LMFDB - Embedded newform 403.2.h.a.118.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("403.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			118.12
Character	$\chi$	$=$	403.118
Dual form			403.2.h.a.222.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41262 q^{2} +(-1.31623 - 2.27977i) q^{3} -0.00449076 q^{4} +(-1.72422 + 2.98644i) q^{5} +(-1.85934 - 3.22047i) q^{6} +(2.33584 + 4.04580i) q^{7} -2.83159 q^{8} +(-1.96492 + 3.40333i) q^{9} +O(q^{10})$	\(q+1.41262 q^{2} +(-1.31623 - 2.27977i) q^{3} -0.00449076 q^{4} +(-1.72422 + 2.98644i) q^{5} +(-1.85934 - 3.22047i) q^{6} +(2.33584 + 4.04580i) q^{7} -2.83159 q^{8} +(-1.96492 + 3.40333i) q^{9} +(-2.43568 + 4.21871i) q^{10} +(-0.595937 + 1.03219i) q^{11} +(0.00591087 + 0.0102379i) q^{12} +(0.500000 - 0.866025i) q^{13} +(3.29967 + 5.71520i) q^{14} +9.07787 q^{15} -3.99100 q^{16} +(-0.625797 - 1.08391i) q^{17} +(-2.77569 + 4.80763i) q^{18} +(3.21698 + 5.57198i) q^{19} +(0.00774306 - 0.0134114i) q^{20} +(6.14901 - 10.6504i) q^{21} +(-0.841835 + 1.45810i) q^{22} -4.73779 q^{23} +(3.72702 + 6.45540i) q^{24} +(-3.44587 - 5.96842i) q^{25} +(0.706312 - 1.22337i) q^{26} +2.44774 q^{27} +(-0.0104897 - 0.0181687i) q^{28} +0.751364 q^{29} +12.8236 q^{30} +(-2.50877 - 4.97052i) q^{31} +0.0254035 q^{32} +3.13756 q^{33} +(-0.884017 - 1.53116i) q^{34} -16.1100 q^{35} +(0.00882397 - 0.0152836i) q^{36} +(4.39058 + 7.60470i) q^{37} +(4.54439 + 7.87112i) q^{38} -2.63246 q^{39} +(4.88229 - 8.45637i) q^{40} +(-3.83672 + 6.64540i) q^{41} +(8.68624 - 15.0450i) q^{42} +(5.02607 + 8.70541i) q^{43} +(0.00267621 - 0.00463533i) q^{44} +(-6.77589 - 11.7362i) q^{45} -6.69271 q^{46} -5.76087 q^{47} +(5.25307 + 9.09858i) q^{48} +(-7.41234 + 12.8385i) q^{49} +(-4.86772 - 8.43114i) q^{50} +(-1.64738 + 2.85335i) q^{51} +(-0.00224538 + 0.00388911i) q^{52} +(5.63583 - 9.76155i) q^{53} +3.45774 q^{54} +(-2.05505 - 3.55946i) q^{55} +(-6.61416 - 11.4561i) q^{56} +(8.46857 - 14.6680i) q^{57} +1.06140 q^{58} +(-0.868681 - 1.50460i) q^{59} -0.0407666 q^{60} +0.317485 q^{61} +(-3.54396 - 7.02148i) q^{62} -18.3589 q^{63} +8.01788 q^{64} +(1.72422 + 2.98644i) q^{65} +4.43219 q^{66} +(3.31754 - 5.74614i) q^{67} +(0.00281031 + 0.00486759i) q^{68} +(6.23601 + 10.8011i) q^{69} -22.7574 q^{70} +(4.63711 - 8.03172i) q^{71} +(5.56384 - 9.63686i) q^{72} +(0.928944 - 1.60898i) q^{73} +(6.20224 + 10.7426i) q^{74} +(-9.07110 + 15.7116i) q^{75} +(-0.0144467 - 0.0250224i) q^{76} -5.56806 q^{77} -3.71867 q^{78} +(-5.91597 - 10.2468i) q^{79} +(6.88136 - 11.9189i) q^{80} +(2.67296 + 4.62971i) q^{81} +(-5.41985 + 9.38746i) q^{82} +(0.162344 - 0.281187i) q^{83} +(-0.0276137 + 0.0478284i) q^{84} +4.31605 q^{85} +(7.09995 + 12.2975i) q^{86} +(-0.988967 - 1.71294i) q^{87} +(1.68745 - 2.92275i) q^{88} +8.13779 q^{89} +(-9.57179 - 16.5788i) q^{90} +4.67169 q^{91} +0.0212763 q^{92} +(-8.02954 + 12.2618i) q^{93} -8.13794 q^{94} -22.1871 q^{95} +(-0.0334369 - 0.0579143i) q^{96} -2.38172 q^{97} +(-10.4709 + 18.1360i) q^{98} +(-2.34193 - 4.05634i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9}+O(q^{10}) $ 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9	\( 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9} - 3 q^{10} - 3 q^{11} + 12 q^{12} + 15 q^{13} + 3 q^{14} + 4 q^{15} + 22 q^{16} + 4 q^{17} - 6 q^{18} + 5 q^{19} + 10 q^{20} - 15 q^{21} + 2 q^{22} - 6 q^{23} - 6 q^{24} - 20 q^{25} - 3 q^{26} + 4 q^{27} + 13 q^{28} + 26 q^{29} + 28 q^{30} + 19 q^{31} - 74 q^{32} + 2 q^{33} - 21 q^{34} - 30 q^{35} + 37 q^{36} - 4 q^{37} - 4 q^{38} - 4 q^{39} - 17 q^{40} + 7 q^{41} + 44 q^{42} + 15 q^{43} - 70 q^{44} + 15 q^{45} - 58 q^{46} - 24 q^{47} + 31 q^{48} - 29 q^{49} + 2 q^{50} + 25 q^{51} + 11 q^{52} + 4 q^{53} + 34 q^{54} + 13 q^{55} - 41 q^{56} + 8 q^{57} - 46 q^{58} + 27 q^{59} + 78 q^{60} + 8 q^{61} + 20 q^{62} - 112 q^{63} + 60 q^{64} - 7 q^{65} + 60 q^{66} + 29 q^{67} + 41 q^{68} - 23 q^{69} - 112 q^{70} + 29 q^{71} + 14 q^{72} - 10 q^{73} + 25 q^{74} - 18 q^{75} + 24 q^{76} - 72 q^{77} + 9 q^{79} - 11 q^{81} - 38 q^{82} - 13 q^{83} - 62 q^{84} + 108 q^{85} - 38 q^{86} - 18 q^{87} + 32 q^{88} + 6 q^{89} + 7 q^{90} + 12 q^{91} + 2 q^{92} + 37 q^{93} - 154 q^{94} - 28 q^{95} - 105 q^{96} - 84 q^{97} + 50 q^{98} + 10 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9 - 3 * q^10 - 3 * q^11 + 12 * q^12 + 15 * q^13 + 3 * q^14 + 4 * q^15 + 22 * q^16 + 4 * q^17 - 6 * q^18 + 5 * q^19 + 10 * q^20 - 15 * q^21 + 2 * q^22 - 6 * q^23 - 6 * q^24 - 20 * q^25 - 3 * q^26 + 4 * q^27 + 13 * q^28 + 26 * q^29 + 28 * q^30 + 19 * q^31 - 74 * q^32 + 2 * q^33 - 21 * q^34 - 30 * q^35 + 37 * q^36 - 4 * q^37 - 4 * q^38 - 4 * q^39 - 17 * q^40 + 7 * q^41 + 44 * q^42 + 15 * q^43 - 70 * q^44 + 15 * q^45 - 58 * q^46 - 24 * q^47 + 31 * q^48 - 29 * q^49 + 2 * q^50 + 25 * q^51 + 11 * q^52 + 4 * q^53 + 34 * q^54 + 13 * q^55 - 41 * q^56 + 8 * q^57 - 46 * q^58 + 27 * q^59 + 78 * q^60 + 8 * q^61 + 20 * q^62 - 112 * q^63 + 60 * q^64 - 7 * q^65 + 60 * q^66 + 29 * q^67 + 41 * q^68 - 23 * q^69 - 112 * q^70 + 29 * q^71 + 14 * q^72 - 10 * q^73 + 25 * q^74 - 18 * q^75 + 24 * q^76 - 72 * q^77 + 9 * q^79 - 11 * q^81 - 38 * q^82 - 13 * q^83 - 62 * q^84 + 108 * q^85 - 38 * q^86 - 18 * q^87 + 32 * q^88 + 6 * q^89 + 7 * q^90 + 12 * q^91 + 2 * q^92 + 37 * q^93 - 154 * q^94 - 28 * q^95 - 105 * q^96 - 84 * q^97 + 50 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.41262			0.998877			0.499438	−	0.866349i	$-0.333540\pi$
$2$	1.41262			0.998877			0.499438	+	0.866349i	$0.333540\pi$
$3$	−1.31623	−	2.27977i	−0.759925	−	1.31623i	−0.942888	−	0.333109i	$-0.891902\pi$
$3$	−1.31623	−	2.27977i	−0.759925	−	1.31623i	0.182963	−	0.983120i	$-0.441431\pi$
$4$	−0.00449076			−0.00224538
$5$	−1.72422	+	2.98644i	−0.771095	+	1.33558i	0.165869	+	0.986148i	$0.446957\pi$
$5$	−1.72422	+	2.98644i	−0.771095	+	1.33558i	−0.936964	+	0.349427i	$0.886376\pi$
$6$	−1.85934	−	3.22047i	−0.759071	−	1.31475i
$7$	2.33584	+	4.04580i	0.882866	+	1.52917i	0.848140	+	0.529772i	$0.177723\pi$
$7$	2.33584	+	4.04580i	0.882866	+	1.52917i	0.0347261	+	0.999397i	$0.488944\pi$
$8$	−2.83159			−1.00112
$9$	−1.96492	+	3.40333i	−0.654972	+	1.13444i
$10$	−2.43568	+	4.21871i	−0.770228	+	1.33407i
$11$	−0.595937	+	1.03219i	−0.179682	+	0.311218i	−0.941772	−	0.336253i	$-0.890840\pi$
$11$	−0.595937	+	1.03219i	−0.179682	+	0.311218i	0.762090	+	0.647471i	$0.224173\pi$
$12$	0.00591087	+	0.0102379i	0.00170632	+	0.00295543i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i
$14$	3.29967	+	5.71520i	0.881874	+	1.52745i
$15$	9.07787			2.34390
$16$	−3.99100			−0.997750
$17$	−0.625797	−	1.08391i	−0.151778	−	0.262888i	0.780103	−	0.625651i	$-0.215167\pi$
$17$	−0.625797	−	1.08391i	−0.151778	−	0.262888i	−0.931881	+	0.362764i	$0.881833\pi$
$18$	−2.77569	+	4.80763i	−0.654236	+	1.13317i
$19$	3.21698	+	5.57198i	0.738027	+	1.27830i	0.953383	+	0.301764i	$0.0975754\pi$
$19$	3.21698	+	5.57198i	0.738027	+	1.27830i	−0.215356	+	0.976536i	$0.569091\pi$
$20$	0.00774306	−	0.0134114i	0.00173140	−	0.00299887i
$21$	6.14901	−	10.6504i	1.34182	−	2.32411i
$22$	−0.841835	+	1.45810i	−0.179480	+	0.310868i
$23$	−4.73779			−0.987897			−0.493948	−	0.869491i	$-0.664447\pi$
$23$	−4.73779			−0.987897			−0.493948	+	0.869491i	$0.664447\pi$
$24$	3.72702	+	6.45540i	0.760776	+	1.31770i
$25$	−3.44587	−	5.96842i	−0.689174	−	1.19368i
$26$	0.706312	−	1.22337i	0.138519	−	0.239922i
$27$	2.44774			0.471067
$28$	−0.0104897	−	0.0181687i	−0.00198237	−	0.00343357i
$29$	0.751364			0.139525			0.0697624	−	0.997564i	$-0.477776\pi$
$29$	0.751364			0.139525			0.0697624	+	0.997564i	$0.477776\pi$
$30$	12.8236			2.34126
$31$	−2.50877	−	4.97052i	−0.450589	−	0.892732i
$31$	−2.50877	−	4.97052i	−0.450589	−	0.892732i
$32$	0.0254035			0.00449075
$33$	3.13756			0.546179
$34$	−0.884017	−	1.53116i	−0.151608	−	0.262592i
$35$	−16.1100			−2.72309
$36$	0.00882397	−	0.0152836i	0.00147066	−	0.00254726i
$37$	4.39058	+	7.60470i	0.721806	+	1.25020i	0.960275	+	0.279055i	$0.0900211\pi$
$37$	4.39058	+	7.60470i	0.721806	+	1.25020i	−0.238469	+	0.971150i	$0.576646\pi$
$38$	4.54439	+	7.87112i	0.737197	+	1.27686i
$39$	−2.63246			−0.421530
$40$	4.88229	−	8.45637i	0.771958	−	1.33707i
$41$	−3.83672	+	6.64540i	−0.599196	+	1.03784i	0.393744	+	0.919220i	$0.371180\pi$
$41$	−3.83672	+	6.64540i	−0.599196	+	1.03784i	−0.992940	+	0.118617i	$0.962154\pi$
$42$	8.68624	−	15.0450i	1.34032	−	2.32150i
$43$	5.02607	+	8.70541i	0.766469	+	1.32756i	0.939467	+	0.342640i	$0.111321\pi$
$43$	5.02607	+	8.70541i	0.766469	+	1.32756i	−0.172998	+	0.984922i	$0.555345\pi$
$44$	0.00267621	−	0.00463533i	0.000403454	−	0.000698803i
$45$	−6.77589	−	11.7362i	−1.01009	−	1.74953i
$46$	−6.69271			−0.986787
$47$	−5.76087			−0.840309			−0.420154	−	0.907453i	$-0.638024\pi$
$47$	−5.76087			−0.840309			−0.420154	+	0.907453i	$0.638024\pi$
$48$	5.25307	+	9.09858i	0.758215	+	1.31327i
$49$	−7.41234	+	12.8385i	−1.05891	+	1.83408i
$50$	−4.86772	−	8.43114i	−0.688400	−	1.19234i
$51$	−1.64738	+	2.85335i	−0.230680	+	0.399550i
$52$	−0.00224538	+	0.00388911i	−0.000311378	+	0.000539323i
$53$	5.63583	−	9.76155i	0.774141	−	1.34085i	−0.161135	−	0.986932i	$-0.551515\pi$
$53$	5.63583	−	9.76155i	0.774141	−	1.34085i	0.935276	−	0.353920i	$-0.115151\pi$
$54$	3.45774			0.470538
$55$	−2.05505	−	3.55946i	−0.277103	−	0.479957i
$56$	−6.61416	−	11.4561i	−0.883855	−	1.53088i
$57$	8.46857	−	14.6680i	1.12169	−	1.94282i
$58$	1.06140			0.139368
$59$	−0.868681	−	1.50460i	−0.113093	−	0.195882i	0.803923	−	0.594733i	$-0.202742\pi$
$59$	−0.868681	−	1.50460i	−0.113093	−	0.195882i	−0.917016	+	0.398851i	$0.869409\pi$
$60$	−0.0407666			−0.00526294
$61$	0.317485			0.0406498			0.0203249	−	0.999793i	$-0.493530\pi$
$61$	0.317485			0.0406498			0.0203249	+	0.999793i	$0.493530\pi$
$62$	−3.54396	−	7.02148i	−0.450083	−	0.891729i
$63$	−18.3589			−2.31301
$64$	8.01788			1.00224
$65$	1.72422	+	2.98644i	0.213863	+	0.370422i
$66$	4.43219			0.545565
$67$	3.31754	−	5.74614i	0.405302	−	0.702003i	−0.589055	−	0.808093i	$-0.700500\pi$
$67$	3.31754	−	5.74614i	0.405302	−	0.702003i	0.994357	+	0.106090i	$0.0338331\pi$
$68$	0.00281031	+	0.00486759i	0.000340800	+	0.000590283i
$69$	6.23601	+	10.8011i	0.750727	+	1.30030i
$70$	−22.7574			−2.72003
$71$	4.63711	−	8.03172i	0.550324	−	0.953189i	−0.447927	−	0.894070i	$-0.647837\pi$
$71$	4.63711	−	8.03172i	0.550324	−	0.953189i	0.998251	−	0.0591191i	$-0.0188292\pi$
$72$	5.56384	−	9.63686i	0.655705	−	1.13571i
$73$	0.928944	−	1.60898i	0.108725	−	0.188317i	−0.806529	−	0.591194i	$-0.798657\pi$
$73$	0.928944	−	1.60898i	0.108725	−	0.188317i	0.915254	+	0.402878i	$0.131990\pi$
$74$	6.20224	+	10.7426i	0.720995	+	1.24880i
$75$	−9.07110	+	15.7116i	−1.04744	+	1.81422i
$76$	−0.0144467	−	0.0250224i	−0.00165715	−	0.00287027i
$77$	−5.56806			−0.634540
$78$	−3.71867			−0.421057
$79$	−5.91597	−	10.2468i	−0.665598	−	1.15285i	−0.979123	−	0.203270i	$-0.934843\pi$
$79$	−5.91597	−	10.2468i	−0.665598	−	1.15285i	0.313525	−	0.949580i	$-0.398490\pi$
$80$	6.88136	−	11.9189i	0.769359	−	1.33257i
$81$	2.67296	+	4.62971i	0.296996	+	0.514412i
$82$	−5.41985	+	9.38746i	−0.598523	+	1.03667i
$83$	0.162344	−	0.281187i	0.0178195	−	0.0308643i	−0.856978	−	0.515353i	$-0.827661\pi$
$83$	0.162344	−	0.281187i	0.0178195	−	0.0308643i	0.874798	+	0.484488i	$0.160994\pi$
$84$	−0.0276137	+	0.0478284i	−0.00301291	+	0.00521851i
$85$	4.31605			0.468141
$86$	7.09995	+	12.2975i	0.765608	+	1.32607i
$87$	−0.988967	−	1.71294i	−0.106028	−	0.183647i
$88$	1.68745	−	2.92275i	0.179883	−	0.311566i
$89$	8.13779			0.862604			0.431302	−	0.902208i	$-0.358054\pi$
$89$	8.13779			0.862604			0.431302	+	0.902208i	$0.358054\pi$
$90$	−9.57179	−	16.5788i	−1.00896	−	1.74756i
$91$	4.67169			0.489726
$92$	0.0212763			0.00221820
$93$	−8.02954	+	12.2618i	−0.832625	+	1.27149i
$94$	−8.13794			−0.839365
$95$	−22.1871			−2.27635
$96$	−0.0334369	−	0.0579143i	−0.00341264	−	0.00591086i
$97$	−2.38172			−0.241827			−0.120913	−	0.992663i	$-0.538582\pi$
$97$	−2.38172			−0.241827			−0.120913	+	0.992663i	$0.538582\pi$
$98$	−10.4709	+	18.1360i	−1.05772	+	1.83202i
$99$	−2.34193	−	4.05634i	−0.235373	−	0.407678i
$100$	0.0154746	+	0.0268028i	0.00154746	+	0.00268028i
$101$	11.8445			1.17857			0.589284	−	0.807926i	$-0.299410\pi$
$101$	11.8445			1.17857			0.589284	+	0.807926i	$0.299410\pi$
$102$	−2.32714	+	4.03072i	−0.230421	+	0.399101i
$103$	−6.59417	+	11.4214i	−0.649742	+	1.12539i	0.333442	+	0.942771i	$0.391790\pi$
$103$	−6.59417	+	11.4214i	−0.649742	+	1.12539i	−0.983184	+	0.182616i	$0.941543\pi$
$104$	−1.41580	+	2.45223i	−0.138830	+	0.240461i
$105$	21.2045	+	36.7273i	2.06935	+	3.58421i
$106$	7.96132	−	13.7894i	0.773272	−	1.33935i
$107$	−0.243674	−	0.422055i	−0.0235568	−	0.0408016i	0.854007	−	0.520262i	$-0.174166\pi$
$107$	−0.243674	−	0.422055i	−0.0235568	−	0.0408016i	−0.877563	+	0.479460i	$0.840832\pi$
$108$	−0.0109922			−0.00105773
$109$	9.67837			0.927020			0.463510	−	0.886092i	$-0.346590\pi$
$109$	9.67837			0.927020			0.463510	+	0.886092i	$0.346590\pi$
$110$	−2.90302	−	5.02818i	−0.276792	−	0.479418i
$111$	11.5580	−	20.0190i	1.09704	−	1.90012i
$112$	−9.32235	−	16.1468i	−0.880879	−	1.52573i
$113$	9.58272	−	16.5978i	0.901466	−	1.56139i	0.0758748	−	0.997117i	$-0.475825\pi$
$113$	9.58272	−	16.5978i	0.901466	−	1.56139i	0.825592	−	0.564268i	$-0.190842\pi$
$114$	11.9629	−	20.7204i	1.12043	−	1.94064i
$115$	8.16899	−	14.1491i	0.761762	−	1.31941i
$116$	−0.00337420			−0.000313286
$117$	1.96492	+	3.40333i	0.181656	+	0.314638i
$118$	−1.22712	−	2.12544i	−0.112966	−	0.195662i
$119$	2.92353	−	5.06370i	0.268000	−	0.464189i
$120$	−25.7048			−2.34652
$121$	4.78972	+	8.29604i	0.435429	+	0.754185i
$122$	0.448488			0.0406042
$123$	20.2000			1.82137
$124$	0.0112663	+	0.0223214i	0.00101174	+	0.00200452i
$125$	6.52354			0.583484
$126$	−25.9343			−2.31041
$127$	2.09027	+	3.62046i	0.185482	+	0.321264i	0.943739	−	0.330692i	$-0.107282\pi$
$127$	2.09027	+	3.62046i	0.185482	+	0.321264i	−0.758257	+	0.651956i	$0.773949\pi$
$128$	11.2755			0.996619
$129$	13.2309	−	22.9166i	1.16492	−	2.01770i
$130$	2.43568	+	4.21871i	0.213623	+	0.370006i
$131$	6.15215	+	10.6558i	0.537516	+	0.931005i	0.999037	+	0.0438754i	$0.0139705\pi$
$131$	6.15215	+	10.6558i	0.537516	+	0.931005i	−0.461521	+	0.887129i	$0.652696\pi$
$132$	−0.0140900			−0.00122638
$133$	−15.0287	+	26.0305i	−1.30316	+	2.25713i
$134$	4.68644	−	8.11715i	0.404847	−	0.701215i
$135$	−4.22044	+	7.31001i	−0.363237	+	0.629146i
$136$	1.77200	+	3.06920i	0.151948	+	0.263182i
$137$	−8.66399	+	15.0065i	−0.740215	+	1.28209i	0.212182	+	0.977230i	$0.431943\pi$
$137$	−8.66399	+	15.0065i	−0.740215	+	1.28209i	−0.952397	+	0.304860i	$0.901390\pi$
$138$	8.80914	+	15.2579i	0.749884	+	1.29884i
$139$	−16.4122			−1.39207			−0.696033	−	0.718010i	$-0.745053\pi$
$139$	−16.4122			−1.39207			−0.696033	+	0.718010i	$0.745053\pi$
$140$	0.0723463			0.00611438
$141$	7.58262	+	13.1335i	0.638571	+	1.10604i
$142$	6.55050	−	11.3458i	0.549706	−	0.952119i
$143$	0.595937	+	1.03219i	0.0498347	+	0.0863163i
$144$	7.84197	−	13.5827i	0.653498	−	1.13189i
$145$	−1.29552	+	2.24390i	−0.107587	+	0.186346i
$146$	1.31225	−	2.27288i	0.108602	−	0.188105i
$147$	39.0253			3.21875
$148$	−0.0197170	−	0.0341509i	−0.00162073	−	0.00280719i
$149$	8.87759	+	15.3764i	0.727280	+	1.25969i	0.958028	+	0.286673i	$0.0925494\pi$
$149$	8.87759	+	15.3764i	0.727280	+	1.25969i	−0.230748	+	0.973014i	$0.574117\pi$
$150$	−12.8141	+	22.1946i	−1.04626	+	1.81218i
$151$	12.7523			1.03777			0.518883	−	0.854845i	$-0.326348\pi$
$151$	12.7523			1.03777			0.518883	+	0.854845i	$0.326348\pi$
$152$	−9.10919	−	15.7776i	−0.738853	−	1.27973i
$153$	4.91856			0.397642
$154$	−7.86559			−0.633827
$155$	19.1698	+	1.07798i	1.53976	+	0.0865851i
$156$	0.0118217			0.000946497
$157$	−3.08319			−0.246066			−0.123033	−	0.992403i	$-0.539262\pi$
$157$	−3.08319			−0.246066			−0.123033	+	0.992403i	$0.539262\pi$
$158$	−8.35704	−	14.4748i	−0.664851	−	1.15155i
$159$	−29.6722			−2.35316
$160$	−0.0438013	+	0.0758661i	−0.00346280	+	0.00599774i
$161$	−11.0667	−	19.1681i	−0.872181	−	1.51066i
$162$	3.77589	+	6.54004i	0.296662	+	0.513834i
$163$	7.30364			0.572065			0.286033	−	0.958220i	$-0.407663\pi$
$163$	7.30364			0.572065			0.286033	+	0.958220i	$0.407663\pi$
$164$	0.0172298	−	0.0298429i	0.00134542	−	0.00233034i
$165$	−5.40984	+	9.37011i	−0.421155	+	0.729462i
$166$	0.229331	−	0.397212i	0.0177995	−	0.0308297i
$167$	−8.94382	−	15.4912i	−0.692094	−	1.19874i	−0.971151	−	0.238467i	$-0.923355\pi$
$167$	−8.94382	−	15.4912i	−0.692094	−	1.19874i	0.279057	−	0.960275i	$-0.409978\pi$
$168$	−17.4115	+	30.1576i	−1.34333	+	2.32671i
$169$	−0.500000	−	0.866025i	−0.0384615	−	0.0666173i
$170$	6.09696			0.467615
$171$	−25.2844			−1.93355
$172$	−0.0225709	−	0.0390939i	−0.00172101	−	0.00298088i
$173$	0.421358	−	0.729813i	0.0320352	−	0.0554866i	−0.849563	−	0.527487i	$-0.823134\pi$
$173$	0.421358	−	0.729813i	0.0320352	−	0.0554866i	0.881599	+	0.472000i	$0.156468\pi$
$174$	−1.39704	−	2.41974i	−0.105909	−	0.183440i
$175$	16.0980	−	27.8826i	1.21690	−	2.10773i
$176$	2.37838	−	4.11948i	0.179277	−	0.310518i
$177$	−2.28677	+	3.96080i	−0.171884	+	0.297712i
$178$	11.4956			0.861635
$179$	6.53603	+	11.3207i	0.488526	+	0.846152i	0.999913	−	0.0131985i	$-0.00420134\pi$
$179$	6.53603	+	11.3207i	0.488526	+	0.846152i	−0.511387	+	0.859351i	$0.670868\pi$
$180$	0.0304289	+	0.0527044i	0.00226804	+	0.00392836i
$181$	−3.33127	+	5.76993i	−0.247612	+	0.428876i	−0.962863	−	0.269992i	$-0.912979\pi$
$181$	−3.33127	+	5.76993i	−0.247612	+	0.428876i	0.715251	+	0.698868i	$0.246312\pi$
$182$	6.59934			0.489176
$183$	−0.417883	−	0.723795i	−0.0308908	−	0.0535045i
$184$	13.4155			0.989003
$185$	−30.2813			−2.22632
$186$	−11.3427	+	17.3213i	−0.831690	+	1.27006i
$187$	1.49174			0.109087
$188$	0.0258707			0.00188681
$189$	5.71753	+	9.90306i	0.415889	+	0.720342i
$190$	−31.3421			−2.27380
$191$	−5.54667	+	9.60711i	−0.401343	+	0.695146i	−0.993888	−	0.110391i	$-0.964790\pi$
$191$	−5.54667	+	9.60711i	−0.401343	+	0.695146i	0.592545	+	0.805537i	$0.298123\pi$
$192$	−10.5534	−	18.2790i	−0.761624	−	1.31917i
$193$	1.86995	+	3.23886i	0.134602	+	0.233138i	0.925445	−	0.378881i	$-0.123691\pi$
$193$	1.86995	+	3.23886i	0.134602	+	0.233138i	−0.790843	+	0.612019i	$0.790358\pi$
$194$	−3.36448			−0.241555
$195$	4.53893	−	7.86167i	0.325040	−	0.562986i
$196$	0.0332870	−	0.0576548i	0.00237765	−	0.00411820i
$197$	3.04433	−	5.27294i	0.216900	−	0.375681i	−0.736959	−	0.675938i	$-0.763739\pi$
$197$	3.04433	−	5.27294i	0.216900	−	0.375681i	0.953859	+	0.300256i	$0.0970722\pi$
$198$	−3.30827	−	5.73009i	−0.235109	−	0.407220i
$199$	−2.45003	+	4.24358i	−0.173678	+	0.300819i	−0.939703	−	0.341992i	$-0.888899\pi$
$199$	−2.45003	+	4.24358i	−0.173678	+	0.300819i	0.766025	+	0.642811i	$0.222232\pi$
$200$	9.75730	+	16.9001i	0.689945	+	1.19502i
$201$	−17.4666			−1.23200
$202$	16.7318			1.17724
$203$	1.75507	+	3.03987i	0.123182	+	0.213357i
$204$	0.00739801	−	0.0128137i	0.000517965	−	0.000897141i
$205$	−13.2307	−	22.9163i	−0.924073	−	1.60054i
$206$	−9.31508	+	16.1342i	−0.649013	+	1.12412i
$207$	9.30935	−	16.1243i	0.647044	−	1.12071i
$208$	−1.99550	+	3.45631i	−0.138363	+	0.239652i
$209$	−7.66848			−0.530440
$210$	29.9540	+	51.8818i	2.06702	+	3.58019i
$211$	−4.59133	−	7.95242i	−0.316080	−	0.547467i	0.663586	−	0.748100i	$-0.269034\pi$
$211$	−4.59133	−	7.95242i	−0.316080	−	0.547467i	−0.979667	+	0.200633i	$0.935700\pi$
$212$	−0.0253092	+	0.0438368i	−0.00173824	+	0.00301072i
$213$	−24.4140			−1.67282
$214$	−0.344219	−	0.596205i	−0.0235303	−	0.0407558i
$215$	−34.6642			−2.36408
$216$	−6.93100			−0.471595
$217$	14.2496	−	21.7604i	0.967328	−	1.47719i
$218$	13.6719			0.925979
$219$	−4.89081			−0.330490
$220$	0.00922875	+	0.0159847i	0.000622202	+	0.00107769i
$221$	−1.25159			−0.0841914
$222$	16.3271	−	28.2794i	1.09580	−	1.89799i
$223$	−1.70601	−	2.95489i	−0.114243	−	0.197874i	0.803234	−	0.595663i	$-0.203111\pi$
$223$	−1.70601	−	2.95489i	−0.114243	−	0.197874i	−0.917477	+	0.397789i	$0.869777\pi$
$224$	0.0593387	+	0.102778i	0.00396473	+	0.00686712i
$225$	27.0834			1.80556
$226$	13.5368	−	23.4464i	0.900454	−	1.55963i
$227$	−4.90036	+	8.48768i	−0.325248	+	0.563347i	−0.981563	−	0.191141i	$-0.938781\pi$
$227$	−4.90036	+	8.48768i	−0.325248	+	0.563347i	0.656314	+	0.754488i	$0.272115\pi$
$228$	−0.0380303	+	0.0658705i	−0.00251862	+	0.00436238i
$229$	8.54925	+	14.8077i	0.564950	+	0.978522i	0.997054	+	0.0766987i	$0.0244380\pi$
$229$	8.54925	+	14.8077i	0.564950	+	0.978522i	−0.432104	+	0.901824i	$0.642229\pi$
$230$	11.5397	−	19.9874i	0.760906	−	1.31793i
$231$	7.32884	+	12.6939i	0.482203	+	0.835199i
$232$	−2.12756			−0.139681
$233$	−4.81668			−0.315551			−0.157776	−	0.987475i	$-0.550432\pi$
$233$	−4.81668			−0.315551			−0.157776	+	0.987475i	$0.550432\pi$
$234$	2.77569	+	4.80763i	0.181452	+	0.314285i
$235$	9.93300	−	17.2045i	0.647957	−	1.12230i
$236$	0.00390104	+	0.00675680i	0.000253936	+	0.000439830i
$237$	−15.5735	+	26.9741i	−1.01161	+	1.75216i
$238$	4.12985	−	7.15311i	0.267699	−	0.463667i
$239$	−8.64402	+	14.9719i	−0.559135	+	0.968450i	0.438434	+	0.898763i	$0.355533\pi$
$239$	−8.64402	+	14.9719i	−0.559135	+	0.968450i	−0.997569	+	0.0696869i	$0.977800\pi$
$240$	−36.2298			−2.33862
$241$	1.14125	+	1.97670i	0.0735143	+	0.127331i	0.900439	−	0.434982i	$-0.143245\pi$
$241$	1.14125	+	1.97670i	0.0735143	+	0.127331i	−0.826925	+	0.562312i	$0.809912\pi$
$242$	6.76608	+	11.7192i	0.434940	+	0.753338i
$243$	10.7081	−	18.5469i	0.686923	−	1.18979i
$244$	−0.00142575			−9.12744e−5
$245$	−25.5610	−	44.2729i	−1.63303	−	2.82849i
$246$	28.5351			1.81933
$247$	6.43397			0.409383
$248$	7.10383	+	14.0745i	0.451093	+	0.893731i
$249$	−0.854725			−0.0541660
$250$	9.21532			0.582828
$251$	−0.484047	−	0.838394i	−0.0305528	−	0.0529190i	0.850345	−	0.526226i	$-0.176393\pi$
$251$	−0.484047	−	0.838394i	−0.0305528	−	0.0529190i	−0.880897	+	0.473307i	$0.843060\pi$
$252$	0.0824456			0.00519359
$253$	2.82342	−	4.89031i	0.177507	−	0.307451i
$254$	2.95277	+	5.11435i	0.185273	+	0.320903i
$255$	−5.68091	−	9.83962i	−0.355752	−	0.616181i
$256$	−0.107778			−0.00673611
$257$	6.05132	−	10.4812i	0.377471	−	0.653799i	−0.613223	−	0.789910i	$-0.710127\pi$
$257$	6.05132	−	10.4812i	0.377471	−	0.653799i	0.990694	+	0.136111i	$0.0434605\pi$
$258$	18.6903	−	32.3726i	1.16361	−	2.01543i
$259$	−20.5114	+	35.5268i	−1.27452	+	2.20753i
$260$	−0.00774306	−	0.0134114i	−0.000480204	−	0.000831738i
$261$	−1.47637	+	2.55714i	−0.0913848	+	0.158283i
$262$	8.69068	+	15.0527i	0.536912	+	0.929959i
$263$	−10.6429			−0.656267			−0.328134	−	0.944631i	$-0.606420\pi$
$263$	−10.6429			−0.656267			−0.328134	+	0.944631i	$0.606420\pi$
$264$	−8.88429			−0.546790
$265$	19.4348	+	33.6621i	1.19387	+	2.06785i
$266$	−21.2300	+	36.7714i	−1.30169	+	2.25460i
$267$	−10.7112	−	18.5523i	−0.655514	−	1.13538i
$268$	−0.0148983	+	0.0258046i	−0.000910057	+	0.00157626i
$269$	−4.29379	+	7.43706i	−0.261797	+	0.453445i	−0.966719	−	0.255839i	$-0.917648\pi$
$269$	−4.29379	+	7.43706i	−0.261797	+	0.453445i	0.704923	+	0.709284i	$0.250982\pi$
$270$	−5.96190	+	10.3263i	−0.362829	+	0.628439i
$271$	−11.1412			−0.676777			−0.338388	−	0.941007i	$-0.609882\pi$
$271$	−11.1412			−0.676777			−0.338388	+	0.941007i	$0.609882\pi$
$272$	2.49756	+	4.32589i	0.151437	+	0.262296i
$273$	−6.14901	−	10.6504i	−0.372155	−	0.644591i
$274$	−12.2390	+	21.1985i	−0.739383	+	1.28065i
$275$	8.21408			0.495328
$276$	−0.0280044	−	0.0485051i	−0.00168567	−	0.00291966i
$277$	31.7768			1.90928			0.954642	−	0.297756i	$-0.0962380\pi$
$277$	31.7768			1.90928			0.954642	+	0.297756i	$0.0962380\pi$
$278$	−23.1843			−1.39050
$279$	21.8459	+	1.22846i	1.30788	+	0.0735459i
$280$	45.6171			2.72614
$281$	17.1388			1.02241			0.511206	−	0.859458i	$-0.329199\pi$
$281$	17.1388			1.02241			0.511206	+	0.859458i	$0.329199\pi$
$282$	10.7114	+	18.5527i	0.637854	+	1.10480i
$283$	12.2372			0.727426			0.363713	−	0.931511i	$-0.381509\pi$
$283$	12.2372			0.727426			0.363713	+	0.931511i	$0.381509\pi$
$284$	−0.0208242	+	0.0360685i	−0.00123569	+	0.00214027i
$285$	29.2034	+	50.5817i	1.72986	+	2.99620i
$286$	0.841835	+	1.45810i	0.0497788	+	0.0862194i
$287$	−35.8480			−2.11604
$288$	−0.0499158	+	0.0864567i	−0.00294132	+	0.00509451i
$289$	7.71676	−	13.3658i	0.453927	−	0.786224i
$290$	−1.83008	+	3.16979i	−0.107466	+	0.186137i
$291$	3.13489	+	5.42978i	0.183770	+	0.318300i
$292$	−0.00417166	+	0.00722554i	−0.000244128	+	0.000422842i
$293$	0.806977	+	1.39773i	0.0471441	+	0.0816560i	0.888635	−	0.458616i	$-0.151655\pi$
$293$	0.806977	+	1.39773i	0.0471441	+	0.0816560i	−0.841490	+	0.540272i	$0.818321\pi$
$294$	55.1281			3.21514
$295$	5.99119			0.348821
$296$	−12.4323	−	21.5334i	−0.722614	−	1.25160i
$297$	−1.45870	+	2.52654i	−0.0846422	+	0.146605i
$298$	12.5407	+	21.7211i	0.726464	+	1.25827i
$299$	−2.36889	+	4.10304i	−0.136997	+	0.237285i
$300$	0.0407362	−	0.0705571i	0.00235190	−	0.00407362i
$301$	−23.4802	+	40.6690i	−1.35338	+	2.34412i
$302$	18.0142			1.03660
$303$	−15.5900	−	27.0027i	−0.895624	−	1.55127i
$304$	−12.8390	−	22.2378i	−0.736366	−	1.27542i
$305$	−0.547415	+	0.948150i	−0.0313449	+	0.0542909i
$306$	6.94807			0.397195
$307$	12.1253	+	21.0017i	0.692030	+	1.19863i	0.971172	+	0.238381i	$0.0766167\pi$
$307$	12.1253	+	21.0017i	0.692030	+	1.19863i	−0.279142	+	0.960250i	$0.590050\pi$
$308$	0.0250048			0.00142478
$309$	34.7177			1.97502
$310$	27.0798	+	1.52278i	1.53803	+	0.0864879i
$311$	−22.0546			−1.25060			−0.625301	−	0.780384i	$-0.715024\pi$
$311$	−22.0546			−1.25060			−0.625301	+	0.780384i	$0.715024\pi$
$312$	7.45405			0.422002
$313$	1.75616	+	3.04176i	0.0992641	+	0.171931i	0.911380	−	0.411565i	$-0.135018\pi$
$313$	1.75616	+	3.04176i	0.0992641	+	0.171931i	−0.812116	+	0.583496i	$0.801684\pi$
$314$	−4.35540			−0.245789
$315$	31.6549	−	54.8278i	1.78355	−	3.08920i
$316$	0.0265672	+	0.0460157i	0.00149452	+	0.00258859i
$317$	5.46872	+	9.47211i	0.307154	+	0.532007i	0.977739	−	0.209827i	$-0.0672899\pi$
$317$	5.46872	+	9.47211i	0.307154	+	0.532007i	−0.670584	+	0.741833i	$0.733957\pi$
$318$	−41.9157			−2.35051
$319$	−0.447766	+	0.775553i	−0.0250701	+	0.0434226i
$320$	−13.8246	+	23.9449i	−0.772818	+	1.33856i
$321$	−0.641460	+	1.11104i	−0.0358028	+	0.0620123i
$322$	−15.6331	−	27.0774i	−0.871201	−	1.50896i
$323$	4.02636	−	6.97386i	0.224033	−	0.388036i
$324$	−0.0120036	−	0.0207909i	−0.000666869	−	0.00115505i
$325$	−6.89174			−0.382285
$326$	10.3173			0.571423
$327$	−12.7389	−	22.0645i	−0.704465	−	1.22017i
$328$	10.8640	−	18.8171i	0.599866	−	1.03900i
$329$	−13.4565	−	23.3073i	−0.741880	−	1.28497i
$330$	−7.64207	+	13.2365i	−0.420682	+	0.728643i
$331$	8.56938	−	14.8426i	0.471016	−	0.815823i	−0.528435	−	0.848974i	$-0.677221\pi$
$331$	8.56938	−	14.8426i	0.471016	−	0.815823i	0.999450	+	0.0331508i	$0.0105542\pi$
$332$	−0.000729047		0.00126275i	−4.00116e−5		6.93022e-5i
$333$	−34.5084			−1.89105
$334$	−12.6343	−	21.8832i	−0.691316	−	1.19739i
$335$	11.4403	+	19.8152i	0.625052	+	1.08262i
$336$	−24.5407	+	42.5057i	−1.33880	+	2.31888i
$337$	−5.55718			−0.302719			−0.151359	−	0.988479i	$-0.548365\pi$
$337$	−5.55718			−0.302719			−0.151359	+	0.988479i	$0.548365\pi$
$338$	−0.706312	−	1.22337i	−0.0384183	−	0.0665425i
$339$	−50.4522			−2.74019
$340$	−0.0193824			−0.00105116
$341$	6.62561	+	0.372578i	0.358797	+	0.0201762i
$342$	−35.7174			−1.93137
$343$	−36.5544			−1.97375
$344$	−14.2318	−	24.6502i	−0.767327	−	1.32905i
$345$	−43.0090			−2.31553
$346$	0.595220	−	1.03095i	0.0319992	−	0.0554243i
$347$	4.54287	+	7.86849i	0.243874	+	0.422403i	0.961814	−	0.273702i	$-0.0882483\pi$
$347$	4.54287	+	7.86849i	0.243874	+	0.422403i	−0.717940	+	0.696105i	$0.754915\pi$
$348$	0.00444121	+	0.00769241i	0.000238074	+	0.000412356i
$349$	6.62365			0.354556			0.177278	−	0.984161i	$-0.443271\pi$
$349$	6.62365			0.354556			0.177278	+	0.984161i	$0.443271\pi$
$350$	22.7405	−	39.3877i	1.21553	−	2.10536i
$351$	1.22387	−	2.11980i	0.0653253	−	0.113147i
$352$	−0.0151389	+	0.0262214i	−0.000806906	+	0.00139760i
$353$	−17.7858	−	30.8060i	−0.946645	−	1.63964i	−0.752424	−	0.658679i	$-0.771115\pi$
$353$	−17.7858	−	30.8060i	−0.946645	−	1.63964i	−0.194221	−	0.980958i	$-0.562218\pi$
$354$	−3.23034	+	5.59512i	−0.171691	+	0.297377i
$355$	15.9908	+	27.6969i	0.848704	+	1.47000i
$356$	−0.0365449			−0.00193687
$357$	−15.3921			−0.814638
$358$	9.23297	+	15.9920i	0.487977	+	0.845202i
$359$	5.03974	−	8.72908i	0.265987	−	0.460703i	−0.701835	−	0.712340i	$-0.747635\pi$
$359$	5.03974	−	8.72908i	0.265987	−	0.460703i	0.967822	+	0.251637i	$0.0809688\pi$
$360$	19.1866	+	33.2321i	1.01122	+	1.75149i
$361$	−11.1980	+	19.3954i	−0.589366	+	1.02081i
$362$	−4.70584	+	8.15075i	−0.247333	+	0.428394i
$363$	12.6087	−	21.8390i	0.661787	−	1.14625i
$364$	−0.0209794			−0.00109962
$365$	3.20341	+	5.54846i	0.167674	+	0.290420i
$366$	−0.590312	−	1.02245i	−0.0308561	−	0.0534444i
$367$	11.5165	−	19.9472i	0.601158	−	1.04124i	−0.391488	−	0.920183i	$-0.628040\pi$
$367$	11.5165	−	19.9472i	0.601158	−	1.04124i	0.992646	−	0.121053i	$-0.0386270\pi$
$368$	18.9085			0.985674
$369$	−15.0777	−	26.1153i	−0.784912	−	1.35951i
$370$	−42.7761			−2.22382
$371$	52.6577			2.73385
$372$	0.0360588	−	0.0550647i	0.00186956	−	0.00285497i
$373$	−9.06764			−0.469504			−0.234752	−	0.972055i	$-0.575428\pi$
$373$	−9.06764			−0.469504			−0.234752	+	0.972055i	$0.575428\pi$
$374$	2.10727			0.108965
$375$	−8.58647	−	14.8722i	−0.443404	−	0.767998i
$376$	16.3124			0.841249
$377$	0.375682	−	0.650700i	0.0193486	−	0.0335128i
$378$	8.07673	+	13.9893i	0.415422	+	0.719532i
$379$	−7.01514	−	12.1506i	−0.360343	−	0.624133i	0.627674	−	0.778476i	$-0.284007\pi$
$379$	−7.01514	−	12.1506i	−0.360343	−	0.624133i	−0.988017	+	0.154343i	$0.950674\pi$
$380$	0.0996372			0.00511128
$381$	5.50256	−	9.53071i	0.281905	−	0.488273i
$382$	−7.83536	+	13.5712i	−0.400892	+	0.694365i
$383$	−3.08250	+	5.33904i	−0.157508	+	0.272812i	−0.933970	−	0.357353i	$-0.883679\pi$
$383$	−3.08250	+	5.33904i	−0.157508	+	0.272812i	0.776461	+	0.630165i	$0.217013\pi$
$384$	−14.8411	−	25.7055i	−0.757355	−	1.31178i
$385$	9.60057	−	16.6287i	0.489290	−	0.847475i
$386$	2.64154	+	4.57529i	0.134451	+	0.232876i
$387$	−39.5032			−2.00806
$388$	0.0106957			0.000542994
$389$	−8.64487	−	14.9734i	−0.438312	−	0.759179i	0.559247	−	0.829001i	$-0.311090\pi$
$389$	−8.64487	−	14.9734i	−0.438312	−	0.759179i	−0.997559	+	0.0698217i	$0.977757\pi$
$390$	6.41181	−	11.1056i	0.324675	−	0.562353i
$391$	2.96489	+	5.13535i	0.149941	+	0.259706i
$392$	20.9887	−	36.3535i	1.06009	−	1.83613i
$393$	16.1953	−	28.0510i	0.816943	−	1.41499i
$394$	4.30050	−	7.44869i	0.216656	−	0.375259i
$395$	40.8017			2.05296
$396$	0.0105171	+	0.0182161i	0.000528502	+	0.000915392i
$397$	−14.9179	−	25.8385i	−0.748706	−	1.29680i	−0.948443	−	0.316948i	$-0.897342\pi$
$397$	−14.9179	−	25.8385i	−0.748706	−	1.29680i	0.199736	−	0.979850i	$-0.435991\pi$
$398$	−3.46097	+	5.99458i	−0.173483	+	0.300481i
$399$	79.1250			3.96121
$400$	13.7525	+	23.8200i	0.687623	+	1.19100i
$401$	7.08817			0.353966			0.176983	−	0.984214i	$-0.443366\pi$
$401$	7.08817			0.353966			0.176983	+	0.984214i	$0.443366\pi$
$402$	−24.6737			−1.23061
$403$	−5.55898	−	0.312598i	−0.276913	−	0.0155716i
$404$	−0.0531907			−0.00264634
$405$	−18.4351			−0.916048
$406$	2.47925	+	4.29419i	0.123043	+	0.213117i
$407$	−10.4660			−0.518782
$408$	4.66472	−	8.07954i	0.230938	−	0.399997i
$409$	8.41351	+	14.5726i	0.416021	+	0.720570i	0.995535	−	0.0943924i	$-0.0300908\pi$
$409$	8.41351	+	14.5726i	0.416021	+	0.720570i	−0.579514	+	0.814962i	$0.696758\pi$
$410$	−18.6900	−	32.3721i	−0.923035	−	1.59874i
$411$	45.6152			2.25003
$412$	0.0296128	−	0.0512909i	0.00145892	−	0.00252692i
$413$	4.05821	−	7.02902i	0.199691	−	0.345876i
$414$	13.1506	−	22.7775i	0.646318	−	1.11945i
$415$	0.559832	+	0.969658i	0.0274811	+	0.0475986i
$416$	0.0127018	−	0.0220001i	0.000622755	−	0.00107864i
$417$	21.6022	+	37.4161i	1.05786	+	1.83228i
$418$	−10.8327			−0.529844
$419$	−24.8241			−1.21274			−0.606369	−	0.795183i	$-0.707375\pi$
$419$	−24.8241			−1.21274			−0.606369	+	0.795183i	$0.707375\pi$
$420$	−0.0952243	−	0.164933i	−0.00464647	−	0.00804792i
$421$	−5.12154	+	8.87077i	−0.249609	+	0.432335i	−0.963417	−	0.268006i	$-0.913635\pi$
$421$	−5.12154	+	8.87077i	−0.249609	+	0.432335i	0.713809	+	0.700341i	$0.246969\pi$
$422$	−6.48583	−	11.2338i	−0.315725	−	0.546852i
$423$	11.3196	−	19.6061i	0.550378	−	0.953283i
$424$	−15.9584	+	27.6407i	−0.775008	+	1.34235i
$425$	−4.31283	+	7.47004i	−0.209203	+	0.362350i
$426$	−34.4878			−1.67094
$427$	0.741596	+	1.28448i	0.0358884	+	0.0621605i
$428$	0.00109428	+	0.00189535i	5.28940e−5	+	9.16151e-5i
$429$	1.56878	−	2.71720i	0.0757413	−	0.131188i
$430$	−48.9675			−2.36142
$431$	9.99534	+	17.3124i	0.481459	+	0.833911i	0.999774	−	0.0212788i	$-0.00677377\pi$
$431$	9.99534	+	17.3124i	0.481459	+	0.833911i	−0.518315	+	0.855190i	$0.673440\pi$
$432$	−9.76892			−0.470007
$433$	24.6035			1.18237			0.591184	−	0.806537i	$-0.298661\pi$
$433$	24.6035			1.18237			0.591184	+	0.806537i	$0.298661\pi$
$434$	20.1294	−	30.7392i	0.966241	−	1.47553i
$435$	6.82078			0.327032
$436$	−0.0434633			−0.00208151
$437$	−15.2414	−	26.3988i	−0.729094	−	1.26283i
$438$	−6.90888			−0.330119
$439$	−7.67986	+	13.3019i	−0.366540	+	0.634865i	−0.989022	−	0.147769i	$-0.952791\pi$
$439$	−7.67986	+	13.3019i	−0.366540	+	0.634865i	0.622482	+	0.782634i	$0.286124\pi$
$440$	5.81907	+	10.0789i	0.277413	+	0.480494i
$441$	−29.1292	−	50.4533i	−1.38711	−	2.40254i
$442$	−1.76803			−0.0840968
$443$	14.5281	−	25.1634i	0.690250	−	1.19555i	−0.281506	−	0.959560i	$-0.590834\pi$
$443$	14.5281	−	25.1634i	0.690250	−	1.19555i	0.971756	−	0.235989i	$-0.0758329\pi$
$444$	−0.0519042	+	0.0899008i	−0.00246327	+	0.00426650i
$445$	−14.0313	+	24.3030i	−0.665149	+	1.15207i
$446$	−2.40995	−	4.17415i	−0.114114	−	0.197652i
$447$	23.3699	−	40.4778i	1.10536	−	1.91453i
$448$	18.7285	+	32.4388i	0.884840	+	1.53259i
$449$	−21.3179			−1.00605			−0.503027	−	0.864270i	$-0.667781\pi$
$449$	−21.3179			−1.00605			−0.503027	+	0.864270i	$0.667781\pi$
$450$	38.2586			1.80353
$451$	−4.57289	−	7.92048i	−0.215329	−	0.372961i
$452$	−0.0430337	+	0.0745366i	−0.00202414	+	0.00350591i
$453$	−16.7849	−	29.0723i	−0.788625	−	1.36594i
$454$	−6.92237	+	11.9899i	−0.324883	+	0.562714i
$455$	−8.05502	+	13.9517i	−0.377625	+	0.654066i
$456$	−23.9795	+	41.5338i	−1.12295	+	1.94500i
$457$	34.5007			1.61387			0.806937	−	0.590637i	$-0.201124\pi$
$457$	34.5007			1.61387			0.806937	+	0.590637i	$0.201124\pi$
$458$	12.0769	+	20.9178i	0.564316	+	0.977423i
$459$	−1.53179	−	2.65313i	−0.0714977	−	0.123838i
$460$	−0.0366850	+	0.0635402i	−0.00171045	+	0.00296258i
$461$	−18.1818			−0.846809			−0.423405	−	0.905941i	$-0.639165\pi$
$461$	−18.1818			−0.846809			−0.423405	+	0.905941i	$0.639165\pi$
$462$	10.3529	+	17.9318i	0.481661	+	0.834261i
$463$	−13.7944			−0.641078			−0.320539	−	0.947235i	$-0.603864\pi$
$463$	−13.7944			−0.641078			−0.320539	+	0.947235i	$0.603864\pi$
$464$	−2.99869			−0.139211
$465$	−22.7743	−	45.1217i	−1.05613	−	2.09247i
$466$	−6.80416			−0.315197
$467$	1.42164			0.0657855			0.0328927	−	0.999459i	$-0.489528\pi$
$467$	1.42164			0.0657855			0.0328927	+	0.999459i	$0.489528\pi$
$468$	−0.00882397	−	0.0152836i	−0.000407888	−	0.000706483i
$469$	30.9970			1.43131
$470$	14.0316	−	24.3035i	0.647230	−	1.12103i
$471$	4.05819	+	7.02899i	0.186991	+	0.323879i
$472$	2.45975	+	4.26042i	0.113219	+	0.196102i
$473$	−11.9809			−0.550882
$474$	−21.9996	+	38.1043i	−1.01047	+	1.75019i
$475$	22.1706	−	38.4006i	1.01726	−	1.76194i
$476$	−0.0131289	+	0.0227399i	−0.000601761	+	0.00104228i
$477$	22.1479	+	38.3612i	1.01408	+	1.75644i
$478$	−12.2108	+	21.1497i	−0.558507	+	0.967362i
$479$	11.1362	+	19.2885i	0.508826	+	0.881312i	0.999948	+	0.0102214i	$0.00325362\pi$
$479$	11.1362	+	19.2885i	0.508826	+	0.881312i	−0.491122	+	0.871091i	$0.663413\pi$
$480$	0.230610			0.0105259
$481$	8.78115			0.400386
$482$	1.61216	+	2.79234i	0.0734318	+	0.127188i
$483$	−29.1327	+	50.4593i	−1.32558	+	2.29598i
$484$	−0.0215095	−	0.0372555i	−0.000977704	−	0.00169343i
$485$	4.10661	−	7.11285i	0.186471	−	0.322978i
$486$	15.1265	−	26.1998i	0.686151	−	1.18845i
$487$	2.83946	−	4.91809i	0.128668	−	0.222860i	−0.794493	−	0.607274i	$-0.792263\pi$
$487$	2.83946	−	4.91809i	0.128668	−	0.222860i	0.923161	+	0.384414i	$0.125596\pi$
$488$	−0.898989			−0.0406953
$489$	−9.61326	−	16.6507i	−0.434727	−	0.752969i
$490$	−36.1081	−	62.5411i	−1.63120	−	2.82532i
$491$	−10.7793	+	18.6704i	−0.486465	+	0.842582i	−0.999879	−	0.0155592i	$-0.995047\pi$
$491$	−10.7793	+	18.6704i	−0.486465	+	0.842582i	0.513414	+	0.858141i	$0.328380\pi$
$492$	−0.0907135			−0.00408968
$493$	−0.470202	−	0.814413i	−0.0211768	−	0.0366793i
$494$	9.08878			0.408924
$495$	16.1520			0.725979
$496$	10.0125	+	19.8373i	0.449575	+	0.890723i
$497$	43.3263			1.94345
$498$	−1.20741			−0.0541052
$499$	−1.47628	−	2.55700i	−0.0660875	−	0.114467i	0.831088	−	0.556140i	$-0.187718\pi$
$499$	−1.47628	−	2.55700i	−0.0660875	−	0.114467i	−0.897176	+	0.441673i	$0.854385\pi$
$500$	−0.0292957			−0.00131014
$501$	−23.5442	+	40.7798i	−1.05188	+	1.82191i
$502$	−0.683777	−	1.18434i	−0.0305185	−	0.0528595i
$503$	−14.2020	−	24.5986i	−0.633235	−	1.09680i	−0.986886	−	0.161418i	$-0.948393\pi$
$503$	−14.2020	−	24.5986i	−0.633235	−	1.09680i	0.353651	−	0.935378i	$-0.384940\pi$
$504$	51.9851			2.31560
$505$	−20.4225	+	35.3727i	−0.908788	+	1.57407i
$506$	3.98844	−	6.90817i	0.177308	−	0.307106i
$507$	−1.31623	+	2.27977i	−0.0584558	+	0.101248i
$508$	−0.00938692	−	0.0162586i	−0.000416477	−	0.000721360i
$509$	−19.2091	+	33.2712i	−0.851430	+	1.47472i	0.0284877	+	0.999594i	$0.490931\pi$
$509$	−19.2091	+	33.2712i	−0.851430	+	1.47472i	−0.879918	+	0.475126i	$0.842402\pi$
$510$	−8.02499	−	13.8997i	−0.355353	−	0.615489i
$511$	8.67947			0.383957
$512$	−22.7032			−1.00335
$513$	7.87433	+	13.6387i	0.347660	+	0.602165i
$514$	8.54824	−	14.8060i	0.377047	−	0.653064i
$515$	−22.7396	−	39.3861i	−1.00203	−	1.73556i
$516$	−0.0594169	+	0.102913i	−0.00261568	+	0.00453050i
$517$	3.43311	−	5.94633i	0.150988	−	0.261519i
$518$	−28.9749	+	50.1860i	−1.27308	+	2.20505i
$519$	−2.21841			−0.0973775
$520$	−4.88229	−	8.45637i	−0.214103	−	0.370837i
$521$	14.7203	+	25.4962i	0.644906	+	1.11701i	0.984323	+	0.176374i	$0.0564368\pi$
$521$	14.7203	+	25.4962i	0.644906	+	1.11701i	−0.339417	+	0.940636i	$0.610230\pi$
$522$	−2.08555	+	3.61228i	−0.0912821	+	0.158105i
$523$	−9.09230			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$523$	−9.09230			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$524$	−0.0276278	−	0.0478528i	−0.00120693	−	0.00209046i
$525$	−84.7547			−3.69900
$526$	−15.0344			−0.655530
$527$	−3.81763	+	5.82983i	−0.166298	+	0.253951i
$528$	−12.5220			−0.544949
$529$	−0.553382			−0.0240601
$530$	27.4541	+	47.5520i	1.19253	+	2.06552i
$531$	6.82754			0.296290
$532$	0.0674905	−	0.116897i	0.00292608	−	0.00506813i
$533$	3.83672	+	6.64540i	0.166187	+	0.287844i
$534$	−15.1309	−	26.2075i	−0.654778	−	1.13411i
$535$	1.68059			0.0726581
$536$	−9.39392	+	16.2707i	−0.405756	+	0.702789i
$537$	17.2058	−	29.8014i	0.742486	−	1.28602i
$538$	−6.06551	+	10.5058i	−0.261503	+	0.452936i
$539$	−8.83457	−	15.3019i	−0.380532	−	0.659100i
$540$	0.0189530	−	0.0328275i	0.000815607	−	0.00141267i
$541$	−10.2939	−	17.8296i	−0.442570	−	0.766554i	0.555309	−	0.831644i	$-0.312600\pi$
$541$	−10.2939	−	17.8296i	−0.442570	−	0.766554i	−0.997879	+	0.0650897i	$0.979267\pi$
$542$	−15.7383			−0.676017
$543$	17.5389			0.752665
$544$	−0.0158975	−	0.0275352i	−0.000681598	−	0.00118056i
$545$	−16.6876	+	28.9038i	−0.714820	+	1.23810i
$546$	−8.68624	−	15.0450i	−0.371737	−	0.643867i
$547$	18.7205	−	32.4248i	0.800429	−	1.38638i	−0.118905	−	0.992906i	$-0.537938\pi$
$547$	18.7205	−	32.4248i	0.800429	−	1.38638i	0.919334	−	0.393478i	$-0.128728\pi$
$548$	0.0389079	−	0.0673905i	0.00166206	−	0.00287878i
$549$	−0.623832	+	1.08051i	−0.0266245	+	0.0461150i
$550$	11.6034			0.494771
$551$	2.41713	+	4.18658i	0.102973	+	0.178354i
$552$	−17.6578	−	30.5843i	−0.751568	−	1.30175i
$553$	27.6376	−	47.8696i	1.17527	−	2.03562i
$554$	44.8887			1.90714
$555$	39.8571	+	69.0345i	1.69184	+	2.93035i
$556$	0.0737033			0.00312572
$557$	−20.4589			−0.866873			−0.433437	−	0.901184i	$-0.642699\pi$
$557$	−20.4589			−0.866873			−0.433437	+	0.901184i	$0.642699\pi$
$558$	30.8600	+	1.73535i	1.30641	+	0.0734632i
$559$	10.0521			0.425160
$560$	64.2951			2.71697
$561$	−1.96347	−	3.40084i	−0.0828980	−	0.143584i
$562$	24.2106			1.02126
$563$	3.66938	−	6.35555i	0.154646	−	0.267855i	−0.778284	−	0.627912i	$-0.783910\pi$
$563$	3.66938	−	6.35555i	0.154646	−	0.267855i	0.932930	+	0.360058i	$0.117243\pi$
$564$	−0.0340517	−	0.0589793i	−0.00143384	−	0.00248348i
$565$	33.0454	+	57.2364i	1.39023	+	2.40795i
$566$	17.2866			0.726608
$567$	−12.4872	+	21.6286i	−0.524415	+	0.908314i
$568$	−13.1304	+	22.7426i	−0.550940	+	0.954256i
$569$	17.0545	−	29.5393i	0.714963	−	1.23835i	−0.248011	−	0.968757i	$-0.579777\pi$
$569$	17.0545	−	29.5393i	0.714963	−	1.23835i	0.962974	−	0.269594i	$-0.0868896\pi$
$570$	41.2534	+	71.4530i	1.72791	+	2.99284i
$571$	11.9751	−	20.7415i	0.501143	−	0.868005i	−0.498856	−	0.866685i	$-0.666246\pi$
$571$	11.9751	−	20.7415i	0.501143	−	0.868005i	0.999999	−	0.00132037i	$-0.000420287\pi$
$572$	−0.00267621	−	0.00463533i	−0.000111898	−	0.000193813i
$573$	29.2027			1.21996
$574$	−50.6397			−2.11366
$575$	16.3258	+	28.2771i	0.680832	+	1.17924i
$576$	−15.7545	+	27.2875i	−0.656436	+	1.13698i
$577$	10.8291	+	18.7566i	0.450822	+	0.780847i	0.998437	−	0.0558832i	$-0.0177975\pi$
$577$	10.8291	+	18.7566i	0.450822	+	0.780847i	−0.547615	+	0.836730i	$0.684464\pi$
$578$	10.9009	−	18.8809i	0.453417	−	0.785341i
$579$	4.92257	−	8.52615i	0.204575	−	0.354335i
$580$	0.00581786	−	0.0100768i	0.000241573	−	0.000418417i
$581$	1.51684			0.0629290
$582$	4.42842	+	7.67025i	0.183564	+	0.317942i
$583$	6.71720	+	11.6345i	0.278198	+	0.481853i
$584$	−2.63039	+	4.55597i	−0.108846	+	0.188527i
$585$	−13.5518			−0.560297
$586$	1.13996	+	1.97446i	0.0470911	+	0.0815643i
$587$	−7.56883			−0.312399			−0.156199	−	0.987726i	$-0.549924\pi$
$587$	−7.56883			−0.312399			−0.156199	+	0.987726i	$0.549924\pi$
$588$	−0.175253			−0.00722733
$589$	19.6249	−	29.9689i	0.808632	−	1.23485i
$590$	8.46330			0.348429
$591$	−16.0282			−0.659310
$592$	−17.5228	−	30.3503i	−0.720182	−	1.24739i
$593$	23.0377			0.946045			0.473022	−	0.881050i	$-0.343163\pi$
$593$	23.0377			0.946045			0.473022	+	0.881050i	$0.343163\pi$
$594$	−2.06059	+	3.56905i	−0.0845471	+	0.146440i
$595$	10.0816	+	17.4619i	0.413306	+	0.715867i
$596$	−0.0398671	−	0.0690519i	−0.00163302	−	0.00282848i
$597$	12.8992			0.527929
$598$	−3.34636	+	5.79606i	−0.136843	+	0.237019i
$599$	−9.90590	+	17.1575i	−0.404744	+	0.701037i	−0.994292	−	0.106696i	$-0.965973\pi$
$599$	−9.90590	+	17.1575i	−0.404744	+	0.701037i	0.589548	+	0.807734i	$0.299306\pi$
$600$	25.6857	−	44.4889i	1.04861	−	1.81625i
$601$	−0.718535	−	1.24454i	−0.0293097	−	0.0507658i	0.850999	−	0.525168i	$-0.175998\pi$
$601$	−0.718535	−	1.24454i	−0.0293097	−	0.0507658i	−0.880308	+	0.474402i	$0.842664\pi$
$602$	−33.1688	+	57.4500i	−1.35186	+	2.34149i
$603$	13.0374	+	22.5814i	0.530922	+	0.919585i
$604$	−0.0572675			−0.00233018
$605$	−33.0341			−1.34303
$606$	−22.0229	−	38.1447i	−0.894617	−	1.54952i
$607$	11.8682	−	20.5563i	0.481714	−	0.834354i	−0.518065	−	0.855341i	$-0.673348\pi$
$607$	11.8682	−	20.5563i	0.481714	−	0.834354i	0.999780	+	0.0209871i	$0.00668091\pi$
$608$	0.0817227	+	0.141548i	0.00331430	+	0.00574053i
$609$	4.62014	−	8.00232i	0.187218	−	0.324271i
$610$	−0.773291	+	1.33938i	−0.0313097	+	0.0542299i
$611$	−2.88043	+	4.98906i	−0.116530	+	0.201836i
$612$	−0.0220881			−0.000892857
$613$	−13.9958	−	24.2414i	−0.565284	−	0.979100i	−0.997023	−	0.0771020i	$-0.975433\pi$
$613$	−13.9958	−	24.2414i	−0.565284	−	0.979100i	0.431739	−	0.901998i	$-0.357900\pi$
$614$	17.1286	+	29.6675i	0.691252	+	1.19728i
$615$	−34.8293	+	60.3261i	−1.40445	+	2.43258i
$616$	15.7665			0.635250
$617$	17.9479	+	31.0867i	0.722555	+	1.25150i	0.959972	+	0.280095i	$0.0903659\pi$
$617$	17.9479	+	31.0867i	0.722555	+	1.25150i	−0.237417	+	0.971408i	$0.576301\pi$
$618$	49.0431			1.97280
$619$	3.52037			0.141495			0.0707477	−	0.997494i	$-0.477461\pi$
$619$	3.52037			0.141495			0.0707477	+	0.997494i	$0.477461\pi$
$620$	−0.0860871	−	0.00484094i	−0.00345734	−	0.000194417i
$621$	−11.5969			−0.465366
$622$	−31.1549			−1.24920
$623$	19.0086	+	32.9239i	0.761564	+	1.31907i
$624$	10.5061			0.420582
$625$	5.98132	−	10.3599i	0.239253	−	0.414398i
$626$	2.48080	+	4.29687i	0.0991526	+	0.171737i
$627$	10.0935	+	17.4824i	0.403094	+	0.698180i
$628$	0.0138459			0.000552511
$629$	5.49522	−	9.51800i	0.219109	−	0.379508i
$630$	44.7164	−	77.4511i	1.78155	−	3.08573i
$631$	−2.29183	+	3.96956i	−0.0912362	+	0.158026i	−0.908032	−	0.418902i	$-0.862415\pi$
$631$	−2.29183	+	3.96956i	−0.0912362	+	0.158026i	0.816795	+	0.576928i	$0.195749\pi$
$632$	16.7516	+	29.0146i	0.666343	+	1.15414i
$633$	−12.0865	+	20.9344i	−0.480395	+	0.832068i
$634$	7.72526	+	13.3805i	0.306809	+	0.531409i
$635$	−14.4164			−0.572096
$636$	0.133251			0.00528373
$637$	7.41234	+	12.8385i	0.293687	+	0.508682i
$638$	−0.632525	+	1.09557i	−0.0250419	+	0.0433738i
$639$	18.2231	+	31.5633i	0.720893	+	1.24862i
$640$	−19.4414	+	33.6734i	−0.768487	+	1.33106i
$641$	−15.6086	+	27.0348i	−0.616502	+	1.06781i	0.373617	+	0.927583i	$0.378117\pi$
$641$	−15.6086	+	27.0348i	−0.616502	+	1.06781i	−0.990119	+	0.140229i	$0.955216\pi$
$642$	−0.906143	+	1.56948i	−0.0357626	+	0.0619426i
$643$	−29.3761			−1.15848			−0.579240	−	0.815157i	$-0.696651\pi$
$643$	−29.3761			−1.15848			−0.579240	+	0.815157i	$0.696651\pi$
$644$	0.0496981	+	0.0860795i	0.00195838	+	0.00339201i
$645$	45.6260	+	79.0266i	1.79652	+	3.11167i
$646$	5.68774	−	9.85145i	0.223781	−	0.387600i
$647$	−2.69402			−0.105913			−0.0529564	−	0.998597i	$-0.516864\pi$
$647$	−2.69402			−0.105913			−0.0529564	+	0.998597i	$0.516864\pi$
$648$	−7.56874	−	13.1095i	−0.297328	−	0.514988i
$649$	2.07072			0.0812828
$650$	−9.73544			−0.381855
$651$	−68.3645	−	3.84434i	−2.67941	−	0.150672i
$652$	−0.0327989			−0.00128450
$653$	5.85334			0.229059			0.114530	−	0.993420i	$-0.463464\pi$
$653$	5.85334			0.229059			0.114530	+	0.993420i	$0.463464\pi$
$654$	−17.9954	−	31.1689i	−0.703674	−	1.21880i
$655$	−42.4306			−1.65790
$656$	15.3124	−	26.5218i	0.597847	−	1.03550i
$657$	3.65059	+	6.32301i	0.142423	+	0.246684i
$658$	−19.0090	−	32.9245i	−0.741047	−	1.28353i
$659$	37.7990			1.47244			0.736220	−	0.676742i	$-0.236609\pi$
$659$	37.7990			1.47244			0.736220	+	0.676742i	$0.236609\pi$
$660$	0.0242943	−	0.0420790i	0.000945654	−	0.00163792i
$661$	6.82547	−	11.8221i	0.265480	−	0.459825i	−0.702209	−	0.711971i	$-0.747803\pi$
$661$	6.82547	−	11.8221i	0.265480	−	0.459825i	0.967689	+	0.252146i	$0.0811362\pi$
$662$	12.1053	−	20.9670i	0.470487	−	0.814907i
$663$	1.64738	+	2.85335i	0.0639791	+	0.110815i
$664$	−0.459691	+	0.796209i	−0.0178395	+	0.0308989i
$665$	−51.8257	−	89.7648i	−2.00972	−	3.48093i
$666$	−48.7475			−1.88893
$667$	−3.55980			−0.137836
$668$	0.0401646	+	0.0695671i	0.00155401	+	0.00269163i
$669$	−4.49099	+	7.77862i	−0.173632	+	0.300739i
$670$	16.1609	+	27.9915i	0.624350	+	1.08141i
$671$	−0.189201	+	0.327706i	−0.00730403	+	0.0126510i
$672$	0.156207	−	0.270558i	0.00602580	−	0.0104370i
$673$	2.22593	−	3.85542i	0.0858032	−	0.148616i	−0.819930	−	0.572464i	$-0.805988\pi$
$673$	2.22593	−	3.85542i	0.0858032	−	0.148616i	0.905733	+	0.423848i	$0.139321\pi$
$674$	−7.85021			−0.302379
$675$	−8.43458	−	14.6091i	−0.324647	−	0.562306i
$676$	0.00224538	+	0.00388911i	8.63608e−5	+	0.000149581i
$677$	19.3893	−	33.5832i	0.745190	−	1.29071i	−0.204916	−	0.978779i	$-0.565692\pi$
$677$	19.3893	−	33.5832i	0.745190	−	1.29071i	0.950106	−	0.311927i	$-0.100974\pi$
$678$	−71.2700			−2.73711
$679$	−5.56333	−	9.63596i	−0.213501	−	0.369794i
$680$	−12.2213			−0.468665
$681$	25.8000			0.988657
$682$	9.35950	+	0.526313i	0.358394	+	0.0201536i
$683$	−42.8753			−1.64058			−0.820290	−	0.571948i	$-0.806188\pi$
$683$	−42.8753			−1.64058			−0.820290	+	0.571948i	$0.806188\pi$
$684$	0.113546			0.00434155
$685$	−29.8773	−	51.7489i	−1.14155	−	1.97723i
$686$	−51.6377			−1.97154
$687$	22.5055	−	38.9807i	0.858639	−	1.48721i
$688$	−20.0590	−	34.7433i	−0.764744	−	1.32458i
$689$	−5.63583	−	9.76155i	−0.214708	−	0.371885i
$690$	−60.7556			−2.31293
$691$	−24.8938	+	43.1173i	−0.947005	+	1.64026i	−0.195318	+	0.980740i	$0.562574\pi$
$691$	−24.8938	+	43.1173i	−0.947005	+	1.64026i	−0.751686	+	0.659521i	$0.770759\pi$
$692$	−0.00189222	+	0.00327742i	−7.19313e−5	+	0.000124589i
$693$	10.9408	−	18.9500i	0.415606	−	0.719850i
$694$	6.41738	+	11.1152i	0.243600	+	0.421928i
$695$	28.2983	−	49.0140i	1.07341	−	1.85921i
$696$	2.80035	+	4.85035i	0.106147	+	0.183852i
$697$	9.60405			0.363779
$698$	9.35673			0.354158
$699$	6.33985	+	10.9809i	0.239795	+	0.415338i
$700$	−0.0722924	+	0.125214i	−0.00273240	+	0.00473265i
$701$	2.20296	+	3.81565i	0.0832048	+	0.144115i	0.904625	−	0.426209i	$-0.140151\pi$
$701$	2.20296	+	3.81565i	0.0832048	+	0.144115i	−0.821420	+	0.570324i	$0.806818\pi$
$702$	1.72887	−	2.99449i	0.0652519	−	0.113020i
$703$	−28.2488	+	48.9284i	−1.06542	+	1.84537i
$704$	−4.77815	+	8.27600i	−0.180083	+	0.311914i
$705$	−52.2964			−1.96960
$706$	−25.1247	−	43.5173i	−0.945582	−	1.63780i
$707$	27.6668	+	47.9204i	1.04052	+	1.80223i
$708$	0.0102693	−	0.0177870i	0.000385945	−	0.000668476i
$709$	0.844722			0.0317242			0.0158621	−	0.999874i	$-0.494951\pi$
$709$	0.844722			0.0317242			0.0158621	+	0.999874i	$0.494951\pi$
$710$	22.5890	+	39.1253i	0.847751	+	1.46835i
$711$	46.4975			1.74379
$712$	−23.0429			−0.863570
$713$	11.8860	+	23.5493i	0.445135	+	0.881927i
$714$	−21.7433			−0.813723
$715$	−4.11011			−0.153709
$716$	−0.0293518	−	0.0508388i	−0.00109693	−	0.00189993i
$717$	45.5100			1.69960
$718$	7.11926	−	12.3309i	0.265688	−	0.460186i
$719$	−4.76062	−	8.24564i	−0.177541	−	0.307511i	0.763497	−	0.645812i	$-0.223481\pi$
$719$	−4.76062	−	8.24564i	−0.177541	−	0.307511i	−0.941038	+	0.338301i	$0.890148\pi$
$720$	27.0426	+	46.8391i	1.00782	+	1.74559i
$721$	−61.6118			−2.29454
$722$	−15.8185	+	27.3985i	−0.588704	+	1.01967i
$723$	3.00429	−	5.20358i	0.111731	−	0.193523i
$724$	0.0149600	−	0.0259114i	0.000555982	−	0.000962990i
$725$	−2.58910	−	4.48446i	−0.0961568	−	0.166549i
$726$	17.8114	−	30.8503i	0.661043	−	1.14496i
$727$	4.93650	+	8.55026i	0.183085	+	0.317112i	0.942929	−	0.332993i	$-0.108058\pi$
$727$	4.93650	+	8.55026i	0.183085	+	0.317112i	−0.759845	+	0.650104i	$0.774725\pi$
$728$	−13.2283			−0.490274
$729$	−40.3393			−1.49405
$730$	4.52521	+	7.83790i	0.167486	+	0.290094i
$731$	6.29060	−	10.8956i	0.232666	−	0.402990i
$732$	0.00187661	+	0.00325039i	6.93617e−5	+	0.000120138i
$733$	20.5464	−	35.5874i	0.758898	−	1.31445i	−0.184515	−	0.982830i	$-0.559071\pi$
$733$	20.5464	−	35.5874i	0.758898	−	1.31445i	0.943413	−	0.331620i	$-0.107595\pi$
$734$	16.2685	−	28.1779i	0.600482	−	1.04007i
$735$	−67.2882	+	116.547i	−2.48196	+	4.29889i
$736$	−0.120357			−0.00443640
$737$	3.95409	+	6.84868i	0.145651	+	0.252274i
$738$	−21.2991	−	36.8911i	−0.784031	−	1.35798i
$739$	4.77295	−	8.26698i	0.175576	−	0.304106i	−0.764785	−	0.644286i	$-0.777155\pi$
$739$	4.77295	−	8.26698i	0.175576	−	0.304106i	0.940360	+	0.340180i	$0.110488\pi$
$740$	0.135986			0.00499894
$741$	−8.46857	−	14.6680i	−0.311101	−	0.538842i
$742$	74.3856			2.73078
$743$	27.2257			0.998812			0.499406	−	0.866368i	$-0.333552\pi$
$743$	27.2257			0.998812			0.499406	+	0.866368i	$0.333552\pi$
$744$	22.7364	−	34.7204i	0.833557	−	1.27291i
$745$	−61.2277			−2.24321
$746$	−12.8092			−0.468977
$747$	0.637983	+	1.10502i	0.0233426	+	0.0404305i
$748$	−0.00669906			−0.000244942
$749$	1.13837	−	1.97171i	0.0415950	−	0.0720447i
$750$	−12.1295	−	21.0089i	−0.442906	−	0.767135i
$751$	−27.0502	−	46.8524i	−0.987078	−	1.70967i	−0.632314	−	0.774712i	$-0.717895\pi$
$751$	−27.0502	−	46.8524i	−0.987078	−	1.70967i	−0.354764	−	0.934956i	$-0.615439\pi$
$752$	22.9916			0.838418
$753$	−1.27423	+	2.20704i	−0.0464356	+	0.0804289i
$754$	0.530698	−	0.919195i	0.0193269	−	0.0334751i
$755$	−21.9878	+	38.0839i	−0.800216	+	1.38602i
$756$	−0.0256761	−	0.0444723i	−0.000933830	−	0.00161744i
$757$	−7.42714	+	12.8642i	−0.269944	+	0.467557i	−0.968847	−	0.247660i	$-0.920339\pi$
$757$	−7.42714	+	12.8642i	−0.269944	+	0.467557i	0.698903	+	0.715216i	$0.253672\pi$
$758$	−9.90976	−	17.1642i	−0.359939	−	0.623432i
$759$	−14.8651			−0.539568
$760$	62.8250			2.27890
$761$	10.1327	+	17.5503i	0.367309	+	0.636197i	0.989144	−	0.146951i	$-0.0469460\pi$
$761$	10.1327	+	17.5503i	0.367309	+	0.636197i	−0.621835	+	0.783148i	$0.713613\pi$
$762$	7.77305	−	13.4633i	0.281588	−	0.487725i
$763$	22.6072	+	39.1568i	0.818434	+	1.41757i
$764$	0.0249088	−	0.0431432i	0.000901167	−	0.00156087i
$765$	−8.48067	+	14.6890i	−0.306619	+	0.531080i
$766$	−4.35441	+	7.54207i	−0.157331	+	0.272506i
$767$	−1.73736			−0.0627325
$768$	0.141860	+	0.245709i	0.00511894	+	0.00886626i
$769$	−3.53573	−	6.12406i	−0.127502	−	0.220839i	0.795206	−	0.606339i	$-0.207362\pi$
$769$	−3.53573	−	6.12406i	−0.127502	−	0.220839i	−0.922708	+	0.385500i	$0.874029\pi$
$770$	13.5620	−	23.4901i	0.488741	−	0.846523i
$771$	−31.8597			−1.14740
$772$	−0.00839752	−	0.0145449i	−0.000302233	−	0.000523483i
$773$	36.2045			1.30218			0.651092	−	0.758999i	$-0.274311\pi$
$773$	36.2045			1.30218			0.651092	+	0.758999i	$0.274311\pi$
$774$	−55.8032			−2.00581
$775$	−21.0212	+	32.1012i	−0.755105	+	1.15311i
$776$	6.74406			0.242098
$777$	107.991			3.87415
$778$	−12.2120	−	21.1517i	−0.437820	−	0.758327i
$779$	−49.3707			−1.76889
$780$	−0.0203833	+	0.0353049i	−0.000729838	+	0.00126412i
$781$	5.52685	+	9.57279i	0.197766	+	0.342541i
$782$	4.18828	+	7.25432i	0.149773	+	0.259414i
$783$	1.83914			0.0657256
$784$	29.5826	−	51.2386i	1.05652	−	1.82995i
$785$	5.31611	−	9.20776i	0.189740	−	0.328639i
$786$	22.8778	−	39.6256i	0.816025	−	1.41340i
$787$	−20.8301	−	36.0788i	−0.742514	−	1.28607i	−0.951347	−	0.308120i	$-0.900300\pi$
$787$	−20.8301	−	36.0788i	−0.742514	−	1.28607i	0.208834	−	0.977951i	$-0.433033\pi$
$788$	−0.0136714	+	0.0236795i	−0.000487023	+	0.000843548i
$789$	14.0084	+	24.2633i	0.498714	+	0.863798i
$790$	57.6375			2.05065
$791$	89.5350			3.18350
$792$	6.63140	+	11.4859i	0.235636	+	0.408134i
$793$	0.158743	−	0.274950i	0.00563712	−	0.00976377i
$794$	−21.0734	−	36.5001i	−0.747865	−	1.29534i
$795$	51.1614	−	88.6141i	1.81451	−	3.14282i
$796$	0.0110025	−	0.0190569i	0.000389973	−	0.000675454i
$797$	−1.78187	+	3.08628i	−0.0631169	+	0.109322i	−0.895857	−	0.444342i	$-0.853437\pi$
$797$	−1.78187	+	3.08628i	−0.0631169	+	0.109322i	0.832740	+	0.553664i	$0.186771\pi$
$798$	111.774			3.95676
$799$	3.60514	+	6.24428i	0.127541	+	0.220907i
$800$	−0.0875373	−	0.151619i	−0.00309491	−	0.00536054i
$801$	−15.9901	+	27.6956i	−0.564981	+	0.978576i
$802$	10.0129			0.353569
$803$	1.10718	+	1.91770i	0.0390717	+	0.0676741i
$804$	0.0784381			0.00276630
$805$	76.3259			2.69013
$806$	−7.85276	−	0.441584i	−0.276602	−	0.0155541i
$807$	22.6064			0.795784
$808$	−33.5387			−1.17989
$809$	−1.08130	−	1.87286i	−0.0380164	−	0.0658464i	0.846391	−	0.532562i	$-0.178771\pi$
$809$	−1.08130	−	1.87286i	−0.0380164	−	0.0658464i	−0.884408	+	0.466715i	$0.845437\pi$
$810$	−26.0419			−0.915019
$811$	−5.49293	+	9.51403i	−0.192883	+	0.334083i	−0.946204	−	0.323570i	$-0.895117\pi$
$811$	−5.49293	+	9.51403i	−0.192883	+	0.334083i	0.753322	+	0.657652i	$0.228450\pi$
$812$	−0.00788160	−	0.0136513i	−0.000276590	−	0.000479068i
$813$	14.6643	+	25.3993i	0.514300	+	0.890793i
$814$	−14.7846			−0.518199
$815$	−12.5931	+	21.8119i	−0.441117	+	0.764036i
$816$	6.57471	−	11.3877i	0.230161	−	0.398650i
$817$	−32.3376	+	56.0103i	−1.13135	+	1.95955i
$818$	11.8851	+	20.5857i	0.415554	+	0.719761i
$819$	−9.17947	+	15.8993i	−0.320757	+	0.555567i
$820$	0.0594160	+	0.102911i	0.00207490	+	0.00359383i
$821$	30.4928			1.06421			0.532103	−	0.846680i	$-0.321402\pi$
$821$	30.4928			1.06421			0.532103	+	0.846680i	$0.321402\pi$
$822$	64.4371			2.24750
$823$	0.305602	+	0.529317i	0.0106526	+	0.0184508i	0.871303	−	0.490746i	$-0.163276\pi$
$823$	0.305602	+	0.529317i	0.0106526	+	0.0184508i	−0.860650	+	0.509197i	$0.829942\pi$
$824$	18.6720	−	32.3408i	0.650470	−	1.12665i
$825$	−10.8116	−	18.7263i	−0.376412	−	0.651965i
$826$	5.73273	−	9.92937i	0.199467	−	0.345487i
$827$	−6.45421	+	11.1790i	−0.224435	+	0.388733i	−0.956150	−	0.292878i	$-0.905387\pi$
$827$	−6.45421	+	11.1790i	−0.224435	+	0.388733i	0.731715	+	0.681611i	$0.238720\pi$
$828$	−0.0418061	+	0.0724102i	−0.00145286	+	0.00251643i
$829$	−19.1627			−0.665550			−0.332775	−	0.943006i	$-0.607985\pi$
$829$	−19.1627			−0.665550			−0.332775	+	0.943006i	$0.607985\pi$
$830$	0.790833	+	1.36976i	0.0274502	+	0.0475452i
$831$	−41.8256	−	72.4440i	−1.45091	−	2.51305i
$832$	4.00894	−	6.94369i	0.138985	−	0.240729i
$833$	18.5545			0.642875
$834$	30.5158	+	52.8550i	1.05668	+	1.83022i
$835$	61.6845			2.13468
$836$	0.0344373			0.00119104
$837$	−6.14082	−	12.1665i	−0.212258	−	0.420537i
$838$	−35.0672			−1.21138
$839$	−19.5629			−0.675387			−0.337694	−	0.941256i	$-0.609647\pi$
$839$	−19.5629			−0.675387			−0.337694	+	0.941256i	$0.609647\pi$
$840$	−60.0425	−	103.997i	−2.07166	−	3.58823i
$841$	−28.4355			−0.980533
$842$	−7.23481	+	12.5311i	−0.249328	+	0.431849i
$843$	−22.5585	−	39.0725i	−0.776957	−	1.34573i
$844$	0.0206186	+	0.0357124i	0.000709721	+	0.00122927i
$845$	3.44844			0.118630
$846$	15.9904	−	27.6961i	0.549760	−	0.952212i
$847$	−22.3761	+	38.7565i	−0.768851	+	1.33169i
$848$	−22.4926	+	38.9583i	−0.772399	+	1.33783i
$849$	−16.1069	−	27.8980i	−0.552789	−	0.957458i
$850$	−6.09241	+	10.5524i	−0.208968	+	0.361943i
$851$	−20.8016	−	36.0294i	−0.713070	−	1.23507i
$852$	0.109637			0.00375612
$853$	25.5525			0.874901			0.437450	−	0.899243i	$-0.355882\pi$
$853$	25.5525			0.874901			0.437450	+	0.899243i	$0.355882\pi$
$854$	1.04760	+	1.81449i	0.0358480	+	0.0620906i
$855$	43.5959	−	75.5102i	1.49095	−	2.58240i
$856$	0.689984	+	1.19509i	0.0235832	+	0.0408473i
$857$	5.25018	−	9.09358i	0.179343	−	0.310631i	−0.762313	−	0.647209i	$-0.775936\pi$
$857$	5.25018	−	9.09358i	0.179343	−	0.310631i	0.941656	+	0.336578i	$0.109270\pi$
$858$	2.21610	−	3.83839i	0.0756563	−	0.131040i
$859$	28.6379	−	49.6023i	0.977112	−	1.69241i	0.304329	−	0.952567i	$-0.401568\pi$
$859$	28.6379	−	49.6023i	0.977112	−	1.69241i	0.672783	−	0.739840i	$-0.265099\pi$
$860$	0.155669			0.00530826
$861$	47.1841	+	81.7253i	1.60803	+	2.78519i
$862$	14.1197	+	24.4560i	0.480918	+	0.832974i
$863$	8.01845	−	13.8884i	0.272951	−	0.472766i	−0.696665	−	0.717397i	$-0.745334\pi$
$863$	8.01845	−	13.8884i	0.272951	−	0.472766i	0.969616	+	0.244631i	$0.0786669\pi$
$864$	0.0621812			0.00211545
$865$	1.45303	+	2.51672i	0.0494044	+	0.0855709i
$866$	34.7555			1.18104
$867$	−40.6281			−1.37980
$868$	−0.0639917	+	0.0977206i	−0.00217202	+	0.00331685i
$869$	14.1022			0.478383
$870$	9.63521			0.326664
$871$	−3.31754	−	5.74614i	−0.112410	−	0.194701i
$872$	−27.4052			−0.928058
$873$	4.67988	−	8.10578i	0.158390	−	0.274339i
$874$	−21.5304	−	37.2917i	−0.728275	−	1.26141i
$875$	15.2380	+	26.3930i	0.515138	+	0.892245i
$876$	0.0219635			0.000742076
$877$	−27.8141	+	48.1754i	−0.939215	+	1.62677i	−0.172276	+	0.985049i	$0.555112\pi$
$877$	−27.8141	+	48.1754i	−0.939215	+	1.62677i	−0.766939	+	0.641720i	$0.778221\pi$
$878$	−10.8488	+	18.7906i	−0.366128	+	0.634152i
$879$	2.12433	−	3.67945i	0.0716520	−	0.124105i
$880$	8.20171	+	14.2058i	0.276480	+	0.478877i
$881$	−21.3290	+	36.9429i	−0.718592	+	1.24464i	0.242966	+	0.970035i	$0.421880\pi$
$881$	−21.3290	+	36.9429i	−0.718592	+	1.24464i	−0.961558	+	0.274602i	$0.911454\pi$
$882$	−41.1487	−	71.2716i	−1.38555	−	2.39984i
$883$	9.66907			0.325390			0.162695	−	0.986676i	$-0.447981\pi$
$883$	9.66907			0.325390			0.162695	+	0.986676i	$0.447981\pi$
$884$	0.00562061			0.000189042
$885$	−7.88578	−	13.6586i	−0.265077	−	0.459128i
$886$	20.5227	−	35.5464i	0.689475	−	1.19421i
$887$	−17.6540	−	30.5777i	−0.592764	−	1.02670i	−0.993858	−	0.110661i	$-0.964703\pi$
$887$	−17.6540	−	30.5777i	−0.592764	−	1.02670i	0.401094	−	0.916037i	$-0.368630\pi$
$888$	−32.7276	+	56.6858i	−1.09827	+	1.90225i
$889$	−9.76511	+	16.9137i	−0.327511	+	0.567266i
$890$	−19.8210	+	34.3310i	−0.664402	+	1.15078i
$891$	−6.37167			−0.213459
$892$	0.00766127	+	0.0132697i	0.000256518	+	0.000444303i
$893$	−18.5326	−	32.0994i	−0.620170	−	1.07417i
$894$	33.0129	−	57.1800i	1.10412	−	1.91238i
$895$	−45.0782			−1.50680
$896$	26.3377	+	45.6182i	0.879881	+	1.52400i
$897$	12.4720			0.416429
$898$	−30.1142			−1.00492
$899$	−1.88500	−	3.73467i	−0.0628683	−	0.124558i
$900$	−0.121625			−0.00405416
$901$	−14.1076			−0.469991
$902$	−6.45978	−	11.1887i	−0.215087	−	0.372542i
$903$	123.621			4.11386
$904$	−27.1344	+	46.9981i	−0.902476	+	1.56313i
$905$	−11.4877	−	19.8973i	−0.381864	−	0.661408i
$906$	−23.7108	−	41.0683i	−0.787739	−	1.36440i
$907$	−29.3414			−0.974264			−0.487132	−	0.873328i	$-0.661957\pi$
$907$	−29.3414			−0.974264			−0.487132	+	0.873328i	$0.661957\pi$
$908$	0.0220064	−	0.0381161i	0.000730307	−	0.00126493i
$909$	−23.2734	+	40.3107i	−0.771929	+	1.33702i
$910$	−11.3787	+	19.7085i	−0.377201	+	0.653331i
$911$	−24.4128	−	42.2841i	−0.808831	−	1.40094i	−0.913674	−	0.406447i	$-0.866768\pi$
$911$	−24.4128	−	42.2841i	−0.808831	−	1.40094i	0.104844	−	0.994489i	$-0.466566\pi$
$912$	−33.7980	+	58.5399i	−1.11917	+	1.93845i
$913$	0.193493	+	0.335140i	0.00640369	+	0.0110915i
$914$	48.7365			1.61206
$915$	2.88209			0.0952790
$916$	−0.0383926	−	0.0664980i	−0.00126853	−	0.00219716i
$917$	−28.7409	+	49.7807i	−0.949109	+	1.64390i
$918$	−2.16384	−	3.74788i	−0.0714174	−	0.123699i
$919$	−14.6298	+	25.3396i	−0.482593	+	0.835876i	−0.999800	−	0.0199840i	$-0.993638\pi$
$919$	−14.6298	+	25.3396i	−0.482593	+	0.835876i	0.517207	+	0.855860i	$0.326972\pi$
$920$	−23.1312	+	40.0645i	−0.762615	+	1.32089i
$921$	31.9194	−	55.2861i	1.05178	−	1.82174i
$922$	−25.6840			−0.845858
$923$	−4.63711	−	8.03172i	−0.152632	−	0.264367i
$924$	−0.0329121	−	0.0570054i	−0.00108273	−	0.00187534i
$925$	30.2587	−	52.4096i	0.994900	−	1.72322i
$926$	−19.4862			−0.640358
$927$	−25.9139	−	44.8843i	−0.851126	−	1.47419i
$928$	0.0190873			0.000626571
$929$	46.4324			1.52340			0.761700	−	0.647930i	$-0.224365\pi$
$929$	46.4324			1.52340			0.761700	+	0.647930i	$0.224365\pi$
$930$	−32.1716	−	63.7401i	−1.05495	−	2.09012i
$931$	−95.3814			−3.12600
$932$	0.0216306			0.000708533
$933$	29.0289	+	50.2795i	0.950363	+	1.64608i
$934$	2.00824			0.0657116
$935$	−2.57209	+	4.45500i	−0.0841164	+	0.145694i
$936$	−5.56384	−	9.63686i	−0.181860	−	0.314990i
$937$	−12.1877	−	21.1097i	−0.398155	−	0.689624i	0.595344	−	0.803471i	$-0.297016\pi$
$937$	−12.1877	−	21.1097i	−0.398155	−	0.689624i	−0.993498	+	0.113847i	$0.963683\pi$
$938$	43.7871			1.42970
$939$	4.62302	−	8.00731i	0.150867	−	0.261309i
$940$	−0.0446067	+	0.0772611i	−0.00145491	+	0.00251998i
$941$	14.7187	−	25.4935i	0.479815	−	0.831063i	−0.519917	−	0.854217i	$-0.674037\pi$
$941$	14.7187	−	25.4935i	0.479815	−	0.831063i	0.999732	+	0.0231534i	$0.00737061\pi$
$942$	5.73270	+	9.92932i	0.186781	+	0.323515i
$943$	18.1776	−	31.4845i	0.591943	−	1.02528i
$944$	3.46691	+	6.00486i	0.112838	+	0.195441i
$945$	−39.4331			−1.28276
$946$	−16.9245			−0.550263
$947$	9.04655	+	15.6691i	0.293973	+	0.509177i	0.974746	−	0.223319i	$-0.0716890\pi$
$947$	9.04655	+	15.6691i	0.293973	+	0.509177i	−0.680772	+	0.732495i	$0.738356\pi$
$948$	0.0699370	−	0.121134i	0.00227145	−	0.00393426i
$949$	−0.928944	−	1.60898i	−0.0301548	−	0.0522296i
$950$	31.3187	−	54.2457i	1.01611	−	1.75996i
$951$	14.3962	−	24.9349i	0.466828	−	0.808570i
$952$	−8.27825	+	14.3384i	−0.268300	+	0.464709i
$953$	34.5592			1.11948			0.559741	−	0.828667i	$-0.310901\pi$
$953$	34.5592			1.11948			0.559741	+	0.828667i	$0.310901\pi$
$954$	31.2866	+	54.1900i	1.01294	+	1.75447i
$955$	−19.1274	−	33.1295i	−0.618947	−	1.07205i
$956$	0.0388182	−	0.0672351i	0.00125547	−	0.00217454i
$957$	2.35745			0.0762054
$958$	15.7313	+	27.2474i	0.508254	+	0.880322i
$959$	−80.9510			−2.61404
$960$	72.7853			2.34914
$961$	−18.4121	+	24.9398i	−0.593939	+	0.804510i
$962$	12.4045			0.399936
$963$	1.91519			0.0617162
$964$	−0.00512508	−	0.00887690i	−0.000165068	−	0.000285906i
$965$	−12.8968			−0.415164
$966$	−41.1536	+	71.2801i	−1.32409	+	2.29340i
$967$	−28.5330	−	49.4207i	−0.917560	−	1.58926i	−0.803109	−	0.595832i	$-0.796822\pi$
$967$	−28.5330	−	49.4207i	−0.917560	−	1.58926i	−0.114451	−	0.993429i	$-0.536511\pi$
$968$	−13.5625	−	23.4910i	−0.435916	−	0.755029i
$969$	−21.1984			−0.680992
$970$	5.80110	−	10.0478i	0.186262	−	0.322615i
$971$	−25.0535	+	43.3939i	−0.804004	+	1.39258i	0.112957	+	0.993600i	$0.463968\pi$
$971$	−25.0535	+	43.3939i	−0.804004	+	1.39258i	−0.916961	+	0.398976i	$0.869366\pi$
$972$	−0.0480874	+	0.0832898i	−0.00154240	+	0.00267152i
$973$	−38.3364	−	66.4005i	−1.22901	−	2.12870i
$974$	4.01110	−	6.94742i	0.128524	−	0.222610i
$975$	9.07110	+	15.7116i	0.290508	+	0.503174i
$976$	−1.26708			−0.0405584
$977$	−15.6998			−0.502281			−0.251141	−	0.967951i	$-0.580806\pi$
$977$	−15.6998			−0.502281			−0.251141	+	0.967951i	$0.580806\pi$
$978$	−13.5799	−	23.5211i	−0.434238	−	0.752123i
$979$	−4.84961	+	8.39977i	−0.154994	+	0.268458i
$980$	0.114788	+	0.198819i	0.00366678	+	0.00635105i
$981$	−19.0172	+	32.9387i	−0.607172	+	1.05165i
$982$	−15.2272	+	26.3742i	−0.485918	+	0.841635i
$983$	−7.37627	+	12.7761i	−0.235267	+	0.407494i	−0.959350	−	0.282219i	$-0.908930\pi$
$983$	−7.37627	+	12.7761i	−0.235267	+	0.407494i	0.724084	+	0.689712i	$0.242263\pi$
$984$	−57.1983			−1.82341
$985$	10.4982	+	18.1834i	0.334501	+	0.579372i
$986$	−0.664219	−	1.15046i	−0.0211530	−	0.0366381i
$987$	−35.4236	+	61.3555i	−1.12755	+	1.95297i
$988$	−0.0288934			−0.000919222
$989$	−23.8124	−	41.2444i	−0.757192	−	1.31149i
$990$	22.8167			0.725164
$991$	44.9038			1.42642			0.713208	−	0.700953i	$-0.247242\pi$
$991$	44.9038			1.42642			0.713208	+	0.700953i	$0.247242\pi$
$992$	−0.0637317	−	0.126269i	−0.00202348	−	0.00400904i
$993$	−45.1171			−1.43175
$994$	61.2038			1.94127
$995$	−8.44878	−	14.6337i	−0.267844	−	0.463920i
$996$	0.00383837			0.000121623
$997$	15.4641	−	26.7845i	0.489752	−	0.848275i	−0.510179	−	0.860068i	$-0.670421\pi$
$997$	15.4641	−	26.7845i	0.489752	−	0.848275i	0.999930	+	0.0117935i	$0.00375408\pi$
$998$	−2.08543	−	3.61208i	−0.0660132	−	0.114338i
$999$	10.7470	+	18.6143i	0.340019	+	0.588931i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.h.a.118.12	✓	30
31.5	even	3	inner	403.2.h.a.222.12	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.h.a.118.12	✓	30	1.1	even	1	trivial
403.2.h.a.222.12	yes	30	31.5	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.41262 q^{2} +(-1.31623 - 2.27977i) q^{3} -0.00449076 q^{4} +(-1.72422 + 2.98644i) q^{5} +(-1.85934 - 3.22047i) q^{6} +(2.33584 + 4.04580i) q^{7} -2.83159 q^{8} +(-1.96492 + 3.40333i) q^{9} +O(q^{10})\)	\(q+1.41262 q^{2} +(-1.31623 - 2.27977i) q^{3} -0.00449076 q^{4} +(-1.72422 + 2.98644i) q^{5} +(-1.85934 - 3.22047i) q^{6} +(2.33584 + 4.04580i) q^{7} -2.83159 q^{8} +(-1.96492 + 3.40333i) q^{9} +(-2.43568 + 4.21871i) q^{10} +(-0.595937 + 1.03219i) q^{11} +(0.00591087 + 0.0102379i) q^{12} +(0.500000 - 0.866025i) q^{13} +(3.29967 + 5.71520i) q^{14} +9.07787 q^{15} -3.99100 q^{16} +(-0.625797 - 1.08391i) q^{17} +(-2.77569 + 4.80763i) q^{18} +(3.21698 + 5.57198i) q^{19} +(0.00774306 - 0.0134114i) q^{20} +(6.14901 - 10.6504i) q^{21} +(-0.841835 + 1.45810i) q^{22} -4.73779 q^{23} +(3.72702 + 6.45540i) q^{24} +(-3.44587 - 5.96842i) q^{25} +(0.706312 - 1.22337i) q^{26} +2.44774 q^{27} +(-0.0104897 - 0.0181687i) q^{28} +0.751364 q^{29} +12.8236 q^{30} +(-2.50877 - 4.97052i) q^{31} +0.0254035 q^{32} +3.13756 q^{33} +(-0.884017 - 1.53116i) q^{34} -16.1100 q^{35} +(0.00882397 - 0.0152836i) q^{36} +(4.39058 + 7.60470i) q^{37} +(4.54439 + 7.87112i) q^{38} -2.63246 q^{39} +(4.88229 - 8.45637i) q^{40} +(-3.83672 + 6.64540i) q^{41} +(8.68624 - 15.0450i) q^{42} +(5.02607 + 8.70541i) q^{43} +(0.00267621 - 0.00463533i) q^{44} +(-6.77589 - 11.7362i) q^{45} -6.69271 q^{46} -5.76087 q^{47} +(5.25307 + 9.09858i) q^{48} +(-7.41234 + 12.8385i) q^{49} +(-4.86772 - 8.43114i) q^{50} +(-1.64738 + 2.85335i) q^{51} +(-0.00224538 + 0.00388911i) q^{52} +(5.63583 - 9.76155i) q^{53} +3.45774 q^{54} +(-2.05505 - 3.55946i) q^{55} +(-6.61416 - 11.4561i) q^{56} +(8.46857 - 14.6680i) q^{57} +1.06140 q^{58} +(-0.868681 - 1.50460i) q^{59} -0.0407666 q^{60} +0.317485 q^{61} +(-3.54396 - 7.02148i) q^{62} -18.3589 q^{63} +8.01788 q^{64} +(1.72422 + 2.98644i) q^{65} +4.43219 q^{66} +(3.31754 - 5.74614i) q^{67} +(0.00281031 + 0.00486759i) q^{68} +(6.23601 + 10.8011i) q^{69} -22.7574 q^{70} +(4.63711 - 8.03172i) q^{71} +(5.56384 - 9.63686i) q^{72} +(0.928944 - 1.60898i) q^{73} +(6.20224 + 10.7426i) q^{74} +(-9.07110 + 15.7116i) q^{75} +(-0.0144467 - 0.0250224i) q^{76} -5.56806 q^{77} -3.71867 q^{78} +(-5.91597 - 10.2468i) q^{79} +(6.88136 - 11.9189i) q^{80} +(2.67296 + 4.62971i) q^{81} +(-5.41985 + 9.38746i) q^{82} +(0.162344 - 0.281187i) q^{83} +(-0.0276137 + 0.0478284i) q^{84} +4.31605 q^{85} +(7.09995 + 12.2975i) q^{86} +(-0.988967 - 1.71294i) q^{87} +(1.68745 - 2.92275i) q^{88} +8.13779 q^{89} +(-9.57179 - 16.5788i) q^{90} +4.67169 q^{91} +0.0212763 q^{92} +(-8.02954 + 12.2618i) q^{93} -8.13794 q^{94} -22.1871 q^{95} +(-0.0334369 - 0.0579143i) q^{96} -2.38172 q^{97} +(-10.4709 + 18.1360i) q^{98} +(-2.34193 - 4.05634i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9}+O(q^{10}) \) 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9	\( 30 q - 6 q^{2} - 2 q^{3} + 22 q^{4} + 7 q^{5} + 6 q^{7} - 24 q^{8} - 13 q^{9} - 3 q^{10} - 3 q^{11} + 12 q^{12} + 15 q^{13} + 3 q^{14} + 4 q^{15} + 22 q^{16} + 4 q^{17} - 6 q^{18} + 5 q^{19} + 10 q^{20} - 15 q^{21} + 2 q^{22} - 6 q^{23} - 6 q^{24} - 20 q^{25} - 3 q^{26} + 4 q^{27} + 13 q^{28} + 26 q^{29} + 28 q^{30} + 19 q^{31} - 74 q^{32} + 2 q^{33} - 21 q^{34} - 30 q^{35} + 37 q^{36} - 4 q^{37} - 4 q^{38} - 4 q^{39} - 17 q^{40} + 7 q^{41} + 44 q^{42} + 15 q^{43} - 70 q^{44} + 15 q^{45} - 58 q^{46} - 24 q^{47} + 31 q^{48} - 29 q^{49} + 2 q^{50} + 25 q^{51} + 11 q^{52} + 4 q^{53} + 34 q^{54} + 13 q^{55} - 41 q^{56} + 8 q^{57} - 46 q^{58} + 27 q^{59} + 78 q^{60} + 8 q^{61} + 20 q^{62} - 112 q^{63} + 60 q^{64} - 7 q^{65} + 60 q^{66} + 29 q^{67} + 41 q^{68} - 23 q^{69} - 112 q^{70} + 29 q^{71} + 14 q^{72} - 10 q^{73} + 25 q^{74} - 18 q^{75} + 24 q^{76} - 72 q^{77} + 9 q^{79} - 11 q^{81} - 38 q^{82} - 13 q^{83} - 62 q^{84} + 108 q^{85} - 38 q^{86} - 18 q^{87} + 32 q^{88} + 6 q^{89} + 7 q^{90} + 12 q^{91} + 2 q^{92} + 37 q^{93} - 154 q^{94} - 28 q^{95} - 105 q^{96} - 84 q^{97} + 50 q^{98} + 10 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 - 2 * q^3 + 22 * q^4 + 7 * q^5 + 6 * q^7 - 24 * q^8 - 13 * q^9 - 3 * q^10 - 3 * q^11 + 12 * q^12 + 15 * q^13 + 3 * q^14 + 4 * q^15 + 22 * q^16 + 4 * q^17 - 6 * q^18 + 5 * q^19 + 10 * q^20 - 15 * q^21 + 2 * q^22 - 6 * q^23 - 6 * q^24 - 20 * q^25 - 3 * q^26 + 4 * q^27 + 13 * q^28 + 26 * q^29 + 28 * q^30 + 19 * q^31 - 74 * q^32 + 2 * q^33 - 21 * q^34 - 30 * q^35 + 37 * q^36 - 4 * q^37 - 4 * q^38 - 4 * q^39 - 17 * q^40 + 7 * q^41 + 44 * q^42 + 15 * q^43 - 70 * q^44 + 15 * q^45 - 58 * q^46 - 24 * q^47 + 31 * q^48 - 29 * q^49 + 2 * q^50 + 25 * q^51 + 11 * q^52 + 4 * q^53 + 34 * q^54 + 13 * q^55 - 41 * q^56 + 8 * q^57 - 46 * q^58 + 27 * q^59 + 78 * q^60 + 8 * q^61 + 20 * q^62 - 112 * q^63 + 60 * q^64 - 7 * q^65 + 60 * q^66 + 29 * q^67 + 41 * q^68 - 23 * q^69 - 112 * q^70 + 29 * q^71 + 14 * q^72 - 10 * q^73 + 25 * q^74 - 18 * q^75 + 24 * q^76 - 72 * q^77 + 9 * q^79 - 11 * q^81 - 38 * q^82 - 13 * q^83 - 62 * q^84 + 108 * q^85 - 38 * q^86 - 18 * q^87 + 32 * q^88 + 6 * q^89 + 7 * q^90 + 12 * q^91 + 2 * q^92 + 37 * q^93 - 154 * q^94 - 28 * q^95 - 105 * q^96 - 84 * q^97 + 50 * q^98 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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