LMFDB - Embedded newform 770.2.n.k.631.1

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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 18 x^{14} - 35 x^{13} + 89 x^{12} - 185 x^{11} + 837 x^{10} - 1660 x^{9} + 4196 x^{8} + \cdots + 25 $ x^16 - 5x^15 + 18x^14 - 35x^13 + 89x^12 - 185x^11 + 837x^10 - 1660x^9 + 4196x^8 - 8420x^7 + 13485x^6 - 14630x^5 + 11615x^4 - 5200x^3 + 1425x^2 - 225*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			631.1
Root			$0.897614 + 2.76257i$ of defining polynomial
Character	$\chi$	$=$	770.631
Dual form			770.2.n.k.421.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-0.897614 + 2.76257i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(2.34998 - 1.70736i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-4.39904 - 3.19609i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.897614 + 2.76257i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(2.34998 - 1.70736i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-4.39904 - 3.19609i) q^{9} -1.00000 q^{10} +(3.20987 + 0.834702i) q^{11} -2.90474 q^{12} +(5.26686 + 3.82660i) q^{13} +(-0.309017 + 0.951057i) q^{14} +(0.897614 + 2.76257i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-5.72647 + 4.16052i) q^{17} +(1.68028 + 5.17138i) q^{18} +(1.22828 - 3.78025i) q^{19} +(0.809017 + 0.587785i) q^{20} +2.90474 q^{21} +(-2.10621 - 2.56200i) q^{22} +9.39994 q^{23} +(2.34998 + 1.70736i) q^{24} +(0.309017 - 0.951057i) q^{25} +(-2.01176 - 6.19157i) q^{26} +(5.72812 - 4.16172i) q^{27} +(0.809017 - 0.587785i) q^{28} +(0.364402 + 1.12151i) q^{29} +(0.897614 - 2.76257i) q^{30} +(1.03837 + 0.754419i) q^{31} +1.00000 q^{32} +(-5.18715 + 8.11826i) q^{33} +7.07831 q^{34} +(-0.809017 - 0.587785i) q^{35} +(1.68028 - 5.17138i) q^{36} +(-0.311511 - 0.958733i) q^{37} +(-3.21567 + 2.33632i) q^{38} +(-15.2989 + 11.1153i) q^{39} +(-0.309017 - 0.951057i) q^{40} +(-1.67841 + 5.16560i) q^{41} +(-2.34998 - 1.70736i) q^{42} -11.2003 q^{43} +(0.198055 + 3.31071i) q^{44} -5.43751 q^{45} +(-7.60471 - 5.52514i) q^{46} +(-3.52015 + 10.8339i) q^{47} +(-0.897614 - 2.76257i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-0.809017 + 0.587785i) q^{50} +(-6.35359 - 19.5543i) q^{51} +(-2.01176 + 6.19157i) q^{52} +(6.27479 + 4.55890i) q^{53} -7.08034 q^{54} +(3.08747 - 1.21143i) q^{55} -1.00000 q^{56} +(9.34069 + 6.78641i) q^{57} +(0.364402 - 1.12151i) q^{58} +(-1.74470 - 5.36963i) q^{59} +(-2.34998 + 1.70736i) q^{60} +(-5.12643 + 3.72457i) q^{61} +(-0.396621 - 1.22068i) q^{62} +(-1.68028 + 5.17138i) q^{63} +(-0.809017 - 0.587785i) q^{64} +6.51020 q^{65} +(8.96829 - 3.51888i) q^{66} +3.88122 q^{67} +(-5.72647 - 4.16052i) q^{68} +(-8.43751 + 25.9680i) q^{69} +(0.309017 + 0.951057i) q^{70} +(0.210285 - 0.152781i) q^{71} +(-4.39904 + 3.19609i) q^{72} +(1.49096 + 4.58872i) q^{73} +(-0.311511 + 0.958733i) q^{74} +(2.34998 + 1.70736i) q^{75} +3.97479 q^{76} +(-0.198055 - 3.31071i) q^{77} +18.9104 q^{78} +(-11.6035 - 8.43046i) q^{79} +(-0.309017 + 0.951057i) q^{80} +(1.31456 + 4.04581i) q^{81} +(4.39413 - 3.19252i) q^{82} +(-3.71745 + 2.70088i) q^{83} +(0.897614 + 2.76257i) q^{84} +(-2.18732 + 6.73187i) q^{85} +(9.06122 + 6.58336i) q^{86} -3.42535 q^{87} +(1.78575 - 2.79483i) q^{88} -1.43088 q^{89} +(4.39904 + 3.19609i) q^{90} +(2.01176 - 6.19157i) q^{91} +(2.90474 + 8.93987i) q^{92} +(-3.01619 + 2.19139i) q^{93} +(9.21588 - 6.69573i) q^{94} +(-1.22828 - 3.78025i) q^{95} +(-0.897614 + 2.76257i) q^{96} +(6.96317 + 5.05904i) q^{97} +1.00000 q^{98} +(-11.4526 - 13.9309i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} - 5 q^{3} - 4 q^{4} + 4 q^{5} + 5 q^{6} + 4 q^{7} - 4 q^{8} + q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 - 5 * q^3 - 4 * q^4 + 4 * q^5 + 5 * q^6 + 4 * q^7 - 4 * q^8 + q^9	\( 16 q - 4 q^{2} - 5 q^{3} - 4 q^{4} + 4 q^{5} + 5 q^{6} + 4 q^{7} - 4 q^{8} + q^{9} - 16 q^{10} - 2 q^{11} + 8 q^{13} + 4 q^{14} + 5 q^{15} - 4 q^{16} - 13 q^{17} - 9 q^{18} + 15 q^{19} + 4 q^{20} - 2 q^{22} + 20 q^{23} + 5 q^{24} - 4 q^{25} - 7 q^{26} + 10 q^{27} + 4 q^{28} - 14 q^{29} + 5 q^{30} - 6 q^{31} + 16 q^{32} - 25 q^{33} + 12 q^{34} - 4 q^{35} - 9 q^{36} + 28 q^{37} - 20 q^{38} + 15 q^{39} + 4 q^{40} + 2 q^{41} - 5 q^{42} - 10 q^{43} + 3 q^{44} - 16 q^{45} - 10 q^{46} - 10 q^{47} - 5 q^{48} - 4 q^{49} - 4 q^{50} - 42 q^{51} - 7 q^{52} - 2 q^{53} - 3 q^{55} - 16 q^{56} + 21 q^{57} - 14 q^{58} + 7 q^{59} - 5 q^{60} + 4 q^{61} + 14 q^{62} + 9 q^{63} - 4 q^{64} + 2 q^{65} - 10 q^{66} + 66 q^{67} - 13 q^{68} - 64 q^{69} - 4 q^{70} + 2 q^{71} + q^{72} + 12 q^{73} + 28 q^{74} + 5 q^{75} + 10 q^{76} - 3 q^{77} + 70 q^{78} + 2 q^{79} + 4 q^{80} - 30 q^{81} - 13 q^{82} - 5 q^{83} + 5 q^{84} - 7 q^{85} + 5 q^{86} - 24 q^{87} - 2 q^{88} + 2 q^{89} - q^{90} + 7 q^{91} - 38 q^{93} + 25 q^{94} - 15 q^{95} - 5 q^{96} + 22 q^{97} + 16 q^{98} - 18 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 5 * q^3 - 4 * q^4 + 4 * q^5 + 5 * q^6 + 4 * q^7 - 4 * q^8 + q^9 - 16 * q^10 - 2 * q^11 + 8 * q^13 + 4 * q^14 + 5 * q^15 - 4 * q^16 - 13 * q^17 - 9 * q^18 + 15 * q^19 + 4 * q^20 - 2 * q^22 + 20 * q^23 + 5 * q^24 - 4 * q^25 - 7 * q^26 + 10 * q^27 + 4 * q^28 - 14 * q^29 + 5 * q^30 - 6 * q^31 + 16 * q^32 - 25 * q^33 + 12 * q^34 - 4 * q^35 - 9 * q^36 + 28 * q^37 - 20 * q^38 + 15 * q^39 + 4 * q^40 + 2 * q^41 - 5 * q^42 - 10 * q^43 + 3 * q^44 - 16 * q^45 - 10 * q^46 - 10 * q^47 - 5 * q^48 - 4 * q^49 - 4 * q^50 - 42 * q^51 - 7 * q^52 - 2 * q^53 - 3 * q^55 - 16 * q^56 + 21 * q^57 - 14 * q^58 + 7 * q^59 - 5 * q^60 + 4 * q^61 + 14 * q^62 + 9 * q^63 - 4 * q^64 + 2 * q^65 - 10 * q^66 + 66 * q^67 - 13 * q^68 - 64 * q^69 - 4 * q^70 + 2 * q^71 + q^72 + 12 * q^73 + 28 * q^74 + 5 * q^75 + 10 * q^76 - 3 * q^77 + 70 * q^78 + 2 * q^79 + 4 * q^80 - 30 * q^81 - 13 * q^82 - 5 * q^83 + 5 * q^84 - 7 * q^85 + 5 * q^86 - 24 * q^87 - 2 * q^88 + 2 * q^89 - q^90 + 7 * q^91 - 38 * q^93 + 25 * q^94 - 15 * q^95 - 5 * q^96 + 22 * q^97 + 16 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−0.897614	+	2.76257i	−0.518238	+	1.59497i	0.259075	+	0.965857i	$0.416582\pi$
$3$	−0.897614	+	2.76257i	−0.518238	+	1.59497i	−0.777313	+	0.629114i	$0.783418\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$6$	2.34998	−	1.70736i	0.959377	−	0.697028i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	−4.39904	−	3.19609i	−1.46635	−	1.06536i
$10$	−1.00000			−0.316228
$11$	3.20987	+	0.834702i	0.967813	+	0.251672i
$11$	3.20987	+	0.834702i	0.967813	+	0.251672i
$12$	−2.90474			−0.838526
$13$	5.26686	+	3.82660i	1.46076	+	1.06131i	0.983163	+	0.182731i	$0.0584938\pi$
$13$	5.26686	+	3.82660i	1.46076	+	1.06131i	0.477602	+	0.878576i	$0.341506\pi$
$14$	−0.309017	+	0.951057i	−0.0825883	+	0.254181i
$15$	0.897614	+	2.76257i	0.231763	+	0.713293i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−5.72647	+	4.16052i	−1.38887	+	1.00908i	−0.392885	+	0.919587i	$0.628523\pi$
$17$	−5.72647	+	4.16052i	−1.38887	+	1.00908i	−0.995988	+	0.0894880i	$0.971477\pi$
$18$	1.68028	+	5.17138i	0.396047	+	1.21891i
$19$	1.22828	−	3.78025i	0.281786	−	0.867249i	−0.705557	−	0.708653i	$-0.749303\pi$
$19$	1.22828	−	3.78025i	0.281786	−	0.867249i	0.987344	−	0.158596i	$-0.0506967\pi$
$20$	0.809017	+	0.587785i	0.180902	+	0.131433i
$21$	2.90474			0.633866
$22$	−2.10621	−	2.56200i	−0.449046	−	0.546221i
$23$	9.39994			1.96002			0.980011	−	0.198943i	$-0.0637509\pi$
$23$	9.39994			1.96002			0.980011	+	0.198943i	$0.0637509\pi$
$24$	2.34998	+	1.70736i	0.479688	+	0.348514i
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	−2.01176	−	6.19157i	−0.394539	−	1.21427i
$27$	5.72812	−	4.16172i	1.10238	−	0.800924i
$28$	0.809017	−	0.587785i	0.152890	−	0.111081i
$29$	0.364402	+	1.12151i	0.0676677	+	0.208260i	0.979173	−	0.203029i	$-0.0650787\pi$
$29$	0.364402	+	1.12151i	0.0676677	+	0.208260i	−0.911505	+	0.411289i	$0.865079\pi$
$30$	0.897614	−	2.76257i	0.163881	−	0.504374i
$31$	1.03837	+	0.754419i	0.186496	+	0.135498i	0.677116	−	0.735876i	$-0.263230\pi$
$31$	1.03837	+	0.754419i	0.186496	+	0.135498i	−0.490620	+	0.871374i	$0.663230\pi$
$32$	1.00000			0.176777
$33$	−5.18715	+	8.11826i	−0.902967	+	1.41321i
$34$	7.07831			1.21392
$35$	−0.809017	−	0.587785i	−0.136749	−	0.0993538i
$36$	1.68028	−	5.17138i	0.280047	−	0.861897i
$37$	−0.311511	−	0.958733i	−0.0512121	−	0.157615i	0.922180	−	0.386762i	$-0.126406\pi$
$37$	−0.311511	−	0.958733i	−0.0512121	−	0.157615i	−0.973392	+	0.229147i	$0.926406\pi$
$38$	−3.21567	+	2.33632i	−0.521651	+	0.379002i
$39$	−15.2989	+	11.1153i	−2.44978	+	1.77987i
$40$	−0.309017	−	0.951057i	−0.0488599	−	0.150375i
$41$	−1.67841	+	5.16560i	−0.262123	+	0.806732i	0.730219	+	0.683213i	$0.239418\pi$
$41$	−1.67841	+	5.16560i	−0.262123	+	0.806732i	−0.992342	+	0.123519i	$0.960582\pi$
$42$	−2.34998	−	1.70736i	−0.362610	−	0.263452i
$43$	−11.2003			−1.70803			−0.854013	−	0.520251i	$-0.825838\pi$
$43$	−11.2003			−1.70803			−0.854013	+	0.520251i	$0.825838\pi$
$44$	0.198055	+	3.31071i	0.0298580	+	0.499108i
$45$	−5.43751			−0.810577
$46$	−7.60471	−	5.52514i	−1.12125	−	0.814638i
$47$	−3.52015	+	10.8339i	−0.513467	+	1.58029i	0.272587	+	0.962131i	$0.412121\pi$
$47$	−3.52015	+	10.8339i	−0.513467	+	1.58029i	−0.786054	+	0.618158i	$0.787879\pi$
$48$	−0.897614	−	2.76257i	−0.129559	−	0.398743i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	−0.809017	+	0.587785i	−0.114412	+	0.0831254i
$51$	−6.35359	−	19.5543i	−0.889680	−	2.73815i
$52$	−2.01176	+	6.19157i	−0.278981	+	0.858616i
$53$	6.27479	+	4.55890i	0.861908	+	0.626213i	0.928403	−	0.371574i	$-0.121182\pi$
$53$	6.27479	+	4.55890i	0.861908	+	0.626213i	−0.0664953	+	0.997787i	$0.521182\pi$
$54$	−7.08034			−0.963513
$55$	3.08747	−	1.21143i	0.416314	−	0.163349i
$56$	−1.00000			−0.133631
$57$	9.34069	+	6.78641i	1.23721	+	0.898882i
$58$	0.364402	−	1.12151i	0.0478483	−	0.147262i
$59$	−1.74470	−	5.36963i	−0.227141	−	0.699067i	−0.998067	−	0.0621428i	$-0.980207\pi$
$59$	−1.74470	−	5.36963i	−0.227141	−	0.699067i	0.770927	−	0.636924i	$-0.219793\pi$
$60$	−2.34998	+	1.70736i	−0.303382	+	0.220420i
$61$	−5.12643	+	3.72457i	−0.656372	+	0.476882i	−0.865436	−	0.501020i	$-0.832958\pi$
$61$	−5.12643	+	3.72457i	−0.656372	+	0.476882i	0.209064	+	0.977902i	$0.432958\pi$
$62$	−0.396621	−	1.22068i	−0.0503710	−	0.155026i
$63$	−1.68028	+	5.17138i	−0.211696	+	0.651533i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	6.51020			0.807491
$66$	8.96829	−	3.51888i	1.10392	−	0.433144i
$67$	3.88122			0.474166			0.237083	−	0.971489i	$-0.423809\pi$
$67$	3.88122			0.474166			0.237083	+	0.971489i	$0.423809\pi$
$68$	−5.72647	−	4.16052i	−0.694437	−	0.504538i
$69$	−8.43751	+	25.9680i	−1.01576	+	3.12618i
$70$	0.309017	+	0.951057i	0.0369346	+	0.113673i
$71$	0.210285	−	0.152781i	0.0249562	−	0.0181317i	−0.575237	−	0.817987i	$-0.695090\pi$
$71$	0.210285	−	0.152781i	0.0249562	−	0.0181317i	0.600193	+	0.799855i	$0.295090\pi$
$72$	−4.39904	+	3.19609i	−0.518432	+	0.376663i
$73$	1.49096	+	4.58872i	0.174504	+	0.537069i	0.999610	−	0.0279089i	$-0.00888484\pi$
$73$	1.49096	+	4.58872i	0.174504	+	0.537069i	−0.825106	+	0.564977i	$0.808885\pi$
$74$	−0.311511	+	0.958733i	−0.0362124	+	0.111450i
$75$	2.34998	+	1.70736i	0.271353	+	0.197149i
$76$	3.97479			0.455940
$77$	−0.198055	−	3.31071i	−0.0225705	−	0.377290i
$78$	18.9104			2.14119
$79$	−11.6035	−	8.43046i	−1.30550	−	0.948501i	−0.305507	−	0.952190i	$-0.598826\pi$
$79$	−11.6035	−	8.43046i	−1.30550	−	0.948501i	−0.999993	+	0.00368850i	$0.998826\pi$
$80$	−0.309017	+	0.951057i	−0.0345492	+	0.106331i
$81$	1.31456	+	4.04581i	0.146062	+	0.449534i
$82$	4.39413	−	3.19252i	0.485250	−	0.352555i
$83$	−3.71745	+	2.70088i	−0.408043	+	0.296460i	−0.772809	−	0.634639i	$-0.781149\pi$
$83$	−3.71745	+	2.70088i	−0.408043	+	0.296460i	0.364766	+	0.931099i	$0.381149\pi$
$84$	0.897614	+	2.76257i	0.0979377	+	0.301421i
$85$	−2.18732	+	6.73187i	−0.237248	+	0.730174i
$86$	9.06122	+	6.58336i	0.977096	+	0.709902i
$87$	−3.42535			−0.367236
$88$	1.78575	−	2.79483i	0.190362	−	0.297930i
$89$	−1.43088			−0.151673			−0.0758366	−	0.997120i	$-0.524163\pi$
$89$	−1.43088			−0.151673			−0.0758366	+	0.997120i	$0.524163\pi$
$90$	4.39904	+	3.19609i	0.463700	+	0.336897i
$91$	2.01176	−	6.19157i	0.210890	−	0.649053i
$92$	2.90474	+	8.93987i	0.302840	+	0.932046i
$93$	−3.01619	+	2.19139i	−0.312764	+	0.227237i
$94$	9.21588	−	6.69573i	0.950545	−	0.690612i
$95$	−1.22828	−	3.78025i	−0.126019	−	0.387845i
$96$	−0.897614	+	2.76257i	−0.0916123	+	0.281954i
$97$	6.96317	+	5.05904i	0.707003	+	0.513667i	0.882205	−	0.470865i	$-0.156058\pi$
$97$	6.96317	+	5.05904i	0.707003	+	0.513667i	−0.175203	+	0.984532i	$0.556058\pi$
$98$	1.00000			0.101015
$99$	−11.4526	−	13.9309i	−1.15103	−	1.40011i
$100$	1.00000			0.100000
$101$	5.77844	+	4.19829i	0.574977	+	0.417745i	0.836910	−	0.547341i	$-0.184360\pi$
$101$	5.77844	+	4.19829i	0.574977	+	0.417745i	−0.261933	+	0.965086i	$0.584360\pi$
$102$	−6.35359	+	19.5543i	−0.629099	+	1.93617i
$103$	0.964531	+	2.96852i	0.0950381	+	0.292497i	0.987264	−	0.159093i	$-0.0508570\pi$
$103$	0.964531	+	2.96852i	0.0950381	+	0.292497i	−0.892226	+	0.451590i	$0.850857\pi$
$104$	5.26686	−	3.82660i	0.516458	−	0.375229i
$105$	2.34998	−	1.70736i	0.229335	−	0.166622i
$106$	−2.39675	−	7.37645i	−0.232793	−	0.716464i
$107$	−1.01725	+	3.13076i	−0.0983409	+	0.302662i	−0.988110	−	0.153749i	$-0.950865\pi$
$107$	−1.01725	+	3.13076i	−0.0983409	+	0.302662i	0.889769	+	0.456411i	$0.150865\pi$
$108$	5.72812	+	4.16172i	0.551188	+	0.400462i
$109$	12.5855			1.20547			0.602736	−	0.797941i	$-0.294077\pi$
$109$	12.5855			1.20547			0.602736	+	0.797941i	$0.294077\pi$
$110$	−3.20987	−	0.834702i	−0.306049	−	0.0795858i
$111$	2.92819			0.277931
$112$	0.809017	+	0.587785i	0.0764449	+	0.0555405i
$113$	0.372334	−	1.14593i	0.0350263	−	0.107800i	−0.932015	−	0.362420i	$-0.881951\pi$
$113$	0.372334	−	1.14593i	0.0350263	−	0.107800i	0.967041	+	0.254620i	$0.0819505\pi$
$114$	−3.56783	−	10.9806i	−0.334158	−	1.02843i
$115$	7.60471	−	5.52514i	0.709143	−	0.515222i
$116$	−0.954016	+	0.693133i	−0.0885782	+	0.0643558i
$117$	−10.9390	−	33.6667i	−1.01131	−	3.11249i
$118$	−1.74470	+	5.36963i	−0.160613	+	0.494315i
$119$	5.72647	+	4.16052i	0.524945	+	0.381395i
$120$	2.90474			0.265165
$121$	9.60654	+	5.35857i	0.873322	+	0.487143i
$122$	6.33662			0.573690
$123$	−12.7638	−	9.27344i	−1.15087	−	0.836158i
$124$	−0.396621	+	1.22068i	−0.0356177	+	0.109620i
$125$	−0.309017	−	0.951057i	−0.0276393	−	0.0850651i
$126$	4.39904	−	3.19609i	0.391898	−	0.284730i
$127$	12.9464	−	9.40609i	1.14880	−	0.834655i	0.160483	−	0.987039i	$-0.448695\pi$
$127$	12.9464	−	9.40609i	1.14880	−	0.834655i	0.988321	+	0.152383i	$0.0486949\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	10.0535	−	30.9416i	0.885164	−	2.72425i
$130$	−5.26686	−	3.82660i	−0.461934	−	0.335615i
$131$	14.6019			1.27577			0.637887	−	0.770130i	$-0.279809\pi$
$131$	14.6019			1.27577			0.637887	+	0.770130i	$0.279809\pi$
$132$	−9.32384	−	2.42459i	−0.811536	−	0.211034i
$133$	−3.97479			−0.344658
$134$	−3.13997	−	2.28132i	−0.271252	−	0.197076i
$135$	2.18795	−	6.73381i	0.188308	−	0.579554i
$136$	2.18732	+	6.73187i	0.187561	+	0.577253i
$137$	−8.17078	+	5.93642i	−0.698077	+	0.507183i	−0.879305	−	0.476258i	$-0.841993\pi$
$137$	−8.17078	+	5.93642i	−0.698077	+	0.507183i	0.181228	+	0.983441i	$0.441993\pi$
$138$	22.0897	−	16.0491i	1.88040	−	1.36619i
$139$	−5.72022	−	17.6050i	−0.485183	−	1.49324i	−0.831716	−	0.555202i	$-0.812641\pi$
$139$	−5.72022	−	17.6050i	−0.485183	−	1.49324i	0.346532	−	0.938038i	$-0.387359\pi$
$140$	0.309017	−	0.951057i	0.0261167	−	0.0803789i
$141$	−26.7697	−	19.4493i	−2.25442	−	1.63793i
$142$	−0.259926			−0.0218125
$143$	13.7119	+	16.6792i	1.14664	+	1.39478i
$144$	5.43751			0.453126
$145$	0.954016	+	0.693133i	0.0792267	+	0.0575616i
$146$	1.49096	−	4.58872i	0.123393	−	0.379765i
$147$	−0.897614	−	2.76257i	−0.0740340	−	0.227853i
$148$	0.815547	−	0.592530i	0.0670375	−	0.0487056i
$149$	−9.31392	+	6.76696i	−0.763026	+	0.554371i	−0.899837	−	0.436226i	$-0.856315\pi$
$149$	−9.31392	+	6.76696i	−0.763026	+	0.554371i	0.136811	+	0.990597i	$0.456315\pi$
$150$	−0.897614	−	2.76257i	−0.0732899	−	0.225563i
$151$	1.67922	−	5.16811i	0.136653	−	0.420575i	−0.859191	−	0.511656i	$-0.829032\pi$
$151$	1.67922	−	5.16811i	0.136653	−	0.420575i	0.995843	+	0.0910813i	$0.0290323\pi$
$152$	−3.21567	−	2.33632i	−0.260826	−	0.189501i
$153$	38.4884			3.11160
$154$	−1.78575	+	2.79483i	−0.143900	+	0.225214i
$155$	1.28349			0.103093
$156$	−15.2989	−	11.1153i	−1.22489	−	0.889934i
$157$	2.46488	−	7.58611i	0.196719	−	0.605438i	−0.803234	−	0.595664i	$-0.796889\pi$
$157$	2.46488	−	7.58611i	0.196719	−	0.605438i	0.999952	−	0.00977361i	$-0.00311109\pi$
$158$	4.43216	+	13.6408i	0.352604	+	1.08520i
$159$	−18.2266	+	13.2424i	−1.44546	+	1.05019i
$160$	0.809017	−	0.587785i	0.0639584	−	0.0464685i
$161$	−2.90474	−	8.93987i	−0.228926	−	0.704560i
$162$	1.31456	−	4.04581i	0.103282	−	0.317869i
$163$	−11.6039	−	8.43072i	−0.908886	−	0.660345i	0.0318466	−	0.999493i	$-0.489861\pi$
$163$	−11.6039	−	8.43072i	−0.908886	−	0.660345i	−0.940733	+	0.339148i	$0.889861\pi$
$164$	−5.43144			−0.424124
$165$	0.575300	+	9.61674i	0.0447870	+	0.748662i
$166$	4.59502			0.356642
$167$	1.54554	+	1.12290i	0.119598	+	0.0868929i	0.645976	−	0.763358i	$-0.276450\pi$
$167$	1.54554	+	1.12290i	0.119598	+	0.0868929i	−0.526378	+	0.850250i	$0.676450\pi$
$168$	0.897614	−	2.76257i	0.0692524	−	0.213137i
$169$	9.07975	+	27.9446i	0.698442	+	2.14958i
$170$	5.72647	−	4.16052i	0.439200	−	0.319098i
$171$	−17.4853	+	12.7038i	−1.33713	+	0.971483i
$172$	−3.46108	−	10.6521i	−0.263905	−	0.812215i
$173$	−4.50935	+	13.8784i	−0.342840	+	1.05515i	0.619890	+	0.784688i	$0.287177\pi$
$173$	−4.50935	+	13.8784i	−0.342840	+	1.05515i	−0.962730	+	0.270464i	$0.912823\pi$
$174$	2.77117	+	2.01337i	0.210082	+	0.152633i
$175$	−1.00000			−0.0755929
$176$	−3.08747	+	1.21143i	−0.232727	+	0.0913147i
$177$	16.4001			1.23270
$178$	1.15761	+	0.841051i	0.0867663	+	0.0630394i
$179$	−0.975544	+	3.00242i	−0.0729156	+	0.224411i	−0.980872	−	0.194653i	$-0.937642\pi$
$179$	−0.975544	+	3.00242i	−0.0729156	+	0.224411i	0.907957	+	0.419064i	$0.137642\pi$
$180$	−1.68028	−	5.17138i	−0.125241	−	0.385452i
$181$	5.73629	−	4.16766i	0.426375	−	0.309780i	−0.353823	−	0.935313i	$-0.615118\pi$
$181$	5.73629	−	4.16766i	0.426375	−	0.309780i	0.780198	+	0.625533i	$0.215118\pi$
$182$	−5.26686	+	3.82660i	−0.390406	+	0.283646i
$183$	−5.68784	−	17.5054i	−0.420457	−	1.29403i
$184$	2.90474	−	8.93987i	0.214140	−	0.659056i
$185$	−0.815547	−	0.592530i	−0.0599602	−	0.0435636i
$186$	3.72822			0.273366
$187$	−21.8540	+	8.57485i	−1.59813	+	0.627055i
$188$	−11.3915			−0.830807
$189$	−5.72812	−	4.16172i	−0.416659	−	0.302721i
$190$	−1.22828	+	3.78025i	−0.0891086	+	0.274248i
$191$	2.35315	+	7.24226i	0.170268	+	0.524032i	0.999386	−	0.0350426i	$-0.0111567\pi$
$191$	2.35315	+	7.24226i	0.170268	+	0.524032i	−0.829118	+	0.559074i	$0.811157\pi$
$192$	2.34998	−	1.70736i	0.169595	−	0.123218i
$193$	6.92116	−	5.02852i	0.498196	−	0.361961i	−0.310131	−	0.950694i	$-0.600373\pi$
$193$	6.92116	−	5.02852i	0.498196	−	0.361961i	0.808328	+	0.588733i	$0.200373\pi$
$194$	−2.65969	−	8.18569i	−0.190955	−	0.587699i
$195$	−5.84365	+	17.9849i	−0.418472	+	1.28792i
$196$	−0.809017	−	0.587785i	−0.0577869	−	0.0419847i
$197$	5.30318			0.377836			0.188918	−	0.981993i	$-0.439502\pi$
$197$	5.30318			0.377836			0.188918	+	0.981993i	$0.439502\pi$
$198$	1.07693	+	18.0020i	0.0765340	+	1.27935i
$199$	27.8463			1.97397			0.986987	−	0.160798i	$-0.0514068\pi$
$199$	27.8463			1.97397			0.986987	+	0.160798i	$0.0514068\pi$
$200$	−0.809017	−	0.587785i	−0.0572061	−	0.0415627i
$201$	−3.48383	+	10.7221i	−0.245731	+	0.756281i
$202$	−2.20717	−	6.79297i	−0.155296	−	0.477952i
$203$	0.954016	−	0.693133i	0.0669588	−	0.0486484i
$204$	16.6339	−	12.0852i	1.16461	−	0.846136i
$205$	1.67841	+	5.16560i	0.117225	+	0.360781i
$206$	0.964531	−	2.96852i	0.0672021	−	0.206827i
$207$	−41.3507	−	30.0430i	−2.87407	−	2.08814i
$208$	−6.51020			−0.451401
$209$	7.09800	−	11.1089i	0.490979	−	0.768417i
$210$	−2.90474			−0.200446
$211$	−7.49743	−	5.44720i	−0.516144	−	0.375001i	0.299005	−	0.954251i	$-0.403345\pi$
$211$	−7.49743	−	5.44720i	−0.516144	−	0.375001i	−0.815149	+	0.579251i	$0.803345\pi$
$212$	−2.39675	+	7.37645i	−0.164610	+	0.506617i
$213$	0.233313	+	0.718064i	0.0159864	+	0.0492009i
$214$	2.66319	−	1.93492i	0.182052	−	0.132268i
$215$	−9.06122	+	6.58336i	−0.617970	+	0.448981i
$216$	−2.18795	−	6.73381i	−0.148871	−	0.458177i
$217$	0.396621	−	1.22068i	0.0269244	−	0.0828648i
$218$	−10.1819	−	7.39757i	−0.689604	−	0.501026i
$219$	−14.0150			−0.947044
$220$	2.10621	+	2.56200i	0.142001	+	0.172730i
$221$	−46.0812			−3.09976
$222$	−2.36895	−	1.72114i	−0.158994	−	0.115516i
$223$	8.03858	−	24.7402i	0.538303	−	1.65673i	−0.198099	−	0.980182i	$-0.563477\pi$
$223$	8.03858	−	24.7402i	0.538303	−	1.65673i	0.736402	−	0.676544i	$-0.236523\pi$
$224$	−0.309017	−	0.951057i	−0.0206471	−	0.0635451i
$225$	−4.39904	+	3.19609i	−0.293269	+	0.213073i
$226$	−0.974784	+	0.708222i	−0.0648417	+	0.0471102i
$227$	−0.0905788	−	0.278773i	−0.00601193	−	0.0185028i	0.948006	−	0.318254i	$-0.103096\pi$
$227$	−0.0905788	−	0.278773i	−0.00601193	−	0.0185028i	−0.954017	+	0.299751i	$0.903096\pi$
$228$	−3.56783	+	10.9806i	−0.236285	+	0.727211i
$229$	16.1441	+	11.7294i	1.06683	+	0.775097i	0.975340	−	0.220709i	$-0.0708370\pi$
$229$	16.1441	+	11.7294i	1.06683	+	0.775097i	0.0914901	+	0.995806i	$0.470837\pi$
$230$	−9.39994			−0.619813
$231$	9.32384	+	2.42459i	0.613464	+	0.159527i
$232$	1.17923			0.0774202
$233$	−0.163064	−	0.118473i	−0.0106827	−	0.00776141i	0.582431	−	0.812880i	$-0.302102\pi$
$233$	−0.163064	−	0.118473i	−0.0106827	−	0.00776141i	−0.593114	+	0.805119i	$0.702102\pi$
$234$	−10.9390	+	33.6667i	−0.715104	+	2.20086i
$235$	3.52015	+	10.8339i	0.229629	+	0.706727i
$236$	4.56768	−	3.31862i	0.297331	−	0.216023i
$237$	33.7053	−	24.4883i	2.18939	−	1.59069i
$238$	−2.18732	−	6.73187i	−0.141783	−	0.436362i
$239$	7.39146	−	22.7486i	0.478114	−	1.47148i	−0.363599	−	0.931556i	$-0.618452\pi$
$239$	7.39146	−	22.7486i	0.478114	−	1.47148i	0.841712	−	0.539927i	$-0.181548\pi$
$240$	−2.34998	−	1.70736i	−0.151691	−	0.110210i
$241$	−18.5851			−1.19717			−0.598586	−	0.801059i	$-0.704270\pi$
$241$	−18.5851			−1.19717			−0.598586	+	0.801059i	$0.704270\pi$
$242$	−4.62217	−	9.98176i	−0.297124	−	0.641652i
$243$	8.88423			0.569924
$244$	−5.12643	−	3.72457i	−0.328186	−	0.238441i
$245$	−0.309017	+	0.951057i	−0.0197424	+	0.0607608i
$246$	4.87533	+	15.0047i	0.310840	+	0.956667i
$247$	20.9347	−	15.2099i	1.33204	−	0.967785i
$248$	1.03837	−	0.754419i	0.0659365	−	0.0479056i
$249$	−4.12455	−	12.6941i	−0.261383	−	0.804453i
$250$	−0.309017	+	0.951057i	−0.0195440	+	0.0601501i
$251$	8.16682	+	5.93354i	0.515485	+	0.374522i	0.814900	−	0.579601i	$-0.196792\pi$
$251$	8.16682	+	5.93354i	0.515485	+	0.374522i	−0.299415	+	0.954123i	$0.596792\pi$
$252$	−5.43751			−0.342531
$253$	30.1726	+	7.84615i	1.89693	+	0.493283i
$254$	−16.0026			−1.00409
$255$	−16.6339	−	12.0852i	−1.04166	−	0.756807i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−1.69131	−	5.20532i	−0.105501	−	0.324699i	0.884347	−	0.466831i	$-0.154604\pi$
$257$	−1.69131	−	5.20532i	−0.105501	−	0.324699i	−0.989848	+	0.142132i	$0.954604\pi$
$258$	−26.3205	+	19.1229i	−1.63864	+	1.19054i
$259$	−0.815547	+	0.592530i	−0.0506756	+	0.0368180i
$260$	2.01176	+	6.19157i	0.124764	+	0.383985i
$261$	1.98144	−	6.09824i	0.122648	−	0.377472i
$262$	−11.8132	−	8.58278i	−0.729821	−	0.530246i
$263$	−12.8440			−0.791998			−0.395999	−	0.918251i	$-0.629602\pi$
$263$	−12.8440			−0.791998			−0.395999	+	0.918251i	$0.629602\pi$
$264$	6.11800	+	7.44195i	0.376537	+	0.458021i
$265$	7.75606			0.476451
$266$	3.21567	+	2.33632i	0.197166	+	0.143249i
$267$	1.28438	−	3.95291i	0.0786027	−	0.241914i
$268$	1.19936	+	3.69126i	0.0732627	+	0.225479i
$269$	−6.37134	+	4.62905i	−0.388468	+	0.282238i	−0.764827	−	0.644235i	$-0.777176\pi$
$269$	−6.37134	+	4.62905i	−0.388468	+	0.282238i	0.376360	+	0.926474i	$0.377176\pi$
$270$	−5.72812	+	4.16172i	−0.348602	+	0.253274i
$271$	3.05292	+	9.39594i	0.185452	+	0.570762i	0.999956	−	0.00939561i	$-0.00299076\pi$
$271$	3.05292	+	9.39594i	0.185452	+	0.570762i	−0.814504	+	0.580158i	$0.802991\pi$
$272$	2.18732	−	6.73187i	0.132626	−	0.408180i
$273$	15.2989	+	11.1153i	0.925929	+	0.672727i
$274$	10.0996			0.610142
$275$	1.78575	−	2.79483i	0.107685	−	0.168535i
$276$	−27.3044			−1.64353
$277$	−21.8669	−	15.8872i	−1.31385	−	0.954570i	−0.999987	−	0.00510267i	$-0.998376\pi$
$277$	−21.8669	−	15.8872i	−1.31385	−	0.954570i	−0.313866	−	0.949467i	$-0.601624\pi$
$278$	−5.72022	+	17.6050i	−0.343076	+	1.05588i
$279$	−2.15663	−	6.63744i	−0.129114	−	0.397373i
$280$	−0.809017	+	0.587785i	−0.0483480	+	0.0351269i
$281$	−11.0365	+	8.01850i	−0.658383	+	0.478343i	−0.866117	−	0.499842i	$-0.833391\pi$
$281$	−11.0365	+	8.01850i	−0.658383	+	0.478343i	0.207733	+	0.978185i	$0.433391\pi$
$282$	10.2251	+	31.4697i	0.608897	+	1.87399i
$283$	5.68127	−	17.4852i	0.337717	−	1.03938i	−0.627652	−	0.778494i	$-0.715984\pi$
$283$	5.68127	−	17.4852i	0.337717	−	1.03938i	0.965368	−	0.260891i	$-0.0840162\pi$
$284$	0.210285	+	0.152781i	0.0124781	+	0.00906586i
$285$	11.5457			0.683910
$286$	−1.28938	−	21.5534i	−0.0762427	−	1.27448i
$287$	5.43144			0.320608
$288$	−4.39904	−	3.19609i	−0.259216	−	0.188331i
$289$	10.2292	−	31.4823i	0.601719	−	1.85190i
$290$	−0.364402	−	1.12151i	−0.0213984	−	0.0658575i
$291$	−20.2262	+	14.6952i	−1.18568	+	0.861447i
$292$	−3.90339	+	2.83598i	−0.228429	+	0.165963i
$293$	3.05137	+	9.39116i	0.178263	+	0.548637i	0.999767	−	0.0215649i	$-0.00686485\pi$
$293$	3.05137	+	9.39116i	0.178263	+	0.548637i	−0.821504	+	0.570202i	$0.806865\pi$
$294$	−0.897614	+	2.76257i	−0.0523499	+	0.161116i
$295$	−4.56768	−	3.31862i	−0.265941	−	0.193217i
$296$	−1.00807			−0.0585930
$297$	21.8603	−	8.57731i	1.26846	−	0.497706i
$298$	11.5126			0.666909
$299$	49.5082	+	35.9698i	2.86313	+	2.08019i
$300$	−0.897614	+	2.76257i	−0.0518238	+	0.159497i
$301$	3.46108	+	10.6521i	0.199493	+	0.613977i
$302$	−4.39625	+	3.19407i	−0.252976	+	0.183798i
$303$	−16.7849	+	12.1949i	−0.964266	+	0.700580i
$304$	1.22828	+	3.78025i	0.0704466	+	0.216812i
$305$	−1.95812	+	6.02648i	−0.112122	+	0.345075i
$306$	−31.1378	−	22.6229i	−1.78003	−	1.29327i
$307$	6.50344			0.371171			0.185585	−	0.982628i	$-0.440582\pi$
$307$	6.50344			0.371171			0.185585	+	0.982628i	$0.440582\pi$
$308$	3.08747	−	1.21143i	0.175925	−	0.0690274i
$309$	−9.06653			−0.515777
$310$	−1.03837	−	0.754419i	−0.0589754	−	0.0428481i
$311$	1.04137	−	3.20502i	0.0590509	−	0.181740i	−0.917180	−	0.398473i	$-0.869540\pi$
$311$	1.04137	−	3.20502i	0.0590509	−	0.181740i	0.976231	+	0.216733i	$0.0695402\pi$
$312$	5.84365	+	17.9849i	0.330831	+	1.01819i
$313$	4.38665	−	3.18709i	0.247948	−	0.180145i	−0.456869	−	0.889534i	$-0.651029\pi$
$313$	4.38665	−	3.18709i	0.247948	−	0.180145i	0.704817	+	0.709389i	$0.251029\pi$
$314$	−6.45313	+	4.68848i	−0.364171	+	0.264586i
$315$	1.68028	+	5.17138i	0.0946733	+	0.291374i
$316$	4.43216	−	13.6408i	0.249328	−	0.767354i
$317$	5.79255	+	4.20853i	0.325342	+	0.236375i	0.738451	−	0.674307i	$-0.235557\pi$
$317$	5.79255	+	4.20853i	0.325342	+	0.236375i	−0.413110	+	0.910681i	$0.635557\pi$
$318$	22.5293			1.26338
$319$	0.233553	+	3.90408i	0.0130764	+	0.218587i
$320$	−1.00000			−0.0559017
$321$	−7.73586	−	5.62043i	−0.431774	−	0.313702i
$322$	−2.90474	+	8.93987i	−0.161875	+	0.498199i
$323$	8.69413	+	26.7578i	0.483754	+	1.48884i
$324$	−3.44157	+	2.50045i	−0.191198	+	0.138914i
$325$	5.26686	−	3.82660i	0.292153	−	0.212262i
$326$	4.43229	+	13.6412i	0.245482	+	0.755515i
$327$	−11.2969	+	34.7683i	−0.624721	+	1.92269i
$328$	4.39413	+	3.19252i	0.242625	+	0.176277i
$329$	11.3915			0.628031
$330$	5.18715	−	8.11826i	0.285543	−	0.446895i
$331$	20.6983			1.13768			0.568842	−	0.822447i	$-0.307392\pi$
$331$	20.6983			1.13768			0.568842	+	0.822447i	$0.307392\pi$
$332$	−3.71745	−	2.70088i	−0.204021	−	0.148230i
$333$	−1.69385	+	5.21312i	−0.0928222	+	0.285677i
$334$	−0.590345	−	1.81690i	−0.0323023	−	0.0994161i
$335$	3.13997	−	2.28132i	0.171555	−	0.124642i
$336$	−2.34998	+	1.70736i	−0.128202	+	0.0931443i
$337$	−2.41371	−	7.42863i	−0.131483	−	0.404663i	0.863543	−	0.504275i	$-0.168240\pi$
$337$	−2.41371	−	7.42863i	−0.131483	−	0.404663i	−0.995026	+	0.0996113i	$0.968240\pi$
$338$	9.07975	−	27.9446i	0.493873	−	1.51999i
$339$	2.83149	+	2.05720i	0.153786	+	0.111732i
$340$	−7.07831			−0.383875
$341$	2.70331	+	3.28832i	0.146393	+	0.178072i
$342$	21.6130			1.16870
$343$	0.809017	+	0.587785i	0.0436828	+	0.0317374i
$344$	−3.46108	+	10.6521i	−0.186609	+	0.574323i
$345$	8.43751	+	25.9680i	0.454260	+	1.39807i
$346$	11.8056	−	8.57730i	0.634675	−	0.461118i
$347$	22.5894	−	16.4121i	1.21266	−	0.881049i	0.217190	−	0.976129i	$-0.430311\pi$
$347$	22.5894	−	16.4121i	1.21266	−	0.881049i	0.995470	+	0.0950802i	$0.0303108\pi$
$348$	−1.05849	−	3.25770i	−0.0567411	−	0.174631i
$349$	6.36381	−	19.5858i	0.340647	−	1.04840i	−0.623226	−	0.782042i	$-0.714178\pi$
$349$	6.36381	−	19.5858i	0.340647	−	1.04840i	0.963873	−	0.266362i	$-0.0858216\pi$
$350$	0.809017	+	0.587785i	0.0432438	+	0.0314184i
$351$	46.0944			2.46034
$352$	3.20987	+	0.834702i	0.171087	+	0.0444898i
$353$	−5.61133			−0.298661			−0.149330	−	0.988787i	$-0.547712\pi$
$353$	−5.61133			−0.298661			−0.149330	+	0.988787i	$0.547712\pi$
$354$	−13.2679	−	9.63971i	−0.705182	−	0.512345i
$355$	0.0803215	−	0.247204i	0.00426302	−	0.0131202i
$356$	−0.442167	−	1.36085i	−0.0234348	−	0.0721249i
$357$	−16.6339	+	12.0852i	−0.880360	+	0.639619i
$358$	2.55401	−	1.85560i	0.134983	−	0.0980712i
$359$	2.54712	+	7.83922i	0.134432	+	0.413738i	0.995501	−	0.0947492i	$-0.0302049\pi$
$359$	2.54712	+	7.83922i	0.134432	+	0.413738i	−0.861070	+	0.508487i	$0.830205\pi$
$360$	−1.68028	+	5.17138i	−0.0885587	+	0.272556i
$361$	2.58970	+	1.88153i	0.136300	+	0.0990276i
$362$	−7.09045			−0.372666
$363$	−23.4264	+	21.7288i	−1.22957	+	1.14047i
$364$	6.51020			0.341227
$365$	3.90339	+	2.83598i	0.204313	+	0.148442i
$366$	−5.68784	+	17.5054i	−0.297308	+	0.915020i
$367$	−1.26950	−	3.90711i	−0.0662672	−	0.203949i	0.912440	−	0.409210i	$-0.134196\pi$
$367$	−1.26950	−	3.90711i	−0.0662672	−	0.203949i	−0.978707	+	0.205261i	$0.934196\pi$
$368$	−7.60471	+	5.52514i	−0.396423	+	0.288018i
$369$	23.8931	−	17.3594i	1.24383	−	0.903692i
$370$	0.311511	+	0.958733i	0.0161947	+	0.0498422i
$371$	2.39675	−	7.37645i	0.124433	−	0.382966i
$372$	−3.01619	−	2.19139i	−0.156382	−	0.113618i
$373$	−26.2182			−1.35753			−0.678764	−	0.734356i	$-0.737484\pi$
$373$	−26.2182			−1.35753			−0.678764	+	0.734356i	$0.737484\pi$
$374$	22.7205	+	5.90828i	1.17485	+	0.305510i
$375$	2.90474			0.150000
$376$	9.21588	+	6.69573i	0.475273	+	0.345306i
$377$	−2.37233	+	7.30128i	−0.122181	+	0.376035i
$378$	2.18795	+	6.73381i	0.112536	+	0.346350i
$379$	−15.9698	+	11.6028i	−0.820316	+	0.595994i	−0.916803	−	0.399340i	$-0.869239\pi$
$379$	−15.9698	+	11.6028i	−0.820316	+	0.595994i	0.0964872	+	0.995334i	$0.469239\pi$
$380$	3.21567	−	2.33632i	0.164961	−	0.119851i
$381$	14.3641	+	44.2083i	0.735898	+	2.26486i
$382$	2.35315	−	7.24226i	0.120398	−	0.370546i
$383$	−28.9660	−	21.0451i	−1.48010	−	1.07535i	−0.977526	−	0.210815i	$-0.932388\pi$
$383$	−28.9660	−	21.0451i	−1.48010	−	1.07535i	−0.502569	−	0.864537i	$-0.667612\pi$
$384$	−2.90474			−0.148232
$385$	−2.10621	−	2.56200i	−0.107343	−	0.130572i
$386$	−8.55503			−0.435439
$387$	49.2705	+	35.7971i	2.50456	+	1.81967i
$388$	−2.65969	+	8.18569i	−0.135025	+	0.415566i
$389$	−8.92549	−	27.4698i	−0.452541	−	1.39278i	−0.873999	−	0.485929i	$-0.838482\pi$
$389$	−8.92549	−	27.4698i	−0.452541	−	1.39278i	0.421458	−	0.906848i	$-0.361518\pi$
$390$	15.2989	−	11.1153i	0.774688	−	0.562844i
$391$	−53.8285	+	39.1087i	−2.72222	+	1.97781i
$392$	0.309017	+	0.951057i	0.0156077	+	0.0480356i
$393$	−13.1069	+	40.3388i	−0.661154	+	2.03482i
$394$	−4.29037	−	3.11713i	−0.216146	−	0.157039i
$395$	−14.3428			−0.721663
$396$	9.71006	−	15.1969i	0.487949	−	0.763675i
$397$	−31.7117			−1.59156			−0.795782	−	0.605583i	$-0.792940\pi$
$397$	−31.7117			−1.59156			−0.795782	+	0.605583i	$0.792940\pi$
$398$	−22.5282	−	16.3677i	−1.12923	−	0.820437i
$399$	3.56783	−	10.9806i	0.178615	−	0.549720i
$400$	0.309017	+	0.951057i	0.0154508	+	0.0475528i
$401$	20.0994	−	14.6031i	1.00372	−	0.729243i	0.0408351	−	0.999166i	$-0.486998\pi$
$401$	20.0994	−	14.6031i	1.00372	−	0.729243i	0.962882	+	0.269923i	$0.0869982\pi$
$402$	9.12079	−	6.62664i	0.454904	−	0.330507i
$403$	2.58208	+	7.94684i	0.128623	+	0.395860i
$404$	−2.20717	+	6.79297i	−0.109811	+	0.337963i
$405$	3.44157	+	2.50045i	0.171013	+	0.124248i
$406$	−1.17923			−0.0585242
$407$	−0.199654	−	3.33743i	−0.00989649	−	0.165430i
$408$	−20.5606			−1.01790
$409$	−14.2689	−	10.3669i	−0.705550	−	0.512612i	0.176185	−	0.984357i	$-0.443624\pi$
$409$	−14.2689	−	10.3669i	−0.705550	−	0.512612i	−0.881735	+	0.471745i	$0.843624\pi$
$410$	1.67841	−	5.16560i	0.0828906	−	0.255111i
$411$	−9.06558	−	27.9010i	−0.447172	−	1.37625i
$412$	−2.52518	+	1.83465i	−0.124406	+	0.0903866i
$413$	−4.56768	+	3.31862i	−0.224761	+	0.163298i
$414$	15.7946	+	48.6107i	0.776260	+	2.38908i
$415$	−1.41994	+	4.37012i	−0.0697020	+	0.214521i
$416$	5.26686	+	3.82660i	0.258229	+	0.187614i
$417$	53.7697			2.63312
$418$	−12.2720	+	4.81517i	−0.600245	+	0.235517i
$419$	6.70771			0.327693			0.163847	−	0.986486i	$-0.447610\pi$
$419$	6.70771			0.327693			0.163847	+	0.986486i	$0.447610\pi$
$420$	2.34998	+	1.70736i	0.114667	+	0.0833108i
$421$	4.95779	−	15.2585i	0.241628	−	0.743655i	−0.754545	−	0.656249i	$-0.772142\pi$
$421$	4.95779	−	15.2585i	0.241628	−	0.743655i	0.996173	−	0.0874061i	$-0.0278578\pi$
$422$	2.86376	+	8.81375i	0.139406	+	0.429047i
$423$	50.1115	−	36.4081i	2.43650	−	1.77022i
$424$	6.27479	−	4.55890i	0.304731	−	0.221400i
$425$	2.18732	+	6.73187i	0.106100	+	0.326544i
$426$	0.233313	−	0.718064i	0.0113041	−	0.0347903i
$427$	5.12643	+	3.72457i	0.248085	+	0.180245i
$428$	−3.29188			−0.159119
$429$	−58.3853	+	22.9086i	−2.81887	+	1.10604i
$430$	11.2003			0.540125
$431$	−25.5229	−	18.5435i	−1.22939	−	0.893207i	−0.232549	−	0.972585i	$-0.574707\pi$
$431$	−25.5229	−	18.5435i	−1.22939	−	0.893207i	−0.996845	+	0.0793776i	$0.974707\pi$
$432$	−2.18795	+	6.73381i	−0.105268	+	0.323980i
$433$	−2.55529	−	7.86439i	−0.122800	−	0.377938i	0.870694	−	0.491825i	$-0.163670\pi$
$433$	−2.55529	−	7.86439i	−0.122800	−	0.377938i	−0.993494	+	0.113887i	$0.963670\pi$
$434$	−1.03837	+	0.754419i	−0.0498433	+	0.0362133i
$435$	−2.77117	+	2.01337i	−0.132867	+	0.0965338i
$436$	3.88913	+	11.9695i	0.186256	+	0.573236i
$437$	11.5457	−	35.5341i	0.552307	−	1.69983i
$438$	11.3383	+	8.23779i	0.541767	+	0.393617i
$439$	11.1008			0.529814			0.264907	−	0.964274i	$-0.414659\pi$
$439$	11.1008			0.529814			0.264907	+	0.964274i	$0.414659\pi$
$440$	−0.198055	−	3.31071i	−0.00944193	−	0.157832i
$441$	5.43751			0.258929
$442$	37.2805	+	27.0858i	1.77325	+	1.28834i
$443$	1.40254	−	4.31657i	0.0666366	−	0.205086i	−0.912194	−	0.409759i	$-0.865613\pi$
$443$	1.40254	−	4.31657i	0.0666366	−	0.205086i	0.978831	+	0.204672i	$0.0656129\pi$
$444$	0.904859	+	2.78487i	0.0429427	+	0.132164i
$445$	−1.15761	+	0.841051i	−0.0548758	+	0.0398696i
$446$	−21.0453	+	15.2903i	−0.996522	+	0.724016i
$447$	−10.3339	−	31.8045i	−0.488777	−	1.50430i
$448$	−0.309017	+	0.951057i	−0.0145997	+	0.0449332i
$449$	7.86344	+	5.71313i	0.371099	+	0.269619i	0.757666	−	0.652642i	$-0.226339\pi$
$449$	7.86344	+	5.71313i	0.371099	+	0.269619i	−0.386568	+	0.922261i	$0.626339\pi$
$450$	5.43751			0.256327
$451$	−9.69921	+	15.1800i	−0.456718	+	0.714796i
$452$	1.20490			0.0566737
$453$	12.7700	+	9.27793i	0.599986	+	0.435915i
$454$	−0.0905788	+	0.278773i	−0.00425107	+	0.0130835i
$455$	−2.01176	−	6.19157i	−0.0943129	−	0.290265i
$456$	9.34069	−	6.78641i	0.437418	−	0.317803i
$457$	−17.1089	+	12.4303i	−0.800321	+	0.581467i	−0.911008	−	0.412388i	$-0.864695\pi$
$457$	−17.1089	+	12.4303i	−0.800321	+	0.581467i	0.110687	+	0.993855i	$0.464695\pi$
$458$	−6.16648	−	18.9785i	−0.288141	−	0.886806i
$459$	−15.4870	+	47.6639i	−0.722869	+	2.22476i
$460$	7.60471	+	5.52514i	0.354571	+	0.257611i
$461$	20.5158			0.955516			0.477758	−	0.878492i	$-0.341450\pi$
$461$	20.5158			0.955516			0.477758	+	0.878492i	$0.341450\pi$
$462$	−6.11800	−	7.44195i	−0.284635	−	0.346231i
$463$	−5.06175			−0.235239			−0.117620	−	0.993059i	$-0.537526\pi$
$463$	−5.06175			−0.235239			−0.117620	+	0.993059i	$0.537526\pi$
$464$	−0.954016	−	0.693133i	−0.0442891	−	0.0321779i
$465$	−1.15208	+	3.54574i	−0.0534265	+	0.164430i
$466$	0.0622848	+	0.191693i	0.00288529	+	0.00888000i
$467$	6.05746	−	4.40100i	0.280306	−	0.203654i	−0.438745	−	0.898612i	$-0.644577\pi$
$467$	6.05746	−	4.40100i	0.280306	−	0.203654i	0.719051	+	0.694958i	$0.244577\pi$
$468$	28.6386	−	20.8072i	1.32382	−	0.961812i
$469$	−1.19936	−	3.69126i	−0.0553814	−	0.170446i
$470$	3.52015	−	10.8339i	0.162373	−	0.499731i
$471$	18.7447	+	13.6188i	0.863709	+	0.627521i
$472$	−5.64597			−0.259877
$473$	−35.9515	−	9.34890i	−1.65305	−	0.429863i
$474$	−41.6620			−1.91360
$475$	−3.21567	−	2.33632i	−0.147545	−	0.107198i
$476$	−2.18732	+	6.73187i	−0.100256	+	0.308555i
$477$	−13.0324	−	40.1096i	−0.596712	−	1.83649i
$478$	−19.3511	+	14.0594i	−0.885098	+	0.643061i
$479$	0.335074	−	0.243446i	0.0153099	−	0.0111233i	−0.580104	−	0.814542i	$-0.696988\pi$
$479$	0.335074	−	0.243446i	0.0153099	−	0.0111233i	0.595414	+	0.803419i	$0.296988\pi$
$480$	0.897614	+	2.76257i	0.0409703	+	0.126094i
$481$	2.02800	−	6.24154i	0.0924688	−	0.284590i
$482$	15.0357	+	10.9240i	0.684855	+	0.497577i
$483$	27.3044			1.24239
$484$	−2.12772	+	10.7923i	−0.0967146	+	0.490557i
$485$	8.60695			0.390821
$486$	−7.18749	−	5.22202i	−0.326031	−	0.236876i
$487$	−7.33384	+	22.5712i	−0.332328	+	1.02280i	0.635695	+	0.771940i	$0.280714\pi$
$487$	−7.33384	+	22.5712i	−0.332328	+	1.02280i	−0.968023	+	0.250861i	$0.919286\pi$
$488$	1.95812	+	6.02648i	0.0886400	+	0.272806i
$489$	33.7063	−	24.4890i	1.52425	−	1.10743i
$490$	0.809017	−	0.587785i	0.0365477	−	0.0265534i
$491$	9.95537	+	30.6395i	0.449279	+	1.38274i	0.877722	+	0.479171i	$0.159063\pi$
$491$	9.95537	+	30.6395i	0.449279	+	1.38274i	−0.428442	+	0.903569i	$0.640937\pi$
$492$	4.87533	−	15.0047i	0.219797	−	0.676466i
$493$	−6.75282	−	4.90621i	−0.304132	−	0.220965i
$494$	−25.8767			−1.16425
$495$	−17.4537	−	4.53871i	−0.784486	−	0.204000i
$496$	−1.28349			−0.0576306
$497$	−0.210285	−	0.152781i	−0.00943255	−	0.00685315i
$498$	−4.12455	+	12.6941i	−0.184826	+	0.568834i
$499$	−1.38745	−	4.27013i	−0.0621108	−	0.191157i	0.915186	−	0.403031i	$-0.132043\pi$
$499$	−1.38745	−	4.27013i	−0.0621108	−	0.191157i	−0.977297	+	0.211874i	$0.932043\pi$
$500$	0.809017	−	0.587785i	0.0361803	−	0.0262866i
$501$	−4.48940	+	3.26174i	−0.200572	+	0.145724i
$502$	−3.11945	−	9.60067i	−0.139228	−	0.428499i
$503$	9.52697	−	29.3210i	0.424787	−	1.30736i	−0.478412	−	0.878136i	$-0.658787\pi$
$503$	9.52697	−	29.3210i	0.424787	−	1.30736i	0.903198	−	0.429223i	$-0.141213\pi$
$504$	4.39904	+	3.19609i	0.195949	+	0.142365i
$505$	7.14255			0.317839
$506$	−19.7983	−	24.0827i	−0.880141	−	1.07061i
$507$	−85.3491			−3.79049
$508$	12.9464	+	9.40609i	0.574402	+	0.417328i
$509$	−0.821003	+	2.52679i	−0.0363903	+	0.111998i	−0.967602	−	0.252482i	$-0.918753\pi$
$509$	−0.821003	+	2.52679i	−0.0363903	+	0.111998i	0.931211	+	0.364480i	$0.118753\pi$
$510$	6.35359	+	19.5543i	0.281342	+	0.865880i
$511$	3.90339	−	2.83598i	0.172676	−	0.125456i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−8.69663	−	26.7655i	−0.383965	−	1.18172i
$514$	−1.69131	+	5.20532i	−0.0746005	+	0.229597i
$515$	2.52518	+	1.83465i	0.111273	+	0.0808442i
$516$	32.5339			1.43222
$517$	−20.3423	+	31.8372i	−0.894655	+	1.40020i
$518$	1.00807			0.0442921
$519$	−34.2923	−	24.9148i	−1.50527	−	1.09364i
$520$	2.01176	−	6.19157i	0.0882216	−	0.271518i
$521$	1.84976	+	5.69297i	0.0810393	+	0.249413i	0.983365	−	0.181642i	$-0.0581413\pi$
$521$	1.84976	+	5.69297i	0.0810393	+	0.249413i	−0.902325	+	0.431056i	$0.858141\pi$
$522$	−5.18748	+	3.76892i	−0.227050	+	0.164961i
$523$	−0.782114	+	0.568239i	−0.0341994	+	0.0248473i	−0.604754	−	0.796413i	$-0.706728\pi$
$523$	−0.782114	+	0.568239i	−0.0341994	+	0.0248473i	0.570554	+	0.821260i	$0.306728\pi$
$524$	4.51224	+	13.8872i	0.197118	+	0.606667i
$525$	0.897614	−	2.76257i	0.0391751	−	0.120569i
$526$	10.3911	+	7.54954i	0.453071	+	0.329176i
$527$	−9.08497			−0.395747
$528$	−0.575300	−	9.61674i	−0.0250367	−	0.418515i
$529$	65.3588			2.84169
$530$	−6.27479	−	4.55890i	−0.272559	−	0.198026i
$531$	−9.48683	+	29.1975i	−0.411693	+	1.26706i
$532$	−1.22828	−	3.78025i	−0.0532526	−	0.163895i
$533$	−28.6066	+	20.7839i	−1.23909	+	0.900252i
$534$	−3.36255	+	2.44303i	−0.145512	+	0.105720i
$535$	1.01725	+	3.13076i	0.0439794	+	0.135355i
$536$	1.19936	−	3.69126i	0.0518045	−	0.159438i
$537$	−7.41873	−	5.39002i	−0.320142	−	0.232597i
$538$	7.87541			0.339533
$539$	−3.08747	+	1.21143i	−0.132987	+	0.0521798i
$540$	7.08034			0.304689
$541$	1.26531	+	0.919302i	0.0543999	+	0.0395239i	0.614653	−	0.788798i	$-0.289296\pi$
$541$	1.26531	+	0.919302i	0.0543999	+	0.0395239i	−0.560253	+	0.828322i	$0.689296\pi$
$542$	3.05292	−	9.39594i	0.131134	−	0.403590i
$543$	6.36448	+	19.5879i	0.273126	+	0.840596i
$544$	−5.72647	+	4.16052i	−0.245520	+	0.178381i
$545$	10.1819	−	7.39757i	0.436144	−	0.316877i
$546$	−5.84365	−	17.9849i	−0.250085	−	0.769682i
$547$	−4.49351	+	13.8296i	−0.192128	+	0.591311i	0.807870	+	0.589361i	$0.200620\pi$
$547$	−4.49351	+	13.8296i	−0.192128	+	0.591311i	−0.999998	+	0.00194934i	$0.999380\pi$
$548$	−8.17078	−	5.93642i	−0.349038	−	0.253591i
$549$	34.4554			1.47052
$550$	−3.08747	+	1.21143i	−0.131650	+	0.0516554i
$551$	4.68719			0.199681
$552$	22.0897	+	16.0491i	0.940200	+	0.683095i
$553$	−4.43216	+	13.6408i	−0.188475	+	0.580065i
$554$	8.35240	+	25.7060i	0.354860	+	1.09215i
$555$	2.36895	−	1.72114i	0.100556	−	0.0730585i
$556$	14.9757	−	10.8805i	0.635113	−	0.461437i
$557$	−11.4349	−	35.1929i	−0.484511	−	1.49117i	−0.832688	−	0.553743i	$-0.813199\pi$
$557$	−11.4349	−	35.1929i	−0.484511	−	1.49117i	0.348176	−	0.937429i	$-0.386801\pi$
$558$	−2.15663	+	6.63744i	−0.0912976	+	0.280985i
$559$	−58.9903	−	42.8590i	−2.49502	−	1.81274i
$560$	1.00000			0.0422577
$561$	−4.07215	−	68.0702i	−0.171926	−	2.87393i
$562$	13.6419			0.575448
$563$	−19.3670	−	14.0709i	−0.816221	−	0.593019i	0.0994065	−	0.995047i	$-0.468306\pi$
$563$	−19.3670	−	14.0709i	−0.816221	−	0.593019i	−0.915628	+	0.402028i	$0.868306\pi$
$564$	10.2251	−	31.4697i	0.430555	−	1.32511i
$565$	−0.372334	−	1.14593i	−0.0156642	−	0.0482095i
$566$	−14.8738	+	10.8064i	−0.625191	+	0.454228i
$567$	3.44157	−	2.50045i	0.144532	−	0.105009i
$568$	−0.0803215	−	0.247204i	−0.00337022	−	0.0103725i
$569$	−8.22221	+	25.3054i	−0.344693	+	1.06086i	0.617055	+	0.786920i	$0.288326\pi$
$569$	−8.22221	+	25.3054i	−0.344693	+	1.06086i	−0.961748	+	0.273936i	$0.911674\pi$
$570$	−9.34069	−	6.78641i	−0.391239	−	0.284251i
$571$	17.4823			0.731610			0.365805	−	0.930692i	$-0.380794\pi$
$571$	17.4823			0.731610			0.365805	+	0.930692i	$0.380794\pi$
$572$	−11.6256	+	18.1949i	−0.486091	+	0.760767i
$573$	−22.1195			−0.924055
$574$	−4.39413	−	3.19252i	−0.183407	−	0.133253i
$575$	2.90474	−	8.93987i	0.121136	−	0.372818i
$576$	1.68028	+	5.17138i	0.0700118	+	0.215474i
$577$	−25.3380	+	18.4091i	−1.05483	+	0.766381i	−0.973126	−	0.230275i	$-0.926037\pi$
$577$	−25.3380	+	18.4091i	−1.05483	+	0.766381i	−0.0817076	+	0.996656i	$0.526037\pi$
$578$	−26.7804	+	19.4571i	−1.11392	+	0.809310i
$579$	7.67911	+	23.6339i	0.319133	+	0.982190i
$580$	−0.364402	+	1.12151i	−0.0151310	+	0.0465683i
$581$	3.71745	+	2.70088i	0.154226	+	0.112051i
$582$	25.0009			1.03632
$583$	16.3359	+	19.8711i	0.676565	+	0.822975i
$584$	4.82486			0.199654
$585$	−28.6386	−	20.8072i	−1.18406	−	0.860271i
$586$	3.05137	−	9.39116i	0.126051	−	0.387945i
$587$	1.25046	+	3.84851i	0.0516118	+	0.158845i	0.973540	−	0.228515i	$-0.0733870\pi$
$587$	1.25046	+	3.84851i	0.0516118	+	0.158845i	−0.921929	+	0.387360i	$0.873387\pi$
$588$	2.34998	−	1.70736i	0.0969117	−	0.0704105i
$589$	4.12730	−	2.99866i	0.170062	−	0.123558i
$590$	1.74470	+	5.36963i	0.0718281	+	0.221064i
$591$	−4.76021	+	14.6504i	−0.195809	+	0.602638i
$592$	0.815547	+	0.592530i	0.0335188	+	0.0243528i
$593$	23.7125			0.973756			0.486878	−	0.873470i	$-0.338136\pi$
$593$	23.7125			0.973756			0.486878	+	0.873470i	$0.338136\pi$
$594$	−22.7270	−	5.90998i	−0.932500	−	0.242489i
$595$	7.07831			0.290182
$596$	−9.31392	−	6.76696i	−0.381513	−	0.277185i
$597$	−24.9953	+	76.9275i	−1.02299	+	3.14843i
$598$	−18.9104	−	58.2003i	−0.773305	−	2.37999i
$599$	8.43294	−	6.12689i	0.344561	−	0.250338i	−0.402023	−	0.915630i	$-0.631693\pi$
$599$	8.43294	−	6.12689i	0.344561	−	0.250338i	0.746584	+	0.665292i	$0.231693\pi$
$600$	2.34998	−	1.70736i	0.0959377	−	0.0697028i
$601$	−4.81848	−	14.8298i	−0.196550	−	0.604919i	−0.999955	−	0.00948588i	$-0.996981\pi$
$601$	−4.81848	−	14.8298i	−0.196550	−	0.604919i	0.803405	−	0.595433i	$-0.203019\pi$
$602$	3.46108	−	10.6521i	0.141063	−	0.434147i
$603$	−17.0736	−	12.4047i	−0.695292	−	0.505159i
$604$	5.43407			0.221109
$605$	10.9215	−	1.31141i	0.444024	−	0.0533163i
$606$	20.7473			0.842799
$607$	2.48340	+	1.80430i	0.100798	+	0.0732342i	0.637043	−	0.770828i	$-0.280157\pi$
$607$	2.48340	+	1.80430i	0.100798	+	0.0732342i	−0.536244	+	0.844063i	$0.680157\pi$
$608$	1.22828	−	3.78025i	0.0498132	−	0.153309i
$609$	1.05849	+	3.25770i	0.0428923	+	0.132009i
$610$	5.12643	−	3.72457i	0.207563	−	0.150803i
$611$	−59.9972	+	43.5905i	−2.42723	+	1.76348i
$612$	11.8936	+	36.6046i	0.480769	+	1.47965i
$613$	7.88838	−	24.2779i	0.318609	−	0.980577i	−0.655635	−	0.755078i	$-0.727599\pi$
$613$	7.88838	−	24.2779i	0.318609	−	0.980577i	0.974243	−	0.225499i	$-0.0724011\pi$
$614$	−5.26139	−	3.82262i	−0.212332	−	0.154269i
$615$	−15.7769			−0.636187
$616$	−3.20987	−	0.834702i	−0.129329	−	0.0336311i
$617$	−14.4437			−0.581483			−0.290741	−	0.956802i	$-0.593902\pi$
$617$	−14.4437			−0.581483			−0.290741	+	0.956802i	$0.593902\pi$
$618$	7.33498	+	5.32917i	0.295056	+	0.214371i
$619$	0.546310	−	1.68137i	0.0219581	−	0.0675800i	−0.939477	−	0.342612i	$-0.888688\pi$
$619$	0.546310	−	1.68137i	0.0219581	−	0.0675800i	0.961435	+	0.275032i	$0.0886884\pi$
$620$	0.396621	+	1.22068i	0.0159287	+	0.0490235i
$621$	53.8439	−	39.1199i	2.16068	−	1.56983i
$622$	−2.72635	+	1.98081i	−0.109317	+	0.0794233i
$623$	0.442167	+	1.36085i	0.0177150	+	0.0545213i
$624$	5.84365	−	17.9849i	0.233933	−	0.719972i
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	−5.42220			−0.216715
$627$	24.3178	+	29.5802i	0.971159	+	1.18132i
$628$	7.97651			0.318297
$629$	5.77269	+	4.19411i	0.230172	+	0.167230i
$630$	1.68028	−	5.17138i	0.0669441	−	0.206033i
$631$	6.59949	+	20.3111i	0.262722	+	0.808574i	0.992210	+	0.124580i	$0.0397584\pi$
$631$	6.59949	+	20.3111i	0.262722	+	0.808574i	−0.729488	+	0.683994i	$0.760242\pi$
$632$	−11.6035	+	8.43046i	−0.461564	+	0.335346i
$633$	21.7781	−	15.8227i	0.865601	−	0.628896i
$634$	−2.21256	−	6.80955i	−0.0878718	−	0.270442i
$635$	4.94507	−	15.2194i	0.196239	−	0.603962i
$636$	−18.2266	−	13.2424i	−0.722732	−	0.525096i
$637$	−6.51020			−0.257943
$638$	2.10581	−	3.29575i	0.0833699	−	0.130480i
$639$	−1.41335			−0.0559113
$640$	0.809017	+	0.587785i	0.0319792	+	0.0232343i
$641$	14.2580	−	43.8815i	0.563156	−	1.73322i	−0.110212	−	0.993908i	$-0.535153\pi$
$641$	14.2580	−	43.8815i	0.563156	−	1.73322i	0.673368	−	0.739308i	$-0.264847\pi$
$642$	2.95484	+	9.09405i	0.116618	+	0.358914i
$643$	−14.9425	+	10.8564i	−0.589274	+	0.428133i	−0.842056	−	0.539391i	$-0.818655\pi$
$643$	−14.9425	+	10.8564i	−0.589274	+	0.428133i	0.252782	+	0.967523i	$0.418655\pi$
$644$	7.60471	−	5.52514i	0.299667	−	0.217721i
$645$	−10.0535	−	30.9416i	−0.395857	−	1.21832i
$646$	8.69413	−	26.7578i	0.342066	−	1.05277i
$647$	−29.4326	−	21.3841i	−1.15712	−	0.840694i	−0.167705	−	0.985837i	$-0.553636\pi$
$647$	−29.4326	−	21.3841i	−1.15712	−	0.840694i	−0.989411	+	0.145143i	$0.953636\pi$
$648$	4.25401			0.167113
$649$	−1.11821	−	18.6921i	−0.0438938	−	0.733730i
$650$	−6.51020			−0.255351
$651$	3.01619	+	2.19139i	0.118214	+	0.0858874i
$652$	4.43229	−	13.6412i	0.173582	−	0.534230i
$653$	−0.894337	−	2.75249i	−0.0349981	−	0.107713i	0.932031	−	0.362378i	$-0.118035\pi$
$653$	−0.894337	−	2.75249i	−0.0349981	−	0.107713i	−0.967029	+	0.254665i	$0.918035\pi$
$654$	29.5757	−	21.4880i	1.15650	−	0.840248i
$655$	11.8132	−	8.58278i	0.461579	−	0.335357i
$656$	−1.67841	−	5.16560i	−0.0655308	−	0.201683i
$657$	8.10714	−	24.9512i	0.316290	−	0.973439i
$658$	−9.21588	−	6.69573i	−0.359272	−	0.261027i
$659$	19.1764			0.747008			0.373504	−	0.927629i	$-0.378156\pi$
$659$	19.1764			0.747008			0.373504	+	0.927629i	$0.378156\pi$
$660$	−8.96829	+	3.51888i	−0.349090	+	0.136972i
$661$	−24.9234			−0.969406			−0.484703	−	0.874679i	$-0.661072\pi$
$661$	−24.9234			−0.969406			−0.484703	+	0.874679i	$0.661072\pi$
$662$	−16.7453	−	12.1662i	−0.650825	−	0.472852i
$663$	41.3631	−	127.303i	1.60641	−	4.94402i
$664$	1.41994	+	4.37012i	0.0551043	+	0.169594i
$665$	−3.21567	+	2.33632i	−0.124698	+	0.0905987i
$666$	4.43455	−	3.22189i	0.171835	−	0.124846i
$667$	3.42535	+	10.5422i	0.132630	+	0.408194i
$668$	−0.590345	+	1.81690i	−0.0228411	+	0.0702978i
$669$	61.1310	+	44.4143i	2.36346	+	1.71716i
$670$	−3.88122			−0.149944
$671$	−19.5641	+	7.67634i	−0.755263	+	0.296342i
$672$	2.90474			0.112053
$673$	−10.7653	−	7.82142i	−0.414970	−	0.301494i	0.360641	−	0.932705i	$-0.382558\pi$
$673$	−10.7653	−	7.82142i	−0.414970	−	0.301494i	−0.775611	+	0.631211i	$0.782558\pi$
$674$	−2.41371	+	7.42863i	−0.0929726	+	0.286140i
$675$	−2.18795	−	6.73381i	−0.0842141	−	0.259184i
$676$	−23.7711	+	17.2707i	−0.914273	+	0.664258i
$677$	−22.8748	+	16.6195i	−0.879149	+	0.638739i	−0.933026	−	0.359809i	$-0.882842\pi$
$677$	−22.8748	+	16.6195i	−0.879149	+	0.638739i	0.0538775	+	0.998548i	$0.482842\pi$
$678$	−1.08153	−	3.32862i	−0.0415361	−	0.127835i
$679$	2.65969	−	8.18569i	0.102070	−	0.314138i
$680$	5.72647	+	4.16052i	0.219600	+	0.159549i
$681$	0.851435			0.0326271
$682$	−0.254203	−	4.24927i	−0.00973394	−	0.162713i
$683$	−20.1040			−0.769259			−0.384629	−	0.923071i	$-0.625671\pi$
$683$	−20.1040			−0.769259			−0.384629	+	0.923071i	$0.625671\pi$
$684$	−17.4853	−	12.7038i	−0.668566	−	0.485741i
$685$	−3.12096	+	9.60533i	−0.119246	+	0.367001i
$686$	−0.309017	−	0.951057i	−0.0117983	−	0.0363115i
$687$	−46.8943	+	34.0707i	−1.78913	+	1.29988i
$688$	9.06122	−	6.58336i	0.345456	−	0.250988i
$689$	15.6033	+	48.0222i	0.594440	+	1.82950i
$690$	8.43751	−	25.9680i	0.321211	−	0.988585i
$691$	1.36612	+	0.992547i	0.0519698	+	0.0377583i	0.613467	−	0.789720i	$-0.289774\pi$
$691$	1.36612	+	0.992547i	0.0519698	+	0.0377583i	−0.561497	+	0.827479i	$0.689774\pi$
$692$	−14.5926			−0.554726
$693$	−9.71006	+	15.1969i	−0.368855	+	0.577284i
$694$	−27.9220			−1.05990
$695$	−14.9757	−	10.8805i	−0.568062	−	0.412721i
$696$	−1.05849	+	3.25770i	−0.0401221	+	0.123483i
$697$	−11.8803	−	36.5637i	−0.449998	−	1.38495i
$698$	−16.6607	+	12.1047i	−0.630616	+	0.458169i
$699$	0.473658	−	0.344133i	0.0179154	−	0.0130163i
$700$	−0.309017	−	0.951057i	−0.0116797	−	0.0359466i
$701$	0.630834	−	1.94151i	0.0238263	−	0.0733298i	−0.938436	−	0.345452i	$-0.887726\pi$
$701$	0.630834	−	1.94151i	0.0238263	−	0.0733298i	0.962263	+	0.272122i	$0.0877256\pi$
$702$	−37.2912	−	27.0936i	−1.40747	−	1.02258i
$703$	−4.00687			−0.151122
$704$	−2.10621	−	2.56200i	−0.0793809	−	0.0965591i
$705$	−33.0892			−1.24621
$706$	4.53966	+	3.29826i	0.170852	+	0.124132i
$707$	2.20717	−	6.79297i	0.0830092	−	0.255476i
$708$	5.06790	+	15.5974i	0.190463	+	0.586186i
$709$	−4.04013	+	2.93533i	−0.151730	+	0.110239i	−0.661060	−	0.750333i	$-0.729893\pi$
$709$	−4.04013	+	2.93533i	−0.151730	+	0.110239i	0.509330	+	0.860571i	$0.329893\pi$
$710$	−0.210285	+	0.152781i	−0.00789184	+	0.00573376i
$711$	24.0999	+	74.1719i	0.903817	+	2.78166i
$712$	−0.442167	+	1.36085i	−0.0165709	+	0.0510000i
$713$	9.76060	+	7.09149i	0.365537	+	0.265578i
$714$	20.5606			0.769463
$715$	20.8969	+	5.43408i	0.781500	+	0.203223i
$716$	−3.15693			−0.117980
$717$	56.2099	+	40.8389i	2.09920	+	1.52516i
$718$	2.54712	−	7.83922i	0.0950575	−	0.292557i
$719$	10.6087	+	32.6502i	0.395638	+	1.21765i	0.928464	+	0.371424i	$0.121130\pi$
$719$	10.6087	+	32.6502i	0.395638	+	1.21765i	−0.532826	+	0.846225i	$0.678870\pi$
$720$	4.39904	−	3.19609i	0.163943	−	0.119111i
$721$	2.52518	−	1.83465i	0.0940424	−	0.0683258i
$722$	−0.989176	−	3.04437i	−0.0368133	−	0.113300i
$723$	16.6822	−	51.3427i	0.620419	−	1.90945i
$724$	5.73629	+	4.16766i	0.213188	+	0.154890i
$725$	1.17923			0.0437955
$726$	31.7243	−	3.80930i	1.17740	−	0.141376i
$727$	26.6447			0.988196			0.494098	−	0.869406i	$-0.335498\pi$
$727$	26.6447			0.988196			0.494098	+	0.869406i	$0.335498\pi$
$728$	−5.26686	−	3.82660i	−0.195203	−	0.141823i
$729$	−11.9183	+	36.6807i	−0.441418	+	1.35855i
$730$	−1.49096	−	4.58872i	−0.0551831	−	0.169836i
$731$	64.1381	−	46.5990i	2.37223	−	1.72353i
$732$	14.8909	−	10.8189i	0.550385	−	0.399878i
$733$	4.36749	+	13.4417i	0.161317	+	0.496482i	0.998746	−	0.0500637i	$-0.0159424\pi$
$733$	4.36749	+	13.4417i	0.161317	+	0.496482i	−0.837429	+	0.546546i	$0.815942\pi$
$734$	−1.26950	+	3.90711i	−0.0468580	+	0.144214i
$735$	−2.34998	−	1.70736i	−0.0866805	−	0.0629770i
$736$	9.39994			0.346486
$737$	12.4582	+	3.23966i	0.458904	+	0.119334i
$738$	−29.5335			−1.08714
$739$	−29.1989	−	21.2142i	−1.07410	−	0.780378i	−0.0974534	−	0.995240i	$-0.531070\pi$
$739$	−29.1989	−	21.2142i	−1.07410	−	0.780378i	−0.976644	+	0.214862i	$0.931070\pi$
$740$	0.311511	−	0.958733i	0.0114514	−	0.0352437i
$741$	23.2273	+	71.4862i	0.853275	+	2.62611i
$742$	−6.27479	+	4.55890i	−0.230355	+	0.167362i
$743$	23.7453	−	17.2520i	0.871131	−	0.632914i	−0.0597589	−	0.998213i	$-0.519033\pi$
$743$	23.7453	−	17.2520i	0.871131	−	0.632914i	0.930890	+	0.365299i	$0.119033\pi$
$744$	1.15208	+	3.54574i	0.0422374	+	0.129993i
$745$	−3.55760	+	10.9492i	−0.130340	+	0.401146i
$746$	21.2110	+	15.4107i	0.776589	+	0.564225i
$747$	24.9855			0.914170
$748$	−14.9084	−	18.1346i	−0.545106	−	0.663068i
$749$	3.29188			0.120283
$750$	−2.34998	−	1.70736i	−0.0858093	−	0.0623441i
$751$	11.3847	−	35.0387i	0.415435	−	1.27858i	−0.496425	−	0.868079i	$-0.665354\pi$
$751$	11.3847	−	35.0387i	0.415435	−	1.27858i	0.911861	−	0.410499i	$-0.134646\pi$
$752$	−3.52015	−	10.8339i	−0.128367	−	0.395072i
$753$	−23.7225	+	17.2354i	−0.864495	+	0.628093i
$754$	6.21084	−	4.51244i	0.226185	−	0.164333i
$755$	−1.67922	−	5.16811i	−0.0611131	−	0.188087i
$756$	2.18795	−	6.73381i	0.0795748	−	0.244906i
$757$	29.7452	+	21.6112i	1.08111	+	0.785471i	0.977876	−	0.209187i	$-0.0670816\pi$
$757$	29.7452	+	21.6112i	1.08111	+	0.785471i	0.103232	+	0.994657i	$0.467082\pi$
$758$	19.7398			0.716982
$759$	−48.7589	+	76.3111i	−1.76984	+	2.76992i
$760$	−3.97479			−0.144181
$761$	−28.8379	−	20.9519i	−1.04537	−	0.759507i	−0.0740451	−	0.997255i	$-0.523591\pi$
$761$	−28.8379	−	20.9519i	−1.04537	−	0.759507i	−0.971327	+	0.237748i	$0.923591\pi$
$762$	14.3641	−	44.2083i	0.520358	−	1.60150i
$763$	−3.88913	−	11.9695i	−0.140796	−	0.433326i
$764$	−6.16064	+	4.47596i	−0.222884	+	0.161935i
$765$	31.1378	−	22.6229i	1.12579	−	0.817933i
$766$	11.0640	+	34.0516i	0.399760	+	1.23033i
$767$	11.3583	−	34.9574i	0.410126	−	1.26224i
$768$	2.34998	+	1.70736i	0.0847977	+	0.0616092i
$769$	30.6264			1.10442			0.552209	−	0.833706i	$-0.313785\pi$
$769$	30.6264			1.10442			0.552209	+	0.833706i	$0.313785\pi$
$770$	0.198055	+	3.31071i	0.00713742	+	0.119310i
$771$	15.8982			0.572560
$772$	6.92116	+	5.02852i	0.249098	+	0.180980i
$773$	−3.31663	+	10.2075i	−0.119291	+	0.367139i	−0.992818	−	0.119636i	$-0.961827\pi$
$773$	−3.31663	+	10.2075i	−0.119291	+	0.367139i	0.873527	+	0.486776i	$0.161827\pi$
$774$	−18.8197	−	57.9209i	−0.676458	−	2.08192i
$775$	1.03837	−	0.754419i	0.0372993	−	0.0270995i
$776$	6.96317	−	5.05904i	0.249963	−	0.181609i
$777$	−0.904859	−	2.78487i	−0.0324616	−	0.0999066i
$778$	−8.92549	+	27.4698i	−0.319994	+	0.984842i
$779$	17.4657	+	12.6896i	0.625775	+	0.454652i
$780$	−18.9104			−0.677102
$781$	0.802513	−	0.314881i	0.0287162	−	0.0112673i
$782$	66.5356			2.37931
$783$	6.75476	+	4.90762i	0.241395	+	0.175384i
$784$	0.309017	−	0.951057i	0.0110363	−	0.0339663i
$785$	−2.46488	−	7.58611i	−0.0879753	−	0.270760i
$786$	34.3142	−	24.9308i	1.22395	−	0.889251i
$787$	14.7731	−	10.7333i	0.526603	−	0.382600i	−0.292482	−	0.956271i	$-0.594481\pi$
$787$	14.7731	−	10.7333i	0.526603	−	0.382600i	0.819086	+	0.573671i	$0.194481\pi$
$788$	1.63877	+	5.04363i	0.0583789	+	0.179672i
$789$	11.5290	−	35.4826i	0.410443	−	1.26321i
$790$	11.6035	+	8.43046i	0.412835	+	0.299942i
$791$	−1.20490			−0.0428413
$792$	−16.7881	+	6.58715i	−0.596540	+	0.234064i
$793$	−41.2526			−1.46492
$794$	25.6553	+	18.6397i	0.910473	+	0.661497i
$795$	−6.96195	+	21.4267i	−0.246915	+	0.759926i
$796$	8.60499	+	26.4834i	0.304996	+	0.938681i
$797$	23.8487	−	17.3271i	0.844763	−	0.613756i	−0.0789342	−	0.996880i	$-0.525152\pi$
$797$	23.8487	−	17.3271i	0.844763	−	0.613756i	0.923697	+	0.383124i	$0.125152\pi$
$798$	−9.34069	+	6.78641i	−0.330657	+	0.240236i
$799$	−24.9167	−	76.6858i	−0.881490	−	2.71295i
$800$	0.309017	−	0.951057i	0.0109254	−	0.0336249i
$801$	6.29451	+	4.57323i	0.222405	+	0.161587i
$802$	−24.8442			−0.877281
$803$	0.955590	+	15.9737i	0.0337221	+	0.563700i
$804$	−11.2739			−0.397601
$805$	−7.60471	−	5.52514i	−0.268031	−	0.194736i
$806$	2.58208	−	7.94684i	0.0909501	−	0.279916i
$807$	−7.06908	−	21.7564i	−0.248843	−	0.765861i
$808$	5.77844	−	4.19829i	0.203285	−	0.147695i
$809$	18.1073	−	13.1557i	0.636619	−	0.462531i	−0.222068	−	0.975031i	$-0.571281\pi$
$809$	18.1073	−	13.1557i	0.636619	−	0.462531i	0.858687	+	0.512501i	$0.171281\pi$
$810$	−1.31456	−	4.04581i	−0.0461890	−	0.142155i
$811$	−8.35328	+	25.7088i	−0.293323	+	0.902756i	0.690456	+	0.723374i	$0.257410\pi$
$811$	−8.35328	+	25.7088i	−0.293323	+	0.902756i	−0.983779	+	0.179382i	$0.942590\pi$
$812$	0.954016	+	0.693133i	0.0334794	+	0.0243242i
$813$	−28.6973			−1.00646
$814$	−1.80017	+	2.81739i	−0.0630958	+	0.0987495i
$815$	−14.3432			−0.502420
$816$	16.6339	+	12.0852i	0.582303	+	0.423068i
$817$	−13.7571	+	42.3399i	−0.481298	+	1.48128i
$818$	5.45022	+	16.7740i	0.190562	+	0.586491i
$819$	−28.6386	+	20.8072i	−1.00071	+	0.727062i
$820$	−4.39413	+	3.19252i	−0.153450	+	0.111488i
$821$	−4.45729	−	13.7181i	−0.155560	−	0.478766i	0.842657	−	0.538451i	$-0.180990\pi$
$821$	−4.45729	−	13.7181i	−0.155560	−	0.478766i	−0.998217	+	0.0596851i	$0.980990\pi$
$822$	−9.06558	+	27.9010i	−0.316198	+	0.973159i
$823$	12.4069	+	9.01414i	0.432477	+	0.314213i	0.782639	−	0.622476i	$-0.213873\pi$
$823$	12.4069	+	9.01414i	0.432477	+	0.314213i	−0.350161	+	0.936689i	$0.613873\pi$
$824$	3.12129			0.108735
$825$	6.11800	+	7.44195i	0.213002	+	0.259096i
$826$	5.64597			0.196448
$827$	−35.7653	−	25.9850i	−1.24368	−	0.903588i	−0.245844	−	0.969309i	$-0.579065\pi$
$827$	−35.7653	−	25.9850i	−1.24368	−	0.903588i	−0.997838	+	0.0657219i	$0.979065\pi$
$828$	15.7946	−	48.6107i	0.548899	−	1.68934i
$829$	−8.64008	−	26.5914i	−0.300082	−	0.923559i	−0.981467	−	0.191633i	$-0.938622\pi$
$829$	−8.64008	−	26.5914i	−0.300082	−	0.923559i	0.681384	−	0.731926i	$-0.261378\pi$
$830$	3.71745	−	2.70088i	0.129034	−	0.0937490i
$831$	63.5176	−	46.1482i	2.20340	−	1.60086i
$832$	−2.01176	−	6.19157i	−0.0697453	−	0.214654i
$833$	2.18732	−	6.73187i	0.0757861	−	0.233245i
$834$	−43.5006	−	31.6051i	−1.50630	−	1.09439i
$835$	1.91040			0.0661120
$836$	12.7586	+	3.31777i	0.441264	+	0.114747i
$837$	9.08758			0.314113
$838$	−5.42665	−	3.94269i	−0.187461	−	0.136198i
$839$	−1.37513	+	4.23222i	−0.0474748	+	0.146112i	−0.971984	−	0.235048i	$-0.924475\pi$
$839$	−1.37513	+	4.23222i	−0.0474748	+	0.146112i	0.924509	+	0.381160i	$0.124475\pi$
$840$	−0.897614	−	2.76257i	−0.0309706	−	0.0953178i
$841$	22.3365	−	16.2284i	0.770224	−	0.559600i
$842$	−12.9797	+	9.43029i	−0.447309	+	0.324989i
$843$	−12.2451	−	37.6867i	−0.421745	−	1.29800i
$844$	2.86376	−	8.81375i	0.0985748	−	0.303382i
$845$	23.7711	+	17.2707i	0.817751	+	0.594131i
$846$	−61.9412			−2.12958
$847$	2.12772	−	10.7923i	0.0731094	−	0.370826i
$848$	−7.75606			−0.266344
$849$	43.2044	+	31.3898i	1.48277	+	1.07730i
$850$	2.18732	−	6.73187i	0.0750244	−	0.230901i
$851$	−2.92819	−	9.01203i	−0.100377	−	0.308928i
$852$	−0.610822	+	0.443788i	−0.0209264	+	0.0152039i
$853$	−1.86997	+	1.35861i	−0.0640265	+	0.0465180i	−0.619338	−	0.785124i	$-0.712599\pi$
$853$	−1.86997	+	1.35861i	−0.0640265	+	0.0465180i	0.555312	+	0.831642i	$0.312599\pi$
$854$	−1.95812	−	6.02648i	−0.0670056	−	0.206222i
$855$	−6.67878	+	20.5552i	−0.228409	+	0.702972i
$856$	2.66319	+	1.93492i	0.0910258	+	0.0661341i
$857$	2.10357			0.0718566			0.0359283	−	0.999354i	$-0.488561\pi$
$857$	2.10357			0.0718566			0.0359283	+	0.999354i	$0.488561\pi$
$858$	60.7001	+	15.7846i	2.07227	+	0.538877i
$859$	−6.91941			−0.236087			−0.118044	−	0.993008i	$-0.537662\pi$
$859$	−6.91941			−0.236087			−0.118044	+	0.993008i	$0.537662\pi$
$860$	−9.06122	−	6.58336i	−0.308985	−	0.224491i
$861$	−4.87533	+	15.0047i	−0.166151	+	0.511360i
$862$	9.74887	+	30.0039i	0.332048	+	1.02194i
$863$	30.4046	−	22.0902i	1.03498	−	0.751959i	0.0656831	−	0.997841i	$-0.479077\pi$
$863$	30.4046	−	22.0902i	1.03498	−	0.751959i	0.969300	+	0.245881i	$0.0790773\pi$
$864$	5.72812	−	4.16172i	0.194875	−	0.141585i
$865$	4.50935	+	13.8784i	0.153323	+	0.471878i
$866$	−2.55529	+	7.86439i	−0.0868324	+	0.267243i
$867$	77.7902	+	56.5179i	2.64189	+	1.91945i
$868$	1.28349			0.0435646
$869$	−30.2089	−	36.7462i	−1.02477	−	1.24653i
$870$	3.42535			0.116130
$871$	20.4418	+	14.8519i	0.692645	+	0.503236i
$872$	3.88913	−	11.9695i	0.131703	−	0.405339i
$873$	−14.4621	−	44.5098i	−0.489469	−	1.50643i
$874$	−30.2271	+	21.9613i	−1.02245	+	0.742852i
$875$	−0.809017	+	0.587785i	−0.0273498	+	0.0198708i
$876$	−4.33086	−	13.3290i	−0.146326	−	0.450346i
$877$	10.5508	−	32.4720i	0.356275	−	1.09650i	−0.598991	−	0.800756i	$-0.704432\pi$
$877$	10.5508	−	32.4720i	0.356275	−	1.09650i	0.955266	−	0.295747i	$-0.0955684\pi$
$878$	−8.98077	−	6.52491i	−0.303086	−	0.220205i
$879$	−28.6827			−0.967443
$880$	−1.78575	+	2.79483i	−0.0601978	+	0.0942138i
$881$	38.7897			1.30686			0.653429	−	0.756987i	$-0.273330\pi$
$881$	38.7897			1.30686			0.653429	+	0.756987i	$0.273330\pi$
$882$	−4.39904	−	3.19609i	−0.148123	−	0.107618i
$883$	0.400498	−	1.23261i	0.0134778	−	0.0414805i	−0.944091	−	0.329684i	$-0.893058\pi$
$883$	0.400498	−	1.23261i	0.0134778	−	0.0414805i	0.957569	+	0.288203i	$0.0930579\pi$
$884$	−14.2399	−	43.8258i	−0.478939	−	1.47402i
$885$	13.2679	−	9.63971i	0.445997	−	0.324035i
$886$	−3.67189	+	2.66779i	−0.123360	+	0.0896261i
$887$	1.99041	+	6.12586i	0.0668316	+	0.205686i	0.978895	−	0.204362i	$-0.0655119\pi$
$887$	1.99041	+	6.12586i	0.0668316	+	0.205686i	−0.912064	+	0.410048i	$0.865512\pi$
$888$	0.904859	−	2.78487i	0.0303651	−	0.0934541i
$889$	−12.9464	−	9.40609i	−0.434207	−	0.315470i
$890$	1.43088			0.0479633
$891$	0.842530	+	14.0838i	0.0282258	+	0.471824i
$892$	26.0134			0.870992
$893$	36.6312	+	26.6141i	1.22582	+	0.890607i
$894$	−10.3339	+	31.8045i	−0.345617	+	1.06370i
$895$	0.975544	+	3.00242i	0.0326088	+	0.100360i
$896$	0.809017	−	0.587785i	0.0270274	−	0.0196365i
$897$	−143.808	+	104.483i	−4.80162	+	3.48858i
$898$	−3.00357	−	9.24403i	−0.100230	−	0.308477i
$899$	−0.467708	+	1.43946i	−0.0155989	+	0.0480085i
$900$	−4.39904	−	3.19609i	−0.146635	−	0.106536i
$901$	−54.8998			−1.82898
$902$	16.7694	−	6.57979i	0.558359	−	0.219083i
$903$	−32.5339			−1.08266
$904$	−0.974784	−	0.708222i	−0.0324208	−	0.0235551i
$905$	2.19107	−	6.74341i	0.0728336	−	0.224159i
$906$	−4.87770	−	15.0120i	−0.162051	−	0.498740i
$907$	−28.5563	+	20.7473i	−0.948195	+	0.688904i	−0.950379	−	0.311094i	$-0.899305\pi$
$907$	−28.5563	+	20.7473i	−0.948195	+	0.688904i	0.00218436	+	0.999998i	$0.499305\pi$
$908$	0.237138	−	0.172291i	0.00786971	−	0.00571768i
$909$	−12.0015	−	36.9369i	−0.398065	−	1.22512i
$910$	−2.01176	+	6.19157i	−0.0666893	+	0.205248i
$911$	29.8760	+	21.7062i	0.989835	+	0.719157i	0.959885	−	0.280394i	$-0.0904652\pi$
$911$	29.8760	+	21.7062i	0.989835	+	0.719157i	0.0299499	+	0.999551i	$0.490465\pi$
$912$	−11.5457			−0.382317
$913$	−14.1870	+	5.56652i	−0.469520	+	0.184225i
$914$	21.1478			0.699506
$915$	−14.8909	−	10.8189i	−0.492280	−	0.357662i
$916$	−6.16648	+	18.9785i	−0.203746	+	0.627067i
$917$	−4.51224	−	13.8872i	−0.149007	−	0.458597i
$918$	40.5454	−	29.4579i	1.33820	−	0.972257i
$919$	28.7007	−	20.8523i	0.946749	−	0.687853i	−0.00328700	−	0.999995i	$-0.501046\pi$
$919$	28.7007	−	20.8523i	0.946749	−	0.687853i	0.950036	+	0.312141i	$0.101046\pi$
$920$	−2.90474	−	8.93987i	−0.0957664	−	0.294739i
$921$	−5.83758	+	17.9662i	−0.192355	+	0.592007i
$922$	−16.5976	−	12.0589i	−0.546614	−	0.397138i
$923$	1.69217			0.0556984
$924$	0.575300	+	9.61674i	0.0189260	+	0.316368i
$925$	−1.00807			−0.0331452
$926$	4.09504	+	2.97522i	0.134571	+	0.0977718i
$927$	5.24465	−	16.1414i	0.172257	−	0.530152i
$928$	0.364402	+	1.12151i	0.0119621	+	0.0368155i
$929$	14.3767	−	10.4453i	0.471684	−	0.342699i	−0.326413	−	0.945227i	$-0.605840\pi$
$929$	14.3767	−	10.4453i	0.471684	−	0.342699i	0.798097	+	0.602529i	$0.205840\pi$
$930$	3.01619	−	2.19139i	0.0989048	−	0.0718585i
$931$	1.22828	+	3.78025i	0.0402552	+	0.123893i
$932$	0.0622848	−	0.191693i	0.00204021	−	0.00627911i
$933$	7.91935	+	5.75374i	0.259268	+	0.188369i
$934$	−7.48743			−0.244996
$935$	−12.6401	+	19.7827i	−0.413376	+	0.646963i
$936$	−35.3993			−1.15706
$937$	−4.86664	−	3.53582i	−0.158986	−	0.115510i	0.505448	−	0.862857i	$-0.331327\pi$
$937$	−4.86664	−	3.53582i	−0.158986	−	0.115510i	−0.664434	+	0.747347i	$0.731327\pi$
$938$	−1.19936	+	3.69126i	−0.0391605	+	0.120524i
$939$	4.86704	+	14.9792i	0.158830	+	0.488828i
$940$	−9.21588	+	6.69573i	−0.300589	+	0.218391i
$941$	−24.8273	+	18.0381i	−0.809348	+	0.588026i	−0.913642	−	0.406521i	$-0.866742\pi$
$941$	−24.8273	+	18.0381i	−0.809348	+	0.588026i	0.104293	+	0.994547i	$0.466742\pi$
$942$	−7.15983	−	22.0357i	−0.233280	−	0.717961i
$943$	−15.7769	+	48.5563i	−0.513767	+	1.58121i
$944$	4.56768	+	3.31862i	0.148665	+	0.108012i
$945$	−7.08034			−0.230324
$946$	23.5902	+	28.6952i	0.766983	+	0.932960i
$947$	32.3767			1.05210			0.526051	−	0.850453i	$-0.323672\pi$
$947$	32.3767			1.05210			0.526051	+	0.850453i	$0.323672\pi$
$948$	33.7053	+	24.4883i	1.09470	+	0.795343i
$949$	−9.70647	+	29.8735i	−0.315085	+	0.969733i
$950$	1.22828	+	3.78025i	0.0398506	+	0.122648i
$951$	−16.8258	+	12.2247i	−0.545615	+	0.396413i
$952$	5.72647	−	4.16052i	0.185596	−	0.134843i
$953$	3.67224	+	11.3020i	0.118956	+	0.366108i	0.992751	−	0.120185i	$-0.0383488\pi$
$953$	3.67224	+	11.3020i	0.118956	+	0.366108i	−0.873796	+	0.486293i	$0.838349\pi$
$954$	−13.0324	+	40.1096i	−0.421939	+	1.29859i
$955$	6.16064	+	4.47596i	0.199353	+	0.144839i
$956$	23.9193			0.773604
$957$	−10.9949	−	2.85915i	−0.355416	−	0.0924232i
$958$	−0.414174			−0.0133814
$959$	8.17078	+	5.93642i	0.263848	+	0.191697i
$960$	0.897614	−	2.76257i	0.0289704	−	0.0891616i
$961$	−9.07047	−	27.9160i	−0.292596	−	0.900517i
$962$	−5.30937	+	3.85749i	−0.171181	+	0.124370i
$963$	14.4811	−	10.5211i	0.466647	−	0.339039i
$964$	−5.74311	−	17.6755i	−0.184973	−	0.569289i
$965$	2.64365	−	8.13631i	0.0851021	−	0.261917i
$966$	−22.0897	−	16.0491i	−0.710724	−	0.516371i
$967$	24.0988			0.774965			0.387483	−	0.921877i	$-0.373345\pi$
$967$	24.0988			0.774965			0.387483	+	0.921877i	$0.373345\pi$
$968$	8.06489	−	7.48048i	0.259215	−	0.240432i
$969$	−81.7242			−2.62536
$970$	−6.96317	−	5.05904i	−0.223574	−	0.162436i
$971$	−0.780102	+	2.40091i	−0.0250347	+	0.0770488i	−0.962793	−	0.270239i	$-0.912897\pi$
$971$	−0.780102	+	2.40091i	−0.0250347	+	0.0770488i	0.937759	+	0.347288i	$0.112897\pi$
$972$	2.74538	+	8.44940i	0.0880580	+	0.271015i
$973$	−14.9757	+	10.8805i	−0.480100	+	0.348813i
$974$	19.2002	−	13.9498i	0.615216	−	0.446980i
$975$	5.84365	+	17.9849i	0.187146	+	0.575978i
$976$	1.95812	−	6.02648i	0.0626780	−	0.192903i
$977$	20.9141	+	15.1950i	0.669103	+	0.486132i	0.869725	−	0.493537i	$-0.164296\pi$
$977$	20.9141	+	15.1950i	0.669103	+	0.486132i	−0.200622	+	0.979669i	$0.564296\pi$
$978$	−41.6632			−1.33224
$979$	−4.59294	−	1.19436i	−0.146791	−	0.0381719i
$980$	−1.00000			−0.0319438
$981$	−55.3641	−	40.2244i	−1.76764	−	1.28427i
$982$	9.95537	−	30.6395i	0.317689	−	0.977745i
$983$	−0.301437	−	0.927729i	−0.00961436	−	0.0295900i	0.946134	−	0.323775i	$-0.104952\pi$
$983$	−0.301437	−	0.927729i	−0.00961436	−	0.0295900i	−0.955749	+	0.294185i	$0.904952\pi$
$984$	−12.7638	+	9.27344i	−0.406895	+	0.295626i
$985$	4.29037	−	3.11713i	0.136702	−	0.0993201i
$986$	2.57935	+	7.93842i	0.0821432	+	0.252811i
$987$	−10.2251	+	31.4697i	−0.325469	+	1.00169i
$988$	20.9347	+	15.2099i	0.666021	+	0.483892i
$989$	−105.282			−3.34777
$990$	11.4526	+	13.9309i	0.363987	+	0.442754i
$991$	3.48309			0.110644			0.0553220	−	0.998469i	$-0.482381\pi$
$991$	3.48309			0.110644			0.0553220	+	0.998469i	$0.482381\pi$
$992$	1.03837	+	0.754419i	0.0329682	+	0.0239528i
$993$	−18.5791	+	57.1806i	−0.589590	+	1.81457i
$994$	0.0803215	+	0.247204i	0.00254764	+	0.00784084i
$995$	22.5282	−	16.3677i	0.714191	−	0.518890i
$996$	10.7982	−	7.84536i	0.342154	−	0.248590i
$997$	13.2883	+	40.8973i	0.420846	+	1.29523i	0.906917	+	0.421310i	$0.138430\pi$
$997$	13.2883	+	40.8973i	0.420846	+	1.29523i	−0.486071	+	0.873919i	$0.661570\pi$
$998$	−1.38745	+	4.27013i	−0.0439190	+	0.135169i
$999$	−5.77435	−	4.19531i	−0.182692	−	0.132734i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.k.631.1	yes	16
11.3	even	5	inner	770.2.n.k.421.1	✓	16
11.5	even	5		8470.2.a.dh.1.1		8
11.6	odd	10		8470.2.a.dg.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.k.421.1	✓	16	11.3	even	5	inner
770.2.n.k.631.1	yes	16	1.1	even	1	trivial
8470.2.a.dg.1.1		8	11.6	odd	10
8470.2.a.dh.1.1		8	11.5	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)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.897614 + 2.76257i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(2.34998 - 1.70736i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-4.39904 - 3.19609i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-0.897614 + 2.76257i) q^{3} +(0.309017 + 0.951057i) q^{4} +(0.809017 - 0.587785i) q^{5} +(2.34998 - 1.70736i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(0.309017 - 0.951057i) q^{8} +(-4.39904 - 3.19609i) q^{9} -1.00000 q^{10} +(3.20987 + 0.834702i) q^{11} -2.90474 q^{12} +(5.26686 + 3.82660i) q^{13} +(-0.309017 + 0.951057i) q^{14} +(0.897614 + 2.76257i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-5.72647 + 4.16052i) q^{17} +(1.68028 + 5.17138i) q^{18} +(1.22828 - 3.78025i) q^{19} +(0.809017 + 0.587785i) q^{20} +2.90474 q^{21} +(-2.10621 - 2.56200i) q^{22} +9.39994 q^{23} +(2.34998 + 1.70736i) q^{24} +(0.309017 - 0.951057i) q^{25} +(-2.01176 - 6.19157i) q^{26} +(5.72812 - 4.16172i) q^{27} +(0.809017 - 0.587785i) q^{28} +(0.364402 + 1.12151i) q^{29} +(0.897614 - 2.76257i) q^{30} +(1.03837 + 0.754419i) q^{31} +1.00000 q^{32} +(-5.18715 + 8.11826i) q^{33} +7.07831 q^{34} +(-0.809017 - 0.587785i) q^{35} +(1.68028 - 5.17138i) q^{36} +(-0.311511 - 0.958733i) q^{37} +(-3.21567 + 2.33632i) q^{38} +(-15.2989 + 11.1153i) q^{39} +(-0.309017 - 0.951057i) q^{40} +(-1.67841 + 5.16560i) q^{41} +(-2.34998 - 1.70736i) q^{42} -11.2003 q^{43} +(0.198055 + 3.31071i) q^{44} -5.43751 q^{45} +(-7.60471 - 5.52514i) q^{46} +(-3.52015 + 10.8339i) q^{47} +(-0.897614 - 2.76257i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-0.809017 + 0.587785i) q^{50} +(-6.35359 - 19.5543i) q^{51} +(-2.01176 + 6.19157i) q^{52} +(6.27479 + 4.55890i) q^{53} -7.08034 q^{54} +(3.08747 - 1.21143i) q^{55} -1.00000 q^{56} +(9.34069 + 6.78641i) q^{57} +(0.364402 - 1.12151i) q^{58} +(-1.74470 - 5.36963i) q^{59} +(-2.34998 + 1.70736i) q^{60} +(-5.12643 + 3.72457i) q^{61} +(-0.396621 - 1.22068i) q^{62} +(-1.68028 + 5.17138i) q^{63} +(-0.809017 - 0.587785i) q^{64} +6.51020 q^{65} +(8.96829 - 3.51888i) q^{66} +3.88122 q^{67} +(-5.72647 - 4.16052i) q^{68} +(-8.43751 + 25.9680i) q^{69} +(0.309017 + 0.951057i) q^{70} +(0.210285 - 0.152781i) q^{71} +(-4.39904 + 3.19609i) q^{72} +(1.49096 + 4.58872i) q^{73} +(-0.311511 + 0.958733i) q^{74} +(2.34998 + 1.70736i) q^{75} +3.97479 q^{76} +(-0.198055 - 3.31071i) q^{77} +18.9104 q^{78} +(-11.6035 - 8.43046i) q^{79} +(-0.309017 + 0.951057i) q^{80} +(1.31456 + 4.04581i) q^{81} +(4.39413 - 3.19252i) q^{82} +(-3.71745 + 2.70088i) q^{83} +(0.897614 + 2.76257i) q^{84} +(-2.18732 + 6.73187i) q^{85} +(9.06122 + 6.58336i) q^{86} -3.42535 q^{87} +(1.78575 - 2.79483i) q^{88} -1.43088 q^{89} +(4.39904 + 3.19609i) q^{90} +(2.01176 - 6.19157i) q^{91} +(2.90474 + 8.93987i) q^{92} +(-3.01619 + 2.19139i) q^{93} +(9.21588 - 6.69573i) q^{94} +(-1.22828 - 3.78025i) q^{95} +(-0.897614 + 2.76257i) q^{96} +(6.96317 + 5.05904i) q^{97} +1.00000 q^{98} +(-11.4526 - 13.9309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} - 5 q^{3} - 4 q^{4} + 4 q^{5} + 5 q^{6} + 4 q^{7} - 4 q^{8} + q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 - 5 * q^3 - 4 * q^4 + 4 * q^5 + 5 * q^6 + 4 * q^7 - 4 * q^8 + q^9	\( 16 q - 4 q^{2} - 5 q^{3} - 4 q^{4} + 4 q^{5} + 5 q^{6} + 4 q^{7} - 4 q^{8} + q^{9} - 16 q^{10} - 2 q^{11} + 8 q^{13} + 4 q^{14} + 5 q^{15} - 4 q^{16} - 13 q^{17} - 9 q^{18} + 15 q^{19} + 4 q^{20} - 2 q^{22} + 20 q^{23} + 5 q^{24} - 4 q^{25} - 7 q^{26} + 10 q^{27} + 4 q^{28} - 14 q^{29} + 5 q^{30} - 6 q^{31} + 16 q^{32} - 25 q^{33} + 12 q^{34} - 4 q^{35} - 9 q^{36} + 28 q^{37} - 20 q^{38} + 15 q^{39} + 4 q^{40} + 2 q^{41} - 5 q^{42} - 10 q^{43} + 3 q^{44} - 16 q^{45} - 10 q^{46} - 10 q^{47} - 5 q^{48} - 4 q^{49} - 4 q^{50} - 42 q^{51} - 7 q^{52} - 2 q^{53} - 3 q^{55} - 16 q^{56} + 21 q^{57} - 14 q^{58} + 7 q^{59} - 5 q^{60} + 4 q^{61} + 14 q^{62} + 9 q^{63} - 4 q^{64} + 2 q^{65} - 10 q^{66} + 66 q^{67} - 13 q^{68} - 64 q^{69} - 4 q^{70} + 2 q^{71} + q^{72} + 12 q^{73} + 28 q^{74} + 5 q^{75} + 10 q^{76} - 3 q^{77} + 70 q^{78} + 2 q^{79} + 4 q^{80} - 30 q^{81} - 13 q^{82} - 5 q^{83} + 5 q^{84} - 7 q^{85} + 5 q^{86} - 24 q^{87} - 2 q^{88} + 2 q^{89} - q^{90} + 7 q^{91} - 38 q^{93} + 25 q^{94} - 15 q^{95} - 5 q^{96} + 22 q^{97} + 16 q^{98} - 18 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 - 5 * q^3 - 4 * q^4 + 4 * q^5 + 5 * q^6 + 4 * q^7 - 4 * q^8 + q^9 - 16 * q^10 - 2 * q^11 + 8 * q^13 + 4 * q^14 + 5 * q^15 - 4 * q^16 - 13 * q^17 - 9 * q^18 + 15 * q^19 + 4 * q^20 - 2 * q^22 + 20 * q^23 + 5 * q^24 - 4 * q^25 - 7 * q^26 + 10 * q^27 + 4 * q^28 - 14 * q^29 + 5 * q^30 - 6 * q^31 + 16 * q^32 - 25 * q^33 + 12 * q^34 - 4 * q^35 - 9 * q^36 + 28 * q^37 - 20 * q^38 + 15 * q^39 + 4 * q^40 + 2 * q^41 - 5 * q^42 - 10 * q^43 + 3 * q^44 - 16 * q^45 - 10 * q^46 - 10 * q^47 - 5 * q^48 - 4 * q^49 - 4 * q^50 - 42 * q^51 - 7 * q^52 - 2 * q^53 - 3 * q^55 - 16 * q^56 + 21 * q^57 - 14 * q^58 + 7 * q^59 - 5 * q^60 + 4 * q^61 + 14 * q^62 + 9 * q^63 - 4 * q^64 + 2 * q^65 - 10 * q^66 + 66 * q^67 - 13 * q^68 - 64 * q^69 - 4 * q^70 + 2 * q^71 + q^72 + 12 * q^73 + 28 * q^74 + 5 * q^75 + 10 * q^76 - 3 * q^77 + 70 * q^78 + 2 * q^79 + 4 * q^80 - 30 * q^81 - 13 * q^82 - 5 * q^83 + 5 * q^84 - 7 * q^85 + 5 * q^86 - 24 * q^87 - 2 * q^88 + 2 * q^89 - q^90 + 7 * q^91 - 38 * q^93 + 25 * q^94 - 15 * q^95 - 5 * q^96 + 22 * q^97 + 16 * q^98 - 18 * q^99

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