LMFDB - Embedded newform 583.2.q.b.21.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [583,2,Mod(21,583)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(583, base_ring=CyclotomicField(52)) chi = DirichletCharacter(H, H._module([26, 31])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("583.21"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 583 = 11 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	583.q (of order $52$, degree $24$, minimal)

Newform invariants

comment:select newform

sage:traces = [1200] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.65527843784$
Analytic rank:	$0$
Dimension:	$1200$
Relative dimension:	$50$ over $\Q(\zeta_{52})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{52}]$

Embedding invariants

Embedding label			21.5
Character	$\chi$	$=$	583.21
Dual form			583.2.q.b.472.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.36779 - 0.737832i) q^{2} +(0.524586 + 0.236097i) q^{3} +(3.41604 + 2.35793i) q^{4} +(0.744767 + 0.0450501i) q^{5} +(-1.06791 - 0.946083i) q^{6} +(-1.95123 + 1.02408i) q^{7} +(-3.28968 - 4.19897i) q^{8} +(-1.76992 - 1.99783i) q^{9} +(-1.73021 - 0.656182i) q^{10} +(0.130277 + 3.31407i) q^{11} +(1.23531 + 2.04345i) q^{12} +(2.39334 - 1.65200i) q^{13} +(5.37569 - 0.985132i) q^{14} +(0.380058 + 0.199470i) q^{15} +(1.74734 + 4.60735i) q^{16} +(0.862195 + 7.10082i) q^{17} +(2.71673 + 6.03633i) q^{18} +(0.406787 - 2.21976i) q^{19} +(2.43793 + 1.91000i) q^{20} +(-1.26537 + 0.0765408i) q^{21} +(2.13675 - 7.94312i) q^{22} +(2.53450 + 2.53450i) q^{23} +(-0.734357 - 2.97941i) q^{24} +(-4.41090 - 0.535580i) q^{25} +(-6.88580 + 2.14570i) q^{26} +(-0.970226 - 3.11356i) q^{27} +(-9.08020 - 1.10254i) q^{28} +(-3.22253 + 0.794281i) q^{29} +(-0.752721 - 0.752721i) q^{30} +(-1.86173 + 3.07969i) q^{31} +(-0.0937330 - 1.54959i) q^{32} +(-0.714099 + 1.76927i) q^{33} +(3.19771 - 17.4494i) q^{34} +(-1.49935 + 0.674801i) q^{35} +(-1.33540 - 10.9980i) q^{36} +(-3.72741 + 1.41362i) q^{37} +(-2.60099 + 4.95578i) q^{38} +(1.64554 - 0.301557i) q^{39} +(-2.26088 - 3.27545i) q^{40} +(0.761441 + 1.25958i) q^{41} +(3.05260 + 0.752399i) q^{42} +(-0.620471 + 1.63605i) q^{43} +(-7.36928 + 11.6282i) q^{44} +(-1.22818 - 1.56765i) q^{45} +(-4.13112 - 7.87119i) q^{46} +(5.34256 + 4.73310i) q^{47} +(-0.171153 + 2.82949i) q^{48} +(-1.21791 + 1.76444i) q^{49} +(10.0489 + 4.52264i) q^{50} +(-1.22419 + 3.92855i) q^{51} +12.0710 q^{52} +(-2.39141 + 6.87613i) q^{53} +8.08811i q^{54} +(-0.0522726 + 2.47408i) q^{55} +(10.7190 + 4.82424i) q^{56} +(0.737474 - 1.06842i) q^{57} +(8.21630 + 0.496994i) q^{58} +(-2.49948 + 2.82133i) q^{59} +(0.827961 + 1.57755i) q^{60} +(-0.141904 - 0.181127i) q^{61} +(6.68048 - 5.91839i) q^{62} +(5.49946 + 2.08567i) q^{63} +(1.43709 - 5.83050i) q^{64} +(1.85690 - 1.12254i) q^{65} +(2.99626 - 3.66237i) q^{66} +(14.9661 - 2.74264i) q^{67} +(-13.7979 + 26.2897i) q^{68} +(0.731176 + 1.92795i) q^{69} +(4.04802 - 0.491519i) q^{70} +(-6.30228 + 2.83643i) q^{71} +(-2.56634 + 14.0040i) q^{72} +(-9.28398 + 11.8501i) q^{73} +(9.86872 - 0.596948i) q^{74} +(-2.18745 - 1.32236i) q^{75} +(6.62364 - 6.62364i) q^{76} +(-3.64808 - 6.33308i) q^{77} +(-4.11879 - 0.500112i) q^{78} +(2.86479 + 9.19344i) q^{79} +(1.09380 + 3.51012i) q^{80} +(-0.739025 + 6.08642i) q^{81} +(-0.873572 - 3.54422i) q^{82} +(6.90228 + 6.90228i) q^{83} +(-4.50304 - 2.72218i) q^{84} +(0.322242 + 5.32730i) q^{85} +(2.67627 - 3.41601i) q^{86} +(-1.87802 - 0.344160i) q^{87} +(13.4871 - 11.4493i) q^{88} +(-0.838215 - 6.90332i) q^{89} +(1.75139 + 4.61805i) q^{90} +(-2.97816 + 5.67441i) q^{91} +(2.68180 + 14.6341i) q^{92} +(-1.70374 + 1.17601i) q^{93} +(-9.15782 - 15.1489i) q^{94} +(0.402962 - 1.63488i) q^{95} +(0.316683 - 0.835024i) q^{96} +(10.3558 - 9.17442i) q^{97} +(4.18560 - 3.27921i) q^{98} +(6.39034 - 6.12590i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1200 q - 48 q^{3} - 52 q^{4} - 44 q^{5} - 52 q^{9} - 26 q^{11} - 64 q^{12} - 28 q^{14} - 28 q^{15} + 72 q^{16} - 52 q^{20} - 12 q^{22} - 68 q^{23} - 52 q^{25} - 80 q^{26} - 72 q^{27} - 56 q^{31} - 28 q^{33}+ \cdots - 258 q^{99}+O(q^{100}) $ 1200 * q - 48 * q^3 - 52 * q^4 - 44 * q^5 - 52 * q^9 - 26 * q^11 - 64 * q^12 - 28 * q^14 - 28 * q^15 + 72 * q^16 - 52 * q^20 - 12 * q^22 - 68 * q^23 - 52 * q^25 - 80 * q^26 - 72 * q^27 - 56 * q^31 - 28 * q^33 - 40 * q^34 - 144 * q^36 - 52 * q^37 - 52 * q^38 + 164 * q^42 - 150 * q^44 + 224 * q^45 - 36 * q^47 - 128 * q^48 - 180 * q^49 + 56 * q^53 - 124 * q^55 + 220 * q^56 - 104 * q^59 - 520 * q^60 + 156 * q^64 - 70 * q^66 + 12 * q^67 - 36 * q^69 - 52 * q^70 - 68 * q^71 + 8 * q^75 - 38 * q^77 - 52 * q^78 - 80 * q^80 + 40 * q^81 - 52 * q^82 - 48 * q^86 - 138 * q^88 - 12 * q^89 - 52 * q^91 - 144 * q^92 + 156 * q^93 + 36 * q^97 - 258 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/583\mathbb{Z}\right)^\times$.

$n$	$266$	$320$
$\chi(n)$	$-1$	$e\left(\frac{31}{52}\right)$

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 $

$2$	−2.36779	−	0.737832i	−1.67428	−	0.521726i	−0.694105	−	0.719874i	$-0.744200\pi$
$2$	−2.36779	−	0.737832i	−1.67428	−	0.521726i	−0.980172	+	0.198148i	$0.936507\pi$
$3$	0.524586	+	0.236097i	0.302870	+	0.136311i	0.556149	−	0.831083i	$-0.312278\pi$
$3$	0.524586	+	0.236097i	0.302870	+	0.136311i	−0.253279	+	0.967393i	$0.581509\pi$
$4$	3.41604	+	2.35793i	1.70802	+	1.17896i
$5$	0.744767	+	0.0450501i	0.333070	+	0.0201470i	0.226067	−	0.974112i	$-0.427413\pi$
$5$	0.744767	+	0.0450501i	0.333070	+	0.0201470i	0.107003	+	0.994259i	$0.465875\pi$
$6$	−1.06791	−	0.946083i	−0.435971	−	0.386237i
$7$	−1.95123	+	1.02408i	−0.737495	+	0.387067i	−0.791255	−	0.611487i	$-0.790572\pi$
$7$	−1.95123	+	1.02408i	−0.737495	+	0.387067i	0.0537596	+	0.998554i	$0.482880\pi$
$8$	−3.28968	−	4.19897i	−1.16308	−	1.48456i
$9$	−1.76992	−	1.99783i	−0.589973	−	0.665942i
$10$	−1.73021	−	0.656182i	−0.547140	−	0.207503i
$11$	0.130277	+	3.31407i	0.0392801	+	0.999228i
$11$	0.130277	+	3.31407i	0.0392801	+	0.999228i
$12$	1.23531	+	2.04345i	0.356603	+	0.589894i
$13$	2.39334	−	1.65200i	0.663792	−	0.458182i	−0.187926	−	0.982183i	$-0.560176\pi$
$13$	2.39334	−	1.65200i	0.663792	−	0.458182i	0.851718	+	0.524001i	$0.175561\pi$
$14$	5.37569	−	0.985132i	1.43671	−	0.263288i
$15$	0.380058	+	0.199470i	0.0981306	+	0.0515029i
$16$	1.74734	+	4.60735i	0.436835	+	1.15184i
$17$	0.862195	+	7.10082i	0.209113	+	1.72220i	0.598497	+	0.801125i	$0.295765\pi$
$17$	0.862195	+	7.10082i	0.209113	+	1.72220i	−0.389384	+	0.921076i	$0.627312\pi$
$18$	2.71673	+	6.03633i	0.640339	+	1.42278i
$19$	0.406787	−	2.21976i	0.0933233	−	0.509249i	−0.903430	−	0.428735i	$-0.858959\pi$
$19$	0.406787	−	2.21976i	0.0933233	−	0.509249i	0.996754	−	0.0805134i	$-0.0256560\pi$
$20$	2.43793	+	1.91000i	0.545138	+	0.427089i
$21$	−1.26537	+	0.0765408i	−0.276127	+	0.0167026i
$22$	2.13675	−	7.94312i	0.455557	−	1.69348i
$23$	2.53450	+	2.53450i	0.528480	+	0.528480i	0.920119	−	0.391639i	$-0.128092\pi$
$23$	2.53450	+	2.53450i	0.528480	+	0.528480i	−0.391639	+	0.920119i	$0.628092\pi$
$24$	−0.734357	−	2.97941i	−0.149900	−	0.608169i
$25$	−4.41090	−	0.535580i	−0.882179	−	0.107116i
$26$	−6.88580	+	2.14570i	−1.35042	+	0.420807i
$27$	−0.970226	−	3.11356i	−0.186720	−	0.599206i
$28$	−9.08020	−	1.10254i	−1.71600	−	0.208360i
$29$	−3.22253	+	0.794281i	−0.598408	+	0.147494i	−0.526873	−	0.849944i	$-0.676636\pi$
$29$	−3.22253	+	0.794281i	−0.598408	+	0.147494i	−0.0715347	+	0.997438i	$0.522790\pi$
$30$	−0.752721	−	0.752721i	−0.137427	−	0.137427i
$31$	−1.86173	+	3.07969i	−0.334377	+	0.553128i	−0.977049	−	0.213014i	$-0.931672\pi$
$31$	−1.86173	+	3.07969i	−0.334377	+	0.553128i	0.642672	+	0.766142i	$0.277826\pi$
$32$	−0.0937330	−	1.54959i	−0.0165698	−	0.273932i
$33$	−0.714099	+	1.76927i	−0.124309	+	0.307990i
$34$	3.19771	−	17.4494i	0.548404	−	2.99254i
$35$	−1.49935	+	0.674801i	−0.253436	+	0.114062i
$36$	−1.33540	−	10.9980i	−0.222566	−	1.83300i
$37$	−3.72741	+	1.41362i	−0.612782	+	0.232398i	−0.641417	−	0.767192i	$-0.721653\pi$
$37$	−3.72741	+	1.41362i	−0.612782	+	0.232398i	0.0286348	+	0.999590i	$0.490884\pi$
$38$	−2.60099	+	4.95578i	−0.421937	+	0.803934i
$39$	1.64554	−	0.301557i	0.263498	−	0.0482878i
$40$	−2.26088	−	3.27545i	−0.357477	−	0.517895i
$41$	0.761441	+	1.25958i	0.118917	+	0.196713i	0.909569	−	0.415553i	$-0.136412\pi$
$41$	0.761441	+	1.25958i	0.118917	+	0.196713i	−0.790652	+	0.612266i	$0.790258\pi$
$42$	3.05260	+	0.752399i	0.471027	+	0.116098i
$43$	−0.620471	+	1.63605i	−0.0946209	+	0.249495i	−0.973968	−	0.226687i	$-0.927210\pi$
$43$	−0.620471	+	1.63605i	−0.0946209	+	0.249495i	0.879347	+	0.476182i	$0.157980\pi$
$44$	−7.36928	+	11.6282i	−1.11096	+	1.75301i
$45$	−1.22818	−	1.56765i	−0.183086	−	0.233691i
$46$	−4.13112	−	7.87119i	−0.609100	−	1.16054i
$47$	5.34256	+	4.73310i	0.779293	+	0.690393i	0.955836	−	0.293899i	$-0.0949531\pi$
$47$	5.34256	+	4.73310i	0.779293	+	0.690393i	−0.176543	+	0.984293i	$0.556492\pi$
$48$	−0.171153	+	2.82949i	−0.0247038	+	0.408402i
$49$	−1.21791	+	1.76444i	−0.173987	+	0.252063i
$50$	10.0489	+	4.52264i	1.42113	+	0.639597i
$51$	−1.22419	+	3.92855i	−0.171420	+	0.550107i
$52$	12.0710			1.67395
$53$	−2.39141	+	6.87613i	−0.328485	+	0.944509i
$53$	−2.39141	+	6.87613i	−0.328485	+	0.944509i
$54$			8.08811i			1.10065i
$55$	−0.0522726	+	2.47408i	−0.00704844	+	0.333604i
$56$	10.7190	+	4.82424i	1.43239	+	0.644666i
$57$	0.737474	−	1.06842i	0.0976808	−	0.141515i
$58$	8.21630	+	0.496994i	1.07885	+	0.0652586i
$59$	−2.49948	+	2.82133i	−0.325404	+	0.367306i	−0.888333	−	0.459200i	$-0.848136\pi$
$59$	−2.49948	+	2.82133i	−0.325404	+	0.367306i	0.562929	+	0.826506i	$0.309675\pi$
$60$	0.827961	+	1.57755i	0.106889	+	0.203660i
$61$	−0.141904	−	0.181127i	−0.0181690	−	0.0231910i	0.778014	−	0.628247i	$-0.216227\pi$
$61$	−0.141904	−	0.181127i	−0.0181690	−	0.0231910i	−0.796183	+	0.605056i	$0.793151\pi$
$62$	6.68048	−	5.91839i	0.848421	−	0.751636i
$63$	5.49946	+	2.08567i	0.692867	+	0.262770i
$64$	1.43709	−	5.83050i	0.179636	−	0.728812i
$65$	1.85690	−	1.12254i	0.230320	−	0.139233i
$66$	2.99626	−	3.66237i	0.368814	−	0.450806i
$67$	14.9661	−	2.74264i	1.82840	−	0.335067i	0.847685	−	0.530499i	$-0.177996\pi$
$67$	14.9661	−	2.74264i	1.82840	−	0.335067i	0.980717	+	0.195432i	$0.0626109\pi$
$68$	−13.7979	+	26.2897i	−1.67324	+	3.18809i
$69$	0.731176	+	1.92795i	0.0880232	+	0.232098i
$70$	4.04802	−	0.491519i	0.483831	−	0.0587477i
$71$	−6.30228	+	2.83643i	−0.747944	+	0.336622i	−0.748285	−	0.663378i	$-0.769122\pi$
$71$	−6.30228	+	2.83643i	−0.747944	+	0.336622i	0.000341014		1.00000i	$0.499891\pi$
$72$	−2.56634	+	14.0040i	−0.302446	+	1.65039i
$73$	−9.28398	+	11.8501i	−1.08661	+	1.38695i	−0.170814	+	0.985303i	$0.554640\pi$
$73$	−9.28398	+	11.8501i	−1.08661	+	1.38695i	−0.915794	+	0.401649i	$0.868437\pi$
$74$	9.86872	−	0.596948i	1.14722	−	0.0693938i
$75$	−2.18745	−	1.32236i	−0.252584	−	0.152693i
$76$	6.62364	−	6.62364i	0.759783	−	0.759783i
$77$	−3.64808	−	6.33308i	−0.415738	−	0.721722i
$78$	−4.11879	−	0.500112i	−0.466361	−	0.0566265i
$79$	2.86479	+	9.19344i	0.322314	+	1.03434i	0.963669	+	0.267098i	$0.0860648\pi$
$79$	2.86479	+	9.19344i	0.322314	+	1.03434i	−0.641355	+	0.767244i	$0.721627\pi$
$80$	1.09380	+	3.51012i	0.122290	+	0.392444i
$81$	−0.739025	+	6.08642i	−0.0821139	+	0.676269i
$82$	−0.873572	−	3.54422i	−0.0964699	−	0.391394i
$83$	6.90228	+	6.90228i	0.757623	+	0.757623i	0.975889	−	0.218266i	$-0.0700400\pi$
$83$	6.90228	+	6.90228i	0.757623	+	0.757623i	−0.218266	+	0.975889i	$0.570040\pi$
$84$	−4.50304	−	2.72218i	−0.491322	−	0.297014i
$85$	0.322242	+	5.32730i	0.0349521	+	0.577826i
$86$	2.67627	−	3.41601i	0.288590	−	0.368357i
$87$	−1.87802	−	0.344160i	−0.201345	−	0.0368978i
$88$	13.4871	−	11.4493i	1.43773	−	1.22049i
$89$	−0.838215	−	6.90332i	−0.0888506	−	0.731751i	−0.967250	−	0.253824i	$-0.918312\pi$
$89$	−0.838215	−	6.90332i	−0.0888506	−	0.731751i	0.878400	−	0.477927i	$-0.158612\pi$
$90$	1.75139	+	4.61805i	0.184613	+	0.486785i
$91$	−2.97816	+	5.67441i	−0.312196	+	0.594839i
$92$	2.68180	+	14.6341i	0.279597	+	1.52571i
$93$	−1.70374	+	1.17601i	−0.176670	+	0.121947i
$94$	−9.15782	−	15.1489i	−0.944557	−	1.56249i
$95$	0.402962	−	1.63488i	0.0413430	−	0.167735i
$96$	0.316683	−	0.835024i	0.0323213	−	0.0852243i
$97$	10.3558	−	9.17442i	1.05147	−	0.931521i	0.0537190	−	0.998556i	$-0.482892\pi$
$97$	10.3558	−	9.17442i	1.05147	−	0.931521i	0.997751	+	0.0670353i	$0.0213540\pi$
$98$	4.18560	−	3.27921i	0.422810	−	0.331250i
$99$	6.39034	−	6.12590i	0.642254	−	0.615676i
$100$	−13.8050	−	12.2301i	−1.38050	−	1.22301i
$101$	−8.45303	−	0.511314i	−0.841108	−	0.0508777i	−0.365796	−	0.930695i	$-0.619203\pi$
$101$	−8.45303	−	0.511314i	−0.841108	−	0.0508777i	−0.475312	+	0.879817i	$0.657665\pi$
$102$	5.79722	−	8.39872i	0.574010	−	0.831597i
$103$	0.517518	−	1.14988i	0.0509926	−	0.113301i	−0.884642	−	0.466271i	$-0.845597\pi$
$103$	0.517518	−	1.14988i	0.0509926	−	0.113301i	0.935635	+	0.352970i	$0.114828\pi$
$104$	−14.8100	−	4.61499i	−1.45224	−	0.452537i
$105$	−0.945855			−0.0923060
$106$	10.7358	−	14.5167i	1.04275	−	1.40999i
$107$			3.12878i			0.302471i	0.988498	+	0.151235i	$0.0483252\pi$
$107$			3.12878i			0.302471i	−0.988498	+	0.151235i	$0.951675\pi$
$108$	4.02722	−	12.9238i	0.387519	−	1.24359i
$109$	2.29413	−	5.09735i	0.219738	−	0.488238i	−0.768748	−	0.639552i	$-0.779120\pi$
$109$	2.29413	−	5.09735i	0.219738	−	0.488238i	0.988486	+	0.151314i	$0.0483506\pi$
$110$	1.94922	−	5.81951i	0.185851	−	0.554869i
$111$	−2.28910	−	0.138465i	−0.217272	−	0.0131425i
$112$	−8.12777	−	7.20058i	−0.768002	−	0.680391i
$113$	5.53410	+	10.5443i	0.520604	+	0.991929i	0.993822	+	0.110983i	$0.0354000\pi$
$113$	5.53410	+	10.5443i	0.520604	+	0.991929i	−0.473218	+	0.880945i	$0.656908\pi$
$114$	−2.53449	+	1.98565i	−0.237377	+	0.185973i
$115$	1.77343	+	2.00179i	0.165373	+	0.186668i
$116$	−12.8811	−	4.88518i	−1.19598	−	0.453577i
$117$	−7.53642	−	1.85756i	−0.696742	−	0.171732i
$118$	7.99989	−	4.83610i	0.736450	−	0.445199i
$119$	−8.95417	−	12.9724i	−0.820828	−	1.18917i
$120$	−0.412703	−	2.25205i	−0.0376744	−	0.205583i
$121$	−10.9661	+	0.863496i	−0.996914	+	0.0784996i
$122$	0.202357	+	0.533572i	0.0183206	+	0.0483074i
$123$	0.102059	+	0.840530i	0.00920234	+	0.0757881i
$124$	−13.6214	+	6.13051i	−1.22324	+	0.550536i
$125$	−6.93050	−	1.27006i	−0.619882	−	0.113598i
$126$	−11.4827	−	8.99609i	−1.02296	−	0.801436i
$127$	−3.07375	+	0.185928i	−0.272751	+	0.0164984i	−0.196188	−	0.980566i	$-0.562856\pi$
$127$	−3.07375	+	0.185928i	−0.272751	+	0.0164984i	−0.0765632	+	0.997065i	$0.524395\pi$
$128$	−9.31090	+	15.4021i	−0.822975	+	1.36137i
$129$	−0.711756	+	0.711756i	−0.0626666	+	0.0626666i
$130$	−5.22498	+	1.28784i	−0.458261	+	0.112951i
$131$	0.831336	−	6.84667i	0.0726341	−	0.598196i	−0.910262	−	0.414033i	$-0.864120\pi$
$131$	0.831336	−	6.84667i	0.0726341	−	0.598196i	0.982896	−	0.184163i	$-0.0589573\pi$
$132$	−6.61120	+	4.36011i	−0.575431	+	0.379499i
$133$	1.47949	+	4.74785i	0.128288	+	0.411691i
$134$	−37.4602	−	4.54849i	−3.23607	−	0.392930i
$135$	−0.582326	−	2.36259i	−0.0501186	−	0.203339i
$136$	26.9798	−	26.9798i	2.31350	−	2.31350i
$137$	−6.49222	+	10.7394i	−0.554668	+	0.917533i	0.445089	+	0.895486i	$0.353172\pi$
$137$	−6.49222	+	10.7394i	−0.554668	+	0.917533i	−0.999757	+	0.0220464i	$0.992982\pi$
$138$	−0.308763	−	5.10446i	−0.0262837	−	0.434521i
$139$	−8.33349	−	6.52887i	−0.706837	−	0.553771i	0.197650	−	0.980273i	$-0.436669\pi$
$139$	−8.33349	−	6.52887i	−0.706837	−	0.553771i	−0.904487	+	0.426501i	$0.859746\pi$
$140$	−6.71296	−	1.23020i	−0.567349	−	0.103971i
$141$	1.68516	+	3.74428i	0.141916	+	0.315325i
$142$	17.0153	−	2.06603i	1.42789	−	0.173377i
$143$	5.78663	+	7.71645i	0.483903	+	0.645282i
$144$	6.11204	−	11.6455i	0.509337	−	0.970460i
$145$	−2.43581	+	0.446379i	−0.202283	+	0.0370698i
$146$	30.7259	−	21.2085i	2.54289	−	1.75523i
$147$	−1.05548	+	0.638058i	−0.0870543	+	0.0526261i
$148$	−16.0662	−	3.95996i	−1.32063	−	0.325507i
$149$	6.19264	−	16.3286i	0.507321	−	1.33769i	−0.399715	−	0.916640i	$-0.630891\pi$
$149$	6.19264	−	16.3286i	0.507321	−	1.33769i	0.907035	−	0.421055i	$-0.138340\pi$
$150$	4.20373	+	4.74503i	0.343233	+	0.387430i
$151$	15.2119	−	11.9178i	1.23793	−	0.969853i	0.237927	−	0.971283i	$-0.423532\pi$
$151$	15.2119	−	11.9178i	1.23793	−	0.969853i	0.999999	+	0.00143009i	$0.000455213\pi$
$152$	−10.6589	+	5.59423i	−0.864552	+	0.453752i
$153$	12.6602	−	14.2904i	1.02351	−	1.15531i
$154$	3.96512	+	17.6871i	0.319519	+	1.42526i
$155$	−1.52530	+	2.20978i	−0.122515	+	0.177494i
$156$	6.33230	+	2.84994i	0.506989	+	0.228177i
$157$	−9.71488	−	3.02728i	−0.775331	−	0.241603i	−0.115793	−	0.993273i	$-0.536941\pi$
$157$	−9.71488	−	3.02728i	−0.775331	−	0.241603i	−0.659539	+	0.751670i	$0.729248\pi$
$158$		−	23.8818i		−	1.89994i
$159$	−2.87793	+	3.04252i	−0.228235	+	0.241287i
$160$		−	1.15831i		−	0.0915723i
$161$	−7.54093	−	2.34985i	−0.594309	−	0.185194i
$162$	6.24061	−	13.8661i	0.490309	−	1.08942i
$163$	5.54542	+	3.82772i	0.434350	+	0.299810i	0.765104	−	0.643907i	$-0.222688\pi$
$163$	5.54542	+	3.82772i	0.434350	+	0.299810i	−0.330754	+	0.943717i	$0.607303\pi$
$164$	−0.368872	+	6.09819i	−0.0288041	+	0.476189i
$165$	−0.611543	+	1.28552i	−0.0476086	+	0.100078i
$166$	−11.2504	−	21.4358i	−0.873200	−	1.66374i
$167$	−0.306693	−	0.391465i	−0.0237326	−	0.0302924i	0.775171	−	0.631751i	$-0.217663\pi$
$167$	−0.306693	−	0.391465i	−0.0237326	−	0.0302924i	−0.798904	+	0.601458i	$0.794587\pi$
$168$	4.48406	+	5.06146i	0.345953	+	0.390500i
$169$	−1.61091	+	4.24763i	−0.123916	+	0.326741i
$170$	3.16765	−	12.8517i	0.242948	−	0.985677i
$171$	−5.15468	+	3.11611i	−0.394188	+	0.238295i
$172$	−5.97723	+	4.12579i	−0.455760	+	0.314588i
$173$	−1.15582	−	6.30708i	−0.0878750	−	0.479518i	−0.997889	−	0.0649411i	$-0.979314\pi$
$173$	−1.15582	−	6.30708i	−0.0878750	−	0.479518i	0.910014	−	0.414577i	$-0.136071\pi$
$174$	4.19282	+	2.20056i	0.317857	+	0.166824i
$175$	9.15515	−	3.47209i	0.692064	−	0.262465i
$176$	−15.0414	+	6.39103i	−1.13379	+	0.481742i
$177$	−1.97730	+	0.889910i	−0.148623	+	0.0668897i
$178$	−3.10878	+	16.9640i	−0.233013	+	1.27151i
$179$	−14.6547	−	11.4812i	−1.09535	−	0.858149i	−0.104686	−	0.994505i	$-0.533384\pi$
$179$	−14.6547	−	11.4812i	−1.09535	−	0.858149i	−0.990660	+	0.136357i	$0.956461\pi$
$180$	−0.499100	−	8.25111i	−0.0372007	−	0.615001i
$181$	19.5955	+	11.8459i	1.45652	+	0.880499i	0.999958	−	0.00919155i	$-0.00292580\pi$
$181$	19.5955	+	11.8459i	1.45652	+	0.880499i	0.456565	+	0.889690i	$0.349080\pi$
$182$	11.2384	−	11.2384i	0.833046	−	0.833046i
$183$	−0.0316774	−	0.128520i	−0.00234166	−	0.00950048i
$184$	2.30459	−	18.9800i	0.169897	−	1.39922i
$185$	−2.83974	+	0.884898i	−0.208782	+	0.0650590i
$186$	4.90180	−	1.52746i	0.359417	−	0.111999i
$187$	−23.4202	+	3.78245i	−1.71266	+	0.276600i
$188$	7.09014	+	28.7658i	0.517102	+	2.09797i
$189$	5.08168	+	5.08168i	0.369638	+	0.369638i
$190$	−2.16039	+	3.57373i	−0.156731	+	0.259265i
$191$	15.3935	−	0.931134i	1.11383	−	0.0673745i	0.506809	−	0.862058i	$-0.330825\pi$
$191$	15.3935	−	0.931134i	1.11383	−	0.0673745i	0.607024	+	0.794684i	$0.292363\pi$
$192$	2.13044	−	2.71931i	0.153751	−	0.196249i
$193$	18.6111	+	3.41061i	1.33966	+	0.245501i	0.801830	−	0.597553i	$-0.203860\pi$
$193$	18.6111	+	3.41061i	1.33966	+	0.245501i	0.537828	+	0.843054i	$0.319245\pi$
$194$	−31.2894	+	14.0822i	−2.24645	+	1.01105i
$195$	1.23913	−	0.150458i	0.0887360	−	0.0107745i
$196$	−8.32085	+	3.15568i	−0.594346	+	0.225406i
$197$	−18.3758	−	9.64438i	−1.30922	−	0.687134i	−0.341675	−	0.939818i	$-0.610994\pi$
$197$	−18.3758	−	9.64438i	−1.30922	−	0.687134i	−0.967549	+	0.252684i	$0.918687\pi$
$198$	−19.6508	+	9.78982i	−1.39652	+	0.695732i
$199$	4.78107	−	3.30013i	0.338921	−	0.233940i	−0.386431	−	0.922318i	$-0.626292\pi$
$199$	4.78107	−	3.30013i	0.338921	−	0.233940i	0.725352	+	0.688378i	$0.241677\pi$
$200$	12.2616	+	20.2831i	0.867023	+	1.43423i
$201$	8.49855	+	2.09470i	0.599441	+	0.147749i
$202$	19.6377	+	7.44760i	1.38170	+	0.524011i
$203$	5.47448	−	4.84996i	0.384233	−	0.340401i
$204$	−13.4451	+	10.5336i	−0.941346	+	0.737497i
$205$	0.510352	+	0.972394i	0.0356445	+	0.0679149i
$206$	−2.07379	+	2.34082i	−0.144488	+	0.163093i
$207$	0.577629	−	9.54935i	0.0401480	−	0.663726i
$208$	11.7933	+	8.14034i	0.817719	+	0.564431i
$209$	7.40943	+	1.05893i	0.512521	+	0.0732479i
$210$	2.23958	+	0.697882i	0.154546	+	0.0481584i
$211$	−24.8797			−1.71279			−0.856393	−	0.516324i	$-0.827300\pi$
$211$	−24.8797			−1.71279			−0.856393	+	0.516324i	$0.827300\pi$
$212$	−24.3826	+	17.8504i	−1.67460	+	1.22597i
$213$	−3.97576			−0.272415
$214$	2.30852	−	7.40829i	0.157807	−	0.506420i
$215$	−0.535810	+	1.19052i	−0.0365420	+	0.0811929i
$216$	−9.88202	+	14.3166i	−0.672386	+	0.974120i
$217$	0.478814	−	7.91574i	0.0325040	−	0.537356i
$218$	−9.19300	+	10.3767i	−0.622628	+	0.702802i
$219$	−7.66803	+	4.02449i	−0.518157	+	0.271950i
$220$	−6.01225	+	8.32830i	−0.405346	+	0.561494i
$221$	13.7941	+	15.5703i	0.927890	+	1.04737i
$222$	5.31793	+	2.01683i	0.356916	+	0.135360i
$223$	4.57256	−	18.5516i	0.306201	−	1.24231i	−0.593154	−	0.805089i	$-0.702117\pi$
$223$	4.57256	−	18.5516i	0.306201	−	1.24231i	0.899355	−	0.437219i	$-0.144037\pi$
$224$	1.76981	+	2.92762i	0.118250	+	0.195610i
$225$	6.73693	+	9.76013i	0.449129	+	0.650676i
$226$	−5.32361	−	29.0500i	−0.354121	−	1.93238i
$227$	11.8562	−	22.5901i	0.786923	−	1.49936i	−0.0777231	−	0.996975i	$-0.524765\pi$
$227$	11.8562	−	22.5901i	0.786923	−	1.49936i	0.864646	−	0.502382i	$-0.167543\pi$
$228$	5.03849	−	1.91085i	0.333682	−	0.126549i
$229$	2.62229	−	0.318404i	0.173286	−	0.0210407i	−0.0334338	−	0.999441i	$-0.510644\pi$
$229$	2.62229	−	0.318404i	0.173286	−	0.0210407i	0.206720	+	0.978400i	$0.433721\pi$
$230$	−2.72212	−	6.04831i	−0.179491	−	0.398814i
$231$	−0.418511	−	4.18355i	−0.0275360	−	0.275257i
$232$	13.9362	+	10.9184i	0.914960	+	0.716825i
$233$	5.12646	−	0.310094i	0.335846	−	0.0203149i	0.108405	−	0.994107i	$-0.465426\pi$
$233$	5.12646	−	0.310094i	0.335846	−	0.0203149i	0.227441	+	0.973792i	$0.426964\pi$
$234$	16.4741	+	9.95891i	1.07694	+	0.651035i
$235$	3.76574	+	3.76574i	0.245650	+	0.245650i
$236$	−15.1908	+	3.74420i	−0.988837	+	0.243727i
$237$	−0.667714	+	5.49912i	−0.0433727	+	0.357206i
$238$	11.6301	+	37.3224i	0.753870	+	2.41925i
$239$	22.6401	−	7.05495i	1.46447	−	0.456347i	0.541329	−	0.840811i	$-0.317921\pi$
$239$	22.6401	−	7.05495i	1.46447	−	0.456347i	0.923140	+	0.384464i	$0.125614\pi$
$240$	−0.254938	+	2.09960i	−0.0164562	+	0.135529i
$241$	−16.3265	+	4.02413i	−1.05168	+	0.259217i	−0.727023	−	0.686613i	$-0.759097\pi$
$241$	−16.3265	+	4.02413i	−1.05168	+	0.259217i	−0.324662	+	0.945830i	$0.605250\pi$
$242$	26.6024	+	6.04653i	1.71007	+	0.388686i
$243$	−6.88614	+	11.3911i	−0.441746	+	0.730737i
$244$	−0.0576664	−	0.953339i	−0.00369171	−	0.0610313i
$245$	−0.986545	+	1.25923i	−0.0630281	+	0.0804494i
$246$	0.378516	−	2.06550i	0.0241333	−	0.131691i
$247$	−2.69347	−	5.98465i	−0.171381	−	0.380794i
$248$	19.0560	−	2.31382i	1.21006	−	0.146928i
$249$	1.99123	+	5.25045i	0.126189	+	0.332734i
$250$	15.4728	+	8.12077i	0.978588	+	0.513603i
$251$	1.43308	+	7.82006i	0.0904552	+	0.493598i	0.997382	+	0.0723101i	$0.0230371\pi$
$251$	1.43308	+	7.82006i	0.0904552	+	0.493598i	−0.906927	+	0.421288i	$0.861578\pi$
$252$	13.8685	+	20.0921i	0.873636	+	1.26568i
$253$	−8.06931	+	8.72969i	−0.507313	+	0.548831i
$254$	7.41516	+	1.82767i	0.465269	+	0.114678i
$255$	−1.08872	+	2.87071i	−0.0681780	+	0.179771i
$256$	24.4208	−	21.6349i	1.52630	−	1.35218i
$257$	−10.8381	−	13.8338i	−0.676059	−	0.862926i	0.320376	−	0.947291i	$-0.396191\pi$
$257$	−10.8381	−	13.8338i	−0.676059	−	0.862926i	−0.996435	+	0.0843649i	$0.973114\pi$
$258$	2.21044	−	1.16013i	0.137616	−	0.0722265i
$259$	5.82536	−	6.57548i	0.361971	−	0.408580i
$260$	8.99011	+	0.543801i	0.557543	+	0.0337251i
$261$	7.29045	+	5.03223i	0.451267	+	0.311487i
$262$	−7.02011	+	15.5980i	−0.433704	+	0.963651i
$263$	−8.41031	+	26.9896i	−0.518602	+	1.66425i	0.208736	+	0.977972i	$0.433065\pi$
$263$	−8.41031	+	26.9896i	−0.518602	+	1.66425i	−0.727338	+	0.686279i	$0.759243\pi$
$264$	9.77827	−	2.82186i	0.601811	−	0.173673i
$265$	−2.09081	+	5.01338i	−0.128438	+	0.307970i
$266$		−	12.3335i		−	0.756216i
$267$	1.19014	−	3.81929i	0.0728353	−	0.233737i
$268$	57.5919	+	25.9200i	3.51798	+	1.58332i
$269$	−3.45770	−	2.38668i	−0.210820	−	0.145518i	0.457976	−	0.888965i	$-0.348575\pi$
$269$	−3.45770	−	2.38668i	−0.210820	−	0.145518i	−0.668796	+	0.743446i	$0.733190\pi$
$270$	−0.364370	+	6.02376i	−0.0221749	+	0.366594i
$271$	−13.9009	−	12.3151i	−0.844418	−	0.748089i	0.125352	−	0.992112i	$-0.459994\pi$
$271$	−13.9009	−	12.3151i	−0.844418	−	0.748089i	−0.969769	+	0.244024i	$0.921533\pi$
$272$	−31.2094	+	16.3800i	−1.89235	+	0.993181i
$273$	−2.90201	+	2.27358i	−0.175638	+	0.137603i
$274$	23.2961	−	20.6385i	1.40737	−	1.24682i
$275$	1.20031	−	14.6878i	0.0723812	−	0.885706i
$276$	−2.04824	+	8.31003i	−0.123289	+	0.500205i
$277$	1.92038	−	1.16091i	0.115385	−	0.0697524i	−0.458469	−	0.888711i	$-0.651602\pi$
$277$	1.92038	−	1.16091i	0.115385	−	0.0697524i	0.573853	+	0.818958i	$0.305448\pi$
$278$	14.9147	+	21.6077i	0.894524	+	1.29594i
$279$	9.44779	−	1.73137i	0.565625	−	0.103655i
$280$	7.76584	+	4.07583i	0.464098	+	0.243577i
$281$	23.6372	−	8.96440i	1.41008	−	0.534771i	0.472122	−	0.881533i	$-0.343488\pi$
$281$	23.6372	−	8.96440i	1.41008	−	0.534771i	0.937953	+	0.346762i	$0.112719\pi$
$282$	−1.22746	−	10.1090i	−0.0730940	−	0.601984i
$283$	2.55504	+	5.67706i	0.151881	+	0.337466i	0.972094	−	0.234593i	$-0.0753756\pi$
$283$	2.55504	+	5.67706i	0.151881	+	0.337466i	−0.820213	+	0.572059i	$0.806145\pi$
$284$	−28.2170	−	5.17095i	−1.67437	−	0.306840i
$285$	0.597379	−	0.762497i	0.0353857	−	0.0451665i
$286$	−8.00806	−	22.5405i	−0.473527	−	1.33285i
$287$	−2.77566	−	1.67794i	−0.163842	−	0.0990458i
$288$	−2.92991	+	2.92991i	−0.172647	+	0.172647i
$289$	−33.1722	+	8.17621i	−1.95131	+	0.480954i
$290$	6.09684	+	0.740290i	0.358019	+	0.0434713i
$291$	7.59855	−	2.36780i	0.445435	−	0.138803i
$292$	−59.6562	+	18.5896i	−3.49112	+	1.08788i
$293$	−2.33204	−	0.283161i	−0.136239	−	0.0165425i	0.0521329	−	0.998640i	$-0.483398\pi$
$293$	−2.33204	−	0.283161i	−0.136239	−	0.0165425i	−0.188372	+	0.982098i	$0.560321\pi$
$294$	2.96992	−	0.732020i	0.173209	−	0.0426923i
$295$	−1.98863	+	1.98863i	−0.115783	+	0.115783i
$296$	18.1977	+	11.0009i	1.05772	+	0.639415i
$297$	10.1922	−	3.62102i	0.591409	−	0.210113i
$298$	−26.7106	+	34.0936i	−1.54731	+	1.97499i
$299$	10.2529	+	1.87891i	0.592941	+	0.108660i
$300$	−4.35439	−	9.67507i	−0.251401	−	0.558590i
$301$	−0.464769	−	3.82772i	−0.0267888	−	0.220626i
$302$	−44.8118	+	16.9949i	−2.57863	+	0.977945i
$303$	−4.31362	−	2.26396i	−0.247811	−	0.130061i
$304$	10.9380	−	2.00447i	0.627339	−	0.114964i
$305$	−0.0975258	−	0.141291i	−0.00558431	−	0.00809027i
$306$	−40.5205	+	24.4955i	−2.31640	+	1.40031i
$307$	−1.69148	+	6.86260i	−0.0965378	+	0.391669i	−0.999256	−	0.0385628i	$-0.987722\pi$
$307$	−1.69148	+	6.86260i	−0.0965378	+	0.391669i	0.902718	+	0.430232i	$0.141568\pi$
$308$	2.47093	−	30.2360i	0.140794	−	1.72286i
$309$	0.542966	−	0.481026i	0.0308883	−	0.0273646i
$310$	5.24202	−	4.10686i	0.297727	−	0.233254i
$311$	1.53235	−	0.804241i	0.0868918	−	0.0456043i	−0.420718	−	0.907192i	$-0.638222\pi$
$311$	1.53235	−	0.804241i	0.0868918	−	0.0456043i	0.507609	+	0.861587i	$0.330529\pi$
$312$	−6.67954	−	5.91756i	−0.378155	−	0.335016i
$313$	0.765656	−	12.6578i	0.0432774	−	0.715461i	−0.910232	−	0.414098i	$-0.864097\pi$
$313$	0.765656	−	12.6578i	0.0432774	−	0.715461i	0.953510	−	0.301363i	$-0.0974415\pi$
$314$	20.7691	+	14.3359i	1.17207	+	0.809021i
$315$	4.00186	+	1.80109i	0.225479	+	0.101480i
$316$	−11.8912	+	38.1602i	−0.668931	+	2.14668i
$317$			6.30043i			0.353867i	0.984223	+	0.176934i	$0.0566178\pi$
$317$			6.30043i			0.353867i	−0.984223	+	0.176934i	$0.943382\pi$
$318$	9.05920	−	5.08060i	0.508014	−	0.284906i
$319$	−3.05212	−	10.5762i	−0.170886	−	0.592153i
$320$	1.33296	−	4.27762i	0.0745148	−	0.239126i
$321$	−0.738696	+	1.64132i	−0.0412300	+	0.0916093i
$322$	16.1215	+	11.1279i	0.898417	+	0.620132i
$323$	16.1129	+	0.974648i	0.896543	+	0.0542309i
$324$	−16.8759	+	19.0489i	−0.937548	+	1.05827i
$325$	−11.4415	+	6.00498i	−0.634662	+	0.333096i
$326$	−10.3061	−	13.1548i	−0.570804	−	0.728578i
$327$	2.40694	−	2.13236i	0.133104	−	0.117920i
$328$	2.78403	−	7.34087i	0.153722	−	0.405332i
$329$	−15.2717	−	3.76413i	−0.841954	−	0.207523i
$330$	2.39650	−	2.59263i	0.131923	−	0.142720i
$331$	−10.9096	−	15.8053i	−0.599647	−	0.868739i	0.399194	−	0.916867i	$-0.369290\pi$
$331$	−10.9096	−	15.8053i	−0.599647	−	0.868739i	−0.998841	+	0.0481274i	$0.984675\pi$
$332$	7.30343	+	39.8535i	0.400828	+	2.18725i
$333$	9.42138	+	4.94472i	0.516289	+	0.270969i
$334$	0.437348	+	1.15319i	0.0239306	+	0.0630998i
$335$	11.2698	−	1.36841i	0.615737	−	0.0747640i
$336$	−2.56368	−	5.69627i	−0.139860	−	0.310757i
$337$	1.45546	−	7.94221i	0.0792842	−	0.432640i	−0.919896	−	0.392162i	$-0.871727\pi$
$337$	1.45546	−	7.94221i	0.0792842	−	0.432640i	0.999180	−	0.0404781i	$-0.0128881\pi$
$338$	6.94833	−	8.86889i	0.377940	−	0.482404i
$339$	0.413623	+	6.83800i	0.0224649	+	0.371389i
$340$	−11.4606	+	18.9581i	−0.621537	+	1.02815i
$341$	−10.4488	−	5.76870i	−0.565835	−	0.312392i
$342$	14.5043	−	3.57500i	0.784305	−	0.193314i
$343$	2.42882	−	20.0031i	0.131144	−	1.08007i
$344$	8.91086	−	2.77674i	0.480442	−	0.149712i
$345$	0.457701	+	1.46881i	0.0246418	+	0.0790783i
$346$	−1.91684	+	15.7866i	−0.103050	+	0.848693i
$347$	−3.66980	+	0.904525i	−0.197005	+	0.0485575i	−0.336584	−	0.941654i	$-0.609271\pi$
$347$	−3.66980	+	0.904525i	−0.197005	+	0.0485575i	0.139578	+	0.990211i	$0.455425\pi$
$348$	−5.60390	−	5.60390i	−0.300400	−	0.300400i
$349$	−0.923299	−	0.558154i	−0.0494231	−	0.0298773i	0.492411	−	0.870363i	$-0.336116\pi$
$349$	−0.923299	−	0.558154i	−0.0494231	−	0.0298773i	−0.541834	+	0.840486i	$0.682270\pi$
$350$	−24.2392	+	1.46620i	−1.29564	+	0.0783719i
$351$	−7.46568	−	5.84899i	−0.398489	−	0.312196i
$352$	5.12324	−	0.512514i	0.273069	−	0.0273171i
$353$	0.831024	+	1.84646i	0.0442310	+	0.0982772i	0.932690	−	0.360678i	$-0.117455\pi$
$353$	0.831024	+	1.84646i	0.0442310	+	0.0982772i	−0.888459	+	0.458955i	$0.848224\pi$
$354$	5.33842	−	0.648202i	0.283734	−	0.0344515i
$355$	−4.82152	+	1.82856i	−0.255899	+	0.0970499i
$356$	13.4141	−	25.5585i	0.710948	−	1.35460i
$357$	−1.63450	−	8.91917i	−0.0865068	−	0.472053i
$358$	26.2280	+	37.9979i	1.38619	+	2.00825i
$359$	6.60735	+	10.9299i	0.348723	+	0.576858i	0.980072	−	0.198640i	$-0.0636526\pi$
$359$	6.60735	+	10.9299i	0.348723	+	0.576858i	−0.631350	+	0.775498i	$0.717499\pi$
$360$	−2.54221	+	10.3141i	−0.133986	+	0.543603i
$361$	13.0034	+	4.93155i	0.684391	+	0.259555i
$362$	−37.6577	−	42.5067i	−1.97924	−	2.23410i
$363$	−5.95651	−	2.13608i	−0.312636	−	0.112115i
$364$	−23.5533	+	12.3618i	−1.23453	+	0.647932i
$365$	−7.44825	+	8.40734i	−0.389859	+	0.440060i
$366$	−0.0198210	+	0.327681i	−0.00103606	+	0.0171281i
$367$	21.3714	−	30.9618i	1.11558	−	1.61619i	0.401961	−	0.915657i	$-0.368329\pi$
$367$	21.3714	−	30.9618i	1.11558	−	1.61619i	0.713617	−	0.700536i	$-0.247056\pi$
$368$	−7.24871	+	16.1060i	−0.377865	+	0.839582i
$369$	1.16873	−	3.75057i	0.0608415	−	0.195247i
$370$	7.37679			0.383501
$371$	−2.37555	−	15.8659i	−0.123332	−	0.823717i
$372$	−8.59301			−0.445527
$373$	11.9828	+	3.73398i	0.620444	+	0.193338i	0.591582	−	0.806245i	$-0.298504\pi$
$373$	11.9828	+	3.73398i	0.620444	+	0.193338i	0.0288626	+	0.999583i	$0.490811\pi$
$374$	58.2449	+	8.32417i	3.01177	+	0.430433i
$375$	−3.33578	−	2.30253i	−0.172259	−	0.118902i
$376$	2.29880	−	38.0037i	0.118551	−	1.95989i
$377$	−6.40043	+	7.22460i	−0.329639	+	0.372086i
$378$	−8.28291	−	15.7818i	−0.426027	−	0.811726i
$379$	4.26285	−	3.33973i	0.218968	−	0.171550i	−0.501241	−	0.865308i	$-0.667123\pi$
$379$	4.26285	−	3.33973i	0.218968	−	0.171550i	0.720209	+	0.693757i	$0.244046\pi$
$380$	5.23146	−	4.63467i	0.268368	−	0.237754i
$381$	−1.65634	−	0.628168i	−0.0848570	−	0.0321820i
$382$	−37.1355	−	9.15307i	−1.90002	−	0.468312i
$383$	11.7468	+	19.4315i	0.600232	+	0.992905i	0.997179	+	0.0750632i	$0.0239158\pi$
$383$	11.7468	+	19.4315i	0.600232	+	0.992905i	−0.396947	+	0.917842i	$0.629930\pi$
$384$	−8.52076	+	5.88146i	−0.434823	+	0.300137i
$385$	−2.43167	−	4.88102i	−0.123929	−	0.248760i
$386$	−41.5507	−	21.8075i	−2.11487	−	1.10997i
$387$	4.36672	−	1.65608i	0.221973	−	0.0841832i
$388$	57.0084	−	6.92207i	2.89416	−	0.351415i
$389$	2.06080	−	0.927492i	0.104487	−	0.0470257i	−0.357495	−	0.933915i	$-0.616369\pi$
$389$	2.06080	−	0.927492i	0.104487	−	0.0470257i	0.461982	+	0.886889i	$0.347138\pi$
$390$	−3.04501	−	0.558019i	−0.154190	−	0.0282564i
$391$	−15.8118	+	20.1823i	−0.799636	+	1.02066i
$392$	11.4154	−	0.690503i	0.576563	−	0.0348756i
$393$	2.05258	−	3.39539i	0.103539	−	0.171275i
$394$	36.3941	+	36.3941i	1.83351	+	1.83351i
$395$	1.71944	+	6.97603i	0.0865142	+	0.351002i
$396$	36.2741	−	5.85839i	1.82284	−	0.294395i
$397$	−17.9407	+	5.59056i	−0.900420	+	0.280582i	−0.712558	−	0.701613i	$-0.752463\pi$
$397$	−17.9407	+	5.59056i	−0.900420	+	0.280582i	−0.187862	+	0.982195i	$0.560156\pi$
$398$	−13.7555	+	4.28638i	−0.689500	+	0.214857i
$399$	−0.344833	+	2.83996i	−0.0172633	+	0.142176i
$400$	−5.23972	−	21.2584i	−0.261986	−	1.06292i
$401$	−5.50474	+	5.50474i	−0.274894	+	0.274894i	−0.831067	−	0.556173i	$-0.812269\pi$
$401$	−5.50474	+	5.50474i	−0.274894	+	0.274894i	0.556173	+	0.831067i	$0.312269\pi$
$402$	−18.5772	−	11.2303i	−0.926547	−	0.560117i
$403$	0.631885	+	10.4463i	0.0314764	+	0.520368i
$404$	−27.6703	−	21.6783i	−1.37665	−	1.07854i
$405$	−0.824596	+	4.49967i	−0.0409745	+	0.223591i
$406$	−16.5408	+	7.44443i	−0.820908	+	0.369461i
$407$	−5.17043	−	12.1687i	−0.256289	−	0.603181i
$408$	20.5230	−	7.78337i	1.01604	−	0.385334i
$409$	−2.50944	−	1.31706i	−0.124084	−	0.0651243i	0.401539	−	0.915842i	$-0.368475\pi$
$409$	−2.50944	−	1.31706i	−0.124084	−	0.0651243i	−0.525623	+	0.850718i	$0.676168\pi$
$410$	−0.490940	−	2.67897i	−0.0242458	−	0.132305i
$411$	−5.94128	+	4.10097i	−0.293062	+	0.202286i
$412$	4.47919	−	2.70777i	0.220674	−	0.133402i
$413$	1.98778	−	8.06473i	0.0978121	−	0.396839i
$414$	−8.41352	+	22.1846i	−0.413502	+	1.09031i
$415$	4.82964	+	5.45154i	0.237078	+	0.267605i
$416$	−2.78426	−	3.55385i	−0.136510	−	0.174242i
$417$	−2.83018	−	5.39247i	−0.138595	−	0.264070i
$418$	−16.7626	−	7.97424i	−0.819887	−	0.390033i
$419$	1.20237	−	19.8775i	0.0587395	−	0.971080i	−0.842757	−	0.538294i	$-0.819069\pi$
$419$	1.20237	−	19.8775i	0.0587395	−	0.971080i	0.901497	−	0.432786i	$-0.142469\pi$
$420$	−3.23108	−	2.23025i	−0.157661	−	0.108825i
$421$	0.785720	−	1.74580i	0.0382936	−	0.0850850i	−0.891760	−	0.452508i	$-0.850529\pi$
$421$	0.785720	−	1.74580i	0.0382936	−	0.0850850i	0.930054	+	0.367423i	$0.119760\pi$
$422$	58.9097	+	18.3570i	2.86768	+	0.893605i
$423$		−	19.0507i		−	0.926278i
$424$	36.7396	−	12.5788i	1.78423	−	0.610882i
$425$		−	31.7827i		−	1.54169i
$426$	9.41375	+	2.93344i	0.456098	+	0.142126i
$427$	0.462377	+	0.208099i	0.0223760	+	0.0100706i
$428$	−7.37744	+	10.6881i	−0.356602	+	0.516627i
$429$	1.21376	+	5.41415i	0.0586007	+	0.261398i
$430$	2.14709	−	2.42356i	0.103542	−	0.116875i
$431$	20.5763	−	10.7993i	0.991124	−	0.520182i	0.110438	−	0.993883i	$-0.464775\pi$
$431$	20.5763	−	10.7993i	0.991124	−	0.520182i	0.880686	+	0.473701i	$0.157082\pi$
$432$	12.6500	−	9.91062i	0.608622	−	0.476825i
$433$	−8.21820	−	9.27643i	−0.394942	−	0.445797i	0.517081	−	0.855936i	$-0.327019\pi$
$433$	−8.21820	−	9.27643i	−0.394942	−	0.445797i	−0.912023	+	0.410139i	$0.865480\pi$
$434$	−6.97422	+	18.3895i	−0.334773	+	0.882724i
$435$	−1.38318	−	0.340924i	−0.0663185	−	0.0163461i
$436$	19.8560	−	12.0034i	0.950931	−	0.574858i
$437$	6.65699	−	4.59499i	0.318447	−	0.219808i
$438$	21.1256	−	3.87142i	1.00942	−	0.184984i
$439$	−7.31452	+	13.9367i	−0.349103	+	0.665160i	−0.995175	−	0.0981162i	$-0.968718\pi$
$439$	−7.31452	+	13.9367i	−0.349103	+	0.665160i	0.646072	+	0.763277i	$0.276411\pi$
$440$	10.5605	−	7.91943i	0.503453	−	0.377544i
$441$	5.68065	−	0.689755i	0.270507	−	0.0328455i
$442$	−21.1731	−	47.0448i	−1.00710	−	2.23769i
$443$	−13.5153	−	2.47676i	−0.642129	−	0.117675i	−0.150683	−	0.988582i	$-0.548147\pi$
$443$	−13.5153	−	2.47676i	−0.642129	−	0.117675i	−0.491447	+	0.870908i	$0.663532\pi$
$444$	−7.49317	−	5.87053i	−0.355610	−	0.278603i
$445$	−0.313280	−	5.17913i	−0.0148509	−	0.245514i
$446$	−24.5148	+	40.5525i	−1.16081	+	1.92022i
$447$	7.10372	−	7.10372i	0.335994	−	0.335994i
$448$	3.16683	+	12.8483i	0.149619	+	0.607027i
$449$	−30.3972	−	3.69089i	−1.43453	−	0.174184i	−0.633936	−	0.773386i	$-0.718562\pi$
$449$	−30.3972	−	3.69089i	−1.43453	−	0.174184i	−0.800598	+	0.599202i	$0.795485\pi$
$450$	−8.75028	−	28.0806i	−0.412492	−	1.32373i
$451$	−4.07512	+	2.68756i	−0.191890	+	0.126552i
$452$	−5.95805	+	49.0689i	−0.280243	+	2.30801i
$453$	10.7937	−	2.66041i	0.507132	−	0.124997i
$454$	−44.7406	+	44.7406i	−2.09978	+	2.09978i
$455$	−2.47367	+	4.09195i	−0.115967	+	0.191833i
$456$	−6.91230	+	0.418117i	−0.323698	+	0.0195801i
$457$	−14.4486	−	11.3197i	−0.675876	−	0.529515i	0.219059	−	0.975712i	$-0.429701\pi$
$457$	−14.4486	−	11.3197i	−0.675876	−	0.529515i	−0.894935	+	0.446196i	$0.852778\pi$
$458$	−6.44395	−	1.18090i	−0.301106	−	0.0551797i
$459$	21.2723	−	9.57389i	0.992907	−	0.446871i
$460$	1.33805	+	11.0198i	0.0623869	+	0.513802i
$461$	4.21670	+	11.1185i	0.196391	+	0.517841i	0.996647	−	0.0818171i	$-0.0260723\pi$
$461$	4.21670	+	11.1185i	0.196391	+	0.517841i	−0.800256	+	0.599658i	$0.795303\pi$
$462$	−2.09581	+	10.2145i	−0.0975060	+	0.475223i
$463$	6.27045	+	34.2167i	0.291413	+	1.59019i	0.724787	+	0.688973i	$0.241938\pi$
$463$	6.27045	+	34.2167i	0.291413	+	1.59019i	−0.433375	+	0.901214i	$0.642677\pi$
$464$	−9.29038	−	13.4594i	−0.431295	−	0.624839i
$465$	−1.32187	+	0.799100i	−0.0613004	+	0.0370574i
$466$	−12.3672	−	3.04823i	−0.572898	−	0.141207i
$467$	34.4590	+	13.0686i	1.59457	+	0.604742i	0.982533	−	0.186086i	$-0.0595803\pi$
$467$	34.4590	+	13.0686i	1.59457	+	0.604742i	0.612039	+	0.790828i	$0.290350\pi$
$468$	−21.3648	−	24.1158i	−0.987586	−	1.11475i
$469$	−26.3936	+	20.6781i	−1.21874	+	0.954825i
$470$	−6.13798	−	11.6949i	−0.283124	−	0.539448i
$471$	−4.38156	−	3.88172i	−0.201892	−	0.178860i
$472$	20.0692	+	1.21396i	0.923758	+	0.0558771i
$473$	−5.50280	−	1.84314i	−0.253019	−	0.0847477i
$474$	5.63843	−	12.5281i	0.258982	−	0.575433i
$475$	−2.98315	+	9.57328i	−0.136876	+	0.439252i
$476$		−	65.4274i		−	2.99886i
$477$	17.9699	−	7.39258i	0.822786	−	0.338483i
$478$	−58.8124			−2.69001
$479$	29.6864	+	9.25067i	1.35641	+	0.422674i	0.887595	−	0.460624i	$-0.152374\pi$
$479$	29.6864	+	9.25067i	1.35641	+	0.422674i	0.468812	+	0.883298i	$0.344682\pi$
$480$	0.273473	−	0.607632i	0.0124823	−	0.0277345i
$481$	−6.58564	+	9.54095i	−0.300279	+	0.435030i
$482$	41.6269	+	2.51796i	1.89605	+	0.114690i
$483$	−3.40108	−	3.01309i	−0.154754	−	0.137100i
$484$	−39.4966	−	22.9074i	−1.79530	−	1.04125i
$485$	8.12595	−	6.36627i	0.368980	−	0.289078i
$486$	24.7096	−	21.8908i	1.12085	−	0.992986i
$487$	5.31732	−	14.0206i	0.240951	−	0.635335i	−0.758924	−	0.651179i	$-0.774275\pi$
$487$	5.31732	−	14.0206i	0.240951	−	0.635335i	0.999874	+	0.0158447i	$0.00504375\pi$
$488$	−0.293729	+	1.19170i	−0.0132965	+	0.0539459i
$489$	2.00533	+	3.31723i	0.0906843	+	0.150010i
$490$	3.26503	−	2.25369i	0.147499	−	0.101811i
$491$	0.310148	+	1.69242i	0.0139968	+	0.0763780i	0.989877	−	0.141930i	$-0.0453308\pi$
$491$	0.310148	+	1.69242i	0.0139968	+	0.0763780i	−0.975880	+	0.218308i	$0.929946\pi$
$492$	−1.63327	+	3.11194i	−0.0736335	+	0.140297i
$493$	−8.41849	−	22.1977i	−0.379150	−	0.999736i
$494$	1.96190	+	16.1577i	0.0882700	+	0.726969i
$495$	5.03529	−	4.27448i	0.226319	−	0.192124i
$496$	−17.4423	−	3.19642i	−0.783181	−	0.143523i
$497$	9.39246	−	11.9886i	0.421309	−	0.537762i
$498$	−0.840863	−	13.9011i	−0.0376800	−	0.622924i
$499$	11.7189	+	7.08430i	0.524609	+	0.317137i	0.754742	−	0.656022i	$-0.227762\pi$
$499$	11.7189	+	7.08430i	0.524609	+	0.317137i	−0.230133	+	0.973159i	$0.573916\pi$
$500$	−20.6802	−	20.6802i	−0.924846	−	0.924846i
$501$	−0.0684632	−	0.277766i	−0.00305871	−	0.0124097i
$502$	2.37666	−	19.5736i	0.106076	−	0.873612i
$503$	7.07491	+	22.7042i	0.315455	+	1.01233i	0.967227	+	0.253915i	$0.0817183\pi$
$503$	7.07491	+	22.7042i	0.315455	+	1.01233i	−0.651772	+	0.758415i	$0.725974\pi$
$504$	−9.33381	−	29.9532i	−0.415761	−	1.33422i
$505$	−6.27250	−	0.761620i	−0.279123	−	0.0338916i
$506$	25.5474	−	14.7162i	1.13572	−	0.654216i
$507$	−1.84792	+	1.84792i	−0.0820688	+	0.0820688i
$508$	−10.9385	−	6.61253i	−0.485316	−	0.293384i
$509$	28.1495	−	1.70273i	1.24770	−	0.0754722i	0.576718	−	0.816943i	$-0.304333\pi$
$509$	28.1495	−	1.70273i	1.24770	−	0.0754722i	0.670985	+	0.741471i	$0.265871\pi$
$510$	4.69594	−	5.99393i	0.207940	−	0.265416i
$511$	5.97965	−	32.6299i	0.264524	−	1.44346i
$512$	−40.9619	+	18.4354i	−1.81028	+	0.814739i
$513$	−7.30605	+	0.887115i	−0.322570	+	0.0391671i
$514$	15.4552	+	40.7520i	0.681700	+	1.79749i
$515$	0.437233	−	0.833078i	0.0192668	−	0.0367098i
$516$	−4.10966	+	0.753123i	−0.180918	+	0.0331544i
$517$	−14.9898	+	18.3222i	−0.659250	+	0.805810i
$518$	−18.6448	+	11.2712i	−0.819206	+	0.495227i
$519$	0.882758	−	3.58149i	0.0387488	−	0.157210i
$520$	−10.8221	−	4.10428i	−0.474581	−	0.179985i
$521$	−10.2655	+	9.09445i	−0.449740	+	0.398435i	−0.857361	−	0.514716i	$-0.827897\pi$
$521$	−10.2655	+	9.09445i	−0.449740	+	0.398435i	0.407620	+	0.913152i	$0.366359\pi$
$522$	−13.5493	−	17.2944i	−0.593036	−	0.756954i
$523$	16.6161	+	31.6593i	0.726571	+	1.38437i	0.915477	+	0.402371i	$0.131814\pi$
$523$	16.6161	+	31.6593i	0.726571	+	1.38437i	−0.188905	+	0.981995i	$0.560494\pi$
$524$	18.9838	−	21.4283i	0.829311	−	0.936099i
$525$	5.62241	+	0.340093i	0.245382	+	0.0148429i
$526$	39.8276	−	57.7002i	1.73657	−	2.51585i
$527$	−23.4735	−	10.5645i	−1.02252	−	0.460199i
$528$	−9.39943	−	0.198592i	−0.409058	−	0.00864262i
$529$		−	10.1526i		−	0.441418i
$530$	8.64963	−	10.3279i	0.375716	−	0.448617i
$531$	10.0604			0.436584
$532$	−6.14107	+	19.7074i	−0.266249	+	0.854424i
$533$	3.90320	+	1.75669i	0.169067	+	0.0760907i
$534$	−5.63598	+	8.16513i	−0.243893	+	0.353340i
$535$	−0.140952	+	2.33021i	−0.00609389	+	0.100744i
$536$	−60.7501	−	53.8199i	−2.62400	−	2.32466i
$537$	−4.97698	−	9.48284i	−0.214773	−	0.409215i
$538$	6.42613	+	8.20235i	0.277050	+	0.353628i
$539$	−6.00614	−	3.80636i	−0.258703	−	0.163951i
$540$	3.58156	−	9.44379i	0.154126	−	0.406396i
$541$	34.6814	+	8.54820i	1.49107	+	0.367516i	0.898849	−	0.438259i	$-0.144405\pi$
$541$	34.6814	+	8.54820i	1.49107	+	0.367516i	0.592222	+	0.805775i	$0.298251\pi$
$542$	23.8278	+	39.4160i	1.02349	+	1.69306i
$543$	7.48275	+	10.8406i	0.321116	+	0.465216i
$544$	10.9225	−	2.00163i	0.468300	−	0.0858192i
$545$	1.93823	−	3.69299i	0.0830246	−	0.158190i
$546$	8.54886	−	3.24216i	0.365857	−	0.138751i
$547$	1.43876	+	11.8493i	0.0615171	+	0.506639i	0.990602	+	0.136773i	$0.0436732\pi$
$547$	1.43876	+	11.8493i	0.0615171	+	0.506639i	−0.929085	+	0.369866i	$0.879404\pi$
$548$	−47.5005	+	21.3782i	−2.02912	+	0.913234i
$549$	−0.110702	+	0.604081i	−0.00472464	+	0.0257816i
$550$	−13.6792	+	33.8919i	−0.583282	+	1.44515i
$551$	0.452236	+	7.47635i	0.0192659	+	0.318503i
$552$	5.69008	−	9.41253i	0.242186	−	0.400624i
$553$	−15.0047	−	15.0047i	−0.638065	−	0.638065i
$554$	−5.40361	+	1.33187i	−0.229577	+	0.0565858i
$555$	−1.69861	−	0.206248i	−0.0721019	−	0.00875475i
$556$	−13.0730	−	41.9526i	−0.554418	−	1.77919i
$557$	2.33856	−	0.728723i	0.0990878	−	0.0308770i	−0.247558	−	0.968873i	$-0.579628\pi$
$557$	2.33856	−	0.728723i	0.0990878	−	0.0308770i	0.346646	+	0.937996i	$0.387320\pi$
$558$	−23.6478	−	2.87136i	−1.00109	−	0.121555i
$559$	1.21776	+	4.94063i	0.0515056	+	0.208966i
$560$	−5.72891	−	5.72891i	−0.242091	−	0.242091i
$561$	−13.1790	−	3.54523i	−0.556416	−	0.149680i
$562$	−62.5820	+	3.78551i	−2.63986	+	0.159682i
$563$	−1.95083	−	1.52838i	−0.0822177	−	0.0644134i	0.574768	−	0.818316i	$-0.305092\pi$
$563$	−1.95083	−	1.52838i	−0.0822177	−	0.0644134i	−0.656986	+	0.753903i	$0.728169\pi$
$564$	−3.07214	+	16.7641i	−0.129360	+	0.705897i
$565$	3.64659	+	8.10239i	0.153413	+	0.340870i
$566$	−1.86107	−	15.3272i	−0.0782264	−	0.644252i
$567$	−4.79100	−	12.6328i	−0.201203	−	0.530529i
$568$	32.6426	+	17.1322i	1.36965	+	0.718849i
$569$	−10.2086	+	1.87079i	−0.427965	+	0.0784275i	−0.389920	−	0.920849i	$-0.627497\pi$
$569$	−10.2086	+	1.87079i	−0.427965	+	0.0784275i	−0.0380445	+	0.999276i	$0.512113\pi$
$570$	−1.97706	+	1.36467i	−0.0828099	+	0.0571595i
$571$	12.1470	+	20.0935i	0.508335	+	0.840889i	0.999545	−	0.0301522i	$-0.00959920\pi$
$571$	12.1470	+	20.0935i	0.508335	+	0.840889i	−0.491210	+	0.871041i	$0.663445\pi$
$572$	1.57258	+	40.0042i	0.0657530	+	1.67266i
$573$	8.29504	+	3.14589i	0.346530	+	0.131422i
$574$	5.33412	+	6.02098i	0.222642	+	0.251311i
$575$	−9.82199	−	12.5368i	−0.409605	−	0.522823i
$576$	−14.1918	+	7.44846i	−0.591327	+	0.310352i
$577$	−5.30482	−	4.69966i	−0.220843	−	0.195650i	0.545446	−	0.838146i	$-0.316360\pi$
$577$	−5.30482	−	4.69966i	−0.220843	−	0.195650i	−0.766289	+	0.642496i	$0.777899\pi$
$578$	84.5773	+	5.11598i	3.51795	+	0.212797i
$579$	8.95790	+	6.18319i	0.372278	+	0.256965i
$580$	−9.37338	−	4.21861i	−0.389208	−	0.175168i
$581$	−20.5364	−	6.39941i	−0.851995	−	0.265492i
$582$	−19.7388			−0.818198
$583$	−23.0995	−	7.02948i	−0.956683	−	0.291131i
$584$	80.2997			3.32282
$585$	−5.52919	−	1.72297i	−0.228604	−	0.0712359i
$586$	5.31285	+	2.39112i	0.219472	+	0.0987763i
$587$	−19.9735	−	13.7867i	−0.824396	−	0.569040i	0.0794787	−	0.996837i	$-0.474674\pi$
$587$	−19.9735	−	13.7867i	−0.824396	−	0.569040i	−0.903875	+	0.427797i	$0.859290\pi$
$588$	−5.11005	−	0.309101i	−0.210735	−	0.0127471i
$589$	6.07884	+	5.38538i	0.250474	+	0.221901i
$590$	6.17592	−	3.24137i	0.254259	−	0.133445i
$591$	−7.36270	−	9.39779i	−0.302861	−	0.386573i
$592$	−13.0261	−	14.7034i	−0.535369	−	0.604307i
$593$	−38.7364	−	14.6908i	−1.59071	−	0.603278i	−0.608920	−	0.793232i	$-0.708397\pi$
$593$	−38.7364	−	14.6908i	−1.59071	−	0.603278i	−0.981793	+	0.189954i	$0.939166\pi$
$594$	−26.8045	+	1.05370i	−1.09980	+	0.0432338i
$595$	−6.08437	−	10.0648i	−0.249435	−	0.412615i
$596$	59.6560	−	41.1776i	2.44361	−	1.68670i
$597$	3.28723	−	0.602408i	0.134537	−	0.0246549i
$598$	−22.8904	−	12.0138i	−0.936056	−	0.491280i
$599$	7.97566	+	21.0301i	0.325877	+	0.859266i	0.993403	+	0.114680i	$0.0365842\pi$
$599$	7.97566	+	21.0301i	0.325877	+	0.859266i	−0.667526	+	0.744587i	$0.732647\pi$
$600$	1.64347	+	13.5352i	0.0670942	+	0.552570i
$601$	12.1013	+	26.8880i	0.493622	+	1.09678i	0.975390	+	0.220485i	$0.0707640\pi$
$601$	12.1013	+	26.8880i	0.493622	+	1.09678i	−0.481768	+	0.876299i	$0.660005\pi$
$602$	−1.72374	+	9.40613i	−0.0702543	+	0.383365i
$603$	−31.9681	−	25.0454i	−1.30184	−	1.01993i
$604$	80.0657	−	4.84308i	3.25783	−	0.197062i
$605$	−8.20606	+	0.149082i	−0.333624	+	0.00606103i
$606$	8.54331	+	8.54331i	0.347048	+	0.347048i
$607$	7.75050	+	31.4450i	0.314583	+	1.27631i	0.889059	+	0.457792i	$0.151360\pi$
$607$	7.75050	+	31.4450i	0.314583	+	1.27631i	−0.574476	+	0.818521i	$0.694794\pi$
$608$	−3.47786	−	0.422288i	−0.141046	−	0.0171260i
$609$	4.01690	−	1.25172i	0.162773	−	0.0507221i
$610$	0.126672	+	0.406503i	0.00512878	+	0.0164588i
$611$	20.6056	+	2.50198i	0.833615	+	0.101219i
$612$	76.9434	−	18.9648i	3.11025	−	0.766608i
$613$	30.0983	+	30.0983i	1.21566	+	1.21566i	0.969137	+	0.246521i	$0.0792876\pi$
$613$	30.0983	+	30.0983i	1.21566	+	1.21566i	0.246521	+	0.969137i	$0.420712\pi$
$614$	9.06850	−	15.0011i	0.365975	−	0.605396i
$615$	0.0381441	+	0.630597i	0.00153812	+	0.0254281i
$616$	−14.5914	+	36.1520i	−0.587904	+	1.45661i
$617$	−3.66484	+	19.9984i	−0.147541	+	0.805104i	0.823704	+	0.567020i	$0.191904\pi$
$617$	−3.66484	+	19.9984i	−0.147541	+	0.805104i	−0.971245	+	0.238084i	$0.923481\pi$
$618$	−1.64054	+	0.738349i	−0.0659923	+	0.0297007i
$619$	−1.59156	−	13.1077i	−0.0639702	−	0.526842i	−0.989106	−	0.147206i	$-0.952972\pi$
$619$	−1.59156	−	13.1077i	−0.0639702	−	0.526842i	0.925136	−	0.379637i	$-0.123951\pi$
$620$	−10.4210	+	3.95216i	−0.418517	+	0.158722i
$621$	5.43229	−	10.3504i	0.217990	−	0.415346i
$622$	−4.22168	+	0.773651i	−0.169274	+	0.0310206i
$623$	8.70513	+	12.6116i	0.348764	+	0.505271i
$624$	4.26470	+	7.05467i	0.170725	+	0.282413i
$625$	16.4665	+	4.05863i	0.658660	+	0.162345i
$626$	−11.1522	+	29.4060i	−0.445733	+	1.17530i
$627$	3.63688	+	2.30485i	0.145243	+	0.0920467i
$628$	−26.0484	−	33.2483i	−1.03944	−	1.32675i
$629$	−13.2516	−	25.2488i	−0.528376	−	1.00674i
$630$	−8.14664	−	7.21729i	−0.324570	−	0.287544i
$631$	−2.31093	+	38.2041i	−0.0919965	+	1.52088i	0.600595	+	0.799553i	$0.294930\pi$
$631$	−2.31093	+	38.2041i	−0.0919965	+	1.52088i	−0.692592	+	0.721330i	$0.743531\pi$
$632$	29.1787	−	42.2727i	1.16067	−	1.68152i
$633$	−13.0515	−	5.87402i	−0.518752	−	0.233471i
$634$	4.64866	−	14.9181i	0.184622	−	0.592472i
$635$	−2.29760			−0.0911776
$636$	−17.0052	+	3.60743i	−0.674299	+	0.143044i
$637$			6.23489i			0.247035i
$638$	−0.576673	+	27.2941i	−0.0228307	+	1.08058i
$639$	16.8212	+	7.57062i	0.665437	+	0.299489i
$640$	−7.62832	+	11.0515i	−0.301536	+	0.436850i
$641$	−18.3792	−	1.11173i	−0.725933	−	0.0439109i	−0.306721	−	0.951799i	$-0.599232\pi$
$641$	−18.3792	−	1.11173i	−0.725933	−	0.0439109i	−0.419212	+	0.907888i	$0.637694\pi$
$642$	2.96009	−	3.34125i	0.116825	−	0.131869i
$643$	11.4623	+	21.8396i	0.452030	+	0.861271i	0.999698	+	0.0245755i	$0.00782342\pi$
$643$	11.4623	+	21.8396i	0.452030	+	0.861271i	−0.547668	+	0.836696i	$0.684484\pi$
$644$	−20.2194	−	25.8081i	−0.796756	−	1.01698i
$645$	−0.562157	+	0.498028i	−0.0221349	+	0.0196098i
$646$	−37.4327	−	14.1963i	−1.47277	−	0.558547i
$647$	−2.00417	+	8.13125i	−0.0787922	+	0.319672i	−0.997091	−	0.0762145i	$-0.975717\pi$
$647$	−2.00417	+	8.13125i	−0.0787922	+	0.319672i	0.918299	+	0.395887i	$0.129563\pi$
$648$	27.9879	−	16.9192i	1.09947	−	0.664651i
$649$	−9.67569	−	7.91588i	−0.379804	−	0.310725i
$650$	31.5218	−	5.77658i	1.23639	−	0.226576i
$651$	2.12006	−	4.03944i	0.0830918	−	0.158318i
$652$	9.91790	+	26.1514i	0.388415	+	1.02417i
$653$	−32.7488	+	3.97643i	−1.28156	+	0.155610i	−0.732843	−	0.680398i	$-0.761807\pi$
$653$	−32.7488	+	3.97643i	−1.28156	+	0.155610i	−0.548718	+	0.836007i	$0.684884\pi$
$654$	−7.27244	+	3.27306i	−0.284375	+	0.127987i
$655$	0.927594	−	5.06172i	0.0362441	−	0.197778i
$656$	−4.47282	+	5.70913i	−0.174634	+	0.222904i
$657$	40.1064	−	2.42599i	1.56470	−	0.0946469i
$658$	33.3827	+	20.1806i	1.30139	+	0.786720i
$659$	−4.60941	+	4.60941i	−0.179557	+	0.179557i	−0.791163	−	0.611606i	$-0.790524\pi$
$659$	−4.60941	+	4.60941i	−0.179557	+	0.179557i	0.611606	+	0.791163i	$0.290524\pi$
$660$	−5.12023	+	2.94943i	−0.199305	+	0.114807i
$661$	28.6036	+	3.47311i	1.11255	+	0.135088i	0.656110	−	0.754665i	$-0.272201\pi$
$661$	28.6036	+	3.47311i	1.11255	+	0.135088i	0.456442	+	0.889753i	$0.349124\pi$
$662$	14.1700	+	45.4731i	0.550732	+	1.76736i
$663$	3.56008	+	11.4247i	0.138262	+	0.443698i
$664$	6.27615	−	51.6888i	0.243562	−	2.00591i
$665$	0.887984	+	3.60269i	0.0344345	+	0.139706i
$666$	−18.6594	−	18.6594i	−0.723038	−	0.723038i
$667$	−10.1806	−	6.15439i	−0.394194	−	0.238299i
$668$	−0.124632	−	2.06042i	−0.00482217	−	0.0797200i
$669$	6.77869	−	8.65235i	0.262079	−	0.334519i
$670$	−27.6942	−	5.07515i	−1.06992	−	0.196070i
$671$	0.581781	−	0.493877i	0.0224594	−	0.0190659i
$672$	0.237214	+	1.95363i	0.00915073	+	0.0753631i
$673$	8.15890	+	21.5132i	0.314502	+	0.829275i	0.995303	+	0.0968062i	$0.0308627\pi$
$673$	8.15890	+	21.5132i	0.314502	+	0.829275i	−0.680801	+	0.732469i	$0.738368\pi$
$674$	−9.30625	+	17.7316i	−0.358463	+	0.682995i
$675$	2.61200	+	14.2532i	0.100536	+	0.548607i
$676$	−15.5185	+	10.7117i	−0.596867	+	0.411988i
$677$	15.4504	+	25.5580i	0.593806	+	0.982274i	0.997721	+	0.0674779i	$0.0214952\pi$
$677$	15.4504	+	25.5580i	0.593806	+	0.982274i	−0.403915	+	0.914796i	$0.632351\pi$
$678$	4.06592	−	16.4961i	0.156151	−	0.633529i
$679$	−10.8111	+	28.5066i	−0.414893	+	1.09398i
$680$	21.3091	−	18.8782i	0.817166	−	0.723946i
$681$	11.5530	−	9.05123i	0.442714	−	0.346844i
$682$	20.4842	+	21.3685i	0.784382	+	0.818242i
$683$	−15.5119	−	13.7424i	−0.593548	−	0.525838i	0.312000	−	0.950082i	$-0.399001\pi$
$683$	−15.5119	−	13.7424i	−0.593548	−	0.525838i	−0.905548	+	0.424245i	$0.860540\pi$
$684$	−24.9562	−	1.50957i	−0.954223	−	0.0577199i
$685$	−5.31901	+	7.70591i	−0.203229	+	0.294428i
$686$	−20.5098	+	45.5710i	−0.783069	+	1.73991i
$687$	1.45079	+	0.452085i	0.0553511	+	0.0172481i
$688$	−8.62202			−0.328711
$689$	5.63593	+	20.4075i	0.214712	+	0.777464i
$690$		−	3.81554i		−	0.145255i
$691$	11.9066	−	38.2095i	0.452947	−	1.45356i	−0.392627	−	0.919698i	$-0.628434\pi$
$691$	11.9066	−	38.2095i	0.452947	−	1.45356i	0.845573	−	0.533859i	$-0.179259\pi$
$692$	10.9233	−	24.2706i	0.415242	−	0.922630i
$693$	−6.19559	+	18.4973i	−0.235351	+	0.702654i
$694$	9.35670	+	0.565976i	0.355175	+	0.0214841i
$695$	−5.91238	−	5.23791i	−0.224269	−	0.198685i
$696$	4.73297	+	9.01792i	0.179403	+	0.341824i
$697$	−8.28751	+	6.49285i	−0.313912	+	0.245934i
$698$	1.77435	+	2.00283i	0.0671601	+	0.0758081i
$699$	2.76248	+	1.04767i	0.104487	+	0.0396266i
$700$	39.4613	+	9.72634i	1.49150	+	0.367621i
$701$	−34.0570	+	20.5882i	−1.28632	+	0.777606i	−0.984437	−	0.175740i	$-0.943768\pi$
$701$	−34.0570	+	20.5882i	−1.28632	+	0.777606i	−0.301880	+	0.953346i	$0.597614\pi$
$702$	13.3616	+	19.3576i	0.504300	+	0.730604i
$703$	1.62164	+	8.84901i	0.0611613	+	0.333747i
$704$	19.5099	+	4.00302i	0.735306	+	0.150870i
$705$	1.08637	+	2.86453i	0.0409152	+	0.107885i
$706$	−0.605310	−	4.98518i	−0.0227811	−	0.187620i
$707$	17.0174	−	7.65892i	0.640006	−	0.288043i
$708$	−8.85288	−	1.62235i	−0.332712	−	0.0609717i
$709$	15.0203	+	11.7677i	0.564100	+	0.441944i	0.857822	−	0.513947i	$-0.171817\pi$
$709$	15.0203	+	11.7677i	0.564100	+	0.441944i	−0.293722	+	0.955891i	$0.594894\pi$
$710$	12.7655	−	0.772169i	0.479080	−	0.0289790i
$711$	13.2964	−	21.9950i	0.498655	−	0.824877i
$712$	−26.2294	+	26.2294i	−0.982988	+	0.982988i
$713$	−12.5240	+	3.08690i	−0.469029	+	0.115605i
$714$	−2.71071	+	22.3247i	−0.101446	+	0.835480i
$715$	3.96207	+	6.00765i	0.148173	+	0.224673i
$716$	−22.9893	−	73.7752i	−0.859150	−	2.75711i
$717$	13.5424	+	1.64434i	0.505749	+	0.0614090i
$718$	−7.58037	−	30.7548i	−0.282897	−	1.14776i
$719$	25.6643	−	25.6643i	0.957117	−	0.957117i	−0.0420007	−	0.999118i	$-0.513373\pi$
$719$	25.6643	−	25.6643i	0.957117	−	0.957117i	0.999118	+	0.0420007i	$0.0133732\pi$
$720$	5.07668	−	8.39785i	0.189197	−	0.312969i
$721$	0.167775	+	2.77366i	0.00624828	+	0.103296i
$722$	−27.1507	−	21.2712i	−1.01044	−	0.791632i
$723$	−9.51476	−	1.74364i	−0.353858	−	0.0648468i
$724$	39.0074	+	86.6709i	1.44970	+	3.22110i
$725$	14.6396	−	1.77757i	0.543702	−	0.0660174i
$726$	12.5277	+	9.45267i	0.464946	+	0.350821i
$727$	7.63942	−	14.5557i	0.283330	−	0.539841i	−0.701647	−	0.712525i	$-0.747552\pi$
$727$	7.63942	−	14.5557i	0.283330	−	0.539841i	0.984977	+	0.172684i	$0.0552439\pi$
$728$	33.6239	−	6.16180i	1.24618	−	0.228372i
$729$	8.83568	−	6.09883i	0.327247	−	0.225883i
$730$	23.8391	−	14.4112i	0.882324	−	0.533383i
$731$	−12.1522	−	2.99526i	−0.449467	−	0.110784i
$732$	0.194830	−	0.513723i	0.00720111	−	0.0189878i
$733$	3.68372	+	4.15806i	0.136061	+	0.153582i	0.812592	−	0.582833i	$-0.198056\pi$
$733$	3.68372	+	4.15806i	0.136061	+	0.153582i	−0.676531	+	0.736415i	$0.736517\pi$
$734$	−73.4475	+	57.5424i	−2.71100	+	2.12393i
$735$	−0.814829	+	0.427655i	−0.0300554	+	0.0157743i
$736$	3.68987	−	4.16501i	0.136011	−	0.153524i
$737$	11.0390	+	49.2414i	0.406629	+	1.81383i
$738$	−5.53459	+	8.01823i	−0.203731	+	0.295155i
$739$	−6.42916	−	2.89353i	−0.236501	−	0.106440i	0.288697	−	0.957420i	$-0.406778\pi$
$739$	−6.42916	−	2.89353i	−0.236501	−	0.106440i	−0.525198	+	0.850980i	$0.676009\pi$
$740$	−11.7872	−	3.67304i	−0.433306	−	0.135023i
$741$		−	3.77538i		−	0.138692i
$742$	−6.08157	+	39.3198i	−0.223262	+	1.44348i
$743$		−	17.1476i		−	0.629083i	−0.949244	−	0.314541i	$-0.898149\pi$
$743$		−	17.1476i		−	0.629083i	0.949244	−	0.314541i	$-0.101851\pi$
$744$	10.5428	+	3.28527i	0.386518	+	0.120444i
$745$	5.34768	−	11.8821i	0.195924	−	0.435325i
$746$	−25.6176	−	17.6825i	−0.937926	−	0.647403i
$747$	1.57307	−	26.0060i	0.0575558	−	0.951511i
$748$	−88.9233	−	42.3022i	−3.25136	−	1.54672i
$749$	−3.20414	−	6.10497i	−0.117077	−	0.223071i
$750$	6.19954	+	7.91313i	0.226375	+	0.288947i
$751$	5.39002	+	6.08408i	0.196685	+	0.222011i	0.838576	−	0.544784i	$-0.183389\pi$
$751$	5.39002	+	6.08408i	0.196685	+	0.222011i	−0.641891	+	0.766795i	$0.721850\pi$
$752$	−12.4718	+	32.8854i	−0.454799	+	1.19921i
$753$	−1.09452	+	4.44064i	−0.0398865	+	0.161826i
$754$	20.4854	−	12.3838i	0.746034	−	0.450993i
$755$	11.8662	−	8.19065i	0.431856	−	0.298088i
$756$	5.37703	+	29.3415i	0.195561	+	1.06714i
$757$	−0.885601	−	0.464799i	−0.0321877	−	0.0168934i	0.448553	−	0.893756i	$-0.351940\pi$
$757$	−0.885601	−	0.464799i	−0.0321877	−	0.0168934i	−0.480740	+	0.876863i	$0.659632\pi$
$758$	−12.5577	+	4.76250i	−0.456115	+	0.172982i
$759$	−6.29410	+	2.67433i	−0.228461	+	0.0970721i
$760$	−8.19043	+	3.68621i	−0.297098	+	0.133713i
$761$	−4.74353	+	25.8846i	−0.171953	+	0.938316i	0.778546	+	0.627588i	$0.215958\pi$
$761$	−4.74353	+	25.8846i	−0.171953	+	0.938316i	−0.950499	+	0.310728i	$0.899427\pi$
$762$	3.45838	+	2.70947i	0.125284	+	0.0981537i
$763$	0.743739	+	12.2955i	0.0269252	+	0.445126i
$764$	54.7804	+	33.1159i	1.98188	+	1.19809i
$765$	10.0727	−	10.0727i	0.364178	−	0.364178i
$766$	−13.4766	−	54.6768i	−0.486930	−	1.97555i
$767$	−1.32126	+	10.8815i	−0.0477078	+	0.392909i
$768$	17.9187	−	5.58370i	0.646587	−	0.201485i
$769$	−50.4424	+	15.7185i	−1.81900	+	0.566824i	−0.999976	−	0.00693395i	$-0.997793\pi$
$769$	−50.4424	+	15.7185i	−1.81900	+	0.566824i	−0.819025	+	0.573758i	$0.805485\pi$
$770$	2.15629	+	13.3514i	0.0777073	+	0.481150i
$771$	−2.41938	−	9.81583i	−0.0871320	−	0.353508i
$772$	55.5345	+	55.5345i	1.99873	+	1.99873i
$773$	15.0685	−	24.9264i	0.541977	−	0.896539i	−0.457995	−	0.888955i	$-0.651432\pi$
$773$	15.0685	−	24.9264i	0.541977	−	0.896539i	0.999971	−	0.00758391i	$-0.00241406\pi$
$774$	−11.5614	+	0.699334i	−0.415565	+	0.0251370i
$775$	9.86133	−	12.5871i	0.354230	−	0.452141i
$776$	−72.5903	−	13.3027i	−2.60584	−	0.477538i
$777$	4.60836	−	2.07405i	0.165324	−	0.0744062i
$778$	−5.56387	+	0.675576i	−0.199474	+	0.0242206i
$779$	3.10570	−	1.17784i	0.111273	−	0.0422004i
$780$	4.58770	+	2.40781i	0.164266	+	0.0862134i
$781$	−10.2212	−	20.5167i	−0.365742	−	0.734144i
$782$	52.3300	−	36.1208i	1.87132	−	1.29168i
$783$	5.59962	+	9.26291i	0.200114	+	0.331029i
$784$	−10.2575	−	2.52825i	−0.366340	−	0.0902946i
$785$	−7.09894	−	2.69227i	−0.253372	−	0.0960913i
$786$	−7.36531	+	6.52509i	−0.262712	+	0.232742i
$787$	11.7363	−	9.19483i	0.418355	−	0.327760i	−0.385369	−	0.922763i	$-0.625926\pi$
$787$	11.7363	−	9.19483i	0.418355	−	0.327760i	0.803724	+	0.595002i	$0.202849\pi$
$788$	−40.0319	−	76.2745i	−1.42608	−	2.71717i
$789$	−10.7841	+	12.1727i	−0.383924	+	0.433361i
$790$	1.07588	−	17.7864i	0.0382780	−	0.632811i
$791$	−21.5966	−	14.9070i	−0.767886	−	0.530034i
$792$	−46.7447	−	6.68060i	−1.66100	−	0.237385i
$793$	−0.638847	−	0.199073i	−0.0226861	−	0.00706928i
$794$	46.6047			1.65394
$795$	−2.28046	+	2.13632i	−0.0808794	+	0.0757673i
$796$	24.1138			0.854691
$797$	−15.8747	+	50.9436i	−0.562309	+	1.80451i	0.0309751	+	0.999520i	$0.490139\pi$
$797$	−15.8747	+	50.9436i	−0.562309	+	1.80451i	−0.593284	+	0.804993i	$0.702169\pi$
$798$	2.91190	−	6.46998i	0.103080	−	0.229035i
$799$	−29.0025	+	42.0174i	−1.02604	+	1.48647i
$800$	−0.416483	+	6.88529i	−0.0147249	+	0.243432i
$801$	−12.3081	+	13.8929i	−0.434884	+	0.490883i
$802$	17.0956	−	8.97247i	0.603667	−	0.316829i
$803$	−40.4816	−	29.2239i	−1.42856	−	1.03129i
$804$	24.0923	+	27.1945i	0.849669	+	0.959078i
$805$	−5.51038	−	2.08981i	−0.194215	−	0.0736561i
$806$	6.21145	−	25.2008i	0.218789	−	0.887662i
$807$	−1.25037	−	2.06837i	−0.0440153	−	0.0728101i
$808$	25.6608	+	37.1761i	0.902744	+	1.30785i
$809$	−2.52345	−	13.7700i	−0.0887199	−	0.484129i	−0.997729	−	0.0673529i	$-0.978545\pi$
$809$	−2.52345	−	13.7700i	−0.0887199	−	0.484129i	0.909009	−	0.416776i	$-0.136840\pi$
$810$	5.27247	−	10.0458i	0.185256	−	0.352975i
$811$	30.6953	−	11.6412i	1.07786	−	0.408778i	0.249154	−	0.968464i	$-0.419847\pi$
$811$	30.6953	−	11.6412i	1.07786	−	0.408778i	0.828705	+	0.559686i	$0.189078\pi$
$812$	30.1369	−	3.65928i	1.05760	−	0.128416i
$813$	−4.38465	−	9.74228i	−0.153776	−	0.341677i
$814$	3.26400	+	32.6278i	0.114403	+	1.14360i
$815$	3.95760	+	3.10058i	0.138629	+	0.108609i
$816$	−20.2393	+	1.22425i	−0.708517	+	0.0428574i
$817$	3.37924	+	2.04282i	0.118225	+	0.0714692i
$818$	4.97006	+	4.97006i	0.173774	+	0.173774i
$819$	16.6076	−	4.09340i	0.580316	−	0.143035i
$820$	−0.549448	+	4.52511i	−0.0191876	+	0.158024i
$821$	−2.81530	−	9.03462i	−0.0982547	−	0.315310i	0.892487	−	0.451074i	$-0.148959\pi$
$821$	−2.81530	−	9.03462i	−0.0982547	−	0.315310i	−0.990741	+	0.135764i	$0.956651\pi$
$822$	17.0935	−	5.32655i	0.596204	−	0.185785i
$823$	5.64545	−	46.4945i	0.196788	−	1.62070i	−0.475023	−	0.879974i	$-0.657560\pi$
$823$	5.64545	−	46.4945i	0.196788	−	1.62070i	0.671811	−	0.740723i	$-0.265517\pi$
$824$	−6.53078	+	1.60969i	−0.227510	+	0.0560763i
$825$	4.09740	−	7.42161i	0.142653	−	0.258387i
$826$	−10.6570	+	17.6289i	−0.370806	+	0.613388i
$827$	−1.11681	−	18.4630i	−0.0388352	−	0.642022i	−0.964566	−	0.263840i	$-0.915011\pi$
$827$	−1.11681	−	18.4630i	−0.0388352	−	0.642022i	0.925731	−	0.378182i	$-0.123451\pi$
$828$	24.4899	−	31.2590i	0.851082	−	1.08633i
$829$	5.20695	−	28.4134i	0.180845	−	0.986838i	−0.760487	−	0.649354i	$-0.775039\pi$
$829$	5.20695	−	28.4134i	0.180845	−	0.986838i	0.941331	−	0.337484i	$-0.109576\pi$
$830$	−7.41324	−	16.4715i	−0.257317	−	0.571735i
$831$	1.28149	−	0.155602i	0.0444545	−	0.00539776i
$832$	−6.19255	−	16.3284i	−0.214688	−	0.566086i
$833$	−13.5791	−	7.12684i	−0.470486	−	0.246930i
$834$	2.72254	+	14.8564i	0.0942737	+	0.514435i
$835$	−0.210779	−	0.305366i	−0.00729432	−	0.0105676i
$836$	22.8141	+	21.0883i	0.789041	+	0.729352i
$837$	11.3951	+	2.80864i	0.393872	+	0.0970808i
$838$	−17.5132	+	46.1785i	−0.604984	+	1.59521i
$839$	−21.4819	+	19.0313i	−0.741638	+	0.657034i	−0.946847	−	0.321684i	$-0.895751\pi$
$839$	−21.4819	+	19.0313i	−0.741638	+	0.657034i	0.205209	+	0.978718i	$0.434213\pi$
$840$	3.11156	+	3.97161i	0.107359	+	0.137034i
$841$	−15.9244	+	8.35779i	−0.549118	+	0.288200i
$842$	−3.14852	+	3.55394i	−0.108505	+	0.122477i
$843$	14.5162	+	0.878068i	0.499965	+	0.0302423i
$844$	−84.9900	−	58.6644i	−2.92548	−	2.01931i
$845$	−1.39111	+	3.09092i	−0.0478557	+	0.106331i
$846$	−14.0562	+	45.1080i	−0.483263	+	1.55085i
$847$	20.5130	−	12.9150i	0.704835	−	0.443766i
$848$	−35.8594	+	0.996869i	−1.23142	+	0.0342326i
$849$			3.58134i			0.122911i
$850$	−23.4503	+	75.2547i	−0.804339	+	2.58121i
$851$	−13.0299	−	5.86430i	−0.446661	−	0.201026i
$852$	−13.5814	−	9.37455i	−0.465291	−	0.321167i
$853$	2.59047	−	42.8256i	0.0886961	−	1.46632i	−0.633022	−	0.774134i	$-0.718186\pi$
$853$	2.59047	−	42.8256i	0.0886961	−	1.46632i	0.721718	−	0.692187i	$-0.243353\pi$
$854$	−0.941268	−	0.833891i	−0.0322095	−	0.0285352i
$855$	−3.97942	+	2.08856i	−0.136093	+	0.0714272i
$856$	13.1377	−	10.2927i	0.449036	−	0.351797i
$857$	29.4155	−	26.0599i	1.00482	−	0.890189i	0.0108565	−	0.999941i	$-0.496544\pi$
$857$	29.4155	−	26.0599i	1.00482	−	0.890189i	0.993959	+	0.109752i	$0.0350057\pi$
$858$	1.12082	−	13.7151i	0.0382641	−	0.468226i
$859$	9.55497	−	38.7660i	0.326011	−	1.32268i	−0.547880	−	0.836557i	$-0.684565\pi$
$859$	9.55497	−	38.7660i	0.326011	−	1.32268i	0.873891	−	0.486122i	$-0.161589\pi$
$860$	−4.63751	+	2.80347i	−0.158138	+	0.0955977i
$861$	−1.05991	−	1.53555i	−0.0361218	−	0.0523314i
$862$	−56.6882	+	10.3885i	−1.93081	+	0.353834i
$863$	14.0510	+	7.37456i	0.478303	+	0.251033i	0.686604	−	0.727032i	$-0.259101\pi$
$863$	14.0510	+	7.37456i	0.478303	+	0.251033i	−0.208300	+	0.978065i	$0.566793\pi$
$864$	−4.73381	+	1.79530i	−0.161047	+	0.0610773i
$865$	−0.576679	−	4.74938i	−0.0196077	−	0.161484i
$866$	12.6145	+	28.0283i	0.428658	+	0.952439i
$867$	−19.3320	−	3.54273i	−0.656551	−	0.120317i
$868$	20.3004	−	25.9115i	0.689040	−	0.879494i
$869$	−30.0944	+	10.6918i	−1.02088	+	0.362695i
$870$	3.02354	+	1.82779i	0.102507	+	0.0619679i
$871$	31.2881	−	31.2881i	1.06016	−	1.06016i
$872$	−28.9506	+	7.13568i	−0.980390	+	0.241645i
$873$	−36.6578	−	4.45106i	−1.24068	−	0.150646i
$874$	−19.1527	+	5.96821i	−0.647848	+	0.201878i
$875$	14.8236	−	4.61923i	0.501130	−	0.156158i
$876$	−35.6838	−	4.33280i	−1.20564	−	0.146392i
$877$	34.1881	−	8.42661i	1.15445	−	0.284546i	0.384792	−	0.923003i	$-0.374273\pi$
$877$	34.1881	−	8.42661i	1.15445	−	0.284546i	0.769658	+	0.638457i	$0.220427\pi$
$878$	27.6021	−	27.6021i	0.931527	−	0.931527i
$879$	−1.15650	−	0.699131i	−0.0390079	−	0.0235811i
$880$	−11.4903	+	4.08221i	−0.387337	+	0.137611i
$881$	−21.9255	+	27.9858i	−0.738689	+	0.942867i	−0.999748	−	0.0224561i	$-0.992851\pi$
$881$	−21.9255	+	27.9858i	−0.738689	+	0.942867i	0.261059	+	0.965323i	$0.415928\pi$
$882$	−13.9595	−	2.55817i	−0.470040	−	0.0861380i
$883$	−10.7819	−	23.9564i	−0.362839	−	0.806196i	−0.999389	−	0.0349602i	$-0.988870\pi$
$883$	−10.7819	−	23.9564i	−0.362839	−	0.806196i	0.636549	−	0.771236i	$-0.280361\pi$
$884$	10.4076	+	85.7142i	0.350045	+	2.88288i
$885$	−1.51272	+	0.573698i	−0.0508494	+	0.0192846i
$886$	30.1738	+	15.8364i	1.01371	+	0.532035i
$887$	−29.2837	+	5.36644i	−0.983251	+	0.180188i	−0.647751	−	0.761852i	$-0.724290\pi$
$887$	−29.2837	+	5.36644i	−0.983251	+	0.180188i	−0.335501	+	0.942040i	$0.608906\pi$
$888$	6.94900	+	10.0674i	0.233193	+	0.337839i
$889$	5.80718	−	3.51056i	0.194767	−	0.117741i
$890$	−3.07955	+	12.4942i	−0.103227	+	0.418807i
$891$	−20.2671	−	1.65625i	−0.678973	−	0.0554866i
$892$	59.3634	−	52.5914i	1.98763	−	1.76089i
$893$	12.6796	−	9.93386i	0.424308	−	0.332424i
$894$	−22.0614	+	11.5787i	−0.737844	+	0.387251i
$895$	−10.3971	−	9.21105i	−0.347538	−	0.307892i
$896$	2.39464	−	39.5882i	0.0799994	−	1.32255i
$897$	4.93493	+	3.40633i	0.164772	+	0.113734i
$898$	69.2509	+	31.1673i	2.31093	+	1.04007i
$899$	3.55335	−	11.4031i	0.118511	−	0.380315i
$900$			49.2262i			1.64087i
$901$	−50.8880	−	11.0524i	−1.69532	−	0.368208i
$902$	11.6320	−	3.35681i	0.387302	−	0.111769i
$903$	0.659901	−	2.11770i	0.0219601	−	0.0704726i
$904$	26.0700	−	57.9251i	0.867074	−	1.92656i
$905$	14.0604	+	9.70521i	0.467385	+	0.322612i
$906$	−27.5201	−	1.66466i	−0.914293	−	0.0553046i
$907$	−23.4340	+	26.4515i	−0.778114	+	0.878309i	−0.995202	−	0.0978434i	$-0.968806\pi$
$907$	−23.4340	+	26.4515i	−0.778114	+	0.878309i	0.217088	+	0.976152i	$0.430344\pi$
$908$	93.7670	−	49.2127i	3.11177	−	1.63318i
$909$	13.9397	+	17.7927i	0.462349	+	0.590145i
$910$	8.87628	−	7.86370i	0.294246	−	0.260679i
$911$	12.5596	−	33.1171i	0.416120	−	1.09722i	−0.549096	−	0.835760i	$-0.685028\pi$
$911$	12.5596	−	33.1171i	0.416120	−	1.09722i	0.965215	−	0.261457i	$-0.0842031\pi$
$912$	6.21118	+	1.53092i	0.205673	+	0.0506938i
$913$	−21.9754	+	23.7738i	−0.727279	+	0.786798i
$914$	25.8591	+	37.4633i	0.855342	+	1.23918i
$915$	−0.0178024	−	0.0971446i	−0.000588530	−	0.00321150i
$916$	9.70863	+	5.09548i	0.320782	+	0.168359i
$917$	5.38943	+	14.2108i	0.177975	+	0.469281i
$918$	−57.4322	+	6.97353i	−1.89555	+	0.230161i
$919$	−14.1275	−	31.3901i	−0.466025	−	1.03546i	−0.983688	−	0.179881i	$-0.942429\pi$
$919$	−14.1275	−	31.3901i	−0.466025	−	1.03546i	0.517664	−	0.855584i	$-0.326802\pi$
$920$	2.57143	−	14.0319i	0.0847776	−	0.462616i
$921$	−2.50756	+	3.20067i	−0.0826271	+	0.105466i
$922$	−1.78064	−	29.4375i	−0.0586423	−	0.969472i
$923$	−10.3977	+	17.1999i	−0.342245	+	0.566142i
$924$	8.43485	−	15.2780i	0.277486	−	0.502610i
$925$	17.1983	−	4.23901i	0.565477	−	0.139378i
$926$	10.3991	−	85.6444i	0.341736	−	2.81445i
$927$	−3.21322	+	1.00128i	−0.105536	+	0.0328864i
$928$	1.53287	+	4.91915i	0.0503189	+	0.161479i
$929$	−0.738539	+	6.08242i	−0.0242307	+	0.199558i	−0.999797	−	0.0201474i	$-0.993586\pi$
$929$	−0.738539	+	6.08242i	−0.0242307	+	0.199558i	0.975566	+	0.219705i	$0.0705095\pi$
$930$	3.71951	−	0.916777i	0.121968	−	0.0300623i
$931$	3.42122	+	3.42122i	0.112126	+	0.112126i
$932$	18.2434	+	11.0285i	0.597583	+	0.361251i
$933$	0.993730	−	0.0601096i	0.0325333	−	0.00196790i
$934$	−71.9491	−	56.3685i	−2.35425	−	1.84443i
$935$	−17.6130	+	1.76196i	−0.576007	+	0.0576222i
$936$	16.9926	+	37.7560i	0.555420	+	1.23409i
$937$	−35.7749	+	4.34386i	−1.16872	+	0.141908i	−0.681798	−	0.731540i	$-0.738802\pi$
$937$	−35.7749	+	4.34386i	−1.16872	+	0.141908i	−0.486917	+	0.873448i	$0.661879\pi$
$938$	77.7514	−	29.4872i	2.53867	−	0.962792i
$939$	3.39012	−	6.45934i	0.110632	−	0.210792i
$940$	3.98460	+	21.7433i	0.129963	+	0.709187i
$941$	2.61329	+	3.78601i	0.0851910	+	0.123420i	0.863262	−	0.504755i	$-0.168417\pi$
$941$	2.61329	+	3.78601i	0.0851910	+	0.123420i	−0.778072	+	0.628176i	$0.783802\pi$
$942$	7.51053	+	12.4239i	0.244706	+	0.404794i
$943$	−1.26253	+	5.12227i	−0.0411135	+	0.166804i
$944$	−17.3663	−	6.58616i	−0.565224	−	0.214361i
$945$	3.55574	+	4.01360i	0.115668	+	0.130562i
$946$	11.6695	+	8.42430i	0.379409	+	0.273898i
$947$	24.6957	−	12.9613i	0.802504	−	0.421186i	−0.0130164	−	0.999915i	$-0.504143\pi$
$947$	24.6957	−	12.9613i	0.802504	−	0.421186i	0.815520	+	0.578729i	$0.196451\pi$
$948$	−15.2474	+	17.2108i	−0.495214	+	0.558981i
$949$	−2.64327	+	43.6985i	−0.0858042	+	1.41851i
$950$	14.1269	−	20.4664i	0.458338	−	0.664018i
$951$	−1.48751	+	3.30512i	−0.0482359	+	0.107176i
$952$	−25.0141	+	80.2732i	−0.810713	+	2.60167i
$953$	−38.1616			−1.23618			−0.618088	−	0.786109i	$-0.712092\pi$
$953$	−38.1616			−1.23618			−0.618088	+	0.786109i	$0.712092\pi$
$954$	−48.0034	+	4.24527i	−1.55417	+	0.137446i
$955$	11.5065			0.372342
$956$	93.9748	+	29.2837i	3.03936	+	0.947103i
$957$	0.895905	−	6.26872i	0.0289605	−	0.202639i
$958$	−63.4657	−	43.8072i	−2.05048	−	1.41535i
$959$	1.66972	−	27.6037i	0.0539179	−	0.891370i
$960$	1.70919	−	1.92927i	0.0551638	−	0.0622670i
$961$	8.38801	+	15.9820i	0.270581	+	0.515549i
$962$	22.6330	−	17.7318i	0.729717	−	0.571697i
$963$	6.25076	−	5.53769i	0.201428	−	0.178450i
$964$	−65.2608	−	24.7501i	−2.10191	−	0.797148i
$965$	13.7073	+	3.37855i	0.441254	+	0.108759i
$966$	5.82986	+	9.64377i	0.187573	+	0.310283i
$967$	0.439174	−	0.303140i	0.0141229	−	0.00974833i	−0.560982	−	0.827828i	$-0.689576\pi$
$967$	0.439174	−	0.303140i	0.0141229	−	0.00974833i	0.575105	+	0.818079i	$0.304961\pi$
$968$	39.7006	+	43.2055i	1.27603	+	1.38868i
$969$	8.22247	+	4.31548i	0.264144	+	0.138633i
$970$	−23.9377	+	9.07839i	−0.768595	+	0.291489i
$971$	−15.1836	+	1.84362i	−0.487265	+	0.0591647i	−0.360483	−	0.932766i	$-0.617388\pi$
$971$	−15.1836	+	1.84362i	−0.487265	+	0.0591647i	−0.126782	+	0.991931i	$0.540465\pi$
$972$	−50.3826	+	22.6754i	−1.61602	+	0.727313i
$973$	22.9466	+	4.20513i	0.735636	+	0.134810i
$974$	−22.9351	+	29.2745i	−0.734889	+	0.938016i
$975$	−7.41983	+	0.448817i	−0.237625	+	0.0143736i
$976$	0.586563	−	0.970294i	0.0187754	−	0.0310584i
$977$	1.63333	+	1.63333i	0.0522548	+	0.0522548i	0.732751	−	0.680496i	$-0.238236\pi$
$977$	1.63333	+	1.63333i	0.0522548	+	0.0522548i	−0.680496	+	0.732751i	$0.738236\pi$
$978$	−2.30064	−	9.33408i	−0.0735665	−	0.298471i
$979$	22.7689	−	3.67725i	0.727696	−	0.117525i
$980$	−6.33926	+	1.97539i	−0.202500	+	0.0631016i
$981$	−14.2440	+	4.43862i	−0.454777	+	0.141714i
$982$	0.514360	−	4.23613i	0.0164139	−	0.135180i
$983$	10.0985	+	40.9711i	0.322091	+	1.30678i	0.879246	+	0.476368i	$0.158047\pi$
$983$	10.0985	+	40.9711i	0.322091	+	1.30678i	−0.557155	+	0.830409i	$0.688107\pi$
$984$	3.19362	−	3.19362i	0.101809	−	0.101809i
$985$	−13.2512	−	8.01065i	−0.422220	−	0.255241i
$986$	3.55499	+	58.7709i	0.113214	+	1.87165i
$987$	−7.12260	−	5.58020i	−0.226715	−	0.177620i
$988$	4.91034	−	26.7948i	0.156219	−	0.852457i
$989$	−5.71915	+	2.57398i	−0.181858	+	0.0818478i
$990$	−15.0763	+	6.40586i	−0.479157	+	0.203592i
$991$	−3.20022	+	1.21368i	−0.101658	+	0.0385539i	−0.404910	−	0.914357i	$-0.632697\pi$
$991$	−3.20022	+	1.21368i	−0.101658	+	0.0385539i	0.303251	+	0.952911i	$0.401928\pi$
$992$	4.94676	+	2.59626i	0.157060	+	0.0824313i
$993$	−1.99145	−	10.8670i	−0.0631967	−	0.344853i
$994$	−31.0849	+	21.4564i	−0.985953	+	0.680554i
$995$	3.70945	−	2.24244i	0.117598	−	0.0710902i
$996$	−5.57802	+	22.6309i	−0.176746	+	0.717089i
$997$	20.8882	−	55.0775i	0.661534	−	1.74432i	−0.00626376	−	0.999980i	$-0.501994\pi$
$997$	20.8882	−	55.0775i	0.661534	−	1.74432i	0.667798	−	0.744342i	$-0.267237\pi$
$998$	−22.5207	−	25.4207i	−0.712882	−	0.804677i
$999$	8.01782	+	10.2340i	0.253673	+	0.323789i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	583.2.q.b.21.5	✓	1200
11.10	odd	2	inner	583.2.q.b.21.46	yes	1200
53.48	odd	52	inner	583.2.q.b.472.46	yes	1200
583.472	even	52	inner	583.2.q.b.472.5	yes	1200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
583.2.q.b.21.5	✓	1200	1.1	even	1	trivial
583.2.q.b.21.46	yes	1200	11.10	odd	2	inner
583.2.q.b.472.5	yes	1200	583.472	even	52	inner
583.2.q.b.472.46	yes	1200	53.48	odd	52	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 583 = 11 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	583.q (of order \(52\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.36779 - 0.737832i) q^{2} +(0.524586 + 0.236097i) q^{3} +(3.41604 + 2.35793i) q^{4} +(0.744767 + 0.0450501i) q^{5} +(-1.06791 - 0.946083i) q^{6} +(-1.95123 + 1.02408i) q^{7} +(-3.28968 - 4.19897i) q^{8} +(-1.76992 - 1.99783i) q^{9} +(-1.73021 - 0.656182i) q^{10} +(0.130277 + 3.31407i) q^{11} +(1.23531 + 2.04345i) q^{12} +(2.39334 - 1.65200i) q^{13} +(5.37569 - 0.985132i) q^{14} +(0.380058 + 0.199470i) q^{15} +(1.74734 + 4.60735i) q^{16} +(0.862195 + 7.10082i) q^{17} +(2.71673 + 6.03633i) q^{18} +(0.406787 - 2.21976i) q^{19} +(2.43793 + 1.91000i) q^{20} +(-1.26537 + 0.0765408i) q^{21} +(2.13675 - 7.94312i) q^{22} +(2.53450 + 2.53450i) q^{23} +(-0.734357 - 2.97941i) q^{24} +(-4.41090 - 0.535580i) q^{25} +(-6.88580 + 2.14570i) q^{26} +(-0.970226 - 3.11356i) q^{27} +(-9.08020 - 1.10254i) q^{28} +(-3.22253 + 0.794281i) q^{29} +(-0.752721 - 0.752721i) q^{30} +(-1.86173 + 3.07969i) q^{31} +(-0.0937330 - 1.54959i) q^{32} +(-0.714099 + 1.76927i) q^{33} +(3.19771 - 17.4494i) q^{34} +(-1.49935 + 0.674801i) q^{35} +(-1.33540 - 10.9980i) q^{36} +(-3.72741 + 1.41362i) q^{37} +(-2.60099 + 4.95578i) q^{38} +(1.64554 - 0.301557i) q^{39} +(-2.26088 - 3.27545i) q^{40} +(0.761441 + 1.25958i) q^{41} +(3.05260 + 0.752399i) q^{42} +(-0.620471 + 1.63605i) q^{43} +(-7.36928 + 11.6282i) q^{44} +(-1.22818 - 1.56765i) q^{45} +(-4.13112 - 7.87119i) q^{46} +(5.34256 + 4.73310i) q^{47} +(-0.171153 + 2.82949i) q^{48} +(-1.21791 + 1.76444i) q^{49} +(10.0489 + 4.52264i) q^{50} +(-1.22419 + 3.92855i) q^{51} +12.0710 q^{52} +(-2.39141 + 6.87613i) q^{53} +8.08811i q^{54} +(-0.0522726 + 2.47408i) q^{55} +(10.7190 + 4.82424i) q^{56} +(0.737474 - 1.06842i) q^{57} +(8.21630 + 0.496994i) q^{58} +(-2.49948 + 2.82133i) q^{59} +(0.827961 + 1.57755i) q^{60} +(-0.141904 - 0.181127i) q^{61} +(6.68048 - 5.91839i) q^{62} +(5.49946 + 2.08567i) q^{63} +(1.43709 - 5.83050i) q^{64} +(1.85690 - 1.12254i) q^{65} +(2.99626 - 3.66237i) q^{66} +(14.9661 - 2.74264i) q^{67} +(-13.7979 + 26.2897i) q^{68} +(0.731176 + 1.92795i) q^{69} +(4.04802 - 0.491519i) q^{70} +(-6.30228 + 2.83643i) q^{71} +(-2.56634 + 14.0040i) q^{72} +(-9.28398 + 11.8501i) q^{73} +(9.86872 - 0.596948i) q^{74} +(-2.18745 - 1.32236i) q^{75} +(6.62364 - 6.62364i) q^{76} +(-3.64808 - 6.33308i) q^{77} +(-4.11879 - 0.500112i) q^{78} +(2.86479 + 9.19344i) q^{79} +(1.09380 + 3.51012i) q^{80} +(-0.739025 + 6.08642i) q^{81} +(-0.873572 - 3.54422i) q^{82} +(6.90228 + 6.90228i) q^{83} +(-4.50304 - 2.72218i) q^{84} +(0.322242 + 5.32730i) q^{85} +(2.67627 - 3.41601i) q^{86} +(-1.87802 - 0.344160i) q^{87} +(13.4871 - 11.4493i) q^{88} +(-0.838215 - 6.90332i) q^{89} +(1.75139 + 4.61805i) q^{90} +(-2.97816 + 5.67441i) q^{91} +(2.68180 + 14.6341i) q^{92} +(-1.70374 + 1.17601i) q^{93} +(-9.15782 - 15.1489i) q^{94} +(0.402962 - 1.63488i) q^{95} +(0.316683 - 0.835024i) q^{96} +(10.3558 - 9.17442i) q^{97} +(4.18560 - 3.27921i) q^{98} +(6.39034 - 6.12590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1200 q - 48 q^{3} - 52 q^{4} - 44 q^{5} - 52 q^{9} - 26 q^{11} - 64 q^{12} - 28 q^{14} - 28 q^{15} + 72 q^{16} - 52 q^{20} - 12 q^{22} - 68 q^{23} - 52 q^{25} - 80 q^{26} - 72 q^{27} - 56 q^{31} - 28 q^{33}+ \cdots - 258 q^{99}+O(q^{100}) \) 1200 * q - 48 * q^3 - 52 * q^4 - 44 * q^5 - 52 * q^9 - 26 * q^11 - 64 * q^12 - 28 * q^14 - 28 * q^15 + 72 * q^16 - 52 * q^20 - 12 * q^22 - 68 * q^23 - 52 * q^25 - 80 * q^26 - 72 * q^27 - 56 * q^31 - 28 * q^33 - 40 * q^34 - 144 * q^36 - 52 * q^37 - 52 * q^38 + 164 * q^42 - 150 * q^44 + 224 * q^45 - 36 * q^47 - 128 * q^48 - 180 * q^49 + 56 * q^53 - 124 * q^55 + 220 * q^56 - 104 * q^59 - 520 * q^60 + 156 * q^64 - 70 * q^66 + 12 * q^67 - 36 * q^69 - 52 * q^70 - 68 * q^71 + 8 * q^75 - 38 * q^77 - 52 * q^78 - 80 * q^80 + 40 * q^81 - 52 * q^82 - 48 * q^86 - 138 * q^88 - 12 * q^89 - 52 * q^91 - 144 * q^92 + 156 * q^93 + 36 * q^97 - 258 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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