LMFDB - Embedded newform 770.2.n.c.71.1

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:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			71.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	770.71
Dual form			770.2.n.c.141.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(-0.500000 - 0.363271i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(-0.190983 + 0.587785i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.809017 - 2.48990i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.500000 - 0.363271i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(-0.190983 + 0.587785i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.809017 - 2.48990i) q^{9} +1.00000 q^{10} +(2.19098 + 2.48990i) q^{11} +0.618034 q^{12} +(-1.61803 - 4.97980i) q^{13} +(0.809017 + 0.587785i) q^{14} +(0.500000 - 0.363271i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.500000 + 1.53884i) q^{17} +(-2.11803 + 1.53884i) q^{18} +(0.309017 + 0.224514i) q^{19} +(-0.309017 - 0.951057i) q^{20} +0.618034 q^{21} +(1.69098 - 2.85317i) q^{22} -8.47214 q^{23} +(-0.190983 - 0.587785i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-4.23607 + 3.07768i) q^{26} +(-1.07295 + 3.30220i) q^{27} +(0.309017 - 0.951057i) q^{28} +(-3.23607 + 2.35114i) q^{29} +(-0.500000 - 0.363271i) q^{30} +(-1.38197 - 4.25325i) q^{31} -1.00000 q^{32} +(-0.190983 - 2.04087i) q^{33} +1.61803 q^{34} +(-0.309017 - 0.951057i) q^{35} +(2.11803 + 1.53884i) q^{36} +(-7.85410 + 5.70634i) q^{37} +(0.118034 - 0.363271i) q^{38} +(-1.00000 + 3.07768i) q^{39} +(-0.809017 + 0.587785i) q^{40} +(-6.97214 - 5.06555i) q^{41} +(-0.190983 - 0.587785i) q^{42} -4.61803 q^{43} +(-3.23607 - 0.726543i) q^{44} +2.61803 q^{45} +(2.61803 + 8.05748i) q^{46} +(5.47214 + 3.97574i) q^{47} +(-0.500000 + 0.363271i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(0.809017 - 0.587785i) q^{51} +(4.23607 + 3.07768i) q^{52} +(-2.00000 - 6.15537i) q^{53} +3.47214 q^{54} +(-3.04508 + 1.31433i) q^{55} -1.00000 q^{56} +(-0.0729490 - 0.224514i) q^{57} +(3.23607 + 2.35114i) q^{58} +(2.92705 - 2.12663i) q^{59} +(-0.190983 + 0.587785i) q^{60} +(-2.47214 + 7.60845i) q^{61} +(-3.61803 + 2.62866i) q^{62} +(2.11803 + 1.53884i) q^{63} +(0.309017 + 0.951057i) q^{64} +5.23607 q^{65} +(-1.88197 + 0.812299i) q^{66} -6.09017 q^{67} +(-0.500000 - 1.53884i) q^{68} +(4.23607 + 3.07768i) q^{69} +(-0.809017 + 0.587785i) q^{70} +(0.763932 - 2.35114i) q^{71} +(0.809017 - 2.48990i) q^{72} +(-3.50000 + 2.54290i) q^{73} +(7.85410 + 5.70634i) q^{74} +(0.190983 + 0.587785i) q^{75} -0.381966 q^{76} +(-3.23607 - 0.726543i) q^{77} +3.23607 q^{78} +(0.527864 + 1.62460i) q^{79} +(0.809017 + 0.587785i) q^{80} +(-4.61803 + 3.35520i) q^{81} +(-2.66312 + 8.19624i) q^{82} +(3.42705 - 10.5474i) q^{83} +(-0.500000 + 0.363271i) q^{84} +(-1.30902 - 0.951057i) q^{85} +(1.42705 + 4.39201i) q^{86} +2.47214 q^{87} +(0.309017 + 3.30220i) q^{88} +9.85410 q^{89} +(-0.809017 - 2.48990i) q^{90} +(4.23607 + 3.07768i) q^{91} +(6.85410 - 4.97980i) q^{92} +(-0.854102 + 2.62866i) q^{93} +(2.09017 - 6.43288i) q^{94} +(-0.309017 + 0.224514i) q^{95} +(0.500000 + 0.363271i) q^{96} +(-3.33688 - 10.2699i) q^{97} -1.00000 q^{98} +(4.42705 - 7.46969i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - 2 q^{3} - q^{4} + q^{5} - 3 q^{6} - q^{7} + q^{8} - q^{9}+O(q^{10}) $ 4 * q + q^2 - 2 * q^3 - q^4 + q^5 - 3 * q^6 - q^7 + q^8 - q^9	\( 4 q + q^{2} - 2 q^{3} - q^{4} + q^{5} - 3 q^{6} - q^{7} + q^{8} - q^{9} + 4 q^{10} + 11 q^{11} - 2 q^{12} - 2 q^{13} + q^{14} + 2 q^{15} - q^{16} - 2 q^{17} - 4 q^{18} - q^{19} + q^{20} - 2 q^{21} + 9 q^{22} - 16 q^{23} - 3 q^{24} - q^{25} - 8 q^{26} - 11 q^{27} - q^{28} - 4 q^{29} - 2 q^{30} - 10 q^{31} - 4 q^{32} - 3 q^{33} + 2 q^{34} + q^{35} + 4 q^{36} - 18 q^{37} - 4 q^{38} - 4 q^{39} - q^{40} - 10 q^{41} - 3 q^{42} - 14 q^{43} - 4 q^{44} + 6 q^{45} + 6 q^{46} + 4 q^{47} - 2 q^{48} - q^{49} + q^{50} + q^{51} + 8 q^{52} - 8 q^{53} - 4 q^{54} - q^{55} - 4 q^{56} - 7 q^{57} + 4 q^{58} + 5 q^{59} - 3 q^{60} + 8 q^{61} - 10 q^{62} + 4 q^{63} - q^{64} + 12 q^{65} - 12 q^{66} - 2 q^{67} - 2 q^{68} + 8 q^{69} - q^{70} + 12 q^{71} + q^{72} - 14 q^{73} + 18 q^{74} + 3 q^{75} - 6 q^{76} - 4 q^{77} + 4 q^{78} + 20 q^{79} + q^{80} - 14 q^{81} + 5 q^{82} + 7 q^{83} - 2 q^{84} - 3 q^{85} - q^{86} - 8 q^{87} - q^{88} + 26 q^{89} - q^{90} + 8 q^{91} + 14 q^{92} + 10 q^{93} - 14 q^{94} + q^{95} + 2 q^{96} - 29 q^{97} - 4 q^{98} + 11 q^{99}+O(q^{100}) \) 4 * q + q^2 - 2 * q^3 - q^4 + q^5 - 3 * q^6 - q^7 + q^8 - q^9 + 4 * q^10 + 11 * q^11 - 2 * q^12 - 2 * q^13 + q^14 + 2 * q^15 - q^16 - 2 * q^17 - 4 * q^18 - q^19 + q^20 - 2 * q^21 + 9 * q^22 - 16 * q^23 - 3 * q^24 - q^25 - 8 * q^26 - 11 * q^27 - q^28 - 4 * q^29 - 2 * q^30 - 10 * q^31 - 4 * q^32 - 3 * q^33 + 2 * q^34 + q^35 + 4 * q^36 - 18 * q^37 - 4 * q^38 - 4 * q^39 - q^40 - 10 * q^41 - 3 * q^42 - 14 * q^43 - 4 * q^44 + 6 * q^45 + 6 * q^46 + 4 * q^47 - 2 * q^48 - q^49 + q^50 + q^51 + 8 * q^52 - 8 * q^53 - 4 * q^54 - q^55 - 4 * q^56 - 7 * q^57 + 4 * q^58 + 5 * q^59 - 3 * q^60 + 8 * q^61 - 10 * q^62 + 4 * q^63 - q^64 + 12 * q^65 - 12 * q^66 - 2 * q^67 - 2 * q^68 + 8 * q^69 - q^70 + 12 * q^71 + q^72 - 14 * q^73 + 18 * q^74 + 3 * q^75 - 6 * q^76 - 4 * q^77 + 4 * q^78 + 20 * q^79 + q^80 - 14 * q^81 + 5 * q^82 + 7 * q^83 - 2 * q^84 - 3 * q^85 - q^86 - 8 * q^87 - q^88 + 26 * q^89 - q^90 + 8 * q^91 + 14 * q^92 + 10 * q^93 - 14 * q^94 + q^95 + 2 * q^96 - 29 * q^97 - 4 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$	$1$

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
$3$	−0.500000	−	0.363271i	−0.288675	−	0.209735i	0.434017	−	0.900905i	$-0.357096\pi$
$3$	−0.500000	−	0.363271i	−0.288675	−	0.209735i	−0.722692	+	0.691170i	$0.757096\pi$
$4$	−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
$6$	−0.190983	+	0.587785i	−0.0779685	+	0.239962i
$7$	−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
$9$	−0.809017	−	2.48990i	−0.269672	−	0.829966i
$10$	1.00000			0.316228
$11$	2.19098	+	2.48990i	0.660606	+	0.750733i
$11$	2.19098	+	2.48990i	0.660606	+	0.750733i
$12$	0.618034			0.178411
$13$	−1.61803	−	4.97980i	−0.448762	−	1.38115i	−0.878305	−	0.478101i	$-0.841325\pi$
$13$	−1.61803	−	4.97980i	−0.448762	−	1.38115i	0.429543	−	0.903046i	$-0.358675\pi$
$14$	0.809017	+	0.587785i	0.216219	+	0.157092i
$15$	0.500000	−	0.363271i	0.129099	−	0.0937962i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−0.500000	+	1.53884i	−0.121268	+	0.373224i	−0.993203	−	0.116398i	$-0.962865\pi$
$17$	−0.500000	+	1.53884i	−0.121268	+	0.373224i	0.871935	+	0.489622i	$0.162865\pi$
$18$	−2.11803	+	1.53884i	−0.499225	+	0.362708i
$19$	0.309017	+	0.224514i	0.0708934	+	0.0515070i	0.622667	−	0.782487i	$-0.286049\pi$
$19$	0.309017	+	0.224514i	0.0708934	+	0.0515070i	−0.551774	+	0.833994i	$0.686049\pi$
$20$	−0.309017	−	0.951057i	−0.0690983	−	0.212663i
$21$	0.618034			0.134866
$22$	1.69098	−	2.85317i	0.360519	−	0.608298i
$23$	−8.47214			−1.76656			−0.883281	−	0.468844i	$-0.844671\pi$
$23$	−8.47214			−1.76656			−0.883281	+	0.468844i	$0.844671\pi$
$24$	−0.190983	−	0.587785i	−0.0389842	−	0.119981i
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	−4.23607	+	3.07768i	−0.830761	+	0.603583i
$27$	−1.07295	+	3.30220i	−0.206489	+	0.635508i
$28$	0.309017	−	0.951057i	0.0583987	−	0.179733i
$29$	−3.23607	+	2.35114i	−0.600923	+	0.436596i	−0.846206	−	0.532855i	$-0.821119\pi$
$29$	−3.23607	+	2.35114i	−0.600923	+	0.436596i	0.245284	+	0.969451i	$0.421119\pi$
$30$	−0.500000	−	0.363271i	−0.0912871	−	0.0663240i
$31$	−1.38197	−	4.25325i	−0.248208	−	0.763907i	−0.995092	−	0.0989523i	$-0.968451\pi$
$31$	−1.38197	−	4.25325i	−0.248208	−	0.763907i	0.746884	−	0.664955i	$-0.231549\pi$
$32$	−1.00000			−0.176777
$33$	−0.190983	−	2.04087i	−0.0332459	−	0.355270i
$34$	1.61803			0.277491
$35$	−0.309017	−	0.951057i	−0.0522334	−	0.160758i
$36$	2.11803	+	1.53884i	0.353006	+	0.256474i
$37$	−7.85410	+	5.70634i	−1.29121	+	0.938116i	−0.999829	−	0.0184918i	$-0.994114\pi$
$37$	−7.85410	+	5.70634i	−1.29121	+	0.938116i	−0.291377	+	0.956608i	$0.594114\pi$
$38$	0.118034	−	0.363271i	0.0191476	−	0.0589304i
$39$	−1.00000	+	3.07768i	−0.160128	+	0.492824i
$40$	−0.809017	+	0.587785i	−0.127917	+	0.0929370i
$41$	−6.97214	−	5.06555i	−1.08886	−	0.791107i	−0.109658	−	0.993969i	$-0.534975\pi$
$41$	−6.97214	−	5.06555i	−1.08886	−	0.791107i	−0.979207	+	0.202863i	$0.934975\pi$
$42$	−0.190983	−	0.587785i	−0.0294693	−	0.0906972i
$43$	−4.61803			−0.704244			−0.352122	−	0.935954i	$-0.614540\pi$
$43$	−4.61803			−0.704244			−0.352122	+	0.935954i	$0.614540\pi$
$44$	−3.23607	−	0.726543i	−0.487856	−	0.109530i
$45$	2.61803			0.390273
$46$	2.61803	+	8.05748i	0.386008	+	1.18801i
$47$	5.47214	+	3.97574i	0.798193	+	0.579921i	0.910383	−	0.413766i	$-0.135787\pi$
$47$	5.47214	+	3.97574i	0.798193	+	0.579921i	−0.112190	+	0.993687i	$0.535787\pi$
$48$	−0.500000	+	0.363271i	−0.0721688	+	0.0524337i
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	−0.309017	+	0.951057i	−0.0437016	+	0.134500i
$51$	0.809017	−	0.587785i	0.113285	−	0.0823064i
$52$	4.23607	+	3.07768i	0.587437	+	0.426798i
$53$	−2.00000	−	6.15537i	−0.274721	−	0.845505i	−0.989293	−	0.145943i	$-0.953378\pi$
$53$	−2.00000	−	6.15537i	−0.274721	−	0.845505i	0.714572	−	0.699562i	$-0.246622\pi$
$54$	3.47214			0.472498
$55$	−3.04508	+	1.31433i	−0.410599	+	0.177224i
$56$	−1.00000			−0.133631
$57$	−0.0729490	−	0.224514i	−0.00966233	−	0.0297376i
$58$	3.23607	+	2.35114i	0.424917	+	0.308720i
$59$	2.92705	−	2.12663i	0.381070	−	0.276863i	−0.380717	−	0.924692i	$-0.624323\pi$
$59$	2.92705	−	2.12663i	0.381070	−	0.276863i	0.761786	+	0.647829i	$0.224323\pi$
$60$	−0.190983	+	0.587785i	−0.0246558	+	0.0758827i
$61$	−2.47214	+	7.60845i	−0.316525	+	0.974162i	0.658598	+	0.752495i	$0.271150\pi$
$61$	−2.47214	+	7.60845i	−0.316525	+	0.974162i	−0.975122	+	0.221667i	$0.928850\pi$
$62$	−3.61803	+	2.62866i	−0.459491	+	0.333840i
$63$	2.11803	+	1.53884i	0.266847	+	0.193876i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	5.23607			0.649454
$66$	−1.88197	+	0.812299i	−0.231654	+	0.0999871i
$67$	−6.09017			−0.744033			−0.372016	−	0.928226i	$-0.621333\pi$
$67$	−6.09017			−0.744033			−0.372016	+	0.928226i	$0.621333\pi$
$68$	−0.500000	−	1.53884i	−0.0606339	−	0.186612i
$69$	4.23607	+	3.07768i	0.509963	+	0.370510i
$70$	−0.809017	+	0.587785i	−0.0966960	+	0.0702538i
$71$	0.763932	−	2.35114i	0.0906621	−	0.279029i	−0.895437	−	0.445189i	$-0.853137\pi$
$71$	0.763932	−	2.35114i	0.0906621	−	0.279029i	0.986099	+	0.166159i	$0.0531366\pi$
$72$	0.809017	−	2.48990i	0.0953436	−	0.293437i
$73$	−3.50000	+	2.54290i	−0.409644	+	0.297624i	−0.773458	−	0.633848i	$-0.781474\pi$
$73$	−3.50000	+	2.54290i	−0.409644	+	0.297624i	0.363814	+	0.931472i	$0.381474\pi$
$74$	7.85410	+	5.70634i	0.913021	+	0.663348i
$75$	0.190983	+	0.587785i	0.0220528	+	0.0678716i
$76$	−0.381966			−0.0438145
$77$	−3.23607	−	0.726543i	−0.368784	−	0.0827972i
$78$	3.23607			0.366413
$79$	0.527864	+	1.62460i	0.0593893	+	0.182782i	0.976350	−	0.216196i	$-0.0693651\pi$
$79$	0.527864	+	1.62460i	0.0593893	+	0.182782i	−0.916961	+	0.398978i	$0.869365\pi$
$80$	0.809017	+	0.587785i	0.0904508	+	0.0657164i
$81$	−4.61803	+	3.35520i	−0.513115	+	0.372800i
$82$	−2.66312	+	8.19624i	−0.294092	+	0.905123i
$83$	3.42705	−	10.5474i	0.376168	−	1.15773i	−0.566520	−	0.824048i	$-0.691711\pi$
$83$	3.42705	−	10.5474i	0.376168	−	1.15773i	0.942687	−	0.333677i	$-0.108289\pi$
$84$	−0.500000	+	0.363271i	−0.0545545	+	0.0396361i
$85$	−1.30902	−	0.951057i	−0.141983	−	0.103157i
$86$	1.42705	+	4.39201i	0.153883	+	0.473603i
$87$	2.47214			0.265041
$88$	0.309017	+	3.30220i	0.0329413	+	0.352015i
$89$	9.85410			1.04453			0.522266	−	0.852782i	$-0.325087\pi$
$89$	9.85410			1.04453			0.522266	+	0.852782i	$0.325087\pi$
$90$	−0.809017	−	2.48990i	−0.0852779	−	0.262458i
$91$	4.23607	+	3.07768i	0.444061	+	0.322629i
$92$	6.85410	−	4.97980i	0.714590	−	0.519180i
$93$	−0.854102	+	2.62866i	−0.0885662	+	0.272579i
$94$	2.09017	−	6.43288i	0.215585	−	0.663501i
$95$	−0.309017	+	0.224514i	−0.0317045	+	0.0230346i
$96$	0.500000	+	0.363271i	0.0510310	+	0.0370762i
$97$	−3.33688	−	10.2699i	−0.338809	−	1.04275i	−0.964815	−	0.262929i	$-0.915312\pi$
$97$	−3.33688	−	10.2699i	−0.338809	−	1.04275i	0.626006	−	0.779818i	$-0.284688\pi$
$98$	−1.00000			−0.101015
$99$	4.42705	−	7.46969i	0.444935	−	0.750733i
$100$	1.00000			0.100000
$101$	5.32624	+	16.3925i	0.529980	+	1.63111i	0.754252	+	0.656585i	$0.228000\pi$
$101$	5.32624	+	16.3925i	0.529980	+	1.63111i	−0.224271	+	0.974527i	$0.572000\pi$
$102$	−0.809017	−	0.587785i	−0.0801046	−	0.0581994i
$103$	−0.236068	+	0.171513i	−0.0232605	+	0.0168997i	−0.599355	−	0.800484i	$-0.704576\pi$
$103$	−0.236068	+	0.171513i	−0.0232605	+	0.0168997i	0.576094	+	0.817383i	$0.304576\pi$
$104$	1.61803	−	4.97980i	0.158661	−	0.488309i
$105$	−0.190983	+	0.587785i	−0.0186380	+	0.0573620i
$106$	−5.23607	+	3.80423i	−0.508572	+	0.369499i
$107$	2.50000	+	1.81636i	0.241684	+	0.175594i	0.702033	−	0.712144i	$-0.252276\pi$
$107$	2.50000	+	1.81636i	0.241684	+	0.175594i	−0.460349	+	0.887738i	$0.652276\pi$
$108$	−1.07295	−	3.30220i	−0.103245	−	0.317754i
$109$	−12.1803			−1.16666			−0.583332	−	0.812233i	$-0.698252\pi$
$109$	−12.1803			−1.16666			−0.583332	+	0.812233i	$0.698252\pi$
$110$	2.19098	+	2.48990i	0.208902	+	0.237402i
$111$	6.00000			0.569495
$112$	0.309017	+	0.951057i	0.0291994	+	0.0898664i
$113$	−11.1631	−	8.11048i	−1.05014	−	0.762970i	−0.0778992	−	0.996961i	$-0.524821\pi$
$113$	−11.1631	−	8.11048i	−1.05014	−	0.762970i	−0.972239	+	0.233991i	$0.924821\pi$
$114$	−0.190983	+	0.138757i	−0.0178872	+	0.0129958i
$115$	2.61803	−	8.05748i	0.244133	−	0.751364i
$116$	1.23607	−	3.80423i	0.114766	−	0.353214i
$117$	−11.0902	+	8.05748i	−1.02529	+	0.744914i
$118$	−2.92705	−	2.12663i	−0.269457	−	0.195772i
$119$	−0.500000	−	1.53884i	−0.0458349	−	0.141065i
$120$	0.618034			0.0564185
$121$	−1.39919	+	10.9106i	−0.127199	+	0.991877i
$122$	8.00000			0.724286
$123$	1.64590	+	5.06555i	0.148406	+	0.456746i
$124$	3.61803	+	2.62866i	0.324909	+	0.236060i
$125$	0.809017	−	0.587785i	0.0723607	−	0.0525731i
$126$	0.809017	−	2.48990i	0.0720730	−	0.221818i
$127$	4.38197	−	13.4863i	0.388837	−	1.19672i	−0.544822	−	0.838552i	$-0.683403\pi$
$127$	4.38197	−	13.4863i	0.388837	−	1.19672i	0.933659	−	0.358164i	$-0.116597\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	2.30902	+	1.67760i	0.203298	+	0.147704i
$130$	−1.61803	−	4.97980i	−0.141911	−	0.436757i
$131$	14.8541			1.29781			0.648904	−	0.760870i	$-0.275227\pi$
$131$	14.8541			1.29781			0.648904	+	0.760870i	$0.275227\pi$
$132$	1.35410	+	1.53884i	0.117859	+	0.133939i
$133$	−0.381966			−0.0331207
$134$	1.88197	+	5.79210i	0.162577	+	0.500361i
$135$	−2.80902	−	2.04087i	−0.241762	−	0.175650i
$136$	−1.30902	+	0.951057i	−0.112247	+	0.0815524i
$137$	−1.89919	+	5.84510i	−0.162258	+	0.499380i	−0.998824	−	0.0484869i	$-0.984560\pi$
$137$	−1.89919	+	5.84510i	−0.162258	+	0.499380i	0.836565	+	0.547867i	$0.184560\pi$
$138$	1.61803	−	4.97980i	0.137736	−	0.423908i
$139$	8.47214	−	6.15537i	0.718597	−	0.522091i	−0.167339	−	0.985899i	$-0.553517\pi$
$139$	8.47214	−	6.15537i	0.718597	−	0.522091i	0.885936	+	0.463808i	$0.153517\pi$
$140$	0.809017	+	0.587785i	0.0683744	+	0.0496769i
$141$	−1.29180	−	3.97574i	−0.108789	−	0.334818i
$142$	−2.47214			−0.207457
$143$	8.85410	−	14.9394i	0.740417	−	1.24929i
$144$	−2.61803			−0.218169
$145$	−1.23607	−	3.80423i	−0.102650	−	0.315924i
$146$	3.50000	+	2.54290i	0.289662	+	0.210452i
$147$	−0.500000	+	0.363271i	−0.0412393	+	0.0299621i
$148$	3.00000	−	9.23305i	0.246598	−	0.758952i
$149$	1.76393	−	5.42882i	0.144507	−	0.444747i	−0.852440	−	0.522825i	$-0.824878\pi$
$149$	1.76393	−	5.42882i	0.144507	−	0.444747i	0.996947	+	0.0780779i	$0.0248783\pi$
$150$	0.500000	−	0.363271i	0.0408248	−	0.0296610i
$151$	1.76393	+	1.28157i	0.143547	+	0.104293i	0.657241	−	0.753681i	$-0.271723\pi$
$151$	1.76393	+	1.28157i	0.143547	+	0.104293i	−0.513694	+	0.857973i	$0.671723\pi$
$152$	0.118034	+	0.363271i	0.00957382	+	0.0294652i
$153$	4.23607			0.342466
$154$	0.309017	+	3.30220i	0.0249013	+	0.266099i
$155$	4.47214			0.359211
$156$	−1.00000	−	3.07768i	−0.0800641	−	0.246412i
$157$	−13.0902	−	9.51057i	−1.04471	−	0.759026i	−0.0735100	−	0.997294i	$-0.523420\pi$
$157$	−13.0902	−	9.51057i	−1.04471	−	0.759026i	−0.971199	+	0.238269i	$0.923420\pi$
$158$	1.38197	−	1.00406i	0.109943	−	0.0798785i
$159$	−1.23607	+	3.80423i	−0.0980266	+	0.301695i
$160$	0.309017	−	0.951057i	0.0244299	−	0.0751876i
$161$	6.85410	−	4.97980i	0.540179	−	0.392463i
$162$	4.61803	+	3.35520i	0.362827	+	0.263609i
$163$	−6.29837	−	19.3844i	−0.493327	−	1.51830i	−0.819548	−	0.573010i	$-0.805776\pi$
$163$	−6.29837	−	19.3844i	−0.493327	−	1.51830i	0.326222	−	0.945293i	$-0.394224\pi$
$164$	8.61803			0.672955
$165$	2.00000	+	0.449028i	0.155700	+	0.0349568i
$166$	−11.0902			−0.860764
$167$	3.09017	+	9.51057i	0.239125	+	0.735950i	0.996547	+	0.0830251i	$0.0264582\pi$
$167$	3.09017	+	9.51057i	0.239125	+	0.735950i	−0.757423	+	0.652925i	$0.773542\pi$
$168$	0.500000	+	0.363271i	0.0385758	+	0.0280270i
$169$	−11.6631	+	8.47375i	−0.897163	+	0.651827i
$170$	−0.500000	+	1.53884i	−0.0383482	+	0.118024i
$171$	0.309017	−	0.951057i	0.0236311	−	0.0727291i
$172$	3.73607	−	2.71441i	0.284873	−	0.206972i
$173$	−7.47214	−	5.42882i	−0.568096	−	0.412746i	0.266317	−	0.963885i	$-0.414193\pi$
$173$	−7.47214	−	5.42882i	−0.568096	−	0.412746i	−0.834413	+	0.551140i	$0.814193\pi$
$174$	−0.763932	−	2.35114i	−0.0579135	−	0.178240i
$175$	1.00000			0.0755929
$176$	3.04508	−	1.31433i	0.229532	−	0.0990712i
$177$	−2.23607			−0.168073
$178$	−3.04508	−	9.37181i	−0.228239	−	0.702447i
$179$	12.0172	+	8.73102i	0.898209	+	0.652587i	0.938005	−	0.346621i	$-0.112671\pi$
$179$	12.0172	+	8.73102i	0.898209	+	0.652587i	−0.0397962	+	0.999208i	$0.512671\pi$
$180$	−2.11803	+	1.53884i	−0.157869	+	0.114698i
$181$	5.29180	−	16.2865i	0.393336	−	1.21056i	−0.536914	−	0.843637i	$-0.680410\pi$
$181$	5.29180	−	16.2865i	0.393336	−	1.21056i	0.930250	−	0.366927i	$-0.119590\pi$
$182$	1.61803	−	4.97980i	0.119937	−	0.369127i
$183$	4.00000	−	2.90617i	0.295689	−	0.214830i
$184$	−6.85410	−	4.97980i	−0.505291	−	0.367115i
$185$	−3.00000	−	9.23305i	−0.220564	−	0.678827i
$186$	2.76393			0.202661
$187$	−4.92705	+	2.12663i	−0.360302	+	0.155514i
$188$	−6.76393			−0.493310
$189$	−1.07295	−	3.30220i	−0.0780456	−	0.240200i
$190$	0.309017	+	0.224514i	0.0224184	+	0.0162880i
$191$	1.61803	−	1.17557i	0.117077	−	0.0850613i	−0.527706	−	0.849427i	$-0.676948\pi$
$191$	1.61803	−	1.17557i	0.117077	−	0.0850613i	0.644783	+	0.764366i	$0.276948\pi$
$192$	0.190983	−	0.587785i	0.0137830	−	0.0424197i
$193$	−3.85410	+	11.8617i	−0.277424	+	0.853824i	0.711143	+	0.703047i	$0.248178\pi$
$193$	−3.85410	+	11.8617i	−0.277424	+	0.853824i	−0.988568	+	0.150777i	$0.951822\pi$
$194$	−8.73607	+	6.34712i	−0.627213	+	0.455697i
$195$	−2.61803	−	1.90211i	−0.187481	−	0.136213i
$196$	0.309017	+	0.951057i	0.0220726	+	0.0679326i
$197$	21.4164			1.52586			0.762928	−	0.646484i	$-0.223761\pi$
$197$	21.4164			1.52586			0.762928	+	0.646484i	$0.223761\pi$
$198$	−8.47214	−	1.90211i	−0.602088	−	0.135177i
$199$	−1.23607			−0.0876225			−0.0438113	−	0.999040i	$-0.513950\pi$
$199$	−1.23607			−0.0876225			−0.0438113	+	0.999040i	$0.513950\pi$
$200$	−0.309017	−	0.951057i	−0.0218508	−	0.0672499i
$201$	3.04508	+	2.21238i	0.214784	+	0.156050i
$202$	13.9443	−	10.1311i	0.981116	−	0.712822i
$203$	1.23607	−	3.80423i	0.0867550	−	0.267004i
$204$	−0.309017	+	0.951057i	−0.0216355	+	0.0665873i
$205$	6.97214	−	5.06555i	0.486955	−	0.353794i
$206$	0.236068	+	0.171513i	0.0164476	+	0.0119499i
$207$	6.85410	+	21.0948i	0.476393	+	1.46619i
$208$	−5.23607			−0.363056
$209$	0.118034	+	1.26133i	0.00816458	+	0.0872478i
$210$	0.618034			0.0426484
$211$	5.22542	+	16.0822i	0.359733	+	1.10714i	0.953214	+	0.302296i	$0.0977533\pi$
$211$	5.22542	+	16.0822i	0.359733	+	1.10714i	−0.593481	+	0.804848i	$0.702247\pi$
$212$	5.23607	+	3.80423i	0.359615	+	0.261275i
$213$	−1.23607	+	0.898056i	−0.0846940	+	0.0615338i
$214$	0.954915	−	2.93893i	0.0652766	−	0.200901i
$215$	1.42705	−	4.39201i	0.0973241	−	0.299533i
$216$	−2.80902	+	2.04087i	−0.191129	+	0.138864i
$217$	3.61803	+	2.62866i	0.245608	+	0.178445i
$218$	3.76393	+	11.5842i	0.254926	+	0.784580i
$219$	2.67376			0.180676
$220$	1.69098	−	2.85317i	0.114006	−	0.192361i
$221$	8.47214			0.569898
$222$	−1.85410	−	5.70634i	−0.124439	−	0.382984i
$223$	4.09017	+	2.97168i	0.273898	+	0.198999i	0.716252	−	0.697842i	$-0.245856\pi$
$223$	4.09017	+	2.97168i	0.273898	+	0.198999i	−0.442353	+	0.896841i	$0.645856\pi$
$224$	0.809017	−	0.587785i	0.0540547	−	0.0392731i
$225$	−0.809017	+	2.48990i	−0.0539345	+	0.165993i
$226$	−4.26393	+	13.1230i	−0.283633	+	0.872931i
$227$	−6.92705	+	5.03280i	−0.459765	+	0.334038i	−0.793439	−	0.608650i	$-0.791711\pi$
$227$	−6.92705	+	5.03280i	−0.459765	+	0.334038i	0.333674	+	0.942688i	$0.391711\pi$
$228$	0.190983	+	0.138757i	0.0126482	+	0.00918943i
$229$	−1.76393	−	5.42882i	−0.116564	−	0.358747i	0.875706	−	0.482845i	$-0.160396\pi$
$229$	−1.76393	−	5.42882i	−0.116564	−	0.358747i	−0.992270	+	0.124098i	$0.960396\pi$
$230$	−8.47214			−0.558636
$231$	1.35410	+	1.53884i	0.0890934	+	0.101248i
$232$	−4.00000			−0.262613
$233$	1.13525	+	3.49396i	0.0743730	+	0.228897i	0.981332	−	0.192323i	$-0.0616021\pi$
$233$	1.13525	+	3.49396i	0.0743730	+	0.228897i	−0.906959	+	0.421220i	$0.861602\pi$
$234$	11.0902	+	8.05748i	0.724987	+	0.526734i
$235$	−5.47214	+	3.97574i	−0.356963	+	0.259349i
$236$	−1.11803	+	3.44095i	−0.0727778	+	0.223987i
$237$	0.326238	−	1.00406i	0.0211914	−	0.0652205i
$238$	−1.30902	+	0.951057i	−0.0848510	+	0.0616478i
$239$	−14.3262	−	10.4086i	−0.926687	−	0.673278i	0.0184922	−	0.999829i	$-0.494113\pi$
$239$	−14.3262	−	10.4086i	−0.926687	−	0.673278i	−0.945179	+	0.326551i	$0.894113\pi$
$240$	−0.190983	−	0.587785i	−0.0123279	−	0.0379414i
$241$	−7.14590			−0.460308			−0.230154	−	0.973154i	$-0.573923\pi$
$241$	−7.14590			−0.460308			−0.230154	+	0.973154i	$0.573923\pi$
$242$	10.8090	−	2.04087i	0.694830	−	0.131192i
$243$	13.9443			0.894525
$244$	−2.47214	−	7.60845i	−0.158262	−	0.487081i
$245$	0.809017	+	0.587785i	0.0516862	+	0.0375522i
$246$	4.30902	−	3.13068i	0.274733	−	0.199605i
$247$	0.618034	−	1.90211i	0.0393246	−	0.121029i
$248$	1.38197	−	4.25325i	0.0877549	−	0.270082i
$249$	−5.54508	+	4.02874i	−0.351405	+	0.255311i
$250$	−0.809017	−	0.587785i	−0.0511667	−	0.0371748i
$251$	−5.52786	−	17.0130i	−0.348916	−	1.07385i	−0.959454	−	0.281865i	$-0.909047\pi$
$251$	−5.52786	−	17.0130i	−0.348916	−	1.07385i	0.610538	−	0.791987i	$-0.290953\pi$
$252$	−2.61803			−0.164921
$253$	−18.5623	−	21.0948i	−1.16700	−	1.32622i
$254$	−14.1803			−0.889754
$255$	0.309017	+	0.951057i	0.0193514	+	0.0595575i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	20.6803	−	15.0251i	1.29000	−	0.937243i	0.290199	−	0.956966i	$-0.406279\pi$
$257$	20.6803	−	15.0251i	1.29000	−	0.937243i	0.999805	+	0.0197235i	$0.00627860\pi$
$258$	0.881966	−	2.71441i	0.0549088	−	0.168992i
$259$	3.00000	−	9.23305i	0.186411	−	0.573714i
$260$	−4.23607	+	3.07768i	−0.262710	+	0.190870i
$261$	8.47214	+	6.15537i	0.524412	+	0.381008i
$262$	−4.59017	−	14.1271i	−0.283582	−	0.872775i
$263$	−12.0000			−0.739952			−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000			−0.739952			−0.369976	+	0.929041i	$0.620634\pi$
$264$	1.04508	−	1.76336i	0.0643205	−	0.108527i
$265$	6.47214			0.397580
$266$	0.118034	+	0.363271i	0.00723713	+	0.0222736i
$267$	−4.92705	−	3.57971i	−0.301531	−	0.219075i
$268$	4.92705	−	3.57971i	0.300968	−	0.218666i
$269$	4.32624	−	13.3148i	0.263775	−	0.811817i	−0.728198	−	0.685367i	$-0.759642\pi$
$269$	4.32624	−	13.3148i	0.263775	−	0.811817i	0.991973	−	0.126450i	$-0.0403583\pi$
$270$	−1.07295	+	3.30220i	−0.0652976	+	0.200965i
$271$	−15.9443	+	11.5842i	−0.968546	+	0.703690i	−0.955120	−	0.296220i	$-0.904274\pi$
$271$	−15.9443	+	11.5842i	−0.968546	+	0.703690i	−0.0134259	+	0.999910i	$0.504274\pi$
$272$	1.30902	+	0.951057i	0.0793708	+	0.0576663i
$273$	−1.00000	−	3.07768i	−0.0605228	−	0.186270i
$274$	6.14590			0.371287
$275$	−0.309017	−	3.30220i	−0.0186344	−	0.199130i
$276$	−5.23607			−0.315174
$277$	7.14590	+	21.9928i	0.429355	+	1.32142i	0.898762	+	0.438438i	$0.144468\pi$
$277$	7.14590	+	21.9928i	0.429355	+	1.32142i	−0.469406	+	0.882982i	$0.655532\pi$
$278$	−8.47214	−	6.15537i	−0.508125	−	0.369174i
$279$	−9.47214	+	6.88191i	−0.567082	+	0.412009i
$280$	0.309017	−	0.951057i	0.0184673	−	0.0568365i
$281$	−2.10081	+	6.46564i	−0.125324	+	0.385708i	−0.993960	−	0.109743i	$-0.964997\pi$
$281$	−2.10081	+	6.46564i	−0.125324	+	0.385708i	0.868636	+	0.495451i	$0.164997\pi$
$282$	−3.38197	+	2.45714i	−0.201393	+	0.146321i
$283$	20.9443	+	15.2169i	1.24501	+	0.904551i	0.997921	−	0.0644424i	$-0.0205269\pi$
$283$	20.9443	+	15.2169i	1.24501	+	0.904551i	0.247086	+	0.968993i	$0.420527\pi$
$284$	0.763932	+	2.35114i	0.0453310	+	0.139515i
$285$	0.236068			0.0139835
$286$	−16.9443	−	3.80423i	−1.00194	−	0.224949i
$287$	8.61803			0.508706
$288$	0.809017	+	2.48990i	0.0476718	+	0.146719i
$289$	11.6353	+	8.45351i	0.684427	+	0.497265i
$290$	−3.23607	+	2.35114i	−0.190028	+	0.138064i
$291$	−2.06231	+	6.34712i	−0.120895	+	0.372075i
$292$	1.33688	−	4.11450i	0.0782350	−	0.240783i
$293$	−1.85410	+	1.34708i	−0.108318	+	0.0786975i	−0.640626	−	0.767853i	$-0.721325\pi$
$293$	−1.85410	+	1.34708i	−0.108318	+	0.0786975i	0.532308	+	0.846551i	$0.321325\pi$
$294$	0.500000	+	0.363271i	0.0291606	+	0.0211864i
$295$	1.11803	+	3.44095i	0.0650945	+	0.200340i
$296$	−9.70820			−0.564278
$297$	−10.5729	+	4.56352i	−0.613505	+	0.264803i
$298$	−5.70820			−0.330667
$299$	13.7082	+	42.1895i	0.792766	+	2.43988i
$300$	−0.500000	−	0.363271i	−0.0288675	−	0.0209735i
$301$	3.73607	−	2.71441i	0.215343	−	0.156456i
$302$	0.673762	−	2.07363i	0.0387707	−	0.119324i
$303$	3.29180	−	10.1311i	0.189109	−	0.582017i
$304$	0.309017	−	0.224514i	0.0177233	−	0.0128768i
$305$	−6.47214	−	4.70228i	−0.370593	−	0.269252i
$306$	−1.30902	−	4.02874i	−0.0748315	−	0.230308i
$307$	34.5066			1.96939			0.984697	−	0.174274i	$-0.0557578\pi$
$307$	34.5066			1.96939			0.984697	+	0.174274i	$0.0557578\pi$
$308$	3.04508	−	1.31433i	0.173510	−	0.0748908i
$309$	0.180340			0.0102592
$310$	−1.38197	−	4.25325i	−0.0784904	−	0.241569i
$311$	−2.61803	−	1.90211i	−0.148455	−	0.107859i	0.511078	−	0.859534i	$-0.329246\pi$
$311$	−2.61803	−	1.90211i	−0.148455	−	0.107859i	−0.659534	+	0.751675i	$0.729246\pi$
$312$	−2.61803	+	1.90211i	−0.148217	+	0.107686i
$313$	1.02786	−	3.16344i	0.0580983	−	0.178808i	−0.917796	−	0.397053i	$-0.870033\pi$
$313$	1.02786	−	3.16344i	0.0580983	−	0.178808i	0.975894	+	0.218244i	$0.0700330\pi$
$314$	−5.00000	+	15.3884i	−0.282166	+	0.868419i
$315$	−2.11803	+	1.53884i	−0.119338	+	0.0867039i
$316$	−1.38197	−	1.00406i	−0.0777417	−	0.0564826i
$317$	−5.52786	−	17.0130i	−0.310476	−	0.955546i	−0.977577	−	0.210579i	$-0.932465\pi$
$317$	−5.52786	−	17.0130i	−0.310476	−	0.955546i	0.667101	−	0.744967i	$-0.267535\pi$
$318$	4.00000			0.224309
$319$	−12.9443	−	2.90617i	−0.724740	−	0.162714i
$320$	−1.00000			−0.0559017
$321$	−0.590170	−	1.81636i	−0.0329401	−	0.101379i
$322$	−6.85410	−	4.97980i	−0.381964	−	0.277513i
$323$	−0.500000	+	0.363271i	−0.0278207	+	0.0202130i
$324$	1.76393	−	5.42882i	0.0979962	−	0.301601i
$325$	−1.61803	+	4.97980i	−0.0897524	+	0.276229i
$326$	−16.4894	+	11.9802i	−0.913261	+	0.663523i
$327$	6.09017	+	4.42477i	0.336787	+	0.244690i
$328$	−2.66312	−	8.19624i	−0.147046	−	0.452562i
$329$	−6.76393			−0.372908
$330$	−0.190983	−	2.04087i	−0.0105133	−	0.112346i
$331$	12.3262			0.677511			0.338756	−	0.940874i	$-0.389994\pi$
$331$	12.3262			0.677511			0.338756	+	0.940874i	$0.389994\pi$
$332$	3.42705	+	10.5474i	0.188084	+	0.578863i
$333$	20.5623	+	14.9394i	1.12681	+	0.818674i
$334$	8.09017	−	5.87785i	0.442674	−	0.321622i
$335$	1.88197	−	5.79210i	0.102823	−	0.316456i
$336$	0.190983	−	0.587785i	0.0104190	−	0.0320663i
$337$	−26.1074	+	18.9681i	−1.42216	+	1.03326i	−0.430750	+	0.902471i	$0.641751\pi$
$337$	−26.1074	+	18.9681i	−1.42216	+	1.03326i	−0.991410	+	0.130789i	$0.958249\pi$
$338$	11.6631	+	8.47375i	0.634390	+	0.460911i
$339$	2.63525	+	8.11048i	0.143127	+	0.440501i
$340$	1.61803			0.0877502
$341$	7.56231	−	12.7598i	0.409522	−	0.690980i
$342$	−1.00000			−0.0540738
$343$	0.309017	+	0.951057i	0.0166853	+	0.0513522i
$344$	−3.73607	−	2.71441i	−0.201435	−	0.146351i
$345$	−4.23607	+	3.07768i	−0.228062	+	0.165697i
$346$	−2.85410	+	8.78402i	−0.153437	+	0.472232i
$347$	−8.35410	+	25.7113i	−0.448472	+	1.38025i	0.430159	+	0.902753i	$0.358457\pi$
$347$	−8.35410	+	25.7113i	−0.448472	+	1.38025i	−0.878631	+	0.477501i	$0.841543\pi$
$348$	−2.00000	+	1.45309i	−0.107211	+	0.0778935i
$349$	−8.47214	−	6.15537i	−0.453503	−	0.329489i	0.337474	−	0.941335i	$-0.390427\pi$
$349$	−8.47214	−	6.15537i	−0.453503	−	0.329489i	−0.790977	+	0.611846i	$0.790427\pi$
$350$	−0.309017	−	0.951057i	−0.0165177	−	0.0508361i
$351$	18.1803			0.970395
$352$	−2.19098	−	2.48990i	−0.116780	−	0.132712i
$353$	17.0344			0.906652			0.453326	−	0.891345i	$-0.350237\pi$
$353$	17.0344			0.906652			0.453326	+	0.891345i	$0.350237\pi$
$354$	0.690983	+	2.12663i	0.0367253	+	0.113029i
$355$	2.00000	+	1.45309i	0.106149	+	0.0771217i
$356$	−7.97214	+	5.79210i	−0.422522	+	0.306980i
$357$	−0.309017	+	0.951057i	−0.0163549	+	0.0503352i
$358$	4.59017	−	14.1271i	0.242598	−	0.746640i
$359$	−20.7984	+	15.1109i	−1.09770	+	0.797523i	−0.980682	−	0.195607i	$-0.937332\pi$
$359$	−20.7984	+	15.1109i	−1.09770	+	0.797523i	−0.117014	+	0.993130i	$0.537332\pi$
$360$	2.11803	+	1.53884i	0.111630	+	0.0811041i
$361$	−5.82624	−	17.9313i	−0.306644	−	0.943754i
$362$	−17.1246			−0.900050
$363$	4.66312	−	4.94704i	0.244750	−	0.259652i
$364$	−5.23607			−0.274445
$365$	−1.33688	−	4.11450i	−0.0699756	−	0.215363i
$366$	−4.00000	−	2.90617i	−0.209083	−	0.151908i
$367$	−8.94427	+	6.49839i	−0.466887	+	0.339213i	−0.796227	−	0.604998i	$-0.793174\pi$
$367$	−8.94427	+	6.49839i	−0.466887	+	0.339213i	0.329340	+	0.944211i	$0.393174\pi$
$368$	−2.61803	+	8.05748i	−0.136474	+	0.420025i
$369$	−6.97214	+	21.4580i	−0.362955	+	1.11706i
$370$	−7.85410	+	5.70634i	−0.408315	+	0.296658i
$371$	5.23607	+	3.80423i	0.271843	+	0.197506i
$372$	−0.854102	−	2.62866i	−0.0442831	−	0.136289i
$373$	−4.94427			−0.256005			−0.128002	−	0.991774i	$-0.540857\pi$
$373$	−4.94427			−0.256005			−0.128002	+	0.991774i	$0.540857\pi$
$374$	3.54508	+	4.02874i	0.183312	+	0.208321i
$375$	−0.618034			−0.0319151
$376$	2.09017	+	6.43288i	0.107792	+	0.331751i
$377$	16.9443	+	12.3107i	0.872674	+	0.634035i
$378$	−2.80902	+	2.04087i	−0.144480	+	0.104971i
$379$	−3.13525	+	9.64932i	−0.161047	+	0.495652i	−0.998723	−	0.0505150i	$-0.983914\pi$
$379$	−3.13525	+	9.64932i	−0.161047	+	0.495652i	0.837676	+	0.546167i	$0.183914\pi$
$380$	0.118034	−	0.363271i	0.00605502	−	0.0186354i
$381$	−7.09017	+	5.15131i	−0.363240	+	0.263910i
$382$	−1.61803	−	1.17557i	−0.0827858	−	0.0601474i
$383$	5.47214	+	16.8415i	0.279613	+	0.860561i	0.987962	+	0.154698i	$0.0494404\pi$
$383$	5.47214	+	16.8415i	0.279613	+	0.860561i	−0.708349	+	0.705863i	$0.750560\pi$
$384$	−0.618034			−0.0315389
$385$	1.69098	−	2.85317i	0.0861805	−	0.145411i
$386$	12.4721			0.634815
$387$	3.73607	+	11.4984i	0.189915	+	0.584498i
$388$	8.73607	+	6.34712i	0.443507	+	0.322226i
$389$	−6.47214	+	4.70228i	−0.328150	+	0.238415i	−0.739645	−	0.672997i	$-0.765007\pi$
$389$	−6.47214	+	4.70228i	−0.328150	+	0.238415i	0.411495	+	0.911412i	$0.365007\pi$
$390$	−1.00000	+	3.07768i	−0.0506370	+	0.155845i
$391$	4.23607	−	13.0373i	0.214227	−	0.659323i
$392$	0.809017	−	0.587785i	0.0408615	−	0.0296876i
$393$	−7.42705	−	5.39607i	−0.374645	−	0.272196i
$394$	−6.61803	−	20.3682i	−0.333412	−	1.02614i
$395$	−1.70820			−0.0859491
$396$	0.809017	+	8.64527i	0.0406546	+	0.434441i
$397$	−34.5410			−1.73356			−0.866782	−	0.498687i	$-0.833816\pi$
$397$	−34.5410			−1.73356			−0.866782	+	0.498687i	$0.833816\pi$
$398$	0.381966	+	1.17557i	0.0191462	+	0.0589260i
$399$	0.190983	+	0.138757i	0.00956111	+	0.00694655i
$400$	−0.809017	+	0.587785i	−0.0404508	+	0.0293893i
$401$	−3.24671	+	9.99235i	−0.162133	+	0.498994i	−0.998814	−	0.0486970i	$-0.984493\pi$
$401$	−3.24671	+	9.99235i	−0.162133	+	0.498994i	0.836681	+	0.547691i	$0.184493\pi$
$402$	1.16312	−	3.57971i	0.0580111	−	0.178540i
$403$	−18.9443	+	13.7638i	−0.943681	+	0.685625i
$404$	−13.9443	−	10.1311i	−0.693753	−	0.504041i
$405$	−1.76393	−	5.42882i	−0.0876505	−	0.269760i
$406$	−4.00000			−0.198517
$407$	−31.4164	−	7.05342i	−1.55725	−	0.349625i
$408$	1.00000			0.0495074
$409$	−9.67376	−	29.7728i	−0.478337	−	1.47217i	−0.841404	−	0.540406i	$-0.818271\pi$
$409$	−9.67376	−	29.7728i	−0.478337	−	1.47217i	0.363067	−	0.931763i	$-0.381729\pi$
$410$	−6.97214	−	5.06555i	−0.344329	−	0.250170i
$411$	3.07295	−	2.23263i	0.151577	−	0.110127i
$412$	0.0901699	−	0.277515i	0.00444235	−	0.0136722i
$413$	−1.11803	+	3.44095i	−0.0550149	+	0.169318i
$414$	17.9443	−	13.0373i	0.881913	−	0.640747i
$415$	8.97214	+	6.51864i	0.440425	+	0.319987i
$416$	1.61803	+	4.97980i	0.0793306	+	0.244155i
$417$	−6.47214			−0.316942
$418$	1.16312	−	0.502029i	0.0568900	−	0.0245550i
$419$	27.7426			1.35532			0.677658	−	0.735377i	$-0.262995\pi$
$419$	27.7426			1.35532			0.677658	+	0.735377i	$0.262995\pi$
$420$	−0.190983	−	0.587785i	−0.00931902	−	0.0286810i
$421$	0.381966	+	0.277515i	0.0186159	+	0.0135252i	0.597054	−	0.802201i	$-0.296338\pi$
$421$	0.381966	+	0.277515i	0.0186159	+	0.0135252i	−0.578438	+	0.815726i	$0.696338\pi$
$422$	13.6803	−	9.93935i	0.665949	−	0.483840i
$423$	5.47214	−	16.8415i	0.266064	−	0.818862i
$424$	2.00000	−	6.15537i	0.0971286	−	0.298931i
$425$	1.30902	−	0.951057i	0.0634967	−	0.0461330i
$426$	1.23607	+	0.898056i	0.0598877	+	0.0435110i
$427$	−2.47214	−	7.60845i	−0.119635	−	0.368199i
$428$	−3.09017			−0.149369
$429$	−9.85410	+	4.25325i	−0.475761	+	0.205349i
$430$	−4.61803			−0.222701
$431$	1.94427	+	5.98385i	0.0936523	+	0.288232i	0.986900	−	0.161333i	$-0.0515792\pi$
$431$	1.94427	+	5.98385i	0.0936523	+	0.288232i	−0.893248	+	0.449565i	$0.851579\pi$
$432$	2.80902	+	2.04087i	0.135149	+	0.0981914i
$433$	−20.8713	+	15.1639i	−1.00301	+	0.728731i	−0.962732	−	0.270458i	$-0.912825\pi$
$433$	−20.8713	+	15.1639i	−1.00301	+	0.728731i	−0.0402799	+	0.999188i	$0.512825\pi$
$434$	1.38197	−	4.25325i	0.0663365	−	0.204163i
$435$	−0.763932	+	2.35114i	−0.0366277	+	0.112729i
$436$	9.85410	−	7.15942i	0.471926	−	0.342874i
$437$	−2.61803	−	1.90211i	−0.125238	−	0.0909904i
$438$	−0.826238	−	2.54290i	−0.0394792	−	0.121504i
$439$	−20.3607			−0.971762			−0.485881	−	0.874025i	$-0.661501\pi$
$439$	−20.3607			−0.971762			−0.485881	+	0.874025i	$0.661501\pi$
$440$	−3.23607	−	0.726543i	−0.154273	−	0.0346366i
$441$	−2.61803			−0.124668
$442$	−2.61803	−	8.05748i	−0.124527	−	0.383255i
$443$	23.1525	+	16.8213i	1.10001	+	0.799202i	0.981061	−	0.193699i	$-0.0620484\pi$
$443$	23.1525	+	16.8213i	1.10001	+	0.799202i	0.118946	+	0.992901i	$0.462048\pi$
$444$	−4.85410	+	3.52671i	−0.230365	+	0.167370i
$445$	−3.04508	+	9.37181i	−0.144351	+	0.444266i
$446$	1.56231	−	4.80828i	0.0739773	−	0.227679i
$447$	−2.85410	+	2.07363i	−0.134994	+	0.0980792i
$448$	−0.809017	−	0.587785i	−0.0382225	−	0.0277702i
$449$	−4.55573	−	14.0211i	−0.214998	−	0.661696i	−0.999154	−	0.0411319i	$-0.986904\pi$
$449$	−4.55573	−	14.0211i	−0.214998	−	0.661696i	0.784156	−	0.620564i	$-0.213096\pi$
$450$	2.61803			0.123415
$451$	−2.66312	−	28.4585i	−0.125401	−	1.34006i
$452$	13.7984			0.649021
$453$	−0.416408	−	1.28157i	−0.0195645	−	0.0602135i
$454$	6.92705	+	5.03280i	0.325103	+	0.236201i
$455$	−4.23607	+	3.07768i	−0.198590	+	0.144284i
$456$	0.0729490	−	0.224514i	0.00341615	−	0.0105138i
$457$	−7.89919	+	24.3112i	−0.369508	+	1.13723i	0.577601	+	0.816319i	$0.303989\pi$
$457$	−7.89919	+	24.3112i	−0.369508	+	1.13723i	−0.947109	+	0.320911i	$0.896011\pi$
$458$	−4.61803	+	3.35520i	−0.215787	+	0.156778i
$459$	−4.54508	−	3.30220i	−0.212146	−	0.154133i
$460$	2.61803	+	8.05748i	0.122066	+	0.375682i
$461$	−1.12461			−0.0523784			−0.0261892	−	0.999657i	$-0.508337\pi$
$461$	−1.12461			−0.0523784			−0.0261892	+	0.999657i	$0.508337\pi$
$462$	1.04508	−	1.76336i	0.0486218	−	0.0820387i
$463$	0.652476			0.0303231			0.0151616	−	0.999885i	$-0.495174\pi$
$463$	0.652476			0.0303231			0.0151616	+	0.999885i	$0.495174\pi$
$464$	1.23607	+	3.80423i	0.0573830	+	0.176607i
$465$	−2.23607	−	1.62460i	−0.103695	−	0.0753390i
$466$	2.97214	−	2.15938i	0.137682	−	0.100031i
$467$	5.23607	−	16.1150i	0.242296	−	0.745711i	−0.753773	−	0.657135i	$-0.771768\pi$
$467$	5.23607	−	16.1150i	0.242296	−	0.745711i	0.996069	−	0.0885766i	$-0.0282318\pi$
$468$	4.23607	−	13.0373i	0.195812	−	0.602648i
$469$	4.92705	−	3.57971i	0.227510	−	0.165296i
$470$	5.47214	+	3.97574i	0.252411	+	0.183387i
$471$	3.09017	+	9.51057i	0.142388	+	0.438224i
$472$	3.61803			0.166534
$473$	−10.1180	−	11.4984i	−0.465228	−	0.528699i
$474$	−1.05573			−0.0484912
$475$	−0.118034	−	0.363271i	−0.00541577	−	0.0166680i
$476$	1.30902	+	0.951057i	0.0599987	+	0.0435916i
$477$	−13.7082	+	9.95959i	−0.627656	+	0.456018i
$478$	−5.47214	+	16.8415i	−0.250290	+	0.770312i
$479$	−5.29180	+	16.2865i	−0.241788	+	0.744148i	0.754360	+	0.656461i	$0.227947\pi$
$479$	−5.29180	+	16.2865i	−0.241788	+	0.744148i	−0.996148	+	0.0876867i	$0.972053\pi$
$480$	−0.500000	+	0.363271i	−0.0228218	+	0.0165810i
$481$	41.1246	+	29.8788i	1.87512	+	1.36236i
$482$	2.20820	+	6.79615i	0.100581	+	0.309556i
$483$	−5.23607			−0.238249
$484$	−5.28115	−	9.64932i	−0.240052	−	0.438606i
$485$	10.7984			0.490329
$486$	−4.30902	−	13.2618i	−0.195461	−	0.601567i
$487$	−30.5623	−	22.2048i	−1.38491	−	1.00620i	−0.996402	−	0.0847509i	$-0.972991\pi$
$487$	−30.5623	−	22.2048i	−1.38491	−	1.00620i	−0.388508	−	0.921445i	$-0.627009\pi$
$488$	−6.47214	+	4.70228i	−0.292980	+	0.212862i
$489$	−3.89261	+	11.9802i	−0.176030	+	0.541764i
$490$	0.309017	−	0.951057i	0.0139600	−	0.0429644i
$491$	30.6803	−	22.2906i	1.38458	−	1.00596i	0.388149	−	0.921597i	$-0.373115\pi$
$491$	30.6803	−	22.2906i	1.38458	−	1.00596i	0.996435	−	0.0843629i	$-0.0268855\pi$
$492$	−4.30902	−	3.13068i	−0.194265	−	0.141142i
$493$	−2.00000	−	6.15537i	−0.0900755	−	0.277224i
$494$	−2.00000			−0.0899843
$495$	5.73607	+	6.51864i	0.257817	+	0.292991i
$496$	−4.47214			−0.200805
$497$	0.763932	+	2.35114i	0.0342670	+	0.105463i
$498$	5.54508	+	4.02874i	0.248481	+	0.180532i
$499$	−0.500000	+	0.363271i	−0.0223831	+	0.0162623i	−0.598921	−	0.800808i	$-0.704403\pi$
$499$	−0.500000	+	0.363271i	−0.0223831	+	0.0162623i	0.576537	+	0.817071i	$0.304403\pi$
$500$	−0.309017	+	0.951057i	−0.0138197	+	0.0425325i
$501$	1.90983	−	5.87785i	0.0853249	−	0.262603i
$502$	−14.4721	+	10.5146i	−0.645923	+	0.469291i
$503$	20.7984	+	15.1109i	0.927354	+	0.673762i	0.945343	−	0.326076i	$-0.105727\pi$
$503$	20.7984	+	15.1109i	0.927354	+	0.673762i	−0.0179898	+	0.999838i	$0.505727\pi$
$504$	0.809017	+	2.48990i	0.0360365	+	0.110909i
$505$	−17.2361			−0.766995
$506$	−14.3262	+	24.1724i	−0.636879	+	1.07460i
$507$	8.90983			0.395699
$508$	4.38197	+	13.4863i	0.194418	+	0.598358i
$509$	−22.7984	−	16.5640i	−1.01052	−	0.734186i	−0.0462020	−	0.998932i	$-0.514712\pi$
$509$	−22.7984	−	16.5640i	−1.01052	−	0.734186i	−0.964318	+	0.264746i	$0.914712\pi$
$510$	0.809017	−	0.587785i	0.0358239	−	0.0260276i
$511$	1.33688	−	4.11450i	0.0591401	−	0.182015i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	−1.07295	+	0.779543i	−0.0473719	+	0.0344177i
$514$	−20.6803	−	15.0251i	−0.912171	−	0.662731i
$515$	−0.0901699	−	0.277515i	−0.00397336	−	0.0122288i
$516$	−2.85410			−0.125645
$517$	2.09017	+	22.3358i	0.0919256	+	0.982329i
$518$	−9.70820			−0.426554
$519$	1.76393	+	5.42882i	0.0774280	+	0.238299i
$520$	4.23607	+	3.07768i	0.185764	+	0.134965i
$521$	−14.1074	+	10.2496i	−0.618056	+	0.449044i	−0.852242	−	0.523148i	$-0.824758\pi$
$521$	−14.1074	+	10.2496i	−0.618056	+	0.449044i	0.234186	+	0.972192i	$0.424758\pi$
$522$	3.23607	−	9.95959i	0.141639	−	0.435920i
$523$	8.93769	−	27.5074i	0.390818	−	1.20281i	−0.541353	−	0.840796i	$-0.682088\pi$
$523$	8.93769	−	27.5074i	0.390818	−	1.20281i	0.932171	−	0.362019i	$-0.117912\pi$
$524$	−12.0172	+	8.73102i	−0.524975	+	0.381416i
$525$	−0.500000	−	0.363271i	−0.0218218	−	0.0158545i
$526$	3.70820	+	11.4127i	0.161685	+	0.497616i
$527$	7.23607			0.315208
$528$	−2.00000	−	0.449028i	−0.0870388	−	0.0195414i
$529$	48.7771			2.12074
$530$	−2.00000	−	6.15537i	−0.0868744	−	0.267372i
$531$	−7.66312	−	5.56758i	−0.332551	−	0.241612i
$532$	0.309017	−	0.224514i	0.0133976	−	0.00973392i
$533$	−13.9443	+	42.9161i	−0.603993	+	1.85890i
$534$	−1.88197	+	5.79210i	−0.0814406	+	0.250648i
$535$	−2.50000	+	1.81636i	−0.108084	+	0.0785279i
$536$	−4.92705	−	3.57971i	−0.212816	−	0.154620i
$537$	−2.83688	−	8.73102i	−0.122420	−	0.376771i
$538$	−14.0000			−0.603583
$539$	3.04508	−	1.31433i	0.131161	−	0.0566121i
$540$	3.47214			0.149417
$541$	12.4164	+	38.2138i	0.533823	+	1.64294i	0.746178	+	0.665746i	$0.231887\pi$
$541$	12.4164	+	38.2138i	0.533823	+	1.64294i	−0.212355	+	0.977193i	$0.568113\pi$
$542$	15.9443	+	11.5842i	0.684865	+	0.497584i
$543$	−8.56231	+	6.22088i	−0.367444	+	0.266963i
$544$	0.500000	−	1.53884i	0.0214373	−	0.0659773i
$545$	3.76393	−	11.5842i	0.161229	−	0.496212i
$546$	−2.61803	+	1.90211i	−0.112042	+	0.0814029i
$547$	−30.8156	−	22.3888i	−1.31758	−	0.957278i	−0.999959	−	0.00905984i	$-0.997116\pi$
$547$	−30.8156	−	22.3888i	−1.31758	−	0.957278i	−0.317621	−	0.948218i	$-0.602884\pi$
$548$	−1.89919	−	5.84510i	−0.0811292	−	0.249690i
$549$	20.9443			0.893880
$550$	−3.04508	+	1.31433i	−0.129843	+	0.0560431i
$551$	−1.52786			−0.0650892
$552$	1.61803	+	4.97980i	0.0688681	+	0.211954i
$553$	−1.38197	−	1.00406i	−0.0587672	−	0.0426969i
$554$	18.7082	−	13.5923i	0.794835	−	0.577482i
$555$	−1.85410	+	5.70634i	−0.0787022	+	0.242221i
$556$	−3.23607	+	9.95959i	−0.137240	+	0.422381i
$557$	32.6525	−	23.7234i	1.38353	−	1.00519i	0.386989	−	0.922084i	$-0.373515\pi$
$557$	32.6525	−	23.7234i	1.38353	−	1.00519i	0.996540	−	0.0831091i	$-0.0264850\pi$
$558$	9.47214	+	6.88191i	0.400987	+	0.291334i
$559$	7.47214	+	22.9969i	0.316038	+	0.972664i
$560$	−1.00000			−0.0422577
$561$	3.23607	+	0.726543i	0.136627	+	0.0306746i
$562$	6.79837			0.286772
$563$	−5.15654	−	15.8702i	−0.217322	−	0.668849i	−0.998981	−	0.0451423i	$-0.985626\pi$
$563$	−5.15654	−	15.8702i	−0.217322	−	0.668849i	0.781658	−	0.623707i	$-0.214374\pi$
$564$	3.38197	+	2.45714i	0.142406	+	0.103464i
$565$	11.1631	−	8.11048i	0.469636	−	0.341210i
$566$	8.00000	−	24.6215i	0.336265	−	1.03492i
$567$	1.76393	−	5.42882i	0.0740782	−	0.227989i
$568$	2.00000	−	1.45309i	0.0839181	−	0.0609701i
$569$	−29.4894	−	21.4253i	−1.23626	−	0.898194i	−0.238915	−	0.971040i	$-0.576792\pi$
$569$	−29.4894	−	21.4253i	−1.23626	−	0.898194i	−0.997343	+	0.0728464i	$0.976792\pi$
$570$	−0.0729490	−	0.224514i	−0.00305550	−	0.00940386i
$571$	−26.8328			−1.12292			−0.561459	−	0.827504i	$-0.689760\pi$
$571$	−26.8328			−1.12292			−0.561459	+	0.827504i	$0.689760\pi$
$572$	1.61803	+	17.2905i	0.0676534	+	0.722953i
$573$	−1.23607			−0.0516375
$574$	−2.66312	−	8.19624i	−0.111156	−	0.342104i
$575$	6.85410	+	4.97980i	0.285836	+	0.207672i
$576$	2.11803	−	1.53884i	0.0882514	−	0.0641184i
$577$	2.68034	−	8.24924i	0.111584	−	0.343420i	−0.879635	−	0.475649i	$-0.842213\pi$
$577$	2.68034	−	8.24924i	0.111584	−	0.343420i	0.991219	+	0.132229i	$0.0422133\pi$
$578$	4.44427	−	13.6781i	0.184857	−	0.568932i
$579$	6.23607	−	4.53077i	0.259162	−	0.188292i
$580$	3.23607	+	2.35114i	0.134370	+	0.0976258i
$581$	3.42705	+	10.5474i	0.142178	+	0.437579i
$582$	6.67376			0.276636
$583$	10.9443	−	18.4661i	0.453265	−	0.764788i
$584$	−4.32624			−0.179021
$585$	−4.23607	−	13.0373i	−0.175140	−	0.539025i
$586$	1.85410	+	1.34708i	0.0765922	+	0.0556475i
$587$	6.78115	−	4.92680i	0.279888	−	0.203351i	−0.438980	−	0.898497i	$-0.644660\pi$
$587$	6.78115	−	4.92680i	0.279888	−	0.203351i	0.718869	+	0.695146i	$0.244660\pi$
$588$	0.190983	−	0.587785i	0.00787601	−	0.0242399i
$589$	0.527864	−	1.62460i	0.0217503	−	0.0669404i
$590$	2.92705	−	2.12663i	0.120505	−	0.0875518i
$591$	−10.7082	−	7.77997i	−0.440477	−	0.320025i
$592$	3.00000	+	9.23305i	0.123299	+	0.379476i
$593$	−10.3820			−0.426336			−0.213168	−	0.977016i	$-0.568378\pi$
$593$	−10.3820			−0.426336			−0.213168	+	0.977016i	$0.568378\pi$
$594$	7.60739	+	8.64527i	0.312135	+	0.354720i
$595$	1.61803			0.0663329
$596$	1.76393	+	5.42882i	0.0722535	+	0.222373i
$597$	0.618034	+	0.449028i	0.0252944	+	0.0183775i
$598$	35.8885	−	26.0746i	1.46759	−	1.06627i
$599$	7.41641	−	22.8254i	0.303026	−	0.932619i	−0.677380	−	0.735633i	$-0.736885\pi$
$599$	7.41641	−	22.8254i	0.303026	−	0.932619i	0.980406	−	0.196986i	$-0.0631152\pi$
$600$	−0.190983	+	0.587785i	−0.00779685	+	0.0239962i
$601$	10.9721	−	7.97172i	0.447563	−	0.325173i	−0.341070	−	0.940038i	$-0.610789\pi$
$601$	10.9721	−	7.97172i	0.447563	−	0.325173i	0.788633	+	0.614865i	$0.210789\pi$
$602$	−3.73607	−	2.71441i	−0.152271	−	0.110631i
$603$	4.92705	+	15.1639i	0.200645	+	0.617522i
$604$	−2.18034			−0.0887168
$605$	−9.94427	−	4.70228i	−0.404292	−	0.191175i
$606$	−10.6525			−0.432727
$607$	−10.5066	−	32.3359i	−0.426449	−	1.31247i	−0.901600	−	0.432570i	$-0.857607\pi$
$607$	−10.5066	−	32.3359i	−0.426449	−	1.31247i	0.475151	−	0.879904i	$-0.342393\pi$
$608$	−0.309017	−	0.224514i	−0.0125323	−	0.00910524i
$609$	−2.00000	+	1.45309i	−0.0810441	+	0.0588820i
$610$	−2.47214	+	7.60845i	−0.100094	+	0.308057i
$611$	10.9443	−	33.6830i	0.442758	−	1.36267i
$612$	−3.42705	+	2.48990i	−0.138530	+	0.100648i
$613$	8.14590	+	5.91834i	0.329010	+	0.239040i	0.740010	−	0.672596i	$-0.234821\pi$
$613$	8.14590	+	5.91834i	0.329010	+	0.239040i	−0.411001	+	0.911635i	$0.634821\pi$
$614$	−10.6631	−	32.8177i	−0.430328	−	1.32441i
$615$	−5.32624			−0.214775
$616$	−2.19098	−	2.48990i	−0.0882772	−	0.100321i
$617$	37.7984			1.52171			0.760853	−	0.648925i	$-0.224781\pi$
$617$	37.7984			1.52171			0.760853	+	0.648925i	$0.224781\pi$
$618$	−0.0557281	−	0.171513i	−0.00224171	−	0.00689928i
$619$	−32.8156	−	23.8419i	−1.31897	−	0.958288i	−0.999944	−	0.0105418i	$-0.996644\pi$
$619$	−32.8156	−	23.8419i	−1.31897	−	0.958288i	−0.319026	−	0.947746i	$-0.603356\pi$
$620$	−3.61803	+	2.62866i	−0.145304	+	0.105569i
$621$	9.09017	−	27.9767i	0.364776	−	1.12266i
$622$	−1.00000	+	3.07768i	−0.0400963	+	0.123404i
$623$	−7.97214	+	5.79210i	−0.319397	+	0.232055i
$624$	2.61803	+	1.90211i	0.104805	+	0.0761455i
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	−3.32624			−0.132943
$627$	0.399187	−	0.673542i	0.0159420	−	0.0268987i
$628$	16.1803			0.645666
$629$	−4.85410	−	14.9394i	−0.193546	−	0.595672i
$630$	2.11803	+	1.53884i	0.0843845	+	0.0613089i
$631$	20.4164	−	14.8334i	0.812764	−	0.590508i	−0.101866	−	0.994798i	$-0.532481\pi$
$631$	20.4164	−	14.8334i	0.812764	−	0.590508i	0.914631	+	0.404290i	$0.132481\pi$
$632$	−0.527864	+	1.62460i	−0.0209973	+	0.0646231i
$633$	3.22949	−	9.93935i	0.128361	−	0.395054i
$634$	−14.4721	+	10.5146i	−0.574762	+	0.417589i
$635$	11.4721	+	8.33499i	0.455258	+	0.330764i
$636$	−1.23607	−	3.80423i	−0.0490133	−	0.150847i
$637$	−5.23607			−0.207461
$638$	1.23607	+	13.2088i	0.0489364	+	0.522941i
$639$	−6.47214			−0.256034
$640$	0.309017	+	0.951057i	0.0122150	+	0.0375938i
$641$	−32.6246	−	23.7032i	−1.28859	−	0.936219i	−0.288819	−	0.957384i	$-0.593262\pi$
$641$	−32.6246	−	23.7032i	−1.28859	−	0.936219i	−0.999776	+	0.0211650i	$0.993262\pi$
$642$	−1.54508	+	1.12257i	−0.0609796	+	0.0443043i
$643$	−4.19098	+	12.8985i	−0.165276	+	0.508668i	−0.999057	−	0.0434284i	$-0.986172\pi$
$643$	−4.19098	+	12.8985i	−0.165276	+	0.508668i	0.833780	+	0.552096i	$0.186172\pi$
$644$	−2.61803	+	8.05748i	−0.103165	+	0.317509i
$645$	−2.30902	+	1.67760i	−0.0909175	+	0.0660554i
$646$	0.500000	+	0.363271i	0.0196722	+	0.0142927i
$647$	8.61803	+	26.5236i	0.338810	+	1.04275i	0.964815	+	0.262930i	$0.0846890\pi$
$647$	8.61803	+	26.5236i	0.338810	+	1.04275i	−0.626005	+	0.779819i	$0.715311\pi$
$648$	−5.70820			−0.224239
$649$	11.7082	+	2.62866i	0.459587	+	0.103184i
$650$	5.23607			0.205375
$651$	−0.854102	−	2.62866i	−0.0334749	−	0.103025i
$652$	16.4894	+	11.9802i	0.645773	+	0.469182i
$653$	4.85410	−	3.52671i	0.189956	−	0.138011i	−0.488743	−	0.872428i	$-0.662544\pi$
$653$	4.85410	−	3.52671i	0.189956	−	0.138011i	0.678698	+	0.734417i	$0.262544\pi$
$654$	2.32624	−	7.15942i	0.0909631	−	0.279956i
$655$	−4.59017	+	14.1271i	−0.179353	+	0.551991i
$656$	−6.97214	+	5.06555i	−0.272216	+	0.197777i
$657$	9.16312	+	6.65740i	0.357487	+	0.259730i
$658$	2.09017	+	6.43288i	0.0814833	+	0.250780i
$659$	9.90983			0.386032			0.193016	−	0.981196i	$-0.438173\pi$
$659$	9.90983			0.386032			0.193016	+	0.981196i	$0.438173\pi$
$660$	−1.88197	+	0.812299i	−0.0732554	+	0.0316187i
$661$	−33.7771			−1.31378			−0.656888	−	0.753988i	$-0.728128\pi$
$661$	−33.7771			−1.31378			−0.656888	+	0.753988i	$0.728128\pi$
$662$	−3.80902	−	11.7229i	−0.148042	−	0.455625i
$663$	−4.23607	−	3.07768i	−0.164515	−	0.119527i
$664$	8.97214	−	6.51864i	0.348186	−	0.252972i
$665$	0.118034	−	0.363271i	0.00457716	−	0.0140871i
$666$	7.85410	−	24.1724i	0.304340	−	0.936663i
$667$	27.4164	−	19.9192i	1.06157	−	0.771274i
$668$	−8.09017	−	5.87785i	−0.313018	−	0.227421i
$669$	−0.965558	−	2.97168i	−0.0373306	−	0.114892i
$670$	−6.09017			−0.235284
$671$	−24.3607	+	10.5146i	−0.940434	+	0.405912i
$672$	−0.618034			−0.0238412
$673$	2.20820	+	6.79615i	0.0851200	+	0.261972i	0.984553	−	0.175086i	$-0.0560203\pi$
$673$	2.20820	+	6.79615i	0.0851200	+	0.261972i	−0.899433	+	0.437058i	$0.856020\pi$
$674$	26.1074	+	18.9681i	1.00562	+	0.730625i
$675$	2.80902	−	2.04087i	0.108119	−	0.0785531i
$676$	4.45492	−	13.7108i	0.171343	−	0.527339i
$677$	2.14590	−	6.60440i	0.0824736	−	0.253828i	−0.901314	−	0.433167i	$-0.857396\pi$
$677$	2.14590	−	6.60440i	0.0824736	−	0.253828i	0.983787	+	0.179339i	$0.0573960\pi$
$678$	6.89919	−	5.01255i	0.264962	−	0.192506i
$679$	8.73607	+	6.34712i	0.335260	+	0.243580i
$680$	−0.500000	−	1.53884i	−0.0191741	−	0.0590119i
$681$	5.29180			0.202782
$682$	−14.4721	−	3.24920i	−0.554167	−	0.124418i
$683$	17.3050			0.662156			0.331078	−	0.943603i	$-0.392588\pi$
$683$	17.3050			0.662156			0.331078	+	0.943603i	$0.392588\pi$
$684$	0.309017	+	0.951057i	0.0118156	+	0.0363646i
$685$	−4.97214	−	3.61247i	−0.189976	−	0.138025i
$686$	0.809017	−	0.587785i	0.0308884	−	0.0224417i
$687$	−1.09017	+	3.35520i	−0.0415926	+	0.128009i
$688$	−1.42705	+	4.39201i	−0.0544058	+	0.167444i
$689$	−27.4164	+	19.9192i	−1.04448	+	0.758861i
$690$	4.23607	+	3.07768i	0.161264	+	0.117165i
$691$	−8.59017	−	26.4378i	−0.326785	−	1.00574i	−0.970628	−	0.240584i	$-0.922661\pi$
$691$	−8.59017	−	26.4378i	−0.326785	−	1.00574i	0.643843	−	0.765158i	$-0.277339\pi$
$692$	9.23607			0.351103
$693$	0.809017	+	8.64527i	0.0307320	+	0.328406i
$694$	27.0344			1.02621
$695$	3.23607	+	9.95959i	0.122751	+	0.377789i
$696$	2.00000	+	1.45309i	0.0758098	+	0.0550790i
$697$	11.2812	−	8.19624i	0.427304	−	0.310455i
$698$	−3.23607	+	9.95959i	−0.122487	+	0.376976i
$699$	0.701626	−	2.15938i	0.0265379	−	0.0816754i
$700$	−0.809017	+	0.587785i	−0.0305780	+	0.0222162i
$701$	−14.7082	−	10.6861i	−0.555521	−	0.403610i	0.274296	−	0.961645i	$-0.411555\pi$
$701$	−14.7082	−	10.6861i	−0.555521	−	0.403610i	−0.829817	+	0.558036i	$0.811555\pi$
$702$	−5.61803	−	17.2905i	−0.212039	−	0.652589i
$703$	−3.70820			−0.139858
$704$	−1.69098	+	2.85317i	−0.0637313	+	0.107533i
$705$	4.18034			0.157441
$706$	−5.26393	−	16.2007i	−0.198111	−	0.609722i
$707$	−13.9443	−	10.1311i	−0.524428	−	0.381019i
$708$	1.80902	−	1.31433i	0.0679870	−	0.0493955i
$709$	11.5066	−	35.4136i	0.432139	−	1.32999i	−0.463852	−	0.885913i	$-0.653533\pi$
$709$	11.5066	−	35.4136i	0.432139	−	1.32999i	0.895991	−	0.444073i	$-0.146467\pi$
$710$	0.763932	−	2.35114i	0.0286699	−	0.0882367i
$711$	3.61803	−	2.62866i	0.135687	−	0.0985823i
$712$	7.97214	+	5.79210i	0.298768	+	0.217068i
$713$	11.7082	+	36.0341i	0.438476	+	1.34949i
$714$	1.00000			0.0374241
$715$	11.4721	+	13.0373i	0.429034	+	0.487567i
$716$	−14.8541			−0.555124
$717$	3.38197	+	10.4086i	0.126302	+	0.388717i
$718$	20.7984	+	15.1109i	0.776188	+	0.563934i
$719$	−40.7426	+	29.6013i	−1.51944	+	1.10394i	−0.557682	+	0.830055i	$0.688309\pi$
$719$	−40.7426	+	29.6013i	−1.51944	+	1.10394i	−0.961762	+	0.273886i	$0.911691\pi$
$720$	0.809017	−	2.48990i	0.0301503	−	0.0927930i
$721$	0.0901699	−	0.277515i	0.00335810	−	0.0103352i
$722$	−15.2533	+	11.0822i	−0.567669	+	0.412435i
$723$	3.57295	+	2.59590i	0.132879	+	0.0965425i
$724$	5.29180	+	16.2865i	0.196668	+	0.605282i
$725$	4.00000			0.148556
$726$	−6.14590	−	2.90617i	−0.228096	−	0.107858i
$727$	37.3050			1.38356			0.691782	−	0.722106i	$-0.256826\pi$
$727$	37.3050			1.38356			0.691782	+	0.722106i	$0.256826\pi$
$728$	1.61803	+	4.97980i	0.0599683	+	0.184564i
$729$	6.88197	+	5.00004i	0.254888	+	0.185187i
$730$	−3.50000	+	2.54290i	−0.129541	+	0.0941169i
$731$	2.30902	−	7.10642i	0.0854021	−	0.262841i
$732$	−1.52786	+	4.70228i	−0.0564715	+	0.173801i
$733$	11.9443	−	8.67802i	0.441172	−	0.320530i	−0.344929	−	0.938629i	$-0.612097\pi$
$733$	11.9443	−	8.67802i	0.441172	−	0.320530i	0.786100	+	0.618099i	$0.212097\pi$
$734$	8.94427	+	6.49839i	0.330139	+	0.239860i
$735$	−0.190983	−	0.587785i	−0.00704451	−	0.0216808i
$736$	8.47214			0.312287
$737$	−13.3435	−	15.1639i	−0.491513	−	0.558570i
$738$	22.5623			0.830530
$739$	6.17376	+	19.0009i	0.227106	+	0.698959i	0.998071	+	0.0620820i	$0.0197740\pi$
$739$	6.17376	+	19.0009i	0.227106	+	0.698959i	−0.770966	+	0.636877i	$0.780226\pi$
$740$	7.85410	+	5.70634i	0.288723	+	0.209769i
$741$	−1.00000	+	0.726543i	−0.0367359	+	0.0266902i
$742$	2.00000	−	6.15537i	0.0734223	−	0.225971i
$743$	−6.79837	+	20.9232i	−0.249408	+	0.767599i	0.745472	+	0.666537i	$0.232224\pi$
$743$	−6.79837	+	20.9232i	−0.249408	+	0.767599i	−0.994880	+	0.101062i	$0.967776\pi$
$744$	−2.23607	+	1.62460i	−0.0819782	+	0.0595607i
$745$	4.61803	+	3.35520i	0.169192	+	0.122925i
$746$	1.52786	+	4.70228i	0.0559391	+	0.172163i
$747$	−29.0344			−1.06231
$748$	2.73607	−	4.61653i	0.100041	−	0.168797i
$749$	−3.09017			−0.112912
$750$	0.190983	+	0.587785i	0.00697371	+	0.0214629i
$751$	18.2705	+	13.2743i	0.666700	+	0.484386i	0.868919	−	0.494954i	$-0.164815\pi$
$751$	18.2705	+	13.2743i	0.666700	+	0.484386i	−0.202219	+	0.979340i	$0.564815\pi$
$752$	5.47214	−	3.97574i	0.199548	−	0.144980i
$753$	−3.41641	+	10.5146i	−0.124501	+	0.383174i
$754$	6.47214	−	19.9192i	0.235701	−	0.725414i
$755$	−1.76393	+	1.28157i	−0.0641961	+	0.0466412i
$756$	2.80902	+	2.04087i	0.102163	+	0.0742257i
$757$	−9.90983	−	30.4993i	−0.360179	−	1.10852i	−0.952945	−	0.303142i	$-0.901964\pi$
$757$	−9.90983	−	30.4993i	−0.360179	−	1.10852i	0.592766	−	0.805374i	$-0.298036\pi$
$758$	10.1459			0.368516
$759$	1.61803	+	17.2905i	0.0587309	+	0.627607i
$760$	−0.381966			−0.0138554
$761$	12.4443	+	38.2995i	0.451105	+	1.38836i	0.875648	+	0.482949i	$0.160435\pi$
$761$	12.4443	+	38.2995i	0.451105	+	1.38836i	−0.424544	+	0.905407i	$0.639565\pi$
$762$	7.09017	+	5.15131i	0.256850	+	0.186612i
$763$	9.85410	−	7.15942i	0.356742	−	0.259189i
$764$	−0.618034	+	1.90211i	−0.0223597	+	0.0688160i
$765$	−1.30902	+	4.02874i	−0.0473276	+	0.145659i
$766$	14.3262	−	10.4086i	0.517628	−	0.376079i
$767$	−15.3262	−	11.1352i	−0.553398	−	0.402067i
$768$	0.190983	+	0.587785i	0.00689151	+	0.0212099i
$769$	−1.41641			−0.0510770			−0.0255385	−	0.999674i	$-0.508130\pi$
$769$	−1.41641			−0.0510770			−0.0255385	+	0.999674i	$0.508130\pi$
$770$	−3.23607	−	0.726543i	−0.116620	−	0.0261828i
$771$	−15.7984			−0.568965
$772$	−3.85410	−	11.8617i	−0.138712	−	0.426912i
$773$	6.76393	+	4.91428i	0.243282	+	0.176755i	0.702744	−	0.711443i	$-0.251958\pi$
$773$	6.76393	+	4.91428i	0.243282	+	0.176755i	−0.459462	+	0.888197i	$0.651958\pi$
$774$	9.78115	−	7.10642i	0.351576	−	0.255435i
$775$	−1.38197	+	4.25325i	−0.0496417	+	0.152781i
$776$	3.33688	−	10.2699i	0.119787	−	0.368667i
$777$	−4.85410	+	3.52671i	−0.174140	+	0.126520i
$778$	6.47214	+	4.70228i	0.232037	+	0.168585i
$779$	−1.01722	−	3.13068i	−0.0364457	−	0.112168i
$780$	3.23607			0.115870
$781$	7.52786	−	3.24920i	0.269368	−	0.116265i
$782$	−13.7082			−0.490204
$783$	−4.29180	−	13.2088i	−0.153376	−	0.472044i
$784$	−0.809017	−	0.587785i	−0.0288935	−	0.0209923i
$785$	13.0902	−	9.51057i	0.467208	−	0.339447i
$786$	−2.83688	+	8.73102i	−0.101188	+	0.311425i
$787$	−4.64590	+	14.2986i	−0.165608	+	0.509690i	−0.999081	−	0.0428712i	$-0.986350\pi$
$787$	−4.64590	+	14.2986i	−0.165608	+	0.509690i	0.833472	+	0.552561i	$0.186350\pi$
$788$	−17.3262	+	12.5882i	−0.617222	+	0.448438i
$789$	6.00000	+	4.35926i	0.213606	+	0.155194i
$790$	0.527864	+	1.62460i	0.0187806	+	0.0578006i
$791$	13.7984			0.490614
$792$	7.97214	−	3.44095i	0.283278	−	0.122269i
$793$	41.8885			1.48751
$794$	10.6738	+	32.8505i	0.378798	+	1.16582i
$795$	−3.23607	−	2.35114i	−0.114772	−	0.0833864i
$796$	1.00000	−	0.726543i	0.0354441	−	0.0257516i
$797$	7.88854	−	24.2784i	0.279427	−	0.859987i	−0.708588	−	0.705623i	$-0.750667\pi$
$797$	7.88854	−	24.2784i	0.279427	−	0.859987i	0.988014	−	0.154364i	$-0.0493327\pi$
$798$	0.0729490	−	0.224514i	0.00258237	−	0.00794771i
$799$	−8.85410	+	6.43288i	−0.313236	+	0.227579i
$800$	0.809017	+	0.587785i	0.0286031	+	0.0207813i
$801$	−7.97214	−	24.5357i	−0.281682	−	0.866927i
$802$	10.5066			0.371000
$803$	−14.0000	−	3.14320i	−0.494049	−	0.110921i
$804$	−3.76393			−0.132744
$805$	2.61803	+	8.05748i	0.0922736	+	0.283989i
$806$	18.9443	+	13.7638i	0.667284	+	0.484810i
$807$	−7.00000	+	5.08580i	−0.246412	+	0.179029i
$808$	−5.32624	+	16.3925i	−0.187376	+	0.576685i
$809$	14.3885	−	44.2834i	0.505874	−	1.55692i	−0.293422	−	0.955983i	$-0.594794\pi$
$809$	14.3885	−	44.2834i	0.505874	−	1.55692i	0.799296	−	0.600938i	$-0.205206\pi$
$810$	−4.61803	+	3.35520i	−0.162261	+	0.117890i
$811$	−20.3885	−	14.8131i	−0.715939	−	0.520160i	0.169145	−	0.985591i	$-0.445899\pi$
$811$	−20.3885	−	14.8131i	−0.715939	−	0.520160i	−0.885084	+	0.465431i	$0.845899\pi$
$812$	1.23607	+	3.80423i	0.0433775	+	0.133502i
$813$	12.1803			0.427183
$814$	3.00000	+	32.0584i	0.105150	+	1.12365i
$815$	20.3820			0.713949
$816$	−0.309017	−	0.951057i	−0.0108178	−	0.0332936i
$817$	−1.42705	−	1.03681i	−0.0499262	−	0.0362735i
$818$	−25.3262	+	18.4006i	−0.885511	+	0.643362i
$819$	4.23607	−	13.0373i	0.148020	−	0.455559i
$820$	−2.66312	+	8.19624i	−0.0930001	+	0.286225i
$821$	28.7082	−	20.8577i	1.00192	−	0.727940i	0.0394235	−	0.999223i	$-0.487448\pi$
$821$	28.7082	−	20.8577i	1.00192	−	0.727940i	0.962500	+	0.271283i	$0.0874478\pi$
$822$	−3.07295	−	2.23263i	−0.107181	−	0.0778718i
$823$	−10.3475	−	31.8464i	−0.360692	−	1.11010i	−0.952635	−	0.304116i	$-0.901639\pi$
$823$	−10.3475	−	31.8464i	−0.360692	−	1.11010i	0.591943	−	0.805980i	$-0.298361\pi$
$824$	−0.291796			−0.0101652
$825$	−1.04508	+	1.76336i	−0.0363852	+	0.0613922i
$826$	3.61803			0.125888
$827$	−5.17376	−	15.9232i	−0.179909	−	0.553704i	0.819914	−	0.572486i	$-0.194021\pi$
$827$	−5.17376	−	15.9232i	−0.179909	−	0.553704i	−0.999824	+	0.0187823i	$0.994021\pi$
$828$	−17.9443	−	13.0373i	−0.623607	−	0.453077i
$829$	12.0902	−	8.78402i	0.419909	−	0.305082i	−0.357692	−	0.933840i	$-0.616436\pi$
$829$	12.0902	−	8.78402i	0.419909	−	0.305082i	0.777601	+	0.628758i	$0.216436\pi$
$830$	3.42705	−	10.5474i	0.118955	−	0.366105i
$831$	4.41641	−	13.5923i	0.153203	−	0.471512i
$832$	4.23607	−	3.07768i	0.146859	−	0.106699i
$833$	1.30902	+	0.951057i	0.0453548	+	0.0329522i
$834$	2.00000	+	6.15537i	0.0692543	+	0.213143i
$835$	−10.0000			−0.346064
$836$	−0.836881	−	0.951057i	−0.0289441	−	0.0328930i
$837$	15.5279			0.536721
$838$	−8.57295	−	26.3848i	−0.296148	−	0.911449i
$839$	−16.7082	−	12.1392i	−0.576831	−	0.419092i	0.260749	−	0.965407i	$-0.416030\pi$
$839$	−16.7082	−	12.1392i	−0.576831	−	0.419092i	−0.837580	+	0.546314i	$0.816030\pi$
$840$	−0.500000	+	0.363271i	−0.0172516	+	0.0125340i
$841$	−4.01722	+	12.3637i	−0.138525	+	0.426336i
$842$	0.145898	−	0.449028i	0.00502798	−	0.0154745i
$843$	3.39919	−	2.46965i	0.117074	−	0.0850594i
$844$	−13.6803	−	9.93935i	−0.470897	−	0.342126i
$845$	−4.45492	−	13.7108i	−0.153254	−	0.471667i
$846$	−17.7082			−0.608821
$847$	−5.28115	−	9.64932i	−0.181463	−	0.331555i
$848$	−6.47214			−0.222254
$849$	−4.94427	−	15.2169i	−0.169687	−	0.522243i
$850$	−1.30902	−	0.951057i	−0.0448989	−	0.0326210i
$851$	66.5410	−	48.3449i	2.28100	−	1.65724i
$852$	0.472136	−	1.45309i	0.0161751	−	0.0497819i
$853$	−15.3607	+	47.2753i	−0.525940	+	1.61868i	0.236511	+	0.971629i	$0.423996\pi$
$853$	−15.3607	+	47.2753i	−0.525940	+	1.61868i	−0.762450	+	0.647047i	$0.776004\pi$
$854$	−6.47214	+	4.70228i	−0.221472	+	0.160909i
$855$	0.809017	+	0.587785i	0.0276678	+	0.0201018i
$856$	0.954915	+	2.93893i	0.0326383	+	0.100450i
$857$	−12.6869			−0.433377			−0.216688	−	0.976241i	$-0.569526\pi$
$857$	−12.6869			−0.433377			−0.216688	+	0.976241i	$0.569526\pi$
$858$	7.09017	+	8.05748i	0.242054	+	0.275078i
$859$	37.1459			1.26740			0.633701	−	0.773578i	$-0.281535\pi$
$859$	37.1459			1.26740			0.633701	+	0.773578i	$0.281535\pi$
$860$	1.42705	+	4.39201i	0.0486620	+	0.149766i
$861$	−4.30902	−	3.13068i	−0.146851	−	0.106693i
$862$	5.09017	−	3.69822i	0.173372	−	0.125962i
$863$	−12.4377	+	38.2793i	−0.423384	+	1.30304i	0.481149	+	0.876639i	$0.340220\pi$
$863$	−12.4377	+	38.2793i	−0.423384	+	1.30304i	−0.904533	+	0.426403i	$0.859780\pi$
$864$	1.07295	−	3.30220i	0.0365025	−	0.112343i
$865$	7.47214	−	5.42882i	0.254060	−	0.184586i
$866$	20.8713	+	15.1639i	0.709236	+	0.515290i
$867$	−2.74671	−	8.45351i	−0.0932832	−	0.287096i
$868$	−4.47214			−0.151794
$869$	−2.88854	+	4.87380i	−0.0979871	+	0.165332i
$870$	2.47214			0.0838133
$871$	9.85410	+	30.3278i	0.333894	+	1.02762i
$872$	−9.85410	−	7.15942i	−0.333702	−	0.242449i
$873$	−22.8713	+	16.6170i	−0.774077	+	0.562400i
$874$	−1.00000	+	3.07768i	−0.0338255	+	0.104104i
$875$	−0.309017	+	0.951057i	−0.0104467	+	0.0321516i
$876$	−2.16312	+	1.57160i	−0.0730850	+	0.0530994i
$877$	−15.4721	−	11.2412i	−0.522457	−	0.379587i	0.295072	−	0.955475i	$-0.404656\pi$
$877$	−15.4721	−	11.2412i	−0.522457	−	0.379587i	−0.817529	+	0.575888i	$0.804656\pi$
$878$	6.29180	+	19.3642i	0.212338	+	0.653509i
$879$	1.41641			0.0477743
$880$	0.309017	+	3.30220i	0.0104170	+	0.111317i
$881$	−57.3394			−1.93181			−0.965907	−	0.258891i	$-0.916643\pi$
$881$	−57.3394			−1.93181			−0.965907	+	0.258891i	$0.916643\pi$
$882$	0.809017	+	2.48990i	0.0272410	+	0.0838392i
$883$	−29.6246	−	21.5235i	−0.996948	−	0.724325i	−0.0355160	−	0.999369i	$-0.511307\pi$
$883$	−29.6246	−	21.5235i	−0.996948	−	0.724325i	−0.961432	+	0.275044i	$0.911307\pi$
$884$	−6.85410	+	4.97980i	−0.230528	+	0.167489i
$885$	0.690983	−	2.12663i	0.0232271	−	0.0714858i
$886$	8.84346	−	27.2174i	0.297102	−	0.914385i
$887$	17.7984	−	12.9313i	0.597611	−	0.434190i	−0.247419	−	0.968909i	$-0.579582\pi$
$887$	17.7984	−	12.9313i	0.597611	−	0.434190i	0.845030	+	0.534719i	$0.179582\pi$
$888$	4.85410	+	3.52671i	0.162893	+	0.118349i
$889$	4.38197	+	13.4863i	0.146966	+	0.452316i
$890$	9.85410			0.330310
$891$	−18.4721	−	4.14725i	−0.618840	−	0.138938i
$892$	−5.05573			−0.169278
$893$	0.798374	+	2.45714i	0.0267166	+	0.0822251i
$894$	2.85410	+	2.07363i	0.0954554	+	0.0693524i
$895$	−12.0172	+	8.73102i	−0.401691	+	0.291846i
$896$	−0.309017	+	0.951057i	−0.0103235	+	0.0317726i
$897$	8.47214	−	26.0746i	0.282876	−	0.870604i
$898$	−11.9271	+	8.66551i	−0.398011	+	0.289172i
$899$	14.4721	+	10.5146i	0.482673	+	0.350682i
$900$	−0.809017	−	2.48990i	−0.0269672	−	0.0829966i
$901$	10.4721			0.348877
$902$	−26.2426	+	11.3269i	−0.873785	+	0.377145i
$903$	−2.85410			−0.0949786
$904$	−4.26393	−	13.1230i	−0.141816	−	0.436466i
$905$	13.8541	+	10.0656i	0.460526	+	0.334592i
$906$	−1.09017	+	0.792055i	−0.0362185	+	0.0263143i
$907$	−1.17376	+	3.61247i	−0.0389741	+	0.119950i	−0.968651	−	0.248427i	$-0.920086\pi$
$907$	−1.17376	+	3.61247i	−0.0389741	+	0.119950i	0.929677	+	0.368377i	$0.120086\pi$
$908$	2.64590	−	8.14324i	0.0878072	−	0.270243i
$909$	36.5066	−	26.5236i	1.21085	−	0.879732i
$910$	4.23607	+	3.07768i	0.140424	+	0.102024i
$911$	9.90983	+	30.4993i	0.328327	+	1.01049i	0.969916	+	0.243439i	$0.0782755\pi$
$911$	9.90983	+	30.4993i	0.328327	+	1.01049i	−0.641589	+	0.767049i	$0.721724\pi$
$912$	−0.236068			−0.00781699
$913$	33.7705	−	14.5761i	1.11764	−	0.482399i
$914$	25.5623			0.845526
$915$	1.52786	+	4.70228i	0.0505096	+	0.155453i
$916$	4.61803	+	3.35520i	0.152584	+	0.110859i
$917$	−12.0172	+	8.73102i	−0.396844	+	0.288324i
$918$	−1.73607	+	5.34307i	−0.0572988	+	0.176348i
$919$	−5.18034	+	15.9434i	−0.170884	+	0.525926i	−0.999422	−	0.0340071i	$-0.989173\pi$
$919$	−5.18034	+	15.9434i	−0.170884	+	0.525926i	0.828538	+	0.559933i	$0.189173\pi$
$920$	6.85410	−	4.97980i	0.225973	−	0.164179i
$921$	−17.2533	−	12.5352i	−0.568515	−	0.413050i
$922$	0.347524	+	1.06957i	0.0114451	+	0.0352244i
$923$	−12.9443			−0.426066
$924$	−2.00000	−	0.449028i	−0.0657952	−	0.0147719i
$925$	9.70820			0.319204
$926$	−0.201626	−	0.620541i	−0.00662585	−	0.0203923i
$927$	0.618034	+	0.449028i	0.0202989	+	0.0147480i
$928$	3.23607	−	2.35114i	0.106229	−	0.0771800i
$929$	10.9164	−	33.5972i	0.358156	−	1.10229i	−0.596001	−	0.802983i	$-0.703245\pi$
$929$	10.9164	−	33.5972i	0.358156	−	1.10229i	0.954157	−	0.299307i	$-0.0967553\pi$
$930$	−0.854102	+	2.62866i	−0.0280071	+	0.0861970i
$931$	0.309017	−	0.224514i	0.0101276	−	0.00735815i
$932$	−2.97214	−	2.15938i	−0.0973556	−	0.0707329i
$933$	0.618034	+	1.90211i	0.0202335	+	0.0622724i
$934$	−16.9443			−0.554434
$935$	−0.500000	−	5.34307i	−0.0163517	−	0.174737i
$936$	−13.7082			−0.448067
$937$	14.0279	+	43.1733i	0.458270	+	1.41041i	0.867252	+	0.497869i	$0.165884\pi$
$937$	14.0279	+	43.1733i	0.458270	+	1.41041i	−0.408982	+	0.912542i	$0.634116\pi$
$938$	−4.92705	−	3.57971i	−0.160874	−	0.116882i
$939$	−1.66312	+	1.20833i	−0.0542738	+	0.0394323i
$940$	2.09017	−	6.43288i	0.0681738	−	0.209817i
$941$	−5.49342	+	16.9070i	−0.179080	+	0.551153i	−0.999796	−	0.0201837i	$-0.993575\pi$
$941$	−5.49342	+	16.9070i	−0.179080	+	0.551153i	0.820716	+	0.571337i	$0.193575\pi$
$942$	8.09017	−	5.87785i	0.263592	−	0.191511i
$943$	59.0689	+	42.9161i	1.92355	+	1.39754i
$944$	−1.11803	−	3.44095i	−0.0363889	−	0.111994i
$945$	3.47214			0.112949
$946$	−7.80902	+	13.1760i	−0.253893	+	0.428390i
$947$	−40.3394			−1.31085			−0.655427	−	0.755258i	$-0.727511\pi$
$947$	−40.3394			−1.31085			−0.655427	+	0.755258i	$0.727511\pi$
$948$	0.326238	+	1.00406i	0.0105957	+	0.0326103i
$949$	18.3262	+	13.3148i	0.594895	+	0.432216i
$950$	−0.309017	+	0.224514i	−0.0100258	+	0.00728420i
$951$	−3.41641	+	10.5146i	−0.110785	+	0.340960i
$952$	0.500000	−	1.53884i	0.0162051	−	0.0498741i
$953$	−27.3885	+	19.8989i	−0.887202	+	0.644590i	−0.935147	−	0.354260i	$-0.884733\pi$
$953$	−27.3885	+	19.8989i	−0.887202	+	0.644590i	0.0479450	+	0.998850i	$0.484733\pi$
$954$	13.7082	+	9.95959i	0.443819	+	0.322454i
$955$	0.618034	+	1.90211i	0.0199991	+	0.0615509i
$956$	17.7082			0.572724
$957$	5.41641	+	6.15537i	0.175088	+	0.198975i
$958$	17.1246			0.553271
$959$	−1.89919	−	5.84510i	−0.0613279	−	0.188748i
$960$	0.500000	+	0.363271i	0.0161374	+	0.0117245i
$961$	8.89919	−	6.46564i	0.287071	−	0.208569i
$962$	15.7082	−	48.3449i	0.506453	−	1.55870i
$963$	2.50000	−	7.69421i	0.0805614	−	0.247942i
$964$	5.78115	−	4.20025i	0.186198	−	0.135281i
$965$	−10.0902	−	7.33094i	−0.324814	−	0.235991i
$966$	1.61803	+	4.97980i	0.0520594	+	0.160222i
$967$	−26.0000			−0.836104			−0.418052	−	0.908423i	$-0.637287\pi$
$967$	−26.0000			−0.836104			−0.418052	+	0.908423i	$0.637287\pi$
$968$	−7.54508	+	8.00448i	−0.242508	+	0.257274i
$969$	0.381966			0.0122705
$970$	−3.33688	−	10.2699i	−0.107141	−	0.329745i
$971$	−33.4164	−	24.2784i	−1.07238	−	0.779132i	−0.0960444	−	0.995377i	$-0.530619\pi$
$971$	−33.4164	−	24.2784i	−1.07238	−	0.779132i	−0.976339	+	0.216245i	$0.930619\pi$
$972$	−11.2812	+	8.19624i	−0.361843	+	0.262894i
$973$	−3.23607	+	9.95959i	−0.103744	+	0.319290i
$974$	−11.6738	+	35.9281i	−0.374051	+	1.15121i
$975$	2.61803	−	1.90211i	0.0838442	−	0.0609164i
$976$	6.47214	+	4.70228i	0.207168	+	0.150516i
$977$	12.5066	+	38.4913i	0.400121	+	1.23145i	0.924901	+	0.380208i	$0.124147\pi$
$977$	12.5066	+	38.4913i	0.400121	+	1.23145i	−0.524780	+	0.851238i	$0.675853\pi$
$978$	12.5967			0.402800
$979$	21.5902	+	24.5357i	0.690025	+	0.784165i
$980$	−1.00000			−0.0319438
$981$	9.85410	+	30.3278i	0.314617	+	0.968292i
$982$	−30.6803	−	22.2906i	−0.979049	−	0.711321i
$983$	−21.6525	+	15.7314i	−0.690607	+	0.501755i	−0.876860	−	0.480747i	$-0.840366\pi$
$983$	−21.6525	+	15.7314i	−0.690607	+	0.501755i	0.186253	+	0.982502i	$0.440366\pi$
$984$	−1.64590	+	5.06555i	−0.0524693	+	0.161484i
$985$	−6.61803	+	20.3682i	−0.210868	+	0.648985i
$986$	−5.23607	+	3.80423i	−0.166750	+	0.121151i
$987$	3.38197	+	2.45714i	0.107649	+	0.0782117i
$988$	0.618034	+	1.90211i	0.0196623	+	0.0605143i
$989$	39.1246			1.24409
$990$	4.42705	−	7.46969i	0.140701	−	0.237402i
$991$	−56.7639			−1.80317			−0.901583	−	0.432606i	$-0.857594\pi$
$991$	−56.7639			−1.80317			−0.901583	+	0.432606i	$0.857594\pi$
$992$	1.38197	+	4.25325i	0.0438775	+	0.135041i
$993$	−6.16312	−	4.47777i	−0.195581	−	0.142098i
$994$	2.00000	−	1.45309i	0.0634361	−	0.0460891i
$995$	0.381966	−	1.17557i	0.0121091	−	0.0372681i
$996$	2.11803	−	6.51864i	0.0671125	−	0.206551i
$997$	−42.9787	+	31.2259i	−1.36115	+	0.988933i	−0.362779	+	0.931875i	$0.618172\pi$
$997$	−42.9787	+	31.2259i	−1.36115	+	0.988933i	−0.998371	+	0.0570577i	$0.981828\pi$
$998$	0.500000	+	0.363271i	0.0158272	+	0.0114992i
$999$	−10.4164	−	32.0584i	−0.329561	−	1.01428i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.n.c.71.1	✓	4
11.3	even	5		8470.2.a.bk.1.2		2
11.8	odd	10		8470.2.a.bx.1.2		2
11.9	even	5	inner	770.2.n.c.141.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.c.71.1	✓	4	1.1	even	1	trivial
770.2.n.c.141.1	yes	4	11.9	even	5	inner
8470.2.a.bk.1.2		2	11.3	even	5
8470.2.a.bx.1.2		2	11.8	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)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.500000 - 0.363271i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(-0.190983 + 0.587785i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.809017 - 2.48990i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.500000 - 0.363271i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(-0.190983 + 0.587785i) q^{6} +(-0.809017 + 0.587785i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.809017 - 2.48990i) q^{9} +1.00000 q^{10} +(2.19098 + 2.48990i) q^{11} +0.618034 q^{12} +(-1.61803 - 4.97980i) q^{13} +(0.809017 + 0.587785i) q^{14} +(0.500000 - 0.363271i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.500000 + 1.53884i) q^{17} +(-2.11803 + 1.53884i) q^{18} +(0.309017 + 0.224514i) q^{19} +(-0.309017 - 0.951057i) q^{20} +0.618034 q^{21} +(1.69098 - 2.85317i) q^{22} -8.47214 q^{23} +(-0.190983 - 0.587785i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-4.23607 + 3.07768i) q^{26} +(-1.07295 + 3.30220i) q^{27} +(0.309017 - 0.951057i) q^{28} +(-3.23607 + 2.35114i) q^{29} +(-0.500000 - 0.363271i) q^{30} +(-1.38197 - 4.25325i) q^{31} -1.00000 q^{32} +(-0.190983 - 2.04087i) q^{33} +1.61803 q^{34} +(-0.309017 - 0.951057i) q^{35} +(2.11803 + 1.53884i) q^{36} +(-7.85410 + 5.70634i) q^{37} +(0.118034 - 0.363271i) q^{38} +(-1.00000 + 3.07768i) q^{39} +(-0.809017 + 0.587785i) q^{40} +(-6.97214 - 5.06555i) q^{41} +(-0.190983 - 0.587785i) q^{42} -4.61803 q^{43} +(-3.23607 - 0.726543i) q^{44} +2.61803 q^{45} +(2.61803 + 8.05748i) q^{46} +(5.47214 + 3.97574i) q^{47} +(-0.500000 + 0.363271i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(0.809017 - 0.587785i) q^{51} +(4.23607 + 3.07768i) q^{52} +(-2.00000 - 6.15537i) q^{53} +3.47214 q^{54} +(-3.04508 + 1.31433i) q^{55} -1.00000 q^{56} +(-0.0729490 - 0.224514i) q^{57} +(3.23607 + 2.35114i) q^{58} +(2.92705 - 2.12663i) q^{59} +(-0.190983 + 0.587785i) q^{60} +(-2.47214 + 7.60845i) q^{61} +(-3.61803 + 2.62866i) q^{62} +(2.11803 + 1.53884i) q^{63} +(0.309017 + 0.951057i) q^{64} +5.23607 q^{65} +(-1.88197 + 0.812299i) q^{66} -6.09017 q^{67} +(-0.500000 - 1.53884i) q^{68} +(4.23607 + 3.07768i) q^{69} +(-0.809017 + 0.587785i) q^{70} +(0.763932 - 2.35114i) q^{71} +(0.809017 - 2.48990i) q^{72} +(-3.50000 + 2.54290i) q^{73} +(7.85410 + 5.70634i) q^{74} +(0.190983 + 0.587785i) q^{75} -0.381966 q^{76} +(-3.23607 - 0.726543i) q^{77} +3.23607 q^{78} +(0.527864 + 1.62460i) q^{79} +(0.809017 + 0.587785i) q^{80} +(-4.61803 + 3.35520i) q^{81} +(-2.66312 + 8.19624i) q^{82} +(3.42705 - 10.5474i) q^{83} +(-0.500000 + 0.363271i) q^{84} +(-1.30902 - 0.951057i) q^{85} +(1.42705 + 4.39201i) q^{86} +2.47214 q^{87} +(0.309017 + 3.30220i) q^{88} +9.85410 q^{89} +(-0.809017 - 2.48990i) q^{90} +(4.23607 + 3.07768i) q^{91} +(6.85410 - 4.97980i) q^{92} +(-0.854102 + 2.62866i) q^{93} +(2.09017 - 6.43288i) q^{94} +(-0.309017 + 0.224514i) q^{95} +(0.500000 + 0.363271i) q^{96} +(-3.33688 - 10.2699i) q^{97} -1.00000 q^{98} +(4.42705 - 7.46969i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - 2 q^{3} - q^{4} + q^{5} - 3 q^{6} - q^{7} + q^{8} - q^{9}+O(q^{10}) \) 4 * q + q^2 - 2 * q^3 - q^4 + q^5 - 3 * q^6 - q^7 + q^8 - q^9	\( 4 q + q^{2} - 2 q^{3} - q^{4} + q^{5} - 3 q^{6} - q^{7} + q^{8} - q^{9} + 4 q^{10} + 11 q^{11} - 2 q^{12} - 2 q^{13} + q^{14} + 2 q^{15} - q^{16} - 2 q^{17} - 4 q^{18} - q^{19} + q^{20} - 2 q^{21} + 9 q^{22} - 16 q^{23} - 3 q^{24} - q^{25} - 8 q^{26} - 11 q^{27} - q^{28} - 4 q^{29} - 2 q^{30} - 10 q^{31} - 4 q^{32} - 3 q^{33} + 2 q^{34} + q^{35} + 4 q^{36} - 18 q^{37} - 4 q^{38} - 4 q^{39} - q^{40} - 10 q^{41} - 3 q^{42} - 14 q^{43} - 4 q^{44} + 6 q^{45} + 6 q^{46} + 4 q^{47} - 2 q^{48} - q^{49} + q^{50} + q^{51} + 8 q^{52} - 8 q^{53} - 4 q^{54} - q^{55} - 4 q^{56} - 7 q^{57} + 4 q^{58} + 5 q^{59} - 3 q^{60} + 8 q^{61} - 10 q^{62} + 4 q^{63} - q^{64} + 12 q^{65} - 12 q^{66} - 2 q^{67} - 2 q^{68} + 8 q^{69} - q^{70} + 12 q^{71} + q^{72} - 14 q^{73} + 18 q^{74} + 3 q^{75} - 6 q^{76} - 4 q^{77} + 4 q^{78} + 20 q^{79} + q^{80} - 14 q^{81} + 5 q^{82} + 7 q^{83} - 2 q^{84} - 3 q^{85} - q^{86} - 8 q^{87} - q^{88} + 26 q^{89} - q^{90} + 8 q^{91} + 14 q^{92} + 10 q^{93} - 14 q^{94} + q^{95} + 2 q^{96} - 29 q^{97} - 4 q^{98} + 11 q^{99}+O(q^{100}) \) 4 * q + q^2 - 2 * q^3 - q^4 + q^5 - 3 * q^6 - q^7 + q^8 - q^9 + 4 * q^10 + 11 * q^11 - 2 * q^12 - 2 * q^13 + q^14 + 2 * q^15 - q^16 - 2 * q^17 - 4 * q^18 - q^19 + q^20 - 2 * q^21 + 9 * q^22 - 16 * q^23 - 3 * q^24 - q^25 - 8 * q^26 - 11 * q^27 - q^28 - 4 * q^29 - 2 * q^30 - 10 * q^31 - 4 * q^32 - 3 * q^33 + 2 * q^34 + q^35 + 4 * q^36 - 18 * q^37 - 4 * q^38 - 4 * q^39 - q^40 - 10 * q^41 - 3 * q^42 - 14 * q^43 - 4 * q^44 + 6 * q^45 + 6 * q^46 + 4 * q^47 - 2 * q^48 - q^49 + q^50 + q^51 + 8 * q^52 - 8 * q^53 - 4 * q^54 - q^55 - 4 * q^56 - 7 * q^57 + 4 * q^58 + 5 * q^59 - 3 * q^60 + 8 * q^61 - 10 * q^62 + 4 * q^63 - q^64 + 12 * q^65 - 12 * q^66 - 2 * q^67 - 2 * q^68 + 8 * q^69 - q^70 + 12 * q^71 + q^72 - 14 * q^73 + 18 * q^74 + 3 * q^75 - 6 * q^76 - 4 * q^77 + 4 * q^78 + 20 * q^79 + q^80 - 14 * q^81 + 5 * q^82 + 7 * q^83 - 2 * q^84 - 3 * q^85 - q^86 - 8 * q^87 - q^88 + 26 * q^89 - q^90 + 8 * q^91 + 14 * q^92 + 10 * q^93 - 14 * q^94 + q^95 + 2 * q^96 - 29 * q^97 - 4 * q^98 + 11 * q^99

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