LMFDB - Embedded newform 950.2.h.d.381.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(191,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(10))

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("950.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.h (of order $5$, degree $4$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			381.3
Character	$\chi$	$=$	950.381
Dual form			950.2.h.d.571.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(-1.70816 + 1.24105i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(2.12953 - 0.681987i) q^{5} +(1.70816 + 1.24105i) q^{6} -1.90564 q^{7} +(0.809017 + 0.587785i) q^{8} +(0.450556 - 1.38667i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(-1.70816 + 1.24105i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(2.12953 - 0.681987i) q^{5} +(1.70816 + 1.24105i) q^{6} -1.90564 q^{7} +(0.809017 + 0.587785i) q^{8} +(0.450556 - 1.38667i) q^{9} +(-1.30667 - 1.81456i) q^{10} +(-0.863322 - 2.65703i) q^{11} +(0.652460 - 2.00806i) q^{12} +(-0.845292 + 2.60154i) q^{13} +(0.588874 + 1.81237i) q^{14} +(-2.79120 + 3.80780i) q^{15} +(0.309017 - 0.951057i) q^{16} +(1.29413 + 0.940243i) q^{17} -1.45803 q^{18} +(0.809017 + 0.587785i) q^{19} +(-1.32196 + 1.80344i) q^{20} +(3.25513 - 2.36499i) q^{21} +(-2.26021 + 1.64214i) q^{22} +(1.80589 + 5.55796i) q^{23} -2.11140 q^{24} +(4.06979 - 2.90462i) q^{25} +2.73542 q^{26} +(-1.00607 - 3.09638i) q^{27} +(1.54169 - 1.12010i) q^{28} +(-3.33856 + 2.42560i) q^{29} +(4.48396 + 1.47791i) q^{30} +(-8.43160 - 6.12591i) q^{31} -1.00000 q^{32} +(4.77221 + 3.46721i) q^{33} +(0.494315 - 1.52134i) q^{34} +(-4.05811 + 1.29962i) q^{35} +(0.450556 + 1.38667i) q^{36} +(-1.70339 + 5.24251i) q^{37} +(0.309017 - 0.951057i) q^{38} +(-1.78475 - 5.49290i) q^{39} +(2.12369 + 0.699967i) q^{40} +(0.770341 - 2.37086i) q^{41} +(-3.25513 - 2.36499i) q^{42} -3.72132 q^{43} +(2.26021 + 1.64214i) q^{44} +(0.0137821 - 3.26022i) q^{45} +(4.72788 - 3.43501i) q^{46} +(-7.52799 + 5.46941i) q^{47} +(0.652460 + 2.00806i) q^{48} -3.36855 q^{49} +(-4.02009 - 2.97302i) q^{50} -3.37748 q^{51} +(-0.845292 - 2.60154i) q^{52} +(-6.05891 + 4.40205i) q^{53} +(-2.63394 + 1.91367i) q^{54} +(-3.65053 - 5.06945i) q^{55} +(-1.54169 - 1.12010i) q^{56} -2.11140 q^{57} +(3.33856 + 2.42560i) q^{58} +(-1.19371 + 3.67386i) q^{59} +(0.0199581 - 4.72120i) q^{60} +(1.03612 + 3.18884i) q^{61} +(-3.22058 + 9.91194i) q^{62} +(-0.858595 + 2.64248i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-0.0258567 + 6.11653i) q^{65} +(1.82282 - 5.61007i) q^{66} +(1.45531 + 1.05735i) q^{67} -1.59964 q^{68} +(-9.98247 - 7.25269i) q^{69} +(2.49003 + 3.45788i) q^{70} +(-2.19103 + 1.59188i) q^{71} +(1.17957 - 0.857008i) q^{72} +(1.06439 + 3.27585i) q^{73} +5.51230 q^{74} +(-3.34707 + 10.0124i) q^{75} -1.00000 q^{76} +(1.64518 + 5.06334i) q^{77} +(-4.67254 + 3.39480i) q^{78} +(-10.6404 + 7.73072i) q^{79} +(0.00945254 - 2.23605i) q^{80} +(9.10002 + 6.61155i) q^{81} -2.49287 q^{82} +(7.38311 + 5.36414i) q^{83} +(-1.24335 + 3.82664i) q^{84} +(3.39713 + 1.11969i) q^{85} +(1.14995 + 3.53919i) q^{86} +(2.69249 - 8.28665i) q^{87} +(0.863322 - 2.65703i) q^{88} +(-0.470174 - 1.44705i) q^{89} +(-3.10491 + 0.994357i) q^{90} +(1.61082 - 4.95759i) q^{91} +(-4.72788 - 3.43501i) q^{92} +22.0051 q^{93} +(7.52799 + 5.46941i) q^{94} +(2.12369 + 0.699967i) q^{95} +(1.70816 - 1.24105i) q^{96} +(1.64693 - 1.19657i) q^{97} +(1.04094 + 3.20368i) q^{98} -4.07340 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 11 q^{5} + q^{6} - 10 q^{7} + 11 q^{8}+O(q^{10}) $ 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 11 * q^5 + q^6 - 10 * q^7 + 11 * q^8	\( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 11 q^{5} + q^{6} - 10 q^{7} + 11 q^{8} - 4 q^{10} + 7 q^{11} + 4 q^{12} + 10 q^{13} - 5 q^{14} - 20 q^{15} - 11 q^{16} + 11 q^{17} - 50 q^{18} + 11 q^{19} + 4 q^{20} + 9 q^{21} + 8 q^{22} - 7 q^{23} + 6 q^{24} - 3 q^{25} + 10 q^{26} + 5 q^{27} - 20 q^{29} - 10 q^{30} - 11 q^{31} - 44 q^{32} - 2 q^{33} - q^{34} + 5 q^{35} + 43 q^{37} - 11 q^{38} - 33 q^{39} - 4 q^{40} - 32 q^{41} - 9 q^{42} - 74 q^{43} - 8 q^{44} + 10 q^{45} - 8 q^{46} - 19 q^{47} + 4 q^{48} + 54 q^{49} + 18 q^{50} + 34 q^{51} + 10 q^{52} + 23 q^{53} - 40 q^{54} + 2 q^{55} + 6 q^{57} + 20 q^{58} + 24 q^{59} - 35 q^{60} - 12 q^{61} + q^{62} - 44 q^{63} - 11 q^{64} + 43 q^{65} - 8 q^{66} + 35 q^{67} - 24 q^{68} + 29 q^{69} - 5 q^{70} - 2 q^{71} + 25 q^{72} + 22 q^{73} + 72 q^{74} + 7 q^{75} - 44 q^{76} - 3 q^{77} - 22 q^{78} - 19 q^{79} - q^{80} - 26 q^{81} - 58 q^{82} - 24 q^{83} - 21 q^{84} - 18 q^{85} - 6 q^{86} + 83 q^{87} - 7 q^{88} - 8 q^{89} + 60 q^{90} - 30 q^{91} + 8 q^{92} - 72 q^{93} + 19 q^{94} - 4 q^{95} + q^{96} - 16 q^{97} + q^{98} + 84 q^{99}+O(q^{100}) \) 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 11 * q^5 + q^6 - 10 * q^7 + 11 * q^8 - 4 * q^10 + 7 * q^11 + 4 * q^12 + 10 * q^13 - 5 * q^14 - 20 * q^15 - 11 * q^16 + 11 * q^17 - 50 * q^18 + 11 * q^19 + 4 * q^20 + 9 * q^21 + 8 * q^22 - 7 * q^23 + 6 * q^24 - 3 * q^25 + 10 * q^26 + 5 * q^27 - 20 * q^29 - 10 * q^30 - 11 * q^31 - 44 * q^32 - 2 * q^33 - q^34 + 5 * q^35 + 43 * q^37 - 11 * q^38 - 33 * q^39 - 4 * q^40 - 32 * q^41 - 9 * q^42 - 74 * q^43 - 8 * q^44 + 10 * q^45 - 8 * q^46 - 19 * q^47 + 4 * q^48 + 54 * q^49 + 18 * q^50 + 34 * q^51 + 10 * q^52 + 23 * q^53 - 40 * q^54 + 2 * q^55 + 6 * q^57 + 20 * q^58 + 24 * q^59 - 35 * q^60 - 12 * q^61 + q^62 - 44 * q^63 - 11 * q^64 + 43 * q^65 - 8 * q^66 + 35 * q^67 - 24 * q^68 + 29 * q^69 - 5 * q^70 - 2 * q^71 + 25 * q^72 + 22 * q^73 + 72 * q^74 + 7 * q^75 - 44 * q^76 - 3 * q^77 - 22 * q^78 - 19 * q^79 - q^80 - 26 * q^81 - 58 * q^82 - 24 * q^83 - 21 * q^84 - 18 * q^85 - 6 * q^86 + 83 * q^87 - 7 * q^88 - 8 * q^89 + 60 * q^90 - 30 * q^91 + 8 * q^92 - 72 * q^93 + 19 * q^94 - 4 * q^95 + q^96 - 16 * q^97 + q^98 + 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	−1.70816	+	1.24105i	−0.986208	+	0.716522i	−0.959087	−	0.283110i	$-0.908634\pi$
$3$	−1.70816	+	1.24105i	−0.986208	+	0.716522i	−0.0271205	+	0.999632i	$0.508634\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	2.12953	−	0.681987i	0.952354	−	0.304994i
$5$	2.12953	−	0.681987i	0.952354	−	0.304994i
$6$	1.70816	+	1.24105i	0.697354	+	0.506658i
$7$	−1.90564			−0.720263			−0.360131	−	0.932902i	$-0.617268\pi$
$7$	−1.90564			−0.720263			−0.360131	+	0.932902i	$0.617268\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	0.450556	−	1.38667i	0.150185	−	0.462223i
$10$	−1.30667	−	1.81456i	−0.413205	−	0.573813i
$11$	−0.863322	−	2.65703i	−0.260301	−	0.801125i	−0.992739	−	0.120291i	$-0.961617\pi$
$11$	−0.863322	−	2.65703i	−0.260301	−	0.801125i	0.732437	−	0.680834i	$-0.238383\pi$
$12$	0.652460	−	2.00806i	0.188349	−	0.579678i
$13$	−0.845292	+	2.60154i	−0.234442	+	0.721538i	0.762753	+	0.646690i	$0.223847\pi$
$13$	−0.845292	+	2.60154i	−0.234442	+	0.721538i	−0.997195	+	0.0748478i	$0.976153\pi$
$14$	0.588874	+	1.81237i	0.157383	+	0.484376i
$15$	−2.79120	+	3.80780i	−0.720685	+	0.983170i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	1.29413	+	0.940243i	0.313873	+	0.228042i	0.733557	−	0.679628i	$-0.237859\pi$
$17$	1.29413	+	0.940243i	0.313873	+	0.228042i	−0.419683	+	0.907671i	$0.637859\pi$
$18$	−1.45803			−0.343661
$19$	0.809017	+	0.587785i	0.185601	+	0.134847i
$19$	0.809017	+	0.587785i	0.185601	+	0.134847i
$20$	−1.32196	+	1.80344i	−0.295600	+	0.403263i
$21$	3.25513	−	2.36499i	0.710329	−	0.516084i
$22$	−2.26021	+	1.64214i	−0.481878	+	0.350105i
$23$	1.80589	+	5.55796i	0.376554	+	1.15891i	0.942424	+	0.334420i	$0.108540\pi$
$23$	1.80589	+	5.55796i	0.376554	+	1.15891i	−0.565870	+	0.824494i	$0.691460\pi$
$24$	−2.11140			−0.430989
$25$	4.06979	−	2.90462i	0.813958	−	0.580924i
$26$	2.73542			0.536460
$27$	−1.00607	−	3.09638i	−0.193619	−	0.595898i
$28$	1.54169	−	1.12010i	0.291352	−	0.211680i
$29$	−3.33856	+	2.42560i	−0.619954	+	0.450423i	−0.852906	−	0.522065i	$-0.825162\pi$
$29$	−3.33856	+	2.42560i	−0.619954	+	0.450423i	0.232951	+	0.972488i	$0.425162\pi$
$30$	4.48396	+	1.47791i	0.818656	+	0.269829i
$31$	−8.43160	−	6.12591i	−1.51436	−	1.10025i	−0.964196	−	0.265190i	$-0.914565\pi$
$31$	−8.43160	−	6.12591i	−1.51436	−	1.10025i	−0.550163	−	0.835057i	$-0.685435\pi$
$32$	−1.00000			−0.176777
$33$	4.77221	+	3.46721i	0.830735	+	0.603564i
$34$	0.494315	−	1.52134i	0.0847743	−	0.260908i
$35$	−4.05811	+	1.29962i	−0.685945	+	0.219676i
$36$	0.450556	+	1.38667i	0.0750926	+	0.231111i
$37$	−1.70339	+	5.24251i	−0.280036	+	0.861863i	0.707806	+	0.706406i	$0.249685\pi$
$37$	−1.70339	+	5.24251i	−0.280036	+	0.861863i	−0.987843	+	0.155457i	$0.950315\pi$
$38$	0.309017	−	0.951057i	0.0501292	−	0.154282i
$39$	−1.78475	−	5.49290i	−0.285789	−	0.879569i
$40$	2.12369	+	0.699967i	0.335784	+	0.110674i
$41$	0.770341	−	2.37086i	0.120307	−	0.370267i	−0.872710	−	0.488239i	$-0.837639\pi$
$41$	0.770341	−	2.37086i	0.120307	−	0.370267i	0.993017	+	0.117972i	$0.0376394\pi$
$42$	−3.25513	−	2.36499i	−0.502278	−	0.364926i
$43$	−3.72132			−0.567496			−0.283748	−	0.958899i	$-0.591578\pi$
$43$	−3.72132			−0.567496			−0.283748	+	0.958899i	$0.591578\pi$
$44$	2.26021	+	1.64214i	0.340739	+	0.247561i
$45$	0.0137821	−	3.26022i	0.00205451	−	0.486005i
$46$	4.72788	−	3.43501i	0.697088	−	0.506464i
$47$	−7.52799	+	5.46941i	−1.09807	+	0.797795i	−0.980744	−	0.195298i	$-0.937433\pi$
$47$	−7.52799	+	5.46941i	−1.09807	+	0.797795i	−0.117327	+	0.993093i	$0.537433\pi$
$48$	0.652460	+	2.00806i	0.0941745	+	0.289839i
$49$	−3.36855			−0.481222
$50$	−4.02009	−	2.97302i	−0.568527	−	0.420449i
$51$	−3.37748			−0.472942
$52$	−0.845292	−	2.60154i	−0.117221	−	0.360769i
$53$	−6.05891	+	4.40205i	−0.832255	+	0.604668i	−0.920196	−	0.391457i	$-0.871971\pi$
$53$	−6.05891	+	4.40205i	−0.832255	+	0.604668i	0.0879416	+	0.996126i	$0.471971\pi$
$54$	−2.63394	+	1.91367i	−0.358433	+	0.260417i
$55$	−3.65053	−	5.06945i	−0.492237	−	0.683565i
$56$	−1.54169	−	1.12010i	−0.206017	−	0.149680i
$57$	−2.11140			−0.279662
$58$	3.33856	+	2.42560i	0.438374	+	0.318497i
$59$	−1.19371	+	3.67386i	−0.155408	+	0.478296i	−0.998202	−	0.0599401i	$-0.980909\pi$
$59$	−1.19371	+	3.67386i	−0.155408	+	0.478296i	0.842794	+	0.538236i	$0.180909\pi$
$60$	0.0199581	−	4.72120i	0.00257659	−	0.609505i
$61$	1.03612	+	3.18884i	0.132661	+	0.408289i	0.995219	−	0.0976694i	$-0.0311388\pi$
$61$	1.03612	+	3.18884i	0.132661	+	0.408289i	−0.862558	+	0.505959i	$0.831139\pi$
$62$	−3.22058	+	9.91194i	−0.409015	+	1.25882i
$63$	−0.858595	+	2.64248i	−0.108173	+	0.332922i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−0.0258567	+	6.11653i	−0.00320713	+	0.758663i
$66$	1.82282	−	5.61007i	0.224374	−	0.690552i
$67$	1.45531	+	1.05735i	0.177795	+	0.129176i	0.673123	−	0.739530i	$-0.264952\pi$
$67$	1.45531	+	1.05735i	0.177795	+	0.129176i	−0.495328	+	0.868706i	$0.664952\pi$
$68$	−1.59964			−0.193984
$69$	−9.98247	−	7.25269i	−1.20175	−	0.873121i
$70$	2.49003	+	3.45788i	0.297616	+	0.413296i
$71$	−2.19103	+	1.59188i	−0.260027	+	0.188921i	−0.710159	−	0.704041i	$-0.751377\pi$
$71$	−2.19103	+	1.59188i	−0.260027	+	0.188921i	0.450132	+	0.892962i	$0.351377\pi$
$72$	1.17957	−	0.857008i	0.139014	−	0.100999i
$73$	1.06439	+	3.27585i	0.124577	+	0.383410i	0.993824	−	0.110969i	$-0.0353955\pi$
$73$	1.06439	+	3.27585i	0.124577	+	0.383410i	−0.869247	+	0.494379i	$0.835396\pi$
$74$	5.51230			0.640792
$75$	−3.34707	+	10.0124i	−0.386486	+	1.15613i
$76$	−1.00000			−0.114708
$77$	1.64518	+	5.06334i	0.187485	+	0.577021i
$78$	−4.67254	+	3.39480i	−0.529061	+	0.384386i
$79$	−10.6404	+	7.73072i	−1.19714	+	0.869774i	−0.994000	−	0.109376i	$-0.965115\pi$
$79$	−10.6404	+	7.73072i	−1.19714	+	0.869774i	−0.203141	+	0.979150i	$0.565115\pi$
$80$	0.00945254	−	2.23605i	0.00105683	−	0.249998i
$81$	9.10002	+	6.61155i	1.01111	+	0.734617i
$82$	−2.49287			−0.275292
$83$	7.38311	+	5.36414i	0.810402	+	0.588791i	0.913947	−	0.405834i	$-0.133019\pi$
$83$	7.38311	+	5.36414i	0.810402	+	0.588791i	−0.103545	+	0.994625i	$0.533019\pi$
$84$	−1.24335	+	3.82664i	−0.135661	+	0.417521i
$85$	3.39713	+	1.11969i	0.368470	+	0.121448i
$86$	1.14995	+	3.53919i	0.124002	+	0.381640i
$87$	2.69249	−	8.28665i	0.288666	−	0.888422i
$88$	0.863322	−	2.65703i	0.0920304	−	0.283241i
$89$	−0.470174	−	1.44705i	−0.0498384	−	0.153387i	0.923040	−	0.384704i	$-0.125696\pi$
$89$	−0.470174	−	1.44705i	−0.0498384	−	0.153387i	−0.972878	+	0.231317i	$0.925696\pi$
$90$	−3.10491	+	0.994357i	−0.327287	+	0.104814i
$91$	1.61082	−	4.95759i	0.168860	−	0.519697i
$92$	−4.72788	−	3.43501i	−0.492916	−	0.358124i
$93$	22.0051			2.28182
$94$	7.52799	+	5.46941i	0.776453	+	0.564126i
$95$	2.12369	+	0.699967i	0.217886	+	0.0718151i
$96$	1.70816	−	1.24105i	0.174339	−	0.126664i
$97$	1.64693	−	1.19657i	0.167221	−	0.121493i	−0.501027	−	0.865431i	$-0.667044\pi$
$97$	1.64693	−	1.19657i	0.167221	−	0.121493i	0.668248	+	0.743938i	$0.267044\pi$
$98$	1.04094	+	3.20368i	0.105151	+	0.323621i
$99$	−4.07340			−0.409392
$100$	−1.58523	+	4.74205i	−0.158523	+	0.474205i
$101$	−11.2279			−1.11722			−0.558608	−	0.829432i	$-0.688664\pi$
$101$	−11.2279			−1.11722			−0.558608	+	0.829432i	$0.688664\pi$
$102$	1.04370	+	3.21217i	0.103342	+	0.318053i
$103$	−10.9232	+	7.93617i	−1.07630	+	0.781974i	−0.977033	−	0.213087i	$-0.931648\pi$
$103$	−10.9232	+	7.93617i	−1.07630	+	0.781974i	−0.0992619	+	0.995061i	$0.531648\pi$
$104$	−2.21300	+	1.60784i	−0.217003	+	0.157662i
$105$	5.31901	−	7.25628i	0.519082	−	0.708141i
$106$	6.05891	+	4.40205i	0.588493	+	0.427565i
$107$	−18.9778			−1.83466			−0.917328	−	0.398133i	$-0.869658\pi$
$107$	−18.9778			−1.83466			−0.917328	+	0.398133i	$0.869658\pi$
$108$	2.63394	+	1.91367i	0.253451	+	0.184143i
$109$	2.97462	−	9.15495i	0.284917	−	0.876885i	−0.701506	−	0.712663i	$-0.747489\pi$
$109$	2.97462	−	9.15495i	0.284917	−	0.876885i	0.986423	−	0.164222i	$-0.0525113\pi$
$110$	−3.69326	+	5.03841i	−0.352139	+	0.480393i
$111$	−3.59655	−	11.0691i	−0.341370	−	1.05063i
$112$	−0.588874	+	1.81237i	−0.0556433	+	0.171253i
$113$	−2.06754	+	6.36322i	−0.194498	+	0.598602i	0.805485	+	0.592617i	$0.201905\pi$
$113$	−2.06754	+	6.36322i	−0.194498	+	0.598602i	−0.999982	+	0.00598508i	$0.998095\pi$
$114$	0.652460	+	2.00806i	0.0611085	+	0.188073i
$115$	7.63615	+	10.6042i	0.712074	+	0.988850i
$116$	1.27521	−	3.92471i	0.118401	−	0.364400i
$117$	3.22662	+	2.34428i	0.298301	+	0.216729i
$118$	3.86292			0.355611
$119$	−2.46615	−	1.79176i	−0.226071	−	0.164250i
$120$	−4.49630	+	1.43995i	−0.410454	+	0.131449i
$121$	2.58469	−	1.87789i	0.234972	−	0.170717i
$122$	2.71259	−	1.97081i	0.245586	−	0.178429i
$123$	1.62650	+	5.00585i	0.146657	+	0.451363i
$124$	10.4220			0.935926
$125$	6.68582	−	8.96102i	0.597998	−	0.801498i
$126$	2.77847			0.247526
$127$	−2.93762	−	9.04107i	−0.260672	−	0.802265i	−0.992659	−	0.120947i	$-0.961407\pi$
$127$	−2.93762	−	9.04107i	−0.260672	−	0.802265i	0.731987	−	0.681318i	$-0.238593\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	6.35662	−	4.61835i	0.559669	−	0.406623i
$130$	5.82516	−	1.86552i	0.510900	−	0.163617i
$131$	−0.756379	−	0.549542i	−0.0660852	−	0.0480137i	0.554252	−	0.832349i	$-0.313004\pi$
$131$	−0.756379	−	0.549542i	−0.0660852	−	0.0480137i	−0.620337	+	0.784335i	$0.713004\pi$
$132$	−5.89878			−0.513423
$133$	−1.54169	−	1.12010i	−0.133682	−	0.0971254i
$134$	0.555881	−	1.71083i	0.0480208	−	0.147793i
$135$	−4.25415	−	5.90770i	−0.366139	−	0.508454i
$136$	0.494315	+	1.52134i	0.0423871	+	0.130454i
$137$	2.34170	−	7.20701i	0.200065	−	0.615736i	−0.799815	−	0.600246i	$-0.795069\pi$
$137$	2.34170	−	7.20701i	0.200065	−	0.615736i	0.999880	−	0.0154898i	$-0.00493077\pi$
$138$	−3.81296	+	11.7351i	−0.324581	+	0.998958i
$139$	−2.64801	−	8.14975i	−0.224602	−	0.691253i	−0.998332	−	0.0577374i	$-0.981611\pi$
$139$	−2.64801	−	8.14975i	−0.224602	−	0.691253i	0.773730	−	0.633515i	$-0.218389\pi$
$140$	2.51918	−	3.43671i	0.212910	−	0.290455i
$141$	6.07121	−	18.6853i	0.511288	−	1.57358i
$142$	2.19103	+	1.59188i	0.183867	+	0.133587i
$143$	7.64214			0.639067
$144$	−1.17957	−	0.857008i	−0.0982975	−	0.0714173i
$145$	−5.45532	+	7.44224i	−0.453040	+	0.618045i
$146$	2.78661	−	2.02459i	0.230621	−	0.167556i
$147$	5.75403	−	4.18055i	0.474585	−	0.344806i
$148$	−1.70339	−	5.24251i	−0.140018	−	0.430932i
$149$	1.53435			0.125699			0.0628494	−	0.998023i	$-0.479981\pi$
$149$	1.53435			0.125699			0.0628494	+	0.998023i	$0.479981\pi$
$150$	10.5566	+	0.0892547i	0.861946	+	0.00728762i
$151$	−5.85825			−0.476738			−0.238369	−	0.971175i	$-0.576613\pi$
$151$	−5.85825			−0.476738			−0.238369	+	0.971175i	$0.576613\pi$
$152$	0.309017	+	0.951057i	0.0250646	+	0.0771409i
$153$	1.88688	−	1.37090i	0.152545	−	0.110831i
$154$	4.30713	−	3.12931i	0.347078	−	0.252167i
$155$	−22.1331	−	7.29507i	−1.77778	−	0.585954i
$156$	4.67254	+	3.39480i	0.374103	+	0.271802i
$157$	−8.29488			−0.662004			−0.331002	−	0.943630i	$-0.607387\pi$
$157$	−8.29488			−0.662004			−0.331002	+	0.943630i	$0.607387\pi$
$158$	10.6404	+	7.73072i	0.846507	+	0.615023i
$159$	4.88642	−	15.0388i	0.387518	−	1.19266i
$160$	−2.12953	+	0.681987i	−0.168354	+	0.0539158i
$161$	−3.44137	−	10.5914i	−0.271218	−	0.834723i
$162$	3.47590	−	10.6977i	0.273092	−	0.840492i
$163$	4.15607	−	12.7911i	0.325528	−	1.00187i	−0.645673	−	0.763614i	$-0.723423\pi$
$163$	4.15607	−	12.7911i	0.325528	−	1.00187i	0.971202	−	0.238260i	$-0.0765769\pi$
$164$	0.770341	+	2.37086i	0.0601535	+	0.185133i
$165$	12.5272	+	4.12895i	0.975238	+	0.321438i
$166$	2.82010	−	8.67937i	0.218882	−	0.673649i
$167$	14.3068	+	10.3945i	1.10710	+	0.804352i	0.982204	−	0.187818i	$-0.0601415\pi$
$167$	14.3068	+	10.3945i	1.10710	+	0.804352i	0.124892	+	0.992170i	$0.460142\pi$
$168$	4.02357			0.310425
$169$	4.46373	+	3.24309i	0.343364	+	0.249468i
$170$	0.0151206	−	3.57686i	0.00115970	−	0.274333i
$171$	1.17957	−	0.857008i	0.0902040	−	0.0655370i
$172$	3.01061	−	2.18734i	0.229557	−	0.166783i
$173$	2.93217	+	9.02430i	0.222929	+	0.686105i	0.998495	+	0.0548386i	$0.0174644\pi$
$173$	2.93217	+	9.02430i	0.222929	+	0.686105i	−0.775566	+	0.631266i	$0.782536\pi$
$174$	−8.71309			−0.660538
$175$	−7.75553	+	5.53515i	−0.586263	+	0.418418i
$176$	−2.79377			−0.210588
$177$	−2.52040	−	7.75700i	−0.189445	−	0.583052i
$178$	−1.23093	+	0.894325i	−0.0922623	+	0.0670325i
$179$	17.0397	−	12.3801i	1.27361	−	0.925331i	0.274269	−	0.961653i	$-0.411564\pi$
$179$	17.0397	−	12.3801i	1.27361	−	0.925331i	0.999340	+	0.0363220i	$0.0115642\pi$
$180$	1.90516	+	2.64568i	0.142002	+	0.197197i
$181$	18.4369	+	13.3952i	1.37040	+	0.995657i	0.997705	+	0.0677048i	$0.0215676\pi$
$181$	18.4369	+	13.3952i	1.37040	+	0.995657i	0.372699	+	0.927952i	$0.378432\pi$
$182$	−5.21272			−0.386392
$183$	−5.72738	−	4.16118i	−0.423380	−	0.307604i
$184$	−1.80589	+	5.55796i	−0.133132	+	0.409738i
$185$	−0.0521053	+	12.3258i	−0.00383086	+	0.906208i
$186$	−6.79995	−	20.9281i	−0.498597	−	1.53452i
$187$	1.38100	−	4.25029i	0.100989	−	0.310812i
$188$	2.87544	−	8.84969i	0.209713	−	0.645430i
$189$	1.91721	+	5.90057i	0.139457	+	0.429203i
$190$	0.00945254	−	2.23605i	0.000685760	−	0.162220i
$191$	0.693246	−	2.13359i	0.0501615	−	0.154381i	−0.922838	−	0.385188i	$-0.874137\pi$
$191$	0.693246	−	2.13359i	0.0501615	−	0.154381i	0.973000	+	0.230807i	$0.0741366\pi$
$192$	−1.70816	−	1.24105i	−0.123276	−	0.0895652i
$193$	8.33573			0.600019			0.300010	−	0.953936i	$-0.403010\pi$
$193$	8.33573			0.600019			0.300010	+	0.953936i	$0.403010\pi$
$194$	−1.64693	−	1.19657i	−0.118243	−	0.0859085i
$195$	−7.54677	−	10.4801i	−0.540436	−	0.750497i
$196$	2.72522	−	1.97999i	0.194658	−	0.141428i
$197$	5.19438	−	3.77394i	0.370084	−	0.268882i	−0.387162	−	0.922012i	$-0.626544\pi$
$197$	5.19438	−	3.77394i	0.370084	−	0.268882i	0.757246	+	0.653130i	$0.226544\pi$
$198$	1.25875	+	3.87403i	0.0894554	+	0.275315i
$199$	26.9358			1.90943			0.954714	−	0.297526i	$-0.0961616\pi$
$199$	26.9358			1.90943			0.954714	+	0.297526i	$0.0961616\pi$
$200$	4.99982	+	0.0422727i	0.353541	+	0.00298913i
$201$	−3.79814			−0.267900
$202$	3.46961	+	10.6784i	0.244121	+	0.751327i
$203$	6.36207	−	4.62232i	0.446530	−	0.324423i
$204$	2.73244	−	1.98523i	0.191309	−	0.138994i
$205$	0.0235640	−	5.57419i	0.00164578	−	0.389318i
$206$	10.9232	+	7.93617i	0.761056	+	0.552939i
$207$	8.52069			0.592229
$208$	2.21300	+	1.60784i	0.153444	+	0.111484i
$209$	0.863322	−	2.65703i	0.0597172	−	0.183791i
$210$	−8.54480	−	2.81636i	−0.589647	−	0.194348i
$211$	8.27879	+	25.4795i	0.569935	+	1.75408i	0.652812	+	0.757520i	$0.273589\pi$
$211$	8.27879	+	25.4795i	0.569935	+	1.75408i	−0.0828769	+	0.996560i	$0.526411\pi$
$212$	2.31430	−	7.12267i	0.158947	−	0.489187i
$213$	1.76703	−	5.43836i	0.121075	−	0.372630i
$214$	5.86447	+	18.0490i	0.400887	+	1.23380i
$215$	−7.92466	+	2.53789i	−0.540457	+	0.173083i
$216$	1.00607	−	3.09638i	0.0684547	−	0.210682i
$217$	16.0676	+	11.6738i	1.09074	+	0.792467i
$218$	−9.62609			−0.651961
$219$	−5.88365	−	4.27472i	−0.397580	−	0.288859i
$220$	5.93309	+	1.95555i	0.400009	+	0.131843i
$221$	−3.54000	+	2.57196i	−0.238126	+	0.173009i
$222$	−9.41590	+	6.84105i	−0.631954	+	0.459141i
$223$	−2.33004	−	7.17113i	−0.156031	−	0.480214i	0.842233	−	0.539114i	$-0.181241\pi$
$223$	−2.33004	−	7.17113i	−0.156031	−	0.480214i	−0.998264	+	0.0588998i	$0.981241\pi$
$224$	1.90564			0.127326
$225$	−2.19408	−	6.95214i	−0.146272	−	0.463476i
$226$	6.69069			0.445058
$227$	−3.99062	−	12.2819i	−0.264867	−	0.815177i	−0.991724	−	0.128388i	$-0.959020\pi$
$227$	−3.99062	−	12.2819i	−0.264867	−	0.815177i	0.726857	−	0.686789i	$-0.240980\pi$
$228$	1.70816	−	1.24105i	0.113126	−	0.0821907i
$229$	−14.8656	+	10.8005i	−0.982347	+	0.713717i	−0.958232	−	0.285993i	$-0.907677\pi$
$229$	−14.8656	+	10.8005i	−0.982347	+	0.713717i	−0.0241148	+	0.999709i	$0.507677\pi$
$230$	7.72553	−	10.5393i	0.509406	−	0.694941i
$231$	−9.09409	−	6.60725i	−0.598347	−	0.434725i
$232$	−4.12668			−0.270930
$233$	−11.0362	−	8.01826i	−0.723004	−	0.525293i	0.164338	−	0.986404i	$-0.447451\pi$
$233$	−11.0362	−	8.01826i	−0.723004	−	0.525293i	−0.887343	+	0.461111i	$0.847451\pi$
$234$	1.23246	−	3.79312i	0.0805684	−	0.247964i
$235$	−12.3010	+	16.7813i	−0.802430	+	1.09469i
$236$	−1.19371	−	3.67386i	−0.0777038	−	0.239148i
$237$	8.58134	−	26.4106i	0.557418	−	1.71556i
$238$	−0.941984	+	2.89913i	−0.0610598	+	0.187923i
$239$	−6.90367	−	21.2473i	−0.446561	−	1.37437i	−0.880762	−	0.473559i	$-0.842969\pi$
$239$	−6.90367	−	21.2473i	−0.446561	−	1.37437i	0.434201	−	0.900816i	$-0.357031\pi$
$240$	2.75891	+	3.83126i	0.178087	+	0.247307i
$241$	0.310279	−	0.954940i	0.0199868	−	0.0615131i	−0.940566	−	0.339612i	$-0.889704\pi$
$241$	0.310279	−	0.954940i	0.0199868	−	0.0615131i	0.960552	+	0.278099i	$0.0897043\pi$
$242$	−2.58469	−	1.87789i	−0.166150	−	0.120715i
$243$	−13.9824			−0.896972
$244$	−2.71259	−	1.97081i	−0.173656	−	0.126168i
$245$	−7.17343	+	2.29731i	−0.458294	+	0.146770i
$246$	4.25823	−	3.09379i	0.271495	−	0.197253i
$247$	−2.21300	+	1.60784i	−0.140810	+	0.102304i
$248$	−3.22058	−	9.91194i	−0.204507	−	0.629409i
$249$	−19.2687			−1.22111
$250$	−10.5885	−	3.58948i	−0.669673	−	0.227019i
$251$	−6.70822			−0.423419			−0.211710	−	0.977333i	$-0.567903\pi$
$251$	−6.70822			−0.423419			−0.211710	+	0.977333i	$0.567903\pi$
$252$	−0.858595	−	2.64248i	−0.0540864	−	0.166461i
$253$	13.2086	−	9.59661i	0.830418	−	0.603334i
$254$	−7.69079	+	5.58769i	−0.482563	+	0.350603i
$255$	−7.19244	+	2.30340i	−0.450408	+	0.144244i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	12.7664			0.796348			0.398174	−	0.917310i	$-0.369644\pi$
$257$	12.7664			0.796348			0.398174	+	0.917310i	$0.369644\pi$
$258$	−6.35662	−	4.61835i	−0.395746	−	0.287526i
$259$	3.24605	−	9.99031i	0.201700	−	0.620768i
$260$	−3.57429	−	4.96358i	−0.221668	−	0.307828i
$261$	1.85930	+	5.72234i	0.115088	+	0.354204i
$262$	−0.288911	+	0.889177i	−0.0178490	+	0.0549336i
$263$	−3.17141	+	9.76060i	−0.195558	+	0.601864i	0.804412	+	0.594072i	$0.202481\pi$
$263$	−3.17141	+	9.76060i	−0.195558	+	0.601864i	−0.999970	+	0.00779266i	$0.997519\pi$
$264$	1.82282	+	5.61007i	0.112187	+	0.345276i
$265$	−9.90047	+	13.5064i	−0.608181	+	0.829691i
$266$	−0.588874	+	1.81237i	−0.0361062	+	0.111123i
$267$	2.59900	+	1.88828i	0.159056	+	0.115561i
$268$	−1.79887			−0.109883
$269$	−15.7607	−	11.4509i	−0.960950	−	0.698171i	−0.00757859	−	0.999971i	$-0.502412\pi$
$269$	−15.7607	−	11.4509i	−0.960950	−	0.698171i	−0.953371	+	0.301800i	$0.902412\pi$
$270$	−4.30395	+	5.87152i	−0.261930	+	0.357329i
$271$	12.8808	−	9.35848i	0.782456	−	0.568487i	−0.123259	−	0.992375i	$-0.539335\pi$
$271$	12.8808	−	9.35848i	0.782456	−	0.568487i	0.905715	+	0.423887i	$0.139335\pi$
$272$	1.29413	−	0.940243i	0.0784683	−	0.0570106i
$273$	3.40109	+	10.4675i	0.205843	+	0.633520i
$274$	−7.57789			−0.457797
$275$	−11.2312	−	8.30593i	−0.677268	−	0.500867i
$276$	12.3390			0.742721
$277$	1.93529	+	5.95620i	0.116280	+	0.357874i	0.992212	−	0.124562i	$-0.0397524\pi$
$277$	1.93529	+	5.95620i	0.116280	+	0.357874i	−0.875932	+	0.482435i	$0.839752\pi$
$278$	−6.93259	+	5.03682i	−0.415789	+	0.302088i
$279$	−12.2935	+	8.93176i	−0.735993	+	0.534730i
$280$	−4.04697	−	1.33388i	−0.241853	−	0.0797147i
$281$	−4.84720	−	3.52169i	−0.289159	−	0.210087i	0.433743	−	0.901037i	$-0.357193\pi$
$281$	−4.84720	−	3.52169i	−0.289159	−	0.210087i	−0.722903	+	0.690950i	$0.757193\pi$
$282$	−19.6469			−1.16995
$283$	24.2524	+	17.6204i	1.44166	+	1.04743i	0.987693	+	0.156405i	$0.0499905\pi$
$283$	24.2524	+	17.6204i	1.44166	+	1.04743i	0.453964	+	0.891020i	$0.350009\pi$
$284$	0.836898	−	2.57571i	0.0496608	−	0.152840i
$285$	−4.49630	+	1.43995i	−0.266338	+	0.0852953i
$286$	−2.36155	−	7.26810i	−0.139641	−	0.429772i
$287$	−1.46799	+	4.51800i	−0.0866526	+	0.266689i
$288$	−0.450556	+	1.38667i	−0.0265492	+	0.0817102i
$289$	−4.46256	−	13.7344i	−0.262504	−	0.807904i
$290$	8.76378	+	2.88854i	0.514627	+	0.169621i
$291$	−1.32823	+	4.08786i	−0.0778620	+	0.239635i
$292$	−2.78661	−	2.02459i	−0.163074	−	0.118480i
$293$	−20.5329			−1.19954			−0.599772	−	0.800171i	$-0.704742\pi$
$293$	−20.5329			−1.19954			−0.599772	+	0.800171i	$0.704742\pi$
$294$	−5.75403	−	4.18055i	−0.335582	−	0.243815i
$295$	−0.0365145	+	8.63768i	−0.00212595	+	0.502905i
$296$	−4.45954	+	3.24005i	−0.259206	+	0.188324i
$297$	−7.35861	+	5.34634i	−0.426990	+	0.310226i
$298$	−0.474140	−	1.45925i	−0.0274662	−	0.0845322i
$299$	−15.9858			−0.924480
$300$	−3.17730	−	10.0675i	−0.183441	−	0.581250i
$301$	7.09148			0.408746
$302$	1.81030	+	5.57153i	0.104171	+	0.320605i
$303$	19.1791	−	13.9344i	1.10181	−	0.800510i
$304$	0.809017	−	0.587785i	0.0464003	−	0.0337118i
$305$	4.38119	+	6.08411i	0.250866	+	0.348375i
$306$	−1.88688	−	1.37090i	−0.107866	−	0.0783692i
$307$	−24.3326			−1.38874			−0.694368	−	0.719620i	$-0.744316\pi$
$307$	−24.3326			−1.38874			−0.694368	+	0.719620i	$0.744316\pi$
$308$	−4.30713	−	3.12931i	−0.245422	−	0.178309i
$309$	8.80940	−	27.1125i	0.501149	−	1.54238i
$310$	−0.0985147	+	23.3042i	−0.00559526	+	1.32359i
$311$	7.22196	+	22.2269i	0.409520	+	1.26037i	0.917062	+	0.398745i	$0.130554\pi$
$311$	7.22196	+	22.2269i	0.409520	+	1.26037i	−0.507542	+	0.861627i	$0.669446\pi$
$312$	1.78475	−	5.49290i	0.101042	−	0.310974i
$313$	6.07629	−	18.7009i	0.343452	−	1.05704i	−0.618955	−	0.785426i	$-0.712444\pi$
$313$	6.07629	−	18.7009i	0.343452	−	1.05704i	0.962407	−	0.271611i	$-0.0875563\pi$
$314$	2.56326	+	7.88890i	0.144653	+	0.445196i
$315$	−0.0262636	+	6.21280i	−0.00147979	+	0.350051i
$316$	4.06428	−	12.5086i	0.228634	−	0.703662i
$317$	−0.857850	−	0.623264i	−0.0481816	−	0.0350060i	0.563434	−	0.826161i	$-0.309480\pi$
$317$	−0.857850	−	0.623264i	−0.0481816	−	0.0350060i	−0.611615	+	0.791155i	$0.709480\pi$
$318$	−15.8128			−0.886736
$319$	9.32715	+	6.77657i	0.522220	+	0.379415i
$320$	1.30667	+	1.81456i	0.0730450	+	0.101437i
$321$	32.4172	−	23.5525i	1.80935	−	1.31457i
$322$	−9.00962	+	6.54587i	−0.502086	+	0.364787i
$323$	0.494315	+	1.52134i	0.0275044	+	0.0846499i
$324$	−11.2482			−0.624902
$325$	4.11633	+	13.0430i	0.228333	+	0.723494i
$326$	−13.4493			−0.744889
$327$	6.28063	+	19.3298i	0.347320	+	1.06894i
$328$	2.01678	−	1.46527i	0.111358	−	0.0809063i
$329$	14.3456	−	10.4227i	0.790899	−	0.574622i
$330$	0.0557584	−	13.1899i	0.00306940	−	0.726083i
$331$	23.0419	+	16.7409i	1.26650	+	0.920163i	0.999057	−	0.0434122i	$-0.0138229\pi$
$331$	23.0419	+	16.7409i	1.26650	+	0.920163i	0.267438	+	0.963575i	$0.413823\pi$
$332$	−9.12603			−0.500856
$333$	6.50214	+	4.72408i	0.356315	+	0.258878i
$334$	5.46472	−	16.8187i	0.299016	−	0.920278i
$335$	3.82023	+	1.25915i	0.208722	+	0.0687946i
$336$	−1.24335	−	3.82664i	−0.0678303	−	0.208760i
$337$	−8.67569	+	26.7010i	−0.472595	+	1.45450i	0.376579	+	0.926384i	$0.377100\pi$
$337$	−8.67569	+	26.7010i	−0.472595	+	1.45450i	−0.849174	+	0.528113i	$0.822900\pi$
$338$	1.70499	−	5.24742i	0.0927393	−	0.285422i
$339$	−4.36541	−	13.4353i	−0.237096	−	0.729708i
$340$	−3.40647	+	1.09093i	−0.184742	+	0.0591640i
$341$	−8.99757	+	27.6917i	−0.487246	+	1.49959i
$342$	−1.17957	−	0.857008i	−0.0637838	−	0.0463417i
$343$	19.7587			1.06687
$344$	−3.01061	−	2.18734i	−0.162321	−	0.117933i
$345$	−26.2042	−	8.63690i	−1.41079	−	0.464995i
$346$	7.67653	−	5.57732i	0.412693	−	0.299839i
$347$	−17.1199	+	12.4383i	−0.919044	+	0.667724i	−0.943286	−	0.331982i	$-0.892283\pi$
$347$	−17.1199	+	12.4383i	−0.919044	+	0.667724i	0.0242420	+	0.999706i	$0.492283\pi$
$348$	2.69249	+	8.28665i	0.144333	+	0.444211i
$349$	15.7129			0.841092			0.420546	−	0.907271i	$-0.361839\pi$
$349$	15.7129			0.841092			0.420546	+	0.907271i	$0.361839\pi$
$350$	7.66083	+	5.66549i	0.409489	+	0.302833i
$351$	8.90578			0.475355
$352$	0.863322	+	2.65703i	0.0460152	+	0.141620i
$353$	4.59717	−	3.34004i	0.244682	−	0.177772i	−0.458684	−	0.888599i	$-0.651679\pi$
$353$	4.59717	−	3.34004i	0.244682	−	0.177772i	0.703367	+	0.710827i	$0.251679\pi$
$354$	−6.59850	+	4.79409i	−0.350706	+	0.254803i
$355$	−3.58022	+	4.88420i	−0.190018	+	0.259226i
$356$	1.23093	+	0.894325i	0.0652393	+	0.0473991i
$357$	6.43625			0.340642
$358$	−17.0397	−	12.3801i	−0.900578	−	0.654308i
$359$	2.04560	−	6.29572i	0.107963	−	0.332275i	−0.882452	−	0.470403i	$-0.844108\pi$
$359$	2.04560	−	6.29572i	0.107963	−	0.332275i	0.990414	+	0.138128i	$0.0441085\pi$
$360$	1.92746	−	2.62947i	0.101586	−	0.138585i
$361$	0.309017	+	0.951057i	0.0162641	+	0.0500556i
$362$	7.04227	−	21.6739i	0.370134	−	1.13915i
$363$	−2.08451	+	6.41548i	−0.109409	+	0.336725i
$364$	1.61082	+	4.95759i	0.0844298	+	0.259848i
$365$	4.50074	+	6.25012i	0.235579	+	0.327146i
$366$	−2.18766	+	6.73294i	−0.114351	+	0.351936i
$367$	26.7959	+	19.4684i	1.39873	+	1.01624i	0.994842	+	0.101434i	$0.0323430\pi$
$367$	26.7959	+	19.4684i	1.39873	+	1.01624i	0.403892	+	0.914807i	$0.367657\pi$
$368$	5.84398			0.304639
$369$	−2.94052	−	2.13641i	−0.153077	−	0.111217i
$370$	11.7386	−	3.75932i	0.610261	−	0.195438i
$371$	11.5461	−	8.38871i	0.599442	−	0.435520i
$372$	−17.8025	+	12.9343i	−0.923017	+	0.670611i
$373$	−5.26616	−	16.2076i	−0.272671	−	0.839196i	−0.989826	−	0.142282i	$-0.954556\pi$
$373$	−5.26616	−	16.2076i	−0.272671	−	0.839196i	0.717155	−	0.696914i	$-0.245444\pi$
$374$	−4.46901			−0.231087
$375$	−0.299365	+	23.6043i	−0.0154591	+	1.21892i
$376$	−9.30511			−0.479875
$377$	−3.48825	−	10.7357i	−0.179654	−	0.552918i
$378$	5.01932	−	3.64675i	0.258166	−	0.187569i
$379$	−8.16337	+	5.93104i	−0.419324	+	0.304657i	−0.777366	−	0.629049i	$-0.783445\pi$
$379$	−8.16337	+	5.93104i	−0.419324	+	0.304657i	0.358042	+	0.933706i	$0.383445\pi$
$380$	−2.12953	+	0.681987i	−0.109243	+	0.0349852i
$381$	16.2384	+	11.7979i	0.831917	+	0.604423i
$382$	−2.24339			−0.114782
$383$	3.06736	+	2.22857i	0.156735	+	0.113874i	0.663388	−	0.748275i	$-0.269118\pi$
$383$	3.06736	+	2.22857i	0.156735	+	0.113874i	−0.506654	+	0.862150i	$0.669118\pi$
$384$	−0.652460	+	2.00806i	−0.0332957	+	0.102474i
$385$	6.95658	+	9.66053i	0.354540	+	0.492346i
$386$	−2.57588	−	7.92775i	−0.131109	−	0.403512i
$387$	−1.67666	+	5.16024i	−0.0852295	+	0.262310i
$388$	−0.629072	+	1.93609i	−0.0319363	+	0.0982899i
$389$	−9.85646	−	30.3351i	−0.499743	−	1.53805i	−0.809433	−	0.587212i	$-0.800225\pi$
$389$	−9.85646	−	30.3351i	−0.499743	−	1.53805i	0.309691	−	0.950837i	$-0.399775\pi$
$390$	−7.63511	+	10.4159i	−0.386619	+	0.527432i
$391$	−2.88877	+	8.89071i	−0.146091	+	0.449623i
$392$	−2.72522	−	1.97999i	−0.137644	−	0.100004i
$393$	1.97403			0.0995766
$394$	−5.19438	−	3.77394i	−0.261689	−	0.190128i
$395$	−17.3868	+	23.7194i	−0.874827	+	1.19345i
$396$	3.29545	−	2.39428i	0.165602	−	0.120317i
$397$	−16.2749	+	11.8244i	−0.816812	+	0.593448i	−0.915797	−	0.401641i	$-0.868440\pi$
$397$	−16.2749	+	11.8244i	−0.816812	+	0.593448i	0.0989859	+	0.995089i	$0.468440\pi$
$398$	−8.32362	−	25.6175i	−0.417225	−	1.28409i
$399$	4.02357			0.201430
$400$	−1.50483	−	4.76818i	−0.0752413	−	0.238409i
$401$	−21.2835			−1.06285			−0.531424	−	0.847106i	$-0.678343\pi$
$401$	−21.2835			−1.06285			−0.531424	+	0.847106i	$0.678343\pi$
$402$	1.17369	+	3.61224i	0.0585383	+	0.180162i
$403$	23.0640	−	16.7570i	1.14890	−	0.834724i
$404$	9.08355	−	6.59959i	0.451924	−	0.328342i
$405$	23.8877	+	7.87339i	1.18699	+	0.391232i
$406$	−6.36207	−	4.62232i	−0.315744	−	0.229402i
$407$	15.4001			0.763354
$408$	−2.73244	−	1.98523i	−0.135276	−	0.0982837i
$409$	3.47653	−	10.6997i	0.171903	−	0.529064i	−0.827575	−	0.561355i	$-0.810280\pi$
$409$	3.47653	−	10.6997i	0.171903	−	0.529064i	0.999479	+	0.0322907i	$0.0102802\pi$
$410$	−5.30865	+	1.70011i	−0.262175	+	0.0839623i
$411$	4.94427	+	15.2169i	0.243883	+	0.750595i
$412$	4.17229	−	12.8410i	0.205554	−	0.632630i
$413$	2.27477	−	7.00104i	0.111934	−	0.344498i
$414$	−2.63304	−	8.10366i	−0.129407	−	0.398273i
$415$	19.3808	+	6.38791i	0.951367	+	0.313570i
$416$	0.845292	−	2.60154i	0.0414438	−	0.127551i
$417$	14.6375	+	10.6348i	0.716801	+	0.520787i
$418$	−2.79377			−0.136648
$419$	−3.94626	−	2.86712i	−0.192787	−	0.140068i	0.487204	−	0.873288i	$-0.338017\pi$
$419$	−3.94626	−	2.86712i	−0.192787	−	0.140068i	−0.679992	+	0.733220i	$0.738017\pi$
$420$	−0.0380330	+	8.99689i	−0.00185582	+	0.439003i
$421$	−5.37088	+	3.90217i	−0.261760	+	0.190180i	−0.710923	−	0.703270i	$-0.751722\pi$
$421$	−5.37088	+	3.90217i	−0.261760	+	0.190180i	0.449162	+	0.893450i	$0.351722\pi$
$422$	21.6741	−	15.7472i	1.05508	−	0.766561i
$423$	4.19247	+	12.9031i	0.203845	+	0.627370i
$424$	−7.48922			−0.363709
$425$	7.99790	+	0.0676209i	0.387955	+	0.00328010i
$426$	−5.71823			−0.277049
$427$	−1.97446	−	6.07677i	−0.0955510	−	0.294076i
$428$	15.3534	−	11.1549i	0.742134	−	0.539192i
$429$	−13.0540	+	9.48429i	−0.630253	+	0.457906i
$430$	4.86253	+	6.75255i	0.234492	+	0.325637i
$431$	−2.61891	−	1.90275i	−0.126148	−	0.0916522i	0.522922	−	0.852381i	$-0.324842\pi$
$431$	−2.61891	−	1.90275i	−0.126148	−	0.0916522i	−0.649070	+	0.760728i	$0.724842\pi$
$432$	−3.25572			−0.156641
$433$	17.4761	+	12.6971i	0.839847	+	0.610185i	0.922328	−	0.386408i	$-0.126284\pi$
$433$	17.4761	+	12.6971i	0.839847	+	0.610185i	−0.0824807	+	0.996593i	$0.526284\pi$
$434$	6.13726	−	18.8885i	0.294598	−	0.906679i
$435$	0.0823609	−	19.4829i	0.00394890	−	0.934133i
$436$	2.97462	+	9.15495i	0.142459	+	0.438443i
$437$	−1.80589	+	5.55796i	−0.0863874	+	0.265873i
$438$	−2.24736	+	6.91665i	−0.107383	+	0.330490i
$439$	11.5937	+	35.6819i	0.553339	+	1.70300i	0.700290	+	0.713859i	$0.253054\pi$
$439$	11.5937	+	35.6819i	0.553339	+	1.70300i	−0.146951	+	0.989144i	$0.546946\pi$
$440$	0.0264082	−	6.24700i	0.00125896	−	0.297814i
$441$	−1.51772	+	4.67106i	−0.0722724	+	0.222432i
$442$	3.54000	+	2.57196i	0.168381	+	0.122336i
$443$	−35.7068			−1.69648			−0.848239	−	0.529613i	$-0.822337\pi$
$443$	−35.7068			−1.69648			−0.848239	+	0.529613i	$0.822337\pi$
$444$	9.41590	+	6.84105i	0.446859	+	0.324662i
$445$	−1.98812	−	2.76088i	−0.0942458	−	0.130878i
$446$	−6.10012	+	4.43200i	−0.288849	+	0.209861i
$447$	−2.62092	+	1.90421i	−0.123965	+	0.0900659i
$448$	−0.588874	−	1.81237i	−0.0278217	−	0.0856263i
$449$	4.31865			0.203809			0.101905	−	0.994794i	$-0.467506\pi$
$449$	4.31865			0.203809			0.101905	+	0.994794i	$0.467506\pi$
$450$	−5.93387	+	4.23502i	−0.279725	+	0.199641i
$451$	−6.96452			−0.327946
$452$	−2.06754	−	6.36322i	−0.0972488	−	0.299301i
$453$	10.0068	−	7.27039i	0.470162	−	0.341593i
$454$	−10.4476	+	7.59062i	−0.490330	+	0.356245i
$455$	0.0492734	−	11.6559i	0.00230997	−	0.546436i
$456$	−1.70816	−	1.24105i	−0.0799920	−	0.0581176i
$457$	−3.54275			−0.165723			−0.0828615	−	0.996561i	$-0.526406\pi$
$457$	−3.54275			−0.165723			−0.0828615	+	0.996561i	$0.526406\pi$
$458$	14.8656	+	10.8005i	0.694624	+	0.504674i
$459$	1.60935	−	4.95308i	0.0751182	−	0.231190i
$460$	−12.4108	−	4.09059i	−0.578656	−	0.190725i
$461$	4.41013	+	13.5730i	0.205400	+	0.632157i	0.999697	+	0.0246266i	$0.00783967\pi$
$461$	4.41013	+	13.5730i	0.205400	+	0.632157i	−0.794297	+	0.607530i	$0.792160\pi$
$462$	−3.47363	+	10.6907i	−0.161608	+	0.497379i
$463$	−1.22271	+	3.76312i	−0.0568243	+	0.174887i	−0.975440	−	0.220265i	$-0.929308\pi$
$463$	−1.22271	+	3.76312i	−0.0568243	+	0.174887i	0.918616	+	0.395152i	$0.129308\pi$
$464$	1.27521	+	3.92471i	0.0592004	+	0.182200i
$465$	46.8605	−	15.0072i	2.17311	−	0.695942i
$466$	−4.21545	+	12.9738i	−0.195277	+	0.601000i
$467$	−12.4911	−	9.07531i	−0.578019	−	0.419955i	0.259991	−	0.965611i	$-0.416281\pi$
$467$	−12.4911	−	9.07531i	−0.578019	−	0.419955i	−0.838009	+	0.545656i	$0.816281\pi$
$468$	−3.98832			−0.184360
$469$	−2.77330	−	2.01492i	−0.128059	−	0.0930404i
$470$	19.7611	+	6.51327i	0.911514	+	0.300435i
$471$	14.1690	−	10.2944i	0.652873	−	0.474340i
$472$	−3.12517	+	2.27057i	−0.143848	+	0.104511i
$473$	3.21270	+	9.88767i	0.147720	+	0.454636i
$474$	−27.7698			−1.27551
$475$	4.99982	+	0.0422727i	0.229408	+	0.00193960i
$476$	3.04832			0.139720
$477$	3.37431	+	10.3851i	0.154499	+	0.475499i
$478$	−18.0740	+	13.1316i	−0.826688	+	0.600624i
$479$	28.5151	−	20.7174i	1.30289	−	0.946604i	0.302909	−	0.953019i	$-0.402042\pi$
$479$	28.5151	−	20.7174i	1.30289	−	0.946604i	0.999979	+	0.00641543i	$0.00204211\pi$
$480$	2.79120	−	3.80780i	0.127400	−	0.173802i
$481$	−12.1987	−	8.86290i	−0.556214	−	0.404113i
$482$	−1.00408			−0.0457348
$483$	19.0229	+	13.8210i	0.865574	+	0.628876i
$484$	−0.987265	+	3.03849i	−0.0448757	+	0.138113i
$485$	2.69115	−	3.67131i	0.122199	−	0.166706i
$486$	4.32080	+	13.2981i	0.195996	+	0.603212i
$487$	5.47099	−	16.8380i	0.247914	−	0.763002i	−0.747229	−	0.664567i	$-0.768616\pi$
$487$	5.47099	−	16.8380i	0.247914	−	0.763002i	0.995143	−	0.0984354i	$-0.0313838\pi$
$488$	−1.03612	+	3.18884i	−0.0469028	+	0.144352i
$489$	8.77514	+	27.0071i	0.396826	+	1.22130i
$490$	4.40158	+	6.11243i	0.198843	+	0.276131i
$491$	−5.44224	+	16.7495i	−0.245605	+	0.755894i	0.749932	+	0.661515i	$0.230086\pi$
$491$	−5.44224	+	16.7495i	−0.245605	+	0.755894i	−0.995536	+	0.0943785i	$0.969914\pi$
$492$	−4.25823	−	3.09379i	−0.191976	−	0.139479i
$493$	−6.60119			−0.297303
$494$	2.21300	+	1.60784i	0.0995677	+	0.0723402i
$495$	−8.67441	+	2.77800i	−0.389886	+	0.124862i
$496$	−8.43160	+	6.12591i	−0.378590	+	0.275062i
$497$	4.17530	−	3.03353i	0.187288	−	0.136073i
$498$	5.95437	+	18.3257i	0.266821	+	0.821192i
$499$	11.3619			0.508627			0.254313	−	0.967122i	$-0.418151\pi$
$499$	11.3619			0.508627			0.254313	+	0.967122i	$0.418151\pi$
$500$	−0.141785	+	11.1794i	−0.00634081	+	0.499960i
$501$	−37.3385			−1.66816
$502$	2.07295	+	6.37990i	0.0925205	+	0.284749i
$503$	15.6278	−	11.3543i	0.696809	−	0.506262i	−0.182082	−	0.983283i	$-0.558284\pi$
$503$	15.6278	−	11.3543i	0.696809	−	0.506262i	0.878892	+	0.477022i	$0.158284\pi$
$504$	−2.24783	+	1.63314i	−0.100126	+	0.0727460i
$505$	−23.9101	+	7.65727i	−1.06399	+	0.340744i
$506$	−13.2086	−	9.59661i	−0.587194	−	0.426622i
$507$	−11.6496			−0.517377
$508$	7.69079	+	5.58769i	0.341224	+	0.247914i
$509$	−10.8759	+	33.4726i	−0.482066	+	1.48365i	0.354119	+	0.935200i	$0.384781\pi$
$509$	−10.8759	+	33.4726i	−0.482066	+	1.48365i	−0.836185	+	0.548447i	$0.815219\pi$
$510$	4.41325	+	6.12863i	0.195422	+	0.271380i
$511$	−2.02834	−	6.24258i	−0.0897284	−	0.276156i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	1.00607	−	3.09638i	0.0444193	−	0.136708i
$514$	−3.94505	−	12.1416i	−0.174009	−	0.535543i
$515$	−17.8489	+	24.3498i	−0.786517	+	1.07298i
$516$	−2.42801	+	7.47265i	−0.106887	+	0.328965i
$517$	21.0315	+	15.2803i	0.924963	+	0.672025i
$518$	−10.5044			−0.461538
$519$	−16.2083	−	11.7760i	−0.711463	−	0.516908i
$520$	−3.61613	+	4.93318i	−0.158578	+	0.216334i
$521$	2.16383	−	1.57211i	0.0947991	−	0.0688756i	−0.539376	−	0.842065i	$-0.681340\pi$
$521$	2.16383	−	1.57211i	0.0947991	−	0.0688756i	0.634175	+	0.773189i	$0.281340\pi$
$522$	4.86771	−	3.53660i	0.213054	−	0.154793i
$523$	−7.16233	−	22.0434i	−0.313187	−	0.963890i	−0.976494	−	0.215543i	$-0.930848\pi$
$523$	−7.16233	−	22.0434i	−0.313187	−	0.963890i	0.663308	−	0.748347i	$-0.269152\pi$
$524$	0.934936			0.0408429
$525$	6.37829	−	19.0800i	0.278372	−	0.832718i
$526$	10.2629			0.447484
$527$	−5.15176	−	15.8555i	−0.224414	−	0.690676i
$528$	4.77221	−	3.46721i	0.207684	−	0.150891i
$529$	−9.02226	+	6.55505i	−0.392272	+	0.285002i
$530$	15.9048	+	5.24220i	0.690859	+	0.227707i
$531$	4.55659	+	3.31056i	0.197739	+	0.143666i
$532$	1.90564			0.0826198
$533$	5.51674	+	4.00814i	0.238956	+	0.173612i
$534$	0.992728	−	3.05530i	0.0429595	−	0.132216i
$535$	−40.4138	+	12.9426i	−1.74724	+	0.559559i
$536$	0.555881	+	1.71083i	0.0240104	+	0.0738964i
$537$	−13.7423	+	42.2944i	−0.593023	+	1.82514i
$538$	−6.02007	+	18.5279i	−0.259544	+	0.798793i
$539$	2.90815	+	8.95035i	0.125263	+	0.385519i
$540$	6.91414	+	2.27890i	0.297537	+	0.0980682i
$541$	−12.2552	+	37.7176i	−0.526892	+	1.62161i	0.233651	+	0.972320i	$0.424933\pi$
$541$	−12.2552	+	37.7176i	−0.526892	+	1.62161i	−0.760544	+	0.649287i	$0.775067\pi$
$542$	−12.8808	−	9.35848i	−0.553280	−	0.401981i
$543$	−48.1174			−2.06491
$544$	−1.29413	−	0.940243i	−0.0554855	−	0.0403126i
$545$	0.0909910	−	21.5244i	0.00389763	−	0.922004i
$546$	8.90417	−	6.46926i	0.381063	−	0.276859i
$547$	19.0248	−	13.8223i	0.813441	−	0.591000i	−0.101385	−	0.994847i	$-0.532327\pi$
$547$	19.0248	−	13.8223i	0.813441	−	0.591000i	0.914826	+	0.403848i	$0.132327\pi$
$548$	2.34170	+	7.20701i	0.100032	+	0.307868i
$549$	4.88869			0.208644
$550$	−4.42878	+	13.2482i	−0.188844	+	0.564905i
$551$	−4.12668			−0.175803
$552$	−3.81296	−	11.7351i	−0.162290	−	0.499479i
$553$	20.2768	−	14.7319i	0.862256	−	0.626466i
$554$	5.06665	−	3.68114i	0.215261	−	0.156396i
$555$	−15.2079	−	21.1191i	−0.645540	−	0.896455i
$556$	6.93259	+	5.03682i	0.294007	+	0.213609i
$557$	10.4726			0.443739			0.221869	−	0.975076i	$-0.428784\pi$
$557$	10.4726			0.443739			0.221869	+	0.975076i	$0.428784\pi$
$558$	12.2935	+	8.93176i	0.520426	+	0.378111i
$559$	3.14560	−	9.68117i	0.133045	−	0.409470i
$560$	−0.0180131	+	4.26109i	−0.000761193	+	0.180064i
$561$	2.91585	+	8.97407i	0.123107	+	0.378886i
$562$	−1.85146	+	5.69822i	−0.0780993	+	0.240365i
$563$	−6.38648	+	19.6556i	−0.269158	+	0.828383i	0.721548	+	0.692364i	$0.243431\pi$
$563$	−6.38648	+	19.6556i	−0.269158	+	0.828383i	−0.990706	+	0.136019i	$0.956569\pi$
$564$	6.07121	+	18.6853i	0.255644	+	0.786792i
$565$	−0.0632440	+	14.9607i	−0.00266070	+	0.629402i
$566$	9.26360	−	28.5104i	0.389378	−	1.19838i
$567$	−17.3413	−	12.5992i	−0.728267	−	0.529117i
$568$	−2.70826			−0.113636
$569$	−24.5507	−	17.8371i	−1.02922	−	0.747772i	−0.0610674	−	0.998134i	$-0.519450\pi$
$569$	−24.5507	−	17.8371i	−1.02922	−	0.747772i	−0.968152	+	0.250362i	$0.919450\pi$
$570$	2.75891	+	3.83126i	0.115558	+	0.160474i
$571$	−3.71358	+	2.69807i	−0.155408	+	0.112911i	−0.662772	−	0.748821i	$-0.730620\pi$
$571$	−3.71358	+	2.69807i	−0.155408	+	0.112911i	0.507364	+	0.861732i	$0.330620\pi$
$572$	−6.18262	+	4.49193i	−0.258508	+	0.187817i
$573$	1.46372	+	4.50487i	0.0611479	+	0.188194i
$574$	4.75051			0.198282
$575$	23.4934	+	17.3743i	0.979740	+	0.724557i
$576$	1.45803			0.0607512
$577$	−9.51650	−	29.2888i	−0.396177	−	1.21931i	−0.928041	−	0.372478i	$-0.878508\pi$
$577$	−9.51650	−	29.2888i	−0.396177	−	1.21931i	0.531864	−	0.846830i	$-0.321492\pi$
$578$	−11.6831	+	8.48830i	−0.485955	+	0.353067i
$579$	−14.2388	+	10.3451i	−0.591743	+	0.429927i
$580$	0.0390076	−	9.22746i	0.00161970	−	0.383149i
$581$	−14.0695	−	10.2221i	−0.583702	−	0.424084i
$582$	4.29823			0.178167
$583$	16.9272	+	12.2983i	0.701052	+	0.509344i
$584$	−1.06439	+	3.27585i	−0.0440447	+	0.135556i
$585$	8.46995	+	2.79169i	0.350189	+	0.115422i
$586$	6.34501	+	19.5279i	0.262110	+	0.806692i
$587$	2.48488	−	7.64767i	0.102562	−	0.315653i	−0.886589	−	0.462559i	$-0.846931\pi$
$587$	2.48488	−	7.64767i	0.102562	−	0.315653i	0.989151	+	0.146906i	$0.0469314\pi$
$588$	−2.19785	+	6.76427i	−0.0906376	+	0.278954i
$589$	−3.22058	−	9.91194i	−0.132702	−	0.408414i
$590$	8.22621	−	2.63446i	0.338668	−	0.108459i
$591$	−4.18919	+	12.8930i	−0.172320	+	0.530347i
$592$	4.45954	+	3.24005i	0.183286	+	0.133165i
$593$	1.49689			0.0614699			0.0307349	−	0.999528i	$-0.490215\pi$
$593$	1.49689			0.0614699			0.0307349	+	0.999528i	$0.490215\pi$
$594$	7.35861	+	5.34634i	0.301927	+	0.219363i
$595$	−6.47369	−	2.13373i	−0.265395	−	0.0874742i
$596$	−1.24131	+	0.901868i	−0.0508462	+	0.0369419i
$597$	−46.0107	+	33.4287i	−1.88309	+	1.36815i
$598$	4.93987	+	15.2034i	0.202006	+	0.621711i
$599$	25.5934			1.04572			0.522860	−	0.852419i	$-0.324865\pi$
$599$	25.5934			1.04572			0.522860	+	0.852419i	$0.324865\pi$
$600$	−8.59297	+	6.13283i	−0.350806	+	0.250372i
$601$	−15.2670			−0.622755			−0.311377	−	0.950286i	$-0.600790\pi$
$601$	−15.2670			−0.622755			−0.311377	+	0.950286i	$0.600790\pi$
$602$	−2.19139	−	6.74440i	−0.0893143	−	0.274881i
$603$	2.12189	−	1.54164i	0.0864101	−	0.0627806i
$604$	4.73942	−	3.44339i	0.192844	−	0.140110i
$605$	4.22348	−	5.76174i	0.171709	−	0.234248i
$606$	−19.1791	−	13.9344i	−0.779096	−	0.566046i
$607$	−34.6920			−1.40811			−0.704053	−	0.710148i	$-0.748628\pi$
$607$	−34.6920			−1.40811			−0.704053	+	0.710148i	$0.748628\pi$
$608$	−0.809017	−	0.587785i	−0.0328100	−	0.0238378i
$609$	−5.13091	+	15.7913i	−0.207915	+	0.639897i
$610$	4.43247	−	6.04686i	0.179466	−	0.244830i
$611$	−7.86554	−	24.2076i	−0.318205	−	0.979336i
$612$	−0.720725	+	2.21816i	−0.0291336	+	0.0896640i
$613$	12.7738	−	39.3138i	0.515930	−	1.58787i	−0.265653	−	0.964069i	$-0.585588\pi$
$613$	12.7738	−	39.3138i	0.515930	−	1.58787i	0.781583	−	0.623801i	$-0.214412\pi$
$614$	7.51919	+	23.1417i	0.303450	+	0.933923i
$615$	6.87761	+	9.55086i	0.277332	+	0.385128i
$616$	−1.64518	+	5.06334i	−0.0662861	+	0.204008i
$617$	−2.14649	−	1.55952i	−0.0864144	−	0.0627837i	0.543739	−	0.839254i	$-0.317008\pi$
$617$	−2.14649	−	1.55952i	−0.0864144	−	0.0627837i	−0.630154	+	0.776471i	$0.717008\pi$
$618$	−28.5078			−1.14675
$619$	−19.5766	−	14.2232i	−0.786851	−	0.571680i	0.120177	−	0.992753i	$-0.461654\pi$
$619$	−19.5766	−	14.2232i	−0.786851	−	0.571680i	−0.907027	+	0.421072i	$0.861654\pi$
$620$	22.1940	−	7.10769i	0.891333	−	0.285452i
$621$	15.3927	−	11.1834i	0.617687	−	0.448776i
$622$	18.9073	−	13.7370i	0.758115	−	0.550803i
$623$	0.895981	+	2.75755i	0.0358967	+	0.110479i
$624$	−5.77558			−0.231208
$625$	8.12634	−	23.6424i	0.325054	−	0.945696i
$626$	−19.6633			−0.785903
$627$	1.82282	+	5.61007i	0.0727965	+	0.224045i
$628$	6.71070	−	4.87561i	0.267786	−	0.194558i
$629$	−7.13365	+	5.18290i	−0.284437	+	0.206656i
$630$	5.91684	−	1.89488i	0.235732	−	0.0754939i
$631$	10.3230	+	7.50008i	0.410951	+	0.298573i	0.773987	−	0.633202i	$-0.218260\pi$
$631$	10.3230	+	7.50008i	0.410951	+	0.298573i	−0.363036	+	0.931775i	$0.618260\pi$
$632$	−13.1523			−0.523170
$633$	−45.7629	−	33.2487i	−1.81891	−	1.32152i
$634$	−0.327669	+	1.00846i	−0.0130134	+	0.0400512i
$635$	−12.4216	−	17.2498i	−0.492938	−	0.684537i
$636$	4.88642	+	15.0388i	0.193759	+	0.596329i
$637$	2.84741	−	8.76343i	0.112818	−	0.347220i
$638$	3.56266	−	10.9647i	0.141047	−	0.434098i
$639$	1.22022	+	3.75546i	0.0482712	+	0.148564i
$640$	1.32196	−	1.80344i	0.0522552	−	0.0712874i
$641$	6.79498	−	20.9128i	0.268385	−	0.826006i	−0.722509	−	0.691362i	$-0.757011\pi$
$641$	6.79498	−	20.9128i	0.268385	−	0.826006i	0.990894	−	0.134644i	$-0.0429890\pi$
$642$	−32.4172	−	23.5525i	−1.27940	−	0.929542i
$643$	5.34308			0.210710			0.105355	−	0.994435i	$-0.466402\pi$
$643$	5.34308			0.210710			0.105355	+	0.994435i	$0.466402\pi$
$644$	9.00962	+	6.54587i	0.355029	+	0.257943i
$645$	10.3869	−	14.1701i	0.408986	−	0.557945i
$646$	1.29413	−	0.940243i	0.0509170	−	0.0369934i
$647$	9.91391	−	7.20288i	0.389756	−	0.283174i	−0.375599	−	0.926782i	$-0.622563\pi$
$647$	9.91391	−	7.20288i	0.389756	−	0.283174i	0.765356	+	0.643608i	$0.222563\pi$
$648$	3.47590	+	10.6977i	0.136546	+	0.420246i
$649$	10.7921			0.423628
$650$	11.1326	−	7.94537i	0.436656	−	0.311643i
$651$	−41.9337			−1.64351
$652$	4.15607	+	12.7911i	0.162764	+	0.500937i
$653$	−28.6168	+	20.7913i	−1.11986	+	0.813627i	−0.984188	−	0.177126i	$-0.943320\pi$
$653$	−28.6168	+	20.7913i	−1.11986	+	0.813627i	−0.135674	+	0.990754i	$0.543320\pi$
$654$	16.4429	−	11.9465i	0.642969	−	0.467144i
$655$	−1.98551	−	0.654424i	−0.0775804	−	0.0255705i
$656$	−2.01678	−	1.46527i	−0.0787419	−	0.0572094i
$657$	5.02209			0.195930
$658$	−14.3456	−	10.4227i	−0.559250	−	0.406319i
$659$	−12.0127	+	36.9712i	−0.467947	+	1.44019i	0.387290	+	0.921958i	$0.373411\pi$
$659$	−12.0127	+	36.9712i	−0.467947	+	1.44019i	−0.855238	+	0.518236i	$0.826589\pi$
$660$	−12.5616	+	4.02289i	−0.488960	+	0.156591i
$661$	−3.96139	−	12.1919i	−0.154080	−	0.474210i	0.843986	−	0.536365i	$-0.180203\pi$
$661$	−3.96139	−	12.1919i	−0.154080	−	0.474210i	−0.998067	+	0.0621548i	$0.980203\pi$
$662$	8.80121	−	27.0873i	0.342069	−	1.05278i
$663$	2.85496	−	8.78665i	0.110877	−	0.341245i
$664$	2.82010	+	8.67937i	0.109441	+	0.336825i
$665$	−4.04697	−	1.33388i	−0.156935	−	0.0517257i
$666$	2.48360	−	7.64373i	0.0962375	−	0.296188i
$667$	−19.5105	−	14.1752i	−0.755448	−	0.548865i
$668$	−17.6842			−0.684223
$669$	12.8798	+	9.35774i	0.497963	+	0.361791i
$670$	0.0170039	−	4.02236i	0.000656917	−	0.155397i
$671$	7.57835	−	5.50600i	0.292559	−	0.212557i
$672$	−3.25513	+	2.36499i	−0.125570	+	0.0912316i
$673$	−7.52203	−	23.1504i	−0.289953	−	0.892383i	−0.984870	−	0.173294i	$-0.944559\pi$
$673$	−7.52203	−	23.1504i	−0.289953	−	0.892383i	0.694917	−	0.719090i	$-0.255441\pi$
$674$	28.0751			1.08141
$675$	−13.0883	−	9.67934i	−0.503770	−	0.372558i
$676$	−5.51747			−0.212210
$677$	9.64719	+	29.6910i	0.370772	+	1.14112i	0.946287	+	0.323327i	$0.104801\pi$
$677$	9.64719	+	29.6910i	0.370772	+	1.14112i	−0.575516	+	0.817791i	$0.695199\pi$
$678$	−11.4288	+	8.30350i	−0.438920	+	0.318894i
$679$	−3.13845	+	2.28022i	−0.120443	+	0.0875068i
$680$	2.09020	+	2.90263i	0.0801553	+	0.111311i
$681$	22.0591	+	16.0269i	0.845306	+	0.614151i
$682$	29.1167			1.11494
$683$	16.7339	+	12.1579i	0.640306	+	0.465210i	0.859955	−	0.510369i	$-0.170491\pi$
$683$	16.7339	+	12.1579i	0.640306	+	0.465210i	−0.219649	+	0.975579i	$0.570491\pi$
$684$	−0.450556	+	1.38667i	−0.0172274	+	0.0530206i
$685$	0.0716304	−	16.9445i	0.00273686	−	0.647417i
$686$	−6.10577	−	18.7916i	−0.233119	−	0.717468i
$687$	11.9889	−	36.8980i	0.457404	−	1.40775i
$688$	−1.14995	+	3.53919i	−0.0438415	+	0.134930i
$689$	−6.33058	−	19.4835i	−0.241176	−	0.742263i
$690$	−0.116635	+	27.5906i	−0.00444022	+	1.05036i
$691$	−14.8979	+	45.8511i	−0.566743	+	1.74426i	0.0959703	+	0.995384i	$0.469405\pi$
$691$	−14.8979	+	45.8511i	−0.566743	+	1.74426i	−0.662714	+	0.748873i	$0.730595\pi$
$692$	−7.67653	−	5.57732i	−0.291818	−	0.212018i
$693$	7.76241			0.294869
$694$	17.1199	+	12.4383i	0.649862	+	0.472152i
$695$	−11.1970	−	15.5492i	−0.424728	−	0.589815i
$696$	7.04904	−	5.12143i	0.267193	−	0.194127i
$697$	3.22611	−	2.34391i	0.122198	−	0.0887818i
$698$	−4.85555	−	14.9439i	−0.183785	−	0.565633i
$699$	28.8027			1.08942
$700$	3.02088	−	9.03662i	0.114178	−	0.341552i
$701$	−21.2060			−0.800939			−0.400469	−	0.916310i	$-0.631153\pi$
$701$	−21.2060			−0.800939			−0.400469	+	0.916310i	$0.631153\pi$
$702$	−2.75204	−	8.46990i	−0.103869	−	0.319676i
$703$	−4.45954	+	3.24005i	−0.168195	+	0.122201i
$704$	2.26021	−	1.64214i	0.0851847	−	0.0618903i
$705$	0.185713	−	43.9313i	0.00699435	−	1.65455i
$706$	−4.59717	−	3.34004i	−0.173017	−	0.125704i
$707$	21.3963			0.804689
$708$	6.59850	+	4.79409i	0.247987	+	0.180173i
$709$	−0.352493	+	1.08486i	−0.0132381	+	0.0407428i	−0.957457	−	0.288575i	$-0.906819\pi$
$709$	−0.352493	+	1.08486i	−0.0132381	+	0.0407428i	0.944219	+	0.329318i	$0.106819\pi$
$710$	5.75150	+	1.89569i	0.215850	+	0.0711441i
$711$	5.92584	+	18.2379i	0.222236	+	0.683973i
$712$	0.470174	−	1.44705i	0.0176205	−	0.0542304i
$713$	18.8210	−	57.9252i	0.704853	−	2.16931i
$714$	−1.98891	−	6.12123i	−0.0744331	−	0.229081i
$715$	16.2741	−	5.21184i	0.608619	−	0.194912i
$716$	−6.50860	+	20.0314i	−0.243238	+	0.748609i
$717$	38.1616	+	27.7260i	1.42517	+	1.03545i
$718$	−6.61971			−0.247045
$719$	41.3965	+	30.0763i	1.54383	+	1.12166i	0.947877	+	0.318636i	$0.103225\pi$
$719$	41.3965	+	30.0763i	1.54383	+	1.12166i	0.595951	+	0.803021i	$0.296775\pi$
$720$	−3.09640	−	1.02057i	−0.115396	−	0.0380345i
$721$	20.8156	−	15.1235i	0.775215	−	0.563227i
$722$	0.809017	−	0.587785i	0.0301085	−	0.0218751i
$723$	0.655124	+	2.01627i	0.0243643	+	0.0749857i
$724$	−22.7893			−0.846956
$725$	−6.54175	+	19.5689i	−0.242955	+	0.726772i
$726$	6.74563			0.250354
$727$	−6.83710	−	21.0424i	−0.253574	−	0.780420i	−0.994107	−	0.108401i	$-0.965427\pi$
$727$	−6.83710	−	21.0424i	−0.253574	−	0.780420i	0.740533	−	0.672020i	$-0.234573\pi$
$728$	4.21718	−	3.06396i	0.156299	−	0.113558i
$729$	−3.41583	+	2.48175i	−0.126512	+	0.0919166i
$730$	4.55342	−	6.21185i	0.168530	−	0.229911i
$731$	−4.81588	−	3.49894i	−0.178122	−	0.129413i
$732$	7.07943			0.261663
$733$	−13.9369	−	10.1258i	−0.514771	−	0.374003i	0.299859	−	0.953983i	$-0.403060\pi$
$733$	−13.9369	−	10.1258i	−0.514771	−	0.374003i	−0.814631	+	0.579980i	$0.803060\pi$
$734$	10.2351	−	31.5005i	0.377785	−	1.16270i
$735$	9.40230	−	12.8268i	0.346809	−	0.473123i
$736$	−1.80589	−	5.55796i	−0.0665660	−	0.204869i
$737$	1.55300	−	4.77965i	0.0572056	−	0.176061i
$738$	−1.12318	+	3.45679i	−0.0413448	+	0.127246i
$739$	−3.75239	−	11.5487i	−0.138034	−	0.424824i	0.858016	−	0.513623i	$-0.171697\pi$
$739$	−3.75239	−	11.5487i	−0.138034	−	0.424824i	−0.996050	+	0.0887990i	$0.971697\pi$
$740$	−7.20275	−	10.0024i	−0.264778	−	0.367695i
$741$	1.78475	−	5.49290i	0.0655645	−	0.201787i
$742$	−11.5461	−	8.38871i	−0.423869	−	0.307959i
$743$	−40.2084			−1.47510			−0.737551	−	0.675292i	$-0.764018\pi$
$743$	−40.2084			−1.47510			−0.737551	+	0.675292i	$0.764018\pi$
$744$	17.8025	+	12.9343i	0.652672	+	0.474194i
$745$	3.26744	−	1.04641i	0.119710	−	0.0383373i
$746$	−13.7870	+	10.0168i	−0.504777	+	0.366742i
$747$	10.7648	−	7.82107i	0.393863	−	0.286158i
$748$	1.38100	+	4.25029i	0.0504944	+	0.155406i
$749$	36.1648			1.32143
$750$	22.5416	−	7.00942i	0.823101	−	0.255948i
$751$	19.2517			0.702505			0.351253	−	0.936281i	$-0.385756\pi$
$751$	19.2517			0.702505			0.351253	+	0.936281i	$0.385756\pi$
$752$	2.87544	+	8.84969i	0.104856	+	0.322715i
$753$	11.4587	−	8.32525i	0.417579	−	0.303389i
$754$	−9.13236	+	6.63505i	−0.332581	+	0.241634i
$755$	−12.4753	+	3.99525i	−0.454023	+	0.145402i
$756$	−5.01932	−	3.64675i	−0.182551	−	0.132631i
$757$	−36.2224			−1.31652			−0.658262	−	0.752789i	$-0.728708\pi$
$757$	−36.2224			−1.31652			−0.658262	+	0.752789i	$0.728708\pi$
$758$	8.16337	+	5.93104i	0.296507	+	0.215425i
$759$	−10.6525	+	32.7851i	−0.386663	+	1.19003i
$760$	1.30667	+	1.81456i	0.0473979	+	0.0658209i
$761$	10.6616	+	32.8130i	0.386482	+	1.18947i	0.935399	+	0.353593i	$0.115040\pi$
$761$	10.6616	+	32.8130i	0.386482	+	1.18947i	−0.548917	+	0.835877i	$0.684960\pi$
$762$	6.20251	−	19.0893i	0.224693	−	0.691534i
$763$	−5.66855	+	17.4460i	−0.205215	+	0.631588i
$764$	0.693246	+	2.13359i	0.0250808	+	0.0771906i
$765$	3.08324	−	4.20620i	0.111475	−	0.152076i
$766$	1.17163	−	3.60589i	0.0423326	−	0.130286i
$767$	−8.54866	−	6.21097i	−0.308674	−	0.224265i
$768$	2.11140			0.0761887
$769$	15.6849	+	11.3958i	0.565613	+	0.410942i	0.833509	−	0.552506i	$-0.186328\pi$
$769$	15.6849	+	11.3958i	0.565613	+	0.410942i	−0.267896	+	0.963448i	$0.586328\pi$
$770$	7.03801	−	9.60137i	0.253632	−	0.346009i
$771$	−21.8071	+	15.8438i	−0.785365	+	0.570601i
$772$	−6.74375	+	4.89962i	−0.242713	+	0.176341i
$773$	1.78914	+	5.50641i	0.0643509	+	0.198052i	0.978063	−	0.208311i	$-0.0667968\pi$
$773$	1.78914	+	5.50641i	0.0643509	+	0.198052i	−0.913712	+	0.406363i	$0.866797\pi$
$774$	5.42579			0.195026
$775$	−52.1083	−	0.440567i	−1.87178	−	0.0158256i
$776$	2.03572			0.0730781
$777$	6.85372	+	21.0936i	0.245876	+	0.756728i
$778$	−25.8046	+	18.7481i	−0.925138	+	0.672152i
$779$	2.01678	−	1.46527i	0.0722586	−	0.0524989i
$780$	12.2655	+	4.04271i	0.439176	+	0.144752i
$781$	6.12123	+	4.44733i	0.219035	+	0.159138i
$782$	9.34825			0.334293
$783$	10.8694	+	7.89710i	0.388441	+	0.282219i
$784$	−1.04094	+	3.20368i	−0.0371764	+	0.114417i
$785$	−17.6642	+	5.65700i	−0.630462	+	0.201907i
$786$	−0.610008	−	1.87741i	−0.0217583	−	0.0669651i
$787$	3.57291	−	10.9963i	0.127361	−	0.391976i	−0.866963	−	0.498372i	$-0.833931\pi$
$787$	3.57291	−	10.9963i	0.127361	−	0.391976i	0.994324	+	0.106397i	$0.0339313\pi$
$788$	−1.98408	+	6.10636i	−0.0706798	+	0.217530i
$789$	−6.69613	−	20.6086i	−0.238389	−	0.733685i
$790$	27.9313	+	9.20616i	0.993752	+	0.327541i
$791$	3.93997	−	12.1260i	0.140089	−	0.431151i
$792$	−3.29545	−	2.39428i	−0.117099	−	0.0850771i
$793$	−9.17172			−0.325697
$794$	16.2749	+	11.8244i	0.577573	+	0.419631i
$795$	0.149471	−	35.3581i	0.00530119	−	1.25402i
$796$	−21.7915	+	15.8325i	−0.772380	+	0.561167i
$797$	−14.0256	+	10.1902i	−0.496813	+	0.360955i	−0.807798	−	0.589459i	$-0.799341\pi$
$797$	−14.0256	+	10.1902i	−0.496813	+	0.360955i	0.310986	+	0.950415i	$0.399341\pi$
$798$	−1.24335	−	3.82664i	−0.0440141	−	0.135462i
$799$	−14.8848			−0.526586
$800$	−4.06979	+	2.90462i	−0.143889	+	0.102694i
$801$	−2.21841			−0.0783838
$802$	6.57696	+	20.2418i	0.232241	+	0.714763i
$803$	7.78514	−	5.65623i	0.274731	−	0.199604i
$804$	3.07276	−	2.23249i	0.108368	−	0.0787338i
$805$	−14.5517	−	20.2078i	−0.512881	−	0.712232i
$806$	−23.0640	−	16.7570i	−0.812394	−	0.590239i
$807$	41.1330			1.44795
$808$	−9.08355	−	6.59959i	−0.319558	−	0.232173i
$809$	0.802234	−	2.46902i	0.0282050	−	0.0868062i	−0.935963	−	0.352098i	$-0.885468\pi$
$809$	0.802234	−	2.46902i	0.0282050	−	0.0868062i	0.964168	+	0.265292i	$0.0854683\pi$
$810$	0.106324	−	25.1516i	0.00373586	−	0.883737i
$811$	−7.53202	−	23.1812i	−0.264485	−	0.814001i	−0.991812	−	0.127710i	$-0.959237\pi$
$811$	−7.53202	−	23.1812i	−0.264485	−	0.814001i	0.727326	−	0.686292i	$-0.240763\pi$
$812$	−2.43010	+	7.47906i	−0.0852796	+	0.262464i
$813$	−10.3882	+	31.9716i	−0.364330	+	1.12129i
$814$	−4.75889	−	14.6464i	−0.166799	−	0.513355i
$815$	0.127130	−	30.0733i	0.00445318	−	1.05342i
$816$	−1.04370	+	3.21217i	−0.0365368	+	0.112449i
$817$	−3.01061	−	2.18734i	−0.105328	−	0.0765253i
$818$	−11.2503			−0.393357
$819$	−6.14877	−	4.46734i	−0.214855	−	0.156101i
$820$	3.25736	+	4.52346i	0.113752	+	0.157966i
$821$	−5.80028	+	4.21415i	−0.202431	+	0.147075i	−0.684383	−	0.729123i	$-0.739928\pi$
$821$	−5.80028	+	4.21415i	−0.202431	+	0.147075i	0.481951	+	0.876198i	$0.339928\pi$
$822$	12.9443	−	9.40456i	0.451483	−	0.328022i
$823$	−16.0572	−	49.4190i	−0.559719	−	1.72264i	−0.683145	−	0.730283i	$-0.739388\pi$
$823$	−16.0572	−	49.4190i	−0.559719	−	1.72264i	0.123426	−	0.992354i	$-0.460612\pi$
$824$	−13.5018			−0.470358
$825$	29.4928	+	0.249357i	1.02681	+	0.00868150i
$826$	−7.36133			−0.256133
$827$	2.98010	+	9.17179i	0.103628	+	0.318934i	0.989406	−	0.145175i	$-0.0463745\pi$
$827$	2.98010	+	9.17179i	0.103628	+	0.318934i	−0.885778	+	0.464109i	$0.846374\pi$
$828$	−6.89339	+	5.00834i	−0.239562	+	0.174052i
$829$	43.3280	−	31.4796i	1.50484	−	1.09333i	0.536443	−	0.843937i	$-0.319768\pi$
$829$	43.3280	−	31.4796i	1.50484	−	1.09333i	0.968401	−	0.249397i	$-0.0802323\pi$
$830$	0.0862642	−	20.4062i	0.00299427	−	0.708311i
$831$	−10.6977	−	7.77237i	−0.371101	−	0.269620i
$832$	−2.73542			−0.0948337
$833$	−4.35936	−	3.16726i	−0.151043	−	0.109739i
$834$	5.59103	−	17.2074i	0.193601	−	0.595844i
$835$	37.5557	+	12.3784i	1.29967	+	0.428371i
$836$	0.863322	+	2.65703i	0.0298586	+	0.0918954i
$837$	−10.4853	+	32.2705i	−0.362426	+	1.11543i
$838$	−1.50734	+	4.63910i	−0.0520700	+	0.160255i
$839$	16.6605	+	51.2756i	0.575183	+	1.77023i	0.635556	+	0.772055i	$0.280771\pi$
$839$	16.6605	+	51.2756i	0.575183	+	1.77023i	−0.0603730	+	0.998176i	$0.519229\pi$
$840$	8.56830	−	2.74402i	0.295635	−	0.0946777i
$841$	−3.69909	+	11.3846i	−0.127555	+	0.392573i
$842$	5.37088	+	3.90217i	0.185093	+	0.134478i
$843$	12.6504			0.435703
$844$	−21.6741	−	15.7472i	−0.746055	−	0.542040i
$845$	11.7174	+	3.86204i	0.403090	+	0.132858i
$846$	10.9760	−	7.97455i	0.377364	−	0.274171i
$847$	−4.92548	+	3.57857i	−0.169242	+	0.122961i
$848$	2.31430	+	7.12267i	0.0794733	+	0.244594i
$849$	−63.2949			−2.17228
$850$	−2.40717	−	7.62735i	−0.0825654	−	0.261616i
$851$	−32.2138			−1.10427
$852$	1.76703	+	5.43836i	0.0605375	+	0.186315i
$853$	23.2983	−	16.9272i	0.797719	−	0.579577i	−0.112525	−	0.993649i	$-0.535894\pi$
$853$	23.2983	−	16.9272i	0.797719	−	0.579577i	0.910244	+	0.414072i	$0.135894\pi$
$854$	−5.16921	+	3.75565i	−0.176887	+	0.128516i
$855$	1.92746	−	2.62947i	0.0659178	−	0.0899261i
$856$	−15.3534	−	11.1549i	−0.524768	−	0.381266i
$857$	−30.6877			−1.04827			−0.524136	−	0.851635i	$-0.675611\pi$
$857$	−30.6877			−1.04827			−0.524136	+	0.851635i	$0.675611\pi$
$858$	13.0540	+	9.48429i	0.445656	+	0.323788i
$859$	−12.9382	+	39.8196i	−0.441444	+	1.35863i	0.444892	+	0.895584i	$0.353242\pi$
$859$	−12.9382	+	39.8196i	−0.441444	+	1.35863i	−0.886336	+	0.463042i	$0.846758\pi$
$860$	4.91945	−	6.71120i	0.167752	−	0.228850i
$861$	−3.09952	−	9.53933i	−0.105631	−	0.325100i
$862$	−1.00033	+	3.07871i	−0.0340715	+	0.104861i
$863$	−2.28962	+	7.04671i	−0.0779394	+	0.239873i	−0.982433	−	0.186613i	$-0.940249\pi$
$863$	−2.28962	+	7.04671i	−0.0779394	+	0.239873i	0.904494	+	0.426486i	$0.140249\pi$
$864$	1.00607	+	3.09638i	0.0342273	+	0.105341i
$865$	12.3986	+	17.2178i	0.421565	+	0.585423i
$866$	6.67527	−	20.5444i	0.226835	−	0.698126i
$867$	24.6678	+	17.9222i	0.837764	+	0.608671i
$868$	−19.8606			−0.674112
$869$	29.7269	+	21.5978i	1.00842	+	0.732657i
$870$	−18.5548	+	5.94222i	−0.629066	+	0.201460i
$871$	−3.98090	+	2.89229i	−0.134888	+	0.0980016i
$872$	7.78767	−	5.65807i	0.263724	−	0.191606i
$873$	−0.917206	−	2.82287i	−0.0310427	−	0.0955396i
$874$	5.84398			0.197676
$875$	−12.7407	+	17.0764i	−0.430715	+	0.577289i
$876$	7.27260			0.245718
$877$	−6.10425	−	18.7870i	−0.206126	−	0.634390i	−0.999665	−	0.0258714i	$-0.991764\pi$
$877$	−6.10425	−	18.7870i	−0.206126	−	0.634390i	0.793539	−	0.608519i	$-0.208236\pi$
$878$	30.3528	−	22.0526i	1.02436	−	0.744239i
$879$	35.0735	−	25.4824i	1.18300	−	0.859500i
$880$	−5.94941	+	1.90531i	−0.200555	+	0.0642281i
$881$	−8.51261	−	6.18477i	−0.286797	−	0.208370i	0.435080	−	0.900392i	$-0.356720\pi$
$881$	−8.51261	−	6.18477i	−0.286797	−	0.208370i	−0.721877	+	0.692022i	$0.756720\pi$
$882$	4.91145			0.165377
$883$	37.2787	+	27.0845i	1.25453	+	0.911467i	0.998476	−	0.0551958i	$-0.0175783\pi$
$883$	37.2787	+	27.0845i	1.25453	+	0.911467i	0.256052	+	0.966663i	$0.417578\pi$
$884$	1.35216	−	4.16152i	0.0454780	−	0.139967i
$885$	−10.6574	−	14.7999i	−0.358246	−	0.497492i
$886$	11.0340	+	33.9591i	0.370694	+	1.14088i
$887$	8.38492	−	25.8061i	0.281538	−	0.866485i	−0.705877	−	0.708334i	$-0.749447\pi$
$887$	8.38492	−	25.8061i	0.281538	−	0.866485i	0.987415	−	0.158150i	$-0.0505530\pi$
$888$	3.59655	−	11.0691i	0.120692	−	0.371453i
$889$	5.59804	+	17.2290i	0.187752	+	0.577841i
$890$	−2.01139	+	2.74397i	−0.0674219	+	0.0919781i
$891$	9.71085	−	29.8869i	0.325326	−	1.00125i
$892$	6.10012	+	4.43200i	0.204247	+	0.148394i
$893$	−9.30511			−0.311384
$894$	2.62092	+	1.90421i	0.0876566	+	0.0636862i
$895$	27.8435	−	37.9846i	0.930707	−	1.26969i
$896$	−1.54169	+	1.12010i	−0.0515043	+	0.0374201i
$897$	27.3063	−	19.8392i	0.911729	−	0.662410i
$898$	−1.33453	−	4.10728i	−0.0445340	−	0.137062i
$899$	43.0084			1.43441
$900$	5.86141	+	4.33475i	0.195380	+	0.144492i
$901$	−11.9800			−0.399113
$902$	2.15215	+	6.62365i	0.0716589	+	0.220543i
$903$	−12.1134	+	8.80090i	−0.403109	+	0.292876i
$904$	−5.41288	+	3.93269i	−0.180030	+	0.130799i
$905$	48.3973	+	15.9517i	1.60878	+	0.530253i
$906$	−10.0068	−	7.27039i	−0.332455	−	0.241543i
$907$	21.0353			0.698466			0.349233	−	0.937036i	$-0.386442\pi$
$907$	21.0353			0.698466			0.349233	+	0.937036i	$0.386442\pi$
$908$	10.4476	+	7.59062i	0.346716	+	0.251904i
$909$	−5.05879	+	15.5694i	−0.167789	+	0.516403i
$910$	−11.1006	+	3.55500i	−0.367982	+	0.117847i
$911$	3.15828	+	9.72018i	0.104638	+	0.322044i	0.989645	−	0.143534i	$-0.0458466\pi$
$911$	3.15828	+	9.72018i	0.104638	+	0.322044i	−0.885007	+	0.465578i	$0.845847\pi$
$912$	−0.652460	+	2.00806i	−0.0216051	+	0.0664937i
$913$	7.87870	−	24.2481i	0.260747	−	0.802496i
$914$	1.09477	+	3.36936i	0.0362118	+	0.111448i
$915$	−15.0345	−	4.95536i	−0.497025	−	0.163819i
$916$	5.67815	−	17.4756i	0.187612	−	0.577409i
$917$	1.44138	+	1.04723i	0.0475987	+	0.0345825i
$918$	−5.20798			−0.171889
$919$	−21.6995	−	15.7656i	−0.715800	−	0.520059i	0.169240	−	0.985575i	$-0.445869\pi$
$919$	−21.6995	−	15.7656i	−0.715800	−	0.520059i	−0.885039	+	0.465516i	$0.845869\pi$
$920$	−0.0552405	+	13.0674i	−0.00182123	+	0.430820i
$921$	41.5641	−	30.1981i	1.36958	−	0.995060i
$922$	11.5459	−	8.38857i	0.380243	−	0.276263i
$923$	−2.28927	−	7.04565i	−0.0753522	−	0.231910i
$924$	11.2409			0.369799
$925$	8.29505	+	26.2836i	0.272740	+	0.864200i
$926$	3.95678			0.130028
$927$	6.08332	+	18.7225i	0.199802	+	0.614929i
$928$	3.33856	−	2.42560i	0.109593	−	0.0796243i
$929$	−16.5535	+	12.0268i	−0.543102	+	0.394587i	−0.825236	−	0.564789i	$-0.808958\pi$
$929$	−16.5535	+	12.0268i	−0.543102	+	0.394587i	0.282134	+	0.959375i	$0.408958\pi$
$930$	−28.7534	−	39.9295i	−0.942861	−	1.30934i
$931$	−2.72522	−	1.97999i	−0.0893153	−	0.0648914i
$932$	13.6415			0.446841
$933$	−39.9210	−	29.0043i	−1.30696	−	0.949559i
$934$	−4.77117	+	14.6842i	−0.156118	+	0.480480i
$935$	0.0422436	−	9.99293i	0.00138151	−	0.326804i
$936$	1.23246	+	3.79312i	0.0402842	+	0.123982i
$937$	−6.12903	+	18.8632i	−0.200227	+	0.616234i	0.799649	+	0.600467i	$0.205019\pi$
$937$	−6.12903	+	18.8632i	−0.200227	+	0.616234i	−0.999876	+	0.0157664i	$0.994981\pi$
$938$	−1.05931	+	3.26021i	−0.0345876	+	0.106450i
$939$	12.8295	+	39.4852i	0.418675	+	1.28855i
$940$	0.0879570	−	20.8067i	0.00286884	−	0.678639i
$941$	9.09479	−	27.9909i	0.296482	−	0.912477i	−0.686238	−	0.727377i	$-0.740739\pi$
$941$	9.09479	−	27.9909i	0.296482	−	0.912477i	0.982720	−	0.185100i	$-0.0592609\pi$
$942$	−14.1690	−	10.2944i	−0.461651	−	0.335409i
$943$	14.5683			0.474410
$944$	3.12517	+	2.27057i	0.101716	+	0.0739007i
$945$	8.10687	+	11.2579i	0.263716	+	0.366220i
$946$	8.41095	−	6.11092i	0.273464	−	0.198683i
$947$	2.57789	−	1.87295i	0.0837702	−	0.0608626i	−0.545112	−	0.838363i	$-0.683513\pi$
$947$	2.57789	−	1.87295i	0.0837702	−	0.0608626i	0.628882	+	0.777501i	$0.283513\pi$
$948$	8.58134	+	26.4106i	0.278709	+	0.857778i
$949$	−9.42198			−0.305850
$950$	−1.50483	−	4.76818i	−0.0488230	−	0.154700i
$951$	2.23885			0.0725997
$952$	−0.941984	−	2.89913i	−0.0305299	−	0.0939613i
$953$	31.3060	−	22.7451i	1.01410	−	0.736786i	0.0490343	−	0.998797i	$-0.484386\pi$
$953$	31.3060	−	22.7451i	1.01410	−	0.736786i	0.965065	+	0.262011i	$0.0843856\pi$
$954$	8.83406	−	6.41832i	0.286013	−	0.207801i
$955$	0.0212058	−	5.01633i	0.000686202	−	0.162325i
$956$	18.0740	+	13.1316i	0.584556	+	0.424705i
$957$	−24.3424			−0.786877
$958$	−28.5151	−	20.7174i	−0.921281	−	0.669350i
$959$	−4.46242	+	13.7339i	−0.144099	+	0.443492i
$960$	−4.48396	−	1.47791i	−0.144719	−	0.0476994i
$961$	23.9855	+	73.8197i	0.773725	+	2.38128i
$962$	−4.65950	+	14.3405i	−0.150228	+	0.462355i
$963$	−8.55057	+	26.3159i	−0.275538	+	0.848019i
$964$	0.310279	+	0.954940i	0.00999341	+	0.0307566i
$965$	17.7512	−	5.68486i	0.571431	−	0.183002i
$966$	7.26612	−	22.3628i	0.233784	−	0.719512i
$967$	0.832408	+	0.604780i	0.0267684	+	0.0194484i	0.601089	−	0.799182i	$-0.294734\pi$
$967$	0.832408	+	0.604780i	0.0267684	+	0.0194484i	−0.574321	+	0.818630i	$0.694734\pi$
$968$	3.19486			0.102687
$969$	−2.73244	−	1.98523i	−0.0877786	−	0.0637749i
$970$	−4.32323	−	1.42494i	−0.138811	−	0.0457520i
$971$	−11.6351	+	8.45342i	−0.373389	+	0.271283i	−0.758615	−	0.651539i	$-0.774124\pi$
$971$	−11.6351	+	8.45342i	−0.373389	+	0.271283i	0.385226	+	0.922822i	$0.374124\pi$
$972$	11.3120	−	8.21865i	0.362833	−	0.263613i
$973$	5.04615	+	15.5305i	0.161772	+	0.497883i
$974$	−17.7045			−0.567289
$975$	−23.2184	−	17.1709i	−0.743583	−	0.549910i
$976$	3.35295			0.107325
$977$	−6.59903	−	20.3097i	−0.211122	−	0.649766i	−0.999406	−	0.0344549i	$-0.989030\pi$
$977$	−6.59903	−	20.3097i	−0.211122	−	0.649766i	0.788285	−	0.615311i	$-0.210970\pi$
$978$	22.9736	−	16.6913i	0.734615	−	0.533729i
$979$	−3.43894	+	2.49854i	−0.109909	+	0.0798536i
$980$	4.45310	−	6.07500i	0.142249	−	0.194059i
$981$	−11.3546	−	8.24963i	−0.362526	−	0.263390i
$982$	17.6115			0.562004
$983$	−11.4330	−	8.30653i	−0.364655	−	0.264937i	0.390336	−	0.920672i	$-0.372359\pi$
$983$	−11.4330	−	8.30653i	−0.364655	−	0.264937i	−0.754991	+	0.655735i	$0.772359\pi$
$984$	−1.62650	+	5.00585i	−0.0518509	+	0.159581i
$985$	8.48781	−	11.5792i	0.270444	−	0.368944i
$986$	2.03988	+	6.27811i	0.0649630	+	0.199936i
$987$	−11.5695	+	35.6073i	−0.368262	+	1.13339i
$988$	0.845292	−	2.60154i	0.0268923	−	0.0827660i
$989$	−6.72029	−	20.6829i	−0.213693	−	0.657679i
$990$	5.32258	+	7.39141i	0.169163	+	0.234914i
$991$	12.7753	−	39.3184i	0.405822	−	1.24899i	−0.514386	−	0.857559i	$-0.671980\pi$
$991$	12.7753	−	39.3184i	0.405822	−	1.24899i	0.920207	−	0.391431i	$-0.128020\pi$
$992$	8.43160	+	6.12591i	0.267703	+	0.194498i
$993$	−60.1356			−1.90834
$994$	−4.17530	−	3.03353i	−0.132433	−	0.0962179i
$995$	57.3605	−	18.3699i	1.81845	−	0.582364i
$996$	15.5887	−	11.3259i	0.493948	−	0.358874i
$997$	11.1851	−	8.12643i	0.354235	−	0.257367i	−0.396409	−	0.918074i	$-0.629744\pi$
$997$	11.1851	−	8.12643i	0.354235	−	0.257367i	0.750643	+	0.660708i	$0.229744\pi$
$998$	−3.51101	−	10.8058i	−0.111139	−	0.342051i
$999$	17.9465			0.567803

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.h.d.381.3	✓	44
25.21	even	5	inner	950.2.h.d.571.3	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.h.d.381.3	✓	44	1.1	even	1	trivial
950.2.h.d.571.3	yes	44	25.21	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-1.70816 + 1.24105i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(2.12953 - 0.681987i) q^{5} +(1.70816 + 1.24105i) q^{6} -1.90564 q^{7} +(0.809017 + 0.587785i) q^{8} +(0.450556 - 1.38667i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-1.70816 + 1.24105i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(2.12953 - 0.681987i) q^{5} +(1.70816 + 1.24105i) q^{6} -1.90564 q^{7} +(0.809017 + 0.587785i) q^{8} +(0.450556 - 1.38667i) q^{9} +(-1.30667 - 1.81456i) q^{10} +(-0.863322 - 2.65703i) q^{11} +(0.652460 - 2.00806i) q^{12} +(-0.845292 + 2.60154i) q^{13} +(0.588874 + 1.81237i) q^{14} +(-2.79120 + 3.80780i) q^{15} +(0.309017 - 0.951057i) q^{16} +(1.29413 + 0.940243i) q^{17} -1.45803 q^{18} +(0.809017 + 0.587785i) q^{19} +(-1.32196 + 1.80344i) q^{20} +(3.25513 - 2.36499i) q^{21} +(-2.26021 + 1.64214i) q^{22} +(1.80589 + 5.55796i) q^{23} -2.11140 q^{24} +(4.06979 - 2.90462i) q^{25} +2.73542 q^{26} +(-1.00607 - 3.09638i) q^{27} +(1.54169 - 1.12010i) q^{28} +(-3.33856 + 2.42560i) q^{29} +(4.48396 + 1.47791i) q^{30} +(-8.43160 - 6.12591i) q^{31} -1.00000 q^{32} +(4.77221 + 3.46721i) q^{33} +(0.494315 - 1.52134i) q^{34} +(-4.05811 + 1.29962i) q^{35} +(0.450556 + 1.38667i) q^{36} +(-1.70339 + 5.24251i) q^{37} +(0.309017 - 0.951057i) q^{38} +(-1.78475 - 5.49290i) q^{39} +(2.12369 + 0.699967i) q^{40} +(0.770341 - 2.37086i) q^{41} +(-3.25513 - 2.36499i) q^{42} -3.72132 q^{43} +(2.26021 + 1.64214i) q^{44} +(0.0137821 - 3.26022i) q^{45} +(4.72788 - 3.43501i) q^{46} +(-7.52799 + 5.46941i) q^{47} +(0.652460 + 2.00806i) q^{48} -3.36855 q^{49} +(-4.02009 - 2.97302i) q^{50} -3.37748 q^{51} +(-0.845292 - 2.60154i) q^{52} +(-6.05891 + 4.40205i) q^{53} +(-2.63394 + 1.91367i) q^{54} +(-3.65053 - 5.06945i) q^{55} +(-1.54169 - 1.12010i) q^{56} -2.11140 q^{57} +(3.33856 + 2.42560i) q^{58} +(-1.19371 + 3.67386i) q^{59} +(0.0199581 - 4.72120i) q^{60} +(1.03612 + 3.18884i) q^{61} +(-3.22058 + 9.91194i) q^{62} +(-0.858595 + 2.64248i) q^{63} +(0.309017 + 0.951057i) q^{64} +(-0.0258567 + 6.11653i) q^{65} +(1.82282 - 5.61007i) q^{66} +(1.45531 + 1.05735i) q^{67} -1.59964 q^{68} +(-9.98247 - 7.25269i) q^{69} +(2.49003 + 3.45788i) q^{70} +(-2.19103 + 1.59188i) q^{71} +(1.17957 - 0.857008i) q^{72} +(1.06439 + 3.27585i) q^{73} +5.51230 q^{74} +(-3.34707 + 10.0124i) q^{75} -1.00000 q^{76} +(1.64518 + 5.06334i) q^{77} +(-4.67254 + 3.39480i) q^{78} +(-10.6404 + 7.73072i) q^{79} +(0.00945254 - 2.23605i) q^{80} +(9.10002 + 6.61155i) q^{81} -2.49287 q^{82} +(7.38311 + 5.36414i) q^{83} +(-1.24335 + 3.82664i) q^{84} +(3.39713 + 1.11969i) q^{85} +(1.14995 + 3.53919i) q^{86} +(2.69249 - 8.28665i) q^{87} +(0.863322 - 2.65703i) q^{88} +(-0.470174 - 1.44705i) q^{89} +(-3.10491 + 0.994357i) q^{90} +(1.61082 - 4.95759i) q^{91} +(-4.72788 - 3.43501i) q^{92} +22.0051 q^{93} +(7.52799 + 5.46941i) q^{94} +(2.12369 + 0.699967i) q^{95} +(1.70816 - 1.24105i) q^{96} +(1.64693 - 1.19657i) q^{97} +(1.04094 + 3.20368i) q^{98} -4.07340 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 11 q^{5} + q^{6} - 10 q^{7} + 11 q^{8}+O(q^{10}) \) 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 11 * q^5 + q^6 - 10 * q^7 + 11 * q^8	\( 44 q + 11 q^{2} - q^{3} - 11 q^{4} - 11 q^{5} + q^{6} - 10 q^{7} + 11 q^{8} - 4 q^{10} + 7 q^{11} + 4 q^{12} + 10 q^{13} - 5 q^{14} - 20 q^{15} - 11 q^{16} + 11 q^{17} - 50 q^{18} + 11 q^{19} + 4 q^{20} + 9 q^{21} + 8 q^{22} - 7 q^{23} + 6 q^{24} - 3 q^{25} + 10 q^{26} + 5 q^{27} - 20 q^{29} - 10 q^{30} - 11 q^{31} - 44 q^{32} - 2 q^{33} - q^{34} + 5 q^{35} + 43 q^{37} - 11 q^{38} - 33 q^{39} - 4 q^{40} - 32 q^{41} - 9 q^{42} - 74 q^{43} - 8 q^{44} + 10 q^{45} - 8 q^{46} - 19 q^{47} + 4 q^{48} + 54 q^{49} + 18 q^{50} + 34 q^{51} + 10 q^{52} + 23 q^{53} - 40 q^{54} + 2 q^{55} + 6 q^{57} + 20 q^{58} + 24 q^{59} - 35 q^{60} - 12 q^{61} + q^{62} - 44 q^{63} - 11 q^{64} + 43 q^{65} - 8 q^{66} + 35 q^{67} - 24 q^{68} + 29 q^{69} - 5 q^{70} - 2 q^{71} + 25 q^{72} + 22 q^{73} + 72 q^{74} + 7 q^{75} - 44 q^{76} - 3 q^{77} - 22 q^{78} - 19 q^{79} - q^{80} - 26 q^{81} - 58 q^{82} - 24 q^{83} - 21 q^{84} - 18 q^{85} - 6 q^{86} + 83 q^{87} - 7 q^{88} - 8 q^{89} + 60 q^{90} - 30 q^{91} + 8 q^{92} - 72 q^{93} + 19 q^{94} - 4 q^{95} + q^{96} - 16 q^{97} + q^{98} + 84 q^{99}+O(q^{100}) \) 44 * q + 11 * q^2 - q^3 - 11 * q^4 - 11 * q^5 + q^6 - 10 * q^7 + 11 * q^8 - 4 * q^10 + 7 * q^11 + 4 * q^12 + 10 * q^13 - 5 * q^14 - 20 * q^15 - 11 * q^16 + 11 * q^17 - 50 * q^18 + 11 * q^19 + 4 * q^20 + 9 * q^21 + 8 * q^22 - 7 * q^23 + 6 * q^24 - 3 * q^25 + 10 * q^26 + 5 * q^27 - 20 * q^29 - 10 * q^30 - 11 * q^31 - 44 * q^32 - 2 * q^33 - q^34 + 5 * q^35 + 43 * q^37 - 11 * q^38 - 33 * q^39 - 4 * q^40 - 32 * q^41 - 9 * q^42 - 74 * q^43 - 8 * q^44 + 10 * q^45 - 8 * q^46 - 19 * q^47 + 4 * q^48 + 54 * q^49 + 18 * q^50 + 34 * q^51 + 10 * q^52 + 23 * q^53 - 40 * q^54 + 2 * q^55 + 6 * q^57 + 20 * q^58 + 24 * q^59 - 35 * q^60 - 12 * q^61 + q^62 - 44 * q^63 - 11 * q^64 + 43 * q^65 - 8 * q^66 + 35 * q^67 - 24 * q^68 + 29 * q^69 - 5 * q^70 - 2 * q^71 + 25 * q^72 + 22 * q^73 + 72 * q^74 + 7 * q^75 - 44 * q^76 - 3 * q^77 - 22 * q^78 - 19 * q^79 - q^80 - 26 * q^81 - 58 * q^82 - 24 * q^83 - 21 * q^84 - 18 * q^85 - 6 * q^86 + 83 * q^87 - 7 * q^88 - 8 * q^89 + 60 * q^90 - 30 * q^91 + 8 * q^92 - 72 * q^93 + 19 * q^94 - 4 * q^95 + q^96 - 16 * q^97 + q^98 + 84 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more