LMFDB - Embedded newform 966.2.r.b.113.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(113,966)]

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([11, 0, 13]))

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

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

chi := DirichletCharacter("966.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.r (of order $22$, 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:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			113.17
Character	$\chi$	$=$	966.113
Dual form			966.2.r.b.701.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.540641 - 0.841254i) q^{2} +(-0.613526 + 1.61975i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(1.38055 + 0.405366i) q^{5} +(1.03092 + 1.39183i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(-2.24717 - 1.98752i) q^{9} +O(q^{10})$	\(q+(0.540641 - 0.841254i) q^{2} +(-0.613526 + 1.61975i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(1.38055 + 0.405366i) q^{5} +(1.03092 + 1.39183i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(-2.24717 - 1.98752i) q^{9} +(1.08740 - 0.942236i) q^{10} +(-3.77859 + 2.42835i) q^{11} +(1.72824 - 0.114785i) q^{12} +(-4.08260 - 4.71158i) q^{13} +(-0.959493 + 0.281733i) q^{14} +(-1.50360 + 1.98744i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(2.06295 - 4.51723i) q^{17} +(-2.88692 + 0.815909i) q^{18} +(-7.86057 + 3.58980i) q^{19} +(-0.204767 - 1.42419i) q^{20} +(1.52438 - 0.822350i) q^{21} +4.49162i q^{22} +(4.63022 + 1.24942i) q^{23} +(0.837796 - 1.51595i) q^{24} +(-2.46467 - 1.58395i) q^{25} +(-6.17085 + 0.887234i) q^{26} +(4.59797 - 2.42046i) q^{27} +(-0.281733 + 0.959493i) q^{28} +(1.26764 + 0.578911i) q^{29} +(0.859038 + 2.33940i) q^{30} +(-0.279329 + 1.94277i) q^{31} +(0.281733 + 0.959493i) q^{32} +(-1.61506 - 7.61023i) q^{33} +(-2.68482 - 4.17766i) q^{34} +(-0.777892 - 1.21042i) q^{35} +(-0.874399 + 2.86974i) q^{36} +(-3.37806 - 11.5046i) q^{37} +(-1.22981 + 8.55353i) q^{38} +(10.1364 - 3.72212i) q^{39} +(-1.30881 - 0.597713i) q^{40} +(-1.64576 + 5.60494i) q^{41} +(0.132338 - 1.72699i) q^{42} +(2.67569 - 0.384706i) q^{43} +(3.77859 + 2.42835i) q^{44} +(-2.29666 - 3.65479i) q^{45} +(3.55436 - 3.21971i) q^{46} -10.6326i q^{47} +(-0.822350 - 1.52438i) q^{48} +(0.142315 + 0.989821i) q^{49} +(-2.66500 + 1.21707i) q^{50} +(6.05110 + 6.11290i) q^{51} +(-2.58982 + 5.67093i) q^{52} +(-4.26105 + 4.91752i) q^{53} +(0.449632 - 5.17666i) q^{54} +(-6.20091 + 1.82075i) q^{55} +(0.654861 + 0.755750i) q^{56} +(-0.991913 - 14.9346i) q^{57} +(1.17235 - 0.753422i) q^{58} +(-7.28307 + 6.31082i) q^{59} +(2.43246 + 0.542105i) q^{60} +(-3.62509 - 0.521210i) q^{61} +(1.48335 + 1.28533i) q^{62} +(0.396753 + 2.97365i) q^{63} +(0.959493 + 0.281733i) q^{64} +(-3.72633 - 8.15952i) q^{65} +(-7.27530 - 2.75573i) q^{66} +(-1.13903 + 1.77236i) q^{67} -4.96600 q^{68} +(-4.86450 + 6.73325i) q^{69} -1.43883 q^{70} +(4.56458 - 7.10262i) q^{71} +(1.94145 + 2.28709i) q^{72} +(4.23611 + 9.27579i) q^{73} +(-11.5046 - 3.37806i) q^{74} +(4.07773 - 3.02035i) q^{75} +(6.53080 + 5.65897i) q^{76} +(4.44590 + 0.639224i) q^{77} +(2.34888 - 10.5396i) q^{78} +(2.65120 - 2.29728i) q^{79} +(-1.21042 + 0.777892i) q^{80} +(1.09956 + 8.93258i) q^{81} +(3.82541 + 4.41476i) q^{82} +(-6.36785 + 1.86977i) q^{83} +(-1.38129 - 1.04501i) q^{84} +(4.67914 - 5.40001i) q^{85} +(1.12295 - 2.45892i) q^{86} +(-1.71542 + 1.69808i) q^{87} +(4.08572 - 1.86589i) q^{88} +(-0.0941349 - 0.654723i) q^{89} +(-4.31628 - 0.0438558i) q^{90} +6.23431i q^{91} +(-0.786956 - 4.73082i) q^{92} +(-2.97543 - 1.64438i) q^{93} +(-8.94473 - 5.74843i) q^{94} +(-12.3071 + 1.76949i) q^{95} +(-1.72699 - 0.132338i) q^{96} +(-4.41422 + 15.0334i) q^{97} +(0.909632 + 0.415415i) q^{98} +(13.3175 + 2.05309i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{3} + 24 q^{4} + 4 q^{5} + 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^3 + 24 * q^4 + 4 * q^5 + 4 * q^9	$ 240 q - 4 q^{3} + 24 q^{4} + 4 q^{5} + 4 q^{9} + 4 q^{12} - 8 q^{13} - 24 q^{14} + 26 q^{15} - 24 q^{16} - 32 q^{17} + 40 q^{18} - 4 q^{20} + 8 q^{23} + 12 q^{25} + 116 q^{27} + 4 q^{30} + 16 q^{31} + 2 q^{33} - 4 q^{36} + 22 q^{37} + 8 q^{39} - 154 q^{41} - 4 q^{42} + 22 q^{43} - 24 q^{45} + 4 q^{46} - 4 q^{48} + 24 q^{49} - 88 q^{50} - 24 q^{51} + 8 q^{52} + 108 q^{53} + 12 q^{54} - 16 q^{55} + 24 q^{56} - 70 q^{57} - 4 q^{58} - 22 q^{59} - 26 q^{60} + 4 q^{63} + 24 q^{64} - 76 q^{66} - 44 q^{67} + 32 q^{68} - 86 q^{69} + 4 q^{70} + 4 q^{72} - 12 q^{73} + 16 q^{74} - 26 q^{75} - 78 q^{78} + 4 q^{80} - 168 q^{81} + 8 q^{82} - 16 q^{83} - 28 q^{85} - 16 q^{86} + 156 q^{87} - 24 q^{89} - 126 q^{90} - 8 q^{92} - 16 q^{93} - 8 q^{94} + 132 q^{97} - 172 q^{99}+O(q^{100}) $ 240 * q - 4 * q^3 + 24 * q^4 + 4 * q^5 + 4 * q^9 + 4 * q^12 - 8 * q^13 - 24 * q^14 + 26 * q^15 - 24 * q^16 - 32 * q^17 + 40 * q^18 - 4 * q^20 + 8 * q^23 + 12 * q^25 + 116 * q^27 + 4 * q^30 + 16 * q^31 + 2 * q^33 - 4 * q^36 + 22 * q^37 + 8 * q^39 - 154 * q^41 - 4 * q^42 + 22 * q^43 - 24 * q^45 + 4 * q^46 - 4 * q^48 + 24 * q^49 - 88 * q^50 - 24 * q^51 + 8 * q^52 + 108 * q^53 + 12 * q^54 - 16 * q^55 + 24 * q^56 - 70 * q^57 - 4 * q^58 - 22 * q^59 - 26 * q^60 + 4 * q^63 + 24 * q^64 - 76 * q^66 - 44 * q^67 + 32 * q^68 - 86 * q^69 + 4 * q^70 + 4 * q^72 - 12 * q^73 + 16 * q^74 - 26 * q^75 - 78 * q^78 + 4 * q^80 - 168 * q^81 + 8 * q^82 - 16 * q^83 - 28 * q^85 - 16 * q^86 + 156 * q^87 - 24 * q^89 - 126 * q^90 - 8 * q^92 - 16 * q^93 - 8 * q^94 + 132 * q^97 - 172 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$1$	$e\left(\frac{13}{22}\right)$

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 $

$2$	0.540641	−	0.841254i	0.382291	−	0.594856i
$2$	0.540641	−	0.841254i	0.382291	−	0.594856i
$3$	−0.613526	+	1.61975i	−0.354219	+	0.935162i
$3$	−0.613526	+	1.61975i	−0.354219	+	0.935162i
$4$	−0.415415	−	0.909632i	−0.207708	−	0.454816i
$5$	1.38055	+	0.405366i	0.617401	+	0.181285i	0.575453	−	0.817835i	$-0.304826\pi$
$5$	1.38055	+	0.405366i	0.617401	+	0.181285i	0.0419475	+	0.999120i	$0.486644\pi$
$6$	1.03092	+	1.39183i	0.420872	+	0.568214i
$7$	−0.755750	−	0.654861i	−0.285646	−	0.247514i
$7$	−0.755750	−	0.654861i	−0.285646	−	0.247514i
$8$	−0.989821	−	0.142315i	−0.349955	−	0.0503159i
$9$	−2.24717	−	1.98752i	−0.749057	−	0.662505i
$10$	1.08740	−	0.942236i	0.343865	−	0.297961i
$11$	−3.77859	+	2.42835i	−1.13929	+	0.732176i	−0.967478	−	0.252954i	$-0.918598\pi$
$11$	−3.77859	+	2.42835i	−1.13929	+	0.732176i	−0.171810	+	0.985130i	$0.554962\pi$
$12$	1.72824	−	0.114785i	0.498901	−	0.0331356i
$13$	−4.08260	−	4.71158i	−1.13231	−	1.30676i	−0.945964	−	0.324272i	$-0.894881\pi$
$13$	−4.08260	−	4.71158i	−1.13231	−	1.30676i	−0.186346	−	0.982484i	$-0.559665\pi$
$14$	−0.959493	+	0.281733i	−0.256435	+	0.0752962i
$15$	−1.50360	+	1.98744i	−0.388227	+	0.513155i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	2.06295	−	4.51723i	0.500339	−	1.09559i	−0.476020	−	0.879434i	$-0.657921\pi$
$17$	2.06295	−	4.51723i	0.500339	−	1.09559i	0.976359	−	0.216155i	$-0.0693516\pi$
$18$	−2.88692	+	0.815909i	−0.680453	+	0.192312i
$19$	−7.86057	+	3.58980i	−1.80334	+	0.823557i	−0.846824	+	0.531873i	$0.821488\pi$
$19$	−7.86057	+	3.58980i	−1.80334	+	0.823557i	−0.956515	+	0.291685i	$0.905784\pi$
$20$	−0.204767	−	1.42419i	−0.0457874	−	0.318458i
$21$	1.52438	−	0.822350i	0.332647	−	0.179452i
$22$			4.49162i			0.957617i
$23$	4.63022	+	1.24942i	0.965468	+	0.260521i
$23$	4.63022	+	1.24942i	0.965468	+	0.260521i
$24$	0.837796	−	1.51595i	0.171014	−	0.309442i
$25$	−2.46467	−	1.58395i	−0.492934	−	0.316789i
$26$	−6.17085	+	0.887234i	−1.21020	+	0.174001i
$27$	4.59797	−	2.42046i	0.884881	−	0.465818i
$28$	−0.281733	+	0.959493i	−0.0532424	+	0.181327i
$29$	1.26764	+	0.578911i	0.235394	+	0.107501i	0.529620	−	0.848235i	$-0.322334\pi$
$29$	1.26764	+	0.578911i	0.235394	+	0.107501i	−0.294226	+	0.955736i	$0.595062\pi$
$30$	0.859038	+	2.33940i	0.156838	+	0.427114i
$31$	−0.279329	+	1.94277i	−0.0501689	+	0.348932i	0.949240	+	0.314553i	$0.101855\pi$
$31$	−0.279329	+	1.94277i	−0.0501689	+	0.348932i	−0.999409	+	0.0343795i	$0.989055\pi$
$32$	0.281733	+	0.959493i	0.0498038	+	0.169616i
$33$	−1.61506	−	7.61023i	−0.281146	−	1.32477i
$34$	−2.68482	−	4.17766i	−0.460443	−	0.716463i
$35$	−0.777892	−	1.21042i	−0.131488	−	0.204599i
$36$	−0.874399	+	2.86974i	−0.145733	+	0.478291i
$37$	−3.37806	−	11.5046i	−0.555350	−	1.89135i	−0.439935	−	0.898030i	$-0.644998\pi$
$37$	−3.37806	−	11.5046i	−0.555350	−	1.89135i	−0.115415	−	0.993317i	$-0.536820\pi$
$38$	−1.22981	+	8.55353i	−0.199502	+	1.38757i
$39$	10.1364	−	3.72212i	1.62312	−	0.596016i
$40$	−1.30881	−	0.597713i	−0.206941	−	0.0945067i
$41$	−1.64576	+	5.60494i	−0.257024	+	0.875344i	0.725344	+	0.688387i	$0.241681\pi$
$41$	−1.64576	+	5.60494i	−0.257024	+	0.875344i	−0.982368	+	0.186957i	$0.940137\pi$
$42$	0.132338	−	1.72699i	0.0204202	−	0.266480i
$43$	2.67569	−	0.384706i	0.408039	−	0.0586671i	0.0647605	−	0.997901i	$-0.479372\pi$
$43$	2.67569	−	0.384706i	0.408039	−	0.0586671i	0.343278	+	0.939234i	$0.388463\pi$
$44$	3.77859	+	2.42835i	0.569644	+	0.366088i
$45$	−2.29666	−	3.65479i	−0.342366	−	0.544825i
$46$	3.55436	−	3.21971i	0.524062	−	0.474720i
$47$		−	10.6326i		−	1.55093i	−0.631393	−	0.775463i	$-0.717516\pi$
$47$		−	10.6326i		−	1.55093i	0.631393	−	0.775463i	$-0.282484\pi$
$48$	−0.822350	−	1.52438i	−0.118696	−	0.220026i
$49$	0.142315	+	0.989821i	0.0203307	+	0.141403i
$50$	−2.66500	+	1.21707i	−0.376888	+	0.172119i
$51$	6.05110	+	6.11290i	0.847324	+	0.855977i
$52$	−2.58982	+	5.67093i	−0.359144	+	0.786416i
$53$	−4.26105	+	4.91752i	−0.585301	+	0.675473i	−0.968736	−	0.248095i	$-0.920196\pi$
$53$	−4.26105	+	4.91752i	−0.585301	+	0.675473i	0.383435	+	0.923568i	$0.374741\pi$
$54$	0.449632	−	5.17666i	0.0611872	−	0.704454i
$55$	−6.20091	+	1.82075i	−0.836131	+	0.245510i
$56$	0.654861	+	0.755750i	0.0875094	+	0.100991i
$57$	−0.991913	−	14.9346i	−0.131382	−	1.97813i
$58$	1.17235	−	0.753422i	0.153937	−	0.0989291i
$59$	−7.28307	+	6.31082i	−0.948175	+	0.821598i	−0.984074	−	0.177757i	$-0.943116\pi$
$59$	−7.28307	+	6.31082i	−0.948175	+	0.821598i	0.0358995	+	0.999355i	$0.488570\pi$
$60$	2.43246	+	0.542105i	0.314029	+	0.0699855i
$61$	−3.62509	−	0.521210i	−0.464146	−	0.0667341i	−0.0937248	−	0.995598i	$-0.529877\pi$
$61$	−3.62509	−	0.521210i	−0.464146	−	0.0667341i	−0.370421	+	0.928864i	$0.620786\pi$
$62$	1.48335	+	1.28533i	0.188385	+	0.163237i
$63$	0.396753	+	2.97365i	0.0499861	+	0.374645i
$64$	0.959493	+	0.281733i	0.119937	+	0.0352166i
$65$	−3.72633	−	8.15952i	−0.462194	−	1.01206i
$66$	−7.27530	−	2.75573i	−0.895527	−	0.339207i
$67$	−1.13903	+	1.77236i	−0.139154	+	0.216528i	−0.903835	−	0.427881i	$-0.859260\pi$
$67$	−1.13903	+	1.77236i	−0.139154	+	0.216528i	0.764681	+	0.644409i	$0.222897\pi$
$68$	−4.96600			−0.602216
$69$	−4.86450	+	6.73325i	−0.585617	+	0.810588i
$70$	−1.43883			−0.171973
$71$	4.56458	−	7.10262i	0.541716	−	0.842926i	−0.457206	−	0.889361i	$-0.651150\pi$
$71$	4.56458	−	7.10262i	0.541716	−	0.842926i	0.998921	+	0.0464350i	$0.0147861\pi$
$72$	1.94145	+	2.28709i	0.228802	+	0.269536i
$73$	4.23611	+	9.27579i	0.495799	+	1.08565i	0.977812	+	0.209485i	$0.0671787\pi$
$73$	4.23611	+	9.27579i	0.495799	+	1.08565i	−0.482012	+	0.876164i	$0.660094\pi$
$74$	−11.5046	−	3.37806i	−1.33738	−	0.392691i
$75$	4.07773	−	3.02035i	0.470856	−	0.348760i
$76$	6.53080	+	5.65897i	0.749134	+	0.649128i
$77$	4.44590	+	0.639224i	0.506658	+	0.0728464i
$78$	2.34888	−	10.5396i	0.265958	−	1.19337i
$79$	2.65120	−	2.29728i	0.298283	−	0.258464i	−0.492841	−	0.870119i	$-0.664042\pi$
$79$	2.65120	−	2.29728i	0.298283	−	0.258464i	0.791124	+	0.611656i	$0.209496\pi$
$80$	−1.21042	+	0.777892i	−0.135329	+	0.0869710i
$81$	1.09956	+	8.93258i	0.122173	+	0.992509i
$82$	3.82541	+	4.41476i	0.422446	+	0.487528i
$83$	−6.36785	+	1.86977i	−0.698963	+	0.205234i	−0.611861	−	0.790966i	$-0.709579\pi$
$83$	−6.36785	+	1.86977i	−0.698963	+	0.205234i	−0.0871018	+	0.996199i	$0.527761\pi$
$84$	−1.38129	−	1.04501i	−0.150711	−	0.114020i
$85$	4.67914	−	5.40001i	0.507524	−	0.585714i
$86$	1.12295	−	2.45892i	0.121091	−	0.265152i
$87$	−1.71542	+	1.69808i	−0.183912	+	0.182053i
$88$	4.08572	−	1.86589i	0.435540	−	0.198904i
$89$	−0.0941349	−	0.654723i	−0.00997828	−	0.0694005i	0.984224	−	0.176928i	$-0.0566158\pi$
$89$	−0.0941349	−	0.654723i	−0.00997828	−	0.0694005i	−0.994202	+	0.107527i	$0.965707\pi$
$90$	−4.31628	−	0.0438558i	−0.454976	−	0.00462280i
$91$			6.23431i			0.653533i
$92$	−0.786956	−	4.73082i	−0.0820458	−	0.493223i
$93$	−2.97543	−	1.64438i	−0.308538	−	0.170515i
$94$	−8.94473	−	5.74843i	−0.922578	−	0.592905i
$95$	−12.3071	+	1.76949i	−1.26268	+	0.181546i
$96$	−1.72699	−	0.132338i	−0.176260	−	0.0135067i
$97$	−4.41422	+	15.0334i	−0.448196	+	1.52641i	0.357401	+	0.933951i	$0.383663\pi$
$97$	−4.41422	+	15.0334i	−0.448196	+	1.52641i	−0.805597	+	0.592464i	$0.798155\pi$
$98$	0.909632	+	0.415415i	0.0918867	+	0.0419633i
$99$	13.3175	+	2.05309i	1.33846	+	0.206343i
$100$	−0.416948	+	2.89994i	−0.0416948	+	0.289994i
$101$	−0.135691	−	0.462122i	−0.0135018	−	0.0459829i	0.952467	−	0.304643i	$-0.0985372\pi$
$101$	−0.135691	−	0.462122i	−0.0135018	−	0.0459829i	−0.965968	+	0.258660i	$0.916719\pi$
$102$	8.41397	−	1.78563i	0.833107	−	0.176804i
$103$	−10.3934	−	16.1725i	−1.02409	−	1.59352i	−0.782013	−	0.623263i	$-0.785807\pi$
$103$	−10.3934	−	16.1725i	−1.02409	−	1.59352i	−0.242080	−	0.970256i	$-0.577830\pi$
$104$	3.37052	+	5.24463i	0.330507	+	0.514279i
$105$	2.43784	−	0.517363i	0.237909	−	0.0504895i
$106$	1.83318	+	6.24324i	0.178054	+	0.606397i
$107$	0.436387	−	3.03514i	0.0421871	−	0.293418i	−0.957795	−	0.287452i	$-0.907192\pi$
$107$	0.436387	−	3.03514i	0.0421871	−	0.293418i	0.999982	−	0.00596589i	$-0.00189901\pi$
$108$	−4.11180	−	3.17697i	−0.395658	−	0.305704i
$109$	−7.15563	−	3.26787i	−0.685385	−	0.313005i	0.0421145	−	0.999113i	$-0.486591\pi$
$109$	−7.15563	−	3.26787i	−0.685385	−	0.313005i	−0.727500	+	0.686108i	$0.759318\pi$
$110$	−1.82075	+	6.20091i	−0.173602	+	0.591234i
$111$	20.7071	+	1.58677i	1.96543	+	0.150610i
$112$	0.989821	−	0.142315i	0.0935293	−	0.0134475i
$113$	−1.45074	−	0.932331i	−0.136474	−	0.0877064i	0.470622	−	0.882335i	$-0.344029\pi$
$113$	−1.45074	−	0.932331i	−0.136474	−	0.0877064i	−0.607096	+	0.794628i	$0.707666\pi$
$114$	−13.1000	−	7.23980i	−1.22693	−	0.678069i
$115$	5.88579	+	3.60182i	0.548852	+	0.335871i
$116$		−	1.39357i		−	0.129390i
$117$	−0.190022	+	18.7020i	−0.0175676	+	1.72900i
$118$	1.37147	+	9.53879i	0.126254	+	0.878117i
$119$	−4.51723	+	2.06295i	−0.414094	+	0.189110i
$120$	1.77113	−	1.75323i	0.161682	−	0.160047i
$121$	3.81129	−	8.34557i	0.346481	−	0.758688i
$122$	−2.39834	+	2.76783i	−0.217136	+	0.250588i
$123$	−8.06887	−	6.10449i	−0.727546	−	0.550423i
$124$	1.88325	−	0.552971i	0.169120	−	0.0496583i
$125$	−7.47170	−	8.62280i	−0.668289	−	0.771247i
$126$	2.71609	+	1.27391i	0.241969	+	0.113489i
$127$	4.95191	−	3.18240i	0.439411	−	0.282392i	−0.302172	−	0.953253i	$-0.597712\pi$
$127$	4.95191	−	3.18240i	0.439411	−	0.282392i	0.741583	+	0.670861i	$0.234075\pi$
$128$	0.755750	−	0.654861i	0.0667995	−	0.0578821i
$129$	−1.01848	+	4.56997i	−0.0896720	+	0.402364i
$130$	−8.87883	−	1.27658i	−0.778725	−	0.111964i
$131$	5.17064	+	4.48039i	0.451761	+	0.391453i	0.850808	−	0.525477i	$-0.176113\pi$
$131$	5.17064	+	4.48039i	0.451761	+	0.391453i	−0.399046	+	0.916931i	$0.630659\pi$
$132$	−6.25159	+	4.63051i	−0.544131	+	0.403034i
$133$	8.29144	+	2.43459i	0.718959	+	0.211106i
$134$	0.875201	+	1.91642i	0.0756058	+	0.165554i
$135$	7.32891	−	1.47770i	0.630772	−	0.127180i
$136$	−2.68482	+	4.17766i	−0.230221	+	0.358232i
$137$	13.3896			1.14395			0.571974	−	0.820272i	$-0.306178\pi$
$137$	13.3896			1.14395			0.571974	+	0.820272i	$0.306178\pi$
$138$	3.03442	+	7.73255i	0.258307	+	0.658238i
$139$	−7.19913			−0.610622			−0.305311	−	0.952253i	$-0.598760\pi$
$139$	−7.19913			−0.610622			−0.305311	+	0.952253i	$0.598760\pi$
$140$	−0.777892	+	1.21042i	−0.0657439	+	0.102299i
$141$	17.2222	+	6.52339i	1.45037	+	0.549368i
$142$	−3.50731	−	7.67993i	−0.294327	−	0.644486i
$143$	26.8679	+	7.88912i	2.24680	+	0.659721i
$144$	2.97365	−	0.396753i	0.247804	−	0.0330627i
$145$	1.51537	+	1.31307i	0.125844	+	0.109045i
$146$	10.0935	+	1.45123i	0.835345	+	0.120104i
$147$	−1.69058	−	0.376767i	−0.139436	−	0.0310752i
$148$	−9.06167	+	7.85198i	−0.744865	+	0.645429i
$149$	9.27406	−	5.96008i	0.759761	−	0.488269i	−0.102500	−	0.994733i	$-0.532684\pi$
$149$	9.27406	−	5.96008i	0.759761	−	0.488269i	0.862261	+	0.506464i	$0.169048\pi$
$150$	−0.336292	−	5.06333i	−0.0274581	−	0.413420i
$151$	6.19697	+	7.15169i	0.504303	+	0.581996i	0.949631	−	0.313371i	$-0.101458\pi$
$151$	6.19697	+	7.15169i	0.504303	+	0.581996i	−0.445328	+	0.895367i	$0.646913\pi$
$152$	8.29144	−	2.43459i	0.672525	−	0.197471i
$153$	−13.6139	+	6.05084i	−1.10062	+	0.489182i
$154$	2.94139	−	3.39454i	0.237024	−	0.273540i
$155$	−1.17316	+	2.56887i	−0.0942306	+	0.206336i
$156$	−7.59655	−	7.67413i	−0.608211	−	0.614422i
$157$	−7.37650	+	3.36874i	−0.588709	+	0.268854i	−0.687418	−	0.726262i	$-0.741256\pi$
$157$	−7.37650	+	3.36874i	−0.588709	+	0.268854i	0.0987091	+	0.995116i	$0.468529\pi$
$158$	−0.499246	−	3.47233i	−0.0397179	−	0.276244i
$159$	−5.35088	−	9.91886i	−0.424352	−	0.786617i
$160$			1.43883i			0.113750i
$161$	−2.68110	−	3.97640i	−0.211300	−	0.313384i
$162$	8.10903	+	3.90431i	0.637106	+	0.306751i
$163$	3.02130	+	1.94167i	0.236647	+	0.152084i	0.653590	−	0.756849i	$-0.273262\pi$
$163$	3.02130	+	1.94167i	0.236647	+	0.152084i	−0.416943	+	0.908933i	$0.636899\pi$
$164$	5.78210	−	0.831341i	0.451506	−	0.0649168i
$165$	0.855260	−	11.1610i	0.0665819	−	0.868882i
$166$	−1.86977	+	6.36785i	−0.145122	+	0.494241i
$167$	19.3926	+	8.85630i	1.50064	+	0.685321i	0.985169	−	0.171585i	$-0.0548887\pi$
$167$	19.3926	+	8.85630i	1.50064	+	0.685321i	0.515474	+	0.856905i	$0.327616\pi$
$168$	−1.62590	+	0.597038i	−0.125441	+	0.0460625i
$169$	−3.68120	+	25.6033i	−0.283169	+	1.96948i
$170$	−2.01305	−	6.85581i	−0.154394	−	0.525817i
$171$	24.7988	+	7.55611i	1.89642	+	0.577830i
$172$	−1.46146	−	2.27408i	−0.111436	−	0.173397i
$173$	−1.06322	−	1.65440i	−0.0808348	−	0.125781i	0.798482	−	0.602019i	$-0.205637\pi$
$173$	−1.06322	−	1.65440i	−0.0808348	−	0.125781i	−0.879317	+	0.476237i	$0.842000\pi$
$174$	0.501088	+	2.36115i	0.0379874	+	0.178998i
$175$	0.825408	+	2.81108i	0.0623950	+	0.212498i
$176$	0.639224	−	4.44590i	0.0481834	−	0.335123i
$177$	−5.75358	−	15.6686i	−0.432466	−	1.17772i
$178$	−0.601681	−	0.274779i	−0.0450979	−	0.0205955i
$179$	1.74706	−	5.94993i	0.130581	−	0.444719i	−0.868081	−	0.496422i	$-0.834647\pi$
$179$	1.74706	−	5.94993i	0.130581	−	0.444719i	0.998662	+	0.0517034i	$0.0164650\pi$
$180$	−2.37045	+	3.60737i	−0.176683	+	0.268878i
$181$	5.28057	−	0.759231i	0.392501	−	0.0564332i	0.0567611	−	0.998388i	$-0.481923\pi$
$181$	5.28057	−	0.759231i	0.392501	−	0.0564332i	0.335740	+	0.941955i	$0.391014\pi$
$182$	5.24463	+	3.37052i	0.388758	+	0.249840i
$183$	3.06832	−	5.55196i	0.226817	−	0.410413i
$184$	−4.40528	−	1.89565i	−0.324762	−	0.139749i
$185$		−	17.2521i		−	1.26840i
$186$	−2.99198	+	1.61407i	−0.219383	+	0.118349i
$187$	3.17439	+	22.0783i	0.232134	+	1.61453i
$188$	−9.67177	+	4.41695i	−0.705386	+	0.322139i
$189$	−5.05998	−	1.18177i	−0.368060	−	0.0859612i
$190$	−5.16513	+	11.3101i	−0.374718	+	0.820518i
$191$	−15.2106	+	17.5539i	−1.10060	+	1.27016i	−0.140627	+	0.990063i	$0.544912\pi$
$191$	−15.2106	+	17.5539i	−1.10060	+	1.27016i	−0.959972	+	0.280096i	$0.909634\pi$
$192$	−1.04501	+	1.38129i	−0.0754171	+	0.0996858i
$193$	8.63363	−	2.53506i	0.621462	−	0.182478i	0.0441814	−	0.999024i	$-0.485932\pi$
$193$	8.63363	−	2.53506i	0.621462	−	0.182478i	0.577281	+	0.816546i	$0.304114\pi$
$194$	10.2604	+	11.8412i	0.736656	+	0.850146i
$195$	15.5026	−	1.02964i	1.11016	−	0.0737338i
$196$	0.841254	−	0.540641i	0.0600895	−	0.0386172i
$197$	5.53852	−	4.79915i	0.394603	−	0.341926i	−0.434849	−	0.900503i	$-0.643198\pi$
$197$	5.53852	−	4.79915i	0.394603	−	0.341926i	0.829452	+	0.558578i	$0.188653\pi$
$198$	8.92717	−	10.0934i	0.634426	−	0.717310i
$199$	22.4693	+	3.23060i	1.59281	+	0.229011i	0.880915	−	0.473275i	$-0.156928\pi$
$199$	22.4693	+	3.23060i	1.59281	+	0.229011i	0.711894	+	0.702287i	$0.247837\pi$
$200$	2.21416	+	1.91858i	0.156565	+	0.135664i
$201$	−2.17196	−	2.93233i	−0.153198	−	0.206831i
$202$	−0.462122	−	0.135691i	−0.0325148	−	0.00954721i
$203$	−0.578911	−	1.26764i	−0.0406316	−	0.0889707i
$204$	3.04677	−	8.04367i	0.213316	−	0.563169i
$205$	−4.54410	+	7.07076i	−0.317374	+	0.493843i
$206$	−19.2242			−1.33942
$207$	−7.92167	−	12.0103i	−0.550594	−	0.834773i
$208$	6.23431			0.432271
$209$	20.9846	−	32.6527i	1.45153	−	2.25863i
$210$	0.882762	−	2.33055i	0.0609164	−	0.160823i
$211$	−6.92388	−	15.1612i	−0.476659	−	1.04374i	−0.983369	−	0.181621i	$-0.941865\pi$
$211$	−6.92388	−	15.1612i	−0.476659	−	1.04374i	0.506709	−	0.862117i	$-0.330862\pi$
$212$	6.24324	+	1.83318i	0.428787	+	0.125903i
$213$	8.70397	+	11.7511i	0.596386	+	0.805173i
$214$	−2.31739	−	2.00803i	−0.158414	−	0.137266i
$215$	3.84987	+	0.553528i	0.262559	+	0.0377503i
$216$	−4.89564	+	1.74146i	−0.333106	+	0.118492i
$217$	1.48335	−	1.28533i	0.100696	−	0.0872538i
$218$	−6.61773	+	4.25296i	−0.448209	+	0.288047i
$219$	−17.6234	+	1.17050i	−1.19088	+	0.0790948i
$220$	4.23217	+	4.88418i	0.285333	+	0.329291i
$221$	−29.7055	+	8.72231i	−1.99821	+	0.586726i
$222$	12.5300	−	16.5621i	0.840958	−	1.11157i
$223$	−12.0727	+	13.9326i	−0.808447	+	0.932998i	−0.998813	−	0.0487154i	$-0.984487\pi$
$223$	−12.0727	+	13.9326i	−0.808447	+	0.932998i	0.190365	+	0.981713i	$0.439033\pi$
$224$	0.415415	−	0.909632i	0.0277561	−	0.0607773i
$225$	2.39041	+	8.45797i	0.159361	+	0.563865i
$226$	−1.56865	+	0.716380i	−0.104345	+	0.0476529i
$227$	2.74516	+	19.0930i	0.182203	+	1.26725i	0.851540	+	0.524289i	$0.175669\pi$
$227$	2.74516	+	19.0930i	0.182203	+	1.26725i	−0.669338	+	0.742958i	$0.733422\pi$
$228$	−13.1729	+	7.10633i	−0.872398	+	0.470628i
$229$		−	16.2753i		−	1.07550i	−0.843104	−	0.537751i	$-0.819274\pi$
$229$		−	16.2753i		−	1.07550i	0.843104	−	0.537751i	$-0.180726\pi$
$230$	6.21214	−	3.00415i	0.409616	−	0.198088i
$231$	−3.76306	+	6.80907i	−0.247591	+	0.448004i
$232$	−1.17235	−	0.753422i	−0.0769684	−	0.0494646i
$233$	4.43314	−	0.637389i	0.290425	−	0.0417567i	0.00443726	−	0.999990i	$-0.498588\pi$
$233$	4.43314	−	0.637389i	0.290425	−	0.0417567i	0.285987	+	0.958233i	$0.407678\pi$
$234$	15.6304	+	10.2709i	1.02179	+	0.671430i
$235$	4.31010	−	14.6789i	0.281160	−	0.957544i
$236$	8.76602	+	4.00331i	0.570619	+	0.260593i
$237$	2.09443	+	5.70372i	0.136048	+	0.370496i
$238$	−0.706735	+	4.91545i	−0.0458108	+	0.318621i
$239$	−3.79471	−	12.9236i	−0.245459	−	0.835957i	−0.986397	−	0.164383i	$-0.947437\pi$
$239$	−3.79471	−	12.9236i	−0.245459	−	0.835957i	0.740937	−	0.671574i	$-0.234381\pi$
$240$	−0.517363	−	2.43784i	−0.0333956	−	0.157362i
$241$	1.76284	+	2.74304i	0.113555	+	0.176695i	0.893379	−	0.449304i	$-0.148328\pi$
$241$	1.76284	+	2.74304i	0.113555	+	0.176695i	−0.779824	+	0.625998i	$0.784692\pi$
$242$	−4.96020	−	7.71822i	−0.318854	−	0.496146i
$243$	−15.1431	−	3.69936i	−0.971433	−	0.237314i
$244$	1.03181	+	3.51402i	0.0660548	+	0.224962i
$245$	−0.204767	+	1.42419i	−0.0130821	+	0.0909881i
$246$	−9.49778	+	3.48763i	−0.605556	+	0.222363i
$247$	49.0052	+	22.3799i	3.11813	+	1.42400i
$248$	0.552971	−	1.88325i	0.0351137	−	0.119586i
$249$	0.878286	−	11.4615i	0.0556591	−	0.726341i
$250$	−11.2935	+	1.62376i	−0.714262	+	0.102695i
$251$	−16.2723	−	10.4576i	−1.02710	−	0.660077i	−0.0853356	−	0.996352i	$-0.527196\pi$
$251$	−16.2723	−	10.4576i	−1.02710	−	0.660077i	−0.941764	+	0.336276i	$0.890833\pi$
$252$	2.54011	−	1.59620i	0.160012	−	0.100551i
$253$	−20.5297	+	6.52279i	−1.29069	+	0.410084i
$254$		−	5.88635i		−	0.369342i
$255$	5.87589	+	10.8921i	0.367963	+	0.682088i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	−9.22035	+	4.21079i	−0.575150	+	0.262662i	−0.681684	−	0.731647i	$-0.738752\pi$
$257$	−9.22035	+	4.21079i	−0.575150	+	0.262662i	0.106534	+	0.994309i	$0.466025\pi$
$258$	3.29388	+	3.32751i	0.205068	+	0.207162i
$259$	−4.98095	+	10.9068i	−0.309501	+	0.677714i
$260$	−5.87419	+	6.77917i	−0.364302	+	0.420426i
$261$	−1.69800	−	3.82036i	−0.105104	−	0.236474i
$262$	6.56460	−	1.92754i	0.405562	−	0.119084i
$263$	9.31138	+	10.7459i	0.574165	+	0.662621i	0.966340	−	0.257269i	$-0.0828228\pi$
$263$	9.31138	+	10.7459i	0.574165	+	0.662621i	−0.392175	+	0.919891i	$0.628277\pi$
$264$	0.515571	+	7.76261i	0.0317312	+	0.477756i
$265$	−7.87600	+	5.06160i	−0.483819	+	0.310931i
$266$	6.53080	−	5.65897i	0.400429	−	0.346974i
$267$	1.11824	+	0.249215i	0.0684352	+	0.0152517i
$268$	2.08537	+	0.299830i	0.127384	+	0.0183151i
$269$	−18.1204	−	15.7014i	−1.10482	−	0.957332i	−0.105508	−	0.994418i	$-0.533647\pi$
$269$	−18.1204	−	15.7014i	−1.10482	−	0.957332i	−0.999312	+	0.0370863i	$0.988192\pi$
$270$	2.71918	−	6.96438i	0.165484	−	0.423839i
$271$	−2.94702	−	0.865324i	−0.179019	−	0.0525647i	0.190995	−	0.981591i	$-0.438829\pi$
$271$	−2.94702	−	0.865324i	−0.179019	−	0.0525647i	−0.370013	+	0.929026i	$0.620647\pi$
$272$	2.06295	+	4.51723i	0.125085	+	0.273897i
$273$	−10.0980	−	3.82491i	−0.611159	−	0.231494i
$274$	7.23895	−	11.2640i	0.437321	−	0.680485i
$275$	13.1594			0.793540
$276$	8.14556	+	1.62781i	0.490305	+	0.0979828i
$277$	−10.3912			−0.624349			−0.312174	−	0.950025i	$-0.601057\pi$
$277$	−10.3912			−0.624349			−0.312174	+	0.950025i	$0.601057\pi$
$278$	−3.89214	+	6.05629i	−0.233435	+	0.363232i
$279$	4.48899	−	3.81057i	0.268749	−	0.228133i
$280$	0.597713	+	1.30881i	0.0357202	+	0.0782163i
$281$	8.34522	+	2.45038i	0.497834	+	0.146177i	0.521004	−	0.853554i	$-0.325558\pi$
$281$	8.34522	+	2.45038i	0.497834	+	0.146177i	−0.0231697	+	0.999732i	$0.507376\pi$
$282$	14.7988	−	10.9614i	0.881257	−	0.652742i
$283$	−4.29126	−	3.71839i	−0.255089	−	0.221036i	0.517923	−	0.855427i	$-0.326705\pi$
$283$	−4.29126	−	3.71839i	−0.255089	−	0.221036i	−0.773012	+	0.634392i	$0.781251\pi$
$284$	−8.35696	−	1.20155i	−0.495895	−	0.0712989i
$285$	4.68459	−	21.0200i	0.277491	−	1.24512i
$286$	21.1626	−	18.3375i	1.25137	−	1.08432i
$287$	4.91423	−	3.15819i	0.290078	−	0.186422i
$288$	1.27391	−	2.71609i	0.0750657	−	0.160047i
$289$	−5.01697	−	5.78989i	−0.295116	−	0.340582i
$290$	1.92390	−	0.564907i	0.112975	−	0.0331725i
$291$	−21.6422	−	16.3733i	−1.26869	−	0.959822i
$292$	6.67781	−	7.70661i	0.390789	−	0.450995i
$293$	4.71285	−	10.3197i	0.275327	−	0.602883i	−0.720569	−	0.693383i	$-0.756119\pi$
$293$	4.71285	−	10.3197i	0.275327	−	0.602883i	0.995896	+	0.0905003i	$0.0288466\pi$
$294$	−1.23095	+	1.21851i	−0.0717905	+	0.0710648i
$295$	−12.6128	+	5.76009i	−0.734348	+	0.335365i
$296$	1.70640	+	11.8683i	0.0991824	+	0.689829i
$297$	−11.4961	+	20.3114i	−0.667074	+	1.17859i
$298$		−	11.0241i		−	0.638609i
$299$	−13.0166	−	26.9165i	−0.752772	−	1.55662i
$300$	−4.44136	−	2.45454i	−0.256422	−	0.141713i
$301$	−2.27408	−	1.46146i	−0.131076	−	0.0842373i
$302$	9.36672	−	1.34673i	0.538994	−	0.0774957i
$303$	0.831772	+	0.0637382i	0.0477841	+	0.00366167i
$304$	2.43459	−	8.29144i	0.139633	−	0.475547i
$305$	−4.79334	−	2.18905i	−0.274466	−	0.125344i
$306$	−2.26992	+	14.7240i	−0.129763	+	0.841718i
$307$	−2.35329	+	16.3675i	−0.134309	+	0.934142i	0.805537	+	0.592545i	$0.201877\pi$
$307$	−2.35329	+	16.3675i	−0.134309	+	0.934142i	−0.939847	+	0.341597i	$0.889032\pi$
$308$	−1.26544	−	4.30968i	−0.0721049	−	0.245567i
$309$	32.5719	−	6.91248i	1.85295	−	0.393237i
$310$	1.52681	+	2.37576i	0.0867169	+	0.134934i
$311$	−16.7231	−	26.0217i	−0.948280	−	1.47555i	−0.878360	−	0.478000i	$-0.841362\pi$
$311$	−16.7231	−	26.0217i	−0.948280	−	1.47555i	−0.0699206	−	0.997553i	$-0.522275\pi$
$312$	−10.5629	+	2.24168i	−0.598006	+	0.126910i
$313$	−3.59244	−	12.2347i	−0.203057	−	0.691548i	−0.996552	−	0.0829714i	$-0.973559\pi$
$313$	−3.59244	−	12.2347i	−0.203057	−	0.691548i	0.793495	−	0.608577i	$-0.208259\pi$
$314$	−1.15408	+	8.02678i	−0.0651284	+	0.452978i
$315$	−0.657680	+	4.26610i	−0.0370561	+	0.240368i
$316$	−3.19102	−	1.45729i	−0.179509	−	0.0819791i
$317$	8.40792	−	28.6347i	0.472236	−	1.60829i	−0.287313	−	0.957837i	$-0.592762\pi$
$317$	8.40792	−	28.6347i	0.472236	−	1.60829i	0.759549	−	0.650451i	$-0.225420\pi$
$318$	−11.2372	−	0.861098i	−0.630150	−	0.0482880i
$319$	−6.19569	+	0.890805i	−0.346892	+	0.0498755i
$320$	1.21042	+	0.777892i	0.0676647	+	0.0434855i
$321$	4.64842	+	2.56897i	0.259450	+	0.143386i
$322$	−4.79467	+	0.105679i	−0.267196	+	0.00588928i
$323$			42.9136i			2.38778i
$324$	7.66859	−	4.71092i	0.426033	−	0.261718i
$325$	2.59938	+	18.0791i	0.144188	+	1.00285i
$326$	3.26688	−	1.49193i	0.180936	−	0.0826305i
$327$	9.68329	−	9.58540i	0.535487	−	0.530074i
$328$	2.42667	−	5.31367i	0.133991	−	0.293398i
$329$	−6.96288	+	8.03560i	−0.383876	+	0.443017i
$330$	−8.92684	−	6.75358i	−0.491406	−	0.371772i
$331$	−32.4511	+	9.52850i	−1.78367	+	0.523734i	−0.995755	−	0.0920449i	$-0.970660\pi$
$331$	−32.4511	+	9.52850i	−1.78367	+	0.523734i	−0.787919	+	0.615779i	$0.788841\pi$
$332$	4.34610	+	5.01567i	0.238523	+	0.275271i
$333$	−15.2745	+	32.5668i	−0.837039	+	1.78465i
$334$	17.9348	−	11.5260i	0.981349	−	0.630675i
$335$	−2.29094	+	1.98511i	−0.125168	+	0.108458i
$336$	−0.376767	+	1.69058i	−0.0205543	+	0.0922285i
$337$	−13.4860	−	1.93899i	−0.734627	−	0.105623i	−0.235160	−	0.971957i	$-0.575562\pi$
$337$	−13.4860	−	1.93899i	−0.734627	−	0.105623i	−0.499467	+	0.866333i	$0.666471\pi$
$338$	19.5487	+	16.9390i	1.06331	+	0.921361i
$339$	2.40021	−	1.77782i	0.130361	−	0.0965578i
$340$	−6.85581	−	2.01305i	−0.371808	−	0.109173i
$341$	−3.66227	−	8.01926i	−0.198323	−	0.434267i
$342$	19.7639	−	16.7770i	1.06871	−	0.907195i
$343$	0.540641	−	0.841254i	0.0291919	−	0.0454234i
$344$	−2.70321			−0.145747
$345$	−9.44512	+	7.32369i	−0.508508	+	0.394294i
$346$	−1.96658			−0.105724
$347$	10.3724	−	16.1398i	0.556822	−	0.866432i	−0.442721	−	0.896659i	$-0.645987\pi$
$347$	10.3724	−	16.1398i	0.556822	−	0.866432i	0.999543	+	0.0302274i	$0.00962315\pi$
$348$	2.25724	+	0.854993i	0.121001	+	0.0458324i
$349$	5.30566	+	11.6178i	0.284006	+	0.621885i	0.996839	−	0.0794479i	$-0.0253157\pi$
$349$	5.30566	+	11.6178i	0.284006	+	0.621885i	−0.712833	+	0.701333i	$0.752588\pi$
$350$	2.81108	+	0.825408i	0.150259	+	0.0441199i
$351$	−30.1759	−	11.7819i	−1.61067	−	0.628873i
$352$	−3.39454	−	2.94139i	−0.180930	−	0.156776i
$353$	14.1690	+	2.03720i	0.754142	+	0.108429i	0.508655	−	0.860971i	$-0.330143\pi$
$353$	14.1690	+	2.03720i	0.754142	+	0.108429i	0.245487	+	0.969400i	$0.421052\pi$
$354$	−16.2919	−	3.63086i	−0.865904	−	0.192978i
$355$	9.18079	−	7.95520i	0.487266	−	0.422218i
$356$	−0.556452	+	0.357610i	−0.0294919	+	0.0189533i
$357$	−0.570022	−	8.58245i	−0.0301687	−	0.454231i
$358$	−4.06087	−	4.68649i	−0.214624	−	0.247689i
$359$	1.54332	−	0.453160i	0.0814534	−	0.0239169i	−0.240752	−	0.970587i	$-0.577394\pi$
$359$	1.54332	−	0.453160i	0.0814534	−	0.0239169i	0.322205	+	0.946670i	$0.395576\pi$
$360$	1.75315	+	3.94444i	0.0923993	+	0.207890i
$361$	36.4596	−	42.0766i	1.91892	−	2.21456i
$362$	2.21618	−	4.85277i	0.116480	−	0.255056i
$363$	11.1794	+	11.2936i	0.586766	+	0.592758i
$364$	5.67093	−	2.58982i	0.297237	−	0.135744i
$365$	2.08807	+	14.5229i	0.109295	+	0.760162i
$366$	−3.01175	−	5.58285i	−0.157427	−	0.291820i
$367$		−	8.77493i		−	0.458048i	−0.973421	−	0.229024i	$-0.926447\pi$
$367$		−	8.77493i		−	0.458048i	0.973421	−	0.229024i	$-0.0735534\pi$
$368$	−3.97640	+	2.68110i	−0.207284	+	0.139762i
$369$	14.8382	−	9.32428i	0.772446	−	0.485403i
$370$	−14.5134	−	9.32717i	−0.754513	−	0.484896i
$371$	6.44058	−	0.926016i	0.334378	−	0.0480763i
$372$	−0.259747	+	3.38965i	−0.0134672	+	0.175745i
$373$	5.78963	−	19.7177i	0.299776	−	1.02094i	−0.662544	−	0.749023i	$-0.730523\pi$
$373$	5.78963	−	19.7177i	0.299776	−	1.02094i	0.962320	−	0.271919i	$-0.0876584\pi$
$374$	20.2897	+	9.26599i	1.04915	+	0.479133i
$375$	18.5509	−	6.81196i	0.957962	−	0.351768i
$376$	−1.51318	+	10.5244i	−0.0780363	+	0.542754i
$377$	−2.44768	−	8.33603i	−0.126062	−	0.429327i
$378$	−3.72980	+	3.61781i	−0.191840	+	0.186080i
$379$	4.61119	+	7.17515i	0.236861	+	0.368563i	0.939252	−	0.343228i	$-0.111521\pi$
$379$	4.61119	+	7.17515i	0.236861	+	0.368563i	−0.702391	+	0.711791i	$0.747884\pi$
$380$	6.72214	+	10.4599i	0.344839	+	0.536579i
$381$	2.11656	+	9.97334i	0.108435	+	0.510950i
$382$	6.54386	+	22.2863i	0.334813	+	1.14027i
$383$	−2.91887	+	20.3012i	−0.149147	+	1.03734i	0.768472	+	0.639883i	$0.221017\pi$
$383$	−2.91887	+	20.3012i	−0.149147	+	1.03734i	−0.917620	+	0.397460i	$0.869892\pi$
$384$	0.597038	+	1.62590i	0.0304675	+	0.0829713i
$385$	5.87868	+	2.68470i	0.299605	+	0.136825i
$386$	2.53506	−	8.63363i	0.129031	−	0.439440i
$387$	−6.77735	−	4.45348i	−0.344512	−	0.226383i
$388$	15.5086	−	2.22980i	0.787331	−	0.113201i
$389$	−3.21705	−	2.06747i	−0.163111	−	0.104825i	0.456539	−	0.889704i	$-0.349089\pi$
$389$	−3.21705	−	2.06747i	−0.163111	−	0.104825i	−0.619650	+	0.784878i	$0.712725\pi$
$390$	7.51514	−	13.5983i	0.380544	−	0.688574i
$391$	15.1958	−	18.3383i	0.768485	−	0.927408i
$392$		−	1.00000i		−	0.0505076i
$393$	−10.4294	+	5.62631i	−0.526095	+	0.283810i
$394$	−1.04296	−	7.25392i	−0.0525434	−	0.365447i
$395$	4.59135	−	2.09680i	0.231016	−	0.105501i
$396$	−3.66475	−	12.9669i	−0.184161	−	0.651613i
$397$	3.13519	−	6.86511i	0.157351	−	0.344550i	−0.814494	−	0.580172i	$-0.802985\pi$
$397$	3.13519	−	6.86511i	0.157351	−	0.344550i	0.971845	+	0.235622i	$0.0757127\pi$
$398$	14.8656	−	17.1558i	0.745145	−	0.859943i
$399$	−9.03044	+	11.9364i	−0.452087	+	0.597566i
$400$	2.81108	−	0.825408i	0.140554	−	0.0412704i
$401$	5.50484	+	6.35293i	0.274899	+	0.317250i	0.876364	−	0.481649i	$-0.159962\pi$
$401$	5.50484	+	6.35293i	0.274899	+	0.317250i	−0.601466	+	0.798899i	$0.705416\pi$
$402$	−3.64108	+	0.241830i	−0.181601	+	0.0120614i
$403$	10.2939	−	6.61549i	0.512776	−	0.329541i
$404$	−0.363993	+	0.315402i	−0.0181093	+	0.0156918i
$405$	−2.10297	+	12.7776i	−0.104497	+	0.634924i
$406$	−1.37939	−	0.198326i	−0.0684578	−	0.00984275i
$407$	40.7016	+	35.2681i	2.01750	+	1.74818i
$408$	−5.11956	−	6.91184i	−0.253456	−	0.342187i
$409$	−5.12536	−	1.50494i	−0.253433	−	0.0744145i	0.152549	−	0.988296i	$-0.451252\pi$
$409$	−5.12536	−	1.50494i	−0.253433	−	0.0744145i	−0.405981	+	0.913881i	$0.633070\pi$
$410$	3.49158	+	7.64549i	0.172437	+	0.377584i
$411$	−8.21485	+	21.6877i	−0.405209	+	1.06978i
$412$	−10.3934	+	16.1725i	−0.512046	+	0.796759i
$413$	9.63688			0.474200
$414$	−14.3865	+	0.170880i	−0.707057	+	0.00839830i
$415$	−9.54908			−0.468746
$416$	3.37052	−	5.24463i	0.165253	−	0.257139i
$417$	4.41685	−	11.6608i	0.216294	−	0.571031i
$418$	−16.1240	−	35.3067i	−0.788652	−	1.72691i
$419$	−33.2503	−	9.76316i	−1.62438	−	0.476961i	−0.662190	−	0.749336i	$-0.730373\pi$
$419$	−33.2503	−	9.76316i	−1.62438	−	0.476961i	−0.962191	+	0.272375i	$0.912191\pi$
$420$	−1.48333	−	2.00262i	−0.0723789	−	0.0977177i
$421$	9.62857	+	8.34320i	0.469268	+	0.406623i	0.857135	−	0.515093i	$-0.172242\pi$
$421$	9.62857	+	8.34320i	0.469268	+	0.406623i	−0.387867	+	0.921715i	$0.626788\pi$
$422$	−16.4977	−	2.37201i	−0.803097	−	0.115468i
$423$	−21.1325	+	23.8933i	−1.02750	+	1.16173i
$424$	4.91752	−	4.26105i	0.238816	−	0.206935i
$425$	−12.2395	+	7.86587i	−0.593705	+	0.381551i
$426$	14.5914	−	0.969118i	0.706955	−	0.0469539i
$427$	2.39834	+	2.76783i	0.116064	+	0.133945i
$428$	−2.94214	+	0.863890i	−0.142214	+	0.0417577i
$429$	−29.2625	+	38.6790i	−1.41281	+	1.86744i
$430$	2.54706	−	2.93946i	0.122830	−	0.141753i
$431$	−13.4085	+	29.3606i	−0.645867	+	1.41425i	0.249258	+	0.968437i	$0.419813\pi$
$431$	−13.4085	+	29.3606i	−0.645867	+	1.41425i	−0.895125	+	0.445814i	$0.852914\pi$
$432$	−1.18177	+	5.05998i	−0.0568580	+	0.243448i
$433$	−23.2054	+	10.5976i	−1.11518	+	0.509286i	−0.885808	−	0.464052i	$-0.846395\pi$
$433$	−23.2054	+	10.5976i	−1.11518	+	0.509286i	−0.229373	+	0.973339i	$0.573668\pi$
$434$	−0.279329	−	1.94277i	−0.0134082	−	0.0932561i
$435$	−3.05657	+	1.64891i	−0.146551	+	0.0790591i
$436$			7.86651i			0.376738i
$437$	−40.8814	+	6.80047i	−1.95562	+	0.325311i
$438$	−8.54325	+	15.4586i	−0.408212	+	0.738639i
$439$	−6.51215	−	4.18510i	−0.310808	−	0.199744i	0.375932	−	0.926647i	$-0.377323\pi$
$439$	−6.51215	−	4.18510i	−0.310808	−	0.199744i	−0.686740	+	0.726903i	$0.740959\pi$
$440$	6.39692	−	0.919738i	0.304961	−	0.0438468i
$441$	1.64748	−	2.50715i	0.0784514	−	0.119388i
$442$	−8.72231	+	29.7055i	−0.414878	+	1.41295i
$443$	−22.4067	−	10.2328i	−1.06457	−	0.486175i	−0.195422	−	0.980719i	$-0.562608\pi$
$443$	−22.4067	−	10.2328i	−1.06457	−	0.486175i	−0.869153	+	0.494544i	$0.835335\pi$
$444$	−7.15867	−	19.4950i	−0.339735	−	0.925193i
$445$	0.135444	−	0.942037i	0.00642068	−	0.0446568i
$446$	5.19388	+	17.6887i	0.245938	+	0.837586i
$447$	3.96395	+	18.6783i	0.187488	+	0.883454i
$448$	−0.540641	−	0.841254i	−0.0255429	−	0.0397455i
$449$	2.77637	+	4.32011i	0.131025	+	0.203879i	0.900567	−	0.434718i	$-0.143152\pi$
$449$	2.77637	+	4.32011i	0.131025	+	0.203879i	−0.769542	+	0.638596i	$0.779515\pi$
$450$	8.40765	+	2.56178i	0.396341	+	0.120763i
$451$	−7.39212	−	25.1752i	−0.348081	−	1.18546i
$452$	−0.245421	+	1.70694i	−0.0115436	+	0.0802877i
$453$	−15.3859	+	5.64979i	−0.722895	+	0.265450i
$454$	17.5462	+	8.01308i	0.823484	+	0.376073i
$455$	−2.52718	+	8.60678i	−0.118476	+	0.403492i
$456$	−1.14360	+	14.9237i	−0.0535538	+	0.698868i
$457$	−13.9651	+	2.00788i	−0.653259	+	0.0939245i	−0.460973	−	0.887414i	$-0.652499\pi$
$457$	−13.9651	+	2.00788i	−0.653259	+	0.0939245i	−0.192287	+	0.981339i	$0.561590\pi$
$458$	−13.6917	−	8.79909i	−0.639769	−	0.411155i
$459$	−1.44838	−	25.7634i	−0.0676047	−	1.20253i
$460$	0.831284	−	6.85015i	0.0387588	−	0.319390i
$461$		−	14.4729i		−	0.674070i	−0.941492	−	0.337035i	$-0.890576\pi$
$461$		−	14.4729i		−	0.674070i	0.941492	−	0.337035i	$-0.109424\pi$
$462$	3.69369	+	6.84695i	0.171846	+	0.318549i
$463$	−1.86092	−	12.9430i	−0.0864842	−	0.601511i	−0.986265	−	0.165169i	$-0.947183\pi$
$463$	−1.86092	−	12.9430i	−0.0864842	−	0.601511i	0.899781	−	0.436342i	$-0.143726\pi$
$464$	−1.26764	+	0.578911i	−0.0588486	+	0.0268753i
$465$	−3.44115	−	3.47629i	−0.159580	−	0.161209i
$466$	1.86053	−	4.07399i	0.0861874	−	0.188724i
$467$	−20.3588	+	23.4953i	−0.942091	+	1.08723i	0.0539680	+	0.998543i	$0.482813\pi$
$467$	−20.3588	+	23.4953i	−0.942091	+	1.08723i	−0.996059	+	0.0886888i	$0.971732\pi$
$468$	17.0908	−	7.59622i	0.790024	−	0.351136i
$469$	2.02147	−	0.593557i	0.0933428	−	0.0274079i
$470$	−10.0184	−	11.5619i	−0.462116	−	0.533310i
$471$	−0.930829	−	14.0149i	−0.0428903	−	0.645772i
$472$	8.10706	−	5.21009i	0.373158	−	0.239814i
$473$	−9.17614	+	7.95117i	−0.421919	+	0.365595i
$474$	5.93061	+	1.32171i	0.272402	+	0.0607083i
$475$	25.0598	+	3.60305i	1.14982	+	0.165319i
$476$	3.75305	+	3.25204i	0.172021	+	0.149057i
$477$	19.3490	−	2.58159i	0.885928	−	0.118203i
$478$	−12.9236	−	3.79471i	−0.591111	−	0.173566i
$479$	6.17140	+	13.5135i	0.281978	+	0.617446i	0.996629	−	0.0820347i	$-0.0261418\pi$
$479$	6.17140	+	13.5135i	0.281978	+	0.617446i	−0.714651	+	0.699481i	$0.753415\pi$
$480$	−2.33055	−	0.882762i	−0.106375	−	0.0402924i
$481$	−40.4136	+	62.8848i	−1.84270	+	2.86730i
$482$	3.26065			0.148519
$483$	8.08568	−	1.90308i	0.367911	−	0.0865931i
$484$	−9.17467			−0.417030
$485$	−12.1881	+	18.9651i	−0.553433	+	0.861159i
$486$	−11.2991	+	10.7392i	−0.512538	+	0.487140i
$487$	−16.0495	−	35.1435i	−0.727272	−	1.59250i	−0.803423	−	0.595408i	$-0.796990\pi$
$487$	−16.0495	−	35.1435i	−0.727272	−	1.59250i	0.0761510	−	0.997096i	$-0.475737\pi$
$488$	3.51402	+	1.03181i	0.159072	+	0.0467078i
$489$	−4.99867	+	3.70248i	−0.226048	+	0.167432i
$490$	1.08740	+	0.942236i	0.0491236	+	0.0425659i
$491$	12.3827	+	1.78037i	0.558824	+	0.0803468i	0.415939	−	0.909392i	$-0.363453\pi$
$491$	12.3827	+	1.78037i	0.558824	+	0.0803468i	0.142885	+	0.989739i	$0.454362\pi$
$492$	−2.20091	+	9.87560i	−0.0992245	+	0.445226i
$493$	5.23014	−	4.53195i	0.235554	−	0.204109i
$494$	45.3214	−	29.1263i	2.03911	−	1.31045i
$495$	17.5533	+	8.23287i	0.788961	+	0.370040i
$496$	−1.28533	−	1.48335i	−0.0577130	−	0.0666043i
$497$	−8.10090	+	2.37864i	−0.363375	+	0.106697i
$498$	−9.16717	−	6.93540i	−0.410791	−	0.310783i
$499$	19.9550	−	23.0293i	0.893307	−	1.03093i	−0.106024	−	0.994364i	$-0.533812\pi$
$499$	19.9550	−	23.0293i	0.893307	−	1.03093i	0.999331	−	0.0365677i	$-0.0116425\pi$
$500$	−4.73972	+	10.3785i	−0.211967	+	0.464142i
$501$	−26.2428	+	25.9775i	−1.17244	+	1.16059i
$502$	−17.5950	+	8.03534i	−0.785301	+	0.358635i
$503$	0.627503	+	4.36438i	0.0279790	+	0.194598i	0.999017	−	0.0443266i	$-0.0141142\pi$
$503$	0.627503	+	4.36438i	0.0279790	+	0.194598i	−0.971038	+	0.238925i	$0.923205\pi$
$504$	0.0304801	−	2.99985i	0.00135769	−	0.133624i
$505$		−	0.692988i		−	0.0308376i
$506$	−5.61190	+	20.7972i	−0.249479	+	0.924549i
$507$	−39.2124	−	21.6709i	−1.74148	−	0.962439i
$508$	−4.95191	−	3.18240i	−0.219706	−	0.141196i
$509$	19.0916	−	2.74496i	0.846222	−	0.121668i	0.294453	−	0.955666i	$-0.404862\pi$
$509$	19.0916	−	2.74496i	0.846222	−	0.121668i	0.551768	+	0.833998i	$0.313953\pi$
$510$	12.3397	+	0.945587i	0.546413	+	0.0418713i
$511$	2.87291	−	9.78424i	0.127090	−	0.432829i
$512$	−0.909632	−	0.415415i	−0.0402004	−	0.0183589i
$513$	−27.4537	+	35.5320i	−1.21211	+	1.56878i
$514$	−1.44255	+	10.0332i	−0.0636283	+	0.442545i
$515$	−7.79285	−	26.5400i	−0.343394	−	1.16949i
$516$	4.58009	−	0.971995i	0.201627	−	0.0427897i
$517$	25.8198	+	40.1763i	1.13555	+	1.76695i
$518$	6.48245	+	10.0869i	0.284822	+	0.443192i
$519$	3.33202	−	0.707127i	0.146259	−	0.0310394i
$520$	2.52718	+	8.60678i	0.110824	+	0.377432i
$521$	−0.379965	+	2.64272i	−0.0166466	+	0.115780i	−0.996450	−	0.0841815i	$-0.973172\pi$
$521$	−0.379965	+	2.64272i	−0.0166466	+	0.115780i	0.979804	+	0.199961i	$0.0640815\pi$
$522$	−4.13190	−	0.636991i	−0.180848	−	0.0278803i
$523$	−34.6992	−	15.8466i	−1.51729	−	0.692923i	−0.529442	−	0.848346i	$-0.677599\pi$
$523$	−34.6992	−	15.8466i	−1.51729	−	0.692923i	−0.987848	+	0.155423i	$0.950326\pi$
$524$	1.92754	−	6.56460i	0.0842050	−	0.286776i
$525$	−5.05966	−	0.387718i	−0.220822	−	0.0169214i
$526$	14.0741	−	2.02356i	0.613662	−	0.0882313i
$527$	8.19971	+	5.26964i	0.357185	+	0.229549i
$528$	6.80907	+	3.76306i	0.296327	+	0.163766i
$529$	19.8779	+	11.5701i	0.864258	+	0.503050i
$530$			9.36222i			0.406669i
$531$	28.9092	+	0.293733i	1.25455	+	0.0127469i
$532$	−1.22981	−	8.55353i	−0.0533191	−	0.370842i
$533$	33.1270	−	15.1286i	1.43489	−	0.655293i
$534$	0.814219	−	0.805988i	0.0352347	−	0.0348785i
$535$	1.83280	−	4.01326i	0.0792387	−	0.173508i
$536$	1.37967	−	1.59222i	0.0595926	−	0.0687735i
$537$	8.56553	+	6.48023i	0.369630	+	0.279643i
$538$	−23.0055	+	6.75502i	−0.991837	+	0.291230i
$539$	−2.94139	−	3.39454i	−0.126694	−	0.146213i
$540$	−4.38871	−	6.05275i	−0.188860	−	0.260469i
$541$	21.1429	−	13.5877i	0.909004	−	0.584181i	−0.000443565	−	1.00000i	$-0.500141\pi$
$541$	21.1429	−	13.5877i	0.909004	−	0.584181i	0.909448	+	0.415818i	$0.136505\pi$
$542$	−2.32124	+	2.01136i	−0.0997057	+	0.0863955i
$543$	−2.01000	+	9.01900i	−0.0862574	+	0.387042i
$544$	4.91545	+	0.706735i	0.210748	+	0.0303010i
$545$	−8.55403	−	7.41211i	−0.366414	−	0.317500i
$546$	−8.67712	+	6.42708i	−0.371346	+	0.275054i
$547$	6.25572	+	1.83685i	0.267475	+	0.0785379i	0.412720	−	0.910858i	$-0.364579\pi$
$547$	6.25572	+	1.83685i	0.267475	+	0.0785379i	−0.145245	+	0.989396i	$0.546397\pi$
$548$	−5.56223	−	12.1796i	−0.237607	−	0.520286i
$549$	7.11029	+	8.37618i	0.303460	+	0.357487i
$550$	7.11449	−	11.0704i	0.303363	−	0.472042i
$551$	−12.0425			−0.513029
$552$	5.77323	−	5.97242i	0.245725	−	0.254203i
$553$	−3.50804			−0.149177
$554$	−5.61793	+	8.74166i	−0.238683	+	0.371398i
$555$	27.9440	+	10.5846i	1.18616	+	0.449291i
$556$	2.99063	+	6.54856i	0.126831	+	0.277721i
$557$	−31.3372	−	9.20144i	−1.32780	−	0.389877i	−0.460499	−	0.887660i	$-0.652329\pi$
$557$	−31.3372	−	9.20144i	−1.32780	−	0.389877i	−0.867302	+	0.497783i	$0.834148\pi$
$558$	−0.778727	−	5.83653i	−0.0329661	−	0.247080i
$559$	−12.7364	−	11.0361i	−0.538690	−	0.466778i
$560$	1.42419	+	0.204767i	0.0601829	+	0.00865300i
$561$	−37.7089	−	8.40393i	−1.59207	−	0.354814i
$562$	6.57316	−	5.69567i	0.277272	−	0.240258i
$563$	16.3181	−	10.4870i	0.687726	−	0.441975i	−0.149551	−	0.988754i	$-0.547783\pi$
$563$	16.3181	−	10.4870i	0.687726	−	0.441975i	0.837277	+	0.546779i	$0.184146\pi$
$564$	−1.22046	−	18.3757i	−0.0513908	−	0.773759i
$565$	−1.62488	−	1.87521i	−0.0683592	−	0.0788907i
$566$	−5.44814	+	1.59972i	−0.229002	+	0.0672412i
$567$	5.01860	−	7.47085i	0.210762	−	0.313746i
$568$	−5.52892	+	6.38072i	−0.231989	+	0.267729i
$569$	4.48272	−	9.81579i	0.187925	−	0.411499i	−0.792095	−	0.610398i	$-0.791009\pi$
$569$	4.48272	−	9.81579i	0.187925	−	0.411499i	0.980020	+	0.198899i	$0.0637366\pi$
$570$	−15.1505	−	15.3052i	−0.634585	−	0.641065i
$571$	29.6396	−	13.5359i	1.24038	−	0.566461i	0.316297	−	0.948660i	$-0.397560\pi$
$571$	29.6396	−	13.5359i	1.24038	−	0.566461i	0.924080	+	0.382199i	$0.124833\pi$
$572$	−3.98512	−	27.7171i	−0.166626	−	1.15891i
$573$	−19.1009	−	35.4071i	−0.797951	−	1.47915i
$574$		−	5.84156i		−	0.243822i
$575$	−9.43296	−	10.4134i	−0.393382	−	0.434270i
$576$	−1.59620	−	2.54011i	−0.0665082	−	0.105838i
$577$	−21.8649	−	14.0517i	−0.910249	−	0.584982i	−0.000436036	−	1.00000i	$-0.500139\pi$
$577$	−21.8649	−	14.0517i	−0.910249	−	0.584982i	−0.909813	+	0.415018i	$0.863775\pi$
$578$	−7.58314	+	1.09029i	−0.315417	+	0.0453501i
$579$	−1.19079	+	15.5396i	−0.0494877	+	0.645805i
$580$	0.564907	−	1.92390i	0.0234565	−	0.0798854i
$581$	6.03694	+	2.75698i	0.250454	+	0.114379i
$582$	−25.4748	+	9.35445i	−1.05596	+	0.387755i
$583$	4.15931	−	28.9286i	0.172261	−	1.19810i
$584$	−2.87291	−	9.78424i	−0.118882	−	0.404875i
$585$	−7.84348	+	25.7420i	−0.324288	+	1.06430i
$586$	−6.13352	−	9.54395i	−0.253373	−	0.394257i
$587$	25.5754	+	39.7962i	1.05561	+	1.64256i	0.710026	+	0.704176i	$0.248683\pi$
$587$	25.5754	+	39.7962i	1.05561	+	1.64256i	0.345585	+	0.938387i	$0.387680\pi$
$588$	0.359571	+	1.69432i	0.0148285	+	0.0698724i
$589$	−4.77849	−	16.2740i	−0.196894	−	0.670560i
$590$	−1.97332	+	13.7247i	−0.0812402	+	0.565038i
$591$	4.37540	+	11.9154i	0.179980	+	0.490135i
$592$	10.9068	+	4.98095i	0.448265	+	0.204716i
$593$	3.32770	−	11.3331i	0.136652	−	0.465394i	−0.862522	−	0.506019i	$-0.831117\pi$
$593$	3.32770	−	11.3331i	0.136652	−	0.465394i	0.999174	+	0.0406246i	$0.0129348\pi$
$594$	10.8718	+	20.6524i	0.446075	+	0.847377i
$595$	−7.07251	+	1.01687i	−0.289945	+	0.0416878i
$596$	−9.27406	−	5.96008i	−0.379880	−	0.244134i
$597$	−19.0183	+	34.4126i	−0.778367	+	1.40841i
$598$	−29.6809	−	3.60186i	−1.21374	−	0.147291i
$599$		−	19.1662i		−	0.783111i	−0.920155	−	0.391555i	$-0.871937\pi$
$599$		−	19.1662i		−	0.783111i	0.920155	−	0.391555i	$-0.128063\pi$
$600$	−4.46607	+	2.40929i	−0.182327	+	0.0983587i
$601$	1.03625	+	7.20731i	0.0422697	+	0.293992i	0.999980	+	0.00625943i	$0.00199245\pi$
$601$	1.03625	+	7.20731i	0.0422697	+	0.293992i	−0.957711	+	0.287733i	$0.907098\pi$
$602$	−2.45892	+	1.12295i	−0.100218	+	0.0457681i
$603$	6.08219	−	1.71897i	0.247686	−	0.0700017i
$604$	3.93109	−	8.60789i	0.159954	−	0.350250i
$605$	8.64470	−	9.97651i	0.351457	−	0.405603i
$606$	0.503310	−	0.665272i	0.0204456	−	0.0270248i
$607$	−28.2070	+	8.28232i	−1.14489	+	0.336169i	−0.798542	−	0.601939i	$-0.794395\pi$
$607$	−28.2070	+	8.28232i	−1.14489	+	0.336169i	−0.346344	+	0.938108i	$0.612577\pi$
$608$	−5.65897	−	6.53080i	−0.229502	−	0.264859i
$609$	2.40843	−	0.159961i	0.0975945	−	0.00648195i
$610$	−4.43302	+	2.84893i	−0.179488	+	0.115350i
$611$	−50.0964	+	43.4088i	−2.02668	+	1.75613i
$612$	11.1594	+	9.87000i	0.451094	+	0.398971i
$613$	7.87915	+	1.13285i	0.318236	+	0.0457554i	0.299582	−	0.954071i	$-0.403153\pi$
$613$	7.87915	+	1.13285i	0.318236	+	0.0457554i	0.0186539	+	0.999826i	$0.494062\pi$
$614$	12.4969	+	10.8286i	0.504335	+	0.437009i
$615$	−8.66493	−	11.6984i	−0.349404	−	0.471725i
$616$	−4.30968	−	1.26544i	−0.173642	−	0.0509859i
$617$	−6.94314	−	15.2034i	−0.279520	−	0.612064i	0.716846	−	0.697231i	$-0.245585\pi$
$617$	−6.94314	−	15.2034i	−0.279520	−	0.612064i	−0.996367	+	0.0851668i	$0.972858\pi$
$618$	11.7946	−	31.1384i	0.474447	−	1.25257i
$619$	8.68506	−	13.5142i	0.349082	−	0.543182i	−0.621666	−	0.783282i	$-0.713544\pi$
$619$	8.68506	−	13.5142i	0.349082	−	0.543182i	0.970748	+	0.240100i	$0.0771803\pi$
$620$	2.82407			0.113417
$621$	24.3138	−	5.46249i	0.975679	−	0.219202i
$622$	−30.9320			−1.24026
$623$	−0.357610	+	0.556452i	−0.0143273	+	0.0222938i
$624$	−3.82491	+	10.0980i	−0.153119	+	0.404244i
$625$	−0.734340	−	1.60798i	−0.0293736	−	0.0643192i
$626$	−12.2347	−	3.59244i	−0.488998	−	0.143583i
$627$	40.0145	+	54.0230i	1.59803	+	2.15747i
$628$	6.12862	+	5.31048i	0.244559	+	0.211911i
$629$	−58.9378	−	8.47397i	−2.35000	−	0.337879i
$630$	3.23331	+	2.85970i	0.128818	+	0.113933i
$631$	1.92398	−	1.66713i	0.0765923	−	0.0663676i	−0.615723	−	0.787962i	$-0.711136\pi$
$631$	1.92398	−	1.66713i	0.0765923	−	0.0663676i	0.692316	+	0.721595i	$0.256591\pi$
$632$	−2.95115	+	1.89659i	−0.117390	+	0.0754423i
$633$	28.8053	−	1.91316i	1.14491	−	0.0760414i
$634$	−19.5434	−	22.5543i	−0.776168	−	0.895746i
$635$	8.12640	−	2.38613i	0.322486	−	0.0946906i
$636$	−6.79968	+	8.98777i	−0.269625	+	0.356388i
$637$	4.08260	−	4.71158i	0.161759	−	0.186679i
$638$	−2.60025	+	5.69375i	−0.102945	+	0.225418i
$639$	−24.3740	+	6.88864i	−0.964219	+	0.272510i
$640$	1.30881	−	0.597713i	0.0517352	−	0.0236267i
$641$	−4.26092	−	29.6354i	−0.168296	−	1.17053i	−0.882405	−	0.470491i	$-0.844077\pi$
$641$	−4.26092	−	29.6354i	−0.168296	−	1.17053i	0.714108	−	0.700035i	$-0.246832\pi$
$642$	4.67428	−	2.52161i	0.184479	−	0.0995200i
$643$		−	28.6974i		−	1.13171i	−0.824503	−	0.565857i	$-0.808545\pi$
$643$		−	28.6974i		−	1.13171i	0.824503	−	0.565857i	$-0.191455\pi$
$644$	−2.50329	+	4.09067i	−0.0986434	+	0.161195i
$645$	−3.25857	+	5.89622i	−0.128306	+	0.232164i
$646$	36.1012	+	23.2008i	1.42038	+	0.912825i
$647$	23.2240	−	3.33911i	0.913031	−	0.131274i	0.330241	−	0.943897i	$-0.392870\pi$
$647$	23.2240	−	3.33911i	0.913031	−	0.131274i	0.582790	+	0.812623i	$0.301961\pi$
$648$	0.182871	−	8.99814i	0.00718385	−	0.353480i
$649$	12.1949	−	41.5319i	0.478690	−	1.63027i
$650$	16.6144	+	7.58756i	0.651672	+	0.297609i
$651$	1.17184	+	3.19123i	0.0459279	+	0.125074i
$652$	0.511114	−	3.55487i	0.0200168	−	0.139220i
$653$	−0.320880	−	1.09282i	−0.0125570	−	0.0427652i	0.952976	−	0.303045i	$-0.0980033\pi$
$653$	−0.320880	−	1.09282i	−0.0125570	−	0.0427652i	−0.965533	+	0.260280i	$0.916185\pi$
$654$	−2.82857	−	13.3284i	−0.110606	−	0.521180i
$655$	5.32214	+	8.28141i	0.207953	+	0.323581i
$656$	−3.15819	−	4.91423i	−0.123306	−	0.191869i
$657$	8.91651	−	29.2636i	0.347866	−	1.14168i
$658$	2.99555	+	10.2019i	0.116779	+	0.397712i
$659$	−4.30999	+	29.9766i	−0.167893	+	1.16772i	0.715336	+	0.698781i	$0.246274\pi$
$659$	−4.30999	+	29.9766i	−0.167893	+	1.16772i	−0.883229	+	0.468942i	$0.844635\pi$
$660$	−10.5077	+	3.85847i	−0.409011	+	0.150191i
$661$	−20.6151	−	9.41460i	−0.801835	−	0.366186i	−0.0280277	−	0.999607i	$-0.508923\pi$
$661$	−20.6151	−	9.41460i	−0.801835	−	0.366186i	−0.773807	+	0.633422i	$0.781650\pi$
$662$	−9.52850	+	32.4511i	−0.370336	+	1.26125i
$663$	4.09713	−	53.4668i	0.159119	−	2.07648i
$664$	6.56913	−	0.944499i	0.254932	−	0.0366537i
$665$	10.4599	+	6.72214i	0.405616	+	0.260674i
$666$	19.1389	+	30.4567i	0.741617	+	1.18017i
$667$	5.14614	+	4.26429i	0.199259	+	0.165114i
$668$		−	21.3192i		−	0.824863i
$669$	−15.1604	−	28.1028i	−0.586137	−	1.08652i
$670$	0.431406	+	3.00050i	0.0166667	+	0.115919i
$671$	14.9634	−	6.83357i	0.577657	−	0.263807i
$672$	1.21851	+	1.23095i	0.0470049	+	0.0474850i
$673$	15.7762	−	34.5450i	0.608128	−	1.33161i	−0.315720	−	0.948852i	$-0.602246\pi$
$673$	15.7762	−	34.5450i	0.608128	−	1.33161i	0.923847	−	0.382761i	$-0.125027\pi$
$674$	−8.92224	+	10.2968i	−0.343672	+	0.396618i
$675$	−15.1664	−	1.31731i	−0.583754	−	0.0507034i
$676$	24.8188	−	7.28746i	0.954570	−	0.280287i
$677$	−4.86262	−	5.61177i	−0.186886	−	0.215678i	0.654573	−	0.755999i	$-0.272848\pi$
$677$	−4.86262	−	5.61177i	−0.186886	−	0.215678i	−0.841459	+	0.540321i	$0.818303\pi$
$678$	−0.197946	−	2.98034i	−0.00760207	−	0.114459i
$679$	13.1809	−	8.47082i	0.505835	−	0.325080i
$680$	−5.40001	+	4.67914i	−0.207081	+	0.179437i
$681$	−32.6101	−	7.26759i	−1.24962	−	0.278495i
$682$	−8.72620	−	1.25464i	−0.334144	−	0.0480426i
$683$	−1.51196	−	1.31012i	−0.0578535	−	0.0501304i	0.625454	−	0.780261i	$-0.284914\pi$
$683$	−1.51196	−	1.31012i	−0.0578535	−	0.0501304i	−0.683308	+	0.730131i	$0.739459\pi$
$684$	−3.42853	−	25.6967i	−0.131093	−	0.982540i
$685$	18.4850	+	5.42768i	0.706275	+	0.207381i
$686$	−0.415415	−	0.909632i	−0.0158606	−	0.0347299i
$687$	26.3619	+	9.98532i	1.00577	+	0.380964i
$688$	−1.46146	+	2.27408i	−0.0557178	+	0.0866985i
$689$	40.5655			1.54542
$690$	1.05466	+	11.9052i	0.0401502	+	0.453224i
$691$	19.6533			0.747646			0.373823	−	0.927500i	$-0.378047\pi$
$691$	19.6533			0.747646			0.373823	+	0.927500i	$0.378047\pi$
$692$	−1.06322	+	1.65440i	−0.0404174	+	0.0628907i
$693$	−8.72024	−	10.2728i	−0.331254	−	0.390230i
$694$	−7.96993	−	17.4517i	−0.302534	−	0.662458i
$695$	−9.93876	−	2.91828i	−0.376999	−	0.110697i
$696$	1.93962	−	1.43666i	0.0735211	−	0.0544566i
$697$	21.9237	+	18.9970i	0.830418	+	0.719561i
$698$	12.6420	+	1.81764i	0.478505	+	0.0687986i
$699$	−1.68744	+	7.57163i	−0.0638247	+	0.286385i
$700$	2.21416	−	1.91858i	0.0836875	−	0.0725156i
$701$	−8.25764	+	5.30686i	−0.311887	+	0.200437i	−0.687214	−	0.726455i	$-0.741167\pi$
$701$	−8.25764	+	5.30686i	−0.311887	+	0.200437i	0.375328	+	0.926892i	$0.377530\pi$
$702$	−26.2259	+	19.0158i	−0.989833	+	0.717704i
$703$	67.8528	+	78.3063i	2.55912	+	2.95338i
$704$	−4.30968	+	1.26544i	−0.162427	+	0.0476929i
$705$	21.1317	+	15.9872i	0.795866	+	0.602111i
$706$	9.37416	−	10.8184i	0.352801	−	0.407154i
$707$	−0.200077	+	0.438108i	−0.00752467	+	0.0164767i
$708$	−11.8625	+	11.7426i	−0.445821	+	0.441314i
$709$	−17.8594	+	8.15612i	−0.670724	+	0.306309i	−0.721514	−	0.692400i	$-0.756553\pi$
$709$	−17.8594	+	8.15612i	−0.670724	+	0.306309i	0.0507899	+	0.998709i	$0.483826\pi$
$710$	−1.72883	−	12.0243i	−0.0648819	−	0.451263i
$711$	−10.5236	−	0.106925i	−0.394665	−	0.00401001i
$712$			0.661455i			0.0247891i
$713$	−3.72068	+	8.64648i	−0.139341	+	0.323813i
$714$	−7.52819	−	4.16049i	−0.281736	−	0.155702i
$715$	33.8945	+	21.7827i	1.26758	+	0.814625i
$716$	−6.13800	+	0.882511i	−0.229388	+	0.0329810i
$717$	23.2611	+	1.78248i	0.868702	+	0.0665681i
$718$	0.453160	−	1.54332i	0.0169118	−	0.0575963i
$719$	−12.6834	−	5.79233i	−0.473012	−	0.216017i	0.164622	−	0.986357i	$-0.447360\pi$
$719$	−12.6834	−	5.79233i	−0.473012	−	0.216017i	−0.637634	+	0.770339i	$0.720087\pi$
$720$	4.26610	+	0.657680i	0.158988	+	0.0245103i
$721$	−2.73589	+	19.0286i	−0.101890	+	0.708660i
$722$	−15.6855	−	53.4200i	−0.583755	−	1.98809i
$723$	−5.52458	+	1.17244i	−0.205461	+	0.0436034i
$724$	−2.88425	−	4.48798i	−0.107192	−	0.166794i
$725$	−2.20734	−	3.43469i	−0.0819787	−	0.127561i
$726$	15.5448	−	3.29895i	0.576921	−	0.122435i
$727$	−11.6590	−	39.7068i	−0.432408	−	1.47264i	−0.831392	−	0.555687i	$-0.812455\pi$
$727$	−11.6590	−	39.7068i	−0.432408	−	1.47264i	0.398984	−	0.916958i	$-0.369363\pi$
$728$	0.887234	−	6.17085i	0.0328831	−	0.228707i
$729$	15.2827	−	22.2584i	0.566028	−	0.824386i
$730$	13.3463	+	6.09506i	0.493969	+	0.225588i
$731$	3.78201	−	12.8803i	0.139883	−	0.476396i
$732$	−6.32487	−	0.484671i	−0.233774	−	0.0179140i
$733$	−31.6995	+	4.55770i	−1.17085	+	0.168342i	−0.700178	−	0.713968i	$-0.746896\pi$
$733$	−31.6995	+	4.55770i	−1.17085	+	0.168342i	−0.470668	+	0.882310i	$0.655987\pi$
$734$	−7.38194	−	4.74409i	−0.272472	−	0.175107i
$735$	−2.18120	−	1.20545i	−0.0804547	−	0.0444636i
$736$	0.105679	+	4.79467i	0.00389540	+	0.176734i
$737$		−	9.46300i		−	0.348574i
$738$	0.178051	−	17.5238i	0.00655416	−	0.645059i
$739$	−1.71600	−	11.9350i	−0.0631241	−	0.439038i	−0.996735	−	0.0807481i	$-0.974269\pi$
$739$	−1.71600	−	11.9350i	−0.0631241	−	0.439038i	0.933610	−	0.358290i	$-0.116640\pi$
$740$	−15.6930	+	7.16676i	−0.576887	+	0.263455i
$741$	−66.3158	+	65.6455i	−2.43617	+	2.41155i
$742$	2.70303	−	5.91880i	0.0992312	−	0.217286i
$743$	−3.73196	+	4.30692i	−0.136913	+	0.158005i	−0.820065	−	0.572270i	$-0.806063\pi$
$743$	−3.73196	+	4.30692i	−0.136913	+	0.158005i	0.683153	+	0.730276i	$0.260608\pi$
$744$	2.71112	+	2.05109i	0.0993946	+	0.0751968i
$745$	15.2193	−	4.46880i	0.557593	−	0.163724i
$746$	−13.4574	−	15.5307i	−0.492712	−	0.568620i
$747$	18.0259	+	8.45451i	0.659531	+	0.309334i
$748$	18.7645	−	12.0592i	0.686097	−	0.440928i
$749$	−2.31739	+	2.00803i	−0.0846756	+	0.0733718i
$750$	4.29876	−	19.2888i	0.156969	−	0.704327i
$751$	−28.4978	−	4.09737i	−1.03990	−	0.149515i	−0.398852	−	0.917015i	$-0.630591\pi$
$751$	−28.4978	−	4.09737i	−1.03990	−	0.149515i	−0.641049	+	0.767500i	$0.721500\pi$
$752$	8.03560	+	6.96288i	0.293028	+	0.253910i
$753$	26.9221	−	19.9411i	0.981097	−	0.726692i
$754$	−8.33603	−	2.44768i	−0.303580	−	0.0891392i
$755$	5.65618	+	12.3853i	0.205850	+	0.450748i
$756$	1.02702	+	5.09365i	0.0373522	+	0.185254i
$757$	0.468889	−	0.729606i	0.0170421	−	0.0265180i	−0.832628	−	0.553833i	$-0.813165\pi$
$757$	0.468889	−	0.729606i	0.0170421	−	0.0265180i	0.849670	+	0.527315i	$0.176801\pi$
$758$	8.52912			0.309792
$759$	2.03026	−	37.2549i	0.0736937	−	1.35227i
$760$	12.4337			0.451016
$761$	22.7170	−	35.3483i	0.823489	−	1.28137i	−0.133442	−	0.991057i	$-0.542603\pi$
$761$	22.7170	−	35.3483i	0.823489	−	1.28137i	0.956931	−	0.290317i	$-0.0937608\pi$
$762$	9.53441	+	3.61143i	0.345395	+	0.130828i
$763$	3.26787	+	7.15563i	0.118305	+	0.259051i
$764$	22.2863	+	6.54386i	0.806291	+	0.236748i
$765$	−21.2474	+	2.83489i	−0.768203	+	0.102496i
$766$	15.5004	+	13.4312i	0.560052	+	0.485288i
$767$	59.4678	+	8.55017i	2.14726	+	0.308729i
$768$	1.69058	+	0.376767i	0.0610034	+	0.0135954i
$769$	7.75415	−	6.71901i	0.279622	−	0.242294i	−0.503746	−	0.863852i	$-0.668045\pi$
$769$	7.75415	−	6.71901i	0.279622	−	0.242294i	0.783368	+	0.621558i	$0.213500\pi$
$770$	5.43677	−	3.49400i	0.195927	−	0.125915i
$771$	−1.16350	−	17.5181i	−0.0419025	−	0.630898i
$772$	−5.89251	−	6.80032i	−0.212076	−	0.244749i
$773$	22.2023	−	6.51919i	0.798562	−	0.234479i	0.143101	−	0.989708i	$-0.454293\pi$
$773$	22.2023	−	6.51919i	0.798562	−	0.234479i	0.655461	+	0.755229i	$0.272474\pi$
$774$	−7.41061	+	3.29373i	−0.266369	+	0.118391i
$775$	3.76570	−	4.34585i	0.135268	−	0.156108i
$776$	6.50877	−	14.2522i	0.233651	−	0.511625i
$777$	−14.6103	−	14.7595i	−0.524141	−	0.529493i
$778$	−3.47854	+	1.58860i	−0.124712	+	0.0569539i
$779$	−7.18402	−	49.9659i	−0.257394	−	1.79022i
$780$	−7.37659	−	13.6739i	−0.264124	−	0.489604i
$781$			37.9223i			1.35697i
$782$	−7.21168	−	22.6980i	−0.257889	−	0.811677i
$783$	7.22979	−	0.406449i	0.258372	−	0.0145253i
$784$	−0.841254	−	0.540641i	−0.0300448	−	0.0193086i
$785$	−11.5492	+	1.66053i	−0.412209	+	0.0592667i
$786$	−0.905423	+	11.8156i	−0.0322954	+	0.421449i
$787$	0.583610	−	1.98759i	0.0208034	−	0.0708500i	−0.948437	−	0.316965i	$-0.897336\pi$
$787$	0.583610	−	1.98759i	0.0208034	−	0.0708500i	0.969241	+	0.246115i	$0.0791542\pi$
$788$	−6.66625	−	3.04437i	−0.237475	−	0.108451i
$789$	−23.1185	+	8.48921i	−0.823039	+	0.302224i
$790$	0.718332	−	4.99611i	0.0255571	−	0.177754i
$791$	0.485846	+	1.65464i	0.0172747	+	0.0588322i
$792$	−12.8898	−	3.92747i	−0.458019	−	0.139557i
$793$	12.3441	+	19.2078i	0.438352	+	0.682089i
$794$	−4.08028	−	6.34905i	−0.144804	−	0.225319i
$795$	−3.36638	−	15.8626i	−0.119393	−	0.562587i
$796$	−6.39544	−	21.7809i	−0.226680	−	0.772002i
$797$	3.25518	−	22.6403i	0.115304	−	0.801960i	−0.847313	−	0.531094i	$-0.821781\pi$
$797$	3.25518	−	22.6403i	0.115304	−	0.801960i	0.962617	−	0.270866i	$-0.0873099\pi$
$798$	5.15929	+	14.0502i	0.182637	+	0.497371i
$799$	−48.0300	−	21.9346i	−1.69918	−	0.775989i
$800$	0.825408	−	2.81108i	0.0291826	−	0.0993868i
$801$	−1.08973	+	1.65837i	−0.0385039	+	0.0585956i
$802$	8.32056	−	1.19632i	0.293809	−	0.0422434i
$803$	−38.5314	−	24.7627i	−1.35975	−	0.873855i
$804$	−1.76508	+	3.19382i	−0.0622495	+	0.112637i
$805$	−2.08949	−	6.57644i	−0.0736449	−	0.231789i
$806$		−	12.2364i		−	0.431009i
$807$	36.5497	−	19.7173i	1.28661	−	0.694081i
$808$	0.0685434	+	0.476730i	0.00241135	+	0.0167713i
$809$	6.58994	−	3.00953i	0.231690	−	0.105809i	−0.296187	−	0.955130i	$-0.595715\pi$
$809$	6.58994	−	3.00953i	0.231690	−	0.105809i	0.527877	+	0.849321i	$0.322988\pi$
$810$	9.61225	+	8.67722i	0.337740	+	0.304887i
$811$	9.38734	−	20.5554i	0.329634	−	0.721798i	−0.670157	−	0.742219i	$-0.733773\pi$
$811$	9.38734	−	20.5554i	0.329634	−	0.721798i	0.999791	+	0.0204210i	$0.00650065\pi$
$812$	−0.912595	+	1.05319i	−0.0320258	+	0.0369598i
$813$	3.20968	−	4.24254i	0.112568	−	0.148792i
$814$	51.6744	−	15.1730i	1.81119	−	0.531812i
$815$	3.38397	+	3.90531i	0.118535	+	0.136797i
$816$	−8.58245	+	0.570022i	−0.300446	+	0.0199548i
$817$	−19.6514	+	12.6292i	−0.687517	+	0.441840i
$818$	−4.03701	+	3.49809i	−0.141151	+	0.122308i
$819$	12.3908	−	14.0096i	0.432969	−	0.489534i
$820$	8.31948	+	1.19616i	0.290529	+	0.0417717i
$821$	41.6724	+	36.1093i	1.45438	+	1.26022i	0.905518	+	0.424309i	$0.139483\pi$
$821$	41.6724	+	36.1093i	1.45438	+	1.26022i	0.548858	+	0.835915i	$0.315063\pi$
$822$	13.8036	+	18.6361i	0.481456	+	0.650007i
$823$	−20.2834	−	5.95575i	−0.707035	−	0.207604i	−0.0916048	−	0.995795i	$-0.529200\pi$
$823$	−20.2834	−	5.95575i	−0.707035	−	0.207604i	−0.615431	+	0.788191i	$0.711018\pi$
$824$	7.98603	+	17.4870i	0.278207	+	0.609188i
$825$	−8.07361	+	21.3149i	−0.281087	+	0.742088i
$826$	5.21009	−	8.10706i	0.181282	−	0.282081i
$827$	−7.71440			−0.268256			−0.134128	−	0.990964i	$-0.542823\pi$
$827$	−7.71440			−0.268256			−0.134128	+	0.990964i	$0.542823\pi$
$828$	−7.63416	+	12.1951i	−0.265306	+	0.423808i
$829$	−9.33101			−0.324080			−0.162040	−	0.986784i	$-0.551807\pi$
$829$	−9.33101			−0.324080			−0.162040	+	0.986784i	$0.551807\pi$
$830$	−5.16262	+	8.03320i	−0.179197	+	0.278836i
$831$	6.37529	−	16.8312i	0.221156	−	0.583867i
$832$	−2.58982	−	5.67093i	−0.0897860	−	0.196604i
$833$	4.76484	+	1.39908i	0.165092	+	0.0484753i
$834$	−7.42174	−	10.0200i	−0.256994	−	0.346964i
$835$	23.1824	+	20.0877i	0.802260	+	0.695162i
$836$	−38.4192	−	5.52385i	−1.32876	−	0.191046i
$837$	3.41806	+	9.60893i	0.118145	+	0.332133i
$838$	−26.1897	+	22.6935i	−0.904709	+	0.783935i
$839$	−31.0090	+	19.9283i	−1.07055	+	0.688000i	−0.952355	−	0.304991i	$-0.901347\pi$
$839$	−31.0090	+	19.9283i	−1.07055	+	0.688000i	−0.118193	+	0.992991i	$0.537710\pi$
$840$	−2.48665	+	0.165156i	−0.0857977	+	0.00569844i
$841$	−17.7192	−	20.4490i	−0.611007	−	0.705139i
$842$	12.2243	−	3.58939i	0.421279	−	0.123699i
$843$	−9.08901	+	12.0138i	−0.313042	+	0.413777i
$844$	−10.9148	+	12.5964i	−0.375703	+	0.433585i
$845$	−15.4608	+	33.8544i	−0.531868	+	1.16463i
$846$	8.67524	+	30.6955i	0.298261	+	1.05533i
$847$	−8.34557	+	3.81129i	−0.286757	+	0.130958i
$848$	−0.926016	−	6.44058i	−0.0317995	−	0.221170i
$849$	8.65566	−	4.66942i	0.297062	−	0.160254i
$850$			14.5492i			0.499032i
$851$	−1.26713	−	57.4895i	−0.0434366	−	1.97072i
$852$	7.07342	−	12.7990i	0.242332	−	0.438486i
$853$	9.70581	+	6.23754i	0.332320	+	0.213569i	0.696150	−	0.717896i	$-0.254895\pi$
$853$	9.70581	+	6.23754i	0.332320	+	0.213569i	−0.363830	+	0.931465i	$0.618531\pi$
$854$	3.62509	−	0.521210i	0.124048	−	0.0178354i
$855$	31.1731	+	20.4842i	1.06610	+	0.700545i
$856$	−0.863890	+	2.94214i	−0.0295271	+	0.100560i
$857$	18.8405	+	8.60415i	0.643578	+	0.293912i	0.710342	−	0.703857i	$-0.248540\pi$
$857$	18.8405	+	8.60415i	0.643578	+	0.293912i	−0.0667642	+	0.997769i	$0.521268\pi$
$858$	16.7183	+	45.5287i	0.570755	+	1.55432i
$859$	−6.25813	+	43.5262i	−0.213525	+	1.48510i	0.547737	+	0.836651i	$0.315489\pi$
$859$	−6.25813	+	43.5262i	−0.213525	+	1.48510i	−0.761262	+	0.648445i	$0.775420\pi$
$860$	−1.09579	−	3.73191i	−0.0373661	−	0.127257i
$861$	2.10046	+	9.89745i	0.0715834	+	0.337304i
$862$	17.4505	+	27.1535i	0.594367	+	0.924853i
$863$	−3.20546	−	4.98779i	−0.109115	−	0.169786i	0.782402	−	0.622774i	$-0.213994\pi$
$863$	−3.20546	−	4.98779i	−0.109115	−	0.169786i	−0.891517	+	0.452988i	$0.850358\pi$
$864$	3.61781	+	3.72980i	0.123081	+	0.126890i
$865$	−0.797187	−	2.71497i	−0.0271052	−	0.0923117i
$866$	−3.63056	+	25.2511i	−0.123372	+	0.858068i
$867$	12.4562	−	4.57398i	0.423035	−	0.155340i
$868$	−1.78538	−	0.815356i	−0.0605998	−	0.0276750i
$869$	−4.43920	+	15.1185i	−0.150590	+	0.512861i
$870$	−0.265353	+	3.46281i	−0.00899632	+	0.117400i
$871$	13.0008	−	1.86924i	0.440516	−	0.0633366i
$872$	6.61773	+	4.25296i	0.224105	+	0.144023i
$873$	39.7987	−	25.0094i	1.34698	−	0.846440i
$874$	−16.3812	+	38.0682i	−0.554103	+	1.28768i
$875$			11.4096i			0.385715i
$876$	8.38575	+	15.5446i	0.283328	+	0.525203i
$877$	−2.25024	−	15.6507i	−0.0759851	−	0.528488i	−0.991891	−	0.127094i	$-0.959435\pi$
$877$	−2.25024	−	15.6507i	−0.0759851	−	0.528488i	0.915906	−	0.401394i	$-0.131474\pi$
$878$	−7.04147	+	3.21573i	−0.237638	+	0.108526i
$879$	13.8239	+	13.9650i	0.466267	+	0.471029i
$880$	2.68470	−	5.87868i	0.0905013	−	0.198170i
$881$	−14.9481	+	17.2510i	−0.503613	+	0.581201i	−0.949452	−	0.313913i	$-0.898360\pi$
$881$	−14.9481	+	17.2510i	−0.503613	+	0.581201i	0.445838	+	0.895113i	$0.352906\pi$
$882$	−1.21846	−	2.74142i	−0.0410275	−	0.0923083i
$883$	15.7595	−	4.62741i	0.530350	−	0.155725i	−0.00558446	−	0.999984i	$-0.501778\pi$
$883$	15.7595	−	4.62741i	0.530350	−	0.155725i	0.535934	+	0.844260i	$0.319959\pi$
$884$	20.2742	+	23.3977i	0.681895	+	0.786949i
$885$	−1.59159	−	23.9636i	−0.0535008	−	0.805527i
$886$	−20.7224	+	13.3175i	−0.696181	+	0.447409i
$887$	30.1383	−	26.1149i	1.01194	−	0.876854i	0.0195312	−	0.999809i	$-0.493783\pi$
$887$	30.1383	−	26.1149i	1.01194	−	0.876854i	0.992412	+	0.122955i	$0.0392372\pi$
$888$	−20.2705	−	4.51755i	−0.680234	−	0.151599i
$889$	−5.82643	−	0.837715i	−0.195412	−	0.0280961i
$890$	−0.719265	−	0.623247i	−0.0241098	−	0.0208913i
$891$	−25.8463	−	31.0825i	−0.865882	−	1.04130i
$892$	17.6887	+	5.19388i	0.592263	+	0.173904i
$893$	38.1690	+	83.5785i	1.27728	+	2.79685i
$894$	17.8563	+	6.76357i	0.597203	+	0.226208i
$895$	4.82380	−	7.50598i	0.161242	−	0.250897i
$896$	−1.00000			−0.0334077
$897$	51.5840	−	4.56972i	1.72234	−	0.152578i
$898$	5.13533			0.171368
$899$	−1.47878	+	2.30103i	−0.0493201	+	0.0767435i
$900$	6.70063	−	5.68797i	0.223354	−	0.189599i
$901$	13.4232	+	29.3928i	0.447192	+	0.979215i
$902$	−25.1752	−	7.39212i	−0.838244	−	0.246131i
$903$	3.76241	−	2.78679i	0.125205	−	0.0927387i
$904$	1.30328	+	1.12930i	0.0433466	+	0.0375601i
$905$	7.59786	+	1.09241i	0.252561	+	0.0363128i
$906$	−3.56536	+	15.9980i	−0.118451	+	0.531498i
$907$	−39.1971	+	33.9644i	−1.30152	+	1.12777i	−0.317778	+	0.948165i	$0.602937\pi$
$907$	−39.1971	+	33.9644i	−1.30152	+	1.12777i	−0.983739	+	0.179606i	$0.942518\pi$
$908$	16.2272	−	10.4286i	0.538519	−	0.346085i
$909$	−0.613554	+	1.30816i	−0.0203503	+	0.0433888i
$910$	5.87419	+	6.77917i	0.194727	+	0.224727i
$911$	−20.0727	+	5.89386i	−0.665037	+	0.195272i	−0.596792	−	0.802396i	$-0.703558\pi$
$911$	−20.0727	+	5.89386i	−0.665037	+	0.195272i	−0.0682451	+	0.997669i	$0.521740\pi$
$912$	11.9364	+	9.03044i	0.395253	+	0.299028i
$913$	19.5211	−	22.5285i	0.646053	−	0.745584i
$914$	−5.86096	+	12.8337i	−0.193863	+	0.424502i
$915$	6.48655	−	6.42097i	0.214439	−	0.212271i
$916$	−14.8045	+	6.76100i	−0.489156	+	0.223390i
$917$	−0.973681	−	6.77210i	−0.0321538	−	0.223635i
$918$	−22.4566	−	12.7103i	−0.741178	−	0.419502i
$919$			30.3056i			0.999688i	0.866115	+	0.499844i	$0.166609\pi$
$919$			30.3056i			0.999688i	−0.866115	+	0.499844i	$0.833391\pi$
$920$	−5.31329	−	4.40279i	−0.175174	−	0.145156i
$921$	−25.0674	−	13.8536i	−0.825999	−	0.456492i
$922$	−12.1754	−	7.82464i	−0.400975	−	0.257691i
$923$	−52.0999	+	7.49083i	−1.71489	+	0.246564i
$924$	7.75698	+	0.594412i	0.255186	+	0.0195547i
$925$	−9.89690	+	33.7057i	−0.325408	+	1.10824i
$926$	−11.8944	−	5.43200i	−0.390875	−	0.178506i
$927$	−8.78725	+	56.9993i	−0.288611	+	1.87210i
$928$	−0.198326	+	1.37939i	−0.00651037	+	0.0452806i
$929$	1.18149	+	4.02377i	0.0387633	+	0.132016i	0.976601	−	0.215057i	$-0.0689938\pi$
$929$	1.18149	+	4.02377i	0.0387633	+	0.132016i	−0.937838	+	0.347073i	$0.887176\pi$
$930$	−4.78487	+	1.01546i	−0.156902	+	0.0332981i
$931$	−4.67194	−	7.26968i	−0.153117	−	0.238254i
$932$	−2.42138	−	3.76774i	−0.0793150	−	0.123417i
$933$	52.4086	−	11.1223i	1.71578	−	0.364126i
$934$	8.75870	+	29.8294i	0.286593	+	0.976047i
$935$	−4.56741	+	31.7671i	−0.149370	+	1.03889i
$936$	2.84965	−	18.4846i	0.0931439	−	0.604187i
$937$	−26.5256	−	12.1138i	−0.866553	−	0.395741i	−0.0680138	−	0.997684i	$-0.521666\pi$
$937$	−26.5256	−	12.1138i	−0.866553	−	0.395741i	−0.798539	+	0.601943i	$0.794393\pi$
$938$	0.593557	−	2.02147i	0.0193803	−	0.0660033i
$939$	22.0213	+	1.68748i	0.718636	+	0.0550687i
$940$	−15.1428	+	2.17721i	−0.493905	+	0.0710129i
$941$	42.8532	+	27.5401i	1.39697	+	0.897781i	0.999801	−	0.0199626i	$-0.00635473\pi$
$941$	42.8532	+	27.5401i	1.39697	+	0.897781i	0.397174	+	0.917744i	$0.369991\pi$
$942$	−12.2933	−	6.79396i	−0.400538	−	0.221359i
$943$	−14.6231	+	23.8959i	−0.476194	+	0.778156i
$944$		−	9.63688i		−	0.313654i
$945$	−6.50651	−	3.68264i	−0.211657	−	0.119796i
$946$	1.72795	+	12.0182i	0.0561807	+	0.390745i
$947$	−36.7712	+	16.7929i	−1.19490	+	0.545695i	−0.910700	−	0.413069i	$-0.864457\pi$
$947$	−36.7712	+	16.7929i	−1.19490	+	0.545695i	−0.284205	+	0.958764i	$0.591730\pi$
$948$	4.31822	−	4.27457i	0.140249	−	0.138832i
$949$	26.4092	−	57.8281i	0.857280	−	1.87718i
$950$	16.5794	−	19.1337i	0.537907	−	0.620778i
$951$	41.2226	+	31.1869i	1.33673	+	1.01130i
$952$	4.76484	−	1.39908i	0.154429	−	0.0453445i
$953$	3.66254	+	4.22680i	0.118641	+	0.136919i	0.811963	−	0.583709i	$-0.198399\pi$
$953$	3.66254	+	4.22680i	0.118641	+	0.136919i	−0.693322	+	0.720628i	$0.743854\pi$
$954$	8.28907	−	17.6731i	0.268368	−	0.572188i
$955$	−28.1147	+	18.0683i	−0.909772	+	0.584675i
$956$	−10.1793	+	8.82044i	−0.329223	+	0.285273i
$957$	2.35833	−	10.5820i	0.0762341	−	0.342067i
$958$	14.7048	+	2.11423i	0.475089	+	0.0683075i
$959$	−10.1192	−	8.76831i	−0.326765	−	0.283143i
$960$	−2.00262	+	1.48333i	−0.0646342	+	0.0478741i
$961$	26.0479	+	7.64836i	0.840256	+	0.246721i
$962$	31.0528	+	67.9961i	1.00118	+	2.19228i
$963$	−7.01302	+	5.95315i	−0.225991	+	0.191837i
$964$	1.76284	−	2.74304i	0.0567773	−	0.0883473i
$965$	12.9468			0.416772
$966$	2.77048	−	7.83099i	0.0891387	−	0.251958i
$967$	52.1063			1.67562			0.837812	−	0.545959i	$-0.183834\pi$
$967$	52.1063			1.67562			0.837812	+	0.545959i	$0.183834\pi$
$968$	−4.96020	+	7.71822i	−0.159427	+	0.248073i
$969$	−69.5092	−	26.3286i	−2.23296	−	0.845797i
$970$	9.36503	+	20.5066i	0.300693	+	0.658426i
$971$	17.5167	+	5.14336i	0.562136	+	0.165058i	0.550442	−	0.834873i	$-0.314459\pi$
$971$	17.5167	+	5.14336i	0.562136	+	0.165058i	0.0116945	+	0.999932i	$0.496277\pi$
$972$	2.92563	+	15.3115i	0.0938397	+	0.491115i
$973$	5.44074	+	4.71443i	0.174422	+	0.151138i
$974$	−38.2416	−	5.49831i	−1.22534	−	0.176177i
$975$	−30.8784	−	6.88165i	−0.988900	−	0.220389i
$976$	2.76783	−	2.39834i	0.0885962	−	0.0767691i
$977$	−10.1321	+	6.51152i	−0.324156	+	0.208322i	−0.692590	−	0.721332i	$-0.743530\pi$
$977$	−10.1321	+	6.51152i	−0.324156	+	0.208322i	0.368434	+	0.929654i	$0.379894\pi$
$978$	0.412242	+	6.20686i	0.0131820	+	0.198474i
$979$	1.94560	+	2.24534i	0.0621815	+	0.0717613i
$980$	1.38055	−	0.405366i	0.0441001	−	0.0129489i
$981$	9.58499	+	21.5654i	0.306025	+	0.688530i
$982$	8.19234	−	9.45447i	0.261428	−	0.301704i
$983$	0.778465	−	1.70460i	0.0248292	−	0.0543683i	−0.896811	−	0.442414i	$-0.854122\pi$
$983$	0.778465	−	1.70460i	0.0248292	−	0.0543683i	0.921640	+	0.388045i	$0.126850\pi$
$984$	7.11798	+	7.19067i	0.226913	+	0.229230i
$985$	9.59162	−	4.38035i	0.305614	−	0.139569i
$986$	−0.984886	−	6.85003i	−0.0313652	−	0.218149i
$987$	−8.74374	−	16.2082i	−0.278316	−	0.515912i
$988$		−	53.8737i		−	1.71395i
$989$	12.8697	+	1.56177i	0.409233	+	0.0496615i
$990$	16.4160	−	10.3157i	0.521733	−	0.327856i
$991$	−1.88052	−	1.20854i	−0.0597367	−	0.0383905i	0.510432	−	0.859918i	$-0.329486\pi$
$991$	−1.88052	−	1.20854i	−0.0597367	−	0.0383905i	−0.570168	+	0.821528i	$0.693122\pi$
$992$	−1.94277	+	0.279329i	−0.0616831	+	0.00886869i
$993$	4.47582	−	58.4086i	0.142036	−	1.85354i
$994$	−2.37864	+	8.10090i	−0.0754459	+	0.256945i
$995$	29.7105	+	13.5683i	0.941885	+	0.430145i
$996$	−10.7906	+	3.96235i	−0.341912	+	0.125552i
$997$	−1.32455	+	9.21243i	−0.0419488	+	0.291760i	0.958038	+	0.286641i	$0.0925387\pi$
$997$	−1.32455	+	9.21243i	−0.0419488	+	0.291760i	−0.999987	+	0.00511950i	$0.998370\pi$
$998$	−8.58498	−	29.2377i	−0.271753	−	0.925505i
$999$	−43.3787	−	44.7215i	−1.37244	−	1.41492i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.r.b.113.17	yes	240
3.2	odd	2		966.2.r.a.113.10	✓	240
23.11	odd	22		966.2.r.a.701.10	yes	240
69.11	even	22	inner	966.2.r.b.701.17	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.r.a.113.10	✓	240	3.2	odd	2
966.2.r.a.701.10	yes	240	23.11	odd	22
966.2.r.b.113.17	yes	240	1.1	even	1	trivial
966.2.r.b.701.17	yes	240	69.11	even	22	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.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.540641 - 0.841254i) q^{2} +(-0.613526 + 1.61975i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(1.38055 + 0.405366i) q^{5} +(1.03092 + 1.39183i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(-2.24717 - 1.98752i) q^{9} +O(q^{10})\)	\(q+(0.540641 - 0.841254i) q^{2} +(-0.613526 + 1.61975i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(1.38055 + 0.405366i) q^{5} +(1.03092 + 1.39183i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(-0.989821 - 0.142315i) q^{8} +(-2.24717 - 1.98752i) q^{9} +(1.08740 - 0.942236i) q^{10} +(-3.77859 + 2.42835i) q^{11} +(1.72824 - 0.114785i) q^{12} +(-4.08260 - 4.71158i) q^{13} +(-0.959493 + 0.281733i) q^{14} +(-1.50360 + 1.98744i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(2.06295 - 4.51723i) q^{17} +(-2.88692 + 0.815909i) q^{18} +(-7.86057 + 3.58980i) q^{19} +(-0.204767 - 1.42419i) q^{20} +(1.52438 - 0.822350i) q^{21} +4.49162i q^{22} +(4.63022 + 1.24942i) q^{23} +(0.837796 - 1.51595i) q^{24} +(-2.46467 - 1.58395i) q^{25} +(-6.17085 + 0.887234i) q^{26} +(4.59797 - 2.42046i) q^{27} +(-0.281733 + 0.959493i) q^{28} +(1.26764 + 0.578911i) q^{29} +(0.859038 + 2.33940i) q^{30} +(-0.279329 + 1.94277i) q^{31} +(0.281733 + 0.959493i) q^{32} +(-1.61506 - 7.61023i) q^{33} +(-2.68482 - 4.17766i) q^{34} +(-0.777892 - 1.21042i) q^{35} +(-0.874399 + 2.86974i) q^{36} +(-3.37806 - 11.5046i) q^{37} +(-1.22981 + 8.55353i) q^{38} +(10.1364 - 3.72212i) q^{39} +(-1.30881 - 0.597713i) q^{40} +(-1.64576 + 5.60494i) q^{41} +(0.132338 - 1.72699i) q^{42} +(2.67569 - 0.384706i) q^{43} +(3.77859 + 2.42835i) q^{44} +(-2.29666 - 3.65479i) q^{45} +(3.55436 - 3.21971i) q^{46} -10.6326i q^{47} +(-0.822350 - 1.52438i) q^{48} +(0.142315 + 0.989821i) q^{49} +(-2.66500 + 1.21707i) q^{50} +(6.05110 + 6.11290i) q^{51} +(-2.58982 + 5.67093i) q^{52} +(-4.26105 + 4.91752i) q^{53} +(0.449632 - 5.17666i) q^{54} +(-6.20091 + 1.82075i) q^{55} +(0.654861 + 0.755750i) q^{56} +(-0.991913 - 14.9346i) q^{57} +(1.17235 - 0.753422i) q^{58} +(-7.28307 + 6.31082i) q^{59} +(2.43246 + 0.542105i) q^{60} +(-3.62509 - 0.521210i) q^{61} +(1.48335 + 1.28533i) q^{62} +(0.396753 + 2.97365i) q^{63} +(0.959493 + 0.281733i) q^{64} +(-3.72633 - 8.15952i) q^{65} +(-7.27530 - 2.75573i) q^{66} +(-1.13903 + 1.77236i) q^{67} -4.96600 q^{68} +(-4.86450 + 6.73325i) q^{69} -1.43883 q^{70} +(4.56458 - 7.10262i) q^{71} +(1.94145 + 2.28709i) q^{72} +(4.23611 + 9.27579i) q^{73} +(-11.5046 - 3.37806i) q^{74} +(4.07773 - 3.02035i) q^{75} +(6.53080 + 5.65897i) q^{76} +(4.44590 + 0.639224i) q^{77} +(2.34888 - 10.5396i) q^{78} +(2.65120 - 2.29728i) q^{79} +(-1.21042 + 0.777892i) q^{80} +(1.09956 + 8.93258i) q^{81} +(3.82541 + 4.41476i) q^{82} +(-6.36785 + 1.86977i) q^{83} +(-1.38129 - 1.04501i) q^{84} +(4.67914 - 5.40001i) q^{85} +(1.12295 - 2.45892i) q^{86} +(-1.71542 + 1.69808i) q^{87} +(4.08572 - 1.86589i) q^{88} +(-0.0941349 - 0.654723i) q^{89} +(-4.31628 - 0.0438558i) q^{90} +6.23431i q^{91} +(-0.786956 - 4.73082i) q^{92} +(-2.97543 - 1.64438i) q^{93} +(-8.94473 - 5.74843i) q^{94} +(-12.3071 + 1.76949i) q^{95} +(-1.72699 - 0.132338i) q^{96} +(-4.41422 + 15.0334i) q^{97} +(0.909632 + 0.415415i) q^{98} +(13.3175 + 2.05309i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{3} + 24 q^{4} + 4 q^{5} + 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^3 + 24 * q^4 + 4 * q^5 + 4 * q^9	\( 240 q - 4 q^{3} + 24 q^{4} + 4 q^{5} + 4 q^{9} + 4 q^{12} - 8 q^{13} - 24 q^{14} + 26 q^{15} - 24 q^{16} - 32 q^{17} + 40 q^{18} - 4 q^{20} + 8 q^{23} + 12 q^{25} + 116 q^{27} + 4 q^{30} + 16 q^{31} + 2 q^{33} - 4 q^{36} + 22 q^{37} + 8 q^{39} - 154 q^{41} - 4 q^{42} + 22 q^{43} - 24 q^{45} + 4 q^{46} - 4 q^{48} + 24 q^{49} - 88 q^{50} - 24 q^{51} + 8 q^{52} + 108 q^{53} + 12 q^{54} - 16 q^{55} + 24 q^{56} - 70 q^{57} - 4 q^{58} - 22 q^{59} - 26 q^{60} + 4 q^{63} + 24 q^{64} - 76 q^{66} - 44 q^{67} + 32 q^{68} - 86 q^{69} + 4 q^{70} + 4 q^{72} - 12 q^{73} + 16 q^{74} - 26 q^{75} - 78 q^{78} + 4 q^{80} - 168 q^{81} + 8 q^{82} - 16 q^{83} - 28 q^{85} - 16 q^{86} + 156 q^{87} - 24 q^{89} - 126 q^{90} - 8 q^{92} - 16 q^{93} - 8 q^{94} + 132 q^{97} - 172 q^{99}+O(q^{100}) \) 240 * q - 4 * q^3 + 24 * q^4 + 4 * q^5 + 4 * q^9 + 4 * q^12 - 8 * q^13 - 24 * q^14 + 26 * q^15 - 24 * q^16 - 32 * q^17 + 40 * q^18 - 4 * q^20 + 8 * q^23 + 12 * q^25 + 116 * q^27 + 4 * q^30 + 16 * q^31 + 2 * q^33 - 4 * q^36 + 22 * q^37 + 8 * q^39 - 154 * q^41 - 4 * q^42 + 22 * q^43 - 24 * q^45 + 4 * q^46 - 4 * q^48 + 24 * q^49 - 88 * q^50 - 24 * q^51 + 8 * q^52 + 108 * q^53 + 12 * q^54 - 16 * q^55 + 24 * q^56 - 70 * q^57 - 4 * q^58 - 22 * q^59 - 26 * q^60 + 4 * q^63 + 24 * q^64 - 76 * q^66 - 44 * q^67 + 32 * q^68 - 86 * q^69 + 4 * q^70 + 4 * q^72 - 12 * q^73 + 16 * q^74 - 26 * q^75 - 78 * q^78 + 4 * q^80 - 168 * q^81 + 8 * q^82 - 16 * q^83 - 28 * q^85 - 16 * q^86 + 156 * q^87 - 24 * q^89 - 126 * q^90 - 8 * q^92 - 16 * q^93 - 8 * q^94 + 132 * q^97 - 172 * q^99

Introduction

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