LMFDB - Embedded newform 770.2.n.i.141.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(71,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("770.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.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:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 11 x^{10} - 21 x^{9} + 61 x^{8} - 34 x^{7} + 141 x^{6} + 192 x^{5} + 289 x^{4} + \cdots + 1 $ x^12 - 3x^11 + 11x^10 - 21x^9 + 61x^8 - 34x^7 + 141x^6 + 192x^5 + 289x^4 - 55x^3 + 222x^2 - 24*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			141.3
Root			$2.26282 - 1.64404i$ of defining polynomial
Character	$\chi$	$=$	770.141
Dual form			770.2.n.i.71.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.309017 - 0.951057i) q^{2} +(2.13924 - 1.55425i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-0.817115 - 2.51482i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(1.23360 - 3.79662i) q^{9} +O(q^{10})$	\(q+(0.309017 - 0.951057i) q^{2} +(2.13924 - 1.55425i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-0.817115 - 2.51482i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(1.23360 - 3.79662i) q^{9} +1.00000 q^{10} +(1.10093 - 3.12857i) q^{11} -2.64424 q^{12} +(0.945705 - 2.91058i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(2.13924 + 1.55425i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.0211240 - 0.0650130i) q^{17} +(-3.22960 - 2.34644i) q^{18} +(-2.24162 + 1.62863i) q^{19} +(0.309017 - 0.951057i) q^{20} -2.64424 q^{21} +(-2.63524 - 2.01383i) q^{22} +1.83120 q^{23} +(-0.817115 + 2.51482i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(-2.47589 - 1.79884i) q^{26} +(-0.810584 - 2.49472i) q^{27} +(0.309017 + 0.951057i) q^{28} +(-2.67733 - 1.94520i) q^{29} +(2.13924 - 1.55425i) q^{30} +(1.27491 - 3.92378i) q^{31} +1.00000 q^{32} +(-2.50741 - 8.40387i) q^{33} -0.0683587 q^{34} +(0.309017 - 0.951057i) q^{35} +(-3.22960 + 2.34644i) q^{36} +(4.55839 + 3.31186i) q^{37} +(0.856222 + 2.63518i) q^{38} +(-2.50067 - 7.69627i) q^{39} +(-0.809017 - 0.587785i) q^{40} +(4.15234 - 3.01685i) q^{41} +(-0.817115 + 2.51482i) q^{42} +2.84053 q^{43} +(-2.72960 + 1.88395i) q^{44} +3.99201 q^{45} +(0.565872 - 1.74157i) q^{46} +(-9.64311 + 7.00613i) q^{47} +(2.13924 + 1.55425i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.309017 + 0.951057i) q^{50} +(-0.146235 - 0.106246i) q^{51} +(-2.47589 + 1.79884i) q^{52} +(0.0382035 - 0.117578i) q^{53} -2.62310 q^{54} +(3.31565 + 0.0802696i) q^{55} +1.00000 q^{56} +(-2.26406 + 6.96805i) q^{57} +(-2.67733 + 1.94520i) q^{58} +(9.05528 + 6.57904i) q^{59} +(-0.817115 - 2.51482i) q^{60} +(0.783832 + 2.41239i) q^{61} +(-3.33777 - 2.42503i) q^{62} +(-3.22960 + 2.34644i) q^{63} +(0.309017 - 0.951057i) q^{64} +3.06037 q^{65} +(-8.76738 - 0.212252i) q^{66} -2.20818 q^{67} +(-0.0211240 + 0.0650130i) q^{68} +(3.91737 - 2.84613i) q^{69} +(-0.809017 - 0.587785i) q^{70} +(4.24118 + 13.0530i) q^{71} +(1.23360 + 3.79662i) q^{72} +(-5.65426 - 4.10806i) q^{73} +(4.55839 - 3.31186i) q^{74} +(-0.817115 + 2.51482i) q^{75} +2.77079 q^{76} +(-2.72960 + 1.88395i) q^{77} -8.09234 q^{78} +(-3.83620 + 11.8066i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(4.07737 + 2.96238i) q^{81} +(-1.58605 - 4.88137i) q^{82} +(-0.943632 - 2.90420i) q^{83} +(2.13924 + 1.55425i) q^{84} +(0.0553034 - 0.0401802i) q^{85} +(0.877773 - 2.70151i) q^{86} -8.75076 q^{87} +(0.948252 + 3.17818i) q^{88} +13.5707 q^{89} +(1.23360 - 3.79662i) q^{90} +(-2.47589 + 1.79884i) q^{91} +(-1.48147 - 1.07635i) q^{92} +(-3.37118 - 10.3754i) q^{93} +(3.68334 + 11.3362i) q^{94} +(-2.24162 - 1.62863i) q^{95} +(2.13924 - 1.55425i) q^{96} +(-0.848181 + 2.61043i) q^{97} +1.00000 q^{98} +(-10.5199 - 8.03923i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} + 2 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} - 15 q^{9}+O(q^{10}) $ 12 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 - 15 * q^9	\( 12 q - 3 q^{2} + 2 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} - 15 q^{9} + 12 q^{10} + q^{11} + 2 q^{12} - 6 q^{13} - 3 q^{14} + 2 q^{15} - 3 q^{16} - 6 q^{17} - 13 q^{19} - 3 q^{20} + 2 q^{21} + q^{22} - 12 q^{23} - 3 q^{24} - 3 q^{25} + 4 q^{26} - 7 q^{27} - 3 q^{28} - 26 q^{29} + 2 q^{30} + 12 q^{32} - 15 q^{33} + 14 q^{34} - 3 q^{35} - 18 q^{37} + 2 q^{38} - 40 q^{39} - 3 q^{40} + 16 q^{41} - 3 q^{42} + 38 q^{43} + 6 q^{44} + 30 q^{45} + 8 q^{46} - 26 q^{47} + 2 q^{48} - 3 q^{49} - 3 q^{50} - 13 q^{51} + 4 q^{52} + 8 q^{54} + 11 q^{55} + 12 q^{56} - 41 q^{57} - 26 q^{58} + 21 q^{59} - 3 q^{60} + 4 q^{61} - 3 q^{64} + 4 q^{65} - 30 q^{66} + 10 q^{67} - 6 q^{68} + 18 q^{69} - 3 q^{70} - 4 q^{71} - 15 q^{72} - 14 q^{73} - 18 q^{74} - 3 q^{75} + 22 q^{76} + 6 q^{77} + 40 q^{78} - 2 q^{79} - 3 q^{80} + 26 q^{81} - 29 q^{82} + 35 q^{83} + 2 q^{84} - q^{85} - 37 q^{86} + 28 q^{87} - 19 q^{88} + 2 q^{89} - 15 q^{90} + 4 q^{91} - 2 q^{92} + 6 q^{93} + 4 q^{94} - 13 q^{95} + 2 q^{96} + 19 q^{97} + 12 q^{98} - 81 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 - 15 * q^9 + 12 * q^10 + q^11 + 2 * q^12 - 6 * q^13 - 3 * q^14 + 2 * q^15 - 3 * q^16 - 6 * q^17 - 13 * q^19 - 3 * q^20 + 2 * q^21 + q^22 - 12 * q^23 - 3 * q^24 - 3 * q^25 + 4 * q^26 - 7 * q^27 - 3 * q^28 - 26 * q^29 + 2 * q^30 + 12 * q^32 - 15 * q^33 + 14 * q^34 - 3 * q^35 - 18 * q^37 + 2 * q^38 - 40 * q^39 - 3 * q^40 + 16 * q^41 - 3 * q^42 + 38 * q^43 + 6 * q^44 + 30 * q^45 + 8 * q^46 - 26 * q^47 + 2 * q^48 - 3 * q^49 - 3 * q^50 - 13 * q^51 + 4 * q^52 + 8 * q^54 + 11 * q^55 + 12 * q^56 - 41 * q^57 - 26 * q^58 + 21 * q^59 - 3 * q^60 + 4 * q^61 - 3 * q^64 + 4 * q^65 - 30 * q^66 + 10 * q^67 - 6 * q^68 + 18 * q^69 - 3 * q^70 - 4 * q^71 - 15 * q^72 - 14 * q^73 - 18 * q^74 - 3 * q^75 + 22 * q^76 + 6 * q^77 + 40 * q^78 - 2 * q^79 - 3 * q^80 + 26 * q^81 - 29 * q^82 + 35 * q^83 + 2 * q^84 - q^85 - 37 * q^86 + 28 * q^87 - 19 * q^88 + 2 * q^89 - 15 * q^90 + 4 * q^91 - 2 * q^92 + 6 * q^93 + 4 * q^94 - 13 * q^95 + 2 * q^96 + 19 * q^97 + 12 * q^98 - 81 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$	$1$

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 $

$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$2$	0.309017	−	0.951057i	0.218508	−	0.672499i
$3$	2.13924	−	1.55425i	1.23509	−	0.897344i	0.237827	−	0.971307i	$-0.423565\pi$
$3$	2.13924	−	1.55425i	1.23509	−	0.897344i	0.997261	+	0.0739635i	$0.0235648\pi$
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	0.309017	+	0.951057i	0.138197	+	0.425325i
$5$	0.309017	+	0.951057i	0.138197	+	0.425325i
$6$	−0.817115	−	2.51482i	−0.333586	−	1.02667i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	1.23360	−	3.79662i	0.411199	−	1.26554i
$10$	1.00000			0.316228
$11$	1.10093	−	3.12857i	0.331944	−	0.943299i
$11$	1.10093	−	3.12857i	0.331944	−	0.943299i
$12$	−2.64424			−0.763326
$13$	0.945705	−	2.91058i	0.262291	−	0.807250i	−0.730014	−	0.683433i	$-0.760486\pi$
$13$	0.945705	−	2.91058i	0.262291	−	0.807250i	0.992305	−	0.123817i	$-0.0395137\pi$
$14$	−0.809017	+	0.587785i	−0.216219	+	0.157092i
$15$	2.13924	+	1.55425i	0.552348	+	0.401304i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−0.0211240	−	0.0650130i	−0.00512332	−	0.0157680i	0.948462	−	0.316890i	$-0.102639\pi$
$17$	−0.0211240	−	0.0650130i	−0.00512332	−	0.0157680i	−0.953585	+	0.301122i	$0.902639\pi$
$18$	−3.22960	−	2.34644i	−0.761224	−	0.553062i
$19$	−2.24162	+	1.62863i	−0.514263	+	0.373634i	−0.814438	−	0.580250i	$-0.802955\pi$
$19$	−2.24162	+	1.62863i	−0.514263	+	0.373634i	0.300176	+	0.953884i	$0.402955\pi$
$20$	0.309017	−	0.951057i	0.0690983	−	0.212663i
$21$	−2.64424			−0.577021
$22$	−2.63524	−	2.01383i	−0.561835	−	0.429350i
$23$	1.83120			0.381831			0.190916	−	0.981606i	$-0.438854\pi$
$23$	1.83120			0.381831			0.190916	+	0.981606i	$0.438854\pi$
$24$	−0.817115	+	2.51482i	−0.166793	+	0.513336i
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$	−2.47589	−	1.79884i	−0.485561	−	0.352781i
$27$	−0.810584	−	2.49472i	−0.155997	−	0.480109i
$28$	0.309017	+	0.951057i	0.0583987	+	0.179733i
$29$	−2.67733	−	1.94520i	−0.497168	−	0.361214i	0.310766	−	0.950486i	$-0.399414\pi$
$29$	−2.67733	−	1.94520i	−0.497168	−	0.361214i	−0.807934	+	0.589272i	$0.799414\pi$
$30$	2.13924	−	1.55425i	0.390569	−	0.283765i
$31$	1.27491	−	3.92378i	0.228981	−	0.704733i	−0.768881	−	0.639391i	$-0.779186\pi$
$31$	1.27491	−	3.92378i	0.228981	−	0.704733i	0.997863	−	0.0653412i	$-0.0208136\pi$
$32$	1.00000			0.176777
$33$	−2.50741	−	8.40387i	−0.436484	−	1.46293i
$34$	−0.0683587			−0.0117234
$35$	0.309017	−	0.951057i	0.0522334	−	0.160758i
$36$	−3.22960	+	2.34644i	−0.538267	+	0.391074i
$37$	4.55839	+	3.31186i	0.749395	+	0.544467i	0.895639	−	0.444781i	$-0.146719\pi$
$37$	4.55839	+	3.31186i	0.749395	+	0.544467i	−0.146244	+	0.989248i	$0.546719\pi$
$38$	0.856222	+	2.63518i	0.138898	+	0.427483i
$39$	−2.50067	−	7.69627i	−0.400428	−	1.23239i
$40$	−0.809017	−	0.587785i	−0.127917	−	0.0929370i
$41$	4.15234	−	3.01685i	0.648486	−	0.471153i	−0.214269	−	0.976775i	$-0.568737\pi$
$41$	4.15234	−	3.01685i	0.648486	−	0.471153i	0.862755	+	0.505622i	$0.168737\pi$
$42$	−0.817115	+	2.51482i	−0.126084	+	0.388045i
$43$	2.84053			0.433177			0.216589	−	0.976263i	$-0.430507\pi$
$43$	2.84053			0.433177			0.216589	+	0.976263i	$0.430507\pi$
$44$	−2.72960	+	1.88395i	−0.411503	+	0.284017i
$45$	3.99201			0.595093
$46$	0.565872	−	1.74157i	0.0834332	−	0.256781i
$47$	−9.64311	+	7.00613i	−1.40659	+	1.02195i	−0.412785	+	0.910829i	$0.635444\pi$
$47$	−9.64311	+	7.00613i	−1.40659	+	1.02195i	−0.993807	+	0.111120i	$0.964556\pi$
$48$	2.13924	+	1.55425i	0.308772	+	0.224336i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	0.309017	+	0.951057i	0.0437016	+	0.134500i
$51$	−0.146235	−	0.106246i	−0.0204770	−	0.0148774i
$52$	−2.47589	+	1.79884i	−0.343344	+	0.249454i
$53$	0.0382035	−	0.117578i	0.00524765	−	0.0161506i	−0.948398	−	0.317081i	$-0.897297\pi$
$53$	0.0382035	−	0.117578i	0.00524765	−	0.0161506i	0.953646	+	0.300931i	$0.0972972\pi$
$54$	−2.62310			−0.356959
$55$	3.31565	+	0.0802696i	0.447083	+	0.0108235i
$56$	1.00000			0.133631
$57$	−2.26406	+	6.96805i	−0.299882	+	0.922941i
$58$	−2.67733	+	1.94520i	−0.351551	+	0.255417i
$59$	9.05528	+	6.57904i	1.17890	+	0.856519i	0.992047	−	0.125870i	$-0.0401722\pi$
$59$	9.05528	+	6.57904i	1.17890	+	0.856519i	0.186850	+	0.982388i	$0.440172\pi$
$60$	−0.817115	−	2.51482i	−0.105489	−	0.324662i
$61$	0.783832	+	2.41239i	0.100359	+	0.308874i	0.988613	−	0.150478i	$-0.0480814\pi$
$61$	0.783832	+	2.41239i	0.100359	+	0.308874i	−0.888254	+	0.459353i	$0.848081\pi$
$62$	−3.33777	−	2.42503i	−0.423897	−	0.307979i
$63$	−3.22960	+	2.34644i	−0.406891	+	0.295624i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	3.06037			0.379592
$66$	−8.76738	−	0.212252i	−1.07919	−	0.0261264i
$67$	−2.20818			−0.269773			−0.134886	−	0.990861i	$-0.543067\pi$
$67$	−2.20818			−0.269773			−0.134886	+	0.990861i	$0.543067\pi$
$68$	−0.0211240	+	0.0650130i	−0.00256166	+	0.00788398i
$69$	3.91737	−	2.84613i	0.471595	−	0.342634i
$70$	−0.809017	−	0.587785i	−0.0966960	−	0.0702538i
$71$	4.24118	+	13.0530i	0.503335	+	1.54911i	0.803551	+	0.595235i	$0.202941\pi$
$71$	4.24118	+	13.0530i	0.503335	+	1.54911i	−0.300216	+	0.953871i	$0.597059\pi$
$72$	1.23360	+	3.79662i	0.145381	+	0.447436i
$73$	−5.65426	−	4.10806i	−0.661781	−	0.480812i	0.205483	−	0.978661i	$-0.434124\pi$
$73$	−5.65426	−	4.10806i	−0.661781	−	0.480812i	−0.867264	+	0.497848i	$0.834124\pi$
$74$	4.55839	−	3.31186i	0.529902	−	0.384996i
$75$	−0.817115	+	2.51482i	−0.0943523	+	0.290387i
$76$	2.77079			0.317832
$77$	−2.72960	+	1.88395i	−0.311067	+	0.214696i
$78$	−8.09234			−0.916277
$79$	−3.83620	+	11.8066i	−0.431607	+	1.32835i	0.464918	+	0.885354i	$0.346084\pi$
$79$	−3.83620	+	11.8066i	−0.431607	+	1.32835i	−0.896524	+	0.442995i	$0.853916\pi$
$80$	−0.809017	+	0.587785i	−0.0904508	+	0.0657164i
$81$	4.07737	+	2.96238i	0.453041	+	0.329153i
$82$	−1.58605	−	4.88137i	−0.175150	−	0.539057i
$83$	−0.943632	−	2.90420i	−0.103577	−	0.318778i	0.885817	−	0.464035i	$-0.153599\pi$
$83$	−0.943632	−	2.90420i	−0.103577	−	0.318778i	−0.989394	+	0.145258i	$0.953599\pi$
$84$	2.13924	+	1.55425i	0.233410	+	0.169582i
$85$	0.0553034	−	0.0401802i	0.00599849	−	0.00435816i
$86$	0.877773	−	2.70151i	0.0946527	−	0.291311i
$87$	−8.75076			−0.938180
$88$	0.948252	+	3.17818i	0.101084	+	0.338795i
$89$	13.5707			1.43849			0.719246	−	0.694756i	$-0.244487\pi$
$89$	13.5707			1.43849			0.719246	+	0.694756i	$0.244487\pi$
$90$	1.23360	−	3.79662i	0.130033	−	0.400199i
$91$	−2.47589	+	1.79884i	−0.259544	+	0.188569i
$92$	−1.48147	−	1.07635i	−0.154454	−	0.112217i
$93$	−3.37118	−	10.3754i	−0.349575	−	1.07588i
$94$	3.68334	+	11.3362i	0.379907	+	1.16923i
$95$	−2.24162	−	1.62863i	−0.229985	−	0.167094i
$96$	2.13924	−	1.55425i	0.218335	−	0.158630i
$97$	−0.848181	+	2.61043i	−0.0861197	+	0.265049i	−0.984838	−	0.173478i	$-0.944500\pi$
$97$	−0.848181	+	2.61043i	−0.0861197	+	0.265049i	0.898718	+	0.438527i	$0.144500\pi$
$98$	1.00000			0.101015
$99$	−10.5199	−	8.03923i	−1.05729	−	0.807973i
$100$	1.00000			0.100000
$101$	−1.71183	+	5.26848i	−0.170334	+	0.524234i	−0.999390	−	0.0349321i	$-0.988879\pi$
$101$	−1.71183	+	5.26848i	−0.170334	+	0.524234i	0.829056	+	0.559166i	$0.188879\pi$
$102$	−0.146235	+	0.106246i	−0.0144795	+	0.0105199i
$103$	2.92619	+	2.12600i	0.288326	+	0.209481i	0.722541	−	0.691328i	$-0.242974\pi$
$103$	2.92619	+	2.12600i	0.288326	+	0.209481i	−0.434215	+	0.900809i	$0.642974\pi$
$104$	0.945705	+	2.91058i	0.0927340	+	0.285406i
$105$	−0.817115	−	2.51482i	−0.0797423	−	0.245421i
$106$	−0.100018	−	0.0726674i	−0.00971461	−	0.00705808i
$107$	−5.32480	+	3.86870i	−0.514768	+	0.374001i	−0.814629	−	0.579982i	$-0.803060\pi$
$107$	−5.32480	+	3.86870i	−0.514768	+	0.374001i	0.299861	+	0.953983i	$0.403060\pi$
$108$	−0.810584	+	2.49472i	−0.0779984	+	0.240055i
$109$	1.14986			0.110137			0.0550683	−	0.998483i	$-0.482462\pi$
$109$	1.14986			0.110137			0.0550683	+	0.998483i	$0.482462\pi$
$110$	1.10093	−	3.12857i	0.104970	−	0.298297i
$111$	14.8989			1.41414
$112$	0.309017	−	0.951057i	0.0291994	−	0.0898664i
$113$	9.83248	−	7.14372i	0.924962	−	0.672024i	−0.0197919	−	0.999804i	$-0.506300\pi$
$113$	9.83248	−	7.14372i	0.924962	−	0.672024i	0.944754	+	0.327780i	$0.106300\pi$
$114$	5.92738	+	4.30649i	0.555150	+	0.403340i
$115$	0.565872	+	1.74157i	0.0527678	+	0.162403i
$116$	1.02265	+	3.14739i	0.0949507	+	0.292228i
$117$	−9.88376	−	7.18097i	−0.913754	−	0.663881i
$118$	9.05528	−	6.57904i	0.833606	−	0.605650i
$119$	−0.0211240	+	0.0650130i	−0.00193643	+	0.00595973i
$120$	−2.64424			−0.241385
$121$	−8.57589	−	6.88870i	−0.779626	−	0.626245i
$122$	2.53653			0.229647
$123$	4.19390	−	12.9075i	0.378151	−	1.16383i
$124$	−3.33777	+	2.42503i	−0.299741	+	0.217774i
$125$	−0.809017	−	0.587785i	−0.0723607	−	0.0525731i
$126$	1.23360	+	3.79662i	0.109898	+	0.338230i
$127$	4.25873	+	13.1070i	0.377901	+	1.16306i	0.941501	+	0.337011i	$0.109416\pi$
$127$	4.25873	+	13.1070i	0.377901	+	1.16306i	−0.563600	+	0.826048i	$0.690584\pi$
$128$	−0.809017	−	0.587785i	−0.0715077	−	0.0519534i
$129$	6.07657	−	4.41489i	0.535012	−	0.388709i
$130$	0.945705	−	2.91058i	0.0829438	−	0.255275i
$131$	4.89161			0.427382			0.213691	−	0.976901i	$-0.431452\pi$
$131$	4.89161			0.427382			0.213691	+	0.976901i	$0.431452\pi$
$132$	−2.91113	+	8.27269i	−0.253382	+	0.720045i
$133$	2.77079			0.240258
$134$	−0.682366	+	2.10011i	−0.0589475	+	0.181422i
$135$	2.12214	−	1.54182i	0.182644	−	0.132699i
$136$	0.0553034	+	0.0401802i	0.00474222	+	0.00344543i
$137$	−5.88858	−	18.1232i	−0.503096	−	1.54837i	−0.803949	−	0.594698i	$-0.797271\pi$
$137$	−5.88858	−	18.1232i	−0.503096	−	1.54837i	0.300853	−	0.953670i	$-0.402729\pi$
$138$	−1.49630	−	4.60514i	−0.127374	−	0.392016i
$139$	−6.19156	−	4.49843i	−0.525161	−	0.381552i	0.293384	−	0.955995i	$-0.405219\pi$
$139$	−6.19156	−	4.49843i	−0.525161	−	0.381552i	−0.818545	+	0.574443i	$0.805219\pi$
$140$	−0.809017	+	0.587785i	−0.0683744	+	0.0496769i
$141$	−9.73963	+	29.9755i	−0.820225	+	2.52439i
$142$	13.7247			1.15175
$143$	−8.06479	−	6.16306i	−0.674412	−	0.515381i
$144$	3.99201			0.332667
$145$	1.02265	−	3.14739i	0.0849265	−	0.261377i
$146$	−5.65426	+	4.10806i	−0.467950	+	0.339986i
$147$	2.13924	+	1.55425i	0.176441	+	0.128192i
$148$	−1.74115	−	5.35871i	−0.143122	−	0.440483i
$149$	−4.53555	−	13.9590i	−0.371567	−	1.14357i	−0.945766	−	0.324850i	$-0.894686\pi$
$149$	−4.53555	−	13.9590i	−0.371567	−	1.14357i	0.574199	−	0.818716i	$-0.305314\pi$
$150$	2.13924	+	1.55425i	0.174668	+	0.126904i
$151$	8.97481	−	6.52058i	0.730360	−	0.530637i	−0.159318	−	0.987227i	$-0.550929\pi$
$151$	8.97481	−	6.52058i	0.730360	−	0.530637i	0.889677	+	0.456590i	$0.150929\pi$
$152$	0.856222	−	2.63518i	0.0694488	−	0.213741i
$153$	−0.272888			−0.0220617
$154$	0.948252	+	3.17818i	0.0764123	+	0.256105i
$155$	4.12571			0.331385
$156$	−2.50067	+	7.69627i	−0.200214	+	0.616195i
$157$	−10.6743	+	7.75530i	−0.851899	+	0.618941i	−0.925669	−	0.378335i	$-0.876497\pi$
$157$	−10.6743	+	7.75530i	−0.851899	+	0.618941i	0.0737701	+	0.997275i	$0.476497\pi$
$158$	10.0433	+	7.29689i	0.799003	+	0.580510i
$159$	−0.101019	−	0.310905i	−0.00801135	−	0.0246564i
$160$	0.309017	+	0.951057i	0.0244299	+	0.0751876i
$161$	−1.48147	−	1.07635i	−0.116756	−	0.0848284i
$162$	4.07737	−	2.96238i	0.320348	−	0.232747i
$163$	−1.14609	+	3.52729i	−0.0897685	+	0.276279i	−0.985855	−	0.167600i	$-0.946398\pi$
$163$	−1.14609	+	3.52729i	−0.0897685	+	0.276279i	0.896087	+	0.443879i	$0.146398\pi$
$164$	−5.13257			−0.400787
$165$	7.21772	−	4.98162i	0.561899	−	0.387819i
$166$	−3.05366			−0.237010
$167$	−2.70523	+	8.32583i	−0.209337	+	0.644272i	0.790171	+	0.612887i	$0.209992\pi$
$167$	−2.70523	+	8.32583i	−0.209337	+	0.644272i	−0.999507	+	0.0313851i	$0.990008\pi$
$168$	2.13924	−	1.55425i	0.165046	−	0.119913i
$169$	2.94010	+	2.13611i	0.226162	+	0.164316i
$170$	−0.0211240	−	0.0650130i	−0.00162014	−	0.00498627i
$171$	3.41804	+	10.5197i	0.261384	+	0.804458i
$172$	−2.29804	−	1.66962i	−0.175224	−	0.127308i
$173$	2.45841	−	1.78614i	0.186910	−	0.135798i	−0.490396	−	0.871500i	$-0.663148\pi$
$173$	2.45841	−	1.78614i	0.186910	−	0.135798i	0.677305	+	0.735702i	$0.263148\pi$
$174$	−2.70413	+	8.32247i	−0.205000	+	0.630925i
$175$	1.00000			0.0755929
$176$	3.31565	+	0.0802696i	0.249927	+	0.00605055i
$177$	29.5968			2.22463
$178$	4.19358	−	12.9065i	0.314322	−	0.967384i
$179$	5.90572	−	4.29075i	0.441414	−	0.320706i	−0.344783	−	0.938683i	$-0.612047\pi$
$179$	5.90572	−	4.29075i	0.441414	−	0.320706i	0.786197	+	0.617977i	$0.212047\pi$
$180$	−3.22960	−	2.34644i	−0.240720	−	0.174894i
$181$	3.37913	+	10.3999i	0.251169	+	0.773018i	0.994560	+	0.104162i	$0.0332160\pi$
$181$	3.37913	+	10.3999i	0.251169	+	0.773018i	−0.743391	+	0.668857i	$0.766784\pi$
$182$	0.945705	+	2.91058i	0.0701003	+	0.215747i
$183$	5.42624	+	3.94239i	0.401119	+	0.291430i
$184$	−1.48147	+	1.07635i	−0.109216	+	0.0793497i
$185$	−1.74115	+	5.35871i	−0.128012	+	0.393980i
$186$	−10.9094			−0.799914
$187$	−0.226654	−	0.00548713i	−0.0165746	−	0.000401258i
$188$	11.9195			0.869322
$189$	−0.810584	+	2.49472i	−0.0589613	+	0.181464i
$190$	−2.24162	+	1.62863i	−0.162624	+	0.118153i
$191$	−18.3258	−	13.3145i	−1.32601	−	0.963403i	−0.999836	−	0.0180930i	$-0.994241\pi$
$191$	−18.3258	−	13.3145i	−1.32601	−	0.963403i	−0.326174	−	0.945310i	$-0.605759\pi$
$192$	−0.817115	−	2.51482i	−0.0589702	−	0.181492i
$193$	−5.24600	−	16.1455i	−0.377615	−	1.16218i	−0.941697	−	0.336461i	$-0.890770\pi$
$193$	−5.24600	−	16.1455i	−0.377615	−	1.16218i	0.564082	−	0.825718i	$-0.309230\pi$
$194$	2.22057	+	1.61334i	0.159427	+	0.115831i
$195$	6.54684	−	4.75656i	0.468829	−	0.340624i
$196$	0.309017	−	0.951057i	0.0220726	−	0.0679326i
$197$	26.3241			1.87551			0.937757	−	0.347293i	$-0.112899\pi$
$197$	26.3241			1.87551			0.937757	+	0.347293i	$0.112899\pi$
$198$	−10.8966	+	7.52075i	−0.774387	+	0.534477i
$199$	16.9127			1.19891			0.599456	−	0.800408i	$-0.295384\pi$
$199$	16.9127			1.19891			0.599456	+	0.800408i	$0.295384\pi$
$200$	0.309017	−	0.951057i	0.0218508	−	0.0672499i
$201$	−4.72383	+	3.43206i	−0.333193	+	0.242079i
$202$	4.48164	+	3.25610i	0.315327	+	0.229099i
$203$	1.02265	+	3.14739i	0.0717760	+	0.220904i
$204$	0.0558569	+	0.171910i	0.00391077	+	0.0120361i
$205$	4.15234	+	3.01685i	0.290012	+	0.210706i
$206$	2.92619	−	2.12600i	0.203877	−	0.148125i
$207$	2.25896	−	6.95237i	0.157009	−	0.483223i
$208$	3.06037			0.212198
$209$	2.62741	+	8.80607i	0.181742	+	0.609129i
$210$	−2.64424			−0.182470
$211$	−5.08280	+	15.6432i	−0.349914	+	1.07693i	0.608986	+	0.793181i	$0.291577\pi$
$211$	−5.08280	+	15.6432i	−0.349914	+	1.07693i	−0.958900	+	0.283744i	$0.908423\pi$
$212$	−0.100018	+	0.0726674i	−0.00686927	+	0.00499082i
$213$	29.3604	+	21.3316i	2.01174	+	1.46162i
$214$	2.03389	+	6.25968i	0.139034	+	0.427903i
$215$	0.877773	+	2.70151i	0.0598636	+	0.184241i
$216$	2.12214	+	1.54182i	0.144393	+	0.104908i
$217$	−3.33777	+	2.42503i	−0.226583	+	0.164622i
$218$	0.355326	−	1.09358i	0.0240657	−	0.0740667i
$219$	−18.4807			−1.24881
$220$	−2.63524	−	2.01383i	−0.177668	−	0.135772i
$221$	−0.209203			−0.0140725
$222$	4.60402	−	14.1697i	0.309002	−	0.951009i
$223$	−16.5585	+	12.0305i	−1.10884	+	0.805620i	−0.982481	−	0.186364i	$-0.940330\pi$
$223$	−16.5585	+	12.0305i	−1.10884	+	0.805620i	−0.126361	+	0.991984i	$0.540330\pi$
$224$	−0.809017	−	0.587785i	−0.0540547	−	0.0392731i
$225$	1.23360	+	3.79662i	0.0822399	+	0.253108i
$226$	−3.75567	−	11.5588i	−0.249824	−	0.768878i
$227$	−19.1770	−	13.9329i	−1.27282	−	0.924759i	−0.273510	−	0.961869i	$-0.588185\pi$
$227$	−19.1770	−	13.9329i	−1.27282	−	0.924759i	−0.999311	+	0.0371106i	$0.988185\pi$
$228$	5.92738	−	4.30649i	0.392550	−	0.285204i
$229$	−8.23123	+	25.3331i	−0.543935	+	1.67406i	0.179573	+	0.983745i	$0.442528\pi$
$229$	−8.23123	+	25.3331i	−0.543935	+	1.67406i	−0.723508	+	0.690316i	$0.757472\pi$
$230$	1.83120			0.120746
$231$	−2.91113	+	8.27269i	−0.191539	+	0.544303i
$232$	3.30937			0.217271
$233$	9.37458	−	28.8520i	0.614149	−	1.89016i	0.200604	−	0.979672i	$-0.435710\pi$
$233$	9.37458	−	28.8520i	0.614149	−	1.89016i	0.413545	−	0.910484i	$-0.364290\pi$
$234$	−9.88376	+	7.18097i	−0.646122	+	0.469435i
$235$	−9.64311	−	7.00613i	−0.629047	−	0.457029i
$236$	−3.45881	−	10.6451i	−0.225149	−	0.692938i
$237$	10.1438	+	31.2195i	0.658914	+	2.02793i
$238$	0.0553034	+	0.0401802i	0.00358478	+	0.00260450i
$239$	8.05118	−	5.84952i	0.520787	−	0.378374i	−0.296113	−	0.955153i	$-0.595691\pi$
$239$	8.05118	−	5.84952i	0.520787	−	0.378374i	0.816900	+	0.576779i	$0.195691\pi$
$240$	−0.817115	+	2.51482i	−0.0527446	+	0.162331i
$241$	−30.1849			−1.94438			−0.972191	−	0.234189i	$-0.924757\pi$
$241$	−30.1849			−1.94438			−0.972191	+	0.234189i	$0.924757\pi$
$242$	−9.20164	+	6.02743i	−0.591504	+	0.387458i
$243$	21.1960			1.35973
$244$	0.783832	−	2.41239i	0.0501797	−	0.154437i
$245$	−0.809017	+	0.587785i	−0.0516862	+	0.0375522i
$246$	−10.9798	−	7.97728i	−0.700045	−	0.508613i
$247$	2.62035	+	8.06462i	0.166729	+	0.513139i
$248$	1.27491	+	3.92378i	0.0809572	+	0.249161i
$249$	−6.53249	−	4.74614i	−0.413980	−	0.300774i
$250$	−0.809017	+	0.587785i	−0.0511667	+	0.0371748i
$251$	−0.361544	+	1.11272i	−0.0228204	+	0.0702341i	−0.961818	−	0.273689i	$-0.911756\pi$
$251$	−0.361544	+	1.11272i	−0.0228204	+	0.0702341i	0.938998	+	0.343923i	$0.111756\pi$
$252$	3.99201			0.251473
$253$	2.01603	−	5.72903i	0.126747	−	0.360181i
$254$	13.7815			0.864730
$255$	0.0558569	−	0.171910i	0.00349790	−	0.0107654i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	0.793578	+	0.576568i	0.0495020	+	0.0359653i	0.612261	−	0.790656i	$-0.290260\pi$
$257$	0.793578	+	0.576568i	0.0495020	+	0.0359653i	−0.562759	+	0.826621i	$0.690260\pi$
$258$	−2.32104	−	7.14344i	−0.144502	−	0.444731i
$259$	−1.74115	−	5.35871i	−0.108190	−	0.332974i
$260$	−2.47589	−	1.79884i	−0.153548	−	0.111559i
$261$	−10.6879	+	7.76524i	−0.661567	+	0.480656i
$262$	1.51159	−	4.65219i	0.0933863	−	0.287413i
$263$	−15.9923			−0.986125			−0.493063	−	0.869994i	$-0.664123\pi$
$263$	−15.9923			−0.986125			−0.493063	+	0.869994i	$0.664123\pi$
$264$	6.96820	+	5.32505i	0.428863	+	0.327734i
$265$	0.123629			0.00759448
$266$	0.856222	−	2.63518i	0.0524983	−	0.161573i
$267$	29.0309	−	21.0922i	1.77666	−	1.29082i
$268$	1.78646	+	1.29794i	0.109125	+	0.0792842i
$269$	4.66762	+	14.3655i	0.284590	+	0.875878i	0.986521	+	0.163633i	$0.0523214\pi$
$269$	4.66762	+	14.3655i	0.284590	+	0.875878i	−0.701931	+	0.712245i	$0.747679\pi$
$270$	−0.810584	−	2.49472i	−0.0493305	−	0.151824i
$271$	0.404143	+	0.293627i	0.0245499	+	0.0178366i	0.599993	−	0.800006i	$-0.295170\pi$
$271$	0.404143	+	0.293627i	0.0245499	+	0.0178366i	−0.575443	+	0.817842i	$0.695170\pi$
$272$	0.0553034	−	0.0401802i	0.00335326	−	0.00243628i
$273$	−2.50067	+	7.69627i	−0.151347	+	0.465800i
$274$	−19.0559			−1.15121
$275$	0.948252	+	3.17818i	0.0571818	+	0.191651i
$276$	−4.84213			−0.291462
$277$	−3.43198	+	10.5625i	−0.206208	+	0.634642i	0.793454	+	0.608630i	$0.208281\pi$
$277$	−3.43198	+	10.5625i	−0.206208	+	0.634642i	−0.999662	+	0.0260116i	$0.991719\pi$
$278$	−6.19156	+	4.49843i	−0.371345	+	0.269798i
$279$	−13.3244	−	9.68075i	−0.797711	−	0.579571i
$280$	0.309017	+	0.951057i	0.0184673	+	0.0568365i
$281$	4.77469	+	14.6950i	0.284834	+	0.876629i	0.986448	+	0.164072i	$0.0524629\pi$
$281$	4.77469	+	14.6950i	0.284834	+	0.876629i	−0.701614	+	0.712557i	$0.747537\pi$
$282$	25.4987	+	18.5259i	1.51843	+	1.10320i
$283$	−11.5802	+	8.41353i	−0.688373	+	0.500132i	−0.876125	−	0.482084i	$-0.839880\pi$
$283$	−11.5802	+	8.41353i	−0.688373	+	0.500132i	0.187752	+	0.982216i	$0.439880\pi$
$284$	4.24118	−	13.0530i	0.251668	−	0.774553i
$285$	−7.32664			−0.433993
$286$	−8.35358	+	5.76558i	−0.493957	+	0.340926i
$287$	−5.13257			−0.302966
$288$	1.23360	−	3.79662i	0.0726905	−	0.223718i
$289$	13.7495	−	9.98960i	0.808795	−	0.587624i
$290$	−2.67733	−	1.94520i	−0.157218	−	0.114226i
$291$	2.24279	+	6.90261i	0.131475	+	0.404638i
$292$	2.15974	+	6.64698i	0.126389	+	0.388985i
$293$	14.2184	+	10.3302i	0.830645	+	0.603499i	0.919742	−	0.392524i	$-0.128398\pi$
$293$	14.2184	+	10.3302i	0.830645	+	0.603499i	−0.0890967	+	0.996023i	$0.528398\pi$
$294$	2.13924	−	1.55425i	0.124763	−	0.0906454i
$295$	−3.45881	+	10.6451i	−0.201380	+	0.619783i
$296$	−5.63448			−0.327498
$297$	−8.69730	−	0.210555i	−0.504669	−	0.0122177i
$298$	−14.6774			−0.850237
$299$	1.73177	−	5.32985i	0.100151	−	0.308233i
$300$	2.13924	−	1.55425i	0.123509	−	0.0897344i
$301$	−2.29804	−	1.66962i	−0.132457	−	0.0962355i
$302$	−3.42807	−	10.5505i	−0.197263	−	0.607114i
$303$	4.52650	+	13.9311i	0.260041	+	0.800323i
$304$	−2.24162	−	1.62863i	−0.128566	−	0.0934084i
$305$	−2.05210	+	1.49094i	−0.117503	+	0.0853708i
$306$	−0.0843272	+	0.259532i	−0.00482066	+	0.0148365i
$307$	5.38032			0.307071			0.153536	−	0.988143i	$-0.450934\pi$
$307$	5.38032			0.307071			0.153536	+	0.988143i	$0.450934\pi$
$308$	3.31565	+	0.0802696i	0.188927	+	0.00457378i
$309$	9.56413			0.544084
$310$	1.27491	−	3.92378i	0.0724103	−	0.222856i
$311$	−13.6747	+	9.93522i	−0.775419	+	0.563375i	−0.903601	−	0.428376i	$-0.859086\pi$
$311$	−13.6747	+	9.93522i	−0.775419	+	0.563375i	0.128182	+	0.991751i	$0.459086\pi$
$312$	6.54684	+	4.75656i	0.370642	+	0.269287i
$313$	−0.418788	−	1.28890i	−0.0236713	−	0.0728528i	0.938523	−	0.345217i	$-0.112195\pi$
$313$	−0.418788	−	1.28890i	−0.0236713	−	0.0728528i	−0.962194	+	0.272364i	$0.912195\pi$
$314$	4.07721	+	12.5483i	0.230090	+	0.708144i
$315$	−3.22960	−	2.34644i	−0.181967	−	0.132207i
$316$	10.0433	−	7.29689i	0.564980	−	0.410482i
$317$	9.06089	−	27.8866i	0.508910	−	1.56627i	−0.285185	−	0.958472i	$-0.592055\pi$
$317$	9.06089	−	27.8866i	0.508910	−	1.56627i	0.794096	−	0.607793i	$-0.207945\pi$
$318$	−0.326905			−0.0183319
$319$	−9.03325	+	6.23469i	−0.505765	+	0.349076i
$320$	1.00000			0.0559017
$321$	−5.37810	+	16.5521i	−0.300176	+	0.923848i
$322$	−1.48147	+	1.07635i	−0.0825592	+	0.0599827i
$323$	0.153234	+	0.111331i	0.00852618	+	0.00619463i
$324$	−1.55742	−	4.79323i	−0.0865231	−	0.266291i
$325$	0.945705	+	2.91058i	0.0524583	+	0.161450i
$326$	3.00050	+	2.17999i	0.166182	+	0.120738i
$327$	2.45982	−	1.78717i	0.136028	−	0.0988305i
$328$	−1.58605	+	4.88137i	−0.0875751	+	0.269528i
$329$	11.9195			0.657145
$330$	−2.50741	−	8.40387i	−0.138028	−	0.462618i
$331$	7.10546			0.390551			0.195276	−	0.980748i	$-0.437440\pi$
$331$	7.10546			0.390551			0.195276	+	0.980748i	$0.437440\pi$
$332$	−0.943632	+	2.90420i	−0.0517886	+	0.159389i
$333$	18.1971	−	13.2210i	0.997196	−	0.724506i
$334$	7.08237	+	5.14564i	0.387530	+	0.281557i
$335$	−0.682366	−	2.10011i	−0.0372817	−	0.114741i
$336$	−0.817115	−	2.51482i	−0.0445773	−	0.137195i
$337$	−23.2713	−	16.9076i	−1.26767	−	0.921016i	−0.268563	−	0.963262i	$-0.586549\pi$
$337$	−23.2713	−	16.9076i	−1.26767	−	0.921016i	−0.999107	+	0.0422456i	$0.986549\pi$
$338$	2.94010	−	2.13611i	0.159920	−	0.116189i
$339$	9.93091	−	30.5642i	0.539373	−	1.66002i
$340$	−0.0683587			−0.00370727
$341$	−10.8722	−	8.30849i	−0.588764	−	0.449930i
$342$	11.0610			0.598112
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$	−2.29804	+	1.66962i	−0.123902	+	0.0900201i
$345$	3.91737	+	2.84613i	0.210904	+	0.153231i
$346$	−0.939030	−	2.89004i	−0.0504825	−	0.155369i
$347$	−7.96934	−	24.5271i	−0.427817	−	1.31668i	−0.900271	−	0.435329i	$-0.856632\pi$
$347$	−7.96934	−	24.5271i	−0.427817	−	1.31668i	0.472455	−	0.881355i	$-0.343368\pi$
$348$	7.07951	+	5.14357i	0.379502	+	0.275724i
$349$	−29.6887	+	21.5701i	−1.58920	+	1.15462i	−0.684131	+	0.729359i	$0.739818\pi$
$349$	−29.6887	+	21.5701i	−1.58920	+	1.15462i	−0.905070	+	0.425263i	$0.860182\pi$
$350$	0.309017	−	0.951057i	0.0165177	−	0.0508361i
$351$	−8.02766			−0.428485
$352$	1.10093	−	3.12857i	0.0586800	−	0.166753i
$353$	16.9704			0.903241			0.451620	−	0.892210i	$-0.350846\pi$
$353$	16.9704			0.903241			0.451620	+	0.892210i	$0.350846\pi$
$354$	9.14592	−	28.1482i	0.486100	−	1.49606i
$355$	−11.1035	+	8.06720i	−0.589315	+	0.428162i
$356$	−10.9789	−	7.97666i	−0.581882	−	0.422762i
$357$	0.0558569	+	0.171910i	0.00295626	+	0.00909844i
$358$	−2.25578	−	6.94259i	−0.119222	−	0.366927i
$359$	−17.1365	−	12.4504i	−0.904430	−	0.657107i	0.0351697	−	0.999381i	$-0.488803\pi$
$359$	−17.1365	−	12.4504i	−0.904430	−	0.657107i	−0.939600	+	0.342274i	$0.888803\pi$
$360$	−3.22960	+	2.34644i	−0.170215	+	0.123668i
$361$	−3.49891	+	10.7685i	−0.184153	+	0.566765i
$362$	10.9351			0.574736
$363$	−29.0526	−	1.40751i	−1.52486	−	0.0738750i
$364$	3.06037			0.160407
$365$	2.15974	−	6.64698i	0.113046	−	0.347919i
$366$	5.42624	−	3.94239i	0.283634	−	0.206072i
$367$	−29.5264	−	21.4522i	−1.54126	−	1.11979i	−0.949537	−	0.313656i	$-0.898446\pi$
$367$	−29.5264	−	21.4522i	−1.54126	−	1.11979i	−0.591728	−	0.806138i	$-0.701554\pi$
$368$	0.565872	+	1.74157i	0.0294981	+	0.0907858i
$369$	−6.33153	−	19.4864i	−0.329606	−	1.01442i
$370$	4.55839	+	3.31186i	0.236979	+	0.172176i
$371$	−0.100018	+	0.0726674i	−0.00519268	+	0.00377270i
$372$	−3.37118	+	10.3754i	−0.174788	+	0.537941i
$373$	−6.23055			−0.322606			−0.161303	−	0.986905i	$-0.551570\pi$
$373$	−6.23055			−0.322606			−0.161303	+	0.986905i	$0.551570\pi$
$374$	−0.0752584	+	0.213865i	−0.00389152	+	0.0110587i
$375$	−2.64424			−0.136548
$376$	3.68334	−	11.3362i	0.189954	−	0.584617i
$377$	−8.19362	+	5.95301i	−0.421993	+	0.306596i
$378$	2.12214	+	1.54182i	0.109151	+	0.0793027i
$379$	0.143280	+	0.440972i	0.00735982	+	0.0226512i	0.954669	−	0.297669i	$-0.0962093\pi$
$379$	0.143280	+	0.440972i	0.00735982	+	0.0226512i	−0.947309	+	0.320321i	$0.896209\pi$
$380$	0.856222	+	2.63518i	0.0439233	+	0.135182i
$381$	29.4819	+	21.4199i	1.51041	+	1.09737i
$382$	−18.3258	+	13.3145i	−0.937631	+	0.681229i
$383$	9.42337	−	29.0022i	0.481512	−	1.48194i	−0.355458	−	0.934692i	$-0.615675\pi$
$383$	9.42337	−	29.0022i	0.481512	−	1.48194i	0.836970	−	0.547249i	$-0.184325\pi$
$384$	−2.64424			−0.134938
$385$	−2.63524	−	2.01383i	−0.134304	−	0.102634i
$386$	−16.9764			−0.864076
$387$	3.50408	−	10.7844i	0.178122	−	0.548204i
$388$	2.22057	−	1.61334i	0.112732	−	0.0819047i
$389$	11.3092	+	8.21658i	0.573397	+	0.416597i	0.836338	−	0.548215i	$-0.184692\pi$
$389$	11.3092	+	8.21658i	0.573397	+	0.416597i	−0.262941	+	0.964812i	$0.584692\pi$
$390$	−2.50067	−	7.69627i	−0.126626	−	0.389716i
$391$	−0.0386823	−	0.119052i	−0.00195625	−	0.00602071i
$392$	−0.809017	−	0.587785i	−0.0408615	−	0.0296876i
$393$	10.4643	−	7.60275i	0.527854	−	0.383508i
$394$	8.13459	−	25.0357i	0.409815	−	1.26128i
$395$	−12.4142			−0.624627
$396$	3.78543	+	12.6873i	0.190225	+	0.637561i
$397$	−11.9510			−0.599801			−0.299901	−	0.953970i	$-0.596953\pi$
$397$	−11.9510			−0.599801			−0.299901	+	0.953970i	$0.596953\pi$
$398$	5.22632	−	16.0850i	0.261972	−	0.806267i
$399$	5.92738	−	4.30649i	0.296740	−	0.215594i
$400$	−0.809017	−	0.587785i	−0.0404508	−	0.0293893i
$401$	−4.46772	−	13.7502i	−0.223107	−	0.686654i	−0.998478	−	0.0551475i	$-0.982437\pi$
$401$	−4.46772	−	13.7502i	−0.223107	−	0.686654i	0.775371	−	0.631506i	$-0.217563\pi$
$402$	1.80434	+	5.55319i	0.0899923	+	0.276968i
$403$	−10.2148	−	7.42148i	−0.508835	−	0.369690i
$404$	4.48164	−	3.25610i	0.222970	−	0.161997i
$405$	−1.55742	+	4.79323i	−0.0773886	+	0.238178i
$406$	3.30937			0.164241
$407$	15.3799	−	10.6151i	0.762353	−	0.526171i
$408$	0.180757			0.00894880
$409$	−1.09522	+	3.37073i	−0.0541550	+	0.166672i	−0.974476	−	0.224492i	$-0.927928\pi$
$409$	−1.09522	+	3.37073i	−0.0541550	+	0.166672i	0.920321	+	0.391164i	$0.127928\pi$
$410$	4.15234	−	3.01685i	0.205069	−	0.148992i
$411$	−40.7650	−	29.6175i	−2.01079	−	1.46092i
$412$	−1.11770	−	3.43994i	−0.0550653	−	0.169474i
$413$	−3.45881	−	10.6451i	−0.170197	−	0.523812i
$414$	−5.91404	−	4.29680i	−0.290659	−	0.211176i
$415$	2.47046	−	1.79490i	0.121270	−	0.0881080i
$416$	0.945705	−	2.91058i	0.0463670	−	0.142703i
$417$	−20.2369			−0.991003
$418$	9.18699	+	0.222410i	0.449350	+	0.0108784i
$419$	−35.5085			−1.73471			−0.867353	−	0.497694i	$-0.834180\pi$
$419$	−35.5085			−1.73471			−0.867353	+	0.497694i	$0.834180\pi$
$420$	−0.817115	+	2.51482i	−0.0398711	+	0.122711i
$421$	21.5352	−	15.6463i	1.04956	−	0.762552i	0.0774331	−	0.996998i	$-0.475328\pi$
$421$	21.5352	−	15.6463i	1.04956	−	0.762552i	0.972129	+	0.234446i	$0.0753276\pi$
$422$	13.3069	+	9.66806i	0.647772	+	0.470634i
$423$	14.7039	+	45.2540i	0.714929	+	2.20032i
$424$	0.0382035	+	0.117578i	0.00185533	+	0.00571011i
$425$	0.0553034	+	0.0401802i	0.00268261	+	0.00194903i
$426$	29.3604	−	21.3316i	1.42252	−	1.03352i
$427$	0.783832	−	2.41239i	0.0379323	−	0.116744i
$428$	6.58182			0.318144
$429$	−26.8314	−	0.649569i	−1.29543	−	0.0313615i
$430$	2.84053			0.136983
$431$	8.04799	−	24.7692i	0.387658	−	1.19309i	−0.546875	−	0.837214i	$-0.684183\pi$
$431$	8.04799	−	24.7692i	0.387658	−	1.19309i	0.934534	−	0.355875i	$-0.115817\pi$
$432$	2.12214	−	1.54182i	0.102101	−	0.0741809i
$433$	−1.36900	−	0.994636i	−0.0657899	−	0.0477992i	0.554404	−	0.832248i	$-0.312946\pi$
$433$	−1.36900	−	0.994636i	−0.0657899	−	0.0477992i	−0.620194	+	0.784448i	$0.712946\pi$
$434$	1.27491	+	3.92378i	0.0611979	+	0.188348i
$435$	−2.70413	−	8.32247i	−0.129653	−	0.399032i
$436$	−0.930257	−	0.675871i	−0.0445512	−	0.0323684i
$437$	−4.10485	+	2.98235i	−0.196362	+	0.142665i
$438$	−5.71086	+	17.5762i	−0.272876	+	0.839824i
$439$	12.8065			0.611223			0.305611	−	0.952156i	$-0.401139\pi$
$439$	12.8065			0.611223			0.305611	+	0.952156i	$0.401139\pi$
$440$	−2.72960	+	1.88395i	−0.130129	+	0.0898139i
$441$	3.99201			0.190096
$442$	−0.0646472	+	0.198964i	−0.00307495	+	0.00946373i
$443$	−0.569870	+	0.414035i	−0.0270753	+	0.0196714i	−0.601241	−	0.799068i	$-0.705327\pi$
$443$	−0.569870	+	0.414035i	−0.0270753	+	0.0196714i	0.574165	+	0.818739i	$0.305327\pi$
$444$	−12.0535	−	8.75737i	−0.572033	−	0.415606i
$445$	4.19358	+	12.9065i	0.198795	+	0.611827i
$446$	6.32480	+	19.4657i	0.299488	+	0.921729i
$447$	−31.3983	−	22.8122i	−1.48509	−	1.07898i
$448$	−0.809017	+	0.587785i	−0.0382225	+	0.0277702i
$449$	−5.68794	+	17.5057i	−0.268431	+	0.826144i	0.722453	+	0.691421i	$0.243015\pi$
$449$	−5.68794	+	17.5057i	−0.268431	+	0.826144i	−0.990883	+	0.134724i	$0.956985\pi$
$450$	3.99201			0.188185
$451$	−4.86697	−	16.3122i	−0.229177	−	0.768113i
$452$	−12.1536			−0.571658
$453$	9.06465	−	27.8981i	0.425894	−	1.31077i
$454$	−19.1770	+	13.9329i	−0.900020	+	0.653903i
$455$	−2.47589	−	1.79884i	−0.116071	−	0.0843308i
$456$	−2.26406	−	6.96805i	−0.106024	−	0.326309i
$457$	5.25190	+	16.1637i	0.245673	+	0.756105i	0.995525	+	0.0944988i	$0.0301248\pi$
$457$	5.25190	+	16.1637i	0.245673	+	0.756105i	−0.749852	+	0.661606i	$0.769875\pi$
$458$	21.5496	+	15.6567i	1.00695	+	0.731591i
$459$	−0.145066	+	0.105397i	−0.00677112	+	0.00491951i
$460$	0.565872	−	1.74157i	0.0263839	−	0.0812013i
$461$	13.3276			0.620729			0.310364	−	0.950618i	$-0.399549\pi$
$461$	13.3276			0.620729			0.310364	+	0.950618i	$0.399549\pi$
$462$	6.96820	+	5.32505i	0.324190	+	0.247744i
$463$	−34.9814			−1.62572			−0.812861	−	0.582457i	$-0.802091\pi$
$463$	−34.9814			−1.62572			−0.812861	+	0.582457i	$0.802091\pi$
$464$	1.02265	−	3.14739i	0.0474754	−	0.146114i
$465$	8.82587	−	6.41237i	0.409290	−	0.297366i
$466$	−24.5430	−	17.8315i	−1.13693	−	0.826028i
$467$	−1.10585	−	3.40346i	−0.0511728	−	0.157494i	0.922204	−	0.386703i	$-0.126386\pi$
$467$	−1.10585	−	3.40346i	−0.0511728	−	0.157494i	−0.973377	+	0.229209i	$0.926386\pi$
$468$	3.77526	+	11.6191i	0.174511	+	0.537091i
$469$	1.78646	+	1.29794i	0.0824910	+	0.0599332i
$470$	−9.64311	+	7.00613i	−0.444803	+	0.323169i
$471$	−10.7811	+	33.1808i	−0.496767	+	1.52889i
$472$	−11.1929			−0.515197
$473$	3.12724	−	8.88681i	0.143791	−	0.408616i
$474$	32.8262			1.50776
$475$	0.856222	−	2.63518i	0.0392862	−	0.120910i
$476$	0.0553034	−	0.0401802i	0.00253483	−	0.00184166i
$477$	−0.399273	−	0.290089i	−0.0182814	−	0.0132822i
$478$	−3.07528	−	9.46472i	−0.140660	−	0.432906i
$479$	5.66428	+	17.4328i	0.258807	+	0.796527i	0.993056	+	0.117646i	$0.0375348\pi$
$479$	5.66428	+	17.4328i	0.258807	+	0.796527i	−0.734248	+	0.678881i	$0.762465\pi$
$480$	2.13924	+	1.55425i	0.0976423	+	0.0709413i
$481$	13.9503	−	10.1355i	0.636081	−	0.462140i
$482$	−9.32766	+	28.7076i	−0.424863	+	1.30759i
$483$	−4.84213			−0.220325
$484$	2.88896	+	10.6139i	0.131317	+	0.482448i
$485$	−2.74477			−0.124634
$486$	6.54993	−	20.1586i	0.297111	−	0.914414i
$487$	−0.394025	+	0.286276i	−0.0178550	+	0.0129724i	−0.596677	−	0.802482i	$-0.703513\pi$
$487$	−0.394025	+	0.286276i	−0.0178550	+	0.0129724i	0.578822	+	0.815454i	$0.303513\pi$
$488$	−2.05210	−	1.49094i	−0.0928941	−	0.0674915i
$489$	3.03053	+	9.32701i	0.137045	+	0.421782i
$490$	0.309017	+	0.951057i	0.0139600	+	0.0429644i
$491$	−4.92827	−	3.58060i	−0.222410	−	0.161590i	0.471001	−	0.882133i	$-0.343893\pi$
$491$	−4.92827	−	3.58060i	−0.222410	−	0.161590i	−0.693411	+	0.720543i	$0.743893\pi$
$492$	−10.9798	+	7.97728i	−0.495007	+	0.359643i
$493$	−0.0699071	+	0.215152i	−0.00314846	+	0.00968995i
$494$	8.47964			0.381517
$495$	4.39494	−	12.4893i	0.197538	−	0.561351i
$496$	4.12571			0.185250
$497$	4.24118	−	13.0530i	0.190243	−	0.585507i
$498$	−6.53249	+	4.74614i	−0.292728	+	0.212679i
$499$	−34.2328	−	24.8716i	−1.53247	−	1.11341i	−0.954844	−	0.297106i	$-0.903978\pi$
$499$	−34.2328	−	24.8716i	−1.53247	−	1.11341i	−0.577628	−	0.816300i	$-0.696022\pi$
$500$	0.309017	+	0.951057i	0.0138197	+	0.0425325i
$501$	7.15327	+	22.0155i	0.319584	+	0.983580i
$502$	0.946534	+	0.687697i	0.0422459	+	0.0306934i
$503$	−26.1860	+	19.0253i	−1.16758	+	0.848294i	−0.990717	−	0.135942i	$-0.956594\pi$
$503$	−26.1860	+	19.0253i	−1.16758	+	0.848294i	−0.176860	+	0.984236i	$0.556594\pi$
$504$	1.23360	−	3.79662i	0.0549488	−	0.169115i
$505$	−5.53961			−0.246510
$506$	−4.82565	−	3.68773i	−0.214526	−	0.163939i
$507$	9.60960			0.426777
$508$	4.25873	−	13.1070i	0.188950	−	0.581530i
$509$	−19.1995	+	13.9493i	−0.851005	+	0.618291i	−0.925423	−	0.378936i	$-0.876290\pi$
$509$	−19.1995	+	13.9493i	−0.851005	+	0.618291i	0.0744182	+	0.997227i	$0.476290\pi$
$510$	−0.146235	−	0.106246i	−0.00647541	−	0.00470466i
$511$	2.15974	+	6.64698i	0.0955411	+	0.294045i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	5.88000	+	4.27207i	0.259608	+	0.188616i
$514$	0.793578	−	0.576568i	0.0350032	−	0.0254313i
$515$	−1.11770	+	3.43994i	−0.0492519	+	0.151582i
$516$	−7.51106			−0.330656
$517$	11.3027	+	37.8824i	0.497093	+	1.66607i
$518$	−5.63448			−0.247565
$519$	2.48302	−	7.64195i	0.108992	−	0.335444i
$520$	−2.47589	+	1.79884i	−0.108575	+	0.0788842i
$521$	24.9355	+	18.1167i	1.09244	+	0.793706i	0.979810	−	0.199930i	$-0.0640716\pi$
$521$	24.9355	+	18.1167i	1.09244	+	0.793706i	0.112633	+	0.993637i	$0.464072\pi$
$522$	4.08243	+	12.5644i	0.178683	+	0.549930i
$523$	11.6215	+	35.7673i	0.508172	+	1.56399i	0.795372	+	0.606122i	$0.207276\pi$
$523$	11.6215	+	35.7673i	0.508172	+	1.56399i	−0.287200	+	0.957871i	$0.592724\pi$
$524$	−3.95739	−	2.87521i	−0.172879	−	0.125604i
$525$	2.13924	−	1.55425i	0.0933639	−	0.0678328i
$526$	−4.94188	+	15.2095i	−0.215476	+	0.663168i
$527$	−0.282028			−0.0122853
$528$	7.21772	−	4.98162i	0.314111	−	0.216797i
$529$	−19.6467			−0.854205
$530$	0.0382035	−	0.117578i	0.00165945	−	0.00510727i
$531$	36.1487	−	26.2636i	1.56872	−	1.13974i
$532$	−2.24162	−	1.62863i	−0.0971865	−	0.0706101i
$533$	−4.85390	−	14.9388i	−0.210246	−	0.647070i
$534$	−11.0888	−	34.1279i	−0.479861	−	1.47686i
$535$	−5.32480	−	3.86870i	−0.230211	−	0.167258i
$536$	1.78646	−	1.29794i	0.0771633	−	0.0560624i
$537$	5.96483	−	18.3579i	0.257401	−	0.792200i
$538$	15.1048			0.651212
$539$	3.31565	+	0.0802696i	0.142815	+	0.00345746i
$540$	−2.62310			−0.112880
$541$	−2.22132	+	6.83651i	−0.0955018	+	0.293924i	−0.987384	−	0.158343i	$-0.949385\pi$
$541$	−2.22132	+	6.83651i	−0.0955018	+	0.293924i	0.891882	+	0.452268i	$0.149385\pi$
$542$	0.404143	−	0.293627i	0.0173594	−	0.0126124i
$543$	23.3928	+	16.9958i	1.00388	+	0.729361i
$544$	−0.0211240	−	0.0650130i	−0.000905684	−	0.00278741i
$545$	0.355326	+	1.09358i	0.0152205	+	0.0468439i
$546$	6.54684	+	4.75656i	0.280179	+	0.203562i
$547$	−13.8145	+	10.0368i	−0.590666	+	0.429144i	−0.842554	−	0.538612i	$-0.818949\pi$
$547$	−13.8145	+	10.0368i	−0.590666	+	0.429144i	0.251888	+	0.967757i	$0.418949\pi$
$548$	−5.88858	+	18.1232i	−0.251548	+	0.774184i
$549$	10.1259			0.432161
$550$	3.31565	+	0.0802696i	0.141380	+	0.00342271i
$551$	9.16957			0.390637
$552$	−1.49630	+	4.60514i	−0.0636868	+	0.196008i
$553$	10.0433	−	7.29689i	0.427085	−	0.310295i
$554$	8.98504	+	6.52801i	0.381738	+	0.277349i
$555$	4.60402	+	14.1697i	0.195430	+	0.601471i
$556$	2.36496	+	7.27861i	0.100297	+	0.308682i
$557$	−28.9135	−	21.0069i	−1.22510	−	0.890090i	−0.228591	−	0.973523i	$-0.573412\pi$
$557$	−28.9135	−	21.0069i	−1.22510	−	0.890090i	−0.996513	+	0.0834323i	$0.973412\pi$
$558$	−13.3244	+	9.68075i	−0.564067	+	0.409819i
$559$	2.68631	−	8.26760i	0.113619	−	0.349682i
$560$	1.00000			0.0422577
$561$	−0.493394	+	0.340537i	−0.0208311	+	0.0143775i
$562$	15.4512			0.651770
$563$	−5.76610	+	17.7462i	−0.243012	+	0.747915i	0.752945	+	0.658084i	$0.228633\pi$
$563$	−5.76610	+	17.7462i	−0.243012	+	0.747915i	−0.995957	+	0.0898311i	$0.971367\pi$
$564$	25.4987	−	18.5259i	1.07369	−	0.780081i
$565$	9.83248	+	7.14372i	0.413656	+	0.300538i
$566$	4.42325	+	13.6134i	0.185923	+	0.572213i
$567$	−1.55742	−	4.79323i	−0.0654053	−	0.201297i
$568$	−11.1035	−	8.06720i	−0.465894	−	0.338492i
$569$	−32.1499	+	23.3582i	−1.34779	+	0.979228i	−0.348674	+	0.937244i	$0.613368\pi$
$569$	−32.1499	+	23.3582i	−1.34779	+	0.979228i	−0.999118	+	0.0419841i	$0.986632\pi$
$570$	−2.26406	+	6.96805i	−0.0948309	+	0.291860i
$571$	13.3763			0.559779			0.279890	−	0.960032i	$-0.409702\pi$
$571$	13.3763			0.559779			0.279890	+	0.960032i	$0.409702\pi$
$572$	2.90200	+	9.72639i	0.121339	+	0.406681i
$573$	−59.8972			−2.50224
$574$	−1.58605	+	4.88137i	−0.0662005	+	0.203744i
$575$	−1.48147	+	1.07635i	−0.0617816	+	0.0448870i
$576$	−3.22960	−	2.34644i	−0.134567	−	0.0977684i
$577$	6.14182	+	18.9026i	0.255688	+	0.786925i	0.993693	+	0.112131i	$0.0357676\pi$
$577$	6.14182	+	18.9026i	0.255688	+	0.786925i	−0.738006	+	0.674794i	$0.764232\pi$
$578$	−5.25184	−	16.1635i	−0.218448	−	0.672314i
$579$	−36.3165	−	26.3855i	−1.50926	−	1.09654i
$580$	−2.67733	+	1.94520i	−0.111170	+	0.0807699i
$581$	−0.943632	+	2.90420i	−0.0391485	+	0.120487i
$582$	7.25783			0.300847
$583$	−0.325792	−	0.248968i	−0.0134929	−	0.0103112i
$584$	6.98905			0.289209
$585$	3.77526	−	11.6191i	0.156088	−	0.480389i
$586$	14.2184	−	10.3302i	0.587355	−	0.426738i
$587$	−4.60014	−	3.34220i	−0.189868	−	0.137947i	0.488790	−	0.872401i	$-0.337438\pi$
$587$	−4.60014	−	3.34220i	−0.189868	−	0.137947i	−0.678658	+	0.734454i	$0.737438\pi$
$588$	−0.817115	−	2.51482i	−0.0336973	−	0.103710i
$589$	3.53253	+	10.8720i	0.145555	+	0.447973i
$590$	9.05528	+	6.57904i	0.372800	+	0.270855i
$591$	56.3134	−	40.9141i	2.31642	−	1.68298i
$592$	−1.74115	+	5.35871i	−0.0715608	+	0.220242i
$593$	28.1824			1.15731			0.578656	−	0.815571i	$-0.303577\pi$
$593$	28.1824			1.15731			0.578656	+	0.815571i	$0.303577\pi$
$594$	−2.88786	+	8.20656i	−0.118491	+	0.336719i
$595$	−0.0683587			−0.00280243
$596$	−4.53555	+	13.9590i	−0.185784	+	0.571783i
$597$	36.1803	−	26.2866i	1.48076	−	1.07584i
$598$	−4.53384	−	3.29403i	−0.185403	−	0.134703i
$599$	11.1923	+	34.4463i	0.457304	+	1.40744i	0.868409	+	0.495848i	$0.165143\pi$
$599$	11.1923	+	34.4463i	0.457304	+	1.40744i	−0.411105	+	0.911588i	$0.634857\pi$
$600$	−0.817115	−	2.51482i	−0.0333586	−	0.102667i
$601$	11.6031	+	8.43018i	0.473302	+	0.343874i	0.798727	−	0.601694i	$-0.205507\pi$
$601$	11.6031	+	8.43018i	0.473302	+	0.343874i	−0.325425	+	0.945568i	$0.605507\pi$
$602$	−2.29804	+	1.66962i	−0.0936611	+	0.0680488i
$603$	−2.72401	+	8.38364i	−0.110930	+	0.341408i
$604$	−11.0935			−0.451387
$605$	3.90144	−	10.2849i	0.158616	−	0.418140i
$606$	14.6481			0.595037
$607$	−1.09589	+	3.37280i	−0.0444808	+	0.136898i	−0.970831	−	0.239767i	$-0.922929\pi$
$607$	−1.09589	+	3.37280i	−0.0444808	+	0.136898i	0.926350	+	0.376664i	$0.122929\pi$
$608$	−2.24162	+	1.62863i	−0.0909096	+	0.0660497i
$609$	7.07951	+	5.14357i	0.286876	+	0.208428i
$610$	0.783832	+	2.41239i	0.0317364	+	0.0976746i
$611$	11.2724	+	34.6928i	0.456031	+	1.40352i
$612$	0.220771	+	0.160400i	0.00892415	+	0.00648378i
$613$	16.5302	−	12.0099i	0.667648	−	0.485075i	−0.201589	−	0.979470i	$-0.564610\pi$
$613$	16.5302	−	12.0099i	0.667648	−	0.485075i	0.869237	+	0.494395i	$0.164610\pi$
$614$	1.66261	−	5.11699i	0.0670976	−	0.206505i
$615$	13.5718			0.547266
$616$	1.10093	−	3.12857i	0.0443579	−	0.126054i
$617$	19.3755			0.780028			0.390014	−	0.920809i	$-0.372470\pi$
$617$	19.3755			0.780028			0.390014	+	0.920809i	$0.372470\pi$
$618$	2.95548	−	9.09603i	0.118887	−	0.365896i
$619$	4.85833	−	3.52978i	0.195273	−	0.141874i	−0.485853	−	0.874041i	$-0.661491\pi$
$619$	4.85833	−	3.52978i	0.195273	−	0.141874i	0.681125	+	0.732167i	$0.261491\pi$
$620$	−3.33777	−	2.42503i	−0.134048	−	0.0973916i
$621$	−1.48434	−	4.56833i	−0.0595645	−	0.183321i
$622$	5.22326	+	16.0755i	0.209433	+	0.644570i
$623$	−10.9789	−	7.97666i	−0.439862	−	0.319578i
$624$	6.54684	−	4.75656i	0.262083	−	0.190415i
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	−1.35523			−0.0541658
$627$	19.3075	+	14.7546i	0.771065	+	0.589243i
$628$	13.1941			0.526502
$629$	0.119023	−	0.366314i	0.00474575	−	0.0146059i
$630$	−3.22960	+	2.34644i	−0.128670	+	0.0934845i
$631$	−17.6308	−	12.8095i	−0.701872	−	0.509940i	0.178669	−	0.983909i	$-0.442821\pi$
$631$	−17.6308	−	12.8095i	−0.701872	−	0.509940i	−0.880541	+	0.473969i	$0.842821\pi$
$632$	−3.83620	−	11.8066i	−0.152596	−	0.469642i
$633$	13.4401	+	41.3645i	0.534198	+	1.64409i
$634$	−23.7217	−	17.2348i	−0.942110	−	0.684483i
$635$	−11.1495	+	8.10058i	−0.442454	+	0.321462i
$636$	−0.101019	+	0.310905i	−0.00400567	+	0.0123282i
$637$	3.06037			0.121256
$638$	3.13811	+	10.5178i	0.124239	+	0.416402i
$639$	54.7892			2.16743
$640$	0.309017	−	0.951057i	0.0122150	−	0.0375938i
$641$	33.1975	−	24.1194i	1.31122	−	0.952659i	0.311225	−	0.950336i	$-0.399261\pi$
$641$	33.1975	−	24.1194i	1.31122	−	0.952659i	0.999997	−	0.00232283i	$-0.000739380\pi$
$642$	14.0801	+	10.2298i	0.555696	+	0.403736i
$643$	−7.65201	−	23.5505i	−0.301766	−	0.928739i	−0.980864	−	0.194692i	$-0.937629\pi$
$643$	−7.65201	−	23.5505i	−0.301766	−	0.928739i	0.679099	−	0.734047i	$-0.262371\pi$
$644$	0.565872	+	1.74157i	0.0222985	+	0.0686276i
$645$	6.07657	+	4.41489i	0.239265	+	0.173836i
$646$	0.153234	−	0.111331i	0.00602892	−	0.00438026i
$647$	13.6308	−	41.9513i	0.535883	−	1.64928i	−0.205852	−	0.978583i	$-0.565996\pi$
$647$	13.6308	−	41.9513i	0.535883	−	1.64928i	0.741734	−	0.670694i	$-0.234004\pi$
$648$	−5.03990			−0.197986
$649$	30.5523	−	21.0870i	1.19928	−	0.827736i
$650$	3.06037			0.120037
$651$	−3.37118	+	10.3754i	−0.132127	+	0.406645i
$652$	3.00050	−	2.17999i	0.117508	−	0.0853749i
$653$	17.8215	+	12.9481i	0.697410	+	0.506698i	0.879088	−	0.476660i	$-0.158153\pi$
$653$	17.8215	+	12.9481i	0.697410	+	0.506698i	−0.181678	+	0.983358i	$0.558153\pi$
$654$	−0.939569	−	2.89169i	−0.0367400	−	0.113074i
$655$	1.51159	+	4.65219i	0.0590627	+	0.181776i
$656$	4.15234	+	3.01685i	0.162122	+	0.117788i
$657$	−22.5719	+	16.3994i	−0.880612	+	0.639802i
$658$	3.68334	−	11.3362i	0.143592	−	0.441929i
$659$	19.5066			0.759868			0.379934	−	0.925014i	$-0.375947\pi$
$659$	19.5066			0.759868			0.379934	+	0.925014i	$0.375947\pi$
$660$	−8.76738	−	0.212252i	−0.341270	−	0.00826190i
$661$	8.75637			0.340583			0.170292	−	0.985394i	$-0.445529\pi$
$661$	8.75637			0.340583			0.170292	+	0.985394i	$0.445529\pi$
$662$	2.19571	−	6.75769i	0.0853386	−	0.262645i
$663$	−0.447534	+	0.325152i	−0.0173808	+	0.0126279i
$664$	2.47046	+	1.79490i	0.0958725	+	0.0696555i
$665$	0.856222	+	2.63518i	0.0332029	+	0.102188i
$666$	−6.95068	−	21.3920i	−0.269334	−	0.828923i
$667$	−4.90273	−	3.56204i	−0.189835	−	0.137923i
$668$	7.08237	−	5.14564i	0.274025	−	0.199091i
$669$	−16.7243	+	51.4721i	−0.646598	+	1.99002i
$670$	−2.20818			−0.0853096
$671$	8.41026	+	0.203606i	0.324675	+	0.00786014i
$672$	−2.64424			−0.102004
$673$	−0.744987	+	2.29283i	−0.0287171	+	0.0883822i	−0.964388	−	0.264492i	$-0.914796\pi$
$673$	−0.744987	+	2.29283i	−0.0287171	+	0.0883822i	0.935671	+	0.352874i	$0.114796\pi$
$674$	−23.2713	+	16.9076i	−0.896378	+	0.651257i
$675$	2.12214	+	1.54182i	0.0816810	+	0.0593447i
$676$	−1.12302	−	3.45630i	−0.0431930	−	0.132934i
$677$	0.717826	+	2.20924i	0.0275883	+	0.0849080i	0.963903	−	0.266255i	$-0.0857863\pi$
$677$	0.717826	+	2.20924i	0.0275883	+	0.0849080i	−0.936314	+	0.351163i	$0.885786\pi$
$678$	−25.9994	−	18.8897i	−0.998503	−	0.725455i
$679$	2.22057	−	1.61334i	0.0852175	−	0.0619142i
$680$	−0.0211240	+	0.0650130i	−0.000810069	+	0.00249313i
$681$	−62.6792			−2.40187
$682$	−11.2615	+	7.77265i	−0.431227	+	0.297630i
$683$	−4.35856			−0.166776			−0.0833879	−	0.996517i	$-0.526574\pi$
$683$	−4.35856			−0.166776			−0.0833879	+	0.996517i	$0.526574\pi$
$684$	3.41804	−	10.5197i	0.130692	−	0.402229i
$685$	15.4165	−	11.2007i	0.589034	−	0.427959i
$686$	−0.809017	−	0.587785i	−0.0308884	−	0.0224417i
$687$	21.7654	+	66.9869i	0.830400	+	2.55571i
$688$	0.877773	+	2.70151i	0.0334648	+	0.102994i
$689$	−0.306092	−	0.222389i	−0.0116612	−	0.00847233i
$690$	3.91737	−	2.84613i	0.149132	−	0.108350i
$691$	−6.32981	+	19.4811i	−0.240797	+	0.741098i	0.755502	+	0.655146i	$0.227393\pi$
$691$	−6.32981	+	19.4811i	−0.240797	+	0.741098i	−0.996299	+	0.0859513i	$0.972607\pi$
$692$	−3.03876			−0.115516
$693$	3.78543	+	12.6873i	0.143797	+	0.481951i
$694$	−25.7893			−0.978950
$695$	2.36496	−	7.27861i	0.0897082	−	0.276093i
$696$	7.07951	−	5.14357i	0.268348	−	0.194966i
$697$	−0.283848	−	0.206228i	−0.0107515	−	0.00781144i
$698$	11.3401	+	34.9012i	0.429228	+	1.32103i
$699$	−24.7886	−	76.2916i	−0.937592	−	2.88561i
$700$	−0.809017	−	0.587785i	−0.0305780	−	0.0222162i
$701$	20.6987	−	15.0385i	0.781780	−	0.567996i	−0.123733	−	0.992316i	$-0.539487\pi$
$701$	20.6987	−	15.0385i	0.781780	−	0.567996i	0.905513	+	0.424319i	$0.139487\pi$
$702$	−2.48068	+	7.63475i	−0.0936273	+	0.288155i
$703$	−15.6120			−0.588817
$704$	−2.63524	−	2.01383i	−0.0993193	−	0.0758991i
$705$	−31.5181			−1.18704
$706$	5.24413	−	16.1398i	0.197365	−	0.607428i
$707$	4.48164	−	3.25610i	0.168549	−	0.122458i
$708$	−23.9443	−	17.3966i	−0.899883	−	0.653803i
$709$	−6.22550	−	19.1601i	−0.233803	−	0.719573i	−0.997278	−	0.0737348i	$-0.976508\pi$
$709$	−6.22550	−	19.1601i	−0.233803	−	0.719573i	0.763474	−	0.645838i	$-0.223492\pi$
$710$	4.24118	+	13.0530i	0.159169	+	0.489870i
$711$	40.0930	+	29.1292i	1.50360	+	1.09243i
$712$	−10.9789	+	7.97666i	−0.411453	+	0.298938i
$713$	2.33462	−	7.18523i	0.0874323	−	0.269089i
$714$	0.180757			0.00676465
$715$	3.36926	−	9.57456i	0.126003	−	0.358068i
$716$	−7.29987			−0.272809
$717$	8.13177	−	25.0270i	0.303686	−	0.934651i
$718$	−17.1365	+	12.4504i	−0.639529	+	0.464645i
$719$	33.4860	+	24.3290i	1.24882	+	0.907318i	0.998153	−	0.0607563i	$-0.0193512\pi$
$719$	33.4860	+	24.3290i	1.24882	+	0.907318i	0.250663	+	0.968074i	$0.419351\pi$
$720$	1.23360	+	3.79662i	0.0459735	+	0.141492i
$721$	−1.11770	−	3.43994i	−0.0416255	−	0.128110i
$722$	9.16026	+	6.65532i	0.340910	+	0.247685i
$723$	−64.5727	+	46.9148i	−2.40148	+	1.74478i
$724$	3.37913	−	10.3999i	0.125584	−	0.386509i
$725$	3.30937			0.122907
$726$	−10.3164	+	27.1957i	−0.382876	+	1.00933i
$727$	−18.3813			−0.681723			−0.340862	−	0.940113i	$-0.610719\pi$
$727$	−18.3813			−0.681723			−0.340862	+	0.940113i	$0.610719\pi$
$728$	0.945705	−	2.91058i	0.0350502	−	0.107873i
$729$	33.1112	−	24.0567i	1.22634	−	0.890988i
$730$	−5.65426	−	4.10806i	−0.209274	−	0.152046i
$731$	−0.0600035	−	0.184672i	−0.00221931	−	0.00683033i
$732$	−2.07264	−	6.37893i	−0.0766069	−	0.235772i
$733$	−38.3326	−	27.8503i	−1.41585	−	1.02867i	−0.992440	−	0.122734i	$-0.960834\pi$
$733$	−38.3326	−	27.8503i	−1.41585	−	1.02867i	−0.423408	−	0.905939i	$-0.639166\pi$
$734$	−29.5264	+	21.4522i	−1.08984	+	0.791814i
$735$	−0.817115	+	2.51482i	−0.0301397	+	0.0927606i
$736$	1.83120			0.0674989
$737$	−2.43107	+	6.90846i	−0.0895494	+	0.254476i
$738$	−20.4893			−0.754220
$739$	−11.2774	+	34.7082i	−0.414845	+	1.27676i	0.497544	+	0.867439i	$0.334235\pi$
$739$	−11.2774	+	34.7082i	−0.414845	+	1.27676i	−0.912389	+	0.409324i	$0.865765\pi$
$740$	4.55839	−	3.31186i	0.167570	−	0.121747i
$741$	18.1399	+	13.1794i	0.666387	+	0.484159i
$742$	0.0382035	+	0.117578i	0.00140249	+	0.00431643i
$743$	6.01175	+	18.5023i	0.220550	+	0.678782i	0.998713	+	0.0507200i	$0.0161516\pi$
$743$	6.01175	+	18.5023i	0.220550	+	0.678782i	−0.778163	+	0.628062i	$0.783848\pi$
$744$	8.82587	+	6.41237i	0.323572	+	0.235089i
$745$	11.8742	−	8.62714i	0.435038	−	0.316074i
$746$	−1.92535	+	5.92561i	−0.0704920	+	0.216952i
$747$	−12.1902			−0.446017
$748$	0.180142	+	0.137663i	0.00658663	+	0.00503345i
$749$	6.58182			0.240494
$750$	−0.817115	+	2.51482i	−0.0298368	+	0.0918283i
$751$	27.5796	−	20.0378i	1.00639	−	0.731188i	0.0429442	−	0.999077i	$-0.486326\pi$
$751$	27.5796	−	20.0378i	1.00639	−	0.731188i	0.963450	+	0.267890i	$0.0863262\pi$
$752$	−9.64311	−	7.00613i	−0.351648	−	0.255487i
$753$	0.956009	+	2.94229i	0.0348389	+	0.107223i
$754$	3.12968	+	9.63218i	0.113976	+	0.350783i
$755$	8.97481	+	6.52058i	0.326627	+	0.237308i
$756$	2.12214	−	1.54182i	0.0771813	−	0.0560755i
$757$	−2.61742	+	8.05559i	−0.0951318	+	0.292786i	−0.987288	−	0.158941i	$-0.949192\pi$
$757$	−2.61742	+	8.05559i	−0.0951318	+	0.292786i	0.892156	+	0.451727i	$0.149192\pi$
$758$	0.463665			0.0168411
$759$	−4.59156	−	15.3892i	−0.166663	−	0.558591i
$760$	2.77079			0.100507
$761$	4.60323	−	14.1673i	0.166867	−	0.513564i	−0.832302	−	0.554322i	$-0.812977\pi$
$761$	4.60323	−	14.1673i	0.166867	−	0.513564i	0.999169	+	0.0407586i	$0.0129774\pi$
$762$	29.4819	−	21.4199i	1.06802	−	0.775961i
$763$	−0.930257	−	0.675871i	−0.0336776	−	0.0244682i
$764$	6.99984	+	21.5433i	0.253245	+	0.779409i
$765$	−0.0843272	−	0.259532i	−0.00304885	−	0.00938341i
$766$	−24.6707	−	17.9243i	−0.891389	−	0.647632i
$767$	27.7125	−	20.1343i	1.00064	−	0.727007i
$768$	−0.817115	+	2.51482i	−0.0294851	+	0.0907458i
$769$	26.5771			0.958396			0.479198	−	0.877707i	$-0.340928\pi$
$769$	26.5771			0.958396			0.479198	+	0.877707i	$0.340928\pi$
$770$	−2.72960	+	1.88395i	−0.0983680	+	0.0678929i
$771$	2.59378			0.0934126
$772$	−5.24600	+	16.1455i	−0.188807	+	0.581090i
$773$	−19.0316	+	13.8273i	−0.684519	+	0.497332i	−0.874854	−	0.484387i	$-0.839043\pi$
$773$	−19.0316	+	13.8273i	−0.684519	+	0.497332i	0.190335	+	0.981719i	$0.439043\pi$
$774$	−9.17379	−	6.66515i	−0.329745	−	0.239574i
$775$	1.27491	+	3.92378i	0.0457963	+	0.140947i
$776$	−0.848181	−	2.61043i	−0.0304479	−	0.0937091i
$777$	−12.0535	−	8.75737i	−0.432416	−	0.314169i
$778$	11.3092	−	8.21658i	0.405453	−	0.294579i
$779$	−4.39462	+	13.5253i	−0.157454	+	0.484593i
$780$	−8.09234			−0.289752
$781$	45.5065	+	1.10168i	1.62835	+	0.0394212i
$782$	−0.125178			−0.00447637
$783$	−2.68252	+	8.25594i	−0.0958654	+	0.295043i
$784$	−0.809017	+	0.587785i	−0.0288935	+	0.0209923i
$785$	−10.6743	−	7.75530i	−0.380981	−	0.276799i
$786$	−3.99700	−	12.3015i	−0.142568	−	0.438781i
$787$	3.04634	+	9.37567i	0.108590	+	0.334206i	0.990556	−	0.137106i	$-0.0437803\pi$
$787$	3.04634	+	9.37567i	0.108590	+	0.334206i	−0.881966	+	0.471313i	$0.843780\pi$
$788$	−21.2966	−	15.4729i	−0.758661	−	0.551200i
$789$	−34.2112	+	24.8559i	−1.21795	+	0.884894i
$790$	−3.83620	+	11.8066i	−0.136486	+	0.420061i
$791$	−12.1536			−0.432133
$792$	13.2361	+	0.320437i	0.470325	+	0.0113862i
$793$	7.76271			0.275662
$794$	−3.69305	+	11.3660i	−0.131061	+	0.403365i
$795$	0.264472	−	0.192150i	0.00937985	−	0.00681486i
$796$	−13.6827	−	9.94106i	−0.484970	−	0.352352i
$797$	−11.9392	−	36.7451i	−0.422908	−	1.30158i	−0.904983	−	0.425447i	$-0.860117\pi$
$797$	−11.9392	−	36.7451i	−0.422908	−	1.30158i	0.482075	−	0.876130i	$-0.339883\pi$
$798$	−2.26406	−	6.96805i	−0.0801468	−	0.246666i
$799$	0.659190	+	0.478930i	0.0233205	+	0.0169433i
$800$	−0.809017	+	0.587785i	−0.0286031	+	0.0207813i
$801$	16.7408	−	51.5229i	0.591507	−	1.82047i
$802$	−14.4578			−0.510524
$803$	−19.0773	+	13.1670i	−0.673224	+	0.464655i
$804$	5.83897			0.205925
$805$	0.565872	−	1.74157i	0.0199444	−	0.0613824i
$806$	−10.2148	+	7.42148i	−0.359801	+	0.261411i
$807$	32.3126	+	23.4765i	1.13746	+	0.826412i
$808$	−1.71183	−	5.26848i	−0.0602221	−	0.185345i
$809$	9.56697	+	29.4441i	0.336357	+	1.03520i	0.966050	+	0.258356i	$0.0831807\pi$
$809$	9.56697	+	29.4441i	0.336357	+	1.03520i	−0.629693	+	0.776844i	$0.716819\pi$
$810$	4.07737	+	2.96238i	0.143264	+	0.104087i
$811$	39.9921	−	29.0559i	1.40431	−	1.02029i	0.410193	−	0.911999i	$-0.365461\pi$
$811$	39.9921	−	29.0559i	1.40431	−	1.02029i	0.994119	−	0.108293i	$-0.0345386\pi$
$812$	1.02265	−	3.14739i	0.0358880	−	0.110452i
$813$	1.32092			0.0463268
$814$	−5.34291	−	17.9074i	−0.187269	−	0.627653i
$815$	−3.70882			−0.129914
$816$	0.0558569	−	0.171910i	0.00195538	−	0.00601805i
$817$	−6.36740	+	4.62618i	−0.222767	+	0.161850i
$818$	2.86731	+	2.08322i	0.100253	+	0.0728383i
$819$	3.77526	+	11.6191i	0.131918	+	0.406003i
$820$	−1.58605	−	4.88137i	−0.0553873	−	0.170465i
$821$	−18.7108	−	13.5942i	−0.653012	−	0.474441i	0.211284	−	0.977425i	$-0.432236\pi$
$821$	−18.7108	−	13.5942i	−0.653012	−	0.474441i	−0.864296	+	0.502984i	$0.832236\pi$
$822$	−40.7650	+	29.6175i	−1.42184	+	1.03303i
$823$	−11.1417	+	34.2907i	−0.388376	+	1.19530i	0.545625	+	0.838030i	$0.316292\pi$
$823$	−11.1417	+	34.2907i	−0.388376	+	1.19530i	−0.934001	+	0.357270i	$0.883708\pi$
$824$	−3.61697			−0.126003
$825$	6.96820	+	5.32505i	0.242602	+	0.185395i
$826$	−11.1929			−0.389452
$827$	−3.21066	+	9.88141i	−0.111646	+	0.343610i	−0.991233	−	0.132128i	$-0.957819\pi$
$827$	−3.21066	+	9.88141i	−0.111646	+	0.343610i	0.879587	+	0.475738i	$0.157819\pi$
$828$	−5.91404	+	4.29680i	−0.205527	+	0.149324i
$829$	−30.2879	−	22.0054i	−1.05194	−	0.764280i	−0.0793608	−	0.996846i	$-0.525288\pi$
$829$	−30.2879	−	22.0054i	−1.05194	−	0.764280i	−0.972581	+	0.232566i	$0.925288\pi$
$830$	−0.943632	−	2.90420i	−0.0327540	−	0.100806i
$831$	9.07498	+	27.9299i	0.314807	+	0.968878i
$832$	−2.47589	−	1.79884i	−0.0858360	−	0.0623635i
$833$	0.0553034	−	0.0401802i	0.00191615	−	0.00139216i
$834$	−6.25353	+	19.2464i	−0.216542	+	0.666448i
$835$	−8.75429			−0.302955
$836$	3.05046	−	8.66862i	0.105502	−	0.299810i
$837$	−10.8222			−0.374069
$838$	−10.9727	+	33.7706i	−0.379047	+	1.16659i
$839$	26.4257	−	19.1994i	0.912317	−	0.662837i	−0.0292827	−	0.999571i	$-0.509322\pi$
$839$	26.4257	−	19.1994i	0.912317	−	0.662837i	0.941600	+	0.336734i	$0.109322\pi$
$840$	2.13924	+	1.55425i	0.0738106	+	0.0536266i
$841$	−5.57717	−	17.1648i	−0.192316	−	0.591888i
$842$	−8.22572	−	25.3162i	−0.283477	−	0.872453i
$843$	33.0538	+	24.0150i	1.13843	+	0.827120i
$844$	13.3069	−	9.66806i	0.458044	−	0.332788i
$845$	−1.12302	+	3.45630i	−0.0386330	+	0.118900i
$846$	47.5829			1.63593
$847$	2.88896	+	10.6139i	0.0992660	+	0.364696i
$848$	0.123629			0.00424544
$849$	−11.6961	+	35.9970i	−0.401411	+	1.23541i
$850$	0.0553034	−	0.0401802i	0.00189689	−	0.00137817i
$851$	8.34732	+	6.06468i	0.286142	+	0.207895i
$852$	−11.2147	−	34.5153i	−0.384209	−	1.18247i
$853$	−6.62142	−	20.3786i	−0.226713	−	0.697751i	−0.998113	−	0.0614007i	$-0.980443\pi$
$853$	−6.62142	−	20.3786i	−0.226713	−	0.697751i	0.771400	−	0.636350i	$-0.219557\pi$
$854$	−2.05210	−	1.49094i	−0.0702213	−	0.0510188i
$855$	−8.94856	+	6.50151i	−0.306034	+	0.222347i
$856$	2.03389	−	6.25968i	0.0695171	−	0.213951i
$857$	−46.6805			−1.59457			−0.797287	−	0.603600i	$-0.793732\pi$
$857$	−46.6805			−1.59457			−0.797287	+	0.603600i	$0.793732\pi$
$858$	−8.90913	+	25.3174i	−0.304153	+	0.864323i
$859$	34.0149			1.16057			0.580287	−	0.814412i	$-0.302940\pi$
$859$	34.0149			1.16057			0.580287	+	0.814412i	$0.302940\pi$
$860$	0.877773	−	2.70151i	0.0299318	−	0.0921207i
$861$	−10.9798	+	7.97728i	−0.374190	+	0.271865i
$862$	−21.0699	−	15.3082i	−0.717644	−	0.521399i
$863$	−1.71772	−	5.28659i	−0.0584718	−	0.179958i	0.917555	−	0.397610i	$-0.130160\pi$
$863$	−1.71772	−	5.28659i	−0.0584718	−	0.179958i	−0.976026	+	0.217652i	$0.930160\pi$
$864$	−0.810584	−	2.49472i	−0.0275766	−	0.0848721i
$865$	2.45841	+	1.78614i	0.0835885	+	0.0607306i
$866$	−1.36900	+	0.994636i	−0.0465205	+	0.0337991i
$867$	13.8871	−	42.7402i	0.471632	−	1.45153i
$868$	4.12571			0.140036
$869$	32.7144	+	25.0001i	1.10976	+	0.848072i
$870$	−8.75076			−0.296679
$871$	−2.08829	+	6.42710i	−0.0707590	+	0.217774i
$872$	−0.930257	+	0.675871i	−0.0315025	+	0.0228879i
$873$	8.86452	+	6.44045i	0.300018	+	0.217976i
$874$	1.56791	+	4.82554i	0.0530355	+	0.163226i
$875$	0.309017	+	0.951057i	0.0104467	+	0.0321516i
$876$	14.9512	+	10.8627i	0.505155	+	0.367017i
$877$	14.8198	−	10.7672i	0.500429	−	0.363583i	−0.308752	−	0.951143i	$-0.599911\pi$
$877$	14.8198	−	10.7672i	0.500429	−	0.363583i	0.809181	+	0.587560i	$0.199911\pi$
$878$	3.95744	−	12.1797i	0.133557	−	0.411047i
$879$	46.4721			1.56747
$880$	0.948252	+	3.17818i	0.0319656	+	0.107136i
$881$	−0.0269589			−0.000908270			−0.000454135	−	1.00000i	$-0.500145\pi$
$881$	−0.0269589			−0.000908270			−0.000454135		1.00000i	$0.500145\pi$
$882$	1.23360	−	3.79662i	0.0415374	−	0.127839i
$883$	4.27433	−	3.10548i	0.143843	−	0.104508i	−0.513537	−	0.858068i	$-0.671665\pi$
$883$	4.27433	−	3.10548i	0.143843	−	0.104508i	0.657379	+	0.753560i	$0.271665\pi$
$884$	0.169248	+	0.122966i	0.00569244	+	0.00413580i
$885$	9.14592	+	28.1482i	0.307437	+	0.946193i
$886$	0.217671	+	0.669922i	0.00731280	+	0.0225065i
$887$	−32.1629	−	23.3677i	−1.07992	−	0.784611i	−0.102255	−	0.994758i	$-0.532606\pi$
$887$	−32.1629	−	23.3677i	−1.07992	−	0.784611i	−0.977670	+	0.210147i	$0.932606\pi$
$888$	−12.0535	+	8.75737i	−0.404488	+	0.293878i
$889$	4.25873	−	13.1070i	0.142833	−	0.439595i
$890$	13.5707			0.454891
$891$	13.7569	−	9.49494i	0.460874	−	0.318092i
$892$	20.4675			0.685302
$893$	10.2058	−	31.4101i	0.341523	−	1.05110i
$894$	−31.3983	+	22.8122i	−1.05012	+	0.762955i
$895$	5.90572	+	4.29075i	0.197406	+	0.143424i
$896$	0.309017	+	0.951057i	0.0103235	+	0.0317726i
$897$	−4.57923	−	14.0934i	−0.152896	−	0.470565i
$898$	14.8912	+	10.8191i	0.496927	+	0.361038i
$899$	−11.0459	+	8.02532i	−0.368402	+	0.267659i
$900$	1.23360	−	3.79662i	0.0411199	−	0.126554i
$901$	−0.00845113			−0.000281548
$902$	−17.0178	−	0.411989i	−0.566632	−	0.0137177i
$903$	−7.51106			−0.249952
$904$	−3.75567	+	11.5588i	−0.124912	+	0.384439i
$905$	−8.84668	+	6.42749i	−0.294074	+	0.213657i
$906$	−23.7315	−	17.2420i	−0.788428	−	0.572826i
$907$	−1.73541	−	5.34105i	−0.0576234	−	0.177347i	0.918102	−	0.396344i	$-0.129721\pi$
$907$	−1.73541	−	5.34105i	−0.0576234	−	0.177347i	−0.975725	+	0.218998i	$0.929721\pi$
$908$	7.32496	+	22.5439i	0.243087	+	0.748145i
$909$	17.8907	+	12.9984i	0.593398	+	0.431129i
$910$	−2.47589	+	1.79884i	−0.0820749	+	0.0596309i
$911$	−8.69844	+	26.7710i	−0.288192	+	0.886964i	0.697232	+	0.716846i	$0.254415\pi$
$911$	−8.69844	+	26.7710i	−0.288192	+	0.886964i	−0.985424	+	0.170118i	$0.945585\pi$
$912$	−7.32664			−0.242609
$913$	−10.1249	−	0.245116i	−0.335084	−	0.00811215i
$914$	16.9955			0.562161
$915$	−2.07264	+	6.37893i	−0.0685193	+	0.210881i
$916$	21.5496	−	15.6567i	0.712020	−	0.517313i
$917$	−3.95739	−	2.87521i	−0.130685	−	0.0949479i
$918$	0.0554104	+	0.170536i	0.00182882	+	0.00562852i
$919$	14.7101	+	45.2732i	0.485243	+	1.49342i	0.831629	+	0.555332i	$0.187409\pi$
$919$	14.7101	+	45.2732i	0.485243	+	1.49342i	−0.346386	+	0.938092i	$0.612591\pi$
$920$	−1.48147	−	1.07635i	−0.0488427	−	0.0354863i
$921$	11.5098	−	8.36235i	0.379260	−	0.275549i
$922$	4.11846	−	12.6753i	0.135634	−	0.417439i
$923$	42.0027			1.38254
$924$	7.21772	−	4.98162i	0.237446	−	0.163883i
$925$	−5.63448			−0.185261
$926$	−10.8098	+	33.2693i	−0.355233	+	1.09330i
$927$	11.6814	−	8.48701i	0.383666	−	0.278750i
$928$	−2.67733	−	1.94520i	−0.0878878	−	0.0638542i
$929$	−11.7997	−	36.3159i	−0.387137	−	1.19149i	−0.934918	−	0.354863i	$-0.884527\pi$
$929$	−11.7997	−	36.3159i	−0.387137	−	1.19149i	0.547781	−	0.836622i	$-0.315473\pi$
$930$	−3.37118	−	10.3754i	−0.110545	−	0.340224i
$931$	−2.24162	−	1.62863i	−0.0734661	−	0.0533762i
$932$	−24.5430	+	17.8315i	−0.803931	+	0.584090i
$933$	−13.8115	+	42.5076i	−0.452170	+	1.39163i
$934$	−3.57861			−0.117096
$935$	−0.0648213	−	0.217256i	−0.00211988	−	0.00710504i
$936$	12.2170			0.399325
$937$	−0.122864	+	0.378135i	−0.00401378	+	0.0123531i	−0.953043	−	0.302834i	$-0.902067\pi$
$937$	−0.122864	+	0.378135i	−0.00401378	+	0.0123531i	0.949030	+	0.315187i	$0.102067\pi$
$938$	1.78646	−	1.29794i	0.0583299	−	0.0423792i
$939$	−2.89915	−	2.10636i	−0.0946102	−	0.0687383i
$940$	3.68334	+	11.3362i	0.120137	+	0.369745i
$941$	−2.09448	−	6.44616i	−0.0682782	−	0.210139i	0.911096	−	0.412195i	$-0.135238\pi$
$941$	−2.09448	−	6.44616i	−0.0682782	−	0.210139i	−0.979374	+	0.202056i	$0.935238\pi$
$942$	28.2253	+	20.5069i	0.919630	+	0.668151i
$943$	7.60376	−	5.52445i	0.247612	−	0.179901i
$944$	−3.45881	+	10.6451i	−0.112575	+	0.346469i
$945$	−2.62310			−0.0853296
$946$	−7.48549	−	5.72036i	−0.243374	−	0.185985i
$947$	−10.5378			−0.342432			−0.171216	−	0.985234i	$-0.554770\pi$
$947$	−10.5378			−0.342432			−0.171216	+	0.985234i	$0.554770\pi$
$948$	10.1438	−	31.2195i	0.329457	−	1.01396i
$949$	−17.3041	+	12.5722i	−0.561715	+	0.408110i
$950$	−2.24162	−	1.62863i	−0.0727277	−	0.0528398i
$951$	−23.9592	−	73.7388i	−0.776929	−	2.39114i
$952$	−0.0211240	−	0.0650130i	−0.000684633	−	0.00210708i
$953$	7.64368	+	5.55346i	0.247603	+	0.179894i	0.704664	−	0.709541i	$-0.251098\pi$
$953$	7.64368	+	5.55346i	0.247603	+	0.179894i	−0.457061	+	0.889435i	$0.651098\pi$
$954$	−0.399273	+	0.290089i	−0.0129269	+	0.00939197i
$955$	6.99984	−	21.5433i	0.226510	−	0.697125i
$956$	−9.95180			−0.321864
$957$	−9.63401	+	27.3774i	−0.311423	+	0.884984i
$958$	18.3300			0.592215
$959$	−5.88858	+	18.1232i	−0.190152	+	0.585228i
$960$	2.13924	−	1.55425i	0.0690435	−	0.0501631i
$961$	11.3088	+	8.21636i	0.364802	+	0.265044i
$962$	−5.32856	−	16.3996i	−0.171800	−	0.528745i
$963$	8.11932	+	24.9887i	0.261641	+	0.805249i
$964$	24.4201	+	17.7423i	0.786519	+	0.571440i
$965$	13.7342	−	9.97848i	0.442119	−	0.321218i
$966$	−1.49630	+	4.60514i	−0.0481427	+	0.148168i
$967$	47.0752			1.51384			0.756918	−	0.653509i	$-0.226704\pi$
$967$	47.0752			1.51384			0.756918	+	0.653509i	$0.226704\pi$
$968$	10.9871	+	0.532292i	0.353139	+	0.0171085i
$969$	0.500840			0.0160893
$970$	−0.848181	+	2.61043i	−0.0272334	+	0.0838159i
$971$	−13.9160	+	10.1106i	−0.446587	+	0.324464i	−0.788247	−	0.615359i	$-0.789011\pi$
$971$	−13.9160	+	10.1106i	−0.446587	+	0.324464i	0.341660	+	0.939824i	$0.389011\pi$
$972$	−17.1479	−	12.4587i	−0.550021	−	0.399613i
$973$	2.36496	+	7.27861i	0.0758173	+	0.233342i
$974$	0.150504	+	0.463204i	0.00482246	+	0.0148420i
$975$	6.54684	+	4.75656i	0.209667	+	0.152332i
$976$	−2.05210	+	1.49094i	−0.0656860	+	0.0477237i
$977$	−2.08833	+	6.42722i	−0.0668116	+	0.205625i	−0.978889	−	0.204394i	$-0.934478\pi$
$977$	−2.08833	+	6.42722i	−0.0668116	+	0.205625i	0.912077	+	0.410019i	$0.134478\pi$
$978$	9.80700			0.313593
$979$	14.9405	−	42.4569i	0.477499	−	1.35693i
$980$	1.00000			0.0319438
$981$	1.41847	−	4.36559i	0.0452881	−	0.139382i
$982$	−4.92827	+	3.58060i	−0.157267	+	0.114261i
$983$	36.7956	+	26.7336i	1.17360	+	0.852669i	0.991435	−	0.130600i	$-0.0416903\pi$
$983$	36.7956	+	26.7336i	1.17360	+	0.852669i	0.182162	+	0.983268i	$0.441690\pi$
$984$	4.19390	+	12.9075i	0.133697	+	0.411476i
$985$	8.13459	+	25.0357i	0.259190	+	0.797703i
$986$	0.183019	+	0.132971i	0.00582852	+	0.00423466i
$987$	25.4987	−	18.5259i	0.811632	−	0.589685i
$988$	2.62035	−	8.06462i	0.0833645	−	0.256570i
$989$	5.20158			0.165401
$990$	−10.5199	−	8.03923i	−0.334344	−	0.255503i
$991$	−11.7391			−0.372906			−0.186453	−	0.982464i	$-0.559699\pi$
$991$	−11.7391			−0.372906			−0.186453	+	0.982464i	$0.559699\pi$
$992$	1.27491	−	3.92378i	0.0404786	−	0.124580i
$993$	15.2002	−	11.0436i	0.482365	−	0.350459i
$994$	−11.1035	−	8.06720i	−0.352183	−	0.255876i
$995$	5.22632	+	16.0850i	0.165686	+	0.509928i
$996$	2.49519	+	7.67941i	0.0790632	+	0.243331i
$997$	13.8846	+	10.0878i	0.439730	+	0.319482i	0.785528	−	0.618827i	$-0.212392\pi$
$997$	13.8846	+	10.0878i	0.439730	+	0.319482i	−0.345798	+	0.938309i	$0.612392\pi$
$998$	−34.2328	+	24.8716i	−1.08362	+	0.787297i
$999$	4.56722	−	14.0565i	0.144500	−	0.444726i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.i.141.3	yes	12
11.4	even	5		8470.2.a.de.1.2		6
11.5	even	5	inner	770.2.n.i.71.3	✓	12
11.7	odd	10		8470.2.a.cy.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.i.71.3	✓	12	11.5	even	5	inner
770.2.n.i.141.3	yes	12	1.1	even	1	trivial
8470.2.a.cy.1.2		6	11.7	odd	10
8470.2.a.de.1.2		6	11.4	even	5

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 - 0.951057i) q^{2} +(2.13924 - 1.55425i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-0.817115 - 2.51482i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(1.23360 - 3.79662i) q^{9} +O(q^{10})\)	\(q+(0.309017 - 0.951057i) q^{2} +(2.13924 - 1.55425i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-0.817115 - 2.51482i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(1.23360 - 3.79662i) q^{9} +1.00000 q^{10} +(1.10093 - 3.12857i) q^{11} -2.64424 q^{12} +(0.945705 - 2.91058i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(2.13924 + 1.55425i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.0211240 - 0.0650130i) q^{17} +(-3.22960 - 2.34644i) q^{18} +(-2.24162 + 1.62863i) q^{19} +(0.309017 - 0.951057i) q^{20} -2.64424 q^{21} +(-2.63524 - 2.01383i) q^{22} +1.83120 q^{23} +(-0.817115 + 2.51482i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(-2.47589 - 1.79884i) q^{26} +(-0.810584 - 2.49472i) q^{27} +(0.309017 + 0.951057i) q^{28} +(-2.67733 - 1.94520i) q^{29} +(2.13924 - 1.55425i) q^{30} +(1.27491 - 3.92378i) q^{31} +1.00000 q^{32} +(-2.50741 - 8.40387i) q^{33} -0.0683587 q^{34} +(0.309017 - 0.951057i) q^{35} +(-3.22960 + 2.34644i) q^{36} +(4.55839 + 3.31186i) q^{37} +(0.856222 + 2.63518i) q^{38} +(-2.50067 - 7.69627i) q^{39} +(-0.809017 - 0.587785i) q^{40} +(4.15234 - 3.01685i) q^{41} +(-0.817115 + 2.51482i) q^{42} +2.84053 q^{43} +(-2.72960 + 1.88395i) q^{44} +3.99201 q^{45} +(0.565872 - 1.74157i) q^{46} +(-9.64311 + 7.00613i) q^{47} +(2.13924 + 1.55425i) q^{48} +(0.309017 + 0.951057i) q^{49} +(0.309017 + 0.951057i) q^{50} +(-0.146235 - 0.106246i) q^{51} +(-2.47589 + 1.79884i) q^{52} +(0.0382035 - 0.117578i) q^{53} -2.62310 q^{54} +(3.31565 + 0.0802696i) q^{55} +1.00000 q^{56} +(-2.26406 + 6.96805i) q^{57} +(-2.67733 + 1.94520i) q^{58} +(9.05528 + 6.57904i) q^{59} +(-0.817115 - 2.51482i) q^{60} +(0.783832 + 2.41239i) q^{61} +(-3.33777 - 2.42503i) q^{62} +(-3.22960 + 2.34644i) q^{63} +(0.309017 - 0.951057i) q^{64} +3.06037 q^{65} +(-8.76738 - 0.212252i) q^{66} -2.20818 q^{67} +(-0.0211240 + 0.0650130i) q^{68} +(3.91737 - 2.84613i) q^{69} +(-0.809017 - 0.587785i) q^{70} +(4.24118 + 13.0530i) q^{71} +(1.23360 + 3.79662i) q^{72} +(-5.65426 - 4.10806i) q^{73} +(4.55839 - 3.31186i) q^{74} +(-0.817115 + 2.51482i) q^{75} +2.77079 q^{76} +(-2.72960 + 1.88395i) q^{77} -8.09234 q^{78} +(-3.83620 + 11.8066i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(4.07737 + 2.96238i) q^{81} +(-1.58605 - 4.88137i) q^{82} +(-0.943632 - 2.90420i) q^{83} +(2.13924 + 1.55425i) q^{84} +(0.0553034 - 0.0401802i) q^{85} +(0.877773 - 2.70151i) q^{86} -8.75076 q^{87} +(0.948252 + 3.17818i) q^{88} +13.5707 q^{89} +(1.23360 - 3.79662i) q^{90} +(-2.47589 + 1.79884i) q^{91} +(-1.48147 - 1.07635i) q^{92} +(-3.37118 - 10.3754i) q^{93} +(3.68334 + 11.3362i) q^{94} +(-2.24162 - 1.62863i) q^{95} +(2.13924 - 1.55425i) q^{96} +(-0.848181 + 2.61043i) q^{97} +1.00000 q^{98} +(-10.5199 - 8.03923i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} + 2 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} - 15 q^{9}+O(q^{10}) \) 12 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 - 15 * q^9	\( 12 q - 3 q^{2} + 2 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{7} - 3 q^{8} - 15 q^{9} + 12 q^{10} + q^{11} + 2 q^{12} - 6 q^{13} - 3 q^{14} + 2 q^{15} - 3 q^{16} - 6 q^{17} - 13 q^{19} - 3 q^{20} + 2 q^{21} + q^{22} - 12 q^{23} - 3 q^{24} - 3 q^{25} + 4 q^{26} - 7 q^{27} - 3 q^{28} - 26 q^{29} + 2 q^{30} + 12 q^{32} - 15 q^{33} + 14 q^{34} - 3 q^{35} - 18 q^{37} + 2 q^{38} - 40 q^{39} - 3 q^{40} + 16 q^{41} - 3 q^{42} + 38 q^{43} + 6 q^{44} + 30 q^{45} + 8 q^{46} - 26 q^{47} + 2 q^{48} - 3 q^{49} - 3 q^{50} - 13 q^{51} + 4 q^{52} + 8 q^{54} + 11 q^{55} + 12 q^{56} - 41 q^{57} - 26 q^{58} + 21 q^{59} - 3 q^{60} + 4 q^{61} - 3 q^{64} + 4 q^{65} - 30 q^{66} + 10 q^{67} - 6 q^{68} + 18 q^{69} - 3 q^{70} - 4 q^{71} - 15 q^{72} - 14 q^{73} - 18 q^{74} - 3 q^{75} + 22 q^{76} + 6 q^{77} + 40 q^{78} - 2 q^{79} - 3 q^{80} + 26 q^{81} - 29 q^{82} + 35 q^{83} + 2 q^{84} - q^{85} - 37 q^{86} + 28 q^{87} - 19 q^{88} + 2 q^{89} - 15 q^{90} + 4 q^{91} - 2 q^{92} + 6 q^{93} + 4 q^{94} - 13 q^{95} + 2 q^{96} + 19 q^{97} + 12 q^{98} - 81 q^{99}+O(q^{100}) \) 12 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^7 - 3 * q^8 - 15 * q^9 + 12 * q^10 + q^11 + 2 * q^12 - 6 * q^13 - 3 * q^14 + 2 * q^15 - 3 * q^16 - 6 * q^17 - 13 * q^19 - 3 * q^20 + 2 * q^21 + q^22 - 12 * q^23 - 3 * q^24 - 3 * q^25 + 4 * q^26 - 7 * q^27 - 3 * q^28 - 26 * q^29 + 2 * q^30 + 12 * q^32 - 15 * q^33 + 14 * q^34 - 3 * q^35 - 18 * q^37 + 2 * q^38 - 40 * q^39 - 3 * q^40 + 16 * q^41 - 3 * q^42 + 38 * q^43 + 6 * q^44 + 30 * q^45 + 8 * q^46 - 26 * q^47 + 2 * q^48 - 3 * q^49 - 3 * q^50 - 13 * q^51 + 4 * q^52 + 8 * q^54 + 11 * q^55 + 12 * q^56 - 41 * q^57 - 26 * q^58 + 21 * q^59 - 3 * q^60 + 4 * q^61 - 3 * q^64 + 4 * q^65 - 30 * q^66 + 10 * q^67 - 6 * q^68 + 18 * q^69 - 3 * q^70 - 4 * q^71 - 15 * q^72 - 14 * q^73 - 18 * q^74 - 3 * q^75 + 22 * q^76 + 6 * q^77 + 40 * q^78 - 2 * q^79 - 3 * q^80 + 26 * q^81 - 29 * q^82 + 35 * q^83 + 2 * q^84 - q^85 - 37 * q^86 + 28 * q^87 - 19 * q^88 + 2 * q^89 - 15 * q^90 + 4 * q^91 - 2 * q^92 + 6 * q^93 + 4 * q^94 - 13 * q^95 + 2 * q^96 + 19 * q^97 + 12 * q^98 - 81 * q^99

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