LMFDB - Embedded newform 56.2.p.a.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [56,2,Mod(37,56)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(56, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("56.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$56 = 2^{3} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	56.p (of order $6$ , degree $2$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.447162251319$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			37.1
Root			$-0.390636 - 1.35919i$ of defining polynomial
Character	$\chi$	$=$	56.37
Dual form			56.2.p.a.53.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40955 - 0.114773i) q^{2} +(-0.591141 + 0.341295i) q^{3} +(1.97365 + 0.323556i) q^{4} +(2.80486 + 1.61939i) q^{5} +(0.872413 - 0.413225i) q^{6} +(1.47779 - 2.19457i) q^{7} +(-2.74483 - 0.682591i) q^{8} +(-1.26704 + 2.19457i) q^{9} +(-3.76772 - 2.60453i) q^{10} +(-2.08913 + 1.20616i) q^{11} +(-1.27714 + 0.482332i) q^{12} -3.09491i q^{13} +(-2.33490 + 2.92374i) q^{14} -2.21076 q^{15} +(3.79062 + 1.27718i) q^{16} +(-1.97779 - 3.42563i) q^{17} +(2.03782 - 2.94793i) q^{18} +(-2.33831 - 1.35002i) q^{19} +(5.01186 + 4.10364i) q^{20} +(-0.124586 + 1.80166i) q^{21} +(3.08317 - 1.46037i) q^{22} +(-1.37241 + 2.37709i) q^{23} +(1.85554 - 0.533289i) q^{24} +(2.74483 + 4.75418i) q^{25} +(-0.355213 + 4.36243i) q^{26} -3.77750i q^{27} +(3.62672 - 3.85317i) q^{28} -2.01745i q^{29} +(3.11617 + 0.253735i) q^{30} +(1.10538 + 1.91457i) q^{31} +(-5.19648 - 2.23530i) q^{32} +(0.823314 - 1.42602i) q^{33} +(2.39462 + 5.05560i) q^{34} +(7.69885 - 3.76234i) q^{35} +(-3.21076 + 3.92136i) q^{36} +(-4.30285 - 2.48425i) q^{37} +(3.14101 + 2.17130i) q^{38} +(1.05628 + 1.82953i) q^{39} +(-6.59347 - 6.35951i) q^{40} -2.11256 q^{41} +(0.382393 - 2.52523i) q^{42} +11.5899i q^{43} +(-4.51349 + 1.70459i) q^{44} +(-7.10771 + 4.10364i) q^{45} +(2.20731 - 3.19311i) q^{46} +(3.31613 - 5.74371i) q^{47} +(-2.67669 + 0.538731i) q^{48} +(-2.63227 - 6.48623i) q^{49} +(-3.32331 - 7.01628i) q^{50} +(2.33831 + 1.35002i) q^{51} +(1.00138 - 6.10829i) q^{52} +(-2.23998 + 1.29325i) q^{53} +(-0.433555 + 5.32458i) q^{54} -7.81297 q^{55} +(-5.55427 + 5.01498i) q^{56} +1.84302 q^{57} +(-0.231549 + 2.84370i) q^{58} +(10.6283 - 6.13625i) q^{59} +(-4.36327 - 0.715304i) q^{60} +(7.54801 + 4.35784i) q^{61} +(-1.33834 - 2.82555i) q^{62} +(2.94372 + 6.02371i) q^{63} +(7.06814 + 3.74718i) q^{64} +(5.01186 - 8.68080i) q^{65} +(-1.32417 + 1.91555i) q^{66} +(-5.01858 + 2.89748i) q^{67} +(-2.79509 - 7.40094i) q^{68} -1.87359i q^{69} +(-11.2837 + 4.41959i) q^{70} +6.64663 q^{71} +(4.97578 - 5.15884i) q^{72} +(4.77890 + 8.27729i) q^{73} +(5.77995 + 3.99553i) q^{74} +(-3.24516 - 1.87359i) q^{75} +(-4.17820 - 3.42105i) q^{76} +(-0.440297 + 6.36720i) q^{77} +(-1.27890 - 2.70004i) q^{78} +(-0.838343 + 1.45205i) q^{79} +(8.56392 + 9.72078i) q^{80} +(-2.51186 - 4.35067i) q^{81} +(2.97775 + 0.242465i) q^{82} +6.47755i q^{83} +(-0.828830 + 3.51555i) q^{84} -12.8112i q^{85} +(1.33021 - 16.3365i) q^{86} +(0.688547 + 1.19260i) q^{87} +(6.55762 - 1.88468i) q^{88} +(-6.98965 + 12.1064i) q^{89} +(10.4897 - 4.96851i) q^{90} +(-6.79200 - 4.57363i) q^{91} +(-3.47779 + 4.24750i) q^{92} +(-1.30687 - 0.754520i) q^{93} +(-5.33347 + 7.71544i) q^{94} +(-4.37241 - 7.57324i) q^{95} +(3.83475 - 0.452156i) q^{96} -1.37709 q^{97} +(2.96587 + 9.44477i) q^{98} -6.11300i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$12 q - 2 q^{2} - 8 q^{6} - 4 q^{7} + 4 q^{8} - 8 q^{10} - 2 q^{12} - 16 q^{14} - 20 q^{15} + 8 q^{16} - 2 q^{17} + 6 q^{18} + 8 q^{20} + 12 q^{22} + 2 q^{23} + 18 q^{24} - 4 q^{25} - 2 q^{26} + 26 q^{28}+ \cdots + 52 q^{98}+O(q^{100})$ 12 * q - 2 * q^2 - 8 * q^6 - 4 * q^7 + 4 * q^8 - 8 * q^10 - 2 * q^12 - 16 * q^14 - 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 + 26 * q^28 + 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 + 22 * q^42 - 30 * q^44 - 4 * q^46 + 30 * q^47 - 56 * q^48 - 12 * q^49 - 16 * q^50 - 32 * q^52 + 2 * q^54 + 4 * q^55 - 40 * q^56 - 4 * q^57 - 22 * q^58 + 6 * q^60 - 28 * q^62 + 44 * q^63 + 24 * q^64 + 8 * q^65 - 38 * q^66 + 4 * q^68 - 48 * q^70 + 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 + 56 * q^84 + 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 + 52 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/56\mathbb{Z}\right)^\times$ .

$n$	$15$	$17$	$29$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−1.40955	−	0.114773i	−0.996701	−	0.0811568i
$2$	−1.40955	−	0.114773i	−0.996701	−	0.0811568i
$3$	−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	$0.396468\pi$
$4$	1.97365	+	0.323556i	0.986827	+	0.161778i
$5$	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
$7$	1.47779	−	2.19457i	0.558552	−	0.829469i
$7$	1.47779	−	2.19457i	0.558552	−	0.829469i
$8$	−2.74483	−	0.682591i	−0.970443	−	0.241332i
$9$	−1.26704	+	2.19457i	−0.422345	+	0.731523i
$10$	−3.76772	−	2.60453i	−1.19146	−	0.823624i
$11$	−2.08913	+	1.20616i	−0.629897	+	0.363671i	−0.780712	−	0.624891i	$-0.785144\pi$
$11$	−2.08913	+	1.20616i	−0.629897	+	0.363671i	0.150815	+	0.988562i	$0.451810\pi$
$12$	−1.27714	+	0.482332i	−0.368677	+	0.139237i
$13$		−	3.09491i		−	0.858375i	−0.903216	−	0.429187i	$-0.858800\pi$
$13$		−	3.09491i		−	0.858375i	0.903216	−	0.429187i	$-0.141200\pi$
$14$	−2.33490	+	2.92374i	−0.624027	+	0.781403i
$15$	−2.21076			−0.570815
$16$	3.79062	+	1.27718i	0.947656	+	0.319294i
$17$	−1.97779	−	3.42563i	−0.479685	−	0.830838i	0.520044	−	0.854140i	$-0.325916\pi$
$17$	−1.97779	−	3.42563i	−0.479685	−	0.830838i	−0.999728	+	0.0233012i	$0.992582\pi$
$18$	2.03782	−	2.94793i	0.480320	−	0.694834i
$19$	−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
$21$	−0.124586	+	1.80166i	−0.0271870	+	0.393155i
$22$	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	$0.259048\pi$
$24$	1.85554	−	0.533289i	0.378761	−	0.108857i
$25$	2.74483	+	4.75418i	0.548965	+	0.950836i
$26$	−0.355213	+	4.36243i	−0.0696629	+	0.855543i
$27$		−	3.77750i		−	0.726981i
$28$	3.62672	−	3.85317i	0.685385	−	0.728181i
$29$		−	2.01745i		−	0.374631i	−0.982300	−	0.187316i	$-0.940021\pi$
$29$		−	2.01745i		−	0.374631i	0.982300	−	0.187316i	$-0.0599787\pi$
$30$	3.11617	+	0.253735i	0.568932	+	0.0463255i
$31$	1.10538	+	1.91457i	0.198532	+	0.343867i	0.948053	−	0.318114i	$-0.103049\pi$
$31$	1.10538	+	1.91457i	0.198532	+	0.343867i	−0.749521	+	0.661981i	$0.769716\pi$
$32$	−5.19648	−	2.23530i	−0.918617	−	0.395150i
$33$	0.823314	−	1.42602i	0.143321	−	0.248239i
$34$	2.39462	+	5.05560i	0.410674	+	0.867027i
$35$	7.69885	−	3.76234i	1.30134	−	0.635952i
$36$	−3.21076	+	3.92136i	−0.535126	+	0.653561i
$37$	−4.30285	−	2.48425i	−0.707385	−	0.408409i	0.102707	−	0.994712i	$-0.467249\pi$
$37$	−4.30285	−	2.48425i	−0.707385	−	0.408409i	−0.810092	+	0.586303i	$0.800583\pi$
$38$	3.14101	+	2.17130i	0.509539	+	0.352231i
$39$	1.05628	+	1.82953i	0.169140	+	0.292959i
$40$	−6.59347	−	6.35951i	−1.04252	−	1.00553i
$41$	−2.11256			−0.329926			−0.164963	−	0.986300i	$-0.552751\pi$
$41$	−2.11256			−0.329926			−0.164963	+	0.986300i	$0.552751\pi$
$42$	0.382393	−	2.52523i	0.0590045	−	0.389652i
$43$			11.5899i			1.76745i	0.468011	+	0.883723i	$0.344971\pi$
$43$			11.5899i			1.76745i	−0.468011	+	0.883723i	$0.655029\pi$
$44$	−4.51349	+	1.70459i	−0.680434	+	0.256977i
$45$	−7.10771	+	4.10364i	−1.05956	+	0.611734i
$46$	2.20731	−	3.19311i	0.325450	−	0.470798i
$47$	3.31613	−	5.74371i	0.483708	−	0.837807i	−0.516117	−	0.856518i	$-0.672623\pi$
$47$	3.31613	−	5.74371i	0.483708	−	0.837807i	0.999825	+	0.0187115i	$0.00595640\pi$
$48$	−2.67669	+	0.538731i	−0.386346	+	0.0777591i
$49$	−2.63227	−	6.48623i	−0.376038	−	0.926604i
$50$	−3.32331	−	7.01628i	−0.469988	−	0.992251i
$51$	2.33831	+	1.35002i	0.327428	+	0.189041i
$52$	1.00138	−	6.10829i	0.138866	−	0.847067i
$53$	−2.23998	+	1.29325i	−0.307684	+	0.177642i	−0.645890	−	0.763431i	$-0.723513\pi$
$53$	−2.23998	+	1.29325i	−0.307684	+	0.177642i	0.338205	+	0.941072i	$0.390180\pi$
$54$	−0.433555	+	5.32458i	−0.0589994	+	0.724583i
$55$	−7.81297			−1.05350
$56$	−5.55427	+	5.01498i	−0.742221	+	0.670156i
$57$	1.84302			0.244114
$58$	−0.231549	+	2.84370i	−0.0304039	+	0.373396i
$59$	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	$0.0387638\pi$
$60$	−4.36327	−	0.715304i	−0.563295	−	0.0923453i
$61$	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
$63$	2.94372	+	6.02371i	0.370874	+	0.758916i
$64$	7.06814	+	3.74718i	0.883518	+	0.468398i
$65$	5.01186	−	8.68080i	0.621645	−	1.07672i
$66$	−1.32417	+	1.91555i	−0.162994	+	0.235788i
$67$	−5.01858	+	2.89748i	−0.613117	+	0.353983i	−0.774184	−	0.632960i	$-0.781840\pi$
$67$	−5.01858	+	2.89748i	−0.613117	+	0.353983i	0.161067	+	0.986943i	$0.448506\pi$
$68$	−2.79509	−	7.40094i	−0.338954	−	0.897496i
$69$		−	1.87359i		−	0.225554i
$70$	−11.2837	+	4.41959i	−1.34866	+	0.528242i
$71$	6.64663			0.788810			0.394405	−	0.918937i	$-0.370951\pi$
$71$	6.64663			0.788810			0.394405	+	0.918937i	$0.370951\pi$
$72$	4.97578	−	5.15884i	0.586402	−	0.607976i
$73$	4.77890	+	8.27729i	0.559328	+	0.968784i	0.997553	+	0.0699184i	$0.0222739\pi$
$73$	4.77890	+	8.27729i	0.559328	+	0.968784i	−0.438225	+	0.898865i	$0.644393\pi$
$74$	5.77995	+	3.99553i	0.671906	+	0.464470i
$75$	−3.24516	−	1.87359i	−0.374718	−	0.216344i
$76$	−4.17820	−	3.42105i	−0.479272	−	0.392421i
$77$	−0.440297	+	6.36720i	−0.0501765	+	0.725610i
$78$	−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	$0.196735\pi$
$80$	8.56392	+	9.72078i	0.957476	+	1.08682i
$81$	−2.51186	−	4.35067i	−0.279096	−	0.483408i
$82$	2.97775	+	0.242465i	0.328838	+	0.0267757i
$83$			6.47755i			0.711003i	0.934676	+	0.355502i	$0.115690\pi$
$83$			6.47755i			0.711003i	−0.934676	+	0.355502i	$0.884310\pi$
$84$	−0.828830	+	3.51555i	−0.0904327	+	0.383578i
$85$		−	12.8112i		−	1.38957i
$86$	1.33021	−	16.3365i	0.143440	−	1.76161i
$87$	0.688547	+	1.19260i	0.0738200	+	0.127860i
$88$	6.55762	−	1.88468i	0.699045	−	0.200908i
$89$	−6.98965	+	12.1064i	−0.740902	+	1.28328i	0.211184	+	0.977446i	$0.432268\pi$
$89$	−6.98965	+	12.1064i	−0.740902	+	1.28328i	−0.952085	+	0.305833i	$0.901065\pi$
$90$	10.4897	−	4.96851i	1.10571	−	0.523726i
$91$	−6.79200	−	4.57363i	−0.711995	−	0.479447i
$92$	−3.47779	+	4.24750i	−0.362585	+	0.442832i
$93$	−1.30687	−	0.754520i	−0.135516	−	0.0782401i
$94$	−5.33347	+	7.71544i	−0.550106	+	0.795787i
$95$	−4.37241	−	7.57324i	−0.448600	−	0.776998i
$96$	3.83475	−	0.452156i	0.391383	−	0.0461479i
$97$	−1.37709			−0.139823			−0.0699113	−	0.997553i	$-0.522272\pi$
$97$	−1.37709			−0.139823			−0.0699113	+	0.997553i	$0.522272\pi$
$98$	2.96587	+	9.44477i	0.299598	+	0.954066i
$99$		−	6.11300i		−	0.614379i
$100$	3.87909	+	10.2712i	0.387909	+	1.02712i
$101$	−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	$0.345945\pi$
$102$	−3.14101	−	2.17130i	−0.311006	−	0.214990i
$103$	1.32799	−	2.30015i	0.130851	−	0.226641i	−0.793154	−	0.609022i	$-0.791562\pi$
$103$	1.32799	−	2.30015i	0.130851	−	0.226641i	0.924005	+	0.382381i	$0.124896\pi$
$104$	−2.11256	+	8.49500i	−0.207153	+	0.833003i
$105$	−3.26704	+	4.85166i	−0.318830	+	0.473473i
$106$	3.30579	−	1.56581i	0.321086	−	0.152085i
$107$	−4.70287	−	2.71520i	−0.454643	−	0.262489i	0.255146	−	0.966903i	$-0.417877\pi$
$107$	−4.70287	−	2.71520i	−0.454643	−	0.262489i	−0.709789	+	0.704414i	$0.751210\pi$
$108$	1.22224	−	7.45549i	0.117610	−	0.717405i
$109$	11.9614	−	6.90593i	1.14570	−	0.661468i	0.197862	−	0.980230i	$-0.436600\pi$
$109$	11.9614	−	6.90593i	1.14570	−	0.661468i	0.947835	+	0.318762i	$0.103267\pi$
$110$	11.0128	+	0.896718i	1.05003	+	0.0854987i
$111$	3.39145			0.321903
$112$	8.40460	−	6.43138i	0.794160	−	0.607709i
$113$	4.53407			0.426529			0.213265	−	0.976994i	$-0.431590\pi$
$113$	4.53407			0.426529			0.213265	+	0.976994i	$0.431590\pi$
$114$	−2.59783	−	0.211529i	−0.243309	−	0.0198115i
$115$	−7.69885	+	4.44493i	−0.717922	+	0.414492i
$116$	0.652759	−	3.98175i	0.0606072	−	0.369697i
$117$	6.79200	+	3.92136i	0.627921	+	0.362530i
$118$	−15.6854	+	7.42950i	−1.44396	+	0.683941i
$119$	−10.4406	−	0.721973i	−0.957084	−	0.0661831i
$120$	6.06814	+	1.50904i	0.553943	+	0.137756i
$121$	−2.59035	+	4.48662i	−0.235486	+	0.407874i
$122$	−10.1391	−	7.00890i	−0.917953	−	0.634556i
$123$	1.24882	−	0.721006i	0.112602	−	0.0650109i
$124$	1.56216	+	4.13635i	0.140286	+	0.371455i
$125$			1.58587i			0.141845i
$126$	−3.45796	−	8.82857i	−0.308059	−	0.786512i
$127$	−15.4897			−1.37448			−0.687242	−	0.726428i	$-0.741179\pi$
$127$	−15.4897			−1.37448			−0.687242	+	0.726428i	$0.741179\pi$
$128$	−9.53281	−	6.09307i	−0.842589	−	0.538556i
$129$	−3.95558	−	6.85127i	−0.348270	−	0.603221i
$130$	−8.06078	+	11.6608i	−0.706977	+	1.02272i
$131$	−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
$133$	−6.41824	+	3.13652i	−0.556532	+	0.271971i
$134$	7.40648	−	3.50814i	0.639823	−	0.303057i
$135$	6.11724	−	10.5954i	0.526488	−	0.911904i
$136$	3.09039	+	10.7528i	0.264998	+	0.922044i
$137$	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	$0.821263\pi$
$138$	−0.215038	+	2.64092i	−0.0183052	+	0.224810i
$139$			2.44264i			0.207182i	0.994620	+	0.103591i	$0.0330333\pi$
$139$			2.44264i			0.207182i	−0.994620	+	0.103591i	$0.966967\pi$
$140$	16.4122	−	4.93455i	1.38708	−	0.417046i
$141$			4.52712i			0.381253i
$142$	−9.36875	−	0.762854i	−0.786208	−	0.0640172i
$143$	3.73296	+	6.46568i	0.312166	+	0.540688i
$144$	−7.60570	+	6.70056i	−0.633809	+	0.558380i
$145$	3.26704	−	5.65867i	0.271312	−	0.469927i
$146$	−5.78608	−	12.2157i	−0.478859	−	1.01098i
$147$	3.76976	+	2.93589i	0.310925	+	0.242148i
$148$	−7.68855	−	6.29527i	−0.631995	−	0.517468i
$149$	8.16541	+	4.71430i	0.668936	+	0.386210i	0.795673	−	0.605726i	$-0.207117\pi$
$149$	8.16541	+	4.71430i	0.668936	+	0.386210i	−0.126737	+	0.991936i	$0.540451\pi$
$150$	4.35917	+	3.01338i	0.355925	+	0.246041i
$151$	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	$0.740671\pi$
$152$	5.49673	+	5.30168i	0.445844	+	0.430023i
$153$	10.0237			0.810370
$154$	1.35140	−	8.92434i	0.108899	−	0.719144i
$155$			7.16014i			0.575116i
$156$	1.49277	+	3.95262i	0.119518	+	0.316463i
$157$	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	$0.220264\pi$
$158$	1.34834	−	1.95052i	0.107268	−	0.155175i
$159$	0.882761	−	1.52899i	0.0700075	−	0.121257i
$160$	−10.9556	−	14.6848i	−0.866115	−	1.16094i
$161$	3.18855	+	6.52470i	0.251293	+	0.514218i
$162$	3.04125	+	6.42078i	0.238943	+	0.504464i
$163$	17.1711	+	9.91376i	1.34495	+	0.776505i	0.987529	−	0.157439i	$-0.0503239\pi$
$163$	17.1711	+	9.91376i	1.34495	+	0.776505i	0.357418	+	0.933945i	$0.383657\pi$
$164$	−4.16946	−	0.683532i	−0.325580	−	0.0533748i
$165$	4.61856	−	2.66653i	0.359555	−	0.207589i
$166$	0.743448	−	9.13042i	0.0577027	−	0.708658i
$167$	22.1600			1.71479			0.857396	−	0.514657i	$-0.172081\pi$
$167$	22.1600			1.71479			0.857396	+	0.514657i	$0.172081\pi$
$168$	1.57177	−	4.86021i	0.121264	−	0.374973i
$169$	3.42151			0.263193
$170$	−1.47038	+	18.0581i	−0.112773	+	1.38499i
$171$	5.92543	−	3.42105i	0.453129	−	0.261614i
$172$	−3.74999	+	22.8745i	−0.285934	+	1.74416i
$173$	−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
$175$	14.4897	+	1.00197i	1.09531	+	0.0757419i
$176$	−9.45960	+	1.90391i	−0.713044	+	0.143513i
$177$	−4.18855	+	7.25478i	−0.314830	+	0.545302i
$178$	11.2417	−	16.2624i	0.842604	−	1.21892i
$179$	3.27141	−	1.88875i	0.244517	−	0.141172i	−0.372734	−	0.927938i	$-0.621580\pi$
$179$	3.27141	−	1.88875i	0.244517	−	0.141172i	0.617251	+	0.786766i	$0.288246\pi$
$180$	−15.3559	+	5.79942i	−1.14456	+	0.432263i
$181$			14.0326i			1.04303i	0.853242	+	0.521516i	$0.174633\pi$
$181$			14.0326i			1.04303i	−0.853242	+	0.521516i	$0.825367\pi$
$182$	9.04873	+	7.22630i	0.670736	+	0.535649i
$183$	−5.94925			−0.439781
$184$	5.38961	−	5.58790i	0.397328	−	0.411945i
$185$	−8.04593	−	13.9360i	−0.591549	−	1.02459i
$186$	1.75550	+	1.21353i	0.128719	+	0.0889801i
$187$	8.26374	+	4.77107i	0.604304	+	0.348895i
$188$	8.40332	−	10.2631i	0.612875	−	0.748517i
$189$	−8.28999	−	5.58236i	−0.603008	−	0.406057i
$190$	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	$0.251491\pi$
$192$	−5.45716	+	0.197209i	−0.393837	+	0.0142324i
$193$	−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	$0.944823\pi$
$194$	1.94108	+	0.158053i	0.139361	+	0.0113476i
$195$			6.84210i			0.489973i
$196$	−3.09653	−	13.6533i	−0.221180	−	0.975233i
$197$			11.6667i			0.831221i	0.909543	+	0.415611i	$0.136432\pi$
$197$			11.6667i			0.831221i	−0.909543	+	0.415611i	$0.863568\pi$
$198$	−0.701607	+	8.61656i	−0.0498610	+	0.612353i
$199$	−9.48247	−	16.4241i	−0.672195	−	1.16428i	−0.977280	−	0.211950i	$-0.932018\pi$
$199$	−9.48247	−	16.4241i	−0.672195	−	1.16428i	0.305086	−	0.952325i	$-0.401315\pi$
$200$	−4.28891	−	14.9230i	−0.303272	−	1.05521i
$201$	1.97779	−	3.42563i	0.139503	−	0.241626i
$202$	1.01753	−	0.481960i	0.0715930	−	0.0339106i
$203$	−4.42744	−	2.98137i	−0.310745	−	0.209251i
$204$	4.17820	+	3.42105i	0.292532	+	0.239521i
$205$	−5.92543	−	3.42105i	−0.413850	−	0.238936i
$206$	−2.13587	+	3.08976i	−0.148813	+	0.215274i
$207$	−3.47779	−	6.02371i	−0.241723	−	0.418677i
$208$	3.95275	−	11.7316i	0.274074	−	0.813443i
$209$	6.51337			0.450540
$210$	5.16188	−	6.46368i	0.356204	−	0.446036i
$211$		−	16.1268i		−	1.11022i	−0.831778	−	0.555109i	$-0.812677\pi$
$211$		−	16.1268i		−	1.11022i	0.831778	−	0.555109i	$-0.187323\pi$
$212$	−4.83938	+	1.82767i	−0.332370	+	0.125525i
$213$	−3.92909	+	2.26846i	−0.269217	+	0.155433i
$214$	6.31729	+	4.36697i	0.431841	+	0.298520i
$215$	−18.7685	+	32.5081i	−1.28000	+	2.21703i
$216$	−2.57849	+	10.3686i	−0.175444	+	0.705493i
$217$	5.83518	+	0.403507i	0.396118	+	0.0273918i
$218$	−17.6528	+	8.36140i	−1.19560	+	0.566305i
$219$	−5.65000	−	3.26203i	−0.381792	−	0.220428i
$220$	−15.4201	−	2.52793i	−1.03962	−	0.170433i
$221$	−10.6020	+	6.12109i	−0.713170	+	0.411749i
$222$	−4.78042	−	0.389247i	−0.320841	−	0.0261246i
$223$	−7.71477			−0.516619			−0.258310	−	0.966062i	$-0.583165\pi$
$223$	−7.71477			−0.516619			−0.258310	+	0.966062i	$0.583165\pi$
$224$	−12.5848	+	8.10073i	−0.840860	+	0.541253i
$225$	−13.9112			−0.927411
$226$	−6.39099	−	0.520389i	−0.425122	−	0.0346158i
$227$	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	$0.310871\pi$
$228$	3.63749	+	0.596322i	0.240899	+	0.0394924i
$229$	−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
$231$	−1.91282	−	3.91418i	−0.125854	−	0.257534i
$232$	−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	$0.0732945\pi$
$234$	−9.12359	−	6.30689i	−0.596428	−	0.412294i
$235$	18.6026	−	10.7402i	1.21350	−	0.700614i
$236$	22.9620	−	8.67199i	1.49470	−	0.564498i
$237$		−	1.14449i		−	0.0743426i
$238$	14.6336	+	2.21595i	0.948556	+	0.143639i
$239$	5.93489			0.383896			0.191948	−	0.981405i	$-0.438520\pi$
$239$	5.93489			0.383896			0.191948	+	0.981405i	$0.438520\pi$
$240$	−8.38014	−	2.82353i	−0.540936	−	0.182258i
$241$	5.34302	+	9.25439i	0.344174	+	0.596128i	0.985203	−	0.171389i	$-0.0548255\pi$
$241$	5.34302	+	9.25439i	0.344174	+	0.596128i	−0.641029	+	0.767517i	$0.721492\pi$
$242$	4.16617	−	6.02680i	0.267811	−	0.387418i
$243$	12.7840	+	7.38083i	0.820092	+	0.473480i
$244$	13.4872	+	11.0431i	0.863426	+	0.706961i
$245$	3.12057	−	22.4556i	0.199366	−	1.43464i
$246$	−1.84302	+	0.872962i	−0.117507	+	0.0556581i
$247$	−4.17820	+	7.23685i	−0.265852	+	0.460470i
$248$	−1.72720	−	6.00968i	−0.109677	−	0.381615i
$249$	−2.21076	−	3.82914i	−0.140101	−	0.242662i
$250$	0.182015	−	2.23536i	0.0115117	−	0.141377i
$251$			3.82402i			0.241370i	0.992691	+	0.120685i	$0.0385091\pi$
$251$			3.82402i			0.241370i	−0.992691	+	0.120685i	$0.961491\pi$
$252$	3.86088	+	12.8412i	0.243212	+	0.808918i
$253$		−	6.62141i		−	0.416284i
$254$	21.8334	+	1.77779i	1.36995	+	0.111549i
$255$	4.37241	+	7.57324i	0.273811	+	0.474255i
$256$	12.7376	+	9.68259i	0.796103	+	0.605162i
$257$	−6.20291	+	10.7438i	−0.386927	+	0.670177i	−0.992034	−	0.125967i	$-0.959797\pi$
$257$	−6.20291	+	10.7438i	−0.386927	+	0.670177i	0.605108	+	0.796144i	$0.293130\pi$
$258$	4.78924	+	10.1112i	0.298165	+	0.629495i
$259$	−11.8106	+	5.77170i	−0.733874	+	0.358636i
$260$	12.7004	−	15.5113i	0.787646	−	0.961968i
$261$	4.42744	+	2.55618i	0.274052	+	0.158224i
$262$	19.5547	+	13.5176i	1.20809	+	0.835123i
$263$	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	$0.820140\pi$
$264$	−3.23324	+	3.35220i	−0.198992	+	0.206313i
$265$	−8.37709			−0.514601
$266$	9.40681	−	3.68444i	0.576769	−	0.225908i
$267$		−	9.54214i		−	0.583970i
$268$	−10.8424	+	4.09483i	−0.662307	+	0.250131i
$269$	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	$0.314396\pi$
$270$	−9.83861	+	14.2326i	−0.598759	+	0.866168i
$271$	13.0190	−	22.5496i	0.790850	−	1.36979i	−0.134590	−	0.990901i	$-0.542972\pi$
$271$	13.0190	−	22.5496i	0.790850	−	1.36979i	0.925441	−	0.378892i	$-0.123695\pi$
$272$	−3.12192	−	15.5113i	−0.189294	−	0.940509i
$273$	5.57599	+	0.385584i	0.337474	+	0.0233366i
$274$	−0.537238	−	1.13423i	−0.0324557	−	0.0685214i
$275$	−11.4686	−	6.62141i	−0.691583	−	0.399286i
$276$	0.606212	−	3.69782i	0.0364897	−	0.222583i
$277$	−13.9578	+	8.05852i	−0.838641	+	0.484189i	−0.856802	−	0.515646i	$-0.827552\pi$
$277$	−13.9578	+	8.05852i	−0.838641	+	0.484189i	0.0181613	+	0.999835i	$0.494219\pi$
$278$	0.280349	−	3.44302i	0.0168142	−	0.206499i
$279$	−5.60221			−0.335396
$280$	−23.7002	+	5.07182i	−1.41635	+	0.303099i
$281$	−16.1313			−0.962312			−0.481156	−	0.876635i	$-0.659783\pi$
$281$	−16.1313			−0.962312			−0.481156	+	0.876635i	$0.659783\pi$
$282$	0.519592	−	6.38120i	0.0309412	−	0.379995i
$283$	−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	$0.619296\pi$
$284$	13.1181	+	2.15056i	0.778419	+	0.127612i
$285$	5.16942	+	2.98457i	0.306210	+	0.176791i
$286$	−4.51971	−	9.54214i	−0.267256	−	0.564239i
$287$	−3.12192	+	4.63616i	−0.184281	+	0.273664i
$288$	11.4897	−	8.57183i	0.677034	−	0.505100i
$289$	0.676686	−	1.17205i	0.0398050	−	0.0689444i
$290$	−5.25451	+	7.60120i	−0.308555	+	0.446358i
$291$	0.814056	−	0.469996i	0.0477208	−	0.0275516i
$292$	6.75372	+	17.8828i	0.395232	+	1.04651i
$293$		−	9.64929i		−	0.563718i	−0.959456	−	0.281859i	$-0.909049\pi$
$293$		−	9.64929i		−	0.563718i	0.959456	−	0.281859i	$-0.0909510\pi$
$294$	−4.97670	−	4.57095i	−0.290247	−	0.266583i
$295$	39.7479			2.31421
$296$	10.1149	+	9.75593i	0.587914	+	0.567052i
$297$	4.55628	+	7.89171i	0.264382	+	0.457923i
$298$	−10.9685	−	7.58220i	−0.635386	−	0.439225i
$299$	7.35688	+	4.24750i	0.425460	+	0.245639i
$300$	−5.79861	−	4.74781i	−0.334783	−	0.274115i
$301$	25.4349	+	17.1275i	1.46604	+	0.987211i
$302$	−4.27020	−	9.01537i	−0.245723	−	0.518777i
$303$	0.271716	−	0.470626i	0.0156097	−	0.0270367i
$304$	−7.13942	−	8.10385i	−0.409474	−	0.464788i
$305$	14.1141	+	24.4463i	0.808169	+	1.39979i
$306$	−14.1289	−	1.15045i	−0.807697	−	0.0657670i
$307$		−	25.2741i		−	1.44247i	−0.692691	−	0.721235i	$-0.743575\pi$
$307$		−	25.2741i		−	1.44247i	0.692691	−	0.721235i	$-0.256425\pi$
$308$	−2.92914	+	12.4242i	−0.166903	+	0.707934i
$309$			1.81295i			0.103135i
$310$	0.821790	−	10.0926i	0.0466746	−	0.573219i
$311$	−11.2742	−	19.5275i	−0.639302	−	1.10730i	−0.985586	−	0.169174i	$-0.945890\pi$
$311$	−11.2742	−	19.5275i	−0.639302	−	1.10730i	0.346284	−	0.938130i	$-0.387443\pi$
$312$	−1.65048	−	5.74275i	−0.0934402	−	0.325119i
$313$	12.6901	−	21.9798i	0.717285	−	1.24237i	−0.244787	−	0.969577i	$-0.578718\pi$
$313$	12.6901	−	21.9798i	0.717285	−	1.24237i	0.962072	−	0.272797i	$-0.0879486\pi$
$314$	−11.1394	+	5.27629i	−0.628635	+	0.297758i
$315$	−1.49799	+	21.6627i	−0.0844023	+	1.22055i
$316$	−2.12442	+	2.59460i	−0.119508	+	0.145958i
$317$	14.8384	+	8.56693i	0.833405	+	0.481167i	0.855017	−	0.518600i	$-0.173547\pi$
$317$	14.8384	+	8.56693i	0.833405	+	0.481167i	−0.0216120	+	0.999766i	$0.506880\pi$
$318$	−1.41978	+	2.05386i	−0.0796174	+	0.115175i
$319$	2.43337	+	4.21473i	0.136243	+	0.235979i
$320$	13.7570	+	21.9564i	0.769040	+	1.22740i
$321$	3.70674			0.206890
$322$	−3.74555	−	9.56284i	−0.208731	−	0.532916i
$323$			10.6802i			0.594264i
$324$	−3.54986	−	9.39945i	−0.197214	−	0.522192i
$325$	14.7138	−	8.49500i	0.816173	−	0.471218i
$326$	−23.0657	−	15.9447i	−1.27749	−	0.883095i
$327$	−4.71392	+	8.16475i	−0.260681	+	0.451512i
$328$	5.79861	+	1.44201i	0.320174	+	0.0796218i
$329$	−7.70442	−	15.7655i	−0.424758	−	0.869180i
$330$	−6.81613	+	3.22851i	−0.375216	+	0.177724i
$331$	−7.43566	−	4.29298i	−0.408701	−	0.235963i	0.281531	−	0.959552i	$-0.409158\pi$
$331$	−7.43566	−	4.29298i	−0.408701	−	0.235963i	−0.690231	+	0.723589i	$0.742491\pi$
$332$	−2.09585	+	12.7844i	−0.115025	+	0.701637i
$333$	10.9037	−	6.29527i	0.597521	−	0.344979i
$334$	−31.2356	−	2.54337i	−1.70914	−	0.139167i
$335$	−18.7685			−1.02544
$336$	−2.77330	+	6.67030i	−0.151296	+	0.363895i
$337$	−3.18070			−0.173264			−0.0866319	−	0.996240i	$-0.527610\pi$
$337$	−3.18070			−0.173264			−0.0866319	+	0.996240i	$0.527610\pi$
$338$	−4.82279	−	0.392697i	−0.262325	−	0.0213599i
$339$	−2.68027	+	1.54746i	−0.145572	+	0.0840463i
$340$	4.14515	−	25.2849i	0.224803	−	1.37127i
$341$	−4.61856	−	2.66653i	−0.250109	−	0.144401i
$342$	−8.74483	+	4.14206i	−0.472866	+	0.223977i
$343$	−18.1244	−	3.80860i	−0.978627	−	0.205645i
$344$	7.91116	−	31.8123i	0.426541	−	1.71520i
$345$	3.03407	−	5.25516i	0.163349	−	0.282929i
$346$	25.2806	+	17.4758i	1.35909	+	0.939503i
$347$	−19.0373	+	10.9912i	−1.02198	+	0.590039i	−0.914676	−	0.404187i	$-0.867554\pi$
$347$	−19.0373	+	10.9912i	−1.02198	+	0.590039i	−0.107302	+	0.994226i	$0.534221\pi$
$348$	0.973081	+	2.57656i	0.0521626	+	0.138118i
$349$			15.5480i			0.832265i	0.909304	+	0.416132i	$0.136615\pi$
$349$			15.5480i			0.832265i	−0.909304	+	0.416132i	$0.863385\pi$
$350$	−20.3089	−	3.07535i	−1.08555	−	0.164384i
$351$	−11.6910			−0.624022
$352$	13.5523	−	1.59795i	0.722339	−	0.0851710i
$353$	13.2804	+	23.0023i	0.706845	+	1.22429i	0.966022	+	0.258461i	$0.0832155\pi$
$353$	13.2804	+	23.0023i	0.706845	+	1.22429i	−0.259177	+	0.965830i	$0.583451\pi$
$354$	6.73661	−	9.74523i	0.358047	−	0.517953i
$355$	18.6429	+	10.7635i	0.989460	+	0.571265i
$356$	−17.7123	+	21.6324i	−0.938748	+	1.14651i
$357$	6.41824	−	3.13652i	0.339689	−	0.166002i
$358$	−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	$-0.138464\pi$
$360$	22.3105	−	6.41212i	1.17587	−	0.337948i
$361$	−5.85488	−	10.1410i	−0.308152	−	0.533735i
$362$	1.61056	−	19.7796i	0.0846491	−	1.03959i
$363$		−	3.53630i		−	0.185607i
$364$	−11.9252	−	11.2244i	−0.625052	−	0.588317i
$365$			30.9555i			1.62029i
$366$	8.38575	+	0.682813i	0.438330	+	0.0356912i
$367$	6.38677	+	11.0622i	0.333387	+	0.577443i	0.983174	−	0.182674i	$-0.0584751\pi$
$367$	6.38677	+	11.0622i	0.333387	+	0.577443i	−0.649787	+	0.760117i	$0.725142\pi$
$368$	−8.23826	+	7.25783i	−0.429449	+	0.378341i
$369$	2.67669	−	4.63616i	0.139343	−	0.241349i
$370$	9.74166	+	20.5669i	0.506445	+	1.06922i
$371$	−0.472088	+	6.82694i	−0.0245096	+	0.354437i
$372$	−2.33518	−	1.91201i	−0.121073	−	0.0991330i
$373$	−5.73431	−	3.31070i	−0.296911	−	0.171422i	0.344143	−	0.938917i	$-0.388169\pi$
$373$	−5.73431	−	3.31070i	−0.296911	−	0.171422i	−0.641054	+	0.767495i	$0.721503\pi$
$374$	−11.1005	−	7.67351i	−0.573996	−	0.396788i
$375$	−0.541251	−	0.937474i	−0.0279501	−	0.0484109i
$376$	−13.0228	+	13.5019i	−0.671600	+	0.696309i
$377$	−6.24384			−0.321574
$378$	11.0444	+	8.82008i	0.568065	+	0.453656i
$379$		−	18.7804i		−	0.964683i	−0.875983	−	0.482341i	$-0.839786\pi$
$379$		−	18.7804i		−	0.964683i	0.875983	−	0.482341i	$-0.160214\pi$
$380$	−6.17926	−	16.3617i	−0.316989	−	0.839337i
$381$	9.15656	−	5.28654i	0.469105	−	0.270838i
$382$	5.85347	−	8.46767i	0.299490	−	0.433244i
$383$	10.2179	−	17.6980i	0.522112	−	0.904325i	−0.477557	−	0.878601i	$-0.658478\pi$
$383$	10.2179	−	17.6980i	0.522112	−	0.904325i	0.999669	−	0.0257240i	$-0.00818910\pi$
$384$	7.71477	+	0.348359i	0.393693	+	0.0177771i
$385$	−11.5459	+	17.1461i	−0.588435	+	0.873846i
$386$	5.77172	+	12.1854i	0.293773	+	0.620221i
$387$	−25.4349	−	14.6848i	−1.29293	−	0.746472i
$388$	−2.71791	−	0.445567i	−0.137981	−	0.0226203i
$389$	−2.05734	+	1.18781i	−0.104311	+	0.0602242i	−0.551248	−	0.834341i	$-0.685848\pi$
$389$	−2.05734	+	1.18781i	−0.104311	+	0.0602242i	0.446937	+	0.894566i	$0.352515\pi$
$390$	0.785288	−	9.64427i	0.0397646	−	0.488357i
$391$	10.8574			0.549082
$392$	2.79768	+	19.6003i	0.141304	+	0.989966i
$393$	11.4740			0.578785
$394$	1.33903	−	16.4448i	0.0674592	−	0.828479i
$395$	−4.70287	+	2.71520i	−0.236627	+	0.136617i
$396$	1.97790	−	12.0649i	0.0993931	−	0.606286i
$397$	−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
$399$	2.72360	−	4.04464i	0.136351	−	0.202485i
$400$	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	$0.938448\pi$
$402$	−3.18096	+	4.60160i	−0.158652	+	0.229507i
$403$	5.92543	−	3.42105i	0.295167	−	0.170415i
$404$	−1.48957	+	0.562562i	−0.0741090	+	0.0279885i
$405$		−	16.2707i		−	0.808497i
$406$	5.89851	+	4.71054i	0.292738	+	0.233780i
$407$	11.9856			0.594106
$408$	−5.49673	−	5.30168i	−0.272129	−	0.262472i
$409$	0.331162	+	0.573590i	0.0163749	+	0.0283622i	0.874097	−	0.485752i	$-0.161454\pi$
$409$	0.331162	+	0.573590i	0.0163749	+	0.0283622i	−0.857722	+	0.514114i	$0.828121\pi$
$410$	7.95954	+	5.50221i	0.393094	+	0.271735i
$411$	−0.524603	−	0.302880i	−0.0258768	−	0.0149399i
$412$	3.36523	−	4.11003i	0.165793	−	0.202487i
$413$	2.23998	−	32.3926i	0.110222	−	1.59394i
$414$	4.21076	+	8.88987i	0.206947	+	0.436913i
$415$	−10.4897	+	18.1686i	−0.514917	+	0.891862i
$416$	−6.91807	+	16.0827i	−0.339186	+	0.788517i
$417$	−0.833662	−	1.44395i	−0.0408246	−	0.0707103i
$418$	−9.18092	−	0.747560i	−0.449053	−	0.0365643i
$419$		−	7.55501i		−	0.369086i	−0.982824	−	0.184543i	$-0.940919\pi$
$419$		−	7.55501i		−	0.369086i	0.982824	−	0.184543i	$-0.0590805\pi$
$420$	−8.01778	+	8.51842i	−0.391228	+	0.415657i
$421$			12.5905i			0.613625i	0.951770	+	0.306813i	$0.0992625\pi$
$421$			12.5905i			0.613625i	−0.951770	+	0.306813i	$0.900737\pi$
$422$	−1.85093	+	22.7316i	−0.0901017	+	1.10656i
$423$	8.40332	+	14.5550i	0.408583	+	0.707687i
$424$	7.03111	−	2.02076i	0.341461	−	0.0981369i
$425$	10.8574	−	18.8055i	0.526661	−	0.912203i
$426$	5.79861	−	2.74655i	0.280943	−	0.133071i
$427$	20.7180	−	10.1246i	1.00261	−	0.489966i
$428$	−8.40332	−	6.88051i	−0.406190	−	0.332582i
$429$	−4.41342	−	2.54809i	−0.213082	−	0.123023i
$430$	30.1862	−	43.6676i	1.45571	−	2.10584i
$431$	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	$0.732736\pi$
$432$	4.82454	−	14.3191i	0.232121	−	0.688928i
$433$	−40.5815			−1.95022			−0.975112	−	0.221715i	$-0.928835\pi$
$433$	−40.5815			−1.95022			−0.975112	+	0.221715i	$0.928835\pi$
$434$	−8.17865	−	1.23848i	−0.392588	−	0.0594491i
$435$			4.46009i			0.213845i
$436$	25.8422	−	9.75973i	1.23762	−	0.467406i
$437$	6.41824	−	3.70557i	0.307026	−	0.177262i
$438$	7.58956	+	5.24646i	0.362643	+	0.250685i
$439$	−18.2273	+	31.5706i	−0.869941	+	1.50678i	−0.00788596	+	0.999969i	$0.502510\pi$
$439$	−18.2273	+	31.5706i	−0.869941	+	1.50678i	−0.862055	+	0.506814i	$0.830823\pi$
$440$	21.4452	+	5.33306i	1.02236	+	0.254244i
$441$	17.5697	+	2.44159i	0.836650	+	0.116266i
$442$	15.6466	−	7.41115i	0.744234	−	0.352512i
$443$	28.1274	+	16.2393i	1.33637	+	0.771555i	0.986267	−	0.165156i	$-0.0528128\pi$
$443$	28.1274	+	16.2393i	1.33637	+	0.771555i	0.350104	+	0.936711i	$0.386146\pi$
$444$	6.69356	+	1.09733i	0.317662	+	0.0520768i
$445$	−39.2100	+	22.6379i	−1.85873	+	1.07314i
$446$	10.8743	+	0.885447i	0.514915	+	0.0419271i
$447$	−6.43587			−0.304406
$448$	18.6687	−	9.97397i	0.882013	−	0.471226i
$449$	25.9823			1.22618			0.613091	−	0.790012i	$-0.289926\pi$
$449$	25.9823			1.22618			0.613091	+	0.790012i	$0.289926\pi$
$450$	19.6085	+	1.59663i	0.924352	+	0.0752657i
$451$	4.41342	−	2.54809i	0.207820	−	0.119985i
$452$	8.94869	+	1.46703i	0.420911	+	0.0690031i
$453$	−4.16978	−	2.40742i	−0.195913	−	0.113111i
$454$	−2.71544	+	1.28619i	−0.127442	+	0.0603638i
$455$	−11.6441	−	23.8273i	−0.545885	−	1.11704i
$456$	−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	$0.0802221\pi$
$458$	10.8979	+	7.53344i	0.509226	+	0.352014i
$459$	−12.9403	+	7.47111i	−0.604004	+	0.348722i
$460$	−16.6331	+	6.28175i	−0.775520	+	0.292888i
$461$		−	25.1973i		−	1.17355i	−0.809749	−	0.586777i	$-0.800396\pi$
$461$		−	25.1973i		−	1.17355i	0.809749	−	0.586777i	$-0.199604\pi$
$462$	2.24697	+	5.73677i	0.104538	+	0.266899i
$463$	−31.8223			−1.47891			−0.739454	−	0.673207i	$-0.764916\pi$
$463$	−31.8223			−1.47891			−0.739454	+	0.673207i	$0.764916\pi$
$464$	2.57664	−	7.64740i	0.119618	−	0.355022i
$465$	−2.44372	−	4.23265i	−0.113325	−	0.196284i
$466$	−7.09868	+	10.2690i	−0.328840	+	0.475702i
$467$	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
$469$	−1.05770	+	15.2955i	−0.0488398	+	0.706280i
$470$	−27.4539	+	13.0038i	−1.26636	+	0.599819i
$471$	−2.97462	+	5.15220i	−0.137063	+	0.237401i
$472$	−33.3614	+	9.58817i	−1.53558	+	0.441331i
$473$	−13.9793	−	24.2129i	−0.642769	−	1.11331i
$474$	−0.131357	+	1.61321i	−0.00603341	+	0.0740974i
$475$		−	14.8223i		−	0.680094i
$476$	−20.3724	−	4.80303i	−0.933769	−	0.220147i
$477$		−	6.55438i		−	0.300104i
$478$	−8.36551	−	0.681165i	−0.382630	−	0.0311558i
$479$	5.77020	+	9.99428i	0.263647	+	0.456650i	0.967208	−	0.253984i	$-0.0817412\pi$
$479$	5.77020	+	9.99428i	0.263647	+	0.456650i	−0.703561	+	0.710635i	$0.748408\pi$
$480$	11.4882	+	4.94171i	0.524360	+	0.225557i
$481$	−7.68855	+	13.3170i	−0.350568	+	0.607201i
$482$	−6.46910	−	13.6577i	−0.294659	−	0.622093i
$483$	−4.11173	−	2.76878i	−0.187090	−	0.125984i
$484$	−6.56413	+	8.01691i	−0.298369	+	0.364405i
$485$	−3.86255	−	2.23005i	−0.175390	−	0.101261i
$486$	−17.1725	−	11.8709i	−0.778961	−	0.538475i
$487$	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	$0.702642\pi$
$488$	−17.7433	−	17.1137i	−0.803204	−	0.774702i
$489$	−13.5341			−0.612032
$490$	−6.97590	+	31.2941i	−0.315139	+	1.41372i
$491$		−	26.8502i		−	1.21173i	−0.795567	−	0.605866i	$-0.792827\pi$
$491$		−	26.8502i		−	1.21173i	0.795567	−	0.605866i	$-0.207173\pi$
$492$	2.69802	−	1.01895i	0.121636	−	0.0459380i
$493$	−6.91105	+	3.99010i	−0.311258	+	0.179705i
$494$	6.71997	−	9.72115i	0.302346	−	0.437375i
$495$	9.89930	−	17.1461i	0.444941	−	0.770660i
$496$	1.74483	+	8.66918i	0.0783450	+	0.389258i
$497$	9.82233	−	14.5865i	0.440592	−	0.654293i
$498$	2.67669	+	5.65110i	0.119945	+	0.253232i
$499$	2.21925	+	1.28129i	0.0993474	+	0.0573583i	0.548851	−	0.835921i	$-0.315066\pi$
$499$	2.21925	+	1.28129i	0.0993474	+	0.0573583i	−0.449503	+	0.893279i	$0.648399\pi$
$500$	−0.513119	+	3.12996i	−0.0229474	+	0.139976i
$501$	−13.0997	+	7.56310i	−0.585251	+	0.337895i
$502$	0.438894	−	5.39014i	0.0195888	−	0.240574i
$503$	−14.6941			−0.655176			−0.327588	−	0.944821i	$-0.606236\pi$
$503$	−14.6941			−0.655176			−0.327588	+	0.944821i	$0.606236\pi$
$504$	−3.96827	−	18.5434i	−0.176761	−	0.825988i
$505$	−2.57849			−0.114741
$506$	−0.759959	+	9.33319i	−0.0337843	+	0.414911i
$507$	−2.02259	+	1.16775i	−0.0898266	+	0.0518614i
$508$	−30.5712	−	5.01177i	−1.35638	−	0.222362i
$509$	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
$511$	25.2273	+	1.74449i	1.11599	+	0.0771716i
$512$	−16.8430	−	15.1100i	−0.744364	−	0.667775i
$513$	−5.09971	+	8.83296i	−0.225158	+	0.389985i
$514$	9.97639	−	14.4319i	0.440040	−	0.636564i
$515$	7.44968	−	4.30107i	0.328272	−	0.189528i
$516$	−5.59018	−	14.8019i	−0.246094	−	0.651617i
$517$			15.9992i			0.703643i
$518$	17.3100	−	6.77996i	0.760559	−	0.297894i
$519$	14.8337			0.651126
$520$	−19.6821	+	20.4062i	−0.863118	+	0.894872i
$521$	−17.0134	−	29.4680i	−0.745369	−	1.29102i	−0.950022	−	0.312183i	$-0.898940\pi$
$521$	−17.0134	−	29.4680i	−0.745369	−	1.29102i	0.204652	−	0.978835i	$-0.434394\pi$
$522$	−5.94731	−	4.11121i	−0.260307	−	0.179943i
$523$	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
$525$	−8.90739	+	4.35294i	−0.388750	+	0.189978i
$526$	−0.813634	−	1.71777i	−0.0354761	−	0.0748982i
$527$	4.37241	−	7.57324i	0.190465	−	0.329896i
$528$	4.94216	−	4.35399i	0.215080	−	0.189483i
$529$	7.73296	+	13.3939i	0.336216	+	0.582343i
$530$	11.8079	+	0.961464i	0.512903	+	0.0417633i
$531$			31.0994i			1.34960i
$532$	−13.6822	+	4.11375i	−0.593200	+	0.178354i
$533$			6.53819i			0.283200i
$534$	−1.09518	+	13.4501i	−0.0473931	+	0.582043i
$535$	−8.79392	−	15.2315i	−0.380195	−	0.658516i
$536$	15.7529	−	4.52744i	0.680422	−	0.195556i
$537$	−1.28924	+	2.23304i	−0.0556350	+	0.0963626i
$538$	−2.49282	+	1.18074i	−0.107473	+	0.0509055i
$539$	13.3226	+	10.3757i	0.573845	+	0.446911i
$540$	15.5015	−	18.9323i	0.667079	−	0.814718i
$541$	−21.3952	−	12.3525i	−0.919852	−	0.531077i	−0.0362640	−	0.999342i	$-0.511546\pi$
$541$	−21.3952	−	12.3525i	−0.919852	−	0.531077i	−0.883588	+	0.468266i	$0.844879\pi$
$542$	−20.9391	+	30.2906i	−0.899410	+	1.30109i
$543$	−4.78924	−	8.29521i	−0.205526	−	0.355982i
$544$	2.62022	+	22.2222i	0.112341	+	0.952769i
$545$	44.7335			1.91617
$546$	−7.81537	−	1.18347i	−0.334467	−	0.0506479i
$547$			27.5793i			1.17920i	0.807694	+	0.589602i	$0.200716\pi$
$547$			27.5793i			1.17920i	−0.807694	+	0.589602i	$0.799284\pi$
$548$	0.627083	+	1.66041i	0.0267877	+	0.0709294i
$549$	−19.1272	+	11.0431i	−0.816328	+	0.471307i
$550$	15.4056	+	10.6495i	0.656897	+	0.454095i
$551$	−2.72360	+	4.71742i	−0.116029	+	0.200969i
$552$	−1.27890	+	5.14268i	−0.0544334	+	0.218887i
$553$	1.94773	+	3.98563i	0.0828261	+	0.169486i
$554$	20.5990	−	9.75690i	0.875169	−	0.414531i
$555$	9.51256	+	5.49208i	0.403785	+	0.233126i
$556$	−0.790332	+	4.82093i	−0.0335175	+	0.204453i
$557$	39.1575	−	22.6076i	1.65916	−	0.957914i	0.686050	−	0.727555i	$-0.259343\pi$
$557$	39.1575	−	22.6076i	1.65916	−	0.957914i	0.973106	−	0.230359i	$-0.0739902\pi$
$558$	7.89659	+	0.642983i	0.334289	+	0.0272196i
$559$	35.8698			1.51713
$560$	33.9886	−	4.42883i	1.43628	−	0.187152i
$561$	−6.51337			−0.274995
$562$	22.7378	+	1.85144i	0.959137	+	0.0780981i
$563$	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	$0.229337\pi$
$564$	−1.46478	+	8.93498i	−0.0616783	+	0.376230i
$565$	12.7174	+	7.34241i	0.535026	+	0.308898i
$566$	33.6410	−	15.9343i	1.41404	−	0.669769i
$567$	−13.2599	−	0.916930i	−0.556862	−	0.0385074i
$568$	−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	$0.262078\pi$
$570$	−6.94400	−	4.80020i	−0.290852	−	0.201058i
$571$	19.2480	−	11.1129i	0.805505	−	0.465058i	−0.0398876	−	0.999204i	$-0.512700\pi$
$571$	19.2480	−	11.1129i	0.805505	−	0.465058i	0.845392	+	0.534146i	$0.179367\pi$
$572$	5.27557	+	13.9689i	0.220583	+	0.584067i
$573$		−	4.96851i		−	0.207562i
$574$	4.93260	−	6.17657i	0.205883	−	0.257805i
$575$	−15.0681			−0.628385
$576$	−17.1790	+	10.7637i	−0.715793	+	0.448488i
$577$	−4.68070	−	8.10721i	−0.194860	−	0.337507i	0.751995	−	0.659169i	$-0.229092\pi$
$577$	−4.68070	−	8.10721i	−0.194860	−	0.337507i	−0.946855	+	0.321662i	$0.895759\pi$
$578$	−1.08834	+	1.57440i	−0.0452690	+	0.0654865i
$579$	5.63598	+	3.25393i	0.234223	+	0.135229i
$580$	8.27890	−	10.1112i	0.343762	−	0.419844i
$581$	14.2154	+	9.57246i	0.589755	+	0.397133i
$582$	−1.20139	+	0.569050i	−0.0497994	+	0.0235879i
$583$	3.11974	−	5.40355i	0.129206	−	0.223792i
$584$	−7.46724	−	25.9818i	−0.308997	−	1.07513i
$585$	12.7004	+	21.9978i	0.525097	+	0.909495i
$586$	−1.10748	+	13.6011i	−0.0457495	+	0.561858i
$587$			13.0157i			0.537217i	0.963249	+	0.268608i	$0.0865637\pi$
$587$			13.0157i			0.537217i	−0.963249	+	0.268608i	$0.913436\pi$
$588$	6.49028	+	7.01417i	0.267654	+	0.289259i
$589$		−	5.96914i		−	0.245954i
$590$	−56.0265	−	4.56198i	−2.30658	−	0.187814i
$591$	−3.98180	−	6.89669i	−0.163790	−	0.283692i
$592$	−13.1377	−	14.9124i	−0.539954	−	0.612894i
$593$	0.698895	−	1.21052i	0.0287002	−	0.0497101i	−0.851319	−	0.524649i	$-0.824197\pi$
$593$	0.698895	−	1.21052i	0.0287002	−	0.0497101i	0.880019	+	0.474939i	$0.157530\pi$
$594$	−5.51654	−	11.6467i	−0.226346	−	0.477869i
$595$	−28.1151	−	18.9323i	−1.15261	−	0.776150i
$596$	14.5903	+	11.9464i	0.597644	+	0.489342i
$597$	11.2110	+	6.47265i	0.458834	+	0.264908i
$598$	−9.88239	−	6.83143i	−0.404121	−	0.279358i
$599$	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	$0.607729\pi$
$600$	7.62850	+	7.35780i	0.311432	+	0.300381i
$601$	34.4927			1.40699			0.703493	−	0.710702i	$-0.251623\pi$
$601$	34.4927			1.40699			0.703493	+	0.710702i	$0.251623\pi$
$602$	−33.8859	−	27.0612i	−1.38109	−	1.10293i
$603$		−	14.6848i		−	0.598012i
$604$	4.98434	+	13.1977i	0.202810	+	0.537007i
$605$	−14.5311	+	8.38955i	−0.590775	+	0.341084i
$606$	−0.437012	+	0.632184i	−0.0177524	+	0.0256807i
$607$	4.61573	−	7.99467i	0.187347	−	0.324494i	−0.757018	−	0.653394i	$-0.773345\pi$
$607$	4.61573	−	7.99467i	0.187347	−	0.324494i	0.944365	+	0.328900i	$0.106678\pi$
$608$	9.13325	+	12.2422i	0.370402	+	0.496486i
$609$	3.63477	+	0.251347i	0.147288	+	0.0101851i
$610$	−17.0887	−	36.0781i	−0.691901	−	1.46076i
$611$	−17.7763	−	10.2631i	−0.719152	−	0.415202i
$612$	19.7834	+	3.24324i	0.799695	+	0.131100i
$613$	28.0431	−	16.1907i	1.13265	−	0.653935i	0.188049	−	0.982160i	$-0.439784\pi$
$613$	28.0431	−	16.1907i	1.13265	−	0.653935i	0.944600	+	0.328225i	$0.106450\pi$
$614$	−2.90079	+	35.6251i	−0.117066	+	1.43771i
$615$	4.67035			0.188327
$616$	5.55473	−	17.1763i	0.223806	−	0.692054i
$617$	−10.1600			−0.409026			−0.204513	−	0.978864i	$-0.565561\pi$
$617$	−10.1600			−0.409026			−0.204513	+	0.978864i	$0.565561\pi$
$618$	0.208078	−	2.55545i	0.00837013	−	0.102795i
$619$	−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	$0.601797\pi$
$620$	−2.31671	+	14.1316i	−0.0930412	+	0.567540i
$621$	8.97946	+	5.18430i	0.360333	+	0.208039i
$622$	13.6503	+	28.8190i	0.547328	+	1.15553i
$623$	16.2392	+	33.2301i	0.650608	+	1.33133i
$624$	1.66732	+	8.28411i	0.0667464	+	0.331630i
$625$	11.1560	−	19.3227i	0.446240	−	0.772910i
$626$	−20.4099	+	29.5252i	−0.815746	+	1.18006i
$627$	−3.85032	+	2.22298i	−0.153767	+	0.0887774i
$628$	16.3072	−	6.15867i	0.650727	−	0.245758i
$629$			19.6533i			0.783630i
$630$	4.59778	−	30.3627i	0.183180	−	1.20968i
$631$	−7.31198			−0.291085			−0.145543	−	0.989352i	$-0.546493\pi$
$631$	−7.31198			−0.291085			−0.145543	+	0.989352i	$0.546493\pi$
$632$	3.29226	−	3.41339i	0.130959	−	0.135777i
$633$	5.50401	+	9.53323i	0.218765	+	0.378912i
$634$	−19.9321	−	13.7785i	−0.791606	−	0.547216i
$635$	−43.4463	−	25.0837i	−1.72411	−	0.995418i
$636$	2.23698	−	2.73207i	0.0887019	−	0.108334i
$637$	−20.0743	+	8.14664i	−0.795373	+	0.322782i
$638$	−2.94622	−	6.22015i	−0.116642	−	0.246258i
$639$	−8.42151	+	14.5865i	−0.333150	+	0.577032i
$640$	−16.8712	−	32.5275i	−0.666891	−	1.28576i
$641$	−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	$0.920586\pi$
$642$	−5.22483	−	0.425434i	−0.206208	−	0.0167905i
$643$		−	30.5812i		−	1.20600i	−0.797740	−	0.603002i	$-0.793971\pi$
$643$		−	30.5812i		−	1.20600i	0.797740	−	0.603002i	$-0.206029\pi$
$644$	4.18198	+	13.9092i	0.164793	+	0.548098i
$645$		−	25.6225i		−	1.00888i
$646$	1.22580	−	15.0543i	0.0482286	−	0.592304i
$647$	−21.2979	−	36.8891i	−0.837308	−	1.45026i	−0.892137	−	0.451765i	$-0.850795\pi$
$647$	−21.2979	−	36.8891i	−0.837308	−	1.45026i	0.0548287	−	0.998496i	$-0.482539\pi$
$648$	3.92490	+	13.6564i	0.154184	+	0.536474i
$649$	−14.8026	+	25.6389i	−0.581054	+	1.00641i
$650$	−21.7148	+	10.2854i	−0.851723	+	0.403425i
$651$	−3.58712	+	1.75299i	−0.140591	+	0.0687050i
$652$	30.6822	+	25.1222i	1.20161	+	0.983859i
$653$	26.9273	+	15.5465i	1.05375	+	0.608381i	0.923696	−	0.383126i	$-0.125152\pi$
$653$	26.9273	+	15.5465i	1.05375	+	0.608381i	0.130051	+	0.991507i	$0.458486\pi$
$654$	7.58160	−	10.9676i	0.296464	−	0.428867i
$655$	−27.2210	−	47.1481i	−1.06361	−	1.84223i
$656$	−8.00791	−	2.69811i	−0.312656	−	0.105343i
$657$	−24.2201			−0.944917
$658$	9.05030	+	23.1065i	0.352818	+	0.900785i
$659$			35.8472i			1.39641i	0.715899	+	0.698204i	$0.246017\pi$
$659$			35.8472i			1.39641i	−0.715899	+	0.698204i	$0.753983\pi$
$660$	9.97822	−	3.76844i	0.388402	−	0.146686i
$661$	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	$0.155287\pi$
$662$	9.98820	+	6.90457i	0.388202	+	0.268354i
$663$	4.17820	−	7.23685i	0.162268	−	0.281056i
$664$	4.42151	−	17.7797i	0.171588	−	0.689988i
$665$	−23.0815	−	1.59611i	−0.895063	−	0.0618943i
$666$	−16.0919	+	7.62204i	−0.623547	+	0.295348i
$667$	4.79566	+	2.76878i	0.185689	+	0.107208i
$668$	43.7362	+	7.17001i	1.69220	+	0.277416i
$669$	4.56051	−	2.63301i	0.176320	−	0.101798i
$670$	26.4552	+	2.15412i	1.02205	+	0.0832210i
$671$	−21.0251			−0.811663
$672$	4.67467	−	9.08382i	0.180329	−	0.350416i
$673$	−32.2963			−1.24493			−0.622465	−	0.782648i	$-0.713869\pi$
$673$	−32.2963			−1.24493			−0.622465	+	0.782648i	$0.713869\pi$
$674$	4.48335	+	0.365058i	0.172692	+	0.0140615i
$675$	17.9589	−	10.3686i	0.691239	−	0.399087i
$676$	6.75288	+	1.10705i	0.259726	+	0.0425789i
$677$	−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
$679$	−2.03506	+	3.02213i	−0.0780983	+	0.115979i
$680$	−8.74483	+	35.1646i	−0.335349	+	1.34850i
$681$	−0.725117	+	1.25594i	−0.0277865	+	0.0481277i
$682$	6.20404	+	4.28869i	0.237565	+	0.164222i
$683$	−16.5012	+	9.52698i	−0.631401	+	0.364540i	−0.781295	−	0.624162i	$-0.785440\pi$
$683$	−16.5012	+	9.52698i	−0.631401	+	0.364540i	0.149893	+	0.988702i	$0.452107\pi$
$684$	12.8017	−	4.83476i	0.489483	−	0.184862i
$685$			2.87422i			0.109818i
$686$	25.1101	+	7.44860i	0.958709	+	0.284389i
$687$	6.39448			0.243965
$688$	−14.8024	+	43.9330i	−0.564335	+	1.67493i
$689$	4.00250	+	6.93253i	0.152483	+	0.264108i
$690$	−4.87982	+	7.05918i	−0.185772	+	0.268738i
$691$	−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
$693$	−13.4154	−	9.03373i	−0.509609	−	0.343163i
$694$	28.0956	−	13.3077i	1.06649	−	0.505153i
$695$	−3.95558	+	6.85127i	−0.150044	+	0.259883i
$696$	−1.07589	−	3.74347i	−0.0407813	−	0.141896i
$697$	4.17820	+	7.23685i	0.158261	+	0.274115i
$698$	1.78449	−	21.9156i	0.0675439	−	0.829519i
$699$			6.02545i			0.227903i
$700$	28.2734	+	6.66576i	1.06863	+	0.251942i
$701$		−	33.5258i		−	1.26625i	−0.774048	−	0.633127i	$-0.781771\pi$
$701$		−	33.5258i		−	1.26625i	0.774048	−	0.633127i	$-0.218229\pi$
$702$	16.4791	+	1.34182i	0.621963	+	0.0506436i
$703$	6.70759	+	11.6179i	0.252981	+	0.438177i
$704$	−19.2860	+	0.696952i	−0.726868	+	0.0262674i
$705$	−7.33116	+	12.6979i	−0.276108	+	0.478232i
$706$	−16.0793	−	33.9472i	−0.605154	−	1.27762i
$707$	−0.145310	+	2.10135i	−0.00546494	+	0.0790293i
$708$	−10.6141	+	12.9632i	−0.398901	+	0.487186i
$709$	−7.16576	−	4.13715i	−0.269116	−	0.155374i	0.359370	−	0.933195i	$-0.382992\pi$
$709$	−7.16576	−	4.13715i	−0.269116	−	0.155374i	−0.628486	+	0.777821i	$0.716325\pi$
$710$	−25.0427	−	17.3113i	−0.939834	−	0.649682i
$711$	−2.12442	−	3.67960i	−0.0796720	−	0.137996i
$712$	27.4491	−	28.4590i	1.02870	−	1.06655i
$713$	−6.06814			−0.227254
$714$	−9.40681	+	3.68444i	−0.352041	+	0.137887i
$715$			24.1805i			0.904298i
$716$	7.06776	−	2.66926i	0.264135	−	0.0997548i
$717$	−3.50835	+	2.02555i	−0.131022	+	0.0756455i
$718$	−24.9393	+	36.0773i	−0.930725	+	1.34639i
$719$	1.81462	−	3.14301i	0.0676739	−	0.117215i	−0.830203	−	0.557461i	$-0.811776\pi$
$719$	1.81462	−	3.14301i	0.0676739	−	0.117215i	0.897877	+	0.440246i	$0.145109\pi$
$720$	−32.1837	+	6.47755i	−1.19942	+	0.241404i
$721$	−3.08535	−	6.31352i	−0.114904	−	0.235128i
$722$	7.08884	+	14.9662i	0.263819	+	0.556983i
$723$	−6.31696	−	3.64710i	−0.234930	−	0.135637i
$724$	−4.54032	+	27.6954i	−0.168740	+	1.02929i
$725$	9.59133	−	5.53756i	0.356213	−	0.205660i
$726$	−0.405871	+	4.98458i	−0.0150633	+	0.184995i
$727$	28.1550			1.04421			0.522106	−	0.852881i	$-0.325147\pi$
$727$	28.1550			1.04421			0.522106	+	0.852881i	$0.325147\pi$
$728$	15.5209	+	17.1900i	0.575244	+	0.637103i
$729$	4.99500			0.185000
$730$	3.55286	−	43.6333i	0.131497	−	1.61494i
$731$	39.7028	−	22.9224i	1.46846	−	0.847816i
$732$	−11.7418	−	1.92492i	−0.433988	−	0.0711470i
$733$	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
$735$	5.81930	+	14.3395i	0.214648	+	0.528919i
$736$	12.4452	−	9.28474i	0.458737	−	0.342240i
$737$	6.98965	−	12.1064i	0.257467	−	0.445946i
$738$	−4.30502	+	6.22768i	−0.158470	+	0.229244i
$739$	−11.2457	+	6.49271i	−0.413680	+	0.238838i	−0.692370	−	0.721543i	$-0.743433\pi$
$739$	−11.2457	+	6.49271i	−0.413680	+	0.238838i	0.278690	+	0.960381i	$0.410100\pi$
$740$	−11.3708	−	30.1081i	−0.418000	−	1.10680i
$741$		−	5.70400i		−	0.209542i
$742$	1.44898	−	9.56872i	0.0531937	−	0.351279i
$743$	21.8510			0.801637			0.400819	−	0.916157i	$-0.368726\pi$
$743$	21.8510			0.801637			0.400819	+	0.916157i	$0.368726\pi$
$744$	3.07210	+	2.96308i	0.112629	+	0.108632i
$745$	15.2685	+	26.4459i	0.559396	+	0.968903i
$746$	7.70280	+	5.32474i	0.282020	+	0.194953i
$747$	−14.2154	−	8.20728i	−0.520115	−	0.300289i
$748$	14.7660	+	12.0902i	0.539900	+	0.442062i
$749$	−12.9086	+	6.30827i	−0.471668	+	0.230499i
$750$	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	$0.237371\pi$
$752$	19.9059	−	17.5370i	0.725895	−	0.639507i
$753$	−1.30512	−	2.26053i	−0.0475612	−	0.0823783i
$754$	8.80100	+	0.716624i	0.320513	+	0.0260979i
$755$			22.8456i			0.831436i
$756$	−14.5554	−	13.6999i	−0.529374	−	0.498262i
$757$		−	27.2309i		−	0.989725i	−0.868971	−	0.494862i	$-0.835218\pi$
$757$		−	27.2309i		−	0.989725i	0.868971	−	0.494862i	$-0.164782\pi$
$758$	−2.15548	+	26.4718i	−0.0782905	+	0.961501i
$759$	2.25985	+	3.91418i	0.0820275	+	0.142076i
$760$	6.83209	+	23.7718i	0.247826	+	0.862294i
$761$	−15.2423	+	26.4005i	−0.552534	+	0.957017i	0.445557	+	0.895254i	$0.353006\pi$
$761$	−15.2423	+	26.4005i	−0.552534	+	0.957017i	−0.998091	+	0.0617632i	$0.980328\pi$
$762$	−13.5134	+	6.40072i	−0.489538	+	0.231873i
$763$	2.52094	−	36.4557i	0.0912642	−	1.31978i
$764$	−9.22262	+	11.2638i	−0.333663	+	0.407509i
$765$	28.1151	+	16.2323i	1.01650	+	0.586879i
$766$	−16.4339	+	23.7734i	−0.593782	+	0.858969i
$767$	−18.9912	−	32.8937i	−0.685731	−	1.18772i
$768$	−10.8344	−	1.37648i	−0.390951	−	0.0496693i
$769$	36.6991			1.32340			0.661701	−	0.749768i	$-0.269835\pi$
$769$	36.6991			1.32340			0.661701	+	0.749768i	$0.269835\pi$
$770$	18.2425	−	22.8431i	0.657413	−	0.823208i
$771$		−	8.46809i		−	0.304971i
$772$	−6.73696	−	17.8384i	−0.242468	−	0.642017i
$773$	−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	$0.535928\pi$
$774$	34.1663	+	23.6182i	1.22808	+	0.848939i
$775$	−6.06814	+	10.5103i	−0.217974	+	0.377542i
$776$	3.77988	+	0.939991i	0.135690	+	0.0337437i
$777$	5.01186	−	7.44278i	0.179800	−	0.267008i
$778$	3.03625	−	1.43814i	0.108855	−	0.0515600i
$779$	4.93981	+	2.85200i	0.176987	+	0.102183i
$780$	−2.21380	+	13.5039i	−0.0792669	+	0.483518i
$781$	−13.8857	+	8.01691i	−0.496869	+	0.286867i
$782$	−15.3040	−	1.24613i	−0.547270	−	0.0445617i
$783$	−7.62093			−0.272350
$784$	−1.69387	−	27.9487i	−0.0604955	−	0.998168i
$785$	28.2281			1.00751
$786$	−16.1731	−	1.31690i	−0.576875	−	0.0469723i
$787$	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	$0.233492\pi$
$788$	−3.77485	+	23.0261i	−0.134473	+	0.820271i
$789$	−0.794499	−	0.458704i	−0.0282849	−	0.0163303i
$790$	6.94055	−	3.28745i	0.246934	−	0.116962i
$791$	6.70041	−	9.95033i	0.238239	−	0.353793i
$792$	−4.17267	+	16.7791i	−0.148269	+	0.596220i
$793$	13.4872	−	23.3604i	0.478943	−	0.829553i
$794$	25.7901	+	17.8280i	0.915255	+	0.632691i
$795$	4.95204	−	2.85906i	0.175631	−	0.101400i
$796$	−13.4010	−	35.4837i	−0.474986	−	1.25768i
$797$			41.7331i			1.47826i	0.673561	+	0.739131i	$0.264764\pi$
$797$			41.7331i			1.47826i	−0.673561	+	0.739131i	$0.735236\pi$
$798$	−4.30327	+	5.38852i	−0.152334	+	0.190752i
$799$	−26.2345			−0.928109
$800$	−3.63641	−	30.8405i	−0.128566	−	1.09038i
$801$	−17.7123	−	30.6786i	−0.625832	−	1.08397i
$802$	21.1633	−	30.6150i	0.747304	−	1.08105i
$803$	−19.9675	−	11.5282i	−0.704638	−	0.406823i
$804$	5.01186	−	6.12109i	0.176755	−	0.215874i
$805$	−1.62258	+	23.4643i	−0.0571884	+	0.827010i
$806$	−8.74483	+	4.14206i	−0.308023	+	0.145898i
$807$	−0.665670	+	1.15297i	−0.0234327	+	0.0405866i
$808$	2.16419	−	0.621995i	0.0761360	−	0.0218817i
$809$	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	$0.778645\pi$
$810$	−1.86744	+	22.9343i	−0.0656150	+	0.805831i
$811$			55.3405i			1.94327i	0.236492	+	0.971633i	$0.424002\pi$
$811$			55.3405i			1.94327i	−0.236492	+	0.971633i	$0.575998\pi$
$812$	−7.77359	−	7.31672i	−0.272800	−	0.256767i
$813$			17.7733i			0.623339i
$814$	−16.8943	−	1.37563i	−0.592146	−	0.0482157i
$815$	32.1084	+	55.6134i	1.12471	+	1.94805i
$816$	7.13942	+	8.10385i	0.249930	+	0.283692i
$817$	15.6466	−	27.1008i	0.547406	−	0.948135i
$818$	−0.400957	−	0.846511i	−0.0140191	−	0.0295976i
$819$	18.6429	−	9.11056i	0.651434	−	0.318349i
$820$	−10.5878	−	8.66918i	−0.369744	−	0.302741i
$821$	−36.5157	−	21.0823i	−1.27441	−	0.735779i	−0.298592	−	0.954381i	$-0.596517\pi$
$821$	−36.5157	−	21.0823i	−1.27441	−	0.735779i	−0.975814	+	0.218602i	$0.929850\pi$
$822$	0.704691	+	0.487134i	0.0245789	+	0.0169907i
$823$	−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	$0.918758\pi$
$824$	−5.21518	+	5.40705i	−0.181679	+	0.188363i
$825$	9.03942			0.314712
$826$	−6.87516	+	45.4019i	−0.239217	+	1.57973i
$827$			1.24390i			0.0432548i	0.999766	+	0.0216274i	$0.00688475\pi$
$827$			1.24390i			0.0432548i	−0.999766	+	0.0216274i	$0.993115\pi$
$828$	−4.91495	−	13.0140i	−0.170806	−	0.452267i
$829$	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	$0.212692\pi$
$830$	16.8709	−	24.4056i	0.585599	−	0.847131i
$831$	5.50067	−	9.52744i	0.190816	−	0.330503i
$832$	11.5972	−	21.8753i	0.402061	−	0.758389i
$833$	−17.0134	+	21.8456i	−0.589478	+	0.756905i
$834$	1.00936	+	2.13099i	0.0349513	+	0.0737902i
$835$	62.1557	+	35.8856i	2.15099	+	1.24187i
$836$	12.8551	+	2.10744i	0.444605	+	0.0728874i
$837$	7.23230	−	4.17557i	0.249985	−	0.144329i
$838$	−0.867111	+	10.6492i	−0.0299539	+	0.367869i
$839$	−20.9379			−0.722857			−0.361429	−	0.932400i	$-0.617711\pi$
$839$	−20.9379			−0.722857			−0.361429	+	0.932400i	$0.617711\pi$
$840$	12.2791	−	11.0869i	0.423671	−	0.382535i
$841$	24.9299			0.859651
$842$	1.44505	−	17.7470i	0.0497999	−	0.611601i
$843$	9.53586	−	5.50553i	0.328432	−	0.189621i
$844$	5.21794	−	31.8288i	0.179609	−	1.09559i
$845$	9.59686	+	5.54075i	0.330142	+	0.190608i
$846$	−10.1744	−	21.4804i	−0.349802	−	0.738512i
$847$	6.01820	+	12.3150i	0.206788	+	0.423148i
$848$	−10.1426	+	2.04138i	−0.348299	+	0.0701013i
$849$	8.98332	−	15.5596i	0.308307	−	0.534003i
$850$	−17.4624	+	25.2612i	−0.598955	+	0.866452i
$851$	11.8106	−	6.81884i	0.404861	−	0.233747i
$852$	−8.48865	+	3.20588i	−0.290816	+	0.109832i
$853$		−	17.4758i		−	0.598361i	−0.954197	−	0.299180i	$-0.903287\pi$
$853$		−	17.4758i		−	0.598361i	0.954197	−	0.299180i	$-0.0967133\pi$
$854$	−30.3650	+	11.8933i	−1.03907	+	0.406981i
$855$	22.1600			0.757856
$856$	11.0552	+	10.6629i	0.377858	+	0.364450i
$857$	−1.75517	−	3.04005i	−0.0599556	−	0.103846i	0.834490	−	0.551024i	$-0.185763\pi$
$857$	−1.75517	−	3.04005i	−0.0599556	−	0.103846i	−0.894445	+	0.447177i	$0.852429\pi$
$858$	5.92847	+	4.09819i	0.202395	+	0.139910i
$859$	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
$861$	0.263196	−	3.80612i	0.00896970	−	0.129712i
$862$	−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	$-0.0737962\pi$
$864$	−8.44387	+	19.6297i	−0.287266	+	0.667817i
$865$	−35.1916	−	60.9536i	−1.19655	−	2.07248i
$866$	57.2016	+	4.65766i	1.94379	+	0.158274i
$867$			0.923798i			0.0313738i
$868$	11.3861	+	2.68439i	0.386468	+	0.0911142i
$869$		−	4.04471i		−	0.137207i
$870$	0.511898	−	6.28672i	0.0173550	−	0.213140i
$871$	8.96744	+	15.5321i	0.303850	+	0.526284i
$872$	−37.5460	+	10.7908i	−1.27147	+	0.365423i
$873$	1.74483	−	3.02213i	0.0590534	−	0.102284i
$874$	−9.47212	+	4.48655i	−0.320399	+	0.151760i
$875$	3.48031	+	2.34359i	0.117656	+	0.0792277i
$876$	−10.0957	−	8.26621i	−0.341102	−	0.279289i
$877$	−36.3471	−	20.9850i	−1.22735	−	0.708613i	−0.260878	−	0.965372i	$-0.584012\pi$
$877$	−36.3471	−	20.9850i	−1.22735	−	0.708613i	−0.966476	+	0.256759i	$0.917345\pi$
$878$	29.3157	−	42.4083i	0.989357	−	1.43121i
$879$	3.29326	+	5.70409i	0.111079	+	0.192394i
$880$	−29.6160	−	9.97854i	−0.998355	−	0.336376i
$881$	−16.5992			−0.559241			−0.279620	−	0.960111i	$-0.590209\pi$
$881$	−16.5992			−0.559241			−0.279620	+	0.960111i	$0.590209\pi$
$882$	−24.4851	−	5.45806i	−0.824455	−	0.183782i
$883$			12.8210i			0.431462i	0.976453	+	0.215731i	$0.0692135\pi$
$883$			12.8210i			0.431462i	−0.976453	+	0.215731i	$0.930787\pi$
$884$	−22.9053	+	8.65056i	−0.770388	+	0.290950i
$885$	−23.4966	+	13.5658i	−0.789829	+	0.456008i
$886$	−37.7831	−	26.1184i	−1.26935	−	0.877465i
$887$	−4.14980	+	7.18766i	−0.139337	+	0.241338i	−0.927246	−	0.374454i	$-0.877830\pi$
$887$	−4.14980	+	7.18766i	−0.139337	+	0.241338i	0.787909	+	0.615792i	$0.211164\pi$
$888$	−9.30895	−	2.31497i	−0.312388	−	0.0776855i
$889$	−22.8905	+	33.9931i	−0.767722	+	1.14009i
$890$	57.8666	−	27.4090i	1.93969	−	0.918751i
$891$	10.4952	+	6.05942i	0.351603	+	0.202998i
$892$	−15.2263	−	2.49616i	−0.509814	−	0.0835777i
$893$	−15.5083	+	8.95370i	−0.518964	+	0.299624i
$894$	9.07168	+	0.738664i	0.303402	+	0.0247046i
$895$	12.2345			0.408954
$896$	−27.4592	+	11.9161i	−0.917346	+	0.398090i
$897$	−5.79861			−0.193610
$898$	−36.6234	−	2.98207i	−1.22214	−	0.0995130i
$899$	3.86255	−	2.23005i	0.128823	−	0.0743762i
$900$	−27.4558	−	4.50104i	−0.915194	−	0.150035i
$901$	8.86041	+	5.11556i	0.295183	+	0.170424i
$902$	−6.51337	+	3.08511i	−0.216872	+	0.102723i
$903$	−20.8811	−	1.44395i	−0.694880	−	0.0480515i
$904$	−12.4452	−	3.09491i	−0.413922	−	0.102935i
$905$	−22.7241	+	39.3593i	−0.755376	+	1.30835i
$906$	5.60120	+	3.87196i	0.186087	+	0.128637i
$907$	14.2277	−	8.21434i	0.472422	−	0.272753i	−0.244831	−	0.969566i	$-0.578733\pi$
$907$	14.2277	−	8.21434i	0.472422	−	0.272753i	0.717253	+	0.696813i	$0.245399\pi$
$908$	3.97516	−	1.50129i	0.131920	−	0.0498219i
$909$		−	2.01745i		−	0.0669147i
$910$	13.6782	+	34.9221i	0.453429	+	1.15766i
$911$	−37.1630			−1.23127			−0.615633	−	0.788033i	$-0.711100\pi$
$911$	−37.1630			−1.23127			−0.615633	+	0.788033i	$0.711100\pi$
$912$	6.98621	+	2.35387i	0.231336	+	0.0779443i
$913$	−7.81297	−	13.5325i	−0.258571	−	0.447859i
$914$	−9.22300	+	13.3420i	−0.305070	+	0.441316i
$915$	−16.6868	−	9.63413i	−0.551649	−	0.318495i
$916$	−14.4965	−	11.8695i	−0.478978	−	0.392180i
$917$	−39.9575	+	19.5268i	−1.31951	+	0.644831i
$918$	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	$-0.0376914\pi$
$920$	24.1661	−	6.94541i	0.796732	−	0.228983i
$921$	8.62593	+	14.9406i	0.284234	+	0.492308i
$922$	−2.89197	+	35.5168i	−0.0952419	+	1.16968i
$923$		−	20.5707i		−	0.677094i
$924$	−2.50878	−	8.34415i	−0.0825329	−	0.274502i
$925$		−	27.2754i		−	0.896809i
$926$	44.8551	+	3.65234i	1.47403	+	0.120023i
$927$	3.36523	+	5.82875i	0.110529	+	0.191441i
$928$	−4.50962	+	10.4837i	−0.148035	+	0.344143i
$929$	10.8263	−	18.7518i	0.355201	−	0.615226i	−0.631952	−	0.775008i	$-0.717746\pi$
$929$	10.8263	−	18.7518i	0.355201	−	0.615226i	0.987152	+	0.159782i	$0.0510792\pi$
$930$	2.95875	+	6.24660i	0.0970212	+	0.204834i
$931$	−2.60150	+	18.7204i	−0.0852608	+	0.613536i
$932$	11.1845	−	13.6599i	0.366362	−	0.447445i
$933$	13.3293	+	7.69567i	0.436382	+	0.251945i
$934$	−16.5344	−	11.4298i	−0.541022	−	0.373994i
$935$	15.4524	+	26.7644i	0.505348	+	0.875288i
$936$	−15.9662	−	15.3996i	−0.521871	−	0.503352i
$937$	−15.8637			−0.518245			−0.259123	−	0.965844i	$-0.583433\pi$
$937$	−15.8637			−0.518245			−0.259123	+	0.965844i	$0.583433\pi$
$938$	3.24638	−	21.4383i	0.105998	−	0.699986i
$939$			17.3242i			0.565355i
$940$	40.1901	−	15.1785i	1.31086	−	0.495067i
$941$	−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	$0.410304\pi$
$942$	4.78421	−	6.92087i	0.155878	−	0.225494i
$943$	2.89930	−	5.02174i	0.0944143	−	0.163530i
$944$	48.1249	−	9.68600i	1.56633	−	0.315252i
$945$	−14.2123	−	29.0824i	−0.462325	−	0.946052i
$946$	16.9255	+	35.7337i	0.550296	+	1.16180i
$947$	−12.0598	−	6.96270i	−0.391889	−	0.226257i	0.291089	−	0.956696i	$-0.405982\pi$
$947$	−12.0598	−	6.96270i	−0.391889	−	0.226257i	−0.682978	+	0.730439i	$0.739316\pi$
$948$	0.370307	−	2.25883i	0.0120270	−	0.0733633i
$949$	25.6175	−	14.7903i	0.831579	−	0.480112i
$950$	−1.70120	+	20.8927i	−0.0551942	+	0.677850i
$951$	−11.6954			−0.379250
$952$	28.1647	+	9.10831i	0.912823	+	0.295202i
$953$	11.2883			0.365663			0.182831	−	0.983144i	$-0.441474\pi$
$953$	11.2883			0.365663			0.182831	+	0.983144i	$0.441474\pi$
$954$	−0.752266	+	9.23871i	−0.0243555	+	0.299114i
$955$	−20.4163	+	11.7873i	−0.660655	+	0.381430i
$956$	11.7134	+	1.92027i	0.378839	+	0.0621060i
$957$	−2.87693	−	1.66100i	−0.0929980	−	0.0536924i
$958$	−6.98631	−	14.7497i	−0.225717	−	0.476541i
$959$	2.34236	+	0.161976i	0.0756386	+	0.00523047i
$960$	−15.6259	−	8.28411i	−0.504325	−	0.267369i
$961$	13.0563	−	22.6141i	0.421170	−	0.729488i
$962$	12.3658	−	17.8885i	0.398690	−	0.576747i
$963$	11.9174	−	6.88051i	0.384033	−	0.221721i
$964$	7.55097	+	19.9937i	0.243200	+	0.643955i
$965$		−	30.8787i		−	0.994020i
$966$	5.47790	+	4.37464i	0.176249	+	0.140752i
$967$	−36.4276			−1.17143			−0.585716	−	0.810517i	$-0.699187\pi$
$967$	−36.4276			−1.17143			−0.585716	+	0.810517i	$0.699187\pi$
$968$	10.1726	−	10.5468i	0.326959	−	0.338988i
$969$	−3.64512	−	6.31352i	−0.117098	−	0.202820i
$970$	5.18851	+	3.58668i	0.166593	+	0.115161i
$971$	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
$973$	5.36055	+	3.60971i	0.171851	+	0.115722i
$974$	−10.6647	−	22.5156i	−0.341719	−	0.721446i
$975$	−5.79861	+	10.0435i	−0.185704	+	0.321649i
$976$	23.0459	+	26.1591i	0.737682	+	0.837332i
$977$	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	$0.574265\pi$
$978$	19.0769	+	1.55335i	0.610013	+	0.0496705i
$979$		−	33.7226i		−	1.07778i
$980$	13.4246	−	43.3100i	0.428833	−	1.38349i
$981$			35.0002i			1.11747i
$982$	−3.08168	+	37.8466i	−0.0983402	+	1.20773i
$983$	9.26538	+	16.0481i	0.295520	+	0.511855i	0.975106	−	0.221741i	$-0.0711738\pi$
$983$	9.26538	+	16.0481i	0.295520	+	0.511855i	−0.679586	+	0.733596i	$0.737841\pi$
$984$	−3.91994	+	1.12660i	−0.124963	+	0.0359148i
$985$	−18.8930	+	32.7236i	−0.601980	+	1.04266i
$986$	10.1994	−	4.83104i	0.324816	−	0.153852i
$987$	9.93508	+	6.69014i	0.316237	+	0.212950i
$988$	−10.5878	+	12.9312i	−0.336844	+	0.411395i
$989$	−27.5503	−	15.9061i	−0.876047	−	0.505786i
$990$	−15.9215	+	23.0321i	−0.506017	+	0.732008i
$991$	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	$0.636626\pi$
$992$	−1.46443	−	12.4199i	−0.0464957	−	0.394332i
$993$	5.86069			0.185983
$994$	−15.5192	+	19.4330i	−0.492239	+	0.616378i
$995$		−	61.4232i		−	1.94724i
$996$	−3.12433	−	8.27271i	−0.0989980	−	0.262131i
$997$	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	$0.255297\pi$
$998$	−2.98109	−	2.06075i	−0.0943647	−	0.0652318i
$999$	−9.38427	+	16.2540i	−0.296905	+	0.514255i

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

)

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.p.a.37.1	✓	12	1.1	even	1	trivial
56.2.p.a.37.5	yes	12	8.5	even	2	inner
56.2.p.a.53.1	yes	12	56.53	even	6	inner
56.2.p.a.53.5	yes	12	7.4	even	3	inner
224.2.t.a.81.3		12	28.11	odd	6
224.2.t.a.81.4		12	56.11	odd	6
224.2.t.a.177.3		12	8.3	odd	2
224.2.t.a.177.4		12	4.3	odd	2
392.2.b.e.197.3		6	56.37	even	6
392.2.b.e.197.4		6	7.2	even	3
392.2.b.f.197.3		6	56.5	odd	6
392.2.b.f.197.4		6	7.5	odd	6
392.2.p.g.165.1		12	56.45	odd	6
392.2.p.g.165.5		12	7.3	odd	6
392.2.p.g.373.1		12	7.6	odd	2
392.2.p.g.373.5		12	56.13	odd	2
504.2.cj.c.37.2		12	24.5	odd	2
504.2.cj.c.37.6		12	3.2	odd	2
504.2.cj.c.109.2		12	21.11	odd	6
504.2.cj.c.109.6		12	168.53	odd	6
1568.2.b.e.785.3		6	28.19	even	6
1568.2.b.e.785.4		6	56.19	even	6
1568.2.b.f.785.3		6	56.51	odd	6
1568.2.b.f.785.4		6	28.23	odd	6
1568.2.t.g.177.3		12	28.27	even	2
1568.2.t.g.177.4		12	56.27	even	2
1568.2.t.g.753.3		12	56.3	even	6
1568.2.t.g.753.4		12	28.3	even	6
2016.2.cr.c.1297.1		12	12.11	even	2
2016.2.cr.c.1297.6		12	24.11	even	2
2016.2.cr.c.1873.1		12	168.11	even	6
2016.2.cr.c.1873.6		12	84.11	even	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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	56.2.p.a.37.1

Level	$56$
Weight	$2$
Character	56.37
Analytic conductor	$0.447$
Analytic rank	$0$
Dimension	$12$
Inner twists	$4$