LMFDB - Embedded newform 385.2.n.e.36.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [385,2,Mod(36,385)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(385, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("385.36");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 385 = 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	385.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.07424047782$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			36.5
Character	$\chi$	$=$	385.36
Dual form			385.2.n.e.246.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.42900 - 1.03823i) q^{2} +(0.0755236 + 0.232438i) q^{3} +(0.346092 - 1.06516i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.349248 + 0.253743i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.480344 + 1.47835i) q^{8} +(2.37873 - 1.72825i) q^{9} +O(q^{10})$	\(q+(1.42900 - 1.03823i) q^{2} +(0.0755236 + 0.232438i) q^{3} +(0.346092 - 1.06516i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.349248 + 0.253743i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.480344 + 1.47835i) q^{8} +(2.37873 - 1.72825i) q^{9} +1.76635 q^{10} +(-2.63287 + 2.01693i) q^{11} +0.273722 q^{12} +(3.66127 - 2.66007i) q^{13} +(-0.545831 - 1.67989i) q^{14} +(-0.0755236 + 0.232438i) q^{15} +(4.03344 + 2.93047i) q^{16} +(2.43256 + 1.76736i) q^{17} +(1.60489 - 4.93934i) q^{18} +(-1.80403 - 5.55223i) q^{19} +(0.906080 - 0.658306i) q^{20} +0.244400 q^{21} +(-1.66835 + 5.61572i) q^{22} -8.86129 q^{23} +(-0.307346 + 0.223300i) q^{24} +(0.309017 + 0.951057i) q^{25} +(2.47020 - 7.60249i) q^{26} +(1.17453 + 0.853346i) q^{27} +(-0.906080 - 0.658306i) q^{28} +(-1.69839 + 5.22710i) q^{29} +(0.133401 + 0.410565i) q^{30} +(-2.16975 + 1.57642i) q^{31} +5.69745 q^{32} +(-0.667654 - 0.459653i) q^{33} +5.31107 q^{34} +(0.809017 - 0.587785i) q^{35} +(-1.01760 - 3.13186i) q^{36} +(0.590577 - 1.81761i) q^{37} +(-8.34247 - 6.06116i) q^{38} +(0.894812 + 0.650119i) q^{39} +(-0.480344 + 1.47835i) q^{40} +(-0.754900 - 2.32334i) q^{41} +(0.349248 - 0.253743i) q^{42} -5.76656 q^{43} +(1.23714 + 3.50247i) q^{44} +2.94027 q^{45} +(-12.6628 + 9.20008i) q^{46} +(0.548983 + 1.68960i) q^{47} +(-0.376531 + 1.15884i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(1.42900 + 1.03823i) q^{50} +(-0.227085 + 0.698897i) q^{51} +(-1.56627 - 4.82047i) q^{52} +(-8.52494 + 6.19373i) q^{53} +2.56438 q^{54} +(-3.31556 + 0.0841643i) q^{55} +1.55443 q^{56} +(1.15430 - 0.838649i) q^{57} +(2.99994 + 9.23287i) q^{58} +(2.33693 - 7.19234i) q^{59} +(0.221446 + 0.160890i) q^{60} +(-6.83758 - 4.96779i) q^{61} +(-1.46390 + 4.50541i) q^{62} +(-0.908593 - 2.79636i) q^{63} +(0.0747997 - 0.0543452i) q^{64} +4.52558 q^{65} +(-1.43131 + 0.0363332i) q^{66} +1.17722 q^{67} +(2.72441 - 1.97940i) q^{68} +(-0.669237 - 2.05970i) q^{69} +(0.545831 - 1.67989i) q^{70} +(4.05595 + 2.94682i) q^{71} +(3.69755 + 2.68643i) q^{72} +(-3.54187 + 10.9008i) q^{73} +(-1.04316 - 3.21052i) q^{74} +(-0.197723 + 0.143654i) q^{75} -6.53838 q^{76} +(1.10461 + 3.12727i) q^{77} +1.95366 q^{78} +(-1.39386 + 1.01270i) q^{79} +(1.54064 + 4.74159i) q^{80} +(2.61613 - 8.05163i) q^{81} +(-3.49092 - 2.53630i) q^{82} +(1.69753 + 1.23333i) q^{83} +(0.0845847 - 0.260325i) q^{84} +(0.929157 + 2.85965i) q^{85} +(-8.24043 + 5.98702i) q^{86} -1.34324 q^{87} +(-4.24640 - 2.92348i) q^{88} -4.47761 q^{89} +(4.20165 - 3.05268i) q^{90} +(-1.39848 - 4.30408i) q^{91} +(-3.06682 + 9.43870i) q^{92} +(-0.530287 - 0.385276i) q^{93} +(2.53869 + 1.84447i) q^{94} +(1.80403 - 5.55223i) q^{95} +(0.430292 + 1.32430i) q^{96} +(-6.25938 + 4.54770i) q^{97} -1.76635 q^{98} +(-2.77714 + 9.34797i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 3 q^{2} - 3 q^{4} + 7 q^{5} + 7 q^{6} - 7 q^{7} - q^{8} - q^{9}+O(q^{10}) $ 28 * q + 3 * q^2 - 3 * q^4 + 7 * q^5 + 7 * q^6 - 7 * q^7 - q^8 - q^9	\( 28 q + 3 q^{2} - 3 q^{4} + 7 q^{5} + 7 q^{6} - 7 q^{7} - q^{8} - q^{9} + 2 q^{10} - 3 q^{11} + 30 q^{12} - 5 q^{13} - 2 q^{14} - 33 q^{16} + 7 q^{17} - 17 q^{18} - 13 q^{19} + 18 q^{20} + 10 q^{21} + 3 q^{22} + 16 q^{23} + 39 q^{24} - 7 q^{25} + 44 q^{26} - 18 q^{27} - 18 q^{28} + 7 q^{29} + 8 q^{30} + 7 q^{31} - 84 q^{32} + 4 q^{33} + 32 q^{34} + 7 q^{35} + 6 q^{36} - 24 q^{37} - 15 q^{38} - 18 q^{39} + q^{40} - 4 q^{41} + 7 q^{42} + q^{44} - 34 q^{45} + 3 q^{46} - 33 q^{47} + 83 q^{48} - 7 q^{49} + 3 q^{50} + 14 q^{51} + 24 q^{52} - 8 q^{53} - 114 q^{54} - 17 q^{55} - 6 q^{56} + 57 q^{57} - 16 q^{58} - 3 q^{59} + 15 q^{60} - 21 q^{61} - 19 q^{62} - 16 q^{63} - 19 q^{64} - 20 q^{65} - 126 q^{66} + 90 q^{67} - 7 q^{68} - 55 q^{69} + 2 q^{70} - 37 q^{71} + 117 q^{72} + 17 q^{73} + 49 q^{74} - 5 q^{75} - 10 q^{76} - 3 q^{77} + 104 q^{78} - 45 q^{79} - 2 q^{80} + 8 q^{81} - 48 q^{82} + q^{83} + 18 q^{85} + 134 q^{86} + 46 q^{87} + 74 q^{88} - 30 q^{89} - 38 q^{90} - 5 q^{91} + 18 q^{92} - 57 q^{93} + 43 q^{94} + 13 q^{95} - 119 q^{96} - 82 q^{97} - 2 q^{98} - 72 q^{99}+O(q^{100}) \) 28 * q + 3 * q^2 - 3 * q^4 + 7 * q^5 + 7 * q^6 - 7 * q^7 - q^8 - q^9 + 2 * q^10 - 3 * q^11 + 30 * q^12 - 5 * q^13 - 2 * q^14 - 33 * q^16 + 7 * q^17 - 17 * q^18 - 13 * q^19 + 18 * q^20 + 10 * q^21 + 3 * q^22 + 16 * q^23 + 39 * q^24 - 7 * q^25 + 44 * q^26 - 18 * q^27 - 18 * q^28 + 7 * q^29 + 8 * q^30 + 7 * q^31 - 84 * q^32 + 4 * q^33 + 32 * q^34 + 7 * q^35 + 6 * q^36 - 24 * q^37 - 15 * q^38 - 18 * q^39 + q^40 - 4 * q^41 + 7 * q^42 + q^44 - 34 * q^45 + 3 * q^46 - 33 * q^47 + 83 * q^48 - 7 * q^49 + 3 * q^50 + 14 * q^51 + 24 * q^52 - 8 * q^53 - 114 * q^54 - 17 * q^55 - 6 * q^56 + 57 * q^57 - 16 * q^58 - 3 * q^59 + 15 * q^60 - 21 * q^61 - 19 * q^62 - 16 * q^63 - 19 * q^64 - 20 * q^65 - 126 * q^66 + 90 * q^67 - 7 * q^68 - 55 * q^69 + 2 * q^70 - 37 * q^71 + 117 * q^72 + 17 * q^73 + 49 * q^74 - 5 * q^75 - 10 * q^76 - 3 * q^77 + 104 * q^78 - 45 * q^79 - 2 * q^80 + 8 * q^81 - 48 * q^82 + q^83 + 18 * q^85 + 134 * q^86 + 46 * q^87 + 74 * q^88 - 30 * q^89 - 38 * q^90 - 5 * q^91 + 18 * q^92 - 57 * q^93 + 43 * q^94 + 13 * q^95 - 119 * q^96 - 82 * q^97 - 2 * q^98 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/385\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$276$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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 $

$2$	1.42900	−	1.03823i	1.01046	−	0.734141i	0.0461530	−	0.998934i	$-0.485304\pi$
$2$	1.42900	−	1.03823i	1.01046	−	0.734141i	0.964305	+	0.264794i	$0.0853038\pi$
$3$	0.0755236	+	0.232438i	0.0436036	+	0.134198i	0.970488	−	0.241148i	$-0.0775239\pi$
$3$	0.0755236	+	0.232438i	0.0436036	+	0.134198i	−0.926885	+	0.375346i	$0.877524\pi$
$4$	0.346092	−	1.06516i	0.173046	−	0.532581i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$5$	0.809017	+	0.587785i	0.361803	+	0.262866i
$6$	0.349248	+	0.253743i	0.142580	+	0.103590i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i
$8$	0.480344	+	1.47835i	0.169827	+	0.522674i
$9$	2.37873	−	1.72825i	0.792909	−	0.576082i
$10$	1.76635			0.558568
$11$	−2.63287	+	2.01693i	−0.793841	+	0.608126i
$11$	−2.63287	+	2.01693i	−0.793841	+	0.608126i
$12$	0.273722			0.0790167
$13$	3.66127	−	2.66007i	1.01545	−	0.737770i	0.0501074	−	0.998744i	$-0.484044\pi$
$13$	3.66127	−	2.66007i	1.01545	−	0.737770i	0.965346	+	0.260974i	$0.0840436\pi$
$14$	−0.545831	−	1.67989i	−0.145879	−	0.448971i
$15$	−0.0755236	+	0.232438i	−0.0195001	+	0.0600152i
$16$	4.03344	+	2.93047i	1.00836	+	0.732616i
$17$	2.43256	+	1.76736i	0.589983	+	0.428648i	0.842309	−	0.538994i	$-0.181196\pi$
$17$	2.43256	+	1.76736i	0.589983	+	0.428648i	−0.252326	+	0.967642i	$0.581196\pi$
$18$	1.60489	−	4.93934i	0.378276	−	1.16421i
$19$	−1.80403	−	5.55223i	−0.413873	−	1.27377i	−0.913255	−	0.407388i	$-0.866440\pi$
$19$	−1.80403	−	5.55223i	−0.413873	−	1.27377i	0.499383	−	0.866382i	$-0.333560\pi$
$20$	0.906080	−	0.658306i	0.202606	−	0.147202i
$21$	0.244400			0.0533323
$22$	−1.66835	+	5.61572i	−0.355693	+	1.19728i
$23$	−8.86129			−1.84771			−0.923854	−	0.382746i	$-0.874978\pi$
$23$	−8.86129			−1.84771			−0.923854	+	0.382746i	$0.874978\pi$
$24$	−0.307346	+	0.223300i	−0.0627368	+	0.0455809i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	2.47020	−	7.60249i	0.484446	−	1.49097i
$27$	1.17453	+	0.853346i	0.226038	+	0.164227i
$28$	−0.906080	−	0.658306i	−0.171233	−	0.124408i
$29$	−1.69839	+	5.22710i	−0.315383	+	0.970649i	0.660214	+	0.751078i	$0.270466\pi$
$29$	−1.69839	+	5.22710i	−0.315383	+	0.970649i	−0.975597	+	0.219571i	$0.929534\pi$
$30$	0.133401	+	0.410565i	0.0243555	+	0.0749586i
$31$	−2.16975	+	1.57642i	−0.389699	+	0.283133i	−0.765332	−	0.643635i	$-0.777425\pi$
$31$	−2.16975	+	1.57642i	−0.389699	+	0.283133i	0.375633	+	0.926768i	$0.377425\pi$
$32$	5.69745			1.00718
$33$	−0.667654	−	0.459653i	−0.116224	−	0.0800153i
$34$	5.31107			0.910841
$35$	0.809017	−	0.587785i	0.136749	−	0.0993538i
$36$	−1.01760	−	3.13186i	−0.169601	−	0.521977i
$37$	0.590577	−	1.81761i	0.0970902	−	0.298813i	−0.890703	−	0.454587i	$-0.849787\pi$
$37$	0.590577	−	1.81761i	0.0970902	−	0.298813i	0.987793	+	0.155774i	$0.0497870\pi$
$38$	−8.34247	−	6.06116i	−1.35333	−	0.983250i
$39$	0.894812	+	0.650119i	0.143285	+	0.104102i
$40$	−0.480344	+	1.47835i	−0.0759490	+	0.233747i
$41$	−0.754900	−	2.32334i	−0.117896	−	0.362845i	0.874644	−	0.484765i	$-0.161095\pi$
$41$	−0.754900	−	2.32334i	−0.117896	−	0.362845i	−0.992540	+	0.121920i	$0.961095\pi$
$42$	0.349248	−	0.253743i	0.0538901	−	0.0391535i
$43$	−5.76656			−0.879392			−0.439696	−	0.898147i	$-0.644914\pi$
$43$	−5.76656			−0.879392			−0.439696	+	0.898147i	$0.644914\pi$
$44$	1.23714	+	3.50247i	0.186505	+	0.528018i
$45$	2.94027			0.438309
$46$	−12.6628	+	9.20008i	−1.86703	+	1.35648i
$47$	0.548983	+	1.68960i	0.0800774	+	0.246453i	0.983078	−	0.183186i	$-0.0586410\pi$
$47$	0.548983	+	1.68960i	0.0800774	+	0.246453i	−0.903001	+	0.429639i	$0.858641\pi$
$48$	−0.376531	+	1.15884i	−0.0543476	+	0.167265i
$49$	−0.809017	−	0.587785i	−0.115574	−	0.0839693i
$50$	1.42900	+	1.03823i	0.202092	+	0.146828i
$51$	−0.227085	+	0.698897i	−0.0317983	+	0.0978652i
$52$	−1.56627	−	4.82047i	−0.217202	−	0.668479i
$53$	−8.52494	+	6.19373i	−1.17099	+	0.850775i	−0.991127	−	0.132917i	$-0.957566\pi$
$53$	−8.52494	+	6.19373i	−1.17099	+	0.850775i	−0.179864	+	0.983692i	$0.557566\pi$
$54$	2.56438			0.348968
$55$	−3.31556	+	0.0841643i	−0.447070	+	0.0113487i
$56$	1.55443			0.207719
$57$	1.15430	−	0.838649i	0.152891	−	0.111082i
$58$	2.99994	+	9.23287i	0.393912	+	1.21234i
$59$	2.33693	−	7.19234i	0.304243	−	0.936363i	−0.675716	−	0.737162i	$-0.736165\pi$
$59$	2.33693	−	7.19234i	0.304243	−	0.936363i	0.979959	−	0.199201i	$-0.0638347\pi$
$60$	0.221446	+	0.160890i	0.0285885	+	0.0207708i
$61$	−6.83758	−	4.96779i	−0.875463	−	0.636061i	0.0565846	−	0.998398i	$-0.481979\pi$
$61$	−6.83758	−	4.96779i	−0.875463	−	0.636061i	−0.932047	+	0.362337i	$0.881979\pi$
$62$	−1.46390	+	4.50541i	−0.185915	+	0.572188i
$63$	−0.908593	−	2.79636i	−0.114472	−	0.352308i
$64$	0.0747997	−	0.0543452i	0.00934996	−	0.00679315i
$65$	4.52558			0.561329
$66$	−1.43131	+	0.0363332i	−0.176182	+	0.00447231i
$67$	1.17722			0.143821			0.0719103	−	0.997411i	$-0.477090\pi$
$67$	1.17722			0.143821			0.0719103	+	0.997411i	$0.477090\pi$
$68$	2.72441	−	1.97940i	0.330384	−	0.240038i
$69$	−0.669237	−	2.05970i	−0.0805666	−	0.247959i
$70$	0.545831	−	1.67989i	0.0652393	−	0.200786i
$71$	4.05595	+	2.94682i	0.481353	+	0.349723i	0.801849	−	0.597526i	$-0.203850\pi$
$71$	4.05595	+	2.94682i	0.481353	+	0.349723i	−0.320496	+	0.947250i	$0.603850\pi$
$72$	3.69755	+	2.68643i	0.435761	+	0.316599i
$73$	−3.54187	+	10.9008i	−0.414545	+	1.27584i	0.498113	+	0.867112i	$0.334026\pi$
$73$	−3.54187	+	10.9008i	−0.414545	+	1.27584i	−0.912658	+	0.408725i	$0.865974\pi$
$74$	−1.04316	−	3.21052i	−0.121265	−	0.373216i
$75$	−0.197723	+	0.143654i	−0.0228311	+	0.0165878i
$76$	−6.53838			−0.750004
$77$	1.10461	+	3.12727i	0.125882	+	0.356386i
$78$	1.95366			0.221209
$79$	−1.39386	+	1.01270i	−0.156822	+	0.113938i	−0.663429	−	0.748239i	$-0.730899\pi$
$79$	−1.39386	+	1.01270i	−0.156822	+	0.113938i	0.506607	+	0.862177i	$0.330899\pi$
$80$	1.54064	+	4.74159i	0.172248	+	0.530126i
$81$	2.61613	−	8.05163i	0.290682	−	0.894626i
$82$	−3.49092	−	2.53630i	−0.385508	−	0.280088i
$83$	1.69753	+	1.23333i	0.186328	+	0.135376i	0.677039	−	0.735947i	$-0.263263\pi$
$83$	1.69753	+	1.23333i	0.186328	+	0.135376i	−0.490711	+	0.871323i	$0.663263\pi$
$84$	0.0845847	−	0.260325i	0.00922894	−	0.0284038i
$85$	0.929157	+	2.85965i	0.100781	+	0.310173i
$86$	−8.24043	+	5.98702i	−0.888589	+	0.645597i
$87$	−1.34324			−0.144011
$88$	−4.24640	−	2.92348i	−0.452668	−	0.311644i
$89$	−4.47761			−0.474626			−0.237313	−	0.971433i	$-0.576267\pi$
$89$	−4.47761			−0.474626			−0.237313	+	0.971433i	$0.576267\pi$
$90$	4.20165	−	3.05268i	0.442893	−	0.321781i
$91$	−1.39848	−	4.30408i	−0.146601	−	0.451190i
$92$	−3.06682	+	9.43870i	−0.319738	+	0.984053i
$93$	−0.530287	−	0.385276i	−0.0549882	−	0.0399512i
$94$	2.53869	+	1.84447i	0.261846	+	0.190242i
$95$	1.80403	−	5.55223i	0.185089	−	0.569647i
$96$	0.430292	+	1.32430i	0.0439165	+	0.135161i
$97$	−6.25938	+	4.54770i	−0.635543	+	0.461749i	−0.858316	−	0.513121i	$-0.828489\pi$
$97$	−6.25938	+	4.54770i	−0.635543	+	0.461749i	0.222773	+	0.974870i	$0.428489\pi$
$98$	−1.76635			−0.178428
$99$	−2.77714	+	9.34797i	−0.279113	+	0.939506i
$100$	1.11998			0.111998
$101$	14.8301	−	10.7747i	1.47565	−	1.07213i	0.496728	−	0.867906i	$-0.334535\pi$
$101$	14.8301	−	10.7747i	1.47565	−	1.07213i	0.978925	−	0.204219i	$-0.0654655\pi$
$102$	0.401111	+	1.23449i	0.0397159	+	0.122233i
$103$	2.84622	−	8.75978i	0.280447	−	0.863126i	−0.707280	−	0.706934i	$-0.750078\pi$
$103$	2.84622	−	8.75978i	0.280447	−	0.863126i	0.987727	−	0.156193i	$-0.0499221\pi$
$104$	5.69117	+	4.13488i	0.558065	+	0.405458i
$105$	0.197723	+	0.143654i	0.0192958	+	0.0140192i
$106$	−5.75164	+	17.7017i	−0.558649	+	1.71934i
$107$	2.95783	+	9.10327i	0.285944	+	0.880047i	0.986114	+	0.166070i	$0.0531077\pi$
$107$	2.95783	+	9.10327i	0.285944	+	0.880047i	−0.700170	+	0.713977i	$0.746892\pi$
$108$	1.31545	−	0.955728i	0.126579	−	0.0919649i
$109$	11.2276			1.07541			0.537705	−	0.843133i	$-0.319291\pi$
$109$	11.2276			1.07541			0.537705	+	0.843133i	$0.319291\pi$
$110$	−4.65056	+	3.56259i	−0.443414	+	0.339679i
$111$	0.467083			0.0443336
$112$	4.03344	−	2.93047i	0.381124	−	0.276903i
$113$	−1.01209	−	3.11488i	−0.0952091	−	0.293023i	0.892099	−	0.451840i	$-0.149232\pi$
$113$	−1.01209	−	3.11488i	−0.0952091	−	0.293023i	−0.987308	+	0.158816i	$0.949232\pi$
$114$	0.778789	−	2.39686i	0.0729402	−	0.224487i
$115$	−7.16894	−	5.20854i	−0.668507	−	0.485699i
$116$	4.97991	+	3.61812i	0.462373	+	0.335934i
$117$	4.11191	−	12.6552i	0.380146	−	1.16997i
$118$	−4.12783	−	12.7042i	−0.379998	−	1.16951i
$119$	2.43256	−	1.76736i	0.222993	−	0.162014i
$120$	−0.379901			−0.0346800
$121$	2.86402	−	10.6206i	0.260366	−	0.965510i
$122$	−14.9286			−1.35158
$123$	0.483020	−	0.350934i	0.0435524	−	0.0316427i
$124$	0.928205	+	2.85672i	0.0833553	+	0.256541i
$125$	−0.309017	+	0.951057i	−0.0276393	+	0.0850651i
$126$	−4.20165	−	3.05268i	−0.374313	−	0.271954i
$127$	8.36488	+	6.07744i	0.742263	+	0.539286i	0.893419	−	0.449224i	$-0.148300\pi$
$127$	8.36488	+	6.07744i	0.742263	+	0.539286i	−0.151156	+	0.988510i	$0.548300\pi$
$128$	−3.47075	+	10.6819i	−0.306774	+	0.944154i
$129$	−0.435511	−	1.34037i	−0.0383446	−	0.118013i
$130$	6.46707	−	4.69860i	0.567199	−	0.412094i
$131$	11.5559			1.00964			0.504821	−	0.863224i	$-0.331558\pi$
$131$	11.5559			1.00964			0.504821	+	0.863224i	$0.331558\pi$
$132$	−0.720674	+	0.552076i	−0.0627266	+	0.0480521i
$133$	−5.83796			−0.506215
$134$	1.68226	−	1.22223i	0.145325	−	0.105585i
$135$	0.448631	+	1.38074i	0.0386120	+	0.118835i
$136$	−1.44430	+	4.44511i	−0.123848	+	0.381165i
$137$	−13.3622	−	9.70823i	−1.14161	−	0.829430i	−0.154270	−	0.988029i	$-0.549303\pi$
$137$	−13.3622	−	9.70823i	−1.14161	−	0.829430i	−0.987343	+	0.158598i	$0.949303\pi$
$138$	−3.09479	−	2.24849i	−0.263446	−	0.191405i
$139$	−0.881762	+	2.71378i	−0.0747901	+	0.230180i	−0.981462	−	0.191656i	$-0.938614\pi$
$139$	−0.881762	+	2.71378i	−0.0747901	+	0.230180i	0.906672	+	0.421836i	$0.138614\pi$
$140$	−0.346092	−	1.06516i	−0.0292501	−	0.0900225i
$141$	−0.351265	+	0.255209i	−0.0295818	+	0.0214924i
$142$	8.85545			0.743133
$143$	−4.27449	+	14.3881i	−0.357451	+	1.20320i
$144$	14.6590			1.22159
$145$	−4.44644	+	3.23053i	−0.369257	+	0.268281i
$146$	6.25617	+	19.2545i	0.517764	+	1.59351i
$147$	0.0755236	−	0.232438i	0.00622908	−	0.0191711i
$148$	−1.73165	−	1.25812i	−0.142341	−	0.103417i
$149$	17.4876	+	12.7055i	1.43264	+	1.04087i	0.989518	+	0.144408i	$0.0461278\pi$
$149$	17.4876	+	12.7055i	1.43264	+	1.04087i	0.443118	+	0.896463i	$0.353872\pi$
$150$	−0.133401	+	0.410565i	−0.0108921	+	0.0335225i
$151$	−4.88464	−	15.0334i	−0.397506	−	1.22340i	−0.926993	−	0.375080i	$-0.877615\pi$
$151$	−4.88464	−	15.0334i	−0.397506	−	1.22340i	0.529486	−	0.848318i	$-0.322385\pi$
$152$	7.34157	−	5.33396i	0.595480	−	0.432641i
$153$	8.84084			0.714740
$154$	4.82532	+	3.32205i	0.388836	+	0.267698i
$155$	−2.68196			−0.215420
$156$	1.00217	−	0.728118i	0.0802377	−	0.0582961i
$157$	−2.87800	−	8.85756i	−0.229689	−	0.706910i	−0.997782	−	0.0665714i	$-0.978794\pi$
$157$	−2.87800	−	8.85756i	−0.229689	−	0.706910i	0.768093	−	0.640339i	$-0.221206\pi$
$158$	−0.940416	+	2.89430i	−0.0748155	+	0.230258i
$159$	−2.08349	−	1.51375i	−0.165232	−	0.120048i
$160$	4.60934	+	3.34888i	0.364400	+	0.264752i
$161$	−2.73829	+	8.42759i	−0.215807	+	0.664187i
$162$	−4.62100	−	14.2220i	−0.363060	−	1.11738i
$163$	−3.23024	+	2.34691i	−0.253012	+	0.183824i	−0.707061	−	0.707153i	$-0.749979\pi$
$163$	−3.23024	+	2.34691i	−0.253012	+	0.183824i	0.454049	+	0.890977i	$0.349979\pi$
$164$	−2.73600			−0.213646
$165$	−0.269966	−	0.764304i	−0.0210168	−	0.0595010i
$166$	3.70626			0.287662
$167$	−16.3129	+	11.8520i	−1.26233	+	0.917139i	−0.998870	−	0.0475309i	$-0.984865\pi$
$167$	−16.3129	+	11.8520i	−1.26233	+	0.917139i	−0.263463	+	0.964669i	$0.584865\pi$
$168$	0.117396	+	0.361307i	0.00905728	+	0.0278755i
$169$	2.31171	−	7.11471i	0.177824	−	0.547285i
$170$	4.29675	+	3.12177i	0.329546	+	0.239429i
$171$	−13.8869	−	10.0894i	−1.06196	−	0.771559i
$172$	−1.99576	+	6.14231i	−0.152175	+	0.468347i
$173$	−5.19491	−	15.9883i	−0.394962	−	1.21557i	−0.928991	−	0.370101i	$-0.879323\pi$
$173$	−5.19491	−	15.9883i	−0.394962	−	1.21557i	0.534030	−	0.845466i	$-0.320677\pi$
$174$	−1.91950	+	1.39460i	−0.145517	+	0.105724i
$175$	1.00000			0.0755929
$176$	−16.5301	+	0.419610i	−1.24600	+	0.0316293i
$177$	1.84827			0.138924
$178$	−6.39853	+	4.64880i	−0.479590	+	0.348442i
$179$	−5.58466	−	17.1878i	−0.417417	−	1.28468i	−0.910071	−	0.414452i	$-0.863973\pi$
$179$	−5.58466	−	17.1878i	−0.417417	−	1.28468i	0.492654	−	0.870225i	$-0.336027\pi$
$180$	1.01760	−	3.13186i	0.0758477	−	0.233435i
$181$	−5.30254	−	3.85252i	−0.394134	−	0.286355i	0.373013	−	0.927826i	$-0.378325\pi$
$181$	−5.30254	−	3.85252i	−0.394134	−	0.286355i	−0.767148	+	0.641471i	$0.778325\pi$
$182$	−6.46707	−	4.69860i	−0.479371	−	0.348283i
$183$	0.638304	−	1.96450i	0.0471848	−	0.145220i
$184$	−4.25647	−	13.1001i	−0.313791	−	0.965749i
$185$	1.54615	−	1.12334i	0.113675	−	0.0825899i
$186$	−1.15779			−0.0848931
$187$	−9.96926	+	0.253066i	−0.729025	+	0.0185060i
$188$	1.98969			0.145113
$189$	1.17453	−	0.853346i	0.0854345	−	0.0620718i
$190$	−3.18654	−	9.80716i	−0.231176	−	0.711486i
$191$	−0.746495	+	2.29748i	−0.0540145	+	0.166239i	−0.974425	−	0.224715i	$-0.927855\pi$
$191$	−0.746495	+	2.29748i	−0.0540145	+	0.166239i	0.920410	+	0.390954i	$0.127855\pi$
$192$	0.0182810	+	0.0132819i	0.00131932	+	0.000958541i
$193$	0.207148	+	0.150502i	0.0149108	+	0.0108334i	0.595216	−	0.803566i	$-0.297067\pi$
$193$	0.207148	+	0.150502i	0.0149108	+	0.0108334i	−0.580305	+	0.814399i	$0.697067\pi$
$194$	−4.22310	+	12.9974i	−0.303201	+	0.933156i
$195$	0.341788	+	1.05192i	0.0244759	+	0.0753292i
$196$	−0.906080	+	0.658306i	−0.0647200	+	0.0470218i
$197$	20.7891			1.48116			0.740582	−	0.671966i	$-0.234550\pi$
$197$	20.7891			1.48116			0.740582	+	0.671966i	$0.234550\pi$
$198$	5.73682	+	16.2416i	0.407698	+	1.15424i
$199$	17.8132			1.26274			0.631371	−	0.775481i	$-0.282493\pi$
$199$	17.8132			1.26274			0.631371	+	0.775481i	$0.282493\pi$
$200$	−1.25756	+	0.913668i	−0.0889227	+	0.0646061i
$201$	0.0889081	+	0.273631i	0.00627109	+	0.0193004i
$202$	10.0057	−	30.7942i	0.703995	−	2.16668i
$203$	4.44644	+	3.23053i	0.312079	+	0.226739i
$204$	0.665846	+	0.483765i	0.0466185	+	0.0338703i
$205$	0.754900	−	2.32334i	0.0527245	−	0.162269i
$206$	−5.02741	−	15.4728i	−0.350277	−	1.07804i
$207$	−21.0786	+	15.3145i	−1.46506	+	1.06443i
$208$	22.5627			1.56444
$209$	15.9482	+	10.9797i	1.10316	+	0.759483i
$210$	0.431694			0.0297897
$211$	10.2175	−	7.42343i	0.703400	−	0.511050i	−0.177638	−	0.984096i	$-0.556846\pi$
$211$	10.2175	−	7.42343i	0.703400	−	0.511050i	0.881038	+	0.473046i	$0.156846\pi$
$212$	3.64691	+	11.2240i	0.250471	+	0.770870i
$213$	−0.378632	+	1.16531i	−0.0259435	+	0.0798458i
$214$	13.6781	+	9.93769i	0.935013	+	0.679327i
$215$	−4.66524	−	3.38950i	−0.318167	−	0.231162i
$216$	−0.697363	+	2.14626i	−0.0474495	+	0.146035i
$217$	0.828772	+	2.55070i	0.0562607	+	0.173153i
$218$	16.0443	−	11.6569i	1.08666	−	0.789502i
$219$	−2.80124			−0.189290
$220$	−1.05784	+	3.56073i	−0.0713195	+	0.240064i
$221$	13.6076			0.915344
$222$	0.667464	−	0.484941i	0.0447972	−	0.0325471i
$223$	−0.209706	−	0.645409i	−0.0140429	−	0.0432198i	0.943790	−	0.330547i	$-0.107233\pi$
$223$	−0.209706	−	0.645409i	−0.0140429	−	0.0432198i	−0.957832	+	0.287327i	$0.907233\pi$
$224$	1.76061	−	5.41860i	0.117636	−	0.362045i
$225$	2.37873	+	1.72825i	0.158582	+	0.115216i
$226$	−4.68024	−	3.40040i	−0.311325	−	0.226191i
$227$	6.94871	−	21.3859i	0.461202	−	1.41943i	−0.402495	−	0.915422i	$-0.631857\pi$
$227$	6.94871	−	21.3859i	0.461202	−	1.41943i	0.863697	−	0.504011i	$-0.168143\pi$
$228$	−0.493802	−	1.51977i	−0.0327028	−	0.100649i
$229$	−19.8180	+	14.3986i	−1.30961	+	0.951485i	−0.309608	+	0.950864i	$0.600198\pi$
$229$	−19.8180	+	14.3986i	−1.30961	+	0.951485i	−1.00000		0.000621034i	$0.999802\pi$
$230$	−15.6521			−1.03207
$231$	−0.643472	+	0.492936i	−0.0423374	+	0.0324328i
$232$	−8.54328			−0.560894
$233$	−18.0694	+	13.1282i	−1.18376	+	0.860054i	−0.992591	−	0.121503i	$-0.961229\pi$
$233$	−18.0694	+	13.1282i	−1.18376	+	0.860054i	−0.191172	+	0.981557i	$0.561229\pi$
$234$	−7.26305	−	22.3534i	−0.474800	−	1.46129i
$235$	−0.548983	+	1.68960i	−0.0358117	+	0.110217i
$236$	−6.85221	−	4.97842i	−0.446041	−	0.324068i
$237$	−0.340659	−	0.247503i	−0.0221282	−	0.0160771i
$238$	1.64121	−	5.05113i	0.106384	−	0.327416i
$239$	2.59319	+	7.98101i	0.167739	+	0.516248i	0.999228	−	0.0392937i	$-0.0125108\pi$
$239$	2.59319	+	7.98101i	0.167739	+	0.516248i	−0.831488	+	0.555542i	$0.812511\pi$
$240$	−0.985771	+	0.716204i	−0.0636312	+	0.0462308i
$241$	18.2784			1.17742			0.588708	−	0.808346i	$-0.299637\pi$
$241$	18.2784			1.17742			0.588708	+	0.808346i	$0.299637\pi$
$242$	−6.93396	−	18.1504i	−0.445732	−	1.16675i
$243$	6.42448			0.412131
$244$	−7.65793	+	5.56381i	−0.490249	+	0.356187i
$245$	−0.309017	−	0.951057i	−0.0197424	−	0.0607608i
$246$	0.325886	−	1.00297i	0.0207777	−	0.0639472i
$247$	−21.3743	−	15.5294i	−1.36002	−	0.988110i
$248$	−3.37272	−	2.45042i	−0.214168	−	0.155602i
$249$	−0.158469	+	0.487716i	−0.0100425	+	0.0309078i
$250$	0.545831	+	1.67989i	0.0345214	+	0.106246i
$251$	21.7936	−	15.8340i	1.37560	−	0.999434i	0.378327	−	0.925672i	$-0.376500\pi$
$251$	21.7936	−	15.8340i	1.37560	−	0.999434i	0.997276	−	0.0737619i	$-0.0235005\pi$
$252$	−3.29303			−0.207442
$253$	23.3306	−	17.8726i	1.46678	−	1.12364i
$254$	18.2632			1.14594
$255$	−0.594517	+	0.431942i	−0.0372301	+	0.0270493i
$256$	6.18769	+	19.0438i	0.386731	+	1.19023i
$257$	−3.41408	+	10.5075i	−0.212965	+	0.655437i	0.786327	+	0.617810i	$0.211980\pi$
$257$	−3.41408	+	10.5075i	−0.212965	+	0.655437i	−0.999292	+	0.0376273i	$0.988020\pi$
$258$	−2.01396	−	1.46323i	−0.125384	−	0.0910965i
$259$	−1.54615	−	1.12334i	−0.0960731	−	0.0698012i
$260$	1.56627	−	4.82047i	0.0971357	−	0.298953i
$261$	4.99372	+	15.3691i	0.309104	+	0.951323i
$262$	16.5134	−	11.9977i	1.02020	−	0.741220i
$263$	−10.7248			−0.661317			−0.330658	−	0.943751i	$-0.607271\pi$
$263$	−10.7248			−0.661317			−0.330658	+	0.943751i	$0.607271\pi$
$264$	0.358823	−	1.20781i	0.0220840	−	0.0743359i
$265$	−10.5374			−0.647308
$266$	−8.34247	+	6.06116i	−0.511510	+	0.371633i
$267$	−0.338166	−	1.04077i	−0.0206954	−	0.0636939i
$268$	0.407427	−	1.25393i	0.0248876	−	0.0765961i
$269$	16.5998	+	12.0605i	1.01211	+	0.735340i	0.964650	−	0.263533i	$-0.0848879\pi$
$269$	16.5998	+	12.0605i	1.01211	+	0.735340i	0.0474583	+	0.998873i	$0.484888\pi$
$270$	2.07463	+	1.50730i	0.126258	+	0.0917316i
$271$	0.614768	−	1.89206i	0.0373445	−	0.114935i	−0.930646	−	0.365920i	$-0.880754\pi$
$271$	0.614768	−	1.89206i	0.0373445	−	0.114935i	0.967991	+	0.250985i	$0.0807545\pi$
$272$	4.63241	+	14.2571i	0.280881	+	0.864463i
$273$	0.894812	−	0.650119i	0.0541565	−	0.0393470i
$274$	−29.1741			−1.76247
$275$	−2.73181	−	1.88075i	−0.164734	−	0.113413i
$276$	−2.42553			−0.146000
$277$	0.915394	−	0.665073i	0.0550007	−	0.0399603i	−0.559945	−	0.828530i	$-0.689178\pi$
$277$	0.915394	−	0.665073i	0.0550007	−	0.0399603i	0.614946	+	0.788569i	$0.289178\pi$
$278$	1.55750	+	4.79348i	0.0934124	+	0.287494i
$279$	−2.43681	+	7.49974i	−0.145888	+	0.448997i
$280$	1.25756	+	0.913668i	0.0751534	+	0.0546021i
$281$	21.4248	+	15.5660i	1.27810	+	0.928591i	0.999494	−	0.0318158i	$-0.0101290\pi$
$281$	21.4248	+	15.5660i	1.27810	+	0.928591i	0.278602	+	0.960407i	$0.410129\pi$
$282$	−0.236993	+	0.729388i	−0.0141127	+	0.0434344i
$283$	8.61154	+	26.5036i	0.511903	+	1.57548i	0.788847	+	0.614590i	$0.210678\pi$
$283$	8.61154	+	26.5036i	0.511903	+	1.57548i	−0.276944	+	0.960886i	$0.589322\pi$
$284$	4.54257	−	3.30037i	0.269552	−	0.195841i
$285$	1.42679			0.0845160
$286$	8.82994	+	24.9986i	0.522126	+	1.47820i
$287$	−2.44291			−0.144200
$288$	13.5527	−	9.84660i	0.798600	−	0.580217i
$289$	−2.45949	−	7.56953i	−0.144676	−	0.445266i
$290$	−2.99994	+	9.23287i	−0.176163	+	0.542173i
$291$	−1.52979	−	1.11146i	−0.0896778	−	0.0651547i
$292$	10.3852	+	7.54532i	0.607751	+	0.441557i
$293$	−8.56913	+	26.3731i	−0.500614	+	1.54073i	0.307408	+	0.951578i	$0.400538\pi$
$293$	−8.56913	+	26.3731i	−0.500614	+	1.54073i	−0.808022	+	0.589153i	$0.799462\pi$
$294$	−0.133401	−	0.410565i	−0.00778009	−	0.0239447i
$295$	6.11817	−	4.44511i	0.356214	−	0.258804i
$296$	2.97073			0.172670
$297$	−4.81352	+	0.122190i	−0.279309	+	0.00709016i
$298$	38.1810			2.21177
$299$	−32.4436	+	23.5716i	−1.87626	+	1.36318i
$300$	0.0845847	+	0.260325i	0.00488350	+	0.0150299i
$301$	−1.78196	+	5.48432i	−0.102711	+	0.316111i
$302$	−22.5883	−	16.4113i	−1.29981	−	0.944367i
$303$	3.62448	+	2.63334i	0.208221	+	0.151281i
$304$	8.99418	−	27.6812i	0.515852	−	1.58763i
$305$	−2.61172	−	8.03806i	−0.149547	−	0.460258i
$306$	12.6336	−	9.17884i	0.722214	−	0.524720i
$307$	26.3127			1.50174			0.750872	−	0.660448i	$-0.229633\pi$
$307$	26.3127			1.50174			0.750872	+	0.660448i	$0.229633\pi$
$308$	3.71335	−	0.0942620i	0.211588	−	0.00537108i
$309$	2.25106			0.128058
$310$	−3.83253	+	2.78450i	−0.217673	+	0.158149i
$311$	0.0795586	+	0.244856i	0.00451135	+	0.0138845i	0.953287	−	0.302067i	$-0.0976765\pi$
$311$	0.0795586	+	0.244856i	0.00451135	+	0.0138845i	−0.948776	+	0.315951i	$0.897676\pi$
$312$	−0.531284	+	1.63512i	−0.0300780	+	0.0925706i
$313$	13.6984	+	9.95246i	0.774279	+	0.562547i	0.903257	−	0.429101i	$-0.141170\pi$
$313$	13.6984	+	9.95246i	0.774279	+	0.562547i	−0.128978	+	0.991647i	$0.541170\pi$
$314$	−13.3089	−	9.66946i	−0.751063	−	0.545679i
$315$	0.908593	−	2.79636i	0.0511934	−	0.157557i
$316$	0.596284	+	1.83517i	0.0335436	+	0.103237i
$317$	8.93382	−	6.49080i	0.501774	−	0.364560i	−0.307920	−	0.951412i	$-0.599633\pi$
$317$	8.93382	−	6.49080i	0.501774	−	0.364560i	0.809694	+	0.586852i	$0.199633\pi$
$318$	−4.54894			−0.255092
$319$	−6.07104	−	17.1878i	−0.339913	−	0.962333i
$320$	0.0924575			0.00516853
$321$	−1.89256	+	1.37502i	−0.105632	+	0.0767463i
$322$	4.83677	+	14.8860i	0.269542	+	0.829566i
$323$	5.42438	−	16.6945i	0.301821	−	0.928908i
$324$	−7.67086	−	5.57321i	−0.426159	−	0.309623i
$325$	3.66127	+	2.66007i	0.203091	+	0.147554i
$326$	−2.17939	+	6.70748i	−0.120705	+	0.371493i
$327$	0.847949	+	2.60972i	0.0468917	+	0.144318i
$328$	3.07209	−	2.23201i	0.169628	−	0.123242i
$329$	1.77655			0.0979441
$330$	−1.17931	−	0.811906i	−0.0649187	−	0.0446940i
$331$	−15.1885			−0.834838			−0.417419	−	0.908714i	$-0.637065\pi$
$331$	−15.1885			−0.834838			−0.417419	+	0.908714i	$0.637065\pi$
$332$	1.90120	−	1.38130i	0.104342	−	0.0758087i
$333$	−1.73645	−	5.34426i	−0.0951571	−	0.292863i
$334$	−11.0061	+	33.8732i	−0.602226	+	1.85346i
$335$	0.952393	+	0.691954i	0.0520348	+	0.0378055i
$336$	0.985771	+	0.716204i	0.0537782	+	0.0390722i
$337$	2.67590	−	8.23559i	0.145766	−	0.448621i	−0.851343	−	0.524610i	$-0.824211\pi$
$337$	2.67590	−	8.23559i	0.145766	−	0.448621i	0.997109	+	0.0759887i	$0.0242113\pi$
$338$	−4.08328	−	12.5670i	−0.222101	−	0.683557i
$339$	0.647580	−	0.470494i	0.0351717	−	0.0255537i
$340$	3.36756			0.182632
$341$	2.53316	−	8.52674i	0.137178	−	0.461749i
$342$	−30.3196			−1.63950
$343$	−0.809017	+	0.587785i	−0.0436828	+	0.0317374i
$344$	−2.76993	−	8.52497i	−0.149345	−	0.459636i
$345$	0.669237	−	2.05970i	0.0360305	−	0.110890i
$346$	−24.0231	−	17.4538i	−1.29149	−	0.938322i
$347$	14.2718	+	10.3691i	0.766150	+	0.556641i	0.900791	−	0.434254i	$-0.142988\pi$
$347$	14.2718	+	10.3691i	0.766150	+	0.556641i	−0.134640	+	0.990895i	$0.542988\pi$
$348$	−0.464886	+	1.43077i	−0.0249205	+	0.0766974i
$349$	4.87057	+	14.9901i	0.260716	+	0.802401i	0.992649	+	0.121025i	$0.0386181\pi$
$349$	4.87057	+	14.9901i	0.260716	+	0.802401i	−0.731934	+	0.681376i	$0.761382\pi$
$350$	1.42900	−	1.03823i	0.0763835	−	0.0554958i
$351$	6.57023			0.350693
$352$	−15.0007	+	11.4913i	−0.799538	+	0.612490i
$353$	−12.2580			−0.652429			−0.326214	−	0.945296i	$-0.605773\pi$
$353$	−12.2580			−0.652429			−0.326214	+	0.945296i	$0.605773\pi$
$354$	2.64118	−	1.91893i	0.140377	−	0.101990i
$355$	1.54924	+	4.76806i	0.0822249	+	0.253062i
$356$	−1.54967	+	4.76938i	−0.0821321	+	0.252777i
$357$	0.594517	+	0.431942i	0.0314652	+	0.0228608i
$358$	−25.8254	−	18.7633i	−1.36492	−	0.991670i
$359$	−5.38760	+	16.5813i	−0.284347	+	0.875129i	0.702247	+	0.711933i	$0.252180\pi$
$359$	−5.38760	+	16.5813i	−0.284347	+	0.875129i	−0.986594	+	0.163196i	$0.947820\pi$
$360$	1.41234	+	4.34674i	0.0744369	+	0.229093i
$361$	−12.2014	+	8.86485i	−0.642180	+	0.466571i
$362$	−11.5772			−0.608482
$363$	2.68493	−	0.136400i	0.140922	−	0.00715915i
$364$	−5.06854			−0.265664
$365$	−9.27274	+	6.73704i	−0.485357	+	0.352633i
$366$	−1.12747	−	3.46998i	−0.0589336	−	0.181379i
$367$	−1.51057	+	4.64907i	−0.0788513	+	0.242679i	−0.982710	−	0.185152i	$-0.940722\pi$
$367$	−1.51057	+	4.64907i	−0.0788513	+	0.242679i	0.903859	+	0.427831i	$0.140722\pi$
$368$	−35.7415	−	25.9677i	−1.86315	−	1.35366i
$369$	−5.81101	−	4.22194i	−0.302509	−	0.219786i
$370$	1.04316	−	3.21052i	0.0542314	−	0.166907i
$371$	3.25624	+	10.0217i	0.169055	+	0.520299i
$372$	−0.593909	+	0.431500i	−0.0307927	+	0.0223722i
$373$	−8.28818			−0.429146			−0.214573	−	0.976708i	$-0.568836\pi$
$373$	−8.28818			−0.429146			−0.214573	+	0.976708i	$0.568836\pi$
$374$	−13.9834	+	10.7120i	−0.723063	+	0.553906i
$375$	−0.244400			−0.0126207
$376$	−2.23411	+	1.62317i	−0.115215	+	0.0837088i
$377$	7.68619	+	23.6557i	0.395859	+	1.21833i
$378$	0.792437	−	2.43887i	0.0407585	−	0.125442i
$379$	−23.0130	−	16.7199i	−1.18210	−	0.858844i	−0.189691	−	0.981844i	$-0.560749\pi$
$379$	−23.0130	−	16.7199i	−1.18210	−	0.858844i	−0.992407	+	0.123000i	$0.960749\pi$
$380$	−5.28966	−	3.84316i	−0.271354	−	0.197150i
$381$	−0.780881	+	2.40330i	−0.0400057	+	0.123125i
$382$	1.31857	+	4.05814i	0.0674638	+	0.207632i
$383$	−27.4574	+	19.9490i	−1.40301	+	1.01935i	−0.408717	+	0.912661i	$0.634024\pi$
$383$	−27.4574	+	19.9490i	−1.40301	+	1.01935i	−0.994293	+	0.106685i	$0.965976\pi$
$384$	−2.74500			−0.140080
$385$	−0.944518	+	3.17929i	−0.0481371	+	0.162032i
$386$	0.452271			0.0230200
$387$	−13.7171	+	9.96603i	−0.697278	+	0.506602i
$388$	2.67772	+	8.24117i	0.135940	+	0.418382i
$389$	−2.30758	+	7.10200i	−0.116999	+	0.360086i	−0.992359	−	0.123387i	$-0.960625\pi$
$389$	−2.30758	+	7.10200i	−0.116999	+	0.360086i	0.875360	+	0.483472i	$0.160625\pi$
$390$	1.58055	+	1.14834i	0.0800342	+	0.0581482i
$391$	−21.5557	−	15.6611i	−1.09012	−	0.792016i
$392$	0.480344	−	1.47835i	0.0242610	−	0.0746678i
$393$	0.872743	+	2.68603i	0.0440240	+	0.135492i
$394$	29.7077	−	21.5839i	1.49665	−	1.08738i
$395$	−1.72291			−0.0866889
$396$	8.99595	+	6.19335i	0.452063	+	0.311228i
$397$	24.6303			1.23616			0.618079	−	0.786116i	$-0.287911\pi$
$397$	24.6303			1.23616			0.618079	+	0.786116i	$0.287911\pi$
$398$	25.4551	−	18.4942i	1.27595	−	0.927030i
$399$	−0.440904	−	1.35696i	−0.0220728	−	0.0679331i
$400$	−1.54064	+	4.74159i	−0.0770318	+	0.237080i
$401$	−0.256945	−	0.186681i	−0.0128312	−	0.00932243i	0.581351	−	0.813653i	$-0.302524\pi$
$401$	−0.256945	−	0.186681i	−0.0128312	−	0.00932243i	−0.594182	+	0.804330i	$0.702524\pi$
$402$	0.411142	+	0.298712i	0.0205059	+	0.0148984i
$403$	−3.75067	+	11.5434i	−0.186834	+	0.575017i
$404$	−6.34423	−	19.5255i	−0.315637	−	0.971431i
$405$	6.84913	−	4.97618i	0.340336	−	0.247269i
$406$	9.70802			0.481801
$407$	2.11107	+	5.97668i	0.104642	+	0.296253i
$408$	−1.14229			−0.0565518
$409$	4.16577	−	3.02661i	0.205984	−	0.149656i	−0.480011	−	0.877263i	$-0.659367\pi$
$409$	4.16577	−	3.02661i	0.205984	−	0.149656i	0.685995	+	0.727607i	$0.259367\pi$
$410$	−1.33341	−	4.10382i	−0.0658526	−	0.202673i
$411$	1.24740	−	3.83909i	0.0615295	−	0.189368i
$412$	−8.34552	−	6.06337i	−0.411154	−	0.298721i
$413$	−6.11817	−	4.44511i	−0.301056	−	0.218730i
$414$	−14.2214	+	43.7690i	−0.698943	+	2.15113i
$415$	0.648400	+	1.99557i	0.0318287	+	0.0979587i
$416$	20.8599	−	15.1556i	1.02274	−	0.743065i
$417$	−0.697380			−0.0341508
$418$	34.1895	−	0.867890i	1.67227	−	0.0424499i
$419$	−28.2458			−1.37990			−0.689948	−	0.723859i	$-0.742367\pi$
$419$	−28.2458			−1.37990			−0.689948	+	0.723859i	$0.742367\pi$
$420$	0.221446	−	0.160890i	0.0108054	−	0.00785061i
$421$	−5.17078	−	15.9140i	−0.252008	−	0.775601i	−0.994404	−	0.105640i	$-0.966311\pi$
$421$	−5.17078	−	15.9140i	−0.252008	−	0.775601i	0.742396	−	0.669961i	$-0.233689\pi$
$422$	6.89356	−	21.2162i	0.335573	−	1.03279i
$423$	4.22592	+	3.07031i	0.205471	+	0.149284i
$424$	−13.2514	−	9.62769i	−0.643544	−	0.467562i
$425$	−0.929157	+	2.85965i	−0.0450707	+	0.138713i
$426$	0.668796	+	2.05834i	0.0324033	+	0.0997270i
$427$	−6.83758	+	4.96779i	−0.330894	+	0.240408i
$428$	10.7201			0.518177
$429$	−3.66717	+	0.0930898i	−0.177053	+	0.00449442i
$430$	−10.1857			−0.491200
$431$	−18.4686	+	13.4183i	−0.889603	+	0.646335i	−0.935775	−	0.352599i	$-0.885298\pi$
$431$	−18.4686	+	13.4183i	−0.889603	+	0.646335i	0.0461712	+	0.998934i	$0.485298\pi$
$432$	2.23669	+	6.88384i	0.107613	+	0.331199i
$433$	7.73886	−	23.8178i	0.371906	−	1.14461i	−0.573637	−	0.819110i	$-0.694468\pi$
$433$	7.73886	−	23.8178i	0.371906	−	1.14461i	0.945543	−	0.325499i	$-0.105532\pi$
$434$	3.83253	+	2.78450i	0.183967	+	0.133660i
$435$	−1.08671	−	0.789539i	−0.0521036	−	0.0378555i
$436$	3.88578	−	11.9592i	0.186095	−	0.572742i
$437$	15.9860	+	49.1999i	0.764716	+	2.35355i
$438$	−4.00298	+	2.90834i	−0.191270	+	0.138966i
$439$	−31.7525			−1.51546			−0.757732	−	0.652565i	$-0.773693\pi$
$439$	−31.7525			−1.51546			−0.757732	+	0.652565i	$0.773693\pi$
$440$	−1.71703	−	4.86111i	−0.0818562	−	0.231744i
$441$	−2.94027			−0.140013
$442$	19.4453	−	14.1278i	0.924917	−	0.671991i
$443$	5.86513	+	18.0510i	0.278661	+	0.857630i	0.988227	+	0.152992i	$0.0488907\pi$
$443$	5.86513	+	18.0510i	0.278661	+	0.857630i	−0.709567	+	0.704638i	$0.751109\pi$
$444$	0.161654	−	0.497519i	0.00767174	−	0.0236112i
$445$	−3.62247	−	2.63188i	−0.171721	−	0.124763i
$446$	−0.969754	−	0.704568i	−0.0459192	−	0.0333622i
$447$	−1.63250	+	5.02433i	−0.0772148	+	0.237643i
$448$	−0.0285710	−	0.0879323i	−0.00134985	−	0.00415441i
$449$	0.0900686	−	0.0654387i	0.00425060	−	0.00308824i	−0.585658	−	0.810558i	$-0.699164\pi$
$449$	0.0900686	−	0.0654387i	0.00425060	−	0.00308824i	0.589909	+	0.807470i	$0.299164\pi$
$450$	5.19353			0.244825
$451$	6.67356	+	4.59448i	0.314246	+	0.216346i
$452$	−3.66813			−0.172534
$453$	3.12542	−	2.27075i	0.146845	−	0.106689i
$454$	−12.2738	−	37.7749i	−0.576039	−	1.77287i
$455$	1.39848	−	4.30408i	0.0655618	−	0.201778i
$456$	1.79428	+	1.30362i	0.0840246	+	0.0610475i
$457$	−11.6791	−	8.48538i	−0.546326	−	0.396929i	0.280103	−	0.959970i	$-0.409631\pi$
$457$	−11.6791	−	8.48538i	−0.546326	−	0.396929i	−0.826429	+	0.563041i	$0.809631\pi$
$458$	−13.3709	+	41.1513i	−0.624779	+	1.92287i
$459$	1.34895	+	4.15164i	0.0629635	+	0.193782i
$460$	−8.02904	+	5.83344i	−0.374356	+	0.271986i
$461$	−23.1164			−1.07664			−0.538319	−	0.842741i	$-0.680940\pi$
$461$	−23.1164			−1.07664			−0.538319	+	0.842741i	$0.680940\pi$
$462$	−0.407743	+	1.37248i	−0.0189699	+	0.0638536i
$463$	27.2088			1.26450			0.632251	−	0.774763i	$-0.282131\pi$
$463$	27.2088			1.26450			0.632251	+	0.774763i	$0.282131\pi$
$464$	−22.1682	+	16.1061i	−1.02913	+	0.747709i
$465$	−0.202551	−	0.623389i	−0.00939310	−	0.0289090i
$466$	−12.1911	+	37.5204i	−0.564742	+	1.73810i
$467$	11.2364	+	8.16374i	0.519959	+	0.377773i	0.816589	−	0.577220i	$-0.195863\pi$
$467$	11.2364	+	8.16374i	0.519959	+	0.377773i	−0.296629	+	0.954993i	$0.595863\pi$
$468$	−12.0567	−	8.75969i	−0.557320	−	0.404917i
$469$	0.363782	−	1.11961i	0.0167979	−	0.0516986i
$470$	0.969693	+	2.98441i	0.0447286	+	0.137661i
$471$	1.84147	−	1.33791i	0.0848507	−	0.0616476i
$472$	11.7553			0.541082
$473$	15.1826	−	11.6307i	0.698097	−	0.534781i
$474$	−0.743769			−0.0341624
$475$	4.72301	−	3.43147i	0.216707	−	0.157447i
$476$	−1.04063	−	3.20274i	−0.0476974	−	0.146797i
$477$	−9.57421	+	29.4664i	−0.438373	+	1.34917i
$478$	11.9918	+	8.71256i	0.548492	+	0.398503i
$479$	7.89538	+	5.73633i	0.360749	+	0.262099i	0.753364	−	0.657603i	$-0.228430\pi$
$479$	7.89538	+	5.73633i	0.360749	+	0.262099i	−0.392615	+	0.919703i	$0.628430\pi$
$480$	−0.430292	+	1.32430i	−0.0196401	+	0.0604459i
$481$	−2.67270	−	8.22573i	−0.121865	−	0.375061i
$482$	26.1199	−	18.9772i	1.18973	−	0.864390i
$483$	−2.16570			−0.0985426
$484$	−10.3214	−	6.72635i	−0.469157	−	0.305743i
$485$	−7.73701			−0.351320
$486$	9.18060	−	6.67010i	0.416441	−	0.302562i
$487$	13.2955	+	40.9193i	0.602476	+	1.85423i	0.513292	+	0.858214i	$0.328426\pi$
$487$	13.2955	+	40.9193i	0.602476	+	1.85423i	0.0891838	+	0.996015i	$0.471574\pi$
$488$	4.05973	−	12.4946i	0.183775	−	0.565602i
$489$	−0.789470	−	0.573583i	−0.0357011	−	0.0259383i
$490$	−1.42900	−	1.03823i	−0.0645558	−	0.0469025i
$491$	1.85595	−	5.71202i	0.0837578	−	0.257780i	−0.900403	−	0.435056i	$-0.856729\pi$
$491$	1.85595	−	5.71202i	0.0837578	−	0.257780i	0.984161	+	0.177276i	$0.0567285\pi$
$492$	−0.206632	−	0.635949i	−0.00931571	−	0.0286708i
$493$	−13.3696	+	9.71360i	−0.602137	+	0.437478i
$494$	−46.6671			−2.09965
$495$	−7.74135	+	5.93030i	−0.347948	+	0.266547i
$496$	−13.3712			−0.600385
$497$	4.05595	−	2.94682i	0.181934	−	0.132183i
$498$	0.279910	+	0.861475i	0.0125431	+	0.0386036i
$499$	10.6068	−	32.6443i	0.474824	−	1.46136i	−0.371371	−	0.928484i	$-0.621112\pi$
$499$	10.6068	−	32.6443i	0.474824	−	1.46136i	0.846195	−	0.532873i	$-0.178888\pi$
$500$	0.906080	+	0.658306i	0.0405211	+	0.0294403i
$501$	−3.98687	−	2.89663i	−0.178120	−	0.129412i
$502$	14.7038	−	45.2537i	0.656264	−	2.01977i
$503$	3.10549	+	9.55772i	0.138467	+	0.426158i	0.996113	−	0.0880825i	$-0.0280739\pi$
$503$	3.10549	+	9.55772i	0.138467	+	0.426158i	−0.857646	+	0.514240i	$0.828074\pi$
$504$	3.69755	−	2.68643i	0.164702	−	0.119663i
$505$	18.3311			0.815721
$506$	14.7837	−	49.7626i	0.657216	−	2.21222i
$507$	1.82832			0.0811984
$508$	9.36847	−	6.80659i	0.415659	−	0.301994i
$509$	−4.61356	−	14.1991i	−0.204492	−	0.629363i	−0.999734	−	0.0230699i	$-0.992656\pi$
$509$	−4.61356	−	14.1991i	−0.204492	−	0.629363i	0.795242	−	0.606293i	$-0.207344\pi$
$510$	−0.401111	+	1.23449i	−0.0177615	+	0.0546643i
$511$	9.27274	+	6.73704i	0.410202	+	0.298029i
$512$	10.4410	+	7.58581i	0.461430	+	0.335248i
$513$	2.61909	−	8.06072i	0.115636	−	0.355890i
$514$	6.03045	+	18.5598i	0.265992	+	0.818638i
$515$	7.45151	−	5.41384i	0.328353	−	0.238562i
$516$	−1.57843			−0.0694866
$517$	−4.85319	−	3.34123i	−0.213443	−	0.146947i
$518$	−3.37574			−0.148322
$519$	3.32394	−	2.41499i	0.145905	−	0.106006i
$520$	2.17383	+	6.69037i	0.0953289	+	0.293392i
$521$	13.8036	−	42.4831i	0.604747	−	1.86122i	0.106227	−	0.994342i	$-0.466123\pi$
$521$	13.8036	−	42.4831i	0.604747	−	1.86122i	0.498520	−	0.866878i	$-0.333877\pi$
$522$	23.0927	+	16.7778i	1.01074	+	0.734346i
$523$	9.39093	+	6.82291i	0.410637	+	0.298345i	0.773860	−	0.633357i	$-0.218324\pi$
$523$	9.39093	+	6.82291i	0.410637	+	0.298345i	−0.363223	+	0.931702i	$0.618324\pi$
$524$	3.99940	−	12.3089i	0.174715	−	0.537716i
$525$	0.0755236	+	0.232438i	0.00329612	+	0.0101444i
$526$	−15.3257	+	11.1348i	−0.668233	+	0.485499i
$527$	−8.06416			−0.351280
$528$	−1.34594	−	3.81052i	−0.0585746	−	0.165832i
$529$	55.5225			2.41402
$530$	−15.0580	+	10.9403i	−0.654077	+	0.475215i
$531$	−6.87121	−	21.1474i	−0.298185	−	0.917720i
$532$	−2.02047	+	6.21837i	−0.0875985	+	0.269601i
$533$	−8.94414	−	6.49830i	−0.387414	−	0.281472i
$534$	−1.56380	−	1.13617i	−0.0676721	−	0.0491667i
$535$	−2.95783	+	9.10327i	−0.127878	+	0.393569i
$536$	0.565472	+	1.74034i	0.0244247	+	0.0751714i
$537$	3.57332	−	2.59617i	0.154200	−	0.112033i
$538$	36.2428			1.56254
$539$	3.31556	−	0.0841643i	0.142811	−	0.00362521i
$540$	1.62598			0.0699711
$541$	−0.413844	+	0.300675i	−0.0177926	+	0.0129270i	−0.596646	−	0.802505i	$-0.703500\pi$
$541$	−0.413844	+	0.300675i	−0.0177926	+	0.0129270i	0.578853	+	0.815432i	$0.303500\pi$
$542$	−1.08589	−	3.34204i	−0.0466431	−	0.143553i
$543$	0.495004	−	1.52347i	0.0212427	−	0.0653782i
$544$	13.8594	+	10.0695i	0.594217	+	0.431724i
$545$	9.08332	+	6.59942i	0.389087	+	0.282688i
$546$	0.603716	−	1.85805i	0.0258366	−	0.0795170i
$547$	3.37043	+	10.3731i	0.144109	+	0.443522i	0.996895	−	0.0787379i	$-0.0250890\pi$
$547$	3.37043	+	10.3731i	0.144109	+	0.443522i	−0.852786	+	0.522260i	$0.825089\pi$
$548$	−14.9654	+	10.8730i	−0.639290	+	0.464471i
$549$	−24.8503			−1.06059
$550$	−5.85642	+	0.148663i	−0.249719	+	0.00633902i
$551$	32.0860			1.36691
$552$	2.72348	−	1.97873i	0.115919	−	0.0842202i
$553$	0.532408	+	1.63858i	0.0226403	+	0.0696796i
$554$	0.617602	−	1.90078i	0.0262394	−	0.0807565i
$555$	0.377878	+	0.274545i	0.0160400	+	0.0116538i
$556$	2.58545	+	1.87844i	0.109647	+	0.0796635i
$557$	8.09985	−	24.9288i	0.343202	−	1.05627i	−0.619338	−	0.785125i	$-0.712599\pi$
$557$	8.09985	−	24.9288i	0.343202	−	1.05627i	0.962539	−	0.271141i	$-0.0874011\pi$
$558$	4.30425	+	13.2471i	0.182214	+	0.560796i
$559$	−21.1129	+	15.3394i	−0.892981	+	0.648789i
$560$	4.98561			0.210680
$561$	−0.811737	−	2.29812i	−0.0342716	−	0.0970267i
$562$	46.7772			1.97318
$563$	31.6963	−	23.0287i	1.33584	−	0.970545i	0.336255	−	0.941771i	$-0.390839\pi$
$563$	31.6963	−	23.0287i	1.33584	−	0.970545i	0.999586	−	0.0287746i	$-0.00916051\pi$
$564$	0.150269	+	0.462479i	0.00632745	+	0.0194739i
$565$	1.01209	−	3.11488i	0.0425788	−	0.131044i
$566$	39.8228	+	28.9330i	1.67388	+	1.21614i
$567$	−6.84913	−	4.97618i	−0.287636	−	0.208980i
$568$	−2.40817	+	7.41159i	−0.101045	+	0.310983i
$569$	−13.3214	−	40.9990i	−0.558462	−	1.71877i	−0.686622	−	0.727015i	$-0.740907\pi$
$569$	−13.3214	−	40.9990i	−0.558462	−	1.71877i	0.128160	−	0.991753i	$-0.459093\pi$
$570$	2.03890	−	1.48134i	0.0853999	−	0.0620467i
$571$	5.74809			0.240550			0.120275	−	0.992741i	$-0.461622\pi$
$571$	5.74809			0.240550			0.120275	+	0.992741i	$0.461622\pi$
$572$	13.8463	+	9.53263i	0.578943	+	0.398579i
$573$	−0.590398			−0.0246642
$574$	−3.49092	+	2.53630i	−0.145708	+	0.105863i
$575$	−2.73829	−	8.42759i	−0.114195	−	0.351455i
$576$	0.0840063	−	0.258545i	0.00350026	−	0.0107727i
$577$	−10.0839	−	7.32637i	−0.419798	−	0.305001i	0.357759	−	0.933814i	$-0.383541\pi$
$577$	−10.0839	−	7.32637i	−0.419798	−	0.305001i	−0.777556	+	0.628813i	$0.783541\pi$
$578$	−11.3735	−	8.26336i	−0.473077	−	0.343710i
$579$	−0.0193378	+	0.0595155i	−0.000803650	+	0.00247338i
$580$	1.90216	+	5.85423i	0.0789827	+	0.243084i
$581$	1.69753	−	1.23333i	0.0704255	−	0.0511671i
$582$	−3.34002			−0.138448
$583$	9.95277	−	33.5015i	0.412202	−	1.38749i
$584$	−17.8164			−0.737248
$585$	10.7651	−	7.82131i	0.445083	−	0.323372i
$586$	15.1360	+	46.5839i	0.625264	+	1.92436i
$587$	7.94788	−	24.4610i	0.328044	−	1.00962i	−0.642004	−	0.766701i	$-0.721897\pi$
$587$	7.94788	−	24.4610i	0.328044	−	1.00962i	0.970048	−	0.242914i	$-0.0781033\pi$
$588$	−0.221446	−	0.160890i	−0.00913226	−	0.00663498i
$589$	12.6669	+	9.20307i	0.521932	+	0.379206i
$590$	4.12783	−	12.7042i	0.169940	−	0.523022i
$591$	1.57007	+	4.83218i	0.0645840	+	0.198769i
$592$	7.70849	−	5.60055i	0.316817	−	0.230181i
$593$	−3.09255			−0.126996			−0.0634978	−	0.997982i	$-0.520226\pi$
$593$	−3.09255			−0.126996			−0.0634978	+	0.997982i	$0.520226\pi$
$594$	−6.75168	+	5.17216i	−0.277025	+	0.212216i
$595$	3.00681			0.123267
$596$	19.5857	−	14.2298i	0.802260	−	0.582876i
$597$	1.34531	+	4.14045i	0.0550600	+	0.169457i
$598$	−21.8892	+	67.3679i	−0.895114	+	2.75488i
$599$	17.6873	+	12.8506i	0.722683	+	0.525060i	0.887240	−	0.461308i	$-0.152620\pi$
$599$	17.6873	+	12.8506i	0.722683	+	0.525060i	−0.164557	+	0.986368i	$0.552620\pi$
$600$	−0.307346	−	0.223300i	−0.0125474	−	0.00911619i
$601$	4.79574	−	14.7598i	0.195622	−	0.602064i	−0.804346	−	0.594161i	$-0.797484\pi$
$601$	4.79574	−	14.7598i	0.195622	−	0.602064i	0.999969	−	0.00790316i	$-0.00251568\pi$
$602$	3.14756	+	9.68721i	0.128285	+	0.394821i
$603$	2.80029	−	2.03453i	0.114037	−	0.0828525i
$604$	−17.7035			−0.720345
$605$	8.55968	−	6.90883i	0.348001	−	0.280884i
$606$	7.91341			0.321460
$607$	−10.4656	+	7.60367i	−0.424784	+	0.308624i	−0.779560	−	0.626328i	$-0.784557\pi$
$607$	−10.4656	+	7.60367i	−0.424784	+	0.308624i	0.354776	+	0.934951i	$0.384557\pi$
$608$	−10.2784	−	31.6336i	−0.416843	−	1.28291i
$609$	−0.415085	+	1.27750i	−0.0168201	+	0.0517670i
$610$	−12.0775	−	8.77484i	−0.489005	−	0.355283i
$611$	6.50441	+	4.72573i	0.263140	+	0.191183i
$612$	3.05974	−	9.41692i	0.123683	−	0.380656i
$613$	−5.52370	−	17.0002i	−0.223100	−	0.686632i	−0.998479	−	0.0551355i	$-0.982441\pi$
$613$	−5.52370	−	17.0002i	−0.223100	−	0.686632i	0.775379	−	0.631497i	$-0.217559\pi$
$614$	37.6009	−	27.3187i	1.51745	−	1.10249i
$615$	0.597045			0.0240752
$616$	−4.09260	+	3.13516i	−0.164896	+	0.126319i
$617$	−26.9337			−1.08431			−0.542156	−	0.840278i	$-0.682392\pi$
$617$	−26.9337			−1.08431			−0.542156	+	0.840278i	$0.682392\pi$
$618$	3.21677	−	2.33712i	0.129398	−	0.0940128i
$619$	−8.65386	−	26.6338i	−0.347828	−	1.07050i	−0.960052	−	0.279820i	$-0.909725\pi$
$619$	−8.65386	−	26.6338i	−0.347828	−	1.07050i	0.612224	−	0.790684i	$-0.290275\pi$
$620$	−0.928205	+	2.85672i	−0.0372776	+	0.114729i
$621$	−10.4079	−	7.56175i	−0.417653	−	0.303443i
$622$	0.367907	+	0.267300i	0.0147517	+	0.0107178i
$623$	−1.38366	+	4.25846i	−0.0554351	+	0.170612i
$624$	1.70402	+	5.24443i	0.0682154	+	0.209945i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	29.9080			1.19536
$627$	−1.34763	+	4.53619i	−0.0538193	+	0.181158i
$628$	−10.4308			−0.416233
$629$	4.64898	−	3.37769i	0.185367	−	0.134677i
$630$	−1.60489	−	4.93934i	−0.0639403	−	0.196788i
$631$	−14.3936	+	44.2989i	−0.572999	+	1.76351i	0.0698950	+	0.997554i	$0.477734\pi$
$631$	−14.3936	+	44.2989i	−0.572999	+	1.76351i	−0.642894	+	0.765955i	$0.722266\pi$
$632$	−2.16665	−	1.57417i	−0.0861848	−	0.0626169i
$633$	2.49714	+	1.81428i	0.0992526	+	0.0721112i
$634$	6.02751	−	18.5508i	0.239383	−	0.736745i
$635$	3.19510	+	9.83350i	0.126794	+	0.390231i
$636$	−2.33346	+	1.69536i	−0.0925278	+	0.0672254i
$637$	−4.52558			−0.179310
$638$	−26.5205	−	18.2583i	−1.04996	−	0.722853i
$639$	14.7408			0.583139
$640$	−9.08655	+	6.60176i	−0.359177	+	0.260958i
$641$	−0.645954	−	1.98804i	−0.0255136	−	0.0785229i	0.937489	−	0.348015i	$-0.113144\pi$
$641$	−0.645954	−	1.98804i	−0.0255136	−	0.0785229i	−0.963003	+	0.269492i	$0.913144\pi$
$642$	−1.27688	+	3.92983i	−0.0503944	+	0.155098i
$643$	−40.7151	−	29.5813i	−1.60565	−	1.16657i	−0.875412	−	0.483377i	$-0.839410\pi$
$643$	−40.7151	−	29.5813i	−1.60565	−	1.16657i	−0.730236	−	0.683195i	$-0.760590\pi$
$644$	8.02904	+	5.83344i	0.316389	+	0.229870i
$645$	0.435511	−	1.34037i	0.0171482	−	0.0527769i
$646$	−9.58133	−	29.4883i	−0.376972	−	1.16020i
$647$	10.6089	−	7.70780i	0.417078	−	0.303025i	−0.359383	−	0.933190i	$-0.617013\pi$
$647$	10.6089	−	7.70780i	0.417078	−	0.303025i	0.776461	+	0.630165i	$0.217013\pi$
$648$	13.1597			0.516964
$649$	8.35358	+	23.6499i	0.327907	+	0.928341i
$650$	7.99373			0.313540
$651$	−0.530287	+	0.385276i	−0.0207836	+	0.0151001i
$652$	1.38188	+	4.25297i	0.0541184	+	0.166559i
$653$	−4.34382	+	13.3689i	−0.169987	+	0.523166i	−0.999369	−	0.0355157i	$-0.988693\pi$
$653$	−4.34382	+	13.3689i	−0.169987	+	0.523166i	0.829382	+	0.558682i	$0.188693\pi$
$654$	3.92122	+	2.84893i	0.153332	+	0.111402i
$655$	9.34891	+	6.79238i	0.365292	+	0.265400i
$656$	3.76363	−	11.5833i	0.146945	−	0.452251i
$657$	10.4141	+	32.0512i	0.406291	+	1.25043i
$658$	2.53869	−	1.84447i	0.0989684	−	0.0719048i
$659$	−0.264837			−0.0103166			−0.00515830	−	0.999987i	$-0.501642\pi$
$659$	−0.264837			−0.0103166			−0.00515830	+	0.999987i	$0.501642\pi$
$660$	−0.907540	+	0.0230376i	−0.0353259	+	0.000896737i
$661$	−6.99569			−0.272101			−0.136050	−	0.990702i	$-0.543441\pi$
$661$	−6.99569			−0.272101			−0.136050	+	0.990702i	$0.543441\pi$
$662$	−21.7045	+	15.7692i	−0.843569	+	0.612888i
$663$	1.02769	+	3.16291i	0.0399123	+	0.122837i
$664$	−1.00789	+	3.10196i	−0.0391137	+	0.120380i
$665$	−4.72301	−	3.43147i	−0.183150	−	0.133067i
$666$	−8.02998	−	5.83412i	−0.311155	−	0.226068i
$667$	15.0499	−	46.3189i	0.582735	−	1.79347i
$668$	6.97856	+	21.4778i	0.270009	+	0.831001i
$669$	0.134180	−	0.0974872i	0.00518768	−	0.00376907i
$670$	2.07938			0.0803335
$671$	28.0221	−	0.711332i	1.08178	−	0.0274607i
$672$	1.39245			0.0537151
$673$	12.6471	−	9.18867i	0.487511	−	0.354197i	−0.316715	−	0.948521i	$-0.602580\pi$
$673$	12.6471	−	9.18867i	0.487511	−	0.354197i	0.804226	+	0.594323i	$0.202580\pi$
$674$	−4.72657	−	14.5469i	−0.182061	−	0.560325i
$675$	−0.448631	+	1.38074i	−0.0172678	+	0.0531448i
$676$	−6.77825	−	4.92469i	−0.260702	−	0.189411i
$677$	−28.3969	−	20.6315i	−1.09138	−	0.792934i	−0.111748	−	0.993737i	$-0.535645\pi$
$677$	−28.3969	−	20.6315i	−1.09138	−	0.792934i	−0.979632	+	0.200803i	$0.935645\pi$
$678$	0.436912	−	1.34468i	0.0167795	−	0.0516420i
$679$	2.39087	+	7.35834i	0.0917531	+	0.282387i
$680$	−3.78124	+	2.74723i	−0.145004	+	0.105351i
$681$	5.49569			0.210595
$682$	−5.23283	−	14.8147i	−0.200375	−	0.567286i
$683$	9.86944			0.377643			0.188822	−	0.982011i	$-0.439533\pi$
$683$	9.86944			0.377643			0.188822	+	0.982011i	$0.439533\pi$
$684$	−15.5530	+	11.2999i	−0.594685	+	0.432064i
$685$	−5.10392	−	15.7083i	−0.195011	−	0.600182i
$686$	−0.545831	+	1.67989i	−0.0208399	+	0.0641387i
$687$	−4.84350	−	3.51901i	−0.184791	−	0.134259i
$688$	−23.2591	−	16.8987i	−0.886743	−	0.644257i
$689$	−14.7364	+	45.3538i	−0.561410	+	1.72784i
$690$	−1.18210	−	3.63814i	−0.0450019	−	0.138502i
$691$	−23.0100	+	16.7177i	−0.875341	+	0.635973i	−0.932015	−	0.362420i	$-0.881951\pi$
$691$	−23.0100	+	16.7177i	−0.875341	+	0.635973i	0.0566737	+	0.998393i	$0.481951\pi$
$692$	−18.8280			−0.715734
$693$	8.03226	+	5.52990i	0.305120	+	0.210063i
$694$	31.1600			1.18282
$695$	−2.30848	+	1.67721i	−0.0875658	+	0.0636203i
$696$	−0.645219	−	1.98578i	−0.0244570	−	0.0752708i
$697$	2.26984	−	6.98586i	0.0859764	−	0.264608i
$698$	22.5232	+	16.3641i	0.852518	+	0.619390i
$699$	−4.41614	−	3.20851i	−0.167034	−	0.121357i
$700$	0.346092	−	1.06516i	0.0130810	−	0.0402593i
$701$	15.5574	+	47.8808i	0.587596	+	1.80843i	0.588587	+	0.808434i	$0.299684\pi$
$701$	15.5574	+	47.8808i	0.587596	+	1.80843i	−0.000991898		1.00000i	$0.500316\pi$
$702$	9.38888	−	6.82142i	0.354360	−	0.257458i
$703$	−11.1572			−0.420802
$704$	−0.0873278	+	0.293949i	−0.00329129	+	0.0110786i
$705$	−0.434187			−0.0163524
$706$	−17.5168	+	12.7267i	−0.659252	+	0.478975i
$707$	−5.66461	−	17.4339i	−0.213039	−	0.655668i
$708$	0.639670	−	1.96870i	0.0240403	−	0.0739883i
$709$	4.46219	+	3.24197i	0.167581	+	0.121755i	0.668415	−	0.743789i	$-0.266973\pi$
$709$	4.46219	+	3.24197i	0.167581	+	0.121755i	−0.500834	+	0.865544i	$0.666973\pi$
$710$	7.16421	+	5.20511i	0.268868	+	0.195344i
$711$	−1.56542	+	4.81787i	−0.0587079	+	0.180684i
$712$	−2.15079	−	6.61947i	−0.0806044	−	0.248075i
$713$	19.2268	−	13.9691i	0.720050	−	0.523147i
$714$	1.29802			0.0485773
$715$	−11.9153	+	9.12775i	−0.445606	+	0.341359i
$716$	−20.2406			−0.756427
$717$	−1.65924	+	1.20551i	−0.0619655	+	0.0450205i
$718$	9.51637	+	29.2884i	0.355148	+	1.09303i
$719$	13.5638	−	41.7450i	0.505843	−	1.55683i	−0.293505	−	0.955958i	$-0.594822\pi$
$719$	13.5638	−	41.7450i	0.505843	−	1.55683i	0.799348	−	0.600868i	$-0.205178\pi$
$720$	11.8594	+	8.61636i	0.441974	+	0.321113i
$721$	−7.45151	−	5.41384i	−0.277509	−	0.201622i
$722$	−8.23211	+	25.3358i	−0.306367	+	0.942902i
$723$	1.38045	+	4.24860i	0.0513396	+	0.158007i
$724$	−5.93872	+	4.31473i	−0.220711	+	0.160356i
$725$	−5.49610			−0.204120
$726$	3.69516	−	2.98250i	0.137140	−	0.110691i
$727$	−37.9460			−1.40734			−0.703670	−	0.710527i	$-0.748457\pi$
$727$	−37.9460			−1.40734			−0.703670	+	0.710527i	$0.748457\pi$
$728$	5.69117	−	4.13488i	0.210929	−	0.153249i
$729$	−7.36320	−	22.6616i	−0.272711	−	0.839319i
$730$	−6.25617	+	19.2545i	−0.231551	+	0.712641i
$731$	−14.0275	−	10.1916i	−0.518827	−	0.376950i
$732$	−1.87159	−	1.35979i	−0.0691761	−	0.0502594i
$733$	16.5168	−	50.8335i	0.610063	−	1.87758i	0.152774	−	0.988261i	$-0.451179\pi$
$733$	16.5168	−	50.8335i	0.610063	−	1.87758i	0.457289	−	0.889318i	$-0.348821\pi$
$734$	2.66819	+	8.21186i	0.0984848	+	0.303105i
$735$	0.197723	−	0.143654i	0.00729314	−	0.00529877i
$736$	−50.4868			−1.86097
$737$	−3.09948	+	2.37437i	−0.114171	+	0.0874611i
$738$	−12.6873			−0.467026
$739$	−35.1556	+	25.5420i	−1.29322	+	0.939579i	−0.999865	−	0.0164254i	$-0.994771\pi$
$739$	−35.1556	+	25.5420i	−1.29322	+	0.939579i	−0.293354	+	0.956004i	$0.594771\pi$
$740$	−0.661432	−	2.03568i	−0.0243147	−	0.0748330i
$741$	1.99534	−	6.14104i	0.0733008	−	0.225597i
$742$	15.0580	+	10.9403i	0.552796	+	0.401630i
$743$	25.2771	+	18.3649i	0.927326	+	0.673742i	0.945337	−	0.326096i	$-0.105733\pi$
$743$	25.2771	+	18.3649i	0.927326	+	0.673742i	−0.0180109	+	0.999838i	$0.505733\pi$
$744$	0.314851	−	0.969012i	0.0115430	−	0.0355257i
$745$	6.67965	+	20.5579i	0.244723	+	0.753181i
$746$	−11.8438	+	8.60506i	−0.433634	+	0.315053i
$747$	6.16947			0.225729
$748$	−3.18072	+	10.7065i	−0.116299	+	0.391467i
$749$	9.57175			0.349744
$750$	−0.349248	+	0.253743i	−0.0127527	+	0.00926540i
$751$	−5.04480	−	15.5263i	−0.184088	−	0.566563i	0.815844	−	0.578272i	$-0.196273\pi$
$751$	−5.04480	−	15.5263i	−0.184088	−	0.566563i	−0.999931	+	0.0117090i	$0.996273\pi$
$752$	−2.73701	+	8.42365i	−0.0998085	+	0.307179i
$753$	5.32636	+	3.86982i	0.194103	+	0.141024i
$754$	35.5437	+	25.8240i	1.29442	+	0.940454i
$755$	4.88464	−	15.0334i	0.177770	−	0.547120i
$756$	−0.502456	−	1.54640i	−0.0182741	−	0.0562420i
$757$	−21.5949	+	15.6896i	−0.784882	+	0.570250i	−0.906440	−	0.422334i	$-0.861211\pi$
$757$	−21.5949	+	15.6896i	−0.784882	+	0.570250i	0.121559	+	0.992584i	$0.461211\pi$
$758$	−50.2448			−1.82497
$759$	5.91627	+	4.07312i	0.214747	+	0.147845i
$760$	9.07467			0.329173
$761$	16.2122	−	11.7789i	0.587692	−	0.426983i	−0.253797	−	0.967258i	$-0.581679\pi$
$761$	16.2122	−	11.7789i	0.587692	−	0.426983i	0.841489	+	0.540274i	$0.181679\pi$
$762$	1.37931	+	4.24506i	0.0499670	+	0.153782i
$763$	3.46952	−	10.6781i	0.125605	−	0.386573i
$764$	2.18883	+	1.59028i	0.0791889	+	0.0575341i
$765$	7.15239	+	5.19652i	0.258595	+	0.187880i
$766$	−18.5251	+	57.0144i	−0.669339	+	2.06001i
$767$	−10.5760	−	32.5495i	−0.381876	−	1.17529i
$768$	−3.95917	+	2.87651i	−0.142864	+	0.103797i
$769$	−26.8572			−0.968496			−0.484248	−	0.874931i	$-0.660907\pi$
$769$	−26.8572			−0.968496			−0.484248	+	0.874931i	$0.660907\pi$
$770$	1.95112	+	5.52385i	0.0703135	+	0.199066i
$771$	−2.70017			−0.0972444
$772$	0.232001	−	0.168559i	0.00834990	−	0.00606656i
$773$	10.5625	+	32.5080i	0.379907	+	1.16923i	0.940108	+	0.340876i	$0.110724\pi$
$773$	10.5625	+	32.5080i	0.379907	+	1.16923i	−0.560201	+	0.828356i	$0.689276\pi$
$774$	−9.25469	+	28.4830i	−0.332653	+	1.02380i
$775$	−2.16975	−	1.57642i	−0.0779398	−	0.0566266i
$776$	−9.72973	−	7.06906i	−0.349277	−	0.253765i
$777$	0.144337	−	0.444223i	0.00517805	−	0.0159364i
$778$	4.07598	+	12.5446i	0.146131	+	0.449745i
$779$	−11.5379	+	8.38275i	−0.413387	+	0.300343i
$780$	1.23875			0.0443543
$781$	−16.6223	+	0.421952i	−0.594793	+	0.0150986i
$782$	−47.0630			−1.68297
$783$	−6.45534	+	4.69008i	−0.230695	+	0.167610i
$784$	−1.54064	−	4.74159i	−0.0550227	−	0.169343i
$785$	2.87800	−	8.85756i	0.102720	−	0.316140i
$786$	4.03587	+	2.93223i	0.143955	+	0.104589i
$787$	−11.3456	−	8.24303i	−0.404426	−	0.293832i	0.366916	−	0.930254i	$-0.380414\pi$
$787$	−11.3456	−	8.24303i	−0.404426	−	0.293832i	−0.771341	+	0.636422i	$0.780414\pi$
$788$	7.19494	−	22.1438i	0.256309	−	0.788839i
$789$	−0.809972	−	2.49284i	−0.0288358	−	0.0887474i
$790$	−2.46204	+	1.78878i	−0.0875955	+	0.0636418i
$791$	−3.27518			−0.116452
$792$	−15.1535	+	0.384667i	−0.538457	+	0.0136685i
$793$	−38.2489			−1.35826
$794$	35.1968	−	25.5720i	1.24909	−	0.907515i
$795$	−0.795823	−	2.44929i	−0.0282249	−	0.0868674i
$796$	6.16499	−	18.9739i	0.218512	−	0.672511i
$797$	8.92409	+	6.48373i	0.316107	+	0.229666i	0.734513	−	0.678595i	$-0.237411\pi$
$797$	8.92409	+	6.48373i	0.316107	+	0.229666i	−0.418405	+	0.908260i	$0.637411\pi$
$798$	−2.03890	−	1.48134i	−0.0721761	−	0.0524390i
$799$	−1.65069	+	5.08030i	−0.0583972	+	0.179728i
$800$	1.76061	+	5.41860i	0.0622469	+	0.191576i
$801$	−10.6510	+	7.73842i	−0.376335	+	0.273424i
$802$	−0.560994			−0.0198094
$803$	−12.6607	−	35.8440i	−0.446787	−	1.26491i
$804$	0.322231			0.0113642
$805$	−7.16894	+	5.20854i	−0.252672	+	0.183577i
$806$	6.62498	+	20.3896i	0.233355	+	0.718193i
$807$	−1.54963	+	4.76927i	−0.0545496	+	0.167886i
$808$	23.0523	+	16.7485i	0.810978	+	0.589210i
$809$	11.3615	+	8.25461i	0.399449	+	0.290217i	0.769316	−	0.638868i	$-0.220597\pi$
$809$	11.3615	+	8.25461i	0.399449	+	0.290217i	−0.369868	+	0.929084i	$0.620597\pi$
$810$	4.62100	−	14.2220i	0.162365	−	0.499709i
$811$	−3.31163	−	10.1921i	−0.116287	−	0.357895i	0.875926	−	0.482445i	$-0.160251\pi$
$811$	−3.31163	−	10.1921i	−0.116287	−	0.357895i	−0.992213	+	0.124550i	$0.960251\pi$
$812$	4.97991	−	3.61812i	0.174761	−	0.126971i
$813$	0.486216			0.0170524
$814$	9.22190	+	6.34892i	0.323227	+	0.222529i
$815$	−3.99280			−0.139862
$816$	−2.96403	+	2.15349i	−0.103762	+	0.0753873i
$817$	10.4030	+	32.0173i	0.363956	+	1.12014i
$818$	2.81058	−	8.65006i	0.0982695	−	0.302442i
$819$	−10.7651	−	7.82131i	−0.376164	−	0.273299i
$820$	−2.21347	−	1.60818i	−0.0772977	−	0.0561601i
$821$	12.0481	−	37.0802i	0.420481	−	1.29411i	−0.486775	−	0.873527i	$-0.661827\pi$
$821$	12.0481	−	37.0802i	0.420481	−	1.29411i	0.907256	−	0.420579i	$-0.138173\pi$
$822$	−2.20333	−	6.78116i	−0.0768500	−	0.236520i
$823$	−3.02408	+	2.19712i	−0.105413	+	0.0765869i	−0.639243	−	0.769005i	$-0.720752\pi$
$823$	−3.02408	+	2.19712i	−0.105413	+	0.0765869i	0.533830	+	0.845592i	$0.320752\pi$
$824$	14.3171			0.498761
$825$	0.230840	−	0.777017i	0.00803681	−	0.0270523i
$826$	−13.3579			−0.464782
$827$	41.5745	−	30.2057i	1.44569	−	1.05035i	0.458873	−	0.888502i	$-0.348253\pi$
$827$	41.5745	−	30.2057i	1.44569	−	1.05035i	0.986815	−	0.161852i	$-0.0517467\pi$
$828$	9.01728	+	27.7523i	0.313372	+	0.964460i
$829$	−5.19743	+	15.9960i	−0.180514	+	0.555565i	−0.999842	−	0.0177596i	$-0.994347\pi$
$829$	−5.19743	+	15.9960i	−0.180514	+	0.555565i	0.819328	+	0.573325i	$0.194347\pi$
$830$	2.99843	+	2.17849i	0.104077	+	0.0756164i
$831$	0.223722	+	0.162543i	0.00776082	+	0.00563857i
$832$	0.129300	−	0.397945i	0.00448267	−	0.0137962i
$833$	−0.929157	−	2.85965i	−0.0321934	−	0.0990810i
$834$	−0.996558	+	0.724042i	−0.0345080	+	0.0250715i
$835$	−20.1639			−0.697800
$836$	17.2147	−	13.1874i	0.595383	−	0.456097i
$837$	−3.89367			−0.134585
$838$	−40.3633	+	29.3257i	−1.39433	+	1.01304i
$839$	−9.46063	−	29.1168i	−0.326617	−	1.00522i	−0.970705	−	0.240273i	$-0.922763\pi$
$839$	−9.46063	−	29.1168i	−0.326617	−	1.00522i	0.644088	−	0.764951i	$-0.277237\pi$
$840$	−0.117396	+	0.361307i	−0.00405054	+	0.0124663i
$841$	−0.976593	−	0.709536i	−0.0336756	−	0.0244668i
$842$	−23.9115	−	17.3727i	−0.824044	−	0.598703i
$843$	−2.00005	+	6.15553i	−0.0688855	+	0.212008i
$844$	−4.37096	−	13.4524i	−0.150455	−	0.463052i
$845$	6.05213	−	4.39713i	0.208200	−	0.151266i
$846$	9.22654			0.317215
$847$	−9.21577	−	6.00580i	−0.316658	−	0.206362i
$848$	−52.5354			−1.80407
$849$	−5.51006	+	4.00330i	−0.189105	+	0.137393i
$850$	1.64121	+	5.05113i	0.0562931	+	0.173252i
$851$	−5.23327	+	16.1064i	−0.179394	+	0.552119i
$852$	1.11020	+	0.806609i	0.0380349	+	0.0276340i
$853$	−26.3253	−	19.1265i	−0.901362	−	0.654878i	0.0374537	−	0.999298i	$-0.488075\pi$
$853$	−26.3253	−	19.1265i	−0.901362	−	0.654878i	−0.938815	+	0.344421i	$0.888075\pi$
$854$	−4.61321	+	14.1980i	−0.157861	+	0.485845i
$855$	−5.30433	−	16.3251i	−0.181404	−	0.558305i
$856$	−12.0370	+	8.74540i	−0.411417	+	0.298912i
$857$	4.88099			0.166731			0.0833657	−	0.996519i	$-0.473433\pi$
$857$	4.88099			0.166731			0.0833657	+	0.996519i	$0.473433\pi$
$858$	−5.14375	+	3.94040i	−0.175605	+	0.134523i
$859$	27.5522			0.940068			0.470034	−	0.882648i	$-0.344242\pi$
$859$	27.5522			0.940068			0.470034	+	0.882648i	$0.344242\pi$
$860$	−5.22496	+	3.79616i	−0.178170	+	0.129448i
$861$	−0.184497	−	0.567824i	−0.00628764	−	0.0193514i
$862$	−12.4605	+	38.3495i	−0.424406	+	1.30619i
$863$	35.3264	+	25.6661i	1.20253	+	0.873686i	0.994531	−	0.104444i	$-0.0333064\pi$
$863$	35.3264	+	25.6661i	1.20253	+	0.873686i	0.207994	+	0.978130i	$0.433306\pi$
$864$	6.69183	+	4.86190i	0.227661	+	0.165405i
$865$	5.19491	−	15.9883i	0.176632	−	0.543618i
$866$	−13.6695	−	42.0704i	−0.464508	−	1.42961i
$867$	1.57369	−	1.14336i	0.0534455	−	0.0388304i
$868$	3.00374			0.101953
$869$	1.62732	−	5.47762i	0.0552030	−	0.185816i
$870$	−2.37263			−0.0804398
$871$	4.31013	−	3.13149i	0.146043	−	0.106107i
$872$	5.39311	+	16.5983i	0.182634	+	0.562089i
$873$	−7.02980	+	21.6355i	−0.237923	+	0.732250i
$874$	73.9250	+	53.7097i	2.50055	+	1.81676i
$875$	0.809017	+	0.587785i	0.0273498	+	0.0198708i
$876$	−0.969487	+	2.98377i	−0.0327559	+	0.100812i
$877$	−13.0986	−	40.3134i	−0.442309	−	1.36129i	−0.885409	−	0.464814i	$-0.846121\pi$
$877$	−13.0986	−	40.3134i	−0.442309	−	1.36129i	0.443100	−	0.896472i	$-0.353879\pi$
$878$	−45.3745	+	32.9665i	−1.53131	+	1.11256i
$879$	−6.77727			−0.228591
$880$	−13.6197	−	9.37665i	−0.459121	−	0.316087i
$881$	−28.8743			−0.972799			−0.486399	−	0.873737i	$-0.661690\pi$
$881$	−28.8743			−0.972799			−0.486399	+	0.873737i	$0.661690\pi$
$882$	−4.20165	+	3.05268i	−0.141477	+	0.102789i
$883$	−9.90178	−	30.4746i	−0.333222	−	1.02555i	−0.967591	−	0.252521i	$-0.918740\pi$
$883$	−9.90178	−	30.4746i	−0.333222	−	1.02555i	0.634370	−	0.773030i	$-0.281260\pi$
$884$	4.70947	−	14.4943i	0.158397	−	0.487494i
$885$	1.49528	+	1.08638i	0.0502632	+	0.0365184i
$886$	27.1224	+	19.7056i	0.911196	+	0.662023i
$887$	−5.07897	+	15.6315i	−0.170535	+	0.524853i	−0.999401	−	0.0345937i	$-0.988986\pi$
$887$	−5.07897	+	15.6315i	−0.170535	+	0.524853i	0.828866	+	0.559447i	$0.188986\pi$
$888$	0.224361	+	0.690511i	0.00752905	+	0.0231720i
$889$	8.36488	−	6.07744i	0.280549	−	0.203831i
$890$	−7.90902			−0.265111
$891$	9.35160	+	26.4755i	0.313290	+	0.886961i
$892$	−0.760042			−0.0254481
$893$	8.39064	−	6.09616i	0.280782	−	0.204000i
$894$	2.88357	+	8.87470i	0.0964409	+	0.296814i
$895$	5.58466	−	17.1878i	0.186675	−	0.574525i
$896$	9.08655	+	6.60176i	0.303560	+	0.220549i
$897$	−7.92919	−	5.76090i	−0.264748	−	0.192351i
$898$	0.0607679	−	0.187024i	0.00202785	−	0.00624108i
$899$	−4.55501	−	14.0189i	−0.151918	−	0.467556i
$900$	2.66412	−	1.93560i	0.0888040	−	0.0645199i
$901$	−31.6840			−1.05555
$902$	14.3067	−	0.363170i	0.476360	−	0.0120922i
$903$	−1.40934			−0.0469000
$904$	4.11872	−	2.99243i	0.136987	−	0.0995267i
$905$	−2.02539	−	6.23351i	−0.0673262	−	0.207209i
$906$	2.10867	−	6.48981i	0.0700558	−	0.215610i
$907$	14.4959	+	10.5319i	0.481330	+	0.349707i	0.801840	−	0.597538i	$-0.203854\pi$
$907$	14.4959	+	10.5319i	0.481330	+	0.349707i	−0.320511	+	0.947245i	$0.603854\pi$
$908$	−20.3746	−	14.8030i	−0.676154	−	0.491254i
$909$	16.6555	−	51.2603i	0.552427	−	1.70020i
$910$	−2.47020	−	7.60249i	−0.0818863	−	0.252020i
$911$	−11.1339	+	8.08928i	−0.368884	+	0.268010i	−0.756748	−	0.653707i	$-0.773213\pi$
$911$	−11.1339	+	8.08928i	−0.368884	+	0.268010i	0.387864	+	0.921717i	$0.373213\pi$
$912$	7.11344			0.235549
$913$	−6.95692	+	0.176599i	−0.230240	+	0.00584457i
$914$	−25.4993			−0.843442
$915$	1.67110	−	1.21413i	0.0552449	−	0.0401378i
$916$	8.47798	+	26.0925i	0.280120	+	0.862122i
$917$	3.57097	−	10.9903i	0.117924	−	0.362932i
$918$	6.23801	+	4.53218i	0.205885	+	0.149584i
$919$	14.0830	+	10.2319i	0.464557	+	0.337520i	0.795316	−	0.606195i	$-0.207305\pi$
$919$	14.0830	+	10.2319i	0.464557	+	0.337520i	−0.330759	+	0.943715i	$0.607305\pi$
$920$	4.25647	−	13.1001i	0.140332	−	0.431896i
$921$	1.98723	+	6.11606i	0.0654814	+	0.201531i
$922$	−33.0334	+	24.0002i	−1.08790	+	0.790404i
$923$	22.6887			0.746807
$924$	0.302355	+	0.856003i	0.00994676	+	0.0281604i
$925$	1.91115			0.0628381
$926$	38.8815	−	28.2491i	1.27773	−	0.928323i
$927$	−8.36866	−	25.7561i	−0.274863	−	0.845941i
$928$	−9.67649	+	29.7812i	−0.317646	+	0.977615i
$929$	9.14530	+	6.64445i	0.300048	+	0.217997i	0.727614	−	0.685986i	$-0.240629\pi$
$929$	9.14530	+	6.64445i	0.300048	+	0.217997i	−0.427567	+	0.903984i	$0.640629\pi$
$930$	−0.936669	−	0.680530i	−0.0307146	−	0.0223155i
$931$	−1.80403	+	5.55223i	−0.0591247	+	0.181967i
$932$	7.72994	+	23.7903i	0.253203	+	0.779278i
$933$	−0.0509052	+	0.0369848i	−0.00166656	+	0.00121083i
$934$	24.5327			0.802735
$935$	−8.21405	−	5.65505i	−0.268628	−	0.184940i
$936$	20.6838			0.676072
$937$	9.68708	−	7.03807i	0.316463	−	0.229924i	−0.418202	−	0.908354i	$-0.637339\pi$
$937$	9.68708	−	7.03807i	0.316463	−	0.229924i	0.734665	+	0.678430i	$0.237339\pi$
$938$	−0.642564	−	1.97761i	−0.0209805	−	0.0645712i
$939$	−1.27878	+	3.93567i	−0.0417313	+	0.128436i
$940$	1.60969	+	1.16951i	0.0525024	+	0.0381452i
$941$	−14.8287	−	10.7737i	−0.483401	−	0.351211i	0.319240	−	0.947674i	$-0.396572\pi$
$941$	−14.8287	−	10.7737i	−0.483401	−	0.351211i	−0.802641	+	0.596463i	$0.796572\pi$
$942$	1.24241	−	3.82376i	0.0404800	−	0.124585i
$943$	6.68939	+	20.5878i	0.217836	+	0.670431i
$944$	30.5028	−	22.1616i	0.992781	−	0.721298i
$945$	1.45180			0.0472270
$946$	9.62061	−	32.3834i	0.312793	−	1.05288i
$947$	−34.7247			−1.12840			−0.564201	−	0.825637i	$-0.690816\pi$
$947$	−34.7247			−1.12840			−0.564201	+	0.825637i	$0.690816\pi$
$948$	−0.381530	+	0.277198i	−0.0123915	+	0.00900297i
$949$	16.0290	+	49.3322i	0.520324	+	1.60139i
$950$	3.18654	−	9.80716i	0.103385	−	0.318186i
$951$	2.18342	+	1.58635i	0.0708023	+	0.0514409i
$952$	3.78124	+	2.74723i	0.122551	+	0.0890382i
$953$	−3.84372	+	11.8297i	−0.124510	+	0.383203i	−0.993812	−	0.111079i	$-0.964569\pi$
$953$	−3.84372	+	11.8297i	−0.124510	+	0.383203i	0.869301	+	0.494283i	$0.164569\pi$
$954$	16.9114	+	52.0478i	0.547526	+	1.68511i
$955$	−1.95435	+	1.41992i	−0.0632413	+	0.0459475i
$956$	9.39854			0.303970
$957$	3.53659	−	2.70922i	0.114322	−	0.0875768i
$958$	17.2382			0.556940
$959$	−13.3622	+	9.70823i	−0.431489	+	0.313495i
$960$	0.00698273	+	0.0214906i	0.000225367	+	0.000693607i
$961$	−7.35679	+	22.6419i	−0.237316	+	0.730383i
$962$	−12.3595	−	8.97971i	−0.398487	−	0.289517i
$963$	22.7686	+	16.5423i	0.733707	+	0.533069i
$964$	6.32601	−	19.4695i	0.203747	−	0.627069i
$965$	0.0791235	+	0.243517i	0.00254708	+	0.00783910i
$966$	−3.09479	+	2.24849i	−0.0995731	+	0.0723441i
$967$	6.51655			0.209558			0.104779	−	0.994496i	$-0.466586\pi$
$967$	6.51655			0.209558			0.104779	+	0.994496i	$0.466586\pi$
$968$	17.0767	−	0.867529i	0.548865	−	0.0278834i
$969$	4.29011			0.137818
$970$	−11.0562	+	8.03281i	−0.354994	+	0.257918i
$971$	2.88124	+	8.86754i	0.0924634	+	0.284573i	0.986584	−	0.163253i	$-0.0521985\pi$
$971$	2.88124	+	8.86754i	0.0924634	+	0.284573i	−0.894121	+	0.447826i	$0.852199\pi$
$972$	2.22346	−	6.84311i	0.0713175	−	0.219493i
$973$	2.30848	+	1.67721i	0.0740066	+	0.0537689i
$974$	61.4830	+	44.6700i	1.97004	+	1.43132i
$975$	−0.341788	+	1.05192i	−0.0109460	+	0.0336882i
$976$	−13.0210	−	40.0746i	−0.416793	−	1.28276i
$977$	−12.6976	+	9.22535i	−0.406232	+	0.295145i	−0.772075	−	0.635532i	$-0.780781\pi$
$977$	−12.6976	+	9.22535i	−0.406232	+	0.295145i	0.365842	+	0.930677i	$0.380781\pi$
$978$	−1.72367			−0.0551168
$979$	11.7890	−	9.03102i	0.376778	−	0.288633i
$980$	−1.11998			−0.0357763
$981$	26.7074	−	19.4041i	0.852702	−	0.619524i
$982$	−3.27825	−	10.0894i	−0.104613	−	0.321966i
$983$	6.18680	−	19.0410i	0.197328	−	0.607314i	−0.802613	−	0.596500i	$-0.796558\pi$
$983$	6.18680	−	19.0410i	0.197328	−	0.607314i	0.999942	−	0.0108145i	$-0.00344242\pi$
$984$	0.750818	+	0.545501i	0.0239352	+	0.0173899i
$985$	16.8187	+	12.2195i	0.535890	+	0.389347i
$986$	−9.02027	+	27.7615i	−0.287264	+	0.884107i
$987$	0.134171	+	0.412936i	0.00427071	+	0.0131439i
$988$	−23.9388	+	17.3925i	−0.761594	+	0.553330i
$989$	51.0992			1.62486
$990$	−4.90539	+	16.5117i	−0.155903	+	0.524778i
$991$	17.7142			0.562711			0.281356	−	0.959604i	$-0.409216\pi$
$991$	17.7142			0.562711			0.281356	+	0.959604i	$0.409216\pi$
$992$	−12.3621	+	8.98156i	−0.392496	+	0.285165i
$993$	−1.14709	−	3.53039i	−0.0364019	−	0.112034i
$994$	2.73649	−	8.42204i	0.0867961	−	0.267131i
$995$	14.4111	+	10.4703i	0.456864	+	0.331931i
$996$	0.464652	+	0.337589i	0.0147231	+	0.0106969i
$997$	−4.37961	+	13.4790i	−0.138704	+	0.426886i	−0.996148	−	0.0876915i	$-0.972051\pi$
$997$	−4.37961	+	13.4790i	−0.138704	+	0.426886i	0.857444	+	0.514577i	$0.172051\pi$
$998$	−18.7352	−	57.6610i	−0.593053	−	1.82523i
$999$	2.24470	−	1.63087i	0.0710191	−	0.0515984i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	385.2.n.e.36.5	✓	28
11.2	odd	10		4235.2.a.bn.1.11		14
11.4	even	5	inner	385.2.n.e.246.5	yes	28
11.9	even	5		4235.2.a.bm.1.4		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.n.e.36.5	✓	28	1.1	even	1	trivial
385.2.n.e.246.5	yes	28	11.4	even	5	inner
4235.2.a.bm.1.4		14	11.9	even	5
4235.2.a.bn.1.11		14	11.2	odd	10

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:	\( N \)	\(=\)	\( 385 = 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	385.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.42900 - 1.03823i) q^{2} +(0.0755236 + 0.232438i) q^{3} +(0.346092 - 1.06516i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.349248 + 0.253743i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.480344 + 1.47835i) q^{8} +(2.37873 - 1.72825i) q^{9} +O(q^{10})\)	\(q+(1.42900 - 1.03823i) q^{2} +(0.0755236 + 0.232438i) q^{3} +(0.346092 - 1.06516i) q^{4} +(0.809017 + 0.587785i) q^{5} +(0.349248 + 0.253743i) q^{6} +(0.309017 - 0.951057i) q^{7} +(0.480344 + 1.47835i) q^{8} +(2.37873 - 1.72825i) q^{9} +1.76635 q^{10} +(-2.63287 + 2.01693i) q^{11} +0.273722 q^{12} +(3.66127 - 2.66007i) q^{13} +(-0.545831 - 1.67989i) q^{14} +(-0.0755236 + 0.232438i) q^{15} +(4.03344 + 2.93047i) q^{16} +(2.43256 + 1.76736i) q^{17} +(1.60489 - 4.93934i) q^{18} +(-1.80403 - 5.55223i) q^{19} +(0.906080 - 0.658306i) q^{20} +0.244400 q^{21} +(-1.66835 + 5.61572i) q^{22} -8.86129 q^{23} +(-0.307346 + 0.223300i) q^{24} +(0.309017 + 0.951057i) q^{25} +(2.47020 - 7.60249i) q^{26} +(1.17453 + 0.853346i) q^{27} +(-0.906080 - 0.658306i) q^{28} +(-1.69839 + 5.22710i) q^{29} +(0.133401 + 0.410565i) q^{30} +(-2.16975 + 1.57642i) q^{31} +5.69745 q^{32} +(-0.667654 - 0.459653i) q^{33} +5.31107 q^{34} +(0.809017 - 0.587785i) q^{35} +(-1.01760 - 3.13186i) q^{36} +(0.590577 - 1.81761i) q^{37} +(-8.34247 - 6.06116i) q^{38} +(0.894812 + 0.650119i) q^{39} +(-0.480344 + 1.47835i) q^{40} +(-0.754900 - 2.32334i) q^{41} +(0.349248 - 0.253743i) q^{42} -5.76656 q^{43} +(1.23714 + 3.50247i) q^{44} +2.94027 q^{45} +(-12.6628 + 9.20008i) q^{46} +(0.548983 + 1.68960i) q^{47} +(-0.376531 + 1.15884i) q^{48} +(-0.809017 - 0.587785i) q^{49} +(1.42900 + 1.03823i) q^{50} +(-0.227085 + 0.698897i) q^{51} +(-1.56627 - 4.82047i) q^{52} +(-8.52494 + 6.19373i) q^{53} +2.56438 q^{54} +(-3.31556 + 0.0841643i) q^{55} +1.55443 q^{56} +(1.15430 - 0.838649i) q^{57} +(2.99994 + 9.23287i) q^{58} +(2.33693 - 7.19234i) q^{59} +(0.221446 + 0.160890i) q^{60} +(-6.83758 - 4.96779i) q^{61} +(-1.46390 + 4.50541i) q^{62} +(-0.908593 - 2.79636i) q^{63} +(0.0747997 - 0.0543452i) q^{64} +4.52558 q^{65} +(-1.43131 + 0.0363332i) q^{66} +1.17722 q^{67} +(2.72441 - 1.97940i) q^{68} +(-0.669237 - 2.05970i) q^{69} +(0.545831 - 1.67989i) q^{70} +(4.05595 + 2.94682i) q^{71} +(3.69755 + 2.68643i) q^{72} +(-3.54187 + 10.9008i) q^{73} +(-1.04316 - 3.21052i) q^{74} +(-0.197723 + 0.143654i) q^{75} -6.53838 q^{76} +(1.10461 + 3.12727i) q^{77} +1.95366 q^{78} +(-1.39386 + 1.01270i) q^{79} +(1.54064 + 4.74159i) q^{80} +(2.61613 - 8.05163i) q^{81} +(-3.49092 - 2.53630i) q^{82} +(1.69753 + 1.23333i) q^{83} +(0.0845847 - 0.260325i) q^{84} +(0.929157 + 2.85965i) q^{85} +(-8.24043 + 5.98702i) q^{86} -1.34324 q^{87} +(-4.24640 - 2.92348i) q^{88} -4.47761 q^{89} +(4.20165 - 3.05268i) q^{90} +(-1.39848 - 4.30408i) q^{91} +(-3.06682 + 9.43870i) q^{92} +(-0.530287 - 0.385276i) q^{93} +(2.53869 + 1.84447i) q^{94} +(1.80403 - 5.55223i) q^{95} +(0.430292 + 1.32430i) q^{96} +(-6.25938 + 4.54770i) q^{97} -1.76635 q^{98} +(-2.77714 + 9.34797i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 3 q^{2} - 3 q^{4} + 7 q^{5} + 7 q^{6} - 7 q^{7} - q^{8} - q^{9}+O(q^{10}) \) 28 * q + 3 * q^2 - 3 * q^4 + 7 * q^5 + 7 * q^6 - 7 * q^7 - q^8 - q^9	\( 28 q + 3 q^{2} - 3 q^{4} + 7 q^{5} + 7 q^{6} - 7 q^{7} - q^{8} - q^{9} + 2 q^{10} - 3 q^{11} + 30 q^{12} - 5 q^{13} - 2 q^{14} - 33 q^{16} + 7 q^{17} - 17 q^{18} - 13 q^{19} + 18 q^{20} + 10 q^{21} + 3 q^{22} + 16 q^{23} + 39 q^{24} - 7 q^{25} + 44 q^{26} - 18 q^{27} - 18 q^{28} + 7 q^{29} + 8 q^{30} + 7 q^{31} - 84 q^{32} + 4 q^{33} + 32 q^{34} + 7 q^{35} + 6 q^{36} - 24 q^{37} - 15 q^{38} - 18 q^{39} + q^{40} - 4 q^{41} + 7 q^{42} + q^{44} - 34 q^{45} + 3 q^{46} - 33 q^{47} + 83 q^{48} - 7 q^{49} + 3 q^{50} + 14 q^{51} + 24 q^{52} - 8 q^{53} - 114 q^{54} - 17 q^{55} - 6 q^{56} + 57 q^{57} - 16 q^{58} - 3 q^{59} + 15 q^{60} - 21 q^{61} - 19 q^{62} - 16 q^{63} - 19 q^{64} - 20 q^{65} - 126 q^{66} + 90 q^{67} - 7 q^{68} - 55 q^{69} + 2 q^{70} - 37 q^{71} + 117 q^{72} + 17 q^{73} + 49 q^{74} - 5 q^{75} - 10 q^{76} - 3 q^{77} + 104 q^{78} - 45 q^{79} - 2 q^{80} + 8 q^{81} - 48 q^{82} + q^{83} + 18 q^{85} + 134 q^{86} + 46 q^{87} + 74 q^{88} - 30 q^{89} - 38 q^{90} - 5 q^{91} + 18 q^{92} - 57 q^{93} + 43 q^{94} + 13 q^{95} - 119 q^{96} - 82 q^{97} - 2 q^{98} - 72 q^{99}+O(q^{100}) \) 28 * q + 3 * q^2 - 3 * q^4 + 7 * q^5 + 7 * q^6 - 7 * q^7 - q^8 - q^9 + 2 * q^10 - 3 * q^11 + 30 * q^12 - 5 * q^13 - 2 * q^14 - 33 * q^16 + 7 * q^17 - 17 * q^18 - 13 * q^19 + 18 * q^20 + 10 * q^21 + 3 * q^22 + 16 * q^23 + 39 * q^24 - 7 * q^25 + 44 * q^26 - 18 * q^27 - 18 * q^28 + 7 * q^29 + 8 * q^30 + 7 * q^31 - 84 * q^32 + 4 * q^33 + 32 * q^34 + 7 * q^35 + 6 * q^36 - 24 * q^37 - 15 * q^38 - 18 * q^39 + q^40 - 4 * q^41 + 7 * q^42 + q^44 - 34 * q^45 + 3 * q^46 - 33 * q^47 + 83 * q^48 - 7 * q^49 + 3 * q^50 + 14 * q^51 + 24 * q^52 - 8 * q^53 - 114 * q^54 - 17 * q^55 - 6 * q^56 + 57 * q^57 - 16 * q^58 - 3 * q^59 + 15 * q^60 - 21 * q^61 - 19 * q^62 - 16 * q^63 - 19 * q^64 - 20 * q^65 - 126 * q^66 + 90 * q^67 - 7 * q^68 - 55 * q^69 + 2 * q^70 - 37 * q^71 + 117 * q^72 + 17 * q^73 + 49 * q^74 - 5 * q^75 - 10 * q^76 - 3 * q^77 + 104 * q^78 - 45 * q^79 - 2 * q^80 + 8 * q^81 - 48 * q^82 + q^83 + 18 * q^85 + 134 * q^86 + 46 * q^87 + 74 * q^88 - 30 * q^89 - 38 * q^90 - 5 * q^91 + 18 * q^92 - 57 * q^93 + 43 * q^94 + 13 * q^95 - 119 * q^96 - 82 * q^97 - 2 * q^98 - 72 * q^99

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