LMFDB - Embedded newform 114.2.i.c.73.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,2,Mod(25,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("114.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	114.i (of order $9$, degree $6$, 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:	$0.910294583043$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			73.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	114.73
Dual form			114.2.i.c.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.766044 + 0.642788i) q^{2} +(0.939693 - 0.342020i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.613341 + 3.47843i) q^{5} +(0.939693 + 0.342020i) q^{6} +(-1.85844 - 3.21891i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.766044 - 0.642788i) q^{9} +(-2.70574 + 2.27038i) q^{10} +(2.64543 - 4.58202i) q^{11} +(0.500000 + 0.866025i) q^{12} +(0.213011 + 0.0775297i) q^{13} +(0.645430 - 3.66041i) q^{14} +(0.613341 + 3.47843i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-1.26604 - 1.06234i) q^{17} +1.00000 q^{18} +(-4.17752 - 1.24432i) q^{19} -3.53209 q^{20} +(-2.84730 - 2.38917i) q^{21} +(4.97178 - 1.80958i) q^{22} +(1.50727 + 8.54818i) q^{23} +(-0.173648 + 0.984808i) q^{24} +(-7.02481 - 2.55682i) q^{25} +(0.113341 + 0.196312i) q^{26} +(0.500000 - 0.866025i) q^{27} +(2.84730 - 2.38917i) q^{28} +(0.0923963 - 0.0775297i) q^{29} +(-1.76604 + 3.05888i) q^{30} +(-1.56031 - 2.70253i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(0.918748 - 5.21048i) q^{33} +(-0.286989 - 1.62760i) q^{34} +(12.3366 - 4.49016i) q^{35} +(0.766044 + 0.642788i) q^{36} +5.12836 q^{37} +(-2.40033 - 3.63846i) q^{38} +0.226682 q^{39} +(-2.70574 - 2.27038i) q^{40} +(-6.67752 + 2.43042i) q^{41} +(-0.645430 - 3.66041i) q^{42} +(-0.929892 + 5.27368i) q^{43} +(4.97178 + 1.80958i) q^{44} +(1.76604 + 3.05888i) q^{45} +(-4.34002 + 7.51714i) q^{46} +(-1.92262 + 1.61327i) q^{47} +(-0.766044 + 0.642788i) q^{48} +(-3.40760 + 5.90214i) q^{49} +(-3.73783 - 6.47410i) q^{50} +(-1.55303 - 0.565258i) q^{51} +(-0.0393628 + 0.223238i) q^{52} +(1.03074 + 5.84564i) q^{53} +(0.939693 - 0.342020i) q^{54} +(14.3157 + 12.0123i) q^{55} +3.71688 q^{56} +(-4.35117 + 0.259515i) q^{57} +0.120615 q^{58} +(0.167718 + 0.140732i) q^{59} +(-3.31908 + 1.20805i) q^{60} +(-0.273318 - 1.55007i) q^{61} +(0.541889 - 3.07321i) q^{62} +(-3.49273 - 1.27125i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.400330 + 0.693392i) q^{65} +(4.05303 - 3.40090i) q^{66} +(11.8589 - 9.95080i) q^{67} +(0.826352 - 1.43128i) q^{68} +(4.34002 + 7.51714i) q^{69} +(12.3366 + 4.49016i) q^{70} +(-0.235300 + 1.33445i) q^{71} +(0.173648 + 0.984808i) q^{72} +(-2.27972 + 0.829748i) q^{73} +(3.92855 + 3.29644i) q^{74} -7.47565 q^{75} +(0.500000 - 4.33013i) q^{76} -19.6655 q^{77} +(0.173648 + 0.145708i) q^{78} +(2.69207 - 0.979832i) q^{79} +(-0.613341 - 3.47843i) q^{80} +(0.173648 - 0.984808i) q^{81} +(-6.67752 - 2.43042i) q^{82} +(-0.960637 - 1.66387i) q^{83} +(1.85844 - 3.21891i) q^{84} +(4.47178 - 3.75227i) q^{85} +(-4.10220 + 3.44215i) q^{86} +(0.0603074 - 0.104455i) q^{87} +(2.64543 + 4.58202i) q^{88} +(11.4226 + 4.15749i) q^{89} +(-0.613341 + 3.47843i) q^{90} +(-0.146307 - 0.829748i) q^{91} +(-8.15657 + 2.96875i) q^{92} +(-2.39053 - 2.00589i) q^{93} -2.50980 q^{94} +(6.89053 - 13.7680i) q^{95} -1.00000 q^{96} +(13.4081 + 11.2507i) q^{97} +(-6.40420 + 2.33094i) q^{98} +(-0.918748 - 5.21048i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{5} - 3 q^{7} - 3 q^{8} - 6 q^{10} + 3 q^{12} + 9 q^{13} - 12 q^{14} - 3 q^{15} - 3 q^{17} + 6 q^{18} - 12 q^{20} - 15 q^{21} + 15 q^{22} + 27 q^{23} - 15 q^{25} - 6 q^{26} + 3 q^{27} + 15 q^{28}+ \cdots - 3 q^{99}+O(q^{100}) $ 6 * q + 3 * q^5 - 3 * q^7 - 3 * q^8 - 6 * q^10 + 3 * q^12 + 9 * q^13 - 12 * q^14 - 3 * q^15 - 3 * q^17 + 6 * q^18 - 12 * q^20 - 15 * q^21 + 15 * q^22 + 27 * q^23 - 15 * q^25 - 6 * q^26 + 3 * q^27 + 15 * q^28 - 3 * q^29 - 6 * q^30 - 15 * q^31 + 3 * q^33 + 6 * q^34 + 12 * q^35 - 6 * q^37 - 12 * q^39 - 6 * q^40 - 15 * q^41 + 12 * q^42 + 3 * q^43 + 15 * q^44 + 6 * q^45 - 6 * q^46 + 15 * q^47 - 24 * q^49 - 3 * q^50 + 3 * q^51 - 9 * q^52 + 6 * q^53 + 27 * q^55 + 6 * q^56 + 12 * q^58 - 27 * q^59 - 3 * q^60 - 15 * q^61 - 3 * q^62 - 3 * q^63 - 3 * q^64 + 12 * q^65 + 12 * q^66 - 3 * q^67 + 6 * q^68 + 6 * q^69 + 12 * q^70 + 3 * q^71 + 12 * q^73 + 24 * q^74 - 6 * q^75 + 3 * q^76 - 42 * q^77 + 27 * q^79 + 3 * q^80 - 15 * q^82 + 3 * q^83 + 3 * q^84 + 12 * q^85 - 24 * q^86 + 6 * q^87 + 42 * q^89 + 3 * q^90 - 42 * q^91 - 27 * q^92 + 3 * q^93 - 18 * q^94 + 24 * q^95 - 6 * q^96 + 18 * q^97 - 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	0.939693	−	0.342020i	0.542532	−	0.197465i
$3$	0.939693	−	0.342020i	0.542532	−	0.197465i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−0.613341	+	3.47843i	−0.274294	+	1.55560i	0.466900	+	0.884310i	$0.345371\pi$
$5$	−0.613341	+	3.47843i	−0.274294	+	1.55560i	−0.741194	+	0.671290i	$0.765740\pi$
$6$	0.939693	+	0.342020i	0.383628	+	0.139629i
$7$	−1.85844	−	3.21891i	−0.702425	−	1.21664i	−0.967613	−	0.252438i	$-0.918767\pi$
$7$	−1.85844	−	3.21891i	−0.702425	−	1.21664i	0.265188	−	0.964197i	$-0.414566\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	0.766044	−	0.642788i	0.255348	−	0.214263i
$10$	−2.70574	+	2.27038i	−0.855629	+	0.717958i
$11$	2.64543	−	4.58202i	0.797627	−	1.38153i	−0.123531	−	0.992341i	$-0.539422\pi$
$11$	2.64543	−	4.58202i	0.797627	−	1.38153i	0.921158	−	0.389190i	$-0.127245\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	0.213011	+	0.0775297i	0.0590786	+	0.0215029i	0.371390	−	0.928477i	$-0.378881\pi$
$13$	0.213011	+	0.0775297i	0.0590786	+	0.0215029i	−0.312312	+	0.949980i	$0.601103\pi$
$14$	0.645430	−	3.66041i	0.172498	−	0.978287i
$15$	0.613341	+	3.47843i	0.158364	+	0.898126i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−1.26604	−	1.06234i	−0.307061	−	0.257655i	0.476215	−	0.879329i	$-0.342008\pi$
$17$	−1.26604	−	1.06234i	−0.307061	−	0.257655i	−0.783276	+	0.621674i	$0.786453\pi$
$18$	1.00000			0.235702
$19$	−4.17752	−	1.24432i	−0.958388	−	0.285467i
$19$	−4.17752	−	1.24432i	−0.958388	−	0.285467i
$20$	−3.53209			−0.789799
$21$	−2.84730	−	2.38917i	−0.621331	−	0.521359i
$22$	4.97178	−	1.80958i	1.05999	−	0.385804i
$23$	1.50727	+	8.54818i	0.314288	+	1.78242i	0.576182	+	0.817321i	$0.304542\pi$
$23$	1.50727	+	8.54818i	0.314288	+	1.78242i	−0.261894	+	0.965097i	$0.584347\pi$
$24$	−0.173648	+	0.984808i	−0.0354458	+	0.201023i
$25$	−7.02481	−	2.55682i	−1.40496	−	0.511365i
$26$	0.113341	+	0.196312i	0.0222280	+	0.0385000i
$27$	0.500000	−	0.866025i	0.0962250	−	0.166667i
$28$	2.84730	−	2.38917i	0.538088	−	0.451510i
$29$	0.0923963	−	0.0775297i	0.0171576	−	0.0143969i	−0.634169	−	0.773195i	$-0.718657\pi$
$29$	0.0923963	−	0.0775297i	0.0171576	−	0.0143969i	0.651326	+	0.758798i	$0.274213\pi$
$30$	−1.76604	+	3.05888i	−0.322434	+	0.558472i
$31$	−1.56031	−	2.70253i	−0.280239	−	0.485389i	0.691204	−	0.722660i	$-0.257081\pi$
$31$	−1.56031	−	2.70253i	−0.280239	−	0.485389i	−0.971444	+	0.237271i	$0.923747\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	0.918748	−	5.21048i	0.159934	−	0.907028i
$34$	−0.286989	−	1.62760i	−0.0492182	−	0.279130i
$35$	12.3366	−	4.49016i	2.08527	−	0.758976i
$36$	0.766044	+	0.642788i	0.127674	+	0.107131i
$37$	5.12836			0.843096			0.421548	−	0.906806i	$-0.361487\pi$
$37$	5.12836			0.843096			0.421548	+	0.906806i	$0.361487\pi$
$38$	−2.40033	−	3.63846i	−0.389385	−	0.590237i
$39$	0.226682			0.0362981
$40$	−2.70574	−	2.27038i	−0.427815	−	0.358979i
$41$	−6.67752	+	2.43042i	−1.04285	+	0.379568i	−0.805961	−	0.591968i	$-0.798351\pi$
$41$	−6.67752	+	2.43042i	−1.04285	+	0.379568i	−0.236892	+	0.971536i	$0.576129\pi$
$42$	−0.645430	−	3.66041i	−0.0995920	−	0.564814i
$43$	−0.929892	+	5.27368i	−0.141807	+	0.804229i	0.828068	+	0.560627i	$0.189440\pi$
$43$	−0.929892	+	5.27368i	−0.141807	+	0.804229i	−0.969875	+	0.243602i	$0.921671\pi$
$44$	4.97178	+	1.80958i	0.749524	+	0.272805i
$45$	1.76604	+	3.05888i	0.263266	+	0.455991i
$46$	−4.34002	+	7.51714i	−0.639901	+	1.10834i
$47$	−1.92262	+	1.61327i	−0.280443	+	0.235319i	−0.772149	−	0.635442i	$-0.780818\pi$
$47$	−1.92262	+	1.61327i	−0.280443	+	0.235319i	0.491706	+	0.870761i	$0.336374\pi$
$48$	−0.766044	+	0.642788i	−0.110569	+	0.0927784i
$49$	−3.40760	+	5.90214i	−0.486801	+	0.843163i
$50$	−3.73783	−	6.47410i	−0.528608	−	0.915577i
$51$	−1.55303	−	0.565258i	−0.217468	−	0.0791519i
$52$	−0.0393628	+	0.223238i	−0.00545864	+	0.0309575i
$53$	1.03074	+	5.84564i	0.141584	+	0.802961i	0.970047	+	0.242918i	$0.0781044\pi$
$53$	1.03074	+	5.84564i	0.141584	+	0.802961i	−0.828463	+	0.560043i	$0.810784\pi$
$54$	0.939693	−	0.342020i	0.127876	−	0.0465430i
$55$	14.3157	+	12.0123i	1.93033	+	1.61974i
$56$	3.71688			0.496689
$57$	−4.35117	+	0.259515i	−0.576326	+	0.0343736i
$58$	0.120615			0.0158375
$59$	0.167718	+	0.140732i	0.0218351	+	0.0183218i	0.653640	−	0.756806i	$-0.273241\pi$
$59$	0.167718	+	0.140732i	0.0218351	+	0.0183218i	−0.631805	+	0.775128i	$0.717686\pi$
$60$	−3.31908	+	1.20805i	−0.428491	+	0.155958i
$61$	−0.273318	−	1.55007i	−0.0349948	−	0.198466i	0.962298	−	0.271997i	$-0.0876841\pi$
$61$	−0.273318	−	1.55007i	−0.0349948	−	0.198466i	−0.997293	+	0.0735316i	$0.976573\pi$
$62$	0.541889	−	3.07321i	0.0688200	−	0.390298i
$63$	−3.49273	−	1.27125i	−0.440042	−	0.160162i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−0.400330	+	0.693392i	−0.0496548	+	0.0860046i
$66$	4.05303	−	3.40090i	0.498894	−	0.418622i
$67$	11.8589	−	9.95080i	1.44880	−	1.21568i	0.515343	−	0.856984i	$-0.327664\pi$
$67$	11.8589	−	9.95080i	1.44880	−	1.21568i	0.933453	−	0.358701i	$-0.116780\pi$
$68$	0.826352	−	1.43128i	0.100210	−	0.173569i
$69$	4.34002	+	7.51714i	0.522477	+	0.904957i
$70$	12.3366	+	4.49016i	1.47451	+	0.536677i
$71$	−0.235300	+	1.33445i	−0.0279249	+	0.158370i	−0.995582	−	0.0939008i	$-0.970066\pi$
$71$	−0.235300	+	1.33445i	−0.0279249	+	0.158370i	0.967657	+	0.252271i	$0.0811775\pi$
$72$	0.173648	+	0.984808i	0.0204646	+	0.116061i
$73$	−2.27972	+	0.829748i	−0.266820	+	0.0971147i	−0.471966	−	0.881617i	$-0.656455\pi$
$73$	−2.27972	+	0.829748i	−0.266820	+	0.0971147i	0.205145	+	0.978731i	$0.434233\pi$
$74$	3.92855	+	3.29644i	0.456684	+	0.383204i
$75$	−7.47565			−0.863214
$76$	0.500000	−	4.33013i	0.0573539	−	0.496700i
$77$	−19.6655			−2.24109
$78$	0.173648	+	0.145708i	0.0196618	+	0.0164982i
$79$	2.69207	−	0.979832i	0.302881	−	0.110240i	−0.186109	−	0.982529i	$-0.559588\pi$
$79$	2.69207	−	0.979832i	0.302881	−	0.110240i	0.488990	+	0.872289i	$0.337365\pi$
$80$	−0.613341	−	3.47843i	−0.0685736	−	0.388900i
$81$	0.173648	−	0.984808i	0.0192942	−	0.109423i
$82$	−6.67752	−	2.43042i	−0.737409	−	0.268395i
$83$	−0.960637	−	1.66387i	−0.105444	−	0.182634i	0.808476	−	0.588530i	$-0.200293\pi$
$83$	−0.960637	−	1.66387i	−0.105444	−	0.182634i	−0.913919	+	0.405896i	$0.866960\pi$
$84$	1.85844	−	3.21891i	0.202773	−	0.351212i
$85$	4.47178	−	3.75227i	0.485033	−	0.406991i
$86$	−4.10220	+	3.44215i	−0.442351	+	0.371177i
$87$	0.0603074	−	0.104455i	0.00646563	−	0.0111988i
$88$	2.64543	+	4.58202i	0.282004	+	0.488445i
$89$	11.4226	+	4.15749i	1.21080	+	0.440693i	0.866980	−	0.498344i	$-0.166058\pi$
$89$	11.4226	+	4.15749i	1.21080	+	0.440693i	0.343816	+	0.939037i	$0.388280\pi$
$90$	−0.613341	+	3.47843i	−0.0646518	+	0.366659i
$91$	−0.146307	−	0.829748i	−0.0153371	−	0.0869813i
$92$	−8.15657	+	2.96875i	−0.850382	+	0.309514i
$93$	−2.39053	−	2.00589i	−0.247886	−	0.208001i
$94$	−2.50980			−0.258866
$95$	6.89053	−	13.7680i	0.706953	−	1.41257i
$96$	−1.00000			−0.102062
$97$	13.4081	+	11.2507i	1.36138	+	1.14234i	0.975552	+	0.219767i	$0.0705296\pi$
$97$	13.4081	+	11.2507i	1.36138	+	1.14234i	0.385831	+	0.922570i	$0.373915\pi$
$98$	−6.40420	+	2.33094i	−0.646922	+	0.235460i
$99$	−0.918748	−	5.21048i	−0.0923377	−	0.523673i
$100$	1.29813	−	7.36208i	0.129813	−	0.736208i
$101$	−14.1099	−	5.13560i	−1.40399	−	0.511011i	−0.474631	−	0.880185i	$-0.657418\pi$
$101$	−14.1099	−	5.13560i	−1.40399	−	0.511011i	−0.929360	+	0.369174i	$0.879641\pi$
$102$	−0.826352	−	1.43128i	−0.0818210	−	0.141718i
$103$	−3.33022	+	5.76811i	−0.328137	+	0.568349i	−0.982142	−	0.188141i	$-0.939754\pi$
$103$	−3.33022	+	5.76811i	−0.328137	+	0.568349i	0.654006	+	0.756490i	$0.273087\pi$
$104$	−0.173648	+	0.145708i	−0.0170276	+	0.0142879i
$105$	10.0569	−	8.43874i	0.981453	−	0.823537i
$106$	−2.96791	+	5.14057i	−0.288269	+	0.499297i
$107$	−4.04323	−	7.00309i	−0.390874	−	0.677014i	0.601691	−	0.798729i	$-0.294494\pi$
$107$	−4.04323	−	7.00309i	−0.390874	−	0.677014i	−0.992565	+	0.121715i	$0.961161\pi$
$108$	0.939693	+	0.342020i	0.0904220	+	0.0329109i
$109$	2.64796	−	15.0173i	0.253628	−	1.43840i	−0.545941	−	0.837823i	$-0.683828\pi$
$109$	2.64796	−	15.0173i	0.253628	−	1.43840i	0.799570	−	0.600573i	$-0.205061\pi$
$110$	3.24510	+	18.4039i	0.309408	+	1.75474i
$111$	4.81908	−	1.75400i	0.457407	−	0.166482i
$112$	2.84730	+	2.38917i	0.269044	+	0.225755i
$113$	0.815207			0.0766883			0.0383441	−	0.999265i	$-0.487792\pi$
$113$	0.815207			0.0766883			0.0383441	+	0.999265i	$0.487792\pi$
$114$	−3.50000	−	2.59808i	−0.327805	−	0.243332i
$115$	−30.6587			−2.85894
$116$	0.0923963	+	0.0775297i	0.00857878	+	0.00719845i
$117$	0.213011	−	0.0775297i	0.0196929	−	0.00716762i
$118$	0.0380187	+	0.215615i	0.00349990	+	0.0198489i
$119$	−1.06670	+	6.04958i	−0.0977846	+	0.554564i
$120$	−3.31908	−	1.20805i	−0.302989	−	0.110279i
$121$	−8.49660	−	14.7165i	−0.772418	−	1.33787i
$122$	0.786989	−	1.36310i	0.0712506	−	0.123410i
$123$	−5.44356	+	4.56769i	−0.490830	+	0.411855i
$124$	2.39053	−	2.00589i	0.214676	−	0.180134i
$125$	4.37211	−	7.57272i	0.391054	−	0.677325i
$126$	−1.85844	−	3.21891i	−0.165563	−	0.286764i
$127$	−10.3969	−	3.78417i	−0.922578	−	0.335791i	−0.163314	−	0.986574i	$-0.552218\pi$
$127$	−10.3969	−	3.78417i	−0.922578	−	0.335791i	−0.759264	+	0.650783i	$0.774441\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	0.929892	+	5.27368i	0.0818725	+	0.464322i
$130$	−0.752374	+	0.273842i	−0.0659876	+	0.0240175i
$131$	−11.0307	−	9.25589i	−0.963761	−	0.808691i	0.0178001	−	0.999842i	$-0.494334\pi$
$131$	−11.0307	−	9.25589i	−0.963761	−	0.808691i	−0.981561	+	0.191150i	$0.938778\pi$
$132$	5.29086			0.460510
$133$	3.75830	+	15.7596i	0.325886	+	1.36653i
$134$	15.4807			1.33733
$135$	2.70574	+	2.27038i	0.232873	+	0.195403i
$136$	1.55303	−	0.565258i	0.133172	−	0.0484705i
$137$	−0.0821293	−	0.465778i	−0.00701678	−	0.0397941i	0.981098	−	0.193510i	$-0.0619871\pi$
$137$	−0.0821293	−	0.465778i	−0.00701678	−	0.0397941i	−0.988115	+	0.153716i	$0.950876\pi$
$138$	−1.50727	+	8.54818i	−0.128308	+	0.727669i
$139$	9.57057	+	3.48340i	0.811766	+	0.295458i	0.714353	−	0.699786i	$-0.246721\pi$
$139$	9.57057	+	3.48340i	0.811766	+	0.295458i	0.0974126	+	0.995244i	$0.468943\pi$
$140$	6.56418	+	11.3695i	0.554774	+	0.960897i
$141$	−1.25490	+	2.17355i	−0.105682	+	0.183046i
$142$	−1.03802	+	0.871001i	−0.0871086	+	0.0730928i
$143$	0.918748	−	0.770921i	0.0768296	−	0.0644677i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	0.213011	+	0.368946i	0.0176896	+	0.0306393i
$146$	−2.27972	−	0.829748i	−0.188671	−	0.0686705i
$147$	−1.18345	+	6.71167i	−0.0976092	+	0.553569i
$148$	0.890530	+	5.05044i	0.0732011	+	0.415144i
$149$	−4.58987	+	1.67058i	−0.376017	+	0.136859i	−0.523113	−	0.852263i	$-0.675229\pi$
$149$	−4.58987	+	1.67058i	−0.376017	+	0.136859i	0.147096	+	0.989122i	$0.453007\pi$
$150$	−5.72668	−	4.80526i	−0.467582	−	0.392348i
$151$	9.04189			0.735818			0.367909	−	0.929862i	$-0.380074\pi$
$151$	9.04189			0.735818			0.367909	+	0.929862i	$0.380074\pi$
$152$	3.16637	−	2.99568i	0.256827	−	0.242981i
$153$	−1.65270			−0.133613
$154$	−15.0646	−	12.6407i	−1.21394	−	1.01862i
$155$	10.3576	−	3.76984i	0.831940	−	0.302801i
$156$	0.0393628	+	0.223238i	0.00315155	+	0.0178733i
$157$	0.0577812	−	0.327693i	0.00461144	−	0.0261528i	−0.982415	−	0.186709i	$-0.940218\pi$
$157$	0.0577812	−	0.327693i	0.00461144	−	0.0261528i	0.987027	+	0.160556i	$0.0513289\pi$
$158$	2.69207	+	0.979832i	0.214169	+	0.0779513i
$159$	2.96791	+	5.14057i	0.235371	+	0.407674i
$160$	1.76604	−	3.05888i	0.139618	−	0.241826i
$161$	24.7147	−	20.7381i	1.94779	−	1.63439i
$162$	0.766044	−	0.642788i	0.0601861	−	0.0505022i
$163$	−1.97044	+	3.41290i	−0.154337	+	0.267319i	−0.932817	−	0.360350i	$-0.882657\pi$
$163$	−1.97044	+	3.41290i	−0.154337	+	0.267319i	0.778481	+	0.627669i	$0.215991\pi$
$164$	−3.55303	−	6.15403i	−0.277445	−	0.480549i
$165$	17.5608	+	6.39160i	1.36710	+	0.497585i
$166$	0.333626	−	1.89209i	0.0258944	−	0.146854i
$167$	1.04071	+	5.90214i	0.0805323	+	0.456722i	0.998232	+	0.0594456i	$0.0189333\pi$
$167$	1.04071	+	5.90214i	0.0805323	+	0.456722i	−0.917699	+	0.397276i	$0.869956\pi$
$168$	3.49273	−	1.27125i	0.269470	−	0.0980789i
$169$	−9.91921	−	8.32321i	−0.763017	−	0.640247i
$170$	5.83750			0.447716
$171$	−4.00000	+	1.73205i	−0.305888	+	0.132453i
$172$	−5.35504			−0.408318
$173$	9.39306	+	7.88171i	0.714141	+	0.599235i	0.925758	−	0.378117i	$-0.123428\pi$
$173$	9.39306	+	7.88171i	0.714141	+	0.599235i	−0.211617	+	0.977353i	$0.567873\pi$
$174$	0.113341	−	0.0412527i	0.00859234	−	0.00312736i
$175$	4.82501	+	27.3640i	0.364736	+	2.06852i
$176$	−0.918748	+	5.21048i	−0.0692532	+	0.392755i
$177$	0.205737	+	0.0748822i	0.0154641	+	0.00562849i
$178$	6.07785	+	10.5271i	0.455554	+	0.789043i
$179$	−4.03209	+	6.98378i	−0.301372	+	0.521992i	−0.976447	−	0.215757i	$-0.930778\pi$
$179$	−4.03209	+	6.98378i	−0.301372	+	0.521992i	0.675075	+	0.737749i	$0.264111\pi$
$180$	−2.70574	+	2.27038i	−0.201674	+	0.169224i
$181$	0.145430	−	0.122030i	0.0108097	−	0.00907042i	−0.637367	−	0.770561i	$-0.719976\pi$
$181$	0.145430	−	0.122030i	0.0108097	−	0.00907042i	0.648176	+	0.761490i	$0.275532\pi$
$182$	0.421274	−	0.729669i	0.0312269	−	0.0540866i
$183$	−0.786989	−	1.36310i	−0.0581759	−	0.100764i
$184$	−8.15657	−	2.96875i	−0.601311	−	0.218859i
$185$	−3.14543	+	17.8386i	−0.231257	+	1.31152i
$186$	−0.541889	−	3.07321i	−0.0397332	−	0.225338i
$187$	−8.21688	+	2.99070i	−0.600878	+	0.218702i
$188$	−1.92262	−	1.61327i	−0.140221	−	0.117660i
$189$	−3.71688			−0.270363
$190$	14.1284	−	6.11776i	1.02498	−	0.443829i
$191$	18.0378			1.30517			0.652584	−	0.757717i	$-0.273685\pi$
$191$	18.0378			1.30517			0.652584	+	0.757717i	$0.273685\pi$
$192$	−0.766044	−	0.642788i	−0.0552845	−	0.0463892i
$193$	16.3871	−	5.96443i	1.17957	−	0.429329i	0.323521	−	0.946221i	$-0.395133\pi$
$193$	16.3871	−	5.96443i	1.17957	−	0.429329i	0.856050	+	0.516892i	$0.172911\pi$
$194$	3.03936	+	17.2371i	0.218214	+	1.23755i
$195$	−0.139033	+	0.788496i	−0.00995637	+	0.0564654i
$196$	−6.40420	−	2.33094i	−0.457443	−	0.166496i
$197$	5.24035	+	9.07656i	0.373360	+	0.646678i	0.990080	−	0.140504i	$-0.0448724\pi$
$197$	5.24035	+	9.07656i	0.373360	+	0.646678i	−0.616720	+	0.787182i	$0.711539\pi$
$198$	2.64543	−	4.58202i	0.188003	−	0.325630i
$199$	−10.4593	+	8.77639i	−0.741440	+	0.622142i	−0.933224	−	0.359295i	$-0.883017\pi$
$199$	−10.4593	+	8.77639i	−0.741440	+	0.622142i	0.191784	+	0.981437i	$0.438573\pi$
$200$	5.72668	−	4.80526i	0.404938	−	0.339783i
$201$	7.74035	−	13.4067i	0.545962	−	0.945635i
$202$	−7.50774	−	13.0038i	−0.528243	−	0.914943i
$203$	−0.421274	−	0.153331i	−0.0295677	−	0.0107617i
$204$	0.286989	−	1.62760i	0.0200932	−	0.113954i
$205$	−4.35844	−	24.7179i	−0.304407	−	1.72638i
$206$	−6.25877	+	2.27801i	−0.436069	+	0.158716i
$207$	6.64930	+	5.57943i	0.462158	+	0.387797i
$208$	−0.226682			−0.0157175
$209$	−16.7528	+	15.8497i	−1.15882	+	1.09635i
$210$	13.1284			0.905943
$211$	−12.2023	−	10.2390i	−0.840043	−	0.704880i	0.117530	−	0.993069i	$-0.462502\pi$
$211$	−12.2023	−	10.2390i	−0.840043	−	0.704880i	−0.957573	+	0.288189i	$0.906947\pi$
$212$	−5.57785	+	2.03017i	−0.383088	+	0.139433i
$213$	0.235300	+	1.33445i	0.0161225	+	0.0914351i
$214$	1.40420	−	7.96361i	0.0959891	−	0.544382i
$215$	−17.7738	−	6.46913i	−1.21216	−	0.441191i
$216$	0.500000	+	0.866025i	0.0340207	+	0.0589256i
$217$	−5.79948	+	10.0450i	−0.393694	+	0.681898i
$218$	11.6814	−	9.80185i	0.791163	−	0.663865i
$219$	−1.85844	+	1.55942i	−0.125582	+	0.105376i
$220$	−9.34389	+	16.1841i	−0.629965	+	1.09113i
$221$	−0.187319	−	0.324446i	−0.0126004	−	0.0218246i
$222$	4.81908	+	1.75400i	0.323435	+	0.117721i
$223$	3.23261	−	18.3331i	0.216472	−	1.22767i	−0.661863	−	0.749625i	$-0.730234\pi$
$223$	3.23261	−	18.3331i	0.216472	−	1.22767i	0.878334	−	0.478047i	$-0.158655\pi$
$224$	0.645430	+	3.66041i	0.0431246	+	0.244572i
$225$	−7.02481	+	2.55682i	−0.468321	+	0.170455i
$226$	0.624485	+	0.524005i	0.0415401	+	0.0348563i
$227$	−5.79292			−0.384490			−0.192245	−	0.981347i	$-0.561577\pi$
$227$	−5.79292			−0.384490			−0.192245	+	0.981347i	$0.561577\pi$
$228$	−1.01114	−	4.24000i	−0.0669647	−	0.280801i
$229$	−8.12836			−0.537137			−0.268568	−	0.963261i	$-0.586551\pi$
$229$	−8.12836			−0.537137			−0.268568	+	0.963261i	$0.586551\pi$
$230$	−23.4859	−	19.7070i	−1.54862	−	1.29944i
$231$	−18.4795	+	6.72600i	−1.21586	+	0.442538i
$232$	0.0209445	+	0.118782i	0.00137508	+	0.00779844i
$233$	−2.95677	+	16.7687i	−0.193704	+	1.09855i	0.720548	+	0.693405i	$0.243890\pi$
$233$	−2.95677	+	16.7687i	−0.193704	+	1.09855i	−0.914252	+	0.405146i	$0.867221\pi$
$234$	0.213011	+	0.0775297i	0.0139250	+	0.00506827i
$235$	−4.43242	−	7.67717i	−0.289139	−	0.500804i
$236$	−0.109470	+	0.189608i	−0.00712592	+	0.0123424i
$237$	2.19459	−	1.84148i	0.142554	−	0.119617i
$238$	−4.70574	+	3.94858i	−0.305028	+	0.255949i
$239$	7.50980	−	13.0074i	0.485769	−	0.841376i	−0.514098	−	0.857732i	$-0.671873\pi$
$239$	7.50980	−	13.0074i	0.485769	−	0.841376i	0.999866	+	0.0163558i	$0.00520644\pi$
$240$	−1.76604	−	3.05888i	−0.113998	−	0.197450i
$241$	20.1596	+	7.33748i	1.29859	+	0.472649i	0.896538	−	0.442967i	$-0.146074\pi$
$241$	20.1596	+	7.33748i	1.29859	+	0.472649i	0.402054	+	0.915616i	$0.368296\pi$
$242$	2.95084	−	16.7350i	0.189687	−	1.07577i
$243$	−0.173648	−	0.984808i	−0.0111395	−	0.0631754i
$244$	1.47906	−	0.538332i	0.0946868	−	0.0344632i
$245$	−18.4402	−	15.4731i	−1.17810	−	0.988542i
$246$	−7.10607			−0.453066
$247$	−0.793386	−	0.588936i	−0.0504819	−	0.0374731i
$248$	3.12061			0.198159
$249$	−1.47178	−	1.23497i	−0.0932704	−	0.0782631i
$250$	8.21688	−	2.99070i	0.519681	−	0.189148i
$251$	−4.43969	−	25.1787i	−0.280231	−	1.58927i	−0.721839	−	0.692061i	$-0.756703\pi$
$251$	−4.43969	−	25.1787i	−0.280231	−	1.58927i	0.441608	−	0.897208i	$-0.354408\pi$
$252$	0.645430	−	3.66041i	0.0406582	−	0.230584i
$253$	43.1553	+	15.7072i	2.71315	+	0.987506i
$254$	−5.53209	−	9.58186i	−0.347114	−	0.601219i
$255$	2.91875	−	5.05542i	0.182779	−	0.316583i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	2.13950	−	1.79525i	0.133458	−	0.111985i	−0.573615	−	0.819125i	$-0.694459\pi$
$257$	2.13950	−	1.79525i	0.133458	−	0.111985i	0.707073	+	0.707140i	$0.250015\pi$
$258$	−2.67752	+	4.63760i	−0.166695	+	0.288724i
$259$	−9.53074	−	16.5077i	−0.592212	−	1.02574i
$260$	−0.752374	−	0.273842i	−0.0466602	−	0.0169829i
$261$	0.0209445	−	0.118782i	0.00129643	−	0.00735244i
$262$	−2.50047	−	14.1809i	−0.154479	−	0.876096i
$263$	−1.30066	+	0.473401i	−0.0802021	+	0.0291912i	−0.381810	−	0.924241i	$-0.624699\pi$
$263$	−1.30066	+	0.473401i	−0.0802021	+	0.0291912i	0.301608	+	0.953432i	$0.402477\pi$
$264$	4.05303	+	3.40090i	0.249447	+	0.209311i
$265$	−20.9659			−1.28792
$266$	−7.25103	+	14.4883i	−0.444589	+	0.888336i
$267$	12.1557			0.743917
$268$	11.8589	+	9.95080i	0.724398	+	0.607842i
$269$	16.0471	−	5.84067i	0.978409	−	0.356112i	0.197188	−	0.980366i	$-0.436819\pi$
$269$	16.0471	−	5.84067i	0.978409	−	0.356112i	0.781221	+	0.624254i	$0.214597\pi$
$270$	0.613341	+	3.47843i	0.0373267	+	0.211690i
$271$	−4.46064	+	25.2975i	−0.270964	+	1.53672i	0.480531	+	0.876978i	$0.340444\pi$
$271$	−4.46064	+	25.2975i	−0.270964	+	1.53672i	−0.751496	+	0.659738i	$0.770667\pi$
$272$	1.55303	+	0.565258i	0.0941665	+	0.0342738i
$273$	−0.421274	−	0.729669i	−0.0254967	−	0.0441615i
$274$	0.236482	−	0.409598i	0.0142864	−	0.0247447i
$275$	−30.2991	+	25.4239i	−1.82710	+	1.53312i
$276$	−6.64930	+	5.57943i	−0.400241	+	0.335842i
$277$	−11.1125	+	19.2474i	−0.667683	+	1.15646i	0.310867	+	0.950453i	$0.399381\pi$
$277$	−11.1125	+	19.2474i	−0.667683	+	1.15646i	−0.978550	+	0.206008i	$0.933953\pi$
$278$	5.09240	+	8.82029i	0.305422	+	0.529006i
$279$	−2.93242	−	1.06731i	−0.175559	−	0.0638984i
$280$	−2.27972	+	12.9289i	−0.136239	+	0.772650i
$281$	0.268104	+	1.52049i	0.0159937	+	0.0907050i	0.991760	−	0.128111i	$-0.0408915\pi$
$281$	0.268104	+	1.52049i	0.0159937	+	0.0907050i	−0.975766	+	0.218816i	$0.929780\pi$
$282$	−2.35844	+	0.858402i	−0.140443	+	0.0511171i
$283$	7.88326	+	6.61484i	0.468611	+	0.393211i	0.846288	−	0.532726i	$-0.178832\pi$
$283$	7.88326	+	6.61484i	0.468611	+	0.393211i	−0.377677	+	0.925938i	$0.623277\pi$
$284$	−1.35504			−0.0804067
$285$	1.76604	−	15.2944i	0.104611	−	0.905962i
$286$	1.19934			0.0709185
$287$	20.2331	+	16.9776i	1.19432	+	1.00215i
$288$	−0.939693	+	0.342020i	−0.0553719	+	0.0201537i
$289$	−2.47771	−	14.0518i	−0.145748	−	0.826576i
$290$	−0.0739780	+	0.419550i	−0.00434413	+	0.0246368i
$291$	16.4474	+	5.98638i	0.964166	+	0.350928i
$292$	−1.21301	−	2.10100i	−0.0709861	−	0.122952i
$293$	14.2515	−	24.6843i	0.832581	−	1.44207i	−0.0634033	−	0.997988i	$-0.520195\pi$
$293$	14.2515	−	24.6843i	0.832581	−	1.44207i	0.895985	−	0.444085i	$-0.146471\pi$
$294$	−5.22075	+	4.38073i	−0.304480	+	0.255489i
$295$	−0.592396	+	0.497079i	−0.0344906	+	0.0289411i
$296$	−2.56418	+	4.44129i	−0.149040	+	0.258145i
$297$	−2.64543	−	4.58202i	−0.153503	−	0.265876i
$298$	−4.58987	−	1.67058i	−0.265884	−	0.0967739i
$299$	−0.341671	+	1.93771i	−0.0197594	+	0.112061i
$300$	−1.29813	−	7.36208i	−0.0749478	−	0.425050i
$301$	18.7037	−	6.80758i	1.07806	−	0.392382i
$302$	6.92649	+	5.81201i	0.398575	+	0.334444i
$303$	−15.0155			−0.862617
$304$	4.35117	−	0.259515i	0.249557	−	0.0148842i
$305$	5.55943			0.318332
$306$	−1.26604	−	1.06234i	−0.0723749	−	0.0607298i
$307$	24.0180	−	8.74184i	1.37078	−	0.498923i	0.451410	−	0.892317i	$-0.350921\pi$
$307$	24.0180	−	8.74184i	1.37078	−	0.498923i	0.919370	+	0.393394i	$0.128699\pi$
$308$	−3.41488	−	19.3667i	−0.194581	−	1.10352i
$309$	−1.15657	+	6.55926i	−0.0657952	+	0.373143i
$310$	10.3576	+	3.76984i	0.588270	+	0.214113i
$311$	−5.18732	−	8.98470i	−0.294146	−	0.509476i	0.680640	−	0.732618i	$-0.261702\pi$
$311$	−5.18732	−	8.98470i	−0.294146	−	0.509476i	−0.974786	+	0.223142i	$0.928368\pi$
$312$	−0.113341	+	0.196312i	−0.00641666	+	0.0111140i
$313$	−11.8250	+	9.92236i	−0.668389	+	0.560845i	−0.912588	−	0.408880i	$-0.865919\pi$
$313$	−11.8250	+	9.92236i	−0.668389	+	0.560845i	0.244199	+	0.969725i	$0.421475\pi$
$314$	0.254900	−	0.213887i	0.0143848	−	0.0120703i
$315$	6.56418	−	11.3695i	0.369850	−	0.640598i
$316$	1.43242	+	2.48102i	0.0805798	+	0.139568i
$317$	−26.6844	−	9.71232i	−1.49874	−	0.545498i	−0.543009	−	0.839727i	$-0.682715\pi$
$317$	−26.6844	−	9.71232i	−1.49874	−	0.545498i	−0.955735	+	0.294229i	$0.904937\pi$
$318$	−1.03074	+	5.84564i	−0.0578013	+	0.327807i
$319$	−0.110815	−	0.628461i	−0.00620443	−	0.0351870i
$320$	3.31908	−	1.20805i	0.185542	−	0.0675318i
$321$	−6.19459	−	5.19788i	−0.345748	−	0.290117i
$322$	32.2627			1.79793
$323$	3.96703	+	6.01330i	0.220732	+	0.334589i
$324$	1.00000			0.0555556
$325$	−1.29813	−	1.08926i	−0.0720075	−	0.0604215i
$326$	−3.70321	+	1.34786i	−0.205102	+	0.0746510i
$327$	−2.64796	−	15.0173i	−0.146432	−	0.830459i
$328$	1.23396	−	6.99811i	0.0681338	−	0.386406i
$329$	8.76604	+	3.19058i	0.483288	+	0.175902i
$330$	9.34389	+	16.1841i	0.514364	+	0.890905i
$331$	12.9611	−	22.4493i	0.712407	−	1.23392i	−0.251545	−	0.967846i	$-0.580938\pi$
$331$	12.9611	−	22.4493i	0.712407	−	1.23392i	0.963951	−	0.266079i	$-0.0857282\pi$
$332$	1.47178	−	1.23497i	0.0807745	−	0.0677779i
$333$	3.92855	−	3.29644i	0.215283	−	0.180644i
$334$	−2.99660	+	5.19026i	−0.163966	+	0.283998i
$335$	27.3396	+	47.3536i	1.49372	+	2.58720i
$336$	3.49273	+	1.27125i	0.190544	+	0.0693523i
$337$	−4.08260	+	23.1536i	−0.222393	+	1.26125i	0.645213	+	0.764003i	$0.276769\pi$
$337$	−4.08260	+	23.1536i	−0.222393	+	1.26125i	−0.867606	+	0.497252i	$0.834343\pi$
$338$	−2.24850	−	12.7519i	−0.122302	−	0.693612i
$339$	0.766044	−	0.278817i	0.0416058	−	0.0151433i
$340$	4.47178	+	3.75227i	0.242516	+	0.203495i
$341$	−16.5107			−0.894106
$342$	−4.17752	−	1.24432i	−0.225894	−	0.0672853i
$343$	−0.686852			−0.0370865
$344$	−4.10220	−	3.44215i	−0.221176	−	0.185588i
$345$	−28.8097	+	10.4859i	−1.55106	+	0.564541i
$346$	2.12923	+	12.0755i	0.114468	+	0.649182i
$347$	−0.417566	+	2.36813i	−0.0224161	+	0.127128i	−0.993962	−	0.109722i	$-0.965004\pi$
$347$	−0.417566	+	2.36813i	−0.0224161	+	0.127128i	0.971546	+	0.236850i	$0.0761150\pi$
$348$	0.113341	+	0.0412527i	0.00607570	+	0.00221138i
$349$	−2.59879	−	4.50124i	−0.139110	−	0.240946i	0.788050	−	0.615611i	$-0.211091\pi$
$349$	−2.59879	−	4.50124i	−0.139110	−	0.240946i	−0.927160	+	0.374665i	$0.877758\pi$
$350$	−13.8931	+	24.0635i	−0.742615	+	1.28625i
$351$	0.173648	−	0.145708i	0.00926865	−	0.00777732i
$352$	−4.05303	+	3.40090i	−0.216027	+	0.181269i
$353$	−4.13816	+	7.16750i	−0.220252	+	0.381487i	−0.954884	−	0.296978i	$-0.904021\pi$
$353$	−4.13816	+	7.16750i	−0.220252	+	0.381487i	0.734633	+	0.678465i	$0.237355\pi$
$354$	0.109470	+	0.189608i	0.00581829	+	0.0100776i
$355$	−4.49747	−	1.63695i	−0.238701	−	0.0868801i
$356$	−2.11081	+	11.9710i	−0.111873	+	0.634463i
$357$	1.06670	+	6.04958i	0.0564560	+	0.320178i
$358$	−7.57785	+	2.75811i	−0.400502	+	0.145771i
$359$	−1.75877	−	1.47578i	−0.0928244	−	0.0778889i	0.595195	−	0.803582i	$-0.297075\pi$
$359$	−1.75877	−	1.47578i	−0.0928244	−	0.0778889i	−0.688019	+	0.725693i	$0.741519\pi$
$360$	−3.53209			−0.186157
$361$	15.9033	+	10.3964i	0.837017	+	0.547177i
$362$	0.189845			0.00997803
$363$	−13.0175	−	10.9230i	−0.683244	−	0.573310i
$364$	0.791737	−	0.288169i	0.0414983	−	0.0151041i
$365$	−1.48798	−	8.43874i	−0.0778843	−	0.441704i
$366$	0.273318	−	1.55007i	0.0142866	−	0.0810232i
$367$	−28.0638	−	10.2144i	−1.46492	−	0.533186i	−0.518202	−	0.855258i	$-0.673398\pi$
$367$	−28.0638	−	10.2144i	−1.46492	−	0.533186i	−0.946715	+	0.322072i	$0.895621\pi$
$368$	−4.34002	−	7.51714i	−0.226239	−	0.391858i
$369$	−3.55303	+	6.15403i	−0.184964	+	0.320366i
$370$	−13.8760	+	11.6433i	−0.721378	+	0.605308i
$371$	16.9010	−	14.1817i	0.877459	−	0.736275i
$372$	1.56031	−	2.70253i	0.0808982	−	0.140120i
$373$	9.92649	+	17.1932i	0.513974	+	0.890229i	0.999869	+	0.0162118i	$0.00516060\pi$
$373$	9.92649	+	17.1932i	0.513974	+	0.890229i	−0.485894	+	0.874017i	$0.661506\pi$
$374$	−8.21688	−	2.99070i	−0.424885	−	0.154645i
$375$	1.51842	−	8.61138i	0.0784108	−	0.444690i
$376$	−0.435822	−	2.47167i	−0.0224758	−	0.127467i
$377$	0.0256923	−	0.00935122i	0.00132322	−	0.000481612i
$378$	−2.84730	−	2.38917i	−0.146449	−	0.122885i
$379$	25.8256			1.32657			0.663287	−	0.748365i	$-0.269161\pi$
$379$	25.8256			1.32657			0.663287	+	0.748365i	$0.269161\pi$
$380$	14.7554	+	4.39506i	0.756934	+	0.225462i
$381$	−11.0642			−0.566835
$382$	13.8177	+	11.5945i	0.706977	+	0.593224i
$383$	−18.9201	+	6.88635i	−0.966772	+	0.351876i	−0.776684	−	0.629891i	$-0.783100\pi$
$383$	−18.9201	+	6.88635i	−0.966772	+	0.351876i	−0.190088	+	0.981767i	$0.560877\pi$
$384$	−0.173648	−	0.984808i	−0.00886145	−	0.0502558i
$385$	12.0617	−	68.4050i	0.614719	−	3.48624i
$386$	16.3871	+	5.96443i	0.834083	+	0.303581i
$387$	2.67752	+	4.63760i	0.136106	+	0.235742i
$388$	−8.75150	+	15.1580i	−0.444290	+	0.769533i
$389$	8.68139	−	7.28455i	0.440164	−	0.369341i	−0.395607	−	0.918420i	$-0.629466\pi$
$389$	8.68139	−	7.28455i	0.440164	−	0.369341i	0.835771	+	0.549079i	$0.185021\pi$
$390$	−0.613341	+	0.514654i	−0.0310577	+	0.0260605i
$391$	7.17277	−	12.4236i	0.362743	−	0.628289i
$392$	−3.40760	−	5.90214i	−0.172110	−	0.298103i
$393$	−13.5312	−	4.92496i	−0.682559	−	0.248431i
$394$	−1.81996	+	10.3215i	−0.0916880	+	0.519989i
$395$	1.75712	+	9.96513i	0.0884104	+	0.501400i
$396$	4.97178	−	1.80958i	0.249841	−	0.0909348i
$397$	10.0307	+	8.41679i	0.503429	+	0.422427i	0.858810	−	0.512295i	$-0.171204\pi$
$397$	10.0307	+	8.41679i	0.503429	+	0.422427i	−0.355381	+	0.934722i	$0.615649\pi$
$398$	−13.6536			−0.684395
$399$	8.92174	+	13.5237i	0.446646	+	0.677034i
$400$	7.47565			0.373783
$401$	16.2554	+	13.6399i	0.811754	+	0.681143i	0.951026	−	0.309112i	$-0.100032\pi$
$401$	16.2554	+	13.6399i	0.811754	+	0.681143i	−0.139272	+	0.990254i	$0.544476\pi$
$402$	14.5471	−	5.29471i	0.725544	−	0.264076i
$403$	−0.122836	−	0.696639i	−0.00611891	−	0.0347021i
$404$	2.60741	−	14.7874i	0.129724	−	0.735699i
$405$	3.31908	+	1.20805i	0.164926	+	0.0600283i
$406$	−0.224155	−	0.388249i	−0.0111246	−	0.0192684i
$407$	13.5667	−	23.4982i	0.672477	−	1.16476i
$408$	1.26604	−	1.06234i	0.0626785	−	0.0525935i
$409$	−22.2763	+	18.6920i	−1.10149	+	0.924262i	−0.997525	−	0.0703185i	$-0.977598\pi$
$409$	−22.2763	+	18.6920i	−1.10149	+	0.924262i	−0.103968	+	0.994581i	$0.533154\pi$
$410$	12.5496	−	21.7366i	0.619782	−	1.07349i
$411$	−0.236482	−	0.409598i	−0.0116648	−	0.0202040i
$412$	−6.25877	−	2.27801i	−0.308347	−	0.112229i
$413$	0.141311	−	0.801414i	0.00695345	−	0.0394350i
$414$	1.50727	+	8.54818i	0.0740785	+	0.420120i
$415$	6.37686	−	2.32099i	0.313028	−	0.113933i
$416$	−0.173648	−	0.145708i	−0.00851380	−	0.00714393i
$417$	10.1848			0.498751
$418$	−23.0214	+	1.37306i	−1.12601	+	0.0671584i
$419$	40.4962			1.97837			0.989184	−	0.146679i	$-0.0468586\pi$
$419$	40.4962			1.97837			0.989184	+	0.146679i	$0.0468586\pi$
$420$	10.0569	+	8.43874i	0.490727	+	0.411769i
$421$	−29.3491	+	10.6822i	−1.43039	+	0.520619i	−0.937043	−	0.349215i	$-0.886448\pi$
$421$	−29.3491	+	10.6822i	−1.43039	+	0.520619i	−0.493345	+	0.869834i	$0.664226\pi$
$422$	−2.76604	−	15.6870i	−0.134649	−	0.763632i
$423$	−0.435822	+	2.47167i	−0.0211904	+	0.120177i
$424$	−5.57785	−	2.03017i	−0.270884	−	0.0985938i
$425$	6.17752	+	10.6998i	0.299654	+	0.519015i
$426$	−0.677519	+	1.17350i	−0.0328259	+	0.0568561i
$427$	−4.48158	+	3.76049i	−0.216879	+	0.181983i
$428$	6.19459	−	5.19788i	0.299427	−	0.251249i
$429$	0.599670	−	1.03866i	0.0289524	−	0.0501469i
$430$	−9.45723	−	16.3804i	−0.456068	−	0.789933i
$431$	−24.4513	−	8.89955i	−1.17778	−	0.428676i	−0.322361	−	0.946617i	$-0.604477\pi$
$431$	−24.4513	−	8.89955i	−1.17778	−	0.428676i	−0.855417	+	0.517941i	$0.826699\pi$
$432$	−0.173648	+	0.984808i	−0.00835465	+	0.0473816i
$433$	−4.69965	−	26.6530i	−0.225851	−	1.28086i	−0.861053	−	0.508516i	$-0.830194\pi$
$433$	−4.69965	−	26.6530i	−0.225851	−	1.28086i	0.635202	−	0.772346i	$-0.280917\pi$
$434$	−10.8995	+	3.96708i	−0.523190	+	0.190426i
$435$	0.326352	+	0.273842i	0.0156474	+	0.0131297i
$436$	15.2490			0.730293
$437$	4.34002	−	37.5857i	0.207611	−	1.79797i
$438$	−2.42602			−0.115920
$439$	−2.25284	−	1.89036i	−0.107522	−	0.0902219i	0.587442	−	0.809267i	$-0.300135\pi$
$439$	−2.25284	−	1.89036i	−0.107522	−	0.0902219i	−0.694964	+	0.719045i	$0.744580\pi$
$440$	−17.5608	+	6.39160i	−0.837177	+	0.304708i
$441$	1.18345	+	6.71167i	0.0563547	+	0.319603i
$442$	0.0650551	−	0.368946i	0.00309436	−	0.0175490i
$443$	−25.9402	−	9.44145i	−1.23245	−	0.448577i	−0.358017	−	0.933715i	$-0.616547\pi$
$443$	−25.9402	−	9.44145i	−1.23245	−	0.448577i	−0.874437	+	0.485138i	$0.838769\pi$
$444$	2.56418	+	4.44129i	0.121690	+	0.210774i
$445$	−21.4675	+	37.1828i	−1.01766	+	1.76263i
$446$	14.2606	−	11.9660i	0.675258	−	0.566609i
$447$	−3.74170	+	3.13966i	−0.176976	+	0.148501i
$448$	−1.85844	+	3.21891i	−0.0878031	+	0.152079i
$449$	−8.46110	−	14.6551i	−0.399304	−	0.691615i	0.594336	−	0.804217i	$-0.297415\pi$
$449$	−8.46110	−	14.6551i	−0.399304	−	0.691615i	−0.993640	+	0.112602i	$0.964082\pi$
$450$	−7.02481	−	2.55682i	−0.331153	−	0.120530i
$451$	−6.52869	+	37.0260i	−0.307424	+	1.74349i
$452$	0.141559	+	0.802823i	0.00665839	+	0.0377616i
$453$	8.49660	−	3.09251i	0.399205	−	0.145299i
$454$	−4.43763	−	3.72362i	−0.208268	−	0.174758i
$455$	2.97596			0.139515
$456$	1.95084	−	3.89798i	0.0913563	−	0.182540i
$457$	9.19160			0.429965			0.214982	−	0.976618i	$-0.431031\pi$
$457$	9.19160			0.429965			0.214982	+	0.976618i	$0.431031\pi$
$458$	−6.22668	−	5.22481i	−0.290954	−	0.244139i
$459$	−1.55303	+	0.565258i	−0.0724894	+	0.0263840i
$460$	−5.32383	−	30.1929i	−0.248225	−	1.40775i
$461$	−2.68210	+	15.2110i	−0.124918	+	0.708445i	0.856438	+	0.516249i	$0.172672\pi$
$461$	−2.68210	+	15.2110i	−0.124918	+	0.708445i	−0.981357	+	0.192196i	$0.938439\pi$
$462$	−18.4795	−	6.72600i	−0.859745	−	0.312922i
$463$	−14.9907	−	25.9646i	−0.696675	−	1.20668i	−0.969613	−	0.244645i	$-0.921328\pi$
$463$	−14.9907	−	25.9646i	−0.696675	−	1.20668i	0.272937	−	0.962032i	$-0.412005\pi$
$464$	−0.0603074	+	0.104455i	−0.00279970	+	0.00484922i
$465$	8.44356	−	7.08499i	0.391561	−	0.328559i
$466$	−13.0437	+	10.9450i	−0.604238	+	0.507016i
$467$	−14.4427	+	25.0155i	−0.668328	+	1.15758i	0.310044	+	0.950722i	$0.399656\pi$
$467$	−14.4427	+	25.0155i	−0.668328	+	1.15758i	−0.978372	+	0.206855i	$0.933677\pi$
$468$	0.113341	+	0.196312i	0.00523918	+	0.00907453i
$469$	−54.0699	−	19.6798i	−2.49671	−	0.908730i
$470$	1.53936	−	8.73016i	0.0710055	−	0.402692i
$471$	−0.0577812	−	0.327693i	−0.00266242	−	0.0150993i
$472$	−0.205737	+	0.0748822i	−0.00946982	+	0.00344673i
$473$	21.7041	+	18.2119i	0.997958	+	0.837386i
$474$	2.86484			0.131586
$475$	26.1648	+	19.4223i	1.20052	+	0.891157i
$476$	−6.14290			−0.281560
$477$	4.54710	+	3.81547i	0.208198	+	0.174699i
$478$	14.1138	−	5.13701i	0.645551	−	0.234961i
$479$	2.37211	+	13.4529i	0.108385	+	0.614679i	0.989814	+	0.142364i	$0.0454704\pi$
$479$	2.37211	+	13.4529i	0.108385	+	0.614679i	−0.881430	+	0.472315i	$0.843418\pi$
$480$	0.613341	−	3.47843i	0.0279950	−	0.158768i
$481$	1.09240	+	0.397600i	0.0498090	+	0.0181290i
$482$	10.7267	+	18.5792i	0.488587	+	0.846257i
$483$	16.1313	−	27.9403i	0.734002	−	1.27133i
$484$	13.0175	−	10.9230i	0.591706	−	0.496501i
$485$	−47.3585	+	39.7385i	−2.15044	+	1.80443i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	3.08899	+	5.35029i	0.139976	+	0.242445i	0.927487	−	0.373855i	$-0.121964\pi$
$487$	3.08899	+	5.35029i	0.139976	+	0.242445i	−0.787512	+	0.616300i	$0.788631\pi$
$488$	1.47906	+	0.538332i	0.0669537	+	0.0243692i
$489$	−0.684326	+	3.88100i	−0.0309463	+	0.175505i
$490$	−4.18004	−	23.7062i	−0.188835	−	1.07094i
$491$	−3.85591	+	1.40344i	−0.174015	+	0.0633363i	−0.427558	−	0.903988i	$-0.640626\pi$
$491$	−3.85591	+	1.40344i	−0.174015	+	0.0633363i	0.253543	+	0.967324i	$0.418404\pi$
$492$	−5.44356	−	4.56769i	−0.245415	−	0.205927i
$493$	−0.199340			−0.00897784
$494$	−0.229208	−	0.961130i	−0.0103125	−	0.0432433i
$495$	18.6878			0.839953
$496$	2.39053	+	2.00589i	0.107338	+	0.0900672i
$497$	4.73277	−	1.72259i	0.212294	−	0.0772687i
$498$	−0.333626	−	1.89209i	−0.0149501	−	0.0847864i
$499$	4.61540	−	26.1752i	0.206614	−	1.17176i	−0.688266	−	0.725458i	$-0.741628\pi$
$499$	4.61540	−	26.1752i	0.206614	−	1.17176i	0.894880	−	0.446306i	$-0.147261\pi$
$500$	8.21688	+	2.99070i	0.367470	+	0.133748i
$501$	2.99660	+	5.19026i	0.133878	+	0.231884i
$502$	12.7836	−	22.1418i	0.570559	−	0.988238i
$503$	−19.8746	+	16.6768i	−0.886166	+	0.743582i	−0.967437	−	0.253110i	$-0.918546\pi$
$503$	−19.8746	+	16.6768i	−0.886166	+	0.743582i	0.0812712	+	0.996692i	$0.474102\pi$
$504$	2.84730	−	2.38917i	0.126829	−	0.106422i
$505$	26.5180	−	45.9305i	1.18004	−	2.04388i
$506$	22.9624	+	39.7721i	1.02081	+	1.76809i
$507$	−12.1677	−	4.42869i	−0.540387	−	0.196685i
$508$	1.92127	−	10.8961i	0.0852428	−	0.483436i
$509$	−4.37551	−	24.8148i	−0.193941	−	1.09990i	−0.913918	−	0.405898i	$-0.866959\pi$
$509$	−4.37551	−	24.8148i	−0.193941	−	1.09990i	0.719977	−	0.693998i	$-0.244152\pi$
$510$	5.48545	−	1.99654i	0.242900	−	0.0884083i
$511$	6.90760	+	5.79617i	0.305574	+	0.256407i
$512$	1.00000			0.0441942
$513$	−3.16637	+	2.99568i	−0.139799	+	0.132262i
$514$	2.79292			0.123190
$515$	−18.0214	−	15.1218i	−0.794118	−	0.666344i
$516$	−5.03209	+	1.83153i	−0.221525	+	0.0806286i
$517$	2.30587	+	13.0773i	0.101412	+	0.575137i
$518$	3.30999	−	18.7719i	0.145433	−	0.824790i
$519$	11.5223	+	4.19377i	0.505772	+	0.184086i
$520$	−0.400330	−	0.693392i	−0.0175556	−	0.0304072i
$521$	1.38800	−	2.40409i	0.0608095	−	0.105325i	−0.834018	−	0.551737i	$-0.813965\pi$
$521$	1.38800	−	2.40409i	0.0608095	−	0.105325i	0.894827	+	0.446412i	$0.147298\pi$
$522$	0.0923963	−	0.0775297i	0.00404407	−	0.00339338i
$523$	8.60678	−	7.22195i	0.376348	−	0.315794i	−0.434919	−	0.900470i	$-0.643223\pi$
$523$	8.60678	−	7.22195i	0.376348	−	0.315794i	0.811267	+	0.584676i	$0.198778\pi$
$524$	7.19981	−	12.4704i	0.314525	−	0.544773i
$525$	13.8931	+	24.0635i	0.606343	+	1.05022i
$526$	−1.30066	−	0.473401i	−0.0567115	−	0.0206413i
$527$	−0.895582	+	5.07910i	−0.0390122	+	0.221249i
$528$	0.918748	+	5.21048i	0.0399834	+	0.226757i
$529$	−49.1865	+	17.9024i	−2.13854	+	0.778366i
$530$	−16.0608	−	13.4766i	−0.697635	−	0.585386i
$531$	0.218941			0.00950122
$532$	−14.8675	+	6.43783i	−0.644589	+	0.279115i
$533$	−1.61081			−0.0697721
$534$	9.31180	+	7.81353i	0.402961	+	0.338125i
$535$	26.8396	−	9.76882i	1.16038	−	0.422343i
$536$	2.68820	+	15.2455i	0.116112	+	0.658506i
$537$	−1.40033	+	7.94166i	−0.0604287	+	0.342708i
$538$	16.0471	+	5.84067i	0.691840	+	0.251809i
$539$	18.0292	+	31.2274i	0.776571	+	1.34506i
$540$	−1.76604	+	3.05888i	−0.0759985	+	0.131633i
$541$	−16.8628	+	14.1496i	−0.724987	+	0.608337i	−0.928760	−	0.370682i	$-0.879124\pi$
$541$	−16.8628	+	14.1496i	−0.724987	+	0.608337i	0.203773	+	0.979018i	$0.434680\pi$
$542$	−19.6780	+	16.5118i	−0.845242	+	0.709242i
$543$	0.0949225	−	0.164411i	0.00407351	−	0.00705553i
$544$	0.826352	+	1.43128i	0.0354295	+	0.0613658i
$545$	50.6125	+	18.4215i	2.16800	+	0.789088i
$546$	0.146307	−	0.829748i	0.00626136	−	0.0355100i
$547$	5.93107	+	33.6368i	0.253594	+	1.43821i	0.799655	+	0.600460i	$0.205016\pi$
$547$	5.93107	+	33.6368i	0.253594	+	1.43821i	−0.546061	+	0.837746i	$0.683873\pi$
$548$	0.444440	−	0.161763i	0.0189856	−	0.00691018i
$549$	−1.20574	−	1.01173i	−0.0514596	−	0.0431797i
$550$	−39.5526			−1.68653
$551$	−0.482459	+	0.208911i	−0.0205534	+	0.00889990i
$552$	−8.68004			−0.369447
$553$	−8.15704	−	6.84457i	−0.346873	−	0.291061i
$554$	−20.8846	+	7.60137i	−0.887302	+	0.322951i
$555$	3.14543	+	17.8386i	0.133516	+	0.757207i
$556$	−1.76857	+	10.0301i	−0.0750041	+	0.425369i
$557$	35.5774	+	12.9491i	1.50746	+	0.548672i	0.957981	−	0.286832i	$-0.0926023\pi$
$557$	35.5774	+	12.9491i	1.50746	+	0.548672i	0.549484	+	0.835504i	$0.314824\pi$
$558$	−1.56031	−	2.70253i	−0.0660531	−	0.114407i
$559$	−0.606944	+	1.05126i	−0.0256710	+	0.0444635i
$560$	−10.0569	+	8.43874i	−0.424982	+	0.356602i
$561$	−6.69846	+	5.62068i	−0.282809	+	0.237305i
$562$	−0.771974	+	1.33710i	−0.0325638	+	0.0564021i
$563$	−5.86231	−	10.1538i	−0.247067	−	0.427933i	0.715644	−	0.698465i	$-0.246133\pi$
$563$	−5.86231	−	10.1538i	−0.247067	−	0.427933i	−0.962711	+	0.270533i	$0.912800\pi$
$564$	−2.35844	−	0.858402i	−0.0993083	−	0.0361453i
$565$	−0.500000	+	2.83564i	−0.0210352	+	0.119296i
$566$	1.78699	+	10.1345i	0.0751127	+	0.425986i
$567$	−3.49273	+	1.27125i	−0.146681	+	0.0533874i
$568$	−1.03802	−	0.871001i	−0.0435543	−	0.0365464i
$569$	14.8972			0.624524			0.312262	−	0.949996i	$-0.398913\pi$
$569$	14.8972			0.624524			0.312262	+	0.949996i	$0.398913\pi$
$570$	11.1839	−	10.5810i	0.468443	−	0.443189i
$571$	12.9409			0.541559			0.270779	−	0.962641i	$-0.412719\pi$
$571$	12.9409			0.541559			0.270779	+	0.962641i	$0.412719\pi$
$572$	0.918748	+	0.770921i	0.0384148	+	0.0322338i
$573$	16.9500	−	6.16928i	0.708095	−	0.257725i
$574$	4.58647	+	26.0111i	0.191435	+	1.08568i
$575$	11.2679	−	63.9032i	0.469902	−	2.66495i
$576$	−0.939693	−	0.342020i	−0.0391539	−	0.0142508i
$577$	−11.3657	−	19.6860i	−0.473161	−	0.819539i	0.526367	−	0.850257i	$-0.323554\pi$
$577$	−11.3657	−	19.6860i	−0.473161	−	0.819539i	−0.999528	+	0.0307187i	$0.990220\pi$
$578$	7.13429	−	12.3569i	0.296747	−	0.513981i
$579$	13.3589	−	11.2095i	0.555177	−	0.465849i
$580$	−0.326352	+	0.273842i	−0.0135510	+	0.0113707i
$581$	−3.57057	+	6.18442i	−0.148132	+	0.256573i
$582$	8.75150	+	15.1580i	0.362761	+	0.628321i
$583$	29.5116	+	10.7413i	1.22225	+	0.444861i
$584$	0.421274	−	2.38917i	0.0174325	−	0.0988644i
$585$	0.139033	+	0.788496i	0.00574831	+	0.0326003i
$586$	26.7841	−	9.74860i	1.10644	−	0.402711i
$587$	−8.08899	−	6.78747i	−0.333868	−	0.280149i	0.460405	−	0.887709i	$-0.347704\pi$
$587$	−8.08899	−	6.78747i	−0.333868	−	0.280149i	−0.794274	+	0.607560i	$0.792148\pi$
$588$	−6.81521			−0.281054
$589$	3.15539	+	13.2314i	0.130016	+	0.545190i
$590$	−0.773318			−0.0318370
$591$	8.02869	+	6.73687i	0.330256	+	0.277118i
$592$	−4.81908	+	1.75400i	−0.198063	+	0.0720890i
$593$	−1.86808	−	10.5944i	−0.0767128	−	0.435060i	−0.998839	−	0.0481709i	$-0.984661\pi$
$593$	−1.86808	−	10.5944i	−0.0767128	−	0.435060i	0.922126	−	0.386889i	$-0.126450\pi$
$594$	0.918748	−	5.21048i	0.0376967	−	0.213789i
$595$	−20.3888	−	7.42091i	−0.835858	−	0.304228i
$596$	−2.44222	−	4.23005i	−0.100037	−	0.173269i
$597$	−6.82682	+	11.8244i	−0.279403	+	0.483940i
$598$	−1.50727	+	1.26475i	−0.0616370	+	0.0517196i
$599$	−18.7153	+	15.7040i	−0.764686	+	0.641648i	−0.939342	−	0.342982i	$-0.888563\pi$
$599$	−18.7153	+	15.7040i	−0.764686	+	0.641648i	0.174656	+	0.984630i	$0.444119\pi$
$600$	3.73783	−	6.47410i	0.152596	−	0.264304i
$601$	13.2057	+	22.8730i	0.538673	+	0.933009i	0.998976	+	0.0452473i	$0.0144076\pi$
$601$	13.2057	+	22.8730i	0.538673	+	0.933009i	−0.460303	+	0.887762i	$0.652259\pi$
$602$	18.7037	+	6.80758i	0.762305	+	0.277456i
$603$	2.68820	−	15.2455i	0.109472	−	0.620845i
$604$	1.57011	+	8.90452i	0.0638868	+	0.362320i
$605$	56.4017	−	20.5286i	2.29306	−	0.834604i
$606$	−11.5025	−	9.65177i	−0.467258	−	0.392076i
$607$	−16.3618			−0.664107			−0.332053	−	0.943261i	$-0.607741\pi$
$607$	−16.3618			−0.664107			−0.332053	+	0.943261i	$0.607741\pi$
$608$	3.50000	+	2.59808i	0.141944	+	0.105366i
$609$	−0.448311			−0.0181665
$610$	4.25877	+	3.57353i	0.172433	+	0.144688i
$611$	−0.534615	+	0.194584i	−0.0216282	+	0.00787203i
$612$	−0.286989	−	1.62760i	−0.0116008	−	0.0657916i
$613$	1.03162	−	5.85062i	0.0416668	−	0.236304i	−0.956861	−	0.290546i	$-0.906163\pi$
$613$	1.03162	−	5.85062i	0.0416668	−	0.236304i	0.998528	+	0.0542418i	$0.0172742\pi$
$614$	24.0180	+	8.74184i	0.969288	+	0.352792i
$615$	−12.5496	−	21.7366i	−0.506050	−	0.876504i
$616$	9.83275	−	17.0308i	0.396173	−	0.686191i
$617$	−26.1438	+	21.9373i	−1.05251	+	0.883162i	−0.993355	−	0.115087i	$-0.963285\pi$
$617$	−26.1438	+	21.9373i	−1.05251	+	0.883162i	−0.0591558	+	0.998249i	$0.518841\pi$
$618$	−5.10220	+	4.28125i	−0.205240	+	0.172217i
$619$	−16.1506	+	27.9737i	−0.649149	+	1.12436i	0.334177	+	0.942510i	$0.391542\pi$
$619$	−16.1506	+	27.9737i	−0.649149	+	1.12436i	−0.983326	+	0.181849i	$0.941792\pi$
$620$	5.51114	+	9.54558i	0.221333	+	0.383360i
$621$	8.15657	+	2.96875i	0.327312	+	0.119132i
$622$	1.80154	−	10.2170i	0.0722350	−	0.409665i
$623$	−7.84565	−	44.4949i	−0.314329	−	1.78265i
$624$	−0.213011	+	0.0775297i	−0.00852727	+	0.00310367i
$625$	−4.97384	−	4.17355i	−0.198954	−	0.166942i
$626$	−15.4365			−0.616965
$627$	−10.3216	+	20.6237i	−0.412205	+	0.823629i
$628$	0.332748			0.0132781
$629$	−6.49273	−	5.44804i	−0.258882	−	0.217228i
$630$	12.3366	−	4.49016i	0.491503	−	0.178892i
$631$	3.13058	+	17.7544i	0.124626	+	0.706791i	0.981529	+	0.191313i	$0.0612745\pi$
$631$	3.13058	+	17.7544i	0.124626	+	0.706791i	−0.856903	+	0.515478i	$0.827614\pi$
$632$	−0.497474	+	2.82131i	−0.0197884	+	0.112226i
$633$	−14.9684	−	5.44804i	−0.594940	−	0.216540i
$634$	−14.1985	−	24.5925i	−0.563893	−	0.976691i
$635$	19.5398	−	33.8440i	0.775414	−	1.34306i
$636$	−4.54710	+	3.81547i	−0.180304	+	0.151293i
$637$	−1.18345	+	0.993031i	−0.0468899	+	0.0393453i
$638$	0.319078	−	0.552659i	0.0126324	−	0.0218800i
$639$	0.677519	+	1.17350i	0.0268022	+	0.0464228i
$640$	3.31908	+	1.20805i	0.131198	+	0.0477522i
$641$	0.449493	−	2.54920i	0.0177539	−	0.100687i	−0.974643	−	0.223765i	$-0.928165\pi$
$641$	0.449493	−	2.54920i	0.0177539	−	0.100687i	0.992397	+	0.123077i	$0.0392764\pi$
$642$	−1.40420	−	7.96361i	−0.0554194	−	0.314299i
$643$	−15.2160	+	5.53817i	−0.600061	+	0.218404i	−0.624149	−	0.781306i	$-0.714554\pi$
$643$	−15.2160	+	5.53817i	−0.600061	+	0.218404i	0.0240880	+	0.999710i	$0.492332\pi$
$644$	24.7147	+	20.7381i	0.973894	+	0.817194i
$645$	−18.9145			−0.744756
$646$	−0.826352	+	7.15642i	−0.0325124	+	0.281565i
$647$	0.477407			0.0187688			0.00938439	−	0.999956i	$-0.497013\pi$
$647$	0.477407			0.0187688			0.00938439	+	0.999956i	$0.497013\pi$
$648$	0.766044	+	0.642788i	0.0300931	+	0.0252511i
$649$	1.08853	−	0.396191i	0.0427284	−	0.0155519i
$650$	−0.294263	−	1.66885i	−0.0115419	−	0.0654576i
$651$	−2.01414	+	11.4227i	−0.0789403	+	0.447693i
$652$	−3.70321	−	1.34786i	−0.145029	−	0.0527862i
$653$	−8.05097	−	13.9447i	−0.315059	−	0.545698i	0.664391	−	0.747385i	$-0.268691\pi$
$653$	−8.05097	−	13.9447i	−0.315059	−	0.545698i	−0.979450	+	0.201687i	$0.935358\pi$
$654$	7.62449	−	13.2060i	0.298141	−	0.516395i
$655$	38.9616	−	32.6926i	1.52235	−	1.27741i
$656$	5.44356	−	4.56769i	0.212535	−	0.178338i
$657$	−1.21301	+	2.10100i	−0.0473241	+	0.0819677i
$658$	4.66431	+	8.07883i	0.181834	+	0.314946i
$659$	13.6630	+	4.97291i	0.532234	+	0.193717i	0.594135	−	0.804365i	$-0.297494\pi$
$659$	13.6630	+	4.97291i	0.532234	+	0.193717i	−0.0619017	+	0.998082i	$0.519717\pi$
$660$	−3.24510	+	18.4039i	−0.126315	+	0.716370i
$661$	−2.52915	−	14.3435i	−0.0983726	−	0.557899i	−0.993662	−	0.112413i	$-0.964142\pi$
$661$	−2.52915	−	14.3435i	−0.0983726	−	0.557899i	0.895289	−	0.445486i	$-0.146969\pi$
$662$	24.3589	−	8.86592i	0.946736	−	0.344584i
$663$	−0.286989	−	0.240812i	−0.0111457	−	0.00935238i
$664$	1.92127			0.0745599
$665$	−57.1237	+	3.40700i	−2.21516	+	0.132118i
$666$	5.12836			0.198720
$667$	0.802004	+	0.672961i	0.0310537	+	0.0260572i
$668$	−5.63176	+	2.04979i	−0.217899	+	0.0793089i
$669$	−3.23261	−	18.3331i	−0.124980	−	0.708797i
$670$	−9.49495	+	53.8485i	−0.366822	+	2.08035i
$671$	−7.82547	−	2.84824i	−0.302099	−	0.109955i
$672$	1.85844	+	3.21891i	0.0716909	+	0.124172i
$673$	−12.4324	+	21.5336i	−0.479235	+	0.830059i	−0.999716	−	0.0238142i	$-0.992419\pi$
$673$	−12.4324	+	21.5336i	−0.479235	+	0.830059i	0.520482	+	0.853873i	$0.325752\pi$
$674$	−18.0103	+	15.1124i	−0.693730	+	0.582108i
$675$	−5.72668	+	4.80526i	−0.220420	+	0.184954i
$676$	6.47431	−	11.2138i	0.249012	−	0.431301i
$677$	−23.2271	−	40.2306i	−0.892692	−	1.54619i	−0.836636	−	0.547760i	$-0.815481\pi$
$677$	−23.2271	−	40.2306i	−0.892692	−	1.54619i	−0.0560563	−	0.998428i	$-0.517853\pi$
$678$	0.766044	+	0.278817i	0.0294198	+	0.0107079i
$679$	11.2970	−	64.0682i	0.433537	−	2.45871i
$680$	1.01367	+	5.74881i	0.0388725	+	0.220457i
$681$	−5.44356	+	1.98129i	−0.208598	+	0.0759234i
$682$	−12.6480	−	10.6129i	−0.484315	−	0.406389i
$683$	−26.0000			−0.994862			−0.497431	−	0.867503i	$-0.665723\pi$
$683$	−26.0000			−0.994862			−0.497431	+	0.867503i	$0.665723\pi$
$684$	−2.40033	−	3.63846i	−0.0917789	−	0.139120i
$685$	1.67055			0.0638284
$686$	−0.526159	−	0.441500i	−0.0200888	−	0.0168565i
$687$	−7.63816	+	2.78006i	−0.291414	+	0.106066i
$688$	−0.929892	−	5.27368i	−0.0354518	−	0.201057i
$689$	−0.233651	+	1.32510i	−0.00890139	+	0.0504823i
$690$	−28.8097	−	10.4859i	−1.09677	−	0.399191i
$691$	8.03478	+	13.9166i	0.305657	+	0.529414i	0.977407	−	0.211364i	$-0.0677905\pi$
$691$	8.03478	+	13.9166i	0.305657	+	0.529414i	−0.671750	+	0.740778i	$0.734457\pi$
$692$	−6.13088	+	10.6190i	−0.233061	+	0.403674i
$693$	−15.0646	+	12.6407i	−0.572259	+	0.480182i
$694$	−1.84208	+	1.54569i	−0.0699245	+	0.0586736i
$695$	−17.9868	+	31.1540i	−0.682278	+	1.18174i
$696$	0.0603074	+	0.104455i	0.00228595	+	0.00395937i
$697$	11.0360	+	4.01676i	0.418017	+	0.152146i
$698$	0.902551	−	5.11862i	0.0341621	−	0.193743i
$699$	2.95677	+	16.7687i	0.111835	+	0.634249i
$700$	−26.1104	+	9.50341i	−0.986881	+	0.359195i
$701$	−7.59240	−	6.37078i	−0.286761	−	0.240621i	0.488048	−	0.872817i	$-0.337709\pi$
$701$	−7.59240	−	6.37078i	−0.286761	−	0.240621i	−0.774808	+	0.632196i	$0.782154\pi$
$702$	0.226682			0.00855555
$703$	−21.4238	−	6.38133i	−0.808014	−	0.240676i
$704$	−5.29086			−0.199407
$705$	−6.79086	−	5.69821i	−0.255759	−	0.214607i
$706$	−7.77719	+	2.83067i	−0.292698	+	0.106533i
$707$	9.69144	+	54.9629i	0.364484	+	2.06709i
$708$	−0.0380187	+	0.215615i	−0.00142883	+	0.00810329i
$709$	25.8148	+	9.39582i	0.969495	+	0.352867i	0.777747	−	0.628577i	$-0.216362\pi$
$709$	25.8148	+	9.39582i	0.969495	+	0.352867i	0.191748	+	0.981444i	$0.438584\pi$
$710$	−2.39306	−	4.14489i	−0.0898098	−	0.155555i
$711$	1.43242	−	2.48102i	0.0537199	−	0.0930456i
$712$	−9.31180	+	7.81353i	−0.348975	+	0.292824i
$713$	20.7499	−	17.4112i	0.777090	−	0.652056i
$714$	−3.07145	+	5.31991i	−0.114946	+	0.199093i
$715$	2.11809	+	3.66864i	0.0792120	+	0.137199i
$716$	−7.57785	−	2.75811i	−0.283197	−	0.103075i
$717$	2.60813	−	14.7914i	0.0974023	−	0.552396i
$718$	−0.398681	−	2.26103i	−0.0148786	−	0.0843810i
$719$	−11.5239	+	4.19437i	−0.429770	+	0.156424i	−0.547843	−	0.836581i	$-0.684551\pi$
$719$	−11.5239	+	4.19437i	−0.429770	+	0.156424i	0.118072	+	0.993005i	$0.462329\pi$
$720$	−2.70574	−	2.27038i	−0.100837	−	0.0846122i
$721$	24.7561			0.921965
$722$	5.50000	+	18.1865i	0.204689	+	0.676833i
$723$	21.4534			0.797859
$724$	0.145430	+	0.122030i	0.00540485	+	0.00453521i
$725$	−0.847296	+	0.308391i	−0.0314678	+	0.0114533i
$726$	−2.95084	−	16.7350i	−0.109516	−	0.621095i
$727$	4.90719	−	27.8301i	0.181998	−	1.03216i	−0.747755	−	0.663975i	$-0.768868\pi$
$727$	4.90719	−	27.8301i	0.181998	−	1.03216i	0.929752	−	0.368185i	$-0.120021\pi$
$728$	0.791737	+	0.288169i	0.0293437	+	0.0106802i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	4.28446	−	7.42091i	0.158575	−	0.274660i
$731$	6.77972	−	5.68886i	0.250757	−	0.210410i
$732$	1.20574	−	1.01173i	0.0445653	−	0.0373947i
$733$	11.2883	−	19.5520i	0.416944	−	0.722168i	−0.578686	−	0.815550i	$-0.696434\pi$
$733$	11.2883	−	19.5520i	0.416944	−	0.722168i	0.995630	+	0.0933819i	$0.0297677\pi$
$734$	−14.9324	−	25.8637i	−0.551166	−	0.954647i
$735$	−22.6202	−	8.23308i	−0.834359	−	0.303682i
$736$	1.50727	−	8.54818i	0.0555589	−	0.315090i
$737$	−14.2229	−	80.6619i	−0.523906	−	2.97122i
$738$	−6.67752	+	2.43042i	−0.245803	+	0.0894649i
$739$	20.2986	+	17.0325i	0.746696	+	0.626552i	0.934627	−	0.355630i	$-0.115734\pi$
$739$	20.2986	+	17.0325i	0.746696	+	0.626552i	−0.187931	+	0.982182i	$0.560178\pi$
$740$	−18.1138			−0.665877
$741$	−0.946967	−	0.282065i	−0.0347877	−	0.0103619i
$742$	22.0627			0.809949
$743$	−21.1536	−	17.7500i	−0.776052	−	0.651185i	0.166199	−	0.986092i	$-0.446850\pi$
$743$	−21.1536	−	17.7500i	−0.776052	−	0.651185i	−0.942251	+	0.334907i	$0.891295\pi$
$744$	2.93242	−	1.06731i	0.107508	−	0.0391296i
$745$	−2.99582	−	16.9902i	−0.109759	−	0.622472i
$746$	−3.44743	+	19.5514i	−0.126220	+	0.715826i
$747$	−1.80541	−	0.657115i	−0.0660564	−	0.0240426i
$748$	−4.37211	−	7.57272i	−0.159860	−	0.276886i
$749$	−15.0282	+	26.0296i	−0.549119	+	0.951102i
$750$	6.69846	−	5.62068i	0.244593	−	0.205238i
$751$	0.988140	−	0.829148i	0.0360578	−	0.0302561i	−0.624581	−	0.780960i	$-0.714730\pi$
$751$	0.988140	−	0.829148i	0.0360578	−	0.0302561i	0.660638	+	0.750704i	$0.270286\pi$
$752$	1.25490	−	2.17355i	0.0457615	−	0.0792612i
$753$	−12.7836	−	22.1418i	−0.465860	−	0.806893i
$754$	0.0256923	+	0.00935122i	0.000935657	+	0.000340551i
$755$	−5.54576	+	31.4516i	−0.201831	+	1.14464i
$756$	−0.645430	−	3.66041i	−0.0234741	−	0.133128i
$757$	24.3259	−	8.85392i	0.884141	−	0.321801i	0.140262	−	0.990114i	$-0.455206\pi$
$757$	24.3259	−	8.85392i	0.884141	−	0.321801i	0.743880	+	0.668313i	$0.232983\pi$
$758$	19.7836	+	16.6004i	0.718572	+	0.602954i
$759$	45.9249			1.66697
$760$	8.47818	+	12.8514i	0.307536	+	0.466168i
$761$	11.3396			0.411059			0.205529	−	0.978651i	$-0.434108\pi$
$761$	11.3396			0.411059			0.205529	+	0.978651i	$0.434108\pi$
$762$	−8.47565	−	7.11192i	−0.307040	−	0.257638i
$763$	−53.2605	+	19.3852i	−1.92816	+	0.701792i
$764$	3.13223	+	17.7637i	0.113320	+	0.642669i
$765$	1.01367	−	5.74881i	0.0366493	−	0.207849i
$766$	−18.9201	−	6.88635i	−0.683611	−	0.248814i
$767$	0.0248149	+	0.0429807i	0.000896015	+	0.00155194i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	16.4283	−	13.7850i	0.592420	−	0.497099i	−0.296579	−	0.955008i	$-0.595846\pi$
$769$	16.4283	−	13.7850i	0.592420	−	0.497099i	0.888999	+	0.457909i	$0.151401\pi$
$770$	53.2097	−	44.6482i	1.91754	−	1.60901i
$771$	1.39646	−	2.41874i	0.0502923	−	0.0871087i
$772$	8.71941	+	15.1025i	0.313818	+	0.543549i
$773$	−3.99108	−	1.45263i	−0.143549	−	0.0522476i	0.269246	−	0.963071i	$-0.413225\pi$
$773$	−3.99108	−	1.45263i	−0.143549	−	0.0522476i	−0.412796	+	0.910824i	$0.635448\pi$
$774$	−0.929892	+	5.27368i	−0.0334243	+	0.189559i
$775$	4.05097	+	22.9742i	0.145515	+	0.825258i
$776$	−16.4474	+	5.98638i	−0.590428	+	0.214898i
$777$	−14.6019	−	12.2525i	−0.523842	−	0.439556i
$778$	11.3327			0.406299
$779$	30.9197	−	1.84413i	1.10781	−	0.0660728i
$780$	−0.800660			−0.0286682
$781$	5.49201	+	4.60834i	0.196520	+	0.164900i
$782$	13.4804	−	4.90646i	0.482058	−	0.175455i
$783$	−0.0209445	−	0.118782i	−0.000748497	−	0.00424493i
$784$	1.18345	−	6.71167i	0.0422660	−	0.239702i
$785$	1.10442	+	0.401975i	0.0394184	+	0.0143471i
$786$	−7.19981	−	12.4704i	−0.256809	−	0.444806i
$787$	5.41013	−	9.37062i	0.192850	−	0.334027i	−0.753343	−	0.657627i	$-0.771560\pi$
$787$	5.41013	−	9.37062i	0.192850	−	0.334027i	0.946194	+	0.323601i	$0.104893\pi$
$788$	−8.02869	+	6.73687i	−0.286010	+	0.239991i
$789$	−1.06031	+	0.889704i	−0.0377479	+	0.0316743i
$790$	−5.05943	+	8.76319i	−0.180006	+	0.311780i
$791$	−1.51501	−	2.62408i	−0.0538677	−	0.0933016i
$792$	4.97178	+	1.80958i	0.176665	+	0.0643006i
$793$	0.0619563	−	0.351371i	0.00220013	−	0.0124776i
$794$	2.27379	+	12.8953i	0.0806936	+	0.457636i
$795$	−19.7015	+	7.17074i	−0.698739	+	0.254320i
$796$	−10.4593	−	8.77639i	−0.370720	−	0.311071i
$797$	22.0327			0.780439			0.390219	−	0.920722i	$-0.372399\pi$
$797$	22.0327			0.780439			0.390219	+	0.920722i	$0.372399\pi$
$798$	−1.85844	+	16.0946i	−0.0657881	+	0.569742i
$799$	4.14796			0.146744
$800$	5.72668	+	4.80526i	0.202469	+	0.169891i
$801$	11.4226	−	4.15749i	0.403598	−	0.146898i
$802$	3.68479	+	20.8975i	0.130115	+	0.737916i
$803$	−2.22890	+	12.6407i	−0.0786563	+	0.446082i
$804$	14.5471	+	5.29471i	0.513037	+	0.186730i
$805$	56.9774	+	98.6877i	2.00819	+	3.47828i
$806$	0.353693	−	0.612614i	0.0124583	−	0.0215784i
$807$	13.0817	−	10.9769i	0.460498	−	0.386404i
$808$	11.5025	−	9.65177i	0.404657	−	0.339548i
$809$	−3.34343	+	5.79098i	−0.117549	+	0.203600i	−0.918796	−	0.394733i	$-0.870837\pi$
$809$	−3.34343	+	5.79098i	−0.117549	+	0.203600i	0.801247	+	0.598334i	$0.204170\pi$
$810$	1.76604	+	3.05888i	0.0620525	+	0.107478i
$811$	−23.9530	−	8.71816i	−0.841102	−	0.306136i	−0.114695	−	0.993401i	$-0.536589\pi$
$811$	−23.9530	−	8.71816i	−0.841102	−	0.306136i	−0.726407	+	0.687265i	$0.758811\pi$
$812$	0.0778483	−	0.441500i	0.00273194	−	0.0154936i
$813$	4.46064	+	25.2975i	0.156441	+	0.887223i
$814$	25.4971	−	9.28017i	0.893672	−	0.325270i
$815$	−10.6630	−	8.94729i	−0.373508	−	0.313410i
$816$	1.65270			0.0578562
$817$	10.4468	−	20.8738i	0.365487	−	0.730282i
$818$	−29.0797			−1.01675
$819$	−0.645430	−	0.541580i	−0.0225531	−	0.0189243i
$820$	23.5856	−	8.58445i	0.823644	−	0.299782i
$821$	−7.34348	−	41.6470i	−0.256289	−	1.45349i	−0.792741	−	0.609558i	$-0.791347\pi$
$821$	−7.34348	−	41.6470i	−0.256289	−	1.45349i	0.536452	−	0.843931i	$-0.319764\pi$
$822$	0.0821293	−	0.465778i	0.00286459	−	0.0162459i
$823$	0.506397	+	0.184313i	0.0176519	+	0.00642476i	0.350831	−	0.936439i	$-0.385899\pi$
$823$	0.506397	+	0.184313i	0.0176519	+	0.00642476i	−0.333179	+	0.942864i	$0.608121\pi$
$824$	−3.33022	−	5.76811i	−0.116014	−	0.200942i
$825$	−19.7763	+	34.2536i	−0.688523	+	1.19256i
$826$	0.623389	−	0.523086i	0.0216905	−	0.0182005i
$827$	−12.2745	+	10.2995i	−0.426826	+	0.358150i	−0.830753	−	0.556642i	$-0.812090\pi$
$827$	−12.2745	+	10.2995i	−0.426826	+	0.358150i	0.403926	+	0.914791i	$0.367645\pi$
$828$	−4.34002	+	7.51714i	−0.150826	+	0.261239i
$829$	10.0517	+	17.4100i	0.349110	+	0.604676i	0.986092	−	0.166203i	$-0.0531508\pi$
$829$	10.0517	+	17.4100i	0.349110	+	0.604676i	−0.636982	+	0.770879i	$0.719817\pi$
$830$	6.37686	+	2.32099i	0.221344	+	0.0805626i
$831$	−3.85932	+	21.8873i	−0.133878	+	0.759261i
$832$	−0.0393628	−	0.223238i	−0.00136466	−	0.00773938i
$833$	10.5842	−	3.85235i	0.366722	−	0.133476i
$834$	7.80200	+	6.54666i	0.270161	+	0.226692i
$835$	−21.1685			−0.732566
$836$	−18.5180	−	13.7461i	−0.640459	−	0.475417i
$837$	−3.12061			−0.107864
$838$	31.0219	+	26.0304i	1.07163	+	0.899207i
$839$	−29.1031	+	10.5927i	−1.00475	+	0.365700i	−0.791415	−	0.611279i	$-0.790655\pi$
$839$	−29.1031	+	10.5927i	−1.00475	+	0.365700i	−0.213337	+	0.976979i	$0.568433\pi$
$840$	2.27972	+	12.9289i	0.0786576	+	0.446090i
$841$	−5.03327	+	28.5451i	−0.173561	+	0.984314i
$842$	−29.3491	−	10.6822i	−1.01144	−	0.368133i
$843$	0.771974	+	1.33710i	0.0265882	+	0.0460521i
$844$	7.96451	−	13.7949i	0.274150	−	0.474841i
$845$	35.0355	−	29.3983i	1.20526	−	1.01133i
$846$	−1.92262	+	1.61327i	−0.0661010	+	0.0554653i
$847$	−31.5808	+	54.6996i	−1.08513	+	1.87950i
$848$	−2.96791	−	5.14057i	−0.101918	−	0.176528i
$849$	9.67024	+	3.51968i	0.331882	+	0.120795i
$850$	−2.14543	+	12.1673i	−0.0735876	+	0.417336i
$851$	7.72984	+	43.8381i	0.264975	+	1.50275i
$852$	−1.27332	+	0.463450i	−0.0436232	+	0.0158775i
$853$	−16.3209	−	13.6949i	−0.558817	−	0.468903i	0.319097	−	0.947722i	$-0.396620\pi$
$853$	−16.3209	−	13.6949i	−0.558817	−	0.468903i	−0.877913	+	0.478819i	$0.841065\pi$
$854$	−5.85029			−0.200193
$855$	−3.57145	−	14.9761i	−0.122141	−	0.512170i
$856$	8.08647			0.276390
$857$	42.5551	+	35.7080i	1.45366	+	1.21976i	0.929857	+	0.367920i	$0.119930\pi$
$857$	42.5551	+	35.7080i	1.45366	+	1.21976i	0.523799	+	0.851842i	$0.324514\pi$
$858$	1.12701	−	0.410199i	0.0384755	−	0.0140039i
$859$	−4.11902	−	23.3601i	−0.140539	−	0.797038i	−0.970841	−	0.239724i	$-0.922943\pi$
$859$	−4.11902	−	23.3601i	−0.140539	−	0.797038i	0.830302	−	0.557314i	$-0.188168\pi$
$860$	3.28446	−	18.6271i	0.111999	−	0.635179i
$861$	24.8195	+	9.03358i	0.845848	+	0.307863i
$862$	−13.0103	−	22.5344i	−0.443131	−	0.767526i
$863$	−10.5410	+	18.2576i	−0.358820	+	0.621495i	−0.987764	−	0.155956i	$-0.950154\pi$
$863$	−10.5410	+	18.2576i	−0.358820	+	0.621495i	0.628944	+	0.777451i	$0.283488\pi$
$864$	−0.766044	+	0.642788i	−0.0260614	+	0.0218681i
$865$	−33.1771	+	27.8389i	−1.12806	+	0.946551i
$866$	13.5321	−	23.4383i	0.459839	−	0.796465i
$867$	−7.13429	−	12.3569i	−0.242293	−	0.419664i
$868$	−10.8995	−	3.96708i	−0.369952	−	0.134651i
$869$	2.63206	−	14.9272i	0.0892866	−	0.506370i
$870$	0.0739780	+	0.419550i	0.00250809	+	0.0142241i
$871$	3.29756	−	1.20021i	0.111734	−	0.0406677i
$872$	11.6814	+	9.80185i	0.395582	+	0.331932i
$873$	17.5030			0.592387
$874$	27.4843	−	26.0026i	0.929669	−	0.879551i
$875$	−32.5012			−1.09874
$876$	−1.85844	−	1.55942i	−0.0627909	−	0.0526878i
$877$	48.1134	−	17.5118i	1.62467	−	0.591333i	0.640409	−	0.768034i	$-0.278765\pi$
$877$	48.1134	−	17.5118i	1.62467	−	0.591333i	0.984265	+	0.176701i	$0.0565425\pi$
$878$	−0.510678	−	2.89620i	−0.0172345	−	0.0977419i
$879$	4.94949	−	28.0700i	0.166942	−	0.946777i
$880$	−17.5608	−	6.39160i	−0.591974	−	0.215461i
$881$	17.0804	+	29.5841i	0.575452	+	0.996713i	0.995992	+	0.0894388i	$0.0285074\pi$
$881$	17.0804	+	29.5841i	0.575452	+	0.996713i	−0.420540	+	0.907274i	$0.638159\pi$
$882$	−3.40760	+	5.90214i	−0.114740	+	0.198735i
$883$	21.5403	−	18.0745i	0.724889	−	0.608254i	−0.203844	−	0.979003i	$-0.565344\pi$
$883$	21.5403	−	18.0745i	0.724889	−	0.608254i	0.928733	+	0.370750i	$0.120899\pi$
$884$	0.286989	−	0.240812i	0.00965248	−	0.00809940i
$885$	−0.386659	+	0.669713i	−0.0129974	+	0.0225122i
$886$	−13.8025	−	23.9066i	−0.463703	−	0.803157i
$887$	33.4298	+	12.1674i	1.12246	+	0.408543i	0.835550	−	0.549414i	$-0.185149\pi$
$887$	33.4298	+	12.1674i	1.12246	+	0.408543i	0.286912	+	0.957957i	$0.407371\pi$
$888$	−0.890530	+	5.05044i	−0.0298842	+	0.169482i
$889$	7.14115	+	40.4995i	0.239506	+	1.35831i
$890$	−40.3457	+	14.6846i	−1.35239	+	0.492230i
$891$	−4.05303	−	3.40090i	−0.135782	−	0.113934i
$892$	18.6159			0.623305
$893$	10.0392	−	4.34710i	0.335949	−	0.145470i
$894$	−4.88444			−0.163360
$895$	−21.8195	−	18.3088i	−0.729347	−	0.611995i
$896$	−3.49273	+	1.27125i	−0.116684	+	0.0424694i
$897$	0.341671	+	1.93771i	0.0114081	+	0.0646984i
$898$	2.93851	−	16.6651i	0.0980594	−	0.556122i
$899$	−0.353693	−	0.128734i	−0.0117963	−	0.00429351i
$900$	−3.73783	−	6.47410i	−0.124594	−	0.215803i
$901$	4.90508	−	8.49584i	0.163412	−	0.283038i
$902$	−28.8011	+	24.1670i	−0.958973	+	0.804674i
$903$	15.2474	−	12.7941i	0.507401	−	0.425760i
$904$	−0.407604	+	0.705990i	−0.0135567	+	0.0234809i
$905$	0.335275	+	0.580713i	0.0111449	+	0.0193035i
$906$	8.49660	+	3.09251i	0.282281	+	0.102742i
$907$	−1.61422	+	9.15469i	−0.0535992	+	0.303976i	−0.999808	−	0.0195795i	$-0.993767\pi$
$907$	−1.61422	+	9.15469i	−0.0535992	+	0.303976i	0.946209	+	0.323556i	$0.104878\pi$
$908$	−1.00593	−	5.70491i	−0.0333830	−	0.189324i
$909$	−14.1099	+	5.13560i	−0.467997	+	0.170337i
$910$	2.27972	+	1.91291i	0.0755718	+	0.0634123i
$911$	3.79055			0.125587			0.0627933	−	0.998027i	$-0.479999\pi$
$911$	3.79055			0.125587			0.0627933	+	0.998027i	$0.479999\pi$
$912$	4.00000	−	1.73205i	0.132453	−	0.0573539i
$913$	−10.1652			−0.336419
$914$	7.04117	+	5.90825i	0.232901	+	0.195427i
$915$	5.22416	−	1.90144i	0.172705	−	0.0628596i
$916$	−1.41147	−	8.00487i	−0.0466364	−	0.264488i
$917$	−9.29394	+	52.7085i	−0.306913	+	1.74059i
$918$	−1.55303	−	0.565258i	−0.0512577	−	0.0186563i
$919$	2.21554	+	3.83742i	0.0730838	+	0.126585i	0.900251	−	0.435370i	$-0.143383\pi$
$919$	2.21554	+	3.83742i	0.0730838	+	0.126585i	−0.827168	+	0.561955i	$0.810049\pi$
$920$	15.3293	−	26.5512i	0.505394	−	0.875367i
$921$	19.5797	−	16.4293i	0.645172	−	0.541363i
$922$	−11.8320	+	9.92825i	−0.389667	+	0.326970i
$923$	−0.153581	+	0.266010i	−0.00505518	+	0.00875583i
$924$	−9.83275	−	17.0308i	−0.323474	−	0.560273i
$925$	−36.0257	−	13.1123i	−1.18452	−	0.431130i
$926$	5.20620	−	29.5258i	0.171086	−	0.970280i
$927$	1.15657	+	6.55926i	0.0379869	+	0.215434i
$928$	−0.113341	+	0.0412527i	−0.00372059	+	0.00135419i
$929$	23.3384	+	19.5833i	0.765709	+	0.642506i	0.939606	−	0.342258i	$-0.111192\pi$
$929$	23.3384	+	19.5833i	0.765709	+	0.642506i	−0.173897	+	0.984764i	$0.555636\pi$
$930$	11.0223			0.361435
$931$	21.5795	−	20.4162i	0.707239	−	0.669112i
$932$	−17.0273			−0.557749
$933$	−7.94743	−	6.66869i	−0.260187	−	0.218323i
$934$	−27.1434	+	9.87938i	−0.888158	+	0.323263i
$935$	−5.36319	−	30.4162i	−0.175395	−	0.994715i
$936$	−0.0393628	+	0.223238i	−0.00128661	+	0.00729676i
$937$	1.34477	+	0.489456i	0.0439317	+	0.0159898i	0.363893	−	0.931441i	$-0.381448\pi$
$937$	1.34477	+	0.489456i	0.0439317	+	0.0159898i	−0.319961	+	0.947431i	$0.603670\pi$
$938$	−28.7700	−	49.8311i	−0.939373	−	1.62704i
$939$	−7.71823	+	13.3684i	−0.251875	+	0.436260i
$940$	6.79086	−	5.69821i	0.221493	−	0.185855i
$941$	3.47384	−	2.91490i	0.113244	−	0.0950230i	−0.584407	−	0.811460i	$-0.698673\pi$
$941$	3.47384	−	2.91490i	0.113244	−	0.0950230i	0.697651	+	0.716437i	$0.254229\pi$
$942$	0.166374	−	0.288169i	0.00542076	−	0.00938904i
$943$	−30.8405	−	53.4173i	−1.00430	−	1.73951i
$944$	−0.205737	−	0.0748822i	−0.00669617	−	0.00243721i
$945$	2.27972	−	12.9289i	0.0741591	−	0.420577i
$946$	4.91993	+	27.9023i	0.159961	+	0.907182i
$947$	−0.388881	+	0.141541i	−0.0126369	+	0.00459946i	−0.348331	−	0.937372i	$-0.613251\pi$
$947$	−0.388881	+	0.141541i	−0.0126369	+	0.00459946i	0.335694	+	0.941971i	$0.391029\pi$
$948$	2.19459	+	1.84148i	0.0712771	+	0.0598086i
$949$	−0.549935			−0.0178516
$950$	7.55896	+	31.6968i	0.245245	+	1.02838i
$951$	−28.3969			−0.920833
$952$	−4.70574	−	3.94858i	−0.152514	−	0.127974i
$953$	−13.3678	+	4.86549i	−0.433027	+	0.157609i	−0.549331	−	0.835605i	$-0.685117\pi$
$953$	−13.3678	+	4.86549i	−0.433027	+	0.157609i	0.116304	+	0.993214i	$0.462895\pi$
$954$	1.03074	+	5.84564i	0.0333716	+	0.189260i
$955$	−11.0633	+	62.7431i	−0.358000	+	2.03032i
$956$	14.1138	+	5.13701i	0.456473	+	0.166143i
$957$	−0.319078	−	0.552659i	−0.0103143	−	0.0178649i
$958$	−6.83022	+	11.8303i	−0.220674	+	0.382219i
$959$	−1.34667	+	1.12999i	−0.0434862	+	0.0364892i
$960$	2.70574	−	2.27038i	0.0873273	−	0.0732763i
$961$	10.6309	−	18.4132i	0.342932	−	0.593975i
$962$	0.581252	+	1.00676i	0.0187403	+	0.0324592i
$963$	−7.59879	−	2.76573i	−0.244868	−	0.0891245i
$964$	−3.72534	+	21.1274i	−0.119985	+	0.680469i
$965$	10.6959	+	60.6597i	0.344314	+	1.95270i
$966$	30.3170	−	11.0345i	0.975434	−	0.355029i
$967$	−43.5376	−	36.5324i	−1.40008	−	1.17480i	−0.961066	−	0.276320i	$-0.910885\pi$
$967$	−43.5376	−	36.5324i	−1.40008	−	1.17480i	−0.439009	−	0.898482i	$-0.644671\pi$
$968$	16.9932			0.546182
$969$	5.78446	+	4.29385i	0.185824	+	0.137938i
$970$	−61.8221			−1.98499
$971$	−6.94356	−	5.82634i	−0.222830	−	0.186976i	0.524538	−	0.851387i	$-0.324238\pi$
$971$	−6.94356	−	5.82634i	−0.222830	−	0.186976i	−0.747368	+	0.664411i	$0.768683\pi$
$972$	0.939693	−	0.342020i	0.0301407	−	0.0109703i
$973$	−6.57357	−	37.2806i	−0.210739	−	1.19516i
$974$	−1.07280	+	6.08413i	−0.0343746	+	0.194948i
$975$	−1.59240	−	0.579585i	−0.0509975	−	0.0185616i
$976$	0.786989	+	1.36310i	0.0251909	+	0.0436319i
$977$	1.32635	−	2.29731i	0.0424338	−	0.0734974i	−0.844028	−	0.536298i	$-0.819822\pi$
$977$	1.32635	−	2.29731i	0.0424338	−	0.0734974i	0.886462	+	0.462801i	$0.153156\pi$
$978$	−3.01889	+	2.53315i	−0.0965333	+	0.0810011i
$979$	49.2674	−	41.3403i	1.57459	−	1.32124i
$980$	12.0360	−	20.8469i	0.384475	−	0.665930i
$981$	−7.62449	−	13.2060i	−0.243431	−	0.421635i
$982$	−3.85591	−	1.40344i	−0.123047	−	0.0447855i
$983$	−9.34183	+	52.9802i	−0.297958	+	1.68980i	0.356972	+	0.934115i	$0.383809\pi$
$983$	−9.34183	+	52.9802i	−0.297958	+	1.68980i	−0.654930	+	0.755690i	$0.727302\pi$
$984$	−1.23396	−	6.99811i	−0.0393371	−	0.223092i
$985$	−34.7863	+	12.6612i	−1.10838	+	0.403418i
$986$	−0.152704	−	0.128134i	−0.00486307	−	0.00408060i
$987$	9.32863			0.296934
$988$	0.442219	−	0.883600i	0.0140689	−	0.0281111i
$989$	−46.4820			−1.47804
$990$	14.3157	+	12.0123i	0.454982	+	0.381775i
$991$	−50.3598	+	18.3295i	−1.59973	+	0.582255i	−0.979373	−	0.202062i	$-0.935236\pi$
$991$	−50.3598	+	18.3295i	−1.59973	+	0.582255i	−0.620360	+	0.784317i	$0.713014\pi$
$992$	0.541889	+	3.07321i	0.0172050	+	0.0975744i
$993$	4.50134	−	25.5284i	0.142846	−	0.810119i
$994$	4.73277	+	1.72259i	0.150114	+	0.0546372i
$995$	−24.1129	−	41.7648i	−0.764431	−	1.32403i
$996$	0.960637	−	1.66387i	0.0304390	−	0.0527218i
$997$	13.8938	−	11.6583i	0.440020	−	0.369221i	−0.395697	−	0.918381i	$-0.629497\pi$
$997$	13.8938	−	11.6583i	0.440020	−	0.369221i	0.835717	+	0.549160i	$0.185052\pi$
$998$	20.3607	−	17.0847i	0.644507	−	0.540806i
$999$	2.56418	−	4.44129i	0.0811270	−	0.140516i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.2.i.c.73.1	yes	6
3.2	odd	2		342.2.u.b.73.1		6
4.3	odd	2		912.2.bo.d.529.1		6
19.5	even	9		2166.2.a.r.1.1		3
19.6	even	9	inner	114.2.i.c.25.1	✓	6
19.14	odd	18		2166.2.a.p.1.1		3
57.5	odd	18		6498.2.a.bp.1.3		3
57.14	even	18		6498.2.a.bu.1.3		3
57.44	odd	18		342.2.u.b.253.1		6
76.63	odd	18		912.2.bo.d.481.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.c.25.1	✓	6	19.6	even	9	inner
114.2.i.c.73.1	yes	6	1.1	even	1	trivial
342.2.u.b.73.1		6	3.2	odd	2
342.2.u.b.253.1		6	57.44	odd	18
912.2.bo.d.481.1		6	76.63	odd	18
912.2.bo.d.529.1		6	4.3	odd	2
2166.2.a.p.1.1		3	19.14	odd	18
2166.2.a.r.1.1		3	19.5	even	9
6498.2.a.bp.1.3		3	57.5	odd	18
6498.2.a.bu.1.3		3	57.14	even	18

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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(0.939693 - 0.342020i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.613341 + 3.47843i) q^{5} +(0.939693 + 0.342020i) q^{6} +(-1.85844 - 3.21891i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(0.766044 - 0.642788i) q^{9} +(-2.70574 + 2.27038i) q^{10} +(2.64543 - 4.58202i) q^{11} +(0.500000 + 0.866025i) q^{12} +(0.213011 + 0.0775297i) q^{13} +(0.645430 - 3.66041i) q^{14} +(0.613341 + 3.47843i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-1.26604 - 1.06234i) q^{17} +1.00000 q^{18} +(-4.17752 - 1.24432i) q^{19} -3.53209 q^{20} +(-2.84730 - 2.38917i) q^{21} +(4.97178 - 1.80958i) q^{22} +(1.50727 + 8.54818i) q^{23} +(-0.173648 + 0.984808i) q^{24} +(-7.02481 - 2.55682i) q^{25} +(0.113341 + 0.196312i) q^{26} +(0.500000 - 0.866025i) q^{27} +(2.84730 - 2.38917i) q^{28} +(0.0923963 - 0.0775297i) q^{29} +(-1.76604 + 3.05888i) q^{30} +(-1.56031 - 2.70253i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(0.918748 - 5.21048i) q^{33} +(-0.286989 - 1.62760i) q^{34} +(12.3366 - 4.49016i) q^{35} +(0.766044 + 0.642788i) q^{36} +5.12836 q^{37} +(-2.40033 - 3.63846i) q^{38} +0.226682 q^{39} +(-2.70574 - 2.27038i) q^{40} +(-6.67752 + 2.43042i) q^{41} +(-0.645430 - 3.66041i) q^{42} +(-0.929892 + 5.27368i) q^{43} +(4.97178 + 1.80958i) q^{44} +(1.76604 + 3.05888i) q^{45} +(-4.34002 + 7.51714i) q^{46} +(-1.92262 + 1.61327i) q^{47} +(-0.766044 + 0.642788i) q^{48} +(-3.40760 + 5.90214i) q^{49} +(-3.73783 - 6.47410i) q^{50} +(-1.55303 - 0.565258i) q^{51} +(-0.0393628 + 0.223238i) q^{52} +(1.03074 + 5.84564i) q^{53} +(0.939693 - 0.342020i) q^{54} +(14.3157 + 12.0123i) q^{55} +3.71688 q^{56} +(-4.35117 + 0.259515i) q^{57} +0.120615 q^{58} +(0.167718 + 0.140732i) q^{59} +(-3.31908 + 1.20805i) q^{60} +(-0.273318 - 1.55007i) q^{61} +(0.541889 - 3.07321i) q^{62} +(-3.49273 - 1.27125i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.400330 + 0.693392i) q^{65} +(4.05303 - 3.40090i) q^{66} +(11.8589 - 9.95080i) q^{67} +(0.826352 - 1.43128i) q^{68} +(4.34002 + 7.51714i) q^{69} +(12.3366 + 4.49016i) q^{70} +(-0.235300 + 1.33445i) q^{71} +(0.173648 + 0.984808i) q^{72} +(-2.27972 + 0.829748i) q^{73} +(3.92855 + 3.29644i) q^{74} -7.47565 q^{75} +(0.500000 - 4.33013i) q^{76} -19.6655 q^{77} +(0.173648 + 0.145708i) q^{78} +(2.69207 - 0.979832i) q^{79} +(-0.613341 - 3.47843i) q^{80} +(0.173648 - 0.984808i) q^{81} +(-6.67752 - 2.43042i) q^{82} +(-0.960637 - 1.66387i) q^{83} +(1.85844 - 3.21891i) q^{84} +(4.47178 - 3.75227i) q^{85} +(-4.10220 + 3.44215i) q^{86} +(0.0603074 - 0.104455i) q^{87} +(2.64543 + 4.58202i) q^{88} +(11.4226 + 4.15749i) q^{89} +(-0.613341 + 3.47843i) q^{90} +(-0.146307 - 0.829748i) q^{91} +(-8.15657 + 2.96875i) q^{92} +(-2.39053 - 2.00589i) q^{93} -2.50980 q^{94} +(6.89053 - 13.7680i) q^{95} -1.00000 q^{96} +(13.4081 + 11.2507i) q^{97} +(-6.40420 + 2.33094i) q^{98} +(-0.918748 - 5.21048i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} - 3 q^{7} - 3 q^{8} - 6 q^{10} + 3 q^{12} + 9 q^{13} - 12 q^{14} - 3 q^{15} - 3 q^{17} + 6 q^{18} - 12 q^{20} - 15 q^{21} + 15 q^{22} + 27 q^{23} - 15 q^{25} - 6 q^{26} + 3 q^{27} + 15 q^{28}+ \cdots - 3 q^{99}+O(q^{100}) \) 6 * q + 3 * q^5 - 3 * q^7 - 3 * q^8 - 6 * q^10 + 3 * q^12 + 9 * q^13 - 12 * q^14 - 3 * q^15 - 3 * q^17 + 6 * q^18 - 12 * q^20 - 15 * q^21 + 15 * q^22 + 27 * q^23 - 15 * q^25 - 6 * q^26 + 3 * q^27 + 15 * q^28 - 3 * q^29 - 6 * q^30 - 15 * q^31 + 3 * q^33 + 6 * q^34 + 12 * q^35 - 6 * q^37 - 12 * q^39 - 6 * q^40 - 15 * q^41 + 12 * q^42 + 3 * q^43 + 15 * q^44 + 6 * q^45 - 6 * q^46 + 15 * q^47 - 24 * q^49 - 3 * q^50 + 3 * q^51 - 9 * q^52 + 6 * q^53 + 27 * q^55 + 6 * q^56 + 12 * q^58 - 27 * q^59 - 3 * q^60 - 15 * q^61 - 3 * q^62 - 3 * q^63 - 3 * q^64 + 12 * q^65 + 12 * q^66 - 3 * q^67 + 6 * q^68 + 6 * q^69 + 12 * q^70 + 3 * q^71 + 12 * q^73 + 24 * q^74 - 6 * q^75 + 3 * q^76 - 42 * q^77 + 27 * q^79 + 3 * q^80 - 15 * q^82 + 3 * q^83 + 3 * q^84 + 12 * q^85 - 24 * q^86 + 6 * q^87 + 42 * q^89 + 3 * q^90 - 42 * q^91 - 27 * q^92 + 3 * q^93 - 18 * q^94 + 24 * q^95 - 6 * q^96 + 18 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

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