LMFDB - Embedded newform 627.2.r.c.100.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [627,2,Mod(100,627)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(627, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("627.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 627 = 3 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	627.r (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:	$5.00662020673$
Analytic rank:	$0$
Dimension:	$54$
Relative dimension:	$9$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			100.6
Character	$\chi$	$=$	627.100
Dual form			627.2.r.c.232.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.14605 - 0.417129i) q^{2} +(0.173648 - 0.984808i) q^{3} +(-0.392648 + 0.329471i) q^{4} +(-1.91969 - 1.61081i) q^{5} +(-0.211782 - 1.20108i) q^{6} +(-0.627651 - 1.08712i) q^{7} +(-1.53217 + 2.65379i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(-2.87198 - 1.04531i) q^{10} +(0.500000 - 0.866025i) q^{11} +(0.256283 + 0.443895i) q^{12} +(-0.498897 - 2.82939i) q^{13} +(-1.17279 - 0.984089i) q^{14} +(-1.91969 + 1.61081i) q^{15} +(-0.470959 + 2.67094i) q^{16} +(-5.25098 + 1.91120i) q^{17} -1.21960 q^{18} +(-4.33060 + 0.495920i) q^{19} +1.28448 q^{20} +(-1.17960 + 0.429338i) q^{21} +(0.211782 - 1.20108i) q^{22} +(-0.572409 + 0.480308i) q^{23} +(2.34742 + 1.96972i) q^{24} +(0.222251 + 1.26045i) q^{25} +(-1.75198 - 3.03452i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(0.604621 + 0.220064i) q^{28} +(4.02109 + 1.46356i) q^{29} +(-1.52815 + 2.64683i) q^{30} +(-4.14491 - 7.17919i) q^{31} +(-0.489849 - 2.77807i) q^{32} +(-0.766044 - 0.642788i) q^{33} +(-5.22068 + 4.38067i) q^{34} +(-0.546254 + 3.09796i) q^{35} +(0.481654 - 0.175308i) q^{36} -7.13754 q^{37} +(-4.75623 + 2.37477i) q^{38} -2.87303 q^{39} +(7.21603 - 2.62642i) q^{40} +(-0.138834 + 0.787365i) q^{41} +(-1.17279 + 0.984089i) q^{42} +(0.668091 + 0.560595i) q^{43} +(0.0890061 + 0.504779i) q^{44} +(1.25299 + 2.17024i) q^{45} +(-0.455660 + 0.789227i) q^{46} +(10.0214 + 3.64748i) q^{47} +(2.54858 + 0.927608i) q^{48} +(2.71211 - 4.69751i) q^{49} +(0.780482 + 1.35183i) q^{50} +(0.970341 + 5.50308i) q^{51} +(1.12809 + 0.946581i) q^{52} +(8.77332 - 7.36169i) q^{53} +(-0.211782 + 1.20108i) q^{54} +(-2.35484 + 0.857093i) q^{55} +3.84667 q^{56} +(-0.263614 + 4.35092i) q^{57} +5.21887 q^{58} +(1.33898 - 0.487350i) q^{59} +(0.223047 - 1.26496i) q^{60} +(1.17222 - 0.983611i) q^{61} +(-7.74493 - 6.49877i) q^{62} +(0.217981 + 1.23623i) q^{63} +(-4.43235 - 7.67706i) q^{64} +(-3.59987 + 6.23516i) q^{65} +(-1.14605 - 0.417129i) q^{66} +(1.88620 + 0.686521i) q^{67} +(1.43210 - 2.48047i) q^{68} +(0.373613 + 0.647117i) q^{69} +(0.666213 + 3.77828i) q^{70} +(5.89580 + 4.94716i) q^{71} +(2.34742 - 1.96972i) q^{72} +(1.66902 - 9.46548i) q^{73} +(-8.18000 + 2.97728i) q^{74} +1.27989 q^{75} +(1.53701 - 1.62153i) q^{76} -1.25530 q^{77} +(-3.29265 + 1.19843i) q^{78} +(0.571565 - 3.24151i) q^{79} +(5.20646 - 4.36874i) q^{80} +(0.766044 + 0.642788i) q^{81} +(0.169322 + 0.960274i) q^{82} +(-8.00749 - 13.8694i) q^{83} +(0.321712 - 0.557222i) q^{84} +(13.1588 + 4.78941i) q^{85} +(0.999509 + 0.363791i) q^{86} +(2.13958 - 3.70585i) q^{87} +(1.53217 + 2.65379i) q^{88} +(1.32646 + 7.52272i) q^{89} +(2.34126 + 1.96455i) q^{90} +(-2.76276 + 2.31823i) q^{91} +(0.0665078 - 0.377184i) q^{92} +(-7.78987 + 2.83528i) q^{93} +13.0065 q^{94} +(9.11221 + 6.02375i) q^{95} -2.82093 q^{96} +(-6.23168 + 2.26814i) q^{97} +(1.14875 - 6.51490i) q^{98} +(-0.766044 + 0.642788i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 3 q^{2} + 3 q^{4} + 3 q^{6} - 18 q^{7} - 12 q^{8} + 30 q^{10} + 27 q^{11} - 33 q^{12} + 9 q^{14} - 21 q^{16} - 24 q^{17} + 6 q^{18} + 3 q^{19} + 30 q^{20} - 3 q^{22} + 12 q^{23} - 39 q^{24} + 30 q^{25}+ \cdots - 54 q^{98}+O(q^{100}) $ 54 * q + 3 * q^2 + 3 * q^4 + 3 * q^6 - 18 * q^7 - 12 * q^8 + 30 * q^10 + 27 * q^11 - 33 * q^12 + 9 * q^14 - 21 * q^16 - 24 * q^17 + 6 * q^18 + 3 * q^19 + 30 * q^20 - 3 * q^22 + 12 * q^23 - 39 * q^24 + 30 * q^25 - 6 * q^26 - 27 * q^27 - 30 * q^28 + 33 * q^29 + 15 * q^30 + 15 * q^31 + 39 * q^32 + 3 * q^34 - 27 * q^35 + 3 * q^36 - 24 * q^37 + 15 * q^38 + 6 * q^39 + 84 * q^40 - 15 * q^41 + 9 * q^42 - 48 * q^43 + 6 * q^44 - 36 * q^46 + 3 * q^47 + 24 * q^48 - 21 * q^49 - 30 * q^50 + 3 * q^51 - 45 * q^52 - 21 * q^53 + 3 * q^54 + 21 * q^57 + 90 * q^58 + 45 * q^59 - 39 * q^60 - 21 * q^61 - 87 * q^62 - 9 * q^63 - 54 * q^64 + 6 * q^65 - 3 * q^66 + 9 * q^67 - 39 * q^69 + 15 * q^70 - 57 * q^71 - 39 * q^72 - 30 * q^73 - 105 * q^74 + 54 * q^75 - 6 * q^76 - 36 * q^77 + 51 * q^78 - 27 * q^79 - 3 * q^80 + 102 * q^82 - 63 * q^83 - 51 * q^84 + 60 * q^85 - 42 * q^86 - 27 * q^87 + 12 * q^88 + 21 * q^89 - 6 * q^90 - 72 * q^91 + 78 * q^92 - 6 * q^93 - 36 * q^94 + 63 * q^95 + 114 * q^96 + 45 * q^97 - 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/627\mathbb{Z}\right)^\times$.

$n$	$343$	$419$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{9}\right)$

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 $

$2$	1.14605	−	0.417129i	0.810382	−	0.294955i	0.0966003	−	0.995323i	$-0.469203\pi$
$2$	1.14605	−	0.417129i	0.810382	−	0.294955i	0.713782	+	0.700368i	$0.246981\pi$
$3$	0.173648	−	0.984808i	0.100256	−	0.568579i
$3$	0.173648	−	0.984808i	0.100256	−	0.568579i
$4$	−0.392648	+	0.329471i	−0.196324	+	0.164735i
$5$	−1.91969	−	1.61081i	−0.858510	−	0.720375i	0.103137	−	0.994667i	$-0.467112\pi$
$5$	−1.91969	−	1.61081i	−0.858510	−	0.720375i	−0.961646	+	0.274292i	$0.911556\pi$
$6$	−0.211782	−	1.20108i	−0.0864597	−	0.490337i
$7$	−0.627651	−	1.08712i	−0.237230	−	0.410894i	0.722689	−	0.691174i	$-0.242906\pi$
$7$	−0.627651	−	1.08712i	−0.237230	−	0.410894i	−0.959918	+	0.280280i	$0.909573\pi$
$8$	−1.53217	+	2.65379i	−0.541703	+	0.938257i
$9$	−0.939693	−	0.342020i	−0.313231	−	0.114007i
$10$	−2.87198	−	1.04531i	−0.908199	−	0.330557i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	0.256283	+	0.443895i	0.0739825	+	0.128141i
$13$	−0.498897	−	2.82939i	−0.138369	−	0.784730i	−0.972454	−	0.233094i	$-0.925115\pi$
$13$	−0.498897	−	2.82939i	−0.138369	−	0.784730i	0.834085	−	0.551636i	$-0.185996\pi$
$14$	−1.17279	−	0.984089i	−0.313442	−	0.263009i
$15$	−1.91969	+	1.61081i	−0.495661	+	0.415909i
$16$	−0.470959	+	2.67094i	−0.117740	+	0.667735i
$17$	−5.25098	+	1.91120i	−1.27355	+	0.463534i	−0.888294	−	0.459276i	$-0.848109\pi$
$17$	−5.25098	+	1.91120i	−1.27355	+	0.463534i	−0.385255	+	0.922810i	$0.625887\pi$
$18$	−1.21960			−0.287463
$19$	−4.33060	+	0.495920i	−0.993507	+	0.113772i
$19$	−4.33060	+	0.495920i	−0.993507	+	0.113772i
$20$	1.28448			0.287217
$21$	−1.17960	+	0.429338i	−0.257409	+	0.0936893i
$22$	0.211782	−	1.20108i	0.0451521	−	0.256070i
$23$	−0.572409	+	0.480308i	−0.119356	+	0.100151i	−0.700512	−	0.713641i	$-0.747045\pi$
$23$	−0.572409	+	0.480308i	−0.119356	+	0.100151i	0.581156	+	0.813792i	$0.302600\pi$
$24$	2.34742	+	1.96972i	0.479165	+	0.402067i
$25$	0.222251	+	1.26045i	0.0444502	+	0.252090i
$26$	−1.75198	−	3.03452i	−0.343592	−	0.595119i
$27$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i
$28$	0.604621	+	0.220064i	0.114263	+	0.0415882i
$29$	4.02109	+	1.46356i	0.746697	+	0.271776i	0.687215	−	0.726454i	$-0.258833\pi$
$29$	4.02109	+	1.46356i	0.746697	+	0.271776i	0.0594818	+	0.998229i	$0.481055\pi$
$30$	−1.52815	+	2.64683i	−0.279000	+	0.483242i
$31$	−4.14491	−	7.17919i	−0.744447	−	1.28942i	−0.950453	−	0.310869i	$-0.899380\pi$
$31$	−4.14491	−	7.17919i	−0.744447	−	1.28942i	0.206006	−	0.978551i	$-0.433953\pi$
$32$	−0.489849	−	2.77807i	−0.0865939	−	0.491098i
$33$	−0.766044	−	0.642788i	−0.133351	−	0.111895i
$34$	−5.22068	+	4.38067i	−0.895339	+	0.751279i
$35$	−0.546254	+	3.09796i	−0.0923337	+	0.523651i
$36$	0.481654	−	0.175308i	0.0802757	−	0.0292180i
$37$	−7.13754			−1.17340			−0.586702	−	0.809803i	$-0.699574\pi$
$37$	−7.13754			−1.17340			−0.586702	+	0.809803i	$0.699574\pi$
$38$	−4.75623	+	2.37477i	−0.771562	+	0.385238i
$39$	−2.87303			−0.460054
$40$	7.21603	−	2.62642i	1.14095	−	0.415273i
$41$	−0.138834	+	0.787365i	−0.0216822	+	0.122966i	−0.993728	−	0.111827i	$-0.964330\pi$
$41$	−0.138834	+	0.787365i	−0.0216822	+	0.122966i	0.972046	+	0.234792i	$0.0754410\pi$
$42$	−1.17279	+	0.984089i	−0.180966	+	0.151848i
$43$	0.668091	+	0.560595i	0.101883	+	0.0854900i	0.692306	−	0.721604i	$-0.256595\pi$
$43$	0.668091	+	0.560595i	0.101883	+	0.0854900i	−0.590423	+	0.807094i	$0.701039\pi$
$44$	0.0890061	+	0.504779i	0.0134182	+	0.0760983i
$45$	1.25299	+	2.17024i	0.186784	+	0.323520i
$46$	−0.455660	+	0.789227i	−0.0671835	+	0.116365i
$47$	10.0214	+	3.64748i	1.46177	+	0.532039i	0.945851	−	0.324600i	$-0.105230\pi$
$47$	10.0214	+	3.64748i	1.46177	+	0.532039i	0.515915	+	0.856640i	$0.327452\pi$
$48$	2.54858	+	0.927608i	0.367856	+	0.133889i
$49$	2.71211	−	4.69751i	0.387444	−	0.671073i
$50$	0.780482	+	1.35183i	0.110377	+	0.191178i
$51$	0.970341	+	5.50308i	0.135875	+	0.770585i
$52$	1.12809	+	0.946581i	0.156438	+	0.131267i
$53$	8.77332	−	7.36169i	1.20511	−	1.01121i	0.205639	−	0.978628i	$-0.434073\pi$
$53$	8.77332	−	7.36169i	1.20511	−	1.01121i	0.999469	−	0.0325775i	$-0.0103716\pi$
$54$	−0.211782	+	1.20108i	−0.0288199	+	0.163446i
$55$	−2.35484	+	0.857093i	−0.317527	+	0.115570i
$56$	3.84667			0.514032
$57$	−0.263614	+	4.35092i	−0.0349166	+	0.576293i
$58$	5.21887			0.685271
$59$	1.33898	−	0.487350i	0.174321	−	0.0634476i	−0.253385	−	0.967365i	$-0.581544\pi$
$59$	1.33898	−	0.487350i	0.174321	−	0.0634476i	0.427706	+	0.903918i	$0.359322\pi$
$60$	0.223047	−	1.26496i	0.0287952	−	0.163306i
$61$	1.17222	−	0.983611i	0.150088	−	0.125939i	−0.564652	−	0.825329i	$-0.690990\pi$
$61$	1.17222	−	0.983611i	0.150088	−	0.125939i	0.714740	+	0.699391i	$0.246545\pi$
$62$	−7.74493	−	6.49877i	−0.983607	−	0.825344i
$63$	0.217981	+	1.23623i	0.0274630	+	0.155750i
$64$	−4.43235	−	7.67706i	−0.554044	−	0.959632i
$65$	−3.59987	+	6.23516i	−0.446509	+	0.773376i
$66$	−1.14605	−	0.417129i	−0.141069	−	0.0513451i
$67$	1.88620	+	0.686521i	0.230436	+	0.0838718i	0.454657	−	0.890666i	$-0.349762\pi$
$67$	1.88620	+	0.686521i	0.230436	+	0.0838718i	−0.224221	+	0.974538i	$0.571984\pi$
$68$	1.43210	−	2.48047i	0.173668	−	0.300802i
$69$	0.373613	+	0.647117i	0.0449778	+	0.0779038i
$70$	0.666213	+	3.77828i	0.0796277	+	0.451591i
$71$	5.89580	+	4.94716i	0.699703	+	0.587120i	0.921689	−	0.387930i	$-0.126810\pi$
$71$	5.89580	+	4.94716i	0.699703	+	0.587120i	−0.221986	+	0.975050i	$0.571254\pi$
$72$	2.34742	−	1.96972i	0.276646	−	0.232133i
$73$	1.66902	−	9.46548i	0.195344	−	1.10785i	−0.716584	−	0.697500i	$-0.754296\pi$
$73$	1.66902	−	9.46548i	0.195344	−	1.10785i	0.911928	−	0.410350i	$-0.134593\pi$
$74$	−8.18000	+	2.97728i	−0.950905	+	0.346101i
$75$	1.27989			0.147789
$76$	1.53701	−	1.62153i	0.176307	−	0.186002i
$77$	−1.25530			−0.143055
$78$	−3.29265	+	1.19843i	−0.372819	+	0.135695i
$79$	0.571565	−	3.24151i	0.0643061	−	0.364698i	−0.935625	−	0.352994i	$-0.885163\pi$
$79$	0.571565	−	3.24151i	0.0643061	−	0.364698i	0.999932	−	0.0117035i	$-0.00372541\pi$
$80$	5.20646	−	4.36874i	0.582100	−	0.488440i
$81$	0.766044	+	0.642788i	0.0851160	+	0.0714208i
$82$	0.169322	+	0.960274i	0.0186985	+	0.106044i
$83$	−8.00749	−	13.8694i	−0.878936	−	1.52236i	−0.852510	−	0.522711i	$-0.824921\pi$
$83$	−8.00749	−	13.8694i	−0.878936	−	1.52236i	−0.0264258	−	0.999651i	$-0.508413\pi$
$84$	0.321712	−	0.557222i	0.0351017	−	0.0607979i
$85$	13.1588	+	4.78941i	1.42727	+	0.519485i
$86$	0.999509	+	0.363791i	0.107780	+	0.0392286i
$87$	2.13958	−	3.70585i	0.229387	−	0.397309i
$88$	1.53217	+	2.65379i	0.163330	+	0.282895i
$89$	1.32646	+	7.52272i	0.140604	+	0.797406i	0.970792	+	0.239922i	$0.0771220\pi$
$89$	1.32646	+	7.52272i	0.140604	+	0.797406i	−0.830188	+	0.557484i	$0.811767\pi$
$90$	2.34126	+	1.96455i	0.246790	+	0.207081i
$91$	−2.76276	+	2.31823i	−0.289616	+	0.243016i
$92$	0.0665078	−	0.377184i	0.00693391	−	0.0393242i
$93$	−7.78987	+	2.83528i	−0.807772	+	0.294005i
$94$	13.0065			1.34152
$95$	9.11221	+	6.02375i	0.934894	+	0.618023i
$96$	−2.82093			−0.287910
$97$	−6.23168	+	2.26814i	−0.632731	+	0.230295i	−0.638419	−	0.769689i	$-0.720411\pi$
$97$	−6.23168	+	2.26814i	−0.632731	+	0.230295i	0.00568863	+	0.999984i	$0.498189\pi$
$98$	1.14875	−	6.51490i	0.116041	−	0.658104i
$99$	−0.766044	+	0.642788i	−0.0769904	+	0.0646026i
$100$	−0.502548	−	0.421688i	−0.0502548	−	0.0421688i
$101$	−1.98990	−	11.2853i	−0.198002	−	1.12293i	−0.908078	−	0.418801i	$-0.862450\pi$
$101$	−1.98990	−	11.2853i	−0.198002	−	1.12293i	0.710076	−	0.704125i	$-0.248661\pi$
$102$	3.40756	+	5.90206i	0.337398	+	0.584391i
$103$	−2.50253	+	4.33450i	−0.246581	+	0.427091i	−0.962575	−	0.271015i	$-0.912641\pi$
$103$	−2.50253	+	4.33450i	−0.246581	+	0.427091i	0.715994	+	0.698107i	$0.245974\pi$
$104$	8.27300	+	3.01112i	0.811234	+	0.295265i
$105$	2.95604	+	1.07591i	0.288480	+	0.104998i
$106$	6.98391	−	12.0965i	0.678337	−	1.17491i
$107$	4.93566	+	8.54882i	0.477148	+	0.826445i	0.999657	−	0.0261888i	$-0.00833710\pi$
$107$	4.93566	+	8.54882i	0.477148	+	0.826445i	−0.522509	+	0.852634i	$0.675004\pi$
$108$	−0.0890061	−	0.504779i	−0.00856462	−	0.0485724i
$109$	2.58969	+	2.17301i	0.248047	+	0.208136i	0.758331	−	0.651870i	$-0.226015\pi$
$109$	2.58969	+	2.17301i	0.248047	+	0.208136i	−0.510284	+	0.860006i	$0.670460\pi$
$110$	−2.34126	+	1.96455i	−0.223230	+	0.187312i
$111$	−1.23942	+	7.02910i	−0.117641	+	0.667173i
$112$	3.19924	−	1.16443i	0.302300	−	0.110028i
$113$	−8.77811			−0.825776			−0.412888	−	0.910782i	$-0.635480\pi$
$113$	−8.77811			−0.825776			−0.412888	+	0.910782i	$0.635480\pi$
$114$	1.51278	+	5.09635i	0.141685	+	0.477317i
$115$	1.87253			0.174614
$116$	−2.06107	+	0.750169i	−0.191366	+	0.0696514i
$117$	−0.498897	+	2.82939i	−0.0461230	+	0.261577i
$118$	1.33126	−	1.11706i	0.122552	−	0.102834i
$119$	5.37349	+	4.50889i	0.492587	+	0.413329i
$120$	−1.33347	−	7.56247i	−0.121728	−	0.690356i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	0.933136	−	1.61624i	0.0844821	−	0.146327i
$123$	0.751295	+	0.273449i	0.0677420	+	0.0246561i
$124$	3.99282	+	1.45327i	0.358566	+	0.130507i
$125$	−4.66124	+	8.07350i	−0.416914	+	0.722116i
$126$	0.765485	+	1.32586i	0.0681949	+	0.118117i
$127$	0.231828	+	1.31476i	0.0205714	+	0.116666i	0.993364	−	0.115010i	$-0.0366901\pi$
$127$	0.231828	+	1.31476i	0.0205714	+	0.116666i	−0.972793	+	0.231676i	$0.925579\pi$
$128$	−3.96012	−	3.32294i	−0.350029	−	0.293709i
$129$	0.668091	−	0.560595i	0.0588222	−	0.0493577i
$130$	−1.52478	+	8.64743i	−0.133732	+	0.758430i
$131$	−12.4360	+	4.52632i	−1.08653	+	0.395466i	−0.822336	−	0.569002i	$-0.807330\pi$
$131$	−12.4360	+	4.52632i	−1.08653	+	0.395466i	−0.264199	+	0.964468i	$0.585107\pi$
$132$	0.512566			0.0446131
$133$	3.25723	+	4.39663i	0.282437	+	0.381236i
$134$	2.44805			0.211480
$135$	2.35484	−	0.857093i	0.202673	−	0.0737668i
$136$	2.97345	−	16.8633i	0.254971	−	1.44601i
$137$	−7.44578	+	6.24775i	−0.636136	+	0.533782i	−0.902829	−	0.430000i	$-0.858514\pi$
$137$	−7.44578	+	6.24775i	−0.636136	+	0.533782i	0.266693	+	0.963782i	$0.414069\pi$
$138$	0.698112	+	0.585786i	0.0594273	+	0.0498654i
$139$	−3.63256	−	20.6013i	−0.308110	−	1.74738i	−0.608494	−	0.793558i	$-0.708226\pi$
$139$	−3.63256	−	20.6013i	−0.308110	−	1.74738i	0.300384	−	0.953818i	$-0.402885\pi$
$140$	−0.806202	−	1.39638i	−0.0681365	−	0.118016i
$141$	5.33226	−	9.23574i	0.449057	−	0.777790i
$142$	8.82050	+	3.21040i	0.740200	+	0.269411i
$143$	−2.69977	−	0.982635i	−0.225766	−	0.0821721i
$144$	1.35607	−	2.34879i	0.113006	−	0.195732i
$145$	−5.36172	−	9.28676i	−0.445266	−	0.771224i
$146$	−2.03554	−	11.5441i	−0.168463	−	0.955399i
$147$	−4.15519	−	3.48662i	−0.342714	−	0.287572i
$148$	2.80254	−	2.35161i	0.230368	−	0.193301i
$149$	−2.53115	+	14.3549i	−0.207360	+	1.17600i	0.686323	+	0.727297i	$0.259224\pi$
$149$	−2.53115	+	14.3549i	−0.207360	+	1.17600i	−0.893683	+	0.448699i	$0.851887\pi$
$150$	1.46683	−	0.533881i	0.119766	−	0.0435912i
$151$	−19.6797			−1.60151			−0.800757	−	0.598989i	$-0.795569\pi$
$151$	−19.6797			−1.60151			−0.800757	+	0.598989i	$0.795569\pi$
$152$	5.31913	−	12.2523i	0.431439	−	0.993796i
$153$	5.58797			0.451761
$154$	−1.43864	+	0.523623i	−0.115929	+	0.0421947i
$155$	−3.60737	+	20.4584i	−0.289751	+	1.64326i
$156$	1.12809	−	0.946581i	0.0903196	−	0.0757871i
$157$	0.450640	+	0.378132i	0.0359650	+	0.0301782i	0.660593	−	0.750744i	$-0.270305\pi$
$157$	0.450640	+	0.378132i	0.0359650	+	0.0301782i	−0.624628	+	0.780922i	$0.714749\pi$
$158$	−0.697083	−	3.95335i	−0.0554569	−	0.314512i
$159$	−5.72638	−	9.91837i	−0.454131	−	0.786578i
$160$	−3.53458	+	6.12208i	−0.279433	+	0.483993i
$161$	0.881427	+	0.320813i	0.0694662	+	0.0252836i
$162$	1.14605	+	0.417129i	0.0900424	+	0.0327728i
$163$	8.85457	−	15.3366i	0.693544	−	1.20125i	−0.277126	−	0.960834i	$-0.589382\pi$
$163$	8.85457	−	15.3366i	0.693544	−	1.20125i	0.970669	−	0.240419i	$-0.0772849\pi$
$164$	−0.204901	−	0.354899i	−0.0160001	−	0.0277130i
$165$	0.435157	+	2.46790i	0.0338770	+	0.192126i
$166$	−14.9623	−	12.5549i	−1.16130	−	0.974448i
$167$	−1.25451	+	1.05266i	−0.0970771	+	0.0814574i	−0.690035	−	0.723776i	$-0.742405\pi$
$167$	−1.25451	+	1.05266i	−0.0970771	+	0.0814574i	0.592957	+	0.805234i	$0.297960\pi$
$168$	0.667966	−	3.78823i	0.0515347	−	0.292268i
$169$	4.45948	−	1.62312i	0.343037	−	0.124855i
$170$	17.0785			1.30986
$171$	4.23904	+	1.01514i	0.324168	+	0.0776296i
$172$	−0.447025			−0.0340853
$173$	−2.76148	+	1.00510i	−0.209951	+	0.0764160i	−0.444855	−	0.895603i	$-0.646745\pi$
$173$	−2.76148	+	1.00510i	−0.209951	+	0.0764160i	0.234904	+	0.972019i	$0.424523\pi$
$174$	0.906247	−	5.13958i	0.0687024	−	0.389631i
$175$	1.23077	−	1.03274i	0.0930373	−	0.0780675i
$176$	2.07762	+	1.74333i	0.156607	+	0.131409i
$177$	−0.247434	−	1.40327i	−0.0185983	−	0.105476i
$178$	4.65814	+	8.06813i	0.349142	+	0.604732i
$179$	4.24187	−	7.34713i	0.317052	−	0.549151i	−0.662819	−	0.748779i	$-0.730640\pi$
$179$	4.24187	−	7.34713i	0.317052	−	0.549151i	0.979872	+	0.199629i	$0.0639736\pi$
$180$	−1.20701	−	0.439316i	−0.0899654	−	0.0327447i
$181$	16.2668	+	5.92062i	1.20910	+	0.440076i	0.866392	−	0.499365i	$-0.166433\pi$
$181$	16.2668	+	5.92062i	1.20910	+	0.440076i	0.342709	+	0.939442i	$0.388656\pi$
$182$	−2.19927	+	3.80924i	−0.163020	+	0.282360i
$183$	−0.765114	−	1.32522i	−0.0565588	−	0.0979628i
$184$	−0.397612	−	2.25497i	−0.0293123	−	0.166238i
$185$	13.7018	+	11.4972i	1.00738	+	0.845291i
$186$	−7.74493	+	6.49877i	−0.567886	+	0.476513i
$187$	−0.970341	+	5.50308i	−0.0709584	+	0.402425i
$188$	−5.13661	+	1.86957i	−0.374626	+	0.136353i
$189$	1.25530			0.0913098
$190$	12.9558	+	3.10256i	0.939910	+	0.225084i
$191$	13.7533			0.995150			0.497575	−	0.867421i	$-0.334224\pi$
$191$	13.7533			0.995150			0.497575	+	0.867421i	$0.334224\pi$
$192$	−8.33010	+	3.03191i	−0.601173	+	0.218809i
$193$	−0.966625	+	5.48200i	−0.0695792	+	0.394603i	0.930052	+	0.367429i	$0.119762\pi$
$193$	−0.966625	+	5.48200i	−0.0695792	+	0.394603i	−0.999631	+	0.0271740i	$0.991349\pi$
$194$	−6.19572	+	5.19883i	−0.444827	+	0.373254i
$195$	5.51532	+	4.62790i	0.394960	+	0.331411i
$196$	0.482789	+	2.73803i	0.0344849	+	0.195574i
$197$	2.41477	+	4.18251i	0.172045	+	0.297991i	0.939135	−	0.343549i	$-0.111629\pi$
$197$	2.41477	+	4.18251i	0.172045	+	0.297991i	−0.767089	+	0.641540i	$0.778296\pi$
$198$	−0.609802	+	1.05621i	−0.0433367	+	0.0750614i
$199$	−23.2949	−	8.47864i	−1.65133	−	0.601035i	−0.662364	−	0.749182i	$-0.730447\pi$
$199$	−23.2949	−	8.47864i	−1.65133	−	0.601035i	−0.988965	+	0.148148i	$0.952669\pi$
$200$	−3.68550	−	1.34141i	−0.260604	−	0.0948521i
$201$	1.00363	−	1.73833i	0.0707903	−	0.122612i
$202$	−6.98795	−	12.1035i	−0.491670	−	0.851598i
$203$	−0.932773	−	5.29002i	−0.0654678	−	0.371286i
$204$	−2.19411	−	1.84107i	−0.153618	−	0.128901i
$205$	1.53481	−	1.28786i	0.107196	−	0.0899480i
$206$	−1.05998	+	6.01145i	−0.0738524	+	0.418838i
$207$	0.702163	−	0.255567i	0.0488037	−	0.0177631i
$208$	7.79208			0.540284
$209$	−1.73582	+	3.99837i	−0.120069	+	0.276573i
$210$	3.83657			0.264748
$211$	17.4850	−	6.36401i	1.20371	−	0.438116i	0.339195	−	0.940716i	$-0.389845\pi$
$211$	17.4850	−	6.36401i	1.20371	−	0.438116i	0.864519	+	0.502600i	$0.167623\pi$
$212$	−1.01937	+	5.78111i	−0.0700103	+	0.397048i
$213$	5.89580	−	4.94716i	0.403973	−	0.338974i
$214$	9.22249	+	7.73859i	0.630436	+	0.528999i
$215$	−0.379514	−	2.15233i	−0.0258827	−	0.146788i
$216$	−1.53217	−	2.65379i	−0.104251	−	0.180568i
$217$	−5.20311	+	9.01204i	−0.353210	+	0.611777i
$218$	3.87435	+	1.41015i	0.262404	+	0.0955072i
$219$	−9.03185	−	3.28733i	−0.610316	−	0.222137i
$220$	0.642238	−	1.11239i	0.0432997	−	0.0749972i
$221$	8.02722	+	13.9035i	0.539969	+	0.935254i
$222$	1.51160	+	8.57272i	0.101452	+	0.575363i
$223$	−20.3103	−	17.0424i	−1.36008	−	1.14124i	−0.975958	−	0.217958i	$-0.930060\pi$
$223$	−20.3103	−	17.0424i	−1.36008	−	1.14124i	−0.384120	−	0.923283i	$-0.625495\pi$
$224$	−2.71265	+	2.27619i	−0.181247	+	0.152084i
$225$	0.222251	−	1.26045i	0.0148167	−	0.0840300i
$226$	−10.0602	+	3.66161i	−0.669194	+	0.243567i
$227$	11.7161			0.777623			0.388811	−	0.921317i	$-0.372886\pi$
$227$	11.7161			0.777623			0.388811	+	0.921317i	$0.372886\pi$
$228$	−1.32999	−	1.79523i	−0.0880810	−	0.118892i
$229$	11.2574			0.743910			0.371955	−	0.928251i	$-0.378688\pi$
$229$	11.2574			0.743910			0.371955	+	0.928251i	$0.378688\pi$
$230$	2.14602	−	0.781087i	0.141504	−	0.0515033i
$231$	−0.217981	+	1.23623i	−0.0143421	+	0.0813380i
$232$	−10.0450	+	8.42872i	−0.659483	+	0.553372i
$233$	−0.215867	−	0.181134i	−0.0141419	−	0.0118665i	0.635689	−	0.771945i	$-0.280716\pi$
$233$	−0.215867	−	0.181134i	−0.0141419	−	0.0118665i	−0.649831	+	0.760079i	$0.725160\pi$
$234$	0.608457	+	3.45073i	0.0397761	+	0.225581i
$235$	−13.3625	−	23.1445i	−0.871672	−	1.50978i
$236$	−0.365182	+	0.632513i	−0.0237713	+	0.0411731i
$237$	−3.09301	−	1.12576i	−0.200912	−	0.0731262i
$238$	8.03909	+	2.92599i	0.521097	+	0.189664i
$239$	−11.7070	+	20.2771i	−0.757264	+	1.31162i	0.186978	+	0.982364i	$0.440131\pi$
$239$	−11.7070	+	20.2771i	−0.757264	+	1.31162i	−0.944241	+	0.329255i	$0.893203\pi$
$240$	−3.39828	−	5.88599i	−0.219358	−	0.379939i
$241$	1.44446	+	8.19194i	0.0930459	+	0.527690i	0.995329	+	0.0965447i	$0.0307791\pi$
$241$	1.44446	+	8.19194i	0.0930459	+	0.527690i	−0.902283	+	0.431145i	$0.858110\pi$
$242$	−0.934271	−	0.783946i	−0.0600572	−	0.0503940i
$243$	0.766044	−	0.642788i	0.0491418	−	0.0412348i
$244$	−0.136200	+	0.772426i	−0.00871929	+	0.0494495i
$245$	−12.7732	+	4.64906i	−0.816049	+	0.297017i
$246$	0.975088			0.0621693
$247$	3.56367	+	12.0055i	0.226751	+	0.763893i
$248$	25.4028			1.61308
$249$	−15.0492	+	5.47744i	−0.953701	+	0.347119i
$250$	−1.97433	+	11.1970i	−0.124868	+	0.708161i
$251$	−0.289866	+	0.243227i	−0.0182962	+	0.0153523i	−0.651890	−	0.758314i	$-0.726024\pi$
$251$	−0.289866	+	0.243227i	−0.0182962	+	0.0153523i	0.633594	+	0.773666i	$0.281579\pi$
$252$	−0.492892	−	0.413585i	−0.0310493	−	0.0260534i
$253$	0.129755	+	0.735875i	0.00815760	+	0.0462640i
$254$	0.814112	+	1.41008i	0.0510819	+	0.0884764i
$255$	7.00165	−	12.1272i	0.438460	−	0.759436i
$256$	10.7356	+	3.90744i	0.670974	+	0.244215i
$257$	−11.7975	−	4.29395i	−0.735909	−	0.267849i	−0.0532451	−	0.998581i	$-0.516956\pi$
$257$	−11.7975	−	4.29395i	−0.735909	−	0.267849i	−0.682664	+	0.730733i	$0.739179\pi$
$258$	0.531828	−	0.921152i	0.0331101	−	0.0573484i
$259$	4.47988	+	7.75938i	0.278366	+	0.482145i
$260$	−0.640821	−	3.63428i	−0.0397420	−	0.225388i
$261$	−3.27802	−	2.75059i	−0.202904	−	0.170257i
$262$	−12.3642	+	10.3748i	−0.763863	+	0.640957i
$263$	1.56537	−	8.87768i	0.0965251	−	0.547421i	−0.897744	−	0.440517i	$-0.854795\pi$
$263$	1.56537	−	8.87768i	0.0965251	−	0.547421i	0.994269	−	0.106904i	$-0.0340938\pi$
$264$	2.87953	−	1.04806i	0.177223	−	0.0645039i
$265$	−28.7003			−1.76304
$266$	5.56692	+	3.68008i	0.341330	+	0.225640i
$267$	7.63877			0.467485
$268$	−0.966802	+	0.351887i	−0.0590568	+	0.0214949i
$269$	4.84085	−	27.4538i	0.295152	−	1.67389i	−0.371434	−	0.928459i	$-0.621134\pi$
$269$	4.84085	−	27.4538i	0.295152	−	1.67389i	0.666586	−	0.745429i	$-0.267755\pi$
$270$	2.34126	−	1.96455i	0.142484	−	0.119559i
$271$	21.2191	+	17.8049i	1.28897	+	1.08157i	0.991941	+	0.126701i	$0.0404389\pi$
$271$	21.2191	+	17.8049i	1.28897	+	1.08157i	0.297025	+	0.954870i	$0.404006\pi$
$272$	−2.63171	−	14.9251i	−0.159571	−	0.904970i
$273$	1.80326	+	3.12334i	0.109138	+	0.189033i
$274$	−5.92714	+	10.2661i	−0.358072	+	0.620198i
$275$	1.20271	+	0.437749i	0.0725259	+	0.0263973i
$276$	−0.359905	−	0.130995i	−0.0216637	−	0.00788496i
$277$	−7.75580	+	13.4334i	−0.466001	+	0.807137i	−0.999246	−	0.0388234i	$-0.987639\pi$
$277$	−7.75580	+	13.4334i	−0.466001	+	0.807137i	0.533245	+	0.845961i	$0.320972\pi$
$278$	−12.7565	−	22.0949i	−0.765084	−	1.32516i
$279$	1.43951	+	8.16387i	0.0861812	+	0.488758i
$280$	−7.38439	−	6.19624i	−0.441302	−	0.370296i
$281$	−11.6311	+	9.75962i	−0.693851	+	0.582210i	−0.920017	−	0.391879i	$-0.871825\pi$
$281$	−11.6311	+	9.75962i	−0.693851	+	0.582210i	0.226166	+	0.974089i	$0.427381\pi$
$282$	2.25855	−	12.8089i	0.134495	−	0.762758i
$283$	−6.91298	+	2.51612i	−0.410934	+	0.149568i	−0.539211	−	0.842171i	$-0.681278\pi$
$283$	−6.91298	+	2.51612i	−0.410934	+	0.149568i	0.128277	+	0.991738i	$0.459055\pi$
$284$	−3.94492			−0.234088
$285$	7.51455	−	7.92777i	0.445124	−	0.469600i
$286$	−3.50396			−0.207194
$287$	0.943102	−	0.343261i	0.0556695	−	0.0202621i
$288$	−0.489849	+	2.77807i	−0.0288646	+	0.163699i
$289$	10.8973	−	9.14394i	0.641019	−	0.537879i
$290$	−10.0186	−	8.40660i	−0.588312	−	0.493652i
$291$	1.15157	+	6.53086i	0.0675061	+	0.382846i
$292$	2.46326	+	4.26650i	0.144152	+	0.249678i
$293$	−8.96686	+	15.5311i	−0.523849	+	0.907334i	0.475765	+	0.879572i	$0.342171\pi$
$293$	−8.96686	+	15.5311i	−0.523849	+	0.907334i	−0.999615	+	0.0277614i	$0.991162\pi$
$294$	−6.21644	−	2.26260i	−0.362550	−	0.131957i
$295$	−3.35545	−	1.22129i	−0.195362	−	0.0711060i
$296$	10.9359	−	18.9415i	0.635637	−	1.10095i
$297$	0.500000	+	0.866025i	0.0290129	+	0.0502519i
$298$	3.08700	+	17.5073i	0.178825	+	1.01417i
$299$	1.64455	+	1.37994i	0.0951068	+	0.0798041i
$300$	−0.502548	+	0.421688i	−0.0290146	+	0.0243462i
$301$	0.190108	−	1.07816i	0.0109576	−	0.0621439i
$302$	−22.5540	+	8.20899i	−1.29784	+	0.472374i
$303$	−11.4594			−0.658324
$304$	0.714960	−	11.8003i	0.0410058	−	0.676795i
$305$	−3.83471			−0.219575
$306$	6.40411	−	2.33091i	0.366099	−	0.133249i
$307$	−0.284278	+	1.61222i	−0.0162246	+	0.0920142i	−0.991845	−	0.127451i	$-0.959320\pi$
$307$	−0.284278	+	1.61222i	−0.0162246	+	0.0920142i	0.975620	+	0.219466i	$0.0704314\pi$
$308$	0.492892	−	0.413585i	0.0280851	−	0.0235662i
$309$	3.83409	+	3.21719i	0.218114	+	0.183019i
$310$	4.39957	+	24.9512i	0.249879	+	1.41713i
$311$	−14.0959	−	24.4149i	−0.799307	−	1.38444i	−0.920068	−	0.391759i	$-0.871867\pi$
$311$	−14.0959	−	24.4149i	−0.799307	−	1.38444i	0.120760	−	0.992682i	$-0.461467\pi$
$312$	4.40197	−	7.62443i	0.249212	−	0.431649i
$313$	−8.33537	−	3.03383i	−0.471143	−	0.171482i	0.0955272	−	0.995427i	$-0.469546\pi$
$313$	−8.33537	−	3.03383i	−0.471143	−	0.171482i	−0.566670	+	0.823945i	$0.691769\pi$
$314$	0.674187	+	0.245384i	0.0380466	+	0.0138478i
$315$	1.57288	−	2.72430i	0.0886215	−	0.153497i
$316$	0.843558	+	1.46109i	0.0474538	+	0.0821925i
$317$	3.75332	+	21.2861i	0.210808	+	1.19555i	0.888035	+	0.459775i	$0.152070\pi$
$317$	3.75332	+	21.2861i	0.210808	+	1.19555i	−0.677228	+	0.735773i	$0.736819\pi$
$318$	−10.7000	−	8.97834i	−0.600025	−	0.503481i
$319$	3.27802	−	2.75059i	0.183534	−	0.154003i
$320$	−3.85754	+	21.8772i	−0.215643	+	1.22297i
$321$	9.27601	−	3.37619i	0.517736	−	0.188441i
$322$	1.14398			0.0637517
$323$	21.7921	−	10.8807i	1.21254	−	0.605418i
$324$	−0.512566			−0.0284759
$325$	3.45542	−	1.25767i	0.191672	−	0.0697629i
$326$	3.75048	−	21.2700i	0.207720	−	1.17804i
$327$	2.58969	−	2.17301i	0.143210	−	0.120168i
$328$	−1.87679	−	1.57481i	−0.103628	−	0.0869544i
$329$	−2.32466	−	13.1838i	−0.128163	−	0.726846i
$330$	1.52815	+	2.64683i	0.0841217	+	0.145703i
$331$	13.3176	−	23.0667i	0.731999	−	1.26786i	−0.224028	−	0.974583i	$-0.571921\pi$
$331$	13.3176	−	23.0667i	0.731999	−	1.26786i	0.956028	−	0.293277i	$-0.0947458\pi$
$332$	7.71368	+	2.80755i	0.423343	+	0.154084i
$333$	6.70709	+	2.44118i	0.367546	+	0.133776i
$334$	−0.998642	+	1.72970i	−0.0546433	+	0.0946449i
$335$	−2.51506	−	4.35621i	−0.137412	−	0.238005i
$336$	−0.591196	−	3.35284i	−0.0322524	−	0.182912i
$337$	−19.4868	−	16.3514i	−1.06151	−	0.890715i	−0.0672559	−	0.997736i	$-0.521424\pi$
$337$	−19.4868	−	16.3514i	−1.06151	−	0.890715i	−0.994257	+	0.107021i	$0.965869\pi$
$338$	4.43375	−	3.72036i	0.241164	−	0.202361i
$339$	−1.52430	+	8.64476i	−0.0827888	+	0.469519i
$340$	−6.74475	+	2.45489i	−0.365786	+	0.133135i
$341$	−8.28981			−0.448918
$342$	5.28161	−	0.604826i	0.285597	−	0.0327052i
$343$	−15.5961			−0.842112
$344$	−2.51133	+	0.914050i	−0.135402	+	0.0492823i
$345$	0.325161	−	1.84408i	0.0175061	−	0.0992820i
$346$	−2.74554	+	2.30378i	−0.147601	+	0.123852i
$347$	−23.2906	−	19.5431i	−1.25030	−	1.04913i	−0.996646	−	0.0818365i	$-0.973921\pi$
$347$	−23.2906	−	19.5431i	−1.25030	−	1.04913i	−0.253659	−	0.967294i	$-0.581634\pi$
$348$	0.380871	+	2.16002i	0.0204168	+	0.115789i
$349$	7.10004	+	12.2976i	0.380056	+	0.658277i	0.991070	−	0.133343i	$-0.0425713\pi$
$349$	7.10004	+	12.2976i	0.380056	+	0.658277i	−0.611014	+	0.791620i	$0.709238\pi$
$350$	0.979740	−	1.69696i	0.0523693	−	0.0907063i
$351$	2.69977	+	0.982635i	0.144103	+	0.0524492i
$352$	−2.65081	−	0.964814i	−0.141288	−	0.0514248i
$353$	−8.53272	+	14.7791i	−0.454151	+	0.786613i	−0.998639	−	0.0521560i	$-0.983391\pi$
$353$	−8.53272	+	14.7791i	−0.454151	+	0.786613i	0.544488	+	0.838769i	$0.316724\pi$
$354$	−0.868917	−	1.50501i	−0.0461824	−	0.0799903i
$355$	−3.34915	−	18.9940i	−0.177755	−	1.00810i
$356$	−2.99935	−	2.51675i	−0.158965	−	0.133388i
$357$	5.37349	−	4.50889i	0.284395	−	0.238636i
$358$	1.79670	−	10.1896i	0.0949587	−	0.538538i
$359$	6.38837	−	2.32518i	0.337165	−	0.122718i	−0.167888	−	0.985806i	$-0.553695\pi$
$359$	6.38837	−	2.32518i	0.337165	−	0.122718i	0.505054	+	0.863088i	$0.331473\pi$
$360$	−7.67914			−0.404726
$361$	18.5081	−	4.29526i	0.974112	−	0.226066i
$362$	21.1123			1.10964
$363$	−0.939693	+	0.342020i	−0.0493211	+	0.0179514i
$364$	0.321003	−	1.82050i	0.0168251	−	0.0954200i
$365$	−18.4511	+	15.4823i	−0.965772	+	0.810379i
$366$	−1.42965	−	1.19962i	−0.0747288	−	0.0627049i
$367$	5.07881	+	28.8034i	0.265112	+	1.50352i	0.768716	+	0.639590i	$0.220896\pi$
$367$	5.07881	+	28.8034i	0.265112	+	1.50352i	−0.503604	+	0.863935i	$0.667993\pi$
$368$	−1.01329	−	1.75508i	−0.0528216	−	0.0914897i
$369$	0.399756	−	0.692397i	0.0208105	−	0.0360448i
$370$	20.4988	+	7.46097i	1.06568	+	0.387877i
$371$	−13.5096	−	4.91711i	−0.701386	−	0.255283i
$372$	2.12454	−	3.67981i	0.110152	−	0.190789i
$373$	2.35615	+	4.08097i	0.121997	+	0.211305i	0.920555	−	0.390613i	$-0.127737\pi$
$373$	2.35615	+	4.08097i	0.121997	+	0.211305i	−0.798558	+	0.601918i	$0.794404\pi$
$374$	1.18343	+	6.71158i	0.0611938	+	0.347047i
$375$	7.14143	+	5.99237i	0.368782	+	0.309445i
$376$	−25.0341	+	21.0061i	−1.29103	+	1.08331i
$377$	2.13486	−	12.1074i	0.109951	−	0.623561i
$378$	1.43864	−	0.523623i	0.0739958	−	0.0269323i
$379$	−15.9670			−0.820171			−0.410086	−	0.912047i	$-0.634501\pi$
$379$	−15.9670			−0.820171			−0.410086	+	0.912047i	$0.634501\pi$
$380$	−5.56254	+	0.636997i	−0.285353	+	0.0326773i
$381$	1.33504			0.0683963
$382$	15.7620	−	5.73688i	0.806452	−	0.293524i
$383$	3.58942	−	20.3566i	0.183411	−	1.04018i	−0.744569	−	0.667545i	$-0.767345\pi$
$383$	3.58942	−	20.3566i	0.183411	−	1.04018i	0.927980	−	0.372630i	$-0.121544\pi$
$384$	−3.96012	+	3.32294i	−0.202089	+	0.169573i
$385$	2.40978	+	2.02205i	0.122814	+	0.103053i
$386$	1.17890	+	6.68587i	0.0600044	+	0.340302i
$387$	−0.436066	−	0.755288i	−0.0221665	−	0.0383934i
$388$	1.69957	−	2.94374i	0.0862825	−	0.149446i
$389$	6.67462	+	2.42936i	0.338417	+	0.123174i	0.505638	−	0.862746i	$-0.331257\pi$
$389$	6.67462	+	2.42936i	0.338417	+	0.123174i	−0.167221	+	0.985919i	$0.553479\pi$
$390$	8.25128	+	3.00322i	0.417820	+	0.152074i
$391$	2.08774	−	3.61607i	0.105582	−	0.182873i
$392$	8.31081	+	14.3947i	0.419759	+	0.727045i
$393$	2.29807	+	13.0330i	0.115922	+	0.657429i
$394$	4.51210	+	3.78610i	0.227316	+	0.190741i
$395$	−6.31867	+	5.30199i	−0.317927	+	0.266772i
$396$	0.0890061	−	0.504779i	0.00447273	−	0.0253661i
$397$	−8.13670	+	2.96152i	−0.408369	+	0.148634i	−0.538033	−	0.842924i	$-0.680832\pi$
$397$	−8.13670	+	2.96152i	−0.408369	+	0.148634i	0.129664	+	0.991558i	$0.458610\pi$
$398$	−30.2338			−1.51549
$399$	4.89544	−	2.44428i	0.245079	−	0.122367i
$400$	−3.47126			−0.173563
$401$	−1.74876	+	0.636496i	−0.0873288	+	0.0317851i	−0.385315	−	0.922785i	$-0.625907\pi$
$401$	−1.74876	+	0.636496i	−0.0873288	+	0.0317851i	0.297986	+	0.954570i	$0.403685\pi$
$402$	0.425100	−	2.41086i	0.0212021	−	0.120243i
$403$	−18.2448	+	15.3092i	−0.908839	+	0.762606i
$404$	4.49950	+	3.77553i	0.223859	+	0.187840i
$405$	−0.435157	−	2.46790i	−0.0216231	−	0.122631i
$406$	−3.27563	−	5.67355i	−0.162567	−	0.281574i
$407$	−3.56877	+	6.18129i	−0.176897	+	0.306395i
$408$	−16.0908	−	5.85656i	−0.796611	−	0.289943i
$409$	−6.58062	−	2.39515i	−0.325391	−	0.118433i	0.174159	−	0.984717i	$-0.444279\pi$
$409$	−6.58062	−	2.39515i	−0.325391	−	0.118433i	−0.499550	+	0.866285i	$0.666501\pi$
$410$	1.22177	−	2.11617i	0.0603390	−	0.104510i
$411$	4.85989	+	8.41758i	0.239721	+	0.415208i
$412$	−0.445481	−	2.52645i	−0.0219473	−	0.124469i
$413$	−1.37022	−	1.14975i	−0.0674243	−	0.0565757i
$414$	0.698112	−	0.585786i	0.0343103	−	0.0287898i
$415$	−6.96903	+	39.5234i	−0.342096	+	1.94013i
$416$	−7.61585	+	2.77194i	−0.373398	+	0.135906i
$417$	−20.9191			−1.02441
$418$	−0.321505	+	5.30640i	−0.0157253	+	0.259545i
$419$	34.9701			1.70840			0.854200	−	0.519945i	$-0.174048\pi$
$419$	34.9701			1.70840			0.854200	+	0.519945i	$0.174048\pi$
$420$	−1.51516	+	0.551475i	−0.0739324	+	0.0269092i
$421$	−1.92891	+	10.9394i	−0.0940094	+	0.533154i	0.901037	+	0.433742i	$0.142807\pi$
$421$	−1.92891	+	10.9394i	−0.0940094	+	0.533154i	−0.995046	+	0.0994117i	$0.968304\pi$
$422$	17.3841	−	14.5870i	0.846244	−	0.710083i
$423$	−8.16949	−	6.85502i	−0.397214	−	0.333302i
$424$	6.09420	+	34.5619i	0.295960	+	1.67847i
$425$	−3.57601	−	6.19382i	−0.173462	−	0.300445i
$426$	4.69329	−	8.12902i	0.227391	−	0.393852i
$427$	−1.80505	−	0.656985i	−0.0873526	−	0.0317938i
$428$	−4.75457	−	1.73052i	−0.229821	−	0.0836479i
$429$	−1.43652	+	2.48812i	−0.0693557	+	0.120128i
$430$	−1.33274	−	2.30838i	−0.0642707	−	0.111320i
$431$	−6.47368	−	36.7141i	−0.311826	−	1.76845i	−0.589490	−	0.807776i	$-0.700671\pi$
$431$	−6.47368	−	36.7141i	−0.311826	−	1.76845i	0.277663	−	0.960678i	$-0.410440\pi$
$432$	−2.07762	−	1.74333i	−0.0999597	−	0.0838761i
$433$	13.1969	−	11.0735i	0.634203	−	0.532159i	−0.268029	−	0.963411i	$-0.586372\pi$
$433$	13.1969	−	11.0735i	0.634203	−	0.532159i	0.902232	+	0.431252i	$0.141928\pi$
$434$	−2.20385	+	12.4986i	−0.105788	+	0.599954i
$435$	−10.0767	+	3.66763i	−0.483142	+	0.175849i
$436$	−1.73278			−0.0829852
$437$	2.24068	−	2.36389i	0.107186	−	0.113080i
$438$	−11.7222			−0.560109
$439$	12.4561	−	4.53364i	0.594496	−	0.216379i	−0.0272099	−	0.999630i	$-0.508662\pi$
$439$	12.4561	−	4.53364i	0.594496	−	0.216379i	0.621706	+	0.783251i	$0.286440\pi$
$440$	1.33347	−	7.56247i	0.0635706	−	0.360527i
$441$	−4.15519	+	3.48662i	−0.197866	+	0.166030i
$442$	14.9992	+	12.5858i	0.713439	+	0.598646i
$443$	−1.07787	−	6.11289i	−0.0512110	−	0.290432i	0.948437	−	0.316966i	$-0.102664\pi$
$443$	−1.07787	−	6.11289i	−0.0512110	−	0.290432i	−0.999648	+	0.0265338i	$0.991553\pi$
$444$	−1.82923	−	3.16832i	−0.0868114	−	0.150362i
$445$	9.57127	−	16.5779i	0.453721	−	0.785869i
$446$	−30.3855	−	11.0594i	−1.43880	−	0.523679i
$447$	13.6973	+	4.98539i	0.647858	+	0.235801i
$448$	−5.56394	+	9.63703i	−0.262871	+	0.455307i
$449$	−14.5112	−	25.1342i	−0.684827	−	1.18615i	−0.973491	−	0.228724i	$-0.926545\pi$
$449$	−14.5112	−	25.1342i	−0.684827	−	1.18615i	0.288664	−	0.957430i	$-0.406789\pi$
$450$	−0.271059	−	1.53725i	−0.0127778	−	0.0724666i
$451$	0.612461	+	0.513916i	0.0288397	+	0.0241994i
$452$	3.44671	−	2.89213i	0.162120	−	0.136035i
$453$	−3.41735	+	19.3808i	−0.160561	+	0.910587i
$454$	13.4272	−	4.88711i	0.630171	−	0.229364i
$455$	9.03785			0.423701
$456$	−11.1425	−	7.36592i	−0.521797	−	0.344941i
$457$	−3.30144			−0.154435			−0.0772175	−	0.997014i	$-0.524604\pi$
$457$	−3.30144			−0.154435			−0.0772175	+	0.997014i	$0.524604\pi$
$458$	12.9016	−	4.69579i	0.602851	−	0.219420i
$459$	0.970341	−	5.50308i	0.0452917	−	0.256862i
$460$	−0.735245	+	0.616944i	−0.0342810	+	0.0287652i
$461$	31.7828	+	26.6690i	1.48027	+	1.24210i	0.905891	+	0.423511i	$0.139203\pi$
$461$	31.7828	+	26.6690i	1.48027	+	1.24210i	0.574383	+	0.818586i	$0.305242\pi$
$462$	0.265850	+	1.50771i	0.0123685	+	0.0701451i
$463$	−13.0644	−	22.6282i	−0.607154	−	1.05162i	−0.991707	−	0.128519i	$-0.958978\pi$
$463$	−13.0644	−	22.6282i	−0.607154	−	1.05162i	0.384553	−	0.923103i	$-0.374356\pi$
$464$	−5.80284	+	10.0508i	−0.269390	+	0.466597i
$465$	19.5212	+	7.10514i	0.905274	+	0.329493i
$466$	−0.322952	−	0.117545i	−0.0149605	−	0.00544516i
$467$	6.24557	−	10.8176i	0.289010	−	0.500581i	−0.684563	−	0.728953i	$-0.740007\pi$
$467$	6.24557	−	10.8176i	0.289010	−	0.500581i	0.973574	+	0.228373i	$0.0733404\pi$
$468$	−0.736309	−	1.27533i	−0.0340359	−	0.0589519i
$469$	−0.437542	−	2.48143i	−0.0202038	−	0.114582i
$470$	−24.9684	−	20.9509i	−1.15170	−	0.966395i
$471$	0.450640	−	0.378132i	0.0207644	−	0.0174234i
$472$	−0.758221	+	4.30009i	−0.0349000	+	0.197927i
$473$	0.819536	−	0.298287i	0.0376823	−	0.0137152i
$474$	−4.01434			−0.184385
$475$	−1.58756	−	5.34828i	−0.0728424	−	0.245396i
$476$	−3.59544			−0.164797
$477$	−10.7621	+	3.91707i	−0.492761	+	0.179350i
$478$	−4.95867	+	28.1220i	−0.226804	+	1.28627i
$479$	13.6070	−	11.4177i	0.621721	−	0.521686i	−0.276623	−	0.960979i	$-0.589215\pi$
$479$	13.6070	−	11.4177i	0.621721	−	0.521686i	0.898344	+	0.439293i	$0.144771\pi$
$480$	5.41530	+	4.54397i	0.247173	+	0.207403i
$481$	3.56090	+	20.1948i	0.162363	+	0.920806i
$482$	5.07253	+	8.78588i	0.231047	+	0.400186i
$483$	0.468997	−	0.812327i	0.0213401	−	0.0369622i
$484$	0.481654	+	0.175308i	0.0218934	+	0.00796854i
$485$	15.6164	+	5.68391i	0.709104	+	0.258093i
$486$	0.609802	−	1.05621i	0.0276612	−	0.0479106i
$487$	−5.86342	−	10.1557i	−0.265697	−	0.460201i	0.702049	−	0.712129i	$-0.252269\pi$
$487$	−5.86342	−	10.1557i	−0.265697	−	0.460201i	−0.967746	+	0.251928i	$0.918935\pi$
$488$	0.814259	+	4.61789i	0.0368598	+	0.209042i
$489$	−13.5660	−	11.3832i	−0.613475	−	0.514767i
$490$	−12.6995	+	10.6561i	−0.573704	+	0.481395i
$491$	4.07169	−	23.0917i	0.183753	−	1.04211i	−0.743794	−	0.668408i	$-0.766976\pi$
$491$	4.07169	−	23.0917i	0.183753	−	1.04211i	0.927547	−	0.373706i	$-0.121913\pi$
$492$	−0.385088	+	0.140161i	−0.0173611	+	0.00631893i
$493$	−23.9118			−1.07693
$494$	9.09200	+	12.2724i	0.409069	+	0.552163i
$495$	2.50597			0.112635
$496$	21.1273	−	7.68970i	0.948642	−	0.345278i
$497$	1.67767	−	9.51455i	0.0752539	−	0.426786i
$498$	−14.9623	+	12.5549i	−0.670478	+	0.562598i
$499$	7.72602	+	6.48290i	0.345864	+	0.290215i	0.799127	−	0.601162i	$-0.205296\pi$
$499$	7.72602	+	6.48290i	0.345864	+	0.290215i	−0.453263	+	0.891377i	$0.649740\pi$
$500$	−0.829758	−	4.70579i	−0.0371079	−	0.210449i
$501$	0.818825	+	1.41825i	0.0365824	+	0.0633626i
$502$	−0.230745	+	0.399663i	−0.0102987	+	0.0178378i
$503$	−17.5060	−	6.37165i	−0.780552	−	0.284098i	−0.0791491	−	0.996863i	$-0.525220\pi$
$503$	−17.5060	−	6.37165i	−0.780552	−	0.284098i	−0.701403	+	0.712765i	$0.747443\pi$
$504$	−3.61468	−	1.31564i	−0.161011	−	0.0586031i
$505$	−14.3584	+	24.8695i	−0.638942	+	1.10668i
$506$	0.455660	+	0.789227i	0.0202566	+	0.0350854i
$507$	−0.824078	−	4.67358i	−0.0365986	−	0.207561i
$508$	−0.524202	−	0.439858i	−0.0232577	−	0.0195155i
$509$	−2.82381	+	2.36946i	−0.125163	+	0.105025i	−0.703221	−	0.710972i	$-0.748255\pi$
$509$	−2.82381	+	2.36946i	−0.125163	+	0.105025i	0.578057	+	0.815996i	$0.303811\pi$
$510$	2.96565	−	16.8190i	0.131321	−	0.744759i
$511$	−11.3377	+	4.12658i	−0.501550	+	0.182549i
$512$	24.2726			1.07271
$513$	1.73582	−	3.99837i	0.0766383	−	0.176532i
$514$	−15.3117			−0.675371
$515$	11.7861	−	4.28980i	0.519358	−	0.189031i
$516$	−0.0776250	+	0.440234i	−0.00341725	+	0.0193802i
$517$	8.16949	−	6.85502i	0.359294	−	0.301483i
$518$	8.37085	+	7.02397i	0.367794	+	0.308616i
$519$	0.510300	+	2.89406i	0.0223997	+	0.127035i
$520$	−11.0312	−	19.1066i	−0.483751	−	0.837881i
$521$	12.6447	−	21.9013i	0.553976	−	0.959515i	−0.444006	−	0.896024i	$-0.646443\pi$
$521$	12.6447	−	21.9013i	0.553976	−	0.959515i	0.997982	−	0.0634910i	$-0.0202234\pi$
$522$	−4.90413	−	1.78496i	−0.214648	−	0.0781255i
$523$	10.7859	+	3.92576i	0.471636	+	0.171661i	0.566893	−	0.823791i	$-0.308145\pi$
$523$	10.7859	+	3.92576i	0.471636	+	0.171661i	−0.0952573	+	0.995453i	$0.530367\pi$
$524$	3.39167	−	5.87454i	0.148166	−	0.256630i
$525$	−0.803326	−	1.39140i	−0.0350600	−	0.0607258i
$526$	−1.90914	−	10.8273i	−0.0832423	−	0.472091i
$527$	35.4857	+	29.7760i	1.54578	+	1.29706i
$528$	2.07762	−	1.74333i	0.0904169	−	0.0758688i
$529$	−3.89695	+	22.1007i	−0.169433	+	0.960901i
$530$	−32.8920	+	11.9717i	−1.42874	+	0.520018i
$531$	−1.42492			−0.0618361
$532$	−2.72751	−	0.653165i	−0.118252	−	0.0283183i
$533$	2.29702			0.0994951
$534$	8.75443	−	3.18635i	0.378841	−	0.137887i
$535$	4.29558	−	24.3614i	0.185714	−	1.05324i
$536$	−4.71186	+	3.95372i	−0.203521	+	0.170775i
$537$	−6.49892	−	5.45324i	−0.280449	−	0.235325i
$538$	−5.90392	−	33.4828i	−0.254536	−	1.44354i
$539$	−2.71211	−	4.69751i	−0.116819	−	0.202336i
$540$	−0.642238	+	1.11239i	−0.0276375	+	0.0478696i
$541$	26.3888	+	9.60474i	1.13454	+	0.412940i	0.839940	−	0.542680i	$-0.182590\pi$
$541$	26.3888	+	9.60474i	1.13454	+	0.412940i	0.294604	+	0.955620i	$0.404812\pi$
$542$	31.7451	+	11.5543i	1.36357	+	0.496299i
$543$	8.65537	−	14.9915i	0.371438	−	0.643349i
$544$	7.88164	+	13.6514i	0.337922	+	0.585299i
$545$	−1.47109	−	8.34299i	−0.0630147	−	0.357374i
$546$	3.36947	+	2.82732i	0.144200	+	0.120998i
$547$	−19.6037	+	16.4495i	−0.838195	+	0.703329i	−0.957157	−	0.289570i	$-0.906488\pi$
$547$	−19.6037	+	16.4495i	−0.838195	+	0.703329i	0.118962	+	0.992899i	$0.462043\pi$
$548$	0.865120	−	4.90634i	0.0369561	−	0.209588i
$549$	−1.43794	+	0.523369i	−0.0613699	+	0.0223368i
$550$	1.56096			0.0665597
$551$	−18.1395	−	4.34393i	−0.772769	−	0.185058i
$552$	−2.28975			−0.0974584
$553$	−3.88266	+	1.41317i	−0.165107	+	0.0600942i
$554$	−3.28508	+	18.6306i	−0.139570	+	0.791539i
$555$	13.7018	−	11.4972i	0.581610	−	0.488029i
$556$	8.21384	+	6.89223i	0.348344	+	0.292296i
$557$	6.41170	+	36.3626i	0.271673	+	1.54073i	0.749337	+	0.662189i	$0.230372\pi$
$557$	6.41170	+	36.3626i	0.271673	+	1.54073i	−0.477664	+	0.878542i	$0.658517\pi$
$558$	5.05514	+	8.75577i	0.214001	+	0.370661i
$559$	1.25283	−	2.16997i	0.0529891	−	0.0917799i
$560$	−8.01720	−	2.91802i	−0.338789	−	0.123309i
$561$	5.25098	+	1.91120i	0.221696	+	0.0806909i
$562$	−9.25879	+	16.0367i	−0.390558	+	0.676467i
$563$	−13.8998	−	24.0751i	−0.585806	−	1.01465i	−0.994774	−	0.102097i	$-0.967445\pi$
$563$	−13.8998	−	24.0751i	−0.585806	−	1.01465i	0.408968	−	0.912549i	$-0.365889\pi$
$564$	0.949207	+	5.38322i	0.0399688	+	0.226674i
$565$	16.8512	+	14.1399i	0.708936	+	0.594868i
$566$	−6.87309	+	5.76721i	−0.288898	+	0.242414i
$567$	0.217981	−	1.23623i	0.00915433	−	0.0519168i
$568$	−22.1621	+	8.06634i	−0.929901	+	0.338456i
$569$	45.0113			1.88697			0.943487	−	0.331411i	$-0.107525\pi$
$569$	45.0113			1.88697			0.943487	+	0.331411i	$0.107525\pi$
$570$	5.30517	−	12.2202i	0.222209	−	0.511847i
$571$	−17.2748			−0.722928			−0.361464	−	0.932386i	$-0.617723\pi$
$571$	−17.2748			−0.722928			−0.361464	+	0.932386i	$0.617723\pi$
$572$	1.38381	−	0.503665i	0.0578600	−	0.0210593i
$573$	2.38823	−	13.5443i	0.0997696	−	0.565822i
$574$	0.937661	−	0.786791i	0.0391372	−	0.0328400i
$575$	−0.732623	−	0.614743i	−0.0305525	−	0.0256366i
$576$	1.53934	+	8.73003i	0.0641392	+	0.363751i
$577$	−8.83572	−	15.3039i	−0.367836	−	0.637111i	0.621391	−	0.783501i	$-0.286568\pi$
$577$	−8.83572	−	15.3039i	−0.367836	−	0.637111i	−0.989227	+	0.146390i	$0.953235\pi$
$578$	8.67470	−	15.0250i	0.360820	−	0.624959i
$579$	5.23087	+	1.90388i	0.217387	+	0.0791225i
$580$	5.16499	+	1.87990i	0.214464	+	0.0780587i
$581$	−10.0518	+	17.4102i	−0.417019	+	0.722299i
$582$	4.04397	+	7.00436i	0.167628	+	0.290340i
$583$	−1.98875	−	11.2788i	−0.0823656	−	0.467118i
$584$	22.5622	+	18.9319i	0.933630	+	0.783409i
$585$	5.51532	−	4.62790i	0.228030	−	0.191340i
$586$	−3.79804	+	21.5397i	−0.156896	+	0.889799i
$587$	30.3398	−	11.0428i	1.25226	−	0.455784i	0.371093	−	0.928596i	$-0.378983\pi$
$587$	30.3398	−	11.0428i	1.25226	−	0.455784i	0.881164	+	0.472811i	$0.156761\pi$
$588$	2.78027			0.114656
$589$	21.5102	+	29.0346i	0.886313	+	1.19635i
$590$	−4.35496			−0.179291
$591$	4.53829	−	1.65180i	0.186680	−	0.0679460i
$592$	3.36149	−	19.0639i	0.138156	−	0.783523i
$593$	−20.0248	+	16.8028i	−0.822319	+	0.690008i	−0.953514	−	0.301349i	$-0.902563\pi$
$593$	−20.0248	+	16.8028i	−0.822319	+	0.690008i	0.131195	+	0.991357i	$0.458119\pi$
$594$	0.934271	+	0.783946i	0.0383336	+	0.0321657i
$595$	−3.05245	−	17.3113i	−0.125138	−	0.709695i
$596$	−3.73566	−	6.47035i	−0.153019	−	0.265036i
$597$	−12.3949	+	21.4687i	−0.507291	+	0.878654i
$598$	2.46036	+	0.895496i	0.100611	+	0.0366196i
$599$	8.65599	+	3.15052i	0.353674	+	0.128727i	0.512746	−	0.858540i	$-0.328628\pi$
$599$	8.65599	+	3.15052i	0.353674	+	0.128727i	−0.159072	+	0.987267i	$0.550850\pi$
$600$	−1.96101	+	3.39657i	−0.0800580	+	0.138664i
$601$	−19.6932	−	34.1096i	−0.803301	−	1.39136i	−0.917432	−	0.397892i	$-0.869742\pi$
$601$	−19.6932	−	34.1096i	−0.803301	−	1.39136i	0.114132	−	0.993466i	$-0.463591\pi$
$602$	−0.231856	−	1.31492i	−0.00944976	−	0.0535923i
$603$	−1.53764	−	1.29024i	−0.0626177	−	0.0525425i
$604$	7.72721	−	6.48390i	0.314416	−	0.263826i
$605$	−0.435157	+	2.46790i	−0.0176917	+	0.100334i
$606$	−13.1330	+	4.78004i	−0.533493	+	0.194176i
$607$	2.65783			0.107878			0.0539389	−	0.998544i	$-0.482822\pi$
$607$	2.65783			0.107878			0.0539389	+	0.998544i	$0.482822\pi$
$608$	3.49904	+	11.7878i	0.141905	+	0.478058i
$609$	−5.37163			−0.217669
$610$	−4.39478	+	1.59957i	−0.177939	+	0.0647646i
$611$	5.32049	−	30.1740i	0.215244	−	1.22071i
$612$	−2.19411	+	1.84107i	−0.0886915	+	0.0744210i
$613$	22.2706	+	18.6873i	0.899502	+	0.754772i	0.970093	−	0.242734i	$-0.0780441\pi$
$613$	22.2706	+	18.6873i	0.899502	+	0.754772i	−0.0705911	+	0.997505i	$0.522489\pi$
$614$	0.346706	+	1.96627i	0.0139919	+	0.0793522i
$615$	−1.00178	−	1.73513i	−0.0403955	−	0.0699671i
$616$	1.92333	−	3.33131i	0.0774933	−	0.134222i
$617$	23.5983	+	8.58909i	0.950033	+	0.345784i	0.770120	−	0.637899i	$-0.220196\pi$
$617$	23.5983	+	8.58909i	0.950033	+	0.345784i	0.179913	+	0.983683i	$0.442418\pi$
$618$	5.73606	+	2.08775i	0.230738	+	0.0839818i
$619$	−5.70768	+	9.88598i	−0.229411	+	0.397351i	−0.957634	−	0.287989i	$-0.907013\pi$
$619$	−5.70768	+	9.88598i	−0.229411	+	0.397351i	0.728223	+	0.685340i	$0.240347\pi$
$620$	−5.32403	−	9.22149i	−0.213818	−	0.370344i
$621$	−0.129755	−	0.735875i	−0.00520687	−	0.0295296i
$622$	−26.3389	−	22.1009i	−1.05609	−	0.886166i
$623$	7.34557	−	6.16366i	0.294294	−	0.246942i
$624$	1.35308	−	7.67370i	0.0541666	−	0.307194i
$625$	27.9665	−	10.1790i	1.11866	−	0.407159i
$626$	−10.8183			−0.432385
$627$	3.63620	+	2.40376i	0.145216	+	0.0959968i
$628$	−0.301526			−0.0120322
$629$	37.4790	−	13.6413i	1.49439	−	0.543913i
$630$	0.666213	−	3.77828i	0.0265426	−	0.150530i
$631$	31.2943	−	26.2591i	1.24581	−	1.04536i	0.248760	−	0.968565i	$-0.419977\pi$
$631$	31.2943	−	26.2591i	1.24581	−	1.04536i	0.997047	−	0.0767917i	$-0.0244676\pi$
$632$	7.72655	+	6.48334i	0.307346	+	0.257894i
$633$	−3.23109	−	18.3244i	−0.128424	−	0.728331i
$634$	13.1806	+	22.8294i	0.523468	+	0.906672i
$635$	1.67279	−	2.89736i	0.0663826	−	0.114978i
$636$	5.51627	+	2.00776i	0.218734	+	0.0796128i
$637$	−14.6441	−	5.33003i	−0.580222	−	0.211183i
$638$	2.60944	−	4.51967i	0.103309	−	0.178936i
$639$	−3.84821	−	6.66529i	−0.152233	−	0.263675i
$640$	2.24958	+	12.7580i	0.0889224	+	0.504304i
$641$	14.8592	+	12.4683i	0.586903	+	0.492470i	0.887206	−	0.461374i	$-0.152643\pi$
$641$	14.8592	+	12.4683i	0.586903	+	0.492470i	−0.300303	+	0.953844i	$0.597088\pi$
$642$	9.22249	−	7.73859i	0.363983	−	0.305418i
$643$	4.46362	−	25.3145i	0.176028	−	0.998305i	−0.760922	−	0.648843i	$-0.775253\pi$
$643$	4.46362	−	25.3145i	0.176028	−	0.998305i	0.936950	−	0.349462i	$-0.113636\pi$
$644$	−0.451789	+	0.164438i	−0.0178030	+	0.00647976i
$645$	−2.18554			−0.0860554
$646$	20.4362	−	21.5600i	0.804051	−	0.848265i
$647$	37.0389			1.45615			0.728075	−	0.685498i	$-0.240415\pi$
$647$	37.0389			1.45615			0.728075	+	0.685498i	$0.240415\pi$
$648$	−2.87953	+	1.04806i	−0.113119	+	0.0411719i
$649$	0.247434	−	1.40327i	0.00971264	−	0.0550831i
$650$	3.43548	−	2.88271i	0.134751	−	0.113069i
$651$	7.97162	+	6.68898i	0.312432	+	0.262162i
$652$	1.57622	+	8.93920i	0.0617296	+	0.350086i
$653$	−21.2195	−	36.7533i	−0.830384	−	1.43827i	−0.897734	−	0.440537i	$-0.854788\pi$
$653$	−21.2195	−	36.7533i	−0.830384	−	1.43827i	0.0673509	−	0.997729i	$-0.478545\pi$
$654$	2.06150	−	3.57062i	0.0806109	−	0.139622i
$655$	31.1642	+	11.3428i	1.21768	+	0.443201i
$656$	−2.03762	−	0.741633i	−0.0795557	−	0.0289559i
$657$	−4.80575	+	8.32380i	−0.187490	+	0.324742i
$658$	−8.16353	−	14.1396i	−0.318248	−	0.551221i
$659$	6.86683	+	38.9437i	0.267494	+	1.51703i	0.761839	+	0.647766i	$0.224297\pi$
$659$	6.86683	+	38.9437i	0.267494	+	1.51703i	−0.494346	+	0.869265i	$0.664592\pi$
$660$	−0.983965	−	0.825645i	−0.0383008	−	0.0321382i
$661$	34.3266	−	28.8034i	1.33515	−	1.12032i	0.352305	−	0.935885i	$-0.385398\pi$
$661$	34.3266	−	28.8034i	1.33515	−	1.12032i	0.982844	−	0.184438i	$-0.0590465\pi$
$662$	5.64084	−	31.9908i	0.219237	−	1.24336i
$663$	15.0862	−	5.49094i	0.585901	−	0.213250i
$664$	49.0753			1.90449
$665$	0.829265	−	13.6869i	0.0321575	−	0.530756i
$666$	8.70497			0.337311
$667$	−3.00466	+	1.09361i	−0.116341	+	0.0423447i
$668$	0.145761	−	0.826651i	0.00563966	−	0.0319841i
$669$	−20.3103	+	17.0424i	−0.785241	+	0.658896i
$670$	−4.69949	−	3.94334i	−0.181557	−	0.152345i
$671$	−0.265721	−	1.50698i	−0.0102581	−	0.0581763i
$672$	1.77056	+	3.06670i	0.0683008	+	0.118300i
$673$	9.99114	−	17.3052i	0.385130	−	0.667065i	−0.606657	−	0.794964i	$-0.707490\pi$
$673$	9.99114	−	17.3052i	0.385130	−	0.667065i	0.991787	+	0.127899i	$0.0408233\pi$
$674$	−29.1535	−	10.6110i	−1.12295	−	0.408721i
$675$	−1.20271	−	0.437749i	−0.0462922	−	0.0168490i
$676$	−1.21624	+	2.10658i	−0.0467783	+	0.0810224i
$677$	−1.44899	−	2.50973i	−0.0556893	−	0.0964566i	0.836837	−	0.547452i	$-0.184402\pi$
$677$	−1.44899	−	2.50973i	−0.0556893	−	0.0964566i	−0.892526	+	0.450996i	$0.851069\pi$
$678$	1.85905	+	10.5432i	0.0713963	+	0.404908i
$679$	6.37707	+	5.35100i	0.244729	+	0.205352i
$680$	−32.8716	+	27.5825i	−1.26057	+	1.05774i
$681$	2.03447	−	11.5381i	0.0779612	−	0.442140i
$682$	−9.50056	+	3.45792i	−0.363795	+	0.132411i
$683$	16.1643			0.618511			0.309255	−	0.950979i	$-0.399920\pi$
$683$	16.1643			0.618511			0.309255	+	0.950979i	$0.399920\pi$
$684$	−1.99891	+	0.998049i	−0.0764303	+	0.0381614i
$685$	24.3575			0.930652
$686$	−17.8740	+	6.50561i	−0.682433	+	0.248385i
$687$	1.95483	−	11.0864i	0.0745813	−	0.422972i
$688$	−1.81196	+	1.52042i	−0.0690804	+	0.0579653i
$689$	−25.2060	−	21.1504i	−0.960273	−	0.805765i
$690$	−0.396568	−	2.24905i	−0.0150971	−	0.0856198i
$691$	3.31507	+	5.74186i	0.126111	+	0.218431i	0.922167	−	0.386793i	$-0.126417\pi$
$691$	3.31507	+	5.74186i	0.126111	+	0.218431i	−0.796056	+	0.605223i	$0.793084\pi$
$692$	0.753139	−	1.30448i	0.0286301	−	0.0495887i
$693$	1.17960	+	0.429338i	0.0448092	+	0.0163092i
$694$	−34.8443	−	12.6823i	−1.32267	−	0.481413i
$695$	−26.2113	+	45.3993i	−0.994251	+	1.72209i
$696$	6.55638	+	11.3560i	0.248519	+	0.430447i
$697$	−0.775799	−	4.39978i	−0.0293855	−	0.166653i
$698$	13.2667	+	11.1321i	0.502153	+	0.421356i
$699$	−0.215867	+	0.181134i	−0.00816485	+	0.00685112i
$700$	−0.143002	+	0.811004i	−0.00540497	+	0.0306531i
$701$	−21.0380	+	7.65720i	−0.794594	+	0.289208i	−0.707244	−	0.706969i	$-0.750062\pi$
$701$	−21.0380	+	7.65720i	−0.794594	+	0.289208i	−0.0873494	+	0.996178i	$0.527840\pi$
$702$	3.50396			0.132249
$703$	30.9098	−	3.53965i	1.16579	−	0.133500i
$704$	−8.86471			−0.334101
$705$	−25.1133	+	9.14048i	−0.945820	+	0.344250i
$706$	−3.61416	+	20.4969i	−0.136021	+	0.771411i
$707$	−11.0195	+	9.24648i	−0.414432	+	0.347750i
$708$	0.559491	+	0.469468i	0.0210269	+	0.0176437i
$709$	5.82268	+	33.0221i	0.218675	+	1.24017i	0.874413	+	0.485182i	$0.161247\pi$
$709$	5.82268	+	33.0221i	0.218675	+	1.24017i	−0.655738	+	0.754989i	$0.727642\pi$
$710$	−11.7613	−	20.3711i	−0.441392	−	0.764514i
$711$	−1.64576	+	2.85053i	−0.0617206	+	0.106903i
$712$	−21.9961	−	8.00592i	−0.824338	−	0.300035i
$713$	5.82080	+	2.11860i	0.217991	+	0.0793421i
$714$	4.27751	−	7.40887i	0.160082	−	0.277270i
$715$	3.59987	+	6.23516i	0.134628	+	0.233182i
$716$	0.755105	+	4.28241i	0.0282196	+	0.160041i
$717$	17.9362	+	15.0502i	0.669839	+	0.562062i
$718$	6.35151	−	5.32955i	0.237036	−	0.198897i
$719$	1.23330	−	6.99437i	0.0459942	−	0.260846i	−0.953136	−	0.302542i	$-0.902165\pi$
$719$	1.23330	−	6.99437i	0.0459942	−	0.260846i	0.999130	+	0.0416957i	$0.0132760\pi$
$720$	−6.38667	+	2.32456i	−0.238017	+	0.0866312i
$721$	6.28285			0.233986
$722$	19.4196	−	12.6429i	0.722723	−	0.470519i
$723$	8.31832			0.309362
$724$	−8.33779	+	3.03471i	−0.309872	+	0.112784i
$725$	−0.951047	+	5.39365i	−0.0353210	+	0.200315i
$726$	−0.934271	+	0.783946i	−0.0346740	+	0.0290950i
$727$	−15.4956	−	13.0024i	−0.574702	−	0.482232i	0.308501	−	0.951224i	$-0.400173\pi$
$727$	−15.4956	−	13.0024i	−0.574702	−	0.482232i	−0.883202	+	0.468992i	$0.844617\pi$
$728$	−1.91909	−	10.8837i	−0.0711262	−	0.403377i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	−14.6878	+	25.4400i	−0.543619	+	0.941576i
$731$	−4.57954	−	1.66682i	−0.169380	−	0.0616495i
$732$	0.737041	+	0.268261i	0.0272418	+	0.00991521i
$733$	−15.1831	+	26.2979i	−0.560800	+	0.971334i	0.436627	+	0.899643i	$0.356173\pi$
$733$	−15.1831	+	26.2979i	−0.560800	+	0.971334i	−0.997427	+	0.0716911i	$0.977160\pi$
$734$	17.8353	+	30.8917i	0.658314	+	1.14023i
$735$	2.36039	+	13.3864i	0.0870642	+	0.493766i
$736$	1.61472	+	1.35491i	0.0595195	+	0.0499428i
$737$	1.53764	−	1.29024i	0.0566398	−	0.0475265i
$738$	0.169322	−	0.960274i	0.00623284	−	0.0353482i
$739$	−18.0322	+	6.56319i	−0.663326	+	0.241431i	−0.651672	−	0.758501i	$-0.725932\pi$
$739$	−18.0322	+	6.56319i	−0.663326	+	0.241431i	−0.0116544	+	0.999932i	$0.503710\pi$
$740$	−9.16799			−0.337022
$741$	12.4419	−	1.42479i	0.457066	−	0.0523411i
$742$	−17.5338			−0.643687
$743$	9.57223	−	3.48401i	0.351171	−	0.127816i	−0.160411	−	0.987050i	$-0.551282\pi$
$743$	9.57223	−	3.48401i	0.351171	−	0.127816i	0.511582	+	0.859235i	$0.329060\pi$
$744$	4.41114	−	25.0168i	0.161720	−	0.917162i
$745$	27.9819	−	23.4796i	1.02518	−	0.860227i
$746$	4.40256	+	3.69419i	0.161189	+	0.135254i
$747$	2.78097	+	15.7717i	0.101750	+	0.577055i
$748$	−1.43210	−	2.48047i	−0.0523628	−	0.0906951i
$749$	6.19574	−	10.7313i	0.226388	−	0.392115i
$750$	10.6841	+	3.88868i	0.390127	+	0.141994i
$751$	−2.06244	−	0.750667i	−0.0752595	−	0.0273922i	0.304116	−	0.952635i	$-0.401639\pi$
$751$	−2.06244	−	0.750667i	−0.0752595	−	0.0273922i	−0.379376	+	0.925243i	$0.623861\pi$
$752$	−14.4619	+	25.0487i	−0.527369	+	0.913431i
$753$	0.189197	+	0.327699i	0.00689472	+	0.0119420i
$754$	−2.60368	−	14.7662i	−0.0948204	−	0.537753i
$755$	37.7789	+	31.7003i	1.37492	+	1.15369i
$756$	−0.492892	+	0.413585i	−0.0179263	+	0.0150420i
$757$	−4.18042	+	23.7083i	−0.151940	+	0.861694i	0.809590	+	0.586995i	$0.199689\pi$
$757$	−4.18042	+	23.7083i	−0.151940	+	0.861694i	−0.961530	+	0.274699i	$0.911422\pi$
$758$	−18.2991	+	6.66032i	−0.664652	+	0.241914i
$759$	0.747227			0.0271226
$760$	−29.9472	+	14.9525i	−1.08630	+	0.542386i
$761$	−18.2139			−0.660253			−0.330127	−	0.943937i	$-0.607091\pi$
$761$	−18.2139			−0.660253			−0.330127	+	0.943937i	$0.607091\pi$
$762$	1.53003	−	0.556885i	0.0554271	−	0.0201738i
$763$	0.736906	−	4.17920i	0.0266778	−	0.151297i
$764$	−5.40019	+	4.53130i	−0.195372	+	0.163937i
$765$	−10.7272	−	9.00115i	−0.387841	−	0.325437i
$766$	−4.37768	−	24.8270i	−0.158172	−	0.897037i
$767$	−2.04692	−	3.54536i	−0.0739098	−	0.128016i
$768$	5.71229	−	9.89397i	0.206124	−	0.357018i
$769$	9.95947	+	3.62495i	0.359148	+	0.130719i	0.515291	−	0.857015i	$-0.327684\pi$
$769$	9.95947	+	3.62495i	0.359148	+	0.130719i	−0.156143	+	0.987734i	$0.549906\pi$
$770$	3.60520	+	1.31218i	0.129922	+	0.0472878i
$771$	−6.27733	+	10.8727i	−0.226072	+	0.391569i
$772$	−1.42662	−	2.47097i	−0.0513451	−	0.0889323i
$773$	−0.816172	−	4.62874i	−0.0293556	−	0.166484i	0.966606	−	0.256269i	$-0.0824932\pi$
$773$	−0.816172	−	4.62874i	−0.0293556	−	0.166484i	−0.995961	+	0.0897847i	$0.971382\pi$
$774$	−0.814807	−	0.683704i	−0.0292876	−	0.0245752i
$775$	8.12779	−	6.82003i	0.291959	−	0.244983i
$776$	3.52879	−	20.0128i	0.126676	−	0.718416i
$777$	8.41942	−	3.06442i	0.302045	−	0.109935i
$778$	8.66282			0.310577
$779$	0.210763	−	3.47861i	0.00755136	−	0.124634i
$780$	−3.69034			−0.132135
$781$	7.23227	−	2.63233i	0.258791	−	0.0941922i
$782$	0.884292	−	5.01507i	0.0316222	−	0.179339i
$783$	−3.27802	+	2.75059i	−0.117147	+	0.0982979i
$784$	11.2695	+	9.45622i	0.402481	+	0.337722i
$785$	−0.255989	−	1.45179i	−0.00913665	−	0.0518165i
$786$	8.07016	+	13.9779i	0.287853	+	0.498576i
$787$	27.5192	−	47.6647i	0.980954	−	1.69906i	0.322259	−	0.946652i	$-0.395558\pi$
$787$	27.5192	−	47.6647i	0.980954	−	1.69906i	0.658695	−	0.752410i	$-0.271109\pi$
$788$	−2.32617	−	0.846657i	−0.0828664	−	0.0301609i
$789$	−8.47098	−	3.08319i	−0.301575	−	0.109764i
$790$	−5.02991	+	8.71206i	−0.178956	+	0.309961i
$791$	5.50959	+	9.54289i	0.195898	+	0.339306i
$792$	−0.532116	−	3.01778i	−0.0189079	−	0.107232i
$793$	−3.36783	−	2.82595i	−0.119595	−	0.100352i
$794$	−8.08976	+	6.78811i	−0.287095	+	0.240901i
$795$	−4.98375	+	28.2643i	−0.176755	+	1.00243i
$796$	11.9402	−	4.34586i	0.423207	−	0.154035i
$797$	−10.8736			−0.385164			−0.192582	−	0.981281i	$-0.561686\pi$
$797$	−10.8736			−0.385164			−0.192582	+	0.981281i	$0.561686\pi$
$798$	4.59086	−	4.84330i	0.162515	−	0.171451i
$799$	−59.5930			−2.10825
$800$	3.39275	−	1.23486i	0.119952	−	0.0436589i
$801$	1.32646	−	7.52272i	0.0468681	−	0.265802i
$802$	−1.73867	+	1.45892i	−0.0613945	+	0.0515161i
$803$	−7.36283	−	6.17815i	−0.259829	−	0.218022i
$804$	0.178658	+	1.01322i	0.00630077	+	0.0357335i
$805$	−1.17529	−	2.03567i	−0.0414237	−	0.0717479i
$806$	−14.5236	+	25.1556i	−0.511572	+	0.886068i
$807$	−26.1961	−	9.53461i	−0.922147	−	0.335634i
$808$	32.9976	+	12.0102i	1.16085	+	0.422516i
$809$	−6.56793	+	11.3760i	−0.230916	+	0.399959i	−0.958078	−	0.286507i	$-0.907506\pi$
$809$	−6.56793	+	11.3760i	−0.230916	+	0.399959i	0.727162	+	0.686466i	$0.240839\pi$
$810$	−1.52815	−	2.64683i	−0.0536936	−	0.0930000i
$811$	2.47373	+	14.0292i	0.0868646	+	0.492633i	0.996939	+	0.0781878i	$0.0249134\pi$
$811$	2.47373	+	14.0292i	0.0868646	+	0.492633i	−0.910074	+	0.414446i	$0.863976\pi$
$812$	2.10916	+	1.76979i	0.0740170	+	0.0621076i
$813$	21.2191	−	17.8049i	0.744185	−	0.624445i
$814$	−1.51160	+	8.57272i	−0.0529816	+	0.300474i
$815$	−41.7023	+	15.1784i	−1.46077	+	0.531675i
$816$	−15.1554			−0.530545
$817$	−3.17124	−	2.09639i	−0.110948	−	0.0733435i
$818$	−8.54083			−0.298623
$819$	3.38902	−	1.23350i	0.118422	−	0.0431021i
$820$	−0.178329	+	1.01135i	−0.00622750	+	0.0353179i
$821$	−16.5809	+	13.9131i	−0.578679	+	0.485569i	−0.884513	−	0.466516i	$-0.845509\pi$
$821$	−16.5809	+	13.9131i	−0.578679	+	0.485569i	0.305834	+	0.952085i	$0.401065\pi$
$822$	9.08091	+	7.61979i	0.316733	+	0.265771i
$823$	−4.22828	−	23.9798i	−0.147389	−	0.835882i	−0.965418	−	0.260706i	$-0.916045\pi$
$823$	−4.22828	−	23.9798i	−0.147389	−	0.835882i	0.818030	−	0.575176i	$-0.195066\pi$
$824$	−7.66858	−	13.2824i	−0.267148	−	0.462714i
$825$	0.639947	−	1.10842i	0.0222801	−	0.0385903i
$826$	−2.04994	−	0.746119i	−0.0713267	−	0.0259608i
$827$	−35.2325	−	12.8236i	−1.22516	−	0.445920i	−0.353220	−	0.935540i	$-0.614913\pi$
$827$	−35.2325	−	12.8236i	−1.22516	−	0.445920i	−0.871936	+	0.489620i	$0.837135\pi$
$828$	−0.191501	+	0.331690i	−0.00665514	+	0.0115270i
$829$	5.48387	+	9.49834i	0.190463	+	0.329891i	0.945404	−	0.325902i	$-0.105668\pi$
$829$	5.48387	+	9.49834i	0.190463	+	0.329891i	−0.754941	+	0.655793i	$0.772335\pi$
$830$	8.49946	+	48.2028i	0.295021	+	1.67315i
$831$	11.8826	+	9.97067i	0.412202	+	0.345879i
$832$	−19.5101	+	16.3709i	−0.676390	+	0.567559i
$833$	−5.26334	+	29.8499i	−0.182364	+	1.03424i
$834$	−23.9744	+	8.72596i	−0.830164	+	0.302155i
$835$	4.10390			0.142021
$836$	−0.635779	−	2.14185i	−0.0219889	−	0.0740775i
$837$	8.28981			0.286538
$838$	40.0775	−	14.5870i	1.38446	−	0.503901i
$839$	−2.39319	+	13.5725i	−0.0826221	+	0.468573i	0.915222	+	0.402949i	$0.132015\pi$
$839$	−2.39319	+	13.5725i	−0.0826221	+	0.468573i	−0.997844	+	0.0656239i	$0.979096\pi$
$840$	−7.38439	+	6.19624i	−0.254786	+	0.213791i
$841$	−8.18815	−	6.87067i	−0.282350	−	0.236920i
$842$	2.35251	+	13.3417i	0.0810728	+	0.459787i
$843$	7.59164	+	13.1491i	0.261470	+	0.452879i
$844$	−4.76868	+	8.25960i	−0.164145	+	0.284307i
$845$	−11.1753	−	4.06749i	−0.384443	−	0.139926i
$846$	−12.2221	−	4.44848i	−0.420204	−	0.152942i
$847$	−0.627651	+	1.08712i	−0.0215663	+	0.0373540i
$848$	15.5308	+	26.9001i	0.533328	+	0.923752i
$849$	1.27747	+	7.24488i	0.0438426	+	0.248643i
$850$	−6.68192	−	5.60679i	−0.229188	−	0.192311i
$851$	4.08559	−	3.42822i	0.140052	−	0.117518i
$852$	−0.685028	+	3.88499i	−0.0234687	+	0.133098i
$853$	30.7242	−	11.1827i	1.05198	−	0.382888i	0.242568	−	0.970134i	$-0.422010\pi$
$853$	30.7242	−	11.1827i	1.05198	−	0.382888i	0.809408	+	0.587246i	$0.199788\pi$
$854$	−2.34273			−0.0801667
$855$	−6.50244	−	8.77703i	−0.222379	−	0.300168i
$856$	−30.2490			−1.03389
$857$	8.59406	−	3.12798i	0.293568	−	0.106850i	−0.191038	−	0.981583i	$-0.561185\pi$
$857$	8.59406	−	3.12798i	0.293568	−	0.106850i	0.484606	+	0.874733i	$0.338963\pi$
$858$	−0.608457	+	3.45073i	−0.0207724	+	0.117806i
$859$	4.38782	−	3.68182i	0.149711	−	0.125622i	−0.564856	−	0.825189i	$-0.691068\pi$
$859$	4.38782	−	3.68182i	0.149711	−	0.125622i	0.714567	+	0.699567i	$0.246624\pi$
$860$	0.858147	+	0.720071i	0.0292626	+	0.0245542i
$861$	−0.174278	−	0.988381i	−0.00593938	−	0.0336839i
$862$	−22.7337	−	39.3759i	−0.774312	−	1.34115i
$863$	3.84115	−	6.65306i	0.130754	−	0.226473i	−0.793213	−	0.608944i	$-0.791593\pi$
$863$	3.84115	−	6.65306i	0.130754	−	0.226473i	0.923968	+	0.382471i	$0.124927\pi$
$864$	2.65081	+	0.964814i	0.0901822	+	0.0328237i
$865$	6.92018	+	2.51874i	0.235293	+	0.0856397i
$866$	10.5053	−	18.1956i	0.356983	−	0.618313i
$867$	−7.11272	−	12.3196i	−0.241561	−	0.418395i
$868$	−0.926217	−	5.25284i	−0.0314378	−	0.178293i
$869$	−2.52144	−	2.11574i	−0.0855341	−	0.0717716i
$870$	−10.0186	+	8.40660i	−0.339662	+	0.285010i
$871$	1.00141	−	5.67929i	0.0339315	−	0.192435i
$872$	−9.73456	+	3.54309i	−0.329654	+	0.119984i
$873$	6.63161			0.224446
$874$	1.58189	−	3.64379i	0.0535082	−	0.123253i
$875$	11.7025			0.395618
$876$	4.62942	−	1.68497i	0.156414	−	0.0569299i
$877$	4.54125	−	25.7547i	0.153347	−	0.869674i	−0.806935	−	0.590641i	$-0.798875\pi$
$877$	4.54125	−	25.7547i	0.153347	−	0.869674i	0.960281	−	0.279033i	$-0.0900139\pi$
$878$	12.3842	−	10.3916i	0.417947	−	0.350699i
$879$	13.7380	+	11.5276i	0.463372	+	0.388815i
$880$	−1.18021	−	6.69330i	−0.0397849	−	0.225631i
$881$	−3.26808	−	5.66049i	−0.110105	−	0.190707i	0.805708	−	0.592313i	$-0.201785\pi$
$881$	−3.26808	−	5.66049i	−0.110105	−	0.190707i	−0.915812	+	0.401607i	$0.868452\pi$
$882$	−3.30770	+	5.72910i	−0.111376	+	0.192909i
$883$	14.7451	+	5.36678i	0.496213	+	0.180607i	0.577990	−	0.816044i	$-0.303837\pi$
$883$	14.7451	+	5.36678i	0.496213	+	0.180607i	−0.0817772	+	0.996651i	$0.526060\pi$
$884$	−7.73269	−	2.81447i	−0.260078	−	0.0946608i
$885$	−1.78540	+	3.09240i	−0.0600155	+	0.103950i
$886$	−3.78516	−	6.55609i	−0.127165	−	0.220256i
$887$	4.71281	+	26.7277i	0.158241	+	0.897428i	0.955763	+	0.294138i	$0.0950326\pi$
$887$	4.71281	+	26.7277i	0.158241	+	0.897428i	−0.797522	+	0.603290i	$0.793856\pi$
$888$	−16.7548	−	14.0589i	−0.562254	−	0.471787i
$889$	1.28380	−	1.07724i	0.0430572	−	0.0361293i
$890$	4.05404	−	22.9916i	0.135892	−	0.770681i
$891$	0.939693	−	0.342020i	0.0314809	−	0.0114581i
$892$	13.5898			0.455019
$893$	−45.2073	−	10.8260i	−1.51281	−	0.362277i
$894$	17.7773			0.594563
$895$	−19.9779	+	7.27135i	−0.667787	+	0.243055i
$896$	−1.12687	+	6.39079i	−0.0376460	+	0.213501i
$897$	1.64455	−	1.37994i	0.0549099	−	0.0460749i
$898$	−27.1148	−	22.7520i	−0.904833	−	0.759245i
$899$	−6.15988	−	34.9344i	−0.205444	−	1.16513i
$900$	0.328015	+	0.568139i	0.0109338	+	0.0189380i
$901$	−31.9988	+	55.4236i	−1.06604	+	1.84643i
$902$	0.916283	+	0.333500i	0.0305089	+	0.0111043i
$903$	−1.02876	−	0.374440i	−0.0342351	−	0.0124606i
$904$	13.4495	−	23.2953i	0.447325	−	0.774790i
$905$	−21.6901	−	37.5684i	−0.721004	−	1.24882i
$906$	4.16781	+	23.6368i	0.138466	+	0.785282i
$907$	−32.2853	−	27.0906i	−1.07201	−	0.899527i	−0.0767813	−	0.997048i	$-0.524464\pi$
$907$	−32.2853	−	27.0906i	−1.07201	−	0.899527i	−0.995233	+	0.0975208i	$0.968909\pi$
$908$	−4.60029	+	3.86011i	−0.152666	+	0.128102i
$909$	−1.98990	+	11.2853i	−0.0660008	+	0.374309i
$910$	10.3578	−	3.76995i	0.343359	−	0.124973i
$911$	−16.2810			−0.539413			−0.269707	−	0.962943i	$-0.586927\pi$
$911$	−16.2810			−0.539413			−0.269707	+	0.962943i	$0.586927\pi$
$912$	−11.4969	−	2.75320i	−0.380700	−	0.0911677i
$913$	−16.0150			−0.530018
$914$	−3.78363	+	1.37713i	−0.125151	+	0.0455513i
$915$	−0.665890	+	3.77645i	−0.0220136	+	0.124846i
$916$	−4.42020	+	3.70899i	−0.146048	+	0.122548i
$917$	12.7261	+	10.6785i	0.420253	+	0.352634i
$918$	−1.18343	−	6.71158i	−0.0390591	−	0.221515i
$919$	−18.7809	−	32.5294i	−0.619524	−	1.07305i	−0.989573	−	0.144034i	$-0.953992\pi$
$919$	−18.7809	−	32.5294i	−0.619524	−	1.07305i	0.370049	−	0.929012i	$-0.379341\pi$
$920$	−2.86903	+	4.96930i	−0.0945891	+	0.163833i
$921$	1.53836	+	0.559918i	0.0506907	+	0.0184499i
$922$	47.5492	+	17.3065i	1.56595	+	0.569959i
$923$	11.0560	−	19.1496i	0.363914	−	0.630317i
$924$	−0.321712	−	0.557222i	−0.0105836	−	0.0183313i
$925$	−1.58633	−	8.99651i	−0.0521581	−	0.295803i
$926$	−24.4114	−	20.4836i	−0.802208	−	0.673132i
$927$	3.83409	−	3.21719i	0.125928	−	0.105666i
$928$	2.09614	−	11.8878i	0.0688091	−	0.390236i
$929$	−15.5780	+	5.66993i	−0.511098	+	0.186024i	−0.584679	−	0.811265i	$-0.698779\pi$
$929$	−15.5780	+	5.66993i	−0.511098	+	0.186024i	0.0735812	+	0.997289i	$0.476557\pi$
$930$	25.3361			0.830803
$931$	−9.41546	+	21.6880i	−0.308579	+	0.710796i
$932$	0.144438			0.00473124
$933$	−26.4917	+	9.64219i	−0.867299	+	0.315671i
$934$	2.64540	−	15.0028i	0.0865601	−	0.490907i
$935$	10.7272	−	9.00115i	0.350815	−	0.294369i
$936$	−6.74421	−	5.65906i	−0.220441	−	0.184972i
$937$	3.81937	+	21.6607i	0.124773	+	0.707624i	0.981442	+	0.191758i	$0.0614189\pi$
$937$	3.81937	+	21.6607i	0.124773	+	0.707624i	−0.856669	+	0.515867i	$0.827470\pi$
$938$	−1.53652	−	2.66133i	−0.0501692	−	0.0868956i
$939$	−4.43516	+	7.68192i	−0.144736	+	0.250690i
$940$	12.8722	+	4.68510i	0.419845	+	0.152811i
$941$	1.18598	+	0.431660i	0.0386618	+	0.0140717i	0.361279	−	0.932458i	$-0.382340\pi$
$941$	1.18598	+	0.431660i	0.0386618	+	0.0140717i	−0.322617	+	0.946530i	$0.604563\pi$
$942$	0.358727	−	0.621334i	0.0116880	−	0.0202442i
$943$	−0.298708	−	0.517378i	−0.00972728	−	0.0168481i
$944$	0.671077	+	3.80587i	0.0218417	+	0.123870i
$945$	−2.40978	−	2.02205i	−0.0783903	−	0.0657773i
$946$	0.814807	−	0.683704i	0.0264917	−	0.0222291i
$947$	6.24771	−	35.4325i	0.203023	−	1.15140i	−0.697496	−	0.716588i	$-0.745703\pi$
$947$	6.24771	−	35.4325i	0.203023	−	1.15140i	0.900520	−	0.434815i	$-0.143186\pi$
$948$	1.58537	−	0.577028i	0.0514904	−	0.0187410i
$949$	−27.6142			−0.896393
$950$	−4.05035	−	5.46719i	−0.131411	−	0.177379i
$951$	21.6145			0.700899
$952$	−20.1988	+	7.35174i	−0.654645	+	0.238271i
$953$	−1.85596	+	10.5256i	−0.0601203	+	0.340959i	−1.00000		0.000546995i	$-0.999826\pi$
$953$	−1.85596	+	10.5256i	−0.0601203	+	0.340959i	0.939880	+	0.341506i	$0.110937\pi$
$954$	−10.7000	+	8.97834i	−0.346424	+	0.290685i
$955$	−26.4019	−	22.1538i	−0.854346	−	0.716882i
$956$	−2.08399	−	11.8189i	−0.0674011	−	0.382251i
$957$	−2.13958	−	3.70585i	−0.0691627	−	0.119793i
$958$	10.8317	−	18.7611i	0.349958	−	0.606145i
$959$	11.4654	+	4.17307i	0.370238	+	0.134756i
$960$	20.8750	+	7.59787i	0.673737	+	0.245220i
$961$	−18.8605	+	32.6673i	−0.608403	+	1.05378i
$962$	12.5048	+	21.6590i	0.403172	+	0.698315i
$963$	−1.71414	−	9.72135i	−0.0552373	−	0.313266i
$964$	−3.26617	−	2.74064i	−0.105196	−	0.0882702i
$965$	10.6861	−	8.96667i	0.343997	−	0.288647i
$966$	0.198650	−	1.12660i	0.00639147	−	0.0362479i
$967$	−15.3965	+	5.60386i	−0.495117	+	0.180208i	−0.577497	−	0.816393i	$-0.695970\pi$
$967$	−15.3965	+	5.60386i	−0.495117	+	0.180208i	0.0823794	+	0.996601i	$0.473748\pi$
$968$	3.06434			0.0984915
$969$	−6.93124	−	23.3504i	−0.222664	−	0.750123i
$970$	20.2681			0.650771
$971$	14.4139	−	5.24622i	0.462563	−	0.168359i	−0.100218	−	0.994966i	$-0.531954\pi$
$971$	14.4139	−	5.24622i	0.462563	−	0.168359i	0.562780	+	0.826606i	$0.309732\pi$
$972$	−0.0890061	+	0.504779i	−0.00285487	+	0.0161908i
$973$	−20.1161	+	16.8794i	−0.644894	+	0.541130i
$974$	−10.9561	−	9.19322i	−0.351055	−	0.294570i
$975$	−0.638535	−	3.62131i	−0.0204495	−	0.115975i
$976$	2.07510	+	3.59418i	0.0664223	+	0.115047i
$977$	−11.1597	+	19.3292i	−0.357031	+	0.618396i	−0.987463	−	0.157848i	$-0.949544\pi$
$977$	−11.1597	+	19.3292i	−0.357031	+	0.618396i	0.630432	+	0.776244i	$0.282878\pi$
$978$	−20.2956	−	7.38700i	−0.648982	−	0.236210i
$979$	7.17809	+	2.61261i	0.229413	+	0.0834994i
$980$	3.48364	−	6.03384i	0.111281	−	0.192744i
$981$	−1.69030	−	2.92769i	−0.0539672	−	0.0934738i
$982$	−4.96585	−	28.1627i	−0.158467	−	0.898709i
$983$	16.2167	+	13.6075i	0.517234	+	0.434011i	0.863666	−	0.504064i	$-0.168163\pi$
$983$	16.2167	+	13.6075i	0.517234	+	0.434011i	−0.346432	+	0.938075i	$0.612607\pi$
$984$	−1.87679	+	1.57481i	−0.0598298	+	0.0502032i
$985$	2.10161	−	11.9188i	0.0669629	−	0.379766i
$986$	−27.4042	+	9.97430i	−0.872726	+	0.317646i
$987$	−13.3872			−0.426119
$988$	−5.35474	−	3.53982i	−0.170357	−	0.112617i
$989$	−0.651680			−0.0207222
$990$	2.87198	−	1.04531i	0.0912774	−	0.0332223i
$991$	8.41611	−	47.7301i	0.267347	−	1.51620i	−0.494922	−	0.868937i	$-0.664803\pi$
$991$	8.41611	−	47.7301i	0.267347	−	1.51620i	0.762269	−	0.647261i	$-0.224086\pi$
$992$	−17.9139	+	15.0316i	−0.568768	+	0.477253i
$993$	−20.4037	−	17.1207i	−0.647491	−	0.543310i
$994$	−2.04610	−	11.6040i	−0.0648982	−	0.368056i
$995$	31.0614	+	53.7999i	0.984711	+	1.70557i
$996$	4.10436	−	7.10897i	0.130052	−	0.225256i
$997$	−45.2094	−	16.4549i	−1.43180	−	0.521131i	−0.494351	−	0.869262i	$-0.664594\pi$
$997$	−45.2094	−	16.4549i	−1.43180	−	0.521131i	−0.937446	+	0.348131i	$0.886816\pi$
$998$	11.5586	+	4.20700i	0.365882	+	0.133170i
$999$	3.56877	−	6.18129i	0.112911	−	0.195567i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	627.2.r.c.100.6	✓	54
19.4	even	9	inner	627.2.r.c.232.6	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
627.2.r.c.100.6	✓	54	1.1	even	1	trivial
627.2.r.c.232.6	yes	54	19.4	even	9	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:	\( N \)	\(=\)	\( 627 = 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	627.r (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.14605 - 0.417129i) q^{2} +(0.173648 - 0.984808i) q^{3} +(-0.392648 + 0.329471i) q^{4} +(-1.91969 - 1.61081i) q^{5} +(-0.211782 - 1.20108i) q^{6} +(-0.627651 - 1.08712i) q^{7} +(-1.53217 + 2.65379i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(-2.87198 - 1.04531i) q^{10} +(0.500000 - 0.866025i) q^{11} +(0.256283 + 0.443895i) q^{12} +(-0.498897 - 2.82939i) q^{13} +(-1.17279 - 0.984089i) q^{14} +(-1.91969 + 1.61081i) q^{15} +(-0.470959 + 2.67094i) q^{16} +(-5.25098 + 1.91120i) q^{17} -1.21960 q^{18} +(-4.33060 + 0.495920i) q^{19} +1.28448 q^{20} +(-1.17960 + 0.429338i) q^{21} +(0.211782 - 1.20108i) q^{22} +(-0.572409 + 0.480308i) q^{23} +(2.34742 + 1.96972i) q^{24} +(0.222251 + 1.26045i) q^{25} +(-1.75198 - 3.03452i) q^{26} +(-0.500000 + 0.866025i) q^{27} +(0.604621 + 0.220064i) q^{28} +(4.02109 + 1.46356i) q^{29} +(-1.52815 + 2.64683i) q^{30} +(-4.14491 - 7.17919i) q^{31} +(-0.489849 - 2.77807i) q^{32} +(-0.766044 - 0.642788i) q^{33} +(-5.22068 + 4.38067i) q^{34} +(-0.546254 + 3.09796i) q^{35} +(0.481654 - 0.175308i) q^{36} -7.13754 q^{37} +(-4.75623 + 2.37477i) q^{38} -2.87303 q^{39} +(7.21603 - 2.62642i) q^{40} +(-0.138834 + 0.787365i) q^{41} +(-1.17279 + 0.984089i) q^{42} +(0.668091 + 0.560595i) q^{43} +(0.0890061 + 0.504779i) q^{44} +(1.25299 + 2.17024i) q^{45} +(-0.455660 + 0.789227i) q^{46} +(10.0214 + 3.64748i) q^{47} +(2.54858 + 0.927608i) q^{48} +(2.71211 - 4.69751i) q^{49} +(0.780482 + 1.35183i) q^{50} +(0.970341 + 5.50308i) q^{51} +(1.12809 + 0.946581i) q^{52} +(8.77332 - 7.36169i) q^{53} +(-0.211782 + 1.20108i) q^{54} +(-2.35484 + 0.857093i) q^{55} +3.84667 q^{56} +(-0.263614 + 4.35092i) q^{57} +5.21887 q^{58} +(1.33898 - 0.487350i) q^{59} +(0.223047 - 1.26496i) q^{60} +(1.17222 - 0.983611i) q^{61} +(-7.74493 - 6.49877i) q^{62} +(0.217981 + 1.23623i) q^{63} +(-4.43235 - 7.67706i) q^{64} +(-3.59987 + 6.23516i) q^{65} +(-1.14605 - 0.417129i) q^{66} +(1.88620 + 0.686521i) q^{67} +(1.43210 - 2.48047i) q^{68} +(0.373613 + 0.647117i) q^{69} +(0.666213 + 3.77828i) q^{70} +(5.89580 + 4.94716i) q^{71} +(2.34742 - 1.96972i) q^{72} +(1.66902 - 9.46548i) q^{73} +(-8.18000 + 2.97728i) q^{74} +1.27989 q^{75} +(1.53701 - 1.62153i) q^{76} -1.25530 q^{77} +(-3.29265 + 1.19843i) q^{78} +(0.571565 - 3.24151i) q^{79} +(5.20646 - 4.36874i) q^{80} +(0.766044 + 0.642788i) q^{81} +(0.169322 + 0.960274i) q^{82} +(-8.00749 - 13.8694i) q^{83} +(0.321712 - 0.557222i) q^{84} +(13.1588 + 4.78941i) q^{85} +(0.999509 + 0.363791i) q^{86} +(2.13958 - 3.70585i) q^{87} +(1.53217 + 2.65379i) q^{88} +(1.32646 + 7.52272i) q^{89} +(2.34126 + 1.96455i) q^{90} +(-2.76276 + 2.31823i) q^{91} +(0.0665078 - 0.377184i) q^{92} +(-7.78987 + 2.83528i) q^{93} +13.0065 q^{94} +(9.11221 + 6.02375i) q^{95} -2.82093 q^{96} +(-6.23168 + 2.26814i) q^{97} +(1.14875 - 6.51490i) q^{98} +(-0.766044 + 0.642788i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 3 q^{2} + 3 q^{4} + 3 q^{6} - 18 q^{7} - 12 q^{8} + 30 q^{10} + 27 q^{11} - 33 q^{12} + 9 q^{14} - 21 q^{16} - 24 q^{17} + 6 q^{18} + 3 q^{19} + 30 q^{20} - 3 q^{22} + 12 q^{23} - 39 q^{24} + 30 q^{25}+ \cdots - 54 q^{98}+O(q^{100}) \) 54 * q + 3 * q^2 + 3 * q^4 + 3 * q^6 - 18 * q^7 - 12 * q^8 + 30 * q^10 + 27 * q^11 - 33 * q^12 + 9 * q^14 - 21 * q^16 - 24 * q^17 + 6 * q^18 + 3 * q^19 + 30 * q^20 - 3 * q^22 + 12 * q^23 - 39 * q^24 + 30 * q^25 - 6 * q^26 - 27 * q^27 - 30 * q^28 + 33 * q^29 + 15 * q^30 + 15 * q^31 + 39 * q^32 + 3 * q^34 - 27 * q^35 + 3 * q^36 - 24 * q^37 + 15 * q^38 + 6 * q^39 + 84 * q^40 - 15 * q^41 + 9 * q^42 - 48 * q^43 + 6 * q^44 - 36 * q^46 + 3 * q^47 + 24 * q^48 - 21 * q^49 - 30 * q^50 + 3 * q^51 - 45 * q^52 - 21 * q^53 + 3 * q^54 + 21 * q^57 + 90 * q^58 + 45 * q^59 - 39 * q^60 - 21 * q^61 - 87 * q^62 - 9 * q^63 - 54 * q^64 + 6 * q^65 - 3 * q^66 + 9 * q^67 - 39 * q^69 + 15 * q^70 - 57 * q^71 - 39 * q^72 - 30 * q^73 - 105 * q^74 + 54 * q^75 - 6 * q^76 - 36 * q^77 + 51 * q^78 - 27 * q^79 - 3 * q^80 + 102 * q^82 - 63 * q^83 - 51 * q^84 + 60 * q^85 - 42 * q^86 - 27 * q^87 + 12 * q^88 + 21 * q^89 - 6 * q^90 - 72 * q^91 + 78 * q^92 - 6 * q^93 - 36 * q^94 + 63 * q^95 + 114 * q^96 + 45 * q^97 - 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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