LMFDB - Embedded newform 403.2.h.b.118.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(118,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("403.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.h (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			118.13
Character	$\chi$	$=$	403.118
Dual form			403.2.h.b.222.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.55799 q^{2} +(-1.19850 - 2.07586i) q^{3} +0.427341 q^{4} +(-0.908804 + 1.57410i) q^{5} +(-1.86725 - 3.23417i) q^{6} +(-1.80502 - 3.12639i) q^{7} -2.45019 q^{8} +(-1.37279 + 2.37775i) q^{9} +O(q^{10})$	\(q+1.55799 q^{2} +(-1.19850 - 2.07586i) q^{3} +0.427341 q^{4} +(-0.908804 + 1.57410i) q^{5} +(-1.86725 - 3.23417i) q^{6} +(-1.80502 - 3.12639i) q^{7} -2.45019 q^{8} +(-1.37279 + 2.37775i) q^{9} +(-1.41591 + 2.45243i) q^{10} +(-0.657884 + 1.13949i) q^{11} +(-0.512167 - 0.887099i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-2.81221 - 4.87090i) q^{14} +4.35680 q^{15} -4.67206 q^{16} +(-0.822939 - 1.42537i) q^{17} +(-2.13880 + 3.70451i) q^{18} +(-3.67118 - 6.35867i) q^{19} +(-0.388369 + 0.672675i) q^{20} +(-4.32663 + 7.49395i) q^{21} +(-1.02498 + 1.77532i) q^{22} +2.76670 q^{23} +(2.93655 + 5.08625i) q^{24} +(0.848150 + 1.46904i) q^{25} +(-0.778996 + 1.34926i) q^{26} -0.609825 q^{27} +(-0.771360 - 1.33603i) q^{28} +0.753167 q^{29} +6.78786 q^{30} +(3.74350 - 4.12143i) q^{31} -2.37865 q^{32} +3.15389 q^{33} +(-1.28213 - 2.22072i) q^{34} +6.56165 q^{35} +(-0.586650 + 1.01611i) q^{36} +(0.869574 + 1.50615i) q^{37} +(-5.71967 - 9.90677i) q^{38} +2.39700 q^{39} +(2.22674 - 3.85683i) q^{40} +(1.45616 - 2.52214i) q^{41} +(-6.74086 + 11.6755i) q^{42} +(-4.15151 - 7.19062i) q^{43} +(-0.281141 + 0.486950i) q^{44} +(-2.49520 - 4.32182i) q^{45} +4.31049 q^{46} +4.25594 q^{47} +(5.59945 + 9.69854i) q^{48} +(-3.01622 + 5.22425i) q^{49} +(1.32141 + 2.28875i) q^{50} +(-1.97258 + 3.41661i) q^{51} +(-0.213670 + 0.370088i) q^{52} +(4.95058 - 8.57466i) q^{53} -0.950103 q^{54} +(-1.19578 - 2.07114i) q^{55} +(4.42265 + 7.66026i) q^{56} +(-8.79981 + 15.2417i) q^{57} +1.17343 q^{58} +(2.40825 + 4.17121i) q^{59} +1.86184 q^{60} -10.1129 q^{61} +(5.83235 - 6.42116i) q^{62} +9.91170 q^{63} +5.63820 q^{64} +(-0.908804 - 1.57410i) q^{65} +4.91374 q^{66} +(-0.609051 + 1.05491i) q^{67} +(-0.351675 - 0.609119i) q^{68} +(-3.31588 - 5.74328i) q^{69} +10.2230 q^{70} +(-2.33787 + 4.04931i) q^{71} +(3.36361 - 5.82594i) q^{72} +(1.17426 - 2.03388i) q^{73} +(1.35479 + 2.34656i) q^{74} +(2.03301 - 3.52128i) q^{75} +(-1.56885 - 2.71732i) q^{76} +4.74999 q^{77} +3.73450 q^{78} +(-5.15237 - 8.92417i) q^{79} +(4.24599 - 7.35427i) q^{80} +(4.84926 + 8.39916i) q^{81} +(2.26868 - 3.92947i) q^{82} +(1.38928 - 2.40631i) q^{83} +(-1.84895 + 3.20247i) q^{84} +2.99156 q^{85} +(-6.46802 - 11.2029i) q^{86} +(-0.902669 - 1.56347i) q^{87} +(1.61194 - 2.79197i) q^{88} -15.2748 q^{89} +(-3.88751 - 6.73336i) q^{90} +3.61005 q^{91} +1.18232 q^{92} +(-13.0421 - 2.83145i) q^{93} +6.63073 q^{94} +13.3455 q^{95} +(2.85081 + 4.93775i) q^{96} +14.0402 q^{97} +(-4.69925 + 8.13934i) q^{98} +(-1.80628 - 3.12857i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9}+O(q^{10}) $ 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9} - 7 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 7 q^{14} + 8 q^{15} + 18 q^{16} - 8 q^{17} + 6 q^{18} + 3 q^{19} - 8 q^{20} + 13 q^{21} + 12 q^{22} - 14 q^{23} - 6 q^{24} - 26 q^{25} - 3 q^{26} + 28 q^{27} - 7 q^{28} - 18 q^{29} - 60 q^{30} - 9 q^{31} + 58 q^{32} - 14 q^{33} - 15 q^{34} + 50 q^{35} - 49 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 29 q^{40} - 5 q^{41} + 8 q^{42} - q^{43} - 22 q^{44} + 13 q^{45} + 34 q^{46} + 16 q^{47} - 49 q^{48} + 3 q^{49} - 35 q^{51} - 17 q^{52} + 30 q^{53} - 2 q^{54} + 21 q^{55} - 7 q^{56} + 34 q^{58} - 9 q^{59} - 38 q^{60} - 28 q^{61} - 62 q^{62} + 88 q^{63} + 56 q^{64} - 5 q^{65} + 140 q^{66} - 31 q^{67} - 39 q^{68} + 5 q^{69} + 56 q^{70} + q^{71} - 32 q^{72} - 10 q^{73} - 39 q^{74} - 2 q^{75} - 16 q^{76} + 76 q^{77} - 23 q^{79} - 22 q^{80} - 29 q^{81} - 10 q^{82} + 3 q^{83} + 52 q^{84} - 32 q^{85} + 4 q^{86} + 18 q^{87} - 10 q^{88} + 26 q^{89} + 35 q^{90} + 4 q^{91} - 94 q^{92} - 41 q^{93} + 70 q^{94} + 28 q^{95} - 23 q^{96} + 32 q^{97} - 38 q^{98} - 70 q^{99}+O(q^{100}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9 - 7 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 7 * q^14 + 8 * q^15 + 18 * q^16 - 8 * q^17 + 6 * q^18 + 3 * q^19 - 8 * q^20 + 13 * q^21 + 12 * q^22 - 14 * q^23 - 6 * q^24 - 26 * q^25 - 3 * q^26 + 28 * q^27 - 7 * q^28 - 18 * q^29 - 60 * q^30 - 9 * q^31 + 58 * q^32 - 14 * q^33 - 15 * q^34 + 50 * q^35 - 49 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 29 * q^40 - 5 * q^41 + 8 * q^42 - q^43 - 22 * q^44 + 13 * q^45 + 34 * q^46 + 16 * q^47 - 49 * q^48 + 3 * q^49 - 35 * q^51 - 17 * q^52 + 30 * q^53 - 2 * q^54 + 21 * q^55 - 7 * q^56 + 34 * q^58 - 9 * q^59 - 38 * q^60 - 28 * q^61 - 62 * q^62 + 88 * q^63 + 56 * q^64 - 5 * q^65 + 140 * q^66 - 31 * q^67 - 39 * q^68 + 5 * q^69 + 56 * q^70 + q^71 - 32 * q^72 - 10 * q^73 - 39 * q^74 - 2 * q^75 - 16 * q^76 + 76 * q^77 - 23 * q^79 - 22 * q^80 - 29 * q^81 - 10 * q^82 + 3 * q^83 + 52 * q^84 - 32 * q^85 + 4 * q^86 + 18 * q^87 - 10 * q^88 + 26 * q^89 + 35 * q^90 + 4 * q^91 - 94 * q^92 - 41 * q^93 + 70 * q^94 + 28 * q^95 - 23 * q^96 + 32 * q^97 - 38 * q^98 - 70 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.55799			1.10167			0.550834	−	0.834615i	$-0.314310\pi$
$2$	1.55799			1.10167			0.550834	+	0.834615i	$0.314310\pi$
$3$	−1.19850	−	2.07586i	−0.691953	−	1.19850i	−0.971197	−	0.238278i	$-0.923417\pi$
$3$	−1.19850	−	2.07586i	−0.691953	−	1.19850i	0.279244	−	0.960220i	$-0.409916\pi$
$4$	0.427341			0.213670
$5$	−0.908804	+	1.57410i	−0.406430	+	0.703957i	−0.994487	−	0.104863i	$-0.966560\pi$
$5$	−0.908804	+	1.57410i	−0.406430	+	0.703957i	0.588057	+	0.808819i	$0.299893\pi$
$6$	−1.86725	−	3.23417i	−0.762302	−	1.32035i
$7$	−1.80502	−	3.12639i	−0.682235	−	1.18167i	−0.974297	−	0.225266i	$-0.927675\pi$
$7$	−1.80502	−	3.12639i	−0.682235	−	1.18167i	0.292063	−	0.956399i	$-0.405658\pi$
$8$	−2.45019			−0.866274
$9$	−1.37279	+	2.37775i	−0.457598	+	0.792583i
$10$	−1.41591	+	2.45243i	−0.447750	+	0.775526i
$11$	−0.657884	+	1.13949i	−0.198360	+	0.343569i	−0.947997	−	0.318280i	$-0.896895\pi$
$11$	−0.657884	+	1.13949i	−0.198360	+	0.343569i	0.749637	+	0.661849i	$0.230228\pi$
$12$	−0.512167	−	0.887099i	−0.147850	−	0.256083i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i
$14$	−2.81221	−	4.87090i	−0.751596	−	1.30180i
$15$	4.35680			1.12492
$16$	−4.67206			−1.16802
$17$	−0.822939	−	1.42537i	−0.199592	−	0.345704i	0.748804	−	0.662791i	$-0.230628\pi$
$17$	−0.822939	−	1.42537i	−0.199592	−	0.345704i	−0.948396	+	0.317088i	$0.897295\pi$
$18$	−2.13880	+	3.70451i	−0.504121	+	0.873162i
$19$	−3.67118	−	6.35867i	−0.842227	−	1.45878i	−0.888008	−	0.459828i	$-0.847911\pi$
$19$	−3.67118	−	6.35867i	−0.842227	−	1.45878i	0.0457808	−	0.998952i	$-0.485422\pi$
$20$	−0.388369	+	0.672675i	−0.0868419	+	0.150415i
$21$	−4.32663	+	7.49395i	−0.944149	+	1.63531i
$22$	−1.02498	+	1.77532i	−0.218526	+	0.378498i
$23$	2.76670			0.576896			0.288448	−	0.957495i	$-0.406861\pi$
$23$	2.76670			0.576896			0.288448	+	0.957495i	$0.406861\pi$
$24$	2.93655	+	5.08625i	0.599421	+	1.03823i
$25$	0.848150	+	1.46904i	0.169630	+	0.293808i
$26$	−0.778996	+	1.34926i	−0.152774	+	0.264612i
$27$	−0.609825			−0.117361
$28$	−0.771360	−	1.33603i	−0.145773	−	0.252487i
$29$	0.753167			0.139860			0.0699298	−	0.997552i	$-0.477722\pi$
$29$	0.753167			0.139860			0.0699298	+	0.997552i	$0.477722\pi$
$30$	6.78786			1.23929
$31$	3.74350	−	4.12143i	0.672353	−	0.740231i
$31$	3.74350	−	4.12143i	0.672353	−	0.740231i
$32$	−2.37865			−0.420490
$33$	3.15389			0.549022
$34$	−1.28213	−	2.22072i	−0.219884	−	0.380850i
$35$	6.56165			1.10912
$36$	−0.586650	+	1.01611i	−0.0977751	+	0.169351i
$37$	0.869574	+	1.50615i	0.142957	+	0.247609i	0.928609	−	0.371060i	$-0.121006\pi$
$37$	0.869574	+	1.50615i	0.142957	+	0.247609i	−0.785652	+	0.618669i	$0.787672\pi$
$38$	−5.71967	−	9.90677i	−0.927854	−	1.60709i
$39$	2.39700			0.383826
$40$	2.22674	−	3.85683i	0.352079	−	0.609819i
$41$	1.45616	−	2.52214i	0.227413	−	0.393891i	−0.729627	−	0.683845i	$-0.760307\pi$
$41$	1.45616	−	2.52214i	0.227413	−	0.393891i	0.957041	+	0.289954i	$0.0936398\pi$
$42$	−6.74086	+	11.6755i	−1.04014	+	1.80157i
$43$	−4.15151	−	7.19062i	−0.633099	−	1.09656i	−0.986914	−	0.161245i	$-0.948449\pi$
$43$	−4.15151	−	7.19062i	−0.633099	−	1.09656i	0.353815	−	0.935315i	$-0.384884\pi$
$44$	−0.281141	+	0.486950i	−0.0423835	+	0.0734104i
$45$	−2.49520	−	4.32182i	−0.371963	−	0.644258i
$46$	4.31049			0.635548
$47$	4.25594			0.620793			0.310396	−	0.950607i	$-0.399538\pi$
$47$	4.25594			0.620793			0.310396	+	0.950607i	$0.399538\pi$
$48$	5.59945	+	9.69854i	0.808212	+	1.39986i
$49$	−3.01622	+	5.22425i	−0.430889	+	0.746321i
$50$	1.32141	+	2.28875i	0.186876	+	0.323678i
$51$	−1.97258	+	3.41661i	−0.276217	+	0.478421i
$52$	−0.213670	+	0.370088i	−0.0296307	+	0.0513219i
$53$	4.95058	−	8.57466i	0.680015	−	1.17782i	−0.294961	−	0.955509i	$-0.595307\pi$
$53$	4.95058	−	8.57466i	0.680015	−	1.17782i	0.974976	−	0.222311i	$-0.0713600\pi$
$54$	−0.950103			−0.129293
$55$	−1.19578	−	2.07114i	−0.161238	−	0.279273i
$56$	4.42265	+	7.66026i	0.591002	+	1.02365i
$57$	−8.79981	+	15.2417i	−1.16556	+	2.01881i
$58$	1.17343			0.154079
$59$	2.40825	+	4.17121i	0.313528	+	0.543046i	0.979123	−	0.203267i	$-0.0651558\pi$
$59$	2.40825	+	4.17121i	0.313528	+	0.543046i	−0.665596	+	0.746312i	$0.731823\pi$
$60$	1.86184			0.240362
$61$	−10.1129			−1.29483			−0.647415	−	0.762138i	$-0.724150\pi$
$61$	−10.1129			−1.29483			−0.647415	+	0.762138i	$0.724150\pi$
$62$	5.83235	−	6.42116i	0.740709	−	0.815488i
$63$	9.91170			1.24876
$64$	5.63820			0.704775
$65$	−0.908804	−	1.57410i	−0.112723	−	0.195242i
$66$	4.91374			0.604839
$67$	−0.609051	+	1.05491i	−0.0744074	+	0.128877i	−0.900828	−	0.434175i	$-0.857040\pi$
$67$	−0.609051	+	1.05491i	−0.0744074	+	0.128877i	0.826421	+	0.563053i	$0.190373\pi$
$68$	−0.351675	−	0.609119i	−0.0426469	−	0.0738666i
$69$	−3.31588	−	5.74328i	−0.399185	−	0.691409i
$70$	10.2230			1.22188
$71$	−2.33787	+	4.04931i	−0.277454	+	0.480565i	−0.970751	−	0.240087i	$-0.922824\pi$
$71$	−2.33787	+	4.04931i	−0.277454	+	0.480565i	0.693297	+	0.720652i	$0.256157\pi$
$72$	3.36361	−	5.82594i	0.396405	−	0.686594i
$73$	1.17426	−	2.03388i	0.137437	−	0.238048i	−0.789089	−	0.614279i	$-0.789447\pi$
$73$	1.17426	−	2.03388i	0.137437	−	0.238048i	0.926526	+	0.376231i	$0.122780\pi$
$74$	1.35479	+	2.34656i	0.157491	+	0.272783i
$75$	2.03301	−	3.52128i	0.234752	−	0.406602i
$76$	−1.56885	−	2.71732i	−0.179959	−	0.311698i
$77$	4.74999			0.541311
$78$	3.73450			0.422849
$79$	−5.15237	−	8.92417i	−0.579687	−	1.00405i	−0.995515	−	0.0946040i	$-0.969842\pi$
$79$	−5.15237	−	8.92417i	−0.579687	−	1.00405i	0.415828	−	0.909443i	$-0.363492\pi$
$80$	4.24599	−	7.35427i	0.474716	−	0.822232i
$81$	4.84926	+	8.39916i	0.538806	+	0.933240i
$82$	2.26868	−	3.92947i	0.250534	−	0.433937i
$83$	1.38928	−	2.40631i	0.152494	−	0.264127i	−0.779650	−	0.626216i	$-0.784603\pi$
$83$	1.38928	−	2.40631i	0.152494	−	0.264127i	0.932144	+	0.362089i	$0.117936\pi$
$84$	−1.84895	+	3.20247i	−0.201737	+	0.349418i
$85$	2.99156			0.324481
$86$	−6.46802	−	11.2029i	−0.697464	−	1.20804i
$87$	−0.902669	−	1.56347i	−0.0967763	−	0.167622i
$88$	1.61194	−	2.79197i	0.171834	−	0.297625i
$89$	−15.2748			−1.61913			−0.809563	−	0.587033i	$-0.800296\pi$
$89$	−15.2748			−1.61913			−0.809563	+	0.587033i	$0.800296\pi$
$90$	−3.88751	−	6.73336i	−0.409779	−	0.709758i
$91$	3.61005			0.378436
$92$	1.18232			0.123266
$93$	−13.0421	−	2.83145i	−1.35240	−	0.293608i
$94$	6.63073			0.683907
$95$	13.3455			1.36922
$96$	2.85081	+	4.93775i	0.290960	+	0.503957i
$97$	14.0402			1.42557			0.712785	−	0.701382i	$-0.247433\pi$
$97$	14.0402			1.42557			0.712785	+	0.701382i	$0.247433\pi$
$98$	−4.69925	+	8.13934i	−0.474696	+	0.822197i
$99$	−1.80628	−	3.12857i	−0.181538	−	0.314433i
$100$	0.362449	+	0.627780i	0.0362449	+	0.0627780i
$101$	9.11956			0.907430			0.453715	−	0.891147i	$-0.350098\pi$
$101$	9.11956			0.907430			0.453715	+	0.891147i	$0.350098\pi$
$102$	−3.07327	+	5.32306i	−0.304299	+	0.527061i
$103$	1.77800	−	3.07958i	0.175191	−	0.303440i	−0.765036	−	0.643987i	$-0.777279\pi$
$103$	1.77800	−	3.07958i	0.175191	−	0.303440i	0.940227	+	0.340547i	$0.110612\pi$
$104$	1.22510	−	2.12193i	0.120131	−	0.208072i
$105$	−7.86413	−	13.6211i	−0.767460	−	1.32928i
$106$	7.71297	−	13.3593i	0.749150	−	1.29757i
$107$	5.51002	+	9.54364i	0.532674	+	0.922618i	0.999272	+	0.0381489i	$0.0121461\pi$
$107$	5.51002	+	9.54364i	0.532674	+	0.922618i	−0.466598	+	0.884469i	$0.654521\pi$
$108$	−0.260603			−0.0250765
$109$	−17.6509			−1.69065			−0.845326	−	0.534250i	$-0.820594\pi$
$109$	−17.6509			−1.69065			−0.845326	+	0.534250i	$0.820594\pi$
$110$	−1.86301	−	3.22683i	−0.177631	−	0.307666i
$111$	2.08437	−	3.61023i	0.197839	−	0.342668i
$112$	8.43318	+	14.6067i	0.796861	+	1.38020i
$113$	−2.95440	+	5.11717i	−0.277926	+	0.481383i	−0.970869	−	0.239610i	$-0.922980\pi$
$113$	−2.95440	+	5.11717i	−0.277926	+	0.481383i	0.692943	+	0.720993i	$0.256314\pi$
$114$	−13.7100	+	23.7465i	−1.28406	+	2.22406i
$115$	−2.51439	+	4.35505i	−0.234468	+	0.406110i
$116$	0.321859			0.0298839
$117$	−1.37279	−	2.37775i	−0.126915	−	0.219823i
$118$	3.75204	+	6.49872i	0.345403	+	0.598256i
$119$	−2.97085	+	5.14566i	−0.272337	+	0.471702i
$120$	−10.6750			−0.974489
$121$	4.63438	+	8.02698i	0.421307	+	0.729725i
$122$	−15.7559			−1.42647
$123$	−6.98080			−0.629437
$124$	1.59975	−	1.76125i	0.143662	−	0.158165i
$125$	−12.1713			−1.08863
$126$	15.4424			1.37571
$127$	7.95139	+	13.7722i	0.705572	+	1.22209i	0.966485	+	0.256724i	$0.0826431\pi$
$127$	7.95139	+	13.7722i	0.705572	+	1.22209i	−0.260913	+	0.965362i	$0.584024\pi$
$128$	13.5416			1.19692
$129$	−9.95115	+	17.2359i	−0.876150	+	1.51754i
$130$	−1.41591	−	2.45243i	−0.124184	−	0.215092i
$131$	−8.44698	−	14.6306i	−0.738016	−	1.27828i	−0.953387	−	0.301749i	$-0.902429\pi$
$131$	−8.44698	−	14.6306i	−0.738016	−	1.27828i	0.215371	−	0.976532i	$-0.430904\pi$
$132$	1.34779			0.117310
$133$	−13.2531	+	22.9551i	−1.14919	+	1.99046i
$134$	−0.948897	+	1.64354i	−0.0819722	+	0.141980i
$135$	0.554212	−	0.959923i	0.0476989	−	0.0826170i
$136$	2.01636	+	3.49244i	0.172901	+	0.299474i
$137$	−4.65469	+	8.06215i	−0.397677	+	0.688796i	−0.993439	−	0.114365i	$-0.963517\pi$
$137$	−4.65469	+	8.06215i	−0.397677	+	0.688796i	0.595762	+	0.803161i	$0.296850\pi$
$138$	−5.16612	−	8.94798i	−0.439769	−	0.761703i
$139$	−10.8658			−0.921623			−0.460811	−	0.887498i	$-0.652442\pi$
$139$	−10.8658			−0.921623			−0.460811	+	0.887498i	$0.652442\pi$
$140$	2.80406			0.236986
$141$	−5.10074	−	8.83474i	−0.429560	−	0.744019i
$142$	−3.64239	+	6.30880i	−0.305662	+	0.529423i
$143$	−0.657884	−	1.13949i	−0.0550150	−	0.0952888i
$144$	6.41378	−	11.1090i	0.534481	−	0.925749i
$145$	−0.684482	+	1.18556i	−0.0568431	+	0.0984552i
$146$	1.82949	−	3.16877i	0.151410	−	0.262250i
$147$	14.4597			1.19262
$148$	0.371604	+	0.643637i	0.0305457	+	0.0529067i
$149$	−6.60854	−	11.4463i	−0.541392	−	0.937719i	−0.998824	−	0.0484746i	$-0.984564\pi$
$149$	−6.60854	−	11.4463i	−0.541392	−	0.937719i	0.457432	−	0.889245i	$-0.348769\pi$
$150$	3.16742	−	5.48613i	0.258618	−	0.447940i
$151$	−5.14020			−0.418304			−0.209152	−	0.977883i	$-0.567070\pi$
$151$	−5.14020			−0.418304			−0.209152	+	0.977883i	$0.567070\pi$
$152$	8.99510	+	15.5800i	0.729599	+	1.26370i
$153$	4.51890			0.365332
$154$	7.40044			0.596345
$155$	3.08542	+	9.63820i	0.247827	+	0.774159i
$156$	1.02433			0.0820123
$157$	18.3368			1.46344			0.731720	−	0.681606i	$-0.238718\pi$
$157$	18.3368			1.46344			0.731720	+	0.681606i	$0.238718\pi$
$158$	−8.02735	−	13.9038i	−0.638622	−	1.10613i
$159$	−23.7330			−1.88215
$160$	2.16173	−	3.74423i	0.170900	−	0.296007i
$161$	−4.99396	−	8.64978i	−0.393579	−	0.681698i
$162$	7.55510	+	13.0858i	0.593585	+	1.02812i
$163$	−7.63039			−0.597658			−0.298829	−	0.954307i	$-0.596596\pi$
$163$	−7.63039			−0.597658			−0.298829	+	0.954307i	$0.596596\pi$
$164$	0.622274	−	1.07781i	0.0485915	−	0.0841629i
$165$	−2.86627	+	4.96452i	−0.223139	+	0.386488i
$166$	2.16449	−	3.74901i	0.167997	−	0.290980i
$167$	−6.39847	−	11.0825i	−0.495128	−	0.857587i	0.504856	−	0.863204i	$-0.331546\pi$
$167$	−6.39847	−	11.0825i	−0.495128	−	0.857587i	−0.999984	+	0.00561623i	$0.998212\pi$
$168$	10.6011	−	18.3616i	0.817891	−	1.41663i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	4.66083			0.357469
$171$	20.1591			1.54161
$172$	−1.77411	−	3.07285i	−0.135274	−	0.234302i
$173$	7.90130	−	13.6855i	0.600725	−	1.04049i	−0.391987	−	0.919971i	$-0.628212\pi$
$173$	7.90130	−	13.6855i	0.600725	−	1.04049i	0.992712	−	0.120515i	$-0.0384546\pi$
$174$	−1.40635	−	2.43587i	−0.106615	−	0.184663i
$175$	3.06186	−	5.30330i	0.231455	−	0.400892i
$176$	3.07368	−	5.32376i	0.231687	−	0.401294i
$177$	5.77257	−	9.99838i	0.433893	−	0.751524i
$178$	−23.7980			−1.78374
$179$	−4.39967	−	7.62046i	−0.328847	−	0.569580i	0.653436	−	0.756981i	$-0.273327\pi$
$179$	−4.39967	−	7.62046i	−0.328847	−	0.569580i	−0.982283	+	0.187402i	$0.939993\pi$
$180$	−1.06630	−	1.84689i	−0.0794774	−	0.137659i
$181$	−8.00823	+	13.8707i	−0.595247	+	1.03100i	0.398265	+	0.917270i	$0.369612\pi$
$181$	−8.00823	+	13.8707i	−0.595247	+	1.03100i	−0.993512	+	0.113728i	$0.963721\pi$
$182$	5.62443			0.416910
$183$	12.1203	+	20.9930i	0.895961	+	1.55185i
$184$	−6.77894			−0.499750
$185$	−3.16109			−0.232408
$186$	−20.3195	−	4.41138i	−1.48990	−	0.323458i
$187$	2.16559			0.158364
$188$	1.81874			0.132645
$189$	1.10075	+	1.90655i	0.0800677	+	0.138681i
$190$	20.7923			1.50843
$191$	−8.40550	+	14.5587i	−0.608200	+	1.05343i	0.383337	+	0.923609i	$0.374775\pi$
$191$	−8.40550	+	14.5587i	−0.608200	+	1.05343i	−0.991537	+	0.129825i	$0.958558\pi$
$192$	−6.75737	−	11.7041i	−0.487671	−	0.844671i
$193$	−10.9057	−	18.8892i	−0.785009	−	1.35967i	−0.928994	−	0.370095i	$-0.879325\pi$
$193$	−10.9057	−	18.8892i	−0.785009	−	1.35967i	0.143985	−	0.989580i	$-0.454008\pi$
$194$	21.8746			1.57050
$195$	−2.17840	+	3.77310i	−0.155998	+	0.270197i
$196$	−1.28895	+	2.23253i	−0.0920681	+	0.159467i
$197$	−0.395261	+	0.684613i	−0.0281612	+	0.0487766i	−0.879763	−	0.475413i	$-0.842299\pi$
$197$	−0.395261	+	0.684613i	−0.0281612	+	0.0487766i	0.851601	+	0.524190i	$0.175632\pi$
$198$	−2.81417	−	4.87428i	−0.199994	−	0.346400i
$199$	9.59845	−	16.6250i	0.680416	−	1.17852i	−0.294438	−	0.955671i	$-0.595132\pi$
$199$	9.59845	−	16.6250i	0.680416	−	1.17852i	0.974854	−	0.222845i	$-0.0715343\pi$
$200$	−2.07813	−	3.59943i	−0.146946	−	0.254518i
$201$	2.91978			0.205946
$202$	14.2082			0.999686
$203$	−1.35948	−	2.35470i	−0.0954171	−	0.165267i
$204$	−0.842964	+	1.46006i	−0.0590193	+	0.102224i
$205$	2.64672	+	4.58425i	0.184855	+	0.320178i
$206$	2.77011	−	4.79797i	0.193002	−	0.334290i
$207$	−3.79811	+	6.57851i	−0.263987	+	0.457238i
$208$	2.33603	−	4.04612i	0.161975	−	0.280548i
$209$	9.66085			0.668255
$210$	−12.2522	−	21.2215i	−0.845485	−	1.46442i
$211$	9.22963	+	15.9862i	0.635394	+	1.10053i	0.986432	+	0.164173i	$0.0524955\pi$
$211$	9.22963	+	15.9862i	0.635394	+	1.10053i	−0.351038	+	0.936361i	$0.614171\pi$
$212$	2.11558	−	3.66430i	0.145299	−	0.251665i
$213$	11.2077			0.767942
$214$	8.58457	+	14.8689i	0.586829	+	1.01642i
$215$	15.0916			1.02924
$216$	1.49419			0.101667
$217$	−19.6423	−	4.26437i	−1.33341	−	0.289484i
$218$	−27.5000			−1.86254
$219$	−5.62941			−0.380400
$220$	−0.511004	−	0.885084i	−0.0344518	−	0.0596724i
$221$	1.64588			0.110714
$222$	3.24743	−	5.62471i	0.217953	−	0.377506i
$223$	6.02421	+	10.4342i	0.403411	+	0.698728i	0.994135	−	0.108145i	$-0.0344911\pi$
$223$	6.02421	+	10.4342i	0.403411	+	0.698728i	−0.590724	+	0.806874i	$0.701158\pi$
$224$	4.29352	+	7.43660i	0.286873	+	0.496879i
$225$	−4.65734			−0.310489
$226$	−4.60293	+	7.97251i	−0.306182	+	0.530323i
$227$	4.79198	−	8.29995i	0.318055	−	0.550887i	−0.662027	−	0.749480i	$-0.730304\pi$
$227$	4.79198	−	8.29995i	0.318055	−	0.550887i	0.980082	+	0.198593i	$0.0636370\pi$
$228$	−3.76051	+	6.51340i	−0.249046	+	0.431361i
$229$	−1.50303	−	2.60333i	−0.0993231	−	0.172033i	0.812082	−	0.583544i	$-0.198334\pi$
$229$	−1.50303	−	2.60333i	−0.0993231	−	0.172033i	−0.911405	+	0.411511i	$0.865001\pi$
$230$	−3.91740	+	6.78513i	−0.258305	+	0.447398i
$231$	−5.69285	−	9.86030i	−0.374562	−	0.648760i
$232$	−1.84540			−0.121157
$233$	23.6608			1.55007			0.775034	−	0.631920i	$-0.217733\pi$
$233$	23.6608			1.55007			0.775034	+	0.631920i	$0.217733\pi$
$234$	−2.13880	−	3.70451i	−0.139818	−	0.242172i
$235$	−3.86782	+	6.69926i	−0.252309	+	0.437011i
$236$	1.02914	+	1.78253i	0.0669915	+	0.116033i
$237$	−12.3502	+	21.3912i	−0.802232	+	1.38951i
$238$	−4.62856	+	8.01690i	−0.300025	+	0.519659i
$239$	0.991011	−	1.71648i	0.0641032	−	0.111030i	−0.832193	−	0.554487i	$-0.812915\pi$
$239$	0.991011	−	1.71648i	0.0641032	−	0.111030i	0.896296	+	0.443457i	$0.146248\pi$
$240$	−20.3552			−1.31392
$241$	−12.3362	−	21.3669i	−0.794643	−	1.37636i	−0.923066	−	0.384643i	$-0.874325\pi$
$241$	−12.3362	−	21.3669i	−0.794643	−	1.37636i	0.128422	−	0.991720i	$-0.459009\pi$
$242$	7.22032	+	12.5060i	0.464140	+	0.803914i
$243$	10.7089	−	18.5484i	0.686977	−	1.18988i
$244$	−4.32167			−0.276667
$245$	−5.48231	−	9.49563i	−0.350252	−	0.606654i
$246$	−10.8760			−0.693430
$247$	7.34236			0.467183
$248$	−9.17229	+	10.0983i	−0.582441	+	0.641243i
$249$	−6.66021			−0.422074
$250$	−18.9627			−1.19931
$251$	9.59668	+	16.6219i	0.605737	+	1.04917i	0.991935	+	0.126751i	$0.0404550\pi$
$251$	9.59668	+	16.6219i	0.605737	+	1.04917i	−0.386197	+	0.922416i	$0.626212\pi$
$252$	4.23567			0.266822
$253$	−1.82017	+	3.15262i	−0.114433	+	0.198204i
$254$	12.3882	+	21.4570i	0.777305	+	1.34633i
$255$	−3.58538	−	6.21006i	−0.224525	−	0.388889i
$256$	9.82128			0.613830
$257$	13.9975	−	24.2444i	0.873141	−	1.51232i	0.0144108	−	0.999896i	$-0.495413\pi$
$257$	13.9975	−	24.2444i	0.873141	−	1.51232i	0.858730	−	0.512428i	$-0.171254\pi$
$258$	−15.5038	+	26.8534i	−0.965225	+	1.67182i
$259$	3.13920	−	5.43726i	0.195061	−	0.337855i
$260$	−0.388369	−	0.672675i	−0.0240856	−	0.0417175i
$261$	−1.03394	+	1.79084i	−0.0639995	+	0.110850i
$262$	−13.1603	−	22.7944i	−0.813048	−	1.40824i
$263$	2.79753			0.172503			0.0862514	−	0.996273i	$-0.472511\pi$
$263$	2.79753			0.172503			0.0862514	+	0.996273i	$0.472511\pi$
$264$	−7.72764			−0.475603
$265$	8.99822	+	15.5854i	0.552756	+	0.957402i
$266$	−20.6483	+	35.7639i	−1.26603	+	2.19282i
$267$	18.3068	+	31.7083i	1.12036	+	1.94052i
$268$	−0.260272	+	0.450805i	−0.0158987	+	0.0275373i
$269$	12.4313	−	21.5316i	0.757948	−	1.31280i	−0.185947	−	0.982560i	$-0.559535\pi$
$269$	12.4313	−	21.5316i	0.757948	−	1.31280i	0.943895	−	0.330245i	$-0.107131\pi$
$270$	0.863457	−	1.49555i	0.0525483	−	0.0910164i
$271$	−20.9959			−1.27541			−0.637704	−	0.770281i	$-0.720116\pi$
$271$	−20.9959			−1.27541			−0.637704	+	0.770281i	$0.720116\pi$
$272$	3.84482	+	6.65943i	0.233127	+	0.403787i
$273$	−4.32663	−	7.49395i	−0.261860	−	0.453554i
$274$	−7.25197	+	12.5608i	−0.438107	+	0.758824i
$275$	−2.23194			−0.134591
$276$	−1.41701	−	2.45433i	−0.0852940	−	0.147734i
$277$	5.93564			0.356638			0.178319	−	0.983973i	$-0.442934\pi$
$277$	5.93564			0.356638			0.178319	+	0.983973i	$0.442934\pi$
$278$	−16.9288			−1.01532
$279$	4.66067	+	14.5590i	0.279027	+	0.871623i
$280$	−16.0773			−0.960803
$281$	6.61510			0.394624			0.197312	−	0.980341i	$-0.436779\pi$
$281$	6.61510			0.394624			0.197312	+	0.980341i	$0.436779\pi$
$282$	−7.94691	−	13.7645i	−0.473232	−	0.819661i
$283$	6.44100			0.382878			0.191439	−	0.981505i	$-0.438685\pi$
$283$	6.44100			0.382878			0.191439	+	0.981505i	$0.438685\pi$
$284$	−0.999068	+	1.73044i	−0.0592838	+	0.102682i
$285$	−15.9946	−	27.7035i	−0.947439	−	1.64101i
$286$	−1.02498	−	1.77532i	−0.0606083	−	0.104977i
$287$	−10.5136			−0.620597
$288$	3.26540	−	5.65584i	0.192416	−	0.333274i
$289$	7.14554	−	12.3764i	0.420326	−	0.728026i
$290$	−1.06642	+	1.84709i	−0.0626222	+	0.108465i
$291$	−16.8272	−	29.1456i	−0.986428	−	1.70854i
$292$	0.501810	−	0.869161i	0.0293662	−	0.0508638i
$293$	−13.4604	−	23.3142i	−0.786367	−	1.36203i	−0.928179	−	0.372135i	$-0.878626\pi$
$293$	−13.4604	−	23.3142i	−0.786367	−	1.36203i	0.141811	−	0.989894i	$-0.454707\pi$
$294$	22.5282			1.31387
$295$	−8.75451			−0.509708
$296$	−2.13062	−	3.69035i	−0.123840	−	0.214497i
$297$	0.401194	−	0.694889i	0.0232797	−	0.0403215i
$298$	−10.2961	−	17.8333i	−0.596434	−	1.03305i
$299$	−1.38335	+	2.39603i	−0.0800011	+	0.138566i
$300$	0.868788	−	1.50479i	0.0501595	−	0.0868788i
$301$	−14.9871	+	25.9585i	−0.863845	+	1.49622i
$302$	−8.00839			−0.460831
$303$	−10.9298	−	18.9309i	−0.627899	−	1.08755i
$304$	17.1520	+	29.7081i	0.983734	+	1.70388i
$305$	9.19068	−	15.9187i	0.526257	−	0.911504i
$306$	7.04042			0.402474
$307$	4.92019	+	8.52203i	0.280810	+	0.486378i	0.971585	−	0.236693i	$-0.0760635\pi$
$307$	4.92019	+	8.52203i	0.280810	+	0.486378i	−0.690774	+	0.723071i	$0.742730\pi$
$308$	2.02986			0.115662
$309$	−8.52371			−0.484897
$310$	4.80705	+	15.0162i	0.273022	+	0.852865i
$311$	25.0139			1.41841			0.709205	−	0.705002i	$-0.249054\pi$
$311$	25.0139			1.41841			0.709205	+	0.705002i	$0.249054\pi$
$312$	−5.87310			−0.332499
$313$	−4.59944	−	7.96647i	−0.259976	−	0.450291i	0.706259	−	0.707953i	$-0.250381\pi$
$313$	−4.59944	−	7.96647i	−0.259976	−	0.450291i	−0.966235	+	0.257662i	$0.917048\pi$
$314$	28.5687			1.61222
$315$	−9.00780	+	15.6020i	−0.507532	+	0.879071i
$316$	−2.20182	−	3.81366i	−0.123862	−	0.214535i
$317$	13.6909	+	23.7134i	0.768958	+	1.33187i	0.938128	+	0.346288i	$0.112558\pi$
$317$	13.6909	+	23.7134i	0.768958	+	1.33187i	−0.169170	+	0.985587i	$0.554109\pi$
$318$	−36.9759			−2.07351
$319$	−0.495497	+	0.858226i	−0.0277425	+	0.0480514i
$320$	−5.12402	+	8.87506i	−0.286441	+	0.496131i
$321$	13.2075	−	22.8761i	0.737171	−	1.27682i
$322$	−7.78054	−	13.4763i	−0.433593	−	0.751005i
$323$	−6.04232	+	10.4656i	−0.336204	+	0.582322i
$324$	2.07228	+	3.58930i	0.115127	+	0.199406i
$325$	−1.69630			−0.0940938
$326$	−11.8881			−0.658421
$327$	21.1546	+	36.6409i	1.16985	+	2.02624i
$328$	−3.56786	+	6.17971i	−0.197002	+	0.341218i
$329$	−7.68208	−	13.3057i	−0.423527	−	0.733570i
$330$	−4.46563	+	7.73469i	−0.245825	+	0.425781i
$331$	−8.55812	+	14.8231i	−0.470397	+	0.814751i	−0.999427	−	0.0338522i	$-0.989222\pi$
$331$	−8.55812	+	14.8231i	−0.470397	+	0.814751i	0.529030	+	0.848603i	$0.322556\pi$
$332$	0.593697	−	1.02831i	0.0325834	−	0.0564360i
$333$	−4.77498			−0.261667
$334$	−9.96876	−	17.2664i	−0.545467	−	0.944776i
$335$	−1.10702	−	1.91741i	−0.0604828	−	0.104759i
$336$	20.2143	−	35.0122i	1.10278	−	1.91007i
$337$	9.62912			0.524531			0.262266	−	0.964996i	$-0.415530\pi$
$337$	9.62912			0.524531			0.262266	+	0.964996i	$0.415530\pi$
$338$	−0.778996	−	1.34926i	−0.0423718	−	0.0733901i
$339$	14.1634			0.769248
$340$	1.27842			0.0693318
$341$	2.23354	+	6.97710i	0.120953	+	0.377831i
$342$	31.4077			1.69834
$343$	−3.49294			−0.188601
$344$	10.1720	+	17.6184i	0.548437	+	0.949921i
$345$	12.0539			0.648963
$346$	12.3102	−	21.3218i	0.661799	−	1.14627i
$347$	−5.38246	−	9.32270i	−0.288946	−	0.500469i	0.684613	−	0.728907i	$-0.259971\pi$
$347$	−5.38246	−	9.32270i	−0.288946	−	0.500469i	−0.973558	+	0.228438i	$0.926638\pi$
$348$	−0.385747	−	0.668134i	−0.0206782	−	0.0358157i
$349$	−6.64494			−0.355695			−0.177848	−	0.984058i	$-0.556913\pi$
$349$	−6.64494			−0.355695			−0.177848	+	0.984058i	$0.556913\pi$
$350$	4.77036	−	8.26250i	0.254986	−	0.441649i
$351$	0.304913	−	0.528124i	0.0162750	−	0.0281892i
$352$	1.56488	−	2.71045i	0.0834083	−	0.144467i
$353$	15.3324	+	26.5564i	0.816059	+	1.41346i	0.908565	+	0.417744i	$0.137179\pi$
$353$	15.3324	+	26.5564i	0.816059	+	1.41346i	−0.0925054	+	0.995712i	$0.529488\pi$
$354$	8.99362	−	15.5774i	0.478005	−	0.827929i
$355$	−4.24934	−	7.36007i	−0.225531	−	0.390632i
$356$	−6.52754			−0.345959
$357$	14.2422			0.753778
$358$	−6.85466	−	11.8726i	−0.362280	−	0.627487i
$359$	9.03091	−	15.6420i	0.476633	−	0.825553i	−0.523008	−	0.852328i	$-0.675190\pi$
$359$	9.03091	−	15.6420i	0.476633	−	0.825553i	0.999641	+	0.0267748i	$0.00852369\pi$
$360$	6.11372	+	10.5893i	0.322221	+	0.558104i
$361$	−17.4552	+	30.2332i	−0.918693	+	1.59122i
$362$	−12.4768	+	21.6104i	−0.655764	+	1.13582i
$363$	11.1086	−	19.2406i	0.583049	−	1.00987i
$364$	1.54272			0.0808605
$365$	2.13435	+	3.69680i	0.111717	+	0.193499i
$366$	18.8834	+	32.7070i	0.987051	+	1.70962i
$367$	7.52229	−	13.0290i	0.392660	−	0.680108i	−0.600139	−	0.799896i	$-0.704888\pi$
$367$	7.52229	−	13.0290i	0.392660	−	0.680108i	0.992799	+	0.119788i	$0.0382215\pi$
$368$	−12.9262			−0.673824
$369$	3.99800	+	6.92474i	0.208128	+	0.360488i
$370$	−4.92495			−0.256036
$371$	−35.7437			−1.85572
$372$	−5.57341	−	1.20999i	−0.288968	−	0.0627353i
$373$	18.4221			0.953861			0.476930	−	0.878941i	$-0.341749\pi$
$373$	18.4221			0.953861			0.476930	+	0.878941i	$0.341749\pi$
$374$	3.37398			0.174464
$375$	14.5872	+	25.2658i	0.753281	+	1.30472i
$376$	−10.4279			−0.537777
$377$	−0.376584	+	0.652262i	−0.0193950	+	0.0335932i
$378$	1.71496	+	2.97039i	0.0882079	+	0.152781i
$379$	11.8445	+	20.5153i	0.608411	+	1.05380i	0.991502	+	0.130089i	$0.0415262\pi$
$379$	11.8445	+	20.5153i	0.608411	+	1.05380i	−0.383091	+	0.923711i	$0.625141\pi$
$380$	5.70309			0.292562
$381$	19.0594	−	33.0119i	0.976445	−	1.69125i
$382$	−13.0957	+	22.6824i	−0.670034	+	1.16053i
$383$	17.4730	−	30.2641i	0.892829	−	1.54642i	0.0563600	−	0.998411i	$-0.482051\pi$
$383$	17.4730	−	30.2641i	0.892829	−	1.54642i	0.836469	−	0.548014i	$-0.184616\pi$
$384$	−16.2296	−	28.1104i	−0.828211	−	1.43450i
$385$	−4.31681	+	7.47693i	−0.220005	+	0.381060i
$386$	−16.9910	−	29.4292i	−0.864818	−	1.49791i
$387$	22.7967			1.15882
$388$	5.99996			0.304602
$389$	−5.56378	−	9.63675i	−0.282095	−	0.488603i	0.689806	−	0.723995i	$-0.257696\pi$
$389$	−5.56378	−	9.63675i	−0.282095	−	0.488603i	−0.971901	+	0.235392i	$0.924363\pi$
$390$	−3.39393	+	5.87846i	−0.171858	+	0.297667i
$391$	−2.27682	−	3.94358i	−0.115144	−	0.199435i
$392$	7.39032	−	12.8004i	0.373267	−	0.646518i
$393$	−20.2474	+	35.0695i	−1.02135	+	1.76902i
$394$	−0.615814	+	1.06662i	−0.0310243	+	0.0537356i
$395$	18.7300			0.942408
$396$	−0.771896	−	1.33696i	−0.0387892	−	0.0671849i
$397$	−15.3987	−	26.6714i	−0.772840	−	1.33860i	−0.936000	−	0.351999i	$-0.885502\pi$
$397$	−15.3987	−	26.6714i	−0.772840	−	1.33860i	0.163160	−	0.986600i	$-0.447831\pi$
$398$	14.9543	−	25.9016i	0.749592	−	1.29833i
$399$	63.5354			3.18075
$400$	−3.96261	−	6.86344i	−0.198130	−	0.343172i
$401$	27.2777			1.36218			0.681091	−	0.732199i	$-0.261506\pi$
$401$	27.2777			1.36218			0.681091	+	0.732199i	$0.261506\pi$
$402$	4.54900			0.226884
$403$	1.69751	+	5.30268i	0.0845592	+	0.264145i
$404$	3.89716			0.193891
$405$	−17.6281			−0.875947
$406$	−2.11807	−	3.66860i	−0.105118	−	0.182070i
$407$	−2.28832			−0.113428
$408$	4.83320	−	8.37135i	0.239279	−	0.414444i
$409$	15.1406	+	26.2242i	0.748652	+	1.29670i	0.948469	+	0.316870i	$0.102632\pi$
$409$	15.1406	+	26.2242i	0.748652	+	1.29670i	−0.199817	+	0.979833i	$0.564035\pi$
$410$	4.12357	+	7.14223i	0.203649	+	0.352730i
$411$	22.3145			1.10069
$412$	0.759811	−	1.31603i	0.0374332	−	0.0648362i
$413$	8.69390	−	15.0583i	0.427799	−	0.740969i
$414$	−5.91742	+	10.2493i	−0.290825	+	0.503724i
$415$	2.52517	+	4.37373i	0.123956	+	0.214698i
$416$	1.18933	−	2.05997i	0.0583115	−	0.100999i
$417$	13.0226	+	22.5558i	0.637720	+	1.10456i
$418$	15.0515			0.736195
$419$	34.1128			1.66652			0.833261	−	0.552881i	$-0.186471\pi$
$419$	34.1128			1.66652			0.833261	+	0.552881i	$0.186471\pi$
$420$	−3.36066	−	5.82083i	−0.163983	−	0.284028i
$421$	−10.9407	+	18.9498i	−0.533216	+	0.923557i	0.466032	+	0.884768i	$0.345683\pi$
$421$	−10.9407	+	18.9498i	−0.533216	+	0.923557i	−0.999247	+	0.0387886i	$0.987650\pi$
$422$	14.3797	+	24.9064i	0.699992	+	1.21242i
$423$	−5.84253	+	10.1196i	−0.284074	+	0.492030i
$424$	−12.1299	+	21.0096i	−0.589079	+	1.02031i
$425$	1.39595	−	2.41786i	0.0677136	−	0.117283i
$426$	17.4616			0.846016
$427$	18.2541	+	31.6170i	0.883378	+	1.53006i
$428$	2.35466	+	4.07838i	0.113817	+	0.197136i
$429$	−1.57695	+	2.73135i	−0.0761356	+	0.131871i
$430$	23.5127			1.13388
$431$	−13.7622	−	23.8368i	−0.662902	−	1.14818i	−0.979850	−	0.199737i	$-0.935991\pi$
$431$	−13.7622	−	23.8368i	−0.662902	−	1.14818i	0.316948	−	0.948443i	$-0.397342\pi$
$432$	2.84914			0.137079
$433$	3.53679			0.169967			0.0849835	−	0.996382i	$-0.472916\pi$
$433$	3.53679			0.169967			0.0849835	+	0.996382i	$0.472916\pi$
$434$	−30.6026	−	6.64386i	−1.46897	−	0.318915i
$435$	3.28140			0.157331
$436$	−7.54296			−0.361242
$437$	−10.1571	−	17.5925i	−0.485878	−	0.841565i
$438$	−8.77057			−0.419074
$439$	−10.5977	+	18.3557i	−0.505799	+	0.876070i	0.494178	+	0.869361i	$0.335469\pi$
$439$	−10.5977	+	18.3557i	−0.505799	+	0.876070i	−0.999977	+	0.00670944i	$0.997864\pi$
$440$	2.92988	+	5.07470i	0.139677	+	0.241927i
$441$	−8.28130	−	14.3436i	−0.394347	−	0.683030i
$442$	2.56427			0.121970
$443$	−2.70926	+	4.69257i	−0.128721	+	0.222951i	−0.923181	−	0.384365i	$-0.874420\pi$
$443$	−2.70926	+	4.69257i	−0.128721	+	0.222951i	0.794461	+	0.607316i	$0.207754\pi$
$444$	0.890734	−	1.54280i	0.0422724	−	0.0732179i
$445$	13.8818	−	24.0440i	0.658061	−	1.13979i
$446$	9.38568	+	16.2565i	0.444425	+	0.769766i
$447$	−15.8406	+	27.4368i	−0.749236	+	1.29772i
$448$	−10.1771	−	17.6272i	−0.480822	−	0.832808i
$449$	−9.81440			−0.463170			−0.231585	−	0.972815i	$-0.574391\pi$
$449$	−9.81440			−0.463170			−0.231585	+	0.972815i	$0.574391\pi$
$450$	−7.25610			−0.342056
$451$	1.91596	+	3.31855i	0.0902192	+	0.156264i
$452$	−1.26253	+	2.18677i	−0.0593846	+	0.102857i
$453$	6.16052	+	10.6703i	0.289446	+	0.501336i
$454$	7.46587	−	12.9313i	0.350391	−	0.606894i
$455$	−3.28083	+	5.68256i	−0.153807	+	0.266402i
$456$	21.5612	−	37.3451i	1.00970	−	1.74885i
$457$	3.45047			0.161406			0.0807031	−	0.996738i	$-0.474283\pi$
$457$	3.45047			0.161406			0.0807031	+	0.996738i	$0.474283\pi$
$458$	−2.34171	−	4.05596i	−0.109421	−	0.189523i
$459$	0.501849	+	0.869228i	0.0234243	+	0.0405721i
$460$	−1.07450	+	1.86109i	−0.0500988	+	0.0867737i
$461$	−28.8701			−1.34462			−0.672308	−	0.740272i	$-0.734697\pi$
$461$	−28.8701			−1.34462			−0.672308	+	0.740272i	$0.734697\pi$
$462$	−8.86941	−	15.3623i	−0.412642	−	0.714718i
$463$	3.37024			0.156628			0.0783141	−	0.996929i	$-0.475046\pi$
$463$	3.37024			0.156628			0.0783141	+	0.996929i	$0.475046\pi$
$464$	−3.51884			−0.163358
$465$	16.3097	−	17.9563i	0.756343	−	0.832701i
$466$	36.8633			1.70766
$467$	−4.74977			−0.219793			−0.109897	−	0.993943i	$-0.535052\pi$
$467$	−4.74977			−0.219793			−0.109897	+	0.993943i	$0.535052\pi$
$468$	−0.586650	−	1.01611i	−0.0271179	−	0.0469696i
$469$	4.39741			0.203053
$470$	−6.02603	+	10.4374i	−0.277960	+	0.481441i
$471$	−21.9767	−	38.0647i	−1.01263	−	1.75393i
$472$	−5.90068	−	10.2203i	−0.271601	−	0.470426i
$473$	10.9248			0.502325
$474$	−19.2415	+	33.3273i	−0.883793	+	1.53077i
$475$	6.22743	−	10.7862i	0.285734	−	0.494906i
$476$	−1.26956	+	2.19895i	−0.0581904	+	0.100789i
$477$	13.5923	+	23.5425i	0.622347	+	1.07794i
$478$	1.54399	−	2.67426i	0.0706203	−	0.122318i
$479$	−3.43966	−	5.95766i	−0.157162	−	0.272212i	0.776682	−	0.629893i	$-0.216901\pi$
$479$	−3.43966	−	5.95766i	−0.157162	−	0.272212i	−0.933844	+	0.357680i	$0.883568\pi$
$480$	−10.3633			−0.473018
$481$	−1.73915			−0.0792983
$482$	−19.2197	−	33.2894i	−0.875432	−	1.51629i
$483$	−11.9705	+	20.7335i	−0.544676	+	0.943407i
$484$	1.98046	+	3.43025i	0.0900208	+	0.155921i
$485$	−12.7598	+	22.1007i	−0.579394	+	1.00354i
$486$	16.6844	−	28.8982i	0.756820	−	1.31085i
$487$	10.7364	−	18.5961i	0.486515	−	0.842668i	−0.513365	−	0.858170i	$-0.671601\pi$
$487$	10.7364	−	18.5961i	0.486515	−	0.842668i	0.999880	+	0.0155020i	$0.00493463\pi$
$488$	24.7786			1.12168
$489$	9.14501	+	15.8396i	0.413552	+	0.716292i
$490$	−8.54139	−	14.7941i	−0.385861	−	0.668330i
$491$	2.75897	−	4.77868i	0.124511	−	0.215659i	−0.797031	−	0.603938i	$-0.793597\pi$
$491$	2.75897	−	4.77868i	0.124511	−	0.215659i	0.921542	+	0.388280i	$0.126931\pi$
$492$	−2.98318			−0.134492
$493$	−0.619811	−	1.07354i	−0.0279149	−	0.0483500i
$494$	11.4393			0.514681
$495$	6.56621			0.295129
$496$	−17.4899	+	19.2556i	−0.785318	+	0.864601i
$497$	16.8797			0.757156
$498$	−10.3766			−0.464985
$499$	−11.7781	−	20.4003i	−0.527261	−	0.913243i	−0.999495	−	0.0317696i	$-0.989886\pi$
$499$	−11.7781	−	20.4003i	−0.527261	−	0.913243i	0.472234	−	0.881473i	$-0.343448\pi$
$500$	−5.20127			−0.232608
$501$	−15.3371	+	26.5646i	−0.685211	+	1.18682i
$502$	14.9516	+	25.8969i	0.667321	+	1.15583i
$503$	−0.951184	−	1.64750i	−0.0424112	−	0.0734584i	0.844041	−	0.536279i	$-0.180171\pi$
$503$	−0.951184	−	1.64750i	−0.0424112	−	0.0734584i	−0.886452	+	0.462821i	$0.846837\pi$
$504$	−24.2856			−1.08177
$505$	−8.28789	+	14.3551i	−0.368806	+	0.638791i
$506$	−2.83581	+	4.91176i	−0.126067	+	0.218354i
$507$	−1.19850	+	2.07586i	−0.0532272	+	0.0921921i
$508$	3.39795	+	5.88542i	0.150760	+	0.261123i
$509$	3.94397	−	6.83116i	0.174814	−	0.302786i	−0.765283	−	0.643694i	$-0.777401\pi$
$509$	3.94397	−	6.83116i	0.174814	−	0.302786i	0.940097	+	0.340908i	$0.110734\pi$
$510$	−5.58600	−	9.67523i	−0.247352	−	0.428426i
$511$	−8.47829			−0.375057
$512$	−11.7817			−0.520682
$513$	2.23878	+	3.87768i	0.0988445	+	0.171204i
$514$	21.8080	−	37.7726i	0.961911	−	1.66608i
$515$	3.23170	+	5.59747i	0.142406	+	0.246654i
$516$	−4.25253	+	7.36560i	−0.187207	+	0.324252i
$517$	−2.79992	+	4.84960i	−0.123140	+	0.213285i
$518$	4.89086	−	8.47121i	0.214892	−	0.372204i
$519$	−37.8788			−1.66269
$520$	2.22674	+	3.85683i	0.0976492	+	0.169133i
$521$	−0.441868	−	0.765338i	−0.0193586	−	0.0335301i	0.856184	−	0.516671i	$-0.172829\pi$
$521$	−0.441868	−	0.765338i	−0.0193586	−	0.0335301i	−0.875542	+	0.483141i	$0.839496\pi$
$522$	−1.61088	+	2.79012i	−0.0705061	+	0.122120i
$523$	−31.5128			−1.37796			−0.688980	−	0.724780i	$-0.741941\pi$
$523$	−31.5128			−1.37796			−0.688980	+	0.724780i	$0.741941\pi$
$524$	−3.60974	−	6.25225i	−0.157692	−	0.273131i
$525$	−14.6785			−0.640624
$526$	4.35852			0.190041
$527$	−8.95525	−	1.94420i	−0.390097	−	0.0846905i
$528$	−14.7352			−0.641266
$529$	−15.3454			−0.667190
$530$	14.0192	+	24.2819i	0.608953	+	1.05474i
$531$	−13.2241			−0.573878
$532$	−5.66360	+	9.80965i	−0.245548	+	0.425302i
$533$	1.45616	+	2.52214i	0.0630731	+	0.109246i
$534$	28.5219	+	49.4014i	1.23426	+	2.13781i
$535$	−20.0301			−0.865978
$536$	1.49229	−	2.58472i	0.0644572	−	0.111643i
$537$	−10.5460	+	18.2662i	−0.455093	+	0.788245i
$538$	19.3678	−	33.5461i	0.835007	−	1.44627i
$539$	−3.96865	−	6.87390i	−0.170942	−	0.296080i
$540$	0.236837	−	0.410214i	0.0101918	−	0.0176528i
$541$	−2.46123	−	4.26298i	−0.105817	−	0.183280i	0.808255	−	0.588833i	$-0.200412\pi$
$541$	−2.46123	−	4.26298i	−0.105817	−	0.183280i	−0.914072	+	0.405553i	$0.867079\pi$
$542$	−32.7114			−1.40508
$543$	38.3914			1.64753
$544$	1.95749	+	3.39047i	0.0839266	+	0.145365i
$545$	16.0412	−	27.7842i	0.687131	−	1.19015i
$546$	−6.74086	−	11.6755i	−0.288482	−	0.499666i
$547$	−10.7523	+	18.6235i	−0.459735	+	0.796284i	−0.998947	−	0.0458861i	$-0.985389\pi$
$547$	−10.7523	+	18.6235i	−0.459735	+	0.796284i	0.539212	+	0.842170i	$0.318722\pi$
$548$	−1.98914	+	3.44529i	−0.0849717	+	0.147175i
$549$	13.8830	−	24.0460i	0.592511	−	1.02626i
$550$	−3.47734			−0.148274
$551$	−2.76501	−	4.78915i	−0.117794	−	0.204024i
$552$	8.12455	+	14.0721i	0.345804	+	0.598949i
$553$	−18.6003	+	32.2167i	−0.790965	+	1.36999i
$554$	9.24768			0.392896
$555$	3.78856	+	6.56198i	0.160815	+	0.278540i
$556$	−4.64339			−0.196923
$557$	−28.9206			−1.22541			−0.612703	−	0.790313i	$-0.709918\pi$
$557$	−28.9206			−1.22541			−0.612703	+	0.790313i	$0.709918\pi$
$558$	7.26130	+	22.6828i	0.307395	+	0.960239i
$559$	8.30302			0.351180
$560$	−30.6564			−1.29547
$561$	−2.59546	−	4.49547i	−0.109580	−	0.189799i
$562$	10.3063			0.434744
$563$	−6.39717	+	11.0802i	−0.269609	+	0.466976i	−0.968761	−	0.247997i	$-0.920228\pi$
$563$	−6.39717	+	11.0802i	−0.269609	+	0.466976i	0.699152	+	0.714973i	$0.253561\pi$
$564$	−2.17975	−	3.77544i	−0.0917841	−	0.158975i
$565$	−5.36994	−	9.30101i	−0.225915	−	0.391296i
$566$	10.0350			0.421804
$567$	17.5060	−	30.3214i	0.735185	−	1.27338i
$568$	5.72823	−	9.92159i	0.240351	−	0.416301i
$569$	−19.8445	+	34.3716i	−0.831923	+	1.44093i	0.0645884	+	0.997912i	$0.479427\pi$
$569$	−19.8445	+	34.3716i	−0.831923	+	1.44093i	−0.896511	+	0.443021i	$0.853907\pi$
$570$	−24.9195	−	43.1618i	−1.04376	−	1.80785i
$571$	−4.43236	+	7.67707i	−0.185488	+	0.321275i	−0.943741	−	0.330686i	$-0.892720\pi$
$571$	−4.43236	+	7.67707i	−0.185488	+	0.321275i	0.758253	+	0.651961i	$0.226053\pi$
$572$	−0.281141	−	0.486950i	−0.0117551	−	0.0203604i
$573$	40.2959			1.68338
$574$	−16.3801			−0.683691
$575$	2.34657	+	4.06439i	0.0978589	+	0.169497i
$576$	−7.74008	+	13.4062i	−0.322504	+	0.558593i
$577$	14.0345	+	24.3084i	0.584263	+	1.01197i	0.994967	+	0.100205i	$0.0319498\pi$
$577$	14.0345	+	24.3084i	0.584263	+	1.01197i	−0.410704	+	0.911769i	$0.634717\pi$
$578$	11.1327	−	19.2824i	0.463059	−	0.802042i
$579$	−26.1409	+	45.2773i	−1.08638	+	1.88166i
$580$	−0.292507	+	0.506637i	−0.0121457	+	0.0210369i
$581$	−10.0308			−0.416146
$582$	−26.2166	−	45.4086i	−1.08672	−	1.88225i
$583$	6.51382	+	11.2823i	0.269775	+	0.467264i
$584$	−2.87717	+	4.98340i	−0.119058	+	0.206215i
$585$	4.99040			0.206328
$586$	−20.9713	−	36.3233i	−0.866315	−	1.50050i
$587$	−17.8159			−0.735341			−0.367670	−	0.929956i	$-0.619845\pi$
$587$	−17.8159			−0.735341			−0.367670	+	0.929956i	$0.619845\pi$
$588$	6.17923			0.254827
$589$	−39.9499	−	8.67318i	−1.64611	−	0.357372i
$590$	−13.6395			−0.561528
$591$	1.89488			0.0779449
$592$	−4.06270	−	7.03681i	−0.166976	−	0.289211i
$593$	15.9926			0.656738			0.328369	−	0.944550i	$-0.393501\pi$
$593$	15.9926			0.656738			0.328369	+	0.944550i	$0.393501\pi$
$594$	0.625058	−	1.08263i	0.0256464	−	0.0444209i
$595$	−5.39984	−	9.35280i	−0.221372	−	0.383427i
$596$	−2.82410	−	4.89148i	−0.115679	−	0.200363i
$597$	−46.0149			−1.88326
$598$	−2.15525	+	3.73300i	−0.0881346	+	0.152654i
$599$	−2.70591	+	4.68678i	−0.110561	+	0.191497i	−0.915996	−	0.401186i	$-0.868598\pi$
$599$	−2.70591	+	4.68678i	−0.110561	+	0.191497i	0.805436	+	0.592683i	$0.201931\pi$
$600$	−4.98127	+	8.62781i	−0.203359	+	0.352229i
$601$	4.85581	+	8.41051i	0.198073	+	0.343072i	0.947903	−	0.318558i	$-0.103198\pi$
$601$	4.85581	+	8.41051i	0.198073	+	0.343072i	−0.749831	+	0.661630i	$0.769865\pi$
$602$	−23.3499	+	40.4431i	−0.951669	+	1.64834i
$603$	−1.67220	−	2.89634i	−0.0680974	−	0.117948i
$604$	−2.19662			−0.0893790
$605$	−16.8470			−0.684927
$606$	−17.0285	−	29.4942i	−0.691735	−	1.19812i
$607$	10.4110	−	18.0323i	0.422568	−	0.731909i	−0.573622	−	0.819120i	$-0.694462\pi$
$607$	10.4110	−	18.0323i	0.422568	−	0.731909i	0.996190	+	0.0872109i	$0.0277954\pi$
$608$	8.73247	+	15.1251i	0.354148	+	0.613403i
$609$	−3.25868	+	5.64420i	−0.132048	+	0.228714i
$610$	14.3190	−	24.8013i	0.579760	−	1.00417i
$611$	−2.12797	+	3.68575i	−0.0860885	+	0.149110i
$612$	1.93111			0.0780605
$613$	2.22287	+	3.85012i	0.0897807	+	0.155505i	0.907418	−	0.420228i	$-0.138050\pi$
$613$	2.22287	+	3.85012i	0.0897807	+	0.155505i	−0.817638	+	0.575733i	$0.804717\pi$
$614$	7.66563	+	13.2773i	0.309359	+	0.535826i
$615$	6.34418	−	10.9884i	0.255822	−	0.443097i
$616$	−11.6384			−0.468924
$617$	3.30069	+	5.71696i	0.132881	+	0.230156i	0.924786	−	0.380488i	$-0.124244\pi$
$617$	3.30069	+	5.71696i	0.132881	+	0.230156i	−0.791905	+	0.610644i	$0.790911\pi$
$618$	−13.2799			−0.534195
$619$	−25.5318			−1.02621			−0.513105	−	0.858326i	$-0.671505\pi$
$619$	−25.5318			−1.02621			−0.513105	+	0.858326i	$0.671505\pi$
$620$	1.31852	+	4.11879i	0.0529532	+	0.165415i
$621$	−1.68720			−0.0677051
$622$	38.9715			1.56262
$623$	27.5714	+	47.7550i	1.10462	+	1.91327i
$624$	−11.1989			−0.448315
$625$	6.82053	−	11.8135i	0.272821	−	0.472540i
$626$	−7.16590	−	12.4117i	−0.286407	−	0.496071i
$627$	−11.5785	−	20.0546i	−0.462401	−	0.800902i
$628$	7.83608			0.312694
$629$	1.43121	−	2.47893i	0.0570662	−	0.0988416i
$630$	−14.0341	+	24.3077i	−0.559131	+	0.968443i
$631$	18.1864	−	31.4998i	0.723989	−	1.25399i	−0.235399	−	0.971899i	$-0.575640\pi$
$631$	18.1864	−	31.4998i	0.723989	−	1.25399i	0.959389	−	0.282088i	$-0.0910269\pi$
$632$	12.6243	+	21.8659i	0.502167	+	0.869780i
$633$	22.1234	−	38.3188i	0.879325	−	1.52304i
$634$	21.3303	+	36.9452i	0.847136	+	1.46728i
$635$	−28.9050			−1.14706
$636$	−10.1421			−0.402160
$637$	−3.01622	−	5.22425i	−0.119507	−	0.206992i
$638$	−0.771980	+	1.33711i	−0.0305630	+	0.0529367i
$639$	−6.41883	−	11.1177i	−0.253925	−	0.439811i
$640$	−12.3066	+	21.3157i	−0.486463	+	0.842578i
$641$	21.2262	−	36.7649i	0.838386	−	1.45213i	−0.0528584	−	0.998602i	$-0.516833\pi$
$641$	21.2262	−	36.7649i	0.838386	−	1.45213i	0.891244	−	0.453524i	$-0.149833\pi$
$642$	20.5772	−	35.6407i	0.812117	−	1.40663i
$643$	−23.5031			−0.926871			−0.463435	−	0.886131i	$-0.653383\pi$
$643$	−23.5031			−0.926871			−0.463435	+	0.886131i	$0.653383\pi$
$644$	−2.13412	−	3.69640i	−0.0840961	−	0.145659i
$645$	−18.0873	−	31.3281i	−0.712186	−	1.23354i
$646$	−9.41389	+	16.3053i	−0.370384	+	0.641525i
$647$	−14.2007			−0.558289			−0.279144	−	0.960249i	$-0.590051\pi$
$647$	−14.2007			−0.558289			−0.279144	+	0.960249i	$0.590051\pi$
$648$	−11.8816	−	20.5795i	−0.466754	−	0.808441i
$649$	−6.33740			−0.248765
$650$	−2.64282			−0.103660
$651$	14.6890	+	45.8855i	0.575709	+	1.79840i
$652$	−3.26078			−0.127702
$653$	17.7704			0.695411			0.347706	−	0.937604i	$-0.386961\pi$
$653$	17.7704			0.695411			0.347706	+	0.937604i	$0.386961\pi$
$654$	32.9587	+	57.0862i	1.28879	+	2.23225i
$655$	30.7066			1.19981
$656$	−6.80325	+	11.7836i	−0.265622	+	0.460071i
$657$	3.22404	+	5.58420i	0.125782	+	0.217861i
$658$	−11.9686	−	20.7303i	−0.466585	−	0.808149i
$659$	20.4374			0.796128			0.398064	−	0.917358i	$-0.369682\pi$
$659$	20.4374			0.796128			0.398064	+	0.917358i	$0.369682\pi$
$660$	−1.22487	+	2.12154i	−0.0476781	+	0.0825809i
$661$	13.3303	−	23.0888i	0.518489	−	0.898049i	−0.481280	−	0.876567i	$-0.659828\pi$
$661$	13.3303	−	23.0888i	0.518489	−	0.898049i	0.999769	−	0.0214823i	$-0.00683856\pi$
$662$	−13.3335	+	23.0943i	−0.518220	+	0.897584i
$663$	−1.97258	−	3.41661i	−0.0766087	−	0.132690i
$664$	−3.40401	+	5.89592i	−0.132101	+	0.228806i
$665$	−24.0890	−	41.7234i	−0.934132	−	1.61796i
$666$	−7.43939			−0.288270
$667$	2.08379			0.0806845
$668$	−2.73432	−	4.73599i	−0.105794	−	0.183241i
$669$	14.4400	−	25.0108i	0.558283	−	0.966975i
$670$	−1.72472	−	2.98731i	−0.0666319	−	0.115410i
$671$	6.65314	−	11.5236i	0.256842	−	0.444863i
$672$	10.2916	−	17.8255i	0.397006	−	0.687634i
$673$	20.6041	−	35.6874i	0.794230	−	1.37565i	−0.129097	−	0.991632i	$-0.541208\pi$
$673$	20.6041	−	35.6874i	0.794230	−	1.37565i	0.923327	−	0.384015i	$-0.125459\pi$
$674$	15.0021			0.577859
$675$	−0.517223	−	0.895857i	−0.0199079	−	0.0344815i
$676$	−0.213670	−	0.370088i	−0.00821809	−	0.0142341i
$677$	−11.4837	+	19.8903i	−0.441354	+	0.764448i	−0.997790	−	0.0664425i	$-0.978835\pi$
$677$	−11.4837	+	19.8903i	−0.441354	+	0.764448i	0.556436	+	0.830890i	$0.312168\pi$
$678$	22.0664			0.847455
$679$	−25.3430	−	43.8953i	−0.972574	−	1.68455i
$680$	−7.32990			−0.281089
$681$	−22.9727			−0.880316
$682$	3.47983	+	10.8703i	0.133250	+	0.416244i
$683$	−1.53543			−0.0587514			−0.0293757	−	0.999568i	$-0.509352\pi$
$683$	−1.53543			−0.0587514			−0.0293757	+	0.999568i	$0.509352\pi$
$684$	8.61480			0.329395
$685$	−8.46040	−	14.6538i	−0.323255	−	0.559894i
$686$	−5.44197			−0.207775
$687$	−3.60276	+	6.24016i	−0.137454	+	0.238077i
$688$	19.3961	+	33.5950i	0.739469	+	1.28080i
$689$	4.95058	+	8.57466i	0.188602	+	0.326669i
$690$	18.7800			0.714941
$691$	11.5992	−	20.0904i	0.441255	−	0.764277i	−0.556528	−	0.830829i	$-0.687867\pi$
$691$	11.5992	−	20.0904i	0.441255	−	0.764277i	0.997783	+	0.0665525i	$0.0212000\pi$
$692$	3.37655	−	5.84835i	0.128357	−	0.222321i
$693$	−6.52075	+	11.2943i	−0.247703	+	0.429034i
$694$	−8.38583	−	14.5247i	−0.318322	−	0.551350i
$695$	9.87486	−	17.1038i	0.374575	−	0.648783i
$696$	2.21171	+	3.83080i	0.0838348	+	0.145206i
$697$	−4.79331			−0.181560
$698$	−10.3528			−0.391858
$699$	−28.3574	−	49.1164i	−1.07257	−	1.85775i
$700$	1.30846	−	2.26631i	0.0494550	−	0.0856586i
$701$	−3.24748	−	5.62480i	−0.122656	−	0.212446i	0.798159	−	0.602447i	$-0.205808\pi$
$701$	−3.24748	−	5.62480i	−0.122656	−	0.212446i	−0.920814	+	0.390002i	$0.872474\pi$
$702$	0.475051	−	0.822813i	0.0179297	−	0.0310551i
$703$	6.38473	−	11.0587i	0.240805	−	0.417086i
$704$	−3.70928	+	6.42466i	−0.139799	+	0.242139i
$705$	18.5423			0.698343
$706$	23.8877	+	41.3747i	0.899026	+	1.55716i
$707$	−16.4610	−	28.5113i	−0.619080	−	1.07228i
$708$	2.46685	−	4.27271i	0.0927100	−	0.160578i
$709$	28.3668			1.06534			0.532670	−	0.846323i	$-0.321189\pi$
$709$	28.3668			1.06534			0.532670	+	0.846323i	$0.321189\pi$
$710$	−6.62043	−	11.4669i	−0.248460	−	0.430346i
$711$	28.2926			1.06105
$712$	37.4262			1.40261
$713$	10.3571	−	11.4028i	0.387878	−	0.427037i
$714$	22.1893			0.830413
$715$	2.39155			0.0894390
$716$	−1.88016	−	3.25653i	−0.0702648	−	0.121702i
$717$	−4.75090			−0.177425
$718$	14.0701	−	24.3701i	0.525091	−	0.909484i
$719$	−12.0513	−	20.8734i	−0.449437	−	0.778448i	0.548912	−	0.835880i	$-0.315042\pi$
$719$	−12.0513	−	20.8734i	−0.449437	−	0.778448i	−0.998349	+	0.0574321i	$0.981709\pi$
$720$	11.6577	+	20.1918i	0.434458	+	0.752504i
$721$	−12.8373			−0.478086
$722$	−27.1950	+	47.1031i	−1.01209	+	1.75300i
$723$	−29.5698	+	51.2163i	−1.09971	+	1.90476i
$724$	−3.42224	+	5.92749i	−0.127187	+	0.220294i
$725$	0.638799	+	1.10643i	0.0237244	+	0.0410919i
$726$	17.3071	−	29.9768i	0.642326	−	1.11254i
$727$	15.1624	+	26.2621i	0.562343	+	0.974006i	0.997291	+	0.0735510i	$0.0234332\pi$
$727$	15.1624	+	26.2621i	0.562343	+	0.974006i	−0.434949	+	0.900455i	$0.643233\pi$
$728$	−8.84531			−0.327829
$729$	−22.2429			−0.823810
$730$	3.32530	+	5.75959i	0.123075	+	0.213172i
$731$	−6.83288	+	11.8349i	−0.252723	+	0.437729i
$732$	5.17951	+	8.97118i	0.191440	+	0.331584i
$733$	−21.7834	+	37.7299i	−0.804587	+	1.39358i	0.111983	+	0.993710i	$0.464280\pi$
$733$	−21.7834	+	37.7299i	−0.804587	+	1.39358i	−0.916570	+	0.399875i	$0.869054\pi$
$734$	11.7197	−	20.2991i	0.432581	−	0.749252i
$735$	−13.1411	+	22.7610i	−0.484715	+	0.839552i
$736$	−6.58101			−0.242579
$737$	−0.801370	−	1.38801i	−0.0295188	−	0.0511281i
$738$	6.22886	+	10.7887i	0.229287	+	0.397137i
$739$	−10.5002	+	18.1868i	−0.386255	+	0.669014i	−0.991942	−	0.126689i	$-0.959565\pi$
$739$	−10.5002	+	18.1868i	−0.386255	+	0.669014i	0.605687	+	0.795703i	$0.292898\pi$
$740$	−1.35086			−0.0496587
$741$	−8.79981	−	15.2417i	−0.323269	−	0.559918i
$742$	−55.6884			−2.04438
$743$	−49.1844			−1.80440			−0.902201	−	0.431316i	$-0.858049\pi$
$743$	−49.1844			−1.80440			−0.902201	+	0.431316i	$0.858049\pi$
$744$	31.9556	+	6.93760i	1.17155	+	0.254345i
$745$	24.0235			0.880152
$746$	28.7015			1.05084
$747$	3.81440	+	6.60673i	0.139562	+	0.241728i
$748$	0.925446			0.0338377
$749$	19.8914	−	34.4530i	0.726817	−	1.25888i
$750$	22.7268	+	39.3639i	0.829864	+	1.43737i
$751$	15.8023	+	27.3704i	0.576634	+	0.998760i	0.995862	+	0.0908789i	$0.0289676\pi$
$751$	15.8023	+	27.3704i	0.576634	+	0.998760i	−0.419228	+	0.907881i	$0.637699\pi$
$752$	−19.8840			−0.725096
$753$	23.0032	−	39.8427i	0.838283	−	1.45195i
$754$	−0.586715	+	1.01622i	−0.0213669	+	0.0370085i
$755$	4.67144	−	8.09116i	0.170011	−	0.294468i
$756$	0.470394	+	0.814747i	0.0171081	+	0.0296321i
$757$	24.9598	−	43.2317i	0.907181	−	1.57128i	0.0892186	−	0.996012i	$-0.471563\pi$
$757$	24.9598	−	43.2317i	0.907181	−	1.57128i	0.817962	−	0.575272i	$-0.195104\pi$
$758$	18.4536	+	31.9626i	0.670267	+	1.16094i
$759$	8.72586			0.316729
$760$	−32.6991			−1.18612
$761$	25.1475	+	43.5567i	0.911594	+	1.57893i	0.811812	+	0.583918i	$0.198481\pi$
$761$	25.1475	+	43.5567i	0.911594	+	1.57893i	0.0997821	+	0.995009i	$0.468185\pi$
$762$	29.6945	−	51.4323i	1.07572	−	1.86320i
$763$	31.8604	+	55.1837i	1.15342	+	1.99779i
$764$	−3.59201	+	6.22154i	−0.129954	+	0.225087i
$765$	−4.10680	+	7.11318i	−0.148482	+	0.257178i
$766$	27.2228	−	47.1513i	0.983600	−	1.70365i
$767$	−4.81650			−0.173914
$768$	−11.7708	−	20.3876i	−0.424741	−	0.735674i
$769$	10.5401	+	18.2559i	0.380085	+	0.658326i	0.991074	−	0.133313i	$-0.0425615\pi$
$769$	10.5401	+	18.2559i	0.380085	+	0.658326i	−0.610989	+	0.791639i	$0.709228\pi$
$770$	−6.72555	+	11.6490i	−0.242372	+	0.419801i
$771$	−67.1040			−2.41669
$772$	−4.66044	−	8.07212i	−0.167733	−	0.290522i
$773$	−28.8385			−1.03725			−0.518624	−	0.855002i	$-0.673556\pi$
$773$	−28.8385			−1.03725			−0.518624	+	0.855002i	$0.673556\pi$
$774$	35.5170			1.27663
$775$	9.22959	+	2.00376i	0.331537	+	0.0719770i
$776$	−34.4013			−1.23493
$777$	−15.0493			−0.539891
$778$	−8.66833	−	15.0140i	−0.310775	−	0.538278i
$779$	−21.3832			−0.766134
$780$	−0.930919	+	1.61240i	−0.0333322	+	0.0577331i
$781$	−3.07610	−	5.32796i	−0.110071	−	0.190649i
$782$	−3.54728	−	6.14406i	−0.126850	−	0.219711i
$783$	−0.459300			−0.0164141
$784$	14.0920	−	24.4080i	0.503284	−	0.871714i
$785$	−16.6646	+	28.8639i	−0.594785	+	1.03020i
$786$	−31.5453	+	54.6380i	−1.12518	+	1.94887i
$787$	−6.08991	−	10.5480i	−0.217082	−	0.375997i	0.736833	−	0.676075i	$-0.236321\pi$
$787$	−6.08991	−	10.5480i	−0.217082	−	0.375997i	−0.953915	+	0.300078i	$0.902987\pi$
$788$	−0.168911	+	0.292563i	−0.00601721	+	0.0104221i
$789$	−3.35283	−	5.80727i	−0.119364	−	0.206744i
$790$	29.1812			1.03822
$791$	21.3310			0.758444
$792$	4.42573	+	7.66559i	0.157261	+	0.272385i
$793$	5.05647	−	8.75806i	0.179561	−	0.311008i
$794$	−23.9911	−	41.5538i	−0.851413	−	1.47469i
$795$	21.5687	−	37.3581i	0.764963	−	1.32495i
$796$	4.10181	−	7.10454i	0.145385	−	0.251814i
$797$	−14.8197	+	25.6685i	−0.524941	+	0.909225i	0.474637	+	0.880182i	$0.342579\pi$
$797$	−14.8197	+	25.6685i	−0.524941	+	0.909225i	−0.999578	+	0.0290431i	$0.990754\pi$
$798$	98.9877			3.50413
$799$	−3.50238	−	6.06630i	−0.123905	−	0.214610i
$800$	−2.01745	−	3.49433i	−0.0713278	−	0.123543i
$801$	20.9692	−	36.3196i	0.740909	−	1.28329i
$802$	42.4984			1.50067
$803$	1.54506	+	2.67612i	0.0545239	+	0.0944382i
$804$	1.24774			0.0440045
$805$	18.1541			0.639848
$806$	2.64471	+	8.26154i	0.0931561	+	0.291000i
$807$	−59.5954			−2.09786
$808$	−22.3447			−0.786083
$809$	11.6291	+	20.1423i	0.408859	+	0.708165i	0.994762	−	0.102216i	$-0.0325934\pi$
$809$	11.6291	+	20.1423i	0.408859	+	0.708165i	−0.585903	+	0.810381i	$0.699260\pi$
$810$	−27.4644			−0.965002
$811$	2.25928	−	3.91319i	0.0793341	−	0.137411i	−0.823629	−	0.567129i	$-0.808054\pi$
$811$	2.25928	−	3.91319i	0.0793341	−	0.137411i	0.902963	+	0.429719i	$0.141387\pi$
$812$	−0.580963	−	1.00626i	−0.0203878	−	0.0353127i
$813$	25.1635	+	43.5845i	0.882523	+	1.52857i
$814$	−3.56518			−0.124959
$815$	6.93453	−	12.0110i	0.242906	−	0.420726i
$816$	9.21602	−	15.9626i	0.322625	−	0.558803i
$817$	−30.4819	+	52.7962i	−1.06643	+	1.84710i
$818$	23.5889	+	40.8571i	0.824765	+	1.42854i
$819$	−4.95585	+	8.58378i	−0.173171	+	0.299942i
$820$	1.13105	+	1.95904i	0.0394980	+	0.0684126i
$821$	38.1094			1.33003			0.665014	−	0.746830i	$-0.268425\pi$
$821$	38.1094			1.33003			0.665014	+	0.746830i	$0.268425\pi$
$822$	34.7659			1.21260
$823$	−3.93028	−	6.80744i	−0.137001	−	0.237292i	0.789359	−	0.613932i	$-0.210413\pi$
$823$	−3.93028	−	6.80744i	−0.137001	−	0.237292i	−0.926360	+	0.376639i	$0.877080\pi$
$824$	−4.35643	+	7.54557i	−0.151764	+	0.262862i
$825$	2.67497	+	4.63319i	0.0931306	+	0.161307i
$826$	13.5450	−	23.4607i	0.471292	−	0.816301i
$827$	−14.1807	+	24.5616i	−0.493110	+	0.854092i	−0.999968	−	0.00793772i	$-0.997473\pi$
$827$	−14.1807	+	24.5616i	−0.493110	+	0.854092i	0.506859	+	0.862029i	$0.330807\pi$
$828$	−1.62308	+	2.81127i	−0.0564061	+	0.0976982i
$829$	−4.94571			−0.171771			−0.0858857	−	0.996305i	$-0.527372\pi$
$829$	−4.94571			−0.171771			−0.0858857	+	0.996305i	$0.527372\pi$
$830$	3.93420	+	6.81423i	0.136558	+	0.236526i
$831$	−7.11385	−	12.3216i	−0.246777	−	0.427430i
$832$	−2.81910	+	4.88282i	−0.0977347	+	0.169281i
$833$	9.92866			0.344008
$834$	20.2891	+	35.1418i	0.702555	+	1.21686i
$835$	23.2598			0.804939
$836$	4.12847			0.142786
$837$	−2.28288	+	2.51335i	−0.0789079	+	0.0868742i
$838$	53.1475			1.83595
$839$	21.2232			0.732707			0.366354	−	0.930476i	$-0.380606\pi$
$839$	21.2232			0.732707			0.366354	+	0.930476i	$0.380606\pi$
$840$	19.2686	+	33.3742i	0.664830	+	1.15152i
$841$	−28.4327			−0.980439
$842$	−17.0455	+	29.5236i	−0.587426	+	1.01745i
$843$	−7.92819	−	13.7320i	−0.273061	−	0.472956i
$844$	3.94419	+	6.83154i	0.135765	+	0.235151i
$845$	1.81761			0.0625276
$846$	−9.10262	+	15.7662i	−0.312955	+	0.542053i
$847$	16.7303	−	28.9778i	0.574861	−	0.995688i
$848$	−23.1294	+	40.0613i	−0.794268	+	1.37571i
$849$	−7.71952	−	13.3706i	−0.264933	−	0.458878i
$850$	2.17488	−	3.76701i	0.0745978	−	0.129207i
$851$	2.40585	+	4.16705i	0.0824714	+	0.142845i
$852$	4.78952			0.164086
$853$	−55.2548			−1.89189			−0.945945	−	0.324327i	$-0.894862\pi$
$853$	−55.2548			−1.89189			−0.945945	+	0.324327i	$0.894862\pi$
$854$	28.4397	+	49.2591i	0.973188	+	1.68561i
$855$	−18.3207	+	31.7323i	−0.626554	+	1.08522i
$856$	−13.5006	−	23.3837i	−0.461441	−	0.799240i
$857$	−14.4802	+	25.0804i	−0.494633	+	0.856730i	−0.999981	−	0.00618594i	$-0.998031\pi$
$857$	−14.4802	+	25.0804i	−0.494633	+	0.856730i	0.505348	+	0.862916i	$0.331364\pi$
$858$	−2.45687	+	4.25542i	−0.0838761	+	0.145278i
$859$	11.8904	−	20.5948i	0.405695	−	0.702684i	−0.588707	−	0.808346i	$-0.700363\pi$
$859$	11.8904	−	20.5948i	0.405695	−	0.702684i	0.994402	+	0.105662i	$0.0336962\pi$
$860$	6.44927			0.219918
$861$	12.6005	+	21.8247i	0.429424	+	0.743784i
$862$	−21.4414	−	37.1376i	−0.730297	−	1.26491i
$863$	17.6789	−	30.6207i	0.601796	−	1.04234i	−0.390752	−	0.920496i	$-0.627785\pi$
$863$	17.6789	−	30.6207i	0.601796	−	1.04234i	0.992549	−	0.121846i	$-0.0388815\pi$
$864$	1.45056			0.0493491
$865$	14.3615	+	24.8748i	0.488305	+	0.845768i
$866$	5.51028			0.187247
$867$	−34.2557			−1.16338
$868$	−8.39396	−	1.82234i	−0.284910	−	0.0618542i
$869$	13.5587			0.459946
$870$	5.11240			0.173326
$871$	−0.609051	−	1.05491i	−0.0206369	−	0.0357442i
$872$	43.2482			1.46457
$873$	−19.2744	+	33.3842i	−0.652338	+	1.12988i
$874$	−15.8246	−	27.4090i	−0.535275	−	0.927124i
$875$	21.9694	+	38.0521i	0.742701	+	1.28640i
$876$	−2.40567			−0.0812802
$877$	−1.43640	+	2.48792i	−0.0485037	+	0.0840110i	−0.889258	−	0.457406i	$-0.848779\pi$
$877$	−1.43640	+	2.48792i	−0.0485037	+	0.0840110i	0.840754	+	0.541417i	$0.182112\pi$
$878$	−16.5111	+	28.5981i	−0.557222	+	0.965138i
$879$	−32.2646	+	55.8840i	−1.08826	+	1.88492i
$880$	5.58674	+	9.67651i	0.188329	+	0.326195i
$881$	−11.8062	+	20.4490i	−0.397762	+	0.688945i	−0.993450	−	0.114272i	$-0.963547\pi$
$881$	−11.8062	+	20.4490i	−0.397762	+	0.688945i	0.595687	+	0.803217i	$0.296880\pi$
$882$	−12.9022	−	22.3473i	−0.434440	−	0.752471i
$883$	−1.44603			−0.0486628			−0.0243314	−	0.999704i	$-0.507746\pi$
$883$	−1.44603			−0.0486628			−0.0243314	+	0.999704i	$0.507746\pi$
$884$	0.703351			0.0236562
$885$	10.4923	+	18.1731i	0.352694	+	0.610883i
$886$	−4.22100	+	7.31099i	−0.141807	+	0.245617i
$887$	−22.0896	−	38.2604i	−0.741697	−	1.28466i	−0.951722	−	0.306961i	$-0.900688\pi$
$887$	−22.0896	−	38.2604i	−0.741697	−	1.28466i	0.210025	−	0.977696i	$-0.432646\pi$
$888$	−5.10709	+	8.84575i	−0.171383	+	0.296844i
$889$	28.7049	−	49.7183i	0.962731	−	1.66750i
$890$	21.6278	−	37.4604i	0.724964	−	1.25567i
$891$	−12.7610			−0.427509
$892$	2.57439	+	4.45897i	0.0861970	+	0.149298i
$893$	−15.6243	−	27.0621i	−0.522849	−	0.905600i
$894$	−24.6796	+	42.7463i	−0.825409	+	1.42965i
$895$	15.9938			0.534613
$896$	−24.4429	−	42.3363i	−0.816579	−	1.41436i
$897$	6.63176			0.221428
$898$	−15.2908			−0.510259
$899$	2.81948	−	3.10413i	0.0940350	−	0.103528i
$900$	−1.99027			−0.0663423
$901$	−16.2961			−0.542902
$902$	2.98506	+	5.17027i	0.0993915	+	0.172151i
$903$	71.8482			2.39096
$904$	7.23884	−	12.5380i	0.240760	−	0.417009i
$905$	−14.5558	−	25.2114i	−0.483852	−	0.838056i
$906$	9.59804	+	16.6243i	0.318874	+	0.552305i
$907$	36.6210			1.21598			0.607991	−	0.793944i	$-0.291976\pi$
$907$	36.6210			1.21598			0.607991	+	0.793944i	$0.291976\pi$
$908$	2.04781	−	3.54691i	0.0679589	−	0.117708i
$909$	−12.5193	+	21.6840i	−0.415238	+	0.719213i
$910$	−5.11150	+	8.85338i	−0.169445	+	0.293487i
$911$	16.3081	+	28.2465i	0.540312	+	0.935848i	0.998886	+	0.0471916i	$0.0150271\pi$
$911$	16.3081	+	28.2465i	0.540312	+	0.935848i	−0.458574	+	0.888656i	$0.651640\pi$
$912$	41.1132	−	71.2102i	1.36140	−	2.35801i
$913$	1.82797	+	3.16615i	0.0604971	+	0.104784i
$914$	5.37581			0.177816
$915$	−44.0601			−1.45658
$916$	−0.642306	−	1.11251i	−0.0212224	−	0.0367583i
$917$	−30.4940	+	52.8172i	−1.00700	+	1.74418i
$918$	0.781877	+	1.35425i	0.0258058	+	0.0446969i
$919$	21.9264	−	37.9777i	0.723286	−	1.25277i	−0.236389	−	0.971658i	$-0.575964\pi$
$919$	21.9264	−	37.9777i	0.723286	−	1.25277i	0.959676	−	0.281110i	$-0.0907026\pi$
$920$	6.16073	−	10.6707i	0.203113	−	0.351802i
$921$	11.7937	−	20.4273i	0.388615	−	0.673101i
$922$	−44.9794			−1.48132
$923$	−2.33787	−	4.04931i	−0.0769520	−	0.133285i
$924$	−2.43278	−	4.21371i	−0.0800327	−	0.138621i
$925$	−1.47506	+	2.55488i	−0.0484996	+	0.0840038i
$926$	5.25080			0.172552
$927$	4.88165	+	8.45526i	0.160334	+	0.277707i
$928$	−1.79152			−0.0588096
$929$	47.3557			1.55369			0.776844	−	0.629693i	$-0.216819\pi$
$929$	47.3557			1.55369			0.776844	+	0.629693i	$0.216819\pi$
$930$	25.4104	−	27.9757i	0.833239	−	0.917359i
$931$	44.2924			1.45162
$932$	10.1112			0.331203
$933$	−29.9792	−	51.9254i	−0.981473	−	1.69996i
$934$	−7.40011			−0.242139
$935$	−1.96810	+	3.40885i	−0.0643638	+	0.111481i
$936$	3.36361	+	5.82594i	0.109943	+	0.190427i
$937$	−11.3306	−	19.6252i	−0.370156	−	0.641128i	0.619434	−	0.785049i	$-0.287362\pi$
$937$	−11.3306	−	19.6252i	−0.370156	−	0.641128i	−0.989589	+	0.143921i	$0.954029\pi$
$938$	6.85112			0.223697
$939$	−11.0248	+	19.0956i	−0.359782	+	0.623161i
$940$	−1.65288	+	2.86286i	−0.0539109	+	0.0933763i
$941$	5.74172	−	9.94495i	0.187175	−	0.324196i	−0.757133	−	0.653261i	$-0.773400\pi$
$941$	5.74172	−	9.94495i	0.187175	−	0.324196i	0.944307	+	0.329065i	$0.106734\pi$
$942$	−34.2395	−	59.3045i	−1.11558	−	1.93225i
$943$	4.02874	−	6.97799i	0.131194	−	0.227234i
$944$	−11.2515	−	19.4882i	−0.366205	−	0.634286i
$945$	−4.00146			−0.130167
$946$	17.0208			0.553395
$947$	−9.60539	−	16.6370i	−0.312133	−	0.540631i	0.666691	−	0.745335i	$-0.267710\pi$
$947$	−9.60539	−	16.6370i	−0.312133	−	0.540631i	−0.978824	+	0.204704i	$0.934377\pi$
$948$	−5.27774	+	9.14132i	−0.171413	+	0.296896i
$949$	1.17426	+	2.03388i	0.0381182	+	0.0660226i
$950$	9.70228	−	16.8048i	0.314784	−	0.545221i
$951$	32.8171	−	56.8408i	1.06417	−	1.84319i
$952$	7.27915	−	12.6079i	0.235919	−	0.408623i
$953$	33.8494			1.09649			0.548245	−	0.836318i	$-0.315296\pi$
$953$	33.8494			1.09649			0.548245	+	0.836318i	$0.315296\pi$
$954$	21.1766	+	36.6790i	0.685619	+	1.18753i
$955$	−15.2779	−	26.4621i	−0.494381	−	0.856293i
$956$	0.423499	−	0.733522i	0.0136969	−	0.0237238i
$957$	2.37541			0.0767860
$958$	−5.35896	−	9.28199i	−0.173140	−	0.299887i
$959$	33.6073			1.08524
$960$	24.5645			0.792816
$961$	−2.97240	−	30.8572i	−0.0958839	−	0.995393i
$962$	−2.70958			−0.0873604
$963$	−30.2565			−0.975002
$964$	−5.27175	−	9.13094i	−0.169792	−	0.294088i
$965$	39.6445			1.27620
$966$	−18.6499	+	32.3026i	−0.600052	+	1.03932i
$967$	−28.7393	−	49.7780i	−0.924195	−	1.60075i	−0.792851	−	0.609416i	$-0.791404\pi$
$967$	−28.7393	−	49.7780i	−0.924195	−	1.60075i	−0.131345	−	0.991337i	$-0.541929\pi$
$968$	−11.3551	−	19.6676i	−0.364967	−	0.632142i
$969$	28.9668			0.930549
$970$	−19.8797	+	34.4327i	−0.638299	+	1.10557i
$971$	−19.6852	+	34.0957i	−0.631727	+	1.09418i	0.355471	+	0.934687i	$0.384320\pi$
$971$	−19.6852	+	34.0957i	−0.631727	+	1.09418i	−0.987198	+	0.159497i	$0.949013\pi$
$972$	4.57635	−	7.92647i	0.146786	−	0.254242i
$973$	19.6130	+	33.9707i	0.628763	+	1.08905i
$974$	16.7273	−	28.9725i	0.535977	−	0.928340i
$975$	2.03301	+	3.52128i	0.0651085	+	0.112771i
$976$	47.2483			1.51238
$977$	−59.3397			−1.89845			−0.949223	−	0.314604i	$-0.898128\pi$
$977$	−59.3397			−1.89845			−0.949223	+	0.314604i	$0.898128\pi$
$978$	14.2479	+	24.6780i	0.455596	+	0.789116i
$979$	10.0491	−	17.4055i	0.321169	−	0.556281i
$980$	−2.34281	−	4.05787i	−0.0748384	−	0.129624i
$981$	24.2311	−	41.9695i	0.773639	−	1.33998i
$982$	4.29846	−	7.44514i	0.137169	−	0.237584i
$983$	−15.3534	+	26.5929i	−0.489698	+	0.848181i	−0.999930	−	0.0118554i	$-0.996226\pi$
$983$	−15.3534	+	26.5929i	−0.489698	+	0.848181i	0.510232	+	0.860037i	$0.329560\pi$
$984$	17.1043			0.545265
$985$	−0.718430	−	1.24436i	−0.0228911	−	0.0396485i
$986$	−0.965661	−	1.67257i	−0.0307529	−	0.0532656i
$987$	−18.4139	+	31.8938i	−0.586121	+	1.01519i
$988$	3.13769			0.0998232
$989$	−11.4860	−	19.8943i	−0.365233	−	0.632601i
$990$	10.2301			0.325134
$991$	−29.2370			−0.928744			−0.464372	−	0.885640i	$-0.653720\pi$
$991$	−29.2370			−0.928744			−0.464372	+	0.885640i	$0.653720\pi$
$992$	−8.90449	+	9.80346i	−0.282718	+	0.311260i
$993$	41.0275			1.30197
$994$	26.2984			0.834134
$995$	17.4462	+	30.2178i	0.553083	+	0.957967i
$996$	−2.84618			−0.0901846
$997$	−22.1221	+	38.3166i	−0.700614	+	1.21350i	0.267637	+	0.963520i	$0.413757\pi$
$997$	−22.1221	+	38.3166i	−0.700614	+	1.21350i	−0.968251	+	0.249980i	$0.919576\pi$
$998$	−18.3502	−	31.7835i	−0.580866	−	1.00609i
$999$	−0.530288	−	0.918486i	−0.0167776	−	0.0290596i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.h.b.118.13	✓	34
31.5	even	3	inner	403.2.h.b.222.13	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.h.b.118.13	✓	34	1.1	even	1	trivial
403.2.h.b.222.13	yes	34	31.5	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.55799 q^{2} +(-1.19850 - 2.07586i) q^{3} +0.427341 q^{4} +(-0.908804 + 1.57410i) q^{5} +(-1.86725 - 3.23417i) q^{6} +(-1.80502 - 3.12639i) q^{7} -2.45019 q^{8} +(-1.37279 + 2.37775i) q^{9} +O(q^{10})\)	\(q+1.55799 q^{2} +(-1.19850 - 2.07586i) q^{3} +0.427341 q^{4} +(-0.908804 + 1.57410i) q^{5} +(-1.86725 - 3.23417i) q^{6} +(-1.80502 - 3.12639i) q^{7} -2.45019 q^{8} +(-1.37279 + 2.37775i) q^{9} +(-1.41591 + 2.45243i) q^{10} +(-0.657884 + 1.13949i) q^{11} +(-0.512167 - 0.887099i) q^{12} +(-0.500000 + 0.866025i) q^{13} +(-2.81221 - 4.87090i) q^{14} +4.35680 q^{15} -4.67206 q^{16} +(-0.822939 - 1.42537i) q^{17} +(-2.13880 + 3.70451i) q^{18} +(-3.67118 - 6.35867i) q^{19} +(-0.388369 + 0.672675i) q^{20} +(-4.32663 + 7.49395i) q^{21} +(-1.02498 + 1.77532i) q^{22} +2.76670 q^{23} +(2.93655 + 5.08625i) q^{24} +(0.848150 + 1.46904i) q^{25} +(-0.778996 + 1.34926i) q^{26} -0.609825 q^{27} +(-0.771360 - 1.33603i) q^{28} +0.753167 q^{29} +6.78786 q^{30} +(3.74350 - 4.12143i) q^{31} -2.37865 q^{32} +3.15389 q^{33} +(-1.28213 - 2.22072i) q^{34} +6.56165 q^{35} +(-0.586650 + 1.01611i) q^{36} +(0.869574 + 1.50615i) q^{37} +(-5.71967 - 9.90677i) q^{38} +2.39700 q^{39} +(2.22674 - 3.85683i) q^{40} +(1.45616 - 2.52214i) q^{41} +(-6.74086 + 11.6755i) q^{42} +(-4.15151 - 7.19062i) q^{43} +(-0.281141 + 0.486950i) q^{44} +(-2.49520 - 4.32182i) q^{45} +4.31049 q^{46} +4.25594 q^{47} +(5.59945 + 9.69854i) q^{48} +(-3.01622 + 5.22425i) q^{49} +(1.32141 + 2.28875i) q^{50} +(-1.97258 + 3.41661i) q^{51} +(-0.213670 + 0.370088i) q^{52} +(4.95058 - 8.57466i) q^{53} -0.950103 q^{54} +(-1.19578 - 2.07114i) q^{55} +(4.42265 + 7.66026i) q^{56} +(-8.79981 + 15.2417i) q^{57} +1.17343 q^{58} +(2.40825 + 4.17121i) q^{59} +1.86184 q^{60} -10.1129 q^{61} +(5.83235 - 6.42116i) q^{62} +9.91170 q^{63} +5.63820 q^{64} +(-0.908804 - 1.57410i) q^{65} +4.91374 q^{66} +(-0.609051 + 1.05491i) q^{67} +(-0.351675 - 0.609119i) q^{68} +(-3.31588 - 5.74328i) q^{69} +10.2230 q^{70} +(-2.33787 + 4.04931i) q^{71} +(3.36361 - 5.82594i) q^{72} +(1.17426 - 2.03388i) q^{73} +(1.35479 + 2.34656i) q^{74} +(2.03301 - 3.52128i) q^{75} +(-1.56885 - 2.71732i) q^{76} +4.74999 q^{77} +3.73450 q^{78} +(-5.15237 - 8.92417i) q^{79} +(4.24599 - 7.35427i) q^{80} +(4.84926 + 8.39916i) q^{81} +(2.26868 - 3.92947i) q^{82} +(1.38928 - 2.40631i) q^{83} +(-1.84895 + 3.20247i) q^{84} +2.99156 q^{85} +(-6.46802 - 11.2029i) q^{86} +(-0.902669 - 1.56347i) q^{87} +(1.61194 - 2.79197i) q^{88} -15.2748 q^{89} +(-3.88751 - 6.73336i) q^{90} +3.61005 q^{91} +1.18232 q^{92} +(-13.0421 - 2.83145i) q^{93} +6.63073 q^{94} +13.3455 q^{95} +(2.85081 + 4.93775i) q^{96} +14.0402 q^{97} +(-4.69925 + 8.13934i) q^{98} +(-1.80628 - 3.12857i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9}+O(q^{10}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9	\( 34 q + 6 q^{2} - 2 q^{3} + 34 q^{4} - 5 q^{5} - 2 q^{7} + 36 q^{8} - 23 q^{9} - 7 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 7 q^{14} + 8 q^{15} + 18 q^{16} - 8 q^{17} + 6 q^{18} + 3 q^{19} - 8 q^{20} + 13 q^{21} + 12 q^{22} - 14 q^{23} - 6 q^{24} - 26 q^{25} - 3 q^{26} + 28 q^{27} - 7 q^{28} - 18 q^{29} - 60 q^{30} - 9 q^{31} + 58 q^{32} - 14 q^{33} - 15 q^{34} + 50 q^{35} - 49 q^{36} - 6 q^{37} + 2 q^{38} + 4 q^{39} - 29 q^{40} - 5 q^{41} + 8 q^{42} - q^{43} - 22 q^{44} + 13 q^{45} + 34 q^{46} + 16 q^{47} - 49 q^{48} + 3 q^{49} - 35 q^{51} - 17 q^{52} + 30 q^{53} - 2 q^{54} + 21 q^{55} - 7 q^{56} + 34 q^{58} - 9 q^{59} - 38 q^{60} - 28 q^{61} - 62 q^{62} + 88 q^{63} + 56 q^{64} - 5 q^{65} + 140 q^{66} - 31 q^{67} - 39 q^{68} + 5 q^{69} + 56 q^{70} + q^{71} - 32 q^{72} - 10 q^{73} - 39 q^{74} - 2 q^{75} - 16 q^{76} + 76 q^{77} - 23 q^{79} - 22 q^{80} - 29 q^{81} - 10 q^{82} + 3 q^{83} + 52 q^{84} - 32 q^{85} + 4 q^{86} + 18 q^{87} - 10 q^{88} + 26 q^{89} + 35 q^{90} + 4 q^{91} - 94 q^{92} - 41 q^{93} + 70 q^{94} + 28 q^{95} - 23 q^{96} + 32 q^{97} - 38 q^{98} - 70 q^{99}+O(q^{100}) \) 34 * q + 6 * q^2 - 2 * q^3 + 34 * q^4 - 5 * q^5 - 2 * q^7 + 36 * q^8 - 23 * q^9 - 7 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 7 * q^14 + 8 * q^15 + 18 * q^16 - 8 * q^17 + 6 * q^18 + 3 * q^19 - 8 * q^20 + 13 * q^21 + 12 * q^22 - 14 * q^23 - 6 * q^24 - 26 * q^25 - 3 * q^26 + 28 * q^27 - 7 * q^28 - 18 * q^29 - 60 * q^30 - 9 * q^31 + 58 * q^32 - 14 * q^33 - 15 * q^34 + 50 * q^35 - 49 * q^36 - 6 * q^37 + 2 * q^38 + 4 * q^39 - 29 * q^40 - 5 * q^41 + 8 * q^42 - q^43 - 22 * q^44 + 13 * q^45 + 34 * q^46 + 16 * q^47 - 49 * q^48 + 3 * q^49 - 35 * q^51 - 17 * q^52 + 30 * q^53 - 2 * q^54 + 21 * q^55 - 7 * q^56 + 34 * q^58 - 9 * q^59 - 38 * q^60 - 28 * q^61 - 62 * q^62 + 88 * q^63 + 56 * q^64 - 5 * q^65 + 140 * q^66 - 31 * q^67 - 39 * q^68 + 5 * q^69 + 56 * q^70 + q^71 - 32 * q^72 - 10 * q^73 - 39 * q^74 - 2 * q^75 - 16 * q^76 + 76 * q^77 - 23 * q^79 - 22 * q^80 - 29 * q^81 - 10 * q^82 + 3 * q^83 + 52 * q^84 - 32 * q^85 + 4 * q^86 + 18 * q^87 - 10 * q^88 + 26 * q^89 + 35 * q^90 + 4 * q^91 - 94 * q^92 - 41 * q^93 + 70 * q^94 + 28 * q^95 - 23 * q^96 + 32 * q^97 - 38 * q^98 - 70 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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