LMFDB - Embedded newform 430.2.q.b.31.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(31,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.q (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			31.4
Character	$\chi$	$=$	430.31
Dual form			430.2.q.b.111.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.900969 + 0.433884i) q^{2} +(2.64426 - 1.80282i) q^{3} +(0.623490 - 0.781831i) q^{4} +(0.733052 + 0.680173i) q^{5} +(-1.60018 + 2.77159i) q^{6} +(-0.952135 - 1.64915i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(2.64590 - 6.74164i) q^{9} +O(q^{10})$	\(q+(-0.900969 + 0.433884i) q^{2} +(2.64426 - 1.80282i) q^{3} +(0.623490 - 0.781831i) q^{4} +(0.733052 + 0.680173i) q^{5} +(-1.60018 + 2.77159i) q^{6} +(-0.952135 - 1.64915i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(2.64590 - 6.74164i) q^{9} +(-0.955573 - 0.294755i) q^{10} +(-3.96139 - 4.96742i) q^{11} +(0.239163 - 3.19141i) q^{12} +(-1.49830 + 0.462164i) q^{13} +(1.57338 + 1.07271i) q^{14} +(3.16461 + 0.476988i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(0.279587 - 0.259418i) q^{17} +(0.541215 + 7.22202i) q^{18} +(2.57779 + 6.56811i) q^{19} +(0.988831 - 0.149042i) q^{20} +(-5.49081 - 2.64423i) q^{21} +(5.72437 + 2.75671i) q^{22} +(4.39919 - 0.663072i) q^{23} +(1.16922 + 2.97913i) q^{24} +(0.0747301 + 0.997204i) q^{25} +(1.14940 - 1.06648i) q^{26} +(-3.02111 - 13.2364i) q^{27} +(-1.88300 - 0.283817i) q^{28} +(5.19388 + 3.54113i) q^{29} +(-3.05817 + 0.943321i) q^{30} +(-0.477364 + 6.36998i) q^{31} +(0.623490 + 0.781831i) q^{32} +(-19.4303 - 5.99345i) q^{33} +(-0.139341 + 0.355036i) q^{34} +(0.423740 - 1.85653i) q^{35} +(-3.62113 - 6.27199i) q^{36} +(-1.30379 + 2.25824i) q^{37} +(-5.17231 - 4.79920i) q^{38} +(-3.12869 + 3.92325i) q^{39} +(-0.826239 + 0.563320i) q^{40} +(-5.01530 + 2.41524i) q^{41} +6.09434 q^{42} +(6.53675 + 0.520533i) q^{43} -6.35357 q^{44} +(6.52506 - 3.14230i) q^{45} +(-3.67584 + 2.50614i) q^{46} +(5.53234 - 6.93734i) q^{47} +(-2.34603 - 2.17679i) q^{48} +(1.68688 - 2.92176i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(0.271613 - 1.19001i) q^{51} +(-0.572840 + 1.45957i) q^{52} +(6.58507 + 2.03122i) q^{53} +(8.46497 + 10.6147i) q^{54} +(0.474803 - 6.33580i) q^{55} +(1.81967 - 0.561293i) q^{56} +(18.6575 + 12.7205i) q^{57} +(-6.21596 - 0.936906i) q^{58} +(-1.96083 - 8.59098i) q^{59} +(2.34603 - 2.17679i) q^{60} +(0.844754 + 11.2725i) q^{61} +(-2.33374 - 5.94628i) q^{62} +(-13.6372 + 2.05548i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(-1.41268 - 0.680312i) q^{65} +(20.1066 - 3.03058i) q^{66} +(2.87616 + 7.32835i) q^{67} +(-0.0285021 - 0.380334i) q^{68} +(10.4372 - 9.68430i) q^{69} +(0.423740 + 1.85653i) q^{70} +(-2.23187 - 0.336401i) q^{71} +(5.98384 + 4.07971i) q^{72} +(-6.16777 + 1.90251i) q^{73} +(0.194865 - 2.60030i) q^{74} +(1.99539 + 2.50214i) q^{75} +(6.74238 + 2.07975i) q^{76} +(-4.42023 + 11.2626i) q^{77} +(1.11662 - 4.89221i) q^{78} +(-1.70317 - 2.94998i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-15.9246 - 14.7758i) q^{81} +(3.47069 - 4.35211i) q^{82} +(10.0315 - 6.83936i) q^{83} +(-5.49081 + 2.64423i) q^{84} +0.381401 q^{85} +(-6.11526 + 2.36720i) q^{86} +20.1180 q^{87} +(5.72437 - 2.75671i) q^{88} +(-12.9668 + 8.84059i) q^{89} +(-4.51548 + 5.66223i) q^{90} +(2.18876 + 2.03087i) q^{91} +(2.22444 - 3.85285i) q^{92} +(10.2217 + 17.7045i) q^{93} +(-1.97447 + 8.65072i) q^{94} +(-2.57779 + 6.56811i) q^{95} +(3.05817 + 0.943321i) q^{96} +(-5.52187 - 6.92420i) q^{97} +(-0.252121 + 3.36432i) q^{98} +(-43.9700 + 13.5629i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9}+O(q^{10}) $ 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9	\( 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9} - 4 q^{10} - 9 q^{11} - q^{12} - 11 q^{13} + 7 q^{14} - 6 q^{15} - 8 q^{16} - 11 q^{17} - 15 q^{18} + 31 q^{19} - 4 q^{20} + 4 q^{21} + 12 q^{22} + 4 q^{23} + 6 q^{24} + 4 q^{25} + 31 q^{26} + 44 q^{27} + 13 q^{29} + q^{30} - q^{31} - 8 q^{32} - 30 q^{33} - 25 q^{34} + 14 q^{35} - 36 q^{36} - 27 q^{37} - 4 q^{38} + 4 q^{39} - 4 q^{40} + 16 q^{41} + 4 q^{42} - 7 q^{43} - 30 q^{44} + 12 q^{45} - 52 q^{46} - 43 q^{47} - q^{48} - 23 q^{49} - 24 q^{50} - 7 q^{51} - 25 q^{52} + 73 q^{53} - 61 q^{54} + 27 q^{55} + 7 q^{56} + 136 q^{57} - 36 q^{58} + 58 q^{59} + q^{60} - 61 q^{61} + 27 q^{62} + 32 q^{63} - 8 q^{64} - q^{65} + 12 q^{66} + 39 q^{67} + 17 q^{68} - 34 q^{69} + 14 q^{70} + 60 q^{71} + 27 q^{72} + 3 q^{73} + 29 q^{74} - 12 q^{75} + 17 q^{76} - 27 q^{77} - 17 q^{78} - 2 q^{79} + 24 q^{80} - 165 q^{81} + 2 q^{82} + 74 q^{83} + 4 q^{84} - 8 q^{85} + 14 q^{86} + 88 q^{87} + 12 q^{88} + 23 q^{89} - 2 q^{90} - 39 q^{91} + 4 q^{92} - 46 q^{93} + 55 q^{94} - 31 q^{95} - q^{96} - 85 q^{97} + 33 q^{98} - 168 q^{99}+O(q^{100}) \) 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9 - 4 * q^10 - 9 * q^11 - q^12 - 11 * q^13 + 7 * q^14 - 6 * q^15 - 8 * q^16 - 11 * q^17 - 15 * q^18 + 31 * q^19 - 4 * q^20 + 4 * q^21 + 12 * q^22 + 4 * q^23 + 6 * q^24 + 4 * q^25 + 31 * q^26 + 44 * q^27 + 13 * q^29 + q^30 - q^31 - 8 * q^32 - 30 * q^33 - 25 * q^34 + 14 * q^35 - 36 * q^36 - 27 * q^37 - 4 * q^38 + 4 * q^39 - 4 * q^40 + 16 * q^41 + 4 * q^42 - 7 * q^43 - 30 * q^44 + 12 * q^45 - 52 * q^46 - 43 * q^47 - q^48 - 23 * q^49 - 24 * q^50 - 7 * q^51 - 25 * q^52 + 73 * q^53 - 61 * q^54 + 27 * q^55 + 7 * q^56 + 136 * q^57 - 36 * q^58 + 58 * q^59 + q^60 - 61 * q^61 + 27 * q^62 + 32 * q^63 - 8 * q^64 - q^65 + 12 * q^66 + 39 * q^67 + 17 * q^68 - 34 * q^69 + 14 * q^70 + 60 * q^71 + 27 * q^72 + 3 * q^73 + 29 * q^74 - 12 * q^75 + 17 * q^76 - 27 * q^77 - 17 * q^78 - 2 * q^79 + 24 * q^80 - 165 * q^81 + 2 * q^82 + 74 * q^83 + 4 * q^84 - 8 * q^85 + 14 * q^86 + 88 * q^87 + 12 * q^88 + 23 * q^89 - 2 * q^90 - 39 * q^91 + 4 * q^92 - 46 * q^93 + 55 * q^94 - 31 * q^95 - q^96 - 85 * q^97 + 33 * q^98 - 168 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{17}{21}\right)$

Coefficient data

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

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

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

$2$	−0.900969	+	0.433884i	−0.637081	+	0.306802i
$2$	−0.900969	+	0.433884i	−0.637081	+	0.306802i
$3$	2.64426	−	1.80282i	1.52666	−	1.04086i	0.547735	−	0.836652i	$-0.315490\pi$
$3$	2.64426	−	1.80282i	1.52666	−	1.04086i	0.978927	−	0.204209i	$-0.0654622\pi$
$4$	0.623490	−	0.781831i	0.311745	−	0.390916i
$5$	0.733052	+	0.680173i	0.327831	+	0.304182i
$5$	0.733052	+	0.680173i	0.327831	+	0.304182i
$6$	−1.60018	+	2.77159i	−0.653270	+	1.13150i
$7$	−0.952135	−	1.64915i	−0.359873	−	0.623318i	0.628066	−	0.778160i	$-0.283847\pi$
$7$	−0.952135	−	1.64915i	−0.359873	−	0.623318i	−0.987939	+	0.154841i	$0.950513\pi$
$8$	−0.222521	+	0.974928i	−0.0786730	+	0.344689i
$9$	2.64590	−	6.74164i	0.881966	−	2.24721i
$10$	−0.955573	−	0.294755i	−0.302179	−	0.0932098i
$11$	−3.96139	−	4.96742i	−1.19440	−	1.49773i	−0.821832	−	0.569730i	$-0.807048\pi$
$11$	−3.96139	−	4.96742i	−1.19440	−	1.49773i	−0.372570	−	0.928004i	$-0.621523\pi$
$12$	0.239163	−	3.19141i	0.0690403	−	0.921279i
$13$	−1.49830	+	0.462164i	−0.415554	+	0.128181i	−0.495480	−	0.868619i	$-0.665008\pi$
$13$	−1.49830	+	0.462164i	−0.415554	+	0.128181i	0.0799262	+	0.996801i	$0.474532\pi$
$14$	1.57338	+	1.07271i	0.420504	+	0.286695i
$15$	3.16461	+	0.476988i	0.817099	+	0.123158i
$16$	−0.222521	−	0.974928i	−0.0556302	−	0.243732i
$17$	0.279587	−	0.259418i	0.0678097	−	0.0629182i	−0.645540	−	0.763726i	$-0.723368\pi$
$17$	0.279587	−	0.259418i	0.0678097	−	0.0629182i	0.713350	+	0.700808i	$0.247177\pi$
$18$	0.541215	+	7.22202i	0.127566	+	1.70225i
$19$	2.57779	+	6.56811i	0.591386	+	1.50683i	0.842405	+	0.538845i	$0.181139\pi$
$19$	2.57779	+	6.56811i	0.591386	+	1.50683i	−0.251019	+	0.967982i	$0.580766\pi$
$20$	0.988831	−	0.149042i	0.221109	−	0.0333269i
$21$	−5.49081	−	2.64423i	−1.19819	−	0.577019i
$22$	5.72437	+	2.75671i	1.22044	+	0.587733i
$23$	4.39919	−	0.663072i	0.917295	−	0.138260i	0.326607	−	0.945160i	$-0.394095\pi$
$23$	4.39919	−	0.663072i	0.917295	−	0.138260i	0.590688	+	0.806900i	$0.298856\pi$
$24$	1.16922	+	2.97913i	0.238666	+	0.608112i
$25$	0.0747301	+	0.997204i	0.0149460	+	0.199441i
$26$	1.14940	−	1.06648i	0.225415	−	0.209155i
$27$	−3.02111	−	13.2364i	−0.581413	−	2.54734i
$28$	−1.88300	−	0.283817i	−0.355854	−	0.0536363i
$29$	5.19388	+	3.54113i	0.964479	+	0.657571i	0.939656	−	0.342121i	$-0.111145\pi$
$29$	5.19388	+	3.54113i	0.964479	+	0.657571i	0.0248234	+	0.999692i	$0.492098\pi$
$30$	−3.05817	+	0.943321i	−0.558343	+	0.172226i
$31$	−0.477364	+	6.36998i	−0.0857371	+	1.14408i	0.773945	+	0.633253i	$0.218281\pi$
$31$	−0.477364	+	6.36998i	−0.0857371	+	1.14408i	−0.859682	+	0.510830i	$0.829338\pi$
$32$	0.623490	+	0.781831i	0.110218	+	0.138210i
$33$	−19.4303	−	5.99345i	−3.38238	−	1.04333i
$34$	−0.139341	+	0.355036i	−0.0238968	+	0.0608882i
$35$	0.423740	−	1.85653i	0.0716251	−	0.313810i
$36$	−3.62113	−	6.27199i	−0.603522	−	1.04533i
$37$	−1.30379	+	2.25824i	−0.214342	+	0.371252i	−0.953069	−	0.302753i	$-0.902094\pi$
$37$	−1.30379	+	2.25824i	−0.214342	+	0.371252i	0.738727	+	0.674005i	$0.235427\pi$
$38$	−5.17231	−	4.79920i	−0.839059	−	0.778533i
$39$	−3.12869	+	3.92325i	−0.500991	+	0.628223i
$40$	−0.826239	+	0.563320i	−0.130640	+	0.0890687i
$41$	−5.01530	+	2.41524i	−0.783258	+	0.377197i	−0.782379	−	0.622802i	$-0.785994\pi$
$41$	−5.01530	+	2.41524i	−0.783258	+	0.377197i	−0.000878928		1.00000i	$0.500280\pi$
$42$	6.09434			0.940377
$43$	6.53675	+	0.520533i	0.996844	+	0.0793806i
$43$	6.53675	+	0.520533i	0.996844	+	0.0793806i
$44$	−6.35357			−0.957837
$45$	6.52506	−	3.14230i	0.972698	−	0.468427i
$46$	−3.67584	+	2.50614i	−0.541973	+	0.369511i
$47$	5.53234	−	6.93734i	0.806975	−	1.01191i	−0.192556	−	0.981286i	$-0.561678\pi$
$47$	5.53234	−	6.93734i	0.806975	−	1.01191i	0.999531	−	0.0306285i	$-0.00975086\pi$
$48$	−2.34603	−	2.17679i	−0.338620	−	0.314193i
$49$	1.68688	−	2.92176i	0.240983	−	0.417394i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	0.271613	−	1.19001i	0.0380334	−	0.166635i
$52$	−0.572840	+	1.45957i	−0.0794386	+	0.202406i
$53$	6.58507	+	2.03122i	0.904529	+	0.279010i	0.711916	−	0.702265i	$-0.247828\pi$
$53$	6.58507	+	2.03122i	0.904529	+	0.279010i	0.192613	+	0.981275i	$0.438304\pi$
$54$	8.46497	+	10.6147i	1.15194	+	1.44448i
$55$	0.474803	−	6.33580i	0.0640224	−	0.854319i
$56$	1.81967	−	0.561293i	0.243163	−	0.0750060i
$57$	18.6575	+	12.7205i	2.47124	+	1.68487i
$58$	−6.21596	−	0.936906i	−0.816196	−	0.123022i
$59$	−1.96083	−	8.59098i	−0.255279	−	1.11845i	−0.926233	−	0.376951i	$-0.876972\pi$
$59$	−1.96083	−	8.59098i	−0.255279	−	1.11845i	0.670954	−	0.741499i	$-0.265885\pi$
$60$	2.34603	−	2.17679i	0.302871	−	0.281023i
$61$	0.844754	+	11.2725i	0.108160	+	1.44329i	0.742297	+	0.670071i	$0.233736\pi$
$61$	0.844754	+	11.2725i	0.108160	+	1.44329i	−0.634138	+	0.773220i	$0.718645\pi$
$62$	−2.33374	−	5.94628i	−0.296385	−	0.755178i
$63$	−13.6372	+	2.05548i	−1.71812	+	0.258966i
$64$	−0.900969	−	0.433884i	−0.112621	−	0.0542355i
$65$	−1.41268	−	0.680312i	−0.175222	−	0.0843824i
$66$	20.1066	−	3.03058i	2.47495	−	0.373038i
$67$	2.87616	+	7.32835i	0.351379	+	0.895300i	0.991861	+	0.127326i	$0.0406396\pi$
$67$	2.87616	+	7.32835i	0.351379	+	0.895300i	−0.640482	+	0.767974i	$0.721265\pi$
$68$	−0.0285021	−	0.380334i	−0.00345639	−	0.0461223i
$69$	10.4372	−	9.68430i	1.25649	−	1.16585i
$70$	0.423740	+	1.85653i	0.0506466	+	0.221897i
$71$	−2.23187	−	0.336401i	−0.264875	−	0.0399234i	0.0152621	−	0.999884i	$-0.495142\pi$
$71$	−2.23187	−	0.336401i	−0.264875	−	0.0399234i	−0.280137	+	0.959960i	$0.590380\pi$
$72$	5.98384	+	4.07971i	0.705203	+	0.480799i
$73$	−6.16777	+	1.90251i	−0.721883	+	0.222671i	−0.633861	−	0.773447i	$-0.718531\pi$
$73$	−6.16777	+	1.90251i	−0.721883	+	0.222671i	−0.0880221	+	0.996119i	$0.528055\pi$
$74$	0.194865	−	2.60030i	0.0226526	−	0.302278i
$75$	1.99539	+	2.50214i	0.230408	+	0.288922i
$76$	6.74238	+	2.07975i	0.773404	+	0.238564i
$77$	−4.42023	+	11.2626i	−0.503732	+	1.28349i
$78$	1.11662	−	4.89221i	0.126432	−	0.553934i
$79$	−1.70317	−	2.94998i	−0.191622	−	0.331899i	0.754166	−	0.656684i	$-0.228041\pi$
$79$	−1.70317	−	2.94998i	−0.191622	−	0.331899i	−0.945788	+	0.324785i	$0.894708\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−15.9246	−	14.7758i	−1.76939	−	1.64176i
$82$	3.47069	−	4.35211i	0.383274	−	0.480611i
$83$	10.0315	−	6.83936i	1.10110	−	0.750717i	0.130507	−	0.991447i	$-0.458339\pi$
$83$	10.0315	−	6.83936i	1.10110	−	0.750717i	0.970592	+	0.240730i	$0.0773870\pi$
$84$	−5.49081	+	2.64423i	−0.599096	+	0.288510i
$85$	0.381401			0.0413687
$86$	−6.11526	+	2.36720i	−0.659425	+	0.255262i
$87$	20.1180			2.15687
$88$	5.72437	−	2.75671i	0.610220	−	0.293866i
$89$	−12.9668	+	8.84059i	−1.37447	+	0.937100i	−0.374523	+	0.927218i	$0.622193\pi$
$89$	−12.9668	+	8.84059i	−1.37447	+	0.937100i	−0.999951	+	0.00988248i	$0.996854\pi$
$90$	−4.51548	+	5.66223i	−0.475973	+	0.596852i
$91$	2.18876	+	2.03087i	0.229444	+	0.212893i
$92$	2.22444	−	3.85285i	0.231914	−	0.401687i
$93$	10.2217	+	17.7045i	1.05994	+	1.83587i
$94$	−1.97447	+	8.65072i	−0.203651	+	0.892253i
$95$	−2.57779	+	6.56811i	−0.264476	+	0.673874i
$96$	3.05817	+	0.943321i	0.312123	+	0.0962773i
$97$	−5.52187	−	6.92420i	−0.560660	−	0.703046i	0.418019	−	0.908438i	$-0.362724\pi$
$97$	−5.52187	−	6.92420i	−0.560660	−	0.703046i	−0.978680	+	0.205392i	$0.934153\pi$
$98$	−0.252121	+	3.36432i	−0.0254681	+	0.339848i
$99$	−43.9700	+	13.5629i	−4.41915	+	1.36313i
$100$	0.826239	+	0.563320i	0.0826239	+	0.0563320i
$101$	−10.7368	−	1.61831i	−1.06835	−	0.161028i	−0.408753	−	0.912645i	$-0.634036\pi$
$101$	−10.7368	−	1.61831i	−1.06835	−	0.161028i	−0.659600	+	0.751617i	$0.729274\pi$
$102$	0.271613	+	1.19001i	0.0268937	+	0.117829i
$103$	1.72918	−	1.60445i	0.170382	−	0.158091i	−0.590373	−	0.807130i	$-0.701019\pi$
$103$	1.72918	−	1.60445i	0.170382	−	0.158091i	0.760755	+	0.649039i	$0.224829\pi$
$104$	−0.117174	−	1.56358i	−0.0114898	−	0.153321i
$105$	−2.22651	−	5.67306i	−0.217285	−	0.553634i
$106$	−6.81426	+	1.02708i	−0.661859	+	0.0997592i
$107$	−6.24938	−	3.00954i	−0.604150	−	0.290944i	0.106695	−	0.994292i	$-0.465973\pi$
$107$	−6.24938	−	3.00954i	−0.604150	−	0.290944i	−0.710845	+	0.703348i	$0.751687\pi$
$108$	−12.2322	−	5.89073i	−1.17705	−	0.566836i
$109$	6.45512	−	0.972953i	0.618288	−	0.0931920i	0.167573	−	0.985860i	$-0.446407\pi$
$109$	6.45512	−	0.972953i	0.618288	−	0.0931920i	0.450715	+	0.892668i	$0.351169\pi$
$110$	2.32122	+	5.91437i	0.221320	+	0.563913i
$111$	0.623638	+	8.32187i	0.0591931	+	0.789877i
$112$	−1.39593	+	1.29523i	−0.131903	+	0.122388i
$113$	1.22610	+	5.37190i	0.115342	+	0.505346i	0.999287	+	0.0377554i	$0.0120208\pi$
$113$	1.22610	+	5.37190i	0.115342	+	0.505346i	−0.883945	+	0.467591i	$0.845122\pi$
$114$	−22.3290	−	3.36556i	−2.09130	−	0.315213i
$115$	3.67584	+	2.50614i	0.342774	+	0.233699i
$116$	6.00690	−	1.85288i	0.557726	−	0.172036i
$117$	−0.848604	+	11.3238i	−0.0784535	+	1.04689i
$118$	5.49414	+	6.88943i	0.505776	+	0.634223i
$119$	−0.694023	−	0.214078i	−0.0636210	−	0.0196245i
$120$	−1.16922	+	2.97913i	−0.106735	+	0.271956i
$121$	−6.53496	+	28.6315i	−0.594087	+	2.60287i
$122$	−5.65203	−	9.78961i	−0.511711	−	0.886310i
$123$	−8.90749	+	15.4282i	−0.803161	+	1.39112i
$124$	4.68262	+	4.34484i	0.420512	+	0.390178i
$125$	−0.623490	+	0.781831i	−0.0557666	+	0.0699291i
$126$	11.3948	−	7.76888i	1.01513	−	0.692106i
$127$	1.73631	−	0.836160i	0.154072	−	0.0741972i	−0.355259	−	0.934768i	$-0.615607\pi$
$127$	1.73631	−	0.836160i	0.154072	−	0.0741972i	0.509331	+	0.860571i	$0.329893\pi$
$128$	1.00000			0.0883883
$129$	18.2233	−	10.4082i	1.60447	−	0.916389i
$130$	1.56796			0.137519
$131$	−14.4969	+	6.98132i	−1.26660	+	0.609961i	−0.941911	−	0.335861i	$-0.890973\pi$
$131$	−14.4969	+	6.98132i	−1.26660	+	0.609961i	−0.324685	+	0.945822i	$0.605258\pi$
$132$	−16.8005	+	11.4544i	−1.46229	+	0.996974i
$133$	8.37736	−	10.5049i	0.726409	−	0.910889i
$134$	−5.77098	−	5.35469i	−0.498537	−	0.462575i
$135$	6.78838	−	11.7578i	0.584251	−	1.01195i
$136$	0.190700	+	0.330303i	0.0163524	+	0.0283232i
$137$	2.87632	−	12.6020i	0.245741	−	1.07666i	−0.689955	−	0.723852i	$-0.742370\pi$
$137$	2.87632	−	12.6020i	0.245741	−	1.07666i	0.935696	−	0.352808i	$-0.114773\pi$
$138$	−5.20173	+	13.2538i	−0.442800	+	1.12824i
$139$	4.83562	+	1.49159i	0.410152	+	0.126515i	0.492963	−	0.870050i	$-0.335914\pi$
$139$	4.83562	+	1.49159i	0.410152	+	0.126515i	−0.0828111	+	0.996565i	$0.526390\pi$
$140$	−1.18729	−	1.48882i	−0.100345	−	0.125828i
$141$	2.12214	−	28.3179i	0.178716	−	2.38480i
$142$	2.15681	−	0.665287i	0.180995	−	0.0558297i
$143$	8.23111	+	5.61187i	0.688320	+	0.469288i
$144$	−7.16138	−	1.07940i	−0.596781	−	0.0899503i
$145$	1.39881	+	6.12857i	0.116164	+	0.508950i
$146$	4.73150	−	4.39019i	0.391582	−	0.363335i
$147$	−0.806877	−	10.7670i	−0.0665501	−	0.888050i
$148$	0.952659	+	2.42733i	0.0783081	+	0.199526i
$149$	−17.2629	+	2.60196i	−1.41423	+	0.213161i	−0.811299	−	0.584631i	$-0.801239\pi$
$149$	−17.2629	+	2.60196i	−1.41423	+	0.213161i	−0.602932	+	0.797792i	$0.706001\pi$
$150$	−2.88342	−	1.38858i	−0.235430	−	0.113377i
$151$	7.97882	+	3.84240i	0.649307	+	0.312690i	0.729390	−	0.684099i	$-0.239804\pi$
$151$	7.97882	+	3.84240i	0.649307	+	0.312690i	−0.0800828	+	0.996788i	$0.525518\pi$
$152$	−6.97705	+	1.05162i	−0.565913	+	0.0852977i
$153$	−1.00915	−	2.57127i	−0.0815847	−	0.207875i
$154$	−0.904152	−	12.0651i	−0.0728587	−	0.972231i
$155$	−4.68262	+	4.34484i	−0.376117	+	0.348986i
$156$	1.11662	+	4.89221i	0.0894008	+	0.391691i
$157$	9.08185	+	1.36887i	0.724811	+	0.109248i	0.501077	−	0.865403i	$-0.332937\pi$
$157$	9.08185	+	1.36887i	0.724811	+	0.109248i	0.223734	+	0.974650i	$0.428175\pi$
$158$	2.81446	+	1.91886i	0.223906	+	0.152657i
$159$	21.0746	−	6.50064i	1.67132	−	0.515534i
$160$	−0.0747301	+	0.997204i	−0.00590793	+	0.0788359i
$161$	−5.28212	−	6.62358i	−0.416290	−	0.522011i
$162$	20.7585	+	6.40315i	1.63094	+	0.503079i
$163$	−2.51391	+	6.40534i	−0.196905	+	0.501705i	−0.994889	−	0.100973i	$-0.967804\pi$
$163$	−2.51391	+	6.40534i	−0.196905	+	0.501705i	0.797984	+	0.602678i	$0.205900\pi$
$164$	−1.23868	+	5.42700i	−0.0967244	+	0.423777i
$165$	−10.1668	−	17.6095i	−0.791487	−	1.37090i
$166$	−6.07058	+	10.5145i	−0.471168	+	0.816087i
$167$	5.69798	+	5.28695i	0.440923	+	0.409116i	0.869145	−	0.494557i	$-0.164670\pi$
$167$	5.69798	+	5.28695i	0.440923	+	0.409116i	−0.428223	+	0.903673i	$0.640860\pi$
$168$	3.79976	−	4.76474i	0.293158	−	0.367608i
$169$	−8.70980	+	5.93824i	−0.669984	+	0.456788i
$170$	−0.343630	+	0.165484i	−0.0263552	+	0.0126920i
$171$	51.1004			3.90774
$172$	4.48256	−	4.78609i	0.341792	−	0.364936i
$173$	−2.81166			−0.213767			−0.106883	−	0.994272i	$-0.534087\pi$
$173$	−2.81166			−0.213767			−0.106883	+	0.994272i	$0.534087\pi$
$174$	−18.1257	+	8.72887i	−1.37410	+	0.661734i
$175$	1.57338	−	1.07271i	0.118936	−	0.0810895i
$176$	−3.96139	+	4.96742i	−0.298601	+	0.374433i
$177$	−20.6730	−	19.1817i	−1.55388	−	1.44179i
$178$	7.84686	−	13.5912i	0.588147	−	1.01870i
$179$	−2.67349	−	4.63062i	−0.199826	−	0.346109i	0.748646	−	0.662970i	$-0.230704\pi$
$179$	−2.67349	−	4.63062i	−0.199826	−	0.346109i	−0.948472	+	0.316861i	$0.897371\pi$
$180$	1.61156	−	7.06069i	0.120118	−	0.526273i
$181$	5.69408	−	14.5083i	0.423238	−	1.07839i	−0.547192	−	0.837007i	$-0.684303\pi$
$181$	5.69408	−	14.5083i	0.423238	−	1.07839i	0.970429	−	0.241385i	$-0.0776016\pi$
$182$	−2.85317	−	0.880085i	−0.211491	−	0.0652363i
$183$	22.5560	+	28.2843i	1.66739	+	2.09084i
$184$	−0.332465	+	4.43644i	−0.0245097	+	0.327059i
$185$	−2.49174	+	0.768600i	−0.183196	+	0.0565086i
$186$	−16.8911	−	11.5162i	−1.23852	−	0.844406i
$187$	−2.39619	−	0.361168i	−0.175227	−	0.0264112i
$188$	−1.97447	−	8.65072i	−0.144003	−	0.630918i
$189$	−18.9522	+	17.5851i	−1.37857	+	1.27912i
$190$	−0.527285	−	7.03612i	−0.0382532	−	0.510454i
$191$	2.33075	+	5.93864i	0.168647	+	0.429705i	0.990063	−	0.140624i	$-0.0449109\pi$
$191$	2.33075	+	5.93864i	0.168647	+	0.429705i	−0.821416	+	0.570329i	$0.806816\pi$
$192$	−3.16461	+	0.476988i	−0.228386	+	0.0344236i
$193$	−12.8113	−	6.16958i	−0.922175	−	0.444096i	−0.0883276	−	0.996091i	$-0.528152\pi$
$193$	−12.8113	−	6.16958i	−0.922175	−	0.444096i	−0.833847	+	0.551996i	$0.813867\pi$
$194$	7.97933	+	3.84264i	0.572882	+	0.275886i
$195$	−4.96198	+	0.747898i	−0.355335	+	0.0535581i
$196$	−1.23257	−	3.14054i	−0.0880409	−	0.224325i
$197$	1.44604	+	19.2961i	0.103026	+	1.37479i	0.773942	+	0.633256i	$0.218282\pi$
$197$	1.44604	+	19.2961i	0.103026	+	1.37479i	−0.670916	+	0.741533i	$0.734099\pi$
$198$	33.7308	−	31.2976i	2.39715	−	2.22423i
$199$	2.89960	+	12.7040i	0.205547	+	0.900562i	0.967488	+	0.252916i	$0.0813895\pi$
$199$	2.89960	+	12.7040i	0.205547	+	0.900562i	−0.761941	+	0.647647i	$0.775753\pi$
$200$	−0.988831	−	0.149042i	−0.0699209	−	0.0105389i
$201$	20.8170	+	14.1928i	1.46832	+	1.00108i
$202$	10.3757	−	3.20048i	0.730031	−	0.225185i
$203$	0.894562	−	11.9371i	0.0627859	−	0.837820i
$204$	−0.761043	−	0.954317i	−0.0532837	−	0.0668156i
$205$	−5.31926	−	1.64077i	−0.371513	−	0.114597i
$206$	−0.861797	+	2.19582i	−0.0600443	+	0.152990i
$207$	7.16962	−	31.4122i	0.498323	−	2.18330i
$208$	0.783980	+	1.35789i	0.0543592	+	0.0941529i
$209$	22.4149	−	38.8238i	1.55047	−	2.68550i
$210$	4.46746	+	4.14520i	0.308284	+	0.286046i
$211$	0.240292	−	0.301316i	0.0165424	−	0.0207435i	−0.773492	−	0.633807i	$-0.781491\pi$
$211$	0.240292	−	0.301316i	0.0165424	−	0.0207435i	0.790034	+	0.613063i	$0.210063\pi$
$212$	5.69380	−	3.88197i	0.391052	−	0.266615i
$213$	−6.50812	+	3.13415i	−0.445929	+	0.214748i
$214$	6.93629			0.474155
$215$	4.43772	+	4.82769i	0.302650	+	0.329246i
$216$	13.5768			0.923781
$217$	10.9595	−	5.27784i	0.743982	−	0.358283i
$218$	−5.39371	+	3.67737i	−0.365308	+	0.249063i
$219$	−12.8793	+	16.1501i	−0.870301	+	1.09132i
$220$	−4.65750	−	4.32152i	−0.314008	−	0.291357i
$221$	−0.299011	+	0.517902i	−0.0201136	+	0.0348378i
$222$	−4.17260	−	7.22716i	−0.280047	−	0.485055i
$223$	0.0769226	−	0.337020i	0.00515112	−	0.0225685i	−0.972287	−	0.233790i	$-0.924887\pi$
$223$	0.0769226	−	0.337020i	0.00515112	−	0.0225685i	0.977438	+	0.211222i	$0.0677442\pi$
$224$	0.695708	−	1.77263i	0.0464839	−	0.118439i
$225$	6.92051	+	2.13470i	0.461368	+	0.142313i
$226$	−3.43546	−	4.30793i	−0.228524	−	0.286559i
$227$	1.52824	−	20.3930i	0.101433	−	1.35353i	−0.681680	−	0.731651i	$-0.738750\pi$
$227$	1.52824	−	20.3930i	0.101433	−	1.35353i	0.783113	−	0.621880i	$-0.213631\pi$
$228$	21.5780	−	6.65593i	1.42904	−	0.440800i
$229$	−18.9650	−	12.9301i	−1.25324	−	0.854447i	−0.259458	−	0.965755i	$-0.583544\pi$
$229$	−18.9650	−	12.9301i	−1.25324	−	0.854447i	−0.993786	+	0.111308i	$0.964496\pi$
$230$	−4.39919	−	0.663072i	−0.290074	−	0.0437216i
$231$	8.61619	+	37.7500i	0.566903	+	2.48377i
$232$	−4.60809	+	4.27568i	−0.302536	+	0.280712i
$233$	−0.357440	−	4.76970i	−0.0234166	−	0.312473i	−0.996597	−	0.0824295i	$-0.973732\pi$
$233$	−0.357440	−	4.76970i	−0.0234166	−	0.312473i	0.973180	−	0.230044i	$-0.0738870\pi$
$234$	−4.14866	−	10.5706i	−0.271206	−	0.691023i
$235$	8.77408	−	1.32248i	0.572358	−	0.0862691i
$236$	−7.93926	−	3.82334i	−0.516802	−	0.248878i
$237$	−9.82193	−	4.72999i	−0.638003	−	0.307246i
$238$	0.718178	−	0.108248i	0.0465526	−	0.00701667i
$239$	8.65237	+	22.0459i	0.559675	+	1.42603i	0.878283	+	0.478142i	$0.158690\pi$
$239$	8.65237	+	22.0459i	0.559675	+	1.42603i	−0.318607	+	0.947887i	$0.603215\pi$
$240$	−0.239163	−	3.19141i	−0.0154379	−	0.206004i
$241$	6.60828	−	6.13159i	0.425677	−	0.394970i	−0.438034	−	0.898958i	$-0.644325\pi$
$241$	6.60828	−	6.13159i	0.425677	−	0.394970i	0.863711	+	0.503988i	$0.168135\pi$
$242$	−6.53496	−	28.6315i	−0.420083	−	1.84050i
$243$	−28.4715	−	4.29138i	−1.82644	−	0.275292i
$244$	9.33986	+	6.36781i	0.597923	+	0.407657i
$245$	3.22387	−	0.994433i	0.205966	−	0.0635320i
$246$	1.33131	−	17.7652i	0.0848815	−	1.13266i
$247$	−6.89785	−	8.64963i	−0.438900	−	0.550363i
$248$	−6.10405	−	1.88285i	−0.387608	−	0.119561i
$249$	14.1957	−	36.1700i	0.899615	−	2.29218i
$250$	0.222521	−	0.974928i	0.0140735	−	0.0616599i
$251$	0.436112	+	0.755367i	0.0275271	+	0.0476784i	0.879461	−	0.475971i	$-0.157903\pi$
$251$	0.436112	+	0.755367i	0.0275271	+	0.0476784i	−0.851934	+	0.523650i	$0.824570\pi$
$252$	−6.89561	+	11.9436i	−0.434383	+	0.752373i
$253$	−20.7207	−	19.2260i	−1.30270	−	1.20873i
$254$	−1.20156	+	1.50671i	−0.0753926	+	0.0945393i
$255$	1.00852	−	0.687599i	0.0631561	−	0.0430591i
$256$	−0.900969	+	0.433884i	−0.0563106	+	0.0271177i
$257$	−11.1035			−0.692615			−0.346308	−	0.938121i	$-0.612565\pi$
$257$	−11.1035			−0.692615			−0.346308	+	0.938121i	$0.612565\pi$
$258$	−11.9027	+	17.2842i	−0.741027	+	1.07607i
$259$	4.96555			0.308544
$260$	−1.41268	+	0.680312i	−0.0876109	+	0.0421912i
$261$	37.6155	−	25.6458i	2.32834	−	1.58743i
$262$	10.0321	−	12.5799i	0.619788	−	0.777189i
$263$	−7.78612	−	7.22447i	−0.480113	−	0.445480i	0.402611	−	0.915371i	$-0.368103\pi$
$263$	−7.78612	−	7.22447i	−0.480113	−	0.445480i	−0.882724	+	0.469891i	$0.844293\pi$
$264$	10.1668	−	17.6095i	0.625725	−	1.08379i
$265$	3.44561	+	5.96798i	0.211662	+	0.366610i
$266$	−2.98985	+	13.0994i	−0.183319	+	0.803174i
$267$	−18.3494	+	46.7536i	−1.12297	+	2.86127i
$268$	7.52279	+	2.32047i	0.459528	+	0.141745i
$269$	−13.0621	−	16.3794i	−0.796413	−	0.998670i	−0.999808	−	0.0195737i	$-0.993769\pi$
$269$	−13.0621	−	16.3794i	−0.796413	−	0.998670i	0.203395	−	0.979097i	$-0.434802\pi$
$270$	−1.01459	+	13.5388i	−0.0617461	+	0.823945i
$271$	−8.95704	+	2.76288i	−0.544101	+	0.167833i	−0.554608	−	0.832112i	$-0.687132\pi$
$271$	−8.95704	+	2.76288i	−0.544101	+	0.167833i	0.0105066	+	0.999945i	$0.496656\pi$
$272$	−0.315128	−	0.214851i	−0.0191075	−	0.0130272i
$273$	9.44895	+	1.42420i	0.571876	+	0.0861965i
$274$	2.87632	+	12.6020i	0.173765	+	0.761314i
$275$	4.65750	−	4.32152i	0.280858	−	0.260598i
$276$	−1.06401	−	14.1982i	−0.0640457	−	0.854630i
$277$	8.56916	+	21.8339i	0.514871	+	1.31187i	0.917947	+	0.396703i	$0.129846\pi$
$277$	8.56916	+	21.8339i	0.514871	+	1.31187i	−0.403076	+	0.915166i	$0.632059\pi$
$278$	−5.00393	+	0.754220i	−0.300116	+	0.0452351i
$279$	41.6810	+	20.0725i	2.49538	+	1.20171i
$280$	1.71569	+	0.826231i	0.102532	+	0.0493768i
$281$	11.9732	−	1.80467i	0.714259	−	0.107657i	0.218147	−	0.975916i	$-0.429999\pi$
$281$	11.9732	−	1.80467i	0.714259	−	0.107657i	0.496112	+	0.868259i	$0.334761\pi$
$282$	10.3747	+	26.4343i	0.617805	+	1.57414i
$283$	0.0240761	+	0.321273i	0.00143118	+	0.0190977i	0.997874	−	0.0651778i	$-0.0207615\pi$
$283$	0.0240761	+	0.321273i	0.00143118	+	0.0190977i	−0.996442	+	0.0842755i	$0.973142\pi$
$284$	−1.65456	+	1.53521i	−0.0981801	+	0.0910978i
$285$	5.02480	+	22.0151i	0.297643	+	1.30406i
$286$	−9.85087	−	1.48478i	−0.582494	−	0.0877969i
$287$	8.75832	+	5.97132i	0.516987	+	0.352476i
$288$	6.92051	−	2.13470i	0.407795	−	0.125788i
$289$	−1.25954	+	16.8074i	−0.0740906	+	0.988671i
$290$	−3.91937	−	4.91473i	−0.230153	−	0.288603i
$291$	−27.0843	−	8.35441i	−1.58771	−	0.489744i
$292$	−2.35810	+	6.00835i	−0.137998	+	0.351612i
$293$	5.12527	−	22.4553i	0.299421	−	1.31185i	−0.571571	−	0.820553i	$-0.693666\pi$
$293$	5.12527	−	22.4553i	0.299421	−	1.31185i	0.870992	−	0.491297i	$-0.163477\pi$
$294$	5.39861	+	9.35067i	0.314853	+	0.545342i
$295$	4.40595	−	7.63134i	0.256525	−	0.444314i
$296$	−1.91150	−	1.77361i	−0.111104	−	0.103089i
$297$	−53.7828	+	67.4415i	−3.12079	+	3.91335i
$298$	14.4244	−	9.83438i	0.835582	−	0.569690i
$299$	−6.28486	+	3.02663i	−0.363463	+	0.175035i
$300$	3.20035			0.184773
$301$	−5.36543	−	11.2757i	−0.309258	−	0.649918i
$302$	−8.85582			−0.509595
$303$	−31.3084	+	15.0773i	−1.79862	+	0.866170i
$304$	5.82982	−	3.97470i	0.334363	−	0.227965i
$305$	−7.04797	+	8.83788i	−0.403566	+	0.506055i
$306$	2.02484	+	1.87878i	0.115752	+	0.107403i
$307$	−0.315654	+	0.546729i	−0.0180153	+	0.0312035i	−0.874893	−	0.484317i	$-0.839068\pi$
$307$	−0.315654	+	0.546729i	−0.0180153	+	0.0312035i	0.856877	+	0.515521i	$0.172401\pi$
$308$	6.04945	+	10.4780i	0.344700	+	0.597037i
$309$	1.67987	−	7.35999i	0.0955645	−	0.418695i
$310$	2.33374	−	5.94628i	0.132548	−	0.337726i
$311$	−14.2725	−	4.40249i	−0.809321	−	0.249642i	−0.137639	−	0.990482i	$-0.543952\pi$
$311$	−14.2725	−	4.40249i	−0.809321	−	0.249642i	−0.671682	+	0.740840i	$0.734428\pi$
$312$	−3.12869	−	3.92325i	−0.177127	−	0.222110i
$313$	−0.346698	+	4.62636i	−0.0195965	+	0.261497i	0.978797	+	0.204834i	$0.0656653\pi$
$313$	−0.346698	+	4.62636i	−0.0195965	+	0.261497i	−0.998393	+	0.0566637i	$0.981954\pi$
$314$	−8.77640	+	2.70716i	−0.495281	+	0.152774i
$315$	−11.3948	−	7.76888i	−0.642027	−	0.437727i
$316$	−3.36830	−	0.507690i	−0.189482	−	0.0285598i
$317$	0.256746	+	1.12488i	0.0144203	+	0.0631794i	0.981626	−	0.190814i	$-0.0611129\pi$
$317$	0.256746	+	1.12488i	0.0144203	+	0.0631794i	−0.967206	+	0.253994i	$0.918256\pi$
$318$	−16.1670	+	15.0008i	−0.906600	+	0.841202i
$319$	−2.98469	−	39.8280i	−0.167111	−	2.22994i
$320$	−0.365341	−	0.930874i	−0.0204232	−	0.0520374i
$321$	−21.9506	+	3.30853i	−1.22517	+	0.184664i
$322$	7.63289	+	3.67581i	0.425364	+	0.204845i
$323$	2.42461	+	1.16763i	0.134909	+	0.0649686i
$324$	−21.4810	+	3.23774i	−1.19339	+	0.179874i
$325$	−0.572840	−	1.45957i	−0.0317754	−	0.0809625i
$326$	−0.514218	−	6.86176i	−0.0284799	−	0.380038i
$327$	15.3149	−	14.2102i	0.846918	−	0.785825i
$328$	−1.23868	−	5.42700i	−0.0683945	−	0.299656i
$329$	−16.7082	−	2.51836i	−0.921153	−	0.138842i
$330$	16.8005	+	11.4544i	0.924835	+	0.630542i
$331$	−26.5771	+	8.19794i	−1.46081	+	0.450600i	−0.920458	−	0.390841i	$-0.872184\pi$
$331$	−26.5771	+	8.19794i	−1.46081	+	0.450600i	−0.540350	+	0.841441i	$0.681708\pi$
$332$	0.907310	−	12.1072i	0.0497951	−	0.664469i
$333$	11.7745	+	14.7648i	0.645239	+	0.809104i
$334$	−7.42762	−	2.29112i	−0.406421	−	0.125364i
$335$	−2.87616	+	7.32835i	−0.157142	+	0.400390i
$336$	−1.35612	+	5.94154i	−0.0739823	+	0.324138i
$337$	−4.35384	−	7.54107i	−0.237169	−	0.410788i	0.722732	−	0.691128i	$-0.242886\pi$
$337$	−4.35384	−	7.54107i	−0.237169	−	0.410788i	−0.959901	+	0.280340i	$0.909553\pi$
$338$	5.27075	−	9.12921i	0.286691	−	0.496563i
$339$	12.9267	+	11.9942i	0.702083	+	0.651438i
$340$	0.237800	−	0.298191i	0.0128965	−	0.0161717i
$341$	33.5334	−	22.8627i	1.81594	−	1.23808i
$342$	−46.0398	+	22.1716i	−2.48955	+	1.19890i
$343$	−19.7544			−1.06664
$344$	−1.96205	+	6.25703i	−0.105786	+	0.337356i
$345$	14.2380			0.766548
$346$	2.53322	−	1.21994i	0.136187	−	0.0655841i
$347$	8.92816	−	6.08712i	0.479289	−	0.326774i	−0.299461	−	0.954109i	$-0.596807\pi$
$347$	8.92816	−	6.08712i	0.479289	−	0.326774i	0.778749	+	0.627335i	$0.215854\pi$
$348$	12.5434	−	15.7289i	0.672395	−	0.843156i
$349$	−3.19745	−	2.96680i	−0.171155	−	0.158809i	0.589944	−	0.807444i	$-0.299150\pi$
$349$	−3.19745	−	2.96680i	−0.171155	−	0.158809i	−0.761100	+	0.648635i	$0.775340\pi$
$350$	−0.952135	+	1.64915i	−0.0508937	+	0.0881505i
$351$	10.6439	+	18.4358i	0.568130	+	0.984030i
$352$	1.41380	−	6.19427i	0.0753559	−	0.330156i
$353$	−4.92212	+	12.5414i	−0.261978	+	0.667509i	−0.999973	−	0.00729657i	$-0.997677\pi$
$353$	−4.92212	+	12.5414i	−0.261978	+	0.667509i	0.737995	+	0.674806i	$0.235773\pi$
$354$	26.9483	+	8.31246i	1.43229	+	0.441802i
$355$	−1.40727	−	1.76466i	−0.0746901	−	0.0936584i
$356$	−1.17279	+	15.6498i	−0.0621579	+	0.829440i
$357$	−2.22112	+	0.685125i	−0.117554	+	0.0362606i
$358$	4.41789	+	3.01206i	0.233493	+	0.159192i
$359$	32.8774	+	4.95547i	1.73520	+	0.261539i	0.939105	−	0.343631i	$-0.111657\pi$
$359$	32.8774	+	4.95547i	1.73520	+	0.261539i	0.796096	+	0.605170i	$0.206895\pi$
$360$	1.61156	+	7.06069i	0.0849365	+	0.372131i
$361$	−22.5671	+	20.9392i	−1.18774	+	1.10206i
$362$	1.16472	+	15.5421i	0.0612162	+	0.816874i
$363$	34.3375	+	87.4905i	1.80225	+	4.59206i
$364$	2.95247	−	0.445013i	0.154751	−	0.0233250i
$365$	−5.81533	−	2.80051i	−0.304388	−	0.146586i
$366$	−32.5944	−	15.6966i	−1.70374	−	0.820476i
$367$	−25.6935	+	3.87267i	−1.34119	+	0.202152i	−0.780127	−	0.625621i	$-0.784846\pi$
$367$	−25.6935	+	3.87267i	−1.34119	+	0.202152i	−0.561063	+	0.827773i	$0.689608\pi$
$368$	−1.62536	−	4.14135i	−0.0847277	−	0.215883i
$369$	3.01271	+	40.2018i	0.156835	+	2.09282i
$370$	1.91150	−	1.77361i	0.0993740	−	0.0922056i
$371$	−2.92009	−	12.7937i	−0.151603	−	0.664218i
$372$	20.2150	+	3.04692i	1.04810	+	0.157976i
$373$	−26.3358	−	17.9554i	−1.36361	−	0.929696i	−0.363616	−	0.931549i	$-0.618458\pi$
$373$	−26.3358	−	17.9554i	−1.36361	−	0.929696i	−0.999998	+	0.00185275i	$0.999410\pi$
$374$	2.31560	−	0.714267i	0.119737	−	0.0369339i
$375$	−0.239163	+	3.19141i	−0.0123503	+	0.164803i
$376$	5.53234	+	6.93734i	0.285309	+	0.357766i
$377$	−9.41857	−	2.90524i	−0.485081	−	0.149628i
$378$	9.44546	−	24.0666i	0.485822	−	1.23785i
$379$	6.41229	−	28.0941i	0.329377	−	1.44310i	−0.490944	−	0.871191i	$-0.663348\pi$
$379$	6.41229	−	28.0941i	0.329377	−	1.44310i	0.820321	−	0.571904i	$-0.193795\pi$
$380$	3.52793	+	6.11055i	0.180979	+	0.313465i
$381$	3.08379	−	5.34128i	0.157987	−	0.273642i
$382$	−4.67661	−	4.33926i	−0.239276	−	0.222016i
$383$	11.2195	−	14.0688i	0.573289	−	0.718881i	−0.407663	−	0.913132i	$-0.633656\pi$
$383$	11.2195	−	14.0688i	0.573289	−	0.718881i	0.980952	+	0.194251i	$0.0622277\pi$
$384$	2.64426	−	1.80282i	0.134939	−	0.0920000i
$385$	−10.9007	+	5.24952i	−0.555553	+	0.267540i
$386$	14.2194			0.723750
$387$	20.8048	−	42.6911i	1.05757	−	2.17011i
$388$	−8.85638			−0.449615
$389$	30.8278	−	14.8459i	1.56303	−	0.752716i	0.565622	−	0.824665i	$-0.308636\pi$
$389$	30.8278	−	14.8459i	1.56303	−	0.752716i	0.997408	+	0.0719488i	$0.0229218\pi$
$390$	4.14609	−	2.82676i	0.209945	−	0.143138i
$391$	1.05794	−	1.32662i	0.0535024	−	0.0670899i
$392$	2.47314	+	2.29474i	0.124912	+	0.115902i
$393$	−25.7473	+	44.5957i	−1.29878	+	2.24956i
$394$	−9.67510	−	16.7578i	−0.487424	−	0.844244i
$395$	0.757984	−	3.32094i	0.0381383	−	0.167095i
$396$	−16.8109	+	42.8335i	−0.844779	+	2.15246i
$397$	4.39478	+	1.35561i	0.220568	+	0.0680361i	0.403069	−	0.915169i	$-0.367943\pi$
$397$	4.39478	+	1.35561i	0.220568	+	0.0680361i	−0.182502	+	0.983206i	$0.558420\pi$
$398$	−8.12451	−	10.1878i	−0.407245	−	0.510669i
$399$	3.21345	−	42.8805i	0.160874	−	2.14671i
$400$	0.955573	−	0.294755i	0.0477786	−	0.0147378i
$401$	−6.34111	−	4.32329i	−0.316660	−	0.215895i	0.394551	−	0.918874i	$-0.370900\pi$
$401$	−6.34111	−	4.32329i	−0.316660	−	0.215895i	−0.711210	+	0.702979i	$0.751853\pi$
$402$	−24.9135	−	3.75511i	−1.24257	−	0.187288i
$403$	−2.22874	−	9.76476i	−0.111022	−	0.486417i
$404$	−7.95954	+	7.38537i	−0.396002	+	0.367436i
$405$	−1.62341	−	21.6629i	−0.0806679	−	1.07644i
$406$	4.37334	+	11.1431i	0.217045	+	0.553022i
$407$	16.3824	−	2.46926i	0.812048	−	0.122396i
$408$	1.09974	+	0.529606i	0.0544452	+	0.0262194i
$409$	−9.72231	−	4.68202i	−0.480737	−	0.231511i	0.177789	−	0.984069i	$-0.443106\pi$
$409$	−9.72231	−	4.68202i	−0.480737	−	0.231511i	−0.658526	+	0.752558i	$0.728820\pi$
$410$	5.50439	−	0.829653i	0.271842	−	0.0409736i
$411$	−15.1134	−	38.5084i	−0.745490	−	1.89948i
$412$	−0.176280	−	2.35229i	−0.00868468	−	0.115889i
$413$	−12.3008	+	11.4135i	−0.605282	+	0.561620i
$414$	7.16962	+	31.4122i	0.352368	+	1.54382i
$415$	12.0055	+	1.80955i	0.589329	+	0.0888271i
$416$	−1.29551	−	0.883263i	−0.0635176	−	0.0433055i
$417$	15.4757	−	4.77363i	0.757849	−	0.233765i
$418$	−3.35014	+	44.7045i	−0.163861	+	2.18657i
$419$	11.6838	+	14.6511i	0.570792	+	0.715751i	0.980512	−	0.196461i	$-0.0629448\pi$
$419$	11.6838	+	14.6511i	0.570792	+	0.715751i	−0.409719	+	0.912212i	$0.634373\pi$
$420$	−5.82358	−	1.79634i	−0.284162	−	0.0876523i
$421$	−8.52171	+	21.7130i	−0.415323	+	1.05822i	0.558215	+	0.829696i	$0.311487\pi$
$421$	−8.52171	+	21.7130i	−0.415323	+	1.05822i	−0.973537	+	0.228528i	$0.926609\pi$
$422$	−0.0857591	+	0.375735i	−0.00417469	+	0.0182905i
$423$	−32.1310	−	55.6525i	−1.56226	−	2.70592i
$424$	−3.44561	+	5.96798i	−0.167334	+	0.289831i
$425$	0.279587	+	0.259418i	0.0135619	+	0.0125836i
$426$	4.50376	−	5.64754i	0.218208	−	0.273624i
$427$	17.7856	−	12.1260i	0.860706	−	0.586819i
$428$	−6.24938	+	3.00954i	−0.302075	+	0.145472i
$429$	31.8824			1.53930
$430$	−6.09291	−	2.42415i	−0.293826	−	0.116903i
$431$	−13.0083			−0.626587			−0.313294	−	0.949656i	$-0.601432\pi$
$431$	−13.0083			−0.626587			−0.313294	+	0.949656i	$0.601432\pi$
$432$	−12.2322	+	5.89073i	−0.588524	+	0.283418i
$433$	29.1687	−	19.8869i	1.40176	−	0.955704i	0.402573	−	0.915388i	$-0.368116\pi$
$433$	29.1687	−	19.8869i	1.40176	−	0.955704i	0.999187	−	0.0403160i	$-0.0128365\pi$
$434$	−7.58424	+	9.51033i	−0.364055	+	0.456511i
$435$	14.7475	+	13.6837i	0.707090	+	0.656083i
$436$	3.26402	−	5.65344i	0.156318	−	0.270751i
$437$	15.6953	+	27.1851i	0.750810	+	1.30044i
$438$	4.59656	−	20.1389i	0.219632	−	0.962272i
$439$	13.8053	−	35.1753i	0.658890	−	1.67882i	−0.0729403	−	0.997336i	$-0.523238\pi$
$439$	13.8053	−	35.1753i	0.658890	−	1.67882i	0.731830	−	0.681487i	$-0.238667\pi$
$440$	6.07130	+	1.87275i	0.289438	+	0.0892797i
$441$	−15.2341	−	19.1030i	−0.725435	−	0.909667i
$442$	0.0446902	−	0.596349i	0.00212570	−	0.0283654i
$443$	−4.18656	+	1.29138i	−0.198909	+	0.0613554i	−0.392609	−	0.919705i	$-0.628427\pi$
$443$	−4.18656	+	1.29138i	−0.198909	+	0.0613554i	0.193700	+	0.981061i	$0.437951\pi$
$444$	6.89513	+	4.70102i	0.327228	+	0.223101i
$445$	−15.5184	−	2.33903i	−0.735644	−	0.110881i
$446$	0.0769226	+	0.337020i	0.00364239	+	0.0159584i
$447$	−40.9566	+	38.0022i	−1.93718	+	1.79744i
$448$	0.142306	+	1.89894i	0.00672334	+	0.0897167i
$449$	11.5433	+	29.4118i	0.544762	+	1.38803i	0.892759	+	0.450535i	$0.148767\pi$
$449$	11.5433	+	29.4118i	0.544762	+	1.38803i	−0.347997	+	0.937496i	$0.613138\pi$
$450$	−7.16138	+	1.07940i	−0.337591	+	0.0508836i
$451$	31.8650	+	15.3454i	1.50047	+	0.722587i
$452$	4.96439	+	2.39072i	0.233505	+	0.112450i
$453$	28.0252	−	4.22412i	1.31674	−	0.198466i
$454$	7.47129	+	19.0365i	0.350645	+	0.893429i
$455$	0.223130	+	2.97747i	0.0104605	+	0.139586i
$456$	−16.5532	+	15.3591i	−0.775175	+	0.719258i
$457$	1.29466	+	5.67228i	0.0605617	+	0.265338i	0.996140	−	0.0877820i	$-0.0279779\pi$
$457$	1.29466	+	5.67228i	0.0605617	+	0.265338i	−0.935578	+	0.353120i	$0.885121\pi$
$458$	22.6971	+	3.42103i	1.06056	+	0.159854i
$459$	−4.27842	−	2.91698i	−0.199700	−	0.136153i
$460$	4.25123	−	1.31133i	0.198215	−	0.0611411i
$461$	0.256103	−	3.41746i	0.0119279	−	0.159167i	−0.988059	−	0.154075i	$-0.950760\pi$
$461$	0.256103	−	3.41746i	0.0119279	−	0.159167i	0.999987	−	0.00509178i	$-0.00162077\pi$
$462$	−24.1420	−	30.2731i	−1.12319	−	1.40843i
$463$	23.3400	+	7.19945i	1.08470	+	0.334587i	0.785032	−	0.619455i	$-0.212647\pi$
$463$	23.3400	+	7.19945i	1.08470	+	0.334587i	0.299672	+	0.954042i	$0.403123\pi$
$464$	2.29660	−	5.85163i	0.106617	−	0.271655i
$465$	−4.54908	+	19.9308i	−0.210958	+	0.924269i
$466$	2.39154	+	4.14226i	0.110786	+	0.191887i
$467$	15.6471	−	27.1016i	0.724063	−	1.25411i	−0.235296	−	0.971924i	$-0.575606\pi$
$467$	15.6471	−	27.1016i	0.724063	−	1.25411i	0.959359	−	0.282190i	$-0.0910608\pi$
$468$	8.32423	+	7.72376i	0.384788	+	0.357031i
$469$	9.34701	−	11.7208i	0.431605	−	0.541216i
$470$	−7.33137	+	4.99844i	−0.338171	+	0.230561i
$471$	26.4826	−	12.7533i	1.22025	−	0.587643i
$472$	8.81191			0.405601
$473$	−23.3089	−	34.5328i	−1.07174	−	1.58782i
$474$	10.9015			0.500723
$475$	−6.35710	+	3.06142i	−0.291684	+	0.140468i
$476$	−0.600089	+	0.409134i	−0.0275050	+	0.0187526i
$477$	31.1172	−	39.0197i	1.42476	−	1.78659i
$478$	−17.3609	−	16.1085i	−0.794067	−	0.736787i
$479$	−6.18424	+	10.7114i	−0.282565	+	0.489418i	−0.972016	−	0.234915i	$-0.924519\pi$
$479$	−6.18424	+	10.7114i	−0.282565	+	0.489418i	0.689451	+	0.724333i	$0.257852\pi$
$480$	1.60018	+	2.77159i	0.0730378	+	0.126505i
$481$	0.909797	−	3.98608i	0.0414832	−	0.181750i
$482$	−3.29346	+	8.39159i	−0.150013	+	0.382227i
$483$	−25.9084	−	7.99169i	−1.17887	−	0.363635i
$484$	18.3105	+	22.9607i	0.832298	+	1.04367i
$485$	0.661838	−	8.83162i	0.0300525	−	0.401023i
$486$	27.5139	−	8.48690i	1.24805	−	0.384974i
$487$	−6.74071	−	4.59574i	−0.305451	−	0.208253i	0.400887	−	0.916127i	$-0.368702\pi$
$487$	−6.74071	−	4.59574i	−0.305451	−	0.208253i	−0.706338	+	0.707874i	$0.749654\pi$
$488$	−11.1778	−	1.68478i	−0.505996	−	0.0762666i
$489$	4.90027	+	21.4695i	0.221598	+	0.970885i
$490$	−2.47314	+	2.29474i	−0.111725	+	0.103666i
$491$	−0.397825	−	5.30861i	−0.0179536	−	0.239574i	−0.998960	−	0.0455980i	$-0.985481\pi$
$491$	−0.397825	−	5.30861i	−0.0179536	−	0.239574i	0.981006	−	0.193976i	$-0.0621384\pi$
$492$	6.50854	+	16.5835i	0.293428	+	0.747641i
$493$	2.37077	−	0.357337i	0.106774	−	0.0160936i
$494$	9.96768	+	4.80018i	0.448467	+	0.215970i
$495$	−41.4574	−	19.9648i	−1.86337	−	0.897352i
$496$	6.31650	−	0.952059i	0.283619	−	0.0427487i
$497$	1.57027	+	4.00098i	0.0704363	+	0.179469i
$498$	2.90371	+	38.7474i	0.130118	+	1.73631i
$499$	11.8211	−	10.9684i	0.529186	−	0.491013i	−0.369727	−	0.929140i	$-0.620549\pi$
$499$	11.8211	−	10.9684i	0.529186	−	0.491013i	0.898913	+	0.438128i	$0.144358\pi$
$500$	0.222521	+	0.974928i	0.00995144	+	0.0436001i
$501$	24.5984	+	3.70760i	1.09897	+	0.165644i
$502$	−0.720665	−	0.491341i	−0.0321648	−	0.0219296i
$503$	−34.0207	+	10.4940i	−1.51691	+	0.467905i	−0.937751	−	0.347309i	$-0.887095\pi$
$503$	−34.0207	+	10.4940i	−1.51691	+	0.467905i	−0.579160	+	0.815214i	$0.696619\pi$
$504$	1.03062	−	13.7527i	0.0459075	−	0.612592i
$505$	−6.76990	−	8.48919i	−0.301257	−	0.377764i
$506$	27.0105	+	8.33163i	1.20076	+	0.370386i
$507$	−12.3253	+	31.4045i	−0.547388	+	1.39472i
$508$	0.428832	−	1.87884i	0.0190263	−	0.0833598i
$509$	0.157953	+	0.273583i	0.00700115	+	0.0121263i	0.869505	−	0.493925i	$-0.164438\pi$
$509$	0.157953	+	0.273583i	0.00700115	+	0.0121263i	−0.862504	+	0.506051i	$0.831105\pi$
$510$	−0.610309	+	1.05709i	−0.0270249	+	0.0468086i
$511$	9.01006	+	8.36011i	0.398581	+	0.369829i
$512$	0.623490	−	0.781831i	0.0275546	−	0.0345524i
$513$	79.1501	−	53.9636i	3.49456	−	2.38255i
$514$	10.0039	−	4.81762i	0.441252	−	0.212496i
$515$	2.35888			0.103945
$516$	3.22458	−	20.7369i	0.141954	−	0.912892i
$517$	−56.3764			−2.47943
$518$	−4.47381	+	2.15447i	−0.196568	+	0.0946620i
$519$	−7.43476	+	5.06894i	−0.326350	+	0.222502i
$520$	0.977607	−	1.22588i	0.0428709	−	0.0537584i
$521$	12.6016	+	11.6926i	0.552085	+	0.512260i	0.906148	−	0.422962i	$-0.139010\pi$
$521$	12.6016	+	11.6926i	0.552085	+	0.512260i	−0.354062	+	0.935222i	$0.615200\pi$
$522$	−22.7631	+	39.4268i	−0.996313	+	1.72566i
$523$	−0.984059	−	1.70444i	−0.0430299	−	0.0745300i	0.843708	−	0.536802i	$-0.180368\pi$
$523$	−0.984059	−	1.70444i	−0.0430299	−	0.0745300i	−0.886738	+	0.462272i	$0.847034\pi$
$524$	−3.58043	+	15.6869i	−0.156412	+	0.685285i
$525$	2.22651	−	5.67306i	0.0971729	−	0.247593i
$526$	10.1496	+	3.13075i	0.442545	+	0.136507i
$527$	1.51903	+	1.90480i	0.0661698	+	0.0829743i
$528$	−1.51954	+	20.2768i	−0.0661294	+	0.882435i
$529$	−3.06495	+	0.945411i	−0.133259	+	0.0411048i
$530$	−5.69380	−	3.88197i	−0.247323	−	0.168622i
$531$	−63.1054	−	9.51161i	−2.73854	−	0.412769i
$532$	−2.98985	−	13.0994i	−0.129626	−	0.567930i
$533$	6.39818	−	5.93665i	0.277136	−	0.257145i
$534$	−3.75335	−	50.0850i	−0.162423	−	2.16739i
$535$	−2.53411	−	6.45681i	−0.109559	−	0.279152i
$536$	−7.78462	+	1.17334i	−0.336244	+	0.0506807i
$537$	−15.4176	−	7.42472i	−0.665318	−	0.320400i
$538$	18.8753	+	9.08989i	0.813774	+	0.391893i
$539$	−21.1960	+	3.19478i	−0.912976	+	0.137609i
$540$	−4.96015	−	12.6382i	−0.213451	−	0.543864i
$541$	1.74804	+	23.3260i	0.0751542	+	1.00286i	0.899541	+	0.436837i	$0.143901\pi$
$541$	1.74804	+	23.3260i	0.0751542	+	1.00286i	−0.824387	+	0.566027i	$0.808480\pi$
$542$	6.87125	−	6.37558i	0.295145	−	0.273855i
$543$	−11.0993	−	48.6290i	−0.476315	−	2.08687i
$544$	0.377141	+	0.0568448i	0.0161698	+	0.00243720i
$545$	5.39371	+	3.67737i	0.231041	+	0.157521i
$546$	−9.13114	+	2.81658i	−0.390777	+	0.120539i
$547$	1.35968	−	18.1437i	0.0581357	−	0.775767i	−0.889606	−	0.456728i	$-0.849021\pi$
$547$	1.35968	−	18.1437i	0.0581357	−	0.775767i	0.947742	−	0.319038i	$-0.103360\pi$
$548$	−8.05927	−	10.1060i	−0.344275	−	0.431707i
$549$	78.2300	+	24.1307i	3.33877	+	1.02988i
$550$	−2.32122	+	5.91437i	−0.0989771	+	0.252190i
$551$	−9.86976	+	43.2423i	−0.420466	+	1.84218i
$552$	7.11900	+	12.3305i	0.303005	+	0.524820i
$553$	−3.24330	+	5.61756i	−0.137919	+	0.238883i
$554$	−17.1939	−	15.9536i	−0.730499	−	0.677804i
$555$	−5.20315	+	6.52454i	−0.220861	+	0.276951i
$556$	4.18114	−	2.85065i	0.177320	−	0.120895i
$557$	−37.7980	+	18.2025i	−1.60155	+	0.771267i	−0.999628	−	0.0272866i	$-0.991313\pi$
$557$	−37.7980	+	18.2025i	−1.60155	+	0.771267i	−0.601924	+	0.798553i	$0.705599\pi$
$558$	−46.2625			−1.95845
$559$	−10.0346	+	2.24114i	−0.424417	+	0.0947899i
$560$	−1.90427			−0.0804701
$561$	−6.98727	+	3.36489i	−0.295003	+	0.142066i
$562$	−10.0044	+	6.82091i	−0.422012	+	0.287723i
$563$	−15.0399	+	18.8594i	−0.633855	+	0.794829i	−0.990220	−	0.139518i	$-0.955445\pi$
$563$	−15.0399	+	18.8594i	−0.633855	+	0.794829i	0.356365	+	0.934347i	$0.384016\pi$
$564$	−20.8167	−	19.3151i	−0.876542	−	0.813312i
$565$	−2.75503	+	4.77185i	−0.115905	+	0.200753i
$566$	−0.161087	−	0.279011i	−0.00677099	−	0.0117277i
$567$	−9.20517	+	40.3305i	−0.386581	+	1.69372i
$568$	0.824605	−	2.10106i	0.0345997	−	0.0881585i
$569$	17.6598	+	5.44733i	0.740338	+	0.228364i	0.641910	−	0.766780i	$-0.278142\pi$
$569$	17.6598	+	5.44733i	0.740338	+	0.228364i	0.0984280	+	0.995144i	$0.468619\pi$
$570$	−14.0792	−	17.6547i	−0.589711	−	0.739475i
$571$	−2.33240	+	31.1237i	−0.0976077	+	1.30248i	0.706378	+	0.707835i	$0.250328\pi$
$571$	−2.33240	+	31.1237i	−0.0976077	+	1.30248i	−0.803985	+	0.594649i	$0.797291\pi$
$572$	9.51955	−	2.93639i	0.398032	−	0.122777i
$573$	16.8694	+	11.5014i	0.704730	+	0.480477i
$574$	−10.4818	−	1.57988i	−0.437503	−	0.0659430i
$575$	0.989970	+	4.33734i	0.0412846	+	0.180880i
$576$	−5.30896	+	4.92599i	−0.221207	+	0.205250i
$577$	−1.77371	−	23.6685i	−0.0738404	−	0.985332i	−0.903924	−	0.427693i	$-0.859326\pi$
$577$	−1.77371	−	23.6685i	−0.0738404	−	0.985332i	0.830084	−	0.557639i	$-0.188293\pi$
$578$	−6.15765	−	15.6894i	−0.256125	−	0.652595i
$579$	−44.9989	+	6.78250i	−1.87009	+	0.281871i
$580$	5.66365	+	2.72747i	0.235170	+	0.113252i
$581$	−20.8304	−	10.0314i	−0.864192	−	0.416173i
$582$	28.0270	−	4.22439i	1.16176	−	0.175107i
$583$	−15.9960	−	40.7573i	−0.662489	−	1.68799i
$584$	−0.482347	−	6.43648i	−0.0199597	−	0.266343i
$585$	−8.32423	+	7.72376i	−0.344165	+	0.319338i
$586$	5.12527	+	22.4553i	0.211723	+	0.927618i
$587$	−27.6049	−	4.16078i	−1.13938	−	0.171734i	−0.447867	−	0.894100i	$-0.647816\pi$
$587$	−27.6049	−	4.16078i	−1.13938	−	0.171734i	−0.691510	+	0.722366i	$0.743054\pi$
$588$	−8.92108	−	6.08229i	−0.367899	−	0.250829i
$589$	−43.0693	+	13.2851i	−1.77464	+	0.547404i
$590$	−0.658515	+	8.78727i	−0.0271106	+	0.361766i
$591$	38.6112	+	48.4169i	1.58825	+	1.99160i
$592$	2.49174	+	0.768600i	0.102410	+	0.0315893i
$593$	−9.15335	+	23.3223i	−0.375883	+	0.957734i	0.610314	+	0.792159i	$0.291043\pi$
$593$	−9.15335	+	23.3223i	−0.375883	+	0.957734i	−0.986197	+	0.165575i	$0.947052\pi$
$594$	19.1948	−	84.0981i	0.787574	−	3.45059i
$595$	−0.363145	−	0.628986i	−0.0148875	−	0.0257859i
$596$	−8.72894	+	15.1190i	−0.357551	+	0.619297i
$597$	30.5704	+	28.3651i	1.25116	+	1.16091i
$598$	4.34926	−	5.45380i	0.177854	−	0.223022i
$599$	5.36135	−	3.65530i	0.219059	−	0.149352i	−0.448819	−	0.893623i	$-0.648155\pi$
$599$	5.36135	−	3.65530i	0.219059	−	0.149352i	0.667878	+	0.744271i	$0.267203\pi$
$600$	−2.88342	+	1.38858i	−0.117715	+	0.0566886i
$601$	−18.4497			−0.752580			−0.376290	−	0.926502i	$-0.622800\pi$
$601$	−18.4497			−0.752580			−0.376290	+	0.926502i	$0.622800\pi$
$602$	9.72641	+	7.83105i	0.396419	+	0.319170i
$603$	57.0151			2.32183
$604$	7.97882	−	3.84240i	0.324653	−	0.156345i
$605$	−24.2648	+	16.5435i	−0.986506	+	0.672589i
$606$	21.6661	−	27.1684i	0.880125	−	1.10364i
$607$	24.6560	+	22.8774i	1.00076	+	0.928566i	0.997446	−	0.0714285i	$-0.0227558\pi$
$607$	24.6560	+	22.8774i	1.00076	+	0.928566i	0.00331043	+	0.999995i	$0.498946\pi$
$608$	−3.52793	+	6.11055i	−0.143076	+	0.247815i
$609$	−19.1550	−	33.1775i	−0.776201	−	1.34442i
$610$	2.51539	−	11.0207i	0.101845	−	0.446213i
$611$	−5.08292	+	12.9511i	−0.205633	+	0.523944i
$612$	−2.63949	−	0.814175i	−0.106695	−	0.0329111i
$613$	10.6649	+	13.3734i	0.430753	+	0.540148i	0.949080	−	0.315035i	$-0.102016\pi$
$613$	10.6649	+	13.3734i	0.430753	+	0.540148i	−0.518327	+	0.855183i	$0.673445\pi$
$614$	0.0471777	−	0.629543i	0.00190394	−	0.0254063i
$615$	−17.0235	+	5.25105i	−0.686454	+	0.211743i
$616$	−9.99659	−	6.81556i	−0.402774	−	0.274607i
$617$	7.78804	+	1.17386i	0.313535	+	0.0472578i	0.303925	−	0.952696i	$-0.401703\pi$
$617$	7.78804	+	1.17386i	0.313535	+	0.0472578i	0.00961007	+	0.999954i	$0.496941\pi$
$618$	1.67987	+	7.35999i	0.0675743	+	0.296062i
$619$	25.6464	−	23.7964i	1.03082	−	0.956458i	0.0317427	−	0.999496i	$-0.489894\pi$
$619$	25.6464	−	23.7964i	1.03082	−	0.956458i	0.999073	+	0.0430385i	$0.0137038\pi$
$620$	0.477364	+	6.36998i	0.0191714	+	0.255825i
$621$	−22.0671	−	56.2261i	−0.885523	−	2.25627i
$622$	14.7693	−	2.22611i	0.592194	−	0.0892589i
$623$	26.9255	+	12.9666i	1.07875	+	0.519498i
$624$	4.52109	+	2.17724i	0.180988	+	0.0871594i
$625$	−0.988831	+	0.149042i	−0.0395532	+	0.00596169i
$626$	−1.69494	−	4.31863i	−0.0677433	−	0.172607i
$627$	−10.7216	−	143.070i	−0.428181	−	5.71367i
$628$	6.73267	−	6.24700i	0.268663	−	0.249283i
$629$	0.221305	+	0.969601i	0.00882401	+	0.0386605i
$630$	13.6372	+	2.05548i	0.543319	+	0.0818921i
$631$	−7.16048	−	4.88193i	−0.285054	−	0.194347i	0.412348	−	0.911026i	$-0.364709\pi$
$631$	−7.16048	−	4.88193i	−0.285054	−	0.194347i	−0.697403	+	0.716680i	$0.745661\pi$
$632$	3.25501	−	1.00404i	0.129477	−	0.0399385i
$633$	0.0921728	−	1.22996i	0.00366354	−	0.0488865i
$634$	−0.719386	−	0.902082i	−0.0285705	−	0.0358263i
$635$	1.84154	+	0.568038i	0.0730791	+	0.0225419i
$636$	8.05737	−	20.5298i	0.319495	−	0.814061i
$637$	−1.17712	+	5.15729i	−0.0466391	+	0.204339i
$638$	19.9698	+	34.5887i	0.790613	+	1.36938i
$639$	−8.17320	+	14.1564i	−0.323327	+	0.560019i
$640$	0.733052	+	0.680173i	0.0289764	+	0.0268862i
$641$	13.8667	−	17.3883i	0.547703	−	0.686798i	−0.428529	−	0.903528i	$-0.640968\pi$
$641$	13.8667	−	17.3883i	0.547703	−	0.686798i	0.976231	+	0.216731i	$0.0695393\pi$
$642$	18.3413	−	12.5049i	0.723875	−	0.493529i
$643$	5.27123	−	2.53849i	0.207877	−	0.100108i	−0.327048	−	0.945008i	$-0.606054\pi$
$643$	5.27123	−	2.53849i	0.207877	−	0.100108i	0.534925	+	0.844899i	$0.320340\pi$
$644$	−8.47187			−0.333838
$645$	20.4380	+	4.76523i	0.804744	+	0.187631i
$646$	−2.69111			−0.105880
$647$	−16.1197	+	7.76284i	−0.633731	+	0.305189i	−0.723030	−	0.690816i	$-0.757251\pi$
$647$	−16.1197	+	7.76284i	−0.633731	+	0.305189i	0.0892998	+	0.996005i	$0.471537\pi$
$648$	17.9489	−	12.2374i	0.705100	−	0.480729i
$649$	−34.9074	+	43.7725i	−1.37023	+	1.71822i
$650$	1.14940	+	1.06648i	0.0450830	+	0.0418309i
$651$	19.4648	−	33.7141i	0.762887	−	1.32136i
$652$	3.44050	+	5.95912i	0.134740	+	0.233377i
$653$	3.05421	−	13.3814i	0.119521	−	0.523654i	−0.879352	−	0.476173i	$-0.842024\pi$
$653$	3.05421	−	13.3814i	0.119521	−	0.523654i	0.998872	−	0.0474807i	$-0.0151193\pi$
$654$	−7.63271	+	19.4478i	−0.298463	+	0.760470i
$655$	−15.3755	−	4.74270i	−0.600769	−	0.185313i
$656$	3.47069	+	4.35211i	0.135508	+	0.169921i
$657$	−3.49329	+	46.6147i	−0.136286	+	1.81861i
$658$	16.1463	−	4.98046i	0.629446	−	0.194159i
$659$	−16.3091	−	11.1194i	−0.635314	−	0.433150i	0.202367	−	0.979310i	$-0.435137\pi$
$659$	−16.3091	−	11.1194i	−0.635314	−	0.433150i	−0.837681	+	0.546160i	$0.816089\pi$
$660$	−20.1066	−	3.03058i	−0.782647	−	0.117965i
$661$	−0.702074	−	3.07599i	−0.0273075	−	0.119642i	0.959437	−	0.281923i	$-0.0909722\pi$
$661$	−0.702074	−	3.07599i	−0.0273075	−	0.119642i	−0.986745	+	0.162281i	$0.948115\pi$
$662$	20.3882	−	18.9174i	0.792408	−	0.735247i
$663$	0.143024	+	1.90853i	0.00555461	+	0.0741211i
$664$	4.43566	+	11.3019i	0.172137	+	0.438598i
$665$	13.2862	−	2.00257i	0.515216	−	0.0776563i
$666$	−17.0147	−	8.19383i	−0.659305	−	0.317504i
$667$	25.1969	+	12.1342i	0.975628	+	0.469838i
$668$	7.68613	−	1.15850i	0.297385	−	0.0448236i
$669$	−0.404184	−	1.02984i	−0.0156267	−	0.0398161i
$670$	−0.588316	−	7.85053i	−0.0227286	−	0.303293i
$671$	52.6486	−	48.8508i	2.03248	−	1.88586i
$672$	−1.35612	−	5.94154i	−0.0523134	−	0.229200i
$673$	43.6377	+	6.57733i	1.68211	+	0.253537i	0.919435	−	0.393243i	$-0.128647\pi$
$673$	43.6377	+	6.57733i	1.68211	+	0.253537i	0.762676	+	0.646781i	$0.223885\pi$
$674$	7.19462	+	4.90521i	0.277127	+	0.188942i
$675$	12.9736	−	4.00182i	0.499353	−	0.154030i
$676$	−0.787767	+	10.5120i	−0.0302987	+	0.404309i
$677$	26.0432	+	32.6571i	1.00092	+	1.25511i	0.966757	+	0.255697i	$0.0823051\pi$
$677$	26.0432	+	32.6571i	1.00092	+	1.25511i	0.0341629	+	0.999416i	$0.489123\pi$
$678$	−16.8507	−	5.19775i	−0.647147	−	0.199618i
$679$	−6.16145	+	15.6991i	−0.236455	+	0.602477i
$680$	−0.0848697	+	0.371838i	−0.00325460	+	0.0142593i
$681$	−32.7239	−	56.6795i	−1.25398	−	2.17196i
$682$	−20.2928	+	35.1482i	−0.777052	+	1.34589i
$683$	23.6194	+	21.9156i	0.903770	+	0.838576i	0.987452	−	0.157917i	$-0.0504777\pi$
$683$	23.6194	+	21.9156i	0.903770	+	0.838576i	−0.0836826	+	0.996492i	$0.526668\pi$
$684$	31.8606	−	39.9519i	1.21822	−	1.52760i
$685$	10.6800	−	7.28151i	0.408062	−	0.278212i
$686$	17.7981	−	8.57113i	0.679536	−	0.327247i
$687$	−73.4591			−2.80264
$688$	−0.947080	−	6.48869i	−0.0361071	−	0.247379i
$689$	−10.8052			−0.411644
$690$	−12.8280	+	6.17764i	−0.488353	+	0.235179i
$691$	30.6619	−	20.9049i	1.16643	−	0.795262i	0.184194	−	0.982890i	$-0.441032\pi$
$691$	30.6619	−	20.9049i	1.16643	−	0.795262i	0.982240	+	0.187628i	$0.0600800\pi$
$692$	−1.75304	+	2.19825i	−0.0666407	+	0.0835648i
$693$	64.2326	+	59.5991i	2.43999	+	2.26398i
$694$	−5.40289	+	9.35809i	−0.205091	+	0.355228i
$695$	2.53022	+	4.38248i	0.0959768	+	0.166237i
$696$	−4.47667	+	19.6136i	−0.169688	+	0.743451i
$697$	−0.775652	+	1.97633i	−0.0293799	+	0.0748588i
$698$	4.16804	+	1.28567i	0.157763	+	0.0486634i
$699$	−9.54409	−	11.9679i	−0.360991	−	0.452668i
$700$	0.142306	−	1.89894i	0.00537867	−	0.0717734i
$701$	24.9553	−	7.69769i	0.942548	−	0.290738i	0.214859	−	0.976645i	$-0.431071\pi$
$701$	24.9553	−	7.69769i	0.942548	−	0.290738i	0.727689	+	0.685907i	$0.240595\pi$
$702$	−17.5888	−	11.9919i	−0.663847	−	0.452603i
$703$	−18.1933	−	2.74219i	−0.686172	−	0.103424i
$704$	1.41380	+	6.19427i	0.0532847	+	0.233455i
$705$	20.8167	−	19.3151i	0.784003	−	0.727449i
$706$	−1.00681	−	13.4350i	−0.0378920	−	0.505633i
$707$	7.55405	+	19.2474i	0.284099	+	0.723873i
$708$	−27.8862	+	4.20318i	−1.04803	+	0.157965i
$709$	32.2322	+	15.5222i	1.21051	+	0.582949i	0.926652	−	0.375919i	$-0.122673\pi$
$709$	32.2322	+	15.5222i	1.21051	+	0.582949i	0.283853	+	0.958868i	$0.408387\pi$
$710$	2.03356	+	0.979312i	0.0763182	+	0.0367529i
$711$	−24.3941	+	3.67683i	−0.914852	+	0.137892i
$712$	−5.73356	−	14.6089i	−0.214874	−	0.547491i
$713$	2.12374	+	28.3393i	0.0795346	+	1.06132i
$714$	1.70389	−	1.58098i	0.0637667	−	0.0591668i
$715$	2.21678	+	9.71237i	0.0829031	+	0.363222i
$716$	−5.28726	−	0.796927i	−0.197594	−	0.0297825i
$717$	62.6239	+	42.6962i	2.33873	+	1.59452i
$718$	−31.7716	+	9.80023i	−1.18570	+	0.365742i
$719$	−2.10806	+	28.1302i	−0.0786175	+	1.04908i	0.808792	+	0.588095i	$0.200122\pi$
$719$	−2.10806	+	28.1302i	−0.0786175	+	1.04908i	−0.887409	+	0.460982i	$0.847497\pi$
$720$	−4.51548	−	5.66223i	−0.168282	−	0.211019i
$721$	−4.29239	−	1.32403i	−0.159857	−	0.0493093i
$722$	11.2470	−	28.6570i	0.418572	−	1.06650i
$723$	6.41982	−	28.1271i	0.238756	−	1.04606i
$724$	−7.79283	−	13.4976i	−0.289618	−	0.501633i
$725$	−3.14309	+	5.44399i	−0.116731	+	0.202185i
$726$	−68.8977	−	63.9277i	−2.55703	−	2.37258i
$727$	−16.9039	+	21.1968i	−0.626930	+	0.786145i	−0.989301	−	0.145889i	$-0.953396\pi$
$727$	−16.9039	+	21.1968i	−0.626930	+	0.786145i	0.362371	+	0.932034i	$0.381967\pi$
$728$	−2.46700	+	1.68197i	−0.0914330	+	0.0623380i
$729$	−24.3055	+	11.7049i	−0.900204	+	0.433515i
$730$	6.45453			0.238893
$731$	1.96262	−	1.55022i	0.0725902	−	0.0573369i
$732$	36.1770			1.33714
$733$	27.5089	−	13.2476i	1.01607	−	0.489311i	0.149705	−	0.988731i	$-0.452168\pi$
$733$	27.5089	−	13.2476i	1.01607	−	0.489311i	0.866360	+	0.499419i	$0.166453\pi$
$734$	21.4688	−	14.6372i	0.792427	−	0.540267i
$735$	6.73196	−	8.44161i	0.248312	−	0.311373i
$736$	3.26126	+	3.02601i	0.120212	+	0.111540i
$737$	25.0094	−	43.3175i	0.921232	−	1.59562i
$738$	−20.1573	−	34.9134i	−0.741999	−	1.28518i
$739$	0.978755	−	4.28821i	0.0360041	−	0.157744i	−0.953730	−	0.300664i	$-0.902792\pi$
$739$	0.978755	−	4.28821i	0.0360041	−	0.157744i	0.989734	+	0.142919i	$0.0456490\pi$
$740$	−0.952659	+	2.42733i	−0.0350204	+	0.0892306i
$741$	−33.8335	−	10.4362i	−1.24290	−	0.383385i
$742$	8.18190	+	10.2598i	0.300367	+	0.376648i
$743$	0.350477	−	4.67679i	0.0128577	−	0.171575i	−0.987078	−	0.160240i	$-0.948773\pi$
$743$	0.350477	−	4.67679i	0.0128577	−	0.171575i	0.999936	−	0.0113343i	$-0.00360790\pi$
$744$	−19.5351	+	6.02579i	−0.716192	+	0.220916i
$745$	−14.4244	−	9.83438i	−0.528468	−	0.360304i
$746$	31.5183	+	4.75061i	1.15397	+	0.173932i
$747$	−19.5662	−	85.7249i	−0.715888	−	3.13651i
$748$	−1.77637	+	1.64823i	−0.0649506	+	0.0602654i
$749$	0.987077	+	13.1716i	0.0360670	+	0.481281i
$750$	−1.16922	−	2.97913i	−0.0426939	−	0.108782i
$751$	−42.4726	+	6.40171i	−1.54985	+	0.233602i	−0.867504	−	0.497431i	$-0.834277\pi$
$751$	−42.4726	+	6.40171i	−1.54985	+	0.233602i	−0.682343	+	0.731032i	$0.739039\pi$
$752$	−7.99446	−	3.84993i	−0.291528	−	0.140393i
$753$	2.51499	+	1.21115i	0.0916512	+	0.0441369i
$754$	9.74638	−	1.46903i	0.354942	−	0.0534989i
$755$	3.23539	+	8.24365i	0.117748	+	0.300017i
$756$	1.93206	+	25.7815i	0.0702682	+	0.937665i
$757$	−6.68025	+	6.19836i	−0.242798	+	0.225283i	−0.792180	−	0.610288i	$-0.791054\pi$
$757$	−6.68025	+	6.19836i	−0.242798	+	0.225283i	0.549382	+	0.835571i	$0.314863\pi$
$758$	6.41229	+	28.0941i	0.232905	+	1.02042i
$759$	−89.4517	−	13.4827i	−3.24689	−	0.489390i
$760$	−5.82982	−	3.97470i	−0.211470	−	0.144178i
$761$	−15.4841	+	4.77620i	−0.561297	+	0.173137i	−0.562405	−	0.826862i	$-0.690124\pi$
$761$	−15.4841	+	4.77620i	−0.561297	+	0.173137i	0.00110749	+	0.999999i	$0.499647\pi$
$762$	−0.460903	+	6.15033i	−0.0166968	+	0.222803i
$763$	−7.75068	−	9.71905i	−0.280594	−	0.351853i
$764$	6.09621	+	1.88043i	0.220553	+	0.0680317i
$765$	1.00915	−	2.57127i	0.0364858	−	0.0929643i
$766$	−4.00419	+	17.5435i	−0.144677	+	0.633872i
$767$	6.90836	+	11.9656i	0.249446	+	0.432054i
$768$	−1.60018	+	2.77159i	−0.0577414	+	0.100011i
$769$	−19.3101	−	17.9172i	−0.696342	−	0.646111i	0.250386	−	0.968146i	$-0.419442\pi$
$769$	−19.3101	−	17.9172i	−0.696342	−	0.646111i	−0.946728	+	0.322036i	$0.895633\pi$
$770$	7.54354	−	9.45931i	0.271850	−	0.340890i
$771$	−29.3604	+	20.0176i	−1.05739	+	0.720916i
$772$	−12.8113	+	6.16958i	−0.461087	+	0.222048i
$773$	42.8494			1.54119			0.770594	−	0.637327i	$-0.219960\pi$
$773$	42.8494			1.54119			0.770594	+	0.637327i	$0.219960\pi$
$774$	−0.221512	+	47.4902i	−0.00796209	+	1.70700i
$775$	−6.38784			−0.229458
$776$	7.97933	−	3.84264i	0.286441	−	0.137943i
$777$	13.1302	−	8.95201i	0.471043	−	0.321152i
$778$	−21.3335	+	26.7513i	−0.764842	+	0.959082i
$779$	−28.7920	−	26.7150i	−1.03158	−	0.957166i
$780$	−2.50901	+	4.34574i	−0.0898371	+	0.155602i
$781$	7.17027	+	12.4193i	0.256572	+	0.444396i
$782$	−0.377575	+	1.65427i	−0.0135021	+	0.0591564i
$783$	31.1803	−	79.4462i	1.11429	−	2.83918i
$784$	−3.22387	−	0.994433i	−0.115138	−	0.0355155i
$785$	5.72640	+	7.18068i	0.204384	+	0.256289i
$786$	3.84820	−	51.3507i	0.137261	−	1.83162i
$787$	−4.86080	+	1.49936i	−0.173269	+	0.0534463i	−0.380176	−	0.924914i	$-0.624136\pi$
$787$	−4.86080	+	1.49936i	−0.173269	+	0.0534463i	0.206907	+	0.978361i	$0.433660\pi$
$788$	15.9879	+	10.9004i	0.569545	+	0.388309i
$789$	−33.6129	−	5.06634i	−1.19665	−	0.180366i
$790$	0.757984	+	3.32094i	0.0269679	+	0.118154i
$791$	7.69164	−	7.13680i	0.273483	−	0.253755i
$792$	−3.43865	−	45.8856i	−0.122187	−	1.63047i
$793$	−6.47542	−	16.4991i	−0.229949	−	0.585901i
$794$	−4.54773	+	0.685461i	−0.161393	+	0.0243261i
$795$	19.8703	+	9.56903i	0.704727	+	0.339379i
$796$	11.7403	+	5.65381i	0.416122	+	0.200394i
$797$	−17.6829	+	2.66526i	−0.626359	+	0.0944085i	−0.454549	−	0.890722i	$-0.650200\pi$
$797$	−17.6829	+	2.66526i	−0.626359	+	0.0944085i	−0.171810	+	0.985130i	$0.554962\pi$
$798$	15.7099	+	40.0283i	0.556126	+	1.41699i
$799$	−0.252905	−	3.37478i	−0.00894712	−	0.119391i
$800$	−0.733052	+	0.680173i	−0.0259173	+	0.0240477i
$801$	25.2913	+	110.808i	0.893624	+	3.91522i
$802$	7.58895	+	1.14385i	0.267975	+	0.0403907i
$803$	33.8835	+	23.1013i	1.19572	+	0.815229i
$804$	24.0756	−	7.42634i	0.849081	−	0.261907i
$805$	0.633104	−	8.44818i	0.0223140	−	0.297759i
$806$	6.24480	+	7.83073i	0.219964	+	0.275826i
$807$	−64.0689	−	19.7626i	−2.25533	−	0.695677i
$808$	3.96690	−	10.1075i	0.139555	−	0.355581i
$809$	4.56756	−	20.0118i	0.160587	−	0.703577i	−0.828953	−	0.559318i	$-0.811063\pi$
$809$	4.56756	−	20.0118i	0.160587	−	0.703577i	0.989540	−	0.144259i	$-0.0460799\pi$
$810$	10.8618	+	18.8132i	0.381645	+	0.661029i
$811$	11.5304	−	19.9713i	0.404889	−	0.701288i	−0.589420	−	0.807827i	$-0.700644\pi$
$811$	11.5304	−	19.9713i	0.404889	−	0.701288i	0.994309	+	0.106539i	$0.0339769\pi$
$812$	−8.77505	−	8.14205i	−0.307944	−	0.285730i
$813$	−18.7037	+	23.4537i	−0.655968	+	0.822558i
$814$	−13.6887	+	9.33280i	−0.479789	+	0.327114i
$815$	−6.19957	+	2.98555i	−0.217161	+	0.104579i
$816$	−1.22062			−0.0427302
$817$	13.4315	+	44.2759i	0.469907	+	1.54902i
$818$	10.7909			0.377297
$819$	19.4826	−	9.38234i	0.680778	−	0.327846i
$820$	−4.59931	+	3.13576i	−0.160615	+	0.109505i
$821$	−3.03409	+	3.80463i	−0.105890	+	0.132782i	−0.831953	−	0.554847i	$-0.812777\pi$
$821$	−3.03409	+	3.80463i	−0.105890	+	0.132782i	0.726062	+	0.687629i	$0.241348\pi$
$822$	30.3249	+	28.1374i	1.05770	+	0.981404i
$823$	−15.3128	+	26.5225i	−0.533769	+	0.924515i	0.465453	+	0.885073i	$0.345892\pi$
$823$	−15.3128	+	26.5225i	−0.533769	+	0.924515i	−0.999222	+	0.0394426i	$0.987442\pi$
$824$	1.17944	+	2.04285i	0.0410878	+	0.0711662i
$825$	4.52467	−	19.8239i	0.157529	−	0.690178i
$826$	6.13051	−	15.6203i	0.213308	−	0.543499i
$827$	−6.59312	−	2.03371i	−0.229265	−	0.0707189i	0.177994	−	0.984032i	$-0.443039\pi$
$827$	−6.59312	−	2.03371i	−0.229265	−	0.0707189i	−0.407259	+	0.913313i	$0.633515\pi$
$828$	−20.0888	−	25.1906i	−0.698135	−	0.875434i
$829$	0.964237	−	12.8668i	0.0334893	−	0.446884i	−0.955104	−	0.296272i	$-0.904257\pi$
$829$	0.964237	−	12.8668i	0.0334893	−	0.446884i	0.988593	−	0.150612i	$-0.0481245\pi$
$830$	−11.6018	+	3.57867i	−0.402703	+	0.124217i
$831$	62.0217	+	42.2857i	2.15151	+	1.46687i
$832$	1.55045	+	0.233692i	0.0537521	+	0.00810182i
$833$	−0.286330	−	1.25449i	−0.00992074	−	0.0434656i
$834$	−11.8719	+	11.0155i	−0.411092	+	0.381437i
$835$	0.580873	+	7.75122i	0.0201020	+	0.268242i
$836$	−16.3782	−	41.7309i	−0.566451	−	1.44329i
$837$	85.7575	−	12.9259i	2.96421	−	0.446783i
$838$	−16.8836	−	8.13072i	−0.583235	−	0.280871i
$839$	48.8799	+	23.5393i	1.68752	+	0.812668i	0.995905	+	0.0904041i	$0.0288159\pi$
$839$	48.8799	+	23.5393i	1.68752	+	0.812668i	0.691618	+	0.722264i	$0.256898\pi$
$840$	6.02627	−	0.908314i	0.207926	−	0.0313398i
$841$	3.84192	+	9.78905i	0.132480	+	0.337553i
$842$	−1.74311	−	23.2601i	−0.0600714	−	0.801597i
$843$	28.4066	−	26.3575i	0.978377	−	0.907801i
$844$	−0.0857591	−	0.375735i	−0.00295195	−	0.0129333i
$845$	−10.4238	−	1.57113i	−0.358588	−	0.0540485i
$846$	53.0957	+	36.2001i	1.82547	+	1.24458i
$847$	53.4397	−	16.4840i	1.83621	−	0.566396i
$848$	0.514982	−	6.87196i	0.0176846	−	0.235984i
$849$	0.642862	+	0.806124i	0.0220630	+	0.0276661i
$850$	−0.364456	−	0.112420i	−0.0125007	−	0.00385597i
$851$	−4.23827	+	10.7989i	−0.145286	+	0.370182i
$852$	−1.60737	+	7.04236i	−0.0550677	+	0.241267i
$853$	−12.3098	−	21.3213i	−0.421481	−	0.730026i	0.574604	−	0.818432i	$-0.305156\pi$
$853$	−12.3098	−	21.3213i	−0.421481	−	0.730026i	−0.996085	+	0.0884055i	$0.971823\pi$
$854$	−10.7630	+	18.6421i	−0.368302	+	0.637918i
$855$	37.4592	+	34.7571i	1.28108	+	1.18867i
$856$	4.32471	−	5.42301i	0.147815	−	0.185355i
$857$	−16.7044	+	11.3888i	−0.570610	+	0.389035i	−0.813975	−	0.580899i	$-0.802701\pi$
$857$	−16.7044	+	11.3888i	−0.570610	+	0.389035i	0.243365	+	0.969935i	$0.421749\pi$
$858$	−28.7250	+	13.8332i	−0.980656	+	0.472259i
$859$	−30.3443			−1.03534			−0.517668	−	0.855582i	$-0.673200\pi$
$859$	−30.3443			−1.03534			−0.517668	+	0.855582i	$0.673200\pi$
$860$	6.54132	−	0.459532i	0.223057	−	0.0156699i
$861$	33.9245			1.15614
$862$	11.7201	−	5.64409i	0.399187	−	0.192238i
$863$	−29.3739	+	20.0268i	−0.999899	+	0.681720i	−0.948440	−	0.316955i	$-0.897339\pi$
$863$	−29.3739	+	20.0268i	−0.999899	+	0.681720i	−0.0514587	+	0.998675i	$0.516387\pi$
$864$	8.46497	−	10.6147i	0.287984	−	0.361121i
$865$	−2.06110	−	1.91242i	−0.0700794	−	0.0650242i
$866$	−17.6515	+	30.5733i	−0.599823	+	1.03892i
$867$	26.9702	+	46.7138i	0.915957	+	1.58648i
$868$	2.70678	−	11.8592i	0.0918742	−	0.402527i
$869$	−7.90688	+	20.1464i	−0.268223	+	0.683420i
$870$	−19.2242	−	5.92988i	−0.651761	−	0.201042i
$871$	−7.69626	−	9.65080i	−0.260778	−	0.327005i
$872$	−0.487840	+	6.50978i	−0.0165204	+	0.220449i
$873$	−61.2907	+	18.9057i	−2.07438	+	0.639861i
$874$	−25.9362	−	17.6830i	−0.877304	−	0.598136i
$875$	1.88300	+	0.283817i	0.0636570	+	0.00959475i
$876$	4.59656	+	20.1389i	0.155304	+	0.680429i
$877$	−18.9545	+	17.5872i	−0.640048	+	0.593877i	−0.931957	−	0.362569i	$-0.881900\pi$
$877$	−18.9545	+	17.5872i	−0.640048	+	0.593877i	0.291910	+	0.956446i	$0.405709\pi$
$878$	2.82385	+	37.6817i	0.0953004	+	1.27170i
$879$	−26.9304	−	68.6174i	−0.908338	−	2.31441i
$880$	−6.28260	+	0.946950i	−0.211787	+	0.0319217i
$881$	−33.2509	−	16.0128i	−1.12025	−	0.539484i	−0.220280	−	0.975437i	$-0.570697\pi$
$881$	−33.2509	−	16.0128i	−1.12025	−	0.539484i	−0.899970	+	0.435953i	$0.856411\pi$
$882$	22.0140	+	10.6014i	0.741249	+	0.356967i
$883$	58.5611	−	8.82666i	1.97074	−	0.297041i	0.972906	−	0.231200i	$-0.0742651\pi$
$883$	58.5611	−	8.82666i	1.97074	−	0.297041i	0.997830	−	0.0658409i	$-0.0209730\pi$
$884$	0.218482	+	0.556682i	0.00734833	+	0.0187233i
$885$	−2.10748	−	28.1224i	−0.0708422	−	0.945323i
$886$	3.21165	−	2.97998i	0.107897	−	0.100114i
$887$	−9.70084	−	42.5021i	−0.325722	−	1.42708i	−0.827198	−	0.561911i	$-0.810067\pi$
$887$	−9.70084	−	42.5021i	−0.325722	−	1.42708i	0.501476	−	0.865172i	$-0.332791\pi$
$888$	−8.25200	−	1.24379i	−0.276919	−	0.0417388i
$889$	−3.03215	−	2.06728i	−0.101695	−	0.0693344i
$890$	14.9965	−	4.62580i	0.502684	−	0.155057i
$891$	−10.3144	+	137.637i	−0.345547	+	4.61100i
$892$	−0.215532	−	0.270269i	−0.00721655	−	0.00904927i
$893$	59.8264	+	18.4540i	2.00201	+	0.617540i
$894$	20.4121	−	52.0092i	0.682683	−	1.73945i
$895$	1.18982	−	5.21292i	0.0397712	−	0.174249i
$896$	−0.952135	−	1.64915i	−0.0318086	−	0.0550941i
$897$	−11.1623	+	19.3337i	−0.372699	+	0.645533i
$898$	−23.1615	−	21.4907i	−0.772908	−	0.717154i
$899$	−25.0363	+	31.3945i	−0.835007	+	1.04707i
$900$	5.98384	−	4.07971i	0.199461	−	0.135990i
$901$	2.36803	−	1.14039i	0.0788907	−	0.0379917i
$902$	−35.3675			−1.17761
$903$	−34.5156	−	20.1428i	−1.14861	−	0.670311i
$904$	−5.51005			−0.183262
$905$	14.0422	−	6.76236i	0.466778	−	0.224789i
$906$	−23.4171	+	15.9655i	−0.777980	+	0.530418i
$907$	−6.33610	+	7.94521i	−0.210387	+	0.263816i	−0.875817	−	0.482644i	$-0.839677\pi$
$907$	−6.33610	+	7.94521i	−0.210387	+	0.263816i	0.665430	+	0.746460i	$0.268248\pi$
$908$	−14.9910	−	13.9096i	−0.497495	−	0.461608i
$909$	−39.3186	+	68.1018i	−1.30411	+	2.25879i
$910$	−1.49291	−	2.58579i	−0.0494894	−	0.0857182i
$911$	2.71369	−	11.8895i	0.0899086	−	0.393915i	−0.909871	−	0.414890i	$-0.863820\pi$
$911$	2.71369	−	11.8895i	0.0899086	−	0.393915i	0.999780	+	0.0209751i	$0.00667708\pi$
$912$	8.24985	−	21.0203i	0.273180	−	0.696051i
$913$	−73.7126	−	22.7373i	−2.43953	−	0.752495i
$914$	−3.62756	−	4.54881i	−0.119989	−	0.150461i
$915$	−2.70351	+	36.0759i	−0.0893754	+	1.19263i
$916$	−21.9337	+	6.76564i	−0.724709	+	0.223543i
$917$	25.3162	+	17.2603i	0.836014	+	0.569985i
$918$	5.12035	+	0.771769i	0.168997	+	0.0254722i
$919$	−3.85073	−	16.8712i	−0.127024	−	0.556528i	−0.997885	−	0.0649996i	$-0.979295\pi$
$919$	−3.85073	−	16.8712i	−0.127024	−	0.556528i	0.870861	−	0.491529i	$-0.163562\pi$
$920$	−3.26126	+	3.02601i	−0.107521	+	0.0997646i
$921$	0.150985	+	2.01476i	0.00497514	+	0.0663886i
$922$	1.25204	+	3.19014i	0.0412337	+	0.105062i
$923$	3.49949	−	0.527463i	0.115187	−	0.0173617i
$924$	34.8862	+	16.8003i	1.14767	+	0.552690i
$925$	−2.34936	−	1.13139i	−0.0772463	−	0.0371999i
$926$	−24.1524	+	3.64039i	−0.793696	+	0.119630i
$927$	−6.24137	−	15.9027i	−0.204993	−	0.522315i
$928$	0.469766	+	6.26860i	0.0154208	+	0.205777i
$929$	−6.41357	+	5.95092i	−0.210422	+	0.195243i	−0.778342	−	0.627841i	$-0.783939\pi$
$929$	−6.41357	+	5.95092i	−0.210422	+	0.195243i	0.567920	+	0.823084i	$0.307748\pi$
$930$	−4.54908	−	19.9308i	−0.149170	−	0.653557i
$931$	23.5389	+	3.54791i	0.771455	+	0.116278i
$932$	−3.95196	−	2.69440i	−0.129451	−	0.0882580i
$933$	−45.6772	+	14.0895i	−1.49540	+	0.461271i
$934$	−2.33862	+	31.2068i	−0.0765221	+	1.02112i
$935$	−1.51088	−	1.89458i	−0.0494109	−	0.0619593i
$936$	−10.8511	−	3.34712i	−0.354679	−	0.109404i
$937$	−0.892856	+	2.27496i	−0.0291683	+	0.0743197i	−0.944716	−	0.327890i	$-0.893662\pi$
$937$	−0.892856	+	2.27496i	−0.0291683	+	0.0743197i	0.915548	+	0.402210i	$0.131758\pi$
$938$	−3.33591	+	14.6156i	−0.108921	+	0.477216i
$939$	7.42375	+	12.8583i	0.242265	+	0.419615i
$940$	4.43659	−	7.68440i	0.144706	−	0.250638i
$941$	−24.2859	−	22.5340i	−0.791697	−	0.734587i	0.176629	−	0.984278i	$-0.443481\pi$
$941$	−24.2859	−	22.5340i	−0.791697	−	0.734587i	−0.968326	+	0.249690i	$0.919671\pi$
$942$	−18.3265	+	22.9807i	−0.597110	+	0.748752i
$943$	−20.4618	+	13.9506i	−0.666327	+	0.454294i
$944$	−7.93926	+	3.82334i	−0.258401	+	0.124439i
$945$	−25.8538			−0.841024
$946$	35.9838	+	20.9996i	1.16993	+	0.682757i
$947$	31.6368			1.02806			0.514030	−	0.857772i	$-0.328152\pi$
$947$	31.6368			1.02806			0.514030	+	0.857772i	$0.328152\pi$
$948$	−9.82193	+	4.72999i	−0.319001	+	0.153623i
$949$	8.36190	−	5.70105i	0.271439	−	0.185064i
$950$	4.39925	−	5.51649i	0.142731	−	0.178979i
$951$	2.70686	+	2.51160i	0.0877759	+	0.0814441i
$952$	0.363145	−	0.628986i	0.0117696	−	0.0203855i
$953$	−6.54157	−	11.3303i	−0.211902	−	0.367025i	0.740408	−	0.672158i	$-0.234633\pi$
$953$	−6.54157	−	11.3303i	−0.211902	−	0.367025i	−0.952310	+	0.305133i	$0.901299\pi$
$954$	−11.1056	+	48.6568i	−0.359557	+	1.57532i
$955$	−2.33075	+	5.93864i	−0.0754212	+	0.192170i
$956$	22.6308	+	6.98068i	0.731933	+	0.225771i
$957$	−79.6951	−	99.9345i	−2.57618	−	3.23042i
$958$	0.924298	−	12.3339i	0.0298627	−	0.398490i
$959$	−23.5211	+	7.25531i	−0.759537	+	0.234286i
$960$	−2.64426	−	1.80282i	−0.0853430	−	0.0581859i
$961$	−9.69503	−	1.46129i	−0.312743	−	0.0471384i
$962$	0.909797	+	3.98608i	0.0293330	+	0.128516i
$963$	−36.8245	+	34.1681i	−1.18665	+	1.10105i
$964$	−0.673673	−	8.98954i	−0.0216975	−	0.289534i
$965$	−5.19494	−	13.2365i	−0.167231	−	0.426098i
$966$	26.8102	−	4.04098i	0.862603	−	0.130016i
$967$	12.0642	+	5.80982i	0.387959	+	0.186831i	0.617688	−	0.786424i	$-0.288070\pi$
$967$	12.0642	+	5.80982i	0.387959	+	0.186831i	−0.229729	+	0.973255i	$0.573784\pi$
$968$	−26.4595	−	12.7422i	−0.850441	−	0.409551i
$969$	8.51631	−	1.28363i	0.273583	−	0.0412360i
$970$	3.23560	+	8.24418i	0.103889	+	0.264705i
$971$	−3.60613	−	48.1204i	−0.115726	−	1.54426i	−0.688920	−	0.724838i	$-0.741915\pi$
$971$	−3.60613	−	48.1204i	−0.115726	−	1.54426i	0.573193	−	0.819420i	$-0.305704\pi$
$972$	−21.1068	+	19.5843i	−0.677001	+	0.628165i
$973$	−2.14431	−	9.39485i	−0.0687435	−	0.301185i
$974$	8.06719	+	1.21593i	0.258489	+	0.0389610i
$975$	−4.14609	−	2.82676i	−0.132781	−	0.0905286i
$976$	10.8019	−	3.33193i	0.345759	−	0.106653i
$977$	1.30376	−	17.3975i	0.0417111	−	0.556596i	−0.936728	−	0.350059i	$-0.886162\pi$
$977$	1.30376	−	17.3975i	0.0417111	−	0.556596i	0.978439	−	0.206537i	$-0.0662194\pi$
$978$	−13.7303	−	17.2172i	−0.439045	−	0.550546i
$979$	95.2812	+	29.3904i	3.04520	+	0.939320i
$980$	1.23257	−	3.14054i	0.0393731	−	0.100321i
$981$	10.5203	−	46.0924i	0.335887	−	1.47162i
$982$	2.66175	+	4.61028i	0.0849397	+	0.147120i
$983$	−1.51377	+	2.62192i	−0.0482817	+	0.0836264i	−0.889156	−	0.457604i	$-0.848708\pi$
$983$	−1.51377	+	2.62192i	−0.0482817	+	0.0836264i	0.840875	+	0.541230i	$0.182041\pi$
$984$	−13.0593	−	12.1173i	−0.416315	−	0.386284i
$985$	−12.0646	+	15.1286i	−0.384412	+	0.482037i
$986$	−1.98095	+	1.35059i	−0.0630863	+	0.0430115i
$987$	−48.7210	+	23.4628i	−1.55081	+	0.746828i
$988$	−11.0633			−0.351970
$989$	29.1016	−	2.04440i	0.925376	−	0.0650083i
$990$	46.0142			1.46243
$991$	−2.26256	+	1.08959i	−0.0718725	+	0.0346120i	−0.469475	−	0.882946i	$-0.655557\pi$
$991$	−2.26256	+	1.08959i	−0.0718725	+	0.0346120i	0.397602	+	0.917558i	$0.369842\pi$
$992$	−5.27788	+	3.59840i	−0.167573	+	0.114249i
$993$	−55.4972	+	69.5912i	−1.76115	+	2.20841i
$994$	−3.15073	−	2.92345i	−0.0999350	−	0.0927261i
$995$	−6.51535	+	11.2849i	−0.206550	+	0.357756i
$996$	−19.4280	−	33.6503i	−0.615600	−	1.06625i
$997$	−3.66848	+	16.0727i	−0.116182	+	0.509027i	0.883029	+	0.469318i	$0.155500\pi$
$997$	−3.66848	+	16.0727i	−0.116182	+	0.509027i	−0.999211	+	0.0397088i	$0.987357\pi$
$998$	−5.89145	+	15.0112i	−0.186491	+	0.475170i
$999$	33.8298	+	10.4351i	1.07033	+	0.330152i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.b.31.4	✓	48
43.25	even	21	inner	430.2.q.b.111.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.b.31.4	✓	48	1.1	even	1	trivial
430.2.q.b.111.4	yes	48	43.25	even	21	inner

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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.900969 + 0.433884i) q^{2} +(2.64426 - 1.80282i) q^{3} +(0.623490 - 0.781831i) q^{4} +(0.733052 + 0.680173i) q^{5} +(-1.60018 + 2.77159i) q^{6} +(-0.952135 - 1.64915i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(2.64590 - 6.74164i) q^{9} +O(q^{10})\)	\(q+(-0.900969 + 0.433884i) q^{2} +(2.64426 - 1.80282i) q^{3} +(0.623490 - 0.781831i) q^{4} +(0.733052 + 0.680173i) q^{5} +(-1.60018 + 2.77159i) q^{6} +(-0.952135 - 1.64915i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(2.64590 - 6.74164i) q^{9} +(-0.955573 - 0.294755i) q^{10} +(-3.96139 - 4.96742i) q^{11} +(0.239163 - 3.19141i) q^{12} +(-1.49830 + 0.462164i) q^{13} +(1.57338 + 1.07271i) q^{14} +(3.16461 + 0.476988i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(0.279587 - 0.259418i) q^{17} +(0.541215 + 7.22202i) q^{18} +(2.57779 + 6.56811i) q^{19} +(0.988831 - 0.149042i) q^{20} +(-5.49081 - 2.64423i) q^{21} +(5.72437 + 2.75671i) q^{22} +(4.39919 - 0.663072i) q^{23} +(1.16922 + 2.97913i) q^{24} +(0.0747301 + 0.997204i) q^{25} +(1.14940 - 1.06648i) q^{26} +(-3.02111 - 13.2364i) q^{27} +(-1.88300 - 0.283817i) q^{28} +(5.19388 + 3.54113i) q^{29} +(-3.05817 + 0.943321i) q^{30} +(-0.477364 + 6.36998i) q^{31} +(0.623490 + 0.781831i) q^{32} +(-19.4303 - 5.99345i) q^{33} +(-0.139341 + 0.355036i) q^{34} +(0.423740 - 1.85653i) q^{35} +(-3.62113 - 6.27199i) q^{36} +(-1.30379 + 2.25824i) q^{37} +(-5.17231 - 4.79920i) q^{38} +(-3.12869 + 3.92325i) q^{39} +(-0.826239 + 0.563320i) q^{40} +(-5.01530 + 2.41524i) q^{41} +6.09434 q^{42} +(6.53675 + 0.520533i) q^{43} -6.35357 q^{44} +(6.52506 - 3.14230i) q^{45} +(-3.67584 + 2.50614i) q^{46} +(5.53234 - 6.93734i) q^{47} +(-2.34603 - 2.17679i) q^{48} +(1.68688 - 2.92176i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(0.271613 - 1.19001i) q^{51} +(-0.572840 + 1.45957i) q^{52} +(6.58507 + 2.03122i) q^{53} +(8.46497 + 10.6147i) q^{54} +(0.474803 - 6.33580i) q^{55} +(1.81967 - 0.561293i) q^{56} +(18.6575 + 12.7205i) q^{57} +(-6.21596 - 0.936906i) q^{58} +(-1.96083 - 8.59098i) q^{59} +(2.34603 - 2.17679i) q^{60} +(0.844754 + 11.2725i) q^{61} +(-2.33374 - 5.94628i) q^{62} +(-13.6372 + 2.05548i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(-1.41268 - 0.680312i) q^{65} +(20.1066 - 3.03058i) q^{66} +(2.87616 + 7.32835i) q^{67} +(-0.0285021 - 0.380334i) q^{68} +(10.4372 - 9.68430i) q^{69} +(0.423740 + 1.85653i) q^{70} +(-2.23187 - 0.336401i) q^{71} +(5.98384 + 4.07971i) q^{72} +(-6.16777 + 1.90251i) q^{73} +(0.194865 - 2.60030i) q^{74} +(1.99539 + 2.50214i) q^{75} +(6.74238 + 2.07975i) q^{76} +(-4.42023 + 11.2626i) q^{77} +(1.11662 - 4.89221i) q^{78} +(-1.70317 - 2.94998i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-15.9246 - 14.7758i) q^{81} +(3.47069 - 4.35211i) q^{82} +(10.0315 - 6.83936i) q^{83} +(-5.49081 + 2.64423i) q^{84} +0.381401 q^{85} +(-6.11526 + 2.36720i) q^{86} +20.1180 q^{87} +(5.72437 - 2.75671i) q^{88} +(-12.9668 + 8.84059i) q^{89} +(-4.51548 + 5.66223i) q^{90} +(2.18876 + 2.03087i) q^{91} +(2.22444 - 3.85285i) q^{92} +(10.2217 + 17.7045i) q^{93} +(-1.97447 + 8.65072i) q^{94} +(-2.57779 + 6.56811i) q^{95} +(3.05817 + 0.943321i) q^{96} +(-5.52187 - 6.92420i) q^{97} +(-0.252121 + 3.36432i) q^{98} +(-43.9700 + 13.5629i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9}+O(q^{10}) \) 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9	\( 48 q - 8 q^{2} - q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} - 7 q^{7} - 8 q^{8} - q^{9} - 4 q^{10} - 9 q^{11} - q^{12} - 11 q^{13} + 7 q^{14} - 6 q^{15} - 8 q^{16} - 11 q^{17} - 15 q^{18} + 31 q^{19} - 4 q^{20} + 4 q^{21} + 12 q^{22} + 4 q^{23} + 6 q^{24} + 4 q^{25} + 31 q^{26} + 44 q^{27} + 13 q^{29} + q^{30} - q^{31} - 8 q^{32} - 30 q^{33} - 25 q^{34} + 14 q^{35} - 36 q^{36} - 27 q^{37} - 4 q^{38} + 4 q^{39} - 4 q^{40} + 16 q^{41} + 4 q^{42} - 7 q^{43} - 30 q^{44} + 12 q^{45} - 52 q^{46} - 43 q^{47} - q^{48} - 23 q^{49} - 24 q^{50} - 7 q^{51} - 25 q^{52} + 73 q^{53} - 61 q^{54} + 27 q^{55} + 7 q^{56} + 136 q^{57} - 36 q^{58} + 58 q^{59} + q^{60} - 61 q^{61} + 27 q^{62} + 32 q^{63} - 8 q^{64} - q^{65} + 12 q^{66} + 39 q^{67} + 17 q^{68} - 34 q^{69} + 14 q^{70} + 60 q^{71} + 27 q^{72} + 3 q^{73} + 29 q^{74} - 12 q^{75} + 17 q^{76} - 27 q^{77} - 17 q^{78} - 2 q^{79} + 24 q^{80} - 165 q^{81} + 2 q^{82} + 74 q^{83} + 4 q^{84} - 8 q^{85} + 14 q^{86} + 88 q^{87} + 12 q^{88} + 23 q^{89} - 2 q^{90} - 39 q^{91} + 4 q^{92} - 46 q^{93} + 55 q^{94} - 31 q^{95} - q^{96} - 85 q^{97} + 33 q^{98} - 168 q^{99}+O(q^{100}) \) 48 * q - 8 * q^2 - q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 - 7 * q^7 - 8 * q^8 - q^9 - 4 * q^10 - 9 * q^11 - q^12 - 11 * q^13 + 7 * q^14 - 6 * q^15 - 8 * q^16 - 11 * q^17 - 15 * q^18 + 31 * q^19 - 4 * q^20 + 4 * q^21 + 12 * q^22 + 4 * q^23 + 6 * q^24 + 4 * q^25 + 31 * q^26 + 44 * q^27 + 13 * q^29 + q^30 - q^31 - 8 * q^32 - 30 * q^33 - 25 * q^34 + 14 * q^35 - 36 * q^36 - 27 * q^37 - 4 * q^38 + 4 * q^39 - 4 * q^40 + 16 * q^41 + 4 * q^42 - 7 * q^43 - 30 * q^44 + 12 * q^45 - 52 * q^46 - 43 * q^47 - q^48 - 23 * q^49 - 24 * q^50 - 7 * q^51 - 25 * q^52 + 73 * q^53 - 61 * q^54 + 27 * q^55 + 7 * q^56 + 136 * q^57 - 36 * q^58 + 58 * q^59 + q^60 - 61 * q^61 + 27 * q^62 + 32 * q^63 - 8 * q^64 - q^65 + 12 * q^66 + 39 * q^67 + 17 * q^68 - 34 * q^69 + 14 * q^70 + 60 * q^71 + 27 * q^72 + 3 * q^73 + 29 * q^74 - 12 * q^75 + 17 * q^76 - 27 * q^77 - 17 * q^78 - 2 * q^79 + 24 * q^80 - 165 * q^81 + 2 * q^82 + 74 * q^83 + 4 * q^84 - 8 * q^85 + 14 * q^86 + 88 * q^87 + 12 * q^88 + 23 * q^89 - 2 * q^90 - 39 * q^91 + 4 * q^92 - 46 * q^93 + 55 * q^94 - 31 * q^95 - q^96 - 85 * q^97 + 33 * q^98 - 168 * q^99

Introduction

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