LMFDB - Embedded newform 403.2.f.b.94.11

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:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			94.11
Character	$\chi$	$=$	403.94
Dual form			403.2.f.b.373.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.578965 + 1.00280i) q^{2} +(-0.235957 - 0.408690i) q^{3} +(0.329599 - 0.570882i) q^{4} -3.25594 q^{5} +(0.273222 - 0.473235i) q^{6} +(0.0133059 - 0.0230465i) q^{7} +3.07917 q^{8} +(1.38865 - 2.40521i) q^{9} +O(q^{10})$	\(q+(0.578965 + 1.00280i) q^{2} +(-0.235957 - 0.408690i) q^{3} +(0.329599 - 0.570882i) q^{4} -3.25594 q^{5} +(0.273222 - 0.473235i) q^{6} +(0.0133059 - 0.0230465i) q^{7} +3.07917 q^{8} +(1.38865 - 2.40521i) q^{9} +(-1.88508 - 3.26505i) q^{10} +(-1.99508 - 3.45558i) q^{11} -0.311085 q^{12} +(1.93078 - 3.04501i) q^{13} +0.0308146 q^{14} +(0.768263 + 1.33067i) q^{15} +(1.12353 + 1.94601i) q^{16} +(-2.63341 + 4.56120i) q^{17} +3.21592 q^{18} +(4.34124 - 7.51924i) q^{19} +(-1.07315 + 1.85876i) q^{20} -0.0125585 q^{21} +(2.31017 - 4.00132i) q^{22} +(2.12725 + 3.68450i) q^{23} +(-0.726552 - 1.25842i) q^{24} +5.60115 q^{25} +(4.17138 + 0.173228i) q^{26} -2.72639 q^{27} +(-0.00877122 - 0.0151922i) q^{28} +(-2.84203 - 4.92255i) q^{29} +(-0.889595 + 1.54082i) q^{30} -1.00000 q^{31} +(1.77819 - 3.07992i) q^{32} +(-0.941508 + 1.63074i) q^{33} -6.09860 q^{34} +(-0.0433232 + 0.0750380i) q^{35} +(-0.915394 - 1.58551i) q^{36} +(2.46125 + 4.26302i) q^{37} +10.0537 q^{38} +(-1.70005 - 0.0705992i) q^{39} -10.0256 q^{40} +(-2.71441 - 4.70150i) q^{41} +(-0.00727093 - 0.0125936i) q^{42} +(-3.26031 + 5.64702i) q^{43} -2.63031 q^{44} +(-4.52136 + 7.83122i) q^{45} +(-2.46320 + 4.26639i) q^{46} -1.95563 q^{47} +(0.530211 - 0.918352i) q^{48} +(3.49965 + 6.06156i) q^{49} +(3.24287 + 5.61682i) q^{50} +2.48549 q^{51} +(-1.10196 - 2.10588i) q^{52} +10.7054 q^{53} +(-1.57848 - 2.73402i) q^{54} +(6.49587 + 11.2512i) q^{55} +(0.0409710 - 0.0709639i) q^{56} -4.09739 q^{57} +(3.29088 - 5.69997i) q^{58} +(-6.64385 + 11.5075i) q^{59} +1.01287 q^{60} +(-0.438981 + 0.760337i) q^{61} +(-0.578965 - 1.00280i) q^{62} +(-0.0369544 - 0.0640069i) q^{63} +8.61218 q^{64} +(-6.28651 + 9.91437i) q^{65} -2.18040 q^{66} +(-2.37747 - 4.11790i) q^{67} +(1.73594 + 3.00673i) q^{68} +(1.00388 - 1.73877i) q^{69} -0.100331 q^{70} +(3.50797 - 6.07598i) q^{71} +(4.27588 - 7.40604i) q^{72} -12.5998 q^{73} +(-2.84996 + 4.93627i) q^{74} +(-1.32163 - 2.28914i) q^{75} +(-2.86173 - 4.95667i) q^{76} -0.106185 q^{77} +(-0.913471 - 1.74568i) q^{78} +13.8937 q^{79} +(-3.65815 - 6.33611i) q^{80} +(-3.52263 - 6.10138i) q^{81} +(3.14310 - 5.44401i) q^{82} +0.690405 q^{83} +(-0.00413926 + 0.00716942i) q^{84} +(8.57422 - 14.8510i) q^{85} -7.55042 q^{86} +(-1.34120 + 2.32302i) q^{87} +(-6.14319 - 10.6403i) q^{88} +(6.83075 + 11.8312i) q^{89} -10.4708 q^{90} +(-0.0444860 - 0.0850143i) q^{91} +2.80455 q^{92} +(0.235957 + 0.408690i) q^{93} +(-1.13224 - 1.96110i) q^{94} +(-14.1348 + 24.4822i) q^{95} -1.67831 q^{96} +(-5.63529 + 9.76061i) q^{97} +(-4.05235 + 7.01887i) q^{98} -11.0819 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 4 q^{2} - 20 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} - 12 q^{8} - 17 q^{9}+O(q^{10}) $ 34 * q + 4 * q^2 - 20 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 - 12 * q^8 - 17 * q^9	\( 34 q + 4 q^{2} - 20 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} - 12 q^{8} - 17 q^{9} - 6 q^{10} + 13 q^{11} + 8 q^{12} - 3 q^{13} + 4 q^{15} - 34 q^{16} + 6 q^{17} + 24 q^{18} + 4 q^{19} + 28 q^{20} - 36 q^{21} + 34 q^{22} + 8 q^{23} + 40 q^{24} + 16 q^{25} - 26 q^{26} - 6 q^{27} + 21 q^{28} + 6 q^{29} - 19 q^{30} - 34 q^{31} + 6 q^{32} + 7 q^{33} - 48 q^{34} + 9 q^{35} + 14 q^{37} + 22 q^{38} - 21 q^{39} - 20 q^{40} + 43 q^{41} - 33 q^{42} - 18 q^{43} - 56 q^{44} + 26 q^{45} + 7 q^{46} - 12 q^{47} + 95 q^{48} + q^{49} + 44 q^{50} + 52 q^{51} - 24 q^{52} - 10 q^{53} + 27 q^{54} - 39 q^{55} - 39 q^{56} - 92 q^{57} + 8 q^{58} - q^{59} - 42 q^{60} + 19 q^{61} - 4 q^{62} + 5 q^{63} + 84 q^{64} - 32 q^{65} + 52 q^{66} + 10 q^{67} - 34 q^{68} - 32 q^{69} + 48 q^{70} + 35 q^{71} - 26 q^{72} - 22 q^{73} + 68 q^{74} + 62 q^{75} + 2 q^{76} + 42 q^{77} - 81 q^{78} + 2 q^{79} + 49 q^{80} - 37 q^{81} - 35 q^{82} - 48 q^{83} - 34 q^{84} - 13 q^{85} - 152 q^{86} + 22 q^{87} + 37 q^{88} + 42 q^{89} + 30 q^{90} - 39 q^{91} + 30 q^{92} - 42 q^{94} - 34 q^{95} - 66 q^{96} - 38 q^{97} + 8 q^{98} - 34 q^{99}+O(q^{100}) \) 34 * q + 4 * q^2 - 20 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 - 12 * q^8 - 17 * q^9 - 6 * q^10 + 13 * q^11 + 8 * q^12 - 3 * q^13 + 4 * q^15 - 34 * q^16 + 6 * q^17 + 24 * q^18 + 4 * q^19 + 28 * q^20 - 36 * q^21 + 34 * q^22 + 8 * q^23 + 40 * q^24 + 16 * q^25 - 26 * q^26 - 6 * q^27 + 21 * q^28 + 6 * q^29 - 19 * q^30 - 34 * q^31 + 6 * q^32 + 7 * q^33 - 48 * q^34 + 9 * q^35 + 14 * q^37 + 22 * q^38 - 21 * q^39 - 20 * q^40 + 43 * q^41 - 33 * q^42 - 18 * q^43 - 56 * q^44 + 26 * q^45 + 7 * q^46 - 12 * q^47 + 95 * q^48 + q^49 + 44 * q^50 + 52 * q^51 - 24 * q^52 - 10 * q^53 + 27 * q^54 - 39 * q^55 - 39 * q^56 - 92 * q^57 + 8 * q^58 - q^59 - 42 * q^60 + 19 * q^61 - 4 * q^62 + 5 * q^63 + 84 * q^64 - 32 * q^65 + 52 * q^66 + 10 * q^67 - 34 * q^68 - 32 * q^69 + 48 * q^70 + 35 * q^71 - 26 * q^72 - 22 * q^73 + 68 * q^74 + 62 * q^75 + 2 * q^76 + 42 * q^77 - 81 * q^78 + 2 * q^79 + 49 * q^80 - 37 * q^81 - 35 * q^82 - 48 * q^83 - 34 * q^84 - 13 * q^85 - 152 * q^86 + 22 * q^87 + 37 * q^88 + 42 * q^89 + 30 * q^90 - 39 * q^91 + 30 * q^92 - 42 * q^94 - 34 * q^95 - 66 * q^96 - 38 * q^97 + 8 * q^98 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.578965	+	1.00280i	0.409390	+	0.709085i	0.994822	−	0.101637i	$-0.0324082\pi$
$2$	0.578965	+	1.00280i	0.409390	+	0.709085i	−0.585431	+	0.810722i	$0.699075\pi$
$3$	−0.235957	−	0.408690i	−0.136230	−	0.235957i	0.789837	−	0.613317i	$-0.210165\pi$
$3$	−0.235957	−	0.408690i	−0.136230	−	0.235957i	−0.926067	+	0.377360i	$0.876832\pi$
$4$	0.329599	−	0.570882i	0.164799	−	0.285441i
$5$	−3.25594			−1.45610			−0.728051	−	0.685523i	$-0.759573\pi$
$5$	−3.25594			−1.45610			−0.728051	+	0.685523i	$0.759573\pi$
$6$	0.273222	−	0.473235i	0.111542	−	0.193197i
$7$	0.0133059	−	0.0230465i	0.00502916	−	0.00871075i	−0.863500	−	0.504349i	$-0.831732\pi$
$7$	0.0133059	−	0.0230465i	0.00502916	−	0.00871075i	0.868529	+	0.495638i	$0.165066\pi$
$8$	3.07917			1.08865
$9$	1.38865	−	2.40521i	0.462883	−	0.801736i
$10$	−1.88508	−	3.26505i	−0.596114	−	1.03250i
$11$	−1.99508	−	3.45558i	−0.601540	−	1.04190i	−0.992588	−	0.121527i	$-0.961221\pi$
$11$	−1.99508	−	3.45558i	−0.601540	−	1.04190i	0.391048	−	0.920370i	$-0.372113\pi$
$12$	−0.311085			−0.0898025
$13$	1.93078	−	3.04501i	0.535503	−	0.844534i
$13$	1.93078	−	3.04501i	0.535503	−	0.844534i
$14$	0.0308146			0.00823555
$15$	0.768263	+	1.33067i	0.198365	+	0.343578i
$16$	1.12353	+	1.94601i	0.280883	+	0.486503i
$17$	−2.63341	+	4.56120i	−0.638695	+	1.10625i	0.347024	+	0.937856i	$0.387192\pi$
$17$	−2.63341	+	4.56120i	−0.638695	+	1.10625i	−0.985719	+	0.168396i	$0.946141\pi$
$18$	3.21592			0.757999
$19$	4.34124	−	7.51924i	0.995948	−	1.72503i	0.420094	−	0.907480i	$-0.361997\pi$
$19$	4.34124	−	7.51924i	0.995948	−	1.72503i	0.575854	−	0.817553i	$-0.304670\pi$
$20$	−1.07315	+	1.85876i	−0.239965	+	0.415631i
$21$	−0.0125585			−0.00274049
$22$	2.31017	−	4.00132i	0.492529	−	0.853085i
$23$	2.12725	+	3.68450i	0.443562	+	0.768272i	0.997951	−	0.0639861i	$-0.0203813\pi$
$23$	2.12725	+	3.68450i	0.443562	+	0.768272i	−0.554389	+	0.832258i	$0.687048\pi$
$24$	−0.726552	−	1.25842i	−0.148307	−	0.256875i
$25$	5.60115			1.12023
$26$	4.17138	+	0.173228i	0.818075	+	0.0339728i
$27$	−2.72639			−0.524694
$28$	−0.00877122	−	0.0151922i	−0.00165760	−	0.00287105i
$29$	−2.84203	−	4.92255i	−0.527753	−	0.914094i	−0.999477	−	0.0323480i	$-0.989702\pi$
$29$	−2.84203	−	4.92255i	−0.527753	−	0.914094i	0.471724	−	0.881746i	$-0.343632\pi$
$30$	−0.889595	+	1.54082i	−0.162417	+	0.281315i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	1.77819	−	3.07992i	0.314343	−	0.544459i
$33$	−0.941508	+	1.63074i	−0.163896	+	0.283875i
$34$	−6.09860			−1.04590
$35$	−0.0433232	+	0.0750380i	−0.00732296	+	0.0126837i
$36$	−0.915394	−	1.58551i	−0.152566	−	0.264251i
$37$	2.46125	+	4.26302i	0.404628	+	0.700835i	0.994278	−	0.106823i	$-0.0340678\pi$
$37$	2.46125	+	4.26302i	0.404628	+	0.700835i	−0.589651	+	0.807659i	$0.700735\pi$
$38$	10.0537			1.63093
$39$	−1.70005	−	0.0705992i	−0.272225	−	0.0113049i
$40$	−10.0256			−1.58518
$41$	−2.71441	−	4.70150i	−0.423920	−	0.734251i	0.572399	−	0.819975i	$-0.306013\pi$
$41$	−2.71441	−	4.70150i	−0.423920	−	0.734251i	−0.996319	+	0.0857240i	$0.972680\pi$
$42$	−0.00727093	−	0.0125936i	−0.00112193	−	0.00194324i
$43$	−3.26031	+	5.64702i	−0.497192	+	0.861163i	−0.999995	−	0.00323891i	$-0.998969\pi$
$43$	−3.26031	+	5.64702i	−0.497192	+	0.861163i	0.502802	+	0.864401i	$0.332302\pi$
$44$	−2.63031			−0.396534
$45$	−4.52136	+	7.83122i	−0.674004	+	1.16741i
$46$	−2.46320	+	4.26639i	−0.363180	+	0.629046i
$47$	−1.95563			−0.285258			−0.142629	−	0.989776i	$-0.545556\pi$
$47$	−1.95563			−0.285258			−0.142629	+	0.989776i	$0.545556\pi$
$48$	0.530211	−	0.918352i	0.0765293	−	0.132553i
$49$	3.49965	+	6.06156i	0.499949	+	0.865938i
$50$	3.24287	+	5.61682i	0.458612	+	0.794338i
$51$	2.48549			0.348038
$52$	−1.10196	−	2.10588i	−0.152814	−	0.292033i
$53$	10.7054			1.47051			0.735253	−	0.677792i	$-0.237063\pi$
$53$	10.7054			1.47051			0.735253	+	0.677792i	$0.237063\pi$
$54$	−1.57848	−	2.73402i	−0.214805	−	0.372052i
$55$	6.49587	+	11.2512i	0.875903	+	1.51711i
$56$	0.0409710	−	0.0709639i	0.00547499	−	0.00948295i
$57$	−4.09739			−0.542712
$58$	3.29088	−	5.69997i	0.432113	−	0.748442i
$59$	−6.64385	+	11.5075i	−0.864955	+	1.49815i	0.00213619	+	0.999998i	$0.499320\pi$
$59$	−6.64385	+	11.5075i	−0.864955	+	1.49815i	−0.867092	+	0.498149i	$0.834013\pi$
$60$	1.01287			0.130762
$61$	−0.438981	+	0.760337i	−0.0562057	+	0.0973512i	−0.892759	−	0.450534i	$-0.851234\pi$
$61$	−0.438981	+	0.760337i	−0.0562057	+	0.0973512i	0.836554	+	0.547885i	$0.184567\pi$
$62$	−0.578965	−	1.00280i	−0.0735286	−	0.127355i
$63$	−0.0369544	−	0.0640069i	−0.00465582	−	0.00806411i
$64$	8.61218			1.07652
$65$	−6.28651	+	9.91437i	−0.779746	+	1.22973i
$66$	−2.18040			−0.268389
$67$	−2.37747	−	4.11790i	−0.290454	−	0.503082i	0.683463	−	0.729985i	$-0.260473\pi$
$67$	−2.37747	−	4.11790i	−0.290454	−	0.503082i	−0.973917	+	0.226904i	$0.927140\pi$
$68$	1.73594	+	3.00673i	0.210513	+	0.364620i
$69$	1.00388	−	1.73877i	0.120853	−	0.209323i
$70$	−0.100331			−0.0119918
$71$	3.50797	−	6.07598i	0.416319	−	0.721086i	−0.579247	−	0.815152i	$-0.696653\pi$
$71$	3.50797	−	6.07598i	0.416319	−	0.721086i	0.995566	+	0.0940661i	$0.0299865\pi$
$72$	4.27588	−	7.40604i	0.503917	−	0.872810i
$73$	−12.5998			−1.47469			−0.737347	−	0.675514i	$-0.763922\pi$
$73$	−12.5998			−1.47469			−0.737347	+	0.675514i	$0.763922\pi$
$74$	−2.84996	+	4.93627i	−0.331301	+	0.573830i
$75$	−1.32163	−	2.28914i	−0.152609	−	0.264327i
$76$	−2.86173	−	4.95667i	−0.328263	−	0.568569i
$77$	−0.106185			−0.0121009
$78$	−0.913471	−	1.74568i	−0.103430	−	0.197659i
$79$	13.8937			1.56317			0.781583	−	0.623801i	$-0.214412\pi$
$79$	13.8937			1.56317			0.781583	+	0.623801i	$0.214412\pi$
$80$	−3.65815	−	6.33611i	−0.408994	−	0.708398i
$81$	−3.52263	−	6.10138i	−0.391404	−	0.677931i
$82$	3.14310	−	5.44401i	0.347098	−	0.601191i
$83$	0.690405			0.0757818			0.0378909	−	0.999282i	$-0.487936\pi$
$83$	0.690405			0.0757818			0.0378909	+	0.999282i	$0.487936\pi$
$84$	−0.00413926	+	0.00716942i	−0.000451631	+	0.000782247i
$85$	8.57422	−	14.8510i	0.930005	−	1.61082i
$86$	−7.55042			−0.814183
$87$	−1.34120	+	2.32302i	−0.143791	+	0.249054i
$88$	−6.14319	−	10.6403i	−0.654866	−	1.13426i
$89$	6.83075	+	11.8312i	0.724058	+	1.25410i	0.959361	+	0.282183i	$0.0910584\pi$
$89$	6.83075	+	11.8312i	0.724058	+	1.25410i	−0.235303	+	0.971922i	$0.575608\pi$
$90$	−10.4708			−1.10372
$91$	−0.0444860	−	0.0850143i	−0.00466340	−	0.00891192i
$92$	2.80455			0.292395
$93$	0.235957	+	0.408690i	0.0244676	+	0.0423792i
$94$	−1.13224	−	1.96110i	−0.116782	−	0.202272i
$95$	−14.1348	+	24.4822i	−1.45020	+	2.51182i
$96$	−1.67831			−0.171292
$97$	−5.63529	+	9.76061i	−0.572177	+	0.991040i	0.424165	+	0.905585i	$0.360568\pi$
$97$	−5.63529	+	9.76061i	−0.572177	+	0.991040i	−0.996342	+	0.0854547i	$0.972766\pi$
$98$	−4.05235	+	7.01887i	−0.409349	+	0.709013i
$99$	−11.0819			−1.11377
$100$	1.84613	−	3.19760i	0.184613	−	0.319760i
$101$	−1.75107	−	3.03295i	−0.174238	−	0.301790i	0.765659	−	0.643247i	$-0.222413\pi$
$101$	−1.75107	−	3.03295i	−0.174238	−	0.301790i	−0.939897	+	0.341457i	$0.889080\pi$
$102$	1.43901	+	2.49244i	0.142483	+	0.246788i
$103$	17.7478			1.74874			0.874370	−	0.485260i	$-0.161275\pi$
$103$	17.7478			1.74874			0.874370	+	0.485260i	$0.161275\pi$
$104$	5.94520	−	9.37609i	0.582974	−	0.919401i
$105$	0.0408897			0.00399043
$106$	6.19808	+	10.7354i	0.602011	+	1.04271i
$107$	1.64893	+	2.85603i	0.159408	+	0.276103i	0.934655	−	0.355555i	$-0.115708\pi$
$107$	1.64893	+	2.85603i	0.159408	+	0.276103i	−0.775247	+	0.631658i	$0.782375\pi$
$108$	−0.898615	+	1.55645i	−0.0864693	+	0.149769i
$109$	−2.37542			−0.227524			−0.113762	−	0.993508i	$-0.536290\pi$
$109$	−2.37542			−0.227524			−0.113762	+	0.993508i	$0.536290\pi$
$110$	−7.52176	+	13.0281i	−0.717172	+	1.24218i
$111$	1.16150	−	2.01178i	0.110245	−	0.190950i
$112$	0.0597984			0.00565041
$113$	−2.47749	+	4.29114i	−0.233062	+	0.403676i	−0.958708	−	0.284393i	$-0.908208\pi$
$113$	−2.47749	+	4.29114i	−0.233062	+	0.403676i	0.725645	+	0.688069i	$0.241541\pi$
$114$	−2.37224	−	4.10885i	−0.222181	−	0.384829i
$115$	−6.92619	−	11.9965i	−0.645871	−	1.11868i
$116$	−3.74693			−0.347893
$117$	−4.64271	−	8.87238i	−0.429218	−	0.820252i
$118$	−15.3862			−1.41642
$119$	0.0700797	+	0.121382i	0.00642419	+	0.0111270i
$120$	2.36561	+	4.09736i	0.215950	+	0.374036i
$121$	−2.46071	+	4.26207i	−0.223700	+	0.387461i
$122$	−1.01662			−0.0920403
$123$	−1.28097	+	2.21871i	−0.115501	+	0.200054i
$124$	−0.329599	+	0.570882i	−0.0295989	+	0.0512667i
$125$	−1.95732			−0.175068
$126$	0.0427906	−	0.0741155i	0.00381209	−	0.00660274i
$127$	−0.502713	−	0.870724i	−0.0446085	−	0.0772643i	0.842859	−	0.538134i	$-0.180871\pi$
$127$	−0.502713	−	0.870724i	−0.0446085	−	0.0772643i	−0.887468	+	0.460870i	$0.847537\pi$
$128$	1.42976	+	2.47642i	0.126374	+	0.218886i
$129$	3.07717			0.270930
$130$	−13.5818	−	0.564021i	−1.19120	−	0.0494679i
$131$	5.29571			0.462688			0.231344	−	0.972872i	$-0.425688\pi$
$131$	5.29571			0.462688			0.231344	+	0.972872i	$0.425688\pi$
$132$	0.620640	+	1.07498i	0.0540198	+	0.0935650i
$133$	−0.115528	−	0.200101i	−0.0100176	−	0.0173509i
$134$	2.75294	−	4.76824i	0.237818	−	0.411913i
$135$	8.87697			0.764008
$136$	−8.10870	+	14.0447i	−0.695315	+	1.20432i
$137$	5.13620	−	8.89616i	0.438815	−	0.760050i	−0.558783	−	0.829314i	$-0.688732\pi$
$137$	5.13620	−	8.89616i	0.438815	−	0.760050i	0.997598	+	0.0692636i	$0.0220649\pi$
$138$	2.32484			0.197904
$139$	7.49442	−	12.9807i	0.635668	−	1.10101i	−0.350705	−	0.936486i	$-0.614058\pi$
$139$	7.49442	−	12.9807i	0.635668	−	1.10101i	0.986373	−	0.164524i	$-0.0526088\pi$
$140$	0.0285586	+	0.0494649i	0.00241364	+	0.00418055i
$141$	0.461445	+	0.799246i	0.0388607	+	0.0673086i
$142$	8.12397			0.681748
$143$	−14.3744	−	0.596935i	−1.20204	−	0.0499182i
$144$	6.24076			0.520063
$145$	9.25350	+	16.0275i	0.768461	+	1.33101i
$146$	−7.29484	−	12.6350i	−0.603725	−	1.04568i
$147$	1.65153	−	2.86054i	0.136216	−	0.235933i
$148$	3.24490			0.266730
$149$	5.88313	−	10.1899i	0.481965	−	0.834788i	−0.517821	−	0.855489i	$-0.673257\pi$
$149$	5.88313	−	10.1899i	0.481965	−	0.834788i	0.999786	+	0.0207014i	$0.00658993\pi$
$150$	1.53036	−	2.65066i	0.124953	−	0.216425i
$151$	7.45932			0.607031			0.303515	−	0.952827i	$-0.401840\pi$
$151$	7.45932			0.607031			0.303515	+	0.952827i	$0.401840\pi$
$152$	13.3674	−	23.1530i	1.08424	−	1.87796i
$153$	7.31375	+	12.6678i	0.591282	+	1.02413i
$154$	−0.0614776	−	0.106482i	−0.00495401	−	0.00858060i
$155$	3.25594			0.261524
$156$	−0.600637	+	0.947257i	−0.0480895	+	0.0758412i
$157$	−6.00213			−0.479022			−0.239511	−	0.970894i	$-0.576987\pi$
$157$	−6.00213			−0.479022			−0.239511	+	0.970894i	$0.576987\pi$
$158$	8.04398	+	13.9326i	0.639945	+	1.10842i
$159$	−2.52603	−	4.37521i	−0.200327	−	0.346977i
$160$	−5.78970	+	10.0280i	−0.457716	+	0.792787i
$161$	0.113220			0.00892296
$162$	4.07896	−	7.06497i	0.320474	−	0.555077i
$163$	5.42888	−	9.40309i	0.425223	−	0.736507i	−0.571219	−	0.820798i	$-0.693529\pi$
$163$	5.42888	−	9.40309i	0.425223	−	0.736507i	0.996441	+	0.0842909i	$0.0268625\pi$
$164$	−3.57867			−0.279447
$165$	3.06550	−	5.30960i	0.238649	−	0.413351i
$166$	0.399720	+	0.692336i	0.0310243	+	0.0537357i
$167$	−0.0221913	−	0.0384365i	−0.00171721	−	0.00297430i	0.865166	−	0.501486i	$-0.167213\pi$
$167$	−0.0221913	−	0.0384365i	−0.00171721	−	0.00297430i	−0.866883	+	0.498512i	$0.833880\pi$
$168$	−0.0386697			−0.00298343
$169$	−5.54416	−	11.7585i	−0.426474	−	0.904500i
$170$	19.8567			1.52294
$171$	−12.0569	−	20.8832i	−0.922015	−	1.59698i
$172$	2.14919	+	3.72250i	0.163874	+	0.283838i
$173$	−2.63020	+	4.55564i	−0.199970	+	0.346359i	−0.948519	−	0.316722i	$-0.897418\pi$
$173$	−2.63020	+	4.55564i	−0.199970	+	0.346359i	0.748548	+	0.663080i	$0.230751\pi$
$174$	−3.10603			−0.235467
$175$	0.0745284	−	0.129087i	0.00563382	−	0.00975805i
$176$	4.48307	−	7.76491i	0.337924	−	0.585302i
$177$	6.27066			0.471331
$178$	−7.90953	+	13.6997i	−0.592844	+	1.02684i
$179$	11.8231	+	20.4782i	0.883701	+	1.53062i	0.847195	+	0.531282i	$0.178290\pi$
$179$	11.8231	+	20.4782i	0.883701	+	1.53062i	0.0365067	+	0.999333i	$0.488377\pi$
$180$	2.98047	+	5.16232i	0.222151	+	0.384777i
$181$	−1.85175			−0.137640			−0.0688199	−	0.997629i	$-0.521923\pi$
$181$	−1.85175			−0.137640			−0.0688199	+	0.997629i	$0.521923\pi$
$182$	0.0594963	−	0.0938307i	0.00441016	−	0.00695520i
$183$	0.414323			0.0306276
$184$	6.55015	+	11.3452i	0.482883	+	0.836378i
$185$	−8.01370	−	13.8801i	−0.589179	−	1.02049i
$186$	−0.273222	+	0.473235i	−0.0200336	+	0.0346992i
$187$	21.0155			1.53680
$188$	−0.644573	+	1.11643i	−0.0470103	+	0.0814242i
$189$	−0.0362771	+	0.0628337i	−0.00263877	+	0.00457048i
$190$	−32.7343			−2.37479
$191$	−5.31997	+	9.21445i	−0.384939	+	0.666734i	−0.991761	−	0.128104i	$-0.959111\pi$
$191$	−5.31997	+	9.21445i	−0.384939	+	0.666734i	0.606821	+	0.794838i	$0.292444\pi$
$192$	−2.03211	−	3.51971i	−0.146655	−	0.254013i
$193$	−6.17034	−	10.6874i	−0.444151	−	0.769292i	0.553842	−	0.832622i	$-0.313161\pi$
$193$	−6.17034	−	10.6874i	−0.444151	−	0.769292i	−0.997993	+	0.0633298i	$0.979828\pi$
$194$	−13.0505			−0.936974
$195$	5.53525	+	0.229867i	0.396388	+	0.0164611i
$196$	4.61392			0.329566
$197$	8.09113	+	14.0143i	0.576469	+	0.998474i	0.995880	+	0.0906777i	$0.0289033\pi$
$197$	8.09113	+	14.0143i	0.576469	+	0.998474i	−0.419411	+	0.907796i	$0.637763\pi$
$198$	−6.41602	−	11.1129i	−0.455966	−	0.789757i
$199$	3.71721	−	6.43839i	0.263506	−	0.456405i	−0.703665	−	0.710532i	$-0.748455\pi$
$199$	3.71721	−	6.43839i	0.263506	−	0.456405i	0.967171	+	0.254126i	$0.0817879\pi$
$200$	17.2469			1.21954
$201$	−1.12196	+	1.94330i	−0.0791372	+	0.137070i
$202$	2.02762	−	3.51194i	0.142663	−	0.247100i
$203$	−0.151263			−0.0106166
$204$	0.819214	−	1.41892i	0.0573564	−	0.0993443i
$205$	8.83797	+	15.3078i	0.617271	+	1.06914i
$206$	10.2753	+	17.7974i	0.715917	+	1.24000i
$207$	11.8160			0.821268
$208$	8.09492	+	0.336164i	0.561282	+	0.0233088i
$209$	−34.6445			−2.39641
$210$	0.0236737	+	0.0410041i	0.00163364	+	0.00282955i
$211$	8.94181	+	15.4877i	0.615580	+	1.06622i	0.990282	+	0.139071i	$0.0444115\pi$
$211$	8.94181	+	15.4877i	0.615580	+	1.06622i	−0.374703	+	0.927145i	$0.622255\pi$
$212$	3.52850	−	6.11155i	0.242339	−	0.419743i
$213$	−3.31092			−0.226861
$214$	−1.90934	+	3.30708i	−0.130520	+	0.226067i
$215$	10.6154	−	18.3864i	0.723962	−	1.25394i
$216$	−8.39501			−0.571208
$217$	−0.0133059	+	0.0230465i	−0.000903263	+	0.00156450i
$218$	−1.37529	−	2.38206i	−0.0931461	−	0.161334i
$219$	2.97301	+	5.14941i	0.200898	+	0.347965i
$220$	8.56413			0.577393
$221$	8.80435	+	16.8254i	0.592245	+	1.13180i
$222$	2.68987			0.180533
$223$	5.42156	+	9.39042i	0.363055	+	0.628829i	0.988462	−	0.151469i	$-0.0484005\pi$
$223$	5.42156	+	9.39042i	0.363055	+	0.628829i	−0.625407	+	0.780298i	$0.715067\pi$
$224$	−0.0473209	−	0.0819623i	−0.00316176	−	0.00547633i
$225$	7.77803	−	13.4720i	0.518536	−	0.898130i
$226$	−5.73752			−0.381654
$227$	9.99802	−	17.3171i	0.663592	−	1.14937i	−0.316073	−	0.948735i	$-0.602365\pi$
$227$	9.99802	−	17.3171i	0.663592	−	1.14937i	0.979665	−	0.200640i	$-0.0643021\pi$
$228$	−1.35049	+	2.33912i	−0.0894387	+	0.154912i
$229$	5.08386			0.335951			0.167975	−	0.985791i	$-0.446277\pi$
$229$	5.08386			0.335951			0.167975	+	0.985791i	$0.446277\pi$
$230$	8.02005	−	13.8911i	0.528826	−	0.915954i
$231$	0.0250552	+	0.0433969i	0.00164851	+	0.00285531i
$232$	−8.75109	−	15.1573i	−0.574537	−	0.995128i
$233$	2.51153			0.164536			0.0822679	−	0.996610i	$-0.473784\pi$
$233$	2.51153			0.164536			0.0822679	+	0.996610i	$0.473784\pi$
$234$	6.20923	−	9.79249i	0.405910	−	0.640155i
$235$	6.36741			0.415364
$236$	4.37961	+	7.58571i	0.285088	+	0.493787i
$237$	−3.27833	−	5.67823i	−0.212950	−	0.368841i
$238$	−0.0811474	+	0.140551i	−0.00526000	+	0.00911059i
$239$	−5.01640			−0.324484			−0.162242	−	0.986751i	$-0.551873\pi$
$239$	−5.01640			−0.324484			−0.162242	+	0.986751i	$0.551873\pi$
$240$	−1.72634	+	2.99010i	−0.111434	+	0.193010i
$241$	−9.82215	+	17.0125i	−0.632700	+	1.09587i	0.354297	+	0.935133i	$0.384720\pi$
$241$	−9.82215	+	17.0125i	−0.632700	+	1.09587i	−0.986997	+	0.160736i	$0.948613\pi$
$242$	−5.69865			−0.366323
$243$	−5.75197	+	9.96270i	−0.368989	+	0.639108i
$244$	0.289375	+	0.501212i	0.0185253	+	0.0320868i
$245$	−11.3946	−	19.7361i	−0.727977	−	1.26089i
$246$	−2.96655			−0.189140
$247$	−14.5142	−	27.7371i	−0.923516	−	1.76487i
$248$	−3.07917			−0.195527
$249$	−0.162906	−	0.282162i	−0.0103238	−	0.0178813i
$250$	−1.13322	−	1.96280i	−0.0716713	−	0.124138i
$251$	−5.19505	+	8.99809i	−0.327908	+	0.567954i	−0.982097	−	0.188378i	$-0.939677\pi$
$251$	−5.19505	+	8.99809i	−0.327908	+	0.567954i	0.654188	+	0.756332i	$0.273010\pi$
$252$	−0.0487205			−0.00306911
$253$	8.48807	−	14.7018i	0.533640	−	0.924292i
$254$	0.582106	−	1.00824i	0.0365246	−	0.0632624i
$255$	−8.09260			−0.506778
$256$	6.95661	−	12.0492i	0.434788	−	0.753075i
$257$	4.29803	+	7.44441i	0.268104	+	0.464369i	0.968372	−	0.249510i	$-0.0802696\pi$
$257$	4.29803	+	7.44441i	0.268104	+	0.464369i	−0.700268	+	0.713880i	$0.746936\pi$
$258$	1.78158	+	3.08578i	0.110916	+	0.192112i
$259$	0.130997			0.00813974
$260$	3.58791	+	6.85662i	0.222513	+	0.425230i
$261$	−15.7863			−0.977150
$262$	3.06603	+	5.31052i	0.189420	+	0.328085i
$263$	6.59268	+	11.4189i	0.406522	+	0.704117i	0.994497	−	0.104762i	$-0.0334081\pi$
$263$	6.59268	+	11.4189i	0.406522	+	0.704117i	−0.587975	+	0.808879i	$0.700075\pi$
$264$	−2.89906	+	5.02132i	−0.178425	+	0.309041i
$265$	−34.8563			−2.14121
$266$	0.133773	−	0.231702i	0.00820218	−	0.0142066i
$267$	3.22353	−	5.58332i	0.197277	−	0.341693i
$268$	−3.13445			−0.191467
$269$	1.24759	−	2.16088i	0.0760667	−	0.131751i	−0.825483	−	0.564427i	$-0.809097\pi$
$269$	1.24759	−	2.16088i	0.0760667	−	0.131751i	0.901550	+	0.432676i	$0.142430\pi$
$270$	5.13945	+	8.90180i	0.312777	+	0.541746i
$271$	2.18311	+	3.78126i	0.132614	+	0.229695i	0.924684	−	0.380736i	$-0.124329\pi$
$271$	2.18311	+	3.78126i	0.132614	+	0.229695i	−0.792069	+	0.610431i	$0.790996\pi$
$272$	−11.8349			−0.717594
$273$	−0.0242477	+	0.0382407i	−0.00146754	+	0.00231443i
$274$	11.8947			0.718586
$275$	−11.1748	−	19.3553i	−0.673864	−	1.16717i
$276$	−0.661755	−	1.14619i	−0.0398330	−	0.0689927i
$277$	3.50611	−	6.07276i	0.210662	−	0.364877i	−0.741260	−	0.671218i	$-0.765771\pi$
$277$	3.50611	−	6.07276i	0.210662	−	0.364877i	0.951922	+	0.306341i	$0.0991048\pi$
$278$	17.3560			1.04095
$279$	−1.38865	+	2.40521i	−0.0831362	+	0.143996i
$280$	−0.133399	+	0.231054i	−0.00797213	+	0.0138081i
$281$	−23.8844			−1.42483			−0.712413	−	0.701761i	$-0.752398\pi$
$281$	−23.8844			−1.42483			−0.712413	+	0.701761i	$0.752398\pi$
$282$	−0.534321	+	0.925471i	−0.0318183	+	0.0551110i
$283$	11.1489	+	19.3105i	0.662733	+	1.14789i	0.979895	+	0.199516i	$0.0639370\pi$
$283$	11.1489	+	19.3105i	0.662733	+	1.14789i	−0.317161	+	0.948372i	$0.602730\pi$
$284$	−2.31245	−	4.00527i	−0.137218	−	0.237669i
$285$	13.3409			0.790244
$286$	−7.72364	−	14.7602i	−0.456709	−	0.872787i
$287$	−0.144471			−0.00852784
$288$	−4.93857	−	8.55386i	−0.291008	−	0.504041i
$289$	−5.36967	−	9.30055i	−0.315863	−	0.547091i
$290$	−10.7149	+	18.5588i	−0.629201	+	1.08981i
$291$	5.31875			0.311791
$292$	−4.15288	+	7.19299i	−0.243029	+	0.420938i
$293$	13.4938	−	23.3719i	0.788316	−	1.36540i	−0.138682	−	0.990337i	$-0.544287\pi$
$293$	13.4938	−	23.3719i	0.788316	−	1.36540i	0.926998	−	0.375066i	$-0.122380\pi$
$294$	3.82472			0.223062
$295$	21.6320	−	37.4677i	1.25946	−	2.18145i
$296$	7.57861	+	13.1265i	0.440497	+	0.762964i
$297$	5.43937	+	9.42127i	0.315624	+	0.546678i
$298$	13.6245			0.789247
$299$	15.3266	+	0.636479i	0.886360	+	0.0368085i
$300$	−1.74244			−0.100600
$301$	0.0867626	+	0.150277i	0.00500092	+	0.00866184i
$302$	4.31869	+	7.48018i	0.248512	+	0.430436i
$303$	−0.826358	+	1.43129i	−0.0474730	+	0.0822257i
$304$	19.5101			1.11898
$305$	1.42930	−	2.47561i	0.0818412	−	0.141753i
$306$	−8.46882	+	14.6684i	−0.484130	+	0.838538i
$307$	13.3522			0.762052			0.381026	−	0.924564i	$-0.375571\pi$
$307$	13.3522			0.762052			0.381026	+	0.924564i	$0.375571\pi$
$308$	−0.0349986	+	0.0606193i	−0.00199423	+	0.00345411i
$309$	−4.18772	−	7.25334i	−0.238231	−	0.412628i
$310$	1.88508	+	3.26505i	0.107065	+	0.185442i
$311$	−7.76620			−0.440381			−0.220190	−	0.975457i	$-0.570668\pi$
$311$	−7.76620			−0.440381			−0.220190	+	0.975457i	$0.570668\pi$
$312$	−5.23473	−	0.217386i	−0.296358	−	0.0123071i
$313$	−30.8675			−1.74473			−0.872367	−	0.488852i	$-0.837416\pi$
$313$	−30.8675			−1.74473			−0.872367	+	0.488852i	$0.837416\pi$
$314$	−3.47502	−	6.01891i	−0.196107	−	0.339667i
$315$	0.120321	+	0.208403i	0.00677934	+	0.0117422i
$316$	4.57936	−	7.93168i	0.257609	−	0.446192i
$317$	−27.7932			−1.56102			−0.780512	−	0.625141i	$-0.785041\pi$
$317$	−27.7932			−1.56102			−0.780512	+	0.625141i	$0.785041\pi$
$318$	2.92497	−	5.06619i	0.164024	−	0.284098i
$319$	−11.3402	+	19.6418i	−0.634928	+	1.09973i
$320$	−28.0407			−1.56752
$321$	0.778153	−	1.34780i	0.0434323	−	0.0752269i
$322$	0.0655503	+	0.113536i	0.00365297	+	0.00632714i
$323$	22.8645	+	39.6025i	1.27221	+	2.20354i
$324$	−4.64422			−0.258012
$325$	10.8146	−	17.0556i	0.599887	−	0.946073i
$326$	12.5725			0.696328
$327$	0.560498	+	0.970811i	0.0309956	+	0.0536860i
$328$	−8.35813	−	14.4767i	−0.461501	−	0.799342i
$329$	−0.0260214	+	0.0450704i	−0.00143461	+	0.00248481i
$330$	7.09926			0.390801
$331$	−1.85251	+	3.20865i	−0.101823	+	0.176363i	−0.912436	−	0.409220i	$-0.865801\pi$
$331$	−1.85251	+	3.20865i	−0.101823	+	0.176363i	0.810613	+	0.585583i	$0.199134\pi$
$332$	0.227557	−	0.394140i	0.0124888	−	0.0216312i
$333$	13.6713			0.749180
$334$	0.0256960	−	0.0445068i	0.00140602	−	0.00243530i
$335$	7.74091	+	13.4076i	0.422931	+	0.732538i
$336$	−0.0141099	−	0.0244390i	−0.000769756	−	0.00133326i
$337$	−25.3047			−1.37844			−0.689218	−	0.724554i	$-0.742046\pi$
$337$	−25.3047			−1.37844			−0.689218	+	0.724554i	$0.742046\pi$
$338$	8.58151	−	12.3674i	0.466773	−	0.672699i
$339$	2.33833			0.127000
$340$	−5.65211	−	9.78974i	−0.306529	−	0.530923i
$341$	1.99508	+	3.45558i	0.108040	+	0.187130i
$342$	13.9611	−	24.1813i	0.754927	−	1.30757i
$343$	0.372546			0.0201156
$344$	−10.0390	+	17.3881i	−0.541268	+	0.937504i
$345$	−3.26857	+	5.66133i	−0.175974	+	0.304796i
$346$	−6.09117			−0.327464
$347$	14.1893	−	24.5766i	0.761723	−	1.31934i	−0.180238	−	0.983623i	$-0.557687\pi$
$347$	14.1893	−	24.5766i	0.761723	−	1.31934i	0.941962	−	0.335720i	$-0.108980\pi$
$348$	0.884114	+	1.53133i	0.0473935	+	0.0820880i
$349$	−17.8000	−	30.8305i	−0.952811	−	1.65032i	−0.739300	−	0.673376i	$-0.764843\pi$
$349$	−17.8000	−	30.8305i	−0.952811	−	1.65032i	−0.213511	−	0.976941i	$-0.568490\pi$
$350$	0.172597			0.00922571
$351$	−5.26407	+	8.30188i	−0.280975	+	0.443122i
$352$	−14.1906			−0.756360
$353$	−7.89796	−	13.6797i	−0.420366	−	0.728096i	0.575609	−	0.817725i	$-0.304765\pi$
$353$	−7.89796	−	13.6797i	−0.420366	−	0.728096i	−0.995975	+	0.0896295i	$0.971432\pi$
$354$	3.63049	+	6.28820i	0.192958	+	0.334214i
$355$	−11.4217	+	19.7830i	−0.606203	+	1.04997i
$356$	9.00563			0.477297
$357$	0.0330716	−	0.0572817i	0.00175034	−	0.00303167i
$358$	−13.6903	+	23.7124i	−0.723557	+	1.25324i
$359$	21.5269			1.13615			0.568074	−	0.822977i	$-0.307689\pi$
$359$	21.5269			1.13615			0.568074	+	0.822977i	$0.307689\pi$
$360$	−13.9220	+	24.1136i	−0.733754	+	1.27090i
$361$	−28.1927	−	48.8312i	−1.48383	−	2.57006i
$362$	−1.07210	−	1.85693i	−0.0563483	−	0.0975982i
$363$	2.32249			0.121899
$364$	−0.0631957	−	0.00262437i	−0.00331235	−	0.000137555i
$365$	41.0242			2.14730
$366$	0.239878	+	0.415482i	0.0125386	+	0.0217176i
$367$	4.37015	+	7.56933i	0.228120	+	0.395116i	0.957251	−	0.289259i	$-0.0934088\pi$
$367$	4.37015	+	7.56933i	0.228120	+	0.395116i	−0.729131	+	0.684374i	$0.760075\pi$
$368$	−4.78006	+	8.27930i	−0.249178	+	0.431589i
$369$	−15.0775			−0.784902
$370$	9.27930	−	16.0722i	0.482408	−	0.835555i
$371$	0.142446	−	0.246723i	0.00739541	−	0.0128092i
$372$	0.311085			0.0161290
$373$	−13.6391	+	23.6237i	−0.706207	+	1.22319i	0.260047	+	0.965596i	$0.416262\pi$
$373$	−13.6391	+	23.6237i	−0.706207	+	1.22319i	−0.966254	+	0.257591i	$0.917071\pi$
$374$	12.1672	+	21.0742i	0.629152	+	1.08972i
$375$	0.461845	+	0.799939i	0.0238496	+	0.0413087i
$376$	−6.02170			−0.310546
$377$	−20.4766	−	0.850345i	−1.05460	−	0.0437950i
$378$	−0.0840126			−0.00432114
$379$	16.8245	+	29.1408i	0.864214	+	1.49686i	0.867826	+	0.496869i	$0.165517\pi$
$379$	16.8245	+	29.1408i	0.864214	+	1.49686i	−0.00361155	+	0.999993i	$0.501150\pi$
$380$	9.31764	+	16.1386i	0.477985	+	0.827894i
$381$	−0.237237	+	0.410907i	−0.0121540	+	0.0210514i
$382$	−12.3203			−0.630361
$383$	−7.42362	+	12.8581i	−0.379329	+	0.657017i	−0.990965	−	0.134122i	$-0.957179\pi$
$383$	−7.42362	+	12.8581i	−0.379329	+	0.657017i	0.611636	+	0.791140i	$0.290512\pi$
$384$	0.674725	−	1.16866i	0.0344319	−	0.0596378i
$385$	0.345733			0.0176202
$386$	7.14483	−	12.3752i	0.363662	−	0.629881i
$387$	9.05484	+	15.6834i	0.460284	+	0.797235i
$388$	3.71477	+	6.43417i	0.188589	+	0.326646i
$389$	−24.2257			−1.22829			−0.614146	−	0.789193i	$-0.710499\pi$
$389$	−24.2257			−1.22829			−0.614146	+	0.789193i	$0.710499\pi$
$390$	2.97421	+	5.68382i	0.150605	+	0.287811i
$391$	−22.4076			−1.13320
$392$	10.7760	+	18.6646i	0.544270	+	0.942703i
$393$	−1.24956	−	2.16430i	−0.0630320	−	0.109175i
$394$	−9.36897	+	16.2275i	−0.472002	+	0.817531i
$395$	−45.2372			−2.27613
$396$	−3.65257	+	6.32644i	−0.183549	+	0.317916i
$397$	10.5094	−	18.2029i	0.527453	−	0.913576i	−0.472035	−	0.881580i	$-0.656480\pi$
$397$	10.5094	−	18.2029i	0.527453	−	0.913576i	0.999488	−	0.0319957i	$-0.0101863\pi$
$398$	8.60853			0.431507
$399$	−0.0545194	+	0.0944304i	−0.00272938	+	0.00472743i
$400$	6.29307	+	10.8999i	0.314654	+	0.544996i
$401$	11.9782	+	20.7469i	0.598164	+	1.03605i	0.993092	+	0.117338i	$0.0374362\pi$
$401$	11.9782	+	20.7469i	0.598164	+	1.03605i	−0.394928	+	0.918712i	$0.629230\pi$
$402$	−2.59831			−0.129592
$403$	−1.93078	+	3.04501i	−0.0961791	+	0.151683i
$404$	−2.30861			−0.114858
$405$	11.4695	+	19.8657i	0.569923	+	0.987136i
$406$	−0.0875761	−	0.151686i	−0.00434633	−	0.00752806i
$407$	9.82080	−	17.0101i	0.486799	−	0.843161i
$408$	7.65323			0.378891
$409$	−10.8730	+	18.8327i	−0.537638	+	0.931216i	0.461393	+	0.887196i	$0.347350\pi$
$409$	−10.8730	+	18.8327i	−0.537638	+	0.931216i	−0.999031	+	0.0440198i	$0.985984\pi$
$410$	−10.2338	+	17.7254i	−0.505409	+	0.875394i
$411$	−4.84770			−0.239119
$412$	5.84964	−	10.1319i	0.288191	−	0.499162i
$413$	0.176805	+	0.306235i	0.00869999	+	0.0150688i
$414$	6.84105	+	11.8490i	0.336219	+	0.582349i
$415$	−2.24792			−0.110346
$416$	−5.94509	−	11.3613i	−0.291482	−	0.557032i
$417$	−7.07345			−0.346388
$418$	−20.0580	−	34.7414i	−0.981067	−	1.69926i
$419$	−13.2286	−	22.9125i	−0.646257	−	1.11935i	−0.984010	−	0.178115i	$-0.943000\pi$
$419$	−13.2286	−	22.9125i	−0.646257	−	1.11935i	0.337752	−	0.941235i	$-0.390333\pi$
$420$	0.0134772	−	0.0233432i	0.000657620	−	0.00113903i
$421$	−29.3326			−1.42958			−0.714792	−	0.699337i	$-0.753479\pi$
$421$	−29.3326			−1.42958			−0.714792	+	0.699337i	$0.753479\pi$
$422$	−10.3540	+	17.9336i	−0.504025	+	0.872996i
$423$	−2.71568	+	4.70370i	−0.132041	+	0.228701i
$424$	32.9638			1.60087
$425$	−14.7501	+	25.5480i	−0.715486	+	1.23926i
$426$	−1.91691	−	3.32018i	−0.0928746	−	0.160863i
$427$	0.0116821	+	0.0202339i	0.000565335	+	0.000979188i
$428$	2.17394			0.105081
$429$	3.14777	+	6.01551i	0.151976	+	0.290431i
$430$	24.5837			1.18553
$431$	−5.67632	−	9.83168i	−0.273419	−	0.473575i	0.696316	−	0.717735i	$-0.254821\pi$
$431$	−5.67632	−	9.83168i	−0.273419	−	0.473575i	−0.969735	+	0.244160i	$0.921488\pi$
$432$	−3.06319	−	5.30559i	−0.147378	−	0.255265i
$433$	−13.8135	+	23.9257i	−0.663836	+	1.14980i	0.315764	+	0.948838i	$0.397739\pi$
$433$	−13.8135	+	23.9257i	−0.663836	+	1.14980i	−0.979599	+	0.200960i	$0.935594\pi$
$434$	−0.0308146			−0.00147915
$435$	4.36686	−	7.56362i	0.209375	−	0.362648i
$436$	−0.782936	+	1.35609i	−0.0374958	+	0.0649447i
$437$	36.9396			1.76706
$438$	−3.44254	+	5.96266i	−0.164491	+	0.284907i
$439$	−9.72226	−	16.8394i	−0.464018	−	0.803703i	0.535139	−	0.844764i	$-0.320259\pi$
$439$	−9.72226	−	16.8394i	−0.464018	−	0.803703i	−0.999157	+	0.0410616i	$0.986926\pi$
$440$	20.0019	+	34.6442i	0.953551	+	1.65160i
$441$	19.4391			0.925672
$442$	−11.7751	+	18.5703i	−0.560083	+	0.883299i
$443$	−16.3973			−0.779058			−0.389529	−	0.921014i	$-0.627362\pi$
$443$	−16.3973			−0.779058			−0.389529	+	0.921014i	$0.627362\pi$
$444$	−0.765659	−	1.32616i	−0.0363366	−	0.0629368i
$445$	−22.2405	−	38.5217i	−1.05430	−	1.82610i
$446$	−6.27779	+	10.8735i	−0.297262	+	0.514873i
$447$	−5.55267			−0.262632
$448$	0.114593	−	0.198480i	0.00541400	−	0.00937732i
$449$	0.425663	−	0.737269i	0.0200883	−	0.0347939i	−0.855807	−	0.517296i	$-0.826939\pi$
$449$	0.425663	−	0.737269i	0.0200883	−	0.0347939i	0.875895	+	0.482502i	$0.160272\pi$
$450$	18.0128			0.849133
$451$	−10.8310	+	18.7598i	−0.510010	+	0.883363i
$452$	1.63315	+	2.82871i	0.0768171	+	0.133051i
$453$	−1.76008	−	3.04855i	−0.0826958	−	0.143233i
$454$	23.1540			1.08667
$455$	0.144844	+	0.276802i	0.00679038	+	0.0129767i
$456$	−12.6165			−0.590823
$457$	9.02560	+	15.6328i	0.422200	+	0.731272i	0.996154	−	0.0876156i	$-0.0279247\pi$
$457$	9.02560	+	15.6328i	0.422200	+	0.731272i	−0.573955	+	0.818887i	$0.694591\pi$
$458$	2.94338	+	5.09808i	0.137535	+	0.238217i
$459$	7.17970	−	12.4356i	0.335120	−	0.580444i
$460$	−9.13146			−0.425757
$461$	−16.3882	+	28.3853i	−0.763277	+	1.32203i	0.177876	+	0.984053i	$0.443077\pi$
$461$	−16.3882	+	28.3853i	−0.763277	+	1.32203i	−0.941153	+	0.337981i	$0.890256\pi$
$462$	−0.0290122	+	0.0502506i	−0.00134977	+	0.00233787i
$463$	−5.85631			−0.272166			−0.136083	−	0.990697i	$-0.543451\pi$
$463$	−5.85631			−0.272166			−0.136083	+	0.990697i	$0.543451\pi$
$464$	6.38623	−	11.0613i	0.296473	−	0.513507i
$465$	−0.768263	−	1.33067i	−0.0356274	−	0.0617084i
$466$	1.45409	+	2.51856i	0.0673594	+	0.116670i
$467$	5.74769			0.265971			0.132986	−	0.991118i	$-0.457544\pi$
$467$	5.74769			0.265971			0.132986	+	0.991118i	$0.457544\pi$
$468$	−6.59531	−	0.273889i	−0.304869	−	0.0126605i
$469$	−0.126537			−0.00584296
$470$	3.68651	+	6.38522i	0.170046	+	0.294528i
$471$	1.41625	+	2.45301i	0.0652572	+	0.113029i
$472$	−20.4575	+	35.4334i	−0.941633	+	1.63096i
$473$	26.0183			1.19632
$474$	3.79607	−	6.57499i	0.174359	−	0.301999i
$475$	24.3159	−	42.1165i	1.11569	−	1.93244i
$476$	0.0923927			0.00423481
$477$	14.8661	−	25.7488i	0.680672	−	1.17896i
$478$	−2.90432	−	5.03043i	−0.132841	−	0.230087i
$479$	−1.19509	−	2.06996i	−0.0546051	−	0.0945789i	0.837431	−	0.546543i	$-0.184057\pi$
$479$	−1.19509	−	2.06996i	−0.0546051	−	0.0945789i	−0.892036	+	0.451965i	$0.850723\pi$
$480$	5.46448			0.249418
$481$	17.7331	+	0.736415i	0.808558	+	0.0335776i
$482$	−22.7467			−1.03608
$483$	−0.0267150	−	0.0462718i	−0.00121558	−	0.00210544i
$484$	1.62209	+	2.80954i	0.0737314	+	0.127707i
$485$	18.3482	−	31.7800i	0.833148	−	1.44305i
$486$	−13.3208			−0.604242
$487$	8.75307	−	15.1608i	0.396639	−	0.687000i	−0.596670	−	0.802487i	$-0.703510\pi$
$487$	8.75307	−	15.1608i	0.396639	−	0.687000i	0.993309	+	0.115487i	$0.0368430\pi$
$488$	−1.35169	+	2.34120i	−0.0611883	+	0.105981i
$489$	−5.12393			−0.231712
$490$	13.1942	−	22.8530i	0.596053	−	1.03239i
$491$	−8.79189	−	15.2280i	−0.396772	−	0.687230i	0.596553	−	0.802573i	$-0.296536\pi$
$491$	−8.79189	−	15.2280i	−0.396772	−	0.687230i	−0.993326	+	0.115344i	$0.963203\pi$
$492$	0.844414	+	1.46257i	0.0380691	+	0.0659376i
$493$	29.9369			1.34829
$494$	19.4115	−	30.6136i	0.873365	−	1.37737i
$495$	36.0819			1.62176
$496$	−1.12353	−	1.94601i	−0.0504481	−	0.0873786i
$497$	−0.0933533	−	0.161693i	−0.00418747	−	0.00725291i
$498$	0.188634	−	0.326723i	0.00845289	−	0.0146408i
$499$	30.4409			1.36272			0.681360	−	0.731948i	$-0.261389\pi$
$499$	30.4409			1.36272			0.681360	+	0.731948i	$0.261389\pi$
$500$	−0.645132	+	1.11740i	−0.0288512	+	0.0499717i
$501$	−0.0104724	+	0.0181387i	−0.000467872	+	0.000810379i
$502$	−12.0310			−0.536970
$503$	4.07083	−	7.05088i	0.181509	−	0.314383i	−0.760886	−	0.648886i	$-0.775235\pi$
$503$	4.07083	−	7.05088i	0.181509	−	0.314383i	0.942395	+	0.334503i	$0.108568\pi$
$504$	−0.113789	−	0.197088i	−0.00506855	−	0.00877899i
$505$	5.70140	+	9.87511i	0.253709	+	0.439437i
$506$	19.6572			0.873868
$507$	−3.49740	+	5.04035i	−0.155325	+	0.223850i
$508$	−0.662774			−0.0294058
$509$	−9.67339	−	16.7548i	−0.428766	−	0.742644i	0.567998	−	0.823030i	$-0.307718\pi$
$509$	−9.67339	−	16.7548i	−0.428766	−	0.742644i	−0.996764	+	0.0803860i	$0.974385\pi$
$510$	−4.68533	−	8.11524i	−0.207470	−	0.359349i
$511$	−0.167651	+	0.290381i	−0.00741646	+	0.0128457i
$512$	21.8296			0.964740
$513$	−11.8359	+	20.5004i	−0.522568	+	0.905115i
$514$	−4.97682	+	8.62011i	−0.219518	+	0.380217i
$515$	−57.7857			−2.54634
$516$	1.01423	−	1.75670i	0.0446491	−	0.0773346i
$517$	3.90164	+	6.75784i	0.171594	+	0.297209i
$518$	0.0758425	+	0.131363i	0.00333233	+	0.00577176i
$519$	2.48246			0.108968
$520$	−19.3572	+	30.5280i	−0.848870	+	1.33874i
$521$	20.1771			0.883973			0.441987	−	0.897022i	$-0.354274\pi$
$521$	20.1771			0.883973			0.441987	+	0.897022i	$0.354274\pi$
$522$	−9.13974	−	15.8305i	−0.400036	−	0.692882i
$523$	−2.92444	−	5.06527i	−0.127877	−	0.221489i	0.794977	−	0.606640i	$-0.207483\pi$
$523$	−2.92444	−	5.06527i	−0.127877	−	0.221489i	−0.922854	+	0.385151i	$0.874150\pi$
$524$	1.74546	−	3.02322i	0.0762508	−	0.132070i
$525$	−0.0703421			−0.00306998
$526$	−7.63387	+	13.2222i	−0.332852	+	0.576517i
$527$	2.63341	−	4.56120i	0.114713	−	0.198689i
$528$	−4.23126			−0.184142
$529$	2.44964	−	4.24289i	0.106506	−	0.184474i
$530$	−20.1806	−	34.9538i	−0.876589	−	1.51830i
$531$	18.4519	+	31.9597i	0.800746	+	1.38693i
$532$	−0.152312			−0.00660355
$533$	−19.5571	−	0.812161i	−0.847110	−	0.0351786i
$534$	7.46524			0.323053
$535$	−5.36881	−	9.29906i	−0.232114	−	0.402033i
$536$	−7.32063	−	12.6797i	−0.316203	−	0.547679i
$537$	5.57950	−	9.66398i	0.240773	−	0.417032i
$538$	2.88924			0.124564
$539$	13.9642	−	24.1866i	0.601479	−	1.04179i
$540$	2.92584	−	5.06770i	0.125908	−	0.218079i
$541$	18.5740			0.798557			0.399279	−	0.916830i	$-0.369261\pi$
$541$	18.5740			0.798557			0.399279	+	0.916830i	$0.369261\pi$
$542$	−2.52789	+	4.37843i	−0.108582	+	0.188070i
$543$	0.436935	+	0.756793i	0.0187507	+	0.0324771i
$544$	9.36542	+	16.2214i	0.401539	+	0.695486i
$545$	7.73423			0.331298
$546$	−0.0523863	−	0.00217548i	−0.00224192	−	9.31021e-5i
$547$	−0.176328			−0.00753926			−0.00376963	−	0.999993i	$-0.501200\pi$
$547$	−0.176328			−0.00753926			−0.00376963	+	0.999993i	$0.501200\pi$
$548$	−3.38577	−	5.86433i	−0.144633	−	0.250512i
$549$	1.21918	+	2.11168i	0.0520333	+	0.0901243i
$550$	12.9396	−	22.4120i	0.551746	−	0.955652i
$551$	−49.3518			−2.10246
$552$	3.09111	−	5.35396i	0.131566	−	0.227880i
$553$	0.184868	−	0.320202i	0.00786141	−	0.0136164i
$554$	8.11967			0.344972
$555$	−3.78178	+	6.55024i	−0.160528	+	0.278042i
$556$	−4.94031	−	8.55686i	−0.209516	−	0.362892i
$557$	−3.44648	−	5.96948i	−0.146032	−	0.252935i	0.783725	−	0.621107i	$-0.213317\pi$
$557$	−3.44648	−	5.96948i	−0.146032	−	0.252935i	−0.929758	+	0.368172i	$0.879984\pi$
$558$	−3.21592			−0.136141
$559$	10.9003	+	20.8308i	0.461033	+	0.881050i
$560$	−0.194700			−0.00822757
$561$	−4.95875	−	8.58881i	−0.209359	−	0.362620i
$562$	−13.8283	−	23.9512i	−0.583310	−	1.01032i
$563$	14.1247	−	24.4648i	0.595287	−	1.03107i	−0.398219	−	0.917290i	$-0.630372\pi$
$563$	14.1247	−	24.4648i	0.595287	−	1.03107i	0.993506	−	0.113777i	$-0.0362949\pi$
$564$	0.608367			0.0256169
$565$	8.06656	−	13.9717i	0.339363	−	0.587793i
$566$	−12.9096	+	22.3602i	−0.542633	+	0.939868i
$567$	−0.187487			−0.00787372
$568$	10.8016	−	18.7090i	0.453226	−	0.785010i
$569$	1.86792	+	3.23532i	0.0783071	+	0.135632i	0.902520	−	0.430649i	$-0.141715\pi$
$569$	1.86792	+	3.23532i	0.0783071	+	0.135632i	−0.824213	+	0.566281i	$0.808382\pi$
$570$	7.72389	+	13.3782i	0.323518	+	0.560350i
$571$	−26.1573			−1.09465			−0.547324	−	0.836921i	$-0.684354\pi$
$571$	−26.1573			−1.09465			−0.547324	+	0.836921i	$0.684354\pi$
$572$	−5.07855	+	8.00931i	−0.212345	+	0.334886i
$573$	5.02114			0.209761
$574$	−0.0836436	−	0.144875i	−0.00349122	−	0.00604696i
$575$	11.9150	+	20.6375i	0.496892	+	0.860642i
$576$	11.9593	−	20.7141i	0.498303	−	0.863087i
$577$	11.6962			0.486917			0.243459	−	0.969911i	$-0.421718\pi$
$577$	11.6962			0.486917			0.243459	+	0.969911i	$0.421718\pi$
$578$	6.21771	−	10.7694i	0.258623	−	0.447947i
$579$	−2.91188	+	5.04352i	−0.121013	+	0.209601i
$580$	12.1998			0.506568
$581$	0.00918646	−	0.0159114i	0.000381118	−	0.000660116i
$582$	3.07937	+	5.33363i	0.127644	+	0.221086i
$583$	−21.3583	−	36.9936i	−0.884568	−	1.53212i
$584$	−38.7968			−1.60542
$585$	15.1164	+	28.8880i	0.624986	+	1.19437i
$586$	31.2497			1.29092
$587$	−4.38840	−	7.60094i	−0.181129	−	0.313724i	0.761136	−	0.648592i	$-0.224642\pi$
$587$	−4.38840	−	7.60094i	−0.181129	−	0.313724i	−0.942265	+	0.334868i	$0.891308\pi$
$588$	−1.08869	−	1.88566i	−0.0448967	−	0.0777634i
$589$	−4.34124	+	7.51924i	−0.178878	+	0.309825i
$590$	50.0966			2.06245
$591$	3.81832	−	6.61353i	0.157065	−	0.272044i
$592$	−5.53059	+	9.57926i	−0.227306	+	0.393705i
$593$	−17.9088			−0.735428			−0.367714	−	0.929939i	$-0.619859\pi$
$593$	−17.9088			−0.735428			−0.367714	+	0.929939i	$0.619859\pi$
$594$	−6.29841	+	10.9092i	−0.258427	+	0.447609i
$595$	−0.228175	−	0.395211i	−0.00935428	−	0.0162021i
$596$	−3.87815	−	6.71715i	−0.158855	−	0.275145i
$597$	−3.50841			−0.143590
$598$	8.23530	+	15.7380i	0.336767	+	0.643573i
$599$	−12.4478			−0.508605			−0.254302	−	0.967125i	$-0.581846\pi$
$599$	−12.4478			−0.508605			−0.254302	+	0.967125i	$0.581846\pi$
$600$	−4.06953	−	7.04863i	−0.166138	−	0.287759i
$601$	10.2313	+	17.7210i	0.417341	+	0.722857i	0.995671	−	0.0929466i	$-0.0296286\pi$
$601$	10.2313	+	17.7210i	0.417341	+	0.722857i	−0.578330	+	0.815803i	$0.696295\pi$
$602$	−0.100465	+	0.174011i	−0.00409465	+	0.00709214i
$603$	−13.2059			−0.537785
$604$	2.45858	−	4.25839i	0.100038	−	0.173272i
$605$	8.01191	−	13.8770i	0.325731	−	0.564182i
$606$	−1.91373			−0.0777399
$607$	2.32819	−	4.03255i	0.0944985	−	0.163676i	−0.814901	−	0.579601i	$-0.803209\pi$
$607$	2.32819	−	4.03255i	0.0944985	−	0.163676i	0.909399	+	0.415924i	$0.136542\pi$
$608$	−15.4391	−	26.7414i	−0.626139	−	1.08451i
$609$	0.0356917	+	0.0618198i	0.00144630	+	0.00250506i
$610$	3.31005			0.134020
$611$	−3.77589	+	5.95491i	−0.152756	+	0.240910i
$612$	9.64242			0.389772
$613$	4.06549	+	7.04164i	0.164204	+	0.284409i	0.936372	−	0.351009i	$-0.114161\pi$
$613$	4.06549	+	7.04164i	0.164204	+	0.284409i	−0.772169	+	0.635418i	$0.780828\pi$
$614$	7.73048	+	13.3896i	0.311977	+	0.540360i
$615$	4.17077	−	7.22398i	0.168182	−	0.291299i
$616$	−0.326962			−0.0131737
$617$	−2.10037	+	3.63794i	−0.0845576	+	0.146458i	−0.905203	−	0.424980i	$-0.860281\pi$
$617$	−2.10037	+	3.63794i	−0.0845576	+	0.146458i	0.820645	+	0.571438i	$0.193614\pi$
$618$	4.84908	−	8.39886i	0.195059	−	0.337852i
$619$	−39.6410			−1.59331			−0.796654	−	0.604436i	$-0.793399\pi$
$619$	−39.6410			−1.59331			−0.796654	+	0.604436i	$0.793399\pi$
$620$	1.07315	−	1.85876i	0.0430989	−	0.0746495i
$621$	−5.79971	−	10.0454i	−0.232734	−	0.403108i
$622$	−4.49636	−	7.78792i	−0.180288	−	0.312267i
$623$	0.363557			0.0145656
$624$	−1.77267	−	3.38763i	−0.0709636	−	0.135614i
$625$	−21.6328			−0.865314
$626$	−17.8712	−	30.9538i	−0.714277	−	1.23716i
$627$	8.17462	+	14.1589i	0.326463	+	0.565451i
$628$	−1.97829	+	3.42651i	−0.0789425	+	0.136732i
$629$	−25.9259			−1.03373
$630$	−0.139324	+	0.241316i	−0.00555079	+	0.00961425i
$631$	−14.1222	+	24.4604i	−0.562197	+	0.973753i	0.435108	+	0.900378i	$0.356710\pi$
$631$	−14.1222	+	24.4604i	−0.562197	+	0.973753i	−0.997304	+	0.0733746i	$0.976623\pi$
$632$	42.7811			1.70174
$633$	4.21977	−	7.30886i	0.167721	−	0.290501i
$634$	−16.0913	−	27.8710i	−0.639067	−	1.10690i
$635$	1.63680	+	2.83503i	0.0649545	+	0.112505i
$636$	−3.33031			−0.132055
$637$	25.2146	+	1.04710i	0.999038	+	0.0414878i
$638$	−26.2623			−1.03973
$639$	−9.74267	−	16.8748i	−0.385414	−	0.667557i
$640$	−4.65522	−	8.06307i	−0.184014	−	0.318721i
$641$	21.9731	−	38.0585i	0.867884	−	1.50322i	0.00372931	−	0.999993i	$-0.498813\pi$
$641$	21.9731	−	38.0585i	0.867884	−	1.50322i	0.864155	−	0.503226i	$-0.167854\pi$
$642$	1.80209			0.0711230
$643$	2.57014	−	4.45161i	0.101356	−	0.175555i	−0.810887	−	0.585202i	$-0.801015\pi$
$643$	2.57014	−	4.45161i	0.101356	−	0.175555i	0.912244	+	0.409648i	$0.134348\pi$
$644$	0.0373171	−	0.0646351i	0.00147050	−	0.00254698i
$645$	−10.0191			−0.394502
$646$	−26.4755	+	45.8569i	−1.04166	+	1.80422i
$647$	12.8145	+	22.1954i	0.503792	+	0.872593i	0.999990	+	0.00438377i	$0.00139540\pi$
$647$	12.8145	+	22.1954i	0.503792	+	0.872593i	−0.496199	+	0.868209i	$0.665271\pi$
$648$	−10.8468	−	18.7872i	−0.426101	−	0.738029i
$649$	53.0201			2.08122
$650$	23.3646	+	0.970278i	0.916433	+	0.0380574i
$651$	0.0125585			0.000492206
$652$	−3.57870	−	6.19850i	−0.140153	−	0.242752i
$653$	1.02353	+	1.77280i	0.0400538	+	0.0693751i	0.885357	−	0.464911i	$-0.153914\pi$
$653$	1.02353	+	1.77280i	0.0400538	+	0.0693751i	−0.845304	+	0.534286i	$0.820580\pi$
$654$	−0.649017	+	1.12413i	−0.0253786	+	0.0439570i
$655$	−17.2425			−0.673721
$656$	6.09946	−	10.5646i	0.238144	−	0.412477i
$657$	−17.4967	+	30.3051i	−0.682610	+	1.18232i
$658$	−0.0602619			−0.00234925
$659$	7.46786	−	12.9347i	0.290907	−	0.503865i	−0.683118	−	0.730308i	$-0.739376\pi$
$659$	7.46786	−	12.9347i	0.290907	−	0.503865i	0.974024	+	0.226443i	$0.0727098\pi$
$660$	−2.02077	−	3.50007i	−0.0786583	−	0.136240i
$661$	21.9685	+	38.0505i	0.854474	+	1.47999i	0.877132	+	0.480249i	$0.159454\pi$
$661$	21.9685	+	38.0505i	0.854474	+	1.47999i	−0.0226587	+	0.999743i	$0.507213\pi$
$662$	−4.29016			−0.166742
$663$	4.79893	−	7.56833i	0.186375	−	0.293930i
$664$	2.12587			0.0824998
$665$	0.376153	+	0.651516i	0.0145866	+	0.0252647i
$666$	7.91518	+	13.7095i	0.306707	+	0.531232i
$667$	12.0914	−	20.9430i	0.468182	−	0.810914i
$668$	−0.0292569			−0.00113198
$669$	2.55851	−	4.43148i	0.0989179	−	0.171331i
$670$	−8.96343	+	15.5251i	−0.346287	+	0.599787i
$671$	3.50321			0.135240
$672$	−0.0223314	+	0.0386792i	−0.000861454	+	0.00149208i
$673$	6.18230	+	10.7081i	0.238310	+	0.412765i	0.960230	−	0.279212i	$-0.0900732\pi$
$673$	6.18230	+	10.7081i	0.238310	+	0.412765i	−0.721919	+	0.691977i	$0.756740\pi$
$674$	−14.6505	−	25.3755i	−0.564318	−	0.977427i
$675$	−15.2709			−0.587779
$676$	−8.54006	−	0.710525i	−0.328464	−	0.0273279i
$677$	12.6478			0.486094			0.243047	−	0.970015i	$-0.421853\pi$
$677$	12.6478			0.486094			0.243047	+	0.970015i	$0.421853\pi$
$678$	1.35381	+	2.34487i	0.0519927	+	0.0900540i
$679$	0.149965	+	0.259747i	0.00575513	+	0.00996818i
$680$	26.4014	−	45.7286i	1.01245	−	1.75361i
$681$	−9.43642			−0.361604
$682$	−2.31017	+	4.00132i	−0.0884608	+	0.153219i
$683$	−0.826198	+	1.43102i	−0.0316136	+	0.0547563i	−0.881399	−	0.472372i	$-0.843398\pi$
$683$	−0.826198	+	1.43102i	−0.0316136	+	0.0547563i	0.849786	+	0.527128i	$0.176731\pi$
$684$	−15.8958			−0.607790
$685$	−16.7232	+	28.9654i	−0.638959	+	1.10671i
$686$	0.215691	+	0.373588i	0.00823513	+	0.0142637i
$687$	−1.19957	−	2.07772i	−0.0457666	−	0.0792700i
$688$	−14.6522			−0.558611
$689$	20.6699	−	32.5982i	0.787460	−	1.24189i
$690$	−7.56956			−0.288168
$691$	14.8963	+	25.8011i	0.566681	+	0.981520i	0.996891	+	0.0787912i	$0.0251060\pi$
$691$	14.8963	+	25.8011i	0.566681	+	0.981520i	−0.430210	+	0.902729i	$0.641561\pi$
$692$	1.73382	+	3.00307i	0.0659100	+	0.114159i
$693$	−0.147454	+	0.255398i	−0.00560132	+	0.00970177i
$694$	32.8605			1.24737
$695$	−24.4014	+	42.2645i	−0.925598	+	1.60318i
$696$	−4.12977	+	7.15297i	−0.156538	+	0.271133i
$697$	28.5926			1.08302
$698$	20.6111	−	35.6995i	0.780143	−	1.35125i
$699$	−0.592614	−	1.02644i	−0.0224147	−	0.0388234i
$700$	−0.0491289	−	0.0850938i	−0.00185690	−	0.00321624i
$701$	41.7850			1.57820			0.789099	−	0.614266i	$-0.210548\pi$
$701$	41.7850			1.57820			0.789099	+	0.614266i	$0.210548\pi$
$702$	−11.3728	−	0.472288i	−0.429239	−	0.0178253i
$703$	42.7395			1.61195
$704$	−17.1820	−	29.7601i	−0.647571	−	1.12163i
$705$	−1.50244	−	2.60230i	−0.0565851	−	0.0980082i
$706$	9.14529	−	15.8401i	0.344188	−	0.596150i
$707$	−0.0931985			−0.00350509
$708$	2.06680	−	3.57981i	0.0776752	−	0.134537i
$709$	−2.52080	+	4.36616i	−0.0946707	+	0.163974i	−0.909471	−	0.415767i	$-0.863513\pi$
$709$	−2.52080	+	4.36616i	−0.0946707	+	0.163974i	0.814800	+	0.579742i	$0.196846\pi$
$710$	−26.4512			−0.992694
$711$	19.2935	−	33.4173i	0.723563	−	1.25325i
$712$	21.0330	+	36.4302i	0.788245	+	1.36528i
$713$	−2.12725	−	3.68450i	−0.0796660	−	0.137986i
$714$	0.0765893			0.00286628
$715$	46.8020	+	1.94358i	1.75030	+	0.0726859i
$716$	15.5875			0.582534
$717$	1.18366	+	2.05015i	0.0442045	+	0.0765644i
$718$	12.4633	+	21.5872i	0.465128	+	0.805625i
$719$	−1.41202	+	2.44569i	−0.0526593	+	0.0912087i	−0.891153	−	0.453702i	$-0.850103\pi$
$719$	−1.41202	+	2.44569i	−0.0526593	+	0.0912087i	0.838494	+	0.544911i	$0.183436\pi$
$720$	−20.3195			−0.757265
$721$	0.236150	−	0.409024i	0.00879468	−	0.0152328i
$722$	32.6452	−	56.5431i	1.21493	−	2.10432i
$723$	9.27043			0.344771
$724$	−0.610336	+	1.05713i	−0.0226830	+	0.0392880i
$725$	−15.9187	−	27.5720i	−0.591205	−	1.02400i
$726$	1.34464	+	2.32898i	0.0499042	+	0.0864366i
$727$	42.3089			1.56915			0.784575	−	0.620034i	$-0.212881\pi$
$727$	42.3089			1.56915			0.784575	+	0.620034i	$0.212881\pi$
$728$	−0.136980	−	0.261773i	−0.00507680	−	0.00970196i
$729$	−15.7069			−0.581738
$730$	23.7516	+	41.1389i	0.879085	+	1.52262i
$731$	−17.1714	−	29.7418i	−0.635109	−	1.10004i
$732$	0.136560	−	0.236529i	0.00504741	−	0.00874238i
$733$	10.5872			0.391049			0.195524	−	0.980699i	$-0.437359\pi$
$733$	10.5872			0.391049			0.195524	+	0.980699i	$0.437359\pi$
$734$	−5.06033	+	8.76475i	−0.186780	+	0.323513i
$735$	−5.37730	+	9.31375i	−0.198345	+	0.343543i
$736$	15.1306			0.557723
$737$	−9.48650	+	16.4311i	−0.349440	+	0.605247i
$738$	−8.72933	−	15.1196i	−0.321331	−	0.556562i
$739$	−3.55792	−	6.16250i	−0.130880	−	0.226691i	0.793136	−	0.609045i	$-0.208447\pi$
$739$	−3.55792	−	6.16250i	−0.130880	−	0.226691i	−0.924016	+	0.382354i	$0.875114\pi$
$740$	−10.5652			−0.388385
$741$	−7.91116	+	12.4766i	−0.290624	+	0.458339i
$742$	0.329884			0.0121104
$743$	11.5153	+	19.9450i	0.422454	+	0.731711i	0.996179	−	0.0873365i	$-0.0278355\pi$
$743$	11.5153	+	19.9450i	0.422454	+	0.731711i	−0.573725	+	0.819048i	$0.694502\pi$
$744$	0.726552	+	1.25842i	0.0266367	+	0.0461361i
$745$	−19.1551	+	33.1777i	−0.701790	+	1.21554i
$746$	−31.5863			−1.15646
$747$	0.958730	−	1.66057i	0.0350781	−	0.0607570i
$748$	6.92667	−	11.9973i	0.253264	−	0.438666i
$749$	0.0877619			0.00320675
$750$	−0.534784	+	0.926274i	−0.0195276	+	0.0338227i
$751$	18.9088	+	32.7509i	0.689991	+	1.19510i	0.971840	+	0.235640i	$0.0757187\pi$
$751$	18.9088	+	32.7509i	0.689991	+	1.19510i	−0.281850	+	0.959459i	$0.590948\pi$
$752$	−2.19721	−	3.80568i	−0.0801240	−	0.138779i
$753$	4.90324			0.178684
$754$	−11.0025	−	21.0261i	−0.400687	−	0.765727i
$755$	−24.2871			−0.883899
$756$	0.0239138	+	0.0414198i	0.000869735	+	0.00150643i
$757$	−16.8858	−	29.2470i	−0.613724	−	1.06300i	−0.990607	−	0.136741i	$-0.956337\pi$
$757$	−16.8858	−	29.2470i	−0.613724	−	1.06300i	0.376883	−	0.926261i	$-0.376996\pi$
$758$	−19.4815	+	33.7430i	−0.707601	+	1.22560i
$759$	−8.01129			−0.290791
$760$	−43.5234	+	75.3848i	−1.57876	+	2.73449i
$761$	11.0717	−	19.1768i	0.401350	−	0.695159i	−0.592539	−	0.805542i	$-0.701874\pi$
$761$	11.0717	−	19.1768i	0.401350	−	0.695159i	0.993889	+	0.110383i	$0.0352077\pi$
$762$	−0.549409			−0.0199030
$763$	−0.0316071	+	0.0547451i	−0.00114425	+	0.00198191i
$764$	3.50691	+	6.07415i	0.126876	+	0.219755i
$765$	−23.8132	−	41.2456i	−0.860967	−	1.49124i
$766$	−17.1921			−0.621174
$767$	22.2126	+	42.4490i	0.802049	+	1.53275i
$768$	−6.56585			−0.236925
$769$	2.87611	+	4.98156i	0.103715	+	0.179640i	0.913213	−	0.407484i	$-0.133594\pi$
$769$	2.87611	+	4.98156i	0.103715	+	0.179640i	−0.809497	+	0.587123i	$0.800260\pi$
$770$	0.200168	+	0.346700i	0.00721354	+	0.0124942i
$771$	2.02830	−	3.51313i	0.0730476	−	0.126522i
$772$	−8.13495			−0.292783
$773$	14.1880	−	24.5744i	0.510308	−	0.883879i	−0.489621	−	0.871936i	$-0.662865\pi$
$773$	14.1880	−	24.5744i	0.510308	−	0.883879i	0.999929	−	0.0119438i	$-0.00380191\pi$
$774$	−10.4849	+	18.1603i	−0.376871	+	0.652760i
$775$	−5.60115			−0.201199
$776$	−17.3520	+	30.0545i	−0.622900	+	1.07889i
$777$	−0.0309096	−	0.0535370i	−0.00110888	−	0.00192063i
$778$	−14.0258	−	24.2935i	−0.502851	−	0.870963i
$779$	−47.1357			−1.68881
$780$	1.95564	−	3.08421i	0.0700231	−	0.110433i
$781$	−27.9947			−1.00173
$782$	−12.9732	−	22.4703i	−0.463922	−	0.803537i
$783$	7.74850	+	13.4208i	0.276909	+	0.479620i
$784$	−7.86392	+	13.6207i	−0.280854	+	0.486454i
$785$	19.5426			0.697504
$786$	1.44690	−	2.50611i	0.0516094	−	0.0893901i
$787$	−22.2635	+	38.5615i	−0.793608	+	1.37457i	0.130112	+	0.991499i	$0.458466\pi$
$787$	−22.2635	+	38.5615i	−0.793608	+	1.37457i	−0.923720	+	0.383069i	$0.874867\pi$
$788$	10.6673			0.380007
$789$	3.11118	−	5.38873i	0.110761	−	0.191844i
$790$	−26.1907	−	45.3637i	−0.931825	−	1.61397i
$791$	0.0659304	+	0.114195i	0.00234421	+	0.00406030i
$792$	−34.1229			−1.21250
$793$	1.46766	+	2.80474i	0.0521180	+	0.0995994i
$794$	24.3384			0.863736
$795$	8.22460	+	14.2454i	0.291697	+	0.505233i
$796$	−2.45037	−	4.24417i	−0.0868512	−	0.150431i
$797$	−15.1512	+	26.2426i	−0.536682	+	0.929561i	0.462398	+	0.886673i	$0.346989\pi$
$797$	−15.1512	+	26.2426i	−0.536682	+	0.929561i	−0.999080	+	0.0428880i	$0.986344\pi$
$798$	−0.126259			−0.00446953
$799$	5.14997	−	8.92000i	0.182193	−	0.315567i
$800$	9.95994	−	17.2511i	0.352137	−	0.609919i
$801$	37.9420			1.34062
$802$	−13.8699	+	24.0235i	−0.489765	+	0.848298i
$803$	25.1376	+	43.5396i	0.887087	+	1.53648i
$804$	0.739596	+	1.28102i	0.0260835	+	0.0451780i
$805$	−0.368637			−0.0129927
$806$	−4.17138	−	0.173228i	−0.146931	−	0.00610170i
$807$	−1.17751			−0.0414503
$808$	−5.39185	−	9.33896i	−0.189685	−	0.328543i
$809$	7.48868	+	12.9708i	0.263288	+	0.456028i	0.967114	−	0.254345i	$-0.0818597\pi$
$809$	7.48868	+	12.9708i	0.263288	+	0.456028i	−0.703826	+	0.710373i	$0.748526\pi$
$810$	−13.2809	+	23.0031i	−0.466642	+	0.808248i
$811$	8.19580			0.287793			0.143897	−	0.989593i	$-0.454037\pi$
$811$	8.19580			0.287793			0.143897	+	0.989593i	$0.454037\pi$
$812$	−0.0498562	+	0.0863535i	−0.00174961	+	0.00303041i
$813$	1.03024	−	1.78443i	0.0361321	−	0.0625827i
$814$	22.7436			0.797163
$815$	−17.6761	+	30.6159i	−0.619167	+	1.07243i
$816$	2.79252	+	4.83679i	0.0977579	+	0.169322i
$817$	28.3076	+	49.0301i	0.990356	+	1.71535i
$818$	−25.1805			−0.880414
$819$	−0.266253	−	0.0110569i	−0.00930362	−	0.000386358i
$820$	11.6519			0.406904
$821$	7.17069	+	12.4200i	0.250259	+	0.433461i	0.963597	−	0.267359i	$-0.0861509\pi$
$821$	7.17069	+	12.4200i	0.250259	+	0.433461i	−0.713338	+	0.700820i	$0.752818\pi$
$822$	−2.80665	−	4.86125i	−0.0978930	−	0.169556i
$823$	4.01110	−	6.94743i	0.139818	−	0.242172i	−0.787610	−	0.616175i	$-0.788682\pi$
$823$	4.01110	−	6.94743i	0.139818	−	0.242172i	0.927428	+	0.374003i	$0.122015\pi$
$824$	54.6483			1.90376
$825$	−5.27353	+	9.13403i	−0.183601	+	0.318006i
$826$	−0.204727	+	0.354598i	−0.00712338	+	0.0123381i
$827$	−18.8582			−0.655766			−0.327883	−	0.944718i	$-0.606335\pi$
$827$	−18.8582			−0.655766			−0.327883	+	0.944718i	$0.606335\pi$
$828$	3.89454	−	6.74554i	0.135345	−	0.234424i
$829$	12.1520	+	21.0480i	0.422058	+	0.731026i	0.996141	−	0.0877715i	$-0.0279745\pi$
$829$	12.1520	+	21.0480i	0.422058	+	0.731026i	−0.574083	+	0.818797i	$0.694641\pi$
$830$	−1.30147	−	2.25421i	−0.0451745	−	0.0782446i
$831$	−3.30917			−0.114794
$832$	16.6282	−	26.2242i	0.576480	−	0.909159i
$833$	−36.8640			−1.27726
$834$	−4.09528	−	7.09324i	−0.141808	−	0.245619i
$835$	0.0722536	+	0.125147i	0.00250044	+	0.00433089i
$836$	−11.4188	+	19.7779i	−0.394927	+	0.684034i
$837$	2.72639			0.0942378
$838$	15.3177	−	26.5311i	0.529143	−	0.916502i
$839$	16.6829	−	28.8957i	0.575959	−	0.997591i	−0.419977	−	0.907535i	$-0.637962\pi$
$839$	16.6829	−	28.8957i	0.575959	−	0.997591i	0.995937	−	0.0900562i	$-0.0287047\pi$
$840$	0.125906			0.00434418
$841$	−1.65432	+	2.86536i	−0.0570455	+	0.0988057i
$842$	−16.9826	−	29.4146i	−0.585257	−	1.01370i
$843$	5.63571	+	9.76133i	0.194104	+	0.336198i
$844$	11.7888			0.405789
$845$	18.0515	+	38.2850i	0.620989	+	1.31704i
$846$	−6.28913			−0.216225
$847$	0.0654838	+	0.113421i	0.00225005	+	0.00389720i
$848$	12.0279	+	20.8329i	0.413040	+	0.715406i
$849$	5.26133	−	9.11289i	0.180568	−	0.312754i
$850$	−34.1592			−1.17165
$851$	−10.4714	+	18.1370i	−0.358955	+	0.621728i
$852$	−1.09128	+	1.89015i	−0.0373865	+	0.0647554i
$853$	13.6534			0.467483			0.233741	−	0.972299i	$-0.424903\pi$
$853$	13.6534			0.467483			0.233741	+	0.972299i	$0.424903\pi$
$854$	−0.0135270	+	0.0234295i	−0.000462885	+	0.000801740i
$855$	39.2566	+	67.9944i	1.34255	+	2.32536i
$856$	5.07732	+	8.79418i	0.173539	+	0.300579i
$857$	−55.6364			−1.90050			−0.950251	−	0.311484i	$-0.899174\pi$
$857$	−55.6364			−1.90050			−0.950251	+	0.311484i	$0.899174\pi$
$858$	−4.20988	+	6.63934i	−0.143723	+	0.226663i
$859$	−29.2170			−0.996872			−0.498436	−	0.866926i	$-0.666092\pi$
$859$	−29.2170			−0.996872			−0.498436	+	0.866926i	$0.666092\pi$
$860$	−6.99763	−	12.1203i	−0.238617	−	0.413297i
$861$	0.0340889	+	0.0590438i	0.00116175	+	0.00201221i
$862$	6.57278	−	11.3844i	0.223870	−	0.387754i
$863$	−14.0275			−0.477502			−0.238751	−	0.971081i	$-0.576738\pi$
$863$	−14.0275			−0.477502			−0.238751	+	0.971081i	$0.576738\pi$
$864$	−4.84805	+	8.39707i	−0.164934	+	0.285674i
$865$	8.56378	−	14.8329i	0.291177	−	0.504334i
$866$	−31.9902			−1.08707
$867$	−2.53403	+	4.38906i	−0.0860601	+	0.149060i
$868$	0.00877122	+	0.0151922i	0.000297714	+	0.000515657i
$869$	−27.7191	−	48.0109i	−0.940307	−	1.62866i
$870$	10.1130			0.342864
$871$	−17.1294	−	0.711347i	−0.580408	−	0.0241031i
$872$	−7.31431			−0.247694
$873$	15.6509	+	27.1081i	0.529702	+	0.917470i
$874$	21.3867	+	37.0429i	0.723416	+	1.25299i
$875$	−0.0260440	+	0.0451095i	−0.000880446	+	0.00152498i
$876$	3.91961			0.132431
$877$	8.39834	−	14.5464i	0.283592	−	0.491195i	−0.688675	−	0.725070i	$-0.741807\pi$
$877$	8.39834	−	14.5464i	0.283592	−	0.491195i	0.972267	+	0.233875i	$0.0751406\pi$
$878$	11.2577	−	19.4989i	0.379929	−	0.658056i
$879$	−12.7358			−0.429569
$880$	−14.5966	+	25.2821i	−0.492052	+	0.852260i
$881$	5.97558	+	10.3500i	0.201323	+	0.348701i	0.948955	−	0.315412i	$-0.102143\pi$
$881$	5.97558	+	10.3500i	0.201323	+	0.348701i	−0.747632	+	0.664113i	$0.768809\pi$
$882$	11.2546	+	19.4935i	0.378961	+	0.656380i
$883$	−34.2201			−1.15160			−0.575800	−	0.817591i	$-0.695309\pi$
$883$	−34.2201			−1.15160			−0.575800	+	0.817591i	$0.695309\pi$
$884$	12.5072	+	0.519398i	0.420664	+	0.0174692i
$885$	−20.4169			−0.686306
$886$	−9.49345	−	16.4431i	−0.318939	−	0.552418i
$887$	7.76450	+	13.4485i	0.260707	+	0.451557i	0.966430	−	0.256931i	$-0.0827112\pi$
$887$	7.76450	+	13.4485i	0.260707	+	0.451557i	−0.705723	+	0.708488i	$0.749378\pi$
$888$	3.57645	−	6.19460i	0.120018	−	0.207877i
$889$	−0.0267562			−0.000897373
$890$	25.7530	−	44.6054i	0.863241	−	1.49518i
$891$	−14.0559	+	24.3455i	−0.470890	+	0.815605i
$892$	7.14776			0.239325
$893$	−8.48985	+	14.7048i	−0.284102	+	0.492079i
$894$	−3.21480	−	5.56820i	−0.107519	−	0.186229i
$895$	−38.4954	−	66.6760i	−1.28676	−	2.22873i
$896$	0.0760969			0.00254222
$897$	−3.35630	−	6.41401i	−0.112064	−	0.214157i
$898$	0.985775			0.0328957
$899$	2.84203	+	4.92255i	0.0947872	+	0.164176i
$900$	−5.12726	−	8.88068i	−0.170909	−	0.296023i
$901$	−28.1918	+	48.8297i	−0.939206	+	1.62675i
$902$	−25.0830			−0.835172
$903$	0.0409446	−	0.0709181i	0.00136255	−	0.00236001i
$904$	−7.62860	+	13.2131i	−0.253723	+	0.439462i
$905$	6.02920			0.200417
$906$	2.03805	−	3.53001i	0.0677097	−	0.117277i
$907$	−15.4879	−	26.8258i	−0.514268	−	0.890738i	−0.999863	−	0.0165539i	$-0.994730\pi$
$907$	−15.4879	−	26.8258i	−0.514268	−	0.890738i	0.485595	−	0.874184i	$-0.338603\pi$
$908$	−6.59067	−	11.4154i	−0.218719	−	0.378833i
$909$	−9.72651			−0.322608
$910$	−0.193716	+	0.305507i	−0.00642163	+	0.0101275i
$911$	−5.45736			−0.180810			−0.0904051	−	0.995905i	$-0.528816\pi$
$911$	−5.45736			−0.180810			−0.0904051	+	0.995905i	$0.528816\pi$
$912$	−4.60354	−	7.97357i	−0.152439	−	0.264031i
$913$	−1.37741	−	2.38575i	−0.0455858	−	0.0789569i
$914$	−10.4510	+	18.1017i	−0.345689	+	0.598751i
$915$	−1.34901			−0.0445969
$916$	1.67563	−	2.90228i	0.0553645	−	0.0958941i
$917$	0.0704641	−	0.122047i	0.00232693	−	0.00403036i
$918$	16.6272			0.548779
$919$	−1.48414	+	2.57061i	−0.0489574	+	0.0847966i	−0.889466	−	0.457002i	$-0.848923\pi$
$919$	−1.48414	+	2.57061i	−0.0489574	+	0.0847966i	0.840508	+	0.541799i	$0.182257\pi$
$920$	−21.3269	−	36.9393i	−0.703127	−	1.21785i
$921$	−3.15056	−	5.45693i	−0.103814	−	0.179812i
$922$	−37.9529			−1.24991
$923$	−11.7283	−	22.4132i	−0.386042	−	0.737739i
$924$	0.0330327			0.00108670
$925$	13.7859	+	23.8778i	0.453276	+	0.785098i
$926$	−3.39060	−	5.87269i	−0.111422	−	0.192989i
$927$	24.6454	−	42.6871i	0.809461	−	1.40203i
$928$	−20.2148			−0.663582
$929$	11.0310	−	19.1063i	0.361916	−	0.626857i	−0.626360	−	0.779534i	$-0.715456\pi$
$929$	11.0310	−	19.1063i	0.361916	−	0.626857i	0.988276	+	0.152677i	$0.0487894\pi$
$930$	0.889595	−	1.54082i	0.0291710	−	0.0505256i
$931$	60.7712			1.99170
$932$	0.827798	−	1.43379i	0.0271154	−	0.0469653i
$933$	1.83249	+	3.17397i	0.0599931	+	0.103911i
$934$	3.32771	+	5.76376i	0.108886	+	0.188596i
$935$	−68.4251			−2.23774
$936$	−14.2957	−	27.3195i	−0.467268	−	0.892967i
$937$	−14.3207			−0.467838			−0.233919	−	0.972256i	$-0.575155\pi$
$937$	−14.3207			−0.467838			−0.233919	+	0.972256i	$0.575155\pi$
$938$	−0.0732608	−	0.126891i	−0.00239205	−	0.00414315i
$939$	7.28341	+	12.6152i	0.237685	+	0.411683i
$940$	2.09869	−	3.63504i	0.0684518	−	0.118562i
$941$	28.4878			0.928676			0.464338	−	0.885658i	$-0.346292\pi$
$941$	28.4878			0.928676			0.464338	+	0.885658i	$0.346292\pi$
$942$	−1.63991	+	2.84041i	−0.0534313	+	0.0925457i
$943$	11.5485	−	20.0025i	0.376070	−	0.651372i
$944$	−29.8583			−0.971805
$945$	0.118116	−	0.204583i	0.00384231	−	0.00665508i
$946$	15.0637	+	26.0911i	0.489763	+	0.848295i
$947$	1.66643	+	2.88634i	0.0541517	+	0.0937935i	0.891831	−	0.452370i	$-0.149421\pi$
$947$	1.66643	+	2.88634i	0.0541517	+	0.0937935i	−0.837679	+	0.546163i	$0.816088\pi$
$948$	−4.32213			−0.140376
$949$	−24.3274	+	38.3665i	−0.789702	+	1.24543i
$950$	56.3123			1.82701
$951$	6.55801	+	11.3588i	0.212658	+	0.368335i
$952$	0.215787	+	0.373754i	0.00699370	+	0.0121134i
$953$	6.76468	−	11.7168i	0.219130	−	0.379543i	−0.735413	−	0.677620i	$-0.763012\pi$
$953$	6.76468	−	11.7168i	0.219130	−	0.379543i	0.954542	+	0.298076i	$0.0963449\pi$
$954$	34.4278			1.11464
$955$	17.3215	−	30.0017i	0.560511	−	0.970833i
$956$	−1.65340	+	2.86377i	−0.0534748	+	0.0926211i
$957$	10.7032			0.345985
$958$	1.38383	−	2.39687i	0.0447096	−	0.0774393i
$959$	−0.136683	−	0.236743i	−0.00441374	−	0.00764482i
$960$	6.61642	+	11.4600i	0.213544	+	0.369869i
$961$	1.00000			0.0322581
$962$	9.52835	+	18.2090i	0.307206	+	0.587082i
$963$	9.15913			0.295149
$964$	6.47474	+	11.2146i	0.208537	+	0.361197i
$965$	20.0903	+	34.7974i	0.646729	+	1.12017i
$966$	0.0309341	−	0.0535795i	0.000995289	−	0.00172389i
$967$	5.06198			0.162782			0.0813912	−	0.996682i	$-0.474064\pi$
$967$	5.06198			0.162782			0.0813912	+	0.996682i	$0.474064\pi$
$968$	−7.57692	+	13.1236i	−0.243531	+	0.421809i
$969$	10.7901	−	18.6890i	0.346628	−	0.600377i
$970$	42.4918			1.36433
$971$	2.09327	−	3.62565i	0.0671763	−	0.116353i	−0.830481	−	0.557047i	$-0.811934\pi$
$971$	2.09327	−	3.62565i	0.0671763	−	0.116353i	0.897657	+	0.440694i	$0.145268\pi$
$972$	3.79168	+	6.56739i	0.121618	+	0.210649i
$973$	−0.199440	−	0.345440i	−0.00639375	−	0.0110743i
$974$	20.2709			0.649521
$975$	−9.52223	−	0.395437i	−0.304955	−	0.0126641i
$976$	−1.97283			−0.0631489
$977$	4.01450	+	6.95332i	0.128435	+	0.222456i	0.923071	−	0.384631i	$-0.125671\pi$
$977$	4.01450	+	6.95332i	0.128435	+	0.222456i	−0.794635	+	0.607087i	$0.792338\pi$
$978$	−2.96658	−	5.13826i	−0.0948607	−	0.164304i
$979$	27.2558	−	47.2084i	0.871099	−	1.50879i
$980$	−15.0226			−0.479881
$981$	−3.29862	+	5.71339i	−0.105317	+	0.182414i
$982$	10.1804	−	17.6330i	0.324869	−	0.562690i
$983$	45.9330			1.46503			0.732517	−	0.680748i	$-0.238345\pi$
$983$	45.9330			1.46503			0.732517	+	0.680748i	$0.238345\pi$
$984$	−3.94432	+	6.83177i	−0.125740	+	0.217789i
$985$	−26.3443	−	45.6296i	−0.839398	−	1.45388i
$986$	17.3324	+	30.0207i	0.551977	+	0.956053i
$987$	0.0245597			0.000781745
$988$	−20.6185	−	0.856240i	−0.655961	−	0.0272406i
$989$	−27.7419			−0.882142
$990$	20.8902	+	36.1828i	0.663933	+	1.14997i
$991$	−8.43458	−	14.6091i	−0.267933	−	0.464074i	0.700395	−	0.713756i	$-0.253007\pi$
$991$	−8.43458	−	14.6091i	−0.267933	−	0.464074i	−0.968328	+	0.249682i	$0.919674\pi$
$992$	−1.77819	+	3.07992i	−0.0564577	+	0.0977877i
$993$	1.74846			0.0554856
$994$	0.108097	−	0.187229i	0.00342862	−	0.00593854i
$995$	−12.1030	+	20.9630i	−0.383691	+	0.664572i
$996$	−0.214775			−0.00680540
$997$	−17.7798	+	30.7955i	−0.563091	+	0.975302i	0.434134	+	0.900848i	$0.357055\pi$
$997$	−17.7798	+	30.7955i	−0.563091	+	0.975302i	−0.997224	+	0.0744535i	$0.976279\pi$
$998$	17.6242	+	30.5260i	0.557884	+	0.966284i
$999$	−6.71034	−	11.6226i	−0.212306	−	0.367724i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.f.b.94.11	✓	34
13.3	even	3		5239.2.a.m.1.7		17
13.9	even	3	inner	403.2.f.b.373.11	yes	34
13.10	even	6		5239.2.a.n.1.11		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.f.b.94.11	✓	34	1.1	even	1	trivial
403.2.f.b.373.11	yes	34	13.9	even	3	inner
5239.2.a.m.1.7		17	13.3	even	3
5239.2.a.n.1.11		17	13.10	even	6

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)

\(f(q)\)	\(=\)	\(q+(0.578965 + 1.00280i) q^{2} +(-0.235957 - 0.408690i) q^{3} +(0.329599 - 0.570882i) q^{4} -3.25594 q^{5} +(0.273222 - 0.473235i) q^{6} +(0.0133059 - 0.0230465i) q^{7} +3.07917 q^{8} +(1.38865 - 2.40521i) q^{9} +O(q^{10})\)	\(q+(0.578965 + 1.00280i) q^{2} +(-0.235957 - 0.408690i) q^{3} +(0.329599 - 0.570882i) q^{4} -3.25594 q^{5} +(0.273222 - 0.473235i) q^{6} +(0.0133059 - 0.0230465i) q^{7} +3.07917 q^{8} +(1.38865 - 2.40521i) q^{9} +(-1.88508 - 3.26505i) q^{10} +(-1.99508 - 3.45558i) q^{11} -0.311085 q^{12} +(1.93078 - 3.04501i) q^{13} +0.0308146 q^{14} +(0.768263 + 1.33067i) q^{15} +(1.12353 + 1.94601i) q^{16} +(-2.63341 + 4.56120i) q^{17} +3.21592 q^{18} +(4.34124 - 7.51924i) q^{19} +(-1.07315 + 1.85876i) q^{20} -0.0125585 q^{21} +(2.31017 - 4.00132i) q^{22} +(2.12725 + 3.68450i) q^{23} +(-0.726552 - 1.25842i) q^{24} +5.60115 q^{25} +(4.17138 + 0.173228i) q^{26} -2.72639 q^{27} +(-0.00877122 - 0.0151922i) q^{28} +(-2.84203 - 4.92255i) q^{29} +(-0.889595 + 1.54082i) q^{30} -1.00000 q^{31} +(1.77819 - 3.07992i) q^{32} +(-0.941508 + 1.63074i) q^{33} -6.09860 q^{34} +(-0.0433232 + 0.0750380i) q^{35} +(-0.915394 - 1.58551i) q^{36} +(2.46125 + 4.26302i) q^{37} +10.0537 q^{38} +(-1.70005 - 0.0705992i) q^{39} -10.0256 q^{40} +(-2.71441 - 4.70150i) q^{41} +(-0.00727093 - 0.0125936i) q^{42} +(-3.26031 + 5.64702i) q^{43} -2.63031 q^{44} +(-4.52136 + 7.83122i) q^{45} +(-2.46320 + 4.26639i) q^{46} -1.95563 q^{47} +(0.530211 - 0.918352i) q^{48} +(3.49965 + 6.06156i) q^{49} +(3.24287 + 5.61682i) q^{50} +2.48549 q^{51} +(-1.10196 - 2.10588i) q^{52} +10.7054 q^{53} +(-1.57848 - 2.73402i) q^{54} +(6.49587 + 11.2512i) q^{55} +(0.0409710 - 0.0709639i) q^{56} -4.09739 q^{57} +(3.29088 - 5.69997i) q^{58} +(-6.64385 + 11.5075i) q^{59} +1.01287 q^{60} +(-0.438981 + 0.760337i) q^{61} +(-0.578965 - 1.00280i) q^{62} +(-0.0369544 - 0.0640069i) q^{63} +8.61218 q^{64} +(-6.28651 + 9.91437i) q^{65} -2.18040 q^{66} +(-2.37747 - 4.11790i) q^{67} +(1.73594 + 3.00673i) q^{68} +(1.00388 - 1.73877i) q^{69} -0.100331 q^{70} +(3.50797 - 6.07598i) q^{71} +(4.27588 - 7.40604i) q^{72} -12.5998 q^{73} +(-2.84996 + 4.93627i) q^{74} +(-1.32163 - 2.28914i) q^{75} +(-2.86173 - 4.95667i) q^{76} -0.106185 q^{77} +(-0.913471 - 1.74568i) q^{78} +13.8937 q^{79} +(-3.65815 - 6.33611i) q^{80} +(-3.52263 - 6.10138i) q^{81} +(3.14310 - 5.44401i) q^{82} +0.690405 q^{83} +(-0.00413926 + 0.00716942i) q^{84} +(8.57422 - 14.8510i) q^{85} -7.55042 q^{86} +(-1.34120 + 2.32302i) q^{87} +(-6.14319 - 10.6403i) q^{88} +(6.83075 + 11.8312i) q^{89} -10.4708 q^{90} +(-0.0444860 - 0.0850143i) q^{91} +2.80455 q^{92} +(0.235957 + 0.408690i) q^{93} +(-1.13224 - 1.96110i) q^{94} +(-14.1348 + 24.4822i) q^{95} -1.67831 q^{96} +(-5.63529 + 9.76061i) q^{97} +(-4.05235 + 7.01887i) q^{98} -11.0819 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 4 q^{2} - 20 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} - 12 q^{8} - 17 q^{9}+O(q^{10}) \) 34 * q + 4 * q^2 - 20 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 - 12 * q^8 - 17 * q^9	\( 34 q + 4 q^{2} - 20 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} - 12 q^{8} - 17 q^{9} - 6 q^{10} + 13 q^{11} + 8 q^{12} - 3 q^{13} + 4 q^{15} - 34 q^{16} + 6 q^{17} + 24 q^{18} + 4 q^{19} + 28 q^{20} - 36 q^{21} + 34 q^{22} + 8 q^{23} + 40 q^{24} + 16 q^{25} - 26 q^{26} - 6 q^{27} + 21 q^{28} + 6 q^{29} - 19 q^{30} - 34 q^{31} + 6 q^{32} + 7 q^{33} - 48 q^{34} + 9 q^{35} + 14 q^{37} + 22 q^{38} - 21 q^{39} - 20 q^{40} + 43 q^{41} - 33 q^{42} - 18 q^{43} - 56 q^{44} + 26 q^{45} + 7 q^{46} - 12 q^{47} + 95 q^{48} + q^{49} + 44 q^{50} + 52 q^{51} - 24 q^{52} - 10 q^{53} + 27 q^{54} - 39 q^{55} - 39 q^{56} - 92 q^{57} + 8 q^{58} - q^{59} - 42 q^{60} + 19 q^{61} - 4 q^{62} + 5 q^{63} + 84 q^{64} - 32 q^{65} + 52 q^{66} + 10 q^{67} - 34 q^{68} - 32 q^{69} + 48 q^{70} + 35 q^{71} - 26 q^{72} - 22 q^{73} + 68 q^{74} + 62 q^{75} + 2 q^{76} + 42 q^{77} - 81 q^{78} + 2 q^{79} + 49 q^{80} - 37 q^{81} - 35 q^{82} - 48 q^{83} - 34 q^{84} - 13 q^{85} - 152 q^{86} + 22 q^{87} + 37 q^{88} + 42 q^{89} + 30 q^{90} - 39 q^{91} + 30 q^{92} - 42 q^{94} - 34 q^{95} - 66 q^{96} - 38 q^{97} + 8 q^{98} - 34 q^{99}+O(q^{100}) \) 34 * q + 4 * q^2 - 20 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 - 12 * q^8 - 17 * q^9 - 6 * q^10 + 13 * q^11 + 8 * q^12 - 3 * q^13 + 4 * q^15 - 34 * q^16 + 6 * q^17 + 24 * q^18 + 4 * q^19 + 28 * q^20 - 36 * q^21 + 34 * q^22 + 8 * q^23 + 40 * q^24 + 16 * q^25 - 26 * q^26 - 6 * q^27 + 21 * q^28 + 6 * q^29 - 19 * q^30 - 34 * q^31 + 6 * q^32 + 7 * q^33 - 48 * q^34 + 9 * q^35 + 14 * q^37 + 22 * q^38 - 21 * q^39 - 20 * q^40 + 43 * q^41 - 33 * q^42 - 18 * q^43 - 56 * q^44 + 26 * q^45 + 7 * q^46 - 12 * q^47 + 95 * q^48 + q^49 + 44 * q^50 + 52 * q^51 - 24 * q^52 - 10 * q^53 + 27 * q^54 - 39 * q^55 - 39 * q^56 - 92 * q^57 + 8 * q^58 - q^59 - 42 * q^60 + 19 * q^61 - 4 * q^62 + 5 * q^63 + 84 * q^64 - 32 * q^65 + 52 * q^66 + 10 * q^67 - 34 * q^68 - 32 * q^69 + 48 * q^70 + 35 * q^71 - 26 * q^72 - 22 * q^73 + 68 * q^74 + 62 * q^75 + 2 * q^76 + 42 * q^77 - 81 * q^78 + 2 * q^79 + 49 * q^80 - 37 * q^81 - 35 * q^82 - 48 * q^83 - 34 * q^84 - 13 * q^85 - 152 * q^86 + 22 * q^87 + 37 * q^88 + 42 * q^89 + 30 * q^90 - 39 * q^91 + 30 * q^92 - 42 * q^94 - 34 * q^95 - 66 * q^96 - 38 * q^97 + 8 * q^98 - 34 * q^99

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