LMFDB - Embedded newform 585.2.i.f.196.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(196,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("585.196");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.i (of order $3$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 11 x^{14} - 4 x^{13} + 74 x^{12} - 18 x^{11} + 289 x^{10} - 4 x^{9} + 784 x^{8} + \cdots + 81 $ x^16 - x^15 + 11x^14 - 4x^13 + 74x^12 - 18x^11 + 289x^10 - 4x^9 + 784x^8 - 9x^7 + 1221x^6 + 133x^5 + 1245x^4 - 14x^3 + 391x^2 + 63x + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			196.3
Root			$-0.624867 + 1.08230i$ of defining polynomial
Character	$\chi$	$=$	585.196
Dual form			585.2.i.f.391.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.624867 + 1.08230i) q^{2} +(1.28189 + 1.16480i) q^{3} +(0.219082 + 0.379462i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.06168 + 0.659540i) q^{6} +(0.148724 - 0.257597i) q^{7} -3.04706 q^{8} +(0.286466 + 2.98629i) q^{9} +O(q^{10})$	\(q+(-0.624867 + 1.08230i) q^{2} +(1.28189 + 1.16480i) q^{3} +(0.219082 + 0.379462i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.06168 + 0.659540i) q^{6} +(0.148724 - 0.257597i) q^{7} -3.04706 q^{8} +(0.286466 + 2.98629i) q^{9} +1.24973 q^{10} +(-1.85005 + 3.20439i) q^{11} +(-0.161160 + 0.741615i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(0.185865 + 0.321928i) q^{14} +(0.367806 - 1.69255i) q^{15} +(1.46584 - 2.53891i) q^{16} -3.47312 q^{17} +(-3.41107 - 1.55599i) q^{18} -3.33464 q^{19} +(0.219082 - 0.379462i) q^{20} +(0.490698 - 0.156976i) q^{21} +(-2.31207 - 4.00463i) q^{22} +(4.29737 + 7.44327i) q^{23} +(-3.90598 - 3.54922i) q^{24} +(-0.500000 + 0.866025i) q^{25} +1.24973 q^{26} +(-3.11123 + 4.16176i) q^{27} +0.130331 q^{28} +(-2.94125 + 5.09439i) q^{29} +(1.60202 + 1.45569i) q^{30} +(3.44361 + 5.96450i) q^{31} +(-1.21515 - 2.10469i) q^{32} +(-6.10404 + 1.95271i) q^{33} +(2.17024 - 3.75896i) q^{34} -0.297448 q^{35} +(-1.07042 + 0.762946i) q^{36} +9.40767 q^{37} +(2.08371 - 3.60909i) q^{38} +(0.367806 - 1.69255i) q^{39} +(1.52353 + 2.63883i) q^{40} +(-5.14943 - 8.91907i) q^{41} +(-0.136725 + 0.629172i) q^{42} +(2.74744 - 4.75870i) q^{43} -1.62126 q^{44} +(2.44297 - 1.74123i) q^{45} -10.7411 q^{46} +(5.77951 - 10.0104i) q^{47} +(4.83638 - 1.54718i) q^{48} +(3.45576 + 5.98556i) q^{49} +(-0.624867 - 1.08230i) q^{50} +(-4.45215 - 4.04550i) q^{51} +(0.219082 - 0.379462i) q^{52} +2.01496 q^{53} +(-2.56018 - 5.96783i) q^{54} +3.70011 q^{55} +(-0.453170 + 0.784914i) q^{56} +(-4.27463 - 3.88420i) q^{57} +(-3.67578 - 6.36663i) q^{58} +(7.46570 + 12.9310i) q^{59} +(0.722837 - 0.231239i) q^{60} +(1.86466 - 3.22969i) q^{61} -8.60718 q^{62} +(0.811865 + 0.370340i) q^{63} +8.90058 q^{64} +(-0.500000 + 0.866025i) q^{65} +(1.70079 - 7.82659i) q^{66} +(-3.59788 - 6.23171i) q^{67} +(-0.760899 - 1.31792i) q^{68} +(-3.16120 + 14.5470i) q^{69} +(0.185865 - 0.321928i) q^{70} -13.2587 q^{71} +(-0.872877 - 9.09940i) q^{72} +1.78880 q^{73} +(-5.87854 + 10.1819i) q^{74} +(-1.64969 + 0.527744i) q^{75} +(-0.730561 - 1.26537i) q^{76} +(0.550294 + 0.953138i) q^{77} +(1.60202 + 1.45569i) q^{78} +(0.213468 - 0.369738i) q^{79} -2.93168 q^{80} +(-8.83588 + 1.71094i) q^{81} +12.8708 q^{82} +(2.05068 - 3.55188i) q^{83} +(0.167070 + 0.151810i) q^{84} +(1.73656 + 3.00781i) q^{85} +(3.43357 + 5.94711i) q^{86} +(-9.70431 + 3.10445i) q^{87} +(5.63722 - 9.76395i) q^{88} +5.14366 q^{89} +(0.358006 + 3.73207i) q^{90} -0.297448 q^{91} +(-1.88296 + 3.26138i) q^{92} +(-2.53316 + 11.6569i) q^{93} +(7.22285 + 12.5103i) q^{94} +(1.66732 + 2.88788i) q^{95} +(0.893876 - 4.11338i) q^{96} +(2.53649 - 4.39333i) q^{97} -8.63757 q^{98} +(-10.0992 - 4.60685i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + q^{2} - 2 q^{3} - 5 q^{4} - 8 q^{5} - 13 q^{6} + 6 q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) $ 16 * q + q^2 - 2 * q^3 - 5 * q^4 - 8 * q^5 - 13 * q^6 + 6 * q^7 - 12 * q^8 + 4 * q^9	\( 16 q + q^{2} - 2 q^{3} - 5 q^{4} - 8 q^{5} - 13 q^{6} + 6 q^{7} - 12 q^{8} + 4 q^{9} - 2 q^{10} + 9 q^{11} - 16 q^{12} - 8 q^{13} - 3 q^{14} + q^{15} + 13 q^{16} + 12 q^{17} + 23 q^{18} - 22 q^{19} - 5 q^{20} + 15 q^{21} + 4 q^{22} + 3 q^{23} - 12 q^{24} - 8 q^{25} - 2 q^{26} + 22 q^{27} - 26 q^{28} + 8 q^{29} + 8 q^{30} + 18 q^{31} + 3 q^{32} - 26 q^{33} + 9 q^{34} - 12 q^{35} + 5 q^{36} - 36 q^{37} - 8 q^{38} + q^{39} + 6 q^{40} - 17 q^{41} - 45 q^{42} + 17 q^{43} + 10 q^{44} + q^{45} + 6 q^{46} + 11 q^{47} + 35 q^{48} + 16 q^{49} + q^{50} - 16 q^{51} - 5 q^{52} + 20 q^{53} + 44 q^{54} - 18 q^{55} - q^{56} - 25 q^{57} + 10 q^{58} + 7 q^{59} + 5 q^{60} + 21 q^{61} - 58 q^{62} - 30 q^{63} - 20 q^{64} - 8 q^{65} + 68 q^{66} + 13 q^{67} - 16 q^{68} - 13 q^{69} - 3 q^{70} - 68 q^{71} + 36 q^{72} - 32 q^{73} - 4 q^{74} + q^{75} + 2 q^{76} + 18 q^{77} + 8 q^{78} + 37 q^{79} - 26 q^{80} - 32 q^{81} + 2 q^{82} + 3 q^{83} + 27 q^{84} - 6 q^{85} - 2 q^{86} - 20 q^{87} + 19 q^{88} + 28 q^{89} - 16 q^{90} - 12 q^{91} - 14 q^{92} + 19 q^{93} + 44 q^{94} + 11 q^{95} - 35 q^{96} + 17 q^{97} + 90 q^{98} - 44 q^{99}+O(q^{100}) \) 16 * q + q^2 - 2 * q^3 - 5 * q^4 - 8 * q^5 - 13 * q^6 + 6 * q^7 - 12 * q^8 + 4 * q^9 - 2 * q^10 + 9 * q^11 - 16 * q^12 - 8 * q^13 - 3 * q^14 + q^15 + 13 * q^16 + 12 * q^17 + 23 * q^18 - 22 * q^19 - 5 * q^20 + 15 * q^21 + 4 * q^22 + 3 * q^23 - 12 * q^24 - 8 * q^25 - 2 * q^26 + 22 * q^27 - 26 * q^28 + 8 * q^29 + 8 * q^30 + 18 * q^31 + 3 * q^32 - 26 * q^33 + 9 * q^34 - 12 * q^35 + 5 * q^36 - 36 * q^37 - 8 * q^38 + q^39 + 6 * q^40 - 17 * q^41 - 45 * q^42 + 17 * q^43 + 10 * q^44 + q^45 + 6 * q^46 + 11 * q^47 + 35 * q^48 + 16 * q^49 + q^50 - 16 * q^51 - 5 * q^52 + 20 * q^53 + 44 * q^54 - 18 * q^55 - q^56 - 25 * q^57 + 10 * q^58 + 7 * q^59 + 5 * q^60 + 21 * q^61 - 58 * q^62 - 30 * q^63 - 20 * q^64 - 8 * q^65 + 68 * q^66 + 13 * q^67 - 16 * q^68 - 13 * q^69 - 3 * q^70 - 68 * q^71 + 36 * q^72 - 32 * q^73 - 4 * q^74 + q^75 + 2 * q^76 + 18 * q^77 + 8 * q^78 + 37 * q^79 - 26 * q^80 - 32 * q^81 + 2 * q^82 + 3 * q^83 + 27 * q^84 - 6 * q^85 - 2 * q^86 - 20 * q^87 + 19 * q^88 + 28 * q^89 - 16 * q^90 - 12 * q^91 - 14 * q^92 + 19 * q^93 + 44 * q^94 + 11 * q^95 - 35 * q^96 + 17 * q^97 + 90 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	−0.624867	+	1.08230i	−0.441848	+	0.765303i	−0.997827	−	0.0658937i	$-0.979010\pi$
$2$	−0.624867	+	1.08230i	−0.441848	+	0.765303i	0.555979	+	0.831196i	$0.312344\pi$
$3$	1.28189	+	1.16480i	0.740097	+	0.672500i
$3$	1.28189	+	1.16480i	0.740097	+	0.672500i
$4$	0.219082	+	0.379462i	0.109541	+	0.189731i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−2.06168	+	0.659540i	−0.841676	+	0.269256i
$7$	0.148724	−	0.257597i	0.0562124	−	0.0973627i	−0.836550	−	0.547891i	$-0.815431\pi$
$7$	0.148724	−	0.257597i	0.0562124	−	0.0973627i	0.892762	+	0.450528i	$0.148764\pi$
$8$	−3.04706			−1.07730
$9$	0.286466	+	2.98629i	0.0954885	+	0.995431i
$10$	1.24973			0.395201
$11$	−1.85005	+	3.20439i	−0.557812	+	0.966159i	0.439867	+	0.898063i	$0.355026\pi$
$11$	−1.85005	+	3.20439i	−0.557812	+	0.966159i	−0.997679	+	0.0680957i	$0.978308\pi$
$12$	−0.161160	+	0.741615i	−0.0465228	+	0.214086i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i
$14$	0.185865	+	0.321928i	0.0496746	+	0.0860390i
$15$	0.367806	−	1.69255i	0.0949672	−	0.437014i
$16$	1.46584	−	2.53891i	0.366460	−	0.634728i
$17$	−3.47312			−0.842355			−0.421178	−	0.906978i	$-0.638383\pi$
$17$	−3.47312			−0.842355			−0.421178	+	0.906978i	$0.638383\pi$
$18$	−3.41107	−	1.55599i	−0.803997	−	0.366751i
$19$	−3.33464			−0.765019			−0.382510	−	0.923951i	$-0.624940\pi$
$19$	−3.33464			−0.765019			−0.382510	+	0.923951i	$0.624940\pi$
$20$	0.219082	−	0.379462i	0.0489883	−	0.0848502i
$21$	0.490698	−	0.156976i	0.107079	−	0.0342551i
$22$	−2.31207	−	4.00463i	−0.492936	−	0.853790i
$23$	4.29737	+	7.44327i	0.896064	+	1.55203i	0.832482	+	0.554051i	$0.186919\pi$
$23$	4.29737	+	7.44327i	0.896064	+	1.55203i	0.0635814	+	0.997977i	$0.479748\pi$
$24$	−3.90598	−	3.54922i	−0.797305	−	0.724482i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	1.24973			0.245093
$27$	−3.11123	+	4.16176i	−0.598756	+	0.800932i
$28$	0.130331			0.0246303
$29$	−2.94125	+	5.09439i	−0.546176	+	0.946004i	0.452356	+	0.891837i	$0.350584\pi$
$29$	−2.94125	+	5.09439i	−0.546176	+	0.946004i	−0.998532	+	0.0541670i	$0.982750\pi$
$30$	1.60202	+	1.45569i	0.292487	+	0.265772i
$31$	3.44361	+	5.96450i	0.618490	+	1.07126i	0.989761	+	0.142731i	$0.0455885\pi$
$31$	3.44361	+	5.96450i	0.618490	+	1.07126i	−0.371272	+	0.928524i	$0.621078\pi$
$32$	−1.21515	−	2.10469i	−0.214809	−	0.372061i
$33$	−6.10404	+	1.95271i	−1.06258	+	0.339923i
$34$	2.17024	−	3.75896i	0.372193	−	0.644657i
$35$	−0.297448			−0.0502779
$36$	−1.07042	+	0.762946i	−0.178404	+	0.127158i
$37$	9.40767			1.54661			0.773306	−	0.634033i	$-0.218602\pi$
$37$	9.40767			1.54661			0.773306	+	0.634033i	$0.218602\pi$
$38$	2.08371	−	3.60909i	0.338022	−	0.585471i
$39$	0.367806	−	1.69255i	0.0588961	−	0.271025i
$40$	1.52353	+	2.63883i	0.240891	+	0.417236i
$41$	−5.14943	−	8.91907i	−0.804206	−	1.39293i	−0.916826	−	0.399287i	$-0.869258\pi$
$41$	−5.14943	−	8.91907i	−0.804206	−	1.39293i	0.112620	−	0.993638i	$-0.464076\pi$
$42$	−0.136725	+	0.629172i	−0.0210971	+	0.0970834i
$43$	2.74744	−	4.75870i	0.418980	−	0.725695i	−0.576857	−	0.816845i	$-0.695721\pi$
$43$	2.74744	−	4.75870i	0.418980	−	0.725695i	0.995837	+	0.0911500i	$0.0290543\pi$
$44$	−1.62126			−0.244413
$45$	2.44297	−	1.74123i	0.364177	−	0.259568i
$46$	−10.7411			−1.58370
$47$	5.77951	−	10.0104i	0.843028	−	1.46017i	−0.0442943	−	0.999019i	$-0.514104\pi$
$47$	5.77951	−	10.0104i	0.843028	−	1.46017i	0.887323	−	0.461149i	$-0.152563\pi$
$48$	4.83638	−	1.54718i	0.698071	−	0.223316i
$49$	3.45576	+	5.98556i	0.493680	+	0.855079i
$50$	−0.624867	−	1.08230i	−0.0883695	−	0.153061i
$51$	−4.45215	−	4.04550i	−0.623425	−	0.566484i
$52$	0.219082	−	0.379462i	0.0303812	−	0.0526219i
$53$	2.01496			0.276776			0.138388	−	0.990378i	$-0.455808\pi$
$53$	2.01496			0.276776			0.138388	+	0.990378i	$0.455808\pi$
$54$	−2.56018	−	5.96783i	−0.348396	−	0.812119i
$55$	3.70011			0.498922
$56$	−0.453170	+	0.784914i	−0.0605574	+	0.104889i
$57$	−4.27463	−	3.88420i	−0.566189	−	0.514475i
$58$	−3.67578	−	6.36663i	−0.482653	−	0.835980i
$59$	7.46570	+	12.9310i	0.971951	+	1.68347i	0.689650	+	0.724143i	$0.257764\pi$
$59$	7.46570	+	12.9310i	0.971951	+	1.68347i	0.282301	+	0.959326i	$0.408902\pi$
$60$	0.722837	−	0.231239i	0.0933178	−	0.0298528i
$61$	1.86466	−	3.22969i	0.238746	−	0.413519i	−0.721609	−	0.692301i	$-0.756597\pi$
$61$	1.86466	−	3.22969i	0.238746	−	0.413519i	0.960355	+	0.278781i	$0.0899305\pi$
$62$	−8.60718			−1.09311
$63$	0.811865	+	0.370340i	0.102285	+	0.0466585i
$64$	8.90058			1.11257
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$	1.70079	−	7.82659i	0.209353	−	0.963387i
$67$	−3.59788	−	6.23171i	−0.439551	−	0.761324i	0.558104	−	0.829771i	$-0.311529\pi$
$67$	−3.59788	−	6.23171i	−0.439551	−	0.761324i	−0.997655	+	0.0684468i	$0.978196\pi$
$68$	−0.760899	−	1.31792i	−0.0922726	−	0.159821i
$69$	−3.16120	+	14.5470i	−0.380564	+	1.75125i
$70$	0.185865	−	0.321928i	0.0222152	−	0.0384778i
$71$	−13.2587			−1.57352			−0.786761	−	0.617258i	$-0.788244\pi$
$71$	−13.2587			−1.57352			−0.786761	+	0.617258i	$0.788244\pi$
$72$	−0.872877	−	9.09940i	−0.102870	−	1.07237i
$73$	1.78880			0.209364			0.104682	−	0.994506i	$-0.466618\pi$
$73$	1.78880			0.209364			0.104682	+	0.994506i	$0.466618\pi$
$74$	−5.87854	+	10.1819i	−0.683367	+	1.18363i
$75$	−1.64969	+	0.527744i	−0.190490	+	0.0609387i
$76$	−0.730561	−	1.26537i	−0.0838011	−	0.145148i
$77$	0.550294	+	0.953138i	0.0627119	+	0.108620i
$78$	1.60202	+	1.45569i	0.181393	+	0.164825i
$79$	0.213468	−	0.369738i	0.0240170	−	0.0415987i	−0.853767	−	0.520655i	$-0.825688\pi$
$79$	0.213468	−	0.369738i	0.0240170	−	0.0415987i	0.877784	+	0.479056i	$0.159021\pi$
$80$	−2.93168			−0.327772
$81$	−8.83588	+	1.71094i	−0.981764	+	0.190104i
$82$	12.8708			1.42135
$83$	2.05068	−	3.55188i	0.225091	−	0.389870i	−0.731256	−	0.682104i	$-0.761065\pi$
$83$	2.05068	−	3.55188i	0.225091	−	0.389870i	0.956347	+	0.292234i	$0.0943986\pi$
$84$	0.167070	+	0.151810i	0.0182288	+	0.0165638i
$85$	1.73656	+	3.00781i	0.188356	+	0.326243i
$86$	3.43357	+	5.94711i	0.370251	+	0.641294i
$87$	−9.70431	+	3.10445i	−1.04041	+	0.332832i
$88$	5.63722	−	9.76395i	0.600930	−	1.04084i
$89$	5.14366			0.545227			0.272613	−	0.962124i	$-0.412112\pi$
$89$	5.14366			0.545227			0.272613	+	0.962124i	$0.412112\pi$
$90$	0.358006	+	3.73207i	0.0377371	+	0.393395i
$91$	−0.297448			−0.0311810
$92$	−1.88296	+	3.26138i	−0.196312	+	0.340022i
$93$	−2.53316	+	11.6569i	−0.262676	+	1.20877i
$94$	7.22285	+	12.5103i	0.744980	+	1.29034i
$95$	1.66732	+	2.88788i	0.171064	+	0.296291i
$96$	0.893876	−	4.11338i	0.0912309	−	0.419821i
$97$	2.53649	−	4.39333i	0.257541	−	0.446075i	−0.708041	−	0.706171i	$-0.750421\pi$
$97$	2.53649	−	4.39333i	0.257541	−	0.446075i	0.965583	+	0.260096i	$0.0837543\pi$
$98$	−8.63757			−0.872526
$99$	−10.0992	−	4.60685i	−1.01501	−	0.463006i
$100$	−0.438165			−0.0438165
$101$	7.69345	−	13.3254i	0.765527	−	1.32593i	−0.174441	−	0.984668i	$-0.555812\pi$
$101$	7.69345	−	13.3254i	0.765527	−	1.32593i	0.939968	−	0.341264i	$-0.110855\pi$
$102$	7.16045	−	2.29066i	0.708991	−	0.226809i
$103$	5.56701	+	9.64235i	0.548534	+	0.950089i	0.998375	+	0.0569805i	$0.0181473\pi$
$103$	5.56701	+	9.64235i	0.548534	+	0.950089i	−0.449841	+	0.893109i	$0.648519\pi$
$104$	1.52353	+	2.63883i	0.149394	+	0.258758i
$105$	−0.381294	−	0.346468i	−0.0372105	−	0.0338118i
$106$	−1.25908	+	2.18079i	−0.122293	+	0.211817i
$107$	12.6654			1.22441			0.612203	−	0.790701i	$-0.290284\pi$
$107$	12.6654			1.22441			0.612203	+	0.790701i	$0.290284\pi$
$108$	−2.26084	−	0.268823i	−0.217550	−	0.0258675i
$109$	−5.43656			−0.520728			−0.260364	−	0.965511i	$-0.583843\pi$
$109$	−5.43656			−0.520728			−0.260364	+	0.965511i	$0.583843\pi$
$110$	−2.31207	+	4.00463i	−0.220448	+	0.381827i
$111$	12.0596	+	10.9581i	1.14464	+	1.04010i
$112$	−0.436011	−	0.755194i	−0.0411992	−	0.0713591i
$113$	−2.10870	−	3.65238i	−0.198370	−	0.343587i	0.749630	−	0.661857i	$-0.230231\pi$
$113$	−2.10870	−	3.65238i	−0.198370	−	0.343587i	−0.948000	+	0.318270i	$0.896898\pi$
$114$	6.87496	−	2.19933i	0.643899	−	0.205986i
$115$	4.29737	−	7.44327i	0.400732	−	0.694088i
$116$	−2.57750			−0.239315
$117$	2.44297	−	1.74123i	0.225853	−	0.160977i
$118$	−18.6603			−1.71782
$119$	−0.516536	+	0.894667i	−0.0473508	+	0.0820140i
$120$	−1.12073	+	5.15729i	−0.102308	+	0.470794i
$121$	−1.34539	−	2.33029i	−0.122309	−	0.211845i
$122$	2.33033	+	4.03625i	0.210978	+	0.365425i
$123$	3.78798	−	17.4313i	0.341551	−	1.57173i
$124$	−1.50887	+	2.61343i	−0.135500	+	0.234693i
$125$	1.00000			0.0894427
$126$	−0.908128	+	0.647270i	−0.0809025	+	0.0576634i
$127$	1.95972			0.173897			0.0869485	−	0.996213i	$-0.472288\pi$
$127$	1.95972			0.173897			0.0869485	+	0.996213i	$0.472288\pi$
$128$	−3.13139	+	5.42373i	−0.276778	+	0.479394i
$129$	9.06486	−	2.89989i	0.798116	−	0.255321i
$130$	−0.624867	−	1.08230i	−0.0548045	−	0.0949241i
$131$	2.26354	+	3.92057i	0.197766	+	0.342542i	0.947804	−	0.318854i	$-0.103298\pi$
$131$	2.26354	+	3.92057i	0.197766	+	0.342542i	−0.750037	+	0.661395i	$0.769965\pi$
$132$	−2.07827	−	1.88844i	−0.180890	−	0.164368i
$133$	−0.495941	+	0.858995i	−0.0430036	+	0.0744843i
$134$	8.99278			0.776858
$135$	5.15981	+	0.613520i	0.444085	+	0.0528034i
$136$	10.5828			0.907467
$137$	−7.76913	+	13.4565i	−0.663762	+	1.14967i	0.315858	+	0.948806i	$0.397708\pi$
$137$	−7.76913	+	13.4565i	−0.663762	+	1.14967i	−0.979620	+	0.200862i	$0.935626\pi$
$138$	−13.7689	−	12.5113i	−1.17209	−	1.06503i
$139$	7.68678	+	13.3139i	0.651985	+	1.12927i	0.982641	+	0.185519i	$0.0593966\pi$
$139$	7.68678	+	13.3139i	0.651985	+	1.12927i	−0.330656	+	0.943751i	$0.607270\pi$
$140$	−0.0651656	−	0.112870i	−0.00550750	−	0.00953926i
$141$	19.0688	−	6.10021i	1.60589	−	0.513730i
$142$	8.28495	−	14.3499i	0.695257	−	1.20422i
$143$	3.70011			0.309418
$144$	8.00184	+	3.65012i	0.666820	+	0.304177i
$145$	5.88249			0.488515
$146$	−1.11776	+	1.93602i	−0.0925068	+	0.160226i
$147$	−2.54210	+	11.6981i	−0.209669	+	0.964842i
$148$	2.06105	+	3.56985i	0.169418	+	0.293440i
$149$	8.83487	+	15.3024i	0.723781	+	1.25363i	0.959474	+	0.281798i	$0.0909307\pi$
$149$	8.83487	+	15.3024i	0.723781	+	1.25363i	−0.235693	+	0.971828i	$0.575736\pi$
$150$	0.459660	−	2.11523i	0.0375311	−	0.172708i
$151$	−5.49711	+	9.52128i	−0.447349	+	0.774831i	−0.998213	−	0.0597645i	$-0.980965\pi$
$151$	−5.49711	+	9.52128i	−0.447349	+	0.774831i	0.550864	+	0.834595i	$0.314298\pi$
$152$	10.1608			0.824154
$153$	−0.994929	−	10.3718i	−0.0804353	−	0.838506i
$154$	−1.37544			−0.110836
$155$	3.44361	−	5.96450i	0.276597	−	0.479080i
$156$	0.722837	−	0.231239i	0.0578733	−	0.0185139i
$157$	−7.46655	−	12.9324i	−0.595895	−	1.03212i	−0.993420	−	0.114529i	$-0.963464\pi$
$157$	−7.46655	−	12.9324i	−0.595895	−	1.03212i	0.397525	−	0.917592i	$-0.369869\pi$
$158$	0.266778	+	0.462074i	0.0212238	+	0.0367606i
$159$	2.58295	+	2.34703i	0.204841	+	0.186131i
$160$	−1.21515	+	2.10469i	−0.0960657	+	0.166391i
$161$	2.55649			0.201479
$162$	3.66950	−	10.6322i	0.288303	−	0.835344i
$163$	0.105825			0.00828886			0.00414443	−	0.999991i	$-0.498681\pi$
$163$	0.105825			0.00828886			0.00414443	+	0.999991i	$0.498681\pi$
$164$	2.25630	−	3.90802i	0.176187	−	0.305165i
$165$	4.74312	+	4.30990i	0.369251	+	0.335525i
$166$	2.56280	+	4.43891i	0.198912	+	0.344526i
$167$	3.52556	+	6.10645i	0.272816	+	0.472531i	0.969582	−	0.244767i	$-0.0787116\pi$
$167$	3.52556	+	6.10645i	0.272816	+	0.472531i	−0.696766	+	0.717299i	$0.745378\pi$
$168$	−1.49518	+	0.478316i	−0.115356	+	0.0369029i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	−4.34048			−0.332899
$171$	−0.955260	−	9.95821i	−0.0730506	−	0.761524i
$172$	2.40766			0.183582
$173$	−3.91958	+	6.78891i	−0.298000	+	0.516151i	−0.975678	−	0.219207i	$-0.929653\pi$
$173$	−3.91958	+	6.78891i	−0.298000	+	0.516151i	0.677678	+	0.735358i	$0.262986\pi$
$174$	2.70395	−	12.4429i	0.204986	−	0.943291i
$175$	0.148724	+	0.257597i	0.0112425	+	0.0194725i
$176$	5.42377	+	9.39424i	0.408832	+	0.708118i
$177$	−5.49186	+	25.2721i	−0.412794	+	1.89957i
$178$	−3.21410	+	5.56699i	−0.240907	+	0.417264i
$179$	22.1988			1.65922			0.829609	−	0.558345i	$-0.188563\pi$
$179$	22.1988			1.65922			0.829609	+	0.558345i	$0.188563\pi$
$180$	1.19594	+	0.545541i	0.0891403	+	0.0406622i
$181$	−6.98625			−0.519284			−0.259642	−	0.965705i	$-0.583605\pi$
$181$	−6.98625			−0.519284			−0.259642	+	0.965705i	$0.583605\pi$
$182$	0.185865	−	0.321928i	0.0137773	−	0.0238629i
$183$	6.15224	−	1.96813i	0.454787	−	0.145488i
$184$	−13.0943	−	22.6801i	−0.965327	−	1.67200i
$185$	−4.70383	−	8.14728i	−0.345833	−	0.599000i
$186$	−11.0334	−	10.0257i	−0.809010	−	0.735118i
$187$	6.42546	−	11.1292i	0.469876	−	0.813849i
$188$	5.06475			0.369385
$189$	0.609345	+	1.42040i	0.0443234	+	0.103319i
$190$	−4.16742			−0.302336
$191$	7.25055	−	12.5583i	0.524632	−	0.908688i	−0.474957	−	0.880009i	$-0.657536\pi$
$191$	7.25055	−	12.5583i	0.524632	−	0.908688i	0.999589	−	0.0286796i	$-0.00913024\pi$
$192$	11.4095	+	10.3674i	0.823412	+	0.748205i
$193$	−0.391910	−	0.678809i	−0.0282103	−	0.0488617i	0.851576	−	0.524232i	$-0.175647\pi$
$193$	−0.391910	−	0.678809i	−0.0282103	−	0.0488617i	−0.879786	+	0.475370i	$0.842314\pi$
$194$	3.16994	+	5.49049i	0.227588	+	0.394194i
$195$	−1.64969	+	0.527744i	−0.118137	+	0.0377926i
$196$	−1.51419	+	2.62266i	−0.108157	+	0.187333i
$197$	−16.4670			−1.17322			−0.586612	−	0.809868i	$-0.699539\pi$
$197$	−16.4670			−1.17322			−0.586612	+	0.809868i	$0.699539\pi$
$198$	11.2967	−	8.05172i	0.802819	−	0.572211i
$199$	−24.6743			−1.74911			−0.874556	−	0.484925i	$-0.838847\pi$
$199$	−24.6743			−1.74911			−0.874556	+	0.484925i	$0.838847\pi$
$200$	1.52353	−	2.63883i	0.107730	−	0.186593i
$201$	2.64664	−	12.1792i	0.186680	−	0.859052i
$202$	9.61477	+	16.6533i	0.676493	+	1.17172i
$203$	0.874868	+	1.51532i	0.0614037	+	0.106354i
$204$	0.559727	−	2.57572i	0.0391887	−	0.180336i
$205$	−5.14943	+	8.91907i	−0.359652	+	0.622935i
$206$	−13.9146			−0.969474
$207$	−20.9967	+	14.9654i	−1.45937	+	1.04017i
$208$	−2.93168			−0.203276
$209$	6.16927	−	10.6855i	0.426737	−	0.739130i
$210$	0.613242	−	0.196179i	0.0423177	−	0.0135376i
$211$	11.1549	+	19.3209i	0.767937	+	1.33011i	0.938680	+	0.344790i	$0.112050\pi$
$211$	11.1549	+	19.3209i	0.767937	+	1.33011i	−0.170743	+	0.985316i	$0.554617\pi$
$212$	0.441441	+	0.764599i	0.0303183	+	0.0525129i
$213$	−16.9962	−	15.4438i	−1.16456	−	1.05819i
$214$	−7.91416	+	13.7077i	−0.541001	+	0.937041i
$215$	−5.49488			−0.374747
$216$	9.48009	−	12.6811i	0.645038	−	0.862842i
$217$	2.04859			0.139067
$218$	3.39713	−	5.88400i	0.230082	−	0.398515i
$219$	2.29304	+	2.08360i	0.154949	+	0.140797i
$220$	0.810628	+	1.40405i	0.0546525	+	0.0946609i
$221$	1.73656	+	3.00781i	0.116814	+	0.202327i
$222$	−19.3956	+	6.20474i	−1.30175	+	0.416435i
$223$	7.10460	−	12.3055i	0.475760	−	0.824040i	−0.523855	−	0.851808i	$-0.675507\pi$
$223$	7.10460	−	12.3055i	0.475760	−	0.824040i	0.999614	+	0.0277678i	$0.00883992\pi$
$224$	−0.722885			−0.0482998
$225$	−2.72944	−	1.24506i	−0.181962	−	0.0830040i
$226$	5.27063			0.350597
$227$	11.4770	−	19.8787i	0.761753	−	1.31940i	−0.180193	−	0.983631i	$-0.557672\pi$
$227$	11.4770	−	19.8787i	0.761753	−	1.31940i	0.941946	−	0.335764i	$-0.108994\pi$
$228$	0.537410	−	2.47302i	0.0355908	−	0.163780i
$229$	3.20629	+	5.55346i	0.211878	+	0.366983i	0.952302	−	0.305156i	$-0.0987088\pi$
$229$	3.20629	+	5.55346i	0.211878	+	0.366983i	−0.740424	+	0.672140i	$0.765375\pi$
$230$	5.37057	+	9.30210i	0.354125	+	0.613362i
$231$	−0.404803	+	1.86280i	−0.0266341	+	0.122563i
$232$	8.96215	−	15.5229i	0.588394	−	1.01913i
$233$	3.12251			0.204563			0.102281	−	0.994756i	$-0.467386\pi$
$233$	3.12251			0.204563			0.102281	+	0.994756i	$0.467386\pi$
$234$	0.358006	+	3.73207i	0.0234036	+	0.243973i
$235$	−11.5590			−0.754027
$236$	−3.27120	+	5.66589i	−0.212937	+	0.368818i
$237$	0.704314	−	0.225313i	0.0457501	−	0.0146357i
$238$	−0.645533	−	1.11810i	−0.0418437	−	0.0724754i
$239$	−0.536167	−	0.928669i	−0.0346818	−	0.0600706i	0.848164	−	0.529735i	$-0.177708\pi$
$239$	−0.536167	−	0.928669i	−0.0346818	−	0.0600706i	−0.882845	+	0.469664i	$0.844375\pi$
$240$	−3.75808	−	3.41483i	−0.242583	−	0.220427i
$241$	−1.65732	+	2.87057i	−0.106758	+	0.184910i	−0.914455	−	0.404688i	$-0.867380\pi$
$241$	−1.65732	+	2.87057i	−0.106758	+	0.184910i	0.807697	+	0.589597i	$0.200714\pi$
$242$	3.36277			0.216167
$243$	−13.3195	−	8.09883i	−0.854446	−	0.519540i
$244$	1.63406			0.104610
$245$	3.45576	−	5.98556i	0.220781	−	0.382403i
$246$	16.4990	+	14.9920i	1.05193	+	0.955855i
$247$	1.66732	+	2.88788i	0.106089	+	0.183752i
$248$	−10.4929	−	18.1742i	−0.666297	−	1.15406i
$249$	6.76598	−	2.16447i	0.428777	−	0.137168i
$250$	−0.624867	+	1.08230i	−0.0395201	+	0.0684508i
$251$	8.79695			0.555258			0.277629	−	0.960688i	$-0.410451\pi$
$251$	8.79695			0.555258			0.277629	+	0.960688i	$0.410451\pi$
$252$	0.0373354	+	0.389207i	0.00235191	+	0.0245177i
$253$	−31.8015			−1.99934
$254$	−1.22456	+	2.12101i	−0.0768360	+	0.133084i
$255$	−1.27744	+	5.87842i	−0.0799961	+	0.368121i
$256$	4.98718	+	8.63805i	0.311699	+	0.539878i
$257$	−5.37796	−	9.31489i	−0.335468	−	0.581047i	0.648107	−	0.761549i	$-0.275561\pi$
$257$	−5.37796	−	9.31489i	−0.335468	−	0.581047i	−0.983575	+	0.180502i	$0.942228\pi$
$258$	−2.52577	+	11.6230i	−0.157248	+	0.723613i
$259$	1.39915	−	2.42339i	0.0869387	−	0.150582i
$260$	−0.438165			−0.0271738
$261$	−16.0559	−	7.32406i	−0.993835	−	0.453348i
$262$	−5.65765			−0.349531
$263$	−10.0372	+	17.3850i	−0.618923	+	1.07201i	0.370759	+	0.928729i	$0.379097\pi$
$263$	−10.0372	+	17.3850i	−0.618923	+	1.07201i	−0.989683	+	0.143277i	$0.954236\pi$
$264$	18.5994	−	5.95002i	1.14471	−	0.366199i
$265$	−1.00748	−	1.74500i	−0.0618889	−	0.107195i
$266$	−0.619795	−	1.07352i	−0.0380020	−	0.0658215i
$267$	6.59359	+	5.99135i	0.403521	+	0.366665i
$268$	1.57646	−	2.73051i	0.0962978	−	0.166793i
$269$	−6.11669			−0.372941			−0.186471	−	0.982461i	$-0.559705\pi$
$269$	−6.11669			−0.372941			−0.186471	+	0.982461i	$0.559705\pi$
$270$	−3.88821	+	5.20110i	−0.236629	+	0.316529i
$271$	−22.9998			−1.39714			−0.698568	−	0.715544i	$-0.746179\pi$
$271$	−22.9998			−1.39714			−0.698568	+	0.715544i	$0.746179\pi$
$272$	−5.09104	+	8.81795i	−0.308690	+	0.534667i
$273$	−0.381294	−	0.346468i	−0.0230770	−	0.0209692i
$274$	−9.70935	−	16.8171i	−0.586563	−	1.01596i
$275$	−1.85005	−	3.20439i	−0.111562	−	0.193232i
$276$	−6.21260	+	1.98744i	−0.373954	+	0.119630i
$277$	−9.18658	+	15.9116i	−0.551968	+	0.956037i	0.446165	+	0.894951i	$0.352790\pi$
$277$	−9.18658	+	15.9116i	−0.551968	+	0.956037i	−0.998133	+	0.0610856i	$0.980544\pi$
$278$	−19.2129			−1.15231
$279$	−16.8253	+	11.9922i	−1.00730	+	0.717956i
$280$	0.906341			0.0541642
$281$	6.95953	−	12.0543i	0.415171	−	0.719097i	−0.580276	−	0.814420i	$-0.697055\pi$
$281$	6.95953	−	12.0543i	0.415171	−	0.719097i	0.995446	+	0.0953233i	$0.0303885\pi$
$282$	−5.31322	+	24.4500i	−0.316398	+	1.45598i
$283$	−7.73532	−	13.3980i	−0.459817	−	0.796427i	0.539134	−	0.842220i	$-0.318752\pi$
$283$	−7.73532	−	13.3980i	−0.459817	−	0.796427i	−0.998951	+	0.0457934i	$0.985418\pi$
$284$	−2.90475	−	5.03118i	−0.172365	−	0.298546i
$285$	−1.22650	+	5.64404i	−0.0726517	+	0.334324i
$286$	−2.31207	+	4.00463i	−0.136716	+	0.236799i
$287$	−3.06337			−0.180825
$288$	5.93713	−	4.23170i	0.349849	−	0.249355i
$289$	−4.93743			−0.290437
$290$	−3.67578	+	6.36663i	−0.215849	+	0.373862i
$291$	8.36886	−	2.67724i	0.490591	−	0.156942i
$292$	0.391895	+	0.678782i	0.0229339	+	0.0397227i
$293$	12.4203	+	21.5125i	0.725599	+	1.25678i	0.958727	+	0.284329i	$0.0917708\pi$
$293$	12.4203	+	21.5125i	0.725599	+	1.25678i	−0.233127	+	0.972446i	$0.574896\pi$
$294$	−11.0724	−	10.0611i	−0.645754	−	0.586774i
$295$	7.46570	−	12.9310i	0.434670	−	0.752870i
$296$	−28.6657			−1.66616
$297$	−7.57996	−	17.6691i	−0.439834	−	1.02526i
$298$	−22.0825			−1.27920
$299$	4.29737	−	7.44327i	0.248523	−	0.430455i
$300$	−0.561677	−	0.510376i	−0.0324284	−	0.0294666i
$301$	−0.817220	−	1.41547i	−0.0471038	−	0.0815861i
$302$	−6.86993	−	11.8991i	−0.395320	−	0.684714i
$303$	25.3837	−	8.12035i	1.45825	−	0.466502i
$304$	−4.88806	+	8.46636i	−0.280349	+	0.485579i
$305$	−3.72932			−0.213541
$306$	11.8471	+	5.40415i	0.677251	+	0.308935i
$307$	−3.77804			−0.215624			−0.107812	−	0.994171i	$-0.534384\pi$
$307$	−3.77804			−0.215624			−0.107812	+	0.994171i	$0.534384\pi$
$308$	−0.241120	+	0.417631i	−0.0137391	+	0.0237967i
$309$	−4.09516	+	18.8449i	−0.232966	+	1.07205i
$310$	4.30359	+	7.45404i	0.244428	+	0.423361i
$311$	−11.1614	−	19.3322i	−0.632908	−	1.09623i	−0.986954	−	0.161000i	$-0.948528\pi$
$311$	−11.1614	−	19.3322i	−0.632908	−	1.09623i	0.354047	−	0.935228i	$-0.384805\pi$
$312$	−1.12073	+	5.15729i	−0.0634487	+	0.291974i
$313$	5.49171	−	9.51192i	0.310410	−	0.537645i	−0.668041	−	0.744124i	$-0.732867\pi$
$313$	5.49171	−	9.51192i	0.310410	−	0.537645i	0.978451	+	0.206479i	$0.0662004\pi$
$314$	18.6624			1.05318
$315$	−0.0852086	−	0.888266i	−0.00480096	−	0.0500481i
$316$	0.187068			0.0105234
$317$	−7.60683	+	13.1754i	−0.427242	+	0.740005i	−0.996627	−	0.0820661i	$-0.973848\pi$
$317$	−7.60683	+	13.1754i	−0.427242	+	0.740005i	0.569385	+	0.822071i	$0.307181\pi$
$318$	−4.15419	+	1.32894i	−0.232955	+	0.0745235i
$319$	−10.8829	−	18.8498i	−0.609327	−	1.05539i
$320$	−4.45029	−	7.70813i	−0.248779	−	0.430898i
$321$	16.2355	+	14.7526i	0.906180	+	0.823413i
$322$	−1.59747	+	2.76689i	−0.0890233	+	0.154193i
$323$	11.5816			0.644418
$324$	−2.58502	−	2.97804i	−0.143612	−	0.165447i
$325$	1.00000			0.0554700
$326$	−0.0661266	+	0.114535i	−0.00366241	+	0.00634349i
$327$	−6.96905	−	6.33252i	−0.385389	−	0.350189i
$328$	15.6906	+	27.1769i	0.866369	+	1.50060i
$329$	−1.71910	−	2.97757i	−0.0947772	−	0.164159i
$330$	−7.62843	+	2.44037i	−0.419931	+	0.134338i
$331$	10.5277	−	18.2345i	0.578655	−	1.00226i	−0.416979	−	0.908916i	$-0.636911\pi$
$331$	10.5277	−	18.2345i	0.578655	−	1.00226i	0.995634	−	0.0933439i	$-0.0297556\pi$
$332$	1.79707			0.0986271
$333$	2.69497	+	28.0940i	0.147684	+	1.53954i
$334$	−8.81203			−0.482173
$335$	−3.59788	+	6.23171i	−0.196573	+	0.340475i
$336$	0.320735	−	1.47594i	0.0174976	−	0.0805192i
$337$	−1.78238	−	3.08716i	−0.0970922	−	0.168169i	0.813388	−	0.581722i	$-0.197621\pi$
$337$	−1.78238	−	3.08716i	−0.0970922	−	0.168169i	−0.910480	+	0.413553i	$0.864287\pi$
$338$	−0.624867	−	1.08230i	−0.0339883	−	0.0588694i
$339$	1.55119	−	7.13815i	0.0842489	−	0.387691i
$340$	−0.760899	+	1.31792i	−0.0412656	+	0.0714740i
$341$	−25.4834			−1.38000
$342$	11.3747	+	5.18868i	0.615073	+	0.280572i
$343$	4.13795			0.223428
$344$	−8.37160	+	14.5000i	−0.451366	+	0.781790i
$345$	14.1787	−	4.53583i	0.763355	−	0.244201i
$346$	−4.89843	−	8.48433i	−0.263341	−	0.456120i
$347$	−15.1211	−	26.1905i	−0.811742	−	1.40598i	−0.911644	−	0.410981i	$-0.865186\pi$
$347$	−15.1211	−	26.1905i	−0.811742	−	1.40598i	0.0999017	−	0.994997i	$-0.468147\pi$
$348$	−3.30406	−	3.00228i	−0.177116	−	0.160939i
$349$	3.44330	−	5.96397i	0.184315	−	0.319244i	−0.759030	−	0.651055i	$-0.774327\pi$
$349$	3.44330	−	5.96397i	0.184315	−	0.319244i	0.943346	+	0.331812i	$0.107660\pi$
$350$	−0.371731			−0.0198698
$351$	5.15981	+	0.613520i	0.275410	+	0.0327473i
$352$	8.99234			0.479293
$353$	4.92240	−	8.52585i	0.261993	−	0.453785i	−0.704778	−	0.709428i	$-0.748954\pi$
$353$	4.92240	−	8.52585i	0.261993	−	0.453785i	0.966771	+	0.255642i	$0.0822869\pi$
$354$	−23.9204	−	21.7356i	−1.27135	−	1.15523i
$355$	6.62937	+	11.4824i	0.351850	+	0.609423i
$356$	1.12688	+	1.95182i	0.0597248	+	0.103446i
$357$	−1.70425	+	0.545198i	−0.0901986	+	0.0288549i
$358$	−13.8713	+	24.0258i	−0.733122	+	1.26980i
$359$	20.5087			1.08241			0.541205	−	0.840891i	$-0.317968\pi$
$359$	20.5087			1.08241			0.541205	+	0.840891i	$0.317968\pi$
$360$	−7.44388	+	5.30563i	−0.392327	+	0.279632i
$361$	−7.88016			−0.414745
$362$	4.36548	−	7.56123i	0.229444	−	0.397409i
$363$	0.989688	−	4.55429i	0.0519452	−	0.239038i
$364$	−0.0651656	−	0.112870i	−0.00341560	−	0.00591600i
$365$	−0.894401	−	1.54915i	−0.0468151	−	0.0810862i
$366$	−1.71422	+	7.88840i	−0.0896038	+	0.412333i
$367$	4.22991	−	7.32643i	0.220800	−	0.382436i	−0.734251	−	0.678878i	$-0.762467\pi$
$367$	4.22991	−	7.32643i	0.220800	−	0.382436i	0.955051	+	0.296441i	$0.0958000\pi$
$368$	25.1971			1.31349
$369$	25.1598	−	17.9327i	1.30977	−	0.933539i
$370$	11.7571			0.611222
$371$	0.299672	−	0.519048i	0.0155582	−	0.0269476i
$372$	−4.97833	+	1.59259i	−0.258114	+	0.0825720i
$373$	9.51631	+	16.4827i	0.492736	+	0.853444i	0.999965	−	0.00836753i	$-0.00266350\pi$
$373$	9.51631	+	16.4827i	0.492736	+	0.853444i	−0.507229	+	0.861811i	$0.669330\pi$
$374$	8.03011	+	13.9086i	0.415227	+	0.719195i
$375$	1.28189	+	1.16480i	0.0661963	+	0.0601502i
$376$	−17.6105	+	30.5023i	−0.908192	+	1.57304i
$377$	5.88249			0.302964
$378$	−1.91806	−	0.228064i	−0.0986543	−	0.0117304i
$379$	−24.9153			−1.27981			−0.639907	−	0.768453i	$-0.721027\pi$
$379$	−24.9153			−1.27981			−0.639907	+	0.768453i	$0.721027\pi$
$380$	−0.730561	+	1.26537i	−0.0374770	+	0.0649121i
$381$	2.51214	+	2.28269i	0.128701	+	0.116946i
$382$	9.06126	+	15.6946i	0.463615	+	0.803004i
$383$	−13.4646	−	23.3214i	−0.688011	−	1.19167i	−0.972480	−	0.232985i	$-0.925151\pi$
$383$	−13.4646	−	23.3214i	−0.688011	−	1.19167i	0.284469	−	0.958685i	$-0.408183\pi$
$384$	−10.3317	+	3.30515i	−0.527235	+	0.168665i
$385$	0.550294	−	0.953138i	0.0280456	−	0.0485764i
$386$	0.979568			0.0498587
$387$	14.9979	+	6.84145i	0.762387	+	0.347770i
$388$	2.22280			0.112846
$389$	10.0944	−	17.4840i	0.511806	−	0.886474i	−0.488101	−	0.872787i	$-0.662310\pi$
$389$	10.0944	−	17.4840i	0.511806	−	0.886474i	0.999906	−	0.0136862i	$-0.00435660\pi$
$390$	0.459660	−	2.11523i	0.0232758	−	0.107109i
$391$	−14.9253	−	25.8514i	−0.754804	−	1.30736i
$392$	−10.5299	−	18.2383i	−0.531841	−	0.921175i
$393$	−1.66509	+	7.66230i	−0.0839926	+	0.386512i
$394$	10.2897	−	17.8222i	0.518387	−	0.897872i
$395$	−0.426936			−0.0214815
$396$	−0.464434	−	4.84154i	−0.0233387	−	0.243297i
$397$	10.2906			0.516471			0.258235	−	0.966082i	$-0.416859\pi$
$397$	10.2906			0.516471			0.258235	+	0.966082i	$0.416859\pi$
$398$	15.4181	−	26.7050i	0.772841	−	1.33860i
$399$	−1.63630	+	0.523460i	−0.0819175	+	0.0262058i
$400$	1.46584	+	2.53891i	0.0732921	+	0.126946i
$401$	−11.3794	−	19.7097i	−0.568259	−	0.984254i	−0.996738	−	0.0807023i	$-0.974284\pi$
$401$	−11.3794	−	19.7097i	−0.568259	−	0.984254i	0.428479	−	0.903552i	$-0.359050\pi$
$402$	11.5277	+	10.4748i	0.574951	+	0.522437i
$403$	3.44361	−	5.96450i	0.171538	−	0.297113i
$404$	6.74200			0.335427
$405$	5.89965	+	6.79662i	0.293156	+	0.337727i
$406$	−2.18670			−0.108524
$407$	−17.4047	+	30.1458i	−0.862718	+	1.49427i
$408$	13.5659	+	12.3269i	0.671614	+	0.610272i
$409$	8.08946	+	14.0114i	0.399998	+	0.692817i	0.993725	−	0.111849i	$-0.0356774\pi$
$409$	8.08946	+	14.0114i	0.399998	+	0.692817i	−0.593727	+	0.804667i	$0.702344\pi$
$410$	−6.43542	−	11.1465i	−0.317823	−	0.550485i
$411$	−25.6334	+	8.20023i	−1.26440	+	0.404487i
$412$	−2.43927	+	4.22494i	−0.120174	+	0.208148i
$413$	4.44131			0.218543
$414$	−3.07697	−	32.0762i	−0.151225	−	1.57646i
$415$	−4.10136			−0.201328
$416$	−1.21515	+	2.10469i	−0.0595774	+	0.103191i
$417$	−5.65449	+	26.0205i	−0.276902	+	1.27423i
$418$	7.70994	+	13.3540i	0.377106	+	0.653166i
$419$	−13.9453	−	24.1540i	−0.681274	−	1.18000i	−0.974592	−	0.223987i	$-0.928093\pi$
$419$	−13.9453	−	24.1540i	−0.681274	−	1.18000i	0.293318	−	0.956015i	$-0.405241\pi$
$420$	0.0479366	−	0.220592i	0.00233907	−	0.0107638i
$421$	−9.33408	+	16.1671i	−0.454915	+	0.787937i	−0.998683	−	0.0512990i	$-0.983664\pi$
$421$	−9.33408	+	16.1671i	−0.454915	+	0.787937i	0.543768	+	0.839236i	$0.316997\pi$
$422$	−27.8814			−1.35724
$423$	31.5496	+	14.3917i	1.53400	+	0.699747i
$424$	−6.13969			−0.298170
$425$	1.73656	−	3.00781i	0.0842355	−	0.145900i
$426$	27.3352	−	8.74467i	1.32440	−	0.423681i
$427$	−0.554640	−	0.960664i	−0.0268409	−	0.0464898i
$428$	2.77475	+	4.80602i	0.134123	+	0.232308i
$429$	4.74312	+	4.30990i	0.229000	+	0.208084i
$430$	3.43357	−	5.94711i	0.165581	−	0.286795i
$431$	33.5486			1.61598			0.807989	−	0.589198i	$-0.200556\pi$
$431$	33.5486			1.61598			0.807989	+	0.589198i	$0.200556\pi$
$432$	6.00578	+	13.9996i	0.288953	+	0.673557i
$433$	−15.6360			−0.751420			−0.375710	−	0.926737i	$-0.622601\pi$
$433$	−15.6360			−0.751420			−0.375710	+	0.926737i	$0.622601\pi$
$434$	−1.28009	+	2.21719i	−0.0614465	+	0.106428i
$435$	7.54069	+	6.85195i	0.361548	+	0.328526i
$436$	−1.19105	−	2.06297i	−0.0570411	−	0.0987981i
$437$	−14.3302	−	24.8206i	−0.685506	−	1.18733i
$438$	−3.68793	+	1.17979i	−0.176216	+	0.0563724i
$439$	4.78950	−	8.29567i	0.228591	−	0.395931i	−0.728800	−	0.684727i	$-0.759922\pi$
$439$	4.78950	−	8.29567i	0.228591	−	0.395931i	0.957391	+	0.288796i	$0.0932550\pi$
$440$	−11.2744			−0.537488
$441$	−16.8847	+	12.0346i	−0.804031	+	0.573075i
$442$	−4.34048			−0.206455
$443$	6.80475	−	11.7862i	0.323303	−	0.559978i	−0.657864	−	0.753137i	$-0.728540\pi$
$443$	6.80475	−	11.7862i	0.323303	−	0.559978i	0.981167	+	0.193159i	$0.0618733\pi$
$444$	−1.51614	+	6.97686i	−0.0719527	+	0.331107i
$445$	−2.57183	−	4.45454i	−0.121916	−	0.211165i
$446$	8.87887	+	15.3786i	0.420427	+	0.728200i
$447$	−6.49904	+	29.9069i	−0.307394	+	1.41455i
$448$	1.32373	−	2.29277i	0.0625404	−	0.108323i
$449$	17.0372			0.804035			0.402018	−	0.915632i	$-0.368309\pi$
$449$	17.0372			0.804035			0.402018	+	0.915632i	$0.368309\pi$
$450$	3.05307	−	2.17608i	0.143923	−	0.102581i
$451$	38.1069			1.79438
$452$	0.923958	−	1.60034i	0.0434593	−	0.0752738i
$453$	−18.1371	+	5.80214i	−0.852155	+	0.272608i
$454$	14.3432	+	24.8431i	0.673158	+	1.16594i
$455$	0.148724	+	0.257597i	0.00697229	+	0.0120764i
$456$	13.0251	+	11.8354i	0.609954	+	0.554243i
$457$	−2.35369	+	4.07671i	−0.110101	+	0.190701i	−0.915811	−	0.401610i	$-0.868451\pi$
$457$	−2.35369	+	4.07671i	−0.110101	+	0.190701i	0.805710	+	0.592310i	$0.201784\pi$
$458$	−8.01403			−0.374471
$459$	10.8057	−	14.4543i	0.504365	−	0.674669i
$460$	3.76591			0.175587
$461$	−6.83654	+	11.8412i	−0.318409	+	0.551501i	−0.980156	−	0.198226i	$-0.936482\pi$
$461$	−6.83654	+	11.8412i	−0.318409	+	0.551501i	0.661747	+	0.749727i	$0.269815\pi$
$462$	−1.76316	−	1.60212i	−0.0820297	−	0.0745374i
$463$	−4.66006	−	8.07146i	−0.216571	−	0.375112i	0.737186	−	0.675690i	$-0.236154\pi$
$463$	−4.66006	−	8.07146i	−0.216571	−	0.375112i	−0.953757	+	0.300577i	$0.902821\pi$
$464$	8.62280	+	14.9351i	0.400304	+	0.693346i
$465$	11.3618	−	3.63469i	0.526890	−	0.168555i
$466$	−1.95116	+	3.37950i	−0.0903855	+	0.156552i
$467$	29.3963			1.36030			0.680148	−	0.733075i	$-0.261915\pi$
$467$	29.3963			1.36030			0.680148	+	0.733075i	$0.261915\pi$
$468$	1.19594	+	0.545541i	0.0552825	+	0.0252176i
$469$	−2.14036			−0.0988328
$470$	7.22285	−	12.5103i	0.333165	−	0.577059i
$471$	5.49248	−	25.2750i	0.253080	−	1.16461i
$472$	−22.7484	−	39.4014i	−1.04708	−	1.81360i
$473$	10.1658	+	17.6077i	0.467425	+	0.809603i
$474$	−0.196246	+	0.903071i	−0.00901386	+	0.0414794i
$475$	1.66732	−	2.88788i	0.0765019	−	0.132505i
$476$	−0.452656			−0.0207474
$477$	0.577216	+	6.01725i	0.0264289	+	0.275511i
$478$	1.34013			0.0612963
$479$	−11.6755	+	20.2225i	−0.533467	+	0.923991i	0.465769	+	0.884906i	$0.345778\pi$
$479$	−11.6755	+	20.2225i	−0.533467	+	0.923991i	−0.999236	+	0.0390851i	$0.987556\pi$
$480$	−4.00923	+	1.28257i	−0.182996	+	0.0585412i
$481$	−4.70383	−	8.14728i	−0.214476	−	0.371484i
$482$	−2.07121	−	3.58745i	−0.0943412	−	0.163404i
$483$	3.27713	+	2.97781i	0.149114	+	0.135495i
$484$	0.589504	−	1.02105i	0.0267956	−	0.0464114i
$485$	−5.07298			−0.230352
$486$	17.0883	−	9.35502i	0.775141	−	0.424352i
$487$	17.7085			0.802451			0.401225	−	0.915979i	$-0.368584\pi$
$487$	17.7085			0.802451			0.401225	+	0.915979i	$0.368584\pi$
$488$	−5.68173	+	9.84105i	−0.257200	+	0.445483i
$489$	0.135656	+	0.123265i	0.00613456	+	0.00557425i
$490$	4.31878	+	7.48035i	0.195103	+	0.337928i
$491$	8.11258	+	14.0514i	0.366116	+	0.634131i	0.988955	−	0.148219i	$-0.0473542\pi$
$491$	8.11258	+	14.0514i	0.366116	+	0.634131i	−0.622839	+	0.782350i	$0.714021\pi$
$492$	7.44440	−	2.38150i	0.335619	−	0.107366i
$493$	10.2153	−	17.6934i	0.460074	−	0.796872i
$494$	−4.16742			−0.187501
$495$	1.05995	+	11.0496i	0.0476413	+	0.496642i
$496$	20.1911			0.906608
$497$	−1.97189	+	3.41542i	−0.0884514	+	0.153202i
$498$	−1.88523	+	8.67534i	−0.0844792	+	0.388751i
$499$	0.146733	+	0.254150i	0.00656869	+	0.0113773i	0.869291	−	0.494301i	$-0.164576\pi$
$499$	0.146733	+	0.254150i	0.00656869	+	0.0113773i	−0.862722	+	0.505678i	$0.831242\pi$
$500$	0.219082	+	0.379462i	0.00979766	+	0.0169700i
$501$	−2.59345	+	11.9344i	−0.115867	+	0.533188i
$502$	−5.49692	+	9.52095i	−0.245340	+	0.424941i
$503$	16.6687			0.743222			0.371611	−	0.928389i	$-0.378806\pi$
$503$	16.6687			0.743222			0.371611	+	0.928389i	$0.378806\pi$
$504$	−2.47380	−	1.12845i	−0.110192	−	0.0502651i
$505$	−15.3869			−0.684708
$506$	19.8717	−	34.4188i	0.883404	−	1.53010i
$507$	−1.64969	+	0.527744i	−0.0732654	+	0.0234380i
$508$	0.429340	+	0.743638i	0.0190489	+	0.0329936i
$509$	−3.70438	−	6.41618i	−0.164194	−	0.284392i	0.772175	−	0.635410i	$-0.219169\pi$
$509$	−3.70438	−	6.41618i	−0.164194	−	0.284392i	−0.936369	+	0.351018i	$0.885836\pi$
$510$	−5.56400	−	5.05580i	−0.246378	−	0.223875i
$511$	0.266038	−	0.460791i	0.0117688	−	0.0203842i
$512$	−24.9909			−1.10445
$513$	10.3748	−	13.8780i	0.458060	−	0.612728i
$514$	13.4420			0.592903
$515$	5.56701	−	9.64235i	0.245312	−	0.424893i
$516$	3.08635	+	2.80445i	0.135869	+	0.123459i
$517$	21.3848	+	37.0396i	0.940503	+	1.62900i
$518$	1.74856	+	3.02860i	0.0768273	+	0.133069i
$519$	−12.9322	+	4.13707i	−0.567660	+	0.181597i
$520$	1.52353	−	2.63883i	0.0668112	−	0.115720i
$521$	6.70235			0.293635			0.146818	−	0.989164i	$-0.453097\pi$
$521$	6.70235			0.293635			0.146818	+	0.989164i	$0.453097\pi$
$522$	17.9596	−	12.8008i	0.786072	−	0.560274i
$523$	17.6159			0.770290			0.385145	−	0.922856i	$-0.374151\pi$
$523$	17.6159			0.770290			0.385145	+	0.922856i	$0.374151\pi$
$524$	−0.991803	+	1.71785i	−0.0433271	+	0.0750448i
$525$	−0.109403	+	0.503445i	−0.00477475	+	0.0219721i
$526$	−12.5439	−	21.7267i	−0.546940	−	0.947327i
$527$	−11.9601	−	20.7154i	−0.520988	−	0.902378i
$528$	−3.98979	+	18.3600i	−0.173633	+	0.799015i
$529$	−25.4348	+	44.0544i	−1.10586	+	1.91541i
$530$	2.51816			0.109382
$531$	−36.4770	+	25.9990i	−1.58297	+	1.12826i
$532$	−0.434608			−0.0188426
$533$	−5.14943	+	8.91907i	−0.223047	+	0.386328i
$534$	−10.6046	+	3.39245i	−0.458904	+	0.146806i
$535$	−6.33268	−	10.9685i	−0.273785	−	0.474210i
$536$	10.9629	+	18.9884i	0.473527	+	0.820173i
$537$	28.4564	+	25.8573i	1.22798	+	1.11582i
$538$	3.82212	−	6.62011i	0.164783	−	0.285413i
$539$	−25.5734			−1.10152
$540$	0.897615	+	2.09236i	0.0386272	+	0.0900408i
$541$	26.5563			1.14174			0.570872	−	0.821039i	$-0.306605\pi$
$541$	26.5563			1.14174			0.570872	+	0.821039i	$0.306605\pi$
$542$	14.3718	−	24.8927i	0.617321	−	1.06923i
$543$	−8.95558	−	8.13761i	−0.384321	−	0.349218i
$544$	4.22035	+	7.30986i	0.180946	+	0.313407i
$545$	2.71828	+	4.70820i	0.116438	+	0.201677i
$546$	0.613242	−	0.196179i	0.0262443	−	0.00839568i
$547$	5.77969	−	10.0107i	0.247122	−	0.428027i	−0.715604	−	0.698506i	$-0.753849\pi$
$547$	5.77969	−	10.0107i	0.247122	−	0.428027i	0.962726	+	0.270479i	$0.0871819\pi$
$548$	−6.80831			−0.290837
$549$	10.1790	+	4.64323i	0.434427	+	0.198168i
$550$	4.62415			0.197174
$551$	9.80801	−	16.9880i	0.417835	−	0.723712i
$552$	9.63236	−	44.3256i	0.409980	−	1.88662i
$553$	−0.0634957	−	0.109978i	−0.00270011	−	0.00467673i
$554$	−11.4808	−	19.8853i	−0.487772	−	0.844845i
$555$	3.46020	−	15.9229i	0.146877	−	0.675891i
$556$	−3.36808	+	5.83368i	−0.142838	+	0.247403i
$557$	0.0154083			0.000652871			0.000326435	−	1.00000i	$-0.499896\pi$
$557$	0.0154083			0.000652871			0.000326435		1.00000i	$0.499896\pi$
$558$	−2.46566	−	25.7036i	−0.104380	−	1.08812i
$559$	−5.49488			−0.232408
$560$	−0.436011	+	0.755194i	−0.0184248	+	0.0319128i
$561$	21.2001	−	6.78200i	0.895067	−	0.286336i
$562$	8.69756	+	15.0646i	0.366885	+	0.635463i
$563$	12.0589	+	20.8866i	0.508221	+	0.880265i	0.999955	+	0.00951951i	$0.00303020\pi$
$563$	12.0589	+	20.8866i	0.508221	+	0.880265i	−0.491733	+	0.870746i	$0.663636\pi$
$564$	6.49244	+	5.89944i	0.273381	+	0.248411i
$565$	−2.10870	+	3.65238i	−0.0887137	+	0.153657i
$566$	19.3342			0.812677
$567$	−0.873373	+	2.53056i	−0.0366782	+	0.106273i
$568$	40.4001			1.69515
$569$	−5.03079	+	8.71359i	−0.210902	+	0.365293i	−0.951997	−	0.306107i	$-0.900973\pi$
$569$	−5.03079	+	8.71359i	−0.210902	+	0.365293i	0.741095	+	0.671400i	$0.234307\pi$
$570$	−5.34215	−	4.85422i	−0.223758	−	0.203321i
$571$	−15.3057	−	26.5103i	−0.640525	−	1.10942i	−0.985316	−	0.170742i	$-0.945384\pi$
$571$	−15.3057	−	26.5103i	−0.640525	−	1.10942i	0.344791	−	0.938679i	$-0.387950\pi$
$572$	0.810628	+	1.40405i	0.0338941	+	0.0587062i
$573$	23.9224	−	7.65288i	0.999371	−	0.319704i
$574$	1.91420	−	3.31549i	0.0798972	−	0.138386i
$575$	−8.59474			−0.358426
$576$	2.54971	+	26.5797i	0.106238	+	1.10749i
$577$	7.54909			0.314273			0.157136	−	0.987577i	$-0.449774\pi$
$577$	7.54909			0.314273			0.157136	+	0.987577i	$0.449774\pi$
$578$	3.08524	−	5.34379i	0.128329	−	0.222272i
$579$	0.288294	−	1.32665i	0.0119811	−	0.0551339i
$580$	1.28875	+	2.23218i	0.0535124	+	0.0926863i
$581$	−0.609970	−	1.05650i	−0.0253058	−	0.0438310i
$582$	−2.33185	+	10.7305i	−0.0966581	+	0.444795i
$583$	−3.72778	+	6.45670i	−0.154389	+	0.267409i
$584$	−5.45059			−0.225547
$585$	−2.72944	−	1.24506i	−0.112848	−	0.0514769i
$586$	−31.0441			−1.28242
$587$	−22.5477	+	39.0537i	−0.930643	+	1.61192i	−0.148418	+	0.988925i	$0.547418\pi$
$587$	−22.5477	+	39.0537i	−0.930643	+	1.61192i	−0.782225	+	0.622996i	$0.785915\pi$
$588$	−4.99590	+	1.59821i	−0.206028	+	0.0659092i
$589$	−11.4832	−	19.8895i	−0.473157	−	0.819531i
$590$	9.33014	+	16.1603i	0.384116	+	0.665308i
$591$	−21.1088	−	19.1808i	−0.868300	−	0.788993i
$592$	13.7902	−	23.8852i	0.566772	−	0.981677i
$593$	24.9853			1.02602			0.513011	−	0.858382i	$-0.328530\pi$
$593$	24.9853			1.02602			0.513011	+	0.858382i	$0.328530\pi$
$594$	23.8597	+	2.83701i	0.978976	+	0.116404i
$595$	1.03307			0.0423518
$596$	−3.87113	+	6.70499i	−0.158568	+	0.274647i
$597$	−31.6296	−	28.7407i	−1.29451	−	1.17628i
$598$	5.37057	+	9.30210i	0.219619	+	0.380391i
$599$	−17.3796	−	30.1024i	−0.710111	−	1.22995i	−0.964815	−	0.262930i	$-0.915311\pi$
$599$	−17.3796	−	30.1024i	−0.710111	−	1.22995i	0.254704	−	0.967019i	$-0.418022\pi$
$600$	5.02671	−	1.60807i	0.205215	−	0.0656491i
$601$	−4.57560	+	7.92518i	−0.186643	+	0.323275i	−0.944129	−	0.329577i	$-0.893094\pi$
$601$	−4.57560	+	7.92518i	−0.186643	+	0.323275i	0.757486	+	0.652851i	$0.226427\pi$
$602$	2.04261			0.0832508
$603$	17.5790	−	12.5295i	0.715873	−	0.510240i
$604$	−4.81728			−0.196012
$605$	−1.34539	+	2.33029i	−0.0546980	+	0.0947398i
$606$	−7.07274	+	32.5469i	−0.287311	+	1.32213i
$607$	−13.7691	−	23.8488i	−0.558871	−	0.967993i	−0.997591	−	0.0693691i	$-0.977901\pi$
$607$	−13.7691	−	23.8488i	−0.558871	−	0.967993i	0.438720	−	0.898624i	$-0.355432\pi$
$608$	4.05208	+	7.01840i	0.164333	+	0.284634i
$609$	−0.643564	+	2.96151i	−0.0260785	+	0.120007i
$610$	2.33033	−	4.03625i	0.0943524	−	0.163423i
$611$	−11.5590			−0.467628
$612$	3.71771	−	2.64980i	0.150280	−	0.107112i
$613$	−46.2262			−1.86706			−0.933529	−	0.358503i	$-0.883287\pi$
$613$	−46.2262			−1.86706			−0.933529	+	0.358503i	$0.883287\pi$
$614$	2.36077	−	4.08898i	0.0952730	−	0.165018i
$615$	−16.9900	+	5.43517i	−0.685101	+	0.219167i
$616$	−1.67678	−	2.90427i	−0.0675593	−	0.117016i
$617$	−2.48622	−	4.30626i	−0.100091	−	0.173363i	0.811631	−	0.584171i	$-0.198580\pi$
$617$	−2.48622	−	4.30626i	−0.100091	−	0.173363i	−0.911722	+	0.410807i	$0.865247\pi$
$618$	−17.8369	−	16.2077i	−0.717505	−	0.651971i
$619$	14.5074	−	25.1276i	0.583102	−	1.00996i	−0.412008	−	0.911180i	$-0.635172\pi$
$619$	14.5074	−	25.1276i	0.583102	−	1.00996i	0.995109	−	0.0987813i	$-0.0314944\pi$
$620$	3.01773			0.121195
$621$	−44.3472	−	5.27305i	−1.77959	−	0.211600i
$622$	27.8977			1.11860
$623$	0.764985	−	1.32499i	0.0306485	−	0.0530847i
$624$	−3.75808	−	3.41483i	−0.150444	−	0.136703i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	6.86318	+	11.8874i	0.274308	+	0.475115i
$627$	20.3548	−	6.51159i	0.812892	−	0.260048i
$628$	3.27158	−	5.66654i	0.130550	−	0.226119i
$629$	−32.6740			−1.30280
$630$	1.01462	+	0.462827i	0.0404233	+	0.0184395i
$631$	−4.63524			−0.184526			−0.0922630	−	0.995735i	$-0.529410\pi$
$631$	−4.63524			−0.184526			−0.0922630	+	0.995735i	$0.529410\pi$
$632$	−0.650450	+	1.12661i	−0.0258735	+	0.0448142i
$633$	−8.20570	+	37.7605i	−0.326147	+	1.50084i
$634$	−9.50652	−	16.4658i	−0.377552	−	0.653939i
$635$	−0.979859	−	1.69717i	−0.0388845	−	0.0673500i
$636$	−0.324730	+	1.49432i	−0.0128764	+	0.0592537i
$637$	3.45576	−	5.98556i	0.136922	−	0.237156i
$638$	27.2015			1.07692
$639$	−3.79817	−	39.5944i	−0.150253	−	1.56633i
$640$	6.26278			0.247558
$641$	2.34622	−	4.06378i	0.0926702	−	0.160509i	−0.815964	−	0.578103i	$-0.803793\pi$
$641$	2.34622	−	4.06378i	0.0926702	−	0.160509i	0.908634	+	0.417594i	$0.137126\pi$
$642$	−26.1119	+	8.35331i	−1.03055	+	0.329679i
$643$	6.53616	+	11.3210i	0.257761	+	0.446455i	0.965642	−	0.259877i	$-0.0836819\pi$
$643$	6.53616	+	11.3210i	0.257761	+	0.446455i	−0.707881	+	0.706332i	$0.750349\pi$
$644$	0.560081	+	0.970089i	0.0220703	+	0.0382269i
$645$	−7.04381	−	6.40045i	−0.277350	−	0.252018i
$646$	−7.23697	+	12.5348i	−0.284735	+	0.493175i
$647$	0.680937			0.0267704			0.0133852	−	0.999910i	$-0.495739\pi$
$647$	0.680937			0.0267704			0.0133852	+	0.999910i	$0.495739\pi$
$648$	26.9234	−	5.21333i	1.05765	−	0.204799i
$649$	−55.2478			−2.16866
$650$	−0.624867	+	1.08230i	−0.0245093	+	0.0424514i
$651$	2.62605	+	2.38620i	0.102923	+	0.0935226i
$652$	0.0231844	+	0.0401566i	0.000907971	+	0.00157265i
$653$	−4.27083	−	7.39729i	−0.167130	−	0.289478i	0.770279	−	0.637707i	$-0.220117\pi$
$653$	−4.27083	−	7.39729i	−0.167130	−	0.289478i	−0.937410	+	0.348228i	$0.886783\pi$
$654$	11.2084	−	3.58563i	0.438284	−	0.140209i
$655$	2.26354	−	3.92057i	0.0884439	−	0.153189i
$656$	−30.1930			−1.17884
$657$	0.512430	+	5.34189i	0.0199918	+	0.208407i
$658$	4.29684			0.167508
$659$	11.3653	−	19.6852i	0.442728	−	0.766827i	−0.555163	−	0.831741i	$-0.687344\pi$
$659$	11.3653	−	19.6852i	0.442728	−	0.766827i	0.997891	+	0.0649148i	$0.0206776\pi$
$660$	−0.596308	+	2.74405i	−0.0232113	+	0.106812i
$661$	21.4416	+	37.1380i	0.833983	+	1.44450i	0.894856	+	0.446356i	$0.147278\pi$
$661$	21.4416	+	37.1380i	0.833983	+	1.44450i	−0.0608726	+	0.998146i	$0.519388\pi$
$662$	13.1568	+	22.7883i	0.511355	+	0.885693i
$663$	−1.27744	+	5.87842i	−0.0496115	+	0.228299i
$664$	−6.24854	+	10.8228i	−0.242490	+	0.420006i
$665$	0.991882			0.0384635
$666$	−32.0902	−	14.6383i	−1.24347	−	0.567221i
$667$	−50.5585			−1.95763
$668$	−1.54478	+	2.67563i	−0.0597692	+	0.103523i
$669$	23.4408	−	7.49883i	0.906275	−	0.289922i
$670$	−4.49639	−	7.78798i	−0.173711	−	0.300876i
$671$	6.89945	+	11.9502i	0.266350	+	0.461332i
$672$	−0.926656	−	0.842019i	−0.0357465	−	0.0324816i
$673$	0.735479	−	1.27389i	0.0283506	−	0.0491047i	−0.851502	−	0.524351i	$-0.824308\pi$
$673$	0.735479	−	1.27389i	0.0283506	−	0.0491047i	0.879853	+	0.475247i	$0.157641\pi$
$674$	4.45499			0.171600
$675$	−2.04858	−	4.77528i	−0.0788498	−	0.183801i
$676$	−0.438165			−0.0168525
$677$	9.91398	−	17.1715i	0.381025	−	0.659955i	−0.610184	−	0.792260i	$-0.708904\pi$
$677$	9.91398	−	17.1715i	0.381025	−	0.659955i	0.991209	+	0.132305i	$0.0422378\pi$
$678$	6.75635	+	6.13925i	0.259476	+	0.235776i
$679$	−0.754473	−	1.30679i	−0.0289540	−	0.0501499i
$680$	−5.29140	−	9.16497i	−0.202916	−	0.351461i
$681$	37.8669	−	12.1138i	1.45106	−	0.464202i
$682$	15.9237	−	27.5807i	0.609752	−	1.05612i
$683$	21.0542			0.805617			0.402808	−	0.915284i	$-0.368034\pi$
$683$	21.0542			0.805617			0.402808	+	0.915284i	$0.368034\pi$
$684$	3.56948	−	2.54415i	0.136482	−	0.0972781i
$685$	15.5383			0.593686
$686$	−2.58567	+	4.47851i	−0.0987214	+	0.170990i
$687$	−2.35859	+	10.8536i	−0.0899858	+	0.414091i
$688$	−8.05462	−	13.9510i	−0.307079	−	0.531877i
$689$	−1.00748	−	1.74500i	−0.0383819	−	0.0664793i
$690$	−3.95066	+	18.1799i	−0.150399	+	0.692097i
$691$	−1.90512	+	3.29977i	−0.0724742	+	0.125529i	−0.899985	−	0.435921i	$-0.856423\pi$
$691$	−1.90512	+	3.29977i	−0.0724742	+	0.125529i	0.827511	+	0.561450i	$0.189756\pi$
$692$	−3.43484			−0.130573
$693$	−2.68871	+	1.91638i	−0.102136	+	0.0727973i
$694$	37.7947			1.43467
$695$	7.68678	−	13.3139i	0.291576	−	0.505025i
$696$	29.5696	−	9.45945i	1.12083	−	0.358560i
$697$	17.8846	+	30.9770i	0.677427	+	1.17334i
$698$	4.30321	+	7.45337i	0.162879	+	0.282114i
$699$	4.00271	+	3.63711i	0.151396	+	0.137568i
$700$	−0.0651656	+	0.112870i	−0.00246303	+	0.00426609i
$701$	−0.907151			−0.0342626			−0.0171313	−	0.999853i	$-0.505453\pi$
$701$	−0.907151			−0.0342626			−0.0171313	+	0.999853i	$0.505453\pi$
$702$	−3.88821	+	5.20110i	−0.146751	+	0.196303i
$703$	−31.3712			−1.18319
$704$	−16.4666	+	28.5209i	−0.620607	+	1.07492i
$705$	−14.8174	−	13.4640i	−0.558054	−	0.507083i
$706$	6.15170	+	10.6551i	0.231522	+	0.401008i
$707$	−2.28840	−	3.96363i	−0.0860642	−	0.149068i
$708$	−10.7930	+	3.45272i	−0.405624	+	0.129761i
$709$	−5.81125	+	10.0654i	−0.218246	+	0.378014i	−0.954272	−	0.298940i	$-0.903367\pi$
$709$	−5.81125	+	10.0654i	−0.218246	+	0.378014i	0.736026	+	0.676954i	$0.236700\pi$
$710$	−16.5699			−0.621857
$711$	1.16530	+	0.531561i	0.0437020	+	0.0199351i
$712$	−15.6730			−0.587372
$713$	−29.5969	+	51.2633i	−1.10841	+	1.91983i
$714$	0.474862	−	2.18519i	0.0177713	−	0.0817787i
$715$	−1.85005	−	3.20439i	−0.0691881	−	0.119837i
$716$	4.86337	+	8.42360i	0.181753	+	0.314805i
$717$	0.394411	−	1.81498i	0.0147296	−	0.0677816i
$718$	−12.8152	+	22.1966i	−0.478260	+	0.828371i
$719$	31.3794			1.17026			0.585128	−	0.810941i	$-0.301044\pi$
$719$	31.3794			1.17026			0.585128	+	0.810941i	$0.301044\pi$
$720$	−0.839826	−	8.75486i	−0.0312985	−	0.326274i
$721$	3.31179			0.123338
$722$	4.92405	−	8.52871i	0.183254	−	0.317406i
$723$	−5.46815	+	1.74929i	−0.203363	+	0.0650567i
$724$	−1.53056	−	2.65101i	−0.0568829	−	0.0985241i
$725$	−2.94125	−	5.09439i	−0.109235	−	0.189201i
$726$	4.31069	+	3.91697i	0.159985	+	0.145372i
$727$	17.1485	−	29.7020i	0.636002	−	1.10159i	−0.350300	−	0.936638i	$-0.613920\pi$
$727$	17.1485	−	29.7020i	0.636002	−	1.10159i	0.986302	−	0.164950i	$-0.0527463\pi$
$728$	0.906341			0.0335912
$729$	−7.64054	−	25.8964i	−0.282983	−	0.959125i
$730$	2.23553			0.0827406
$731$	−9.54218	+	16.5275i	−0.352930	+	0.611293i
$732$	2.09468	+	1.90336i	0.0774215	+	0.0703501i
$733$	11.5052	+	19.9276i	0.424955	+	0.736044i	0.996416	−	0.0845849i	$-0.0269564\pi$
$733$	11.5052	+	19.9276i	0.424955	+	0.736044i	−0.571461	+	0.820629i	$0.693623\pi$
$734$	5.28627	+	9.15608i	0.195120	+	0.337957i
$735$	11.4019	−	3.64752i	0.420565	−	0.134541i
$736$	10.4439	−	18.0893i	0.384966	−	0.666781i
$737$	26.6251			0.980747
$738$	3.68705	+	38.4361i	0.135722	+	1.41485i
$739$	−0.517286			−0.0190287			−0.00951434	−	0.999955i	$-0.503029\pi$
$739$	−0.517286			−0.0190287			−0.00951434	+	0.999955i	$0.503029\pi$
$740$	2.06105	−	3.56985i	0.0757658	−	0.131230i
$741$	−1.22650	+	5.64404i	−0.0450567	+	0.207339i
$742$	0.374511	+	0.648671i	0.0137487	+	0.0238135i
$743$	21.9775	+	38.0662i	0.806278	+	1.39651i	0.915425	+	0.402488i	$0.131855\pi$
$743$	21.9775	+	38.0662i	0.806278	+	1.39651i	−0.109147	+	0.994026i	$0.534812\pi$
$744$	7.71868	−	35.5193i	0.282981	−	1.30220i
$745$	8.83487	−	15.3024i	0.323685	−	0.560638i
$746$	−23.7857			−0.870857
$747$	11.1944	+	5.10644i	0.409582	+	0.186835i
$748$	5.63082			0.205883
$749$	1.88364	−	3.26256i	0.0688268	−	0.119211i
$750$	−2.06168	+	0.659540i	−0.0752818	+	0.0240830i
$751$	−6.41225	−	11.1063i	−0.233986	−	0.405276i	0.724991	−	0.688758i	$-0.241844\pi$
$751$	−6.41225	−	11.1063i	−0.233986	−	0.405276i	−0.958978	+	0.283482i	$0.908510\pi$
$752$	−16.9437	−	29.3473i	−0.617873	−	1.07019i
$753$	11.2767	+	10.2467i	0.410945	+	0.373411i
$754$	−3.67578	+	6.36663i	−0.133864	+	0.231859i
$755$	10.9942			0.400121
$756$	−0.405490	+	0.542407i	−0.0147475	+	0.0197272i
$757$	45.0965			1.63906			0.819530	−	0.573037i	$-0.194235\pi$
$757$	45.0965			1.63906			0.819530	+	0.573037i	$0.194235\pi$
$758$	15.5688	−	26.9659i	0.565483	−	0.979445i
$759$	−40.7659	−	37.0425i	−1.47971	−	1.34456i
$760$	−5.08042	−	8.79955i	−0.184286	−	0.319193i
$761$	−5.34539	−	9.25849i	−0.193770	−	0.335620i	0.752726	−	0.658333i	$-0.228738\pi$
$761$	−5.34539	−	9.25849i	−0.193770	−	0.335620i	−0.946497	+	0.322714i	$0.895405\pi$
$762$	−4.04031	+	1.29251i	−0.146365	+	0.0468228i
$763$	−0.808547	+	1.40044i	−0.0292714	+	0.0506995i
$764$	6.35387			0.229875
$765$	−8.48473	+	6.04751i	−0.306766	+	0.218648i
$766$	33.6544			1.21598
$767$	7.46570	−	12.9310i	0.269571	−	0.466910i
$768$	−3.66863	+	16.8821i	−0.132380	+	0.609179i
$769$	−8.03126	−	13.9106i	−0.289615	−	0.501627i	0.684103	−	0.729385i	$-0.260194\pi$
$769$	−8.03126	−	13.9106i	−0.289615	−	0.501627i	−0.973718	+	0.227758i	$0.926861\pi$
$770$	0.687722	+	1.19117i	0.0247838	+	0.0429268i
$771$	3.95609	−	18.2049i	0.142475	−	0.655633i
$772$	0.171721	−	0.297430i	0.00618038	−	0.0107047i
$773$	−27.8349			−1.00115			−0.500576	−	0.865693i	$-0.666878\pi$
$773$	−27.8349			−1.00115			−0.500576	+	0.865693i	$0.666878\pi$
$774$	−16.7762	+	11.9573i	−0.603009	+	0.429795i
$775$	−6.88721			−0.247396
$776$	−7.72883	+	13.3867i	−0.277449	+	0.480555i
$777$	4.61632	−	1.47678i	0.165610	−	0.0529793i
$778$	12.6153	+	21.8503i	0.452280	+	0.783373i
$779$	17.1715	+	29.7419i	0.615233	+	1.06561i
$780$	−0.561677	−	0.510376i	−0.0201113	−	0.0182744i
$781$	24.5294	−	42.4861i	0.877730	−	1.52027i
$782$	37.3053			1.33403
$783$	−12.0508	−	28.0906i	−0.430659	−	1.00388i
$784$	20.2624			0.723657
$785$	−7.46655	+	12.9324i	−0.266492	+	0.461579i
$786$	−7.25246	−	6.59005i	−0.258687	−	0.235059i
$787$	−10.2615	−	17.7735i	−0.365784	−	0.633556i	0.623118	−	0.782128i	$-0.285866\pi$
$787$	−10.2615	−	17.7735i	−0.365784	−	0.633556i	−0.988902	+	0.148572i	$0.952532\pi$
$788$	−3.60763	−	6.24859i	−0.128516	−	0.222597i
$789$	−33.1167	+	10.5942i	−1.17899	+	0.377164i
$790$	0.266778	−	0.462074i	0.00949155	−	0.0164398i
$791$	−1.25446			−0.0446034
$792$	30.7729	+	14.0373i	1.09347	+	0.498795i
$793$	−3.72932			−0.132432
$794$	−6.43026	+	11.1375i	−0.228201	+	0.395256i
$795$	0.741113	−	3.41041i	0.0262846	−	0.120955i
$796$	−5.40569	−	9.36294i	−0.191600	−	0.331860i
$797$	8.55060	+	14.8101i	0.302878	+	0.524600i	0.976787	−	0.214215i	$-0.0687192\pi$
$797$	8.55060	+	14.8101i	0.302878	+	0.524600i	−0.673909	+	0.738815i	$0.735386\pi$
$798$	0.455929	−	2.09806i	0.0161397	−	0.0742707i
$799$	−20.0729	+	34.7673i	−0.710129	+	1.22998i
$800$	2.43029			0.0859238
$801$	1.47348	+	15.3605i	0.0520629	+	0.542735i
$802$	28.4424			1.00434
$803$	−3.30938	+	5.73202i	−0.116786	+	0.202278i
$804$	5.20136	−	1.66394i	0.183438	−	0.0586826i
$805$	−1.27824	−	2.21398i	−0.0450522	−	0.0780327i
$806$	4.30359	+	7.45404i	0.151588	+	0.262557i
$807$	−7.84090	−	7.12474i	−0.276013	−	0.250803i
$808$	−23.4424	+	40.6034i	−0.824700	+	1.42842i
$809$	−2.51316			−0.0883579			−0.0441790	−	0.999024i	$-0.514067\pi$
$809$	−2.51316			−0.0883579			−0.0441790	+	0.999024i	$0.514067\pi$
$810$	−11.0425	+	2.13822i	−0.387994	+	0.0751294i
$811$	39.9682			1.40347			0.701736	−	0.712437i	$-0.252409\pi$
$811$	39.9682			1.40347			0.701736	+	0.712437i	$0.252409\pi$
$812$	−0.383336	+	0.663958i	−0.0134525	+	0.0233003i
$813$	−29.4831	−	26.7902i	−1.03402	−	0.939573i
$814$	−21.7512	−	37.6742i	−0.762380	−	1.32048i
$815$	−0.0529125	−	0.0916472i	−0.00185345	−	0.00321026i
$816$	−16.7973	+	5.37354i	−0.588024	+	0.188112i
$817$	−9.16172	+	15.8686i	−0.320528	+	0.555171i
$818$	−20.2194			−0.706953
$819$	−0.0852086	−	0.888266i	−0.00297743	−	0.0310385i
$820$	−4.51260			−0.157587
$821$	2.95732	−	5.12223i	0.103211	−	0.178767i	−0.809795	−	0.586713i	$-0.800422\pi$
$821$	2.95732	−	5.12223i	0.103211	−	0.178767i	0.913006	+	0.407946i	$0.133755\pi$
$822$	7.14232	−	32.8671i	0.249117	−	1.14637i
$823$	−1.58203	−	2.74016i	−0.0551462	−	0.0955160i	0.837134	−	0.546997i	$-0.184229\pi$
$823$	−1.58203	−	2.74016i	−0.0551462	−	0.0955160i	−0.892281	+	0.451481i	$0.850896\pi$
$824$	−16.9630	−	29.3808i	−0.590934	−	1.02353i
$825$	1.36092	−	6.26261i	0.0473812	−	0.218036i
$826$	−2.77523	+	4.80684i	−0.0965626	+	0.167251i
$827$	−31.5111			−1.09575			−0.547875	−	0.836560i	$-0.684563\pi$
$827$	−31.5111			−1.09575			−0.547875	+	0.836560i	$0.684563\pi$
$828$	−10.2788	−	4.68878i	−0.357214	−	0.162946i
$829$	0.505503			0.0175568			0.00877842	−	0.999961i	$-0.497206\pi$
$829$	0.505503			0.0175568			0.00877842	+	0.999961i	$0.497206\pi$
$830$	2.56280	−	4.43891i	0.0889562	−	0.154077i
$831$	−30.3101	+	9.69633i	−1.05144	+	0.336362i
$832$	−4.45029	−	7.70813i	−0.154286	−	0.267231i
$833$	−12.0023	−	20.7886i	−0.415854	−	0.720281i
$834$	−24.6287	−	22.3792i	−0.852823	−	0.774929i
$835$	3.52556	−	6.10645i	0.122007	−	0.211323i
$836$	5.40631			0.186981
$837$	−35.5367	−	4.22544i	−1.22833	−	0.146053i
$838$	34.8559			1.20408
$839$	−17.7544	+	30.7515i	−0.612950	+	1.06166i	0.377791	+	0.925891i	$0.376684\pi$
$839$	−17.7544	+	30.7515i	−0.612950	+	1.06166i	−0.990740	+	0.135769i	$0.956649\pi$
$840$	1.16183	+	1.05571i	0.0400868	+	0.0364254i
$841$	−2.80187	−	4.85298i	−0.0966163	−	0.167344i
$842$	−11.6651	−	20.2046i	−0.402007	−	0.696296i
$843$	22.9622	−	7.34571i	0.790859	−	0.253000i
$844$	−4.88769	+	8.46573i	−0.168241	+	0.291402i
$845$	1.00000			0.0344010
$846$	−35.2904	+	25.1533i	−1.21331	+	0.864789i
$847$	−0.800369			−0.0275010
$848$	2.95361	−	5.11580i	0.101427	−	0.175677i
$849$	5.69020	−	26.1848i	0.195287	−	0.898660i
$850$	2.17024	+	3.75896i	0.0744386	+	0.128931i
$851$	40.4282	+	70.0238i	1.38586	+	2.40038i
$852$	2.13677	−	9.83287i	0.0732046	−	0.336869i
$853$	−22.3604	+	38.7293i	−0.765604	+	1.32607i	0.174322	+	0.984689i	$0.444227\pi$
$853$	−22.3604	+	38.7293i	−0.765604	+	1.32607i	−0.939926	+	0.341377i	$0.889107\pi$
$854$	1.38630			0.0474384
$855$	−8.14644	+	5.80639i	−0.278602	+	0.198574i
$856$	−38.5921			−1.31905
$857$	2.40863	−	4.17186i	0.0822771	−	0.142508i	−0.821951	−	0.569559i	$-0.807114\pi$
$857$	2.40863	−	4.17186i	0.0822771	−	0.142508i	0.904228	+	0.427051i	$0.140447\pi$
$858$	−7.62843	+	2.44037i	−0.260430	+	0.0833128i
$859$	5.56161	+	9.63299i	0.189760	+	0.328673i	0.945170	−	0.326579i	$-0.105896\pi$
$859$	5.56161	+	9.63299i	0.189760	+	0.328673i	−0.755410	+	0.655252i	$0.772562\pi$
$860$	−1.20383	−	2.08509i	−0.0410503	−	0.0711011i
$861$	−3.92690	−	3.56823i	−0.133828	−	0.121605i
$862$	−20.9634	+	36.3097i	−0.714016	+	1.23671i
$863$	−9.37409			−0.319098			−0.159549	−	0.987190i	$-0.551004\pi$
$863$	−9.37409			−0.319098			−0.159549	+	0.987190i	$0.551004\pi$
$864$	12.5398	+	1.49103i	0.426614	+	0.0507259i
$865$	7.83915			0.266539
$866$	9.77044	−	16.9229i	0.332013	−	0.575063i
$867$	−6.32923	−	5.75114i	−0.214952	−	0.195319i
$868$	0.448809	+	0.777360i	0.0152336	+	0.0263853i
$869$	0.789855	+	1.36807i	0.0267940	+	0.0464086i
$870$	−12.1278	+	3.87974i	−0.411171	+	0.131536i
$871$	−3.59788	+	6.23171i	−0.121909	+	0.211153i
$872$	16.5655			0.560979
$873$	13.8464	+	6.31616i	0.468629	+	0.213770i
$874$	35.8179			1.21156
$875$	0.148724	−	0.257597i	0.00502779	−	0.00870838i
$876$	−0.288283	+	1.32660i	−0.00974018	+	0.0448217i
$877$	3.43696	+	5.95300i	0.116058	+	0.201018i	0.918202	−	0.396112i	$-0.129641\pi$
$877$	3.43696	+	5.95300i	0.116058	+	0.201018i	−0.802144	+	0.597130i	$0.796307\pi$
$878$	5.98561	+	10.3674i	0.202004	+	0.349882i
$879$	−9.13650	+	42.0438i	−0.308166	+	1.41810i
$880$	5.42377	−	9.39424i	0.182835	−	0.316680i
$881$	20.5232			0.691445			0.345722	−	0.938337i	$-0.387634\pi$
$881$	20.5232			0.691445			0.345722	+	0.938337i	$0.387634\pi$
$882$	−2.47437	−	25.7943i	−0.0833162	−	0.868539i
$883$	−20.4330			−0.687624			−0.343812	−	0.939038i	$-0.611718\pi$
$883$	−20.4330			−0.687624			−0.343812	+	0.939038i	$0.611718\pi$
$884$	−0.760899	+	1.31792i	−0.0255918	+	0.0443263i
$885$	24.6322	−	7.87996i	0.828003	−	0.264882i
$886$	8.50412	+	14.7296i	0.285702	+	0.494850i
$887$	−12.8721	−	22.2951i	−0.432203	−	0.748597i	0.564860	−	0.825187i	$-0.308930\pi$
$887$	−12.8721	−	22.2951i	−0.432203	−	0.748597i	−0.997063	+	0.0765899i	$0.975597\pi$
$888$	−36.7462	−	33.3899i	−1.23312	−	1.12049i
$889$	0.291457	−	0.504819i	0.00977516	−	0.0169311i
$890$	6.42821			0.215474
$891$	10.8643	−	31.4789i	0.363969	−	1.05458i
$892$	6.22597			0.208461
$893$	−19.2726	+	33.3811i	−0.644933	+	1.11706i
$894$	−28.3072	−	25.7218i	−0.946735	−	0.860264i
$895$	−11.0994	−	19.2247i	−0.371012	−	0.642612i
$896$	0.931425	+	1.61328i	0.0311167	+	0.0538958i
$897$	14.1787	−	4.53583i	0.473412	−	0.151447i
$898$	−10.6460	+	18.4394i	−0.355261	+	0.615331i
$899$	−40.5140			−1.35122
$900$	−0.125519	−	1.30849i	−0.00418397	−	0.0436162i
$901$	−6.99819			−0.233143
$902$	−23.8117	+	41.2431i	−0.792844	+	1.37325i
$903$	0.601157	−	2.76637i	0.0200053	−	0.0920589i
$904$	6.42533	+	11.1290i	0.213703	+	0.370145i
$905$	3.49312	+	6.05027i	0.116115	+	0.201118i
$906$	5.05361	−	23.2554i	0.167895	−	0.772608i
$907$	−13.4403	+	23.2793i	−0.446278	+	0.772976i	−0.998140	−	0.0609590i	$-0.980584\pi$
$907$	−13.4403	+	23.2793i	−0.446278	+	0.772976i	0.551862	+	0.833935i	$0.313917\pi$
$908$	10.0576			0.333773
$909$	41.9976	+	19.1576i	1.39297	+	0.635418i
$910$	−0.371731			−0.0123228
$911$	−5.38848	+	9.33311i	−0.178528	+	0.309220i	−0.941377	−	0.337357i	$-0.890467\pi$
$911$	−5.38848	+	9.33311i	−0.178528	+	0.309220i	0.762848	+	0.646577i	$0.223800\pi$
$912$	−16.1276	+	5.15929i	−0.534038	+	0.170841i
$913$	7.58773	+	13.1423i	0.251117	+	0.434948i
$914$	−2.94149	−	5.09481i	−0.0972958	−	0.168521i
$915$	−4.78057	−	4.34393i	−0.158041	−	0.143606i
$916$	−1.40488	+	2.43333i	−0.0464187	+	0.0803995i
$917$	1.34657			0.0444677
$918$	8.89181	+	20.7270i	0.293473	+	0.684093i
$919$	−2.40175			−0.0792264			−0.0396132	−	0.999215i	$-0.512613\pi$
$919$	−2.40175			−0.0792264			−0.0396132	+	0.999215i	$0.512613\pi$
$920$	−13.0943	+	22.6801i	−0.431708	+	0.747739i
$921$	−4.84302	−	4.40067i	−0.159583	−	0.145007i
$922$	−8.54385	−	14.7984i	−0.281377	−	0.487359i
$923$	6.62937	+	11.4824i	0.218208	+	0.377948i
$924$	−0.795546	+	0.254499i	−0.0261715	+	0.00837240i
$925$	−4.70383	+	8.14728i	−0.154661	+	0.267881i
$926$	11.6477			0.382766
$927$	−27.2001	+	19.3869i	−0.893369	+	0.636750i
$928$	14.2962			0.469295
$929$	−4.80524	+	8.32292i	−0.157655	+	0.273066i	−0.934023	−	0.357214i	$-0.883727\pi$
$929$	−4.80524	+	8.32292i	−0.157655	+	0.273066i	0.776368	+	0.630280i	$0.217060\pi$
$930$	−3.16578	+	14.5681i	−0.103810	+	0.477706i
$931$	−11.5237	−	19.9597i	−0.377675	−	0.654152i
$932$	0.684087	+	1.18487i	0.0224080	+	0.0388118i
$933$	8.21050	−	37.7826i	0.268800	−	1.23695i
$934$	−18.3688	+	31.8156i	−0.601044	+	1.04104i
$935$	−12.8509			−0.420270
$936$	−7.44388	+	5.30563i	−0.243311	+	0.173420i
$937$	−8.19764			−0.267805			−0.133903	−	0.990994i	$-0.542751\pi$
$937$	−8.19764			−0.267805			−0.133903	+	0.990994i	$0.542751\pi$
$938$	1.33744	−	2.31652i	0.0436690	−	0.0756370i
$939$	18.1193	−	5.79644i	0.591300	−	0.189160i
$940$	−2.53238	−	4.38621i	−0.0825970	−	0.143062i
$941$	24.8432	+	43.0297i	0.809866	+	1.40273i	0.912956	+	0.408057i	$0.133794\pi$
$941$	24.8432	+	43.0297i	0.809866	+	1.40273i	−0.103090	+	0.994672i	$0.532873\pi$
$942$	23.9231	+	21.7380i	0.779456	+	0.708263i
$943$	44.2580	−	76.6571i	1.44124	−	2.49630i
$944$	43.7741			1.42473
$945$	0.925428	−	1.23791i	0.0301042	−	0.0402691i
$946$	−25.4091			−0.826122
$947$	−13.4244	+	23.2517i	−0.436234	+	0.755580i	−0.997395	−	0.0721264i	$-0.977021\pi$
$947$	−13.4244	+	23.2517i	−0.436234	+	0.755580i	0.561161	+	0.827707i	$0.310355\pi$
$948$	0.239800	+	0.217898i	0.00778836	+	0.00707699i
$949$	−0.894401	−	1.54915i	−0.0290335	−	0.0502875i
$950$	2.08371	+	3.60909i	0.0676044	+	0.117094i
$951$	−25.0979	+	8.02892i	−0.813854	+	0.260356i
$952$	1.57392	−	2.72610i	0.0510109	−	0.0883535i
$953$	−51.4277			−1.66591			−0.832954	−	0.553342i	$-0.813352\pi$
$953$	−51.4277			−1.66591			−0.832954	+	0.553342i	$0.813352\pi$
$954$	−6.87316	−	3.13526i	−0.222527	−	0.101508i
$955$	−14.5011			−0.469245
$956$	0.234929	−	0.406910i	0.00759816	−	0.0131604i
$957$	8.00562	−	36.8398i	0.258785	−	1.19086i
$958$	−14.5913	−	25.2728i	−0.471422	−	0.816527i
$959$	2.31091	+	4.00262i	0.0746232	+	0.129251i
$960$	3.27369	−	15.0647i	0.105658	−	0.486210i
$961$	−8.21683	+	14.2320i	−0.265059	+	0.459096i
$962$	11.7571			0.379064
$963$	3.62819	+	37.8224i	0.116917	+	1.21881i
$964$	−1.45236			−0.0467774
$965$	−0.391910	+	0.678809i	−0.0126160	+	0.0218516i
$966$	−5.27065	+	1.68611i	−0.169580	+	0.0542496i
$967$	17.8101	+	30.8480i	0.572733	+	0.992003i	0.996284	+	0.0861307i	$0.0274503\pi$
$967$	17.8101	+	30.8480i	0.572733	+	0.992003i	−0.423551	+	0.905872i	$0.639216\pi$
$968$	4.09949	+	7.10053i	0.131763	+	0.228220i
$969$	14.8463	+	13.4903i	0.476932	+	0.433371i
$970$	3.16994	−	5.49049i	0.101781	−	0.176289i
$971$	53.3540			1.71221			0.856105	−	0.516802i	$-0.172878\pi$
$971$	53.3540			1.71221			0.856105	+	0.516802i	$0.172878\pi$
$972$	0.155129	−	6.82855i	0.00497577	−	0.219026i
$973$	4.57284			0.146598
$974$	−11.0655	+	19.1660i	−0.354561	+	0.614118i
$975$	1.28189	+	1.16480i	0.0410532	+	0.0373036i
$976$	−5.46660	−	9.46843i	−0.174982	−	0.303077i
$977$	4.79134	+	8.29884i	0.153289	+	0.265504i	0.932435	−	0.361339i	$-0.117680\pi$
$977$	4.79134	+	8.29884i	0.153289	+	0.265504i	−0.779146	+	0.626842i	$0.784347\pi$
$978$	−0.218177	+	0.0697959i	−0.00697653	+	0.00223183i
$979$	−9.51604	+	16.4823i	−0.304134	+	0.526776i
$980$	3.02839			0.0967382
$981$	−1.55739	−	16.2352i	−0.0497235	−	0.518349i
$982$	−20.2771			−0.647069
$983$	−2.80079	+	4.85111i	−0.0893314	+	0.154726i	−0.907229	−	0.420638i	$-0.861806\pi$
$983$	−2.80079	+	4.85111i	−0.0893314	+	0.154726i	0.817897	+	0.575364i	$0.195140\pi$
$984$	−11.5422	+	53.1142i	−0.367952	+	1.69322i
$985$	8.23349	+	14.2608i	0.262341	+	0.454388i
$986$	12.7664	+	22.1121i	0.406566	+	0.704192i
$987$	1.26459	−	5.81933i	0.0402525	−	0.185231i
$988$	−0.730561	+	1.26537i	−0.0232422	+	0.0402567i
$989$	47.2270			1.50173
$990$	−12.6213	−	5.75734i	−0.401132	−	0.182980i
$991$	19.9861			0.634879			0.317440	−	0.948279i	$-0.397177\pi$
$991$	19.9861			0.634879			0.317440	+	0.948279i	$0.397177\pi$
$992$	8.36896	−	14.4955i	0.265715	−	0.460232i
$993$	34.7350	−	11.1119i	1.10228	−	0.352625i
$994$	−2.46434	−	4.26836i	−0.0781641	−	0.135384i
$995$	12.3371	+	21.3685i	0.391113	+	0.677428i
$996$	2.30364	+	2.09323i	0.0729936	+	0.0663267i
$997$	−14.8014	+	25.6368i	−0.468765	+	0.811924i	−0.999363	−	0.0356993i	$-0.988634\pi$
$997$	−14.8014	+	25.6368i	−0.468765	+	0.811924i	0.530598	+	0.847624i	$0.321967\pi$
$998$	−0.366755			−0.0116094
$999$	−29.2694	+	39.1525i	−0.926043	+	1.23873i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.f.196.3	✓	16
3.2	odd	2		1755.2.i.e.586.6		16
9.2	odd	6		5265.2.a.be.1.3		8
9.4	even	3	inner	585.2.i.f.391.3	yes	16
9.5	odd	6		1755.2.i.e.1171.6		16
9.7	even	3		5265.2.a.bb.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.f.196.3	✓	16	1.1	even	1	trivial
585.2.i.f.391.3	yes	16	9.4	even	3	inner
1755.2.i.e.586.6		16	3.2	odd	2
1755.2.i.e.1171.6		16	9.5	odd	6
5265.2.a.bb.1.6		8	9.7	even	3
5265.2.a.be.1.3		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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.624867 + 1.08230i) q^{2} +(1.28189 + 1.16480i) q^{3} +(0.219082 + 0.379462i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.06168 + 0.659540i) q^{6} +(0.148724 - 0.257597i) q^{7} -3.04706 q^{8} +(0.286466 + 2.98629i) q^{9} +O(q^{10})\)	\(q+(-0.624867 + 1.08230i) q^{2} +(1.28189 + 1.16480i) q^{3} +(0.219082 + 0.379462i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.06168 + 0.659540i) q^{6} +(0.148724 - 0.257597i) q^{7} -3.04706 q^{8} +(0.286466 + 2.98629i) q^{9} +1.24973 q^{10} +(-1.85005 + 3.20439i) q^{11} +(-0.161160 + 0.741615i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(0.185865 + 0.321928i) q^{14} +(0.367806 - 1.69255i) q^{15} +(1.46584 - 2.53891i) q^{16} -3.47312 q^{17} +(-3.41107 - 1.55599i) q^{18} -3.33464 q^{19} +(0.219082 - 0.379462i) q^{20} +(0.490698 - 0.156976i) q^{21} +(-2.31207 - 4.00463i) q^{22} +(4.29737 + 7.44327i) q^{23} +(-3.90598 - 3.54922i) q^{24} +(-0.500000 + 0.866025i) q^{25} +1.24973 q^{26} +(-3.11123 + 4.16176i) q^{27} +0.130331 q^{28} +(-2.94125 + 5.09439i) q^{29} +(1.60202 + 1.45569i) q^{30} +(3.44361 + 5.96450i) q^{31} +(-1.21515 - 2.10469i) q^{32} +(-6.10404 + 1.95271i) q^{33} +(2.17024 - 3.75896i) q^{34} -0.297448 q^{35} +(-1.07042 + 0.762946i) q^{36} +9.40767 q^{37} +(2.08371 - 3.60909i) q^{38} +(0.367806 - 1.69255i) q^{39} +(1.52353 + 2.63883i) q^{40} +(-5.14943 - 8.91907i) q^{41} +(-0.136725 + 0.629172i) q^{42} +(2.74744 - 4.75870i) q^{43} -1.62126 q^{44} +(2.44297 - 1.74123i) q^{45} -10.7411 q^{46} +(5.77951 - 10.0104i) q^{47} +(4.83638 - 1.54718i) q^{48} +(3.45576 + 5.98556i) q^{49} +(-0.624867 - 1.08230i) q^{50} +(-4.45215 - 4.04550i) q^{51} +(0.219082 - 0.379462i) q^{52} +2.01496 q^{53} +(-2.56018 - 5.96783i) q^{54} +3.70011 q^{55} +(-0.453170 + 0.784914i) q^{56} +(-4.27463 - 3.88420i) q^{57} +(-3.67578 - 6.36663i) q^{58} +(7.46570 + 12.9310i) q^{59} +(0.722837 - 0.231239i) q^{60} +(1.86466 - 3.22969i) q^{61} -8.60718 q^{62} +(0.811865 + 0.370340i) q^{63} +8.90058 q^{64} +(-0.500000 + 0.866025i) q^{65} +(1.70079 - 7.82659i) q^{66} +(-3.59788 - 6.23171i) q^{67} +(-0.760899 - 1.31792i) q^{68} +(-3.16120 + 14.5470i) q^{69} +(0.185865 - 0.321928i) q^{70} -13.2587 q^{71} +(-0.872877 - 9.09940i) q^{72} +1.78880 q^{73} +(-5.87854 + 10.1819i) q^{74} +(-1.64969 + 0.527744i) q^{75} +(-0.730561 - 1.26537i) q^{76} +(0.550294 + 0.953138i) q^{77} +(1.60202 + 1.45569i) q^{78} +(0.213468 - 0.369738i) q^{79} -2.93168 q^{80} +(-8.83588 + 1.71094i) q^{81} +12.8708 q^{82} +(2.05068 - 3.55188i) q^{83} +(0.167070 + 0.151810i) q^{84} +(1.73656 + 3.00781i) q^{85} +(3.43357 + 5.94711i) q^{86} +(-9.70431 + 3.10445i) q^{87} +(5.63722 - 9.76395i) q^{88} +5.14366 q^{89} +(0.358006 + 3.73207i) q^{90} -0.297448 q^{91} +(-1.88296 + 3.26138i) q^{92} +(-2.53316 + 11.6569i) q^{93} +(7.22285 + 12.5103i) q^{94} +(1.66732 + 2.88788i) q^{95} +(0.893876 - 4.11338i) q^{96} +(2.53649 - 4.39333i) q^{97} -8.63757 q^{98} +(-10.0992 - 4.60685i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + q^{2} - 2 q^{3} - 5 q^{4} - 8 q^{5} - 13 q^{6} + 6 q^{7} - 12 q^{8} + 4 q^{9}+O(q^{10}) \) 16 * q + q^2 - 2 * q^3 - 5 * q^4 - 8 * q^5 - 13 * q^6 + 6 * q^7 - 12 * q^8 + 4 * q^9	\( 16 q + q^{2} - 2 q^{3} - 5 q^{4} - 8 q^{5} - 13 q^{6} + 6 q^{7} - 12 q^{8} + 4 q^{9} - 2 q^{10} + 9 q^{11} - 16 q^{12} - 8 q^{13} - 3 q^{14} + q^{15} + 13 q^{16} + 12 q^{17} + 23 q^{18} - 22 q^{19} - 5 q^{20} + 15 q^{21} + 4 q^{22} + 3 q^{23} - 12 q^{24} - 8 q^{25} - 2 q^{26} + 22 q^{27} - 26 q^{28} + 8 q^{29} + 8 q^{30} + 18 q^{31} + 3 q^{32} - 26 q^{33} + 9 q^{34} - 12 q^{35} + 5 q^{36} - 36 q^{37} - 8 q^{38} + q^{39} + 6 q^{40} - 17 q^{41} - 45 q^{42} + 17 q^{43} + 10 q^{44} + q^{45} + 6 q^{46} + 11 q^{47} + 35 q^{48} + 16 q^{49} + q^{50} - 16 q^{51} - 5 q^{52} + 20 q^{53} + 44 q^{54} - 18 q^{55} - q^{56} - 25 q^{57} + 10 q^{58} + 7 q^{59} + 5 q^{60} + 21 q^{61} - 58 q^{62} - 30 q^{63} - 20 q^{64} - 8 q^{65} + 68 q^{66} + 13 q^{67} - 16 q^{68} - 13 q^{69} - 3 q^{70} - 68 q^{71} + 36 q^{72} - 32 q^{73} - 4 q^{74} + q^{75} + 2 q^{76} + 18 q^{77} + 8 q^{78} + 37 q^{79} - 26 q^{80} - 32 q^{81} + 2 q^{82} + 3 q^{83} + 27 q^{84} - 6 q^{85} - 2 q^{86} - 20 q^{87} + 19 q^{88} + 28 q^{89} - 16 q^{90} - 12 q^{91} - 14 q^{92} + 19 q^{93} + 44 q^{94} + 11 q^{95} - 35 q^{96} + 17 q^{97} + 90 q^{98} - 44 q^{99}+O(q^{100}) \) 16 * q + q^2 - 2 * q^3 - 5 * q^4 - 8 * q^5 - 13 * q^6 + 6 * q^7 - 12 * q^8 + 4 * q^9 - 2 * q^10 + 9 * q^11 - 16 * q^12 - 8 * q^13 - 3 * q^14 + q^15 + 13 * q^16 + 12 * q^17 + 23 * q^18 - 22 * q^19 - 5 * q^20 + 15 * q^21 + 4 * q^22 + 3 * q^23 - 12 * q^24 - 8 * q^25 - 2 * q^26 + 22 * q^27 - 26 * q^28 + 8 * q^29 + 8 * q^30 + 18 * q^31 + 3 * q^32 - 26 * q^33 + 9 * q^34 - 12 * q^35 + 5 * q^36 - 36 * q^37 - 8 * q^38 + q^39 + 6 * q^40 - 17 * q^41 - 45 * q^42 + 17 * q^43 + 10 * q^44 + q^45 + 6 * q^46 + 11 * q^47 + 35 * q^48 + 16 * q^49 + q^50 - 16 * q^51 - 5 * q^52 + 20 * q^53 + 44 * q^54 - 18 * q^55 - q^56 - 25 * q^57 + 10 * q^58 + 7 * q^59 + 5 * q^60 + 21 * q^61 - 58 * q^62 - 30 * q^63 - 20 * q^64 - 8 * q^65 + 68 * q^66 + 13 * q^67 - 16 * q^68 - 13 * q^69 - 3 * q^70 - 68 * q^71 + 36 * q^72 - 32 * q^73 - 4 * q^74 + q^75 + 2 * q^76 + 18 * q^77 + 8 * q^78 + 37 * q^79 - 26 * q^80 - 32 * q^81 + 2 * q^82 + 3 * q^83 + 27 * q^84 - 6 * q^85 - 2 * q^86 - 20 * q^87 + 19 * q^88 + 28 * q^89 - 16 * q^90 - 12 * q^91 - 14 * q^92 + 19 * q^93 + 44 * q^94 + 11 * q^95 - 35 * q^96 + 17 * q^97 + 90 * q^98 - 44 * q^99

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