LMFDB - Embedded newform 130.2.l.b.121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [130,2,Mod(101,130)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(130, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("130.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	130.l (of order $6$, degree $2$, 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:	$1.03805522628$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			121.3
Root			$-1.27597 - 0.609843i$ of defining polynomial
Character	$\chi$	$=$	130.121
Dual form			130.2.l.b.101.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-1.66612 + 2.88581i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(-2.88581 + 1.66612i) q^{6} +(-1.24653 + 0.719687i) q^{7} +1.00000i q^{8} +(-4.05193 - 7.01815i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-1.66612 + 2.88581i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(-2.88581 + 1.66612i) q^{6} +(-1.24653 + 0.719687i) q^{7} +1.00000i q^{8} +(-4.05193 - 7.01815i) q^{9} +(0.500000 - 0.866025i) q^{10} +(3.49837 + 2.01978i) q^{11} -3.33225 q^{12} +(3.13234 + 1.78561i) q^{13} -1.43937 q^{14} +(2.88581 + 1.66612i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.15376 + 1.99837i) q^{17} -8.10387i q^{18} +(-0.346241 + 0.199902i) q^{19} +(0.866025 - 0.500000i) q^{20} -4.79635i q^{21} +(2.01978 + 3.49837i) q^{22} +(0.780313 - 1.35154i) q^{23} +(-2.88581 - 1.66612i) q^{24} -1.00000 q^{25} +(1.81988 + 3.11256i) q^{26} +17.0073 q^{27} +(-1.24653 - 0.719687i) q^{28} +(3.93244 - 6.81119i) q^{29} +(1.66612 + 2.88581i) q^{30} -3.10713i q^{31} +(-0.866025 + 0.500000i) q^{32} +(-11.6574 + 6.73042i) q^{33} +2.30752i q^{34} +(0.719687 + 1.24653i) q^{35} +(4.05193 - 7.01815i) q^{36} +(-5.40029 - 3.11786i) q^{37} -0.399804 q^{38} +(-10.3718 + 6.06430i) q^{39} +1.00000 q^{40} +(-0.659061 - 0.380509i) q^{41} +(2.39817 - 4.15376i) q^{42} +(-5.50367 - 9.53264i) q^{43} +4.03957i q^{44} +(-7.01815 + 4.05193i) q^{45} +(1.35154 - 0.780313i) q^{46} +5.84016i q^{47} +(-1.66612 - 2.88581i) q^{48} +(-2.46410 + 4.26795i) q^{49} +(-0.866025 - 0.500000i) q^{50} -7.68922 q^{51} +(0.0197847 + 3.60550i) q^{52} +10.6249 q^{53} +(14.7288 + 8.50367i) q^{54} +(2.01978 - 3.49837i) q^{55} +(-0.719687 - 1.24653i) q^{56} -1.33225i q^{57} +(6.81119 - 3.93244i) q^{58} +(-3.00000 + 1.73205i) q^{59} +3.33225i q^{60} +(2.84624 + 4.92983i) q^{61} +(1.55356 - 2.69085i) q^{62} +(10.1017 + 5.83225i) q^{63} -1.00000 q^{64} +(1.78561 - 3.13234i) q^{65} -13.4608 q^{66} +(-9.00734 - 5.20039i) q^{67} +(-1.15376 + 1.99837i) q^{68} +(2.60020 + 4.50367i) q^{69} +1.43937i q^{70} +(5.19615 - 3.00000i) q^{71} +(7.01815 - 4.05193i) q^{72} -13.4608i q^{73} +(-3.11786 - 5.40029i) q^{74} +(1.66612 - 2.88581i) q^{75} +(-0.346241 - 0.199902i) q^{76} -5.81445 q^{77} +(-12.0144 + 0.0659276i) q^{78} +0.931464 q^{79} +(0.866025 + 0.500000i) q^{80} +(-16.1805 + 28.0255i) q^{81} +(-0.380509 - 0.659061i) q^{82} +10.3867i q^{83} +(4.15376 - 2.39817i) q^{84} +(1.99837 - 1.15376i) q^{85} -11.0073i q^{86} +(13.1039 + 22.6966i) q^{87} +(-2.01978 + 3.49837i) q^{88} +(-0.840939 - 0.485517i) q^{89} -8.10387 q^{90} +(-5.18966 + 0.0284776i) q^{91} +1.56063 q^{92} +(8.96658 + 5.17686i) q^{93} +(-2.92008 + 5.05772i) q^{94} +(0.199902 + 0.346241i) q^{95} -3.33225i q^{96} +(-10.6680 + 6.15919i) q^{97} +(-4.26795 + 2.46410i) q^{98} -32.7361i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 + 4 * q^4 - 6 * q^6 - 4 * q^9	$ 8 q - 2 q^{3} + 4 q^{4} - 6 q^{6} - 4 q^{9} + 4 q^{10} - 6 q^{11} - 4 q^{12} - 2 q^{13} + 6 q^{15} - 4 q^{16} + 6 q^{17} - 6 q^{19} + 6 q^{22} + 12 q^{23} - 6 q^{24} - 8 q^{25} + 40 q^{27} + 2 q^{30} - 42 q^{33} + 4 q^{36} - 30 q^{37} - 12 q^{38} - 40 q^{39} + 8 q^{40} + 12 q^{41} - 6 q^{42} + 4 q^{43} - 12 q^{45} - 2 q^{48} + 8 q^{49} - 10 q^{52} + 60 q^{53} + 36 q^{54} + 6 q^{55} - 24 q^{59} + 26 q^{61} + 18 q^{62} + 12 q^{63} - 8 q^{64} + 6 q^{65} - 12 q^{66} + 24 q^{67} - 6 q^{68} + 12 q^{69} + 12 q^{72} + 6 q^{74} + 2 q^{75} - 6 q^{76} - 60 q^{77} - 6 q^{78} + 20 q^{79} - 28 q^{81} + 30 q^{84} - 18 q^{85} + 48 q^{87} - 6 q^{88} - 24 q^{89} - 8 q^{90} - 66 q^{91} + 24 q^{92} + 48 q^{93} + 6 q^{95} - 6 q^{97} - 48 q^{98}+O(q^{100}) $ 8 * q - 2 * q^3 + 4 * q^4 - 6 * q^6 - 4 * q^9 + 4 * q^10 - 6 * q^11 - 4 * q^12 - 2 * q^13 + 6 * q^15 - 4 * q^16 + 6 * q^17 - 6 * q^19 + 6 * q^22 + 12 * q^23 - 6 * q^24 - 8 * q^25 + 40 * q^27 + 2 * q^30 - 42 * q^33 + 4 * q^36 - 30 * q^37 - 12 * q^38 - 40 * q^39 + 8 * q^40 + 12 * q^41 - 6 * q^42 + 4 * q^43 - 12 * q^45 - 2 * q^48 + 8 * q^49 - 10 * q^52 + 60 * q^53 + 36 * q^54 + 6 * q^55 - 24 * q^59 + 26 * q^61 + 18 * q^62 + 12 * q^63 - 8 * q^64 + 6 * q^65 - 12 * q^66 + 24 * q^67 - 6 * q^68 + 12 * q^69 + 12 * q^72 + 6 * q^74 + 2 * q^75 - 6 * q^76 - 60 * q^77 - 6 * q^78 + 20 * q^79 - 28 * q^81 + 30 * q^84 - 18 * q^85 + 48 * q^87 - 6 * q^88 - 24 * q^89 - 8 * q^90 - 66 * q^91 + 24 * q^92 + 48 * q^93 + 6 * q^95 - 6 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/130\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−1.66612	+	2.88581i	−0.961937	+	1.66612i	−0.244308	+	0.969698i	$0.578561\pi$
$3$	−1.66612	+	2.88581i	−0.961937	+	1.66612i	−0.717629	+	0.696425i	$0.754773\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−2.88581	+	1.66612i	−1.17813	+	0.680192i
$7$	−1.24653	+	0.719687i	−0.471146	+	0.272016i	−0.716719	−	0.697362i	$-0.754357\pi$
$7$	−1.24653	+	0.719687i	−0.471146	+	0.272016i	0.245574	+	0.969378i	$0.421024\pi$
$8$			1.00000i			0.353553i
$9$	−4.05193	−	7.01815i	−1.35064	−	2.33938i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	3.49837	+	2.01978i	1.05480	+	0.608988i	0.923989	−	0.382420i	$-0.124909\pi$
$11$	3.49837	+	2.01978i	1.05480	+	0.608988i	0.130809	+	0.991408i	$0.458242\pi$
$12$	−3.33225			−0.961937
$13$	3.13234	+	1.78561i	0.868756	+	0.495240i
$13$	3.13234	+	1.78561i	0.868756	+	0.495240i
$14$	−1.43937			−0.384689
$15$	2.88581	+	1.66612i	0.745113	+	0.430191i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.15376	+	1.99837i	0.279828	+	0.484676i	0.971342	−	0.237687i	$-0.0763893\pi$
$17$	1.15376	+	1.99837i	0.279828	+	0.484676i	−0.691514	+	0.722363i	$0.743056\pi$
$18$		−	8.10387i		−	1.91010i
$19$	−0.346241	+	0.199902i	−0.0794331	+	0.0458607i	−0.539190	−	0.842184i	$-0.681270\pi$
$19$	−0.346241	+	0.199902i	−0.0794331	+	0.0458607i	0.459757	+	0.888045i	$0.347936\pi$
$20$	0.866025	−	0.500000i	0.193649	−	0.111803i
$21$		−	4.79635i		−	1.04665i
$22$	2.01978	+	3.49837i	0.430620	+	0.745855i
$23$	0.780313	−	1.35154i	0.162707	−	0.281816i	−0.773132	−	0.634245i	$-0.781311\pi$
$23$	0.780313	−	1.35154i	0.162707	−	0.281816i	0.935838	+	0.352429i	$0.114644\pi$
$24$	−2.88581	−	1.66612i	−0.589064	−	0.340096i
$25$	−1.00000			−0.200000
$26$	1.81988	+	3.11256i	0.356908	+	0.610423i
$27$	17.0073			3.27306
$28$	−1.24653	−	0.719687i	−0.235573	−	0.136008i
$29$	3.93244	−	6.81119i	0.730236	−	1.26481i	−0.226546	−	0.974000i	$-0.572743\pi$
$29$	3.93244	−	6.81119i	0.730236	−	1.26481i	0.956782	−	0.290806i	$-0.0939233\pi$
$30$	1.66612	+	2.88581i	0.304191	+	0.526874i
$31$		−	3.10713i		−	0.558057i	−0.960283	−	0.279028i	$-0.909988\pi$
$31$		−	3.10713i		−	0.558057i	0.960283	−	0.279028i	$-0.0900123\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−11.6574	+	6.73042i	−2.02930	+	1.17162i
$34$			2.30752i			0.395736i
$35$	0.719687	+	1.24653i	0.121649	+	0.210703i
$36$	4.05193	−	7.01815i	0.675322	−	1.16969i
$37$	−5.40029	−	3.11786i	−0.887803	−	0.512573i	−0.0145796	−	0.999894i	$-0.504641\pi$
$37$	−5.40029	−	3.11786i	−0.887803	−	0.512573i	−0.873223	+	0.487321i	$0.837974\pi$
$38$	−0.399804			−0.0648568
$39$	−10.3718	+	6.06430i	−1.66082	+	0.971065i
$40$	1.00000			0.158114
$41$	−0.659061	−	0.380509i	−0.102928	−	0.0594255i	0.447652	−	0.894208i	$-0.352260\pi$
$41$	−0.659061	−	0.380509i	−0.102928	−	0.0594255i	−0.550580	+	0.834782i	$0.685594\pi$
$42$	2.39817	−	4.15376i	0.370046	−	0.640939i
$43$	−5.50367	−	9.53264i	−0.839302	−	1.45371i	−0.890479	−	0.455024i	$-0.849631\pi$
$43$	−5.50367	−	9.53264i	−0.839302	−	1.45371i	0.0511772	−	0.998690i	$-0.483703\pi$
$44$			4.03957i			0.608988i
$45$	−7.01815	+	4.05193i	−1.04620	+	0.604027i
$46$	1.35154	−	0.780313i	0.199274	−	0.115051i
$47$			5.84016i			0.851874i	0.904753	+	0.425937i	$0.140056\pi$
$47$			5.84016i			0.851874i	−0.904753	+	0.425937i	$0.859944\pi$
$48$	−1.66612	−	2.88581i	−0.240484	−	0.416531i
$49$	−2.46410	+	4.26795i	−0.352015	+	0.609707i
$50$	−0.866025	−	0.500000i	−0.122474	−	0.0707107i
$51$	−7.68922			−1.07671
$52$	0.0197847	+	3.60550i	0.00274365	+	0.499992i
$53$	10.6249			1.45945			0.729723	−	0.683743i	$-0.239649\pi$
$53$	10.6249			1.45945			0.729723	+	0.683743i	$0.239649\pi$
$54$	14.7288	+	8.50367i	2.00433	+	1.15720i
$55$	2.01978	−	3.49837i	0.272348	−	0.471720i
$56$	−0.719687	−	1.24653i	−0.0961722	−	0.166575i
$57$		−	1.33225i		−	0.176460i
$58$	6.81119	−	3.93244i	0.894353	−	0.516355i
$59$	−3.00000	+	1.73205i	−0.390567	+	0.225494i	−0.682406	−	0.730974i	$-0.739066\pi$
$59$	−3.00000	+	1.73205i	−0.390567	+	0.225494i	0.291839	+	0.956467i	$0.405733\pi$
$60$			3.33225i			0.430191i
$61$	2.84624	+	4.92983i	0.364424	+	0.631200i	0.988684	−	0.150016i	$-0.0479326\pi$
$61$	2.84624	+	4.92983i	0.364424	+	0.631200i	−0.624260	+	0.781217i	$0.714599\pi$
$62$	1.55356	−	2.69085i	0.197303	−	0.341738i
$63$	10.1017	+	5.83225i	1.27270	+	0.734794i
$64$	−1.00000			−0.125000
$65$	1.78561	−	3.13234i	0.221478	−	0.388519i
$66$	−13.4608			−1.65692
$67$	−9.00734	−	5.20039i	−1.10042	−	0.635329i	−0.164090	−	0.986445i	$-0.552469\pi$
$67$	−9.00734	−	5.20039i	−1.10042	−	0.635329i	−0.936332	+	0.351116i	$0.885802\pi$
$68$	−1.15376	+	1.99837i	−0.139914	+	0.242338i
$69$	2.60020	+	4.50367i	0.313027	+	0.542178i
$70$			1.43937i			0.172038i
$71$	5.19615	−	3.00000i	0.616670	−	0.356034i	−0.158901	−	0.987294i	$-0.550795\pi$
$71$	5.19615	−	3.00000i	0.616670	−	0.356034i	0.775571	+	0.631260i	$0.217462\pi$
$72$	7.01815	−	4.05193i	0.827097	−	0.477525i
$73$		−	13.4608i		−	1.57547i	−0.616013	−	0.787736i	$-0.711253\pi$
$73$		−	13.4608i		−	1.57547i	0.616013	−	0.787736i	$-0.288747\pi$
$74$	−3.11786	−	5.40029i	−0.362444	−	0.627771i
$75$	1.66612	−	2.88581i	0.192387	−	0.333225i
$76$	−0.346241	−	0.199902i	−0.0397165	−	0.0229303i
$77$	−5.81445			−0.662618
$78$	−12.0144	+	0.0659276i	−1.36036	+	0.00746483i
$79$	0.931464			0.104798			0.0523989	−	0.998626i	$-0.483313\pi$
$79$	0.931464			0.104798			0.0523989	+	0.998626i	$0.483313\pi$
$80$	0.866025	+	0.500000i	0.0968246	+	0.0559017i
$81$	−16.1805	+	28.0255i	−1.79784	+	3.11394i
$82$	−0.380509	−	0.659061i	−0.0420202	−	0.0727811i
$83$			10.3867i			1.14008i	0.821616	+	0.570042i	$0.193073\pi$
$83$			10.3867i			1.14008i	−0.821616	+	0.570042i	$0.806927\pi$
$84$	4.15376	−	2.39817i	0.453212	−	0.261662i
$85$	1.99837	−	1.15376i	0.216754	−	0.125143i
$86$		−	11.0073i		−	1.18695i
$87$	13.1039	+	22.6966i	1.40488	+	2.43333i
$88$	−2.01978	+	3.49837i	−0.215310	+	0.372927i
$89$	−0.840939	−	0.485517i	−0.0891394	−	0.0514647i	0.454768	−	0.890610i	$-0.349722\pi$
$89$	−0.840939	−	0.485517i	−0.0891394	−	0.0514647i	−0.543907	+	0.839145i	$0.683056\pi$
$90$	−8.10387			−0.854223
$91$	−5.18966	+	0.0284776i	−0.544024	+	0.00298526i
$92$	1.56063			0.162707
$93$	8.96658	+	5.17686i	0.929791	+	0.536815i
$94$	−2.92008	+	5.05772i	−0.301183	+	0.521664i
$95$	0.199902	+	0.346241i	0.0205095	+	0.0355235i
$96$		−	3.33225i		−	0.340096i
$97$	−10.6680	+	6.15919i	−1.08317	+	0.625371i	−0.931751	−	0.363098i	$-0.881719\pi$
$97$	−10.6680	+	6.15919i	−1.08317	+	0.625371i	−0.151424	+	0.988469i	$0.548386\pi$
$98$	−4.26795	+	2.46410i	−0.431128	+	0.248912i
$99$		−	32.7361i		−	3.29011i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	2.41747	−	4.18718i	0.240547	−	0.416640i	−0.720323	−	0.693639i	$-0.756006\pi$
$101$	2.41747	−	4.18718i	0.240547	−	0.416640i	0.960870	+	0.276999i	$0.0893398\pi$
$102$	−6.65906	−	3.84461i	−0.659345	−	0.380673i
$103$	−5.73205			−0.564796			−0.282398	−	0.959297i	$-0.591130\pi$
$103$	−5.73205			−0.564796			−0.282398	+	0.959297i	$0.591130\pi$
$104$	−1.78561	+	3.13234i	−0.175094	+	0.307152i
$105$	−4.79635			−0.468076
$106$	9.20145	+	5.31246i	0.893724	+	0.515992i
$107$	6.43774	−	11.1505i	0.622360	−	1.07796i	−0.366685	−	0.930345i	$-0.619507\pi$
$107$	6.43774	−	11.1505i	0.622360	−	1.07796i	0.989045	−	0.147614i	$-0.0471594\pi$
$108$	8.50367	+	14.7288i	0.818266	+	1.41728i
$109$		−	0.214254i		−	0.0205219i	−0.999947	−	0.0102609i	$-0.996734\pi$
$109$		−	0.214254i		−	0.0205219i	0.999947	−	0.0102609i	$-0.00326621\pi$
$110$	3.49837	−	2.01978i	0.333556	−	0.192579i
$111$	17.9951	−	10.3895i	1.70802	−	0.986126i
$112$		−	1.43937i		−	0.136008i
$113$	0.0642973	+	0.111366i	0.00604858	+	0.0104765i	0.869034	−	0.494753i	$-0.164741\pi$
$113$	0.0642973	+	0.111366i	0.00604858	+	0.0104765i	−0.862985	+	0.505229i	$0.831408\pi$
$114$	0.666123	−	1.15376i	0.0623882	−	0.108059i
$115$	−1.35154	−	0.780313i	−0.126032	−	0.0727646i
$116$	7.86488			0.730236
$117$	−0.160333	−	29.2185i	−0.0148228	−	2.70125i
$118$	−3.46410			−0.318896
$119$	−2.87640	−	1.66069i	−0.263679	−	0.152235i
$120$	−1.66612	+	2.88581i	−0.152096	+	0.263437i
$121$	2.65906	+	4.60563i	0.241733	+	0.418693i
$122$			5.69248i			0.515373i
$123$	2.19615	−	1.26795i	0.198020	−	0.114327i
$124$	2.69085	−	1.55356i	0.241646	−	0.139514i
$125$			1.00000i			0.0894427i
$126$	5.83225	+	10.1017i	0.519578	+	0.899935i
$127$	−8.06218	+	13.9641i	−0.715403	+	1.23911i	0.247401	+	0.968913i	$0.420423\pi$
$127$	−8.06218	+	13.9641i	−0.715403	+	1.23911i	−0.962804	+	0.270201i	$0.912910\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	36.6792			3.22942
$130$	3.11256	−	1.81988i	0.272990	−	0.159614i
$131$	2.78010			0.242898			0.121449	−	0.992598i	$-0.461246\pi$
$131$	2.78010			0.242898			0.121449	+	0.992598i	$0.461246\pi$
$132$	−11.6574	−	6.73042i	−1.01465	−	0.585808i
$133$	0.287734	−	0.498370i	0.0249497	−	0.0432141i
$134$	−5.20039	−	9.00734i	−0.449245	−	0.778116i
$135$		−	17.0073i		−	1.46376i
$136$	−1.99837	+	1.15376i	−0.171359	+	0.0989340i
$137$	−4.73487	+	2.73368i	−0.404528	+	0.233554i	−0.688436	−	0.725297i	$-0.741702\pi$
$137$	−4.73487	+	2.73368i	−0.404528	+	0.233554i	0.283908	+	0.958851i	$0.408369\pi$
$138$			5.20039i			0.442687i
$139$	0.107258	+	0.185777i	0.00909753	+	0.0157574i	0.870538	−	0.492101i	$-0.163771\pi$
$139$	0.107258	+	0.185777i	0.00909753	+	0.0157574i	−0.861441	+	0.507858i	$0.830437\pi$
$140$	−0.719687	+	1.24653i	−0.0608246	+	0.105351i
$141$	−16.8536	−	9.73042i	−1.41933	−	0.819449i
$142$	6.00000			0.503509
$143$	7.35154	+	12.5734i	0.614767	+	1.05144i
$144$	8.10387			0.675322
$145$	−6.81119	−	3.93244i	−0.565639	−	0.326572i
$146$	6.73042	−	11.6574i	0.557014	−	0.964776i
$147$	−8.21099	−	14.2219i	−0.677231	−	1.17300i
$148$		−	6.23572i		−	0.512573i
$149$	14.3149	−	8.26469i	1.17272	−	0.677070i	0.218400	−	0.975859i	$-0.429916\pi$
$149$	14.3149	−	8.26469i	1.17272	−	0.677070i	0.954319	+	0.298790i	$0.0965829\pi$
$150$	2.88581	−	1.66612i	0.235625	−	0.136038i
$151$			6.70830i			0.545914i	0.962026	+	0.272957i	$0.0880016\pi$
$151$			6.70830i			0.545914i	−0.962026	+	0.272957i	$0.911998\pi$
$152$	−0.199902	−	0.346241i	−0.0162142	−	0.0280838i
$153$	9.34991	−	16.1945i	0.755896	−	1.30925i
$154$	−5.03546	−	2.90723i	−0.405769	−	0.234271i
$155$	−3.10713			−0.249570
$156$	−10.4377	−	5.95011i	−0.835688	−	0.476390i
$157$	5.81684			0.464234			0.232117	−	0.972688i	$-0.425435\pi$
$157$	5.81684			0.464234			0.232117	+	0.972688i	$0.425435\pi$
$158$	0.806671	+	0.465732i	0.0641753	+	0.0370516i
$159$	−17.7024	+	30.6615i	−1.40389	+	2.43162i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$			2.24632i			0.177035i
$162$	−28.0255	+	16.1805i	−2.20189	+	1.27126i
$163$	3.61341	−	2.08620i	0.283024	−	0.163404i	−0.351768	−	0.936087i	$-0.614419\pi$
$163$	3.61341	−	2.08620i	0.283024	−	0.163404i	0.634792	+	0.772683i	$0.281086\pi$
$164$		−	0.761018i		−	0.0594255i
$165$	6.73042	+	11.6574i	0.523963	+	0.907530i
$166$	−5.19333	+	8.99511i	−0.403080	+	0.698156i
$167$	−13.5174	−	7.80426i	−1.04601	−	0.603912i	−0.124477	−	0.992222i	$-0.539725\pi$
$167$	−13.5174	−	7.80426i	−1.04601	−	0.603912i	−0.921528	+	0.388311i	$0.873059\pi$
$168$	4.79635			0.370046
$169$	6.62316	+	11.1863i	0.509474	+	0.860486i
$170$	2.30752			0.176979
$171$	2.80589	+	1.61998i	0.214572	+	0.123883i
$172$	5.50367	−	9.53264i	0.419651	−	0.726857i
$173$	2.90723	+	5.03546i	0.221032	+	0.382839i	0.955122	−	0.296214i	$-0.0957241\pi$
$173$	2.90723	+	5.03546i	0.221032	+	0.382839i	−0.734089	+	0.679053i	$0.762391\pi$
$174$			26.2077i			1.98680i
$175$	1.24653	−	0.719687i	0.0942291	−	0.0544032i
$176$	−3.49837	+	2.01978i	−0.263700	+	0.152247i
$177$		−	11.5432i		−	0.867643i
$178$	−0.485517	−	0.840939i	−0.0363910	−	0.0630311i
$179$	−8.43611	+	14.6118i	−0.630545	+	1.09214i	0.356896	+	0.934144i	$0.383835\pi$
$179$	−8.43611	+	14.6118i	−0.630545	+	1.09214i	−0.987441	+	0.157991i	$0.949498\pi$
$180$	−7.01815	−	4.05193i	−0.523102	−	0.302013i
$181$	12.6207			0.938088			0.469044	−	0.883175i	$-0.344599\pi$
$181$	12.6207			0.938088			0.469044	+	0.883175i	$0.344599\pi$
$182$	−4.50861	−	2.57017i	−0.334201	−	0.190513i
$183$	−18.9688			−1.40221
$184$	1.35154	+	0.780313i	0.0996370	+	0.0575254i
$185$	−3.11786	+	5.40029i	−0.229230	+	0.397037i
$186$	5.17686	+	8.96658i	0.379586	+	0.657461i
$187$			9.32138i			0.681647i
$188$	−5.05772	+	2.92008i	−0.368872	+	0.212969i
$189$	−21.2002	+	12.2400i	−1.54209	+	0.890326i
$190$			0.399804i			0.0290049i
$191$	−0.670362	−	1.16110i	−0.0485057	−	0.0840143i	0.840753	−	0.541419i	$-0.182113\pi$
$191$	−0.670362	−	1.16110i	−0.0485057	−	0.0840143i	−0.889259	+	0.457404i	$0.848779\pi$
$192$	1.66612	−	2.88581i	0.120242	−	0.208265i
$193$	−14.5004	−	8.37182i	−1.04376	−	0.602616i	−0.122866	−	0.992423i	$-0.539208\pi$
$193$	−14.5004	−	8.37182i	−1.04376	−	0.602616i	−0.920897	+	0.389807i	$0.872542\pi$
$194$	−12.3184			−0.884408
$195$	6.06430	+	10.3718i	0.434273	+	0.742741i
$196$	−4.92820			−0.352015
$197$	0.863202	+	0.498370i	0.0615006	+	0.0355074i	0.530435	−	0.847726i	$-0.322029\pi$
$197$	0.863202	+	0.498370i	0.0615006	+	0.0355074i	−0.468934	+	0.883233i	$0.655362\pi$
$198$	16.3681	−	28.3503i	1.16323	−	2.01477i
$199$	−1.30752	−	2.26469i	−0.0926875	−	0.160540i	0.815954	−	0.578117i	$-0.196212\pi$
$199$	−1.30752	−	2.26469i	−0.0926875	−	0.160540i	−0.908641	+	0.417578i	$0.862879\pi$
$200$		−	1.00000i		−	0.0707107i
$201$	30.0147	−	17.3290i	2.11707	−	1.22229i
$202$	4.18718	−	2.41747i	0.294609	−	0.170093i
$203$			11.3205i			0.794544i
$204$	−3.84461	−	6.65906i	−0.269177	−	0.466227i
$205$	−0.380509	+	0.659061i	−0.0265759	+	0.0460308i
$206$	−4.96410	−	2.86603i	−0.345865	−	0.199685i
$207$	−12.6471			−0.879035
$208$	−3.11256	+	1.81988i	−0.215817	+	0.126186i
$209$	−1.61504			−0.111714
$210$	−4.15376	−	2.39817i	−0.286637	−	0.165490i
$211$	4.56691	−	7.91011i	0.314399	−	0.544555i	−0.664911	−	0.746923i	$-0.731530\pi$
$211$	4.56691	−	7.91011i	0.314399	−	0.544555i	0.979310	+	0.202368i	$0.0648638\pi$
$212$	5.31246	+	9.20145i	0.364861	+	0.631958i
$213$			19.9935i			1.36993i
$214$	11.1505	−	6.43774i	0.762232	−	0.440075i
$215$	−9.53264	+	5.50367i	−0.650121	+	0.375347i
$216$			17.0073i			1.15720i
$217$	2.23616	+	3.87314i	0.151800	+	0.262926i
$218$	0.107127	−	0.185550i	0.00725557	−	0.0125670i
$219$	38.8454	+	22.4274i	2.62493	+	1.51550i
$220$	4.03957			0.272348
$221$	0.0456536	+	8.31975i	0.00307099	+	0.559647i
$222$	20.7790			1.39459
$223$	5.03326	+	2.90595i	0.337052	+	0.194597i	0.658968	−	0.752171i	$-0.270993\pi$
$223$	5.03326	+	2.90595i	0.337052	+	0.194597i	−0.321916	+	0.946768i	$0.604327\pi$
$224$	0.719687	−	1.24653i	0.0480861	−	0.0832876i
$225$	4.05193	+	7.01815i	0.270129	+	0.467877i
$226$			0.128595i			0.00855399i
$227$	−9.99674	+	5.77162i	−0.663507	+	0.383076i	−0.793612	−	0.608424i	$-0.791802\pi$
$227$	−9.99674	+	5.77162i	−0.663507	+	0.383076i	0.130105	+	0.991500i	$0.458469\pi$
$228$	1.15376	−	0.666123i	0.0764096	−	0.0441151i
$229$			12.8755i			0.850836i	0.904997	+	0.425418i	$0.139873\pi$
$229$			12.8755i			0.850836i	−0.904997	+	0.425418i	$0.860127\pi$
$230$	−0.780313	−	1.35154i	−0.0514523	−	0.0891180i
$231$	9.68759	−	16.7794i	0.637397	−	1.10400i
$232$	6.81119	+	3.93244i	0.447177	+	0.258177i
$233$	−10.4149			−0.682303			−0.341152	−	0.940008i	$-0.610817\pi$
$233$	−10.4149			−0.682303			−0.341152	+	0.940008i	$0.610817\pi$
$234$	14.4704	−	25.3841i	0.945958	−	1.65941i
$235$	5.84016			0.380970
$236$	−3.00000	−	1.73205i	−0.195283	−	0.112747i
$237$	−1.55193	+	2.68803i	−0.100809	+	0.174606i
$238$	−1.66069	−	2.87640i	−0.107647	−	0.186449i
$239$		−	18.3801i		−	1.18891i	−0.804128	−	0.594456i	$-0.797367\pi$
$239$		−	18.3801i		−	1.18891i	0.804128	−	0.594456i	$-0.202633\pi$
$240$	−2.88581	+	1.66612i	−0.186278	+	0.107548i
$241$	0.536681	−	0.309853i	0.0345707	−	0.0199594i	−0.482615	−	0.875833i	$-0.660313\pi$
$241$	0.536681	−	0.309853i	0.0345707	−	0.0199594i	0.517186	+	0.855873i	$0.326980\pi$
$242$			5.31812i			0.341862i
$243$	−28.4065	−	49.2015i	−1.82228	−	3.15628i
$244$	−2.84624	+	4.92983i	−0.182212	+	0.315600i
$245$	4.26795	+	2.46410i	0.272669	+	0.157426i
$246$	2.53590			0.161683
$247$	−1.44149	+	0.00791002i	−0.0917200	+	0.000503302i
$248$	3.10713			0.197303
$249$	−29.9739	−	17.3055i	−1.89952	−	1.09669i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	−2.65376	−	4.59645i	−0.167504	−	0.290125i	0.770038	−	0.637998i	$-0.220237\pi$
$251$	−2.65376	−	4.59645i	−0.167504	−	0.290125i	−0.937542	+	0.347873i	$0.886904\pi$
$252$			11.6645i			0.734794i
$253$	5.45965	−	3.15213i	0.343245	−	0.198173i
$254$	−13.9641	+	8.06218i	−0.876186	+	0.505866i
$255$			7.68922i			0.481518i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	12.3686	−	21.4230i	0.771529	−	1.33633i	−0.165195	−	0.986261i	$-0.552825\pi$
$257$	12.3686	−	21.4230i	0.771529	−	1.33633i	0.936725	−	0.350067i	$-0.113841\pi$
$258$	31.7651	+	18.3396i	1.97761	+	1.14177i
$259$	8.97553			0.557713
$260$	3.60550	−	0.0197847i	0.223603	−	0.00122700i
$261$	−63.7360			−3.94516
$262$	2.40764	+	1.39005i	0.148744	+	0.0858775i
$263$	−2.56466	+	4.44211i	−0.158143	+	0.273912i	−0.934199	−	0.356752i	$-0.883884\pi$
$263$	−2.56466	+	4.44211i	−0.158143	+	0.273912i	0.776056	+	0.630664i	$0.217218\pi$
$264$	−6.73042	−	11.6574i	−0.414229	−	0.717465i
$265$		−	10.6249i		−	0.652684i
$266$	0.498370	−	0.287734i	0.0305570	−	0.0176421i
$267$	2.80222	−	1.61786i	0.171493	−	0.0990115i
$268$		−	10.4008i		−	0.635329i
$269$	−3.40687	−	5.90087i	−0.207720	−	0.359782i	0.743276	−	0.668985i	$-0.233271\pi$
$269$	−3.40687	−	5.90087i	−0.207720	−	0.359782i	−0.950996	+	0.309203i	$0.899938\pi$
$270$	8.50367	−	14.7288i	0.517517	−	0.896366i
$271$	−19.0709	−	11.0106i	−1.15848	−	0.668846i	−0.207538	−	0.978227i	$-0.566545\pi$
$271$	−19.0709	−	11.0106i	−1.15848	−	0.668846i	−0.950938	+	0.309381i	$0.899878\pi$
$272$	−2.30752			−0.139914
$273$	8.56443	−	15.0238i	0.518343	−	0.909283i
$274$	−5.46736			−0.330295
$275$	−3.49837	−	2.01978i	−0.210960	−	0.121798i
$276$	−2.60020	+	4.50367i	−0.156513	+	0.271089i
$277$	12.7152	+	22.0233i	0.763980	+	1.32325i	0.940784	+	0.339006i	$0.110091\pi$
$277$	12.7152	+	22.0233i	0.763980	+	1.32325i	−0.176805	+	0.984246i	$0.556576\pi$
$278$			0.214517i			0.0128659i
$279$	−21.8063	+	12.5899i	−1.30551	+	0.753736i
$280$	−1.24653	+	0.719687i	−0.0744947	+	0.0430095i
$281$			25.0954i			1.49707i	0.663098	+	0.748533i	$0.269241\pi$
$281$			25.0954i			1.49707i	−0.663098	+	0.748533i	$0.730759\pi$
$282$	−9.73042	−	16.8536i	−0.579438	−	1.00362i
$283$	0.882986	−	1.52938i	0.0524881	−	0.0909120i	−0.838588	−	0.544767i	$-0.816618\pi$
$283$	0.882986	−	1.52938i	0.0524881	−	0.0909120i	0.891076	+	0.453855i	$0.149952\pi$
$284$	5.19615	+	3.00000i	0.308335	+	0.178017i
$285$	−1.33225			−0.0789155
$286$	0.0799217	+	14.5647i	0.00472587	+	0.861226i
$287$	1.09539			0.0646588
$288$	7.01815	+	4.05193i	0.413549	+	0.238762i
$289$	5.83768	−	10.1112i	0.343393	−	0.594774i
$290$	−3.93244	−	6.81119i	−0.230921	−	0.399967i
$291$		−	41.0479i		−	2.40627i
$292$	11.6574	−	6.73042i	0.682200	−	0.393868i
$293$	−15.9374	+	9.20145i	−0.931072	+	0.537555i	−0.887150	−	0.461480i	$-0.847318\pi$
$293$	−15.9374	+	9.20145i	−0.931072	+	0.537555i	−0.0439215	+	0.999035i	$0.513985\pi$
$294$		−	16.4220i		−	0.957750i
$295$	1.73205	+	3.00000i	0.100844	+	0.174667i
$296$	3.11786	−	5.40029i	0.181222	−	0.313886i
$297$	59.4980	+	34.3512i	3.45242	+	1.99326i
$298$	16.5294			0.957521
$299$	4.85754	−	2.84016i	0.280919	−	0.164250i
$300$	3.33225			0.192387
$301$	13.7210	+	7.92184i	0.790867	+	0.456607i
$302$	−3.35415	+	5.80956i	−0.193010	+	0.334303i
$303$	8.05560	+	13.9527i	0.462782	+	0.801563i
$304$		−	0.399804i		−	0.0229303i
$305$	4.92983	−	2.84624i	0.282281	−	0.162975i
$306$	16.1945	−	9.34991i	0.925779	−	0.534499i
$307$		−	8.40730i		−	0.479830i	−0.970794	−	0.239915i	$-0.922880\pi$
$307$		−	8.40730i		−	0.479830i	0.970794	−	0.239915i	$-0.0771196\pi$
$308$	−2.90723	−	5.03546i	−0.165655	−	0.286922i
$309$	9.55030	−	16.5416i	0.543298	−	0.941019i
$310$	−2.69085	−	1.55356i	−0.152830	−	0.0882365i
$311$	−33.6601			−1.90869			−0.954344	−	0.298708i	$-0.903444\pi$
$311$	−33.6601			−1.90869			−0.954344	+	0.298708i	$0.903444\pi$
$312$	−6.06430	−	10.3718i	−0.343323	−	0.587188i
$313$	27.0008			1.52618			0.763088	−	0.646294i	$-0.223682\pi$
$313$	27.0008			1.52618			0.763088	+	0.646294i	$0.223682\pi$
$314$	5.03753	+	2.90842i	0.284284	+	0.164132i
$315$	5.83225	−	10.1017i	0.328610	−	0.569169i
$316$	0.465732	+	0.806671i	0.0261995	+	0.0453788i
$317$		−	10.2569i		−	0.576086i	−0.957617	−	0.288043i	$-0.906995\pi$
$317$		−	10.2569i		−	0.576086i	0.957617	−	0.288043i	$-0.0930047\pi$
$318$	−30.6615	+	17.7024i	−1.71941	+	0.992703i
$319$	27.5143	−	15.8854i	1.54050	−	0.889410i
$320$			1.00000i			0.0559017i
$321$	21.4521	+	37.1562i	1.19734	+	2.07386i
$322$	−1.12316	+	1.94537i	−0.0625914	+	0.108411i
$323$	−0.798957	−	0.461278i	−0.0444551	−	0.0256662i
$324$	−32.3611			−1.79784
$325$	−3.13234	−	1.78561i	−0.173751	−	0.0990481i
$326$	4.17240			0.231088
$327$	0.618298	+	0.356974i	0.0341919	+	0.0197407i
$328$	0.380509	−	0.659061i	0.0210101	−	0.0363905i
$329$	−4.20308	−	7.27995i	−0.231724	−	0.401357i
$330$			13.4608i			0.740995i
$331$	−3.92256	+	2.26469i	−0.215603	+	0.124479i	−0.603913	−	0.797050i	$-0.706392\pi$
$331$	−3.92256	+	2.26469i	−0.215603	+	0.124479i	0.388310	+	0.921529i	$0.373059\pi$
$332$	−8.99511	+	5.19333i	−0.493671	+	0.285021i
$333$			50.5335i			2.76922i
$334$	−7.80426	−	13.5174i	−0.427030	−	0.739638i
$335$	−5.20039	+	9.00734i	−0.284128	+	0.492124i
$336$	4.15376	+	2.39817i	0.226606	+	0.130831i
$337$	6.72755			0.366473			0.183236	−	0.983069i	$-0.441343\pi$
$337$	6.72755			0.366473			0.183236	+	0.983069i	$0.441343\pi$
$338$	0.142667	+	12.9992i	0.00776009	+	0.707064i
$339$	−0.428509			−0.0232734
$340$	1.99837	+	1.15376i	0.108377	+	0.0625714i
$341$	6.27573	−	10.8699i	0.339850	−	0.588637i
$342$	1.61998	+	2.80589i	0.0875985	+	0.151725i
$343$		−	17.1691i		−	0.927047i
$344$	9.53264	−	5.50367i	0.513965	−	0.296738i
$345$	4.50367	−	2.60020i	0.242469	−	0.139990i
$346$			5.81445i			0.312587i
$347$	−1.57286	−	2.72427i	−0.0844355	−	0.146247i	0.820715	−	0.571338i	$-0.193575\pi$
$347$	−1.57286	−	2.72427i	−0.0844355	−	0.146247i	−0.905151	+	0.425091i	$0.860242\pi$
$348$	−13.1039	+	22.6966i	−0.702441	+	1.21666i
$349$	−9.09752	−	5.25246i	−0.486979	−	0.281158i	0.236341	−	0.971670i	$-0.424052\pi$
$349$	−9.09752	−	5.25246i	−0.486979	−	0.281158i	−0.723320	+	0.690513i	$0.757385\pi$
$350$	1.43937			0.0769378
$351$	53.2729	+	30.3686i	2.84349	+	1.62095i
$352$	−4.03957			−0.215310
$353$	−28.5767	−	16.4988i	−1.52099	−	0.878141i	−0.999693	−	0.0247633i	$-0.992117\pi$
$353$	−28.5767	−	16.4988i	−1.52099	−	0.878141i	−0.521292	−	0.853378i	$-0.674550\pi$
$354$	5.77162	−	9.99674i	0.306758	−	0.531321i
$355$	−3.00000	−	5.19615i	−0.159223	−	0.275783i
$356$		−	0.971033i		−	0.0514647i
$357$	9.58488	−	5.53383i	0.507285	−	0.292881i
$358$	−14.6118	+	8.43611i	−0.772256	+	0.445862i
$359$			24.2487i			1.27980i	0.768459	+	0.639899i	$0.221024\pi$
$359$			24.2487i			1.27980i	−0.768459	+	0.639899i	$0.778976\pi$
$360$	−4.05193	−	7.01815i	−0.213556	−	0.369889i
$361$	−9.42008	+	16.3161i	−0.495794	+	0.858740i
$362$	10.9298	+	6.31034i	0.574459	+	0.331664i
$363$	−17.7213			−0.930127
$364$	−2.61949	−	4.48014i	−0.137299	−	0.234823i
$365$	−13.4608			−0.704573
$366$	−16.4274	−	9.48438i	−0.858675	−	0.495756i
$367$	9.89924	−	17.1460i	0.516736	−	0.895013i	−0.483075	−	0.875579i	$-0.660480\pi$
$367$	9.89924	−	17.1460i	0.516736	−	0.895013i	0.999811	−	0.0194340i	$-0.00618643\pi$
$368$	0.780313	+	1.35154i	0.0406766	+	0.0704540i
$369$			6.16719i			0.321051i
$370$	−5.40029	+	3.11786i	−0.280748	+	0.162090i
$371$	−13.2443	+	7.64662i	−0.687611	+	0.396993i
$372$			10.3537i			0.536815i
$373$	−2.39557	−	4.14924i	−0.124038	−	0.214840i	0.797319	−	0.603559i	$-0.206251\pi$
$373$	−2.39557	−	4.14924i	−0.124038	−	0.214840i	−0.921356	+	0.388719i	$0.872918\pi$
$374$	−4.66069	+	8.07255i	−0.240999	+	0.417422i
$375$	−2.88581	−	1.66612i	−0.149023	−	0.0860382i
$376$	−5.84016			−0.301183
$377$	24.4799	−	14.3132i	1.26078	−	0.737166i
$378$	−24.4799			−1.25911
$379$	−16.8833	−	9.74760i	−0.867239	−	0.500700i	−0.000808945	−	1.00000i	$-0.500257\pi$
$379$	−16.8833	−	9.74760i	−0.867239	−	0.500700i	−0.866430	+	0.499299i	$0.833591\pi$
$380$	−0.199902	+	0.346241i	−0.0102548	+	0.0177618i
$381$	−26.8652	−	46.5318i	−1.37634	−	2.38390i
$382$		−	1.34072i		−	0.0685974i
$383$	11.1383	−	6.43068i	0.569139	−	0.328592i	−0.187667	−	0.982233i	$-0.560092\pi$
$383$	11.1383	−	6.43068i	0.569139	−	0.328592i	0.756805	+	0.653640i	$0.226759\pi$
$384$	2.88581	−	1.66612i	0.147266	−	0.0850240i
$385$			5.81445i			0.296332i
$386$	−8.37182	−	14.5004i	−0.426114	−	0.738051i
$387$	−44.6010	+	77.2512i	−2.26720	+	3.92690i
$388$	−10.6680	−	6.15919i	−0.541587	−	0.312686i
$389$	6.94233			0.351990			0.175995	−	0.984391i	$-0.443686\pi$
$389$	6.94233			0.351990			0.175995	+	0.984391i	$0.443686\pi$
$390$	0.0659276	+	12.0144i	0.00333837	+	0.608373i
$391$	3.60117			0.182119
$392$	−4.26795	−	2.46410i	−0.215564	−	0.124456i
$393$	−4.63199	+	8.02284i	−0.233653	+	0.404699i
$394$	0.498370	+	0.863202i	0.0251075	+	0.0434875i
$395$		−	0.931464i		−	0.0468670i
$396$	28.3503	−	16.3681i	1.42466	−	0.822526i
$397$	−3.75184	+	2.16612i	−0.188299	+	0.108715i	−0.591186	−	0.806535i	$-0.701340\pi$
$397$	−3.75184	+	2.16612i	−0.188299	+	0.108715i	0.402887	+	0.915250i	$0.368007\pi$
$398$		−	2.61504i		−	0.131080i
$399$	0.958800	+	1.66069i	0.0480001	+	0.0831385i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	−20.5448	−	11.8616i	−1.02596	−	0.592339i	−0.110136	−	0.993917i	$-0.535129\pi$
$401$	−20.5448	−	11.8616i	−1.02596	−	0.592339i	−0.915825	+	0.401578i	$0.868462\pi$
$402$	34.6580			1.72858
$403$	5.54813	−	9.73259i	0.276372	−	0.484815i
$404$	4.83494			0.240547
$405$	28.0255	+	16.1805i	1.39260	+	0.804017i
$406$	−5.66025	+	9.80385i	−0.280914	+	0.486557i
$407$	−12.5948	−	21.8149i	−0.624302	−	1.08132i
$408$		−	7.68922i		−	0.380673i
$409$	−33.2373	+	19.1896i	−1.64348	+	0.948864i	−0.663897	+	0.747824i	$0.731099\pi$
$409$	−33.2373	+	19.1896i	−1.64348	+	0.948864i	−0.979583	+	0.201039i	$0.935568\pi$
$410$	−0.659061	+	0.380509i	−0.0325487	+	0.0187920i
$411$		−	18.2186i		−	0.898657i
$412$	−2.86603	−	4.96410i	−0.141199	−	0.244564i
$413$	2.49307	−	4.31812i	0.122676	−	0.212481i
$414$	−10.9527	−	6.32355i	−0.538297	−	0.310786i
$415$	10.3867			0.509861
$416$	−3.60550	+	0.0197847i	−0.176774	+	0.000970026i
$417$	−0.714822			−0.0350050
$418$	−1.39866	−	0.807519i	−0.0684109	−	0.0394970i
$419$	19.2946	−	33.4192i	0.942602	−	1.63263i	0.182120	−	0.983276i	$-0.441704\pi$
$419$	19.2946	−	33.4192i	0.942602	−	1.63263i	0.760482	−	0.649359i	$-0.224963\pi$
$420$	−2.39817	−	4.15376i	−0.117019	−	0.202683i
$421$			40.6199i			1.97969i	0.142134	+	0.989847i	$0.454603\pi$
$421$			40.6199i			1.97969i	−0.142134	+	0.989847i	$0.545397\pi$
$422$	7.91011	−	4.56691i	0.385058	−	0.222314i
$423$	40.9871	−	23.6639i	1.99286	−	1.15058i
$424$			10.6249i			0.515992i
$425$	−1.15376	−	1.99837i	−0.0559655	−	0.0969352i
$426$	−9.99674	+	17.3149i	−0.484344	+	0.838908i
$427$	−7.09587	−	4.09680i	−0.343393	−	0.198258i
$428$	12.8755			0.622360
$429$	−48.5330	+	0.266319i	−2.34320	+	0.0128580i
$430$	−11.0073			−0.530821
$431$	10.1945	+	5.88581i	0.491053	+	0.283509i	0.725011	−	0.688737i	$-0.241835\pi$
$431$	10.1945	+	5.88581i	0.491053	+	0.283509i	−0.233958	+	0.972247i	$0.575168\pi$
$432$	−8.50367	+	14.7288i	−0.409133	+	0.708639i
$433$	−16.5004	−	28.5795i	−0.792959	−	1.37345i	−0.924127	−	0.382085i	$-0.875206\pi$
$433$	−16.5004	−	28.5795i	−0.792959	−	1.37345i	0.131168	−	0.991360i	$-0.458127\pi$
$434$			4.47232i			0.214678i
$435$	22.6966	−	13.1039i	1.08822	−	0.628282i
$436$	0.185550	−	0.107127i	0.00888622	−	0.00513046i
$437$			0.623945i			0.0298473i
$438$	22.4274	+	38.8454i	1.07162	+	1.85611i
$439$	0.348718	−	0.603998i	0.0166434	−	0.0288272i	−0.857584	−	0.514344i	$-0.828035\pi$
$439$	0.348718	−	0.603998i	0.0166434	−	0.0288272i	0.874227	+	0.485517i	$0.161369\pi$
$440$	3.49837	+	2.01978i	0.166778	+	0.0962895i
$441$	39.9375			1.90179
$442$	−4.12034	+	7.22794i	−0.195985	+	0.343798i
$443$	28.6297			1.36024			0.680120	−	0.733101i	$-0.261928\pi$
$443$	28.6297			1.36024			0.680120	+	0.733101i	$0.261928\pi$
$444$	17.9951	+	10.3895i	0.854010	+	0.493063i
$445$	−0.485517	+	0.840939i	−0.0230157	+	0.0398644i
$446$	2.90595	+	5.03326i	0.137601	+	0.238332i
$447$			55.0800i			2.60519i
$448$	1.24653	−	0.719687i	0.0588932	−	0.0340020i
$449$	−5.87601	+	3.39251i	−0.277306	+	0.160103i	−0.632203	−	0.774803i	$-0.717849\pi$
$449$	−5.87601	+	3.39251i	−0.277306	+	0.160103i	0.354897	+	0.934905i	$0.384516\pi$
$450$			8.10387i			0.382020i
$451$	−1.53709	−	2.66232i	−0.0723788	−	0.125364i
$452$	−0.0642973	+	0.111366i	−0.00302429	+	0.00523823i
$453$	−19.3589	−	11.1769i	−0.909560	−	0.525135i
$454$	−11.5432			−0.541751
$455$	0.0284776	+	5.18966i	0.00133505	+	0.243295i
$456$	1.33225			0.0623882
$457$	15.5355	+	8.96940i	0.726718	+	0.419571i	0.817220	−	0.576325i	$-0.195514\pi$
$457$	15.5355	+	8.96940i	0.726718	+	0.419571i	−0.0905021	+	0.995896i	$0.528847\pi$
$458$	−6.43774	+	11.1505i	−0.300816	+	0.521029i
$459$	19.6224	+	33.9870i	0.915894	+	1.58638i
$460$		−	1.56063i		−	0.0727646i
$461$	−23.2937	+	13.4486i	−1.08489	+	0.626364i	−0.932213	−	0.361911i	$-0.882124\pi$
$461$	−23.2937	+	13.4486i	−1.08489	+	0.626364i	−0.152682	+	0.988275i	$0.548791\pi$
$462$	16.7794	−	9.68759i	0.780648	−	0.450708i
$463$		−	26.8402i		−	1.24737i	−0.781677	−	0.623684i	$-0.785635\pi$
$463$		−	26.8402i		−	1.24737i	0.781677	−	0.623684i	$-0.214365\pi$
$464$	3.93244	+	6.81119i	0.182559	+	0.316202i
$465$	5.17686	−	8.96658i	0.240071	−	0.415815i
$466$	−9.01957	−	5.20745i	−0.417824	−	0.241231i
$467$	9.48726			0.439018			0.219509	−	0.975610i	$-0.429554\pi$
$467$	9.48726			0.439018			0.219509	+	0.975610i	$0.429554\pi$
$468$	25.2238	−	14.7481i	1.16597	−	0.681731i
$469$	14.9706			0.691279
$470$	5.05772	+	2.92008i	0.233295	+	0.134693i
$471$	−9.69157	+	16.7863i	−0.446564	+	0.773471i
$472$	−1.73205	−	3.00000i	−0.0797241	−	0.138086i
$473$		−	44.4649i		−	2.04450i
$474$	−2.68803	+	1.55193i	−0.123465	+	0.0712827i
$475$	0.346241	−	0.199902i	0.0158866	−	0.00917214i
$476$		−	3.32138i		−	0.152235i
$477$	−43.0515	−	74.5674i	−1.97119	−	3.41420i
$478$	9.19007	−	15.9177i	0.420344	−	0.728057i
$479$	9.71206	+	5.60726i	0.443755	+	0.256202i	0.705189	−	0.709019i	$-0.250862\pi$
$479$	9.71206	+	5.60726i	0.443755	+	0.256202i	−0.261434	+	0.965221i	$0.584195\pi$
$480$	−3.33225			−0.152096
$481$	−11.3483	−	19.4091i	−0.517437	−	0.884977i
$482$	0.619706			0.0282268
$483$	−6.48247	−	3.74265i	−0.294962	−	0.170297i
$484$	−2.65906	+	4.60563i	−0.120866	+	0.209347i
$485$	6.15919	+	10.6680i	0.279674	+	0.484410i
$486$		−	56.8130i		−	2.57709i
$487$	24.0137	−	13.8643i	1.08816	−	0.628252i	0.155077	−	0.987902i	$-0.450437\pi$
$487$	24.0137	−	13.8643i	1.08816	−	0.628252i	0.933087	+	0.359650i	$0.117104\pi$
$488$	−4.92983	+	2.84624i	−0.223163	+	0.128843i
$489$			13.9035i			0.628737i
$490$	2.46410	+	4.26795i	0.111317	+	0.192806i
$491$	13.9377	−	24.1409i	0.629002	−	1.08946i	−0.358751	−	0.933433i	$-0.616797\pi$
$491$	13.9377	−	24.1409i	0.629002	−	1.08946i	0.987752	−	0.156029i	$-0.0498694\pi$
$492$	2.19615	+	1.26795i	0.0990102	+	0.0571636i
$493$	18.1484			0.817361
$494$	−1.25232	−	0.713896i	−0.0563448	−	0.0321197i
$495$	−32.7361			−1.47138
$496$	2.69085	+	1.55356i	0.120823	+	0.0697571i
$497$	−4.31812	+	7.47921i	−0.193694	+	0.335488i
$498$	−17.3055	−	29.9739i	−0.775476	−	1.34316i
$499$			36.8040i			1.64757i	0.566901	+	0.823786i	$0.308142\pi$
$499$			36.8040i			1.64757i	−0.566901	+	0.823786i	$0.691858\pi$
$500$	−0.866025	+	0.500000i	−0.0387298	+	0.0223607i
$501$	45.0432	−	26.0057i	2.01238	−	1.16185i
$502$		−	5.30752i		−	0.236886i
$503$	19.2848	+	33.4022i	0.859865	+	1.48933i	0.872057	+	0.489404i	$0.162785\pi$
$503$	19.2848	+	33.4022i	0.859865	+	1.48933i	−0.0121928	+	0.999926i	$0.503881\pi$
$504$	−5.83225	+	10.1017i	−0.259789	+	0.449968i
$505$	−4.18718	−	2.41747i	−0.186327	−	0.107576i
$506$	6.30426			0.280258
$507$	−43.3166	+	0.475403i	−1.92376	+	0.0211134i
$508$	−16.1244			−0.715403
$509$	24.9870	+	14.4262i	1.10753	+	0.639431i	0.938188	−	0.346126i	$-0.112503\pi$
$509$	24.9870	+	14.4262i	1.10753	+	0.639431i	0.169340	+	0.985558i	$0.445837\pi$
$510$	−3.84461	+	6.65906i	−0.170242	+	0.294868i
$511$	9.68759	+	16.7794i	0.428554	+	0.742277i
$512$		−	1.00000i		−	0.0441942i
$513$	−5.88863	+	3.39980i	−0.259990	+	0.150105i
$514$	21.4230	−	12.3686i	0.944927	−	0.545554i
$515$			5.73205i			0.252584i
$516$	18.3396	+	31.7651i	0.807355	+	1.39838i
$517$	−11.7959	+	20.4310i	−0.518781	+	0.898556i
$518$	7.77304	+	4.48777i	0.341528	+	0.197181i
$519$	−19.3752			−0.850476
$520$	3.13234	+	1.78561i	0.137362	+	0.0783044i
$521$	−10.6422			−0.466241			−0.233121	−	0.972448i	$-0.574894\pi$
$521$	−10.6422			−0.466241			−0.233121	+	0.972448i	$0.574894\pi$
$522$	−55.1970	−	31.8680i	−2.41591	−	1.39482i
$523$	−19.0759	+	33.0404i	−0.834130	+	1.44476i	0.0606070	+	0.998162i	$0.480696\pi$
$523$	−19.0759	+	33.0404i	−0.834130	+	1.44476i	−0.894737	+	0.446594i	$0.852637\pi$
$524$	1.39005	+	2.40764i	0.0607246	+	0.105178i
$525$			4.79635i			0.209330i
$526$	−4.44211	+	2.56466i	−0.193685	+	0.111824i
$527$	6.20919	−	3.58488i	0.270477	−	0.156160i
$528$		−	13.4608i		−	0.585808i
$529$	10.2822	+	17.8093i	0.447053	+	0.774319i
$530$	5.31246	−	9.20145i	0.230759	−	0.399686i
$531$	24.3116	+	14.0363i	1.05503	+	0.609124i
$532$	0.575468			0.0249497
$533$	−1.38496	−	2.36871i	−0.0599894	−	0.102600i
$534$	3.23572			0.140023
$535$	−11.1505	−	6.43774i	−0.482078	−	0.278328i
$536$	5.20039	−	9.00734i	0.224623	−	0.389058i
$537$	−28.1112	−	48.6900i	−1.21309	−	2.10113i
$538$		−	6.81373i		−	0.293761i
$539$	−17.2407	+	9.95391i	−0.742609	+	0.428745i
$540$	14.7288	−	8.50367i	0.633826	−	0.365940i
$541$			1.46593i			0.0630252i	0.999503	+	0.0315126i	$0.0100324\pi$
$541$			1.46593i			0.0630252i	−0.999503	+	0.0315126i	$0.989968\pi$
$542$	−11.0106	−	19.0709i	−0.472946	−	0.819166i
$543$	−21.0276	+	36.4209i	−0.902381	+	1.56297i
$544$	−1.99837	−	1.15376i	−0.0856794	−	0.0494670i
$545$	−0.214254			−0.00917765
$546$	14.9289	−	8.72879i	0.638899	−	0.373558i
$547$	−16.2374			−0.694262			−0.347131	−	0.937817i	$-0.612844\pi$
$547$	−16.2374			−0.694262			−0.347131	+	0.937817i	$0.612844\pi$
$548$	−4.73487	−	2.73368i	−0.202264	−	0.116777i
$549$	23.0656	−	39.9507i	0.984414	−	1.70505i
$550$	−2.01978	−	3.49837i	−0.0861239	−	0.149171i
$551$			3.14441i			0.133957i
$552$	−4.50367	+	2.60020i	−0.191689	+	0.110672i
$553$	−1.16110	+	0.670362i	−0.0493751	+	0.0285067i
$554$			25.4303i			1.08043i
$555$	−10.3895	−	17.9951i	−0.441009	−	0.763850i
$556$	−0.107258	+	0.185777i	−0.00454877	+	0.00787869i
$557$	28.8599	+	16.6623i	1.22283	+	0.706004i	0.965521	−	0.260324i	$-0.0838293\pi$
$557$	28.8599	+	16.6623i	1.22283	+	0.706004i	0.257314	+	0.966328i	$0.417163\pi$
$558$	−25.1797			−1.06594
$559$	−0.217777	−	39.6869i	−0.00921099	−	1.67858i
$560$	−1.43937			−0.0608246
$561$	−26.8997	−	15.5306i	−1.13571	−	0.655701i
$562$	−12.5477	+	21.7332i	−0.529293	+	0.916762i
$563$	3.75678	+	6.50693i	0.158329	+	0.274234i	0.934266	−	0.356576i	$-0.116056\pi$
$563$	3.75678	+	6.50693i	0.158329	+	0.274234i	−0.775937	+	0.630810i	$0.782723\pi$
$564$		−	19.4608i		−	0.819449i
$565$	0.111366	−	0.0642973i	0.00468521	−	0.00270501i
$566$	1.52938	−	0.882986i	0.0642845	−	0.0371147i
$567$		−	46.5797i		−	1.95616i
$568$	3.00000	+	5.19615i	0.125877	+	0.218026i
$569$	6.45619	−	11.1825i	0.270658	−	0.468793i	−0.698373	−	0.715734i	$-0.746092\pi$
$569$	6.45619	−	11.1825i	0.270658	−	0.468793i	0.969030	+	0.246941i	$0.0794255\pi$
$570$	−1.15376	−	0.666123i	−0.0483257	−	0.0279008i
$571$	3.47470			0.145412			0.0727059	−	0.997353i	$-0.476837\pi$
$571$	3.47470			0.145412			0.0727059	+	0.997353i	$0.476837\pi$
$572$	−7.21311	+	12.6533i	−0.301595	+	0.529062i
$573$	4.46762			0.186638
$574$	0.948635	+	0.547694i	0.0395952	+	0.0228603i
$575$	−0.780313	+	1.35154i	−0.0325413	+	0.0563632i
$576$	4.05193	+	7.01815i	0.168831	+	0.292423i
$577$			8.80287i			0.366468i	0.983069	+	0.183234i	$0.0586566\pi$
$577$			8.80287i			0.366468i	−0.983069	+	0.183234i	$0.941343\pi$
$578$	10.1112	−	5.83768i	0.420569	−	0.242815i
$579$	48.3189	−	27.8970i	2.00807	−	1.15936i
$580$		−	7.86488i		−	0.326572i
$581$	−7.47514	−	12.9473i	−0.310121	−	0.537146i
$582$	20.5239	−	35.5485i	0.850745	−	1.47353i
$583$	37.1699	+	21.4601i	1.53942	+	0.888785i
$584$	13.4608			0.557014
$585$	−29.2185	+	0.160333i	−1.20803	+	0.00662894i
$586$	−18.4029			−0.760217
$587$	30.9967	+	17.8960i	1.27937	+	0.738646i	0.976733	−	0.214459i	$-0.0687989\pi$
$587$	30.9967	+	17.8960i	1.27937	+	0.738646i	0.302639	+	0.953105i	$0.402132\pi$
$588$	8.21099	−	14.2219i	0.338616	−	0.586500i
$589$	0.621121	+	1.07581i	0.0255929	+	0.0443281i
$590$			3.46410i			0.142615i
$591$	−2.87640	+	1.66069i	−0.118319	+	0.0683117i
$592$	5.40029	−	3.11786i	0.221951	−	0.128143i
$593$		−	3.93555i		−	0.161613i	−0.996730	−	0.0808067i	$-0.974250\pi$
$593$		−	3.93555i		−	0.161613i	0.996730	−	0.0808067i	$-0.0257497\pi$
$594$	34.3512	+	59.4980i	1.40945	+	2.44123i
$595$	−1.66069	+	2.87640i	−0.0680817	+	0.117921i
$596$	14.3149	+	8.26469i	0.586360	+	0.338535i
$597$	8.71395			0.356638
$598$	5.62683	−	0.0308766i	0.230098	−	0.00126264i
$599$	−9.50704			−0.388447			−0.194223	−	0.980957i	$-0.562219\pi$
$599$	−9.50704			−0.388447			−0.194223	+	0.980957i	$0.562219\pi$
$600$	2.88581	+	1.66612i	0.117813	+	0.0680192i
$601$	−17.4935	+	30.2996i	−0.713574	+	1.23595i	0.249933	+	0.968263i	$0.419591\pi$
$601$	−17.4935	+	30.2996i	−0.713574	+	1.23595i	−0.963507	+	0.267683i	$0.913742\pi$
$602$	7.92184	+	13.7210i	0.322870	+	0.559227i
$603$			84.2866i			3.43241i
$604$	−5.80956	+	3.35415i	−0.236388	+	0.136478i
$605$	4.60563	−	2.65906i	0.187245	−	0.108106i
$606$			16.1112i			0.654473i
$607$	8.08054	+	13.9959i	0.327979	+	0.568076i	0.982111	−	0.188304i	$-0.0602991\pi$
$607$	8.08054	+	13.9959i	0.327979	+	0.568076i	−0.654132	+	0.756381i	$0.726966\pi$
$608$	0.199902	−	0.346241i	0.00810710	−	0.0140419i
$609$	−32.6688	−	18.8614i	−1.32381	−	0.764301i
$610$	5.69248			0.230482
$611$	−10.4283	+	18.2934i	−0.421883	+	0.740071i
$612$	18.6998			0.755896
$613$	−7.68335	−	4.43598i	−0.310327	−	0.179168i	0.336746	−	0.941596i	$-0.390674\pi$
$613$	−7.68335	−	4.43598i	−0.310327	−	0.179168i	−0.647073	+	0.762428i	$0.724007\pi$
$614$	4.20365	−	7.28094i	0.169646	−	0.293835i
$615$	−1.26795	−	2.19615i	−0.0511286	−	0.0885574i
$616$		−	5.81445i		−	0.234271i
$617$	−9.39557	+	5.42453i	−0.378251	+	0.218383i	−0.677057	−	0.735930i	$-0.736745\pi$
$617$	−9.39557	+	5.42453i	−0.378251	+	0.218383i	0.298806	+	0.954314i	$0.403412\pi$
$618$	16.5416	−	9.55030i	0.665401	−	0.384170i
$619$			5.82727i			0.234218i	0.993119	+	0.117109i	$0.0373627\pi$
$619$			5.82727i			0.234218i	−0.993119	+	0.117109i	$0.962637\pi$
$620$	−1.55356	−	2.69085i	−0.0623926	−	0.108067i
$621$	13.2711	−	22.9861i	0.532549	−	0.922402i
$622$	−29.1505	−	16.8300i	−1.16883	−	0.674823i
$623$	1.39768			0.0559969
$624$	−0.0659276	−	12.0144i	−0.00263921	−	0.480961i
$625$	1.00000			0.0400000
$626$	23.3834	+	13.5004i	0.934589	+	0.539585i
$627$	2.69085	−	4.66069i	0.107462	−	0.186130i
$628$	2.90842	+	5.03753i	0.116059	+	0.201019i
$629$		−	14.3890i		−	0.573729i
$630$	10.1017	−	5.83225i	0.402463	−	0.232362i
$631$	−8.17169	+	4.71793i	−0.325310	+	0.187818i	−0.653757	−	0.756705i	$-0.726808\pi$
$631$	−8.17169	+	4.71793i	−0.325310	+	0.187818i	0.328447	+	0.944522i	$0.393475\pi$
$632$			0.931464i			0.0370516i
$633$	15.2181	+	26.3584i	0.604863	+	1.04765i
$634$	5.12846	−	8.88276i	0.203677	−	0.352779i
$635$	13.9641	+	8.06218i	0.554148	+	0.319938i
$636$	−35.4049			−1.40389
$637$	−15.3393	+	8.96875i	−0.607766	+	0.355355i
$638$	31.7707			1.25782
$639$	−42.1089	−	24.3116i	−1.66580	−	0.961752i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	20.2877	+	35.1392i	0.801314	+	1.38792i	0.918751	+	0.394837i	$0.129199\pi$
$641$	20.2877	+	35.1392i	0.801314	+	1.38792i	−0.117437	+	0.993080i	$0.537468\pi$
$642$			42.9043i			1.69330i
$643$	−5.08527	+	2.93598i	−0.200543	+	0.115784i	−0.596909	−	0.802309i	$-0.703605\pi$
$643$	−5.08527	+	2.93598i	−0.200543	+	0.115784i	0.396365	+	0.918093i	$0.370271\pi$
$644$	−1.94537	+	1.12316i	−0.0766585	+	0.0442588i
$645$		−	36.6792i		−	1.44424i
$646$	−0.461278	−	0.798957i	−0.0181487	−	0.0314345i
$647$	19.3652	−	33.5416i	0.761326	−	1.31866i	−0.180841	−	0.983512i	$-0.557882\pi$
$647$	19.3652	−	33.5416i	0.761326	−	1.31866i	0.942167	−	0.335143i	$-0.108785\pi$
$648$	−28.0255	−	16.1805i	−1.10095	−	0.635631i
$649$	−13.9935			−0.549292
$650$	−1.81988	−	3.11256i	−0.0713817	−	0.122085i
$651$	−14.9029			−0.584089
$652$	3.61341	+	2.08620i	0.141512	+	0.0817020i
$653$	6.45492	−	11.1802i	0.252601	−	0.437517i	−0.711641	−	0.702544i	$-0.752047\pi$
$653$	6.45492	−	11.1802i	0.252601	−	0.437517i	0.964241	+	0.265027i	$0.0853808\pi$
$654$	0.356974	+	0.618298i	0.0139588	+	0.0241774i
$655$		−	2.78010i		−	0.108627i
$656$	0.659061	−	0.380509i	0.0257320	−	0.0148564i
$657$	−94.4703	+	54.5424i	−3.68564	+	2.12790i
$658$		−	8.40617i		−	0.327707i
$659$	3.20654	+	5.55389i	0.124909	+	0.216349i	0.921697	−	0.387910i	$-0.126803\pi$
$659$	3.20654	+	5.55389i	0.124909	+	0.216349i	−0.796788	+	0.604259i	$0.793469\pi$
$660$	−6.73042	+	11.6574i	−0.261981	+	0.453765i
$661$	−6.05300	−	3.49470i	−0.235434	−	0.135928i	0.377642	−	0.925952i	$-0.376735\pi$
$661$	−6.05300	−	3.49470i	−0.235434	−	0.135928i	−0.613076	+	0.790024i	$0.710068\pi$
$662$	−4.52938			−0.176039
$663$	−24.0853	−	13.7300i	−0.935395	−	0.533228i
$664$	−10.3867			−0.403080
$665$	−0.498370	−	0.287734i	−0.0193260	−	0.0111578i
$666$	−25.2667	+	43.7633i	−0.979066	+	1.69579i
$667$	−6.13707	−	10.6297i	−0.237628	−	0.411584i
$668$		−	15.6085i		−	0.603912i
$669$	−16.7721	+	9.68335i	−0.648445	+	0.374380i
$670$	−9.00734	+	5.20039i	−0.347984	+	0.200909i
$671$			22.9952i			0.887719i
$672$	2.39817	+	4.15376i	0.0925116	+	0.160235i
$673$	−23.3083	+	40.3712i	−0.898470	+	1.55620i	−0.0690207	+	0.997615i	$0.521987\pi$
$673$	−23.3083	+	40.3712i	−0.898470	+	1.55620i	−0.829450	+	0.558581i	$0.811346\pi$
$674$	5.82623	+	3.36377i	0.224418	+	0.129568i
$675$	−17.0073			−0.654613
$676$	−6.37605	+	11.3290i	−0.245233	+	0.435730i
$677$	6.85102			0.263306			0.131653	−	0.991296i	$-0.457972\pi$
$677$	6.85102			0.263306			0.131653	+	0.991296i	$0.457972\pi$
$678$	−0.371100	−	0.214254i	−0.0142520	−	0.00822839i
$679$	8.86538	−	15.3553i	0.340222	−	0.589282i
$680$	1.15376	+	1.99837i	0.0442446	+	0.0766340i
$681$		−	38.4649i		−	1.47398i
$682$	10.8699	−	6.27573i	0.416229	−	0.240310i
$683$	−21.2374	+	12.2614i	−0.812627	+	0.469171i	−0.847867	−	0.530208i	$-0.822114\pi$
$683$	−21.2374	+	12.2614i	−0.812627	+	0.469171i	0.0352402	+	0.999379i	$0.488780\pi$
$684$			3.23996i			0.123883i
$685$	2.73368	+	4.73487i	0.104449	+	0.180910i
$686$	8.58457	−	14.8689i	0.327760	−	0.567698i
$687$	−37.1562	−	21.4521i	−1.41760	−	0.818451i
$688$	11.0073			0.419651
$689$	33.2809	+	18.9720i	1.26790	+	0.722776i
$690$	5.20039			0.197976
$691$	8.72060	+	5.03484i	0.331747	+	0.191534i	0.656617	−	0.754225i	$-0.271987\pi$
$691$	8.72060	+	5.03484i	0.331747	+	0.191534i	−0.324869	+	0.945759i	$0.605320\pi$
$692$	−2.90723	+	5.03546i	−0.110516	+	0.191420i
$693$	23.5598	+	40.8067i	0.894961	+	1.55012i
$694$		−	3.14572i		−	0.119410i
$695$	0.185777	−	0.107258i	0.00704692	−	0.00406854i
$696$	−22.6966	+	13.1039i	−0.860311	+	0.496701i
$697$		−	1.75606i		−	0.0665156i
$698$	−5.25246	−	9.09752i	−0.198808	−	0.344346i
$699$	17.3525	−	30.0554i	0.656333	−	1.13680i
$700$	1.24653	+	0.719687i	0.0471146	+	0.0272016i
$701$	−10.4149			−0.393366			−0.196683	−	0.980467i	$-0.563017\pi$
$701$	−10.4149			−0.393366			−0.196683	+	0.980467i	$0.563017\pi$
$702$	30.9514	+	52.9364i	1.16818	+	1.99795i
$703$	2.49307			0.0940279
$704$	−3.49837	−	2.01978i	−0.131850	−	0.0761235i
$705$	−9.73042	+	16.8536i	−0.366469	+	0.634743i
$706$	−16.4988	−	28.5767i	−0.620940	−	1.07550i
$707$			6.95928i			0.261731i
$708$	9.99674	−	5.77162i	0.375700	−	0.216911i
$709$	−0.325446	+	0.187896i	−0.0122224	+	0.00705660i	−0.506099	−	0.862476i	$-0.668913\pi$
$709$	−0.325446	+	0.187896i	−0.0122224	+	0.00705660i	0.493876	+	0.869532i	$0.335580\pi$
$710$		−	6.00000i		−	0.225176i
$711$	−3.77423	−	6.53716i	−0.141545	−	0.245163i
$712$	0.485517	−	0.840939i	0.0181955	−	0.0315155i
$713$	−4.19941	−	2.42453i	−0.157269	−	0.0907994i
$714$	11.0677			0.414197
$715$	12.5734	−	7.35154i	0.470219	−	0.274932i
$716$	−16.8722			−0.630545
$717$	53.0416	+	30.6236i	1.98087	+	1.14366i
$718$	−12.1244	+	21.0000i	−0.452477	+	0.783713i
$719$	−9.66547	−	16.7411i	−0.360461	−	0.624337i	0.627576	−	0.778556i	$-0.284047\pi$
$719$	−9.66547	−	16.7411i	−0.360461	−	0.624337i	−0.988037	+	0.154218i	$0.950714\pi$
$720$		−	8.10387i		−	0.302013i
$721$	7.14520	−	4.12528i	0.266101	−	0.153634i
$722$	−16.3161	+	9.42008i	−0.607221	+	0.350579i
$723$			2.06501i			0.0767987i
$724$	6.31034	+	10.9298i	0.234522	+	0.406204i
$725$	−3.93244	+	6.81119i	−0.146047	+	0.252961i
$726$	−15.3471	−	8.86065i	−0.569584	−	0.328849i
$727$	31.3390			1.16230			0.581150	−	0.813797i	$-0.302603\pi$
$727$	31.3390			1.16230			0.581150	+	0.813797i	$0.302603\pi$
$728$	−0.0284776	−	5.18966i	−0.00105545	−	0.192342i
$729$	92.2317			3.41599
$730$	−11.6574	−	6.73042i	−0.431461	−	0.249104i
$731$	12.6998	−	21.9967i	0.469720	−	0.813579i
$732$	−9.48438	−	16.4274i	−0.350553	−	0.607175i
$733$			19.6207i			0.724707i	0.932041	+	0.362353i	$0.118027\pi$
$733$			19.6207i			0.724707i	−0.932041	+	0.362353i	$0.881973\pi$
$734$	17.1460	−	9.89924i	0.632870	−	0.365387i
$735$	−14.2219	+	8.21099i	−0.524581	+	0.302867i
$736$			1.56063i			0.0575254i
$737$	−21.0073	−	36.3858i	−0.773815	−	1.34029i
$738$	−3.08359	+	5.34094i	−0.113509	+	0.196603i
$739$	−10.3601	−	5.98141i	−0.381103	−	0.220030i	0.297195	−	0.954817i	$-0.403949\pi$
$739$	−10.3601	−	5.98141i	−0.381103	−	0.220030i	−0.678298	+	0.734787i	$0.737282\pi$
$740$	−6.23572			−0.229230
$741$	2.37888	−	4.17305i	0.0873903	−	0.153301i
$742$	−15.2932			−0.561432
$743$	−17.2540	−	9.96162i	−0.632989	−	0.365457i	0.148920	−	0.988849i	$-0.452420\pi$
$743$	−17.2540	−	9.96162i	−0.632989	−	0.365457i	−0.781909	+	0.623393i	$0.785754\pi$
$744$	−5.17686	+	8.96658i	−0.189793	+	0.328731i
$745$	−8.26469	−	14.3149i	−0.302795	−	0.524456i
$746$		−	4.79113i		−	0.175416i
$747$	72.8952	−	42.0860i	2.66709	−	1.53985i
$748$	−8.07255	+	4.66069i	−0.295162	+	0.170412i
$749$			18.5326i			0.677168i
$750$	−1.66612	−	2.88581i	−0.0608382	−	0.105375i
$751$	21.4608	−	37.1713i	0.783117	−	1.35640i	−0.147000	−	0.989136i	$-0.546962\pi$
$751$	21.4608	−	37.1713i	0.783117	−	1.35640i	0.930117	−	0.367262i	$-0.119705\pi$
$752$	−5.05772	−	2.92008i	−0.184436	−	0.106484i
$753$	17.6860			0.644512
$754$	28.3568	−	0.155605i	1.03269	−	0.00566678i
$755$	6.70830			0.244140
$756$	−21.2002	−	12.2400i	−0.771045	−	0.445163i
$757$	17.8750	−	30.9604i	0.649678	−	1.12528i	−0.333522	−	0.942742i	$-0.608237\pi$
$757$	17.8750	−	30.9604i	0.649678	−	1.12528i	0.983200	−	0.182533i	$-0.0584295\pi$
$758$	−9.74760	−	16.8833i	−0.354049	−	0.613230i
$759$			21.0073i			0.762518i
$760$	−0.346241	+	0.199902i	−0.0125595	+	0.00725121i
$761$	26.1232	−	15.0822i	0.946965	−	0.546731i	0.0548284	−	0.998496i	$-0.482539\pi$
$761$	26.1232	−	15.0822i	0.946965	−	0.546731i	0.892137	+	0.451765i	$0.149205\pi$
$762$		−	53.7303i		−	1.94644i
$763$	0.154196	+	0.267076i	0.00558227	+	0.00966878i
$764$	0.670362	−	1.16110i	0.0242529	−	0.0420072i
$765$	−16.1945	−	9.34991i	−0.585514	−	0.338047i
$766$	12.8614			0.464700
$767$	−12.4898	+	0.0685363i	−0.450981	+	0.00247470i
$768$	3.33225			0.120242
$769$	−21.0236	−	12.1380i	−0.758132	−	0.437708i	0.0704928	−	0.997512i	$-0.477543\pi$
$769$	−21.0236	−	12.1380i	−0.758132	−	0.437708i	−0.828625	+	0.559805i	$0.810876\pi$
$770$	−2.90723	+	5.03546i	−0.104769	+	0.181465i
$771$	41.2151	+	71.3866i	1.48432	+	2.57093i
$772$		−	16.7436i		−	0.602616i
$773$	−38.5671	+	22.2667i	−1.38716	+	0.800879i	−0.992995	−	0.118160i	$-0.962300\pi$
$773$	−38.5671	+	22.2667i	−1.38716	+	0.800879i	−0.394168	+	0.919038i	$0.628967\pi$
$774$	−77.2512	+	44.6010i	−2.77674	+	1.60315i
$775$			3.10713i			0.111611i
$776$	−6.15919	−	10.6680i	−0.221102	−	0.382960i
$777$	−14.9543	+	25.9017i	−0.536484	+	0.929218i
$778$	6.01223	+	3.47116i	0.215549	+	0.124447i
$779$	0.304258			0.0109012
$780$	−5.95011	+	10.4377i	−0.213048	+	0.373731i
$781$	24.2374			0.867283
$782$	3.11871	+	1.80059i	0.111525	+	0.0643889i
$783$	66.8804	−	115.840i	2.39011	−	4.13979i
$784$	−2.46410	−	4.26795i	−0.0880036	−	0.152427i
$785$		−	5.81684i		−	0.207612i
$786$	−8.02284	+	4.63199i	−0.286165	+	0.165217i
$787$	−15.0864	+	8.71015i	−0.537773	+	0.310483i	−0.744176	−	0.667984i	$-0.767158\pi$
$787$	−15.0864	+	8.71015i	−0.537773	+	0.310483i	0.206403	+	0.978467i	$0.433824\pi$
$788$			0.996740i			0.0355074i
$789$	−8.54606	−	14.8022i	−0.304248	−	0.526973i
$790$	0.465732	−	0.806671i	0.0165700	−	0.0287001i
$791$	−0.160298	−	0.0925479i	−0.00569953	−	0.00329062i
$792$	32.7361			1.16323
$793$	0.112624	+	20.5242i	0.00399940	+	0.728837i
$794$	−4.33225			−0.153746
$795$	30.6615	+	17.7024i	1.08745	+	0.627841i
$796$	1.30752	−	2.26469i	0.0463438	−	0.0802698i
$797$	16.4801	+	28.5444i	0.583756	+	1.01110i	0.995029	+	0.0995834i	$0.0317510\pi$
$797$	16.4801	+	28.5444i	0.583756	+	1.01110i	−0.411273	+	0.911512i	$0.634916\pi$
$798$			1.91760i			0.0678823i
$799$	−11.6708	+	6.73813i	−0.412883	+	0.238378i
$800$	0.866025	−	0.500000i	0.0306186	−	0.0176777i
$801$			7.86912i			0.278042i
$802$	−11.8616	−	20.5448i	−0.418847	−	0.725464i
$803$	27.1880	−	47.0910i	0.959444	−	1.66181i
$804$	30.0147	+	17.3290i	1.05854	+	0.611146i
$805$	2.24632			0.0791725
$806$	9.67112	−	5.65461i	0.340651	−	0.199175i
$807$	22.7050			0.799255
$808$	4.18718	+	2.41747i	0.147304	+	0.0850463i
$809$	−12.6664	+	21.9389i	−0.445327	+	0.771329i	−0.998075	−	0.0620195i	$-0.980246\pi$
$809$	−12.6664	+	21.9389i	−0.445327	+	0.771329i	0.552748	+	0.833348i	$0.313579\pi$
$810$	16.1805	+	28.0255i	0.568526	+	0.984716i
$811$		−	42.4806i		−	1.49170i	−0.666117	−	0.745848i	$-0.732045\pi$
$811$		−	42.4806i		−	1.49170i	0.666117	−	0.745848i	$-0.267955\pi$
$812$	−9.80385	+	5.66025i	−0.344048	+	0.198636i
$813$	63.5490	−	36.6900i	2.22876	−	1.28678i
$814$		−	25.1896i		−	0.882896i
$815$	−2.08620	−	3.61341i	−0.0730765	−	0.126572i
$816$	3.84461	−	6.65906i	0.134588	−	0.233114i
$817$	3.81119	+	2.20039i	0.133337	+	0.0769820i
$818$	−38.3792			−1.34190
$819$	21.2280	+	36.3064i	0.741767	+	1.26865i
$820$	−0.761018			−0.0265759
$821$	15.3744	+	8.87640i	0.536569	+	0.309789i	0.743687	−	0.668527i	$-0.233075\pi$
$821$	15.3744	+	8.87640i	0.536569	+	0.309789i	−0.207118	+	0.978316i	$0.566408\pi$
$822$	9.10930	−	15.7778i	0.317723	−	0.550313i
$823$	16.2840	+	28.2048i	0.567626	+	0.983157i	0.996800	+	0.0799351i	$0.0254713\pi$
$823$	16.2840	+	28.2048i	0.567626	+	0.983157i	−0.429174	+	0.903222i	$0.641195\pi$
$824$		−	5.73205i		−	0.199685i
$825$	11.6574	−	6.73042i	0.405860	−	0.234323i
$826$	4.31812	−	2.49307i	0.150247	−	0.0867449i
$827$		−	26.6419i		−	0.926429i	−0.886246	−	0.463215i	$-0.846696\pi$
$827$		−	26.6419i		−	0.926429i	0.886246	−	0.463215i	$-0.153304\pi$
$828$	−6.32355	−	10.9527i	−0.219759	−	0.380633i
$829$	−8.58281	+	14.8659i	−0.298093	+	0.516313i	−0.975700	−	0.219112i	$-0.929684\pi$
$829$	−8.58281	+	14.8659i	−0.298093	+	0.516313i	0.677606	+	0.735425i	$0.263017\pi$
$830$	8.99511	+	5.19333i	0.312225	+	0.180263i
$831$	−84.7401			−2.93960
$832$	−3.13234	−	1.78561i	−0.108595	−	0.0619050i
$833$	−11.3719			−0.394014
$834$	−0.619054	−	0.357411i	−0.0214361	−	0.0123761i
$835$	−7.80426	+	13.5174i	−0.270077	+	0.467788i
$836$	−0.807519	−	1.39866i	−0.0279286	−	0.0483738i
$837$		−	52.8440i		−	1.82656i
$838$	33.4192	−	19.2946i	1.15445	−	0.666520i
$839$	−38.9951	+	22.5138i	−1.34626	+	0.777264i	−0.987718	−	0.156249i	$-0.950060\pi$
$839$	−38.9951	+	22.5138i	−1.34626	+	0.777264i	−0.358543	+	0.933513i	$0.616726\pi$
$840$		−	4.79635i		−	0.165490i
$841$	−16.4282	−	28.4545i	−0.566490	−	0.981189i
$842$	−20.3100	+	35.1779i	−0.699928	+	1.21231i
$843$	−72.4205	−	41.8120i	−2.49430	−	1.44008i
$844$	9.13381			0.314399
$845$	11.1863	−	6.62316i	0.384821	−	0.227844i
$846$	47.3279			1.62717
$847$	−6.62922	−	3.82738i	−0.227783	−	0.131510i
$848$	−5.31246	+	9.20145i	−0.182431	+	0.315979i
$849$	2.94233	+	5.09626i	0.100980	+	0.174903i
$850$		−	2.30752i		−	0.0791472i
$851$	−8.42784	+	4.86582i	−0.288903	+	0.166798i
$852$	−17.3149	+	9.99674i	−0.593197	+	0.342483i
$853$		−	31.0013i		−	1.06146i	−0.847540	−	0.530731i	$-0.821917\pi$
$853$		−	31.0013i		−	1.06146i	0.847540	−	0.530731i	$-0.178083\pi$
$854$	−4.09680	−	7.09587i	−0.140190	−	0.242816i
$855$	1.61998	−	2.80589i	0.0554022	−	0.0959594i
$856$	11.1505	+	6.43774i	0.381116	+	0.220038i
$857$	−27.3813			−0.935326			−0.467663	−	0.883907i	$-0.654904\pi$
$857$	−27.3813			−0.935326			−0.467663	+	0.883907i	$0.654904\pi$
$858$	−42.1640	−	24.0359i	−1.43945	−	0.820571i
$859$	8.36050			0.285256			0.142628	−	0.989776i	$-0.454445\pi$
$859$	8.36050			0.285256			0.142628	+	0.989776i	$0.454445\pi$
$860$	−9.53264	−	5.50367i	−0.325060	−	0.187674i
$861$	−1.82505	+	3.16108i	−0.0621976	+	0.107729i
$862$	5.88581	+	10.1945i	0.200471	+	0.347227i
$863$		−	40.2398i		−	1.36978i	−0.728647	−	0.684889i	$-0.759850\pi$
$863$		−	40.2398i		−	1.36978i	0.728647	−	0.684889i	$-0.240150\pi$
$864$	−14.7288	+	8.50367i	−0.501084	+	0.289301i
$865$	5.03546	−	2.90723i	0.171211	−	0.0988486i
$866$		−	33.0008i		−	1.12141i
$867$	19.4526	+	33.6929i	0.660644	+	1.14427i
$868$	−2.23616	+	3.87314i	−0.0759002	+	0.131463i
$869$	3.25860	+	1.88136i	0.110541	+	0.0638206i
$870$	26.2077			0.888525
$871$	−18.9282	−	32.3731i	−0.641358	−	1.09692i
$872$	0.214254			0.00725557
$873$	86.4523	+	49.9133i	2.92597	+	1.68931i
$874$	−0.311973	+	0.540352i	−0.0105526	+	0.0182777i
$875$	−0.719687	−	1.24653i	−0.0243299	−	0.0421405i
$876$			44.8548i			1.51550i
$877$	−45.0918	+	26.0338i	−1.52264	+	0.879098i	−0.523000	+	0.852333i	$0.675187\pi$
$877$	−45.0918	+	26.0338i	−1.52264	+	0.879098i	−0.999642	+	0.0267652i	$0.991479\pi$
$878$	0.603998	−	0.348718i	0.0203839	−	0.0117687i
$879$		−	61.3230i		−	2.06837i
$880$	2.01978	+	3.49837i	0.0680869	+	0.117930i
$881$	−17.2542	+	29.8852i	−0.581310	+	1.00686i	0.414015	+	0.910270i	$0.364126\pi$
$881$	−17.2542	+	29.8852i	−0.581310	+	1.00686i	−0.995324	+	0.0965881i	$0.969207\pi$
$882$	34.5869	+	19.9688i	1.16460	+	0.672383i
$883$	−28.2064			−0.949222			−0.474611	−	0.880196i	$-0.657411\pi$
$883$	−28.2064			−0.949222			−0.474611	+	0.880196i	$0.657411\pi$
$884$	−7.18229	+	4.19941i	−0.241567	+	0.141242i
$885$	−11.5432			−0.388022
$886$	24.7941	+	14.3149i	0.832973	+	0.480917i
$887$	−1.06098	+	1.83768i	−0.0356244	+	0.0617032i	−0.883288	−	0.468831i	$-0.844675\pi$
$887$	−1.06098	+	1.83768i	−0.0356244	+	0.0617032i	0.847664	+	0.530534i	$0.178009\pi$
$888$	10.3895	+	17.9951i	0.348648	+	0.603876i
$889$		−	23.2090i		−	0.778404i
$890$	−0.840939	+	0.485517i	−0.0281884	+	0.0162746i
$891$	−113.211	+	65.3624i	−3.79271	+	2.18972i
$892$			5.81191i			0.194597i
$893$	−1.16746	−	2.02210i	−0.0390676	−	0.0676670i
$894$	−27.5400	+	47.7006i	−0.921075	+	1.59535i
$895$	14.6118	+	8.43611i	0.488418	+	0.281988i
$896$	1.43937			0.0480861
$897$	0.102888	+	18.7500i	0.00343534	+	0.626044i
$898$	−6.78503			−0.226419
$899$	−21.1632	−	12.2186i	−0.705833	−	0.407513i
$900$	−4.05193	+	7.01815i	−0.135064	+	0.233938i
$901$	12.2586	+	21.2325i	0.408393	+	0.707358i
$902$		−	3.07418i		−	0.102359i
$903$	−45.7218	+	26.3975i	−1.52153	+	0.878455i
$904$	−0.111366	+	0.0642973i	−0.00370398	+	0.00213850i
$905$		−	12.6207i		−	0.419526i
$906$	−11.1769	−	19.3589i	−0.371326	−	0.643156i
$907$	14.7272	−	25.5082i	0.489007	−	0.846986i	−0.510913	−	0.859633i	$-0.670692\pi$
$907$	14.7272	−	25.5082i	0.489007	−	0.846986i	0.999920	+	0.0126471i	$0.00402580\pi$
$908$	−9.99674	−	5.77162i	−0.331753	−	0.191538i
$909$	−39.1817			−1.29958
$910$	−2.57017	+	4.50861i	−0.0852002	+	0.149459i
$911$	19.9986			0.662582			0.331291	−	0.943529i	$-0.392516\pi$
$911$	19.9986			0.662582			0.331291	+	0.943529i	$0.392516\pi$
$912$	1.15376	+	0.666123i	0.0382048	+	0.0220575i
$913$	−20.9788	+	36.3364i	−0.694297	+	1.20256i
$914$	8.96940	+	15.5355i	0.296681	+	0.513867i
$915$			18.9688i			0.627088i
$916$	−11.1505	+	6.43774i	−0.368423	+	0.212709i
$917$	−3.46549	+	2.00080i	−0.114440	+	0.0660722i
$918$			39.2448i			1.29527i
$919$	14.8564	+	25.7321i	0.490068	+	0.848822i	0.999935	−	0.0114312i	$-0.00363874\pi$
$919$	14.8564	+	25.7321i	0.490068	+	0.848822i	−0.509867	+	0.860253i	$0.670305\pi$
$920$	0.780313	−	1.35154i	0.0257262	−	0.0445590i
$921$	24.2619	+	14.0076i	0.799456	+	0.461566i
$922$	−26.8972			−0.885813
$923$	21.6330	−	0.118708i	0.712058	−	0.00390733i
$924$	19.3752			0.637397
$925$	5.40029	+	3.11786i	0.177561	+	0.102515i
$926$	13.4201	−	23.2443i	0.441011	−	0.763854i
$927$	23.2259	+	40.2284i	0.762838	+	1.32127i
$928$			7.86488i			0.258177i
$929$	−7.99348	+	4.61504i	−0.262258	+	0.151414i	−0.625364	−	0.780333i	$-0.715049\pi$
$929$	−7.99348	+	4.61504i	−0.262258	+	0.151414i	0.363106	+	0.931748i	$0.381716\pi$
$930$	8.96658	−	5.17686i	0.294026	−	0.169756i
$931$		−	1.97032i		−	0.0645745i
$932$	−5.20745	−	9.01957i	−0.170576	−	0.295446i
$933$	56.0819	−	97.1366i	1.83604	−	3.18011i
$934$	8.21621	+	4.74363i	0.268843	+	0.155216i
$935$	9.32138			0.304842
$936$	29.2185	−	0.160333i	0.955035	−	0.00524064i
$937$	−4.58731			−0.149861			−0.0749305	−	0.997189i	$-0.523873\pi$
$937$	−4.58731			−0.149861			−0.0749305	+	0.997189i	$0.523873\pi$
$938$	12.9649	+	7.48531i	0.423320	+	0.244404i
$939$	−44.9867	+	77.9192i	−1.46809	+	2.54280i
$940$	2.92008	+	5.05772i	0.0952425	+	0.164965i
$941$		−	9.00734i		−	0.293631i	−0.989164	−	0.146815i	$-0.953098\pi$
$941$		−	9.00734i		−	0.293631i	0.989164	−	0.146815i	$-0.0469024\pi$
$942$	−16.7863	+	9.69157i	−0.546927	+	0.315768i
$943$	−1.02855	+	0.593832i	−0.0334941	+	0.0193378i
$944$		−	3.46410i		−	0.112747i
$945$	12.2400	+	21.2002i	0.398166	+	0.689644i
$946$	22.2325	−	38.5078i	0.722840	−	1.25200i
$947$	47.3100	+	27.3144i	1.53737	+	0.887600i	0.998992	+	0.0448946i	$0.0142952\pi$
$947$	47.3100	+	27.3144i	1.53737	+	0.887600i	0.538376	+	0.842705i	$0.319038\pi$
$948$	−3.10387			−0.100809
$949$	24.0359	−	42.1640i	0.780237	−	1.36870i
$950$	0.399804			0.0129714
$951$	29.5995	+	17.0893i	0.959831	+	0.554159i
$952$	1.66069	−	2.87640i	0.0538233	−	0.0932247i
$953$	−9.46862	−	16.4001i	−0.306719	−	0.531252i	0.670924	−	0.741526i	$-0.265898\pi$
$953$	−9.46862	−	16.4001i	−0.306719	−	0.531252i	−0.977643	+	0.210274i	$0.932564\pi$
$954$		−	86.1030i		−	2.78769i
$955$	−1.16110	+	0.670362i	−0.0375724	+	0.0216924i
$956$	15.9177	−	9.19007i	0.514814	−	0.297228i
$957$			105.868i			3.42223i
$958$	5.60726	+	9.71206i	0.181162	+	0.313782i
$959$	3.93479	−	6.81525i	0.127061	−	0.220076i
$960$	−2.88581	−	1.66612i	−0.0931391	−	0.0537739i
$961$	21.3458			0.688573
$962$	−0.123372	−	22.4829i	−0.00397767	−	0.724877i
$963$	−104.341			−3.36235
$964$	0.536681	+	0.309853i	0.0172853	+	0.00997970i
$965$	−8.37182	+	14.5004i	−0.269498	+	0.466785i
$966$	−3.74265	−	6.48247i	−0.120418	−	0.208570i
$967$			19.1583i			0.616089i	0.951372	+	0.308044i	$0.0996745\pi$
$967$			19.1583i			0.616089i	−0.951372	+	0.308044i	$0.900325\pi$
$968$	−4.60563	+	2.65906i	−0.148030	+	0.0854654i
$969$	2.66232	−	1.53709i	0.0855261	−	0.0493785i
$970$			12.3184i			0.395519i
$971$	−11.1876	−	19.3775i	−0.359027	−	0.621853i	0.628772	−	0.777590i	$-0.283558\pi$
$971$	−11.1876	−	19.3775i	−0.359027	−	0.621853i	−0.987799	+	0.155737i	$0.950225\pi$
$972$	28.4065	−	49.2015i	0.911139	−	1.57814i
$973$	−0.267402	−	0.154385i	−0.00857253	−	0.00494935i
$974$	27.7286			0.888483
$975$	10.3718	−	6.06430i	0.332164	−	0.194213i
$976$	−5.69248			−0.182212
$977$	3.91962	+	2.26299i	0.125400	+	0.0723996i	0.561388	−	0.827553i	$-0.310268\pi$
$977$	3.91962	+	2.26299i	0.125400	+	0.0723996i	−0.435988	+	0.899952i	$0.643601\pi$
$978$	−6.95174	+	12.0408i	−0.222292	+	0.385021i
$979$	−1.96128	−	3.39703i	−0.0626827	−	0.108570i
$980$			4.92820i			0.157426i
$981$	−1.50367	+	0.868145i	−0.0480085	+	0.0277177i
$982$	24.1409	−	13.9377i	0.770366	−	0.444771i
$983$			12.1598i			0.387839i	0.981017	+	0.193919i	$0.0621200\pi$
$983$			12.1598i			0.387839i	−0.981017	+	0.193919i	$0.937880\pi$
$984$	1.26795	+	2.19615i	0.0404207	+	0.0700108i
$985$	0.498370	−	0.863202i	0.0158794	−	0.0275039i
$986$	15.7169	+	9.07418i	0.500530	+	0.288981i
$987$	28.0114			0.891613
$988$	−0.727597	−	1.24441i	−0.0231479	−	0.0395901i
$989$	−17.1783			−0.546240
$990$	−28.3503	−	16.3681i	−0.901032	−	0.520211i
$991$	28.1367	−	48.7341i	0.893790	−	1.54809i	0.0584955	−	0.998288i	$-0.481370\pi$
$991$	28.1367	−	48.7341i	0.893790	−	1.54809i	0.835295	−	0.549802i	$-0.185297\pi$
$992$	1.55356	+	2.69085i	0.0493257	+	0.0854346i
$993$		−	15.0930i		−	0.478962i
$994$	−7.47921	+	4.31812i	−0.237226	+	0.136962i
$995$	−2.26469	+	1.30752i	−0.0717955	+	0.0414511i
$996$		−	34.6109i		−	1.09669i
$997$	2.33056	+	4.03665i	0.0738097	+	0.127842i	0.900568	−	0.434715i	$-0.143151\pi$
$997$	2.33056	+	4.03665i	0.0738097	+	0.127842i	−0.826758	+	0.562557i	$0.809818\pi$
$998$	−18.4020	+	31.8732i	−0.582504	+	1.00893i
$999$	−91.8446	−	53.0265i	−2.90584	−	1.67769i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.2.l.b.121.3	yes	8
3.2	odd	2		1170.2.bs.g.901.1		8
4.3	odd	2		1040.2.da.d.641.4		8
5.2	odd	4		650.2.n.d.199.4		8
5.3	odd	4		650.2.n.e.199.1		8
5.4	even	2		650.2.m.c.251.2		8
13.2	odd	12		1690.2.e.t.991.1		8
13.3	even	3		1690.2.l.j.361.1		8
13.4	even	6		1690.2.d.k.1351.8		8
13.5	odd	4		1690.2.e.t.191.1		8
13.6	odd	12		1690.2.a.t.1.4		4
13.7	odd	12		1690.2.a.u.1.4		4
13.8	odd	4		1690.2.e.s.191.1		8
13.9	even	3		1690.2.d.k.1351.4		8
13.10	even	6	inner	130.2.l.b.101.3	✓	8
13.11	odd	12		1690.2.e.s.991.1		8
13.12	even	2		1690.2.l.j.1161.1		8
39.23	odd	6		1170.2.bs.g.361.1		8
52.23	odd	6		1040.2.da.d.881.4		8
65.19	odd	12		8450.2.a.cm.1.1		4
65.23	odd	12		650.2.n.d.49.4		8
65.49	even	6		650.2.m.c.101.2		8
65.59	odd	12		8450.2.a.ci.1.1		4
65.62	odd	12		650.2.n.e.49.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.l.b.101.3	✓	8	13.10	even	6	inner
130.2.l.b.121.3	yes	8	1.1	even	1	trivial
650.2.m.c.101.2		8	65.49	even	6
650.2.m.c.251.2		8	5.4	even	2
650.2.n.d.49.4		8	65.23	odd	12
650.2.n.d.199.4		8	5.2	odd	4
650.2.n.e.49.1		8	65.62	odd	12
650.2.n.e.199.1		8	5.3	odd	4
1040.2.da.d.641.4		8	4.3	odd	2
1040.2.da.d.881.4		8	52.23	odd	6
1170.2.bs.g.361.1		8	39.23	odd	6
1170.2.bs.g.901.1		8	3.2	odd	2
1690.2.a.t.1.4		4	13.6	odd	12
1690.2.a.u.1.4		4	13.7	odd	12
1690.2.d.k.1351.4		8	13.9	even	3
1690.2.d.k.1351.8		8	13.4	even	6
1690.2.e.s.191.1		8	13.8	odd	4
1690.2.e.s.991.1		8	13.11	odd	12
1690.2.e.t.191.1		8	13.5	odd	4
1690.2.e.t.991.1		8	13.2	odd	12
1690.2.l.j.361.1		8	13.3	even	3
1690.2.l.j.1161.1		8	13.12	even	2
8450.2.a.ci.1.1		4	65.59	odd	12
8450.2.a.cm.1.1		4	65.19	odd	12

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:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	130.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-1.66612 + 2.88581i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(-2.88581 + 1.66612i) q^{6} +(-1.24653 + 0.719687i) q^{7} +1.00000i q^{8} +(-4.05193 - 7.01815i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-1.66612 + 2.88581i) q^{3} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(-2.88581 + 1.66612i) q^{6} +(-1.24653 + 0.719687i) q^{7} +1.00000i q^{8} +(-4.05193 - 7.01815i) q^{9} +(0.500000 - 0.866025i) q^{10} +(3.49837 + 2.01978i) q^{11} -3.33225 q^{12} +(3.13234 + 1.78561i) q^{13} -1.43937 q^{14} +(2.88581 + 1.66612i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.15376 + 1.99837i) q^{17} -8.10387i q^{18} +(-0.346241 + 0.199902i) q^{19} +(0.866025 - 0.500000i) q^{20} -4.79635i q^{21} +(2.01978 + 3.49837i) q^{22} +(0.780313 - 1.35154i) q^{23} +(-2.88581 - 1.66612i) q^{24} -1.00000 q^{25} +(1.81988 + 3.11256i) q^{26} +17.0073 q^{27} +(-1.24653 - 0.719687i) q^{28} +(3.93244 - 6.81119i) q^{29} +(1.66612 + 2.88581i) q^{30} -3.10713i q^{31} +(-0.866025 + 0.500000i) q^{32} +(-11.6574 + 6.73042i) q^{33} +2.30752i q^{34} +(0.719687 + 1.24653i) q^{35} +(4.05193 - 7.01815i) q^{36} +(-5.40029 - 3.11786i) q^{37} -0.399804 q^{38} +(-10.3718 + 6.06430i) q^{39} +1.00000 q^{40} +(-0.659061 - 0.380509i) q^{41} +(2.39817 - 4.15376i) q^{42} +(-5.50367 - 9.53264i) q^{43} +4.03957i q^{44} +(-7.01815 + 4.05193i) q^{45} +(1.35154 - 0.780313i) q^{46} +5.84016i q^{47} +(-1.66612 - 2.88581i) q^{48} +(-2.46410 + 4.26795i) q^{49} +(-0.866025 - 0.500000i) q^{50} -7.68922 q^{51} +(0.0197847 + 3.60550i) q^{52} +10.6249 q^{53} +(14.7288 + 8.50367i) q^{54} +(2.01978 - 3.49837i) q^{55} +(-0.719687 - 1.24653i) q^{56} -1.33225i q^{57} +(6.81119 - 3.93244i) q^{58} +(-3.00000 + 1.73205i) q^{59} +3.33225i q^{60} +(2.84624 + 4.92983i) q^{61} +(1.55356 - 2.69085i) q^{62} +(10.1017 + 5.83225i) q^{63} -1.00000 q^{64} +(1.78561 - 3.13234i) q^{65} -13.4608 q^{66} +(-9.00734 - 5.20039i) q^{67} +(-1.15376 + 1.99837i) q^{68} +(2.60020 + 4.50367i) q^{69} +1.43937i q^{70} +(5.19615 - 3.00000i) q^{71} +(7.01815 - 4.05193i) q^{72} -13.4608i q^{73} +(-3.11786 - 5.40029i) q^{74} +(1.66612 - 2.88581i) q^{75} +(-0.346241 - 0.199902i) q^{76} -5.81445 q^{77} +(-12.0144 + 0.0659276i) q^{78} +0.931464 q^{79} +(0.866025 + 0.500000i) q^{80} +(-16.1805 + 28.0255i) q^{81} +(-0.380509 - 0.659061i) q^{82} +10.3867i q^{83} +(4.15376 - 2.39817i) q^{84} +(1.99837 - 1.15376i) q^{85} -11.0073i q^{86} +(13.1039 + 22.6966i) q^{87} +(-2.01978 + 3.49837i) q^{88} +(-0.840939 - 0.485517i) q^{89} -8.10387 q^{90} +(-5.18966 + 0.0284776i) q^{91} +1.56063 q^{92} +(8.96658 + 5.17686i) q^{93} +(-2.92008 + 5.05772i) q^{94} +(0.199902 + 0.346241i) q^{95} -3.33225i q^{96} +(-10.6680 + 6.15919i) q^{97} +(-4.26795 + 2.46410i) q^{98} -32.7361i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 + 4 * q^4 - 6 * q^6 - 4 * q^9	\( 8 q - 2 q^{3} + 4 q^{4} - 6 q^{6} - 4 q^{9} + 4 q^{10} - 6 q^{11} - 4 q^{12} - 2 q^{13} + 6 q^{15} - 4 q^{16} + 6 q^{17} - 6 q^{19} + 6 q^{22} + 12 q^{23} - 6 q^{24} - 8 q^{25} + 40 q^{27} + 2 q^{30} - 42 q^{33} + 4 q^{36} - 30 q^{37} - 12 q^{38} - 40 q^{39} + 8 q^{40} + 12 q^{41} - 6 q^{42} + 4 q^{43} - 12 q^{45} - 2 q^{48} + 8 q^{49} - 10 q^{52} + 60 q^{53} + 36 q^{54} + 6 q^{55} - 24 q^{59} + 26 q^{61} + 18 q^{62} + 12 q^{63} - 8 q^{64} + 6 q^{65} - 12 q^{66} + 24 q^{67} - 6 q^{68} + 12 q^{69} + 12 q^{72} + 6 q^{74} + 2 q^{75} - 6 q^{76} - 60 q^{77} - 6 q^{78} + 20 q^{79} - 28 q^{81} + 30 q^{84} - 18 q^{85} + 48 q^{87} - 6 q^{88} - 24 q^{89} - 8 q^{90} - 66 q^{91} + 24 q^{92} + 48 q^{93} + 6 q^{95} - 6 q^{97} - 48 q^{98}+O(q^{100}) \) 8 * q - 2 * q^3 + 4 * q^4 - 6 * q^6 - 4 * q^9 + 4 * q^10 - 6 * q^11 - 4 * q^12 - 2 * q^13 + 6 * q^15 - 4 * q^16 + 6 * q^17 - 6 * q^19 + 6 * q^22 + 12 * q^23 - 6 * q^24 - 8 * q^25 + 40 * q^27 + 2 * q^30 - 42 * q^33 + 4 * q^36 - 30 * q^37 - 12 * q^38 - 40 * q^39 + 8 * q^40 + 12 * q^41 - 6 * q^42 + 4 * q^43 - 12 * q^45 - 2 * q^48 + 8 * q^49 - 10 * q^52 + 60 * q^53 + 36 * q^54 + 6 * q^55 - 24 * q^59 + 26 * q^61 + 18 * q^62 + 12 * q^63 - 8 * q^64 + 6 * q^65 - 12 * q^66 + 24 * q^67 - 6 * q^68 + 12 * q^69 + 12 * q^72 + 6 * q^74 + 2 * q^75 - 6 * q^76 - 60 * q^77 - 6 * q^78 + 20 * q^79 - 28 * q^81 + 30 * q^84 - 18 * q^85 + 48 * q^87 - 6 * q^88 - 24 * q^89 - 8 * q^90 - 66 * q^91 + 24 * q^92 + 48 * q^93 + 6 * q^95 - 6 * q^97 - 48 * q^98

Introduction

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