LMFDB - Embedded newform 299.2.i.b.231.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [299,2,Mod(231,299)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(299, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0]))

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

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

chi := DirichletCharacter("299.231");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 299 = 13 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	299.i (of order $6$, 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:	$2.38752702044$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			231.1
Character	$\chi$	$=$	299.231
Dual form			299.2.i.b.277.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.30697 + 1.33193i) q^{2} +(0.800132 + 1.38587i) q^{3} +(2.54808 - 4.41341i) q^{4} -0.558810i q^{5} +(-3.69177 - 2.13144i) q^{6} +(-2.36396 - 1.36484i) q^{7} +8.24775i q^{8} +(0.219577 - 0.380318i) q^{9} +O(q^{10})$	\(q+(-2.30697 + 1.33193i) q^{2} +(0.800132 + 1.38587i) q^{3} +(2.54808 - 4.41341i) q^{4} -0.558810i q^{5} +(-3.69177 - 2.13144i) q^{6} +(-2.36396 - 1.36484i) q^{7} +8.24775i q^{8} +(0.219577 - 0.380318i) q^{9} +(0.744297 + 1.28916i) q^{10} +(4.99132 - 2.88174i) q^{11} +8.15521 q^{12} +(-3.38873 - 1.23148i) q^{13} +7.27147 q^{14} +(0.774438 - 0.447122i) q^{15} +(-5.88927 - 10.2005i) q^{16} +(2.84079 - 4.92039i) q^{17} +1.16984i q^{18} +(-3.97411 - 2.29445i) q^{19} +(-2.46626 - 1.42389i) q^{20} -4.36819i q^{21} +(-7.67656 + 13.2962i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(-11.4303 + 6.59929i) q^{24} +4.68773 q^{25} +(9.45794 - 1.67256i) q^{26} +5.50356 q^{27} +(-12.0471 + 6.95542i) q^{28} +(2.65869 + 4.60499i) q^{29} +(-1.19107 + 2.06300i) q^{30} -1.11426i q^{31} +(12.8873 + 7.44046i) q^{32} +(7.98743 + 4.61155i) q^{33} +15.1349i q^{34} +(-0.762684 + 1.32101i) q^{35} +(-1.11900 - 1.93816i) q^{36} +(-0.473870 + 0.273589i) q^{37} +12.2242 q^{38} +(-1.00476 - 5.68168i) q^{39} +4.60893 q^{40} +(-1.94596 + 1.12350i) q^{41} +(5.81813 + 10.0773i) q^{42} +(-2.37585 + 4.11509i) q^{43} -29.3716i q^{44} +(-0.212526 - 0.122702i) q^{45} +(2.30697 + 1.33193i) q^{46} +10.4136i q^{47} +(9.42439 - 16.3235i) q^{48} +(0.225550 + 0.390664i) q^{49} +(-10.8145 + 6.24373i) q^{50} +9.09202 q^{51} +(-14.0698 + 11.8179i) q^{52} -2.18803 q^{53} +(-12.6965 + 7.33036i) q^{54} +(-1.61035 - 2.78920i) q^{55} +(11.2568 - 19.4974i) q^{56} -7.34346i q^{57} +(-12.2671 - 7.08240i) q^{58} +(-6.99415 - 4.03808i) q^{59} -4.55721i q^{60} +(6.74264 - 11.6786i) q^{61} +(1.48412 + 2.57056i) q^{62} +(-1.03814 + 0.599372i) q^{63} -16.0836 q^{64} +(-0.688162 + 1.89365i) q^{65} -24.5691 q^{66} +(8.25743 - 4.76743i) q^{67} +(-14.4771 - 25.0751i) q^{68} +(0.800132 - 1.38587i) q^{69} -4.06337i q^{70} +(9.07200 + 5.23772i) q^{71} +(3.13677 + 1.81101i) q^{72} -4.46497i q^{73} +(0.728804 - 1.26233i) q^{74} +(3.75081 + 6.49658i) q^{75} +(-20.2527 + 11.6929i) q^{76} -15.7324 q^{77} +(9.88556 + 11.7692i) q^{78} -8.71615 q^{79} +(-5.70015 + 3.29098i) q^{80} +(3.74484 + 6.48626i) q^{81} +(2.99285 - 5.18377i) q^{82} -3.95807i q^{83} +(-19.2786 - 11.1305i) q^{84} +(-2.74956 - 1.58746i) q^{85} -12.6579i q^{86} +(-4.25461 + 7.36921i) q^{87} +(23.7679 + 41.1672i) q^{88} +(6.61753 - 3.82063i) q^{89} +0.653721 q^{90} +(6.33006 + 7.53622i) q^{91} -5.09616 q^{92} +(1.54422 - 0.891555i) q^{93} +(-13.8702 - 24.0239i) q^{94} +(-1.28216 + 2.22077i) q^{95} +23.8134i q^{96} +(0.0736356 + 0.0425135i) q^{97} +(-1.04068 - 0.600834i) q^{98} -2.53105i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} + 16 q^{4} - 9 q^{6} - 3 q^{7} - 16 q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 + 16 * q^4 - 9 * q^6 - 3 * q^7 - 16 * q^9	$ 30 q - 3 q^{3} + 16 q^{4} - 9 q^{6} - 3 q^{7} - 16 q^{9} + 23 q^{10} - 4 q^{12} - 2 q^{13} + 4 q^{14} - 6 q^{15} - 26 q^{16} + 13 q^{17} - 12 q^{19} + 6 q^{20} - 16 q^{22} - 15 q^{23} + 6 q^{24} - 52 q^{25} - 25 q^{26} + 54 q^{27} - 24 q^{28} - q^{29} + 20 q^{30} - 39 q^{32} - 18 q^{33} + 20 q^{35} + 23 q^{36} - 30 q^{37} + 18 q^{38} - 60 q^{39} + 124 q^{40} - 6 q^{41} - 12 q^{42} + 33 q^{43} + 18 q^{45} + 34 q^{48} + 48 q^{49} - 60 q^{50} + 20 q^{51} - 39 q^{52} + 62 q^{53} + 45 q^{54} - 16 q^{55} - 5 q^{56} - 66 q^{58} - 21 q^{59} - 18 q^{61} + 46 q^{62} - 117 q^{63} - 16 q^{64} - 4 q^{65} + 52 q^{66} + 24 q^{67} - 18 q^{68} - 3 q^{69} + 54 q^{71} - 54 q^{72} + 42 q^{74} + 4 q^{75} - 18 q^{76} - 20 q^{77} + 72 q^{79} + 114 q^{80} - 15 q^{81} + 14 q^{82} - 159 q^{84} - 39 q^{85} + 40 q^{87} + 93 q^{88} - 51 q^{89} - 78 q^{90} - 34 q^{91} - 32 q^{92} + 6 q^{93} + 8 q^{94} - 24 q^{95} - 6 q^{97} - 123 q^{98}+O(q^{100}) $ 30 * q - 3 * q^3 + 16 * q^4 - 9 * q^6 - 3 * q^7 - 16 * q^9 + 23 * q^10 - 4 * q^12 - 2 * q^13 + 4 * q^14 - 6 * q^15 - 26 * q^16 + 13 * q^17 - 12 * q^19 + 6 * q^20 - 16 * q^22 - 15 * q^23 + 6 * q^24 - 52 * q^25 - 25 * q^26 + 54 * q^27 - 24 * q^28 - q^29 + 20 * q^30 - 39 * q^32 - 18 * q^33 + 20 * q^35 + 23 * q^36 - 30 * q^37 + 18 * q^38 - 60 * q^39 + 124 * q^40 - 6 * q^41 - 12 * q^42 + 33 * q^43 + 18 * q^45 + 34 * q^48 + 48 * q^49 - 60 * q^50 + 20 * q^51 - 39 * q^52 + 62 * q^53 + 45 * q^54 - 16 * q^55 - 5 * q^56 - 66 * q^58 - 21 * q^59 - 18 * q^61 + 46 * q^62 - 117 * q^63 - 16 * q^64 - 4 * q^65 + 52 * q^66 + 24 * q^67 - 18 * q^68 - 3 * q^69 + 54 * q^71 - 54 * q^72 + 42 * q^74 + 4 * q^75 - 18 * q^76 - 20 * q^77 + 72 * q^79 + 114 * q^80 - 15 * q^81 + 14 * q^82 - 159 * q^84 - 39 * q^85 + 40 * q^87 + 93 * q^88 - 51 * q^89 - 78 * q^90 - 34 * q^91 - 32 * q^92 + 6 * q^93 + 8 * q^94 - 24 * q^95 - 6 * q^97 - 123 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/299\mathbb{Z}\right)^\times$.

$n$	$93$	$235$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−2.30697	+	1.33193i	−1.63128	+	0.941818i	−0.647576	+	0.762001i	$0.724217\pi$
$2$	−2.30697	+	1.33193i	−1.63128	+	0.941818i	−0.983700	+	0.179816i	$0.942450\pi$
$3$	0.800132	+	1.38587i	0.461957	+	0.800132i	0.999058	−	0.0433851i	$-0.0138143\pi$
$3$	0.800132	+	1.38587i	0.461957	+	0.800132i	−0.537102	+	0.843517i	$0.680481\pi$
$4$	2.54808	−	4.41341i	1.27404	−	2.20670i
$5$		−	0.558810i		−	0.249908i	−0.992163	−	0.124954i	$-0.960122\pi$
$5$		−	0.558810i		−	0.249908i	0.992163	−	0.124954i	$-0.0398783\pi$
$6$	−3.69177	−	2.13144i	−1.50716	−	0.870158i
$7$	−2.36396	−	1.36484i	−0.893494	−	0.515859i	−0.0184105	−	0.999831i	$-0.505861\pi$
$7$	−2.36396	−	1.36484i	−0.893494	−	0.515859i	−0.875084	+	0.483971i	$0.839194\pi$
$8$			8.24775i			2.91602i
$9$	0.219577	−	0.380318i	0.0731922	−	0.126773i
$10$	0.744297	+	1.28916i	0.235367	+	0.407668i
$11$	4.99132	−	2.88174i	1.50494	−	0.868877i	0.504956	−	0.863145i	$-0.331509\pi$
$11$	4.99132	−	2.88174i	1.50494	−	0.868877i	0.999984	−	0.00573255i	$-0.00182474\pi$
$12$	8.15521			2.35421
$13$	−3.38873	−	1.23148i	−0.939863	−	0.341550i
$13$	−3.38873	−	1.23148i	−0.939863	−	0.341550i
$14$	7.27147			1.94338
$15$	0.774438	−	0.447122i	0.199959	−	0.115446i
$16$	−5.88927	−	10.2005i	−1.47232	−	2.55013i
$17$	2.84079	−	4.92039i	0.688992	−	1.19337i	−0.283172	−	0.959069i	$-0.591387\pi$
$17$	2.84079	−	4.92039i	0.688992	−	1.19337i	0.972164	−	0.234300i	$-0.0752799\pi$
$18$			1.16984i			0.275735i
$19$	−3.97411	−	2.29445i	−0.911722	−	0.526383i	−0.0307374	−	0.999527i	$-0.509786\pi$
$19$	−3.97411	−	2.29445i	−0.911722	−	0.526383i	−0.880985	+	0.473144i	$0.843119\pi$
$20$	−2.46626	−	1.42389i	−0.551472	−	0.318392i
$21$		−	4.36819i		−	0.953218i
$22$	−7.67656	+	13.2962i	−1.63665	+	2.83476i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$24$	−11.4303	+	6.59929i	−2.33320	+	1.34707i
$25$	4.68773			0.937546
$26$	9.45794	−	1.67256i	1.85485	−	0.328017i
$27$	5.50356			1.05916
$28$	−12.0471	+	6.95542i	−2.27670	+	1.31445i
$29$	2.65869	+	4.60499i	0.493707	+	0.855126i	0.999974	−	0.00725116i	$-0.00230814\pi$
$29$	2.65869	+	4.60499i	0.493707	+	0.855126i	−0.506267	+	0.862377i	$0.668975\pi$
$30$	−1.19107	+	2.06300i	−0.217459	+	0.376650i
$31$		−	1.11426i		−	0.200127i	−0.994981	−	0.100063i	$-0.968095\pi$
$31$		−	1.11426i		−	0.200127i	0.994981	−	0.100063i	$-0.0319046\pi$
$32$	12.8873	+	7.44046i	2.27817	+	1.31530i
$33$	7.98743	+	4.61155i	1.39043	+	0.802767i
$34$			15.1349i			2.59562i
$35$	−0.762684	+	1.32101i	−0.128917	+	0.223291i
$36$	−1.11900	−	1.93816i	−0.186500	−	0.323027i
$37$	−0.473870	+	0.273589i	−0.0779038	+	0.0449778i	−0.538446	−	0.842660i	$-0.680988\pi$
$37$	−0.473870	+	0.273589i	−0.0779038	+	0.0449778i	0.460542	+	0.887638i	$0.347655\pi$
$38$	12.2242			1.98303
$39$	−1.00476	−	5.68168i	−0.160891	−	0.909797i
$40$	4.60893			0.728735
$41$	−1.94596	+	1.12350i	−0.303908	+	0.175461i	−0.644197	−	0.764860i	$-0.722808\pi$
$41$	−1.94596	+	1.12350i	−0.303908	+	0.175461i	0.340289	+	0.940321i	$0.389475\pi$
$42$	5.81813	+	10.0773i	0.897758	+	1.55496i
$43$	−2.37585	+	4.11509i	−0.362313	+	0.627545i	−0.988341	−	0.152256i	$-0.951346\pi$
$43$	−2.37585	+	4.11509i	−0.362313	+	0.627545i	0.626028	+	0.779801i	$0.284680\pi$
$44$		−	29.3716i		−	4.42794i
$45$	−0.212526	−	0.122702i	−0.0316814	−	0.0182913i
$46$	2.30697	+	1.33193i	0.340145	+	0.196383i
$47$			10.4136i			1.51898i	0.650517	+	0.759491i	$0.274552\pi$
$47$			10.4136i			1.51898i	−0.650517	+	0.759491i	$0.725448\pi$
$48$	9.42439	−	16.3235i	1.36029	−	2.35610i
$49$	0.225550	+	0.390664i	0.0322214	+	0.0558092i
$50$	−10.8145	+	6.24373i	−1.52940	+	0.882997i
$51$	9.09202			1.27314
$52$	−14.0698	+	11.8179i	−1.95112	+	1.63885i
$53$	−2.18803			−0.300549			−0.150274	−	0.988644i	$-0.548016\pi$
$53$	−2.18803			−0.300549			−0.150274	+	0.988644i	$0.548016\pi$
$54$	−12.6965	+	7.33036i	−1.72778	+	0.997535i
$55$	−1.61035	−	2.78920i	−0.217139	−	0.376096i
$56$	11.2568	−	19.4974i	1.50426	−	2.60545i
$57$		−	7.34346i		−	0.972665i
$58$	−12.2671	−	7.08240i	−1.61075	−	0.929964i
$59$	−6.99415	−	4.03808i	−0.910561	−	0.525713i	−0.0299495	−	0.999551i	$-0.509535\pi$
$59$	−6.99415	−	4.03808i	−0.910561	−	0.525713i	−0.880612	+	0.473839i	$0.842868\pi$
$60$		−	4.55721i		−	0.588334i
$61$	6.74264	−	11.6786i	0.863306	−	1.49529i	−0.00541251	−	0.999985i	$-0.501723\pi$
$61$	6.74264	−	11.6786i	0.863306	−	1.49529i	0.868719	−	0.495305i	$-0.164944\pi$
$62$	1.48412	+	2.57056i	0.188483	+	0.326462i
$63$	−1.03814	+	0.599372i	−0.130794	+	0.0755138i
$64$	−16.0836			−2.01045
$65$	−0.688162	+	1.89365i	−0.0853560	+	0.234879i
$66$	−24.5691			−3.02424
$67$	8.25743	−	4.76743i	1.00881	−	0.582434i	0.0979642	−	0.995190i	$-0.468767\pi$
$67$	8.25743	−	4.76743i	1.00881	−	0.582434i	0.910842	+	0.412756i	$0.135434\pi$
$68$	−14.4771	−	25.0751i	−1.75561	−	3.04080i
$69$	0.800132	−	1.38587i	0.0963246	−	0.166839i
$70$		−	4.06337i		−	0.485665i
$71$	9.07200	+	5.23772i	1.07665	+	0.621603i	0.929990	−	0.367584i	$-0.119815\pi$
$71$	9.07200	+	5.23772i	1.07665	+	0.621603i	0.146658	+	0.989187i	$0.453148\pi$
$72$	3.13677	+	1.81101i	0.369672	+	0.213430i
$73$		−	4.46497i		−	0.522585i	−0.965260	−	0.261293i	$-0.915851\pi$
$73$		−	4.46497i		−	0.522585i	0.965260	−	0.261293i	$-0.0841488\pi$
$74$	0.728804	−	1.26233i	0.0847217	−	0.146742i
$75$	3.75081	+	6.49658i	0.433106	+	0.750161i
$76$	−20.2527	+	11.6929i	−2.32314	+	1.34127i
$77$	−15.7324			−1.79287
$78$	9.88556	+	11.7692i	1.11932	+	1.33260i
$79$	−8.71615			−0.980644			−0.490322	−	0.871541i	$-0.663121\pi$
$79$	−8.71615			−0.980644			−0.490322	+	0.871541i	$0.663121\pi$
$80$	−5.70015	+	3.29098i	−0.637296	+	0.367943i
$81$	3.74484	+	6.48626i	0.416094	+	0.720695i
$82$	2.99285	−	5.18377i	0.330505	−	0.572452i
$83$		−	3.95807i		−	0.434454i	−0.976121	−	0.217227i	$-0.930299\pi$
$83$		−	3.95807i		−	0.434454i	0.976121	−	0.217227i	$-0.0697012\pi$
$84$	−19.2786	−	11.1305i	−2.10347	−	1.21444i
$85$	−2.74956	−	1.58746i	−0.298232	−	0.172184i
$86$		−	12.6579i		−	1.36493i
$87$	−4.25461	+	7.36921i	−0.456143	+	0.790062i
$88$	23.7679	+	41.1672i	2.53366	+	4.38843i
$89$	6.61753	−	3.82063i	0.701457	−	0.404986i	−0.106433	−	0.994320i	$-0.533943\pi$
$89$	6.61753	−	3.82063i	0.701457	−	0.404986i	0.807890	+	0.589334i	$0.200610\pi$
$90$	0.653721			0.0689082
$91$	6.33006	+	7.53622i	0.663571	+	0.790011i
$92$	−5.09616			−0.531312
$93$	1.54422	−	0.891555i	0.160128	−	0.0924499i
$94$	−13.8702	−	24.0239i	−1.43060	−	2.47788i
$95$	−1.28216	+	2.22077i	−0.131547	+	0.227846i
$96$			23.8134i			2.43045i
$97$	0.0736356	+	0.0425135i	0.00747656	+	0.00431659i	0.503734	−	0.863859i	$-0.331959\pi$
$97$	0.0736356	+	0.0425135i	0.00747656	+	0.00431659i	−0.496257	+	0.868176i	$0.665293\pi$
$98$	−1.04068	−	0.600834i	−0.105124	−	0.0606934i
$99$		−	2.53105i		−	0.254380i
$100$	11.9447	−	20.6889i	1.19447	−	2.06889i
$101$	−1.63653	−	2.83456i	−0.162841	−	0.282049i	0.773045	−	0.634351i	$-0.218733\pi$
$101$	−1.63653	−	2.83456i	−0.162841	−	0.282049i	−0.935887	+	0.352301i	$0.885399\pi$
$102$	−20.9750	+	12.1100i	−2.07684	+	1.19906i
$103$	−6.76941			−0.667010			−0.333505	−	0.942748i	$-0.608231\pi$
$103$	−6.76941			−0.667010			−0.333505	+	0.942748i	$0.608231\pi$
$104$	10.1569	−	27.9494i	0.995968	−	2.74066i
$105$	−2.44099			−0.238216
$106$	5.04772	−	2.91430i	0.490278	−	0.283062i
$107$	7.31816	+	12.6754i	0.707473	+	1.22538i	0.965792	+	0.259320i	$0.0834983\pi$
$107$	7.31816	+	12.6754i	0.707473	+	1.22538i	−0.258318	+	0.966060i	$0.583168\pi$
$108$	14.0235	−	24.2894i	1.34941	−	2.33725i
$109$		−	7.08148i		−	0.678283i	−0.940735	−	0.339141i	$-0.889864\pi$
$109$		−	7.08148i		−	0.678283i	0.940735	−	0.339141i	$-0.110136\pi$
$110$	7.43005	+	4.28974i	0.708427	+	0.409011i
$111$	−0.758318	−	0.437815i	−0.0719764	−	0.0415556i
$112$			32.1515i			3.03803i
$113$	−3.06945	+	5.31644i	−0.288749	+	0.500128i	−0.973511	−	0.228638i	$-0.926573\pi$
$113$	−3.06945	+	5.31644i	−0.288749	+	0.500128i	0.684762	+	0.728767i	$0.259906\pi$
$114$	9.78098	+	16.9412i	0.916073	+	1.58668i
$115$	−0.483944	+	0.279405i	−0.0451280	+	0.0260547i
$116$	27.0983			2.51601
$117$	−1.21244	+	1.01839i	−0.112090	+	0.0941501i
$118$	21.5138			1.98050
$119$	−13.4310	+	7.75441i	−1.23122	+	0.710846i
$120$	3.68775	+	6.38737i	0.336644	+	0.583085i
$121$	11.1089	−	19.2411i	1.00990	−	1.74919i
$122$			35.9229i			3.25231i
$123$	−3.11405	−	1.79790i	−0.280785	−	0.162111i
$124$	−4.91768	−	2.83922i	−0.441620	−	0.254970i
$125$		−	5.41360i		−	0.484207i
$126$	1.59664	−	2.76547i	0.142240	−	0.246368i
$127$	−4.69744	−	8.13620i	−0.416830	−	0.721971i	0.578789	−	0.815478i	$-0.303526\pi$
$127$	−4.69744	−	8.13620i	−0.416830	−	0.721971i	−0.995619	+	0.0935068i	$0.970192\pi$
$128$	11.3300	−	6.54137i	1.00144	−	0.578181i
$129$	−7.60396			−0.669492
$130$	−0.934646	−	5.28519i	−0.0819739	−	0.463542i
$131$	−6.00048			−0.524264			−0.262132	−	0.965032i	$-0.584426\pi$
$131$	−6.00048			−0.524264			−0.262132	+	0.965032i	$0.584426\pi$
$132$	40.7053	−	23.5012i	3.54294	−	2.04552i
$133$	6.26309	+	10.8480i	0.543079	+	0.940641i
$134$	−12.6998	+	21.9967i	−1.09709	+	1.90022i
$135$		−	3.07544i		−	0.264692i
$136$	40.5821	+	23.4301i	3.47989	+	2.00911i
$137$	−4.24555	−	2.45117i	−0.362722	−	0.209418i	0.307552	−	0.951531i	$-0.400490\pi$
$137$	−4.24555	−	2.45117i	−0.362722	−	0.209418i	−0.670274	+	0.742114i	$0.733823\pi$
$138$			4.26288i			0.362881i
$139$	−8.73666	+	15.1323i	−0.741034	+	1.28351i	0.210991	+	0.977488i	$0.432331\pi$
$139$	−8.73666	+	15.1323i	−0.741034	+	1.28351i	−0.952025	+	0.306020i	$0.901003\pi$
$140$	3.88676	+	6.73207i	0.328491	+	0.568963i
$141$	−14.4319	+	8.33228i	−1.21539	+	0.701704i
$142$	−27.9051			−2.34175
$143$	−20.4630	+	3.61873i	−1.71120	+	0.302613i
$144$	−5.17259			−0.431049
$145$	2.57332	−	1.48571i	0.213702	−	0.123381i
$146$	5.94703	+	10.3006i	0.492180	+	0.852481i
$147$	−0.360940	+	0.625166i	−0.0297698	+	0.0515628i
$148$			2.78851i			0.229214i
$149$	12.3147	+	7.10989i	1.00886	+	0.582465i	0.910857	−	0.412721i	$-0.135422\pi$
$149$	12.3147	+	7.10989i	1.00886	+	0.582465i	0.0980015	+	0.995186i	$0.468755\pi$
$150$	−17.3060	−	9.99163i	−1.41303	−	0.815813i
$151$			15.0221i			1.22248i	0.791444	+	0.611242i	$0.209330\pi$
$151$			15.0221i			1.22248i	−0.791444	+	0.611242i	$0.790670\pi$
$152$	18.9241	−	32.7774i	1.53494	−	2.65860i
$153$	−1.24754	−	2.16081i	−0.100858	−	0.174691i
$154$	36.2942	−	20.9545i	2.92467	−	1.68856i
$155$	−0.622659			−0.0500132
$156$	−27.6358	−	10.0430i	−2.21263	−	0.804080i
$157$	−3.93803			−0.314289			−0.157145	−	0.987576i	$-0.550229\pi$
$157$	−3.93803			−0.314289			−0.157145	+	0.987576i	$0.550229\pi$
$158$	20.1079	−	11.6093i	1.59970	−	0.923588i
$159$	−1.75071	−	3.03232i	−0.138841	−	0.240479i
$160$	4.15780	−	7.20153i	0.328703	−	0.569331i
$161$			2.72967i			0.215128i
$162$	−17.2785	−	9.97574i	−1.35753	−	0.783768i
$163$	8.16660	+	4.71499i	0.639657	+	0.369306i	0.784482	−	0.620151i	$-0.212929\pi$
$163$	8.16660	+	4.71499i	0.639657	+	0.369306i	−0.144825	+	0.989457i	$0.546262\pi$
$164$			11.4511i			0.894179i
$165$	2.57698	−	4.46346i	0.200618	−	0.347480i
$166$	5.27187	+	9.13115i	0.409177	+	0.708715i
$167$	20.6421	−	11.9177i	1.59733	−	0.922219i	0.605332	−	0.795973i	$-0.293040\pi$
$167$	20.6421	−	11.9177i	1.59733	−	0.922219i	0.991999	−	0.126246i	$-0.0402930\pi$
$168$	36.0278			2.77960
$169$	9.96692	+	8.34628i	0.766687	+	0.642022i
$170$	8.45756			0.648665
$171$	−1.74524	+	1.00762i	−0.133462	+	0.0770543i
$172$	12.1077	+	20.9711i	0.923203	+	1.59903i
$173$	0.937299	−	1.62345i	0.0712616	−	0.123429i	−0.828193	−	0.560443i	$-0.810631\pi$
$173$	0.937299	−	1.62345i	0.0712616	−	0.123429i	0.899454	+	0.437015i	$0.143964\pi$
$174$		−	22.6674i		−	1.71841i
$175$	−11.0816	−	6.39798i	−0.837692	−	0.483642i
$176$	−58.7905	−	33.9427i	−4.43150	−	2.55853i
$177$		−	12.9240i		−	0.971426i
$178$	−10.1776	+	17.6282i	−0.762846	+	1.32129i
$179$	−1.82905	−	3.16800i	−0.136709	−	0.236788i	0.789540	−	0.613699i	$-0.210319\pi$
$179$	−1.82905	−	3.16800i	−0.136709	−	0.236788i	−0.926249	+	0.376912i	$0.876986\pi$
$180$	−1.08306	+	0.625308i	−0.0807269	+	0.0466077i
$181$	0.693990			0.0515839			0.0257919	−	0.999667i	$-0.491789\pi$
$181$	0.693990			0.0515839			0.0257919	+	0.999667i	$0.491789\pi$
$182$	−24.6410	−	8.95465i	−1.82651	−	0.663763i
$183$	21.5800			1.59524
$184$	7.14276	−	4.12387i	0.526571	−	0.304016i
$185$	0.152884	+	0.264804i	0.0112403	+	0.0194687i
$186$	−2.37498	+	4.11358i	−0.174142	+	0.301623i
$187$		−	32.7457i		−	2.39460i
$188$	45.9595	+	26.5348i	3.35194	+	1.93525i
$189$	−13.0102	−	7.51145i	−0.946353	−	0.546377i
$190$		−	6.83101i		−	0.495573i
$191$	−7.09885	+	12.2956i	−0.513655	+	0.889676i	0.486220	+	0.873837i	$0.338375\pi$
$191$	−7.09885	+	12.2956i	−0.513655	+	0.889676i	−0.999875	+	0.0158396i	$0.994958\pi$
$192$	−12.8690	−	22.2898i	−0.928742	−	1.60863i
$193$	−22.5921	+	13.0436i	−1.62622	+	0.938897i	−0.641009	+	0.767533i	$0.721484\pi$
$193$	−22.5921	+	13.0436i	−1.62622	+	0.938897i	−0.985208	+	0.171364i	$0.945183\pi$
$194$	−0.226500			−0.0162618
$195$	−3.17498	+	0.561471i	−0.227365	+	0.0402078i
$196$	2.29888			0.164206
$197$	12.3621	−	7.13724i	0.880761	−	0.508507i	0.00985156	−	0.999951i	$-0.496864\pi$
$197$	12.3621	−	7.13724i	0.880761	−	0.508507i	0.870909	+	0.491444i	$0.163531\pi$
$198$	3.37119	+	5.83907i	0.239580	+	0.414964i
$199$	−9.06467	+	15.7005i	−0.642577	+	1.11298i	0.342278	+	0.939599i	$0.388801\pi$
$199$	−9.06467	+	15.7005i	−0.642577	+	1.11298i	−0.984855	+	0.173378i	$0.944532\pi$
$200$			38.6632i			2.73390i
$201$	13.2141	+	7.62915i	0.932049	+	0.538119i
$202$	7.55088	+	4.35950i	0.531278	+	0.306734i
$203$		−	14.5147i		−	1.01873i
$204$	23.1672	−	40.1268i	1.62203	−	2.80944i
$205$	0.627824	+	1.08742i	0.0438491	+	0.0759489i
$206$	15.6168	−	9.01639i	1.08808	−	0.628202i
$207$	−0.439153			−0.0305233
$208$	7.39542	+	41.8193i	0.512780	+	2.89964i
$209$	−26.4480			−1.82945
$210$	5.63130	−	3.25123i	0.388597	−	0.224356i
$211$	8.98193	+	15.5572i	0.618342	+	1.07100i	0.989788	+	0.142545i	$0.0455285\pi$
$211$	8.98193	+	15.5572i	0.618342	+	1.07100i	−0.371447	+	0.928454i	$0.621138\pi$
$212$	−5.57528	+	9.65666i	−0.382912	+	0.663222i
$213$			16.7635i			1.14862i
$214$	−33.7656	−	19.4946i	−2.30817	−	1.33262i
$215$	2.29955	+	1.32765i	0.156828	+	0.0905448i
$216$			45.3919i			3.08853i
$217$	−1.52078	+	2.63407i	−0.103237	+	0.178812i
$218$	9.43204	+	16.3368i	0.638819	+	1.10647i
$219$	6.18787	−	3.57257i	0.418137	−	0.241412i
$220$	−16.4132			−1.10658
$221$	−15.6860	+	13.1755i	−1.05515	+	0.886279i
$222$	2.33256			0.156551
$223$	−5.23742	+	3.02382i	−0.350723	+	0.202490i	−0.665004	−	0.746840i	$-0.731570\pi$
$223$	−5.23742	+	3.02382i	−0.350723	+	0.202490i	0.314280	+	0.949330i	$0.398237\pi$
$224$	−20.3100	−	35.1779i	−1.35702	−	2.35043i
$225$	1.02932	−	1.78283i	0.0686211	−	0.118855i
$226$		−	16.3532i		−	1.08780i
$227$	7.31633	+	4.22408i	0.485602	+	0.280362i	0.722748	−	0.691112i	$-0.242879\pi$
$227$	7.31633	+	4.22408i	0.485602	+	0.280362i	−0.237146	+	0.971474i	$0.576212\pi$
$228$	−32.4097	−	18.7117i	−2.14638	−	1.23921i
$229$		−	0.620033i		−	0.0409729i	−0.999790	−	0.0204865i	$-0.993479\pi$
$229$		−	0.620033i		−	0.0409729i	0.999790	−	0.0204865i	$-0.00652150\pi$
$230$	0.744297	−	1.28916i	0.0490775	−	0.0850047i
$231$	−12.5880	−	21.8031i	−0.828230	−	1.43454i
$232$	−37.9808	+	21.9282i	−2.49356	+	1.43966i
$233$	−19.2851			−1.26341			−0.631705	−	0.775209i	$-0.717645\pi$
$233$	−19.2851			−1.26341			−0.631705	+	0.775209i	$0.717645\pi$
$234$	1.44064	−	3.96428i	0.0941774	−	0.259153i
$235$	5.81924			0.379605
$236$	−35.6433	+	20.5787i	−2.32018	+	1.33956i
$237$	−6.97408	−	12.0795i	−0.453015	−	0.784645i
$238$	20.6567	−	35.7784i	1.33897	−	2.31917i
$239$			18.9646i			1.22672i	0.789803	+	0.613360i	$0.210183\pi$
$239$			18.9646i			1.22672i	−0.789803	+	0.613360i	$0.789817\pi$
$240$	−9.12175	−	5.26645i	−0.588807	−	0.339948i
$241$	15.6066	+	9.01046i	1.00531	+	0.580415i	0.909815	−	0.415015i	$-0.136224\pi$
$241$	15.6066	+	9.01046i	1.00531	+	0.580415i	0.0954937	+	0.995430i	$0.469557\pi$
$242$			59.1849i			3.80455i
$243$	2.26259	−	3.91893i	0.145146	−	0.251399i
$244$	−34.3616	−	59.5160i	−2.19977	−	3.81012i
$245$	0.218307	−	0.126040i	0.0139471	−	0.00805238i
$246$	9.57871			0.610716
$247$	10.6416	+	12.6693i	0.677108	+	0.806127i
$248$	9.19013			0.583574
$249$	5.48536	−	3.16698i	0.347621	−	0.200699i
$250$	7.21055	+	12.4890i	0.456035	+	0.789876i
$251$	4.10379	−	7.10797i	0.259029	−	0.448651i	−0.706953	−	0.707260i	$-0.749931\pi$
$251$	4.10379	−	7.10797i	0.259029	−	0.448651i	0.965982	+	0.258609i	$0.0832642\pi$
$252$			6.10899i			0.384830i
$253$	−4.99132	−	2.88174i	−0.313802	−	0.181173i
$254$	21.6737	+	12.5133i	1.35993	+	0.785156i
$255$		−	5.08072i		−	0.318167i
$256$	−1.34167	+	2.32384i	−0.0838544	+	0.145240i
$257$	−10.3559	−	17.9369i	−0.645982	−	1.11887i	−0.984074	−	0.177760i	$-0.943115\pi$
$257$	−10.3559	−	17.9369i	−0.645982	−	1.11887i	0.338092	−	0.941113i	$-0.390219\pi$
$258$	17.5421	−	10.1280i	1.09213	−	0.630539i
$259$	1.49362			0.0928088
$260$	6.60397	+	7.86232i	0.409561	+	0.487601i
$261$	2.33515			0.144542
$262$	13.8429	−	7.99223i	0.855220	−	0.493761i
$263$	10.3883	+	17.9931i	0.640572	+	1.10950i	0.985305	+	0.170803i	$0.0546362\pi$
$263$	10.3883	+	17.9931i	0.640572	+	1.10950i	−0.344733	+	0.938701i	$0.612030\pi$
$264$	−38.0349	+	65.8783i	−2.34089	+	4.05453i
$265$			1.22269i			0.0751094i
$266$	−28.8976	−	16.6840i	−1.77182	−	1.02296i
$267$	10.5898	+	6.11402i	0.648085	+	0.374172i
$268$		−	48.5912i		−	2.96818i
$269$	−4.63167	+	8.02229i	−0.282398	+	0.489128i	−0.971975	−	0.235085i	$-0.924463\pi$
$269$	−4.63167	+	8.02229i	−0.282398	+	0.489128i	0.689577	+	0.724213i	$0.257797\pi$
$270$	4.09628	+	7.09496i	0.249292	+	0.431786i
$271$	−12.7302	+	7.34981i	−0.773307	+	0.446469i	−0.834053	−	0.551684i	$-0.813985\pi$
$271$	−12.7302	+	7.34981i	−0.773307	+	0.446469i	0.0607461	+	0.998153i	$0.480652\pi$
$272$	−66.9207			−4.05766
$273$	−5.37933	+	14.8026i	−0.325572	+	0.895895i
$274$	13.0592			0.788933
$275$	23.3980	−	13.5088i	1.41095	−	0.814613i
$276$	−4.07760	−	7.06262i	−0.245443	−	0.425120i
$277$	1.36006	−	2.35569i	0.0817180	−	0.141540i	−0.822270	−	0.569098i	$-0.807293\pi$
$277$	1.36006	−	2.35569i	0.0817180	−	0.141540i	0.903988	+	0.427558i	$0.140626\pi$
$278$		−	46.5465i		−	2.79167i
$279$	−0.423773	−	0.244665i	−0.0253706	−	0.0146477i
$280$	−10.8953	−	6.29042i	−0.651121	−	0.375925i
$281$		−	5.48808i		−	0.327391i	−0.986511	−	0.163696i	$-0.947659\pi$
$281$		−	5.48808i		−	0.327391i	0.986511	−	0.163696i	$-0.0523415\pi$
$282$	22.1960	−	38.4447i	1.32175	−	2.28935i
$283$	−5.91222	−	10.2403i	−0.351445	−	0.608721i	0.635058	−	0.772465i	$-0.280976\pi$
$283$	−5.91222	−	10.2403i	−0.351445	−	0.608721i	−0.986503	+	0.163744i	$0.947643\pi$
$284$	46.2324	−	26.6923i	2.74339	−	1.58390i
$285$	−4.10360			−0.243076
$286$	42.3877	−	35.6036i	2.50644	−	2.10529i
$287$	6.13357			0.362053
$288$	5.65948	−	3.26750i	0.333488	−	0.192539i
$289$	−7.64015	−	13.2331i	−0.449421	−	0.778419i
$290$	−3.95771	+	6.85496i	−0.232405	+	0.402537i
$291$			0.136066i			0.00797632i
$292$	−19.7057	−	11.3771i	−1.15319	−	0.665795i
$293$	−4.58102	−	2.64485i	−0.267626	−	0.154514i	0.360182	−	0.932882i	$-0.382714\pi$
$293$	−4.58102	−	2.64485i	−0.267626	−	0.154514i	−0.627808	+	0.778368i	$0.716048\pi$
$294$		−	1.92299i		−	0.112151i
$295$	−2.25652	+	3.90840i	−0.131380	+	0.227556i
$296$	−2.25650	−	3.90836i	−0.131156	−	0.227169i
$297$	27.4700	−	15.8598i	1.59397	−	0.920280i
$298$	−37.8795			−2.19430
$299$	0.627872	+	3.55046i	0.0363108	+	0.205328i
$300$	38.2294			2.20718
$301$	11.2328	−	6.48528i	0.647449	−	0.373805i
$302$	−20.0085	−	34.6557i	−1.15136	−	1.99421i
$303$	2.61889	−	4.53605i	0.150451	−	0.260589i
$304$			54.0506i			3.10001i
$305$	−6.52612	−	3.76786i	−0.373684	−	0.215747i
$306$	5.75609	+	3.32328i	0.329054	+	0.189979i
$307$		−	18.3626i		−	1.04801i	−0.851715	−	0.524005i	$-0.824437\pi$
$307$		−	18.3626i		−	1.04801i	0.851715	−	0.524005i	$-0.175563\pi$
$308$	−40.0874	+	69.4335i	−2.28419	+	3.95634i
$309$	−5.41642	−	9.38152i	−0.308130	−	0.533696i
$310$	1.43646	−	0.829339i	0.0815853	−	0.0471033i
$311$	12.2571			0.695035			0.347518	−	0.937673i	$-0.387025\pi$
$311$	12.2571			0.695035			0.347518	+	0.937673i	$0.387025\pi$
$312$	46.8611	−	8.28702i	2.65298	−	0.469160i
$313$	31.9255			1.80454			0.902268	−	0.431175i	$-0.141901\pi$
$313$	31.9255			1.80454			0.902268	+	0.431175i	$0.141901\pi$
$314$	9.08493	−	5.24519i	0.512692	−	0.296003i
$315$	0.334935	+	0.580125i	0.0188715	+	0.0326863i
$316$	−22.2095	+	38.4679i	−1.24938	+	2.16399i
$317$			23.7008i			1.33117i	0.746323	+	0.665584i	$0.231818\pi$
$317$			23.7008i			1.33117i	−0.746323	+	0.665584i	$0.768182\pi$
$318$	8.07769	+	4.66366i	0.452975	+	0.261525i
$319$	26.5408	+	15.3233i	1.48600	+	0.857942i
$320$			8.98769i			0.502427i
$321$	−11.7110	+	20.2840i	−0.653644	+	1.13214i
$322$	−3.63573	−	6.29727i	−0.202611	−	0.350933i
$323$	−22.5792	+	13.0361i	−1.25634	+	0.725348i
$324$	38.1686			2.12048
$325$	−15.8854	−	5.77284i	−0.881165	−	0.320219i
$326$	−25.1201			−1.39128
$327$	9.81401	−	5.66612i	0.542716	−	0.313337i
$328$	−9.26635	−	16.0498i	−0.511649	−	0.886201i
$329$	14.2129	−	24.6174i	0.783581	−	1.35720i
$330$			13.7294i			0.755781i
$331$	19.5689	+	11.2981i	1.07560	+	0.621000i	0.929707	−	0.368300i	$-0.120060\pi$
$331$	19.5689	+	11.2981i	1.07560	+	0.621000i	0.145897	+	0.989300i	$0.453393\pi$
$332$	−17.4686	−	10.0855i	−0.958711	−	0.553512i
$333$			0.240295i			0.0131681i
$334$	−31.7471	+	54.9876i	−1.73712	+	3.00879i
$335$	−2.66409	−	4.61434i	−0.145555	−	0.252108i
$336$	−44.5578	+	25.7255i	−2.43083	+	1.40344i
$337$	7.54955			0.411250			0.205625	−	0.978631i	$-0.434077\pi$
$337$	7.54955			0.411250			0.205625	+	0.978631i	$0.434077\pi$
$338$	−34.1101	−	5.97938i	−1.85534	−	0.325236i
$339$	−9.82385			−0.533558
$340$	−14.0122	+	8.08996i	−0.759919	+	0.438740i
$341$	−3.21100	−	5.56162i	−0.173886	−	0.301179i
$342$	2.68415	−	4.64908i	0.145142	−	0.251394i
$343$			17.8763i			0.965232i
$344$	−33.9402	−	19.5954i	−1.82993	−	1.05651i
$345$	−0.774438	−	0.447122i	−0.0416943	−	0.0240722i
$346$			4.99367i			0.268462i
$347$	−8.09992	+	14.0295i	−0.434827	+	0.753142i	−0.997281	−	0.0736862i	$-0.976524\pi$
$347$	−8.09992	+	14.0295i	−0.434827	+	0.753142i	0.562455	+	0.826828i	$0.309857\pi$
$348$	21.6822	+	37.5547i	1.16229	+	2.01314i
$349$	−0.0270492	+	0.0156169i	−0.00144791	+	0.000835951i	−0.500724	−	0.865607i	$-0.666933\pi$
$349$	−0.0270492	+	0.0156169i	−0.00144791	+	0.000835951i	0.499276	+	0.866443i	$0.333599\pi$
$350$	34.0867			1.82201
$351$	−18.6500	−	6.77751i	−0.995465	−	0.361757i
$352$	85.7659			4.57134
$353$	13.0263	−	7.52073i	0.693319	−	0.400288i	−0.111535	−	0.993760i	$-0.535577\pi$
$353$	13.0263	−	7.52073i	0.693319	−	0.400288i	0.804854	+	0.593473i	$0.202243\pi$
$354$	17.2138	+	29.8153i	0.914906	+	1.58466i
$355$	2.92689	−	5.06953i	0.155343	−	0.269063i
$356$		−	38.9411i		−	2.06388i
$357$	−21.4932	−	12.4091i	−1.13754	−	0.656760i
$358$	8.43912	+	4.87233i	0.446021	+	0.257511i
$359$			15.9636i			0.842528i	0.906938	+	0.421264i	$0.138413\pi$
$359$			15.9636i			0.842528i	−0.906938	+	0.421264i	$0.861587\pi$
$360$	1.01201	−	1.75286i	0.0533377	−	0.0923837i
$361$	1.02901	+	1.78229i	0.0541583	+	0.0938050i
$362$	−1.60102	+	0.924347i	−0.0841475	+	0.0485826i
$363$	35.5542			1.86611
$364$	49.3899	−	8.73423i	2.58873	−	0.457798i
$365$	−2.49507			−0.130598
$366$	−49.7845	+	28.7431i	−2.60228	+	1.50243i
$367$	12.6209	+	21.8601i	0.658807	+	1.14109i	0.980925	+	0.194388i	$0.0622720\pi$
$367$	12.6209	+	21.8601i	0.658807	+	1.14109i	−0.322118	+	0.946700i	$0.604395\pi$
$368$	−5.88927	+	10.2005i	−0.306999	+	0.531739i
$369$			0.986778i			0.0513696i
$370$	−0.705400	−	0.407263i	−0.0366720	−	0.0211726i
$371$	5.17242	+	2.98630i	0.268539	+	0.155041i
$372$		−	9.08701i		−	0.471140i
$373$	17.3857	−	30.1129i	0.900196	−	1.55918i	0.0729563	−	0.997335i	$-0.476757\pi$
$373$	17.3857	−	30.1129i	0.900196	−	1.55918i	0.827239	−	0.561850i	$-0.189910\pi$
$374$	43.6150	+	75.5433i	2.25528	+	3.90625i
$375$	7.50255	−	4.33160i	0.387430	−	0.223683i
$376$	−85.8889			−4.42938
$377$	−3.33864	−	18.8792i	−0.171949	−	0.972327i
$378$	40.0189			2.05835
$379$	3.98579	−	2.30120i	0.204737	−	0.118205i	−0.394126	−	0.919056i	$-0.628953\pi$
$379$	3.98579	−	2.30120i	0.204737	−	0.118205i	0.598863	+	0.800852i	$0.295619\pi$
$380$	6.53411	+	11.3174i	0.335193	+	0.580571i
$381$	7.51714	−	13.0201i	0.385115	−	0.667038i
$382$		−	37.8207i		−	1.93508i
$383$	31.9942	+	18.4718i	1.63482	+	0.943866i	0.982576	+	0.185862i	$0.0595076\pi$
$383$	31.9942	+	18.4718i	1.63482	+	0.943866i	0.652249	+	0.758005i	$0.273826\pi$
$384$	18.1310	+	10.4679i	0.925242	+	0.534189i
$385$			8.79143i			0.448053i
$386$	34.7463	−	60.1823i	1.76854	−	3.06320i
$387$	1.04336	+	1.80715i	0.0530370	+	0.0918628i
$388$	0.375259	−	0.216656i	0.0190509	−	0.0109990i
$389$	−28.6821			−1.45424			−0.727121	−	0.686509i	$-0.759142\pi$
$389$	−28.6821			−1.45424			−0.727121	+	0.686509i	$0.759142\pi$
$390$	6.57675	−	5.52415i	0.333027	−	0.279726i
$391$	−5.68158			−0.287330
$392$	−3.22210	+	1.86028i	−0.162741	+	0.0939583i
$393$	−4.80118	−	8.31588i	−0.242187	−	0.419481i
$394$	−19.0126	+	32.9308i	−0.957842	+	1.65903i
$395$			4.87068i			0.245070i
$396$	−11.1706	−	6.44933i	−0.561342	−	0.324091i
$397$	−8.09152	−	4.67164i	−0.406102	−	0.234463i	0.283012	−	0.959116i	$-0.408667\pi$
$397$	−8.09152	−	4.67164i	−0.406102	−	0.234463i	−0.689113	+	0.724653i	$0.742000\pi$
$398$		−	48.2940i		−	2.42076i
$399$	−10.0226	+	17.3597i	−0.501758	+	0.869070i
$400$	−27.6073	−	47.8173i	−1.38037	−	2.39086i
$401$	−10.5084	+	6.06703i	−0.524764	+	0.302973i	−0.738882	−	0.673835i	$-0.764646\pi$
$401$	−10.5084	+	6.06703i	−0.524764	+	0.302973i	0.214117	+	0.976808i	$0.431312\pi$
$402$	−40.6460			−2.02724
$403$	−1.37219	+	3.77592i	−0.0683534	+	0.188092i
$404$	−16.6801			−0.829865
$405$	3.62459	−	2.09266i	0.180107	−	0.103985i
$406$	19.3326	+	33.4851i	0.959461	+	1.66184i
$407$	−1.57683	+	2.73114i	−0.0781604	+	0.135378i
$408$			74.9887i			3.71250i
$409$	6.03267	+	3.48297i	0.298296	+	0.172222i	0.641677	−	0.766975i	$-0.278239\pi$
$409$	6.03267	+	3.48297i	0.298296	+	0.172222i	−0.343381	+	0.939196i	$0.611572\pi$
$410$	−2.89674	−	1.67244i	−0.143060	−	0.0825957i
$411$		−	7.84504i		−	0.386967i
$412$	−17.2490	+	29.8762i	−0.849798	+	1.47189i
$413$	11.0226	+	19.0917i	0.542387	+	0.939443i
$414$	1.01311	−	0.584922i	0.0497919	−	0.0287473i
$415$	−2.21181			−0.108573
$416$	−34.5086	−	41.0840i	−1.69192	−	2.01431i
$417$	−27.9619			−1.36930
$418$	61.0149	−	35.2270i	2.98434	−	1.72301i
$419$	14.6905	+	25.4447i	0.717677	+	1.24305i	0.961918	+	0.273339i	$0.0881281\pi$
$419$	14.6905	+	25.4447i	0.717677	+	1.24305i	−0.244240	+	0.969715i	$0.578539\pi$
$420$	−6.21984	+	10.7731i	−0.303497	+	0.525673i
$421$		−	3.72153i		−	0.181376i	−0.995879	−	0.0906882i	$-0.971093\pi$
$421$		−	3.72153i		−	0.181376i	0.995879	−	0.0906882i	$-0.0289067\pi$
$422$	−41.4421	−	23.9266i	−2.01737	−	1.16473i
$423$	3.96049	+	2.28659i	0.192565	+	0.111178i
$424$		−	18.0463i		−	0.876407i
$425$	13.3168	−	23.0655i	0.645962	−	1.11884i
$426$	−22.3278	−	38.6729i	−1.08179	−	1.87371i
$427$	−31.8787	+	18.4052i	−1.54272	+	0.890689i
$428$	74.5890			3.60540
$429$	−21.3882	−	25.4636i	−1.03263	−	1.22939i
$430$	−7.07334			−0.341107
$431$	−2.74790	+	1.58650i	−0.132362	+	0.0764192i	−0.564719	−	0.825283i	$-0.691015\pi$
$431$	−2.74790	+	1.58650i	−0.132362	+	0.0764192i	0.432357	+	0.901703i	$0.357682\pi$
$432$	−32.4119	−	56.1391i	−1.55942	−	2.70099i
$433$	−0.647589	+	1.12166i	−0.0311211	+	0.0539034i	−0.881166	−	0.472806i	$-0.843241\pi$
$433$	−0.647589	+	1.12166i	−0.0311211	+	0.0539034i	0.850045	+	0.526710i	$0.176574\pi$
$434$		−	8.10230i		−	0.388923i
$435$	4.11799	+	2.37752i	0.197442	+	0.113993i
$436$	−31.2534	−	18.0442i	−1.49677	−	0.864160i
$437$			4.58890i			0.219517i
$438$	−9.51683	+	16.4836i	−0.454732	+	0.787618i
$439$	11.5494	+	20.0042i	0.551224	+	0.954748i	0.998187	+	0.0601955i	$0.0191724\pi$
$439$	11.5494	+	20.0042i	0.551224	+	0.954748i	−0.446962	+	0.894553i	$0.647494\pi$
$440$	23.0046	−	13.2817i	1.09670	−	0.633182i
$441$	0.198102			0.00943343
$442$	18.6383	−	51.2881i	0.886535	−	2.43953i
$443$	−37.2235			−1.76854			−0.884272	−	0.466973i	$-0.845345\pi$
$443$	−37.2235			−1.76854			−0.884272	+	0.466973i	$0.845345\pi$
$444$	−3.86451	+	2.23118i	−0.183402	+	0.105887i
$445$	−2.13501	−	3.69794i	−0.101209	−	0.175299i
$446$	8.05505	−	13.9518i	0.381418	−	0.660635i
$447$			22.7554i			1.07629i
$448$	38.0211	+	21.9515i	1.79633	+	1.03711i
$449$	30.9960	+	17.8955i	1.46279	+	0.844542i	0.999140	−	0.0414757i	$-0.0132059\pi$
$449$	30.9960	+	17.8955i	1.46279	+	0.844542i	0.463651	+	0.886018i	$0.346539\pi$
$450$			5.48391i			0.258514i
$451$	−6.47527	+	11.2155i	−0.304909	+	0.528117i
$452$	15.6424	+	27.0934i	0.735756	+	1.27437i
$453$	−20.8187	+	12.0197i	−0.978149	+	0.564735i
$454$	−22.5048			−1.05620
$455$	4.21132	−	3.53730i	0.197430	−	0.165831i
$456$	60.5670			2.83631
$457$	−25.2246	+	14.5634i	−1.17996	+	0.681249i	−0.956005	−	0.293352i	$-0.905229\pi$
$457$	−25.2246	+	14.5634i	−1.17996	+	0.681249i	−0.223952	+	0.974600i	$0.571896\pi$
$458$	0.825841	+	1.43040i	0.0385890	+	0.0668381i
$459$	15.6344	−	27.0796i	0.729753	−	1.26397i
$460$			2.84779i			0.132779i
$461$	−11.8444	−	6.83839i	−0.551651	−	0.318496i	0.198137	−	0.980174i	$-0.436511\pi$
$461$	−11.8444	−	6.83839i	−0.551651	−	0.318496i	−0.749788	+	0.661679i	$0.769844\pi$
$462$	58.0804	+	33.5327i	2.70214	+	1.56008i
$463$		−	35.9093i		−	1.66885i	−0.551122	−	0.834425i	$-0.685800\pi$
$463$		−	35.9093i		−	1.66885i	0.551122	−	0.834425i	$-0.314200\pi$
$464$	31.3155	−	54.2401i	1.45379	−	2.51803i
$465$	−0.498210	−	0.862925i	−0.0231039	−	0.0400172i
$466$	44.4903	−	25.6865i	2.06097	−	1.18990i
$467$	−22.6718			−1.04912			−0.524562	−	0.851372i	$-0.675771\pi$
$467$	−22.6718			−1.04912			−0.524562	+	0.851372i	$0.675771\pi$
$468$	1.40518	+	7.94592i	0.0649542	+	0.367300i
$469$	−26.0270			−1.20182
$470$	−13.4248	+	7.75082i	−0.619241	+	0.357519i
$471$	−3.15095	−	5.45760i	−0.145188	−	0.251473i
$472$	33.3050	−	57.6860i	1.53299	−	2.65521i
$473$			27.3863i			1.25922i
$474$	32.1780	+	18.5780i	1.47798	+	0.853315i
$475$	−18.6295	−	10.7558i	−0.854782	−	0.493508i
$476$			79.0355i			3.62259i
$477$	−0.480440	+	0.832147i	−0.0219978	+	0.0381014i
$478$	−25.2596	−	43.7509i	−1.15535	−	2.00112i
$479$	12.4047	−	7.16185i	0.566785	−	0.327233i	−0.189079	−	0.981962i	$-0.560550\pi$
$479$	12.4047	−	7.16185i	0.566785	−	0.327233i	0.755864	+	0.654728i	$0.227217\pi$
$480$	13.3072			0.607387
$481$	1.94274	−	0.343558i	0.0885811	−	0.0156649i
$482$	−48.0053			−2.18658
$483$	−3.78297	+	2.18410i	−0.172131	+	0.0993799i
$484$	−56.6125	−	98.0558i	−2.57330	−	4.45708i
$485$	0.0237570	−	0.0411483i	0.00107875	−	0.00186845i
$486$			12.0545i			0.546802i
$487$	−30.5273	−	17.6249i	−1.38332	−	0.798661i	−0.390771	−	0.920488i	$-0.627792\pi$
$487$	−30.5273	−	17.6249i	−1.38332	−	0.798661i	−0.992551	+	0.121827i	$0.961125\pi$
$488$	96.3221	+	55.6116i	4.36030	+	2.51742i
$489$			15.0905i			0.682414i
$490$	−0.335752	+	0.581540i	−0.0151677	+	0.0262713i
$491$	−3.78223	−	6.55101i	−0.170690	−	0.295643i	0.767972	−	0.640484i	$-0.221266\pi$
$491$	−3.78223	−	6.55101i	−0.170690	−	0.295643i	−0.938661	+	0.344841i	$0.887933\pi$
$492$	−15.8697	+	9.16238i	−0.715462	+	0.413072i
$493$	30.2111			1.36064
$494$	−41.4245	−	15.0538i	−1.86377	−	0.677304i
$495$	−1.41438			−0.0635715
$496$	−11.3660	+	6.56217i	−0.510349	+	0.294650i
$497$	−14.2973	−	24.7636i	−0.641320	−	1.11080i
$498$	−8.43639	+	14.6123i	−0.378044	+	0.654791i
$499$		−	18.0491i		−	0.807989i	−0.914761	−	0.403995i	$-0.867621\pi$
$499$		−	18.0491i		−	0.807989i	0.914761	−	0.403995i	$-0.132379\pi$
$500$	−23.8924	−	13.7943i	−1.06850	−	0.616900i
$501$	33.0328	+	19.0715i	1.47580	+	0.852051i
$502$			21.8639i			0.975832i
$503$	21.5080	−	37.2530i	0.958995	−	1.66103i	0.234045	−	0.972226i	$-0.424804\pi$
$503$	21.5080	−	37.2530i	0.958995	−	1.66103i	0.724950	−	0.688802i	$-0.241863\pi$
$504$	−4.94347	−	8.56234i	−0.220200	−	0.381397i
$505$	−1.58398	+	0.914512i	−0.0704863	+	0.0406953i
$506$	15.3531			0.682529
$507$	−3.59200	+	20.4910i	−0.159526	+	0.910037i
$508$	−47.8778			−2.12423
$509$	−15.3954	+	8.88853i	−0.682388	+	0.393977i	−0.800754	−	0.598993i	$-0.795568\pi$
$509$	−15.3954	+	8.88853i	−0.682388	+	0.393977i	0.118366	+	0.992970i	$0.462234\pi$
$510$	6.76716	+	11.7211i	0.299655	+	0.519018i
$511$	−6.09395	+	10.5550i	−0.269580	+	0.466927i
$512$			19.0174i			0.840459i
$513$	−21.8717	−	12.6276i	−0.965659	−	0.557524i
$514$	47.7815	+	27.5866i	2.10755	+	1.21679i
$515$			3.78282i			0.166691i
$516$	−19.3755	+	33.5594i	−0.852959	+	1.47737i
$517$	30.0094	+	51.9777i	1.31981	+	2.28598i
$518$	−3.44573	+	1.98939i	−0.151397	+	0.0874090i
$519$	2.99985			0.131679
$520$	−15.6184	−	5.67579i	−0.684912	−	0.248900i
$521$	21.0124			0.920569			0.460285	−	0.887771i	$-0.347747\pi$
$521$	21.0124			0.920569			0.460285	+	0.887771i	$0.347747\pi$
$522$	−5.38712	+	3.11026i	−0.235788	+	0.136132i
$523$	−6.70643	−	11.6159i	−0.293252	−	0.507927i	0.681325	−	0.731981i	$-0.261404\pi$
$523$	−6.70643	−	11.6159i	−0.293252	−	0.507927i	−0.974577	+	0.224054i	$0.928071\pi$
$524$	−15.2897	+	26.4826i	−0.667934	+	1.15690i
$525$		−	20.4769i		−	0.893686i
$526$	−47.9312	−	27.6731i	−2.08990	−	1.20660i
$527$	−5.48259	−	3.16537i	−0.238825	−	0.137886i
$528$		−	108.635i		−	4.72771i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	−1.62854	−	2.82072i	−0.0707394	−	0.122524i
$531$	−3.07151	+	1.77333i	−0.133292	+	0.0769562i
$532$	63.8355			2.76762
$533$	7.97789	−	1.41083i	0.345561	−	0.0611098i
$534$	−32.5738			−1.40961
$535$	7.08316	−	4.08946i	0.306232	−	0.176803i
$536$	39.3206	+	68.1052i	1.69839	+	2.94170i
$537$	2.92696	−	5.06964i	0.126308	−	0.218771i
$538$		−	24.6763i		−	1.06387i
$539$	2.25159	+	1.29995i	0.0969826	+	0.0559930i
$540$	−13.5732	−	7.83648i	−0.584097	−	0.337228i
$541$		−	28.0210i		−	1.20472i	−0.798225	−	0.602359i	$-0.794228\pi$
$541$		−	28.0210i		−	1.20472i	0.798225	−	0.602359i	$-0.205772\pi$
$542$	19.5789	−	33.9116i	0.840985	−	1.45663i
$543$	0.555284	+	0.961780i	0.0238295	+	0.0412739i
$544$	73.2199	−	42.2735i	3.13928	−	1.81246i
$545$	−3.95720			−0.169508
$546$	−7.30609	−	41.3141i	−0.312672	−	1.76808i
$547$	11.8641			0.507270			0.253635	−	0.967300i	$-0.418374\pi$
$547$	11.8641			0.507270			0.253635	+	0.967300i	$0.418374\pi$
$548$	−21.6360	+	12.4916i	−0.924245	+	0.533613i
$549$	−2.96105	−	5.12869i	−0.126375	−	0.218887i
$550$	−35.9856	+	62.3290i	−1.53443	+	2.65772i
$551$		−	24.4010i		−	1.03952i
$552$	11.4303	+	6.59929i	0.486506	+	0.280884i
$553$	20.6047	+	11.8961i	0.876200	+	0.505874i
$554$			7.24601i			0.307854i
$555$	−0.244656	+	0.423756i	−0.0103850	+	0.0179874i
$556$	44.5234	+	77.1168i	1.88821	+	3.27048i
$557$	−5.00797	+	2.89135i	−0.212194	+	0.122511i	−0.602331	−	0.798247i	$-0.705761\pi$
$557$	−5.00797	+	2.89135i	−0.212194	+	0.122511i	0.390136	+	0.920757i	$0.372428\pi$
$558$	1.30351			0.0551819
$559$	13.1187	−	11.0191i	0.554863	−	0.466058i
$560$	17.9666			0.759228
$561$	45.3812	−	26.2009i	1.91600	−	1.10620i
$562$	7.30974	+	12.6608i	0.308343	+	0.534065i
$563$	−1.83486	+	3.17807i	−0.0773301	+	0.133940i	−0.902097	−	0.431533i	$-0.857973\pi$
$563$	−1.83486	+	3.17807i	−0.0773301	+	0.133940i	0.824767	+	0.565473i	$0.191306\pi$
$564$			84.9252i			3.57600i
$565$	2.97088	+	1.71524i	0.124986	+	0.0721606i
$566$	27.2787	+	15.7493i	1.14661	+	0.661994i
$567$		−	20.4444i		−	0.858583i
$568$	−43.1994	+	74.8236i	−1.81261	+	3.13953i
$569$	13.6417	+	23.6281i	0.571889	+	0.990541i	0.996372	+	0.0851048i	$0.0271225\pi$
$569$	13.6417	+	23.6281i	0.571889	+	0.990541i	−0.424483	+	0.905436i	$0.639544\pi$
$570$	9.46689	−	5.46571i	0.396524	−	0.228933i
$571$	−1.89469			−0.0792902			−0.0396451	−	0.999214i	$-0.512623\pi$
$571$	−1.89469			−0.0792902			−0.0396451	+	0.999214i	$0.512623\pi$
$572$	−36.1705	+	99.5324i	−1.51237	+	4.16166i
$573$	−22.7201			−0.949145
$574$	−14.1500	+	8.16950i	−0.590609	+	0.340988i
$575$	−2.34387	−	4.05969i	−0.0977460	−	0.169301i
$576$	−3.53159	+	6.11689i	−0.147150	+	0.254870i
$577$		−	5.86384i		−	0.244115i	−0.992523	−	0.122058i	$-0.961051\pi$
$577$		−	5.86384i		−	0.244115i	0.992523	−	0.122058i	$-0.0389492\pi$
$578$	35.2512	+	20.3523i	1.46626	+	0.846545i
$579$	−36.1534	−	20.8732i	−1.50248	−	0.867459i
$580$		−	15.1428i		−	0.628770i
$581$	−5.40211	+	9.35673i	−0.224117	+	0.388182i
$582$	−0.181230	−	0.313900i	−0.00751223	−	0.0130116i
$583$	−10.9212	+	6.30533i	−0.452308	+	0.261140i
$584$	36.8260			1.52387
$585$	0.569086	+	0.677523i	0.0235288	+	0.0280121i
$586$	14.0910			0.582096
$587$	−2.86010	+	1.65128i	−0.118049	+	0.0681556i	−0.557862	−	0.829934i	$-0.688378\pi$
$587$	−2.86010	+	1.65128i	−0.118049	+	0.0681556i	0.439813	+	0.898089i	$0.355045\pi$
$588$	1.83941	+	3.18595i	0.0758559	+	0.131386i
$589$	−2.55661	+	4.42818i	−0.105343	+	0.182460i
$590$		−	12.0221i		−	0.494942i
$591$	19.7826	+	11.4215i	0.813746	+	0.469817i
$592$	5.58150	+	3.22248i	0.229398	+	0.132443i
$593$			10.6290i			0.436479i	0.975895	+	0.218240i	$0.0700314\pi$
$593$			10.6290i			0.436479i	−0.975895	+	0.218240i	$0.929969\pi$
$594$	−42.2484	+	73.1763i	−1.73347	+	3.00246i
$595$	4.33325	+	7.50540i	0.177646	+	0.307691i
$596$	62.7577	−	36.2332i	2.57065	−	1.48417i
$597$	−29.0117			−1.18737
$598$	−6.17745	−	7.35453i	−0.252615	−	0.300749i
$599$	17.9815			0.734703			0.367352	−	0.930082i	$-0.380265\pi$
$599$	17.9815			0.734703			0.367352	+	0.930082i	$0.380265\pi$
$600$	−53.5822	+	30.9357i	−2.18748	+	1.26294i
$601$	15.3562	+	26.5977i	0.626392	+	1.08494i	0.988270	+	0.152718i	$0.0488025\pi$
$601$	15.3562	+	26.5977i	0.626392	+	1.08494i	−0.361877	+	0.932226i	$0.617864\pi$
$602$	−17.2759	+	29.9227i	−0.704112	+	1.21956i
$603$		−	4.18727i		−	0.170519i
$604$	66.2988	+	38.2776i	2.69766	+	1.55749i
$605$	−10.7521	−	6.20774i	−0.437136	−	0.252381i
$606$			13.9527i			0.566790i
$607$	−9.10024	+	15.7621i	−0.369367	+	0.639763i	−0.989467	−	0.144760i	$-0.953759\pi$
$607$	−9.10024	+	15.7621i	−0.369367	+	0.639763i	0.620099	+	0.784523i	$0.287092\pi$
$608$	−34.1435	−	59.1383i	−1.38470	−	2.39838i
$609$	20.1155	−	11.6137i	0.815122	−	0.470611i
$610$	20.0741			0.812776
$611$	12.8241	−	35.2889i	0.518809	−	1.42764i
$612$	−12.7153			−0.513987
$613$	−8.46467	+	4.88708i	−0.341885	+	0.197387i	−0.661105	−	0.750293i	$-0.729912\pi$
$613$	−8.46467	+	4.88708i	−0.341885	+	0.197387i	0.319220	+	0.947680i	$0.396579\pi$
$614$	24.4578	+	42.3621i	0.987035	+	1.70959i
$615$	−1.00468	+	1.74016i	−0.0405128	+	0.0701702i
$616$		−	129.757i		−	5.22805i
$617$	3.32362	+	1.91889i	0.133804	+	0.0772516i	0.565408	−	0.824812i	$-0.308719\pi$
$617$	3.32362	+	1.91889i	0.133804	+	0.0772516i	−0.431604	+	0.902063i	$0.642052\pi$
$618$	24.9911	+	14.4286i	1.00529	+	0.580404i
$619$		−	17.6828i		−	0.710732i	−0.934727	−	0.355366i	$-0.884356\pi$
$619$		−	17.6828i		−	0.710732i	0.934727	−	0.355366i	$-0.115644\pi$
$620$	−1.58659	+	2.74805i	−0.0637188	+	0.110364i
$621$	−2.75178	−	4.76622i	−0.110425	−	0.191262i
$622$	−28.2767	+	16.3256i	−1.13379	+	0.654596i
$623$	−20.8581			−0.835664
$624$	−52.0387	+	43.7100i	−2.08322	+	1.74980i
$625$	20.4135			0.816539
$626$	−73.6513	+	42.5226i	−2.94370	+	1.69954i
$627$	−21.1619	−	36.6535i	−0.845126	−	1.46380i
$628$	−10.0344	+	17.3801i	−0.400417	+	0.693543i
$629$			3.10884i			0.123957i
$630$	−1.54537	−	0.892221i	−0.0615691	−	0.0355469i
$631$	3.56689	+	2.05935i	0.141996	+	0.0819813i	0.569315	−	0.822120i	$-0.307209\pi$
$631$	3.56689	+	2.05935i	0.141996	+	0.0819813i	−0.427319	+	0.904101i	$0.640542\pi$
$632$		−	71.8887i		−	2.85958i
$633$	−14.3735	+	24.8956i	−0.571294	+	0.989510i
$634$	−31.5678	−	54.6770i	−1.25372	−	2.17150i
$635$	−4.54659	+	2.62498i	−0.180426	+	0.104169i
$636$	−17.8438			−0.707554
$637$	−0.283233	−	1.60161i	−0.0112221	−	0.0634582i
$638$	−81.6385			−3.23210
$639$	3.98400	−	2.30016i	0.157605	−	0.0909931i
$640$	−3.65538	−	6.33131i	−0.144492	−	0.250267i
$641$	−1.00661	+	1.74350i	−0.0397588	+	0.0688642i	−0.885220	−	0.465173i	$-0.845992\pi$
$641$	−1.00661	+	1.74350i	−0.0397588	+	0.0688642i	0.845461	+	0.534037i	$0.179326\pi$
$642$		−	62.3929i		−	2.46245i
$643$	1.52120	+	0.878266i	0.0599903	+	0.0346354i	0.529695	−	0.848188i	$-0.322306\pi$
$643$	1.52120	+	0.878266i	0.0599903	+	0.0346354i	−0.469705	+	0.882824i	$0.655640\pi$
$644$	12.0471	+	6.95542i	0.474724	+	0.274082i
$645$			4.24917i			0.167311i
$646$	34.7264	−	60.1478i	1.36629	−	2.36648i
$647$	−6.72569	−	11.6492i	−0.264414	−	0.457979i	0.702996	−	0.711194i	$-0.251845\pi$
$647$	−6.72569	−	11.6492i	−0.264414	−	0.457979i	−0.967410	+	0.253215i	$0.918512\pi$
$648$	−53.4970	+	30.8865i	−2.10156	+	1.21334i
$649$	−46.5467			−1.82712
$650$	44.3363	−	7.84053i	1.73901	−	0.307531i
$651$	−4.86730			−0.190765
$652$	41.6183	−	24.0283i	1.62990	−	0.941022i
$653$	−11.1820	−	19.3678i	−0.437585	−	0.757919i	0.559918	−	0.828548i	$-0.310833\pi$
$653$	−11.1820	−	19.3678i	−0.437585	−	0.757919i	−0.997503	+	0.0706292i	$0.977499\pi$
$654$	−15.0938	+	26.1432i	−0.590213	+	1.02228i
$655$			3.35313i			0.131018i
$656$	22.9206	+	13.2332i	0.894898	+	0.516670i
$657$	−1.69811	−	0.980403i	−0.0662495	−	0.0382492i
$658$			75.7223i			2.95196i
$659$	−11.2912	+	19.5569i	−0.439843	+	0.761831i	−0.997677	−	0.0681220i	$-0.978299\pi$
$659$	−11.2912	+	19.5569i	−0.439843	+	0.761831i	0.557834	+	0.829953i	$0.311633\pi$
$660$	−13.1327	−	22.7465i	−0.511190	−	0.885407i
$661$	19.5828	−	11.3061i	0.761683	−	0.439758i	−0.0682169	−	0.997671i	$-0.521731\pi$
$661$	19.5828	−	11.3061i	0.761683	−	0.439758i	0.829900	+	0.557913i	$0.188398\pi$
$662$	−60.1932			−2.33948
$663$	−30.8104	−	11.1966i	−1.19658	−	0.434841i
$664$	32.6451			1.26688
$665$	6.06197	−	3.49988i	0.235073	−	0.135720i
$666$	−0.320057	−	0.554354i	−0.0124019	−	0.0214808i
$667$	2.65869	−	4.60499i	0.102945	−	0.178306i
$668$		−	121.469i		−	4.69978i
$669$	−8.38125	−	4.83892i	−0.324038	−	0.187083i
$670$	12.2920	+	7.09677i	0.474880	+	0.274172i
$671$		−	77.7221i		−	3.00043i
$672$	32.5014	−	56.2940i	1.25377	−	2.17159i
$673$	17.6443	+	30.5608i	0.680136	+	1.17803i	0.974939	+	0.222472i	$0.0714127\pi$
$673$	17.6443	+	30.5608i	0.680136	+	1.17803i	−0.294803	+	0.955558i	$0.595254\pi$
$674$	−17.4166	+	10.0555i	−0.670862	+	0.387322i
$675$	25.7992			0.993011
$676$	62.2321	−	22.7211i	2.39354	−	0.873888i
$677$	28.5288			1.09645			0.548226	−	0.836331i	$-0.315304\pi$
$677$	28.5288			1.09645			0.548226	+	0.836331i	$0.315304\pi$
$678$	22.6634	−	13.0847i	0.870381	−	0.502515i
$679$	−0.116048	−	0.201001i	−0.00445351	−	0.00771370i
$680$	13.0930	−	22.6777i	0.502093	−	0.869650i
$681$			13.5193i			0.518061i
$682$	14.8154	+	8.55367i	0.567311	+	0.327537i
$683$	−22.7007	−	13.1063i	−0.868619	−	0.501497i	−0.00172976	−	0.999999i	$-0.500551\pi$
$683$	−22.7007	−	13.1063i	−0.868619	−	0.501497i	−0.866889	+	0.498501i	$0.833884\pi$
$684$			10.2699i			0.392681i
$685$	−1.36974	+	2.37246i	−0.0523350	+	0.0906469i
$686$	−23.8101	−	41.2402i	−0.909072	−	1.57456i
$687$	0.859284	−	0.496108i	0.0327837	−	0.0189277i
$688$	55.9680			2.13376
$689$	7.41463	+	2.69451i	0.282475	+	0.102653i
$690$	2.38214			0.0906866
$691$	−2.15074	+	1.24173i	−0.0818182	+	0.0472377i	−0.540351	−	0.841440i	$-0.681709\pi$
$691$	−2.15074	+	1.24173i	−0.0818182	+	0.0472377i	0.458533	+	0.888678i	$0.348375\pi$
$692$	−4.77663	−	8.27336i	−0.181580	−	0.314506i
$693$	−3.45447	+	5.98332i	−0.131224	+	0.227287i
$694$		−	43.1542i		−	1.63811i
$695$	8.45610	+	4.88213i	0.320758	+	0.185190i
$696$	−60.7794	−	35.0910i	−2.30384	−	1.33012i
$697$			12.7665i			0.483566i
$698$	0.0416012	−	0.0720553i	0.00157463	−	0.00272733i
$699$	−15.4307	−	26.7267i	−0.583641	−	1.01090i
$700$	−56.4738	+	32.6051i	−2.13451	+	1.23236i
$701$	9.72477			0.367299			0.183650	−	0.982992i	$-0.441209\pi$
$701$	9.72477			0.367299			0.183650	+	0.982992i	$0.441209\pi$
$702$	52.0523	−	9.20505i	1.96459	−	0.347422i
$703$	2.51095			0.0947022
$704$	−80.2785	+	46.3488i	−3.02561	+	1.74684i
$705$	4.65616	+	8.06471i	0.175361	+	0.303734i
$706$	−20.0342	+	34.7002i	−0.753996	+	1.30596i
$707$			8.93440i			0.336013i
$708$	−57.0388	−	32.9313i	−2.14365	−	1.23764i
$709$	−31.5049	−	18.1894i	−1.18319	−	0.683117i	−0.226442	−	0.974025i	$-0.572709\pi$
$709$	−31.5049	−	18.1894i	−1.18319	−	0.683117i	−0.956751	+	0.290908i	$0.906043\pi$
$710$			15.5937i			0.585220i
$711$	−1.91386	+	3.31491i	−0.0717755	+	0.124319i
$712$	31.5116	+	54.5797i	1.18095	+	2.04546i
$713$	−0.964977	+	0.557129i	−0.0361387	+	0.0208647i
$714$	66.1123			2.47419
$715$	2.02218	+	11.4349i	0.0756253	+	0.427643i
$716$	−18.6422			−0.696693
$717$	−26.2825	+	15.1742i	−0.981539	+	0.566692i
$718$	−21.2624	−	36.8276i	−0.793507	−	1.37439i
$719$	−5.06134	+	8.76650i	−0.188756	+	0.326935i	−0.944836	−	0.327544i	$-0.893779\pi$
$719$	−5.06134	+	8.76650i	−0.188756	+	0.326935i	0.756080	+	0.654480i	$0.227112\pi$
$720$			2.89049i			0.107722i
$721$	16.0026	+	9.23913i	0.595970	+	0.344083i
$722$	−4.74779	−	2.74114i	−0.176694	−	0.102015i
$723$			28.8383i			1.07251i
$724$	1.76834	−	3.06286i	0.0657199	−	0.113830i
$725$	12.4632	+	21.5870i	0.462873	+	0.801720i
$726$	−82.0226	+	47.3558i	−3.04414	+	1.75754i
$727$	−21.1534			−0.784537			−0.392269	−	0.919851i	$-0.628310\pi$
$727$	−21.1534			−0.784537			−0.392269	+	0.919851i	$0.628310\pi$
$728$	−62.1569	+	52.2088i	−2.30369	+	1.93499i
$729$	29.7106			1.10039
$730$	5.75606	−	3.32326i	0.213041	−	0.122999i
$731$	13.4985	+	23.3802i	0.499262	+	0.864747i
$732$	54.9876	−	95.2413i	2.03240	−	3.52022i
$733$		−	17.4731i		−	0.645385i	−0.946504	−	0.322693i	$-0.895412\pi$
$733$		−	17.4731i		−	0.645385i	0.946504	−	0.322693i	$-0.104588\pi$
$734$	−58.2323	−	33.6204i	−2.14939	−	1.24095i
$735$	0.349349	+	0.201697i	0.0128859	+	0.00743970i
$736$		−	14.8809i		−	0.548518i
$737$	27.4770	−	47.5916i	1.01213	−	1.75306i
$738$	−1.31432	−	2.27647i	−0.0483808	−	0.0837980i
$739$	−24.5193	+	14.1562i	−0.901958	+	0.520746i	−0.877835	−	0.478963i	$-0.841013\pi$
$739$	−24.5193	+	14.1562i	−0.901958	+	0.520746i	−0.0241233	+	0.999709i	$0.507679\pi$
$740$	1.55825			0.0572823
$741$	−9.04330	+	24.8850i	−0.332214	+	0.914172i
$742$	−15.9102			−0.584081
$743$	22.8540	−	13.1948i	0.838431	−	0.484068i	−0.0182995	−	0.999833i	$-0.505825\pi$
$743$	22.8540	−	13.1948i	0.838431	−	0.484068i	0.856731	+	0.515764i	$0.172492\pi$
$744$	7.35332	+	12.7363i	0.269586	+	0.466936i
$745$	3.97308	−	6.88158i	0.145562	−	0.252121i
$746$			92.6260i			3.39128i
$747$	−1.50532	−	0.869099i	−0.0550769	−	0.0317987i
$748$	−144.520	−	83.4386i	−5.28417	−	3.05082i
$749$		−	39.9523i		−	1.45983i
$750$	−11.5388	+	19.9858i	−0.421337	+	0.729777i
$751$	−11.7088	−	20.2803i	−0.427262	−	0.740039i	0.569367	−	0.822084i	$-0.307188\pi$
$751$	−11.7088	−	20.2803i	−0.427262	−	0.740039i	−0.996629	+	0.0820444i	$0.973855\pi$
$752$	106.224	−	61.3286i	3.87360	−	2.23643i
$753$	13.1343			0.478640
$754$	32.8479	+	39.1069i	1.19625	+	1.42419i
$755$	8.39452			0.305508
$756$	−66.3021	+	38.2795i	−2.41138	+	1.39221i
$757$	15.1878	+	26.3061i	0.552011	+	0.956112i	0.998129	+	0.0611376i	$0.0194728\pi$
$757$	15.1878	+	26.3061i	0.552011	+	0.956112i	−0.446118	+	0.894974i	$0.647194\pi$
$758$	−6.13008	+	10.6176i	−0.222654	+	0.385649i
$759$		−	9.22309i		−	0.334777i
$760$	−18.3164	−	10.5750i	−0.664404	−	0.383594i
$761$	38.6979	+	22.3423i	1.40280	+	0.809906i	0.994679	−	0.103023i	$-0.0328514\pi$
$761$	38.6979	+	22.3423i	1.40280	+	0.809906i	0.408119	+	0.912929i	$0.366185\pi$
$762$			40.0493i			1.45083i
$763$	−9.66505	+	16.7404i	−0.349898	+	0.606042i
$764$	36.1769	+	62.6602i	1.30883	+	2.26697i
$765$	−1.20748	+	0.697139i	−0.0436565	+	0.0252051i
$766$	−98.4128			−3.55580
$767$	18.7285	+	22.2971i	0.676246	+	0.805101i
$768$	−4.29406			−0.154948
$769$	35.5269	−	20.5115i	1.28113	−	0.739663i	0.304078	−	0.952647i	$-0.401652\pi$
$769$	35.5269	−	20.5115i	1.28113	−	0.739663i	0.977056	+	0.212985i	$0.0683185\pi$
$770$	−11.7096	−	20.2816i	−0.421984	−	0.730897i
$771$	16.5721	−	28.7038i	0.596831	−	1.03374i
$772$			132.944i			4.78477i
$773$	−32.0632	−	18.5117i	−1.15323	−	0.665819i	−0.203560	−	0.979062i	$-0.565251\pi$
$773$	−32.0632	−	18.5117i	−1.15323	−	0.665819i	−0.949673	+	0.313243i	$0.898585\pi$
$774$	−4.81401	−	2.77937i	−0.173036	−	0.0999023i
$775$		−	5.22335i		−	0.187628i
$776$	−0.350641	+	0.607328i	−0.0125873	+	0.0218018i
$777$	1.19509	+	2.06996i	0.0428736	+	0.0742593i
$778$	66.1689	−	38.2026i	2.37227	−	1.36963i
$779$	10.3113			0.369440
$780$	−5.61211	+	15.4431i	−0.200946	+	0.552953i
$781$	60.3750			2.16039
$782$	13.1072	−	7.56747i	0.468714	−	0.270612i
$783$	14.6323	+	25.3438i	0.522915	+	0.905715i
$784$	2.65665	−	4.60145i	0.0948804	−	0.164338i
$785$			2.20061i			0.0785432i
$786$	22.1524	+	12.7897i	0.790149	+	0.456193i
$787$	25.3796	+	14.6529i	0.904684	+	0.522320i	0.878717	−	0.477343i	$-0.158400\pi$
$787$	25.3796	+	14.6529i	0.904684	+	0.522320i	0.0259673	+	0.999663i	$0.491733\pi$
$788$		−	72.7451i		−	2.59144i
$789$	−16.6241	+	28.7938i	−0.591833	+	1.02509i
$790$	−6.48740	−	11.2365i	−0.230812	−	0.399777i
$791$	14.5121	−	8.37858i	0.515992	−	0.297908i
$792$	20.8755			0.741778
$793$	−37.2309	+	31.2721i	−1.32211	+	1.11051i
$794$	24.8892			0.883286
$795$	−1.69449	+	0.978316i	−0.0600975	+	0.0346973i
$796$	46.1950	+	80.0121i	1.63734	+	2.83595i
$797$	−3.44520	+	5.96726i	−0.122035	+	0.211371i	−0.920570	−	0.390577i	$-0.872275\pi$
$797$	−3.44520	+	5.96726i	−0.122035	+	0.211371i	0.798535	+	0.601948i	$0.205609\pi$
$798$		−	53.3977i		−	1.89026i
$799$	51.2391	+	29.5829i	1.81271	+	1.04657i
$800$	60.4120	+	34.8789i	2.13589	+	1.23315i
$801$		−	3.35569i		−	0.118567i
$802$	16.1617	−	27.9929i	0.570690	−	0.988465i
$803$	−12.8669	−	22.2861i	−0.454063	−	0.786460i
$804$	67.3411	−	38.8794i	2.37494	−	1.37117i
$805$	1.52537			0.0537621
$806$	−1.86367	−	10.5386i	−0.0656450	−	0.371206i
$807$	−14.8238			−0.521822
$808$	23.3787	−	13.4977i	0.822461	−	0.474848i
$809$	−9.19896	−	15.9331i	−0.323418	−	0.560177i	0.657773	−	0.753216i	$-0.271499\pi$
$809$	−9.19896	−	15.9331i	−0.323418	−	0.560177i	−0.981191	+	0.193040i	$0.938165\pi$
$810$	−5.57455	+	9.65540i	−0.195870	+	0.339256i
$811$		−	18.5293i		−	0.650653i	−0.945602	−	0.325326i	$-0.894526\pi$
$811$		−	18.5293i		−	0.650653i	0.945602	−	0.325326i	$-0.105474\pi$
$812$	−64.0593	−	36.9847i	−2.24804	−	1.29791i
$813$	−20.3718	−	11.7616i	−0.714468	−	0.412499i
$814$		−	8.40090i		−	0.294451i
$815$	2.63478	−	4.56358i	0.0922924	−	0.159855i
$816$	−53.5454	−	92.7433i	−1.87446	−	3.24667i
$817$	18.8837	−	10.9025i	0.660658	−	0.381431i
$818$	−18.5563			−0.648805
$819$	4.25609	−	0.752658i	0.148720	−	0.0263000i
$820$	6.39898			0.223462
$821$	15.2888	−	8.82698i	0.533582	−	0.308064i	−0.208892	−	0.977939i	$-0.566986\pi$
$821$	15.2888	−	8.82698i	0.533582	−	0.308064i	0.742474	+	0.669875i	$0.233652\pi$
$822$	10.4491	+	18.0983i	0.364453	+	0.631251i
$823$	6.29069	−	10.8958i	0.219280	−	0.379804i	−0.735308	−	0.677733i	$-0.762963\pi$
$823$	6.29069	−	10.8958i	0.219280	−	0.379804i	0.954588	+	0.297929i	$0.0962960\pi$
$824$		−	55.8324i		−	1.94501i
$825$	37.4429	+	21.6177i	1.30360	+	0.752631i
$826$	−50.8577	−	29.3627i	−1.76957	−	1.02166i
$827$			42.6931i			1.48458i	0.670077	+	0.742291i	$0.266261\pi$
$827$			42.6931i			1.48458i	−0.670077	+	0.742291i	$0.733739\pi$
$828$	−1.11900	+	1.93816i	−0.0388879	+	0.0673558i
$829$	−18.0369	−	31.2409i	−0.626449	−	1.08504i	−0.988259	−	0.152790i	$-0.951174\pi$
$829$	−18.0369	−	31.2409i	−0.626449	−	1.08504i	0.361810	−	0.932252i	$-0.382159\pi$
$830$	5.10258	−	2.94598i	0.177113	−	0.102256i
$831$	4.35291			0.151001
$832$	54.5030	+	19.8066i	1.88955	+	0.686671i
$833$	2.56296			0.0888013
$834$	64.5074	−	37.2434i	2.23371	−	1.28963i
$835$	−6.65973	−	11.5350i	−0.230470	−	0.399185i
$836$	−67.3918	+	116.726i	−2.33079	+	4.03705i
$837$		−	6.13239i		−	0.211966i
$838$	−67.7811	−	39.1334i	−2.34146	−	1.35184i
$839$	−10.2142	−	5.89714i	−0.352632	−	0.203592i	0.313212	−	0.949683i	$-0.398595\pi$
$839$	−10.2142	−	5.89714i	−0.352632	−	0.203592i	−0.665844	+	0.746091i	$0.731928\pi$
$840$		−	20.1327i		−	0.694644i
$841$	0.362688	−	0.628193i	0.0125065	−	0.0216618i
$842$	4.95683	+	8.58548i	0.170824	+	0.295875i
$843$	7.60576	−	4.39119i	0.261956	−	0.151241i
$844$	91.5467			3.15117
$845$	4.66399	−	5.56962i	0.160446	−	0.191601i
$846$	−12.1823			−0.418837
$847$	−52.5219	+	30.3235i	−1.80467	+	1.04193i
$848$	12.8859	+	22.3190i	0.442504	+	0.766439i
$849$	9.46112	−	16.3871i	0.324705	−	0.562405i
$850$			70.9485i			2.43351i
$851$	0.473870	+	0.273589i	0.0162441	+	0.00937852i
$852$	73.9841	+	42.7147i	2.53465	+	1.46338i
$853$			35.9009i			1.22922i	0.788830	+	0.614612i	$0.210687\pi$
$853$			35.9009i			1.22922i	−0.788830	+	0.614612i	$0.789313\pi$
$854$	49.0289	−	84.9205i	1.67773	−	2.90592i
$855$	0.563066	+	0.975259i	0.0192564	+	0.0333531i
$856$	−104.544	+	60.3583i	−3.57323	+	2.06301i
$857$	−32.0049			−1.09327			−0.546633	−	0.837372i	$-0.684091\pi$
$857$	−32.0049			−1.09327			−0.546633	+	0.837372i	$0.684091\pi$
$858$	83.2578	+	30.2562i	2.84237	+	1.03293i
$859$	−57.7067			−1.96893			−0.984463	−	0.175590i	$-0.943817\pi$
$859$	−57.7067			−1.96893			−0.984463	+	0.175590i	$0.943817\pi$
$860$	11.7189	−	6.76590i	0.399611	−	0.230715i
$861$	4.90767	+	8.50033i	0.167253	+	0.289691i
$862$	4.22622	−	7.32004i	0.143946	−	0.249321i
$863$			7.70095i			0.262143i	0.991373	+	0.131072i	$0.0418418\pi$
$863$			7.70095i			0.262143i	−0.991373	+	0.131072i	$0.958158\pi$
$864$	70.9257	+	40.9490i	2.41294	+	1.39311i
$865$	−0.907200	−	0.523772i	−0.0308457	−	0.0178088i
$866$		−	3.45018i		−	0.117242i
$867$	12.2263	−	21.1765i	0.415226	−	0.719192i
$868$	7.75014	+	13.4236i	0.263057	+	0.455628i
$869$	−43.5051	+	25.1177i	−1.47581	+	0.852059i
$870$	−12.6668			−0.429444
$871$	−33.8532	+	5.98667i	−1.14707	+	0.202851i
$872$	58.4063			1.97789
$873$	0.0323373	−	0.0186700i	0.00109445	−	0.000631882i
$874$	−6.11210	−	10.5865i	−0.206745	−	0.358093i
$875$	−7.38868	+	12.7976i	−0.249783	+	0.432637i
$876$		−	36.4128i		−	1.23027i
$877$	1.67966	+	0.969750i	0.0567180	+	0.0327461i	0.528091	−	0.849188i	$-0.322908\pi$
$877$	1.67966	+	0.969750i	0.0567180	+	0.0327461i	−0.471373	+	0.881934i	$0.656241\pi$
$878$	−53.2884	−	30.7661i	−1.79840	−	1.03831i
$879$		−	8.46493i		−	0.285515i
$880$	−18.9675	+	32.8527i	−0.639395	+	1.10747i
$881$	2.67207	+	4.62816i	0.0900243	+	0.155927i	0.907521	−	0.420006i	$-0.137972\pi$
$881$	2.67207	+	4.62816i	0.0900243	+	0.155927i	−0.817497	+	0.575933i	$0.804639\pi$
$882$	−0.457016	+	0.263858i	−0.0153885	+	0.00888457i
$883$	14.6898			0.494350			0.247175	−	0.968971i	$-0.420498\pi$
$883$	14.6898			0.494350			0.247175	+	0.968971i	$0.420498\pi$
$884$	18.1795	+	102.801i	0.611444	+	3.45757i
$885$	−7.22205			−0.242767
$886$	85.8736	−	49.5792i	2.88498	−	1.66564i
$887$	−5.58115	−	9.66683i	−0.187397	−	0.324580i	0.756985	−	0.653432i	$-0.226672\pi$
$887$	−5.58115	−	9.66683i	−0.187397	−	0.324580i	−0.944382	+	0.328852i	$0.893338\pi$
$888$	3.61099	−	6.25442i	0.121177	−	0.209884i
$889$			25.6449i			0.860102i
$890$	9.85081	+	5.68737i	0.330200	+	0.190641i
$891$	37.3834	+	21.5833i	1.25239	+	0.723069i
$892$			30.8198i			1.03192i
$893$	23.8935	−	41.3848i	0.799567	−	1.38489i
$894$	−30.3086	−	52.4961i	−1.01367	−	1.75573i
$895$	−1.77031	+	1.02209i	−0.0591750	+	0.0341647i
$896$	−35.7115			−1.19304
$897$	−4.41810	+	3.71099i	−0.147516	+	0.123906i
$898$	−95.3425			−3.18162
$899$	5.13116	−	2.96247i	0.171134	−	0.0988040i
$900$	−5.24556	−	9.08558i	−0.174852	−	0.302853i
$901$	−6.21573	+	10.7660i	−0.207076	+	0.358666i
$902$		−	34.4985i		−	1.14867i
$903$	17.9755	+	10.3782i	0.598187	+	0.345363i
$904$	−43.8486	−	25.3160i	−1.45838	−	0.841998i
$905$		−	0.387809i		−	0.0128912i
$906$	32.0188	−	55.4582i	1.06375	−	1.84248i
$907$	7.60096	+	13.1652i	0.252386	+	0.437145i	0.964182	−	0.265241i	$-0.0854515\pi$
$907$	7.60096	+	13.1652i	0.252386	+	0.437145i	−0.711797	+	0.702386i	$0.752118\pi$
$908$	37.2852	−	21.5266i	1.23735	−	0.714386i
$909$	−1.43738			−0.0476749
$910$	−5.00395	+	13.7696i	−0.165879	+	0.456459i
$911$	−28.9747			−0.959973			−0.479987	−	0.877276i	$-0.659358\pi$
$911$	−28.9747			−0.959973			−0.479987	+	0.877276i	$0.659358\pi$
$912$	−74.9071	+	43.2476i	−2.48042	+	1.43207i
$913$	−11.4061	−	19.7560i	−0.377487	−	0.653827i
$914$	38.7950	−	67.1949i	1.28322	−	2.22261i
$915$		−	12.0591i		−	0.398663i
$916$	−2.73646	−	1.57989i	−0.0904150	−	0.0522011i
$917$	14.1849	+	8.18967i	0.468427	+	0.270447i
$918$			83.2960i			2.74918i
$919$	19.7022	−	34.1251i	0.649914	−	1.12568i	−0.333229	−	0.942846i	$-0.608138\pi$
$919$	19.7022	−	34.1251i	0.649914	−	1.12568i	0.983143	−	0.182838i	$-0.0585284\pi$
$920$	−2.30446	−	3.99145i	−0.0759759	−	0.131594i
$921$	25.4482	−	14.6925i	0.838547	−	0.484135i
$922$	36.4331			1.19986
$923$	−24.2924	−	28.9212i	−0.799594	−	0.951952i
$924$	−128.301			−4.22079
$925$	−2.22138	+	1.28251i	−0.0730384	+	0.0421688i
$926$	47.8288	+	82.8419i	1.57175	+	2.72235i
$927$	−1.48640	+	2.57453i	−0.0488199	+	0.0845586i
$928$			79.1276i			2.59749i
$929$	36.6075	+	21.1354i	1.20105	+	0.693429i	0.960790	−	0.277278i	$-0.0894325\pi$
$929$	36.6075	+	21.1354i	1.20105	+	0.693429i	0.240265	+	0.970707i	$0.422766\pi$
$930$	2.29871	+	1.32716i	0.0753777	+	0.0435194i
$931$		−	2.07005i		−	0.0678433i
$932$	−49.1401	+	85.1131i	−1.60964	+	2.78797i
$933$	9.80729	+	16.9867i	0.321076	+	0.556120i
$934$	52.3031	−	30.1972i	1.71141	−	0.988083i
$935$	−18.2986			−0.598428
$936$	−8.39942	−	9.99989i	−0.274544	−	0.326857i
$937$	6.59440			0.215430			0.107715	−	0.994182i	$-0.465647\pi$
$937$	6.59440			0.215430			0.107715	+	0.994182i	$0.465647\pi$
$938$	60.0436	−	34.6662i	1.96049	−	1.13189i
$939$	25.5446	+	44.2446i	0.833618	+	1.44387i
$940$	14.8279	−	25.6827i	0.483632	−	0.837676i
$941$		−	6.07797i		−	0.198136i	−0.995081	−	0.0990680i	$-0.968414\pi$
$941$		−	6.07797i		−	0.198136i	0.995081	−	0.0990680i	$-0.0315861\pi$
$942$	14.5383	+	8.39369i	0.473683	+	0.273481i
$943$	1.94596	+	1.12350i	0.0633692	+	0.0365862i
$944$			95.1253i			3.09606i
$945$	−4.19747	+	7.27024i	−0.136544	+	0.236501i
$946$	−36.4766	−	63.1794i	−1.18596	−	2.05414i
$947$	6.03663	−	3.48525i	0.196164	−	0.113255i	−0.398701	−	0.917081i	$-0.630539\pi$
$947$	6.03663	−	3.48525i	0.196164	−	0.113255i	0.594865	+	0.803826i	$0.297205\pi$
$948$	−71.0820			−2.30864
$949$	−5.49851	+	15.1306i	−0.178489	+	0.491159i
$950$	57.3038			1.85918
$951$	−32.8462	+	18.9638i	−1.06511	+	0.614942i
$952$	−63.9565	−	110.776i	−2.07284	−	3.59027i
$953$	10.6190	−	18.3927i	0.343983	−	0.595796i	−0.641185	−	0.767386i	$-0.721557\pi$
$953$	10.6190	−	18.3927i	0.343983	−	0.595796i	0.985169	+	0.171590i	$0.0548903\pi$
$954$		−	2.55965i		−	0.0828718i
$955$	6.87089	+	3.96691i	0.222337	+	0.128366i
$956$	83.6986	+	48.3234i	2.70701	+	1.56289i
$957$			49.0428i			1.58533i
$958$	−19.0782	+	33.0444i	−0.616388	+	1.06762i
$959$	6.69089	+	11.5890i	0.216060	+	0.374227i
$960$	−12.4558	+	7.19134i	−0.402008	+	0.232100i
$961$	29.7584			0.959949
$962$	−4.02424	+	3.38017i	−0.129747	+	0.108981i
$963$	6.42759			0.207126
$964$	79.5337	−	45.9188i	2.56161	−	1.47894i
$965$	7.28888	+	12.6247i	0.234637	+	0.406404i
$966$	5.81813	−	10.0773i	0.187195	−	0.324232i
$967$		−	30.1147i		−	0.968424i	−0.874951	−	0.484212i	$-0.839106\pi$
$967$		−	30.1147i		−	0.968424i	0.874951	−	0.484212i	$-0.160894\pi$
$968$	158.696	+	91.6231i	5.10068	+	2.94488i
$969$	−36.1327	−	20.8612i	−1.16075	−	0.670158i
$970$			0.126571i			0.00406394i
$971$	8.51997	−	14.7570i	0.273419	−	0.473575i	−0.696316	−	0.717735i	$-0.745179\pi$
$971$	8.51997	−	14.7570i	0.273419	−	0.473575i	0.969735	+	0.244160i	$0.0785122\pi$
$972$	−11.5305	−	19.9715i	−0.369843	−	0.640586i
$973$	41.3063	−	23.8482i	1.32422	−	0.764538i
$974$	93.9007			3.00877
$975$	−4.71005	−	26.6342i	−0.150842	−	0.852976i
$976$	−158.837			−5.08425
$977$	−31.4974	+	18.1850i	−1.00769	+	0.581791i	−0.910515	−	0.413476i	$-0.864315\pi$
$977$	−31.4974	+	18.1850i	−1.00769	+	0.581791i	−0.0971767	+	0.995267i	$0.530981\pi$
$978$	−20.0994	−	34.8133i	−0.642709	−	1.11321i
$979$	22.0201	−	38.1400i	0.703767	−	1.21896i
$980$		−	1.28464i		−	0.0410362i
$981$	−2.69321	−	1.55493i	−0.0859877	−	0.0496450i
$982$	17.4510	+	10.0753i	0.556884	+	0.321517i
$983$		−	45.5728i		−	1.45355i	−0.686877	−	0.726774i	$-0.741019\pi$
$983$		−	45.5728i		−	1.45355i	0.686877	−	0.726774i	$-0.258981\pi$
$984$	14.8286	−	25.6839i	0.472719	−	0.818773i
$985$	−3.98836	−	6.90805i	−0.127080	−	0.220109i
$986$	−69.6963	+	40.2392i	−2.21958	+	1.28148i
$987$	45.4887			1.44792
$988$	83.0303	−	14.6833i	2.64155	−	0.467137i
$989$	4.75169			0.151095
$990$	3.26293	−	1.88385i	0.103703	−	0.0598728i
$991$	−24.5935	−	42.5971i	−0.781237	−	1.35314i	−0.931221	−	0.364454i	$-0.881256\pi$
$991$	−24.5935	−	42.5971i	−0.781237	−	1.35314i	0.149984	−	0.988688i	$-0.452078\pi$
$992$	8.29060	−	14.3597i	0.263227	−	0.455922i
$993$			36.1599i			1.14750i
$994$	65.9668	+	38.0859i	2.09234	+	1.20801i
$995$	8.77358	+	5.06543i	0.278141	+	0.160585i
$996$		−	32.2788i		−	1.02279i
$997$	−2.71549	+	4.70337i	−0.0860006	+	0.148957i	−0.905817	−	0.423669i	$-0.860742\pi$
$997$	−2.71549	+	4.70337i	−0.0860006	+	0.148957i	0.819817	+	0.572626i	$0.194075\pi$
$998$	24.0402	+	41.6388i	0.760978	+	1.31805i
$999$	−2.60797	+	1.50571i	−0.0825126	+	0.0476387i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	299.2.i.b.231.1	✓	30
13.2	odd	12		3887.2.a.u.1.1		30
13.4	even	6	inner	299.2.i.b.277.1	yes	30
13.11	odd	12		3887.2.a.u.1.30		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
299.2.i.b.231.1	✓	30	1.1	even	1	trivial
299.2.i.b.277.1	yes	30	13.4	even	6	inner
3887.2.a.u.1.1		30	13.2	odd	12
3887.2.a.u.1.30		30	13.11	odd	12

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:	\( N \)	\(=\)	\( 299 = 13 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	299.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.30697 + 1.33193i) q^{2} +(0.800132 + 1.38587i) q^{3} +(2.54808 - 4.41341i) q^{4} -0.558810i q^{5} +(-3.69177 - 2.13144i) q^{6} +(-2.36396 - 1.36484i) q^{7} +8.24775i q^{8} +(0.219577 - 0.380318i) q^{9} +O(q^{10})\)	\(q+(-2.30697 + 1.33193i) q^{2} +(0.800132 + 1.38587i) q^{3} +(2.54808 - 4.41341i) q^{4} -0.558810i q^{5} +(-3.69177 - 2.13144i) q^{6} +(-2.36396 - 1.36484i) q^{7} +8.24775i q^{8} +(0.219577 - 0.380318i) q^{9} +(0.744297 + 1.28916i) q^{10} +(4.99132 - 2.88174i) q^{11} +8.15521 q^{12} +(-3.38873 - 1.23148i) q^{13} +7.27147 q^{14} +(0.774438 - 0.447122i) q^{15} +(-5.88927 - 10.2005i) q^{16} +(2.84079 - 4.92039i) q^{17} +1.16984i q^{18} +(-3.97411 - 2.29445i) q^{19} +(-2.46626 - 1.42389i) q^{20} -4.36819i q^{21} +(-7.67656 + 13.2962i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(-11.4303 + 6.59929i) q^{24} +4.68773 q^{25} +(9.45794 - 1.67256i) q^{26} +5.50356 q^{27} +(-12.0471 + 6.95542i) q^{28} +(2.65869 + 4.60499i) q^{29} +(-1.19107 + 2.06300i) q^{30} -1.11426i q^{31} +(12.8873 + 7.44046i) q^{32} +(7.98743 + 4.61155i) q^{33} +15.1349i q^{34} +(-0.762684 + 1.32101i) q^{35} +(-1.11900 - 1.93816i) q^{36} +(-0.473870 + 0.273589i) q^{37} +12.2242 q^{38} +(-1.00476 - 5.68168i) q^{39} +4.60893 q^{40} +(-1.94596 + 1.12350i) q^{41} +(5.81813 + 10.0773i) q^{42} +(-2.37585 + 4.11509i) q^{43} -29.3716i q^{44} +(-0.212526 - 0.122702i) q^{45} +(2.30697 + 1.33193i) q^{46} +10.4136i q^{47} +(9.42439 - 16.3235i) q^{48} +(0.225550 + 0.390664i) q^{49} +(-10.8145 + 6.24373i) q^{50} +9.09202 q^{51} +(-14.0698 + 11.8179i) q^{52} -2.18803 q^{53} +(-12.6965 + 7.33036i) q^{54} +(-1.61035 - 2.78920i) q^{55} +(11.2568 - 19.4974i) q^{56} -7.34346i q^{57} +(-12.2671 - 7.08240i) q^{58} +(-6.99415 - 4.03808i) q^{59} -4.55721i q^{60} +(6.74264 - 11.6786i) q^{61} +(1.48412 + 2.57056i) q^{62} +(-1.03814 + 0.599372i) q^{63} -16.0836 q^{64} +(-0.688162 + 1.89365i) q^{65} -24.5691 q^{66} +(8.25743 - 4.76743i) q^{67} +(-14.4771 - 25.0751i) q^{68} +(0.800132 - 1.38587i) q^{69} -4.06337i q^{70} +(9.07200 + 5.23772i) q^{71} +(3.13677 + 1.81101i) q^{72} -4.46497i q^{73} +(0.728804 - 1.26233i) q^{74} +(3.75081 + 6.49658i) q^{75} +(-20.2527 + 11.6929i) q^{76} -15.7324 q^{77} +(9.88556 + 11.7692i) q^{78} -8.71615 q^{79} +(-5.70015 + 3.29098i) q^{80} +(3.74484 + 6.48626i) q^{81} +(2.99285 - 5.18377i) q^{82} -3.95807i q^{83} +(-19.2786 - 11.1305i) q^{84} +(-2.74956 - 1.58746i) q^{85} -12.6579i q^{86} +(-4.25461 + 7.36921i) q^{87} +(23.7679 + 41.1672i) q^{88} +(6.61753 - 3.82063i) q^{89} +0.653721 q^{90} +(6.33006 + 7.53622i) q^{91} -5.09616 q^{92} +(1.54422 - 0.891555i) q^{93} +(-13.8702 - 24.0239i) q^{94} +(-1.28216 + 2.22077i) q^{95} +23.8134i q^{96} +(0.0736356 + 0.0425135i) q^{97} +(-1.04068 - 0.600834i) q^{98} -2.53105i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} + 16 q^{4} - 9 q^{6} - 3 q^{7} - 16 q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 + 16 * q^4 - 9 * q^6 - 3 * q^7 - 16 * q^9	\( 30 q - 3 q^{3} + 16 q^{4} - 9 q^{6} - 3 q^{7} - 16 q^{9} + 23 q^{10} - 4 q^{12} - 2 q^{13} + 4 q^{14} - 6 q^{15} - 26 q^{16} + 13 q^{17} - 12 q^{19} + 6 q^{20} - 16 q^{22} - 15 q^{23} + 6 q^{24} - 52 q^{25} - 25 q^{26} + 54 q^{27} - 24 q^{28} - q^{29} + 20 q^{30} - 39 q^{32} - 18 q^{33} + 20 q^{35} + 23 q^{36} - 30 q^{37} + 18 q^{38} - 60 q^{39} + 124 q^{40} - 6 q^{41} - 12 q^{42} + 33 q^{43} + 18 q^{45} + 34 q^{48} + 48 q^{49} - 60 q^{50} + 20 q^{51} - 39 q^{52} + 62 q^{53} + 45 q^{54} - 16 q^{55} - 5 q^{56} - 66 q^{58} - 21 q^{59} - 18 q^{61} + 46 q^{62} - 117 q^{63} - 16 q^{64} - 4 q^{65} + 52 q^{66} + 24 q^{67} - 18 q^{68} - 3 q^{69} + 54 q^{71} - 54 q^{72} + 42 q^{74} + 4 q^{75} - 18 q^{76} - 20 q^{77} + 72 q^{79} + 114 q^{80} - 15 q^{81} + 14 q^{82} - 159 q^{84} - 39 q^{85} + 40 q^{87} + 93 q^{88} - 51 q^{89} - 78 q^{90} - 34 q^{91} - 32 q^{92} + 6 q^{93} + 8 q^{94} - 24 q^{95} - 6 q^{97} - 123 q^{98}+O(q^{100}) \) 30 * q - 3 * q^3 + 16 * q^4 - 9 * q^6 - 3 * q^7 - 16 * q^9 + 23 * q^10 - 4 * q^12 - 2 * q^13 + 4 * q^14 - 6 * q^15 - 26 * q^16 + 13 * q^17 - 12 * q^19 + 6 * q^20 - 16 * q^22 - 15 * q^23 + 6 * q^24 - 52 * q^25 - 25 * q^26 + 54 * q^27 - 24 * q^28 - q^29 + 20 * q^30 - 39 * q^32 - 18 * q^33 + 20 * q^35 + 23 * q^36 - 30 * q^37 + 18 * q^38 - 60 * q^39 + 124 * q^40 - 6 * q^41 - 12 * q^42 + 33 * q^43 + 18 * q^45 + 34 * q^48 + 48 * q^49 - 60 * q^50 + 20 * q^51 - 39 * q^52 + 62 * q^53 + 45 * q^54 - 16 * q^55 - 5 * q^56 - 66 * q^58 - 21 * q^59 - 18 * q^61 + 46 * q^62 - 117 * q^63 - 16 * q^64 - 4 * q^65 + 52 * q^66 + 24 * q^67 - 18 * q^68 - 3 * q^69 + 54 * q^71 - 54 * q^72 + 42 * q^74 + 4 * q^75 - 18 * q^76 - 20 * q^77 + 72 * q^79 + 114 * q^80 - 15 * q^81 + 14 * q^82 - 159 * q^84 - 39 * q^85 + 40 * q^87 + 93 * q^88 - 51 * q^89 - 78 * q^90 - 34 * q^91 - 32 * q^92 + 6 * q^93 + 8 * q^94 - 24 * q^95 - 6 * q^97 - 123 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more