LMFDB - Embedded newform 731.2.e.a.307.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(307,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("731.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$58$
Relative dimension:	$29$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			307.3
Character	$\chi$	$=$	731.307
Dual form			731.2.e.a.681.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.32507 q^{2} +(1.39344 - 2.41351i) q^{3} +3.40595 q^{4} +(1.48534 - 2.57269i) q^{5} +(-3.23985 + 5.61158i) q^{6} +(1.79579 + 3.11040i) q^{7} -3.26893 q^{8} +(-2.38336 - 4.12809i) q^{9} +O(q^{10})$	\(q-2.32507 q^{2} +(1.39344 - 2.41351i) q^{3} +3.40595 q^{4} +(1.48534 - 2.57269i) q^{5} +(-3.23985 + 5.61158i) q^{6} +(1.79579 + 3.11040i) q^{7} -3.26893 q^{8} +(-2.38336 - 4.12809i) q^{9} +(-3.45353 + 5.98168i) q^{10} +0.503913 q^{11} +(4.74599 - 8.22030i) q^{12} +(1.43942 + 2.49315i) q^{13} +(-4.17534 - 7.23190i) q^{14} +(-4.13948 - 7.16978i) q^{15} +0.788599 q^{16} +(0.500000 + 0.866025i) q^{17} +(5.54147 + 9.59811i) q^{18} +(2.51253 - 4.35183i) q^{19} +(5.05901 - 8.76246i) q^{20} +10.0093 q^{21} -1.17163 q^{22} +(3.29078 - 5.69981i) q^{23} +(-4.55507 + 7.88961i) q^{24} +(-1.91249 - 3.31253i) q^{25} +(-3.34676 - 5.79676i) q^{26} -4.92362 q^{27} +(6.11638 + 10.5939i) q^{28} +(-2.23638 - 3.87352i) q^{29} +(9.62457 + 16.6702i) q^{30} +(-3.21859 + 5.57477i) q^{31} +4.70432 q^{32} +(0.702173 - 1.21620i) q^{33} +(-1.16254 - 2.01357i) q^{34} +10.6695 q^{35} +(-8.11759 - 14.0601i) q^{36} +(3.83987 - 6.65085i) q^{37} +(-5.84181 + 10.1183i) q^{38} +8.02301 q^{39} +(-4.85549 + 8.40995i) q^{40} +4.22141 q^{41} -23.2724 q^{42} +(-3.41951 + 5.59526i) q^{43} +1.71630 q^{44} -14.1604 q^{45} +(-7.65130 + 13.2524i) q^{46} -9.51331 q^{47} +(1.09887 - 1.90329i) q^{48} +(-2.94974 + 5.10909i) q^{49} +(4.44667 + 7.70186i) q^{50} +2.78688 q^{51} +(4.90260 + 8.49156i) q^{52} +(-2.74262 + 4.75036i) q^{53} +11.4478 q^{54} +(0.748484 - 1.29641i) q^{55} +(-5.87032 - 10.1677i) q^{56} +(-7.00213 - 12.1280i) q^{57} +(5.19973 + 9.00620i) q^{58} -2.40870 q^{59} +(-14.0989 - 24.4199i) q^{60} +(-2.28404 - 3.95607i) q^{61} +(7.48346 - 12.9617i) q^{62} +(8.56002 - 14.8264i) q^{63} -12.5151 q^{64} +8.55215 q^{65} +(-1.63260 + 2.82775i) q^{66} +(0.943401 - 1.63402i) q^{67} +(1.70298 + 2.94964i) q^{68} +(-9.17103 - 15.8847i) q^{69} -24.8073 q^{70} +(6.37565 + 11.0430i) q^{71} +(7.79103 + 13.4945i) q^{72} +(1.74386 + 3.02046i) q^{73} +(-8.92797 + 15.4637i) q^{74} -10.6598 q^{75} +(8.55755 - 14.8221i) q^{76} +(0.904923 + 1.56737i) q^{77} -18.6541 q^{78} +(2.32739 + 4.03115i) q^{79} +(1.17134 - 2.02882i) q^{80} +(0.289298 - 0.501079i) q^{81} -9.81508 q^{82} +(5.65525 - 9.79519i) q^{83} +34.0913 q^{84} +2.97069 q^{85} +(7.95060 - 13.0094i) q^{86} -12.4650 q^{87} -1.64726 q^{88} +(4.14612 - 7.18130i) q^{89} +32.9239 q^{90} +(-5.16981 + 8.95437i) q^{91} +(11.2082 - 19.4133i) q^{92} +(8.96984 + 15.5362i) q^{93} +22.1191 q^{94} +(-7.46394 - 12.9279i) q^{95} +(6.55519 - 11.3539i) q^{96} -10.2402 q^{97} +(6.85835 - 11.8790i) q^{98} +(-1.20100 - 2.08020i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9}+O(q^{10}) $ 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9} + 4 q^{10} + 16 q^{11} + 12 q^{12} + 2 q^{13} - 11 q^{14} + 7 q^{15} + 30 q^{16} + 29 q^{17} + 8 q^{18} + 8 q^{19} - 33 q^{20} - 26 q^{21} - 22 q^{22} - 5 q^{23} + 12 q^{24} - 36 q^{25} - 12 q^{27} + 15 q^{28} + 2 q^{29} + 11 q^{30} + 3 q^{31} - 40 q^{32} + 17 q^{33} - 3 q^{34} + 38 q^{35} - 7 q^{36} + 2 q^{37} + q^{38} - 54 q^{39} + 5 q^{40} + 14 q^{41} - 112 q^{42} + 31 q^{43} - 24 q^{44} - 46 q^{45} - 13 q^{46} - 28 q^{47} - 28 q^{49} - 13 q^{50} + 6 q^{51} + 85 q^{52} - 10 q^{53} + 34 q^{54} + 36 q^{55} - 54 q^{56} - 23 q^{57} + 3 q^{58} + 12 q^{59} + 2 q^{60} - q^{61} - q^{62} - 14 q^{63} + 28 q^{64} + 80 q^{65} - 74 q^{66} + 11 q^{67} + 27 q^{68} - 11 q^{69} + 2 q^{70} + 16 q^{71} + 21 q^{72} + 14 q^{73} + 21 q^{74} - 54 q^{75} + 44 q^{76} + 25 q^{77} + 88 q^{78} - 4 q^{79} - 112 q^{80} + 11 q^{81} - 176 q^{82} - 3 q^{83} + 100 q^{84} - 2 q^{85} + 44 q^{86} + 8 q^{87} - 106 q^{88} + 82 q^{89} + 54 q^{90} - 15 q^{91} + 42 q^{92} + 88 q^{94} + 29 q^{95} + 20 q^{96} + 20 q^{97} + 44 q^{98} - 54 q^{99}+O(q^{100}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9 + 4 * q^10 + 16 * q^11 + 12 * q^12 + 2 * q^13 - 11 * q^14 + 7 * q^15 + 30 * q^16 + 29 * q^17 + 8 * q^18 + 8 * q^19 - 33 * q^20 - 26 * q^21 - 22 * q^22 - 5 * q^23 + 12 * q^24 - 36 * q^25 - 12 * q^27 + 15 * q^28 + 2 * q^29 + 11 * q^30 + 3 * q^31 - 40 * q^32 + 17 * q^33 - 3 * q^34 + 38 * q^35 - 7 * q^36 + 2 * q^37 + q^38 - 54 * q^39 + 5 * q^40 + 14 * q^41 - 112 * q^42 + 31 * q^43 - 24 * q^44 - 46 * q^45 - 13 * q^46 - 28 * q^47 - 28 * q^49 - 13 * q^50 + 6 * q^51 + 85 * q^52 - 10 * q^53 + 34 * q^54 + 36 * q^55 - 54 * q^56 - 23 * q^57 + 3 * q^58 + 12 * q^59 + 2 * q^60 - q^61 - q^62 - 14 * q^63 + 28 * q^64 + 80 * q^65 - 74 * q^66 + 11 * q^67 + 27 * q^68 - 11 * q^69 + 2 * q^70 + 16 * q^71 + 21 * q^72 + 14 * q^73 + 21 * q^74 - 54 * q^75 + 44 * q^76 + 25 * q^77 + 88 * q^78 - 4 * q^79 - 112 * q^80 + 11 * q^81 - 176 * q^82 - 3 * q^83 + 100 * q^84 - 2 * q^85 + 44 * q^86 + 8 * q^87 - 106 * q^88 + 82 * q^89 + 54 * q^90 - 15 * q^91 + 42 * q^92 + 88 * q^94 + 29 * q^95 + 20 * q^96 + 20 * q^97 + 44 * q^98 - 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.32507			−1.64407			−0.822036	−	0.569435i	$-0.807162\pi$
$2$	−2.32507			−1.64407			−0.822036	+	0.569435i	$0.807162\pi$
$3$	1.39344	−	2.41351i	0.804504	−	1.39344i	−0.112122	−	0.993694i	$-0.535765\pi$
$3$	1.39344	−	2.41351i	0.804504	−	1.39344i	0.916626	−	0.399747i	$-0.130902\pi$
$4$	3.40595			1.70298
$5$	1.48534	−	2.57269i	0.664266	−	1.15054i	−0.315218	−	0.949019i	$-0.602078\pi$
$5$	1.48534	−	2.57269i	0.664266	−	1.15054i	0.979484	−	0.201523i	$-0.0645890\pi$
$6$	−3.23985	+	5.61158i	−1.32266	+	2.29092i
$7$	1.79579	+	3.11040i	0.678746	+	1.17562i	0.975359	+	0.220624i	$0.0708094\pi$
$7$	1.79579	+	3.11040i	0.678746	+	1.17562i	−0.296613	+	0.954998i	$0.595857\pi$
$8$	−3.26893			−1.15574
$9$	−2.38336	−	4.12809i	−0.794452	−	1.37603i
$10$	−3.45353	+	5.98168i	−1.09210	+	1.89157i
$11$	0.503913			0.151935			0.0759677	−	0.997110i	$-0.475795\pi$
$11$	0.503913			0.151935			0.0759677	+	0.997110i	$0.475795\pi$
$12$	4.74599	−	8.22030i	1.37005	−	2.37300i
$13$	1.43942	+	2.49315i	0.399224	+	0.691477i	0.993630	−	0.112688i	$-0.0359462\pi$
$13$	1.43942	+	2.49315i	0.399224	+	0.691477i	−0.594406	+	0.804165i	$0.702613\pi$
$14$	−4.17534	−	7.23190i	−1.11591	−	1.93281i
$15$	−4.13948	−	7.16978i	−1.06881	−	1.85123i
$16$	0.788599			0.197150
$17$	0.500000	+	0.866025i	0.121268	+	0.210042i
$17$	0.500000	+	0.866025i	0.121268	+	0.210042i
$18$	5.54147	+	9.59811i	1.30614	+	2.26230i
$19$	2.51253	−	4.35183i	0.576414	−	0.998378i	−0.419472	−	0.907768i	$-0.637785\pi$
$19$	2.51253	−	4.35183i	0.576414	−	0.998378i	0.995886	−	0.0906103i	$-0.0288818\pi$
$20$	5.05901	−	8.76246i	1.13123	−	1.95934i
$21$	10.0093			2.18421
$22$	−1.17163			−0.249793
$23$	3.29078	−	5.69981i	0.686176	−	1.18849i	−0.286890	−	0.957964i	$-0.592621\pi$
$23$	3.29078	−	5.69981i	0.686176	−	1.18849i	0.973066	−	0.230528i	$-0.0740453\pi$
$24$	−4.55507	+	7.88961i	−0.929799	+	1.61046i
$25$	−1.91249	−	3.31253i	−0.382498	−	0.662506i
$26$	−3.34676	−	5.79676i	−0.656354	−	1.13684i
$27$	−4.92362			−0.947550
$28$	6.11638	+	10.5939i	1.15589	+	2.00205i
$29$	−2.23638	−	3.87352i	−0.415285	−	0.719294i	0.580174	−	0.814493i	$-0.302985\pi$
$29$	−2.23638	−	3.87352i	−0.415285	−	0.719294i	−0.995458	+	0.0951986i	$0.969651\pi$
$30$	9.62457	+	16.6702i	1.75720	+	3.04356i
$31$	−3.21859	+	5.57477i	−0.578077	+	1.00126i	0.417623	+	0.908620i	$0.362863\pi$
$31$	−3.21859	+	5.57477i	−0.578077	+	1.00126i	−0.995700	+	0.0926378i	$0.970470\pi$
$32$	4.70432			0.831614
$33$	0.702173	−	1.21620i	0.122233	−	0.211713i
$34$	−1.16254	−	2.01357i	−0.199373	−	0.345324i
$35$	10.6695			1.80347
$36$	−8.11759	−	14.0601i	−1.35293	−	2.34335i
$37$	3.83987	−	6.65085i	0.631271	−	1.09339i	−0.356021	−	0.934478i	$-0.615867\pi$
$37$	3.83987	−	6.65085i	0.631271	−	1.09339i	0.987292	−	0.158915i	$-0.0507997\pi$
$38$	−5.84181	+	10.1183i	−0.947667	+	1.64141i
$39$	8.02301			1.28471
$40$	−4.85549	+	8.40995i	−0.767720	+	1.32973i
$41$	4.22141			0.659274			0.329637	−	0.944108i	$-0.393074\pi$
$41$	4.22141			0.659274			0.329637	+	0.944108i	$0.393074\pi$
$42$	−23.2724			−3.59100
$43$	−3.41951	+	5.59526i	−0.521470	+	0.853270i
$43$	−3.41951	+	5.59526i	−0.521470	+	0.853270i
$44$	1.71630			0.258742
$45$	−14.1604			−2.11091
$46$	−7.65130	+	13.2524i	−1.12812	+	1.95397i
$47$	−9.51331			−1.38766			−0.693829	−	0.720140i	$-0.744078\pi$
$47$	−9.51331			−1.38766			−0.693829	+	0.720140i	$0.744078\pi$
$48$	1.09887	−	1.90329i	0.158608	−	0.274716i
$49$	−2.94974	+	5.10909i	−0.421391	+	0.729871i
$50$	4.44667	+	7.70186i	0.628854	+	1.08921i
$51$	2.78688			0.390242
$52$	4.90260	+	8.49156i	0.679869	+	1.17757i
$53$	−2.74262	+	4.75036i	−0.376728	+	0.652512i	−0.990584	−	0.136906i	$-0.956284\pi$
$53$	−2.74262	+	4.75036i	−0.376728	+	0.652512i	0.613856	+	0.789418i	$0.289618\pi$
$54$	11.4478			1.55784
$55$	0.748484	−	1.29641i	0.100926	−	0.174808i
$56$	−5.87032	−	10.1677i	−0.784455	−	1.35872i
$57$	−7.00213	−	12.1280i	−0.927454	−	1.60640i
$58$	5.19973	+	9.00620i	0.682758	+	1.18257i
$59$	−2.40870			−0.313585			−0.156793	−	0.987632i	$-0.550115\pi$
$59$	−2.40870			−0.313585			−0.156793	+	0.987632i	$0.550115\pi$
$60$	−14.0989	−	24.4199i	−1.82015	−	3.15260i
$61$	−2.28404	−	3.95607i	−0.292441	−	0.506522i	0.681946	−	0.731403i	$-0.261134\pi$
$61$	−2.28404	−	3.95607i	−0.292441	−	0.506522i	−0.974386	+	0.224881i	$0.927801\pi$
$62$	7.48346	−	12.9617i	0.950400	−	1.64614i
$63$	8.56002	−	14.8264i	1.07846	−	1.86795i
$64$	−12.5151			−1.56438
$65$	8.55215			1.06076
$66$	−1.63260	+	2.82775i	−0.200959	+	0.348072i
$67$	0.943401	−	1.63402i	0.115255	−	0.199627i	−0.802627	−	0.596482i	$-0.796565\pi$
$67$	0.943401	−	1.63402i	0.115255	−	0.199627i	0.917882	+	0.396854i	$0.129898\pi$
$68$	1.70298	+	2.94964i	0.206516	+	0.357696i
$69$	−9.17103	−	15.8847i	−1.10406	−	1.91229i
$70$	−24.8073			−2.96504
$71$	6.37565	+	11.0430i	0.756651	+	1.31056i	0.944549	+	0.328369i	$0.106499\pi$
$71$	6.37565	+	11.0430i	0.756651	+	1.31056i	−0.187899	+	0.982188i	$0.560168\pi$
$72$	7.79103	+	13.4945i	0.918182	+	1.59034i
$73$	1.74386	+	3.02046i	0.204104	+	0.353518i	0.949847	−	0.312716i	$-0.101239\pi$
$73$	1.74386	+	3.02046i	0.204104	+	0.353518i	−0.745743	+	0.666234i	$0.767905\pi$
$74$	−8.92797	+	15.4637i	−1.03786	+	1.79762i
$75$	−10.6598			−1.23088
$76$	8.55755	−	14.8221i	0.981619	−	1.70021i
$77$	0.904923	+	1.56737i	0.103126	+	0.178619i
$78$	−18.6541			−2.11216
$79$	2.32739	+	4.03115i	0.261852	+	0.453540i	0.966734	−	0.255784i	$-0.0823336\pi$
$79$	2.32739	+	4.03115i	0.261852	+	0.453540i	−0.704882	+	0.709324i	$0.749000\pi$
$80$	1.17134	−	2.02882i	0.130960	−	0.226829i
$81$	0.289298	−	0.501079i	0.0321442	−	0.0556755i
$82$	−9.81508			−1.08389
$83$	5.65525	−	9.79519i	0.620745	−	1.07516i	−0.368602	−	0.929587i	$-0.620164\pi$
$83$	5.65525	−	9.79519i	0.620745	−	1.07516i	0.989347	−	0.145574i	$-0.0465030\pi$
$84$	34.0913			3.71966
$85$	2.97069			0.322216
$86$	7.95060	−	13.0094i	0.857335	−	1.40284i
$87$	−12.4650			−1.33639
$88$	−1.64726			−0.175598
$89$	4.14612	−	7.18130i	0.439488	−	0.761216i	−0.558162	−	0.829732i	$-0.688493\pi$
$89$	4.14612	−	7.18130i	0.439488	−	0.761216i	0.997650	+	0.0685162i	$0.0218265\pi$
$90$	32.9239			3.47049
$91$	−5.16981	+	8.95437i	−0.541943	+	0.938673i
$92$	11.2082	−	19.4133i	1.16854	−	2.02397i
$93$	8.96984	+	15.5362i	0.930129	+	1.61103i
$94$	22.1191			2.28141
$95$	−7.46394	−	12.9279i	−0.765784	−	1.32638i
$96$	6.55519	−	11.3539i	0.669037	−	1.15881i
$97$	−10.2402			−1.03973			−0.519867	−	0.854247i	$-0.674018\pi$
$97$	−10.2402			−1.03973			−0.519867	+	0.854247i	$0.674018\pi$
$98$	6.85835	−	11.8790i	0.692798	−	1.19996i
$99$	−1.20100	−	2.08020i	−0.120705	−	0.209068i
$100$	−6.51384	−	11.2823i	−0.651384	−	1.12823i
$101$	6.61995	+	11.4661i	0.658709	+	1.14092i	0.980950	+	0.194260i	$0.0622307\pi$
$101$	6.61995	+	11.4661i	0.658709	+	1.14092i	−0.322241	+	0.946658i	$0.604436\pi$
$102$	−6.47970			−0.641585
$103$	−7.17269	−	12.4235i	−0.706746	−	1.22412i	−0.966058	−	0.258327i	$-0.916829\pi$
$103$	−7.17269	−	12.4235i	−0.706746	−	1.22412i	0.259311	−	0.965794i	$-0.416504\pi$
$104$	−4.70538	−	8.14996i	−0.461400	−	0.799169i
$105$	14.8673	−	25.7509i	1.45090	−	2.51303i
$106$	6.37679	−	11.0449i	0.619368	−	1.07278i
$107$	−12.0291			−1.16290			−0.581451	−	0.813582i	$-0.697515\pi$
$107$	−12.0291			−1.16290			−0.581451	+	0.813582i	$0.697515\pi$
$108$	−16.7696			−1.61365
$109$	−6.41856	+	11.1173i	−0.614786	+	1.06484i	0.375635	+	0.926767i	$0.377424\pi$
$109$	−6.41856	+	11.1173i	−0.614786	+	1.06484i	−0.990422	+	0.138074i	$0.955909\pi$
$110$	−1.74028	+	3.01425i	−0.165929	+	0.287397i
$111$	−10.7013	−	18.5351i	−1.01572	−	1.75928i
$112$	1.41616	+	2.45286i	0.133814	+	0.231773i
$113$	−4.82605			−0.453997			−0.226998	−	0.973895i	$-0.572891\pi$
$113$	−4.82605			−0.453997			−0.226998	+	0.973895i	$0.572891\pi$
$114$	16.2804	+	28.1985i	1.52480	+	2.64103i
$115$	−9.77589	−	16.9323i	−0.911606	−	1.57895i
$116$	−7.61699	−	13.1930i	−0.707220	−	1.22494i
$117$	6.86132	−	11.8841i	0.634329	−	1.09869i
$118$	5.60039			0.515557
$119$	−1.79579	+	3.11040i	−0.164620	+	0.285130i
$120$	13.5317	+	23.4375i	1.23527	+	2.13955i
$121$	−10.7461			−0.976916
$122$	5.31054	+	9.19813i	0.480794	+	0.832759i
$123$	5.88229	−	10.1884i	0.530388	−	0.918660i
$124$	−10.9624	+	18.9874i	−0.984450	+	1.70512i
$125$	3.49062			0.312210
$126$	−19.9027	+	34.4724i	−1.77307	+	3.07105i
$127$	16.4456			1.45931			0.729654	−	0.683817i	$-0.239681\pi$
$127$	16.4456			1.45931			0.729654	+	0.683817i	$0.239681\pi$
$128$	19.6898			1.74035
$129$	8.73934	+	16.0497i	0.769456	+	1.41310i
$130$	−19.8843			−1.74397
$131$	−11.6217			−1.01539			−0.507697	−	0.861536i	$-0.669503\pi$
$131$	−11.6217			−1.01539			−0.507697	+	0.861536i	$0.669503\pi$
$132$	2.39157	−	4.14231i	0.208159	−	0.360542i
$133$	18.0479			1.56495
$134$	−2.19347	+	3.79921i	−0.189487	+	0.328202i
$135$	−7.31326	+	12.6669i	−0.629425	+	1.09020i
$136$	−1.63447	−	2.83098i	−0.140154	−	0.242755i
$137$	−5.12027			−0.437455			−0.218727	−	0.975786i	$-0.570191\pi$
$137$	−5.12027			−0.437455			−0.218727	+	0.975786i	$0.570191\pi$
$138$	21.3233	+	36.9330i	1.81516	+	3.14395i
$139$	−11.0870	+	19.2033i	−0.940390	+	1.62880i	−0.175661	+	0.984451i	$0.556206\pi$
$139$	−11.0870	+	19.2033i	−0.940390	+	1.62880i	−0.764729	+	0.644352i	$0.777127\pi$
$140$	36.3397			3.07126
$141$	−13.2562	+	22.9605i	−1.11638	+	1.93362i
$142$	−14.8238	−	25.6756i	−1.24399	−	2.15465i
$143$	0.725344	+	1.25633i	0.0606563	+	0.105060i
$144$	−1.87951	−	3.25541i	−0.156626	−	0.271284i
$145$	−13.2871			−1.10344
$146$	−4.05460	−	7.02278i	−0.335561	−	0.581209i
$147$	8.22057	+	14.2384i	0.678021	+	1.17437i
$148$	13.0784	−	22.6525i	1.07504	−	1.86202i
$149$	−8.58539	+	14.8703i	−0.703343	+	1.21823i	0.263943	+	0.964538i	$0.414977\pi$
$149$	−8.58539	+	14.8703i	−0.703343	+	1.21823i	−0.967286	+	0.253687i	$0.918357\pi$
$150$	24.7847			2.02366
$151$	−1.84274			−0.149960			−0.0749799	−	0.997185i	$-0.523889\pi$
$151$	−1.84274			−0.149960			−0.0749799	+	0.997185i	$0.523889\pi$
$152$	−8.21330	+	14.2258i	−0.666186	+	1.15387i
$153$	2.38336	−	4.12809i	0.192683	−	0.333737i
$154$	−2.10401	−	3.64425i	−0.169546	−	0.293662i
$155$	9.56144	+	16.5609i	0.767993	+	1.33020i
$156$	27.3260			2.18783
$157$	3.20156	+	5.54526i	0.255512	+	0.442560i	0.965035	−	0.262123i	$-0.0844226\pi$
$157$	3.20156	+	5.54526i	0.255512	+	0.442560i	−0.709522	+	0.704683i	$0.751089\pi$
$158$	−5.41134	−	9.37271i	−0.430503	−	0.745653i
$159$	7.64336	+	13.2387i	0.606158	+	1.04990i
$160$	6.98753	−	12.1028i	0.552413	−	0.956807i
$161$	23.6383			1.86296
$162$	−0.672638	+	1.16504i	−0.0528475	+	0.0915345i
$163$	10.5226	+	18.2258i	0.824197	+	1.42755i	0.902531	+	0.430624i	$0.141707\pi$
$163$	10.5226	+	18.2258i	0.824197	+	1.42755i	−0.0783343	+	0.996927i	$0.524960\pi$
$164$	14.3779			1.12273
$165$	−2.08594	−	3.61295i	−0.162390	−	0.281268i
$166$	−13.1489	+	22.7745i	−1.02055	+	1.76764i
$167$	4.65036	−	8.05466i	0.359856	−	0.623289i	−0.628081	−	0.778148i	$-0.716159\pi$
$167$	4.65036	−	8.05466i	0.359856	−	0.623289i	0.987936	+	0.154860i	$0.0494926\pi$
$168$	−32.7198			−2.52439
$169$	2.35612	−	4.08092i	0.181240	−	0.313917i
$170$	−6.90705			−0.529747
$171$	−23.9530			−1.83173
$172$	−11.6467	+	19.0572i	−0.888051	+	1.45310i
$173$	11.0411			0.839443			0.419721	−	0.907653i	$-0.362128\pi$
$173$	11.0411			0.839443			0.419721	+	0.907653i	$0.362128\pi$
$174$	28.9821			2.19713
$175$	6.86887	−	11.8972i	0.519237	−	0.899346i
$176$	0.397385			0.0299540
$177$	−3.35638	+	5.81341i	−0.252281	+	0.436963i
$178$	−9.64003	+	16.6970i	−0.722551	+	1.25149i
$179$	0.475587	+	0.823741i	0.0355470	+	0.0615693i	0.883252	−	0.468899i	$-0.155349\pi$
$179$	0.475587	+	0.823741i	0.0355470	+	0.0615693i	−0.847705	+	0.530469i	$0.822016\pi$
$180$	−48.2296			−3.59483
$181$	11.2289	+	19.4491i	0.834640	+	1.44564i	0.894323	+	0.447422i	$0.147658\pi$
$181$	11.2289	+	19.4491i	0.834640	+	1.44564i	−0.0596826	+	0.998217i	$0.519009\pi$
$182$	12.0202	−	20.8195i	0.890994	−	1.54325i
$183$	−12.7307			−0.941079
$184$	−10.7574	+	18.6323i	−0.793043	+	1.37359i
$185$	−11.4071	−	19.7576i	−0.838663	−	1.45261i
$186$	−20.8555	−	36.1228i	−1.52920	−	2.64865i
$187$	0.251956	+	0.436401i	0.0184249	+	0.0319128i
$188$	−32.4019			−2.36315
$189$	−8.84179	−	15.3144i	−0.643146	−	1.11396i
$190$	17.3542	+	30.0583i	1.25900	+	2.18066i
$191$	−9.97449	+	17.2763i	−0.721729	+	1.25007i	0.238578	+	0.971123i	$0.423319\pi$
$191$	−9.97449	+	17.2763i	−0.721729	+	1.25007i	−0.960306	+	0.278947i	$0.910014\pi$
$192$	−17.4390	+	30.2053i	−1.25855	+	2.17988i
$193$	−15.0663			−1.08449			−0.542247	−	0.840219i	$-0.682426\pi$
$193$	−15.0663			−1.08449			−0.542247	+	0.840219i	$0.682426\pi$
$194$	23.8092			1.70940
$195$	11.9169	−	20.6407i	0.853388	−	1.47811i
$196$	−10.0467	+	17.4013i	−0.717619	+	1.24295i
$197$	−10.8742	−	18.8346i	−0.774752	−	1.34191i	−0.934934	−	0.354823i	$-0.884541\pi$
$197$	−10.8742	−	18.8346i	−0.774752	−	1.34191i	0.160181	−	0.987088i	$-0.448792\pi$
$198$	2.79242	+	4.83661i	0.198448	+	0.343723i
$199$	17.8288			1.26385			0.631927	−	0.775028i	$-0.282264\pi$
$199$	17.8288			1.26385			0.631927	+	0.775028i	$0.282264\pi$
$200$	6.25180	+	10.8284i	0.442069	+	0.765686i
$201$	−2.62915	−	4.55382i	−0.185446	−	0.321201i
$202$	−15.3918	−	26.6595i	−1.08297	−	1.87575i
$203$	8.03213	−	13.9121i	0.563745	−	0.976436i
$204$	9.49198			0.664572
$205$	6.27025	−	10.8604i	0.437933	−	0.758523i
$206$	16.6770	+	28.8854i	1.16194	+	2.01254i
$207$	−31.3724			−2.18054
$208$	1.13513	+	1.96610i	0.0787069	+	0.136324i
$209$	1.26610	−	2.19294i	0.0875777	−	0.151689i
$210$	−34.5675	+	59.8726i	−2.38538	+	4.13160i
$211$	−13.6092			−0.936896			−0.468448	−	0.883491i	$-0.655187\pi$
$211$	−13.6092			−0.936896			−0.468448	+	0.883491i	$0.655187\pi$
$212$	−9.34123	+	16.1795i	−0.641559	+	1.11121i
$213$	35.5364			2.43491
$214$	27.9686			1.91189
$215$	9.31573	+	17.1082i	0.635328	+	1.16677i
$216$	16.0950			1.09512
$217$	−23.1197			−1.56947
$218$	14.9236	−	25.8484i	1.01075	−	1.75068i
$219$	9.71988			0.656809
$220$	2.54930	−	4.41551i	0.171874	−	0.297694i
$221$	−1.43942	+	2.49315i	−0.0968261	+	0.167708i
$222$	24.8812	+	43.0955i	1.66992	+	2.89238i
$223$	5.89939			0.395052			0.197526	−	0.980298i	$-0.436709\pi$
$223$	5.89939			0.395052			0.197526	+	0.980298i	$0.436709\pi$
$224$	8.44798	+	14.6323i	0.564454	+	0.977664i
$225$	−9.11629	+	15.7899i	−0.607752	+	1.05266i
$226$	11.2209			0.746403
$227$	−8.20693	+	14.2148i	−0.544713	+	0.943471i	0.453912	+	0.891047i	$0.350028\pi$
$227$	−8.20693	+	14.2148i	−0.544713	+	0.943471i	−0.998625	+	0.0524241i	$0.983305\pi$
$228$	−23.8489	−	41.3075i	−1.57943	−	2.73566i
$229$	−1.06288	−	1.84097i	−0.0702373	−	0.121655i	0.828768	−	0.559592i	$-0.189042\pi$
$229$	−1.06288	−	1.84097i	−0.0702373	−	0.121655i	−0.899005	+	0.437938i	$0.855709\pi$
$230$	22.7296	+	39.3689i	1.49875	+	2.59591i
$231$	5.04383			0.331859
$232$	7.31057	+	12.6623i	0.479962	+	0.831319i
$233$	−1.53910	−	2.66580i	−0.100830	−	0.174643i	0.811197	−	0.584773i	$-0.198816\pi$
$233$	−1.53910	−	2.66580i	−0.100830	−	0.174643i	−0.912027	+	0.410131i	$0.865483\pi$
$234$	−15.9530	+	27.6315i	−1.04288	+	1.80633i
$235$	−14.1305	+	24.4748i	−0.921774	+	1.59656i
$236$	−8.20390			−0.534028
$237$	12.9723			0.842642
$238$	4.17534	−	7.23190i	0.270647	−	0.468775i
$239$	14.5834	−	25.2592i	0.943322	−	1.63388i	0.184244	−	0.982880i	$-0.441016\pi$
$239$	14.5834	−	25.2592i	0.943322	−	1.63388i	0.759077	−	0.651000i	$-0.225650\pi$
$240$	−3.26439	−	5.65408i	−0.210715	−	0.364969i
$241$	−7.66282	−	13.2724i	−0.493606	−	0.854950i	0.506367	−	0.862318i	$-0.330988\pi$
$241$	−7.66282	−	13.2724i	−0.493606	−	0.854950i	−0.999973	+	0.00736776i	$0.997655\pi$
$242$	24.9854			1.60612
$243$	−8.19166	−	14.1884i	−0.525496	−	0.910185i
$244$	−7.77931	−	13.4742i	−0.498019	−	0.862595i
$245$	8.76275	+	15.1775i	0.559831	+	0.969656i
$246$	−13.6767	+	23.6888i	−0.871997	+	1.51034i
$247$	14.4664			0.920474
$248$	10.5214	−	18.2236i	0.668108	−	1.15720i
$249$	−15.7605	−	27.2980i	−0.998783	−	1.72994i
$250$	−8.11593			−0.513297
$251$	8.69612	+	15.0621i	0.548895	+	0.950713i	0.998351	+	0.0574108i	$0.0182845\pi$
$251$	8.69612	+	15.0621i	0.548895	+	0.950713i	−0.449456	+	0.893302i	$0.648382\pi$
$252$	29.1550	−	50.4980i	1.83659	−	3.18107i
$253$	1.65827	−	2.87221i	0.104254	−	0.180574i
$254$	−38.2371			−2.39921
$255$	4.13948	−	7.16978i	0.259224	−	0.448989i
$256$	−20.7500			−1.29687
$257$	4.79336			0.299002			0.149501	−	0.988762i	$-0.452233\pi$
$257$	4.79336			0.299002			0.149501	+	0.988762i	$0.452233\pi$
$258$	−20.3196	−	37.3166i	−1.26504	−	2.32323i
$259$	27.5824			1.71389
$260$	29.1282			1.80645
$261$	−10.6602	+	18.4639i	−0.659847	+	1.14289i
$262$	27.0213			1.66938
$263$	1.15106	−	1.99370i	0.0709776	−	0.122937i	−0.828352	−	0.560207i	$-0.810721\pi$
$263$	1.15106	−	1.99370i	0.0709776	−	0.122937i	0.899330	+	0.437271i	$0.144055\pi$
$264$	−2.29536	+	3.97567i	−0.141269	+	0.244686i
$265$	8.14747	+	14.1118i	0.500495	+	0.866883i
$266$	−41.9627			−2.57290
$267$	−11.5548	−	20.0134i	−0.707140	−	1.22480i
$268$	3.21318	−	5.56539i	0.196276	−	0.339960i
$269$	6.49631			0.396087			0.198044	−	0.980193i	$-0.436541\pi$
$269$	6.49631			0.396087			0.198044	+	0.980193i	$0.436541\pi$
$270$	17.0038	−	29.4515i	1.03482	−	1.79236i
$271$	5.26818	+	9.12476i	0.320019	+	0.554289i	0.980492	−	0.196561i	$-0.0629773\pi$
$271$	5.26818	+	9.12476i	0.320019	+	0.554289i	−0.660472	+	0.750850i	$0.729644\pi$
$272$	0.394299	+	0.682946i	0.0239079	+	0.0414097i
$273$	14.4076	+	24.9548i	0.871991	+	1.51033i
$274$	11.9050			0.719207
$275$	−0.963728	−	1.66923i	−0.0581150	−	0.100658i
$276$	−31.2361	−	54.1025i	−1.88019	−	3.25659i
$277$	13.4475	−	23.2917i	0.807980	−	1.39946i	−0.106281	−	0.994336i	$-0.533894\pi$
$277$	13.4475	−	23.2917i	0.807980	−	1.39946i	0.914261	−	0.405126i	$-0.132772\pi$
$278$	25.7781	−	44.6490i	1.54607	−	2.67787i
$279$	30.6842			1.83702
$280$	−34.8778			−2.08435
$281$	2.97549	−	5.15370i	0.177503	−	0.307444i	−0.763522	−	0.645782i	$-0.776531\pi$
$281$	2.97549	−	5.15370i	0.177503	−	0.307444i	0.941025	+	0.338338i	$0.109865\pi$
$282$	30.8217	−	53.3847i	1.83540	−	3.17901i
$283$	9.49026	+	16.4376i	0.564138	+	0.977115i	0.997129	+	0.0757170i	$0.0241246\pi$
$283$	9.49026	+	16.4376i	0.564138	+	0.977115i	−0.432992	+	0.901398i	$0.642542\pi$
$284$	21.7152	+	37.6118i	1.28856	+	2.23185i
$285$	−41.6022			−2.46430
$286$	−1.68648	−	2.92106i	−0.0997234	−	0.172726i
$287$	7.58078	+	13.1303i	0.447479	+	0.775057i
$288$	−11.2121	−	19.4199i	−0.660678	−	1.14433i
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$	30.8935			1.81413
$291$	−14.2691	+	24.7148i	−0.836469	+	1.44881i
$292$	5.93951	+	10.2875i	0.347584	+	0.602032i
$293$	−4.11101			−0.240168			−0.120084	−	0.992764i	$-0.538316\pi$
$293$	−4.11101			−0.240168			−0.120084	+	0.992764i	$0.538316\pi$
$294$	−19.1134	−	33.1054i	−1.11472	−	1.93075i
$295$	−3.57774	+	6.19683i	−0.208304	+	0.360793i
$296$	−12.5523	+	21.7412i	−0.729587	+	1.26368i
$297$	−2.48107			−0.143967
$298$	19.9616	−	34.5746i	1.15635	−	2.00285i
$299$	18.9473			1.09575
$300$	−36.3066			−2.09616
$301$	−23.5442	−	0.588121i	−1.35707	−	0.0338988i
$302$	4.28449			0.246545
$303$	36.8980			2.11974
$304$	1.98138	−	3.43185i	0.113640	−	0.196830i
$305$	−13.5703			−0.777034
$306$	−5.54147	+	9.59811i	−0.316785	+	0.548687i
$307$	7.22796	−	12.5192i	0.412521	−	0.714508i	−0.582643	−	0.812728i	$-0.697982\pi$
$307$	7.22796	−	12.5192i	0.412521	−	0.714508i	0.995165	+	0.0982201i	$0.0313149\pi$
$308$	3.08212	+	5.33839i	0.175620	+	0.304183i
$309$	−39.9789			−2.27432
$310$	−22.2310	−	38.5052i	−1.26264	−	2.18695i
$311$	5.40542	−	9.36246i	0.306513	−	0.530896i	−0.671084	−	0.741381i	$-0.734171\pi$
$311$	5.40542	−	9.36246i	0.306513	−	0.530896i	0.977597	+	0.210485i	$0.0675044\pi$
$312$	−26.2267			−1.48479
$313$	13.4845	−	23.3558i	0.762187	−	1.32015i	−0.179534	−	0.983752i	$-0.557459\pi$
$313$	13.4845	−	23.3558i	0.762187	−	1.32015i	0.941721	−	0.336395i	$-0.109208\pi$
$314$	−7.44385	−	12.8931i	−0.420081	−	0.727601i
$315$	−25.4291	−	44.0446i	−1.43277	−	2.48163i
$316$	7.92697	+	13.7299i	0.445927	+	0.772368i
$317$	−19.2227			−1.07965			−0.539826	−	0.841777i	$-0.681510\pi$
$317$	−19.2227			−1.07965			−0.539826	+	0.841777i	$0.681510\pi$
$318$	−17.7714	−	30.7809i	−0.996568	−	1.72611i
$319$	−1.12694	−	1.95192i	−0.0630965	−	0.109286i
$320$	−18.5892	+	32.1974i	−1.03917	+	1.79989i
$321$	−16.7619	+	29.0325i	−0.935558	+	1.62043i
$322$	−54.9606			−3.06283
$323$	5.02506			0.279602
$324$	0.985335	−	1.70665i	0.0547408	−	0.0948139i
$325$	5.50576	−	9.53626i	0.305405	−	0.528977i
$326$	−24.4659	−	42.3762i	−1.35504	−	2.34700i
$327$	17.8878	+	30.9825i	0.989196	+	1.71334i
$328$	−13.7995			−0.761951
$329$	−17.0839	−	29.5902i	−0.941867	−	1.63136i
$330$	4.84995	+	8.40035i	0.266981	+	0.462424i
$331$	15.9850	+	27.6868i	0.878613	+	1.52180i	0.852863	+	0.522135i	$0.174864\pi$
$331$	15.9850	+	27.6868i	0.878613	+	1.52180i	0.0257503	+	0.999668i	$0.491803\pi$
$332$	19.2615	−	33.3619i	1.05711	−	1.83097i
$333$	−36.6071			−2.00606
$334$	−10.8124	+	18.7277i	−0.591629	+	1.02473i
$335$	−2.80255	−	4.85416i	−0.153120	−	0.265211i
$336$	7.89334			0.430617
$337$	13.6496	+	23.6418i	0.743541	+	1.28785i	0.950874	+	0.309580i	$0.100188\pi$
$337$	13.6496	+	23.6418i	0.743541	+	1.28785i	−0.207333	+	0.978270i	$0.566478\pi$
$338$	−5.47815	+	9.48843i	−0.297972	+	0.516102i
$339$	−6.72482	+	11.6477i	−0.365242	+	0.632618i
$340$	10.1180			0.548726
$341$	−1.62189	+	2.80920i	−0.0878303	+	0.152127i
$342$	55.6924			3.01150
$343$	3.95263			0.213422
$344$	11.1781	−	18.2905i	0.602685	−	0.986160i
$345$	−54.4885			−2.93356
$346$	−25.6714			−1.38011
$347$	−2.25420	+	3.90439i	−0.121012	+	0.209599i	−0.920167	−	0.391526i	$-0.871947\pi$
$347$	−2.25420	+	3.90439i	−0.121012	+	0.209599i	0.799155	+	0.601125i	$0.205281\pi$
$348$	−42.4553			−2.27584
$349$	0.902306	−	1.56284i	0.0482993	−	0.0836569i	−0.840865	−	0.541245i	$-0.817953\pi$
$349$	0.902306	−	1.56284i	0.0482993	−	0.0836569i	0.889164	+	0.457588i	$0.151287\pi$
$350$	−15.9706	+	27.6619i	−0.853664	+	1.47859i
$351$	−7.08717	−	12.2753i	−0.378285	−	0.655209i
$352$	2.37057			0.126352
$353$	−15.8692	−	27.4862i	−0.844631	−	1.46294i	−0.885942	−	0.463797i	$-0.846487\pi$
$353$	−15.8692	−	27.4862i	−0.844631	−	1.46294i	0.0413108	−	0.999146i	$-0.486847\pi$
$354$	7.80381	−	13.5166i	0.414768	−	0.718399i
$355$	37.8801			2.01047
$356$	14.1215	−	24.4591i	0.748438	−	1.29633i
$357$	5.00466	+	8.66833i	0.264875	+	0.458776i
$358$	−1.10577	−	1.91525i	−0.0584419	−	0.101224i
$359$	15.5614	+	26.9532i	0.821301	+	1.42253i	0.904714	+	0.426019i	$0.140085\pi$
$359$	15.5614	+	26.9532i	0.821301	+	1.42253i	−0.0834133	+	0.996515i	$0.526582\pi$
$360$	46.2894			2.43967
$361$	−3.12562	−	5.41373i	−0.164506	−	0.284933i
$362$	−26.1081	−	45.2205i	−1.37221	−	2.37674i
$363$	−14.9740	+	25.9358i	−0.785932	+	1.36127i
$364$	−17.6081	+	30.4982i	−0.922916	+	1.59854i
$365$	10.3609			0.542316
$366$	29.5997			1.54720
$367$	12.9247	−	22.3863i	0.674664	−	1.16855i	−0.301903	−	0.953339i	$-0.597622\pi$
$367$	12.9247	−	22.3863i	0.674664	−	1.16855i	0.976567	−	0.215214i	$-0.0690449\pi$
$368$	2.59511	−	4.49486i	0.135279	−	0.234311i
$369$	−10.0611	−	17.4264i	−0.523762	−	0.907182i
$370$	26.5222	+	45.9378i	1.37882	+	2.38819i
$371$	−19.7007			−1.02281
$372$	30.5508	+	52.9156i	1.58399	+	2.74355i
$373$	11.7173	+	20.2950i	0.606701	+	1.05084i	0.991780	+	0.127954i	$0.0408409\pi$
$373$	11.7173	+	20.2950i	0.606701	+	1.05084i	−0.385079	+	0.922884i	$0.625826\pi$
$374$	−0.585816	−	1.01466i	−0.0302918	−	0.0524670i
$375$	4.86397	−	8.42465i	0.251174	−	0.435047i
$376$	31.0984			1.60378
$377$	6.43819	−	11.1513i	0.331583	−	0.574319i
$378$	20.5578	+	35.6071i	1.05738	+	1.83143i
$379$	15.0200			0.771525			0.385762	−	0.922598i	$-0.373938\pi$
$379$	15.0200			0.771525			0.385762	+	0.922598i	$0.373938\pi$
$380$	−25.4218	−	44.0319i	−1.30411	−	2.25879i
$381$	22.9159	−	39.6915i	1.17402	−	2.03346i
$382$	23.1914	−	40.1687i	1.18657	−	2.05521i
$383$	−13.4675			−0.688155			−0.344078	−	0.938941i	$-0.611808\pi$
$383$	−13.4675			−0.688155			−0.344078	+	0.938941i	$0.611808\pi$
$384$	27.4365	−	47.5215i	1.40012	−	2.42507i
$385$	5.37648			0.274011
$386$	35.0301			1.78299
$387$	31.2477	+	0.780548i	1.58841	+	0.0396775i
$388$	−34.8776			−1.77064
$389$	−33.1441			−1.68047			−0.840236	−	0.542221i	$-0.817583\pi$
$389$	−33.1441			−1.68047			−0.840236	+	0.542221i	$0.817583\pi$
$390$	−27.7077	+	47.9911i	−1.40303	+	2.43012i
$391$	6.58157			0.332844
$392$	9.64250	−	16.7013i	0.487020	−	0.843543i
$393$	−16.1942	+	28.0491i	−0.816888	+	1.41489i
$394$	25.2832	+	43.7918i	1.27375	+	2.20620i
$395$	13.8279			0.695756
$396$	−4.09056	−	7.08506i	−0.205558	−	0.356037i
$397$	−6.22428	+	10.7808i	−0.312388	+	0.541071i	−0.978879	−	0.204442i	$-0.934462\pi$
$397$	−6.22428	+	10.7808i	−0.312388	+	0.541071i	0.666491	+	0.745513i	$0.267795\pi$
$398$	−41.4533			−2.07787
$399$	25.1487	−	43.5589i	1.25901	−	2.18067i
$400$	−1.50819	−	2.61226i	−0.0754093	−	0.130613i
$401$	−7.18772	−	12.4495i	−0.358938	−	0.621699i	0.628846	−	0.777530i	$-0.283528\pi$
$401$	−7.18772	−	12.4495i	−0.358938	−	0.621699i	−0.987784	+	0.155831i	$0.950194\pi$
$402$	6.11295	+	10.5879i	0.304886	+	0.528079i
$403$	−18.5317			−0.923129
$404$	22.5472	+	39.0529i	1.12177	+	1.94296i
$405$	−0.859414	−	1.48855i	−0.0427046	−	0.0739666i
$406$	−18.6753	+	32.3465i	−0.926838	+	1.60533i
$407$	1.93496	−	3.35145i	0.0959124	−	0.166125i
$408$	−9.11013			−0.451019
$409$	12.2907			0.607738			0.303869	−	0.952714i	$-0.401722\pi$
$409$	12.2907			0.607738			0.303869	+	0.952714i	$0.401722\pi$
$410$	−14.5788	+	25.2512i	−0.719994	+	1.24707i
$411$	−7.13480	+	12.3578i	−0.351934	+	0.609567i
$412$	−24.4298	−	42.3137i	−1.20357	−	2.08465i
$413$	−4.32552	−	7.49201i	−0.212845	−	0.368658i
$414$	72.9431			3.58496
$415$	−16.8000	−	29.0984i	−0.824679	−	1.42839i
$416$	6.77151	+	11.7286i	0.332001	+	0.575042i
$417$	30.8983	+	53.5173i	1.51309	+	2.62076i
$418$	−2.94376	+	5.09875i	−0.143984	+	0.249388i
$419$	−10.2081			−0.498696			−0.249348	−	0.968414i	$-0.580216\pi$
$419$	−10.2081			−0.498696			−0.249348	+	0.968414i	$0.580216\pi$
$420$	50.6372	−	87.7062i	2.47084	−	4.27963i
$421$	−5.73239	−	9.92879i	−0.279380	−	0.483900i	0.691851	−	0.722040i	$-0.256795\pi$
$421$	−5.73239	−	9.92879i	−0.279380	−	0.483900i	−0.971231	+	0.238141i	$0.923462\pi$
$422$	31.6423			1.54032
$423$	22.6736	+	39.2718i	1.10243	+	1.90946i
$424$	8.96545	−	15.5286i	0.435401	−	0.754136i
$425$	1.91249	−	3.31253i	0.0927694	−	0.160681i
$426$	−82.6246			−4.00317
$427$	8.20330	−	14.2085i	0.396986	−	0.687599i
$428$	−40.9707			−1.98039
$429$	4.04290			0.195193
$430$	−21.6597	−	39.7778i	−1.04452	−	1.91826i
$431$	12.6265			0.608196			0.304098	−	0.952641i	$-0.401645\pi$
$431$	12.6265			0.608196			0.304098	+	0.952641i	$0.401645\pi$
$432$	−3.88276			−0.186809
$433$	−4.74544	+	8.21934i	−0.228051	+	0.394996i	−0.957230	−	0.289326i	$-0.906569\pi$
$433$	−4.74544	+	8.21934i	−0.228051	+	0.394996i	0.729179	+	0.684323i	$0.239902\pi$
$434$	53.7549			2.58032
$435$	−18.5149	+	32.0687i	−0.887719	+	1.53758i
$436$	−21.8613	+	37.8649i	−1.04697	+	1.81340i
$437$	−16.5364	−	28.6419i	−0.791043	−	1.37013i
$438$	−22.5994			−1.07984
$439$	7.16534	+	12.4107i	0.341983	+	0.592332i	0.984801	−	0.173687i	$-0.0555681\pi$
$439$	7.16534	+	12.4107i	0.341983	+	0.592332i	−0.642818	+	0.766019i	$0.722235\pi$
$440$	−2.44674	+	4.23788i	−0.116644	+	0.202033i
$441$	28.1211			1.33910
$442$	3.34676	−	5.79676i	0.159189	−	0.275724i
$443$	−0.108587	−	0.188078i	−0.00515913	−	0.00893587i	0.863434	−	0.504461i	$-0.168309\pi$
$443$	−0.108587	−	0.188078i	−0.00515913	−	0.00893587i	−0.868593	+	0.495525i	$0.834976\pi$
$444$	−36.4480	−	63.1298i	−1.72974	−	2.99601i
$445$	−12.3168	−	21.3334i	−0.583874	−	1.01130i
$446$	−13.7165			−0.649495
$447$	23.9265	+	41.4419i	1.13168	+	1.96013i
$448$	−22.4745	−	38.9269i	−1.06182	−	1.83912i
$449$	−20.0777	+	34.7756i	−0.947526	+	1.64116i	−0.196913	+	0.980421i	$0.563092\pi$
$449$	−20.0777	+	34.7756i	−0.947526	+	1.64116i	−0.750613	+	0.660742i	$0.770242\pi$
$450$	21.1960	−	36.7126i	0.999189	−	1.73065i
$451$	2.12722			0.100167
$452$	−16.4373			−0.773145
$453$	−2.56774	+	4.44746i	−0.120643	+	0.208960i
$454$	19.0817	−	33.0504i	0.895548	−	1.55113i
$455$	15.3579	+	26.6006i	0.719989	+	1.24706i
$456$	22.8895	+	39.6458i	1.07190	+	1.85658i
$457$	20.9761			0.981222			0.490611	−	0.871379i	$-0.336774\pi$
$457$	20.9761			0.981222			0.490611	+	0.871379i	$0.336774\pi$
$458$	2.47128	+	4.28038i	0.115475	+	0.200009i
$459$	−2.46181	−	4.26398i	−0.114907	−	0.199025i
$460$	−33.2962	−	57.6707i	−1.55244	−	2.68891i
$461$	3.26361	−	5.65274i	0.152002	−	0.263274i	−0.779962	−	0.625827i	$-0.784761\pi$
$461$	3.26361	−	5.65274i	0.152002	−	0.263274i	0.931963	+	0.362553i	$0.118095\pi$
$462$	−11.7272			−0.545601
$463$	6.92572	−	11.9957i	0.321865	−	0.557487i	−0.659008	−	0.752136i	$-0.729023\pi$
$463$	6.92572	−	11.9957i	0.321865	−	0.557487i	0.980873	+	0.194649i	$0.0623568\pi$
$464$	−1.76360	−	3.05465i	−0.0818732	−	0.141809i
$465$	53.2932			2.47141
$466$	3.57852	+	6.19818i	0.165772	+	0.287125i
$467$	1.81086	−	3.13651i	0.0837968	−	0.145140i	−0.821081	−	0.570812i	$-0.806629\pi$
$467$	1.81086	−	3.13651i	0.0837968	−	0.145140i	0.904878	+	0.425671i	$0.139962\pi$
$468$	23.3693	−	40.4768i	1.08025	−	1.87104i
$469$	6.77661			0.312915
$470$	32.8545	−	56.9056i	1.51546	−	2.62486i
$471$	17.8447			0.822242
$472$	7.87387			0.362424
$473$	−1.72313	+	2.81952i	−0.0792298	+	0.129642i
$474$	−30.1615			−1.38536
$475$	−19.2208			−0.881909
$476$	−6.11638	+	10.5939i	−0.280344	+	0.485570i
$477$	26.1466			1.19717
$478$	−33.9074	+	58.7294i	−1.55089	+	2.68622i
$479$	−8.02385	+	13.8977i	−0.366619	+	0.635003i	−0.989035	−	0.147684i	$-0.952818\pi$
$479$	−8.02385	+	13.8977i	−0.366619	+	0.635003i	0.622416	+	0.782687i	$0.286151\pi$
$480$	−19.4734	−	33.7290i	−0.888836	−	1.53951i
$481$	22.1088			1.00807
$482$	17.8166	+	30.8593i	0.811524	+	1.40560i
$483$	32.9385	−	57.0512i	1.49875	−	2.59592i
$484$	−36.6006			−1.66366
$485$	−15.2102	+	26.3448i	−0.690659	+	1.19626i
$486$	19.0462	+	32.9890i	0.863953	+	1.49641i
$487$	0.348282	+	0.603242i	0.0157822	+	0.0273355i	0.873809	−	0.486270i	$-0.161643\pi$
$487$	0.348282	+	0.603242i	0.0157822	+	0.0273355i	−0.858026	+	0.513605i	$0.828310\pi$
$488$	7.46636	+	12.9321i	0.337986	+	0.585409i
$489$	58.6507			2.65228
$490$	−20.3740	−	35.2888i	−0.920403	−	1.59419i
$491$	17.9222	+	31.0422i	0.808819	+	1.40092i	0.913682	+	0.406429i	$0.133226\pi$
$491$	17.9222	+	31.0422i	0.808819	+	1.40092i	−0.104863	+	0.994487i	$0.533441\pi$
$492$	20.0348	−	34.7013i	0.903238	−	1.56445i
$493$	2.23638	−	3.87352i	0.100721	−	0.174454i
$494$	−33.6353			−1.51333
$495$	−7.13561			−0.320722
$496$	−2.53818	+	4.39625i	−0.113968	+	0.197398i
$497$	−22.8987	+	39.6617i	−1.02715	+	1.77907i
$498$	36.6443	+	63.4698i	1.64207	+	2.84415i
$499$	0.985814	+	1.70748i	0.0441311	+	0.0764373i	0.887247	−	0.461294i	$-0.152615\pi$
$499$	0.985814	+	1.70748i	0.0441311	+	0.0764373i	−0.843116	+	0.537732i	$0.819281\pi$
$500$	11.8889			0.531687
$501$	−12.9600	−	22.4474i	−0.579011	−	1.00288i
$502$	−20.2191	−	35.0205i	−0.902423	−	1.56304i
$503$	−5.79508	−	10.0374i	−0.258390	−	0.447544i	0.707421	−	0.706792i	$-0.249859\pi$
$503$	−5.79508	−	10.0374i	−0.258390	−	0.447544i	−0.965811	+	0.259248i	$0.916525\pi$
$504$	−27.9821	+	48.4665i	−1.24642	+	2.15887i
$505$	39.3316			1.75023
$506$	−3.85559	+	6.67808i	−0.171402	+	0.296877i
$507$	−6.56623	−	11.3730i	−0.291617	−	0.505095i
$508$	56.0128			2.48516
$509$	−20.1338	−	34.8727i	−0.892414	−	1.54571i	−0.836973	−	0.547244i	$-0.815677\pi$
$509$	−20.1338	−	34.8727i	−0.892414	−	1.54571i	−0.0554402	−	0.998462i	$-0.517656\pi$
$510$	−9.62457	+	16.6702i	−0.426183	+	0.738171i
$511$	−6.26323	+	10.8482i	−0.277069	+	0.479897i
$512$	8.86557			0.391807
$513$	−12.3707	+	21.4267i	−0.546181	+	0.946014i
$514$	−11.1449			−0.491581
$515$	−42.6156			−1.87787
$516$	29.7658	+	54.6644i	1.31036	+	2.40647i
$517$	−4.79388			−0.210835
$518$	−64.1311			−2.81776
$519$	15.3852	−	26.6479i	0.675335	−	1.16971i
$520$	−27.9564			−1.22597
$521$	−20.6123	+	35.7015i	−0.903041	+	1.56411i	−0.0795149	+	0.996834i	$0.525337\pi$
$521$	−20.6123	+	35.7015i	−0.903041	+	1.56411i	−0.823526	+	0.567279i	$0.807996\pi$
$522$	24.7856	−	42.9300i	1.08484	−	1.87899i
$523$	15.2683	+	26.4454i	0.667635	+	1.15638i	0.978564	+	0.205944i	$0.0660265\pi$
$523$	15.2683	+	26.4454i	0.667635	+	1.15638i	−0.310929	+	0.950433i	$0.600640\pi$
$524$	−39.5830			−1.72919
$525$	−19.1427	−	33.1562i	−0.835457	−	1.44705i
$526$	−2.67630	+	4.63550i	−0.116692	+	0.202117i
$527$	−6.43719			−0.280408
$528$	0.553733	−	0.959093i	0.0240981	−	0.0417392i
$529$	−10.1585	−	17.5951i	−0.441675	−	0.765003i
$530$	−18.9434	−	32.8110i	−0.822850	−	1.42522i
$531$	5.74078	+	9.94332i	0.249129	+	0.431503i
$532$	61.4703			2.66508
$533$	6.07640	+	10.5246i	0.263198	+	0.455873i
$534$	26.8656	+	46.5326i	1.16259	+	2.01366i
$535$	−17.8674	+	30.9473i	−0.772476	+	1.33797i
$536$	−3.08392	+	5.34150i	−0.133205	+	0.230718i
$537$	2.65081			0.114391
$538$	−15.1044			−0.651196
$539$	−1.48641	+	2.57454i	−0.0640242	+	0.110893i
$540$	−24.9086	+	43.1430i	−1.07190	+	1.85658i
$541$	−19.0950	−	33.0735i	−0.820957	−	1.42194i	−0.904970	−	0.425475i	$-0.860107\pi$
$541$	−19.0950	−	33.0735i	−0.820957	−	1.42194i	0.0840131	−	0.996465i	$-0.473226\pi$
$542$	−12.2489	−	21.2157i	−0.526135	−	0.911292i
$543$	62.5874			2.68588
$544$	2.35216	+	4.07406i	0.100848	+	0.174674i
$545$	19.0675	+	33.0259i	0.816763	+	1.41468i
$546$	−33.4988	−	58.0216i	−1.43362	−	2.48310i
$547$	−19.3109	+	33.4474i	−0.825674	+	1.43011i	0.0757291	+	0.997128i	$0.475872\pi$
$547$	−19.3109	+	33.4474i	−0.825674	+	1.43011i	−0.901403	+	0.432981i	$0.857462\pi$
$548$	−17.4394			−0.744974
$549$	−10.8873	+	18.8574i	−0.464660	+	0.804815i
$550$	2.24074	+	3.88107i	0.0955453	+	0.165489i
$551$	−22.4759			−0.957504
$552$	29.9795	+	51.9260i	1.27601	+	2.21012i
$553$	−8.35901	+	14.4782i	−0.355461	+	0.615677i
$554$	−31.2663	+	54.1548i	−1.32838	+	2.30082i
$555$	−63.5802			−2.69883
$556$	−37.7619	+	65.4055i	−1.60146	+	2.77381i
$557$	23.3874			0.990956			0.495478	−	0.868621i	$-0.334993\pi$
$557$	23.3874			0.990956			0.495478	+	0.868621i	$0.334993\pi$
$558$	−71.3430			−3.02019
$559$	−18.8720	−	0.471411i	−0.798199	−	0.0199386i
$560$	8.41393			0.355553
$561$	1.40435			0.0592915
$562$	−6.91822	+	11.9827i	−0.291827	+	0.505460i
$563$	1.78677			0.0753032			0.0376516	−	0.999291i	$-0.488012\pi$
$563$	1.78677			0.0753032			0.0376516	+	0.999291i	$0.488012\pi$
$564$	−45.1501	+	78.2022i	−1.90116	+	3.29291i
$565$	−7.16834	+	12.4159i	−0.301574	+	0.522342i
$566$	−22.0655	−	38.2186i	−0.927483	−	1.60645i
$567$	2.07808			0.0872710
$568$	−20.8416	−	36.0987i	−0.874494	−	1.51467i
$569$	15.8375	−	27.4314i	0.663944	−	1.14998i	−0.315627	−	0.948883i	$-0.602215\pi$
$569$	15.8375	−	27.4314i	0.663944	−	1.14998i	0.979571	−	0.201101i	$-0.0644518\pi$
$570$	96.7281			4.05150
$571$	1.82524	−	3.16141i	0.0763838	−	0.132301i	−0.825303	−	0.564690i	$-0.808996\pi$
$571$	1.82524	−	3.16141i	0.0763838	−	0.132301i	0.901687	+	0.432389i	$0.142329\pi$
$572$	2.47049	+	4.27901i	0.103296	+	0.178914i
$573$	27.7977	+	48.1471i	1.16127	+	2.01137i
$574$	−17.6258	−	30.5289i	−0.735689	−	1.27425i
$575$	−25.1744			−1.04984
$576$	29.8279	+	51.6634i	1.24283	+	2.15264i
$577$	−8.86014	−	15.3462i	−0.368852	−	0.638871i	0.620534	−	0.784180i	$-0.286916\pi$
$577$	−8.86014	−	15.3462i	−0.368852	−	0.638871i	−0.989386	+	0.145308i	$0.953583\pi$
$578$	1.16254	−	2.01357i	0.0483551	−	0.0837535i
$579$	−20.9939	+	36.3626i	−0.872479	+	1.51118i
$580$	−45.2554			−1.87913
$581$	40.6226			1.68531
$582$	33.1767	−	57.4636i	1.37522	−	2.38194i
$583$	−1.38204	+	2.39377i	−0.0572384	+	0.0991397i
$584$	−5.70057	−	9.87368i	−0.235891	−	0.408576i
$585$	−20.3828	−	35.3041i	−0.842726	−	1.45964i
$586$	9.55838			0.394853
$587$	−9.08044	−	15.7278i	−0.374790	−	0.649155i	0.615506	−	0.788132i	$-0.288952\pi$
$587$	−9.08044	−	15.7278i	−0.374790	−	0.649155i	−0.990296	+	0.138977i	$0.955618\pi$
$588$	27.9989	+	48.4954i	1.15465	+	1.99992i
$589$	16.1736	+	28.0136i	0.666423	+	1.15428i
$590$	8.31850	−	14.4081i	0.342467	−	0.593170i
$591$	−60.6101			−2.49316
$592$	3.02812	−	5.24485i	0.124455	−	0.215562i
$593$	−8.63919	−	14.9635i	−0.354769	−	0.614478i	0.632309	−	0.774716i	$-0.282107\pi$
$593$	−8.63919	−	14.9635i	−0.354769	−	0.614478i	−0.987078	+	0.160238i	$0.948774\pi$
$594$	5.76867			0.236691
$595$	5.33474	+	9.24003i	0.218703	+	0.378804i
$596$	−29.2414	+	50.6476i	−1.19778	+	2.07461i
$597$	24.8434	−	43.0301i	1.01677	−	1.76110i
$598$	−44.0539			−1.80150
$599$	−0.129072	+	0.223559i	−0.00527373	+	0.00913437i	−0.868650	−	0.495426i	$-0.835012\pi$
$599$	−0.129072	+	0.223559i	−0.00527373	+	0.00913437i	0.863376	+	0.504560i	$0.168345\pi$
$600$	34.8461			1.42258
$601$	−16.1648			−0.659375			−0.329687	−	0.944090i	$-0.606943\pi$
$601$	−16.1648			−0.659375			−0.329687	+	0.944090i	$0.606943\pi$
$602$	54.7420	+	1.36742i	2.23112	+	0.0557320i
$603$	−8.99384			−0.366257
$604$	−6.27627			−0.255378
$605$	−15.9616	+	27.6463i	−0.648932	+	1.12398i
$606$	−85.7905			−3.48500
$607$	−11.6809	+	20.2319i	−0.474112	+	0.821186i	−0.999561	−	0.0296392i	$-0.990564\pi$
$607$	−11.6809	+	20.2319i	−0.474112	+	0.821186i	0.525449	+	0.850825i	$0.323897\pi$
$608$	11.8197	−	20.4724i	0.479354	−	0.830266i
$609$	−22.3846	−	38.7713i	−0.907070	−	1.57109i
$610$	31.5519			1.27750
$611$	−13.6937	−	23.7181i	−0.553987	−	0.959533i
$612$	8.11759	−	14.0601i	0.328134	−	0.568345i
$613$	−21.3899			−0.863931			−0.431965	−	0.901890i	$-0.642180\pi$
$613$	−21.3899			−0.863931			−0.431965	+	0.901890i	$0.642180\pi$
$614$	−16.8055	+	29.1080i	−0.678215	+	1.17470i
$615$	−17.4744	−	30.2666i	−0.704638	−	1.22047i
$616$	−2.95813	−	5.12364i	−0.119187	−	0.206437i
$617$	−11.0481	−	19.1358i	−0.444779	−	0.770380i	0.553258	−	0.833010i	$-0.313385\pi$
$617$	−11.0481	−	19.1358i	−0.444779	−	0.770380i	−0.998037	+	0.0626300i	$0.980051\pi$
$618$	92.9537			3.73915
$619$	−9.14363	−	15.8372i	−0.367513	−	0.636552i	0.621663	−	0.783285i	$-0.286457\pi$
$619$	−9.14363	−	15.8372i	−0.367513	−	0.636552i	−0.989176	+	0.146733i	$0.953124\pi$
$620$	32.5658	+	56.4056i	1.30787	+	2.26530i
$621$	−16.2026	+	28.0637i	−0.650186	+	1.12616i
$622$	−12.5680	+	21.7684i	−0.503930	+	0.872832i
$623$	29.7823			1.19320
$624$	6.32693			0.253280
$625$	14.7472	−	25.5429i	0.589889	−	1.02172i
$626$	−31.3523	+	54.3038i	−1.25309	+	2.17042i
$627$	−3.52846	−	6.11147i	−0.140913	−	0.244069i
$628$	10.9044	+	18.8869i	0.435131	+	0.753669i
$629$	7.67974			0.306211
$630$	59.1245	+	102.407i	2.35558	+	4.07998i
$631$	−10.5426	−	18.2603i	−0.419693	−	0.726930i	0.576215	−	0.817298i	$-0.304529\pi$
$631$	−10.5426	−	18.2603i	−0.419693	−	0.726930i	−0.995908	+	0.0903679i	$0.971196\pi$
$632$	−7.60807	−	13.1776i	−0.302633	−	0.524176i
$633$	−18.9636	+	32.8459i	−0.753736	+	1.30551i
$634$	44.6940			1.77503
$635$	24.4273	−	42.3093i	0.969368	−	1.67899i
$636$	26.0329	+	45.0903i	1.03227	+	1.78795i
$637$	−16.9837			−0.672918
$638$	2.62021	+	4.53834i	0.103735	+	0.179675i
$639$	30.3909	−	52.6386i	1.20225	−	2.08235i
$640$	29.2461	−	50.6557i	1.15605	−	2.00234i
$641$	34.1434			1.34858			0.674291	−	0.738466i	$-0.264449\pi$
$641$	34.1434			1.34858			0.674291	+	0.738466i	$0.264449\pi$
$642$	38.9726	−	67.5025i	1.53813	−	2.66411i
$643$	28.8469			1.13761			0.568804	−	0.822473i	$-0.307406\pi$
$643$	28.8469			1.13761			0.568804	+	0.822473i	$0.307406\pi$
$644$	80.5107			3.17257
$645$	54.2718	+	1.35568i	2.13695	+	0.0533798i
$646$	−11.6836			−0.459686
$647$	18.7741			0.738084			0.369042	−	0.929413i	$-0.379686\pi$
$647$	18.7741			0.738084			0.369042	+	0.929413i	$0.379686\pi$
$648$	−0.945696	+	1.63799i	−0.0371505	+	0.0643465i
$649$	−1.21377			−0.0476448
$650$	−12.8013	+	22.1725i	−0.502108	+	0.869676i
$651$	−32.2159	+	55.7997i	−1.26264	+	2.18696i
$652$	35.8396	+	62.0760i	1.40359	+	2.43108i
$653$	−43.6976			−1.71002			−0.855010	−	0.518612i	$-0.826449\pi$
$653$	−43.6976			−1.71002			−0.855010	+	0.518612i	$0.826449\pi$
$654$	−41.5903	−	72.0365i	−1.62631	−	2.81685i
$655$	−17.2622	+	29.8991i	−0.674491	+	1.16825i
$656$	3.32900			0.129976
$657$	8.31249	−	14.3977i	0.324301	−	0.561706i
$658$	39.7213	+	68.7993i	1.54850	+	2.68208i
$659$	9.68199	+	16.7697i	0.377157	+	0.653255i	0.990647	−	0.136447i	$-0.0435684\pi$
$659$	9.68199	+	16.7697i	0.377157	+	0.653255i	−0.613490	+	0.789702i	$0.710235\pi$
$660$	−7.10459	−	12.3055i	−0.276546	−	0.478992i
$661$	−6.86779			−0.267126			−0.133563	−	0.991040i	$-0.542642\pi$
$661$	−6.86779			−0.267126			−0.133563	+	0.991040i	$0.542642\pi$
$662$	−37.1662	−	64.3737i	−1.44450	−	2.50195i
$663$	4.01150	+	6.94813i	0.155794	+	0.269843i
$664$	−18.4867	+	32.0198i	−0.717421	+	1.24261i
$665$	26.8074	−	46.4317i	1.03955	−	1.80054i
$666$	85.1141			3.29810
$667$	−29.4377			−1.13983
$668$	15.8389	−	27.4338i	0.612826	−	1.06144i
$669$	8.22045	−	14.2382i	0.317821	−	0.550482i
$670$	6.51612	+	11.2863i	0.251740	+	0.436026i
$671$	−1.15095	−	1.99351i	−0.0444321	−	0.0769587i
$672$	47.0871			1.81642
$673$	−16.0618	−	27.8199i	−0.619138	−	1.07238i	−0.989643	−	0.143548i	$-0.954149\pi$
$673$	−16.0618	−	27.8199i	−0.619138	−	1.07238i	0.370505	−	0.928830i	$-0.379184\pi$
$674$	−31.7363	−	54.9688i	−1.22243	−	2.11732i
$675$	9.41636	+	16.3096i	0.362436	+	0.627758i
$676$	8.02483	−	13.8994i	0.308647	−	0.534593i
$677$	−4.98440			−0.191566			−0.0957831	−	0.995402i	$-0.530536\pi$
$677$	−4.98440			−0.191566			−0.0957831	+	0.995402i	$0.530536\pi$
$678$	15.6357	−	27.0818i	0.600484	−	1.04007i
$679$	−18.3892	−	31.8511i	−0.705714	−	1.22233i
$680$	−9.71098			−0.372399
$681$	22.8717	+	39.6150i	0.876447	+	1.51805i
$682$	3.77101	−	6.53158i	0.144399	−	0.250107i
$683$	−24.4049	+	42.2705i	−0.933827	+	1.61743i	−0.157113	+	0.987581i	$0.550219\pi$
$683$	−24.4049	+	42.2705i	−0.933827	+	1.61743i	−0.776713	+	0.629854i	$0.783115\pi$
$684$	−81.5828			−3.11940
$685$	−7.60537	+	13.1729i	−0.290586	+	0.503310i
$686$	−9.19014			−0.350881
$687$	−5.92426			−0.226025
$688$	−2.69662	+	4.41242i	−0.102808	+	0.168222i
$689$	−15.7912			−0.601596
$690$	126.690			4.82299
$691$	3.93880	−	6.82220i	0.149839	−	0.259529i	−0.781329	−	0.624120i	$-0.785458\pi$
$691$	3.93880	−	6.82220i	0.149839	−	0.259529i	0.931168	+	0.364591i	$0.118791\pi$
$692$	37.6056			1.42955
$693$	4.31351	−	7.47121i	0.163857	−	0.283808i
$694$	5.24118	−	9.07799i	0.198952	−	0.344596i
$695$	32.9361	+	57.0470i	1.24934	+	2.16392i
$696$	40.7474			1.54453
$697$	2.11071	+	3.65585i	0.0799487	+	0.138475i
$698$	−2.09793	+	3.63371i	−0.0794076	+	0.137538i
$699$	−8.57860			−0.324472
$700$	23.3950	−	40.5214i	0.884249	−	1.53156i
$701$	−1.09638	−	1.89899i	−0.0414097	−	0.0717237i	0.844578	−	0.535433i	$-0.179852\pi$
$701$	−1.09638	−	1.89899i	−0.0414097	−	0.0717237i	−0.885987	+	0.463709i	$0.846518\pi$
$702$	16.4782	+	28.5410i	0.621928	+	1.07721i
$703$	−19.2956	−	33.4209i	−0.727747	−	1.26049i
$704$	−6.30651			−0.237685
$705$	39.3801	+	68.2084i	1.48314	+	2.56888i
$706$	36.8969	+	63.9074i	1.38863	+	2.40519i
$707$	−23.7761	+	41.1814i	−0.894192	+	1.54879i
$708$	−11.4316	+	19.8002i	−0.429628	+	0.744137i
$709$	13.0818			0.491298			0.245649	−	0.969359i	$-0.420999\pi$
$709$	13.0818			0.491298			0.245649	+	0.969359i	$0.420999\pi$
$710$	−88.0740			−3.30536
$711$	11.0940	−	19.2153i	0.416057	−	0.720632i
$712$	−13.5534	+	23.4752i	−0.507935	+	0.879770i
$713$	21.1834	+	36.6907i	0.793325	+	1.37408i
$714$	−11.6362	−	20.1545i	−0.435473	−	0.754262i
$715$	4.30954			0.161168
$716$	1.61983	+	2.80562i	0.0605357	+	0.104851i
$717$	−40.6422	−	70.3944i	−1.51781	−	2.62893i
$718$	−36.1814	−	62.6680i	−1.35028	−	2.33875i
$719$	6.34936	−	10.9974i	0.236791	−	0.410134i	−0.723000	−	0.690848i	$-0.757238\pi$
$719$	6.34936	−	10.9974i	0.236791	−	0.410134i	0.959792	+	0.280713i	$0.0905709\pi$
$720$	−11.1669			−0.416165
$721$	25.7613	−	44.6199i	0.959402	−	1.66173i
$722$	7.26728	+	12.5873i	0.270460	+	0.468451i
$723$	−42.7108			−1.58843
$724$	38.2452	+	66.2426i	1.42137	+	2.46189i
$725$	−8.55409	+	14.8161i	−0.317691	+	0.550257i
$726$	34.8156	−	60.3025i	1.29213	−	2.23803i
$727$	−14.5455			−0.539464			−0.269732	−	0.962935i	$-0.586935\pi$
$727$	−14.5455			−0.539464			−0.269732	+	0.962935i	$0.586935\pi$
$728$	16.8998	−	29.2713i	0.626347	−	1.08486i
$729$	−43.9226			−1.62676
$730$	−24.0899			−0.891607
$731$	−6.55539	−	0.163750i	−0.242460	−	0.00605651i
$732$	−43.3600			−1.60263
$733$	30.1939			1.11524			0.557619	−	0.830097i	$-0.311715\pi$
$733$	30.1939			1.11524			0.557619	+	0.830097i	$0.311715\pi$
$734$	−30.0509	+	52.0496i	−1.10920	+	1.92119i
$735$	48.8415			1.80154
$736$	15.4809	−	26.8137i	0.570634	−	0.988367i
$737$	0.475392	−	0.823403i	0.0175113	−	0.0303304i
$738$	23.3928	+	40.5176i	0.861102	+	1.49147i
$739$	−4.33258			−0.159376			−0.0796882	−	0.996820i	$-0.525392\pi$
$739$	−4.33258			−0.159376			−0.0796882	+	0.996820i	$0.525392\pi$
$740$	−38.8519	−	67.2934i	−1.42822	−	2.47375i
$741$	20.1580	−	34.9148i	0.740524	−	1.28263i
$742$	45.8055			1.68157
$743$	−2.05226	+	3.55461i	−0.0752900	+	0.130406i	−0.901212	−	0.433378i	$-0.857322\pi$
$743$	−2.05226	+	3.55461i	−0.0752900	+	0.130406i	0.825922	+	0.563784i	$0.190655\pi$
$744$	−29.3218	−	50.7869i	−1.07499	−	1.86194i
$745$	25.5045	+	44.1751i	0.934413	+	1.61845i
$746$	−27.2437	−	47.1874i	−0.997461	−	1.72765i
$747$	−53.9139			−1.97261
$748$	0.858151	+	1.48636i	0.0313771	+	0.0543468i
$749$	−21.6018	−	37.4155i	−0.789314	−	1.36713i
$750$	−11.3091	+	19.5879i	−0.412949	+	0.715249i
$751$	6.04133	−	10.4639i	0.220451	−	0.381833i	−0.734494	−	0.678616i	$-0.762580\pi$
$751$	6.04133	−	10.4639i	0.220451	−	0.381833i	0.954945	+	0.296782i	$0.0959136\pi$
$752$	−7.50218			−0.273576
$753$	48.4701			1.76635
$754$	−14.9692	+	25.9275i	−0.545147	+	0.944223i
$755$	−2.73710	+	4.74079i	−0.0996131	+	0.172535i
$756$	−30.1147	−	52.1602i	−1.09526	−	1.89705i
$757$	−4.87313	−	8.44051i	−0.177117	−	0.306775i	0.763775	−	0.645483i	$-0.223344\pi$
$757$	−4.87313	−	8.44051i	−0.177117	−	0.306775i	−0.940892	+	0.338707i	$0.890010\pi$
$758$	−34.9225			−1.26844
$759$	−4.62140	−	8.00450i	−0.167746	−	0.290545i
$760$	24.3991	+	42.2605i	0.885049	+	1.53295i
$761$	−9.68749	−	16.7792i	−0.351171	−	0.608246i	0.635284	−	0.772279i	$-0.280883\pi$
$761$	−9.68749	−	16.7792i	−0.351171	−	0.608246i	−0.986455	+	0.164032i	$0.947550\pi$
$762$	−53.2811	+	92.2856i	−1.93017	+	3.34315i
$763$	−46.1056			−1.66913
$764$	−33.9726	+	58.8423i	−1.22909	+	2.12884i
$765$	−7.08020	−	12.2633i	−0.255985	−	0.443380i
$766$	31.3128			1.13138
$767$	−3.46713	−	6.00525i	−0.125191	−	0.216837i
$768$	−28.9139	+	50.0803i	−1.04334	+	1.80712i
$769$	−1.21136	+	2.09814i	−0.0436828	+	0.0756609i	−0.887040	−	0.461692i	$-0.847242\pi$
$769$	−1.21136	+	2.09814i	−0.0436828	+	0.0756609i	0.843357	+	0.537353i	$0.180576\pi$
$770$	−12.5007			−0.450494
$771$	6.67927	−	11.5688i	0.240548	−	0.416641i
$772$	−51.3149			−1.84686
$773$	38.7186			1.39261			0.696306	−	0.717745i	$-0.254826\pi$
$773$	38.7186			1.39261			0.696306	+	0.717745i	$0.254826\pi$
$774$	−72.6530	−	1.81483i	−2.61146	−	0.0652327i
$775$	24.6221			0.884452
$776$	33.4745			1.20166
$777$	38.4345	−	66.5705i	1.37883	−	2.38820i
$778$	77.0623			2.76282
$779$	10.6064	−	18.3709i	0.380015	−	0.658205i
$780$	40.5884	−	70.3012i	1.45330	−	2.51719i
$781$	3.21277	+	5.56469i	0.114962	+	0.199120i
$782$	−15.3026			−0.547220
$783$	11.0111	+	19.0717i	0.393503	+	0.681568i
$784$	−2.32616	+	4.02902i	−0.0830771	+	0.143894i
$785$	19.0217			0.678912
$786$	37.6526	−	65.2162i	1.34302	−	2.32618i
$787$	−1.55343	−	2.69062i	−0.0553738	−	0.0959102i	0.837010	−	0.547188i	$-0.184302\pi$
$787$	−1.55343	−	2.69062i	−0.0553738	−	0.0959102i	−0.892384	+	0.451278i	$0.850968\pi$
$788$	−37.0369	−	64.1498i	−1.31938	−	2.28524i
$789$	−3.20788	−	5.55621i	−0.114204	−	0.197806i
$790$	−32.1508			−1.14387
$791$	−8.66658	−	15.0110i	−0.308148	−	0.533728i
$792$	3.92600	+	6.80003i	0.139504	+	0.241629i
$793$	6.57539	−	11.3889i	0.233499	−	0.404432i
$794$	14.4719	−	25.0660i	0.513588	−	0.889560i
$795$	45.4121			1.61060
$796$	60.7242			2.15231
$797$	−7.82501	+	13.5533i	−0.277176	+	0.480083i	−0.970682	−	0.240368i	$-0.922732\pi$
$797$	−7.82501	+	13.5533i	−0.277176	+	0.480083i	0.693506	+	0.720451i	$0.256065\pi$
$798$	−58.4725	+	101.277i	−2.06991	+	3.58518i
$799$	−4.75665	−	8.23877i	−0.168278	−	0.291467i
$800$	−8.99696	−	15.5832i	−0.318091	−	0.550949i
$801$	−39.5268			−1.39661
$802$	16.7120	+	28.9460i	0.590120	+	1.02212i
$803$	0.878755	+	1.52205i	0.0310106	+	0.0537119i
$804$	−8.95475	−	15.5101i	−0.315810	−	0.546998i
$805$	35.1109	−	60.8139i	1.23750	−	2.14341i
$806$	43.0875			1.51769
$807$	9.05223	−	15.6789i	0.318654	−	0.551924i
$808$	−21.6402	−	37.4819i	−0.761298	−	1.31861i
$809$	−15.0932			−0.530648			−0.265324	−	0.964159i	$-0.585479\pi$
$809$	−15.0932			−0.530648			−0.265324	+	0.964159i	$0.585479\pi$
$810$	1.99820	+	3.46098i	0.0702095	+	0.121606i
$811$	−18.9865	+	32.8856i	−0.666706	+	1.15477i	0.312113	+	0.950045i	$0.398963\pi$
$811$	−18.9865	+	32.8856i	−0.666706	+	1.15477i	−0.978820	+	0.204724i	$0.934370\pi$
$812$	27.3571	−	47.3838i	0.960044	−	1.66285i
$813$	29.3636			1.02983
$814$	−4.49892	+	7.79235i	−0.157687	+	0.273122i
$815$	62.5190			2.18994
$816$	2.19773			0.0769360
$817$	15.7580	+	28.9394i	0.551303	+	1.01246i
$818$	−28.5768			−0.999165
$819$	49.2860			1.72219
$820$	21.3562	−	36.9900i	0.745789	−	1.29175i
$821$	−21.5513			−0.752146			−0.376073	−	0.926590i	$-0.622726\pi$
$821$	−21.5513			−0.752146			−0.376073	+	0.926590i	$0.622726\pi$
$822$	16.5889	−	28.7328i	0.578605	−	1.00217i
$823$	−0.486184	+	0.842095i	−0.0169473	+	0.0293536i	−0.874375	−	0.485251i	$-0.838728\pi$
$823$	−0.486184	+	0.842095i	−0.0169473	+	0.0293536i	0.857427	+	0.514605i	$0.172061\pi$
$824$	23.4471	+	40.6115i	0.816817	+	1.41477i
$825$	−5.37159			−0.187015
$826$	10.0571	+	17.4195i	0.349932	+	0.606100i
$827$	−5.35696	+	9.27853i	−0.186280	+	0.322646i	−0.944007	−	0.329925i	$-0.892976\pi$
$827$	−5.35696	+	9.27853i	−0.186280	+	0.322646i	0.757727	+	0.652571i	$0.226310\pi$
$828$	−106.853			−3.71340
$829$	−17.0147	+	29.4704i	−0.590946	+	1.02355i	0.403159	+	0.915130i	$0.367912\pi$
$829$	−17.0147	+	29.4704i	−0.590946	+	1.02355i	−0.994105	+	0.108419i	$0.965421\pi$
$830$	39.0611	+	67.6559i	1.35583	+	2.34837i
$831$	−37.4765	−	64.9112i	−1.30005	−	2.25175i
$832$	−18.0145	−	31.2020i	−0.624540	−	1.08173i
$833$	−5.89947			−0.204405
$834$	−71.8406	−	124.432i	−2.48764	−	4.30871i
$835$	−13.8148	−	23.9279i	−0.478080	−	0.828058i
$836$	4.31226	−	7.46906i	0.149143	−	0.258323i
$837$	15.8471	−	27.4480i	0.547757	−	0.948743i
$838$	23.7344			0.819892
$839$	−30.5573			−1.05496			−0.527478	−	0.849569i	$-0.676862\pi$
$839$	−30.5573			−1.05496			−0.527478	+	0.849569i	$0.676862\pi$
$840$	−48.6001	+	84.1779i	−1.67686	+	2.90441i
$841$	4.49724	−	7.78945i	0.155077	−	0.268602i
$842$	13.3282	+	23.0851i	0.459320	+	0.795566i
$843$	−8.29233	−	14.3627i	−0.285603	−	0.494679i
$844$	−46.3523			−1.59551
$845$	−6.99930	−	12.1231i	−0.240783	−	0.417049i
$846$	−52.7177	−	91.3097i	−1.81247	−	3.13929i
$847$	−19.2977	−	33.4246i	−0.663077	−	1.14848i
$848$	−2.16283	+	3.74613i	−0.0742718	+	0.128643i
$849$	52.8965			1.81540
$850$	−4.44667	+	7.70186i	−0.152520	+	0.264172i
$851$	−25.2724	−	43.7730i	−0.866326	−	1.50052i
$852$	121.035			4.14660
$853$	−2.05349	−	3.55674i	−0.0703100	−	0.121781i	0.828727	−	0.559653i	$-0.189066\pi$
$853$	−2.05349	−	3.55674i	−0.0703100	−	0.121781i	−0.899037	+	0.437872i	$0.855732\pi$
$854$	−19.0733	+	33.0359i	−0.652673	+	1.13046i
$855$	−35.5785	+	61.6237i	−1.21676	+	2.10749i
$856$	39.3225			1.34401
$857$	−16.5200	+	28.6135i	−0.564314	+	0.977420i	0.432799	+	0.901490i	$0.357526\pi$
$857$	−16.5200	+	28.6135i	−0.564314	+	0.977420i	−0.997113	+	0.0759298i	$0.975808\pi$
$858$	−9.40002			−0.320911
$859$	−12.4751			−0.425645			−0.212822	−	0.977091i	$-0.568266\pi$
$859$	−12.4751			−0.425645			−0.212822	+	0.977091i	$0.568266\pi$
$860$	31.7289	+	58.2698i	1.08195	+	1.98698i
$861$	42.2535			1.43999
$862$	−29.3574			−0.999918
$863$	−22.2856	+	38.5998i	−0.758612	+	1.31395i	0.184947	+	0.982748i	$0.440789\pi$
$863$	−22.2856	+	38.5998i	−0.758612	+	1.31395i	−0.943559	+	0.331205i	$0.892545\pi$
$864$	−23.1623			−0.787996
$865$	16.3999	−	28.4054i	0.557613	−	0.965814i
$866$	11.0335	−	19.1105i	0.374933	−	0.649403i
$867$	1.39344	+	2.41351i	0.0473237	+	0.0819671i
$868$	−78.7446			−2.67277
$869$	1.17280	+	2.03135i	0.0397845	+	0.0689088i
$870$	43.0483	−	74.5619i	1.45948	−	2.52789i
$871$	5.43181			0.184050
$872$	20.9818	−	36.3416i	0.710535	−	1.23068i
$873$	24.4060	+	42.2724i	0.826018	+	1.43071i
$874$	38.4483	+	66.5943i	1.30053	+	2.25259i
$875$	6.26843	+	10.8572i	0.211911	+	0.367041i
$876$	33.1054			1.11853
$877$	−3.04763	−	5.27866i	−0.102911	−	0.178248i	0.809972	−	0.586469i	$-0.199482\pi$
$877$	−3.04763	−	5.27866i	−0.102911	−	0.178248i	−0.912883	+	0.408221i	$0.866149\pi$
$878$	−16.6599	−	28.8558i	−0.562245	−	0.973837i
$879$	−5.72845	+	9.92196i	−0.193216	+	0.334659i
$880$	0.590253	−	1.02235i	0.0198974	−	0.0344634i
$881$	−17.7513			−0.598055			−0.299028	−	0.954244i	$-0.596662\pi$
$881$	−17.7513			−0.598055			−0.299028	+	0.954244i	$0.596662\pi$
$882$	−65.3835			−2.20158
$883$	16.5651	−	28.6916i	0.557460	−	0.965549i	−0.440248	−	0.897876i	$-0.645109\pi$
$883$	16.5651	−	28.6916i	0.557460	−	0.965549i	0.997708	−	0.0676727i	$-0.0215574\pi$
$884$	−4.90260	+	8.49156i	−0.164892	+	0.285602i
$885$	9.97074	+	17.2698i	0.335163	+	0.580519i
$886$	0.252473	+	0.437295i	0.00848198	+	0.0146912i
$887$	48.4779			1.62773			0.813863	−	0.581056i	$-0.197360\pi$
$887$	48.4779			1.62773			0.813863	+	0.581056i	$0.197360\pi$
$888$	34.9817	+	60.5901i	1.17391	+	2.03327i
$889$	29.5328	+	51.1523i	0.990499	+	1.71559i
$890$	28.6375	+	49.6016i	0.959931	+	1.66265i
$891$	0.145781	−	0.252500i	0.00488385	−	0.00845908i
$892$	20.0930			0.672764
$893$	−23.9025	+	41.4003i	−0.799866	+	1.38541i
$894$	−55.6307	−	96.3553i	−1.86057	−	3.22260i
$895$	2.82564			0.0944507
$896$	35.3587	+	61.2431i	1.18125	+	2.04599i
$897$	26.4020	−	45.7296i	0.881536	−	1.52687i
$898$	46.6821	−	80.8558i	1.55780	−	2.69819i
$899$	28.7920			0.960266
$900$	−31.0496	+	53.7795i	−1.03499	+	1.79265i
$901$	−5.48524			−0.182740
$902$	−4.94595			−0.164682
$903$	−34.2270	+	56.0048i	−1.13900	+	1.86372i
$904$	15.7760			0.524703
$905$	66.7153			2.21769
$906$	5.97018	−	10.3407i	0.198346	−	0.343545i
$907$	7.49684			0.248928			0.124464	−	0.992224i	$-0.460279\pi$
$907$	7.49684			0.248928			0.124464	+	0.992224i	$0.460279\pi$
$908$	−27.9524	+	48.4150i	−0.927633	+	1.60671i
$909$	31.5554	−	54.6555i	1.04663	−	1.81281i
$910$	−35.7082	−	61.8483i	−1.18371	−	2.05025i
$911$	36.4154			1.20649			0.603247	−	0.797554i	$-0.293873\pi$
$911$	36.4154			1.20649			0.603247	+	0.797554i	$0.293873\pi$
$912$	−5.52187	−	9.56415i	−0.182847	−	0.316701i
$913$	2.84976	−	4.93592i	0.0943131	−	0.163355i
$914$	−48.7710			−1.61320
$915$	−18.9094	+	32.7521i	−0.625126	+	1.08275i
$916$	−3.62013	−	6.27024i	−0.119612	−	0.207175i
$917$	−20.8702	−	36.1482i	−0.689194	−	1.19372i
$918$	5.72388	+	9.91404i	0.188916	+	0.327212i
$919$	20.8956			0.689282			0.344641	−	0.938735i	$-0.388001\pi$
$919$	20.8956			0.689282			0.344641	+	0.938735i	$0.388001\pi$
$920$	31.9567	+	55.3507i	1.05358	+	1.82486i
$921$	−20.1435	−	34.8895i	−0.663750	−	1.14965i
$922$	−7.58812	+	13.1430i	−0.249902	+	0.432842i
$923$	−18.3545	+	31.7910i	−0.604147	+	1.04641i
$924$	17.1790			0.565148
$925$	−29.3748			−0.965839
$926$	−16.1028	+	27.8908i	−0.529170	+	0.916550i
$927$	−34.1901	+	59.2191i	−1.12295	+	1.94501i
$928$	−10.5206	−	18.2223i	−0.345357	−	0.598175i
$929$	−17.1962	−	29.7847i	−0.564190	−	0.977206i	−0.997125	−	0.0757805i	$-0.975855\pi$
$929$	−17.1962	−	29.7847i	−0.564190	−	0.977206i	0.432934	−	0.901425i	$-0.357478\pi$
$930$	−123.910			−4.06318
$931$	14.8226	+	25.6735i	0.485791	+	0.841415i
$932$	−5.24211	−	9.07960i	−0.171711	−	0.297412i
$933$	−15.0643	−	26.0921i	−0.493182	−	0.854216i
$934$	−4.21038	+	7.29260i	−0.137768	+	0.238621i
$935$	1.49697			0.0489561
$936$	−22.4292	+	38.8485i	−0.733121	+	1.26980i
$937$	24.6378	+	42.6739i	0.804882	+	1.39410i	0.916371	+	0.400330i	$0.131105\pi$
$937$	24.6378	+	42.6739i	0.804882	+	1.39410i	−0.111490	+	0.993766i	$0.535562\pi$
$938$	−15.7561			−0.514454
$939$	−37.5796	−	65.0898i	−1.22636	−	2.12413i
$940$	−48.1279	+	83.3599i	−1.56976	+	2.71890i
$941$	−17.0483	+	29.5285i	−0.555759	+	0.962602i	0.442085	+	0.896973i	$0.354239\pi$
$941$	−17.0483	+	29.5285i	−0.555759	+	0.962602i	−0.997844	+	0.0656294i	$0.979094\pi$
$942$	−41.4903			−1.35183
$943$	13.8918	−	24.0612i	0.452378	−	0.783542i
$944$	−1.89949			−0.0618233
$945$	−52.5324			−1.70888
$946$	4.00641	−	6.55559i	0.130260	−	0.213141i
$947$	30.3688			0.986855			0.493427	−	0.869787i	$-0.335744\pi$
$947$	30.3688			0.986855			0.493427	+	0.869787i	$0.335744\pi$
$948$	44.1830			1.43500
$949$	−5.02031	+	8.69544i	−0.162966	+	0.282266i
$950$	44.6896			1.44992
$951$	−26.7856	+	46.3941i	−0.868584	+	1.50443i
$952$	5.87032	−	10.1677i	0.190258	−	0.329537i
$953$	−13.9581	−	24.1762i	−0.452149	−	0.783145i	0.546370	−	0.837544i	$-0.316009\pi$
$953$	−13.9581	−	24.1762i	−0.452149	−	0.783145i	−0.998519	+	0.0543989i	$0.982676\pi$
$954$	−60.7926			−1.96823
$955$	29.6311	+	51.3225i	0.958839	+	1.66076i
$956$	49.6703	−	86.0315i	1.60645	−	2.78246i
$957$	−6.28129			−0.203045
$958$	18.6560	−	32.3132i	0.602748	−	1.04399i
$959$	−9.19495	−	15.9261i	−0.296920	−	0.514281i
$960$	51.8058	+	89.7304i	1.67203	+	2.89603i
$961$	−5.21870	−	9.03906i	−0.168345	−	0.291583i
$962$	−51.4045			−1.65735
$963$	28.6697	+	49.6574i	0.923869	+	1.60019i
$964$	−26.0992	−	45.2051i	−0.840598	−	1.45596i
$965$	−22.3786	+	38.7608i	−0.720392	+	1.24775i
$966$	−76.5843	+	132.648i	−2.46406	+	4.26788i
$967$	−52.7063			−1.69492			−0.847459	−	0.530860i	$-0.821869\pi$
$967$	−52.7063			−1.69492			−0.847459	+	0.530860i	$0.821869\pi$
$968$	35.1282			1.12906
$969$	7.00213	−	12.1280i	0.224941	−	0.389609i
$970$	35.3648	−	61.2536i	1.13549	−	1.96673i
$971$	−12.5472	−	21.7324i	−0.402658	−	0.697425i	0.591388	−	0.806388i	$-0.298580\pi$
$971$	−12.5472	−	21.7324i	−0.402658	−	0.697425i	−0.994046	+	0.108963i	$0.965247\pi$
$972$	−27.9004	−	48.3249i	−0.894906	−	1.55002i
$973$	−79.6400			−2.55314
$974$	−0.809780	−	1.40258i	−0.0259470	−	0.0449415i
$975$	−15.3439	−	26.5764i	−0.491399	−	0.851127i
$976$	−1.80119	−	3.11975i	−0.0576546	−	0.0998607i
$977$	−13.0026	+	22.5211i	−0.415990	+	0.720515i	−0.995532	−	0.0944272i	$-0.969898\pi$
$977$	−13.0026	+	22.5211i	−0.415990	+	0.720515i	0.579542	+	0.814942i	$0.303231\pi$
$978$	−136.367			−4.36054
$979$	2.08929	−	3.61875i	0.0667739	−	0.115656i
$980$	29.8455	+	51.6939i	0.953379	+	1.65130i
$981$	61.1908			1.95367
$982$	−41.6704	−	72.1753i	−1.32976	−	2.30321i
$983$	9.71576	−	16.8282i	0.309885	−	0.536736i	−0.668452	−	0.743755i	$-0.733043\pi$
$983$	9.71576	−	16.8282i	0.309885	−	0.536736i	0.978337	+	0.207019i	$0.0663762\pi$
$984$	−19.2288	+	33.3053i	−0.612992	+	1.06173i
$985$	−64.6075			−2.05857
$986$	−5.19973	+	9.00620i	−0.165593	+	0.286816i
$987$	−95.2217			−3.03094
$988$	49.2718			1.56754
$989$	20.6390	+	37.9033i	0.656283	+	1.20526i
$990$	16.5908			0.527290
$991$	37.5650			1.19329			0.596646	−	0.802504i	$-0.296500\pi$
$991$	37.5650			1.19329			0.596646	+	0.802504i	$0.296500\pi$
$992$	−15.1413	+	26.2255i	−0.480737	+	0.832661i
$993$	89.0964			2.82739
$994$	53.2411	−	92.2162i	1.68870	−	2.92492i
$995$	26.4820	−	45.8681i	0.839534	−	1.45412i
$996$	−53.6796	−	92.9758i	−1.70090	−	2.94605i
$997$	−17.1424			−0.542906			−0.271453	−	0.962452i	$-0.587504\pi$
$997$	−17.1424			−0.542906			−0.271453	+	0.962452i	$0.587504\pi$
$998$	−2.29209	−	3.97001i	−0.0725548	−	0.125669i
$999$	−18.9060	+	32.7462i	−0.598161	+	1.03605i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.e.a.307.3	✓	58
43.36	even	3	inner	731.2.e.a.681.3	yes	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.e.a.307.3	✓	58	1.1	even	1	trivial
731.2.e.a.681.3	yes	58	43.36	even	3	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.32507 q^{2} +(1.39344 - 2.41351i) q^{3} +3.40595 q^{4} +(1.48534 - 2.57269i) q^{5} +(-3.23985 + 5.61158i) q^{6} +(1.79579 + 3.11040i) q^{7} -3.26893 q^{8} +(-2.38336 - 4.12809i) q^{9} +O(q^{10})\)	\(q-2.32507 q^{2} +(1.39344 - 2.41351i) q^{3} +3.40595 q^{4} +(1.48534 - 2.57269i) q^{5} +(-3.23985 + 5.61158i) q^{6} +(1.79579 + 3.11040i) q^{7} -3.26893 q^{8} +(-2.38336 - 4.12809i) q^{9} +(-3.45353 + 5.98168i) q^{10} +0.503913 q^{11} +(4.74599 - 8.22030i) q^{12} +(1.43942 + 2.49315i) q^{13} +(-4.17534 - 7.23190i) q^{14} +(-4.13948 - 7.16978i) q^{15} +0.788599 q^{16} +(0.500000 + 0.866025i) q^{17} +(5.54147 + 9.59811i) q^{18} +(2.51253 - 4.35183i) q^{19} +(5.05901 - 8.76246i) q^{20} +10.0093 q^{21} -1.17163 q^{22} +(3.29078 - 5.69981i) q^{23} +(-4.55507 + 7.88961i) q^{24} +(-1.91249 - 3.31253i) q^{25} +(-3.34676 - 5.79676i) q^{26} -4.92362 q^{27} +(6.11638 + 10.5939i) q^{28} +(-2.23638 - 3.87352i) q^{29} +(9.62457 + 16.6702i) q^{30} +(-3.21859 + 5.57477i) q^{31} +4.70432 q^{32} +(0.702173 - 1.21620i) q^{33} +(-1.16254 - 2.01357i) q^{34} +10.6695 q^{35} +(-8.11759 - 14.0601i) q^{36} +(3.83987 - 6.65085i) q^{37} +(-5.84181 + 10.1183i) q^{38} +8.02301 q^{39} +(-4.85549 + 8.40995i) q^{40} +4.22141 q^{41} -23.2724 q^{42} +(-3.41951 + 5.59526i) q^{43} +1.71630 q^{44} -14.1604 q^{45} +(-7.65130 + 13.2524i) q^{46} -9.51331 q^{47} +(1.09887 - 1.90329i) q^{48} +(-2.94974 + 5.10909i) q^{49} +(4.44667 + 7.70186i) q^{50} +2.78688 q^{51} +(4.90260 + 8.49156i) q^{52} +(-2.74262 + 4.75036i) q^{53} +11.4478 q^{54} +(0.748484 - 1.29641i) q^{55} +(-5.87032 - 10.1677i) q^{56} +(-7.00213 - 12.1280i) q^{57} +(5.19973 + 9.00620i) q^{58} -2.40870 q^{59} +(-14.0989 - 24.4199i) q^{60} +(-2.28404 - 3.95607i) q^{61} +(7.48346 - 12.9617i) q^{62} +(8.56002 - 14.8264i) q^{63} -12.5151 q^{64} +8.55215 q^{65} +(-1.63260 + 2.82775i) q^{66} +(0.943401 - 1.63402i) q^{67} +(1.70298 + 2.94964i) q^{68} +(-9.17103 - 15.8847i) q^{69} -24.8073 q^{70} +(6.37565 + 11.0430i) q^{71} +(7.79103 + 13.4945i) q^{72} +(1.74386 + 3.02046i) q^{73} +(-8.92797 + 15.4637i) q^{74} -10.6598 q^{75} +(8.55755 - 14.8221i) q^{76} +(0.904923 + 1.56737i) q^{77} -18.6541 q^{78} +(2.32739 + 4.03115i) q^{79} +(1.17134 - 2.02882i) q^{80} +(0.289298 - 0.501079i) q^{81} -9.81508 q^{82} +(5.65525 - 9.79519i) q^{83} +34.0913 q^{84} +2.97069 q^{85} +(7.95060 - 13.0094i) q^{86} -12.4650 q^{87} -1.64726 q^{88} +(4.14612 - 7.18130i) q^{89} +32.9239 q^{90} +(-5.16981 + 8.95437i) q^{91} +(11.2082 - 19.4133i) q^{92} +(8.96984 + 15.5362i) q^{93} +22.1191 q^{94} +(-7.46394 - 12.9279i) q^{95} +(6.55519 - 11.3539i) q^{96} -10.2402 q^{97} +(6.85835 - 11.8790i) q^{98} +(-1.20100 - 2.08020i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9}+O(q^{10}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9	\( 58 q - 6 q^{2} + 3 q^{3} + 54 q^{4} - q^{5} + 12 q^{6} + 7 q^{7} - 12 q^{8} - 22 q^{9} + 4 q^{10} + 16 q^{11} + 12 q^{12} + 2 q^{13} - 11 q^{14} + 7 q^{15} + 30 q^{16} + 29 q^{17} + 8 q^{18} + 8 q^{19} - 33 q^{20} - 26 q^{21} - 22 q^{22} - 5 q^{23} + 12 q^{24} - 36 q^{25} - 12 q^{27} + 15 q^{28} + 2 q^{29} + 11 q^{30} + 3 q^{31} - 40 q^{32} + 17 q^{33} - 3 q^{34} + 38 q^{35} - 7 q^{36} + 2 q^{37} + q^{38} - 54 q^{39} + 5 q^{40} + 14 q^{41} - 112 q^{42} + 31 q^{43} - 24 q^{44} - 46 q^{45} - 13 q^{46} - 28 q^{47} - 28 q^{49} - 13 q^{50} + 6 q^{51} + 85 q^{52} - 10 q^{53} + 34 q^{54} + 36 q^{55} - 54 q^{56} - 23 q^{57} + 3 q^{58} + 12 q^{59} + 2 q^{60} - q^{61} - q^{62} - 14 q^{63} + 28 q^{64} + 80 q^{65} - 74 q^{66} + 11 q^{67} + 27 q^{68} - 11 q^{69} + 2 q^{70} + 16 q^{71} + 21 q^{72} + 14 q^{73} + 21 q^{74} - 54 q^{75} + 44 q^{76} + 25 q^{77} + 88 q^{78} - 4 q^{79} - 112 q^{80} + 11 q^{81} - 176 q^{82} - 3 q^{83} + 100 q^{84} - 2 q^{85} + 44 q^{86} + 8 q^{87} - 106 q^{88} + 82 q^{89} + 54 q^{90} - 15 q^{91} + 42 q^{92} + 88 q^{94} + 29 q^{95} + 20 q^{96} + 20 q^{97} + 44 q^{98} - 54 q^{99}+O(q^{100}) \) 58 * q - 6 * q^2 + 3 * q^3 + 54 * q^4 - q^5 + 12 * q^6 + 7 * q^7 - 12 * q^8 - 22 * q^9 + 4 * q^10 + 16 * q^11 + 12 * q^12 + 2 * q^13 - 11 * q^14 + 7 * q^15 + 30 * q^16 + 29 * q^17 + 8 * q^18 + 8 * q^19 - 33 * q^20 - 26 * q^21 - 22 * q^22 - 5 * q^23 + 12 * q^24 - 36 * q^25 - 12 * q^27 + 15 * q^28 + 2 * q^29 + 11 * q^30 + 3 * q^31 - 40 * q^32 + 17 * q^33 - 3 * q^34 + 38 * q^35 - 7 * q^36 + 2 * q^37 + q^38 - 54 * q^39 + 5 * q^40 + 14 * q^41 - 112 * q^42 + 31 * q^43 - 24 * q^44 - 46 * q^45 - 13 * q^46 - 28 * q^47 - 28 * q^49 - 13 * q^50 + 6 * q^51 + 85 * q^52 - 10 * q^53 + 34 * q^54 + 36 * q^55 - 54 * q^56 - 23 * q^57 + 3 * q^58 + 12 * q^59 + 2 * q^60 - q^61 - q^62 - 14 * q^63 + 28 * q^64 + 80 * q^65 - 74 * q^66 + 11 * q^67 + 27 * q^68 - 11 * q^69 + 2 * q^70 + 16 * q^71 + 21 * q^72 + 14 * q^73 + 21 * q^74 - 54 * q^75 + 44 * q^76 + 25 * q^77 + 88 * q^78 - 4 * q^79 - 112 * q^80 + 11 * q^81 - 176 * q^82 - 3 * q^83 + 100 * q^84 - 2 * q^85 + 44 * q^86 + 8 * q^87 - 106 * q^88 + 82 * q^89 + 54 * q^90 - 15 * q^91 + 42 * q^92 + 88 * q^94 + 29 * q^95 + 20 * q^96 + 20 * q^97 + 44 * q^98 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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