LMFDB - Embedded newform 430.2.q.a.31.1

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:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			31.1
Character	$\chi$	$=$	430.31
Dual form			430.2.q.a.111.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.900969 + 0.433884i) q^{2} +(-1.94282 + 1.32459i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-0.733052 - 0.680173i) q^{5} +(1.17570 - 2.03638i) q^{6} +(1.33082 + 2.30504i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(0.923984 - 2.35427i) q^{9} +O(q^{10})$	\(q+(-0.900969 + 0.433884i) q^{2} +(-1.94282 + 1.32459i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-0.733052 - 0.680173i) q^{5} +(1.17570 - 2.03638i) q^{6} +(1.33082 + 2.30504i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(0.923984 - 2.35427i) q^{9} +(0.955573 + 0.294755i) q^{10} +(2.03611 + 2.55320i) q^{11} +(-0.175721 + 2.34483i) q^{12} +(-2.20188 + 0.679191i) q^{13} +(-2.19914 - 1.49935i) q^{14} +(2.32514 + 0.350459i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(-3.42111 + 3.17433i) q^{17} +(0.189000 + 2.52203i) q^{18} +(-1.33932 - 3.41253i) q^{19} +(-0.988831 + 0.149042i) q^{20} +(-5.63878 - 2.71549i) q^{21} +(-2.94227 - 1.41692i) q^{22} +(-0.878056 + 0.132346i) q^{23} +(-0.859064 - 2.18886i) q^{24} +(0.0747301 + 0.997204i) q^{25} +(1.68914 - 1.56729i) q^{26} +(-0.246393 - 1.07952i) q^{27} +(2.63190 + 0.396696i) q^{28} +(-5.38956 - 3.67454i) q^{29} +(-2.24694 + 0.693088i) q^{30} +(0.0946169 - 1.26257i) q^{31} +(0.623490 + 0.781831i) q^{32} +(-7.33776 - 2.26340i) q^{33} +(1.70502 - 4.34433i) q^{34} +(0.592269 - 2.59490i) q^{35} +(-1.26455 - 2.19026i) q^{36} +(0.861119 - 1.49150i) q^{37} +(2.68732 + 2.49347i) q^{38} +(3.37821 - 4.23615i) q^{39} +(0.826239 - 0.563320i) q^{40} +(-8.53107 + 4.10835i) q^{41} +6.25857 q^{42} +(0.0655539 - 6.55711i) q^{43} +3.26567 q^{44} +(-2.27864 + 1.09733i) q^{45} +(0.733679 - 0.500214i) q^{46} +(-5.86764 + 7.35779i) q^{47} +(1.72370 + 1.59936i) q^{48} +(-0.0421428 + 0.0729934i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(2.44191 - 10.6987i) q^{51} +(-0.841839 + 2.14497i) q^{52} +(-6.72985 - 2.07589i) q^{53} +(0.690377 + 0.865705i) q^{54} +(0.244044 - 3.25654i) q^{55} +(-2.54338 + 0.784530i) q^{56} +(7.12227 + 4.85588i) q^{57} +(6.45015 + 0.972203i) q^{58} +(0.719210 + 3.15106i) q^{59} +(1.72370 - 1.59936i) q^{60} +(0.202599 + 2.70350i) q^{61} +(0.462564 + 1.17859i) q^{62} +(6.65635 - 1.00328i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(2.07606 + 0.999779i) q^{65} +(7.59314 - 1.14448i) q^{66} +(2.88593 + 7.35322i) q^{67} +(0.348761 + 4.65389i) q^{68} +(1.53060 - 1.42019i) q^{69} +(0.592269 + 2.59490i) q^{70} +(-5.36519 - 0.808673i) q^{71} +(2.08964 + 1.42469i) q^{72} +(-7.51740 + 2.31881i) q^{73} +(-0.128703 + 1.71742i) q^{74} +(-1.46608 - 1.83840i) q^{75} +(-3.50307 - 1.08055i) q^{76} +(-3.17555 + 8.09117i) q^{77} +(-1.20567 + 5.28239i) q^{78} +(1.20165 + 2.08132i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(7.47050 + 6.93161i) q^{81} +(5.90368 - 7.40298i) q^{82} +(10.4297 - 7.11087i) q^{83} +(-5.63878 + 2.71549i) q^{84} +4.66694 q^{85} +(2.78596 + 5.93620i) q^{86} +15.3382 q^{87} +(-2.94227 + 1.41692i) q^{88} +(-14.1990 + 9.68073i) q^{89} +(1.57687 - 1.97733i) q^{90} +(-4.49587 - 4.17155i) q^{91} +(-0.443987 + 0.769008i) q^{92} +(1.48857 + 2.57829i) q^{93} +(2.09414 - 9.17501i) q^{94} +(-1.33932 + 3.41253i) q^{95} +(-2.24694 - 0.693088i) q^{96} +(11.8716 + 14.8865i) q^{97} +(0.00629867 - 0.0840499i) q^{98} +(7.89227 - 2.43444i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) $ 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9	\( 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9} + 3 q^{10} + 9 q^{11} - 16 q^{12} + 21 q^{13} - 6 q^{14} + 5 q^{15} - 6 q^{16} - 37 q^{17} + 19 q^{18} + 7 q^{19} + 3 q^{20} - 8 q^{21} + 16 q^{22} + 13 q^{23} + 5 q^{24} + 3 q^{25} - 21 q^{26} - 28 q^{27} - 6 q^{28} + 4 q^{29} - 2 q^{30} + 13 q^{31} - 6 q^{32} - 54 q^{33} - 23 q^{34} - 2 q^{35} - 9 q^{36} + 17 q^{37} + 28 q^{38} + 8 q^{39} + 3 q^{40} + 10 q^{41} - 50 q^{42} + 14 q^{43} - 26 q^{44} + 4 q^{45} - 8 q^{46} + 13 q^{47} - 2 q^{48} + 5 q^{49} - 18 q^{50} + 17 q^{51} - 7 q^{52} - 71 q^{53} + 7 q^{54} - 29 q^{55} + q^{56} - 70 q^{57} + 25 q^{58} + 8 q^{59} - 2 q^{60} + 25 q^{61} - 15 q^{62} + 88 q^{63} - 6 q^{64} + 7 q^{65} + 44 q^{66} + 26 q^{67} - 9 q^{68} + 78 q^{69} - 2 q^{70} - 60 q^{71} - 23 q^{72} + 7 q^{73} + 17 q^{74} - 10 q^{75} - 35 q^{76} - 5 q^{77} + 57 q^{78} + 52 q^{79} - 18 q^{80} + q^{81} - 4 q^{82} - 101 q^{83} - 8 q^{84} - 24 q^{85} + 49 q^{86} - 18 q^{87} + 16 q^{88} + 14 q^{89} - 3 q^{90} + 35 q^{91} + 6 q^{92} + 28 q^{93} - 15 q^{94} + 7 q^{95} - 2 q^{96} + 11 q^{97} + 12 q^{98} + 78 q^{99}+O(q^{100}) \) 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9 + 3 * q^10 + 9 * q^11 - 16 * q^12 + 21 * q^13 - 6 * q^14 + 5 * q^15 - 6 * q^16 - 37 * q^17 + 19 * q^18 + 7 * q^19 + 3 * q^20 - 8 * q^21 + 16 * q^22 + 13 * q^23 + 5 * q^24 + 3 * q^25 - 21 * q^26 - 28 * q^27 - 6 * q^28 + 4 * q^29 - 2 * q^30 + 13 * q^31 - 6 * q^32 - 54 * q^33 - 23 * q^34 - 2 * q^35 - 9 * q^36 + 17 * q^37 + 28 * q^38 + 8 * q^39 + 3 * q^40 + 10 * q^41 - 50 * q^42 + 14 * q^43 - 26 * q^44 + 4 * q^45 - 8 * q^46 + 13 * q^47 - 2 * q^48 + 5 * q^49 - 18 * q^50 + 17 * q^51 - 7 * q^52 - 71 * q^53 + 7 * q^54 - 29 * q^55 + q^56 - 70 * q^57 + 25 * q^58 + 8 * q^59 - 2 * q^60 + 25 * q^61 - 15 * q^62 + 88 * q^63 - 6 * q^64 + 7 * q^65 + 44 * q^66 + 26 * q^67 - 9 * q^68 + 78 * q^69 - 2 * q^70 - 60 * q^71 - 23 * q^72 + 7 * q^73 + 17 * q^74 - 10 * q^75 - 35 * q^76 - 5 * q^77 + 57 * q^78 + 52 * q^79 - 18 * q^80 + q^81 - 4 * q^82 - 101 * q^83 - 8 * q^84 - 24 * q^85 + 49 * q^86 - 18 * q^87 + 16 * q^88 + 14 * q^89 - 3 * q^90 + 35 * q^91 + 6 * q^92 + 28 * q^93 - 15 * q^94 + 7 * q^95 - 2 * q^96 + 11 * q^97 + 12 * q^98 + 78 * 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
$3$	−1.94282	+	1.32459i	−1.12169	+	0.764754i	−0.974507	−	0.224356i	$-0.927972\pi$
$3$	−1.94282	+	1.32459i	−1.12169	+	0.764754i	−0.147181	+	0.989110i	$0.547020\pi$
$4$	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
$6$	1.17570	−	2.03638i	0.479978	−	0.831347i
$7$	1.33082	+	2.30504i	0.503001	+	0.871224i	0.999994	+	0.00346895i	$0.00110420\pi$
$7$	1.33082	+	2.30504i	0.503001	+	0.871224i	−0.496993	+	0.867755i	$0.665562\pi$
$8$	−0.222521	+	0.974928i	−0.0786730	+	0.344689i
$9$	0.923984	−	2.35427i	0.307995	−	0.784757i
$10$	0.955573	+	0.294755i	0.302179	+	0.0932098i
$11$	2.03611	+	2.55320i	0.613911	+	0.769820i	0.987474	−	0.157785i	$-0.0504353\pi$
$11$	2.03611	+	2.55320i	0.613911	+	0.769820i	−0.373562	+	0.927605i	$0.621864\pi$
$12$	−0.175721	+	2.34483i	−0.0507262	+	0.676894i
$13$	−2.20188	+	0.679191i	−0.610693	+	0.188374i	−0.584648	−	0.811287i	$-0.698767\pi$
$13$	−2.20188	+	0.679191i	−0.610693	+	0.188374i	−0.0260446	+	0.999661i	$0.508291\pi$
$14$	−2.19914	−	1.49935i	−0.587746	−	0.400718i
$15$	2.32514	+	0.350459i	0.600349	+	0.0904880i
$16$	−0.222521	−	0.974928i	−0.0556302	−	0.243732i
$17$	−3.42111	+	3.17433i	−0.829741	+	0.769887i	−0.975632	−	0.219414i	$-0.929586\pi$
$17$	−3.42111	+	3.17433i	−0.829741	+	0.769887i	0.145891	+	0.989301i	$0.453395\pi$
$18$	0.189000	+	2.52203i	0.0445477	+	0.594447i
$19$	−1.33932	−	3.41253i	−0.307261	−	0.782888i	−0.998200	−	0.0599747i	$-0.980898\pi$
$19$	−1.33932	−	3.41253i	−0.307261	−	0.782888i	0.690939	−	0.722913i	$-0.257197\pi$
$20$	−0.988831	+	0.149042i	−0.221109	+	0.0333269i
$21$	−5.63878	−	2.71549i	−1.23048	−	0.592569i
$22$	−2.94227	−	1.41692i	−0.627294	−	0.302089i
$23$	−0.878056	+	0.132346i	−0.183087	+	0.0275960i	−0.239946	−	0.970786i	$-0.577130\pi$
$23$	−0.878056	+	0.132346i	−0.183087	+	0.0275960i	0.0568585	+	0.998382i	$0.481892\pi$
$24$	−0.859064	−	2.18886i	−0.175356	−	0.446799i
$25$	0.0747301	+	0.997204i	0.0149460	+	0.199441i
$26$	1.68914	−	1.56729i	0.331267	−	0.307371i
$27$	−0.246393	−	1.07952i	−0.0474183	−	0.207753i
$28$	2.63190	+	0.396696i	0.497383	+	0.0749684i
$29$	−5.38956	−	3.67454i	−1.00082	−	0.682345i	−0.0521548	−	0.998639i	$-0.516609\pi$
$29$	−5.38956	−	3.67454i	−1.00082	−	0.682345i	−0.948661	+	0.316294i	$0.897561\pi$
$30$	−2.24694	+	0.693088i	−0.410233	+	0.126540i
$31$	0.0946169	−	1.26257i	0.0169937	−	0.226765i	−0.982240	−	0.187628i	$-0.939920\pi$
$31$	0.0946169	−	1.26257i	0.0169937	−	0.226765i	0.999234	−	0.0391371i	$-0.0124609\pi$
$32$	0.623490	+	0.781831i	0.110218	+	0.138210i
$33$	−7.33776	−	2.26340i	−1.27734	−	0.394007i
$34$	1.70502	−	4.34433i	0.292409	−	0.745047i
$35$	0.592269	−	2.59490i	0.100112	−	0.438618i
$36$	−1.26455	−	2.19026i	−0.210758	−	0.365044i
$37$	0.861119	−	1.49150i	0.141567	−	0.245201i	−0.786520	−	0.617565i	$-0.788119\pi$
$37$	0.861119	−	1.49150i	0.141567	−	0.245201i	0.928087	+	0.372364i	$0.121453\pi$
$38$	2.68732	+	2.49347i	0.435942	+	0.404495i
$39$	3.37821	−	4.23615i	0.540947	−	0.678326i
$40$	0.826239	−	0.563320i	0.130640	−	0.0890687i
$41$	−8.53107	+	4.10835i	−1.33233	+	0.641616i	−0.958290	−	0.285797i	$-0.907742\pi$
$41$	−8.53107	+	4.10835i	−1.33233	+	0.641616i	−0.374039	+	0.927413i	$0.622027\pi$
$42$	6.25857			0.965719
$43$	0.0655539	−	6.55711i	0.00999687	−	0.999950i
$43$	0.0655539	−	6.55711i	0.00999687	−	0.999950i
$44$	3.26567			0.492318
$45$	−2.27864	+	1.09733i	−0.339679	+	0.163581i
$46$	0.733679	−	0.500214i	0.108175	−	0.0737525i
$47$	−5.86764	+	7.35779i	−0.855883	+	1.07324i	0.140651	+	0.990059i	$0.455080\pi$
$47$	−5.86764	+	7.35779i	−0.855883	+	1.07324i	−0.996534	+	0.0831842i	$0.973491\pi$
$48$	1.72370	+	1.59936i	0.248795	+	0.230848i
$49$	−0.0421428	+	0.0729934i	−0.00602040	+	0.0104276i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	2.44191	−	10.6987i	0.341936	−	1.49812i
$52$	−0.841839	+	2.14497i	−0.116742	+	0.297454i
$53$	−6.72985	−	2.07589i	−0.924417	−	0.285145i	−0.204228	−	0.978923i	$-0.565468\pi$
$53$	−6.72985	−	2.07589i	−0.924417	−	0.285145i	−0.720188	+	0.693779i	$0.755945\pi$
$54$	0.690377	+	0.865705i	0.0939484	+	0.117808i
$55$	0.244044	−	3.25654i	0.0329069	−	0.439112i
$56$	−2.54338	+	0.784530i	−0.339874	+	0.104837i
$57$	7.12227	+	4.85588i	0.943367	+	0.643177i
$58$	6.45015	+	0.972203i	0.846946	+	0.127657i
$59$	0.719210	+	3.15106i	0.0936332	+	0.410234i	0.999923	−	0.0124234i	$-0.00395460\pi$
$59$	0.719210	+	3.15106i	0.0936332	+	0.410234i	−0.906290	+	0.422657i	$0.861097\pi$
$60$	1.72370	−	1.59936i	0.222529	−	0.206477i
$61$	0.202599	+	2.70350i	0.0259402	+	0.346148i	0.995040	+	0.0994781i	$0.0317173\pi$
$61$	0.202599	+	2.70350i	0.0259402	+	0.346148i	−0.969100	+	0.246670i	$0.920664\pi$
$62$	0.462564	+	1.17859i	0.0587457	+	0.149681i
$63$	6.65635	−	1.00328i	0.838621	−	0.126402i
$64$	−0.900969	−	0.433884i	−0.112621	−	0.0542355i
$65$	2.07606	+	0.999779i	0.257504	+	0.124007i
$66$	7.59314	−	1.14448i	0.934651	−	0.140876i
$67$	2.88593	+	7.35322i	0.352572	+	0.898339i	0.991622	+	0.129173i	$0.0412324\pi$
$67$	2.88593	+	7.35322i	0.352572	+	0.898339i	−0.639050	+	0.769165i	$0.720672\pi$
$68$	0.348761	+	4.65389i	0.0422935	+	0.564367i
$69$	1.53060	−	1.42019i	0.184263	−	0.170971i
$70$	0.592269	+	2.59490i	0.0707897	+	0.310150i
$71$	−5.36519	−	0.808673i	−0.636731	−	0.0959718i	−0.177259	−	0.984164i	$-0.556723\pi$
$71$	−5.36519	−	0.808673i	−0.636731	−	0.0959718i	−0.459472	+	0.888192i	$0.651961\pi$
$72$	2.08964	+	1.42469i	0.246266	+	0.167902i
$73$	−7.51740	+	2.31881i	−0.879845	+	0.271396i	−0.701584	−	0.712587i	$-0.747523\pi$
$73$	−7.51740	+	2.31881i	−0.879845	+	0.271396i	−0.178261	+	0.983983i	$0.557047\pi$
$74$	−0.128703	+	1.71742i	−0.0149614	+	0.199646i
$75$	−1.46608	−	1.83840i	−0.169288	−	0.212280i
$76$	−3.50307	−	1.08055i	−0.401830	−	0.123948i
$77$	−3.17555	+	8.09117i	−0.361887	+	0.922074i
$78$	−1.20567	+	5.28239i	−0.136515	+	0.598113i
$79$	1.20165	+	2.08132i	0.135196	+	0.234167i	0.925672	−	0.378326i	$-0.123500\pi$
$79$	1.20165	+	2.08132i	0.135196	+	0.234167i	−0.790476	+	0.612493i	$0.790167\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	7.47050	+	6.93161i	0.830055	+	0.770179i
$82$	5.90368	−	7.40298i	0.651953	−	0.817523i
$83$	10.4297	−	7.11087i	1.14481	−	0.780520i	0.166171	−	0.986097i	$-0.446860\pi$
$83$	10.4297	−	7.11087i	1.14481	−	0.780520i	0.978641	+	0.205577i	$0.0659072\pi$
$84$	−5.63878	+	2.71549i	−0.615241	+	0.296285i
$85$	4.66694			0.506201
$86$	2.78596	+	5.93620i	0.300418	+	0.640116i
$87$	15.3382			1.64443
$88$	−2.94227	+	1.41692i	−0.313647	+	0.151044i
$89$	−14.1990	+	9.68073i	−1.50509	+	1.02616i	−0.519994	+	0.854170i	$0.674066\pi$
$89$	−14.1990	+	9.68073i	−1.50509	+	1.02616i	−0.985099	+	0.171986i	$0.944982\pi$
$90$	1.57687	−	1.97733i	0.166216	−	0.208429i
$91$	−4.49587	−	4.17155i	−0.471295	−	0.437298i
$92$	−0.443987	+	0.769008i	−0.0462888	+	0.0801746i
$93$	1.48857	+	2.57829i	0.154358	+	0.267356i
$94$	2.09414	−	9.17501i	0.215994	−	0.946330i
$95$	−1.33932	+	3.41253i	−0.137411	+	0.350118i
$96$	−2.24694	−	0.693088i	−0.229327	−	0.0707380i
$97$	11.8716	+	14.8865i	1.20538	+	1.51150i	0.802953	+	0.596042i	$0.203261\pi$
$97$	11.8716	+	14.8865i	1.20538	+	1.51150i	0.402424	+	0.915453i	$0.368168\pi$
$98$	0.00629867	−	0.0840499i	0.000636261	−	0.00849032i
$99$	7.89227	−	2.43444i	0.793203	−	0.244671i
$100$	0.826239	+	0.563320i	0.0826239	+	0.0563320i
$101$	13.8797	+	2.09203i	1.38109	+	0.208165i	0.797222	−	0.603686i	$-0.206302\pi$
$101$	13.8797	+	2.09203i	1.38109	+	0.208165i	0.583864	+	0.811851i	$0.301540\pi$
$102$	2.44191	+	10.6987i	0.241785	+	1.05933i
$103$	−3.39210	+	3.14741i	−0.334233	+	0.310123i	−0.829379	−	0.558687i	$-0.811305\pi$
$103$	−3.39210	+	3.14741i	−0.334233	+	0.310123i	0.495145	+	0.868810i	$0.335115\pi$
$104$	−0.172197	−	2.29781i	−0.0168853	−	0.225319i
$105$	2.28651	+	5.82594i	0.223141	+	0.568554i
$106$	6.96408	−	1.04967i	0.676411	−	0.101953i
$107$	−6.77913	−	3.26466i	−0.655363	−	0.315606i	0.0764882	−	0.997070i	$-0.475629\pi$
$107$	−6.77913	−	3.26466i	−0.655363	−	0.315606i	−0.731852	+	0.681464i	$0.761344\pi$
$108$	−0.997624	−	0.480430i	−0.0959964	−	0.0462294i
$109$	5.45424	−	0.822095i	0.522422	−	0.0787424i	0.117463	−	0.993077i	$-0.462524\pi$
$109$	5.45424	−	0.822095i	0.522422	−	0.0787424i	0.404959	+	0.914335i	$0.367286\pi$
$110$	1.19308	+	3.03993i	0.113756	+	0.289846i
$111$	0.302633	+	4.03835i	0.0287246	+	0.383304i
$112$	1.95111	−	1.81037i	0.184363	−	0.171064i
$113$	−2.83140	−	12.4052i	−0.266356	−	1.16698i	−0.914218	−	0.405223i	$-0.867194\pi$
$113$	−2.83140	−	12.4052i	−0.266356	−	1.16698i	0.647862	−	0.761758i	$-0.275663\pi$
$114$	−8.52383	−	1.28476i	−0.798329	−	0.120329i
$115$	0.733679	+	0.500214i	0.0684159	+	0.0466452i
$116$	−6.23321	+	1.92269i	−0.578739	+	0.178517i
$117$	−0.435504	+	5.81139i	−0.0402623	+	0.537264i
$118$	−2.01518	−	2.52696i	−0.185513	−	0.232625i
$119$	−11.8698	−	3.66135i	−1.08810	−	0.335636i
$120$	−0.859064	+	2.18886i	−0.0784215	+	0.199815i
$121$	0.0746316	−	0.326982i	0.00678469	−	0.0297257i
$122$	−1.35554	−	2.34787i	−0.122725	−	0.212566i
$123$	11.1325	−	19.2820i	1.00378	−	1.73860i
$124$	−0.928128	−	0.861177i	−0.0833483	−	0.0773360i
$125$	0.623490	−	0.781831i	0.0557666	−	0.0699291i
$126$	−5.56185	+	3.79201i	−0.495489	+	0.337819i
$127$	3.83479	−	1.84674i	0.340282	−	0.163871i	−0.255936	−	0.966694i	$-0.582384\pi$
$127$	3.83479	−	1.84674i	0.340282	−	0.163871i	0.596218	+	0.802822i	$0.296669\pi$
$128$	1.00000			0.0883883
$129$	8.55814	+	12.8261i	0.753502	+	1.12928i
$130$	−2.30426			−0.202097
$131$	−1.12126	+	0.539968i	−0.0979646	+	0.0471773i	−0.482224	−	0.876048i	$-0.660171\pi$
$131$	−1.12126	+	0.539968i	−0.0979646	+	0.0471773i	0.384260	+	0.923225i	$0.374457\pi$
$132$	−6.34461	+	4.32568i	−0.552228	+	0.376503i
$133$	6.08363	−	7.62863i	0.527518	−	0.661486i
$134$	−5.79057	−	5.37286i	−0.500229	−	0.464145i
$135$	−0.553639	+	0.958931i	−0.0476497	+	0.0825317i
$136$	−2.33347	−	4.04169i	−0.200093	−	0.346572i
$137$	2.44867	−	10.7283i	0.209204	−	0.916582i	−0.755894	−	0.654694i	$-0.772798\pi$
$137$	2.44867	−	10.7283i	0.209204	−	0.916582i	0.965098	−	0.261888i	$-0.0843452\pi$
$138$	−0.762827	+	1.94365i	−0.0649361	+	0.165455i
$139$	10.1586	+	3.13352i	0.861644	+	0.265782i	0.693920	−	0.720052i	$-0.255882\pi$
$139$	10.1586	+	3.13352i	0.861644	+	0.265782i	0.167724	+	0.985834i	$0.446358\pi$
$140$	−1.65950	−	2.08095i	−0.140253	−	0.175872i
$141$	1.65370	−	22.0671i	0.139267	−	1.85838i
$142$	5.18474	−	1.59928i	0.435094	−	0.134209i
$143$	−6.21740	−	4.23895i	−0.519925	−	0.354479i
$144$	−2.50085	−	0.376943i	−0.208404	−	0.0314119i
$145$	1.45151	+	6.35946i	0.120541	+	0.528124i
$146$	5.76685	−	5.35085i	0.477268	−	0.442840i
$147$	−0.0148107	−	0.197635i	−0.00122157	−	0.0163007i
$148$	−0.629204	−	1.60319i	−0.0517203	−	0.131781i
$149$	1.06360	−	0.160312i	0.0871335	−	0.0131333i	−0.105331	−	0.994437i	$-0.533590\pi$
$149$	1.06360	−	0.160312i	0.0871335	−	0.0131333i	0.192464	+	0.981304i	$0.438352\pi$
$150$	2.11854	+	1.02024i	0.172978	+	0.0833019i
$151$	11.7117	+	5.64007i	0.953087	+	0.458982i	0.844767	−	0.535134i	$-0.179739\pi$
$151$	11.7117	+	5.64007i	0.953087	+	0.458982i	0.108319	+	0.994116i	$0.465453\pi$
$152$	3.62499	−	0.546380i	0.294026	−	0.0443173i
$153$	4.31218	+	10.9872i	0.348619	+	0.888266i
$154$	−0.649555	−	8.66771i	−0.0523426	−	0.698464i
$155$	−0.928128	+	0.861177i	−0.0745490	+	0.0691714i
$156$	−1.20567	−	5.28239i	−0.0965309	−	0.422930i
$157$	−16.7217	−	2.52039i	−1.33454	−	0.201149i	−0.557277	−	0.830327i	$-0.688154\pi$
$157$	−16.7217	−	2.52039i	−1.33454	−	0.201149i	−0.777262	+	0.629177i	$0.783392\pi$
$158$	−1.98570	−	1.35383i	−0.157974	−	0.107705i
$159$	15.8246	−	4.88124i	1.25497	−	0.387108i
$160$	0.0747301	−	0.997204i	0.00590793	−	0.0788359i
$161$	−1.47359	−	1.84783i	−0.116135	−	0.145629i
$162$	−9.73820	−	3.00384i	−0.765105	−	0.236004i
$163$	−0.224592	+	0.572251i	−0.0175914	+	0.0448222i	−0.939400	−	0.342824i	$-0.888617\pi$
$163$	−0.224592	+	0.572251i	−0.0175914	+	0.0448222i	0.921808	+	0.387646i	$0.126712\pi$
$164$	−2.10700	+	9.23137i	−0.164529	+	0.720849i
$165$	3.83946	+	6.65013i	0.298901	+	0.517712i
$166$	−6.31157	+	10.9320i	−0.489873	+	0.848485i
$167$	−2.69489	−	2.50049i	−0.208537	−	0.193494i	0.568989	−	0.822345i	$-0.307335\pi$
$167$	−2.69489	−	2.50049i	−0.208537	−	0.193494i	−0.777525	+	0.628851i	$0.783525\pi$
$168$	3.90216	−	4.89315i	0.301058	−	0.377515i
$169$	−6.35411	+	4.33216i	−0.488778	+	0.333243i
$170$	−4.20477	+	2.02491i	−0.322491	+	0.155303i
$171$	−9.27153			−0.709011
$172$	−5.08568	−	4.13954i	−0.387780	−	0.315637i
$173$	−17.7704			−1.35106			−0.675530	−	0.737333i	$-0.736085\pi$
$173$	−17.7704			−1.35106			−0.675530	+	0.737333i	$0.736085\pi$
$174$	−13.8193	+	6.65500i	−1.04763	+	0.504514i
$175$	−2.19914	+	1.49935i	−0.166240	+	0.113340i
$176$	2.03611	−	2.55320i	0.153478	−	0.192455i
$177$	−5.57117	−	5.16929i	−0.418755	−	0.388548i
$178$	8.59257	−	14.8828i	0.644040	−	1.11551i
$179$	9.65656	+	16.7257i	0.721765	+	1.25013i	0.960292	+	0.278998i	$0.0900024\pi$
$179$	9.65656	+	16.7257i	0.721765	+	1.25013i	−0.238526	+	0.971136i	$0.576664\pi$
$180$	−0.562777	+	2.46569i	−0.0419470	+	0.183782i
$181$	−3.34874	+	8.53246i	−0.248910	+	0.634213i	−0.999652	−	0.0263831i	$-0.991601\pi$
$181$	−3.34874	+	8.53246i	−0.248910	+	0.634213i	0.750742	+	0.660596i	$0.229696\pi$
$182$	5.86060	+	1.80776i	0.434417	+	0.134000i
$183$	−3.97465	−	4.98406i	−0.293815	−	0.368432i
$184$	0.0663584	−	0.885491i	0.00489200	−	0.0652793i
$185$	−1.64572	+	0.507639i	−0.120996	+	0.0373223i
$186$	−2.45983	−	1.67709i	−0.180364	−	0.122970i
$187$	−15.0705	−	2.27151i	−1.10206	−	0.166109i
$188$	2.09414	+	9.17501i	0.152731	+	0.669156i
$189$	2.16043	−	2.00458i	0.157148	−	0.145812i
$190$	−0.273956	−	3.65569i	−0.0198749	−	0.265212i
$191$	9.30202	+	23.7012i	0.673070	+	1.71496i	0.698831	+	0.715287i	$0.253704\pi$
$191$	9.30202	+	23.7012i	0.673070	+	1.71496i	−0.0257603	+	0.999668i	$0.508201\pi$
$192$	2.32514	−	0.350459i	0.167803	−	0.0252922i
$193$	−7.19895	−	3.46683i	−0.518192	−	0.249548i	0.156460	−	0.987684i	$-0.449992\pi$
$193$	−7.19895	−	3.46683i	−0.518192	−	0.249548i	−0.674652	+	0.738136i	$0.735706\pi$
$194$	−17.1549	−	8.26139i	−1.23165	−	0.593133i
$195$	−5.35772	+	0.807546i	−0.383674	+	0.0578296i
$196$	0.0307930	+	0.0784592i	0.00219950	+	0.00560423i
$197$	1.85787	+	24.7915i	0.132368	+	1.76632i	0.529261	+	0.848459i	$0.322469\pi$
$197$	1.85787	+	24.7915i	0.132368	+	1.76632i	−0.396893	+	0.917865i	$0.629912\pi$
$198$	−6.05443	+	5.61769i	−0.430269	+	0.399232i
$199$	−1.52737	−	6.69185i	−0.108272	−	0.474372i	−0.999772	−	0.0213510i	$-0.993203\pi$
$199$	−1.52737	−	6.69185i	−0.108272	−	0.474372i	0.891500	−	0.453021i	$-0.149654\pi$
$200$	−0.988831	−	0.149042i	−0.0699209	−	0.0105389i
$201$	−15.3469	−	10.4633i	−1.08248	−	0.738025i
$202$	−13.4129	+	4.13734i	−0.943729	+	0.291102i
$203$	1.29745	−	17.3133i	0.0910633	−	1.21515i
$204$	−6.84209	−	8.57971i	−0.479042	−	0.600700i
$205$	9.04810	+	2.79097i	0.631947	+	0.194930i
$206$	1.69057	−	4.30749i	0.117787	−	0.300117i
$207$	−0.499732	+	2.18947i	−0.0347338	+	0.152179i
$208$	1.15213	+	1.99554i	0.0798857	+	0.138366i
$209$	5.98588	−	10.3678i	0.414052	−	0.717159i
$210$	−4.58786	−	4.25691i	−0.316592	−	0.293755i
$211$	1.43904	−	1.80451i	0.0990679	−	0.124227i	−0.729826	−	0.683633i	$-0.760399\pi$
$211$	1.43904	−	1.80451i	0.0990679	−	0.124227i	0.828894	+	0.559405i	$0.188970\pi$
$212$	−5.81899	+	3.96732i	−0.399650	+	0.272477i
$213$	11.4948	−	5.53559i	0.787609	−	0.379292i
$214$	7.52427			0.514348
$215$	−4.50802	+	4.76211i	−0.307445	+	0.324774i
$216$	1.10728			0.0753408
$217$	3.03620	−	1.46216i	0.206111	−	0.0992578i
$218$	−4.55741	+	3.10719i	−0.308667	+	0.210445i
$219$	11.5335	−	14.4625i	0.779360	−	0.977287i
$220$	−2.39391	−	2.22122i	−0.161397	−	0.149755i
$221$	5.37691	−	9.31308i	0.361690	−	0.626466i
$222$	−2.02484	−	3.50712i	−0.135898	−	0.235383i
$223$	0.728903	−	3.19353i	0.0488110	−	0.213855i	−0.944641	−	0.328106i	$-0.893590\pi$
$223$	0.728903	−	3.19353i	0.0488110	−	0.213855i	0.993452	+	0.114251i	$0.0364469\pi$
$224$	−0.972403	+	2.47764i	−0.0649714	+	0.165545i
$225$	2.41674	+	0.745465i	0.161116	+	0.0496977i
$226$	7.93341	+	9.94818i	0.527723	+	0.661743i
$227$	0.714267	−	9.53124i	0.0474076	−	0.632610i	−0.922006	−	0.387176i	$-0.873450\pi$
$227$	0.714267	−	9.53124i	0.0474076	−	0.632610i	0.969413	−	0.245434i	$-0.0789305\pi$
$228$	8.23714	−	2.54082i	0.545518	−	0.168270i
$229$	−17.0929	−	11.6537i	−1.12953	−	0.770099i	−0.153587	−	0.988135i	$-0.549083\pi$
$229$	−17.0929	−	11.6537i	−1.12953	−	0.770099i	−0.975941	+	0.218036i	$0.930035\pi$
$230$	−0.878056	−	0.132346i	−0.0578973	−	0.00872661i
$231$	−4.54798	−	19.9260i	−0.299235	−	1.31103i
$232$	4.78170	−	4.43677i	0.313934	−	0.291288i
$233$	−0.263571	−	3.51711i	−0.0172671	−	0.230414i	−0.999160	−	0.0409772i	$-0.986953\pi$
$233$	−0.263571	−	3.51711i	−0.0172671	−	0.230414i	0.981893	−	0.189437i	$-0.0606661\pi$
$234$	−2.12909	−	5.42484i	−0.139183	−	0.354633i
$235$	9.30585	−	1.40263i	0.607047	−	0.0914976i
$236$	2.91202	+	1.40236i	0.189556	+	0.0912856i
$237$	−5.09149	−	2.45193i	−0.330728	−	0.159270i
$238$	12.2829	−	1.85135i	0.796185	−	0.120006i
$239$	6.35283	+	16.1867i	0.410930	+	1.04703i	0.975177	+	0.221427i	$0.0710714\pi$
$239$	6.35283	+	16.1867i	0.410930	+	1.04703i	−0.564247	+	0.825606i	$0.690833\pi$
$240$	−0.175721	−	2.34483i	−0.0113427	−	0.151358i
$241$	0.763943	−	0.708836i	0.0492099	−	0.0456601i	−0.655185	−	0.755469i	$-0.727409\pi$
$241$	0.763943	−	0.708836i	0.0492099	−	0.0456601i	0.704394	+	0.709809i	$0.251219\pi$
$242$	0.0746316	+	0.326982i	0.00479750	+	0.0210192i
$243$	−20.4107	−	3.07641i	−1.30934	−	0.197352i
$244$	2.24000	+	1.52721i	0.143401	+	0.0977694i
$245$	0.0805410	−	0.0248436i	0.00514557	−	0.00158720i
$246$	−1.66386	+	22.2026i	−0.106084	+	1.41559i
$247$	5.26678	+	6.60434i	0.335117	+	0.420224i
$248$	1.20986	+	0.373194i	0.0768265	+	0.0236978i
$249$	−10.8441	+	27.6303i	−0.687217	+	1.75100i
$250$	−0.222521	+	0.974928i	−0.0140735	+	0.0616599i
$251$	6.17764	+	10.7000i	0.389929	+	0.675377i	0.992440	−	0.122734i	$-0.0391662\pi$
$251$	6.17764	+	10.7000i	0.389929	+	0.675377i	−0.602511	+	0.798111i	$0.705833\pi$
$252$	3.36577	−	5.82968i	0.212023	−	0.367235i
$253$	−2.12573	−	1.97239i	−0.133643	−	0.124003i
$254$	−2.65376	+	3.32770i	−0.166511	+	0.208799i
$255$	−9.06703	+	6.18179i	−0.567799	+	0.387119i
$256$	−0.900969	+	0.433884i	−0.0563106	+	0.0271177i
$257$	24.0192			1.49827			0.749137	−	0.662415i	$-0.230469\pi$
$257$	24.0192			1.49827			0.749137	+	0.662415i	$0.230469\pi$
$258$	−13.2757	−	7.84270i	−0.826507	−	0.488265i
$259$	4.58396			0.284834
$260$	2.07606	−	0.999779i	0.128752	−	0.0620037i
$261$	−13.6307	+	9.29327i	−0.843721	+	0.575239i
$262$	0.775933	−	0.972989i	0.0479373	−	0.0601115i
$263$	9.53868	+	8.85060i	0.588180	+	0.545751i	0.917126	−	0.398597i	$-0.130503\pi$
$263$	9.53868	+	8.85060i	0.588180	+	0.545751i	−0.328946	+	0.944349i	$0.606693\pi$
$264$	3.83946	−	6.65013i	0.236302	−	0.409287i
$265$	3.52137	+	6.09919i	0.216316	+	0.374671i
$266$	−2.17122	+	9.51275i	−0.133126	+	0.583264i
$267$	14.7631	−	37.6159i	0.903489	−	2.30205i
$268$	7.54832	+	2.32835i	0.461087	+	0.142227i
$269$	−10.4967	−	13.1625i	−0.639996	−	0.802530i	0.351006	−	0.936373i	$-0.385840\pi$
$269$	−10.4967	−	13.1625i	−0.639996	−	0.802530i	−0.991003	+	0.133843i	$0.957268\pi$
$270$	0.0827470	−	1.10418i	0.00503582	−	0.0671984i
$271$	−29.1118	+	8.97980i	−1.76841	+	0.545484i	−0.995977	−	0.0896070i	$-0.971439\pi$
$271$	−29.1118	+	8.97980i	−1.76841	+	0.545484i	−0.772438	+	0.635091i	$0.780963\pi$
$272$	3.85601	+	2.62898i	0.233805	+	0.159405i
$273$	14.2603	+	2.14939i	0.863071	+	0.130087i
$274$	2.44867	+	10.7283i	0.147929	+	0.648121i
$275$	−2.39391	+	2.22122i	−0.144358	+	0.133945i
$276$	−0.156035	−	2.08215i	−0.00939222	−	0.125331i
$277$	−6.81478	−	17.3638i	−0.409460	−	1.04329i	−0.975712	−	0.219056i	$-0.929702\pi$
$277$	−6.81478	−	17.3638i	−0.409460	−	1.04329i	0.566252	−	0.824232i	$-0.308393\pi$
$278$	−10.5122	+	1.58446i	−0.630480	+	0.0950296i
$279$	−2.88502	−	1.38935i	−0.172722	−	0.0831783i
$280$	2.39805	+	1.15484i	0.143311	+	0.0690148i
$281$	16.9539	−	2.55539i	1.01139	−	0.152442i	0.377615	−	0.925963i	$-0.376744\pi$
$281$	16.9539	−	2.55539i	1.01139	−	0.152442i	0.633771	+	0.773520i	$0.281506\pi$
$282$	8.08462	+	20.5993i	0.481432	+	1.22667i
$283$	2.29850	+	30.6714i	0.136632	+	1.82323i	0.472516	+	0.881322i	$0.343346\pi$
$283$	2.29850	+	30.6714i	0.136632	+	1.82323i	−0.335884	+	0.941903i	$0.609035\pi$
$284$	−3.97739	+	3.69048i	−0.236015	+	0.218990i
$285$	−1.91815	−	8.40398i	−0.113622	−	0.497809i
$286$	7.44089	+	1.12153i	0.439989	+	0.0663177i
$287$	−20.8232	−	14.1970i	−1.22915	−	0.838023i
$288$	2.41674	−	0.745465i	0.142408	−	0.0439269i
$289$	0.357234	−	4.76696i	0.0210138	−	0.280409i
$290$	−4.06703	−	5.09989i	−0.238824	−	0.299476i
$291$	−42.7829	−	13.1968i	−2.50798	−	0.773609i
$292$	−2.87410	+	7.32309i	−0.168194	+	0.428552i
$293$	−5.03015	+	22.0385i	−0.293864	+	1.28750i	0.585234	+	0.810864i	$0.301002\pi$
$293$	−5.03015	+	22.0385i	−0.293864	+	1.28750i	−0.879099	+	0.476640i	$0.841855\pi$
$294$	0.0990947	+	0.171637i	0.00577932	+	0.0100101i
$295$	1.61605	−	2.79908i	0.0940901	−	0.162969i
$296$	1.26249	+	1.17142i	0.0733807	+	0.0680874i
$297$	2.25454	−	2.82711i	0.130822	−	0.164046i
$298$	−0.888714	+	0.605915i	−0.0514818	+	0.0350997i
$299$	1.84349	−	0.887778i	0.106612	−	0.0513415i
$300$	−2.35140			−0.135758
$301$	15.2016	−	8.57520i	0.876209	−	0.494267i
$302$	−12.9990			−0.748010
$303$	−29.7369	+	14.3206i	−1.70834	+	0.822695i
$304$	−3.02894	+	2.06510i	−0.173722	+	0.118441i
$305$	1.69033	−	2.11961i	0.0967882	−	0.121369i
$306$	−8.65232	−	8.02818i	−0.494620	−	0.458941i
$307$	11.6097	−	20.1086i	0.662600	−	1.14766i	−0.317330	−	0.948315i	$-0.602786\pi$
$307$	11.6097	−	20.1086i	0.662600	−	1.14766i	0.979930	−	0.199341i	$-0.0638803\pi$
$308$	4.34601	+	7.52751i	0.247637	+	0.428919i
$309$	2.42121	−	10.6080i	0.137738	−	0.603468i
$310$	0.462564	−	1.17859i	0.0262719	−	0.0669396i
$311$	9.62946	+	2.97029i	0.546036	+	0.168430i	0.555487	−	0.831525i	$-0.312532\pi$
$311$	9.62946	+	2.97029i	0.546036	+	0.168430i	−0.00945031	+	0.999955i	$0.503008\pi$
$312$	3.37821	+	4.23615i	0.191254	+	0.239825i
$313$	−0.281220	+	3.75262i	−0.0158955	+	0.212111i	0.983600	+	0.180362i	$0.0577268\pi$
$313$	−0.281220	+	3.75262i	−0.0158955	+	0.212111i	−0.999496	+	0.0317490i	$0.989892\pi$
$314$	16.1593	−	4.98449i	0.911922	−	0.281291i
$315$	−5.56185	−	3.79201i	−0.313375	−	0.213655i
$316$	2.37646	+	0.358193i	0.133686	+	0.0201500i
$317$	−3.79338	−	16.6199i	−0.213058	−	0.933467i	−0.962475	−	0.271369i	$-0.912524\pi$
$317$	−3.79338	−	16.6199i	−0.213058	−	0.933467i	0.749418	−	0.662098i	$-0.230334\pi$
$318$	−12.1396	+	11.2639i	−0.680754	+	0.631647i
$319$	−1.59190	−	21.2424i	−0.0891293	−	1.18935i
$320$	0.365341	+	0.930874i	0.0204232	+	0.0520374i
$321$	17.4950	−	2.63694i	0.976475	−	0.147180i
$322$	2.12940	+	1.02547i	0.118667	+	0.0571470i
$323$	15.4144	+	7.42320i	0.857682	+	0.413038i
$324$	10.0771	−	1.51888i	0.559841	−	0.0843824i
$325$	−0.841839	−	2.14497i	−0.0466968	−	0.118982i
$326$	−0.0459400	−	0.613027i	−0.00254438	−	0.0339524i
$327$	−9.50768	+	8.82183i	−0.525776	+	0.487849i
$328$	−2.10700	−	9.23137i	−0.116340	−	0.509717i
$329$	−24.7687	−	3.73329i	−1.36555	−	0.205823i
$330$	−6.34461	−	4.32568i	−0.349260	−	0.238121i
$331$	−14.0501	+	4.33389i	−0.772265	+	0.238212i	−0.655751	−	0.754977i	$-0.727648\pi$
$331$	−14.0501	+	4.33389i	−0.772265	+	0.238212i	−0.116513	+	0.993189i	$0.537172\pi$
$332$	0.943329	−	12.5879i	0.0517719	−	0.690848i
$333$	−2.71574	−	3.40543i	−0.148822	−	0.186617i
$334$	3.51294	+	1.08360i	0.192219	+	0.0592918i
$335$	2.88593	−	7.35322i	0.157675	−	0.401749i
$336$	−1.39266	+	6.10166i	−0.0759760	+	0.332873i
$337$	5.18812	+	8.98608i	0.282615	+	0.489503i	0.972028	−	0.234865i	$-0.0754649\pi$
$337$	5.18812	+	8.98608i	0.282615	+	0.489503i	−0.689413	+	0.724368i	$0.742132\pi$
$338$	3.84520	−	6.66009i	0.209151	−	0.362261i
$339$	21.9327	+	20.3506i	1.19122	+	1.10529i
$340$	2.90979	−	3.64876i	0.157805	−	0.197882i
$341$	3.41626	−	2.32917i	0.185001	−	0.126132i
$342$	8.35336	−	4.02276i	0.451698	−	0.217526i
$343$	18.4071			0.993889
$344$	6.37812	+	1.52300i	0.343885	+	0.0821149i
$345$	−2.08799			−0.112413
$346$	16.0106	−	7.71030i	0.860735	−	0.414508i
$347$	−2.10297	+	1.43378i	−0.112893	+	0.0769694i	−0.618451	−	0.785824i	$-0.712239\pi$
$347$	−2.10297	+	1.43378i	−0.112893	+	0.0769694i	0.505557	+	0.862793i	$0.331287\pi$
$348$	9.56322	−	11.9919i	0.512642	−	0.642833i
$349$	−3.36204	−	3.11952i	−0.179966	−	0.166984i	0.585046	−	0.811000i	$-0.301076\pi$
$349$	−3.36204	−	3.11952i	−0.179966	−	0.166984i	−0.765012	+	0.644016i	$0.777267\pi$
$350$	1.33082	−	2.30504i	0.0711351	−	0.123210i
$351$	1.27573	+	2.20962i	0.0680932	+	0.117941i
$352$	−0.726680	+	3.18379i	−0.0387322	+	0.169697i
$353$	−12.2786	+	31.2854i	−0.653525	+	1.66515i	0.0895802	+	0.995980i	$0.471447\pi$
$353$	−12.2786	+	31.2854i	−0.653525	+	1.66515i	−0.743105	+	0.669175i	$0.766648\pi$
$354$	7.26233	+	2.24013i	0.385988	+	0.119062i
$355$	3.38293	+	4.24206i	0.179547	+	0.225145i
$356$	−1.28425	+	17.1371i	−0.0680650	+	0.908264i
$357$	27.9107	−	8.60932i	1.47719	−	0.455654i
$358$	−15.9573	−	10.8795i	−0.843367	−	0.574998i
$359$	5.41421	+	0.816060i	0.285751	+	0.0430700i	0.290354	−	0.956919i	$-0.406227\pi$
$359$	5.41421	+	0.816060i	0.285751	+	0.0430700i	−0.00460284	+	0.999989i	$0.501465\pi$
$360$	−0.562777	−	2.46569i	−0.0296610	−	0.129953i
$361$	4.07641	−	3.78236i	0.214548	−	0.199072i
$362$	−0.684982	−	9.14044i	−0.0360018	−	0.480411i
$363$	0.288123	+	0.734125i	0.0151225	+	0.0385315i
$364$	−6.06458	+	0.914088i	−0.317870	+	0.0479112i
$365$	7.08783	+	3.41332i	0.370994	+	0.178661i
$366$	5.74354	+	2.76594i	0.300220	+	0.144578i
$367$	20.4156	−	3.07716i	1.06569	−	0.160627i	0.407291	−	0.913298i	$-0.366473\pi$
$367$	20.4156	−	3.07716i	1.06569	−	0.160627i	0.658396	+	0.752672i	$0.271235\pi$
$368$	0.324413	+	0.826592i	0.0169112	+	0.0430891i
$369$	1.78960	+	23.8805i	0.0931626	+	1.24317i
$370$	1.26249	−	1.17142i	0.0656337	−	0.0608992i
$371$	−4.17120	−	18.2752i	−0.216558	−	0.948802i
$372$	2.94389	+	0.443721i	0.152634	+	0.0230058i
$373$	−0.575340	−	0.392260i	−0.0297900	−	0.0203105i	0.548334	−	0.836260i	$-0.315262\pi$
$373$	−0.575340	−	0.392260i	−0.0297900	−	0.0203105i	−0.578123	+	0.815949i	$0.696215\pi$
$374$	14.5636	−	4.49227i	0.753065	−	0.232290i
$375$	−0.175721	+	2.34483i	−0.00907417	+	0.121086i
$376$	−5.86764	−	7.35779i	−0.302600	−	0.379449i
$377$	14.3629	+	4.43037i	0.739727	+	0.228176i
$378$	−1.07672	+	2.74344i	−0.0553806	+	0.141107i
$379$	−4.23024	+	18.5339i	−0.217293	+	0.952022i	0.742175	+	0.670206i	$0.233794\pi$
$379$	−4.23024	+	18.5339i	−0.217293	+	0.952022i	−0.959468	+	0.281817i	$0.909063\pi$
$380$	1.83297	+	3.17480i	0.0940294	+	0.162864i
$381$	−5.00413	+	8.66741i	−0.256369	+	0.444045i
$382$	−18.6644	−	17.3180i	−0.954952	−	0.886066i
$383$	−20.7249	+	25.9882i	−1.05899	+	1.32793i	−0.116690	+	0.993168i	$0.537228\pi$
$383$	−20.7249	+	25.9882i	−1.05899	+	1.32793i	−0.942302	+	0.334765i	$0.891343\pi$
$384$	−1.94282	+	1.32459i	−0.0991442	+	0.0675953i
$385$	7.83124	−	3.77132i	0.399117	−	0.192204i
$386$	7.99024			0.406692
$387$	−15.3766	−	6.21299i	−0.781639	−	0.315824i
$388$	19.0406			0.966638
$389$	7.45023	−	3.58784i	0.377742	−	0.181911i	−0.235372	−	0.971905i	$-0.575631\pi$
$389$	7.45023	−	3.58784i	0.377742	−	0.181911i	0.613114	+	0.789995i	$0.289917\pi$
$390$	4.47676	−	3.05220i	0.226689	−	0.154554i
$391$	2.58382	−	3.24000i	0.130669	−	0.163854i
$392$	−0.0617857	−	0.0573287i	−0.00312065	−	0.00289554i
$393$	1.46316	−	2.53427i	0.0738067	−	0.127837i
$394$	−12.4305	−	21.5303i	−0.626241	−	1.08468i
$395$	0.534785	−	2.34304i	0.0269079	−	0.117891i
$396$	3.01743	−	7.68828i	0.151631	−	0.386350i
$397$	−33.6562	−	10.3816i	−1.68916	−	0.521036i	−0.706697	−	0.707516i	$-0.749816\pi$
$397$	−33.6562	−	10.3816i	−1.68916	−	0.521036i	−0.982459	+	0.186481i	$0.940292\pi$
$398$	4.27960	+	5.36644i	0.214517	+	0.268996i
$399$	−1.71457	+	22.8794i	−0.0858360	+	1.14540i
$400$	0.955573	−	0.294755i	0.0477786	−	0.0147378i
$401$	21.3577	+	14.5614i	1.06655	+	0.727163i	0.963553	−	0.267519i	$-0.0862037\pi$
$401$	21.3577	+	14.5614i	1.06655	+	0.727163i	0.102999	+	0.994681i	$0.467156\pi$
$402$	18.3669	+	2.76836i	0.916058	+	0.138073i
$403$	0.649194	+	2.84431i	0.0323387	+	0.141685i
$404$	10.2895	−	9.54726i	0.511922	−	0.474994i
$405$	−0.761571	−	10.1625i	−0.0378428	−	0.504977i
$406$	6.34299	+	16.1617i	0.314797	+	0.802091i
$407$	5.56145	−	0.838253i	0.275671	−	0.0415507i
$408$	9.88711	+	4.76138i	0.489485	+	0.235723i
$409$	33.0446	+	15.9134i	1.63395	+	0.786869i	0.999908	+	0.0135705i	$0.00431975\pi$
$409$	33.0446	+	15.9134i	1.63395	+	0.786869i	0.634042	+	0.773298i	$0.281395\pi$
$410$	−9.36301	+	1.41125i	−0.462406	+	0.0696965i
$411$	9.45333	+	24.0867i	0.466298	+	1.18811i
$412$	0.345803	+	4.61442i	0.0170365	+	0.227336i
$413$	−6.30620	+	5.85130i	−0.310308	+	0.287923i
$414$	−0.499732	−	2.18947i	−0.0245605	−	0.107606i
$415$	−12.4822	−	1.88138i	−0.612725	−	0.0923534i
$416$	−1.90387	−	1.29803i	−0.0933447	−	0.0636413i
$417$	−23.8871	+	7.36818i	−1.16975	+	0.360821i
$418$	−0.894650	+	11.9383i	−0.0437588	+	0.583920i
$419$	13.1956	+	16.5467i	0.644645	+	0.808359i	0.991575	−	0.129532i	$-0.0413474\pi$
$419$	13.1956	+	16.5467i	0.644645	+	0.808359i	−0.346930	+	0.937891i	$0.612776\pi$
$420$	5.98052	+	1.84475i	0.291820	+	0.0900144i
$421$	−8.01365	+	20.4185i	−0.390562	+	0.995135i	0.591455	+	0.806338i	$0.298554\pi$
$421$	−8.01365	+	20.4185i	−0.390562	+	0.995135i	−0.982016	+	0.188796i	$0.939541\pi$
$422$	−0.513589	+	2.25018i	−0.0250011	+	0.109537i
$423$	11.9006	+	20.6125i	0.578628	+	1.00221i
$424$	3.52137	−	6.09919i	0.171013	−	0.296203i
$425$	−3.42111	−	3.17433i	−0.165948	−	0.153977i
$426$	−7.95463	+	9.97479i	−0.385403	+	0.483280i
$427$	−5.96206	+	4.06486i	−0.288524	+	0.196713i
$428$	−6.77913	+	3.26466i	−0.327682	+	0.157803i
$429$	17.6942			0.854283
$430$	1.99538	−	6.24647i	0.0962260	−	0.301232i
$431$	15.8658			0.764229			0.382115	−	0.924115i	$-0.375196\pi$
$431$	15.8658			0.764229			0.382115	+	0.924115i	$0.375196\pi$
$432$	−0.997624	+	0.480430i	−0.0479982	+	0.0231147i
$433$	10.6095	−	7.23345i	0.509861	−	0.347618i	−0.280905	−	0.959736i	$-0.590635\pi$
$433$	10.6095	−	7.23345i	0.509861	−	0.347618i	0.790766	+	0.612118i	$0.209682\pi$
$434$	−2.10112	+	2.63472i	−0.100857	+	0.126471i
$435$	−11.2437	−	10.4326i	−0.539095	−	0.500207i
$436$	2.75793	−	4.77687i	0.132081	−	0.228770i
$437$	1.62763	+	2.81914i	0.0778601	+	0.134858i
$438$	−4.11625	+	18.0345i	−0.196682	+	0.861720i
$439$	1.83348	−	4.67163i	0.0875071	−	0.222964i	−0.880420	−	0.474194i	$-0.842740\pi$
$439$	1.83348	−	4.67163i	0.0875071	−	0.222964i	0.967928	+	0.251229i	$0.0808348\pi$
$440$	3.12059	+	0.962573i	0.148768	+	0.0458889i
$441$	0.132907	+	0.166660i	0.00632891	+	0.00793620i
$442$	−0.803634	+	10.7238i	−0.0382250	+	0.510077i
$443$	25.3536	−	7.82055i	1.20459	−	0.371565i	0.373458	−	0.927647i	$-0.378172\pi$
$443$	25.3536	−	7.82055i	1.20459	−	0.371565i	0.831127	+	0.556082i	$0.187696\pi$
$444$	3.34600	+	2.28126i	0.158794	+	0.108264i
$445$	16.9932	+	2.56131i	0.805555	+	0.121418i
$446$	0.728903	+	3.19353i	0.0345146	+	0.151218i
$447$	−1.85404	+	1.72029i	−0.0876929	+	0.0813672i
$448$	−0.198904	−	2.65419i	−0.00939733	−	0.125399i
$449$	−10.3089	−	26.2667i	−0.486507	−	1.23960i	−0.937785	−	0.347217i	$-0.887127\pi$
$449$	−10.3089	−	26.2667i	−0.486507	−	1.23960i	0.451277	−	0.892384i	$-0.350968\pi$
$450$	−2.50085	+	0.376943i	−0.117891	+	0.0177692i
$451$	−27.8597	−	13.4165i	−1.31186	−	0.631759i
$452$	−11.4641	−	5.52082i	−0.539226	−	0.259678i
$453$	−30.2246	+	4.55562i	−1.42007	+	0.214042i
$454$	3.49192	+	8.89725i	0.163884	+	0.417569i
$455$	0.458326	+	6.11593i	0.0214866	+	0.286719i
$456$	−6.31898	+	5.86316i	−0.295914	+	0.274568i
$457$	7.07027	+	30.9769i	0.330733	+	1.44904i	0.817714	+	0.575625i	$0.195241\pi$
$457$	7.07027	+	30.9769i	0.330733	+	1.44904i	−0.486980	+	0.873413i	$0.661902\pi$
$458$	20.4565	+	3.08332i	0.955869	+	0.144074i
$459$	4.26967	+	2.91101i	0.199291	+	0.135875i
$460$	0.848524	−	0.261735i	0.0395626	−	0.0122035i
$461$	0.515509	−	6.87899i	0.0240097	−	0.320387i	−0.972248	−	0.233953i	$-0.924834\pi$
$461$	0.515509	−	6.87899i	0.0240097	−	0.320387i	0.996258	−	0.0864337i	$-0.0275471\pi$
$462$	12.7432	+	15.9794i	0.592865	+	0.743430i
$463$	13.9950	+	4.31690i	0.650404	+	0.200623i	0.602363	−	0.798222i	$-0.294226\pi$
$463$	13.9950	+	4.31690i	0.650404	+	0.200623i	0.0480411	+	0.998845i	$0.484702\pi$
$464$	−2.38312	+	6.07209i	−0.110634	+	0.281890i
$465$	0.662478	−	2.90250i	0.0307217	−	0.134600i
$466$	1.76349	+	3.05445i	0.0816920	+	0.141495i
$467$	2.28779	−	3.96258i	0.105867	−	0.183366i	−0.808225	−	0.588873i	$-0.799572\pi$
$467$	2.28779	−	3.96258i	0.105867	−	0.183366i	0.914092	+	0.405507i	$0.132905\pi$
$468$	4.27200	+	3.96384i	0.197473	+	0.183228i
$469$	−13.1088	+	16.4380i	−0.605310	+	0.759034i
$470$	−7.77570	+	5.30138i	−0.358666	+	0.244535i
$471$	35.8258	−	17.2528i	1.65077	−	0.794967i
$472$	−3.23210			−0.148769
$473$	16.8751	−	13.1836i	0.775919	−	0.606185i
$474$	5.65113			0.259565
$475$	3.30290	−	1.59059i	0.151547	−	0.0729814i
$476$	−10.2633	+	6.99738i	−0.470416	+	0.320724i
$477$	−11.1055	+	13.9258i	−0.508485	+	0.637620i
$478$	−12.7469	−	11.8274i	−0.583028	−	0.540971i
$479$	7.62275	−	13.2030i	0.348292	−	0.603260i	−0.637654	−	0.770323i	$-0.720095\pi$
$479$	7.62275	−	13.2030i	0.348292	−	0.603260i	0.985946	+	0.167063i	$0.0534283\pi$
$480$	1.17570	+	2.03638i	0.0536632	+	0.0929474i
$481$	−0.883069	+	3.86898i	−0.0402645	+	0.176410i
$482$	−0.380737	+	0.970102i	−0.0173421	+	0.0441869i
$483$	5.31055	+	1.63809i	0.241638	+	0.0745355i
$484$	−0.209113	−	0.262219i	−0.00950514	−	0.0119191i
$485$	1.42290	−	18.9873i	0.0646107	−	0.862169i
$486$	19.7242	−	6.08410i	0.894707	−	0.275981i
$487$	−33.8601	−	23.0854i	−1.53435	−	1.04610i	−0.976334	−	0.216268i	$-0.930612\pi$
$487$	−33.8601	−	23.0854i	−1.53435	−	1.04610i	−0.558013	−	0.829832i	$-0.688436\pi$
$488$	−2.68080	−	0.404066i	−0.121354	−	0.0182912i
$489$	−0.321658	−	1.40927i	−0.0145459	−	0.0637296i
$490$	−0.0617857	+	0.0573287i	−0.00279119	+	0.00258985i
$491$	0.0454349	+	0.606287i	0.00205045	+	0.0273613i	0.998135	−	0.0610424i	$-0.0194425\pi$
$491$	0.0454349	+	0.606287i	0.00205045	+	0.0273613i	−0.996085	+	0.0884037i	$0.971823\pi$
$492$	−8.13428	−	20.7258i	−0.366722	−	0.934392i
$493$	30.1025	−	4.53721i	1.35575	−	0.204346i
$494$	−7.61072	−	3.66513i	−0.342423	−	0.164902i
$495$	−7.44129	−	3.58353i	−0.334461	−	0.161068i
$496$	−1.25197	+	0.188705i	−0.0562153	+	0.00847309i
$497$	−5.27606	−	13.4432i	−0.236664	−	0.603009i
$498$	−2.21815	−	29.5991i	−0.0993975	−	1.32637i
$499$	−19.5820	+	18.1694i	−0.876609	+	0.813374i	−0.983502	−	0.180896i	$-0.942100\pi$
$499$	−19.5820	+	18.1694i	−0.876609	+	0.813374i	0.106893	+	0.994271i	$0.465910\pi$
$500$	−0.222521	−	0.974928i	−0.00995144	−	0.0436001i
$501$	8.54783	+	1.28838i	0.381889	+	0.0575605i
$502$	−10.2084	−	6.95998i	−0.455624	−	0.310639i
$503$	−30.2480	+	9.33026i	−1.34869	+	0.416016i	−0.883183	−	0.469028i	$-0.844604\pi$
$503$	−30.2480	+	9.33026i	−1.34869	+	0.416016i	−0.465507	+	0.885044i	$0.654128\pi$
$504$	−0.503048	+	6.71271i	−0.0224075	+	0.299008i
$505$	−8.75163	−	10.9742i	−0.389442	−	0.488345i
$506$	2.77100	+	0.854740i	0.123186	+	0.0379978i
$507$	6.60655	−	16.8332i	0.293407	−	0.747590i
$508$	0.947114	−	4.14958i	0.0420214	−	0.184108i
$509$	−16.4746	−	28.5348i	−0.730222	−	1.26478i	−0.956788	−	0.290785i	$-0.906083\pi$
$509$	−16.4746	−	28.5348i	−0.730222	−	1.26478i	0.226567	−	0.973996i	$-0.427250\pi$
$510$	5.48693	−	9.50364i	0.242965	−	0.420828i
$511$	−15.3492	−	14.2420i	−0.679010	−	0.630029i
$512$	0.623490	−	0.781831i	0.0275546	−	0.0345524i
$513$	−3.35388	+	2.28664i	−0.148078	+	0.100958i
$514$	−21.6405	+	10.4215i	−0.954522	+	0.459674i
$515$	4.62736			0.203906
$516$	15.3638	+	1.30593i	0.676353	+	0.0574905i
$517$	−30.7331			−1.35164
$518$	−4.13001	+	1.98891i	−0.181462	+	0.0873876i
$519$	34.5247	−	23.5386i	1.51547	−	1.03323i
$520$	−1.43668	+	1.80154i	−0.0630026	+	0.0790027i
$521$	−30.4553	−	28.2584i	−1.33427	−	1.23802i	−0.949021	−	0.315213i	$-0.897924\pi$
$521$	−30.4553	−	28.2584i	−1.33427	−	1.23802i	−0.385252	−	0.922812i	$-0.625885\pi$
$522$	8.24866	−	14.2871i	0.361034	−	0.625329i
$523$	−2.04125	−	3.53555i	−0.0892578	−	0.154599i	0.817940	−	0.575304i	$-0.195116\pi$
$523$	−2.04125	−	3.53555i	−0.0892578	−	0.154599i	−0.907198	+	0.420705i	$0.861783\pi$
$524$	−0.276927	+	1.21330i	−0.0120976	+	0.0530032i
$525$	2.28651	−	5.82594i	0.0997916	−	0.254265i
$526$	−12.4342	−	3.83544i	−0.542156	−	0.167233i
$527$	3.68413	+	4.61975i	0.160483	+	0.201239i
$528$	−0.573846	+	7.65744i	−0.0249734	+	0.333247i
$529$	−21.2247	+	6.54696i	−0.922813	+	0.284650i
$530$	−5.81899	−	3.96732i	−0.252761	−	0.172329i
$531$	8.08300	+	1.21832i	0.350772	+	0.0528704i
$532$	−2.17122	−	9.51275i	−0.0941344	−	0.412430i
$533$	15.9941	−	14.8403i	0.692780	−	0.642806i
$534$	3.01978	+	40.2962i	0.130679	+	1.74379i
$535$	2.74892	+	7.00414i	0.118846	+	0.302816i
$536$	−7.81104	+	1.17732i	−0.337385	+	0.0508527i
$537$	−40.9157	−	19.7039i	−1.76564	−	0.850288i
$538$	15.1682	+	7.30462i	0.653947	+	0.314924i
$539$	−0.272175	+	0.0410237i	−0.0117234	+	0.00176702i
$540$	0.404534	+	1.03074i	0.0174084	+	0.0443558i
$541$	1.32199	+	17.6407i	0.0568367	+	0.758433i	0.950704	+	0.310101i	$0.100363\pi$
$541$	1.32199	+	17.6407i	0.0568367	+	0.758433i	−0.893867	+	0.448332i	$0.852018\pi$
$542$	22.3326	−	20.7216i	0.959268	−	0.890071i
$543$	−4.79603	−	21.0128i	−0.205817	−	0.901744i
$544$	−4.61481	−	0.695571i	−0.197859	−	0.0298224i
$545$	−4.55741	−	3.10719i	−0.195218	−	0.133097i
$546$	−13.7806	+	4.25077i	−0.589757	+	0.181916i
$547$	−1.05295	+	14.0507i	−0.0450210	+	0.600763i	0.928377	+	0.371641i	$0.121205\pi$
$547$	−1.05295	+	14.0507i	−0.0450210	+	0.600763i	−0.973398	+	0.229122i	$0.926414\pi$
$548$	−6.86102	−	8.60344i	−0.293088	−	0.367521i
$549$	6.55198	+	2.02102i	0.279632	+	0.0862549i
$550$	1.19308	−	3.03993i	0.0508733	−	0.129623i
$551$	−5.32113	+	23.3134i	−0.226688	+	0.993184i
$552$	1.04399	+	1.80825i	0.0444353	+	0.0769642i
$553$	−3.19835	+	5.53971i	−0.136008	+	0.235572i
$554$	13.6738	+	12.6874i	0.580942	+	0.539036i
$555$	2.52493	−	3.16617i	0.107177	−	0.134396i
$556$	8.78370	−	5.98862i	0.372512	−	0.253974i
$557$	26.2666	−	12.6493i	1.11295	−	0.535969i	0.215243	−	0.976561i	$-0.430946\pi$
$557$	26.2666	−	12.6493i	1.11295	−	0.535969i	0.897708	+	0.440592i	$0.145231\pi$
$558$	3.20213			0.135557
$559$	4.30919	+	14.4825i	0.182259	+	0.612545i
$560$	−2.66163			−0.112474
$561$	32.2880	−	15.5491i	1.36320	−	0.656483i
$562$	−14.1662	+	9.65837i	−0.597566	+	0.407414i
$563$	20.5733	−	25.7981i	0.867060	−	1.08726i	−0.128366	−	0.991727i	$-0.540973\pi$
$563$	20.5733	−	25.7981i	0.867060	−	1.08726i	0.995426	−	0.0955320i	$-0.0304552\pi$
$564$	−16.2217	−	15.0515i	−0.683056	−	0.633783i
$565$	−6.36210	+	11.0195i	−0.267656	+	0.463593i
$566$	−15.3787	−	26.6367i	−0.646415	−	1.11962i
$567$	−6.03579	+	26.4445i	−0.253479	+	1.11056i
$568$	1.98227	−	5.05073i	0.0831740	−	0.211924i
$569$	−34.7092	−	10.7064i	−1.45508	−	0.448834i	−0.536446	−	0.843935i	$-0.680233\pi$
$569$	−34.7092	−	10.7064i	−1.45508	−	0.448834i	−0.918638	+	0.395101i	$0.870710\pi$
$570$	5.37455	+	6.73947i	0.225115	+	0.282285i
$571$	−1.74160	+	23.2400i	−0.0728835	+	0.972563i	0.834159	+	0.551524i	$0.185953\pi$
$571$	−1.74160	+	23.2400i	−0.0728835	+	0.972563i	−0.907043	+	0.421039i	$0.861666\pi$
$572$	−7.19063	+	2.21802i	−0.300655	+	0.0927399i
$573$	−49.4665	−	33.7257i	−2.06649	−	1.40891i
$574$	24.9209	+	3.75622i	1.04018	+	0.156782i
$575$	−0.197593	−	0.865711i	−0.00824019	−	0.0361026i
$576$	−1.85396	+	1.72022i	−0.0772484	+	0.0716760i
$577$	1.97685	+	26.3792i	0.0822974	+	1.09818i	0.873563	+	0.486710i	$0.161803\pi$
$577$	1.97685	+	26.3792i	0.0822974	+	1.09818i	−0.791266	+	0.611472i	$0.790578\pi$
$578$	1.74645	+	4.44988i	0.0726427	+	0.185091i
$579$	18.5784	−	2.80025i	0.772093	−	0.116374i
$580$	5.87702	+	2.83023i	0.244030	+	0.117519i
$581$	30.2709	+	14.5777i	1.25585	+	0.604785i
$582$	44.2720	−	6.67292i	1.83513	−	0.276602i
$583$	−8.40258	−	21.4094i	−0.347999	−	0.886688i
$584$	−0.587894	−	7.84490i	−0.0243272	−	0.324624i
$585$	4.27200	−	3.96384i	0.176625	−	0.163884i
$586$	−5.03015	−	22.0385i	−0.207793	−	0.910403i
$587$	−32.9937	−	4.97300i	−1.36179	−	0.205258i	−0.572819	−	0.819682i	$-0.694150\pi$
$587$	−32.9937	−	4.97300i	−1.36179	−	0.205258i	−0.788976	+	0.614424i	$0.789388\pi$
$588$	−0.163752	−	0.111644i	−0.00675301	−	0.00460412i
$589$	−4.43529	+	1.36811i	−0.182753	+	0.0563719i
$590$	−0.241535	+	3.22306i	−0.00994385	+	0.132691i
$591$	−36.4482	−	45.7046i	−1.49928	−	1.88004i
$592$	−1.64572	−	0.507639i	−0.0676388	−	0.0208638i
$593$	−6.57276	+	16.7471i	−0.269911	+	0.687721i	0.730080	+	0.683362i	$0.239483\pi$
$593$	−6.57276	+	16.7471i	−0.269911	+	0.687721i	−0.999990	+	0.00435938i	$0.998612\pi$
$594$	−0.804638	+	3.52535i	−0.0330147	+	0.144647i
$595$	6.21084	+	10.7575i	0.254620	+	0.441014i
$596$	0.537807	−	0.931509i	0.0220294	−	0.0381561i
$597$	11.8314	+	10.9779i	0.484226	+	0.449296i
$598$	−1.27573	+	1.59972i	−0.0521687	+	0.0654174i
$599$	−26.8389	+	18.2985i	−1.09661	+	0.747655i	−0.969710	−	0.244261i	$-0.921455\pi$
$599$	−26.8389	+	18.2985i	−1.09661	+	0.747655i	−0.126899	+	0.991916i	$0.540502\pi$
$600$	2.11854	−	1.02024i	0.0864891	−	0.0416510i
$601$	−37.5793			−1.53289			−0.766446	−	0.642309i	$-0.777977\pi$
$601$	−37.5793			−1.53289			−0.766446	+	0.642309i	$0.777977\pi$
$602$	−9.97557	+	14.3217i	−0.406574	+	0.583711i
$603$	19.9780			0.813568
$604$	11.7117	−	5.64007i	0.476543	−	0.229491i
$605$	−0.277113	+	0.188933i	−0.0112663	+	0.00768120i
$606$	20.5786	−	25.8048i	0.835949	−	1.04825i
$607$	7.28587	+	6.76030i	0.295724	+	0.274392i	0.814054	−	0.580789i	$-0.197256\pi$
$607$	7.28587	+	6.76030i	0.295724	+	0.274392i	−0.518330	+	0.855181i	$0.673446\pi$
$608$	1.83297	−	3.17480i	0.0743368	−	0.128755i
$609$	20.4123	+	35.3552i	0.827150	+	1.43267i
$610$	−0.603273	+	2.64311i	−0.0244258	+	0.107016i
$611$	7.92251	−	20.1862i	0.320511	−	0.816648i
$612$	11.2788	+	3.47904i	0.455917	+	0.140632i
$613$	−0.179700	−	0.225337i	−0.00725802	−	0.00910127i	0.778189	−	0.628030i	$-0.216138\pi$
$613$	−0.179700	−	0.225337i	−0.00725802	−	0.00910127i	−0.785447	+	0.618929i	$0.787567\pi$
$614$	−1.73519	+	23.1544i	−0.0700264	+	0.934437i
$615$	−21.2757	+	6.56270i	−0.857921	+	0.264633i
$616$	−7.18168	−	4.89639i	−0.289358	−	0.197281i
$617$	−20.3448	−	3.06648i	−0.819050	−	0.123452i	−0.273865	−	0.961768i	$-0.588302\pi$
$617$	−20.3448	−	3.06648i	−0.819050	−	0.123452i	−0.545184	+	0.838316i	$0.683540\pi$
$618$	2.42121	+	10.6080i	0.0973951	+	0.426716i
$619$	−1.28529	+	1.19257i	−0.0516601	+	0.0479335i	−0.705580	−	0.708630i	$-0.749314\pi$
$619$	−1.28529	+	1.19257i	−0.0516601	+	0.0479335i	0.653920	+	0.756563i	$0.273123\pi$
$620$	0.0946169	+	1.26257i	0.00379991	+	0.0507062i
$621$	0.359216	+	0.915267i	0.0144148	+	0.0367284i
$622$	−9.96460	+	1.50192i	−0.399544	+	0.0602216i
$623$	−41.2108	−	19.8461i	−1.65107	−	0.795116i
$624$	−4.88166	−	2.35088i	−0.195423	−	0.0941107i
$625$	−0.988831	+	0.149042i	−0.0395532	+	0.00596169i
$626$	−1.37483	−	3.50301i	−0.0549493	−	0.140008i
$627$	2.10368	+	28.0717i	0.0840131	+	1.12108i
$628$	−12.3963	+	11.5021i	−0.494668	+	0.458985i
$629$	1.78853	+	7.83606i	0.0713134	+	0.312444i
$630$	6.65635	+	1.00328i	0.265195	+	0.0399717i
$631$	−18.0142	−	12.2818i	−0.717132	−	0.488933i	0.148943	−	0.988846i	$-0.452413\pi$
$631$	−18.0142	−	12.2818i	−0.717132	−	0.488933i	−0.866076	+	0.499913i	$0.833365\pi$
$632$	−2.29653	+	0.708385i	−0.0913510	+	0.0281781i
$633$	−0.405572	+	5.41198i	−0.0161200	+	0.215107i
$634$	10.6288	+	13.3281i	0.422125	+	0.529327i
$635$	−4.06720	−	1.25456i	−0.161402	−	0.0497859i
$636$	6.05017	−	15.4156i	0.239905	−	0.611267i
$637$	0.0432170	−	0.189346i	0.00171232	−	0.00750216i
$638$	10.6510	+	18.4481i	0.421677	+	0.730366i
$639$	−6.86118	+	11.8839i	−0.271424	+	0.470121i
$640$	−0.733052	−	0.680173i	−0.0289764	−	0.0268862i
$641$	−2.24997	+	2.82137i	−0.0888683	+	0.111437i	−0.824278	−	0.566186i	$-0.808418\pi$
$641$	−2.24997	+	2.82137i	−0.0888683	+	0.111437i	0.735409	+	0.677623i	$0.236990\pi$
$642$	−14.6183	+	9.96659i	−0.576938	+	0.393350i
$643$	24.2806	−	11.6929i	0.957535	−	0.461125i	0.111213	−	0.993797i	$-0.464526\pi$
$643$	24.2806	−	11.6929i	0.957535	−	0.461125i	0.846322	+	0.532672i	$0.178812\pi$
$644$	−2.36346			−0.0931334
$645$	2.45042	−	15.2232i	0.0964851	−	0.599414i
$646$	−17.1087			−0.673134
$647$	39.9982	−	19.2621i	1.57249	−	0.757273i	0.574375	−	0.818592i	$-0.305245\pi$
$647$	39.9982	−	19.2621i	1.57249	−	0.757273i	0.998118	+	0.0613195i	$0.0195308\pi$
$648$	−8.42016	+	5.74077i	−0.330775	+	0.225519i
$649$	−6.58092	+	8.25221i	−0.258324	+	0.323928i
$650$	1.68914	+	1.56729i	0.0662535	+	0.0614742i
$651$	−3.96204	+	6.86245i	−0.155284	+	0.268960i
$652$	0.307373	+	0.532386i	0.0120377	+	0.0208498i
$653$	5.09442	−	22.3201i	0.199360	−	0.873454i	−0.771959	−	0.635673i	$-0.780723\pi$
$653$	5.09442	−	22.3201i	0.199360	−	0.873454i	0.971319	−	0.237781i	$-0.0764201\pi$
$654$	4.73847	−	12.0734i	0.185289	−	0.472108i
$655$	1.18921	+	0.366823i	0.0464663	+	0.0143330i
$656$	5.90368	+	7.40298i	0.230500	+	0.289038i
$657$	−1.48684	+	19.8405i	−0.0580073	+	0.774053i
$658$	23.9357	−	7.38318i	0.933110	−	0.287826i
$659$	−35.8450	−	24.4387i	−1.39632	−	0.951997i	−0.999417	−	0.0341373i	$-0.989132\pi$
$659$	−35.8450	−	24.4387i	−1.39632	−	0.951997i	−0.396906	−	0.917859i	$-0.629916\pi$
$660$	7.59314	+	1.14448i	0.295563	+	0.0445489i
$661$	−2.40200	−	10.5239i	−0.0934271	−	0.409331i	0.906490	−	0.422228i	$-0.138752\pi$
$661$	−2.40200	−	10.5239i	−0.0934271	−	0.409331i	−0.999917	+	0.0128970i	$0.995895\pi$
$662$	10.7783	−	10.0008i	0.418911	−	0.388693i
$663$	1.88967	+	25.2159i	0.0733886	+	0.979303i
$664$	4.61175	+	11.7506i	0.178971	+	0.456010i
$665$	−9.64840	+	1.45426i	−0.374149	+	0.0563939i
$666$	3.92436	+	1.88987i	0.152066	+	0.0732311i
$667$	5.21864	+	2.51317i	0.202067	+	0.0973102i
$668$	−3.63520	+	0.547918i	−0.140650	+	0.0211996i
$669$	2.81400	+	7.16996i	0.108796	+	0.277207i
$670$	0.590313	+	7.87718i	0.0228058	+	0.304322i
$671$	−6.49008	+	6.02191i	−0.250547	+	0.232473i
$672$	−1.39266	−	6.10166i	−0.0537231	−	0.235376i
$673$	27.9571	+	4.21386i	1.07767	+	0.162432i	0.663804	−	0.747906i	$-0.268941\pi$
$673$	27.9571	+	4.21386i	1.07767	+	0.162432i	0.413864	+	0.910339i	$0.364179\pi$
$674$	−8.57325	−	5.84514i	−0.330229	−	0.225146i
$675$	1.05809	−	0.326376i	0.0407257	−	0.0125622i
$676$	−0.574705	+	7.66890i	−0.0221040	+	0.294958i
$677$	−18.8292	−	23.6111i	−0.723667	−	0.907449i	0.274872	−	0.961481i	$-0.411364\pi$
$677$	−18.8292	−	23.6111i	−0.723667	−	0.907449i	−0.998539	+	0.0540313i	$0.982793\pi$
$678$	−28.5905	−	8.81900i	−1.09801	−	0.338692i
$679$	−18.5151	+	47.1757i	−0.710544	+	1.81044i
$680$	−1.03849	+	4.54993i	−0.0398243	+	0.174482i
$681$	11.2373	+	19.4636i	0.430615	+	0.745847i
$682$	−2.06736	+	3.58077i	−0.0791632	+	0.137115i
$683$	24.2446	+	22.4957i	0.927693	+	0.860773i	0.990536	−	0.137250i	$-0.0438264\pi$
$683$	24.2446	+	22.4957i	0.927693	+	0.860773i	−0.0628433	+	0.998023i	$0.520017\pi$
$684$	−5.78070	+	7.24877i	−0.221031	+	0.277164i
$685$	−9.09211	+	6.19890i	−0.347392	+	0.236848i
$686$	−16.5842	+	7.98654i	−0.633188	+	0.304927i
$687$	48.6448			1.85591
$688$	−6.40730	+	1.39518i	−0.244276	+	0.0531909i
$689$	16.2283			0.618248
$690$	1.88121	−	0.905943i	0.0716164	−	0.0344887i
$691$	−3.97073	+	2.70720i	−0.151054	+	0.102987i	−0.636489	−	0.771286i	$-0.719614\pi$
$691$	−3.97073	+	2.70720i	−0.151054	+	0.102987i	0.485435	+	0.874273i	$0.338661\pi$
$692$	−11.0797	+	13.8935i	−0.421186	+	0.528151i
$693$	16.1147	+	14.9522i	0.612145	+	0.567988i
$694$	1.27262	−	2.20424i	0.0483078	−	0.0836716i
$695$	−5.31547	−	9.20666i	−0.201627	−	0.349229i
$696$	−3.41307	+	14.9537i	−0.129372	+	0.566817i
$697$	16.1445	−	41.1355i	0.611516	−	1.55812i
$698$	4.38260	+	1.35185i	0.165884	+	0.0511684i
$699$	5.17082	+	6.48400i	0.195578	+	0.245247i
$700$	−0.198904	+	2.65419i	−0.00751787	+	0.100319i
$701$	31.4099	−	9.68867i	1.18634	−	0.365936i	0.362076	−	0.932149i	$-0.382068\pi$
$701$	31.4099	−	9.68867i	1.18634	−	0.365936i	0.824259	+	0.566213i	$0.191592\pi$
$702$	−2.10811	−	1.43728i	−0.0795655	−	0.0542468i
$703$	−6.24311	−	0.940997i	−0.235463	−	0.0354904i
$704$	−0.726680	−	3.18379i	−0.0273878	−	0.119994i
$705$	−16.2217	+	15.0515i	−0.610944	+	0.566873i
$706$	−2.51158	−	33.5147i	−0.0945245	−	1.26134i
$707$	13.6492	+	34.7775i	0.513329	+	1.30794i
$708$	−7.51509	+	1.13272i	−0.282434	+	0.0425701i
$709$	9.77111	+	4.70552i	0.366962	+	0.176719i	0.608272	−	0.793729i	$-0.291863\pi$
$709$	9.77111	+	4.70552i	0.366962	+	0.176719i	−0.241310	+	0.970448i	$0.577577\pi$
$710$	−4.88847	−	2.35416i	−0.183461	−	0.0883502i
$711$	6.01030	−	0.905906i	0.225404	−	0.0339741i
$712$	−6.27844	−	15.9972i	−0.235294	−	0.599520i
$713$	0.0840173	+	1.12113i	0.00314647	+	0.0419868i
$714$	−21.4113	+	19.8667i	−0.801296	+	0.743494i
$715$	1.67446	+	7.33627i	0.0626211	+	0.274361i
$716$	19.0974	+	2.87847i	0.713704	+	0.107574i
$717$	−33.7832	−	23.0330i	−1.26166	−	0.860184i
$718$	−5.23211	+	1.61389i	−0.195260	+	0.0602299i
$719$	1.15828	−	15.4562i	0.0431967	−	0.576420i	−0.933048	−	0.359751i	$-0.882862\pi$
$719$	1.15828	−	15.4562i	0.0431967	−	0.576420i	0.976245	−	0.216669i	$-0.0695192\pi$
$720$	1.57687	+	1.97733i	0.0587664	+	0.0736907i
$721$	−11.7692	−	3.63030i	−0.438306	−	0.135200i
$722$	−2.03162	+	5.17648i	−0.0756090	+	0.192649i
$723$	−0.545286	+	2.38906i	−0.0202794	+	0.0888499i
$724$	4.58304	+	7.93805i	0.170327	+	0.295015i
$725$	3.26150	−	5.64909i	0.121129	−	0.209802i
$726$	−0.578114	−	0.536412i	−0.0214558	−	0.0199081i
$727$	32.6700	−	40.9668i	1.21166	−	1.51938i	0.421074	−	0.907026i	$-0.361653\pi$
$727$	32.6700	−	40.9668i	1.21166	−	1.51938i	0.790587	−	0.612349i	$-0.209775\pi$
$728$	5.06739	−	3.45489i	0.187810	−	0.128047i
$729$	16.1841	−	7.79383i	0.599410	−	0.288661i
$730$	−7.86690			−0.291167
$731$	20.5901	+	22.6407i	0.761554	+	0.837396i
$732$	−6.37485			−0.235621
$733$	14.7399	−	7.09837i	0.544432	−	0.262184i	−0.141390	−	0.989954i	$-0.545157\pi$
$733$	14.7399	−	7.09837i	0.544432	−	0.262184i	0.685822	+	0.727770i	$0.259443\pi$
$734$	−17.0587	+	11.6304i	−0.629649	+	0.429287i
$735$	−0.123569	+	0.154951i	−0.00455791	+	0.00571544i
$736$	−0.650931	−	0.603976i	−0.0239936	−	0.0222628i
$737$	−12.8982	+	22.3403i	−0.475111	+	0.822917i
$738$	−11.9737	−	20.7391i	−0.440759	−	0.763417i
$739$	0.755406	−	3.30965i	0.0277880	−	0.121747i	−0.959132	−	0.282960i	$-0.908683\pi$
$739$	0.755406	−	3.30965i	0.0277880	−	0.121747i	0.986920	+	0.161213i	$0.0515406\pi$
$740$	−0.629204	+	1.60319i	−0.0231300	+	0.0589343i
$741$	−18.9805	−	5.85470i	−0.697265	−	0.215078i
$742$	11.6874	+	14.6556i	0.429059	+	0.538023i
$743$	−0.575240	+	7.67604i	−0.0211035	+	0.281607i	0.976661	+	0.214785i	$0.0689050\pi$
$743$	−0.575240	+	7.67604i	−0.0211035	+	0.281607i	−0.997765	+	0.0668220i	$0.978714\pi$
$744$	−2.84488	+	0.877530i	−0.104298	+	0.0321718i
$745$	−0.888714	−	0.605915i	−0.0325600	−	0.0221990i
$746$	0.688559	+	0.103784i	0.0252099	+	0.00379978i
$747$	−7.10402	−	31.1248i	−0.259923	−	1.13880i
$748$	−11.1722	+	10.3663i	−0.408497	+	0.379030i
$749$	−1.49661	−	19.9708i	−0.0546848	−	0.729718i
$750$	−0.859064	−	2.18886i	−0.0313686	−	0.0799259i
$751$	−26.4547	+	3.98741i	−0.965347	+	0.145503i	−0.612754	−	0.790274i	$-0.709938\pi$
$751$	−26.4547	+	3.98741i	−0.965347	+	0.145503i	−0.352593	+	0.935777i	$0.614700\pi$
$752$	8.47898	+	4.08326i	0.309197	+	0.148901i
$753$	−26.1752	−	12.6053i	−0.953876	−	0.459363i
$754$	−14.8628	+	2.24020i	−0.541271	+	0.0815834i
$755$	−4.74908	−	12.1005i	−0.172837	−	0.440381i
$756$	−0.220242	−	2.93893i	−0.00801013	−	0.106888i
$757$	32.7323	−	30.3712i	1.18968	−	1.10386i	0.197335	−	0.980336i	$-0.436771\pi$
$757$	32.7323	−	30.3712i	1.18968	−	1.10386i	0.992342	−	0.123523i	$-0.0394193\pi$
$758$	−4.23024	−	18.5339i	−0.153649	−	0.673181i
$759$	6.74251	+	1.01627i	0.244738	+	0.0368883i
$760$	−3.02894	−	2.06510i	−0.109871	−	0.0749090i
$761$	47.5092	−	14.6546i	1.72221	−	0.531230i	0.733317	−	0.679887i	$-0.237971\pi$
$761$	47.5092	−	14.6546i	1.72221	−	0.531230i	0.988889	+	0.148657i	$0.0474951\pi$
$762$	0.747918	−	9.98028i	0.0270942	−	0.361547i
$763$	9.15356	+	11.4782i	0.331381	+	0.415539i
$764$	24.3300	+	7.50482i	0.880229	+	0.271515i
$765$	4.31218	−	10.9872i	0.155907	−	0.397245i
$766$	7.39662	−	32.4067i	0.267251	−	1.17090i
$767$	−3.72379	−	6.44980i	−0.134458	−	0.232889i
$768$	1.17570	−	2.03638i	0.0424245	−	0.0734814i
$769$	35.2474	+	32.7049i	1.27106	+	1.17937i	0.974509	+	0.224349i	$0.0720255\pi$
$769$	35.2474	+	32.7049i	1.27106	+	1.17937i	0.296547	+	0.955018i	$0.404165\pi$
$770$	−5.41938	+	6.79569i	−0.195301	+	0.244900i
$771$	−46.6649	+	31.8156i	−1.68060	+	1.14581i
$772$	−7.19895	+	3.46683i	−0.259096	+	0.124774i
$773$	−27.7805			−0.999196			−0.499598	−	0.866258i	$-0.666519\pi$
$773$	−27.7805			−0.999196			−0.499598	+	0.866258i	$0.666519\pi$
$774$	16.5496	−	1.07396i	0.594863	−	0.0386028i
$775$	1.26611			0.0454802
$776$	−17.1549	+	8.26139i	−0.615827	+	0.296566i
$777$	−8.90582	+	6.07189i	−0.319495	+	0.217828i
$778$	−5.15572	+	6.46506i	−0.184841	+	0.231784i
$779$	25.4457	+	23.6101i	0.911685	+	0.845921i
$780$	−2.70912	+	4.69233i	−0.0970020	+	0.168012i
$781$	−8.85943	−	15.3450i	−0.317015	−	0.549087i
$782$	−0.922154	+	4.04022i	−0.0329762	+	0.144478i
$783$	−2.63878	+	6.72350i	−0.0943023	+	0.240278i
$784$	0.0805410	+	0.0248436i	0.00287646	+	0.000887271i
$785$	10.5436	+	13.2212i	0.376317	+	0.471886i
$786$	−0.218684	+	2.91814i	−0.00780021	+	0.104087i
$787$	−11.9940	+	3.69966i	−0.427540	+	0.131879i	−0.501055	−	0.865416i	$-0.667055\pi$
$787$	−11.9940	+	3.69966i	−0.427540	+	0.131879i	0.0735150	+	0.997294i	$0.476578\pi$
$788$	20.5412	+	14.0047i	0.731749	+	0.498898i
$789$	−30.2554	−	4.56027i	−1.07712	−	0.162350i
$790$	0.534785	+	2.34304i	0.0190268	+	0.0833618i
$791$	24.8264	−	23.0355i	0.882724	−	0.819048i
$792$	0.617211	+	8.23611i	0.0219316	+	0.292657i
$793$	−2.28230	−	5.81519i	−0.0810467	−	0.206504i
$794$	34.8276	−	5.24941i	1.23598	−	0.186295i
$795$	−14.9203	−	7.18526i	−0.529170	−	0.254835i
$796$	−6.18420	−	2.97815i	−0.219193	−	0.105558i
$797$	−5.20879	+	0.785099i	−0.184505	+	0.0278096i	−0.240645	−	0.970613i	$-0.577359\pi$
$797$	−5.20879	+	0.785099i	−0.184505	+	0.0278096i	0.0561398	+	0.998423i	$0.482121\pi$
$798$	−8.38222	−	21.3575i	−0.296727	−	0.756049i
$799$	−3.28218	−	43.7976i	−0.116115	−	1.54945i
$800$	−0.733052	+	0.680173i	−0.0259173	+	0.0240477i
$801$	9.67141	+	42.3732i	0.341722	+	1.49718i
$802$	−25.5606	−	3.85264i	−0.902575	−	0.136041i
$803$	−21.2267	−	14.4721i	−0.749073	−	0.510709i
$804$	−17.7492	+	5.47489i	−0.625964	+	0.193084i
$805$	−0.176622	+	2.35685i	−0.00622509	+	0.0830681i
$806$	−1.81900	−	2.28096i	−0.0640716	−	0.0803432i
$807$	37.8282	+	11.6684i	1.33161	+	0.410749i
$808$	−5.12812	+	13.0662i	−0.180406	+	0.459668i
$809$	−0.920022	+	4.03088i	−0.0323462	+	0.141718i	−0.988523	−	0.151073i	$-0.951727\pi$
$809$	−0.920022	+	4.03088i	−0.0323462	+	0.141718i	0.956176	+	0.292791i	$0.0945842\pi$
$810$	5.09548	+	8.82563i	0.179037	+	0.310101i
$811$	−16.8095	+	29.1150i	−0.590263	+	1.02237i	0.403934	+	0.914788i	$0.367643\pi$
$811$	−16.8095	+	29.1150i	−0.590263	+	1.02237i	−0.994197	+	0.107577i	$0.965691\pi$
$812$	−12.7271	−	11.8090i	−0.446635	−	0.414416i
$813$	44.6644	−	56.0074i	1.56645	−	1.96426i
$814$	−4.64699	+	3.16826i	−0.162877	+	0.111047i
$815$	0.553867	−	0.266728i	0.0194011	−	0.00934309i
$816$	−10.9739			−0.384162
$817$	−22.4641	+	8.55835i	−0.785920	+	0.299419i
$818$	−36.6767			−1.28237
$819$	−13.9751	+	6.73004i	−0.488329	+	0.235167i
$820$	7.82347	−	5.33395i	0.273207	−	0.186270i
$821$	21.8454	−	27.3932i	0.762409	−	0.956030i	−0.237473	−	0.971394i	$-0.576319\pi$
$821$	21.8454	−	27.3932i	0.762409	−	0.956030i	0.999882	+	0.0153637i	$0.00489060\pi$
$822$	−18.9680	−	17.5997i	−0.661584	−	0.613860i
$823$	−11.7483	+	20.3486i	−0.409519	+	0.709307i	−0.994836	−	0.101497i	$-0.967637\pi$
$823$	−11.7483	+	20.3486i	−0.409519	+	0.709307i	0.585317	+	0.810804i	$0.300970\pi$
$824$	−2.31368	−	4.00741i	−0.0806009	−	0.139605i
$825$	1.70872	−	7.48638i	0.0594899	−	0.260642i
$826$	3.14291	−	8.00799i	0.109356	−	0.278634i
$827$	40.4454	+	12.4757i	1.40642	+	0.433824i	0.902785	−	0.430091i	$-0.141519\pi$
$827$	40.4454	+	12.4757i	1.40642	+	0.433824i	0.503637	+	0.863915i	$0.331995\pi$
$828$	1.40022	+	1.75582i	0.0486609	+	0.0610189i
$829$	−0.114900	+	1.53323i	−0.00399063	+	0.0532513i	−0.998844	−	0.0480778i	$-0.984690\pi$
$829$	−0.114900	+	1.53323i	−0.00399063	+	0.0532513i	0.994853	+	0.101329i	$0.0323095\pi$
$830$	12.0623	−	3.72074i	0.418690	−	0.129149i
$831$	36.2398	+	24.7079i	1.25715	+	0.857107i
$832$	2.27852	+	0.343431i	0.0789934	+	0.0119063i
$833$	−0.0875298	−	0.383493i	−0.00303273	−	0.0132873i
$834$	18.3246	−	17.0027i	0.634528	−	0.588756i
$835$	0.274727	+	3.66598i	0.00950734	+	0.126867i
$836$	−4.37377	−	11.1442i	−0.151270	−	0.385430i
$837$	−1.38628	+	0.208949i	−0.0479170	+	0.00722232i
$838$	−19.0681	−	9.18273i	−0.658698	−	0.317212i
$839$	−0.555066	−	0.267306i	−0.0191630	−	0.00922842i	0.424278	−	0.905532i	$-0.360528\pi$
$839$	−0.555066	−	0.267306i	−0.0191630	−	0.00922842i	−0.443441	+	0.896304i	$0.646242\pi$
$840$	−6.18867	+	0.932792i	−0.213529	+	0.0321844i
$841$	4.95022	+	12.6130i	0.170697	+	0.434929i
$842$	−1.63918	−	21.8734i	−0.0564900	−	0.753807i
$843$	−29.5536	+	27.4217i	−1.01788	+	0.944454i
$844$	−0.513589	−	2.25018i	−0.0176785	−	0.0774544i
$845$	7.60451	+	1.14620i	0.261603	+	0.0394303i
$846$	−19.6655	−	13.4077i	−0.676114	−	0.460967i
$847$	0.853029	−	0.263125i	0.0293104	−	0.00904106i
$848$	−0.526305	+	7.02305i	−0.0180734	+	0.241173i
$849$	−45.0927	−	56.5445i	−1.54758	−	1.94060i
$850$	4.45960	+	1.37560i	0.152963	+	0.0471829i
$851$	−0.558717	+	1.42359i	−0.0191526	+	0.0488000i
$852$	2.83897	−	12.4384i	0.0972616	−	0.426131i
$853$	−5.51871	−	9.55869i	−0.188957	−	0.327283i	0.755946	−	0.654634i	$-0.227177\pi$
$853$	−5.51871	−	9.55869i	−0.188957	−	0.327283i	−0.944903	+	0.327351i	$0.893844\pi$
$854$	3.60795	−	6.24916i	0.123462	−	0.213842i
$855$	6.79651	+	6.30624i	0.232436	+	0.215669i
$856$	4.69130	−	5.88271i	0.160345	−	0.201067i
$857$	15.0233	−	10.2427i	0.513187	−	0.349885i	−0.278873	−	0.960328i	$-0.589961\pi$
$857$	15.0233	−	10.2427i	0.513187	−	0.349885i	0.792060	+	0.610443i	$0.209009\pi$
$858$	−15.9419	+	7.67721i	−0.544247	+	0.262096i
$859$	−35.2182			−1.20163			−0.600815	−	0.799388i	$-0.705157\pi$
$859$	−35.2182			−1.20163			−0.600815	+	0.799388i	$0.705157\pi$
$860$	0.912465	+	6.49364i	0.0311148	+	0.221431i
$861$	59.2610			2.01961
$862$	−14.2946	+	6.88392i	−0.486876	+	0.234467i
$863$	6.29571	−	4.29234i	0.214308	−	0.146113i	−0.451408	−	0.892317i	$-0.649078\pi$
$863$	6.29571	−	4.29234i	0.214308	−	0.146113i	0.665717	+	0.746204i	$0.268126\pi$
$864$	0.690377	−	0.865705i	0.0234871	−	0.0294519i
$865$	13.0266	+	12.0870i	0.442919	+	0.410969i
$866$	−6.42038	+	11.1204i	−0.218173	+	0.377887i
$867$	5.62024	+	9.73454i	0.190873	+	0.330602i
$868$	0.749880	−	3.28544i	0.0254526	−	0.111515i
$869$	−2.86734	+	7.30586i	−0.0972678	+	0.247834i
$870$	14.6568	+	4.52102i	0.496911	+	0.153277i
$871$	−11.3487	−	14.2308i	−0.384536	−	0.482193i
$872$	−0.412200	+	5.50043i	−0.0139589	+	0.186268i
$873$	46.0160	−	14.1941i	1.55741	−	0.480396i
$874$	−2.68962	−	1.83375i	−0.0909778	−	0.0620276i
$875$	2.63190	+	0.396696i	0.0889746	+	0.0134108i
$876$	−4.11625	−	18.0345i	−0.139075	−	0.609328i
$877$	2.38413	−	2.21215i	0.0805062	−	0.0746988i	−0.638893	−	0.769295i	$-0.720608\pi$
$877$	2.38413	−	2.21215i	0.0805062	−	0.0746988i	0.719400	+	0.694596i	$0.244417\pi$
$878$	0.375036	+	5.00450i	0.0126568	+	0.168894i
$879$	−19.4194	−	49.4798i	−0.655000	−	1.66891i
$880$	−3.22920	+	0.486723i	−0.108856	+	0.0164074i
$881$	11.9816	+	5.77001i	0.403669	+	0.194397i	0.624691	−	0.780872i	$-0.285225\pi$
$881$	11.9816	+	5.77001i	0.403669	+	0.194397i	−0.221022	+	0.975269i	$0.570939\pi$
$882$	−0.192056	−	0.0924895i	−0.00646687	−	0.00311428i
$883$	5.75174	−	0.866935i	0.193562	−	0.0291747i	−0.0515459	−	0.998671i	$-0.516415\pi$
$883$	5.75174	−	0.866935i	0.193562	−	0.0291747i	0.245107	+	0.969496i	$0.421177\pi$
$884$	−3.92881	−	10.0105i	−0.132140	−	0.336688i
$885$	0.567947	+	7.57872i	0.0190913	+	0.254756i
$886$	−19.4496	+	18.0466i	−0.653422	+	0.606287i
$887$	6.31929	+	27.6866i	0.212181	+	0.929626i	0.963081	+	0.269210i	$0.0867626\pi$
$887$	6.31929	+	27.6866i	0.212181	+	0.929626i	−0.750900	+	0.660415i	$0.770380\pi$
$888$	−4.00445	−	0.603573i	−0.134380	−	0.0202546i
$889$	9.36020	+	6.38168i	0.313931	+	0.214035i
$890$	−16.4217	+	5.06541i	−0.550455	+	0.169793i
$891$	−2.48704	+	33.1873i	−0.0833190	+	1.11181i
$892$	−2.04234	−	2.56101i	−0.0683826	−	0.0857491i
$893$	32.9673	+	10.1691i	1.10321	+	0.340295i
$894$	0.924022	−	2.35437i	0.0309039	−	0.0787419i
$895$	4.29757	−	18.8289i	0.143652	−	0.629381i
$896$	1.33082	+	2.30504i	0.0444594	+	0.0770060i
$897$	−2.40563	+	4.16667i	−0.0803215	+	0.139121i
$898$	20.6847	+	19.1926i	0.690257	+	0.640465i
$899$	−5.14932	+	6.45705i	−0.171740	+	0.215355i
$900$	2.08964	−	1.42469i	0.0696547	−	0.0474897i
$901$	29.6131	−	14.2609i	0.986555	−	0.475100i
$902$	30.9219			1.02959
$903$	−18.1754	+	36.7961i	−0.604840	+	1.22450i
$904$	12.7242			0.423201
$905$	8.25835	−	3.97701i	0.274517	−	0.132200i
$906$	25.2548	−	17.2184i	0.839034	−	0.572044i
$907$	−28.0465	+	35.1692i	−0.931268	+	1.16777i	0.0543058	+	0.998524i	$0.482705\pi$
$907$	−28.0465	+	35.1692i	−0.931268	+	1.16777i	−0.985573	+	0.169248i	$0.945866\pi$
$908$	−7.00648	−	6.50106i	−0.232518	−	0.215745i
$909$	17.7499	−	30.7437i	0.588726	−	1.01970i
$910$	−3.06654	−	5.31140i	−0.101655	−	0.176071i
$911$	10.2127	−	44.7449i	0.338363	−	1.48246i	−0.464112	−	0.885777i	$-0.653626\pi$
$911$	10.2127	−	44.7449i	0.338363	−	1.48246i	0.802474	−	0.596687i	$-0.203516\pi$
$912$	3.14928	−	8.02423i	0.104283	−	0.265709i
$913$	39.3916	+	12.1507i	1.30367	+	0.402130i
$914$	−19.8105	−	24.8415i	−0.655272	−	0.821685i
$915$	−0.476393	+	6.35702i	−0.0157491	+	0.210157i
$916$	−19.7685	+	6.09776i	−0.653168	+	0.201476i
$917$	−2.73683	−	1.86594i	−0.0903782	−	0.0616188i
$918$	−5.10989	−	0.770191i	−0.168651	−	0.0254201i
$919$	−7.38318	−	32.3478i	−0.243549	−	1.06706i	−0.937760	−	0.347285i	$-0.887104\pi$
$919$	−7.38318	−	32.3478i	−0.243549	−	1.06706i	0.694211	−	0.719771i	$-0.255753\pi$
$920$	−0.650931	+	0.603976i	−0.0214606	+	0.0199125i
$921$	4.08012	+	54.4454i	0.134445	+	1.79404i
$922$	2.52022	+	6.42143i	0.0829992	+	0.211478i
$923$	12.3628	−	1.86339i	0.406926	−	0.0613342i
$924$	−18.4144	−	8.86791i	−0.605789	−	0.291733i
$925$	1.55168	+	0.747251i	0.0510190	+	0.0245695i
$926$	−14.4821	+	2.18283i	−0.475912	+	0.0717322i
$927$	4.27561	+	10.8941i	0.140429	+	0.357808i
$928$	−0.487465	−	6.50476i	−0.0160018	−	0.213529i
$929$	−9.92997	+	9.21367i	−0.325792	+	0.302291i	−0.826063	−	0.563578i	$-0.809424\pi$
$929$	−9.92997	+	9.21367i	−0.325792	+	0.302291i	0.500271	+	0.865869i	$0.333234\pi$
$930$	0.662478	+	2.90250i	0.0217235	+	0.0951768i
$931$	0.305535	+	0.0460519i	0.0100135	+	0.00150929i
$932$	−2.91412	−	1.98682i	−0.0954553	−	0.0650803i
$933$	−22.6427	+	6.98436i	−0.741290	+	0.228658i
$934$	−0.341934	+	4.56280i	−0.0111884	+	0.149299i
$935$	9.50242	+	11.9157i	0.310762	+	0.389683i
$936$	−5.56878	−	1.71774i	−0.182021	−	0.0561461i
$937$	−0.803801	+	2.04805i	−0.0262590	+	0.0669069i	−0.943402	−	0.331652i	$-0.892394\pi$
$937$	−0.803801	+	2.04805i	−0.0262590	+	0.0669069i	0.917143	+	0.398558i	$0.130489\pi$
$938$	4.67849	−	20.4978i	0.152758	−	0.669277i
$939$	−4.42433	−	7.66317i	−0.144383	−	0.250078i
$940$	4.70548	−	8.15013i	0.153476	−	0.265828i
$941$	−26.9325	−	24.9897i	−0.877975	−	0.814642i	0.105737	−	0.994394i	$-0.466280\pi$
$941$	−26.9325	−	24.9897i	−0.877975	−	0.814642i	−0.983712	+	0.179752i	$0.942470\pi$
$942$	−24.7922	+	31.0885i	−0.807774	+	1.01292i
$943$	6.94704	−	4.73641i	0.226227	−	0.154239i
$944$	2.91202	−	1.40236i	0.0947782	−	0.0456428i
$945$	−2.94717			−0.0958714
$946$	−9.48379	+	19.1999i	−0.308345	+	0.624242i
$947$	−28.8963			−0.939002			−0.469501	−	0.882932i	$-0.655566\pi$
$947$	−28.8963			−0.939002			−0.469501	+	0.882932i	$0.655566\pi$
$948$	−5.09149	+	2.45193i	−0.165364	+	0.0796351i
$949$	14.9775	−	10.2115i	0.486191	−	0.331479i
$950$	−2.28568	+	2.86615i	−0.0741571	+	0.0929901i
$951$	29.3845	+	27.2648i	0.952857	+	0.884122i
$952$	6.21084	−	10.7575i	0.201294	−	0.348652i
$953$	−10.0145	−	17.3456i	−0.324402	−	0.561880i	0.656989	−	0.753900i	$-0.271830\pi$
$953$	−10.0145	−	17.3456i	−0.324402	−	0.561880i	−0.981391	+	0.192020i	$0.938496\pi$
$954$	3.96350	−	17.3652i	0.128323	−	0.562220i
$955$	9.30202	−	23.7012i	0.301006	−	0.766951i
$956$	16.6162	+	5.12543i	0.537407	+	0.165768i
$957$	31.2303	+	39.1616i	1.00953	+	1.26591i
$958$	−1.13930	+	15.2029i	−0.0368090	+	0.491182i
$959$	27.9879	−	8.63314i	0.903778	−	0.278778i
$960$	−1.94282	−	1.32459i	−0.0627043	−	0.0427510i
$961$	29.0686	+	4.38139i	0.937697	+	0.141335i
$962$	−0.883069	−	3.86898i	−0.0284713	−	0.124741i
$963$	−13.9497	+	12.9434i	−0.449523	+	0.417096i
$964$	−0.0778793	−	1.03923i	−0.00250832	−	0.0334712i
$965$	2.91916	+	7.43790i	0.0939711	+	0.239435i
$966$	−5.49538	+	0.828295i	−0.176811	+	0.0266499i
$967$	42.2708	+	20.3565i	1.35934	+	0.654622i	0.964489	−	0.264124i	$-0.0850829\pi$
$967$	42.2708	+	20.3565i	1.35934	+	0.654622i	0.394848	+	0.918746i	$0.370797\pi$
$968$	0.302177	+	0.145521i	0.00971234	+	0.00467722i
$969$	−39.7802	+	5.99590i	−1.27792	+	0.192616i
$970$	6.95630	+	17.7244i	0.223353	+	0.569095i
$971$	3.95088	+	52.7209i	0.126790	+	1.69189i	0.591401	+	0.806378i	$0.298575\pi$
$971$	3.95088	+	52.7209i	0.126790	+	1.69189i	−0.464611	+	0.885515i	$0.653806\pi$
$972$	−15.1311	+	14.0396i	−0.485330	+	0.450320i
$973$	6.29637	+	27.5862i	0.201853	+	0.884374i
$974$	40.5233	+	6.10790i	1.29845	+	0.195710i
$975$	4.47676	+	3.05220i	0.143371	+	0.0977486i
$976$	2.59064	−	0.799106i	0.0829243	−	0.0255788i
$977$	−0.914386	+	12.2016i	−0.0292538	+	0.390365i	0.963289	+	0.268467i	$0.0865170\pi$
$977$	−0.914386	+	12.2016i	−0.0292538	+	0.390365i	−0.992543	+	0.121898i	$0.961102\pi$
$978$	0.901264	+	1.13015i	0.0288193	+	0.0361382i
$979$	−53.6277	−	16.5420i	−1.71395	−	0.528683i
$980$	0.0307930	−	0.0784592i	0.000983645	−	0.00250629i
$981$	3.10420	−	13.6004i	0.0991094	−	0.434226i
$982$	−0.303993	−	0.526532i	−0.00970082	−	0.0168023i
$983$	19.9262	−	34.5132i	0.635548	−	1.10080i	−0.350851	−	0.936431i	$-0.614108\pi$
$983$	19.9262	−	34.5132i	0.635548	−	1.10080i	0.986399	−	0.164370i	$-0.0525589\pi$
$984$	16.3213	+	15.1440i	0.520305	+	0.482772i
$985$	15.5006	−	19.4372i	0.493891	−	0.619319i
$986$	−25.1527	+	17.1489i	−0.801027	+	0.546131i
$987$	53.0663	−	25.5554i	1.68912	−	0.813437i
$988$	8.44726			0.268743
$989$	0.810245	+	5.76619i	0.0257643	+	0.183354i
$990$	8.25921			0.262495
$991$	−5.74713	+	2.76767i	−0.182564	+	0.0879180i	−0.522933	−	0.852374i	$-0.675162\pi$
$991$	−5.74713	+	2.76767i	−0.182564	+	0.0879180i	0.340369	+	0.940292i	$0.389448\pi$
$992$	1.04611	−	0.713228i	0.0332141	−	0.0226450i
$993$	21.5562	−	27.0307i	0.684067	−	0.857792i
$994$	10.5863	+	9.82269i	0.335778	+	0.311557i
$995$	−3.43197	+	5.94435i	−0.108801	+	0.188448i
$996$	14.8411	+	25.7055i	0.470257	+	0.814509i
$997$	0.742027	−	3.25103i	0.0235002	−	0.102961i	−0.961818	−	0.273691i	$-0.911755\pi$
$997$	0.742027	−	3.25103i	0.0235002	−	0.102961i	0.985318	+	0.170730i	$0.0546125\pi$
$998$	9.75933	−	24.8664i	0.308926	−	0.787131i
$999$	−1.82228	−	0.562097i	−0.0576542	−	0.0177840i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.a.31.1	✓	36
43.25	even	21	inner	430.2.q.a.111.1	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.a.31.1	✓	36	1.1	even	1	trivial
430.2.q.a.111.1	yes	36	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)

\(f(q)\)	\(=\)	\(q+(-0.900969 + 0.433884i) q^{2} +(-1.94282 + 1.32459i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-0.733052 - 0.680173i) q^{5} +(1.17570 - 2.03638i) q^{6} +(1.33082 + 2.30504i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(0.923984 - 2.35427i) q^{9} +O(q^{10})\)	\(q+(-0.900969 + 0.433884i) q^{2} +(-1.94282 + 1.32459i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-0.733052 - 0.680173i) q^{5} +(1.17570 - 2.03638i) q^{6} +(1.33082 + 2.30504i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(0.923984 - 2.35427i) q^{9} +(0.955573 + 0.294755i) q^{10} +(2.03611 + 2.55320i) q^{11} +(-0.175721 + 2.34483i) q^{12} +(-2.20188 + 0.679191i) q^{13} +(-2.19914 - 1.49935i) q^{14} +(2.32514 + 0.350459i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(-3.42111 + 3.17433i) q^{17} +(0.189000 + 2.52203i) q^{18} +(-1.33932 - 3.41253i) q^{19} +(-0.988831 + 0.149042i) q^{20} +(-5.63878 - 2.71549i) q^{21} +(-2.94227 - 1.41692i) q^{22} +(-0.878056 + 0.132346i) q^{23} +(-0.859064 - 2.18886i) q^{24} +(0.0747301 + 0.997204i) q^{25} +(1.68914 - 1.56729i) q^{26} +(-0.246393 - 1.07952i) q^{27} +(2.63190 + 0.396696i) q^{28} +(-5.38956 - 3.67454i) q^{29} +(-2.24694 + 0.693088i) q^{30} +(0.0946169 - 1.26257i) q^{31} +(0.623490 + 0.781831i) q^{32} +(-7.33776 - 2.26340i) q^{33} +(1.70502 - 4.34433i) q^{34} +(0.592269 - 2.59490i) q^{35} +(-1.26455 - 2.19026i) q^{36} +(0.861119 - 1.49150i) q^{37} +(2.68732 + 2.49347i) q^{38} +(3.37821 - 4.23615i) q^{39} +(0.826239 - 0.563320i) q^{40} +(-8.53107 + 4.10835i) q^{41} +6.25857 q^{42} +(0.0655539 - 6.55711i) q^{43} +3.26567 q^{44} +(-2.27864 + 1.09733i) q^{45} +(0.733679 - 0.500214i) q^{46} +(-5.86764 + 7.35779i) q^{47} +(1.72370 + 1.59936i) q^{48} +(-0.0421428 + 0.0729934i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(2.44191 - 10.6987i) q^{51} +(-0.841839 + 2.14497i) q^{52} +(-6.72985 - 2.07589i) q^{53} +(0.690377 + 0.865705i) q^{54} +(0.244044 - 3.25654i) q^{55} +(-2.54338 + 0.784530i) q^{56} +(7.12227 + 4.85588i) q^{57} +(6.45015 + 0.972203i) q^{58} +(0.719210 + 3.15106i) q^{59} +(1.72370 - 1.59936i) q^{60} +(0.202599 + 2.70350i) q^{61} +(0.462564 + 1.17859i) q^{62} +(6.65635 - 1.00328i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(2.07606 + 0.999779i) q^{65} +(7.59314 - 1.14448i) q^{66} +(2.88593 + 7.35322i) q^{67} +(0.348761 + 4.65389i) q^{68} +(1.53060 - 1.42019i) q^{69} +(0.592269 + 2.59490i) q^{70} +(-5.36519 - 0.808673i) q^{71} +(2.08964 + 1.42469i) q^{72} +(-7.51740 + 2.31881i) q^{73} +(-0.128703 + 1.71742i) q^{74} +(-1.46608 - 1.83840i) q^{75} +(-3.50307 - 1.08055i) q^{76} +(-3.17555 + 8.09117i) q^{77} +(-1.20567 + 5.28239i) q^{78} +(1.20165 + 2.08132i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(7.47050 + 6.93161i) q^{81} +(5.90368 - 7.40298i) q^{82} +(10.4297 - 7.11087i) q^{83} +(-5.63878 + 2.71549i) q^{84} +4.66694 q^{85} +(2.78596 + 5.93620i) q^{86} +15.3382 q^{87} +(-2.94227 + 1.41692i) q^{88} +(-14.1990 + 9.68073i) q^{89} +(1.57687 - 1.97733i) q^{90} +(-4.49587 - 4.17155i) q^{91} +(-0.443987 + 0.769008i) q^{92} +(1.48857 + 2.57829i) q^{93} +(2.09414 - 9.17501i) q^{94} +(-1.33932 + 3.41253i) q^{95} +(-2.24694 - 0.693088i) q^{96} +(11.8716 + 14.8865i) q^{97} +(0.00629867 - 0.0840499i) q^{98} +(7.89227 - 2.43444i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) \) 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9	\( 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9} + 3 q^{10} + 9 q^{11} - 16 q^{12} + 21 q^{13} - 6 q^{14} + 5 q^{15} - 6 q^{16} - 37 q^{17} + 19 q^{18} + 7 q^{19} + 3 q^{20} - 8 q^{21} + 16 q^{22} + 13 q^{23} + 5 q^{24} + 3 q^{25} - 21 q^{26} - 28 q^{27} - 6 q^{28} + 4 q^{29} - 2 q^{30} + 13 q^{31} - 6 q^{32} - 54 q^{33} - 23 q^{34} - 2 q^{35} - 9 q^{36} + 17 q^{37} + 28 q^{38} + 8 q^{39} + 3 q^{40} + 10 q^{41} - 50 q^{42} + 14 q^{43} - 26 q^{44} + 4 q^{45} - 8 q^{46} + 13 q^{47} - 2 q^{48} + 5 q^{49} - 18 q^{50} + 17 q^{51} - 7 q^{52} - 71 q^{53} + 7 q^{54} - 29 q^{55} + q^{56} - 70 q^{57} + 25 q^{58} + 8 q^{59} - 2 q^{60} + 25 q^{61} - 15 q^{62} + 88 q^{63} - 6 q^{64} + 7 q^{65} + 44 q^{66} + 26 q^{67} - 9 q^{68} + 78 q^{69} - 2 q^{70} - 60 q^{71} - 23 q^{72} + 7 q^{73} + 17 q^{74} - 10 q^{75} - 35 q^{76} - 5 q^{77} + 57 q^{78} + 52 q^{79} - 18 q^{80} + q^{81} - 4 q^{82} - 101 q^{83} - 8 q^{84} - 24 q^{85} + 49 q^{86} - 18 q^{87} + 16 q^{88} + 14 q^{89} - 3 q^{90} + 35 q^{91} + 6 q^{92} + 28 q^{93} - 15 q^{94} + 7 q^{95} - 2 q^{96} + 11 q^{97} + 12 q^{98} + 78 q^{99}+O(q^{100}) \) 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9 + 3 * q^10 + 9 * q^11 - 16 * q^12 + 21 * q^13 - 6 * q^14 + 5 * q^15 - 6 * q^16 - 37 * q^17 + 19 * q^18 + 7 * q^19 + 3 * q^20 - 8 * q^21 + 16 * q^22 + 13 * q^23 + 5 * q^24 + 3 * q^25 - 21 * q^26 - 28 * q^27 - 6 * q^28 + 4 * q^29 - 2 * q^30 + 13 * q^31 - 6 * q^32 - 54 * q^33 - 23 * q^34 - 2 * q^35 - 9 * q^36 + 17 * q^37 + 28 * q^38 + 8 * q^39 + 3 * q^40 + 10 * q^41 - 50 * q^42 + 14 * q^43 - 26 * q^44 + 4 * q^45 - 8 * q^46 + 13 * q^47 - 2 * q^48 + 5 * q^49 - 18 * q^50 + 17 * q^51 - 7 * q^52 - 71 * q^53 + 7 * q^54 - 29 * q^55 + q^56 - 70 * q^57 + 25 * q^58 + 8 * q^59 - 2 * q^60 + 25 * q^61 - 15 * q^62 + 88 * q^63 - 6 * q^64 + 7 * q^65 + 44 * q^66 + 26 * q^67 - 9 * q^68 + 78 * q^69 - 2 * q^70 - 60 * q^71 - 23 * q^72 + 7 * q^73 + 17 * q^74 - 10 * q^75 - 35 * q^76 - 5 * q^77 + 57 * q^78 + 52 * q^79 - 18 * q^80 + q^81 - 4 * q^82 - 101 * q^83 - 8 * q^84 - 24 * q^85 + 49 * q^86 - 18 * q^87 + 16 * q^88 + 14 * q^89 - 3 * q^90 + 35 * q^91 + 6 * q^92 + 28 * q^93 - 15 * q^94 + 7 * q^95 - 2 * q^96 + 11 * q^97 + 12 * q^98 + 78 * q^99

Introduction

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