LMFDB - Embedded newform 966.2.y.b.25.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(25,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 6]))

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

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

chi := DirichletCharacter("966.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.y (of order $33$, degree $20$, 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:	$160$
Relative dimension:	$8$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			25.4
Character	$\chi$	$=$	966.25
Dual form			966.2.y.b.541.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0475819 + 0.998867i) q^{2} +(0.928368 + 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(0.0842779 + 0.347398i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(0.863387 - 2.50091i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +O(q^{10})$	\(q+(-0.0475819 + 0.998867i) q^{2} +(0.928368 + 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(0.0842779 + 0.347398i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(0.863387 - 2.50091i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +(-0.351015 + 0.0676526i) q^{10} +(0.312736 + 6.56513i) q^{11} +(-0.888835 - 0.458227i) q^{12} +(-3.08311 - 3.55809i) q^{13} +(2.45700 + 0.981408i) q^{14} +(-0.0508740 + 0.353836i) q^{15} +(0.981929 + 0.189251i) q^{16} +(2.42855 + 3.41042i) q^{17} +(-0.723734 + 0.690079i) q^{18} +(-4.10985 + 5.77148i) q^{19} +(-0.0508740 - 0.353836i) q^{20} +(1.73104 - 2.00088i) q^{21} -6.57258 q^{22} +(3.98660 + 2.66590i) q^{23} +(0.500000 - 0.866025i) q^{24} +(4.33059 - 2.23258i) q^{25} +(3.70076 - 2.91031i) q^{26} +(0.415415 + 0.909632i) q^{27} +(-1.09720 + 2.40752i) q^{28} +(1.12567 - 2.46486i) q^{29} +(-0.351015 - 0.0676526i) q^{30} +(4.04472 + 3.18080i) q^{31} +(-0.235759 + 0.971812i) q^{32} +(-2.14968 + 6.21109i) q^{33} +(-3.52211 + 2.26352i) q^{34} +(0.941577 + 0.0891676i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(8.32621 + 7.93903i) q^{37} +(-5.56939 - 4.37982i) q^{38} +(-1.53985 - 4.44910i) q^{39} +(0.355856 - 0.0339801i) q^{40} +(2.74531 + 0.806094i) q^{41} +(1.91625 + 1.82428i) q^{42} +(0.545147 + 3.79158i) q^{43} +(0.312736 - 6.56513i) q^{44} +(-0.178737 + 0.309582i) q^{45} +(-2.85257 + 3.85523i) q^{46} +(-0.221595 - 0.383813i) q^{47} +(0.841254 + 0.540641i) q^{48} +(-5.50912 - 4.31851i) q^{49} +(2.02399 + 4.43192i) q^{50} +(0.987062 + 4.06872i) q^{51} +(2.73093 + 3.83505i) q^{52} +(-0.237587 - 0.686463i) q^{53} +(-0.928368 + 0.371662i) q^{54} +(-2.25436 + 0.661939i) q^{55} +(-2.35258 - 1.21052i) q^{56} +(-5.96050 + 3.83058i) q^{57} +(2.40851 + 1.24167i) q^{58} +(-2.17722 + 0.419625i) q^{59} +(0.0842779 - 0.347398i) q^{60} +(-3.83511 + 1.53535i) q^{61} +(-3.36966 + 3.88879i) q^{62} +(2.35069 - 1.21419i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(0.976238 - 1.37093i) q^{65} +(-6.10177 - 2.44278i) q^{66} +(-0.284864 + 0.146857i) q^{67} +(-2.09337 - 3.62582i) q^{68} +(2.71021 + 3.95661i) q^{69} +(-0.133869 + 0.936268i) q^{70} +(-11.5116 - 7.39804i) q^{71} +(0.786053 - 0.618159i) q^{72} +(-12.2744 - 1.17206i) q^{73} +(-8.32621 + 7.93903i) q^{74} +(4.85015 - 0.463133i) q^{75} +(4.63986 - 5.35468i) q^{76} +(16.6888 + 4.88613i) q^{77} +(4.51732 - 1.32641i) q^{78} +(5.15608 - 14.8975i) q^{79} +(0.0170093 + 0.357070i) q^{80} +(0.0475819 + 0.998867i) q^{81} +(-0.935808 + 2.70384i) q^{82} +(8.65945 - 2.54264i) q^{83} +(-1.91339 + 1.82727i) q^{84} +(-0.980100 + 1.13110i) q^{85} +(-3.81322 + 0.364119i) q^{86} +(1.96113 - 1.86993i) q^{87} +(6.54282 + 0.624763i) q^{88} +(-9.98511 + 7.85237i) q^{89} +(-0.300727 - 0.193265i) q^{90} +(-11.5604 + 4.63856i) q^{91} +(-3.71514 - 3.03278i) q^{92} +(2.57280 + 4.45623i) q^{93} +(0.393922 - 0.203081i) q^{94} +(-2.35137 - 0.941347i) q^{95} +(-0.580057 + 0.814576i) q^{96} +(4.48578 + 1.31714i) q^{97} +(4.57576 - 5.29740i) q^{98} +(-4.30412 + 4.96722i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 8 q^{2} + 8 q^{3} + 8 q^{4} + 6 q^{5} + 16 q^{6} - 10 q^{7} + 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 + 6 * q^5 + 16 * q^6 - 10 * q^7 + 16 * q^8 + 8 * q^9	\( 160 q - 8 q^{2} + 8 q^{3} + 8 q^{4} + 6 q^{5} + 16 q^{6} - 10 q^{7} + 16 q^{8} + 8 q^{9} - 6 q^{10} + 8 q^{11} + 8 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 8 q^{16} + 9 q^{17} - 8 q^{18} - 8 q^{19} + 10 q^{20} - 3 q^{21} - 28 q^{22} + 22 q^{23} + 80 q^{24} + 46 q^{25} + 2 q^{26} - 16 q^{27} - 14 q^{28} + 62 q^{29} - 6 q^{30} + 7 q^{31} - 8 q^{32} - 14 q^{33} - 4 q^{34} + 24 q^{35} - 16 q^{36} + 15 q^{37} + 19 q^{38} - 2 q^{39} + 5 q^{40} - 14 q^{41} + 10 q^{42} - 56 q^{43} + 8 q^{44} - 16 q^{45} + 66 q^{47} - 16 q^{48} + 42 q^{49} + 4 q^{50} + 9 q^{51} - 2 q^{52} + 12 q^{53} - 8 q^{54} - 14 q^{55} + 10 q^{56} - 6 q^{57} - 13 q^{58} + 62 q^{59} + 6 q^{60} + 16 q^{61} - 8 q^{62} + 2 q^{63} - 16 q^{64} + 70 q^{65} - 8 q^{66} - 14 q^{67} - 46 q^{68} + 22 q^{69} + 24 q^{70} - 108 q^{71} - 8 q^{72} + 40 q^{73} - 15 q^{74} + 2 q^{75} + 16 q^{76} + 29 q^{77} + 18 q^{78} + 22 q^{79} + 6 q^{80} + 8 q^{81} - 7 q^{82} - 18 q^{83} - 9 q^{84} + 26 q^{85} - 6 q^{86} + 2 q^{87} + 3 q^{88} + 112 q^{89} + 12 q^{90} + 18 q^{91} - 66 q^{92} - 26 q^{93} + 23 q^{95} - 8 q^{96} + 8 q^{97} + 9 q^{98} + 28 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 + 6 * q^5 + 16 * q^6 - 10 * q^7 + 16 * q^8 + 8 * q^9 - 6 * q^10 + 8 * q^11 + 8 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 8 * q^16 + 9 * q^17 - 8 * q^18 - 8 * q^19 + 10 * q^20 - 3 * q^21 - 28 * q^22 + 22 * q^23 + 80 * q^24 + 46 * q^25 + 2 * q^26 - 16 * q^27 - 14 * q^28 + 62 * q^29 - 6 * q^30 + 7 * q^31 - 8 * q^32 - 14 * q^33 - 4 * q^34 + 24 * q^35 - 16 * q^36 + 15 * q^37 + 19 * q^38 - 2 * q^39 + 5 * q^40 - 14 * q^41 + 10 * q^42 - 56 * q^43 + 8 * q^44 - 16 * q^45 + 66 * q^47 - 16 * q^48 + 42 * q^49 + 4 * q^50 + 9 * q^51 - 2 * q^52 + 12 * q^53 - 8 * q^54 - 14 * q^55 + 10 * q^56 - 6 * q^57 - 13 * q^58 + 62 * q^59 + 6 * q^60 + 16 * q^61 - 8 * q^62 + 2 * q^63 - 16 * q^64 + 70 * q^65 - 8 * q^66 - 14 * q^67 - 46 * q^68 + 22 * q^69 + 24 * q^70 - 108 * q^71 - 8 * q^72 + 40 * q^73 - 15 * q^74 + 2 * q^75 + 16 * q^76 + 29 * q^77 + 18 * q^78 + 22 * q^79 + 6 * q^80 + 8 * q^81 - 7 * q^82 - 18 * q^83 - 9 * q^84 + 26 * q^85 - 6 * q^86 + 2 * q^87 + 3 * q^88 + 112 * q^89 + 12 * q^90 + 18 * q^91 - 66 * q^92 - 26 * q^93 + 23 * q^95 - 8 * q^96 + 8 * q^97 + 9 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{11}\right)$

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 $

$2$	−0.0475819	+	0.998867i	−0.0336455	+	0.706306i
$2$	−0.0475819	+	0.998867i	−0.0336455	+	0.706306i
$3$	0.928368	+	0.371662i	0.535993	+	0.214579i
$3$	0.928368	+	0.371662i	0.535993	+	0.214579i
$4$	−0.995472	−	0.0950560i	−0.497736	−	0.0475280i
$5$	0.0842779	+	0.347398i	0.0376902	+	0.155361i	0.987547	−	0.157324i	$-0.0502867\pi$
$5$	0.0842779	+	0.347398i	0.0376902	+	0.155361i	−0.949857	+	0.312685i	$0.898772\pi$
$6$	−0.415415	+	0.909632i	−0.169592	+	0.371356i
$7$	0.863387	−	2.50091i	0.326330	−	0.945256i
$7$	0.863387	−	2.50091i	0.326330	−	0.945256i
$8$	0.142315	−	0.989821i	0.0503159	−	0.349955i
$9$	0.723734	+	0.690079i	0.241245	+	0.230026i
$10$	−0.351015	+	0.0676526i	−0.111001	+	0.0213936i
$11$	0.312736	+	6.56513i	0.0942934	+	1.97946i	0.181937	+	0.983310i	$0.441763\pi$
$11$	0.312736	+	6.56513i	0.0942934	+	1.97946i	−0.0876433	+	0.996152i	$0.527934\pi$
$12$	−0.888835	−	0.458227i	−0.256585	−	0.132279i
$13$	−3.08311	−	3.55809i	−0.855100	−	0.986838i	0.144897	−	0.989447i	$-0.453715\pi$
$13$	−3.08311	−	3.55809i	−0.855100	−	0.986838i	−0.999997	+	0.00260901i	$0.999170\pi$
$14$	2.45700	+	0.981408i	0.656660	+	0.262292i
$15$	−0.0508740	+	0.353836i	−0.0131356	+	0.0913601i
$16$	0.981929	+	0.189251i	0.245482	+	0.0473128i
$17$	2.42855	+	3.41042i	0.589009	+	0.827148i	0.996281	−	0.0861589i	$-0.0274593\pi$
$17$	2.42855	+	3.41042i	0.589009	+	0.827148i	−0.407272	+	0.913307i	$0.633520\pi$
$18$	−0.723734	+	0.690079i	−0.170586	+	0.162653i
$19$	−4.10985	+	5.77148i	−0.942865	+	1.32407i	0.00316711	+	0.999995i	$0.498992\pi$
$19$	−4.10985	+	5.77148i	−0.942865	+	1.32407i	−0.946032	+	0.324073i	$0.894948\pi$
$20$	−0.0508740	−	0.353836i	−0.0113758	−	0.0791202i
$21$	1.73104	−	2.00088i	0.377743	−	0.436627i
$22$	−6.57258			−1.40128
$23$	3.98660	+	2.66590i	0.831263	+	0.555879i
$23$	3.98660	+	2.66590i	0.831263	+	0.555879i
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	4.33059	−	2.23258i	0.866119	−	0.446515i
$26$	3.70076	−	2.91031i	0.725780	−	0.570759i
$27$	0.415415	+	0.909632i	0.0799467	+	0.175059i
$28$	−1.09720	+	2.40752i	−0.207352	+	0.454978i
$29$	1.12567	−	2.46486i	0.209031	−	0.457713i	−0.775857	−	0.630909i	$-0.782682\pi$
$29$	1.12567	−	2.46486i	0.209031	−	0.457713i	0.984887	+	0.173196i	$0.0554093\pi$
$30$	−0.351015	−	0.0676526i	−0.0640862	−	0.0123516i
$31$	4.04472	+	3.18080i	0.726453	+	0.571289i	0.911431	−	0.411453i	$-0.134979\pi$
$31$	4.04472	+	3.18080i	0.726453	+	0.571289i	−0.184977	+	0.982743i	$0.559221\pi$
$32$	−0.235759	+	0.971812i	−0.0416767	+	0.171794i
$33$	−2.14968	+	6.21109i	−0.374211	+	1.08121i
$34$	−3.52211	+	2.26352i	−0.604037	+	0.388191i
$35$	0.941577	+	0.0891676i	0.159156	+	0.0150721i
$36$	−0.654861	−	0.755750i	−0.109143	−	0.125958i
$37$	8.32621	+	7.93903i	1.36882	+	1.30517i	0.908783	+	0.417269i	$0.137013\pi$
$37$	8.32621	+	7.93903i	1.36882	+	1.30517i	0.460038	+	0.887899i	$0.347836\pi$
$38$	−5.56939	−	4.37982i	−0.903474	−	0.710500i
$39$	−1.53985	−	4.44910i	−0.246573	−	0.712425i
$40$	0.355856	−	0.0339801i	0.0562658	−	0.00537273i
$41$	2.74531	+	0.806094i	0.428745	+	0.125891i	0.488983	−	0.872293i	$-0.337368\pi$
$41$	2.74531	+	0.806094i	0.428745	+	0.125891i	−0.0602385	+	0.998184i	$0.519186\pi$
$42$	1.91625	+	1.82428i	0.295683	+	0.281493i
$43$	0.545147	+	3.79158i	0.0831341	+	0.578210i	0.988227	+	0.152996i	$0.0488922\pi$
$43$	0.545147	+	3.79158i	0.0831341	+	0.578210i	−0.905093	+	0.425214i	$0.860199\pi$
$44$	0.312736	−	6.56513i	0.0471467	−	0.989731i
$45$	−0.178737	+	0.309582i	−0.0266446	+	0.0461498i
$46$	−2.85257	+	3.85523i	−0.420589	+	0.568423i
$47$	−0.221595	−	0.383813i	−0.0323229	−	0.0559849i	0.849411	−	0.527731i	$-0.176957\pi$
$47$	−0.221595	−	0.383813i	−0.0323229	−	0.0559849i	−0.881734	+	0.471746i	$0.843624\pi$
$48$	0.841254	+	0.540641i	0.121424	+	0.0780348i
$49$	−5.50912	−	4.31851i	−0.787018	−	0.616930i
$50$	2.02399	+	4.43192i	0.286235	+	0.626768i
$51$	0.987062	+	4.06872i	0.138216	+	0.569735i
$52$	2.73093	+	3.83505i	0.378711	+	0.531826i
$53$	−0.237587	−	0.686463i	−0.0326351	−	0.0942930i	0.927506	−	0.373807i	$-0.121948\pi$
$53$	−0.237587	−	0.686463i	−0.0326351	−	0.0942930i	−0.960142	+	0.279514i	$0.909827\pi$
$54$	−0.928368	+	0.371662i	−0.126335	+	0.0505769i
$55$	−2.25436	+	0.661939i	−0.303978	+	0.0892559i
$56$	−2.35258	−	1.21052i	−0.314377	−	0.161762i
$57$	−5.96050	+	3.83058i	−0.789487	+	0.507373i
$58$	2.40851	+	1.24167i	0.316253	+	0.163040i
$59$	−2.17722	+	0.419625i	−0.283450	+	0.0546305i	−0.328995	−	0.944332i	$-0.606710\pi$
$59$	−2.17722	+	0.419625i	−0.283450	+	0.0546305i	0.0455447	+	0.998962i	$0.485498\pi$
$60$	0.0842779	−	0.347398i	0.0108802	−	0.0448489i
$61$	−3.83511	+	1.53535i	−0.491036	+	0.196581i	−0.603948	−	0.797024i	$-0.706406\pi$
$61$	−3.83511	+	1.53535i	−0.491036	+	0.196581i	0.112912	+	0.993605i	$0.463982\pi$
$62$	−3.36966	+	3.88879i	−0.427947	+	0.493877i
$63$	2.35069	−	1.21419i	0.296159	−	0.152974i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	0.976238	−	1.37093i	0.121087	−	0.170043i
$66$	−6.10177	−	2.44278i	−0.751076	−	0.300685i
$67$	−0.284864	+	0.146857i	−0.0348016	+	0.0179415i	−0.475540	−	0.879694i	$-0.657747\pi$
$67$	−0.284864	+	0.146857i	−0.0348016	+	0.0179415i	0.440738	+	0.897636i	$0.354717\pi$
$68$	−2.09337	−	3.62582i	−0.253858	−	0.439696i
$69$	2.71021	+	3.95661i	0.326272	+	0.476319i
$70$	−0.133869	+	0.936268i	−0.0160004	+	0.111905i
$71$	−11.5116	−	7.39804i	−1.36617	−	0.877986i	−0.367527	−	0.930013i	$-0.619795\pi$
$71$	−11.5116	−	7.39804i	−1.36617	−	0.877986i	−0.998646	+	0.0520270i	$0.983432\pi$
$72$	0.786053	−	0.618159i	0.0926372	−	0.0728507i
$73$	−12.2744	−	1.17206i	−1.43661	−	0.137179i	−0.652493	−	0.757795i	$-0.726277\pi$
$73$	−12.2744	−	1.17206i	−1.43661	−	0.137179i	−0.784115	+	0.620615i	$0.786883\pi$
$74$	−8.32621	+	7.93903i	−0.967903	+	0.922893i
$75$	4.85015	−	0.463133i	0.560047	−	0.0534780i
$76$	4.63986	−	5.35468i	0.532228	−	0.614224i
$77$	16.6888	+	4.88613i	1.90187	+	0.556826i
$78$	4.51732	−	1.32641i	0.511486	−	0.150186i
$79$	5.15608	−	14.8975i	0.580104	−	1.67610i	−0.146639	−	0.989190i	$-0.546846\pi$
$79$	5.15608	−	14.8975i	0.580104	−	1.67610i	0.726743	−	0.686910i	$-0.241033\pi$
$80$	0.0170093	+	0.357070i	0.00190170	+	0.0399216i
$81$	0.0475819	+	0.998867i	0.00528688	+	0.110985i
$82$	−0.935808	+	2.70384i	−0.103343	+	0.298589i
$83$	8.65945	−	2.54264i	0.950498	−	0.279092i	0.230504	−	0.973071i	$-0.425963\pi$
$83$	8.65945	−	2.54264i	0.950498	−	0.279092i	0.719994	+	0.693980i	$0.244144\pi$
$84$	−1.91339	+	1.82727i	−0.208768	+	0.199372i
$85$	−0.980100	+	1.13110i	−0.106307	+	0.122685i
$86$	−3.81322	+	0.364119i	−0.411190	+	0.0392639i
$87$	1.96113	−	1.86993i	0.210255	−	0.200478i
$88$	6.54282	+	0.624763i	0.697467	+	0.0666000i
$89$	−9.98511	+	7.85237i	−1.05842	+	0.832350i	−0.986286	−	0.165045i	$-0.947223\pi$
$89$	−9.98511	+	7.85237i	−1.05842	+	0.832350i	−0.0721331	+	0.997395i	$0.522981\pi$
$90$	−0.300727	−	0.193265i	−0.0316994	−	0.0203720i
$91$	−11.5604	+	4.63856i	−1.21186	+	0.486254i
$92$	−3.71514	−	3.03278i	−0.387330	−	0.316189i
$93$	2.57280	+	4.45623i	0.266787	+	0.462089i
$94$	0.393922	−	0.203081i	0.0406300	−	0.0209462i
$95$	−2.35137	−	0.941347i	−0.241246	−	0.0965802i
$96$	−0.580057	+	0.814576i	−0.0592018	+	0.0831373i
$97$	4.48578	+	1.31714i	0.455462	+	0.133736i	0.501413	−	0.865208i	$-0.332814\pi$
$97$	4.48578	+	1.31714i	0.455462	+	0.133736i	−0.0459514	+	0.998944i	$0.514632\pi$
$98$	4.57576	−	5.29740i	0.462221	−	0.535118i
$99$	−4.30412	+	4.96722i	−0.432581	+	0.499225i
$100$	−4.52321	+	1.81082i	−0.452321	+	0.181082i
$101$	3.61047	−	14.8825i	0.359255	−	1.48087i	−0.449797	−	0.893131i	$-0.648504\pi$
$101$	3.61047	−	14.8825i	0.359255	−	1.48087i	0.809052	−	0.587737i	$-0.199981\pi$
$102$	−4.11108	+	0.792346i	−0.407058	+	0.0784539i
$103$	−10.2811	−	5.30028i	−1.01303	−	0.522252i	−0.129971	−	0.991518i	$-0.541488\pi$
$103$	−10.2811	−	5.30028i	−1.01303	−	0.522252i	−0.883057	+	0.469266i	$0.844519\pi$
$104$	−3.96065	+	2.54535i	−0.388374	+	0.249593i
$105$	0.840989	+	0.432729i	0.0820722	+	0.0422300i
$106$	0.696991	−	0.204655i	0.0676977	−	0.0198778i
$107$	7.09087	−	2.83876i	0.685501	−	0.274433i	−0.00265472	−	0.999996i	$-0.500845\pi$
$107$	7.09087	−	2.83876i	0.685501	−	0.274433i	0.688155	+	0.725563i	$0.258421\pi$
$108$	−0.327068	−	0.945001i	−0.0314721	−	0.0909327i
$109$	−2.31772	−	3.25478i	−0.221997	−	0.311751i	0.688524	−	0.725213i	$-0.258259\pi$
$109$	−2.31772	−	3.25478i	−0.221997	−	0.311751i	−0.910521	+	0.413462i	$0.864319\pi$
$110$	−0.553923	−	2.28330i	−0.0528145	−	0.217704i
$111$	4.77915	+	10.4649i	0.453617	+	0.993283i
$112$	1.32109	−	2.29232i	0.124831	−	0.216604i
$113$	0.592704	+	0.380908i	0.0557569	+	0.0358328i	0.568222	−	0.822875i	$-0.307631\pi$
$113$	0.592704	+	0.380908i	0.0557569	+	0.0358328i	−0.512465	+	0.858708i	$0.671268\pi$
$114$	−3.54263	−	6.13601i	−0.331798	−	0.574690i
$115$	−0.590147	+	1.60961i	−0.0550315	+	0.150097i
$116$	−1.35487	+	2.34670i	−0.125796	+	0.217886i
$117$	0.224017	−	4.70270i	0.0207104	−	0.434765i
$118$	−0.315553	−	2.19472i	−0.0290490	−	0.202040i
$119$	10.6259	−	3.12907i	0.974078	−	0.286842i
$120$	0.342995	+	0.100712i	0.0313110	+	0.00919373i
$121$	−32.0530	+	3.06069i	−2.91391	+	0.278244i
$122$	−1.35113	−	3.90382i	−0.122325	−	0.353436i
$123$	2.24906	+	1.76868i	0.202791	+	0.159476i
$124$	−3.72405	−	3.55088i	−0.334430	−	0.318878i
$125$	2.31105	+	2.66709i	0.206706	+	0.238552i
$126$	1.10096	+	2.40580i	0.0980817	+	0.214326i
$127$	7.19951	−	4.62684i	0.638853	−	0.410566i	−0.180725	−	0.983534i	$-0.557844\pi$
$127$	7.19951	−	4.62684i	0.638853	−	0.410566i	0.819578	+	0.572968i	$0.194208\pi$
$128$	0.327068	−	0.945001i	0.0289090	−	0.0835271i
$129$	−0.903091	+	3.72259i	−0.0795127	+	0.327756i
$130$	1.32293	+	1.04036i	0.116029	+	0.0912459i
$131$	7.10427	+	1.36924i	0.620703	+	0.119631i	0.489901	−	0.871778i	$-0.337033\pi$
$131$	7.10427	+	1.36924i	0.620703	+	0.119631i	0.130801	+	0.991409i	$0.458245\pi$
$132$	2.73035	−	5.97863i	0.237646	−	0.520373i
$133$	10.8856	+	15.2614i	0.943899	+	1.32333i
$134$	−0.133137	−	0.291529i	−0.0115013	−	0.0251842i
$135$	−0.280994	+	0.220976i	−0.0241841	+	0.0190186i
$136$	3.72132	−	1.91848i	0.319101	−	0.164508i
$137$	6.90109	−	11.9530i	0.589600	−	1.02122i	−0.404685	−	0.914456i	$-0.632619\pi$
$137$	6.90109	−	11.9530i	0.589600	−	1.02122i	0.994285	−	0.106760i	$-0.0340478\pi$
$138$	−4.08108	+	2.51888i	−0.347405	+	0.214421i
$139$	13.3290			1.13055			0.565274	−	0.824903i	$-0.308770\pi$
$139$	13.3290			1.13055			0.565274	+	0.824903i	$0.308770\pi$
$140$	−0.928837	−	0.178266i	−0.0785011	−	0.0150663i
$141$	−0.0630724	−	0.438678i	−0.00531165	−	0.0369434i
$142$	7.93740	−	11.1465i	0.666092	−	0.935396i
$143$	22.3952	−	21.3537i	1.87278	−	1.78569i
$144$	0.580057	+	0.814576i	0.0483381	+	0.0678813i
$145$	0.951157	+	0.183321i	0.0789893	+	0.0152239i
$146$	1.75477	−	12.2047i	0.145226	−	1.01007i
$147$	−3.50947	−	6.05670i	−0.289456	−	0.499548i
$148$	−7.53386	−	8.69454i	−0.619279	−	0.714687i
$149$	−4.66819	−	2.40662i	−0.382433	−	0.197158i	0.256281	−	0.966602i	$-0.417503\pi$
$149$	−4.66819	−	2.40662i	−0.382433	−	0.197158i	−0.638714	+	0.769445i	$0.720533\pi$
$150$	0.231829	+	4.86669i	0.0189288	+	0.397364i
$151$	3.73562	−	0.719982i	0.304000	−	0.0585913i	−0.0349699	−	0.999388i	$-0.511134\pi$
$151$	3.73562	−	0.719982i	0.304000	−	0.0585913i	0.338970	+	0.940797i	$0.389921\pi$
$152$	5.12784	+	4.88939i	0.415923	+	0.396582i
$153$	−0.595835	+	4.14413i	−0.0481704	+	0.335033i
$154$	−5.67468	+	16.4374i	−0.457279	+	1.32457i
$155$	−0.764125	+	1.67320i	−0.0613760	+	0.134395i
$156$	1.10996	+	4.57532i	0.0888680	+	0.366319i
$157$	−3.74547	−	0.357649i	−0.298921	−	0.0285435i	−0.0554821	−	0.998460i	$-0.517670\pi$
$157$	−3.74547	−	0.357649i	−0.298921	−	0.0285435i	−0.243439	+	0.969916i	$0.578276\pi$
$158$	14.6353	+	5.85909i	1.16432	+	0.466124i
$159$	0.0345642	−	0.725593i	0.00274112	−	0.0575433i
$160$	−0.357475			−0.0282609
$161$	10.1092	−	7.66843i	0.796714	−	0.604357i
$162$	−1.00000			−0.0785674
$163$	−0.0566053	+	1.18829i	−0.00443367	+	0.0930741i	−1.00000		0.000993186i	$-0.999684\pi$
$163$	−0.0566053	+	1.18829i	−0.00443367	+	0.0930741i	0.995566	+	0.0940673i	$0.0299869\pi$
$164$	−2.65625	−	1.06340i	−0.207418	−	0.0830378i
$165$	−2.33889	−	0.223337i	−0.182083	−	0.0173868i
$166$	2.12773	+	8.77063i	0.165144	+	0.680733i
$167$	−7.87272	+	17.2388i	−0.609209	+	1.33398i	0.313904	+	0.949455i	$0.398363\pi$
$167$	−7.87272	+	17.2388i	−0.609209	+	1.33398i	−0.923114	+	0.384527i	$0.874364\pi$
$168$	−1.73416	−	1.99817i	−0.133793	−	0.154162i
$169$	−1.30440	+	9.07228i	−0.100338	+	0.697868i
$170$	−1.08318	−	1.03281i	−0.0830761	−	0.0792129i
$171$	−6.95722	+	1.34089i	−0.532032	+	0.102541i
$172$	−0.182266	−	3.82623i	−0.0138976	−	0.291747i
$173$	−1.24635	−	0.642540i	−0.0947586	−	0.0488514i	0.410196	−	0.911997i	$-0.365460\pi$
$173$	−1.24635	−	0.642540i	−0.0947586	−	0.0488514i	−0.504954	+	0.863146i	$0.668491\pi$
$174$	1.77450	+	2.04788i	0.134524	+	0.155250i
$175$	−1.84450	−	12.7580i	−0.139431	−	0.964415i
$176$	−0.935375	+	6.50568i	−0.0705066	+	0.490384i
$177$	−2.17722	−	0.419625i	−0.163650	−	0.0315409i
$178$	−7.36837	−	10.3474i	−0.552283	−	0.775572i
$179$	−11.4568	+	10.9240i	−0.856320	+	0.816500i	−0.984524	−	0.175248i	$-0.943927\pi$
$179$	−11.4568	+	10.9240i	−0.856320	+	0.816500i	0.128204	+	0.991748i	$0.459079\pi$
$180$	0.207356	−	0.291190i	0.0154554	−	0.0217041i
$181$	−1.78425	−	12.4098i	−0.132622	−	0.922410i	−0.942117	−	0.335283i	$-0.891168\pi$
$181$	−1.78425	−	12.4098i	−0.132622	−	0.922410i	0.809495	−	0.587127i	$-0.199741\pi$
$182$	−4.08324	−	11.7680i	−0.302670	−	0.872303i
$183$	−4.13103			−0.305374
$184$	3.20612	−	3.56662i	0.236358	−	0.262935i
$185$	−2.05629	+	3.56160i	−0.151181	+	0.261854i
$186$	−4.57360	+	2.35785i	−0.335353	+	0.172886i
$187$	−21.6304	+	17.0103i	−1.58177	+	1.24392i
$188$	0.184107	+	0.403139i	0.0134274	+	0.0294019i
$189$	2.63357	−	0.253552i	0.191564	−	0.0184432i
$190$	1.05216	−	2.30392i	0.0763320	−	0.167144i
$191$	10.4070	+	2.00579i	0.753028	+	0.145134i	0.551300	−	0.834307i	$-0.314132\pi$
$191$	10.4070	+	2.00579i	0.753028	+	0.145134i	0.201728	+	0.979442i	$0.435344\pi$
$192$	−0.786053	−	0.618159i	−0.0567285	−	0.0446118i
$193$	−0.833082	+	3.43401i	−0.0599665	+	0.247185i	−0.993904	−	0.110252i	$-0.964834\pi$
$193$	−0.833082	+	3.43401i	−0.0599665	+	0.247185i	0.933937	+	0.357437i	$0.116349\pi$
$194$	−1.52909	+	4.41802i	−0.109782	+	0.317196i
$195$	1.41583	−	0.909900i	0.101390	−	0.0651593i
$196$	5.07368	+	4.82263i	0.362406	+	0.344474i
$197$	1.07856	+	1.24472i	0.0768441	+	0.0886828i	0.792870	−	0.609391i	$-0.208586\pi$
$197$	1.07856	+	1.24472i	0.0768441	+	0.0886828i	−0.716026	+	0.698074i	$0.754041\pi$
$198$	−4.75680	−	4.53560i	−0.338051	−	0.322331i
$199$	2.16858	+	1.70539i	0.153727	+	0.120892i	0.692060	−	0.721840i	$-0.256703\pi$
$199$	2.16858	+	1.70539i	0.153727	+	0.120892i	−0.538333	+	0.842732i	$0.680946\pi$
$200$	−1.59354	−	4.60424i	−0.112681	−	0.325569i
$201$	−0.319040	+	0.0304646i	−0.0225033	+	0.00214881i
$202$	14.6939	+	4.31452i	1.03386	+	0.303568i
$203$	−5.19252	−	4.94332i	−0.364443	−	0.346953i
$204$	−0.595835	−	4.14413i	−0.0417168	−	0.290147i
$205$	−0.0486672	+	1.02165i	−0.00339906	+	0.0713551i
$206$	5.78347	−	10.0173i	0.402953	−	0.697936i
$207$	1.04555	+	4.68047i	0.0726711	+	0.325315i
$208$	−2.35402	−	4.07728i	−0.163222	−	0.282708i
$209$	−39.1758	−	25.1768i	−2.70985	−	1.74151i
$210$	−0.472255	+	0.819447i	−0.0325887	+	0.0565472i
$211$	7.31843	+	16.0251i	0.503822	+	1.10322i	0.975208	+	0.221289i	$0.0710264\pi$
$211$	7.31843	+	16.0251i	0.503822	+	1.10322i	−0.471387	+	0.881927i	$0.656246\pi$
$212$	0.171259	+	0.705939i	0.0117621	+	0.0484841i
$213$	−7.93740	−	11.1465i	−0.543862	−	0.763747i
$214$	2.49814	+	7.21791i	0.170770	+	0.493406i
$215$	−1.27124	+	0.508929i	−0.0866981	+	0.0347087i
$216$	0.959493	−	0.281733i	0.0652852	−	0.0191695i
$217$	11.4471	−	7.36923i	0.777078	−	0.500256i
$218$	3.36137	−	2.16022i	0.227661	−	0.146309i
$219$	−10.9595	−	5.65003i	−0.740577	−	0.381794i
$220$	2.30707	−	0.444652i	0.155543	−	0.0299784i
$221$	4.64712	−	19.1557i	0.312599	−	1.28855i
$222$	−10.6804	+	4.27580i	−0.716824	+	0.286973i
$223$	−3.98804	+	4.60244i	−0.267059	+	0.308202i	−0.873401	−	0.487001i	$-0.838091\pi$
$223$	−3.98804	+	4.60244i	−0.267059	+	0.308202i	0.606342	+	0.795204i	$0.292636\pi$
$224$	2.22686	+	1.42866i	0.148789	+	0.0954565i
$225$	4.67485	+	1.37266i	0.311657	+	0.0915107i
$226$	−0.408678	+	0.573908i	−0.0271849	+	0.0381758i
$227$	12.1593	+	4.86784i	0.807040	+	0.323090i	0.738238	−	0.674540i	$-0.235658\pi$
$227$	12.1593	+	4.86784i	0.807040	+	0.323090i	0.0688020	+	0.997630i	$0.478082\pi$
$228$	6.29763	−	3.24665i	0.417071	−	0.215015i
$229$	−1.02389	−	1.77343i	−0.0676605	−	0.117191i	0.830211	−	0.557450i	$-0.188220\pi$
$229$	−1.02389	−	1.77343i	−0.0676605	−	0.117191i	−0.897871	+	0.440258i	$0.854887\pi$
$230$	−1.57971	−	0.666067i	−0.104163	−	0.0439192i
$231$	13.6774	+	10.7387i	0.899906	+	0.706557i
$232$	−2.27957	−	1.46499i	−0.149661	−	0.0961816i
$233$	12.4564	−	9.79579i	0.816043	−	0.641744i	−0.120336	−	0.992733i	$-0.538397\pi$
$233$	12.4564	−	9.79579i	0.816043	−	0.641744i	0.936379	+	0.350990i	$0.114155\pi$
$234$	4.68671	+	0.447527i	0.306380	+	0.0292558i
$235$	0.114660	−	0.109328i	0.00747962	−	0.00713180i
$236$	2.20725	−	0.210767i	0.143680	−	0.0137197i
$237$	10.3236	−	11.9140i	0.670588	−	0.773900i
$238$	2.61993	+	10.7628i	0.169825	+	0.697648i
$239$	3.67128	−	1.07798i	0.237475	−	0.0697290i	−0.160829	−	0.986982i	$-0.551417\pi$
$239$	3.67128	−	1.07798i	0.237475	−	0.0697290i	0.398305	+	0.917253i	$0.369599\pi$
$240$	−0.116919	+	0.337814i	−0.00754706	+	0.0218058i
$241$	−1.15607	−	24.2688i	−0.0744688	−	1.56329i	−0.659138	−	0.752022i	$-0.729079\pi$
$241$	−1.15607	−	24.2688i	−0.0744688	−	1.56329i	0.584669	−	0.811272i	$-0.301224\pi$
$242$	−1.53208	−	32.1623i	−0.0984858	−	2.06747i
$243$	−0.327068	+	0.945001i	−0.0209814	+	0.0606218i
$244$	3.96369	−	1.16384i	0.253749	−	0.0745075i
$245$	1.03595	−	2.27781i	0.0661841	−	0.145524i
$246$	−1.87369	+	2.16235i	−0.119462	+	0.137867i
$247$	33.2066	−	3.17084i	2.11288	−	0.201756i
$248$	3.72405	−	3.55088i	0.236478	−	0.225481i
$249$	8.98416	+	0.857884i	0.569348	+	0.0543662i
$250$	−2.77403	+	2.18152i	−0.175445	+	0.137972i
$251$	−11.7967	−	7.58130i	−0.744603	−	0.478527i	0.112513	−	0.993650i	$-0.464110\pi$
$251$	−11.7967	−	7.58130i	−0.744603	−	0.478527i	−0.857116	+	0.515123i	$0.827746\pi$
$252$	−2.45546	+	0.985245i	−0.154680	+	0.0620646i
$253$	−16.2552	+	27.0063i	−1.02196	+	1.69787i
$254$	4.27903	+	7.41151i	0.268491	+	0.465039i
$255$	−1.33028	+	0.685807i	−0.0833053	+	0.0429469i
$256$	0.928368	+	0.371662i	0.0580230	+	0.0232289i
$257$	7.22641	−	10.1481i	0.450771	−	0.633020i	−0.525185	−	0.850988i	$-0.676004\pi$
$257$	7.22641	−	10.1481i	0.450771	−	0.633020i	0.975956	+	0.217969i	$0.0699431\pi$
$258$	−3.67540	−	1.07920i	−0.228821	−	0.0671878i
$259$	27.0436	−	13.9687i	1.68041	−	0.867971i
$260$	−1.10213	+	1.27193i	−0.0683514	+	0.0788817i
$261$	2.51563	−	1.00711i	0.155714	−	0.0623384i
$262$	−1.70572	+	7.03107i	−0.105380	+	0.434381i
$263$	12.5834	−	2.42525i	0.775924	−	0.149547i	0.214109	−	0.976810i	$-0.431315\pi$
$263$	12.5834	−	2.42525i	0.775924	−	0.149547i	0.561815	+	0.827263i	$0.310103\pi$
$264$	5.84194	+	3.01173i	0.359547	+	0.185359i
$265$	0.218453	−	0.140391i	0.0134194	−	0.00862415i
$266$	−15.7621	+	10.1471i	−0.966435	+	0.622157i
$267$	−12.1883	+	3.57880i	−0.745911	+	0.219019i
$268$	0.297533	−	0.119114i	0.0181747	−	0.00727607i
$269$	1.70582	+	4.92864i	0.104006	+	0.300505i	0.984982	−	0.172655i	$-0.0552346\pi$
$269$	1.70582	+	4.92864i	0.104006	+	0.300505i	−0.880977	+	0.473160i	$0.843113\pi$
$270$	−0.207356	−	0.291190i	−0.0126193	−	0.0177213i
$271$	−4.17287	−	17.2008i	−0.253484	−	1.04488i	−0.946179	−	0.323645i	$-0.895092\pi$
$271$	−4.17287	−	17.2008i	−0.253484	−	1.04488i	0.692695	−	0.721231i	$-0.256423\pi$
$272$	1.73924	+	3.80839i	0.105457	+	0.230918i
$273$	−12.4563	+	0.00972945i	−0.753888	+	0.000588853i
$274$	11.6111	+	7.46202i	0.701454	+	0.450797i
$275$	16.0115	+	27.7327i	0.965529	+	1.67235i
$276$	−2.32184	−	4.19631i	−0.139759	−	0.252588i
$277$	4.25229	−	7.36518i	0.255495	−	0.442531i	−0.709535	−	0.704671i	$-0.751095\pi$
$277$	4.25229	−	7.36518i	0.255495	−	0.442531i	0.965030	+	0.262140i	$0.0844282\pi$
$278$	−0.634218	+	13.3139i	−0.0380379	+	0.798513i
$279$	0.732297	+	5.09323i	0.0438414	+	0.304924i
$280$	0.222260	−	0.919303i	0.0132826	−	0.0549389i
$281$	21.3760	+	6.27655i	1.27518	+	0.374427i	0.848125	−	0.529797i	$-0.177732\pi$
$281$	21.3760	+	6.27655i	1.27518	+	0.374427i	0.427058	+	0.904224i	$0.359550\pi$
$282$	0.441182	−	0.0421278i	0.0262720	−	0.00250867i
$283$	−6.29619	−	18.1917i	−0.374270	−	1.08138i	−0.962170	−	0.272448i	$-0.912167\pi$
$283$	−6.29619	−	18.1917i	−0.374270	−	1.08138i	0.587901	−	0.808933i	$-0.299955\pi$
$284$	10.7562	+	8.45879i	0.638264	+	0.501937i
$285$	−1.83307	−	1.74783i	−0.108582	−	0.103533i
$286$	20.2640	+	23.3859i	1.19823	+	1.38283i
$287$	4.38623	−	6.16980i	0.258911	−	0.364192i
$288$	−0.841254	+	0.540641i	−0.0495713	+	0.0318576i
$289$	−0.172953	+	0.499716i	−0.0101737	+	0.0293951i
$290$	−0.228371	+	0.941357i	−0.0134104	+	0.0552784i
$291$	3.67492	+	2.88999i	0.215428	+	0.169414i
$292$	12.1074	+	2.33351i	0.708532	+	0.136558i
$293$	1.38281	−	3.02793i	0.0807846	−	0.176894i	−0.864929	−	0.501893i	$-0.832637\pi$
$293$	1.38281	−	3.02793i	0.0807846	−	0.176894i	0.945714	+	0.325000i	$0.105364\pi$
$294$	6.21683	−	3.21730i	0.362573	−	0.187637i
$295$	−0.329268	−	0.720997i	−0.0191707	−	0.0419781i
$296$	9.04317	−	7.11162i	0.525623	−	0.413355i
$297$	−5.84194	+	3.01173i	−0.338984	+	0.174758i
$298$	2.62601	−	4.54839i	0.152121	−	0.263481i
$299$	−2.80558	−	22.4040i	−0.162251	−	1.29565i
$300$	−4.87221			−0.281297
$301$	9.95308	+	1.91024i	0.573686	+	0.110104i
$302$	0.541418	+	3.76565i	0.0311551	+	0.216689i
$303$	8.88312	−	12.4746i	0.510322	−	0.716647i
$304$	−5.12784	+	4.88939i	−0.294102	+	0.280426i
$305$	−0.856592	−	1.20292i	−0.0490483	−	0.0688787i
$306$	−4.11108	−	0.792346i	−0.235015	−	0.0452954i
$307$	1.00441	−	6.98583i	0.0573248	−	0.398703i	−0.940876	−	0.338750i	$-0.889996\pi$
$307$	1.00441	−	6.98583i	0.0573248	−	0.398703i	0.998201	−	0.0599526i	$-0.0190950\pi$
$308$	−16.1488	−	6.45038i	−0.920164	−	0.367544i
$309$	−7.57473	−	8.74171i	−0.430912	−	0.497298i
$310$	−1.63495	−	0.842874i	−0.0928587	−	0.0478720i
$311$	−0.174460	−	3.66237i	−0.00989274	−	0.207674i	−0.998402	−	0.0565129i	$-0.982002\pi$
$311$	−0.174460	−	3.66237i	−0.00989274	−	0.207674i	0.988509	−	0.151161i	$-0.0483012\pi$
$312$	−4.62295	+	0.891001i	−0.261723	+	0.0504430i
$313$	−16.1440	−	15.3933i	−0.912515	−	0.870081i	0.0794184	−	0.996841i	$-0.474694\pi$
$313$	−16.1440	−	15.3933i	−0.912515	−	0.870081i	−0.991933	+	0.126760i	$0.959542\pi$
$314$	0.535461	−	3.72421i	0.0302178	−	0.210169i
$315$	0.619919	+	0.714296i	0.0349285	+	0.0402460i
$316$	−6.54883	+	14.3399i	−0.368400	+	0.806684i
$317$	7.90637	+	32.5905i	0.444066	+	1.83047i	0.548785	+	0.835964i	$0.315091\pi$
$317$	7.90637	+	32.5905i	0.444066	+	1.83047i	−0.104718	+	0.994502i	$0.533394\pi$
$318$	0.723126	+	0.0690502i	0.0405509	+	0.00387214i
$319$	16.5342	+	6.61929i	0.925737	+	0.370609i
$320$	0.0170093	−	0.357070i	0.000950851	−	0.0199608i
$321$	7.63800			0.426311
$322$	7.17873	+	10.4626i	0.400055	+	0.583058i
$323$	−29.6641			−1.65056
$324$	0.0475819	−	0.998867i	0.00264344	−	0.0554926i
$325$	−21.2954	−	8.52539i	−1.18126	−	0.472904i
$326$	−1.18425	−	0.113082i	−0.0655896	−	0.00626305i
$327$	−0.942016	−	3.88304i	−0.0520936	−	0.214733i
$328$	1.18859	−	2.60264i	0.0656288	−	0.143707i
$329$	−1.15120	+	0.222809i	−0.0634680	+	0.0122839i
$330$	0.334373	−	2.32562i	0.0184066	−	0.128021i
$331$	21.8580	+	20.8415i	1.20142	+	1.14555i	0.985595	+	0.169123i	$0.0540935\pi$
$331$	21.8580	+	20.8415i	1.20142	+	1.14555i	0.215828	+	0.976431i	$0.430755\pi$
$332$	−8.86194	+	1.70800i	−0.486362	+	0.0937386i
$333$	0.547407	+	11.4915i	0.0299977	+	0.629730i
$334$	−16.8447	−	8.68406i	−0.921702	−	0.475170i
$335$	−0.0750257	−	0.0865843i	−0.00409909	−	0.00473060i
$336$	2.07842	−	1.63712i	0.113387	−	0.0893122i
$337$	3.81706	−	26.5482i	0.207928	−	1.44617i	−0.571973	−	0.820272i	$-0.693822\pi$
$337$	3.81706	−	26.5482i	0.207928	−	1.44617i	0.779902	−	0.625902i	$-0.215269\pi$
$338$	−8.99994	−	1.73460i	−0.489532	−	0.0943496i
$339$	0.408678	+	0.573908i	0.0221963	+	0.0311704i
$340$	1.08318	−	1.03281i	0.0587437	−	0.0560120i
$341$	−19.6175	+	27.5489i	−1.06235	+	1.49186i
$342$	−1.00834	−	7.01314i	−0.0545246	−	0.379227i
$343$	−15.5567	+	10.0493i	−0.839984	+	0.542611i
$344$	3.83057			0.206530
$345$	−1.14611	+	1.27498i	−0.0617043	+	0.0686425i
$346$	0.701116	−	1.21437i	0.0376923	−	0.0652849i
$347$	−14.2813	+	7.36253i	−0.766661	+	0.395241i	−0.796752	−	0.604306i	$-0.793450\pi$
$347$	−14.2813	+	7.36253i	−0.766661	+	0.395241i	0.0300914	+	0.999547i	$0.490420\pi$
$348$	−2.13000	+	1.67505i	−0.114180	+	0.0897920i
$349$	−13.7600	−	30.1303i	−0.736558	−	1.61284i	−0.789134	−	0.614221i	$-0.789470\pi$
$349$	−13.7600	−	30.1303i	−0.736558	−	1.61284i	0.0525760	−	0.998617i	$-0.483257\pi$
$350$	12.8313	−	1.23536i	0.685863	−	0.0660327i
$351$	1.95579	−	4.28258i	0.104392	−	0.228587i
$352$	−6.45380	−	1.24387i	−0.343989	−	0.0662984i
$353$	−11.1911	−	8.80082i	−0.595645	−	0.468420i	0.274249	−	0.961659i	$-0.411571\pi$
$353$	−11.1911	−	8.80082i	−0.595645	−	0.468420i	−0.869894	+	0.493238i	$0.835813\pi$
$354$	0.522746	−	2.15479i	0.0277836	−	0.114526i
$355$	1.59989	−	4.62259i	0.0849136	−	0.245342i
$356$	10.6863	−	6.86767i	0.566373	−	0.363986i
$357$	11.0277	+	1.04433i	0.583650	+	0.0552718i
$358$	−10.3665	−	11.9636i	−0.547887	−	0.632296i
$359$	−2.21995	−	2.11672i	−0.117164	−	0.111716i	0.629232	−	0.777217i	$-0.283369\pi$
$359$	−2.21995	−	2.11672i	−0.117164	−	0.111716i	−0.746397	+	0.665501i	$0.768218\pi$
$360$	0.280994	+	0.220976i	0.0148097	+	0.0116465i
$361$	−10.2048	−	29.4848i	−0.537095	−	1.55183i
$362$	12.4806	−	1.19175i	0.655966	−	0.0626371i
$363$	−30.8945	−	9.07144i	−1.62154	−	0.476127i
$364$	11.9490	−	3.51868i	0.626296	−	0.184429i
$365$	−0.627287	−	4.36288i	−0.0328337	−	0.228363i
$366$	0.196562	−	4.12635i	0.0102745	−	0.215688i
$367$	−13.0925	+	22.6770i	−0.683426	+	1.18373i	0.290503	+	0.956874i	$0.406177\pi$
$367$	−13.0925	+	22.6770i	−0.683426	+	1.18373i	−0.973929	+	0.226854i	$0.927156\pi$
$368$	3.41003	+	3.37219i	0.177760	+	0.175788i
$369$	1.43060	+	2.47788i	0.0744742	+	0.128993i
$370$	−3.45972	−	2.22343i	−0.179862	−	0.115590i
$371$	−1.92191	+	0.00150118i	−0.0997808	+	7.79376e-5i
$372$	−2.13756	−	4.68061i	−0.110827	−	0.242678i
$373$	0.0919500	+	0.379023i	0.00476099	+	0.0196251i	0.974143	−	0.225934i	$-0.0725435\pi$
$373$	0.0919500	+	0.379023i	0.00476099	+	0.0196251i	−0.969382	+	0.245559i	$0.921028\pi$
$374$	−15.9618	−	22.4152i	−0.825366	−	1.15906i
$375$	1.15424	+	3.33497i	0.0596049	+	0.172217i
$376$	−0.411443	+	0.164717i	−0.0212185	+	0.00849462i
$377$	−12.2408	+	3.59421i	−0.630431	+	0.185111i
$378$	0.127954	+	2.64266i	0.00658125	+	0.135924i
$379$	8.52356	−	5.47776i	0.437826	−	0.281374i	−0.303102	−	0.952958i	$-0.598022\pi$
$379$	8.52356	−	5.47776i	0.437826	−	0.281374i	0.740928	+	0.671584i	$0.234386\pi$
$380$	2.25124	+	1.16060i	0.115486	+	0.0595374i
$381$	8.40341	−	1.61963i	0.430520	−	0.0829759i
$382$	−2.49871	+	10.2998i	−0.127845	+	0.526985i
$383$	9.78744	−	3.91830i	0.500115	−	0.200216i	−0.107869	−	0.994165i	$-0.534403\pi$
$383$	9.78744	−	3.91830i	0.500115	−	0.200216i	0.607984	+	0.793949i	$0.291978\pi$
$384$	0.654861	−	0.755750i	0.0334182	−	0.0385667i
$385$	−0.290932	+	6.20946i	−0.0148273	+	0.316464i
$386$	−3.39048	−	0.995535i	−0.172571	−	0.0506714i
$387$	−2.22195	+	3.12029i	−0.112948	+	0.158613i
$388$	−4.34026	−	1.73758i	−0.220343	−	0.0882122i
$389$	−0.371873	+	0.191714i	−0.0188547	+	0.00972029i	−0.467628	−	0.883925i	$-0.654891\pi$
$389$	−0.371873	+	0.191714i	−0.0188547	+	0.00972029i	0.448773	+	0.893646i	$0.351861\pi$
$390$	0.841502	+	1.45752i	0.0426111	+	0.0738046i
$391$	0.589807	+	20.0702i	0.0298278	+	1.01500i
$392$	−5.05859	+	4.83846i	−0.255497	+	0.244379i
$393$	6.08648	+	3.91154i	0.307022	+	0.197311i
$394$	−1.29463	+	1.01811i	−0.0652226	+	0.0512916i
$395$	5.60991	+	0.535681i	0.282265	+	0.0269531i
$396$	4.75680	−	4.53560i	0.239038	−	0.227922i
$397$	−20.2227	+	1.93104i	−1.01495	+	0.0969160i	−0.589252	−	0.807949i	$-0.700578\pi$
$397$	−20.2227	+	1.93104i	−1.01495	+	0.0969160i	−0.425698	+	0.904865i	$0.639971\pi$
$398$	−1.80665	+	2.08498i	−0.0905590	+	0.104511i
$399$	4.43372	+	18.2140i	0.221964	+	0.911838i
$400$	4.67485	−	1.37266i	0.233743	−	0.0686330i
$401$	−1.83515	+	5.30233i	−0.0916432	+	0.264786i	−0.981502	−	0.191449i	$-0.938681\pi$
$401$	−1.83515	+	5.30233i	−0.0916432	+	0.264786i	0.889859	+	0.456235i	$0.150802\pi$
$402$	−0.0152496	−	0.320128i	−0.000760579	−	0.0159665i
$403$	−1.15271	−	24.1983i	−0.0574203	−	1.20540i
$404$	−5.00879	+	14.4720i	−0.249197	+	0.720007i
$405$	−0.342995	+	0.100712i	−0.0170435	+	0.00500443i
$406$	5.18479	−	4.95143i	0.257317	−	0.245735i
$407$	−49.5169	+	57.1455i	−2.45446	+	2.83260i
$408$	4.16778	−	0.397975i	0.206336	−	0.0197027i
$409$	−16.9900	+	16.1999i	−0.840101	+	0.801035i	−0.982007	−	0.188845i	$-0.939526\pi$
$409$	−16.9900	+	16.1999i	−0.840101	+	0.801035i	0.141906	+	0.989880i	$0.454677\pi$
$410$	−1.01818	−	0.0972241i	−0.0502842	−	0.00480156i
$411$	10.8492	−	8.53194i	0.535154	−	0.420849i
$412$	9.73073	+	6.25356i	0.479399	+	0.308091i
$413$	−0.830339	+	5.80734i	−0.0408583	+	0.285760i
$414$	−4.72492	+	0.821664i	−0.232217	+	0.0403826i
$415$	1.61311	+	2.79399i	0.0791845	+	0.137152i
$416$	4.18467	−	2.15735i	0.205170	−	0.105773i
$417$	12.3742	+	4.95388i	0.605967	+	0.242593i
$418$	27.0123	−	37.9335i	1.32122	−	1.85539i
$419$	9.15256	+	2.68743i	0.447132	+	0.131290i	0.497544	−	0.867439i	$-0.334235\pi$
$419$	9.15256	+	2.68743i	0.447132	+	0.131290i	−0.0504122	+	0.998728i	$0.516054\pi$
$420$	−0.796048	−	0.510711i	−0.0388432	−	0.0249201i
$421$	−12.2946	+	14.1887i	−0.599202	+	0.691516i	−0.971619	−	0.236549i	$-0.923984\pi$
$421$	−12.2946	+	14.1887i	−0.599202	+	0.691516i	0.372417	+	0.928065i	$0.378529\pi$
$422$	−16.3552	+	6.54764i	−0.796159	+	0.318734i
$423$	0.104486	−	0.430696i	0.00508027	−	0.0209412i
$424$	−0.713288	+	0.137475i	−0.0346403	+	0.00667638i
$425$	18.1311	+	9.34722i	0.879486	+	0.453407i
$426$	11.5116	−	7.39804i	0.557738	−	0.358436i
$427$	0.528582	+	10.9169i	0.0255799	+	0.528305i
$428$	−7.32861	+	2.15187i	−0.354242	+	0.104015i
$429$	28.7273	−	11.5007i	1.38697	−	0.555259i
$430$	−0.447864	−	1.29402i	−0.0215979	−	0.0624032i
$431$	−1.76786	−	2.48261i	−0.0851547	−	0.119583i	0.769801	−	0.638284i	$-0.220355\pi$
$431$	−1.76786	−	2.48261i	−0.0851547	−	0.119583i	−0.854956	+	0.518701i	$0.826416\pi$
$432$	0.235759	+	0.971812i	0.0113430	+	0.0467563i
$433$	11.7160	+	25.6544i	0.563034	+	1.23287i	0.950424	+	0.310956i	$0.100649\pi$
$433$	11.7160	+	25.6544i	0.563034	+	1.23287i	−0.387391	+	0.921916i	$0.626624\pi$
$434$	6.81621	+	11.7848i	0.327188	+	0.565686i
$435$	0.814891	+	0.523698i	0.0390710	+	0.0251094i
$436$	1.99784	+	3.46036i	0.0956790	+	0.165721i
$437$	−31.7705	+	12.0521i	−1.51979	+	0.576531i
$438$	6.16511	−	10.6783i	0.294580	−	0.510228i
$439$	0.186243	−	3.90971i	0.00888888	−	0.186600i	−0.990056	−	0.140674i	$-0.955073\pi$
$439$	0.186243	−	3.90971i	0.00888888	−	0.186600i	0.998945	−	0.0459263i	$-0.0146240\pi$
$440$	0.334373	+	2.32562i	0.0159406	+	0.110869i
$441$	−1.00703	−	6.92719i	−0.0479536	−	0.329866i
$442$	18.9129	+	5.55332i	0.899593	+	0.264144i
$443$	−10.4252	+	0.995487i	−0.495317	+	0.0472970i	−0.339726	−	0.940525i	$-0.610334\pi$
$443$	−10.4252	+	0.995487i	−0.495317	+	0.0472970i	−0.155591	+	0.987822i	$0.549728\pi$
$444$	−3.76276	−	10.8718i	−0.178573	−	0.515952i
$445$	−3.56942	−	2.80703i	−0.169207	−	0.133066i
$446$	−4.40747	−	4.20252i	−0.208700	−	0.198995i
$447$	−3.43935	−	3.96922i	−0.162675	−	0.187737i
$448$	−1.53300	+	2.15636i	−0.0724276	+	0.101879i
$449$	19.8922	−	12.7840i	0.938773	−	0.603313i	0.0207262	−	0.999785i	$-0.493402\pi$
$449$	19.8922	−	12.7840i	0.938773	−	0.603313i	0.918047	+	0.396473i	$0.129766\pi$
$450$	−1.59354	+	4.60424i	−0.0751204	+	0.217046i
$451$	−4.43356	+	18.2754i	−0.208768	+	0.860555i
$452$	−0.553812	−	0.435523i	−0.0260491	−	0.0204853i
$453$	3.73562	+	0.719982i	0.175515	+	0.0338277i
$454$	−5.44089	+	11.9139i	−0.255354	+	0.559147i
$455$	−2.58571	−	3.62513i	−0.121220	−	0.169949i
$456$	2.94332	+	6.44498i	0.137834	+	0.301814i
$457$	−17.2390	+	13.5569i	−0.806405	+	0.634164i	−0.933843	−	0.357683i	$-0.883567\pi$
$457$	−17.2390	+	13.5569i	−0.806405	+	0.634164i	0.127439	+	0.991846i	$0.459324\pi$
$458$	1.82014	−	0.938346i	0.0850494	−	0.0438460i
$459$	−2.09337	+	3.62582i	−0.0977102	+	0.169239i
$460$	0.740478	−	1.54623i	0.0345250	−	0.0720933i
$461$	−22.2536			−1.03645			−0.518226	−	0.855244i	$-0.673407\pi$
$461$	−22.2536			−1.03645			−0.518226	+	0.855244i	$0.673407\pi$
$462$	−11.3774	+	13.1509i	−0.529323	+	0.611837i
$463$	0.162710	+	1.13167i	0.00756175	+	0.0525932i	0.993253	−	0.115968i	$-0.0369970\pi$
$463$	0.162710	+	1.13167i	0.00756175	+	0.0525932i	−0.985691	+	0.168561i	$0.946088\pi$
$464$	1.57180	−	2.20729i	0.0729690	−	0.102471i
$465$	−1.33125	+	1.26935i	−0.0617355	+	0.0588647i
$466$	9.19200	+	12.9084i	0.425811	+	0.597968i
$467$	−24.5959	−	4.74048i	−1.13816	−	0.219363i	−0.414855	−	0.909888i	$-0.636168\pi$
$467$	−24.5959	−	4.74048i	−1.13816	−	0.219363i	−0.723309	+	0.690524i	$0.757380\pi$
$468$	−0.670023	+	4.66011i	−0.0309718	+	0.215414i
$469$	0.121330	+	0.839214i	0.00560249	+	0.0387513i
$470$	0.103749	+	0.119733i	0.00478558	+	0.00552285i
$471$	−3.34425	−	1.72408i	−0.154095	−	0.0794415i
$472$	0.105503	+	2.21478i	0.00485616	+	0.101943i
$473$	−24.7217	+	4.76472i	−1.13671	+	0.219082i
$474$	11.4093	+	10.8788i	0.524048	+	0.499679i
$475$	−4.91283	+	34.1695i	−0.225416	+	1.56780i
$476$	−10.8753	+	2.10485i	−0.498467	+	0.0964754i
$477$	0.301764	−	0.660771i	0.0138168	−	0.0302546i
$478$	0.902077	+	3.71841i	0.0412600	+	0.170076i
$479$	39.2699	+	3.74982i	1.79429	+	0.171334i	0.938336	−	0.345725i	$-0.112367\pi$
$479$	39.2699	+	3.74982i	1.79429	+	0.171334i	0.855950	+	0.517059i	$0.172973\pi$
$480$	−0.331868	−	0.132860i	−0.0151476	−	0.00606420i
$481$	2.57721	−	54.1023i	0.117511	−	2.46685i
$482$	24.2964			1.10667
$483$	12.2351	−	3.36193i	0.556716	−	0.152973i
$484$	32.1988			1.46358
$485$	−0.0795212	+	1.66936i	−0.00361087	+	0.0758016i
$486$	−0.928368	−	0.371662i	−0.0421116	−	0.0168590i
$487$	−20.9557	−	2.00102i	−0.949591	−	0.0906750i	−0.391248	−	0.920285i	$-0.627957\pi$
$487$	−20.9557	−	2.00102i	−0.949591	−	0.0906750i	−0.558343	+	0.829610i	$0.688563\pi$
$488$	0.973926	+	4.01458i	0.0440876	+	0.181731i
$489$	−0.494194	+	1.08213i	−0.0223482	+	0.0489357i
$490$	2.22594	+	1.14316i	0.100558	+	0.0516425i
$491$	−0.240737	+	1.67436i	−0.0108643	+	0.0755628i	−0.994532	−	0.104430i	$-0.966698\pi$
$491$	−0.240737	+	1.67436i	−0.0108643	+	0.0755628i	0.983668	+	0.179993i	$0.0576074\pi$
$492$	−2.07075	−	1.97446i	−0.0933567	−	0.0890154i
$493$	11.1399	−	2.14705i	0.501718	−	0.0966982i
$494$	1.58722	+	33.3198i	0.0714124	+	1.49913i
$495$	−2.08835	−	1.07662i	−0.0938642	−	0.0483904i
$496$	3.36966	+	3.88879i	0.151302	+	0.174612i
$497$	−28.4408	+	22.4021i	−1.27574	+	1.00487i
$498$	−1.28440	+	8.93317i	−0.0575551	+	0.400305i
$499$	1.49934	+	0.288975i	0.0671198	+	0.0129363i	0.222701	−	0.974887i	$-0.428513\pi$
$499$	1.49934	+	0.288975i	0.0671198	+	0.0129363i	−0.155581	+	0.987823i	$0.549725\pi$
$500$	−2.04706	−	2.87469i	−0.0915473	−	0.128560i
$501$	−13.7158	+	13.0780i	−0.612777	+	0.584282i
$502$	8.13402	−	11.4226i	0.363039	−	0.509817i
$503$	−3.35838	−	23.3581i	−0.149743	−	1.04149i	−0.916640	−	0.399715i	$-0.869109\pi$
$503$	−3.35838	−	23.3581i	−0.149743	−	1.04149i	0.766897	−	0.641771i	$-0.221800\pi$
$504$	−0.867293	−	2.49956i	−0.0386323	−	0.111339i
$505$	5.47445			0.243610
$506$	−26.2022	−	17.5218i	−1.16483	−	0.778941i
$507$	−4.58279	+	7.93762i	−0.203529	+	0.352522i
$508$	−7.60672	+	3.92153i	−0.337493	+	0.173990i
$509$	−2.20803	+	1.73642i	−0.0978694	+	0.0769654i	−0.665895	−	0.746046i	$-0.731950\pi$
$509$	−2.20803	+	1.73642i	−0.0978694	+	0.0769654i	0.568025	+	0.823011i	$0.307708\pi$
$510$	−0.621733	−	1.36140i	−0.0275308	−	0.0602840i
$511$	−13.5288	+	29.6852i	−0.598478	+	1.31320i
$512$	−0.415415	+	0.909632i	−0.0183589	+	0.0402004i
$513$	−6.95722	−	1.34089i	−0.307169	−	0.0592019i
$514$	9.79273	+	7.70109i	0.431939	+	0.339681i
$515$	0.974837	−	4.01833i	0.0429565	−	0.177069i
$516$	1.25286	−	3.61989i	0.0551539	−	0.159357i
$517$	2.45048	−	1.57483i	0.107772	−	0.0692609i
$518$	12.6661	+	27.6776i	0.556515	+	1.21608i
$519$	−0.918267	−	1.05974i	−0.0403075	−	0.0465173i
$520$	−1.21805	−	1.16141i	−0.0534149	−	0.0509310i
$521$	11.0390	+	8.68115i	0.483626	+	0.380328i	0.829995	−	0.557770i	$-0.188343\pi$
$521$	11.0390	+	8.68115i	0.483626	+	0.380328i	−0.346369	+	0.938098i	$0.612585\pi$
$522$	0.886268	+	2.56070i	0.0387909	+	0.112079i
$523$	25.7538	−	2.45919i	1.12613	−	0.107533i	0.484678	−	0.874693i	$-0.338937\pi$
$523$	25.7538	−	2.45919i	1.12613	−	0.107533i	0.641456	+	0.767160i	$0.278331\pi$
$524$	−6.94194	−	2.03834i	−0.303260	−	0.0890452i
$525$	3.02930	−	12.5297i	0.132210	−	0.546839i
$526$	1.82376	+	12.6845i	0.0795197	+	0.553072i
$527$	−1.02507	+	21.5189i	−0.0446529	+	0.937379i
$528$	−3.28629	+	5.69202i	−0.143017	+	0.247713i
$529$	8.78594	+	21.2558i	0.381997	+	0.924163i
$530$	0.129838	+	0.224885i	0.00563979	+	0.00976840i
$531$	−1.86530	−	1.19876i	−0.0809472	−	0.0520216i
$532$	−9.38559	−	16.2270i	−0.406917	−	0.703531i
$533$	−5.59591	−	12.2533i	−0.242386	−	0.530751i
$534$	−2.99481	−	12.3448i	−0.129598	−	0.534210i
$535$	1.58378	+	2.22411i	0.0684729	+	0.0961567i
$536$	0.104822	+	0.302864i	0.00452763	+	0.0130817i
$537$	−14.6962	+	5.88346i	−0.634186	+	0.253890i
$538$	−5.00423	+	1.46937i	−0.215748	+	0.0633492i
$539$	26.6287	−	37.5187i	1.14698	−	1.61604i
$540$	0.300727	−	0.193265i	0.0129412	−	0.00831682i
$541$	21.0979	+	10.8767i	0.907068	+	0.467626i	0.847619	−	0.530605i	$-0.178035\pi$
$541$	21.0979	+	10.8767i	0.907068	+	0.467626i	0.0594490	+	0.998231i	$0.481066\pi$
$542$	17.3799	−	3.34970i	0.746530	−	0.143882i
$543$	2.95580	−	12.1840i	0.126845	−	0.522864i
$544$	−3.88684	+	1.55605i	−0.166647	+	0.0667153i
$545$	0.935372	−	1.07948i	0.0400669	−	0.0462397i
$546$	0.582975	−	12.4426i	0.0249490	−	0.532496i
$547$	−5.85693	−	1.71975i	−0.250424	−	0.0735312i	0.154111	−	0.988053i	$-0.450749\pi$
$547$	−5.85693	−	1.71975i	−0.250424	−	0.0735312i	−0.404535	+	0.914522i	$0.632567\pi$
$548$	−8.00605	+	11.2429i	−0.342001	+	0.480274i
$549$	−3.83511	−	1.53535i	−0.163679	−	0.0655270i
$550$	−28.4632	+	14.6738i	−1.21367	+	0.625692i
$551$	9.59959	+	16.6270i	0.408956	+	0.708333i
$552$	4.30204	−	2.11955i	0.183107	−	0.0902138i
$553$	−32.8057	−	25.7572i	−1.39504	−	1.09531i
$554$	7.15450	+	4.59792i	0.303966	+	0.195347i
$555$	−3.23270	+	2.54223i	−0.137221	+	0.107912i
$556$	−13.2686	−	1.26700i	−0.562715	−	0.0537327i
$557$	−28.1412	+	26.8325i	−1.19238	+	1.13693i	−0.204966	+	0.978769i	$0.565708\pi$
$557$	−28.1412	+	26.8325i	−1.19238	+	1.13693i	−0.987413	+	0.158162i	$0.949443\pi$
$558$	−5.12231	+	0.489121i	−0.216845	+	0.0207062i
$559$	11.8100	−	13.6295i	0.499512	−	0.576467i
$560$	0.907686	+	0.265751i	0.0383567	+	0.0112300i
$561$	−26.4030	+	7.75263i	−1.11474	+	0.327316i
$562$	−7.28655	+	21.0531i	−0.307364	+	0.888071i
$563$	−1.50873	−	31.6721i	−0.0635853	−	1.33482i	−0.774962	−	0.632008i	$-0.782231\pi$
$563$	−1.50873	−	31.6721i	−0.0635853	−	1.33482i	0.711376	−	0.702811i	$-0.248072\pi$
$564$	0.0210878	+	0.442687i	0.000887956	+	0.0186405i
$565$	−0.0823748	+	0.238006i	−0.00346553	+	0.0100130i
$566$	18.4706	−	5.42347i	0.776379	−	0.227965i
$567$	2.53916	+	0.743411i	0.106635	+	0.0312203i
$568$	−8.96101	+	10.3416i	−0.375996	+	0.433922i
$569$	−31.5881	+	3.01630i	−1.32424	+	0.126450i	−0.733102	−	0.680118i	$-0.761928\pi$
$569$	−31.5881	+	3.01630i	−1.32424	+	0.126450i	−0.591141	+	0.806568i	$0.701322\pi$
$570$	1.83307	−	1.74783i	0.0767790	−	0.0732087i
$571$	37.7796	+	3.60751i	1.58103	+	0.150970i	0.848286	−	0.529539i	$-0.177635\pi$
$571$	37.7796	+	3.60751i	1.58103	+	0.150970i	0.732740	+	0.680508i	$0.238241\pi$
$572$	−24.3236	+	19.1283i	−1.01702	+	0.799793i
$573$	8.91609	+	5.73002i	0.372475	+	0.239375i
$574$	5.95410	+	4.67484i	0.248519	+	0.195124i
$575$	23.2162	+	2.64455i	0.968181	+	0.110285i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−15.6952	+	8.09146i	−0.653402	+	0.336852i	−0.752851	−	0.658191i	$-0.771322\pi$
$577$	−15.6952	+	8.09146i	−0.653402	+	0.336852i	0.0994497	+	0.995043i	$0.468292\pi$
$578$	−0.490921	−	0.196535i	−0.0204196	−	0.00817478i
$579$	−2.04970	+	2.87840i	−0.0851826	+	0.119622i
$580$	−0.929425	−	0.272904i	−0.0385923	−	0.0113317i
$581$	1.11753	−	23.8518i	0.0463630	−	0.989540i
$582$	−3.06157	+	3.53324i	−0.126906	+	0.146458i
$583$	4.43242	−	1.77447i	0.183572	−	0.0734912i
$584$	−2.90696	+	11.9826i	−0.120291	+	0.495845i
$585$	1.65259	−	0.318510i	0.0683262	−	0.0131688i
$586$	2.95871	+	1.52532i	0.122223	+	0.0630103i
$587$	26.7963	−	17.2209i	1.10600	−	0.710784i	0.145584	−	0.989346i	$-0.453494\pi$
$587$	26.7963	−	17.2209i	1.10600	−	0.710784i	0.960418	+	0.278562i	$0.0898576\pi$
$588$	2.91785	+	6.36287i	0.120330	+	0.262400i
$589$	−34.9812	+	10.2714i	−1.44137	+	0.423225i
$590$	0.735848	−	0.294589i	0.0302944	−	0.0121280i
$591$	0.538682	+	1.55642i	0.0221584	+	0.0640226i
$592$	6.67328	+	9.37131i	0.274270	+	0.385158i
$593$	1.00602	+	4.14687i	0.0413123	+	0.170292i	0.988730	−	0.149706i	$-0.0478329\pi$
$593$	1.00602	+	4.14687i	0.0413123	+	0.170292i	−0.947418	+	0.319998i	$0.896318\pi$
$594$	−2.73035	−	5.97863i	−0.112028	−	0.245306i
$595$	1.98257	+	3.42772i	0.0812773	+	0.140523i
$596$	4.41829	+	2.83946i	0.180980	+	0.116309i
$597$	1.37941	+	2.38921i	0.0564556	+	0.0977839i
$598$	22.5121	−	1.73638i	0.920587	−	0.0710058i
$599$	4.17726	−	7.23522i	0.170678	−	0.295623i	−0.767979	−	0.640475i	$-0.778738\pi$
$599$	4.17726	−	7.23522i	0.170678	−	0.295623i	0.938657	+	0.344852i	$0.112071\pi$
$600$	0.231829	−	4.86669i	0.00946439	−	0.198682i
$601$	−5.74910	−	39.9859i	−0.234511	−	1.63106i	−0.678200	−	0.734877i	$-0.737240\pi$
$601$	−5.74910	−	39.9859i	−0.234511	−	1.63106i	0.443690	−	0.896181i	$-0.353669\pi$
$602$	−2.38166	+	9.85091i	−0.0970692	+	0.401493i
$603$	−0.307509	−	0.0902927i	−0.0125227	−	0.00367700i
$604$	−3.78714	+	0.361628i	−0.154097	+	0.0147144i
$605$	−3.76463	−	10.8772i	−0.153054	−	0.442221i
$606$	12.0378	+	9.46663i	0.489002	+	0.384555i
$607$	29.7519	+	28.3683i	1.20759	+	1.15144i	0.984266	+	0.176691i	$0.0565394\pi$
$607$	29.7519	+	28.3683i	1.20759	+	1.15144i	0.223324	+	0.974744i	$0.428309\pi$
$608$	−4.63986	−	5.35468i	−0.188171	−	0.217161i
$609$	−2.98332	−	6.51909i	−0.120890	−	0.264167i
$610$	1.24231	−	0.798385i	0.0502997	−	0.0323257i
$611$	−0.682443	+	1.97179i	−0.0276087	+	0.0797701i
$612$	0.987062	−	4.06872i	0.0398996	−	0.164468i
$613$	−35.6875	−	28.0650i	−1.44141	−	1.13353i	−0.967473	−	0.252974i	$-0.918591\pi$
$613$	−35.6875	−	28.0650i	−1.44141	−	1.13353i	−0.473933	−	0.880561i	$-0.657166\pi$
$614$	6.93013	+	1.33567i	0.279677	+	0.0539034i
$615$	−0.424890	+	0.930379i	−0.0171332	+	0.0375165i
$616$	7.21146	−	15.8236i	0.290558	−	0.637551i
$617$	20.4458	+	44.7700i	0.823117	+	1.80237i	0.535220	+	0.844713i	$0.320229\pi$
$617$	20.4458	+	44.7700i	0.823117	+	1.80237i	0.287897	+	0.957661i	$0.407044\pi$
$618$	9.09223	−	7.15021i	0.365743	−	0.287624i
$619$	25.7951	−	13.2983i	1.03679	−	0.534503i	0.146175	−	0.989259i	$-0.453304\pi$
$619$	25.7951	−	13.2983i	1.03679	−	0.534503i	0.890616	+	0.454755i	$0.150273\pi$
$620$	0.919713	−	1.59299i	0.0369366	−	0.0639760i
$621$	−0.768896	+	4.73379i	−0.0308547	+	0.189961i
$622$	3.66653			0.147014
$623$	11.0171	+	31.7515i	0.441390	+	1.27210i
$624$	−0.670023	−	4.66011i	−0.0268224	−	0.186554i
$625$	13.3990	−	18.8163i	0.535961	−	0.752652i
$626$	16.1440	−	15.3933i	0.645246	−	0.615240i
$627$	−27.0123	−	37.9335i	−1.07877	−	1.51492i
$628$	3.69452	+	0.712060i	0.147427	+	0.0284143i
$629$	−6.85480	+	47.6762i	−0.273319	+	1.90097i
$630$	−0.742984	+	0.585229i	−0.0296012	+	0.0233161i
$631$	−29.7107	−	34.2879i	−1.18276	−	1.36498i	−0.915980	−	0.401224i	$-0.868585\pi$
$631$	−29.7107	−	34.2879i	−1.18276	−	1.36498i	−0.266782	−	0.963757i	$-0.585960\pi$
$632$	−14.0121	−	7.22373i	−0.557371	−	0.287345i
$633$	0.838258	+	17.5972i	0.0333178	+	0.699426i
$634$	−32.9298	+	6.34670i	−1.30781	+	0.252060i
$635$	2.21412	+	2.11115i	0.0878645	+	0.0837786i
$636$	−0.103380	+	0.719022i	−0.00409927	+	0.0285111i
$637$	1.61954	+	32.9164i	0.0641687	+	1.30420i
$638$	−7.39852	+	16.2005i	−0.292910	+	0.641384i
$639$	−3.22609	−	13.2981i	−0.127622	−	0.526065i
$640$	0.355856	+	0.0339801i	0.0140664	+	0.00134318i
$641$	0.584688	+	0.234074i	0.0230938	+	0.00924536i	0.383181	−	0.923673i	$-0.374829\pi$
$641$	0.584688	+	0.234074i	0.0230938	+	0.00924536i	−0.360087	+	0.932919i	$0.617253\pi$
$642$	−0.363431	+	7.62935i	−0.0143435	+	0.301106i
$643$	14.8971			0.587484			0.293742	−	0.955885i	$-0.405099\pi$
$643$	14.8971			0.587484			0.293742	+	0.955885i	$0.405099\pi$
$644$	−10.7923	+	6.67277i	−0.425277	+	0.262944i
$645$	−1.36933			−0.0539174
$646$	1.41148	−	29.6305i	0.0555338	−	1.16580i
$647$	2.56292	+	1.02604i	0.100759	+	0.0403378i	0.421494	−	0.906831i	$-0.361506\pi$
$647$	2.56292	+	1.02604i	0.100759	+	0.0403378i	−0.320735	+	0.947169i	$0.603930\pi$
$648$	0.995472	+	0.0950560i	0.0391058	+	0.00373415i
$649$	−3.43579	−	14.1625i	−0.134866	−	0.555927i
$650$	9.52901	−	20.8656i	0.373759	−	0.818417i
$651$	13.3660	−	2.58691i	0.523853	−	0.101389i
$652$	0.169303	−	1.17753i	0.00663042	−	0.0461156i
$653$	26.2952	+	25.0724i	1.02901	+	0.981160i	0.999830	−	0.0184138i	$-0.00586162\pi$
$653$	26.2952	+	25.0724i	1.02901	+	0.981160i	0.0291809	+	0.999574i	$0.490710\pi$
$654$	3.92347	−	0.756186i	0.153420	−	0.0295692i
$655$	0.123063	+	2.58341i	0.00480846	+	0.100942i
$656$	2.54314	+	1.31108i	0.0992929	+	0.0511891i
$657$	−8.07457	−	9.31856i	−0.315019	−	0.363551i
$658$	−0.167780	−	1.16050i	−0.00654076	−	0.0452411i
$659$	−4.76808	+	33.1627i	−0.185738	+	1.29184i	0.657155	+	0.753755i	$0.271760\pi$
$659$	−4.76808	+	33.1627i	−0.185738	+	1.29184i	−0.842893	+	0.538081i	$0.819149\pi$
$660$	2.30707	+	0.444652i	0.0898027	+	0.0173080i
$661$	18.7519	+	26.3334i	0.729366	+	1.02425i	0.998135	+	0.0610467i	$0.0194438\pi$
$661$	18.7519	+	26.3334i	0.729366	+	1.02425i	−0.268769	+	0.963205i	$0.586617\pi$
$662$	−21.8580	+	20.8415i	−0.849534	+	0.810029i
$663$	11.4337	−	16.0564i	0.444048	−	0.623577i
$664$	−1.28440	−	8.93317i	−0.0498442	−	0.346674i
$665$	−4.38437	+	5.06783i	−0.170019	+	0.196522i
$666$	−11.5045			−0.445791
$667$	11.0587	−	6.82551i	0.428193	−	0.264285i
$668$	9.47573	−	16.4124i	0.366627	−	0.635016i
$669$	−5.41293	+	2.79056i	−0.209276	+	0.107889i
$670$	0.0900561	−	0.0708209i	0.00347917	−	0.00273605i
$671$	−11.2791	−	24.6979i	−0.435426	−	0.953451i
$672$	1.53637	+	2.15397i	0.0592667	+	0.0830910i
$673$	17.1114	−	37.4687i	0.659595	−	1.44431i	−0.223304	−	0.974749i	$-0.571684\pi$
$673$	17.1114	−	37.4687i	0.659595	−	1.44431i	0.882899	−	0.469562i	$-0.155588\pi$
$674$	26.3365	+	5.07595i	1.01445	+	0.195518i
$675$	3.82982	+	3.01180i	0.147410	+	0.115924i
$676$	2.16087	−	8.90721i	0.0831103	−	0.342585i
$677$	−14.8477	+	42.8996i	−0.570644	+	1.64877i	0.176651	+	0.984274i	$0.443474\pi$
$677$	−14.8477	+	42.8996i	−0.570644	+	1.64877i	−0.747295	+	0.664493i	$0.768648\pi$
$678$	−0.592704	+	0.380908i	−0.0227626	+	0.0146287i
$679$	7.16702	−	10.0813i	0.275045	−	0.386886i
$680$	0.980100	+	1.13110i	0.0375851	+	0.0433756i
$681$	9.47910	+	9.03830i	0.363240	+	0.346348i
$682$	−26.5842	−	20.9061i	−1.01796	−	0.800535i
$683$	−10.5349	−	30.4385i	−0.403105	−	1.16470i	−0.945796	−	0.324763i	$-0.894716\pi$
$683$	−10.5349	−	30.4385i	−0.403105	−	1.16470i	0.542691	−	0.839933i	$-0.317406\pi$
$684$	7.05317	−	0.673497i	0.269685	−	0.0257518i
$685$	4.73407	+	1.39005i	0.180880	+	0.0531110i
$686$	−9.29769	−	16.0173i	−0.354987	−	0.611542i
$687$	−0.291429	−	2.02693i	−0.0111187	−	0.0773324i
$688$	−0.182266	+	3.82623i	−0.00694882	+	0.145874i
$689$	−1.70999	+	2.96180i	−0.0651456	+	0.112835i
$690$	−1.21900	−	1.20547i	−0.0464065	−	0.0458916i
$691$	2.24668	+	3.89137i	0.0854678	+	0.148035i	0.905590	−	0.424153i	$-0.139428\pi$
$691$	2.24668	+	3.89137i	0.0854678	+	0.148035i	−0.820123	+	0.572188i	$0.806095\pi$
$692$	1.17963	+	0.758104i	0.0448429	+	0.0288188i
$693$	8.70646	+	15.0529i	0.330731	+	0.571811i
$694$	−6.67466	−	14.6155i	−0.253366	−	0.554795i
$695$	1.12334	+	4.63046i	0.0426106	+	0.175643i
$696$	−1.57180	−	2.20729i	−0.0595790	−	0.0836670i
$697$	3.91799	+	11.3203i	0.148404	+	0.428786i
$698$	30.7509	−	12.3108i	1.16394	−	0.465971i
$699$	15.2048	−	4.46454i	0.575099	−	0.168864i
$700$	0.623419	+	12.8756i	0.0235630	+	0.486651i
$701$	−27.7077	+	17.8066i	−1.04650	+	0.672548i	−0.946587	−	0.322448i	$-0.895494\pi$
$701$	−27.7077	+	17.8066i	−1.04650	+	0.672548i	−0.0999175	+	0.994996i	$0.531858\pi$
$702$	4.18467	+	2.15735i	0.157940	+	0.0814238i
$703$	−80.0395	+	15.4263i	−3.01875	+	0.581816i
$704$	1.54954	−	6.38731i	0.0584006	−	0.240731i
$705$	0.147080	−	0.0588821i	0.00553937	−	0.00221763i
$706$	9.32334	−	10.7597i	0.350889	−	0.404947i
$707$	−34.1027	−	21.8789i	−1.28256	−	0.822839i
$708$	2.12747	+	0.624683i	0.0799554	+	0.0234770i
$709$	26.2546	−	36.8694i	0.986011	−	1.38466i	0.0638031	−	0.997963i	$-0.479677\pi$
$709$	26.2546	−	36.8694i	0.986011	−	1.38466i	0.922207	−	0.386696i	$-0.126384\pi$
$710$	4.54123	+	1.81803i	0.170429	+	0.0682296i
$711$	14.0121	−	7.22373i	0.525494	−	0.270911i
$712$	6.35142	+	11.0010i	0.238030	+	0.412279i
$713$	7.64497	+	23.4634i	0.286306	+	0.878712i
$714$	−1.56787	+	10.9656i	−0.0586760	+	0.410376i
$715$	9.30567	+	5.98039i	0.348012	+	0.223654i
$716$	12.4433	−	9.78552i	0.465028	−	0.365702i
$717$	3.80894	+	0.363710i	0.142248	+	0.0135830i
$718$	2.21995	−	2.11672i	0.0828477	−	0.0789952i
$719$	20.4097	−	1.94889i	0.761154	−	0.0726814i	0.292742	−	0.956192i	$-0.405432\pi$
$719$	20.4097	−	1.94889i	0.761154	−	0.0726814i	0.468412	+	0.883510i	$0.344826\pi$
$720$	−0.234096	+	0.270161i	−0.00872425	+	0.0100683i
$721$	−22.1321	+	21.1360i	−0.824243	+	0.787144i
$722$	29.9370	−	8.79030i	1.11414	−	0.327141i
$723$	7.94656	−	22.9601i	0.295536	−	0.853895i
$724$	0.596552	+	12.5232i	0.0221707	+	0.465420i
$725$	−0.628196	−	13.1875i	−0.0233306	−	0.489770i
$726$	10.5312	−	30.4279i	0.390849	−	1.12928i
$727$	1.32375	−	0.388689i	0.0490953	−	0.0144157i	−0.257093	−	0.966387i	$-0.582765\pi$
$727$	1.32375	−	0.388689i	0.0490953	−	0.0144157i	0.306188	+	0.951971i	$0.400946\pi$
$728$	2.94613	+	12.1029i	0.109191	+	0.448562i
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$	4.38778	−	0.418983i	0.162399	−	0.0155072i
$731$	−11.6070	+	11.0672i	−0.429299	+	0.409335i
$732$	4.11232	+	0.392679i	0.151996	+	0.0145138i
$733$	−22.3356	+	17.5649i	−0.824985	+	0.648775i	−0.938699	−	0.344739i	$-0.887968\pi$
$733$	−22.3356	+	17.5649i	−0.824985	+	0.648775i	0.113714	+	0.993513i	$0.463725\pi$
$734$	−22.0283	−	14.1567i	−0.813080	−	0.522535i
$735$	1.80832	−	1.72963i	0.0667008	−	0.0637983i
$736$	−3.53063	+	3.24571i	−0.130141	+	0.119639i
$737$	−1.05323	−	1.82424i	−0.0387961	−	0.0671967i
$738$	−2.54314	+	1.31108i	−0.0936143	+	0.0482615i
$739$	14.5943	+	5.84267i	0.536860	+	0.214926i	0.624217	−	0.781251i	$-0.285418\pi$
$739$	14.5943	+	5.84267i	0.536860	+	0.214926i	−0.0873575	+	0.996177i	$0.527842\pi$
$740$	2.38553	−	3.35001i	0.0876938	−	0.123149i
$741$	32.0064	+	9.39793i	1.17578	+	0.345242i
$742$	0.0899489	−	1.91981i	0.00330213	−	0.0704784i
$743$	9.50101	−	10.9648i	0.348558	−	0.402258i	−0.554216	−	0.832373i	$-0.686982\pi$
$743$	9.50101	−	10.9648i	0.348558	−	0.402258i	0.902774	+	0.430115i	$0.141527\pi$
$744$	4.77702	−	1.91243i	0.175134	−	0.0701131i
$745$	0.442630	−	1.82454i	0.0162167	−	0.0668461i
$746$	−0.382969	+	0.0738112i	−0.0140215	+	0.00270242i
$747$	8.02177	+	4.13551i	0.293501	+	0.151310i
$748$	23.1493	−	14.8772i	0.846424	−	0.543964i
$749$	−0.977313	−	20.1846i	−0.0357102	−	0.737529i
$750$	−3.38612	+	0.994253i	−0.123643	+	0.0363050i
$751$	−14.4272	+	5.77578i	−0.526456	+	0.210761i	−0.619638	−	0.784888i	$-0.712721\pi$
$751$	−14.4272	+	5.77578i	−0.526456	+	0.210761i	0.0931816	+	0.995649i	$0.470296\pi$
$752$	−0.144953	−	0.418814i	−0.00528589	−	0.0152726i
$753$	−8.13402	−	11.4226i	−0.296420	−	0.416264i
$754$	−3.00770	−	12.3979i	−0.109534	−	0.451505i
$755$	0.564950	+	1.23707i	0.0205606	+	0.0450215i
$756$	−2.64575	+	0.00206656i	−0.0962250	+	7.51602e-5i
$757$	−17.6239	−	11.3262i	−0.640550	−	0.411656i	0.179652	−	0.983730i	$-0.442503\pi$
$757$	−17.6239	−	11.3262i	−0.640550	−	0.411656i	−0.820202	+	0.572074i	$0.806139\pi$
$758$	5.06599	+	8.77455i	0.184005	+	0.318706i
$759$	−25.1281	+	19.0303i	−0.912091	+	0.690756i
$760$	−1.26640	+	2.19347i	−0.0459372	+	0.0795655i
$761$	−0.235290	+	4.93934i	−0.00852924	+	0.179051i	0.990583	+	0.136916i	$0.0437190\pi$
$761$	−0.235290	+	4.93934i	−0.00852924	+	0.179051i	−0.999112	+	0.0421350i	$0.986584\pi$
$762$	1.21794	+	8.47096i	0.0441213	+	0.306871i
$763$	−10.1410	+	2.98627i	−0.367129	+	0.108110i
$764$	−10.1693	−	2.98596i	−0.367911	−	0.108028i
$765$	−1.48988	+	0.142266i	−0.0538666	+	0.00514364i
$766$	3.44816	+	9.96279i	0.124587	+	0.359970i
$767$	8.20566	+	6.45301i	0.296289	+	0.233005i
$768$	0.723734	+	0.690079i	0.0261155	+	0.0249011i
$769$	−24.5001	−	28.2747i	−0.883497	−	1.01961i	−0.999652	−	0.0263793i	$-0.991602\pi$
$769$	−24.5001	−	28.2747i	−0.883497	−	1.01961i	0.116155	−	0.993231i	$-0.462943\pi$
$770$	−6.18859	−	0.586061i	−0.223021	−	0.0211202i
$771$	10.4804	−	6.73536i	0.377443	−	0.242568i
$772$	1.15573	−	3.33927i	0.0415957	−	0.120183i
$773$	10.9786	−	45.2543i	0.394872	−	1.62768i	−0.333676	−	0.942688i	$-0.608289\pi$
$773$	10.9786	−	45.2543i	0.394872	−	1.62768i	0.728548	−	0.684995i	$-0.240196\pi$
$774$	−3.01103	−	2.36790i	−0.108229	−	0.0851124i
$775$	24.6174	+	4.74462i	0.884285	+	0.170432i
$776$	1.94213	−	4.25267i	0.0697183	−	0.152662i
$777$	30.2980	−	2.91699i	1.08694	−	0.104647i
$778$	−0.173803	−	0.380574i	−0.00623112	−	0.0136443i
$779$	−15.9352	+	12.5315i	−0.570936	+	0.448989i
$780$	−1.49591	+	0.771197i	−0.0535623	+	0.0276133i
$781$	44.9690	−	77.8887i	1.60912	−	2.78708i
$782$	−20.0756	−	0.365842i	−0.717901	−	0.0130825i
$783$	2.70974			0.0968381
$784$	−4.59228	−	5.28308i	−0.164010	−	0.188681i
$785$	−0.191414	−	1.33131i	−0.00683185	−	0.0475166i
$786$	−4.19672	+	5.89347i	−0.149692	+	0.210213i
$787$	24.9171	−	23.7584i	0.888200	−	0.846897i	−0.100786	−	0.994908i	$-0.532136\pi$
$787$	24.9171	−	23.7584i	0.888200	−	0.846897i	0.988986	+	0.148011i	$0.0472872\pi$
$788$	−0.955356	−	1.34161i	−0.0340331	−	0.0477929i
$789$	12.5834	+	2.42525i	0.447980	+	0.0863411i
$790$	−0.802005	+	5.57807i	−0.0285340	+	0.198459i
$791$	1.46435	−	1.15343i	0.0520663	−	0.0410112i
$792$	4.30412	+	4.96722i	0.152940	+	0.176503i
$793$	17.2870	+	8.91205i	0.613878	+	0.316476i
$794$	−0.966614	−	20.2917i	−0.0343038	−	0.720126i
$795$	0.254983	−	0.0491439i	0.00904330	−	0.00174295i
$796$	−1.99666	−	1.90381i	−0.0707696	−	0.0674786i
$797$	−1.54807	+	10.7671i	−0.0548354	+	0.381389i	0.943861	+	0.330343i	$0.107164\pi$
$797$	−1.54807	+	10.7671i	−0.0548354	+	0.381389i	−0.998696	+	0.0510456i	$0.983745\pi$
$798$	−18.4043	+	3.56205i	−0.651505	+	0.126095i
$799$	0.770810	−	1.68784i	0.0272693	−	0.0597114i
$800$	1.14867	+	4.73487i	0.0406115	+	0.167403i
$801$	−12.6453	−	1.20748i	−0.446800	−	0.0426643i
$802$	−5.20900	−	2.08537i	−0.183936	−	0.0736370i
$803$	3.85610	−	80.9495i	0.136079	−	2.85665i
$804$	0.320491			0.0113028
$805$	3.51598	+	2.86563i	0.123922	+	0.101000i
$806$	24.2257			0.853314
$807$	−0.248163	+	5.20958i	−0.00873575	+	0.183386i
$808$	−14.2172	−	5.69172i	−0.500161	−	0.200234i
$809$	−9.30404	−	0.888428i	−0.327112	−	0.0312355i	−0.0697920	−	0.997562i	$-0.522234\pi$
$809$	−9.30404	−	0.888428i	−0.327112	−	0.0312355i	−0.257321	+	0.966326i	$0.582840\pi$
$810$	−0.0842779	−	0.347398i	−0.00296122	−	0.0122063i
$811$	−1.32524	+	2.90186i	−0.0465353	+	0.101898i	−0.931472	−	0.363814i	$-0.881474\pi$
$811$	−1.32524	+	2.90186i	−0.0465353	+	0.101898i	0.884936	+	0.465712i	$0.154202\pi$
$812$	4.69912	+	5.41452i	0.164907	+	0.190012i
$813$	2.51894	−	17.5196i	0.0883430	−	0.614439i
$814$	−54.7247	−	52.1799i	−1.91810	−	1.82890i
$815$	−0.417581	+	0.0804821i	−0.0146272	+	0.00281916i
$816$	0.199213	+	4.18200i	0.00697386	+	0.146399i
$817$	−24.1235	−	12.4365i	−0.843974	−	0.435099i
$818$	−15.3732	−	17.7416i	−0.537510	−	0.620320i
$819$	−11.5676	−	4.62050i	−0.404206	−	0.161453i
$820$	0.145561	−	1.01240i	0.00508321	−	0.0353545i
$821$	31.9466	+	6.15721i	1.11494	+	0.214888i	0.713266	−	0.700893i	$-0.247215\pi$
$821$	31.9466	+	6.15721i	1.11494	+	0.214888i	0.401678	+	0.915781i	$0.368427\pi$
$822$	8.00605	+	11.2429i	0.279243	+	0.392142i
$823$	26.4071	−	25.1791i	0.920492	−	0.877688i	−0.0723185	−	0.997382i	$-0.523040\pi$
$823$	26.4071	−	25.1791i	0.920492	−	0.877688i	0.992811	+	0.119694i	$0.0381913\pi$
$824$	−6.70948	+	9.42215i	−0.233736	+	0.328236i
$825$	4.55735	+	31.6970i	0.158666	+	1.10355i
$826$	−5.76125	−	1.10572i	−0.200459	−	0.0384730i
$827$	11.2622			0.391627			0.195813	−	0.980641i	$-0.437265\pi$
$827$	11.2622			0.391627			0.195813	+	0.980641i	$0.437265\pi$
$828$	−0.595913	−	4.75866i	−0.0207094	−	0.165375i
$829$	−8.01743	+	13.8866i	−0.278457	+	0.482301i	−0.971001	−	0.239074i	$-0.923156\pi$
$829$	−8.01743	+	13.8866i	−0.278457	+	0.482301i	0.692545	+	0.721375i	$0.256490\pi$
$830$	−2.86758	+	1.47834i	−0.0995351	+	0.0513139i
$831$	6.68505	−	5.25718i	0.231902	−	0.182370i
$832$	1.95579	+	4.28258i	0.0678047	+	0.148472i
$833$	1.34876	−	29.2761i	0.0467317	−	1.01436i
$834$	−5.53706	+	12.1245i	−0.191733	+	0.419836i
$835$	−6.65224	−	1.28211i	−0.230210	−	0.0443694i
$836$	36.6052	+	28.7867i	1.26602	+	0.995608i
$837$	−1.21312	+	5.00056i	−0.0419317	+	0.172845i
$838$	−3.11989	+	9.01432i	−0.107775	+	0.311394i
$839$	−36.4712	+	23.4386i	−1.25913	+	0.809192i	−0.988164	−	0.153398i	$-0.950978\pi$
$839$	−36.4712	+	23.4386i	−1.25913	+	0.809192i	−0.270962	+	0.962590i	$0.587342\pi$
$840$	0.548010	−	0.770846i	0.0189081	−	0.0265967i
$841$	14.1825	+	16.3675i	0.489053	+	0.564397i
$842$	−13.5877	−	12.9558i	−0.468261	−	0.446486i
$843$	17.5120	+	13.7716i	0.603145	+	0.474319i
$844$	−5.76201	−	16.6482i	−0.198337	−	0.573056i
$845$	−3.26163	+	0.311448i	−0.112203	+	0.0107141i
$846$	0.425237	+	0.124861i	0.0146199	+	0.00429280i
$847$	−20.0196	+	82.8043i	−0.687882	+	2.84519i
$848$	−0.103380	−	0.719022i	−0.00355007	−	0.0246913i
$849$	0.915971	−	19.2286i	0.0314361	−	0.659924i
$850$	−10.1993	+	17.6658i	−0.349835	+	0.605931i
$851$	12.0286	+	53.8466i	0.412335	+	1.84584i
$852$	6.84192	+	11.8505i	0.234400	+	0.405993i
$853$	−0.281459	−	0.180882i	−0.00963696	−	0.00619330i	0.535813	−	0.844336i	$-0.320005\pi$
$853$	−0.281459	−	0.180882i	−0.00963696	−	0.00619330i	−0.545450	+	0.838143i	$0.683641\pi$
$854$	−10.9297	+	0.00853703i	−0.374005	+	0.000292131i
$855$	−1.05216	−	2.30392i	−0.0359832	−	0.0787923i
$856$	−1.80073	−	7.42270i	−0.0615476	−	0.253702i
$857$	−5.74257	−	8.06432i	−0.196163	−	0.275472i	0.704765	−	0.709440i	$-0.251052\pi$
$857$	−5.74257	−	8.06432i	−0.196163	−	0.275472i	−0.900928	+	0.433969i	$0.857113\pi$
$858$	10.1208	+	29.2420i	0.345517	+	0.998306i
$859$	−6.70192	+	2.68304i	−0.228667	+	0.0915443i	−0.483166	−	0.875529i	$-0.660513\pi$
$859$	−6.70192	+	2.68304i	−0.228667	+	0.0915443i	0.254500	+	0.967073i	$0.418089\pi$
$860$	1.31386	−	0.385785i	0.0448024	−	0.0131552i
$861$	6.36512	−	4.09764i	0.216923	−	0.139647i
$862$	2.56391	−	1.64773i	0.0873272	−	0.0561218i
$863$	−9.47844	−	4.88647i	−0.322650	−	0.166338i	0.289291	−	0.957241i	$-0.406581\pi$
$863$	−9.47844	−	4.88647i	−0.322650	−	0.166338i	−0.611941	+	0.790904i	$0.709611\pi$
$864$	−0.981929	+	0.189251i	−0.0334059	+	0.00643846i
$865$	0.118177	−	0.487133i	0.00401815	−	0.0165630i
$866$	−26.1828	+	10.4820i	−0.889728	+	0.356193i
$867$	−0.346290	+	0.399640i	−0.0117606	+	0.0135725i
$868$	−12.0957	+	6.24775i	−0.410556	+	0.212062i
$869$	99.4166	+	29.1913i	3.37248	+	0.990248i
$870$	−0.561879	+	0.789049i	−0.0190495	+	0.0267513i
$871$	1.40080	+	0.560795i	0.0474642	+	0.0190018i
$872$	−3.55150	+	1.83092i	−0.120269	+	0.0620029i
$873$	2.33758	+	4.04880i	0.0791150	+	0.137031i
$874$	−10.5268	−	32.3080i	−0.356073	−	1.09283i
$875$	8.66549	−	3.47699i	0.292947	−	0.117544i
$876$	10.3728	+	6.66622i	0.350466	+	0.225231i
$877$	38.9339	−	30.6180i	1.31471	−	1.03390i	0.318405	−	0.947955i	$-0.396853\pi$
$877$	38.9339	−	30.6180i	1.31471	−	1.03390i	0.996300	−	0.0859411i	$-0.0273897\pi$
$878$	3.89642	+	0.372063i	0.131498	+	0.0125565i
$879$	2.40913	−	2.29710i	0.0812578	−	0.0774791i
$880$	−2.33889	+	0.223337i	−0.0788440	+	0.00752869i
$881$	−6.06406	+	6.99830i	−0.204303	+	0.235779i	−0.848650	−	0.528955i	$-0.822584\pi$
$881$	−6.06406	+	6.99830i	−0.204303	+	0.235779i	0.644346	+	0.764734i	$0.277129\pi$
$882$	6.96726	−	0.676277i	0.234600	−	0.0227714i
$883$	−19.9474	+	5.85708i	−0.671283	+	0.197106i	−0.599574	−	0.800319i	$-0.704663\pi$
$883$	−19.9474	+	5.85708i	−0.671283	+	0.197106i	−0.0717087	+	0.997426i	$0.522845\pi$
$884$	−6.44694	+	18.6272i	−0.216834	+	0.626501i
$885$	−0.0377146	−	0.791727i	−0.00126776	−	0.0266136i
$886$	−0.498308	−	10.4608i	−0.0167410	−	0.351437i
$887$	16.2402	−	46.9230i	0.545293	−	1.57552i	−0.249331	−	0.968418i	$-0.580211\pi$
$887$	16.2402	−	46.9230i	0.545293	−	1.57552i	0.794624	−	0.607102i	$-0.207668\pi$
$888$	11.0385	−	3.24120i	0.370428	−	0.108768i
$889$	−5.35536	−	22.0001i	−0.179613	−	0.737859i
$890$	2.97369	−	3.43182i	0.0996782	−	0.115035i
$891$	−6.54282	+	0.624763i	−0.219193	+	0.0209304i
$892$	4.40747	−	4.20252i	0.147573	−	0.140711i
$893$	3.12589	+	0.298486i	0.104604	+	0.00998846i
$894$	4.12837	−	3.24659i	0.138073	−	0.108582i
$895$	−4.76054	−	3.05941i	−0.159127	−	0.102265i
$896$	−2.08098	−	1.63387i	−0.0695206	−	0.0545838i
$897$	5.72210	−	21.8418i	0.191055	−	0.729278i
$898$	11.8230	+	20.4780i	0.394538	+	0.683360i
$899$	12.3932	−	6.38916i	0.413338	−	0.213091i
$900$	−4.52321	−	1.81082i	−0.150774	−	0.0603606i
$901$	1.76414	−	2.47738i	0.0587719	−	0.0825335i
$902$	−18.0437	−	5.29812i	−0.600791	−	0.176408i
$903$	8.53015	+	5.47259i	0.283866	+	0.182116i
$904$	0.461381	−	0.532462i	0.0153453	−	0.0177094i
$905$	4.16075	−	1.66571i	0.138308	−	0.0553702i
$906$	−0.896914	+	3.69713i	−0.0297980	+	0.122829i
$907$	2.23800	−	0.431339i	0.0743116	−	0.0143224i	−0.151960	−	0.988387i	$-0.548558\pi$
$907$	2.23800	−	0.431339i	0.0743116	−	0.0143224i	0.226271	+	0.974064i	$0.427346\pi$
$908$	−11.6415	−	6.00162i	−0.386337	−	0.199171i
$909$	12.8831	−	8.27949i	0.427307	−	0.274614i
$910$	3.74406	−	2.41030i	0.124114	−	0.0799005i
$911$	16.8427	−	4.94546i	0.558023	−	0.163850i	0.00945363	−	0.999955i	$-0.496991\pi$
$911$	16.8427	−	4.94546i	0.558023	−	0.163850i	0.548570	+	0.836105i	$0.315173\pi$
$912$	−6.57773	+	2.63332i	−0.217810	+	0.0871981i
$913$	19.4009	+	56.0553i	0.642077	+	1.85516i
$914$	−12.7213	−	17.8645i	−0.420782	−	0.590905i
$915$	−0.348154	−	1.43511i	−0.0115096	−	0.0474433i
$916$	0.850678	+	1.86272i	0.0281072	+	0.0615461i
$917$	9.55807	−	16.5850i	0.315635	−	0.547684i
$918$	−3.52211	−	2.26352i	−0.116247	−	0.0747074i
$919$	−7.03774	−	12.1897i	−0.232154	−	0.402102i	0.726288	−	0.687391i	$-0.241244\pi$
$919$	−7.03774	−	12.1897i	−0.232154	−	0.402102i	−0.958442	+	0.285289i	$0.907911\pi$
$920$	1.50924	+	0.813212i	0.0497583	+	0.0268108i
$921$	3.52883	−	6.11212i	0.116279	−	0.201401i
$922$	1.05887	−	22.2284i	0.0348720	−	0.732052i
$923$	9.16849	+	63.7682i	0.301784	+	2.09896i
$924$	−12.5947	−	11.9902i	−0.414334	−	0.394450i
$925$	53.7820	+	15.7918i	1.76834	+	0.519231i
$926$	−1.13813	+	0.108678i	−0.0374013	+	0.00357139i
$927$	−3.78318	−	10.9308i	−0.124256	−	0.359013i
$928$	2.13000	+	1.67505i	0.0699206	+	0.0549861i
$929$	−32.3143	−	30.8116i	−1.06020	−	1.01090i	−0.999919	−	0.0127141i	$-0.995953\pi$
$929$	−32.3143	−	30.8116i	−1.06020	−	1.01090i	−0.0602778	−	0.998182i	$-0.519199\pi$
$930$	−1.20457	−	1.39015i	−0.0394993	−	0.0455847i
$931$	47.5659	−	14.0474i	1.55891	−	0.460384i
$932$	−13.3311	+	8.56738i	−0.436675	+	0.280634i
$933$	1.19920	−	3.46487i	0.0392601	−	0.113435i
$934$	5.90543	−	24.3425i	0.193232	−	0.796511i
$935$	−7.73231	−	6.08075i	−0.252874	−	0.198862i
$936$	−4.62295	−	0.891001i	−0.151106	−	0.0291233i
$937$	−0.268570	+	0.588085i	−0.00877378	+	0.0192119i	−0.913968	−	0.405786i	$-0.866998\pi$
$937$	−0.268570	+	0.588085i	−0.00877378	+	0.0192119i	0.905194	+	0.424998i	$0.139725\pi$
$938$	−0.844036	+	0.0812610i	−0.0275588	+	0.00265327i
$939$	−9.26649	−	20.2908i	−0.302401	−	0.662165i
$940$	−0.124534	+	0.0979343i	−0.00406184	+	0.00319426i
$941$	21.3001	−	10.9810i	0.694364	−	0.357970i	−0.0746425	−	0.997210i	$-0.523782\pi$
$941$	21.3001	−	10.9810i	0.694364	−	0.357970i	0.769007	+	0.639241i	$0.220751\pi$
$942$	1.88125	−	3.25843i	0.0612946	−	0.106165i
$943$	8.79546	+	10.5323i	0.286420	+	0.342979i
$944$	−2.21729			−0.0721666
$945$	0.310035	+	0.893530i	0.0100855	+	0.0290665i
$946$	−3.58302	−	24.9204i	−0.116494	−	0.810233i
$947$	−20.5386	+	28.8424i	−0.667414	+	0.937252i	−0.999983	−	0.00582717i	$-0.998145\pi$
$947$	−20.5386	+	28.8424i	−0.667414	+	0.937252i	0.332569	+	0.943079i	$0.392085\pi$
$948$	−11.4093	+	10.8788i	−0.370558	+	0.353326i
$949$	33.6729	+	47.2870i	1.09307	+	1.53500i
$950$	−33.8970	−	6.53312i	−1.09977	−	0.211962i
$951$	−4.77265	+	33.1945i	−0.154764	+	1.07641i
$952$	−1.58500	−	10.9631i	−0.0513700	−	0.355316i
$953$	−7.12897	−	8.22727i	−0.230930	−	0.266507i	0.628444	−	0.777855i	$-0.283692\pi$
$953$	−7.12897	−	8.22727i	−0.230930	−	0.266507i	−0.859374	+	0.511347i	$0.829147\pi$
$954$	0.645664	+	0.332863i	0.0209041	+	0.0107768i
$955$	0.180275	+	3.78443i	0.00583356	+	0.122461i
$956$	−3.75712	+	0.724126i	−0.121514	+	0.0234199i
$957$	12.8897	+	12.2903i	0.416664	+	0.397288i
$958$	−5.61411	+	39.0470i	−0.181384	+	1.26155i
$959$	−23.9352	−	27.5791i	−0.772907	−	0.890576i
$960$	0.148500	−	0.325171i	0.00479283	−	0.0104948i
$961$	−1.06627	−	4.39522i	−0.0343958	−	0.141781i
$962$	53.9184	+	5.14858i	1.73840	+	0.165997i
$963$	7.09087	+	2.83876i	0.228500	+	0.0914777i
$964$	−1.15607	+	24.2688i	−0.0372344	+	0.781647i
$965$	−1.26318			−0.0406632
$966$	2.77595	+	12.3812i	0.0893147	+	0.398359i
$967$	17.2832			0.555790			0.277895	−	0.960611i	$-0.410363\pi$
$967$	17.2832			0.555790			0.277895	+	0.960611i	$0.410363\pi$
$968$	−1.53208	+	32.1623i	−0.0492429	+	1.03374i
$969$	−27.5392	−	11.0250i	−0.884688	−	0.354176i
$970$	−1.66368	−	0.158862i	−0.0534176	−	0.00510076i
$971$	11.7040	+	48.2444i	0.375598	+	1.54824i	0.775300	+	0.631593i	$0.217598\pi$
$971$	11.7040	+	48.2444i	0.375598	+	1.54824i	−0.399702	+	0.916645i	$0.630886\pi$
$972$	0.415415	−	0.909632i	0.0133244	−	0.0291765i
$973$	11.5081	−	33.3346i	0.368932	−	1.06866i
$974$	2.99587	−	20.8367i	0.0959937	−	0.667651i
$975$	−16.6014	−	15.8294i	−0.531670	−	0.506947i
$976$	−4.05637	+	0.781802i	−0.129841	+	0.0250249i
$977$	−2.46604	−	51.7685i	−0.0788956	−	1.65622i	−0.597989	−	0.801505i	$-0.704033\pi$
$977$	−2.46604	−	51.7685i	−0.0788956	−	1.65622i	0.519093	−	0.854718i	$-0.326270\pi$
$978$	−1.05739	−	0.545124i	−0.0338117	−	0.0174311i
$979$	−54.6746	−	63.0978i	−1.74741	−	2.01662i
$980$	−1.24778	+	2.16903i	−0.0398587	+	0.0692871i
$981$	0.568644	−	3.95500i	0.0181554	−	0.126274i
$982$	−1.66101	−	0.320133i	−0.0530049	−	0.0102159i
$983$	2.64678	+	3.71689i	0.0844193	+	0.118550i	0.854626	−	0.519244i	$-0.173786\pi$
$983$	2.64678	+	3.71689i	0.0844193	+	0.118550i	−0.770207	+	0.637794i	$0.779847\pi$
$984$	2.07075	−	1.97446i	0.0660131	−	0.0629434i
$985$	−0.341516	+	0.479592i	−0.0108816	+	0.0152811i
$986$	1.61456	+	11.2295i	0.0514180	+	0.357620i
$987$	−1.15155	−	0.221011i	−0.0366543	−	0.00703484i
$988$	−33.3576			−1.06125
$989$	−7.93469	+	16.5688i	−0.252309	+	0.526857i
$990$	1.17477	−	2.03475i	0.0373365	−	0.0646687i
$991$	4.42442	−	2.28095i	0.140546	−	0.0724567i	−0.386519	−	0.922281i	$-0.626323\pi$
$991$	4.42442	−	2.28095i	0.140546	−	0.0724567i	0.527065	+	0.849825i	$0.323292\pi$
$992$	−4.04472	+	3.18080i	−0.128420	+	0.100991i
$993$	12.5462	+	27.4724i	0.398142	+	0.871810i
$994$	−21.0234	−	29.4745i	−0.666823	−	0.934875i
$995$	−0.409687	+	0.897089i	−0.0129879	+	0.0284396i
$996$	−8.86194	−	1.70800i	−0.280801	−	0.0541200i
$997$	20.9460	+	16.4721i	0.663368	+	0.521678i	0.892115	−	0.451808i	$-0.149221\pi$
$997$	20.9460	+	16.4721i	0.663368	+	0.521678i	−0.228748	+	0.973486i	$0.573463\pi$
$998$	−0.359989	+	1.48390i	−0.0113953	+	0.0469719i
$999$	−3.76276	+	10.8718i	−0.119048	+	0.343968i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.b.25.4	✓	160
7.2	even	3	inner	966.2.y.b.163.4	yes	160
23.12	even	11	inner	966.2.y.b.403.4	yes	160
161.58	even	33	inner	966.2.y.b.541.4	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.b.25.4	✓	160	1.1	even	1	trivial
966.2.y.b.163.4	yes	160	7.2	even	3	inner
966.2.y.b.403.4	yes	160	23.12	even	11	inner
966.2.y.b.541.4	yes	160	161.58	even	33	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.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0475819 + 0.998867i) q^{2} +(0.928368 + 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(0.0842779 + 0.347398i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(0.863387 - 2.50091i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +O(q^{10})\)	\(q+(-0.0475819 + 0.998867i) q^{2} +(0.928368 + 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(0.0842779 + 0.347398i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(0.863387 - 2.50091i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +(-0.351015 + 0.0676526i) q^{10} +(0.312736 + 6.56513i) q^{11} +(-0.888835 - 0.458227i) q^{12} +(-3.08311 - 3.55809i) q^{13} +(2.45700 + 0.981408i) q^{14} +(-0.0508740 + 0.353836i) q^{15} +(0.981929 + 0.189251i) q^{16} +(2.42855 + 3.41042i) q^{17} +(-0.723734 + 0.690079i) q^{18} +(-4.10985 + 5.77148i) q^{19} +(-0.0508740 - 0.353836i) q^{20} +(1.73104 - 2.00088i) q^{21} -6.57258 q^{22} +(3.98660 + 2.66590i) q^{23} +(0.500000 - 0.866025i) q^{24} +(4.33059 - 2.23258i) q^{25} +(3.70076 - 2.91031i) q^{26} +(0.415415 + 0.909632i) q^{27} +(-1.09720 + 2.40752i) q^{28} +(1.12567 - 2.46486i) q^{29} +(-0.351015 - 0.0676526i) q^{30} +(4.04472 + 3.18080i) q^{31} +(-0.235759 + 0.971812i) q^{32} +(-2.14968 + 6.21109i) q^{33} +(-3.52211 + 2.26352i) q^{34} +(0.941577 + 0.0891676i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(8.32621 + 7.93903i) q^{37} +(-5.56939 - 4.37982i) q^{38} +(-1.53985 - 4.44910i) q^{39} +(0.355856 - 0.0339801i) q^{40} +(2.74531 + 0.806094i) q^{41} +(1.91625 + 1.82428i) q^{42} +(0.545147 + 3.79158i) q^{43} +(0.312736 - 6.56513i) q^{44} +(-0.178737 + 0.309582i) q^{45} +(-2.85257 + 3.85523i) q^{46} +(-0.221595 - 0.383813i) q^{47} +(0.841254 + 0.540641i) q^{48} +(-5.50912 - 4.31851i) q^{49} +(2.02399 + 4.43192i) q^{50} +(0.987062 + 4.06872i) q^{51} +(2.73093 + 3.83505i) q^{52} +(-0.237587 - 0.686463i) q^{53} +(-0.928368 + 0.371662i) q^{54} +(-2.25436 + 0.661939i) q^{55} +(-2.35258 - 1.21052i) q^{56} +(-5.96050 + 3.83058i) q^{57} +(2.40851 + 1.24167i) q^{58} +(-2.17722 + 0.419625i) q^{59} +(0.0842779 - 0.347398i) q^{60} +(-3.83511 + 1.53535i) q^{61} +(-3.36966 + 3.88879i) q^{62} +(2.35069 - 1.21419i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(0.976238 - 1.37093i) q^{65} +(-6.10177 - 2.44278i) q^{66} +(-0.284864 + 0.146857i) q^{67} +(-2.09337 - 3.62582i) q^{68} +(2.71021 + 3.95661i) q^{69} +(-0.133869 + 0.936268i) q^{70} +(-11.5116 - 7.39804i) q^{71} +(0.786053 - 0.618159i) q^{72} +(-12.2744 - 1.17206i) q^{73} +(-8.32621 + 7.93903i) q^{74} +(4.85015 - 0.463133i) q^{75} +(4.63986 - 5.35468i) q^{76} +(16.6888 + 4.88613i) q^{77} +(4.51732 - 1.32641i) q^{78} +(5.15608 - 14.8975i) q^{79} +(0.0170093 + 0.357070i) q^{80} +(0.0475819 + 0.998867i) q^{81} +(-0.935808 + 2.70384i) q^{82} +(8.65945 - 2.54264i) q^{83} +(-1.91339 + 1.82727i) q^{84} +(-0.980100 + 1.13110i) q^{85} +(-3.81322 + 0.364119i) q^{86} +(1.96113 - 1.86993i) q^{87} +(6.54282 + 0.624763i) q^{88} +(-9.98511 + 7.85237i) q^{89} +(-0.300727 - 0.193265i) q^{90} +(-11.5604 + 4.63856i) q^{91} +(-3.71514 - 3.03278i) q^{92} +(2.57280 + 4.45623i) q^{93} +(0.393922 - 0.203081i) q^{94} +(-2.35137 - 0.941347i) q^{95} +(-0.580057 + 0.814576i) q^{96} +(4.48578 + 1.31714i) q^{97} +(4.57576 - 5.29740i) q^{98} +(-4.30412 + 4.96722i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 8 q^{2} + 8 q^{3} + 8 q^{4} + 6 q^{5} + 16 q^{6} - 10 q^{7} + 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 + 6 * q^5 + 16 * q^6 - 10 * q^7 + 16 * q^8 + 8 * q^9	\( 160 q - 8 q^{2} + 8 q^{3} + 8 q^{4} + 6 q^{5} + 16 q^{6} - 10 q^{7} + 16 q^{8} + 8 q^{9} - 6 q^{10} + 8 q^{11} + 8 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 8 q^{16} + 9 q^{17} - 8 q^{18} - 8 q^{19} + 10 q^{20} - 3 q^{21} - 28 q^{22} + 22 q^{23} + 80 q^{24} + 46 q^{25} + 2 q^{26} - 16 q^{27} - 14 q^{28} + 62 q^{29} - 6 q^{30} + 7 q^{31} - 8 q^{32} - 14 q^{33} - 4 q^{34} + 24 q^{35} - 16 q^{36} + 15 q^{37} + 19 q^{38} - 2 q^{39} + 5 q^{40} - 14 q^{41} + 10 q^{42} - 56 q^{43} + 8 q^{44} - 16 q^{45} + 66 q^{47} - 16 q^{48} + 42 q^{49} + 4 q^{50} + 9 q^{51} - 2 q^{52} + 12 q^{53} - 8 q^{54} - 14 q^{55} + 10 q^{56} - 6 q^{57} - 13 q^{58} + 62 q^{59} + 6 q^{60} + 16 q^{61} - 8 q^{62} + 2 q^{63} - 16 q^{64} + 70 q^{65} - 8 q^{66} - 14 q^{67} - 46 q^{68} + 22 q^{69} + 24 q^{70} - 108 q^{71} - 8 q^{72} + 40 q^{73} - 15 q^{74} + 2 q^{75} + 16 q^{76} + 29 q^{77} + 18 q^{78} + 22 q^{79} + 6 q^{80} + 8 q^{81} - 7 q^{82} - 18 q^{83} - 9 q^{84} + 26 q^{85} - 6 q^{86} + 2 q^{87} + 3 q^{88} + 112 q^{89} + 12 q^{90} + 18 q^{91} - 66 q^{92} - 26 q^{93} + 23 q^{95} - 8 q^{96} + 8 q^{97} + 9 q^{98} + 28 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 + 6 * q^5 + 16 * q^6 - 10 * q^7 + 16 * q^8 + 8 * q^9 - 6 * q^10 + 8 * q^11 + 8 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 8 * q^16 + 9 * q^17 - 8 * q^18 - 8 * q^19 + 10 * q^20 - 3 * q^21 - 28 * q^22 + 22 * q^23 + 80 * q^24 + 46 * q^25 + 2 * q^26 - 16 * q^27 - 14 * q^28 + 62 * q^29 - 6 * q^30 + 7 * q^31 - 8 * q^32 - 14 * q^33 - 4 * q^34 + 24 * q^35 - 16 * q^36 + 15 * q^37 + 19 * q^38 - 2 * q^39 + 5 * q^40 - 14 * q^41 + 10 * q^42 - 56 * q^43 + 8 * q^44 - 16 * q^45 + 66 * q^47 - 16 * q^48 + 42 * q^49 + 4 * q^50 + 9 * q^51 - 2 * q^52 + 12 * q^53 - 8 * q^54 - 14 * q^55 + 10 * q^56 - 6 * q^57 - 13 * q^58 + 62 * q^59 + 6 * q^60 + 16 * q^61 - 8 * q^62 + 2 * q^63 - 16 * q^64 + 70 * q^65 - 8 * q^66 - 14 * q^67 - 46 * q^68 + 22 * q^69 + 24 * q^70 - 108 * q^71 - 8 * q^72 + 40 * q^73 - 15 * q^74 + 2 * q^75 + 16 * q^76 + 29 * q^77 + 18 * q^78 + 22 * q^79 + 6 * q^80 + 8 * q^81 - 7 * q^82 - 18 * q^83 - 9 * q^84 + 26 * q^85 - 6 * q^86 + 2 * q^87 + 3 * q^88 + 112 * q^89 + 12 * q^90 + 18 * q^91 - 66 * q^92 - 26 * q^93 + 23 * q^95 - 8 * q^96 + 8 * q^97 + 9 * q^98 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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