0.485752i	$-0.838546\pi$
$409$	−0.331162	+	0.573590i	−0.0163749	+	0.0283622i	0.857722	+	0.514114i	$0.171879\pi$
$410$	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	$0.0590805\pi$
$419$			7.55501i			0.369086i	−0.982824	+	0.184543i	$0.940919\pi$
$420$		0			0
$421$			12.5905i			0.613625i	0.951770	+	0.306813i	$0.0992625\pi$
$421$			12.5905i			0.613625i	−0.951770	+	0.306813i	$0.900737\pi$
$422$	−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	−0.667734	−	0.744400i	$-0.732736\pi$
$431$	6.45241	−	11.1759i	0.310802	−	0.538325i	0.978536	+	0.206075i	$0.0660691\pi$
$432$	−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	0.862055	+	0.506814i	$0.169177\pi$
$439$	18.2273	+	31.5706i	0.869941	+	1.50678i	0.00788596	+	0.999969i	$0.497490\pi$
$440$	−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	−0.986267	−	0.165156i	$-0.947187\pi$
$443$	−28.1274	+	16.2393i	−1.33637	+	0.771555i	−0.350104	+	0.936711i	$0.613854\pi$
$444$	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	0.968409	−	0.249366i	$-0.0802221\pi$
$457$	5.73448	+	9.93241i	0.268248	+	0.464618i	−0.700162	+	0.713984i	$0.746889\pi$
$458$	−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	$0.199604\pi$
$461$			25.1973i			1.17355i	−0.809749	+	0.586777i	$0.800396\pi$
$462$		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	−0.187396	−	0.982284i	$-0.560005\pi$
$467$	12.3089	−	7.10656i	0.569589	−	0.328852i	0.756985	+	0.653432i	$0.226671\pi$
$468$	−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	−0.967208	−	0.253984i	$-0.918259\pi$
$479$	−5.77020	+	9.99428i	−0.263647	+	0.456650i	0.703561	+	0.710635i	$0.251592\pi$
$480$	−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	−0.594479	−	0.804111i	$-0.702642\pi$
$487$	8.80829	−	15.2564i	0.399142	−	0.691333i	0.993620	+	0.112778i	$0.0359749\pi$
$488$	−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	$-0.792827\pi$
$491$		−	26.8502i		−	1.21173i	0.795567	−	0.605866i	$-0.207173\pi$
$492$	−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	−0.548851	−	0.835921i	$-0.684934\pi$
$499$	−2.21925	+	1.28129i	−0.0993474	+	0.0573583i	0.449503	+	0.893279i	$0.351601\pi$
$500$	−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	−0.235264	−	0.971932i	$-0.575595\pi$
$509$	11.0283	−	6.36720i	0.488821	−	0.282221i	0.724085	+	0.689710i	$0.242262\pi$
$510$	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	−0.204652	−	0.978835i	$-0.565606\pi$
$521$	17.0134	−	29.4680i	0.745369	−	1.29102i	0.950022	−	0.312183i	$-0.101060\pi$
$522$	−0.586762	+	7.20613i	−0.0256819	+	0.315404i
$523$	5.88515	−	3.39779i	0.257340	−	0.148575i	−0.365781	−	0.930701i	$-0.619198\pi$
$523$	5.88515	−	3.39779i	0.257340	−	0.148575i	0.623120	+	0.782126i	$0.285865\pi$
$524$	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	0.0362640	−	0.999342i	$-0.488454\pi$
$541$	21.3952	−	12.3525i	0.919852	−	0.531077i	0.883588	+	0.468266i	$0.155121\pi$
$542$	−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	$0.200716\pi$
$547$			27.5793i			1.17920i	−0.807694	+	0.589602i	$0.799284\pi$
$548$	−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	−0.973106	−	0.230359i	$-0.926010\pi$
$557$	−39.1575	−	22.6076i	−1.65916	−	0.957914i	−0.686050	−	0.727555i	$-0.740657\pi$
$558$	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	0.751487	−	0.659748i	$-0.229337\pi$
$563$	13.1895	+	7.61497i	0.555872	+	0.320933i	−0.195615	+	0.980681i	$0.562670\pi$
$564$	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	0.679773	−	0.733423i	$-0.262078\pi$
$569$	−7.04343	−	12.1996i	−0.295276	−	0.511433i	−0.975049	+	0.221989i	$0.928745\pi$
$570$	0.685096	−	8.41379i	0.0286955	−	0.352415i
$571$	−19.2480	−	11.1129i	−0.805505	−	0.465058i	0.0398876	−	0.999204i	$-0.487300\pi$
$571$	−19.2480	−	11.1129i	−0.805505	−	0.465058i	−0.845392	+	0.534146i	$0.820633\pi$
$572$	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	−0.751995	−	0.659169i	$-0.770908\pi$
$577$	4.68070	−	8.10721i	0.194860	−	0.337507i	0.946855	+	0.321662i	$0.104241\pi$
$578$	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	$-0.913436\pi$
$587$		−	13.0157i		−	0.537217i	0.963249	−	0.268608i	$-0.0865637\pi$
$588$		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	0.851319	−	0.524649i	$-0.175803\pi$
$593$	−0.698895	−	1.21052i	−0.0287002	−	0.0497101i	−0.880019	+	0.474939i	$0.842470\pi$
$594$	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	−0.332017	−	0.943274i	$-0.607729\pi$
$599$	15.9302	−	27.5919i	0.650891	−	1.12738i	0.982907	−	0.184102i	$-0.0589377\pi$
$600$	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	0.757018	−	0.653394i	$-0.226655\pi$
$607$	−4.61573	−	7.99467i	−0.187347	−	0.324494i	−0.944365	+	0.328900i	$0.893322\pi$
$608$	−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	−0.188049	−	0.982160i	$-0.560216\pi$
$613$	−28.0431	−	16.1907i	−1.13265	−	0.653935i	−0.944600	+	0.328225i	$0.893550\pi$
$614$	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	−0.314382	−	0.949297i	$-0.601797\pi$
$619$	−32.1866	−	18.5829i	−1.29369	−	0.746911i	−0.979306	+	0.202385i	$0.935131\pi$
$620$	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	−0.969039	−	0.246907i	$-0.920586\pi$
$641$	−6.85337	+	11.8704i	−0.270692	+	0.468852i	0.698347	+	0.715759i	$0.253919\pi$
$642$	−2.98085	+	4.31212i	−0.117645	+	0.170186i
$643$			30.5812i			1.20600i	0.797740	+	0.603002i	$0.206029\pi$
$643$			30.5812i			1.20600i	−0.797740	+	0.603002i	$0.793971\pi$
$644$		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	−0.0548287	−	0.998496i	$-0.517461\pi$
$647$	21.2979	−	36.8891i	0.837308	−	1.45026i	0.892137	−	0.451765i	$-0.149205\pi$
$648$	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	−0.923696	−	0.383126i	$-0.874848\pi$
$653$	−26.9273	+	15.5465i	−1.05375	+	0.608381i	−0.130051	+	0.991507i	$0.541514\pi$
$654$	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	$0.246017\pi$
$659$			35.8472i			1.39641i	−0.715899	+	0.698204i	$0.753983\pi$
$660$	−1.72554	+	10.5256i	−0.0671667	+	0.409709i
$661$	23.6297	+	13.6426i	0.919087	+	0.530635i	0.883344	−	0.468726i	$-0.155287\pi$
$661$	23.6297	+	13.6426i	0.919087	+	0.530635i	0.0357432	+	0.999361i	$0.488620\pi$
$662$	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	−0.737697	−	0.675132i	$-0.764086\pi$
$677$	−13.5785	+	7.83953i	−0.521863	+	0.301298i	0.215834	+	0.976430i	$0.430753\pi$
$678$	−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	0.781295	−	0.624162i	$-0.214560\pi$
$683$	16.5012	+	9.52698i	0.631401	+	0.364540i	−0.149893	+	0.988702i	$0.547893\pi$
$684$	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	−0.915138	−	0.403142i	$-0.867918\pi$
$691$	−26.9066	+	15.5345i	−1.02358	+	0.590961i	−0.108438	+	0.994103i	$0.534585\pi$
$692$	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	$-0.781771\pi$
$701$		−	33.5258i		−	1.26625i	0.774048	−	0.633127i	$-0.218229\pi$
$702$	−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	−0.359370	−	0.933195i	$-0.617008\pi$
$709$	7.16576	−	4.13715i	0.269116	−	0.155374i	0.628486	+	0.777821i	$0.283675\pi$
$710$	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	0.830203	−	0.557461i	$-0.188224\pi$
$719$	−1.81462	−	3.14301i	−0.0676739	−	0.117215i	−0.897877	+	0.440246i	$0.854891\pi$
$720$	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	0.0494525	−	0.998776i	$-0.484252\pi$
$733$	25.4264	−	14.6799i	0.939145	−	0.542215i	0.889692	+	0.456561i	$0.150919\pi$
$734$	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	0.692370	−	0.721543i	$-0.256567\pi$
$739$	11.2457	+	6.49271i	0.413680	+	0.238838i	−0.278690	+	0.960381i	$0.589900\pi$
$740$	−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	0.734598	−	0.678503i	$-0.237371\pi$
$751$	−6.03724	−	10.4568i	−0.220302	−	0.381574i	−0.954900	+	0.296929i	$0.904038\pi$
$752$	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	$-0.835218\pi$
$757$		−	27.2309i		−	0.989725i	0.868971	−	0.494862i	$-0.164782\pi$
$758$	−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	0.998091	+	0.0617632i	$0.0196724\pi$
$761$	15.2423	+	26.4005i	0.552534	+	0.957017i	−0.445557	+	0.895254i	$0.646994\pi$
$762$	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	−0.112631	−	0.993637i	$-0.535928\pi$
$773$	−28.6220	−	16.5249i	−1.02946	−	0.594359i	−0.916830	+	0.399277i	$0.869261\pi$
$774$	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	0.742811	−	0.669501i	$-0.233492\pi$
$787$	14.9922	+	8.65572i	0.534413	+	0.308543i	−0.208399	+	0.978044i	$0.566825\pi$
$788$	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	$-0.735236\pi$
$797$		−	41.7331i		−	1.47826i	0.673561	−	0.739131i	$-0.264764\pi$
$798$		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	−0.767793	−	0.640698i	$-0.778645\pi$
$809$	4.86273	−	8.42250i	0.170965	−	0.296119i	0.938757	+	0.344579i	$0.111978\pi$
$810$	18.9280	+	13.0844i	0.665062	+	0.459740i
$811$		−	55.3405i		−	1.94327i	−0.236492	−	0.971633i	$-0.575998\pi$
$811$		−	55.3405i		−	1.94327i	0.236492	−	0.971633i	$-0.424002\pi$
$812$		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	0.298592	−	0.954381i	$-0.403483\pi$
$821$	36.5157	−	21.0823i	1.27441	−	0.735779i	0.975814	+	0.218602i	$0.0701496\pi$
$822$	−0.0695248	+	0.853847i	−0.00242496	+	0.0297813i
$823$	−7.60689	+	13.1755i	−0.265160	+	0.459270i	−0.967605	−	0.252467i	$-0.918758\pi$
$823$	−7.60689	+	13.1755i	−0.265160	+	0.459270i	0.702446	+	0.711737i	$0.252091\pi$
$824$	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	$0.00688475\pi$
$827$			1.24390i			0.0432548i	−0.999766	+	0.0216274i	$0.993115\pi$
$828$	13.7279	+	2.25052i	0.477078	+	0.0782110i
$829$	18.4517	+	10.6531i	0.640855	+	0.369998i	0.784944	−	0.619567i	$-0.212692\pi$
$829$	18.4517	+	10.6531i	0.640855	+	0.369998i	−0.144089	+	0.989565i	$0.546025\pi$
$830$	−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	$0.0967133\pi$
$853$			17.4758i			0.598361i	−0.954197	+	0.299180i	$0.903287\pi$
$854$		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	−0.834490	−	0.551024i	$-0.814237\pi$
$857$	1.75517	−	3.04005i	0.0599556	−	0.103846i	0.894445	+	0.447177i	$0.147571\pi$
$858$	0.584903	−	7.18330i	0.0199683	−	0.245234i
$859$	4.45370	−	2.57134i	0.151958	−	0.0877331i	−0.422093	−	0.906553i	$-0.638704\pi$
$859$	4.45370	−	2.57134i	0.151958	−	0.0877331i	0.574051	+	0.818819i	$0.305371\pi$
$860$	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	0.973246	+	0.229766i	$0.0737962\pi$
$863$	20.1410	+	34.8852i	0.685606	+	1.18750i	−0.287640	+	0.957739i	$0.592871\pi$
$864$	−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	0.260878	−	0.965372i	$-0.415988\pi$
$877$	36.3471	−	20.9850i	1.22735	−	0.708613i	0.966476	+	0.256759i	$0.0826546\pi$
$878$	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	$0.0692135\pi$
$883$			12.8210i			0.431462i	−0.976453	+	0.215731i	$0.930787\pi$
$884$	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	0.927246	−	0.374454i	$-0.122170\pi$
$887$	4.14980	+	7.18766i	0.139337	+	0.241338i	−0.787909	+	0.615792i	$0.788836\pi$
$888$	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	0.244831	−	0.969566i	$-0.421267\pi$
$907$	−14.2277	−	8.21434i	−0.472422	−	0.272753i	−0.717253	+	0.696813i	$0.754601\pi$
$908$	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	0.992998	+	0.118135i	$0.0376914\pi$
$919$	18.1528	+	31.4416i	0.598806	+	1.03716i	−0.394191	+	0.919028i	$0.628975\pi$
$920$	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	0.631952	−	0.775008i	$-0.282254\pi$
$929$	−10.8263	−	18.7518i	−0.355201	−	0.615226i	−0.987152	+	0.159782i	$0.948921\pi$
$930$	−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	0.278075	−	0.960559i	$-0.410304\pi$
$941$	−12.7230	−	7.34561i	−0.414757	−	0.239460i	−0.692832	+	0.721099i	$0.743637\pi$
$942$	−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	−0.291089	−	0.956696i	$-0.594018\pi$
$947$	12.0598	−	6.96270i	0.391889	−	0.226257i	0.682978	+	0.730439i	$0.260684\pi$
$948$	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	−0.404806	−	0.914403i	$-0.632661\pi$
$971$	5.75503	−	3.32267i	0.184688	−	0.106629i	0.589493	+	0.807773i	$0.299327\pi$
$972$	−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	−0.231201	−	0.972906i	$-0.574265\pi$
$977$	22.7226	−	39.3567i	0.726961	−	1.25913i	0.958162	−	0.286227i	$-0.0924012\pi$
$978$	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	−0.975106	−	0.221741i	$-0.928826\pi$
$983$	−9.26538	+	16.0481i	−0.295520	+	0.511855i	0.679586	+	0.733596i	$0.262159\pi$
$984$	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	−0.416164	−	0.909290i	$-0.636626\pi$
$991$	18.2392	−	31.5911i	0.579386	−	1.00353i	0.995550	−	0.0942363i	$-0.0300409\pi$
$992$	−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	0.695243	−	0.718775i	$-0.255297\pi$
$997$	13.2738	+	7.66365i	0.420386	+	0.242710i	−0.274856	+	0.961485i	$0.588630\pi$
$998$	−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.165.5		12
4.3	odd	2		1568.2.t.g.753.4		12
7.2	even	3	inner	392.2.p.g.373.1		12
7.3	odd	6		392.2.b.e.197.4		6
7.4	even	3		392.2.b.f.197.4		6
7.5	odd	6		56.2.p.a.37.1	✓	12
7.6	odd	2		56.2.p.a.53.5	yes	12
8.3	odd	2		1568.2.t.g.753.3		12
8.5	even	2	inner	392.2.p.g.165.1		12
21.5	even	6		504.2.cj.c.37.6		12
21.20	even	2		504.2.cj.c.109.2		12
28.3	even	6		1568.2.b.f.785.4		6
28.11	odd	6		1568.2.b.e.785.3		6
28.19	even	6		224.2.t.a.177.4		12
28.23	odd	6		1568.2.t.g.177.3		12
28.27	even	2		224.2.t.a.81.3		12
56.3	even	6		1568.2.b.f.785.3		6
56.5	odd	6		56.2.p.a.37.5	yes	12
56.11	odd	6		1568.2.b.e.785.4		6
56.13	odd	2		56.2.p.a.53.1	yes	12
56.19	even	6		224.2.t.a.177.3		12
56.27	even	2		224.2.t.a.81.4		12
56.37	even	6	inner	392.2.p.g.373.5		12
56.45	odd	6		392.2.b.e.197.3		6
56.51	odd	6		1568.2.t.g.177.4		12
56.53	even	6		392.2.b.f.197.3		6
84.47	odd	6		2016.2.cr.c.1297.1		12
84.83	odd	2		2016.2.cr.c.1873.6		12
168.5	even	6		504.2.cj.c.37.2		12
168.83	odd	2		2016.2.cr.c.1873.1		12
168.125	even	2		504.2.cj.c.109.6		12
168.131	odd	6		2016.2.cr.c.1297.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.p.a.37.1	✓	12	7.5	odd	6
56.2.p.a.37.5	yes	12	56.5	odd	6
56.2.p.a.53.1	yes	12	56.13	odd	2
56.2.p.a.53.5	yes	12	7.6	odd	2
224.2.t.a.81.3		12	28.27	even	2
224.2.t.a.81.4		12	56.27	even	2
224.2.t.a.177.3		12	56.19	even	6
224.2.t.a.177.4		12	28.19	even	6
392.2.b.e.197.3		6	56.45	odd	6
392.2.b.e.197.4		6	7.3	odd	6
392.2.b.f.197.3		6	56.53	even	6
392.2.b.f.197.4		6	7.4	even	3
392.2.p.g.165.1		12	8.5	even	2	inner
392.2.p.g.165.5		12	1.1	even	1	trivial
392.2.p.g.373.1		12	7.2	even	3	inner
392.2.p.g.373.5		12	56.37	even	6	inner
504.2.cj.c.37.2		12	168.5	even	6
504.2.cj.c.37.6		12	21.5	even	6
504.2.cj.c.109.2		12	21.20	even	2
504.2.cj.c.109.6		12	168.125	even	2
1568.2.b.e.785.3		6	28.11	odd	6
1568.2.b.e.785.4		6	56.11	odd	6
1568.2.b.f.785.3		6	56.3	even	6
1568.2.b.f.785.4		6	28.3	even	6
1568.2.t.g.177.3		12	28.23	odd	6
1568.2.t.g.177.4		12	56.51	odd	6
1568.2.t.g.753.3		12	8.3	odd	2
1568.2.t.g.753.4		12	4.3	odd	2
2016.2.cr.c.1297.1		12	84.47	odd	6
2016.2.cr.c.1297.6		12	168.131	odd	6
2016.2.cr.c.1873.1		12	168.83	odd	2
2016.2.cr.c.1873.6		12	84.83	odd	2

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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