LMFDB - Embedded newform 966.2.q.i.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(85,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("966.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.q (of order $11$, degree $10$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			127.1
Character	$\chi$	$=$	966.127
Dual form			966.2.q.i.715.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.841254 - 0.540641i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-2.99676 + 0.879928i) q^{5} +(0.415415 + 0.909632i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(0.841254 - 0.540641i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-2.99676 + 0.879928i) q^{5} +(0.415415 + 0.909632i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(-2.04531 + 2.36041i) q^{10} +(1.95438 + 1.25600i) q^{11} +(0.841254 + 0.540641i) q^{12} +(-0.263405 + 0.303986i) q^{13} +(-0.959493 - 0.281733i) q^{14} +(-0.444488 - 3.09148i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-3.09599 - 6.77928i) q^{17} +(-0.959493 + 0.281733i) q^{18} +(2.47859 - 5.42735i) q^{19} +(-0.444488 + 3.09148i) q^{20} +(0.841254 - 0.540641i) q^{21} +2.32317 q^{22} +(3.41917 - 3.36292i) q^{23} +1.00000 q^{24} +(4.00002 - 2.57066i) q^{25} +(-0.0572434 + 0.398137i) q^{26} +(0.415415 - 0.909632i) q^{27} +(-0.959493 + 0.281733i) q^{28} +(-1.38990 - 3.04345i) q^{29} +(-2.04531 - 2.36041i) q^{30} +(-1.06286 - 7.39237i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(-1.52135 + 1.75574i) q^{33} +(-6.26967 - 4.02927i) q^{34} +(2.62746 + 1.68857i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(5.93672 + 1.74318i) q^{37} +(-0.849126 - 5.90580i) q^{38} +(-0.263405 - 0.303986i) q^{39} +(1.29745 + 2.84103i) q^{40} +(-8.21616 + 2.41248i) q^{41} +(0.415415 - 0.909632i) q^{42} +(-1.03096 + 7.17046i) q^{43} +(1.95438 - 1.25600i) q^{44} +3.12327 q^{45} +(1.05826 - 4.67762i) q^{46} -4.85915 q^{47} +(0.841254 - 0.540641i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(1.97523 - 4.32515i) q^{50} +(7.15088 - 2.09969i) q^{51} +(0.167093 + 0.365882i) q^{52} +(-6.48551 - 7.48468i) q^{53} +(-0.142315 - 0.989821i) q^{54} +(-6.96198 - 2.04422i) q^{55} +(-0.654861 + 0.755750i) q^{56} +(5.01937 + 3.22575i) q^{57} +(-2.81467 - 1.80888i) q^{58} +(-3.18308 + 3.67347i) q^{59} +(-2.99676 - 0.879928i) q^{60} +(-0.689583 - 4.79616i) q^{61} +(-4.89075 - 5.64423i) q^{62} +(0.415415 + 0.909632i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(0.521876 - 1.14275i) q^{65} +(-0.330622 + 2.29952i) q^{66} +(10.9127 - 7.01315i) q^{67} -7.45277 q^{68} +(2.84209 + 3.86296i) q^{69} +3.12327 q^{70} +(-3.45271 + 2.21892i) q^{71} +(-0.142315 + 0.989821i) q^{72} +(-3.00731 + 6.58509i) q^{73} +(5.93672 - 1.74318i) q^{74} +(1.97523 + 4.32515i) q^{75} +(-3.90725 - 4.50920i) q^{76} +(-0.330622 - 2.29952i) q^{77} +(-0.385938 - 0.113322i) q^{78} +(5.63934 - 6.50814i) q^{79} +(2.62746 + 1.68857i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-5.60759 + 6.47150i) q^{82} +(1.44138 + 0.423226i) q^{83} +(-0.142315 - 0.989821i) q^{84} +(15.2432 + 17.5916i) q^{85} +(3.00935 + 6.58955i) q^{86} +(3.21027 - 0.942621i) q^{87} +(0.965080 - 2.11323i) q^{88} +(-0.994471 + 6.91670i) q^{89} +(2.62746 - 1.68857i) q^{90} +0.402231 q^{91} +(-1.63865 - 4.50720i) q^{92} +7.46838 q^{93} +(-4.08778 + 2.62706i) q^{94} +(-2.65205 + 18.4454i) q^{95} +(0.415415 - 0.909632i) q^{96} +(9.95348 - 2.92261i) q^{97} +(0.415415 + 0.909632i) q^{98} +(-1.52135 - 1.75574i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 40 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 40 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 4 q^{10} - q^{11} - 4 q^{12} - 8 q^{13} - 4 q^{14} - 7 q^{15} - 4 q^{16} - 7 q^{17} - 4 q^{18} + 20 q^{19} - 7 q^{20} - 4 q^{21} + 10 q^{22} + 2 q^{23} + 40 q^{24} - 22 q^{25} + 14 q^{26} - 4 q^{27} - 4 q^{28} + 15 q^{29} + 4 q^{30} - 16 q^{31} - 4 q^{32} - q^{33} - 7 q^{34} - 7 q^{35} - 4 q^{36} - 16 q^{37} - 13 q^{38} - 8 q^{39} + 4 q^{40} - 17 q^{41} - 4 q^{42} + 26 q^{43} - q^{44} + 4 q^{45} - 20 q^{46} + 72 q^{47} - 4 q^{48} - 4 q^{49} + 11 q^{50} - 7 q^{51} - 19 q^{52} + 6 q^{53} - 4 q^{54} + 49 q^{55} - 4 q^{56} + 9 q^{57} - 7 q^{58} - 51 q^{59} + 4 q^{60} - 42 q^{61} - 16 q^{62} - 4 q^{63} - 4 q^{64} + 8 q^{65} - 12 q^{66} + 54 q^{67} + 4 q^{68} + 2 q^{69} + 4 q^{70} - 59 q^{71} - 4 q^{72} - 27 q^{73} - 16 q^{74} + 11 q^{75} - 2 q^{76} - 12 q^{77} - 8 q^{78} - 6 q^{79} - 7 q^{80} - 4 q^{81} - 6 q^{82} - 24 q^{83} - 4 q^{84} + 35 q^{85} - 7 q^{86} - 29 q^{87} - q^{88} + 22 q^{89} - 7 q^{90} + 36 q^{91} - 9 q^{92} + 50 q^{93} - 16 q^{94} + 22 q^{95} - 4 q^{96} + 16 q^{97} - 4 q^{98} - q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 + 4 * q^10 - q^11 - 4 * q^12 - 8 * q^13 - 4 * q^14 - 7 * q^15 - 4 * q^16 - 7 * q^17 - 4 * q^18 + 20 * q^19 - 7 * q^20 - 4 * q^21 + 10 * q^22 + 2 * q^23 + 40 * q^24 - 22 * q^25 + 14 * q^26 - 4 * q^27 - 4 * q^28 + 15 * q^29 + 4 * q^30 - 16 * q^31 - 4 * q^32 - q^33 - 7 * q^34 - 7 * q^35 - 4 * q^36 - 16 * q^37 - 13 * q^38 - 8 * q^39 + 4 * q^40 - 17 * q^41 - 4 * q^42 + 26 * q^43 - q^44 + 4 * q^45 - 20 * q^46 + 72 * q^47 - 4 * q^48 - 4 * q^49 + 11 * q^50 - 7 * q^51 - 19 * q^52 + 6 * q^53 - 4 * q^54 + 49 * q^55 - 4 * q^56 + 9 * q^57 - 7 * q^58 - 51 * q^59 + 4 * q^60 - 42 * q^61 - 16 * q^62 - 4 * q^63 - 4 * q^64 + 8 * q^65 - 12 * q^66 + 54 * q^67 + 4 * q^68 + 2 * q^69 + 4 * q^70 - 59 * q^71 - 4 * q^72 - 27 * q^73 - 16 * q^74 + 11 * q^75 - 2 * q^76 - 12 * q^77 - 8 * q^78 - 6 * q^79 - 7 * q^80 - 4 * q^81 - 6 * q^82 - 24 * q^83 - 4 * q^84 + 35 * q^85 - 7 * q^86 - 29 * q^87 - q^88 + 22 * q^89 - 7 * q^90 + 36 * q^91 - 9 * q^92 + 50 * q^93 - 16 * q^94 + 22 * q^95 - 4 * q^96 + 16 * q^97 - 4 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{10}{11}\right)$

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 $

$2$	0.841254	−	0.540641i	0.594856	−	0.382291i
$2$	0.841254	−	0.540641i	0.594856	−	0.382291i
$3$	−0.142315	+	0.989821i	−0.0821655	+	0.571474i
$3$	−0.142315	+	0.989821i	−0.0821655	+	0.571474i
$4$	0.415415	−	0.909632i	0.207708	−	0.454816i
$5$	−2.99676	+	0.879928i	−1.34019	+	0.393516i	−0.871738	−	0.489973i	$-0.837007\pi$
$5$	−2.99676	+	0.879928i	−1.34019	+	0.393516i	−0.468453	+	0.883488i	$0.655189\pi$
$6$	0.415415	+	0.909632i	0.169592	+	0.371356i
$7$	−0.654861	−	0.755750i	−0.247514	−	0.285646i
$7$	−0.654861	−	0.755750i	−0.247514	−	0.285646i
$8$	−0.142315	−	0.989821i	−0.0503159	−	0.349955i
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$	−2.04531	+	2.36041i	−0.646784	+	0.746428i
$11$	1.95438	+	1.25600i	0.589266	+	0.378699i	0.801032	−	0.598622i	$-0.204285\pi$
$11$	1.95438	+	1.25600i	0.589266	+	0.378699i	−0.211765	+	0.977321i	$0.567921\pi$
$12$	0.841254	+	0.540641i	0.242849	+	0.156070i
$13$	−0.263405	+	0.303986i	−0.0730555	+	0.0843105i	−0.791101	−	0.611686i	$-0.790492\pi$
$13$	−0.263405	+	0.303986i	−0.0730555	+	0.0843105i	0.718045	+	0.695996i	$0.245037\pi$
$14$	−0.959493	−	0.281733i	−0.256435	−	0.0752962i
$15$	−0.444488	−	3.09148i	−0.114766	−	0.798217i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	−3.09599	−	6.77928i	−0.750888	−	1.64422i	−0.764762	−	0.644313i	$-0.777144\pi$
$17$	−3.09599	−	6.77928i	−0.750888	−	1.64422i	0.0138738	−	0.999904i	$-0.495584\pi$
$18$	−0.959493	+	0.281733i	−0.226155	+	0.0664050i
$19$	2.47859	−	5.42735i	0.568627	−	1.24512i	−0.378898	−	0.925438i	$-0.623697\pi$
$19$	2.47859	−	5.42735i	0.568627	−	1.24512i	0.947525	−	0.319681i	$-0.103576\pi$
$20$	−0.444488	+	3.09148i	−0.0993906	+	0.691277i
$21$	0.841254	−	0.540641i	0.183577	−	0.117977i
$22$	2.32317			0.495302
$23$	3.41917	−	3.36292i	0.712947	−	0.701218i
$23$	3.41917	−	3.36292i	0.712947	−	0.701218i
$24$	1.00000			0.204124
$25$	4.00002	−	2.57066i	0.800005	−	0.514132i
$26$	−0.0572434	+	0.398137i	−0.0112264	+	0.0780811i
$27$	0.415415	−	0.909632i	0.0799467	−	0.175059i
$28$	−0.959493	+	0.281733i	−0.181327	+	0.0532424i
$29$	−1.38990	−	3.04345i	−0.258097	−	0.565154i	0.735579	−	0.677439i	$-0.236910\pi$
$29$	−1.38990	−	3.04345i	−0.258097	−	0.565154i	−0.993676	+	0.112285i	$0.964183\pi$
$30$	−2.04531	−	2.36041i	−0.373421	−	0.430950i
$31$	−1.06286	−	7.39237i	−0.190896	−	1.32771i	−0.829644	−	0.558293i	$-0.811457\pi$
$31$	−1.06286	−	7.39237i	−0.190896	−	1.32771i	0.638748	−	0.769416i	$-0.279452\pi$
$32$	−0.959493	−	0.281733i	−0.169616	−	0.0498038i
$33$	−1.52135	+	1.75574i	−0.264834	+	0.305634i
$34$	−6.26967	−	4.02927i	−1.07524	−	0.691014i
$35$	2.62746	+	1.68857i	0.444123	+	0.285420i
$36$	−0.654861	+	0.755750i	−0.109143	+	0.125958i
$37$	5.93672	+	1.74318i	0.975992	+	0.286577i	0.730569	−	0.682839i	$-0.239255\pi$
$37$	5.93672	+	1.74318i	0.975992	+	0.286577i	0.245423	+	0.969416i	$0.421073\pi$
$38$	−0.849126	−	5.90580i	−0.137746	−	0.958048i
$39$	−0.263405	−	0.303986i	−0.0421786	−	0.0486767i
$40$	1.29745	+	2.84103i	0.205146	+	0.449206i
$41$	−8.21616	+	2.41248i	−1.28315	+	0.376766i	−0.851062	−	0.525066i	$-0.824041\pi$
$41$	−8.21616	+	2.41248i	−1.28315	+	0.376766i	−0.432087	+	0.901832i	$0.642223\pi$
$42$	0.415415	−	0.909632i	0.0640999	−	0.140359i
$43$	−1.03096	+	7.17046i	−0.157219	+	1.09349i	0.746508	+	0.665377i	$0.231729\pi$
$43$	−1.03096	+	7.17046i	−0.157219	+	1.09349i	−0.903727	+	0.428109i	$0.859180\pi$
$44$	1.95438	−	1.25600i	0.294633	−	0.189349i
$45$	3.12327			0.465590
$46$	1.05826	−	4.67762i	0.156032	−	0.689677i
$47$	−4.85915			−0.708780			−0.354390	−	0.935098i	$-0.615311\pi$
$47$	−4.85915			−0.708780			−0.354390	+	0.935098i	$0.615311\pi$
$48$	0.841254	−	0.540641i	0.121424	−	0.0780348i
$49$	−0.142315	+	0.989821i	−0.0203307	+	0.141403i
$50$	1.97523	−	4.32515i	0.279340	−	0.611669i
$51$	7.15088	−	2.09969i	1.00132	−	0.294015i
$52$	0.167093	+	0.365882i	0.0231716	+	0.0507387i
$53$	−6.48551	−	7.48468i	−0.890853	−	1.02810i	−0.999421	−	0.0340105i	$-0.989172\pi$
$53$	−6.48551	−	7.48468i	−0.890853	−	1.02810i	0.108568	−	0.994089i	$-0.465373\pi$
$54$	−0.142315	−	0.989821i	−0.0193666	−	0.134698i
$55$	−6.96198	−	2.04422i	−0.938754	−	0.275643i
$56$	−0.654861	+	0.755750i	−0.0875094	+	0.100991i
$57$	5.01937	+	3.22575i	0.664831	+	0.427261i
$58$	−2.81467	−	1.80888i	−0.369584	−	0.237517i
$59$	−3.18308	+	3.67347i	−0.414402	+	0.478245i	−0.924123	−	0.382094i	$-0.875203\pi$
$59$	−3.18308	+	3.67347i	−0.414402	+	0.478245i	0.509721	+	0.860340i	$0.329748\pi$
$60$	−2.99676	−	0.879928i	−0.386880	−	0.113598i
$61$	−0.689583	−	4.79616i	−0.0882921	−	0.614085i	−0.985141	−	0.171748i	$-0.945059\pi$
$61$	−0.689583	−	4.79616i	−0.0882921	−	0.614085i	0.896849	−	0.442337i	$-0.145851\pi$
$62$	−4.89075	−	5.64423i	−0.621126	−	0.716818i
$63$	0.415415	+	0.909632i	0.0523374	+	0.114603i
$64$	−0.959493	+	0.281733i	−0.119937	+	0.0352166i
$65$	0.521876	−	1.14275i	0.0647308	−	0.141741i
$66$	−0.330622	+	2.29952i	−0.0406967	+	0.283052i
$67$	10.9127	−	7.01315i	1.33320	−	0.856793i	0.336796	−	0.941577i	$-0.390657\pi$
$67$	10.9127	−	7.01315i	1.33320	−	0.856793i	0.996399	+	0.0847846i	$0.0270202\pi$
$68$	−7.45277			−0.903781
$69$	2.84209	+	3.86296i	0.342148	+	0.465046i
$70$	3.12327			0.373303
$71$	−3.45271	+	2.21892i	−0.409761	+	0.263337i	−0.729243	−	0.684255i	$-0.760128\pi$
$71$	−3.45271	+	2.21892i	−0.409761	+	0.263337i	0.319482	+	0.947592i	$0.396491\pi$
$72$	−0.142315	+	0.989821i	−0.0167720	+	0.116652i
$73$	−3.00731	+	6.58509i	−0.351979	+	0.770726i	0.647980	+	0.761657i	$0.275614\pi$
$73$	−3.00731	+	6.58509i	−0.351979	+	0.770726i	−0.999959	+	0.00906877i	$0.997113\pi$
$74$	5.93672	−	1.74318i	0.690130	−	0.202641i
$75$	1.97523	+	4.32515i	0.228080	+	0.499426i
$76$	−3.90725	−	4.50920i	−0.448192	−	0.517241i
$77$	−0.330622	−	2.29952i	−0.0376778	−	0.262055i
$78$	−0.385938	−	0.113322i	−0.0436988	−	0.0128311i
$79$	5.63934	−	6.50814i	0.634475	−	0.732223i	−0.343913	−	0.939002i	$-0.611753\pi$
$79$	5.63934	−	6.50814i	0.634475	−	0.732223i	0.978388	+	0.206779i	$0.0662980\pi$
$80$	2.62746	+	1.68857i	0.293759	+	0.188788i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	−5.60759	+	6.47150i	−0.619254	+	0.714658i
$83$	1.44138	+	0.423226i	0.158211	+	0.0464551i	0.359879	−	0.932999i	$-0.382818\pi$
$83$	1.44138	+	0.423226i	0.158211	+	0.0464551i	−0.201668	+	0.979454i	$0.564636\pi$
$84$	−0.142315	−	0.989821i	−0.0155278	−	0.107998i
$85$	15.2432	+	17.5916i	1.65336	+	1.90808i
$86$	3.00935	+	6.58955i	0.324506	+	0.710570i
$87$	3.21027	−	0.942621i	0.344177	−	0.101060i
$88$	0.965080	−	2.11323i	0.102878	−	0.225271i
$89$	−0.994471	+	6.91670i	−0.105414	+	0.733169i	0.866729	+	0.498779i	$0.166218\pi$
$89$	−0.994471	+	6.91670i	−0.105414	+	0.733169i	−0.972143	+	0.234389i	$0.924691\pi$
$90$	2.62746	−	1.68857i	0.276959	−	0.177991i
$91$	0.402231			0.0421653
$92$	−1.63865	−	4.50720i	−0.170841	−	0.469908i
$93$	7.46838			0.774435
$94$	−4.08778	+	2.62706i	−0.421622	+	0.270960i
$95$	−2.65205	+	18.4454i	−0.272095	+	1.89246i
$96$	0.415415	−	0.909632i	0.0423981	−	0.0928389i
$97$	9.95348	−	2.92261i	1.01062	−	0.296746i	0.265815	−	0.964024i	$-0.414359\pi$
$97$	9.95348	−	2.92261i	1.01062	−	0.296746i	0.744808	+	0.667279i	$0.232541\pi$
$98$	0.415415	+	0.909632i	0.0419633	+	0.0918867i
$99$	−1.52135	−	1.75574i	−0.152902	−	0.176458i
$100$	−0.676684	−	4.70644i	−0.0676684	−	0.470644i
$101$	14.5264	+	4.26534i	1.44543	+	0.424417i	0.908028	−	0.418909i	$-0.137587\pi$
$101$	14.5264	+	4.26534i	1.44543	+	0.424417i	0.537403	+	0.843326i	$0.319406\pi$
$102$	4.88053	−	5.63243i	0.483244	−	0.557693i
$103$	−6.52284	−	4.19198i	−0.642715	−	0.413048i	0.178283	−	0.983979i	$-0.442946\pi$
$103$	−6.52284	−	4.19198i	−0.642715	−	0.413048i	−0.820998	+	0.570932i	$0.806582\pi$
$104$	0.338378	+	0.217462i	0.0331807	+	0.0213240i
$105$	−2.04531	+	2.36041i	−0.199602	+	0.230353i
$106$	−9.50248	−	2.79018i	−0.922962	−	0.271006i
$107$	0.147988	+	1.02928i	0.0143066	+	0.0995043i	0.995724	−	0.0923828i	$-0.0294483\pi$
$107$	0.147988	+	1.02928i	0.0143066	+	0.0995043i	−0.981417	+	0.191887i	$0.938539\pi$
$108$	−0.654861	−	0.755750i	−0.0630140	−	0.0727220i
$109$	−6.23939	−	13.6624i	−0.597625	−	1.30862i	−0.930723	−	0.365724i	$-0.880821\pi$
$109$	−6.23939	−	13.6624i	−0.597625	−	1.30862i	0.333098	−	0.942892i	$-0.391906\pi$
$110$	−6.96198	+	2.04422i	−0.663799	+	0.194909i
$111$	−2.57032	+	5.62822i	−0.243964	+	0.534207i
$112$	−0.142315	+	0.989821i	−0.0134475	+	0.0935293i
$113$	−15.4812	+	9.94917i	−1.45635	+	0.935940i	−0.457442	+	0.889240i	$0.651234\pi$
$113$	−15.4812	+	9.94917i	−1.45635	+	0.935940i	−0.998909	+	0.0467000i	$0.985130\pi$
$114$	5.96653			0.558817
$115$	−7.28731	+	13.0865i	−0.679545	+	1.22032i
$116$	−3.34580			−0.310650
$117$	0.338378	−	0.217462i	0.0312831	−	0.0201044i
$118$	−0.691750	+	4.81123i	−0.0636807	+	0.442909i
$119$	−3.09599	+	6.77928i	−0.283809	+	0.621455i
$120$	−2.99676	+	0.879928i	−0.273565	+	0.0803261i
$121$	−2.32752	−	5.09656i	−0.211593	−	0.463323i
$122$	−3.17311	−	3.66197i	−0.287280	−	0.331539i
$123$	−1.21864	−	8.47586i	−0.109882	−	0.764243i
$124$	−7.16586	−	2.10409i	−0.643513	−	0.188953i
$125$	0.501434	−	0.578686i	0.0448496	−	0.0517593i
$126$	0.841254	+	0.540641i	0.0749448	+	0.0481641i
$127$	8.39993	+	5.39831i	0.745374	+	0.479022i	0.857379	−	0.514685i	$-0.172091\pi$
$127$	8.39993	+	5.39831i	0.745374	+	0.479022i	−0.112006	+	0.993708i	$0.535728\pi$
$128$	−0.654861	+	0.755750i	−0.0578821	+	0.0667995i
$129$	−6.95076	−	2.04093i	−0.611980	−	0.179694i
$130$	−0.178787	−	1.24349i	−0.0156806	−	0.109061i
$131$	−3.18263	−	3.67295i	−0.278068	−	0.320907i	0.599486	−	0.800385i	$-0.295372\pi$
$131$	−3.18263	−	3.67295i	−0.278068	−	0.320907i	−0.877554	+	0.479478i	$0.840826\pi$
$132$	0.965080	+	2.11323i	0.0839994	+	0.183933i
$133$	−5.72485	+	1.68097i	−0.496407	+	0.145758i
$134$	5.38873	−	11.7997i	0.465516	−	1.01934i
$135$	−0.444488	+	3.09148i	−0.0382554	+	0.266072i
$136$	−6.26967	+	4.02927i	−0.537620	+	0.345507i
$137$	15.7678			1.34714			0.673569	−	0.739125i	$-0.264761\pi$
$137$	15.7678			1.34714			0.673569	+	0.739125i	$0.264761\pi$
$138$	4.47940	+	1.71318i	0.381312	+	0.145836i
$139$	−15.3564			−1.30251			−0.651255	−	0.758859i	$-0.725757\pi$
$139$	−15.3564			−1.30251			−0.651255	+	0.758859i	$0.725757\pi$
$140$	2.62746	−	1.68857i	0.222061	−	0.142710i
$141$	0.691529	−	4.80969i	0.0582373	−	0.405049i
$142$	−1.70496	+	3.73335i	−0.143077	+	0.313296i
$143$	−0.896599	+	0.263265i	−0.0749774	+	0.0220154i
$144$	0.415415	+	0.909632i	0.0346179	+	0.0758027i
$145$	6.84320	+	7.89747i	0.568297	+	0.655849i
$146$	1.03026	+	7.16560i	0.0852647	+	0.593029i
$147$	−0.959493	−	0.281733i	−0.0791376	−	0.0232369i
$148$	4.05186	−	4.67609i	0.333061	−	0.384372i
$149$	−4.56049	−	2.93085i	−0.373610	−	0.240105i	0.340338	−	0.940303i	$-0.389458\pi$
$149$	−4.56049	−	2.93085i	−0.373610	−	0.240105i	−0.713948	+	0.700199i	$0.753095\pi$
$150$	4.00002	+	2.57066i	0.326601	+	0.209893i
$151$	−8.33889	+	9.62359i	−0.678609	+	0.783156i	−0.985697	−	0.168525i	$-0.946100\pi$
$151$	−8.33889	+	9.62359i	−0.678609	+	0.783156i	0.307089	+	0.951681i	$0.400645\pi$
$152$	−5.72485	−	1.68097i	−0.464346	−	0.136344i
$153$	1.06064	+	7.37691i	0.0857476	+	0.596388i
$154$	−1.52135	−	1.75574i	−0.122594	−	0.141481i
$155$	9.68989	+	21.2179i	0.778311	+	1.70426i
$156$	−0.385938	+	0.113322i	−0.0308998	+	0.00907299i
$157$	3.28399	−	7.19093i	0.262091	−	0.573898i	−0.732141	−	0.681153i	$-0.761479\pi$
$157$	3.28399	−	7.19093i	0.262091	−	0.573898i	0.994232	+	0.107255i	$0.0342061\pi$
$158$	1.22554	−	8.52385i	0.0974991	−	0.678121i
$159$	8.33148	−	5.35432i	0.660729	−	0.424625i
$160$	3.12327			0.246916
$161$	−4.78061	−	0.381792i	−0.376765	−	0.0300894i
$162$	1.00000			0.0785674
$163$	4.32041	−	2.77656i	0.338401	−	0.217477i	−0.360392	−	0.932801i	$-0.617357\pi$
$163$	4.32041	−	2.77656i	0.338401	−	0.217477i	0.698793	+	0.715324i	$0.253721\pi$
$164$	−1.21864	+	8.47586i	−0.0951602	+	0.661854i
$165$	3.01421	−	6.60020i	0.234656	−	0.513825i
$166$	1.44138	−	0.423226i	0.111872	−	0.0328487i
$167$	3.28020	+	7.18264i	0.253830	+	0.555809i	0.993055	−	0.117649i	$-0.0375356\pi$
$167$	3.28020	+	7.18264i	0.253830	+	0.555809i	−0.739226	+	0.673458i	$0.764808\pi$
$168$	−0.654861	−	0.755750i	−0.0505236	−	0.0583073i
$169$	1.82707	+	12.7075i	0.140544	+	0.977503i
$170$	22.3342	+	6.55790i	1.71295	+	0.502968i
$171$	−3.90725	+	4.50920i	−0.298795	+	0.344828i
$172$	6.09421	+	3.91651i	0.464679	+	0.298631i
$173$	16.9473	+	10.8914i	1.28848	+	0.828057i	0.991909	−	0.126952i	$-0.0405196\pi$
$173$	16.9473	+	10.8914i	1.28848	+	0.828057i	0.296574	+	0.955010i	$0.404156\pi$
$174$	2.19103	−	2.52859i	0.166102	−	0.191692i
$175$	−4.56223	−	1.33959i	−0.344872	−	0.101264i
$176$	−0.330622	−	2.29952i	−0.0249215	−	0.173333i
$177$	−3.18308	−	3.67347i	−0.239255	−	0.276115i
$178$	2.90285	+	6.35635i	0.217578	+	0.476429i
$179$	−11.6968	+	3.43450i	−0.874261	+	0.256706i	−0.687927	−	0.725780i	$-0.741479\pi$
$179$	−11.6968	+	3.43450i	−0.874261	+	0.256706i	−0.186335	+	0.982486i	$0.559661\pi$
$180$	1.29745	−	2.84103i	0.0967066	−	0.211758i
$181$	0.804792	−	5.59745i	0.0598198	−	0.416056i	−0.937804	−	0.347164i	$-0.887145\pi$
$181$	0.804792	−	5.59745i	0.0598198	−	0.416056i	0.997624	−	0.0688914i	$-0.0219462\pi$
$182$	0.338378	−	0.217462i	0.0250823	−	0.0161194i
$183$	4.84548			0.358188
$184$	−3.81529	−	2.90578i	−0.281267	−	0.214217i
$185$	−19.3248			−1.42079
$186$	6.28280	−	4.03771i	0.460678	−	0.296060i
$187$	2.46405	−	17.1378i	0.180189	−	1.25324i
$188$	−2.01856	+	4.42004i	−0.147219	+	0.322365i
$189$	−0.959493	+	0.281733i	−0.0697928	+	0.0204930i
$190$	7.74131	+	16.9511i	0.561613	+	1.22976i
$191$	−9.30669	−	10.7405i	−0.673409	−	0.777155i	0.311497	−	0.950247i	$-0.399170\pi$
$191$	−9.30669	−	10.7405i	−0.673409	−	0.777155i	−0.984906	+	0.173092i	$0.944624\pi$
$192$	−0.142315	−	0.989821i	−0.0102707	−	0.0714342i
$193$	−5.31380	−	1.56027i	−0.382496	−	0.112311i	0.0848315	−	0.996395i	$-0.472965\pi$
$193$	−5.31380	−	1.56027i	−0.382496	−	0.112311i	−0.467327	+	0.884084i	$0.654783\pi$
$194$	6.79332	−	7.83991i	0.487732	−	0.562873i
$195$	1.05685	+	0.679195i	0.0756824	+	0.0486381i
$196$	0.841254	+	0.540641i	0.0600895	+	0.0386172i
$197$	−4.31918	+	4.98460i	−0.307729	+	0.355138i	−0.888457	−	0.458959i	$-0.848222\pi$
$197$	−4.31918	+	4.98460i	−0.307729	+	0.355138i	0.580728	+	0.814097i	$0.302768\pi$
$198$	−2.22907	−	0.654513i	−0.158413	−	0.0465142i
$199$	0.0347928	+	0.241989i	0.00246639	+	0.0171541i	0.991017	−	0.133732i	$-0.0426963\pi$
$199$	0.0347928	+	0.241989i	0.00246639	+	0.0171541i	−0.988551	+	0.150887i	$0.951787\pi$
$200$	−3.11376	−	3.59347i	−0.220176	−	0.254096i
$201$	5.38873	+	11.7997i	0.380092	+	0.832285i
$202$	14.5264	−	4.26534i	1.02207	−	0.300108i
$203$	−1.38990	+	3.04345i	−0.0975516	+	0.213608i
$204$	1.06064	−	7.37691i	0.0742596	−	0.516487i
$205$	22.4990	−	14.4593i	1.57140	−	1.00988i
$206$	−7.75372			−0.540227
$207$	−4.22812	+	2.26341i	−0.293874	+	0.157318i
$208$	0.402231			0.0278897
$209$	11.6608	−	7.49397i	0.806598	−	0.518369i
$210$	−0.444488	+	3.09148i	−0.0306726	+	0.213333i
$211$	2.86756	−	6.27908i	0.197411	−	0.432270i	−0.784876	−	0.619653i	$-0.787273\pi$
$211$	2.86756	−	6.27908i	0.197411	−	0.432270i	0.982287	+	0.187383i	$0.0600007\pi$
$212$	−9.50248	+	2.79018i	−0.652633	+	0.191630i
$213$	−1.70496	−	3.73335i	−0.116822	−	0.255805i
$214$	0.680967	+	0.785877i	0.0465499	+	0.0537215i
$215$	−3.21996	−	22.3953i	−0.219599	−	1.52735i
$216$	−0.959493	−	0.281733i	−0.0652852	−	0.0191695i
$217$	−4.89075	+	5.64423i	−0.332006	+	0.383155i
$218$	−12.6353	−	8.12024i	−0.855773	−	0.549972i
$219$	−6.09007	−	3.91385i	−0.411529	−	0.264474i
$220$	−4.75160	+	5.48364i	−0.320353	+	0.369707i
$221$	2.87631	+	0.844559i	0.193481	+	0.0568112i
$222$	0.880553	+	6.12438i	0.0590988	+	0.411041i
$223$	−2.97776	−	3.43652i	−0.199406	−	0.230127i	0.647236	−	0.762290i	$-0.275925\pi$
$223$	−2.97776	−	3.43652i	−0.199406	−	0.230127i	−0.846642	+	0.532163i	$0.821379\pi$
$224$	0.415415	+	0.909632i	0.0277561	+	0.0607773i
$225$	−4.56223	+	1.33959i	−0.304149	+	0.0893062i
$226$	−7.64470	+	16.7396i	−0.508518	+	1.11350i
$227$	−3.29538	+	22.9199i	−0.218722	+	1.52125i	0.524042	+	0.851692i	$0.324423\pi$
$227$	−3.29538	+	22.9199i	−0.218722	+	1.52125i	−0.742764	+	0.669553i	$0.766486\pi$
$228$	5.01937	−	3.22575i	0.332416	−	0.213631i
$229$	2.35405			0.155560			0.0777801	−	0.996971i	$-0.475217\pi$
$229$	2.35405			0.155560			0.0777801	+	0.996971i	$0.475217\pi$
$230$	0.944622	+	14.9489i	0.0622865	+	0.985700i
$231$	2.32317			0.152853
$232$	−2.81467	+	1.80888i	−0.184792	+	0.118759i
$233$	0.426061	−	2.96332i	0.0279122	−	0.194134i	−0.971094	−	0.238696i	$-0.923280\pi$
$233$	0.426061	−	2.96332i	0.0279122	−	0.194134i	0.999007	+	0.0445621i	$0.0141893\pi$
$234$	0.167093	−	0.365882i	0.0109232	−	0.0239185i
$235$	14.5617	−	4.27570i	0.949901	−	0.278916i
$236$	2.01921	+	4.42145i	0.131439	+	0.287812i
$237$	5.63934	+	6.50814i	0.366314	+	0.422749i
$238$	1.06064	+	7.37691i	0.0687511	+	0.478174i
$239$	−27.8069	−	8.16485i	−1.79868	−	0.528140i	−0.801156	−	0.598456i	$-0.795781\pi$
$239$	−27.8069	−	8.16485i	−1.79868	−	0.528140i	−0.997525	+	0.0703154i	$0.977599\pi$
$240$	−2.04531	+	2.36041i	−0.132024	+	0.152364i
$241$	14.1906	+	9.11972i	0.914094	+	0.587453i	0.910938	−	0.412542i	$-0.135359\pi$
$241$	14.1906	+	9.11972i	0.914094	+	0.587453i	0.00315584	+	0.999995i	$0.498995\pi$
$242$	−4.71344	−	3.02914i	−0.302991	−	0.194721i
$243$	−0.654861	+	0.755750i	−0.0420093	+	0.0484814i
$244$	−4.64920	−	1.36513i	−0.297635	−	0.0873934i
$245$	−0.444488	−	3.09148i	−0.0283973	−	0.197508i
$246$	−5.60759	−	6.47150i	−0.357527	−	0.412608i
$247$	0.996965	+	2.18305i	0.0634353	+	0.138904i
$248$	−7.16586	+	2.10409i	−0.455033	+	0.133610i
$249$	−0.624047	+	1.36647i	−0.0395474	+	0.0865967i
$250$	0.108972	−	0.757918i	0.00689200	−	0.0479349i
$251$	−15.8789	+	10.2048i	−1.00227	+	0.644120i	−0.935381	−	0.353641i	$-0.884944\pi$
$251$	−15.8789	+	10.2048i	−1.00227	+	0.644120i	−0.0668885	+	0.997760i	$0.521307\pi$
$252$	1.00000			0.0629941
$253$	10.9062	−	2.27793i	0.685666	−	0.143212i
$254$	9.98502			0.626516
$255$	−19.5819	+	12.5845i	−1.22627	+	0.788073i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	11.5835	−	25.3643i	0.722559	−	1.58218i	−0.0877237	−	0.996145i	$-0.527959\pi$
$257$	11.5835	−	25.3643i	0.722559	−	1.58218i	0.810283	−	0.586039i	$-0.199313\pi$
$258$	−6.95076	+	2.04093i	−0.432735	+	0.127063i
$259$	−2.57032	−	5.62822i	−0.159712	−	0.349720i
$260$	−0.822687	−	0.949431i	−0.0510209	−	0.0588812i
$261$	0.476157	+	3.31175i	0.0294734	+	0.204992i
$262$	−4.66315	−	1.36922i	−0.288090	−	0.0845910i
$263$	6.31477	−	7.28763i	0.389385	−	0.449375i	−0.526884	−	0.849937i	$-0.676640\pi$
$263$	6.31477	−	7.28763i	0.389385	−	0.449375i	0.916269	+	0.400562i	$0.131185\pi$
$264$	1.95438	+	1.25600i	0.120284	+	0.0773015i
$265$	26.0215	+	16.7230i	1.59849	+	1.02729i
$266$	−3.90725	+	4.50920i	−0.239569	+	0.276477i
$267$	−6.70477	−	1.96870i	−0.410325	−	0.120482i
$268$	−1.84610	−	12.8399i	−0.112768	−	0.784321i
$269$	−4.96554	−	5.73054i	−0.302755	−	0.349397i	0.583903	−	0.811823i	$-0.301525\pi$
$269$	−4.96554	−	5.73054i	−0.302755	−	0.349397i	−0.886658	+	0.462426i	$0.846979\pi$
$270$	1.29745	+	2.84103i	0.0789606	+	0.172900i
$271$	12.8981	−	3.78723i	0.783505	−	0.230058i	0.134572	−	0.990904i	$-0.457034\pi$
$271$	12.8981	−	3.78723i	0.783505	−	0.230058i	0.648933	+	0.760846i	$0.275216\pi$
$272$	−3.09599	+	6.77928i	−0.187722	+	0.411054i
$273$	−0.0572434	+	0.398137i	−0.00346453	+	0.0240963i
$274$	13.2647	−	8.52474i	0.801353	−	0.514998i
$275$	11.0463			0.666117
$276$	4.69453	−	0.980527i	0.282577	−	0.0590208i
$277$	−17.5067			−1.05187			−0.525936	−	0.850524i	$-0.676285\pi$
$277$	−17.5067			−1.05187			−0.525936	+	0.850524i	$0.676285\pi$
$278$	−12.9186	+	8.30227i	−0.774806	+	0.497937i
$279$	−1.06286	+	7.39237i	−0.0636319	+	0.442569i
$280$	1.29745	−	2.84103i	0.0775377	−	0.169784i
$281$	24.1520	−	7.09167i	1.44079	−	0.423053i	0.534303	−	0.845293i	$-0.320574\pi$
$281$	24.1520	−	7.09167i	1.44079	−	0.423053i	0.906484	+	0.422240i	$0.138756\pi$
$282$	−2.01856	−	4.42004i	−0.120204	−	0.263210i
$283$	16.5068	+	19.0499i	0.981227	+	1.13240i	0.991190	+	0.132446i	$0.0422832\pi$
$283$	16.5068	+	19.0499i	0.981227	+	1.13240i	−0.00996279	+	0.999950i	$0.503171\pi$
$284$	0.584095	+	4.06247i	0.0346596	+	0.241063i
$285$	−17.8803	−	5.25012i	−1.05914	−	0.310990i
$286$	−0.611935	+	0.706211i	−0.0361845	+	0.0417591i
$287$	7.20367	+	4.62952i	0.425219	+	0.273272i
$288$	0.841254	+	0.540641i	0.0495713	+	0.0318576i
$289$	−25.2408	+	29.1294i	−1.48475	+	1.71350i
$290$	10.0266	+	2.94406i	0.588780	+	0.172881i
$291$	1.47633	+	10.2681i	0.0865440	+	0.601927i
$292$	4.74072	+	5.47109i	0.277430	+	0.320171i
$293$	−11.0153	−	24.1202i	−0.643522	−	1.40912i	−0.897111	−	0.441805i	$-0.854338\pi$
$293$	−11.0153	−	24.1202i	−0.643522	−	1.40912i	0.253589	−	0.967312i	$-0.418389\pi$
$294$	−0.959493	+	0.281733i	−0.0559588	+	0.0164310i
$295$	6.30654	−	13.8094i	0.367181	−	0.804014i
$296$	0.880553	−	6.12438i	0.0511811	−	0.355972i
$297$	1.95438	−	1.25600i	0.113404	−	0.0728806i
$298$	−5.42107			−0.314034
$299$	0.121653	+	1.92519i	0.00703538	+	0.111337i
$300$	4.75484			0.274521
$301$	6.09421	−	3.91651i	0.351264	−	0.225744i
$302$	−1.81221	+	12.6042i	−0.104281	+	0.725291i
$303$	−6.28924	+	13.7715i	−0.361308	+	0.791153i
$304$	−5.72485	+	1.68097i	−0.328342	+	0.0964101i
$305$	6.28679	+	13.7661i	0.359980	+	0.788247i
$306$	4.88053	+	5.63243i	0.279001	+	0.321984i
$307$	−1.38661	−	9.64406i	−0.0791378	−	0.550415i	−0.990362	−	0.138504i	$-0.955771\pi$
$307$	−1.38661	−	9.64406i	−0.0791378	−	0.550415i	0.911224	−	0.411911i	$-0.135139\pi$
$308$	−2.22907	−	0.654513i	−0.127013	−	0.0372943i
$309$	5.07761	−	5.85987i	0.288855	−	0.333356i
$310$	19.6229	+	12.6109i	1.11451	+	0.716250i
$311$	0.0607801	+	0.0390610i	0.00344652	+	0.00221495i	0.542363	−	0.840144i	$-0.317530\pi$
$311$	0.0607801	+	0.0390610i	0.00344652	+	0.00221495i	−0.538916	+	0.842359i	$0.681166\pi$
$312$	−0.263405	+	0.303986i	−0.0149124	+	0.0172098i
$313$	23.2865	+	6.83752i	1.31623	+	0.386480i	0.863131	−	0.504981i	$-0.168500\pi$
$313$	23.2865	+	6.83752i	1.31623	+	0.386480i	0.453098	+	0.891460i	$0.350319\pi$
$314$	−1.12504	−	7.82485i	−0.0634899	−	0.441582i
$315$	−2.04531	−	2.36041i	−0.115240	−	0.132994i
$316$	−3.57735	−	7.83330i	−0.201242	−	0.440657i
$317$	1.75679	−	0.515839i	0.0986709	−	0.0289724i	−0.232024	−	0.972710i	$-0.574535\pi$
$317$	1.75679	−	0.515839i	0.0986709	−	0.0289724i	0.330695	+	0.943738i	$0.392717\pi$
$318$	4.11412	−	9.00867i	0.230709	−	0.505181i
$319$	1.10619	−	7.69375i	0.0619350	−	0.430767i
$320$	2.62746	−	1.68857i	0.146880	−	0.0943939i
$321$	−1.03986			−0.0580396
$322$	−4.22812	+	2.26341i	−0.235624	+	0.126135i
$323$	−44.4672			−2.47422
$324$	0.841254	−	0.540641i	0.0467363	−	0.0300356i
$325$	−0.272183	+	1.89308i	−0.0150980	+	0.105009i
$326$	2.13344	−	4.67158i	0.118160	−	0.258735i
$327$	14.4113	−	4.23153i	0.796944	−	0.234004i
$328$	3.55721	+	7.78920i	0.196414	+	0.430086i
$329$	3.18207	+	3.67230i	0.175433	+	0.202461i
$330$	−1.03262	−	7.18204i	−0.0568440	−	0.395358i
$331$	22.4555	+	6.59352i	1.23426	+	0.362412i	0.832857	−	0.553488i	$-0.186703\pi$
$331$	22.4555	+	6.59352i	1.23426	+	0.362412i	0.401406	+	0.915900i	$0.368522\pi$
$332$	0.983749	−	1.13531i	0.0539902	−	0.0623080i
$333$	−5.20514	−	3.34514i	−0.285240	−	0.183312i
$334$	6.64271	+	4.26901i	0.363473	+	0.233590i
$335$	−26.5316	+	30.6191i	−1.44958	+	1.67290i
$336$	−0.959493	−	0.281733i	−0.0523446	−	0.0153698i
$337$	3.80511	+	26.4651i	0.207277	+	1.44165i	0.781990	+	0.623291i	$0.214205\pi$
$337$	3.80511	+	26.4651i	0.207277	+	1.44165i	−0.574712	+	0.818355i	$0.694886\pi$
$338$	8.40724	+	9.70247i	0.457294	+	0.527745i
$339$	−7.64470	−	16.7396i	−0.415203	−	0.909168i
$340$	22.3342	−	6.55790i	1.21124	−	0.355652i
$341$	7.20759	−	15.7824i	0.390313	−	0.854666i
$342$	−0.849126	+	5.90580i	−0.0459155	+	0.319349i
$343$	0.841254	−	0.540641i	0.0454234	−	0.0291919i
$344$	7.24420			0.390581
$345$	−11.9162	−	9.07554i	−0.641547	−	0.488610i
$346$	20.1453			1.08302
$347$	23.5296	−	15.1216i	1.26314	−	0.811768i	0.274426	−	0.961608i	$-0.411512\pi$
$347$	23.5296	−	15.1216i	1.26314	−	0.811768i	0.988710	+	0.149840i	$0.0478758\pi$
$348$	0.476157	−	3.31175i	0.0255247	−	0.177528i
$349$	12.1616	−	26.6301i	0.650993	−	1.42548i	−0.239690	−	0.970850i	$-0.577046\pi$
$349$	12.1616	−	26.6301i	0.650993	−	1.42548i	0.890682	−	0.454626i	$-0.150227\pi$
$350$	−4.56223	+	1.33959i	−0.243862	+	0.0716042i
$351$	0.167093	+	0.365882i	0.00891875	+	0.0195293i
$352$	−1.52135	−	1.75574i	−0.0810884	−	0.0935810i
$353$	2.70902	+	18.8416i	0.144187	+	1.00284i	0.925513	+	0.378717i	$0.123634\pi$
$353$	2.70902	+	18.8416i	0.144187	+	1.00284i	−0.781326	+	0.624123i	$0.785456\pi$
$354$	−4.66381	−	1.36942i	−0.247879	−	0.0727837i
$355$	8.39444	−	9.68770i	0.445531	−	0.514170i
$356$	5.87853	+	3.77790i	0.311562	+	0.200229i
$357$	−6.26967	−	4.02927i	−0.331826	−	0.213252i
$358$	−7.98316	+	9.21306i	−0.421923	+	0.486925i
$359$	−2.39321	−	0.702710i	−0.126309	−	0.0370876i	0.217967	−	0.975956i	$-0.430057\pi$
$359$	−2.39321	−	0.702710i	−0.126309	−	0.0370876i	−0.344276	+	0.938868i	$0.611876\pi$
$360$	−0.444488	−	3.09148i	−0.0234266	−	0.162935i
$361$	−10.8704	−	12.5451i	−0.572125	−	0.660267i
$362$	−2.34918	−	5.14398i	−0.123470	−	0.270362i
$363$	5.37592	−	1.57851i	0.282163	−	0.0828504i
$364$	0.167093	−	0.365882i	0.00875804	−	0.0191774i
$365$	3.21778	−	22.3801i	0.168426	−	1.17143i
$366$	4.07628	−	2.61966i	0.213070	−	0.136932i
$367$	−32.3055			−1.68633			−0.843165	−	0.537654i	$-0.819311\pi$
$367$	−32.3055			−1.68633			−0.843165	+	0.537654i	$0.819311\pi$
$368$	−4.78061	−	0.381792i	−0.249207	−	0.0199023i
$369$	8.56302			0.445773
$370$	−16.2571	+	10.4478i	−0.845164	+	0.543154i
$371$	−1.40944	+	9.80284i	−0.0731743	+	0.508938i
$372$	3.10248	−	6.79348i	0.160856	−	0.352226i
$373$	−4.60406	+	1.35187i	−0.238389	+	0.0699974i	−0.398745	−	0.917062i	$-0.630554\pi$
$373$	−4.60406	+	1.35187i	−0.238389	+	0.0699974i	0.160356	+	0.987059i	$0.448736\pi$
$374$	−7.19252	−	15.7494i	−0.371916	−	0.814383i
$375$	0.501434	+	0.578686i	0.0258940	+	0.0298832i
$376$	0.691529	+	4.80969i	0.0356629	+	0.248041i
$377$	1.29127	+	0.379151i	0.0665039	+	0.0195273i
$378$	−0.654861	+	0.755750i	−0.0336824	+	0.0388716i
$379$	−15.0301	−	9.65923i	−0.772042	−	0.496161i	0.0943417	−	0.995540i	$-0.469925\pi$
$379$	−15.0301	−	9.65923i	−0.772042	−	0.496161i	−0.866384	+	0.499378i	$0.833562\pi$
$380$	15.6769	+	10.0749i	0.804206	+	0.516832i
$381$	−6.53880	+	7.54617i	−0.334993	+	0.386602i
$382$	−13.6360	−	4.00390i	−0.697680	−	0.204857i
$383$	−4.49802	−	31.2844i	−0.229838	−	1.59856i	−0.698785	−	0.715332i	$-0.746276\pi$
$383$	−4.49802	−	31.2844i	−0.229838	−	1.59856i	0.468947	−	0.883226i	$-0.344634\pi$
$384$	−0.654861	−	0.755750i	−0.0334182	−	0.0385667i
$385$	3.01421	+	6.60020i	0.153618	+	0.336377i
$386$	−5.31380	+	1.56027i	−0.270465	+	0.0794158i
$387$	3.00935	−	6.58955i	0.152974	−	0.334966i
$388$	1.47633	−	10.2681i	0.0749493	−	0.521284i
$389$	14.5248	−	9.33455i	0.736439	−	0.473281i	−0.117881	−	0.993028i	$-0.537610\pi$
$389$	14.5248	−	9.33455i	0.736439	−	0.473281i	0.854320	+	0.519747i	$0.173974\pi$
$390$	1.25628			0.0636141
$391$	−33.3839	−	12.7679i	−1.68830	−	0.645702i
$392$	1.00000			0.0505076
$393$	4.08850	−	2.62752i	0.206238	−	0.132541i
$394$	−0.938648	+	6.52844i	−0.0472884	+	0.328898i
$395$	−11.1730	+	24.4655i	−0.562176	+	1.23099i
$396$	−2.22907	+	0.654513i	−0.112015	+	0.0328905i
$397$	4.54806	+	9.95887i	0.228261	+	0.499821i	0.988759	−	0.149519i	$-0.0477724\pi$
$397$	4.54806	+	9.95887i	0.228261	+	0.499821i	−0.760498	+	0.649340i	$0.775045\pi$
$398$	0.160099	+	0.184764i	0.00802502	+	0.00926137i
$399$	−0.849126	−	5.90580i	−0.0425095	−	0.295660i
$400$	−4.56223	−	1.33959i	−0.228112	−	0.0669796i
$401$	16.5574	−	19.1082i	0.826836	−	0.954220i	−0.172691	−	0.984976i	$-0.555246\pi$
$401$	16.5574	−	19.1082i	0.826836	−	0.954220i	0.999527	+	0.0307565i	$0.00979163\pi$
$402$	10.9127	+	7.01315i	0.544275	+	0.349784i
$403$	2.52714	+	1.62409i	0.125886	+	0.0809019i
$404$	9.91437	−	11.4418i	0.493258	−	0.569251i
$405$	−2.99676	−	0.879928i	−0.148910	−	0.0437240i
$406$	0.476157	+	3.31175i	0.0236313	+	0.164359i
$407$	9.41316	+	10.8634i	0.466593	+	0.538477i
$408$	−3.09599	−	6.77928i	−0.153274	−	0.335624i
$409$	32.3905	−	9.51069i	1.60160	−	0.470274i	0.645612	−	0.763665i	$-0.276602\pi$
$409$	32.3905	−	9.51069i	1.60160	−	0.470274i	0.955992	+	0.293392i	$0.0947840\pi$
$410$	11.1101	−	24.3278i	0.548690	−	1.20146i
$411$	−2.24400	+	15.6073i	−0.110688	+	0.769853i
$412$	−6.52284	+	4.19198i	−0.321357	+	0.206524i
$413$	4.86070			0.239179
$414$	−2.33323	+	4.18999i	−0.114672	+	0.205927i
$415$	−4.69186			−0.230314
$416$	0.338378	−	0.217462i	0.0165904	−	0.0106620i
$417$	2.18544	−	15.2001i	0.107021	−	0.744350i
$418$	5.75818	−	12.6087i	0.281642	−	0.616710i
$419$	13.0461	−	3.83068i	0.637344	−	0.187141i	0.0529319	−	0.998598i	$-0.483143\pi$
$419$	13.0461	−	3.83068i	0.637344	−	0.187141i	0.584412	+	0.811457i	$0.301325\pi$
$420$	1.29745	+	2.84103i	0.0633093	+	0.138628i
$421$	21.7508	+	25.1018i	1.06007	+	1.22339i	0.973870	+	0.227108i	$0.0729270\pi$
$421$	21.7508	+	25.1018i	1.06007	+	1.22339i	0.0862002	+	0.996278i	$0.472528\pi$
$422$	−0.982382	−	6.83262i	−0.0478216	−	0.332607i
$423$	4.66232	+	1.36898i	0.226690	+	0.0665621i
$424$	−6.48551	+	7.48468i	−0.314964	+	0.363488i
$425$	−29.8113	−	19.1585i	−1.44606	−	0.929325i
$426$	−3.45271	−	2.21892i	−0.167284	−	0.107507i
$427$	−3.17311	+	3.66197i	−0.153558	+	0.177215i
$428$	0.997743	+	0.292964i	0.0482277	+	0.0141609i
$429$	−0.132986	−	0.924940i	−0.00642064	−	0.0446565i
$430$	−14.8166	−	17.0993i	−0.714521	−	0.824601i
$431$	−2.13803	−	4.68163i	−0.102985	−	0.225506i	0.851124	−	0.524964i	$-0.175921\pi$
$431$	−2.13803	−	4.68163i	−0.102985	−	0.225506i	−0.954109	+	0.299458i	$0.903194\pi$
$432$	−0.959493	+	0.281733i	−0.0461636	+	0.0135549i
$433$	6.17072	−	13.5120i	0.296546	−	0.649345i	−0.701444	−	0.712725i	$-0.747461\pi$
$433$	6.17072	−	13.5120i	0.296546	−	0.649345i	0.997989	+	0.0633800i	$0.0201880\pi$
$434$	−1.06286	+	7.39237i	−0.0510190	+	0.354845i
$435$	−8.79098	+	5.64962i	−0.421495	+	0.270878i
$436$	−15.0197			−0.719311
$437$	−9.77704	−	26.8923i	−0.467699	−	1.28644i
$438$	−7.23929			−0.345906
$439$	−23.7104	+	15.2377i	−1.13163	+	0.727257i	−0.965900	−	0.258914i	$-0.916635\pi$
$439$	−23.7104	+	15.2377i	−1.13163	+	0.727257i	−0.165733	+	0.986171i	$0.552999\pi$
$440$	−1.03262	+	7.18204i	−0.0492283	+	0.342390i
$441$	0.415415	−	0.909632i	0.0197817	−	0.0433158i
$442$	2.87631	−	0.844559i	0.136812	−	0.0401716i
$443$	−0.795991	−	1.74298i	−0.0378187	−	0.0828114i	0.889780	−	0.456390i	$-0.150858\pi$
$443$	−0.795991	−	1.74298i	−0.0378187	−	0.0828114i	−0.927598	+	0.373579i	$0.878131\pi$
$444$	4.05186	+	4.67609i	0.192293	+	0.221918i
$445$	−3.10601	−	21.6027i	−0.147239	−	1.02407i
$446$	−4.36298	−	1.28109i	−0.206593	−	0.0606612i
$447$	3.55004	−	4.09697i	0.167911	−	0.193780i
$448$	0.841254	+	0.540641i	0.0397455	+	0.0255429i
$449$	12.4327	+	7.99004i	0.586737	+	0.377073i	0.800070	−	0.599906i	$-0.204796\pi$
$449$	12.4327	+	7.99004i	0.586737	+	0.377073i	−0.213333	+	0.976980i	$0.568432\pi$
$450$	−3.11376	+	3.59347i	−0.146784	+	0.169398i
$451$	−19.0875	−	5.60461i	−0.898797	−	0.263911i
$452$	2.61896	+	18.2152i	0.123185	+	0.856773i
$453$	−8.33889	−	9.62359i	−0.391795	−	0.452156i
$454$	9.61917	+	21.0630i	0.451450	+	0.988538i
$455$	−1.20539	+	0.353934i	−0.0565095	+	0.0165927i
$456$	2.47859	−	5.42735i	0.116070	−	0.254159i
$457$	4.24128	−	29.4987i	0.198399	−	1.37989i	−0.610534	−	0.791990i	$-0.709045\pi$
$457$	4.24128	−	29.4987i	0.198399	−	1.37989i	0.808932	−	0.587902i	$-0.200046\pi$
$458$	1.98035	−	1.27270i	0.0925359	−	0.0594692i
$459$	−7.45277			−0.347865
$460$	8.87664	+	12.0651i	0.413875	+	0.562538i
$461$	−5.15401			−0.240046			−0.120023	−	0.992771i	$-0.538297\pi$
$461$	−5.15401			−0.240046			−0.120023	+	0.992771i	$0.538297\pi$
$462$	1.95438	−	1.25600i	0.0909258	−	0.0584345i
$463$	−2.37028	+	16.4856i	−0.110156	+	0.766153i	0.857610	+	0.514301i	$0.171949\pi$
$463$	−2.37028	+	16.4856i	−0.110156	+	0.766153i	−0.967766	+	0.251852i	$0.918960\pi$
$464$	−1.38990	+	3.04345i	−0.0645243	+	0.141289i
$465$	−22.3809	+	6.57164i	−1.03789	+	0.304752i
$466$	−1.24367	−	2.72325i	−0.0576117	−	0.126152i
$467$	−6.67658	−	7.70519i	−0.308955	−	0.356554i	0.579944	−	0.814657i	$-0.303075\pi$
$467$	−6.67658	−	7.70519i	−0.308955	−	0.356554i	−0.888899	+	0.458103i	$0.848529\pi$
$468$	−0.0572434	−	0.398137i	−0.00264608	−	0.0184039i
$469$	−12.4465	−	3.65461i	−0.574725	−	0.168754i
$470$	9.93847	−	11.4696i	0.458427	−	0.529053i
$471$	6.65037	+	4.27393i	0.306433	+	0.196933i
$472$	4.08908	+	2.62789i	0.188215	+	0.120959i
$473$	−11.0210	+	12.7189i	−0.506745	+	0.584815i
$474$	8.26268	+	2.42614i	0.379517	+	0.111436i
$475$	−4.03746	−	28.0811i	−0.185251	−	1.28845i
$476$	4.88053	+	5.63243i	0.223699	+	0.258162i
$477$	4.11412	+	9.00867i	0.188373	+	0.412479i
$478$	−27.8069	+	8.16485i	−1.27186	+	0.373452i
$479$	9.43675	−	20.6636i	0.431176	−	0.944144i	−0.561958	−	0.827166i	$-0.689952\pi$
$479$	9.43675	−	20.6636i	0.431176	−	0.944144i	0.993134	−	0.116979i	$-0.0373209\pi$
$480$	−0.444488	+	3.09148i	−0.0202880	+	0.141106i
$481$	−2.09367	+	1.34552i	−0.0954630	+	0.0613503i
$482$	16.8684			0.768332
$483$	1.05826	−	4.67762i	0.0481524	−	0.212839i
$484$	−5.60288			−0.254676
$485$	−27.2565	+	17.5167i	−1.23765	+	0.795392i
$486$	−0.142315	+	0.989821i	−0.00645553	+	0.0448992i
$487$	0.533096	−	1.16732i	0.0241569	−	0.0528962i	−0.897169	−	0.441687i	$-0.854380\pi$
$487$	0.533096	−	1.16732i	0.0241569	−	0.0528962i	0.921326	+	0.388791i	$0.127107\pi$
$488$	−4.64920	+	1.36513i	−0.210459	+	0.0617965i
$489$	2.13344	+	4.67158i	0.0964775	+	0.211256i
$490$	−2.04531	−	2.36041i	−0.0923976	−	0.106633i
$491$	−4.02087	−	27.9658i	−0.181460	−	1.26208i	−0.853315	−	0.521396i	$-0.825411\pi$
$491$	−4.02087	−	27.9658i	−0.181460	−	1.26208i	0.671855	−	0.740683i	$-0.265498\pi$
$492$	−8.21616	−	2.41248i	−0.370413	−	0.108763i
$493$	−16.3293	+	18.8450i	−0.735433	+	0.848735i
$494$	2.01894	+	1.29750i	0.0908366	+	0.0583772i
$495$	6.10405	+	3.92283i	0.274357	+	0.176318i
$496$	−4.89075	+	5.64423i	−0.219601	+	0.253433i
$497$	3.93799	+	1.15630i	0.176643	+	0.0518671i
$498$	0.213789	+	1.48694i	0.00958012	+	0.0666312i
$499$	−8.04872	−	9.28872i	−0.360310	−	0.415820i	0.546433	−	0.837503i	$-0.315985\pi$
$499$	−8.04872	−	9.28872i	−0.360310	−	0.415820i	−0.906744	+	0.421682i	$0.861440\pi$
$500$	−0.318088	−	0.696516i	−0.0142253	−	0.0311491i
$501$	−7.57635	+	2.22462i	−0.338486	+	0.0993886i
$502$	−7.84110	+	17.1696i	−0.349965	+	0.766317i
$503$	−4.51177	+	31.3801i	−0.201170	+	1.39917i	0.599649	+	0.800263i	$0.295307\pi$
$503$	−4.51177	+	31.3801i	−0.201170	+	1.39917i	−0.800819	+	0.598906i	$0.795602\pi$
$504$	0.841254	−	0.540641i	0.0374724	−	0.0240821i
$505$	−47.2853			−2.10417
$506$	7.94332	−	7.81265i	0.353124	−	0.347314i
$507$	−12.8382			−0.570165
$508$	8.39993	−	5.39831i	0.372687	−	0.239511i
$509$	0.776951	−	5.40381i	0.0344377	−	0.239520i	−0.965331	−	0.261029i	$-0.915938\pi$
$509$	0.776951	−	5.40381i	0.0344377	−	0.239520i	0.999769	+	0.0215095i	$0.00684720\pi$
$510$	−9.66963	+	21.1735i	−0.428178	+	0.937580i
$511$	6.94604	−	2.03954i	0.307275	−	0.0902241i
$512$	0.415415	+	0.909632i	0.0183589	+	0.0402004i
$513$	−3.90725	−	4.50920i	−0.172509	−	0.199086i
$514$	−3.96833	−	27.6004i	−0.175036	−	1.21740i
$515$	23.2360	+	6.82271i	1.02390	+	0.300645i
$516$	−4.74394	+	5.47480i	−0.208840	+	0.241015i
$517$	−9.49661	−	6.10310i	−0.417660	−	0.268414i
$518$	−5.20514	−	3.34514i	−0.228701	−	0.146977i
$519$	−13.1924	+	15.2248i	−0.579082	+	0.668296i
$520$	−1.20539	−	0.353934i	−0.0528598	−	0.0155210i
$521$	4.64936	+	32.3370i	0.203692	+	1.41671i	0.793207	+	0.608952i	$0.208410\pi$
$521$	4.64936	+	32.3370i	0.203692	+	1.41671i	−0.589515	+	0.807758i	$0.700681\pi$
$522$	2.19103	+	2.52859i	0.0958990	+	0.110673i
$523$	7.63219	+	16.7122i	0.333732	+	0.730772i	0.999887	−	0.0150418i	$-0.00478815\pi$
$523$	7.63219	+	16.7122i	0.333732	+	0.730772i	−0.666155	+	0.745814i	$0.732061\pi$
$524$	−4.66315	+	1.36922i	−0.203711	+	0.0598148i
$525$	1.97523	−	4.32515i	0.0862061	−	0.188765i
$526$	1.37233	−	9.54477i	0.0598365	−	0.416172i
$527$	−46.8243	+	30.0921i	−2.03970	+	1.31083i
$528$	2.32317			0.101103
$529$	0.381488	−	22.9968i	0.0165865	−	0.999862i
$530$	30.9318			1.34359
$531$	4.08908	−	2.62789i	0.177451	−	0.114041i
$532$	−0.849126	+	5.90580i	−0.0368143	+	0.256049i
$533$	1.43082	−	3.13306i	0.0619756	−	0.135708i
$534$	−6.70477	+	1.96870i	−0.290144	+	0.0851939i
$535$	−1.34918	−	2.95429i	−0.0583300	−	0.127725i
$536$	−8.49480	−	9.80353i	−0.366920	−	0.423448i
$537$	−1.73491	−	12.0665i	−0.0748668	−	0.520710i
$538$	−7.27545	−	2.13626i	−0.313667	−	0.0921009i
$539$	−1.52135	+	1.75574i	−0.0655293	+	0.0756249i
$540$	2.62746	+	1.68857i	0.113068	+	0.0726644i
$541$	12.6338	+	8.11924i	0.543169	+	0.349073i	0.783277	−	0.621673i	$-0.213547\pi$
$541$	12.6338	+	8.11924i	0.543169	+	0.349073i	−0.240108	+	0.970746i	$0.577183\pi$
$542$	8.80306	−	10.1593i	0.378124	−	0.436378i
$543$	5.42595	+	1.59320i	0.232850	+	0.0683708i
$544$	1.06064	+	7.37691i	0.0454746	+	0.316282i
$545$	30.7198	+	35.4526i	1.31589	+	1.51862i
$546$	0.167093	+	0.365882i	0.00715091	+	0.0156583i
$547$	−22.7919	+	6.69229i	−0.974509	+	0.286142i	−0.729956	−	0.683494i	$-0.760459\pi$
$547$	−22.7919	+	6.69229i	−0.974509	+	0.286142i	−0.244553	+	0.969636i	$0.578641\pi$
$548$	6.55020	−	14.3429i	0.279811	−	0.612700i
$549$	−0.689583	+	4.79616i	−0.0294307	+	0.204695i
$550$	9.29274	−	5.97208i	0.396244	−	0.254650i
$551$	−19.9628			−0.850445
$552$	3.41917	−	3.36292i	0.145530	−	0.143136i
$553$	−8.61150			−0.366198
$554$	−14.7275	+	9.46481i	−0.625713	+	0.402121i
$555$	2.75021	−	19.1281i	0.116740	−	0.811943i
$556$	−6.37926	+	13.9686i	−0.270541	+	0.592402i
$557$	25.8911	−	7.60231i	1.09704	−	0.322120i	0.317365	−	0.948304i	$-0.397202\pi$
$557$	25.8911	−	7.60231i	1.09704	−	0.322120i	0.779676	+	0.626184i	$0.215384\pi$
$558$	3.10248	+	6.79348i	0.131338	+	0.287591i
$559$	−1.90816	−	2.20213i	−0.0807066	−	0.0931403i
$560$	−0.444488	−	3.09148i	−0.0187831	−	0.130639i
$561$	16.6127	+	4.87793i	0.701389	+	0.205947i
$562$	16.4839	−	19.0234i	0.695332	−	0.802455i
$563$	33.2083	+	21.3417i	1.39956	+	0.899444i	0.999852	−	0.0171979i	$-0.00547454\pi$
$563$	33.2083	+	21.3417i	1.39956	+	0.899444i	0.399710	+	0.916642i	$0.369111\pi$
$564$	−4.08778	−	2.62706i	−0.172127	−	0.110619i
$565$	37.6389	−	43.4376i	1.58348	−	1.82743i
$566$	24.1855	+	7.10151i	1.01659	+	0.298499i
$567$	−0.142315	−	0.989821i	−0.00597666	−	0.0415686i
$568$	2.68771	+	3.10178i	0.112774	+	0.130148i
$569$	−17.2306	−	37.7297i	−0.722343	−	1.58171i	−0.810591	−	0.585612i	$-0.800854\pi$
$569$	−17.2306	−	37.7297i	−0.722343	−	1.58171i	0.0882483	−	0.996099i	$-0.471873\pi$
$570$	−17.8803	+	5.25012i	−0.748922	+	0.219903i
$571$	−0.609447	+	1.33450i	−0.0255046	+	0.0558472i	−0.921956	−	0.387296i	$-0.873409\pi$
$571$	−0.609447	+	1.33450i	−0.0255046	+	0.0558472i	0.896451	+	0.443143i	$0.146137\pi$
$572$	−0.132986	+	0.924940i	−0.00556044	+	0.0386737i
$573$	11.9557	−	7.68343i	0.499454	−	0.320980i
$574$	8.56302			0.357414
$575$	5.03184	−	22.2413i	0.209842	−	0.927526i
$576$	1.00000			0.0416667
$577$	−14.0464	+	9.02709i	−0.584761	+	0.375803i	−0.799318	−	0.600909i	$-0.794806\pi$
$577$	−14.0464	+	9.02709i	−0.584761	+	0.375803i	0.214557	+	0.976711i	$0.431169\pi$
$578$	−5.48535	+	38.1515i	−0.228161	+	1.58689i
$579$	2.30062	−	5.03766i	0.0956107	−	0.209358i
$580$	10.0266	−	2.94406i	0.416330	−	0.122246i
$581$	−0.624047	−	1.36647i	−0.0258898	−	0.0566908i
$582$	6.79332	+	7.83991i	0.281592	+	0.324975i
$583$	−3.27436	−	22.7737i	−0.135610	−	0.943189i
$584$	6.94604	+	2.03954i	0.287429	+	0.0843969i
$585$	−0.822687	+	0.949431i	−0.0340139	+	0.0392541i
$586$	−22.3070	−	14.3359i	−0.921495	−	0.592209i
$587$	18.0293	+	11.5868i	0.744151	+	0.478237i	0.856962	−	0.515380i	$-0.172349\pi$
$587$	18.0293	+	11.5868i	0.744151	+	0.478237i	−0.112811	+	0.993616i	$0.535986\pi$
$588$	−0.654861	+	0.755750i	−0.0270060	+	0.0311666i
$589$	−42.7554	−	12.5541i	−1.76170	−	0.517283i
$590$	−2.16052	−	15.0268i	−0.0889474	−	0.618643i
$591$	−4.31918	−	4.98460i	−0.177667	−	0.205039i
$592$	−2.57032	−	5.62822i	−0.105640	−	0.231318i
$593$	−2.72687	+	0.800680i	−0.111979	+	0.0328800i	−0.337242	−	0.941418i	$-0.609494\pi$
$593$	−2.72687	+	0.800680i	−0.111979	+	0.0328800i	0.225263	+	0.974298i	$0.427676\pi$
$594$	0.965080	−	2.11323i	0.0395977	−	0.0867069i
$595$	3.31267	−	23.0401i	0.135806	−	0.944552i
$596$	−4.56049	+	2.93085i	−0.186805	+	0.120052i
$597$	−0.244477			−0.0100058
$598$	1.14318	+	1.55380i	0.0467480	+	0.0635398i
$599$	21.9877			0.898391			0.449196	−	0.893433i	$-0.351711\pi$
$599$	21.9877			0.898391			0.449196	+	0.893433i	$0.351711\pi$
$600$	4.00002	−	2.57066i	0.163300	−	0.104947i
$601$	−2.88629	+	20.0746i	−0.117734	+	0.818859i	0.842307	+	0.538999i	$0.181197\pi$
$601$	−2.88629	+	20.0746i	−0.117734	+	0.818859i	−0.960041	+	0.279860i	$0.909712\pi$
$602$	3.00935	−	6.58955i	0.122652	−	0.268570i
$603$	−12.4465	+	3.65461i	−0.506859	+	0.148827i
$604$	5.28982	+	11.5831i	0.215240	+	0.471310i
$605$	11.4596	+	13.2251i	0.465900	+	0.537677i
$606$	2.15460	+	14.9856i	0.0875246	+	0.608747i
$607$	11.0788	+	3.25302i	0.449673	+	0.132036i	0.498725	−	0.866760i	$-0.333802\pi$
$607$	11.0788	+	3.25302i	0.449673	+	0.132036i	−0.0490519	+	0.998796i	$0.515620\pi$
$608$	−3.90725	+	4.50920i	−0.158460	+	0.182872i
$609$	−2.81467	−	1.80888i	−0.114056	−	0.0732994i
$610$	12.7313	+	8.18192i	0.515476	+	0.331276i
$611$	1.27993	−	1.47711i	0.0517803	−	0.0597576i
$612$	7.15088	+	2.09969i	0.289057	+	0.0848748i
$613$	−5.22806	−	36.3619i	−0.211159	−	1.46864i	−0.769294	−	0.638895i	$-0.779392\pi$
$613$	−5.22806	−	36.3619i	−0.211159	−	1.46864i	0.558135	−	0.829750i	$-0.311517\pi$
$614$	−6.38046	−	7.36344i	−0.257494	−	0.297164i
$615$	11.1101	+	24.3278i	0.448004	+	0.980991i
$616$	−2.22907	+	0.654513i	−0.0898116	+	0.0263711i
$617$	−13.5340	+	29.6352i	−0.544857	+	1.19307i	0.414286	+	0.910147i	$0.364031\pi$
$617$	−13.5340	+	29.6352i	−0.544857	+	1.19307i	−0.959143	+	0.282923i	$0.908696\pi$
$618$	1.10347	−	7.67480i	0.0443880	−	0.308726i
$619$	5.41455	−	3.47972i	0.217629	−	0.139862i	−0.427284	−	0.904117i	$-0.640530\pi$
$619$	5.41455	−	3.47972i	0.217629	−	0.139862i	0.644914	+	0.764256i	$0.276893\pi$
$620$	23.3258			0.936787
$621$	−1.63865	−	4.50720i	−0.0657566	−	0.180868i
$622$	0.0722494			0.00289694
$623$	5.87853	−	3.77790i	0.235518	−	0.151359i
$624$	−0.0572434	+	0.398137i	−0.00229157	+	0.0159382i
$625$	−10.8696	+	23.8012i	−0.434785	+	0.952047i
$626$	23.2865	−	6.83752i	0.930715	−	0.273282i
$627$	5.75818	+	12.6087i	0.229960	+	0.503541i
$628$	−5.17688	−	5.97444i	−0.206580	−	0.238406i
$629$	−6.56256	−	45.6436i	−0.261666	−	1.81993i
$630$	−2.99676	−	0.879928i	−0.119394	−	0.0350572i
$631$	−28.7105	+	33.1337i	−1.14295	+	1.31903i	−0.202426	+	0.979298i	$0.564882\pi$
$631$	−28.7105	+	33.1337i	−1.14295	+	1.31903i	−0.940522	+	0.339734i	$0.889663\pi$
$632$	−7.24446	−	4.65573i	−0.288169	−	0.185195i
$633$	5.80707	+	3.73198i	0.230810	+	0.148333i
$634$	1.19902	−	1.38374i	0.0476191	−	0.0549554i
$635$	−29.9227	−	8.78610i	−1.18745	−	0.348666i
$636$	−1.40944	−	9.80284i	−0.0558878	−	0.388708i
$637$	−0.263405	−	0.303986i	−0.0104365	−	0.0120444i
$638$	−3.22897	−	7.07045i	−0.127836	−	0.279922i
$639$	3.93799	−	1.15630i	0.155785	−	0.0457425i
$640$	1.29745	−	2.84103i	0.0512864	−	0.112302i
$641$	3.39128	−	23.5868i	0.133947	−	0.931625i	−0.806391	−	0.591383i	$-0.798582\pi$
$641$	3.39128	−	23.5868i	0.133947	−	0.931625i	0.940338	−	0.340241i	$-0.110509\pi$
$642$	−0.874790	+	0.562193i	−0.0345252	+	0.0221880i
$643$	1.11768			0.0440769			0.0220385	−	0.999757i	$-0.492984\pi$
$643$	1.11768			0.0440769			0.0220385	+	0.999757i	$0.492984\pi$
$644$	−2.33323	+	4.18999i	−0.0919420	+	0.165109i
$645$	22.6256			0.890882
$646$	−37.4082	+	24.0408i	−1.47181	+	0.945872i
$647$	0.902445	−	6.27664i	0.0354788	−	0.246760i	−0.964362	−	0.264585i	$-0.914765\pi$
$647$	0.902445	−	6.27664i	0.0354788	−	0.246760i	0.999841	+	0.0178248i	$0.00567412\pi$
$648$	0.415415	−	0.909632i	0.0163190	−	0.0357337i
$649$	−10.8348	+	3.18139i	−0.425304	+	0.124881i
$650$	0.794499	+	1.73971i	0.0311628	+	0.0682370i
$651$	−4.89075	−	5.64423i	−0.191684	−	0.221215i
$652$	−0.730884	−	5.08341i	−0.0286236	−	0.199082i
$653$	12.9316	+	3.79707i	0.506054	+	0.148591i	0.524787	−	0.851234i	$-0.324145\pi$
$653$	12.9316	+	3.79707i	0.506054	+	0.148591i	−0.0187329	+	0.999825i	$0.505963\pi$
$654$	9.83578	−	11.3511i	0.384609	−	0.443863i
$655$	12.7695	+	8.20647i	0.498946	+	0.320653i
$656$	7.20367	+	4.62952i	0.281256	+	0.180752i
$657$	4.74072	−	5.47109i	0.184953	−	0.213447i
$658$	4.66232	+	1.36898i	0.181756	+	0.0533684i
$659$	−1.95809	−	13.6188i	−0.0762764	−	0.530514i	−0.991755	−	0.128148i	$-0.959097\pi$
$659$	−1.95809	−	13.6188i	−0.0762764	−	0.530514i	0.915479	−	0.402366i	$-0.131812\pi$
$660$	−4.75160	−	5.48364i	−0.184956	−	0.213450i
$661$	−10.9569	−	23.9922i	−0.426172	−	0.933188i	−0.993932	−	0.109993i	$-0.964917\pi$
$661$	−10.9569	−	23.9922i	−0.426172	−	0.933188i	0.567760	−	0.823194i	$-0.307810\pi$
$662$	22.4555	−	6.59352i	0.872756	−	0.256264i
$663$	−1.24530	+	2.72684i	−0.0483636	+	0.105902i
$664$	0.213789	−	1.48694i	0.00829662	−	0.0577043i
$665$	15.6769	−	10.0749i	0.607922	−	0.390688i
$666$	−6.18736			−0.239755
$667$	−14.9872	−	5.73196i	−0.580306	−	0.221942i
$668$	7.89620			0.305513
$669$	3.82532	−	2.45839i	0.147896	−	0.0950467i
$670$	−5.76587	+	40.1025i	−0.222755	+	1.54929i
$671$	4.67627	−	10.2396i	0.180526	−	0.395296i
$672$	−0.959493	+	0.281733i	−0.0370132	+	0.0108681i
$673$	−0.431578	−	0.945024i	−0.0166361	−	0.0364280i	0.901132	−	0.433546i	$-0.142738\pi$
$673$	−0.431578	−	0.945024i	−0.0166361	−	0.0364280i	−0.917768	+	0.397118i	$0.870010\pi$
$674$	17.5092	+	20.2067i	0.674429	+	0.778332i
$675$	−0.676684	−	4.70644i	−0.0260456	−	0.181151i
$676$	12.3182	+	3.61694i	0.473776	+	0.139113i
$677$	0.902460	−	1.04149i	0.0346843	−	0.0400279i	−0.738142	−	0.674645i	$-0.764297\pi$
$677$	0.902460	−	1.04149i	0.0346843	−	0.0400279i	0.772827	+	0.634617i	$0.218842\pi$
$678$	−15.4812	−	9.94917i	−0.594553	−	0.382096i
$679$	−8.72690	−	5.60844i	−0.334908	−	0.215232i
$680$	15.2432	−	17.5916i	0.584551	−	0.674607i
$681$	−22.2176	−	6.52368i	−0.851380	−	0.249988i
$682$	−2.46921	−	17.1737i	−0.0945509	−	0.657616i
$683$	24.9860	+	28.8353i	0.956062	+	1.10335i	0.994567	+	0.104096i	$0.0331948\pi$
$683$	24.9860	+	28.8353i	0.956062	+	1.10335i	−0.0385057	+	0.999258i	$0.512260\pi$
$684$	2.47859	+	5.42735i	0.0947712	+	0.207520i
$685$	−47.2524	+	13.8746i	−1.80542	+	0.530120i
$686$	0.415415	−	0.909632i	0.0158606	−	0.0347299i
$687$	−0.335017	+	2.33009i	−0.0127817	+	0.0888985i
$688$	6.09421	−	3.91651i	0.232339	−	0.149315i
$689$	3.98355			0.151761
$690$	−14.9312	−	1.19244i	−0.568419	−	0.0453954i
$691$	−13.5510			−0.515505			−0.257752	−	0.966211i	$-0.582982\pi$
$691$	−13.5510			−0.515505			−0.257752	+	0.966211i	$0.582982\pi$
$692$	16.9473	−	10.8914i	0.644241	−	0.414029i
$693$	−0.330622	+	2.29952i	−0.0125593	+	0.0873517i
$694$	11.6190	−	25.4421i	0.441053	−	0.965771i
$695$	46.0193	−	13.5125i	1.74561	−	0.512558i
$696$	−1.38990	−	3.04345i	−0.0526839	−	0.115362i
$697$	41.7920	+	48.2306i	1.58299	+	1.82686i
$698$	−4.16636	−	28.9777i	−0.157699	−	1.09682i
$699$	2.87252	+	0.843449i	0.108649	+	0.0319022i
$700$	−3.11376	+	3.59347i	−0.117689	+	0.135820i
$701$	−8.82997	−	5.67468i	−0.333503	−	0.214330i	0.363162	−	0.931726i	$-0.381697\pi$
$701$	−8.82997	−	5.67468i	−0.333503	−	0.214330i	−0.696665	+	0.717397i	$0.745334\pi$
$702$	0.338378	+	0.217462i	0.0127713	+	0.00820759i
$703$	24.1755	−	27.9001i	0.911798	−	1.05227i
$704$	−2.22907	−	0.654513i	−0.0840111	−	0.0246679i
$705$	2.15984	+	15.0220i	0.0813441	+	0.565761i
$706$	12.4655	+	14.3860i	0.469147	+	0.541424i
$707$	−6.28924	−	13.7715i	−0.236531	−	0.517931i
$708$	−4.66381	+	1.36942i	−0.175277	+	0.0514659i
$709$	13.2681	−	29.0531i	0.498294	−	1.09111i	−0.478726	−	0.877964i	$-0.658901\pi$
$709$	13.2681	−	29.0531i	0.498294	−	1.09111i	0.977020	−	0.213147i	$-0.0683713\pi$
$710$	1.82429	−	12.6882i	0.0684643	−	0.476179i
$711$	−7.24446	+	4.65573i	−0.271688	+	0.174604i
$712$	6.98783			0.261880
$713$	−28.4941	−	21.7015i	−1.06711	−	0.812726i
$714$	−7.45277			−0.278913
$715$	2.45524	−	1.57789i	0.0918207	−	0.0590096i
$716$	−1.73491	+	12.0665i	−0.0648365	+	0.450948i
$717$	12.0391	−	26.3619i	0.449608	−	0.984504i
$718$	−2.39321	+	0.702710i	−0.0893139	+	0.0262249i
$719$	4.73918	+	10.3774i	0.176742	+	0.387010i	0.977182	−	0.212402i	$-0.0681285\pi$
$719$	4.73918	+	10.3774i	0.176742	+	0.387010i	−0.800441	+	0.599412i	$0.795401\pi$
$720$	−2.04531	−	2.36041i	−0.0762242	−	0.0879674i
$721$	1.10347	+	7.67480i	0.0410953	+	0.285824i
$722$	−15.9271	−	4.67662i	−0.592746	−	0.174046i
$723$	−11.0464	+	12.7482i	−0.410821	+	0.474112i
$724$	−4.75730	−	3.05733i	−0.176804	−	0.113625i
$725$	−13.3833	−	8.60092i	−0.497043	−	0.319430i
$726$	3.66910	−	4.23437i	0.136173	−	0.157152i
$727$	32.2883	+	9.48069i	1.19751	+	0.351620i	0.818899	−	0.573938i	$-0.194585\pi$
$727$	32.2883	+	9.48069i	1.19751	+	0.351620i	0.378607	+	0.925557i	$0.376403\pi$
$728$	−0.0572434	−	0.398137i	−0.00212158	−	0.0147559i
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$	−9.39265	−	20.5670i	−0.347637	−	0.761220i
$731$	51.8024	−	15.2106i	1.91598	−	0.562583i
$732$	2.01288	−	4.40760i	0.0743983	−	0.162910i
$733$	−1.33937	+	9.31551i	−0.0494707	+	0.344076i	0.950021	+	0.312187i	$0.101061\pi$
$733$	−1.33937	+	9.31551i	−0.0494707	+	0.344076i	−0.999491	+	0.0318893i	$0.989848\pi$
$734$	−27.1771	+	17.4656i	−1.00312	+	0.644669i
$735$	3.12327			0.115204
$736$	−4.22812	+	2.26341i	−0.155850	+	0.0834304i
$737$	30.1360			1.11007
$738$	7.20367	−	4.62952i	0.265171	−	0.170415i
$739$	7.34637	−	51.0951i	0.270241	−	1.87956i	−0.175614	−	0.984459i	$-0.556191\pi$
$739$	7.34637	−	51.0951i	0.270241	−	1.87956i	0.445854	−	0.895105i	$-0.352900\pi$
$740$	−8.02781	+	17.5785i	−0.295108	+	0.646197i
$741$	−2.30271	+	0.676137i	−0.0845922	+	0.0248385i
$742$	4.11412	+	9.00867i	0.151034	+	0.330719i
$743$	11.0639	+	12.7684i	0.405895	+	0.468428i	0.921489	−	0.388405i	$-0.126974\pi$
$743$	11.0639	+	12.7684i	0.405895	+	0.468428i	−0.515593	+	0.856833i	$0.672429\pi$
$744$	−1.06286	−	7.39237i	−0.0389664	−	0.271017i
$745$	16.2456	+	4.77015i	0.595194	+	0.174765i
$746$	−3.14231	+	3.62641i	−0.115048	+	0.132772i
$747$	−1.26375	−	0.812165i	−0.0462383	−	0.0297156i
$748$	−14.5655	−	9.36069i	−0.532568	−	0.342261i
$749$	0.680967	−	0.785877i	0.0248820	−	0.0287153i
$750$	0.734695	+	0.215726i	0.0268273	+	0.00787719i
$751$	5.05913	+	35.1870i	0.184610	+	1.28399i	0.845689	+	0.533676i	$0.179190\pi$
$751$	5.05913	+	35.1870i	0.184610	+	1.28399i	−0.661078	+	0.750317i	$0.729901\pi$
$752$	3.18207	+	3.67230i	0.116038	+	0.133915i
$753$	−7.84110	−	17.1696i	−0.285745	−	0.625695i
$754$	1.29127	−	0.379151i	0.0470253	−	0.0138079i
$755$	16.5216	−	36.1772i	0.601281	−	1.31662i
$756$	−0.142315	+	0.989821i	−0.00517594	+	0.0359995i
$757$	8.63815	−	5.55140i	0.313959	−	0.201769i	−0.374165	−	0.927362i	$-0.622071\pi$
$757$	8.63815	−	5.55140i	0.313959	−	0.201769i	0.688124	+	0.725593i	$0.258434\pi$
$758$	−17.8663			−0.648932
$759$	0.702634	+	11.1194i	0.0255040	+	0.403607i
$760$	18.6351			0.675967
$761$	−27.0887	+	17.4088i	−0.981964	+	0.631070i	−0.929992	−	0.367579i	$-0.880187\pi$
$761$	−27.0887	+	17.4088i	−0.981964	+	0.631070i	−0.0519712	+	0.998649i	$0.516550\pi$
$762$	−1.42102	+	9.88339i	−0.0514780	+	0.358037i
$763$	−6.23939	+	13.6624i	−0.225881	+	0.494611i
$764$	−13.6360	+	4.00390i	−0.493334	+	0.144856i
$765$	−9.66963	−	21.1735i	−0.349606	−	0.765531i
$766$	−20.6976	−	23.8863i	−0.747835	−	0.863047i
$767$	−0.278243	−	1.93522i	−0.0100468	−	0.0698769i
$768$	−0.959493	−	0.281733i	−0.0346227	−	0.0101661i
$769$	−16.2382	+	18.7399i	−0.585566	+	0.675779i	−0.968792	−	0.247876i	$-0.920267\pi$
$769$	−16.2382	+	18.7399i	−0.585566	+	0.675779i	0.383226	+	0.923654i	$0.374813\pi$
$770$	6.10405	+	3.92283i	0.219975	+	0.141369i
$771$	23.4577	+	15.0753i	0.844807	+	0.542924i
$772$	−3.62671	+	4.18544i	−0.130528	+	0.150637i
$773$	29.7090	+	8.72336i	1.06856	+	0.313757i	0.768293	−	0.640098i	$-0.221106\pi$
$773$	29.7090	+	8.72336i	1.06856	+	0.313757i	0.300266	+	0.953855i	$0.402924\pi$
$774$	−1.03096	−	7.17046i	−0.0370570	−	0.257737i
$775$	−23.2547	−	26.8374i	−0.835334	−	0.964027i
$776$	−4.30939	−	9.43624i	−0.154698	−	0.338741i
$777$	5.93672	−	1.74318i	0.212979	−	0.0625362i
$778$	7.17244	−	15.7055i	0.257144	−	0.563068i
$779$	−7.27109	+	50.5715i	−0.260514	+	1.81191i
$780$	1.05685	−	0.679195i	0.0378412	−	0.0243191i
$781$	−9.53486			−0.341184
$782$	−34.9872	+	7.30764i	−1.25114	+	0.261321i
$783$	−3.34580			−0.119569
$784$	0.841254	−	0.540641i	0.0300448	−	0.0193086i
$785$	−3.51382	+	24.4391i	−0.125414	+	0.872270i
$786$	2.01892	−	4.42082i	0.0720126	−	0.157686i
$787$	−29.1061	+	8.54632i	−1.03752	+	0.304643i	−0.755765	−	0.654843i	$-0.772735\pi$
$787$	−29.1061	+	8.54632i	−1.03752	+	0.304643i	−0.281755	+	0.959486i	$0.590916\pi$
$788$	2.73990	+	5.99955i	0.0976049	+	0.213725i
$789$	6.31477	+	7.28763i	0.224812	+	0.259447i
$790$	3.82771	+	26.6223i	0.136184	+	0.947179i
$791$	17.6571	+	5.18460i	0.627815	+	0.184343i
$792$	−1.52135	+	1.75574i	−0.0540589	+	0.0623873i
$793$	1.63960	+	1.05371i	0.0582240	+	0.0374183i
$794$	9.21025	+	5.91907i	0.326859	+	0.210060i
$795$	−20.2560	+	23.3767i	−0.718407	+	0.829086i
$796$	0.234574	+	0.0688773i	0.00831427	+	0.00244129i
$797$	1.92254	+	13.3716i	0.0680998	+	0.473645i	0.995123	+	0.0986409i	$0.0314495\pi$
$797$	1.92254	+	13.3716i	0.0680998	+	0.473645i	−0.927023	+	0.375004i	$0.877641\pi$
$798$	−3.90725	−	4.50920i	−0.138315	−	0.159624i
$799$	15.0439	+	32.9415i	0.532215	+	1.16539i
$800$	−4.56223	+	1.33959i	−0.161299	+	0.0473617i
$801$	2.90285	−	6.35635i	0.102567	−	0.224591i
$802$	3.59826	−	25.0265i	0.127059	−	0.883715i
$803$	−14.1483	+	9.09255i	−0.499282	+	0.320869i
$804$	12.9719			0.457485
$805$	14.6623	−	3.06245i	0.516778	−	0.107937i
$806$	3.00402			0.105812
$807$	6.37889	−	4.09946i	0.224547	−	0.144308i
$808$	2.15460	−	14.9856i	0.0757985	−	0.527190i
$809$	−1.59288	+	3.48793i	−0.0560028	+	0.122629i	−0.935565	−	0.353156i	$-0.885109\pi$
$809$	−1.59288	+	3.48793i	−0.0560028	+	0.122629i	0.879562	+	0.475785i	$0.157836\pi$
$810$	−2.99676	+	0.879928i	−0.105295	+	0.0309175i
$811$	1.73004	+	3.78826i	0.0607500	+	0.133024i	0.937572	−	0.347791i	$-0.113068\pi$
$811$	1.73004	+	3.78826i	0.0607500	+	0.133024i	−0.876822	+	0.480815i	$0.840341\pi$
$812$	2.19103	+	2.52859i	0.0768902	+	0.0887361i
$813$	1.91309	+	13.3058i	0.0670949	+	0.466655i
$814$	13.7920	+	4.04970i	0.483410	+	0.141942i
$815$	−10.5041	+	12.1223i	−0.367941	+	0.424627i
$816$	−6.26967	−	4.02927i	−0.219482	−	0.141053i
$817$	36.3613	+	23.3680i	1.27212	+	0.817542i
$818$	22.1067	−	25.5125i	0.772943	−	0.892024i
$819$	−0.385938	−	0.113322i	−0.0134858	−	0.00395978i
$820$	−3.80616	−	26.4724i	−0.132917	−	0.924457i
$821$	−5.97620	−	6.89690i	−0.208571	−	0.240704i	0.641820	−	0.766856i	$-0.278180\pi$
$821$	−5.97620	−	6.89690i	−0.208571	−	0.240704i	−0.850391	+	0.526152i	$0.823634\pi$
$822$	6.55020	+	14.3429i	0.228464	+	0.500267i
$823$	6.73858	−	1.97863i	0.234892	−	0.0689706i	−0.162168	−	0.986763i	$-0.551849\pi$
$823$	6.73858	−	1.97863i	0.234892	−	0.0689706i	0.397060	+	0.917793i	$0.370030\pi$
$824$	−3.22101	+	7.05303i	−0.112209	+	0.245704i
$825$	−1.57205	+	10.9339i	−0.0547318	+	0.380668i
$826$	4.08908	−	2.62789i	0.142277	−	0.0914361i
$827$	45.5164			1.58276			0.791380	−	0.611325i	$-0.209363\pi$
$827$	45.5164			1.58276			0.791380	+	0.611325i	$0.209363\pi$
$828$	0.302446	+	4.78629i	0.0105107	+	0.166335i
$829$	34.8663			1.21096			0.605478	−	0.795862i	$-0.292982\pi$
$829$	34.8663			1.21096			0.605478	+	0.795862i	$0.292982\pi$
$830$	−3.94705	+	2.53661i	−0.137004	+	0.0880471i
$831$	2.49146	−	17.3285i	0.0864277	−	0.601118i
$832$	0.167093	−	0.365882i	0.00579290	−	0.0126847i
$833$	7.15088	−	2.09969i	0.247763	−	0.0727499i
$834$	−6.37926	−	13.9686i	−0.220896	−	0.483694i
$835$	−16.1502	−	18.6383i	−0.558900	−	0.645005i
$836$	−1.97267	−	13.7202i	−0.0682261	−	0.474523i
$837$	−7.16586	−	2.10409i	−0.247688	−	0.0727279i
$838$	8.90406	−	10.2758i	0.307586	−	0.354973i
$839$	−42.2901	−	27.1782i	−1.46002	−	0.938295i	−0.998696	−	0.0510616i	$-0.983740\pi$
$839$	−42.2901	−	27.1782i	−1.46002	−	0.938295i	−0.461320	−	0.887234i	$-0.652624\pi$
$840$	2.62746	+	1.68857i	0.0906561	+	0.0582612i
$841$	11.6602	−	13.4566i	0.402076	−	0.464020i
$842$	31.8690	+	9.35758i	1.09828	+	0.322484i
$843$	3.58230	+	24.9154i	0.123381	+	0.858132i
$844$	−4.52042	−	5.21685i	−0.155599	−	0.179571i
$845$	−16.6570	−	36.4737i	−0.573018	−	1.25473i
$846$	4.66232	−	1.36898i	0.160294	−	0.0470665i
$847$	−2.32752	+	5.09656i	−0.0799745	+	0.175120i
$848$	−1.40944	+	9.80284i	−0.0484002	+	0.336631i
$849$	−21.2051	+	13.6277i	−0.727758	+	0.467702i
$850$	−35.4367			−1.21547
$851$	26.1609	−	14.0045i	0.896783	−	0.480069i
$852$	−4.10424			−0.140609
$853$	−12.5821	+	8.08604i	−0.430804	+	0.276861i	−0.738020	−	0.674779i	$-0.764239\pi$
$853$	−12.5821	+	8.08604i	−0.430804	+	0.276861i	0.307216	+	0.951640i	$0.400603\pi$
$854$	−0.689583	+	4.79616i	−0.0235971	+	0.164121i
$855$	7.74131	−	16.9511i	0.264747	−	0.579715i
$856$	0.997743	−	0.292964i	0.0341022	−	0.0100133i
$857$	12.4907	+	27.3508i	0.426674	+	0.934285i	0.993855	+	0.110692i	$0.0353068\pi$
$857$	12.4907	+	27.3508i	0.426674	+	0.934285i	−0.567181	+	0.823593i	$0.691966\pi$
$858$	−0.611935	−	0.706211i	−0.0208911	−	0.0241097i
$859$	4.57273	+	31.8041i	0.156020	+	1.08514i	0.905877	+	0.423541i	$0.139213\pi$
$859$	4.57273	+	31.8041i	0.156020	+	1.08514i	−0.749857	+	0.661600i	$0.769878\pi$
$860$	−21.7091	−	6.37437i	−0.740275	−	0.217364i
$861$	−5.60759	+	6.47150i	−0.191106	+	0.220548i
$862$	−4.32971	−	2.78253i	−0.147470	−	0.0947734i
$863$	2.27062	+	1.45924i	0.0772927	+	0.0496730i	0.578716	−	0.815529i	$-0.303554\pi$
$863$	2.27062	+	1.45924i	0.0772927	+	0.0496730i	−0.501424	+	0.865202i	$0.667190\pi$
$864$	−0.654861	+	0.755750i	−0.0222788	+	0.0257111i
$865$	−60.3707	−	17.7264i	−2.05267	−	0.602717i
$866$	−2.11399	−	14.7032i	−0.0718365	−	0.499634i
$867$	−25.2408	−	29.1294i	−0.857223	−	0.989288i
$868$	3.10248	+	6.79348i	0.105305	+	0.230586i
$869$	19.1956	−	5.63634i	0.651166	−	0.191200i
$870$	−4.34103	+	9.50552i	−0.147175	+	0.322267i
$871$	−0.742558	+	5.16460i	−0.0251606	+	0.174996i
$872$	−12.6353	+	8.12024i	−0.427886	+	0.274986i
$873$	−10.3737			−0.351096
$874$	−22.7641	−	17.3374i	−0.770006	−	0.586447i
$875$	−0.765711			−0.0258858
$876$	−6.09007	+	3.91385i	−0.205765	+	0.132237i
$877$	−4.05547	+	28.2064i	−0.136944	+	0.952463i	0.799255	+	0.600992i	$0.205228\pi$
$877$	−4.05547	+	28.2064i	−0.136944	+	0.952463i	−0.936199	+	0.351471i	$0.885681\pi$
$878$	−11.7083	+	25.6376i	−0.395136	+	0.865226i
$879$	25.4423	−	7.47054i	0.858149	−	0.251975i
$880$	3.01421	+	6.60020i	0.101609	+	0.222493i
$881$	9.39310	+	10.8402i	0.316461	+	0.365216i	0.891587	−	0.452849i	$-0.149592\pi$
$881$	9.39310	+	10.8402i	0.316461	+	0.365216i	−0.575126	+	0.818065i	$0.695047\pi$
$882$	−0.142315	−	0.989821i	−0.00479199	−	0.0333290i
$883$	−20.8450	−	6.12063i	−0.701489	−	0.205976i	−0.0885102	−	0.996075i	$-0.528211\pi$
$883$	−20.8450	−	6.12063i	−0.701489	−	0.205976i	−0.612978	+	0.790100i	$0.710029\pi$
$884$	1.96310	−	2.26554i	0.0660262	−	0.0761982i
$885$	12.7713	+	8.20763i	0.429303	+	0.275896i
$886$	−1.61196	−	1.03594i	−0.0541547	−	0.0348031i
$887$	3.82279	−	4.41173i	0.128357	−	0.148131i	−0.687933	−	0.725774i	$-0.741482\pi$
$887$	3.82279	−	4.41173i	0.128357	−	0.148131i	0.816290	+	0.577643i	$0.196027\pi$
$888$	5.93672	+	1.74318i	0.199223	+	0.0584973i
$889$	−1.42102	−	9.88339i	−0.0476594	−	0.331478i
$890$	−14.2923	−	16.4942i	−0.479078	−	0.552885i
$891$	0.965080	+	2.11323i	0.0323314	+	0.0707959i
$892$	−4.36298	+	1.28109i	−0.146083	+	0.0428939i
$893$	−12.0438	+	26.3723i	−0.403031	+	0.882516i
$894$	0.771498	−	5.36589i	0.0258028	−	0.179462i
$895$	32.0304	−	20.5847i	1.07066	−	0.688071i
$896$	1.00000			0.0334077
$897$	−1.92291	−	0.153569i	−0.0642041	−	0.00512750i
$898$	14.7788			0.493176
$899$	−21.0210	+	13.5094i	−0.701090	+	0.450563i
$900$	−0.676684	+	4.70644i	−0.0225561	+	0.156881i
$901$	−30.6616	+	67.1396i	−1.02149	+	2.23674i
$902$	−19.0875	+	5.60461i	−0.635546	+	0.186613i
$903$	3.00935	+	6.58955i	0.100145	+	0.219287i
$904$	12.0511	+	13.9077i	0.400814	+	0.462564i
$905$	2.51359	+	17.4824i	0.0835545	+	0.581134i
$906$	−12.2180	−	3.58753i	−0.405917	−	0.119188i
$907$	−2.14916	+	2.48026i	−0.0713617	+	0.0823558i	−0.790308	−	0.612710i	$-0.790079\pi$
$907$	−2.14916	+	2.48026i	−0.0713617	+	0.0823558i	0.718946	+	0.695066i	$0.244625\pi$
$908$	19.4797	+	12.5188i	0.646457	+	0.415452i
$909$	−12.7363	−	8.18512i	−0.422436	−	0.271483i
$910$	−0.822687	+	0.949431i	−0.0272718	+	0.0314733i
$911$	54.8029	+	16.0916i	1.81570	+	0.533138i	0.999033	−	0.0439707i	$-0.0140008\pi$
$911$	54.8029	+	16.0916i	1.81570	+	0.533138i	0.816668	+	0.577108i	$0.195819\pi$
$912$	−0.849126	−	5.90580i	−0.0281174	−	0.195561i
$913$	2.28542	+	2.63751i	0.0756363	+	0.0872889i
$914$	−12.3802	−	27.1089i	−0.409501	−	0.896683i
$915$	−14.5207	+	4.26367i	−0.480040	+	0.140953i
$916$	0.977909	−	2.14132i	0.0323110	−	0.0707512i
$917$	−0.691652	+	4.81055i	−0.0228404	+	0.158858i
$918$	−6.26967	+	4.02927i	−0.206930	+	0.132986i
$919$	17.2576			0.569275			0.284637	−	0.958635i	$-0.408127\pi$
$919$	17.2576			0.569275			0.284637	+	0.958635i	$0.408127\pi$
$920$	13.9904	+	5.35073i	0.461249	+	0.176408i
$921$	9.74323			0.321050
$922$	−4.33583	+	2.78647i	−0.142793	+	0.0917675i
$923$	0.234941	−	1.63405i	0.00773317	−	0.0537854i
$924$	0.965080	−	2.11323i	0.0317488	−	0.0695202i
$925$	28.2282	−	8.28854i	0.928136	−	0.272525i
$926$	6.91881	+	15.1501i	0.227366	+	0.497862i
$927$	5.07761	+	5.85987i	0.166770	+	0.192463i
$928$	0.476157	+	3.31175i	0.0156306	+	0.108713i
$929$	42.6022	+	12.5091i	1.39773	+	0.410411i	0.891905	−	0.452224i	$-0.149369\pi$
$929$	42.6022	+	12.5091i	1.39773	+	0.410411i	0.505827	+	0.862635i	$0.331187\pi$
$930$	−15.2752	+	17.6285i	−0.500892	+	0.578060i
$931$	5.01937	+	3.22575i	0.164503	+	0.105720i
$932$	−2.51854	−	1.61857i	−0.0824975	−	0.0530179i
$933$	−0.0473133	+	0.0546025i	−0.00154897	+	0.00178760i
$934$	−9.78244	−	2.87238i	−0.320091	−	0.0939872i
$935$	7.69589	+	53.5261i	0.251683	+	1.75049i
$936$	−0.263405	−	0.303986i	−0.00860967	−	0.00993609i
$937$	12.8616	+	28.1630i	0.420170	+	0.920045i	0.994821	+	0.101646i	$0.0324108\pi$
$937$	12.8616	+	28.1630i	0.420170	+	0.920045i	−0.574650	+	0.818399i	$0.694862\pi$
$938$	−12.4465	+	3.65461i	−0.406392	+	0.119327i
$939$	−10.0819	+	22.0764i	−0.329012	+	0.720435i
$940$	2.15984	−	15.0220i	0.0704461	−	0.489963i
$941$	−31.6689	+	20.3524i	−1.03238	+	0.663468i	−0.943090	−	0.332538i	$-0.892095\pi$
$941$	−31.6689	+	20.3524i	−1.03238	+	0.663468i	−0.0892866	+	0.996006i	$0.528459\pi$
$942$	7.90531			0.257569
$943$	−19.9795	+	35.8790i	−0.650621	+	1.16838i
$944$	4.86070			0.158202
$945$	2.62746	−	1.68857i	0.0854714	−	0.0549292i
$946$	−2.39509	+	16.6582i	−0.0778710	+	0.541605i
$947$	−11.5838	+	25.3650i	−0.376422	+	0.824250i	0.622704	+	0.782458i	$0.286034\pi$
$947$	−11.5838	+	25.3650i	−0.376422	+	0.824250i	−0.999126	+	0.0417926i	$0.986693\pi$
$948$	8.26268	−	2.42614i	0.268359	−	0.0787974i
$949$	−1.20963	−	2.64873i	−0.0392663	−	0.0859813i
$950$	−18.5783	−	21.4405i	−0.602761	−	0.695623i
$951$	0.260572	+	1.81232i	0.00844962	+	0.0587684i
$952$	7.15088	+	2.09969i	0.231761	+	0.0680513i
$953$	−24.4301	+	28.1938i	−0.791368	+	0.913288i	−0.997875	−	0.0651573i	$-0.979245\pi$
$953$	−24.4301	+	28.1938i	−0.791368	+	0.913288i	0.206507	+	0.978445i	$0.433791\pi$
$954$	8.33148	+	5.35432i	0.269742	+	0.173352i
$955$	37.3408	+	23.9975i	1.20832	+	0.776539i
$956$	−18.9784	+	21.9023i	−0.613806	+	0.708370i
$957$	7.45801	+	2.18987i	0.241083	+	0.0707885i
$958$	−3.23289	−	22.4852i	−0.104450	−	0.726465i
$959$	−10.3257	−	11.9165i	−0.333435	−	0.384805i
$960$	1.29745	+	2.84103i	0.0418752	+	0.0916938i
$961$	−23.7731	+	6.98042i	−0.766875	+	0.225175i
$962$	−1.03386	+	2.26384i	−0.0333331	+	0.0729892i
$963$	0.147988	−	1.02928i	0.00476885	−	0.0331681i
$964$	14.1906	−	9.11972i	0.457047	−	0.293726i
$965$	17.2971			0.556814
$966$	−1.63865	−	4.50720i	−0.0527226	−	0.145017i
$967$	11.1484			0.358507			0.179254	−	0.983803i	$-0.442632\pi$
$967$	11.1484			0.358507			0.179254	+	0.983803i	$0.442632\pi$
$968$	−4.71344	+	3.02914i	−0.151496	+	0.0973604i
$969$	6.32834	−	44.0146i	0.203296	−	1.41395i
$970$	−13.4594	+	29.4720i	−0.432155	+	0.946287i
$971$	33.0983	−	9.71853i	1.06217	−	0.311882i	0.296448	−	0.955049i	$-0.404198\pi$
$971$	33.0983	−	9.71853i	1.06217	−	0.311882i	0.765726	+	0.643167i	$0.222380\pi$
$972$	0.415415	+	0.909632i	0.0133244	+	0.0291765i
$973$	10.0563	+	11.6056i	0.322389	+	0.372057i
$974$	−0.182630	−	1.27022i	−0.00585186	−	0.0407006i
$975$	−1.83507	−	0.538826i	−0.0587693	−	0.0172562i
$976$	−3.17311	+	3.66197i	−0.101569	+	0.117217i
$977$	−7.73603	−	4.97164i	−0.247497	−	0.159057i	0.411011	−	0.911630i	$-0.365176\pi$
$977$	−7.73603	−	4.97164i	−0.247497	−	0.159057i	−0.658508	+	0.752574i	$0.728812\pi$
$978$	4.32041	+	2.77656i	0.138152	+	0.0887846i
$979$	−10.6310	+	12.2688i	−0.339767	+	0.392112i
$980$	−2.99676	−	0.879928i	−0.0957280	−	0.0281083i
$981$	2.13752	+	14.8668i	0.0682457	+	0.474660i
$982$	−18.5020	−	21.3525i	−0.590423	−	0.681385i
$983$	−19.1518	−	41.9367i	−0.610849	−	1.33757i	−0.921992	−	0.387210i	$-0.873439\pi$
$983$	−19.1518	−	41.9367i	−0.610849	−	1.33757i	0.311143	−	0.950363i	$-0.399288\pi$
$984$	−8.21616	+	2.41248i	−0.261922	+	0.0769071i
$985$	8.55746	−	18.7382i	0.272663	−	0.597050i
$986$	−3.54869	+	24.6817i	−0.113013	+	0.786025i
$987$	−4.08778	+	2.62706i	−0.130115	+	0.0836201i
$988$	2.39992			0.0763518
$989$	20.5887	+	27.9841i	0.654682	+	0.889842i
$990$	7.25590			0.230608
$991$	−37.4824	+	24.0885i	−1.19067	+	0.765197i	−0.977318	−	0.211779i	$-0.932074\pi$
$991$	−37.4824	+	24.0885i	−1.19067	+	0.765197i	−0.213352	+	0.976975i	$0.568438\pi$
$992$	−1.06286	+	7.39237i	−0.0337459	+	0.234708i
$993$	−9.72215	+	21.2885i	−0.308523	+	0.675571i
$994$	3.93799	−	1.15630i	0.124906	−	0.0366756i
$995$	−0.317198	−	0.694568i	−0.0100559	−	0.0220193i
$996$	0.983749	+	1.13531i	0.0311713	+	0.0359736i
$997$	1.36661	+	9.50497i	0.0432809	+	0.301025i	0.999951	+	0.00985281i	$0.00313630\pi$
$997$	1.36661	+	9.50497i	0.0432809	+	0.301025i	−0.956671	+	0.291173i	$0.905955\pi$
$998$	−11.7929	−	3.46270i	−0.373297	−	0.109610i
$999$	4.05186	−	4.67609i	0.128195	−	0.147945i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.i.127.1	✓	40
23.2	even	11	inner	966.2.q.i.715.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.i.127.1	✓	40	1.1	even	1	trivial
966.2.q.i.715.1	yes	40	23.2	even	11	inner

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.841254 - 0.540641i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-2.99676 + 0.879928i) q^{5} +(0.415415 + 0.909632i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(0.841254 - 0.540641i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-2.99676 + 0.879928i) q^{5} +(0.415415 + 0.909632i) q^{6} +(-0.654861 - 0.755750i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(-2.04531 + 2.36041i) q^{10} +(1.95438 + 1.25600i) q^{11} +(0.841254 + 0.540641i) q^{12} +(-0.263405 + 0.303986i) q^{13} +(-0.959493 - 0.281733i) q^{14} +(-0.444488 - 3.09148i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-3.09599 - 6.77928i) q^{17} +(-0.959493 + 0.281733i) q^{18} +(2.47859 - 5.42735i) q^{19} +(-0.444488 + 3.09148i) q^{20} +(0.841254 - 0.540641i) q^{21} +2.32317 q^{22} +(3.41917 - 3.36292i) q^{23} +1.00000 q^{24} +(4.00002 - 2.57066i) q^{25} +(-0.0572434 + 0.398137i) q^{26} +(0.415415 - 0.909632i) q^{27} +(-0.959493 + 0.281733i) q^{28} +(-1.38990 - 3.04345i) q^{29} +(-2.04531 - 2.36041i) q^{30} +(-1.06286 - 7.39237i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(-1.52135 + 1.75574i) q^{33} +(-6.26967 - 4.02927i) q^{34} +(2.62746 + 1.68857i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(5.93672 + 1.74318i) q^{37} +(-0.849126 - 5.90580i) q^{38} +(-0.263405 - 0.303986i) q^{39} +(1.29745 + 2.84103i) q^{40} +(-8.21616 + 2.41248i) q^{41} +(0.415415 - 0.909632i) q^{42} +(-1.03096 + 7.17046i) q^{43} +(1.95438 - 1.25600i) q^{44} +3.12327 q^{45} +(1.05826 - 4.67762i) q^{46} -4.85915 q^{47} +(0.841254 - 0.540641i) q^{48} +(-0.142315 + 0.989821i) q^{49} +(1.97523 - 4.32515i) q^{50} +(7.15088 - 2.09969i) q^{51} +(0.167093 + 0.365882i) q^{52} +(-6.48551 - 7.48468i) q^{53} +(-0.142315 - 0.989821i) q^{54} +(-6.96198 - 2.04422i) q^{55} +(-0.654861 + 0.755750i) q^{56} +(5.01937 + 3.22575i) q^{57} +(-2.81467 - 1.80888i) q^{58} +(-3.18308 + 3.67347i) q^{59} +(-2.99676 - 0.879928i) q^{60} +(-0.689583 - 4.79616i) q^{61} +(-4.89075 - 5.64423i) q^{62} +(0.415415 + 0.909632i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(0.521876 - 1.14275i) q^{65} +(-0.330622 + 2.29952i) q^{66} +(10.9127 - 7.01315i) q^{67} -7.45277 q^{68} +(2.84209 + 3.86296i) q^{69} +3.12327 q^{70} +(-3.45271 + 2.21892i) q^{71} +(-0.142315 + 0.989821i) q^{72} +(-3.00731 + 6.58509i) q^{73} +(5.93672 - 1.74318i) q^{74} +(1.97523 + 4.32515i) q^{75} +(-3.90725 - 4.50920i) q^{76} +(-0.330622 - 2.29952i) q^{77} +(-0.385938 - 0.113322i) q^{78} +(5.63934 - 6.50814i) q^{79} +(2.62746 + 1.68857i) q^{80} +(0.841254 + 0.540641i) q^{81} +(-5.60759 + 6.47150i) q^{82} +(1.44138 + 0.423226i) q^{83} +(-0.142315 - 0.989821i) q^{84} +(15.2432 + 17.5916i) q^{85} +(3.00935 + 6.58955i) q^{86} +(3.21027 - 0.942621i) q^{87} +(0.965080 - 2.11323i) q^{88} +(-0.994471 + 6.91670i) q^{89} +(2.62746 - 1.68857i) q^{90} +0.402231 q^{91} +(-1.63865 - 4.50720i) q^{92} +7.46838 q^{93} +(-4.08778 + 2.62706i) q^{94} +(-2.65205 + 18.4454i) q^{95} +(0.415415 - 0.909632i) q^{96} +(9.95348 - 2.92261i) q^{97} +(0.415415 + 0.909632i) q^{98} +(-1.52135 - 1.75574i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 40 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9	\( 40 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} - 4 q^{6} - 4 q^{7} - 4 q^{8} - 4 q^{9} + 4 q^{10} - q^{11} - 4 q^{12} - 8 q^{13} - 4 q^{14} - 7 q^{15} - 4 q^{16} - 7 q^{17} - 4 q^{18} + 20 q^{19} - 7 q^{20} - 4 q^{21} + 10 q^{22} + 2 q^{23} + 40 q^{24} - 22 q^{25} + 14 q^{26} - 4 q^{27} - 4 q^{28} + 15 q^{29} + 4 q^{30} - 16 q^{31} - 4 q^{32} - q^{33} - 7 q^{34} - 7 q^{35} - 4 q^{36} - 16 q^{37} - 13 q^{38} - 8 q^{39} + 4 q^{40} - 17 q^{41} - 4 q^{42} + 26 q^{43} - q^{44} + 4 q^{45} - 20 q^{46} + 72 q^{47} - 4 q^{48} - 4 q^{49} + 11 q^{50} - 7 q^{51} - 19 q^{52} + 6 q^{53} - 4 q^{54} + 49 q^{55} - 4 q^{56} + 9 q^{57} - 7 q^{58} - 51 q^{59} + 4 q^{60} - 42 q^{61} - 16 q^{62} - 4 q^{63} - 4 q^{64} + 8 q^{65} - 12 q^{66} + 54 q^{67} + 4 q^{68} + 2 q^{69} + 4 q^{70} - 59 q^{71} - 4 q^{72} - 27 q^{73} - 16 q^{74} + 11 q^{75} - 2 q^{76} - 12 q^{77} - 8 q^{78} - 6 q^{79} - 7 q^{80} - 4 q^{81} - 6 q^{82} - 24 q^{83} - 4 q^{84} + 35 q^{85} - 7 q^{86} - 29 q^{87} - q^{88} + 22 q^{89} - 7 q^{90} + 36 q^{91} - 9 q^{92} + 50 q^{93} - 16 q^{94} + 22 q^{95} - 4 q^{96} + 16 q^{97} - 4 q^{98} - q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 + 4 * q^10 - q^11 - 4 * q^12 - 8 * q^13 - 4 * q^14 - 7 * q^15 - 4 * q^16 - 7 * q^17 - 4 * q^18 + 20 * q^19 - 7 * q^20 - 4 * q^21 + 10 * q^22 + 2 * q^23 + 40 * q^24 - 22 * q^25 + 14 * q^26 - 4 * q^27 - 4 * q^28 + 15 * q^29 + 4 * q^30 - 16 * q^31 - 4 * q^32 - q^33 - 7 * q^34 - 7 * q^35 - 4 * q^36 - 16 * q^37 - 13 * q^38 - 8 * q^39 + 4 * q^40 - 17 * q^41 - 4 * q^42 + 26 * q^43 - q^44 + 4 * q^45 - 20 * q^46 + 72 * q^47 - 4 * q^48 - 4 * q^49 + 11 * q^50 - 7 * q^51 - 19 * q^52 + 6 * q^53 - 4 * q^54 + 49 * q^55 - 4 * q^56 + 9 * q^57 - 7 * q^58 - 51 * q^59 + 4 * q^60 - 42 * q^61 - 16 * q^62 - 4 * q^63 - 4 * q^64 + 8 * q^65 - 12 * q^66 + 54 * q^67 + 4 * q^68 + 2 * q^69 + 4 * q^70 - 59 * q^71 - 4 * q^72 - 27 * q^73 - 16 * q^74 + 11 * q^75 - 2 * q^76 - 12 * q^77 - 8 * q^78 - 6 * q^79 - 7 * q^80 - 4 * q^81 - 6 * q^82 - 24 * q^83 - 4 * q^84 + 35 * q^85 - 7 * q^86 - 29 * q^87 - q^88 + 22 * q^89 - 7 * q^90 + 36 * q^91 - 9 * q^92 + 50 * q^93 - 16 * q^94 + 22 * q^95 - 4 * q^96 + 16 * q^97 - 4 * q^98 - q^99

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