LMFDB - Embedded newform 430.2.q.a.181.2

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			181.2
Character	$\chi$	$=$	430.181
Dual form			430.2.q.a.411.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.623490 + 0.781831i) q^{2} +(1.26688 + 0.190952i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(0.826239 + 0.563320i) q^{5} +(0.640596 + 1.10954i) q^{6} +(-1.20270 + 2.08314i) q^{7} +(-0.900969 + 0.433884i) q^{8} +(-1.29819 - 0.400439i) q^{9} +O(q^{10})$	\(q+(0.623490 + 0.781831i) q^{2} +(1.26688 + 0.190952i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(0.826239 + 0.563320i) q^{5} +(0.640596 + 1.10954i) q^{6} +(-1.20270 + 2.08314i) q^{7} +(-0.900969 + 0.433884i) q^{8} +(-1.29819 - 0.400439i) q^{9} +(0.0747301 + 0.997204i) q^{10} +(0.781839 + 3.42546i) q^{11} +(-0.468072 + 1.19263i) q^{12} +(-0.0764582 + 1.02026i) q^{13} +(-2.37853 + 0.358506i) q^{14} +(0.939180 + 0.871431i) q^{15} +(-0.900969 - 0.433884i) q^{16} +(-0.102826 + 0.0701055i) q^{17} +(-0.496334 - 1.26464i) q^{18} +(5.54821 - 1.71140i) q^{19} +(-0.733052 + 0.680173i) q^{20} +(-1.92146 + 2.40943i) q^{21} +(-2.19066 + 2.74701i) q^{22} +(5.44859 - 5.05555i) q^{23} +(-1.22427 + 0.377638i) q^{24} +(0.365341 + 0.930874i) q^{25} +(-0.845346 + 0.576347i) q^{26} +(-5.03113 - 2.42287i) q^{27} +(-1.76328 - 1.63609i) q^{28} +(1.74853 - 0.263549i) q^{29} +(-0.0957435 + 1.27761i) q^{30} +(0.941882 - 2.39988i) q^{31} +(-0.222521 - 0.974928i) q^{32} +(0.336400 + 4.48894i) q^{33} +(-0.118922 - 0.0366825i) q^{34} +(-2.16719 + 1.04366i) q^{35} +(0.679275 - 1.17654i) q^{36} +(0.228785 + 0.396268i) q^{37} +(4.79728 + 3.27073i) q^{38} +(-0.291685 + 1.27795i) q^{39} +(-0.988831 - 0.149042i) q^{40} +(-2.46217 - 3.08746i) q^{41} -3.08178 q^{42} +(-1.31952 - 6.42331i) q^{43} -3.51355 q^{44} +(-0.847042 - 1.06216i) q^{45} +(7.34973 + 1.10779i) q^{46} +(0.452390 - 1.98205i) q^{47} +(-1.05857 - 0.721721i) q^{48} +(0.607028 + 1.05140i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-0.143655 + 0.0691806i) q^{51} +(-0.977671 - 0.301571i) q^{52} +(0.251100 + 3.35069i) q^{53} +(-1.24259 - 5.44413i) q^{54} +(-1.28364 + 3.27067i) q^{55} +(0.179756 - 2.39867i) q^{56} +(7.35572 - 1.10870i) q^{57} +(1.29624 + 1.20274i) q^{58} +(-1.29825 - 0.625206i) q^{59} +(-1.05857 + 0.721721i) q^{60} +(2.11408 + 5.38658i) q^{61} +(2.46355 - 0.759906i) q^{62} +(2.39551 - 2.22270i) q^{63} +(0.623490 - 0.781831i) q^{64} +(-0.637908 + 0.799911i) q^{65} +(-3.29986 + 3.06182i) q^{66} +(-11.7548 + 3.62588i) q^{67} +(-0.0454669 - 0.115848i) q^{68} +(7.86808 - 5.36437i) q^{69} +(-2.16719 - 1.04366i) q^{70} +(-5.81578 - 5.39626i) q^{71} +(1.34338 - 0.202481i) q^{72} +(0.780669 - 10.4173i) q^{73} +(-0.167169 + 0.425940i) q^{74} +(0.285092 + 1.24907i) q^{75} +(0.433895 + 5.78993i) q^{76} +(-8.07602 - 2.49112i) q^{77} +(-1.18101 + 0.568743i) q^{78} +(2.99808 - 5.19283i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-2.54374 - 1.73429i) q^{81} +(0.878737 - 3.85000i) q^{82} +(-2.08309 - 0.313975i) q^{83} +(-1.92146 - 2.40943i) q^{84} -0.124451 q^{85} +(4.19924 - 5.03651i) q^{86} +2.26551 q^{87} +(-2.19066 - 2.74701i) q^{88} +(9.49754 + 1.43152i) q^{89} +(0.302306 - 1.32449i) q^{90} +(-2.03339 - 1.38634i) q^{91} +(3.71637 + 6.43695i) q^{92} +(1.65151 - 2.86051i) q^{93} +(1.83169 - 0.882096i) q^{94} +(5.54821 + 1.71140i) q^{95} +(-0.0957435 - 1.27761i) q^{96} +(0.351470 + 1.53989i) q^{97} +(-0.443545 + 1.13013i) q^{98} +(0.356712 - 4.75999i) 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 $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.623490	+	0.781831i	0.440874	+	0.552838i
$2$	0.623490	+	0.781831i	0.440874	+	0.552838i
$3$	1.26688	+	0.190952i	0.731434	+	0.110246i	0.504191	−	0.863592i	$-0.331791\pi$
$3$	1.26688	+	0.190952i	0.731434	+	0.110246i	0.227243	+	0.973838i	$0.427029\pi$
$4$	−0.222521	+	0.974928i	−0.111260	+	0.487464i
$5$	0.826239	+	0.563320i	0.369505	+	0.251924i
$5$	0.826239	+	0.563320i	0.369505	+	0.251924i
$6$	0.640596	+	1.10954i	0.261522	+	0.452969i
$7$	−1.20270	+	2.08314i	−0.454578	+	0.787352i	−0.998664	−	0.0516778i	$-0.983543\pi$
$7$	−1.20270	+	2.08314i	−0.454578	+	0.787352i	0.544086	+	0.839029i	$0.316876\pi$
$8$	−0.900969	+	0.433884i	−0.318541	+	0.153401i
$9$	−1.29819	−	0.400439i	−0.432731	−	0.133480i
$10$	0.0747301	+	0.997204i	0.0236317	+	0.315344i
$11$	0.781839	+	3.42546i	0.235733	+	1.03281i	0.944793	+	0.327667i	$0.106262\pi$
$11$	0.781839	+	3.42546i	0.235733	+	1.03281i	−0.709060	+	0.705148i	$0.750881\pi$
$12$	−0.468072	+	1.19263i	−0.135121	+	0.344282i
$13$	−0.0764582	+	1.02026i	−0.0212057	+	0.282970i	0.976513	+	0.215459i	$0.0691249\pi$
$13$	−0.0764582	+	1.02026i	−0.0212057	+	0.282970i	−0.997719	+	0.0675111i	$0.978494\pi$
$14$	−2.37853	+	0.358506i	−0.635690	+	0.0958148i
$15$	0.939180	+	0.871431i	0.242495	+	0.225003i
$16$	−0.900969	−	0.433884i	−0.225242	−	0.108471i
$17$	−0.102826	+	0.0701055i	−0.0249390	+	0.0170031i	−0.575725	−	0.817643i	$-0.695280\pi$
$17$	−0.102826	+	0.0701055i	−0.0249390	+	0.0170031i	0.550786	+	0.834646i	$0.314328\pi$
$18$	−0.496334	−	1.26464i	−0.116987	−	0.298078i
$19$	5.54821	−	1.71140i	1.27285	−	0.392621i	0.416554	−	0.909111i	$-0.363238\pi$
$19$	5.54821	−	1.71140i	1.27285	−	0.392621i	0.856293	+	0.516490i	$0.172762\pi$
$20$	−0.733052	+	0.680173i	−0.163915	+	0.152091i
$21$	−1.92146	+	2.40943i	−0.419296	+	0.525781i
$22$	−2.19066	+	2.74701i	−0.467051	+	0.585664i
$23$	5.44859	−	5.05555i	1.13611	−	1.05416i	0.138143	−	0.990412i	$-0.455887\pi$
$23$	5.44859	−	5.05555i	1.13611	−	1.05416i	0.997966	−	0.0637432i	$-0.0203039\pi$
$24$	−1.22427	+	0.377638i	−0.249903	+	0.0770850i
$25$	0.365341	+	0.930874i	0.0730682	+	0.186175i
$26$	−0.845346	+	0.576347i	−0.165786	+	0.113031i
$27$	−5.03113	−	2.42287i	−0.968242	−	0.466281i
$28$	−1.76328	−	1.63609i	−0.333229	−	0.309191i
$29$	1.74853	−	0.263549i	0.324694	−	0.0489397i	0.0153272	−	0.999883i	$-0.495121\pi$
$29$	1.74853	−	0.263549i	0.324694	−	0.0489397i	0.309367	+	0.950943i	$0.399883\pi$
$30$	−0.0957435	+	1.27761i	−0.0174803	+	0.233258i
$31$	0.941882	−	2.39988i	0.169167	−	0.431031i	−0.820999	−	0.570930i	$-0.806583\pi$
$31$	0.941882	−	2.39988i	0.169167	−	0.431031i	0.990166	+	0.139899i	$0.0446779\pi$
$32$	−0.222521	−	0.974928i	−0.0393365	−	0.172345i
$33$	0.336400	+	4.48894i	0.0585597	+	0.781425i
$34$	−0.118922	−	0.0366825i	−0.0203949	−	0.00629099i
$35$	−2.16719	+	1.04366i	−0.366322	+	0.176411i
$36$	0.679275	−	1.17654i	0.113212	−	0.196090i
$37$	0.228785	+	0.396268i	0.0376121	+	0.0651460i	0.884219	−	0.467073i	$-0.154692\pi$
$37$	0.228785	+	0.396268i	0.0376121	+	0.0651460i	−0.846607	+	0.532219i	$0.821358\pi$
$38$	4.79728	+	3.27073i	0.778221	+	0.530582i
$39$	−0.291685	+	1.27795i	−0.0467069	+	0.204636i
$40$	−0.988831	−	0.149042i	−0.156348	−	0.0235657i
$41$	−2.46217	−	3.08746i	−0.384526	−	0.482180i	0.551468	−	0.834196i	$-0.314068\pi$
$41$	−2.46217	−	3.08746i	−0.384526	−	0.482180i	−0.935994	+	0.352016i	$0.885496\pi$
$42$	−3.08178			−0.475528
$43$	−1.31952	−	6.42331i	−0.201225	−	0.979545i
$43$	−1.31952	−	6.42331i	−0.201225	−	0.979545i
$44$	−3.51355			−0.529688
$45$	−0.847042	−	1.06216i	−0.126270	−	0.158337i
$46$	7.34973	+	1.10779i	1.08366	+	0.163335i
$47$	0.452390	−	1.98205i	0.0659879	−	0.289112i	−0.931157	−	0.364617i	$-0.881200\pi$
$47$	0.452390	−	1.98205i	0.0659879	−	0.289112i	0.997145	+	0.0755053i	$0.0240570\pi$
$48$	−1.05857	−	0.721721i	−0.152791	−	0.104171i
$49$	0.607028	+	1.05140i	0.0867183	+	0.150201i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	−0.143655	+	0.0691806i	−0.0201157	+	0.00968722i
$52$	−0.977671	−	0.301571i	−0.135579	−	0.0418204i
$53$	0.251100	+	3.35069i	0.0344912	+	0.460253i	0.987533	+	0.157414i	$0.0503155\pi$
$53$	0.251100	+	3.35069i	0.0344912	+	0.460253i	−0.953042	+	0.302839i	$0.902065\pi$
$54$	−1.24259	−	5.44413i	−0.169095	−	0.740852i
$55$	−1.28364	+	3.27067i	−0.173087	+	0.441017i
$56$	0.179756	−	2.39867i	0.0240209	−	0.320536i
$57$	7.35572	−	1.10870i	0.974289	−	0.146850i
$58$	1.29624	+	1.20274i	0.170205	+	0.157927i
$59$	−1.29825	−	0.625206i	−0.169018	−	0.0813949i	0.347462	−	0.937694i	$-0.387044\pi$
$59$	−1.29825	−	0.625206i	−0.169018	−	0.0813949i	−0.516480	+	0.856299i	$0.672758\pi$
$60$	−1.05857	+	0.721721i	−0.136661	+	0.0931737i
$61$	2.11408	+	5.38658i	0.270680	+	0.689680i	0.999985	+	0.00549194i	$0.00174815\pi$
$61$	2.11408	+	5.38658i	0.270680	+	0.689680i	−0.729305	+	0.684188i	$0.760157\pi$
$62$	2.46355	−	0.759906i	0.312872	−	0.0965081i
$63$	2.39551	−	2.22270i	0.301805	−	0.280034i
$64$	0.623490	−	0.781831i	0.0779362	−	0.0977289i
$65$	−0.637908	+	0.799911i	−0.0791228	+	0.0992168i
$66$	−3.29986	+	3.06182i	−0.406184	+	0.376884i
$67$	−11.7548	+	3.62588i	−1.43608	+	0.442972i	−0.912525	−	0.409021i	$-0.865870\pi$
$67$	−11.7548	+	3.62588i	−1.43608	+	0.442972i	−0.523554	+	0.851993i	$0.675394\pi$
$68$	−0.0454669	−	0.115848i	−0.00551367	−	0.0140486i
$69$	7.86808	−	5.36437i	0.947206	−	0.645794i
$70$	−2.16719	−	1.04366i	−0.259029	−	0.124742i
$71$	−5.81578	−	5.39626i	−0.690206	−	0.640418i	0.254981	−	0.966946i	$-0.417931\pi$
$71$	−5.81578	−	5.39626i	−0.690206	−	0.640418i	−0.945187	+	0.326528i	$0.894121\pi$
$72$	1.34338	−	0.202481i	0.158318	−	0.0238626i
$73$	0.780669	−	10.4173i	0.0913704	−	1.21925i	−0.743473	−	0.668766i	$-0.766823\pi$
$73$	0.780669	−	10.4173i	0.0913704	−	1.21925i	0.834844	−	0.550487i	$-0.185558\pi$
$74$	−0.167169	+	0.425940i	−0.0194330	+	0.0495146i
$75$	0.285092	+	1.24907i	0.0329196	+	0.144230i
$76$	0.433895	+	5.78993i	0.0497712	+	0.664150i
$77$	−8.07602	−	2.49112i	−0.920348	−	0.283890i
$78$	−1.18101	+	0.568743i	−0.133723	+	0.0643975i
$79$	2.99808	−	5.19283i	0.337311	−	0.584240i	−0.646615	−	0.762816i	$-0.723816\pi$
$79$	2.99808	−	5.19283i	0.337311	−	0.584240i	0.983926	+	0.178577i	$0.0571493\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−2.54374	−	1.73429i	−0.282637	−	0.192699i
$82$	0.878737	−	3.85000i	0.0970403	−	0.425161i
$83$	−2.08309	−	0.313975i	−0.228648	−	0.0344632i	0.0337186	−	0.999431i	$-0.489265\pi$
$83$	−2.08309	−	0.313975i	−0.228648	−	0.0344632i	−0.262367	+	0.964968i	$0.584503\pi$
$84$	−1.92146	−	2.40943i	−0.209648	−	0.262890i
$85$	−0.124451			−0.0134986
$86$	4.19924	−	5.03651i	0.452815	−	0.543101i
$87$	2.26551			0.242888
$88$	−2.19066	−	2.74701i	−0.233526	−	0.292832i
$89$	9.49754	+	1.43152i	1.00674	+	0.151741i	0.631655	−	0.775250i	$-0.282376\pi$
$89$	9.49754	+	1.43152i	1.00674	+	0.151741i	0.375083	+	0.926991i	$0.377614\pi$
$90$	0.302306	−	1.32449i	0.0318658	−	0.139613i
$91$	−2.03339	−	1.38634i	−0.213158	−	0.145328i
$92$	3.71637	+	6.43695i	0.387459	+	0.671098i
$93$	1.65151	−	2.86051i	0.171254	−	0.296621i
$94$	1.83169	−	0.882096i	0.188924	−	0.0909812i
$95$	5.54821	+	1.71140i	0.569234	+	0.175586i
$96$	−0.0957435	−	1.27761i	−0.00977178	−	0.130395i
$97$	0.351470	+	1.53989i	0.0356864	+	0.156352i	0.989632	−	0.143628i	$-0.0458769\pi$
$97$	0.351470	+	1.53989i	0.0356864	+	0.156352i	−0.953945	+	0.299981i	$0.903020\pi$
$98$	−0.443545	+	1.13013i	−0.0448048	+	0.114161i
$99$	0.356712	−	4.75999i	0.0358509	−	0.478397i
$100$	−0.988831	+	0.149042i	−0.0988831	+	0.0149042i
$101$	5.82190	+	5.40194i	0.579301	+	0.537513i	0.914474	−	0.404644i	$-0.132604\pi$
$101$	5.82190	+	5.40194i	0.579301	+	0.537513i	−0.335173	+	0.942156i	$0.608795\pi$
$102$	−0.143655	−	0.0691806i	−0.0142240	−	0.00684990i
$103$	3.42886	−	2.33776i	0.337856	−	0.230346i	−0.382493	−	0.923959i	$-0.624934\pi$
$103$	3.42886	−	2.33776i	0.337856	−	0.230346i	0.720348	+	0.693612i	$0.243982\pi$
$104$	−0.373790	−	0.952400i	−0.0366531	−	0.0933905i
$105$	−2.94486	+	0.908369i	−0.287389	+	0.0886478i
$106$	−2.46312	+	2.28544i	−0.239239	+	0.221982i
$107$	−8.82574	+	11.0671i	−0.853216	+	1.06990i	0.143558	+	0.989642i	$0.454146\pi$
$107$	−8.82574	+	11.0671i	−0.853216	+	1.06990i	−0.996774	+	0.0802574i	$0.974426\pi$
$108$	3.48165	−	4.36585i	0.335022	−	0.420104i
$109$	10.2147	−	9.47786i	0.978391	−	0.907814i	−0.0173648	−	0.999849i	$-0.505528\pi$
$109$	10.2147	−	9.47786i	0.978391	−	0.907814i	0.995756	+	0.0920351i	$0.0293372\pi$
$110$	−3.35745	+	1.03564i	−0.320121	+	0.0987442i
$111$	0.214176	+	0.545711i	0.0203287	+	0.0517966i
$112$	1.98743	−	1.35501i	0.187795	−	0.128036i
$113$	−6.43699	−	3.09989i	−0.605541	−	0.291613i	0.105880	−	0.994379i	$-0.466234\pi$
$113$	−6.43699	−	3.09989i	−0.605541	−	0.291613i	−0.711421	+	0.702766i	$0.751948\pi$
$114$	5.45303	+	5.05967i	0.510723	+	0.473882i
$115$	7.34973	−	1.10779i	0.685366	−	0.103302i
$116$	−0.132144	+	1.76334i	−0.0122692	+	0.163722i
$117$	0.507812	−	1.29388i	0.0469472	−	0.119620i
$118$	−0.320642	−	1.40483i	−0.0295175	−	0.129325i
$119$	−0.0223707	−	0.298516i	−0.00205072	−	0.0273650i
$120$	−1.22427	−	0.377638i	−0.111760	−	0.0344734i
$121$	−1.21184	+	0.583593i	−0.110168	+	0.0530539i
$122$	−2.89329	+	5.01133i	−0.261946	+	0.453704i
$123$	−2.52972	−	4.38160i	−0.228097	−	0.395076i
$124$	2.13012	+	1.45229i	0.191290	+	0.130420i
$125$	−0.222521	+	0.974928i	−0.0199029	+	0.0872002i
$126$	3.23135	+	0.487048i	0.287872	+	0.0433897i
$127$	10.2218	+	12.8177i	0.907037	+	1.13739i	0.990033	+	0.140838i	$0.0449797\pi$
$127$	10.2218	+	12.8177i	0.907037	+	1.13739i	−0.0829959	+	0.996550i	$0.526449\pi$
$128$	1.00000			0.0883883
$129$	−0.445132	−	8.38953i	−0.0391917	−	0.738657i
$130$	−1.02313			−0.0897340
$131$	0.547965	+	0.687126i	0.0478759	+	0.0600345i	0.805193	−	0.593013i	$-0.202062\pi$
$131$	0.547965	+	0.687126i	0.0478759	+	0.0600345i	−0.757317	+	0.653047i	$0.773490\pi$
$132$	−4.45125	−	0.670918i	−0.387432	−	0.0583959i
$133$	−3.10776	+	13.6160i	−0.269477	+	1.18065i
$134$	−10.1638	−	6.92958i	−0.878021	−	0.598625i
$135$	−2.79207	−	4.83600i	−0.240303	−	0.416217i
$136$	0.0622253	−	0.107777i	0.00533578	−	0.00924184i
$137$	−12.5104	+	6.02471i	−1.06884	+	0.514725i	−0.883732	−	0.467993i	$-0.844977\pi$
$137$	−12.5104	+	6.02471i	−1.06884	+	0.514725i	−0.185106	+	0.982719i	$0.559263\pi$
$138$	9.09970	+	2.80689i	0.774618	+	0.238938i
$139$	−1.58937	−	21.2087i	−0.134809	−	1.79890i	−0.497996	−	0.867179i	$-0.665931\pi$
$139$	−1.58937	−	21.2087i	−0.134809	−	1.79890i	0.363188	−	0.931716i	$-0.381688\pi$
$140$	−0.535252	−	2.34509i	−0.0452370	−	0.198196i
$141$	0.951601	−	2.42464i	0.0801392	−	0.204191i
$142$	0.592883	−	7.91147i	0.0497536	−	0.663916i
$143$	−3.55465	+	0.535778i	−0.297255	+	0.0448040i
$144$	0.995887	+	0.924048i	0.0829906	+	0.0770040i
$145$	1.59317	+	0.767228i	0.132305	+	0.0637148i
$146$	8.63131	−	5.88473i	0.714332	−	0.487024i
$147$	0.568265	+	1.44792i	0.0468697	+	0.119422i
$148$	−0.437242	+	0.134871i	−0.0359411	+	0.0110864i
$149$	−12.8134	+	11.8891i	−1.04971	+	0.973992i	−0.999694	−	0.0247567i	$-0.992119\pi$
$149$	−12.8134	+	11.8891i	−1.04971	+	0.973992i	−0.0500198	+	0.998748i	$0.515928\pi$
$150$	−0.798810	+	1.00168i	−0.0652225	+	0.0817865i
$151$	14.1497	−	17.7432i	1.15149	−	1.44392i	0.275691	−	0.961246i	$-0.411093\pi$
$151$	14.1497	−	17.7432i	1.15149	−	1.44392i	0.875799	−	0.482676i	$-0.160335\pi$
$152$	−4.25622	+	3.94919i	−0.345225	+	0.320322i
$153$	0.161561	−	0.0498349i	0.0130614	−	0.00402892i
$154$	−3.08768	−	7.86727i	−0.248812	−	0.633963i
$155$	2.13012	−	1.45229i	0.171095	−	0.116651i
$156$	−1.18101	−	0.568743i	−0.0945562	−	0.0455359i
$157$	6.18188	+	5.73595i	0.493368	+	0.457778i	0.887187	−	0.461409i	$-0.152656\pi$
$157$	6.18188	+	5.73595i	0.493368	+	0.457778i	−0.393820	+	0.919188i	$0.628847\pi$
$158$	5.92920	−	0.893683i	0.471702	−	0.0710976i
$159$	−0.321707	+	4.29288i	−0.0255130	+	0.340447i
$160$	0.365341	−	0.930874i	0.0288827	−	0.0735920i
$161$	3.97839	+	17.4305i	0.313541	+	1.37371i
$162$	−0.230071	−	3.07009i	−0.0180761	−	0.241209i
$163$	−15.7517	−	4.85875i	−1.23377	−	0.380566i	−0.391776	−	0.920060i	$-0.628139\pi$
$163$	−15.7517	−	4.85875i	−1.23377	−	0.380566i	−0.841989	+	0.539494i	$0.818616\pi$
$164$	3.55793	−	1.71341i	0.277828	−	0.133795i
$165$	−2.25077	+	3.89844i	−0.175222	+	0.303493i
$166$	−1.05331	−	1.82438i	−0.0817525	−	0.141599i
$167$	−10.5178	−	7.17089i	−0.813889	−	0.554900i	0.0833112	−	0.996524i	$-0.473450\pi$
$167$	−10.5178	−	7.17089i	−0.813889	−	0.554900i	−0.897201	+	0.441623i	$0.854403\pi$
$168$	0.685760	−	3.00451i	0.0529075	−	0.231803i
$169$	11.8197	+	1.78153i	0.909208	+	0.137041i
$170$	−0.0775937	−	0.0972994i	−0.00595117	−	0.00746253i
$171$	−7.88796			−0.603207
$172$	6.55588	+	0.142885i	0.499881	+	0.0108949i
$173$	−8.08341			−0.614570			−0.307285	−	0.951618i	$-0.599421\pi$
$173$	−8.08341			−0.614570			−0.307285	+	0.951618i	$0.599421\pi$
$174$	1.41252	+	1.77124i	0.107083	+	0.134278i
$175$	−2.37853	−	0.358506i	−0.179800	−	0.0271005i
$176$	0.781839	−	3.42546i	0.0589333	−	0.258204i
$177$	−1.52535	−	1.03997i	−0.114652	−	0.0781686i
$178$	4.80241	+	8.31802i	0.359956	+	0.623462i
$179$	2.42572	−	4.20147i	0.181307	−	0.314032i	−0.761019	−	0.648730i	$-0.775301\pi$
$179$	2.42572	−	4.20147i	0.181307	−	0.314032i	0.942326	+	0.334697i	$0.108634\pi$
$180$	1.22401	−	0.589453i	0.0912324	−	0.0439352i
$181$	2.63124	+	0.811630i	0.195579	+	0.0603280i	0.390997	−	0.920392i	$-0.372130\pi$
$181$	2.63124	+	0.811630i	0.195579	+	0.0603280i	−0.195418	+	0.980720i	$0.562606\pi$
$182$	−0.183913	−	2.45414i	−0.0136325	−	0.181913i
$183$	1.64971	+	7.22784i	0.121950	+	0.534297i
$184$	−2.71549	+	6.91895i	−0.200188	+	0.510072i
$185$	−0.0341943	+	0.456291i	−0.00251401	+	0.0335472i
$186$	3.26614	−	0.492291i	0.239485	−	0.0360965i
$187$	−0.320537	−	0.297415i	−0.0234400	−	0.0217491i
$188$	1.83169	+	0.882096i	0.133590	+	0.0643334i
$189$	11.0981	−	7.56656i	0.807268	−	0.550386i
$190$	2.12123	+	5.40480i	0.153890	+	0.392106i
$191$	−14.5858	+	4.49912i	−1.05539	+	0.325545i	−0.773430	−	0.633881i	$-0.781461\pi$
$191$	−14.5858	+	4.49912i	−1.05539	+	0.325545i	−0.281960	+	0.959426i	$0.590985\pi$
$192$	0.939180	−	0.871431i	0.0677794	−	0.0628901i
$193$	−12.0609	+	15.1239i	−0.868165	+	1.08864i	0.127143	+	0.991884i	$0.459419\pi$
$193$	−12.0609	+	15.1239i	−0.868165	+	1.08864i	−0.995308	+	0.0967603i	$0.969152\pi$
$194$	−0.984798	+	1.23490i	−0.0707044	+	0.0886605i
$195$	−0.960898	+	0.891583i	−0.0688113	+	0.0638476i
$196$	−1.16012	+	0.357849i	−0.0828657	+	0.0255607i
$197$	5.08662	+	12.9605i	0.362407	+	0.923397i	0.989510	+	0.144461i	$0.0461449\pi$
$197$	5.08662	+	12.9605i	0.362407	+	0.923397i	−0.627104	+	0.778936i	$0.715760\pi$
$198$	3.94391	−	2.68891i	0.280282	−	0.191093i
$199$	22.1791	+	10.6809i	1.57224	+	0.757149i	0.998100	−	0.0616106i	$-0.0196237\pi$
$199$	22.1791	+	10.6809i	1.57224	+	0.757149i	0.574136	+	0.818760i	$0.305338\pi$
$200$	−0.733052	−	0.680173i	−0.0518346	−	0.0480955i
$201$	−15.5843	+	2.34896i	−1.09923	+	0.165683i
$202$	−0.593507	+	7.91980i	−0.0417590	+	0.557235i
$203$	−1.55395	+	3.95940i	−0.109066	+	0.277895i
$204$	−0.0354799	−	0.155447i	−0.00248409	−	0.0108835i
$205$	−0.295110	−	3.93797i	−0.0206114	−	0.275040i
$206$	3.96559	+	1.22322i	0.276296	+	0.0852260i
$207$	−9.09776	+	4.38125i	−0.632338	+	0.304518i
$208$	0.511563	−	0.886052i	0.0354705	−	0.0614367i
$209$	10.2001	+	17.6671i	0.705557	+	1.22206i
$210$	−2.54628	−	1.73603i	−0.175710	−	0.119797i
$211$	1.60996	−	7.05369i	0.110834	−	0.485596i	−0.888794	−	0.458308i	$-0.848456\pi$
$211$	1.60996	−	7.05369i	0.110834	−	0.485596i	0.999628	−	0.0272880i	$-0.00868711\pi$
$212$	−3.32256	−	0.500795i	−0.228194	−	0.0343947i
$213$	−6.33748	−	7.94695i	−0.434237	−	0.544516i
$214$	−14.1554			−0.967642
$215$	2.52814	−	6.05050i	0.172418	−	0.412640i
$216$	5.58413			0.379952
$217$	3.86647	+	4.84840i	0.262473	+	0.329131i
$218$	13.7788	+	2.07683i	0.933221	+	0.140660i
$219$	2.97821	−	13.0484i	0.201249	−	0.881730i
$220$	−2.90303	−	1.97925i	−0.195722	−	0.133441i
$221$	−0.0636643	−	0.110270i	−0.00428252	−	0.00741755i
$222$	−0.293118	+	0.507695i	−0.0196728	+	0.0340742i
$223$	−10.1999	+	4.91204i	−0.683039	+	0.328934i	−0.743024	−	0.669265i	$-0.766609\pi$
$223$	−10.1999	+	4.91204i	−0.683039	+	0.328934i	0.0599848	+	0.998199i	$0.480895\pi$
$224$	2.29853	+	0.709004i	0.153577	+	0.0473723i
$225$	−0.101525	−	1.35475i	−0.00676830	−	0.0903167i
$226$	−1.58981	−	6.96539i	−0.105752	−	0.463331i
$227$	−8.59128	+	21.8902i	−0.570223	+	1.45290i	0.296948	+	0.954894i	$0.404031\pi$
$227$	−8.59128	+	21.8902i	−0.570223	+	1.45290i	−0.867171	+	0.498011i	$0.834064\pi$
$228$	−0.555902	+	7.41800i	−0.0368155	+	0.491269i
$229$	−19.9239	+	3.00305i	−1.31661	+	0.198447i	−0.769518	−	0.638625i	$-0.779503\pi$
$229$	−19.9239	+	3.00305i	−1.31661	+	0.198447i	−0.547092	+	0.837072i	$0.684265\pi$
$230$	5.44859	+	5.05555i	0.359269	+	0.333353i
$231$	−9.75567	−	4.69808i	−0.641876	−	0.309111i
$232$	−1.46102	+	0.996108i	−0.0959208	+	0.0653977i
$233$	1.08605	+	2.76722i	0.0711496	+	0.181286i	0.962025	−	0.272962i	$-0.0880032\pi$
$233$	1.08605	+	2.76722i	0.0711496	+	0.181286i	−0.890875	+	0.454248i	$0.849908\pi$
$234$	1.32821	−	0.409700i	0.0868280	−	0.0267829i
$235$	1.49031	−	1.38281i	0.0972172	−	0.0902044i
$236$	0.898420	−	1.12658i	0.0584822	−	0.0733343i
$237$	4.78980	−	6.00622i	0.311131	−	0.390146i
$238$	0.219442	−	0.203612i	0.0142243	−	0.0131982i
$239$	−12.0806	+	3.72637i	−0.781430	+	0.241039i	−0.659705	−	0.751525i	$-0.729319\pi$
$239$	−12.0806	+	3.72637i	−0.781430	+	0.241039i	−0.121725	+	0.992564i	$0.538843\pi$
$240$	−0.468072	−	1.19263i	−0.0302139	−	0.0769838i
$241$	−15.9638	+	10.8839i	−1.02832	+	0.701096i	−0.955119	−	0.296221i	$-0.904274\pi$
$241$	−15.9638	+	10.8839i	−1.02832	+	0.701096i	−0.0732000	+	0.997317i	$0.523321\pi$
$242$	−1.21184	−	0.583593i	−0.0779003	−	0.0375148i
$243$	9.38893	+	8.71166i	0.602300	+	0.558853i
$244$	−5.72195	+	0.862445i	−0.366310	+	0.0552124i
$245$	−0.0907265	+	1.21066i	−0.00579631	+	0.0773463i
$246$	1.84842	−	4.70970i	0.117851	−	0.300279i
$247$	1.32187	+	5.79149i	0.0841086	+	0.368504i
$248$	0.192661	+	2.57088i	0.0122340	+	0.163251i
$249$	−2.57907	−	0.795537i	−0.163442	−	0.0504151i
$250$	−0.900969	+	0.433884i	−0.0569823	+	0.0274412i
$251$	−6.61639	+	11.4599i	−0.417623	+	0.723344i	−0.995700	−	0.0926385i	$-0.970470\pi$
$251$	−6.61639	+	11.4599i	−0.417623	+	0.723344i	0.578077	+	0.815982i	$0.303803\pi$
$252$	1.63393	+	2.83004i	0.102928	+	0.178276i
$253$	21.5775	+	14.7113i	1.35657	+	0.924891i
$254$	−3.64811	+	15.9834i	−0.228903	+	1.00289i
$255$	−0.157664	−	0.0237641i	−0.00987331	−	0.00148816i
$256$	0.623490	+	0.781831i	0.0389681	+	0.0488645i
$257$	−15.4923			−0.966382			−0.483191	−	0.875515i	$-0.660522\pi$
$257$	−15.4923			−0.966382			−0.483191	+	0.875515i	$0.660522\pi$
$258$	6.28166	−	5.57881i	0.391079	−	0.347321i
$259$	−1.10064			−0.0683904
$260$	−0.637908	−	0.799911i	−0.0395614	−	0.0496084i
$261$	−2.37547	−	0.358044i	−0.147038	−	0.0221624i
$262$	−0.195566	+	0.856832i	−0.0120821	+	0.0529353i
$263$	−8.39798	−	5.72565i	−0.517842	−	0.353058i	0.276025	−	0.961150i	$-0.410983\pi$
$263$	−8.39798	−	5.72565i	−0.517842	−	0.353058i	−0.793867	+	0.608092i	$0.791935\pi$
$264$	−2.25077	−	3.89844i	−0.138525	−	0.239932i
$265$	−1.68004	+	2.90992i	−0.103204	+	0.178755i
$266$	−12.5831	+	6.05968i	−0.771517	+	0.371543i
$267$	11.7589	+	3.62714i	0.719633	+	0.221978i
$268$	−0.919279	−	12.2669i	−0.0561539	−	0.749322i
$269$	4.17035	+	18.2715i	0.254271	+	1.11403i	0.927271	+	0.374391i	$0.122148\pi$
$269$	4.17035	+	18.2715i	0.254271	+	1.11403i	−0.673000	+	0.739642i	$0.734995\pi$
$270$	2.04011	−	5.19812i	0.124157	−	0.316348i
$271$	2.32087	−	30.9699i	0.140983	−	1.88129i	−0.260574	−	0.965454i	$-0.583912\pi$
$271$	2.32087	−	30.9699i	0.140983	−	1.88129i	0.401557	−	0.915834i	$-0.368469\pi$
$272$	0.123061	−	0.0185484i	0.00746165	−	0.00112466i
$273$	−2.31134	−	2.14461i	−0.139889	−	0.129798i
$274$	−12.5104	−	6.02471i	−0.755783	−	0.363966i
$275$	−2.90303	+	1.97925i	−0.175059	+	0.119354i
$276$	3.47906	+	8.86450i	0.209415	+	0.533580i
$277$	20.2259	−	6.23885i	1.21525	−	0.374856i	0.380138	−	0.924930i	$-0.375877\pi$
$277$	20.2259	−	6.23885i	1.21525	−	0.374856i	0.835116	+	0.550074i	$0.185400\pi$
$278$	15.5906	−	14.4660i	0.935065	−	0.867613i
$279$	−2.18375	+	2.73834i	−0.130738	+	0.163940i
$280$	1.49974	−	1.88062i	0.0896267	−	0.112388i
$281$	10.9523	−	10.1622i	0.653357	−	0.606227i	−0.282220	−	0.959350i	$-0.591071\pi$
$281$	10.9523	−	10.1622i	0.653357	−	0.606227i	0.935577	+	0.353123i	$0.114880\pi$
$282$	2.48897	−	0.767746i	0.148216	−	0.0457186i
$283$	−2.58623	−	6.58961i	−0.153735	−	0.391711i	0.833169	−	0.553019i	$-0.186524\pi$
$283$	−2.58623	−	6.58961i	−0.153735	−	0.391711i	−0.986904	+	0.161307i	$0.948429\pi$
$284$	6.55509	−	4.46919i	0.388973	−	0.265198i
$285$	6.70213	+	3.22758i	0.397000	+	0.191185i
$286$	−2.63518	−	2.44509i	−0.155821	−	0.144581i
$287$	9.39285	−	1.41574i	0.554442	−	0.0835687i
$288$	−0.101525	+	1.35475i	−0.00598239	+	0.0798294i
$289$	−6.20514	+	15.8104i	−0.365008	+	0.930026i
$290$	0.393480	+	1.72395i	0.0231059	+	0.101234i
$291$	0.151226	+	2.01797i	0.00886504	+	0.118296i
$292$	9.98240	+	3.07916i	0.584176	+	0.180194i
$293$	12.5949	−	6.06539i	0.735803	−	0.354344i	−0.0281604	−	0.999603i	$-0.508965\pi$
$293$	12.5949	−	6.06539i	0.735803	−	0.354344i	0.763964	+	0.645259i	$0.223251\pi$
$294$	−0.777719	+	1.34705i	−0.0453575	+	0.0785615i
$295$	−0.720477	−	1.24790i	−0.0419478	−	0.0726557i
$296$	−0.378063	−	0.257759i	−0.0219744	−	0.0149819i
$297$	4.36589	−	19.1282i	0.253335	−	1.10993i
$298$	−17.2843	−	2.60518i	−1.00125	−	0.150914i
$299$	4.74141	+	5.94554i	0.274203	+	0.343839i
$300$	−1.28119			−0.0739696
$301$	14.9676	+	4.97657i	0.862719	+	0.286845i
$302$	22.6944			1.30592
$303$	6.34415	+	7.95531i	0.364462	+	0.457021i
$304$	−5.74131	−	0.865364i	−0.329287	−	0.0496320i
$305$	−1.28764	+	5.64150i	−0.0737298	+	0.323031i
$306$	0.139694	+	0.0952418i	0.00798578	+	0.00544461i
$307$	−3.07880	−	5.33264i	−0.175716	−	0.304350i	0.764693	−	0.644395i	$-0.222891\pi$
$307$	−3.07880	−	5.33264i	−0.175716	−	0.304350i	−0.940409	+	0.340046i	$0.889557\pi$
$308$	4.22575	−	7.31921i	0.240784	−	0.417051i
$309$	4.79036	−	2.30692i	0.272514	−	0.131236i
$310$	2.46355	+	0.759906i	0.139920	+	0.0431597i
$311$	0.191358	+	2.55349i	0.0108509	+	0.144795i	0.999998	−	0.00213535i	$-0.000679705\pi$
$311$	0.191358	+	2.55349i	0.0108509	+	0.144795i	−0.989147	+	0.146930i	$0.953061\pi$
$312$	−0.291685	−	1.27795i	−0.0165134	−	0.0723499i
$313$	−5.65227	+	14.4018i	−0.319485	+	0.814036i	0.677433	+	0.735585i	$0.263093\pi$
$313$	−5.65227	+	14.4018i	−0.319485	+	0.814036i	−0.996918	+	0.0784507i	$0.975003\pi$
$314$	−0.630204	+	8.40949i	−0.0355645	+	0.474575i
$315$	3.23135	−	0.487048i	0.182066	−	0.0274421i
$316$	4.39550	+	4.07843i	0.247266	+	0.229430i
$317$	−14.8485	−	7.15064i	−0.833973	−	0.401620i	−0.0323692	−	0.999476i	$-0.510305\pi$
$317$	−14.8485	−	7.15064i	−0.833973	−	0.401620i	−0.801604	+	0.597856i	$0.796020\pi$
$318$	−3.55689	+	2.42504i	−0.199460	+	0.135990i
$319$	2.26984	+	5.78347i	0.127087	+	0.323812i
$320$	0.955573	−	0.294755i	0.0534181	−	0.0164773i
$321$	−13.2944	+	12.3354i	−0.742024	+	0.688497i
$322$	−11.1472	+	13.9781i	−0.621209	+	0.778972i
$323$	−0.450522	+	0.564936i	−0.0250677	+	0.0314339i
$324$	2.25684	−	2.09404i	0.125380	−	0.116336i
$325$	−0.977671	+	0.301571i	−0.0542314	+	0.0167282i
$326$	−6.02228	−	15.3445i	−0.333543	−	0.849855i
$327$	14.7506	−	10.0568i	0.815711	−	0.556143i
$328$	3.55793	+	1.71341i	0.196454	+	0.0946073i
$329$	3.58479	+	3.32620i	0.197636	+	0.183379i
$330$	−4.45125	+	0.670918i	−0.245033	+	0.0369328i
$331$	2.41507	−	32.2268i	0.132744	−	1.77135i	−0.391884	−	0.920015i	$-0.628176\pi$
$331$	2.41507	−	32.2268i	0.132744	−	1.77135i	0.524628	−	0.851332i	$-0.324205\pi$
$332$	0.769633	−	1.96099i	0.0422391	−	0.107623i
$333$	−0.138326	−	0.606047i	−0.00758023	−	0.0332112i
$334$	−0.951292	−	12.6941i	−0.0520524	−	0.694590i
$335$	−11.7548	−	3.62588i	−0.642234	−	0.198103i
$336$	2.77658	−	1.33713i	0.151475	−	0.0729465i
$337$	11.5216	−	19.9560i	0.627622	−	1.08707i	−0.360406	−	0.932796i	$-0.617362\pi$
$337$	11.5216	−	19.9560i	0.627622	−	1.08707i	0.988028	−	0.154277i	$-0.0493049\pi$
$338$	5.97661	+	10.3518i	0.325085	+	0.563063i
$339$	−7.56297	−	5.15635i	−0.410764	−	0.280054i
$340$	0.0276929	−	0.121330i	0.00150186	−	0.00658006i
$341$	8.95708	+	1.35006i	0.485053	+	0.0731100i
$342$	−4.91806	−	6.16705i	−0.265938	−	0.333476i
$343$	−19.7581			−1.06684
$344$	3.97581	+	5.21468i	0.214361	+	0.281157i
$345$	9.52277			0.512689
$346$	−5.03992	−	6.31986i	−0.270948	−	0.339758i
$347$	4.23453	+	0.638252i	0.227321	+	0.0342632i	0.261715	−	0.965145i	$-0.415712\pi$
$347$	4.23453	+	0.638252i	0.227321	+	0.0342632i	−0.0343937	+	0.999408i	$0.510950\pi$
$348$	−0.504122	+	2.20870i	−0.0270238	+	0.118399i
$349$	3.03555	+	2.06960i	0.162489	+	0.110783i	0.641835	−	0.766843i	$-0.278174\pi$
$349$	3.03555	+	2.06960i	0.162489	+	0.110783i	−0.479345	+	0.877626i	$0.659126\pi$
$350$	−1.20270	−	2.08314i	−0.0642870	−	0.111348i
$351$	2.85663	−	4.94784i	0.152476	−	0.264096i
$352$	3.16560	−	1.52447i	0.168727	−	0.0812547i
$353$	−17.6123	−	5.43269i	−0.937411	−	0.289153i	−0.211843	−	0.977304i	$-0.567947\pi$
$353$	−17.6123	−	5.43269i	−0.937411	−	0.289153i	−0.725568	+	0.688151i	$0.758423\pi$
$354$	−0.137962	−	1.84097i	−0.00733260	−	0.0978467i
$355$	−1.76540	−	7.73474i	−0.0936980	−	0.410518i
$356$	−3.50904	+	8.94088i	−0.185978	+	0.473865i
$357$	0.0286612	−	0.382457i	0.00151691	−	0.0202417i
$358$	4.79725	−	0.723069i	0.253543	−	0.0382154i
$359$	−6.06221	−	5.62491i	−0.319951	−	0.296871i	0.503803	−	0.863819i	$-0.331934\pi$
$359$	−6.06221	−	5.62491i	−0.319951	−	0.296871i	−0.823754	+	0.566947i	$0.808124\pi$
$360$	1.22401	+	0.589453i	0.0645110	+	0.0310669i
$361$	12.1552	−	8.28730i	0.639749	−	0.436174i
$362$	1.00599	+	2.56323i	0.0528738	+	0.134720i
$363$	−1.64670	+	0.507940i	−0.0864294	+	0.0266599i
$364$	1.80406	−	1.67392i	0.0945583	−	0.0877373i
$365$	6.51329	−	8.16741i	0.340921	−	0.427502i
$366$	−4.62238	+	5.79628i	−0.241615	+	0.302976i
$367$	16.2784	−	15.1041i	0.849726	−	0.788430i	−0.129420	−	0.991590i	$-0.541312\pi$
$367$	16.2784	−	15.1041i	0.849726	−	0.788430i	0.979146	+	0.203160i	$0.0651211\pi$
$368$	−7.10253	+	2.19084i	−0.370245	+	0.114205i
$369$	1.96003	+	4.99407i	0.102035	+	0.259981i
$370$	−0.378063	+	0.257759i	−0.0196545	+	0.0134002i
$371$	−7.28195	−	3.50680i	−0.378060	−	0.182064i
$372$	2.42129	+	2.24663i	0.125538	+	0.116482i
$373$	7.43931	−	1.12130i	0.385193	−	0.0580585i	0.0464086	−	0.998923i	$-0.485222\pi$
$373$	7.43931	−	1.12130i	0.385193	−	0.0580585i	0.338784	+	0.940864i	$0.389984\pi$
$374$	0.0326768	−	0.436041i	0.00168968	−	0.0225471i
$375$	−0.468072	+	1.19263i	−0.0241711	+	0.0615870i
$376$	0.452390	+	1.98205i	0.0233302	+	0.102216i
$377$	0.135200	+	1.80411i	0.00696314	+	0.0929166i
$378$	12.8353	+	3.95917i	0.660178	+	0.203638i
$379$	2.69289	−	1.29683i	0.138324	−	0.0666135i	−0.363441	−	0.931617i	$-0.618398\pi$
$379$	2.69289	−	1.29683i	0.138324	−	0.0666135i	0.501766	+	0.865004i	$0.332684\pi$
$380$	−2.90308	+	5.02828i	−0.148925	+	0.257946i
$381$	10.5022	+	18.1904i	0.538045	+	0.931922i
$382$	−12.6116	−	8.59847i	−0.645268	−	0.439936i
$383$	7.64202	−	33.4819i	0.390489	−	1.71084i	−0.272449	−	0.962170i	$-0.587834\pi$
$383$	7.64202	−	33.4819i	0.390489	−	1.71084i	0.662938	−	0.748674i	$-0.269309\pi$
$384$	1.26688	+	0.190952i	0.0646503	+	0.00974446i
$385$	−5.26942	−	6.60764i	−0.268555	−	0.336757i
$386$	−19.3442			−0.984596
$387$	−0.859156	+	8.86708i	−0.0436734	+	0.450739i
$388$	−1.57949			−0.0801866
$389$	5.27460	+	6.61414i	0.267433	+	0.335350i	0.897356	−	0.441307i	$-0.145485\pi$
$389$	5.27460	+	6.61414i	0.267433	+	0.335350i	−0.629923	+	0.776657i	$0.716914\pi$
$390$	−1.29618	−	0.195367i	−0.0656345	−	0.00989281i
$391$	−0.205834	+	0.901818i	−0.0104095	+	0.0456069i
$392$	−1.00310	−	0.683902i	−0.0506642	−	0.0345423i
$393$	0.562999	+	0.975142i	0.0283995	+	0.0491894i
$394$	−6.96147	+	12.0576i	−0.350714	+	0.607454i
$395$	5.40236	−	2.60164i	0.271822	−	0.130903i
$396$	4.56127	+	1.40696i	0.229212	+	0.0707026i
$397$	−1.89414	−	25.2755i	−0.0950640	−	1.26854i	−0.817023	−	0.576605i	$-0.804377\pi$
$397$	−1.89414	−	25.2755i	−0.0950640	−	1.26854i	0.721959	−	0.691936i	$-0.243242\pi$
$398$	5.47779	+	23.9998i	0.274577	+	1.20300i
$399$	−6.53715	+	16.6564i	−0.327267	+	0.833863i
$400$	0.0747301	−	0.997204i	0.00373650	−	0.0498602i
$401$	−6.82835	+	1.02921i	−0.340992	+	0.0513962i	−0.317306	−	0.948323i	$-0.602778\pi$
$401$	−6.82835	+	1.02921i	−0.340992	+	0.0513962i	−0.0236858	+	0.999719i	$0.507540\pi$
$402$	−11.5532	−	10.7198i	−0.576219	−	0.534653i
$403$	2.37649	+	1.14446i	0.118382	+	0.0570096i
$404$	−6.56199	+	4.47389i	−0.326471	+	0.222584i
$405$	−1.12477	−	2.86588i	−0.0558904	−	0.142407i
$406$	−4.06445	+	1.25372i	−0.201715	+	0.0622210i
$407$	−1.17853	+	1.09351i	−0.0584174	+	0.0542034i
$408$	0.0994124	−	0.124659i	0.00492165	−	0.00617155i
$409$	−8.15782	+	10.2296i	−0.403378	+	0.505820i	−0.941484	−	0.337057i	$-0.890569\pi$
$409$	−8.15782	+	10.2296i	−0.403378	+	0.505820i	0.538106	+	0.842877i	$0.319140\pi$
$410$	2.89483	−	2.68601i	0.142965	−	0.132653i
$411$	−16.9997	+	5.24370i	−0.838531	+	0.258653i
$412$	1.51615	+	3.86309i	0.0746955	+	0.190321i
$413$	2.86380	−	1.95251i	0.140918	−	0.0960765i
$414$	−9.09776	−	4.38125i	−0.447131	−	0.215327i
$415$	−1.54426	−	1.43286i	−0.0758046	−	0.0703364i
$416$	1.01170	−	0.152489i	0.0496026	−	0.00747638i
$417$	2.03629	−	27.1723i	0.0997174	−	1.33064i
$418$	−7.45305	+	18.9901i	−0.364541	+	0.928834i
$419$	4.14311	+	18.1521i	0.202404	+	0.886790i	0.969468	+	0.245219i	$0.0788598\pi$
$419$	4.14311	+	18.1521i	0.202404	+	0.886790i	−0.767064	+	0.641571i	$0.778283\pi$
$420$	−0.230301	−	3.07316i	−0.0112376	−	0.149955i
$421$	13.5836	+	4.18998i	0.662023	+	0.204207i	0.607518	−	0.794306i	$-0.292165\pi$
$421$	13.5836	+	4.18998i	0.662023	+	0.204207i	0.0545059	+	0.998513i	$0.482642\pi$
$422$	6.51859	−	3.13919i	0.317320	−	0.152813i
$423$	−1.38098	+	2.39193i	−0.0671456	+	0.116300i
$424$	−1.68004	−	2.90992i	−0.0815901	−	0.141318i
$425$	−0.102826	−	0.0701055i	−0.00498779	−	0.00340062i
$426$	2.26182	−	9.90968i	0.109586	−	0.480126i
$427$	−13.7636	−	2.07452i	−0.666066	−	0.100393i
$428$	−8.82574	−	11.0671i	−0.426608	−	0.534950i
$429$	−4.60563			−0.222362
$430$	6.30674	−	1.79584i	0.304138	−	0.0866032i
$431$	33.0338			1.59118			0.795590	−	0.605835i	$-0.207161\pi$
$431$	33.0338			1.59118			0.795590	+	0.605835i	$0.207161\pi$
$432$	3.48165	+	4.36585i	0.167511	+	0.210052i
$433$	−25.9786	−	3.91564i	−1.24845	−	0.188174i	−0.508634	−	0.860983i	$-0.669849\pi$
$433$	−25.9786	−	3.91564i	−1.24845	−	0.188174i	−0.739816	+	0.672809i	$0.765087\pi$
$434$	−1.37993	+	6.04586i	−0.0662386	+	0.290210i
$435$	1.87185	+	1.27620i	0.0897483	+	0.0611893i
$436$	6.96724	+	12.0676i	0.333670	+	0.577934i
$437$	21.5779	−	37.3740i	1.03221	−	1.78784i
$438$	12.0585	−	5.80709i	0.576180	−	0.277473i
$439$	12.3678	+	3.81496i	0.590282	+	0.182078i	0.575485	−	0.817813i	$-0.304813\pi$
$439$	12.3678	+	3.81496i	0.590282	+	0.182078i	0.0147974	+	0.999891i	$0.495290\pi$
$440$	−0.262568	−	3.50373i	−0.0125174	−	0.167034i
$441$	−0.367016	−	1.60800i	−0.0174770	−	0.0765716i
$442$	0.0465184	−	0.118527i	0.00221265	−	0.00563775i
$443$	2.44208	−	32.5873i	0.116027	−	1.54827i	−0.570580	−	0.821242i	$-0.693282\pi$
$443$	2.44208	−	32.5873i	0.116027	−	1.54827i	0.686607	−	0.727029i	$-0.259099\pi$
$444$	−0.579688	+	0.0873739i	−0.0275108	+	0.00414658i
$445$	7.04083	+	6.53294i	0.333767	+	0.309691i
$446$	−10.1999	−	4.91204i	−0.482981	−	0.232592i
$447$	−18.5033	+	12.6153i	−0.875175	+	0.596684i
$448$	0.878791	+	2.23912i	0.0415190	+	0.105789i
$449$	−18.0671	+	5.57296i	−0.852640	+	0.263004i	−0.690115	−	0.723700i	$-0.742440\pi$
$449$	−18.0671	+	5.57296i	−0.852640	+	0.263004i	−0.162525	+	0.986704i	$0.551964\pi$
$450$	0.995887	−	0.924048i	0.0469466	−	0.0435601i
$451$	8.65095	−	10.8480i	0.407357	−	0.510810i
$452$	4.45454	−	5.58581i	0.209524	−	0.262734i
$453$	21.3141	−	19.7766i	1.00143	−	0.929187i
$454$	−22.4710	+	6.93139i	−1.05462	+	0.325306i
$455$	−0.899113	−	2.29090i	−0.0421511	−	0.107399i
$456$	−6.14623	+	4.19043i	−0.287823	+	0.196235i
$457$	−29.1662	−	14.0457i	−1.36434	−	0.657029i	−0.398736	−	0.917066i	$-0.630551\pi$
$457$	−29.1662	−	14.0457i	−1.36434	−	0.657029i	−0.965599	+	0.260036i	$0.916265\pi$
$458$	−14.7702	−	13.7048i	−0.690168	−	0.640383i
$459$	0.687187	−	0.103577i	0.0320751	−	0.00483455i
$460$	−0.555450	+	7.41196i	−0.0258980	+	0.345585i
$461$	−2.23912	+	5.70517i	−0.104286	+	0.265716i	−0.973487	−	0.228743i	$-0.926539\pi$
$461$	−2.23912	+	5.70517i	−0.104286	+	0.265716i	0.869201	+	0.494459i	$0.164634\pi$
$462$	−2.40945	−	10.5565i	−0.112098	−	0.491133i
$463$	0.186019	+	2.48225i	0.00864504	+	0.115360i	0.999857	−	0.0169250i	$-0.00538764\pi$
$463$	0.186019	+	2.48225i	0.00864504	+	0.115360i	−0.991212	+	0.132285i	$0.957769\pi$
$464$	−1.68972	−	0.521210i	−0.0784433	−	0.0241966i
$465$	2.97592	−	1.43313i	0.138005	−	0.0664598i
$466$	−1.48635	+	2.57444i	−0.0688540	+	0.119259i
$467$	10.1675	+	17.6107i	0.470496	+	0.814924i	0.999431	−	0.0337391i	$-0.0107415\pi$
$467$	10.1675	+	17.6107i	0.470496	+	0.814924i	−0.528934	+	0.848663i	$0.677408\pi$
$468$	1.14844	+	0.782996i	0.0530868	+	0.0361940i
$469$	6.58430	−	28.8477i	0.304035	−	1.33206i
$470$	2.01032	+	0.303006i	0.0927290	+	0.0139766i
$471$	6.73642	+	8.44720i	0.310398	+	0.389227i
$472$	1.44095			0.0663253
$473$	20.9711	−	9.54195i	0.964253	−	0.438739i
$474$	7.68224			0.352857
$475$	3.62008	+	4.53944i	0.166101	+	0.208284i
$476$	0.296010	+	0.0446163i	0.0135676	+	0.00204499i
$477$	1.01577	−	4.45039i	0.0465091	−	0.203770i
$478$	−10.4455	−	7.12164i	−0.477768	−	0.325736i
$479$	−0.638074	−	1.10518i	−0.0291543	−	0.0504968i	0.851080	−	0.525036i	$-0.175948\pi$
$479$	−0.638074	−	1.10518i	−0.0291543	−	0.0504968i	−0.880234	+	0.474539i	$0.842615\pi$
$480$	0.640596	−	1.10954i	0.0292391	−	0.0506435i
$481$	−0.421790	+	0.203124i	−0.0192320	+	0.00926164i
$482$	−18.4627	−	5.69498i	−0.840952	−	0.259399i
$483$	1.71177	+	22.8420i	0.0778883	+	1.03935i
$484$	−0.299301	−	1.31132i	−0.0136046	−	0.0596056i
$485$	−0.577054	+	1.47031i	−0.0262027	+	0.0667633i
$486$	−0.957144	+	12.7722i	−0.0434169	+	0.579358i
$487$	17.4813	−	2.63489i	0.792155	−	0.119398i	0.259514	−	0.965739i	$-0.416438\pi$
$487$	17.4813	−	2.63489i	0.792155	−	0.119398i	0.532641	+	0.846341i	$0.321200\pi$
$488$	−4.24186	−	3.93587i	−0.192020	−	0.178169i
$489$	−19.0277	−	9.16326i	−0.860463	−	0.414377i
$490$	−1.00310	+	0.683902i	−0.0453155	+	0.0308956i
$491$	−3.08964	−	7.87227i	−0.139433	−	0.355271i	0.844051	−	0.536263i	$-0.180164\pi$
$491$	−3.08964	−	7.87227i	−0.139433	−	0.355271i	−0.983485	+	0.180992i	$0.942069\pi$
$492$	4.83466	−	1.49129i	0.217963	−	0.0672328i
$493$	−0.161318	+	0.149681i	−0.00726540	+	0.00674131i
$494$	−3.70380	+	4.64442i	−0.166642	+	0.208962i
$495$	2.97612	−	3.73194i	0.133767	−	0.167738i
$496$	−1.88987	+	1.75355i	−0.0848579	+	0.0787366i
$497$	18.2358	−	5.62499i	0.817986	−	0.252315i
$498$	−0.986047	−	2.51241i	−0.0441858	−	0.112584i
$499$	−6.62900	+	4.51958i	−0.296755	+	0.202324i	−0.702540	−	0.711645i	$-0.747951\pi$
$499$	−6.62900	+	4.51958i	−0.296755	+	0.202324i	0.405785	+	0.913969i	$0.366998\pi$
$500$	−0.900969	−	0.433884i	−0.0402926	−	0.0194039i
$501$	−11.9555	−	11.0931i	−0.534131	−	0.495601i
$502$	−13.0850	+	1.97224i	−0.584011	+	0.0880255i
$503$	−0.717745	+	9.57764i	−0.0320027	+	0.427046i	0.958074	+	0.286520i	$0.0924984\pi$
$503$	−0.717745	+	9.57764i	−0.0320027	+	0.427046i	−0.990077	+	0.140526i	$0.955121\pi$
$504$	−1.19388	+	3.04196i	−0.0531797	+	0.135500i
$505$	1.76726	+	7.74288i	0.0786422	+	0.344554i
$506$	1.95160	+	26.0423i	0.0867593	+	1.15772i
$507$	14.6340	+	4.51398i	0.649918	+	0.200473i
$508$	−14.7709	+	7.11329i	−0.655353	+	0.315601i
$509$	−1.79935	+	3.11656i	−0.0797546	+	0.138139i	−0.903144	−	0.429338i	$-0.858747\pi$
$509$	−1.79935	+	3.11656i	−0.0797546	+	0.138139i	0.823389	+	0.567477i	$0.192080\pi$
$510$	−0.0797225	−	0.138083i	−0.00353017	−	0.00611444i
$511$	20.7617	+	14.1551i	0.918446	+	0.626186i
$512$	−0.222521	+	0.974928i	−0.00983413	+	0.0430861i
$513$	−32.0603	−	4.83231i	−1.41550	−	0.213352i
$514$	−9.65928	−	12.1124i	−0.426053	−	0.534253i
$515$	4.14996			0.182869
$516$	8.27824	+	1.43287i	0.364429	+	0.0630788i
$517$	7.14313			0.314155
$518$	−0.686238	−	0.860515i	−0.0301516	−	0.0378089i
$519$	−10.2407	−	1.54354i	−0.449518	−	0.0677539i
$520$	0.227667	−	0.997473i	0.00998385	−	0.0437421i
$521$	−4.94220	−	3.36953i	−0.216522	−	0.147622i	0.450203	−	0.892926i	$-0.351352\pi$
$521$	−4.94220	−	3.36953i	−0.216522	−	0.147622i	−0.666724	+	0.745304i	$0.732304\pi$
$522$	−1.20115	−	2.08045i	−0.0525728	−	0.0910588i
$523$	−5.91384	+	10.2431i	−0.258594	+	0.447898i	−0.965866	−	0.259044i	$-0.916593\pi$
$523$	−5.91384	+	10.2431i	−0.258594	+	0.447898i	0.707271	+	0.706942i	$0.249926\pi$
$524$	−0.791832	+	0.381326i	−0.0345914	+	0.0166583i
$525$	−2.94486	−	0.908369i	−0.128524	−	0.0396445i
$526$	−0.759565	−	10.1357i	−0.0331186	−	0.441937i
$527$	0.0713947	+	0.312801i	0.00311000	+	0.0136258i
$528$	1.64459	−	4.19036i	0.0715718	−	0.182362i
$529$	2.40973	−	32.1556i	0.104771	−	1.39807i
$530$	−3.32256	+	0.500795i	−0.144323	+	0.0217531i
$531$	1.43503	+	1.33151i	0.0622749	+	0.0577826i
$532$	−12.5831	−	6.05968i	−0.545545	−	0.262720i
$533$	3.33828	−	2.27600i	0.144597	−	0.0985845i
$534$	4.49574	+	11.4550i	0.194550	+	0.495705i
$535$	−13.5265	+	4.17237i	−0.584802	+	0.180387i
$536$	9.01751	−	8.36703i	0.389497	−	0.361400i
$537$	3.87537	−	4.85957i	0.167235	−	0.209706i
$538$	−11.6851	+	14.6526i	−0.503779	+	0.631719i
$539$	−3.12694	+	2.90138i	−0.134687	+	0.124971i
$540$	5.33605	−	1.64595i	0.229627	−	0.0708305i
$541$	10.3910	+	26.4759i	0.446746	+	1.13829i	0.959987	+	0.280045i	$0.0903495\pi$
$541$	10.3910	+	26.4759i	0.446746	+	1.13829i	−0.513241	+	0.858245i	$0.671555\pi$
$542$	25.6603	−	17.4949i	1.10220	−	0.751470i
$543$	3.17849	+	1.53068i	0.136402	+	0.0656877i
$544$	0.0912288	+	0.0846479i	0.00391140	+	0.00362925i
$545$	13.7788	−	2.07683i	0.590221	−	0.0889615i
$546$	0.235627	−	3.14423i	0.0100839	−	0.134560i
$547$	8.11222	−	20.6696i	0.346853	−	0.883768i	−0.645881	−	0.763438i	$-0.723510\pi$
$547$	8.11222	−	20.6696i	0.346853	−	0.883768i	0.992734	−	0.120330i	$-0.0383951\pi$
$548$	−3.08982	−	13.5374i	−0.131991	−	0.578289i
$549$	−0.587480	−	7.83937i	−0.0250730	−	0.334576i
$550$	−3.35745	−	1.03564i	−0.143162	−	0.0441597i
$551$	9.25018	−	4.45465i	0.394071	−	0.189775i
$552$	−4.76138	+	8.24696i	−0.202658	+	0.351014i
$553$	7.21159	+	12.4908i	0.306668	+	0.531165i
$554$	17.4883	+	11.9234i	0.743009	+	0.506575i
$555$	−0.130450	+	0.571537i	−0.00553728	+	0.0242604i
$556$	21.0306	+	3.16985i	0.891895	+	0.134432i
$557$	−24.1525	−	30.2863i	−1.02338	−	1.28327i	−0.958413	−	0.285384i	$-0.907879\pi$
$557$	−24.1525	−	30.2863i	−1.02338	−	1.28327i	−0.0649621	−	0.997888i	$-0.520693\pi$
$558$	−3.50246			−0.148271
$559$	6.65436	−	0.855143i	0.281449	−	0.0361687i
$560$	2.40540			0.101647
$561$	−0.349290	−	0.437996i	−0.0147471	−	0.0184922i
$562$	14.7738	+	2.22679i	0.623194	+	0.0939313i
$563$	−8.72039	+	38.2065i	−0.367521	+	1.61021i	0.366047	+	0.930596i	$0.380711\pi$
$563$	−8.72039	+	38.2065i	−0.367521	+	1.61021i	−0.733567	+	0.679617i	$0.762146\pi$
$564$	2.15210	+	1.46727i	0.0906196	+	0.0617834i
$565$	−3.57226	−	6.18734i	−0.150286	−	0.260303i
$566$	3.53947	−	6.13055i	0.148775	−	0.257686i
$567$	6.67212	−	3.21312i	0.280203	−	0.134938i
$568$	7.58119	+	2.33849i	0.318100	+	0.0981207i
$569$	−1.36982	−	18.2790i	−0.0574258	−	0.766294i	−0.949372	−	0.314153i	$-0.898279\pi$
$569$	−1.36982	−	18.2790i	−0.0574258	−	0.766294i	0.891947	−	0.452141i	$-0.149340\pi$
$570$	1.65529	+	7.25230i	0.0693324	+	0.303765i
$571$	4.58404	−	11.6800i	0.191836	−	0.488791i	−0.802301	−	0.596920i	$-0.796391\pi$
$571$	4.58404	−	11.6800i	0.191836	−	0.488791i	0.994137	+	0.108130i	$0.0344861\pi$
$572$	0.268640	−	3.58475i	0.0112324	−	0.149886i
$573$	−19.3376	+	2.91467i	−0.807839	+	0.121762i
$574$	6.96322	+	6.46092i	0.290639	+	0.269674i
$575$	6.69667	+	3.22495i	0.279271	+	0.134490i
$576$	−1.12249	+	0.765298i	−0.0467703	+	0.0318874i
$577$	12.8052	+	32.6271i	0.533088	+	1.35829i	0.903169	+	0.429286i	$0.141235\pi$
$577$	12.8052	+	32.6271i	0.533088	+	1.35829i	−0.370081	+	0.929000i	$0.620670\pi$
$578$	−16.2299	+	5.00627i	−0.675076	+	0.208233i
$579$	−18.1677	+	16.8572i	−0.755024	+	0.700560i
$580$	−1.10251	+	1.38250i	−0.0457790	+	0.0574051i
$581$	3.15938	−	3.96173i	0.131073	−	0.164360i
$582$	−1.48343	+	1.37642i	−0.0614901	+	0.0570544i
$583$	−11.2813	+	3.47983i	−0.467225	+	0.144120i
$584$	3.81654	+	9.72438i	0.157929	+	0.402398i
$585$	1.14844	−	0.782996i	0.0474823	−	0.0323729i
$586$	12.5949	+	6.06539i	0.520291	+	0.250559i
$587$	24.1816	+	22.4372i	0.998081	+	0.926084i	0.997264	−	0.0739162i	$-0.0235497\pi$
$587$	24.1816	+	22.4372i	0.998081	+	0.926084i	0.000816198		1.00000i	$0.499740\pi$
$588$	−1.53807	+	0.231826i	−0.0634287	+	0.00956034i
$589$	1.11862	−	14.9270i	0.0460920	−	0.615055i
$590$	0.526439	−	1.34135i	0.0216732	−	0.0552223i
$591$	3.96931	+	17.3907i	0.163276	+	0.715358i
$592$	−0.0341943	−	0.456291i	−0.00140538	−	0.0187535i
$593$	−9.96702	−	3.07442i	−0.409296	−	0.126251i	0.0832681	−	0.996527i	$-0.473464\pi$
$593$	−9.96702	−	3.07442i	−0.409296	−	0.126251i	−0.492564	+	0.870276i	$0.663940\pi$
$594$	17.6771	−	8.51286i	0.725302	−	0.349287i
$595$	0.149677	−	0.259248i	0.00613615	−	0.0106281i
$596$	−8.73975	−	15.1377i	−0.357994	−	0.620064i
$597$	26.0588	+	17.7666i	1.06651	+	0.727138i
$598$	−1.69219	+	7.41397i	−0.0691988	+	0.303180i
$599$	−27.8603	−	4.19926i	−1.13834	−	0.171577i	−0.447293	−	0.894387i	$-0.647612\pi$
$599$	−27.8603	−	4.19926i	−1.13834	−	0.171577i	−0.691047	+	0.722810i	$0.742850\pi$
$600$	−0.798810	−	1.00168i	−0.0326113	−	0.0408932i
$601$	−47.6367			−1.94314			−0.971571	−	0.236750i	$-0.923918\pi$
$601$	−47.6367			−1.94314			−0.971571	+	0.236750i	$0.923918\pi$
$602$	5.44131	+	14.8050i	0.221771	+	0.603406i
$603$	16.7120			0.680564
$604$	14.1497	+	17.7432i	0.575745	+	0.721961i
$605$	−1.33002	−	0.200469i	−0.0540731	−	0.00815021i
$606$	−2.26420	+	9.92011i	−0.0919769	+	0.402977i
$607$	−10.1854	−	6.94431i	−0.413414	−	0.281861i	0.338699	−	0.940895i	$-0.390013\pi$
$607$	−10.1854	−	6.94431i	−0.413414	−	0.281861i	−0.752113	+	0.659034i	$0.770965\pi$
$608$	−2.90308	−	5.02828i	−0.117735	−	0.203924i
$609$	−2.72472	+	4.71936i	−0.110411	+	0.191238i
$610$	−5.21353	+	2.51070i	−0.211090	+	0.101655i
$611$	1.98763	+	0.613102i	0.0804108	+	0.0248034i
$612$	0.0126348	+	0.168600i	0.000510731	+	0.00681523i
$613$	−1.48728	−	6.51619i	−0.0600705	−	0.263186i	0.935971	−	0.352078i	$-0.114525\pi$
$613$	−1.48728	−	6.51619i	−0.0600705	−	0.263186i	−0.996041	+	0.0888915i	$0.971668\pi$
$614$	2.24962	−	5.73195i	0.0907874	−	0.231323i
$615$	0.378092	−	5.04529i	0.0152461	−	0.203446i
$616$	8.35710	−	1.25963i	0.336717	−	0.0507519i
$617$	−2.93724	−	2.72536i	−0.118249	−	0.109719i	0.618832	−	0.785523i	$-0.287606\pi$
$617$	−2.93724	−	2.72536i	−0.118249	−	0.109719i	−0.737081	+	0.675804i	$0.763796\pi$
$618$	4.79036	+	2.30692i	0.192697	+	0.0927977i
$619$	−11.8858	+	8.10358i	−0.477729	+	0.325710i	−0.778131	−	0.628103i	$-0.783832\pi$
$619$	−11.8858	+	8.10358i	−0.477729	+	0.325710i	0.300401	+	0.953813i	$0.402879\pi$
$620$	0.941882	+	2.39988i	0.0378269	+	0.0963814i
$621$	−39.6615	+	12.2339i	−1.59156	+	0.490931i
$622$	−1.87709	+	1.74168i	−0.0752644	+	0.0698352i
$623$	−14.4048	+	18.0630i	−0.577114	+	0.723678i
$624$	0.817282	−	1.02484i	0.0327175	−	0.0410264i
$625$	−0.733052	+	0.680173i	−0.0293221	+	0.0272069i
$626$	−14.7839	+	4.56022i	−0.590883	+	0.182263i
$627$	9.54878	+	24.3299i	0.381342	+	0.971642i
$628$	−6.96773	+	4.75052i	−0.278043	+	0.189566i
$629$	−0.0513056	−	0.0247075i	−0.00204569	−	0.000985152i
$630$	2.39551	+	2.22270i	0.0954392	+	0.0885547i
$631$	32.5863	−	4.91160i	1.29724	−	0.195528i	0.536123	−	0.844140i	$-0.319888\pi$
$631$	32.5863	−	4.91160i	1.29724	−	0.195528i	0.761119	+	0.648612i	$0.224650\pi$
$632$	−0.448094	+	5.97940i	−0.0178242	+	0.237848i
$633$	3.38654	−	8.62876i	0.134603	−	0.342962i
$634$	−3.66727	−	16.0674i	−0.145646	−	0.638116i
$635$	1.22516	+	16.3486i	0.0486190	+	0.648775i
$636$	−4.11366	−	1.26890i	−0.163117	−	0.0503150i
$637$	−1.11912	+	0.538941i	−0.0443412	+	0.0213536i
$638$	−3.10647	+	5.38057i	−0.122986	+	0.213019i
$639$	5.38913	+	9.33425i	0.213191	+	0.369257i
$640$	0.826239	+	0.563320i	0.0326600	+	0.0222672i
$641$	−11.1136	+	48.6920i	−0.438962	+	1.92322i	−0.0588827	+	0.998265i	$0.518754\pi$
$641$	−11.1136	+	48.6920i	−0.438962	+	1.92322i	−0.380079	+	0.924954i	$0.624103\pi$
$642$	−17.9332	−	2.70299i	−0.707767	−	0.106679i
$643$	28.1328	+	35.2774i	1.10945	+	1.39120i	0.911653	+	0.410961i	$0.134807\pi$
$643$	28.1328	+	35.2774i	1.10945	+	1.39120i	0.197795	+	0.980243i	$0.436622\pi$
$644$	−17.8787			−0.704520
$645$	4.35821	−	7.18251i	0.171604	−	0.282811i
$646$	−0.722581			−0.0284296
$647$	−9.28719	−	11.6458i	−0.365117	−	0.457842i	0.565008	−	0.825085i	$-0.308873\pi$
$647$	−9.28719	−	11.6458i	−0.365117	−	0.457842i	−0.930125	+	0.367243i	$0.880302\pi$
$648$	3.04431	+	0.458856i	0.119592	+	0.0180256i
$649$	1.12659	−	4.93593i	0.0442227	−	0.193752i
$650$	−0.845346	−	0.576347i	−0.0331572	−	0.0226062i
$651$	3.97255	+	6.88066i	0.155696	+	0.269674i
$652$	8.24200	−	14.2756i	0.322782	−	0.559074i
$653$	39.4858	−	19.0154i	1.54520	−	0.744128i	0.549388	−	0.835568i	$-0.314861\pi$
$653$	39.4858	−	19.0154i	1.54520	−	0.744128i	0.995811	+	0.0914393i	$0.0291467\pi$
$654$	17.0596	+	5.26219i	0.667083	+	0.205768i
$655$	0.0656778	+	0.876410i	0.00256625	+	0.0342442i
$656$	0.878737	+	3.85000i	0.0343089	+	0.150317i
$657$	−5.18496	+	13.2111i	−0.202284	+	0.515412i
$658$	−0.365447	+	4.87656i	−0.0142466	+	0.190108i
$659$	22.6044	−	3.40706i	0.880541	−	0.132720i	0.306817	−	0.951769i	$-0.400736\pi$
$659$	22.6044	−	3.40706i	0.880541	−	0.132720i	0.573724	+	0.819049i	$0.305498\pi$
$660$	−3.29986	−	3.06182i	−0.128447	−	0.119181i
$661$	8.98562	+	4.32725i	0.349500	+	0.168310i	0.600394	−	0.799704i	$-0.295010\pi$
$661$	8.98562	+	4.32725i	0.349500	+	0.168310i	−0.250894	+	0.968015i	$0.580725\pi$
$662$	26.7017	−	18.2049i	1.03779	−	0.707554i
$663$	−0.0595989	−	0.151856i	−0.00231463	−	0.00589758i
$664$	2.01302	−	0.620936i	0.0781205	−	0.0240970i
$665$	−10.2379	+	9.49939i	−0.397009	+	0.368370i
$666$	0.387581	−	0.486012i	0.0150185	−	0.0188326i
$667$	8.19464	−	10.2758i	0.317298	−	0.397879i
$668$	9.33153	−	8.65839i	0.361048	−	0.335003i
$669$	−13.8601	+	4.27527i	−0.535862	+	0.165291i
$670$	−4.49418	−	11.4510i	−0.173625	−	0.442390i
$671$	−16.7986	+	11.4531i	−0.648504	+	0.442142i
$672$	2.77658	+	1.33713i	0.107109	+	0.0515810i
$673$	14.0067	+	12.9963i	0.539917	+	0.500970i	0.902329	−	0.431048i	$-0.141856\pi$
$673$	14.0067	+	12.9963i	0.539917	+	0.500970i	−0.362412	+	0.932018i	$0.618047\pi$
$674$	22.7858	−	3.43441i	0.877677	−	0.132289i
$675$	0.417303	−	5.56852i	0.0160620	−	0.214332i
$676$	−4.36700	+	11.1269i	−0.167962	+	0.427959i
$677$	3.51288	+	15.3909i	0.135011	+	0.591521i	0.996489	+	0.0837261i	$0.0266821\pi$
$677$	3.51288	+	15.3909i	0.135011	+	0.591521i	−0.861478	+	0.507795i	$0.830461\pi$
$678$	−0.684042	−	9.12790i	−0.0262705	−	0.350555i
$679$	−3.63052	−	1.11987i	−0.139327	−	0.0429765i
$680$	0.112126	−	0.0539971i	0.00429984	−	0.00207069i
$681$	−15.0641	+	26.0918i	−0.577257	+	0.999839i
$682$	4.52913	+	7.84468i	0.173429	+	0.300388i
$683$	8.72322	+	5.94739i	0.333785	+	0.227571i	0.718601	−	0.695423i	$-0.244783\pi$
$683$	8.72322	+	5.94739i	0.333785	+	0.227571i	−0.384816	+	0.922993i	$0.625735\pi$
$684$	1.75524	−	7.69019i	0.0671131	−	0.294042i
$685$	−13.7304	−	2.06953i	−0.524613	−	0.0790727i
$686$	−12.3190	−	15.4475i	−0.470340	−	0.589788i
$687$	−25.8147			−0.984892
$688$	−1.59812	+	6.35972i	−0.0609279	+	0.242462i
$689$	−3.43779			−0.130969
$690$	5.93735	+	7.44520i	0.226031	+	0.283434i
$691$	12.9260	+	1.94828i	0.491728	+	0.0741160i	0.390225	−	0.920719i	$-0.372397\pi$
$691$	12.9260	+	1.94828i	0.491728	+	0.0741160i	0.101502	+	0.994835i	$0.467635\pi$
$692$	1.79873	−	7.88074i	0.0683774	−	0.299581i
$693$	9.48668	+	6.46791i	0.360369	+	0.245696i
$694$	2.14118	+	3.70863i	0.0812781	+	0.140778i
$695$	10.6341	−	18.4187i	0.403373	−	0.698663i
$696$	−2.04115	+	0.982966i	−0.0773696	+	0.0372592i
$697$	0.469623	+	0.144859i	0.0177882	+	0.00548694i
$698$	0.274554	+	3.66366i	0.0103920	+	0.138672i
$699$	0.847495	+	3.71312i	0.0320552	+	0.140443i
$700$	0.878791	−	2.23912i	0.0332152	−	0.0846309i
$701$	−1.52508	+	20.3508i	−0.0576016	+	0.768639i	0.891370	+	0.453277i	$0.149745\pi$
$701$	−1.52508	+	20.3508i	−0.0576016	+	0.768639i	−0.948971	+	0.315362i	$0.897874\pi$
$702$	5.64946	−	0.851518i	0.213225	−	0.0321385i
$703$	1.94752	+	1.80703i	0.0734521	+	0.0681536i
$704$	3.16560	+	1.52447i	0.119308	+	0.0574557i
$705$	2.15210	−	1.46727i	0.0810527	−	0.0552608i
$706$	−6.73367	−	17.1571i	−0.253425	−	0.645716i
$707$	−18.2550	+	5.63091i	−0.686549	+	0.211772i
$708$	1.35331	−	1.25569i	0.0508607	−	0.0471918i
$709$	−20.5857	+	25.8136i	−0.773111	+	0.969451i	−0.999990	−	0.00447236i	$-0.998576\pi$
$709$	−20.5857	+	25.8136i	−0.773111	+	0.969451i	0.226879	+	0.973923i	$0.427148\pi$
$710$	4.94655	−	6.20278i	0.185641	−	0.232786i
$711$	−5.97151	+	5.54075i	−0.223949	+	0.207794i
$712$	−9.17811	+	2.83107i	−0.343964	+	0.106099i
$713$	−7.00077	−	17.8377i	−0.262181	−	0.668026i
$714$	0.316886	−	0.216050i	0.0118592	−	0.00808545i
$715$	−3.23881	−	1.55973i	−0.121124	−	0.0583305i
$716$	3.55636	+	3.29982i	0.132907	+	0.123320i
$717$	−16.0163	+	2.41406i	−0.598138	+	0.0901548i
$718$	0.618005	−	8.24670i	0.0230637	−	0.307764i
$719$	−17.4206	+	44.3869i	−0.649678	+	1.65535i	0.101163	+	0.994870i	$0.467744\pi$
$719$	−17.4206	+	44.3869i	−0.649678	+	1.65535i	−0.750841	+	0.660483i	$0.770351\pi$
$720$	0.302306	+	1.32449i	0.0112663	+	0.0493607i
$721$	0.745980	+	9.95441i	0.0277817	+	0.370722i
$722$	14.0579	+	4.33630i	0.523182	+	0.161380i
$723$	−22.3026	+	10.7403i	−0.829441	+	0.399438i
$724$	−1.37679	+	2.38466i	−0.0511679	+	0.0886254i
$725$	0.884140	+	1.53138i	0.0328362	+	0.0568739i
$726$	−1.42382	−	0.970747i	−0.0528431	−	0.0360278i
$727$	−5.70572	+	24.9984i	−0.211613	+	0.927139i	0.751857	+	0.659326i	$0.229158\pi$
$727$	−5.70572	+	24.9984i	−0.211613	+	0.927139i	−0.963471	+	0.267813i	$0.913699\pi$
$728$	2.43354	+	0.366797i	0.0901929	+	0.0135944i
$729$	15.9898	+	20.0505i	0.592213	+	0.742612i
$730$	10.4465			0.386643
$731$	0.585990	+	0.567977i	0.0216736	+	0.0210074i
$732$	−7.41371			−0.274019
$733$	2.65388	+	3.32786i	0.0980233	+	0.122917i	0.828424	−	0.560102i	$-0.189238\pi$
$733$	2.65388	+	3.32786i	0.0980233	+	0.122917i	−0.730401	+	0.683019i	$0.760667\pi$
$734$	21.9583	+	3.30968i	0.810496	+	0.122163i
$735$	−0.346118	+	1.51644i	−0.0127667	+	0.0559347i
$736$	−6.14122	−	4.18702i	−0.226369	−	0.154335i
$737$	−21.6107	−	37.4308i	−0.796039	−	1.37878i
$738$	−2.68246	+	4.64616i	−0.0987428	+	0.171028i
$739$	18.5998	−	8.95720i	0.684206	−	0.329496i	−0.0592862	−	0.998241i	$-0.518882\pi$
$739$	18.5998	−	8.95720i	0.684206	−	0.329496i	0.743492	+	0.668745i	$0.233168\pi$
$740$	−0.437242	−	0.134871i	−0.0160733	−	0.00495797i
$741$	0.568758	+	7.58955i	0.0208938	+	0.278809i
$742$	−1.79849	−	7.87971i	−0.0660247	−	0.289273i
$743$	4.03314	−	10.2763i	0.147962	−	0.377000i	−0.837608	−	0.546272i	$-0.816046\pi$
$743$	4.03314	−	10.2763i	0.147962	−	0.377000i	0.985569	+	0.169272i	$0.0541416\pi$
$744$	−0.246836	+	3.29379i	−0.00904943	+	0.120756i
$745$	−17.2843	+	2.60518i	−0.633247	+	0.0954466i
$746$	5.51500	+	5.11717i	0.201918	+	0.187353i
$747$	2.57852	+	1.24175i	0.0943431	+	0.0454332i
$748$	0.361284	−	0.246319i	0.0132099	−	0.00900633i
$749$	−12.4396	−	31.6956i	−0.454534	−	1.15813i
$750$	−1.22427	+	0.377638i	−0.0447041	+	0.0137894i
$751$	−33.0265	+	30.6442i	−1.20516	+	1.11822i	−0.215240	+	0.976561i	$0.569053\pi$
$751$	−33.0265	+	30.6442i	−1.20516	+	1.11822i	−0.989915	+	0.141660i	$0.954756\pi$
$752$	−1.26757	+	1.58948i	−0.0462235	+	0.0579624i
$753$	−10.5705	+	13.2549i	−0.385209	+	0.483037i
$754$	−1.32622	+	1.23055i	−0.0482980	+	0.0448140i
$755$	21.6862	−	6.68930i	0.789241	−	0.243449i
$756$	4.90729	+	12.5036i	0.178476	+	0.454750i
$757$	23.6620	−	16.1324i	0.860008	−	0.586344i	−0.0510153	−	0.998698i	$-0.516246\pi$
$757$	23.6620	−	16.1324i	0.860008	−	0.586344i	0.911024	+	0.412354i	$0.135293\pi$
$758$	2.69289	+	1.29683i	0.0978101	+	0.0471028i
$759$	24.5270	+	22.7577i	0.890273	+	0.826053i
$760$	−5.74131	+	0.865364i	−0.208259	+	0.0313900i
$761$	3.38572	−	45.1793i	0.122732	−	1.63775i	−0.507720	−	0.861522i	$-0.669512\pi$
$761$	3.38572	−	45.1793i	0.122732	−	1.63775i	0.630453	−	0.776228i	$-0.282869\pi$
$762$	−7.67379	+	19.5525i	−0.277992	+	0.708312i
$763$	7.45846	+	32.6776i	0.270014	+	1.18301i
$764$	−1.14067	−	15.2212i	−0.0412681	−	0.550685i
$765$	0.161561	+	0.0498349i	0.00584125	+	0.00180179i
$766$	30.9419	−	14.9008i	1.11798	−	0.538389i
$767$	0.737138	−	1.27676i	0.0266165	−	0.0461011i
$768$	0.640596	+	1.10954i	0.0231155	+	0.0400372i
$769$	−2.72081	−	1.85502i	−0.0981148	−	0.0668936i	0.513269	−	0.858228i	$-0.328434\pi$
$769$	−2.72081	−	1.85502i	−0.0981148	−	0.0668936i	−0.611384	+	0.791334i	$0.709387\pi$
$770$	1.88063	−	8.23960i	0.0677734	−	0.296934i
$771$	−19.6269	−	2.95828i	−0.706845	−	0.106540i
$772$	−12.0609	−	15.1239i	−0.434083	−	0.544322i
$773$	36.6929			1.31975			0.659876	−	0.751374i	$-0.270609\pi$
$773$	36.6929			1.31975			0.659876	+	0.751374i	$0.270609\pi$
$774$	−7.46824	+	4.85682i	−0.268440	+	0.174575i
$775$	2.57809			0.0926078
$776$	−0.984798	−	1.23490i	−0.0353522	−	0.0443302i
$777$	−1.39438	−	0.210169i	−0.0500231	−	0.00753977i
$778$	−1.88248	+	8.24770i	−0.0674903	+	0.295694i
$779$	−18.9445	−	12.9161i	−0.678757	−	0.462769i
$780$	−0.655409	−	1.13520i	−0.0234674	−	0.0406468i
$781$	13.9377	−	24.1407i	0.498729	−	0.863823i
$782$	−0.833405	+	0.401347i	−0.0298025	+	0.0143521i
$783$	−9.43563	−	2.91051i	−0.337202	−	0.104013i
$784$	−0.0907265	−	1.21066i	−0.00324023	−	0.0432379i
$785$	1.87654	+	8.22164i	0.0669764	+	0.293443i
$786$	−0.411373	+	1.04816i	−0.0146732	+	0.0373867i
$787$	−2.01732	+	26.9193i	−0.0719097	+	0.959568i	0.838243	+	0.545296i	$0.183583\pi$
$787$	−2.01732	+	26.9193i	−0.0719097	+	0.959568i	−0.910153	+	0.414272i	$0.864036\pi$
$788$	−13.7674	+	2.07511i	−0.490444	+	0.0739226i
$789$	−9.54592	−	8.85732i	−0.339844	−	0.315329i
$790$	5.40236	+	2.60164i	0.192207	+	0.0925622i
$791$	14.1993	−	9.68089i	0.504868	−	0.344213i
$792$	1.74389	+	4.44337i	0.0619666	+	0.157888i
$793$	−5.65737	+	1.74507i	−0.200899	+	0.0619691i
$794$	18.5802	−	17.2399i	0.659386	−	0.611821i
$795$	−2.68407	+	3.36572i	−0.0951942	+	0.119370i
$796$	−15.3484	+	19.2463i	−0.544011	+	0.682168i
$797$	10.4927	−	9.73580i	0.371671	−	0.344860i	−0.472118	−	0.881535i	$-0.656510\pi$
$797$	10.4927	−	9.73580i	0.371671	−	0.344860i	0.843789	+	0.536675i	$0.180320\pi$
$798$	−17.0983	+	5.27414i	−0.605275	+	0.186703i
$799$	0.0924353	+	0.235521i	0.00327013	+	0.00833215i
$800$	0.826239	−	0.563320i	0.0292120	−	0.0199164i
$801$	−11.7564	−	5.66159i	−0.415392	−	0.200042i
$802$	−5.06208	−	4.69692i	−0.178748	−	0.165854i
$803$	36.2944	−	5.47050i	1.28080	−	0.193050i
$804$	1.17777	−	15.7163i	0.0415368	−	0.554270i
$805$	−6.53183	+	16.6428i	−0.230217	+	0.586583i
$806$	0.586946	+	2.57158i	0.0206743	+	0.0905799i
$807$	1.79437	+	23.9442i	0.0631647	+	0.842874i
$808$	−7.58917	−	2.34095i	−0.266986	−	0.0823543i
$809$	31.4633	−	15.1519i	1.10619	−	0.532714i	0.210592	−	0.977574i	$-0.432461\pi$
$809$	31.4633	−	15.1519i	1.10619	−	0.532714i	0.895600	+	0.444860i	$0.146747\pi$
$810$	1.53935	−	2.66623i	0.0540872	−	0.0936817i
$811$	−21.8718	−	37.8831i	−0.768024	−	1.33026i	−0.938633	−	0.344917i	$-0.887907\pi$
$811$	−21.8718	−	37.8831i	−0.768024	−	1.33026i	0.170610	−	0.985339i	$-0.445426\pi$
$812$	−3.51434	−	2.39604i	−0.123329	−	0.0840844i
$813$	8.85402	−	38.7920i	0.310524	−	1.36050i
$814$	−1.58974	−	0.239615i	−0.0557204	−	0.00839850i
$815$	−10.2776	−	12.8877i	−0.360009	−	0.451437i
$816$	0.159445			0.00558169
$817$	−18.3138	−	33.3796i	−0.640718	−	1.16781i
$818$	−13.0841			−0.457476
$819$	2.08459	+	2.61399i	0.0728415	+	0.0913403i
$820$	3.90490	+	0.588569i	0.136365	+	0.0205537i
$821$	8.99566	−	39.4126i	0.313951	−	1.37551i	−0.534023	−	0.845470i	$-0.679320\pi$
$821$	8.99566	−	39.4126i	0.313951	−	1.37551i	0.847974	−	0.530038i	$-0.177822\pi$
$822$	−14.6988	−	10.0215i	−0.512680	−	0.349539i
$823$	−20.4357	−	35.3957i	−0.712344	−	1.23382i	−0.963975	−	0.265993i	$-0.914300\pi$
$823$	−20.4357	−	35.3957i	−0.712344	−	1.23382i	0.251631	−	0.967823i	$-0.419033\pi$
$824$	−2.07498	+	3.59397i	−0.0722854	+	0.125202i
$825$	−4.05574	+	1.95314i	−0.141203	+	0.0679996i
$826$	3.31208	+	1.02164i	0.115242	+	0.0355475i
$827$	−2.59527	−	34.6315i	−0.0902465	−	1.20426i	−0.840018	−	0.542559i	$-0.817455\pi$
$827$	−2.59527	−	34.6315i	−0.0902465	−	1.20426i	0.749771	−	0.661697i	$-0.230164\pi$
$828$	−2.24696	−	9.84458i	−0.0780873	−	0.342123i
$829$	8.88536	−	22.6395i	0.308601	−	0.786303i	−0.689475	−	0.724309i	$-0.742159\pi$
$829$	8.88536	−	22.6395i	0.308601	−	0.786303i	0.998077	−	0.0619939i	$-0.0197459\pi$
$830$	0.157428	−	2.10072i	0.00546439	−	0.0729172i
$831$	26.8151	−	4.04172i	0.930205	−	0.140206i
$832$	0.750004	+	0.695902i	0.0260017	+	0.0241261i
$833$	−0.136127	−	0.0655555i	−0.00471654	−	0.00227136i
$834$	22.5138	−	15.3497i	0.779589	−	0.531515i
$835$	−4.65068	−	11.8497i	−0.160943	−	0.410077i
$836$	−19.4939	+	6.01308i	−0.674212	+	0.207967i
$837$	−10.5533	+	9.79204i	−0.364776	+	0.338463i
$838$	−11.6087	+	14.5569i	−0.401017	+	0.502859i
$839$	2.36154	−	2.96128i	0.0815294	−	0.102235i	−0.739394	−	0.673273i	$-0.764888\pi$
$839$	2.36154	−	2.96128i	0.0815294	−	0.102235i	0.820923	+	0.571038i	$0.193459\pi$
$840$	2.25910	−	2.09614i	0.0779464	−	0.0723237i
$841$	−24.7237	+	7.62625i	−0.852542	+	0.262974i
$842$	5.19337	+	13.2325i	0.178975	+	0.456022i
$843$	15.8157	−	10.7830i	0.544722	−	0.371385i
$844$	6.51859	+	3.13919i	0.224379	+	0.108055i
$845$	8.76233	+	8.13025i	0.301433	+	0.279689i
$846$	−2.73111	+	0.411649i	−0.0938976	+	0.0141528i
$847$	0.241780	−	3.22632i	0.00830764	−	0.110858i
$848$	1.22758	−	3.12782i	0.0421552	−	0.107410i
$849$	−2.01815	−	8.84209i	−0.0692627	−	0.303460i
$850$	−0.00930021	−	0.124103i	−0.000318994	−	0.00425669i
$851$	3.24991	+	1.00246i	0.111405	+	0.0343640i
$852$	9.15793	−	4.41022i	0.313745	−	0.151092i
$853$	−22.5494	+	39.0567i	−0.772077	+	1.33728i	0.164346	+	0.986403i	$0.447449\pi$
$853$	−22.5494	+	39.0567i	−0.772077	+	1.33728i	−0.936423	+	0.350874i	$0.885885\pi$
$854$	−6.95952	−	12.0542i	−0.238150	−	0.412487i
$855$	−6.51734	−	4.44345i	−0.222888	−	0.151963i
$856$	3.14987	−	13.8005i	0.107660	−	0.471691i
$857$	−32.8756	−	4.95519i	−1.12301	−	0.169266i	−0.438822	−	0.898574i	$-0.644604\pi$
$857$	−32.8756	−	4.95519i	−1.12301	−	0.169266i	−0.684186	+	0.729308i	$0.739842\pi$
$858$	−2.87156	−	3.60083i	−0.0980335	−	0.122930i
$859$	−6.44297			−0.219831			−0.109916	−	0.993941i	$-0.535058\pi$
$859$	−6.44297			−0.219831			−0.109916	+	0.993941i	$0.535058\pi$
$860$	5.33623	+	3.81112i	0.181964	+	0.129958i
$861$	12.1700			0.414751
$862$	20.5962	+	25.8268i	0.701510	+	0.879666i
$863$	−12.3743	−	1.86513i	−0.421228	−	0.0634899i	−0.0649916	−	0.997886i	$-0.520702\pi$
$863$	−12.3743	−	1.86513i	−0.421228	−	0.0634899i	−0.356236	+	0.934396i	$0.615940\pi$
$864$	−1.24259	+	5.44413i	−0.0422737	+	0.185213i
$865$	−6.67882	−	4.55355i	−0.227087	−	0.154825i
$866$	−13.1360	−	22.7522i	−0.446379	−	0.773152i
$867$	−10.8802	+	18.8451i	−0.369511	+	0.640012i
$868$	−5.58721	+	2.69066i	−0.189642	+	0.0913269i
$869$	20.1319	+	6.20986i	0.682927	+	0.210655i
$870$	0.169301	+	2.25917i	0.00573986	+	0.0765931i
$871$	−2.80060	−	12.2702i	−0.0948948	−	0.415761i
$872$	−5.09084	+	12.9712i	−0.172398	+	0.439262i
$873$	0.160357	−	2.13982i	0.00542727	−	0.0724219i
$874$	42.6737	−	6.43203i	1.44346	−	0.217567i
$875$	−1.76328	−	1.63609i	−0.0596098	−	0.0553098i
$876$	12.0585	+	5.80709i	0.407420	+	0.196203i
$877$	−9.80598	+	6.68561i	−0.331125	+	0.225757i	−0.717457	−	0.696603i	$-0.754694\pi$
$877$	−9.80598	+	6.68561i	−0.331125	+	0.225757i	0.386333	+	0.922360i	$0.373742\pi$
$878$	4.72853	+	12.0481i	0.159580	+	0.406604i
$879$	17.1145	−	5.27911i	0.577257	−	0.178060i
$880$	2.57562	−	2.38982i	0.0868240	−	0.0805609i
$881$	6.20171	−	7.77670i	0.208941	−	0.262004i	−0.666308	−	0.745677i	$-0.732126\pi$
$881$	6.20171	−	7.77670i	0.208941	−	0.262004i	0.875249	+	0.483673i	$0.160698\pi$
$882$	1.02836	−	1.28952i	0.0346266	−	0.0434203i
$883$	23.6502	−	21.9442i	0.795893	−	0.738481i	−0.173277	−	0.984873i	$-0.555436\pi$
$883$	23.6502	−	21.9442i	0.795893	−	0.738481i	0.969170	+	0.246392i	$0.0792451\pi$
$884$	0.121672	−	0.0375308i	0.00409226	−	0.00126230i
$885$	−0.674470	−	1.71852i	−0.0226720	−	0.0577674i
$886$	27.0004	−	18.4086i	0.907097	−	0.618448i
$887$	−18.4926	−	8.90558i	−0.620922	−	0.299020i	0.0968497	−	0.995299i	$-0.469123\pi$
$887$	−18.4926	−	8.90558i	−0.620922	−	0.299020i	−0.717771	+	0.696279i	$0.754838\pi$
$888$	−0.429741	−	0.398741i	−0.0144212	−	0.0133809i
$889$	−38.9948	+	5.87752i	−1.30784	+	0.197126i
$890$	−0.717769	+	9.57796i	−0.0240597	+	0.321054i
$891$	3.95195	−	10.0694i	0.132395	−	0.337338i
$892$	−2.51918	−	11.0372i	−0.0843483	−	0.369554i
$893$	−0.882119	−	11.7711i	−0.0295190	−	0.393903i
$894$	−21.3997	−	6.60092i	−0.715712	−	0.220768i
$895$	4.37099	−	2.10496i	0.146106	−	0.0703611i
$896$	−1.20270	+	2.08314i	−0.0401794	+	0.0695927i
$897$	4.87149	+	8.43767i	0.162654	+	0.281726i
$898$	−15.6218	−	10.6507i	−0.521305	−	0.355420i
$899$	1.01443	−	4.44449i	0.0338330	−	0.148232i
$900$	1.34338	+	0.202481i	0.0447792	+	0.00674938i
$901$	−0.260722	−	0.326935i	−0.00868590	−	0.0108918i
$902$	13.8750			0.461989
$903$	18.0119	+	9.16281i	0.599398	+	0.304919i
$904$	7.14452			0.237623
$905$	1.71682	+	2.15283i	0.0570692	+	0.0715625i
$906$	28.7511	+	4.33354i	0.955193	+	0.143972i
$907$	1.55041	−	6.79278i	0.0514804	−	0.225550i	−0.942643	−	0.333802i	$-0.891668\pi$
$907$	1.55041	−	6.79278i	0.0514804	−	0.225550i	0.994123	+	0.108252i	$0.0345253\pi$
$908$	−19.4296	−	13.2469i	−0.644795	−	0.439614i
$909$	−5.39480	−	9.34408i	−0.178934	−	0.309923i
$910$	1.23051	−	2.13131i	0.0407911	−	0.0706522i
$911$	32.4883	−	15.6456i	1.07639	−	0.518360i	0.190227	−	0.981740i	$-0.439078\pi$
$911$	32.4883	−	15.6456i	1.07639	−	0.518360i	0.886160	+	0.463380i	$0.153363\pi$
$912$	−7.10832	−	2.19263i	−0.235380	−	0.0726051i
$913$	−0.553130	−	7.38100i	−0.0183059	−	0.244276i
$914$	−7.20345	−	31.5604i	−0.238269	−	1.04392i
$915$	−2.70853	+	6.90123i	−0.0895414	+	0.228148i
$916$	1.50573	−	20.0926i	0.0497509	−	0.663879i
$917$	−2.09041	+	0.315079i	−0.0690316	+	0.0104048i
$918$	0.509434	+	0.472685i	0.0168138	+	0.0156009i
$919$	−38.9703	−	18.7671i	−1.28551	−	0.619070i	−0.338711	−	0.940890i	$-0.609991\pi$
$919$	−38.9703	−	18.7671i	−1.28551	−	0.619070i	−0.946801	+	0.321820i	$0.895705\pi$
$920$	−6.14122	+	4.18702i	−0.202470	+	0.138042i
$921$	−2.88220	−	7.34372i	−0.0949716	−	0.241984i
$922$	−5.85655	+	1.80651i	−0.192875	+	0.0594941i
$923$	5.95027	−	5.52105i	0.195856	−	0.181727i
$924$	6.75113	−	8.46565i	0.222096	−	0.278500i
$925$	−0.285291	+	0.357743i	−0.00938030	+	0.0117625i
$926$	−1.82472	+	1.69309i	−0.0599641	+	0.0556385i
$927$	−5.38745	+	1.66181i	−0.176947	+	0.0545810i
$928$	−0.646026	−	1.64605i	−0.0212068	−	0.0540341i
$929$	−30.6227	+	20.8782i	−1.00470	+	0.684992i	−0.949592	−	0.313489i	$-0.898502\pi$
$929$	−30.6227	+	20.8782i	−1.00470	+	0.684992i	−0.0551064	+	0.998480i	$0.517550\pi$
$930$	2.97592	+	1.43313i	0.0975844	+	0.0469942i
$931$	5.16729	+	4.79454i	0.169351	+	0.157135i
$932$	−2.93950	+	0.443059i	−0.0962867	+	0.0145129i
$933$	−0.245166	+	3.27151i	−0.00802636	+	0.107104i
$934$	−7.42922	+	18.9293i	−0.243092	+	0.619387i
$935$	−0.0973003	−	0.426301i	−0.00318206	−	0.0139415i
$936$	0.103872	+	1.38608i	0.00339517	+	0.0453054i
$937$	28.4004	+	8.76038i	0.927802	+	0.286189i	0.721592	−	0.692319i	$-0.243411\pi$
$937$	28.4004	+	8.76038i	0.927802	+	0.286189i	0.206210	+	0.978508i	$0.433887\pi$
$938$	26.6593	−	12.8384i	0.870457	−	0.419190i
$939$	−9.91080	+	17.1660i	−0.323427	+	0.560191i
$940$	1.01651	+	1.76065i	0.0331550	+	0.0574261i
$941$	−39.9285	−	27.2228i	−1.30163	−	0.887437i	−0.303765	−	0.952747i	$-0.598244\pi$
$941$	−39.9285	−	27.2228i	−1.30163	−	0.887437i	−0.997865	+	0.0653103i	$0.979196\pi$
$942$	−2.40420	+	10.5335i	−0.0783331	+	0.343200i
$943$	−29.0242	−	4.37469i	−0.945156	−	0.142459i
$944$	0.898420	+	1.12658i	0.0292411	+	0.0366671i
$945$	13.4321			0.436945
$946$	20.5355	+	10.4466i	0.667666	+	0.339648i
$947$	−35.9109			−1.16695			−0.583473	−	0.812132i	$-0.698307\pi$
$947$	−35.9109			−1.16695			−0.583473	+	0.812132i	$0.698307\pi$
$948$	4.78980	+	6.00622i	0.155565	+	0.195073i
$949$	10.5687	+	1.59298i	0.343075	+	0.0517102i
$950$	−1.29199	+	5.66059i	−0.0419178	+	0.183654i
$951$	−17.4458	−	11.8944i	−0.565719	−	0.385701i
$952$	0.149677	+	0.259248i	0.00485105	+	0.00840227i
$953$	23.2336	−	40.2418i	0.752611	−	1.30356i	−0.193942	−	0.981013i	$-0.562127\pi$
$953$	23.2336	−	40.2418i	0.752611	−	1.30356i	0.946553	−	0.322547i	$-0.104539\pi$
$954$	4.11278	−	1.98061i	0.133156	−	0.0641247i
$955$	−14.5858	−	4.49912i	−0.471985	−	0.145588i
$956$	−0.944758	−	12.6069i	−0.0305557	−	0.407737i
$957$	1.77126	+	7.76040i	0.0572567	+	0.250858i
$958$	0.466229	−	1.18793i	0.0150632	−	0.0383804i
$959$	2.49600	−	33.3068i	0.0806001	−	1.07553i
$960$	1.26688	−	0.190952i	0.0408884	−	0.00616294i
$961$	17.8523	+	16.5646i	0.575882	+	0.534340i
$962$	−0.421790	−	0.203124i	−0.0135991	−	0.00654897i
$963$	15.8892	−	10.8331i	0.512023	−	0.349091i
$964$	−7.05878	−	17.9855i	−0.227348	−	0.579273i
$965$	−18.4848	+	5.70181i	−0.595048	+	0.183548i
$966$	−16.7913	+	15.5801i	−0.540252	+	0.501281i
$967$	−17.6749	+	22.1637i	−0.568388	+	0.712735i	−0.980084	−	0.198586i	$-0.936365\pi$
$967$	−17.6749	+	22.1637i	−0.568388	+	0.712735i	0.411696	+	0.911321i	$0.364937\pi$
$968$	0.838622	−	1.05160i	0.0269543	−	0.0337997i
$969$	−0.678633	+	0.629679i	−0.0218008	+	0.0202282i
$970$	−1.50932	+	0.465564i	−0.0484614	+	0.0149484i
$971$	−14.6921	−	37.4350i	−0.471493	−	1.20134i	−0.946886	−	0.321571i	$-0.895789\pi$
$971$	−14.6921	−	37.4350i	−0.471493	−	1.20134i	0.475392	−	0.879774i	$-0.342306\pi$
$972$	−10.5825	+	7.21501i	−0.339433	+	0.231421i
$973$	46.0921	+	22.1968i	1.47764	+	0.711596i
$974$	12.9595	+	12.0246i	0.415248	+	0.385294i
$975$	−1.29618	+	0.195367i	−0.0415109	+	0.00625676i
$976$	0.432432	−	5.77040i	0.0138418	−	0.184706i
$977$	−9.04867	+	23.0556i	−0.289493	+	0.737615i	0.709951	+	0.704252i	$0.248717\pi$
$977$	−9.04867	+	23.0556i	−0.289493	+	0.737615i	−0.999443	+	0.0333639i	$0.989378\pi$
$978$	−4.69946	−	20.5897i	−0.150272	−	0.658385i
$979$	2.52192	+	33.6527i	0.0806009	+	1.07554i
$980$	−1.16012	−	0.357849i	−0.0370586	−	0.0114311i
$981$	−17.0560	+	8.21372i	−0.544555	+	0.262244i
$982$	4.22843	−	7.32386i	0.134935	−	0.233714i
$983$	28.4870	+	49.3410i	0.908595	+	1.57373i	0.816018	+	0.578027i	$0.196177\pi$
$983$	28.4870	+	49.3410i	0.908595	+	1.57373i	0.0925771	+	0.995706i	$0.470490\pi$
$984$	4.18030	+	2.85008i	0.133263	+	0.0908573i
$985$	−3.09814	+	13.5739i	−0.0987151	+	0.432499i
$986$	−0.217606	−	0.0327988i	−0.00692998	−	0.00104453i
$987$	3.90636	+	4.89843i	0.124341	+	0.155919i
$988$	−5.94043			−0.188990
$989$	−39.6629	−	28.3271i	−1.26121	−	0.900748i
$990$	4.77333			0.151707
$991$	18.7599	+	23.5242i	0.595929	+	0.747271i	0.984737	−	0.174047i	$-0.0556846\pi$
$991$	18.7599	+	23.5242i	0.595929	+	0.747271i	−0.388808	+	0.921319i	$0.627113\pi$
$992$	−2.54930	−	0.384245i	−0.0809402	−	0.0121998i
$993$	9.21337	−	40.3664i	0.292377	−	1.28099i
$994$	15.7676	+	10.7502i	0.500118	+	0.340975i
$995$	12.3085	+	21.3189i	0.390205	+	0.675855i
$996$	1.34949	−	2.33738i	0.0427602	−	0.0740628i
$997$	25.2789	−	12.1737i	0.800590	−	0.385544i	0.0115868	−	0.999933i	$-0.496312\pi$
$997$	25.2789	−	12.1737i	0.800590	−	0.385544i	0.789003	+	0.614389i	$0.210597\pi$
$998$	−7.66667	−	2.36485i	−0.242684	−	0.0748581i
$999$	−0.190946	−	2.54799i	−0.00604125	−	0.0806149i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.a.181.2	✓	36
43.24	even	21	inner	430.2.q.a.411.2	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.a.181.2	✓	36	1.1	even	1	trivial
430.2.q.a.411.2	yes	36	43.24	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)

\(f(q)\)	\(=\)	\(q+(0.623490 + 0.781831i) q^{2} +(1.26688 + 0.190952i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(0.826239 + 0.563320i) q^{5} +(0.640596 + 1.10954i) q^{6} +(-1.20270 + 2.08314i) q^{7} +(-0.900969 + 0.433884i) q^{8} +(-1.29819 - 0.400439i) q^{9} +O(q^{10})\)	\(q+(0.623490 + 0.781831i) q^{2} +(1.26688 + 0.190952i) q^{3} +(-0.222521 + 0.974928i) q^{4} +(0.826239 + 0.563320i) q^{5} +(0.640596 + 1.10954i) q^{6} +(-1.20270 + 2.08314i) q^{7} +(-0.900969 + 0.433884i) q^{8} +(-1.29819 - 0.400439i) q^{9} +(0.0747301 + 0.997204i) q^{10} +(0.781839 + 3.42546i) q^{11} +(-0.468072 + 1.19263i) q^{12} +(-0.0764582 + 1.02026i) q^{13} +(-2.37853 + 0.358506i) q^{14} +(0.939180 + 0.871431i) q^{15} +(-0.900969 - 0.433884i) q^{16} +(-0.102826 + 0.0701055i) q^{17} +(-0.496334 - 1.26464i) q^{18} +(5.54821 - 1.71140i) q^{19} +(-0.733052 + 0.680173i) q^{20} +(-1.92146 + 2.40943i) q^{21} +(-2.19066 + 2.74701i) q^{22} +(5.44859 - 5.05555i) q^{23} +(-1.22427 + 0.377638i) q^{24} +(0.365341 + 0.930874i) q^{25} +(-0.845346 + 0.576347i) q^{26} +(-5.03113 - 2.42287i) q^{27} +(-1.76328 - 1.63609i) q^{28} +(1.74853 - 0.263549i) q^{29} +(-0.0957435 + 1.27761i) q^{30} +(0.941882 - 2.39988i) q^{31} +(-0.222521 - 0.974928i) q^{32} +(0.336400 + 4.48894i) q^{33} +(-0.118922 - 0.0366825i) q^{34} +(-2.16719 + 1.04366i) q^{35} +(0.679275 - 1.17654i) q^{36} +(0.228785 + 0.396268i) q^{37} +(4.79728 + 3.27073i) q^{38} +(-0.291685 + 1.27795i) q^{39} +(-0.988831 - 0.149042i) q^{40} +(-2.46217 - 3.08746i) q^{41} -3.08178 q^{42} +(-1.31952 - 6.42331i) q^{43} -3.51355 q^{44} +(-0.847042 - 1.06216i) q^{45} +(7.34973 + 1.10779i) q^{46} +(0.452390 - 1.98205i) q^{47} +(-1.05857 - 0.721721i) q^{48} +(0.607028 + 1.05140i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-0.143655 + 0.0691806i) q^{51} +(-0.977671 - 0.301571i) q^{52} +(0.251100 + 3.35069i) q^{53} +(-1.24259 - 5.44413i) q^{54} +(-1.28364 + 3.27067i) q^{55} +(0.179756 - 2.39867i) q^{56} +(7.35572 - 1.10870i) q^{57} +(1.29624 + 1.20274i) q^{58} +(-1.29825 - 0.625206i) q^{59} +(-1.05857 + 0.721721i) q^{60} +(2.11408 + 5.38658i) q^{61} +(2.46355 - 0.759906i) q^{62} +(2.39551 - 2.22270i) q^{63} +(0.623490 - 0.781831i) q^{64} +(-0.637908 + 0.799911i) q^{65} +(-3.29986 + 3.06182i) q^{66} +(-11.7548 + 3.62588i) q^{67} +(-0.0454669 - 0.115848i) q^{68} +(7.86808 - 5.36437i) q^{69} +(-2.16719 - 1.04366i) q^{70} +(-5.81578 - 5.39626i) q^{71} +(1.34338 - 0.202481i) q^{72} +(0.780669 - 10.4173i) q^{73} +(-0.167169 + 0.425940i) q^{74} +(0.285092 + 1.24907i) q^{75} +(0.433895 + 5.78993i) q^{76} +(-8.07602 - 2.49112i) q^{77} +(-1.18101 + 0.568743i) q^{78} +(2.99808 - 5.19283i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-2.54374 - 1.73429i) q^{81} +(0.878737 - 3.85000i) q^{82} +(-2.08309 - 0.313975i) q^{83} +(-1.92146 - 2.40943i) q^{84} -0.124451 q^{85} +(4.19924 - 5.03651i) q^{86} +2.26551 q^{87} +(-2.19066 - 2.74701i) q^{88} +(9.49754 + 1.43152i) q^{89} +(0.302306 - 1.32449i) q^{90} +(-2.03339 - 1.38634i) q^{91} +(3.71637 + 6.43695i) q^{92} +(1.65151 - 2.86051i) q^{93} +(1.83169 - 0.882096i) q^{94} +(5.54821 + 1.71140i) q^{95} +(-0.0957435 - 1.27761i) q^{96} +(0.351470 + 1.53989i) q^{97} +(-0.443545 + 1.13013i) q^{98} +(0.356712 - 4.75999i) 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

L-functions

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Database

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