LMFDB - Embedded newform 430.2.k.a.391.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(11,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("430.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.k (of order $7$, degree $6$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 6 x^{10} - 16 x^{9} + 44 x^{8} - 70 x^{7} + 141 x^{6} - 182 x^{5} + 270 x^{4} + \cdots + 1 $ x^12 - 3x^11 + 6x^10 - 16x^9 + 44x^8 - 70x^7 + 141x^6 - 182x^5 + 270x^4 - 124x^3 + 115x^2 + 20*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			391.2
Root			$-0.380695 + 1.66794i$ of defining polynomial
Character	$\chi$	$=$	430.391
Dual form			430.2.k.a.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.623490 - 0.781831i) q^{2} +(-0.0568052 - 0.0712315i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(-0.900969 - 0.433884i) q^{5} -0.0911085 q^{6} +0.481895 q^{7} +(-0.900969 - 0.433884i) q^{8} +(0.665716 - 2.91669i) q^{9} +O(q^{10})$	\(q+(0.623490 - 0.781831i) q^{2} +(-0.0568052 - 0.0712315i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(-0.900969 - 0.433884i) q^{5} -0.0911085 q^{6} +0.481895 q^{7} +(-0.900969 - 0.433884i) q^{8} +(0.665716 - 2.91669i) q^{9} +(-0.900969 + 0.433884i) q^{10} +(0.483742 - 2.11941i) q^{11} +(-0.0568052 + 0.0712315i) q^{12} +(-1.12349 - 0.541044i) q^{13} +(0.300456 - 0.376761i) q^{14} +(0.0202736 + 0.0888242i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(-0.238779 + 0.114990i) q^{17} +(-1.86529 - 2.33900i) q^{18} +(-0.805464 - 3.52897i) q^{19} +(-0.222521 + 0.974928i) q^{20} +(-0.0273741 - 0.0343261i) q^{21} +(-1.35541 - 1.69964i) q^{22} +(0.757865 - 3.32042i) q^{23} +(0.0202736 + 0.0888242i) q^{24} +(0.623490 + 0.781831i) q^{25} +(-1.12349 + 0.541044i) q^{26} +(-0.491834 + 0.236855i) q^{27} +(-0.107232 - 0.469813i) q^{28} +(2.06313 - 2.58708i) q^{29} +(0.0820859 + 0.0395305i) q^{30} +(-2.83249 + 3.55183i) q^{31} +(-0.222521 + 0.974928i) q^{32} +(-0.178448 + 0.0859360i) q^{33} +(-0.0589736 + 0.258380i) q^{34} +(-0.434172 - 0.209086i) q^{35} -2.99170 q^{36} +6.79199 q^{37} +(-3.26126 - 1.57054i) q^{38} +(0.0252807 + 0.110762i) q^{39} +(0.623490 + 0.781831i) q^{40} +(-0.298016 + 0.373701i) q^{41} -0.0439047 q^{42} +(-0.947167 + 6.48867i) q^{43} -2.17392 q^{44} +(-1.86529 + 2.33900i) q^{45} +(-2.12349 - 2.66277i) q^{46} +(2.07192 + 9.07769i) q^{47} +(0.0820859 + 0.0395305i) q^{48} -6.76778 q^{49} +1.00000 q^{50} +(0.0217548 + 0.0104766i) q^{51} +(-0.277479 + 1.21572i) q^{52} +(11.3781 - 5.47942i) q^{53} +(-0.121473 + 0.532208i) q^{54} +(-1.35541 + 1.69964i) q^{55} +(-0.434172 - 0.209086i) q^{56} +(-0.205619 + 0.257838i) q^{57} +(-0.736322 - 3.22604i) q^{58} +(6.47294 - 3.11720i) q^{59} +(0.0820859 - 0.0395305i) q^{60} +(3.28029 + 4.11336i) q^{61} +(1.01090 + 4.42906i) q^{62} +(0.320805 - 1.40554i) q^{63} +(0.623490 + 0.781831i) q^{64} +(0.777479 + 0.974928i) q^{65} +(-0.0440730 + 0.193096i) q^{66} +(1.47735 + 6.47268i) q^{67} +(0.165240 + 0.207205i) q^{68} +(-0.279569 + 0.134633i) q^{69} +(-0.434172 + 0.209086i) q^{70} +(1.16523 + 5.10519i) q^{71} +(-1.86529 + 2.33900i) q^{72} +(-0.919736 - 0.442921i) q^{73} +(4.23474 - 5.31019i) q^{74} +(0.0202736 - 0.0888242i) q^{75} +(-3.26126 + 1.57054i) q^{76} +(0.233113 - 1.02133i) q^{77} +(0.102359 + 0.0492937i) q^{78} +7.50816 q^{79} +1.00000 q^{80} +(-8.04147 - 3.87257i) q^{81} +(0.106361 + 0.465997i) q^{82} +(3.90063 + 4.89123i) q^{83} +(-0.0273741 + 0.0343261i) q^{84} +0.265025 q^{85} +(4.48250 + 4.78615i) q^{86} -0.301478 q^{87} +(-1.35541 + 1.69964i) q^{88} +(-9.36256 - 11.7403i) q^{89} +(0.665716 + 2.91669i) q^{90} +(-0.541404 - 0.260726i) q^{91} -3.40581 q^{92} +0.413903 q^{93} +(8.38904 + 4.03995i) q^{94} +(-0.805464 + 3.52897i) q^{95} +(0.0820859 - 0.0395305i) q^{96} +(-0.935545 + 4.09889i) q^{97} +(-4.21964 + 5.29126i) q^{98} +(-5.85963 - 2.82185i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - q^{3} - 2 q^{4} - 2 q^{5} - 8 q^{6} + 4 q^{7} - 2 q^{8} + 7 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 - q^3 - 2 * q^4 - 2 * q^5 - 8 * q^6 + 4 * q^7 - 2 * q^8 + 7 * q^9	\( 12 q - 2 q^{2} - q^{3} - 2 q^{4} - 2 q^{5} - 8 q^{6} + 4 q^{7} - 2 q^{8} + 7 q^{9} - 2 q^{10} + 3 q^{11} - q^{12} - 4 q^{13} - 10 q^{14} - q^{15} - 2 q^{16} - 5 q^{17} - 2 q^{19} - 2 q^{20} + 22 q^{21} - 4 q^{22} - 16 q^{23} - q^{24} - 2 q^{25} - 4 q^{26} + 8 q^{27} + 11 q^{28} + 2 q^{29} + 6 q^{30} + 27 q^{31} - 2 q^{32} + 6 q^{33} + 2 q^{34} - 3 q^{35} - 18 q^{37} - 2 q^{38} + 5 q^{39} - 2 q^{40} + 14 q^{41} - 20 q^{42} + 14 q^{43} - 4 q^{44} - 16 q^{46} + 2 q^{47} + 6 q^{48} - 12 q^{49} + 12 q^{50} - 5 q^{51} - 4 q^{52} + 2 q^{53} - 6 q^{54} - 4 q^{55} - 3 q^{56} - 19 q^{57} + 2 q^{58} + 4 q^{59} + 6 q^{60} + 16 q^{61} - 22 q^{62} + 13 q^{63} - 2 q^{64} + 10 q^{65} - 8 q^{66} + 9 q^{67} + 9 q^{68} - 15 q^{69} - 3 q^{70} + 27 q^{71} + 28 q^{73} + 24 q^{74} - q^{75} - 2 q^{76} + 26 q^{77} + 5 q^{78} + 10 q^{79} + 12 q^{80} - 12 q^{81} + 7 q^{82} - 31 q^{83} + 22 q^{84} - 12 q^{85} - 28 q^{86} - 6 q^{87} - 4 q^{88} - 38 q^{89} + 7 q^{90} + 8 q^{91} + 12 q^{92} - 2 q^{93} - 12 q^{94} - 2 q^{95} + 6 q^{96} - 15 q^{97} - 19 q^{98} - 6 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - q^3 - 2 * q^4 - 2 * q^5 - 8 * q^6 + 4 * q^7 - 2 * q^8 + 7 * q^9 - 2 * q^10 + 3 * q^11 - q^12 - 4 * q^13 - 10 * q^14 - q^15 - 2 * q^16 - 5 * q^17 - 2 * q^19 - 2 * q^20 + 22 * q^21 - 4 * q^22 - 16 * q^23 - q^24 - 2 * q^25 - 4 * q^26 + 8 * q^27 + 11 * q^28 + 2 * q^29 + 6 * q^30 + 27 * q^31 - 2 * q^32 + 6 * q^33 + 2 * q^34 - 3 * q^35 - 18 * q^37 - 2 * q^38 + 5 * q^39 - 2 * q^40 + 14 * q^41 - 20 * q^42 + 14 * q^43 - 4 * q^44 - 16 * q^46 + 2 * q^47 + 6 * q^48 - 12 * q^49 + 12 * q^50 - 5 * q^51 - 4 * q^52 + 2 * q^53 - 6 * q^54 - 4 * q^55 - 3 * q^56 - 19 * q^57 + 2 * q^58 + 4 * q^59 + 6 * q^60 + 16 * q^61 - 22 * q^62 + 13 * q^63 - 2 * q^64 + 10 * q^65 - 8 * q^66 + 9 * q^67 + 9 * q^68 - 15 * q^69 - 3 * q^70 + 27 * q^71 + 28 * q^73 + 24 * q^74 - q^75 - 2 * q^76 + 26 * q^77 + 5 * q^78 + 10 * q^79 + 12 * q^80 - 12 * q^81 + 7 * q^82 - 31 * q^83 + 22 * q^84 - 12 * q^85 - 28 * q^86 - 6 * q^87 - 4 * q^88 - 38 * q^89 + 7 * q^90 + 8 * q^91 + 12 * q^92 - 2 * q^93 - 12 * q^94 - 2 * q^95 + 6 * q^96 - 15 * q^97 - 19 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{2}{7}\right)$

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 $

$2$	0.623490	−	0.781831i	0.440874	−	0.552838i
$2$	0.623490	−	0.781831i	0.440874	−	0.552838i
$3$	−0.0568052	−	0.0712315i	−0.0327965	−	0.0411255i	0.765163	−	0.643837i	$-0.222658\pi$
$3$	−0.0568052	−	0.0712315i	−0.0327965	−	0.0411255i	−0.797959	+	0.602711i	$0.794087\pi$
$4$	−0.222521	−	0.974928i	−0.111260	−	0.487464i
$5$	−0.900969	−	0.433884i	−0.402926	−	0.194039i
$5$	−0.900969	−	0.433884i	−0.402926	−	0.194039i
$6$	−0.0911085			−0.0371949
$7$	0.481895			0.182139			0.0910696	−	0.995845i	$-0.470971\pi$
$7$	0.481895			0.182139			0.0910696	+	0.995845i	$0.470971\pi$
$8$	−0.900969	−	0.433884i	−0.318541	−	0.153401i
$9$	0.665716	−	2.91669i	0.221905	−	0.972230i
$10$	−0.900969	+	0.433884i	−0.284911	+	0.137206i
$11$	0.483742	−	2.11941i	0.145854	−	0.639027i	−0.848157	−	0.529745i	$-0.822288\pi$
$11$	0.483742	−	2.11941i	0.145854	−	0.639027i	0.994011	−	0.109282i	$-0.0348551\pi$
$12$	−0.0568052	+	0.0712315i	−0.0163983	+	0.0205628i
$13$	−1.12349	−	0.541044i	−0.311600	−	0.150059i	0.271547	−	0.962425i	$-0.412465\pi$
$13$	−1.12349	−	0.541044i	−0.311600	−	0.150059i	−0.583147	+	0.812366i	$0.698179\pi$
$14$	0.300456	−	0.376761i	0.0803004	−	0.100693i
$15$	0.0202736	+	0.0888242i	0.00523461	+	0.0229343i
$16$	−0.900969	+	0.433884i	−0.225242	+	0.108471i
$17$	−0.238779	+	0.114990i	−0.0579124	+	0.0278892i	−0.462616	−	0.886559i	$-0.653089\pi$
$17$	−0.238779	+	0.114990i	−0.0579124	+	0.0278892i	0.404703	+	0.914448i	$0.367375\pi$
$18$	−1.86529	−	2.33900i	−0.439654	−	0.551309i
$19$	−0.805464	−	3.52897i	−0.184786	−	0.809601i	−0.979310	−	0.202367i	$-0.935137\pi$
$19$	−0.805464	−	3.52897i	−0.184786	−	0.809601i	0.794524	−	0.607233i	$-0.207721\pi$
$20$	−0.222521	+	0.974928i	−0.0497572	+	0.218001i
$21$	−0.0273741	−	0.0343261i	−0.00597353	−	0.00749057i
$22$	−1.35541	−	1.69964i	−0.288975	−	0.362364i
$23$	0.757865	−	3.32042i	0.158026	−	0.692356i	−0.832385	−	0.554198i	$-0.813025\pi$
$23$	0.757865	−	3.32042i	0.158026	−	0.692356i	0.990410	−	0.138157i	$-0.0441180\pi$
$24$	0.0202736	+	0.0888242i	0.00413832	+	0.0181312i
$25$	0.623490	+	0.781831i	0.124698	+	0.156366i
$26$	−1.12349	+	0.541044i	−0.220334	+	0.106107i
$27$	−0.491834	+	0.236855i	−0.0946535	+	0.0455827i
$28$	−0.107232	−	0.469813i	−0.0202649	−	0.0887862i
$29$	2.06313	−	2.58708i	0.383113	−	0.480409i	−0.552461	−	0.833539i	$-0.686311\pi$
$29$	2.06313	−	2.58708i	0.383113	−	0.480409i	0.935574	+	0.353130i	$0.114883\pi$
$30$	0.0820859	+	0.0395305i	0.0149868	+	0.00721725i
$31$	−2.83249	+	3.55183i	−0.508730	+	0.637928i	−0.968174	−	0.250279i	$-0.919478\pi$
$31$	−2.83249	+	3.55183i	−0.508730	+	0.637928i	0.459443	+	0.888207i	$0.348049\pi$
$32$	−0.222521	+	0.974928i	−0.0393365	+	0.172345i
$33$	−0.178448	+	0.0859360i	−0.0310638	+	0.0149595i
$34$	−0.0589736	+	0.258380i	−0.0101139	+	0.0443118i
$35$	−0.434172	−	0.209086i	−0.0733885	−	0.0353420i
$36$	−2.99170			−0.498617
$37$	6.79199			1.11660			0.558298	−	0.829640i	$-0.311454\pi$
$37$	6.79199			1.11660			0.558298	+	0.829640i	$0.311454\pi$
$38$	−3.26126	−	1.57054i	−0.529046	−	0.254775i
$39$	0.0252807	+	0.110762i	0.00404815	+	0.0177361i
$40$	0.623490	+	0.781831i	0.0985824	+	0.123618i
$41$	−0.298016	+	0.373701i	−0.0465424	+	0.0583623i	−0.804558	−	0.593874i	$-0.797598\pi$
$41$	−0.298016	+	0.373701i	−0.0465424	+	0.0583623i	0.758016	+	0.652236i	$0.226169\pi$
$42$	−0.0439047			−0.00677464
$43$	−0.947167	+	6.48867i	−0.144442	+	0.989513i
$43$	−0.947167	+	6.48867i	−0.144442	+	0.989513i
$44$	−2.17392			−0.327730
$45$	−1.86529	+	2.33900i	−0.278062	+	0.348678i
$46$	−2.12349	−	2.66277i	−0.313091	−	0.392604i
$47$	2.07192	+	9.07769i	0.302221	+	1.32412i	0.866766	+	0.498715i	$0.166194\pi$
$47$	2.07192	+	9.07769i	0.302221	+	1.32412i	−0.564545	+	0.825402i	$0.690948\pi$
$48$	0.0820859	+	0.0395305i	0.0118481	+	0.00570574i
$49$	−6.76778			−0.966825
$50$	1.00000			0.141421
$51$	0.0217548	+	0.0104766i	0.00304628	+	0.00146701i
$52$	−0.277479	+	1.21572i	−0.0384794	+	0.168589i
$53$	11.3781	−	5.47942i	1.56291	−	0.752656i	0.565508	−	0.824743i	$-0.308680\pi$
$53$	11.3781	−	5.47942i	1.56291	−	0.752656i	0.997398	+	0.0720867i	$0.0229658\pi$
$54$	−0.121473	+	0.532208i	−0.0165304	+	0.0724243i
$55$	−1.35541	+	1.69964i	−0.182764	+	0.229179i
$56$	−0.434172	−	0.209086i	−0.0580187	−	0.0279403i
$57$	−0.205619	+	0.257838i	−0.0272349	+	0.0341515i
$58$	−0.736322	−	3.22604i	−0.0966838	−	0.423599i
$59$	6.47294	−	3.11720i	0.842705	−	0.405825i	0.0378405	−	0.999284i	$-0.487952\pi$
$59$	6.47294	−	3.11720i	0.842705	−	0.405825i	0.804865	+	0.593458i	$0.202238\pi$
$60$	0.0820859	−	0.0395305i	0.0105972	−	0.00510337i
$61$	3.28029	+	4.11336i	0.419998	+	0.526661i	0.946150	−	0.323730i	$-0.104937\pi$
$61$	3.28029	+	4.11336i	0.419998	+	0.526661i	−0.526151	+	0.850391i	$0.676365\pi$
$62$	1.01090	+	4.42906i	0.128385	+	0.562491i
$63$	0.320805	−	1.40554i	0.0404176	−	0.177081i
$64$	0.623490	+	0.781831i	0.0779362	+	0.0977289i
$65$	0.777479	+	0.974928i	0.0964344	+	0.120925i
$66$	−0.0440730	+	0.193096i	−0.00542501	+	0.0237685i
$67$	1.47735	+	6.47268i	0.180487	+	0.790764i	0.981399	+	0.191982i	$0.0614914\pi$
$67$	1.47735	+	6.47268i	0.180487	+	0.790764i	−0.800912	+	0.598782i	$0.795651\pi$
$68$	0.165240	+	0.207205i	0.0200383	+	0.0251273i
$69$	−0.279569	+	0.134633i	−0.0336562	+	0.0162080i
$70$	−0.434172	+	0.209086i	−0.0518935	+	0.0249906i
$71$	1.16523	+	5.10519i	0.138287	+	0.605875i	0.995811	+	0.0914314i	$0.0291442\pi$
$71$	1.16523	+	5.10519i	0.138287	+	0.605875i	−0.857524	+	0.514443i	$0.827999\pi$
$72$	−1.86529	+	2.33900i	−0.219827	+	0.275654i
$73$	−0.919736	−	0.442921i	−0.107647	−	0.0518400i	0.379285	−	0.925280i	$-0.376170\pi$
$73$	−0.919736	−	0.442921i	−0.107647	−	0.0518400i	−0.486932	+	0.873440i	$0.661884\pi$
$74$	4.23474	−	5.31019i	0.492278	−	0.617298i
$75$	0.0202736	−	0.0888242i	0.00234099	−	0.0102565i
$76$	−3.26126	+	1.57054i	−0.374092	+	0.180153i
$77$	0.233113	−	1.02133i	0.0265657	−	0.116392i
$78$	0.102359	+	0.0492937i	0.0115899	+	0.00558142i
$79$	7.50816			0.844734			0.422367	−	0.906425i	$-0.361199\pi$
$79$	7.50816			0.844734			0.422367	+	0.906425i	$0.361199\pi$
$80$	1.00000			0.111803
$81$	−8.04147	−	3.87257i	−0.893497	−	0.430285i
$82$	0.106361	+	0.465997i	0.0117456	+	0.0514608i
$83$	3.90063	+	4.89123i	0.428149	+	0.536882i	0.948377	−	0.317145i	$-0.102724\pi$
$83$	3.90063	+	4.89123i	0.428149	+	0.536882i	−0.520228	+	0.854028i	$0.674153\pi$
$84$	−0.0273741	+	0.0343261i	−0.00298676	+	0.00374528i
$85$	0.265025			0.0287460
$86$	4.48250	+	4.78615i	0.483360	+	0.516103i
$87$	−0.301478			−0.0323218
$88$	−1.35541	+	1.69964i	−0.144488	+	0.181182i
$89$	−9.36256	−	11.7403i	−0.992430	−	1.24447i	−0.969592	−	0.244728i	$-0.921301\pi$
$89$	−9.36256	−	11.7403i	−0.992430	−	1.24447i	−0.0228381	−	0.999739i	$-0.507270\pi$
$90$	0.665716	+	2.91669i	0.0701726	+	0.307446i
$91$	−0.541404	−	0.260726i	−0.0567545	−	0.0273315i
$92$	−3.40581			−0.355081
$93$	0.413903			0.0429197
$94$	8.38904	+	4.03995i	0.865264	+	0.416689i
$95$	−0.805464	+	3.52897i	−0.0826388	+	0.362064i
$96$	0.0820859	−	0.0395305i	0.00837786	−	0.00403456i
$97$	−0.935545	+	4.09889i	−0.0949902	+	0.416179i	−0.999957	−	0.00930346i	$-0.997039\pi$
$97$	−0.935545	+	4.09889i	−0.0949902	+	0.416179i	0.904966	+	0.425483i	$0.139896\pi$
$98$	−4.21964	+	5.29126i	−0.426248	+	0.534498i
$99$	−5.85963	−	2.82185i	−0.588915	−	0.283607i
$100$	0.623490	−	0.781831i	0.0623490	−	0.0781831i
$101$	1.19758	+	5.24694i	0.119164	+	0.522090i	0.998911	+	0.0466491i	$0.0148543\pi$
$101$	1.19758	+	5.24694i	0.119164	+	0.522090i	−0.879748	+	0.475441i	$0.842289\pi$
$102$	0.0217548	−	0.0104766i	0.00215405	−	0.00103733i
$103$	1.96220	−	0.944947i	0.193342	−	0.0931084i	−0.334708	−	0.942322i	$-0.608638\pi$
$103$	1.96220	−	0.944947i	0.193342	−	0.0931084i	0.528050	+	0.849213i	$0.322923\pi$
$104$	0.777479	+	0.974928i	0.0762381	+	0.0955995i
$105$	0.00976972	+	0.0428039i	0.000953427	+	0.00417724i
$106$	2.81017	−	12.3121i	0.272947	−	1.19586i
$107$	6.65790	+	8.34874i	0.643644	+	0.807104i	0.991453	−	0.130462i	$-0.0416459\pi$
$107$	6.65790	+	8.34874i	0.643644	+	0.807104i	−0.347810	+	0.937565i	$0.613074\pi$
$108$	0.340360	+	0.426798i	0.0327511	+	0.0410686i
$109$	0.768463	−	3.36686i	0.0736054	−	0.322487i	−0.924699	−	0.380700i	$-0.875683\pi$
$109$	0.768463	−	3.36686i	0.0736054	−	0.322487i	0.998304	+	0.0582132i	$0.0185403\pi$
$110$	0.483742	+	2.11941i	0.0461230	+	0.202078i
$111$	−0.385821	−	0.483804i	−0.0366205	−	0.0459206i
$112$	−0.434172	+	0.209086i	−0.0410254	+	0.0197568i
$113$	4.40321	−	2.12047i	0.414219	−	0.199477i	−0.215155	−	0.976580i	$-0.569026\pi$
$113$	4.40321	−	2.12047i	0.414219	−	0.199477i	0.629374	+	0.777103i	$0.283311\pi$
$114$	0.0733846	+	0.321519i	0.00687310	+	0.0301130i
$115$	−2.12349	+	2.66277i	−0.198016	+	0.248305i
$116$	−2.98131	−	1.43572i	−0.276807	−	0.133303i
$117$	−2.32598	+	2.91669i	−0.215037	+	0.269648i
$118$	1.59868	−	7.00429i	0.147171	−	0.644798i
$119$	−0.115066	+	0.0554130i	−0.0105481	+	0.00507971i
$120$	0.0202736	−	0.0888242i	0.00185071	−	0.00810851i
$121$	5.65276	+	2.72222i	0.513887	+	0.247475i
$122$	5.26118			0.476325
$123$	0.0435482			0.00392661
$124$	4.09307	+	1.97112i	0.367568	+	0.177012i
$125$	−0.222521	−	0.974928i	−0.0199029	−	0.0872002i
$126$	−0.898875	−	1.12715i	−0.0800782	−	0.100415i
$127$	−6.73468	+	8.44502i	−0.597606	+	0.749374i	−0.985003	−	0.172539i	$-0.944803\pi$
$127$	−6.73468	+	8.44502i	−0.597606	+	0.749374i	0.387397	+	0.921913i	$0.373374\pi$
$128$	1.00000			0.0883883
$129$	0.516002	−	0.301122i	0.0454314	−	0.0265123i
$130$	1.24698			0.109367
$131$	5.13133	−	6.43448i	0.448326	−	0.562183i	−0.505390	−	0.862891i	$-0.668651\pi$
$131$	5.13133	−	6.43448i	0.448326	−	0.562183i	0.953716	+	0.300708i	$0.0972228\pi$
$132$	0.123490	+	0.154851i	0.0107484	+	0.0134781i
$133$	−0.388149	−	1.70059i	−0.0336568	−	0.147460i
$134$	5.98166	+	2.88061i	0.516737	+	0.248847i
$135$	0.545895			0.0469831
$136$	0.265025			0.0227257
$137$	−3.24526	−	1.56283i	−0.277261	−	0.133522i	0.290086	−	0.957000i	$-0.406316\pi$
$137$	−3.24526	−	1.56283i	−0.277261	−	0.133522i	−0.567347	+	0.823479i	$0.692030\pi$
$138$	−0.0690479	+	0.302519i	−0.00587775	+	0.0257521i
$139$	−7.15196	+	3.44420i	−0.606621	+	0.292133i	−0.711868	−	0.702313i	$-0.752151\pi$
$139$	−7.15196	+	3.44420i	−0.606621	+	0.292133i	0.105248	+	0.994446i	$0.466437\pi$
$140$	−0.107232	+	0.469813i	−0.00906273	+	0.0397064i
$141$	0.528921	−	0.663246i	0.0445432	−	0.0558554i
$142$	4.71790	+	2.27202i	0.395918	+	0.190664i
$143$	−1.69017	+	2.11941i	−0.141339	+	0.177234i
$144$	0.665716	+	2.91669i	0.0554763	+	0.243058i
$145$	−2.98131	+	1.43572i	−0.247584	+	0.119230i
$146$	−0.919736	+	0.442921i	−0.0761179	+	0.0366564i
$147$	0.384445	+	0.482079i	0.0317085	+	0.0397612i
$148$	−1.51136	−	6.62170i	−0.124233	−	0.544301i
$149$	5.17083	−	22.6549i	0.423611	−	1.85596i	−0.0870897	−	0.996200i	$-0.527757\pi$
$149$	5.17083	−	22.6549i	0.423611	−	1.85596i	0.510700	−	0.859759i	$-0.329386\pi$
$150$	−0.0568052	−	0.0712315i	−0.00463813	−	0.00581603i
$151$	4.83483	+	6.06268i	0.393453	+	0.493374i	0.938620	−	0.344953i	$-0.112105\pi$
$151$	4.83483	+	6.06268i	0.393453	+	0.493374i	−0.545167	+	0.838327i	$0.683534\pi$
$152$	−0.805464	+	3.52897i	−0.0653317	+	0.286237i
$153$	0.176431	+	0.772995i	0.0142636	+	0.0624930i
$154$	−0.653167	−	0.819046i	−0.0526337	−	0.0660006i
$155$	4.09307	−	1.97112i	0.328763	−	0.158324i
$156$	0.102359	−	0.0492937i	0.00819532	−	0.00394666i
$157$	−0.627544	−	2.74945i	−0.0500835	−	0.219430i	0.943693	−	0.330822i	$-0.107326\pi$
$157$	−0.627544	−	2.74945i	−0.0500835	−	0.219430i	−0.993777	+	0.111392i	$0.964469\pi$
$158$	4.68126	−	5.87012i	0.372421	−	0.467001i
$159$	−1.03664	−	0.499222i	−0.0822113	−	0.0395909i
$160$	0.623490	−	0.781831i	0.0492912	−	0.0618092i
$161$	0.365211	−	1.60009i	0.0287827	−	0.126105i
$162$	−8.04147	+	3.87257i	−0.631798	+	0.304258i
$163$	−2.64686	+	11.5967i	−0.207318	+	0.908321i	0.759024	+	0.651062i	$0.225676\pi$
$163$	−2.64686	+	11.5967i	−0.207318	+	0.908321i	−0.966343	+	0.257258i	$0.917181\pi$
$164$	0.430646	+	0.207388i	0.0336278	+	0.0161943i
$165$	0.198062			0.0154191
$166$	6.25612			0.485569
$167$	3.84263	+	1.85051i	0.297352	+	0.143197i	0.576611	−	0.817019i	$-0.304375\pi$
$167$	3.84263	+	1.85051i	0.297352	+	0.143197i	−0.279260	+	0.960216i	$0.590089\pi$
$168$	0.00976972	+	0.0428039i	0.000753750	+	0.00330239i
$169$	−7.13587	−	8.94809i	−0.548913	−	0.688315i
$170$	0.165240	−	0.207205i	0.0126733	−	0.0158919i
$171$	−10.8291			−0.828123
$172$	6.53675	−	0.520446i	0.498423	−	0.0396836i
$173$	3.99124			0.303448			0.151724	−	0.988423i	$-0.451517\pi$
$173$	3.99124			0.303448			0.151724	+	0.988423i	$0.451517\pi$
$174$	−0.187968	+	0.235705i	−0.0142498	+	0.0178687i
$175$	0.300456	+	0.376761i	0.0227124	+	0.0284804i
$176$	0.483742	+	2.11941i	0.0364634	+	0.159757i
$177$	−0.589740	−	0.284004i	−0.0443276	−	0.0213470i
$178$	−15.0164			−1.12553
$179$	−8.68782			−0.649358			−0.324679	−	0.945824i	$-0.605256\pi$
$179$	−8.68782			−0.649358			−0.324679	+	0.945824i	$0.605256\pi$
$180$	2.69543	+	1.29805i	0.200905	+	0.0967509i
$181$	0.720953	−	3.15870i	0.0535880	−	0.234784i	−0.941040	−	0.338294i	$-0.890150\pi$
$181$	0.720953	−	3.15870i	0.0535880	−	0.234784i	0.994628	+	0.103510i	$0.0330073\pi$
$182$	−0.541404	+	0.260726i	−0.0401315	+	0.0193263i
$183$	0.106663	−	0.467320i	0.00788474	−	0.0345453i
$184$	−2.12349	+	2.66277i	−0.156546	+	0.196302i
$185$	−6.11937	−	2.94694i	−0.449905	−	0.216663i
$186$	0.258064	−	0.323602i	0.0189222	−	0.0237277i
$187$	0.128204	+	0.561697i	0.00937517	+	0.0410753i
$188$	8.38904	−	4.03995i	0.611834	−	0.294644i
$189$	−0.237012	+	0.114139i	−0.0172401	+	0.00830240i
$190$	2.25686	+	2.83001i	0.163730	+	0.205311i
$191$	−3.35967	−	14.7197i	−0.243098	−	1.06508i	−0.938179	−	0.346149i	$-0.887489\pi$
$191$	−3.35967	−	14.7197i	−0.243098	−	1.06508i	0.695082	−	0.718931i	$-0.255368\pi$
$192$	0.0202736	−	0.0888242i	0.00146312	−	0.00641034i
$193$	−4.40902	−	5.52874i	−0.317368	−	0.397967i	0.597402	−	0.801942i	$-0.296200\pi$
$193$	−4.40902	−	5.52874i	−0.317368	−	0.397967i	−0.914770	+	0.403975i	$0.867628\pi$
$194$	2.62134	+	3.28706i	0.188201	+	0.235997i
$195$	0.0252807	−	0.110762i	0.00181039	−	0.00793183i
$196$	1.50597	+	6.59810i	0.107569	+	0.471293i
$197$	−5.83599	−	7.31810i	−0.415797	−	0.521393i	0.529189	−	0.848504i	$-0.322496\pi$
$197$	−5.83599	−	7.31810i	−0.415797	−	0.521393i	−0.944986	+	0.327111i	$0.893925\pi$
$198$	−5.85963	+	2.82185i	−0.416426	+	0.200540i
$199$	−18.8210	+	9.06371i	−1.33418	+	0.642509i	−0.958726	−	0.284330i	$-0.908229\pi$
$199$	−18.8210	+	9.06371i	−1.33418	+	0.642509i	−0.375458	+	0.926840i	$0.622514\pi$
$200$	−0.222521	−	0.974928i	−0.0157346	−	0.0689378i
$201$	0.377138	−	0.472916i	0.0266013	−	0.0333569i
$202$	4.84890	+	2.33511i	0.341167	+	0.164298i
$203$	0.994210	−	1.24670i	0.0697799	−	0.0875012i
$204$	0.00537299	−	0.0235406i	0.000376185	−	0.00164817i
$205$	0.430646	−	0.207388i	0.0300776	−	0.0144846i
$206$	0.484624	−	2.12328i	0.0337654	−	0.147936i
$207$	−9.18012	−	4.42091i	−0.638063	−	0.307275i
$208$	1.24698			0.0864625
$209$	−7.86897			−0.544308
$210$	0.0395568	+	0.0190495i	0.00272968	+	0.00131454i
$211$	−0.641331	−	2.80986i	−0.0441511	−	0.193439i	0.948043	−	0.318142i	$-0.103059\pi$
$211$	−0.641331	−	2.80986i	−0.0441511	−	0.193439i	−0.992194	+	0.124704i	$0.960202\pi$
$212$	−7.87391	−	9.87357i	−0.540782	−	0.678120i
$213$	0.297459	−	0.373002i	0.0203816	−	0.0255577i
$214$	10.6784			0.729964
$215$	3.66870	−	5.43513i	0.250203	−	0.370673i
$216$	0.545895			0.0371434
$217$	−1.36496	+	1.71161i	−0.0926597	+	0.116192i
$218$	−2.15319	−	2.70001i	−0.145832	−	0.182868i
$219$	0.0206958	+	0.0906744i	0.00139850	+	0.00612721i
$220$	1.95863	+	0.943227i	0.132051	+	0.0635923i
$221$	0.330480			0.0222305
$222$	−0.618808			−0.0415317
$223$	−7.68426	−	3.70055i	−0.514576	−	0.247807i	0.158528	−	0.987354i	$-0.449325\pi$
$223$	−7.68426	−	3.70055i	−0.514576	−	0.247807i	−0.673104	+	0.739548i	$0.735039\pi$
$224$	−0.107232	+	0.469813i	−0.00716472	+	0.0313907i
$225$	2.69543	−	1.29805i	0.179695	−	0.0865366i
$226$	1.08750	−	4.76466i	0.0723396	−	0.316940i
$227$	−13.1596	+	16.5016i	−0.873432	+	1.09525i	0.121288	+	0.992617i	$0.461298\pi$
$227$	−13.1596	+	16.5016i	−0.873432	+	1.09525i	−0.994719	+	0.102632i	$0.967274\pi$
$228$	0.297128	+	0.143089i	0.0196778	+	0.00947632i
$229$	−1.52595	+	1.91348i	−0.100838	+	0.126447i	−0.829690	−	0.558225i	$-0.811483\pi$
$229$	−1.52595	+	1.91348i	−0.100838	+	0.126447i	0.728852	+	0.684671i	$0.240054\pi$
$230$	0.757865	+	3.32042i	0.0499721	+	0.218942i
$231$	−0.0859931	+	0.0414121i	−0.00565793	+	0.00272472i
$232$	−2.98131	+	1.43572i	−0.195732	+	0.0942597i
$233$	−0.0582865	−	0.0730889i	−0.00381847	−	0.00478822i	0.779919	−	0.625881i	$-0.215260\pi$
$233$	−0.0582865	−	0.0730889i	−0.00381847	−	0.00478822i	−0.783737	+	0.621093i	$0.786689\pi$
$234$	0.830134	+	3.63705i	0.0542676	+	0.237762i
$235$	2.07192	−	9.07769i	0.135157	−	0.592163i
$236$	−4.47941	−	5.61701i	−0.291585	−	0.365636i
$237$	−0.426503	−	0.534818i	−0.0277043	−	0.0347401i
$238$	−0.0284190	+	0.124512i	−0.00184213	+	0.00807091i
$239$	−1.66718	−	7.30441i	−0.107841	−	0.472483i	−0.999793	−	0.0203522i	$-0.993521\pi$
$239$	−1.66718	−	7.30441i	−0.107841	−	0.472483i	0.891952	−	0.452131i	$-0.149336\pi$
$240$	−0.0568052	−	0.0712315i	−0.00366676	−	0.00459797i
$241$	−3.19909	+	1.54060i	−0.206072	+	0.0992389i	−0.534073	−	0.845438i	$-0.679339\pi$
$241$	−3.19909	+	1.54060i	−0.206072	+	0.0992389i	0.328001	+	0.944677i	$0.393625\pi$
$242$	5.65276	−	2.72222i	0.363373	−	0.174991i
$243$	0.545368	+	2.38941i	0.0349854	+	0.153281i
$244$	3.28029	−	4.11336i	0.209999	−	0.263331i
$245$	6.09756	+	2.93643i	0.389559	+	0.187602i
$246$	0.0271518	−	0.0340473i	0.00173114	−	0.00217078i
$247$	−1.00440	+	4.40055i	−0.0639082	+	0.280000i
$248$	4.09307	−	1.97112i	0.259910	−	0.125166i
$249$	0.126834	−	0.555695i	0.00803776	−	0.0352157i
$250$	−0.900969	−	0.433884i	−0.0569823	−	0.0274412i
$251$	20.6185			1.30143			0.650714	−	0.759323i	$-0.274470\pi$
$251$	20.6185			1.30143			0.650714	+	0.759323i	$0.274470\pi$
$252$	−1.44168			−0.0908176
$253$	−6.67073	−	3.21245i	−0.419385	−	0.201965i
$254$	2.40358	+	10.5308i	0.150814	+	0.660759i
$255$	−0.0150548	−	0.0188781i	−0.000942768	−	0.00118219i
$256$	0.623490	−	0.781831i	0.0389681	−	0.0488645i
$257$	0.513451			0.0320282			0.0160141	−	0.999872i	$-0.494902\pi$
$257$	0.513451			0.0320282			0.0160141	+	0.999872i	$0.494902\pi$
$258$	0.0862950	−	0.591173i	0.00537249	−	0.0368048i
$259$	3.27303			0.203376
$260$	0.777479	−	0.974928i	0.0482172	−	0.0604625i
$261$	−6.17226	−	7.73976i	−0.382053	−	0.479079i
$262$	−1.83135	−	8.02367i	−0.113141	−	0.495704i
$263$	4.89128	+	2.35552i	0.301609	+	0.145247i	0.578567	−	0.815635i	$-0.303612\pi$
$263$	4.89128	+	2.35552i	0.301609	+	0.145247i	−0.276958	+	0.960882i	$0.589326\pi$
$264$	0.198062			0.0121899
$265$	−12.6288			−0.775779
$266$	−1.57158	−	0.756834i	−0.0963599	−	0.0464045i
$267$	−0.304435	+	1.33382i	−0.0186311	+	0.0816284i
$268$	5.98166	−	2.88061i	0.365388	−	0.175962i
$269$	3.47004	−	15.2032i	0.211572	−	0.926958i	−0.751927	−	0.659246i	$-0.770875\pi$
$269$	3.47004	−	15.2032i	0.211572	−	0.926958i	0.963499	−	0.267712i	$-0.0862674\pi$
$270$	0.340360	−	0.426798i	0.0207136	−	0.0259741i
$271$	−5.07514	−	2.44406i	−0.308293	−	0.148466i	0.273340	−	0.961917i	$-0.411872\pi$
$271$	−5.07514	−	2.44406i	−0.308293	−	0.148466i	−0.581633	+	0.813452i	$0.697586\pi$
$272$	0.165240	−	0.207205i	0.0100192	−	0.0125636i
$273$	0.0121826	+	0.0533756i	0.000737327	+	0.00323044i
$274$	−3.24526	+	1.56283i	−0.196053	+	0.0944142i
$275$	1.95863	−	0.943227i	0.118110	−	0.0568787i
$276$	0.193468	+	0.242601i	0.0116454	+	0.0146029i
$277$	−3.50972	−	15.3771i	−0.210879	−	0.923920i	−0.963971	−	0.266006i	$-0.914296\pi$
$277$	−3.50972	−	15.3771i	−0.210879	−	0.923920i	0.753093	−	0.657914i	$-0.228561\pi$
$278$	−1.76639	+	7.73905i	−0.105941	+	0.464157i
$279$	8.47396	+	10.6260i	0.507323	+	0.636163i
$280$	0.300456	+	0.376761i	0.0179557	+	0.0225157i
$281$	0.518312	−	2.27087i	0.0309199	−	0.135469i	−0.957112	−	0.289718i	$-0.906439\pi$
$281$	0.518312	−	2.27087i	0.0309199	−	0.135469i	0.988032	+	0.154249i	$0.0492957\pi$
$282$	−0.188770	−	0.827054i	−0.0112411	−	0.0492504i
$283$	−2.78706	−	3.49486i	−0.165673	−	0.207748i	0.692064	−	0.721836i	$-0.256702\pi$
$283$	−2.78706	−	3.49486i	−0.165673	−	0.207748i	−0.857737	+	0.514089i	$0.828130\pi$
$284$	4.71790	−	2.27202i	0.279956	−	0.134820i
$285$	0.297128	−	0.143089i	0.0176004	−	0.00847588i
$286$	0.603216	+	2.64286i	0.0356689	+	0.156276i
$287$	−0.143613	+	0.180084i	−0.00847718	+	0.0106301i
$288$	2.69543	+	1.29805i	0.158830	+	0.0764883i
$289$	−10.5555	+	13.2362i	−0.620914	+	0.778601i
$290$	−0.736322	+	3.22604i	−0.0432383	+	0.189439i
$291$	0.345114	−	0.166198i	0.0202309	−	0.00974271i
$292$	−0.227156	+	0.995235i	−0.0132933	+	0.0582417i
$293$	16.9825	+	8.17832i	0.992126	+	0.477783i	0.858259	−	0.513217i	$-0.171546\pi$
$293$	16.9825	+	8.17832i	0.992126	+	0.477783i	0.133867	+	0.990999i	$0.457261\pi$
$294$	0.616602			0.0359610
$295$	−7.18442			−0.418293
$296$	−6.11937	−	2.94694i	−0.355681	−	0.171287i
$297$	0.264072	+	1.15698i	0.0153230	+	0.0671345i
$298$	−14.4883	−	18.1678i	−0.839287	−	1.05243i
$299$	−2.64795	+	3.32042i	−0.153135	+	0.192025i
$300$	−0.0911085			−0.00526015
$301$	−0.456435	+	3.12686i	−0.0263085	+	0.180229i
$302$	7.75446			0.446219
$303$	0.305719	−	0.383359i	0.0175631	−	0.0220234i
$304$	2.25686	+	2.83001i	0.129440	+	0.162312i
$305$	−1.17072	−	5.12927i	−0.0670354	−	0.293701i
$306$	0.714355	+	0.344015i	0.0408370	+	0.0196660i
$307$	−21.7636			−1.24211			−0.621057	−	0.783765i	$-0.713296\pi$
$307$	−21.7636			−1.24211			−0.621057	+	0.783765i	$0.713296\pi$
$308$	−1.04760			−0.0596925
$309$	−0.178773	−	0.0860927i	−0.0101701	−	0.00489764i
$310$	1.01090	−	4.42906i	0.0574155	−	0.251554i
$311$	26.3188	−	12.6745i	1.49240	−	0.718703i	0.503051	−	0.864257i	$-0.332211\pi$
$311$	26.3188	−	12.6745i	1.49240	−	0.718703i	0.989350	+	0.145554i	$0.0464965\pi$
$312$	0.0252807	−	0.110762i	0.00143124	−	0.00627066i
$313$	−5.44325	+	6.82562i	−0.307671	+	0.385807i	−0.911495	−	0.411310i	$-0.865071\pi$
$313$	−5.44325	+	6.82562i	−0.307671	+	0.385807i	0.603825	+	0.797117i	$0.293643\pi$
$314$	−2.54088	−	1.22362i	−0.143390	−	0.0690529i
$315$	−0.898875	+	1.12715i	−0.0506459	+	0.0635079i
$316$	−1.67072	−	7.31992i	−0.0939855	−	0.411777i
$317$	21.8420	−	10.5186i	1.22677	−	0.590781i	0.295580	−	0.955318i	$-0.404487\pi$
$317$	21.8420	−	10.5186i	1.22677	−	0.590781i	0.931189	+	0.364537i	$0.118773\pi$
$318$	−1.03664	+	0.499222i	−0.0581321	+	0.0279950i
$319$	−4.48507	−	5.62409i	−0.251115	−	0.314889i
$320$	−0.222521	−	0.974928i	−0.0124393	−	0.0545001i
$321$	0.216490	−	0.948505i	0.0120833	−	0.0529404i
$322$	−1.02330	−	1.28318i	−0.0570262	−	0.0715086i
$323$	0.598124	+	0.750023i	0.0332805	+	0.0417324i
$324$	−1.98608	+	8.70158i	−0.110338	+	0.483421i
$325$	−0.277479	−	1.21572i	−0.0153918	−	0.0674357i
$326$	7.41634	+	9.29980i	0.410753	+	0.515068i
$327$	−0.283479	+	0.136516i	−0.0156764	+	0.00754937i
$328$	0.430646	−	0.207388i	0.0237785	−	0.0114511i
$329$	0.998449	+	4.37449i	0.0550463	+	0.241173i
$330$	0.123490	−	0.154851i	0.00679789	−	0.00852428i
$331$	21.3416	+	10.2776i	1.17304	+	0.564907i	0.915876	−	0.401461i	$-0.131497\pi$
$331$	21.3416	+	10.2776i	1.17304	+	0.564907i	0.257165	+	0.966368i	$0.417212\pi$
$332$	3.90063	−	4.89123i	0.214075	−	0.268441i
$333$	4.52154	−	19.8101i	0.247779	−	1.08559i
$334$	3.84263	−	1.85051i	0.210259	−	0.101256i
$335$	1.47735	−	6.47268i	0.0807161	−	0.353640i
$336$	0.0395568	+	0.0190495i	0.00215800	+	0.00103924i
$337$	17.5782			0.957546			0.478773	−	0.877939i	$-0.341082\pi$
$337$	17.5782			0.957546			0.478773	+	0.877939i	$0.341082\pi$
$338$	−11.4450			−0.622528
$339$	−0.401170	−	0.193193i	−0.0217885	−	0.0104928i
$340$	−0.0589736	−	0.258380i	−0.00319829	−	0.0140126i
$341$	6.15760	+	7.72138i	0.333453	+	0.418136i
$342$	−6.75184	+	8.46654i	−0.365098	+	0.457818i
$343$	−6.63462			−0.358236
$344$	3.66870	−	5.43513i	0.197803	−	0.293043i
$345$	0.310299			0.0167059
$346$	2.48850	−	3.12048i	0.133782	−	0.167758i
$347$	−8.97917	−	11.2595i	−0.482027	−	0.604443i	0.480043	−	0.877245i	$-0.340621\pi$
$347$	−8.97917	−	11.2595i	−0.482027	−	0.604443i	−0.962070	+	0.272802i	$0.912050\pi$
$348$	0.0670852	+	0.293919i	0.00359614	+	0.0157557i
$349$	19.2510	+	9.27078i	1.03048	+	0.496253i	0.871173	−	0.490976i	$-0.163360\pi$
$349$	19.2510	+	9.27078i	1.03048	+	0.496253i	0.159307	+	0.987229i	$0.449074\pi$
$350$	0.481895			0.0257584
$351$	0.680720			0.0363341
$352$	1.95863	+	0.943227i	0.104395	+	0.0502742i
$353$	−4.59331	+	20.1246i	−0.244477	+	1.07112i	0.692413	+	0.721501i	$0.256548\pi$
$353$	−4.59331	+	20.1246i	−0.244477	+	1.07112i	−0.936890	+	0.349623i	$0.886310\pi$
$354$	−0.589740	+	0.284004i	−0.0313443	+	0.0150946i
$355$	1.16523	−	5.10519i	0.0618438	−	0.270955i
$356$	−9.36256	+	11.7403i	−0.496215	+	0.622234i
$357$	0.0104835	+	0.00504860i	0.000554847	+	0.000267200i
$358$	−5.41677	+	6.79241i	−0.286285	+	0.358990i
$359$	3.16761	+	13.8782i	0.167180	+	0.732463i	0.987116	+	0.160007i	$0.0511518\pi$
$359$	3.16761	+	13.8782i	0.167180	+	0.732463i	−0.819936	+	0.572455i	$0.805991\pi$
$360$	2.69543	−	1.29805i	0.142062	−	0.0684132i
$361$	5.31357	−	2.55888i	0.279662	−	0.134678i
$362$	−2.02007	−	2.53308i	−0.106172	−	0.133136i
$363$	−0.127198	−	0.557291i	−0.00667617	−	0.0292502i
$364$	−0.133716	+	0.585847i	−0.00700861	+	0.0307067i
$365$	0.636477	+	0.798117i	0.0333147	+	0.0417753i
$366$	−0.298863	−	0.374762i	−0.0156218	−	0.0195891i
$367$	2.36795	−	10.3747i	0.123606	−	0.541553i	−0.874768	−	0.484542i	$-0.838986\pi$
$367$	2.36795	−	10.3747i	0.123606	−	0.541553i	0.998374	−	0.0570102i	$-0.0181568\pi$
$368$	0.757865	+	3.32042i	0.0395064	+	0.173089i
$369$	0.891576	+	1.11800i	0.0464136	+	0.0582008i
$370$	−6.11937	+	2.94694i	−0.318131	+	0.153204i
$371$	5.48306	−	2.64050i	0.284666	−	0.137088i
$372$	−0.0921020	−	0.403525i	−0.00477527	−	0.0209218i
$373$	−12.8124	+	16.0662i	−0.663399	+	0.831876i	−0.993709	−	0.111996i	$-0.964275\pi$
$373$	−12.8124	+	16.0662i	−0.663399	+	0.831876i	0.330309	+	0.943873i	$0.392847\pi$
$374$	0.519086	+	0.249978i	0.0268413	+	0.0129261i
$375$	−0.0568052	+	0.0712315i	−0.00293341	+	0.00367838i
$376$	2.07192	−	9.07769i	0.106851	−	0.468146i
$377$	−3.71763	+	1.79031i	−0.191468	+	0.0922059i
$378$	−0.0585372	+	0.256468i	−0.00301083	+	0.0131913i
$379$	−3.61904	−	1.74284i	−0.185897	−	0.0895235i	0.338620	−	0.940923i	$-0.390040\pi$
$379$	−3.61904	−	1.74284i	−0.185897	−	0.0895235i	−0.524517	+	0.851400i	$0.675754\pi$
$380$	3.61972			0.185688
$381$	0.984116			0.0504178
$382$	−13.6030	−	6.55088i	−0.695992	−	0.335172i
$383$	5.84586	+	25.6124i	0.298709	+	1.30873i	0.872051	+	0.489415i	$0.162790\pi$
$383$	5.84586	+	25.6124i	0.298709	+	1.30873i	−0.573341	+	0.819317i	$0.694353\pi$
$384$	−0.0568052	−	0.0712315i	−0.00289883	−	0.00363502i
$385$	−0.653167	+	0.819046i	−0.0332885	+	0.0417424i
$386$	−7.07152			−0.359931
$387$	18.2949	+	7.08220i	0.929983	+	0.360009i
$388$	4.20430			0.213441
$389$	−8.55174	+	10.7235i	−0.433591	+	0.543706i	−0.949841	−	0.312732i	$-0.898756\pi$
$389$	−8.55174	+	10.7235i	−0.433591	+	0.543706i	0.516251	+	0.856437i	$0.327327\pi$
$390$	−0.0708350	−	0.0888242i	−0.00358687	−	0.00449779i
$391$	0.200853	+	0.879994i	0.0101576	+	0.0445032i
$392$	6.09756	+	2.93643i	0.307973	+	0.148312i
$393$	−0.749824			−0.0378236
$394$	−9.36020			−0.471560
$395$	−6.76462	−	3.25767i	−0.340365	−	0.163911i
$396$	−1.44721	+	6.34064i	−0.0727250	+	0.318629i
$397$	35.0094	−	16.8596i	1.75707	−	0.846161i	0.782317	−	0.622881i	$-0.214038\pi$
$397$	35.0094	−	16.8596i	1.75707	−	0.846161i	0.974754	−	0.223280i	$-0.0716764\pi$
$398$	−4.64840	+	20.3660i	−0.233003	+	1.02085i
$399$	−0.0990867	+	0.124251i	−0.00496054	+	0.00622032i
$400$	−0.900969	−	0.433884i	−0.0450484	−	0.0216942i
$401$	−11.4822	+	14.3983i	−0.573395	+	0.719015i	−0.980971	−	0.194157i	$-0.937803\pi$
$401$	−11.4822	+	14.3983i	−0.573395	+	0.719015i	0.407575	+	0.913172i	$0.366374\pi$
$402$	−0.134599	−	0.589716i	−0.00671318	−	0.0294124i
$403$	5.10397	−	2.45794i	0.254247	−	0.122439i
$404$	4.84890	−	2.33511i	0.241242	−	0.116176i
$405$	5.56487	+	6.97813i	0.276521	+	0.346746i
$406$	−0.354830	−	1.55461i	−0.0176099	−	0.0771540i
$407$	3.28557	−	14.3950i	0.162860	−	0.713535i
$408$	−0.0150548	−	0.0188781i	−0.000745323	−	0.000934606i
$409$	17.5295	+	21.9813i	0.866779	+	1.08691i	0.995456	+	0.0952201i	$0.0303555\pi$
$409$	17.5295	+	21.9813i	0.866779	+	1.08691i	−0.128677	+	0.991687i	$0.541073\pi$
$410$	0.106361	−	0.465997i	0.00525279	−	0.0230140i
$411$	0.0730245	+	0.319941i	0.00360204	+	0.0157815i
$412$	−1.35789	−	1.70274i	−0.0668983	−	0.0838878i
$413$	3.11928	−	1.50216i	0.153490	−	0.0739167i
$414$	−9.18012	+	4.42091i	−0.451178	+	0.217276i
$415$	−1.39212	−	6.09926i	−0.0683363	−	0.299401i
$416$	0.777479	−	0.974928i	0.0381190	−	0.0477998i
$417$	0.651604	+	0.313796i	0.0319092	+	0.0153667i
$418$	−4.90622	+	6.15221i	−0.239971	+	0.300914i
$419$	−0.940425	+	4.12027i	−0.0459427	+	0.201288i	−0.992691	−	0.120688i	$-0.961490\pi$
$419$	−0.940425	+	4.12027i	−0.0459427	+	0.201288i	0.946748	+	0.321976i	$0.104347\pi$
$420$	0.0395568	−	0.0190495i	0.00193017	−	0.000929522i
$421$	−5.35152	+	23.4465i	−0.260817	+	1.14271i	0.659551	+	0.751660i	$0.270746\pi$
$421$	−5.35152	+	23.4465i	−0.260817	+	1.14271i	−0.920368	+	0.391054i	$0.872111\pi$
$422$	−2.59670	−	1.25050i	−0.126405	−	0.0608736i
$423$	27.8561			1.35441
$424$	−12.6288			−0.613307
$425$	−0.238779	−	0.114990i	−0.0115825	−	0.00557783i
$426$	−0.106162	−	0.465126i	−0.00514357	−	0.0225354i
$427$	1.58076	+	1.98221i	0.0764981	+	0.0959256i
$428$	6.65790	−	8.34874i	0.321822	−	0.403552i
$429$	0.246980			0.0119243
$430$	−1.96196	−	6.25705i	−0.0946142	−	0.301742i
$431$	0.750696			0.0361598			0.0180799	−	0.999837i	$-0.494245\pi$
$431$	0.750696			0.0361598			0.0180799	+	0.999837i	$0.494245\pi$
$432$	0.340360	−	0.426798i	0.0163756	−	0.0205343i
$433$	−8.41718	−	10.5548i	−0.404504	−	0.507232i	0.537301	−	0.843390i	$-0.319444\pi$
$433$	−8.41718	−	10.5548i	−0.404504	−	0.507232i	−0.941806	+	0.336158i	$0.890872\pi$
$434$	0.487150	+	2.13434i	0.0233839	+	0.102452i
$435$	0.271622	+	0.130806i	0.0130233	+	0.00627169i
$436$	−3.45344			−0.165390
$437$	−12.3281			−0.589733
$438$	0.0837958	+	0.0403539i	0.00400392	+	0.00192818i
$439$	−6.16124	+	26.9942i	−0.294060	+	1.28836i	0.584760	+	0.811207i	$0.301189\pi$
$439$	−6.16124	+	26.9942i	−0.294060	+	1.28836i	−0.878820	+	0.477154i	$0.841668\pi$
$440$	1.95863	−	0.943227i	0.0933741	−	0.0449666i
$441$	−4.50542	+	19.7395i	−0.214544	+	0.939977i
$442$	0.206051	−	0.258380i	0.00980086	−	0.0122899i
$443$	32.1795	+	15.4968i	1.52889	+	0.736276i	0.994075	−	0.108692i	$-0.0346662\pi$
$443$	32.1795	+	15.4968i	1.52889	+	0.736276i	0.534817	+	0.844968i	$0.320380\pi$
$444$	−0.385821	+	0.483804i	−0.0183102	+	0.0229603i
$445$	3.34146	+	14.6399i	0.158400	+	0.693998i
$446$	−7.68426	+	3.70055i	−0.363860	+	0.175226i
$447$	−1.90747	+	0.918589i	−0.0902202	+	0.0434478i
$448$	0.300456	+	0.376761i	0.0141952	+	0.0178003i
$449$	−1.73499	−	7.60150i	−0.0818794	−	0.358737i	0.917346	−	0.398091i	$-0.130327\pi$
$449$	−1.73499	−	7.60150i	−0.0818794	−	0.358737i	−0.999225	+	0.0393540i	$0.987470\pi$
$450$	0.665716	−	2.91669i	0.0313821	−	0.137494i
$451$	0.647863	+	0.812394i	0.0305067	+	0.0382542i
$452$	−3.04711	−	3.82096i	−0.143324	−	0.179723i
$453$	0.157210	−	0.688784i	0.00738639	−	0.0323619i
$454$	4.69660	+	20.5771i	0.220422	+	0.965733i
$455$	0.374663	+	0.469813i	0.0175645	+	0.0220252i
$456$	0.297128	−	0.143089i	0.0139143	−	0.00670077i
$457$	−11.2906	+	5.43725i	−0.528150	+	0.254344i	−0.678903	−	0.734228i	$-0.737544\pi$
$457$	−11.2906	+	5.43725i	−0.528150	+	0.254344i	0.150753	+	0.988571i	$0.451830\pi$
$458$	0.544606	+	2.38607i	0.0254478	+	0.111494i
$459$	0.0902038	−	0.113112i	0.00421035	−	0.00527961i
$460$	3.06853	+	1.47773i	0.143071	+	0.0688994i
$461$	−26.0363	+	32.6485i	−1.21263	+	1.52059i	−0.424074	+	0.905628i	$0.639400\pi$
$461$	−26.0363	+	32.6485i	−1.21263	+	1.52059i	−0.788556	+	0.614962i	$0.789171\pi$
$462$	−0.0212385	+	0.0930522i	−0.000988107	+	0.00432918i
$463$	−23.2189	+	11.1816i	−1.07908	+	0.519655i	−0.887021	−	0.461729i	$-0.847229\pi$
$463$	−23.2189	+	11.1816i	−1.07908	+	0.519655i	−0.192054	+	0.981384i	$0.561515\pi$
$464$	−0.736322	+	3.22604i	−0.0341829	+	0.149765i
$465$	−0.372913	−	0.179586i	−0.0172934	−	0.00832808i
$466$	−0.0934843			−0.00433057
$467$	5.39533			0.249666			0.124833	−	0.992178i	$-0.460160\pi$
$467$	5.39533			0.249666			0.124833	+	0.992178i	$0.460160\pi$
$468$	3.36114	+	1.61864i	0.155369	+	0.0748217i
$469$	0.711926	+	3.11915i	0.0328737	+	0.144029i
$470$	−5.80540	−	7.27974i	−0.267783	−	0.335789i
$471$	−0.160200	+	0.200884i	−0.00738161	+	0.00925625i
$472$	−7.18442			−0.330690
$473$	13.2940	+	5.14628i	0.611258	+	0.236626i
$474$	−0.684057			−0.0314198
$475$	2.25686	−	2.83001i	0.103552	−	0.129850i
$476$	0.0796284	+	0.0998509i	0.00364976	+	0.00457666i
$477$	−8.40717	−	36.8342i	−0.384938	−	1.68652i
$478$	−6.75029	−	3.25077i	−0.308751	−	0.148687i
$479$	−14.5475			−0.664693			−0.332346	−	0.943157i	$-0.607840\pi$
$479$	−14.5475			−0.664693			−0.332346	+	0.943157i	$0.607840\pi$
$480$	−0.0911085			−0.00415852
$481$	−7.63073	−	3.67477i	−0.347932	−	0.167555i
$482$	−0.790110	+	3.46170i	−0.0359885	+	0.157676i
$483$	−0.134723	+	0.0648792i	−0.00613011	+	0.00295210i
$484$	1.39612	−	6.11678i	0.0634598	−	0.278036i
$485$	2.62134	−	3.28706i	0.119029	−	0.149258i
$486$	2.20815	+	1.06339i	0.100164	+	0.0482363i
$487$	9.34686	−	11.7206i	0.423547	−	0.531111i	−0.523577	−	0.851978i	$-0.675403\pi$
$487$	9.34686	−	11.7206i	0.423547	−	0.531111i	0.947124	+	0.320867i	$0.103974\pi$
$488$	−1.17072	−	5.12927i	−0.0529961	−	0.232191i
$489$	0.976403	−	0.470211i	0.0441545	−	0.0212637i
$490$	6.09756	−	2.93643i	0.275460	−	0.132654i
$491$	−9.77164	−	12.2533i	−0.440988	−	0.552981i	0.510815	−	0.859690i	$-0.329344\pi$
$491$	−9.77164	−	12.2533i	−0.440988	−	0.552981i	−0.951803	+	0.306709i	$0.900772\pi$
$492$	−0.00969038	−	0.0424563i	−0.000436876	−	0.00191408i
$493$	−0.195143	+	0.854979i	−0.00878882	+	0.0385063i
$494$	2.81426	+	3.52897i	0.126619	+	0.158776i
$495$	4.05499	+	5.08480i	0.182258	+	0.228545i
$496$	1.01090	−	4.42906i	0.0453909	−	0.198871i
$497$	0.561516	+	2.46016i	0.0251875	+	0.110353i
$498$	−0.355380	−	0.445633i	−0.0159250	−	0.0199693i
$499$	5.12098	−	2.46613i	0.229247	−	0.110399i	−0.315735	−	0.948847i	$-0.602251\pi$
$499$	5.12098	−	2.46613i	0.229247	−	0.110399i	0.544981	+	0.838448i	$0.316537\pi$
$500$	−0.900969	+	0.433884i	−0.0402926	+	0.0194039i
$501$	−0.0864667	−	0.378835i	−0.00386305	−	0.0169251i
$502$	12.8554	−	16.1202i	0.573766	−	0.719479i
$503$	33.8750	+	16.3133i	1.51041	+	0.727375i	0.991820	−	0.127648i	$-0.0407427\pi$
$503$	33.8750	+	16.3133i	1.51041	+	0.727375i	0.518590	+	0.855023i	$0.326457\pi$
$504$	−0.898875	+	1.12715i	−0.0400391	+	0.0502074i
$505$	1.19758	−	5.24694i	0.0532916	−	0.233486i
$506$	−6.67073	+	3.21245i	−0.296550	+	0.142811i
$507$	−0.232032	+	1.01660i	−0.0103049	+	0.0451487i
$508$	9.73189	+	4.68663i	0.431783	+	0.207936i
$509$	29.4161			1.30385			0.651924	−	0.758284i	$-0.273962\pi$
$509$	29.4161			1.30385			0.651924	+	0.758284i	$0.273962\pi$
$510$	−0.0241460			−0.00106920
$511$	−0.443216	−	0.213442i	−0.0196067	−	0.00944210i
$512$	−0.222521	−	0.974928i	−0.00983413	−	0.0430861i
$513$	1.23201	+	1.54489i	0.0543945	+	0.0682085i
$514$	0.320131	−	0.401432i	0.0141204	−	0.0177064i
$515$	−2.17788			−0.0959689
$516$	−0.408394	−	0.436059i	−0.0179785	−	0.0191964i
$517$	20.2416			0.890226
$518$	2.04070	−	2.55895i	0.0896631	−	0.112434i
$519$	−0.226723	−	0.284302i	−0.00995205	−	0.0124795i
$520$	−0.277479	−	1.21572i	−0.0121683	−	0.0533126i
$521$	−25.7971	−	12.4232i	−1.13019	−	0.544272i	−0.227166	−	0.973856i	$-0.572946\pi$
$521$	−25.7971	−	12.4232i	−1.13019	−	0.544272i	−0.903027	+	0.429584i	$0.858660\pi$
$522$	−9.89953			−0.433291
$523$	−23.8407			−1.04248			−0.521240	−	0.853410i	$-0.674530\pi$
$523$	−23.8407			−1.04248			−0.521240	+	0.853410i	$0.674530\pi$
$524$	−7.41499	−	3.57087i	−0.323925	−	0.155994i
$525$	0.00976972	−	0.0428039i	0.000426385	−	0.00186812i
$526$	4.89128	−	2.35552i	0.213270	−	0.102705i
$527$	0.267915	−	1.17381i	0.0116705	−	0.0511320i
$528$	0.123490	−	0.154851i	0.00537420	−	0.00673904i
$529$	10.2714	+	4.94646i	0.446584	+	0.215064i
$530$	−7.87391	+	9.87357i	−0.342021	+	0.428881i
$531$	−4.78278	−	20.9547i	−0.207555	−	0.909358i
$532$	−1.57158	+	0.756834i	−0.0681367	+	0.0328129i
$533$	0.537007	−	0.258609i	0.0232604	−	0.0112016i
$534$	0.853009	+	1.06964i	0.0369133	+	0.0462878i
$535$	−2.37618	−	10.4107i	−0.102731	−	0.450094i
$536$	1.47735	−	6.47268i	0.0638117	−	0.279577i
$537$	0.493513	+	0.618846i	0.0212967	+	0.0267052i
$538$	−9.72284	−	12.1921i	−0.419181	−	0.525637i
$539$	−3.27386	+	14.3437i	−0.141015	+	0.617827i
$540$	−0.121473	−	0.532208i	−0.00522737	−	0.0229026i
$541$	17.6309	+	22.1085i	0.758012	+	0.950517i	0.999804	−	0.0198109i	$-0.00630641\pi$
$541$	17.6309	+	22.1085i	0.758012	+	0.950517i	−0.241791	+	0.970328i	$0.577735\pi$
$542$	−5.07514	+	2.44406i	−0.217996	+	0.104981i
$543$	−0.265953	+	0.128076i	−0.0114131	+	0.00549627i
$544$	−0.0589736	−	0.258380i	−0.00252847	−	0.0110780i
$545$	−2.15319	+	2.70001i	−0.0922324	+	0.115656i
$546$	0.0493265	+	0.0237544i	0.00211098	+	0.00101659i
$547$	12.4552	−	15.6183i	0.532545	−	0.667791i	−0.440675	−	0.897667i	$-0.645261\pi$
$547$	12.4552	−	15.6183i	0.532545	−	0.667791i	0.973220	+	0.229876i	$0.0738322\pi$
$548$	−0.801512	+	3.51165i	−0.0342389	+	0.150010i
$549$	14.1811	−	6.82927i	0.605236	−	0.291466i
$550$	0.483742	−	2.11941i	0.0206268	−	0.0903720i
$551$	−10.7915	−	5.19691i	−0.459733	−	0.221396i
$552$	0.310299			0.0132072
$553$	3.61814			0.153859
$554$	−14.2106	−	6.84345i	−0.603749	−	0.290750i
$555$	0.137698	+	0.603294i	0.00584495	+	0.0256084i
$556$	4.94931	+	6.20623i	0.209897	+	0.263203i
$557$	3.16847	−	3.97313i	0.134252	−	0.168347i	−0.710161	−	0.704039i	$-0.751378\pi$
$557$	3.16847	−	3.97313i	0.134252	−	0.168347i	0.844413	+	0.535692i	$0.179949\pi$
$558$	13.5912			0.575361
$559$	4.57479	−	6.77750i	0.193493	−	0.286658i
$560$	0.481895			0.0203638
$561$	0.0327279	−	0.0410394i	0.00138177	−	0.00173269i
$562$	−1.45228	−	1.82110i	−0.0612607	−	0.0768184i
$563$	−7.90229	−	34.6222i	−0.333042	−	1.45915i	−0.813208	−	0.581973i	$-0.802281\pi$
$563$	−7.90229	−	34.6222i	−0.333042	−	1.45915i	0.480166	−	0.877178i	$-0.340576\pi$
$564$	−0.764313	−	0.368074i	−0.0321834	−	0.0154987i
$565$	−4.88719			−0.205606
$566$	−4.47009			−0.187892
$567$	−3.87514	−	1.86617i	−0.162741	−	0.0783718i
$568$	1.16523	−	5.10519i	0.0488918	−	0.214209i
$569$	−9.57265	+	4.60994i	−0.401306	+	0.193259i	−0.623640	−	0.781712i	$-0.714347\pi$
$569$	−9.57265	+	4.60994i	−0.401306	+	0.193259i	0.222334	+	0.974971i	$0.428633\pi$
$570$	0.0733846	−	0.321519i	0.00307374	−	0.0134669i
$571$	−24.2309	+	30.3846i	−1.01403	+	1.27156i	−0.0519938	+	0.998647i	$0.516558\pi$
$571$	−24.2309	+	30.3846i	−1.01403	+	1.27156i	−0.962040	+	0.272910i	$0.912014\pi$
$572$	2.44237	+	1.17618i	0.102121	+	0.0491788i
$573$	−0.857659	+	1.07547i	−0.0358292	+	0.0449284i
$574$	0.0512547	+	0.224562i	0.00213933	+	0.00937302i
$575$	3.06853	−	1.47773i	0.127967	−	0.0616255i
$576$	2.69543	−	1.29805i	0.112309	−	0.0540854i
$577$	−21.0086	−	26.3439i	−0.874598	−	1.09671i	−0.994584	−	0.103936i	$-0.966856\pi$
$577$	−21.0086	−	26.3439i	−0.874598	−	1.09671i	0.119986	−	0.992776i	$-0.461715\pi$
$578$	3.76723	+	16.5053i	0.156696	+	0.686530i
$579$	−0.143365	+	0.628123i	−0.00595804	+	0.0261039i
$580$	2.06313	+	2.58708i	0.0856667	+	0.107423i
$581$	1.87969	+	2.35706i	0.0779827	+	0.0977872i
$582$	0.0852361	−	0.373444i	0.00353315	−	0.0154797i
$583$	−6.10907	−	26.7656i	−0.253012	−	1.10852i
$584$	0.636477	+	0.798117i	0.0263376	+	0.0330263i
$585$	3.36114	−	1.61864i	0.138966	−	0.0669226i
$586$	16.9825	−	8.17832i	0.701539	−	0.337843i
$587$	−1.73991	−	7.62303i	−0.0718137	−	0.314636i	0.926245	−	0.376923i	$-0.123018\pi$
$587$	−1.73991	−	7.62303i	−0.0718137	−	0.314636i	−0.998058	+	0.0622867i	$0.980161\pi$
$588$	0.384445	−	0.482079i	0.0158542	−	0.0198806i
$589$	14.8158	+	7.13490i	0.610473	+	0.293988i
$590$	−4.47941	+	5.61701i	−0.184415	+	0.231249i
$591$	−0.189764	+	0.831412i	−0.00780587	+	0.0341997i
$592$	−6.11937	+	2.94694i	−0.251505	+	0.121118i
$593$	−6.28979	+	27.5573i	−0.258291	+	1.13164i	0.664788	+	0.747032i	$0.268522\pi$
$593$	−6.28979	+	27.5573i	−0.258291	+	1.13164i	−0.923078	+	0.384612i	$0.874335\pi$
$594$	1.06921	+	0.514903i	0.0438701	+	0.0211267i
$595$	0.127714			0.00523577
$596$	−23.2375			−0.951844
$597$	1.71475	+	0.825781i	0.0701801	+	0.0337970i
$598$	0.945042	+	4.14050i	0.0386456	+	0.169318i
$599$	−10.4455	−	13.0983i	−0.426793	−	0.535181i	0.521216	−	0.853425i	$-0.325478\pi$
$599$	−10.4455	−	13.0983i	−0.426793	−	0.535181i	−0.948009	+	0.318243i	$0.896907\pi$
$600$	−0.0568052	+	0.0712315i	−0.00231906	+	0.00290801i
$601$	−10.1209			−0.412840			−0.206420	−	0.978463i	$-0.566181\pi$
$601$	−10.1209			−0.412840			−0.206420	+	0.978463i	$0.566181\pi$
$602$	2.16009	+	2.30642i	0.0880388	+	0.0940026i
$603$	19.8623			0.808856
$604$	4.83483	−	6.06268i	0.196726	−	0.246687i
$605$	−3.91183	−	4.90528i	−0.159039	−	0.199428i
$606$	−0.109110	−	0.478041i	−0.00443228	−	0.0194191i
$607$	−9.32241	−	4.48944i	−0.378385	−	0.182221i	0.235017	−	0.971991i	$-0.424485\pi$
$607$	−9.32241	−	4.48944i	−0.378385	−	0.182221i	−0.613402	+	0.789771i	$0.710200\pi$
$608$	3.61972			0.146799
$609$	−0.145281			−0.00588707
$610$	−4.74016	−	2.28274i	−0.191923	−	0.0924255i
$611$	2.58365	−	11.3197i	0.104523	−	0.457946i
$612$	0.714355	−	0.344015i	0.0288761	−	0.0139060i
$613$	5.33581	−	23.3777i	0.215511	−	0.944217i	−0.745238	−	0.666799i	$-0.767664\pi$
$613$	5.33581	−	23.3777i	0.215511	−	0.944217i	0.960749	−	0.277418i	$-0.0894788\pi$
$614$	−13.5694	+	17.0155i	−0.547616	+	0.686688i
$615$	−0.0392355	−	0.0188948i	−0.00158213	−	0.000761914i
$616$	−0.653167	+	0.819046i	−0.0263169	+	0.0330003i
$617$	−6.91617	−	30.3017i	−0.278434	−	1.21990i	−0.899773	−	0.436359i	$-0.856268\pi$
$617$	−6.91617	−	30.3017i	−0.278434	−	1.21990i	0.621338	−	0.783542i	$-0.286589\pi$
$618$	−0.178773	+	0.0860927i	−0.00719132	+	0.00346316i
$619$	0.422918	−	0.203666i	0.0169985	−	0.00818604i	−0.425365	−	0.905022i	$-0.639854\pi$
$619$	0.422918	−	0.203666i	0.0169985	−	0.00818604i	0.442364	+	0.896836i	$0.354140\pi$
$620$	−2.83249	−	3.55183i	−0.113756	−	0.142645i
$621$	0.413714	+	1.81260i	0.0166018	+	0.0727372i
$622$	6.50020	−	28.4792i	0.260634	−	1.14191i
$623$	−4.51177	−	5.65758i	−0.180760	−	0.226666i
$624$	−0.0708350	−	0.0888242i	−0.00283567	−	0.00355581i
$625$	−0.222521	+	0.974928i	−0.00890084	+	0.0389971i
$626$	1.94267	+	8.51141i	0.0776448	+	0.340184i
$627$	0.446999	+	0.560519i	0.0178514	+	0.0223850i
$628$	−2.54088	+	1.22362i	−0.101392	+	0.0488278i
$629$	−1.62179	+	0.781011i	−0.0646648	+	0.0311409i
$630$	0.320805	+	1.40554i	0.0127812	+	0.0559980i
$631$	15.4722	−	19.4015i	0.615938	−	0.772362i	−0.371828	−	0.928302i	$-0.621269\pi$
$631$	15.4722	−	19.4015i	0.615938	−	0.772362i	0.987767	+	0.155939i	$0.0498404\pi$
$632$	−6.76462	−	3.25767i	−0.269082	−	0.129583i
$633$	−0.163719	+	0.205298i	−0.00650726	+	0.00815984i
$634$	5.39453	−	23.6350i	0.214244	−	0.938665i
$635$	9.73189	−	4.68663i	0.386198	−	0.185983i
$636$	−0.256030	+	1.12174i	−0.0101523	+	0.0444799i
$637$	7.60353	+	3.66167i	0.301263	+	0.145081i
$638$	−7.19349			−0.284793
$639$	15.6660			0.619736
$640$	−0.900969	−	0.433884i	−0.0356139	−	0.0171508i
$641$	1.04083	+	4.56017i	0.0411102	+	0.180116i	0.991315	−	0.131512i	$-0.0419831\pi$
$641$	1.04083	+	4.56017i	0.0411102	+	0.180116i	−0.950204	+	0.311627i	$0.899126\pi$
$642$	−0.606592	−	0.760642i	−0.0239403	−	0.0300201i
$643$	−7.70645	+	9.66359i	−0.303913	+	0.381095i	−0.910212	−	0.414142i	$-0.864082\pi$
$643$	−7.70645	+	9.66359i	−0.303913	+	0.381095i	0.606300	+	0.795236i	$0.292653\pi$
$644$	−1.64124			−0.0646741
$645$	−0.595554	+	0.0474171i	−0.0234499	+	0.00186705i
$646$	0.959316			0.0377438
$647$	−16.3307	+	20.4781i	−0.642026	+	0.805076i	−0.991255	−	0.131962i	$-0.957872\pi$
$647$	−16.3307	+	20.4781i	−0.642026	+	0.805076i	0.349228	+	0.937038i	$0.386444\pi$
$648$	5.56487	+	6.97813i	0.218609	+	0.274127i
$649$	−3.47541	−	15.2268i	−0.136422	−	0.597702i
$650$	−1.12349	−	0.541044i	−0.0440669	−	0.0212215i
$651$	0.199458			0.00781736
$652$	11.8949			0.465840
$653$	−15.8981	−	7.65611i	−0.622140	−	0.299607i	0.0961328	−	0.995369i	$-0.469353\pi$
$653$	−15.8981	−	7.65611i	−0.622140	−	0.299607i	−0.718273	+	0.695762i	$0.755067\pi$
$654$	−0.0700136	+	0.306749i	−0.00273775	+	0.0119949i
$655$	−7.41499	+	3.57087i	−0.289727	+	0.139525i
$656$	0.106361	−	0.465997i	0.00415269	−	0.0181941i
$657$	−1.90415	+	2.38773i	−0.0742879	+	0.0931540i
$658$	4.04264	+	1.94683i	0.157598	+	0.0758954i
$659$	−1.77314	+	2.22345i	−0.0690718	+	0.0866133i	−0.815167	−	0.579226i	$-0.803355\pi$
$659$	−1.77314	+	2.22345i	−0.0690718	+	0.0866133i	0.746095	+	0.665839i	$0.231926\pi$
$660$	−0.0440730	−	0.193096i	−0.00171554	−	0.00751627i
$661$	28.1220	−	13.5428i	1.09382	−	0.526755i	0.202108	−	0.979363i	$-0.435221\pi$
$661$	28.1220	−	13.5428i	1.09382	−	0.526755i	0.891709	+	0.452608i	$0.149506\pi$
$662$	21.3416	−	10.2776i	0.829465	−	0.399449i
$663$	−0.0187730	−	0.0235406i	−0.000729084	−	0.000914242i
$664$	−1.39212	−	6.09926i	−0.0540246	−	0.236697i
$665$	−0.388149	+	1.70059i	−0.0150518	+	0.0659461i
$666$	−12.6691	−	15.8865i	−0.490916	−	0.615589i
$667$	−7.02663	−	8.81111i	−0.272072	−	0.341168i
$668$	0.949052	−	4.15807i	0.0367199	−	0.160880i
$669$	0.172911	+	0.757572i	0.00668512	+	0.0292894i
$670$	−4.13944	−	5.19069i	−0.159920	−	0.200534i
$671$	10.3047	−	4.96249i	0.397809	−	0.191575i
$672$	0.0395568	−	0.0190495i	0.00152594	−	0.000734852i
$673$	−3.47034	−	15.2045i	−0.133772	−	0.586092i	−0.996729	−	0.0808152i	$-0.974248\pi$
$673$	−3.47034	−	15.2045i	−0.133772	−	0.586092i	0.862957	−	0.505277i	$-0.168610\pi$
$674$	10.9598	−	13.7432i	0.422157	−	0.529368i
$675$	−0.491834	−	0.236855i	−0.0189307	−	0.00911655i
$676$	−7.13587	+	8.94809i	−0.274456	+	0.344157i
$677$	4.85148	−	21.2557i	0.186458	−	0.816924i	−0.792008	−	0.610511i	$-0.790964\pi$
$677$	4.85148	−	21.2557i	0.186458	−	0.816924i	0.978465	−	0.206413i	$-0.0661789\pi$
$678$	−0.401170	+	0.193193i	−0.0154068	+	0.00741954i
$679$	−0.450834	+	1.97523i	−0.0173014	+	0.0758025i
$680$	−0.238779	−	0.114990i	−0.00915676	−	0.00440966i
$681$	1.92297			0.0736882
$682$	9.87602			0.378172
$683$	−42.4204	−	20.4286i	−1.62317	−	0.781677i	−0.623170	−	0.782087i	$-0.714155\pi$
$683$	−42.4204	−	20.4286i	−1.62317	−	0.781677i	−1.00000		0.000409135i	$0.999870\pi$
$684$	2.40970	+	10.5576i	0.0921374	+	0.403680i
$685$	2.24579	+	2.81613i	0.0858071	+	0.107599i
$686$	−4.13662	+	5.18715i	−0.157937	+	0.198046i
$687$	0.222982			0.00850730
$688$	−1.96196	−	6.25705i	−0.0747991	−	0.238548i
$689$	−15.7478			−0.599944
$690$	0.193468	−	0.242601i	0.00736520	−	0.00923567i
$691$	−25.5139	−	31.9934i	−0.970594	−	1.21709i	−0.976149	−	0.217102i	$-0.930340\pi$
$691$	−25.5139	−	31.9934i	−0.970594	−	1.21709i	0.00555468	−	0.999985i	$-0.498232\pi$
$692$	−0.888134	−	3.89117i	−0.0337618	−	0.147920i
$693$	−2.82373	−	1.35984i	−0.107265	−	0.0516559i
$694$	−14.4015			−0.546672
$695$	7.93807			0.301108
$696$	0.271622	+	0.130806i	0.0102958	+	0.00495820i
$697$	0.0281883	−	0.123501i	0.00106771	−	0.00467793i
$698$	19.2510	−	9.27078i	0.728660	−	0.350904i
$699$	−0.00189526	+	0.00830367i	−7.16852e−5	+	0.000314074i
$700$	0.300456	−	0.376761i	0.0113562	−	0.0142402i
$701$	−35.9168	−	17.2966i	−1.35656	−	0.653285i	−0.392693	−	0.919670i	$-0.628456\pi$
$701$	−35.9168	−	17.2966i	−1.35656	−	0.653285i	−0.963867	+	0.266385i	$0.914171\pi$
$702$	0.424422	−	0.532208i	0.0160188	−	0.0200869i
$703$	−5.47070	−	23.9687i	−0.206331	−	0.903997i
$704$	1.95863	−	0.943227i	0.0738187	−	0.0355492i
$705$	−0.764313	+	0.368074i	−0.0287857	+	0.0138625i
$706$	12.8702	+	16.1387i	0.484375	+	0.607387i
$707$	0.577107	+	2.52847i	0.0217044	+	0.0950930i
$708$	−0.145654	+	0.638151i	−0.00547400	+	0.0239832i
$709$	26.1016	+	32.7304i	0.980268	+	1.22922i	0.973370	+	0.229241i	$0.0736243\pi$
$709$	26.1016	+	32.7304i	0.980268	+	1.22922i	0.00689801	+	0.999976i	$0.497804\pi$
$710$	−3.26489	−	4.09404i	−0.122529	−	0.153647i
$711$	4.99830	−	21.8990i	0.187451	−	0.821276i
$712$	3.34146	+	14.6399i	0.125227	+	0.548653i
$713$	9.64694	+	12.0969i	0.361281	+	0.453032i
$714$	0.0104835	−	0.00504860i	0.000392336	−	0.000188939i
$715$	2.44237	−	1.17618i	0.0913396	−	0.0439868i
$716$	1.93322	+	8.47000i	0.0722479	+	0.316539i
$717$	−0.425599	+	0.533684i	−0.0158943	+	0.0199308i
$718$	12.8254	+	6.17637i	0.478639	+	0.230500i
$719$	10.7520	−	13.4825i	0.400981	−	0.502814i	−0.539817	−	0.841782i	$-0.681507\pi$
$719$	10.7520	−	13.4825i	0.400981	−	0.502814i	0.940798	+	0.338969i	$0.110078\pi$
$720$	0.665716	−	2.91669i	0.0248098	−	0.108699i
$721$	0.945575	−	0.455365i	0.0352151	−	0.0169587i
$722$	1.31234	−	5.74976i	0.0488404	−	0.213984i
$723$	0.291464	+	0.140362i	0.0108397	+	0.00522012i
$724$	−3.23993			−0.120411
$725$	3.30900			0.122893
$726$	−0.515014	−	0.248018i	−0.0191140	−	0.00920481i
$727$	9.65675	+	42.3090i	0.358149	+	1.56915i	0.757801	+	0.652486i	$0.226274\pi$
$727$	9.65675	+	42.3090i	0.358149	+	1.56915i	−0.399652	+	0.916667i	$0.630869\pi$
$728$	0.374663	+	0.469813i	0.0138859	+	0.0174124i
$729$	−16.5554	+	20.7598i	−0.613163	+	0.768882i
$730$	1.02083			0.0377826
$731$	−0.519968	−	1.65827i	−0.0192317	−	0.0613335i
$732$	−0.479338			−0.0177169
$733$	−26.2875	+	32.9635i	−0.970952	+	1.21754i	0.00509721	+	0.999987i	$0.498378\pi$
$733$	−26.2875	+	32.9635i	−0.970952	+	1.21754i	−0.976049	+	0.217549i	$0.930194\pi$
$734$	−6.63484	−	8.31983i	−0.244896	−	0.307090i
$735$	−0.137207	−	0.601143i	−0.00506095	−	0.0221735i
$736$	3.06853	+	1.47773i	0.113108	+	0.0544697i
$737$	14.4329			0.531644
$738$	1.42998			0.0526382
$739$	−10.4015	−	5.00908i	−0.382624	−	0.184262i	0.232678	−	0.972554i	$-0.425251\pi$
$739$	−10.4015	−	5.00908i	−0.382624	−	0.184262i	−0.615301	+	0.788292i	$0.710966\pi$
$740$	−1.51136	+	6.62170i	−0.0555587	+	0.243419i
$741$	0.370513	−	0.178430i	0.0136111	−	0.00655477i
$742$	1.35420	−	5.93316i	0.0497144	−	0.217813i
$743$	−3.60902	+	4.52557i	−0.132402	+	0.166027i	−0.843613	−	0.536952i	$-0.819576\pi$
$743$	−3.60902	+	4.52557i	−0.132402	+	0.166027i	0.711211	+	0.702979i	$0.248147\pi$
$744$	−0.372913	−	0.179586i	−0.0136717	−	0.00658393i
$745$	−14.4883	+	18.1678i	−0.530811	+	0.665617i
$746$	4.57268	+	20.0342i	0.167418	+	0.733505i
$747$	16.8629	−	8.12075i	0.616982	−	0.297123i
$748$	0.519086	−	0.249978i	0.0189797	−	0.00914012i
$749$	3.20841	+	4.02322i	0.117233	+	0.147005i
$750$	0.0202736	+	0.0888242i	0.000740285	+	0.00324340i
$751$	5.28996	−	23.1768i	0.193034	−	0.845735i	−0.781929	−	0.623367i	$-0.785764\pi$
$751$	5.28996	−	23.1768i	0.193034	−	0.845735i	0.974963	−	0.222368i	$-0.0713786\pi$
$752$	−5.80540	−	7.27974i	−0.211701	−	0.265465i
$753$	−1.17124	−	1.46869i	−0.0426823	−	0.0535219i
$754$	−0.918178	+	4.02280i	−0.0334381	+	0.146502i
$755$	−1.72553	−	7.56004i	−0.0627984	−	0.275138i
$756$	0.164018	+	0.205672i	0.00596526	+	0.00748020i
$757$	3.89495	−	1.87571i	0.141564	−	0.0681737i	−0.361761	−	0.932271i	$-0.617824\pi$
$757$	3.89495	−	1.87571i	0.141564	−	0.0681737i	0.503325	+	0.864097i	$0.332110\pi$
$758$	−3.61904	+	1.74284i	−0.131449	+	0.0633027i
$759$	0.150104	+	0.657650i	0.00544844	+	0.0238712i
$760$	2.25686	−	2.83001i	0.0818649	−	0.102655i
$761$	13.9525	+	6.71918i	0.505779	+	0.243570i	0.669331	−	0.742964i	$-0.266581\pi$
$761$	13.9525	+	6.71918i	0.505779	+	0.243570i	−0.163552	+	0.986535i	$0.552295\pi$
$762$	0.613586	−	0.769413i	0.0222279	−	0.0278729i
$763$	0.370318	−	1.62247i	0.0134064	−	0.0587374i
$764$	−13.6030	+	6.55088i	−0.492141	+	0.237003i
$765$	0.176431	−	0.772995i	0.00637888	−	0.0279477i
$766$	23.6694	+	11.3986i	0.855210	+	0.411848i
$767$	−8.95883			−0.323485
$768$	−0.0911085			−0.00328760
$769$	−3.58809	−	1.72793i	−0.129390	−	0.0623109i	0.368069	−	0.929799i	$-0.380019\pi$
$769$	−3.58809	−	1.72793i	−0.129390	−	0.0623109i	−0.497459	+	0.867488i	$0.665733\pi$
$770$	0.233113	+	1.02133i	0.00840080	+	0.0368063i
$771$	−0.0291667	−	0.0365739i	−0.00105041	−	0.00131718i
$772$	−4.40902	+	5.52874i	−0.158684	+	0.198984i
$773$	−39.8174			−1.43213			−0.716066	−	0.698032i	$-0.754059\pi$
$773$	−39.8174			−1.43213			−0.716066	+	0.698032i	$0.754059\pi$
$774$	16.9438	−	9.88785i	0.609032	−	0.355412i
$775$	−4.54296			−0.163188
$776$	2.62134	−	3.28706i	0.0941006	−	0.117998i
$777$	−0.185925	−	0.233143i	−0.00667002	−	0.00836394i
$778$	3.05208	+	13.3720i	0.109422	+	0.479411i
$779$	1.55882	+	0.750688i	0.0558505	+	0.0268962i
$780$	−0.113610			−0.00406791
$781$	11.3837			0.407340
$782$	0.813237	+	0.391634i	0.0290813	+	0.0140048i
$783$	−0.401954	+	1.76108i	−0.0143647	+	0.0629357i
$784$	6.09756	−	2.93643i	0.217770	−	0.104872i
$785$	−0.627544	+	2.74945i	−0.0223980	+	0.0981321i
$786$	−0.467508	+	0.586236i	−0.0166755	+	0.0209104i
$787$	−4.91824	−	2.36850i	−0.175316	−	0.0844279i	0.344167	−	0.938908i	$-0.388161\pi$
$787$	−4.91824	−	2.36850i	−0.175316	−	0.0844279i	−0.519483	+	0.854481i	$0.673876\pi$
$788$	−5.83599	+	7.31810i	−0.207898	+	0.260696i
$789$	−0.110063	−	0.482219i	−0.00391836	−	0.0171674i
$790$	−6.76462	+	3.25767i	−0.240674	+	0.115903i
$791$	2.12188	−	1.02184i	0.0754455	−	0.0363326i
$792$	4.05499	+	5.08480i	0.144088	+	0.180681i
$793$	−1.45987	−	6.39610i	−0.0518414	−	0.227132i
$794$	8.64661	−	37.8833i	0.306857	−	1.34443i
$795$	0.717380	+	0.899566i	0.0254429	+	0.0319043i
$796$	13.0245	+	16.3322i	0.461642	+	0.578881i
$797$	−11.6075	+	50.8556i	−0.411157	+	1.80140i	0.167553	+	0.985863i	$0.446414\pi$
$797$	−11.6075	+	50.8556i	−0.411157	+	1.80140i	−0.578710	+	0.815533i	$0.696444\pi$
$798$	0.0353637	+	0.154938i	0.00125186	+	0.00548476i
$799$	−1.53857	−	1.92931i	−0.0544308	−	0.0682541i
$800$	−0.900969	+	0.433884i	−0.0318541	+	0.0153401i
$801$	−40.4756	+	19.4920i	−1.43013	+	0.688717i
$802$	4.09796	+	17.9543i	0.144704	+	0.633990i
$803$	−1.38365	+	1.73504i	−0.0488279	+	0.0612282i
$804$	−0.544980	−	0.262449i	−0.0192200	−	0.00925585i
$805$	−1.02330	+	1.28318i	−0.0360665	+	0.0452260i
$806$	1.26058	−	5.52295i	0.0444019	−	0.194538i
$807$	−1.28007	+	0.616447i	−0.0450605	+	0.0217000i
$808$	1.19758	−	5.24694i	0.0421307	−	0.184587i
$809$	−45.1324	−	21.7346i	−1.58677	−	0.764148i	−0.587777	−	0.809023i	$-0.699997\pi$
$809$	−45.1324	−	21.7346i	−1.58677	−	0.764148i	−0.998993	+	0.0448749i	$0.985711\pi$
$810$	8.92536			0.313605
$811$	31.3229			1.09989			0.549947	−	0.835199i	$-0.314648\pi$
$811$	31.3229			1.09989			0.549947	+	0.835199i	$0.314648\pi$
$812$	−1.43668	−	0.691866i	−0.0504174	−	0.0242798i
$813$	0.114200	+	0.500345i	0.00400518	+	0.0175479i
$814$	−9.20597	−	11.5439i	−0.322669	−	0.404614i
$815$	7.41634	−	9.29980i	0.259783	−	0.325758i
$816$	−0.0241460			−0.000845279
$817$	23.6612	−	1.88387i	0.827801	−	0.0659083i
$818$	28.1152			0.983024
$819$	−1.12088	+	1.40554i	−0.0391667	+	0.0491135i
$820$	−0.298016	−	0.373701i	−0.0104072	−	0.0130502i
$821$	11.4321	+	50.0875i	0.398985	+	1.74807i	0.631408	+	0.775451i	$0.282477\pi$
$821$	11.4321	+	50.0875i	0.398985	+	1.74807i	−0.232423	+	0.972615i	$0.574665\pi$
$822$	0.295670	+	0.142387i	0.0103127	+	0.00496633i
$823$	−43.7459			−1.52488			−0.762442	−	0.647056i	$-0.776000\pi$
$823$	−43.7459			−1.52488			−0.762442	+	0.647056i	$0.776000\pi$
$824$	−2.17788			−0.0758701
$825$	−0.178448	−	0.0859360i	−0.00621276	−	0.00299191i
$826$	0.770398	−	3.37533i	0.0268056	−	0.117443i
$827$	−20.1035	+	9.68131i	−0.699066	+	0.336652i	−0.749435	−	0.662078i	$-0.769675\pi$
$827$	−20.1035	+	9.68131i	−0.699066	+	0.336652i	0.0503690	+	0.998731i	$0.483960\pi$
$828$	−2.26730	+	9.93371i	−0.0787942	+	0.345220i
$829$	4.67410	−	5.86113i	0.162338	−	0.203565i	−0.694009	−	0.719966i	$-0.744157\pi$
$829$	4.67410	−	5.86113i	0.162338	−	0.203565i	0.856347	+	0.516401i	$0.172729\pi$
$830$	−5.63657	−	2.71443i	−0.195648	−	0.0942192i
$831$	−0.895963	+	1.12350i	−0.0310806	+	0.0389739i
$832$	−0.277479	−	1.21572i	−0.00961986	−	0.0421473i
$833$	1.61600	−	0.778226i	0.0559912	−	0.0269639i
$834$	0.651604	−	0.313796i	0.0225632	−	0.0108659i
$835$	−2.65918	−	3.33451i	−0.0920249	−	0.115396i
$836$	1.75101	+	7.67168i	0.0605600	+	0.265331i
$837$	0.551847	−	2.41780i	0.0190746	−	0.0835714i
$838$	2.63501	+	3.30420i	0.0910250	+	0.114142i
$839$	18.1205	+	22.7224i	0.625590	+	0.784464i	0.989119	−	0.147118i	$-0.0469998\pi$
$839$	18.1205	+	22.7224i	0.625590	+	0.784464i	−0.363529	+	0.931583i	$0.618428\pi$
$840$	0.00976972	−	0.0428039i	0.000337087	−	0.00147688i
$841$	4.01662	+	17.5980i	0.138504	+	0.606826i
$842$	14.9946	+	18.8026i	0.516748	+	0.647982i
$843$	−0.191201	+	0.0920773i	−0.00658530	+	0.00317131i
$844$	−2.59670	+	1.25050i	−0.0893820	+	0.0430441i
$845$	2.54676	+	11.1581i	0.0876113	+	0.383850i
$846$	17.3680	−	21.7788i	0.597124	−	0.748770i
$847$	2.72403	+	1.31183i	0.0935989	+	0.0450749i
$848$	−7.87391	+	9.87357i	−0.270391	+	0.339060i
$849$	−0.0906246	+	0.397052i	−0.00311023	+	0.0136268i
$850$	−0.238779	+	0.114990i	−0.00819005	+	0.00394412i
$851$	5.14741	−	22.5523i	0.176451	−	0.773082i
$852$	−0.429841	−	0.207001i	−0.0147261	−	0.00709172i
$853$	33.6887			1.15348			0.576739	−	0.816929i	$-0.304325\pi$
$853$	33.6887			1.15348			0.576739	+	0.816929i	$0.304325\pi$
$854$	2.53534			0.0867574
$855$	9.75670	+	4.69858i	0.333672	+	0.160688i
$856$	−2.37618	−	10.4107i	−0.0812161	−	0.355831i
$857$	−18.3983	−	23.0708i	−0.628475	−	0.788082i	0.361035	−	0.932552i	$-0.382424\pi$
$857$	−18.3983	−	23.0708i	−0.628475	−	0.788082i	−0.989509	+	0.144470i	$0.953852\pi$
$858$	0.153989	−	0.193096i	0.00525711	−	0.00659220i
$859$	42.3402			1.44463			0.722315	−	0.691565i	$-0.243078\pi$
$859$	42.3402			1.44463			0.722315	+	0.691565i	$0.243078\pi$
$860$	−6.11522	−	2.36728i	−0.208527	−	0.0807237i
$861$	0.0209856			0.000715188
$862$	0.468051	−	0.586918i	0.0159419	−	0.0199905i
$863$	−17.0708	−	21.4061i	−0.581097	−	0.728673i	0.401202	−	0.915989i	$-0.368592\pi$
$863$	−17.0708	−	21.4061i	−0.581097	−	0.728673i	−0.982300	+	0.187317i	$0.940021\pi$
$864$	−0.121473	−	0.532208i	−0.00413260	−	0.0181061i
$865$	−3.59598	−	1.73173i	−0.122267	−	0.0588807i
$866$	−13.5001			−0.458753
$867$	1.54245			0.0523842
$868$	1.97243	+	0.949871i	0.0669486	+	0.0322407i
$869$	3.63201	−	15.9129i	0.123208	−	0.539808i
$870$	0.271622	−	0.130806i	0.00920886	−	0.00443475i
$871$	1.84222	−	8.07130i	0.0624213	−	0.273486i
$872$	−2.15319	+	2.70001i	−0.0729161	+	0.0914339i
$873$	11.3324	+	5.45739i	0.383543	+	0.184705i
$874$	−7.68644	+	9.63849i	−0.259998	+	0.326027i
$875$	−0.107232	−	0.469813i	−0.00362509	−	0.0158826i
$876$	0.0837958	−	0.0403539i	0.00283120	−	0.00136343i
$877$	−24.0295	+	11.5720i	−0.811417	+	0.390758i	−0.793113	−	0.609074i	$-0.791541\pi$
$877$	−24.0295	+	11.5720i	−0.811417	+	0.390758i	−0.0183044	+	0.999832i	$0.505827\pi$
$878$	17.2634	+	21.6476i	0.582612	+	0.730572i
$879$	−0.382138	−	1.67426i	−0.0128892	−	0.0564713i
$880$	0.483742	−	2.11941i	0.0163069	−	0.0714454i
$881$	8.77894	+	11.0084i	0.295770	+	0.370884i	0.907406	−	0.420256i	$-0.138060\pi$
$881$	8.77894	+	11.0084i	0.295770	+	0.370884i	−0.611636	+	0.791139i	$0.709488\pi$
$882$	12.6239	+	15.8299i	0.425069	+	0.533019i
$883$	0.468839	−	2.05412i	0.0157777	−	0.0691266i	−0.966426	−	0.256944i	$-0.917284\pi$
$883$	0.468839	−	2.05412i	0.0157777	−	0.0691266i	0.982204	+	0.187818i	$0.0601414\pi$
$884$	−0.0735388	−	0.322195i	−0.00247338	−	0.0108366i
$885$	0.408113	+	0.511757i	0.0137186	+	0.0172025i
$886$	32.1795	−	15.4968i	1.08109	−	0.520626i
$887$	−42.1858	+	20.3156i	−1.41646	+	0.682132i	−0.976427	−	0.215849i	$-0.930748\pi$
$887$	−42.1858	+	20.3156i	−1.41646	+	0.682132i	−0.440034	+	0.897981i	$0.645034\pi$
$888$	0.137698	+	0.603294i	0.00462084	+	0.0202452i
$889$	−3.24541	+	4.06961i	−0.108847	+	0.136490i
$890$	13.5293	+	6.51537i	0.453503	+	0.218396i
$891$	−12.0976	+	15.1699i	−0.405284	+	0.508210i
$892$	−1.89786	+	8.31505i	−0.0635449	+	0.278409i
$893$	30.3660	−	14.6235i	1.01616	−	0.489357i
$894$	−0.471106	+	2.06405i	−0.0157562	+	0.0690322i
$895$	7.82745	+	3.76950i	0.261643	+	0.126001i
$896$	0.481895			0.0160990
$897$	0.386936			0.0129194
$898$	−7.02484	−	3.38299i	−0.234422	−	0.112892i
$899$	3.34508	+	14.6558i	0.111565	+	0.488797i
$900$	−1.86529	−	2.33900i	−0.0621765	−	0.0779668i
$901$	−2.08678	+	2.61674i	−0.0695208	+	0.0871763i
$902$	1.03909			0.0345980
$903$	0.248659	−	0.145109i	0.00827484	−	0.00482894i
$904$	−4.88719			−0.162546
$905$	−2.02007	+	2.53308i	−0.0671492	+	0.0842025i
$906$	−0.440494	−	0.552362i	−0.0146344	−	0.0183510i
$907$	7.54583	+	33.0604i	0.250555	+	1.09775i	0.931019	+	0.364972i	$0.118921\pi$
$907$	7.54583	+	33.0604i	0.250555	+	1.09775i	−0.680463	+	0.732782i	$0.738222\pi$
$908$	19.0161	+	9.15769i	0.631073	+	0.303909i
$909$	16.1009			0.534035
$910$	0.600913			0.0199201
$911$	−27.2297	−	13.1131i	−0.902159	−	0.434457i	−0.0754906	−	0.997147i	$-0.524052\pi$
$911$	−27.2297	−	13.1131i	−0.902159	−	0.434457i	−0.826668	+	0.562690i	$0.809767\pi$
$912$	0.0733846	−	0.321519i	0.00243001	−	0.0106466i
$913$	12.2534	−	5.90094i	0.405529	−	0.195293i
$914$	−2.78854	+	12.2174i	−0.0922367	+	0.404115i
$915$	−0.298863	+	0.374762i	−0.00988009	+	0.0123892i
$916$	2.20506	+	1.06190i	0.0728574	+	0.0350863i
$917$	2.47276	−	3.10074i	0.0816578	−	0.102396i
$918$	−0.0321934	−	0.141048i	−0.00106254	−	0.00465529i
$919$	23.3432	−	11.2415i	0.770022	−	0.370823i	−0.00726126	−	0.999974i	$-0.502311\pi$
$919$	23.3432	−	11.2415i	0.770022	−	0.370823i	0.777284	+	0.629150i	$0.216597\pi$
$920$	3.06853	−	1.47773i	0.101166	−	0.0487192i
$921$	1.23629	+	1.55025i	0.0407370	+	0.0510826i
$922$	9.29224	+	40.7120i	0.306024	+	1.34078i
$923$	1.45301	−	6.36607i	0.0478265	−	0.209542i
$924$	0.0595091	+	0.0746220i	0.00195771	+	0.00245488i
$925$	4.23474	+	5.31019i	0.139237	+	0.174598i
$926$	−5.73460	+	25.1249i	−0.188451	+	0.825657i
$927$	−1.44985	−	6.35220i	−0.0476193	−	0.208634i
$928$	2.06313	+	2.58708i	0.0677255	+	0.0849250i
$929$	−48.0741	+	23.1513i	−1.57726	+	0.759569i	−0.998437	−	0.0558838i	$-0.982202\pi$
$929$	−48.0741	+	23.1513i	−1.57726	+	0.759569i	−0.578824	+	0.815453i	$0.696488\pi$
$930$	−0.372913	+	0.179586i	−0.0122283	+	0.00588884i
$931$	5.45120	+	23.8833i	0.178656	+	0.782742i
$932$	−0.0582865	+	0.0730889i	−0.00190924	+	0.00239411i
$933$	−2.39787	−	1.15475i	−0.0785026	−	0.0378048i
$934$	3.36393	−	4.21824i	0.110071	−	0.138025i
$935$	0.128204	−	0.561697i	0.00419271	−	0.0183694i
$936$	3.36114	−	1.61864i	0.109862	−	0.0529070i
$937$	−8.73613	+	38.2755i	−0.285397	+	1.25041i	0.605370	+	0.795944i	$0.293025\pi$
$937$	−8.73613	+	38.2755i	−0.285397	+	1.25041i	−0.890767	+	0.454461i	$0.849832\pi$
$938$	2.88253	+	1.38815i	0.0941179	+	0.0453248i
$939$	0.795404			0.0259570
$940$	−9.31114			−0.303696
$941$	−15.5291	−	7.47843i	−0.506235	−	0.243790i	0.163292	−	0.986578i	$-0.447789\pi$
$941$	−15.5291	−	7.47843i	−0.506235	−	0.243790i	−0.669527	+	0.742788i	$0.733503\pi$
$942$	0.0571746	+	0.250498i	0.00186285	+	0.00816168i
$943$	1.01499	+	1.27276i	0.0330526	+	0.0414466i
$944$	−4.47941	+	5.61701i	−0.145793	+	0.182818i
$945$	0.263064			0.00855747
$946$	12.3122	−	7.18500i	0.400304	−	0.233605i
$947$	0.729329			0.0237000			0.0118500	−	0.999930i	$-0.496228\pi$
$947$	0.729329			0.0237000			0.0118500	+	0.999930i	$0.496228\pi$
$948$	−0.426503	+	0.534818i	−0.0138522	+	0.0173701i
$949$	0.793674	+	0.995235i	0.0257637	+	0.0323067i
$950$	−0.805464	−	3.52897i	−0.0261327	−	0.114495i
$951$	−1.98999	−	0.958330i	−0.0645299	−	0.0310760i
$952$	0.127714			0.00413924
$953$	−26.3729			−0.854302			−0.427151	−	0.904180i	$-0.640483\pi$
$953$	−26.3729			−0.854302			−0.427151	+	0.904180i	$0.640483\pi$
$954$	−34.0399	−	16.3928i	−1.10208	−	0.530736i
$955$	−3.35967	+	14.7197i	−0.108717	+	0.476318i
$956$	−6.75029	+	3.25077i	−0.218320	+	0.105137i
$957$	−0.145838	+	0.638956i	−0.00471426	+	0.0206545i
$958$	−9.07023	+	11.3737i	−0.293046	+	0.367468i
$959$	−1.56387	−	0.753121i	−0.0505000	−	0.0243195i
$960$	−0.0568052	+	0.0712315i	−0.00183338	+	0.00229899i
$961$	2.30565	+	10.1017i	0.0743757	+	0.325861i
$962$	−7.63073	+	3.67477i	−0.246025	+	0.118479i
$963$	28.7830	−	13.8612i	0.927519	−	0.446669i
$964$	2.21384	+	2.77607i	0.0713030	+	0.0894111i
$965$	1.57356	+	6.89423i	0.0506548	+	0.221933i
$966$	−0.0332738	+	0.145782i	−0.00107057	+	0.00469047i
$967$	36.2998	+	45.5185i	1.16732	+	1.46378i	0.858615	+	0.512621i	$0.171325\pi$
$967$	36.2998	+	45.5185i	1.16732	+	1.46378i	0.308708	+	0.951157i	$0.400103\pi$
$968$	−3.91183	−	4.90528i	−0.125731	−	0.157662i
$969$	0.0194487	−	0.0852105i	0.000624783	−	0.00273735i
$970$	−0.935545	−	4.09889i	−0.0300385	−	0.131607i
$971$	−6.91628	−	8.67274i	−0.221954	−	0.278321i	0.658370	−	0.752694i	$-0.271246\pi$
$971$	−6.91628	−	8.67274i	−0.221954	−	0.278321i	−0.880324	+	0.474373i	$0.842675\pi$
$972$	2.20815	−	1.06339i	0.0708264	−	0.0341082i
$973$	−3.44649	+	1.65974i	−0.110489	+	0.0532089i
$974$	−3.33586	−	14.6153i	−0.106888	−	0.468306i
$975$	−0.0708350	+	0.0888242i	−0.00226853	+	0.00284465i
$976$	−4.74016	−	2.28274i	−0.151729	−	0.0730688i
$977$	−29.2784	+	36.7140i	−0.936700	+	1.17458i	0.0477390	+	0.998860i	$0.484798\pi$
$977$	−29.2784	+	36.7140i	−0.936700	+	1.17458i	−0.984439	+	0.175725i	$0.943773\pi$
$978$	0.241152	−	1.05655i	0.00771118	−	0.0337849i
$979$	−29.4116	+	14.1639i	−0.939997	+	0.452679i
$980$	1.50597	−	6.59810i	0.0481065	−	0.210768i
$981$	−9.30851	−	4.48274i	−0.297198	−	0.143123i
$982$	−15.6725			−0.500129
$983$	1.88161			0.0600139			0.0300070	−	0.999550i	$-0.490447\pi$
$983$	1.88161			0.0600139			0.0300070	+	0.999550i	$0.490447\pi$
$984$	−0.0392355	−	0.0188948i	−0.00125078	−	0.000602346i
$985$	2.08284	+	9.12552i	0.0663648	+	0.290763i
$986$	0.546780	+	0.685640i	0.0174130	+	0.0218352i
$987$	0.254884	−	0.319615i	0.00811306	−	0.0101735i
$988$	4.51372			0.143600
$989$	20.8273	+	8.06253i	0.662270	+	0.256374i
$990$	6.50370			0.206701
$991$	26.1599	−	32.8034i	0.830996	−	1.04204i	−0.167426	−	0.985885i	$-0.553546\pi$
$991$	26.1599	−	32.8034i	0.830996	−	1.04204i	0.998422	−	0.0561512i	$-0.0178829\pi$
$992$	−2.83249	−	3.55183i	−0.0899317	−	0.112771i
$993$	−0.480228	−	2.10402i	−0.0152396	−	0.0667689i
$994$	2.27353	+	1.09488i	0.0721121	+	0.0347274i
$995$	20.8897			0.662248
$996$	−0.569986			−0.0180607
$997$	19.4134	+	9.34900i	0.614829	+	0.296086i	0.715260	−	0.698858i	$-0.246308\pi$
$997$	19.4134	+	9.34900i	0.614829	+	0.296086i	−0.100432	+	0.994944i	$0.532022\pi$
$998$	1.26478	−	5.54135i	0.0400358	−	0.175408i
$999$	−3.34053	+	1.60872i	−0.105690	+	0.0508975i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.k.a.391.2	yes	12
43.11	even	7	inner	430.2.k.a.11.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.k.a.11.2	✓	12	43.11	even	7	inner
430.2.k.a.391.2	yes	12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.623490 - 0.781831i) q^{2} +(-0.0568052 - 0.0712315i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(-0.900969 - 0.433884i) q^{5} -0.0911085 q^{6} +0.481895 q^{7} +(-0.900969 - 0.433884i) q^{8} +(0.665716 - 2.91669i) q^{9} +O(q^{10})\)	\(q+(0.623490 - 0.781831i) q^{2} +(-0.0568052 - 0.0712315i) q^{3} +(-0.222521 - 0.974928i) q^{4} +(-0.900969 - 0.433884i) q^{5} -0.0911085 q^{6} +0.481895 q^{7} +(-0.900969 - 0.433884i) q^{8} +(0.665716 - 2.91669i) q^{9} +(-0.900969 + 0.433884i) q^{10} +(0.483742 - 2.11941i) q^{11} +(-0.0568052 + 0.0712315i) q^{12} +(-1.12349 - 0.541044i) q^{13} +(0.300456 - 0.376761i) q^{14} +(0.0202736 + 0.0888242i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(-0.238779 + 0.114990i) q^{17} +(-1.86529 - 2.33900i) q^{18} +(-0.805464 - 3.52897i) q^{19} +(-0.222521 + 0.974928i) q^{20} +(-0.0273741 - 0.0343261i) q^{21} +(-1.35541 - 1.69964i) q^{22} +(0.757865 - 3.32042i) q^{23} +(0.0202736 + 0.0888242i) q^{24} +(0.623490 + 0.781831i) q^{25} +(-1.12349 + 0.541044i) q^{26} +(-0.491834 + 0.236855i) q^{27} +(-0.107232 - 0.469813i) q^{28} +(2.06313 - 2.58708i) q^{29} +(0.0820859 + 0.0395305i) q^{30} +(-2.83249 + 3.55183i) q^{31} +(-0.222521 + 0.974928i) q^{32} +(-0.178448 + 0.0859360i) q^{33} +(-0.0589736 + 0.258380i) q^{34} +(-0.434172 - 0.209086i) q^{35} -2.99170 q^{36} +6.79199 q^{37} +(-3.26126 - 1.57054i) q^{38} +(0.0252807 + 0.110762i) q^{39} +(0.623490 + 0.781831i) q^{40} +(-0.298016 + 0.373701i) q^{41} -0.0439047 q^{42} +(-0.947167 + 6.48867i) q^{43} -2.17392 q^{44} +(-1.86529 + 2.33900i) q^{45} +(-2.12349 - 2.66277i) q^{46} +(2.07192 + 9.07769i) q^{47} +(0.0820859 + 0.0395305i) q^{48} -6.76778 q^{49} +1.00000 q^{50} +(0.0217548 + 0.0104766i) q^{51} +(-0.277479 + 1.21572i) q^{52} +(11.3781 - 5.47942i) q^{53} +(-0.121473 + 0.532208i) q^{54} +(-1.35541 + 1.69964i) q^{55} +(-0.434172 - 0.209086i) q^{56} +(-0.205619 + 0.257838i) q^{57} +(-0.736322 - 3.22604i) q^{58} +(6.47294 - 3.11720i) q^{59} +(0.0820859 - 0.0395305i) q^{60} +(3.28029 + 4.11336i) q^{61} +(1.01090 + 4.42906i) q^{62} +(0.320805 - 1.40554i) q^{63} +(0.623490 + 0.781831i) q^{64} +(0.777479 + 0.974928i) q^{65} +(-0.0440730 + 0.193096i) q^{66} +(1.47735 + 6.47268i) q^{67} +(0.165240 + 0.207205i) q^{68} +(-0.279569 + 0.134633i) q^{69} +(-0.434172 + 0.209086i) q^{70} +(1.16523 + 5.10519i) q^{71} +(-1.86529 + 2.33900i) q^{72} +(-0.919736 - 0.442921i) q^{73} +(4.23474 - 5.31019i) q^{74} +(0.0202736 - 0.0888242i) q^{75} +(-3.26126 + 1.57054i) q^{76} +(0.233113 - 1.02133i) q^{77} +(0.102359 + 0.0492937i) q^{78} +7.50816 q^{79} +1.00000 q^{80} +(-8.04147 - 3.87257i) q^{81} +(0.106361 + 0.465997i) q^{82} +(3.90063 + 4.89123i) q^{83} +(-0.0273741 + 0.0343261i) q^{84} +0.265025 q^{85} +(4.48250 + 4.78615i) q^{86} -0.301478 q^{87} +(-1.35541 + 1.69964i) q^{88} +(-9.36256 - 11.7403i) q^{89} +(0.665716 + 2.91669i) q^{90} +(-0.541404 - 0.260726i) q^{91} -3.40581 q^{92} +0.413903 q^{93} +(8.38904 + 4.03995i) q^{94} +(-0.805464 + 3.52897i) q^{95} +(0.0820859 - 0.0395305i) q^{96} +(-0.935545 + 4.09889i) q^{97} +(-4.21964 + 5.29126i) q^{98} +(-5.85963 - 2.82185i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - q^{3} - 2 q^{4} - 2 q^{5} - 8 q^{6} + 4 q^{7} - 2 q^{8} + 7 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 - q^3 - 2 * q^4 - 2 * q^5 - 8 * q^6 + 4 * q^7 - 2 * q^8 + 7 * q^9	\( 12 q - 2 q^{2} - q^{3} - 2 q^{4} - 2 q^{5} - 8 q^{6} + 4 q^{7} - 2 q^{8} + 7 q^{9} - 2 q^{10} + 3 q^{11} - q^{12} - 4 q^{13} - 10 q^{14} - q^{15} - 2 q^{16} - 5 q^{17} - 2 q^{19} - 2 q^{20} + 22 q^{21} - 4 q^{22} - 16 q^{23} - q^{24} - 2 q^{25} - 4 q^{26} + 8 q^{27} + 11 q^{28} + 2 q^{29} + 6 q^{30} + 27 q^{31} - 2 q^{32} + 6 q^{33} + 2 q^{34} - 3 q^{35} - 18 q^{37} - 2 q^{38} + 5 q^{39} - 2 q^{40} + 14 q^{41} - 20 q^{42} + 14 q^{43} - 4 q^{44} - 16 q^{46} + 2 q^{47} + 6 q^{48} - 12 q^{49} + 12 q^{50} - 5 q^{51} - 4 q^{52} + 2 q^{53} - 6 q^{54} - 4 q^{55} - 3 q^{56} - 19 q^{57} + 2 q^{58} + 4 q^{59} + 6 q^{60} + 16 q^{61} - 22 q^{62} + 13 q^{63} - 2 q^{64} + 10 q^{65} - 8 q^{66} + 9 q^{67} + 9 q^{68} - 15 q^{69} - 3 q^{70} + 27 q^{71} + 28 q^{73} + 24 q^{74} - q^{75} - 2 q^{76} + 26 q^{77} + 5 q^{78} + 10 q^{79} + 12 q^{80} - 12 q^{81} + 7 q^{82} - 31 q^{83} + 22 q^{84} - 12 q^{85} - 28 q^{86} - 6 q^{87} - 4 q^{88} - 38 q^{89} + 7 q^{90} + 8 q^{91} + 12 q^{92} - 2 q^{93} - 12 q^{94} - 2 q^{95} + 6 q^{96} - 15 q^{97} - 19 q^{98} - 6 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - q^3 - 2 * q^4 - 2 * q^5 - 8 * q^6 + 4 * q^7 - 2 * q^8 + 7 * q^9 - 2 * q^10 + 3 * q^11 - q^12 - 4 * q^13 - 10 * q^14 - q^15 - 2 * q^16 - 5 * q^17 - 2 * q^19 - 2 * q^20 + 22 * q^21 - 4 * q^22 - 16 * q^23 - q^24 - 2 * q^25 - 4 * q^26 + 8 * q^27 + 11 * q^28 + 2 * q^29 + 6 * q^30 + 27 * q^31 - 2 * q^32 + 6 * q^33 + 2 * q^34 - 3 * q^35 - 18 * q^37 - 2 * q^38 + 5 * q^39 - 2 * q^40 + 14 * q^41 - 20 * q^42 + 14 * q^43 - 4 * q^44 - 16 * q^46 + 2 * q^47 + 6 * q^48 - 12 * q^49 + 12 * q^50 - 5 * q^51 - 4 * q^52 + 2 * q^53 - 6 * q^54 - 4 * q^55 - 3 * q^56 - 19 * q^57 + 2 * q^58 + 4 * q^59 + 6 * q^60 + 16 * q^61 - 22 * q^62 + 13 * q^63 - 2 * q^64 + 10 * q^65 - 8 * q^66 + 9 * q^67 + 9 * q^68 - 15 * q^69 - 3 * q^70 + 27 * q^71 + 28 * q^73 + 24 * q^74 - q^75 - 2 * q^76 + 26 * q^77 + 5 * q^78 + 10 * q^79 + 12 * q^80 - 12 * q^81 + 7 * q^82 - 31 * q^83 + 22 * q^84 - 12 * q^85 - 28 * q^86 - 6 * q^87 - 4 * q^88 - 38 * q^89 + 7 * q^90 + 8 * q^91 + 12 * q^92 - 2 * q^93 - 12 * q^94 - 2 * q^95 + 6 * q^96 - 15 * q^97 - 19 * q^98 - 6 * q^99

Introduction

L-functions

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