LMFDB - Embedded newform 430.2.q.d.31.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$5$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.900969 - 0.433884i) q^{2} +(1.74260 - 1.18809i) q^{3} +(0.623490 - 0.781831i) q^{4} +(0.733052 + 0.680173i) q^{5} +(1.05454 - 1.82652i) q^{6} +(-2.08827 - 3.61700i) q^{7} +(0.222521 - 0.974928i) q^{8} +(0.529092 - 1.34811i) q^{9} +O(q^{10})$	\(q+(0.900969 - 0.433884i) q^{2} +(1.74260 - 1.18809i) q^{3} +(0.623490 - 0.781831i) q^{4} +(0.733052 + 0.680173i) q^{5} +(1.05454 - 1.82652i) q^{6} +(-2.08827 - 3.61700i) q^{7} +(0.222521 - 0.974928i) q^{8} +(0.529092 - 1.34811i) q^{9} +(0.955573 + 0.294755i) q^{10} +(1.97503 + 2.47660i) q^{11} +(0.157612 - 2.10318i) q^{12} +(-3.60399 + 1.11168i) q^{13} +(-3.45082 - 2.35273i) q^{14} +(2.08552 + 0.314342i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(4.74962 - 4.40700i) q^{17} +(-0.108225 - 1.44417i) q^{18} +(1.19470 + 3.04405i) q^{19} +(0.988831 - 0.149042i) q^{20} +(-7.93633 - 3.82194i) q^{21} +(2.85399 + 1.37441i) q^{22} +(-5.35218 + 0.806712i) q^{23} +(-0.770533 - 1.96329i) q^{24} +(0.0747301 + 0.997204i) q^{25} +(-2.76474 + 2.56530i) q^{26} +(0.728275 + 3.19078i) q^{27} +(-4.12990 - 0.622482i) q^{28} +(5.39114 + 3.67562i) q^{29} +(2.01538 - 0.621662i) q^{30} +(-0.619854 + 8.27138i) q^{31} +(-0.623490 - 0.781831i) q^{32} +(6.38411 + 1.96924i) q^{33} +(2.36713 - 6.03136i) q^{34} +(0.929369 - 4.07183i) q^{35} +(-0.724107 - 1.25419i) q^{36} +(2.14375 - 3.71308i) q^{37} +(2.39715 + 2.22423i) q^{38} +(-4.95954 + 6.21907i) q^{39} +(0.826239 - 0.563320i) q^{40} +(9.61462 - 4.63016i) q^{41} -8.80867 q^{42} +(-6.47257 - 1.05162i) q^{43} +3.16770 q^{44} +(1.30480 - 0.628357i) q^{45} +(-4.47213 + 3.04905i) q^{46} +(-7.11477 + 8.92164i) q^{47} +(-1.54606 - 1.43454i) q^{48} +(-5.22177 + 9.04437i) q^{49} +(0.500000 + 0.866025i) q^{50} +(3.04080 - 13.3226i) q^{51} +(-1.37790 + 3.51083i) q^{52} +(-6.07687 - 1.87447i) q^{53} +(2.04058 + 2.55881i) q^{54} +(-0.236722 + 3.15884i) q^{55} +(-3.99099 + 1.23106i) q^{56} +(5.69848 + 3.88516i) q^{57} +(6.45205 + 0.972489i) q^{58} +(-2.90199 - 12.7144i) q^{59} +(1.54606 - 1.43454i) q^{60} +(-0.318209 - 4.24621i) q^{61} +(3.03035 + 7.72120i) q^{62} +(-5.98098 + 0.901488i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(-3.39804 - 1.63641i) q^{65} +(6.60630 - 0.995739i) q^{66} +(-1.62448 - 4.13910i) q^{67} +(-0.484194 - 6.46113i) q^{68} +(-8.36829 + 7.76464i) q^{69} +(-0.929369 - 4.07183i) q^{70} +(8.52747 + 1.28531i) q^{71} +(-1.19657 - 0.815808i) q^{72} +(2.12072 - 0.654155i) q^{73} +(0.320405 - 4.27550i) q^{74} +(1.31499 + 1.64894i) q^{75} +(3.12482 + 0.963878i) q^{76} +(4.83347 - 12.3155i) q^{77} +(-1.77004 + 7.75505i) q^{78} +(5.36444 + 9.29148i) q^{79} +(0.500000 - 0.866025i) q^{80} +(8.24487 + 7.65012i) q^{81} +(6.65352 - 8.34325i) q^{82} +(-11.7427 + 8.00602i) q^{83} +(-7.93633 + 3.82194i) q^{84} +6.47924 q^{85} +(-6.28786 + 1.86087i) q^{86} +13.7616 q^{87} +(2.85399 - 1.37441i) q^{88} +(-5.99923 + 4.09021i) q^{89} +(0.902947 - 1.13226i) q^{90} +(11.5471 + 10.7141i) q^{91} +(-2.70632 + 4.68748i) q^{92} +(8.74695 + 15.1502i) q^{93} +(-2.53923 + 11.1251i) q^{94} +(-1.19470 + 3.04405i) q^{95} +(-2.01538 - 0.621662i) q^{96} +(-3.15651 - 3.95813i) q^{97} +(-0.780447 + 10.4143i) q^{98} +(4.38369 - 1.35219i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} - 6 q^{6} + q^{7} + 10 q^{8} + 8 q^{9}+O(q^{10}) $ 60 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 - 6 * q^6 + q^7 + 10 * q^8 + 8 * q^9	\( 60 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} - 6 q^{6} + q^{7} + 10 q^{8} + 8 q^{9} + 5 q^{10} + 3 q^{11} - q^{12} + 13 q^{13} - 15 q^{14} + q^{15} - 10 q^{16} + 38 q^{17} + 6 q^{18} + 17 q^{19} - 5 q^{20} + 4 q^{21} + 11 q^{22} - 8 q^{23} + q^{24} + 5 q^{25} + 29 q^{26} - 16 q^{27} - 6 q^{28} - 41 q^{29} - q^{30} + 15 q^{31} + 10 q^{32} + 63 q^{33} - 10 q^{34} + 2 q^{35} - 48 q^{36} + 7 q^{37} + 25 q^{38} - 64 q^{39} + 5 q^{40} - 22 q^{41} - 60 q^{42} + 6 q^{43} - 4 q^{44} + 30 q^{45} - 20 q^{46} - 13 q^{47} - q^{48} - 93 q^{49} + 30 q^{50} + 18 q^{51} - 15 q^{52} + 71 q^{53} - 5 q^{54} - 16 q^{55} - q^{56} - 94 q^{57} - 22 q^{58} + 20 q^{59} + q^{60} + 91 q^{61} + 69 q^{62} - 50 q^{63} - 10 q^{64} + 5 q^{65} + 14 q^{66} - 26 q^{67} - 18 q^{68} - 94 q^{69} - 2 q^{70} + 20 q^{71} - 36 q^{72} - 56 q^{73} - 7 q^{74} + 2 q^{75} + 38 q^{76} + 41 q^{77} - 13 q^{78} - 46 q^{79} + 30 q^{80} + 39 q^{81} + 8 q^{82} - 115 q^{83} + 4 q^{84} + 6 q^{85} + 29 q^{86} + 20 q^{87} + 11 q^{88} + 30 q^{89} - 16 q^{90} - 53 q^{91} - 8 q^{92} + 16 q^{93} + 41 q^{94} - 17 q^{95} + q^{96} + 113 q^{97} + 2 q^{98} + 139 q^{99}+O(q^{100}) \) 60 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 - 6 * q^6 + q^7 + 10 * q^8 + 8 * q^9 + 5 * q^10 + 3 * q^11 - q^12 + 13 * q^13 - 15 * q^14 + q^15 - 10 * q^16 + 38 * q^17 + 6 * q^18 + 17 * q^19 - 5 * q^20 + 4 * q^21 + 11 * q^22 - 8 * q^23 + q^24 + 5 * q^25 + 29 * q^26 - 16 * q^27 - 6 * q^28 - 41 * q^29 - q^30 + 15 * q^31 + 10 * q^32 + 63 * q^33 - 10 * q^34 + 2 * q^35 - 48 * q^36 + 7 * q^37 + 25 * q^38 - 64 * q^39 + 5 * q^40 - 22 * q^41 - 60 * q^42 + 6 * q^43 - 4 * q^44 + 30 * q^45 - 20 * q^46 - 13 * q^47 - q^48 - 93 * q^49 + 30 * q^50 + 18 * q^51 - 15 * q^52 + 71 * q^53 - 5 * q^54 - 16 * q^55 - q^56 - 94 * q^57 - 22 * q^58 + 20 * q^59 + q^60 + 91 * q^61 + 69 * q^62 - 50 * q^63 - 10 * q^64 + 5 * q^65 + 14 * q^66 - 26 * q^67 - 18 * q^68 - 94 * q^69 - 2 * q^70 + 20 * q^71 - 36 * q^72 - 56 * q^73 - 7 * q^74 + 2 * q^75 + 38 * q^76 + 41 * q^77 - 13 * q^78 - 46 * q^79 + 30 * q^80 + 39 * q^81 + 8 * q^82 - 115 * q^83 + 4 * q^84 + 6 * q^85 + 29 * q^86 + 20 * q^87 + 11 * q^88 + 30 * q^89 - 16 * q^90 - 53 * q^91 - 8 * q^92 + 16 * q^93 + 41 * q^94 - 17 * q^95 + q^96 + 113 * q^97 + 2 * q^98 + 139 * 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
$3$	1.74260	−	1.18809i	1.00609	−	0.685942i	0.0561677	−	0.998421i	$-0.482112\pi$
$3$	1.74260	−	1.18809i	1.00609	−	0.685942i	0.949925	+	0.312479i	$0.101159\pi$
$4$	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
$6$	1.05454	−	1.82652i	0.430514	−	0.745672i
$7$	−2.08827	−	3.61700i	−0.789293	−	1.36710i	−0.926401	−	0.376540i	$-0.877114\pi$
$7$	−2.08827	−	3.61700i	−0.789293	−	1.36710i	0.137107	−	0.990556i	$-0.456219\pi$
$8$	0.222521	−	0.974928i	0.0786730	−	0.344689i
$9$	0.529092	−	1.34811i	0.176364	−	0.449368i
$10$	0.955573	+	0.294755i	0.302179	+	0.0932098i
$11$	1.97503	+	2.47660i	0.595493	+	0.746724i	0.984668	−	0.174440i	$-0.0558114\pi$
$11$	1.97503	+	2.47660i	0.595493	+	0.746724i	−0.389175	+	0.921164i	$0.627240\pi$
$12$	0.157612	−	2.10318i	0.0454986	−	0.607136i
$13$	−3.60399	+	1.11168i	−0.999566	+	0.308325i	−0.751009	−	0.660292i	$-0.770433\pi$
$13$	−3.60399	+	1.11168i	−0.999566	+	0.308325i	−0.248557	+	0.968617i	$0.579956\pi$
$14$	−3.45082	−	2.35273i	−0.922272	−	0.628794i
$15$	2.08552	+	0.314342i	0.538480	+	0.0811627i
$16$	−0.222521	−	0.974928i	−0.0556302	−	0.243732i
$17$	4.74962	−	4.40700i	1.15195	−	1.06886i	0.155236	−	0.987877i	$-0.450386\pi$
$17$	4.74962	−	4.40700i	1.15195	−	1.06886i	0.996716	−	0.0809782i	$-0.0258044\pi$
$18$	−0.108225	−	1.44417i	−0.0255089	−	0.340393i
$19$	1.19470	+	3.04405i	0.274083	+	0.698353i	0.999945	+	0.0105118i	$0.00334608\pi$
$19$	1.19470	+	3.04405i	0.274083	+	0.698353i	−0.725862	+	0.687841i	$0.758559\pi$
$20$	0.988831	−	0.149042i	0.221109	−	0.0333269i
$21$	−7.93633	−	3.82194i	−1.73185	−	0.834015i
$22$	2.85399	+	1.37441i	0.608474	+	0.293026i
$23$	−5.35218	+	0.806712i	−1.11601	+	0.168211i	−0.681048	−	0.732239i	$-0.738475\pi$
$23$	−5.35218	+	0.806712i	−1.11601	+	0.168211i	−0.434960	+	0.900450i	$0.643237\pi$
$24$	−0.770533	−	1.96329i	−0.157284	−	0.400754i
$25$	0.0747301	+	0.997204i	0.0149460	+	0.199441i
$26$	−2.76474	+	2.56530i	−0.542210	+	0.503097i
$27$	0.728275	+	3.19078i	0.140157	+	0.614066i
$28$	−4.12990	−	0.622482i	−0.780477	−	0.117638i
$29$	5.39114	+	3.67562i	1.00111	+	0.682546i	0.948732	−	0.316082i	$-0.102367\pi$
$29$	5.39114	+	3.67562i	1.00111	+	0.682546i	0.0523785	+	0.998627i	$0.483320\pi$
$30$	2.01538	−	0.621662i	0.367956	−	0.113499i
$31$	−0.619854	+	8.27138i	−0.111329	+	1.48558i	0.609675	+	0.792652i	$0.291300\pi$
$31$	−0.619854	+	8.27138i	−0.111329	+	1.48558i	−0.721004	+	0.692931i	$0.756319\pi$
$32$	−0.623490	−	0.781831i	−0.110218	−	0.138210i
$33$	6.38411	+	1.96924i	1.11133	+	0.342800i
$34$	2.36713	−	6.03136i	0.405960	−	1.03437i
$35$	0.929369	−	4.07183i	0.157092	−	0.688265i
$36$	−0.724107	−	1.25419i	−0.120685	−	0.209032i
$37$	2.14375	−	3.71308i	0.352430	−	0.610426i	−0.634245	−	0.773132i	$-0.718689\pi$
$37$	2.14375	−	3.71308i	0.352430	−	0.610426i	0.986675	+	0.162706i	$0.0520223\pi$
$38$	2.39715	+	2.22423i	0.388869	+	0.360818i
$39$	−4.95954	+	6.21907i	−0.794162	+	0.995848i
$40$	0.826239	−	0.563320i	0.130640	−	0.0890687i
$41$	9.61462	−	4.63016i	1.50155	−	0.723109i	0.510914	−	0.859632i	$-0.329307\pi$
$41$	9.61462	−	4.63016i	1.50155	−	0.723109i	0.990637	+	0.136523i	$0.0435928\pi$
$42$	−8.80867			−1.35921
$43$	−6.47257	−	1.05162i	−0.987057	−	0.160370i
$43$	−6.47257	−	1.05162i	−0.987057	−	0.160370i
$44$	3.16770			0.477548
$45$	1.30480	−	0.628357i	0.194508	−	0.0936699i
$46$	−4.47213	+	3.04905i	−0.659380	+	0.449558i
$47$	−7.11477	+	8.92164i	−1.03780	+	1.30136i	−0.0854481	+	0.996343i	$0.527232\pi$
$47$	−7.11477	+	8.92164i	−1.03780	+	1.30136i	−0.952348	+	0.305013i	$0.901339\pi$
$48$	−1.54606	−	1.43454i	−0.223155	−	0.207058i
$49$	−5.22177	+	9.04437i	−0.745967	+	1.29205i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	3.04080	−	13.3226i	0.425797	−	1.86554i
$52$	−1.37790	+	3.51083i	−0.191080	+	0.486865i
$53$	−6.07687	−	1.87447i	−0.834723	−	0.257478i	−0.152207	−	0.988349i	$-0.548638\pi$
$53$	−6.07687	−	1.87447i	−0.834723	−	0.257478i	−0.682516	+	0.730871i	$0.739114\pi$
$54$	2.04058	+	2.55881i	0.277688	+	0.348210i
$55$	−0.236722	+	3.15884i	−0.0319196	+	0.425938i
$56$	−3.99099	+	1.23106i	−0.533319	+	0.164507i
$57$	5.69848	+	3.88516i	0.754783	+	0.514602i
$58$	6.45205	+	0.972489i	0.847195	+	0.127694i
$59$	−2.90199	−	12.7144i	−0.377807	−	1.65528i	−0.704168	−	0.710033i	$-0.748680\pi$
$59$	−2.90199	−	12.7144i	−0.377807	−	1.65528i	0.326361	−	0.945245i	$-0.394177\pi$
$60$	1.54606	−	1.43454i	0.199596	−	0.185198i
$61$	−0.318209	−	4.24621i	−0.0407425	−	0.543671i	−0.979809	−	0.199936i	$-0.935927\pi$
$61$	−0.318209	−	4.24621i	−0.0407425	−	0.543671i	0.939066	−	0.343736i	$-0.111692\pi$
$62$	3.03035	+	7.72120i	0.384854	+	0.980593i
$63$	−5.98098	+	0.901488i	−0.753533	+	0.113577i
$64$	−0.900969	−	0.433884i	−0.112621	−	0.0542355i
$65$	−3.39804	−	1.63641i	−0.421476	−	0.202972i
$66$	6.60630	−	0.995739i	0.813179	−	0.122567i
$67$	−1.62448	−	4.13910i	−0.198462	−	0.505672i	0.796649	−	0.604443i	$-0.206604\pi$
$67$	−1.62448	−	4.13910i	−0.198462	−	0.505672i	−0.995110	+	0.0987707i	$0.968509\pi$
$68$	−0.484194	−	6.46113i	−0.0587172	−	0.783527i
$69$	−8.36829	+	7.76464i	−1.00742	+	0.934752i
$70$	−0.929369	−	4.07183i	−0.111081	−	0.486677i
$71$	8.52747	+	1.28531i	1.01202	+	0.152538i	0.634062	−	0.773282i	$-0.281387\pi$
$71$	8.52747	+	1.28531i	1.01202	+	0.152538i	0.377963	+	0.925821i	$0.376625\pi$
$72$	−1.19657	−	0.815808i	−0.141017	−	0.0961439i
$73$	2.12072	−	0.654155i	0.248211	−	0.0765630i	−0.168153	−	0.985761i	$-0.553780\pi$
$73$	2.12072	−	0.654155i	0.248211	−	0.0765630i	0.416364	+	0.909198i	$0.363304\pi$
$74$	0.320405	−	4.27550i	0.0372463	−	0.497017i
$75$	1.31499	+	1.64894i	0.151842	+	0.190404i
$76$	3.12482	+	0.963878i	0.358441	+	0.110564i
$77$	4.83347	−	12.3155i	0.550825	−	1.40348i
$78$	−1.77004	+	7.75505i	−0.200418	+	0.878087i
$79$	5.36444	+	9.29148i	0.603547	+	1.04537i	0.992279	+	0.124023i	$0.0395796\pi$
$79$	5.36444	+	9.29148i	0.603547	+	1.04537i	−0.388733	+	0.921351i	$0.627087\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	8.24487	+	7.65012i	0.916096	+	0.850013i
$82$	6.65352	−	8.34325i	0.734758	−	0.921358i
$83$	−11.7427	+	8.00602i	−1.28893	+	0.878775i	−0.996980	−	0.0776604i	$-0.975255\pi$
$83$	−11.7427	+	8.00602i	−1.28893	+	0.878775i	−0.291946	+	0.956435i	$0.594303\pi$
$84$	−7.93633	+	3.82194i	−0.865925	+	0.417008i
$85$	6.47924			0.702773
$86$	−6.28786	+	1.86087i	−0.678037	+	0.200663i
$87$	13.7616			1.47540
$88$	2.85399	−	1.37441i	0.304237	−	0.146513i
$89$	−5.99923	+	4.09021i	−0.635917	+	0.433561i	−0.837897	−	0.545829i	$-0.816215\pi$
$89$	−5.99923	+	4.09021i	−0.635917	+	0.433561i	0.201979	+	0.979390i	$0.435263\pi$
$90$	0.902947	−	1.13226i	0.0951790	−	0.119351i
$91$	11.5471	+	10.7141i	1.21046	+	1.12314i
$92$	−2.70632	+	4.68748i	−0.282153	+	0.488704i
$93$	8.74695	+	15.1502i	0.907017	+	1.57100i
$94$	−2.53923	+	11.1251i	−0.261902	+	1.14747i
$95$	−1.19470	+	3.04405i	−0.122574	+	0.312313i
$96$	−2.01538	−	0.621662i	−0.205694	−	0.0634481i
$97$	−3.15651	−	3.95813i	−0.320495	−	0.401888i	0.595320	−	0.803489i	$-0.297025\pi$
$97$	−3.15651	−	3.95813i	−0.320495	−	0.401888i	−0.915815	+	0.401601i	$0.868454\pi$
$98$	−0.780447	+	10.4143i	−0.0788370	+	1.05201i
$99$	4.38369	−	1.35219i	0.440578	−	0.135900i
$100$	0.826239	+	0.563320i	0.0826239	+	0.0563320i
$101$	−14.1979	−	2.13998i	−1.41274	−	0.212936i	−0.602072	−	0.798442i	$-0.705658\pi$
$101$	−14.1979	−	2.13998i	−1.41274	−	0.212936i	−0.810669	+	0.585505i	$0.800896\pi$
$102$	−3.04080	−	13.3226i	−0.301084	−	1.31914i
$103$	2.15984	−	2.00404i	0.212815	−	0.197463i	−0.566561	−	0.824020i	$-0.691727\pi$
$103$	2.15984	−	2.00404i	0.212815	−	0.197463i	0.779376	+	0.626556i	$0.215536\pi$
$104$	0.281848	+	3.76100i	0.0276375	+	0.368796i
$105$	−3.21817	−	8.19976i	−0.314061	−	0.800214i
$106$	−6.28837	+	0.947820i	−0.610781	+	0.0920604i
$107$	0.993423	+	0.478407i	0.0960378	+	0.0462494i	0.481286	−	0.876564i	$-0.340170\pi$
$107$	0.993423	+	0.478407i	0.0960378	+	0.0462494i	−0.385248	+	0.922813i	$0.625884\pi$
$108$	2.94872	+	1.42003i	0.283741	+	0.136643i
$109$	−0.335346	+	0.0505453i	−0.0321204	+	0.00484137i	−0.165083	−	0.986280i	$-0.552789\pi$
$109$	−0.335346	+	0.0505453i	−0.0321204	+	0.00484137i	0.132962	+	0.991121i	$0.457551\pi$
$110$	1.15729	+	2.94872i	0.110343	+	0.281150i
$111$	−0.675759	−	9.01737i	−0.0641402	−	0.855891i
$112$	−3.06163	+	2.84077i	−0.289296	+	0.268428i
$113$	2.64184	+	11.5746i	0.248523	+	1.08885i	0.933017	+	0.359833i	$0.117166\pi$
$113$	2.64184	+	11.5746i	0.248523	+	1.08885i	−0.684494	+	0.729019i	$0.739977\pi$
$114$	6.81986	+	1.02793i	0.638739	+	0.0962744i
$115$	−4.47213	−	3.04905i	−0.417028	−	0.284325i
$116$	6.23504	−	1.92325i	0.578909	−	0.178570i
$117$	−0.408176	+	5.44673i	−0.0377359	+	0.503551i
$118$	−8.13119	−	10.1962i	−0.748536	−	0.938635i
$119$	−25.8586	−	7.97633i	−2.37046	−	0.731189i
$120$	0.770533	−	1.96329i	0.0703397	−	0.179223i
$121$	0.214890	−	0.941494i	0.0195354	−	0.0855904i
$122$	−2.12906	−	3.68764i	−0.192756	−	0.333863i
$123$	11.2534	−	19.4915i	1.01469	−	1.75749i
$124$	6.08035	+	5.64174i	0.546031	+	0.506643i
$125$	−0.623490	+	0.781831i	−0.0557666	+	0.0699291i
$126$	−4.99754	+	3.40726i	−0.445216	+	0.303543i
$127$	10.6736	−	5.14016i	0.947133	−	0.456115i	0.104453	−	0.994530i	$-0.466691\pi$
$127$	10.6736	−	5.14016i	0.947133	−	0.456115i	0.842680	+	0.538415i	$0.180977\pi$
$128$	−1.00000			−0.0883883
$129$	−12.5285	+	5.85742i	−1.10307	+	0.515717i
$130$	−3.77155			−0.330786
$131$	1.63489	−	0.787320i	0.142841	−	0.0687885i	−0.361098	−	0.932528i	$-0.617598\pi$
$131$	1.63489	−	0.787320i	0.142841	−	0.0687885i	0.503939	+	0.863739i	$0.331884\pi$
$132$	5.52004	−	3.76350i	0.480457	−	0.327570i
$133$	8.51545	−	10.6780i	0.738383	−	0.925903i
$134$	−3.25949	−	3.02437i	−0.281577	−	0.261266i
$135$	−1.63642	+	2.83436i	−0.140841	+	0.243943i
$136$	−3.23962	−	5.61119i	−0.277795	−	0.481155i
$137$	1.09601	−	4.80192i	0.0936381	−	0.410255i	−0.906285	−	0.422667i	$-0.861094\pi$
$137$	1.09601	−	4.80192i	0.0936381	−	0.410255i	0.999923	+	0.0124120i	$0.00395097\pi$
$138$	−4.17062	+	10.6266i	−0.355027	+	0.904593i
$139$	6.62647	+	2.04399i	0.562050	+	0.173369i	0.562745	−	0.826630i	$-0.309745\pi$
$139$	6.62647	+	2.04399i	0.562050	+	0.173369i	−0.000695576		1.00000i	$0.500221\pi$
$140$	−2.60403	−	3.26536i	−0.220081	−	0.275973i
$141$	−1.79854	+	23.9998i	−0.151464	+	2.02115i
$142$	8.24066	−	2.54191i	0.691541	−	0.213312i
$143$	−9.87116	−	6.73004i	−0.825468	−	0.562795i
$144$	−1.43204	−	0.215845i	−0.119337	−	0.0179871i
$145$	1.45193	+	6.36133i	0.120576	+	0.528280i
$146$	1.62687	−	1.50952i	0.134641	−	0.124929i
$147$	1.64602	+	21.9647i	0.135762	+	1.81161i
$148$	−1.56640	−	3.99111i	−0.128757	−	0.328067i
$149$	−10.8584	+	1.63664i	−0.889556	+	0.134079i	−0.577892	−	0.816113i	$-0.696124\pi$
$149$	−10.8584	+	1.63664i	−0.889556	+	0.134079i	−0.311664	+	0.950192i	$0.600886\pi$
$150$	1.90021	+	0.915095i	0.155152	+	0.0747172i
$151$	−20.5241	−	9.88390i	−1.67023	−	0.804340i	−0.997947	−	0.0640450i	$-0.979600\pi$
$151$	−20.5241	−	9.88390i	−1.67023	−	0.804340i	−0.672282	−	0.740295i	$-0.734686\pi$
$152$	3.23357	−	0.487383i	0.262278	−	0.0395320i
$153$	−3.42812	−	8.73470i	−0.277147	−	0.706159i
$154$	−0.988681	−	13.1930i	−0.0796702	−	1.06312i
$155$	−6.08035	+	5.64174i	−0.488385	+	0.453155i
$156$	1.77004	+	7.75505i	0.141717	+	0.620901i
$157$	0.576545	+	0.0869002i	0.0460133	+	0.00693539i	0.172009	−	0.985095i	$-0.444974\pi$
$157$	0.576545	+	0.0869002i	0.0460133	+	0.00693539i	−0.125995	+	0.992031i	$0.540212\pi$
$158$	8.86462	+	6.04379i	0.705231	+	0.480818i
$159$	−12.8166	+	3.95340i	−1.01642	+	0.313525i
$160$	0.0747301	−	0.997204i	0.00590793	−	0.0788359i
$161$	14.0947	+	17.6742i	1.11082	+	1.39292i
$162$	10.7476	+	3.31521i	0.844414	+	0.260467i
$163$	−0.0282312	+	0.0719318i	−0.00221124	+	0.00563414i	−0.931975	−	0.362522i	$-0.881916\pi$
$163$	−0.0282312	+	0.0719318i	−0.00221124	+	0.00563414i	0.929764	+	0.368156i	$0.120011\pi$
$164$	2.37461	−	10.4039i	0.185426	−	0.812405i
$165$	3.34046	+	5.78585i	0.260054	+	0.450428i
$166$	−7.10610	+	12.3081i	−0.551540	+	0.955296i
$167$	2.20088	+	2.04212i	0.170310	+	0.158024i	0.760723	−	0.649077i	$-0.224845\pi$
$167$	2.20088	+	2.04212i	0.170310	+	0.158024i	−0.590413	+	0.807101i	$0.701035\pi$
$168$	−5.49211	+	6.88689i	−0.423726	+	0.531335i
$169$	1.01177	−	0.689816i	0.0778288	−	0.0530628i
$170$	5.83760	−	2.81124i	0.447723	−	0.215612i
$171$	4.73581			0.362156
$172$	−4.85776	+	4.40478i	−0.370401	+	0.335862i
$173$	−0.131324			−0.00998439			−0.00499220	−	0.999988i	$-0.501589\pi$
$173$	−0.131324			−0.00998439			−0.00499220	+	0.999988i	$0.501589\pi$
$174$	12.3988	−	5.97093i	0.939947	−	0.452655i
$175$	3.45082	−	2.35273i	0.260858	−	0.177850i
$176$	1.97503	−	2.47660i	0.148873	−	0.186681i
$177$	−20.1629	−	18.7084i	−1.51553	−	1.40621i
$178$	−3.63045	+	6.28812i	−0.272114	+	0.471314i
$179$	−2.59339	−	4.49188i	−0.193839	−	0.335739i	0.752680	−	0.658386i	$-0.228761\pi$
$179$	−2.59339	−	4.49188i	−0.193839	−	0.335739i	−0.946519	+	0.322647i	$0.895427\pi$
$180$	0.322258	−	1.41191i	0.0240197	−	0.105237i
$181$	8.06614	−	20.5522i	0.599551	−	1.52763i	−0.232306	−	0.972643i	$-0.574627\pi$
$181$	8.06614	−	20.5522i	0.599551	−	1.52763i	0.831858	−	0.554989i	$-0.187278\pi$
$182$	15.0522	+	4.64299i	1.11574	+	0.344162i
$183$	−5.59938	−	7.02140i	−0.413918	−	0.519036i
$184$	−0.404487	+	5.39750i	−0.0298192	+	0.397909i
$185$	4.09701	−	1.26376i	0.301218	−	0.0929135i
$186$	14.4541	+	9.85467i	1.05983	+	0.722579i
$187$	20.2950	+	3.05898i	1.48412	+	0.223695i
$188$	2.53923	+	11.1251i	0.185193	+	0.811382i
$189$	10.0202	−	9.29739i	0.728862	−	0.676286i
$190$	0.244375	+	3.26095i	0.0177288	+	0.236575i
$191$	−7.34997	−	18.7274i	−0.531825	−	1.35507i	−0.904249	−	0.427006i	$-0.859568\pi$
$191$	−7.34997	−	18.7274i	−0.531825	−	1.35507i	0.372423	−	0.928063i	$-0.378527\pi$
$192$	−2.08552	+	0.314342i	−0.150510	+	0.0226857i
$193$	7.38313	+	3.55553i	0.531449	+	0.255932i	0.680308	−	0.732926i	$-0.261846\pi$
$193$	7.38313	+	3.55553i	0.531449	+	0.255932i	−0.148859	+	0.988858i	$0.547560\pi$
$194$	−4.56128	−	2.19660i	−0.327481	−	0.157707i
$195$	−7.86564	+	1.18555i	−0.563270	+	0.0848993i
$196$	3.81545	+	9.72162i	0.272532	+	0.694401i
$197$	−1.01968	−	13.6067i	−0.0726493	−	0.969438i	−0.907796	−	0.419411i	$-0.862237\pi$
$197$	−1.01968	−	13.6067i	−0.0726493	−	0.969438i	0.835147	−	0.550027i	$-0.185383\pi$
$198$	3.36288	−	3.12029i	0.238989	−	0.221750i
$199$	−1.94720	−	8.53124i	−0.138033	−	0.604764i	−0.995866	−	0.0908344i	$-0.971047\pi$
$199$	−1.94720	−	8.53124i	−0.138033	−	0.604764i	0.857833	−	0.513929i	$-0.171811\pi$
$200$	0.988831	+	0.149042i	0.0699209	+	0.0105389i
$201$	−7.74844	−	5.28279i	−0.546532	−	0.372620i
$202$	−13.7203	+	4.23217i	−0.965360	+	0.297774i
$203$	2.03652	−	27.1754i	0.142936	−	1.90734i
$204$	−8.52014	−	10.6839i	−0.596529	−	0.748023i
$205$	10.1973	+	3.14546i	0.712212	+	0.219688i
$206$	1.07643	−	2.74269i	0.0749982	−	0.191092i
$207$	−1.74427	+	7.64213i	−0.121235	+	0.531165i
$208$	1.88577	+	3.26625i	0.130755	+	0.226474i
$209$	−5.17934	+	8.97088i	−0.358262	+	0.620529i
$210$	−6.45721	−	5.99142i	−0.445590	−	0.413447i
$211$	−4.69927	+	5.89270i	−0.323511	+	0.405670i	−0.916817	−	0.399307i	$-0.869251\pi$
$211$	−4.69927	+	5.89270i	−0.323511	+	0.405670i	0.593306	+	0.804977i	$0.297822\pi$
$212$	−5.25439	+	3.58238i	−0.360873	+	0.246039i
$213$	16.3871	−	7.89159i	1.12282	−	0.540723i
$214$	1.10262			0.0753733
$215$	−4.02945	−	5.17335i	−0.274806	−	0.352820i
$216$	3.27284			0.222688
$217$	31.2120	−	15.0309i	2.11881	−	1.02036i
$218$	−0.280206	+	0.191041i	−0.0189779	+	0.0129389i
$219$	2.91838	−	3.65953i	0.197206	−	0.247288i
$220$	2.32209	+	2.15458i	0.156555	+	0.145262i
$221$	−12.2184	+	21.1629i	−0.821897	+	1.42357i
$222$	−4.52133	−	7.83117i	−0.303452	−	0.525594i
$223$	−2.36733	+	10.3720i	−0.158528	+	0.694558i	0.831714	+	0.555204i	$0.187360\pi$
$223$	−2.36733	+	10.3720i	−0.158528	+	0.694558i	−0.990243	+	0.139354i	$0.955497\pi$
$224$	−1.52586	+	3.88784i	−0.101951	+	0.259767i
$225$	1.38387	+	0.426869i	0.0922583	+	0.0284579i
$226$	7.40227	+	9.28215i	0.492391	+	0.617439i
$227$	0.945886	−	12.6220i	0.0627806	−	0.837749i	−0.873573	−	0.486692i	$-0.838203\pi$
$227$	0.945886	−	12.6220i	0.0627806	−	0.837749i	0.936354	−	0.351057i	$-0.114178\pi$
$228$	6.59049	−	2.03290i	0.436466	−	0.134632i
$229$	8.78292	+	5.98809i	0.580392	+	0.395704i	0.817627	−	0.575748i	$-0.195289\pi$
$229$	8.78292	+	5.98809i	0.580392	+	0.395704i	−0.237236	+	0.971452i	$0.576241\pi$
$230$	−5.35218	−	0.806712i	−0.352913	−	0.0531930i
$231$	−6.20904	−	27.2036i	−0.408525	−	1.78986i
$232$	4.78311	−	4.43808i	0.314026	−	0.291374i
$233$	−0.894592	−	11.9375i	−0.0586067	−	0.782052i	−0.946644	−	0.322281i	$-0.895550\pi$
$233$	−0.894592	−	11.9375i	−0.0586067	−	0.782052i	0.888037	−	0.459771i	$-0.152069\pi$
$234$	1.99550	+	5.08444i	0.130450	+	0.332380i
$235$	−11.2838	+	1.70075i	−0.736071	+	0.110945i
$236$	−11.7499	−	5.65846i	−0.764854	−	0.368334i
$237$	20.3872	+	9.81795i	1.32429	+	0.637744i
$238$	−26.7586	+	4.03321i	−1.73450	+	0.261434i
$239$	−1.58633	−	4.04189i	−0.102611	−	0.261448i	0.870344	−	0.492445i	$-0.163897\pi$
$239$	−1.58633	−	4.04189i	−0.102611	−	0.261448i	−0.972955	+	0.230997i	$0.925801\pi$
$240$	−0.157612	−	2.10318i	−0.0101738	−	0.135760i
$241$	−2.08787	+	1.93726i	−0.134491	+	0.124790i	−0.744550	−	0.667566i	$-0.767336\pi$
$241$	−2.08787	+	1.93726i	−0.134491	+	0.124790i	0.610059	+	0.792356i	$0.291146\pi$
$242$	−0.214890	−	0.941494i	−0.0138136	−	0.0605215i
$243$	13.7477	+	2.07213i	0.881914	+	0.132927i
$244$	−3.51822	−	2.39868i	−0.225231	−	0.153560i
$245$	−9.97956	+	3.07829i	−0.637571	+	0.196665i
$246$	1.68194	−	22.4439i	0.107237	−	1.43097i
$247$	−7.68970	−	9.64258i	−0.489284	−	0.613543i
$248$	7.92606	+	2.44487i	0.503306	+	0.155249i
$249$	−10.9510	+	27.9026i	−0.693990	+	1.76826i
$250$	−0.222521	+	0.974928i	−0.0140735	+	0.0616599i
$251$	−11.9640	−	20.7222i	−0.755160	−	1.30798i	−0.945295	−	0.326218i	$-0.894226\pi$
$251$	−11.9640	−	20.7222i	−0.755160	−	1.30798i	0.190135	−	0.981758i	$-0.439108\pi$
$252$	−3.02427	+	5.23819i	−0.190511	+	0.329975i
$253$	−12.5686	−	11.6620i	−0.790182	−	0.733181i
$254$	7.38639	−	9.26224i	0.463463	−	0.581165i
$255$	11.2907	−	7.69790i	0.707054	−	0.482061i
$256$	−0.900969	+	0.433884i	−0.0563106	+	0.0271177i
$257$	12.2027			0.761185			0.380593	−	0.924743i	$-0.375720\pi$
$257$	12.2027			0.761185			0.380593	+	0.924743i	$0.375720\pi$
$258$	−8.74637	+	10.7133i	−0.544525	+	0.666979i
$259$	−17.9069			−1.11268
$260$	−3.39804	+	1.63641i	−0.210738	+	0.101486i
$261$	7.80754	−	5.32309i	0.483274	−	0.329491i
$262$	1.13138	−	1.41870i	0.0698967	−	0.0876477i
$263$	23.5297	+	21.8323i	1.45090	+	1.34624i	0.823147	+	0.567829i	$0.192216\pi$
$263$	23.5297	+	21.8323i	1.45090	+	1.34624i	0.627755	+	0.778411i	$0.283974\pi$
$264$	3.34046	−	5.78585i	0.205591	−	0.356094i
$265$	−3.17970	−	5.50740i	−0.195328	−	0.338317i
$266$	3.03913	−	13.3153i	0.186341	−	0.816413i
$267$	−5.59476	+	14.2552i	−0.342394	+	0.872405i
$268$	−4.24893	−	1.31062i	−0.259545	−	0.0800589i
$269$	−2.68983	−	3.37294i	−0.164002	−	0.205652i	0.693039	−	0.720900i	$-0.256271\pi$
$269$	−2.68983	−	3.37294i	−0.164002	−	0.205652i	−0.857041	+	0.515248i	$0.827700\pi$
$270$	−0.244579	+	3.26369i	−0.0148846	+	0.198622i
$271$	8.82054	−	2.72077i	0.535809	−	0.165275i	−0.0150293	−	0.999887i	$-0.504784\pi$
$271$	8.82054	−	2.72077i	0.535809	−	0.165275i	0.550839	+	0.834612i	$0.314308\pi$
$272$	−5.35340	−	3.64989i	−0.324598	−	0.221307i
$273$	32.8512	+	4.95152i	1.98825	+	0.299680i
$274$	−1.09601	−	4.80192i	−0.0662122	−	0.290094i
$275$	−2.32209	+	2.15458i	−0.140027	+	0.129926i
$276$	0.853095	+	11.3838i	0.0513503	+	0.685222i
$277$	1.77769	+	4.52948i	0.106811	+	0.272150i	0.974280	−	0.225342i	$-0.0723498\pi$
$277$	1.77769	+	4.52948i	0.106811	+	0.272150i	−0.867469	+	0.497491i	$0.834255\pi$
$278$	6.85710	−	1.03354i	0.411261	−	0.0619877i
$279$	10.8227	+	5.21195i	0.647940	+	0.312031i
$280$	−3.76294	−	1.81214i	−0.224879	−	0.108296i
$281$	4.42185	−	0.666487i	0.263786	−	0.0397593i	−0.0158177	−	0.999875i	$-0.505035\pi$
$281$	4.42185	−	0.666487i	0.263786	−	0.0397593i	0.279603	+	0.960116i	$0.409797\pi$
$282$	8.79272	+	22.4035i	0.523599	+	1.33411i
$283$	−1.07473	−	14.3412i	−0.0638858	−	0.852497i	−0.933457	−	0.358690i	$-0.883224\pi$
$283$	−1.07473	−	14.3412i	−0.0638858	−	0.852497i	0.869571	−	0.493808i	$-0.164395\pi$
$284$	6.32169	−	5.86567i	0.375123	−	0.348063i
$285$	1.53470	+	6.72398i	0.0909080	+	0.398294i
$286$	−11.8137	−	1.78062i	−0.698557	−	0.105290i
$287$	−36.8252	−	25.1070i	−2.17372	−	1.48202i
$288$	−1.38387	+	0.426869i	−0.0815456	+	0.0251535i
$289$	1.86680	−	24.9107i	0.109812	−	1.46534i
$290$	4.06822	+	5.10139i	0.238894	+	0.299564i
$291$	−10.2031	−	3.14725i	−0.598119	−	0.184495i
$292$	0.810807	−	2.06590i	0.0474489	−	0.120898i
$293$	−1.48823	+	6.52037i	−0.0869434	+	0.380924i	−0.999614	−	0.0277713i	$-0.991159\pi$
$293$	−1.48823	+	6.52037i	−0.0869434	+	0.380924i	0.912671	+	0.408695i	$0.134016\pi$
$294$	11.0131	+	19.0753i	0.642299	+	1.11249i
$295$	6.52071	−	11.2942i	0.379650	−	0.657573i
$296$	−3.14295	−	2.91623i	−0.182680	−	0.169503i
$297$	−6.46394	+	8.10552i	−0.375076	+	0.470330i
$298$	−9.07298	+	6.18585i	−0.525584	+	0.358337i
$299$	18.3924	−	8.85731i	1.06366	−	0.512231i
$300$	2.10908			0.121768
$301$	9.71280	+	25.6073i	0.559836	+	1.47598i
$302$	−22.7801			−1.31084
$303$	−27.2837	+	13.1392i	−1.56741	+	0.754825i
$304$	2.70188	−	1.84211i	0.154964	−	0.105652i
$305$	2.65489	−	3.32913i	0.152019	−	0.190625i
$306$	−6.87847	−	6.38229i	−0.393216	−	0.364851i
$307$	−14.4192	+	24.9748i	−0.822948	+	1.42539i	0.0805291	+	0.996752i	$0.474339\pi$
$307$	−14.4192	+	24.9748i	−0.822948	+	1.42539i	−0.903477	+	0.428636i	$0.858994\pi$
$308$	−6.61501	−	11.4575i	−0.376925	−	0.652854i
$309$	1.38277	−	6.05831i	0.0786630	−	0.344645i
$310$	−3.03035	+	7.72120i	−0.172112	+	0.438534i
$311$	−29.7512	−	9.17702i	−1.68703	−	0.520381i	−0.705019	−	0.709188i	$-0.749062\pi$
$311$	−29.7512	−	9.17702i	−1.68703	−	0.520381i	−0.982014	+	0.188807i	$0.939538\pi$
$312$	4.95954	+	6.21907i	0.280779	+	0.352085i
$313$	0.998304	−	13.3214i	0.0564275	−	0.752973i	−0.895189	−	0.445686i	$-0.852960\pi$
$313$	0.998304	−	13.3214i	0.0564275	−	0.752973i	0.951617	−	0.307287i	$-0.0994211\pi$
$314$	0.557154	−	0.171859i	0.0314420	−	0.00969858i
$315$	−4.99754	−	3.40726i	−0.281579	−	0.191977i
$316$	10.6090	+	1.59906i	0.596806	+	0.0899540i
$317$	−2.42522	−	10.6256i	−0.136214	−	0.596793i	−0.996247	−	0.0865547i	$-0.972414\pi$
$317$	−2.42522	−	10.6256i	−0.136214	−	0.596793i	0.860033	−	0.510239i	$-0.170443\pi$
$318$	−9.83205	+	9.12281i	−0.551354	+	0.511582i
$319$	1.54459	+	20.6112i	0.0864807	+	1.15400i
$320$	−0.365341	−	0.930874i	−0.0204232	−	0.0520374i
$321$	2.29953	−	0.346599i	0.128347	−	0.0193452i
$322$	20.3674	+	9.80844i	1.13503	+	0.546603i
$323$	19.0895	+	9.19303i	1.06217	+	0.511514i
$324$	11.1217	−	1.67633i	0.617872	−	0.0931292i
$325$	−1.37790	−	3.51083i	−0.0764322	−	0.194746i
$326$	0.00577465	+	0.0770574i	0.000319828	+	0.00426781i
$327$	−0.524323	+	0.486501i	−0.0289952	+	0.0269036i
$328$	−2.37461	−	10.4039i	−0.131116	−	0.574457i
$329$	47.1271	+	7.10327i	2.59820	+	0.391616i
$330$	5.52004	+	3.76350i	0.303868	+	0.207174i
$331$	7.23739	−	2.23244i	0.397803	−	0.122706i	−0.0893978	−	0.995996i	$-0.528494\pi$
$331$	7.23739	−	2.23244i	0.397803	−	0.122706i	0.487201	+	0.873290i	$0.338018\pi$
$332$	−1.06208	+	14.1725i	−0.0582892	+	0.777815i
$333$	−3.87138	−	4.85455i	−0.212150	−	0.266028i
$334$	2.86897	+	0.884961i	0.156983	+	0.0484229i
$335$	1.62448	−	4.13910i	0.0887548	−	0.226143i
$336$	−1.96011	+	8.58782i	−0.106933	+	0.468504i
$337$	1.01084	+	1.75082i	0.0550638	+	0.0953732i	0.892243	−	0.451555i	$-0.149130\pi$
$337$	1.01084	+	1.75082i	0.0550638	+	0.0953732i	−0.837180	+	0.546928i	$0.815797\pi$
$338$	0.612277	−	1.06049i	0.0333035	−	0.0576833i
$339$	18.3554	+	17.0313i	0.996926	+	0.925012i
$340$	4.03974	−	5.06568i	0.219086	−	0.274725i
$341$	−21.7091	+	14.8010i	−1.17562	+	0.801522i
$342$	4.26681	−	2.05479i	0.230723	−	0.111110i
$343$	14.3821			0.776561
$344$	−2.46553	+	6.07628i	−0.132932	+	0.327611i
$345$	−11.4157			−0.614600
$346$	−0.118319	+	0.0569794i	−0.00636087	+	0.00306323i
$347$	−3.60323	+	2.45664i	−0.193432	+	0.131879i	−0.656163	−	0.754619i	$-0.727822\pi$
$347$	−3.60323	+	2.45664i	−0.193432	+	0.131879i	0.462732	+	0.886498i	$0.346869\pi$
$348$	8.58020	−	10.7592i	0.459947	−	0.576756i
$349$	15.7893	+	14.6503i	0.845181	+	0.784213i	0.978367	−	0.206878i	$-0.0663303\pi$
$349$	15.7893	+	14.6503i	0.845181	+	0.784213i	−0.133186	+	0.991091i	$0.542521\pi$
$350$	2.08827	−	3.61700i	0.111623	−	0.193337i
$351$	−6.17183	−	10.6899i	−0.329428	−	0.570586i
$352$	0.704879	−	3.08827i	0.0375702	−	0.164606i
$353$	−3.88084	+	9.88822i	−0.206556	+	0.526297i	−0.996183	−	0.0872909i	$-0.972179\pi$
$353$	−3.88084	+	9.88822i	−0.206556	+	0.526297i	0.789627	+	0.613588i	$0.210274\pi$
$354$	−26.2834	−	8.10735i	−1.39695	−	0.430901i
$355$	5.37685	+	6.74235i	0.285373	+	0.357847i
$356$	−0.542607	+	7.24059i	−0.0287581	+	0.383751i
$357$	−54.5379	+	16.8227i	−2.88645	+	0.890352i
$358$	−4.28552	−	2.92182i	−0.226497	−	0.154423i
$359$	15.5976	+	2.35096i	0.823211	+	0.124079i	0.547122	−	0.837053i	$-0.315723\pi$
$359$	15.5976	+	2.35096i	0.823211	+	0.124079i	0.276089	+	0.961132i	$0.410961\pi$
$360$	−0.322258	−	1.41191i	−0.0169845	−	0.0744139i
$361$	6.08906	−	5.64982i	0.320477	−	0.297359i
$362$	−1.64992	−	22.0166i	−0.0867178	−	1.15717i
$363$	−0.744109	−	1.89596i	−0.0390556	−	0.0995120i
$364$	15.5761	−	2.34772i	0.816409	−	0.123054i
$365$	1.99953	+	0.962925i	0.104660	+	0.0504018i
$366$	−8.09133	−	3.89658i	−0.422941	−	0.203678i
$367$	−7.89010	+	1.18924i	−0.411860	+	0.0620779i	−0.351704	−	0.936111i	$-0.614398\pi$
$367$	−7.89010	+	1.18924i	−0.411860	+	0.0620779i	−0.0601555	+	0.998189i	$0.519160\pi$
$368$	1.97746	+	5.03848i	0.103082	+	0.262649i
$369$	−1.15492	−	15.4113i	−0.0601226	−	0.802280i
$370$	3.14295	−	2.91623i	0.163394	−	0.151608i
$371$	5.91023	+	25.8944i	0.306844	+	1.34437i
$372$	17.2985	+	2.60733i	0.896886	+	0.135184i
$373$	1.65200	+	1.12631i	0.0855372	+	0.0583182i	0.605333	−	0.795972i	$-0.293040\pi$
$373$	1.65200	+	1.12631i	0.0855372	+	0.0583182i	−0.519796	+	0.854290i	$0.673992\pi$
$374$	19.6124	−	6.04963i	1.01413	−	0.312819i
$375$	−0.157612	+	2.10318i	−0.00813903	+	0.108608i
$376$	7.11477	+	8.92164i	0.366916	+	0.460099i
$377$	−23.5157	−	7.25364i	−1.21112	−	0.373582i
$378$	4.99390	−	12.7243i	0.256859	−	0.654465i
$379$	−5.60860	+	24.5729i	−0.288094	+	1.26222i	0.599042	+	0.800717i	$0.295548\pi$
$379$	−5.60860	+	24.5729i	−0.288094	+	1.26222i	−0.887137	+	0.461507i	$0.847309\pi$
$380$	1.63505	+	2.83199i	0.0838763	+	0.145278i
$381$	12.4930	−	21.6385i	0.640034	−	1.10857i
$382$	−14.7476	−	13.6838i	−0.754554	−	0.700124i
$383$	−3.33228	+	4.17854i	−0.170271	+	0.213513i	−0.859644	−	0.510893i	$-0.829315\pi$
$383$	−3.33228	+	4.17854i	−0.170271	+	0.213513i	0.689373	+	0.724407i	$0.257886\pi$
$384$	−1.74260	+	1.18809i	−0.0889268	+	0.0606293i
$385$	11.9198	−	5.74029i	0.607491	−	0.292552i
$386$	8.19465			0.417097
$387$	−4.84227	+	8.16930i	−0.246147	+	0.415269i
$388$	−5.06264			−0.257017
$389$	12.1762	−	5.86375i	0.617358	−	0.297304i	−0.0989456	−	0.995093i	$-0.531547\pi$
$389$	12.1762	−	5.86375i	0.617358	−	0.297304i	0.716303	+	0.697789i	$0.245833\pi$
$390$	−6.57231	+	4.48092i	−0.332802	+	0.226900i
$391$	−21.8657	+	27.4187i	−1.10579	+	1.38662i
$392$	7.65566	+	7.10341i	0.386669	+	0.358776i
$393$	1.91355	−	3.31437i	0.0965261	−	0.167188i
$394$	−6.82243	−	11.8168i	−0.343709	−	0.595322i
$395$	−2.38740	+	10.4599i	−0.120123	+	0.526294i
$396$	1.67600	−	4.27039i	0.0842223	−	0.214595i
$397$	3.18739	+	0.983180i	0.159971	+	0.0493444i	0.373706	−	0.927547i	$-0.378087\pi$
$397$	3.18739	+	0.983180i	0.159971	+	0.0493444i	−0.213735	+	0.976892i	$0.568563\pi$
$398$	−5.45593	−	6.84152i	−0.273481	−	0.342935i
$399$	2.15262	−	28.7247i	0.107766	−	1.43803i
$400$	0.955573	−	0.294755i	0.0477786	−	0.0147378i
$401$	−1.80111	−	1.22798i	−0.0899431	−	0.0613222i	0.517513	−	0.855675i	$-0.326858\pi$
$401$	−1.80111	−	1.22798i	−0.0899431	−	0.0613222i	−0.607457	+	0.794353i	$0.707810\pi$
$402$	−9.27322	−	1.39771i	−0.462506	−	0.0697116i
$403$	−6.96120	−	30.4990i	−0.346762	−	1.51926i
$404$	−10.5253	+	9.76608i	−0.523655	+	0.485881i
$405$	0.840513	+	11.2159i	0.0417654	+	0.557321i
$406$	−9.95614	−	25.3678i	−0.494115	−	1.25898i
$407$	13.4298	−	2.02421i	0.665689	−	0.100336i
$408$	−12.3120	−	5.92912i	−0.609532	−	0.293535i
$409$	11.6592	+	5.61477i	0.576510	+	0.277633i	0.699333	−	0.714796i	$-0.253480\pi$
$409$	11.6592	+	5.61477i	0.576510	+	0.277633i	−0.122823	+	0.992429i	$0.539195\pi$
$410$	10.5522	−	1.59049i	0.521137	−	0.0785488i
$411$	−3.79519	−	9.66998i	−0.187203	−	0.476985i
$412$	−0.220182	−	2.93812i	−0.0108476	−	0.144751i
$413$	−39.9279	+	37.0477i	−1.96472	+	1.82300i
$414$	1.74427	+	7.64213i	0.0857260	+	0.375590i
$415$	−14.0535	−	2.11822i	−0.689857	−	0.103979i
$416$	3.11620	+	2.12459i	0.152784	+	0.104166i
$417$	13.9757	−	4.31095i	0.684395	−	0.211108i
$418$	−0.774105	+	10.3297i	−0.0378627	+	0.505243i
$419$	−3.18776	−	3.99732i	−0.155732	−	0.195282i	0.697844	−	0.716249i	$-0.254143\pi$
$419$	−3.18776	−	3.99732i	−0.155732	−	0.195282i	−0.853577	+	0.520967i	$0.825571\pi$
$420$	−8.41732	−	2.59640i	−0.410723	−	0.126691i
$421$	−13.0083	+	33.1447i	−0.633988	+	1.61537i	0.145788	+	0.989316i	$0.453428\pi$
$421$	−13.0083	+	33.1447i	−0.633988	+	1.61537i	−0.779776	+	0.626059i	$0.784667\pi$
$422$	−1.67715	+	7.34808i	−0.0816424	+	0.357699i
$423$	8.26294	+	14.3118i	0.401758	+	0.695865i
$424$	−3.17970	+	5.50740i	−0.154420	+	0.267463i
$425$	4.74962	+	4.40700i	0.230390	+	0.213771i
$426$	11.3402	−	14.2202i	0.549434	−	0.688969i
$427$	−14.6940	+	10.0182i	−0.711093	+	0.484815i
$428$	0.993423	−	0.478407i	0.0480189	−	0.0231247i
$429$	−25.1974			−1.21654
$430$	−5.87504	−	2.91272i	−0.283320	−	0.140464i
$431$	29.4405			1.41810			0.709050	−	0.705158i	$-0.249124\pi$
$431$	29.4405			1.41810			0.709050	+	0.705158i	$0.249124\pi$
$432$	2.94872	−	1.42003i	0.141871	−	0.0683213i
$433$	4.49309	−	3.06333i	0.215924	−	0.147214i	−0.450528	−	0.892762i	$-0.648764\pi$
$433$	4.49309	−	3.06333i	0.215924	−	0.147214i	0.666452	+	0.745548i	$0.267812\pi$
$434$	21.5993	−	27.0847i	1.03680	−	1.30011i
$435$	10.0880	+	9.36025i	0.483680	+	0.448790i
$436$	−0.169567	+	0.293699i	−0.00812079	+	0.0140656i
$437$	−8.84993	−	15.3285i	−0.423350	−	0.733263i
$438$	1.04156	−	4.56336i	0.0497675	−	0.218046i
$439$	−2.56466	+	6.53464i	−0.122404	+	0.311882i	−0.978921	−	0.204237i	$-0.934529\pi$
$439$	−2.56466	+	6.53464i	−0.122404	+	0.311882i	0.856517	+	0.516119i	$0.172624\pi$
$440$	3.02696	+	0.933695i	0.144305	+	0.0445121i
$441$	9.42996	+	11.8248i	0.449046	+	0.563086i
$442$	−1.82616	+	24.3684i	−0.0868616	+	1.15909i
$443$	−11.9105	+	3.67390i	−0.565885	+	0.174552i	−0.564480	−	0.825447i	$-0.690923\pi$
$443$	−11.9105	+	3.67390i	−0.565885	+	0.174552i	−0.00140455	+	0.999999i	$0.500447\pi$
$444$	−7.47140	−	5.09391i	−0.354577	−	0.241746i
$445$	−7.17980	−	1.08218i	−0.340355	−	0.0513003i
$446$	2.36733	+	10.3720i	0.112096	+	0.491127i
$447$	−16.9774	+	15.7528i	−0.803005	+	0.745080i
$448$	0.312114	+	4.16487i	0.0147460	+	0.196772i
$449$	2.15440	+	5.48932i	0.101672	+	0.259057i	0.972654	−	0.232258i	$-0.0746115\pi$
$449$	2.15440	+	5.48932i	0.101672	+	0.259057i	−0.870982	+	0.491315i	$0.836516\pi$
$450$	1.43204	−	0.215845i	0.0675070	−	0.0101750i
$451$	30.4562	+	14.6669i	1.43413	+	0.690638i
$452$	10.6966	+	5.15120i	0.503125	+	0.242292i
$453$	−47.5083	+	7.16073i	−2.23214	+	0.336440i
$454$	−4.62425	−	11.7824i	−0.217027	−	0.552976i
$455$	1.17715	+	15.7080i	0.0551857	+	0.736402i
$456$	5.05578	−	4.69108i	0.236759	−	0.219680i
$457$	7.40473	+	32.4423i	0.346379	+	1.51758i	0.785332	+	0.619075i	$0.212492\pi$
$457$	7.40473	+	32.4423i	0.346379	+	1.51758i	−0.438953	+	0.898510i	$0.644651\pi$
$458$	10.5113	+	1.58432i	0.491160	+	0.0740304i
$459$	17.5208	+	11.9455i	0.817802	+	0.557568i
$460$	−5.17217	+	1.59540i	−0.241154	+	0.0743861i
$461$	1.67057	−	22.2922i	0.0778060	−	1.03825i	−0.812522	−	0.582930i	$-0.801906\pi$
$461$	1.67057	−	22.2922i	0.0778060	−	1.03825i	0.890328	−	0.455319i	$-0.150475\pi$
$462$	−17.3973	−	21.8156i	−0.809398	−	1.01495i
$463$	22.5248	+	6.94798i	1.04682	+	0.322900i	0.770014	−	0.638027i	$-0.220249\pi$
$463$	22.5248	+	6.94798i	1.04682	+	0.322900i	0.276802	+	0.960927i	$0.410725\pi$
$464$	2.38382	−	6.07388i	0.110666	−	0.281973i
$465$	−3.89276	+	17.0553i	−0.180522	+	0.790920i
$466$	−5.98549	−	10.3672i	−0.277272	−	0.480250i
$467$	−8.62038	+	14.9309i	−0.398904	+	0.690922i	−0.993591	−	0.113036i	$-0.963943\pi$
$467$	−8.62038	+	14.9309i	−0.398904	+	0.690922i	0.594687	+	0.803957i	$0.297276\pi$
$468$	4.00394	+	3.71511i	0.185082	+	0.171731i
$469$	−11.5788	+	14.5193i	−0.534658	+	0.670440i
$470$	−9.42838	+	6.42816i	−0.434899	+	0.296509i
$471$	1.10793	−	0.533553i	0.0510509	−	0.0245848i
$472$	−13.0414			−0.600280
$473$	−10.1790	−	18.1069i	−0.468033	−	0.832558i
$474$	22.6281			1.03934
$475$	−2.94626	+	1.41884i	−0.135184	+	0.0651010i
$476$	−22.3587	+	15.2439i	−1.02481	+	0.698704i
$477$	−5.74220	+	7.20050i	−0.262918	+	0.329688i
$478$	−3.18294	−	2.95334i	−0.145584	−	0.135083i
$479$	18.1351	−	31.4108i	0.828612	−	1.43520i	−0.0705150	−	0.997511i	$-0.522464\pi$
$479$	18.1351	−	31.4108i	0.828612	−	1.43520i	0.899127	−	0.437688i	$-0.144202\pi$
$480$	−1.05454	−	1.82652i	−0.0481329	−	0.0833687i
$481$	−3.59827	+	15.7650i	−0.164067	+	0.718824i
$482$	−1.04056	+	2.65130i	−0.0473961	+	0.120763i
$483$	45.5599	+	14.0534i	2.07305	+	0.639451i
$484$	−0.602108	−	0.755020i	−0.0273685	−	0.0343191i
$485$	0.378332	−	5.04849i	0.0171792	−	0.229240i
$486$	13.2853	−	4.09797i	0.602633	−	0.185888i
$487$	35.7953	+	24.4048i	1.62204	+	1.10589i	0.918640	+	0.395095i	$0.129288\pi$
$487$	35.7953	+	24.4048i	1.62204	+	1.10589i	0.703400	+	0.710794i	$0.251664\pi$
$488$	−4.21056	−	0.634639i	−0.190603	−	0.0287288i
$489$	0.0362655	+	0.158890i	0.00163998	+	0.00718524i
$490$	−7.65566	+	7.10341i	−0.345847	+	0.320899i
$491$	0.768144	+	10.2502i	0.0346659	+	0.462584i	0.987343	+	0.158600i	$0.0506979\pi$
$491$	0.768144	+	10.2502i	0.0346659	+	0.462584i	−0.952677	+	0.303984i	$0.901683\pi$
$492$	−8.22268	−	20.9511i	−0.370707	−	0.944546i
$493$	41.8044	−	6.30099i	1.88277	−	0.283783i
$494$	−11.1119	−	5.35123i	−0.499950	−	0.240763i
$495$	4.13320	+	1.99044i	0.185773	+	0.0894638i
$496$	8.20193	−	1.23624i	0.368277	−	0.0555089i
$497$	−13.1587	−	33.5279i	−0.590250	−	1.50393i
$498$	2.24001	+	29.8908i	0.100377	+	1.33944i
$499$	−6.41829	+	5.95531i	−0.287322	+	0.266596i	−0.810644	−	0.585539i	$-0.800883\pi$
$499$	−6.41829	+	5.95531i	−0.287322	+	0.266596i	0.523322	+	0.852135i	$0.324692\pi$
$500$	0.222521	+	0.974928i	0.00995144	+	0.0436001i
$501$	6.26149	+	0.943767i	0.279743	+	0.0421644i
$502$	−19.7702	−	13.4791i	−0.882388	−	0.601602i
$503$	17.0878	−	5.27087i	0.761905	−	0.235017i	0.110634	−	0.993861i	$-0.464712\pi$
$503$	17.0878	−	5.27087i	0.761905	−	0.235017i	0.651272	+	0.758845i	$0.274236\pi$
$504$	−0.452008	+	6.03162i	−0.0201340	+	0.268670i
$505$	−8.95222	−	11.2257i	−0.398368	−	0.499538i
$506$	−16.3839	−	5.05375i	−0.728351	−	0.224667i
$507$	0.943559	−	2.40415i	0.0419049	−	0.106772i
$508$	2.63617	−	11.5498i	0.116961	−	0.512441i
$509$	−17.5532	−	30.4030i	−0.778032	−	1.34759i	−0.933075	−	0.359683i	$-0.882885\pi$
$509$	−17.5532	−	30.4030i	−0.778032	−	1.34759i	0.155043	−	0.987908i	$-0.450448\pi$
$510$	6.83262	−	11.8344i	0.302553	−	0.524038i
$511$	−6.79471	−	6.30457i	−0.300580	−	0.278898i
$512$	−0.623490	+	0.781831i	−0.0275546	+	0.0345524i
$513$	−8.84282	+	6.02893i	−0.390420	+	0.266184i
$514$	10.9943	−	5.29456i	0.484937	−	0.233533i
$515$	2.94636			0.129832
$516$	−3.23189	+	13.4472i	−0.142276	+	0.591982i
$517$	−36.1472			−1.58975
$518$	−16.1336	+	7.76952i	−0.708868	+	0.341373i
$519$	−0.228846	+	0.156024i	−0.0100452	+	0.00684872i
$520$	−2.35152	+	2.94871i	−0.103121	+	0.129310i
$521$	−10.7863	−	10.0082i	−0.472557	−	0.438469i	0.407594	−	0.913163i	$-0.366368\pi$
$521$	−10.7863	−	10.0082i	−0.472557	−	0.438469i	−0.880151	+	0.474695i	$0.842559\pi$
$522$	4.72475	−	8.18350i	0.206796	−	0.358182i
$523$	−9.27310	−	16.0615i	−0.405484	−	0.702319i	0.588894	−	0.808211i	$-0.299564\pi$
$523$	−9.27310	−	16.0615i	−0.405484	−	0.702319i	−0.994378	+	0.105891i	$0.966230\pi$
$524$	0.403784	−	1.76909i	0.0176394	−	0.0772831i
$525$	3.21817	−	8.19976i	0.140452	−	0.357867i
$526$	30.6722	+	9.46112i	1.33737	+	0.412524i
$527$	33.5079	+	42.0176i	1.45963	+	1.83032i
$528$	0.499266	−	6.66224i	0.0217278	−	0.289937i
$529$	6.01692	−	1.85597i	0.261605	−	0.0806945i
$530$	−5.25439	−	3.58238i	−0.228236	−	0.155609i
$531$	−18.6758	−	2.81493i	−0.810461	−	0.122157i
$532$	−3.03913	−	13.3153i	−0.131763	−	0.577291i
$533$	−29.5037	+	27.3754i	−1.27795	+	1.18576i
$534$	1.14440	+	15.2710i	0.0495231	+	0.660840i
$535$	0.402831	+	1.02640i	0.0174159	+	0.0443750i
$536$	−4.39681	+	0.662712i	−0.189913	+	0.0286248i
$537$	−9.85600	−	4.74640i	−0.425318	−	0.204822i
$538$	−3.88691	−	1.87184i	−0.167577	−	0.0807007i
$539$	−32.7125	+	4.93061i	−1.40903	+	0.212376i
$540$	1.19570	+	3.04660i	0.0514548	+	0.131105i
$541$	2.17521	+	29.0261i	0.0935194	+	1.24793i	0.824631	+	0.565672i	$0.191383\pi$
$541$	2.17521	+	29.0261i	0.0935194	+	1.24793i	−0.731111	+	0.682258i	$0.760998\pi$
$542$	6.76653	−	6.27842i	0.290647	−	0.269681i
$543$	−10.3617	−	45.3976i	−0.444663	−	1.94820i
$544$	−6.40688	−	0.965681i	−0.274693	−	0.0414032i
$545$	−0.280206	−	0.191041i	−0.0120027	−	0.00818330i
$546$	31.7463	−	9.79244i	1.35862	−	0.419078i
$547$	−2.47084	+	32.9710i	−0.105645	+	1.40974i	0.652567	+	0.757731i	$0.273692\pi$
$547$	−2.47084	+	32.9710i	−0.105645	+	1.40974i	−0.758213	+	0.652007i	$0.773927\pi$
$548$	−3.07094	−	3.85084i	−0.131184	−	0.164500i
$549$	−5.89270	−	1.81766i	−0.251494	−	0.0775757i
$550$	−1.15729	+	2.94872i	−0.0493470	+	0.125734i
$551$	−4.74796	+	20.8022i	−0.202270	+	0.886203i
$552$	5.70784	+	9.88627i	0.242942	+	0.420788i
$553$	22.4048	−	38.8063i	0.952750	−	1.65021i
$554$	3.56691	+	3.30961i	0.151543	+	0.140612i
$555$	5.63801	−	7.06984i	0.239320	−	0.300098i
$556$	5.72959	−	3.90637i	0.242989	−	0.165667i
$557$	10.1457	−	4.88592i	0.429888	−	0.207023i	−0.206411	−	0.978465i	$-0.566179\pi$
$557$	10.1457	−	4.88592i	0.429888	−	0.207023i	0.636300	+	0.771442i	$0.280464\pi$
$558$	12.0123			0.508522
$559$	24.4961	−	3.40543i	1.03607	−	0.144034i
$560$	−4.17655			−0.176491
$561$	39.0005	−	18.7817i	1.64660	−	0.792962i
$562$	3.69477	−	2.51905i	0.155855	−	0.106260i
$563$	12.8017	−	16.0528i	0.539526	−	0.676544i	−0.435100	−	0.900382i	$-0.643287\pi$
$563$	12.8017	−	16.0528i	0.539526	−	0.676544i	0.974626	+	0.223838i	$0.0718586\pi$
$564$	17.6425	+	16.3698i	0.742882	+	0.689294i
$565$	−5.93616	+	10.2817i	−0.249736	+	0.432555i
$566$	−7.19072	−	12.4547i	−0.302248	−	0.523510i
$567$	10.4529	−	45.7972i	0.438981	−	1.92330i
$568$	3.15063	−	8.02766i	0.132197	−	0.336833i
$569$	−12.5542	−	3.87246i	−0.526300	−	0.162342i	0.0202084	−	0.999796i	$-0.493567\pi$
$569$	−12.5542	−	3.87246i	−0.526300	−	0.162342i	−0.546508	+	0.837454i	$0.684043\pi$
$570$	4.30014	+	5.39221i	0.180113	+	0.225855i
$571$	−1.66933	+	22.2756i	−0.0698591	+	0.932206i	0.846639	+	0.532167i	$0.178622\pi$
$571$	−1.66933	+	22.2756i	−0.0698591	+	0.932206i	−0.916498	+	0.400038i	$0.868997\pi$
$572$	−11.4163	+	3.52147i	−0.477341	+	0.147240i
$573$	−35.0579	−	23.9021i	−1.46456	−	0.998523i
$574$	−44.0719	−	6.64277i	−1.83952	−	0.277264i
$575$	−1.20443	−	5.27693i	−0.0502280	−	0.220063i
$576$	−1.06162	+	0.985036i	−0.0442340	+	0.0410432i
$577$	2.43860	+	32.5409i	0.101520	+	1.35469i	0.782618	+	0.622502i	$0.213884\pi$
$577$	2.43860	+	32.5409i	0.101520	+	1.35469i	−0.681098	+	0.732192i	$0.738497\pi$
$578$	−9.12643	−	23.2538i	−0.379610	−	0.967229i
$579$	17.0901	−	2.57592i	0.710242	−	0.107052i
$580$	5.87875	+	2.83106i	0.244102	+	0.117553i
$581$	53.4796	+	25.7544i	2.21871	+	1.06847i
$582$	−10.5583	+	1.59140i	−0.437654	+	0.0659657i
$583$	−7.35967	−	18.7521i	−0.304806	−	0.776634i
$584$	−0.165850	−	2.21311i	−0.00686291	−	0.0915791i
$585$	−4.00394	+	3.71511i	−0.165542	+	0.153601i
$586$	1.48823	+	6.52037i	0.0614783	+	0.269354i
$587$	−19.2048	−	2.89466i	−0.792667	−	0.119475i	−0.259787	−	0.965666i	$-0.583652\pi$
$587$	−19.2048	−	2.89466i	−0.792667	−	0.119475i	−0.532880	+	0.846191i	$0.678890\pi$
$588$	18.1989	+	12.4078i	0.750512	+	0.511690i
$589$	−25.9190	+	7.99496i	−1.06797	+	0.329426i
$590$	0.974586	−	13.0049i	0.0401231	−	0.535405i
$591$	−17.9429	−	22.4996i	−0.738070	−	0.925511i
$592$	−4.09701	−	1.26376i	−0.168386	−	0.0519402i
$593$	−16.6486	+	42.4199i	−0.683675	+	1.74198i	−0.0133467	+	0.999911i	$0.504249\pi$
$593$	−16.6486	+	42.4199i	−0.683675	+	1.74198i	−0.670328	+	0.742065i	$0.733847\pi$
$594$	−2.30695	+	10.1074i	−0.0946554	+	0.414713i
$595$	−13.5304	−	23.4354i	−0.554694	−	0.960757i
$596$	−5.49053	+	9.50988i	−0.224901	+	0.389540i
$597$	−13.5290	−	12.5531i	−0.553707	−	0.513765i
$598$	12.7279	−	15.9603i	0.520484	−	0.652666i
$599$	−13.2902	+	9.06112i	−0.543024	+	0.370227i	−0.803548	−	0.595240i	$-0.797057\pi$
$599$	−13.2902	+	9.06112i	−0.543024	+	0.370227i	0.260524	+	0.965467i	$0.416105\pi$
$600$	1.90021	−	0.915095i	0.0775759	−	0.0373586i
$601$	46.2334			1.88590			0.942950	−	0.332935i	$-0.108039\pi$
$601$	46.2334			1.88590			0.942950	+	0.332935i	$0.108039\pi$
$602$	19.8615	+	18.8572i	0.809495	+	0.768560i
$603$	−6.43945			−0.262235
$604$	−20.5241	+	9.88390i	−0.835115	+	0.402170i
$605$	0.797904	−	0.544002i	0.0324394	−	0.0221168i
$606$	−18.8809	+	23.6759i	−0.766985	+	0.961769i
$607$	−0.426838	−	0.396047i	−0.0173248	−	0.0160751i	0.671463	−	0.741038i	$-0.265666\pi$
$607$	−0.426838	−	0.396047i	−0.0173248	−	0.0160751i	−0.688788	+	0.724963i	$0.741857\pi$
$608$	1.63505	−	2.83199i	0.0663100	−	0.114852i
$609$	−28.7379	−	49.7756i	−1.16452	−	2.01701i
$610$	0.947520	−	4.15136i	0.0383640	−	0.168083i
$611$	15.7235	−	40.0628i	0.636105	−	1.62077i
$612$	−8.96646	−	2.76579i	−0.362448	−	0.111800i
$613$	13.0445	+	16.3573i	0.526862	+	0.660664i	0.972050	−	0.234773i	$-0.0754347\pi$
$613$	13.0445	+	16.3573i	0.526862	+	0.660664i	−0.445188	+	0.895437i	$0.646863\pi$
$614$	−2.15510	+	28.7578i	−0.0869727	+	1.16057i
$615$	21.5070	−	6.63402i	0.867244	−	0.267509i
$616$	−10.9312	−	7.45274i	−0.440429	−	0.300279i
$617$	29.4038	+	4.43192i	1.18375	+	0.178422i	0.711271	−	0.702918i	$-0.248120\pi$
$617$	29.4038	+	4.43192i	1.18375	+	0.178422i	0.472483	+	0.881340i	$0.343358\pi$
$618$	−1.38277	−	6.05831i	−0.0556232	−	0.243701i
$619$	17.6897	−	16.4136i	0.711008	−	0.659719i	−0.239330	−	0.970938i	$-0.576928\pi$
$619$	17.6897	−	16.4136i	0.711008	−	0.659719i	0.950338	+	0.311219i	$0.100737\pi$
$620$	0.619854	+	8.27138i	0.0248939	+	0.332186i
$621$	−6.47190	−	16.4901i	−0.259709	−	0.661726i
$622$	−30.7866	+	4.64034i	−1.23443	+	0.186061i
$623$	27.3223	+	13.1577i	1.09464	+	0.527153i
$624$	7.16675	+	3.45132i	0.286899	+	0.138163i
$625$	−0.988831	+	0.149042i	−0.0395532	+	0.00596169i
$626$	−4.88052	−	12.4354i	−0.195065	−	0.497017i
$627$	1.63265	+	21.7862i	0.0652017	+	0.870056i
$628$	0.427411	−	0.396580i	0.0170556	−	0.0158253i
$629$	−6.18156	−	27.0832i	−0.246475	−	1.07988i
$630$	−5.98098	−	0.901488i	−0.238288	−	0.0359161i
$631$	−27.1055	−	18.4802i	−1.07905	−	0.735685i	−0.112887	−	0.993608i	$-0.536010\pi$
$631$	−27.1055	−	18.4802i	−1.07905	−	0.735685i	−0.966166	+	0.257922i	$0.916962\pi$
$632$	10.2522	−	3.16239i	0.407812	−	0.125793i
$633$	−1.18793	+	15.8518i	−0.0472158	+	0.630052i
$634$	−6.79533	−	8.52107i	−0.269877	−	0.338415i
$635$	11.3205	+	3.49192i	0.449241	+	0.138573i
$636$	−4.90013	+	12.4853i	−0.194303	+	0.495076i
$637$	8.76472	−	38.4007i	0.347271	−	1.52149i
$638$	10.3345	+	17.8999i	0.409146	+	0.708662i
$639$	6.24455	−	10.8159i	0.247031	−	0.427870i
$640$	−0.733052	−	0.680173i	−0.0289764	−	0.0268862i
$641$	−14.2986	+	17.9299i	−0.564760	+	0.708187i	−0.979430	−	0.201785i	$-0.935326\pi$
$641$	−14.2986	+	17.9299i	−0.564760	+	0.708187i	0.414670	+	0.909972i	$0.363897\pi$
$642$	1.92142	−	1.31000i	0.0758325	−	0.0517017i
$643$	−38.5781	+	18.5783i	−1.52137	+	0.732655i	−0.993193	−	0.116478i	$-0.962840\pi$
$643$	−38.5781	+	18.5783i	−1.52137	+	0.732655i	−0.528180	+	0.849132i	$0.677125\pi$
$644$	22.6061			0.890807
$645$	−13.1681	−	4.22777i	−0.518494	−	0.166468i
$646$	21.1878			0.833621
$647$	−36.3655	+	17.5127i	−1.42968	+	0.688496i	−0.978938	−	0.204159i	$-0.934554\pi$
$647$	−36.3655	+	17.5127i	−1.42968	+	0.688496i	−0.450740	+	0.892656i	$0.648840\pi$
$648$	9.29297	−	6.33584i	0.365062	−	0.248895i
$649$	25.7571	−	32.2984i	1.01106	−	1.26782i
$650$	−2.76474	−	2.56530i	−0.108442	−	0.100619i
$651$	36.5320	−	63.2754i	1.43180	−	2.47996i
$652$	0.0386367	+	0.0669208i	0.00151313	+	0.00262082i
$653$	6.57325	−	28.7993i	0.257231	−	1.12700i	−0.666966	−	0.745088i	$-0.732407\pi$
$653$	6.57325	−	28.7993i	0.257231	−	1.12700i	0.924197	−	0.381916i	$-0.124735\pi$
$654$	−0.261314	+	0.665818i	−0.0102182	+	0.0260355i
$655$	1.73397	+	0.534859i	0.0677518	+	0.0208987i
$656$	−6.65352	−	8.34325i	−0.259776	−	0.325749i
$657$	0.240186	−	3.20506i	0.00937055	−	0.125041i
$658$	45.5421	−	14.0479i	1.77541	−	0.547643i
$659$	25.0851	+	17.1028i	0.977179	+	0.666229i	0.942863	−	0.333182i	$-0.108122\pi$
$659$	25.0851	+	17.1028i	0.977179	+	0.666229i	0.0343161	+	0.999411i	$0.489075\pi$
$660$	6.60630	+	0.995739i	0.257150	+	0.0387591i
$661$	−8.28793	−	36.3118i	−0.322363	−	1.41236i	−0.833335	−	0.552768i	$-0.813572\pi$
$661$	−8.28793	−	36.3118i	−0.322363	−	1.41236i	0.510972	−	0.859597i	$-0.329285\pi$
$662$	5.55204	−	5.15154i	0.215786	−	0.200220i
$663$	3.85152	+	51.3949i	0.149581	+	1.99601i
$664$	5.19230	+	13.2298i	0.201500	+	0.513414i
$665$	13.5052	−	2.03558i	0.523708	−	0.0789363i
$666$	−5.59430	−	2.69407i	−0.216775	−	0.104393i
$667$	−31.8196	−	15.3235i	−1.23206	−	0.593328i
$668$	2.96882	−	0.447478i	0.114867	−	0.0173135i
$669$	8.19747	+	20.8868i	0.316932	+	0.807531i
$670$	−0.332285	−	4.43404i	−0.0128373	−	0.171302i
$671$	9.88771	−	9.17445i	0.381711	−	0.354176i
$672$	1.96011	+	8.58782i	0.0756130	+	0.331282i
$673$	12.0659	+	1.81864i	0.465106	+	0.0701034i	0.377415	−	0.926044i	$-0.376813\pi$
$673$	12.0659	+	1.81864i	0.465106	+	0.0701034i	0.0876909	+	0.996148i	$0.472051\pi$
$674$	1.67038	+	1.13885i	0.0643408	+	0.0438668i
$675$	−3.12743	+	0.964686i	−0.120375	+	0.0371308i
$676$	0.0915110	−	1.22113i	0.00351966	−	0.0469665i
$677$	−20.1701	−	25.2925i	−0.775201	−	0.972071i	0.224796	−	0.974406i	$-0.427828\pi$
$677$	−20.1701	−	25.2925i	−0.775201	−	0.972071i	−0.999997	+	0.00233442i	$0.999257\pi$
$678$	23.9272	+	7.38056i	0.918919	+	0.283449i
$679$	−7.72490	+	19.6827i	−0.296455	+	0.755354i
$680$	1.44177	−	6.31679i	0.0552892	−	0.242238i
$681$	−13.3477	−	23.1189i	−0.511484	−	0.885917i
$682$	−13.1373	+	22.7545i	−0.503055	+	0.871316i
$683$	22.8584	+	21.2095i	0.874652	+	0.811559i	0.983200	−	0.182533i	$-0.0584295\pi$
$683$	22.8584	+	21.2095i	0.874652	+	0.811559i	−0.108548	+	0.994091i	$0.534620\pi$
$684$	2.95273	−	3.70260i	0.112900	−	0.141573i
$685$	4.06956	−	2.77458i	0.155490	−	0.106011i
$686$	12.9578	−	6.24016i	0.494732	−	0.238250i
$687$	22.4195			0.855358
$688$	0.415032	+	6.54429i	0.0158230	+	0.249499i
$689$	23.9848			0.913747
$690$	−10.2852	+	4.95308i	−0.391550	+	0.188561i
$691$	−0.114903	+	0.0783396i	−0.00437112	+	0.00298018i	−0.565504	−	0.824746i	$-0.691318\pi$
$691$	−0.114903	+	0.0783396i	−0.00437112	+	0.00298018i	0.561133	+	0.827726i	$0.310366\pi$
$692$	−0.0818793	+	0.102673i	−0.00311258	+	0.00390306i
$693$	−14.0452	−	13.0321i	−0.533534	−	0.495047i
$694$	−2.18050	+	3.77674i	−0.0827707	+	0.143363i
$695$	3.46728	+	6.00550i	0.131521	+	0.227801i
$696$	3.06224	−	13.4165i	0.116074	−	0.508553i
$697$	25.2607	−	64.3631i	0.956816	−	2.43793i
$698$	20.5822	+	6.34876i	0.779047	+	0.240304i
$699$	−15.7417	−	19.7395i	−0.595406	−	0.746616i
$700$	0.312114	−	4.16487i	0.0117968	−	0.157417i
$701$	29.0031	−	8.94626i	1.09543	−	0.337896i	0.306184	−	0.951972i	$-0.400948\pi$
$701$	29.0031	−	8.94626i	1.09543	−	0.337896i	0.789246	+	0.614077i	$0.210471\pi$
$702$	−10.1988	−	6.95343i	−0.384929	−	0.262440i
$703$	13.8639	+	2.08965i	0.522888	+	0.0788126i
$704$	−0.704879	−	3.08827i	−0.0265661	−	0.116394i
$705$	−17.6425	+	16.3698i	−0.664454	+	0.616523i
$706$	0.793821	+	10.5928i	0.0298759	+	0.398666i
$707$	21.9087	+	55.8225i	0.823962	+	2.09942i
$708$	−27.1982	+	4.09946i	−1.02217	+	0.154067i
$709$	−25.9401	−	12.4921i	−0.974202	−	0.469151i	−0.122095	−	0.992518i	$-0.538961\pi$
$709$	−25.9401	−	12.4921i	−0.974202	−	0.469151i	−0.852107	+	0.523367i	$0.824676\pi$
$710$	7.76977	+	3.74172i	0.291594	+	0.140424i
$711$	15.3642	−	2.31578i	0.576202	−	0.0868484i
$712$	2.65270	+	6.75898i	0.0994142	+	0.253303i
$713$	−3.35505	−	44.7700i	−0.125647	−	1.67665i
$714$	−41.8378	+	38.8198i	−1.56574	+	1.45280i
$715$	−2.65848	−	11.6476i	−0.0994216	−	0.435594i
$716$	−5.12885	−	0.773050i	−0.191674	−	0.0288902i
$717$	−7.56645	−	5.15872i	−0.282574	−	0.192656i
$718$	15.0730	−	4.64941i	0.562520	−	0.173515i
$719$	0.766335	−	10.2260i	0.0285795	−	0.381367i	−0.964513	−	0.264035i	$-0.914947\pi$
$719$	0.766335	−	10.2260i	0.0285795	−	0.381367i	0.993093	−	0.117332i	$-0.0374342\pi$
$720$	−0.902947	−	1.13226i	−0.0336509	−	0.0421968i
$721$	−11.7589	−	3.62715i	−0.437925	−	0.135082i
$722$	3.03469	−	7.73226i	0.112939	−	0.287765i
$723$	−1.33669	+	5.85644i	−0.0497122	+	0.217803i
$724$	−11.0392	−	19.1204i	−0.410268	−	0.710605i
$725$	−3.26246	+	5.65075i	−0.121165	+	0.209864i
$726$	−1.49304	−	1.38534i	−0.0554121	−	0.0514149i
$727$	17.4642	−	21.8995i	0.647713	−	0.812206i	−0.344231	−	0.938885i	$-0.611860\pi$
$727$	17.4642	−	21.8995i	0.647713	−	0.812206i	0.991944	+	0.126679i	$0.0404318\pi$
$728$	13.0149	−	8.87344i	0.482366	−	0.328871i
$729$	−3.98182	+	1.91754i	−0.147475	+	0.0710202i
$730$	2.21932			0.0821405
$731$	−35.3767	+	23.5299i	−1.30845	+	0.870283i
$732$	−8.98070			−0.331936
$733$	22.7650	−	10.9630i	0.840844	−	0.404929i	0.0366729	−	0.999327i	$-0.488324\pi$
$733$	22.7650	−	10.9630i	0.840844	−	0.404929i	0.804171	+	0.594398i	$0.202610\pi$
$734$	−6.59274	+	4.49485i	−0.243343	+	0.165908i
$735$	−13.7331	+	17.2208i	−0.506555	+	0.635199i
$736$	3.96775	+	3.68153i	0.146253	+	0.135703i
$737$	7.04253	−	12.1980i	0.259415	−	0.449320i
$738$	−7.72725	−	13.3840i	−0.284444	−	0.492672i
$739$	11.8966	−	52.1225i	0.437624	−	1.91736i	0.0415557	−	0.999136i	$-0.486769\pi$
$739$	11.8966	−	52.1225i	0.437624	−	1.91736i	0.396069	−	0.918221i	$-0.370374\pi$
$740$	1.56640	−	3.99111i	0.0575819	−	0.146716i
$741$	−24.8563	−	7.66716i	−0.913120	−	0.281660i
$742$	16.5601	+	20.7657i	0.607940	+	0.762333i
$743$	−0.569494	+	7.59937i	−0.0208927	+	0.278794i	0.976966	+	0.213393i	$0.0684516\pi$
$743$	−0.569494	+	7.59937i	−0.0208927	+	0.278794i	−0.997859	+	0.0654005i	$0.979167\pi$
$744$	16.7167	−	5.15642i	0.612864	−	0.189043i
$745$	−9.07298	−	6.18585i	−0.332408	−	0.226632i
$746$	1.97709	+	0.297998i	0.0723863	+	0.0109105i
$747$	4.58000	+	20.0663i	0.167573	+	0.734187i
$748$	15.0454	−	13.9600i	0.550113	−	0.510430i
$749$	−0.344142	−	4.59225i	−0.0125747	−	0.167797i
$750$	0.770533	+	1.96329i	0.0281359	+	0.0716891i
$751$	14.6804	−	2.21272i	0.535697	−	0.0807433i	0.124378	−	0.992235i	$-0.460306\pi$
$751$	14.6804	−	2.21272i	0.535697	−	0.0807433i	0.411319	+	0.911492i	$0.365068\pi$
$752$	10.2811	+	4.95114i	0.374915	+	0.180549i
$753$	−45.4683	−	21.8964i	−1.65696	−	0.797948i
$754$	−24.3342	+	3.66779i	−0.886199	+	0.133573i
$755$	−8.32249	−	21.2054i	−0.302886	−	0.771742i
$756$	−1.02150	−	13.6309i	−0.0371515	−	0.495752i
$757$	−6.81200	+	6.32062i	−0.247587	+	0.229727i	−0.794197	−	0.607660i	$-0.792108\pi$
$757$	−6.81200	+	6.32062i	−0.247587	+	0.229727i	0.546611	+	0.837387i	$0.315918\pi$
$758$	5.60860	+	24.5729i	0.203714	+	0.892527i
$759$	−35.7575	−	5.38958i	−1.29792	−	0.195629i
$760$	2.70188	+	1.84211i	0.0980076	+	0.0668204i
$761$	−16.9686	+	5.23411i	−0.615111	+	0.189737i	−0.586626	−	0.809858i	$-0.699544\pi$
$761$	−16.9686	+	5.23411i	−0.615111	+	0.189737i	−0.0284843	+	0.999594i	$0.509068\pi$
$762$	1.86720	−	24.9161i	0.0676416	−	0.902614i
$763$	0.883117	+	1.10739i	0.0319710	+	0.0400904i
$764$	−19.2243	−	5.92992i	−0.695512	−	0.214537i
$765$	3.42812	−	8.73470i	0.123944	−	0.315804i
$766$	−1.18928	+	5.21056i	−0.0429703	+	0.188265i
$767$	24.5931	+	42.5966i	0.888007	+	1.53807i
$768$	−1.05454	+	1.82652i	−0.0380524	+	0.0659087i
$769$	−8.46115	−	7.85080i	−0.305117	−	0.283107i	0.512722	−	0.858555i	$-0.328637\pi$
$769$	−8.46115	−	7.85080i	−0.305117	−	0.283107i	−0.817839	+	0.575448i	$0.804828\pi$
$770$	8.24879	−	10.3437i	0.297266	−	0.372759i
$771$	21.2645	−	14.4979i	0.765823	−	0.522129i
$772$	7.38313	−	3.55553i	0.265725	−	0.127966i
$773$	25.1044			0.902943			0.451472	−	0.892285i	$-0.350899\pi$
$773$	25.1044			0.902943			0.451472	+	0.892285i	$0.350899\pi$
$774$	−0.818211	+	9.46127i	−0.0294100	+	0.340078i
$775$	−8.29457			−0.297950
$776$	−4.56128	+	2.19660i	−0.163741	+	0.0788533i
$777$	−31.2046	+	21.2750i	−1.11946	+	0.763235i
$778$	8.42619	−	10.5661i	0.302094	−	0.378813i
$779$	25.5810	+	23.7357i	0.916535	+	0.850420i
$780$	−3.97724	+	6.88879i	−0.142408	+	0.246658i
$781$	13.6588	+	23.6577i	0.488749	+	0.846539i
$782$	−7.80377	+	34.1905i	−0.279062	+	1.22265i
$783$	−7.80186	+	19.8788i	−0.278816	+	0.710411i
$784$	9.97956	+	3.07829i	0.356413	+	0.109939i
$785$	0.363530	+	0.455853i	0.0129750	+	0.0162701i
$786$	0.286000	−	3.81641i	0.0102013	−	0.136127i
$787$	−13.1608	+	4.05957i	−0.469131	+	0.144708i	−0.520303	−	0.853982i	$-0.674181\pi$
$787$	−13.1608	+	4.05957i	−0.469131	+	0.144708i	0.0511711	+	0.998690i	$0.483705\pi$
$788$	−11.2739	−	7.68643i	−0.401617	−	0.273818i
$789$	66.9416	+	10.0898i	2.38318	+	0.359207i
$790$	2.38740	+	10.4599i	0.0849399	+	0.372146i
$791$	36.3486	−	33.7265i	1.29241	−	1.19918i
$792$	−0.342825	−	4.57468i	−0.0121817	−	0.162554i
$793$	5.86726	+	14.9495i	0.208352	+	0.530873i
$794$	3.29833	−	0.497143i	0.117053	−	0.0176429i
$795$	−12.0842	−	5.81946i	−0.428583	−	0.206395i
$796$	−7.88405	−	3.79676i	−0.279443	−	0.134573i
$797$	52.5955	−	7.92750i	1.86303	−	0.280806i	0.881509	−	0.472168i	$-0.156528\pi$
$797$	52.5955	−	7.92750i	1.86303	−	0.280806i	0.981520	+	0.191361i	$0.0612902\pi$
$798$	−10.5237	−	26.8140i	−0.372536	−	0.949206i
$799$	5.52524	+	73.7293i	0.195469	+	2.60835i
$800$	0.733052	−	0.680173i	0.0259173	−	0.0240477i
$801$	2.33988	+	10.2517i	0.0826757	+	0.362226i
$802$	−2.15554	−	0.324896i	−0.0761148	−	0.0114725i
$803$	5.80855	+	3.96020i	0.204979	+	0.139753i
$804$	−8.96132	+	2.76420i	−0.316042	+	0.0974859i
$805$	−1.68936	+	22.5429i	−0.0595421	+	0.794534i
$806$	−19.5048	−	24.4583i	−0.687029	−	0.861507i
$807$	−8.69464	−	2.68194i	−0.306066	−	0.0944088i
$808$	−5.24565	+	13.3657i	−0.184541	+	0.470204i
$809$	7.76375	−	34.0152i	0.272959	−	1.19591i	−0.633542	−	0.773708i	$-0.718400\pi$
$809$	7.76375	−	34.0152i	0.272959	−	1.19591i	0.906501	−	0.422203i	$-0.138743\pi$
$810$	5.62366	+	9.74046i	0.197595	+	0.342245i
$811$	−7.66568	+	13.2773i	−0.269178	+	0.466231i	−0.968650	−	0.248430i	$-0.920085\pi$
$811$	−7.66568	+	13.2773i	−0.269178	+	0.466231i	0.699472	+	0.714660i	$0.253419\pi$
$812$	−19.9769	−	18.5358i	−0.701051	−	0.650480i
$813$	12.1382	−	15.2208i	0.425704	−	0.533816i
$814$	11.2215	−	7.65071i	0.393315	−	0.268157i
$815$	−0.0696210	+	0.0335277i	−0.00243872	+	0.00117442i
$816$	−13.6652			−0.478379
$817$	−4.53161	−	20.9592i	−0.158541	−	0.733269i
$818$	12.9407			0.452462
$819$	20.5532	−	9.89790i	0.718187	−	0.345861i
$820$	8.81714	−	6.01142i	0.307908	−	0.209928i
$821$	−11.1749	+	14.0129i	−0.390007	+	0.489053i	−0.937612	−	0.347684i	$-0.886968\pi$
$821$	−11.1749	+	14.0129i	−0.390007	+	0.489053i	0.547605	+	0.836737i	$0.315540\pi$
$822$	−7.61500	−	7.06568i	−0.265604	−	0.246444i
$823$	−16.8032	+	29.1040i	−0.585723	+	1.01450i	0.409062	+	0.912507i	$0.365856\pi$
$823$	−16.8032	+	29.1040i	−0.585723	+	1.01450i	−0.994785	+	0.101995i	$0.967477\pi$
$824$	−1.47318	−	2.55162i	−0.0513207	−	0.0888901i
$825$	−1.48664	+	6.51342i	−0.0517583	+	0.226768i
$826$	−19.8994	+	50.7029i	−0.692389	+	1.76418i
$827$	9.52734	+	2.93879i	0.331298	+	0.102192i	0.455942	−	0.890010i	$-0.349303\pi$
$827$	9.52734	+	2.93879i	0.331298	+	0.102192i	−0.124644	+	0.992202i	$0.539779\pi$
$828$	4.88733	+	6.12851i	0.169846	+	0.212981i
$829$	−3.74857	+	50.0213i	−0.130193	+	1.73731i	0.424652	+	0.905357i	$0.360396\pi$
$829$	−3.74857	+	50.0213i	−0.130193	+	1.73731i	−0.554845	+	0.831953i	$0.687223\pi$
$830$	−13.5808	+	4.18912i	−0.471396	+	0.145406i
$831$	8.47921	+	5.78103i	0.294141	+	0.200542i
$832$	3.72942	+	0.562120i	0.129294	+	0.0194880i
$833$	15.0572	+	65.9697i	0.521699	+	2.28571i
$834$	10.7213	−	9.94788i	0.371247	−	0.344467i
$835$	0.224367	+	2.99396i	0.00776452	+	0.103610i
$836$	3.78445	+	9.64262i	0.130888	+	0.333497i
$837$	−26.8436	+	4.04602i	−0.927850	+	0.139851i
$838$	−4.60644	−	2.21835i	−0.159127	−	0.0766315i
$839$	−16.0078	−	7.70893i	−0.552649	−	0.266142i	0.136649	−	0.990620i	$-0.456367\pi$
$839$	−16.0078	−	7.70893i	−0.552649	−	0.266142i	−0.689298	+	0.724478i	$0.742081\pi$
$840$	−8.71028	+	1.31286i	−0.300533	+	0.0452981i
$841$	4.95937	+	12.6363i	0.171013	+	0.435733i
$842$	2.66084	+	35.5065i	0.0916987	+	1.22363i
$843$	6.91369	−	6.41497i	0.238120	−	0.220943i
$844$	1.67715	+	7.34808i	0.0577299	+	0.252931i
$845$	1.21088	+	0.182510i	0.0416554	+	0.00627855i
$846$	13.6543	+	9.30936i	0.469445	+	0.320062i
$847$	−3.85413	+	1.18884i	−0.132429	+	0.0408491i
$848$	−0.475239	+	6.34162i	−0.0163198	+	0.217772i
$849$	−18.9114	−	23.7142i	−0.649039	−	0.813869i
$850$	6.19139	+	1.90979i	0.212363	+	0.0655053i
$851$	−8.47834	+	21.6025i	−0.290634	+	0.740523i
$852$	4.04727	−	17.7322i	0.138657	−	0.607497i
$853$	−3.08171	−	5.33769i	−0.105516	−	0.182759i	0.808433	−	0.588588i	$-0.200316\pi$
$853$	−3.08171	−	5.33769i	−0.105516	−	0.182759i	−0.913949	+	0.405829i	$0.866983\pi$
$854$	−8.89211	+	15.4016i	−0.304282	+	0.527031i
$855$	3.47159	+	3.22117i	0.118726	+	0.110162i
$856$	0.687470	−	0.862060i	0.0234972	−	0.0294646i
$857$	−37.7603	+	25.7446i	−1.28987	+	0.879417i	−0.997050	−	0.0767509i	$-0.975545\pi$
$857$	−37.7603	+	25.7446i	−1.28987	+	0.879417i	−0.292818	+	0.956168i	$0.594593\pi$
$858$	−22.7021	+	10.9327i	−0.775036	+	0.373238i
$859$	−14.8938			−0.508171			−0.254086	−	0.967182i	$-0.581775\pi$
$859$	−14.8938			−0.508171			−0.254086	+	0.967182i	$0.581775\pi$
$860$	−6.55701	−	0.0751837i	−0.223592	−	0.00256374i
$861$	−94.0010			−3.20354
$862$	26.5250	−	12.7738i	0.903445	−	0.435076i
$863$	0.773192	−	0.527154i	0.0263198	−	0.0179445i	−0.550089	−	0.835106i	$-0.685406\pi$
$863$	0.773192	−	0.527154i	0.0263198	−	0.0179445i	0.576408	+	0.817162i	$0.304454\pi$
$864$	2.04058	−	2.55881i	0.0694220	−	0.0870524i
$865$	−0.0962674	−	0.0893231i	−0.00327319	−	0.00303708i
$866$	2.71900	−	4.70945i	0.0923954	−	0.160033i
$867$	−26.3430	−	45.6274i	−0.894656	−	1.54959i
$868$	7.70872	−	33.7741i	0.261651	−	1.14637i
$869$	−12.4164	+	31.6365i	−0.421198	+	1.07320i
$870$	13.1502	+	4.05630i	0.445833	+	0.137521i
$871$	10.4560	+	13.1114i	0.354287	+	0.444262i
$872$	−0.0253435	+	0.338186i	−0.000858241	+	0.0114524i
$873$	−7.00606	+	2.16108i	−0.237119	+	0.0731416i
$874$	−14.6243	−	9.97069i	−0.494675	−	0.337264i
$875$	4.12990	+	0.622482i	0.139616	+	0.0210437i
$876$	−1.04156	−	4.56336i	−0.0351909	−	0.154182i
$877$	−15.5059	+	14.3874i	−0.523596	+	0.485826i	−0.897116	−	0.441796i	$-0.854342\pi$
$877$	−15.5059	+	14.3874i	−0.523596	+	0.485826i	0.373519	+	0.927622i	$0.378151\pi$
$878$	0.524598	+	7.00028i	0.0177043	+	0.236248i
$879$	5.15337	+	13.1306i	0.173819	+	0.442883i
$880$	3.13231	−	0.472120i	0.105590	−	0.0159152i
$881$	11.7308	+	5.64923i	0.395219	+	0.190327i	0.620929	−	0.783867i	$-0.286756\pi$
$881$	11.7308	+	5.64923i	0.395219	+	0.190327i	−0.225709	+	0.974195i	$0.572470\pi$
$882$	13.6267	+	6.56227i	0.458835	+	0.220963i
$883$	−9.75106	+	1.46974i	−0.328149	+	0.0494605i	−0.311051	−	0.950393i	$-0.600681\pi$
$883$	−9.75106	+	1.46974i	−0.328149	+	0.0494605i	−0.0170984	+	0.999854i	$0.505443\pi$
$884$	8.92775	+	22.7475i	0.300273	+	0.765082i
$885$	−2.05548	−	27.4285i	−0.0690942	−	0.921997i
$886$	−9.13694	+	8.47784i	−0.306961	+	0.284819i
$887$	−10.1331	−	44.3958i	−0.340235	−	1.49066i	−0.798579	−	0.601890i	$-0.794414\pi$
$887$	−10.1331	−	44.3958i	−0.340235	−	1.49066i	0.458344	−	0.888775i	$-0.348443\pi$
$888$	−8.94166	−	1.34774i	−0.300062	−	0.0452271i
$889$	−40.8814	−	27.8725i	−1.37112	−	0.934812i
$890$	−6.93831	+	2.14019i	−0.232573	+	0.0717392i
$891$	−2.66249	+	35.5285i	−0.0891968	+	1.19025i
$892$	6.63312	+	8.31767i	0.222093	+	0.278496i
$893$	−35.6579	−	10.9990i	−1.19325	−	0.368068i
$894$	−8.46127	+	21.5590i	−0.282987	+	0.721040i
$895$	1.15417	−	5.05674i	0.0385796	−	0.169028i
$896$	2.08827	+	3.61700i	0.0697643	+	0.120835i
$897$	21.5274	−	37.2865i	0.718778	−	1.24496i
$898$	4.32278	+	4.01095i	0.144253	+	0.133847i
$899$	−33.7442	+	42.3138i	−1.12543	+	1.41125i
$900$	1.19657	−	0.815808i	0.0398857	−	0.0271936i
$901$	−37.1236	+	17.8778i	−1.23677	+	0.595596i
$902$	33.8038			1.12554
$903$	47.3492	+	33.0837i	1.57568	+	1.10096i
$904$	11.8723			0.394867
$905$	19.8919	−	9.57945i	0.661230	−	0.318432i
$906$	−39.6966	+	27.0647i	−1.31883	+	0.899164i
$907$	31.8382	−	39.9239i	1.05717	−	1.32565i	0.113950	−	0.993487i	$-0.463650\pi$
$907$	31.8382	−	39.9239i	1.05717	−	1.32565i	0.943221	−	0.332164i	$-0.107779\pi$
$908$	−9.27850	−	8.60919i	−0.307918	−	0.285706i
$909$	−10.3969	+	18.0080i	−0.344844	+	0.597287i
$910$	7.87602	+	13.6417i	0.261087	+	0.452217i
$911$	−7.31444	+	32.0466i	−0.242338	+	1.06175i	0.696544	+	0.717514i	$0.254720\pi$
$911$	−7.31444	+	32.0466i	−0.242338	+	1.06175i	−0.938882	+	0.344239i	$0.888137\pi$
$912$	2.51972	−	6.42014i	0.0834362	−	0.212592i
$913$	−43.0198	−	13.2699i	−1.42375	−	0.439168i
$914$	20.7476	+	26.0167i	0.686270	+	0.860555i
$915$	0.671129	−	8.95559i	0.0221868	−	0.296063i
$916$	10.1577	−	3.13325i	0.335621	−	0.103525i
$917$	−6.26182	−	4.26924i	−0.206784	−	0.140983i
$918$	20.9687	+	3.16052i	0.692069	+	0.104313i
$919$	−4.02613	−	17.6396i	−0.132810	−	0.581877i	−0.996910	−	0.0785568i	$-0.974969\pi$
$919$	−4.02613	−	17.6396i	−0.132810	−	0.581877i	0.864100	−	0.503320i	$-0.167888\pi$
$920$	−3.96775	+	3.68153i	−0.130813	+	0.121376i
$921$	4.54527	+	60.6525i	0.149772	+	1.99857i
$922$	−8.16707	−	20.8094i	−0.268968	−	0.685320i
$923$	−32.1617	+	4.84760i	−1.05862	+	0.159561i
$924$	−25.1399	−	12.1067i	−0.827042	−	0.398282i
$925$	3.86290	+	1.86027i	0.127011	+	0.0611654i
$926$	23.3088	−	3.51323i	0.765973	−	0.115452i
$927$	−1.55890	−	3.97201i	−0.0512009	−	0.130458i
$928$	−0.487608	−	6.50668i	−0.0160065	−	0.213592i
$929$	9.82026	−	9.11187i	0.322192	−	0.298951i	−0.502449	−	0.864607i	$-0.667567\pi$
$929$	9.82026	−	9.11187i	0.322192	−	0.298951i	0.824641	+	0.565656i	$0.191377\pi$
$930$	3.89276	+	17.0553i	0.127649	+	0.559265i
$931$	−33.7700	−	5.09000i	−1.10677	−	0.166818i
$932$	−9.89089	−	6.74349i	−0.323987	−	0.220890i
$933$	−62.7476	+	19.3551i	−2.05426	+	0.633656i
$934$	−1.28840	+	17.1926i	−0.0421579	+	0.562558i
$935$	12.7967	+	16.0465i	0.418496	+	0.524777i
$936$	5.21935	+	1.60996i	0.170600	+	0.0526230i
$937$	12.9935	−	33.1070i	0.424480	−	1.08156i	−0.545443	−	0.838148i	$-0.683639\pi$
$937$	12.9935	−	33.1070i	0.424480	−	1.08156i	0.969924	−	0.243410i	$-0.0782660\pi$
$938$	−4.13241	+	18.1053i	−0.134928	+	0.591159i
$939$	−14.0874	−	24.4001i	−0.459724	−	0.796266i
$940$	−5.70561	+	9.88240i	−0.186096	+	0.322328i
$941$	36.1259	+	33.5199i	1.17767	+	1.09272i	0.993961	+	0.109737i	$0.0350009\pi$
$941$	36.1259	+	33.5199i	1.17767	+	1.09272i	0.183709	+	0.982981i	$0.441190\pi$
$942$	0.766715	−	0.961430i	0.0249809	−	0.0313251i
$943$	−47.7240	+	32.5377i	−1.55411	+	1.05957i
$944$	−11.7499	+	5.65846i	−0.382427	+	0.184167i
$945$	13.6692			0.444658
$946$	−17.0273	−	11.8973i	−0.553606	−	0.386814i
$947$	−2.61191			−0.0848756			−0.0424378	−	0.999099i	$-0.513512\pi$
$947$	−2.61191			−0.0848756			−0.0424378	+	0.999099i	$0.513512\pi$
$948$	20.3872	−	9.81795i	0.662145	−	0.318872i
$949$	−6.91582	+	4.71513i	−0.224497	+	0.153060i
$950$	−2.03887	+	2.55667i	−0.0661498	+	0.0829492i
$951$	−16.8503	−	15.6348i	−0.546410	−	0.506994i
$952$	−13.5304	+	23.4354i	−0.438524	+	0.759545i
$953$	21.4129	+	37.0883i	0.693633	+	1.20141i	0.970640	+	0.240539i	$0.0773242\pi$
$953$	21.4129	+	37.0883i	0.693633	+	1.20141i	−0.277007	+	0.960868i	$0.589343\pi$
$954$	−2.04937	+	8.97887i	−0.0663508	+	0.290702i
$955$	7.34997	−	18.7274i	0.237840	−	0.606005i
$956$	−4.14914	−	1.27984i	−0.134193	−	0.0413929i
$957$	27.1795	+	34.0820i	0.878588	+	1.10171i
$958$	2.71047	−	36.1687i	0.0875713	−	1.16856i
$959$	−19.6573	+	6.06347i	−0.634766	+	0.195800i
$960$	−1.74260	−	1.18809i	−0.0562423	−	0.0383453i
$961$	−37.3777	−	5.63378i	−1.20573	−	0.181735i
$962$	3.59827	+	15.7650i	0.116013	+	0.508285i
$963$	1.17056	−	1.08612i	0.0377206	−	0.0349996i
$964$	0.212845	+	2.84022i	0.00685528	+	0.0914773i
$965$	2.99384	+	7.62819i	0.0963752	+	0.245560i
$966$	47.1456	−	7.10606i	1.51689	−	0.228634i
$967$	28.7364	+	13.8387i	0.924099	+	0.445023i	0.834533	−	0.550958i	$-0.185738\pi$
$967$	28.7364	+	13.8387i	0.924099	+	0.445023i	0.0895664	+	0.995981i	$0.471452\pi$
$968$	−0.870071	−	0.419004i	−0.0279651	−	0.0134673i
$969$	44.1876	−	6.66020i	1.41951	−	0.213957i
$970$	−1.84959	−	4.71268i	−0.0593868	−	0.151315i
$971$	−3.89694	−	52.0011i	−0.125059	−	1.66879i	−0.608603	−	0.793475i	$-0.708270\pi$
$971$	−3.89694	−	52.0011i	−0.125059	−	1.66879i	0.483544	−	0.875320i	$-0.339349\pi$
$972$	10.1916	−	9.45642i	0.326896	−	0.303315i
$973$	−6.44476	−	28.2363i	−0.206609	−	0.905215i
$974$	42.8393	+	6.45699i	1.37266	+	0.206895i
$975$	−6.57231	−	4.48092i	−0.210482	−	0.143504i
$976$	−4.06894	+	1.25510i	−0.130244	+	0.0401748i
$977$	1.05127	−	14.0282i	0.0336331	−	0.448802i	−0.954811	−	0.297214i	$-0.903942\pi$
$977$	1.05127	−	14.0282i	0.0336331	−	0.448802i	0.988444	−	0.151588i	$-0.0484386\pi$
$978$	0.101614	+	0.127420i	0.00324925	+	0.00407443i
$979$	−21.9785	−	6.77946i	−0.702435	−	0.216672i
$980$	−3.81545	+	9.72162i	−0.121880	+	0.310546i
$981$	−0.109289	+	0.478825i	−0.00348932	+	0.0152877i
$982$	5.13946	+	8.90180i	0.164007	+	0.284068i
$983$	3.83028	−	6.63424i	0.122167	−	0.211600i	−0.798455	−	0.602055i	$-0.794349\pi$
$983$	3.83028	−	6.63424i	0.122167	−	0.211600i	0.920622	+	0.390455i	$0.127682\pi$
$984$	−16.4987	−	15.3086i	−0.525959	−	0.488019i
$985$	8.50743	−	10.6680i	0.271069	−	0.339910i
$986$	34.9305	−	23.8152i	1.11241	−	0.758432i
$987$	90.5632	−	43.6129i	2.88266	−	1.38821i
$988$	−12.3333			−0.392375
$989$	35.4907	+	0.406942i	1.12854	+	0.0129400i
$990$	4.58750			0.145800
$991$	18.5320	−	8.92456i	0.588689	−	0.283498i	−0.115731	−	0.993281i	$-0.536921\pi$
$991$	18.5320	−	8.92456i	0.588689	−	0.283498i	0.704421	+	0.709783i	$0.251207\pi$
$992$	6.85329	−	4.67250i	0.217592	−	0.148352i
$993$	9.95956	−	12.4889i	0.316057	−	0.396323i
$994$	−26.4028	−	24.4982i	−0.837447	−	0.777037i
$995$	4.37532	−	7.57827i	0.138707	−	0.240247i
$996$	14.9873	+	25.9588i	0.474892	+	0.822536i
$997$	−6.16943	+	27.0300i	−0.195388	+	0.856050i	0.778251	+	0.627954i	$0.216107\pi$
$997$	−6.16943	+	27.0300i	−0.195388	+	0.856050i	−0.973639	+	0.228096i	$0.926750\pi$
$998$	−3.19877	+	8.15034i	−0.101255	+	0.257994i
$999$	13.4088	+	4.13608i	0.424237	+	0.130860i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.d.31.4	✓	60
43.25	even	21	inner	430.2.q.d.111.4	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.d.31.4	✓	60	1.1	even	1	trivial
430.2.q.d.111.4	yes	60	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)

\(f(q)\)	\(=\)	\(q+(0.900969 - 0.433884i) q^{2} +(1.74260 - 1.18809i) q^{3} +(0.623490 - 0.781831i) q^{4} +(0.733052 + 0.680173i) q^{5} +(1.05454 - 1.82652i) q^{6} +(-2.08827 - 3.61700i) q^{7} +(0.222521 - 0.974928i) q^{8} +(0.529092 - 1.34811i) q^{9} +O(q^{10})\)	\(q+(0.900969 - 0.433884i) q^{2} +(1.74260 - 1.18809i) q^{3} +(0.623490 - 0.781831i) q^{4} +(0.733052 + 0.680173i) q^{5} +(1.05454 - 1.82652i) q^{6} +(-2.08827 - 3.61700i) q^{7} +(0.222521 - 0.974928i) q^{8} +(0.529092 - 1.34811i) q^{9} +(0.955573 + 0.294755i) q^{10} +(1.97503 + 2.47660i) q^{11} +(0.157612 - 2.10318i) q^{12} +(-3.60399 + 1.11168i) q^{13} +(-3.45082 - 2.35273i) q^{14} +(2.08552 + 0.314342i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(4.74962 - 4.40700i) q^{17} +(-0.108225 - 1.44417i) q^{18} +(1.19470 + 3.04405i) q^{19} +(0.988831 - 0.149042i) q^{20} +(-7.93633 - 3.82194i) q^{21} +(2.85399 + 1.37441i) q^{22} +(-5.35218 + 0.806712i) q^{23} +(-0.770533 - 1.96329i) q^{24} +(0.0747301 + 0.997204i) q^{25} +(-2.76474 + 2.56530i) q^{26} +(0.728275 + 3.19078i) q^{27} +(-4.12990 - 0.622482i) q^{28} +(5.39114 + 3.67562i) q^{29} +(2.01538 - 0.621662i) q^{30} +(-0.619854 + 8.27138i) q^{31} +(-0.623490 - 0.781831i) q^{32} +(6.38411 + 1.96924i) q^{33} +(2.36713 - 6.03136i) q^{34} +(0.929369 - 4.07183i) q^{35} +(-0.724107 - 1.25419i) q^{36} +(2.14375 - 3.71308i) q^{37} +(2.39715 + 2.22423i) q^{38} +(-4.95954 + 6.21907i) q^{39} +(0.826239 - 0.563320i) q^{40} +(9.61462 - 4.63016i) q^{41} -8.80867 q^{42} +(-6.47257 - 1.05162i) q^{43} +3.16770 q^{44} +(1.30480 - 0.628357i) q^{45} +(-4.47213 + 3.04905i) q^{46} +(-7.11477 + 8.92164i) q^{47} +(-1.54606 - 1.43454i) q^{48} +(-5.22177 + 9.04437i) q^{49} +(0.500000 + 0.866025i) q^{50} +(3.04080 - 13.3226i) q^{51} +(-1.37790 + 3.51083i) q^{52} +(-6.07687 - 1.87447i) q^{53} +(2.04058 + 2.55881i) q^{54} +(-0.236722 + 3.15884i) q^{55} +(-3.99099 + 1.23106i) q^{56} +(5.69848 + 3.88516i) q^{57} +(6.45205 + 0.972489i) q^{58} +(-2.90199 - 12.7144i) q^{59} +(1.54606 - 1.43454i) q^{60} +(-0.318209 - 4.24621i) q^{61} +(3.03035 + 7.72120i) q^{62} +(-5.98098 + 0.901488i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(-3.39804 - 1.63641i) q^{65} +(6.60630 - 0.995739i) q^{66} +(-1.62448 - 4.13910i) q^{67} +(-0.484194 - 6.46113i) q^{68} +(-8.36829 + 7.76464i) q^{69} +(-0.929369 - 4.07183i) q^{70} +(8.52747 + 1.28531i) q^{71} +(-1.19657 - 0.815808i) q^{72} +(2.12072 - 0.654155i) q^{73} +(0.320405 - 4.27550i) q^{74} +(1.31499 + 1.64894i) q^{75} +(3.12482 + 0.963878i) q^{76} +(4.83347 - 12.3155i) q^{77} +(-1.77004 + 7.75505i) q^{78} +(5.36444 + 9.29148i) q^{79} +(0.500000 - 0.866025i) q^{80} +(8.24487 + 7.65012i) q^{81} +(6.65352 - 8.34325i) q^{82} +(-11.7427 + 8.00602i) q^{83} +(-7.93633 + 3.82194i) q^{84} +6.47924 q^{85} +(-6.28786 + 1.86087i) q^{86} +13.7616 q^{87} +(2.85399 - 1.37441i) q^{88} +(-5.99923 + 4.09021i) q^{89} +(0.902947 - 1.13226i) q^{90} +(11.5471 + 10.7141i) q^{91} +(-2.70632 + 4.68748i) q^{92} +(8.74695 + 15.1502i) q^{93} +(-2.53923 + 11.1251i) q^{94} +(-1.19470 + 3.04405i) q^{95} +(-2.01538 - 0.621662i) q^{96} +(-3.15651 - 3.95813i) q^{97} +(-0.780447 + 10.4143i) q^{98} +(4.38369 - 1.35219i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} - 6 q^{6} + q^{7} + 10 q^{8} + 8 q^{9}+O(q^{10}) \) 60 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 - 6 * q^6 + q^7 + 10 * q^8 + 8 * q^9	\( 60 q + 10 q^{2} - q^{3} - 10 q^{4} - 5 q^{5} - 6 q^{6} + q^{7} + 10 q^{8} + 8 q^{9} + 5 q^{10} + 3 q^{11} - q^{12} + 13 q^{13} - 15 q^{14} + q^{15} - 10 q^{16} + 38 q^{17} + 6 q^{18} + 17 q^{19} - 5 q^{20} + 4 q^{21} + 11 q^{22} - 8 q^{23} + q^{24} + 5 q^{25} + 29 q^{26} - 16 q^{27} - 6 q^{28} - 41 q^{29} - q^{30} + 15 q^{31} + 10 q^{32} + 63 q^{33} - 10 q^{34} + 2 q^{35} - 48 q^{36} + 7 q^{37} + 25 q^{38} - 64 q^{39} + 5 q^{40} - 22 q^{41} - 60 q^{42} + 6 q^{43} - 4 q^{44} + 30 q^{45} - 20 q^{46} - 13 q^{47} - q^{48} - 93 q^{49} + 30 q^{50} + 18 q^{51} - 15 q^{52} + 71 q^{53} - 5 q^{54} - 16 q^{55} - q^{56} - 94 q^{57} - 22 q^{58} + 20 q^{59} + q^{60} + 91 q^{61} + 69 q^{62} - 50 q^{63} - 10 q^{64} + 5 q^{65} + 14 q^{66} - 26 q^{67} - 18 q^{68} - 94 q^{69} - 2 q^{70} + 20 q^{71} - 36 q^{72} - 56 q^{73} - 7 q^{74} + 2 q^{75} + 38 q^{76} + 41 q^{77} - 13 q^{78} - 46 q^{79} + 30 q^{80} + 39 q^{81} + 8 q^{82} - 115 q^{83} + 4 q^{84} + 6 q^{85} + 29 q^{86} + 20 q^{87} + 11 q^{88} + 30 q^{89} - 16 q^{90} - 53 q^{91} - 8 q^{92} + 16 q^{93} + 41 q^{94} - 17 q^{95} + q^{96} + 113 q^{97} + 2 q^{98} + 139 q^{99}+O(q^{100}) \) 60 * q + 10 * q^2 - q^3 - 10 * q^4 - 5 * q^5 - 6 * q^6 + q^7 + 10 * q^8 + 8 * q^9 + 5 * q^10 + 3 * q^11 - q^12 + 13 * q^13 - 15 * q^14 + q^15 - 10 * q^16 + 38 * q^17 + 6 * q^18 + 17 * q^19 - 5 * q^20 + 4 * q^21 + 11 * q^22 - 8 * q^23 + q^24 + 5 * q^25 + 29 * q^26 - 16 * q^27 - 6 * q^28 - 41 * q^29 - q^30 + 15 * q^31 + 10 * q^32 + 63 * q^33 - 10 * q^34 + 2 * q^35 - 48 * q^36 + 7 * q^37 + 25 * q^38 - 64 * q^39 + 5 * q^40 - 22 * q^41 - 60 * q^42 + 6 * q^43 - 4 * q^44 + 30 * q^45 - 20 * q^46 - 13 * q^47 - q^48 - 93 * q^49 + 30 * q^50 + 18 * q^51 - 15 * q^52 + 71 * q^53 - 5 * q^54 - 16 * q^55 - q^56 - 94 * q^57 - 22 * q^58 + 20 * q^59 + q^60 + 91 * q^61 + 69 * q^62 - 50 * q^63 - 10 * q^64 + 5 * q^65 + 14 * q^66 - 26 * q^67 - 18 * q^68 - 94 * q^69 - 2 * q^70 + 20 * q^71 - 36 * q^72 - 56 * q^73 - 7 * q^74 + 2 * q^75 + 38 * q^76 + 41 * q^77 - 13 * q^78 - 46 * q^79 + 30 * q^80 + 39 * q^81 + 8 * q^82 - 115 * q^83 + 4 * q^84 + 6 * q^85 + 29 * q^86 + 20 * q^87 + 11 * q^88 + 30 * q^89 - 16 * q^90 - 53 * q^91 - 8 * q^92 + 16 * q^93 + 41 * q^94 - 17 * q^95 + q^96 + 113 * q^97 + 2 * q^98 + 139 * q^99

Introduction

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