LMFDB - Embedded newform 230.2.e.b.137.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(137,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("230.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.e (of order $4$, 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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.110166016.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 10x^{6} + 19x^{4} + 10x^{2} + 1 $ x^8 + 10x^6 + 19x^4 + 10*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			137.2
Root			$2.77462i$ of defining polynomial
Character	$\chi$	$=$	230.137
Dual form			230.2.e.b.183.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(0.254848 - 0.254848i) q^{3} +1.00000i q^{4} +(1.36041 - 1.77462i) q^{5} -0.360409 q^{6} +(0.812668 - 0.812668i) q^{7} +(0.707107 - 0.707107i) q^{8} +2.87011i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(0.254848 - 0.254848i) q^{3} +1.00000i q^{4} +(1.36041 - 1.77462i) q^{5} -0.360409 q^{6} +(0.812668 - 0.812668i) q^{7} +(0.707107 - 0.707107i) q^{8} +2.87011i q^{9} +(-2.21680 + 0.292893i) q^{10} -3.05380i q^{11} +(0.254848 + 0.254848i) q^{12} +(0.697028 - 0.697028i) q^{13} -1.14929 q^{14} +(-0.105561 - 0.798956i) q^{15} -1.00000 q^{16} +(2.89444 - 2.89444i) q^{17} +(2.02947 - 2.02947i) q^{18} -2.26493 q^{19} +(1.77462 + 1.36041i) q^{20} -0.414214i q^{21} +(-2.15937 + 2.15937i) q^{22} +(1.84214 - 4.42793i) q^{23} -0.360409i q^{24} +(-1.29857 - 4.82843i) q^{25} -0.985746 q^{26} +(1.49598 + 1.49598i) q^{27} +(0.812668 + 0.812668i) q^{28} +6.96346i q^{29} +(-0.490304 + 0.639591i) q^{30} -0.938164 q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.778256 - 0.778256i) q^{33} -4.09335 q^{34} +(-0.336618 - 2.54774i) q^{35} -2.87011 q^{36} +(-4.39193 + 4.39193i) q^{37} +(1.60155 + 1.60155i) q^{38} -0.355272i q^{39} +(-0.292893 - 2.21680i) q^{40} -3.69853 q^{41} +(-0.292893 + 0.292893i) q^{42} +(2.58289 + 2.58289i) q^{43} +3.05380 q^{44} +(5.09335 + 3.90452i) q^{45} +(-4.43361 + 1.82843i) q^{46} +(0.923909 + 0.923909i) q^{47} +(-0.254848 + 0.254848i) q^{48} +5.67914i q^{49} +(-2.49598 + 4.33244i) q^{50} -1.47528i q^{51} +(0.697028 + 0.697028i) q^{52} +(8.88737 + 8.88737i) q^{53} -2.11564i q^{54} +(-5.41935 - 4.15442i) q^{55} -1.14929i q^{56} +(-0.577212 + 0.577212i) q^{57} +(4.92391 - 4.92391i) q^{58} +4.22248i q^{59} +(0.798956 - 0.105561i) q^{60} +10.6590i q^{61} +(0.663382 + 0.663382i) q^{62} +(2.33244 + 2.33244i) q^{63} -1.00000i q^{64} +(-0.288718 - 2.18520i) q^{65} +1.10062i q^{66} +(-2.79478 + 2.79478i) q^{67} +(2.89444 + 2.89444i) q^{68} +(-0.658982 - 1.59791i) q^{69} +(-1.56350 + 2.03955i) q^{70} +4.55438 q^{71} +(2.02947 + 2.02947i) q^{72} +(0.803131 - 0.803131i) q^{73} +6.21112 q^{74} +(-1.56145 - 0.899576i) q^{75} -2.26493i q^{76} +(-2.48173 - 2.48173i) q^{77} +(-0.251215 + 0.251215i) q^{78} -16.8702 q^{79} +(-1.36041 + 1.77462i) q^{80} -7.84782 q^{81} +(2.61526 + 2.61526i) q^{82} +(-8.37177 - 8.37177i) q^{83} +0.414214 q^{84} +(-1.19892 - 9.07416i) q^{85} -3.65276i q^{86} +(1.77462 + 1.77462i) q^{87} +(-2.15937 - 2.15937i) q^{88} +9.61955 q^{89} +(-0.840634 - 6.36246i) q^{90} -1.13290i q^{91} +(4.42793 + 1.84214i) q^{92} +(-0.239089 + 0.239089i) q^{93} -1.30661i q^{94} +(-3.08123 + 4.01939i) q^{95} +0.360409 q^{96} +(4.17254 - 4.17254i) q^{97} +(4.01576 - 4.01576i) q^{98} +8.76474 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} + 4 q^{5} + 4 q^{6}+O(q^{10}) $ 8 * q - 4 * q^3 + 4 * q^5 + 4 * q^6	$ 8 q - 4 q^{3} + 4 q^{5} + 4 q^{6} - 4 q^{12} - 4 q^{14} - 8 q^{16} + 24 q^{17} - 8 q^{18} - 12 q^{19} - 4 q^{20} - 12 q^{22} - 16 q^{23} + 12 q^{26} + 8 q^{27} - 16 q^{30} - 4 q^{31} + 20 q^{33} - 4 q^{34} - 4 q^{35} - 4 q^{36} + 4 q^{37} + 8 q^{38} - 8 q^{40} + 12 q^{41} - 8 q^{42} - 20 q^{43} + 20 q^{44} + 12 q^{45} - 16 q^{47} + 4 q^{48} - 16 q^{50} + 12 q^{55} + 20 q^{57} + 16 q^{58} + 8 q^{60} + 4 q^{62} + 12 q^{65} - 4 q^{67} + 24 q^{68} + 12 q^{69} + 4 q^{70} - 44 q^{71} - 8 q^{72} + 28 q^{73} + 48 q^{74} - 4 q^{75} + 4 q^{77} - 4 q^{78} + 8 q^{79} - 4 q^{80} - 16 q^{81} + 8 q^{82} - 28 q^{83} - 8 q^{84} + 20 q^{85} - 4 q^{87} - 12 q^{88} - 40 q^{89} - 12 q^{90} + 16 q^{92} - 12 q^{93} - 4 q^{95} - 4 q^{96} - 8 q^{97} + 16 q^{98} - 36 q^{99}+O(q^{100}) $ 8 * q - 4 * q^3 + 4 * q^5 + 4 * q^6 - 4 * q^12 - 4 * q^14 - 8 * q^16 + 24 * q^17 - 8 * q^18 - 12 * q^19 - 4 * q^20 - 12 * q^22 - 16 * q^23 + 12 * q^26 + 8 * q^27 - 16 * q^30 - 4 * q^31 + 20 * q^33 - 4 * q^34 - 4 * q^35 - 4 * q^36 + 4 * q^37 + 8 * q^38 - 8 * q^40 + 12 * q^41 - 8 * q^42 - 20 * q^43 + 20 * q^44 + 12 * q^45 - 16 * q^47 + 4 * q^48 - 16 * q^50 + 12 * q^55 + 20 * q^57 + 16 * q^58 + 8 * q^60 + 4 * q^62 + 12 * q^65 - 4 * q^67 + 24 * q^68 + 12 * q^69 + 4 * q^70 - 44 * q^71 - 8 * q^72 + 28 * q^73 + 48 * q^74 - 4 * q^75 + 4 * q^77 - 4 * q^78 + 8 * q^79 - 4 * q^80 - 16 * q^81 + 8 * q^82 - 28 * q^83 - 8 * q^84 + 20 * q^85 - 4 * q^87 - 12 * q^88 - 40 * q^89 - 12 * q^90 + 16 * q^92 - 12 * q^93 - 4 * q^95 - 4 * q^96 - 8 * q^97 + 16 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	0.254848	−	0.254848i	0.147136	−	0.147136i	−0.629701	−	0.776838i	$-0.716823\pi$
$3$	0.254848	−	0.254848i	0.147136	−	0.147136i	0.776838	+	0.629701i	$0.216823\pi$
$4$			1.00000i			0.500000i
$5$	1.36041	−	1.77462i	0.608394	−	0.793635i
$5$	1.36041	−	1.77462i	0.608394	−	0.793635i
$6$	−0.360409			−0.147136
$7$	0.812668	−	0.812668i	0.307160	−	0.307160i	−0.536647	−	0.843807i	$-0.680309\pi$
$7$	0.812668	−	0.812668i	0.307160	−	0.307160i	0.843807	+	0.536647i	$0.180309\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$			2.87011i			0.956702i
$10$	−2.21680	+	0.292893i	−0.701015	+	0.0926210i
$11$		−	3.05380i		−	0.920757i	−0.887723	−	0.460378i	$-0.847714\pi$
$11$		−	3.05380i		−	0.920757i	0.887723	−	0.460378i	$-0.152286\pi$
$12$	0.254848	+	0.254848i	0.0735682	+	0.0735682i
$13$	0.697028	−	0.697028i	0.193321	−	0.193321i	−0.603809	−	0.797129i	$-0.706351\pi$
$13$	0.697028	−	0.697028i	0.193321	−	0.193321i	0.797129	+	0.603809i	$0.206351\pi$
$14$	−1.14929			−0.307160
$15$	−0.105561	−	0.798956i	−0.0272558	−	0.206290i
$16$	−1.00000			−0.250000
$17$	2.89444	−	2.89444i	0.702004	−	0.702004i	−0.262836	−	0.964841i	$-0.584658\pi$
$17$	2.89444	−	2.89444i	0.702004	−	0.702004i	0.964841	+	0.262836i	$0.0846578\pi$
$18$	2.02947	−	2.02947i	0.478351	−	0.478351i
$19$	−2.26493			−0.519610			−0.259805	−	0.965661i	$-0.583658\pi$
$19$	−2.26493			−0.519610			−0.259805	+	0.965661i	$0.583658\pi$
$20$	1.77462	+	1.36041i	0.396818	+	0.304197i
$21$		−	0.414214i		−	0.0903888i
$22$	−2.15937	+	2.15937i	−0.460378	+	0.460378i
$23$	1.84214	−	4.42793i	0.384113	−	0.923286i
$23$	1.84214	−	4.42793i	0.384113	−	0.923286i
$24$		−	0.360409i		−	0.0735682i
$25$	−1.29857	−	4.82843i	−0.259715	−	0.965685i
$26$	−0.985746			−0.193321
$27$	1.49598	+	1.49598i	0.287902	+	0.287902i
$28$	0.812668	+	0.812668i	0.153580	+	0.153580i
$29$			6.96346i			1.29308i	0.762879	+	0.646541i	$0.223785\pi$
$29$			6.96346i			1.29308i	−0.762879	+	0.646541i	$0.776215\pi$
$30$	−0.490304	+	0.639591i	−0.0895169	+	0.116773i
$31$	−0.938164			−0.168499			−0.0842496	−	0.996445i	$-0.526849\pi$
$31$	−0.938164			−0.168499			−0.0842496	+	0.996445i	$0.526849\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−0.778256	−	0.778256i	−0.135477	−	0.135477i
$34$	−4.09335			−0.702004
$35$	−0.336618	−	2.54774i	−0.0568989	−	0.430647i
$36$	−2.87011			−0.478351
$37$	−4.39193	+	4.39193i	−0.722028	+	0.722028i	−0.969018	−	0.246990i	$-0.920559\pi$
$37$	−4.39193	+	4.39193i	−0.722028	+	0.722028i	0.246990	+	0.969018i	$0.420559\pi$
$38$	1.60155	+	1.60155i	0.259805	+	0.259805i
$39$		−	0.355272i		−	0.0568890i
$40$	−0.292893	−	2.21680i	−0.0463105	−	0.350507i
$41$	−3.69853			−0.577614			−0.288807	−	0.957387i	$-0.593259\pi$
$41$	−3.69853			−0.577614			−0.288807	+	0.957387i	$0.593259\pi$
$42$	−0.292893	+	0.292893i	−0.0451944	+	0.0451944i
$43$	2.58289	+	2.58289i	0.393887	+	0.393887i	0.876070	−	0.482183i	$-0.160156\pi$
$43$	2.58289	+	2.58289i	0.393887	+	0.393887i	−0.482183	+	0.876070i	$0.660156\pi$
$44$	3.05380			0.460378
$45$	5.09335	+	3.90452i	0.759272	+	0.582051i
$46$	−4.43361	+	1.82843i	−0.653699	+	0.269587i
$47$	0.923909	+	0.923909i	0.134766	+	0.134766i	0.771272	−	0.636506i	$-0.219621\pi$
$47$	0.923909	+	0.923909i	0.134766	+	0.134766i	−0.636506	+	0.771272i	$0.719621\pi$
$48$	−0.254848	+	0.254848i	−0.0367841	+	0.0367841i
$49$			5.67914i			0.811306i
$50$	−2.49598	+	4.33244i	−0.352985	+	0.612700i
$51$		−	1.47528i		−	0.206581i
$52$	0.697028	+	0.697028i	0.0966603	+	0.0966603i
$53$	8.88737	+	8.88737i	1.22077	+	1.22077i	0.967357	+	0.253417i	$0.0815544\pi$
$53$	8.88737	+	8.88737i	1.22077	+	1.22077i	0.253417	+	0.967357i	$0.418446\pi$
$54$		−	2.11564i		−	0.287902i
$55$	−5.41935	−	4.15442i	−0.730745	−	0.560182i
$56$		−	1.14929i		−	0.153580i
$57$	−0.577212	+	0.577212i	−0.0764536	+	0.0764536i
$58$	4.92391	−	4.92391i	0.646541	−	0.646541i
$59$			4.22248i			0.549720i	0.961484	+	0.274860i	$0.0886316\pi$
$59$			4.22248i			0.549720i	−0.961484	+	0.274860i	$0.911368\pi$
$60$	0.798956	−	0.105561i	0.103145	−	0.0136279i
$61$			10.6590i			1.36474i	0.731006	+	0.682371i	$0.239051\pi$
$61$			10.6590i			1.36474i	−0.731006	+	0.682371i	$0.760949\pi$
$62$	0.663382	+	0.663382i	0.0842496	+	0.0842496i
$63$	2.33244	+	2.33244i	0.293860	+	0.293860i
$64$		−	1.00000i		−	0.125000i
$65$	−0.288718	−	2.18520i	−0.0358111	−	0.271041i
$66$			1.10062i			0.135477i
$67$	−2.79478	+	2.79478i	−0.341437	+	0.341437i	−0.856907	−	0.515470i	$-0.827617\pi$
$67$	−2.79478	+	2.79478i	−0.341437	+	0.341437i	0.515470	+	0.856907i	$0.327617\pi$
$68$	2.89444	+	2.89444i	0.351002	+	0.351002i
$69$	−0.658982	−	1.59791i	−0.0793321	−	0.192366i
$70$	−1.56350	+	2.03955i	−0.186874	+	0.243773i
$71$	4.55438			0.540506			0.270253	−	0.962789i	$-0.412893\pi$
$71$	4.55438			0.540506			0.270253	+	0.962789i	$0.412893\pi$
$72$	2.02947	+	2.02947i	0.239175	+	0.239175i
$73$	0.803131	−	0.803131i	0.0939994	−	0.0939994i	−0.658543	−	0.752543i	$-0.728827\pi$
$73$	0.803131	−	0.803131i	0.0939994	−	0.0939994i	0.752543	+	0.658543i	$0.228827\pi$
$74$	6.21112			0.722028
$75$	−1.56145	−	0.899576i	−0.180301	−	0.103874i
$76$		−	2.26493i		−	0.259805i
$77$	−2.48173	−	2.48173i	−0.282819	−	0.282819i
$78$	−0.251215	+	0.251215i	−0.0284445	+	0.0284445i
$79$	−16.8702			−1.89805			−0.949024	−	0.315204i	$-0.897927\pi$
$79$	−16.8702			−1.89805			−0.949024	+	0.315204i	$0.897927\pi$
$80$	−1.36041	+	1.77462i	−0.152098	+	0.198409i
$81$	−7.84782			−0.871980
$82$	2.61526	+	2.61526i	0.288807	+	0.288807i
$83$	−8.37177	−	8.37177i	−0.918921	−	0.918921i	0.0780300	−	0.996951i	$-0.475137\pi$
$83$	−8.37177	−	8.37177i	−0.918921	−	0.918921i	−0.996951	+	0.0780300i	$0.975137\pi$
$84$	0.414214			0.0451944
$85$	−1.19892	−	9.07416i	−0.130041	−	0.984231i
$86$		−	3.65276i		−	0.393887i
$87$	1.77462	+	1.77462i	0.190260	+	0.190260i
$88$	−2.15937	−	2.15937i	−0.230189	−	0.230189i
$89$	9.61955			1.01967			0.509835	−	0.860272i	$-0.329706\pi$
$89$	9.61955			1.01967			0.509835	+	0.860272i	$0.329706\pi$
$90$	−0.840634	−	6.36246i	−0.0886106	−	0.670662i
$91$		−	1.13290i		−	0.118761i
$92$	4.42793	+	1.84214i	0.461643	+	0.192056i
$93$	−0.239089	+	0.239089i	−0.0247924	+	0.0247924i
$94$		−	1.30661i		−	0.134766i
$95$	−3.08123	+	4.01939i	−0.316127	+	0.412381i
$96$	0.360409			0.0367841
$97$	4.17254	−	4.17254i	0.423657	−	0.423657i	−0.462804	−	0.886461i	$-0.653157\pi$
$97$	4.17254	−	4.17254i	0.423657	−	0.423657i	0.886461	+	0.462804i	$0.153157\pi$
$98$	4.01576	−	4.01576i	0.405653	−	0.405653i
$99$	8.76474			0.880889
$100$	4.82843	−	1.29857i	0.482843	−	0.129857i
$101$	10.6002			1.05475			0.527377	−	0.849631i	$-0.323175\pi$
$101$	10.6002			1.05475			0.527377	+	0.849631i	$0.323175\pi$
$102$	−1.04318	+	1.04318i	−0.103290	+	0.103290i
$103$	−10.4631	−	10.4631i	−1.03096	−	1.03096i	−0.999505	−	0.0314522i	$-0.989987\pi$
$103$	−10.4631	−	10.4631i	−1.03096	−	1.03096i	−0.0314522	−	0.999505i	$-0.510013\pi$
$104$		−	0.985746i		−	0.0966603i
$105$	−0.735073	−	0.563500i	−0.0717358	−	0.0549920i
$106$		−	12.5686i		−	1.22077i
$107$	−7.30661	+	7.30661i	−0.706356	+	0.706356i	−0.965767	−	0.259411i	$-0.916472\pi$
$107$	−7.30661	+	7.30661i	−0.706356	+	0.706356i	0.259411	+	0.965767i	$0.416472\pi$
$108$	−1.49598	+	1.49598i	−0.143951	+	0.143951i
$109$	−3.93013			−0.376438			−0.188219	−	0.982127i	$-0.560272\pi$
$109$	−3.93013			−0.376438			−0.188219	+	0.982127i	$0.560272\pi$
$110$	0.894439	+	6.76968i	0.0852814	+	0.645464i
$111$			2.23855i			0.212473i
$112$	−0.812668	+	0.812668i	−0.0767899	+	0.0767899i
$113$	−2.02016	−	2.02016i	−0.190041	−	0.190041i	0.605673	−	0.795714i	$-0.292904\pi$
$113$	−2.02016	−	2.02016i	−0.190041	−	0.190041i	−0.795714	+	0.605673i	$0.792904\pi$
$114$	0.816301			0.0764536
$115$	−5.35183	−	9.29289i	−0.499061	−	0.866567i
$116$	−6.96346			−0.646541
$117$	2.00054	+	2.00054i	0.184950	+	0.184950i
$118$	2.98575	−	2.98575i	0.274860	−	0.274860i
$119$		−	4.70444i		−	0.431255i
$120$	−0.639591	−	0.490304i	−0.0583864	−	0.0447584i
$121$	1.67428			0.152207
$122$	7.53704	−	7.53704i	0.682371	−	0.682371i
$123$	−0.942563	+	0.942563i	−0.0849881	+	0.0849881i
$124$		−	0.938164i		−	0.0842496i
$125$	−10.3352	−	4.26416i	−0.924411	−	0.381398i
$126$		−	3.29857i		−	0.293860i
$127$	5.81630	+	5.81630i	0.516113	+	0.516113i	0.916393	−	0.400280i	$-0.131087\pi$
$127$	5.81630	+	5.81630i	0.516113	+	0.516113i	−0.400280	+	0.916393i	$0.631087\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	1.31649			0.115910
$130$	−1.34102	+	1.74933i	−0.117615	+	0.153426i
$131$	12.5442			1.09599			0.547997	−	0.836480i	$-0.315391\pi$
$131$	12.5442			1.09599			0.547997	+	0.836480i	$0.315391\pi$
$132$	0.778256	−	0.778256i	0.0677385	−	0.0677385i
$133$	−1.84063	+	1.84063i	−0.159603	+	0.159603i
$134$	3.95242			0.341437
$135$	4.68996	−	0.619657i	0.403647	−	0.0533316i
$136$		−	4.09335i		−	0.351002i
$137$	8.61881	−	8.61881i	0.736355	−	0.736355i	−0.235516	−	0.971870i	$-0.575678\pi$
$137$	8.61881	−	8.61881i	0.736355	−	0.736355i	0.971870	+	0.235516i	$0.0756780\pi$
$138$	−0.663924	+	1.59587i	−0.0565170	+	0.135849i
$139$		−	19.4875i		−	1.65291i	−0.563003	−	0.826455i	$-0.690354\pi$
$139$		−	19.4875i		−	1.65291i	0.563003	−	0.826455i	$-0.309646\pi$
$140$	2.54774	−	0.336618i	0.215323	−	0.0284494i
$141$	0.470913			0.0396580
$142$	−3.22044	−	3.22044i	−0.270253	−	0.270253i
$143$	−2.12859	−	2.12859i	−0.178001	−	0.178001i
$144$		−	2.87011i		−	0.239175i
$145$	12.3575	+	9.47316i	1.02624	+	0.786703i
$146$	−1.13580			−0.0939994
$147$	1.44732	+	1.44732i	0.119373	+	0.119373i
$148$	−4.39193	−	4.39193i	−0.361014	−	0.361014i
$149$	−16.8925			−1.38389			−0.691944	−	0.721951i	$-0.743246\pi$
$149$	−16.8925			−1.38389			−0.691944	+	0.721951i	$0.743246\pi$
$150$	0.468018	+	1.74021i	0.0382135	+	0.142088i
$151$	12.0934			0.984143			0.492072	−	0.870555i	$-0.336240\pi$
$151$	12.0934			0.984143			0.492072	+	0.870555i	$0.336240\pi$
$152$	−1.60155	+	1.60155i	−0.129902	+	0.129902i
$153$	8.30734	+	8.30734i	0.671609	+	0.671609i
$154$			3.50970i			0.282819i
$155$	−1.27629	+	1.66489i	−0.102514	+	0.133727i
$156$	0.355272			0.0284445
$157$	−3.53712	+	3.53712i	−0.282293	+	0.282293i	−0.834023	−	0.551730i	$-0.813968\pi$
$157$	−3.53712	+	3.53712i	−0.282293	+	0.282293i	0.551730	+	0.834023i	$0.313968\pi$
$158$	11.9290	+	11.9290i	0.949024	+	0.949024i
$159$	4.52985			0.359241
$160$	2.21680	−	0.292893i	0.175254	−	0.0231552i
$161$	−2.10139	−	5.09548i	−0.165612	−	0.401580i
$162$	5.54925	+	5.54925i	0.435990	+	0.435990i
$163$	−7.99239	+	7.99239i	−0.626012	+	0.626012i	−0.947062	−	0.321050i	$-0.895964\pi$
$163$	−7.99239	+	7.99239i	−0.626012	+	0.626012i	0.321050	+	0.947062i	$0.395964\pi$
$164$		−	3.69853i		−	0.288807i
$165$	−2.43986	+	0.322364i	−0.189943	+	0.0250960i
$166$			11.8395i			0.918921i
$167$	−13.0165	−	13.0165i	−1.00725	−	1.00725i	−0.999974	−	0.00727320i	$-0.997685\pi$
$167$	−13.0165	−	13.0165i	−1.00725	−	1.00725i	−0.00727320	−	0.999974i	$-0.502315\pi$
$168$	−0.292893	−	0.292893i	−0.0225972	−	0.0225972i
$169$			12.0283i			0.925254i
$170$	−5.56864	+	7.26416i	−0.427095	+	0.557136i
$171$		−	6.50058i		−	0.497112i
$172$	−2.58289	+	2.58289i	−0.196944	+	0.196944i
$173$	−6.56145	+	6.56145i	−0.498858	+	0.498858i	−0.911082	−	0.412224i	$-0.864752\pi$
$173$	−6.56145	+	6.56145i	−0.498858	+	0.498858i	0.412224	+	0.911082i	$0.364752\pi$
$174$		−	2.50970i		−	0.190260i
$175$	−4.97922	−	2.86860i	−0.376394	−	0.216846i
$176$			3.05380i			0.230189i
$177$	1.07609	+	1.07609i	0.0808839	+	0.0808839i
$178$	−6.80205	−	6.80205i	−0.509835	−	0.509835i
$179$			1.70552i			0.127477i	0.997967	+	0.0637383i	$0.0203023\pi$
$179$			1.70552i			0.127477i	−0.997967	+	0.0637383i	$0.979698\pi$
$180$	−3.90452	+	5.09335i	−0.291026	+	0.379636i
$181$			11.8225i			0.878761i	0.898301	+	0.439381i	$0.144802\pi$
$181$			11.8225i			0.878761i	−0.898301	+	0.439381i	$0.855198\pi$
$182$	−0.801084	+	0.801084i	−0.0593803	+	0.0593803i
$183$	2.71642	+	2.71642i	0.200803	+	0.200803i
$184$	−1.82843	−	4.43361i	−0.134793	−	0.326850i
$185$	1.81920	+	13.7688i	0.133750	+	1.01230i
$186$	0.338123			0.0247924
$187$	−8.83905	−	8.83905i	−0.646375	−	0.646375i
$188$	−0.923909	+	0.923909i	−0.0673830	+	0.0673830i
$189$	2.43148			0.176864
$190$	5.02090	−	0.663382i	0.364254	−	0.0481268i
$191$			15.5119i			1.12240i	0.827679	+	0.561202i	$0.189661\pi$
$191$			15.5119i			1.12240i	−0.827679	+	0.561202i	$0.810339\pi$
$192$	−0.254848	−	0.254848i	−0.0183921	−	0.0183921i
$193$	−2.93527	+	2.93527i	−0.211285	+	0.211285i	−0.804813	−	0.593528i	$-0.797735\pi$
$193$	−2.93527	+	2.93527i	−0.211285	+	0.211285i	0.593528	+	0.804813i	$0.297735\pi$
$194$	−5.90086			−0.423657
$195$	−0.630474	−	0.483315i	−0.0451492	−	0.0346109i
$196$	−5.67914			−0.405653
$197$	−16.1422	−	16.1422i	−1.15009	−	1.15009i	−0.986535	−	0.163550i	$-0.947705\pi$
$197$	−16.1422	−	16.1422i	−1.15009	−	1.15009i	−0.163550	−	0.986535i	$-0.552295\pi$
$198$	−6.19761	−	6.19761i	−0.440445	−	0.440445i
$199$	21.0938			1.49530			0.747649	−	0.664094i	$-0.231182\pi$
$199$	21.0938			1.49530			0.747649	+	0.664094i	$0.231182\pi$
$200$	−4.33244	−	2.49598i	−0.306350	−	0.176493i
$201$			1.42449i			0.100476i
$202$	−7.49544	−	7.49544i	−0.527377	−	0.527377i
$203$	5.65898	+	5.65898i	0.397183	+	0.397183i
$204$	1.47528			0.103290
$205$	−5.03152	+	6.56350i	−0.351416	+	0.458415i
$206$			14.7970i			1.03096i
$207$	12.7086	+	5.28713i	0.883310	+	0.367481i
$208$	−0.697028	+	0.697028i	−0.0483302	+	0.0483302i
$209$			6.91664i			0.478434i
$210$	0.121320	+	0.918230i	0.00837190	+	0.0633639i
$211$	13.8007			0.950078			0.475039	−	0.879965i	$-0.342434\pi$
$211$	13.8007			0.950078			0.475039	+	0.879965i	$0.342434\pi$
$212$	−8.88737	+	8.88737i	−0.610387	+	0.610387i
$213$	1.16067	−	1.16067i	0.0795281	−	0.0795281i
$214$	10.3331			0.706356
$215$	8.09745	−	1.06987i	0.552241	−	0.0729644i
$216$	2.11564			0.143951
$217$	−0.762416	+	0.762416i	−0.0517562	+	0.0517562i
$218$	2.77902	+	2.77902i	0.188219	+	0.188219i
$219$		−	0.409353i		−	0.0276615i
$220$	4.15442	−	5.41935i	0.280091	−	0.365373i
$221$		−	4.03501i		−	0.271424i
$222$	1.58289	−	1.58289i	0.106237	−	0.106237i
$223$	−19.2255	+	19.2255i	−1.28743	+	1.28743i	−0.351094	+	0.936340i	$0.614190\pi$
$223$	−19.2255	+	19.2255i	−1.28743	+	1.28743i	−0.936340	+	0.351094i	$0.885810\pi$
$224$	1.14929			0.0767899
$225$	13.8581	−	3.72704i	0.923873	−	0.248469i
$226$			2.85694i			0.190041i
$227$	13.2083	−	13.2083i	0.876668	−	0.876668i	−0.116520	−	0.993188i	$-0.537174\pi$
$227$	13.2083	−	13.2083i	0.876668	−	0.876668i	0.993188	+	0.116520i	$0.0371739\pi$
$228$	−0.577212	−	0.577212i	−0.0382268	−	0.0382268i
$229$	4.10182			0.271056			0.135528	−	0.990774i	$-0.456727\pi$
$229$	4.10182			0.271056			0.135528	+	0.990774i	$0.456727\pi$
$230$	−2.78675	+	10.3554i	−0.183753	+	0.682814i
$231$	−1.26493			−0.0832261
$232$	4.92391	+	4.92391i	0.323270	+	0.323270i
$233$	13.7878	−	13.7878i	0.903268	−	0.903268i	−0.0924491	−	0.995717i	$-0.529470\pi$
$233$	13.7878	−	13.7878i	0.903268	−	0.903268i	0.995717	+	0.0924491i	$0.0294695\pi$
$234$		−	2.82919i		−	0.184950i
$235$	2.89649	−	0.382696i	0.188946	−	0.0249643i
$236$	−4.22248			−0.274860
$237$	−4.29934	+	4.29934i	−0.279272	+	0.279272i
$238$	−3.32654	+	3.32654i	−0.215627	+	0.215627i
$239$		−	15.3810i		−	0.994914i	−0.867489	−	0.497457i	$-0.834267\pi$
$239$		−	15.3810i		−	0.994914i	0.867489	−	0.497457i	$-0.165733\pi$
$240$	0.105561	+	0.798956i	0.00681396	+	0.0515724i
$241$		−	16.7710i		−	1.08031i	−0.841565	−	0.540156i	$-0.818365\pi$
$241$		−	16.7710i		−	1.08031i	0.841565	−	0.540156i	$-0.181635\pi$
$242$	−1.18389	−	1.18389i	−0.0761036	−	0.0761036i
$243$	−6.48795	+	6.48795i	−0.416202	+	0.416202i
$244$	−10.6590			−0.682371
$245$	10.0783	+	7.72596i	0.643881	+	0.493593i
$246$	1.33299			0.0849881
$247$	−1.57872	+	1.57872i	−0.100451	+	0.100451i
$248$	−0.663382	+	0.663382i	−0.0421248	+	0.0421248i
$249$	−4.26706			−0.270414
$250$	4.29289	+	10.3233i	0.271506	+	0.652904i
$251$			21.7250i			1.37127i	0.727945	+	0.685636i	$0.240476\pi$
$251$			21.7250i			1.37127i	−0.727945	+	0.685636i	$0.759524\pi$
$252$	−2.33244	+	2.33244i	−0.146930	+	0.146930i
$253$	−13.5220	−	5.62553i	−0.850122	−	0.353674i
$254$		−	8.22549i		−	0.516113i
$255$	−2.61807	−	2.00699i	−0.163950	−	0.125683i
$256$	1.00000			0.0625000
$257$	−6.92604	−	6.92604i	−0.432034	−	0.432034i	0.457286	−	0.889320i	$-0.348822\pi$
$257$	−6.92604	−	6.92604i	−0.432034	−	0.432034i	−0.889320	+	0.457286i	$0.848822\pi$
$258$	−0.930898	−	0.930898i	−0.0579552	−	0.0579552i
$259$			7.13836i			0.443556i
$260$	2.18520	−	0.288718i	0.135521	−	0.0179055i
$261$	−19.9859			−1.23709
$262$	−8.87011	−	8.87011i	−0.547997	−	0.547997i
$263$	−20.2550	−	20.2550i	−1.24897	−	1.24897i	−0.956173	−	0.292801i	$-0.905413\pi$
$263$	−20.2550	−	20.2550i	−1.24897	−	1.24897i	−0.292801	−	0.956173i	$-0.594587\pi$
$264$	−1.10062			−0.0677385
$265$	27.8622	−	3.68127i	1.71156	−	0.226139i
$266$	2.60305			0.159603
$267$	2.45152	−	2.45152i	0.150031	−	0.150031i
$268$	−2.79478	−	2.79478i	−0.170718	−	0.170718i
$269$		−	0.742062i		−	0.0452443i	−0.999744	−	0.0226222i	$-0.992799\pi$
$269$		−	0.742062i		−	0.0452443i	0.999744	−	0.0226222i	$-0.00720147\pi$
$270$	−3.75446	−	2.87814i	−0.228489	−	0.175158i
$271$	−1.72781			−0.104957			−0.0524784	−	0.998622i	$-0.516712\pi$
$271$	−1.72781			−0.104957			−0.0524784	+	0.998622i	$0.516712\pi$
$272$	−2.89444	+	2.89444i	−0.175501	+	0.175501i
$273$	−0.288718	−	0.288718i	−0.0174740	−	0.0174740i
$274$	−12.1888			−0.736355
$275$	−14.7451	+	3.96559i	−0.889161	+	0.239134i
$276$	1.59791	−	0.658982i	0.0961830	−	0.0396661i
$277$	8.96755	+	8.96755i	0.538808	+	0.538808i	0.923179	−	0.384371i	$-0.125582\pi$
$277$	8.96755	+	8.96755i	0.538808	+	0.538808i	−0.384371	+	0.923179i	$0.625582\pi$
$278$	−13.7798	+	13.7798i	−0.826455	+	0.826455i
$279$		−	2.69263i		−	0.161203i
$280$	−2.03955	−	1.56350i	−0.121886	−	0.0934370i
$281$		−	29.4648i		−	1.75772i	−0.477077	−	0.878861i	$-0.658304\pi$
$281$		−	29.4648i		−	1.75772i	0.477077	−	0.878861i	$-0.341696\pi$
$282$	−0.332986	−	0.332986i	−0.0198290	−	0.0198290i
$283$	14.8551	+	14.8551i	0.883043	+	0.883043i	0.993843	−	0.110800i	$-0.0353412\pi$
$283$	14.8551	+	14.8551i	0.883043	+	0.883043i	−0.110800	+	0.993843i	$0.535341\pi$
$284$			4.55438i			0.270253i
$285$	0.239089	+	1.80958i	0.0141624	+	0.107190i
$286$			3.01027i			0.178001i
$287$	−3.00568	+	3.00568i	−0.177420	+	0.177420i
$288$	−2.02947	+	2.02947i	−0.119588	+	0.119588i
$289$			0.244451i			0.0143795i
$290$	−2.03955	−	15.4366i	−0.119767	−	0.906469i
$291$		−	2.12672i		−	0.124671i
$292$	0.803131	+	0.803131i	0.0469997	+	0.0469997i
$293$	−2.77872	−	2.77872i	−0.162334	−	0.162334i	0.621266	−	0.783600i	$-0.286619\pi$
$293$	−2.77872	−	2.77872i	−0.162334	−	0.162334i	−0.783600	+	0.621266i	$0.786619\pi$
$294$		−	2.04682i		−	0.119373i
$295$	7.49331	+	5.74430i	0.436278	+	0.334446i
$296$			6.21112i			0.361014i
$297$	4.56844	−	4.56844i	0.265088	−	0.265088i
$298$	11.9448	+	11.9448i	0.691944	+	0.691944i
$299$	−1.80236	−	4.37041i	−0.104233	−	0.252747i
$300$	0.899576	−	1.56145i	0.0519370	−	0.0901505i
$301$	4.19807			0.241973
$302$	−8.55129	−	8.55129i	−0.492072	−	0.492072i
$303$	2.70143	−	2.70143i	0.155193	−	0.155193i
$304$	2.26493			0.129902
$305$	18.9157	+	14.5006i	1.08311	+	0.830301i
$306$		−	11.7484i		−	0.671609i
$307$	9.27015	+	9.27015i	0.529075	+	0.529075i	0.920297	−	0.391221i	$-0.127947\pi$
$307$	9.27015	+	9.27015i	0.529075	+	0.529075i	−0.391221	+	0.920297i	$0.627947\pi$
$308$	2.48173	−	2.48173i	0.141410	−	0.141410i
$309$	−5.33299			−0.303383
$310$	2.07972	−	0.274782i	0.118120	−	0.0156066i
$311$	−13.1388			−0.745033			−0.372517	−	0.928025i	$-0.621505\pi$
$311$	−13.1388			−0.745033			−0.372517	+	0.928025i	$0.621505\pi$
$312$	−0.251215	−	0.251215i	−0.0142223	−	0.0142223i
$313$	−3.34798	−	3.34798i	−0.189239	−	0.189239i	0.606128	−	0.795367i	$-0.292722\pi$
$313$	−3.34798	−	3.34798i	−0.189239	−	0.189239i	−0.795367	+	0.606128i	$0.792722\pi$
$314$	5.00224			0.282293
$315$	7.31228	−	0.966130i	0.412001	−	0.0544352i
$316$		−	16.8702i		−	0.949024i
$317$	−10.6829	−	10.6829i	−0.600011	−	0.600011i	0.340305	−	0.940315i	$-0.389470\pi$
$317$	−10.6829	−	10.6829i	−0.600011	−	0.600011i	−0.940315	+	0.340305i	$0.889470\pi$
$318$	−3.20309	−	3.20309i	−0.179620	−	0.179620i
$319$	21.2650			1.19061
$320$	−1.77462	−	1.36041i	−0.0992044	−	0.0760492i
$321$			3.72415i			0.207862i
$322$	−2.11715	+	5.08895i	−0.117984	+	0.283596i
$323$	−6.55569	+	6.55569i	−0.364768	+	0.364768i
$324$		−	7.84782i		−	0.435990i
$325$	−4.27069	−	2.46041i	−0.236895	−	0.136479i
$326$	11.3029			0.626012
$327$	−1.00159	+	1.00159i	−0.0553878	+	0.0553878i
$328$	−2.61526	+	2.61526i	−0.144403	+	0.144403i
$329$	1.50166			0.0827894
$330$	1.95318	+	1.49729i	0.107519	+	0.0824233i
$331$	−0.952100			−0.0523322			−0.0261661	−	0.999658i	$-0.508330\pi$
$331$	−0.952100			−0.0523322			−0.0261661	+	0.999658i	$0.508330\pi$
$332$	8.37177	−	8.37177i	0.459460	−	0.459460i
$333$	−12.6053	−	12.6053i	−0.690766	−	0.690766i
$334$			18.4081i			1.00725i
$335$	1.15764	+	8.76173i	0.0632484	+	0.478704i
$336$			0.414214i			0.0225972i
$337$	14.5701	−	14.5701i	0.793686	−	0.793686i	−0.188405	−	0.982091i	$-0.560332\pi$
$337$	14.5701	−	14.5701i	0.793686	−	0.793686i	0.982091	+	0.188405i	$0.0603318\pi$
$338$	8.50530	−	8.50530i	0.462627	−	0.462627i
$339$	−1.02967			−0.0559238
$340$	9.07416	−	1.19892i	0.492115	−	0.0650203i
$341$			2.86497i			0.155147i
$342$	−4.59660	+	4.59660i	−0.248556	+	0.248556i
$343$	10.3039	+	10.3039i	0.556360	+	0.556360i
$344$	3.65276			0.196944
$345$	−3.73218	−	1.00437i	−0.200934	−	0.0540735i
$346$	9.27930			0.498858
$347$	−0.823485	−	0.823485i	−0.0442070	−	0.0442070i	0.684658	−	0.728865i	$-0.259952\pi$
$347$	−0.823485	−	0.823485i	−0.0442070	−	0.0442070i	−0.728865	+	0.684658i	$0.759952\pi$
$348$	−1.77462	+	1.77462i	−0.0951298	+	0.0951298i
$349$		−	14.2684i		−	0.763768i	−0.924210	−	0.381884i	$-0.875275\pi$
$349$		−	14.2684i		−	0.763768i	0.924210	−	0.381884i	$-0.124725\pi$
$350$	1.49243	+	5.54925i	0.0797739	+	0.296620i
$351$	2.08548			0.111315
$352$	2.15937	−	2.15937i	0.115095	−	0.115095i
$353$	17.4275	−	17.4275i	0.927572	−	0.927572i	−0.0699765	−	0.997549i	$-0.522292\pi$
$353$	17.4275	−	17.4275i	0.927572	−	0.927572i	0.997549	+	0.0699765i	$0.0222924\pi$
$354$		−	1.52182i		−	0.0808839i
$355$	6.19583	−	8.08231i	0.328840	−	0.428965i
$356$			9.61955i			0.509835i
$357$	−1.19892	−	1.19892i	−0.0634533	−	0.0634533i
$358$	1.20599	−	1.20599i	0.0637383	−	0.0637383i
$359$	−22.4365			−1.18415			−0.592075	−	0.805883i	$-0.701691\pi$
$359$	−22.4365			−1.18415			−0.592075	+	0.805883i	$0.701691\pi$
$360$	6.36246	−	0.840634i	0.335331	−	0.0443053i
$361$	−13.8701			−0.730006
$362$	8.35979	−	8.35979i	0.439381	−	0.439381i
$363$	0.426687	−	0.426687i	0.0223952	−	0.0223952i
$364$	1.13290			0.0593803
$365$	−0.332668	−	2.51784i	−0.0174126	−	0.131790i
$366$		−	3.84160i		−	0.200803i
$367$	3.52483	−	3.52483i	0.183995	−	0.183995i	−0.609099	−	0.793094i	$-0.708469\pi$
$367$	3.52483	−	3.52483i	0.183995	−	0.183995i	0.793094	+	0.609099i	$0.208469\pi$
$368$	−1.84214	+	4.42793i	−0.0960281	+	0.230822i
$369$		−	10.6152i		−	0.552604i
$370$	8.44967	−	11.0224i	0.439277	−	0.573027i
$371$	14.4450			0.749945
$372$	−0.239089	−	0.239089i	−0.0123962	−	0.0123962i
$373$	−11.4486	−	11.4486i	−0.592787	−	0.592787i	0.345596	−	0.938383i	$-0.387677\pi$
$373$	−11.4486	−	11.4486i	−0.592787	−	0.592787i	−0.938383	+	0.345596i	$0.887677\pi$
$374$			12.5003i			0.646375i
$375$	−3.72062	+	1.54720i	−0.192132	+	0.0798970i
$376$	1.30661			0.0673830
$377$	4.85372	+	4.85372i	0.249979	+	0.249979i
$378$	−1.71931	−	1.71931i	−0.0884320	−	0.0884320i
$379$	21.0371			1.08060			0.540302	−	0.841471i	$-0.318310\pi$
$379$	21.0371			1.08060			0.540302	+	0.841471i	$0.318310\pi$
$380$	−4.01939	−	3.08123i	−0.206190	−	0.158064i
$381$	2.96454			0.151878
$382$	10.9686	−	10.9686i	0.561202	−	0.561202i
$383$	16.6002	+	16.6002i	0.848228	+	0.848228i	0.989912	−	0.141684i	$-0.0452516\pi$
$383$	16.6002	+	16.6002i	0.848228	+	0.848228i	−0.141684	+	0.989912i	$0.545252\pi$
$384$			0.360409i			0.0183921i
$385$	−7.78030	+	1.02797i	−0.396521	+	0.0523900i
$386$	4.15110			0.211285
$387$	−7.41317	+	7.41317i	−0.376833	+	0.376833i
$388$	4.17254	+	4.17254i	0.211828	+	0.211828i
$389$	−10.4680			−0.530750			−0.265375	−	0.964145i	$-0.585496\pi$
$389$	−10.4680			−0.530750			−0.265375	+	0.964145i	$0.585496\pi$
$390$	0.104057	+	0.787568i	0.00526912	+	0.0398800i
$391$	−7.48440	−	18.1483i	−0.378502	−	0.917800i
$392$	4.01576	+	4.01576i	0.202826	+	0.202826i
$393$	3.19687	−	3.19687i	0.161261	−	0.161261i
$394$			22.8285i			1.15009i
$395$	−22.9504	+	29.9383i	−1.15476	+	1.50636i
$396$			8.76474i			0.440445i
$397$	−19.8627	−	19.8627i	−0.996881	−	0.996881i	0.00311393	−	0.999995i	$-0.499009\pi$
$397$	−19.8627	−	19.8627i	−0.996881	−	0.996881i	−0.999995	+	0.00311393i	$0.999009\pi$
$398$	−14.9156	−	14.9156i	−0.747649	−	0.747649i
$399$			0.938164i			0.0469669i
$400$	1.29857	+	4.82843i	0.0649286	+	0.241421i
$401$		−	23.8437i		−	1.19070i	−0.803467	−	0.595349i	$-0.797014\pi$
$401$		−	23.8437i		−	1.19070i	0.803467	−	0.595349i	$-0.202986\pi$
$402$	1.00727	−	1.00727i	0.0502378	−	0.0502378i
$403$	−0.653926	+	0.653926i	−0.0325744	+	0.0325744i
$404$			10.6002i			0.527377i
$405$	−10.6762	+	13.9269i	−0.530507	+	0.692034i
$406$		−	8.00301i		−	0.397183i
$407$	13.4121	+	13.4121i	0.664812	+	0.664812i
$408$	−1.04318	−	1.04318i	−0.0516452	−	0.0516452i
$409$			17.1274i			0.846897i	0.905920	+	0.423449i	$0.139181\pi$
$409$			17.1274i			0.846897i	−0.905920	+	0.423449i	$0.860819\pi$
$410$	8.19892	−	1.08328i	0.404916	−	0.0534991i
$411$		−	4.39297i		−	0.216689i
$412$	10.4631	−	10.4631i	0.515479	−	0.515479i
$413$	3.43148	+	3.43148i	0.168852	+	0.168852i
$414$	−5.24778	−	12.7249i	−0.257914	−	0.625395i
$415$	−26.2458	+	3.46770i	−1.28835	+	0.170223i
$416$	0.985746			0.0483302
$417$	−4.96635	−	4.96635i	−0.243203	−	0.243203i
$418$	4.89081	−	4.89081i	0.239217	−	0.239217i
$419$	−31.7177			−1.54951			−0.774756	−	0.632260i	$-0.782127\pi$
$419$	−31.7177			−1.54951			−0.774756	+	0.632260i	$0.782127\pi$
$420$	0.563500	−	0.735073i	0.0274960	−	0.0358679i
$421$			18.3502i			0.894334i	0.894450	+	0.447167i	$0.147567\pi$
$421$			18.3502i			0.894334i	−0.894450	+	0.447167i	$0.852433\pi$
$422$	−9.75856	−	9.75856i	−0.475039	−	0.475039i
$423$	−2.65172	+	2.65172i	−0.128931	+	0.128931i
$424$	12.5686			0.610387
$425$	−17.7342	−	10.2169i	−0.860236	−	0.495595i
$426$	−1.64144			−0.0795281
$427$	8.66222	+	8.66222i	0.419194	+	0.419194i
$428$	−7.30661	−	7.30661i	−0.353178	−	0.353178i
$429$	−1.08493			−0.0523810
$430$	−6.48227	−	4.96925i	−0.312603	−	0.239638i
$431$			24.7843i			1.19382i	0.802309	+	0.596909i	$0.203605\pi$
$431$			24.7843i			1.19382i	−0.802309	+	0.596909i	$0.796395\pi$
$432$	−1.49598	−	1.49598i	−0.0719756	−	0.0719756i
$433$	4.42484	+	4.42484i	0.212644	+	0.212644i	0.805390	−	0.592746i	$-0.201956\pi$
$433$	4.42484	+	4.42484i	0.212644	+	0.212644i	−0.592746	+	0.805390i	$0.701956\pi$
$434$	1.07822			0.0517562
$435$	5.56350	−	0.735073i	0.266749	−	0.0352440i
$436$		−	3.93013i		−	0.188219i
$437$	−4.17231	+	10.0289i	−0.199589	+	0.479749i
$438$	−0.289456	+	0.289456i	−0.0138307	+	0.0138307i
$439$		−	22.0184i		−	1.05088i	−0.850830	−	0.525441i	$-0.823900\pi$
$439$		−	22.0184i		−	1.05088i	0.850830	−	0.525441i	$-0.176100\pi$
$440$	−6.76968	+	0.894439i	−0.322732	+	0.0426407i
$441$	−16.2997			−0.776178
$442$	−2.85318	+	2.85318i	−0.135712	+	0.135712i
$443$	27.1908	−	27.1908i	1.29187	−	1.29187i	0.358245	−	0.933628i	$-0.383375\pi$
$443$	27.1908	−	27.1908i	1.29187	−	1.29187i	0.933628	−	0.358245i	$-0.116625\pi$
$444$	−2.23855			−0.106237
$445$	13.0865	−	17.0711i	0.620361	−	0.809246i
$446$	27.1890			1.28743
$447$	−4.30502	+	4.30502i	−0.203620	+	0.203620i
$448$	−0.812668	−	0.812668i	−0.0383950	−	0.0383950i
$449$			0.580878i			0.0274133i	0.999906	+	0.0137067i	$0.00436310\pi$
$449$			0.580878i			0.0274133i	−0.999906	+	0.0137067i	$0.995637\pi$
$450$	−12.4346	−	7.16374i	−0.586171	−	0.337702i
$451$			11.2946i			0.531842i
$452$	2.02016	−	2.02016i	0.0950203	−	0.0950203i
$453$	3.08197	−	3.08197i	0.144803	−	0.144803i
$454$	−18.6794			−0.876668
$455$	−2.01048	−	1.54121i	−0.0942527	−	0.0722532i
$456$			0.816301i			0.0382268i
$457$	−12.9909	+	12.9909i	−0.607688	+	0.607688i	−0.942341	−	0.334653i	$-0.891381\pi$
$457$	−12.9909	+	12.9909i	−0.607688	+	0.607688i	0.334653	+	0.942341i	$0.391381\pi$
$458$	−2.90042	−	2.90042i	−0.135528	−	0.135528i
$459$	8.66007			0.404217
$460$	9.29289	−	5.35183i	0.433283	−	0.249531i
$461$	15.6873			0.730630			0.365315	−	0.930884i	$-0.380961\pi$
$461$	15.6873			0.730630			0.365315	+	0.930884i	$0.380961\pi$
$462$	0.894439	+	0.894439i	0.0416130	+	0.0416130i
$463$	−9.77763	+	9.77763i	−0.454405	+	0.454405i	−0.896814	−	0.442409i	$-0.854124\pi$
$463$	−9.77763	+	9.77763i	−0.454405	+	0.454405i	0.442409	+	0.896814i	$0.354124\pi$
$464$		−	6.96346i		−	0.323270i
$465$	0.0990339	+	0.749552i	0.00459259	+	0.0347596i
$466$	−19.4989			−0.903268
$467$	−15.9737	+	15.9737i	−0.739176	+	0.739176i	−0.972419	−	0.233242i	$-0.925066\pi$
$467$	−15.9737	+	15.9737i	−0.739176	+	0.739176i	0.233242	+	0.972419i	$0.425066\pi$
$468$	−2.00054	+	2.00054i	−0.0924751	+	0.0924751i
$469$			4.54246i			0.209751i
$470$	−2.31873	−	1.77752i	−0.106955	−	0.0819908i
$471$			1.80285i			0.0830712i
$472$	2.98575	+	2.98575i	0.137430	+	0.137430i
$473$	7.88765	−	7.88765i	0.362674	−	0.362674i
$474$	6.08018			0.279272
$475$	2.94117	+	10.9360i	0.134950	+	0.501780i
$476$	4.70444			0.215627
$477$	−25.5077	+	25.5077i	−1.16792	+	1.16792i
$478$	−10.8760	+	10.8760i	−0.497457	+	0.497457i
$479$	35.1636			1.60667			0.803333	−	0.595530i	$-0.203058\pi$
$479$	35.1636			1.60667			0.803333	+	0.595530i	$0.203058\pi$
$480$	0.490304	−	0.639591i	0.0223792	−	0.0291932i
$481$			6.12259i			0.279166i
$482$	−11.8589	+	11.8589i	−0.540156	+	0.540156i
$483$	−1.83411	−	0.763039i	−0.0834547	−	0.0347195i
$484$			1.67428i			0.0761036i
$485$	−1.72832	−	13.0810i	−0.0784790	−	0.593979i
$486$	9.17535			0.416202
$487$	19.6145	+	19.6145i	0.888819	+	0.888819i	0.994410	−	0.105591i	$-0.0336734\pi$
$487$	19.6145	+	19.6145i	0.888819	+	0.888819i	−0.105591	+	0.994410i	$0.533673\pi$
$488$	7.53704	+	7.53704i	0.341186	+	0.341186i
$489$			4.07369i			0.184218i
$490$	−1.66338	−	12.5895i	−0.0751439	−	0.568737i
$491$	−34.8359			−1.57212			−0.786062	−	0.618148i	$-0.787883\pi$
$491$	−34.8359			−1.57212			−0.786062	+	0.618148i	$0.787883\pi$
$492$	−0.942563	−	0.942563i	−0.0424940	−	0.0424940i
$493$	20.1553	+	20.1553i	0.907749	+	0.907749i
$494$	2.23264			0.100451
$495$	11.9236	−	15.5541i	0.535927	−	0.699105i
$496$	0.938164			0.0421248
$497$	3.70120	−	3.70120i	0.166022	−	0.166022i
$498$	3.01726	+	3.01726i	0.135207	+	0.135207i
$499$		−	35.1206i		−	1.57221i	−0.618091	−	0.786106i	$-0.712094\pi$
$499$		−	35.1206i		−	1.57221i	0.618091	−	0.786106i	$-0.287906\pi$
$500$	4.26416	−	10.3352i	0.190699	−	0.462205i
$501$	−6.63445			−0.296406
$502$	15.3619	−	15.3619i	0.685636	−	0.685636i
$503$	7.26752	+	7.26752i	0.324043	+	0.324043i	0.850316	−	0.526273i	$-0.176411\pi$
$503$	7.26752	+	7.26752i	0.324043	+	0.324043i	−0.526273	+	0.850316i	$0.676411\pi$
$504$	3.29857			0.146930
$505$	14.4206	−	18.8113i	0.641706	−	0.837091i
$506$	5.58366	+	13.5394i	0.248224	+	0.601898i
$507$	3.06539	+	3.06539i	0.136139	+	0.136139i
$508$	−5.81630	+	5.81630i	−0.258057	+	0.258057i
$509$			44.5560i			1.97491i	0.157904	+	0.987454i	$0.449526\pi$
$509$			44.5560i			1.97491i	−0.157904	+	0.987454i	$0.550474\pi$
$510$	0.432100	+	3.27041i	0.0191337	+	0.144816i
$511$		−	1.30536i		−	0.0577457i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−3.38829	−	3.38829i	−0.149597	−	0.149597i
$514$			9.79490i			0.432034i
$515$	−32.8021	+	4.33395i	−1.44543	+	0.190977i
$516$			1.31649i			0.0579552i
$517$	2.82144	−	2.82144i	0.124087	−	0.124087i
$518$	5.04758	−	5.04758i	0.221778	−	0.221778i
$519$			3.34434i			0.146800i
$520$	−1.74933	−	1.34102i	−0.0767131	−	0.0588075i
$521$			16.2124i			0.710280i	0.934813	+	0.355140i	$0.115567\pi$
$521$			16.2124i			0.710280i	−0.934813	+	0.355140i	$0.884433\pi$
$522$	14.1321	+	14.1321i	0.618547	+	0.618547i
$523$	3.90861	+	3.90861i	0.170912	+	0.170912i	0.787380	−	0.616468i	$-0.211437\pi$
$523$	3.90861	+	3.90861i	0.170912	+	0.170912i	−0.616468	+	0.787380i	$0.711437\pi$
$524$			12.5442i			0.547997i
$525$	−2.00000	+	0.537886i	−0.0872872	+	0.0234753i
$526$			28.6448i			1.24897i
$527$	−2.71546	+	2.71546i	−0.118287	+	0.118287i
$528$	0.778256	+	0.778256i	0.0338692	+	0.0338692i
$529$	−16.2130	−	16.3137i	−0.704915	−	0.709292i
$530$	−22.3046	−	17.0985i	−0.968850	−	0.742711i
$531$	−12.1190			−0.525918
$532$	−1.84063	−	1.84063i	−0.0798016	−	0.0798016i
$533$	−2.57798	+	2.57798i	−0.111665	+	0.111665i
$534$	−3.46697			−0.150031
$535$	3.02649	+	22.9064i	0.130847	+	0.990332i
$536$			3.95242i			0.170718i
$537$	0.434648	+	0.434648i	0.0187565	+	0.0187565i
$538$	−0.524717	+	0.524717i	−0.0226222	+	0.0226222i
$539$	17.3430			0.747015
$540$	0.619657	+	4.68996i	0.0266658	+	0.201824i
$541$	−19.7184			−0.847758			−0.423879	−	0.905719i	$-0.639332\pi$
$541$	−19.7184			−0.847758			−0.423879	+	0.905719i	$0.639332\pi$
$542$	1.22174	+	1.22174i	0.0524784	+	0.0524784i
$543$	3.01294	+	3.01294i	0.129298	+	0.129298i
$544$	4.09335			0.175501
$545$	−5.34659	+	6.97450i	−0.229023	+	0.298755i
$546$			0.408309i			0.0174740i
$547$	−0.723090	−	0.723090i	−0.0309171	−	0.0309171i	0.691479	−	0.722396i	$-0.256959\pi$
$547$	−0.723090	−	0.723090i	−0.0309171	−	0.0309171i	−0.722396	+	0.691479i	$0.756959\pi$
$548$	8.61881	+	8.61881i	0.368177	+	0.368177i
$549$	−30.5924			−1.30565
$550$	13.2304	+	7.62225i	0.564148	+	0.325014i
$551$		−	15.7717i		−	0.671898i
$552$	−1.59587	−	0.663924i	−0.0679246	−	0.0282585i
$553$	−13.7099	+	13.7099i	−0.583004	+	0.583004i
$554$		−	12.6820i		−	0.538808i
$555$	3.97258	+	3.04534i	0.168626	+	0.129267i
$556$	19.4875			0.826455
$557$	7.40510	−	7.40510i	0.313764	−	0.313764i	−0.532602	−	0.846366i	$-0.678786\pi$
$557$	7.40510	−	7.40510i	0.313764	−	0.313764i	0.846366	+	0.532602i	$0.178786\pi$
$558$	−1.90398	+	1.90398i	−0.0806017	+	0.0806017i
$559$	3.60069			0.152293
$560$	0.336618	+	2.54774i	0.0142247	+	0.107662i
$561$	−4.50523			−0.190211
$562$	−20.8348	+	20.8348i	−0.878861	+	0.878861i
$563$	16.0153	+	16.0153i	0.674962	+	0.674962i	0.958856	−	0.283893i	$-0.0916262\pi$
$563$	16.0153	+	16.0153i	0.674962	+	0.674962i	−0.283893	+	0.958856i	$0.591626\pi$
$564$			0.470913i			0.0198290i
$565$	−6.33326	+	0.836777i	−0.266442	+	0.0352035i
$566$		−	21.0083i		−	0.883043i
$567$	−6.37767	+	6.37767i	−0.267837	+	0.267837i
$568$	3.22044	−	3.22044i	0.135126	−	0.135126i
$569$	0.251153			0.0105289			0.00526443	−	0.999986i	$-0.498324\pi$
$569$	0.251153			0.0105289			0.00526443	+	0.999986i	$0.498324\pi$
$570$	1.11050	−	1.44863i	0.0465139	−	0.0606763i
$571$		−	13.6282i		−	0.570324i	−0.958479	−	0.285162i	$-0.907953\pi$
$571$		−	13.6282i		−	0.570324i	0.958479	−	0.285162i	$-0.0920474\pi$
$572$	2.12859	−	2.12859i	0.0890006	−	0.0890006i
$573$	3.95318	+	3.95318i	0.165147	+	0.165147i
$574$	4.25067			0.177420
$575$	−23.7721	−	3.14465i	−0.991364	−	0.131141i
$576$	2.87011			0.119588
$577$	29.2581	+	29.2581i	1.21803	+	1.21803i	0.968321	+	0.249707i	$0.0803344\pi$
$577$	29.2581	+	29.2581i	1.21803	+	1.21803i	0.249707	+	0.968321i	$0.419666\pi$
$578$	0.172853	−	0.172853i	0.00718973	−	0.00718973i
$579$			1.49609i			0.0621755i
$580$	−9.47316	+	12.3575i	−0.393351	+	0.513118i
$581$	−13.6069			−0.564511
$582$	−1.50382	+	1.50382i	−0.0623354	+	0.0623354i
$583$	27.1403	−	27.1403i	1.12404	−	1.12404i
$584$		−	1.13580i		−	0.0469997i
$585$	6.27176	−	0.828652i	0.259306	−	0.0342605i
$586$			3.92970i			0.162334i
$587$	−9.56129	−	9.56129i	−0.394637	−	0.394637i	0.481700	−	0.876336i	$-0.340020\pi$
$587$	−9.56129	−	9.56129i	−0.394637	−	0.394637i	−0.876336	+	0.481700i	$0.840020\pi$
$588$	−1.44732	+	1.44732i	−0.0596863	+	0.0596863i
$589$	2.12487			0.0875538
$590$	−1.23674	−	9.36041i	−0.0509156	−	0.385362i
$591$	−8.22762			−0.338439
$592$	4.39193	−	4.39193i	0.180507	−	0.180507i
$593$	18.5159	−	18.5159i	0.760358	−	0.760358i	−0.216029	−	0.976387i	$-0.569311\pi$
$593$	18.5159	−	18.5159i	0.760358	−	0.760358i	0.976387	+	0.216029i	$0.0693107\pi$
$594$	−6.46075			−0.265088
$595$	−8.34860	−	6.39996i	−0.342259	−	0.262373i
$596$		−	16.8925i		−	0.691944i
$597$	5.37571	−	5.37571i	0.220013	−	0.220013i
$598$	−1.81588	+	4.36481i	−0.0742569	+	0.178490i
$599$		−	20.5744i		−	0.840646i	−0.907374	−	0.420323i	$-0.861917\pi$
$599$		−	20.5744i		−	0.840646i	0.907374	−	0.420323i	$-0.138083\pi$
$600$	−1.74021	+	0.468018i	−0.0710438	+	0.0191067i
$601$	12.6034			0.514102			0.257051	−	0.966398i	$-0.417249\pi$
$601$	12.6034			0.514102			0.257051	+	0.966398i	$0.417249\pi$
$602$	−2.96848	−	2.96848i	−0.120986	−	0.120986i
$603$	−8.02132	−	8.02132i	−0.326653	−	0.326653i
$604$			12.0934i			0.492072i
$605$	2.27771	−	2.97122i	0.0926019	−	0.120797i
$606$	−3.82039			−0.155193
$607$	20.9098	+	20.9098i	0.848701	+	0.848701i	0.989971	−	0.141270i	$-0.0451185\pi$
$607$	20.9098	+	20.9098i	0.848701	+	0.848701i	−0.141270	+	0.989971i	$0.545118\pi$
$608$	−1.60155	−	1.60155i	−0.0649512	−	0.0649512i
$609$	2.88436			0.116880
$610$	−3.12194	−	23.6289i	−0.126404	−	0.956705i
$611$	1.28798			0.0521061
$612$	−8.30734	+	8.30734i	−0.335804	+	0.335804i
$613$	−0.241759	−	0.241759i	−0.00976456	−	0.00976456i	0.702208	−	0.711972i	$-0.252198\pi$
$613$	−0.241759	−	0.241759i	−0.00976456	−	0.00976456i	−0.711972	+	0.702208i	$0.752198\pi$
$614$		−	13.1100i		−	0.529075i
$615$	0.390422	+	2.95497i	0.0157434	+	0.119156i
$616$	−3.50970			−0.141410
$617$	17.6380	−	17.6380i	0.710078	−	0.710078i	−0.256473	−	0.966551i	$-0.582561\pi$
$617$	17.6380	−	17.6380i	0.710078	−	0.710078i	0.966551	+	0.256473i	$0.0825605\pi$
$618$	3.77099	+	3.77099i	0.151691	+	0.151691i
$619$	17.5344			0.704767			0.352383	−	0.935856i	$-0.385371\pi$
$619$	17.5344			0.704767			0.352383	+	0.935856i	$0.385371\pi$
$620$	−1.66489	−	1.27629i	−0.0668635	−	0.0512569i
$621$	9.37992	−	3.86829i	0.376403	−	0.155229i
$622$	9.29054	+	9.29054i	0.372517	+	0.372517i
$623$	7.81750	−	7.81750i	0.313202	−	0.313202i
$624$			0.355272i			0.0142223i
$625$	−21.6274	+	12.5401i	−0.865097	+	0.501605i
$626$			4.73476i			0.189239i
$627$	1.76269	+	1.76269i	0.0703951	+	0.0703951i
$628$	−3.53712	−	3.53712i	−0.141146	−	0.141146i
$629$			25.4243i			1.01373i
$630$	−5.85372	−	4.48741i	−0.233218	−	0.178783i
$631$			20.3839i			0.811468i	0.913991	+	0.405734i	$0.132984\pi$
$631$			20.3839i			0.811468i	−0.913991	+	0.405734i	$0.867016\pi$
$632$	−11.9290	+	11.9290i	−0.474512	+	0.474512i
$633$	3.51708	−	3.51708i	0.139791	−	0.139791i
$634$			15.1079i			0.600011i
$635$	18.2343	−	2.40919i	0.723606	−	0.0956058i
$636$			4.52985i			0.179620i
$637$	3.95852	+	3.95852i	0.156842	+	0.156842i
$638$	−15.0367	−	15.0367i	−0.595307	−	0.595307i
$639$			13.0716i			0.517103i
$640$	0.292893	+	2.21680i	0.0115776	+	0.0876268i
$641$		−	47.3067i		−	1.86850i	−0.356617	−	0.934251i	$-0.616070\pi$
$641$		−	47.3067i		−	1.86850i	0.356617	−	0.934251i	$-0.383930\pi$
$642$	2.63337	−	2.63337i	0.103931	−	0.103931i
$643$	−25.9299	−	25.9299i	−1.02258	−	1.02258i	−0.999739	−	0.0228373i	$-0.992730\pi$
$643$	−25.9299	−	25.9299i	−1.02258	−	1.02258i	−0.0228373	−	0.999739i	$-0.507270\pi$
$644$	5.09548	−	2.10139i	0.200790	−	0.0828062i
$645$	1.79096	−	2.33627i	0.0705191	−	0.0919906i
$646$	9.27115			0.364768
$647$	−16.6612	−	16.6612i	−0.655020	−	0.655020i	0.299177	−	0.954198i	$-0.403288\pi$
$647$	−16.6612	−	16.6612i	−0.655020	−	0.655020i	−0.954198	+	0.299177i	$0.903288\pi$
$648$	−5.54925	+	5.54925i	−0.217995	+	0.217995i
$649$	12.8946			0.506159
$650$	1.28006	+	4.75960i	0.0502082	+	0.186687i
$651$			0.388600i			0.0152304i
$652$	−7.99239	−	7.99239i	−0.313006	−	0.313006i
$653$	13.5400	−	13.5400i	0.529861	−	0.529861i	−0.390670	−	0.920531i	$-0.627757\pi$
$653$	13.5400	−	13.5400i	0.529861	−	0.529861i	0.920531	+	0.390670i	$0.127757\pi$
$654$	1.41646			0.0553878
$655$	17.0653	−	22.2613i	0.666796	−	0.869820i
$656$	3.69853			0.144403
$657$	2.30507	+	2.30507i	0.0899294	+	0.0899294i
$658$	−1.06184	−	1.06184i	−0.0413947	−	0.0413947i
$659$	−39.6959			−1.54633			−0.773166	−	0.634204i	$-0.781328\pi$
$659$	−39.6959			−1.54633			−0.773166	+	0.634204i	$0.781328\pi$
$660$	−0.322364	−	2.43986i	−0.0125480	−	0.0949713i
$661$		−	12.0576i		−	0.468986i	−0.972118	−	0.234493i	$-0.924657\pi$
$661$		−	12.0576i		−	0.468986i	0.972118	−	0.234493i	$-0.0753429\pi$
$662$	0.673236	+	0.673236i	0.0261661	+	0.0261661i
$663$	−1.02831	−	1.02831i	−0.0399364	−	0.0399364i
$664$	−11.8395			−0.459460
$665$	0.762416	+	5.77045i	0.0295652	+	0.223768i
$666$			17.8266i			0.690766i
$667$	30.8337	+	12.8277i	1.19388	+	0.496689i
$668$	13.0165	−	13.0165i	0.503623	−	0.503623i
$669$			9.79915i			0.378857i
$670$	5.37691	−	7.01405i	0.207728	−	0.270976i
$671$	32.5504			1.25660
$672$	0.292893	−	0.292893i	0.0112986	−	0.0112986i
$673$	7.82931	−	7.82931i	0.301798	−	0.301798i	−0.539919	−	0.841717i	$-0.681545\pi$
$673$	7.82931	−	7.82931i	0.301798	−	0.301798i	0.841717	+	0.539919i	$0.181545\pi$
$674$	−20.6053			−0.793686
$675$	5.28061	−	9.16589i	0.203251	−	0.352795i
$676$	−12.0283			−0.462627
$677$	27.0657	−	27.0657i	1.04022	−	1.04022i	0.0410639	−	0.999157i	$-0.486925\pi$
$677$	27.0657	−	27.0657i	1.04022	−	1.04022i	0.999157	−	0.0410639i	$-0.0130747\pi$
$678$	0.728084	+	0.728084i	0.0279619	+	0.0279619i
$679$		−	6.78177i		−	0.260261i
$680$	−7.26416	−	5.56864i	−0.278568	−	0.213547i
$681$		−	6.73224i		−	0.257980i
$682$	2.02584	−	2.02584i	0.0775734	−	0.0775734i
$683$	−6.29630	+	6.29630i	−0.240921	+	0.240921i	−0.817231	−	0.576310i	$-0.804492\pi$
$683$	−6.29630	+	6.29630i	−0.240921	+	0.240921i	0.576310	+	0.817231i	$0.304492\pi$
$684$	6.50058			0.248556
$685$	−3.57003	−	27.0202i	−0.136404	−	1.03239i
$686$		−	14.5720i		−	0.556360i
$687$	1.04534	−	1.04534i	0.0398822	−	0.0398822i
$688$	−2.58289	−	2.58289i	−0.0984718	−	0.0984718i
$689$	12.3895			0.472002
$690$	1.92885	+	3.34925i	0.0734301	+	0.127504i
$691$	17.7979			0.677064			0.338532	−	0.940955i	$-0.390070\pi$
$691$	17.7979			0.677064			0.338532	+	0.940955i	$0.390070\pi$
$692$	−6.56145	−	6.56145i	−0.249429	−	0.249429i
$693$	7.12283	−	7.12283i	0.270574	−	0.270574i
$694$			1.16458i			0.0442070i
$695$	−34.5830	−	26.5110i	−1.31181	−	1.00562i
$696$	2.50970			0.0951298
$697$	−10.7052	+	10.7052i	−0.405487	+	0.405487i
$698$	−10.0893	+	10.0893i	−0.381884	+	0.381884i
$699$		−	7.02758i		−	0.265807i
$700$	2.86860	−	4.97922i	0.108423	−	0.188197i
$701$			25.4881i			0.962673i	0.876536	+	0.481336i	$0.159848\pi$
$701$			25.4881i			0.962673i	−0.876536	+	0.481336i	$0.840152\pi$
$702$	−1.47466	−	1.47466i	−0.0556574	−	0.0556574i
$703$	9.94739	−	9.94739i	0.375173	−	0.375173i
$704$	−3.05380			−0.115095
$705$	0.640634	−	0.835692i	0.0241277	−	0.0314740i
$706$	−24.6462			−0.927572
$707$	8.61441	−	8.61441i	0.323978	−	0.323978i
$708$	−1.07609	+	1.07609i	−0.0404420	+	0.0404420i
$709$	−13.1303			−0.493118			−0.246559	−	0.969128i	$-0.579300\pi$
$709$	−13.1303			−0.493118			−0.246559	+	0.969128i	$0.579300\pi$
$710$	−10.0962	+	1.33395i	−0.378902	+	0.0500622i
$711$		−	48.4193i		−	1.81587i
$712$	6.80205	−	6.80205i	0.254917	−	0.254917i
$713$	−1.72823	+	4.15412i	−0.0647226	+	0.155573i
$714$			1.69552i			0.0634533i
$715$	−6.67318	+	0.881689i	−0.249563	+	0.0329733i
$716$	−1.70552			−0.0637383
$717$	−3.91982	−	3.91982i	−0.146388	−	0.146388i
$718$	15.8650	+	15.8650i	0.592075	+	0.592075i
$719$			48.8089i			1.82027i	0.414316	+	0.910133i	$0.364021\pi$
$719$			48.8089i			1.82027i	−0.414316	+	0.910133i	$0.635979\pi$
$720$	−5.09335	−	3.90452i	−0.189818	−	0.145513i
$721$	−17.0060			−0.633337
$722$	9.80765	+	9.80765i	0.365003	+	0.365003i
$723$	−4.27404	−	4.27404i	−0.158953	−	0.158953i
$724$	−11.8225			−0.439381
$725$	33.6226	−	9.04256i	1.24871	−	0.335832i
$726$	−0.603426			−0.0223952
$727$	−27.1683	+	27.1683i	−1.00762	+	1.00762i	−0.00764493	+	0.999971i	$0.502433\pi$
$727$	−27.1683	+	27.1683i	−1.00762	+	1.00762i	−0.999971	+	0.00764493i	$0.997567\pi$
$728$	−0.801084	−	0.801084i	−0.0296902	−	0.0296902i
$729$		−	20.2366i		−	0.749503i
$730$	−1.54515	+	2.01562i	−0.0571886	+	0.0746013i
$731$	14.9520			0.553021
$732$	−2.71642	+	2.71642i	−0.100402	+	0.100402i
$733$	−26.1220	−	26.1220i	−0.964837	−	0.964837i	0.0345652	−	0.999402i	$-0.488995\pi$
$733$	−26.1220	−	26.1220i	−0.964837	−	0.964837i	−0.999402	+	0.0345652i	$0.988995\pi$
$734$	−4.98486			−0.183995
$735$	4.53739	−	0.599498i	0.167364	−	0.0221128i
$736$	4.43361	−	1.82843i	0.163425	−	0.0673967i
$737$	8.53472	+	8.53472i	0.314380	+	0.314380i
$738$	−7.50606	+	7.50606i	−0.276302	+	0.276302i
$739$		−	8.74415i		−	0.321659i	−0.986982	−	0.160829i	$-0.948583\pi$
$739$		−	8.74415i		−	0.321659i	0.986982	−	0.160829i	$-0.0514169\pi$
$740$	−13.7688	+	1.81920i	−0.506152	+	0.0668750i
$741$			0.804665i			0.0295601i
$742$	−10.2141	−	10.2141i	−0.374973	−	0.374973i
$743$	−3.35814	−	3.35814i	−0.123198	−	0.123198i	0.642820	−	0.766018i	$-0.277765\pi$
$743$	−3.35814	−	3.35814i	−0.123198	−	0.123198i	−0.766018	+	0.642820i	$0.777765\pi$
$744$			0.338123i			0.0123962i
$745$	−22.9807	+	29.9778i	−0.841949	+	1.09830i
$746$			16.1908i			0.592787i
$747$	24.0279	−	24.0279i	0.879133	−	0.879133i
$748$	8.83905	−	8.83905i	0.323188	−	0.323188i
$749$			11.8757i			0.433928i
$750$	3.72491	+	1.53684i	0.136015	+	0.0561176i
$751$		−	22.6897i		−	0.827959i	−0.910286	−	0.413979i	$-0.864139\pi$
$751$		−	22.6897i		−	0.827959i	0.910286	−	0.413979i	$-0.135861\pi$
$752$	−0.923909	−	0.923909i	−0.0336915	−	0.0336915i
$753$	5.53658	+	5.53658i	0.201764	+	0.201764i
$754$		−	6.86420i		−	0.249979i
$755$	16.4519	−	21.4611i	0.598746	−	0.781051i
$756$			2.43148i			0.0884320i
$757$	−10.7978	+	10.7978i	−0.392452	+	0.392452i	−0.875561	−	0.483108i	$-0.839508\pi$
$757$	−10.7978	+	10.7978i	−0.392452	+	0.392452i	0.483108	+	0.875561i	$0.339508\pi$
$758$	−14.8755	−	14.8755i	−0.540302	−	0.540302i
$759$	−4.87971	+	2.01240i	−0.177122	+	0.0730456i
$760$	0.663382	+	5.02090i	0.0240634	+	0.182127i
$761$	−39.2774			−1.42381			−0.711903	−	0.702278i	$-0.752167\pi$
$761$	−39.2774			−1.42381			−0.711903	+	0.702278i	$0.752167\pi$
$762$	−2.09625	−	2.09625i	−0.0759391	−	0.0759391i
$763$	−3.19389	+	3.19389i	−0.115627	+	0.115627i
$764$	−15.5119			−0.561202
$765$	26.0438	−	3.44101i	0.941615	−	0.124410i
$766$		−	23.4762i		−	0.848228i
$767$	2.94319	+	2.94319i	0.106272	+	0.106272i
$768$	0.254848	−	0.254848i	0.00919603	−	0.00919603i
$769$	24.7615			0.892923			0.446462	−	0.894803i	$-0.352684\pi$
$769$	24.7615			0.892923			0.446462	+	0.894803i	$0.352684\pi$
$770$	6.22839	+	4.77462i	0.224455	+	0.172065i
$771$	−3.53017			−0.127136
$772$	−2.93527	−	2.93527i	−0.105643	−	0.105643i
$773$	32.3049	+	32.3049i	1.16193	+	1.16193i	0.984053	+	0.177873i	$0.0569218\pi$
$773$	32.3049	+	32.3049i	1.16193	+	1.16193i	0.177873	+	0.984053i	$0.443078\pi$
$774$	10.4838			0.376833
$775$	1.21827	+	4.52985i	0.0437617	+	0.162717i
$776$		−	5.90086i		−	0.211828i
$777$	1.81920	+	1.81920i	0.0652633	+	0.0652633i
$778$	7.40201	+	7.40201i	0.265375	+	0.265375i
$779$	8.37691			0.300134
$780$	0.483315	−	0.630474i	0.0173055	−	0.0225746i
$781$		−	13.9082i		−	0.497674i
$782$	−7.54053	+	18.1251i	−0.269649	+	0.648151i
$783$	−10.4172	+	10.4172i	−0.372281	+	0.372281i
$784$		−	5.67914i		−	0.202826i
$785$	1.46512	+	11.0890i	0.0522925	+	0.395783i
$786$	−4.52106			−0.161261
$787$	6.55956	−	6.55956i	0.233823	−	0.233823i	−0.580463	−	0.814286i	$-0.697129\pi$
$787$	6.55956	−	6.55956i	0.233823	−	0.233823i	0.814286	+	0.580463i	$0.197129\pi$
$788$	16.1422	−	16.1422i	0.575043	−	0.575043i
$789$	−10.3239			−0.367539
$790$	37.3979	−	4.94117i	1.33056	−	0.175799i
$791$	−3.28344			−0.116746
$792$	6.19761	−	6.19761i	0.220222	−	0.220222i
$793$	7.42960	+	7.42960i	0.263833	+	0.263833i
$794$			28.0901i			0.996881i
$795$	6.16246	−	8.03878i	0.218560	−	0.285106i
$796$			21.0938i			0.747649i
$797$	9.89605	−	9.89605i	0.350536	−	0.350536i	−0.509773	−	0.860309i	$-0.670271\pi$
$797$	9.89605	−	9.89605i	0.350536	−	0.350536i	0.860309	+	0.509773i	$0.170271\pi$
$798$	0.663382	−	0.663382i	0.0234835	−	0.0234835i
$799$	5.34840			0.189213
$800$	2.49598	−	4.33244i	0.0882464	−	0.153175i
$801$			27.6091i			0.975520i
$802$	−16.8601	+	16.8601i	−0.595349	+	0.595349i
$803$	−2.45261	−	2.45261i	−0.0865506	−	0.0865506i
$804$	−1.42449			−0.0502378
$805$	−11.9013	−	3.20277i	−0.419466	−	0.112883i
$806$	0.924791			0.0325744
$807$	−0.189113	−	0.189113i	−0.00665709	−	0.00665709i
$808$	7.49544	−	7.49544i	0.263689	−	0.263689i
$809$		−	30.8434i		−	1.08439i	−0.840251	−	0.542197i	$-0.817592\pi$
$809$		−	30.8434i		−	1.08439i	0.840251	−	0.542197i	$-0.182408\pi$
$810$	17.3971	−	2.29857i	0.611271	−	0.0807636i
$811$	−32.5399			−1.14263			−0.571315	−	0.820731i	$-0.693567\pi$
$811$	−32.5399			−1.14263			−0.571315	+	0.820731i	$0.693567\pi$
$812$	−5.65898	+	5.65898i	−0.198591	+	0.198591i
$813$	−0.440328	+	0.440328i	−0.0154430	+	0.0154430i
$814$		−	18.9676i		−	0.664812i
$815$	3.31056	+	25.0564i	0.115964	+	0.877687i
$816$			1.47528i			0.0516452i
$817$	−5.85006	−	5.85006i	−0.204668	−	0.204668i
$818$	12.1109	−	12.1109i	0.423449	−	0.423449i
$819$	3.25155			0.113619
$820$	−6.56350	−	5.03152i	−0.229207	−	0.175708i
$821$	19.5704			0.683013			0.341506	−	0.939879i	$-0.389063\pi$
$821$	19.5704			0.683013			0.341506	+	0.939879i	$0.389063\pi$
$822$	−3.10630	+	3.10630i	−0.108345	+	0.108345i
$823$	0.670676	−	0.670676i	0.0233783	−	0.0233783i	−0.695321	−	0.718699i	$-0.744738\pi$
$823$	0.670676	−	0.670676i	0.0233783	−	0.0233783i	0.718699	+	0.695321i	$0.244738\pi$
$824$	−14.7970			−0.515479
$825$	−2.74713	+	4.76837i	−0.0956427	+	0.166013i
$826$		−	4.85284i		−	0.168852i
$827$	−31.3990	+	31.3990i	−1.09185	+	1.09185i	−0.0965203	+	0.995331i	$0.530771\pi$
$827$	−31.3990	+	31.3990i	−1.09185	+	1.09185i	−0.995331	+	0.0965203i	$0.969229\pi$
$828$	−5.28713	+	12.7086i	−0.183741	+	0.441655i
$829$		−	34.4163i		−	1.19533i	−0.801747	−	0.597664i	$-0.796096\pi$
$829$		−	34.4163i		−	1.19533i	0.801747	−	0.597664i	$-0.203904\pi$
$830$	21.0106	+	16.1065i	0.729288	+	0.559066i
$831$	4.57072			0.158557
$832$	−0.697028	−	0.697028i	−0.0241651	−	0.0241651i
$833$	16.4379	+	16.4379i	0.569540	+	0.569540i
$834$			7.02349i			0.243203i
$835$	−40.8071	+	5.39161i	−1.41219	+	0.186584i
$836$	−6.91664			−0.239217
$837$	−1.40348	−	1.40348i	−0.0485113	−	0.0485113i
$838$	22.4278	+	22.4278i	0.774756	+	0.774756i
$839$	16.3790			0.565465			0.282733	−	0.959199i	$-0.408759\pi$
$839$	16.3790			0.565465			0.282733	+	0.959199i	$0.408759\pi$
$840$	−0.918230	+	0.121320i	−0.0316819	+	0.00418595i
$841$	−19.4898			−0.672061
$842$	12.9756	−	12.9756i	0.447167	−	0.447167i
$843$	−7.50904	−	7.50904i	−0.258625	−	0.258625i
$844$			13.8007i			0.475039i
$845$	21.3457	+	16.3634i	0.734315	+	0.562919i
$846$	3.75009			0.128931
$847$	1.36063	−	1.36063i	0.0467519	−	0.0467519i
$848$	−8.88737	−	8.88737i	−0.305193	−	0.305193i
$849$	7.57157			0.259856
$850$	5.31552	+	19.7645i	0.182321	+	0.677915i
$851$	11.3566	+	27.5377i	0.389299	+	0.943979i
$852$	1.16067	+	1.16067i	0.0397641	+	0.0397641i
$853$	−4.42162	+	4.42162i	−0.151393	+	0.151393i	−0.778740	−	0.627347i	$-0.784141\pi$
$853$	−4.42162	+	4.42162i	−0.151393	+	0.151393i	0.627347	+	0.778740i	$0.284141\pi$
$854$		−	12.2502i		−	0.419194i
$855$	−11.5361	−	8.84345i	−0.394525	−	0.302440i
$856$			10.3331i			0.353178i
$857$	−25.8582	−	25.8582i	−0.883301	−	0.883301i	0.110568	−	0.993869i	$-0.464733\pi$
$857$	−25.8582	−	25.8582i	−0.883301	−	0.883301i	−0.993869	+	0.110568i	$0.964733\pi$
$858$	0.767162	+	0.767162i	0.0261905	+	0.0261905i
$859$			51.1948i			1.74674i	0.487053	+	0.873372i	$0.338072\pi$
$859$			51.1948i			1.74674i	−0.487053	+	0.873372i	$0.661928\pi$
$860$	1.06987	+	8.09745i	0.0364822	+	0.276121i
$861$			1.53198i			0.0522098i
$862$	17.5251	−	17.5251i	0.596909	−	0.596909i
$863$	−19.1775	+	19.1775i	−0.652809	+	0.652809i	−0.953668	−	0.300860i	$-0.902726\pi$
$863$	−19.1775	+	19.1775i	−0.652809	+	0.652809i	0.300860	+	0.953668i	$0.402726\pi$
$864$			2.11564i			0.0719756i
$865$	2.71784	+	20.5704i	0.0924094	+	0.699413i
$866$		−	6.25766i		−	0.212644i
$867$	0.0622978	+	0.0622978i	0.00211574	+	0.00211574i
$868$	−0.762416	−	0.762416i	−0.0258781	−	0.0258781i
$869$			51.5183i			1.74764i
$870$	−4.45376	−	3.41421i	−0.150997	−	0.115753i
$871$			3.89608i			0.132014i
$872$	−2.77902	+	2.77902i	−0.0941096	+	0.0941096i
$873$	11.9756	+	11.9756i	0.405313	+	0.405313i
$874$	10.0418	−	4.14125i	0.339669	−	0.140080i
$875$	−11.8645	+	4.93376i	−0.401092	+	0.166792i
$876$	0.409353			0.0138307
$877$	−28.0226	−	28.0226i	−0.946257	−	0.946257i	0.0523705	−	0.998628i	$-0.483322\pi$
$877$	−28.0226	−	28.0226i	−0.946257	−	0.946257i	−0.998628	+	0.0523705i	$0.983322\pi$
$878$	−15.5694	+	15.5694i	−0.525441	+	0.525441i
$879$	−1.41630			−0.0477706
$880$	5.41935	+	4.15442i	0.182686	+	0.140046i
$881$			13.5604i			0.456863i	0.973560	+	0.228431i	$0.0733597\pi$
$881$			13.5604i			0.456863i	−0.973560	+	0.228431i	$0.926640\pi$
$882$	11.5257	+	11.5257i	0.388089	+	0.388089i
$883$	23.1955	−	23.1955i	0.780590	−	0.780590i	−0.199340	−	0.979930i	$-0.563880\pi$
$883$	23.1955	−	23.1955i	0.780590	−	0.780590i	0.979930	+	0.199340i	$0.0638799\pi$
$884$	4.03501			0.135712
$885$	3.37358	−	0.445731i	0.113402	−	0.0149831i
$886$	−38.4536			−1.29187
$887$	−28.9804	−	28.9804i	−0.973067	−	0.973067i	0.0265799	−	0.999647i	$-0.491538\pi$
$887$	−28.9804	−	28.9804i	−0.973067	−	0.973067i	−0.999647	+	0.0265799i	$0.991538\pi$
$888$	1.58289	+	1.58289i	0.0531184	+	0.0531184i
$889$	9.45345			0.317058
$890$	−21.3246	+	2.81750i	−0.714803	+	0.0944428i
$891$			23.9657i			0.802881i
$892$	−19.2255	−	19.2255i	−0.643717	−	0.643717i
$893$	−2.09259	−	2.09259i	−0.0700258	−	0.0700258i
$894$	6.08822			0.203620
$895$	3.02666	+	2.32021i	0.101170	+	0.0775560i
$896$			1.14929i			0.0383950i
$897$	−1.57312	−	0.654460i	−0.0525249	−	0.0218518i
$898$	0.410743	−	0.410743i	0.0137067	−	0.0137067i
$899$		−	6.53286i		−	0.217883i
$900$	3.72704	+	13.8581i	0.124235	+	0.461936i
$901$	51.4479			1.71398
$902$	7.98648	−	7.98648i	0.265921	−	0.265921i
$903$	1.06987	−	1.06987i	0.0356030	−	0.0356030i
$904$	−2.85694			−0.0950203
$905$	20.9805	+	16.0835i	0.697416	+	0.534633i
$906$	−4.35856			−0.144803
$907$	−19.1811	+	19.1811i	−0.636897	+	0.636897i	−0.949789	−	0.312892i	$-0.898702\pi$
$907$	−19.1811	+	19.1811i	−0.636897	+	0.636897i	0.312892	+	0.949789i	$0.398702\pi$
$908$	13.2083	+	13.2083i	0.438334	+	0.438334i
$909$			30.4236i			1.00909i
$910$	0.331820	+	2.51143i	0.0109997	+	0.0832529i
$911$			36.9319i			1.22361i	0.791009	+	0.611805i	$0.209556\pi$
$911$			36.9319i			1.22361i	−0.791009	+	0.611805i	$0.790444\pi$
$912$	0.577212	−	0.577212i	0.0191134	−	0.0191134i
$913$	−25.5657	+	25.5657i	−0.846103	+	0.846103i
$914$	18.3719			0.607688
$915$	8.51606	−	1.12518i	0.281532	−	0.0371972i
$916$			4.10182i			0.135528i
$917$	10.1943	−	10.1943i	0.336645	−	0.336645i
$918$	−6.12359	−	6.12359i	−0.202109	−	0.202109i
$919$	−58.3059			−1.92333			−0.961667	−	0.274219i	$-0.911581\pi$
$919$	−58.3059			−1.92333			−0.961667	+	0.274219i	$0.911581\pi$
$920$	−10.3554	−	2.78675i	−0.341407	−	0.0918764i
$921$	4.72495			0.155693
$922$	−11.0926	−	11.0926i	−0.365315	−	0.365315i
$923$	3.17453	−	3.17453i	0.104491	−	0.104491i
$924$		−	1.26493i		−	0.0416130i
$925$	26.9093	+	15.5029i	0.884774	+	0.509731i
$926$	13.8277			0.454405
$927$	30.0301	−	30.0301i	0.986319	−	0.986319i
$928$	−4.92391	+	4.92391i	−0.161635	+	0.161635i
$929$		−	15.1024i		−	0.495494i	−0.968825	−	0.247747i	$-0.920310\pi$
$929$		−	15.1024i		−	0.495494i	0.968825	−	0.247747i	$-0.0796902\pi$
$930$	0.459986	−	0.600041i	0.0150835	−	0.0196761i
$931$		−	12.8628i		−	0.421563i
$932$	13.7878	+	13.7878i	0.451634	+	0.451634i
$933$	−3.34840	+	3.34840i	−0.109622	+	0.109622i
$934$	22.5903			0.739176
$935$	−27.7107	+	3.66125i	−0.906237	+	0.119736i
$936$	2.82919			0.0924751
$937$	−9.26161	+	9.26161i	−0.302564	+	0.302564i	−0.842016	−	0.539452i	$-0.818631\pi$
$937$	−9.26161	+	9.26161i	−0.302564	+	0.302564i	0.539452	+	0.842016i	$0.318631\pi$
$938$	3.21200	−	3.21200i	0.104876	−	0.104876i
$939$	−1.70645			−0.0556879
$940$	0.382696	+	2.89649i	0.0124822	+	0.0944729i
$941$			38.8905i			1.26779i	0.773418	+	0.633897i	$0.218546\pi$
$941$			38.8905i			1.26779i	−0.773418	+	0.633897i	$0.781454\pi$
$942$	1.27481	−	1.27481i	0.0415356	−	0.0415356i
$943$	−6.81321	+	16.3768i	−0.221869	+	0.533303i
$944$		−	4.22248i		−	0.137430i
$945$	3.30780	−	4.31496i	0.107603	−	0.140365i
$946$	−11.1548			−0.362674
$947$	−13.7163	−	13.7163i	−0.445720	−	0.445720i	0.448209	−	0.893929i	$-0.352062\pi$
$947$	−13.7163	−	13.7163i	−0.445720	−	0.445720i	−0.893929	+	0.448209i	$0.852062\pi$
$948$	−4.29934	−	4.29934i	−0.139636	−	0.139636i
$949$		−	1.11961i		−	0.0363441i
$950$	5.65322	−	9.81267i	0.183415	−	0.318365i
$951$	−5.44502			−0.176567
$952$	−3.32654	−	3.32654i	−0.107814	−	0.107814i
$953$	14.8183	+	14.8183i	0.480013	+	0.480013i	0.905136	−	0.425122i	$-0.139769\pi$
$953$	14.8183	+	14.8183i	0.480013	+	0.480013i	−0.425122	+	0.905136i	$0.639769\pi$
$954$	36.0733			1.16792
$955$	27.5278	+	21.1026i	0.890780	+	0.682864i
$956$	15.3810			0.497457
$957$	5.41935	−	5.41935i	0.175183	−	0.175183i
$958$	−24.8644	−	24.8644i	−0.803333	−	0.803333i
$959$		−	14.0085i		−	0.452357i
$960$	−0.798956	+	0.105561i	−0.0257862	+	0.00340698i
$961$	−30.1198			−0.971608
$962$	4.32932	−	4.32932i	0.139583	−	0.139583i
$963$	−20.9707	−	20.9707i	−0.675772	−	0.675772i
$964$	16.7710			0.540156
$965$	1.21583	+	9.20216i	0.0391389	+	0.296228i
$966$	0.757359	+	1.83646i	0.0243676	+	0.0590871i
$967$	16.6986	+	16.6986i	0.536992	+	0.536992i	0.922644	−	0.385652i	$-0.126023\pi$
$967$	16.6986	+	16.6986i	0.536992	+	0.536992i	−0.385652	+	0.922644i	$0.626023\pi$
$968$	1.18389	−	1.18389i	0.0380518	−	0.0380518i
$969$			3.34141i			0.107342i
$970$	−8.02758	+	10.4718i	−0.257750	+	0.336229i
$971$			4.63581i			0.148770i	0.997230	+	0.0743852i	$0.0236994\pi$
$971$			4.63581i			0.148770i	−0.997230	+	0.0743852i	$0.976301\pi$
$972$	−6.48795	−	6.48795i	−0.208101	−	0.208101i
$973$	−15.8369	−	15.8369i	−0.507707	−	0.507707i
$974$		−	27.7391i		−	0.888819i
$975$	−1.71540	+	0.461347i	−0.0549369	+	0.0147749i
$976$		−	10.6590i		−	0.341186i
$977$	−24.3063	+	24.3063i	−0.777626	+	0.777626i	−0.979427	−	0.201801i	$-0.935321\pi$
$977$	−24.3063	+	24.3063i	−0.777626	+	0.777626i	0.201801	+	0.979427i	$0.435321\pi$
$978$	2.88053	−	2.88053i	0.0921092	−	0.0921092i
$979$		−	29.3762i		−	0.938868i
$980$	−7.72596	+	10.0783i	−0.246797	+	0.321941i
$981$		−	11.2799i		−	0.360139i
$982$	24.6327	+	24.6327i	0.786062	+	0.786062i
$983$	3.10070	+	3.10070i	0.0988970	+	0.0988970i	0.754824	−	0.655927i	$-0.227722\pi$
$983$	3.10070	+	3.10070i	0.0988970	+	0.0988970i	−0.655927	+	0.754824i	$0.727722\pi$
$984$			1.33299i			0.0424940i
$985$	−50.6064	+	6.68633i	−1.61245	+	0.213044i
$986$		−	28.5039i		−	0.907749i
$987$	0.382696	−	0.382696i	0.0121813	−	0.0121813i
$988$	−1.57872	−	1.57872i	−0.0502257	−	0.0502257i
$989$	16.1949	−	6.67881i	0.514968	−	0.212374i
$990$	−19.4297	+	2.56713i	−0.617516	+	0.0815888i
$991$	−1.91539			−0.0608443			−0.0304221	−	0.999537i	$-0.509685\pi$
$991$	−1.91539			−0.0608443			−0.0304221	+	0.999537i	$0.509685\pi$
$992$	−0.663382	−	0.663382i	−0.0210624	−	0.0210624i
$993$	−0.242641	+	0.242641i	−0.00769997	+	0.00769997i
$994$	−5.23429			−0.166022
$995$	28.6962	−	37.4335i	0.909730	−	1.18672i
$996$		−	4.26706i		−	0.135207i
$997$	−36.7069	−	36.7069i	−1.16252	−	1.16252i	−0.983922	−	0.178597i	$-0.942844\pi$
$997$	−36.7069	−	36.7069i	−1.16252	−	1.16252i	−0.178597	−	0.983922i	$-0.557156\pi$
$998$	−24.8340	+	24.8340i	−0.786106	+	0.786106i
$999$	−13.1405			−0.415747

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.e.b.137.2	yes	8
5.2	odd	4		1150.2.e.c.643.3		8
5.3	odd	4		230.2.e.a.183.2	yes	8
5.4	even	2		1150.2.e.b.1057.3		8
23.22	odd	2		230.2.e.a.137.2	✓	8
115.22	even	4		1150.2.e.b.643.3		8
115.68	even	4	inner	230.2.e.b.183.2	yes	8
115.114	odd	2		1150.2.e.c.1057.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.e.a.137.2	✓	8	23.22	odd	2
230.2.e.a.183.2	yes	8	5.3	odd	4
230.2.e.b.137.2	yes	8	1.1	even	1	trivial
230.2.e.b.183.2	yes	8	115.68	even	4	inner
1150.2.e.b.643.3		8	115.22	even	4
1150.2.e.b.1057.3		8	5.4	even	2
1150.2.e.c.643.3		8	5.2	odd	4
1150.2.e.c.1057.3		8	115.114	odd	2

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.254848 - 0.254848i) q^{3} +1.00000i q^{4} +(1.36041 - 1.77462i) q^{5} -0.360409 q^{6} +(0.812668 - 0.812668i) q^{7} +(0.707107 - 0.707107i) q^{8} +2.87011i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.254848 - 0.254848i) q^{3} +1.00000i q^{4} +(1.36041 - 1.77462i) q^{5} -0.360409 q^{6} +(0.812668 - 0.812668i) q^{7} +(0.707107 - 0.707107i) q^{8} +2.87011i q^{9} +(-2.21680 + 0.292893i) q^{10} -3.05380i q^{11} +(0.254848 + 0.254848i) q^{12} +(0.697028 - 0.697028i) q^{13} -1.14929 q^{14} +(-0.105561 - 0.798956i) q^{15} -1.00000 q^{16} +(2.89444 - 2.89444i) q^{17} +(2.02947 - 2.02947i) q^{18} -2.26493 q^{19} +(1.77462 + 1.36041i) q^{20} -0.414214i q^{21} +(-2.15937 + 2.15937i) q^{22} +(1.84214 - 4.42793i) q^{23} -0.360409i q^{24} +(-1.29857 - 4.82843i) q^{25} -0.985746 q^{26} +(1.49598 + 1.49598i) q^{27} +(0.812668 + 0.812668i) q^{28} +6.96346i q^{29} +(-0.490304 + 0.639591i) q^{30} -0.938164 q^{31} +(0.707107 + 0.707107i) q^{32} +(-0.778256 - 0.778256i) q^{33} -4.09335 q^{34} +(-0.336618 - 2.54774i) q^{35} -2.87011 q^{36} +(-4.39193 + 4.39193i) q^{37} +(1.60155 + 1.60155i) q^{38} -0.355272i q^{39} +(-0.292893 - 2.21680i) q^{40} -3.69853 q^{41} +(-0.292893 + 0.292893i) q^{42} +(2.58289 + 2.58289i) q^{43} +3.05380 q^{44} +(5.09335 + 3.90452i) q^{45} +(-4.43361 + 1.82843i) q^{46} +(0.923909 + 0.923909i) q^{47} +(-0.254848 + 0.254848i) q^{48} +5.67914i q^{49} +(-2.49598 + 4.33244i) q^{50} -1.47528i q^{51} +(0.697028 + 0.697028i) q^{52} +(8.88737 + 8.88737i) q^{53} -2.11564i q^{54} +(-5.41935 - 4.15442i) q^{55} -1.14929i q^{56} +(-0.577212 + 0.577212i) q^{57} +(4.92391 - 4.92391i) q^{58} +4.22248i q^{59} +(0.798956 - 0.105561i) q^{60} +10.6590i q^{61} +(0.663382 + 0.663382i) q^{62} +(2.33244 + 2.33244i) q^{63} -1.00000i q^{64} +(-0.288718 - 2.18520i) q^{65} +1.10062i q^{66} +(-2.79478 + 2.79478i) q^{67} +(2.89444 + 2.89444i) q^{68} +(-0.658982 - 1.59791i) q^{69} +(-1.56350 + 2.03955i) q^{70} +4.55438 q^{71} +(2.02947 + 2.02947i) q^{72} +(0.803131 - 0.803131i) q^{73} +6.21112 q^{74} +(-1.56145 - 0.899576i) q^{75} -2.26493i q^{76} +(-2.48173 - 2.48173i) q^{77} +(-0.251215 + 0.251215i) q^{78} -16.8702 q^{79} +(-1.36041 + 1.77462i) q^{80} -7.84782 q^{81} +(2.61526 + 2.61526i) q^{82} +(-8.37177 - 8.37177i) q^{83} +0.414214 q^{84} +(-1.19892 - 9.07416i) q^{85} -3.65276i q^{86} +(1.77462 + 1.77462i) q^{87} +(-2.15937 - 2.15937i) q^{88} +9.61955 q^{89} +(-0.840634 - 6.36246i) q^{90} -1.13290i q^{91} +(4.42793 + 1.84214i) q^{92} +(-0.239089 + 0.239089i) q^{93} -1.30661i q^{94} +(-3.08123 + 4.01939i) q^{95} +0.360409 q^{96} +(4.17254 - 4.17254i) q^{97} +(4.01576 - 4.01576i) q^{98} +8.76474 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} + 4 q^{5} + 4 q^{6}+O(q^{10}) \) 8 * q - 4 * q^3 + 4 * q^5 + 4 * q^6	\( 8 q - 4 q^{3} + 4 q^{5} + 4 q^{6} - 4 q^{12} - 4 q^{14} - 8 q^{16} + 24 q^{17} - 8 q^{18} - 12 q^{19} - 4 q^{20} - 12 q^{22} - 16 q^{23} + 12 q^{26} + 8 q^{27} - 16 q^{30} - 4 q^{31} + 20 q^{33} - 4 q^{34} - 4 q^{35} - 4 q^{36} + 4 q^{37} + 8 q^{38} - 8 q^{40} + 12 q^{41} - 8 q^{42} - 20 q^{43} + 20 q^{44} + 12 q^{45} - 16 q^{47} + 4 q^{48} - 16 q^{50} + 12 q^{55} + 20 q^{57} + 16 q^{58} + 8 q^{60} + 4 q^{62} + 12 q^{65} - 4 q^{67} + 24 q^{68} + 12 q^{69} + 4 q^{70} - 44 q^{71} - 8 q^{72} + 28 q^{73} + 48 q^{74} - 4 q^{75} + 4 q^{77} - 4 q^{78} + 8 q^{79} - 4 q^{80} - 16 q^{81} + 8 q^{82} - 28 q^{83} - 8 q^{84} + 20 q^{85} - 4 q^{87} - 12 q^{88} - 40 q^{89} - 12 q^{90} + 16 q^{92} - 12 q^{93} - 4 q^{95} - 4 q^{96} - 8 q^{97} + 16 q^{98} - 36 q^{99}+O(q^{100}) \) 8 * q - 4 * q^3 + 4 * q^5 + 4 * q^6 - 4 * q^12 - 4 * q^14 - 8 * q^16 + 24 * q^17 - 8 * q^18 - 12 * q^19 - 4 * q^20 - 12 * q^22 - 16 * q^23 + 12 * q^26 + 8 * q^27 - 16 * q^30 - 4 * q^31 + 20 * q^33 - 4 * q^34 - 4 * q^35 - 4 * q^36 + 4 * q^37 + 8 * q^38 - 8 * q^40 + 12 * q^41 - 8 * q^42 - 20 * q^43 + 20 * q^44 + 12 * q^45 - 16 * q^47 + 4 * q^48 - 16 * q^50 + 12 * q^55 + 20 * q^57 + 16 * q^58 + 8 * q^60 + 4 * q^62 + 12 * q^65 - 4 * q^67 + 24 * q^68 + 12 * q^69 + 4 * q^70 - 44 * q^71 - 8 * q^72 + 28 * q^73 + 48 * q^74 - 4 * q^75 + 4 * q^77 - 4 * q^78 + 8 * q^79 - 4 * q^80 - 16 * q^81 + 8 * q^82 - 28 * q^83 - 8 * q^84 + 20 * q^85 - 4 * q^87 - 12 * q^88 - 40 * q^89 - 12 * q^90 + 16 * q^92 - 12 * q^93 - 4 * q^95 - 4 * q^96 - 8 * q^97 + 16 * q^98 - 36 * q^99

Introduction

L-functions

Modular forms

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