LMFDB - Embedded newform 1170.2.j.h.391.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1170,2,Mod(391,1170)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1170, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1170.391"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.j (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,-4,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$9.34249703649$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.856615824.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			391.1
Root			$-0.385731i$ of defining polynomial
Character	$\chi$	$=$	1170.391
Dual form			1170.2.j.h.781.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.42561 + 0.983691i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.56470 + 0.742765i) q^{6} +(-0.425606 - 0.737171i) q^{7} +1.00000 q^{8} +(1.06470 - 2.80471i) q^{9} -1.00000 q^{10} +(0.0743941 + 0.128854i) q^{11} +(-0.139098 - 1.72646i) q^{12} +(0.500000 - 0.866025i) q^{13} +(-0.425606 + 0.737171i) q^{14} +(0.139098 + 1.72646i) q^{15} +(-0.500000 - 0.866025i) q^{16} -0.0580138 q^{17} +(-2.96130 + 0.480295i) q^{18} +1.85121 q^{19} +(0.500000 + 0.866025i) q^{20} +(1.33189 + 0.632251i) q^{21} +(0.0743941 - 0.128854i) q^{22} +(-2.78651 + 4.82637i) q^{23} +(-1.42561 + 0.983691i) q^{24} +(-0.500000 - 0.866025i) q^{25} -1.00000 q^{26} +(1.24112 + 5.04575i) q^{27} +0.851212 q^{28} +(-3.26851 - 5.66122i) q^{29} +(1.42561 - 0.983691i) q^{30} +(-1.59371 + 2.76039i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.232810 - 0.110515i) q^{33} +(0.0290069 + 0.0502414i) q^{34} -0.851212 q^{35} +(1.89660 + 2.32442i) q^{36} +1.73518 q^{37} +(-0.925606 - 1.60320i) q^{38} +(0.139098 + 1.72646i) q^{39} +(0.500000 - 0.866025i) q^{40} +(4.31389 - 7.47188i) q^{41} +(-0.118402 - 1.46958i) q^{42} +(1.27820 + 2.21390i) q^{43} -0.148788 q^{44} +(-1.89660 - 2.32442i) q^{45} +5.57301 q^{46} +(-6.55501 - 11.3536i) q^{47} +(1.56470 + 0.742765i) q^{48} +(3.13772 - 5.43469i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(0.0827048 - 0.0570676i) q^{51} +(0.500000 + 0.866025i) q^{52} -11.8452 q^{53} +(3.74919 - 3.59772i) q^{54} +0.148788 q^{55} +(-0.425606 - 0.737171i) q^{56} +(-2.63910 + 1.82102i) q^{57} +(-3.26851 + 5.66122i) q^{58} +(3.17480 - 5.49891i) q^{59} +(-1.56470 - 0.742765i) q^{60} +(1.10202 + 1.90876i) q^{61} +3.18742 q^{62} +(-2.52070 + 0.408832i) q^{63} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{65} +(0.0206962 + 0.256876i) q^{66} +(2.73281 - 4.73337i) q^{67} +(0.0290069 - 0.0502414i) q^{68} +(-0.775197 - 9.62157i) q^{69} +(0.425606 + 0.737171i) q^{70} +10.8152 q^{71} +(1.06470 - 2.80471i) q^{72} -6.14279 q^{73} +(-0.867592 - 1.50271i) q^{74} +(1.56470 + 0.742765i) q^{75} +(-0.925606 + 1.60320i) q^{76} +(0.0633251 - 0.109682i) q^{77} +(1.42561 - 0.983691i) q^{78} +(-6.67342 - 11.5587i) q^{79} -1.00000 q^{80} +(-6.73281 - 5.97238i) q^{81} -8.62779 q^{82} +(-6.96961 - 12.0717i) q^{83} +(-1.21349 + 0.837329i) q^{84} +(-0.0290069 + 0.0502414i) q^{85} +(1.27820 - 2.21390i) q^{86} +(10.2285 + 4.85547i) q^{87} +(0.0743941 + 0.128854i) q^{88} -5.88985 q^{89} +(-1.06470 + 2.80471i) q^{90} -0.851212 q^{91} +(-2.78651 - 4.82637i) q^{92} +(-0.443365 - 5.50295i) q^{93} +(-6.55501 + 11.3536i) q^{94} +(0.925606 - 1.60320i) q^{95} +(-0.139098 - 1.72646i) q^{96} +(1.31551 + 2.27854i) q^{97} -6.27544 q^{98} +(0.440607 - 0.0714622i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - q^{3} - 4 q^{4} + 4 q^{5} - q^{6} + 7 q^{7} + 8 q^{8} - 5 q^{9} - 8 q^{10} + 11 q^{11} + 2 q^{12} + 4 q^{13} + 7 q^{14} - 2 q^{15} - 4 q^{16} - 8 q^{17} + 4 q^{18} - 6 q^{19} + 4 q^{20}+ \cdots - 29 q^{99}+O(q^{100}) $ 8 * q - 4 * q^2 - q^3 - 4 * q^4 + 4 * q^5 - q^6 + 7 * q^7 + 8 * q^8 - 5 * q^9 - 8 * q^10 + 11 * q^11 + 2 * q^12 + 4 * q^13 + 7 * q^14 - 2 * q^15 - 4 * q^16 - 8 * q^17 + 4 * q^18 - 6 * q^19 + 4 * q^20 + 10 * q^21 + 11 * q^22 - 15 * q^23 - q^24 - 4 * q^25 - 8 * q^26 - 4 * q^27 - 14 * q^28 + 4 * q^29 + q^30 - 3 * q^31 - 4 * q^32 + 11 * q^33 + 4 * q^34 + 14 * q^35 + q^36 - 22 * q^37 + 3 * q^38 - 2 * q^39 + 4 * q^40 + 11 * q^41 + 7 * q^42 + 4 * q^43 - 22 * q^44 - q^45 + 30 * q^46 - 15 * q^47 - q^48 - 3 * q^49 - 4 * q^50 + 10 * q^51 + 4 * q^52 + 16 * q^53 + 20 * q^54 + 22 * q^55 + 7 * q^56 - 18 * q^57 + 4 * q^58 + 5 * q^59 + q^60 - 2 * q^61 + 6 * q^62 - 25 * q^63 + 8 * q^64 - 4 * q^65 + 5 * q^66 + 9 * q^67 + 4 * q^68 + 45 * q^69 - 7 * q^70 + 20 * q^71 - 5 * q^72 + 20 * q^73 + 11 * q^74 - q^75 + 3 * q^76 - 38 * q^77 + q^78 - 8 * q^79 - 8 * q^80 - 41 * q^81 - 22 * q^82 - 27 * q^83 - 17 * q^84 - 4 * q^85 + 4 * q^86 + 67 * q^87 + 11 * q^88 + 14 * q^89 + 5 * q^90 + 14 * q^91 - 15 * q^92 - 21 * q^93 - 15 * q^94 - 3 * q^95 + 2 * q^96 + 7 * q^97 + 6 * q^98 - 29 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−1.42561	+	0.983691i	−0.823074	+	0.567934i
$3$	−1.42561	+	0.983691i	−0.823074	+	0.567934i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	1.56470	+	0.742765i	0.638788	+	0.303233i
$7$	−0.425606	−	0.737171i	−0.160864	−	0.278624i	0.774315	−	0.632801i	$-0.218095\pi$
$7$	−0.425606	−	0.737171i	−0.160864	−	0.278624i	−0.935179	+	0.354176i	$0.884761\pi$
$8$	1.00000			0.353553
$9$	1.06470	−	2.80471i	0.354901	−	0.934904i
$10$	−1.00000			−0.316228
$11$	0.0743941	+	0.128854i	0.0224307	+	0.0388511i	0.877023	−	0.480449i	$-0.159526\pi$
$11$	0.0743941	+	0.128854i	0.0224307	+	0.0388511i	−0.854592	+	0.519300i	$0.826193\pi$
$12$	−0.139098	−	1.72646i	−0.0401542	−	0.498385i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$14$	−0.425606	+	0.737171i	−0.113748	+	0.197017i
$15$	0.139098	+	1.72646i	0.0359151	+	0.445769i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.0580138			−0.0140704			−0.00703521	−	0.999975i	$-0.502239\pi$
$17$	−0.0580138			−0.0140704			−0.00703521	+	0.999975i	$0.502239\pi$
$18$	−2.96130	+	0.480295i	−0.697986	+	0.113207i
$19$	1.85121			0.424697			0.212349	−	0.977194i	$-0.431889\pi$
$19$	1.85121			0.424697			0.212349	+	0.977194i	$0.431889\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	1.33189	+	0.632251i	0.290643	+	0.137968i
$22$	0.0743941	−	0.128854i	0.0158609	−	0.0274718i
$23$	−2.78651	+	4.82637i	−0.581027	+	1.00637i	0.414331	+	0.910126i	$0.364016\pi$
$23$	−2.78651	+	4.82637i	−0.581027	+	1.00637i	−0.995358	+	0.0962420i	$0.969318\pi$
$24$	−1.42561	+	0.983691i	−0.291001	+	0.200795i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−1.00000			−0.196116
$27$	1.24112	+	5.04575i	0.238854	+	0.971056i
$28$	0.851212			0.160864
$29$	−3.26851	−	5.66122i	−0.606947	−	1.05126i	−0.991741	−	0.128260i	$-0.959061\pi$
$29$	−3.26851	−	5.66122i	−0.606947	−	1.05126i	0.384794	−	0.923002i	$-0.374272\pi$
$30$	1.42561	−	0.983691i	0.260279	−	0.179597i
$31$	−1.59371	+	2.76039i	−0.286239	+	0.495780i	−0.972909	−	0.231189i	$-0.925738\pi$
$31$	−1.59371	+	2.76039i	−0.286239	+	0.495780i	0.686670	+	0.726969i	$0.259072\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−0.232810	−	0.110515i	−0.0405269	−	0.0192381i
$34$	0.0290069	+	0.0502414i	0.00497464	+	0.00861633i
$35$	−0.851212			−0.143881
$36$	1.89660	+	2.32442i	0.316100	+	0.387403i
$37$	1.73518			0.285263			0.142631	−	0.989776i	$-0.454444\pi$
$37$	1.73518			0.285263			0.142631	+	0.989776i	$0.454444\pi$
$38$	−0.925606	−	1.60320i	−0.150153	−	0.260073i
$39$	0.139098	+	1.72646i	0.0222736	+	0.276454i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	4.31389	−	7.47188i	0.673717	−	1.16691i	−0.303125	−	0.952951i	$-0.598030\pi$
$41$	4.31389	−	7.47188i	0.673717	−	1.16691i	0.976842	−	0.213961i	$-0.0686367\pi$
$42$	−0.118402	−	1.46958i	−0.0182699	−	0.226761i
$43$	1.27820	+	2.21390i	0.194923	+	0.337617i	0.946875	−	0.321601i	$-0.104221\pi$
$43$	1.27820	+	2.21390i	0.194923	+	0.337617i	−0.751952	+	0.659218i	$0.770888\pi$
$44$	−0.148788			−0.0224307
$45$	−1.89660	−	2.32442i	−0.282728	−	0.346504i
$46$	5.57301			0.821696
$47$	−6.55501	−	11.3536i	−0.956147	−	1.65610i	−0.731721	−	0.681604i	$-0.761283\pi$
$47$	−6.55501	−	11.3536i	−0.956147	−	1.65610i	−0.224426	−	0.974491i	$-0.572051\pi$
$48$	1.56470	+	0.742765i	0.225846	+	0.107209i
$49$	3.13772	−	5.43469i	0.448246	−	0.776384i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	0.0827048	−	0.0570676i	0.0115810	−	0.00799107i
$52$	0.500000	+	0.866025i	0.0693375	+	0.120096i
$53$	−11.8452			−1.62707			−0.813533	−	0.581519i	$-0.802458\pi$
$53$	−11.8452			−1.62707			−0.813533	+	0.581519i	$0.802458\pi$
$54$	3.74919	−	3.59772i	0.510200	−	0.489587i
$55$	0.148788			0.0200626
$56$	−0.425606	−	0.737171i	−0.0568740	−	0.0985086i
$57$	−2.63910	+	1.82102i	−0.349557	+	0.241200i
$58$	−3.26851	+	5.66122i	−0.429176	+	0.743355i
$59$	3.17480	−	5.49891i	0.413323	−	0.715897i	−0.581928	−	0.813241i	$-0.697701\pi$
$59$	3.17480	−	5.49891i	0.413323	−	0.715897i	0.995251	+	0.0973438i	$0.0310346\pi$
$60$	−1.56470	−	0.742765i	−0.202002	−	0.0958906i
$61$	1.10202	+	1.90876i	0.141099	+	0.244391i	0.927911	−	0.372802i	$-0.121603\pi$
$61$	1.10202	+	1.90876i	0.141099	+	0.244391i	−0.786811	+	0.617193i	$0.788270\pi$
$62$	3.18742			0.404803
$63$	−2.52070	+	0.408832i	−0.317578	+	0.0515080i
$64$	1.00000			0.125000
$65$	−0.500000	−	0.866025i	−0.0620174	−	0.107417i
$66$	0.0206962	+	0.256876i	0.00254753	+	0.0316193i
$67$	2.73281	−	4.73337i	0.333866	−	0.578273i	−0.649400	−	0.760447i	$-0.724980\pi$
$67$	2.73281	−	4.73337i	0.333866	−	0.578273i	0.983266	+	0.182174i	$0.0583134\pi$
$68$	0.0290069	−	0.0502414i	0.00351760	−	0.00609267i
$69$	−0.775197	−	9.62157i	−0.0933228	−	1.15830i
$70$	0.425606	+	0.737171i	0.0508696	+	0.0881088i
$71$	10.8152			1.28353			0.641765	−	0.766902i	$-0.278203\pi$
$71$	10.8152			1.28353			0.641765	+	0.766902i	$0.278203\pi$
$72$	1.06470	−	2.80471i	0.125477	−	0.330538i
$73$	−6.14279			−0.718959			−0.359480	−	0.933153i	$-0.617046\pi$
$73$	−6.14279			−0.718959			−0.359480	+	0.933153i	$0.617046\pi$
$74$	−0.867592	−	1.50271i	−0.100856	−	0.174687i
$75$	1.56470	+	0.742765i	0.180676	+	0.0857672i
$76$	−0.925606	+	1.60320i	−0.106174	+	0.183899i
$77$	0.0633251	−	0.109682i	0.00721657	−	0.0124995i
$78$	1.42561	−	0.983691i	0.161418	−	0.111381i
$79$	−6.67342	−	11.5587i	−0.750818	−	1.30045i	−0.947427	−	0.319973i	$-0.896326\pi$
$79$	−6.67342	−	11.5587i	−0.750818	−	1.30045i	0.196609	−	0.980482i	$-0.437007\pi$
$80$	−1.00000			−0.111803
$81$	−6.73281	−	5.97238i	−0.748090	−	0.663597i
$82$	−8.62779			−0.952780
$83$	−6.96961	−	12.0717i	−0.765015	−	1.32504i	−0.940239	−	0.340515i	$-0.889398\pi$
$83$	−6.96961	−	12.0717i	−0.765015	−	1.32504i	0.175224	−	0.984529i	$-0.443935\pi$
$84$	−1.21349	+	0.837329i	−0.132403	+	0.0913601i
$85$	−0.0290069	+	0.0502414i	−0.00314624	+	0.00544945i
$86$	1.27820	−	2.21390i	0.137832	−	0.238731i
$87$	10.2285	+	4.85547i	1.09661	+	0.520561i
$88$	0.0743941	+	0.128854i	0.00793044	+	0.0137359i
$89$	−5.88985			−0.624322			−0.312161	−	0.950029i	$-0.601053\pi$
$89$	−5.88985			−0.624322			−0.312161	+	0.950029i	$0.601053\pi$
$90$	−1.06470	+	2.80471i	−0.112230	+	0.295643i
$91$	−0.851212			−0.0892312
$92$	−2.78651	−	4.82637i	−0.290513	−	0.503184i
$93$	−0.443365	−	5.50295i	−0.0459748	−	0.570629i
$94$	−6.55501	+	11.3536i	−0.676098	+	1.17104i
$95$	0.925606	−	1.60320i	0.0949652	−	0.164484i
$96$	−0.139098	−	1.72646i	−0.0141967	−	0.176206i
$97$	1.31551	+	2.27854i	0.133570	+	0.231350i	0.925050	−	0.379844i	$-0.124022\pi$
$97$	1.31551	+	2.27854i	0.133570	+	0.231350i	−0.791480	+	0.611195i	$0.790689\pi$
$98$	−6.27544			−0.633915
$99$	0.440607	−	0.0714622i	0.0442827	−	0.00718222i
$100$	1.00000			0.100000
$101$	−6.41592	−	11.1127i	−0.638408	−	1.10575i	−0.985782	−	0.168028i	$-0.946260\pi$
$101$	−6.41592	−	11.1127i	−0.638408	−	1.10575i	0.347375	−	0.937726i	$-0.387073\pi$
$102$	−0.0907744	−	0.0430906i	−0.00898801	−	0.00426661i
$103$	−5.41592	+	9.38064i	−0.533646	+	0.924302i	0.465582	+	0.885005i	$0.345845\pi$
$103$	−5.41592	+	9.38064i	−0.533646	+	0.924302i	−0.999228	+	0.0392971i	$0.987488\pi$
$104$	0.500000	−	0.866025i	0.0490290	−	0.0849208i
$105$	1.21349	−	0.837329i	0.118425	−	0.0817150i
$106$	5.92261	+	10.2583i	0.575254	+	0.996370i
$107$	2.27820			0.220242			0.110121	−	0.993918i	$-0.464876\pi$
$107$	2.27820			0.220242			0.110121	+	0.993918i	$0.464876\pi$
$108$	−4.99031	−	1.44803i	−0.480193	−	0.139337i
$109$	−4.56977			−0.437705			−0.218853	−	0.975758i	$-0.570231\pi$
$109$	−4.56977			−0.437705			−0.218853	+	0.975758i	$0.570231\pi$
$110$	−0.0743941	−	0.128854i	−0.00709320	−	0.0122858i
$111$	−2.47369	+	1.70688i	−0.234792	+	0.162010i
$112$	−0.425606	+	0.737171i	−0.0402160	+	0.0696561i
$113$	6.22981	−	10.7903i	0.586051	−	1.01507i	−0.408692	−	0.912672i	$-0.634015\pi$
$113$	6.22981	−	10.7903i	0.586051	−	1.01507i	0.994743	−	0.102398i	$-0.0326516\pi$
$114$	2.89660	+	1.37502i	0.271291	+	0.128782i
$115$	2.78651	+	4.82637i	0.259843	+	0.450062i
$116$	6.53701			0.606947
$117$	−1.89660	−	2.32442i	−0.175341	−	0.214892i
$118$	−6.34959			−0.584527
$119$	0.0246910	+	0.0427661i	0.00226342	+	0.00392036i
$120$	0.139098	+	1.72646i	0.0126979	+	0.157603i
$121$	5.48893	−	9.50711i	0.498994	−	0.864282i
$122$	1.10202	−	1.90876i	0.0997724	−	0.172811i
$123$	1.20011	+	14.8955i	0.108210	+	1.34308i
$124$	−1.59371	−	2.76039i	−0.143119	−	0.247890i
$125$	−1.00000			−0.0894427
$126$	1.61441	+	1.97857i	0.143823	+	0.176265i
$127$	−6.23680			−0.553427			−0.276713	−	0.960952i	$-0.589245\pi$
$127$	−6.23680			−0.553427			−0.276713	+	0.960952i	$0.589245\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−4.00000	−	1.89880i	−0.352180	−	0.167180i
$130$	−0.500000	+	0.866025i	−0.0438529	+	0.0759555i
$131$	−3.14879	+	5.45386i	−0.275111	+	0.476506i	−0.970163	−	0.242453i	$-0.922048\pi$
$131$	−3.14879	+	5.45386i	−0.275111	+	0.476506i	0.695052	+	0.718959i	$0.255381\pi$
$132$	0.212113	−	0.146362i	0.0184621	−	0.0127391i
$133$	−0.787887	−	1.36466i	−0.0683184	−	0.118331i
$134$	−5.46562			−0.472158
$135$	4.99031	+	1.44803i	0.429498	+	0.124627i
$136$	−0.0580138			−0.00497464
$137$	−6.05070	−	10.4801i	−0.516946	−	0.895377i	−0.999806	−	0.0196794i	$-0.993735\pi$
$137$	−6.05070	−	10.4801i	−0.516946	−	0.895377i	0.482860	−	0.875697i	$-0.339598\pi$
$138$	−7.94492	+	5.48212i	−0.676317	+	0.466669i
$139$	−1.41892	+	2.45763i	−0.120351	+	0.208454i	−0.919906	−	0.392139i	$-0.871735\pi$
$139$	−1.41892	+	2.45763i	−0.120351	+	0.208454i	0.799555	+	0.600593i	$0.205069\pi$
$140$	0.425606	−	0.737171i	0.0359703	−	0.0623023i
$141$	20.5133	+	9.73768i	1.72753	+	0.820060i
$142$	−5.40761	−	9.36625i	−0.453796	−	0.785998i
$143$	0.148788			0.0124423
$144$	−2.96130	+	0.480295i	−0.246775	+	0.0400246i
$145$	−6.53701			−0.542869
$146$	3.07139	+	5.31981i	0.254190	+	0.440271i
$147$	0.872903	+	10.8343i	0.0719959	+	0.893596i
$148$	−0.867592	+	1.50271i	−0.0713156	+	0.123522i
$149$	−1.91592	+	3.31846i	−0.156958	+	0.271859i	−0.933770	−	0.357873i	$-0.883502\pi$
$149$	−1.91592	+	3.31846i	−0.156958	+	0.271859i	0.776812	+	0.629732i	$0.216835\pi$
$150$	−0.139098	−	1.72646i	−0.0113573	−	0.140965i
$151$	4.71049	+	8.15881i	0.383334	+	0.663955i	0.991537	−	0.129827i	$-0.0414423\pi$
$151$	4.71049	+	8.15881i	0.383334	+	0.663955i	−0.608202	+	0.793782i	$0.708109\pi$
$152$	1.85121			0.150153
$153$	−0.0617675	+	0.162712i	−0.00499361	+	0.0131545i
$154$	−0.126650			−0.0102058
$155$	1.59371	+	2.76039i	0.128010	+	0.221720i
$156$	−1.56470	−	0.742765i	−0.125277	−	0.0594688i
$157$	−5.34152	+	9.25179i	−0.426300	+	0.738373i	−0.996541	−	0.0831044i	$-0.973516\pi$
$157$	−5.34152	+	9.25179i	−0.426300	+	0.738373i	0.570241	+	0.821477i	$0.306850\pi$
$158$	−6.67342	+	11.5587i	−0.530909	+	0.919561i
$159$	16.8866	−	11.6520i	1.33919	−	0.924066i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	4.74382			0.373865
$162$	−1.80582	+	8.81697i	−0.141879	+	0.692727i
$163$	5.63379			0.441272			0.220636	−	0.975356i	$-0.429187\pi$
$163$	5.63379			0.441272			0.220636	+	0.975356i	$0.429187\pi$
$164$	4.31389	+	7.47188i	0.336859	+	0.583456i
$165$	−0.212113	+	0.146362i	−0.0165130	+	0.0113942i
$166$	−6.96961	+	12.0717i	−0.540947	+	0.936948i
$167$	−6.05232	+	10.4829i	−0.468342	+	0.811193i	−0.999345	−	0.0361770i	$-0.988482\pi$
$167$	−6.05232	+	10.4829i	−0.468342	+	0.811193i	0.531003	+	0.847370i	$0.321815\pi$
$168$	1.33189	+	0.632251i	0.102758	+	0.0487792i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	0.0580138			0.00444945
$171$	1.97099	−	5.19211i	0.150726	−	0.397051i
$172$	−2.55639			−0.194923
$173$	−10.8399	−	18.7753i	−0.824142	−	1.42746i	−0.902573	−	0.430537i	$-0.858324\pi$
$173$	−10.8399	−	18.7753i	−0.824142	−	1.42746i	0.0784304	−	0.996920i	$-0.475009\pi$
$174$	−0.909288	−	11.2859i	−0.0689330	−	0.855580i
$175$	−0.425606	+	0.737171i	−0.0321728	+	0.0557249i
$176$	0.0743941	−	0.128854i	0.00560767	−	0.00971276i
$177$	0.883218	+	10.9623i	0.0663867	+	0.823976i
$178$	2.94492	+	5.10076i	0.220731	+	0.382318i
$179$	4.88721			0.365287			0.182644	−	0.983179i	$-0.441535\pi$
$179$	4.88721			0.365287			0.182644	+	0.983179i	$0.441535\pi$
$180$	2.96130	−	0.480295i	0.220723	−	0.0357990i
$181$	25.6412			1.90589			0.952947	−	0.303138i	$-0.0980344\pi$
$181$	25.6412			1.90589			0.952947	+	0.303138i	$0.0980344\pi$
$182$	0.425606	+	0.737171i	0.0315480	+	0.0546428i
$183$	−3.44868	−	1.63709i	−0.254934	−	0.121017i
$184$	−2.78651	+	4.82637i	−0.205424	+	0.355805i
$185$	0.867592	−	1.50271i	0.0637866	−	0.110482i
$186$	−4.54401	+	3.13544i	−0.333183	+	0.229902i
$187$	−0.00431588	−	0.00747533i	−0.000315609	−	0.000546650i
$188$	13.1100			0.956147
$189$	3.19135	−	3.06242i	0.232137	−	0.222758i
$190$	−1.85121			−0.134301
$191$	−3.90923	−	6.77098i	−0.282862	−	0.489931i	0.689227	−	0.724546i	$-0.257950\pi$
$191$	−3.90923	−	6.77098i	−0.282862	−	0.489931i	−0.972088	+	0.234615i	$0.924617\pi$
$192$	−1.42561	+	0.983691i	−0.102884	+	0.0709918i
$193$	−5.60709	+	9.71177i	−0.403607	+	0.699068i	−0.994158	−	0.107932i	$-0.965577\pi$
$193$	−5.60709	+	9.71177i	−0.403607	+	0.699068i	0.590551	+	0.807000i	$0.298910\pi$
$194$	1.31551	−	2.27854i	0.0944484	−	0.163589i
$195$	1.56470	+	0.742765i	0.112051	+	0.0531905i
$196$	3.13772	+	5.43469i	0.224123	+	0.388192i
$197$	24.8092			1.76758			0.883792	−	0.467881i	$-0.154982\pi$
$197$	24.8092			1.76758			0.883792	+	0.467881i	$0.154982\pi$
$198$	−0.282192	−	0.345846i	−0.0200545	−	0.0245782i
$199$	5.78720			0.410244			0.205122	−	0.978736i	$-0.434241\pi$
$199$	5.78720			0.410244			0.205122	+	0.978736i	$0.434241\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	0.760259	+	9.43615i	0.0536245	+	0.665575i
$202$	−6.41592	+	11.1127i	−0.451422	+	0.781886i
$203$	−2.78219	+	4.81890i	−0.195272	+	0.338220i
$204$	0.00806963	+	0.100158i	0.000564987	+	0.00701248i
$205$	−4.31389	−	7.47188i	−0.301295	−	0.521859i
$206$	10.8318			0.754690
$207$	10.5698	+	12.9540i	0.734650	+	0.900366i
$208$	−1.00000			−0.0693375
$209$	0.137719	+	0.238537i	0.00952624	+	0.0164999i
$210$	−1.33189	−	0.632251i	−0.0919095	−	0.0436294i
$211$	−1.23149	+	2.13301i	−0.0847795	+	0.146842i	−0.905297	−	0.424779i	$-0.860352\pi$
$211$	−1.23149	+	2.13301i	−0.0847795	+	0.146842i	0.820518	+	0.571621i	$0.193685\pi$
$212$	5.92261	−	10.2583i	0.406766	−	0.704540i
$213$	−15.4182	+	10.6388i	−1.05644	+	0.728960i
$214$	−1.13910	−	1.97298i	−0.0778672	−	0.134870i
$215$	2.55639			0.174345
$216$	1.24112	+	5.04575i	0.0844475	+	0.343320i
$217$	2.71317			0.184182
$218$	2.28489	+	3.95754i	0.154752	+	0.268038i
$219$	8.75720	−	6.04261i	0.591757	−	0.408322i
$220$	−0.0743941	+	0.128854i	−0.00501565	+	0.00868736i
$221$	−0.0290069	+	0.0502414i	−0.00195122	+	0.00337960i
$222$	2.71505	+	1.28883i	0.182222	+	0.0865009i
$223$	7.07433	+	12.2531i	0.473732	+	0.820528i	0.999548	−	0.0300703i	$-0.00957311\pi$
$223$	7.07433	+	12.2531i	0.473732	+	0.820528i	−0.525816	+	0.850599i	$0.676240\pi$
$224$	0.851212			0.0568740
$225$	−2.96130	+	0.480295i	−0.197420	+	0.0320196i
$226$	−12.4596			−0.828802
$227$	6.81089	+	11.7968i	0.452055	+	0.782982i	0.998514	−	0.0545040i	$-0.0173577\pi$
$227$	6.81089	+	11.7968i	0.452055	+	0.782982i	−0.546459	+	0.837486i	$0.684024\pi$
$228$	−0.257501	−	3.19604i	−0.0170534	−	0.211663i
$229$	0.765570	−	1.32601i	0.0505903	−	0.0876250i	−0.839621	−	0.543172i	$-0.817223\pi$
$229$	0.765570	−	1.32601i	0.0505903	−	0.0876250i	0.890212	+	0.455547i	$0.150556\pi$
$230$	2.78651	−	4.82637i	0.183737	−	0.318242i
$231$	0.0176169	+	0.218656i	0.00115910	+	0.0143865i
$232$	−3.26851	−	5.66122i	−0.214588	−	0.371677i
$233$	−12.5509			−0.822235			−0.411118	−	0.911582i	$-0.634861\pi$
$233$	−12.5509			−0.822235			−0.411118	+	0.911582i	$0.634861\pi$
$234$	−1.06470	+	2.80471i	−0.0696019	+	0.183350i
$235$	−13.1100			−0.855204
$236$	3.17480	+	5.49891i	0.206662	+	0.357948i
$237$	20.8838	+	9.91357i	1.35655	+	0.643955i
$238$	0.0246910	−	0.0427661i	0.00160048	−	0.00277211i
$239$	−10.1748	+	17.6233i	−0.658153	+	1.13995i	0.322941	+	0.946419i	$0.395329\pi$
$239$	−10.1748	+	17.6233i	−0.658153	+	1.13995i	−0.981093	+	0.193535i	$0.938005\pi$
$240$	1.42561	−	0.983691i	0.0920225	−	0.0634970i
$241$	−5.51638	−	9.55465i	−0.355341	−	0.615469i	0.631835	−	0.775103i	$-0.282302\pi$
$241$	−5.51638	−	9.55465i	−0.355341	−	0.615469i	−0.987176	+	0.159634i	$0.948969\pi$
$242$	−10.9779			−0.705684
$243$	15.4733	+	1.89125i	0.992613	+	0.121324i
$244$	−2.20404			−0.141099
$245$	−3.13772	−	5.43469i	−0.200462	−	0.347210i
$246$	12.2998	−	8.48708i	0.784208	−	0.541116i
$247$	0.925606	−	1.60320i	0.0588949	−	0.102009i
$248$	−1.59371	+	2.76039i	−0.101201	+	0.175285i
$249$	21.8108	+	10.3536i	1.38220	+	0.656131i
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	2.60578			0.164475			0.0822375	−	0.996613i	$-0.473793\pi$
$251$	2.60578			0.164475			0.0822375	+	0.996613i	$0.473793\pi$
$252$	0.906289	−	2.38740i	0.0570908	−	0.150392i
$253$	−0.829199			−0.0521313
$254$	3.11840	+	5.40123i	0.195666	+	0.338903i
$255$	−0.00806963	−	0.100158i	−0.000505340	−	0.00627216i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.187422	−	0.324625i	0.0116911	−	0.0202496i	−0.860121	−	0.510091i	$-0.829612\pi$
$257$	0.187422	−	0.324625i	0.0116911	−	0.0202496i	0.871812	+	0.489841i	$0.162945\pi$
$258$	0.355590	+	4.41350i	0.0221381	+	0.274773i
$259$	−0.738505	−	1.27913i	−0.0458884	−	0.0794811i
$260$	1.00000			0.0620174
$261$	−19.3581	+	3.13969i	−1.19824	+	0.194342i
$262$	6.29758			0.389066
$263$	−2.09509	−	3.62880i	−0.129189	−	0.223762i	0.794174	−	0.607691i	$-0.207904\pi$
$263$	−2.09509	−	3.62880i	−0.129189	−	0.223762i	−0.923363	+	0.383929i	$0.874571\pi$
$264$	−0.232810	−	0.110515i	−0.0143284	−	0.00680171i
$265$	−5.92261	+	10.2583i	−0.363823	+	0.630160i
$266$	−0.787887	+	1.36466i	−0.0483084	+	0.0836727i
$267$	8.39660	−	5.79379i	0.513864	−	0.354574i
$268$	2.73281	+	4.73337i	0.166933	+	0.289136i
$269$	18.9032			1.15255			0.576275	−	0.817256i	$-0.304506\pi$
$269$	18.9032			1.15255			0.576275	+	0.817256i	$0.304506\pi$
$270$	−1.24112	−	5.04575i	−0.0755322	−	0.307075i
$271$	13.0165			0.790696			0.395348	−	0.918531i	$-0.370624\pi$
$271$	13.0165			0.790696			0.395348	+	0.918531i	$0.370624\pi$
$272$	0.0290069	+	0.0502414i	0.00175880	+	0.00304633i
$273$	1.21349	−	0.837329i	0.0734439	−	0.0506775i
$274$	−6.05070	+	10.4801i	−0.365536	+	0.633127i
$275$	0.0743941	−	0.128854i	0.00448613	−	0.00777021i
$276$	8.72012	+	4.13944i	0.524890	+	0.249165i
$277$	−3.69435	−	6.39881i	−0.221972	−	0.384467i	0.733435	−	0.679760i	$-0.237916\pi$
$277$	−3.69435	−	6.39881i	−0.221972	−	0.384467i	−0.955407	+	0.295293i	$0.904583\pi$
$278$	2.83783			0.170202
$279$	6.04526	+	7.40890i	0.361920	+	0.443559i
$280$	−0.851212			−0.0508696
$281$	−11.5190	−	19.9515i	−0.687167	−	1.19021i	−0.972751	−	0.231854i	$-0.925521\pi$
$281$	−11.5190	−	19.9515i	−0.687167	−	1.19021i	0.285584	−	0.958354i	$-0.407812\pi$
$282$	−1.82358	−	22.6339i	−0.108593	−	1.34783i
$283$	6.89522	−	11.9429i	0.409878	−	0.709930i	−0.584997	−	0.811035i	$-0.698905\pi$
$283$	6.89522	−	11.9429i	0.409878	−	0.709930i	0.994876	+	0.101105i	$0.0322378\pi$
$284$	−5.40761	+	9.36625i	−0.320882	+	0.555785i
$285$	0.257501	+	3.19604i	0.0152530	+	0.189317i
$286$	−0.0743941	−	0.128854i	−0.00439902	−	0.00761932i
$287$	−7.34408			−0.433507
$288$	1.89660	+	2.32442i	0.111758	+	0.136968i
$289$	−16.9966			−0.999802
$290$	3.26851	+	5.66122i	0.191933	+	0.332438i
$291$	−4.11678	−	1.95424i	−0.241330	−	0.114559i
$292$	3.07139	−	5.31981i	0.179740	−	0.311318i
$293$	−5.01638	+	8.68863i	−0.293060	+	0.507595i	−0.974532	−	0.224250i	$-0.928007\pi$
$293$	−5.01638	+	8.68863i	−0.293060	+	0.507595i	0.681472	+	0.731844i	$0.261340\pi$
$294$	8.94630	−	6.17309i	0.521759	−	0.360022i
$295$	−3.17480	−	5.49891i	−0.184844	−	0.320159i
$296$	1.73518			0.100856
$297$	−0.557835	+	0.535298i	−0.0323689	+	0.0310611i
$298$	3.83183			0.221972
$299$	2.78651	+	4.82637i	0.161148	+	0.279116i
$300$	−1.42561	+	0.983691i	−0.0823074	+	0.0567934i
$301$	1.08802	−	1.88450i	0.0627122	−	0.108621i
$302$	4.71049	−	8.15881i	0.271058	−	0.469487i
$303$	20.0780	+	9.53104i	1.15345	+	0.547544i
$304$	−0.925606	−	1.60320i	−0.0530871	−	0.0919496i
$305$	2.20404			0.126203
$306$	0.171796	−	0.0278637i	0.00982095	−	0.00159286i
$307$	1.79307			0.102336			0.0511680	−	0.998690i	$-0.483706\pi$
$307$	1.79307			0.102336			0.0511680	+	0.998690i	$0.483706\pi$
$308$	0.0633251	+	0.109682i	0.00360829	+	0.00624973i
$309$	−1.50669	−	18.7007i	−0.0857126	−	1.06384i
$310$	1.59371	−	2.76039i	0.0905167	−	0.156780i
$311$	5.47900	−	9.48991i	0.310686	−	0.538123i	−0.667825	−	0.744318i	$-0.732775\pi$
$311$	5.47900	−	9.48991i	0.310686	−	0.538123i	0.978511	+	0.206195i	$0.0661080\pi$
$312$	0.139098	+	1.72646i	0.00787490	+	0.0977413i
$313$	3.28782	+	5.69468i	0.185839	+	0.321882i	0.943859	−	0.330349i	$-0.107166\pi$
$313$	3.28782	+	5.69468i	0.185839	+	0.321882i	−0.758020	+	0.652231i	$0.773833\pi$
$314$	10.6830			0.602879
$315$	−0.906289	+	2.38740i	−0.0510636	+	0.134515i
$316$	13.3468			0.750818
$317$	6.69942	+	11.6037i	0.376277	+	0.651731i	0.990517	−	0.137388i	$-0.0438707\pi$
$317$	6.69942	+	11.6037i	0.376277	+	0.651731i	−0.614240	+	0.789119i	$0.710537\pi$
$318$	−18.5343	−	8.79821i	−1.03935	−	0.493379i
$319$	0.486315	−	0.842323i	0.0272284	−	0.0471610i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	−3.24781	+	2.24104i	−0.181275	+	0.125083i
$322$	−2.37191	−	4.10827i	−0.132181	−	0.228945i
$323$	−0.107396			−0.00597566
$324$	8.53863	−	2.84460i	0.474369	−	0.158033i
$325$	−1.00000			−0.0554700
$326$	−2.81689	−	4.87900i	−0.156013	−	0.270223i
$327$	6.51470	−	4.49525i	0.360264	−	0.248588i
$328$	4.31389	−	7.47188i	0.238195	−	0.412566i
$329$	−5.57971	+	9.66433i	−0.307619	+	0.532812i
$330$	0.232810	+	0.110515i	0.0128157	+	0.00608364i
$331$	−2.58564	−	4.47846i	−0.142120	−	0.246159i	0.786175	−	0.618004i	$-0.212058\pi$
$331$	−2.58564	−	4.47846i	−0.142120	−	0.246159i	−0.928295	+	0.371845i	$0.878725\pi$
$332$	13.9392			0.765015
$333$	1.84746	−	4.86669i	0.101240	−	0.266693i
$334$	12.1046			0.662336
$335$	−2.73281	−	4.73337i	−0.149309	−	0.258611i
$336$	−0.118402	−	1.46958i	−0.00645937	−	0.0801722i
$337$	10.0644	−	17.4321i	0.548243	−	0.949584i	−0.450152	−	0.892952i	$-0.648630\pi$
$337$	10.0644	−	17.4321i	0.548243	−	0.949584i	0.998395	−	0.0566326i	$-0.0180364\pi$
$338$	−0.500000	+	0.866025i	−0.0271964	+	0.0471056i
$339$	1.73311	+	21.5110i	0.0941298	+	1.16832i
$340$	−0.0290069	−	0.0502414i	−0.00157312	−	0.00272472i
$341$	−0.474251			−0.0256821
$342$	−5.48200	+	0.889127i	−0.296433	+	0.0480785i
$343$	−11.3002			−0.610154
$344$	1.27820	+	2.21390i	0.0689158	+	0.119366i
$345$	−8.72012	−	4.13944i	−0.469476	−	0.222860i
$346$	−10.8399	+	18.7753i	−0.582757	+	1.00936i
$347$	3.71181	−	6.42904i	0.199260	−	0.345129i	−0.749028	−	0.662538i	$-0.769479\pi$
$347$	3.71181	−	6.42904i	0.199260	−	0.345129i	0.948289	+	0.317409i	$0.102813\pi$
$348$	−9.31921	+	6.43040i	−0.499562	+	0.344706i
$349$	16.0259	+	27.7578i	0.857849	+	1.48584i	0.873976	+	0.485968i	$0.161533\pi$
$349$	16.0259	+	27.7578i	0.857849	+	1.48584i	−0.0161272	+	0.999870i	$0.505134\pi$
$350$	0.851212			0.0454992
$351$	4.99031	+	1.44803i	0.266363	+	0.0772904i
$352$	−0.148788			−0.00793044
$353$	−4.65704	−	8.06622i	−0.247869	−	0.429322i	0.715065	−	0.699058i	$-0.246397\pi$
$353$	−4.65704	−	8.06622i	−0.247869	−	0.429322i	−0.962934	+	0.269736i	$0.913064\pi$
$354$	9.05202	−	6.24604i	0.481109	−	0.331973i
$355$	5.40761	−	9.36625i	0.287006	−	0.497109i
$356$	2.94492	−	5.10076i	0.156081	−	0.270340i
$357$	−0.0772683	−	0.0366793i	−0.00408947	−	0.00194127i
$358$	−2.44361	−	4.23245i	−0.129149	−	0.223692i
$359$	−5.03264			−0.265612			−0.132806	−	0.991142i	$-0.542399\pi$
$359$	−5.03264			−0.265612			−0.132806	+	0.991142i	$0.542399\pi$
$360$	−1.89660	−	2.32442i	−0.0999595	−	0.122508i
$361$	−15.5730			−0.819632
$362$	−12.8206	−	22.2059i	−0.673835	−	1.16712i
$363$	1.52700	+	18.9528i	0.0801469	+	0.994764i
$364$	0.425606	−	0.737171i	0.0223078	−	0.0386383i
$365$	−3.07139	+	5.31981i	−0.160764	+	0.278452i
$366$	0.306579	+	3.80519i	0.0160251	+	0.198900i
$367$	4.49331	+	7.78264i	0.234549	+	0.406251i	0.959141	−	0.282927i	$-0.0913054\pi$
$367$	4.49331	+	7.78264i	0.234549	+	0.406251i	−0.724593	+	0.689177i	$0.757972\pi$
$368$	5.57301			0.290513
$369$	−16.3635	−	20.0546i	−0.851847	−	1.04400i
$370$	−1.73518			−0.0902079
$371$	5.04139	+	8.73195i	0.261736	+	0.453340i
$372$	4.98737	+	2.36751i	0.258583	+	0.122750i
$373$	−1.70518	+	2.95346i	−0.0882910	+	0.152924i	−0.906789	−	0.421585i	$-0.861474\pi$
$373$	−1.70518	+	2.95346i	−0.0882910	+	0.152924i	0.818498	+	0.574510i	$0.194807\pi$
$374$	−0.00431588	+	0.00747533i	−0.000223169	+	0.000386540i
$375$	1.42561	−	0.983691i	0.0736180	−	0.0507976i
$376$	−6.55501	−	11.3536i	−0.338049	−	0.585518i
$377$	−6.53701			−0.336673
$378$	−4.24781	−	1.23258i	−0.218484	−	0.0633973i
$379$	30.3956			1.56132			0.780659	−	0.624958i	$-0.214884\pi$
$379$	30.3956			1.56132			0.780659	+	0.624958i	$0.214884\pi$
$380$	0.925606	+	1.60320i	0.0474826	+	0.0822422i
$381$	8.89123	−	6.13509i	0.455511	−	0.314310i
$382$	−3.90923	+	6.77098i	−0.200013	+	0.346433i
$383$	−5.23944	+	9.07497i	−0.267723	+	0.463709i	−0.968273	−	0.249893i	$-0.919604\pi$
$383$	−5.23944	+	9.07497i	−0.267723	+	0.463709i	0.700551	+	0.713603i	$0.252938\pi$
$384$	1.56470	+	0.742765i	0.0798485	+	0.0379041i
$385$	−0.0633251	−	0.109682i	−0.00322735	−	0.00558993i
$386$	11.2142			0.570787
$387$	7.57026	−	1.22782i	0.384818	−	0.0624137i
$388$	−2.63103			−0.133570
$389$	6.42392	+	11.1266i	0.325706	+	0.564139i	0.981655	−	0.190666i	$-0.0610648\pi$
$389$	6.42392	+	11.1266i	0.325706	+	0.564139i	−0.655949	+	0.754805i	$0.727731\pi$
$390$	−0.139098	−	1.72646i	−0.00704352	−	0.0874225i
$391$	0.161656	−	0.279996i	0.00817529	−	0.0141600i
$392$	3.13772	−	5.43469i	0.158479	−	0.274493i
$393$	−0.875983	−	10.8725i	−0.0441875	−	0.548445i
$394$	−12.4046	−	21.4854i	−0.624935	−	1.08242i
$395$	−13.3468			−0.671552
$396$	−0.158415	+	0.417308i	−0.00796068	+	0.0209705i
$397$	6.59515			0.331001			0.165501	−	0.986210i	$-0.447076\pi$
$397$	6.59515			0.331001			0.165501	+	0.986210i	$0.447076\pi$
$398$	−2.89360	−	5.01186i	−0.145043	−	0.251222i
$399$	2.46562	+	1.17043i	0.123435	+	0.0585948i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	7.98494	−	13.8303i	0.398749	−	0.690653i	−0.594823	−	0.803857i	$-0.702778\pi$
$401$	7.98494	−	13.8303i	0.398749	−	0.690653i	0.993572	+	0.113204i	$0.0361112\pi$
$402$	7.79182	−	5.37648i	0.388621	−	0.268154i
$403$	1.59371	+	2.76039i	0.0793884	+	0.137505i
$404$	12.8318			0.638408
$405$	−8.53863	+	2.84460i	−0.424288	+	0.141349i
$406$	5.56438			0.276156
$407$	0.129087	+	0.223586i	0.00639863	+	0.0110828i
$408$	0.0827048	−	0.0570676i	0.00409450	−	0.00282527i
$409$	0.484999	−	0.840043i	0.0239816	−	0.0415374i	−0.853786	−	0.520625i	$-0.825699\pi$
$409$	0.484999	−	0.840043i	0.0239816	−	0.0415374i	0.877767	+	0.479087i	$0.159032\pi$
$410$	−4.31389	+	7.47188i	−0.213048	+	0.369010i
$411$	18.9351	+	8.98850i	0.934000	+	0.443370i
$412$	−5.41592	−	9.38064i	−0.266823	−	0.462151i
$413$	−5.40485			−0.265955
$414$	5.93361	−	15.6307i	0.291621	−	0.768207i
$415$	−13.9392			−0.684250
$416$	0.500000	+	0.866025i	0.0245145	+	0.0424604i
$417$	−0.394738	−	4.89939i	−0.0193304	−	0.239924i
$418$	0.137719	−	0.238537i	0.00673607	−	0.0116672i
$419$	−11.7491	+	20.3501i	−0.573982	+	0.994167i	0.422169	+	0.906517i	$0.361269\pi$
$419$	−11.7491	+	20.3501i	−0.573982	+	0.994167i	−0.996151	+	0.0876496i	$0.972064\pi$
$420$	0.118402	+	1.46958i	0.00577744	+	0.0717082i
$421$	−0.422669	−	0.732084i	−0.0205996	−	0.0356796i	0.855542	−	0.517734i	$-0.173224\pi$
$421$	−0.422669	−	0.732084i	−0.0205996	−	0.0356796i	−0.876141	+	0.482054i	$0.839891\pi$
$422$	2.46299			0.119896
$423$	−38.8228	+	6.29668i	−1.88763	+	0.306155i
$424$	−11.8452			−0.575254
$425$	0.0290069	+	0.0502414i	0.00140704	+	0.00243707i
$426$	16.9226	+	8.03316i	0.819903	+	0.389208i
$427$	0.938054	−	1.62476i	0.0453956	−	0.0786275i
$428$	−1.13910	+	1.97298i	−0.0550604	+	0.0953674i
$429$	−0.212113	+	0.146362i	−0.0102409	+	0.00706641i
$430$	−1.27820	−	2.21390i	−0.0616401	−	0.106764i
$431$	−34.8834			−1.68027			−0.840136	−	0.542375i	$-0.817525\pi$
$431$	−34.8834			−1.68027			−0.840136	+	0.542375i	$0.817525\pi$
$432$	3.74919	−	3.59772i	0.180383	−	0.173095i
$433$	23.7409			1.14092			0.570458	−	0.821327i	$-0.306766\pi$
$433$	23.7409			1.14092			0.570458	+	0.821327i	$0.306766\pi$
$434$	−1.35659	−	2.34968i	−0.0651182	−	0.112788i
$435$	9.31921	−	6.43040i	0.446822	−	0.308314i
$436$	2.28489	−	3.95754i	0.109426	−	0.189532i
$437$	−5.15842	+	8.93464i	−0.246760	+	0.427402i
$438$	−9.61165	−	4.56265i	−0.459262	−	0.218012i
$439$	−19.4279	−	33.6500i	−0.927241	−	1.60603i	−0.787917	−	0.615782i	$-0.788840\pi$
$439$	−19.4279	−	33.6500i	−0.927241	−	1.60603i	−0.139324	−	0.990247i	$-0.544493\pi$
$440$	0.148788			0.00709320
$441$	−11.9020	−	14.5867i	−0.566761	−	0.694606i
$442$	0.0580138			0.00275943
$443$	−8.67180	−	15.0200i	−0.412009	−	0.713621i	0.583100	−	0.812400i	$-0.301840\pi$
$443$	−8.67180	−	15.0200i	−0.412009	−	0.713621i	−0.995109	+	0.0987791i	$0.968506\pi$
$444$	−0.241361	−	2.99572i	−0.0114545	−	0.142171i
$445$	−2.94492	+	5.10076i	−0.139603	+	0.241799i
$446$	7.07433	−	12.2531i	0.334979	−	0.580201i
$447$	−0.533002	−	6.61549i	−0.0252101	−	0.312902i
$448$	−0.425606	−	0.737171i	−0.0201080	−	0.0348281i
$449$	−4.51452			−0.213053			−0.106527	−	0.994310i	$-0.533973\pi$
$449$	−4.51452			−0.213053			−0.106527	+	0.994310i	$0.533973\pi$
$450$	1.89660	+	2.32442i	0.0894065	+	0.109574i
$451$	1.28371			0.0604477
$452$	6.22981	+	10.7903i	0.293026	+	0.507535i
$453$	−14.7411	−	6.99758i	−0.692595	−	0.328775i
$454$	6.81089	−	11.7968i	0.319651	−	0.553652i
$455$	−0.425606	+	0.737171i	−0.0199527	+	0.0345591i
$456$	−2.63910	+	1.82102i	−0.123587	+	0.0852771i
$457$	12.2174	+	21.1612i	0.571507	+	0.989879i	0.996412	+	0.0846410i	$0.0269743\pi$
$457$	12.2174	+	21.1612i	0.571507	+	0.989879i	−0.424904	+	0.905238i	$0.639692\pi$
$458$	−1.53114			−0.0715455
$459$	−0.0720021	−	0.292723i	−0.00336077	−	0.0136632i
$460$	−5.57301			−0.259843
$461$	7.34446	+	12.7210i	0.342066	+	0.592475i	0.984816	−	0.173601i	$-0.0555402\pi$
$461$	7.34446	+	12.7210i	0.342066	+	0.592475i	−0.642751	+	0.766075i	$0.722207\pi$
$462$	0.180553	−	0.124585i	0.00840010	−	0.00579621i
$463$	−1.99400	+	3.45371i	−0.0926691	+	0.160508i	−0.908633	−	0.417595i	$-0.862873\pi$
$463$	−1.99400	+	3.45371i	−0.0926691	+	0.160508i	0.815964	+	0.578102i	$0.196207\pi$
$464$	−3.26851	+	5.66122i	−0.151737	+	0.262816i
$465$	−4.98737	−	2.36751i	−0.231284	−	0.109791i
$466$	6.27544	+	10.8694i	0.290704	+	0.503514i
$467$	29.0599			1.34473			0.672365	−	0.740219i	$-0.265278\pi$
$467$	29.0599			1.34473			0.672365	+	0.740219i	$0.265278\pi$
$468$	2.96130	−	0.480295i	0.136886	−	0.0222016i
$469$	−4.65240			−0.214828
$470$	6.55501	+	11.3536i	0.302360	+	0.523703i
$471$	−1.48599	−	18.4438i	−0.0684710	−	0.849846i
$472$	3.17480	−	5.49891i	0.146132	−	0.253108i
$473$	−0.190181	+	0.329403i	−0.00874451	+	0.0151459i
$474$	−1.85652	−	23.0427i	−0.0852729	−	1.05839i
$475$	−0.925606	−	1.60320i	−0.0424697	−	0.0735597i
$476$	−0.0493820			−0.00226342
$477$	−12.6116	+	33.2224i	−0.577448	+	1.52115i
$478$	20.3496			0.930769
$479$	20.6816	+	35.8216i	0.944967	+	1.63673i	0.755818	+	0.654781i	$0.227239\pi$
$479$	20.6816	+	35.8216i	0.944967	+	1.63673i	0.189148	+	0.981949i	$0.439427\pi$
$480$	−1.56470	−	0.742765i	−0.0714187	−	0.0339024i
$481$	0.867592	−	1.50271i	0.0395588	−	0.0685178i
$482$	−5.51638	+	9.55465i	−0.251264	+	0.435202i
$483$	−6.76281	+	4.66645i	−0.307719	+	0.212331i
$484$	5.48893	+	9.50711i	0.249497	+	0.432141i
$485$	2.63103			0.119469
$486$	−6.09878	−	14.3459i	−0.276646	−	0.650743i
$487$	−42.6109			−1.93088			−0.965442	−	0.260619i	$-0.916073\pi$
$487$	−42.6109			−1.93088			−0.965442	+	0.260619i	$0.916073\pi$
$488$	1.10202	+	1.90876i	0.0498862	+	0.0864054i
$489$	−8.03156	+	5.54191i	−0.363200	+	0.250614i
$490$	−3.13772	+	5.43469i	−0.141748	+	0.245514i
$491$	−6.02732	+	10.4396i	−0.272009	+	0.471134i	−0.969376	−	0.245580i	$-0.921021\pi$
$491$	−6.02732	+	10.4396i	−0.272009	+	0.471134i	0.697367	+	0.716714i	$0.254355\pi$
$492$	−13.4999	−	6.40842i	−0.608624	−	0.288914i
$493$	0.189618	+	0.328429i	0.00853999	+	0.0147917i
$494$	−1.85121			−0.0832900
$495$	0.158415	−	0.417308i	0.00712025	−	0.0187566i
$496$	3.18742			0.143119
$497$	−4.60302	−	7.97266i	−0.206474	−	0.357623i
$498$	−1.93892	−	24.0655i	−0.0868853	−	1.07840i
$499$	−16.7641	+	29.0362i	−0.750463	+	1.29984i	0.197136	+	0.980376i	$0.436836\pi$
$499$	−16.7641	+	29.0362i	−0.750463	+	1.29984i	−0.947599	+	0.319463i	$0.896497\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	−1.68374	−	20.8981i	−0.0752238	−	0.933660i
$502$	−1.30289	−	2.25667i	−0.0581507	−	0.100720i
$503$	2.33310			0.104028			0.0520138	−	0.998646i	$-0.483436\pi$
$503$	2.33310			0.104028			0.0520138	+	0.998646i	$0.483436\pi$
$504$	−2.52070	+	0.408832i	−0.112281	+	0.0182108i
$505$	−12.8318			−0.571009
$506$	0.414600	+	0.718107i	0.0184312	+	0.0319238i
$507$	1.56470	+	0.742765i	0.0694910	+	0.0329874i
$508$	3.11840	−	5.40123i	0.138357	−	0.239641i
$509$	−17.2327	+	29.8480i	−0.763828	+	1.32299i	0.177036	+	0.984204i	$0.443349\pi$
$509$	−17.2327	+	29.8480i	−0.763828	+	1.32299i	−0.940864	+	0.338785i	$0.889984\pi$
$510$	−0.0827048	+	0.0570676i	−0.00366223	+	0.00252700i
$511$	2.61441	+	4.52829i	0.115655	+	0.200320i
$512$	1.00000			0.0441942
$513$	2.29758	+	9.34076i	0.101440	+	0.412404i
$514$	−0.374845			−0.0165337
$515$	5.41592	+	9.38064i	0.238654	+	0.413360i
$516$	3.64441	−	2.51470i	0.160436	−	0.110704i
$517$	0.975309	−	1.68928i	0.0428940	−	0.0742947i
$518$	−0.738505	+	1.27913i	−0.0324480	+	0.0562016i
$519$	33.9225	+	16.1030i	1.48903	+	0.706844i
$520$	−0.500000	−	0.866025i	−0.0219265	−	0.0379777i
$521$	−32.9659			−1.44426			−0.722130	−	0.691757i	$-0.756837\pi$
$521$	−32.9659			−1.44426			−0.722130	+	0.691757i	$0.756837\pi$
$522$	12.3981	+	15.1947i	0.542650	+	0.665056i
$523$	5.71629			0.249956			0.124978	−	0.992160i	$-0.460114\pi$
$523$	5.71629			0.249956			0.124978	+	0.992160i	$0.460114\pi$
$524$	−3.14879	−	5.45386i	−0.137555	−	0.238253i
$525$	−0.118402	−	1.46958i	−0.00516750	−	0.0641377i
$526$	−2.09509	+	3.62880i	−0.0913503	+	0.158223i
$527$	0.0924572	−	0.160141i	0.00402750	−	0.00697584i
$528$	0.0206962	+	0.256876i	0.000900687	+	0.0111791i
$529$	−4.02925	−	6.97886i	−0.175185	−	0.303429i
$530$	11.8452			0.514523
$531$	−12.0426	−	14.7591i	−0.522606	−	0.640490i
$532$	1.57577			0.0683184
$533$	−4.31389	−	7.47188i	−0.186855	−	0.323643i
$534$	−9.21587	−	4.37477i	−0.398810	−	0.189315i
$535$	1.13910	−	1.97298i	0.0492475	−	0.0852992i
$536$	2.73281	−	4.73337i	0.118039	−	0.204450i
$537$	−6.96724	+	4.80751i	−0.300659	+	0.207459i
$538$	−9.45161	−	16.3707i	−0.407488	−	0.705790i
$539$	0.933711			0.0402178
$540$	−3.74919	+	3.59772i	−0.161339	+	0.154821i
$541$	5.80507			0.249579			0.124790	−	0.992183i	$-0.460174\pi$
$541$	5.80507			0.249579			0.124790	+	0.992183i	$0.460174\pi$
$542$	−6.50825	−	11.2726i	−0.279553	−	0.484200i
$543$	−36.5542	+	25.2230i	−1.56869	+	1.08242i
$544$	0.0290069	−	0.0502414i	0.00124366	−	0.00215408i
$545$	−2.28489	+	3.95754i	−0.0978738	+	0.169522i
$546$	−1.33189	−	0.632251i	−0.0569998	−	0.0270578i
$547$	0.902294	+	1.56282i	0.0385793	+	0.0668213i	0.884670	−	0.466217i	$-0.154383\pi$
$547$	0.902294	+	1.56282i	0.0385793	+	0.0668213i	−0.846091	+	0.533038i	$0.821050\pi$
$548$	12.1014			0.516946
$549$	6.52684	−	1.05859i	0.278559	−	0.0451795i
$550$	−0.148788			−0.00634435
$551$	−6.05070	−	10.4801i	−0.257768	−	0.446468i
$552$	−0.775197	−	9.62157i	−0.0329946	−	0.409521i
$553$	−5.68049	+	9.83890i	−0.241559	+	0.418393i
$554$	−3.69435	+	6.39881i	−0.156958	+	0.271859i
$555$	0.241361	+	2.99572i	0.0102452	+	0.127161i
$556$	−1.41892	−	2.45763i	−0.0601754	−	0.104227i
$557$	21.2616			0.900882			0.450441	−	0.892806i	$-0.351267\pi$
$557$	21.2616			0.900882			0.450441	+	0.892806i	$0.351267\pi$
$558$	3.39366	−	8.93980i	0.143665	−	0.378452i
$559$	2.55639			0.108124
$560$	0.425606	+	0.737171i	0.0179851	+	0.0311512i
$561$	0.0135062	+	0.00641138i	0.000570231	+	0.000270689i
$562$	−11.5190	+	19.9515i	−0.485900	+	0.841604i
$563$	−4.58702	+	7.94495i	−0.193320	+	0.334840i	−0.946348	−	0.323148i	$-0.895259\pi$
$563$	−4.58702	+	7.94495i	−0.193320	+	0.334840i	0.753029	+	0.657988i	$0.228592\pi$
$564$	−18.6897	+	12.8962i	−0.786980	+	0.543029i
$565$	−6.22981	−	10.7903i	−0.262090	−	0.453953i
$566$	−13.7904			−0.579655
$567$	−1.53714	+	7.50511i	−0.0645538	+	0.315185i
$568$	10.8152			0.453796
$569$	−10.9471	−	18.9609i	−0.458924	−	0.794881i	0.539980	−	0.841678i	$-0.318432\pi$
$569$	−10.9471	−	18.9609i	−0.458924	−	0.794881i	−0.998904	+	0.0467974i	$0.985098\pi$
$570$	2.63910	−	1.82102i	0.110540	−	0.0762741i
$571$	22.5036	−	38.9773i	0.941745	−	1.63115i	0.179604	−	0.983739i	$-0.442518\pi$
$571$	22.5036	−	38.9773i	0.941745	−	1.63115i	0.762141	−	0.647411i	$-0.224148\pi$
$572$	−0.0743941	+	0.128854i	−0.00311057	+	0.00538767i
$573$	12.2336	+	5.80728i	0.511064	+	0.242602i
$574$	3.67204	+	6.36016i	0.153268	+	0.265468i
$575$	5.57301			0.232411
$576$	1.06470	−	2.80471i	0.0443627	−	0.116863i
$577$	11.0993			0.462069			0.231035	−	0.972946i	$-0.425789\pi$
$577$	11.0993			0.462069			0.231035	+	0.972946i	$0.425789\pi$
$578$	8.49832	+	14.7195i	0.353483	+	0.612251i
$579$	−1.55988	−	19.3608i	−0.0648262	−	0.804607i
$580$	3.26851	−	5.66122i	0.135717	−	0.235069i
$581$	−5.93262	+	10.2756i	−0.246126	+	0.426304i
$582$	0.365972	+	4.54236i	0.0151700	+	0.188287i
$583$	−0.881214	−	1.52631i	−0.0364962	−	0.0632132i
$584$	−6.14279			−0.254190
$585$	−2.96130	+	0.480295i	−0.122435	+	0.0198577i
$586$	10.0328			0.414450
$587$	−9.08672	−	15.7387i	−0.375049	−	0.649604i	0.615285	−	0.788304i	$-0.289041\pi$
$587$	−9.08672	−	15.7387i	−0.375049	−	0.649604i	−0.990334	+	0.138701i	$0.955707\pi$
$588$	−9.81921	−	4.66118i	−0.404937	−	0.192224i
$589$	−2.95030	+	5.11006i	−0.121565	+	0.210557i
$590$	−3.17480	+	5.49891i	−0.130704	+	0.226386i
$591$	−35.3682	+	24.4046i	−1.45485	+	1.00387i
$592$	−0.867592	−	1.50271i	−0.0356578	−	0.0617611i
$593$	−45.0659			−1.85063			−0.925317	−	0.379195i	$-0.876201\pi$
$593$	−45.0659			−1.85063			−0.925317	+	0.379195i	$0.876201\pi$
$594$	0.742499	+	0.215451i	0.0304651	+	0.00884004i
$595$	0.0493820			0.00202447
$596$	−1.91592	−	3.31846i	−0.0784790	−	0.135930i
$597$	−8.25027	+	5.69282i	−0.337661	+	0.232991i
$598$	2.78651	−	4.82637i	0.113949	−	0.197365i
$599$	−22.9386	+	39.7309i	−0.937247	+	1.62336i	−0.166669	+	0.986013i	$0.553301\pi$
$599$	−22.9386	+	39.7309i	−0.937247	+	1.62336i	−0.770578	+	0.637346i	$0.780032\pi$
$600$	1.56470	+	0.742765i	0.0638788	+	0.0303233i
$601$	2.50669	+	4.34172i	0.102250	+	0.177102i	0.912611	−	0.408828i	$-0.134062\pi$
$601$	2.50669	+	4.34172i	0.102250	+	0.177102i	−0.810361	+	0.585930i	$0.800729\pi$
$602$	−2.17603			−0.0886885
$603$	−10.3661	−	12.7044i	−0.422140	−	0.517362i
$604$	−9.42099			−0.383334
$605$	−5.48893	−	9.50711i	−0.223157	−	0.386519i
$606$	−1.78489	−	22.1536i	−0.0725061	−	0.899928i
$607$	5.28213	−	9.14892i	0.214395	−	0.371343i	−0.738690	−	0.674045i	$-0.764555\pi$
$607$	5.28213	−	9.14892i	0.214395	−	0.371343i	0.953085	+	0.302702i	$0.0978887\pi$
$608$	−0.925606	+	1.60320i	−0.0375383	+	0.0650182i
$609$	−0.773997	−	9.60666i	−0.0313639	−	0.389282i
$610$	−1.10202	−	1.90876i	−0.0446196	−	0.0772833i
$611$	−13.1100			−0.530375
$612$	−0.110029	−	0.134848i	−0.00444765	−	0.00545092i
$613$	10.4736			0.423025			0.211513	−	0.977375i	$-0.432161\pi$
$613$	10.4736			0.423025			0.211513	+	0.977375i	$0.432161\pi$
$614$	−0.896536	−	1.55285i	−0.0361813	−	0.0626678i
$615$	13.4999	+	6.40842i	0.544370	+	0.258413i
$616$	0.0633251	−	0.109682i	0.00255144	−	0.00441923i
$617$	11.1967	−	19.3933i	0.450763	−	0.780745i	−0.547670	−	0.836694i	$-0.684485\pi$
$617$	11.1967	−	19.3933i	0.450763	−	0.780745i	0.998434	+	0.0559493i	$0.0178185\pi$
$618$	−15.4419	+	10.6552i	−0.621165	+	0.428614i
$619$	−10.6984	−	18.5302i	−0.430006	−	0.744793i	0.566867	−	0.823809i	$-0.308155\pi$
$619$	−10.6984	−	18.5302i	−0.430006	−	0.744793i	−0.996873	+	0.0790167i	$0.974822\pi$
$620$	−3.18742			−0.128010
$621$	−27.8111	−	8.06992i	−1.11602	−	0.323835i
$622$	−10.9580			−0.439376
$623$	2.50675	+	4.34182i	0.100431	+	0.173951i
$624$	1.42561	−	0.983691i	0.0570699	−	0.0393792i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	3.28782	−	5.69468i	0.131408	−	0.227605i
$627$	−0.430980	−	0.204586i	−0.0172117	−	0.00817039i
$628$	−5.34152	−	9.25179i	−0.213150	−	0.369187i
$629$	−0.100665			−0.00401376
$630$	2.52070	−	0.408832i	0.100427	−	0.0162883i
$631$	0.0358759			0.00142820			0.000714098	−	1.00000i	$-0.499773\pi$
$631$	0.0358759			0.00142820			0.000714098		1.00000i	$0.499773\pi$
$632$	−6.67342	−	11.5587i	−0.265454	−	0.459780i
$633$	−0.342597	−	4.25224i	−0.0136170	−	0.169011i
$634$	6.69942	−	11.6037i	0.266068	−	0.460844i
$635$	−3.11840	+	5.40123i	−0.123750	+	0.214341i
$636$	1.64765	+	20.4502i	0.0653336	+	0.810905i
$637$	−3.13772	−	5.43469i	−0.124321	−	0.215330i
$638$	−0.972631			−0.0385068
$639$	11.5150	−	30.3335i	0.455526	−	1.19998i
$640$	−1.00000			−0.0395285
$641$	16.3066	+	28.2438i	0.644071	+	1.11556i	0.984515	+	0.175299i	$0.0560893\pi$
$641$	16.3066	+	28.2438i	0.644071	+	1.11556i	−0.340444	+	0.940265i	$0.610577\pi$
$642$	3.56470	+	1.69217i	0.140688	+	0.0667845i
$643$	11.0464	−	19.1329i	0.435627	−	0.754529i	−0.561719	−	0.827328i	$-0.689860\pi$
$643$	11.0464	−	19.1329i	0.435627	−	0.754529i	0.997347	+	0.0727990i	$0.0231932\pi$
$644$	−2.37191	+	4.10827i	−0.0934663	+	0.161888i
$645$	−3.64441	+	2.51470i	−0.143498	+	0.0990163i
$646$	0.0536979	+	0.0930075i	0.00211272	+	0.00365933i
$647$	39.0330			1.53455			0.767273	−	0.641321i	$-0.221613\pi$
$647$	39.0330			1.53455			0.767273	+	0.641321i	$0.221613\pi$
$648$	−6.73281	−	5.97238i	−0.264490	−	0.234617i
$649$	0.944744			0.0370845
$650$	0.500000	+	0.866025i	0.0196116	+	0.0339683i
$651$	−3.86791	+	2.66892i	−0.151595	+	0.104603i
$652$	−2.81689	+	4.87900i	−0.110318	+	0.191076i
$653$	20.9333	−	36.2576i	0.819184	−	1.41887i	−0.0871008	−	0.996200i	$-0.527760\pi$
$653$	20.9333	−	36.2576i	0.819184	−	1.41887i	0.906284	−	0.422668i	$-0.138906\pi$
$654$	−7.15035	−	3.39427i	−0.279601	−	0.132726i
$655$	3.14879	+	5.45386i	0.123033	+	0.213100i
$656$	−8.62779			−0.336859
$657$	−6.54025	+	17.2288i	−0.255160	+	0.672158i
$658$	11.1594			0.435039
$659$	3.84521	+	6.66010i	0.149788	+	0.259441i	0.931149	−	0.364639i	$-0.118807\pi$
$659$	3.84521	+	6.66010i	0.149788	+	0.259441i	−0.781361	+	0.624079i	$0.785474\pi$
$660$	−0.0206962	−	0.256876i	−0.000805599	−	0.00999890i
$661$	16.4913	−	28.5638i	0.641437	−	1.11100i	−0.343675	−	0.939089i	$-0.611672\pi$
$661$	16.4913	−	28.5638i	0.641437	−	1.11100i	0.985112	−	0.171913i	$-0.0549949\pi$
$662$	−2.58564	+	4.47846i	−0.100494	+	0.174060i
$663$	−0.00806963	−	0.100158i	−0.000313398	−	0.00388983i
$664$	−6.96961	−	12.0717i	−0.270473	−	0.468474i
$665$	−1.57577			−0.0611059
$666$	−5.13841	+	0.833400i	−0.199109	+	0.0322936i
$667$	36.4309			1.41061
$668$	−6.05232	−	10.4829i	−0.234171	−	0.405596i
$669$	−22.1385	−	10.5091i	−0.855923	−	0.406307i
$670$	−2.73281	+	4.73337i	−0.105578	+	0.182866i
$671$	−0.163968	+	0.284001i	−0.00632991	+	0.0109637i
$672$	−1.21349	+	0.837329i	−0.0468115	+	0.0323007i
$673$	−5.45699	−	9.45178i	−0.210351	−	0.364339i	0.741473	−	0.670983i	$-0.234127\pi$
$673$	−5.45699	−	9.45178i	−0.210351	−	0.364339i	−0.951825	+	0.306643i	$0.900794\pi$
$674$	−20.1288			−0.775332
$675$	3.74919	−	3.59772i	0.144306	−	0.138476i
$676$	1.00000			0.0384615
$677$	14.0987	+	24.4197i	0.541858	+	0.938525i	0.998797	+	0.0490275i	$0.0156122\pi$
$677$	14.0987	+	24.4197i	0.541858	+	0.938525i	−0.456940	+	0.889498i	$0.651054\pi$
$678$	17.7625	−	12.2564i	0.682165	−	0.470705i
$679$	1.11978	−	1.93952i	0.0429733	−	0.0744319i
$680$	−0.0290069	+	0.0502414i	−0.00111236	+	0.00192667i
$681$	−21.3141	−	10.1178i	−0.816757	−	0.387715i
$682$	0.237125	+	0.410713i	0.00908000	+	0.0157270i
$683$	−7.03552			−0.269207			−0.134603	−	0.990900i	$-0.542976\pi$
$683$	−7.03552			−0.269207			−0.134603	+	0.990900i	$0.542976\pi$
$684$	3.51101	+	4.30299i	0.134247	+	0.164529i
$685$	−12.1014			−0.462371
$686$	5.65010	+	9.78627i	0.215722	+	0.373641i
$687$	0.212979	+	2.64345i	0.00812566	+	0.100854i
$688$	1.27820	−	2.21390i	0.0487308	−	0.0844042i
$689$	−5.92261	+	10.2583i	−0.225633	+	0.390808i
$690$	0.775197	+	9.62157i	0.0295113	+	0.366287i
$691$	−10.6764	−	18.4921i	−0.406150	−	0.703472i	0.588305	−	0.808639i	$-0.299796\pi$
$691$	−10.6764	−	18.4921i	−0.406150	−	0.703472i	−0.994455	+	0.105167i	$0.966462\pi$
$692$	21.6798			0.824142
$693$	−0.240205	−	0.294388i	−0.00912463	−	0.0111829i
$694$	−7.42362			−0.281797
$695$	1.41892	+	2.45763i	0.0538225	+	0.0932234i
$696$	10.2285	+	4.85547i	0.387710	+	0.184046i
$697$	−0.250265	+	0.433472i	−0.00947948	+	0.0164189i
$698$	16.0259	−	27.7578i	0.606591	−	1.05065i
$699$	17.8926	−	12.3462i	0.676760	−	0.466976i
$700$	−0.425606	−	0.737171i	−0.0160864	−	0.0278624i
$701$	41.2962			1.55974			0.779868	−	0.625944i	$-0.215286\pi$
$701$	41.2962			1.55974			0.779868	+	0.625944i	$0.215286\pi$
$702$	−1.24112	−	5.04575i	−0.0468431	−	0.190440i
$703$	3.21219			0.121150
$704$	0.0743941	+	0.128854i	0.00280383	+	0.00485638i
$705$	18.6897	−	12.8962i	0.703896	−	0.485700i
$706$	−4.65704	+	8.06622i	−0.175270	+	0.303576i
$707$	−5.46130	+	9.45925i	−0.205393	+	0.355752i
$708$	−9.93523	−	4.71626i	−0.373389	−	0.177248i
$709$	−9.45137	−	16.3703i	−0.354954	−	0.614798i	0.632156	−	0.774841i	$-0.282170\pi$
$709$	−9.45137	−	16.3703i	−0.354954	−	0.614798i	−0.987110	+	0.160043i	$0.948837\pi$
$710$	−10.8152			−0.405888
$711$	−39.5240	+	6.41041i	−1.48227	+	0.240409i
$712$	−5.88985			−0.220731
$713$	−8.88178	−	15.3837i	−0.332625	−	0.576124i
$714$	0.00686896	+	0.0852559i	0.000257064	+	0.00319062i
$715$	0.0743941	−	0.128854i	0.00278218	−	0.00481888i
$716$	−2.44361	+	4.23245i	−0.0913219	+	0.158174i
$717$	−2.83060	−	35.1327i	−0.105711	−	1.31205i
$718$	2.51632	+	4.35839i	0.0939081	+	0.162654i
$719$	40.6689			1.51669			0.758347	−	0.651851i	$-0.226007\pi$
$719$	40.6689			1.51669			0.758347	+	0.651851i	$0.226007\pi$
$720$	−1.06470	+	2.80471i	−0.0396792	+	0.104525i
$721$	9.22018			0.343378
$722$	7.78651	+	13.4866i	0.289784	+	0.501920i
$723$	17.2630	+	8.19475i	0.642018	+	0.304766i
$724$	−12.8206	+	22.2059i	−0.476473	+	0.825276i
$725$	−3.26851	+	5.66122i	−0.121389	+	0.210252i
$726$	15.6501	−	10.7988i	0.580830	−	0.400782i
$727$	7.10610	+	12.3081i	0.263551	+	0.456483i	0.967183	−	0.254081i	$-0.0817731\pi$
$727$	7.10610	+	12.3081i	0.263551	+	0.456483i	−0.703632	+	0.710564i	$0.748440\pi$
$728$	−0.851212			−0.0315480
$729$	−23.9192	+	12.5248i	−0.885898	+	0.463880i
$730$	6.14279			0.227355
$731$	−0.0741530	−	0.128437i	−0.00274265	−	0.00475041i
$732$	3.14210	−	2.16810i	0.116135	−	0.0801352i
$733$	−6.85684	+	11.8764i	−0.253263	+	0.438665i	−0.964422	−	0.264366i	$-0.914837\pi$
$733$	−6.85684	+	11.8764i	−0.253263	+	0.438665i	0.711159	+	0.703031i	$0.248171\pi$
$734$	4.49331	−	7.78264i	0.165851	−	0.287262i
$735$	9.81921	+	4.66118i	0.362187	+	0.171930i
$736$	−2.78651	−	4.82637i	−0.102712	−	0.177902i
$737$	0.813220			0.0299553
$738$	−9.18604	+	24.1985i	−0.338143	+	0.890757i
$739$	−28.9640			−1.06546			−0.532729	−	0.846286i	$-0.678833\pi$
$739$	−28.9640			−1.06546			−0.532729	+	0.846286i	$0.678833\pi$
$740$	0.867592	+	1.50271i	0.0318933	+	0.0552408i
$741$	0.257501	+	3.19604i	0.00945952	+	0.117409i
$742$	5.04139	−	8.73195i	0.185075	−	0.320560i
$743$	17.4459	−	30.2172i	0.640029	−	1.10856i	−0.345396	−	0.938457i	$-0.612256\pi$
$743$	17.4459	−	30.2172i	0.640029	−	1.10856i	0.985426	−	0.170106i	$-0.0544111\pi$
$744$	−0.443365	−	5.50295i	−0.0162546	−	0.201748i
$745$	1.91592	+	3.31846i	0.0701937	+	0.121579i
$746$	3.41036			0.124862
$747$	−41.2783	+	6.69494i	−1.51029	+	0.244955i
$748$	0.00863177			0.000315609
$749$	−0.969614	−	1.67942i	−0.0354289	−	0.0613647i
$750$	−1.56470	−	0.742765i	−0.0571349	−	0.0271220i
$751$	15.0354	−	26.0421i	0.548649	−	0.950288i	−0.449718	−	0.893171i	$-0.648476\pi$
$751$	15.0354	−	26.0421i	0.548649	−	0.950288i	0.998367	−	0.0571179i	$-0.0181911\pi$
$752$	−6.55501	+	11.3536i	−0.239037	+	0.414024i
$753$	−3.71481	+	2.56328i	−0.135375	+	0.0934110i
$754$	3.26851	+	5.66122i	0.119032	+	0.206169i
$755$	9.42099			0.342865
$756$	1.05646	+	4.29500i	0.0384229	+	0.156208i
$757$	−13.6037			−0.494433			−0.247217	−	0.968960i	$-0.579516\pi$
$757$	−13.6037			−0.494433			−0.247217	+	0.968960i	$0.579516\pi$
$758$	−15.1978	−	26.3234i	−0.552009	−	0.956108i
$759$	1.18211	−	0.815676i	0.0429079	−	0.0296071i
$760$	0.925606	−	1.60320i	0.0335753	−	0.0581540i
$761$	10.6087	−	18.3748i	0.384566	−	0.666087i	−0.607143	−	0.794592i	$-0.707685\pi$
$761$	10.6087	−	18.3748i	0.384566	−	0.666087i	0.991709	+	0.128505i	$0.0410179\pi$
$762$	−9.75875	−	4.63248i	−0.353522	−	0.167817i
$763$	1.94492	+	3.36871i	0.0704109	+	0.121955i
$764$	7.81845			0.282862
$765$	0.110029	+	0.134848i	0.00397810	+	0.00487545i
$766$	10.4789			0.378617
$767$	−3.17480	−	5.49891i	−0.114635	−	0.198554i
$768$	−0.139098	−	1.72646i	−0.00501928	−	0.0622981i
$769$	−4.79889	+	8.31193i	−0.173053	+	0.299736i	−0.939486	−	0.342588i	$-0.888696\pi$
$769$	−4.79889	+	8.31193i	−0.173053	+	0.299736i	0.766433	+	0.642324i	$0.222030\pi$
$770$	−0.0633251	+	0.109682i	−0.00228208	+	0.00395268i
$771$	0.0521403	+	0.647153i	0.00187779	+	0.0233066i
$772$	−5.60709	−	9.71177i	−0.201804	−	0.349534i
$773$	48.6082			1.74831			0.874157	−	0.485643i	$-0.161415\pi$
$773$	48.6082			1.74831			0.874157	+	0.485643i	$0.161415\pi$
$774$	−4.84845	−	5.94212i	−0.174274	−	0.213585i
$775$	3.18742			0.114496
$776$	1.31551	+	2.27854i	0.0472242	+	0.0817947i
$777$	2.31108	+	1.09707i	0.0829096	+	0.0393572i
$778$	6.42392	−	11.1266i	0.230309	−	0.398907i
$779$	7.98593	−	13.8320i	0.286126	−	0.495584i
$780$	−1.42561	+	0.983691i	−0.0510449	+	0.0352218i
$781$	0.804588	+	1.39359i	0.0287904	+	0.0498665i
$782$	−0.323312			−0.0115616
$783$	24.5085	−	23.5183i	0.875863	−	0.840477i
$784$	−6.27544			−0.224123
$785$	5.34152	+	9.25179i	0.190647	+	0.330210i
$786$	−8.97786	+	6.19487i	−0.320230	+	0.220964i
$787$	14.8528	−	25.7258i	0.529444	−	0.917024i	−0.469966	−	0.882684i	$-0.655734\pi$
$787$	14.8528	−	25.7258i	0.529444	−	0.917024i	0.999410	−	0.0343396i	$-0.0109328\pi$
$788$	−12.4046	+	21.4854i	−0.441896	+	0.765386i
$789$	6.55639	+	3.11232i	0.233414	+	0.110802i
$790$	6.67342	+	11.5587i	0.237430	+	0.411240i
$791$	−10.6058			−0.377098
$792$	0.440607	−	0.0714622i	0.0156563	−	0.00253930i
$793$	2.20404			0.0782679
$794$	−3.29758	−	5.71157i	−0.117027	−	0.202696i
$795$	−1.64765	−	20.4502i	−0.0584361	−	0.725295i
$796$	−2.89360	+	5.01186i	−0.102561	+	0.177641i
$797$	−15.2340	+	26.3861i	−0.539618	+	0.934645i	0.459307	+	0.888278i	$0.348098\pi$
$797$	−15.2340	+	26.3861i	−0.539618	+	0.934645i	−0.998924	+	0.0463674i	$0.985235\pi$
$798$	−0.219188	−	2.72050i	−0.00775915	−	0.0963048i
$799$	0.380281	+	0.658666i	0.0134534	+	0.0233019i
$800$	1.00000			0.0353553
$801$	−6.27094	+	16.5193i	−0.221573	+	0.583681i
$802$	−15.9699			−0.563916
$803$	−0.456987	−	0.791525i	−0.0161267	−	0.0279323i
$804$	−8.55208	−	4.05967i	−0.301609	−	0.143174i
$805$	2.37191	−	4.10827i	0.0835988	−	0.144797i
$806$	1.59371	−	2.76039i	0.0561361	−	0.0972305i
$807$	−26.9486	+	18.5949i	−0.948634	+	0.654573i
$808$	−6.41592	−	11.1127i	−0.225711	−	0.390943i
$809$	−7.09401			−0.249412			−0.124706	−	0.992194i	$-0.539799\pi$
$809$	−7.09401			−0.249412			−0.124706	+	0.992194i	$0.539799\pi$
$810$	6.73281	+	5.97238i	0.236567	+	0.209848i
$811$	7.57914			0.266140			0.133070	−	0.991107i	$-0.457517\pi$
$811$	7.57914			0.266140			0.133070	+	0.991107i	$0.457517\pi$
$812$	−2.78219	−	4.81890i	−0.0976358	−	0.169110i
$813$	−18.5564	+	12.8042i	−0.650801	+	0.449063i
$814$	0.129087	−	0.223586i	0.00452451	−	0.00783669i
$815$	2.81689	−	4.87900i	0.0986715	−	0.170904i
$816$	−0.0907744	−	0.0430906i	−0.00317774	−	0.00150847i
$817$	2.36621	+	4.09840i	0.0827833	+	0.143385i
$818$	−0.969998			−0.0339152
$819$	−0.906289	+	2.38740i	−0.0316683	+	0.0834226i
$820$	8.62779			0.301295
$821$	6.27582	+	10.8700i	0.219028	+	0.379367i	0.954511	−	0.298176i	$-0.0963782\pi$
$821$	6.27582	+	10.8700i	0.219028	+	0.379367i	−0.735483	+	0.677543i	$0.763045\pi$
$822$	−1.68328	−	20.8925i	−0.0587113	−	0.728711i
$823$	23.9253	−	41.4398i	0.833984	−	1.44450i	−0.0608717	−	0.998146i	$-0.519388\pi$
$823$	23.9253	−	41.4398i	0.833984	−	1.44450i	0.894855	−	0.446356i	$-0.147279\pi$
$824$	−5.41592	+	9.38064i	−0.188672	+	0.326790i
$825$	0.0206962	+	0.256876i	0.000720549	+	0.00894329i
$826$	2.70242	+	4.68073i	0.0940293	+	0.162864i
$827$	−24.9360			−0.867109			−0.433555	−	0.901127i	$-0.642741\pi$
$827$	−24.9360			−0.867109			−0.433555	+	0.901127i	$0.642741\pi$
$828$	−16.5034	+	2.67669i	−0.573532	+	0.0930214i
$829$	10.8598			0.377178			0.188589	−	0.982056i	$-0.439609\pi$
$829$	10.8598			0.377178			0.188589	+	0.982056i	$0.439609\pi$
$830$	6.96961	+	12.0717i	0.241919	+	0.419016i
$831$	11.5611	+	5.48808i	0.401052	+	0.190379i
$832$	0.500000	−	0.866025i	0.0173344	−	0.0300240i
$833$	−0.182031	+	0.315287i	−0.00630700	+	0.0109240i
$834$	−4.04563	+	2.79155i	−0.140089	+	0.0966634i
$835$	6.05232	+	10.4829i	0.209449	+	0.362777i
$836$	−0.275439			−0.00952624
$837$	−15.9062	−	4.61550i	−0.549800	−	0.159535i
$838$	23.4983			0.811734
$839$	9.52163	+	16.4919i	0.328723	+	0.569365i	0.982259	−	0.187531i	$-0.0600484\pi$
$839$	9.52163	+	16.4919i	0.328723	+	0.569365i	−0.653536	+	0.756896i	$0.726715\pi$
$840$	1.21349	−	0.837329i	0.0418695	−	0.0288906i
$841$	−6.86628	+	11.8927i	−0.236768	+	0.410094i
$842$	−0.422669	+	0.732084i	−0.0145661	+	0.0252293i
$843$	36.0477	+	17.1119i	1.24155	+	0.589363i
$844$	−1.23149	−	2.13301i	−0.0423897	−	0.0734212i
$845$	−1.00000			−0.0344010
$846$	24.8645	+	30.4732i	0.854858	+	1.04769i
$847$	−9.34449			−0.321080
$848$	5.92261	+	10.2583i	0.203383	+	0.352270i
$849$	1.91823	+	23.8086i	0.0658334	+	0.817109i
$850$	0.0290069	−	0.0502414i	0.000994928	−	0.00172327i
$851$	−4.83510	+	8.37465i	−0.165745	+	0.287079i
$852$	−1.50438	−	18.6720i	−0.0515392	−	0.639692i
$853$	24.9101	+	43.1456i	0.852905	+	1.47728i	0.878575	+	0.477605i	$0.158495\pi$
$853$	24.9101	+	43.1456i	0.852905	+	1.47728i	−0.0256692	+	0.999670i	$0.508172\pi$
$854$	−1.87611			−0.0641991
$855$	−3.51101	−	4.30299i	−0.120074	−	0.147159i
$856$	2.27820			0.0778672
$857$	−13.5730	−	23.5092i	−0.463645	−	0.803057i	0.535494	−	0.844539i	$-0.320125\pi$
$857$	−13.5730	−	23.5092i	−0.463645	−	0.803057i	−0.999139	+	0.0414818i	$0.986792\pi$
$858$	0.232810	+	0.110515i	0.00794799	+	0.00377291i
$859$	9.94993	−	17.2338i	0.339487	−	0.588009i	−0.644849	−	0.764310i	$-0.723080\pi$
$859$	9.94993	−	17.2338i	0.339487	−	0.588009i	0.984336	+	0.176301i	$0.0564131\pi$
$860$	−1.27820	+	2.21390i	−0.0435861	+	0.0754934i
$861$	10.4698	−	7.22430i	0.356808	−	0.246203i
$862$	17.4417	+	30.2099i	0.594066	+	1.02895i
$863$	−2.24743			−0.0765033			−0.0382517	−	0.999268i	$-0.512179\pi$
$863$	−2.24743			−0.0765033			−0.0382517	+	0.999268i	$0.512179\pi$
$864$	−4.99031	−	1.44803i	−0.169774	−	0.0492631i
$865$	−21.6798			−0.737135
$866$	−11.8705	−	20.5603i	−0.403375	−	0.698666i
$867$	24.2305	−	16.7194i	0.822911	−	0.567822i
$868$	−1.35659	+	2.34968i	−0.0460455	+	0.0797532i
$869$	0.992926	−	1.71980i	0.0336827	−	0.0583402i
$870$	−10.2285	−	4.85547i	−0.346778	−	0.164616i
$871$	−2.73281	−	4.73337i	−0.0925977	−	0.160384i
$872$	−4.56977			−0.154752
$873$	7.79127	−	1.26367i	0.263695	−	0.0427687i
$874$	10.3168			0.348972
$875$	0.425606	+	0.737171i	0.0143881	+	0.0249209i
$876$	0.854452	+	10.6053i	0.0288693	+	0.358318i
$877$	20.5013	−	35.5092i	0.692278	−	1.19906i	−0.278811	−	0.960346i	$-0.589940\pi$
$877$	20.5013	−	35.5092i	0.692278	−	1.19906i	0.971090	−	0.238715i	$-0.0767262\pi$
$878$	−19.4279	+	33.6500i	−0.655658	+	1.13563i
$879$	−1.39554	−	17.3211i	−0.0470704	−	0.584227i
$880$	−0.0743941	−	0.128854i	−0.00250783	−	0.00434368i
$881$	33.9525			1.14389			0.571944	−	0.820293i	$-0.306189\pi$
$881$	33.9525			1.14389			0.571944	+	0.820293i	$0.306189\pi$
$882$	−6.68149	+	17.6008i	−0.224977	+	0.592650i
$883$	27.8138			0.936010			0.468005	−	0.883726i	$-0.344973\pi$
$883$	27.8138			0.936010			0.468005	+	0.883726i	$0.344973\pi$
$884$	−0.0290069	−	0.0502414i	−0.000975608	−	0.00168980i
$885$	9.93523	+	4.71626i	0.333969	+	0.158535i
$886$	−8.67180	+	15.0200i	−0.291335	+	0.504607i
$887$	−23.9454	+	41.4746i	−0.804007	+	1.39258i	0.112952	+	0.993600i	$0.463969\pi$
$887$	−23.9454	+	41.4746i	−0.804007	+	1.39258i	−0.916959	+	0.398981i	$0.869364\pi$
$888$	−2.47369	+	1.70688i	−0.0830116	+	0.0572793i
$889$	2.65442	+	4.59759i	0.0890264	+	0.154198i
$890$	5.88985			0.197428
$891$	0.268685	−	1.31186i	0.00900130	−	0.0439490i
$892$	−14.1487			−0.473732
$893$	−12.1347	−	21.0180i	−0.406073	−	0.703339i
$894$	−5.46268	+	3.76934i	−0.182699	+	0.126066i
$895$	2.44361	−	4.23245i	0.0816808	−	0.141475i
$896$	−0.425606	+	0.737171i	−0.0142185	+	0.0246272i
$897$	−8.72012	−	4.13944i	−0.291156	−	0.138212i
$898$	2.25726	+	3.90969i	0.0753257	+	0.130468i
$899$	20.8362			0.694927
$900$	1.06470	−	2.80471i	0.0354901	−	0.0934904i
$901$	0.687186			0.0228935
$902$	−0.641857	−	1.11173i	−0.0213715	−	0.0370165i
$903$	0.302683	+	3.75682i	0.0100726	+	0.125019i
$904$	6.22981	−	10.7903i	0.207200	−	0.358882i
$905$	12.8206	−	22.2059i	0.426171	−	0.738149i
$906$	1.31044	+	16.2649i	0.0435366	+	0.540366i
$907$	10.7792	+	18.6701i	0.357917	+	0.619931i	0.987613	−	0.156911i	$-0.0501537\pi$
$907$	10.7792	+	18.6701i	0.357917	+	0.619931i	−0.629695	+	0.776842i	$0.716820\pi$
$908$	−13.6218			−0.452055
$909$	−37.9989	+	6.16306i	−1.26035	+	0.204416i
$910$	0.851212			0.0282174
$911$	−19.7802	−	34.2603i	−0.655347	−	1.13510i	−0.981807	−	0.189884i	$-0.939189\pi$
$911$	−19.7802	−	34.2603i	−0.655347	−	1.13510i	0.326459	−	0.945211i	$-0.394144\pi$
$912$	2.89660	+	1.37502i	0.0959160	+	0.0455313i
$913$	1.03700	−	1.79613i	0.0343196	−	0.0594432i
$914$	12.2174	−	21.1612i	0.404116	−	0.699950i
$915$	−3.14210	+	2.16810i	−0.103875	+	0.0716751i
$916$	0.765570	+	1.32601i	0.0252952	+	0.0438125i
$917$	5.36057			0.177022
$918$	−0.217505	+	0.208717i	−0.00717873	+	0.00688870i
$919$	−0.985977			−0.0325244			−0.0162622	−	0.999868i	$-0.505177\pi$
$919$	−0.985977			−0.0325244			−0.0162622	+	0.999868i	$0.505177\pi$
$920$	2.78651	+	4.82637i	0.0918684	+	0.159121i
$921$	−2.55622	+	1.76383i	−0.0842302	+	0.0581202i
$922$	7.34446	−	12.7210i	0.241877	−	0.418943i
$923$	5.40761	−	9.36625i	0.177993	−	0.308294i
$924$	−0.198170	−	0.0940715i	−0.00651932	−	0.00309472i
$925$	−0.867592	−	1.50271i	−0.0285263	−	0.0494089i
$926$	3.98800			0.131054
$927$	20.5436	+	25.1777i	0.674742	+	0.826944i
$928$	6.53701			0.214588
$929$	27.0874	+	46.9168i	0.888709	+	1.53929i	0.841403	+	0.540409i	$0.181730\pi$
$929$	27.0874	+	46.9168i	0.888709	+	1.53929i	0.0473065	+	0.998880i	$0.484936\pi$
$930$	0.443365	+	5.50295i	0.0145385	+	0.180449i
$931$	5.80858	−	10.0608i	0.190369	−	0.329728i
$932$	6.27544	−	10.8694i	0.205559	−	0.356038i
$933$	1.52424	+	18.9185i	0.0499014	+	0.619364i
$934$	−14.5299	−	25.1666i	−0.475434	−	0.823476i
$935$	−0.00863177			−0.000282289
$936$	−1.89660	−	2.32442i	−0.0619923	−	0.0759759i
$937$	8.63366			0.282049			0.141025	−	0.990006i	$-0.454960\pi$
$937$	8.63366			0.282049			0.141025	+	0.990006i	$0.454960\pi$
$938$	2.32620	+	4.02910i	0.0759531	+	0.131555i
$939$	−10.2889	−	4.88416i	−0.335767	−	0.159389i
$940$	6.55501	−	11.3536i	0.213801	−	0.370314i
$941$	1.51107	−	2.61725i	0.0492594	−	0.0853199i	−0.840344	−	0.542053i	$-0.817647\pi$
$941$	1.51107	−	2.61725i	0.0492594	−	0.0853199i	0.889604	+	0.456733i	$0.150981\pi$
$942$	−15.2298	+	10.5088i	−0.496214	+	0.342396i
$943$	24.0414	+	41.6409i	0.782896	+	1.35601i
$944$	−6.34959			−0.206662
$945$	−1.05646	−	4.29500i	−0.0343665	−	0.139716i
$946$	0.380361			0.0123666
$947$	−25.9158	−	44.8875i	−0.842150	−	1.45865i	−0.888073	−	0.459702i	$-0.847956\pi$
$947$	−25.9158	−	44.8875i	−0.842150	−	1.45865i	0.0459233	−	0.998945i	$-0.485377\pi$
$948$	−19.0273	+	13.1292i	−0.617979	+	0.426415i
$949$	−3.07139	+	5.31981i	−0.0997017	+	0.172688i
$950$	−0.925606	+	1.60320i	−0.0300306	+	0.0520146i
$951$	−20.9652	−	9.95220i	−0.679844	−	0.322722i
$952$	0.0246910	+	0.0427661i	0.000800240	+	0.00138606i
$953$	39.5024			1.27961			0.639804	−	0.768538i	$-0.279015\pi$
$953$	39.5024			1.27961			0.639804	+	0.768538i	$0.279015\pi$
$954$	35.0773	−	5.68919i	1.13567	−	0.184194i
$955$	−7.81845			−0.252999
$956$	−10.1748	−	17.6233i	−0.329076	−	0.569977i
$957$	0.135291	+	1.67920i	0.00437335	+	0.0542810i
$958$	20.6816	−	35.8216i	0.668192	−	1.15734i
$959$	−5.15043	+	8.92080i	−0.166316	+	0.288068i
$960$	0.139098	+	1.72646i	0.00448938	+	0.0557211i
$961$	10.4202	+	18.0483i	0.336134	+	0.582202i
$962$	−1.73518			−0.0559446
$963$	2.42561	−	6.38968i	0.0781641	−	0.205905i
$964$	11.0328			0.355341
$965$	5.60709	+	9.71177i	0.180499	+	0.312633i
$966$	7.42267	+	3.52354i	0.238820	+	0.113368i
$967$	−4.86597	+	8.42811i	−0.156479	+	0.271030i	−0.933597	−	0.358326i	$-0.883348\pi$
$967$	−4.86597	+	8.42811i	−0.156479	+	0.271030i	0.777118	+	0.629356i	$0.216681\pi$
$968$	5.48893	−	9.50711i	0.176421	−	0.305570i
$969$	0.153104	−	0.105644i	0.00491841	−	0.00339378i
$970$	−1.31551	−	2.27854i	−0.0422386	−	0.0731594i
$971$	−10.7765			−0.345833			−0.172916	−	0.984937i	$-0.555319\pi$
$971$	−10.7765			−0.345833			−0.172916	+	0.984937i	$0.555319\pi$
$972$	−9.37452	+	12.4546i	−0.300688	+	0.399483i
$973$	2.41559			0.0774404
$974$	21.3054	+	36.9021i	0.682670	+	1.18242i
$975$	1.42561	−	0.983691i	0.0456559	−	0.0315033i
$976$	1.10202	−	1.90876i	0.0352749	−	0.0610979i
$977$	17.9926	−	31.1640i	0.575633	−	0.997026i	−0.420340	−	0.907367i	$-0.638089\pi$
$977$	17.9926	−	31.1640i	0.575633	−	0.997026i	0.995973	−	0.0896587i	$-0.0285776\pi$
$978$	8.81521	+	4.18458i	0.281879	+	0.133808i
$979$	−0.438170	−	0.758932i	−0.0140040	−	0.0242556i
$980$	6.27544			0.200462
$981$	−4.86546	+	12.8169i	−0.155342	+	0.409212i
$982$	12.0546			0.384679
$983$	−11.6844	−	20.2380i	−0.372675	−	0.645492i	0.617301	−	0.786727i	$-0.288226\pi$
$983$	−11.6844	−	20.2380i	−0.372675	−	0.645492i	−0.989976	+	0.141235i	$0.954893\pi$
$984$	1.20011	+	14.8955i	0.0382582	+	0.474851i
$985$	12.4046	−	21.4854i	0.395244	−	0.684582i
$986$	0.189618	−	0.328429i	0.00603868	−	0.0104593i
$987$	−1.55226	−	19.2662i	−0.0494089	−	0.613251i
$988$	0.925606	+	1.60320i	0.0294474	+	0.0510045i
$989$	−14.2468			−0.453023
$990$	−0.440607	+	0.0714622i	−0.0140034	+	0.00227122i
$991$	−13.6196			−0.432642			−0.216321	−	0.976322i	$-0.569406\pi$
$991$	−13.6196			−0.432642			−0.216321	+	0.976322i	$0.569406\pi$
$992$	−1.59371	−	2.76039i	−0.0506004	−	0.0876424i
$993$	8.09153	+	3.84105i	0.256777	+	0.121892i
$994$	−4.60302	+	7.97266i	−0.145999	+	0.252877i
$995$	2.89360	−	5.01186i	0.0917333	−	0.158887i
$996$	−19.8718	+	13.7119i	−0.629664	+	0.434478i
$997$	−14.4871	−	25.0923i	−0.458810	−	0.794682i	0.540088	−	0.841608i	$-0.318391\pi$
$997$	−14.4871	−	25.0923i	−0.458810	−	0.794682i	−0.998898	+	0.0469260i	$0.985058\pi$
$998$	33.5281			1.06131
$999$	2.15357	+	8.75531i	0.0681360	+	0.277006i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.j.h.391.1	✓	8
3.2	odd	2		3510.2.j.h.1171.1		8
9.2	odd	6		3510.2.j.h.2341.1		8
9.7	even	3	inner	1170.2.j.h.781.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1170.2.j.h.391.1	✓	8	1.1	even	1	trivial
1170.2.j.h.781.1	yes	8	9.7	even	3	inner
3510.2.j.h.1171.1		8	3.2	odd	2
3510.2.j.h.2341.1		8	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.42561 + 0.983691i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.56470 + 0.742765i) q^{6} +(-0.425606 - 0.737171i) q^{7} +1.00000 q^{8} +(1.06470 - 2.80471i) q^{9} -1.00000 q^{10} +(0.0743941 + 0.128854i) q^{11} +(-0.139098 - 1.72646i) q^{12} +(0.500000 - 0.866025i) q^{13} +(-0.425606 + 0.737171i) q^{14} +(0.139098 + 1.72646i) q^{15} +(-0.500000 - 0.866025i) q^{16} -0.0580138 q^{17} +(-2.96130 + 0.480295i) q^{18} +1.85121 q^{19} +(0.500000 + 0.866025i) q^{20} +(1.33189 + 0.632251i) q^{21} +(0.0743941 - 0.128854i) q^{22} +(-2.78651 + 4.82637i) q^{23} +(-1.42561 + 0.983691i) q^{24} +(-0.500000 - 0.866025i) q^{25} -1.00000 q^{26} +(1.24112 + 5.04575i) q^{27} +0.851212 q^{28} +(-3.26851 - 5.66122i) q^{29} +(1.42561 - 0.983691i) q^{30} +(-1.59371 + 2.76039i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.232810 - 0.110515i) q^{33} +(0.0290069 + 0.0502414i) q^{34} -0.851212 q^{35} +(1.89660 + 2.32442i) q^{36} +1.73518 q^{37} +(-0.925606 - 1.60320i) q^{38} +(0.139098 + 1.72646i) q^{39} +(0.500000 - 0.866025i) q^{40} +(4.31389 - 7.47188i) q^{41} +(-0.118402 - 1.46958i) q^{42} +(1.27820 + 2.21390i) q^{43} -0.148788 q^{44} +(-1.89660 - 2.32442i) q^{45} +5.57301 q^{46} +(-6.55501 - 11.3536i) q^{47} +(1.56470 + 0.742765i) q^{48} +(3.13772 - 5.43469i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(0.0827048 - 0.0570676i) q^{51} +(0.500000 + 0.866025i) q^{52} -11.8452 q^{53} +(3.74919 - 3.59772i) q^{54} +0.148788 q^{55} +(-0.425606 - 0.737171i) q^{56} +(-2.63910 + 1.82102i) q^{57} +(-3.26851 + 5.66122i) q^{58} +(3.17480 - 5.49891i) q^{59} +(-1.56470 - 0.742765i) q^{60} +(1.10202 + 1.90876i) q^{61} +3.18742 q^{62} +(-2.52070 + 0.408832i) q^{63} +1.00000 q^{64} +(-0.500000 - 0.866025i) q^{65} +(0.0206962 + 0.256876i) q^{66} +(2.73281 - 4.73337i) q^{67} +(0.0290069 - 0.0502414i) q^{68} +(-0.775197 - 9.62157i) q^{69} +(0.425606 + 0.737171i) q^{70} +10.8152 q^{71} +(1.06470 - 2.80471i) q^{72} -6.14279 q^{73} +(-0.867592 - 1.50271i) q^{74} +(1.56470 + 0.742765i) q^{75} +(-0.925606 + 1.60320i) q^{76} +(0.0633251 - 0.109682i) q^{77} +(1.42561 - 0.983691i) q^{78} +(-6.67342 - 11.5587i) q^{79} -1.00000 q^{80} +(-6.73281 - 5.97238i) q^{81} -8.62779 q^{82} +(-6.96961 - 12.0717i) q^{83} +(-1.21349 + 0.837329i) q^{84} +(-0.0290069 + 0.0502414i) q^{85} +(1.27820 - 2.21390i) q^{86} +(10.2285 + 4.85547i) q^{87} +(0.0743941 + 0.128854i) q^{88} -5.88985 q^{89} +(-1.06470 + 2.80471i) q^{90} -0.851212 q^{91} +(-2.78651 - 4.82637i) q^{92} +(-0.443365 - 5.50295i) q^{93} +(-6.55501 + 11.3536i) q^{94} +(0.925606 - 1.60320i) q^{95} +(-0.139098 - 1.72646i) q^{96} +(1.31551 + 2.27854i) q^{97} -6.27544 q^{98} +(0.440607 - 0.0714622i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - q^{3} - 4 q^{4} + 4 q^{5} - q^{6} + 7 q^{7} + 8 q^{8} - 5 q^{9} - 8 q^{10} + 11 q^{11} + 2 q^{12} + 4 q^{13} + 7 q^{14} - 2 q^{15} - 4 q^{16} - 8 q^{17} + 4 q^{18} - 6 q^{19} + 4 q^{20}+ \cdots - 29 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - q^3 - 4 * q^4 + 4 * q^5 - q^6 + 7 * q^7 + 8 * q^8 - 5 * q^9 - 8 * q^10 + 11 * q^11 + 2 * q^12 + 4 * q^13 + 7 * q^14 - 2 * q^15 - 4 * q^16 - 8 * q^17 + 4 * q^18 - 6 * q^19 + 4 * q^20 + 10 * q^21 + 11 * q^22 - 15 * q^23 - q^24 - 4 * q^25 - 8 * q^26 - 4 * q^27 - 14 * q^28 + 4 * q^29 + q^30 - 3 * q^31 - 4 * q^32 + 11 * q^33 + 4 * q^34 + 14 * q^35 + q^36 - 22 * q^37 + 3 * q^38 - 2 * q^39 + 4 * q^40 + 11 * q^41 + 7 * q^42 + 4 * q^43 - 22 * q^44 - q^45 + 30 * q^46 - 15 * q^47 - q^48 - 3 * q^49 - 4 * q^50 + 10 * q^51 + 4 * q^52 + 16 * q^53 + 20 * q^54 + 22 * q^55 + 7 * q^56 - 18 * q^57 + 4 * q^58 + 5 * q^59 + q^60 - 2 * q^61 + 6 * q^62 - 25 * q^63 + 8 * q^64 - 4 * q^65 + 5 * q^66 + 9 * q^67 + 4 * q^68 + 45 * q^69 - 7 * q^70 + 20 * q^71 - 5 * q^72 + 20 * q^73 + 11 * q^74 - q^75 + 3 * q^76 - 38 * q^77 + q^78 - 8 * q^79 - 8 * q^80 - 41 * q^81 - 22 * q^82 - 27 * q^83 - 17 * q^84 - 4 * q^85 + 4 * q^86 + 67 * q^87 + 11 * q^88 + 14 * q^89 + 5 * q^90 + 14 * q^91 - 15 * q^92 - 21 * q^93 - 15 * q^94 - 3 * q^95 + 2 * q^96 + 7 * q^97 + 6 * q^98 - 29 * q^99

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