LMFDB - Embedded newform 403.2.f.b.94.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("403.94");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			94.8
Character	$\chi$	$=$	403.94
Dual form			403.2.f.b.373.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0361865 - 0.0626768i) q^{2} +(1.64544 + 2.84999i) q^{3} +(0.997381 - 1.72751i) q^{4} +2.88575 q^{5} +(0.119086 - 0.206262i) q^{6} +(-0.540773 + 0.936646i) q^{7} -0.289113 q^{8} +(-3.91498 + 6.78094i) q^{9} +O(q^{10})$	\(q+(-0.0361865 - 0.0626768i) q^{2} +(1.64544 + 2.84999i) q^{3} +(0.997381 - 1.72751i) q^{4} +2.88575 q^{5} +(0.119086 - 0.206262i) q^{6} +(-0.540773 + 0.936646i) q^{7} -0.289113 q^{8} +(-3.91498 + 6.78094i) q^{9} +(-0.104425 - 0.180869i) q^{10} +(-0.248486 - 0.430390i) q^{11} +6.56454 q^{12} +(-3.34708 - 1.34054i) q^{13} +0.0782746 q^{14} +(4.74834 + 8.22436i) q^{15} +(-1.98430 - 3.43691i) q^{16} +(1.78037 - 3.08369i) q^{17} +0.566677 q^{18} +(0.404341 - 0.700340i) q^{19} +(2.87819 - 4.98517i) q^{20} -3.55925 q^{21} +(-0.0179836 + 0.0311486i) q^{22} +(-3.65912 - 6.33778i) q^{23} +(-0.475719 - 0.823969i) q^{24} +3.32753 q^{25} +(0.0370980 + 0.258294i) q^{26} -15.8949 q^{27} +(1.07871 + 1.86839i) q^{28} +(1.83722 + 3.18216i) q^{29} +(0.343651 - 0.595221i) q^{30} -1.00000 q^{31} +(-0.432722 + 0.749497i) q^{32} +(0.817740 - 1.41637i) q^{33} -0.257701 q^{34} +(-1.56053 + 2.70292i) q^{35} +(7.80945 + 13.5264i) q^{36} +(4.90446 + 8.49478i) q^{37} -0.0585267 q^{38} +(-1.68689 - 11.7449i) q^{39} -0.834306 q^{40} +(-0.601574 - 1.04196i) q^{41} +(0.128796 + 0.223082i) q^{42} +(1.71236 - 2.96589i) q^{43} -0.991341 q^{44} +(-11.2976 + 19.5681i) q^{45} +(-0.264821 + 0.458684i) q^{46} -6.86116 q^{47} +(6.53011 - 11.3105i) q^{48} +(2.91513 + 5.04915i) q^{49} +(-0.120412 - 0.208559i) q^{50} +11.7180 q^{51} +(-5.65412 + 4.44510i) q^{52} -2.70752 q^{53} +(0.575178 + 0.996238i) q^{54} +(-0.717067 - 1.24200i) q^{55} +(0.156344 - 0.270796i) q^{56} +2.66129 q^{57} +(0.132965 - 0.230302i) q^{58} +(-6.99040 + 12.1077i) q^{59} +18.9436 q^{60} +(5.98240 - 10.3618i) q^{61} +(0.0361865 + 0.0626768i) q^{62} +(-4.23423 - 7.33389i) q^{63} -7.87457 q^{64} +(-9.65882 - 3.86847i) q^{65} -0.118364 q^{66} +(-3.53410 - 6.12124i) q^{67} +(-3.55141 - 6.15123i) q^{68} +(12.0418 - 20.8570i) q^{69} +0.225881 q^{70} +(1.98350 - 3.43553i) q^{71} +(1.13187 - 1.96046i) q^{72} +3.80915 q^{73} +(0.354950 - 0.614792i) q^{74} +(5.47527 + 9.48345i) q^{75} +(-0.806565 - 1.39701i) q^{76} +0.537497 q^{77} +(-0.675093 + 0.530737i) q^{78} +11.9813 q^{79} +(-5.72619 - 9.91805i) q^{80} +(-14.4092 - 24.9574i) q^{81} +(-0.0435377 + 0.0754095i) q^{82} +9.74620 q^{83} +(-3.54992 + 6.14865i) q^{84} +(5.13769 - 8.89874i) q^{85} -0.247857 q^{86} +(-6.04608 + 10.4721i) q^{87} +(0.0718404 + 0.124431i) q^{88} +(4.47774 + 7.75567i) q^{89} +1.63529 q^{90} +(3.06562 - 2.41010i) q^{91} -14.5982 q^{92} +(-1.64544 - 2.84999i) q^{93} +(0.248281 + 0.430035i) q^{94} +(1.16683 - 2.02100i) q^{95} -2.84808 q^{96} +(-7.17134 + 12.4211i) q^{97} +(0.210976 - 0.365422i) q^{98} +3.89127 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 4 q^{2} - 20 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} - 12 q^{8} - 17 q^{9}+O(q^{10}) $ 34 * q + 4 * q^2 - 20 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 - 12 * q^8 - 17 * q^9	\( 34 q + 4 q^{2} - 20 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} - 12 q^{8} - 17 q^{9} - 6 q^{10} + 13 q^{11} + 8 q^{12} - 3 q^{13} + 4 q^{15} - 34 q^{16} + 6 q^{17} + 24 q^{18} + 4 q^{19} + 28 q^{20} - 36 q^{21} + 34 q^{22} + 8 q^{23} + 40 q^{24} + 16 q^{25} - 26 q^{26} - 6 q^{27} + 21 q^{28} + 6 q^{29} - 19 q^{30} - 34 q^{31} + 6 q^{32} + 7 q^{33} - 48 q^{34} + 9 q^{35} + 14 q^{37} + 22 q^{38} - 21 q^{39} - 20 q^{40} + 43 q^{41} - 33 q^{42} - 18 q^{43} - 56 q^{44} + 26 q^{45} + 7 q^{46} - 12 q^{47} + 95 q^{48} + q^{49} + 44 q^{50} + 52 q^{51} - 24 q^{52} - 10 q^{53} + 27 q^{54} - 39 q^{55} - 39 q^{56} - 92 q^{57} + 8 q^{58} - q^{59} - 42 q^{60} + 19 q^{61} - 4 q^{62} + 5 q^{63} + 84 q^{64} - 32 q^{65} + 52 q^{66} + 10 q^{67} - 34 q^{68} - 32 q^{69} + 48 q^{70} + 35 q^{71} - 26 q^{72} - 22 q^{73} + 68 q^{74} + 62 q^{75} + 2 q^{76} + 42 q^{77} - 81 q^{78} + 2 q^{79} + 49 q^{80} - 37 q^{81} - 35 q^{82} - 48 q^{83} - 34 q^{84} - 13 q^{85} - 152 q^{86} + 22 q^{87} + 37 q^{88} + 42 q^{89} + 30 q^{90} - 39 q^{91} + 30 q^{92} - 42 q^{94} - 34 q^{95} - 66 q^{96} - 38 q^{97} + 8 q^{98} - 34 q^{99}+O(q^{100}) \) 34 * q + 4 * q^2 - 20 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 - 12 * q^8 - 17 * q^9 - 6 * q^10 + 13 * q^11 + 8 * q^12 - 3 * q^13 + 4 * q^15 - 34 * q^16 + 6 * q^17 + 24 * q^18 + 4 * q^19 + 28 * q^20 - 36 * q^21 + 34 * q^22 + 8 * q^23 + 40 * q^24 + 16 * q^25 - 26 * q^26 - 6 * q^27 + 21 * q^28 + 6 * q^29 - 19 * q^30 - 34 * q^31 + 6 * q^32 + 7 * q^33 - 48 * q^34 + 9 * q^35 + 14 * q^37 + 22 * q^38 - 21 * q^39 - 20 * q^40 + 43 * q^41 - 33 * q^42 - 18 * q^43 - 56 * q^44 + 26 * q^45 + 7 * q^46 - 12 * q^47 + 95 * q^48 + q^49 + 44 * q^50 + 52 * q^51 - 24 * q^52 - 10 * q^53 + 27 * q^54 - 39 * q^55 - 39 * q^56 - 92 * q^57 + 8 * q^58 - q^59 - 42 * q^60 + 19 * q^61 - 4 * q^62 + 5 * q^63 + 84 * q^64 - 32 * q^65 + 52 * q^66 + 10 * q^67 - 34 * q^68 - 32 * q^69 + 48 * q^70 + 35 * q^71 - 26 * q^72 - 22 * q^73 + 68 * q^74 + 62 * q^75 + 2 * q^76 + 42 * q^77 - 81 * q^78 + 2 * q^79 + 49 * q^80 - 37 * q^81 - 35 * q^82 - 48 * q^83 - 34 * q^84 - 13 * q^85 - 152 * q^86 + 22 * q^87 + 37 * q^88 + 42 * q^89 + 30 * q^90 - 39 * q^91 + 30 * q^92 - 42 * q^94 - 34 * q^95 - 66 * q^96 - 38 * q^97 + 8 * q^98 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.0361865	−	0.0626768i	−0.0255877	−	0.0443192i	0.852948	−	0.521996i	$-0.174812\pi$
$2$	−0.0361865	−	0.0626768i	−0.0255877	−	0.0443192i	−0.878536	+	0.477677i	$0.841479\pi$
$3$	1.64544	+	2.84999i	0.949998	+	1.64544i	0.745420	+	0.666595i	$0.232249\pi$
$3$	1.64544	+	2.84999i	0.949998	+	1.64544i	0.204578	+	0.978850i	$0.434418\pi$
$4$	0.997381	−	1.72751i	0.498691	−	0.863757i
$5$	2.88575			1.29055			0.645273	−	0.763952i	$-0.276744\pi$
$5$	2.88575			1.29055			0.645273	+	0.763952i	$0.276744\pi$
$6$	0.119086	−	0.206262i	0.0486165	−	0.0842063i
$7$	−0.540773	+	0.936646i	−0.204393	+	0.354019i	−0.949939	−	0.312435i	$-0.898855\pi$
$7$	−0.540773	+	0.936646i	−0.204393	+	0.354019i	0.745546	+	0.666454i	$0.232189\pi$
$8$	−0.289113			−0.102217
$9$	−3.91498	+	6.78094i	−1.30499	+	2.26031i
$10$	−0.104425	−	0.180869i	−0.0330221	−	0.0571959i
$11$	−0.248486	−	0.430390i	−0.0749213	−	0.129768i	0.826131	−	0.563478i	$-0.190537\pi$
$11$	−0.248486	−	0.430390i	−0.0749213	−	0.129768i	−0.901052	+	0.433711i	$0.857204\pi$
$12$	6.56454			1.89502
$13$	−3.34708	−	1.34054i	−0.928313	−	0.371800i
$13$	−3.34708	−	1.34054i	−0.928313	−	0.371800i
$14$	0.0782746			0.0209198
$15$	4.74834	+	8.22436i	1.22602	+	2.12352i
$16$	−1.98430	−	3.43691i	−0.496075	−	0.859227i
$17$	1.78037	−	3.08369i	0.431803	−	0.747904i	−0.565226	−	0.824936i	$-0.691211\pi$
$17$	1.78037	−	3.08369i	0.431803	−	0.747904i	0.997029	+	0.0770318i	$0.0245443\pi$
$18$	0.566677			0.133567
$19$	0.404341	−	0.700340i	0.0927623	−	0.160669i	−0.815910	−	0.578179i	$-0.803764\pi$
$19$	0.404341	−	0.700340i	0.0927623	−	0.160669i	0.908672	+	0.417510i	$0.137097\pi$
$20$	2.87819	−	4.98517i	0.643583	−	1.11472i
$21$	−3.55925			−0.776691
$22$	−0.0179836	+	0.0311486i	−0.00383413	+	0.00664090i
$23$	−3.65912	−	6.33778i	−0.762980	−	1.32152i	−0.941308	−	0.337548i	$-0.890402\pi$
$23$	−3.65912	−	6.33778i	−0.762980	−	1.32152i	0.178329	−	0.983971i	$-0.442931\pi$
$24$	−0.475719	−	0.823969i	−0.0971057	−	0.168192i
$25$	3.32753			0.665507
$26$	0.0370980	+	0.258294i	0.00727551	+	0.0506556i
$27$	−15.8949			−3.05897
$28$	1.07871	+	1.86839i	0.203858	+	0.353092i
$29$	1.83722	+	3.18216i	0.341163	+	0.590912i	0.984649	−	0.174546i	$-0.0558459\pi$
$29$	1.83722	+	3.18216i	0.341163	+	0.590912i	−0.643486	+	0.765458i	$0.722513\pi$
$30$	0.343651	−	0.595221i	0.0627418	−	0.108672i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	−0.432722	+	0.749497i	−0.0764952	+	0.132494i
$33$	0.817740	−	1.41637i	0.142350	−	0.246558i
$34$	−0.257701			−0.0441953
$35$	−1.56053	+	2.70292i	−0.263778	+	0.456877i
$36$	7.80945	+	13.5264i	1.30158	+	2.25439i
$37$	4.90446	+	8.49478i	0.806289	+	1.39653i	0.915418	+	0.402506i	$0.131861\pi$
$37$	4.90446	+	8.49478i	0.806289	+	1.39653i	−0.109129	+	0.994028i	$0.534806\pi$
$38$	−0.0585267			−0.00949429
$39$	−1.68689	−	11.7449i	−0.270119	−	1.88070i
$40$	−0.834306			−0.131915
$41$	−0.601574	−	1.04196i	−0.0939501	−	0.162726i	0.815220	−	0.579152i	$-0.196616\pi$
$41$	−0.601574	−	1.04196i	−0.0939501	−	0.162726i	−0.909170	+	0.416425i	$0.863283\pi$
$42$	0.128796	+	0.223082i	0.0198737	+	0.0344223i
$43$	1.71236	−	2.96589i	0.261132	−	0.452294i	−0.705411	−	0.708798i	$-0.749238\pi$
$43$	1.71236	−	2.96589i	0.261132	−	0.452294i	0.966543	+	0.256505i	$0.0825709\pi$
$44$	−0.991341			−0.149450
$45$	−11.2976	+	19.5681i	−1.68415	+	2.91704i
$46$	−0.264821	+	0.458684i	−0.0390458	+	0.0676292i
$47$	−6.86116			−1.00080			−0.500402	−	0.865793i	$-0.666814\pi$
$47$	−6.86116			−1.00080			−0.500402	+	0.865793i	$0.666814\pi$
$48$	6.53011	−	11.3105i	0.942541	−	1.63253i
$49$	2.91513	+	5.04915i	0.416447	+	0.721308i
$50$	−0.120412	−	0.208559i	−0.0170288	−	0.0294947i
$51$	11.7180			1.64085
$52$	−5.65412	+	4.44510i	−0.784086	+	0.616424i
$53$	−2.70752			−0.371906			−0.185953	−	0.982559i	$-0.559537\pi$
$53$	−2.70752			−0.371906			−0.185953	+	0.982559i	$0.559537\pi$
$54$	0.575178	+	0.996238i	0.0782719	+	0.135571i
$55$	−0.717067	−	1.24200i	−0.0966893	−	0.167471i
$56$	0.156344	−	0.270796i	0.0208924	−	0.0361866i
$57$	2.66129			0.352496
$58$	0.132965	−	0.230302i	0.0174591	−	0.0302401i
$59$	−6.99040	+	12.1077i	−0.910072	+	1.57629i	−0.0961121	+	0.995371i	$0.530641\pi$
$59$	−6.99040	+	12.1077i	−0.910072	+	1.57629i	−0.813960	+	0.580921i	$0.802693\pi$
$60$	18.9436			2.44561
$61$	5.98240	−	10.3618i	0.765968	−	1.32670i	−0.173765	−	0.984787i	$-0.555593\pi$
$61$	5.98240	−	10.3618i	0.765968	−	1.32670i	0.939733	−	0.341909i	$-0.111073\pi$
$62$	0.0361865	+	0.0626768i	0.00459568	+	0.00795996i
$63$	−4.23423	−	7.33389i	−0.533462	−	0.923984i
$64$	−7.87457			−0.984321
$65$	−9.65882	−	3.86847i	−1.19803	−	0.479825i
$66$	−0.118364			−0.0145697
$67$	−3.53410	−	6.12124i	−0.431759	−	0.747828i	0.565266	−	0.824909i	$-0.308774\pi$
$67$	−3.53410	−	6.12124i	−0.431759	−	0.747828i	−0.997025	+	0.0770804i	$0.975440\pi$
$68$	−3.55141	−	6.15123i	−0.430672	−	0.745946i
$69$	12.0418	−	20.8570i	1.44966	−	2.51088i
$70$	0.225881			0.0269979
$71$	1.98350	−	3.43553i	0.235398	−	0.407722i	−0.723990	−	0.689811i	$-0.757694\pi$
$71$	1.98350	−	3.43553i	0.235398	−	0.407722i	0.959388	+	0.282088i	$0.0910272\pi$
$72$	1.13187	−	1.96046i	0.133392	−	0.231042i
$73$	3.80915			0.445828			0.222914	−	0.974838i	$-0.428443\pi$
$73$	3.80915			0.445828			0.222914	+	0.974838i	$0.428443\pi$
$74$	0.354950	−	0.614792i	0.0412621	−	0.0714681i
$75$	5.47527	+	9.48345i	0.632230	+	1.09505i
$76$	−0.806565	−	1.39701i	−0.0925193	−	0.160248i
$77$	0.537497			0.0612535
$78$	−0.675093	+	0.530737i	−0.0764392	+	0.0600941i
$79$	11.9813			1.34801			0.674003	−	0.738729i	$-0.264574\pi$
$79$	11.9813			1.34801			0.674003	+	0.738729i	$0.264574\pi$
$80$	−5.72619	−	9.91805i	−0.640207	−	1.10887i
$81$	−14.4092	−	24.9574i	−1.60102	−	2.77305i
$82$	−0.0435377	+	0.0754095i	−0.00480793	+	0.00832758i
$83$	9.74620			1.06978			0.534892	−	0.844920i	$-0.320352\pi$
$83$	9.74620			1.06978			0.534892	+	0.844920i	$0.320352\pi$
$84$	−3.54992	+	6.14865i	−0.387329	+	0.670873i
$85$	5.13769	−	8.89874i	0.557261	−	0.965204i
$86$	−0.247857			−0.0267271
$87$	−6.04608	+	10.4721i	−0.648208	+	1.12273i
$88$	0.0718404	+	0.124431i	0.00765821	+	0.0132644i
$89$	4.47774	+	7.75567i	0.474640	+	0.822100i	0.999578	−	0.0290402i	$-0.00924508\pi$
$89$	4.47774	+	7.75567i	0.474640	+	0.822100i	−0.524939	+	0.851140i	$0.675912\pi$
$90$	1.63529			0.172374
$91$	3.06562	−	2.41010i	0.321365	−	0.252647i
$92$	−14.5982			−1.52196
$93$	−1.64544	−	2.84999i	−0.170625	−	0.295531i
$94$	0.248281	+	0.430035i	0.0256082	+	0.0443548i
$95$	1.16683	−	2.02100i	0.119714	−	0.207351i
$96$	−2.84808			−0.290681
$97$	−7.17134	+	12.4211i	−0.728139	+	1.26117i	0.229530	+	0.973302i	$0.426281\pi$
$97$	−7.17134	+	12.4211i	−0.728139	+	1.26117i	−0.957669	+	0.287872i	$0.907052\pi$
$98$	0.210976	−	0.365422i	0.0213118	−	0.0369132i
$99$	3.89127			0.391087
$100$	3.31882	−	5.74836i	0.331882	−	0.574836i
$101$	−0.512539	−	0.887743i	−0.0509995	−	0.0883337i	0.839399	−	0.543516i	$-0.182907\pi$
$101$	−0.512539	−	0.887743i	−0.0509995	−	0.0883337i	−0.890398	+	0.455182i	$0.849574\pi$
$102$	−0.424033	−	0.734446i	−0.0419855	−	0.0727210i
$103$	−4.92883			−0.485652			−0.242826	−	0.970070i	$-0.578074\pi$
$103$	−4.92883			−0.485652			−0.242826	+	0.970070i	$0.578074\pi$
$104$	0.967683	+	0.387568i	0.0948891	+	0.0380042i
$105$	−10.2711			−1.00235
$106$	0.0979755	+	0.169698i	0.00951622	+	0.0164826i
$107$	−4.63232	−	8.02342i	−0.447824	−	0.775653i	0.550421	−	0.834888i	$-0.314467\pi$
$107$	−4.63232	−	8.02342i	−0.447824	−	0.775653i	−0.998244	+	0.0592344i	$0.981134\pi$
$108$	−15.8532	+	27.4586i	−1.52548	+	2.64220i
$109$	4.45675			0.426879			0.213440	−	0.976956i	$-0.431533\pi$
$109$	4.45675			0.426879			0.213440	+	0.976956i	$0.431533\pi$
$110$	−0.0518962	+	0.0898869i	−0.00494811	+	0.00857038i
$111$	−16.1400	+	27.9554i	−1.53195	+	2.65341i
$112$	4.29222			0.405577
$113$	0.380948	−	0.659822i	0.0358366	−	0.0620708i	−0.847551	−	0.530714i	$-0.821924\pi$
$113$	0.380948	−	0.659822i	0.0358366	−	0.0620708i	0.883387	+	0.468643i	$0.155257\pi$
$114$	−0.0963025	−	0.166801i	−0.00901956	−	0.0156223i
$115$	−10.5593	−	18.2892i	−0.984660	−	1.70548i
$116$	7.32963			0.680539
$117$	22.1939	−	17.4482i	2.05183	−	1.61308i
$118$	1.01183			0.0931466
$119$	1.92555	+	3.33515i	0.176515	+	0.305733i
$120$	−1.37280	−	2.37777i	−0.125319	−	0.217059i
$121$	5.37651	−	9.31239i	0.488774	−	0.846581i
$122$	−0.865928			−0.0783974
$123$	1.97971	−	3.42897i	0.178505	−	0.309179i
$124$	−0.997381	+	1.72751i	−0.0895675	+	0.155135i
$125$	−4.82632			−0.431679
$126$	−0.306443	+	0.530775i	−0.0273001	+	0.0472852i
$127$	5.36595	+	9.29410i	0.476151	+	0.824718i	0.999627	−	0.0273226i	$-0.00869813\pi$
$127$	5.36595	+	9.29410i	0.476151	+	0.824718i	−0.523475	+	0.852041i	$0.675365\pi$
$128$	1.15040	+	1.99255i	0.101682	+	0.176118i
$129$	11.2704			0.992300
$130$	0.107055	+	0.745370i	0.00938937	+	0.0653733i
$131$	−19.2424			−1.68122			−0.840609	−	0.541642i	$-0.817803\pi$
$131$	−19.2424			−1.68122			−0.840609	+	0.541642i	$0.817803\pi$
$132$	−1.63120	−	2.82531i	−0.141977	−	0.245912i
$133$	0.437313	+	0.757449i	0.0379199	+	0.0656792i
$134$	−0.255773	+	0.443012i	−0.0220954	+	0.0382704i
$135$	−45.8685			−3.94773
$136$	−0.514727	+	0.891533i	−0.0441375	+	0.0764483i
$137$	−1.39067	+	2.40872i	−0.118813	+	0.205791i	−0.919298	−	0.393563i	$-0.871242\pi$
$137$	−1.39067	+	2.40872i	−0.118813	+	0.205791i	0.800484	+	0.599354i	$0.204576\pi$
$138$	−1.74300			−0.148374
$139$	4.84101	−	8.38488i	0.410609	−	0.711196i	−0.584347	−	0.811504i	$-0.698649\pi$
$139$	4.84101	−	8.38488i	0.410609	−	0.711196i	0.994956	+	0.100307i	$0.0319826\pi$
$140$	3.11289	+	5.39169i	0.263087	+	0.455681i
$141$	−11.2897	−	19.5543i	−0.950761	−	1.64677i
$142$	−0.287104			−0.0240932
$143$	0.254745	+	1.77366i	0.0213029	+	0.148321i
$144$	31.0740			2.58950
$145$	5.30175	+	9.18290i	0.440286	+	0.762598i
$146$	−0.137840	−	0.238746i	−0.0114077	−	0.0197587i
$147$	−9.59337	+	16.6162i	−0.791248	+	1.37048i
$148$	19.5665			1.60835
$149$	10.5356	−	18.2482i	0.863111	−	1.49495i	−0.00580048	−	0.999983i	$-0.501846\pi$
$149$	10.5356	−	18.2482i	0.863111	−	1.49495i	0.868911	−	0.494968i	$-0.164820\pi$
$150$	0.396261	−	0.686345i	0.0323546	−	0.0560398i
$151$	−14.3786			−1.17011			−0.585057	−	0.810992i	$-0.698928\pi$
$151$	−14.3786			−1.17011			−0.585057	+	0.810992i	$0.698928\pi$
$152$	−0.116900	+	0.202477i	−0.00948186	+	0.0164231i
$153$	13.9402	+	24.1451i	1.12700	+	1.95202i
$154$	−0.0194501	−	0.0336886i	−0.00156734	−	0.00271471i
$155$	−2.88575			−0.231789
$156$	−21.9720	−	8.80006i	−1.75917	−	0.704568i
$157$	9.06348			0.723344			0.361672	−	0.932305i	$-0.382206\pi$
$157$	9.06348			0.723344			0.361672	+	0.932305i	$0.382206\pi$
$158$	−0.433562	−	0.750952i	−0.0344924	−	0.0597425i
$159$	−4.45507	−	7.71641i	−0.353310	−	0.611951i
$160$	−1.24873	+	2.16286i	−0.0987205	+	0.170989i
$161$	7.91501			0.623790
$162$	−1.04283	+	1.80624i	−0.0819328	+	0.141912i
$163$	−8.39170	+	14.5348i	−0.657289	+	1.13846i	0.324026	+	0.946048i	$0.394963\pi$
$163$	−8.39170	+	14.5348i	−0.657289	+	1.13846i	−0.981315	+	0.192409i	$0.938370\pi$
$164$	−2.39999			−0.187408
$165$	2.35979	−	4.08728i	0.183709	−	0.318194i
$166$	−0.352680	−	0.610860i	−0.0273733	−	0.0474120i
$167$	−1.11704	−	1.93476i	−0.0864388	−	0.149716i	0.819565	−	0.572987i	$-0.194215\pi$
$167$	−1.11704	−	1.93476i	−0.0864388	−	0.149716i	−0.906003	+	0.423270i	$0.860882\pi$
$168$	1.02902			0.0793908
$169$	9.40588	+	8.97381i	0.723530	+	0.690293i
$170$	−0.743659			−0.0570361
$171$	3.16598	+	5.48363i	0.242108	+	0.419344i
$172$	−3.41574	−	5.91624i	−0.260448	−	0.451109i
$173$	−10.4891	+	18.1676i	−0.797468	+	1.38126i	0.123792	+	0.992308i	$0.460495\pi$
$173$	−10.4891	+	18.1676i	−0.797468	+	1.38126i	−0.921260	+	0.388947i	$0.872839\pi$
$174$	0.875145			0.0663446
$175$	−1.79944	+	3.11672i	−0.136025	+	0.235602i
$176$	−0.986141	+	1.70805i	−0.0743332	+	0.128749i
$177$	−46.0093			−3.45827
$178$	0.324067	−	0.561301i	0.0242899	−	0.0420713i
$179$	−1.14080	−	1.97593i	−0.0852677	−	0.147688i	0.820238	−	0.572023i	$-0.193841\pi$
$179$	−1.14080	−	1.97593i	−0.0852677	−	0.147688i	−0.905505	+	0.424335i	$0.860508\pi$
$180$	22.5361	+	39.0337i	1.67974	+	2.90940i
$181$	13.0506			0.970041			0.485020	−	0.874503i	$-0.338812\pi$
$181$	13.0506			0.970041			0.485020	+	0.874503i	$0.338812\pi$
$182$	−0.261991	−	0.104930i	−0.0194201	−	0.00777797i
$183$	39.3749			2.91067
$184$	1.05790	+	1.83233i	0.0779893	+	0.135081i
$185$	14.1530	+	24.5138i	1.04055	+	1.80229i
$186$	−0.119086	+	0.206262i	−0.00873178	+	0.0151239i
$187$	−1.76959			−0.129405
$188$	−6.84319	+	11.8528i	−0.499091	+	0.864451i
$189$	8.59550	−	14.8878i	0.625231	−	1.08293i
$190$	−0.168893			−0.0122528
$191$	2.59749	−	4.49898i	0.187948	−	0.325535i	−0.756618	−	0.653857i	$-0.773150\pi$
$191$	2.59749	−	4.49898i	0.187948	−	0.325535i	0.944566	+	0.328322i	$0.106483\pi$
$192$	−12.9572	−	22.4425i	−0.935103	−	1.61965i
$193$	13.4205	+	23.2449i	0.966027	+	1.67321i	0.706830	+	0.707383i	$0.250124\pi$
$193$	13.4205	+	23.2449i	0.966027	+	1.67321i	0.259197	+	0.965825i	$0.416542\pi$
$194$	1.03802			0.0745256
$195$	−4.86795	−	33.8929i	−0.348601	−	2.42712i
$196$	11.6300			0.830713
$197$	−7.99429	−	13.8465i	−0.569569	−	0.986523i	−0.996608	−	0.0822900i	$-0.973777\pi$
$197$	−7.99429	−	13.8465i	−0.569569	−	0.986523i	0.427039	−	0.904233i	$-0.359557\pi$
$198$	−0.140811	−	0.243892i	−0.0100070	−	0.0173327i
$199$	10.4584	−	18.1145i	0.741377	−	1.28410i	−0.210491	−	0.977596i	$-0.567506\pi$
$199$	10.4584	−	18.1145i	0.741377	−	1.28410i	0.951868	−	0.306507i	$-0.0991604\pi$
$200$	−0.962032			−0.0680259
$201$	11.6303	−	20.1443i	0.820340	−	1.42087i
$202$	−0.0370939	+	0.0642486i	−0.00260992	+	0.00452051i
$203$	−3.97407			−0.278925
$204$	11.6873	−	20.2430i	0.818275	−	1.41729i
$205$	−1.73599	−	3.00682i	−0.121247	−	0.210006i
$206$	0.178357	+	0.308923i	0.0124267	+	0.0215237i
$207$	57.3015			3.98273
$208$	2.03428	+	14.1636i	0.141052	+	0.982072i
$209$	−0.401893			−0.0277995
$210$	0.371674	+	0.643758i	0.0256479	+	0.0444235i
$211$	−4.00862	−	6.94314i	−0.275965	−	0.477985i	0.694413	−	0.719577i	$-0.255664\pi$
$211$	−4.00862	−	6.94314i	−0.275965	−	0.477985i	−0.970378	+	0.241591i	$0.922331\pi$
$212$	−2.70043	+	4.67728i	−0.185466	+	0.321237i
$213$	13.0550			0.894512
$214$	−0.335255	+	0.580678i	−0.0229175	+	0.0396943i
$215$	4.94143	−	8.55880i	0.337003	−	0.583706i
$216$	4.59540			0.312678
$217$	0.540773	−	0.936646i	0.0367100	−	0.0635836i
$218$	−0.161274	−	0.279335i	−0.0109229	−	0.0189189i
$219$	6.26775	+	10.8561i	0.423536	+	0.733585i
$220$	−2.86076			−0.192872
$221$	−10.0929	+	7.93469i	−0.678919	+	0.533745i
$222$	2.33620			0.156796
$223$	−4.15392	−	7.19480i	−0.278167	−	0.481799i	0.692762	−	0.721166i	$-0.256393\pi$
$223$	−4.15392	−	7.19480i	−0.278167	−	0.481799i	−0.970929	+	0.239367i	$0.923060\pi$
$224$	−0.468009	−	0.810615i	−0.0312701	−	0.0541615i
$225$	−13.0272	+	22.5638i	−0.868481	+	1.50425i
$226$	−0.0551407			−0.00366790
$227$	−14.1779	+	24.5569i	−0.941021	+	1.62990i	−0.177494	+	0.984122i	$0.556799\pi$
$227$	−14.1779	+	24.5569i	−0.941021	+	1.62990i	−0.763528	+	0.645775i	$0.776534\pi$
$228$	2.65432	−	4.59741i	0.175786	−	0.304471i
$229$	14.3597			0.948915			0.474457	−	0.880278i	$-0.342644\pi$
$229$	14.3597			0.948915			0.474457	+	0.880278i	$0.342644\pi$
$230$	−0.764207	+	1.32365i	−0.0503903	+	0.0872786i
$231$	0.884422	+	1.53186i	0.0581907	+	0.100789i
$232$	−0.531163	−	0.920001i	−0.0348726	−	0.0604010i
$233$	−18.0110			−1.17994			−0.589970	−	0.807425i	$-0.700861\pi$
$233$	−18.0110			−1.17994			−0.589970	+	0.807425i	$0.700861\pi$
$234$	−1.89671	−	0.759655i	−0.123992	−	0.0496602i
$235$	−19.7996			−1.29158
$236$	13.9442	+	24.1520i	0.907689	+	1.57216i
$237$	19.7146	+	34.1467i	1.28060	+	2.21807i
$238$	0.139358	−	0.241374i	0.00903321	−	0.0156460i
$239$	−13.7194			−0.887436			−0.443718	−	0.896167i	$-0.646341\pi$
$239$	−13.7194			−0.887436			−0.443718	+	0.896167i	$0.646341\pi$
$240$	18.8443	−	32.6392i	1.21639	−	2.10685i
$241$	6.80272	−	11.7827i	0.438202	−	0.758988i	−0.559349	−	0.828932i	$-0.688949\pi$
$241$	6.80272	−	11.7827i	0.438202	−	0.758988i	0.997551	+	0.0699445i	$0.0222822\pi$
$242$	−0.778227			−0.0500263
$243$	23.5767	−	40.8361i	1.51245	−	2.61964i
$244$	−11.9335	−	20.6694i	−0.763962	−	1.32322i
$245$	8.41233	+	14.5706i	0.537444	+	0.930880i
$246$	−0.286555			−0.0182701
$247$	−2.29220	+	1.80206i	−0.145849	+	0.114662i
$248$	0.289113			0.0183587
$249$	16.0368	+	27.7766i	1.01629	+	1.76027i
$250$	0.174647	+	0.302498i	0.0110457	+	0.0191317i
$251$	−2.04420	+	3.54066i	−0.129029	+	0.223485i	−0.923301	−	0.384078i	$-0.874519\pi$
$251$	−2.04420	+	3.54066i	−0.129029	+	0.223485i	0.794272	+	0.607563i	$0.207853\pi$
$252$	−16.8925			−1.06413
$253$	−1.81848	+	3.14970i	−0.114327	+	0.198020i
$254$	0.388350	−	0.672641i	0.0243672	−	0.0422053i
$255$	33.8152			2.11759
$256$	−7.79131	+	13.4949i	−0.486957	+	0.843434i
$257$	−2.31857	−	4.01588i	−0.144628	−	0.250504i	0.784606	−	0.619995i	$-0.212865\pi$
$257$	−2.31857	−	4.01588i	−0.144628	−	0.250504i	−0.929234	+	0.369491i	$0.879532\pi$
$258$	−0.407834	−	0.706390i	−0.0253907	−	0.0439779i
$259$	−10.6088			−0.659199
$260$	−16.3164	+	12.8274i	−1.01190	+	0.795523i
$261$	−28.7707			−1.78086
$262$	0.696315	+	1.20605i	0.0430185	+	0.0745102i
$263$	12.9965	+	22.5106i	0.801398	+	1.38806i	0.918696	+	0.394965i	$0.129243\pi$
$263$	12.9965	+	22.5106i	0.801398	+	1.38806i	−0.117299	+	0.993097i	$0.537424\pi$
$264$	−0.236419	+	0.409489i	−0.0145506	+	0.0252023i
$265$	−7.81321			−0.479962
$266$	0.0316496	−	0.0548188i	0.00194056	−	0.00336116i
$267$	−14.7358	+	25.5231i	−0.901813	+	1.56199i
$268$	−14.0994			−0.861256
$269$	−6.13345	+	10.6234i	−0.373963	+	0.647723i	−0.990171	−	0.139861i	$-0.955335\pi$
$269$	−6.13345	+	10.6234i	−0.373963	+	0.647723i	0.616208	+	0.787583i	$0.288668\pi$
$270$	1.65982	+	2.87489i	0.101013	+	0.174960i
$271$	12.4761	+	21.6093i	0.757871	+	1.31267i	0.943934	+	0.330133i	$0.107094\pi$
$271$	12.4761	+	21.6093i	0.757871	+	1.31267i	−0.186064	+	0.982538i	$0.559573\pi$
$272$	−14.1311			−0.856826
$273$	11.9131	+	4.77133i	0.721012	+	0.288774i
$274$	0.201294			0.0121606
$275$	−0.826845	−	1.43214i	−0.0498606	−	0.0863611i
$276$	−24.0205	−	41.6047i	−1.44586	−	2.50431i
$277$	5.51584	−	9.55372i	0.331415	−	0.574027i	−0.651375	−	0.758756i	$-0.725807\pi$
$277$	5.51584	−	9.55372i	0.331415	−	0.574027i	0.982790	+	0.184729i	$0.0591407\pi$
$278$	−0.700717			−0.0420262
$279$	3.91498	−	6.78094i	0.234384	−	0.405964i
$280$	0.451170	−	0.781449i	0.0269625	−	0.0467005i
$281$	−21.3168			−1.27165			−0.635827	−	0.771831i	$-0.719341\pi$
$281$	−21.3168			−1.27165			−0.635827	+	0.771831i	$0.719341\pi$
$282$	−0.817066	+	1.41520i	−0.0486556	+	0.0842739i
$283$	−0.819224	−	1.41894i	−0.0486978	−	0.0843471i	0.840649	−	0.541580i	$-0.182174\pi$
$283$	−0.819224	−	1.41894i	−0.0486978	−	0.0843471i	−0.889347	+	0.457233i	$0.848840\pi$
$284$	−3.95662	−	6.85306i	−0.234782	−	0.406654i
$285$	7.67980			0.454912
$286$	0.101949	−	0.0801489i	0.00602836	−	0.00473931i
$287$	1.30126			0.0768109
$288$	−3.38820	−	5.86853i	−0.199651	−	0.345806i
$289$	2.16058	+	3.74223i	0.127093	+	0.220131i
$290$	0.383703	−	0.664593i	0.0225318	−	0.0390262i
$291$	−47.2002			−2.76692
$292$	3.79918	−	6.58037i	0.222330	−	0.385087i
$293$	8.72440	−	15.1111i	0.509685	−	0.882800i	−0.490252	−	0.871581i	$-0.663095\pi$
$293$	8.72440	−	15.1111i	0.509685	−	0.882800i	0.999937	−	0.0112193i	$-0.00357129\pi$
$294$	1.38860			0.0809848
$295$	−20.1725	+	34.9398i	−1.17449	+	2.03427i
$296$	−1.41794	−	2.45595i	−0.0824162	−	0.142749i
$297$	3.94965	+	6.84099i	0.229182	+	0.396955i
$298$	−1.52499			−0.0883400
$299$	3.75129	+	26.1183i	0.216943	+	1.51046i
$300$	21.8437			1.26115
$301$	1.85199	+	3.20774i	0.106747	+	0.184891i
$302$	0.520310	+	0.901204i	0.0299405	+	0.0518584i
$303$	1.68671	−	2.92146i	0.0968989	−	0.167834i
$304$	−3.20934			−0.184068
$305$	17.2637	−	29.9016i	0.988517	−	1.71216i
$306$	1.00889	−	1.74745i	0.0576746	−	0.0998953i
$307$	−2.30251			−0.131411			−0.0657055	−	0.997839i	$-0.520930\pi$
$307$	−2.30251			−0.131411			−0.0657055	+	0.997839i	$0.520930\pi$
$308$	0.536090	−	0.928535i	0.0305465	−	0.0529082i
$309$	−8.11012	−	14.0471i	−0.461369	−	0.799114i
$310$	0.104425	+	0.180869i	0.00593094	+	0.0102727i
$311$	10.6055			0.601383			0.300691	−	0.953722i	$-0.402783\pi$
$311$	10.6055			0.601383			0.300691	+	0.953722i	$0.402783\pi$
$312$	0.487702	+	3.39561i	0.0276107	+	0.192239i
$313$	−27.4089			−1.54924			−0.774622	−	0.632425i	$-0.782060\pi$
$313$	−27.4089			−1.54924			−0.774622	+	0.632425i	$0.782060\pi$
$314$	−0.327975	−	0.568070i	−0.0185087	−	0.0320580i
$315$	−12.2189	−	21.1638i	−0.688457	−	1.19244i
$316$	11.9500	−	20.6979i	0.672238	−	1.16435i
$317$	−2.78223			−0.156266			−0.0781329	−	0.996943i	$-0.524896\pi$
$317$	−2.78223			−0.156266			−0.0781329	+	0.996943i	$0.524896\pi$
$318$	−0.322426	+	0.558459i	−0.0180808	+	0.0313168i
$319$	0.913046	−	1.58144i	0.0511208	−	0.0885437i
$320$	−22.7240			−1.27031
$321$	15.2445	−	26.4042i	0.850863	−	1.47374i
$322$	−0.286416	−	0.496087i	−0.0159613	−	0.0276459i
$323$	−1.43975	−	2.49373i	−0.0801100	−	0.138755i
$324$	−57.4858			−3.19365
$325$	−11.1375	−	4.46070i	−0.617798	−	0.247435i
$326$	1.21466			0.0672740
$327$	7.33334	+	12.7017i	0.405534	+	0.702406i
$328$	0.173923	+	0.301243i	0.00960327	+	0.0166334i
$329$	3.71033	−	6.42648i	0.204557	−	0.354303i
$330$	−0.341570			−0.0188028
$331$	−9.29827	+	16.1051i	−0.511079	+	0.885215i	0.488839	+	0.872374i	$0.337421\pi$
$331$	−9.29827	+	16.1051i	−0.511079	+	0.885215i	−0.999918	+	0.0128404i	$0.995913\pi$
$332$	9.72068	−	16.8367i	0.533491	−	0.924034i
$333$	−76.8035			−4.20880
$334$	−0.0808431	+	0.140024i	−0.00442354	+	0.00766179i
$335$	−10.1985	−	17.6643i	−0.557204	−	0.965106i
$336$	7.06261	+	12.2328i	0.385297	+	0.667354i
$337$	−19.5914			−1.06721			−0.533605	−	0.845734i	$-0.679163\pi$
$337$	−19.5914			−1.06721			−0.533605	+	0.845734i	$0.679163\pi$
$338$	0.222084	−	0.914261i	0.0120798	−	0.0497292i
$339$	2.50732			0.136179
$340$	−10.2485	−	17.7509i	−0.555802	−	0.962677i
$341$	0.248486	+	0.430390i	0.0134563	+	0.0233069i
$342$	0.229131	−	0.396866i	0.0123900	−	0.0214601i
$343$	−13.8765			−0.749261
$344$	−0.495064	+	0.857476i	−0.0266921	+	0.0462320i
$345$	34.7495	−	60.1879i	1.87085	−	3.24041i
$346$	1.51825			0.0816215
$347$	5.70488	−	9.88115i	0.306254	−	0.530448i	−0.671286	−	0.741199i	$-0.734258\pi$
$347$	5.70488	−	9.88115i	0.306254	−	0.530448i	0.977540	+	0.210751i	$0.0675909\pi$
$348$	12.0605	+	20.8894i	0.646511	+	1.11979i
$349$	9.90740	+	17.1601i	0.530331	+	0.918560i	0.999374	+	0.0353845i	$0.0112656\pi$
$349$	9.90740	+	17.1601i	0.530331	+	0.918560i	−0.469043	+	0.883175i	$0.655401\pi$
$350$	0.260461			0.0139222
$351$	53.2013	+	21.3078i	2.83968	+	1.13732i
$352$	0.430101			0.0229245
$353$	−0.677121	−	1.17281i	−0.0360395	−	0.0624223i	0.847443	−	0.530886i	$-0.178141\pi$
$353$	−0.677121	−	1.17281i	−0.0360395	−	0.0624223i	−0.883483	+	0.468464i	$0.844808\pi$
$354$	1.66491	+	2.88371i	0.0884891	+	0.153268i
$355$	5.72389	−	9.91406i	0.303792	−	0.526184i
$356$	17.8641			0.946793
$357$	−6.33677	+	10.9756i	−0.335377	+	0.580891i
$358$	−0.0825633	+	0.143004i	−0.00436361	+	0.00755799i
$359$	31.5944			1.66749			0.833745	−	0.552149i	$-0.186192\pi$
$359$	31.5944			1.66749			0.833745	+	0.552149i	$0.186192\pi$
$360$	3.26629	−	5.65738i	0.172149	−	0.298170i
$361$	9.17302	+	15.8881i	0.482790	+	0.836217i
$362$	−0.472254	−	0.817967i	−0.0248211	−	0.0429914i
$363$	35.3870			1.85734
$364$	−1.10588	−	7.69970i	−0.0579641	−	0.403574i
$365$	10.9923			0.575361
$366$	−1.42484	−	2.46789i	−0.0744774	−	0.128999i
$367$	12.2847	+	21.2777i	0.641255	+	1.11069i	0.985153	+	0.171680i	$0.0549194\pi$
$367$	12.2847	+	21.2777i	0.641255	+	1.11069i	−0.343898	+	0.939007i	$0.611747\pi$
$368$	−14.5216	+	25.1521i	−0.756990	+	1.31115i
$369$	9.42060			0.490417
$370$	1.02430	−	1.77413i	0.0532506	−	0.0922328i
$371$	1.46415	−	2.53598i	0.0760149	−	0.131662i
$372$	−6.56454			−0.340356
$373$	18.1091	−	31.3659i	0.937654	−	1.62406i	0.167822	−	0.985817i	$-0.446327\pi$
$373$	18.1091	−	31.3659i	0.937654	−	1.62406i	0.769832	−	0.638246i	$-0.220340\pi$
$374$	0.0640350	+	0.110912i	0.00331117	+	0.00573512i
$375$	−7.94144	−	13.7550i	−0.410094	−	0.710304i
$376$	1.98365			0.102299
$377$	−1.88350	−	13.1138i	−0.0970050	−	0.675395i
$378$	−1.24416			−0.0639928
$379$	6.17539	+	10.6961i	0.317208	+	0.549421i	0.979904	−	0.199468i	$-0.0639212\pi$
$379$	6.17539	+	10.6961i	0.317208	+	0.549421i	−0.662696	+	0.748888i	$0.730588\pi$
$380$	−2.32754	−	4.03142i	−0.119400	−	0.206808i
$381$	−17.6588	+	30.5859i	−0.904686	+	1.56696i
$382$	−0.375976			−0.0192366
$383$	0.774226	−	1.34100i	0.0395611	−	0.0685218i	−0.845567	−	0.533869i	$-0.820737\pi$
$383$	0.774226	−	1.34100i	0.0395611	−	0.0685218i	0.885128	+	0.465348i	$0.154071\pi$
$384$	−3.78583	+	6.55725i	−0.193195	+	0.334623i
$385$	1.55108			0.0790504
$386$	0.971279	−	1.68230i	0.0494368	−	0.0856270i
$387$	13.4077	+	23.2228i	0.681551	+	1.18048i
$388$	14.3051	+	24.7772i	0.726232	+	1.25787i
$389$	12.1782			0.617462			0.308731	−	0.951149i	$-0.400096\pi$
$389$	12.1782			0.617462			0.308731	+	0.951149i	$0.400096\pi$
$390$	−1.94815	+	1.53157i	−0.0986483	+	0.0775542i
$391$	−26.0583			−1.31783
$392$	−0.842801	−	1.45977i	−0.0425679	−	0.0737297i
$393$	−31.6624	−	54.8408i	−1.59715	−	2.76635i
$394$	−0.578570	+	1.00211i	−0.0291479	+	0.0504857i
$395$	34.5751			1.73966
$396$	3.88108	−	6.72222i	0.195031	−	0.337804i
$397$	−1.32134	+	2.28862i	−0.0663160	+	0.114863i	−0.897277	−	0.441468i	$-0.854458\pi$
$397$	−1.32134	+	2.28862i	−0.0663160	+	0.114863i	0.830961	+	0.556331i	$0.187791\pi$
$398$	−1.51381			−0.0758805
$399$	−1.43915	+	2.49268i	−0.0720476	+	0.124790i
$400$	−6.60282	−	11.4364i	−0.330141	−	0.571821i
$401$	9.58201	+	16.5965i	0.478503	+	0.828791i	0.999696	−	0.0246473i	$-0.00784626\pi$
$401$	9.58201	+	16.5965i	0.478503	+	0.828791i	−0.521193	+	0.853439i	$0.674513\pi$
$402$	−1.68344			−0.0839624
$403$	3.34708	+	1.34054i	0.166730	+	0.0667772i
$404$	−2.04479			−0.101732
$405$	−41.5812	−	72.0208i	−2.06619	−	3.57874i
$406$	0.143808	+	0.249082i	0.00713705	+	0.0123617i
$407$	2.43738	−	4.22167i	0.120816	−	0.209260i
$408$	−3.38782			−0.167722
$409$	−0.0423579	+	0.0733661i	−0.00209447	+	0.00362772i	−0.867071	−	0.498185i	$-0.834000\pi$
$409$	−0.0423579	+	0.0733661i	−0.00209447	+	0.00362772i	0.864976	+	0.501813i	$0.167333\pi$
$410$	−0.125639	+	0.217613i	−0.00620485	+	0.0107471i
$411$	−9.15310			−0.451489
$412$	−4.91592	+	8.51463i	−0.242190	+	0.419486i
$413$	−7.56043	−	13.0950i	−0.372024	−	0.644365i
$414$	−2.07354	−	3.59147i	−0.101909	−	0.176511i
$415$	28.1251			1.38061
$416$	2.45309	−	1.92854i	0.120273	−	0.0945546i
$417$	31.8625			1.56031
$418$	0.0145431	+	0.0251893i	0.000711325	+	0.00123205i
$419$	−4.26603	−	7.38898i	−0.208409	−	0.360975i	0.742804	−	0.669509i	$-0.233495\pi$
$419$	−4.26603	−	7.38898i	−0.208409	−	0.360975i	−0.951214	+	0.308533i	$0.900162\pi$
$420$	−10.2442	+	17.7434i	−0.499865	+	0.865791i
$421$	−10.1032			−0.492398			−0.246199	−	0.969219i	$-0.579182\pi$
$421$	−10.1032			−0.492398			−0.246199	+	0.969219i	$0.579182\pi$
$422$	−0.290116	+	0.502495i	−0.0141226	+	0.0244611i
$423$	26.8613	−	46.5251i	1.30604	−	2.26213i
$424$	0.782777			0.0380150
$425$	5.92423	−	10.2611i	0.287368	−	0.497735i
$426$	−0.472413	−	0.818244i	−0.0228885	−	0.0396441i
$427$	6.47024	+	11.2068i	0.313117	+	0.542334i
$428$	−18.4808			−0.893301
$429$	−4.63574	+	3.64448i	−0.223816	+	0.175957i
$430$	−0.715251			−0.0344925
$431$	−18.6771	−	32.3497i	−0.899646	−	1.55823i	−0.827947	−	0.560806i	$-0.810491\pi$
$431$	−18.6771	−	32.3497i	−0.899646	−	1.55823i	−0.0716986	−	0.997426i	$-0.522842\pi$
$432$	31.5402	+	54.6292i	1.51748	+	2.62835i
$433$	−5.40368	+	9.35945i	−0.259684	+	0.449787i	−0.966157	−	0.257953i	$-0.916952\pi$
$433$	−5.40368	+	9.35945i	−0.259684	+	0.449787i	0.706473	+	0.707740i	$0.250285\pi$
$434$	−0.0782746			−0.00375730
$435$	−17.4475	+	30.2199i	−0.836542	+	1.44893i
$436$	4.44508	−	7.69910i	0.212881	−	0.368720i
$437$	−5.91814			−0.283103
$438$	0.453616	−	0.785685i	0.0216746	−	0.0375415i
$439$	−5.14658	−	8.91414i	−0.245633	−	0.425449i	0.716677	−	0.697406i	$-0.245662\pi$
$439$	−5.14658	−	8.91414i	−0.245633	−	0.425449i	−0.962309	+	0.271957i	$0.912329\pi$
$440$	0.207313	+	0.359077i	0.00988327	+	0.0171183i
$441$	−45.6507			−2.17384
$442$	0.862545	+	0.345459i	0.0410271	+	0.0164318i
$443$	−22.8335			−1.08485			−0.542426	−	0.840103i	$-0.682494\pi$
$443$	−22.8335			−1.08485			−0.542426	+	0.840103i	$0.682494\pi$
$444$	32.1956	+	55.7643i	1.52793	+	2.64646i
$445$	12.9216	+	22.3809i	0.612544	+	1.06096i
$446$	−0.300631	+	0.520708i	−0.0142353	+	0.0246563i
$447$	69.3430			3.27981
$448$	4.25835	−	7.37568i	0.201188	−	0.348468i
$449$	18.6607	−	32.3213i	0.880653	−	1.52534i	0.0300370	−	0.999549i	$-0.490438\pi$
$449$	18.6607	−	32.3213i	0.880653	−	1.52534i	0.850616	−	0.525787i	$-0.176229\pi$
$450$	1.88564			0.0888897
$451$	−0.298965	+	0.517823i	−0.0140777	+	0.0243833i
$452$	−0.759901	−	1.31619i	−0.0357428	−	0.0619083i
$453$	−23.6592	−	40.9789i	−1.11161	−	1.92536i
$454$	2.05219			0.0963142
$455$	8.84661	−	6.95493i	0.414736	−	0.326052i
$456$	−0.769411			−0.0360310
$457$	−4.87036	−	8.43571i	−0.227826	−	0.394606i	0.729338	−	0.684154i	$-0.239828\pi$
$457$	−4.87036	−	8.43571i	−0.227826	−	0.394606i	−0.957163	+	0.289548i	$0.906495\pi$
$458$	−0.519626	−	0.900019i	−0.0242805	−	0.0420551i
$459$	−28.2987	+	49.0148i	−1.32087	+	2.28781i
$460$	−42.1266			−1.96416
$461$	0.106151	−	0.183858i	0.00494393	−	0.00856314i	−0.863543	−	0.504275i	$-0.831760\pi$
$461$	0.106151	−	0.183858i	0.00494393	−	0.00856314i	0.868487	+	0.495712i	$0.165093\pi$
$462$	0.0640082	−	0.110865i	0.00297793	−	0.00515793i
$463$	23.1227			1.07460			0.537300	−	0.843391i	$-0.319444\pi$
$463$	23.1227			1.07460			0.537300	+	0.843391i	$0.319444\pi$
$464$	7.29119	−	12.6287i	0.338485	−	0.586273i
$465$	−4.74834	−	8.22436i	−0.220199	−	0.381396i
$466$	0.651755	+	1.12887i	0.0301920	+	0.0522940i
$467$	4.32797			0.200275			0.100137	−	0.994974i	$-0.468072\pi$
$467$	4.32797			0.200275			0.100137	+	0.994974i	$0.468072\pi$
$468$	−8.00617	−	55.7427i	−0.370085	−	2.57671i
$469$	7.64457			0.352994
$470$	0.716476	+	1.24097i	0.0330486	+	0.0572418i
$471$	14.9135	+	25.8309i	0.687176	+	1.19022i
$472$	2.02101	−	3.50049i	0.0930246	−	0.161123i
$473$	−1.70199			−0.0782574
$474$	1.42681	−	2.47130i	0.0655353	−	0.113511i
$475$	1.34546	−	2.33040i	0.0617339	−	0.106926i
$476$	7.68202			0.352105
$477$	10.5999	−	18.3595i	0.485335	−	0.840625i
$478$	0.496457	+	0.859889i	0.0227074	+	0.0393304i
$479$	4.83040	+	8.36649i	0.220707	+	0.382275i	0.955023	−	0.296533i	$-0.0958304\pi$
$479$	4.83040	+	8.36649i	0.220707	+	0.382275i	−0.734316	+	0.678808i	$0.762497\pi$
$480$	−8.21884			−0.375137
$481$	−5.02800	−	35.0074i	−0.229257	−	1.59620i
$482$	−0.984665			−0.0448503
$483$	13.0237	+	22.5577i	0.592599	+	1.02641i
$484$	−10.7249	−	18.5760i	−0.487494	−	0.844364i
$485$	−20.6947	+	35.8442i	−0.939696	+	1.62760i
$486$	−3.41263			−0.154800
$487$	−4.32497	+	7.49107i	−0.195983	+	0.339453i	−0.947222	−	0.320577i	$-0.896123\pi$
$487$	−4.32497	+	7.49107i	−0.195983	+	0.339453i	0.751239	+	0.660030i	$0.229456\pi$
$488$	−1.72959	+	2.99573i	−0.0782948	+	0.135611i
$489$	−55.2323			−2.49769
$490$	0.608825	−	1.05452i	0.0275039	−	0.0476381i
$491$	3.26455	+	5.65437i	0.147327	+	0.255178i	0.930239	−	0.366955i	$-0.119600\pi$
$491$	3.26455	+	5.65437i	0.147327	+	0.255178i	−0.782912	+	0.622133i	$0.786266\pi$
$492$	−3.94906	−	6.83997i	−0.178037	−	0.308370i
$493$	13.0837			0.589260
$494$	0.195894	+	0.0784576i	0.00881367	+	0.00352998i
$495$	11.2292			0.504716
$496$	1.98430	+	3.43691i	0.0890977	+	0.154322i
$497$	2.14525	+	3.71568i	0.0962275	+	0.166671i
$498$	1.16063	−	2.01027i	0.0520092	−	0.0900826i
$499$	9.72835			0.435501			0.217750	−	0.976005i	$-0.430128\pi$
$499$	9.72835			0.435501			0.217750	+	0.976005i	$0.430128\pi$
$500$	−4.81368	+	8.33753i	−0.215274	+	0.372866i
$501$	3.67604	−	6.36709i	0.164233	−	0.284461i
$502$	0.295890			0.0132062
$503$	−6.12938	+	10.6164i	−0.273296	+	0.473362i	−0.969704	−	0.244284i	$-0.921447\pi$
$503$	−6.12938	+	10.6164i	−0.273296	+	0.473362i	0.696408	+	0.717646i	$0.254780\pi$
$504$	1.22417	+	2.12032i	0.0545288	+	0.0944466i
$505$	−1.47906	−	2.56180i	−0.0658172	−	0.113999i
$506$	0.263217			0.0117014
$507$	−10.0985	+	41.5726i	−0.448488	+	1.84631i
$508$	21.4076			0.949809
$509$	−1.33169	−	2.30656i	−0.0590263	−	0.102236i	0.835002	−	0.550246i	$-0.185466\pi$
$509$	−1.33169	−	2.30656i	−0.0590263	−	0.102236i	−0.894029	+	0.448010i	$0.852133\pi$
$510$	−1.22365	−	2.11943i	−0.0541842	−	0.0938497i
$511$	−2.05989	+	3.56783i	−0.0911240	+	0.157831i
$512$	5.72935			0.253204
$513$	−6.42695	+	11.1318i	−0.283757	+	0.491481i
$514$	−0.167802	+	0.290641i	−0.00740142	+	0.0128196i
$515$	−14.2234			−0.626756
$516$	11.2408	−	19.4697i	0.494850	−	0.857106i
$517$	1.70490	+	2.95298i	0.0749815	+	0.129872i
$518$	0.383895	+	0.664925i	0.0168674	+	0.0292151i
$519$	−69.0367			−3.03037
$520$	2.79249	+	1.11842i	0.122459	+	0.0490461i
$521$	32.1033			1.40647			0.703236	−	0.710956i	$-0.251738\pi$
$521$	32.1033			1.40647			0.703236	+	0.710956i	$0.251738\pi$
$522$	1.04111	+	1.80325i	0.0455681	+	0.0789263i
$523$	−1.32376	−	2.29283i	−0.0578842	−	0.100258i	0.835631	−	0.549291i	$-0.185102\pi$
$523$	−1.32376	−	2.29283i	−0.0578842	−	0.100258i	−0.893515	+	0.449032i	$0.851769\pi$
$524$	−19.1920	+	33.2416i	−0.838408	+	1.45216i
$525$	−11.8435			−0.516893
$526$	0.940593	−	1.62916i	0.0410118	−	0.0710346i
$527$	−1.78037	+	3.08369i	−0.0775541	+	0.134328i
$528$	−6.49056			−0.282466
$529$	−15.2783	+	26.4629i	−0.664276	+	1.15056i
$530$	0.282732	+	0.489707i	0.0122811	+	0.0212715i
$531$	−54.7345	−	94.8029i	−2.37528	−	4.11410i
$532$	1.74467			0.0756411
$533$	0.616727	+	4.29395i	0.0267134	+	0.185992i
$534$	2.13294			0.0923013
$535$	−13.3677	−	23.1536i	−0.577936	−	1.00102i
$536$	1.02175	+	1.76973i	0.0441330	+	0.0764406i
$537$	3.75426	−	6.50257i	0.162008	−	0.280607i
$538$	0.887791			0.0382754
$539$	1.44874	−	2.50929i	0.0624015	−	0.108083i
$540$	−45.7484	+	79.2386i	−1.96870	+	3.40988i
$541$	−26.9434			−1.15839			−0.579193	−	0.815190i	$-0.696632\pi$
$541$	−26.9434			−1.15839			−0.579193	+	0.815190i	$0.696632\pi$
$542$	0.902934	−	1.56393i	0.0387843	−	0.0671764i
$543$	21.4740	+	37.1940i	0.921537	+	1.59615i
$544$	1.54081	+	2.66876i	0.0660617	+	0.114422i
$545$	12.8610			0.550907
$546$	−0.132041	−	0.919331i	−0.00565083	−	0.0393437i
$547$	−20.6107			−0.881252			−0.440626	−	0.897691i	$-0.645243\pi$
$547$	−20.6107			−0.881252			−0.440626	+	0.897691i	$0.645243\pi$
$548$	2.77406	+	4.80482i	0.118502	+	0.205252i
$549$	46.8420	+	81.1327i	1.99917	+	3.46266i
$550$	−0.0598412	+	0.103648i	−0.00255164	+	0.00441956i
$551$	2.97145			0.126588
$552$	−3.48143	+	6.03001i	−0.148179	+	0.256654i
$553$	−6.47918	+	11.2223i	−0.275523	+	0.477219i
$554$	−0.798395			−0.0339206
$555$	−46.5761	+	80.6722i	−1.97704	+	3.42434i
$556$	−9.65667	−	16.7258i	−0.409534	−	0.709334i
$557$	−15.4552	−	26.7693i	−0.654859	−	1.13425i	−0.981929	−	0.189249i	$-0.939395\pi$
$557$	−15.4552	−	26.7693i	−0.654859	−	1.13425i	0.327070	−	0.945000i	$-0.393939\pi$
$558$	−0.566677			−0.0239893
$559$	−9.70730	+	7.63158i	−0.410575	+	0.322781i
$560$	12.3863			0.523415
$561$	−2.91176	−	5.04331i	−0.122934	−	0.212929i
$562$	0.771380	+	1.33607i	0.0325387	+	0.0563587i
$563$	13.7797	−	23.8671i	0.580743	−	1.00588i	−0.414648	−	0.909982i	$-0.636095\pi$
$563$	13.7797	−	23.8671i	0.580743	−	1.00588i	0.995391	−	0.0958950i	$-0.0305713\pi$
$564$	−45.0404			−1.89654
$565$	1.09932	−	1.90408i	0.0462488	−	0.0801052i
$566$	−0.0592896	+	0.102693i	−0.00249213	+	0.00431649i
$567$	31.1683			1.30895
$568$	−0.573456	+	0.993254i	−0.0240617	+	0.0416760i
$569$	1.82195	+	3.15571i	0.0763802	+	0.132294i	0.901686	−	0.432392i	$-0.142330\pi$
$569$	1.82195	+	3.15571i	0.0763802	+	0.132294i	−0.825305	+	0.564687i	$0.808997\pi$
$570$	−0.277905	−	0.481345i	−0.0116401	−	0.0201613i
$571$	−0.826311			−0.0345801			−0.0172900	−	0.999851i	$-0.505504\pi$
$571$	−0.826311			−0.0345801			−0.0172900	+	0.999851i	$0.505504\pi$
$572$	3.31810	+	1.32894i	0.138737	+	0.0555656i
$573$	17.0961			0.714200
$574$	−0.0470880	−	0.0815587i	−0.00196541	−	0.00340420i
$575$	−12.1758	−	21.0892i	−0.507768	−	0.879480i
$576$	30.8288	−	53.3970i	1.28453	−	2.22487i
$577$	33.2990			1.38626			0.693129	−	0.720814i	$-0.256232\pi$
$577$	33.2990			1.38626			0.693129	+	0.720814i	$0.256232\pi$
$578$	0.156367	−	0.270836i	0.00650402	−	0.0112653i
$579$	−44.1653	+	76.4966i	−1.83545	+	3.17909i
$580$	21.1515			0.878266
$581$	−5.27048	+	9.12874i	−0.218656	+	0.378724i
$582$	1.70801	+	2.95835i	0.0707991	+	0.122628i
$583$	0.672780	+	1.16529i	0.0278637	+	0.0482613i
$584$	−1.10127			−0.0455711
$585$	64.0460	−	50.3509i	2.64797	−	2.08176i
$586$	−1.26282			−0.0521666
$587$	−10.5942	−	18.3497i	−0.437271	−	0.757375i	0.560207	−	0.828352i	$-0.310721\pi$
$587$	−10.5942	−	18.3497i	−0.437271	−	0.757375i	−0.997478	+	0.0709776i	$0.977388\pi$
$588$	19.1365	+	33.1454i	0.789176	+	1.36689i
$589$	−0.404341	+	0.700340i	−0.0166606	+	0.0288570i
$590$	2.91989			0.120210
$591$	26.3083	−	45.5674i	1.08218	−	1.87439i
$592$	19.4639	−	33.7124i	0.799959	−	1.38557i
$593$	31.2778			1.28442			0.642212	−	0.766527i	$-0.278017\pi$
$593$	31.2778			1.28442			0.642212	+	0.766527i	$0.278017\pi$
$594$	0.285847	−	0.495102i	0.0117285	−	0.0203143i
$595$	5.55665	+	9.62439i	0.227800	+	0.394562i
$596$	−21.0160	−	36.4008i	−0.860850	−	1.49104i
$597$	68.8350			2.81723
$598$	1.50126	−	1.18025i	0.0613912	−	0.0482639i
$599$	−26.3423			−1.07632			−0.538159	−	0.842843i	$-0.680880\pi$
$599$	−26.3423			−1.07632			−0.538159	+	0.842843i	$0.680880\pi$
$600$	−1.58297	−	2.74178i	−0.0646245	−	0.111933i
$601$	0.577951	+	1.00104i	0.0235751	+	0.0408333i	0.877572	−	0.479444i	$-0.159162\pi$
$601$	0.577951	+	1.00104i	0.0235751	+	0.0408333i	−0.853997	+	0.520278i	$0.825828\pi$
$602$	0.134034	−	0.232154i	0.00546282	−	0.00946188i
$603$	55.3437			2.25377
$604$	−14.3409	+	24.8392i	−0.583524	+	1.01069i
$605$	15.5152	−	26.8732i	0.630784	−	1.09255i
$606$	−0.244144			−0.00991767
$607$	−3.58170	+	6.20369i	−0.145377	+	0.251800i	−0.929513	−	0.368788i	$-0.879773\pi$
$607$	−3.58170	+	6.20369i	−0.145377	+	0.251800i	0.784137	+	0.620588i	$0.213106\pi$
$608$	0.349935	+	0.606105i	0.0141917	+	0.0245808i
$609$	−6.53911	−	11.3261i	−0.264978	−	0.458956i
$610$	−2.49885			−0.101175
$611$	22.9649	+	9.19769i	0.929059	+	0.372099i
$612$	55.6148			2.24810
$613$	14.8171	+	25.6640i	0.598458	+	1.03656i	0.993049	+	0.117703i	$0.0375531\pi$
$613$	14.8171	+	25.6640i	0.598458	+	1.03656i	−0.394591	+	0.918857i	$0.629114\pi$
$614$	0.0833196	+	0.144314i	0.00336250	+	0.00582403i
$615$	5.71295	−	9.89512i	0.230369	−	0.399010i
$616$	−0.155397			−0.00626113
$617$	3.13869	−	5.43636i	0.126359	−	0.218860i	−0.795905	−	0.605422i	$-0.793004\pi$
$617$	3.13869	−	5.43636i	0.126359	−	0.218860i	0.922263	+	0.386562i	$0.126338\pi$
$618$	−0.586953	+	1.01663i	−0.0236107	+	0.0408949i
$619$	14.9723			0.601787			0.300893	−	0.953658i	$-0.402715\pi$
$619$	14.9723			0.601787			0.300893	+	0.953658i	$0.402715\pi$
$620$	−2.87819	+	4.98517i	−0.115591	+	0.200209i
$621$	58.1612	+	100.738i	2.33393	+	4.04248i
$622$	−0.383775	−	0.664718i	−0.0153880	−	0.0266528i
$623$	−9.68576			−0.388052
$624$	−37.0190	+	29.1032i	−1.48195	+	1.16506i
$625$	−30.5652			−1.22261
$626$	0.991831	+	1.71790i	0.0396415	+	0.0686612i
$627$	−0.661292	−	1.14539i	−0.0264095	−	0.0457425i
$628$	9.03974	−	15.6573i	0.360725	−	0.624794i
$629$	34.9270			1.39263
$630$	−0.884317	+	1.53168i	−0.0352321	+	0.0610237i
$631$	20.7099	−	35.8706i	0.824449	−	1.42799i	−0.0778915	−	0.996962i	$-0.524819\pi$
$631$	20.7099	−	35.8706i	0.824449	−	1.42799i	0.902340	−	0.431025i	$-0.141848\pi$
$632$	−3.46396			−0.137789
$633$	13.1919	−	22.8491i	0.524332	−	0.908170i
$634$	0.100679	+	0.174381i	0.00399848	+	0.00692557i
$635$	15.4848	+	26.8204i	0.614495	+	1.06434i
$636$	−17.7736			−0.704770
$637$	−2.98856	−	20.8078i	−0.118411	−	0.824434i
$638$	−0.132160			−0.00523225
$639$	15.5307	+	26.9000i	0.614387	+	1.06415i
$640$	3.31975	+	5.74998i	0.131225	+	0.227288i
$641$	3.12851	−	5.41874i	0.123569	−	0.214028i	−0.797604	−	0.603182i	$-0.793899\pi$
$641$	3.12851	−	5.41874i	0.123569	−	0.214028i	0.921173	+	0.389154i	$0.127233\pi$
$642$	−2.20657			−0.0870865
$643$	10.1651	−	17.6064i	0.400871	−	0.694329i	−0.592960	−	0.805232i	$-0.702041\pi$
$643$	10.1651	−	17.6064i	0.400871	−	0.694329i	0.993831	+	0.110903i	$0.0353742\pi$
$644$	7.89428	−	13.6733i	0.311078	−	0.538803i
$645$	32.5234			1.28061
$646$	−0.104199	+	0.180478i	−0.00409966	+	0.00710082i
$647$	−10.7433	−	18.6079i	−0.422361	−	0.731551i	0.573809	−	0.818989i	$-0.305465\pi$
$647$	−10.7433	−	18.6079i	−0.422361	−	0.731551i	−0.996170	+	0.0874384i	$0.972132\pi$
$648$	4.16587	+	7.21550i	0.163651	+	0.283452i
$649$	6.94806			0.272735
$650$	0.123445	+	0.859481i	0.00484190	+	0.0337116i
$651$	3.55925			0.139498
$652$	16.7394	+	28.9936i	0.655567	+	1.13548i
$653$	−11.2287	−	19.4487i	−0.439414	−	0.761087i	0.558231	−	0.829686i	$-0.311480\pi$
$653$	−11.2287	−	19.4487i	−0.439414	−	0.761087i	−0.997644	+	0.0685991i	$0.978147\pi$
$654$	0.530735	−	0.919260i	0.0207534	−	0.0359459i
$655$	−55.5288			−2.16969
$656$	−2.38741	+	4.13511i	−0.0932126	+	0.161449i
$657$	−14.9128	+	25.8297i	−0.581802	+	1.00771i
$658$	−0.537054			−0.0209366
$659$	18.4447	−	31.9471i	0.718503	−	1.24448i	−0.243090	−	0.970004i	$-0.578161\pi$
$659$	18.4447	−	31.9471i	0.718503	−	1.24448i	0.961593	−	0.274480i	$-0.0885057\pi$
$660$	−4.70722	−	8.15314i	−0.183228	−	0.317361i
$661$	2.71231	+	4.69786i	0.105497	+	0.182726i	0.913941	−	0.405847i	$-0.133023\pi$
$661$	2.71231	+	4.69786i	0.105497	+	0.182726i	−0.808444	+	0.588573i	$0.799690\pi$
$662$	1.34589			0.0523093
$663$	−39.2211	−	15.7085i	−1.52322	−	0.610067i
$664$	−2.81775			−0.109350
$665$	1.26198	+	2.18581i	0.0489373	+	0.0847619i
$666$	2.77925	+	4.81379i	0.107694	+	0.186531i
$667$	13.4452	−	23.2878i	0.520601	−	0.901707i
$668$	−4.45644			−0.172425
$669$	13.6701	−	23.6773i	0.528516	−	0.915416i
$670$	−0.738096	+	1.27842i	−0.0285151	+	0.0493897i
$671$	−5.94617			−0.229549
$672$	1.54016	−	2.66764i	0.0594131	−	0.102907i
$673$	−6.29464	−	10.9026i	−0.242641	−	0.420266i	0.718825	−	0.695191i	$-0.244680\pi$
$673$	−6.29464	−	10.9026i	−0.242641	−	0.420266i	−0.961466	+	0.274925i	$0.911347\pi$
$674$	0.708943	+	1.22792i	0.0273075	+	0.0472979i
$675$	−52.8907			−2.03576
$676$	24.8836	−	7.29849i	0.957063	−	0.280711i
$677$	−26.1272			−1.00415			−0.502076	−	0.864824i	$-0.667430\pi$
$677$	−26.1272			−1.00415			−0.502076	+	0.864824i	$0.667430\pi$
$678$	−0.0907310	−	0.157151i	−0.00348450	−	0.00603533i
$679$	−7.75612	−	13.4340i	−0.297653	−	0.515550i
$680$	−1.48537	+	2.57274i	−0.0569614	+	0.0986600i
$681$	−93.3159			−3.57587
$682$	0.0179836	−	0.0311486i	0.000688629	−	0.00119274i
$683$	5.31335	−	9.20300i	0.203310	−	0.352143i	−0.746283	−	0.665629i	$-0.768163\pi$
$683$	5.31335	−	9.20300i	0.203310	−	0.352143i	0.949593	+	0.313486i	$0.101497\pi$
$684$	12.6307			0.482948
$685$	−4.01313	+	6.95095i	−0.153334	+	0.265582i
$686$	0.502142	+	0.869735i	0.0191719	+	0.0332066i
$687$	23.6281	+	40.9250i	0.901467	+	1.56139i
$688$	−13.5913			−0.518164
$689$	9.06228	+	3.62955i	0.345245	+	0.138275i
$690$	−5.02984			−0.191483
$691$	10.8576	+	18.8059i	0.413043	+	0.715411i	0.995221	−	0.0976501i	$-0.0311326\pi$
$691$	10.8576	+	18.8059i	0.413043	+	0.715411i	−0.582178	+	0.813061i	$0.697799\pi$
$692$	20.9232	+	36.2400i	0.795380	+	1.37764i
$693$	−2.10429	+	3.64474i	−0.0799354	+	0.138452i
$694$	−0.825758			−0.0313453
$695$	13.9699	−	24.1966i	0.529910	−	0.917831i
$696$	1.74800	−	3.02762i	0.0662577	−	0.114762i
$697$	−4.28409			−0.162272
$698$	0.717027	−	1.24193i	0.0271399	−	0.0470076i
$699$	−29.6361	−	51.3313i	−1.12094	−	1.94153i
$700$	3.58945	+	6.21711i	0.135669	+	0.234985i
$701$	19.8534			0.749853			0.374926	−	0.927055i	$-0.377668\pi$
$701$	19.8534			0.749853			0.374926	+	0.927055i	$0.377668\pi$
$702$	−0.589667	−	4.10554i	−0.0222555	−	0.154954i
$703$	7.93231			0.299173
$704$	1.95672	+	3.38914i	0.0737466	+	0.127733i
$705$	−32.5791	−	56.4287i	−1.22700	−	2.12523i
$706$	−0.0490052	+	0.0848796i	−0.00184434	+	0.00319448i
$707$	1.10867			0.0416957
$708$	−45.8888	+	79.4817i	−1.72461	+	2.98710i
$709$	−16.7449	+	29.0031i	−0.628869	+	1.08923i	0.358910	+	0.933372i	$0.383149\pi$
$709$	−16.7449	+	29.0031i	−0.628869	+	1.08923i	−0.987779	+	0.155861i	$0.950185\pi$
$710$	−0.828509			−0.0310934
$711$	−46.9067	+	81.2447i	−1.75914	+	3.04692i
$712$	−1.29457	−	2.24226i	−0.0485161	−	0.0840324i
$713$	3.65912	+	6.33778i	0.137035	+	0.237352i
$714$	0.917221			0.0343261
$715$	0.735130	+	5.11832i	0.0274923	+	0.191414i
$716$	−4.55127			−0.170089
$717$	−22.5746	−	39.1003i	−0.843062	−	1.46023i
$718$	−1.14329	−	1.98024i	−0.0426672	−	0.0739018i
$719$	−24.9233	+	43.1684i	−0.929481	+	1.60991i	−0.145290	+	0.989389i	$0.546412\pi$
$719$	−24.9233	+	43.1684i	−0.929481	+	1.60991i	−0.784191	+	0.620519i	$0.786922\pi$
$720$	89.6716			3.34186
$721$	2.66538	−	4.61657i	0.0992638	−	0.171930i
$722$	0.663878	−	1.14987i	0.0247070	−	0.0427937i
$723$	44.7740			1.66516
$724$	13.0164	−	22.5450i	0.483750	−	0.837880i
$725$	6.11341	+	10.5887i	0.227046	+	0.393256i
$726$	−1.28053	−	2.21794i	−0.0475249	−	0.0823156i
$727$	26.4407			0.980632			0.490316	−	0.871545i	$-0.336881\pi$
$727$	26.4407			0.980632			0.490316	+	0.871545i	$0.336881\pi$
$728$	−0.886310	+	0.696790i	−0.0328488	+	0.0258247i
$729$	68.7218			2.54525
$730$	−0.397771	−	0.688959i	−0.0147222	−	0.0254995i
$731$	−6.09725	−	10.5608i	−0.225515	−	0.390604i
$732$	39.2717	−	68.0207i	1.45153	−	2.51412i
$733$	−26.7183			−0.986864			−0.493432	−	0.869784i	$-0.664258\pi$
$733$	−26.7183			−0.986864			−0.493432	+	0.869784i	$0.664258\pi$
$734$	0.889078	−	1.53993i	0.0328165	−	0.0568398i
$735$	−27.6840	+	47.9502i	−1.02114	+	1.76867i
$736$	6.33353			0.233457
$737$	−1.75635	+	3.04208i	−0.0646959	+	0.112057i
$738$	−0.340898	−	0.590453i	−0.0125486	−	0.0217349i
$739$	−3.89118	−	6.73972i	−0.143139	−	0.247925i	0.785538	−	0.618814i	$-0.212386\pi$
$739$	−3.89118	−	6.73972i	−0.143139	−	0.247925i	−0.928677	+	0.370889i	$0.879053\pi$
$740$	56.4639			2.07565
$741$	−8.90754	−	3.56757i	−0.327227	−	0.131058i
$742$	−0.211930			−0.00778019
$743$	20.5432	+	35.5819i	0.753658	+	1.30537i	0.946039	+	0.324053i	$0.105046\pi$
$743$	20.5432	+	35.5819i	0.753658	+	1.30537i	−0.192381	+	0.981320i	$0.561621\pi$
$744$	0.475719	+	0.823969i	0.0174407	+	0.0302082i
$745$	30.4031	−	52.6597i	1.11388	−	1.92930i
$746$	−2.62122			−0.0959696
$747$	−38.1562	+	66.0884i	−1.39606	+	2.41805i
$748$	−1.76495	+	3.05699i	−0.0645330	+	0.111774i
$749$	10.0201			0.366128
$750$	−0.574745	+	0.995488i	−0.0209867	+	0.0363501i
$751$	2.95805	+	5.12350i	0.107941	+	0.186959i	0.914936	−	0.403599i	$-0.132241\pi$
$751$	2.95805	+	5.12350i	0.107941	+	0.186959i	−0.806995	+	0.590558i	$0.798908\pi$
$752$	13.6146	+	23.5812i	0.496474	+	0.859917i
$753$	−13.4545			−0.490309
$754$	−0.753774	+	0.592594i	−0.0274508	+	0.0215810i
$755$	−41.4930			−1.51008
$756$	−17.1460	−	29.6977i	−0.623593	−	1.08010i
$757$	−9.20070	−	15.9361i	−0.334405	−	0.579207i	0.648965	−	0.760818i	$-0.275202\pi$
$757$	−9.20070	−	15.9361i	−0.334405	−	0.579207i	−0.983370	+	0.181611i	$0.941869\pi$
$758$	0.446931	−	0.774107i	0.0162333	−	0.0281168i
$759$	−11.9688			−0.434441
$760$	−0.337344	+	0.584297i	−0.0122368	+	0.0211947i
$761$	12.9607	−	22.4487i	0.469827	−	0.813764i	−0.529578	−	0.848261i	$-0.677650\pi$
$761$	12.9607	−	22.4487i	0.469827	−	0.813764i	0.999405	+	0.0344976i	$0.0109831\pi$
$762$	2.55603			0.0925953
$763$	−2.41009	+	4.17439i	−0.0872510	+	0.151123i
$764$	−5.18137	−	8.97440i	−0.187455	−	0.324682i
$765$	40.2279	+	69.6768i	1.45444	+	2.51917i
$766$	−0.112066			−0.00404911
$767$	39.6284	−	31.1546i	1.43090	−	1.12493i
$768$	−51.2807			−1.85043
$769$	−14.1059	−	24.4321i	−0.508671	−	0.881044i	−0.999950	−	0.0100417i	$-0.996804\pi$
$769$	−14.1059	−	24.4321i	−0.508671	−	0.881044i	0.491278	−	0.871003i	$-0.336530\pi$
$770$	−0.0561281	−	0.0972168i	−0.00202272	−	0.00350345i
$771$	7.63016	−	13.2158i	0.274794	−	0.475956i
$772$	53.5413			1.92699
$773$	−10.3226	+	17.8792i	−0.371277	+	0.643071i	−0.989762	−	0.142725i	$-0.954413\pi$
$773$	−10.3226	+	17.8792i	−0.371277	+	0.643071i	0.618485	+	0.785797i	$0.287747\pi$
$774$	0.970353	−	1.68070i	0.0348786	−	0.0604115i
$775$	−3.32753			−0.119529
$776$	2.07332	−	3.59110i	0.0744280	−	0.128913i
$777$	−17.4562	−	30.2350i	−0.626237	−	1.08467i
$778$	−0.440688	−	0.763293i	−0.0157994	−	0.0273654i
$779$	−0.972965			−0.0348601
$780$	−63.4058	−	25.3947i	−2.27029	−	0.909277i
$781$	−1.97149			−0.0705455
$782$	0.942959	+	1.63325i	0.0337201	+	0.0584050i
$783$	−29.2023	−	50.5799i	−1.04361	−	1.80758i
$784$	11.5690	−	20.0381i	0.413178	−	0.715645i
$785$	26.1549			0.933508
$786$	−2.29150	+	3.96899i	−0.0817350	+	0.141569i
$787$	−2.31583	+	4.01113i	−0.0825503	+	0.142981i	−0.904345	−	0.426803i	$-0.859640\pi$
$787$	−2.31583	+	4.01113i	−0.0825503	+	0.142981i	0.821794	+	0.569784i	$0.192973\pi$
$788$	−31.8934			−1.13616
$789$	−42.7700	+	74.0798i	−1.52265	+	2.63731i
$790$	−1.25115	−	2.16706i	−0.0445139	−	0.0771004i
$791$	0.412013	+	0.713627i	0.0146495	+	0.0253737i
$792$	−1.12501			−0.0399756
$793$	−33.9141	+	26.6622i	−1.20432	+	0.946802i
$794$	0.191258			0.00678749
$795$	−12.8562	−	22.2676i	−0.455963	−	0.789750i
$796$	−20.8620	−	36.1341i	−0.739436	−	1.28074i
$797$	8.88560	−	15.3903i	0.314744	−	0.545153i	−0.664639	−	0.747165i	$-0.731415\pi$
$797$	8.88560	−	15.3903i	0.314744	−	0.545153i	0.979383	+	0.202012i	$0.0647480\pi$
$798$	0.208311			0.00737413
$799$	−12.2154	+	21.1577i	−0.432150	+	0.748505i
$800$	−1.43990	+	2.49397i	−0.0509080	+	0.0881753i
$801$	−70.1210			−2.47760
$802$	0.693478	−	1.20114i	0.0244876	−	0.0424137i
$803$	−0.946521	−	1.63942i	−0.0334020	−	0.0578540i
$804$	−23.1997	−	40.1831i	−0.818192	−	1.41715i
$805$	22.8407			0.805029
$806$	−0.0370980	−	0.258294i	−0.00130672	−	0.00909801i
$807$	−40.3690			−1.42106
$808$	0.148181	+	0.256658i	0.00521300	+	0.00902919i
$809$	−21.1397	−	36.6150i	−0.743233	−	1.28732i	−0.951016	−	0.309142i	$-0.899958\pi$
$809$	−21.1397	−	36.6150i	−0.743233	−	1.28732i	0.207783	−	0.978175i	$-0.433375\pi$
$810$	−3.00935	+	5.21235i	−0.105738	+	0.183143i
$811$	−31.2730			−1.09814			−0.549072	−	0.835775i	$-0.685019\pi$
$811$	−31.2730			−1.09814			−0.549072	+	0.835775i	$0.685019\pi$
$812$	−3.96366	+	6.86526i	−0.139097	+	0.240924i
$813$	−41.0576	+	71.1138i	−1.43995	+	2.49407i
$814$	−0.352801			−0.0123657
$815$	−24.2163	+	41.9439i	−0.848260	+	1.46923i
$816$	−23.2520	−	40.2737i	−0.813983	−	1.40986i
$817$	−1.38475	−	2.39846i	−0.0484464	−	0.0839116i
$818$	0.00613114			0.000214370
$819$	4.34088	+	30.2233i	0.151683	+	1.05609i
$820$	−6.92578			−0.241859
$821$	19.7467	+	34.2023i	0.689166	+	1.19367i	0.972108	+	0.234533i	$0.0753562\pi$
$821$	19.7467	+	34.2023i	0.689166	+	1.19367i	−0.282942	+	0.959137i	$0.591310\pi$
$822$	0.331218	+	0.573687i	0.0115526	+	0.0200096i
$823$	18.1546	−	31.4447i	0.632830	−	1.09609i	−0.354141	−	0.935192i	$-0.615227\pi$
$823$	18.1546	−	31.4447i	0.632830	−	1.09609i	0.986971	−	0.160901i	$-0.0514400\pi$
$824$	1.42499			0.0496418
$825$	2.72106	−	4.71301i	0.0947350	−	0.164086i
$826$	−0.547170	+	0.947727i	−0.0190385	+	0.0329756i
$827$	13.6748			0.475520			0.237760	−	0.971324i	$-0.423587\pi$
$827$	13.6748			0.475520			0.237760	+	0.971324i	$0.423587\pi$
$828$	57.1515	−	98.9892i	1.98615	−	3.44011i
$829$	7.42100	+	12.8536i	0.257742	+	0.446423i	0.965637	−	0.259896i	$-0.0836882\pi$
$829$	7.42100	+	12.8536i	0.257742	+	0.446423i	−0.707895	+	0.706318i	$0.750355\pi$
$830$	−1.01775	−	1.76279i	−0.0353265	−	0.0611873i
$831$	36.3041			1.25937
$832$	26.3568	+	10.5562i	0.913758	+	0.365970i
$833$	20.7600			0.719292
$834$	−1.15299	−	1.99704i	−0.0399248	−	0.0691518i
$835$	−3.22348	−	5.58323i	−0.111553	−	0.193216i
$836$	−0.400840	+	0.694275i	−0.0138633	+	0.0240120i
$837$	15.8949			0.549407
$838$	−0.308745	+	0.534762i	−0.0106654	+	0.0184731i
$839$	12.7884	−	22.1501i	0.441504	−	0.764707i	−0.556298	−	0.830983i	$-0.687779\pi$
$839$	12.7884	−	22.1501i	0.441504	−	0.764707i	0.997801	+	0.0662765i	$0.0211119\pi$
$840$	2.96950			0.102457
$841$	7.74925	−	13.4221i	0.267216	−	0.462831i
$842$	0.365597	+	0.633233i	0.0125993	+	0.0218227i
$843$	−35.0757	−	60.7528i	−1.20807	−	2.09244i
$844$	−15.9925			−0.550484
$845$	27.1430	+	25.8962i	0.933747	+	0.890855i
$846$	−3.88806			−0.133674
$847$	5.81494	+	10.0718i	0.199804	+	0.346070i
$848$	5.37253	+	9.30549i	0.184493	+	0.319552i
$849$	2.69598	−	4.66957i	0.0925257	−	0.160259i
$850$	−0.857508			−0.0294123
$851$	35.8921	−	62.1669i	1.23036	−	2.13105i
$852$	13.0208	−	22.5527i	0.446085	−	0.772642i
$853$	21.4065			0.732945			0.366472	−	0.930429i	$-0.380565\pi$
$853$	21.4065			0.732945			0.366472	+	0.930429i	$0.380565\pi$
$854$	0.468270	−	0.811068i	0.0160239	−	0.0277542i
$855$	9.13620	+	15.8244i	0.312452	+	0.541182i
$856$	1.33926	+	2.31967i	0.0457751	+	0.0792847i
$857$	−9.92725			−0.339109			−0.169554	−	0.985521i	$-0.554233\pi$
$857$	−9.92725			−0.339109			−0.169554	+	0.985521i	$0.554233\pi$
$858$	0.396175	+	0.158673i	0.0135252	+	0.00541700i
$859$	−33.1040			−1.12949			−0.564747	−	0.825264i	$-0.691026\pi$
$859$	−33.1040			−1.12949			−0.564747	+	0.825264i	$0.691026\pi$
$860$	−9.85697	−	17.0728i	−0.336120	−	0.582177i
$861$	2.14115	+	3.70858i	0.0729702	+	0.126388i
$862$	−1.35172	+	2.34125i	−0.0460397	+	0.0797431i
$863$	−20.5526			−0.699620			−0.349810	−	0.936821i	$-0.613754\pi$
$863$	−20.5526			−0.699620			−0.349810	+	0.936821i	$0.613754\pi$
$864$	6.87806	−	11.9131i	0.233996	−	0.405293i
$865$	−30.2688	+	52.4270i	−1.02917	+	1.78257i
$866$	0.782160			0.0265789
$867$	−7.11022	+	12.3153i	−0.241476	+	0.418248i
$868$	−1.07871	−	1.86839i	−0.0366139	−	0.0634171i
$869$	−2.97719	−	5.15665i	−0.100994	−	0.174927i
$870$	2.52545			0.0856207
$871$	3.62312	+	25.2259i	0.122765	+	0.854747i
$872$	−1.28850			−0.0436342
$873$	−56.1513	−	97.2568i	−1.90043	−	3.29164i
$874$	0.214156	+	0.370930i	0.00724395	+	0.0125469i
$875$	2.60994	−	4.52055i	0.0882321	−	0.152822i
$876$	25.0054			0.844853
$877$	3.57370	−	6.18982i	0.120675	−	0.209015i	−0.799359	−	0.600854i	$-0.794827\pi$
$877$	3.57370	−	6.18982i	0.120675	−	0.209015i	0.920034	+	0.391838i	$0.128161\pi$
$878$	−0.372473	+	0.645142i	−0.0125704	+	0.0217725i
$879$	57.4221			1.93680
$880$	−2.84575	+	4.92899i	−0.0959303	+	0.166156i
$881$	5.47942	+	9.49064i	0.184606	+	0.319748i	0.943444	−	0.331532i	$-0.107566\pi$
$881$	5.47942	+	9.49064i	0.184606	+	0.319748i	−0.758837	+	0.651280i	$0.774232\pi$
$882$	1.65194	+	2.86124i	0.0556236	+	0.0963429i
$883$	−40.3954			−1.35941			−0.679706	−	0.733484i	$-0.737893\pi$
$883$	−40.3954			−1.35941			−0.679706	+	0.733484i	$0.737893\pi$
$884$	3.64087	+	25.3495i	0.122456	+	0.852595i
$885$	−132.771			−4.46305
$886$	0.826264	+	1.43113i	0.0277589	+	0.0480798i
$887$	2.31887	+	4.01639i	0.0778599	+	0.134857i	0.902326	−	0.431054i	$-0.141858\pi$
$887$	2.31887	+	4.01639i	0.0778599	+	0.134857i	−0.824466	+	0.565911i	$0.808525\pi$
$888$	4.66629	−	8.08225i	0.156590	−	0.271223i
$889$	−11.6070			−0.389288
$890$	0.935176	−	1.61977i	0.0313472	−	0.0542949i
$891$	−7.16095	+	12.4031i	−0.239901	+	0.415521i
$892$	−16.5722			−0.554877
$893$	−2.77425	+	4.80514i	−0.0928368	+	0.160798i
$894$	−2.50928	−	4.34620i	−0.0839228	−	0.145359i
$895$	−3.29207	−	5.70204i	−0.110042	−	0.190598i
$896$	−2.48841			−0.0831320
$897$	−68.2644	+	53.6674i	−2.27928	+	1.79190i
$898$	−2.70106			−0.0901355
$899$	−1.83722	−	3.18216i	−0.0612747	−	0.106131i
$900$	25.9862	+	45.0094i	0.866207	+	1.50031i
$901$	−4.82038	+	8.34914i	−0.160590	+	0.278150i
$902$	0.0432740			0.00144087
$903$	−6.09470	+	10.5563i	−0.202819	+	0.351293i
$904$	−0.110137	+	0.190763i	−0.00366310	+	0.00634468i
$905$	37.6606			1.25188
$906$	−1.71228	+	2.96576i	−0.0568868	+	0.0985309i
$907$	−10.5915	−	18.3450i	−0.351684	−	0.609135i	0.634860	−	0.772627i	$-0.281058\pi$
$907$	−10.5915	−	18.3450i	−0.351684	−	0.609135i	−0.986545	+	0.163492i	$0.947724\pi$
$908$	28.2816	+	48.9851i	0.938557	+	1.62563i
$909$	8.02631			0.266216
$910$	−0.756040	−	0.302803i	−0.0250625	−	0.0100378i
$911$	25.3804			0.840891			0.420446	−	0.907318i	$-0.361874\pi$
$911$	25.3804			0.840891			0.420446	+	0.907318i	$0.361874\pi$
$912$	−5.28079	−	9.14660i	−0.174864	−	0.302874i
$913$	−2.42179	−	4.19467i	−0.0801497	−	0.138823i
$914$	−0.352482	+	0.610517i	−0.0116591	+	0.0201941i
$915$	113.626			3.75636
$916$	14.3221	−	24.8066i	0.473215	−	0.819632i
$917$	10.4058	−	18.0233i	0.343629	−	0.595183i
$918$	4.09612			0.135192
$919$	−13.2465	+	22.9436i	−0.436962	+	0.756841i	−0.997454	−	0.0713196i	$-0.977279\pi$
$919$	−13.2465	+	22.9436i	−0.436962	+	0.756841i	0.560491	+	0.828160i	$0.310612\pi$
$920$	3.05283	+	5.28765i	0.100649	+	0.174329i
$921$	−3.78865	−	6.56213i	−0.124840	−	0.216230i
$922$	−0.0153649			−0.000506015
$923$	−11.2444	+	8.84001i	−0.370114	+	0.290973i
$924$	3.52842			0.116077
$925$	16.3198	+	28.2667i	0.536590	+	0.929402i
$926$	−0.836727	−	1.44925i	−0.0274966	−	0.0476254i
$927$	19.2963	−	33.4221i	0.633772	−	1.09773i
$928$	−3.18002			−0.104389
$929$	16.2108	−	28.0779i	0.531859	−	0.921208i	−0.467449	−	0.884020i	$-0.654827\pi$
$929$	16.2108	−	28.0779i	0.531859	−	0.921208i	0.999308	−	0.0371875i	$-0.0118399\pi$
$930$	−0.343651	+	0.595221i	−0.0112688	+	0.0195181i
$931$	4.71483			0.154522
$932$	−17.9638	+	31.1143i	−0.588425	+	1.01918i
$933$	17.4508	+	30.2256i	0.571312	+	0.989542i
$934$	−0.156614	−	0.271263i	−0.00512457	−	0.00887601i
$935$	−5.10658			−0.167003
$936$	−6.41653	+	5.04448i	−0.209731	+	0.164884i
$937$	−23.1533			−0.756384			−0.378192	−	0.925727i	$-0.623454\pi$
$937$	−23.1533			−0.756384			−0.378192	+	0.925727i	$0.623454\pi$
$938$	−0.276630	−	0.479137i	−0.00903229	−	0.0156444i
$939$	−45.0999	−	78.1152i	−1.47178	−	2.54919i
$940$	−19.7477	+	34.2041i	−0.644100	+	1.11561i
$941$	−33.9978			−1.10830			−0.554149	−	0.832418i	$-0.686956\pi$
$941$	−33.9978			−1.10830			−0.554149	+	0.832418i	$0.686956\pi$
$942$	1.07933	−	1.86945i	0.0351665	−	0.0609101i
$943$	−4.40247	+	7.62529i	−0.143364	+	0.248314i
$944$	55.4842			1.80586
$945$	24.8044	−	42.9625i	0.806888	−	1.39757i
$946$	0.0615888	+	0.106675i	0.00200243	+	0.00346830i
$947$	−1.83628	−	3.18052i	−0.0596710	−	0.103353i	0.834647	−	0.550786i	$-0.185672\pi$
$947$	−1.83628	−	3.18052i	−0.0596710	−	0.103353i	−0.894318	+	0.447432i	$0.852338\pi$
$948$	78.6520			2.55450
$949$	−12.7495	−	5.10634i	−0.413868	−	0.165759i
$950$	−0.194750			−0.00631851
$951$	−4.57801	−	7.92935i	−0.148452	−	0.257127i
$952$	−0.556700	−	0.964233i	−0.0180428	−	0.0312510i
$953$	−11.1787	+	19.3621i	−0.362115	+	0.627202i	−0.988309	−	0.152466i	$-0.951279\pi$
$953$	−11.1787	+	19.3621i	−0.362115	+	0.627202i	0.626194	+	0.779667i	$0.284612\pi$
$954$	−1.53429			−0.0496744
$955$	7.49569	−	12.9829i	0.242555	−	0.420118i
$956$	−13.6835	+	23.7005i	−0.442556	+	0.766529i
$957$	6.00947			0.194258
$958$	0.349590	−	0.605508i	0.0112947	−	0.0195631i
$959$	−1.50408	−	2.60514i	−0.0485691	−	0.0841242i
$960$	−37.3911	−	64.7633i	−1.20679	−	2.09023i
$961$	1.00000			0.0322581
$962$	−2.01220	+	1.58193i	−0.0648760	+	0.0510035i
$963$	72.5418			2.33763
$964$	−13.5698	−	23.5036i	−0.437054	−	0.757000i
$965$	38.7281	+	67.0790i	1.24670	+	2.15935i
$966$	0.942564	−	1.63257i	0.0303265	−	0.0525270i
$967$	9.50245			0.305578			0.152789	−	0.988259i	$-0.451174\pi$
$967$	9.50245			0.305578			0.152789	+	0.988259i	$0.451174\pi$
$968$	−1.55442	+	2.69233i	−0.0499608	+	0.0865347i
$969$	4.73807	−	8.20658i	0.152209	−	0.263633i
$970$	2.99547			0.0961786
$971$	−12.4768	+	21.6104i	−0.400398	+	0.693510i	−0.993774	−	0.111416i	$-0.964462\pi$
$971$	−12.4768	+	21.6104i	−0.400398	+	0.693510i	0.593376	+	0.804926i	$0.297795\pi$
$972$	−47.0300	−	81.4583i	−1.50849	−	2.61278i
$973$	5.23578	+	9.06863i	0.167851	+	0.290727i
$974$	0.626022			0.0200590
$975$	−5.61319	−	39.0817i	−0.179766	−	1.25162i
$976$	−47.4835			−1.51991
$977$	16.0950	+	27.8773i	0.514924	+	0.891875i	0.999850	+	0.0173194i	$0.00551320\pi$
$977$	16.0950	+	27.8773i	0.514924	+	0.891875i	−0.484926	+	0.874555i	$0.661153\pi$
$978$	1.99866	+	3.46178i	0.0639101	+	0.110696i
$979$	2.22531	−	3.85435i	0.0711212	−	0.123186i
$980$	33.5612			1.07207
$981$	−17.4481	+	30.2210i	−0.557074	+	0.964881i
$982$	0.236265	−	0.409223i	0.00753953	−	0.0130588i
$983$	−13.7440			−0.438366			−0.219183	−	0.975684i	$-0.570339\pi$
$983$	−13.7440			−0.438366			−0.219183	+	0.975684i	$0.570339\pi$
$984$	−0.572360	+	0.991357i	−0.0182462	+	0.0316033i
$985$	−23.0695	−	39.9575i	−0.735055	−	1.27315i
$986$	−0.473453	−	0.820045i	−0.0150778	−	0.0261155i
$987$	24.4206			0.777315
$988$	0.826882	+	5.75714i	0.0263066	+	0.183159i
$989$	−25.0629			−0.796953
$990$	−0.406345	−	0.703811i	−0.0129145	−	0.0223686i
$991$	−8.64503	−	14.9736i	−0.274619	−	0.475653i	0.695420	−	0.718603i	$-0.255218\pi$
$991$	−8.64503	−	14.9736i	−0.274619	−	0.475653i	−0.970039	+	0.242950i	$0.921885\pi$
$992$	0.432722	−	0.749497i	0.0137389	−	0.0237965i
$993$	−61.1991			−1.94210
$994$	0.155258	−	0.268914i	0.00492448	−	0.00852945i
$995$	30.1803	−	52.2739i	0.956781	−	1.65719i
$996$	63.9794			2.02726
$997$	−15.4423	+	26.7468i	−0.489061	+	0.847079i	−0.999921	−	0.0125852i	$-0.995994\pi$
$997$	−15.4423	+	26.7468i	−0.489061	+	0.847079i	0.510859	+	0.859664i	$0.329327\pi$
$998$	−0.352034	−	0.609742i	−0.0111435	−	0.0193010i
$999$	−77.9557	−	135.023i	−2.46641	−	4.27195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.f.b.94.8	✓	34
13.3	even	3		5239.2.a.m.1.10		17
13.9	even	3	inner	403.2.f.b.373.8	yes	34
13.10	even	6		5239.2.a.n.1.8		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.f.b.94.8	✓	34	1.1	even	1	trivial
403.2.f.b.373.8	yes	34	13.9	even	3	inner
5239.2.a.m.1.10		17	13.3	even	3
5239.2.a.n.1.8		17	13.10	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.0361865 - 0.0626768i) q^{2} +(1.64544 + 2.84999i) q^{3} +(0.997381 - 1.72751i) q^{4} +2.88575 q^{5} +(0.119086 - 0.206262i) q^{6} +(-0.540773 + 0.936646i) q^{7} -0.289113 q^{8} +(-3.91498 + 6.78094i) q^{9} +O(q^{10})\)	\(q+(-0.0361865 - 0.0626768i) q^{2} +(1.64544 + 2.84999i) q^{3} +(0.997381 - 1.72751i) q^{4} +2.88575 q^{5} +(0.119086 - 0.206262i) q^{6} +(-0.540773 + 0.936646i) q^{7} -0.289113 q^{8} +(-3.91498 + 6.78094i) q^{9} +(-0.104425 - 0.180869i) q^{10} +(-0.248486 - 0.430390i) q^{11} +6.56454 q^{12} +(-3.34708 - 1.34054i) q^{13} +0.0782746 q^{14} +(4.74834 + 8.22436i) q^{15} +(-1.98430 - 3.43691i) q^{16} +(1.78037 - 3.08369i) q^{17} +0.566677 q^{18} +(0.404341 - 0.700340i) q^{19} +(2.87819 - 4.98517i) q^{20} -3.55925 q^{21} +(-0.0179836 + 0.0311486i) q^{22} +(-3.65912 - 6.33778i) q^{23} +(-0.475719 - 0.823969i) q^{24} +3.32753 q^{25} +(0.0370980 + 0.258294i) q^{26} -15.8949 q^{27} +(1.07871 + 1.86839i) q^{28} +(1.83722 + 3.18216i) q^{29} +(0.343651 - 0.595221i) q^{30} -1.00000 q^{31} +(-0.432722 + 0.749497i) q^{32} +(0.817740 - 1.41637i) q^{33} -0.257701 q^{34} +(-1.56053 + 2.70292i) q^{35} +(7.80945 + 13.5264i) q^{36} +(4.90446 + 8.49478i) q^{37} -0.0585267 q^{38} +(-1.68689 - 11.7449i) q^{39} -0.834306 q^{40} +(-0.601574 - 1.04196i) q^{41} +(0.128796 + 0.223082i) q^{42} +(1.71236 - 2.96589i) q^{43} -0.991341 q^{44} +(-11.2976 + 19.5681i) q^{45} +(-0.264821 + 0.458684i) q^{46} -6.86116 q^{47} +(6.53011 - 11.3105i) q^{48} +(2.91513 + 5.04915i) q^{49} +(-0.120412 - 0.208559i) q^{50} +11.7180 q^{51} +(-5.65412 + 4.44510i) q^{52} -2.70752 q^{53} +(0.575178 + 0.996238i) q^{54} +(-0.717067 - 1.24200i) q^{55} +(0.156344 - 0.270796i) q^{56} +2.66129 q^{57} +(0.132965 - 0.230302i) q^{58} +(-6.99040 + 12.1077i) q^{59} +18.9436 q^{60} +(5.98240 - 10.3618i) q^{61} +(0.0361865 + 0.0626768i) q^{62} +(-4.23423 - 7.33389i) q^{63} -7.87457 q^{64} +(-9.65882 - 3.86847i) q^{65} -0.118364 q^{66} +(-3.53410 - 6.12124i) q^{67} +(-3.55141 - 6.15123i) q^{68} +(12.0418 - 20.8570i) q^{69} +0.225881 q^{70} +(1.98350 - 3.43553i) q^{71} +(1.13187 - 1.96046i) q^{72} +3.80915 q^{73} +(0.354950 - 0.614792i) q^{74} +(5.47527 + 9.48345i) q^{75} +(-0.806565 - 1.39701i) q^{76} +0.537497 q^{77} +(-0.675093 + 0.530737i) q^{78} +11.9813 q^{79} +(-5.72619 - 9.91805i) q^{80} +(-14.4092 - 24.9574i) q^{81} +(-0.0435377 + 0.0754095i) q^{82} +9.74620 q^{83} +(-3.54992 + 6.14865i) q^{84} +(5.13769 - 8.89874i) q^{85} -0.247857 q^{86} +(-6.04608 + 10.4721i) q^{87} +(0.0718404 + 0.124431i) q^{88} +(4.47774 + 7.75567i) q^{89} +1.63529 q^{90} +(3.06562 - 2.41010i) q^{91} -14.5982 q^{92} +(-1.64544 - 2.84999i) q^{93} +(0.248281 + 0.430035i) q^{94} +(1.16683 - 2.02100i) q^{95} -2.84808 q^{96} +(-7.17134 + 12.4211i) q^{97} +(0.210976 - 0.365422i) q^{98} +3.89127 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 4 q^{2} - 20 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} - 12 q^{8} - 17 q^{9}+O(q^{10}) \) 34 * q + 4 * q^2 - 20 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 - 12 * q^8 - 17 * q^9	\( 34 q + 4 q^{2} - 20 q^{4} - 14 q^{5} + 6 q^{6} + 6 q^{7} - 12 q^{8} - 17 q^{9} - 6 q^{10} + 13 q^{11} + 8 q^{12} - 3 q^{13} + 4 q^{15} - 34 q^{16} + 6 q^{17} + 24 q^{18} + 4 q^{19} + 28 q^{20} - 36 q^{21} + 34 q^{22} + 8 q^{23} + 40 q^{24} + 16 q^{25} - 26 q^{26} - 6 q^{27} + 21 q^{28} + 6 q^{29} - 19 q^{30} - 34 q^{31} + 6 q^{32} + 7 q^{33} - 48 q^{34} + 9 q^{35} + 14 q^{37} + 22 q^{38} - 21 q^{39} - 20 q^{40} + 43 q^{41} - 33 q^{42} - 18 q^{43} - 56 q^{44} + 26 q^{45} + 7 q^{46} - 12 q^{47} + 95 q^{48} + q^{49} + 44 q^{50} + 52 q^{51} - 24 q^{52} - 10 q^{53} + 27 q^{54} - 39 q^{55} - 39 q^{56} - 92 q^{57} + 8 q^{58} - q^{59} - 42 q^{60} + 19 q^{61} - 4 q^{62} + 5 q^{63} + 84 q^{64} - 32 q^{65} + 52 q^{66} + 10 q^{67} - 34 q^{68} - 32 q^{69} + 48 q^{70} + 35 q^{71} - 26 q^{72} - 22 q^{73} + 68 q^{74} + 62 q^{75} + 2 q^{76} + 42 q^{77} - 81 q^{78} + 2 q^{79} + 49 q^{80} - 37 q^{81} - 35 q^{82} - 48 q^{83} - 34 q^{84} - 13 q^{85} - 152 q^{86} + 22 q^{87} + 37 q^{88} + 42 q^{89} + 30 q^{90} - 39 q^{91} + 30 q^{92} - 42 q^{94} - 34 q^{95} - 66 q^{96} - 38 q^{97} + 8 q^{98} - 34 q^{99}+O(q^{100}) \) 34 * q + 4 * q^2 - 20 * q^4 - 14 * q^5 + 6 * q^6 + 6 * q^7 - 12 * q^8 - 17 * q^9 - 6 * q^10 + 13 * q^11 + 8 * q^12 - 3 * q^13 + 4 * q^15 - 34 * q^16 + 6 * q^17 + 24 * q^18 + 4 * q^19 + 28 * q^20 - 36 * q^21 + 34 * q^22 + 8 * q^23 + 40 * q^24 + 16 * q^25 - 26 * q^26 - 6 * q^27 + 21 * q^28 + 6 * q^29 - 19 * q^30 - 34 * q^31 + 6 * q^32 + 7 * q^33 - 48 * q^34 + 9 * q^35 + 14 * q^37 + 22 * q^38 - 21 * q^39 - 20 * q^40 + 43 * q^41 - 33 * q^42 - 18 * q^43 - 56 * q^44 + 26 * q^45 + 7 * q^46 - 12 * q^47 + 95 * q^48 + q^49 + 44 * q^50 + 52 * q^51 - 24 * q^52 - 10 * q^53 + 27 * q^54 - 39 * q^55 - 39 * q^56 - 92 * q^57 + 8 * q^58 - q^59 - 42 * q^60 + 19 * q^61 - 4 * q^62 + 5 * q^63 + 84 * q^64 - 32 * q^65 + 52 * q^66 + 10 * q^67 - 34 * q^68 - 32 * q^69 + 48 * q^70 + 35 * q^71 - 26 * q^72 - 22 * q^73 + 68 * q^74 + 62 * q^75 + 2 * q^76 + 42 * q^77 - 81 * q^78 + 2 * q^79 + 49 * q^80 - 37 * q^81 - 35 * q^82 - 48 * q^83 - 34 * q^84 - 13 * q^85 - 152 * q^86 + 22 * q^87 + 37 * q^88 + 42 * q^89 + 30 * q^90 - 39 * q^91 + 30 * q^92 - 42 * q^94 - 34 * q^95 - 66 * q^96 - 38 * q^97 + 8 * q^98 - 34 * q^99

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