LMFDB - Embedded newform 770.2.n.f.141.1

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:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.484000000.9
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 16x^{4} + 66x^{2} + 121 $ x^8 + x^6 + 16x^4 + 66x^2 + 121
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			141.1
Root			$-1.73855 - 1.26313i$ of defining polynomial
Character	$\chi$	$=$	770.141
Dual form			770.2.n.f.71.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(-0.929529 + 0.675342i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-0.355049 - 1.09273i) q^{6} +(0.809017 + 0.587785i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.519114 + 1.59767i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.929529 + 0.675342i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-0.355049 - 1.09273i) q^{6} +(0.809017 + 0.587785i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.519114 + 1.59767i) q^{9} -1.00000 q^{10} +(3.22344 + 0.780656i) q^{11} +1.14896 q^{12} +(1.17340 - 3.61136i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(-0.929529 - 0.675342i) q^{15} +(0.309017 + 0.951057i) q^{16} +(2.00153 + 6.16008i) q^{17} +(-1.35906 - 0.987414i) q^{18} +(-2.16808 + 1.57520i) q^{19} +(0.309017 - 0.951057i) q^{20} -1.14896 q^{21} +(-1.73855 + 2.82444i) q^{22} +2.65626 q^{23} +(-0.355049 + 1.09273i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(3.07200 + 2.23194i) q^{26} +(-1.66159 - 5.11384i) q^{27} +(-0.309017 - 0.951057i) q^{28} +(-0.313027 - 0.227427i) q^{29} +(0.929529 - 0.675342i) q^{30} +(-1.85987 + 5.72410i) q^{31} -1.00000 q^{32} +(-3.52349 + 1.45128i) q^{33} -6.47709 q^{34} +(-0.309017 + 0.951057i) q^{35} +(1.35906 - 0.987414i) q^{36} +(-1.93106 - 1.40300i) q^{37} +(-0.828131 - 2.54873i) q^{38} +(1.34819 + 4.14931i) q^{39} +(0.809017 + 0.587785i) q^{40} +(-7.66713 + 5.57050i) q^{41} +(0.355049 - 1.09273i) q^{42} -4.66428 q^{43} +(-2.14896 - 2.52626i) q^{44} -1.67989 q^{45} +(-0.820830 + 2.52626i) q^{46} +(3.62605 - 2.63448i) q^{47} +(-0.929529 - 0.675342i) q^{48} +(0.309017 + 0.951057i) q^{49} +(-0.309017 - 0.951057i) q^{50} +(-6.02065 - 4.37426i) q^{51} +(-3.07200 + 2.23194i) q^{52} +(-1.57543 + 4.84867i) q^{53} +5.37701 q^{54} +(0.253650 + 3.30691i) q^{55} +1.00000 q^{56} +(0.951490 - 2.92839i) q^{57} +(0.313027 - 0.227427i) q^{58} +(-3.83994 - 2.78988i) q^{59} +(0.355049 + 1.09273i) q^{60} +(3.60293 + 11.0887i) q^{61} +(-4.86921 - 3.53769i) q^{62} +(-1.35906 + 0.987414i) q^{63} +(0.309017 - 0.951057i) q^{64} +3.79720 q^{65} +(-0.291435 - 3.79951i) q^{66} +5.71316 q^{67} +(2.00153 - 6.16008i) q^{68} +(-2.46907 + 1.79389i) q^{69} +(-0.809017 - 0.587785i) q^{70} +(1.02940 + 3.16815i) q^{71} +(0.519114 + 1.59767i) q^{72} +(-12.1455 - 8.82425i) q^{73} +(1.93106 - 1.40300i) q^{74} +(0.355049 - 1.09273i) q^{75} +2.67989 q^{76} +(2.14896 + 2.52626i) q^{77} -4.36284 q^{78} +(-1.86533 + 5.74090i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(0.920912 + 0.669082i) q^{81} +(-2.92858 - 9.01325i) q^{82} +(-3.44711 - 10.6091i) q^{83} +(0.929529 + 0.675342i) q^{84} +(-5.24008 + 3.80714i) q^{85} +(1.44134 - 4.43600i) q^{86} +0.444559 q^{87} +(3.06668 - 1.26313i) q^{88} -5.87277 q^{89} +(0.519114 - 1.59767i) q^{90} +(3.07200 - 2.23194i) q^{91} +(-2.14896 - 1.56131i) q^{92} +(-2.13692 - 6.57676i) q^{93} +(1.38503 + 4.26268i) q^{94} +(-2.16808 - 1.57520i) q^{95} +(0.929529 - 0.675342i) q^{96} +(-1.02115 + 3.14277i) q^{97} -1.00000 q^{98} +(-2.92056 + 4.74474i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9	$ 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9} - 8 q^{10} - 8 q^{12} - 2 q^{13} - 2 q^{14} + 2 q^{15} - 2 q^{16} - 6 q^{17} + 8 q^{18} + 6 q^{19} - 2 q^{20} + 8 q^{21} - 2 q^{24} - 2 q^{25} + 12 q^{26} - 4 q^{27} + 2 q^{28} + 20 q^{29} - 2 q^{30} - 6 q^{31} - 8 q^{32} - 8 q^{33} - 24 q^{34} + 2 q^{35} - 8 q^{36} + 16 q^{37} + 4 q^{38} + 20 q^{39} + 2 q^{40} - 12 q^{41} + 2 q^{42} + 20 q^{43} + 12 q^{45} - 16 q^{47} + 2 q^{48} - 2 q^{49} + 2 q^{50} - 20 q^{51} - 12 q^{52} - 30 q^{53} + 44 q^{54} + 8 q^{56} - 20 q^{58} - 18 q^{59} + 2 q^{60} + 8 q^{61} - 24 q^{62} + 8 q^{63} - 2 q^{64} + 28 q^{65} + 18 q^{66} - 6 q^{68} - 28 q^{69} - 2 q^{70} + 22 q^{71} - 2 q^{72} - 50 q^{73} - 16 q^{74} + 2 q^{75} - 4 q^{76} + 60 q^{78} - 34 q^{79} - 2 q^{80} - 28 q^{81} + 12 q^{82} - 34 q^{83} - 2 q^{84} - 6 q^{85} + 4 q^{87} - 8 q^{89} - 2 q^{90} + 12 q^{91} + 56 q^{93} - 24 q^{94} + 6 q^{95} - 2 q^{96} - 8 q^{98} - 24 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9 - 8 * q^10 - 8 * q^12 - 2 * q^13 - 2 * q^14 + 2 * q^15 - 2 * q^16 - 6 * q^17 + 8 * q^18 + 6 * q^19 - 2 * q^20 + 8 * q^21 - 2 * q^24 - 2 * q^25 + 12 * q^26 - 4 * q^27 + 2 * q^28 + 20 * q^29 - 2 * q^30 - 6 * q^31 - 8 * q^32 - 8 * q^33 - 24 * q^34 + 2 * q^35 - 8 * q^36 + 16 * q^37 + 4 * q^38 + 20 * q^39 + 2 * q^40 - 12 * q^41 + 2 * q^42 + 20 * q^43 + 12 * q^45 - 16 * q^47 + 2 * q^48 - 2 * q^49 + 2 * q^50 - 20 * q^51 - 12 * q^52 - 30 * q^53 + 44 * q^54 + 8 * q^56 - 20 * q^58 - 18 * q^59 + 2 * q^60 + 8 * q^61 - 24 * q^62 + 8 * q^63 - 2 * q^64 + 28 * q^65 + 18 * q^66 - 6 * q^68 - 28 * q^69 - 2 * q^70 + 22 * q^71 - 2 * q^72 - 50 * q^73 - 16 * q^74 + 2 * q^75 - 4 * q^76 + 60 * q^78 - 34 * q^79 - 2 * q^80 - 28 * q^81 + 12 * q^82 - 34 * q^83 - 2 * q^84 - 6 * q^85 + 4 * q^87 - 8 * q^89 - 2 * q^90 + 12 * q^91 + 56 * q^93 - 24 * q^94 + 6 * q^95 - 2 * q^96 - 8 * q^98 - 24 * 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
$3$	−0.929529	+	0.675342i	−0.536664	+	0.389909i	−0.822845	−	0.568267i	$-0.807614\pi$
$3$	−0.929529	+	0.675342i	−0.536664	+	0.389909i	0.286181	+	0.958176i	$0.407614\pi$
$4$	−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
$6$	−0.355049	−	1.09273i	−0.144948	−	0.446104i
$7$	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
$9$	−0.519114	+	1.59767i	−0.173038	+	0.532556i
$10$	−1.00000			−0.316228
$11$	3.22344	+	0.780656i	0.971904	+	0.235377i
$11$	3.22344	+	0.780656i	0.971904	+	0.235377i
$12$	1.14896			0.331677
$13$	1.17340	−	3.61136i	0.325443	−	1.00161i	−0.645798	−	0.763509i	$-0.723475\pi$
$13$	1.17340	−	3.61136i	0.325443	−	1.00161i	0.971240	−	0.238101i	$-0.0765250\pi$
$14$	−0.809017	+	0.587785i	−0.216219	+	0.157092i
$15$	−0.929529	−	0.675342i	−0.240003	−	0.174373i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	2.00153	+	6.16008i	0.485443	+	1.49404i	0.831339	+	0.555766i	$0.187575\pi$
$17$	2.00153	+	6.16008i	0.485443	+	1.49404i	−0.345896	+	0.938273i	$0.612425\pi$
$18$	−1.35906	−	0.987414i	−0.320333	−	0.232736i
$19$	−2.16808	+	1.57520i	−0.497391	+	0.361375i	−0.808019	−	0.589156i	$-0.799460\pi$
$19$	−2.16808	+	1.57520i	−0.497391	+	0.361375i	0.310629	+	0.950531i	$0.399460\pi$
$20$	0.309017	−	0.951057i	0.0690983	−	0.212663i
$21$	−1.14896			−0.250724
$22$	−1.73855	+	2.82444i	−0.370659	+	0.602172i
$23$	2.65626			0.553869			0.276934	−	0.960889i	$-0.410682\pi$
$23$	2.65626			0.553869			0.276934	+	0.960889i	$0.410682\pi$
$24$	−0.355049	+	1.09273i	−0.0724740	+	0.223052i
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$	3.07200	+	2.23194i	0.602469	+	0.437720i
$27$	−1.66159	−	5.11384i	−0.319773	−	0.984159i
$28$	−0.309017	−	0.951057i	−0.0583987	−	0.179733i
$29$	−0.313027	−	0.227427i	−0.0581276	−	0.0422322i	0.558342	−	0.829611i	$-0.311438\pi$
$29$	−0.313027	−	0.227427i	−0.0581276	−	0.0422322i	−0.616470	+	0.787379i	$0.711438\pi$
$30$	0.929529	−	0.675342i	0.169708	−	0.123300i
$31$	−1.85987	+	5.72410i	−0.334043	+	1.02808i	0.633149	+	0.774030i	$0.281762\pi$
$31$	−1.85987	+	5.72410i	−0.334043	+	1.02808i	−0.967192	+	0.254048i	$0.918238\pi$
$32$	−1.00000			−0.176777
$33$	−3.52349	+	1.45128i	−0.613361	+	0.252636i
$34$	−6.47709			−1.11081
$35$	−0.309017	+	0.951057i	−0.0522334	+	0.160758i
$36$	1.35906	−	0.987414i	0.226510	−	0.164569i
$37$	−1.93106	−	1.40300i	−0.317464	−	0.230651i	0.417628	−	0.908618i	$-0.362861\pi$
$37$	−1.93106	−	1.40300i	−0.317464	−	0.230651i	−0.735093	+	0.677967i	$0.762861\pi$
$38$	−0.828131	−	2.54873i	−0.134341	−	0.413458i
$39$	1.34819	+	4.14931i	0.215883	+	0.664421i
$40$	0.809017	+	0.587785i	0.127917	+	0.0929370i
$41$	−7.66713	+	5.57050i	−1.19740	+	0.869965i	−0.994027	−	0.109135i	$-0.965192\pi$
$41$	−7.66713	+	5.57050i	−1.19740	+	0.869965i	−0.203377	+	0.979100i	$0.565192\pi$
$42$	0.355049	−	1.09273i	0.0547852	−	0.168611i
$43$	−4.66428			−0.711296			−0.355648	−	0.934620i	$-0.615740\pi$
$43$	−4.66428			−0.711296			−0.355648	+	0.934620i	$0.615740\pi$
$44$	−2.14896	−	2.52626i	−0.323968	−	0.380847i
$45$	−1.67989			−0.250423
$46$	−0.820830	+	2.52626i	−0.121025	+	0.372476i
$47$	3.62605	−	2.63448i	0.528914	−	0.384279i	−0.291037	−	0.956712i	$-0.594000\pi$
$47$	3.62605	−	2.63448i	0.528914	−	0.384279i	0.819951	+	0.572433i	$0.194000\pi$
$48$	−0.929529	−	0.675342i	−0.134166	−	0.0974773i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	−0.309017	−	0.951057i	−0.0437016	−	0.134500i
$51$	−6.02065	−	4.37426i	−0.843059	−	0.612518i
$52$	−3.07200	+	2.23194i	−0.426010	+	0.309514i
$53$	−1.57543	+	4.84867i	−0.216402	+	0.666016i	0.782650	+	0.622463i	$0.213868\pi$
$53$	−1.57543	+	4.84867i	−0.216402	+	0.666016i	−0.999051	+	0.0435529i	$0.986132\pi$
$54$	5.37701			0.731718
$55$	0.253650	+	3.30691i	0.0342022	+	0.445904i
$56$	1.00000			0.133631
$57$	0.951490	−	2.92839i	0.126028	−	0.387874i
$58$	0.313027	−	0.227427i	0.0411024	−	0.0298627i
$59$	−3.83994	−	2.78988i	−0.499918	−	0.363212i	0.309068	−	0.951040i	$-0.399983\pi$
$59$	−3.83994	−	2.78988i	−0.499918	−	0.363212i	−0.808986	+	0.587828i	$0.799983\pi$
$60$	0.355049	+	1.09273i	0.0458366	+	0.141070i
$61$	3.60293	+	11.0887i	0.461308	+	1.41976i	0.863567	+	0.504234i	$0.168225\pi$
$61$	3.60293	+	11.0887i	0.461308	+	1.41976i	−0.402259	+	0.915526i	$0.631775\pi$
$62$	−4.86921	−	3.53769i	−0.618390	−	0.449287i
$63$	−1.35906	+	0.987414i	−0.171225	+	0.124402i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	3.79720			0.470985
$66$	−0.291435	−	3.79951i	−0.0358731	−	0.467688i
$67$	5.71316			0.697974			0.348987	−	0.937128i	$-0.386526\pi$
$67$	5.71316			0.697974			0.348987	+	0.937128i	$0.386526\pi$
$68$	2.00153	−	6.16008i	0.242721	−	0.747020i
$69$	−2.46907	+	1.79389i	−0.297241	+	0.215959i
$70$	−0.809017	−	0.587785i	−0.0966960	−	0.0702538i
$71$	1.02940	+	3.16815i	0.122167	+	0.375991i	0.993374	−	0.114924i	$-0.0366626\pi$
$71$	1.02940	+	3.16815i	0.122167	+	0.375991i	−0.871207	+	0.490915i	$0.836663\pi$
$72$	0.519114	+	1.59767i	0.0611782	+	0.188287i
$73$	−12.1455	−	8.82425i	−1.42153	−	1.03280i	−0.991517	−	0.129976i	$-0.958510\pi$
$73$	−12.1455	−	8.82425i	−1.42153	−	1.03280i	−0.430010	−	0.902824i	$-0.641490\pi$
$74$	1.93106	−	1.40300i	0.224481	−	0.163095i
$75$	0.355049	−	1.09273i	0.0409975	−	0.126177i
$76$	2.67989			0.307404
$77$	2.14896	+	2.52626i	0.244897	+	0.287894i
$78$	−4.36284			−0.493994
$79$	−1.86533	+	5.74090i	−0.209866	+	0.645901i	0.789612	+	0.613606i	$0.210282\pi$
$79$	−1.86533	+	5.74090i	−0.209866	+	0.645901i	−0.999478	+	0.0322952i	$0.989718\pi$
$80$	−0.809017	+	0.587785i	−0.0904508	+	0.0657164i
$81$	0.920912	+	0.669082i	0.102324	+	0.0743425i
$82$	−2.92858	−	9.01325i	−0.323408	−	0.995347i
$83$	−3.44711	−	10.6091i	−0.378370	−	1.16450i	−0.941177	−	0.337914i	$-0.890279\pi$
$83$	−3.44711	−	10.6091i	−0.378370	−	1.16450i	0.562807	−	0.826588i	$-0.309721\pi$
$84$	0.929529	+	0.675342i	0.101420	+	0.0736859i
$85$	−5.24008	+	3.80714i	−0.568366	+	0.412942i
$86$	1.44134	−	4.43600i	0.155424	−	0.478346i
$87$	0.444559			0.0476617
$88$	3.06668	−	1.26313i	0.326909	−	0.134650i
$89$	−5.87277			−0.622513			−0.311256	−	0.950326i	$-0.600750\pi$
$89$	−5.87277			−0.622513			−0.311256	+	0.950326i	$0.600750\pi$
$90$	0.519114	−	1.59767i	0.0547194	−	0.168409i
$91$	3.07200	−	2.23194i	0.322033	−	0.233971i
$92$	−2.14896	−	1.56131i	−0.224045	−	0.162778i
$93$	−2.13692	−	6.57676i	−0.221588	−	0.681979i
$94$	1.38503	+	4.26268i	0.142855	+	0.439662i
$95$	−2.16808	−	1.57520i	−0.222440	−	0.161612i
$96$	0.929529	−	0.675342i	0.0948697	−	0.0689268i
$97$	−1.02115	+	3.14277i	−0.103682	+	0.319100i	−0.989419	−	0.145088i	$-0.953654\pi$
$97$	−1.02115	+	3.14277i	−0.103682	+	0.319100i	0.885737	+	0.464188i	$0.153654\pi$
$98$	−1.00000			−0.101015
$99$	−2.92056	+	4.74474i	−0.293528	+	0.476865i
$100$	1.00000			0.100000
$101$	−1.71943	+	5.29187i	−0.171090	+	0.526561i	−0.999433	−	0.0336601i	$-0.989284\pi$
$101$	−1.71943	+	5.29187i	−0.171090	+	0.526561i	0.828343	+	0.560221i	$0.189284\pi$
$102$	6.02065	−	4.37426i	0.596133	−	0.433116i
$103$	6.43968	+	4.67870i	0.634520	+	0.461006i	0.857963	−	0.513711i	$-0.171730\pi$
$103$	6.43968	+	4.67870i	0.634520	+	0.461006i	−0.223443	+	0.974717i	$0.571730\pi$
$104$	−1.17340	−	3.61136i	−0.115061	−	0.354123i
$105$	−0.355049	−	1.09273i	−0.0346492	−	0.106639i
$106$	−4.12452	−	2.99664i	−0.400609	−	0.291059i
$107$	14.0967	−	10.2418i	1.36278	−	0.990114i	0.364512	−	0.931199i	$-0.381236\pi$
$107$	14.0967	−	10.2418i	1.36278	−	0.990114i	0.998263	−	0.0589157i	$-0.0187643\pi$
$108$	−1.66159	+	5.11384i	−0.159886	+	0.492080i
$109$	4.92398			0.471631			0.235816	−	0.971798i	$-0.424224\pi$
$109$	4.92398			0.471631			0.235816	+	0.971798i	$0.424224\pi$
$110$	−3.22344	−	0.780656i	−0.307343	−	0.0744326i
$111$	2.74248			0.260305
$112$	−0.309017	+	0.951057i	−0.0291994	+	0.0898664i
$113$	9.20855	−	6.69041i	0.866268	−	0.629380i	−0.0633151	−	0.997994i	$-0.520167\pi$
$113$	9.20855	−	6.69041i	0.866268	−	0.629380i	0.929583	+	0.368613i	$0.120167\pi$
$114$	2.49103	+	1.80984i	0.233307	+	0.169507i
$115$	0.820830	+	2.52626i	0.0765428	+	0.235575i
$116$	0.119566	+	0.367985i	0.0111014	+	0.0341665i
$117$	5.16062	+	3.74941i	0.477100	+	0.346633i
$118$	3.83994	−	2.78988i	0.353496	−	0.256830i
$119$	−2.00153	+	6.16008i	−0.183480	+	0.564694i
$120$	−1.14896			−0.104885
$121$	9.78115	+	5.03280i	0.889196	+	0.457527i
$122$	−11.6593			−1.05559
$123$	3.36483	−	10.3559i	0.303396	−	0.933758i
$124$	4.86921	−	3.53769i	0.437268	−	0.317694i
$125$	−0.809017	−	0.587785i	−0.0723607	−	0.0525731i
$126$	−0.519114	−	1.59767i	−0.0462464	−	0.142332i
$127$	−0.444131	−	1.36689i	−0.0394102	−	0.121292i	0.929416	−	0.369034i	$-0.120311\pi$
$127$	−0.444131	−	1.36689i	−0.0394102	−	0.121292i	−0.968826	+	0.247742i	$0.920311\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	4.33559	−	3.14999i	0.381727	−	0.277341i
$130$	−1.17340	+	3.61136i	−0.102914	+	0.316737i
$131$	19.5165			1.70516			0.852582	−	0.522594i	$-0.175036\pi$
$131$	19.5165			1.70516			0.852582	+	0.522594i	$0.175036\pi$
$132$	3.70361	+	0.896943i	0.322358	+	0.0780689i
$133$	−2.67989			−0.232376
$134$	−1.76546	+	5.43354i	−0.152513	+	0.469386i
$135$	4.35009	−	3.16053i	0.374396	−	0.272015i
$136$	5.24008	+	3.80714i	0.449333	+	0.326459i
$137$	5.86541	+	18.0519i	0.501116	+	1.54228i	0.807204	+	0.590273i	$0.200980\pi$
$137$	5.86541	+	18.0519i	0.501116	+	1.54228i	−0.306088	+	0.952003i	$0.599020\pi$
$138$	−0.943102	−	2.90257i	−0.0802822	−	0.247083i
$139$	−5.32813	−	3.87111i	−0.451926	−	0.328344i	0.338430	−	0.940992i	$-0.390104\pi$
$139$	−5.32813	−	3.87111i	−0.451926	−	0.328344i	−0.790356	+	0.612648i	$0.790104\pi$
$140$	0.809017	−	0.587785i	0.0683744	−	0.0496769i
$141$	−1.59134	+	4.89766i	−0.134015	+	0.412457i
$142$	−3.33119			−0.279548
$143$	6.60161	−	10.7250i	0.552055	−	0.896867i
$144$	−1.67989			−0.139991
$145$	0.119566	−	0.367985i	0.00992938	−	0.0305595i
$146$	12.1455	−	8.82425i	1.00517	−	0.730300i
$147$	−0.929529	−	0.675342i	−0.0766663	−	0.0557013i
$148$	0.737600	+	2.27010i	0.0606303	+	0.186601i
$149$	3.12533	+	9.61879i	0.256037	+	0.788002i	0.993623	+	0.112749i	$0.0359656\pi$
$149$	3.12533	+	9.61879i	0.256037	+	0.788002i	−0.737586	+	0.675253i	$0.764034\pi$
$150$	0.929529	+	0.675342i	0.0758957	+	0.0551415i
$151$	9.57353	−	6.95558i	0.779083	−	0.566037i	−0.125621	−	0.992078i	$-0.540092\pi$
$151$	9.57353	−	6.95558i	0.779083	−	0.566037i	0.904704	+	0.426041i	$0.140092\pi$
$152$	−0.828131	+	2.54873i	−0.0671703	+	0.206729i
$153$	−10.8808			−0.879660
$154$	−3.06668	+	1.26313i	−0.247120	+	0.101786i
$155$	−6.01867			−0.483431
$156$	1.34819	−	4.14931i	0.107942	−	0.332210i
$157$	−1.36767	+	0.993674i	−0.109152	+	0.0793038i	−0.641022	−	0.767522i	$-0.721489\pi$
$157$	−1.36767	+	0.993674i	−0.109152	+	0.0793038i	0.531870	+	0.846826i	$0.321489\pi$
$158$	−4.88350	−	3.54807i	−0.388510	−	0.282269i
$159$	−1.81010	−	5.57093i	−0.143551	−	0.441803i
$160$	−0.309017	−	0.951057i	−0.0244299	−	0.0751876i
$161$	2.14896	+	1.56131i	0.169362	+	0.123049i
$162$	−0.920912	+	0.669082i	−0.0723537	+	0.0525681i
$163$	−2.49117	+	7.66703i	−0.195123	+	0.600528i	0.804852	+	0.593476i	$0.202245\pi$
$163$	−2.49117	+	7.66703i	−0.195123	+	0.600528i	−0.999975	+	0.00705197i	$0.997755\pi$
$164$	9.47709			0.740037
$165$	−2.46907	−	2.90257i	−0.192217	−	0.225965i
$166$	11.1551			0.865803
$167$	5.01158	−	15.4241i	0.387808	−	1.19355i	−0.546615	−	0.837384i	$-0.684084\pi$
$167$	5.01158	−	15.4241i	0.387808	−	1.19355i	0.934423	−	0.356166i	$-0.115916\pi$
$168$	−0.929529	+	0.675342i	−0.0717147	+	0.0521038i
$169$	−1.14780	−	0.833925i	−0.0882922	−	0.0641480i
$170$	−2.00153	−	6.16008i	−0.153510	−	0.472457i
$171$	−1.39117	−	4.28157i	−0.106385	−	0.327420i
$172$	3.77348	+	2.74160i	0.287725	+	0.209045i
$173$	−9.83768	+	7.14749i	−0.747945	+	0.543414i	−0.895189	−	0.445686i	$-0.852960\pi$
$173$	−9.83768	+	7.14749i	−0.747945	+	0.543414i	0.147244	+	0.989100i	$0.452960\pi$
$174$	−0.137376	+	0.422800i	−0.0104145	+	0.0320524i
$175$	−1.00000			−0.0755929
$176$	0.253650	+	3.30691i	0.0191196	+	0.249268i
$177$	5.45347			0.409908
$178$	1.81479	−	5.58534i	0.136024	−	0.418639i
$179$	18.8528	−	13.6973i	1.40912	−	1.02379i	0.415673	−	0.909514i	$-0.363546\pi$
$179$	18.8528	−	13.6973i	1.40912	−	1.02379i	0.993449	−	0.114273i	$-0.0364540\pi$
$180$	1.35906	+	0.987414i	0.101298	+	0.0735975i
$181$	6.83818	+	21.0458i	0.508278	+	1.56432i	0.795189	+	0.606362i	$0.207372\pi$
$181$	6.83818	+	21.0458i	0.508278	+	1.56432i	−0.286910	+	0.957957i	$0.592628\pi$
$182$	1.17340	+	3.61136i	0.0869782	+	0.267691i
$183$	−10.8377	−	7.87404i	−0.801144	−	0.582066i
$184$	2.14896	−	1.56131i	0.158424	−	0.115101i
$185$	0.737600	−	2.27010i	0.0542294	−	0.166901i
$186$	6.91522			0.507048
$187$	1.64292	+	21.4192i	0.120142	+	1.56632i
$188$	−4.48205			−0.326887
$189$	1.66159	−	5.11384i	0.120863	−	0.371977i
$190$	2.16808	−	1.57520i	0.157289	−	0.114277i
$191$	−16.4120	−	11.9240i	−1.18753	−	0.862793i	−0.194531	−	0.980896i	$-0.562319\pi$
$191$	−16.4120	−	11.9240i	−1.18753	−	0.862793i	−0.993001	+	0.118103i	$0.962319\pi$
$192$	0.355049	+	1.09273i	0.0256234	+	0.0788608i
$193$	−1.18819	−	3.65689i	−0.0855281	−	0.263228i	0.899142	−	0.437658i	$-0.144192\pi$
$193$	−1.18819	−	3.65689i	−0.0855281	−	0.263228i	−0.984670	+	0.174429i	$0.944192\pi$
$194$	−2.67340	−	1.94234i	−0.191939	−	0.139452i
$195$	−3.52961	+	2.56441i	−0.252761	+	0.183641i
$196$	0.309017	−	0.951057i	0.0220726	−	0.0679326i
$197$	11.8159			0.841846			0.420923	−	0.907096i	$-0.361706\pi$
$197$	11.8159			0.841846			0.420923	+	0.907096i	$0.361706\pi$
$198$	−3.61001	−	4.24383i	−0.256553	−	0.301596i
$199$	12.5496			0.889617			0.444809	−	0.895626i	$-0.353272\pi$
$199$	12.5496			0.889617			0.444809	+	0.895626i	$0.353272\pi$
$200$	−0.309017	+	0.951057i	−0.0218508	+	0.0672499i
$201$	−5.31055	+	3.85834i	−0.374577	+	0.272146i
$202$	−4.50153	−	3.27055i	−0.316727	−	0.230115i
$203$	−0.119566	−	0.367985i	−0.00839186	−	0.0258275i
$204$	2.29968	+	7.07769i	0.161010	+	0.495538i
$205$	−7.66713	−	5.57050i	−0.535495	−	0.389060i
$206$	−6.43968	+	4.67870i	−0.448674	+	0.325980i
$207$	−1.37890	+	4.24383i	−0.0958404	+	0.294966i
$208$	3.79720			0.263289
$209$	−8.21835	+	3.38504i	−0.568475	+	0.234148i
$210$	1.14896			0.0792859
$211$	1.23599	−	3.80397i	0.0850888	−	0.261876i	−0.899455	−	0.437012i	$-0.856037\pi$
$211$	1.23599	−	3.80397i	0.0850888	−	0.261876i	0.984544	+	0.175136i	$0.0560366\pi$
$212$	4.12452	−	2.99664i	0.283273	−	0.205810i
$213$	−3.09644	−	2.24970i	−0.212165	−	0.154147i
$214$	5.38444	+	16.5716i	0.368073	+	1.13281i
$215$	−1.44134	−	4.43600i	−0.0982987	−	0.302532i
$216$	−4.35009	−	3.16053i	−0.295986	−	0.215047i
$217$	−4.86921	+	3.53769i	−0.330543	+	0.240154i
$218$	−1.52159	+	4.68298i	−0.103055	+	0.317171i
$219$	17.2490			1.16558
$220$	1.73855	−	2.82444i	0.117213	−	0.190424i
$221$	24.5948			1.65443
$222$	−0.847473	+	2.60825i	−0.0568787	+	0.175055i
$223$	−14.4637	+	10.5085i	−0.968563	+	0.703702i	−0.955124	−	0.296207i	$-0.904278\pi$
$223$	−14.4637	+	10.5085i	−0.968563	+	0.703702i	−0.0134396	+	0.999910i	$0.504278\pi$
$224$	−0.809017	−	0.587785i	−0.0540547	−	0.0392731i
$225$	−0.519114	−	1.59767i	−0.0346076	−	0.106511i
$226$	3.51735	+	10.8253i	0.233971	+	0.720088i
$227$	4.66159	+	3.38684i	0.309400	+	0.224793i	0.731639	−	0.681692i	$-0.238756\pi$
$227$	4.66159	+	3.38684i	0.309400	+	0.224793i	−0.422239	+	0.906485i	$0.638756\pi$
$228$	−2.49103	+	1.80984i	−0.164973	+	0.119860i
$229$	−2.65018	+	8.15642i	−0.175129	+	0.538992i	−0.999639	−	0.0268553i	$-0.991451\pi$
$229$	−2.65018	+	8.15642i	−0.175129	+	0.538992i	0.824510	+	0.565847i	$0.191451\pi$
$230$	−2.65626			−0.175149
$231$	−3.70361	−	0.896943i	−0.243680	−	0.0590145i
$232$	−0.386922			−0.0254027
$233$	4.45017	−	13.6962i	0.291541	−	0.897270i	−0.692821	−	0.721110i	$-0.743632\pi$
$233$	4.45017	−	13.6962i	0.291541	−	0.897270i	0.984362	−	0.176160i	$-0.0563676\pi$
$234$	−5.16062	+	3.74941i	−0.337360	+	0.245107i
$235$	3.62605	+	2.63448i	0.236538	+	0.171855i
$236$	1.46673	+	4.51413i	0.0954759	+	0.293845i
$237$	−2.14319	−	6.59607i	−0.139215	−	0.428461i
$238$	−5.24008	−	3.80714i	−0.339664	−	0.246780i
$239$	19.4242	−	14.1125i	1.25645	−	0.912862i	0.257869	−	0.966180i	$-0.416980\pi$
$239$	19.4242	−	14.1125i	1.25645	−	0.912862i	0.998578	+	0.0533181i	$0.0169797\pi$
$240$	0.355049	−	1.09273i	0.0229183	−	0.0705352i
$241$	−16.7641			−1.07987			−0.539935	−	0.841707i	$-0.681551\pi$
$241$	−16.7641			−1.07987			−0.539935	+	0.841707i	$0.681551\pi$
$242$	−7.80902	+	7.74721i	−0.501983	+	0.498009i
$243$	14.8232			0.950906
$244$	3.60293	−	11.0887i	0.230654	−	0.709880i
$245$	−0.809017	+	0.587785i	−0.0516862	+	0.0375522i
$246$	8.80923	+	6.40028i	0.561656	+	0.408067i
$247$	3.14458	+	9.67803i	0.200085	+	0.615798i
$248$	1.85987	+	5.72410i	0.118102	+	0.363480i
$249$	10.3690	+	7.53350i	0.657107	+	0.477416i
$250$	0.809017	−	0.587785i	0.0511667	−	0.0371748i
$251$	−0.749330	+	2.30620i	−0.0472973	+	0.145566i	−0.971916	−	0.235328i	$-0.924384\pi$
$251$	−0.749330	+	2.30620i	−0.0472973	+	0.145566i	0.924619	+	0.380894i	$0.124384\pi$
$252$	1.67989			0.105823
$253$	8.56231	+	2.07363i	0.538308	+	0.130368i
$254$	1.43724			0.0901803
$255$	2.29968	−	7.07769i	0.144012	−	0.443222i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−4.19368	−	3.04688i	−0.261594	−	0.190059i	0.449255	−	0.893403i	$-0.351689\pi$
$257$	−4.19368	−	3.04688i	−0.261594	−	0.190059i	−0.710850	+	0.703344i	$0.751689\pi$
$258$	1.65605	+	5.09679i	0.103101	+	0.317312i
$259$	−0.737600	−	2.27010i	−0.0458322	−	0.141057i
$260$	−3.07200	−	2.23194i	−0.190518	−	0.138419i
$261$	0.525850	−	0.382052i	0.0325493	−	0.0236484i
$262$	−6.03093	+	18.5613i	−0.372592	+	1.14672i
$263$	20.3770			1.25650			0.628250	−	0.778011i	$-0.283771\pi$
$263$	20.3770			1.25650			0.628250	+	0.778011i	$0.283771\pi$
$264$	−1.99752	+	3.24517i	−0.122939	+	0.199726i
$265$	−5.09819			−0.313179
$266$	0.828131	−	2.54873i	0.0507760	−	0.156272i
$267$	5.45891	−	3.96613i	0.334080	−	0.242723i
$268$	−4.62204	−	3.35811i	−0.282336	−	0.205129i
$269$	−3.53837	−	10.8900i	−0.215738	−	0.663974i	−0.999100	−	0.0424083i	$-0.986497\pi$
$269$	−3.53837	−	10.8900i	−0.215738	−	0.663974i	0.783362	−	0.621566i	$-0.213503\pi$
$270$	1.66159	+	5.11384i	0.101121	+	0.311218i
$271$	−11.9896	−	8.71094i	−0.728315	−	0.529152i	0.160715	−	0.987001i	$-0.448620\pi$
$271$	−11.9896	−	8.71094i	−0.728315	−	0.529152i	−0.889030	+	0.457849i	$0.848620\pi$
$272$	−5.24008	+	3.80714i	−0.317726	+	0.230842i
$273$	−1.34819	+	4.14931i	−0.0815963	+	0.251127i
$274$	−18.9809			−1.14668
$275$	−3.06668	+	1.26313i	−0.184928	+	0.0761695i
$276$	3.05194			0.183705
$277$	7.57578	−	23.3159i	0.455185	−	1.40091i	−0.415733	−	0.909487i	$-0.636475\pi$
$277$	7.57578	−	23.3159i	0.455185	−	1.40091i	0.870918	−	0.491428i	$-0.163525\pi$
$278$	5.32813	−	3.87111i	0.319560	−	0.232174i
$279$	−8.17972	−	5.94292i	−0.489707	−	0.355793i
$280$	0.309017	+	0.951057i	0.0184673	+	0.0568365i
$281$	−8.83571	−	27.1935i	−0.527094	−	1.62223i	−0.760137	−	0.649762i	$-0.774868\pi$
$281$	−8.83571	−	27.1935i	−0.527094	−	1.62223i	0.233043	−	0.972466i	$-0.425132\pi$
$282$	−4.16619	−	3.02692i	−0.248093	−	0.180250i
$283$	4.20280	−	3.05351i	0.249830	−	0.181512i	−0.455821	−	0.890071i	$-0.650654\pi$
$283$	4.20280	−	3.05351i	0.249830	−	0.181512i	0.705652	+	0.708559i	$0.250654\pi$
$284$	1.02940	−	3.16815i	0.0610834	−	0.187995i
$285$	3.07909			0.182389
$286$	8.16004	+	9.59271i	0.482513	+	0.567229i
$287$	−9.47709			−0.559415
$288$	0.519114	−	1.59767i	0.0305891	−	0.0941435i
$289$	−20.1872	+	14.6668i	−1.18748	+	0.862755i
$290$	0.313027	+	0.227427i	0.0183816	+	0.0133550i
$291$	−1.17326	−	3.61092i	−0.0687777	−	0.211676i
$292$	4.63918	+	14.2779i	0.271488	+	0.835553i
$293$	−14.7407	−	10.7097i	−0.861159	−	0.625668i	0.0670412	−	0.997750i	$-0.478644\pi$
$293$	−14.7407	−	10.7097i	−0.861159	−	0.625668i	−0.928200	+	0.372082i	$0.878644\pi$
$294$	0.929529	−	0.675342i	0.0542112	−	0.0393868i
$295$	1.46673	−	4.51413i	0.0853962	−	0.262823i
$296$	−2.38692			−0.138737
$297$	−1.36388	−	17.7813i	−0.0791404	−	1.03178i
$298$	−10.1138			−0.585876
$299$	3.11686	−	9.59271i	0.180253	−	0.554761i
$300$	−0.929529	+	0.675342i	−0.0536664	+	0.0389909i
$301$	−3.77348	−	2.74160i	−0.217500	−	0.158023i
$302$	3.65676	+	11.2544i	0.210423	+	0.647616i
$303$	−1.97556	−	6.08015i	−0.113493	−	0.349296i
$304$	−2.16808	−	1.57520i	−0.124348	−	0.0903438i
$305$	−9.43259	+	6.85318i	−0.540109	+	0.392412i
$306$	3.36235	−	10.3482i	0.192213	−	0.591570i
$307$	−10.9710			−0.626146			−0.313073	−	0.949729i	$-0.601358\pi$
$307$	−10.9710			−0.626146			−0.313073	+	0.949729i	$0.601358\pi$
$308$	−0.253650	−	3.30691i	−0.0144531	−	0.188429i
$309$	−9.14559			−0.520275
$310$	1.85987	−	5.72410i	0.105634	−	0.325107i
$311$	−16.8831	+	12.2663i	−0.957354	+	0.695558i	−0.952535	−	0.304430i	$-0.901534\pi$
$311$	−16.8831	+	12.2663i	−0.957354	+	0.695558i	−0.00481905	+	0.999988i	$0.501534\pi$
$312$	3.52961	+	2.56441i	0.199825	+	0.145181i
$313$	2.67240	+	8.22479i	0.151053	+	0.464892i	0.997740	−	0.0671990i	$-0.0214062\pi$
$313$	2.67240	+	8.22479i	0.151053	+	0.464892i	−0.846687	+	0.532091i	$0.821406\pi$
$314$	−0.522405	−	1.60780i	−0.0294810	−	0.0907333i
$315$	−1.35906	−	0.987414i	−0.0765743	−	0.0556345i
$316$	4.88350	−	3.54807i	0.274718	−	0.199594i
$317$	1.09288	−	3.36353i	0.0613820	−	0.188915i	−0.915663	−	0.401946i	$-0.868334\pi$
$317$	1.09288	−	3.36353i	0.0613820	−	0.188915i	0.977045	+	0.213032i	$0.0683338\pi$
$318$	5.85762			0.328479
$319$	−0.831481	−	0.977464i	−0.0465540	−	0.0547275i
$320$	1.00000			0.0559017
$321$	−6.18652	+	19.0401i	−0.345298	+	1.06272i
$322$	−2.14896	+	1.56131i	−0.119757	+	0.0870085i
$323$	−14.0428	−	10.2027i	−0.781364	−	0.567694i
$324$	−0.351757	−	1.08260i	−0.0195421	−	0.0601443i
$325$	1.17340	+	3.61136i	0.0650886	+	0.200322i
$326$	−6.52196	−	4.73848i	−0.361218	−	0.262440i
$327$	−4.57698	+	3.32537i	−0.253107	+	0.183893i
$328$	−2.92858	+	9.01325i	−0.161704	+	0.497673i
$329$	4.48205			0.247103
$330$	3.52349	−	1.45128i	0.193962	−	0.0798906i
$331$	10.1966			0.560458			0.280229	−	0.959933i	$-0.409590\pi$
$331$	10.1966			0.560458			0.280229	+	0.959933i	$0.409590\pi$
$332$	−3.44711	+	10.6091i	−0.189185	+	0.582251i
$333$	3.24397	−	2.35688i	0.177768	−	0.129156i
$334$	13.1205	+	9.53260i	0.717922	+	0.521601i
$335$	1.76546	+	5.43354i	0.0964576	+	0.296866i
$336$	−0.355049	−	1.09273i	−0.0193695	−	0.0596131i
$337$	11.4130	+	8.29201i	0.621704	+	0.451695i	0.853516	−	0.521066i	$-0.174465\pi$
$337$	11.4130	+	8.29201i	0.621704	+	0.451695i	−0.231812	+	0.972761i	$0.574465\pi$
$338$	1.14780	−	0.833925i	0.0624320	−	0.0453595i
$339$	−4.04130	+	12.4379i	−0.219493	+	0.675531i
$340$	6.47709			0.351270
$341$	−10.4637	+	16.9994i	−0.566643	+	0.920567i
$342$	4.50191			0.243436
$343$	−0.309017	+	0.951057i	−0.0166853	+	0.0513522i
$344$	−3.77348	+	2.74160i	−0.203453	+	0.147817i
$345$	−2.46907	−	1.79389i	−0.132930	−	0.0965796i
$346$	−3.75766	−	11.5649i	−0.202013	−	0.621732i
$347$	1.28837	+	3.96520i	0.0691634	+	0.212863i	0.979664	−	0.200644i	$-0.0643036\pi$
$347$	1.28837	+	3.96520i	0.0691634	+	0.212863i	−0.910501	+	0.413507i	$0.864304\pi$
$348$	−0.359655	−	0.261305i	−0.0192796	−	0.0140074i
$349$	−6.50234	+	4.72423i	−0.348063	+	0.252882i	−0.748056	−	0.663636i	$-0.769012\pi$
$349$	−6.50234	+	4.72423i	−0.348063	+	0.252882i	0.399993	+	0.916518i	$0.369012\pi$
$350$	0.309017	−	0.951057i	0.0165177	−	0.0508361i
$351$	−20.4176			−1.08981
$352$	−3.22344	−	0.780656i	−0.171810	−	0.0416091i
$353$	15.7957			0.840723			0.420361	−	0.907357i	$-0.361903\pi$
$353$	15.7957			0.840723			0.420361	+	0.907357i	$0.361903\pi$
$354$	−1.68521	+	5.18655i	−0.0895681	+	0.275662i
$355$	−2.69499	+	1.95803i	−0.143035	+	0.103921i
$356$	4.75117	+	3.45193i	0.251812	+	0.182952i
$357$	−2.29968	−	7.07769i	−0.121712	−	0.374591i
$358$	7.20112	+	22.1628i	0.380591	+	1.17134i
$359$	−5.37205	−	3.90303i	−0.283526	−	0.205994i	0.436928	−	0.899497i	$-0.356067\pi$
$359$	−5.37205	−	3.90303i	−0.283526	−	0.205994i	−0.720454	+	0.693503i	$0.756067\pi$
$360$	−1.35906	+	0.987414i	−0.0716287	+	0.0520413i
$361$	−3.65202	+	11.2398i	−0.192212	+	0.591567i
$362$	−22.1288			−1.16307
$363$	−12.4907	+	1.92750i	−0.655593	+	0.101167i
$364$	−3.79720			−0.199028
$365$	4.63918	−	14.2779i	0.242826	−	0.747341i
$366$	10.8377	−	7.87404i	0.566495	−	0.411582i
$367$	−13.4544	−	9.77519i	−0.702314	−	0.510261i	0.178371	−	0.983963i	$-0.442917\pi$
$367$	−13.4544	−	9.77519i	−0.702314	−	0.510261i	−0.880685	+	0.473702i	$0.842917\pi$
$368$	0.820830	+	2.52626i	0.0427887	+	0.131690i
$369$	−4.91969	−	15.1413i	−0.256109	−	0.788222i
$370$	1.93106	+	1.40300i	0.100391	+	0.0729384i
$371$	−4.12452	+	2.99664i	−0.214135	+	0.155578i
$372$	−2.13692	+	6.57676i	−0.110794	+	0.340989i
$373$	−7.30477			−0.378227			−0.189113	−	0.981955i	$-0.560561\pi$
$373$	−7.30477			−0.378227			−0.189113	+	0.981955i	$0.560561\pi$
$374$	−20.8785	−	5.05638i	−1.07960	−	0.261459i
$375$	1.14896			0.0593321
$376$	1.38503	−	4.26268i	0.0714274	−	0.219831i
$377$	−1.18863	+	0.863587i	−0.0612174	+	0.0444770i
$378$	4.35009	+	3.16053i	0.223745	+	0.162560i
$379$	−4.10368	−	12.6298i	−0.210792	−	0.648751i	−0.999426	−	0.0338879i	$-0.989211\pi$
$379$	−4.10368	−	12.6298i	−0.210792	−	0.648751i	0.788634	−	0.614864i	$-0.210789\pi$
$380$	0.828131	+	2.54873i	0.0424822	+	0.130747i
$381$	1.33595	+	0.970628i	0.0684430	+	0.0497268i
$382$	16.4120	−	11.9240i	0.839712	−	0.610087i
$383$	5.28619	−	16.2692i	0.270112	−	0.831319i	−0.720360	−	0.693601i	$-0.756023\pi$
$383$	5.28619	−	16.2692i	0.270112	−	0.831319i	0.990471	−	0.137718i	$-0.0439767\pi$
$384$	−1.14896			−0.0586327
$385$	−1.73855	+	2.82444i	−0.0886045	+	0.143947i
$386$	3.84508			0.195709
$387$	2.42129	−	7.45198i	0.123081	−	0.378805i
$388$	2.67340	−	1.94234i	0.135721	−	0.0986073i
$389$	−6.91464	−	5.02378i	−0.350586	−	0.254716i	0.398529	−	0.917156i	$-0.369521\pi$
$389$	−6.91464	−	5.02378i	−0.350586	−	0.254716i	−0.749115	+	0.662440i	$0.769521\pi$
$390$	−1.34819	−	4.14931i	−0.0682683	−	0.210108i
$391$	5.31659	+	16.3628i	0.268872	+	0.827502i
$392$	0.809017	+	0.587785i	0.0408615	+	0.0296876i
$393$	−18.1411	+	13.1803i	−0.915100	+	0.664859i
$394$	−3.65131	+	11.2376i	−0.183950	+	0.566140i
$395$	−6.03633			−0.303721
$396$	5.15167	−	2.12191i	0.258881	−	0.106630i
$397$	17.0472			0.855572			0.427786	−	0.903880i	$-0.359294\pi$
$397$	17.0472			0.855572			0.427786	+	0.903880i	$0.359294\pi$
$398$	−3.87804	+	11.9354i	−0.194389	+	0.598266i
$399$	2.49103	−	1.80984i	0.124708	−	0.0906054i
$400$	−0.809017	−	0.587785i	−0.0404508	−	0.0293893i
$401$	−0.837599	−	2.57787i	−0.0418277	−	0.128732i	0.927962	−	0.372675i	$-0.121559\pi$
$401$	−0.837599	−	2.57787i	−0.0418277	−	0.128732i	−0.969790	+	0.243942i	$0.921559\pi$
$402$	−2.02845	−	6.24292i	−0.101170	−	0.311369i
$403$	18.4894	+	13.4333i	0.921021	+	0.669161i
$404$	4.50153	−	3.27055i	0.223960	−	0.162716i
$405$	−0.351757	+	1.08260i	−0.0174790	+	0.0537947i
$406$	0.386922			0.0192026
$407$	−5.12940	−	6.02997i	−0.254255	−	0.298895i
$408$	−7.44193			−0.368430
$409$	9.05879	−	27.8801i	0.447928	−	1.37858i	−0.431312	−	0.902203i	$-0.641949\pi$
$409$	9.05879	−	27.8801i	0.447928	−	1.37858i	0.879240	−	0.476379i	$-0.158051\pi$
$410$	7.66713	−	5.57050i	0.378652	−	0.275107i
$411$	−17.6433	−	12.8186i	−0.870279	−	0.632294i
$412$	−2.45974	−	7.57029i	−0.121183	−	0.372962i
$413$	−1.46673	−	4.51413i	−0.0721730	−	0.222126i
$414$	−3.61001	−	2.62283i	−0.177423	−	0.128905i
$415$	9.02466	−	6.55680i	0.443003	−	0.321860i
$416$	−1.17340	+	3.61136i	−0.0575307	+	0.177061i
$417$	7.56698			0.370557
$418$	−0.679755	−	8.86215i	−0.0332479	−	0.433462i
$419$	38.3776			1.87487			0.937434	−	0.348162i	$-0.113194\pi$
$419$	38.3776			1.87487			0.937434	+	0.348162i	$0.113194\pi$
$420$	−0.355049	+	1.09273i	−0.0173246	+	0.0533196i
$421$	30.0635	−	21.8424i	1.46520	−	1.06453i	0.483234	−	0.875491i	$-0.339462\pi$
$421$	30.0635	−	21.8424i	1.46520	−	1.06453i	0.981969	−	0.189041i	$-0.0605380\pi$
$422$	3.23585	+	2.35098i	0.157519	+	0.114444i
$423$	2.32669	+	7.16083i	0.113128	+	0.348171i
$424$	1.57543	+	4.84867i	0.0765095	+	0.235472i
$425$	−5.24008	−	3.80714i	−0.254181	−	0.184673i
$426$	3.09644	−	2.24970i	0.150023	−	0.108998i
$427$	−3.60293	+	11.0887i	−0.174358	+	0.536619i
$428$	−17.4244			−0.842241
$429$	1.10664	+	14.4275i	0.0534289	+	0.696567i
$430$	4.66428			0.224932
$431$	−9.50072	+	29.2402i	−0.457634	+	1.40845i	0.410382	+	0.911914i	$0.365395\pi$
$431$	−9.50072	+	29.2402i	−0.457634	+	1.40845i	−0.868015	+	0.496537i	$0.834605\pi$
$432$	4.35009	−	3.16053i	0.209294	−	0.152061i
$433$	6.91997	+	5.02765i	0.332552	+	0.241613i	0.741513	−	0.670939i	$-0.234109\pi$
$433$	6.91997	+	5.02765i	0.332552	+	0.241613i	−0.408961	+	0.912552i	$0.634109\pi$
$434$	−1.85987	−	5.72410i	−0.0892767	−	0.274765i
$435$	0.137376	+	0.422800i	0.00658668	+	0.0202717i
$436$	−3.98358	−	2.89424i	−0.190779	−	0.138609i
$437$	−5.75898	+	4.18414i	−0.275489	+	0.200155i
$438$	−5.33024	+	16.4048i	−0.254689	+	0.783851i
$439$	−24.5405			−1.17126			−0.585628	−	0.810580i	$-0.699152\pi$
$439$	−24.5405			−1.17126			−0.585628	+	0.810580i	$0.699152\pi$
$440$	2.14896	+	2.52626i	0.102448	+	0.120434i
$441$	−1.67989			−0.0799947
$442$	−7.60022	+	23.3911i	−0.361506	+	1.11260i
$443$	−21.8178	+	15.8516i	−1.03660	+	0.753132i	−0.969618	−	0.244623i	$-0.921336\pi$
$443$	−21.8178	+	15.8516i	−1.03660	+	0.753132i	−0.0669784	+	0.997754i	$0.521336\pi$
$444$	−2.21871	−	1.61199i	−0.105295	−	0.0765017i
$445$	−1.81479	−	5.58534i	−0.0860291	−	0.264770i
$446$	−5.52466	−	17.0031i	−0.261600	−	0.805122i
$447$	−9.40107	−	6.83028i	−0.444655	−	0.323061i
$448$	0.809017	−	0.587785i	0.0382225	−	0.0277702i
$449$	−10.8713	+	33.4585i	−0.513049	+	1.57900i	0.273755	+	0.961800i	$0.411734\pi$
$449$	−10.8713	+	33.4585i	−0.513049	+	1.57900i	−0.786804	+	0.617203i	$0.788266\pi$
$450$	1.67989			0.0791907
$451$	−29.0632	+	11.9708i	−1.36853	+	0.563682i
$452$	−11.3824			−0.535383
$453$	−4.20148	+	12.9308i	−0.197403	+	0.607543i
$454$	−4.66159	+	3.38684i	−0.218779	+	0.158952i
$455$	3.07200	+	2.23194i	0.144018	+	0.104635i
$456$	−0.951490	−	2.92839i	−0.0445576	−	0.137134i
$457$	6.31519	+	19.4362i	0.295412	+	0.909186i	0.983083	+	0.183163i	$0.0586335\pi$
$457$	6.31519	+	19.4362i	0.295412	+	0.909186i	−0.687670	+	0.726023i	$0.741367\pi$
$458$	−6.93827	−	5.04095i	−0.324204	−	0.235548i
$459$	28.1759	−	20.4710i	1.31514	−	0.955506i
$460$	0.820830	−	2.52626i	0.0382714	−	0.117787i
$461$	5.59541			0.260604			0.130302	−	0.991474i	$-0.458405\pi$
$461$	5.59541			0.260604			0.130302	+	0.991474i	$0.458405\pi$
$462$	1.99752	−	3.24517i	0.0929331	−	0.150979i
$463$	−29.5079			−1.37135			−0.685674	−	0.727909i	$-0.740492\pi$
$463$	−29.5079			−1.37135			−0.685674	+	0.727909i	$0.740492\pi$
$464$	0.119566	−	0.367985i	0.00555069	−	0.0170833i
$465$	5.59453	−	4.06466i	0.259440	−	0.188494i
$466$	11.6507	+	8.46474i	0.539709	+	0.392121i
$467$	9.68484	+	29.8069i	0.448161	+	1.37930i	0.878980	+	0.476860i	$0.158225\pi$
$467$	9.68484	+	29.8069i	0.448161	+	1.37930i	−0.430818	+	0.902439i	$0.641775\pi$
$468$	−1.97118	−	6.06667i	−0.0911179	−	0.280432i
$469$	4.62204	+	3.35811i	0.213426	+	0.155063i
$470$	−3.62605	+	2.63448i	−0.167257	+	0.121520i
$471$	0.600223	−	1.84730i	0.0276568	−	0.0851190i
$472$	−4.74643			−0.218472
$473$	−15.0350	−	3.64120i	−0.691312	−	0.167422i
$474$	6.93551			0.318559
$475$	0.828131	−	2.54873i	0.0379973	−	0.116944i
$476$	5.24008	−	3.80714i	0.240179	−	0.174500i
$477$	−6.92874	−	5.03402i	−0.317245	−	0.230492i
$478$	7.41938	+	22.8345i	0.339355	+	1.04443i
$479$	2.08629	+	6.42095i	0.0953252	+	0.293381i	0.987338	−	0.158629i	$-0.0507073\pi$
$479$	2.08629	+	6.42095i	0.0953252	+	0.293381i	−0.892013	+	0.452010i	$0.850707\pi$
$480$	0.929529	+	0.675342i	0.0424270	+	0.0308250i
$481$	−7.33263	+	5.32747i	−0.334339	+	0.242912i
$482$	5.18039	−	15.9436i	0.235960	−	0.726211i
$483$	−3.05194			−0.138868
$484$	−4.95492	−	9.82084i	−0.225223	−	0.446402i
$485$	−3.30450			−0.150050
$486$	−4.58061	+	14.0977i	−0.207781	+	0.639483i
$487$	20.5135	−	14.9040i	0.929558	−	0.675363i	−0.0163269	−	0.999867i	$-0.505197\pi$
$487$	20.5135	−	14.9040i	0.929558	−	0.675363i	0.945884	+	0.324504i	$0.105197\pi$
$488$	9.43259	+	6.85318i	0.426993	+	0.310229i
$489$	−2.86225	−	8.80911i	−0.129436	−	0.398362i
$490$	−0.309017	−	0.951057i	−0.0139600	−	0.0429644i
$491$	−16.0082	−	11.6307i	−0.722442	−	0.524885i	0.164722	−	0.986340i	$-0.447327\pi$
$491$	−16.0082	−	11.6307i	−0.722442	−	0.524885i	−0.887163	+	0.461456i	$0.847327\pi$
$492$	−8.80923	+	6.40028i	−0.397151	+	0.288547i
$493$	0.774437	−	2.38347i	0.0348789	−	0.107346i
$494$	−10.1761			−0.457844
$495$	−5.41502	−	1.31141i	−0.243387	−	0.0589437i
$496$	−6.01867			−0.270246
$497$	−1.02940	+	3.16815i	−0.0461747	+	0.142111i
$498$	−10.3690	+	7.53350i	−0.464645	+	0.337584i
$499$	21.6595	+	15.7366i	0.969614	+	0.704466i	0.955364	−	0.295432i	$-0.0954637\pi$
$499$	21.6595	+	15.7366i	0.969614	+	0.704466i	0.0142506	+	0.999898i	$0.495464\pi$
$500$	0.309017	+	0.951057i	0.0138197	+	0.0425325i
$501$	5.75812	+	17.7217i	0.257254	+	0.791745i
$502$	−1.96177	−	1.42531i	−0.0875582	−	0.0636147i
$503$	0.287272	−	0.208715i	0.0128088	−	0.00930614i	−0.581362	−	0.813645i	$-0.697480\pi$
$503$	0.287272	−	0.208715i	0.0128088	−	0.00930614i	0.594171	+	0.804339i	$0.297480\pi$
$504$	−0.519114	+	1.59767i	−0.0231232	+	0.0711658i
$505$	−5.56420			−0.247604
$506$	−4.61803	+	7.50245i	−0.205297	+	0.333525i
$507$	1.63010			0.0723951
$508$	−0.444131	+	1.36689i	−0.0197051	+	0.0606461i
$509$	19.3956	−	14.0917i	0.859695	−	0.624605i	−0.0681068	−	0.997678i	$-0.521696\pi$
$509$	19.3956	−	14.0917i	0.859695	−	0.624605i	0.927802	+	0.373073i	$0.121696\pi$
$510$	6.02065	+	4.37426i	0.266599	+	0.193695i
$511$	−4.63918	−	14.2779i	−0.205225	−	0.631619i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	11.6578	+	8.46986i	0.514703	+	0.373953i
$514$	4.19368	−	3.04688i	0.184975	−	0.134392i
$515$	−2.45974	+	7.57029i	−0.108389	+	0.333587i
$516$	−5.35908			−0.235920
$517$	13.7450	−	5.66140i	0.604504	−	0.248988i
$518$	2.38692			0.104875
$519$	4.31741	−	13.2876i	0.189513	−	0.583261i
$520$	3.07200	−	2.23194i	0.134716	−	0.0978771i
$521$	5.87027	+	4.26500i	0.257181	+	0.186853i	0.708904	−	0.705305i	$-0.249190\pi$
$521$	5.87027	+	4.26500i	0.257181	+	0.186853i	−0.451722	+	0.892159i	$0.649190\pi$
$522$	0.200857	+	0.618174i	0.00879126	+	0.0270567i
$523$	−5.30654	−	16.3318i	−0.232039	−	0.714142i	−0.997500	−	0.0706604i	$-0.977489\pi$
$523$	−5.30654	−	16.3318i	−0.232039	−	0.714142i	0.765462	−	0.643481i	$-0.222511\pi$
$524$	−15.7892	−	11.4715i	−0.689753	−	0.501135i
$525$	0.929529	−	0.675342i	0.0405680	−	0.0294744i
$526$	−6.29684	+	19.3797i	−0.274555	+	0.844995i
$527$	−38.9835			−1.69815
$528$	−2.46907	−	2.90257i	−0.107453	−	0.126318i
$529$	−15.9443			−0.693229
$530$	1.57543	−	4.84867i	0.0684322	−	0.210613i
$531$	6.45068	−	4.68669i	0.279936	−	0.203385i
$532$	2.16808	+	1.57520i	0.0939980	+	0.0682935i
$533$	11.1204	+	34.2251i	0.481679	+	1.48246i
$534$	2.08512	+	6.41734i	0.0902319	+	0.277705i
$535$	14.0967	+	10.2418i	0.609452	+	0.442793i
$536$	4.62204	−	3.35811i	0.199642	−	0.145048i
$537$	−8.27381	+	25.4642i	−0.357041	+	1.09886i
$538$	11.4504			0.493662
$539$	0.253650	+	3.30691i	0.0109255	+	0.142439i
$540$	−5.37701			−0.231390
$541$	−7.35094	+	22.6239i	−0.316042	+	0.972677i	0.659282	+	0.751896i	$0.270860\pi$
$541$	−7.35094	+	22.6239i	−0.316042	+	0.972677i	−0.975324	+	0.220781i	$0.929140\pi$
$542$	11.9896	−	8.71094i	0.514997	−	0.374167i
$543$	−20.5694	−	14.9445i	−0.882717	−	0.641331i
$544$	−2.00153	−	6.16008i	−0.0858150	−	0.264111i
$545$	1.52159	+	4.68298i	0.0651778	+	0.200597i
$546$	−3.52961	−	2.56441i	−0.151053	−	0.109747i
$547$	31.7492	−	23.0672i	1.35750	−	0.986281i	0.358900	−	0.933376i	$-0.383152\pi$
$547$	31.7492	−	23.0672i	1.35750	−	0.986281i	0.998600	−	0.0529054i	$-0.0168482\pi$
$548$	5.86541	−	18.0519i	0.250558	−	0.771138i
$549$	−19.5864			−0.835926
$550$	−0.253650	−	3.30691i	−0.0108157	−	0.141007i
$551$	1.03691			0.0441738
$552$	−0.943102	+	2.90257i	−0.0401411	+	0.123542i
$553$	−4.88350	+	3.54807i	−0.207667	+	0.150879i
$554$	19.8337	+	14.4100i	0.842651	+	0.612222i
$555$	0.847473	+	2.60825i	0.0359732	+	0.110714i
$556$	2.03516	+	6.26359i	0.0863102	+	0.265636i
$557$	−34.8535	−	25.3225i	−1.47679	−	1.07295i	−0.978574	−	0.205895i	$-0.933989\pi$
$557$	−34.8535	−	25.3225i	−1.47679	−	1.07295i	−0.498214	−	0.867054i	$-0.666011\pi$
$558$	8.17972	−	5.94292i	0.346275	−	0.251584i
$559$	−5.47307	+	16.8444i	−0.231486	+	0.712441i
$560$	−1.00000			−0.0422577
$561$	−15.9924	−	18.8002i	−0.675200	−	0.793745i
$562$	28.5929			1.20612
$563$	12.6244	−	38.8539i	0.532055	−	1.63750i	−0.217874	−	0.975977i	$-0.569912\pi$
$563$	12.6244	−	38.8539i	0.532055	−	1.63750i	0.749929	−	0.661519i	$-0.230088\pi$
$564$	4.16619	−	3.02692i	0.175428	−	0.127456i
$565$	9.20855	+	6.69041i	0.387407	+	0.281467i
$566$	1.60533	+	4.94068i	0.0674769	+	0.207672i
$567$	0.351757	+	1.08260i	0.0147724	+	0.0454648i
$568$	2.69499	+	1.95803i	0.113079	+	0.0821570i
$569$	3.61190	−	2.62420i	0.151419	−	0.110012i	−0.509497	−	0.860473i	$-0.670168\pi$
$569$	3.61190	−	2.62420i	0.151419	−	0.110012i	0.660915	+	0.750461i	$0.270168\pi$
$570$	−0.951490	+	2.92839i	−0.0398535	+	0.122657i
$571$	31.4272			1.31519			0.657593	−	0.753373i	$-0.271575\pi$
$571$	31.4272			1.31519			0.657593	+	0.753373i	$0.271575\pi$
$572$	−11.6448	+	4.79635i	−0.486893	+	0.200546i
$573$	23.3083			0.973717
$574$	2.92858	−	9.01325i	0.122237	−	0.376206i
$575$	−2.14896	+	1.56131i	−0.0896179	+	0.0651112i
$576$	1.35906	+	0.987414i	0.0566274	+	0.0411422i
$577$	2.54706	+	7.83905i	0.106036	+	0.326344i	0.989972	−	0.141263i	$-0.0451163\pi$
$577$	2.54706	+	7.83905i	0.106036	+	0.326344i	−0.883937	+	0.467607i	$0.845116\pi$
$578$	−7.71082	−	23.7314i	−0.320728	−	0.987098i
$579$	3.57411	+	2.59674i	0.148535	+	0.107917i
$580$	−0.313027	+	0.227427i	−0.0129977	+	0.00944340i
$581$	3.44711	−	10.6091i	0.143010	−	0.440140i
$582$	3.79675			0.157380
$583$	−8.86344	+	14.3995i	−0.367086	+	0.596367i
$584$	−15.0127			−0.621230
$585$	−1.97118	+	6.06667i	−0.0814983	+	0.250826i
$586$	14.7407	−	10.7097i	0.608931	−	0.442414i
$587$	−0.897655	−	0.652185i	−0.0370502	−	0.0269185i	0.569106	−	0.822264i	$-0.307289\pi$
$587$	−0.897655	−	0.652185i	−0.0370502	−	0.0269185i	−0.606156	+	0.795346i	$0.707289\pi$
$588$	0.355049	+	1.09273i	0.0146420	+	0.0450633i
$589$	−4.98425	−	15.3399i	−0.205372	−	0.632071i
$590$	3.83994	+	2.78988i	0.158088	+	0.114858i
$591$	−10.9832	+	7.97976i	−0.451788	+	0.328243i
$592$	0.737600	−	2.27010i	0.0303152	−	0.0933005i
$593$	46.0484			1.89098			0.945491	−	0.325648i	$-0.105582\pi$
$593$	46.0484			1.89098			0.945491	+	0.325648i	$0.105582\pi$
$594$	17.3325	+	4.19759i	0.711160	+	0.172229i
$595$	−6.47709			−0.265535
$596$	3.12533	−	9.61879i	0.128019	−	0.394001i
$597$	−11.6652	+	8.47528i	−0.477425	+	0.346870i
$598$	8.16004	+	5.92862i	0.333689	+	0.242439i
$599$	−9.13467	−	28.1136i	−0.373232	−	1.14869i	−0.944663	−	0.328041i	$-0.893611\pi$
$599$	−9.13467	−	28.1136i	−0.373232	−	1.14869i	0.571431	−	0.820650i	$-0.306389\pi$
$600$	−0.355049	−	1.09273i	−0.0144948	−	0.0446104i
$601$	−4.59563	−	3.33892i	−0.187460	−	0.136197i	0.490097	−	0.871668i	$-0.336961\pi$
$601$	−4.59563	−	3.33892i	−0.187460	−	0.136197i	−0.677557	+	0.735470i	$0.736961\pi$
$602$	3.77348	−	2.74160i	0.153796	−	0.111739i
$603$	−2.96578	+	9.12774i	−0.120776	+	0.371710i
$604$	−11.8335			−0.481500
$605$	−1.76393	+	10.8576i	−0.0717140	+	0.441426i
$606$	6.39305			0.259700
$607$	7.51424	−	23.1265i	0.304994	−	0.938674i	−0.674686	−	0.738105i	$-0.735721\pi$
$607$	7.51424	−	23.1265i	0.304994	−	0.938674i	0.979680	−	0.200569i	$-0.0642791\pi$
$608$	2.16808	−	1.57520i	0.0879271	−	0.0638827i
$609$	0.359655	+	0.261305i	0.0145740	+	0.0105886i
$610$	−3.60293	−	11.0887i	−0.145878	−	0.448967i
$611$	−5.25924	−	16.1863i	−0.212766	−	0.654826i
$612$	8.80275	+	6.39557i	0.355830	+	0.258526i
$613$	−24.6250	+	17.8911i	−0.994593	+	0.722614i	−0.960922	−	0.276819i	$-0.910720\pi$
$613$	−24.6250	+	17.8911i	−0.994593	+	0.722614i	−0.0336711	+	0.999433i	$0.510720\pi$
$614$	3.39021	−	10.4340i	0.136818	−	0.421082i
$615$	10.8888			0.439079
$616$	3.22344	+	0.780656i	0.129876	+	0.0314535i
$617$	33.4297			1.34583			0.672914	−	0.739721i	$-0.265043\pi$
$617$	33.4297			1.34583			0.672914	+	0.739721i	$0.265043\pi$
$618$	2.82614	−	8.69797i	0.113684	−	0.349884i
$619$	3.50729	−	2.54819i	0.140970	−	0.102421i	−0.515065	−	0.857151i	$-0.672232\pi$
$619$	3.50729	−	2.54819i	0.140970	−	0.102421i	0.656035	+	0.754730i	$0.272232\pi$
$620$	4.86921	+	3.53769i	0.195552	+	0.142077i
$621$	−4.41361	−	13.5837i	−0.177112	−	0.545095i
$622$	−6.44878	−	19.8473i	−0.258572	−	0.795804i
$623$	−4.75117	−	3.45193i	−0.190352	−	0.138299i
$624$	−3.52961	+	2.56441i	−0.141298	+	0.102659i
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	−8.64805			−0.345646
$627$	5.35314	−	8.69670i	0.213784	−	0.347313i
$628$	1.69054			0.0674599
$629$	4.77750	−	14.7036i	0.190491	−	0.586272i
$630$	1.35906	−	0.987414i	0.0541462	−	0.0393395i
$631$	12.4778	+	9.06567i	0.496735	+	0.360899i	0.807768	−	0.589500i	$-0.200675\pi$
$631$	12.4778	+	9.06567i	0.496735	+	0.360899i	−0.311034	+	0.950399i	$0.600675\pi$
$632$	1.86533	+	5.74090i	0.0741988	+	0.228361i
$633$	1.42010	+	4.37062i	0.0564439	+	0.173716i
$634$	2.86119	+	2.07877i	0.113632	+	0.0825587i
$635$	1.16275	−	0.844787i	0.0461423	−	0.0335244i
$636$	−1.81010	+	5.57093i	−0.0717753	+	0.220902i
$637$	3.79720			0.150451
$638$	1.18657	−	0.488732i	0.0469766	−	0.0193491i
$639$	−5.59603			−0.221376
$640$	−0.309017	+	0.951057i	−0.0122150	+	0.0375938i
$641$	−28.7426	+	20.8827i	−1.13527	+	0.824819i	−0.986453	−	0.164047i	$-0.947545\pi$
$641$	−28.7426	+	20.8827i	−1.13527	+	0.824819i	−0.148813	+	0.988865i	$0.547545\pi$
$642$	−16.1965	−	11.7675i	−0.639225	−	0.464424i
$643$	15.2056	+	46.7981i	0.599652	+	1.84554i	0.530056	+	0.847962i	$0.322171\pi$
$643$	15.2056	+	46.7981i	0.599652	+	1.84554i	0.0695952	+	0.997575i	$0.477829\pi$
$644$	−0.820830	−	2.52626i	−0.0323452	−	0.0995484i
$645$	4.33559	+	3.14999i	0.170714	+	0.124031i
$646$	14.0428	−	10.2027i	0.552507	−	0.401420i
$647$	3.70266	−	11.3956i	0.145566	−	0.448007i	−0.851517	−	0.524327i	$-0.824317\pi$
$647$	3.70266	−	11.3956i	0.145566	−	0.448007i	0.997083	+	0.0763197i	$0.0243170\pi$
$648$	1.13831			0.0447171
$649$	−10.1999	−	11.9907i	−0.400381	−	0.470676i
$650$	−3.79720			−0.148939
$651$	2.13692	−	6.57676i	0.0837525	−	0.257764i
$652$	6.52196	−	4.73848i	0.255420	−	0.185573i
$653$	40.8261	+	29.6619i	1.59765	+	1.16076i	0.891835	+	0.452360i	$0.149418\pi$
$653$	40.8261	+	29.6619i	1.59765	+	1.16076i	0.705812	+	0.708399i	$0.250582\pi$
$654$	−1.74825	−	5.38056i	−0.0683620	−	0.210397i
$655$	6.03093	+	18.5613i	0.235648	+	0.725249i
$656$	−7.66713	−	5.57050i	−0.299351	−	0.217491i
$657$	20.4031	−	14.8238i	0.796002	−	0.578330i
$658$	−1.38503	+	4.26268i	−0.0539941	+	0.166177i
$659$	29.2967			1.14124			0.570618	−	0.821216i	$-0.306704\pi$
$659$	29.2967			1.14124			0.570618	+	0.821216i	$0.306704\pi$
$660$	0.291435	+	3.79951i	0.0113441	+	0.147896i
$661$	35.0445			1.36307			0.681537	−	0.731784i	$-0.261312\pi$
$661$	35.0445			1.36307			0.681537	+	0.731784i	$0.261312\pi$
$662$	−3.15094	+	9.69759i	−0.122465	+	0.376907i
$663$	−22.8616	+	16.6099i	−0.887872	+	0.645077i
$664$	−9.02466	−	6.55680i	−0.350225	−	0.254453i
$665$	−0.828131	−	2.54873i	−0.0321135	−	0.0988353i
$666$	1.23908	+	3.81351i	0.0480136	+	0.147771i
$667$	−0.831481	−	0.604106i	−0.0321951	−	0.0233911i
$668$	−13.1205	+	9.53260i	−0.507647	+	0.368827i
$669$	6.34761	−	19.5359i	0.245413	−	0.755303i
$670$	−5.71316			−0.220719
$671$	2.95739	+	38.5564i	0.114169	+	1.48845i
$672$	1.14896			0.0443221
$673$	11.5802	−	35.6402i	0.446384	−	1.37383i	−0.434574	−	0.900636i	$-0.643101\pi$
$673$	11.5802	−	35.6402i	0.446384	−	1.37383i	0.880958	−	0.473194i	$-0.156899\pi$
$674$	−11.4130	+	8.29201i	−0.439611	+	0.319396i
$675$	4.35009	+	3.16053i	0.167435	+	0.121649i
$676$	0.438420	+	1.34932i	0.0168623	+	0.0518969i
$677$	2.60278	+	8.01055i	0.100033	+	0.307870i	0.988533	−	0.151007i	$-0.0482517\pi$
$677$	2.60278	+	8.01055i	0.100033	+	0.307870i	−0.888500	+	0.458877i	$0.848252\pi$
$678$	−10.5803	−	7.68702i	−0.406333	−	0.295218i
$679$	−2.67340	+	1.94234i	−0.102596	+	0.0745401i
$680$	−2.00153	+	6.16008i	−0.0767552	+	0.236228i
$681$	−6.62036			−0.253693
$682$	−12.9339	−	15.2047i	−0.495264	−	0.582218i
$683$	14.9986			0.573904			0.286952	−	0.957945i	$-0.407358\pi$
$683$	14.9986			0.573904			0.286952	+	0.957945i	$0.407358\pi$
$684$	−1.39117	+	4.28157i	−0.0531926	+	0.163710i
$685$	−15.3558	+	11.1567i	−0.586717	+	0.426275i
$686$	−0.809017	−	0.587785i	−0.0308884	−	0.0224417i
$687$	−3.04496	−	9.37141i	−0.116172	−	0.357542i
$688$	−1.44134	−	4.43600i	−0.0549507	−	0.169121i
$689$	15.6616	+	11.3789i	0.596661	+	0.433500i
$690$	2.46907	−	1.79389i	0.0939960	−	0.0682921i
$691$	13.5639	−	41.7454i	0.515996	−	1.58807i	−0.265468	−	0.964120i	$-0.585526\pi$
$691$	13.5639	−	41.7454i	0.515996	−	1.58807i	0.781463	−	0.623951i	$-0.214474\pi$
$692$	12.1600			0.462255
$693$	−5.15167	+	2.12191i	−0.195696	+	0.0806048i
$694$	−4.16926			−0.158263
$695$	2.03516	−	6.26359i	0.0771982	−	0.237592i
$696$	0.359655	−	0.261305i	0.0136327	−	0.00990474i
$697$	−49.6607	−	36.0806i	−1.88103	−	1.36665i
$698$	−2.48367	−	7.64396i	−0.0940085	−	0.289328i
$699$	5.11308	+	15.7364i	0.193394	+	0.595207i
$700$	0.809017	+	0.587785i	0.0305780	+	0.0222162i
$701$	35.0980	−	25.5002i	1.32563	−	0.963130i	0.325791	−	0.945442i	$-0.394369\pi$
$701$	35.0980	−	25.5002i	1.32563	−	0.963130i	0.999844	−	0.0176883i	$-0.00563067\pi$
$702$	6.30939	−	19.4183i	0.238132	−	0.732896i
$703$	6.39668			0.241256
$704$	1.73855	−	2.82444i	0.0655239	−	0.106450i
$705$	−5.14970			−0.193949
$706$	−4.88115	+	15.0226i	−0.183705	+	0.565385i
$707$	−4.50153	+	3.27055i	−0.169298	+	0.123002i
$708$	−4.41195	−	3.20547i	−0.165811	−	0.120469i
$709$	2.04287	+	6.28732i	0.0767217	+	0.236125i	0.982061	−	0.188564i	$-0.0603833\pi$
$709$	2.04287	+	6.28732i	0.0767217	+	0.236125i	−0.905339	+	0.424689i	$0.860383\pi$
$710$	−1.02940	−	3.16815i	−0.0386325	−	0.118899i
$711$	−8.20373	−	5.96036i	−0.307664	−	0.223531i
$712$	−4.75117	+	3.45193i	−0.178058	+	0.129367i
$713$	−4.94031	+	15.2047i	−0.185016	+	0.569420i
$714$	7.44193			0.278507
$715$	12.2401	+	2.96431i	0.457752	+	0.110859i
$716$	−23.3033			−0.870886
$717$	−8.52458	+	26.2360i	−0.318356	+	0.979800i
$718$	5.37205	−	3.90303i	0.200483	−	0.145660i
$719$	22.2569	+	16.1706i	0.830043	+	0.603062i	0.919571	−	0.392923i	$-0.128536\pi$
$719$	22.2569	+	16.1706i	0.830043	+	0.603062i	−0.0895285	+	0.995984i	$0.528536\pi$
$720$	−0.519114	−	1.59767i	−0.0193462	−	0.0595416i
$721$	2.45974	+	7.57029i	0.0916054	+	0.281933i
$722$	−9.56112	−	6.94656i	−0.355828	−	0.258524i
$723$	15.5827	−	11.3215i	0.579527	−	0.421051i
$724$	6.83818	−	21.0458i	0.254139	−	0.782160i
$725$	0.386922			0.0143699
$726$	2.02669	−	12.4750i	0.0752175	−	0.462991i
$727$	−13.3895			−0.496590			−0.248295	−	0.968685i	$-0.579870\pi$
$727$	−13.3895			−0.496590			−0.248295	+	0.968685i	$0.579870\pi$
$728$	1.17340	−	3.61136i	0.0434891	−	0.133846i
$729$	−16.5413	+	12.0180i	−0.612640	+	0.445109i
$730$	12.1455	+	8.82425i	0.449526	+	0.326600i
$731$	−9.33571	−	28.7323i	−0.345294	−	1.06270i
$732$	4.13963	+	12.7405i	0.153005	+	0.470901i
$733$	37.1376	+	26.9820i	1.37171	+	0.996604i	0.997602	+	0.0692185i	$0.0220506\pi$
$733$	37.1376	+	26.9820i	1.37171	+	0.996604i	0.374107	+	0.927386i	$0.377949\pi$
$734$	13.4544	−	9.77519i	0.496611	−	0.360809i
$735$	0.355049	−	1.09273i	0.0130962	−	0.0403058i
$736$	−2.65626			−0.0979111
$737$	18.4160	+	4.46001i	0.678364	+	0.164287i
$738$	15.9205			0.586040
$739$	−4.80834	+	14.7985i	−0.176878	+	0.544373i	−0.999714	−	0.0239048i	$-0.992390\pi$
$739$	−4.80834	+	14.7985i	−0.176878	+	0.544373i	0.822837	+	0.568278i	$0.192390\pi$
$740$	−1.93106	+	1.40300i	−0.0709872	+	0.0515752i
$741$	−9.45896	−	6.87234i	−0.347484	−	0.252462i
$742$	−1.57543	−	4.84867i	−0.0578357	−	0.178000i
$743$	9.87890	+	30.4041i	0.362422	+	1.11542i	0.951580	+	0.307401i	$0.0994594\pi$
$743$	9.87890	+	30.4041i	0.362422	+	1.11542i	−0.589158	+	0.808018i	$0.700541\pi$
$744$	−5.59453	−	4.06466i	−0.205105	−	0.149018i
$745$	−8.18223	+	5.94474i	−0.299774	+	0.217798i
$746$	2.25730	−	6.94725i	0.0826456	−	0.254357i
$747$	18.7393			0.685635
$748$	11.2607	−	18.2942i	0.411733	−	0.668901i
$749$	17.4244			0.636675
$750$	−0.355049	+	1.09273i	−0.0129645	+	0.0399007i
$751$	−25.6503	+	18.6361i	−0.935994	+	0.680040i	−0.947453	−	0.319895i	$-0.896353\pi$
$751$	−25.6503	+	18.6361i	−0.935994	+	0.680040i	0.0114587	+	0.999934i	$0.496353\pi$
$752$	3.62605	+	2.63448i	0.132229	+	0.0960697i
$753$	−0.860951	−	2.64974i	−0.0313748	−	0.0965617i
$754$	−0.454015	−	1.39731i	−0.0165342	−	0.0508872i
$755$	9.57353	+	6.95558i	0.348417	+	0.253139i
$756$	−4.35009	+	3.16053i	−0.158211	+	0.114947i
$757$	−6.90054	+	21.2377i	−0.250804	+	0.771897i	0.743823	+	0.668377i	$0.233011\pi$
$757$	−6.90054	+	21.2377i	−0.250804	+	0.771897i	−0.994627	+	0.103520i	$0.966989\pi$
$758$	13.2798			0.482344
$759$	−9.35932	+	3.85499i	−0.339722	+	0.139927i
$760$	−2.67989			−0.0972098
$761$	5.36631	−	16.5158i	0.194529	−	0.598697i	−0.805453	−	0.592659i	$-0.798078\pi$
$761$	5.36631	−	16.5158i	0.194529	−	0.598697i	0.999982	−	0.00603791i	$-0.00192194\pi$
$762$	−1.33595	+	0.970628i	−0.0483965	+	0.0351621i
$763$	3.98358	+	2.89424i	0.144215	+	0.104779i
$764$	6.26884	+	19.2935i	0.226799	+	0.698014i
$765$	−3.36235	−	10.3482i	−0.121566	−	0.374142i
$766$	13.8394	+	10.0549i	0.500039	+	0.363300i
$767$	−14.5811	+	10.5938i	−0.526491	+	0.382518i
$768$	0.355049	−	1.09273i	0.0128117	−	0.0394304i
$769$	−36.3673			−1.31144			−0.655720	−	0.755004i	$-0.727635\pi$
$769$	−36.3673			−1.31144			−0.655720	+	0.755004i	$0.727635\pi$
$770$	−2.14896	−	2.52626i	−0.0774432	−	0.0910399i
$771$	5.95584			0.214494
$772$	−1.18819	+	3.65689i	−0.0427640	+	0.131614i
$773$	42.9363	−	31.1951i	1.54431	−	1.12201i	0.596753	−	0.802425i	$-0.296457\pi$
$773$	42.9363	−	31.1951i	1.54431	−	1.12201i	0.947558	−	0.319583i	$-0.103543\pi$
$774$	6.33903	+	4.60557i	0.227852	+	0.165544i
$775$	−1.85987	−	5.72410i	−0.0668086	−	0.205616i
$776$	1.02115	+	3.14277i	0.0366571	+	0.112819i
$777$	2.21871	+	1.61199i	0.0795959	+	0.0578298i
$778$	6.91464	−	5.02378i	0.247902	−	0.180111i
$779$	7.84827	−	24.1545i	0.281194	−	0.865425i
$780$	4.36284			0.156215
$781$	0.844959	+	11.0160i	0.0302350	+	0.394182i
$782$	−17.2049			−0.615244
$783$	−0.642905	+	1.97866i	−0.0229756	+	0.0707115i
$784$	−0.809017	+	0.587785i	−0.0288935	+	0.0209923i
$785$	−1.36767	−	0.993674i	−0.0488144	−	0.0354657i
$786$	−6.92930	−	21.3262i	−0.247160	−	0.760680i
$787$	−11.8467	−	36.4603i	−0.422288	−	1.29967i	−0.905568	−	0.424202i	$-0.860555\pi$
$787$	−11.8467	−	36.4603i	−0.422288	−	1.29967i	0.483280	−	0.875466i	$-0.339445\pi$
$788$	−9.55924	−	6.94520i	−0.340534	−	0.247412i
$789$	−18.9410	+	13.7615i	−0.674318	+	0.489921i
$790$	1.86533	−	5.74090i	0.0663655	−	0.204252i
$791$	11.3824			0.404711
$792$	0.426104	+	5.55524i	0.0151410	+	0.197397i
$793$	44.2728			1.57217
$794$	−5.26786	+	16.2128i	−0.186949	+	0.575371i
$795$	4.73892	−	3.44302i	0.168072	−	0.122111i
$796$	−10.1528	−	7.37647i	−0.359858	−	0.261452i
$797$	−9.42565	−	29.0092i	−0.333874	−	1.02756i	−0.967274	−	0.253734i	$-0.918341\pi$
$797$	−9.42565	−	29.0092i	−0.333874	−	1.02756i	0.633400	−	0.773824i	$-0.281659\pi$
$798$	0.951490	+	2.92839i	0.0336824	+	0.103664i
$799$	23.4863	+	17.0638i	0.830885	+	0.603673i
$800$	0.809017	−	0.587785i	0.0286031	−	0.0207813i
$801$	3.04864	−	9.38274i	0.107718	−	0.331523i
$802$	2.71053			0.0957121
$803$	−32.2617	−	37.9259i	−1.13849	−	1.33838i
$804$	6.56420			0.231501
$805$	−0.820830	+	2.52626i	−0.0289305	+	0.0890388i
$806$	−18.4894	+	13.4333i	−0.651260	+	0.473168i
$807$	10.6435	+	7.73294i	0.374668	+	0.272212i
$808$	1.71943	+	5.29187i	0.0604894	+	0.186167i
$809$	−10.4754	−	32.2399i	−0.368294	−	1.13349i	−0.947892	−	0.318591i	$-0.896790\pi$
$809$	−10.4754	−	32.2399i	−0.368294	−	1.13349i	0.579598	−	0.814903i	$-0.303210\pi$
$810$	−0.920912	−	0.669082i	−0.0323576	−	0.0235091i
$811$	−34.7098	+	25.2181i	−1.21883	+	0.885529i	−0.996002	−	0.0893303i	$-0.971527\pi$
$811$	−34.7098	+	25.2181i	−1.21883	+	0.885529i	−0.222823	+	0.974859i	$0.571527\pi$
$812$	−0.119566	+	0.367985i	−0.00419593	+	0.0129137i
$813$	17.0275			0.597182
$814$	7.31992	−	3.01499i	0.256563	−	0.105675i
$815$	−8.06159			−0.282385
$816$	2.29968	−	7.07769i	0.0805050	−	0.247769i
$817$	10.1125	−	7.34717i	0.353792	−	0.257045i
$818$	23.7162	+	17.2308i	0.829218	+	0.602462i
$819$	1.97118	+	6.06667i	0.0688787	+	0.211987i
$820$	2.92858	+	9.01325i	0.102271	+	0.314756i
$821$	−40.6169	−	29.5099i	−1.41754	−	1.02990i	−0.992171	−	0.124884i	$-0.960144\pi$
$821$	−40.6169	−	29.5099i	−1.41754	−	1.02990i	−0.425369	−	0.905020i	$-0.639856\pi$
$822$	17.6433	−	12.8186i	0.615380	−	0.447100i
$823$	−6.16131	+	18.9626i	−0.214770	+	0.660994i	0.784400	+	0.620255i	$0.212971\pi$
$823$	−6.16131	+	18.9626i	−0.214770	+	0.660994i	−0.999170	+	0.0407384i	$0.987029\pi$
$824$	7.95988			0.277296
$825$	1.99752	−	3.24517i	0.0695448	−	0.112982i
$826$	4.74643			0.165149
$827$	−10.5187	+	32.3734i	−0.365773	+	1.12573i	0.583723	+	0.811953i	$0.301595\pi$
$827$	−10.5187	+	32.3734i	−0.365773	+	1.12573i	−0.949496	+	0.313780i	$0.898405\pi$
$828$	3.61001	−	2.62283i	0.125457	−	0.0911496i
$829$	10.4872	+	7.61943i	0.364237	+	0.264634i	0.754817	−	0.655935i	$-0.227726\pi$
$829$	10.4872	+	7.61943i	0.364237	+	0.264634i	−0.390580	+	0.920569i	$0.627726\pi$
$830$	3.44711	+	10.6091i	0.119651	+	0.368248i
$831$	8.70428	+	26.7890i	0.301948	+	0.929301i
$832$	−3.07200	−	2.23194i	−0.106503	−	0.0773786i
$833$	−5.24008	+	3.80714i	−0.181558	+	0.131910i
$834$	−2.33833	+	7.19663i	−0.0809696	+	0.249199i
$835$	16.2178			0.561241
$836$	8.63846	+	2.09207i	0.298768	+	0.0723558i
$837$	32.3624			1.11861
$838$	−11.8593	+	36.4993i	−0.409674	+	1.26085i
$839$	11.7034	−	8.50305i	0.404048	−	0.293558i	−0.367140	−	0.930166i	$-0.619663\pi$
$839$	11.7034	−	8.50305i	0.404048	−	0.293558i	0.771188	+	0.636608i	$0.219663\pi$
$840$	−0.929529	−	0.675342i	−0.0320718	−	0.0233015i
$841$	−8.91523	−	27.4383i	−0.307422	−	0.946147i
$842$	11.4832	+	35.3417i	0.395738	+	1.21796i
$843$	26.5780	+	19.3100i	0.915394	+	0.665073i
$844$	−3.23585	+	2.35098i	−0.111383	+	0.0809242i
$845$	0.438420	−	1.34932i	0.0150821	−	0.0464180i
$846$	−7.52934			−0.258864
$847$	4.95492	+	9.82084i	0.170253	+	0.337448i
$848$	−5.09819			−0.175073
$849$	−1.84446	+	5.67665i	−0.0633016	+	0.194822i
$850$	5.24008	−	3.80714i	0.179733	−	0.130584i
$851$	−5.12940	−	3.72673i	−0.175834	−	0.127751i
$852$	1.18274	+	3.64009i	0.0405199	+	0.124707i
$853$	−15.8156	−	48.6755i	−0.541517	−	1.66662i	−0.729130	−	0.684375i	$-0.760075\pi$
$853$	−15.8156	−	48.6755i	−0.541517	−	1.66662i	0.187613	−	0.982243i	$-0.439925\pi$
$854$	−9.43259	−	6.85318i	−0.322777	−	0.234511i
$855$	3.64212	−	2.64616i	0.124558	−	0.0904967i
$856$	5.38444	−	16.5716i	0.184037	−	0.566406i
$857$	−50.8960			−1.73857			−0.869287	−	0.494308i	$-0.835422\pi$
$857$	−50.8960			−1.73857			−0.869287	+	0.494308i	$0.835422\pi$
$858$	−14.0634	−	3.40588i	−0.480115	−	0.116275i
$859$	−20.8508			−0.711422			−0.355711	−	0.934596i	$-0.615761\pi$
$859$	−20.8508			−0.711422			−0.355711	+	0.934596i	$0.615761\pi$
$860$	−1.44134	+	4.43600i	−0.0491494	+	0.151266i
$861$	8.80923	−	6.40028i	0.300218	−	0.218121i
$862$	−24.8732	−	18.0714i	−0.847185	−	0.615516i
$863$	16.7105	+	51.4295i	0.568830	+	1.75068i	0.656287	+	0.754512i	$0.272126\pi$
$863$	16.7105	+	51.4295i	0.568830	+	1.75068i	−0.0874560	+	0.996168i	$0.527874\pi$
$864$	1.66159	+	5.11384i	0.0565284	+	0.173976i
$865$	−9.83768	−	7.14749i	−0.334491	−	0.243022i
$866$	−6.91997	+	5.02765i	−0.235150	+	0.170846i
$867$	8.85943	−	27.2665i	0.300882	−	0.926019i
$868$	6.01867			0.204287
$869$	−10.4944	+	17.0493i	−0.356000	+	0.578357i
$870$	−0.444559			−0.0150719
$871$	6.70383	−	20.6323i	0.227150	−	0.699097i
$872$	3.98358	−	2.89424i	0.134901	−	0.0980113i
$873$	−4.49101	−	3.26291i	−0.151998	−	0.110433i
$874$	−2.19973	−	6.77008i	−0.0744071	−	0.229001i
$875$	−0.309017	−	0.951057i	−0.0104467	−	0.0321516i
$876$	−13.9547	−	10.1387i	−0.471487	−	0.342556i
$877$	−2.09156	+	1.51961i	−0.0706270	+	0.0513135i	−0.622539	−	0.782589i	$-0.713899\pi$
$877$	−2.09156	+	1.51961i	−0.0706270	+	0.0513135i	0.551912	+	0.833903i	$0.313899\pi$
$878$	7.58345	−	23.3394i	0.255929	−	0.787668i
$879$	20.9346			0.706107
$880$	−3.06668	+	1.26313i	−0.103378	+	0.0425800i
$881$	42.8631			1.44410			0.722048	−	0.691843i	$-0.243201\pi$
$881$	42.8631			1.44410			0.722048	+	0.691843i	$0.243201\pi$
$882$	0.519114	−	1.59767i	0.0174795	−	0.0537963i
$883$	11.6738	−	8.48154i	0.392856	−	0.285426i	−0.373769	−	0.927522i	$-0.621935\pi$
$883$	11.6738	−	8.48154i	0.392856	−	0.285426i	0.766625	+	0.642095i	$0.221935\pi$
$884$	−19.8976	−	14.4565i	−0.669230	−	0.486224i
$885$	1.68521	+	5.18655i	0.0566478	+	0.174344i
$886$	−8.33367	−	25.6484i	−0.279975	−	0.861675i
$887$	6.87146	+	4.99241i	0.230721	+	0.167629i	0.697139	−	0.716936i	$-0.254456\pi$
$887$	6.87146	+	4.99241i	0.230721	+	0.167629i	−0.466418	+	0.884564i	$0.654456\pi$
$888$	2.21871	−	1.61199i	0.0744552	−	0.0540948i
$889$	0.444131	−	1.36689i	0.0148957	−	0.0458442i
$890$	5.87277			0.196856
$891$	2.44618	+	2.87566i	0.0819503	+	0.0963383i
$892$	17.8782			0.598605
$893$	−3.71172	+	11.4235i	−0.124208	+	0.382273i
$894$	9.40107	−	6.83028i	0.314419	−	0.228439i
$895$	18.8528	+	13.6973i	0.630179	+	0.457852i
$896$	0.309017	+	0.951057i	0.0103235	+	0.0317726i
$897$	3.58115	+	11.0216i	0.119571	+	0.368002i
$898$	−28.4615	−	20.6785i	−0.949772	−	0.690049i
$899$	1.88400	−	1.36881i	0.0628351	−	0.0456523i
$900$	−0.519114	+	1.59767i	−0.0173038	+	0.0532556i
$901$	−33.0214			−1.10010
$902$	−2.40387	−	31.3399i	−0.0800401	−	1.04350i
$903$	5.35908			0.178339
$904$	3.51735	−	10.8253i	0.116985	−	0.360044i
$905$	−17.9026	+	13.0070i	−0.595103	+	0.432367i
$906$	−10.9996	−	7.99169i	−0.365438	−	0.265506i
$907$	−14.6512	−	45.0918i	−0.486485	−	1.49725i	−0.829818	−	0.558034i	$-0.811556\pi$
$907$	−14.6512	−	45.0918i	−0.486485	−	1.49725i	0.343332	−	0.939214i	$-0.388444\pi$
$908$	−1.78057	−	5.48002i	−0.0590902	−	0.181861i
$909$	−7.56207	−	5.49417i	−0.250818	−	0.182230i
$910$	−3.07200	+	2.23194i	−0.101836	+	0.0739881i
$911$	4.56370	−	14.0456i	0.151202	−	0.465352i	−0.846554	−	0.532302i	$-0.821327\pi$
$911$	4.56370	−	14.0456i	0.151202	−	0.465352i	0.997756	+	0.0669505i	$0.0213269\pi$
$912$	3.07909			0.101959
$913$	−2.82949	−	36.8889i	−0.0936426	−	1.22084i
$914$	−20.4364			−0.675976
$915$	4.13963	−	12.7405i	0.136852	−	0.421187i
$916$	6.93827	−	5.04095i	0.229247	−	0.166558i
$917$	15.7892	+	11.4715i	0.521404	+	0.378822i
$918$	10.7623	+	33.1228i	0.355207	+	1.09322i
$919$	9.16694	+	28.2129i	0.302389	+	0.930659i	0.980639	+	0.195827i	$0.0627390\pi$
$919$	9.16694	+	28.2129i	0.302389	+	0.930659i	−0.678249	+	0.734832i	$0.737261\pi$
$920$	2.14896	+	1.56131i	0.0708492	+	0.0514749i
$921$	10.1978	−	7.40916i	0.336030	−	0.244140i
$922$	−1.72908	+	5.32155i	−0.0569441	+	0.175256i
$923$	12.6492			0.416354
$924$	2.46907	+	2.90257i	0.0812265	+	0.0954875i
$925$	2.38692			0.0784815
$926$	9.11844	−	28.0637i	0.299651	−	0.922230i
$927$	−10.8179	+	7.85969i	−0.355308	+	0.258146i
$928$	0.313027	+	0.227427i	0.0102756	+	0.00746566i
$929$	−4.54241	−	13.9801i	−0.149032	−	0.458673i	0.848476	−	0.529234i	$-0.177521\pi$
$929$	−4.54241	−	13.9801i	−0.149032	−	0.458673i	−0.997507	+	0.0705618i	$0.977521\pi$
$930$	2.13692	+	6.57676i	0.0700724	+	0.215661i
$931$	−2.16808	−	1.57520i	−0.0710558	−	0.0516251i
$932$	−11.6507	+	8.46474i	−0.381632	+	0.277272i
$933$	7.40939	−	22.8038i	0.242573	−	0.746562i
$934$	−31.3408			−1.02550
$935$	−19.8632	+	8.18139i	−0.649594	+	0.267560i
$936$	6.37888			0.208500
$937$	16.7647	−	51.5965i	0.547680	−	1.68558i	−0.166852	−	0.985982i	$-0.553360\pi$
$937$	16.7647	−	51.5965i	0.547680	−	1.68558i	0.714532	−	0.699603i	$-0.246640\pi$
$938$	−4.62204	+	3.35811i	−0.150915	+	0.109646i
$939$	−8.03862	−	5.84040i	−0.262330	−	0.190594i
$940$	−1.38503	−	4.26268i	−0.0451747	−	0.139033i
$941$	9.84147	+	30.2889i	0.320823	+	0.987391i	0.973291	+	0.229575i	$0.0737335\pi$
$941$	9.84147	+	30.2889i	0.320823	+	0.987391i	−0.652468	+	0.757816i	$0.726266\pi$
$942$	1.57141	+	1.14169i	0.0511991	+	0.0371984i
$943$	−20.3659	+	14.7967i	−0.663205	+	0.481847i
$944$	1.46673	−	4.51413i	0.0477379	−	0.146922i
$945$	5.37701			0.174914
$946$	8.10907	−	13.1740i	0.263649	−	0.428323i
$947$	−44.7035			−1.45267			−0.726335	−	0.687341i	$-0.758778\pi$
$947$	−44.7035			−1.45267			−0.726335	+	0.687341i	$0.758778\pi$
$948$	−2.14319	+	6.59607i	−0.0696076	+	0.214230i
$949$	−46.1191	+	33.5075i	−1.49709	+	1.08770i
$950$	2.16808	+	1.57520i	0.0703416	+	0.0511062i
$951$	1.25567	+	3.86456i	0.0407180	+	0.125317i
$952$	2.00153	+	6.16008i	0.0648700	+	0.199649i
$953$	36.7503	+	26.7007i	1.19046	+	0.864920i	0.993313	−	0.115454i	$-0.0368323\pi$
$953$	36.7503	+	26.7007i	1.19046	+	0.864920i	0.197147	+	0.980374i	$0.436832\pi$
$954$	6.92874	−	5.03402i	0.224326	−	0.162982i
$955$	6.26884	−	19.2935i	0.202855	−	0.624323i
$956$	−24.0096			−0.776527
$957$	1.43301	+	0.347047i	0.0463226	+	0.0112184i
$958$	−6.75139			−0.218127
$959$	−5.86541	+	18.0519i	−0.189404	+	0.582926i
$960$	−0.929529	+	0.675342i	−0.0300004	+	0.0217966i
$961$	−4.22662	−	3.07082i	−0.136343	−	0.0990587i
$962$	−2.80082	−	8.62002i	−0.0903019	−	0.277921i
$963$	9.04526	+	27.8385i	0.291480	+	0.897082i
$964$	13.5624	+	9.85369i	0.436817	+	0.317366i
$965$	3.11073	−	2.26008i	0.100138	−	0.0727545i
$966$	0.943102	−	2.90257i	0.0303438	−	0.0933886i
$967$	−34.6596			−1.11458			−0.557289	−	0.830319i	$-0.688158\pi$
$967$	−34.6596			−1.11458			−0.557289	+	0.830319i	$0.688158\pi$
$968$	10.8713	−	1.67760i	0.349418	−	0.0539201i
$969$	19.9435			0.640679
$970$	1.02115	−	3.14277i	0.0327871	−	0.100908i
$971$	−3.47214	+	2.52265i	−0.111426	+	0.0809558i	−0.642103	−	0.766618i	$-0.721938\pi$
$971$	−3.47214	+	2.52265i	−0.111426	+	0.0809558i	0.530677	+	0.847574i	$0.321938\pi$
$972$	−11.9922	−	8.71283i	−0.384649	−	0.279464i
$973$	−2.03516	−	6.26359i	−0.0652444	−	0.200802i
$974$	7.83548	+	24.1151i	0.251065	+	0.772698i
$975$	−3.52961	−	2.56441i	−0.113038	−	0.0821269i
$976$	−9.43259	+	6.85318i	−0.301930	+	0.219365i
$977$	−11.6819	+	35.9533i	−0.373739	+	1.15025i	0.570587	+	0.821237i	$0.306716\pi$
$977$	−11.6819	+	35.9533i	−0.373739	+	1.15025i	−0.944326	+	0.329012i	$0.893284\pi$
$978$	9.26245			0.296181
$979$	−18.9305	−	4.58461i	−0.605023	−	0.146525i
$980$	1.00000			0.0319438
$981$	−2.55610	+	7.86688i	−0.0816101	+	0.251170i
$982$	16.0082	−	11.6307i	0.510843	−	0.371149i
$983$	11.6611	+	8.47227i	0.371930	+	0.270223i	0.758011	−	0.652242i	$-0.226171\pi$
$983$	11.6611	+	8.47227i	0.371930	+	0.270223i	−0.386081	+	0.922465i	$0.626171\pi$
$984$	−3.36483	−	10.3559i	−0.107267	−	0.330133i
$985$	3.65131	+	11.2376i	0.116340	+	0.358059i
$986$	2.02750	+	1.47307i	0.0645688	+	0.0469120i
$987$	−4.16619	+	3.02692i	−0.132611	+	0.0963478i
$988$	3.14458	−	9.67803i	0.100042	−	0.307899i
$989$	−12.3896			−0.393965
$990$	2.92056	−	4.74474i	0.0928216	−	0.150798i
$991$	−24.3859			−0.774644			−0.387322	−	0.921944i	$-0.626600\pi$
$991$	−24.3859			−0.774644			−0.387322	+	0.921944i	$0.626600\pi$
$992$	1.85987	−	5.72410i	0.0590510	−	0.181740i
$993$	−9.47808	+	6.88623i	−0.300778	+	0.218528i
$994$	−2.69499	−	1.95803i	−0.0854800	−	0.0621048i
$995$	3.87804	+	11.9354i	0.122942	+	0.378377i
$996$	−3.96060	−	12.1895i	−0.125496	−	0.386238i
$997$	−12.6037	−	9.15716i	−0.399165	−	0.290010i	0.370036	−	0.929017i	$-0.379345\pi$
$997$	−12.6037	−	9.15716i	−0.399165	−	0.290010i	−0.769201	+	0.639007i	$0.779345\pi$
$998$	−21.6595	+	15.7366i	−0.685621	+	0.498133i
$999$	−3.96608	+	12.2063i	−0.125481	+	0.386191i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.f.141.1	yes	8
11.4	even	5		8470.2.a.co.1.4		4
11.5	even	5	inner	770.2.n.f.71.1	✓	8
11.7	odd	10		8470.2.a.cs.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.f.71.1	✓	8	11.5	even	5	inner
770.2.n.f.141.1	yes	8	1.1	even	1	trivial
8470.2.a.co.1.4		4	11.4	even	5
8470.2.a.cs.1.4		4	11.7	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.929529 + 0.675342i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-0.355049 - 1.09273i) q^{6} +(0.809017 + 0.587785i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.519114 + 1.59767i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(-0.929529 + 0.675342i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.309017 + 0.951057i) q^{5} +(-0.355049 - 1.09273i) q^{6} +(0.809017 + 0.587785i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.519114 + 1.59767i) q^{9} -1.00000 q^{10} +(3.22344 + 0.780656i) q^{11} +1.14896 q^{12} +(1.17340 - 3.61136i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(-0.929529 - 0.675342i) q^{15} +(0.309017 + 0.951057i) q^{16} +(2.00153 + 6.16008i) q^{17} +(-1.35906 - 0.987414i) q^{18} +(-2.16808 + 1.57520i) q^{19} +(0.309017 - 0.951057i) q^{20} -1.14896 q^{21} +(-1.73855 + 2.82444i) q^{22} +2.65626 q^{23} +(-0.355049 + 1.09273i) q^{24} +(-0.809017 + 0.587785i) q^{25} +(3.07200 + 2.23194i) q^{26} +(-1.66159 - 5.11384i) q^{27} +(-0.309017 - 0.951057i) q^{28} +(-0.313027 - 0.227427i) q^{29} +(0.929529 - 0.675342i) q^{30} +(-1.85987 + 5.72410i) q^{31} -1.00000 q^{32} +(-3.52349 + 1.45128i) q^{33} -6.47709 q^{34} +(-0.309017 + 0.951057i) q^{35} +(1.35906 - 0.987414i) q^{36} +(-1.93106 - 1.40300i) q^{37} +(-0.828131 - 2.54873i) q^{38} +(1.34819 + 4.14931i) q^{39} +(0.809017 + 0.587785i) q^{40} +(-7.66713 + 5.57050i) q^{41} +(0.355049 - 1.09273i) q^{42} -4.66428 q^{43} +(-2.14896 - 2.52626i) q^{44} -1.67989 q^{45} +(-0.820830 + 2.52626i) q^{46} +(3.62605 - 2.63448i) q^{47} +(-0.929529 - 0.675342i) q^{48} +(0.309017 + 0.951057i) q^{49} +(-0.309017 - 0.951057i) q^{50} +(-6.02065 - 4.37426i) q^{51} +(-3.07200 + 2.23194i) q^{52} +(-1.57543 + 4.84867i) q^{53} +5.37701 q^{54} +(0.253650 + 3.30691i) q^{55} +1.00000 q^{56} +(0.951490 - 2.92839i) q^{57} +(0.313027 - 0.227427i) q^{58} +(-3.83994 - 2.78988i) q^{59} +(0.355049 + 1.09273i) q^{60} +(3.60293 + 11.0887i) q^{61} +(-4.86921 - 3.53769i) q^{62} +(-1.35906 + 0.987414i) q^{63} +(0.309017 - 0.951057i) q^{64} +3.79720 q^{65} +(-0.291435 - 3.79951i) q^{66} +5.71316 q^{67} +(2.00153 - 6.16008i) q^{68} +(-2.46907 + 1.79389i) q^{69} +(-0.809017 - 0.587785i) q^{70} +(1.02940 + 3.16815i) q^{71} +(0.519114 + 1.59767i) q^{72} +(-12.1455 - 8.82425i) q^{73} +(1.93106 - 1.40300i) q^{74} +(0.355049 - 1.09273i) q^{75} +2.67989 q^{76} +(2.14896 + 2.52626i) q^{77} -4.36284 q^{78} +(-1.86533 + 5.74090i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(0.920912 + 0.669082i) q^{81} +(-2.92858 - 9.01325i) q^{82} +(-3.44711 - 10.6091i) q^{83} +(0.929529 + 0.675342i) q^{84} +(-5.24008 + 3.80714i) q^{85} +(1.44134 - 4.43600i) q^{86} +0.444559 q^{87} +(3.06668 - 1.26313i) q^{88} -5.87277 q^{89} +(0.519114 - 1.59767i) q^{90} +(3.07200 - 2.23194i) q^{91} +(-2.14896 - 1.56131i) q^{92} +(-2.13692 - 6.57676i) q^{93} +(1.38503 + 4.26268i) q^{94} +(-2.16808 - 1.57520i) q^{95} +(0.929529 - 0.675342i) q^{96} +(-1.02115 + 3.14277i) q^{97} -1.00000 q^{98} +(-2.92056 + 4.74474i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9	\( 8 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9} - 8 q^{10} - 8 q^{12} - 2 q^{13} - 2 q^{14} + 2 q^{15} - 2 q^{16} - 6 q^{17} + 8 q^{18} + 6 q^{19} - 2 q^{20} + 8 q^{21} - 2 q^{24} - 2 q^{25} + 12 q^{26} - 4 q^{27} + 2 q^{28} + 20 q^{29} - 2 q^{30} - 6 q^{31} - 8 q^{32} - 8 q^{33} - 24 q^{34} + 2 q^{35} - 8 q^{36} + 16 q^{37} + 4 q^{38} + 20 q^{39} + 2 q^{40} - 12 q^{41} + 2 q^{42} + 20 q^{43} + 12 q^{45} - 16 q^{47} + 2 q^{48} - 2 q^{49} + 2 q^{50} - 20 q^{51} - 12 q^{52} - 30 q^{53} + 44 q^{54} + 8 q^{56} - 20 q^{58} - 18 q^{59} + 2 q^{60} + 8 q^{61} - 24 q^{62} + 8 q^{63} - 2 q^{64} + 28 q^{65} + 18 q^{66} - 6 q^{68} - 28 q^{69} - 2 q^{70} + 22 q^{71} - 2 q^{72} - 50 q^{73} - 16 q^{74} + 2 q^{75} - 4 q^{76} + 60 q^{78} - 34 q^{79} - 2 q^{80} - 28 q^{81} + 12 q^{82} - 34 q^{83} - 2 q^{84} - 6 q^{85} + 4 q^{87} - 8 q^{89} - 2 q^{90} + 12 q^{91} + 56 q^{93} - 24 q^{94} + 6 q^{95} - 2 q^{96} - 8 q^{98} - 24 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 + 2 * q^9 - 8 * q^10 - 8 * q^12 - 2 * q^13 - 2 * q^14 + 2 * q^15 - 2 * q^16 - 6 * q^17 + 8 * q^18 + 6 * q^19 - 2 * q^20 + 8 * q^21 - 2 * q^24 - 2 * q^25 + 12 * q^26 - 4 * q^27 + 2 * q^28 + 20 * q^29 - 2 * q^30 - 6 * q^31 - 8 * q^32 - 8 * q^33 - 24 * q^34 + 2 * q^35 - 8 * q^36 + 16 * q^37 + 4 * q^38 + 20 * q^39 + 2 * q^40 - 12 * q^41 + 2 * q^42 + 20 * q^43 + 12 * q^45 - 16 * q^47 + 2 * q^48 - 2 * q^49 + 2 * q^50 - 20 * q^51 - 12 * q^52 - 30 * q^53 + 44 * q^54 + 8 * q^56 - 20 * q^58 - 18 * q^59 + 2 * q^60 + 8 * q^61 - 24 * q^62 + 8 * q^63 - 2 * q^64 + 28 * q^65 + 18 * q^66 - 6 * q^68 - 28 * q^69 - 2 * q^70 + 22 * q^71 - 2 * q^72 - 50 * q^73 - 16 * q^74 + 2 * q^75 - 4 * q^76 + 60 * q^78 - 34 * q^79 - 2 * q^80 - 28 * q^81 + 12 * q^82 - 34 * q^83 - 2 * q^84 - 6 * q^85 + 4 * q^87 - 8 * q^89 - 2 * q^90 + 12 * q^91 + 56 * q^93 - 24 * q^94 + 6 * q^95 - 2 * q^96 - 8 * q^98 - 24 * q^99

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