LMFDB - Embedded newform 770.2.n.d.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.d.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} +(0.809017 - 3.21644i) q^{11} -0.618034 q^{12} +(-0.236068 - 0.726543i) q^{13} +(0.809017 + 0.587785i) q^{14} +(-0.500000 + 0.363271i) q^{15} +(0.309017 - 0.951057i) q^{16} +(0.118034 - 0.363271i) q^{17} +(-2.11803 + 1.53884i) q^{18} +(-0.927051 - 0.673542i) q^{19} +(-0.309017 - 0.951057i) q^{20} -0.618034 q^{21} +(-3.30902 + 0.224514i) q^{22} +8.47214 q^{23} +(0.190983 + 0.587785i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-0.618034 + 0.449028i) q^{26} +(1.07295 - 3.30220i) q^{27} +(0.309017 - 0.951057i) q^{28} +(3.61803 - 2.62866i) q^{29} +(0.500000 + 0.363271i) q^{30} +(-2.00000 - 6.15537i) q^{31} -1.00000 q^{32} +(1.57295 - 1.31433i) q^{33} -0.381966 q^{34} +(-0.309017 - 0.951057i) q^{35} +(2.11803 + 1.53884i) q^{36} +(5.47214 - 3.97574i) q^{37} +(-0.354102 + 1.08981i) q^{38} +(0.145898 - 0.449028i) q^{39} +(-0.809017 + 0.587785i) q^{40} +(3.11803 + 2.26538i) q^{41} +(0.190983 + 0.587785i) q^{42} +9.09017 q^{43} +(1.23607 + 3.07768i) q^{44} +2.61803 q^{45} +(-2.61803 - 8.05748i) q^{46} +(-7.47214 - 5.42882i) q^{47} +(0.500000 - 0.363271i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(0.190983 - 0.138757i) q^{51} +(0.618034 + 0.449028i) q^{52} +(-2.23607 - 6.88191i) q^{53} -3.47214 q^{54} +(2.80902 + 1.76336i) q^{55} -1.00000 q^{56} +(-0.218847 - 0.673542i) q^{57} +(-3.61803 - 2.62866i) q^{58} +(-8.78115 + 6.37988i) q^{59} +(0.190983 - 0.587785i) q^{60} +(0.0901699 - 0.277515i) q^{61} +(-5.23607 + 3.80423i) q^{62} +(2.11803 + 1.53884i) q^{63} +(0.309017 + 0.951057i) q^{64} +0.763932 q^{65} +(-1.73607 - 1.08981i) q^{66} -5.61803 q^{67} +(0.118034 + 0.363271i) q^{68} +(4.23607 + 3.07768i) q^{69} +(-0.809017 + 0.587785i) q^{70} +(-2.14590 + 6.60440i) q^{71} +(0.809017 - 2.48990i) q^{72} +(3.11803 - 2.26538i) q^{73} +(-5.47214 - 3.97574i) q^{74} +(-0.190983 - 0.587785i) q^{75} +1.14590 q^{76} +(1.23607 + 3.07768i) q^{77} -0.472136 q^{78} +(1.23607 + 3.80423i) q^{79} +(0.809017 + 0.587785i) q^{80} +(-4.61803 + 3.35520i) q^{81} +(1.19098 - 3.66547i) q^{82} +(-0.663119 + 2.04087i) q^{83} +(0.500000 - 0.363271i) q^{84} +(0.309017 + 0.224514i) q^{85} +(-2.80902 - 8.64527i) q^{86} +2.76393 q^{87} +(2.54508 - 2.12663i) q^{88} -8.14590 q^{89} +(-0.809017 - 2.48990i) q^{90} +(0.618034 + 0.449028i) q^{91} +(-6.85410 + 4.97980i) q^{92} +(1.23607 - 3.80423i) q^{93} +(-2.85410 + 8.78402i) q^{94} +(0.927051 - 0.673542i) q^{95} +(-0.500000 - 0.363271i) q^{96} +(-3.28115 - 10.0984i) q^{97} -1.00000 q^{98} +(-8.66312 + 0.587785i) 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	\( 4 q + q^{2} + 2 q^{3} - q^{4} + q^{5} + 3 q^{6} - q^{7} + q^{8} - q^{9} + 4 q^{10} + q^{11} + 2 q^{12} + 8 q^{13} + q^{14} - 2 q^{15} - q^{16} - 4 q^{17} - 4 q^{18} + 3 q^{19} + q^{20} + 2 q^{21} - 11 q^{22} + 16 q^{23} + 3 q^{24} - q^{25} + 2 q^{26} + 11 q^{27} - q^{28} + 10 q^{29} + 2 q^{30} - 8 q^{31} - 4 q^{32} + 13 q^{33} - 6 q^{34} + q^{35} + 4 q^{36} + 4 q^{37} + 12 q^{38} + 14 q^{39} - q^{40} + 8 q^{41} + 3 q^{42} + 14 q^{43} - 4 q^{44} + 6 q^{45} - 6 q^{46} - 12 q^{47} + 2 q^{48} - q^{49} + q^{50} + 3 q^{51} - 2 q^{52} + 4 q^{54} + 9 q^{55} - 4 q^{56} - 21 q^{57} - 10 q^{58} - 15 q^{59} + 3 q^{60} - 22 q^{61} - 12 q^{62} + 4 q^{63} - q^{64} + 12 q^{65} + 2 q^{66} - 18 q^{67} - 4 q^{68} + 8 q^{69} - q^{70} - 22 q^{71} + q^{72} + 8 q^{73} - 4 q^{74} - 3 q^{75} + 18 q^{76} - 4 q^{77} + 16 q^{78} - 4 q^{79} + q^{80} - 14 q^{81} + 7 q^{82} + 13 q^{83} + 2 q^{84} - q^{85} - 9 q^{86} + 20 q^{87} - q^{88} - 46 q^{89} - q^{90} - 2 q^{91} - 14 q^{92} - 4 q^{93} + 2 q^{94} - 3 q^{95} - 2 q^{96} + 7 q^{97} - 4 q^{98} - 19 q^{99}+O(q^{100}) \) 4 * q + q^2 + 2 * q^3 - q^4 + q^5 + 3 * q^6 - q^7 + q^8 - q^9 + 4 * q^10 + q^11 + 2 * q^12 + 8 * q^13 + q^14 - 2 * q^15 - q^16 - 4 * q^17 - 4 * q^18 + 3 * q^19 + q^20 + 2 * q^21 - 11 * q^22 + 16 * q^23 + 3 * q^24 - q^25 + 2 * q^26 + 11 * q^27 - q^28 + 10 * q^29 + 2 * q^30 - 8 * q^31 - 4 * q^32 + 13 * q^33 - 6 * q^34 + q^35 + 4 * q^36 + 4 * q^37 + 12 * q^38 + 14 * q^39 - q^40 + 8 * q^41 + 3 * q^42 + 14 * q^43 - 4 * q^44 + 6 * q^45 - 6 * q^46 - 12 * q^47 + 2 * q^48 - q^49 + q^50 + 3 * q^51 - 2 * q^52 + 4 * q^54 + 9 * q^55 - 4 * q^56 - 21 * q^57 - 10 * q^58 - 15 * q^59 + 3 * q^60 - 22 * q^61 - 12 * q^62 + 4 * q^63 - q^64 + 12 * q^65 + 2 * q^66 - 18 * q^67 - 4 * q^68 + 8 * q^69 - q^70 - 22 * q^71 + q^72 + 8 * q^73 - 4 * q^74 - 3 * q^75 + 18 * q^76 - 4 * q^77 + 16 * q^78 - 4 * q^79 + q^80 - 14 * q^81 + 7 * q^82 + 13 * q^83 + 2 * q^84 - q^85 - 9 * q^86 + 20 * q^87 - q^88 - 46 * q^89 - q^90 - 2 * q^91 - 14 * q^92 - 4 * q^93 + 2 * q^94 - 3 * q^95 - 2 * q^96 + 7 * q^97 - 4 * q^98 - 19 * 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	0.722692	−	0.691170i	$-0.242904\pi$
$3$	0.500000	+	0.363271i	0.288675	+	0.209735i	−0.434017	+	0.900905i	$0.642904\pi$
$4$	−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
$11$	0.809017	−	3.21644i	0.243928	−	0.969793i
$11$	0.809017	−	3.21644i	0.243928	−	0.969793i
$12$	−0.618034			−0.178411
$13$	−0.236068	−	0.726543i	−0.0654735	−	0.201507i	0.912968	−	0.408031i	$-0.133785\pi$
$13$	−0.236068	−	0.726543i	−0.0654735	−	0.201507i	−0.978441	+	0.206525i	$0.933785\pi$
$14$	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
$17$	0.118034	−	0.363271i	0.0286274	−	0.0881062i	−0.935722	−	0.352738i	$-0.885251\pi$
$17$	0.118034	−	0.363271i	0.0286274	−	0.0881062i	0.964349	+	0.264632i	$0.0852506\pi$
$18$	−2.11803	+	1.53884i	−0.499225	+	0.362708i
$19$	−0.927051	−	0.673542i	−0.212680	−	0.154521i	0.476345	−	0.879258i	$-0.341961\pi$
$19$	−0.927051	−	0.673542i	−0.212680	−	0.154521i	−0.689025	+	0.724737i	$0.741961\pi$
$20$	−0.309017	−	0.951057i	−0.0690983	−	0.212663i
$21$	−0.618034			−0.134866
$22$	−3.30902	+	0.224514i	−0.705485	+	0.0478665i
$23$	8.47214			1.76656			0.883281	−	0.468844i	$-0.155329\pi$
$23$	8.47214			1.76656			0.883281	+	0.468844i	$0.155329\pi$
$24$	0.190983	+	0.587785i	0.0389842	+	0.119981i
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	−0.618034	+	0.449028i	−0.121206	+	0.0880616i
$27$	1.07295	−	3.30220i	0.206489	−	0.635508i
$28$	0.309017	−	0.951057i	0.0583987	−	0.179733i
$29$	3.61803	−	2.62866i	0.671852	−	0.488129i	−0.198793	−	0.980042i	$-0.563702\pi$
$29$	3.61803	−	2.62866i	0.671852	−	0.488129i	0.870645	+	0.491912i	$0.163702\pi$
$30$	0.500000	+	0.363271i	0.0912871	+	0.0663240i
$31$	−2.00000	−	6.15537i	−0.359211	−	1.10554i	−0.953528	−	0.301306i	$-0.902578\pi$
$31$	−2.00000	−	6.15537i	−0.359211	−	1.10554i	0.594317	−	0.804231i	$-0.297422\pi$
$32$	−1.00000			−0.176777
$33$	1.57295	−	1.31433i	0.273815	−	0.228795i
$34$	−0.381966			−0.0655066
$35$	−0.309017	−	0.951057i	−0.0522334	−	0.160758i
$36$	2.11803	+	1.53884i	0.353006	+	0.256474i
$37$	5.47214	−	3.97574i	0.899614	−	0.653608i	−0.0387531	−	0.999249i	$-0.512339\pi$
$37$	5.47214	−	3.97574i	0.899614	−	0.653608i	0.938367	+	0.345641i	$0.112339\pi$
$38$	−0.354102	+	1.08981i	−0.0574429	+	0.176791i
$39$	0.145898	−	0.449028i	0.0233624	−	0.0719020i
$40$	−0.809017	+	0.587785i	−0.127917	+	0.0929370i
$41$	3.11803	+	2.26538i	0.486955	+	0.353794i	0.804012	−	0.594613i	$-0.202695\pi$
$41$	3.11803	+	2.26538i	0.486955	+	0.353794i	−0.317057	+	0.948406i	$0.602695\pi$
$42$	0.190983	+	0.587785i	0.0294693	+	0.0906972i
$43$	9.09017			1.38624			0.693119	−	0.720823i	$-0.256236\pi$
$43$	9.09017			1.38624			0.693119	+	0.720823i	$0.256236\pi$
$44$	1.23607	+	3.07768i	0.186344	+	0.463978i
$45$	2.61803			0.390273
$46$	−2.61803	−	8.05748i	−0.386008	−	1.18801i
$47$	−7.47214	−	5.42882i	−1.08992	−	0.791875i	−0.110537	−	0.993872i	$-0.535257\pi$
$47$	−7.47214	−	5.42882i	−1.08992	−	0.791875i	−0.979386	+	0.201997i	$0.935257\pi$
$48$	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
$51$	0.190983	−	0.138757i	0.0267430	−	0.0194299i
$52$	0.618034	+	0.449028i	0.0857059	+	0.0622690i
$53$	−2.23607	−	6.88191i	−0.307148	−	0.945303i	−0.978867	−	0.204497i	$-0.934444\pi$
$53$	−2.23607	−	6.88191i	−0.307148	−	0.945303i	0.671720	−	0.740806i	$-0.265556\pi$
$54$	−3.47214			−0.472498
$55$	2.80902	+	1.76336i	0.378768	+	0.237771i
$56$	−1.00000			−0.133631
$57$	−0.218847	−	0.673542i	−0.0289870	−	0.0892128i
$58$	−3.61803	−	2.62866i	−0.475071	−	0.345159i
$59$	−8.78115	+	6.37988i	−1.14321	+	0.830590i	−0.987563	−	0.157223i	$-0.949746\pi$
$59$	−8.78115	+	6.37988i	−1.14321	+	0.830590i	−0.155646	+	0.987813i	$0.549746\pi$
$60$	0.190983	−	0.587785i	0.0246558	−	0.0758827i
$61$	0.0901699	−	0.277515i	0.0115451	−	0.0355321i	−0.945118	−	0.326729i	$-0.894054\pi$
$61$	0.0901699	−	0.277515i	0.0115451	−	0.0355321i	0.956663	+	0.291197i	$0.0940535\pi$
$62$	−5.23607	+	3.80423i	−0.664981	+	0.483137i
$63$	2.11803	+	1.53884i	0.266847	+	0.193876i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	0.763932			0.0947541
$66$	−1.73607	−	1.08981i	−0.213695	−	0.134147i
$67$	−5.61803			−0.686352			−0.343176	−	0.939271i	$-0.611503\pi$
$67$	−5.61803			−0.686352			−0.343176	+	0.939271i	$0.611503\pi$
$68$	0.118034	+	0.363271i	0.0143137	+	0.0440531i
$69$	4.23607	+	3.07768i	0.509963	+	0.370510i
$70$	−0.809017	+	0.587785i	−0.0966960	+	0.0702538i
$71$	−2.14590	+	6.60440i	−0.254671	+	0.783797i	0.739223	+	0.673461i	$0.235193\pi$
$71$	−2.14590	+	6.60440i	−0.254671	+	0.783797i	−0.993894	+	0.110337i	$0.964807\pi$
$72$	0.809017	−	2.48990i	0.0953436	−	0.293437i
$73$	3.11803	−	2.26538i	0.364938	−	0.265143i	−0.390171	−	0.920743i	$-0.627584\pi$
$73$	3.11803	−	2.26538i	0.364938	−	0.265143i	0.755109	+	0.655599i	$0.227584\pi$
$74$	−5.47214	−	3.97574i	−0.636123	−	0.462170i
$75$	−0.190983	−	0.587785i	−0.0220528	−	0.0678716i
$76$	1.14590			0.131444
$77$	1.23607	+	3.07768i	0.140863	+	0.350735i
$78$	−0.472136			−0.0534589
$79$	1.23607	+	3.80423i	0.139069	+	0.428009i	0.996201	−	0.0870877i	$-0.0277560\pi$
$79$	1.23607	+	3.80423i	0.139069	+	0.428009i	−0.857132	+	0.515097i	$0.827756\pi$
$80$	0.809017	+	0.587785i	0.0904508	+	0.0657164i
$81$	−4.61803	+	3.35520i	−0.513115	+	0.372800i
$82$	1.19098	−	3.66547i	0.131522	−	0.404783i
$83$	−0.663119	+	2.04087i	−0.0727868	+	0.224015i	−0.980831	−	0.194859i	$-0.937575\pi$
$83$	−0.663119	+	2.04087i	−0.0727868	+	0.224015i	0.908044	+	0.418874i	$0.137575\pi$
$84$	0.500000	−	0.363271i	0.0545545	−	0.0396361i
$85$	0.309017	+	0.224514i	0.0335176	+	0.0243520i
$86$	−2.80902	−	8.64527i	−0.302904	−	0.932243i
$87$	2.76393			0.296325
$88$	2.54508	−	2.12663i	0.271307	−	0.226699i
$89$	−8.14590			−0.863463			−0.431732	−	0.902002i	$-0.642097\pi$
$89$	−8.14590			−0.863463			−0.431732	+	0.902002i	$0.642097\pi$
$90$	−0.809017	−	2.48990i	−0.0852779	−	0.262458i
$91$	0.618034	+	0.449028i	0.0647876	+	0.0470709i
$92$	−6.85410	+	4.97980i	−0.714590	+	0.519180i
$93$	1.23607	−	3.80423i	0.128174	−	0.394480i
$94$	−2.85410	+	8.78402i	−0.294378	+	0.906003i
$95$	0.927051	−	0.673542i	0.0951134	−	0.0691039i
$96$	−0.500000	−	0.363271i	−0.0510310	−	0.0370762i
$97$	−3.28115	−	10.0984i	−0.333151	−	1.02533i	−0.967626	−	0.252389i	$-0.918784\pi$
$97$	−3.28115	−	10.0984i	−0.333151	−	1.02533i	0.634475	−	0.772943i	$-0.281216\pi$
$98$	−1.00000			−0.101015
$99$	−8.66312	+	0.587785i	−0.870676	+	0.0590746i
$100$	1.00000			0.100000
$101$	0.909830	+	2.80017i	0.0905315	+	0.278627i	0.986063	−	0.166370i	$-0.0532046\pi$
$101$	0.909830	+	2.80017i	0.0905315	+	0.278627i	−0.895532	+	0.444997i	$0.853205\pi$
$102$	−0.190983	−	0.138757i	−0.0189101	−	0.0137390i
$103$	4.85410	−	3.52671i	0.478289	−	0.347497i	−0.322374	−	0.946612i	$-0.604481\pi$
$103$	4.85410	−	3.52671i	0.478289	−	0.347497i	0.800663	+	0.599115i	$0.204481\pi$
$104$	0.236068	−	0.726543i	0.0231484	−	0.0712434i
$105$	0.190983	−	0.587785i	0.0186380	−	0.0573620i
$106$	−5.85410	+	4.25325i	−0.568601	+	0.413113i
$107$	3.11803	+	2.26538i	0.301432	+	0.219003i	0.728211	−	0.685353i	$-0.240352\pi$
$107$	3.11803	+	2.26538i	0.301432	+	0.219003i	−0.426780	+	0.904356i	$0.640352\pi$
$108$	1.07295	+	3.30220i	0.103245	+	0.317754i
$109$	4.00000			0.383131			0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000			0.383131			0.191565	+	0.981480i	$0.438644\pi$
$110$	0.809017	−	3.21644i	0.0771367	−	0.306676i
$111$	4.18034			0.396780
$112$	0.309017	+	0.951057i	0.0291994	+	0.0898664i
$113$	9.16312	+	6.65740i	0.861994	+	0.626275i	0.928427	−	0.371516i	$-0.121162\pi$
$113$	9.16312	+	6.65740i	0.861994	+	0.626275i	−0.0664329	+	0.997791i	$0.521162\pi$
$114$	−0.572949	+	0.416272i	−0.0536616	+	0.0389874i
$115$	−2.61803	+	8.05748i	−0.244133	+	0.751364i
$116$	−1.38197	+	4.25325i	−0.128312	+	0.394905i
$117$	−1.61803	+	1.17557i	−0.149587	+	0.108682i
$118$	8.78115	+	6.37988i	0.808371	+	0.587316i
$119$	0.118034	+	0.363271i	0.0108202	+	0.0333010i
$120$	−0.618034			−0.0564185
$121$	−9.69098	−	5.20431i	−0.880998	−	0.473119i
$122$	−0.291796			−0.0264180
$123$	0.736068	+	2.26538i	0.0663690	+	0.204263i
$124$	5.23607	+	3.80423i	0.470213	+	0.341630i
$125$	0.809017	−	0.587785i	0.0723607	−	0.0525731i
$126$	0.809017	−	2.48990i	0.0720730	−	0.221818i
$127$	1.09017	−	3.35520i	0.0967369	−	0.297726i	−0.890966	−	0.454071i	$-0.849971\pi$
$127$	1.09017	−	3.35520i	0.0967369	−	0.297726i	0.987702	+	0.156345i	$0.0499713\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	4.54508	+	3.30220i	0.400172	+	0.290742i
$130$	−0.236068	−	0.726543i	−0.0207045	−	0.0637220i
$131$	−6.09017			−0.532101			−0.266050	−	0.963959i	$-0.585719\pi$
$131$	−6.09017			−0.532101			−0.266050	+	0.963959i	$0.585719\pi$
$132$	−0.500000	+	1.98787i	−0.0435194	+	0.173022i
$133$	1.14590			0.0993620
$134$	1.73607	+	5.34307i	0.149973	+	0.461571i
$135$	2.80902	+	2.04087i	0.241762	+	0.175650i
$136$	0.309017	−	0.224514i	0.0264980	−	0.0192519i
$137$	−0.572949	+	1.76336i	−0.0489503	+	0.150654i	−0.972544	−	0.232719i	$-0.925238\pi$
$137$	−0.572949	+	1.76336i	−0.0489503	+	0.150654i	0.923594	+	0.383373i	$0.125238\pi$
$138$	1.61803	−	4.97980i	0.137736	−	0.423908i
$139$	−10.4721	+	7.60845i	−0.888235	+	0.645340i	−0.935417	−	0.353546i	$-0.884976\pi$
$139$	−10.4721	+	7.60845i	−0.888235	+	0.645340i	0.0471822	+	0.998886i	$0.484976\pi$
$140$	0.809017	+	0.587785i	0.0683744	+	0.0496769i
$141$	−1.76393	−	5.42882i	−0.148550	−	0.457190i
$142$	6.94427			0.582750
$143$	−2.52786	+	0.171513i	−0.211391	+	0.0143427i
$144$	−2.61803			−0.218169
$145$	1.38197	+	4.25325i	0.114766	+	0.353214i
$146$	−3.11803	−	2.26538i	−0.258050	−	0.187485i
$147$	0.500000	−	0.363271i	0.0412393	−	0.0299621i
$148$	−2.09017	+	6.43288i	−0.171811	+	0.528780i
$149$	−0.527864	+	1.62460i	−0.0432443	+	0.133092i	−0.970348	−	0.241713i	$-0.922291\pi$
$149$	−0.527864	+	1.62460i	−0.0432443	+	0.133092i	0.927103	+	0.374806i	$0.122291\pi$
$150$	−0.500000	+	0.363271i	−0.0408248	+	0.0296610i
$151$	−7.70820	−	5.60034i	−0.627285	−	0.455749i	0.228174	−	0.973620i	$-0.426725\pi$
$151$	−7.70820	−	5.60034i	−0.627285	−	0.455749i	−0.855458	+	0.517871i	$0.826725\pi$
$152$	−0.354102	−	1.08981i	−0.0287215	−	0.0883956i
$153$	−1.00000			−0.0808452
$154$	2.54508	−	2.12663i	0.205089	−	0.171368i
$155$	6.47214			0.519854
$156$	0.145898	+	0.449028i	0.0116812	+	0.0359510i
$157$	−2.38197	−	1.73060i	−0.190102	−	0.138117i	0.488664	−	0.872472i	$-0.337485\pi$
$157$	−2.38197	−	1.73060i	−0.190102	−	0.138117i	−0.678765	+	0.734355i	$0.737485\pi$
$158$	3.23607	−	2.35114i	0.257448	−	0.187047i
$159$	1.38197	−	4.25325i	0.109597	−	0.337305i
$160$	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
$163$	−0.555728	−	1.71036i	−0.0435280	−	0.133965i	0.926931	−	0.375232i	$-0.122437\pi$
$163$	−0.555728	−	1.71036i	−0.0435280	−	0.133965i	−0.970459	+	0.241267i	$0.922437\pi$
$164$	−3.85410			−0.300955
$165$	0.763932	+	1.90211i	0.0594720	+	0.148079i
$166$	2.14590			0.166554
$167$	6.70820	+	20.6457i	0.519096	+	1.59761i	0.775703	+	0.631098i	$0.217396\pi$
$167$	6.70820	+	20.6457i	0.519096	+	1.59761i	−0.256606	+	0.966516i	$0.582604\pi$
$168$	−0.500000	−	0.363271i	−0.0385758	−	0.0280270i
$169$	10.0451	−	7.29818i	0.772699	−	0.561399i
$170$	0.118034	−	0.363271i	0.00905279	−	0.0278616i
$171$	−0.927051	+	2.85317i	−0.0708934	+	0.218187i
$172$	−7.35410	+	5.34307i	−0.560745	+	0.407405i
$173$	12.8541	+	9.33905i	0.977279	+	0.710035i	0.957099	−	0.289761i	$-0.0935760\pi$
$173$	12.8541	+	9.33905i	0.977279	+	0.710035i	0.0201804	+	0.999796i	$0.493576\pi$
$174$	−0.854102	−	2.62866i	−0.0647493	−	0.199278i
$175$	1.00000			0.0755929
$176$	−2.80902	−	1.76336i	−0.211738	−	0.132918i
$177$	−6.70820			−0.504219
$178$	2.51722	+	7.74721i	0.188674	+	0.580678i
$179$	−7.16312	−	5.20431i	−0.535397	−	0.388988i	0.286976	−	0.957938i	$-0.407350\pi$
$179$	−7.16312	−	5.20431i	−0.535397	−	0.388988i	−0.822373	+	0.568949i	$0.807350\pi$
$180$	−2.11803	+	1.53884i	−0.157869	+	0.114698i
$181$	0.944272	−	2.90617i	0.0701872	−	0.216014i	−0.909810	−	0.415025i	$-0.863773\pi$
$181$	0.944272	−	2.90617i	0.0701872	−	0.216014i	0.979997	+	0.199011i	$0.0637729\pi$
$182$	0.236068	−	0.726543i	0.0174985	−	0.0538549i
$183$	0.145898	−	0.106001i	0.0107851	−	0.00783583i
$184$	6.85410	+	4.97980i	0.505291	+	0.367115i
$185$	2.09017	+	6.43288i	0.153672	+	0.472955i
$186$	−4.00000			−0.293294
$187$	−1.07295	−	0.673542i	−0.0784618	−	0.0492543i
$188$	9.23607			0.673609
$189$	1.07295	+	3.30220i	0.0780456	+	0.240200i
$190$	−0.927051	−	0.673542i	−0.0672553	−	0.0488639i
$191$	−2.61803	+	1.90211i	−0.189434	+	0.137632i	−0.678460	−	0.734637i	$-0.737352\pi$
$191$	−2.61803	+	1.90211i	−0.189434	+	0.137632i	0.489026	+	0.872269i	$0.337352\pi$
$192$	−0.190983	+	0.587785i	−0.0137830	+	0.0424197i
$193$	1.67376	−	5.15131i	0.120480	−	0.370799i	−0.872570	−	0.488488i	$-0.837549\pi$
$193$	1.67376	−	5.15131i	0.120480	−	0.370799i	0.993051	+	0.117689i	$0.0375485\pi$
$194$	−8.59017	+	6.24112i	−0.616738	+	0.448087i
$195$	0.381966	+	0.277515i	0.0273532	+	0.0198732i
$196$	0.309017	+	0.951057i	0.0220726	+	0.0679326i
$197$	20.4721			1.45858			0.729290	−	0.684205i	$-0.239851\pi$
$197$	20.4721			1.45858			0.729290	+	0.684205i	$0.239851\pi$
$198$	3.23607	+	8.05748i	0.229977	+	0.572620i
$199$	22.9443			1.62648			0.813238	−	0.581931i	$-0.197703\pi$
$199$	22.9443			1.62648			0.813238	+	0.581931i	$0.197703\pi$
$200$	−0.309017	−	0.951057i	−0.0218508	−	0.0672499i
$201$	−2.80902	−	2.04087i	−0.198133	−	0.143952i
$202$	2.38197	−	1.73060i	0.167595	−	0.121765i
$203$	−1.38197	+	4.25325i	−0.0969950	+	0.298520i
$204$	−0.0729490	+	0.224514i	−0.00510745	+	0.0157191i
$205$	−3.11803	+	2.26538i	−0.217773	+	0.158221i
$206$	−4.85410	−	3.52671i	−0.338201	−	0.245718i
$207$	−6.85410	−	21.0948i	−0.476393	−	1.46619i
$208$	−0.763932			−0.0529692
$209$	−2.91641	+	2.43690i	−0.201732	+	0.168564i
$210$	−0.618034			−0.0426484
$211$	8.13525	+	25.0377i	0.560054	+	1.72367i	0.682208	+	0.731158i	$0.261020\pi$
$211$	8.13525	+	25.0377i	0.560054	+	1.72367i	−0.122154	+	0.992511i	$0.538980\pi$
$212$	5.85410	+	4.25325i	0.402061	+	0.292115i
$213$	−3.47214	+	2.52265i	−0.237907	+	0.172849i
$214$	1.19098	−	3.66547i	0.0814139	−	0.250566i
$215$	−2.80902	+	8.64527i	−0.191573	+	0.589602i
$216$	2.80902	−	2.04087i	0.191129	−	0.138864i
$217$	5.23607	+	3.80423i	0.355447	+	0.258248i
$218$	−1.23607	−	3.80423i	−0.0837171	−	0.257655i
$219$	2.38197			0.160958
$220$	−3.30902	+	0.224514i	−0.223094	+	0.0151367i
$221$	−0.291796			−0.0196283
$222$	−1.29180	−	3.97574i	−0.0866997	−	0.266834i
$223$	21.9443	+	15.9434i	1.46950	+	1.06765i	0.980759	+	0.195222i	$0.0625426\pi$
$223$	21.9443	+	15.9434i	1.46950	+	1.06765i	0.488738	+	0.872431i	$0.337457\pi$
$224$	0.809017	−	0.587785i	0.0540547	−	0.0392731i
$225$	−0.809017	+	2.48990i	−0.0539345	+	0.165993i
$226$	3.50000	−	10.7719i	0.232817	−	0.716536i
$227$	−23.7254	+	17.2375i	−1.57471	+	1.14410i	−0.652252	+	0.758002i	$0.726175\pi$
$227$	−23.7254	+	17.2375i	−1.57471	+	1.14410i	−0.922460	+	0.386093i	$0.873825\pi$
$228$	0.572949	+	0.416272i	0.0379445	+	0.0275683i
$229$	−6.90983	−	21.2663i	−0.456614	−	1.40531i	−0.869229	−	0.494409i	$-0.835384\pi$
$229$	−6.90983	−	21.2663i	−0.456614	−	1.40531i	0.412615	−	0.910906i	$-0.364616\pi$
$230$	8.47214			0.558636
$231$	−0.500000	+	1.98787i	−0.0328976	+	0.130792i
$232$	4.47214			0.293610
$233$	5.04508	+	15.5272i	0.330515	+	1.01722i	0.968890	+	0.247494i	$0.0796069\pi$
$233$	5.04508	+	15.5272i	0.330515	+	1.01722i	−0.638375	+	0.769725i	$0.720393\pi$
$234$	1.61803	+	1.17557i	0.105774	+	0.0768494i
$235$	7.47214	−	5.42882i	0.487428	−	0.354137i
$236$	3.35410	−	10.3229i	0.218333	−	0.671961i
$237$	−0.763932	+	2.35114i	−0.0496227	+	0.152723i
$238$	0.309017	−	0.224514i	0.0200306	−	0.0145531i
$239$	−15.9443	−	11.5842i	−1.03135	−	0.749319i	−0.0627709	−	0.998028i	$-0.519994\pi$
$239$	−15.9443	−	11.5842i	−1.03135	−	0.749319i	−0.968578	+	0.248709i	$0.919994\pi$
$240$	0.190983	+	0.587785i	0.0123279	+	0.0379414i
$241$	15.9787			1.02928			0.514640	−	0.857407i	$-0.327926\pi$
$241$	15.9787			1.02928			0.514640	+	0.857407i	$0.327926\pi$
$242$	−1.95492	+	10.8249i	−0.125667	+	0.695850i
$243$	−13.9443			−0.894525
$244$	0.0901699	+	0.277515i	0.00577254	+	0.0177660i
$245$	0.809017	+	0.587785i	0.0516862	+	0.0375522i
$246$	1.92705	−	1.40008i	0.122864	−	0.0892661i
$247$	−0.270510	+	0.832544i	−0.0172121	+	0.0529735i
$248$	2.00000	−	6.15537i	0.127000	−	0.390866i
$249$	−1.07295	+	0.779543i	−0.0679954	+	0.0494015i
$250$	−0.809017	−	0.587785i	−0.0511667	−	0.0371748i
$251$	6.18034	+	19.0211i	0.390100	+	1.20060i	0.932713	+	0.360620i	$0.117435\pi$
$251$	6.18034	+	19.0211i	0.390100	+	1.20060i	−0.542613	+	0.839983i	$0.682565\pi$
$252$	−2.61803			−0.164921
$253$	6.85410	−	27.2501i	0.430914	−	1.71320i
$254$	−3.52786			−0.221358
$255$	0.0729490	+	0.224514i	0.00456824	+	0.0140596i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−6.59017	+	4.78804i	−0.411084	+	0.298670i	−0.774040	−	0.633136i	$-0.781767\pi$
$257$	−6.59017	+	4.78804i	−0.411084	+	0.298670i	0.362957	+	0.931806i	$0.381767\pi$
$258$	1.73607	−	5.34307i	0.108083	−	0.332645i
$259$	−2.09017	+	6.43288i	−0.129877	+	0.399720i
$260$	−0.618034	+	0.449028i	−0.0383288	+	0.0278475i
$261$	−9.47214	−	6.88191i	−0.586310	−	0.425980i
$262$	1.88197	+	5.79210i	0.116268	+	0.357837i
$263$	−18.3607			−1.13217			−0.566084	−	0.824348i	$-0.691542\pi$
$263$	−18.3607			−1.13217			−0.566084	+	0.824348i	$0.691542\pi$
$264$	2.04508	−	0.138757i	0.125866	−	0.00853992i
$265$	7.23607			0.444508
$266$	−0.354102	−	1.08981i	−0.0217114	−	0.0668208i
$267$	−4.07295	−	2.95917i	−0.249260	−	0.181098i
$268$	4.54508	−	3.30220i	0.277635	−	0.201714i
$269$	3.90983	−	12.0332i	0.238387	−	0.733678i	−0.758268	−	0.651943i	$-0.773954\pi$
$269$	3.90983	−	12.0332i	0.238387	−	0.733678i	0.996654	−	0.0817349i	$-0.0260461\pi$
$270$	1.07295	−	3.30220i	0.0652976	−	0.200965i
$271$	−13.0902	+	9.51057i	−0.795171	+	0.577726i	−0.909494	−	0.415718i	$-0.863530\pi$
$271$	−13.0902	+	9.51057i	−0.795171	+	0.577726i	0.114322	+	0.993444i	$0.463530\pi$
$272$	−0.309017	−	0.224514i	−0.0187369	−	0.0136132i
$273$	0.145898	+	0.449028i	0.00883015	+	0.0271764i
$274$	1.85410			0.112010
$275$	−2.54508	+	2.12663i	−0.153474	+	0.128240i
$276$	−5.23607			−0.315174
$277$	−3.70820	−	11.4127i	−0.222804	−	0.685721i	−0.998507	−	0.0546228i	$-0.982604\pi$
$277$	−3.70820	−	11.4127i	−0.222804	−	0.685721i	0.775703	−	0.631099i	$-0.217396\pi$
$278$	10.4721	+	7.60845i	0.628077	+	0.456325i
$279$	−13.7082	+	9.95959i	−0.820689	+	0.596265i
$280$	0.309017	−	0.951057i	0.0184673	−	0.0568365i
$281$	−1.33688	+	4.11450i	−0.0797516	+	0.245450i	−0.982981	−	0.183708i	$-0.941190\pi$
$281$	−1.33688	+	4.11450i	−0.0797516	+	0.245450i	0.903229	+	0.429159i	$0.141190\pi$
$282$	−4.61803	+	3.35520i	−0.275000	+	0.199799i
$283$	22.9443	+	16.6700i	1.36390	+	0.990928i	0.998186	+	0.0601988i	$0.0191735\pi$
$283$	22.9443	+	16.6700i	1.36390	+	0.990928i	0.365709	+	0.930729i	$0.380827\pi$
$284$	−2.14590	−	6.60440i	−0.127336	−	0.391899i
$285$	0.708204			0.0419504
$286$	0.944272	+	2.35114i	0.0558360	+	0.139026i
$287$	−3.85410			−0.227500
$288$	0.809017	+	2.48990i	0.0476718	+	0.146719i
$289$	13.6353	+	9.90659i	0.802074	+	0.582741i
$290$	3.61803	−	2.62866i	0.212458	−	0.154360i
$291$	2.02786	−	6.24112i	0.118875	−	0.365861i
$292$	−1.19098	+	3.66547i	−0.0696970	+	0.214505i
$293$	−7.70820	+	5.60034i	−0.450318	+	0.327175i	−0.789721	−	0.613466i	$-0.789775\pi$
$293$	−7.70820	+	5.60034i	−0.450318	+	0.327175i	0.339403	+	0.940641i	$0.389775\pi$
$294$	−0.500000	−	0.363271i	−0.0291606	−	0.0211864i
$295$	−3.35410	−	10.3229i	−0.195283	−	0.601020i
$296$	6.76393			0.393146
$297$	−9.75329	−	6.12261i	−0.565943	−	0.355270i
$298$	1.70820			0.0989536
$299$	−2.00000	−	6.15537i	−0.115663	−	0.355974i
$300$	0.500000	+	0.363271i	0.0288675	+	0.0209735i
$301$	−7.35410	+	5.34307i	−0.423883	+	0.307969i
$302$	−2.94427	+	9.06154i	−0.169424	+	0.521433i
$303$	−0.562306	+	1.73060i	−0.0323036	+	0.0994203i
$304$	−0.927051	+	0.673542i	−0.0531700	+	0.0386303i
$305$	0.236068	+	0.171513i	0.0135172	+	0.00982083i
$306$	0.309017	+	0.951057i	0.0176653	+	0.0543683i
$307$	−1.56231			−0.0891655			−0.0445828	−	0.999006i	$-0.514196\pi$
$307$	−1.56231			−0.0891655			−0.0445828	+	0.999006i	$0.514196\pi$
$308$	−2.80902	−	1.76336i	−0.160059	−	0.100477i
$309$	3.70820			0.210952
$310$	−2.00000	−	6.15537i	−0.113592	−	0.349601i
$311$	−16.3262	−	11.8617i	−0.925776	−	0.672616i	0.0191789	−	0.999816i	$-0.493895\pi$
$311$	−16.3262	−	11.8617i	−0.925776	−	0.672616i	−0.944955	+	0.327200i	$0.893895\pi$
$312$	0.381966	−	0.277515i	0.0216246	−	0.0157112i
$313$	0.701626	−	2.15938i	0.0396583	−	0.122056i	−0.929267	−	0.369408i	$-0.879561\pi$
$313$	0.701626	−	2.15938i	0.0396583	−	0.122056i	0.968926	+	0.247352i	$0.0795605\pi$
$314$	−0.909830	+	2.80017i	−0.0513447	+	0.158023i
$315$	−2.11803	+	1.53884i	−0.119338	+	0.0867039i
$316$	−3.23607	−	2.35114i	−0.182043	−	0.132262i
$317$	−4.43769	−	13.6578i	−0.249246	−	0.767099i	−0.994909	−	0.100777i	$-0.967867\pi$
$317$	−4.43769	−	13.6578i	−0.249246	−	0.767099i	0.745663	−	0.666323i	$-0.232133\pi$
$318$	−4.47214			−0.250785
$319$	−5.52786	−	13.7638i	−0.309501	−	0.770626i
$320$	−1.00000			−0.0559017
$321$	0.736068	+	2.26538i	0.0410833	+	0.126441i
$322$	6.85410	+	4.97980i	0.381964	+	0.277513i
$323$	−0.354102	+	0.257270i	−0.0197028	+	0.0143149i
$324$	1.76393	−	5.42882i	0.0979962	−	0.301601i
$325$	−0.236068	+	0.726543i	−0.0130947	+	0.0403013i
$326$	−1.45492	+	1.05706i	−0.0805803	+	0.0585450i
$327$	2.00000	+	1.45309i	0.110600	+	0.0803558i
$328$	1.19098	+	3.66547i	0.0657610	+	0.202392i
$329$	9.23607			0.509201
$330$	1.57295	−	1.31433i	0.0865880	−	0.0723514i
$331$	−30.0344			−1.65084			−0.825421	−	0.564517i	$-0.809062\pi$
$331$	−30.0344			−1.65084			−0.825421	+	0.564517i	$0.809062\pi$
$332$	−0.663119	−	2.04087i	−0.0363934	−	0.112007i
$333$	−14.3262	−	10.4086i	−0.785073	−	0.570389i
$334$	17.5623	−	12.7598i	0.960967	−	0.698183i
$335$	1.73607	−	5.34307i	0.0948515	−	0.291923i
$336$	−0.190983	+	0.587785i	−0.0104190	+	0.0320663i
$337$	20.8713	−	15.1639i	1.13693	−	0.826030i	0.150244	−	0.988649i	$-0.451994\pi$
$337$	20.8713	−	15.1639i	1.13693	−	0.826030i	0.986689	+	0.162618i	$0.0519940\pi$
$338$	−10.0451	−	7.29818i	−0.546381	−	0.396969i
$339$	2.16312	+	6.65740i	0.117484	+	0.361580i
$340$	−0.381966			−0.0207150
$341$	−21.4164	+	1.45309i	−1.15976	+	0.0786890i
$342$	3.00000			0.162221
$343$	0.309017	+	0.951057i	0.0166853	+	0.0513522i
$344$	7.35410	+	5.34307i	0.396507	+	0.288079i
$345$	−4.23607	+	3.07768i	−0.228062	+	0.165697i
$346$	4.90983	−	15.1109i	0.263954	−	0.812367i
$347$	1.20820	−	3.71847i	0.0648598	−	0.199618i	−0.913375	−	0.407120i	$-0.866533\pi$
$347$	1.20820	−	3.71847i	0.0648598	−	0.199618i	0.978235	+	0.207502i	$0.0665332\pi$
$348$	−2.23607	+	1.62460i	−0.119866	+	0.0870876i
$349$	−6.00000	−	4.35926i	−0.321173	−	0.233346i	0.415503	−	0.909592i	$-0.363606\pi$
$349$	−6.00000	−	4.35926i	−0.321173	−	0.233346i	−0.736676	+	0.676246i	$0.763606\pi$
$350$	−0.309017	−	0.951057i	−0.0165177	−	0.0508361i
$351$	−2.65248			−0.141579
$352$	−0.809017	+	3.21644i	−0.0431208	+	0.171437i
$353$	8.56231			0.455726			0.227863	−	0.973693i	$-0.426826\pi$
$353$	8.56231			0.455726			0.227863	+	0.973693i	$0.426826\pi$
$354$	2.07295	+	6.37988i	0.110176	+	0.339087i
$355$	−5.61803	−	4.08174i	−0.298174	−	0.216636i
$356$	6.59017	−	4.78804i	0.349278	−	0.253766i
$357$	−0.0729490	+	0.224514i	−0.00386087	+	0.0118825i
$358$	−2.73607	+	8.42075i	−0.144606	+	0.445051i
$359$	15.8541	−	11.5187i	0.836747	−	0.607933i	−0.0847127	−	0.996405i	$-0.526997\pi$
$359$	15.8541	−	11.5187i	0.836747	−	0.607933i	0.921460	+	0.388473i	$0.126997\pi$
$360$	2.11803	+	1.53884i	0.111630	+	0.0811041i
$361$	−5.46556	−	16.8213i	−0.287661	−	0.885329i
$362$	−3.05573			−0.160606
$363$	−2.95492	−	6.12261i	−0.155093	−	0.321354i
$364$	−0.763932			−0.0400409
$365$	1.19098	+	3.66547i	0.0623389	+	0.191859i
$366$	−0.145898	−	0.106001i	−0.00762621	−	0.00554077i
$367$	16.0902	−	11.6902i	0.839900	−	0.610223i	−0.0824427	−	0.996596i	$-0.526272\pi$
$367$	16.0902	−	11.6902i	0.839900	−	0.610223i	0.922343	+	0.386373i	$0.126272\pi$
$368$	2.61803	−	8.05748i	0.136474	−	0.420025i
$369$	3.11803	−	9.59632i	0.162318	−	0.499565i
$370$	5.47214	−	3.97574i	0.284483	−	0.206689i
$371$	5.85410	+	4.25325i	0.303930	+	0.220818i
$372$	1.23607	+	3.80423i	0.0640871	+	0.197240i
$373$	−16.6525			−0.862233			−0.431116	−	0.902296i	$-0.641880\pi$
$373$	−16.6525			−0.862233			−0.431116	+	0.902296i	$0.641880\pi$
$374$	−0.309017	+	1.22857i	−0.0159789	+	0.0635279i
$375$	0.618034			0.0319151
$376$	−2.85410	−	8.78402i	−0.147189	−	0.453001i
$377$	−2.76393	−	2.00811i	−0.142350	−	0.103423i
$378$	2.80902	−	2.04087i	0.144480	−	0.104971i
$379$	4.13525	−	12.7270i	0.212414	−	0.653742i	−0.786913	−	0.617064i	$-0.788322\pi$
$379$	4.13525	−	12.7270i	0.212414	−	0.653742i	0.999327	−	0.0366788i	$-0.0116779\pi$
$380$	−0.354102	+	1.08981i	−0.0181650	+	0.0559063i
$381$	1.76393	−	1.28157i	0.0903690	−	0.0656569i
$382$	2.61803	+	1.90211i	0.133950	+	0.0973206i
$383$	0.673762	+	2.07363i	0.0344276	+	0.105957i	0.966794	−	0.255558i	$-0.0822593\pi$
$383$	0.673762	+	2.07363i	0.0344276	+	0.105957i	−0.932366	+	0.361516i	$0.882259\pi$
$384$	0.618034			0.0315389
$385$	−3.30902	+	0.224514i	−0.168643	+	0.0114423i
$386$	−5.41641			−0.275688
$387$	−7.35410	−	22.6336i	−0.373830	−	1.15053i
$388$	8.59017	+	6.24112i	0.436100	+	0.316845i
$389$	−9.94427	+	7.22494i	−0.504195	+	0.366319i	−0.810617	−	0.585577i	$-0.800868\pi$
$389$	−9.94427	+	7.22494i	−0.504195	+	0.366319i	0.306422	+	0.951896i	$0.400868\pi$
$390$	0.145898	−	0.449028i	0.00738783	−	0.0227374i
$391$	1.00000	−	3.07768i	0.0505722	−	0.155645i
$392$	0.809017	−	0.587785i	0.0408615	−	0.0296876i
$393$	−3.04508	−	2.21238i	−0.153604	−	0.111600i
$394$	−6.32624	−	19.4702i	−0.318711	−	0.980892i
$395$	−4.00000			−0.201262
$396$	6.66312	−	5.56758i	0.334834	−	0.279782i
$397$	35.8885			1.80119			0.900597	−	0.434655i	$-0.143130\pi$
$397$	35.8885			1.80119			0.900597	+	0.434655i	$0.143130\pi$
$398$	−7.09017	−	21.8213i	−0.355398	−	1.09380i
$399$	0.572949	+	0.416272i	0.0286833	+	0.0208397i
$400$	−0.809017	+	0.587785i	−0.0404508	+	0.0293893i
$401$	−5.42705	+	16.7027i	−0.271014	+	0.834095i	0.719233	+	0.694769i	$0.244494\pi$
$401$	−5.42705	+	16.7027i	−0.271014	+	0.834095i	−0.990247	+	0.139326i	$0.955506\pi$
$402$	−1.07295	+	3.30220i	−0.0535138	+	0.164699i
$403$	−4.00000	+	2.90617i	−0.199254	+	0.144767i
$404$	−2.38197	−	1.73060i	−0.118507	−	0.0861005i
$405$	−1.76393	−	5.42882i	−0.0876505	−	0.269760i
$406$	4.47214			0.221948
$407$	−8.36068	−	20.8172i	−0.414424	−	1.03187i
$408$	0.236068			0.0116871
$409$	−1.56231	−	4.80828i	−0.0772511	−	0.237754i	0.904972	−	0.425471i	$-0.139891\pi$
$409$	−1.56231	−	4.80828i	−0.0772511	−	0.237754i	−0.982223	+	0.187716i	$0.939891\pi$
$410$	3.11803	+	2.26538i	0.153989	+	0.111879i
$411$	−0.927051	+	0.673542i	−0.0457281	+	0.0332234i
$412$	−1.85410	+	5.70634i	−0.0913450	+	0.281131i
$413$	3.35410	−	10.3229i	0.165045	−	0.507955i
$414$	−17.9443	+	13.0373i	−0.881913	+	0.640747i
$415$	−1.73607	−	1.26133i	−0.0852202	−	0.0619161i
$416$	0.236068	+	0.726543i	0.0115742	+	0.0356217i
$417$	−8.00000			−0.391762
$418$	3.21885	+	2.02063i	0.157439	+	0.0988320i
$419$	2.43769			0.119089			0.0595446	−	0.998226i	$-0.481035\pi$
$419$	2.43769			0.119089			0.0595446	+	0.998226i	$0.481035\pi$
$420$	0.190983	+	0.587785i	0.00931902	+	0.0286810i
$421$	−13.6180	−	9.89408i	−0.663702	−	0.482208i	0.204209	−	0.978927i	$-0.434538\pi$
$421$	−13.6180	−	9.89408i	−0.663702	−	0.482208i	−0.867911	+	0.496719i	$0.834538\pi$
$422$	21.2984	−	15.4742i	1.03679	−	0.753271i
$423$	−7.47214	+	22.9969i	−0.363308	+	1.11815i
$424$	2.23607	−	6.88191i	0.108593	−	0.334215i
$425$	−0.309017	+	0.224514i	−0.0149895	+	0.0108905i
$426$	3.47214	+	2.52265i	0.168226	+	0.122223i
$427$	0.0901699	+	0.277515i	0.00436363	+	0.0134299i
$428$	−3.85410			−0.186295
$429$	−1.32624	−	0.832544i	−0.0640314	−	0.0401956i
$430$	9.09017			0.438367
$431$	9.47214	+	29.1522i	0.456257	+	1.40421i	0.869653	+	0.493663i	$0.164342\pi$
$431$	9.47214	+	29.1522i	0.456257	+	1.40421i	−0.413397	+	0.910551i	$0.635658\pi$
$432$	−2.80902	−	2.04087i	−0.135149	−	0.0981914i
$433$	−12.7812	+	9.28605i	−0.614223	+	0.446259i	−0.850899	−	0.525330i	$-0.823942\pi$
$433$	−12.7812	+	9.28605i	−0.614223	+	0.446259i	0.236676	+	0.971589i	$0.423942\pi$
$434$	2.00000	−	6.15537i	0.0960031	−	0.295467i
$435$	−0.854102	+	2.62866i	−0.0409511	+	0.126034i
$436$	−3.23607	+	2.35114i	−0.154980	+	0.112599i
$437$	−7.85410	−	5.70634i	−0.375713	−	0.272971i
$438$	−0.736068	−	2.26538i	−0.0351707	−	0.108244i
$439$	−36.5410			−1.74401			−0.872004	−	0.489499i	$-0.837180\pi$
$439$	−36.5410			−1.74401			−0.872004	+	0.489499i	$0.837180\pi$
$440$	1.23607	+	3.07768i	0.0589272	+	0.146723i
$441$	−2.61803			−0.124668
$442$	0.0901699	+	0.277515i	0.00428895	+	0.0132000i
$443$	6.82624	+	4.95955i	0.324324	+	0.235635i	0.738018	−	0.674780i	$-0.235762\pi$
$443$	6.82624	+	4.95955i	0.324324	+	0.235635i	−0.413694	+	0.910416i	$0.635762\pi$
$444$	−3.38197	+	2.45714i	−0.160501	+	0.116611i
$445$	2.51722	−	7.74721i	0.119328	−	0.367253i
$446$	8.38197	−	25.7970i	0.396898	−	1.22153i
$447$	−0.854102	+	0.620541i	−0.0403976	+	0.0293506i
$448$	−0.809017	−	0.587785i	−0.0382225	−	0.0277702i
$449$	2.79180	+	8.59226i	0.131753	+	0.405494i	0.995071	−	0.0991665i	$-0.0316177\pi$
$449$	2.79180	+	8.59226i	0.131753	+	0.405494i	−0.863318	+	0.504661i	$0.831618\pi$
$450$	2.61803			0.123415
$451$	9.80902	−	8.19624i	0.461889	−	0.385946i
$452$	−11.3262			−0.532741
$453$	−1.81966	−	5.60034i	−0.0854951	−	0.263127i
$454$	23.7254	+	17.2375i	1.11349	+	0.808997i
$455$	−0.618034	+	0.449028i	−0.0289739	+	0.0210508i
$456$	0.218847	−	0.673542i	0.0102485	−	0.0315415i
$457$	6.48278	−	19.9519i	0.303252	−	0.933313i	−0.677072	−	0.735917i	$-0.736752\pi$
$457$	6.48278	−	19.9519i	0.303252	−	0.933313i	0.980324	−	0.197396i	$-0.0632485\pi$
$458$	−18.0902	+	13.1433i	−0.845298	+	0.614145i
$459$	−1.07295	−	0.779543i	−0.0500810	−	0.0363860i
$460$	−2.61803	−	8.05748i	−0.122066	−	0.375682i
$461$	40.9443			1.90696			0.953482	−	0.301449i	$-0.0974702\pi$
$461$	40.9443			1.90696			0.953482	+	0.301449i	$0.0974702\pi$
$462$	2.04508	−	0.138757i	0.0951460	−	0.00645557i
$463$	6.94427			0.322728			0.161364	−	0.986895i	$-0.448411\pi$
$463$	6.94427			0.322728			0.161364	+	0.986895i	$0.448411\pi$
$464$	−1.38197	−	4.25325i	−0.0641562	−	0.197452i
$465$	3.23607	+	2.35114i	0.150069	+	0.109032i
$466$	13.2082	−	9.59632i	0.611858	−	0.444541i
$467$	−1.52786	+	4.70228i	−0.0707011	+	0.217596i	−0.980164	−	0.198191i	$-0.936494\pi$
$467$	−1.52786	+	4.70228i	−0.0707011	+	0.217596i	0.909462	+	0.415786i	$0.136494\pi$
$468$	0.618034	−	1.90211i	0.0285686	−	0.0879252i
$469$	4.54508	−	3.30220i	0.209873	−	0.152481i
$470$	−7.47214	−	5.42882i	−0.344664	−	0.250413i
$471$	−0.562306	−	1.73060i	−0.0259097	−	0.0797418i
$472$	−10.8541			−0.499601
$473$	7.35410	−	29.2380i	0.338142	−	1.34436i
$474$	2.47214			0.113549
$475$	0.354102	+	1.08981i	0.0162473	+	0.0500041i
$476$	−0.309017	−	0.224514i	−0.0141638	−	0.0102906i
$477$	−15.3262	+	11.1352i	−0.701740	+	0.509844i
$478$	−6.09017	+	18.7436i	−0.278558	+	0.857313i
$479$	11.0344	−	33.9605i	0.504177	−	1.55170i	−0.297974	−	0.954574i	$-0.596311\pi$
$479$	11.0344	−	33.9605i	0.504177	−	1.55170i	0.802151	−	0.597122i	$-0.203689\pi$
$480$	0.500000	−	0.363271i	0.0228218	−	0.0165810i
$481$	−4.18034	−	3.03719i	−0.190607	−	0.138484i
$482$	−4.93769	−	15.1967i	−0.224906	−	0.692189i
$483$	−5.23607			−0.238249
$484$	10.8992	−	1.48584i	0.495418	−	0.0675382i
$485$	10.6180			0.482140
$486$	4.30902	+	13.2618i	0.195461	+	0.601567i
$487$	−12.7984	−	9.29856i	−0.579950	−	0.421358i	0.258756	−	0.965943i	$-0.416687\pi$
$487$	−12.7984	−	9.29856i	−0.579950	−	0.421358i	−0.838706	+	0.544585i	$0.816687\pi$
$488$	0.236068	−	0.171513i	0.0106863	−	0.00776405i
$489$	0.343459	−	1.05706i	0.0155317	−	0.0478018i
$490$	0.309017	−	0.951057i	0.0139600	−	0.0429644i
$491$	−26.0623	+	18.9354i	−1.17618	+	0.854541i	−0.991735	−	0.128302i	$-0.959047\pi$
$491$	−26.0623	+	18.9354i	−1.17618	+	0.854541i	−0.184440	+	0.982844i	$0.559047\pi$
$492$	−1.92705	−	1.40008i	−0.0868782	−	0.0631207i
$493$	−0.527864	−	1.62460i	−0.0237738	−	0.0731682i
$494$	0.875388			0.0393856
$495$	2.11803	−	8.42075i	0.0951985	−	0.378485i
$496$	−6.47214			−0.290607
$497$	−2.14590	−	6.60440i	−0.0962567	−	0.296248i
$498$	1.07295	+	0.779543i	0.0480800	+	0.0349322i
$499$	−21.8262	+	15.8577i	−0.977077	+	0.709888i	−0.957053	−	0.289912i	$-0.906374\pi$
$499$	−21.8262	+	15.8577i	−0.977077	+	0.709888i	−0.0200232	+	0.999800i	$0.506374\pi$
$500$	−0.309017	+	0.951057i	−0.0138197	+	0.0425325i
$501$	−4.14590	+	12.7598i	−0.185225	+	0.570064i
$502$	16.1803	−	11.7557i	0.722164	−	0.524683i
$503$	−8.61803	−	6.26137i	−0.384259	−	0.279181i	0.378840	−	0.925462i	$-0.376323\pi$
$503$	−8.61803	−	6.26137i	−0.384259	−	0.279181i	−0.763099	+	0.646282i	$0.776323\pi$
$504$	0.809017	+	2.48990i	0.0360365	+	0.110909i
$505$	−2.94427			−0.131018
$506$	−28.0344	+	1.90211i	−1.24628	+	0.0845592i
$507$	7.67376			0.340804
$508$	1.09017	+	3.35520i	0.0483685	+	0.148863i
$509$	21.9443	+	15.9434i	0.972663	+	0.706681i	0.956057	−	0.293181i	$-0.0947139\pi$
$509$	21.9443	+	15.9434i	0.972663	+	0.706681i	0.0166059	+	0.999862i	$0.494714\pi$
$510$	0.190983	−	0.138757i	0.00845687	−	0.00614428i
$511$	−1.19098	+	3.66547i	−0.0526860	+	0.162151i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	−3.21885	+	2.33863i	−0.142116	+	0.103253i
$514$	6.59017	+	4.78804i	0.290680	+	0.211191i
$515$	1.85410	+	5.70634i	0.0817015	+	0.251451i
$516$	−5.61803			−0.247320
$517$	−23.5066	+	19.6417i	−1.03382	+	0.863840i
$518$	6.76393			0.297190
$519$	3.03444	+	9.33905i	0.133197	+	0.409939i
$520$	0.618034	+	0.449028i	0.0271026	+	0.0196912i
$521$	20.4894	−	14.8864i	0.897655	−	0.652185i	−0.0402076	−	0.999191i	$-0.512802\pi$
$521$	20.4894	−	14.8864i	0.897655	−	0.652185i	0.937863	+	0.347007i	$0.112802\pi$
$522$	−3.61803	+	11.1352i	−0.158357	+	0.487373i
$523$	1.17376	−	3.61247i	0.0513250	−	0.157962i	−0.922109	−	0.386931i	$-0.873535\pi$
$523$	1.17376	−	3.61247i	0.0513250	−	0.157962i	0.973434	+	0.228968i	$0.0735353\pi$
$524$	4.92705	−	3.57971i	0.215239	−	0.156380i
$525$	0.500000	+	0.363271i	0.0218218	+	0.0158545i
$526$	5.67376	+	17.4620i	0.247388	+	0.761381i
$527$	−2.47214			−0.107688
$528$	−0.763932	−	1.90211i	−0.0332459	−	0.0827788i
$529$	48.7771			2.12074
$530$	−2.23607	−	6.88191i	−0.0971286	−	0.298931i
$531$	22.9894	+	16.7027i	0.997653	+	0.724837i
$532$	−0.927051	+	0.673542i	−0.0401928	+	0.0292017i
$533$	0.909830	−	2.80017i	0.0394091	−	0.121289i
$534$	−1.55573	+	4.78804i	−0.0673229	+	0.207199i
$535$	−3.11803	+	2.26538i	−0.134804	+	0.0979411i
$536$	−4.54508	−	3.30220i	−0.196318	−	0.142633i
$537$	−1.69098	−	5.20431i	−0.0729713	−	0.224583i
$538$	−12.6525			−0.545487
$539$	−2.80902	−	1.76336i	−0.120993	−	0.0759531i
$540$	−3.47214			−0.149417
$541$	10.2016	+	31.3974i	0.438602	+	1.34988i	0.889350	+	0.457227i	$0.151157\pi$
$541$	10.2016	+	31.3974i	0.438602	+	1.34988i	−0.450748	+	0.892651i	$0.648843\pi$
$542$	13.0902	+	9.51057i	0.562271	+	0.408514i
$543$	1.52786	−	1.11006i	0.0655669	−	0.0476372i
$544$	−0.118034	+	0.363271i	−0.00506067	+	0.0155751i
$545$	−1.23607	+	3.80423i	−0.0529473	+	0.162955i
$546$	0.381966	−	0.277515i	0.0163466	−	0.0118765i
$547$	23.3435	+	16.9600i	0.998094	+	0.725158i	0.961679	−	0.274179i	$-0.0884060\pi$
$547$	23.3435	+	16.9600i	0.998094	+	0.725158i	0.0364155	+	0.999337i	$0.488406\pi$
$548$	−0.572949	−	1.76336i	−0.0244752	−	0.0753268i
$549$	−0.763932			−0.0326038
$550$	2.80902	+	1.76336i	0.119777	+	0.0751897i
$551$	−5.12461			−0.218316
$552$	1.61803	+	4.97980i	0.0688681	+	0.211954i
$553$	−3.23607	−	2.35114i	−0.137612	−	0.0999807i
$554$	−9.70820	+	7.05342i	−0.412462	+	0.299671i
$555$	−1.29180	+	3.97574i	−0.0548337	+	0.168761i
$556$	4.00000	−	12.3107i	0.169638	−	0.522091i
$557$	−18.7984	+	13.6578i	−0.796513	+	0.578700i	−0.909889	−	0.414852i	$-0.863833\pi$
$557$	−18.7984	+	13.6578i	−0.796513	+	0.578700i	0.113376	+	0.993552i	$0.463833\pi$
$558$	13.7082	+	9.95959i	0.580315	+	0.421623i
$559$	−2.14590	−	6.60440i	−0.0907618	−	0.279336i
$560$	−1.00000			−0.0422577
$561$	−0.291796	−	0.726543i	−0.0123196	−	0.0306746i
$562$	4.32624			0.182491
$563$	8.46149	+	26.0418i	0.356609	+	1.09753i	0.955070	+	0.296379i	$0.0957791\pi$
$563$	8.46149	+	26.0418i	0.356609	+	1.09753i	−0.598461	+	0.801152i	$0.704221\pi$
$564$	4.61803	+	3.35520i	0.194454	+	0.141279i
$565$	−9.16312	+	6.65740i	−0.385495	+	0.280079i
$566$	8.76393	−	26.9726i	0.368376	−	1.13374i
$567$	1.76393	−	5.42882i	0.0740782	−	0.227989i
$568$	−5.61803	+	4.08174i	−0.235727	+	0.171266i
$569$	−23.1976	−	16.8540i	−0.972492	−	0.706557i	−0.0164741	−	0.999864i	$-0.505244\pi$
$569$	−23.1976	−	16.8540i	−0.972492	−	0.706557i	−0.956018	+	0.293307i	$0.905244\pi$
$570$	−0.218847	−	0.673542i	−0.00916649	−	0.0282116i
$571$	18.8328			0.788129			0.394064	−	0.919083i	$-0.371069\pi$
$571$	18.8328			0.788129			0.394064	+	0.919083i	$0.371069\pi$
$572$	1.94427	−	1.62460i	0.0812941	−	0.0679279i
$573$	−2.00000			−0.0835512
$574$	1.19098	+	3.66547i	0.0497107	+	0.152994i
$575$	−6.85410	−	4.97980i	−0.285836	−	0.207672i
$576$	2.11803	−	1.53884i	0.0882514	−	0.0641184i
$577$	14.6459	−	45.0754i	0.609717	−	1.87652i	0.149355	−	0.988784i	$-0.452280\pi$
$577$	14.6459	−	45.0754i	0.609717	−	1.87652i	0.460362	−	0.887731i	$-0.347720\pi$
$578$	5.20820	−	16.0292i	0.216633	−	0.666727i
$579$	2.70820	−	1.96763i	0.112549	−	0.0817717i
$580$	−3.61803	−	2.62866i	−0.150231	−	0.109149i
$581$	−0.663119	−	2.04087i	−0.0275108	−	0.0846696i
$582$	−6.56231			−0.272016
$583$	−23.9443	+	1.62460i	−0.991670	+	0.0672840i
$584$	3.85410			0.159484
$585$	−0.618034	−	1.90211i	−0.0255526	−	0.0786427i
$586$	7.70820	+	5.60034i	0.318423	+	0.231348i
$587$	−34.9615	+	25.4010i	−1.44302	+	1.04841i	−0.455614	+	0.890178i	$0.650580\pi$
$587$	−34.9615	+	25.4010i	−1.44302	+	1.04841i	−0.987402	+	0.158234i	$0.949420\pi$
$588$	−0.190983	+	0.587785i	−0.00787601	+	0.0242399i
$589$	−2.29180	+	7.05342i	−0.0944318	+	0.290631i
$590$	−8.78115	+	6.37988i	−0.361514	+	0.262656i
$591$	10.2361	+	7.43694i	0.421056	+	0.305915i
$592$	−2.09017	−	6.43288i	−0.0859055	−	0.264390i
$593$	−4.96556			−0.203911			−0.101956	−	0.994789i	$-0.532510\pi$
$593$	−4.96556			−0.203911			−0.101956	+	0.994789i	$0.532510\pi$
$594$	−2.80902	+	11.1679i	−0.115255	+	0.458225i
$595$	−0.381966			−0.0156591
$596$	−0.527864	−	1.62460i	−0.0216222	−	0.0665461i
$597$	11.4721	+	8.33499i	0.469523	+	0.341129i
$598$	−5.23607	+	3.80423i	−0.214119	+	0.155566i
$599$	6.81966	−	20.9888i	0.278644	−	0.857577i	−0.709588	−	0.704616i	$-0.751119\pi$
$599$	6.81966	−	20.9888i	0.278644	−	0.857577i	0.988232	−	0.152961i	$-0.0488809\pi$
$600$	0.190983	−	0.587785i	0.00779685	−	0.0239962i
$601$	14.2984	−	10.3884i	0.583243	−	0.423751i	−0.256649	−	0.966505i	$-0.582618\pi$
$601$	14.2984	−	10.3884i	0.583243	−	0.423751i	0.839892	+	0.542754i	$0.182618\pi$
$602$	7.35410	+	5.34307i	0.299731	+	0.217767i
$603$	4.54508	+	13.9883i	0.185090	+	0.569649i
$604$	9.52786			0.387683
$605$	7.94427	−	7.60845i	0.322981	−	0.309328i
$606$	1.81966			0.0739186
$607$	14.4721	+	44.5407i	0.587406	+	1.80785i	0.589386	+	0.807851i	$0.299370\pi$
$607$	14.4721	+	44.5407i	0.587406	+	1.80785i	−0.00198039	+	0.999998i	$0.500630\pi$
$608$	0.927051	+	0.673542i	0.0375969	+	0.0273157i
$609$	−2.23607	+	1.62460i	−0.0906100	+	0.0658321i
$610$	0.0901699	−	0.277515i	0.00365087	−	0.0112362i
$611$	−2.18034	+	6.71040i	−0.0882071	+	0.271474i
$612$	0.809017	−	0.587785i	0.0327026	−	0.0237598i
$613$	1.23607	+	0.898056i	0.0499243	+	0.0362721i	0.612468	−	0.790496i	$-0.290177\pi$
$613$	1.23607	+	0.898056i	0.0499243	+	0.0362721i	−0.562543	+	0.826768i	$0.690177\pi$
$614$	0.482779	+	1.48584i	0.0194834	+	0.0599637i
$615$	−2.38197			−0.0960501
$616$	−0.809017	+	3.21644i	−0.0325962	+	0.129594i
$617$	14.5623			0.586256			0.293128	−	0.956073i	$-0.405304\pi$
$617$	14.5623			0.586256			0.293128	+	0.956073i	$0.405304\pi$
$618$	−1.14590	−	3.52671i	−0.0460948	−	0.141865i
$619$	−7.87132	−	5.71885i	−0.316375	−	0.229860i	0.418252	−	0.908331i	$-0.362643\pi$
$619$	−7.87132	−	5.71885i	−0.316375	−	0.229860i	−0.734627	+	0.678471i	$0.762643\pi$
$620$	−5.23607	+	3.80423i	−0.210286	+	0.152781i
$621$	9.09017	−	27.9767i	0.364776	−	1.12266i
$622$	−6.23607	+	19.1926i	−0.250044	+	0.769555i
$623$	6.59017	−	4.78804i	0.264030	−	0.191829i
$624$	−0.381966	−	0.277515i	−0.0152909	−	0.0111095i
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	−2.27051			−0.0907478
$627$	−2.34346	+	0.159002i	−0.0935887	+	0.00634992i
$628$	2.94427			0.117489
$629$	−0.798374	−	2.45714i	−0.0318333	−	0.0979727i
$630$	2.11803	+	1.53884i	0.0843845	+	0.0613089i
$631$	12.2361	−	8.89002i	0.487110	−	0.353906i	−0.316962	−	0.948438i	$-0.602663\pi$
$631$	12.2361	−	8.89002i	0.487110	−	0.353906i	0.804072	+	0.594532i	$0.202663\pi$
$632$	−1.23607	+	3.80423i	−0.0491681	+	0.151324i
$633$	−5.02786	+	15.4742i	−0.199840	+	0.615043i
$634$	−11.6180	+	8.44100i	−0.461411	+	0.335235i
$635$	2.85410	+	2.07363i	0.113262	+	0.0822894i
$636$	1.38197	+	4.25325i	0.0547985	+	0.168652i
$637$	−0.763932			−0.0302681
$638$	−11.3820	+	9.51057i	−0.450616	+	0.376527i
$639$	18.1803			0.719203
$640$	0.309017	+	0.951057i	0.0122150	+	0.0375938i
$641$	27.6246	+	20.0705i	1.09111	+	0.792735i	0.979586	−	0.201027i	$-0.0644278\pi$
$641$	27.6246	+	20.0705i	1.09111	+	0.792735i	0.111521	+	0.993762i	$0.464428\pi$
$642$	1.92705	−	1.40008i	0.0760546	−	0.0552569i
$643$	−11.9894	+	36.8994i	−0.472814	+	1.45517i	0.376069	+	0.926592i	$0.377276\pi$
$643$	−11.9894	+	36.8994i	−0.472814	+	1.45517i	−0.848883	+	0.528580i	$0.822724\pi$
$644$	2.61803	−	8.05748i	0.103165	−	0.317509i
$645$	−4.54508	+	3.30220i	−0.178963	+	0.130024i
$646$	0.354102	+	0.257270i	0.0139320	+	0.0101222i
$647$	7.50658	+	23.1029i	0.295114	+	0.908268i	0.983183	+	0.182622i	$0.0584586\pi$
$647$	7.50658	+	23.1029i	0.295114	+	0.908268i	−0.688069	+	0.725645i	$0.741541\pi$
$648$	−5.70820			−0.224239
$649$	13.4164	+	33.4055i	0.526640	+	1.31128i
$650$	0.763932			0.0299639
$651$	1.23607	+	3.80423i	0.0484453	+	0.149099i
$652$	1.45492	+	1.05706i	0.0569789	+	0.0413976i
$653$	−10.7984	+	7.84548i	−0.422573	+	0.307017i	−0.778672	−	0.627431i	$-0.784107\pi$
$653$	−10.7984	+	7.84548i	−0.422573	+	0.307017i	0.356099	+	0.934448i	$0.384107\pi$
$654$	0.763932	−	2.35114i	0.0298721	−	0.0919369i
$655$	1.88197	−	5.79210i	0.0735345	−	0.226316i
$656$	3.11803	−	2.26538i	0.121739	−	0.0884484i
$657$	−8.16312	−	5.93085i	−0.318474	−	0.231385i
$658$	−2.85410	−	8.78402i	−0.111264	−	0.342437i
$659$	25.9787			1.01199			0.505994	−	0.862537i	$-0.331126\pi$
$659$	25.9787			1.01199			0.505994	+	0.862537i	$0.331126\pi$
$660$	−1.73607	−	1.08981i	−0.0675764	−	0.0424209i
$661$	24.1803			0.940506			0.470253	−	0.882532i	$-0.344163\pi$
$661$	24.1803			0.940506			0.470253	+	0.882532i	$0.344163\pi$
$662$	9.28115	+	28.5645i	0.360722	+	1.11019i
$663$	−0.145898	−	0.106001i	−0.00566621	−	0.00411674i
$664$	−1.73607	+	1.26133i	−0.0673725	+	0.0489490i
$665$	−0.354102	+	1.08981i	−0.0137315	+	0.0422612i
$666$	−5.47214	+	16.8415i	−0.212041	+	0.652595i
$667$	30.6525	−	22.2703i	1.18687	−	0.862311i
$668$	−17.5623	−	12.7598i	−0.679506	−	0.493690i
$669$	5.18034	+	15.9434i	0.200284	+	0.616409i
$670$	−5.61803			−0.217044
$671$	−0.819660	−	0.514540i	−0.0316426	−	0.0198636i
$672$	0.618034			0.0238412
$673$	−12.5000	−	38.4710i	−0.481840	−	1.48295i	−0.836506	−	0.547957i	$-0.815406\pi$
$673$	−12.5000	−	38.4710i	−0.481840	−	1.48295i	0.354667	−	0.934993i	$-0.384594\pi$
$674$	−20.8713	−	15.1639i	−0.803933	−	0.584092i
$675$	−2.80902	+	2.04087i	−0.108119	+	0.0785531i
$676$	−3.83688	+	11.8087i	−0.147572	+	0.454181i
$677$	−4.76393	+	14.6619i	−0.183093	+	0.563502i	−0.999910	−	0.0133945i	$-0.995736\pi$
$677$	−4.76393	+	14.6619i	−0.183093	+	0.563502i	0.816818	+	0.576896i	$0.195736\pi$
$678$	5.66312	−	4.11450i	0.217491	−	0.158016i
$679$	8.59017	+	6.24112i	0.329660	+	0.239512i
$680$	0.118034	+	0.363271i	0.00452640	+	0.0139308i
$681$	−18.1246			−0.694537
$682$	8.00000	+	19.9192i	0.306336	+	0.762745i
$683$	30.4721			1.16598			0.582992	−	0.812478i	$-0.301882\pi$
$683$	30.4721			1.16598			0.582992	+	0.812478i	$0.301882\pi$
$684$	−0.927051	−	2.85317i	−0.0354467	−	0.109094i
$685$	−1.50000	−	1.08981i	−0.0573121	−	0.0416396i
$686$	0.809017	−	0.587785i	0.0308884	−	0.0224417i
$687$	4.27051	−	13.1433i	0.162930	−	0.501447i
$688$	2.80902	−	8.64527i	0.107093	−	0.329598i
$689$	−4.47214	+	3.24920i	−0.170375	+	0.123785i
$690$	4.23607	+	3.07768i	0.161264	+	0.117165i
$691$	3.88197	+	11.9475i	0.147677	+	0.454503i	0.997346	−	0.0728142i	$-0.0231980\pi$
$691$	3.88197	+	11.9475i	0.147677	+	0.454503i	−0.849669	+	0.527317i	$0.823198\pi$
$692$	−15.8885			−0.603992
$693$	6.66312	−	5.56758i	0.253111	−	0.211495i
$694$	−3.90983			−0.148415
$695$	−4.00000	−	12.3107i	−0.151729	−	0.466973i
$696$	2.23607	+	1.62460i	0.0847579	+	0.0615802i
$697$	1.19098	−	0.865300i	0.0451117	−	0.0327756i
$698$	−2.29180	+	7.05342i	−0.0867458	+	0.266976i
$699$	−3.11803	+	9.59632i	−0.117935	+	0.362966i
$700$	−0.809017	+	0.587785i	−0.0305780	+	0.0222162i
$701$	−15.2361	−	11.0697i	−0.575458	−	0.418095i	0.261626	−	0.965169i	$-0.415741\pi$
$701$	−15.2361	−	11.0697i	−0.575458	−	0.418095i	−0.837084	+	0.547074i	$0.815741\pi$
$702$	0.819660	+	2.52265i	0.0309361	+	0.0952115i
$703$	−7.75078			−0.292326
$704$	3.30902	−	0.224514i	0.124713	−	0.00846169i
$705$	5.70820			0.214983
$706$	−2.64590	−	8.14324i	−0.0995797	−	0.306475i
$707$	−2.38197	−	1.73060i	−0.0895831	−	0.0650859i
$708$	5.42705	−	3.94298i	0.203961	−	0.148186i
$709$	−11.6738	+	35.9281i	−0.438417	+	1.34931i	0.451127	+	0.892460i	$0.351022\pi$
$709$	−11.6738	+	35.9281i	−0.438417	+	1.34931i	−0.889544	+	0.456850i	$0.848978\pi$
$710$	−2.14590	+	6.60440i	−0.0805341	+	0.247859i
$711$	8.47214	−	6.15537i	0.317730	−	0.230844i
$712$	−6.59017	−	4.78804i	−0.246977	−	0.179439i
$713$	−16.9443	−	52.1491i	−0.634568	−	1.95300i
$714$	0.236068			0.00883462
$715$	0.618034	−	2.45714i	0.0231132	−	0.0918919i
$716$	8.85410			0.330893
$717$	−3.76393	−	11.5842i	−0.140567	−	0.432620i
$718$	−15.8541	−	11.5187i	−0.591670	−	0.429873i
$719$	27.5623	−	20.0252i	1.02790	−	0.746813i	0.0600132	−	0.998198i	$-0.480886\pi$
$719$	27.5623	−	20.0252i	1.02790	−	0.746813i	0.967887	+	0.251384i	$0.0808857\pi$
$720$	0.809017	−	2.48990i	0.0301503	−	0.0927930i
$721$	−1.85410	+	5.70634i	−0.0690504	+	0.212515i
$722$	−14.3090	+	10.3961i	−0.532526	+	0.386903i
$723$	7.98936	+	5.80461i	0.297127	+	0.215876i
$724$	0.944272	+	2.90617i	0.0350936	+	0.108007i
$725$	−4.47214			−0.166091
$726$	−4.90983	+	4.70228i	−0.182221	+	0.174518i
$727$	−30.2492			−1.12188			−0.560941	−	0.827856i	$-0.689560\pi$
$727$	−30.2492			−1.12188			−0.560941	+	0.827856i	$0.689560\pi$
$728$	0.236068	+	0.726543i	0.00874926	+	0.0269275i
$729$	6.88197	+	5.00004i	0.254888	+	0.185187i
$730$	3.11803	−	2.26538i	0.115404	−	0.0838456i
$731$	1.07295	−	3.30220i	0.0396845	−	0.122136i
$732$	−0.0557281	+	0.171513i	−0.00205977	+	0.00633932i
$733$	−11.0000	+	7.99197i	−0.406294	+	0.295190i	−0.772100	−	0.635501i	$-0.780794\pi$
$733$	−11.0000	+	7.99197i	−0.406294	+	0.295190i	0.365806	+	0.930691i	$0.380794\pi$
$734$	−16.0902	−	11.6902i	−0.593899	−	0.431493i
$735$	0.190983	+	0.587785i	0.00704451	+	0.0216808i
$736$	−8.47214			−0.312287
$737$	−4.54508	+	18.0701i	−0.167420	+	0.665620i
$738$	−10.0902			−0.371424
$739$	5.20820	+	16.0292i	0.191587	+	0.589644i	0.999999	+	0.00102754i	$0.000327077\pi$
$739$	5.20820	+	16.0292i	0.191587	+	0.589644i	−0.808413	+	0.588616i	$0.799673\pi$
$740$	−5.47214	−	3.97574i	−0.201160	−	0.146151i
$741$	−0.437694	+	0.318003i	−0.0160791	+	0.0116821i
$742$	2.23607	−	6.88191i	0.0820886	−	0.252643i
$743$	12.4377	−	38.2793i	0.456295	−	1.40433i	−0.413314	−	0.910589i	$-0.635629\pi$
$743$	12.4377	−	38.2793i	0.456295	−	1.40433i	0.869608	−	0.493742i	$-0.164371\pi$
$744$	3.23607	−	2.35114i	0.118640	−	0.0861970i
$745$	−1.38197	−	1.00406i	−0.0506313	−	0.0367858i
$746$	5.14590	+	15.8374i	0.188405	+	0.579850i
$747$	5.61803			0.205553
$748$	1.26393	−	0.0857567i	0.0462139	−	0.00313558i
$749$	−3.85410			−0.140826
$750$	−0.190983	−	0.587785i	−0.00697371	−	0.0214629i
$751$	−14.0000	−	10.1716i	−0.510867	−	0.371167i	0.302285	−	0.953218i	$-0.402250\pi$
$751$	−14.0000	−	10.1716i	−0.510867	−	0.371167i	−0.813152	+	0.582051i	$0.802250\pi$
$752$	−7.47214	+	5.42882i	−0.272481	+	0.197969i
$753$	−3.81966	+	11.7557i	−0.139196	+	0.428402i
$754$	−1.05573	+	3.24920i	−0.0384473	+	0.118329i
$755$	7.70820	−	5.60034i	0.280530	−	0.203817i
$756$	−2.80902	−	2.04087i	−0.102163	−	0.0742257i
$757$	4.12461	+	12.6942i	0.149912	+	0.461380i	0.997610	−	0.0690983i	$-0.0220122\pi$
$757$	4.12461	+	12.6942i	0.149912	+	0.461380i	−0.847698	+	0.530479i	$0.822012\pi$
$758$	−13.3820			−0.486055
$759$	13.3262	−	11.1352i	0.483712	−	0.404181i
$760$	1.14590			0.0415661
$761$	15.7016	+	48.3246i	0.569184	+	1.75177i	0.655182	+	0.755471i	$0.272592\pi$
$761$	15.7016	+	48.3246i	0.569184	+	1.75177i	−0.0859981	+	0.996295i	$0.527408\pi$
$762$	−1.76393	−	1.28157i	−0.0639005	−	0.0464264i
$763$	−3.23607	+	2.35114i	−0.117154	+	0.0851170i
$764$	1.00000	−	3.07768i	0.0361787	−	0.111347i
$765$	0.309017	−	0.951057i	0.0111725	−	0.0343855i
$766$	1.76393	−	1.28157i	0.0637335	−	0.0463051i
$767$	6.70820	+	4.87380i	0.242219	+	0.175983i
$768$	−0.190983	−	0.587785i	−0.00689151	−	0.0212099i
$769$	−31.3050			−1.12889			−0.564443	−	0.825472i	$-0.690909\pi$
$769$	−31.3050			−1.12889			−0.564443	+	0.825472i	$0.690909\pi$
$770$	1.23607	+	3.07768i	0.0445448	+	0.110912i
$771$	−5.03444			−0.181311
$772$	1.67376	+	5.15131i	0.0602400	+	0.185400i
$773$	−31.7426	−	23.0624i	−1.14170	−	0.829496i	−0.154348	−	0.988017i	$-0.549328\pi$
$773$	−31.7426	−	23.0624i	−1.14170	−	0.829496i	−0.987356	+	0.158520i	$0.949328\pi$
$774$	−19.2533	+	13.9883i	−0.692045	+	0.502800i
$775$	−2.00000	+	6.15537i	−0.0718421	+	0.221107i
$776$	3.28115	−	10.0984i	0.117787	−	0.362510i
$777$	−3.38197	+	2.45714i	−0.121327	+	0.0881495i
$778$	9.94427	+	7.22494i	0.356519	+	0.259027i
$779$	−1.36475	−	4.20025i	−0.0488971	−	0.150490i
$780$	−0.472136			−0.0169052
$781$	19.5066	+	12.2452i	0.698000	+	0.438168i
$782$	−3.23607			−0.115722
$783$	−4.79837	−	14.7679i	−0.171480	−	0.527761i
$784$	−0.809017	−	0.587785i	−0.0288935	−	0.0209923i
$785$	2.38197	−	1.73060i	0.0850160	−	0.0617677i
$786$	−1.16312	+	3.57971i	−0.0414871	+	0.127684i
$787$	3.00658	−	9.25330i	0.107173	−	0.329844i	−0.883061	−	0.469258i	$-0.844522\pi$
$787$	3.00658	−	9.25330i	0.107173	−	0.329844i	0.990234	+	0.139413i	$0.0445216\pi$
$788$	−16.5623	+	12.0332i	−0.590008	+	0.428666i
$789$	−9.18034	−	6.66991i	−0.326829	−	0.237455i
$790$	1.23607	+	3.80423i	0.0439773	+	0.135348i
$791$	−11.3262			−0.402715
$792$	−7.35410	−	4.61653i	−0.261317	−	0.164041i
$793$	−0.222912			−0.00791585
$794$	−11.0902	−	34.1320i	−0.393575	−	1.21130i
$795$	3.61803	+	2.62866i	0.128318	+	0.0932288i
$796$	−18.5623	+	13.4863i	−0.657923	+	0.478009i
$797$	4.38197	−	13.4863i	0.155217	−	0.477709i	−0.842966	−	0.537967i	$-0.819192\pi$
$797$	4.38197	−	13.4863i	0.155217	−	0.477709i	0.998183	+	0.0602580i	$0.0191923\pi$
$798$	0.218847	−	0.673542i	0.00774710	−	0.0238431i
$799$	−2.85410	+	2.07363i	−0.100971	+	0.0733596i
$800$	0.809017	+	0.587785i	0.0286031	+	0.0207813i
$801$	6.59017	+	20.2825i	0.232852	+	0.716645i
$802$	17.5623			0.620147
$803$	−4.76393	−	11.8617i	−0.168116	−	0.418591i
$804$	3.47214			0.122453
$805$	−2.61803	−	8.05748i	−0.0922736	−	0.283989i
$806$	4.00000	+	2.90617i	0.140894	+	0.102365i
$807$	6.32624	−	4.59628i	0.222694	−	0.161797i
$808$	−0.909830	+	2.80017i	−0.0320077	+	0.0985096i
$809$	−13.0279	+	40.0956i	−0.458035	+	1.40969i	0.409499	+	0.912311i	$0.365703\pi$
$809$	−13.0279	+	40.0956i	−0.458035	+	1.40969i	−0.867534	+	0.497377i	$0.834297\pi$
$810$	−4.61803	+	3.35520i	−0.162261	+	0.117890i
$811$	19.9721	+	14.5106i	0.701317	+	0.509536i	0.880361	−	0.474305i	$-0.157301\pi$
$811$	19.9721	+	14.5106i	0.701317	+	0.509536i	−0.179044	+	0.983841i	$0.557301\pi$
$812$	−1.38197	−	4.25325i	−0.0484975	−	0.149260i
$813$	−10.0000			−0.350715
$814$	−17.2148	+	14.3844i	−0.603378	+	0.504172i
$815$	1.79837			0.0629943
$816$	−0.0729490	−	0.224514i	−0.00255373	−	0.00785956i
$817$	−8.42705	−	6.12261i	−0.294825	−	0.214203i
$818$	−4.09017	+	2.97168i	−0.143009	+	0.103902i
$819$	0.618034	−	1.90211i	0.0215959	−	0.0664652i
$820$	1.19098	−	3.66547i	0.0415909	−	0.128004i
$821$	29.0344	−	21.0948i	1.01331	−	0.736212i	0.0484085	−	0.998828i	$-0.484585\pi$
$821$	29.0344	−	21.0948i	1.01331	−	0.736212i	0.964901	+	0.262616i	$0.0845851\pi$
$822$	0.927051	+	0.673542i	0.0323346	+	0.0234925i
$823$	−8.09017	−	24.8990i	−0.282006	−	0.867924i	−0.987280	−	0.158990i	$-0.949176\pi$
$823$	−8.09017	−	24.8990i	−0.282006	−	0.867924i	0.705275	−	0.708934i	$-0.250824\pi$
$824$	6.00000			0.209020
$825$	−2.04508	+	0.138757i	−0.0712007	+	0.00483091i
$826$	−10.8541			−0.377663
$827$	11.3328	+	34.8788i	0.394081	+	1.21286i	0.929675	+	0.368380i	$0.120088\pi$
$827$	11.3328	+	34.8788i	0.394081	+	1.21286i	−0.535595	+	0.844475i	$0.679912\pi$
$828$	17.9443	+	13.0373i	0.623607	+	0.453077i
$829$	−34.3607	+	24.9645i	−1.19340	+	0.867053i	−0.993619	−	0.112789i	$-0.964022\pi$
$829$	−34.3607	+	24.9645i	−1.19340	+	0.867053i	−0.199777	+	0.979841i	$0.564022\pi$
$830$	−0.663119	+	2.04087i	−0.0230172	+	0.0708396i
$831$	2.29180	−	7.05342i	0.0795015	−	0.244681i
$832$	0.618034	−	0.449028i	0.0214265	−	0.0155672i
$833$	−0.309017	−	0.224514i	−0.0107068	−	0.00777895i
$834$	2.47214	+	7.60845i	0.0856031	+	0.263459i
$835$	−21.7082			−0.751243
$836$	0.927051	−	3.68571i	0.0320627	−	0.127473i
$837$	−22.4721			−0.776751
$838$	−0.753289	−	2.31838i	−0.0260219	−	0.0800873i
$839$	−40.2148	−	29.2177i	−1.38837	−	1.00871i	−0.996042	−	0.0888826i	$-0.971670\pi$
$839$	−40.2148	−	29.2177i	−1.38837	−	1.00871i	−0.392326	−	0.919826i	$-0.628330\pi$
$840$	0.500000	−	0.363271i	0.0172516	−	0.0125340i
$841$	−2.78115	+	8.55951i	−0.0959018	+	0.295155i
$842$	−5.20163	+	16.0090i	−0.179260	+	0.551705i
$843$	−2.16312	+	1.57160i	−0.0745018	+	0.0541287i
$844$	−21.2984	−	15.4742i	−0.733120	−	0.532643i
$845$	3.83688	+	11.8087i	0.131993	+	0.406232i
$846$	24.1803			0.831337
$847$	10.8992	−	1.48584i	0.374500	−	0.0510541i
$848$	−7.23607			−0.248488
$849$	5.41641	+	16.6700i	0.185891	+	0.572113i
$850$	0.309017	+	0.224514i	0.0105992	+	0.00770077i
$851$	46.3607	−	33.6830i	1.58922	−	1.15464i
$852$	1.32624	−	4.08174i	0.0454362	−	0.139838i
$853$	4.14590	−	12.7598i	0.141953	−	0.436886i	−0.854654	−	0.519198i	$-0.826231\pi$
$853$	4.14590	−	12.7598i	0.141953	−	0.436886i	0.996607	+	0.0823125i	$0.0262306\pi$
$854$	0.236068	−	0.171513i	0.00807808	−	0.00586907i
$855$	−2.42705	−	1.76336i	−0.0830034	−	0.0603055i
$856$	1.19098	+	3.66547i	0.0407070	+	0.125283i
$857$	4.43769			0.151589			0.0757944	−	0.997123i	$-0.475851\pi$
$857$	4.43769			0.151589			0.0757944	+	0.997123i	$0.475851\pi$
$858$	−0.381966	+	1.51860i	−0.0130401	+	0.0518441i
$859$	−1.32624			−0.0452507			−0.0226253	−	0.999744i	$-0.507202\pi$
$859$	−1.32624			−0.0452507			−0.0226253	+	0.999744i	$0.507202\pi$
$860$	−2.80902	−	8.64527i	−0.0957867	−	0.294801i
$861$	−1.92705	−	1.40008i	−0.0656737	−	0.0477148i
$862$	24.7984	−	18.0171i	0.844636	−	0.613664i
$863$	−15.4164	+	47.4468i	−0.524781	+	1.61511i	0.239969	+	0.970781i	$0.422863\pi$
$863$	−15.4164	+	47.4468i	−0.524781	+	1.61511i	−0.764749	+	0.644328i	$0.777137\pi$
$864$	−1.07295	+	3.30220i	−0.0365025	+	0.112343i
$865$	−12.8541	+	9.33905i	−0.437053	+	0.317537i
$866$	12.7812	+	9.28605i	0.434321	+	0.315553i
$867$	3.21885	+	9.90659i	0.109318	+	0.336446i
$868$	−6.47214			−0.219679
$869$	13.2361	−	0.898056i	0.449003	−	0.0304645i
$870$	2.76393			0.0937061
$871$	1.32624	+	4.08174i	0.0449379	+	0.138305i
$872$	3.23607	+	2.35114i	0.109587	+	0.0796197i
$873$	−22.4894	+	16.3395i	−0.761149	+	0.553007i
$874$	−3.00000	+	9.23305i	−0.101477	+	0.312313i
$875$	−0.309017	+	0.951057i	−0.0104467	+	0.0321516i
$876$	−1.92705	+	1.40008i	−0.0651090	+	0.0473045i
$877$	5.85410	+	4.25325i	0.197679	+	0.143622i	0.682222	−	0.731145i	$-0.261014\pi$
$877$	5.85410	+	4.25325i	0.197679	+	0.143622i	−0.484543	+	0.874768i	$0.661014\pi$
$878$	11.2918	+	34.7526i	0.381080	+	1.17284i
$879$	−5.88854			−0.198616
$880$	2.54508	−	2.12663i	0.0857948	−	0.0716886i
$881$	30.3262			1.02172			0.510858	−	0.859665i	$-0.329328\pi$
$881$	30.3262			1.02172			0.510858	+	0.859665i	$0.329328\pi$
$882$	0.809017	+	2.48990i	0.0272410	+	0.0838392i
$883$	−6.64590	−	4.82853i	−0.223652	−	0.162493i	0.470317	−	0.882498i	$-0.344140\pi$
$883$	−6.64590	−	4.82853i	−0.223652	−	0.162493i	−0.693969	+	0.720005i	$0.744140\pi$
$884$	0.236068	−	0.171513i	0.00793983	−	0.00576862i
$885$	2.07295	−	6.37988i	0.0696814	−	0.214457i
$886$	2.60739	−	8.02472i	0.0875970	−	0.269596i
$887$	32.7984	−	23.8294i	1.10126	−	0.800113i	0.119996	−	0.992774i	$-0.461712\pi$
$887$	32.7984	−	23.8294i	1.10126	−	0.800113i	0.981265	+	0.192661i	$0.0617118\pi$
$888$	3.38197	+	2.45714i	0.113491	+	0.0824563i
$889$	1.09017	+	3.35520i	0.0365631	+	0.112530i
$890$	−8.14590			−0.273051
$891$	7.05573	+	17.5680i	0.236376	+	0.588552i
$892$	−27.1246			−0.908199
$893$	3.27051	+	10.0656i	0.109443	+	0.336832i
$894$	0.854102	+	0.620541i	0.0285654	+	0.0207540i
$895$	7.16312	−	5.20431i	0.239437	−	0.173961i
$896$	−0.309017	+	0.951057i	−0.0103235	+	0.0317726i
$897$	1.23607	−	3.80423i	0.0412711	−	0.127019i
$898$	7.30902	−	5.31031i	0.243905	−	0.177207i
$899$	−23.4164	−	17.0130i	−0.780981	−	0.567416i
$900$	−0.809017	−	2.48990i	−0.0269672	−	0.0829966i
$901$	−2.76393			−0.0920799
$902$	−10.8262	−	6.79615i	−0.360474	−	0.226287i
$903$	−5.61803			−0.186956
$904$	3.50000	+	10.7719i	0.116408	+	0.358268i
$905$	2.47214	+	1.79611i	0.0821766	+	0.0597048i
$906$	−4.76393	+	3.46120i	−0.158271	+	0.114991i
$907$	5.91641	−	18.2088i	0.196451	−	0.604614i	−0.803505	−	0.595297i	$-0.797034\pi$
$907$	5.91641	−	18.2088i	0.196451	−	0.604614i	0.999957	−	0.00931698i	$-0.00296573\pi$
$908$	9.06231	−	27.8909i	0.300743	−	0.925592i
$909$	6.23607	−	4.53077i	0.206837	−	0.150276i
$910$	0.618034	+	0.449028i	0.0204876	+	0.0148851i
$911$	5.70820	+	17.5680i	0.189121	+	0.582055i	0.999995	−	0.00316581i	$-0.00100771\pi$
$911$	5.70820	+	17.5680i	0.189121	+	0.582055i	−0.810874	+	0.585221i	$0.801008\pi$
$912$	−0.708204			−0.0234510
$913$	6.02786	+	3.78398i	0.199493	+	0.125232i
$914$	−20.9787			−0.693914
$915$	0.0557281	+	0.171513i	0.00184231	+	0.00567006i
$916$	18.0902	+	13.1433i	0.597716	+	0.434266i
$917$	4.92705	−	3.57971i	0.162706	−	0.118213i
$918$	−0.409830	+	1.26133i	−0.0135264	+	0.0416300i
$919$	7.70820	−	23.7234i	0.254270	−	0.782563i	−0.739702	−	0.672934i	$-0.765034\pi$
$919$	7.70820	−	23.7234i	0.254270	−	0.782563i	0.993973	−	0.109629i	$-0.0349663\pi$
$920$	−6.85410	+	4.97980i	−0.225973	+	0.164179i
$921$	−0.781153	−	0.567541i	−0.0257399	−	0.0187011i
$922$	−12.6525	−	38.9403i	−0.416687	−	1.28243i
$923$	5.30495			0.174615
$924$	−0.763932	−	1.90211i	−0.0251315	−	0.0625749i
$925$	−6.76393			−0.222397
$926$	−2.14590	−	6.60440i	−0.0705186	−	0.217034i
$927$	−12.7082	−	9.23305i	−0.417392	−	0.303253i
$928$	−3.61803	+	2.62866i	−0.118768	+	0.0862898i
$929$	6.82624	−	21.0090i	0.223962	−	0.689283i	−0.774434	−	0.632655i	$-0.781965\pi$
$929$	6.82624	−	21.0090i	0.223962	−	0.689283i	0.998395	−	0.0566279i	$-0.0180349\pi$
$930$	1.23607	−	3.80423i	0.0405323	−	0.124745i
$931$	−0.927051	+	0.673542i	−0.0303829	+	0.0220744i
$932$	−13.2082	−	9.59632i	−0.432649	−	0.314338i
$933$	−3.85410	−	11.8617i	−0.126178	−	0.388335i
$934$	4.94427			0.161782
$935$	0.972136	−	0.812299i	0.0317922	−	0.0265650i
$936$	−2.00000			−0.0653720
$937$	2.93769	+	9.04129i	0.0959703	+	0.295366i	0.987505	−	0.157586i	$-0.0503710\pi$
$937$	2.93769	+	9.04129i	0.0959703	+	0.295366i	−0.891535	+	0.452952i	$0.850371\pi$
$938$	−4.54508	−	3.30220i	−0.148402	−	0.107821i
$939$	1.13525	−	0.824811i	0.0370476	−	0.0269167i
$940$	−2.85410	+	8.78402i	−0.0930905	+	0.286503i
$941$	6.29180	−	19.3642i	0.205107	−	0.631253i	−0.794602	−	0.607130i	$-0.792321\pi$
$941$	6.29180	−	19.3642i	0.205107	−	0.631253i	0.999709	−	0.0241232i	$-0.00767940\pi$
$942$	−1.47214	+	1.06957i	−0.0479648	+	0.0348485i
$943$	26.4164	+	19.1926i	0.860237	+	0.624998i
$944$	3.35410	+	10.3229i	0.109167	+	0.335981i
$945$	−3.47214			−0.112949
$946$	−30.0795	+	2.04087i	−0.977970	+	0.0663544i
$947$	24.6312			0.800406			0.400203	−	0.916426i	$-0.368940\pi$
$947$	24.6312			0.800406			0.400203	+	0.916426i	$0.368940\pi$
$948$	−0.763932	−	2.35114i	−0.0248114	−	0.0763615i
$949$	−2.38197	−	1.73060i	−0.0773219	−	0.0561776i
$950$	0.927051	−	0.673542i	0.0300775	−	0.0218526i
$951$	2.74265	−	8.44100i	0.0889364	−	0.273718i
$952$	−0.118034	+	0.363271i	−0.00382550	+	0.0117737i
$953$	4.73607	−	3.44095i	0.153416	−	0.111463i	−0.508429	−	0.861104i	$-0.669774\pi$
$953$	4.73607	−	3.44095i	0.153416	−	0.111463i	0.661845	+	0.749640i	$0.269774\pi$
$954$	15.3262	+	11.1352i	0.496205	+	0.360514i
$955$	−1.00000	−	3.07768i	−0.0323592	−	0.0995915i
$956$	19.7082			0.637409
$957$	2.23607	−	8.89002i	0.0722818	−	0.287374i
$958$	−35.7082			−1.15368
$959$	−0.572949	−	1.76336i	−0.0185015	−	0.0569417i
$960$	−0.500000	−	0.363271i	−0.0161374	−	0.0117245i
$961$	−8.80902	+	6.40013i	−0.284162	+	0.206456i
$962$	−1.59675	+	4.91428i	−0.0514812	+	0.158443i
$963$	3.11803	−	9.59632i	0.100477	−	0.309237i
$964$	−12.9271	+	9.39205i	−0.416352	+	0.302498i
$965$	4.38197	+	3.18368i	0.141060	+	0.102486i
$966$	1.61803	+	4.97980i	0.0520594	+	0.160222i
$967$	48.6525			1.56456			0.782279	−	0.622928i	$-0.214057\pi$
$967$	48.6525			1.56456			0.782279	+	0.622928i	$0.214057\pi$
$968$	−4.78115	−	9.90659i	−0.153672	−	0.318410i
$969$	−0.270510			−0.00869003
$970$	−3.28115	−	10.0984i	−0.105351	−	0.324238i
$971$	−15.2361	−	11.0697i	−0.488949	−	0.355242i	0.315831	−	0.948815i	$-0.397717\pi$
$971$	−15.2361	−	11.0697i	−0.488949	−	0.355242i	−0.804780	+	0.593573i	$0.797717\pi$
$972$	11.2812	−	8.19624i	0.361843	−	0.262894i
$973$	4.00000	−	12.3107i	0.128234	−	0.394664i
$974$	−4.88854	+	15.0454i	−0.156639	+	0.482085i
$975$	−0.381966	+	0.277515i	−0.0122327	+	0.00888758i
$976$	−0.236068	−	0.171513i	−0.00755635	−	0.00549001i
$977$	18.9098	+	58.1985i	0.604979	+	1.86193i	0.496935	+	0.867788i	$0.334459\pi$
$977$	18.9098	+	58.1985i	0.604979	+	1.86193i	0.108045	+	0.994146i	$0.465541\pi$
$978$	−1.11146			−0.0355404
$979$	−6.59017	+	26.2008i	−0.210623	+	0.837381i
$980$	−1.00000			−0.0319438
$981$	−3.23607	−	9.95959i	−0.103320	−	0.317985i
$982$	26.0623	+	18.9354i	0.831682	+	0.604252i
$983$	−7.23607	+	5.25731i	−0.230795	+	0.167682i	−0.697172	−	0.716904i	$-0.745559\pi$
$983$	−7.23607	+	5.25731i	−0.230795	+	0.167682i	0.466378	+	0.884586i	$0.345559\pi$
$984$	−0.736068	+	2.26538i	−0.0234650	+	0.0722178i
$985$	−6.32624	+	19.4702i	−0.201571	+	0.620371i
$986$	−1.38197	+	1.00406i	−0.0440108	+	0.0319757i
$987$	4.61803	+	3.35520i	0.146994	+	0.106797i
$988$	−0.270510	−	0.832544i	−0.00860606	−	0.0264867i
$989$	77.0132			2.44888
$990$	−8.66312	+	0.587785i	−0.275332	+	0.0186810i
$991$	−10.3607			−0.329118			−0.164559	−	0.986367i	$-0.552620\pi$
$991$	−10.3607			−0.329118			−0.164559	+	0.986367i	$0.552620\pi$
$992$	2.00000	+	6.15537i	0.0635001	+	0.195433i
$993$	−15.0172	−	10.9106i	−0.476557	−	0.346239i
$994$	−5.61803	+	4.08174i	−0.178193	+	0.129465i
$995$	−7.09017	+	21.8213i	−0.224773	+	0.691782i
$996$	0.409830	−	1.26133i	0.0129860	−	0.0399667i
$997$	−3.90983	+	2.84066i	−0.123826	+	0.0899645i	−0.647974	−	0.761662i	$-0.724384\pi$
$997$	−3.90983	+	2.84066i	−0.123826	+	0.0899645i	0.524149	+	0.851627i	$0.324384\pi$
$998$	21.8262	+	15.8577i	0.690897	+	0.501966i
$999$	−7.25735	−	22.3358i	−0.229613	−	0.706675i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.n.d.71.1	✓	4	1.1	even	1	trivial
770.2.n.d.141.1	yes	4	11.9	even	5	inner
8470.2.a.bp.1.1		2	11.3	even	5
8470.2.a.cb.1.1		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} +(0.809017 - 3.21644i) q^{11} -0.618034 q^{12} +(-0.236068 - 0.726543i) q^{13} +(0.809017 + 0.587785i) q^{14} +(-0.500000 + 0.363271i) q^{15} +(0.309017 - 0.951057i) q^{16} +(0.118034 - 0.363271i) q^{17} +(-2.11803 + 1.53884i) q^{18} +(-0.927051 - 0.673542i) q^{19} +(-0.309017 - 0.951057i) q^{20} -0.618034 q^{21} +(-3.30902 + 0.224514i) q^{22} +8.47214 q^{23} +(0.190983 + 0.587785i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-0.618034 + 0.449028i) q^{26} +(1.07295 - 3.30220i) q^{27} +(0.309017 - 0.951057i) q^{28} +(3.61803 - 2.62866i) q^{29} +(0.500000 + 0.363271i) q^{30} +(-2.00000 - 6.15537i) q^{31} -1.00000 q^{32} +(1.57295 - 1.31433i) q^{33} -0.381966 q^{34} +(-0.309017 - 0.951057i) q^{35} +(2.11803 + 1.53884i) q^{36} +(5.47214 - 3.97574i) q^{37} +(-0.354102 + 1.08981i) q^{38} +(0.145898 - 0.449028i) q^{39} +(-0.809017 + 0.587785i) q^{40} +(3.11803 + 2.26538i) q^{41} +(0.190983 + 0.587785i) q^{42} +9.09017 q^{43} +(1.23607 + 3.07768i) q^{44} +2.61803 q^{45} +(-2.61803 - 8.05748i) q^{46} +(-7.47214 - 5.42882i) q^{47} +(0.500000 - 0.363271i) q^{48} +(0.309017 - 0.951057i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(0.190983 - 0.138757i) q^{51} +(0.618034 + 0.449028i) q^{52} +(-2.23607 - 6.88191i) q^{53} -3.47214 q^{54} +(2.80902 + 1.76336i) q^{55} -1.00000 q^{56} +(-0.218847 - 0.673542i) q^{57} +(-3.61803 - 2.62866i) q^{58} +(-8.78115 + 6.37988i) q^{59} +(0.190983 - 0.587785i) q^{60} +(0.0901699 - 0.277515i) q^{61} +(-5.23607 + 3.80423i) q^{62} +(2.11803 + 1.53884i) q^{63} +(0.309017 + 0.951057i) q^{64} +0.763932 q^{65} +(-1.73607 - 1.08981i) q^{66} -5.61803 q^{67} +(0.118034 + 0.363271i) q^{68} +(4.23607 + 3.07768i) q^{69} +(-0.809017 + 0.587785i) q^{70} +(-2.14590 + 6.60440i) q^{71} +(0.809017 - 2.48990i) q^{72} +(3.11803 - 2.26538i) q^{73} +(-5.47214 - 3.97574i) q^{74} +(-0.190983 - 0.587785i) q^{75} +1.14590 q^{76} +(1.23607 + 3.07768i) q^{77} -0.472136 q^{78} +(1.23607 + 3.80423i) q^{79} +(0.809017 + 0.587785i) q^{80} +(-4.61803 + 3.35520i) q^{81} +(1.19098 - 3.66547i) q^{82} +(-0.663119 + 2.04087i) q^{83} +(0.500000 - 0.363271i) q^{84} +(0.309017 + 0.224514i) q^{85} +(-2.80902 - 8.64527i) q^{86} +2.76393 q^{87} +(2.54508 - 2.12663i) q^{88} -8.14590 q^{89} +(-0.809017 - 2.48990i) q^{90} +(0.618034 + 0.449028i) q^{91} +(-6.85410 + 4.97980i) q^{92} +(1.23607 - 3.80423i) q^{93} +(-2.85410 + 8.78402i) q^{94} +(0.927051 - 0.673542i) q^{95} +(-0.500000 - 0.363271i) q^{96} +(-3.28115 - 10.0984i) q^{97} -1.00000 q^{98} +(-8.66312 + 0.587785i) 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	\( 4 q + q^{2} + 2 q^{3} - q^{4} + q^{5} + 3 q^{6} - q^{7} + q^{8} - q^{9} + 4 q^{10} + q^{11} + 2 q^{12} + 8 q^{13} + q^{14} - 2 q^{15} - q^{16} - 4 q^{17} - 4 q^{18} + 3 q^{19} + q^{20} + 2 q^{21} - 11 q^{22} + 16 q^{23} + 3 q^{24} - q^{25} + 2 q^{26} + 11 q^{27} - q^{28} + 10 q^{29} + 2 q^{30} - 8 q^{31} - 4 q^{32} + 13 q^{33} - 6 q^{34} + q^{35} + 4 q^{36} + 4 q^{37} + 12 q^{38} + 14 q^{39} - q^{40} + 8 q^{41} + 3 q^{42} + 14 q^{43} - 4 q^{44} + 6 q^{45} - 6 q^{46} - 12 q^{47} + 2 q^{48} - q^{49} + q^{50} + 3 q^{51} - 2 q^{52} + 4 q^{54} + 9 q^{55} - 4 q^{56} - 21 q^{57} - 10 q^{58} - 15 q^{59} + 3 q^{60} - 22 q^{61} - 12 q^{62} + 4 q^{63} - q^{64} + 12 q^{65} + 2 q^{66} - 18 q^{67} - 4 q^{68} + 8 q^{69} - q^{70} - 22 q^{71} + q^{72} + 8 q^{73} - 4 q^{74} - 3 q^{75} + 18 q^{76} - 4 q^{77} + 16 q^{78} - 4 q^{79} + q^{80} - 14 q^{81} + 7 q^{82} + 13 q^{83} + 2 q^{84} - q^{85} - 9 q^{86} + 20 q^{87} - q^{88} - 46 q^{89} - q^{90} - 2 q^{91} - 14 q^{92} - 4 q^{93} + 2 q^{94} - 3 q^{95} - 2 q^{96} + 7 q^{97} - 4 q^{98} - 19 q^{99}+O(q^{100}) \) 4 * q + q^2 + 2 * q^3 - q^4 + q^5 + 3 * q^6 - q^7 + q^8 - q^9 + 4 * q^10 + q^11 + 2 * q^12 + 8 * q^13 + q^14 - 2 * q^15 - q^16 - 4 * q^17 - 4 * q^18 + 3 * q^19 + q^20 + 2 * q^21 - 11 * q^22 + 16 * q^23 + 3 * q^24 - q^25 + 2 * q^26 + 11 * q^27 - q^28 + 10 * q^29 + 2 * q^30 - 8 * q^31 - 4 * q^32 + 13 * q^33 - 6 * q^34 + q^35 + 4 * q^36 + 4 * q^37 + 12 * q^38 + 14 * q^39 - q^40 + 8 * q^41 + 3 * q^42 + 14 * q^43 - 4 * q^44 + 6 * q^45 - 6 * q^46 - 12 * q^47 + 2 * q^48 - q^49 + q^50 + 3 * q^51 - 2 * q^52 + 4 * q^54 + 9 * q^55 - 4 * q^56 - 21 * q^57 - 10 * q^58 - 15 * q^59 + 3 * q^60 - 22 * q^61 - 12 * q^62 + 4 * q^63 - q^64 + 12 * q^65 + 2 * q^66 - 18 * q^67 - 4 * q^68 + 8 * q^69 - q^70 - 22 * q^71 + q^72 + 8 * q^73 - 4 * q^74 - 3 * q^75 + 18 * q^76 - 4 * q^77 + 16 * q^78 - 4 * q^79 + q^80 - 14 * q^81 + 7 * q^82 + 13 * q^83 + 2 * q^84 - q^85 - 9 * q^86 + 20 * q^87 - q^88 - 46 * q^89 - q^90 - 2 * q^91 - 14 * q^92 - 4 * q^93 + 2 * q^94 - 3 * q^95 - 2 * q^96 + 7 * q^97 - 4 * q^98 - 19 * q^99

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