LMFDB - Embedded newform 637.2.bp.a.543.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(88,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([34, 35]))

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

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

chi := DirichletCharacter("637.88");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$637 = 7^{2} \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	637.bp (of order $42$ , degree $12$ , 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$756$
Relative dimension:	$63$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			543.8
Character	$\chi$	$=$	637.543
Dual form			637.2.bp.a.576.8

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.36581 - 0.177293i) q^{2} +(0.532425 - 2.33271i) q^{3} +(3.58796 + 0.540798i) q^{4} +(0.329479 + 1.06814i) q^{5} +(-1.67319 + 5.42434i) q^{6} +(1.40758 - 2.24025i) q^{7} +(-3.76664 - 0.859710i) q^{8} +(-2.45513 - 1.18233i) q^{9} +(-0.590110 - 2.58544i) q^{10} +(1.47161 + 3.05582i) q^{11} +(3.17184 - 8.08173i) q^{12} +(-3.11176 - 1.82124i) q^{13} +(-3.72724 + 5.05046i) q^{14} +(2.66709 - 0.199871i) q^{15} +(1.82415 + 0.562676i) q^{16} +(0.844274 - 2.15118i) q^{17} +(5.59876 + 3.23245i) q^{18} -1.22816i q^{19} +(0.604507 + 4.01064i) q^{20} +(-4.47642 - 4.47623i) q^{21} +(-2.93977 - 7.49040i) q^{22} +(-1.36836 - 3.48652i) q^{23} +(-4.01090 + 8.32872i) q^{24} +(3.09882 - 2.11274i) q^{25} +(7.03895 + 4.86041i) q^{26} +(0.410261 - 0.514451i) q^{27} +(6.26186 - 7.27673i) q^{28} +(0.429523 - 1.09441i) q^{29} -6.34526 q^{30} +(7.21091 + 4.16322i) q^{31} +(2.97703 + 1.16840i) q^{32} +(7.91185 - 1.80583i) q^{33} +(-2.37878 + 4.93959i) q^{34} +(2.85668 + 0.765379i) q^{35} +(-8.16953 - 5.56989i) q^{36} +(-1.06456 - 7.06287i) q^{37} +(-0.217744 + 2.90560i) q^{38} +(-5.90520 + 6.28916i) q^{39} +(-0.322733 - 4.30657i) q^{40} +(-0.0827967 - 0.268420i) q^{41} +(9.79676 + 11.3835i) q^{42} +(-8.44207 - 2.60403i) q^{43} +(3.62749 + 11.7600i) q^{44} +(0.453984 - 3.01199i) q^{45} +(2.61914 + 8.49106i) q^{46} +(-0.702141 + 1.02985i) q^{47} +(2.28378 - 3.95563i) q^{48} +(-3.03746 - 6.30665i) q^{49} +(-7.70579 + 4.44894i) q^{50} +(-4.56855 - 3.11478i) q^{51} +(-10.1800 - 8.21738i) q^{52} +(2.12481 + 5.41394i) q^{53} +(-1.06181 + 1.14436i) q^{54} +(-2.77920 + 2.57872i) q^{55} +(-7.22780 + 7.22811i) q^{56} +(-2.86494 - 0.653903i) q^{57} +(-1.21020 + 2.51301i) q^{58} +(-0.332459 - 0.358306i) q^{59} +(9.67751 + 0.725229i) q^{60} +(-4.04838 - 5.07651i) q^{61} +(-16.3215 - 11.1278i) q^{62} +(-6.10451 + 3.83590i) q^{63} +(-10.2758 - 4.94855i) q^{64} +(0.920088 - 3.92387i) q^{65} +(-19.0381 + 2.86953i) q^{66} -13.3949i q^{67} +(4.19258 - 7.26176i) q^{68} +(-8.86159 + 1.33567i) q^{69} +(-6.62266 - 2.31721i) q^{70} +(-2.63498 + 1.03415i) q^{71} +(8.23114 + 6.56411i) q^{72} +(-0.772794 - 1.13348i) q^{73} +(1.26634 + 16.8981i) q^{74} +(-3.27851 - 8.35351i) q^{75} +(0.664188 - 4.40660i) q^{76} +(8.91721 + 1.00453i) q^{77} +(15.0856 - 13.8320i) q^{78} +(4.37875 + 7.58422i) q^{79} +2.13385i q^{80} +(-6.07865 - 7.62238i) q^{81} +(0.148292 + 0.649711i) q^{82} +(-1.46582 + 3.04381i) q^{83} +(-13.6405 - 18.4814i) q^{84} +(2.57594 + 0.193040i) q^{85} +(19.5107 + 7.65737i) q^{86} +(-2.32424 - 1.58464i) q^{87} +(-2.91588 - 12.7753i) q^{88} +(5.04539 + 7.40023i) q^{89} +(-1.60805 + 7.04531i) q^{90} +(-8.46009 + 4.40760i) q^{91} +(-3.02412 - 13.2495i) q^{92} +(13.5508 - 14.6043i) q^{93} +(1.84372 - 2.31195i) q^{94} +(1.31185 - 0.404653i) q^{95} +(4.31057 - 6.32244i) q^{96} +(8.94651 + 5.16527i) q^{97} +(6.06792 + 15.4589i) q^{98} -9.24238i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$756 q - 18 q^{2} - 11 q^{3} - 68 q^{4} - 15 q^{6} - 19 q^{7} - 121 q^{9} + 11 q^{10} - 21 q^{11} - 26 q^{12} - 10 q^{13} - 38 q^{14} - 6 q^{15} + 52 q^{16} - 18 q^{17} + 9 q^{18} - 15 q^{20} + 16 q^{21}+ \cdots + 24 q^{98}+O(q^{100})$ 756 * q - 18 * q^2 - 11 * q^3 - 68 * q^4 - 15 * q^6 - 19 * q^7 - 121 * q^9 + 11 * q^10 - 21 * q^11 - 26 * q^12 - 10 * q^13 - 38 * q^14 - 6 * q^15 + 52 * q^16 - 18 * q^17 + 9 * q^18 - 15 * q^20 + 16 * q^21 - q^22 - 8 * q^23 - 21 * q^24 - 79 * q^25 - 16 * q^26 - 50 * q^27 - 47 * q^28 - 3 * q^29 + 22 * q^30 + 15 * q^31 - 30 * q^32 - 21 * q^33 - 6 * q^35 - 42 * q^36 + 41 * q^37 - 2 * q^38 + 13 * q^39 - 24 * q^40 - 6 * q^41 - 35 * q^42 - 5 * q^43 - 108 * q^44 + 87 * q^45 - 3 * q^46 - 63 * q^47 - 154 * q^48 - 55 * q^49 + 135 * q^50 + 26 * q^51 - 80 * q^52 + 16 * q^53 - 75 * q^54 + 59 * q^55 - 122 * q^56 + 63 * q^57 - 21 * q^58 - 42 * q^59 - 15 * q^60 - 60 * q^61 - 45 * q^62 + 51 * q^63 + 4 * q^64 - 32 * q^65 + 85 * q^66 - 156 * q^68 + 70 * q^69 + 228 * q^70 - 30 * q^71 - 21 * q^72 - 6 * q^73 + 32 * q^74 - 52 * q^75 + 21 * q^76 + 3 * q^77 - 89 * q^78 + 12 * q^79 - 81 * q^81 + 160 * q^82 - 147 * q^83 - 25 * q^84 + 144 * q^85 + 60 * q^86 - 76 * q^87 - 35 * q^88 - 57 * q^89 + 117 * q^90 - 11 * q^91 + 88 * q^92 - 24 * q^93 - 42 * q^94 + 69 * q^95 + 12 * q^96 - 156 * q^97 + 24 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$ .

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{21}\right)$

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

)

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

$2$	−2.36581	−	0.177293i	−1.67288	−	0.125365i	−0.795753	−	0.605622i	$-0.792924\pi$
$2$	−2.36581	−	0.177293i	−1.67288	−	0.125365i	−0.877128	+	0.480257i	$0.840543\pi$
$3$	0.532425	−	2.33271i	0.307396	−	1.34679i	−0.551302	−	0.834306i	$-0.685869\pi$
$3$	0.532425	−	2.33271i	0.307396	−	1.34679i	0.858698	−	0.512483i	$-0.171274\pi$
$4$	3.58796	+	0.540798i	1.79398	+	0.270399i
$5$	0.329479	+	1.06814i	0.147347	+	0.477689i	0.998916	−	0.0465551i	$-0.0148243\pi$
$5$	0.329479	+	1.06814i	0.147347	+	0.477689i	−0.851568	+	0.524244i	$0.824348\pi$
$6$	−1.67319	+	5.42434i	−0.683076	+	2.21448i
$7$	1.40758	−	2.24025i	0.532014	−	0.846736i
$7$	1.40758	−	2.24025i	0.532014	−	0.846736i
$8$	−3.76664	−	0.859710i	−1.33171	−	0.303953i
$9$	−2.45513	−	1.18233i	−0.818378	−	0.394110i
$10$	−0.590110	−	2.58544i	−0.186609	−	0.817588i
$11$	1.47161	+	3.05582i	0.443706	+	0.921365i	0.996138	+	0.0878067i	$0.0279858\pi$
$11$	1.47161	+	3.05582i	0.443706	+	0.921365i	−0.552432	+	0.833558i	$0.686300\pi$
$12$	3.17184	−	8.08173i	0.915633	−	2.33299i
$13$	−3.11176	−	1.82124i	−0.863048	−	0.505122i
$13$	−3.11176	−	1.82124i	−0.863048	−	0.505122i
$14$	−3.72724	+	5.05046i	−0.996147	+	1.34979i
$15$	2.66709	−	0.199871i	0.688639	−	0.0516064i
$16$	1.82415	+	0.562676i	0.456038	+	0.140669i
$17$	0.844274	−	2.15118i	0.204767	−	0.521737i	−0.791190	−	0.611570i	$-0.790538\pi$
$17$	0.844274	−	2.15118i	0.204767	−	0.521737i	0.995957	+	0.0898334i	$0.0286335\pi$
$18$	5.59876	+	3.23245i	1.31964	+	0.761895i
$19$		−	1.22816i		−	0.281759i	−0.990027	−	0.140880i	$-0.955007\pi$
$19$		−	1.22816i		−	0.281759i	0.990027	−	0.140880i	$-0.0449931\pi$
$20$	0.604507	+	4.01064i	0.135172	+	0.896807i
$21$	−4.47642	−	4.47623i	−0.976835	−	0.976793i
$22$	−2.93977	−	7.49040i	−0.626760	−	1.59696i
$23$	−1.36836	−	3.48652i	−0.285323	−	0.726991i	−0.999631	−	0.0271595i	$-0.991354\pi$
$23$	−1.36836	−	3.48652i	−0.285323	−	0.726991i	0.714308	−	0.699831i	$-0.246741\pi$
$24$	−4.01090	+	8.32872i	−0.818722	+	1.70009i
$25$	3.09882	−	2.11274i	0.619764	−	0.422548i
$26$	7.03895	+	4.86041i	1.38045	+	0.953204i
$27$	0.410261	−	0.514451i	0.0789547	−	0.0990060i
$28$	6.26186	−	7.27673i	1.18338	−	1.37517i
$29$	0.429523	−	1.09441i	0.0797605	−	0.203226i	−0.885431	−	0.464771i	$-0.846137\pi$
$29$	0.429523	−	1.09441i	0.0797605	−	0.203226i	0.965191	+	0.261545i	$0.0842319\pi$
$30$	−6.34526			−1.15848
$31$	7.21091	+	4.16322i	1.29512	+	0.747737i	0.979557	−	0.201168i	$-0.0644738\pi$
$31$	7.21091	+	4.16322i	1.29512	+	0.747737i	0.315562	+	0.948905i	$0.397807\pi$
$32$	2.97703	+	1.16840i	0.526269	+	0.206545i
$33$	7.91185	−	1.80583i	1.37728	−	0.314355i
$34$	−2.37878	+	4.93959i	−0.407958	+	0.847132i
$35$	2.85668	+	0.765379i	0.482867	+	0.129373i
$36$	−8.16953	−	5.56989i	−1.36159	−	0.928315i
$37$	−1.06456	−	7.06287i	−0.175012	−	1.16113i	−0.887963	−	0.459915i	$-0.847880\pi$
$37$	−1.06456	−	7.06287i	−0.175012	−	1.16113i	0.712951	−	0.701214i	$-0.247358\pi$
$38$	−0.217744	+	2.90560i	−0.0353228	+	0.471350i
$39$	−5.90520	+	6.28916i	−0.945589	+	1.00707i
$40$	−0.322733	−	4.30657i	−0.0510285	−	0.680928i
$41$	−0.0827967	−	0.268420i	−0.0129307	−	0.0419202i	0.948878	−	0.315644i	$-0.102221\pi$
$41$	−0.0827967	−	0.268420i	−0.0129307	−	0.0419202i	−0.961808	+	0.273724i	$0.911744\pi$
$42$	9.79676	+	11.3835i	1.51167	+	1.75652i
$43$	−8.44207	−	2.60403i	−1.28740	−	0.397112i	−0.425858	−	0.904790i	$-0.640028\pi$
$43$	−8.44207	−	2.60403i	−1.28740	−	0.397112i	−0.861547	+	0.507679i	$0.830504\pi$
$44$	3.62749	+	11.7600i	0.546864	+	1.77289i
$45$	0.453984	−	3.01199i	0.0676760	−	0.449001i
$46$	2.61914	+	8.49106i	0.386172	+	1.25194i
$47$	−0.702141	+	1.02985i	−0.102418	+	0.150219i	−0.874027	−	0.485878i	$-0.838500\pi$
$47$	−0.702141	+	1.02985i	−0.102418	+	0.150219i	0.771609	+	0.636097i	$0.219452\pi$
$48$	2.28378	−	3.95563i	0.329636	−	0.570946i
$49$	−3.03746	−	6.30665i	−0.433923	−	0.900950i
$50$	−7.70579	+	4.44894i	−1.08976	+	0.629175i
$51$	−4.56855	−	3.11478i	−0.639725	−	0.436157i
$52$	−10.1800	−	8.21738i	−1.41171	−	1.13955i
$53$	2.12481	+	5.41394i	0.291866	+	0.743661i	0.999319	+	0.0369012i	$0.0117487\pi$
$53$	2.12481	+	5.41394i	0.291866	+	0.743661i	−0.707453	+	0.706760i	$0.750156\pi$
$54$	−1.06181	+	1.14436i	−0.144494	+	0.155727i
$55$	−2.77920	+	2.57872i	−0.374747	+	0.347714i
$56$	−7.22780	+	7.22811i	−0.965855	+	0.965896i
$57$	−2.86494	−	0.653903i	−0.379470	−	0.0866116i
$58$	−1.21020	+	2.51301i	−0.158907	+	0.329974i
$59$	−0.332459	−	0.358306i	−0.0432825	−	0.0466475i	0.711039	−	0.703152i	$-0.248225\pi$
$59$	−0.332459	−	0.358306i	−0.0432825	−	0.0466475i	−0.754322	+	0.656505i	$0.772034\pi$
$60$	9.67751	+	0.725229i	1.24936	+	0.0936266i
$61$	−4.04838	−	5.07651i	−0.518342	−	0.649980i	0.451914	−	0.892062i	$-0.350741\pi$
$61$	−4.04838	−	5.07651i	−0.518342	−	0.649980i	−0.970256	+	0.242081i	$0.922170\pi$
$62$	−16.3215	−	11.1278i	−2.07284	−	1.41324i
$63$	−6.10451	+	3.83590i	−0.769096	+	0.483278i
$64$	−10.2758	−	4.94855i	−1.28447	−	0.618568i
$65$	0.920088	−	3.92387i	0.114123	−	0.486697i
$66$	−19.0381	+	2.86953i	−2.34343	+	0.353215i
$67$		−	13.3949i		−	1.63645i	−0.574899	−	0.818224i	$-0.694959\pi$
$67$		−	13.3949i		−	1.63645i	0.574899	−	0.818224i	$-0.305041\pi$
$68$	4.19258	−	7.26176i	0.508425	−	0.880617i
$69$	−8.86159	+	1.33567i	−1.06681	+	0.160796i
$70$	−6.62266	−	2.31721i	−0.791560	−	0.276960i
$71$	−2.63498	+	1.03415i	−0.312715	+	0.122732i	−0.516508	−	0.856282i	$-0.672768\pi$
$71$	−2.63498	+	1.03415i	−0.312715	+	0.122732i	0.203793	+	0.979014i	$0.434673\pi$
$72$	8.23114	+	6.56411i	0.970049	+	0.773588i
$73$	−0.772794	−	1.13348i	−0.0904486	−	0.132664i	0.778348	−	0.627834i	$-0.216058\pi$
$73$	−0.772794	−	1.13348i	−0.0904486	−	0.132664i	−0.868796	+	0.495170i	$0.835106\pi$
$74$	1.26634	+	16.8981i	0.147209	+	1.96437i
$75$	−3.27851	−	8.35351i	−0.378570	−	0.964580i
$76$	0.664188	−	4.40660i	0.0761875	−	0.505471i
$77$	8.91721	+	1.00453i	1.01621	+	0.114477i
$78$	15.0856	−	13.8320i	1.70811	−	1.56617i
$79$	4.37875	+	7.58422i	0.492648	+	0.853292i	0.999964	−	0.00846851i	$-0.00269564\pi$
$79$	4.37875	+	7.58422i	0.492648	+	0.853292i	−0.507316	+	0.861760i	$0.669362\pi$
$80$			2.13385i			0.238571i
$81$	−6.07865	−	7.62238i	−0.675405	−	0.846931i
$82$	0.148292	+	0.649711i	0.0163761	+	0.0717485i
$83$	−1.46582	+	3.04381i	−0.160895	+	0.334101i	−0.965794	−	0.259310i	$-0.916505\pi$
$83$	−1.46582	+	3.04381i	−0.160895	+	0.334101i	0.804899	+	0.593411i	$0.202219\pi$
$84$	−13.6405	−	18.4814i	−1.48830	−	2.01648i
$85$	2.57594	+	0.193040i	0.279399	+	0.0209381i
$86$	19.5107	+	7.65737i	2.10389	+	0.825716i
$87$	−2.32424	−	1.58464i	−0.249185	−	0.169891i
$88$	−2.91588	−	12.7753i	−0.310834	−	1.36185i
$89$	5.04539	+	7.40023i	0.534810	+	0.784423i	0.994620	−	0.103595i	$-0.0330346\pi$
$89$	5.04539	+	7.40023i	0.534810	+	0.784423i	−0.459809	+	0.888018i	$0.652082\pi$
$90$	−1.60805	+	7.04531i	−0.169503	+	0.742641i
$91$	−8.46009	+	4.40760i	−0.886858	+	0.462042i
$92$	−3.02412	−	13.2495i	−0.315286	−	1.38136i
$93$	13.5508	−	14.6043i	1.40516	−	1.51440i
$94$	1.84372	−	2.31195i	0.190165	−	0.238459i
$95$	1.31185	−	0.404653i	0.134593	−	0.0415165i
$96$	4.31057	−	6.32244i	0.439946	−	0.645282i
$97$	8.94651	+	5.16527i	0.908380	+	0.524454i	0.879910	−	0.475141i	$-0.157603\pi$
$97$	8.94651	+	5.16527i	0.908380	+	0.524454i	0.0284706	+	0.999595i	$0.490936\pi$
$98$	6.06792	+	15.4589i	0.612953	+	1.56158i
$99$		−	9.24238i		−	0.928894i
$100$	12.2610	−	5.90459i	1.22610	−	0.590459i
$101$	3.53798	−	15.5009i	0.352042	−	1.54240i	−0.420416	−	0.907332i	$-0.638116\pi$
$101$	3.53798	−	15.5009i	0.352042	−	1.54240i	0.772458	−	0.635066i	$-0.219027\pi$
$102$	10.2561	+	8.17896i	1.01550	+	0.809837i
$103$	−11.6901	+	3.60590i	−1.15186	+	0.355300i	−0.811132	−	0.584863i	$-0.801148\pi$
$103$	−11.6901	+	3.60590i	−1.15186	+	0.355300i	−0.340723	+	0.940164i	$0.610672\pi$
$104$	10.1551	+	9.53517i	0.995794	+	0.935000i
$105$	3.30637	−	6.25628i	0.322669	−	0.610551i
$106$	−4.06705	−	13.1851i	−0.395027	−	1.28065i
$107$	−11.5700	+	7.88829i	−1.11851	+	0.762590i	−0.973918	−	0.226901i	$-0.927141\pi$
$107$	−11.5700	+	7.88829i	−1.11851	+	0.762590i	−0.144596	+	0.989491i	$0.546188\pi$
$108$	1.75021	−	1.62396i	0.168414	−	0.156266i
$109$	−14.0758	−	1.05484i	−1.34822	−	0.101035i	−0.619040	−	0.785359i	$-0.712478\pi$
$109$	−14.0758	−	1.05484i	−1.34822	−	0.101035i	−0.729178	+	0.684324i	$0.760097\pi$
$110$	7.03224	−	5.60802i	0.670497	−	0.534704i
$111$	−17.0424	−	1.27715i	−1.61759	−	0.121222i
$112$	3.82817	−	3.29455i	0.361728	−	0.311306i
$113$	−9.03595	+	6.16060i	−0.850030	+	0.579541i	−0.908091	−	0.418772i	$-0.862461\pi$
$113$	−9.03595	+	6.16060i	−0.850030	+	0.579541i	0.0580610	+	0.998313i	$0.481508\pi$
$114$	6.66197	+	2.05494i	0.623950	+	0.192463i
$115$	3.27327	−	2.61034i	0.305234	−	0.243416i
$116$	2.13297	−	3.69441i	0.198041	−	0.343017i
$117$	5.48649	+	8.15053i	0.507226	+	0.753516i
$118$	0.723011	+	0.906627i	0.0665585	+	0.0834618i
$119$	−3.63079	−	4.91933i	−0.332834	−	0.450954i
$120$	−10.2178	−	1.54008i	−0.932752	−	0.140590i
$121$	−0.314036	+	0.393788i	−0.0285487	+	0.0357989i
$122$	8.67767	+	12.7278i	0.785639	+	1.15232i
$123$	−0.670229	+	0.0502267i	−0.0604325	+	0.00452879i
$124$	23.6210	+	18.8371i	2.12123	+	1.69163i
$125$	7.64738	+	6.09858i	0.684003	+	0.545474i
$126$	15.1222	−	7.99272i	1.34719	−	0.712048i
$127$	1.85887	−	4.73633i	0.164948	−	0.420281i	−0.824370	−	0.566051i	$-0.808471\pi$
$127$	1.85887	−	4.73633i	0.164948	−	0.420281i	0.989319	+	0.145770i	$0.0465658\pi$
$128$	17.8939	+	10.3310i	1.58161	+	0.913144i
$129$	−10.5692	+	18.3064i	−0.930568	+	1.61179i
$130$	−2.87243	+	9.12002i	−0.251929	+	0.799878i
$131$	7.79406	−	7.23183i	0.680970	−	0.631848i	−0.261866	−	0.965104i	$-0.584338\pi$
$131$	7.79406	−	7.23183i	0.680970	−	0.631848i	0.942836	+	0.333256i	$0.108147\pi$
$132$	29.3640	−	2.20053i	2.55581	−	0.191532i
$133$	−2.75139	−	1.72873i	−0.238576	−	0.149900i
$134$	−2.37482	+	31.6898i	−0.205153	+	2.73758i
$135$	0.684680	+	0.268717i	0.0589278	+	0.0231275i
$136$	−5.02946	+	7.37686i	−0.431273	+	0.632561i
$137$	3.90794	+	4.21176i	0.333878	+	0.359835i	0.877569	−	0.479451i	$-0.159164\pi$
$137$	3.90794	+	4.21176i	0.333878	+	0.359835i	−0.543691	+	0.839285i	$0.682974\pi$
$138$	21.2016	−	1.58884i	1.80480	−	0.135251i
$139$	6.85301	+	6.35866i	0.581265	+	0.539335i	0.915064	−	0.403310i	$-0.132140\pi$
$139$	6.85301	+	6.35866i	0.581265	+	0.539335i	−0.333799	+	0.942644i	$0.608331\pi$
$140$	9.83574	+	4.29104i	0.831272	+	0.362659i
$141$	2.02850	+	2.18621i	0.170831	+	0.184112i
$142$	6.41722	−	1.97945i	0.538521	−	0.166112i
$143$	0.986097	−	12.1891i	0.0824616	−	1.01931i
$144$	−3.81327	−	3.53820i	−0.317772	−	0.294850i
$145$	1.31050	+	0.0982087i	0.108831	+	0.00815579i
$146$	1.62732	+	2.81861i	0.134678	+	0.233270i
$147$	−16.3288	+	3.72768i	−1.34678	+	0.307454i
$148$		−	25.9170i		−	2.13037i
$149$	6.74175	+	13.9994i	0.552306	+	1.14687i	0.971073	+	0.238781i	$0.0767479\pi$
$149$	6.74175	+	13.9994i	0.552306	+	1.14687i	−0.418768	+	0.908093i	$0.637538\pi$
$150$	6.27531	+	20.3441i	0.512377	+	1.66109i
$151$	−14.0632	+	5.51941i	−1.14445	+	0.449163i	−0.860386	−	0.509643i	$-0.829778\pi$
$151$	−14.0632	+	5.51941i	−1.14445	+	0.449163i	−0.284063	+	0.958806i	$0.591682\pi$
$152$	−1.05586	+	4.62604i	−0.0856418	+	0.375221i
$153$	−4.61621	+	4.28321i	−0.373198	+	0.346277i
$154$	−20.9183	−	3.95749i	−1.68565	−	0.318904i
$155$	−2.07108	+	9.07399i	−0.166353	+	0.728840i
$156$	−24.5888	+	19.3717i	−1.96868	+	1.55098i
$157$	20.8271	+	6.42432i	1.66219	+	0.512717i	0.976562	−	0.215238i	$-0.0690528\pi$
$157$	20.8271	+	6.42432i	1.66219	+	0.512717i	0.685625	+	0.727955i	$0.259529\pi$
$158$	−9.01467	−	18.7192i	−0.717168	−	1.48922i
$159$	13.7604	−	2.07405i	1.09127	−	0.164483i
$160$	−0.267149	+	3.56486i	−0.0211200	+	0.281827i
$161$	−9.73677	−	1.84208i	−0.767365	−	0.145176i
$162$	13.0295	+	19.1108i	1.02370	+	1.50149i
$163$	10.0977	−	2.30474i	0.790916	−	0.180522i	0.192066	−	0.981382i	$-0.438481\pi$
$163$	10.0977	−	2.30474i	0.790916	−	0.180522i	0.598851	+	0.800861i	$0.295624\pi$
$164$	−0.151910	−	1.00786i	−0.0118622	−	0.0787005i
$165$	4.53567	+	7.85602i	0.353102	+	0.611590i
$166$	4.00750	−	6.94119i	0.311042	−	0.538741i
$167$	10.0915	+	3.96063i	0.780904	+	0.306482i	0.722101	−	0.691787i	$-0.243176\pi$
$167$	10.0915	+	3.96063i	0.780904	+	0.306482i	0.0588030	+	0.998270i	$0.481272\pi$
$168$	13.0128	+	20.7087i	1.00396	+	1.59771i
$169$	6.36616	+	11.3345i	0.489705	+	0.871888i
$170$	−6.05995	−	0.913391i	−0.464777	−	0.0700539i
$171$	−1.45209	+	3.01530i	−0.111044	+	0.230586i
$172$	−28.8816	−	13.9086i	−2.20220	−	1.06052i
$173$	0.758225	−	0.950784i	0.0576468	−	0.0722868i	−0.752172	−	0.658967i	$-0.770994\pi$
$173$	0.758225	−	0.950784i	0.0576468	−	0.0722868i	0.809819	+	0.586680i	$0.199565\pi$
$174$	5.21777	+	4.16103i	0.395558	+	0.315447i
$175$	−0.371244	−	9.91597i	−0.0280634	−	0.749577i
$176$	0.964995	+	6.40232i	0.0727392	+	0.482593i
$177$	−1.01283	+	0.584759i	−0.0761291	+	0.0439532i
$178$	−10.6244	−	18.4020i	−0.796335	−	1.37929i
$179$	−15.9719	−	20.0281i	−1.19379	−	1.49697i	−0.822797	−	0.568335i	$-0.807588\pi$
$179$	−15.9719	−	20.0281i	−1.19379	−	1.49697i	−0.370996	−	0.928634i	$-0.620984\pi$
$180$	3.25776	−	10.5614i	0.242819	−	0.787200i
$181$	21.5831	+	10.3939i	1.60426	+	0.772569i	0.999712	−	0.0240021i	$-0.00764084\pi$
$181$	21.5831	+	10.3939i	1.60426	+	0.772569i	0.604545	+	0.796571i	$0.293355\pi$
$182$	20.7964	−	8.92763i	1.54153	−	0.661760i
$183$	−13.9975	+	6.74082i	−1.03472	+	0.498296i
$184$	2.15671	+	14.3089i	0.158995	+	1.05486i
$185$	7.19341	−	3.46417i	0.528870	−	0.254690i
$186$	−34.6480	+	32.1486i	−2.54051	+	2.35725i
$187$	7.81605	−	0.585732i	0.571566	−	0.0428330i
$188$	−3.07620	+	3.31535i	−0.224355	+	0.241797i
$189$	−0.575026	−	1.64322i	−0.0418270	−	0.119526i
$190$	−3.17534	+	0.724750i	−0.230363	+	0.0525789i
$191$	−1.44981	+	6.35202i	−0.104904	+	0.459616i	0.895004	+	0.446059i	$0.147173\pi$
$191$	−1.44981	+	6.35202i	−0.104904	+	0.459616i	−0.999908	+	0.0135573i	$0.995684\pi$
$192$	−17.0146	+	21.3356i	−1.22792	+	1.53976i
$193$	18.7748	+	4.28522i	1.35144	+	0.308457i	0.836122	−	0.548543i	$-0.184817\pi$
$193$	18.7748	+	4.28522i	1.35144	+	0.308457i	0.515316	+	0.857000i	$0.327675\pi$
$194$	−20.2500	−	13.8062i	−1.45386	−	0.991227i
$195$	−8.66337	−	4.23546i	−0.620397	−	0.303308i
$196$	−7.48766	−	24.2707i	−0.534833	−	1.73362i
$197$	0.156289	−	0.0902333i	0.0111351	−	0.00642886i	−0.494422	−	0.869222i	$-0.664620\pi$
$197$	0.156289	−	0.0902333i	0.0111351	−	0.00642886i	0.505557	+	0.862793i	$0.331287\pi$
$198$	−1.63861	+	21.8657i	−0.116451	+	1.55393i
$199$	12.1057	−	3.73412i	0.858152	−	0.264705i	0.165707	−	0.986175i	$-0.447009\pi$
$199$	12.1057	−	3.73412i	0.858152	−	0.264705i	0.692446	+	0.721470i	$0.256533\pi$
$200$	−13.4885	+	5.29383i	−0.953778	+	0.374330i
$201$	−31.2464	−	7.13178i	−2.20395	−	0.503037i
$202$	−11.1184	+	36.0449i	−0.782287	+	2.53611i
$203$	−1.84716	−	2.50270i	−0.129645	−	0.175655i
$204$	−14.7073	−	13.6464i	−1.02972	−	0.955438i
$205$	0.259432	−	0.176878i	0.0181195	−	0.0123537i
$206$	28.2957	−	6.45832i	1.97146	−	0.449972i
$207$	−0.762716	+	10.1777i	−0.0530124	+	0.707402i
$208$	−4.65156	−	5.07314i	−0.322528	−	0.351759i
$209$	3.75304	−	1.80737i	0.259603	−	0.125018i
$210$	−8.93144	+	14.2150i	−0.616328	+	0.980927i
$211$	0.495760	+	6.61545i	0.0341295	+	0.455427i	0.987921	+	0.154958i	$0.0495241\pi$
$211$	0.495760	+	6.61545i	0.0341295	+	0.455427i	−0.953792	+	0.300469i	$0.902857\pi$
$212$	4.69590	+	20.5741i	0.322516	+	1.41303i
$213$	1.00945	+	6.69725i	0.0691662	+	0.458888i
$214$	28.7709	−	16.6109i	1.96674	−	1.13550i
$215$		−	9.87533i		−	0.673492i
$216$	−1.98758	+	1.58504i	−0.135238	+	0.107848i
$217$	19.4766	−	10.2942i	1.32216	−	0.698816i
$218$	33.1137	+	4.99108i	2.24274	+	0.338039i
$219$	−3.05553	+	1.19921i	−0.206474	+	0.0810349i
$220$	−11.3662	+	7.74936i	−0.766310	+	0.522461i
$221$	−6.54499	+	5.15632i	−0.440264	+	0.346852i
$222$	40.0926	+	6.04299i	2.69084	+	0.405579i
$223$	−2.37859	+	15.7809i	−0.159282	+	1.05677i	0.756179	+	0.654365i	$0.227064\pi$
$223$	−2.37859	+	15.7809i	−0.159282	+	1.05677i	−0.915462	+	0.402405i	$0.868174\pi$
$224$	6.80790	−	5.02468i	0.454872	−	0.335726i
$225$	−10.1060	+	1.52323i	−0.673731	+	0.101549i
$226$	22.4696	−	12.9728i	1.49465	−	0.862938i
$227$	−0.516535	+	0.298221i	−0.0342836	+	0.0197937i	−0.517044	−	0.855959i	$-0.672968\pi$
$227$	−0.516535	+	0.298221i	−0.0342836	+	0.0197937i	0.482760	+	0.875753i	$0.339634\pi$
$228$	−9.92566	−	3.89554i	−0.657343	−	0.257988i
$229$	−5.78727	−	6.23719i	−0.382433	−	0.412165i	0.512271	−	0.858824i	$-0.328804\pi$
$229$	−5.78727	−	6.23719i	−0.382433	−	0.412165i	−0.894704	+	0.446659i	$0.852614\pi$
$230$	−8.20672	+	5.59525i	−0.541135	+	0.368940i
$231$	7.09103	−	20.2664i	0.466555	−	1.33343i
$232$	−2.55873	+	3.75297i	−0.167989	+	0.246395i
$233$	9.85509	−	25.1103i	0.645628	−	1.64503i	−0.113067	−	0.993587i	$-0.536067\pi$
$233$	9.85509	−	25.1103i	0.645628	−	1.64503i	0.758695	−	0.651446i	$-0.225837\pi$
$234$	−11.5350	−	20.2553i	−0.754064	−	1.32413i
$235$	−1.33137	−	0.410673i	−0.0868490	−	0.0267894i
$236$	−0.999081	−	1.46538i	−0.0650346	−	0.0953883i
$237$	20.0231	−	6.17631i	1.30064	−	0.401195i
$238$	7.71761	+	12.2819i	0.500258	+	0.796118i
$239$	0.0825068	−	0.0188316i	0.00533692	−	0.00121812i	−0.219852	−	0.975533i	$-0.570557\pi$
$239$	0.0825068	−	0.0188316i	0.00533692	−	0.00121812i	0.225189	+	0.974315i	$0.427700\pi$
$240$	4.97764	+	1.13611i	0.321305	+	0.0733358i
$241$	0.774128	−	5.13600i	0.0498659	−	0.330839i	−0.949963	−	0.312361i	$-0.898880\pi$
$241$	0.774128	−	5.13600i	0.0498659	−	0.330839i	0.999829	−	0.0184775i	$-0.00588190\pi$
$242$	0.812765	−	0.875952i	0.0522465	−	0.0563083i
$243$	−19.2387	+	9.26485i	−1.23416	+	0.594341i
$244$	−11.7801	−	20.4037i	−0.754142	−	1.30621i
$245$	5.73563	−	5.32235i	0.366436	−	0.340033i
$246$	1.59454			0.101664
$247$	−2.23678	+	3.82175i	−0.142323	+	0.243172i
$248$	−23.5817	−	21.8806i	−1.49744	−	1.38942i
$249$	6.31987	+	5.03993i	0.400505	+	0.319392i
$250$	−17.0110	−	15.7839i	−1.07587	−	0.998262i
$251$	−3.34688	−	1.03238i	−0.211253	−	0.0651630i	0.187322	−	0.982299i	$-0.440019\pi$
$251$	−3.34688	−	1.03238i	−0.211253	−	0.0651630i	−0.398575	+	0.917136i	$0.630495\pi$
$252$	−23.9772	+	10.4618i	−1.51042	+	0.659029i
$253$	8.64051	−	9.31226i	0.543224	−	0.585457i
$254$	−5.23746	+	10.8757i	−0.328627	+	0.682402i
$255$	1.82180	−	5.90612i	0.114085	−	0.369856i
$256$	−21.6550	−	14.7641i	−1.35344	−	0.922759i
$257$	3.70403	−	0.558293i	0.231051	−	0.0348254i	−0.0324961	−	0.999472i	$-0.510346\pi$
$257$	3.70403	−	0.558293i	0.231051	−	0.0348254i	0.263547	+	0.964647i	$0.415108\pi$
$258$	28.2504	−	41.4357i	1.75879	−	2.57967i
$259$	−17.3210	−	7.55665i	−1.07628	−	0.469548i
$260$	5.42327	−	13.5811i	0.336337	−	0.842266i
$261$	−2.34849	+	2.17908i	−0.145368	+	0.134882i
$262$	−19.7214	+	15.7273i	−1.21839	+	0.971636i
$263$	−25.0665			−1.54566			−0.772832	−	0.634611i	$-0.781161\pi$
$263$	−25.0665			−1.54566			−0.772832	+	0.634611i	$0.781161\pi$
$264$	−31.3536			−1.92968
$265$	−5.08278	+	4.05338i	−0.312233	+	0.248997i
$266$	6.20277	+	4.57765i	0.380317	+	0.280674i
$267$	19.9489	−	7.82935i	1.22085	−	0.479148i
$268$	7.24394	−	48.0604i	0.442494	−	2.93576i
$269$	−1.31665	−	17.5695i	−0.0802778	−	1.07123i	−0.881287	−	0.472581i	$-0.843322\pi$
$269$	−1.31665	−	17.5695i	−0.0802778	−	1.07123i	0.801010	−	0.598652i	$-0.204297\pi$
$270$	−1.57218	−	0.757122i	−0.0956798	−	0.0460770i
$271$	11.3673	−	4.46134i	0.690514	−	0.271007i	0.00597431	−	0.999982i	$-0.498098\pi$
$271$	11.3673	−	4.46134i	0.690514	−	0.271007i	0.684540	+	0.728975i	$0.260003\pi$
$272$	2.75050	−	3.44902i	0.166774	−	0.209127i
$273$	5.77728	+	22.0816i	0.349657	+	1.33644i
$274$	−8.49873	−	10.6571i	−0.513427	−	0.643817i
$275$	11.0164	+	6.36032i	0.664314	+	0.383542i
$276$	−32.5174			−1.95732
$277$	−0.216210	+	0.550895i	−0.0129908	+	0.0331001i	−0.937222	−	0.348733i	$-0.886612\pi$
$277$	−0.216210	+	0.550895i	−0.0129908	+	0.0331001i	0.924231	+	0.381833i	$0.124707\pi$
$278$	−15.0856	−	16.2584i	−0.904772	−	0.975113i
$279$	−12.7815	−	18.7470i	−0.765206	−	1.12235i
$280$	−10.1021	−	5.33882i	−0.603714	−	0.319055i
$281$	0.977992	+	2.03082i	0.0583421	+	0.121149i	0.928101	−	0.372328i	$-0.121440\pi$
$281$	0.977992	+	2.03082i	0.0583421	+	0.121149i	−0.869759	+	0.493476i	$0.835726\pi$
$282$	−4.41146	−	5.53179i	−0.262698	−	0.329413i
$283$	17.7015	−	8.52457i	1.05224	−	0.506733i	0.173899	−	0.984764i	$-0.444363\pi$
$283$	17.7015	−	8.52457i	1.05224	−	0.506733i	0.878343	+	0.478030i	$0.158649\pi$
$284$	−10.0135	+	2.28551i	−0.594191	+	0.135620i
$285$	−0.245473	−	3.27561i	−0.0145406	−	0.194031i
$286$	−4.49397	+	28.6624i	−0.265734	+	1.69484i
$287$	−0.717872	−	0.192337i	−0.0423746	−	0.0113533i
$288$	−5.92757	−	6.38840i	−0.349285	−	0.376440i
$289$	8.54712	+	7.93057i	0.502772	+	0.466504i
$290$	−3.08299	−	0.464686i	−0.181039	−	0.0272873i
$291$	16.8124	−	18.1195i	0.985560	−	1.06218i
$292$	−2.15977	−	4.48481i	−0.126391	−	0.262454i
$293$	−26.5682	−	15.3392i	−1.55213	−	0.896123i	−0.997968	−	0.0637141i	$-0.979705\pi$
$293$	−26.5682	−	15.3392i	−1.55213	−	0.896123i	−0.554162	−	0.832409i	$-0.686961\pi$
$294$	39.2917	−	5.92400i	2.29154	−	0.345495i
$295$	0.273184	−	0.473169i	0.0159054	−	0.0275490i
$296$	−2.06222	+	27.5185i	−0.119864	+	1.59948i
$297$	2.17581	+	0.496615i	0.126253	+	0.0288165i
$298$	−13.4677	−	34.3152i	−0.780163	−	1.98782i
$299$	−2.09179	+	13.3414i	−0.120971	+	0.771551i
$300$	−7.24561	−	31.7451i	−0.418325	−	1.83280i
$301$	−17.7166	+	15.2470i	−1.02117	+	0.878822i
$302$	34.2495	−	10.5646i	1.97084	−	0.607922i
$303$	−34.2753	−	16.5061i	−1.96907	−	0.948253i
$304$	0.691057	−	2.24035i	0.0396348	−	0.128493i
$305$	4.08859	−	5.99686i	0.234112	−	0.343379i
$306$	11.6805	−	9.31485i	0.667727	−	0.532495i
$307$	5.23842	+	10.8777i	0.298972	+	0.620822i	0.995293	−	0.0969081i	$-0.0308953\pi$
$307$	5.23842	+	10.8777i	0.298972	+	0.620822i	−0.696321	+	0.717730i	$0.745181\pi$
$308$	31.4514	+	8.42664i	1.79211	+	0.480153i
$309$	2.18744	+	29.1893i	0.124439	+	1.66052i
$310$	6.50853	−	21.1001i	0.369660	−	1.19841i
$311$	5.57396	−	0.840139i	0.316070	−	0.0476399i	0.0109086	−	0.999940i	$-0.496528\pi$
$311$	5.57396	−	0.840139i	0.316070	−	0.0476399i	0.305162	+	0.952301i	$0.401290\pi$
$312$	27.6496	−	18.6122i	1.56535	−	1.05371i
$313$	16.8216	+	29.1359i	0.950815	+	1.64686i	0.743666	+	0.668551i	$0.233085\pi$
$313$	16.8216	+	29.1359i	0.950815	+	1.64686i	0.207149	+	0.978309i	$0.433582\pi$
$314$	−48.1341	−	18.8912i	−2.71636	−	1.06609i
$315$	−6.10860	−	5.25665i	−0.344181	−	0.296178i
$316$	11.6093	+	29.5799i	0.653072	+	1.66400i
$317$	−4.19056	+	27.8025i	−0.235365	+	1.56155i	0.489096	+	0.872230i	$0.337327\pi$
$317$	−4.19056	+	27.8025i	−0.235365	+	1.56155i	−0.724461	+	0.689315i	$0.757911\pi$
$318$	−32.9223	+	2.46718i	−1.84619	+	0.138353i
$319$	3.97640	−	0.297990i	0.222636	−	0.0166843i
$320$	1.90011	−	12.6064i	0.106220	−	0.704721i
$321$	12.2409	+	31.1893i	0.683221	+	1.74082i
$322$	22.7088	+	6.08427i	1.26551	+	0.339063i
$323$	−2.64199	−	1.03690i	−0.147004	−	0.0576949i
$324$	−17.6878	−	30.6361i	−0.982655	−	1.70201i
$325$	−13.4906	+	0.930649i	−0.748324	+	0.0516231i
$326$	−24.2980	+	3.66233i	−1.34574	+	0.202838i
$327$	−9.95493	+	32.2731i	−0.550509	+	1.78471i
$328$	0.0811014	+	1.08222i	0.00447807	+	0.0597558i
$329$	1.31881	+	3.02257i	0.0727084	+	0.166640i
$330$	−9.33773	−	19.3900i	−0.514025	−	1.06738i
$331$	8.14904	−	6.49864i	0.447912	−	0.357198i	−0.373407	−	0.927668i	$-0.621810\pi$
$331$	8.14904	−	6.49864i	0.447912	−	0.357198i	0.821318	+	0.570470i	$0.193239\pi$
$332$	−6.90540	+	10.1284i	−0.378983	+	0.555866i
$333$	−5.73702	+	18.5989i	−0.314387	+	1.01922i
$334$	−23.1724	−	11.1592i	−1.26794	−	0.610607i
$335$	14.3077	−	4.41334i	0.781713	−	0.241126i
$336$	−5.64700	−	10.6841i	−0.308069	−	0.582865i
$337$	−3.09100	−	13.5425i	−0.168377	−	0.737710i	−0.986647	−	0.162875i	$-0.947923\pi$
$337$	−3.09100	−	13.5425i	−0.168377	−	0.737710i	0.818269	−	0.574835i	$-0.194934\pi$
$338$	−13.0516	−	27.9441i	−0.709913	−	1.51996i
$339$	9.55991	+	24.3583i	0.519223	+	1.32296i
$340$	9.13797	+	2.08568i	0.495576	+	0.113112i
$341$	−2.11044	+	28.1619i	−0.114287	+	1.52505i
$342$	3.96997	−	6.87618i	0.214671	−	0.371821i
$343$	−18.4039	−	2.07242i	−0.993719	−	0.111900i
$344$	29.5595	+	17.0662i	1.59374	+	0.920147i
$345$	−4.34639	−	9.02538i	−0.234002	−	0.485910i
$346$	−1.96238	+	2.11495i	−0.105498	+	0.113700i
$347$	22.3733	+	3.37224i	1.20106	+	0.181031i	0.718940	−	0.695072i	$-0.244627\pi$
$347$	22.3733	+	3.37224i	1.20106	+	0.181031i	0.482124	+	0.876103i	$0.339866\pi$
$348$	−7.48232	−	6.94258i	−0.401095	−	0.372161i
$349$	−21.1988	−	22.8469i	−1.13474	−	1.22296i	−0.971668	−	0.236351i	$-0.924049\pi$
$349$	−21.1988	−	22.8469i	−1.13474	−	1.22296i	−0.163077	−	0.986613i	$-0.552142\pi$
$350$	−0.879741	+	23.5251i	−0.0470241	+	1.25747i
$351$	−2.21357	+	0.853665i	−0.118152	+	0.0455653i
$352$	0.810598	+	10.8167i	0.0432050	+	0.576531i
$353$	−20.8551	+	4.76004i	−1.11000	+	0.253351i	−0.737947	−	0.674858i	$-0.764205\pi$
$353$	−20.8551	+	4.76004i	−1.11000	+	0.253351i	−0.372057	+	0.928210i	$0.621348\pi$
$354$	2.49984	−	1.20386i	0.132865	−	0.0639845i
$355$	−1.97280	−	2.47381i	−0.104705	−	0.131296i
$356$	14.1006	+	29.2803i	0.747333	+	1.55185i
$357$	−13.4085	+	5.85040i	−0.709652	+	0.309636i
$358$	34.2356	+	50.2143i	1.80941	+	2.65391i
$359$	−23.7013	−	25.5440i	−1.25091	−	1.34816i	−0.913520	−	0.406793i	$-0.866647\pi$
$359$	−23.7013	−	25.5440i	−1.25091	−	1.34816i	−0.337388	−	0.941366i	$-0.609543\pi$
$360$	−4.29943	+	10.9548i	−0.226600	+	0.577367i
$361$	17.4916			0.920612
$362$	−49.2187	−	28.4164i	−2.58688	−	1.49353i
$363$	0.751392	+	0.942216i	0.0394379	+	0.0494535i
$364$	−32.7381	+	11.2391i	−1.71594	+	0.589089i
$365$	0.956101	−	1.19891i	0.0500446	−	0.0627540i
$366$	34.3104	−	13.4659i	1.79344	−	0.703871i
$367$	24.5438	+	11.8197i	1.28118	+	0.616981i	0.945692	−	0.325065i	$-0.105386\pi$
$367$	24.5438	+	11.8197i	1.28118	+	0.616981i	0.335483	+	0.942046i	$0.391100\pi$
$368$	−0.534312	−	7.12990i	−0.0278529	−	0.371671i
$369$	−0.114084	+	0.756901i	−0.00593900	+	0.0394027i
$370$	−17.6324	+	6.92022i	−0.916666	+	0.359765i
$371$	15.1194	+	2.86041i	0.784961	+	0.148505i
$372$	56.5179	−	45.0715i	2.93032	−	2.33685i
$373$	9.73638			0.504130			0.252065	−	0.967710i	$-0.418890\pi$
$373$	9.73638			0.504130			0.252065	+	0.967710i	$0.418890\pi$
$374$	−18.5951			−0.961531
$375$	18.2979	−	14.5921i	0.944897	−	0.753530i
$376$	3.53008	−	3.27544i	0.182050	−	0.168918i
$377$	−3.32976	+	2.62327i	−0.171491	+	0.135105i
$378$	1.06907	+	3.98948i	0.0549871	+	0.205197i
$379$	2.22930	−	3.26979i	0.114512	−	0.167958i	−0.764704	−	0.644382i	$-0.777115\pi$
$379$	2.22930	−	3.26979i	0.114512	−	0.167958i	0.879216	+	0.476424i	$0.158067\pi$
$380$	4.92572	−	0.742432i	0.252684	−	0.0380860i
$381$	−10.0588	−	6.85794i	−0.515326	−	0.351343i
$382$	4.55614	−	14.7706i	0.233112	−	0.755731i
$383$	−12.4459	+	25.8442i	−0.635956	+	1.32058i	0.295018	+	0.955492i	$0.404674\pi$
$383$	−12.4459	+	25.8442i	−0.635956	+	1.32058i	−0.930974	+	0.365085i	$0.881040\pi$
$384$	33.6264	−	36.2407i	1.71599	−	1.84940i
$385$	1.86505	+	9.85584i	0.0950515	+	0.502300i
$386$	−43.6578	−	13.4667i	−2.22212	−	0.685435i
$387$	17.6476	+	16.3746i	0.897078	+	0.832366i
$388$	29.3064	+	23.3711i	1.48781	+	1.18649i
$389$	24.4420	+	22.6789i	1.23926	+	1.14987i	0.983068	+	0.183240i	$0.0586584\pi$
$389$	24.4420	+	22.6789i	1.23926	+	1.14987i	0.256192	+	0.966626i	$0.417532\pi$
$390$	19.7450	+	11.5563i	0.999825	+	0.585174i
$391$	−8.65540			−0.437722
$392$	6.01911	+	26.3662i	0.304011	+	1.33169i
$393$	−12.7200	−	22.0316i	−0.641638	−	1.11135i
$394$	−0.385747	+	0.185766i	−0.0194337	+	0.00935875i
$395$	−6.65834	+	7.17598i	−0.335017	+	0.361063i
$396$	4.99826	−	33.1613i	0.251172	−	1.66642i
$397$	9.04307	+	2.06402i	0.453858	+	0.103590i	0.443338	−	0.896354i	$-0.353794\pi$
$397$	9.04307	+	2.06402i	0.453858	+	0.103590i	0.0105203	+	0.999945i	$0.496651\pi$
$398$	−29.3019	+	6.68796i	−1.46877	+	0.335237i
$399$	−5.49753	+	5.49776i	−0.275221	+	0.275233i
$400$	6.84150	−	2.11032i	0.342075	−	0.105516i
$401$	−0.800677	−	1.17438i	−0.0399839	−	0.0586456i	0.805726	−	0.592288i	$-0.201775\pi$
$401$	−0.800677	−	1.17438i	−0.0399839	−	0.0586456i	−0.845710	+	0.533642i	$0.820823\pi$
$402$	72.6586	+	22.4122i	3.62388	+	1.11782i
$403$	−14.8564	−	26.0878i	−0.740052	−	1.29953i
$404$	21.0770	−	53.7033i	1.04862	−	2.67184i
$405$	6.13902	−	9.00428i	0.305050	−	0.447426i
$406$	3.92632	+	6.24841i	0.194860	+	0.310103i
$407$	20.0163	−	13.6469i	0.992169	−	0.676450i
$408$	14.5302	+	15.6599i	0.719354	+	0.775280i
$409$	−7.05698	−	2.76966i	−0.348945	−	0.136951i	0.184394	−	0.982852i	$-0.440968\pi$
$409$	−7.05698	−	2.76966i	−0.348945	−	0.136951i	−0.533339	+	0.845902i	$0.679063\pi$
$410$	−0.645126	+	0.372463i	−0.0318605	+	0.0183947i
$411$	11.9055	−	6.87363i	0.587254	−	0.339051i
$412$	−43.8935	+	6.61589i	−2.16248	+	0.325941i
$413$	−1.27066	+	0.240450i	−0.0625250	+	0.0118318i
$414$	3.60888	−	23.9434i	0.177367	−	1.17675i
$415$	−3.73418	−	0.562837i	−0.183304	−	0.0276286i
$416$	−7.13587	−	9.05766i	−0.349865	−	0.444088i
$417$	18.4816	−	12.6005i	0.905048	−	0.617051i
$418$	−9.19942	+	3.61051i	−0.449958	+	0.176596i
$419$	33.8425	+	5.10093i	1.65331	+	0.249197i	0.908442	−	0.418011i	$-0.137273\pi$
$419$	33.8425	+	5.10093i	1.65331	+	0.249197i	0.744871	+	0.667208i	$0.232511\pi$
$420$	15.2465	−	20.6592i	0.743954	−	1.00807i
$421$	6.55429	−	5.22687i	0.319436	−	0.254742i	−0.450623	−	0.892714i	$-0.648798\pi$
$421$	6.55429	−	5.22687i	0.319436	−	0.254742i	0.770059	+	0.637972i	$0.220227\pi$
$422$		−	15.7388i		−	0.766153i
$423$	2.94148	−	1.69826i	0.143019	−	0.0825723i
$424$	−3.34898	−	22.2190i	−0.162641	−	1.07905i
$425$	−1.92862	−	8.44983i	−0.0935518	−	0.409877i
$426$	−1.20079	−	16.0234i	−0.0581783	−	0.776336i
$427$	−17.0711	+	1.92382i	−0.826127	+	0.0931001i
$428$	−45.7787	+	22.0459i	−2.21280	+	1.06563i
$429$	−27.9087	−	8.79008i	−1.34744	−	0.424389i
$430$	−1.75083	+	23.3631i	−0.0844323	+	1.12667i
$431$	−6.22229	+	1.42020i	−0.299717	+	0.0684084i	−0.369735	−	0.929137i	$-0.620551\pi$
$431$	−6.22229	+	1.42020i	−0.299717	+	0.0684084i	0.0700179	+	0.997546i	$0.477694\pi$
$432$	1.03785	−	0.707592i	0.0499334	−	0.0340440i
$433$	0.912674	+	0.846838i	0.0438603	+	0.0406964i	0.701798	−	0.712376i	$-0.252381\pi$
$433$	0.912674	+	0.846838i	0.0438603	+	0.0406964i	−0.657938	+	0.753072i	$0.728571\pi$
$434$	−47.9030	+	20.9011i	−2.29942	+	1.00328i
$435$	0.926837	−	3.00473i	0.0444384	−	0.144066i
$436$	−49.9330	−	11.3969i	−2.39136	−	0.545812i
$437$	−4.28201	+	1.68057i	−0.204836	+	0.0803924i
$438$	7.44142	−	2.29537i	0.355565	−	0.109677i
$439$	−2.73494	+	36.4953i	−0.130532	+	1.74182i	0.420457	+	0.907312i	$0.361870\pi$
$439$	−2.73494	+	36.4953i	−0.130532	+	1.74182i	−0.550989	+	0.834512i	$0.685749\pi$
$440$	12.6852	−	7.32378i	0.604742	−	0.349148i
$441$	0.000822133		19.0750i	3.91492e−5		0.908331i
$442$	16.3984	−	11.0385i	0.779992	−	0.525048i
$443$	−4.40926	−	3.00618i	−0.209490	−	0.142828i	0.454030	−	0.890986i	$-0.349986\pi$
$443$	−4.40926	−	3.00618i	−0.209490	−	0.142828i	−0.663520	+	0.748158i	$0.730938\pi$
$444$	−60.4568	−	13.7989i	−2.86915	−	0.654865i
$445$	−6.24216	+	7.82742i	−0.295907	+	0.371055i
$446$	8.42515	−	36.9130i	0.398943	−	1.74788i
$447$	36.2459	−	8.27290i	1.71437	−	0.391295i
$448$	−25.5499	+	16.0548i	−1.20712	+	0.758520i
$449$	−6.97087	+	7.51281i	−0.328976	+	0.354551i	−0.875781	−	0.482708i	$-0.839653\pi$
$449$	−6.97087	+	7.51281i	−0.328976	+	0.354551i	0.546806	+	0.837260i	$0.315844\pi$
$450$	24.1789	−	1.81196i	1.13980	−	0.0854164i
$451$	0.698400	−	0.648021i	0.0328864	−	0.0305141i
$452$	−35.7523	+	17.2174i	−1.68165	+	0.809838i
$453$	5.38755	+	35.7440i	0.253129	+	1.67940i
$454$	1.27490	−	0.613957i	0.0598338	−	0.0288144i
$455$	−7.49537	−	7.58438i	−0.351388	−	0.355561i
$456$	10.2290	+	4.92603i	0.479017	+	0.230683i
$457$	−6.43171	+	20.8511i	−0.300863	+	0.975374i	0.671323	+	0.741165i	$0.265726\pi$
$457$	−6.43171	+	20.8511i	−0.300863	+	0.975374i	−0.972186	+	0.234209i	$0.924750\pi$
$458$	12.5858	+	15.7820i	0.588094	+	0.737447i
$459$	−0.760301	−	1.31688i	−0.0354878	−	0.0614667i
$460$	13.1560	−	7.59563i	0.613403	−	0.354148i
$461$	5.40071	+	35.8314i	0.251536	+	1.66883i	0.656367	+	0.754442i	$0.272092\pi$
$461$	5.40071	+	35.8314i	0.251536	+	1.66883i	−0.404831	+	0.914392i	$0.632670\pi$
$462$	−20.3691	+	46.6892i	−0.947657	+	2.17218i
$463$	−5.95639	−	4.75006i	−0.276817	−	0.220754i	0.475233	−	0.879860i	$-0.342364\pi$
$463$	−5.95639	−	4.75006i	−0.276817	−	0.220754i	−0.752050	+	0.659106i	$0.770935\pi$
$464$	1.39931	−	1.75468i	0.0649615	−	0.0814591i
$465$	20.0643	+	9.66244i	0.930458	+	0.448085i
$466$	−27.7671	+	57.6591i	−1.28629	+	2.67101i
$467$	13.0719	+	1.97027i	0.604895	+	0.0911733i	0.444347	−	0.895855i	$-0.353436\pi$
$467$	13.0719	+	1.97027i	0.604895	+	0.0911733i	0.160548	+	0.987028i	$0.448674\pi$
$468$	15.2775	+	32.2109i	0.706204	+	1.48895i
$469$	−30.0080	−	18.8544i	−1.38564	−	0.870613i
$470$	3.07696	+	1.20762i	0.141930	+	0.0557033i
$471$	26.0749	−	45.1631i	1.20147	−	2.08101i
$472$	0.944214	+	1.63543i	0.0434610	+	0.0752766i
$473$	−4.46594	−	29.6296i	−0.205344	−	1.36237i
$474$	−48.4659	+	11.0620i	−2.22611	+	0.508096i
$475$	−2.59478	−	3.80585i	−0.119057	−	0.174624i
$476$	−10.3668	−	19.6139i	−0.475161	−	0.899002i
$477$	1.18436	−	15.8042i	0.0542281	−	0.723623i
$478$	−0.198534	+	0.0299242i	−0.00908075	+	0.00136870i
$479$	13.2783	+	27.5727i	0.606701	+	1.25983i	0.947519	+	0.319698i	$0.103582\pi$
$479$	13.2783	+	27.5727i	0.606701	+	1.25983i	−0.340819	+	0.940129i	$0.610704\pi$
$480$	8.17352	+	2.52120i	0.373069	+	0.115076i
$481$	−9.55054	+	23.9168i	−0.435467	+	1.09051i
$482$	−2.74202	+	12.0136i	−0.124895	+	0.547202i
$483$	−9.48112	+	21.7322i	−0.431406	+	0.988851i
$484$	−1.33971	+	1.24307i	−0.0608959	+	0.0565031i
$485$	−2.56957	+	11.2580i	−0.116678	+	0.511200i
$486$	47.1576	−	18.5080i	2.13911	−	0.839540i
$487$	−0.650830	−	2.10994i	−0.0294919	−	0.0956105i	0.939630	−	0.342191i	$-0.111169\pi$
$487$	−0.650830	−	2.10994i	−0.0294919	−	0.0956105i	−0.969122	+	0.246581i	$0.920693\pi$
$488$	10.8845	+	22.6018i	0.492716	+	1.02314i
$489$		−	24.7822i		−	1.12069i
$490$	−14.5130	+	11.5748i	−0.655632	+	0.522895i
$491$	5.41804	+	9.38431i	0.244512	+	0.423508i	0.961994	−	0.273069i	$-0.0880387\pi$
$491$	5.41804	+	9.38431i	0.244512	+	0.423508i	−0.717482	+	0.696577i	$0.754705\pi$
$492$	−2.43192	−	0.182247i	−0.109639	−	0.00821633i
$493$	−1.99163	−	1.84796i	−0.0896984	−	0.0832279i
$494$	5.96936	−	8.64496i	0.268574	−	0.388955i
$495$	9.87219	−	3.04517i	0.443722	−	0.136870i
$496$	10.8113	+	11.6518i	0.485440	+	0.523180i
$497$	−1.39217	+	7.35868i	−0.0624475	+	0.330082i
$498$	−14.0581	−	13.0440i	−0.629957	−	0.584515i
$499$	13.7110	−	1.02750i	0.613789	−	0.0459972i	0.235792	−	0.971804i	$-0.424232\pi$
$499$	13.7110	−	1.02750i	0.613789	−	0.0459972i	0.377998	+	0.925806i	$0.376613\pi$
$500$	24.1404	+	26.0172i	1.07959	+	1.16352i
$501$	14.6119	−	21.4318i	0.652814	−	0.957502i
$502$	7.73505	+	3.03578i	0.345232	+	0.135494i
$503$	−0.385472	+	5.14376i	−0.0171873	+	0.229349i	0.981995	+	0.188909i	$0.0604951\pi$
$503$	−0.385472	+	5.14376i	−0.0171873	+	0.229349i	−0.999182	+	0.0404402i	$0.987124\pi$
$504$	26.2912	−	9.20033i	1.17110	−	0.409815i
$505$	17.7229	−	1.32815i	0.788658	−	0.0591018i
$506$	−22.0928	+	20.4991i	−0.982145	+	0.911298i
$507$	29.8297	−	8.81558i	1.32478	−	0.391514i
$508$	9.23097	−	15.9885i	0.409558	−	0.709375i
$509$	−5.70093	−	3.29143i	−0.252689	−	0.145890i	0.368306	−	0.929705i	$-0.379938\pi$
$509$	−5.70093	−	3.29143i	−0.252689	−	0.145890i	−0.620995	+	0.783814i	$0.713271\pi$
$510$	−5.35714	+	13.6498i	−0.237218	+	0.604422i
$511$	−3.62705	+	0.135793i	−0.160451	+	0.00600712i
$512$	16.3056	+	13.0033i	0.720611	+	0.574668i
$513$	−0.631828	−	0.503866i	−0.0278959	−	0.0222462i
$514$	−8.86202	+	0.664116i	−0.390887	+	0.0292929i
$515$	−7.70325	−	11.2986i	−0.339446	−	0.497875i
$516$	−47.8220	+	59.9670i	−2.10525	+	2.63990i
$517$	−4.18032	−	0.630082i	−0.183850	−	0.0277110i
$518$	39.6386	+	20.9485i	1.74162	+	0.920424i
$519$	−1.81420	−	2.27494i	−0.0796346	−	0.0998587i
$520$	−6.83903	+	13.9888i	−0.299911	+	0.613449i
$521$	17.4821	−	30.2799i	0.765905	−	1.32659i	−0.173862	−	0.984770i	$-0.555625\pi$
$521$	17.4821	−	30.2799i	0.765905	−	1.32659i	0.939767	−	0.341816i	$-0.111042\pi$
$522$	5.94241	−	4.73892i	0.260092	−	0.207417i
$523$	−13.6836	−	4.22082i	−0.598341	−	0.184564i	−0.0192335	−	0.999815i	$-0.506123\pi$
$523$	−13.6836	−	4.22082i	−0.598341	−	0.184564i	−0.579107	+	0.815251i	$0.696599\pi$
$524$	31.8758	−	21.7325i	1.39250	−	0.949390i
$525$	−23.3287	−	4.41351i	−1.01815	−	0.192621i
$526$	59.3025	+	4.44411i	2.58571	+	0.193772i
$527$	15.0438	−	11.9970i	0.655319	−	0.522599i
$528$	15.4485	+	1.15771i	0.672311	+	0.0503827i
$529$	6.57675	−	6.10233i	0.285946	−	0.265319i
$530$	12.7435	−	8.68839i	0.553544	−	0.377400i
$531$	0.392596	+	1.27277i	0.0170372	+	0.0552334i
$532$	−8.93699	−	7.69057i	−0.387468	−	0.333428i
$533$	−0.231214	+	0.986054i	−0.0100150	+	0.0427107i
$534$	−48.5833	+	14.9860i	−2.10240	+	0.648506i
$535$	−12.2379	−	9.75940i	−0.529090	−	0.421936i
$536$	−11.5157	+	50.4537i	−0.497404	+	2.17927i
$537$	−55.2235	+	26.5942i	−2.38307	+	1.14763i
$538$			41.7996i			1.80211i
$539$	14.8021	−	18.5628i	0.637570	−	0.799558i
$540$	2.31128	+	1.33442i	0.0994618	+	0.0574243i
$541$	8.13138	−	11.9266i	0.349596	−	0.512762i	−0.610657	−	0.791895i	$-0.709095\pi$
$541$	8.13138	−	11.9266i	0.349596	−	0.512762i	0.960253	+	0.279133i	$0.0900469\pi$
$542$	−27.6838	+	8.53933i	−1.18912	+	0.366796i
$543$	35.7372	−	44.8130i	1.53363	−	1.92311i
$544$	5.02685	−	5.41766i	0.215525	−	0.232280i
$545$	−3.51096	−	15.3825i	−0.150393	−	0.658916i
$546$	−9.75302	−	53.2652i	−0.417391	−	2.27954i
$547$	−0.134582	+	0.589642i	−0.00575431	+	0.0252113i	−0.977724	−	0.209897i	$-0.932687\pi$
$547$	−0.134582	+	0.589642i	−0.00575431	+	0.0252113i	0.971969	+	0.235108i	$0.0755444\pi$
$548$	11.7438	+	17.2250i	0.501671	+	0.735817i
$549$	3.93721	+	17.2500i	0.168036	+	0.736213i
$550$	−24.9351	−	17.0004i	−1.06323	−	0.724901i
$551$	−1.34411	−	0.527524i	−0.0572609	−	0.0224733i
$552$	34.5267	+	2.58742i	1.46955	+	0.110128i
$553$	23.1540	+	0.865862i	0.984608	+	0.0368202i
$554$	0.609183	−	1.26498i	0.0258817	−	0.0537439i
$555$	−4.25093	−	18.6245i	−0.180442	−	0.790567i
$556$	21.1496	+	26.5207i	0.896942	+	1.12473i
$557$			40.7003i			1.72453i	0.506459	+	0.862264i	$0.330954\pi$
$557$			40.7003i			1.72453i	−0.506459	+	0.862264i	$0.669046\pi$
$558$	26.9148	+	46.6178i	1.13939	+	1.97349i
$559$	21.5272	+	23.4782i	0.910502	+	0.993022i
$560$	4.78036	+	3.00355i	0.202007	+	0.126923i
$561$	2.79512	−	18.5444i	0.118010	−	0.782945i
$562$	−1.95369	−	4.97793i	−0.0824116	−	0.209981i
$563$	−1.31746	−	17.5803i	−0.0555245	−	0.740922i	−0.953599	−	0.301079i	$-0.902653\pi$
$563$	−1.31746	−	17.5803i	−0.0555245	−	0.740922i	0.898075	−	0.439843i	$-0.144966\pi$
$564$	6.09590	+	8.94104i	0.256684	+	0.376486i
$565$	−9.55757	−	7.62190i	−0.402090	−	0.320656i
$566$	−43.3896	+	17.0292i	−1.82380	+	0.715790i
$567$	−25.6322	+	2.88862i	−1.07645	+	0.121310i
$568$	10.8141	−	1.62996i	0.453749	−	0.0683917i
$569$	4.17312	−	7.22806i	0.174946	−	0.303016i	−0.765196	−	0.643797i	$-0.777358\pi$
$569$	4.17312	−	7.22806i	0.174946	−	0.303016i	0.940143	+	0.340781i	$0.110691\pi$
$570$			7.79300i			0.326413i
$571$	−25.4962	+	3.84293i	−1.06698	+	0.160822i	−0.658981	−	0.752159i	$-0.729012\pi$
$571$	−25.4962	+	3.84293i	−1.06698	+	0.160822i	−0.408002	+	0.912981i	$0.633774\pi$
$572$	10.1300	−	43.2009i	0.423555	−	1.80632i
$573$	14.0455	+	6.76395i	0.586758	+	0.282568i
$574$	1.66425	+	0.582305i	0.0694644	+	0.0243050i
$575$	−11.6064	−	7.91312i	−0.484021	−	0.330000i
$576$	19.3776	+	24.2987i	0.807398	+	1.01245i
$577$	27.7169	+	2.07709i	1.15387	+	0.0864705i	0.637888	−	0.770130i	$-0.279808\pi$
$577$	27.7169	+	2.07709i	1.15387	+	0.0864705i	0.515981	+	0.856600i	$0.327428\pi$
$578$	−18.8148	−	20.2776i	−0.782594	−	0.843436i
$579$	19.9923	−	41.5145i	0.830853	−	1.72528i
$580$	4.64893	+	1.06109i	0.193036	+	0.0440593i
$581$	4.75564	+	7.56820i	0.197297	+	0.313982i
$582$	−42.9874	+	39.8865i	−1.78188	+	1.65335i
$583$	−13.4171	+	14.4602i	−0.555681	+	0.598882i
$584$	1.93637	+	4.93379i	0.0801275	+	0.204161i
$585$	−6.89825	+	8.54579i	−0.285208	+	0.353325i
$586$	60.1358	+	40.9999i	2.48419	+	1.69369i
$587$	−0.735853	+	0.424845i	−0.0303719	+	0.0175352i	−0.515109	−	0.857125i	$-0.672249\pi$
$587$	−0.735853	+	0.424845i	−0.0303719	+	0.0175352i	0.484737	+	0.874660i	$0.338915\pi$
$588$	−60.6030	+	4.54419i	−2.49923	+	0.187399i
$589$	5.11311	−	8.85616i	0.210682	−	0.364912i
$590$	−0.730191	+	1.07099i	−0.0300615	+	0.0440921i
$591$	−0.127276	−	0.412618i	−0.00523543	−	0.0169728i
$592$	2.03220	−	13.4827i	0.0835228	−	0.554138i
$593$	13.0712	+	42.3759i	0.536771	+	1.74017i	0.663445	+	0.748225i	$0.269094\pi$
$593$	13.0712	+	42.3759i	0.536771	+	1.74017i	−0.126674	+	0.991944i	$0.540430\pi$
$594$	−5.05951	−	1.56065i	−0.207594	−	0.0640343i
$595$	4.05828	−	5.49903i	0.166373	−	0.225438i
$596$	16.6183	+	53.8752i	0.680712	+	2.20681i
$597$	−2.26522	−	30.2272i	−0.0927092	−	1.23712i
$598$	7.31410	−	31.1923i	0.299096	−	1.27555i
$599$	−1.21246	+	16.1791i	−0.0495397	+	0.661062i	0.916062	+	0.401036i	$0.131350\pi$
$599$	−1.21246	+	16.1791i	−0.0495397	+	0.661062i	−0.965602	+	0.260025i	$0.916269\pi$
$600$	5.16736	+	34.2832i	0.210957	+	1.39961i
$601$	17.2548	+	11.7641i	0.703837	+	0.479868i	0.861586	−	0.507612i	$-0.169471\pi$
$601$	17.2548	+	11.7641i	0.703837	+	0.479868i	−0.157750	+	0.987479i	$0.550424\pi$
$602$	44.6172	−	32.9305i	1.81846	−	1.34215i
$603$	−15.8372	+	32.8863i	−0.644941	+	1.33923i
$604$	−53.4432	+	12.1981i	−2.17457	+	0.496332i
$605$	−0.524091	−	0.205690i	−0.0213073	−	0.00836251i
$606$	78.1625	+	45.1272i	3.17514	+	1.83317i
$607$	−3.16746			−0.128563			−0.0642816	−	0.997932i	$-0.520476\pi$
$607$	−3.16746			−0.128563			−0.0642816	+	0.997932i	$0.520476\pi$
$608$	1.43498	−	3.65627i	0.0581961	−	0.148281i
$609$	−6.82154	+	2.97638i	−0.276423	+	0.120609i
$610$	−10.7360	+	13.4625i	−0.434689	+	0.545083i
$611$	4.06051	−	1.92589i	0.164270	−	0.0779131i
$612$	−18.8791	+	12.8716i	−0.763144	+	0.520303i
$613$	15.2738	−	31.7164i	0.616904	−	1.28101i	−0.325185	−	0.945651i	$-0.605426\pi$
$613$	15.2738	−	31.7164i	0.616904	−	1.28101i	0.942089	−	0.335364i	$-0.108859\pi$
$614$	−10.4646	−	26.6633i	−0.422315	−	1.07604i
$615$	−0.274475	−	0.699352i	−0.0110679	−	0.0282006i
$616$	−32.7243	−	11.4499i	−1.31850	−	0.461331i
$617$	−5.60942	−	37.2161i	−0.225827	−	1.49826i	−0.758350	−	0.651847i	$-0.773994\pi$
$617$	−5.60942	−	37.2161i	−0.225827	−	1.49826i	0.532523	−	0.846415i	$-0.321244\pi$
$618$		−	69.4442i		−	2.79346i
$619$	−16.2664	−	9.39142i	−0.653802	−	0.377473i	0.136109	−	0.990694i	$-0.456540\pi$
$619$	−16.2664	−	9.39142i	−0.653802	−	0.377473i	−0.789912	+	0.613221i	$0.789874\pi$
$620$	−12.3382	+	31.4371i	−0.495512	+	1.26254i
$621$	−2.35503	−	0.726430i	−0.0945040	−	0.0291506i
$622$	−13.3359	+	0.999386i	−0.534720	+	0.0400717i
$623$	23.6802	−	0.886560i	0.948725	−	0.0355193i
$624$	−14.3107	+	8.14966i	−0.572888	+	0.326248i
$625$	2.85656	−	7.27841i	0.114263	−	0.291136i
$626$	−34.6312	−	71.9124i	−1.38414	−	2.87420i
$627$	−2.21785	−	9.71703i	−0.0885724	−	0.388061i
$628$	71.2527	+	34.3135i	2.84329	+	1.36926i
$629$	−16.0922	−	3.67295i	−0.641640	−	0.146450i
$630$	13.5198	+	13.5192i	0.538643	+	0.538619i
$631$	−10.0829	+	32.6880i	−0.401394	+	1.30129i	0.499146	+	0.866518i	$0.333647\pi$
$631$	−10.0829	+	32.6880i	−0.401394	+	1.30129i	−0.900541	+	0.434771i	$0.856829\pi$
$632$	−9.97294	−	32.3315i	−0.396702	−	1.28608i
$633$	15.6959	+	2.36577i	0.623854	+	0.0940309i
$634$	14.8433	−	65.0325i	0.589501	−	2.58277i
$635$	5.67154	+	0.425023i	0.225068	+	0.0168665i
$636$	50.4935			2.00220
$637$	−2.03408	+	25.1568i	−0.0805932	+	0.996747i
$638$	−9.46025			−0.374535
$639$	7.69195	+	0.576432i	0.304289	+	0.0228033i
$640$	−5.13938	+	22.5171i	−0.203152	+	0.890067i
$641$	23.7319	+	3.57701i	0.937353	+	0.141283i	0.599914	−	0.800064i	$-0.295201\pi$
$641$	23.7319	+	3.57701i	0.937353	+	0.141283i	0.337439	+	0.941347i	$0.390439\pi$
$642$	−23.4300	−	75.9582i	−0.924709	−	2.99783i
$643$	−4.30681	+	13.9623i	−0.169844	+	0.550621i	−0.999976	−	0.00694622i	$-0.997789\pi$
$643$	−4.30681	+	13.9623i	−0.169844	+	0.550621i	0.830132	+	0.557567i	$0.188265\pi$
$644$	−33.9390	−	11.8749i	−1.33738	−	0.467938i
$645$	−23.0362	−	5.25787i	−0.907051	−	0.207028i
$646$	6.06661	+	2.92153i	0.238688	+	0.114946i
$647$	5.55730	+	24.3481i	0.218480	+	0.957223i	0.958602	+	0.284750i	$0.0919106\pi$
$647$	5.55730	+	24.3481i	0.218480	+	0.957223i	−0.740122	+	0.672473i	$0.765232\pi$
$648$	16.3430	+	33.9366i	0.642014	+	1.33316i
$649$	0.605670	−	1.54322i	0.0237746	−	0.0605768i
$650$	32.0812	+	0.190050i	1.25833	+	0.00745438i
$651$	−13.6435	−	50.9140i	−0.534733	−	1.99548i
$652$	37.4767	−	2.80849i	1.46770	−	0.109989i
$653$	−37.7521	−	11.6450i	−1.47735	−	0.455703i	−0.551689	−	0.834050i	$-0.686017\pi$
$653$	−37.7521	−	11.6450i	−1.47735	−	0.455703i	−0.925664	+	0.378346i	$0.876493\pi$
$654$	29.2733	−	74.5871i	1.14468	−	2.91659i
$655$	10.2926	+	5.94244i	0.402166	+	0.232190i
$656$		−	0.536227i		−	0.0209362i
$657$	0.557164	+	3.69654i	0.0217370	+	0.144216i
$658$	−2.58417	−	7.38464i	−0.100742	−	0.287883i
$659$	12.3902	+	31.5696i	0.482653	+	1.22978i	0.940209	+	0.340598i	$0.110630\pi$
$659$	12.3902	+	31.5696i	0.482653	+	1.22978i	−0.457557	+	0.889181i	$0.651275\pi$
$660$	12.0253	+	30.6400i	0.468085	+	1.19266i
$661$	−15.1779	+	31.5172i	−0.590351	+	1.22588i	0.365166	+	0.930942i	$0.381012\pi$
$661$	−15.1779	+	31.5172i	−0.590351	+	1.22588i	−0.955517	+	0.294935i	$0.904702\pi$
$662$	−20.4312	+	13.9298i	−0.794083	+	0.541396i
$663$	8.54347	+	18.0129i	0.331801	+	0.699563i
$664$	8.13801	−	10.2047i	0.315816	−	0.396021i
$665$	0.940008	−	3.50846i	0.0364520	−	0.136052i
$666$	16.8702	−	42.9844i	0.653705	−	1.66561i
$667$	−4.40342			−0.170501
$668$	34.0661	+	19.6681i	1.31806	+	0.760980i
$669$	35.5459	+	13.9507i	1.37428	+	0.539366i
$670$	−34.6317	+	7.90447i	−1.33794	+	0.305376i
$671$	9.55528	−	19.8418i	0.368878	−	0.765982i
$672$	−8.09641	−	18.5561i	−0.312326	−	0.715817i
$673$	0.718930	+	0.490158i	0.0277127	+	0.0188942i	0.577097	−	0.816675i	$-0.304185\pi$
$673$	0.718930	+	0.490158i	0.0277127	+	0.0188942i	−0.549384	+	0.835570i	$0.685138\pi$
$674$	4.91172	+	32.5871i	0.189192	+	1.25521i
$675$	0.184424	−	2.46096i	0.00709847	−	0.0947225i
$676$	16.7118	+	44.1108i	0.642763	+	1.69657i
$677$	1.33308	+	17.7888i	0.0512346	+	0.683678i	0.962400	+	0.271637i	$0.0875650\pi$
$677$	1.33308	+	17.7888i	0.0512346	+	0.683678i	−0.911165	+	0.412041i	$0.864816\pi$
$678$	−18.2984	−	59.3219i	−0.702746	−	2.27825i
$679$	24.1644	−	12.7719i	0.927344	−	0.490141i
$680$	−9.53666	−	2.94167i	−0.365714	−	0.112808i
$681$	0.420647	+	1.36370i	0.0161192	+	0.0522572i
$682$	9.98581	−	66.2515i	0.382376	−	2.53690i
$683$	−2.99518	−	9.71014i	−0.114607	−	0.371548i	0.880037	−	0.474905i	$-0.157518\pi$
$683$	−2.99518	−	9.71014i	−0.114607	−	0.371548i	−0.994644	+	0.103357i	$0.967042\pi$
$684$	−6.84072	+	10.0335i	−0.261562	+	0.383640i
$685$	−3.21118	+	5.56193i	−0.122693	+	0.212510i
$686$	43.1728	+	8.16584i	1.64835	+	0.311773i
$687$	−17.6308	+	10.1792i	−0.672657	+	0.388359i
$688$	−13.9344	−	9.50031i	−0.531244	−	0.362196i
$689$	3.24817	−	20.7167i	0.123745	−	0.789243i
$690$	8.68260	+	22.1229i	0.330541	+	0.842205i
$691$	5.73293	−	6.17863i	0.218091	−	0.235046i	−0.614524	−	0.788898i	$-0.710652\pi$
$691$	5.73293	−	6.17863i	0.218091	−	0.235046i	0.832615	+	0.553852i	$0.186843\pi$
$692$	3.23467	−	3.00133i	0.122964	−	0.114094i
$693$	−20.7053	−	13.0094i	−0.786528	−	0.494184i
$694$	−52.3332	−	11.9447i	−1.98654	−	0.453415i
$695$	−4.53405	+	9.41504i	−0.171986	+	0.357133i
$696$	7.39224	+	7.96694i	0.280202	+	0.301986i
$697$	−0.647322	−	0.0485101i	−0.0245191	−	0.00183745i
$698$	46.1017	+	57.8097i	1.74498	+	2.18813i
$699$	−53.3280	−	36.3584i	−2.01705	−	1.37520i
$700$	4.03054	−	35.7789i	0.152340	−	1.35232i
$701$	−45.3306	−	21.8301i	−1.71211	−	0.824510i	−0.991337	−	0.131341i	$-0.958072\pi$
$701$	−45.3306	−	21.8301i	−1.71211	−	0.824510i	−0.720775	−	0.693169i	$-0.756214\pi$
$702$	5.38824	−	1.62716i	0.203366	−	0.0614132i
$703$	−8.67434	+	1.30745i	−0.327159	+	0.0493113i
$704$		−	38.6832i		−	1.45793i
$705$	−1.66684	+	2.88704i	−0.0627766	+	0.108732i
$706$	50.1831	−	7.56389i	1.88867	−	0.284671i
$707$	−29.7460	−	29.7447i	−1.11871	−	1.11866i
$708$	−3.95024	+	1.55036i	−0.148459	+	0.0582659i
$709$	20.1593	+	16.0765i	0.757098	+	0.603765i	0.924082	−	0.382194i	$-0.124831\pi$
$709$	20.1593	+	16.0765i	0.757098	+	0.603765i	−0.166984	+	0.985960i	$0.553403\pi$
$710$	4.22867	+	6.20233i	0.158699	+	0.232769i
$711$	−1.78337	−	23.7974i	−0.0668816	−	0.892473i
$712$	−12.6421	−	32.2115i	−0.473783	−	1.20718i
$713$	4.64805	−	30.8378i	0.174071	−	1.15489i
$714$	32.7591	−	11.4637i	1.22598	−	0.429019i
$715$	13.3447	−	2.96277i	0.499062	−	0.110801i
$716$	−46.4753	−	80.4976i	−1.73686	−	3.00834i
$717$		−	0.202491i		−	0.00756215i
$718$	51.5441	+	64.6342i	1.92361	+	2.41213i
$719$	−0.469082	−	2.05518i	−0.0174938	−	0.0766453i	0.965428	−	0.260672i	$-0.0839440\pi$
$719$	−0.469082	−	2.05518i	−0.0174938	−	0.0766453i	−0.982921	+	0.184026i	$0.941087\pi$
$720$	2.52291	−	5.23888i	0.0940234	−	0.195242i
$721$	−8.37651	+	31.2642i	−0.311957	+	1.16434i
$722$	−41.3819	−	3.10114i	−1.54007	−	0.115413i
$723$	−11.5686	−	4.54035i	−0.430241	−	0.168857i
$724$	71.8183	+	48.9649i	2.66910	+	1.81976i
$725$	−0.981182	−	4.29884i	−0.0364402	−	0.159655i
$726$	−1.61060	−	2.36232i	−0.0597751	−	0.0876739i
$727$	0.360235	−	1.57829i	0.0133604	−	0.0585357i	−0.967808	−	0.251688i	$-0.919014\pi$
$727$	0.360235	−	1.57829i	0.0133604	−	0.0585357i	0.981169	+	0.193153i	$0.0618713\pi$
$728$	35.6553	−	9.32861i	1.32147	−	0.345741i
$729$	4.86070	+	21.2961i	0.180026	+	0.788745i
$730$	−2.47451	+	2.66689i	−0.0915858	+	0.0987060i
$731$	−12.7292	+	15.9619i	−0.470805	+	0.590371i
$732$	−53.8678	+	16.6160i	−1.99101	+	0.614146i
$733$	−7.89958	+	11.5866i	−0.291778	+	0.427959i	−0.943938	−	0.330121i	$-0.892910\pi$
$733$	−7.89958	+	11.5866i	−0.291778	+	0.427959i	0.652161	+	0.758081i	$0.273863\pi$
$734$	−55.9704	−	32.3145i	−2.06590	−	1.19275i
$735$	−9.36169	−	16.2133i	−0.345311	−	0.598037i
$736$		−	11.9783i		−	0.441525i
$737$	40.9325	−	19.7120i	1.50777	−	0.726102i
$738$	0.404095	−	1.77046i	0.0148750	−	0.0651714i
$739$	1.67231	+	1.33363i	0.0615171	+	0.0490582i	0.653766	−	0.756697i	$-0.273188\pi$
$739$	1.67231	+	1.33363i	0.0615171	+	0.0490582i	−0.592249	+	0.805755i	$0.701760\pi$
$740$	27.6831	−	8.53911i	1.01765	−	0.313904i
$741$	7.72410	+	7.25254i	0.283752	+	0.266429i
$742$	−35.2625	−	9.44775i	−1.29453	−	0.346838i
$743$	−9.24306	−	29.9653i	−0.339095	−	1.09932i	−0.951209	−	0.308549i	$-0.900157\pi$
$743$	−9.24306	−	29.9653i	−0.339095	−	1.09932i	0.612114	−	0.790770i	$-0.290319\pi$
$744$	−63.5966	+	43.3594i	−2.33156	+	1.58963i
$745$	−12.7321	+	11.8137i	−0.466468	+	0.432819i
$746$	−23.0344	−	1.72619i	−0.843350	−	0.0632003i
$747$	7.19757	−	5.73987i	0.263345	−	0.210011i
$748$	28.3605	+	2.12532i	1.03696	+	0.0777095i
$749$	1.38610	+	37.0231i	0.0506472	+	1.35279i
$750$	−45.8763	+	31.2779i	−1.67517	+	1.14211i
$751$	−3.34038	−	1.03037i	−0.121892	−	0.0375987i	0.233209	−	0.972427i	$-0.425077\pi$
$751$	−3.34038	−	1.03037i	−0.121892	−	0.0375987i	−0.355101	+	0.934828i	$0.615554\pi$
$752$	−1.86029	+	1.48353i	−0.0678376	+	0.0540987i
$753$	−4.19019	+	7.25762i	−0.152699	+	0.264482i
$754$	8.34266	−	5.61582i	0.303822	−	0.204516i
$755$	−10.5291	−	13.2030i	−0.383192	−	0.480507i
$756$	−1.17452	−	6.20677i	−0.0427170	−	0.225738i
$757$	−38.8125	−	5.85004i	−1.41066	−	0.212623i	−0.600875	−	0.799343i	$-0.705181\pi$
$757$	−38.8125	−	5.85004i	−1.41066	−	0.212623i	−0.809790	+	0.586720i	$0.800419\pi$
$758$	−5.85382	+	7.34046i	−0.212620	+	0.266617i
$759$	−17.1223	−	25.1139i	−0.621501	−	0.911575i
$760$	−5.28916	+	0.396368i	−0.191858	+	0.0143778i
$761$	−16.8763	−	13.4584i	−0.611764	−	0.487866i	0.267909	−	0.963444i	$-0.413667\pi$
$761$	−16.8763	−	13.4584i	−0.611764	−	0.487866i	−0.879673	+	0.475578i	$0.842239\pi$
$762$	22.5812	+	18.0079i	0.818032	+	0.652359i
$763$	−22.1759	+	30.0486i	−0.802821	+	1.08783i
$764$	−8.63702	+	22.0068i	−0.312476	+	0.796176i
$765$	−6.09603	−	3.51955i	−0.220403	−	0.127249i
$766$	34.0266	−	58.9359i	1.22943	−	2.12944i
$767$	0.381974	+	1.72045i	0.0137923	+	0.0621220i
$768$	−45.9701	+	42.6540i	−1.65880	+	1.53914i
$769$	−4.39166	+	0.329109i	−0.158367	+	0.0118680i	−0.153678	−	0.988121i	$-0.549112\pi$
$769$	−4.39166	+	0.329109i	−0.158367	+	0.0118680i	−0.00468950	+	0.999989i	$0.501493\pi$
$770$	−2.66497	−	23.6477i	−0.0960389	−	0.852204i
$771$	0.669785	−	8.93766i	0.0241217	−	0.321882i
$772$	65.0458	+	25.5286i	2.34105	+	0.918794i
$773$	11.1280	−	16.3217i	0.400245	−	0.587051i	−0.572220	−	0.820100i	$-0.693918\pi$
$773$	11.1280	−	16.3217i	0.400245	−	0.587051i	0.972465	+	0.233049i	$0.0748701\pi$
$774$	−38.8478	−	41.8679i	−1.39635	−	1.50491i
$775$	31.1411	−	2.33370i	1.11862	−	0.0838291i
$776$	−29.2576	−	27.1471i	−1.05029	−	0.974524i
$777$	−26.8496	+	36.3816i	−0.963224	+	1.30518i
$778$	−53.8044	−	57.9874i	−1.92898	−	2.07895i
$779$	−0.329663	+	0.101688i	−0.0118114	+	0.00364334i
$780$	−28.7933	−	19.8818i	−1.03097	−	0.711883i
$781$	−7.03785	−	6.53017i	−0.251834	−	0.233668i
$782$	20.4770	+	1.53454i	0.732257	+	0.0548751i
$783$	−0.386802	−	0.669961i	−0.0138232	−	0.0239424i
$784$	−1.99218	−	13.2134i	−0.0711493	−	0.471907i
$785$			24.3631i			0.869555i
$786$	26.1870	+	54.3779i	0.934059	+	1.93959i
$787$	−1.24224	−	4.02724i	−0.0442811	−	0.143556i	0.930733	−	0.365700i	$-0.119170\pi$
$787$	−1.24224	−	4.02724i	−0.0442811	−	0.143556i	−0.975014	+	0.222145i	$0.928694\pi$
$788$	0.609556	−	0.239233i	0.0217145	−	0.00852233i
$789$	−13.3460	+	58.4727i	−0.475130	+	2.08168i
$790$	17.0246	−	15.7965i	0.605708	−	0.562015i
$791$	1.08252	+	28.9143i	0.0384900	+	1.02807i
$792$	−7.94577	+	34.8127i	−0.282341	+	1.23701i
$793$	3.35206	+	23.1700i	0.119035	+	0.822790i
$794$	−21.0282	−	6.48635i	−0.746264	−	0.230192i
$795$	6.74915	+	14.0148i	0.239368	+	0.497052i
$796$	45.4543	−	6.85114i	1.61109	−	0.242832i
$797$	3.21492	−	42.9001i	0.113878	−	1.51960i	−0.588909	−	0.808200i	$-0.700442\pi$
$797$	3.21492	−	42.9001i	0.113878	−	1.51960i	0.702787	−	0.711400i	$-0.251939\pi$
$798$	13.9808	−	12.0320i	0.494916	−	0.425928i
$799$	1.62259	+	2.37991i	0.0574032	+	0.0841950i
$800$	11.6938	−	2.66903i	0.413438	−	0.0943644i
$801$	−3.63760	−	24.1339i	−0.128528	−	0.852729i
$802$	1.68604	+	2.92031i	0.0595362	+	0.103120i
$803$	2.32647	−	4.02956i	0.0820992	−	0.142200i
$804$	−108.254	−	42.4866i	−3.81782	−	1.49839i
$805$	−1.24045	−	11.0072i	−0.0437202	−	0.387953i
$806$	30.5223	+	64.3527i	1.07510	+	2.26673i
$807$	−41.6855	−	6.28308i	−1.46740	−	0.221175i
$808$	−26.6526	+	55.3446i	−0.937634	+	1.94702i
$809$	26.4400	+	12.7328i	0.929581	+	0.447662i	0.836482	−	0.547994i	$-0.184608\pi$
$809$	26.4400	+	12.7328i	0.929581	+	0.447662i	0.0930987	+	0.995657i	$0.470323\pi$
$810$	−16.1201	+	20.2140i	−0.566404	+	0.710248i
$811$	0.585330	+	0.466785i	0.0205537	+	0.0163911i	0.633713	−	0.773568i	$-0.281530\pi$
$811$	0.585330	+	0.466785i	0.0205537	+	0.0163911i	−0.613159	+	0.789959i	$0.710102\pi$
$812$	−5.27409	−	9.97855i	−0.185084	−	0.350178i
$813$	−4.35475	−	28.8919i	−0.152728	−	1.01328i
$814$	−49.7742	+	28.7371i	−1.74458	+	1.00724i
$815$	5.78879	+	10.0265i	0.202773	+	0.351212i
$816$	−6.58111	−	8.25245i	−0.230385	−	0.288894i
$817$	−3.19817	+	10.3682i	−0.111890	+	0.362738i
$818$	16.2044	+	7.80364i	0.566575	+	0.272848i
$819$	25.9819	−	0.818635i	0.907881	−	0.0286054i
$820$	1.02649	−	0.494330i	0.0358465	−	0.0172628i
$821$	−0.166025	−	1.10150i	−0.00579430	−	0.0384427i	0.985747	−	0.168235i	$-0.0538069\pi$
$821$	−0.166025	−	1.10150i	−0.00579430	−	0.0384427i	−0.991541	+	0.129793i	$0.958569\pi$
$822$	−29.3847	+	14.1509i	−1.02491	+	0.493571i
$823$	−5.20197	+	4.82672i	−0.181329	+	0.168249i	−0.765615	−	0.643299i	$-0.777565\pi$
$823$	−5.20197	+	4.82672i	−0.181329	+	0.168249i	0.584286	+	0.811548i	$0.301375\pi$
$824$	47.1322	−	3.53207i	1.64193	−	0.123046i
$825$	20.7022	−	22.3116i	0.720756	−	0.776791i
$826$	3.04877	−	0.343580i	0.106080	−	0.0119547i
$827$	−21.7688	+	4.96859i	−0.756975	+	0.172775i	−0.583555	−	0.812073i	$-0.698339\pi$
$827$	−21.7688	+	4.96859i	−0.756975	+	0.172775i	−0.173420	+	0.984848i	$0.555482\pi$
$828$	−8.24070	+	36.1049i	−0.286384	+	1.25473i
$829$	−34.0572	+	42.7064i	−1.18286	+	1.48325i	−0.343940	+	0.938992i	$0.611762\pi$
$829$	−34.0572	+	42.7064i	−1.18286	+	1.48325i	−0.838915	+	0.544262i	$0.816810\pi$
$830$	8.73458	+	1.99361i	0.303182	+	0.0691992i
$831$	1.16996	+	0.797666i	0.0405855	+	0.0276707i
$832$	22.9633	+	34.1134i	0.796108	+	1.18267i
$833$	−16.1312	+	1.20956i	−0.558912	+	0.0419089i
$834$	−45.9579	+	26.5338i	−1.59139	+	0.918791i
$835$	−0.905580	+	12.0841i	−0.0313389	+	0.418189i
$836$	14.4432	−	4.45514i	0.499528	−	0.154084i
$837$	5.10013	−	2.00165i	0.176286	−	0.0691872i
$838$	−79.1605	−	18.0679i	−2.73455	−	0.624144i
$839$	−14.3296	+	46.4554i	−0.494712	+	1.60382i	0.272318	+	0.962207i	$0.412210\pi$
$839$	−14.3296	+	46.4554i	−0.494712	+	1.60382i	−0.767030	+	0.641611i	$0.778266\pi$
$840$	−17.8325	+	20.7226i	−0.615279	+	0.714999i
$841$	20.2453	+	18.7849i	0.698113	+	0.647754i
$842$	−16.4329	+	11.2037i	−0.566315	+	0.386107i
$843$	5.25802	−	1.20011i	0.181096	−	0.0413339i
$844$	−1.79886	+	24.0041i	−0.0619193	+	0.826255i
$845$	−10.0094	+	10.5345i	−0.344334	+	0.362397i
$846$	−7.26006	+	3.49626i	−0.249606	+	0.120204i
$847$	0.440156	+	1.25781i	0.0151239	+	0.0432187i
$848$	0.829688	+	11.0714i	0.0284916	+	0.380194i
$849$	−10.4606	−	45.8310i	−0.359008	−	1.57292i
$850$	3.06465	+	20.3326i	0.105117	+	0.697403i
$851$	−23.1682	+	13.3761i	−0.794195	+	0.458528i
$852$			24.5754i			0.841939i
$853$	2.88817	−	2.30324i	0.0988892	−	0.0788615i	−0.572797	−	0.819697i	$-0.694142\pi$
$853$	2.88817	−	2.30324i	0.0988892	−	0.0788615i	0.671686	+	0.740836i	$0.265570\pi$
$854$	40.7280	−	1.52481i	1.39368	−	0.0521780i
$855$	−3.69921	−	0.557566i	−0.126510	−	0.0190684i
$856$	50.3616	−	19.7655i	1.72132	−	0.675570i
$857$	−22.6068	+	15.4130i	−0.772232	+	0.526499i	−0.884141	−	0.467220i	$-0.845256\pi$
$857$	−22.6068	+	15.4130i	−0.772232	+	0.526499i	0.111909	+	0.993718i	$0.464303\pi$
$858$	64.4682	+	25.7437i	2.20091	+	0.878875i
$859$	−23.1950	−	3.49608i	−0.791402	−	0.119285i	−0.259113	−	0.965847i	$-0.583430\pi$
$859$	−23.1950	−	3.49608i	−0.791402	−	0.119285i	−0.532290	+	0.846562i	$0.678668\pi$
$860$	5.34056	−	35.4323i	0.182112	−	1.20823i
$861$	−0.830877	+	1.57218i	−0.0283162	+	0.0535797i
$862$	14.9725	−	2.25675i	0.509967	−	0.0768651i
$863$	11.3191	−	6.53510i	0.385308	−	0.222458i	−0.294817	−	0.955554i	$-0.595259\pi$
$863$	11.3191	−	6.53510i	0.385308	−	0.222458i	0.680125	+	0.733096i	$0.261925\pi$
$864$	1.82244	−	1.05219i	0.0620006	−	0.0357961i
$865$	1.26539	+	0.496631i	0.0430247	+	0.0168859i
$866$	−2.00908	−	2.16527i	−0.0682712	−	0.0735788i
$867$	23.0504	−	15.7155i	0.782833	−	0.533726i
$868$	75.4483	−	26.4023i	2.56088	−	0.896154i
$869$	−16.7322	+	24.5417i	−0.567602	+	0.832519i
$870$	−2.72544	+	6.94430i	−0.0924010	+	0.235434i
$871$	−24.3954	+	41.6818i	−0.826605	+	1.41233i
$872$	52.1116	+	16.0743i	1.76472	+	0.544344i
$873$	−15.8578	−	23.2592i	−0.536706	−	0.787203i
$874$	10.4284	−	3.21673i	0.352745	−	0.108808i
$875$	24.4266	−	8.54784i	0.825771	−	0.288970i
$876$	−11.6117	+	2.65029i	−0.392322	+	0.0895448i
$877$	41.7790	+	9.53579i	1.41078	+	0.322001i	0.858993	−	0.511987i	$-0.171090\pi$
$877$	41.7790	+	9.53579i	1.41078	+	0.322001i	0.551784	+	0.833987i	$0.313947\pi$
$878$	12.9407	−	85.8560i	0.436728	−	2.89750i
$879$	−49.9273	+	53.8088i	−1.68401	+	1.81493i
$880$	−6.52066	+	3.14018i	−0.219811	+	0.105856i
$881$	−5.44721	−	9.43485i	−0.183521	−	0.317868i	0.759556	−	0.650442i	$-0.225416\pi$
$881$	−5.44721	−	9.43485i	−0.183521	−	0.317868i	−0.943077	+	0.332574i	$0.892083\pi$
$882$	3.37991	−	45.1279i	0.113807	−	1.51953i
$883$	12.2135			0.411016			0.205508	−	0.978655i	$-0.434115\pi$
$883$	12.2135			0.411016			0.205508	+	0.978655i	$0.434115\pi$
$884$	−26.2717	+	14.9612i	−0.883614	+	0.503199i
$885$	−0.958314	−	0.889185i	−0.0322134	−	0.0298896i
$886$	9.89849	+	7.89378i	0.332546	+	0.265197i
$887$	−36.3307	−	33.7099i	−1.21986	−	1.13187i	−0.987230	−	0.159304i	$-0.949075\pi$
$887$	−36.3307	−	33.7099i	−1.21986	−	1.13187i	−0.232635	−	0.972564i	$-0.574735\pi$
$888$	63.0945	+	19.4621i	2.11731	+	0.653105i
$889$	−7.99407	−	10.8311i	−0.268112	−	0.363263i
$890$	16.1555	−	17.4115i	0.541534	−	0.583635i
$891$	14.3473	−	29.7924i	0.480651	−	0.998083i
$892$	−17.0686	+	55.3351i	−0.571500	+	1.85276i
$893$	1.26482	+	0.862342i	0.0423257	+	0.0288572i
$894$	−87.2177	+	13.1460i	−2.91700	+	0.439667i
$895$	16.1305	−	23.6591i	0.539183	−	0.790836i
$896$	48.3312	−	25.5451i	1.61463	−	0.853402i
$897$	30.0077	+	11.9828i	1.00193	+	0.400094i
$898$	17.8237	−	16.5380i	0.594785	−	0.551880i
$899$	7.65352	−	6.10348i	0.255259	−	0.203562i
$900$	−37.0836			−1.23612
$901$	13.4402			0.447760
$902$	−1.76717	+	1.40927i	−0.0588404	+	0.0469237i
$903$	26.1340	+	49.4454i	0.869686	+	1.64544i
$904$	39.3315	−	15.4365i	1.30814	−	0.513409i
$905$	−3.99097	+	26.4784i	−0.132664	+	0.880171i
$906$	−6.40875	−	85.5188i	−0.212916	−	2.84117i
$907$	−43.7489	−	21.0684i	−1.45266	−	0.699563i	−0.469604	−	0.882877i	$-0.655603\pi$
$907$	−43.7489	−	21.0684i	−1.45266	−	0.699563i	−0.983054	+	0.183314i	$0.941317\pi$
$908$	−2.01458	+	0.790666i	−0.0668564	+	0.0262392i
$909$	−27.0134	+	33.8737i	−0.895978	+	1.12352i
$910$	16.3880	+	19.2721i	0.543256	+	0.638863i
$911$	10.9140	+	13.6857i	0.361598	+	0.453429i	0.929037	−	0.369986i	$-0.120637\pi$
$911$	10.9140	+	13.6857i	0.361598	+	0.453429i	−0.567440	+	0.823415i	$0.692066\pi$
$912$	−4.85815	−	2.80485i	−0.160869	−	0.0928780i
$913$	−11.4584			−0.379219
$914$	18.9130	−	48.1895i	0.625585	−	1.59397i
$915$	−11.8120	−	12.7303i	−0.390494	−	0.420852i
$916$	−17.3914	−	25.5085i	−0.574629	−	0.842826i
$917$	−5.23039	−	27.6400i	−0.172723	−	0.912753i
$918$	1.56525	+	3.25028i	0.0516611	+	0.107275i
$919$	−20.1814	−	25.3067i	−0.665724	−	0.834791i	0.328229	−	0.944598i	$-0.393548\pi$
$919$	−20.1814	−	25.3067i	−0.665724	−	0.834791i	−0.993953	+	0.109807i	$0.964977\pi$
$920$	−14.5733	+	7.01815i	−0.480469	+	0.231382i
$921$	28.1635	−	6.42814i	0.928019	−	0.211814i
$922$	−6.42440	−	85.7277i	−0.211577	−	2.82329i
$923$	10.0829	+	1.58089i	0.331882	+	0.0520358i
$924$	36.4024	−	68.8802i	1.19755	−	2.26599i
$925$	−18.2209	−	19.6374i	−0.599098	−	0.645674i
$926$	13.2495	+	12.2938i	0.435407	+	0.403999i
$927$	32.9640	+	4.96853i	1.08268	+	0.163188i
$928$	2.55740	−	2.75623i	0.0839509	−	0.0904776i
$929$	16.8985	+	35.0901i	0.554423	+	1.15127i	0.970312	+	0.241855i	$0.0777559\pi$
$929$	16.8985	+	35.0901i	0.554423	+	1.15127i	−0.415890	+	0.909415i	$0.636530\pi$
$930$	−45.7551	−	26.4167i	−1.50037	−	0.866239i
$931$	−7.74558	+	3.73049i	−0.253851	+	0.122262i
$932$	48.9393	−	84.7654i	1.60306	−	2.77658i
$933$	1.00792	−	13.4497i	0.0329977	−	0.440324i
$934$	−30.5763	−	6.97884i	−1.00049	−	0.228355i
$935$	3.20087	+	8.15568i	0.104680	+	0.266719i
$936$	−13.6585	−	35.4169i	−0.446443	−	1.15764i
$937$	−7.80572	−	34.1991i	−0.255002	−	1.11724i	−0.926519	−	0.376247i	$-0.877214\pi$
$937$	−7.80572	−	34.1991i	−0.255002	−	1.11724i	0.671518	−	0.740989i	$-0.265643\pi$
$938$	67.6504	+	49.9260i	2.20886	+	1.63014i
$939$	76.9218	−	23.7272i	2.51025	−	0.774309i
$940$	−4.55482	−	2.19348i	−0.148562	−	0.0715436i
$941$	0.990586	−	3.21140i	0.0322922	−	0.104689i	−0.937992	−	0.346657i	$-0.887317\pi$
$941$	0.990586	−	3.21140i	0.0322922	−	0.104689i	0.970284	+	0.241968i	$0.0777930\pi$
$942$	−69.6955	+	102.224i	−2.27080	+	3.33065i
$943$	−0.822558	+	0.655968i	−0.0267862	+	0.0213613i
$944$	−0.404846	−	0.840672i	−0.0131766	−	0.0273615i
$945$	1.56573	−	1.15562i	0.0509333	−	0.0375922i
$946$	5.31245	+	70.8898i	0.172723	+	2.30483i
$947$	13.1526	−	42.6396i	0.427401	−	1.38560i	−0.444438	−	0.895810i	$-0.646597\pi$
$947$	13.1526	−	42.6396i	0.427401	−	1.38560i	0.871839	−	0.489792i	$-0.162927\pi$
$948$	75.1823	−	11.3319i	2.44181	−	0.368043i
$949$	0.340411	+	4.93457i	0.0110502	+	0.160183i
$950$	5.46401	+	9.46395i	0.177276	+	0.307051i
$951$	62.6240	+	24.5781i	2.03072	+	0.796999i
$952$	9.44669	+	21.6508i	0.306169	+	0.701705i
$953$	−1.07750	−	2.74543i	−0.0349038	−	0.0889334i	0.912359	−	0.409391i	$-0.134259\pi$
$953$	−1.07750	−	2.74543i	−0.0349038	−	0.0889334i	−0.947263	+	0.320457i	$0.896163\pi$
$954$	−5.60394	+	37.1797i	−0.181434	+	1.20374i
$955$	−7.26255	+	0.544253i	−0.235011	+	0.0176116i
$956$	0.306216	−	0.0229477i	0.00990372	−	0.000742181i
$957$	1.42201	−	9.43444i	0.0459671	−	0.304972i
$958$	−26.5255	−	67.5858i	−0.857000	−	2.18360i
$959$	14.9361	−	2.82640i	0.482312	−	0.0912692i
$960$	−28.3954	−	11.1444i	−0.916459	−	0.359684i
$961$	19.1648	+	33.1945i	0.618221	+	1.07079i
$962$	26.8350	−	54.8894i	0.865197	−	1.76970i
$963$	37.7325	−	5.68725i	1.21591	−	0.183269i
$964$	5.55508	−	18.0091i	0.178917	−	0.580035i
$965$	1.60866	+	21.4661i	0.0517846	+	0.691017i
$966$	26.2835	−	49.7334i	0.845658	−	1.60015i
$967$	1.29407	+	2.68716i	0.0416144	+	0.0864132i	0.920739	−	0.390178i	$-0.127587\pi$
$967$	1.29407	+	2.68716i	0.0416144	+	0.0864132i	−0.879125	+	0.476591i	$0.841872\pi$
$968$	1.52140	−	1.21328i	0.0488997	−	0.0389962i
$969$	−3.82545	+	5.61091i	−0.122891	+	0.180248i
$970$	8.07507	−	26.1787i	0.259275	−	0.840549i
$971$	−40.5053	−	19.5063i	−1.29988	−	0.625987i	−0.349455	−	0.936953i	$-0.613633\pi$
$971$	−40.5053	−	19.5063i	−1.29988	−	0.625987i	−0.950421	+	0.310966i	$0.899348\pi$
$972$	−74.0380	+	22.8377i	−2.37477	+	0.732520i
$973$	23.8911	−	6.40216i	0.765915	−	0.205244i
$974$	1.16566	+	5.10710i	0.0373502	+	0.163642i
$975$	−5.01180	+	31.9651i	−0.160506	+	1.02370i
$976$	−4.52843	−	11.5383i	−0.144952	−	0.369330i
$977$	42.9500	+	9.80307i	1.37409	+	0.313628i	0.844923	−	0.534888i	$-0.179646\pi$
$977$	42.9500	+	9.80307i	1.37409	+	0.313628i	0.529170	+	0.848516i	$0.322503\pi$
$978$	−4.39370	+	58.6299i	−0.140495	+	1.87478i
$979$	−15.1890	+	26.3080i	−0.485441	+	0.840809i
$980$	23.4576	−	15.9946i	0.749324	−	0.510928i
$981$	33.3108	+	19.2320i	1.06353	+	0.614031i
$982$	−11.1543	−	23.1621i	−0.355947	−	0.739132i
$983$	−22.5343	+	24.2862i	−0.718733	+	0.774610i	−0.981749	−	0.190182i	$-0.939092\pi$
$983$	−22.5343	+	24.2862i	−0.718733	+	0.774610i	0.263016	+	0.964791i	$0.415283\pi$
$984$	2.56769	+	0.387017i	0.0818549	+	0.0123376i
$985$	0.147876	+	0.137209i	0.00471172	+	0.00437184i
$986$	4.38418	+	4.72502i	0.139621	+	0.150475i
$987$	7.75293	−	1.46711i	0.246778	−	0.0466985i
$988$	−10.0923	+	12.5026i	−0.321078	+	0.397762i
$989$	2.47276	+	32.9968i	0.0786294	+	1.04924i
$990$	−23.8956	+	5.45402i	−0.759453	+	0.173340i
$991$	35.6719	−	17.1787i	1.13315	−	0.545698i	0.229222	−	0.973374i	$-0.426382\pi$
$991$	35.6719	−	17.1787i	1.13315	−	0.545698i	0.903932	+	0.427676i	$0.140668\pi$
$992$	16.6028	+	20.8192i	0.527139	+	0.661011i
$993$	−10.8207	−	22.4693i	−0.343384	−	0.713043i
$994$	4.59826	−	17.1624i	0.145848	−	0.544358i
$995$	7.97716	+	11.7003i	0.252893	+	0.370926i
$996$	19.9499	+	21.5009i	0.632136	+	0.681281i
$997$	−19.3000	+	49.1755i	−0.611236	+	1.55740i	0.204430	+	0.978881i	$0.434466\pi$
$997$	−19.3000	+	49.1755i	−0.611236	+	1.55740i	−0.815666	+	0.578523i	$0.803629\pi$
$998$	−32.6198			−1.03256
$999$	−4.07024	−	2.34996i	−0.128777	−	0.0743493i

Display

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a_n

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a_n

instead) (See

a_n

instead) Display

a_n

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n

up to: 50 250 1000 (See only

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a_p

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a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bp.a.543.8	✓	756
13.4	even	6		637.2.bz.a.4.8	yes	756
49.37	even	21		637.2.bz.a.478.8	yes	756
637.576	even	42	inner	637.2.bp.a.576.8	yes	756

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bp.a.543.8	✓	756	1.1	even	1	trivial
637.2.bp.a.576.8	yes	756	637.576	even	42	inner
637.2.bz.a.4.8	yes	756	13.4	even	6
637.2.bz.a.478.8	yes	756	49.37	even	21

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

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	637.2.bp.a.543.8

Level	$637$
Weight	$2$
Character	637.543
Analytic conductor	$5.086$
Analytic rank	$0$
Dimension	$756$
Inner twists	$2$