LMFDB - Embedded newform 403.2.f.c.373.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(94,403)]

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([2, 0]))

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

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

chi := DirichletCharacter("403.94");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.f (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:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			373.2
Character	$\chi$	$=$	403.373
Dual form			403.2.f.c.94.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33157 + 2.30635i) q^{2} +(-1.12120 + 1.94198i) q^{3} +(-2.54616 - 4.41008i) q^{4} +4.27464 q^{5} +(-2.98592 - 5.17177i) q^{6} +(1.44001 + 2.49418i) q^{7} +8.23530 q^{8} +(-1.01419 - 1.75663i) q^{9} +O(q^{10})$	\(q+(-1.33157 + 2.30635i) q^{2} +(-1.12120 + 1.94198i) q^{3} +(-2.54616 - 4.41008i) q^{4} +4.27464 q^{5} +(-2.98592 - 5.17177i) q^{6} +(1.44001 + 2.49418i) q^{7} +8.23530 q^{8} +(-1.01419 - 1.75663i) q^{9} +(-5.69198 + 9.85880i) q^{10} +(0.929182 - 1.60939i) q^{11} +11.4191 q^{12} +(-0.150623 + 3.60240i) q^{13} -7.66992 q^{14} +(-4.79273 + 8.30126i) q^{15} +(-5.87356 + 10.1733i) q^{16} +(2.25889 + 3.91251i) q^{17} +5.40188 q^{18} +(-1.62921 - 2.82188i) q^{19} +(-10.8839 - 18.8515i) q^{20} -6.45819 q^{21} +(2.47454 + 4.28603i) q^{22} +(1.44566 - 2.50396i) q^{23} +(-9.23344 + 15.9928i) q^{24} +13.2725 q^{25} +(-8.10783 - 5.14425i) q^{26} -2.17875 q^{27} +(7.33301 - 12.7011i) q^{28} +(-1.29013 + 2.23457i) q^{29} +(-12.7637 - 22.1074i) q^{30} +1.00000 q^{31} +(-7.40682 - 12.8290i) q^{32} +(2.08360 + 3.60891i) q^{33} -12.0315 q^{34} +(6.15553 + 10.6617i) q^{35} +(-5.16460 + 8.94535i) q^{36} +(2.82583 - 4.89449i) q^{37} +8.67765 q^{38} +(-6.82692 - 4.33153i) q^{39} +35.2029 q^{40} +(4.00686 - 6.94009i) q^{41} +(8.59953 - 14.8948i) q^{42} +(-0.408032 - 0.706732i) q^{43} -9.46339 q^{44} +(-4.33530 - 7.50897i) q^{45} +(3.85000 + 6.66840i) q^{46} -9.93802 q^{47} +(-13.1709 - 22.8127i) q^{48} +(-0.647274 + 1.12111i) q^{49} +(-17.6733 + 30.6110i) q^{50} -10.1307 q^{51} +(16.2704 - 8.50804i) q^{52} -10.5819 q^{53} +(2.90117 - 5.02497i) q^{54} +(3.97191 - 6.87956i) q^{55} +(11.8589 + 20.5403i) q^{56} +7.30672 q^{57} +(-3.43580 - 5.95098i) q^{58} +(-2.65141 - 4.59238i) q^{59} +48.8123 q^{60} +(-2.98864 - 5.17647i) q^{61} +(-1.33157 + 2.30635i) q^{62} +(2.92090 - 5.05915i) q^{63} +15.9566 q^{64} +(-0.643860 + 15.3990i) q^{65} -11.0979 q^{66} +(-0.949280 + 1.64420i) q^{67} +(11.5030 - 19.9238i) q^{68} +(3.24176 + 5.61489i) q^{69} -32.7861 q^{70} +(1.03692 + 1.79600i) q^{71} +(-8.35218 - 14.4664i) q^{72} +5.58655 q^{73} +(7.52559 + 13.0347i) q^{74} +(-14.8812 + 25.7750i) q^{75} +(-8.29648 + 14.3699i) q^{76} +5.35213 q^{77} +(19.0806 - 9.97751i) q^{78} -8.08816 q^{79} +(-25.1073 + 43.4872i) q^{80} +(5.48540 - 9.50100i) q^{81} +(10.6708 + 18.4824i) q^{82} -0.931615 q^{83} +(16.4436 + 28.4811i) q^{84} +(9.65594 + 16.7246i) q^{85} +2.17329 q^{86} +(-2.89299 - 5.01081i) q^{87} +(7.65209 - 13.2538i) q^{88} +(-6.58674 + 11.4086i) q^{89} +23.0911 q^{90} +(-9.20193 + 4.81183i) q^{91} -14.7236 q^{92} +(-1.12120 + 1.94198i) q^{93} +(13.2332 - 22.9205i) q^{94} +(-6.96429 - 12.0625i) q^{95} +33.2182 q^{96} +(-1.00594 - 1.74233i) q^{97} +(-1.72378 - 2.98568i) q^{98} -3.76948 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9}+O(q^{10}) $ 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9} - 3 q^{10} - 17 q^{11} + 8 q^{12} + 8 q^{13} + 4 q^{14} - 12 q^{15} - 17 q^{16} + 7 q^{17} - 14 q^{18} - 4 q^{19} - 15 q^{20} + 28 q^{21} - 30 q^{22} + 4 q^{23} - 48 q^{24} + 24 q^{25} + 25 q^{26} - 6 q^{27} - q^{28} + 15 q^{29} + 35 q^{30} + 36 q^{31} - 35 q^{32} - 17 q^{33} - 6 q^{34} - 17 q^{35} - 35 q^{36} - 3 q^{37} + 14 q^{38} + 3 q^{39} - 2 q^{40} - 44 q^{41} + 57 q^{42} + 4 q^{43} + 64 q^{44} + 5 q^{45} - 13 q^{46} + 24 q^{47} - 89 q^{48} - 44 q^{49} - 84 q^{50} - 28 q^{51} + 50 q^{52} - 28 q^{53} - 21 q^{54} + 29 q^{55} + 11 q^{56} + 32 q^{57} + 49 q^{58} - 11 q^{59} + 54 q^{60} - 4 q^{61} - 5 q^{62} - 9 q^{63} + 34 q^{64} - 5 q^{65} + 52 q^{66} - 16 q^{67} + 53 q^{68} + 4 q^{69} - 44 q^{70} - 5 q^{71} - 27 q^{72} + 64 q^{73} + q^{74} - 98 q^{75} - 42 q^{76} - 22 q^{77} + 143 q^{78} - 6 q^{79} - 2 q^{80} + 10 q^{81} + 22 q^{82} + 36 q^{83} + 38 q^{84} + 2 q^{85} + 84 q^{86} - 34 q^{87} - 69 q^{88} - 54 q^{89} - 32 q^{90} - 43 q^{91} - 86 q^{92} + 44 q^{94} - 2 q^{95} + 170 q^{96} - 28 q^{97} - 29 q^{98} + 154 q^{99}+O(q^{100}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9 - 3 * q^10 - 17 * q^11 + 8 * q^12 + 8 * q^13 + 4 * q^14 - 12 * q^15 - 17 * q^16 + 7 * q^17 - 14 * q^18 - 4 * q^19 - 15 * q^20 + 28 * q^21 - 30 * q^22 + 4 * q^23 - 48 * q^24 + 24 * q^25 + 25 * q^26 - 6 * q^27 - q^28 + 15 * q^29 + 35 * q^30 + 36 * q^31 - 35 * q^32 - 17 * q^33 - 6 * q^34 - 17 * q^35 - 35 * q^36 - 3 * q^37 + 14 * q^38 + 3 * q^39 - 2 * q^40 - 44 * q^41 + 57 * q^42 + 4 * q^43 + 64 * q^44 + 5 * q^45 - 13 * q^46 + 24 * q^47 - 89 * q^48 - 44 * q^49 - 84 * q^50 - 28 * q^51 + 50 * q^52 - 28 * q^53 - 21 * q^54 + 29 * q^55 + 11 * q^56 + 32 * q^57 + 49 * q^58 - 11 * q^59 + 54 * q^60 - 4 * q^61 - 5 * q^62 - 9 * q^63 + 34 * q^64 - 5 * q^65 + 52 * q^66 - 16 * q^67 + 53 * q^68 + 4 * q^69 - 44 * q^70 - 5 * q^71 - 27 * q^72 + 64 * q^73 + q^74 - 98 * q^75 - 42 * q^76 - 22 * q^77 + 143 * q^78 - 6 * q^79 - 2 * q^80 + 10 * q^81 + 22 * q^82 + 36 * q^83 + 38 * q^84 + 2 * q^85 + 84 * q^86 - 34 * q^87 - 69 * q^88 - 54 * q^89 - 32 * q^90 - 43 * q^91 - 86 * q^92 + 44 * q^94 - 2 * q^95 + 170 * q^96 - 28 * q^97 - 29 * q^98 + 154 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−1.33157	+	2.30635i	−0.941563	+	1.63083i	−0.179072	+	0.983836i	$0.557309\pi$
$2$	−1.33157	+	2.30635i	−0.941563	+	1.63083i	−0.762491	+	0.646999i	$0.776024\pi$
$3$	−1.12120	+	1.94198i	−0.647327	+	1.12120i	0.336432	+	0.941708i	$0.390780\pi$
$3$	−1.12120	+	1.94198i	−0.647327	+	1.12120i	−0.983759	+	0.179495i	$0.942554\pi$
$4$	−2.54616	−	4.41008i	−1.27308	−	2.20504i
$5$	4.27464			1.91168			0.955838	−	0.293896i	$-0.0949518\pi$
$5$	4.27464			1.91168			0.955838	+	0.293896i	$0.0949518\pi$
$6$	−2.98592	−	5.17177i	−1.21900	−	2.11137i
$7$	1.44001	+	2.49418i	0.544274	+	0.942710i	0.998652	+	0.0519010i	$0.0165280\pi$
$7$	1.44001	+	2.49418i	0.544274	+	0.942710i	−0.454379	+	0.890809i	$0.650139\pi$
$8$	8.23530			2.91162
$9$	−1.01419	−	1.75663i	−0.338064	−	0.585544i
$10$	−5.69198	+	9.85880i	−1.79996	+	3.11763i
$11$	0.929182	−	1.60939i	0.280159	−	0.485249i	−0.691265	−	0.722601i	$-0.742946\pi$
$11$	0.929182	−	1.60939i	0.280159	−	0.485249i	0.971424	+	0.237352i	$0.0762795\pi$
$12$	11.4191			3.29640
$13$	−0.150623	+	3.60240i	−0.0417754	+	0.999127i
$13$	−0.150623	+	3.60240i	−0.0417754	+	0.999127i
$14$	−7.66992			−2.04987
$15$	−4.79273	+	8.30126i	−1.23748	+	2.14338i
$16$	−5.87356	+	10.1733i	−1.46839	+	2.54333i
$17$	2.25889	+	3.91251i	0.547862	+	0.948924i	0.998421	+	0.0561775i	$0.0178913\pi$
$17$	2.25889	+	3.91251i	0.547862	+	0.948924i	−0.450559	+	0.892747i	$0.648775\pi$
$18$	5.40188			1.27323
$19$	−1.62921	−	2.82188i	−0.373767	−	0.647384i	0.616375	−	0.787453i	$-0.288601\pi$
$19$	−1.62921	−	2.82188i	−0.373767	−	0.647384i	−0.990142	+	0.140069i	$0.955267\pi$
$20$	−10.8839	−	18.8515i	−2.43372	−	4.21532i
$21$	−6.45819			−1.40929
$22$	2.47454	+	4.28603i	0.527574	+	0.913785i
$23$	1.44566	−	2.50396i	0.301441	−	0.522111i	−0.675021	−	0.737798i	$-0.735866\pi$
$23$	1.44566	−	2.50396i	0.301441	−	0.522111i	0.976463	+	0.215687i	$0.0691990\pi$
$24$	−9.23344	+	15.9928i	−1.88477	+	3.26451i
$25$	13.2725			2.65450
$26$	−8.10783	−	5.14425i	−1.59008	−	1.00887i
$27$	−2.17875			−0.419302
$28$	7.33301	−	12.7011i	1.38581	−	2.40029i
$29$	−1.29013	+	2.23457i	−0.239571	+	0.414949i	−0.960591	−	0.277965i	$-0.910340\pi$
$29$	−1.29013	+	2.23457i	−0.239571	+	0.414949i	0.721020	+	0.692914i	$0.243673\pi$
$30$	−12.7637	−	22.1074i	−2.33033	−	4.03625i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	−7.40682	−	12.8290i	−1.30935	−	2.26787i
$33$	2.08360	+	3.60891i	0.362709	+	0.628230i
$34$	−12.0315			−2.06338
$35$	6.15553	+	10.6617i	1.04047	+	1.80215i
$36$	−5.16460	+	8.94535i	−0.860766	+	1.49089i
$37$	2.82583	−	4.89449i	0.464564	−	0.804648i	−0.534618	−	0.845094i	$-0.679544\pi$
$37$	2.82583	−	4.89449i	0.464564	−	0.804648i	0.999182	+	0.0404456i	$0.0128777\pi$
$38$	8.67765			1.40770
$39$	−6.82692	−	4.33153i	−1.09318	−	0.693600i
$40$	35.2029			5.56607
$41$	4.00686	−	6.94009i	0.625767	−	1.08386i	−0.362625	−	0.931935i	$-0.618119\pi$
$41$	4.00686	−	6.94009i	0.625767	−	1.08386i	0.988392	−	0.151925i	$-0.0485473\pi$
$42$	8.59953	−	14.8948i	1.32694	−	2.29832i
$43$	−0.408032	−	0.706732i	−0.0622243	−	0.107776i	0.833235	−	0.552919i	$-0.186486\pi$
$43$	−0.408032	−	0.706732i	−0.0622243	−	0.107776i	−0.895459	+	0.445143i	$0.853153\pi$
$44$	−9.46339			−1.42666
$45$	−4.33530	−	7.50897i	−0.646269	−	1.11937i
$46$	3.85000	+	6.66840i	0.567652	+	0.983201i
$47$	−9.93802			−1.44961			−0.724804	−	0.688955i	$-0.758070\pi$
$47$	−9.93802			−1.44961			−0.724804	+	0.688955i	$0.758070\pi$
$48$	−13.1709	−	22.8127i	−1.90106	−	3.29273i
$49$	−0.647274	+	1.12111i	−0.0924677	+	0.160159i
$50$	−17.6733	+	30.6110i	−2.49938	+	4.32905i
$51$	−10.1307			−1.41858
$52$	16.2704	−	8.50804i	2.25630	−	1.17985i
$53$	−10.5819			−1.45354			−0.726770	−	0.686881i	$-0.758979\pi$
$53$	−10.5819			−1.45354			−0.726770	+	0.686881i	$0.758979\pi$
$54$	2.90117	−	5.02497i	0.394799	−	0.683812i
$55$	3.97191	−	6.87956i	0.535573	−	0.927639i
$56$	11.8589	+	20.5403i	1.58472	+	2.74481i
$57$	7.30672			0.967798
$58$	−3.43580	−	5.95098i	−0.451142	−	0.781401i
$59$	−2.65141	−	4.59238i	−0.345184	−	0.597877i	0.640203	−	0.768206i	$-0.278850\pi$
$59$	−2.65141	−	4.59238i	−0.345184	−	0.597877i	−0.985387	+	0.170329i	$0.945517\pi$
$60$	48.8123			6.30164
$61$	−2.98864	−	5.17647i	−0.382656	−	0.662779i	0.608785	−	0.793335i	$-0.291657\pi$
$61$	−2.98864	−	5.17647i	−0.382656	−	0.662779i	−0.991441	+	0.130556i	$0.958324\pi$
$62$	−1.33157	+	2.30635i	−0.169110	+	0.292907i
$63$	2.92090	−	5.05915i	0.367999	−	0.637393i
$64$	15.9566			1.99458
$65$	−0.643860	+	15.3990i	−0.0798610	+	1.91001i
$66$	−11.0979			−1.36605
$67$	−0.949280	+	1.64420i	−0.115973	+	0.200871i	−0.918168	−	0.396191i	$-0.870332\pi$
$67$	−0.949280	+	1.64420i	−0.115973	+	0.200871i	0.802195	+	0.597062i	$0.203665\pi$
$68$	11.5030	−	19.9238i	1.39494	−	2.41611i
$69$	3.24176	+	5.61489i	0.390262	+	0.675954i
$70$	−32.7861			−3.91869
$71$	1.03692	+	1.79600i	0.123060	+	0.213146i	0.920973	−	0.389627i	$-0.127396\pi$
$71$	1.03692	+	1.79600i	0.123060	+	0.213146i	−0.797913	+	0.602772i	$0.794063\pi$
$72$	−8.35218	−	14.4664i	−0.984314	−	1.70488i
$73$	5.58655			0.653856			0.326928	−	0.945049i	$-0.393987\pi$
$73$	5.58655			0.653856			0.326928	+	0.945049i	$0.393987\pi$
$74$	7.52559	+	13.0347i	0.874832	+	1.51525i
$75$	−14.8812	+	25.7750i	−1.71833	+	2.97624i
$76$	−8.29648	+	14.3699i	−0.951672	+	1.64834i
$77$	5.35213			0.609932
$78$	19.0806	−	9.97751i	2.16045	−	1.12973i
$79$	−8.08816			−0.909989			−0.454994	−	0.890494i	$-0.650359\pi$
$79$	−8.08816			−0.909989			−0.454994	+	0.890494i	$0.650359\pi$
$80$	−25.1073	+	43.4872i	−2.80708	+	4.86201i
$81$	5.48540	−	9.50100i	0.609489	−	1.05567i
$82$	10.6708	+	18.4824i	1.17840	+	2.04104i
$83$	−0.931615			−0.102258			−0.0511290	−	0.998692i	$-0.516282\pi$
$83$	−0.931615			−0.102258			−0.0511290	+	0.998692i	$0.516282\pi$
$84$	16.4436	+	28.4811i	1.79414	+	3.10755i
$85$	9.65594	+	16.7246i	1.04733	+	1.81403i
$86$	2.17329			0.234352
$87$	−2.89299	−	5.01081i	−0.310162	−	0.537216i
$88$	7.65209	−	13.2538i	0.815715	−	1.41286i
$89$	−6.58674	+	11.4086i	−0.698193	+	1.20931i	0.270899	+	0.962608i	$0.412679\pi$
$89$	−6.58674	+	11.4086i	−0.698193	+	1.20931i	−0.969092	+	0.246699i	$0.920654\pi$
$90$	23.0911			2.43401
$91$	−9.20193	+	4.81183i	−0.964624	+	0.504416i
$92$	−14.7236			−1.53504
$93$	−1.12120	+	1.94198i	−0.116263	+	0.201374i
$94$	13.2332	−	22.9205i	1.36490	−	2.36407i
$95$	−6.96429	−	12.0625i	−0.714521	−	1.23759i
$96$	33.2182			3.39032
$97$	−1.00594	−	1.74233i	−0.102137	−	0.176907i	0.810428	−	0.585839i	$-0.199235\pi$
$97$	−1.00594	−	1.74233i	−0.102137	−	0.176907i	−0.912565	+	0.408932i	$0.865901\pi$
$98$	−1.72378	−	2.98568i	−0.174128	−	0.301599i
$99$	−3.76948			−0.378847
$100$	−33.7940	−	58.5328i	−3.37940	−	5.85328i
$101$	5.35770	−	9.27980i	0.533111	−	0.923375i	−0.466141	−	0.884710i	$-0.654356\pi$
$101$	5.35770	−	9.27980i	0.533111	−	0.923375i	0.999252	−	0.0386648i	$-0.0123105\pi$
$102$	13.4897	−	23.3649i	1.33568	−	2.31347i
$103$	−1.45981			−0.143839			−0.0719195	−	0.997410i	$-0.522912\pi$
$103$	−1.45981			−0.143839			−0.0719195	+	0.997410i	$0.522912\pi$
$104$	−1.24043	+	29.6669i	−0.121634	+	2.90908i
$105$	−27.6064			−2.69411
$106$	14.0906	−	24.4056i	1.36860	−	2.37048i
$107$	−6.76418	+	11.7159i	−0.653918	+	1.13262i	0.328246	+	0.944592i	$0.393543\pi$
$107$	−6.76418	+	11.7159i	−0.653918	+	1.13262i	−0.982164	+	0.188027i	$0.939791\pi$
$108$	5.54746	+	9.60849i	0.533805	+	0.924577i
$109$	11.6718			1.11796			0.558979	−	0.829182i	$-0.311193\pi$
$109$	11.6718			1.11796			0.558979	+	0.829182i	$0.311193\pi$
$110$	10.5778	+	18.3212i	1.00855	+	1.74686i
$111$	6.33666	+	10.9754i	0.601450	+	1.04174i
$112$	−33.8320			−3.19682
$113$	−6.96866	−	12.0701i	−0.655556	−	1.13546i	−0.981754	−	0.190155i	$-0.939101\pi$
$113$	−6.96866	−	12.0701i	−0.655556	−	1.13546i	0.326198	−	0.945301i	$-0.394232\pi$
$114$	−9.72941	+	16.8518i	−0.911243	+	1.57832i
$115$	6.17967	−	10.7035i	0.576258	−	0.998107i
$116$	13.1395			1.21997
$117$	6.48086	−	3.38894i	0.599156	−	0.313308i
$118$	14.1222			1.30005
$119$	−6.50566	+	11.2681i	−0.596373	+	1.03295i
$120$	−39.4696	+	68.3633i	−3.60306	+	6.24069i
$121$	3.77324	+	6.53545i	0.343022	+	0.594132i
$122$	15.9183			1.44118
$123$	8.98502	+	15.5625i	0.810152	+	1.40322i
$124$	−2.54616	−	4.41008i	−0.228652	−	0.396037i
$125$	35.3620			3.16287
$126$	7.77877	+	13.4732i	0.692988	+	1.20029i
$127$	0.279582	−	0.484251i	0.0248089	−	0.0429703i	−0.853354	−	0.521331i	$-0.825436\pi$
$127$	0.279582	−	0.484251i	0.0248089	−	0.0429703i	0.878163	+	0.478361i	$0.158769\pi$
$128$	−6.43370	+	11.1435i	−0.568664	+	0.984955i
$129$	1.82995			0.161118
$130$	−34.6580	−	21.9898i	−3.03971	−	1.92863i
$131$	11.0113			0.962059			0.481030	−	0.876704i	$-0.340263\pi$
$131$	11.0113			0.962059			0.481030	+	0.876704i	$0.340263\pi$
$132$	10.6104	−	18.3777i	0.923515	−	1.59958i
$133$	4.69218	−	8.12709i	0.406863	−	0.704708i
$134$	−2.52807	−	4.37874i	−0.218392	−	0.378266i
$135$	−9.31338			−0.801568
$136$	18.6026	+	32.2207i	1.59516	+	2.76290i
$137$	−5.06525	−	8.77326i	−0.432753	−	0.749551i	0.564356	−	0.825531i	$-0.309125\pi$
$137$	−5.06525	−	8.77326i	−0.432753	−	0.749551i	−0.997109	+	0.0759809i	$0.975791\pi$
$138$	−17.2665			−1.46982
$139$	−1.08387	−	1.87731i	−0.0919324	−	0.159232i	0.816392	−	0.577498i	$-0.195971\pi$
$139$	−1.08387	−	1.87731i	−0.0919324	−	0.159232i	−0.908324	+	0.418267i	$0.862638\pi$
$140$	31.3460	−	54.2928i	2.64922	−	4.58858i
$141$	11.1425	−	19.2994i	0.938371	−	1.62531i
$142$	−5.52293			−0.463474
$143$	5.65772	+	3.58970i	0.473122	+	0.300186i
$144$	23.8277			1.98564
$145$	−5.51483	+	9.55197i	−0.457982	+	0.793248i
$146$	−7.43888	+	12.8845i	−0.615646	+	1.06633i
$147$	−1.45145	−	2.51399i	−0.119714	−	0.207350i
$148$	−28.7801			−2.36571
$149$	−5.76236	−	9.98071i	−0.472071	−	0.817651i	0.527418	−	0.849606i	$-0.323160\pi$
$149$	−5.76236	−	9.98071i	−0.472071	−	0.817651i	−0.999489	+	0.0319546i	$0.989827\pi$
$150$	−39.6307	−	68.6424i	−3.23583	−	5.60462i
$151$	18.3774			1.49553			0.747765	−	0.663963i	$-0.231127\pi$
$151$	18.3774			1.49553			0.747765	+	0.663963i	$0.231127\pi$
$152$	−13.4171	−	23.2390i	−1.08827	−	1.88493i
$153$	4.58190	−	7.93609i	0.370425	−	0.641594i
$154$	−7.12675	+	12.3439i	−0.574290	+	0.994699i
$155$	4.27464			0.343347
$156$	−1.71998	+	41.1361i	−0.137708	+	3.29352i
$157$	19.5222			1.55804			0.779020	−	0.626999i	$-0.215717\pi$
$157$	19.5222			1.55804			0.779020	+	0.626999i	$0.215717\pi$
$158$	10.7700	−	18.6541i	0.856812	−	1.48404i
$159$	11.8645	−	20.5499i	0.940915	−	1.62971i
$160$	−31.6615	−	54.8393i	−2.50306	−	4.33542i
$161$	8.32708			0.656266
$162$	14.6084	+	25.3025i	1.14775	+	1.98795i
$163$	2.00343	+	3.47004i	0.156921	+	0.271795i	0.933757	−	0.357908i	$-0.116510\pi$
$163$	2.00343	+	3.47004i	0.156921	+	0.271795i	−0.776836	+	0.629703i	$0.783177\pi$
$164$	−40.8085			−3.18661
$165$	8.90664	+	15.4268i	0.693381	+	1.20097i
$166$	1.24051	−	2.14863i	0.0962823	−	0.166766i
$167$	3.65941	−	6.33828i	0.283173	−	0.490471i	−0.688991	−	0.724770i	$-0.741946\pi$
$167$	3.65941	−	6.33828i	0.283173	−	0.490471i	0.972165	+	0.234299i	$0.0752795\pi$
$168$	−53.1851			−4.10332
$169$	−12.9546	−	1.08521i	−0.996510	−	0.0834778i
$170$	−51.4303			−3.94452
$171$	−3.30467	+	5.72386i	−0.252715	+	0.437714i
$172$	−2.07783	+	3.59891i	−0.158433	+	0.274414i
$173$	−2.24637	−	3.89083i	−0.170789	−	0.295815i	0.767907	−	0.640561i	$-0.221298\pi$
$173$	−2.24637	−	3.89083i	−0.170789	−	0.295815i	−0.938696	+	0.344747i	$0.887965\pi$
$174$	15.4089			1.16815
$175$	19.1126	+	33.1040i	1.44478	+	2.50242i
$176$	10.9152	+	18.9057i	0.822765	+	1.42507i
$177$	11.8911			0.893789
$178$	−17.5414	−	30.3826i	−1.31479	−	2.27728i
$179$	0.261548	−	0.453014i	0.0195490	−	0.0338598i	−0.856085	−	0.516834i	$-0.827110\pi$
$179$	0.261548	−	0.453014i	0.0195490	−	0.0338598i	0.875634	+	0.482975i	$0.160444\pi$
$180$	−22.0768	+	38.2381i	−1.64551	+	2.85010i
$181$	−10.5726			−0.785853			−0.392926	−	0.919570i	$-0.628537\pi$
$181$	−10.5726			−0.785853			−0.392926	+	0.919570i	$0.628537\pi$
$182$	1.15527	−	27.6301i	0.0856342	−	2.04808i
$183$	13.4035			0.990813
$184$	11.9055	−	20.6208i	0.877681	−	1.52019i
$185$	12.0794	−	20.9221i	0.888095	−	1.53823i
$186$	−2.98592	−	5.17177i	−0.218938	−	0.379213i
$187$	8.39568			0.613953
$188$	25.3038	+	43.8275i	1.84547	+	3.19645i
$189$	−3.13744	−	5.43420i	−0.228215	−	0.395280i
$190$	37.0938			2.69107
$191$	−0.554450	−	0.960336i	−0.0401186	−	0.0694875i	0.845269	−	0.534341i	$-0.179440\pi$
$191$	−0.554450	−	0.960336i	−0.0401186	−	0.0694875i	−0.885387	+	0.464854i	$0.846107\pi$
$192$	−17.8906	+	30.9874i	−1.29114	+	2.23632i
$193$	−9.30450	+	16.1159i	−0.669753	+	1.16005i	0.308221	+	0.951315i	$0.400267\pi$
$193$	−9.30450	+	16.1159i	−0.669753	+	1.16005i	−0.977973	+	0.208731i	$0.933067\pi$
$194$	5.35790			0.384675
$195$	−29.1826	−	18.5157i	−2.08981	−	1.32594i
$196$	6.59226			0.470876
$197$	−12.8504	+	22.2575i	−0.915551	+	1.58578i	−0.109460	+	0.993991i	$0.534912\pi$
$197$	−12.8504	+	22.2575i	−0.915551	+	1.58578i	−0.806092	+	0.591790i	$0.798421\pi$
$198$	5.01933	−	8.69373i	0.356708	−	0.617836i
$199$	8.53523	+	14.7835i	0.605047	+	1.04797i	0.992044	+	0.125891i	$0.0401789\pi$
$199$	8.53523	+	14.7835i	0.605047	+	1.04797i	−0.386998	+	0.922081i	$0.626488\pi$
$200$	109.303			7.72889
$201$	−2.12867	−	3.68697i	−0.150145	−	0.260059i
$202$	14.2683	+	24.7134i	1.00391	+	1.73883i
$203$	−7.43121			−0.521569
$204$	25.7944	+	44.6772i	1.80597	+	3.12803i
$205$	17.1279	−	29.6664i	1.19626	−	2.07199i
$206$	1.94383	−	3.36682i	0.135433	−	0.234577i
$207$	−5.86472			−0.407626
$208$	−35.7636	−	22.6913i	−2.47976	−	1.57336i
$209$	−6.05534			−0.418857
$210$	36.7599	−	63.6700i	2.53667	−	4.39365i
$211$	5.28261	−	9.14975i	0.363670	−	0.629895i	−0.624892	−	0.780711i	$-0.714857\pi$
$211$	5.28261	−	9.14975i	0.363670	−	0.629895i	0.988562	+	0.150816i	$0.0481903\pi$
$212$	26.9433	+	46.6672i	1.85047	+	3.20512i
$213$	−4.65039			−0.318639
$214$	−18.0140	−	31.2011i	−1.23141	−	2.13286i
$215$	−1.74419	−	3.02102i	−0.118953	−	0.206032i
$216$	−17.9427			−1.22085
$217$	1.44001	+	2.49418i	0.0977544	+	0.169316i
$218$	−15.5419	+	26.9193i	−1.05263	+	1.82320i
$219$	−6.26365	+	10.8490i	−0.423258	+	0.733105i
$220$	−40.4525			−2.72731
$221$	−14.4347	+	7.54812i	−0.970983	+	0.507742i
$222$	−33.7509			−2.26521
$223$	−2.46794	+	4.27461i	−0.165266	+	0.286249i	−0.936750	−	0.350000i	$-0.886182\pi$
$223$	−2.46794	+	4.27461i	−0.165266	+	0.286249i	0.771484	+	0.636249i	$0.219515\pi$
$224$	21.3318	−	36.9478i	1.42529	−	2.46868i
$225$	−13.4609	−	23.3149i	−0.897392	−	1.55433i
$226$	37.1170			2.46899
$227$	−9.77953	−	16.9387i	−0.649091	−	1.12426i	−0.983340	−	0.181773i	$-0.941816\pi$
$227$	−9.77953	−	16.9387i	−0.649091	−	1.12426i	0.334250	−	0.942484i	$-0.391517\pi$
$228$	−18.6041	−	32.2232i	−1.23209	−	2.13403i
$229$	−4.23687			−0.279980			−0.139990	−	0.990153i	$-0.544707\pi$
$229$	−4.23687			−0.279980			−0.139990	+	0.990153i	$0.544707\pi$
$230$	16.4573	+	28.5050i	1.08517	+	1.87956i
$231$	−6.00083	+	10.3937i	−0.394826	+	0.683858i
$232$	−10.6246	+	18.4023i	−0.697539	+	1.20817i
$233$	1.37441			0.0900404			0.0450202	−	0.998986i	$-0.485665\pi$
$233$	1.37441			0.0900404			0.0450202	+	0.998986i	$0.485665\pi$
$234$	−0.813649	+	19.4597i	−0.0531899	+	1.27212i
$235$	−42.4814			−2.77118
$236$	−13.5019	+	23.3859i	−0.878896	+	1.52229i
$237$	9.06847	−	15.7070i	0.589060	−	1.02028i
$238$	−17.3255	−	30.0087i	−1.12305	−	1.94517i
$239$	−21.0076			−1.35887			−0.679435	−	0.733736i	$-0.737775\pi$
$239$	−21.0076			−1.35887			−0.679435	+	0.733736i	$0.737775\pi$
$240$	−56.3008	−	97.5159i	−3.63420	−	6.29462i
$241$	14.3749	+	24.8980i	0.925968	+	1.60382i	0.789997	+	0.613111i	$0.210082\pi$
$241$	14.3749	+	24.8980i	0.925968	+	1.60382i	0.135972	+	0.990713i	$0.456584\pi$
$242$	−20.0974			−1.29191
$243$	9.03237	+	15.6445i	0.579427	+	1.00360i
$244$	−15.2191	+	26.3603i	−0.974304	+	1.68754i
$245$	−2.76686	+	4.79234i	−0.176768	+	0.306171i
$246$	−47.8567			−3.05123
$247$	10.4109	−	5.44404i	0.662433	−	0.346396i
$248$	8.23530			0.522942
$249$	1.04453	−	1.80918i	0.0661943	−	0.114652i
$250$	−47.0869	+	81.5570i	−2.97804	+	5.15812i
$251$	−2.08348	−	3.60869i	−0.131508	−	0.227778i	0.792750	−	0.609547i	$-0.208649\pi$
$251$	−2.08348	−	3.60869i	−0.131508	−	0.227778i	−0.924258	+	0.381768i	$0.875315\pi$
$252$	−29.7483			−1.87397
$253$	−2.68656	−	4.65327i	−0.168903	−	0.292548i
$254$	0.744568	+	1.28963i	0.0467183	+	0.0809185i
$255$	−43.3051			−2.71187
$256$	−1.17726	−	2.03907i	−0.0735786	−	0.127442i
$257$	0.924440	−	1.60118i	0.0576650	−	0.0998786i	−0.835752	−	0.549107i	$-0.814968\pi$
$257$	0.924440	−	1.60118i	0.0576650	−	0.0998786i	0.893417	+	0.449229i	$0.148301\pi$
$258$	−2.43670	+	4.22049i	−0.151703	+	0.262756i
$259$	16.2769			1.01140
$260$	69.5501	−	36.3688i	4.31331	−	2.25550i
$261$	5.23376			0.323962
$262$	−14.6623	+	25.3958i	−0.905839	+	1.56896i
$263$	6.25884	−	10.8406i	0.385937	−	0.668462i	−0.605962	−	0.795494i	$-0.707212\pi$
$263$	6.25884	−	10.8406i	0.385937	−	0.668462i	0.991899	+	0.127032i	$0.0405450\pi$
$264$	17.1591	+	29.7204i	1.05607	+	1.82917i
$265$	−45.2339			−2.77870
$266$	12.4959	+	21.6436i	0.766175	+	1.32705i
$267$	−14.7702	−	25.5827i	−0.903919	−	1.56563i
$268$	9.66809			0.590572
$269$	2.16690	+	3.75318i	0.132118	+	0.228835i	0.924493	−	0.381199i	$-0.124489\pi$
$269$	2.16690	+	3.75318i	0.132118	+	0.228835i	−0.792375	+	0.610035i	$0.791156\pi$
$270$	12.4014	−	21.4799i	0.754727	−	1.30723i
$271$	3.12854	−	5.41880i	0.190046	−	0.329169i	−0.755220	−	0.655472i	$-0.772470\pi$
$271$	3.12854	−	5.41880i	0.190046	−	0.329169i	0.945265	+	0.326303i	$0.105803\pi$
$272$	−53.0709			−3.21790
$273$	0.972754	−	23.2650i	0.0588737	−	1.40806i
$274$	26.9789			1.62986
$275$	12.3326	−	21.3606i	0.743682	−	1.28810i
$276$	16.5081	−	28.5929i	0.993670	−	1.72109i
$277$	−4.39591	−	7.61394i	−0.264125	−	0.457477i	0.703209	−	0.710983i	$-0.251750\pi$
$277$	−4.39591	−	7.61394i	−0.264125	−	0.457477i	−0.967334	+	0.253506i	$0.918416\pi$
$278$	5.77298			0.346240
$279$	−1.01419	−	1.75663i	−0.0607181	−	0.105167i
$280$	50.6926	+	87.8022i	3.02946	+	5.24719i
$281$	20.3514			1.21406			0.607032	−	0.794677i	$-0.292360\pi$
$281$	20.3514			1.21406			0.607032	+	0.794677i	$0.292360\pi$
$282$	29.6742	+	51.3971i	1.76707	+	3.06065i
$283$	6.49963	−	11.2577i	0.386363	−	0.669200i	−0.605595	−	0.795773i	$-0.707065\pi$
$283$	6.49963	−	11.2577i	0.386363	−	0.669200i	0.991957	+	0.126574i	$0.0403980\pi$
$284$	5.28033	−	9.14580i	0.313330	−	0.542703i
$285$	31.2335			1.85012
$286$	−15.8127	+	8.26873i	−0.935027	+	0.488940i
$287$	23.0797			1.36235
$288$	−15.0239	+	26.0221i	−0.885291	+	1.53337i
$289$	−1.70518	+	2.95345i	−0.100305	+	0.173733i
$290$	−14.6868	−	25.4383i	−0.862438	−	1.49379i
$291$	4.51144			0.264465
$292$	−14.2242	−	24.6371i	−0.832411	−	1.44178i
$293$	15.2231	+	26.3672i	0.889342	+	1.54039i	0.840654	+	0.541572i	$0.182171\pi$
$293$	15.2231	+	26.3672i	0.889342	+	1.54039i	0.0486881	+	0.998814i	$0.484496\pi$
$294$	7.73084			0.450872
$295$	−11.3338	−	19.6308i	−0.659881	−	1.14295i
$296$	23.2716	−	40.3075i	1.35263	−	2.34283i
$297$	−2.02446	+	3.50647i	−0.117471	+	0.203466i
$298$	30.6920			1.77794
$299$	8.80252	+	5.58501i	0.509063	+	0.322989i
$300$	151.560			8.75029
$301$	1.17514	−	2.03541i	0.0677341	−	0.117319i
$302$	−24.4708	+	42.3846i	−1.40814	+	2.43896i
$303$	12.0141	+	20.8091i	0.690194	+	1.19545i
$304$	38.2771			2.19534
$305$	−12.7753	−	22.1275i	−0.731513	−	1.26702i
$306$	12.2023	+	21.1349i	0.697556	+	1.20820i
$307$	20.8458			1.18973			0.594867	−	0.803824i	$-0.297205\pi$
$307$	20.8458			1.18973			0.594867	+	0.803824i	$0.297205\pi$
$308$	−13.6274	−	23.6034i	−0.776493	−	1.34493i
$309$	1.63674	−	2.83491i	0.0931108	−	0.161273i
$310$	−5.69198	+	9.85880i	−0.323283	+	0.559942i
$311$	17.2853			0.980162			0.490081	−	0.871677i	$-0.336967\pi$
$311$	17.2853			0.980162			0.490081	+	0.871677i	$0.336967\pi$
$312$	−56.2217	−	35.6715i	−3.18293	−	2.01950i
$313$	−8.70885			−0.492253			−0.246127	−	0.969238i	$-0.579158\pi$
$313$	−8.70885			−0.492253			−0.246127	+	0.969238i	$0.579158\pi$
$314$	−25.9952	+	45.0250i	−1.46699	+	2.54091i
$315$	12.4858	−	21.6260i	0.703494	−	1.21849i
$316$	20.5938	+	35.6694i	1.15849	+	2.00656i
$317$	−28.6587			−1.60963			−0.804816	−	0.593524i	$-0.797736\pi$
$317$	−28.6587			−1.60963			−0.804816	+	0.593524i	$0.797736\pi$
$318$	31.5968	+	54.7273i	1.77186	+	3.06895i
$319$	2.39753	+	4.15264i	0.134236	+	0.232503i
$320$	68.2087			3.81298
$321$	−15.1680	−	26.2718i	−0.846597	−	1.46635i
$322$	−11.0881	+	19.2052i	−0.617916	+	1.07026i
$323$	7.36043	−	12.7486i	0.409545	−	0.709353i
$324$	−55.8669			−3.10372
$325$	−1.99915	+	47.8129i	−0.110893	+	2.65218i
$326$	−10.6708			−0.591003
$327$	−13.0865	+	22.6664i	−0.723684	+	1.25346i
$328$	32.9977	−	57.1537i	1.82199	−	3.15579i
$329$	−14.3109	−	24.7872i	−0.788984	−	1.36656i
$330$	−47.4393			−2.61145
$331$	0.0296926	+	0.0514291i	0.00163205	+	0.00282680i	0.866840	−	0.498586i	$-0.166147\pi$
$331$	0.0296926	+	0.0514291i	0.00163205	+	0.00282680i	−0.865208	+	0.501413i	$0.832814\pi$
$332$	2.37204	+	4.10850i	0.130183	+	0.225483i
$333$	−11.4638			−0.628210
$334$	9.74552	+	16.8797i	0.533251	+	0.923618i
$335$	−4.05783	+	7.02836i	−0.221703	+	0.384000i
$336$	37.9325	−	65.7011i	2.06939	−	3.58429i
$337$	−5.65334			−0.307957			−0.153979	−	0.988074i	$-0.549209\pi$
$337$	−5.65334			−0.307957			−0.153979	+	0.988074i	$0.549209\pi$
$338$	19.7529	−	28.4328i	1.07441	−	1.54654i
$339$	31.2531			1.69744
$340$	49.1712	−	85.1669i	2.66668	−	4.61883i
$341$	0.929182	−	1.60939i	0.0503180	−	0.0871534i
$342$	−8.80081	−	15.2434i	−0.475893	−	0.824271i
$343$	16.4318			0.887236
$344$	−3.36026	−	5.82015i	−0.181173	−	0.313801i
$345$	13.8573	+	24.0016i	0.746054	+	1.29220i
$346$	11.9648			0.643233
$347$	10.7521	+	18.6231i	0.577201	+	0.999741i	0.995799	+	0.0915692i	$0.0291883\pi$
$347$	10.7521	+	18.6231i	0.577201	+	0.999741i	−0.418598	+	0.908172i	$0.637478\pi$
$348$	−14.7321	+	25.5167i	−0.789722	+	1.36784i
$349$	2.68607	−	4.65241i	0.143782	−	0.249038i	−0.785136	−	0.619324i	$-0.787407\pi$
$349$	2.68607	−	4.65241i	0.143782	−	0.249038i	0.928918	+	0.370286i	$0.120740\pi$
$350$	−101.799			−5.44139
$351$	0.328171	−	7.84875i	0.0175165	−	0.418936i
$352$	−27.5291			−1.46731
$353$	0.0877344	−	0.151960i	0.00466963	−	0.00808804i	−0.863681	−	0.504039i	$-0.831847\pi$
$353$	0.0877344	−	0.151960i	0.00466963	−	0.00808804i	0.868351	+	0.495951i	$0.165180\pi$
$354$	−15.8338	+	27.4250i	−0.841558	+	1.45762i
$355$	4.43245	+	7.67723i	0.235250	+	0.407465i
$356$	67.0837			3.55543
$357$	−14.5883	−	25.2677i	−0.772097	−	1.33731i
$358$	0.696539	+	1.20644i	0.0368132	+	0.0637624i
$359$	0.0394691			0.00208310			0.00104155	−	0.999999i	$-0.499668\pi$
$359$	0.0394691			0.00208310			0.00104155	+	0.999999i	$0.499668\pi$
$360$	−35.7025	−	61.8386i	−1.88169	−	3.25918i
$361$	4.19133	−	7.25959i	0.220596	−	0.382084i
$362$	14.0781	−	24.3840i	0.739930	−	1.28160i
$363$	−16.9223			−0.888190
$364$	44.6501	+	28.3296i	2.34030	+	1.48487i
$365$	23.8804			1.24996
$366$	−17.8477	+	30.9131i	−0.932913	+	1.61585i
$367$	15.6621	−	27.1275i	0.817553	−	1.41604i	−0.0899280	−	0.995948i	$-0.528664\pi$
$367$	15.6621	−	27.1275i	0.817553	−	1.41604i	0.907480	−	0.420094i	$-0.138003\pi$
$368$	16.9824	+	29.4143i	0.885266	+	1.53333i
$369$	−16.2549			−0.846198
$370$	32.1692	+	55.7186i	1.67240	+	2.89667i
$371$	−15.2381	−	26.3932i	−0.791123	−	1.37027i
$372$	11.4191			0.592051
$373$	−6.12396	−	10.6070i	−0.317087	−	0.549210i	0.662792	−	0.748803i	$-0.269371\pi$
$373$	−6.12396	−	10.6070i	−0.317087	−	0.549210i	−0.979879	+	0.199593i	$0.936038\pi$
$374$	−11.1794	+	19.3634i	−0.578075	+	1.00126i
$375$	−39.6479	+	68.6722i	−2.04741	+	3.54622i
$376$	−81.8425			−4.22071
$377$	−7.85550	−	4.98415i	−0.404579	−	0.256697i
$378$	16.7109			0.859514
$379$	13.8330	−	23.9594i	0.710552	−	1.23071i	−0.254099	−	0.967178i	$-0.581779\pi$
$379$	13.8330	−	23.9594i	0.710552	−	1.23071i	0.964650	−	0.263533i	$-0.0848878\pi$
$380$	−35.4644	+	61.4262i	−1.81929	+	3.15110i
$381$	0.626937	+	1.08589i	0.0321190	+	0.0556317i
$382$	2.95316			0.151097
$383$	−5.24610	−	9.08651i	−0.268063	−	0.464299i	0.700298	−	0.713850i	$-0.253050\pi$
$383$	−5.24610	−	9.08651i	−0.268063	−	0.464299i	−0.968362	+	0.249551i	$0.919717\pi$
$384$	−14.4270	−	24.9882i	−0.736223	−	1.27518i
$385$	22.8784			1.16599
$386$	−24.7792	−	42.9188i	−1.26123	−	2.18451i
$387$	−0.827646	+	1.43352i	−0.0420716	+	0.0728701i
$388$	−5.12256	+	8.87253i	−0.260058	+	0.450434i
$389$	−0.505975			−0.0256539			−0.0128270	−	0.999918i	$-0.504083\pi$
$389$	−0.505975			−0.0256539			−0.0128270	+	0.999918i	$0.504083\pi$
$390$	81.5624	−	42.6502i	4.13007	−	2.15968i
$391$	13.0624			0.660592
$392$	−5.33049	+	9.23269i	−0.269231	+	0.466321i
$393$	−12.3459	+	21.3837i	−0.622767	+	1.07866i
$394$	−34.2224	−	59.2749i	−1.72410	−	2.98623i
$395$	−34.5739			−1.73960
$396$	9.59770	+	16.6237i	0.482303	+	0.835373i
$397$	−4.98191	−	8.62892i	−0.250035	−	0.433073i	0.713500	−	0.700655i	$-0.247109\pi$
$397$	−4.98191	−	8.62892i	−0.250035	−	0.433073i	−0.963535	+	0.267582i	$0.913775\pi$
$398$	−45.4611			−2.27876
$399$	10.5218	+	18.2242i	0.526747	+	0.912353i
$400$	−77.9569	+	135.025i	−3.89784	+	6.75126i
$401$	−8.76186	+	15.1760i	−0.437546	+	0.757853i	−0.997500	−	0.0706716i	$-0.977486\pi$
$401$	−8.76186	+	15.1760i	−0.437546	+	0.757853i	0.559953	+	0.828524i	$0.310819\pi$
$402$	11.3379			0.565484
$403$	−0.150623	+	3.60240i	−0.00750308	+	0.179449i
$404$	−54.5663			−2.71477
$405$	23.4481	−	40.6133i	1.16515	−	2.01809i
$406$	9.89519	−	17.1390i	0.491090	−	0.850593i
$407$	−5.25142	−	9.09573i	−0.260303	−	0.450859i
$408$	−83.4294			−4.13037
$409$	−1.89631	−	3.28451i	−0.0937667	−	0.162409i	0.815326	−	0.579001i	$-0.196557\pi$
$409$	−1.89631	−	3.28451i	−0.0937667	−	0.162409i	−0.909093	+	0.416593i	$0.863224\pi$
$410$	45.6140	+	79.0057i	2.25271	+	3.90181i
$411$	22.7167			1.12053
$412$	3.71690	+	6.43786i	0.183119	+	0.317171i
$413$	7.63614	−	13.2262i	0.375750	−	0.650817i
$414$	7.80928	−	13.5261i	0.383805	−	0.664770i
$415$	−3.98231			−0.195484
$416$	47.3309	−	24.7500i	2.32059	−	1.21347i
$417$	4.86094			0.238041
$418$	8.06312	−	13.9657i	0.394380	−	0.683086i
$419$	−8.85032	+	15.3292i	−0.432366	+	0.748881i	−0.997077	−	0.0764087i	$-0.975655\pi$
$419$	−8.85032	+	15.3292i	−0.432366	+	0.748881i	0.564710	+	0.825289i	$0.308988\pi$
$420$	70.2904	+	121.746i	3.42982	+	5.94062i
$421$	−0.387735			−0.0188970			−0.00944852	−	0.999955i	$-0.503008\pi$
$421$	−0.387735			−0.0188970			−0.00944852	+	0.999955i	$0.503008\pi$
$422$	14.0683	+	24.3671i	0.684836	+	1.18617i
$423$	10.0791	+	17.4574i	0.490061	+	0.848810i
$424$	−87.1453			−4.23215
$425$	29.9811	+	51.9289i	1.45430	+	2.51892i
$426$	6.19232	−	10.7254i	0.300019	−	0.519648i
$427$	8.60735	−	14.9084i	0.416539	−	0.721467i
$428$	68.8908			3.32996
$429$	−13.3146	+	6.96239i	−0.642834	+	0.336148i
$430$	9.29004			0.448005
$431$	−8.98534	+	15.5631i	−0.432809	+	0.749646i	−0.997114	−	0.0759198i	$-0.975811\pi$
$431$	−8.98534	+	15.5631i	−0.432809	+	0.749646i	0.564305	+	0.825566i	$0.309144\pi$
$432$	12.7970	−	22.1651i	0.615698	−	1.06642i
$433$	8.15415	+	14.1234i	0.391864	+	0.678728i	0.992695	−	0.120648i	$-0.0384972\pi$
$433$	8.15415	+	14.1234i	0.391864	+	0.678728i	−0.600832	+	0.799376i	$0.705164\pi$
$434$	−7.66992			−0.368168
$435$	−12.3665	−	21.4194i	−0.592928	−	1.02698i
$436$	−29.7183	−	51.4737i	−1.42325	−	2.46514i
$437$	−9.42116			−0.450675
$438$	−16.6810	−	28.8923i	−0.797049	−	1.38053i
$439$	3.10294	−	5.37445i	0.148095	−	0.256509i	−0.782428	−	0.622741i	$-0.786019\pi$
$439$	3.10294	−	5.37445i	0.148095	−	0.256509i	0.930523	+	0.366232i	$0.119352\pi$
$440$	32.7099	−	56.6552i	1.55938	−	2.70093i
$441$	2.62584			0.125040
$442$	1.81222	−	43.3423i	0.0861987	−	2.06158i
$443$	−38.4781			−1.82815			−0.914074	−	0.405548i	$-0.867081\pi$
$443$	−38.4781			−1.82815			−0.914074	+	0.405548i	$0.867081\pi$
$444$	32.2683	−	55.8904i	1.53139	−	2.65244i
$445$	−28.1559	+	48.7675i	−1.33472	+	2.31180i
$446$	−6.57249	−	11.3839i	−0.311216	−	0.539042i
$447$	25.8431			1.22234
$448$	22.9777	+	39.7986i	1.08559	+	1.88031i
$449$	−16.9459	−	29.3511i	−0.799726	−	1.38517i	−0.919794	−	0.392401i	$-0.871645\pi$
$449$	−16.9459	−	29.3511i	−0.799726	−	1.38517i	0.120068	−	0.992766i	$-0.461689\pi$
$450$	71.6965			3.37980
$451$	−7.44621	−	12.8972i	−0.350628	−	0.607306i
$452$	−35.4867	+	61.4647i	−1.66915	+	2.89106i
$453$	−20.6048	+	35.6885i	−0.968097	+	1.67679i
$454$	52.0886			2.44464
$455$	−39.3349	+	20.5688i	−1.84405	+	0.964280i
$456$	60.1730			2.81786
$457$	−5.59589	+	9.69236i	−0.261765	+	0.453390i	−0.966711	−	0.255871i	$-0.917638\pi$
$457$	−5.59589	+	9.69236i	−0.261765	+	0.453390i	0.704946	+	0.709261i	$0.250971\pi$
$458$	5.64169	−	9.77170i	0.263619	−	0.456602i
$459$	−4.92157	−	8.52441i	−0.229719	−	0.397885i
$460$	−62.9378			−2.93449
$461$	−16.5827	−	28.7220i	−0.772332	−	1.33772i	−0.936282	−	0.351250i	$-0.885757\pi$
$461$	−16.5827	−	28.7220i	−0.772332	−	1.33772i	0.163949	−	0.986469i	$-0.447577\pi$
$462$	−15.9811	−	27.6800i	−0.743506	−	1.28779i
$463$	25.2049			1.17137			0.585685	−	0.810539i	$-0.300826\pi$
$463$	25.2049			1.17137			0.585685	+	0.810539i	$0.300826\pi$
$464$	−15.1553	−	26.2498i	−0.703567	−	1.21861i
$465$	−4.79273	+	8.30126i	−0.222258	+	0.384962i
$466$	−1.83012	+	3.16986i	−0.0847787	+	0.146841i
$467$	11.3047			0.523119			0.261559	−	0.965187i	$-0.415763\pi$
$467$	11.3047			0.523119			0.261559	+	0.965187i	$0.415763\pi$
$468$	−31.4468	−	19.9523i	−1.45363	−	0.922297i
$469$	−5.46790			−0.252484
$470$	56.5670	−	97.9769i	2.60924	−	4.51934i
$471$	−21.8883	+	37.9117i	−1.00856	+	1.74688i
$472$	−21.8352	−	37.8196i	−1.00505	−	1.74079i
$473$	−1.51654			−0.0697307
$474$	24.1506	+	41.8301i	1.10927	+	1.92132i
$475$	−21.6237	−	37.4534i	−0.992165	−	1.71848i
$476$	66.2579			3.03693
$477$	10.7321	+	18.5886i	0.491390	+	0.851112i
$478$	27.9731	−	48.4509i	1.27946	−	2.21609i
$479$	−8.00399	+	13.8633i	−0.365712	+	0.633431i	−0.988890	−	0.148649i	$-0.952508\pi$
$479$	−8.00399	+	13.8633i	−0.365712	+	0.633431i	0.623178	+	0.782080i	$0.285841\pi$
$480$	141.996			6.48119
$481$	17.2063	+	10.9170i	0.784539	+	0.497773i
$482$	−76.5648			−3.48743
$483$	−9.33635	+	16.1710i	−0.424819	+	0.735808i
$484$	19.2146	−	33.2806i	0.873390	−	1.51276i
$485$	−4.30001	−	7.44784i	−0.195254	−	0.338189i
$486$	−48.1090			−2.18227
$487$	17.4935	+	30.2996i	0.792706	+	1.37301i	0.924286	+	0.381702i	$0.124662\pi$
$487$	17.4935	+	30.2996i	0.792706	+	1.37301i	−0.131579	+	0.991306i	$0.542005\pi$
$488$	−24.6123	−	42.6298i	−1.11415	−	1.92976i
$489$	−8.98501			−0.406316
$490$	−7.36854	−	12.7627i	−0.332877	−	0.576559i
$491$	2.76928	−	4.79653i	0.124976	−	0.216465i	−0.796748	−	0.604312i	$-0.793448\pi$
$491$	2.76928	−	4.79653i	0.124976	−	0.216465i	0.921724	+	0.387848i	$0.126781\pi$
$492$	45.7546	−	79.2493i	2.06278	−	3.57284i
$493$	−11.6570			−0.525007
$494$	−1.30706	+	31.2604i	−0.0588073	+	1.40647i
$495$	−16.1131			−0.724232
$496$	−5.87356	+	10.1733i	−0.263731	+	0.456795i
$497$	−2.98636	+	5.17252i	−0.133956	+	0.232019i
$498$	2.78173	+	4.81810i	0.124652	+	0.215904i
$499$	11.1336			0.498406			0.249203	−	0.968451i	$-0.419831\pi$
$499$	11.1336			0.498406			0.249203	+	0.968451i	$0.419831\pi$
$500$	−90.0373	−	155.949i	−4.02659	−	6.97426i
$501$	8.20587	+	14.2130i	0.366611	+	0.634990i
$502$	11.0972			0.495292
$503$	2.43104	+	4.21069i	0.108395	+	0.187745i	0.915120	−	0.403181i	$-0.132096\pi$
$503$	2.43104	+	4.21069i	0.108395	+	0.187745i	−0.806725	+	0.590927i	$0.798762\pi$
$504$	24.0545	−	41.6636i	1.07147	−	1.85584i
$505$	22.9022	−	39.6678i	1.01913	−	1.76519i
$506$	14.3094			0.636130
$507$	16.6322	−	23.9409i	0.738663	−	1.06325i
$508$	−2.84745			−0.126335
$509$	4.37775	−	7.58248i	0.194040	−	0.336087i	−0.752545	−	0.658541i	$-0.771174\pi$
$509$	4.37775	−	7.58248i	0.194040	−	0.336087i	0.946585	+	0.322453i	$0.104507\pi$
$510$	57.6638	−	99.8766i	2.55339	−	4.42261i
$511$	8.04470	+	13.9338i	0.355876	+	0.616396i
$512$	−19.4644			−0.860213
$513$	3.54966	+	6.14818i	0.156721	+	0.271449i
$514$	2.46191	+	4.26416i	0.108590	+	0.188084i
$515$	−6.24014			−0.274973
$516$	−4.65934	−	8.07021i	−0.205116	−	0.355271i
$517$	−9.23422	+	15.9941i	−0.406121	+	0.703422i
$518$	−21.6739	+	37.5403i	−0.952296	+	1.64943i
$519$	10.0746			0.442224
$520$	−5.30238	+	126.815i	−0.232525	+	5.56121i
$521$	−0.209766			−0.00919004			−0.00459502	−	0.999989i	$-0.501463\pi$
$521$	−0.209766			−0.00919004			−0.00459502	+	0.999989i	$0.501463\pi$
$522$	−6.96912	+	12.0709i	−0.305030	+	0.528328i
$523$	12.6266	−	21.8699i	0.552123	−	0.956306i	−0.445998	−	0.895034i	$-0.647151\pi$
$523$	12.6266	−	21.8699i	0.552123	−	0.956306i	0.998121	−	0.0612718i	$-0.0195156\pi$
$524$	−28.0365	−	48.5606i	−1.22478	−	2.12138i
$525$	−85.7163			−3.74097
$526$	16.6682	+	28.8701i	0.726767	+	1.25880i
$527$	2.25889	+	3.91251i	0.0983988	+	0.170432i
$528$	−48.9527			−2.13039
$529$	7.32013	+	12.6788i	0.318266	+	0.551254i
$530$	60.2321	−	104.325i	2.61632	−	4.53159i
$531$	−5.37809	+	9.31512i	−0.233389	+	0.404242i
$532$	−47.7882			−2.07188
$533$	24.3975	+	15.4797i	1.05677	+	0.670499i
$534$	78.6700			3.40438
$535$	−28.9144	+	50.0812i	−1.25008	+	2.16520i
$536$	−7.81761	+	13.5405i	−0.337669	+	0.584860i
$537$	0.586496	+	1.01584i	0.0253092	+	0.0438368i
$538$	−11.5415			−0.497590
$539$	1.20287	+	2.08343i	0.0518113	+	0.0897398i
$540$	23.7134	+	41.0728i	1.02046	+	1.76749i
$541$	−21.0964			−0.907003			−0.453502	−	0.891255i	$-0.649825\pi$
$541$	−21.0964			−0.907003			−0.453502	+	0.891255i	$0.649825\pi$
$542$	8.33176	+	14.4310i	0.357880	+	0.619866i
$543$	11.8540	−	20.5317i	0.508704	−	0.881101i
$544$	33.4624	−	57.9586i	1.43469	−	2.48495i
$545$	49.8928			2.13717
$546$	52.3619	+	33.2225i	2.24088	+	1.42179i
$547$	−22.4079			−0.958091			−0.479045	−	0.877790i	$-0.659017\pi$
$547$	−22.4079			−0.958091			−0.479045	+	0.877790i	$0.659017\pi$
$548$	−25.7939	+	44.6763i	−1.10186	+	1.90848i
$549$	−6.06211	+	10.4999i	−0.258724	+	0.448124i
$550$	32.8434	+	56.8864i	1.40045	+	2.42564i
$551$	8.40758			0.358175
$552$	26.6969	+	46.2403i	1.13629	+	1.96812i
$553$	−11.6471	−	20.1733i	−0.495283	−	0.857855i
$554$	23.4139			0.994760
$555$	27.0869	+	46.9159i	1.14978	+	1.99147i
$556$	−5.51940	+	9.55988i	−0.234075	+	0.405429i
$557$	10.6366	−	18.4232i	0.450688	−	0.780615i	−0.547741	−	0.836648i	$-0.684512\pi$
$557$	10.6366	−	18.4232i	0.450688	−	0.780615i	0.998429	+	0.0560333i	$0.0178453\pi$
$558$	5.40188			0.228680
$559$	2.60739	−	1.36345i	0.110281	−	0.0576676i
$560$	−144.619			−6.11129
$561$	−9.41326	+	16.3042i	−0.397428	+	0.688366i
$562$	−27.0994	+	46.9375i	−1.14312	+	1.97994i
$563$	4.23597	+	7.33692i	0.178525	+	0.309214i	0.941376	−	0.337360i	$-0.109534\pi$
$563$	4.23597	+	7.33692i	0.178525	+	0.309214i	−0.762851	+	0.646575i	$0.776201\pi$
$564$	−113.483			−4.77849
$565$	−29.7885	−	51.5951i	−1.25321	−	2.17062i
$566$	17.3094	+	29.9808i	0.727569	+	1.26019i
$567$	31.5962			1.32692
$568$	8.53934	+	14.7906i	0.358303	+	0.620599i
$569$	12.0112	−	20.8039i	0.503534	−	0.872146i	−0.496458	−	0.868061i	$-0.665366\pi$
$569$	12.0112	−	20.8039i	0.503534	−	0.872146i	0.999992	−	0.00408519i	$-0.00130036\pi$
$570$	−41.5897	+	72.0354i	−1.74200	+	3.01723i
$571$	−6.49543			−0.271825			−0.135913	−	0.990721i	$-0.543397\pi$
$571$	−6.49543			−0.271825			−0.135913	+	0.990721i	$0.543397\pi$
$572$	1.42541	−	34.0909i	0.0595993	−	1.42541i
$573$	2.48661			0.103879
$574$	−30.7323	+	53.2299i	−1.28274	+	2.22177i
$575$	19.1875	−	33.2338i	0.800176	−	1.38595i
$576$	−16.1831	−	28.0299i	−0.674295	−	1.16791i
$577$	−8.13454			−0.338645			−0.169323	−	0.985561i	$-0.554158\pi$
$577$	−8.13454			−0.338645			−0.169323	+	0.985561i	$0.554158\pi$
$578$	−4.54113	−	7.86546i	−0.188886	−	0.327160i
$579$	−20.8645	−	36.1383i	−0.867098	−	1.50186i
$580$	56.1666			2.33219
$581$	−1.34154	−	2.32361i	−0.0556563	−	0.0963996i
$582$	−6.00730	+	10.4049i	−0.249011	+	0.431299i
$583$	−9.83254	+	17.0305i	−0.407222	+	0.705329i
$584$	46.0069			1.90378
$585$	27.7033	−	14.4865i	1.14539	−	0.598943i
$586$	−81.0825			−3.34949
$587$	−4.23201	+	7.33005i	−0.174674	+	0.302543i	−0.940048	−	0.341041i	$-0.889220\pi$
$587$	−4.23201	+	7.33005i	−0.174674	+	0.302543i	0.765375	+	0.643585i	$0.222554\pi$
$588$	−7.39126	+	12.8020i	−0.304810	+	0.527947i
$589$	−1.62921	−	2.82188i	−0.0671306	−	0.116274i
$590$	60.3671			2.48528
$591$	−28.8158	−	49.9104i	−1.18532	−	2.05304i
$592$	33.1954	+	57.4961i	1.36432	+	2.36308i
$593$	10.9945			0.451490			0.225745	−	0.974186i	$-0.427518\pi$
$593$	10.9945			0.451490			0.225745	+	0.974186i	$0.427518\pi$
$594$	−5.39142	−	9.33822i	−0.221213	−	0.383152i
$595$	−27.8093	+	48.1672i	−1.14007	+	1.97466i
$596$	−29.3438	+	50.8250i	−1.20197	+	2.08187i
$597$	−38.2789			−1.56665
$598$	−24.6022	+	12.8648i	−1.00606	+	0.526082i
$599$	−31.0927			−1.27041			−0.635207	−	0.772342i	$-0.719085\pi$
$599$	−31.0927			−1.27041			−0.635207	+	0.772342i	$0.719085\pi$
$600$	−122.551	+	212.264i	−5.00312	+	8.66566i
$601$	3.68920	−	6.38988i	0.150486	−	0.260649i	−0.780921	−	0.624630i	$-0.785250\pi$
$601$	3.68920	−	6.38988i	0.150486	−	0.260649i	0.931406	+	0.363982i	$0.118583\pi$
$602$	3.12957	+	5.42057i	0.127552	+	0.220926i
$603$	3.85101			0.156825
$604$	−46.7918	−	81.0458i	−1.90393	−	3.29771i
$605$	16.1292	+	27.9367i	0.655747	+	1.13579i
$606$	−63.9907			−2.59944
$607$	−17.7907	−	30.8145i	−0.722104	−	1.25072i	−0.960155	−	0.279468i	$-0.909842\pi$
$607$	−17.7907	−	30.8145i	−0.722104	−	1.25072i	0.238051	−	0.971253i	$-0.423492\pi$
$608$	−24.1346	+	41.8023i	−0.978787	+	1.69531i
$609$	8.33190	−	14.4313i	0.337626	−	0.584785i
$610$	68.0451			2.75506
$611$	1.49690	−	35.8007i	0.0605580	−	1.44834i
$612$	−46.6651			−1.88632
$613$	3.95699	−	6.85371i	0.159821	−	0.276819i	−0.774983	−	0.631982i	$-0.782242\pi$
$613$	3.95699	−	6.85371i	0.159821	−	0.276819i	0.934804	+	0.355164i	$0.115575\pi$
$614$	−27.7577	+	48.0778i	−1.12021	+	1.94026i
$615$	38.4077	+	66.5240i	1.54875	+	2.68251i
$616$	44.0764			1.77589
$617$	0.644919	+	1.11703i	0.0259635	+	0.0449700i	0.878715	−	0.477346i	$-0.158401\pi$
$617$	0.644919	+	1.11703i	0.0259635	+	0.0449700i	−0.852752	+	0.522316i	$0.825068\pi$
$618$	4.35887	+	7.54978i	0.175339	+	0.303697i
$619$	−39.3137			−1.58015			−0.790076	−	0.613009i	$-0.789959\pi$
$619$	−39.3137			−1.58015			−0.790076	+	0.613009i	$0.789959\pi$
$620$	−10.8839	−	18.8515i	−0.437109	−	0.757094i
$621$	−3.14974	+	5.45551i	−0.126395	+	0.218922i
$622$	−23.0167	+	39.8660i	−0.922884	+	1.59848i
$623$	−37.9400			−1.52003
$624$	84.1643	−	44.0108i	3.36927	−	1.76184i
$625$	84.7969			3.39188
$626$	11.5964	−	20.0856i	0.463487	−	0.802784i
$627$	6.78927	−	11.7594i	0.271137	−	0.469623i
$628$	−49.7067	−	86.0945i	−1.98351	−	3.43554i
$629$	25.5330			1.01807
$630$	33.2514	+	57.5931i	1.32477	+	2.29457i
$631$	13.8829	+	24.0458i	0.552669	+	0.957250i	0.998081	+	0.0619245i	$0.0197238\pi$
$631$	13.8829	+	24.0458i	0.552669	+	0.957250i	−0.445412	+	0.895326i	$0.646943\pi$
$632$	−66.6084			−2.64954
$633$	11.8458	+	20.5175i	0.470827	+	0.815496i
$634$	38.1611	−	66.0969i	1.51557	−	2.62504i
$635$	1.19511	−	2.07000i	0.0474266	−	0.0821453i
$636$	−120.836			−4.79145
$637$	−3.94120	−	2.50061i	−0.156156	−	0.0990777i
$638$	−12.7699			−0.505566
$639$	2.10327	−	3.64297i	0.0832042	−	0.144114i
$640$	−27.5017	+	47.6344i	−1.08710	+	1.88291i
$641$	12.2474	+	21.2131i	0.483743	+	0.837867i	0.999826	−	0.0186718i	$-0.00594378\pi$
$641$	12.2474	+	21.2131i	0.483743	+	0.837867i	−0.516083	+	0.856539i	$0.672610\pi$
$642$	80.7893			3.18850
$643$	13.2208	+	22.8991i	0.521378	+	0.903053i	0.999691	+	0.0248637i	$0.00791519\pi$
$643$	13.2208	+	22.8991i	0.521378	+	0.903053i	−0.478313	+	0.878190i	$0.658751\pi$
$644$	−21.2021	−	36.7231i	−0.835480	−	1.44709i
$645$	7.82235			0.308005
$646$	19.6019	+	33.9514i	0.771225	+	1.33580i
$647$	15.9339	−	27.5984i	0.626428	−	1.08501i	−0.361835	−	0.932242i	$-0.617850\pi$
$647$	15.9339	−	27.5984i	0.626428	−	1.08501i	0.988263	−	0.152763i	$-0.0488171\pi$
$648$	45.1739	−	78.2436i	1.77460	−	3.07370i
$649$	−9.85458			−0.386826
$650$	−107.611	−	68.2770i	−4.22086	−	2.67805i
$651$	−6.45819			−0.253116
$652$	10.2021	−	17.6706i	0.399546	−	0.692034i
$653$	6.10496	−	10.5741i	0.238905	−	0.413796i	−0.721495	−	0.692420i	$-0.756545\pi$
$653$	6.10496	−	10.5741i	0.238905	−	0.413796i	0.960400	+	0.278623i	$0.0898781\pi$
$654$	−34.8511	−	60.3640i	−1.36279	−	2.36042i
$655$	47.0692			1.83914
$656$	47.0691	+	81.5261i	1.83774	+	3.18306i
$657$	−5.66583	−	9.81351i	−0.221045	−	0.382861i
$658$	76.2238			2.97151
$659$	−7.18294	−	12.4412i	−0.279807	−	0.484641i	0.691529	−	0.722348i	$-0.256937\pi$
$659$	−7.18294	−	12.4412i	−0.279807	−	0.484641i	−0.971337	+	0.237708i	$0.923604\pi$
$660$	45.3555	−	78.5580i	1.76546	−	3.05787i
$661$	−19.0709	+	33.0318i	−0.741773	+	1.28479i	0.209914	+	0.977720i	$0.432681\pi$
$661$	−19.0709	+	33.0318i	−0.741773	+	1.28479i	−0.951687	+	0.307069i	$0.900652\pi$
$662$	−0.158151			−0.00614672
$663$	1.52592	−	36.4949i	0.0592618	−	1.41734i
$664$	−7.67212			−0.297736
$665$	20.0573	−	34.7403i	0.777790	−	1.34717i
$666$	15.2648	−	26.4394i	0.591499	−	1.02451i
$667$	3.73018	+	6.46086i	0.144433	+	0.250166i
$668$	−37.2698			−1.44201
$669$	−5.53413	−	9.58540i	−0.213962	−	0.370593i
$670$	−10.8066	−	18.7175i	−0.417494	−	0.723121i
$671$	−11.1079			−0.428818
$672$	47.8346	+	82.8520i	1.84526	+	3.19609i
$673$	−20.6201	+	35.7150i	−0.794845	+	1.37671i	0.128092	+	0.991762i	$0.459115\pi$
$673$	−20.6201	+	35.7150i	−0.794845	+	1.37671i	−0.922937	+	0.384950i	$0.874219\pi$
$674$	7.52783	−	13.0386i	0.289961	−	0.502227i
$675$	−28.9175			−1.11304
$676$	28.1987	+	59.8941i	1.08457	+	2.30362i
$677$	39.4716			1.51702			0.758509	−	0.651662i	$-0.225928\pi$
$677$	39.4716			1.51702			0.758509	+	0.651662i	$0.225928\pi$
$678$	−41.6157	+	72.0806i	−1.59824	+	2.76824i
$679$	2.89712	−	5.01797i	0.111181	−	0.192572i
$680$	79.5195	+	137.732i	3.04943	+	5.28177i
$681$	43.8594			1.68070
$682$	2.47454	+	4.28603i	0.0947551	+	0.164121i
$683$	21.7424	+	37.6590i	0.831950	+	1.44098i	0.896490	+	0.443065i	$0.146109\pi$
$683$	21.7424	+	37.6590i	0.831950	+	1.44098i	−0.0645395	+	0.997915i	$0.520558\pi$
$684$	33.6569			1.28690
$685$	−21.6521	−	37.5025i	−0.827284	−	1.43290i
$686$	−21.8802	+	37.8976i	−0.835389	+	1.44694i
$687$	4.75039	−	8.22792i	0.181239	−	0.313915i
$688$	9.58640			0.365478
$689$	1.59389	−	38.1204i	0.0607222	−	1.45227i
$690$	−73.8081			−2.80983
$691$	−18.7118	+	32.4098i	−0.711830	+	1.23293i	0.252340	+	0.967639i	$0.418800\pi$
$691$	−18.7118	+	32.4098i	−0.711830	+	1.23293i	−0.964170	+	0.265286i	$0.914533\pi$
$692$	−11.4393	+	19.8134i	−0.434855	+	0.753192i
$693$	−5.42810	−	9.40174i	−0.206196	−	0.357142i
$694$	−57.2685			−2.17388
$695$	−4.63314	−	8.02483i	−0.175745	−	0.304399i
$696$	−23.8247	−	41.2655i	−0.903072	−	1.56417i
$697$	36.2043			1.37133
$698$	7.15339	+	12.3900i	0.270760	+	0.468970i
$699$	−1.54099	+	2.66907i	−0.0582856	+	0.100954i
$700$	97.3275	−	168.576i	3.67863	−	6.37158i
$701$	−2.63456			−0.0995059			−0.0497530	−	0.998762i	$-0.515843\pi$
$701$	−2.63456			−0.0995059			−0.0497530	+	0.998762i	$0.515843\pi$
$702$	17.6650	+	11.2081i	0.666722	+	0.423021i
$703$	−18.4155			−0.694555
$704$	14.8266	−	25.6804i	0.558798	−	0.967866i
$705$	47.6303	−	82.4981i	1.79386	−	3.10706i
$706$	0.233649	+	0.404692i	0.00879350	+	0.0152308i
$707$	30.8606			1.16063
$708$	−30.2766	−	52.4407i	−1.13787	−	1.97084i
$709$	−17.4185	−	30.1697i	−0.654165	−	1.13305i	−0.982103	−	0.188347i	$-0.939687\pi$
$709$	−17.4185	−	30.1697i	−0.654165	−	1.13305i	0.327938	−	0.944699i	$-0.393646\pi$
$710$	−23.6085			−0.886011
$711$	8.20295	+	14.2079i	0.307635	+	0.532839i
$712$	−54.2438	+	93.9530i	−2.03287	+	3.52104i
$713$	1.44566	−	2.50396i	0.0541404	−	0.0937740i
$714$	77.7016			2.90791
$715$	24.1847	+	15.3447i	0.904455	+	0.573858i
$716$	−2.66377			−0.0995498
$717$	23.5538	−	40.7964i	0.879633	−	1.52357i
$718$	−0.0525559	+	0.0910295i	−0.00196137	+	0.00339719i
$719$	−3.76203	−	6.51602i	−0.140300	−	0.243007i	0.787310	−	0.616558i	$-0.211473\pi$
$719$	−3.76203	−	6.51602i	−0.140300	−	0.243007i	−0.927610	+	0.373551i	$0.878140\pi$
$720$	101.855			3.79590
$721$	−2.10214	−	3.64101i	−0.0782877	−	0.135598i
$722$	11.1621	+	19.3333i	0.415410	+	0.719512i
$723$	−64.4687			−2.39762
$724$	26.9195	+	46.6259i	1.00045	+	1.73284i
$725$	−17.1233	+	29.6583i	−0.635942	+	1.10148i
$726$	22.5332	−	39.0287i	0.836286	−	1.44849i
$727$	37.7642			1.40060			0.700299	−	0.713850i	$-0.253050\pi$
$727$	37.7642			1.40060			0.700299	+	0.713850i	$0.253050\pi$
$728$	−75.7806	+	39.6268i	−2.80862	+	1.46867i
$729$	−7.59607			−0.281336
$730$	−31.7985	+	55.0766i	−1.17692	+	2.03848i
$731$	1.84340	−	3.19286i	0.0681806	−	0.118092i
$732$	−34.1274	−	59.1104i	−1.26139	−	2.18478i
$733$	−32.0897			−1.18526			−0.592631	−	0.805474i	$-0.701911\pi$
$733$	−32.0897			−1.18526			−0.592631	+	0.805474i	$0.701911\pi$
$734$	41.7103	+	72.2443i	1.53955	+	2.66659i
$735$	−6.20442	−	10.7464i	−0.228854	−	0.396386i
$736$	−42.8310			−1.57877
$737$	1.76411	+	3.05552i	0.0649817	+	0.112552i
$738$	21.6446	−	37.4895i	0.796748	−	1.38001i
$739$	−25.6650	+	44.4531i	−0.944104	+	1.63524i	−0.186567	+	0.982442i	$0.559736\pi$
$739$	−25.6650	+	44.4531i	−0.944104	+	1.63524i	−0.757536	+	0.652793i	$0.773597\pi$
$740$	−123.024			−4.52247
$741$	−1.10056	+	26.3217i	−0.0404301	+	0.966953i
$742$	81.1625			2.97957
$743$	−26.3733	+	45.6798i	−0.967541	+	1.67583i	−0.264914	+	0.964272i	$0.585344\pi$
$743$	−26.3733	+	45.6798i	−0.967541	+	1.67583i	−0.702627	+	0.711559i	$0.747990\pi$
$744$	−9.23344	+	15.9928i	−0.338514	+	0.586324i
$745$	−24.6320	−	42.6639i	−0.902447	−	1.56308i
$746$	32.6179			1.19423
$747$	0.944837	+	1.63651i	0.0345698	+	0.0598766i
$748$	−21.3768	−	37.0256i	−0.781612	−	1.35379i
$749$	−38.9620			−1.42364
$750$	−105.588	−	182.884i	−3.85553	−	6.67798i
$751$	−10.2726	+	17.7926i	−0.374851	+	0.649261i	−0.990305	−	0.138912i	$-0.955639\pi$
$751$	−10.2726	+	17.7926i	−0.374851	+	0.649261i	0.615454	+	0.788173i	$0.288973\pi$
$752$	58.3715	−	101.102i	2.12859	−	3.68683i
$753$	9.34400			0.340514
$754$	21.9553	−	11.4808i	0.799566	−	0.418105i
$755$	78.5566			2.85897
$756$	−15.9768	+	27.6727i	−0.581072	+	1.00645i
$757$	16.3614	−	28.3388i	0.594665	−	1.02999i	−0.398929	−	0.916982i	$-0.630618\pi$
$757$	16.3614	−	28.3388i	0.594665	−	1.02999i	0.993594	−	0.113008i	$-0.0360486\pi$
$758$	36.8391	+	63.8073i	1.33806	+	2.31758i
$759$	12.0487			0.437341
$760$	−57.3530	−	99.3383i	−2.08041	−	3.60338i
$761$	−10.0413	−	17.3921i	−0.363998	−	0.630463i	0.624617	−	0.780932i	$-0.285255\pi$
$761$	−10.0413	−	17.3921i	−0.363998	−	0.630463i	−0.988615	+	0.150468i	$0.951922\pi$
$762$	−3.33925			−0.120968
$763$	16.8076	+	29.1116i	0.608475	+	1.05391i
$764$	−2.82344	+	4.89034i	−0.102148	+	0.176926i
$765$	19.5860	−	33.9239i	0.708132	−	1.22652i
$766$	27.9422			1.00959
$767$	16.9430	−	8.85974i	0.611775	−	0.319907i
$768$	5.27978			0.190518
$769$	−18.9635	+	32.8457i	−0.683840	+	1.18445i	0.289960	+	0.957039i	$0.406358\pi$
$769$	−18.9635	+	32.8457i	−0.683840	+	1.18445i	−0.973800	+	0.227406i	$0.926975\pi$
$770$	−30.4642	+	52.7656i	−1.09786	+	1.90154i
$771$	2.07297	+	3.59049i	0.0746562	+	0.129308i
$772$	94.7631			3.41060
$773$	−17.2296	−	29.8426i	−0.619706	−	1.07336i	−0.989539	−	0.144265i	$-0.953918\pi$
$773$	−17.2296	−	29.8426i	−0.619706	−	1.07336i	0.369833	−	0.929098i	$-0.379415\pi$
$774$	−2.20414	−	3.81768i	−0.0792261	−	0.137224i
$775$	13.2725			0.476763
$776$	−8.28419	−	14.3486i	−0.297385	−	0.515086i
$777$	−18.2498	+	31.6095i	−0.654706	+	1.13398i
$778$	0.673741	−	1.16695i	0.0241548	−	0.0418373i
$779$	−26.1121			−0.935565
$780$	−7.35227	+	175.842i	−0.263254	+	6.29614i
$781$	3.85395			0.137905
$782$	−17.3935	+	30.1264i	−0.621989	+	1.07732i
$783$	2.81088	−	4.86858i	0.100453	−	0.173989i
$784$	−7.60360	−	13.1698i	−0.271557	−	0.470351i
$785$	83.4502			2.97847
$786$	−32.8788	−	56.9478i	−1.17275	−	2.03126i
$787$	−11.1981	−	19.3957i	−0.399169	−	0.691381i	0.594455	−	0.804129i	$-0.297368\pi$
$787$	−11.1981	−	19.3957i	−0.399169	−	0.691381i	−0.993624	+	0.112748i	$0.964035\pi$
$788$	130.877			4.66228
$789$	14.0349	+	24.3091i	0.499654	+	0.865426i
$790$	46.0376	−	79.7395i	1.63795	−	2.83700i
$791$	20.0699	−	34.7621i	0.713604	−	1.23600i
$792$	−31.0428			−1.10306
$793$	19.0979	−	9.98658i	0.678186	−	0.354634i
$794$	26.5351			0.941694
$795$	50.7164	−	87.8433i	1.79872	−	3.11548i
$796$	43.4642	−	75.2822i	1.54055	−	2.66831i
$797$	−26.6161	−	46.1004i	−0.942791	−	1.63296i	−0.760116	−	0.649788i	$-0.774858\pi$
$797$	−26.6161	−	46.1004i	−0.942791	−	1.63296i	−0.182675	−	0.983173i	$-0.558476\pi$
$798$	−56.0419			−1.98386
$799$	−22.4489	−	38.8826i	−0.794185	−	1.37557i
$800$	−98.3071	−	170.273i	−3.47568	−	6.02006i
$801$	26.7209			0.944137
$802$	−23.3341	−	40.4158i	−0.823955	−	1.42713i
$803$	5.19092	−	8.99093i	0.183183	−	0.317283i
$804$	−10.8399	+	18.7752i	−0.382293	+	0.662152i
$805$	35.5952			1.25457
$806$	−8.10783	−	5.14425i	−0.285586	−	0.181198i
$807$	−9.71813			−0.342094
$808$	44.1222	−	76.4220i	1.55221	−	2.68852i
$809$	−10.7215	+	18.5702i	−0.376948	+	0.652893i	−0.990617	−	0.136671i	$-0.956360\pi$
$809$	−10.7215	+	18.5702i	−0.376948	+	0.652893i	0.613669	+	0.789564i	$0.289693\pi$
$810$	62.4456	+	108.159i	2.19412	+	3.80032i
$811$	−19.6817			−0.691118			−0.345559	−	0.938397i	$-0.612311\pi$
$811$	−19.6817			−0.691118			−0.345559	+	0.938397i	$0.612311\pi$
$812$	18.9211	+	32.7723i	0.663999	+	1.15008i
$813$	7.01547	+	12.1511i	0.246043	+	0.426159i
$814$	27.9706			0.980368
$815$	8.56394	+	14.8332i	0.299982	+	0.519583i
$816$	59.5033	−	103.063i	2.08303	−	3.60792i
$817$	−1.32954	+	2.30283i	−0.0465148	+	0.0805660i
$818$	10.1003			0.353149
$819$	17.7851	+	11.2843i	0.621463	+	0.394305i
$820$	−174.441			−6.09176
$821$	−10.1951	+	17.6584i	−0.355812	+	0.616284i	−0.987257	−	0.159137i	$-0.949129\pi$
$821$	−10.1951	+	17.6584i	−0.355812	+	0.616284i	0.631445	+	0.775421i	$0.282462\pi$
$822$	−30.2489	+	52.3926i	−1.05505	+	1.82740i
$823$	6.21556	+	10.7657i	0.216661	+	0.375267i	0.953785	−	0.300490i	$-0.0971501\pi$
$823$	6.21556	+	10.7657i	0.216661	+	0.375267i	−0.737124	+	0.675757i	$0.763817\pi$
$824$	−12.0219			−0.418804
$825$	27.6546	+	47.8992i	0.962811	+	1.66764i
$826$	20.3361	+	35.2232i	0.707584	+	1.22557i
$827$	20.6542			0.718216			0.359108	−	0.933296i	$-0.383081\pi$
$827$	20.6542			0.718216			0.359108	+	0.933296i	$0.383081\pi$
$828$	14.9325	+	25.8639i	0.518941	+	0.898832i
$829$	−10.3594	+	17.9430i	−0.359796	+	0.623185i	−0.987927	−	0.154923i	$-0.950487\pi$
$829$	−10.3594	+	17.9430i	−0.359796	+	0.623185i	0.628131	+	0.778108i	$0.283820\pi$
$830$	5.30273	−	9.18460i	0.184061	−	0.318802i
$831$	19.7148			0.683900
$832$	−2.40344	+	57.4821i	−0.0833242	+	1.99283i
$833$	−5.84848			−0.202638
$834$	−6.47269	+	11.2110i	−0.224131	+	0.388206i
$835$	15.6426	−	27.0938i	0.541335	−	0.937620i
$836$	15.4179	+	26.7045i	0.533238	+	0.923596i
$837$	−2.17875			−0.0753088
$838$	−23.5697	−	40.8238i	−0.814200	−	1.41024i
$839$	14.0741	+	24.3770i	0.485891	+	0.841588i	0.999869	−	0.0162157i	$-0.00516185\pi$
$839$	14.0741	+	24.3770i	0.485891	+	0.841588i	−0.513977	+	0.857804i	$0.671829\pi$
$840$	−227.347			−7.84421
$841$	11.1711	+	19.3490i	0.385211	+	0.667206i
$842$	0.516296	−	0.894251i	0.0177927	−	0.0308179i
$843$	−22.8181	+	39.5221i	−0.785896	+	1.36121i
$844$	−53.8015			−1.85193
$845$	−55.3763	−	4.63889i	−1.90500	−	0.159583i
$846$	−53.6839			−1.84569
$847$	−10.8670	+	18.8223i	−0.373396	+	0.646740i
$848$	62.1536	−	107.653i	2.13436	−	3.69683i
$849$	14.5748	+	25.2443i	0.500206	+	0.866382i
$850$	−159.688			−5.47726
$851$	−8.17039	−	14.1515i	−0.280077	−	0.485108i
$852$	11.8406	+	20.5086i	0.405654	+	0.702613i
$853$	−9.69144			−0.331829			−0.165914	−	0.986140i	$-0.553058\pi$
$853$	−9.69144			−0.331829			−0.165914	+	0.986140i	$0.553058\pi$
$854$	22.9226	+	39.7031i	0.784395	+	1.35861i
$855$	−14.1263	+	24.4674i	−0.483108	+	0.836768i
$856$	−55.7050	+	96.4840i	−1.90396	+	3.29775i
$857$	35.1605			1.20106			0.600530	−	0.799602i	$-0.294956\pi$
$857$	35.1605			1.20106			0.600530	+	0.799602i	$0.294956\pi$
$858$	1.67160	−	39.9790i	0.0570674	−	1.36486i
$859$	18.3163			0.624943			0.312472	−	0.949927i	$-0.398843\pi$
$859$	18.3163			0.624943			0.312472	+	0.949927i	$0.398843\pi$
$860$	−8.88197	+	15.3840i	−0.302873	+	0.524591i
$861$	−25.8771	+	44.8204i	−0.881888	+	1.52748i
$862$	−23.9292	−	41.4466i	−0.815033	−	1.41168i
$863$	−56.7903			−1.93316			−0.966582	−	0.256357i	$-0.917478\pi$
$863$	−56.7903			−1.93316			−0.966582	+	0.256357i	$0.917478\pi$
$864$	16.1377	+	27.9512i	0.549014	+	0.950920i
$865$	−9.60243	−	16.6319i	−0.326492	−	0.565501i
$866$	−43.4313			−1.47586
$867$	−3.82370	−	6.62284i	−0.129860	−	0.224923i
$868$	7.33301	−	12.7011i	0.248899	−	0.431105i
$869$	−7.51537	+	13.0170i	−0.254941	+	0.441571i
$870$	65.8675			2.23312
$871$	−5.78009	−	3.66735i	−0.195851	−	0.124263i
$872$	96.1209			3.25506
$873$	−2.04043	+	3.53412i	−0.0690580	+	0.119612i
$874$	12.5449	−	21.7285i	0.424339	−	0.734977i
$875$	50.9217	+	88.1989i	1.72147	+	2.98167i
$876$	63.7931			2.15537
$877$	1.40654	+	2.43620i	0.0474955	+	0.0822647i	0.888796	−	0.458303i	$-0.151543\pi$
$877$	1.40654	+	2.43620i	0.0474955	+	0.0822647i	−0.841300	+	0.540568i	$0.818209\pi$
$878$	8.26357	+	14.3129i	0.278882	+	0.483038i
$879$	−68.2727			−2.30278
$880$	46.6585	+	80.8149i	1.57286	+	2.72427i
$881$	11.6310	−	20.1454i	0.391857	−	0.678716i	−0.600838	−	0.799371i	$-0.705166\pi$
$881$	11.6310	−	20.1454i	0.391857	−	0.678716i	0.992694	+	0.120655i	$0.0384995\pi$
$882$	−3.49649	+	6.05611i	−0.117733	+	0.203920i
$883$	−18.8589			−0.634652			−0.317326	−	0.948316i	$-0.602785\pi$
$883$	−18.8589			−0.634652			−0.317326	+	0.948316i	$0.602785\pi$
$884$	70.0409	+	44.4395i	2.35573	+	1.49466i
$885$	50.8301			1.70863
$886$	51.2363	−	88.7438i	1.72132	−	2.98141i
$887$	22.2704	−	38.5734i	0.747766	−	1.29517i	−0.201125	−	0.979566i	$-0.564460\pi$
$887$	22.2704	−	38.5734i	0.747766	−	1.29517i	0.948891	−	0.315604i	$-0.102207\pi$
$888$	52.1843	+	90.3859i	1.75119	+	3.03315i
$889$	1.61041			0.0540114
$890$	−74.9832	−	129.875i	−2.51344	−	4.35341i
$891$	−10.1939	−	17.6563i	−0.341508	−	0.591509i
$892$	25.1351			0.841587
$893$	16.1911	+	28.0439i	0.541816	+	0.938453i
$894$	−34.4119	+	59.6032i	−1.15091	+	1.99343i
$895$	1.11802	−	1.93647i	0.0373713	−	0.0647290i
$896$	−37.0585			−1.23804
$897$	−20.7154	+	10.8324i	−0.691667	+	0.361683i
$898$	90.2586			3.01197
$899$	−1.29013	+	2.23457i	−0.0430282	+	0.0745271i
$900$	−68.5472	+	118.727i	−2.28491	+	3.95757i
$901$	−23.9034	−	41.4019i	−0.796339	−	1.37930i
$902$	39.6606			1.32055
$903$	2.63515	+	4.56421i	0.0876922	+	0.151887i
$904$	−57.3890	−	99.4006i	−1.90873	−	3.30602i
$905$	−45.1939			−1.50230
$906$	−54.8734	−	95.0436i	−1.82305	−	3.15761i
$907$	−19.2819	+	33.3973i	−0.640246	+	1.10894i	0.345132	+	0.938554i	$0.387834\pi$
$907$	−19.2819	+	33.3973i	−0.640246	+	1.10894i	−0.985378	+	0.170384i	$0.945499\pi$
$908$	−49.8006	+	86.2571i	−1.65269	+	2.86254i
$909$	−21.7349			−0.720903
$910$	4.93835	−	118.109i	0.163705	−	3.91527i
$911$	2.59812			0.0860795			0.0430398	−	0.999073i	$-0.486296\pi$
$911$	2.59812			0.0860795			0.0430398	+	0.999073i	$0.486296\pi$
$912$	−42.9164	+	74.3334i	−1.42110	+	2.46143i
$913$	−0.865639	+	1.49933i	−0.0286485	+	0.0496206i
$914$	−14.9026	−	25.8121i	−0.492936	−	0.853789i
$915$	57.2950			1.89411
$916$	10.7878	+	18.6849i	0.356438	+	0.617368i
$917$	15.8564	+	27.4640i	0.523623	+	0.906942i
$918$	26.2137			0.865180
$919$	6.79248	+	11.7649i	0.224063	+	0.388089i	0.956038	−	0.293243i	$-0.0947345\pi$
$919$	6.79248	+	11.7649i	0.224063	+	0.388089i	−0.731975	+	0.681332i	$0.761401\pi$
$920$	50.8915	−	88.1466i	1.67784	−	2.90611i
$921$	−23.3724	+	40.4822i	−0.770147	+	1.33393i
$922$	88.3240			2.90880
$923$	−6.62609	+	3.46488i	−0.218100	+	0.114048i
$924$	61.1163			2.01058
$925$	37.5059	−	64.9621i	1.23319	−	2.13594i
$926$	−33.5621	+	58.1312i	−1.10292	+	1.91031i
$927$	1.48052	+	2.56434i	0.0486268	+	0.0842241i
$928$	38.2230			1.25473
$929$	−8.93512	−	15.4761i	−0.293152	−	0.507754i	0.681401	−	0.731910i	$-0.261371\pi$
$929$	−8.93512	−	15.4761i	−0.293152	−	0.507754i	−0.974553	+	0.224156i	$0.928037\pi$
$930$	−12.7637	−	22.1074i	−0.418539	−	0.724931i
$931$	4.21819			0.138246
$932$	−3.49946	−	6.06125i	−0.114629	−	0.198543i
$933$	−19.3804	+	33.5678i	−0.634485	+	1.09896i
$934$	−15.0530	+	26.0725i	−0.492549	+	0.853120i
$935$	35.8885			1.17368
$936$	53.3718	−	27.9089i	1.74451	−	0.912232i
$937$	−15.4776			−0.505631			−0.252815	−	0.967515i	$-0.581357\pi$
$937$	−15.4776			−0.505631			−0.252815	+	0.967515i	$0.581357\pi$
$938$	7.28090	−	12.6109i	0.237730	−	0.411760i
$939$	9.76439	−	16.9124i	0.318649	−	0.551916i
$940$	108.165	+	187.346i	3.52794	+	6.11057i
$941$	15.0215			0.489686			0.244843	−	0.969563i	$-0.421264\pi$
$941$	15.0215			0.489686			0.244843	+	0.969563i	$0.421264\pi$
$942$	−58.2917	−	100.964i	−1.89925	−	3.28959i
$943$	−11.5851	−	20.0660i	−0.377264	−	0.653440i
$944$	62.2929			2.02746
$945$	−13.4114	−	23.2292i	−0.436273	−	0.755646i
$946$	2.01938	−	3.49768i	0.0656558	−	0.113719i
$947$	20.9969	−	36.3677i	0.682308	−	1.18179i	−0.291966	−	0.956429i	$-0.594309\pi$
$947$	20.9969	−	36.3677i	0.682308	−	1.18179i	0.974275	−	0.225364i	$-0.0723572\pi$
$948$	−92.3592			−2.99969
$949$	−0.841464	+	20.1250i	−0.0273151	+	0.653285i
$950$	115.174			3.73674
$951$	32.1322	−	55.6546i	1.04196	−	1.80473i
$952$	−53.5761	+	92.7965i	−1.73641	+	3.00755i
$953$	−5.99448	−	10.3827i	−0.194180	−	0.336330i	0.752451	−	0.658648i	$-0.228871\pi$
$953$	−5.99448	−	10.3827i	−0.194180	−	0.336330i	−0.946631	+	0.322318i	$0.895538\pi$
$954$	−57.1623			−1.85070
$955$	−2.37007	−	4.10509i	−0.0766937	−	0.132837i
$956$	53.4888	+	92.6453i	1.72995	+	2.99636i
$957$	−10.7525			−0.347578
$958$	−21.3158	−	36.9200i	−0.688681	−	1.19283i
$959$	14.5880	−	25.2672i	0.471072	−	0.815921i
$960$	−76.4758	+	132.460i	−2.46824	+	4.27512i
$961$	1.00000			0.0322581
$962$	−48.0898	+	25.1469i	−1.55048	+	0.810768i
$963$	27.4407			0.884265
$964$	73.2016	−	126.789i	2.35767	−	4.08360i
$965$	−39.7733	+	68.8895i	−1.28035	+	2.21763i
$966$	−24.8640	−	43.0658i	−0.799987	−	1.38562i
$967$	−21.5832			−0.694067			−0.347034	−	0.937853i	$-0.612811\pi$
$967$	−21.5832			−0.694067			−0.347034	+	0.937853i	$0.612811\pi$
$968$	31.0738	+	53.8214i	0.998749	+	1.72988i
$969$	16.5051	+	28.5876i	0.530219	+	0.918367i
$970$	22.9031			0.735374
$971$	−9.50321	−	16.4600i	−0.304972	−	0.528228i	0.672283	−	0.740294i	$-0.265314\pi$
$971$	−9.50321	−	16.4600i	−0.304972	−	0.528228i	−0.977255	+	0.212067i	$0.931981\pi$
$972$	45.9958	−	79.6670i	1.47531	−	2.55532i
$973$	3.12156	−	5.40671i	0.100073	−	0.173331i
$974$	−93.1753			−2.98553
$975$	−90.6103	−	57.4903i	−2.90185	−	1.84116i
$976$	70.2157			2.24755
$977$	−3.13496	+	5.42991i	−0.100296	+	0.173718i	−0.911807	−	0.410620i	$-0.865312\pi$
$977$	−3.13496	+	5.42991i	−0.100296	+	0.173718i	0.811510	+	0.584338i	$0.198646\pi$
$978$	11.9642	−	20.7226i	0.382572	−	0.662635i
$979$	12.2406	+	21.2013i	0.391210	+	0.677596i
$980$	28.1795			0.900161
$981$	−11.8375	−	20.5031i	−0.377941	−	0.654614i
$982$	7.37499	+	12.7738i	0.235345	+	0.407630i
$983$	20.5002			0.653853			0.326927	−	0.945050i	$-0.393987\pi$
$983$	20.5002			0.653853			0.326927	+	0.945050i	$0.393987\pi$
$984$	73.9943	+	128.162i	2.35885	+	4.08565i
$985$	−54.9307	+	95.1427i	−1.75024	+	3.03150i
$986$	15.5222	−	26.8852i	0.494327	−	0.856200i
$987$	64.1816			2.04292
$988$	−50.5166	−	32.0517i	−1.60715	−	1.01970i
$989$	−2.35950			−0.0750278
$990$	21.4558	−	37.1625i	0.681910	−	1.18110i
$991$	5.13289	−	8.89043i	0.163052	−	0.282414i	−0.772910	−	0.634516i	$-0.781200\pi$
$991$	5.13289	−	8.89043i	0.163052	−	0.282414i	0.935962	+	0.352102i	$0.114533\pi$
$992$	−7.40682	−	12.8290i	−0.235167	−	0.407321i
$993$	−0.133166			−0.00422589
$994$	−7.95309	−	13.7752i	−0.252257	−	0.436921i
$995$	36.4850	+	63.1939i	1.15665	+	2.00338i
$996$	−10.6382			−0.337083
$997$	−20.4753	−	35.4643i	−0.648459	−	1.12316i	−0.983491	−	0.180957i	$-0.942080\pi$
$997$	−20.4753	−	35.4643i	−0.648459	−	1.12316i	0.335032	−	0.942207i	$-0.391253\pi$
$998$	−14.8251	+	25.6778i	−0.469281	+	0.812818i
$999$	−6.15680	+	10.6639i	−0.194792	+	0.337390i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.f.c.373.2	yes	36
13.3	even	3	inner	403.2.f.c.94.2	✓	36
13.4	even	6		5239.2.a.o.1.2		18
13.9	even	3		5239.2.a.p.1.17		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.f.c.94.2	✓	36	13.3	even	3	inner
403.2.f.c.373.2	yes	36	1.1	even	1	trivial
5239.2.a.o.1.2		18	13.4	even	6
5239.2.a.p.1.17		18	13.9	even	3

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.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33157 + 2.30635i) q^{2} +(-1.12120 + 1.94198i) q^{3} +(-2.54616 - 4.41008i) q^{4} +4.27464 q^{5} +(-2.98592 - 5.17177i) q^{6} +(1.44001 + 2.49418i) q^{7} +8.23530 q^{8} +(-1.01419 - 1.75663i) q^{9} +O(q^{10})\)	\(q+(-1.33157 + 2.30635i) q^{2} +(-1.12120 + 1.94198i) q^{3} +(-2.54616 - 4.41008i) q^{4} +4.27464 q^{5} +(-2.98592 - 5.17177i) q^{6} +(1.44001 + 2.49418i) q^{7} +8.23530 q^{8} +(-1.01419 - 1.75663i) q^{9} +(-5.69198 + 9.85880i) q^{10} +(0.929182 - 1.60939i) q^{11} +11.4191 q^{12} +(-0.150623 + 3.60240i) q^{13} -7.66992 q^{14} +(-4.79273 + 8.30126i) q^{15} +(-5.87356 + 10.1733i) q^{16} +(2.25889 + 3.91251i) q^{17} +5.40188 q^{18} +(-1.62921 - 2.82188i) q^{19} +(-10.8839 - 18.8515i) q^{20} -6.45819 q^{21} +(2.47454 + 4.28603i) q^{22} +(1.44566 - 2.50396i) q^{23} +(-9.23344 + 15.9928i) q^{24} +13.2725 q^{25} +(-8.10783 - 5.14425i) q^{26} -2.17875 q^{27} +(7.33301 - 12.7011i) q^{28} +(-1.29013 + 2.23457i) q^{29} +(-12.7637 - 22.1074i) q^{30} +1.00000 q^{31} +(-7.40682 - 12.8290i) q^{32} +(2.08360 + 3.60891i) q^{33} -12.0315 q^{34} +(6.15553 + 10.6617i) q^{35} +(-5.16460 + 8.94535i) q^{36} +(2.82583 - 4.89449i) q^{37} +8.67765 q^{38} +(-6.82692 - 4.33153i) q^{39} +35.2029 q^{40} +(4.00686 - 6.94009i) q^{41} +(8.59953 - 14.8948i) q^{42} +(-0.408032 - 0.706732i) q^{43} -9.46339 q^{44} +(-4.33530 - 7.50897i) q^{45} +(3.85000 + 6.66840i) q^{46} -9.93802 q^{47} +(-13.1709 - 22.8127i) q^{48} +(-0.647274 + 1.12111i) q^{49} +(-17.6733 + 30.6110i) q^{50} -10.1307 q^{51} +(16.2704 - 8.50804i) q^{52} -10.5819 q^{53} +(2.90117 - 5.02497i) q^{54} +(3.97191 - 6.87956i) q^{55} +(11.8589 + 20.5403i) q^{56} +7.30672 q^{57} +(-3.43580 - 5.95098i) q^{58} +(-2.65141 - 4.59238i) q^{59} +48.8123 q^{60} +(-2.98864 - 5.17647i) q^{61} +(-1.33157 + 2.30635i) q^{62} +(2.92090 - 5.05915i) q^{63} +15.9566 q^{64} +(-0.643860 + 15.3990i) q^{65} -11.0979 q^{66} +(-0.949280 + 1.64420i) q^{67} +(11.5030 - 19.9238i) q^{68} +(3.24176 + 5.61489i) q^{69} -32.7861 q^{70} +(1.03692 + 1.79600i) q^{71} +(-8.35218 - 14.4664i) q^{72} +5.58655 q^{73} +(7.52559 + 13.0347i) q^{74} +(-14.8812 + 25.7750i) q^{75} +(-8.29648 + 14.3699i) q^{76} +5.35213 q^{77} +(19.0806 - 9.97751i) q^{78} -8.08816 q^{79} +(-25.1073 + 43.4872i) q^{80} +(5.48540 - 9.50100i) q^{81} +(10.6708 + 18.4824i) q^{82} -0.931615 q^{83} +(16.4436 + 28.4811i) q^{84} +(9.65594 + 16.7246i) q^{85} +2.17329 q^{86} +(-2.89299 - 5.01081i) q^{87} +(7.65209 - 13.2538i) q^{88} +(-6.58674 + 11.4086i) q^{89} +23.0911 q^{90} +(-9.20193 + 4.81183i) q^{91} -14.7236 q^{92} +(-1.12120 + 1.94198i) q^{93} +(13.2332 - 22.9205i) q^{94} +(-6.96429 - 12.0625i) q^{95} +33.2182 q^{96} +(-1.00594 - 1.74233i) q^{97} +(-1.72378 - 2.98568i) q^{98} -3.76948 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9}+O(q^{10}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9	\( 36 q - 5 q^{2} - 19 q^{4} + 12 q^{5} - 6 q^{6} - 4 q^{7} + 30 q^{8} - 22 q^{9} - 3 q^{10} - 17 q^{11} + 8 q^{12} + 8 q^{13} + 4 q^{14} - 12 q^{15} - 17 q^{16} + 7 q^{17} - 14 q^{18} - 4 q^{19} - 15 q^{20} + 28 q^{21} - 30 q^{22} + 4 q^{23} - 48 q^{24} + 24 q^{25} + 25 q^{26} - 6 q^{27} - q^{28} + 15 q^{29} + 35 q^{30} + 36 q^{31} - 35 q^{32} - 17 q^{33} - 6 q^{34} - 17 q^{35} - 35 q^{36} - 3 q^{37} + 14 q^{38} + 3 q^{39} - 2 q^{40} - 44 q^{41} + 57 q^{42} + 4 q^{43} + 64 q^{44} + 5 q^{45} - 13 q^{46} + 24 q^{47} - 89 q^{48} - 44 q^{49} - 84 q^{50} - 28 q^{51} + 50 q^{52} - 28 q^{53} - 21 q^{54} + 29 q^{55} + 11 q^{56} + 32 q^{57} + 49 q^{58} - 11 q^{59} + 54 q^{60} - 4 q^{61} - 5 q^{62} - 9 q^{63} + 34 q^{64} - 5 q^{65} + 52 q^{66} - 16 q^{67} + 53 q^{68} + 4 q^{69} - 44 q^{70} - 5 q^{71} - 27 q^{72} + 64 q^{73} + q^{74} - 98 q^{75} - 42 q^{76} - 22 q^{77} + 143 q^{78} - 6 q^{79} - 2 q^{80} + 10 q^{81} + 22 q^{82} + 36 q^{83} + 38 q^{84} + 2 q^{85} + 84 q^{86} - 34 q^{87} - 69 q^{88} - 54 q^{89} - 32 q^{90} - 43 q^{91} - 86 q^{92} + 44 q^{94} - 2 q^{95} + 170 q^{96} - 28 q^{97} - 29 q^{98} + 154 q^{99}+O(q^{100}) \) 36 * q - 5 * q^2 - 19 * q^4 + 12 * q^5 - 6 * q^6 - 4 * q^7 + 30 * q^8 - 22 * q^9 - 3 * q^10 - 17 * q^11 + 8 * q^12 + 8 * q^13 + 4 * q^14 - 12 * q^15 - 17 * q^16 + 7 * q^17 - 14 * q^18 - 4 * q^19 - 15 * q^20 + 28 * q^21 - 30 * q^22 + 4 * q^23 - 48 * q^24 + 24 * q^25 + 25 * q^26 - 6 * q^27 - q^28 + 15 * q^29 + 35 * q^30 + 36 * q^31 - 35 * q^32 - 17 * q^33 - 6 * q^34 - 17 * q^35 - 35 * q^36 - 3 * q^37 + 14 * q^38 + 3 * q^39 - 2 * q^40 - 44 * q^41 + 57 * q^42 + 4 * q^43 + 64 * q^44 + 5 * q^45 - 13 * q^46 + 24 * q^47 - 89 * q^48 - 44 * q^49 - 84 * q^50 - 28 * q^51 + 50 * q^52 - 28 * q^53 - 21 * q^54 + 29 * q^55 + 11 * q^56 + 32 * q^57 + 49 * q^58 - 11 * q^59 + 54 * q^60 - 4 * q^61 - 5 * q^62 - 9 * q^63 + 34 * q^64 - 5 * q^65 + 52 * q^66 - 16 * q^67 + 53 * q^68 + 4 * q^69 - 44 * q^70 - 5 * q^71 - 27 * q^72 + 64 * q^73 + q^74 - 98 * q^75 - 42 * q^76 - 22 * q^77 + 143 * q^78 - 6 * q^79 - 2 * q^80 + 10 * q^81 + 22 * q^82 + 36 * q^83 + 38 * q^84 + 2 * q^85 + 84 * q^86 - 34 * q^87 - 69 * q^88 - 54 * q^89 - 32 * q^90 - 43 * q^91 - 86 * q^92 + 44 * q^94 - 2 * q^95 + 170 * q^96 - 28 * q^97 - 29 * q^98 + 154 * q^99

Introduction

L-functions

Modular forms

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