LMFDB - Embedded newform 966.2.y.a.823.6

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			823.6
Character	$\chi$	$=$	966.823
Dual form			966.2.y.a.331.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.235759 - 0.971812i) q^{2} +(0.327068 + 0.945001i) q^{3} +(-0.888835 + 0.458227i) q^{4} +(1.60022 - 0.640630i) q^{5} +(0.841254 - 0.540641i) q^{6} +(2.54430 - 0.725627i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.786053 + 0.618159i) q^{9} +O(q^{10})$	\(q+(-0.235759 - 0.971812i) q^{2} +(0.327068 + 0.945001i) q^{3} +(-0.888835 + 0.458227i) q^{4} +(1.60022 - 0.640630i) q^{5} +(0.841254 - 0.540641i) q^{6} +(2.54430 - 0.725627i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.786053 + 0.618159i) q^{9} +(-0.999838 - 1.40408i) q^{10} +(0.979556 - 4.03779i) q^{11} +(-0.723734 - 0.690079i) q^{12} +(0.835916 - 1.83040i) q^{13} +(-1.30501 - 2.30151i) q^{14} +(1.12878 + 1.30268i) q^{15} +(0.580057 - 0.814576i) q^{16} +(0.205254 + 4.30881i) q^{17} +(0.786053 + 0.618159i) q^{18} +(0.276559 - 5.80569i) q^{19} +(-1.12878 + 1.30268i) q^{20} +(1.51788 + 2.16704i) q^{21} -4.15491 q^{22} +(-4.18787 + 2.33705i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-1.46838 + 1.40010i) q^{25} +(-1.97588 - 0.380820i) q^{26} +(-0.841254 - 0.540641i) q^{27} +(-1.92896 + 1.81083i) q^{28} +(3.94055 - 2.53244i) q^{29} +(0.999838 - 1.40408i) q^{30} +(2.20117 - 0.424241i) q^{31} +(-0.928368 - 0.371662i) q^{32} +(4.13609 - 0.394949i) q^{33} +(4.13896 - 1.21531i) q^{34} +(3.60658 - 2.79112i) q^{35} +(0.415415 - 0.909632i) q^{36} +(0.0568169 - 0.0446813i) q^{37} +(-5.70724 + 1.09998i) q^{38} +(2.00313 + 0.191276i) q^{39} +(1.53208 + 0.789840i) q^{40} +(0.0857628 - 0.596493i) q^{41} +(1.74810 - 1.98599i) q^{42} +(5.53723 - 6.39031i) q^{43} +(0.979556 + 4.03779i) q^{44} +(-0.861844 + 1.49276i) q^{45} +(3.25849 + 3.51884i) q^{46} +(5.84239 + 10.1193i) q^{47} +(0.959493 + 0.281733i) q^{48} +(5.94693 - 3.69243i) q^{49} +(1.70682 + 1.09690i) q^{50} +(-4.00470 + 1.60324i) q^{51} +(0.0957464 + 2.00997i) q^{52} +(-9.10421 - 0.869346i) q^{53} +(-0.327068 + 0.945001i) q^{54} +(-1.01923 - 7.08887i) q^{55} +(2.21456 + 1.44767i) q^{56} +(5.57684 - 1.63751i) q^{57} +(-3.39007 - 3.23243i) q^{58} +(-1.94388 - 2.72979i) q^{59} +(-1.60022 - 0.640630i) q^{60} +(1.54903 - 4.47561i) q^{61} +(-0.931228 - 2.03910i) q^{62} +(-1.55140 + 2.14316i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(0.165037 - 3.46455i) q^{65} +(-1.35894 - 3.92639i) q^{66} +(-8.62614 + 8.22500i) q^{67} +(-2.15685 - 3.73577i) q^{68} +(-3.57823 - 3.19316i) q^{69} +(-3.56272 - 2.84688i) q^{70} +(12.7504 + 3.74386i) q^{71} +(-0.981929 - 0.189251i) q^{72} +(6.32391 - 3.26020i) q^{73} +(-0.0568169 - 0.0446813i) q^{74} +(-1.80336 - 0.929694i) q^{75} +(2.41451 + 5.28703i) q^{76} +(-0.437642 - 10.9841i) q^{77} +(-0.286372 - 1.99176i) q^{78} +(10.6034 - 1.01250i) q^{79} +(0.406375 - 1.67510i) q^{80} +(0.235759 - 0.971812i) q^{81} +(-0.599898 + 0.0572833i) q^{82} +(-0.326923 - 2.27380i) q^{83} +(-2.34214 - 1.23061i) q^{84} +(3.08881 + 6.76354i) q^{85} +(-7.51563 - 3.87458i) q^{86} +(3.68199 + 2.89555i) q^{87} +(3.69303 - 1.90389i) q^{88} +(-4.11341 - 0.792796i) q^{89} +(1.65387 + 0.485619i) q^{90} +(0.798633 - 5.26366i) q^{91} +(2.65143 - 3.99624i) q^{92} +(1.12084 + 1.94135i) q^{93} +(8.45667 - 8.06342i) q^{94} +(-3.27675 - 9.46754i) q^{95} +(0.0475819 - 0.998867i) q^{96} +(0.730897 - 5.08350i) q^{97} +(-4.99039 - 4.90877i) q^{98} +(1.72601 + 3.77944i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} - 16 q^{6} - 2 q^{7} + 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 - 16 * q^6 - 2 * q^7 + 16 * q^8 + 8 * q^9	\( 160 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} - 16 q^{6} - 2 q^{7} + 16 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{12} + 4 q^{13} - 9 q^{14} - 18 q^{15} + 8 q^{16} + 9 q^{17} - 8 q^{18} + 18 q^{20} + 7 q^{21} + 52 q^{22} + 22 q^{23} - 80 q^{24} + 42 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 54 q^{29} + 2 q^{30} - 15 q^{31} - 8 q^{32} + 18 q^{33} + 84 q^{34} + 82 q^{35} - 16 q^{36} + 3 q^{37} + 11 q^{38} + 2 q^{39} - 13 q^{40} + 22 q^{41} - 2 q^{42} - 96 q^{43} + 4 q^{44} - 20 q^{45} - 26 q^{47} + 16 q^{48} - 2 q^{49} - 4 q^{50} + 13 q^{51} - 2 q^{52} + 16 q^{53} + 8 q^{54} - 34 q^{55} + 2 q^{56} - 22 q^{57} - 5 q^{58} - 6 q^{59} - 2 q^{60} + 40 q^{61} - 8 q^{62} - 2 q^{63} - 16 q^{64} - 82 q^{65} + 4 q^{66} + 10 q^{67} - 46 q^{68} - 22 q^{69} + 100 q^{70} + 92 q^{71} - 8 q^{72} + 68 q^{73} - 3 q^{74} + 2 q^{75} - 7 q^{77} - 18 q^{78} - 78 q^{79} + 2 q^{80} + 8 q^{81} + 55 q^{82} - 42 q^{83} - 9 q^{84} + 50 q^{85} + 40 q^{86} + 6 q^{87} + 7 q^{88} - 80 q^{89} + 4 q^{90} - 62 q^{91} + 66 q^{92} + 26 q^{93} + 4 q^{94} - 17 q^{95} + 8 q^{96} - 8 q^{97} - 3 q^{98} + 36 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 - 16 * q^6 - 2 * q^7 + 16 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 8 * q^12 + 4 * q^13 - 9 * q^14 - 18 * q^15 + 8 * q^16 + 9 * q^17 - 8 * q^18 + 18 * q^20 + 7 * q^21 + 52 * q^22 + 22 * q^23 - 80 * q^24 + 42 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 54 * q^29 + 2 * q^30 - 15 * q^31 - 8 * q^32 + 18 * q^33 + 84 * q^34 + 82 * q^35 - 16 * q^36 + 3 * q^37 + 11 * q^38 + 2 * q^39 - 13 * q^40 + 22 * q^41 - 2 * q^42 - 96 * q^43 + 4 * q^44 - 20 * q^45 - 26 * q^47 + 16 * q^48 - 2 * q^49 - 4 * q^50 + 13 * q^51 - 2 * q^52 + 16 * q^53 + 8 * q^54 - 34 * q^55 + 2 * q^56 - 22 * q^57 - 5 * q^58 - 6 * q^59 - 2 * q^60 + 40 * q^61 - 8 * q^62 - 2 * q^63 - 16 * q^64 - 82 * q^65 + 4 * q^66 + 10 * q^67 - 46 * q^68 - 22 * q^69 + 100 * q^70 + 92 * q^71 - 8 * q^72 + 68 * q^73 - 3 * q^74 + 2 * q^75 - 7 * q^77 - 18 * q^78 - 78 * q^79 + 2 * q^80 + 8 * q^81 + 55 * q^82 - 42 * q^83 - 9 * q^84 + 50 * q^85 + 40 * q^86 + 6 * q^87 + 7 * q^88 - 80 * q^89 + 4 * q^90 - 62 * q^91 + 66 * q^92 + 26 * q^93 + 4 * q^94 - 17 * q^95 + 8 * q^96 - 8 * q^97 - 3 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{6}{11}\right)$

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 $

$2$	−0.235759	−	0.971812i	−0.166707	−	0.687175i
$2$	−0.235759	−	0.971812i	−0.166707	−	0.687175i
$3$	0.327068	+	0.945001i	0.188833	+	0.545596i
$3$	0.327068	+	0.945001i	0.188833	+	0.545596i
$4$	−0.888835	+	0.458227i	−0.444418	+	0.229113i
$5$	1.60022	−	0.640630i	0.715639	−	0.286499i	0.0148726	−	0.999889i	$-0.495266\pi$
$5$	1.60022	−	0.640630i	0.715639	−	0.286499i	0.700766	+	0.713391i	$0.252842\pi$
$6$	0.841254	−	0.540641i	0.343440	−	0.220716i
$7$	2.54430	−	0.725627i	0.961655	−	0.274261i
$7$	2.54430	−	0.725627i	0.961655	−	0.274261i
$8$	0.654861	+	0.755750i	0.231528	+	0.267198i
$9$	−0.786053	+	0.618159i	−0.262018	+	0.206053i
$10$	−0.999838	−	1.40408i	−0.316176	−	0.444008i
$11$	0.979556	−	4.03779i	0.295347	−	1.21744i	−0.609874	−	0.792498i	$-0.708780\pi$
$11$	0.979556	−	4.03779i	0.295347	−	1.21744i	0.905222	−	0.424940i	$-0.139705\pi$
$12$	−0.723734	−	0.690079i	−0.208924	−	0.199209i
$13$	0.835916	−	1.83040i	0.231842	−	0.507662i	−0.757578	−	0.652745i	$-0.773617\pi$
$13$	0.835916	−	1.83040i	0.231842	−	0.507662i	0.989420	+	0.145082i	$0.0463448\pi$
$14$	−1.30501	−	2.30151i	−0.348780	−	0.615104i
$15$	1.12878	+	1.30268i	0.291449	+	0.336350i
$16$	0.580057	−	0.814576i	0.145014	−	0.203644i
$17$	0.205254	+	4.30881i	0.0497814	+	1.04504i	0.876189	+	0.481968i	$0.160078\pi$
$17$	0.205254	+	4.30881i	0.0497814	+	1.04504i	−0.826407	+	0.563073i	$0.809619\pi$
$18$	0.786053	+	0.618159i	0.185274	+	0.145701i
$19$	0.276559	−	5.80569i	0.0634470	−	1.33192i	−0.712746	−	0.701422i	$-0.752549\pi$
$19$	0.276559	−	5.80569i	0.0634470	−	1.33192i	0.776193	−	0.630495i	$-0.217148\pi$
$20$	−1.12878	+	1.30268i	−0.252402	+	0.291287i
$21$	1.51788	+	2.16704i	0.331228	+	0.472886i
$22$	−4.15491			−0.885829
$23$	−4.18787	+	2.33705i	−0.873230	+	0.487308i
$23$	−4.18787	+	2.33705i	−0.873230	+	0.487308i
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−1.46838	+	1.40010i	−0.293676	+	0.280020i
$26$	−1.97588	−	0.380820i	−0.387502	−	0.0746849i
$27$	−0.841254	−	0.540641i	−0.161899	−	0.104046i
$28$	−1.92896	+	1.81083i	−0.364540	+	0.342215i
$29$	3.94055	−	2.53244i	0.731742	−	0.470262i	−0.120961	−	0.992657i	$-0.538598\pi$
$29$	3.94055	−	2.53244i	0.731742	−	0.470262i	0.852704	+	0.522395i	$0.174961\pi$
$30$	0.999838	−	1.40408i	0.182545	−	0.256348i
$31$	2.20117	−	0.424241i	0.395342	−	0.0761959i	0.0122940	−	0.999924i	$-0.496087\pi$
$31$	2.20117	−	0.424241i	0.395342	−	0.0761959i	0.383048	+	0.923729i	$0.374874\pi$
$32$	−0.928368	−	0.371662i	−0.164114	−	0.0657013i
$33$	4.13609	−	0.394949i	0.720001	−	0.0687518i
$34$	4.13896	−	1.21531i	0.709826	−	0.208424i
$35$	3.60658	−	2.79112i	0.609622	−	0.471785i
$36$	0.415415	−	0.909632i	0.0692358	−	0.151605i
$37$	0.0568169	−	0.0446813i	0.00934064	−	0.00734556i	−0.613478	−	0.789712i	$-0.710230\pi$
$37$	0.0568169	−	0.0446813i	0.00934064	−	0.00734556i	0.622818	+	0.782366i	$0.285988\pi$
$38$	−5.70724	+	1.09998i	−0.925837	+	0.178440i
$39$	2.00313	+	0.191276i	0.320758	+	0.0306287i
$40$	1.53208	+	0.789840i	0.242242	+	0.124885i
$41$	0.0857628	−	0.596493i	0.0133939	−	0.0931566i	−0.982028	−	0.188735i	$-0.939561\pi$
$41$	0.0857628	−	0.596493i	0.0133939	−	0.0931566i	0.995422	+	0.0955789i	$0.0304702\pi$
$42$	1.74810	−	1.98599i	0.269737	−	0.306445i
$43$	5.53723	−	6.39031i	0.844420	−	0.974513i	−0.155491	−	0.987837i	$-0.549696\pi$
$43$	5.53723	−	6.39031i	0.844420	−	0.974513i	0.999911	+	0.0133243i	$0.00424139\pi$
$44$	0.979556	+	4.03779i	0.147674	+	0.608719i
$45$	−0.861844	+	1.49276i	−0.128476	+	0.222527i
$46$	3.25849	+	3.51884i	0.480439	+	0.518824i
$47$	5.84239	+	10.1193i	0.852200	+	1.47605i	0.879218	+	0.476419i	$0.158065\pi$
$47$	5.84239	+	10.1193i	0.852200	+	1.47605i	−0.0270181	+	0.999635i	$0.508601\pi$
$48$	0.959493	+	0.281733i	0.138491	+	0.0406646i
$49$	5.94693	−	3.69243i	0.849561	−	0.527490i
$50$	1.70682	+	1.09690i	0.241380	+	0.155126i
$51$	−4.00470	+	1.60324i	−0.560770	+	0.224498i
$52$	0.0957464	+	2.00997i	0.0132776	+	0.278732i
$53$	−9.10421	−	0.869346i	−1.25056	−	0.119414i	−0.551315	−	0.834297i	$-0.685874\pi$
$53$	−9.10421	−	0.869346i	−1.25056	−	0.119414i	−0.699244	+	0.714883i	$0.746480\pi$
$54$	−0.327068	+	0.945001i	−0.0445083	+	0.128598i
$55$	−1.01923	−	7.08887i	−0.137432	−	0.955863i
$56$	2.21456	+	1.44767i	0.295932	+	0.193453i
$57$	5.57684	−	1.63751i	0.738670	−	0.216893i
$58$	−3.39007	−	3.23243i	−0.445139	−	0.424439i
$59$	−1.94388	−	2.72979i	−0.253071	−	0.355389i	0.668423	−	0.743782i	$-0.266970\pi$
$59$	−1.94388	−	2.72979i	−0.253071	−	0.355389i	−0.921494	+	0.388393i	$0.873030\pi$
$60$	−1.60022	−	0.640630i	−0.206587	−	0.0827050i
$61$	1.54903	−	4.47561i	0.198332	−	0.573044i	−0.801351	−	0.598194i	$-0.795885\pi$
$61$	1.54903	−	4.47561i	0.198332	−	0.573044i	0.999684	+	0.0251503i	$0.00800642\pi$
$62$	−0.931228	−	2.03910i	−0.118266	−	0.258966i
$63$	−1.55140	+	2.14316i	−0.195458	+	0.270013i
$64$	−0.142315	+	0.989821i	−0.0177894	+	0.123728i
$65$	0.165037	−	3.46455i	0.0204703	−	0.429725i
$66$	−1.35894	−	3.92639i	−0.167274	−	0.483305i
$67$	−8.62614	+	8.22500i	−1.05385	+	1.00484i	−0.0538701	+	0.998548i	$0.517156\pi$
$67$	−8.62614	+	8.22500i	−1.05385	+	1.00484i	−0.999980	+	0.00629624i	$0.997996\pi$
$68$	−2.15685	−	3.73577i	−0.261556	−	0.453029i
$69$	−3.57823	−	3.19316i	−0.430768	−	0.384412i
$70$	−3.56272	−	2.84688i	−0.425827	−	0.340267i
$71$	12.7504	+	3.74386i	1.51320	+	0.444314i	0.929859	−	0.367916i	$-0.119929\pi$
$71$	12.7504	+	3.74386i	1.51320	+	0.444314i	0.583337	+	0.812230i	$0.301747\pi$
$72$	−0.981929	−	0.189251i	−0.115721	−	0.0223035i
$73$	6.32391	−	3.26020i	0.740157	−	0.381578i	−0.0465400	−	0.998916i	$-0.514820\pi$
$73$	6.32391	−	3.26020i	0.740157	−	0.381578i	0.786697	+	0.617339i	$0.211789\pi$
$74$	−0.0568169	−	0.0446813i	−0.00660483	−	0.00519410i
$75$	−1.80336	−	0.929694i	−0.208234	−	0.107352i
$76$	2.41451	+	5.28703i	0.276963	+	0.606464i
$77$	−0.437642	−	10.9841i	−0.0498740	−	1.25176i
$78$	−0.286372	−	1.99176i	−0.0324253	−	0.225523i
$79$	10.6034	−	1.01250i	1.19298	−	0.113915i	0.520386	−	0.853931i	$-0.325788\pi$
$79$	10.6034	−	1.01250i	1.19298	−	0.113915i	0.672590	+	0.740016i	$0.265182\pi$
$80$	0.406375	−	1.67510i	0.0454341	−	0.187282i
$81$	0.235759	−	0.971812i	0.0261954	−	0.107979i
$82$	−0.599898	+	0.0572833i	−0.0662477	+	0.00632589i
$83$	−0.326923	−	2.27380i	−0.0358844	−	0.249582i	0.963981	−	0.265970i	$-0.0856923\pi$
$83$	−0.326923	−	2.27380i	−0.0358844	−	0.249582i	−0.999866	+	0.0163884i	$0.994783\pi$
$84$	−2.34214	−	1.23061i	−0.255548	−	0.134270i
$85$	3.08881	+	6.76354i	0.335028	+	0.733609i
$86$	−7.51563	−	3.87458i	−0.810431	−	0.417806i
$87$	3.68199	+	2.89555i	0.394750	+	0.310435i
$88$	3.69303	−	1.90389i	0.393678	−	0.202955i
$89$	−4.11341	−	0.792796i	−0.436021	−	0.0840362i	−0.0334827	−	0.999439i	$-0.510660\pi$
$89$	−4.11341	−	0.792796i	−0.436021	−	0.0840362i	−0.402538	+	0.915403i	$0.631872\pi$
$90$	1.65387	+	0.485619i	0.174333	+	0.0511888i
$91$	0.798633	−	5.26366i	0.0837195	−	0.551781i
$92$	2.65143	−	3.99624i	0.276430	−	0.416637i
$93$	1.12084	+	1.94135i	0.116226	+	0.201309i
$94$	8.45667	−	8.06342i	0.872239	−	0.831678i
$95$	−3.27675	−	9.46754i	−0.336187	−	0.971349i
$96$	0.0475819	−	0.998867i	0.00485631	−	0.101946i
$97$	0.730897	−	5.08350i	0.0742113	−	0.516151i	−0.918480	−	0.395468i	$-0.870582\pi$
$97$	0.730897	−	5.08350i	0.0742113	−	0.516151i	0.992691	−	0.120683i	$-0.0385085\pi$
$98$	−4.99039	−	4.90877i	−0.504105	−	0.495861i
$99$	1.72601	+	3.77944i	0.173471	+	0.379848i
$100$	0.663587	−	1.91731i	0.0663587	−	0.191731i
$101$	−14.2328	−	5.69797i	−1.41622	−	0.566969i	−0.467757	−	0.883857i	$-0.654938\pi$
$101$	−14.2328	−	5.69797i	−1.41622	−	0.566969i	−0.948463	+	0.316889i	$0.897362\pi$
$102$	2.50219	+	3.51383i	0.247754	+	0.347921i
$103$	1.42119	+	1.35510i	0.140034	+	0.133522i	0.756859	−	0.653578i	$-0.226733\pi$
$103$	1.42119	+	1.35510i	0.140034	+	0.133522i	−0.616825	+	0.787100i	$0.711581\pi$
$104$	1.93073	−	0.566915i	0.189324	−	0.0555906i
$105$	3.81720	+	2.49533i	0.372521	+	0.243519i
$106$	1.30156	+	9.05253i	0.126418	+	0.879259i
$107$	−2.82215	+	8.15406i	−0.272827	+	0.788283i	0.722469	+	0.691403i	$0.243007\pi$
$107$	−2.82215	+	8.15406i	−0.272827	+	0.788283i	−0.995296	+	0.0968792i	$0.969114\pi$
$108$	0.995472	+	0.0950560i	0.0957893	+	0.00914677i
$109$	0.226863	+	4.76245i	0.0217296	+	0.456160i	0.983344	+	0.181755i	$0.0581777\pi$
$109$	0.226863	+	4.76245i	0.0217296	+	0.456160i	−0.961614	+	0.274405i	$0.911519\pi$
$110$	−6.64875	+	2.66176i	−0.633934	+	0.253789i
$111$	0.0608069	+	0.0390782i	0.00577153	+	0.00370914i
$112$	0.884761	−	2.49343i	0.0836020	−	0.235607i
$113$	2.13754	+	0.627638i	0.201083	+	0.0590432i	0.380723	−	0.924689i	$-0.375675\pi$
$113$	2.13754	+	0.627638i	0.201083	+	0.0590432i	−0.179640	+	0.983732i	$0.557493\pi$
$114$	−2.90614	−	5.03358i	−0.272185	−	0.471438i
$115$	−5.20431	+	6.42266i	−0.485305	+	0.598916i
$116$	−2.34207	+	4.05659i	−0.217456	+	0.376645i
$117$	0.474405	+	1.95552i	0.0438587	+	0.180788i
$118$	−2.19456	+	2.53265i	−0.202025	+	0.233150i
$119$	3.64882	+	10.8140i	0.334487	+	0.991315i
$120$	−0.245307	+	1.70614i	−0.0223933	+	0.155749i
$121$	−5.56700	−	2.86999i	−0.506091	−	0.260908i
$122$	−4.71465	−	0.450195i	−0.426844	−	0.0407587i
$123$	0.591737	−	0.114048i	0.0533551	−	0.0102834i
$124$	−1.76208	+	1.38571i	−0.158239	+	0.124441i
$125$	−5.03301	+	11.0208i	−0.450167	+	0.985727i
$126$	2.44851	+	1.00240i	0.218130	+	0.0893009i
$127$	−1.85986	+	0.546103i	−0.165036	+	0.0484588i	−0.363207	−	0.931709i	$-0.618318\pi$
$127$	−1.85986	+	0.546103i	−0.165036	+	0.0484588i	0.198171	+	0.980167i	$0.436500\pi$
$128$	0.995472	−	0.0950560i	0.0879881	−	0.00840185i
$129$	7.84990	+	3.14263i	0.691145	+	0.276693i
$130$	−3.40580	+	0.656415i	−0.298709	+	0.0575714i
$131$	−2.64605	+	3.71586i	−0.231187	+	0.324657i	−0.913831	−	0.406094i	$-0.866890\pi$
$131$	−2.64605	+	3.71586i	−0.231187	+	0.324657i	0.682644	+	0.730751i	$0.260830\pi$
$132$	−3.49533	+	2.24631i	−0.304229	+	0.195516i
$133$	−3.50912	−	14.9721i	−0.304279	−	1.29825i
$134$	10.0268	+	6.44386i	0.866187	+	0.556665i
$135$	−1.69254	−	0.326210i	−0.145671	−	0.0280757i
$136$	−3.12197	+	2.97679i	−0.267707	+	0.255258i
$137$	−11.1327	+	19.2824i	−0.951130	+	1.64740i	−0.208143	+	0.978098i	$0.566742\pi$
$137$	−11.1327	+	19.2824i	−0.951130	+	1.64740i	−0.742987	+	0.669306i	$0.766591\pi$
$138$	−2.25955	+	4.23018i	−0.192346	+	0.360097i
$139$	18.3978			1.56048			0.780239	−	0.625481i	$-0.215097\pi$
$139$	18.3978			1.56048			0.780239	+	0.625481i	$0.215097\pi$
$140$	−1.92669	+	4.13347i	−0.162835	+	0.349342i
$141$	−7.65190	+	8.83077i	−0.644407	+	0.743685i
$142$	0.632302	−	13.2736i	0.0530616	−	1.11390i
$143$	−6.57194	−	5.16823i	−0.549574	−	0.432189i
$144$	0.0475819	+	0.998867i	0.00396516	+	0.0832389i
$145$	4.68338	−	6.57689i	0.388934	−	0.546181i
$146$	−4.65922	−	5.37703i	−0.385600	−	0.445006i
$147$	5.43440	+	4.41218i	0.448222	+	0.363910i
$148$	−0.0300267	+	0.0657494i	−0.00246818	+	0.00540456i
$149$	−15.7671	−	15.0339i	−1.29169	−	1.23162i	−0.957270	−	0.289196i	$-0.906612\pi$
$149$	−15.7671	−	15.0339i	−1.29169	−	1.23162i	−0.334417	−	0.942425i	$-0.608539\pi$
$150$	−0.478331	+	1.97171i	−0.0390555	+	0.160989i
$151$	9.50938	+	13.3541i	0.773862	+	1.08674i	0.993796	+	0.111223i	$0.0354767\pi$
$151$	9.50938	+	13.3541i	0.773862	+	1.08674i	−0.219933	+	0.975515i	$0.570584\pi$
$152$	4.56876	−	3.59291i	0.370575	−	0.291423i
$153$	−2.82487	−	3.26008i	−0.228377	−	0.263561i
$154$	−10.5713	+	3.01491i	−0.851862	+	0.242949i
$155$	3.25057	−	2.08901i	0.261092	−	0.167794i
$156$	−1.86810	+	0.747876i	−0.149568	+	0.0598780i
$157$	−7.87127	+	4.05792i	−0.628196	+	0.323857i	−0.742759	−	0.669558i	$-0.766483\pi$
$157$	−7.87127	+	4.05792i	−0.628196	+	0.323857i	0.114563	+	0.993416i	$0.463453\pi$
$158$	−3.48381	−	10.0658i	−0.277157	−	0.800792i
$159$	−2.15616	−	8.88782i	−0.170995	−	0.704850i
$160$	−1.72369			−0.136270
$161$	−8.95936	+	8.98498i	−0.706097	+	0.708115i
$162$	−1.00000			−0.0785674
$163$	−3.13425	−	12.9196i	−0.245494	−	1.01194i	−0.952453	−	0.304685i	$-0.901449\pi$
$163$	−3.13425	−	12.9196i	−0.245494	−	1.01194i	0.706960	−	0.707254i	$-0.250066\pi$
$164$	0.197100	+	0.569483i	0.0153909	+	0.0444692i
$165$	6.36563	−	3.28171i	0.495564	−	0.255481i
$166$	−2.13263	+	0.853775i	−0.165524	+	0.0662658i
$167$	−9.22091	+	5.92592i	−0.713535	+	0.458561i	−0.846383	−	0.532575i	$-0.821224\pi$
$167$	−9.22091	+	5.92592i	−0.713535	+	0.458561i	0.132847	+	0.991137i	$0.457588\pi$
$168$	−0.643739	+	2.56624i	−0.0496655	+	0.197990i
$169$	5.86158	+	6.76462i	0.450890	+	0.520355i
$170$	5.84468	−	4.59630i	0.448266	−	0.352520i
$171$	3.37145	+	4.73454i	0.257821	+	0.362059i
$172$	−1.99348	+	8.21724i	−0.152002	+	0.626559i
$173$	−2.19442	−	2.09238i	−0.166839	−	0.159081i	0.602060	−	0.798451i	$-0.294347\pi$
$173$	−2.19442	−	2.09238i	−0.166839	−	0.159081i	−0.768899	+	0.639370i	$0.779195\pi$
$174$	1.94586	−	4.26085i	0.147516	−	0.323014i
$175$	−2.72005	+	4.62777i	−0.205617	+	0.349827i
$176$	−2.72089	−	3.14007i	−0.205094	−	0.236692i
$177$	1.94388	−	2.72979i	0.146111	−	0.205184i
$178$	0.199326	+	4.18437i	0.0149401	+	0.313632i
$179$	5.80585	+	4.56577i	0.433949	+	0.341262i	0.811117	−	0.584883i	$-0.198860\pi$
$179$	5.80585	+	4.56577i	0.433949	+	0.341262i	−0.377168	+	0.926145i	$0.623102\pi$
$180$	0.0820164	−	1.72174i	0.00611314	−	0.128331i
$181$	−7.67871	+	8.86171i	−0.570754	+	0.658686i	−0.965591	−	0.260066i	$-0.916256\pi$
$181$	−7.67871	+	8.86171i	−0.570754	+	0.658686i	0.394837	+	0.918751i	$0.370801\pi$
$182$	−5.30357	+	0.464833i	−0.393127	+	0.0344557i
$183$	4.73610			0.350102
$184$	−4.50869	−	1.63454i	−0.332385	−	0.120500i
$185$	0.0622952	−	0.107898i	0.00458003	−	0.00793285i
$186$	1.62238	−	1.54694i	0.118959	−	0.113427i
$187$	17.5991	+	3.39195i	1.28698	+	0.248044i
$188$	−9.82986	−	6.31727i	−0.716916	−	0.460734i
$189$	−2.53271	−	0.765116i	−0.184227	−	0.0556540i
$190$	−8.42814	+	5.41644i	−0.611442	+	0.392950i
$191$	−8.94148	+	12.5566i	−0.646983	+	0.908560i	−0.999630	−	0.0271959i	$-0.991342\pi$
$191$	−8.94148	+	12.5566i	−0.646983	+	0.908560i	0.352647	+	0.935756i	$0.385282\pi$
$192$	−0.981929	+	0.189251i	−0.0708646	+	0.0136580i
$193$	−13.9318	−	5.57747i	−1.00284	−	0.401475i	−0.188628	−	0.982049i	$-0.560404\pi$
$193$	−13.9318	−	5.57747i	−1.00284	−	0.401475i	−0.814208	+	0.580574i	$0.802828\pi$
$194$	−5.11252	+	0.488186i	−0.367057	+	0.0350497i
$195$	3.32798	−	0.977185i	0.238322	−	0.0699776i
$196$	−3.59387	+	6.00700i	−0.256705	+	0.429072i
$197$	−4.67046	+	10.2269i	−0.332756	+	0.728635i	−0.999867	−	0.0163243i	$-0.994804\pi$
$197$	−4.67046	+	10.2269i	−0.332756	+	0.728635i	0.667111	+	0.744959i	$0.267531\pi$
$198$	3.26598	−	2.56839i	0.232103	−	0.182528i
$199$	−11.1822	+	2.15519i	−0.792684	+	0.152777i	−0.569492	−	0.821997i	$-0.692860\pi$
$199$	−11.1822	+	2.15519i	−0.792684	+	0.152777i	−0.223192	+	0.974774i	$0.571648\pi$
$200$	−2.01971	−	0.192859i	−0.142815	−	0.0136372i
$201$	−10.5940	−	5.46157i	−0.747241	−	0.385229i
$202$	−2.18183	+	15.1750i	−0.153513	+	1.06771i
$203$	8.18834	−	9.30266i	0.574709	−	0.652919i
$204$	2.82487	−	3.26008i	0.197781	−	0.228251i
$205$	−0.244893	−	1.00946i	−0.0171040	−	0.0705038i
$206$	0.981845	−	1.70060i	0.0684084	−	0.118487i
$207$	1.84722	−	4.42581i	0.128391	−	0.307615i
$208$	−1.00612	−	1.74265i	−0.0697620	−	0.120831i
$209$	−23.1712	−	6.80369i	−1.60279	−	0.470621i
$210$	1.52505	−	4.29790i	0.105239	−	0.296583i
$211$	18.0015	+	11.5688i	1.23927	+	0.796432i	0.985309	−	0.170782i	$-0.0546293\pi$
$211$	18.0015	+	11.5688i	1.23927	+	0.796432i	0.253963	+	0.967214i	$0.418266\pi$
$212$	8.49050	−	3.39908i	0.583130	−	0.233450i
$213$	0.632302	+	13.2736i	0.0433246	+	0.909495i
$214$	8.58956	+	0.820203i	0.587170	+	0.0560679i
$215$	4.76695	−	13.7732i	0.325103	−	0.939325i
$216$	−0.142315	−	0.989821i	−0.00968330	−	0.0673488i
$217$	5.29260	−	2.67663i	0.359285	−	0.181701i
$218$	4.57471	−	1.34326i	0.309839	−	0.0909769i
$219$	5.14924	+	4.90979i	0.347953	+	0.331773i
$220$	4.15423	+	5.83380i	0.280078	+	0.393315i
$221$	8.05843	+	3.22611i	0.542069	+	0.217012i
$222$	0.0236409	−	0.0683059i	0.00158667	−	0.00458439i
$223$	2.64364	+	5.78876i	0.177031	+	0.387644i	0.977258	−	0.212053i	$-0.0680150\pi$
$223$	2.64364	+	5.78876i	0.177031	+	0.387644i	−0.800227	+	0.599697i	$0.795288\pi$
$224$	−2.63174	−	0.271972i	−0.175840	−	0.0181719i
$225$	0.288742	−	2.00825i	0.0192495	−	0.133883i
$226$	0.106002	−	2.22526i	0.00705115	−	0.148022i
$227$	−3.79486	−	10.9645i	−0.251874	−	0.727741i	−0.998075	−	0.0620207i	$-0.980246\pi$
$227$	−3.79486	−	10.9645i	−0.251874	−	0.727741i	0.746201	−	0.665721i	$-0.231876\pi$
$228$	−4.20654	+	4.01093i	−0.278585	+	0.265630i
$229$	−2.58152	−	4.47132i	−0.170591	−	0.295473i	0.768035	−	0.640407i	$-0.221234\pi$
$229$	−2.58152	−	4.47132i	−0.170591	−	0.295473i	−0.938627	+	0.344934i	$0.887901\pi$
$230$	7.46857	+	3.54341i	0.492463	+	0.233646i
$231$	10.2369	−	4.00613i	0.673537	−	0.263584i
$232$	4.49440	+	1.31968i	0.295072	+	0.0866410i
$233$	29.4384	+	5.67379i	1.92857	+	0.371702i	1.00000		0.000555315i	$0.000176762\pi$
$233$	29.4384	+	5.67379i	1.92857	+	0.371702i	0.928574	+	0.371147i	$0.121035\pi$
$234$	1.78855	−	0.922064i	0.116921	−	0.0602772i
$235$	15.8318	+	12.4503i	1.03276	+	0.812168i
$236$	2.97865	+	1.53560i	0.193893	+	0.0999590i
$237$	4.42485	+	9.68906i	0.287425	+	0.629372i
$238$	9.64890	−	6.09546i	0.625446	−	0.395110i
$239$	−2.13954	−	14.8808i	−0.138395	−	0.962561i	−0.934135	−	0.356921i	$-0.883826\pi$
$239$	−2.13954	−	14.8808i	−0.138395	−	0.962561i	0.795739	−	0.605639i	$-0.207083\pi$
$240$	1.71588	−	0.163847i	0.110760	−	0.0105763i
$241$	−5.96641	+	24.5939i	−0.384330	+	1.58423i	0.370838	+	0.928698i	$0.379071\pi$
$241$	−5.96641	+	24.5939i	−0.384330	+	1.58423i	−0.755168	+	0.655532i	$0.772445\pi$
$242$	−1.47662	+	6.08670i	−0.0949205	+	0.391268i
$243$	0.995472	−	0.0950560i	0.0638596	−	0.00609785i
$244$	0.674017	+	4.68789i	0.0431495	+	0.300111i
$245$	7.15090	−	9.71847i	0.456854	−	0.620890i
$246$	−0.250340	−	0.548169i	−0.0159611	−	0.0349500i
$247$	−10.3956	−	5.35929i	−0.661454	−	0.341003i
$248$	1.76208	+	1.38571i	0.111892	+	0.0879930i
$249$	2.04181	−	1.05263i	0.129395	−	0.0667076i
$250$	11.8967	+	2.29290i	0.752412	+	0.145016i
$251$	−18.4221	−	5.40923i	−1.16279	−	0.341427i	−0.357277	−	0.933999i	$-0.616295\pi$
$251$	−18.4221	−	5.40923i	−1.16279	−	0.341427i	−0.805518	+	0.592571i	$0.798113\pi$
$252$	0.396887	−	2.61581i	0.0250015	−	0.164781i
$253$	5.33424	+	19.1990i	0.335361	+	1.20703i
$254$	0.969187	+	1.67868i	0.0608122	+	0.105330i
$255$	−5.38130	+	5.13106i	−0.336990	+	0.321320i
$256$	−0.327068	−	0.945001i	−0.0204417	−	0.0590626i
$257$	−1.18462	+	24.8682i	−0.0738946	+	1.55124i	0.592458	+	0.805602i	$0.298158\pi$
$257$	−1.18462	+	24.8682i	−0.0738946	+	1.55124i	−0.666352	+	0.745637i	$0.732145\pi$
$258$	1.20336	−	8.36952i	0.0749177	−	0.521064i
$259$	0.112137	−	0.154911i	0.00696787	−	0.00962568i
$260$	1.44086	+	3.15504i	0.0893583	+	0.195667i
$261$	−1.53203	+	4.42652i	−0.0948305	+	0.273995i
$262$	4.23495	+	1.69542i	0.261636	+	0.104743i
$263$	14.8711	+	20.8835i	0.916990	+	1.28773i	0.957464	+	0.288552i	$0.0931739\pi$
$263$	14.8711	+	20.8835i	0.916990	+	1.28773i	−0.0404737	+	0.999181i	$0.512887\pi$
$264$	3.00705	+	2.86721i	0.185071	+	0.176465i
$265$	−15.1256	+	4.44129i	−0.929161	+	0.272826i
$266$	−13.7228	+	6.94001i	−0.841396	+	0.425519i
$267$	−0.596174	−	4.14648i	−0.0364852	−	0.253760i
$268$	3.89830	−	11.2634i	0.238127	−	0.688022i
$269$	1.97923	+	0.188993i	0.120676	+	0.0115231i	0.155219	−	0.987880i	$-0.450392\pi$
$269$	1.97923	+	0.188993i	0.120676	+	0.0115231i	−0.0345435	+	0.999403i	$0.510998\pi$
$270$	0.0820164	+	1.72174i	0.00499136	+	0.104782i
$271$	−16.0384	+	6.42082i	−0.974265	+	0.390037i	−0.803520	−	0.595278i	$-0.797042\pi$
$271$	−16.0384	+	6.42082i	−0.974265	+	0.390037i	−0.170746	+	0.985315i	$0.554618\pi$
$272$	3.62891	+	2.33216i	0.220035	+	0.141408i
$273$	5.23537	−	0.966864i	0.316859	−	0.0585173i
$274$	21.3635	+	6.27288i	1.29061	+	0.378959i
$275$	4.21494	+	7.30049i	0.254170	+	0.440236i
$276$	4.64365	+	1.19856i	0.279515	+	0.0721447i
$277$	10.0041	−	17.3276i	0.601088	−	1.04112i	−0.391568	−	0.920149i	$-0.628067\pi$
$277$	10.0041	−	17.3276i	0.601088	−	1.04112i	0.992657	−	0.120967i	$-0.0385994\pi$
$278$	−4.33744	−	17.8792i	−0.260142	−	1.07232i
$279$	−1.46799	+	1.69415i	−0.0878862	+	0.101426i
$280$	4.47119	+	0.897874i	0.267205	+	0.0536582i
$281$	1.43025	−	9.94758i	0.0853213	−	0.593423i	−0.901643	−	0.432482i	$-0.857638\pi$
$281$	1.43025	−	9.94758i	0.0853213	−	0.593423i	0.986964	−	0.160941i	$-0.0514529\pi$
$282$	10.3858	+	5.35428i	0.618468	+	0.318843i
$283$	−16.6899	−	1.59369i	−0.992111	−	0.0947351i	−0.413642	−	0.910440i	$-0.635743\pi$
$283$	−16.6899	−	1.59369i	−0.992111	−	0.0947351i	−0.578469	+	0.815705i	$0.696350\pi$
$284$	−13.0486	+	2.51490i	−0.774289	+	0.149232i
$285$	7.87512	−	6.19306i	0.466482	−	0.366845i
$286$	−3.47315	+	7.60515i	−0.205372	+	0.449702i
$287$	−0.214625	−	1.57989i	−0.0126689	−	0.0932579i
$288$	0.959493	−	0.281733i	0.0565387	−	0.0166013i
$289$	−1.60071	+	0.152849i	−0.0941593	+	0.00899113i
$290$	−7.49565	−	3.00081i	−0.440160	−	0.176213i
$291$	5.04296	−	0.971952i	0.295624	−	0.0569768i
$292$	−4.12700	+	5.79556i	−0.241515	+	0.339160i
$293$	−2.04092	+	1.31162i	−0.119232	+	0.0766257i	−0.598898	−	0.800826i	$-0.704394\pi$
$293$	−2.04092	+	1.31162i	−0.119232	+	0.0766257i	0.479666	+	0.877451i	$0.340758\pi$
$294$	3.00660	−	6.32142i	0.175348	−	0.368673i
$295$	−4.85941	−	3.12295i	−0.282926	−	0.181825i
$296$	0.0709750	+	0.0136793i	0.00412534	+	0.000795094i
$297$	−3.00705	+	2.86721i	−0.174487	+	0.166373i
$298$	−10.8928	+	18.8670i	−0.631006	+	1.09293i
$299$	0.777027	+	9.61905i	0.0449366	+	0.556284i
$300$	2.02890			0.117138
$301$	9.45141	−	20.2768i	0.544770	−	1.16874i
$302$	10.7357	−	12.3897i	0.617770	−	0.712945i
$303$	0.729479	−	15.3137i	0.0419075	−	0.879747i
$304$	−4.56876	−	3.59291i	−0.262036	−	0.206068i
$305$	−0.388438	−	8.15431i	−0.0222419	−	0.466914i
$306$	−2.50219	+	3.51383i	−0.143041	+	0.200873i
$307$	−7.27336	−	8.39390i	−0.415112	−	0.479065i	0.509229	−	0.860631i	$-0.329930\pi$
$307$	−7.27336	−	8.39390i	−0.415112	−	0.479065i	−0.924342	+	0.381566i	$0.875385\pi$
$308$	5.42221	+	9.56255i	0.308959	+	0.544877i
$309$	−0.815746	+	1.78623i	−0.0464062	+	0.101615i
$310$	−2.79648	−	2.66644i	−0.158829	−	0.151443i
$311$	−2.63703	+	10.8700i	−0.149532	+	0.616380i	0.846883	+	0.531780i	$0.178477\pi$
$311$	−2.63703	+	10.8700i	−0.149532	+	0.616380i	−0.996415	+	0.0846006i	$0.973039\pi$
$312$	1.16722	+	1.63913i	0.0660806	+	0.0927972i
$313$	−24.7957	+	19.4996i	−1.40154	+	1.10218i	−0.420732	+	0.907185i	$0.638227\pi$
$313$	−24.7957	+	19.4996i	−1.40154	+	1.10218i	−0.980804	+	0.194996i	$0.937531\pi$
$314$	5.79926	+	6.69270i	0.327271	+	0.377691i
$315$	−1.10961	+	4.42340i	−0.0625192	+	0.249231i
$316$	−8.96072	+	5.75871i	−0.504080	+	0.323953i
$317$	−17.8422	+	7.14295i	−1.00212	+	0.401188i	−0.813941	−	0.580947i	$-0.802682\pi$
$317$	−17.8422	+	7.14295i	−1.00212	+	0.401188i	−0.188178	+	0.982135i	$0.560258\pi$
$318$	−8.12895	+	4.19076i	−0.455849	+	0.235006i
$319$	−6.36546	−	18.3918i	−0.356397	−	1.02974i
$320$	0.406375	+	1.67510i	0.0227171	+	0.0936410i
$321$	−8.62863			−0.481603
$322$	10.8440	+	6.58853i	0.604310	+	0.367164i
$323$	25.0724			1.39507
$324$	0.235759	+	0.971812i	0.0130977	+	0.0539895i
$325$	1.33530	+	3.85809i	0.0740691	+	0.214009i
$326$	−11.8165	+	6.09181i	−0.654453	+	0.337394i
$327$	−4.42632	+	1.77203i	−0.244776	+	0.0979935i
$328$	0.506962	−	0.325805i	0.0279923	−	0.0179896i
$329$	22.2076	+	21.5072i	1.22435	+	1.18573i
$330$	−4.68996	−	5.41250i	−0.258174	−	0.297948i
$331$	−4.98291	+	3.91860i	−0.273885	+	0.215386i	−0.745648	−	0.666340i	$-0.767860\pi$
$331$	−4.98291	+	3.91860i	−0.273885	+	0.215386i	0.471763	+	0.881725i	$0.343618\pi$
$332$	1.33249	+	1.87123i	0.0731302	+	0.102697i
$333$	−0.0170410	+	0.0702438i	−0.000933839	+	0.00384933i
$334$	7.93279	+	7.56390i	0.434063	+	0.413878i
$335$	−8.53451	+	18.6880i	−0.466290	+	1.02103i
$336$	2.64567	+	0.0205780i	0.144333	+	0.00112262i
$337$	−12.8656	−	14.8477i	−0.700834	−	0.808806i	0.288031	−	0.957621i	$-0.406999\pi$
$337$	−12.8656	−	14.8477i	−0.700834	−	0.808806i	−0.988865	+	0.148816i	$0.952454\pi$
$338$	5.19202	−	7.29117i	0.282408	−	0.396587i
$339$	0.106002	+	2.22526i	0.00575724	+	0.120859i
$340$	−5.84468	−	4.59630i	−0.316972	−	0.249270i
$341$	0.443177	−	9.30342i	0.0239994	−	0.503809i
$342$	3.80623	−	4.39262i	0.205817	−	0.237526i
$343$	12.4515	−	13.7099i	0.672315	−	0.740265i
$344$	8.45559			0.455895
$345$	−7.77158	−	2.81743i	−0.418408	−	0.151686i
$346$	−1.51604	+	2.62586i	−0.0815030	+	0.141167i
$347$	0.611123	−	0.582705i	0.0328068	−	0.0312812i	−0.673498	−	0.739189i	$-0.735209\pi$
$347$	0.611123	−	0.582705i	0.0328068	−	0.0312812i	0.706305	+	0.707908i	$0.250361\pi$
$348$	−4.59950	−	0.886480i	−0.246559	−	0.0475203i
$349$	−18.2551	−	11.7318i	−0.977172	−	0.627991i	−0.0484732	−	0.998824i	$-0.515436\pi$
$349$	−18.2551	−	11.7318i	−0.977172	−	0.627991i	−0.928699	+	0.370834i	$0.879072\pi$
$350$	5.13860	+	1.55234i	0.274670	+	0.0829762i
$351$	−1.69281	+	1.08790i	−0.0903554	+	0.0580679i
$352$	−2.41008	+	3.38449i	−0.128458	+	0.180394i
$353$	−10.7349	+	2.06899i	−0.571363	+	0.110121i	−0.466746	−	0.884392i	$-0.654574\pi$
$353$	−10.7349	+	2.06899i	−0.571363	+	0.110121i	−0.104617	+	0.994513i	$0.533362\pi$
$354$	−3.11113	−	1.24551i	−0.165355	−	0.0661980i
$355$	22.8019	−	2.17731i	1.21020	−	0.115560i
$356$	4.01943	−	1.18021i	0.213029	−	0.0625510i
$357$	−9.02580	+	6.98504i	−0.477696	+	0.369688i
$358$	3.06829	−	6.71861i	0.162164	−	0.355090i
$359$	−4.27912	+	3.36514i	−0.225843	+	0.177605i	−0.724669	−	0.689097i	$-0.758007\pi$
$359$	−4.27912	+	3.36514i	−0.225843	+	0.177605i	0.498825	+	0.866702i	$0.333765\pi$
$360$	−1.69254	+	0.326210i	−0.0892047	+	0.0171928i
$361$	−14.7156	−	1.40517i	−0.774506	−	0.0739563i
$362$	10.4222	+	5.37304i	0.547781	+	0.282400i
$363$	0.891353	−	6.19950i	0.0467839	−	0.325389i
$364$	1.70209	+	5.04448i	0.0892139	+	0.264403i
$365$	8.03104	−	9.26832i	0.420364	−	0.485126i
$366$	−1.11658	−	4.60259i	−0.0583644	−	0.240581i
$367$	14.0279	−	24.2970i	0.732249	−	1.26829i	−0.223670	−	0.974665i	$-0.571804\pi$
$367$	14.0279	−	24.2970i	0.732249	−	1.26829i	0.955920	−	0.293628i	$-0.0948628\pi$
$368$	−0.525499	+	4.76695i	−0.0273935	+	0.248495i
$369$	0.301314	+	0.521890i	0.0156858	+	0.0271685i
$370$	−0.119544	−	0.0351012i	−0.00621478	−	0.00182482i
$371$	−23.7947	+	4.39438i	−1.23536	+	0.228145i
$372$	−1.88582	−	1.21194i	−0.0977753	−	0.0628364i
$373$	4.41761	−	1.76855i	0.228735	−	0.0915718i	−0.254464	−	0.967082i	$-0.581899\pi$
$373$	4.41761	−	1.76855i	0.228735	−	0.0915718i	0.483199	+	0.875510i	$0.339475\pi$
$374$	−0.852811	−	17.9027i	−0.0440978	−	0.925727i
$375$	−12.0608	−	1.15166i	−0.622816	−	0.0594717i
$376$	−3.82172	+	11.0421i	−0.197090	+	0.569454i
$377$	−1.34141	−	9.32970i	−0.0690861	−	0.480504i
$378$	−0.146441	+	2.64170i	−0.00753210	+	0.135874i
$379$	−0.722066	+	0.212018i	−0.0370900	+	0.0108906i	−0.300225	−	0.953868i	$-0.597062\pi$
$379$	−0.722066	+	0.212018i	−0.0370900	+	0.0108906i	0.263135	+	0.964759i	$0.415244\pi$
$380$	7.25077	+	6.91359i	0.371957	+	0.354660i
$381$	−1.12437	−	1.57895i	−0.0576031	−	0.0808922i
$382$	14.3106	+	5.72912i	0.732196	+	0.293127i
$383$	1.34494	−	3.88594i	0.0687231	−	0.198562i	−0.905410	−	0.424539i	$-0.860436\pi$
$383$	1.34494	−	3.88594i	0.0687231	−	0.198562i	0.974133	+	0.225977i	$0.0725573\pi$
$384$	0.415415	+	0.909632i	0.0211991	+	0.0464195i
$385$	−7.73709	−	17.2966i	−0.394319	−	0.881518i
$386$	−2.13569	+	14.8541i	−0.108704	+	0.756052i
$387$	−0.402333	+	8.44601i	−0.0204517	+	0.429335i
$388$	1.67975	+	4.85331i	0.0852762	+	0.246390i
$389$	17.2536	−	16.4512i	0.874790	−	0.834110i	−0.112400	−	0.993663i	$-0.535854\pi$
$389$	17.2536	−	16.4512i	0.874790	−	0.834110i	0.987189	+	0.159553i	$0.0510052\pi$
$390$	−1.73424	−	3.00379i	−0.0878167	−	0.152103i
$391$	−10.9295	−	17.5650i	−0.552727	−	0.888302i
$392$	6.68496	+	2.07636i	0.337642	+	0.104872i
$393$	−4.37693	−	1.28518i	−0.220787	−	0.0648289i
$394$	11.0397	+	2.12773i	0.556172	+	0.107193i
$395$	16.3191	−	8.41308i	0.821103	−	0.423308i
$396$	−3.26598	−	2.56839i	−0.164122	−	0.129067i
$397$	14.4661	+	7.45781i	0.726034	+	0.374297i	0.781284	−	0.624176i	$-0.214565\pi$
$397$	14.4661	+	7.45781i	0.726034	+	0.374297i	−0.0552496	+	0.998473i	$0.517595\pi$
$398$	4.73074	+	10.3589i	0.237130	+	0.519243i
$399$	13.0009	−	8.21302i	0.650861	−	0.411165i
$400$	0.288742	+	2.00825i	0.0144371	+	0.100412i
$401$	20.3827	−	1.94631i	1.01786	−	0.0971942i	0.427237	−	0.904140i	$-0.359487\pi$
$401$	20.3827	−	1.94631i	1.01786	−	0.0971942i	0.590626	+	0.806945i	$0.298881\pi$
$402$	−2.80999	+	11.5830i	−0.140150	+	0.577705i
$403$	1.06346	−	4.38366i	0.0529749	−	0.218365i
$404$	15.2616	−	1.45731i	0.759293	−	0.0725037i
$405$	−0.245307	−	1.70614i	−0.0121894	−	0.0847790i
$406$	−10.9709	−	5.76434i	−0.544477	−	0.286079i
$407$	−0.124758	−	0.273182i	−0.00618404	−	0.0135411i
$408$	−3.83417	−	1.97665i	−0.189820	−	0.0978588i
$409$	−19.7124	−	15.5020i	−0.974714	−	0.766524i	−0.00235086	−	0.999997i	$-0.500748\pi$
$409$	−19.7124	−	15.5020i	−0.974714	−	0.766524i	−0.972363	+	0.233474i	$0.924991\pi$
$410$	−0.923270	+	0.475979i	−0.0455971	+	0.0235069i
$411$	−21.8630	−	4.21375i	−1.07842	−	0.207849i
$412$	−1.88415	−	0.553235i	−0.0928252	−	0.0272559i
$413$	−6.92661	−	5.53488i	−0.340836	−	0.272354i
$414$	−4.73655	−	0.751725i	−0.232789	−	0.0369452i
$415$	−1.97981	−	3.42913i	−0.0971851	−	0.168330i
$416$	−1.45633	+	1.38861i	−0.0714024	+	0.0680821i
$417$	6.01732	+	17.3859i	0.294670	+	0.851392i
$418$	−1.14908	+	24.1221i	−0.0562032	+	1.17985i
$419$	0.759660	−	5.28355i	0.0371118	−	0.258118i	−0.962816	−	0.270159i	$-0.912924\pi$
$419$	0.759660	−	5.28355i	0.0371118	−	0.258118i	0.999928	+	0.0120408i	$0.00383280\pi$
$420$	−4.53629	−	0.468795i	−0.221348	−	0.0228748i
$421$	1.32689	+	2.90549i	0.0646689	+	0.141605i	0.939207	−	0.343352i	$-0.111562\pi$
$421$	1.32689	+	2.90549i	0.0646689	+	0.141605i	−0.874538	+	0.484957i	$0.838835\pi$
$422$	6.99873	−	20.2215i	0.340693	−	0.984367i
$423$	−10.8478	−	4.34279i	−0.527437	−	0.211154i
$424$	−5.30498	−	7.44980i	−0.257633	−	0.361794i
$425$	−6.33415	−	6.03960i	−0.307252	−	0.292964i
$426$	12.7504	−	3.74386i	0.617760	−	0.181391i
$427$	0.693558	−	12.5113i	0.0335636	−	0.605465i
$428$	−1.22798	−	8.54080i	−0.0593567	−	0.412835i
$429$	2.73451	−	7.90086i	0.132024	−	0.381457i
$430$	−14.5088	−	1.38542i	−0.699677	−	0.0668111i
$431$	−1.33975	−	28.1247i	−0.0645333	−	1.35472i	−0.766377	−	0.642391i	$-0.777943\pi$
$431$	−1.33975	−	28.1247i	−0.0645333	−	1.35472i	0.701844	−	0.712331i	$-0.252360\pi$
$432$	−0.928368	+	0.371662i	−0.0446661	+	0.0178816i
$433$	−20.0764	−	12.9023i	−0.964810	−	0.620046i	−0.0394851	−	0.999220i	$-0.512572\pi$
$433$	−20.0764	−	12.9023i	−0.964810	−	0.620046i	−0.925325	+	0.379174i	$0.876208\pi$
$434$	−3.84895	−	4.51237i	−0.184756	−	0.216601i
$435$	7.74695	+	2.27471i	0.371438	+	0.109064i
$436$	−2.38392	−	4.12908i	−0.114169	−	0.197747i
$437$	12.4100	+	24.9598i	0.593650	+	1.19399i
$438$	3.55741	−	6.16162i	0.169980	−	0.294414i
$439$	1.83821	+	7.57719i	0.0877328	+	0.361640i	0.998708	−	0.0508222i	$-0.0161842\pi$
$439$	1.83821	+	7.57719i	0.0877328	+	0.361640i	−0.910975	+	0.412462i	$0.864669\pi$
$440$	4.68996	−	5.41250i	0.223585	−	0.258031i
$441$	−2.39210	+	6.57859i	−0.113909	+	0.313266i
$442$	1.23532	−	8.59186i	0.0587583	−	0.408673i
$443$	21.7207	+	11.1978i	1.03198	+	0.532023i	0.889098	−	0.457716i	$-0.151333\pi$
$443$	21.7207	+	11.1978i	1.03198	+	0.532023i	0.142883	+	0.989740i	$0.454363\pi$
$444$	−0.0719540	−	0.00687077i	−0.00341478	−	0.000326072i
$445$	−7.09025	+	1.36653i	−0.336110	+	0.0647799i
$446$	5.00232	−	3.93387i	0.236867	−	0.186274i
$447$	9.05011	−	19.8170i	0.428055	−	0.937310i
$448$	0.356150	+	2.62167i	0.0168265	+	0.123862i
$449$	−7.24444	+	2.12716i	−0.341886	+	0.100387i	−0.448168	−	0.893949i	$-0.647924\pi$
$449$	−7.24444	+	2.12716i	−0.341886	+	0.100387i	0.106282	+	0.994336i	$0.466105\pi$
$450$	−2.01971	+	0.192859i	−0.0952100	+	0.00909146i
$451$	−2.32450	−	0.930590i	−0.109457	−	0.0438198i
$452$	−2.18752	+	0.421610i	−0.102892	+	0.0198309i
$453$	−9.50938	+	13.3541i	−0.446790	+	0.627428i
$454$	−9.76078	+	6.27287i	−0.458096	+	0.294401i
$455$	−2.09407	−	8.93462i	−0.0981716	−	0.418862i
$456$	4.88960	+	3.14235i	0.228976	+	0.147154i
$457$	10.7230	+	2.06669i	0.501600	+	0.0966755i	0.433774	−	0.901022i	$-0.357182\pi$
$457$	10.7230	+	2.06669i	0.501600	+	0.0966755i	0.0678261	+	0.997697i	$0.478394\pi$
$458$	−3.73666	+	3.56290i	−0.174603	+	0.166483i
$459$	2.15685	−	3.73577i	0.100673	−	0.174371i
$460$	1.68275	−	8.09344i	0.0784585	−	0.377358i
$461$	1.83216			0.0853323			0.0426661	−	0.999089i	$-0.486415\pi$
$461$	1.83216			0.0853323			0.0426661	+	0.999089i	$0.486415\pi$
$462$	−6.30664	−	9.00383i	−0.293411	−	0.418896i
$463$	5.91596	−	6.82738i	0.274938	−	0.317295i	−0.601441	−	0.798917i	$-0.705407\pi$
$463$	5.91596	−	6.82738i	0.274938	−	0.317295i	0.876379	+	0.481622i	$0.159952\pi$
$464$	0.222881	−	4.67884i	0.0103470	−	0.217210i
$465$	3.03728	+	2.38854i	0.140850	+	0.110766i
$466$	−1.42651	−	29.9462i	−0.0660820	−	1.38723i
$467$	−12.6177	+	17.7190i	−0.583876	+	0.819940i	−0.995826	−	0.0912668i	$-0.970908\pi$
$467$	−12.6177	+	17.7190i	−0.583876	+	0.819940i	0.411950	+	0.911206i	$0.364848\pi$
$468$	−1.31774	−	1.52075i	−0.0609125	−	0.0702968i
$469$	−15.9792	+	27.1862i	−0.737851	+	1.25534i
$470$	8.36684	−	18.3208i	0.385934	−	0.845077i
$471$	−6.40918	−	6.11114i	−0.295319	−	0.281587i
$472$	0.790071	−	3.25672i	0.0363660	−	0.149902i
$473$	−20.3787	−	28.6178i	−0.937012	−	1.31585i
$474$	8.37275	−	6.58440i	0.384573	−	0.302432i
$475$	7.72245	+	8.91218i	0.354330	+	0.408919i
$476$	−8.19845	−	7.93986i	−0.375775	−	0.363923i
$477$	7.69378	−	4.94449i	0.352274	−	0.226393i
$478$	−13.9569	+	5.58752i	−0.638376	+	0.255567i
$479$	17.8224	−	9.18811i	0.814328	−	0.419815i	−0.000156690	−	1.00000i	$-0.500050\pi$
$479$	17.8224	−	9.18811i	0.814328	−	0.419815i	0.814485	+	0.580185i	$0.197020\pi$
$480$	−0.563763	−	1.62889i	−0.0257322	−	0.0743482i
$481$	−0.0342906	−	0.141348i	−0.00156352	−	0.00644490i
$482$	25.3072			1.15271
$483$	−11.4211	−	5.52791i	−0.519679	−	0.251529i
$484$	6.26325			0.284693
$485$	−2.08705	−	8.60294i	−0.0947681	−	0.390639i
$486$	−0.327068	−	0.945001i	−0.0148361	−	0.0428661i
$487$	−17.6115	+	9.07934i	−0.798051	+	0.411424i	−0.808481	−	0.588522i	$-0.799710\pi$
$487$	−17.6115	+	9.07934i	−0.798051	+	0.411424i	0.0104303	+	0.999946i	$0.496680\pi$
$488$	4.39684	−	1.76023i	0.199036	−	0.0796818i
$489$	11.1839	−	7.18745i	0.505753	−	0.325028i
$490$	−11.1304	−	4.65811i	−0.502821	−	0.210432i
$491$	5.95272	+	6.86980i	0.268642	+	0.310030i	0.874002	−	0.485922i	$-0.161516\pi$
$491$	5.95272	+	6.86980i	0.268642	+	0.310030i	−0.605360	+	0.795952i	$0.706971\pi$
$492$	−0.473697	+	0.372519i	−0.0213559	+	0.0167945i
$493$	11.7206	+	16.4593i	0.527870	+	0.741290i
$494$	−2.75737	+	11.3660i	−0.124060	+	0.511382i
$495$	5.18321	+	4.94218i	0.232968	+	0.222135i
$496$	0.931228	−	2.03910i	0.0418134	−	0.0915585i
$497$	35.1575	+	0.273455i	1.57703	+	0.0122661i
$498$	−1.50433	−	1.73609i	−0.0674108	−	0.0777962i
$499$	−3.80087	+	5.33758i	−0.170151	+	0.238943i	−0.890842	−	0.454313i	$-0.849885\pi$
$499$	−3.80087	+	5.33758i	−0.170151	+	0.238943i	0.720692	+	0.693256i	$0.243824\pi$
$500$	−0.576485	−	12.1019i	−0.0257812	−	0.541214i
$501$	−8.61586	−	6.77559i	−0.384928	−	0.302711i
$502$	−0.913566	+	19.1781i	−0.0407745	+	0.855961i
$503$	−3.71125	+	4.28301i	−0.165476	+	0.190970i	−0.832432	−	0.554128i	$-0.813052\pi$
$503$	−3.71125	+	4.28301i	−0.165476	+	0.190970i	0.666955	+	0.745098i	$0.267597\pi$
$504$	−2.63565	+	0.231002i	−0.117401	+	0.0102897i
$505$	−26.4259			−1.17594
$506$	17.4002	−	9.71021i	0.773533	−	0.431671i
$507$	−4.47544	+	7.75168i	−0.198761	+	0.344264i
$508$	1.40287	−	1.33763i	0.0622422	−	0.0593478i
$509$	−12.9068	−	2.48759i	−0.572086	−	0.110261i	−0.105000	−	0.994472i	$-0.533484\pi$
$509$	−12.9068	−	2.48759i	−0.572086	−	0.110261i	−0.467086	+	0.884212i	$0.654696\pi$
$510$	6.25512	+	4.01992i	0.276981	+	0.178005i
$511$	13.7242	−	12.8837i	0.607124	−	0.569943i
$512$	−0.841254	+	0.540641i	−0.0371785	+	0.0238932i
$513$	−3.37145	+	4.73454i	−0.148853	+	0.209035i
$514$	24.4465	−	4.71168i	1.07829	−	0.207823i
$515$	3.14233	+	1.25800i	0.138468	+	0.0554341i
$516$	−8.41730	+	0.803755i	−0.370551	+	0.0353833i
$517$	46.5826	−	13.6779i	2.04870	−	0.601553i
$518$	−0.176981	−	0.0724548i	−0.00777611	−	0.00318348i
$519$	1.25957	−	2.75808i	0.0552892	−	0.121066i
$520$	2.72641	−	2.14407i	0.119561	−	0.0940239i
$521$	−20.6695	+	3.98372i	−0.905546	+	0.174530i	−0.620704	−	0.784045i	$-0.713153\pi$
$521$	−20.6695	+	3.98372i	−0.905546	+	0.174530i	−0.284842	+	0.958574i	$0.591941\pi$
$522$	4.66293	+	0.445256i	0.204091	+	0.0194883i
$523$	−13.6607	−	7.04259i	−0.597341	−	0.307951i	0.132912	−	0.991128i	$-0.457567\pi$
$523$	−13.6607	−	7.04259i	−0.597341	−	0.307951i	−0.730253	+	0.683177i	$0.760598\pi$
$524$	0.649200	−	4.51528i	0.0283604	−	0.197251i
$525$	−5.26289	−	1.05686i	−0.229691	−	0.0461251i
$526$	16.7889	−	19.3754i	0.732029	−	0.844806i
$527$	2.27977	+	9.39735i	0.0993085	+	0.409355i
$528$	2.07745	−	3.59825i	0.0904095	−	0.156594i
$529$	12.0764	−	19.5745i	0.525062	−	0.851064i
$530$	7.88210	+	13.6522i	0.342377	+	0.593014i
$531$	3.21543	+	0.944137i	0.139538	+	0.0409720i
$532$	9.97964	+	11.6998i	0.432672	+	0.507249i
$533$	−1.02013	−	0.655599i	−0.0441868	−	0.0283971i
$534$	−3.88904	+	1.55694i	−0.168295	+	0.0673753i
$535$	0.707689	+	14.8562i	0.0305961	+	0.642290i
$536$	−11.8650	−	1.13297i	−0.512488	−	0.0489367i
$537$	−2.41575	+	6.97985i	−0.104247	+	0.301203i
$538$	−0.282955	−	1.96799i	−0.0121990	−	0.0848462i
$539$	−9.08388	−	27.6294i	−0.391270	−	1.19008i
$540$	1.65387	−	0.485619i	0.0711711	−	0.0208977i
$541$	−30.8143	−	29.3814i	−1.32481	−	1.26320i	−0.940412	−	0.340037i	$-0.889560\pi$
$541$	−30.8143	−	29.3814i	−1.32481	−	1.26320i	−0.384398	−	0.923167i	$-0.625591\pi$
$542$	10.0210	+	14.0726i	0.430440	+	0.604469i
$543$	−10.8858	−	4.35801i	−0.467154	−	0.187020i
$544$	1.41087	−	4.07645i	0.0604907	−	0.174776i
$545$	3.41400	+	7.47561i	0.146240	+	0.320220i
$546$	−2.17389	−	4.85984i	−0.0930341	−	0.207982i
$547$	−3.65815	+	25.4430i	−0.156411	+	1.08786i	0.748767	+	0.662833i	$0.230646\pi$
$547$	−3.65815	+	25.4430i	−0.156411	+	1.08786i	−0.905179	+	0.425031i	$0.860263\pi$
$548$	1.05943	−	22.2402i	0.0452566	−	0.950052i
$549$	1.54903	+	4.47561i	0.0661108	+	0.191015i
$550$	6.10099	−	5.81728i	0.260147	−	0.248050i
$551$	−13.6128	−	23.5780i	−0.579923	−	1.00446i
$552$	0.0699917	−	4.79532i	0.00297904	−	0.204102i
$553$	26.2435	−	10.2702i	1.11599	−	0.436734i
$554$	−19.1977	−	5.63696i	−0.815634	−	0.239492i
$555$	0.122339	+	0.0235789i	0.00519300	+	0.00100087i
$556$	−16.3526	+	8.43035i	−0.693504	+	0.357526i
$557$	30.9781	+	24.3614i	1.31258	+	1.03223i	0.996508	+	0.0834923i	$0.0266074\pi$
$557$	30.9781	+	24.3614i	1.31258	+	1.03223i	0.316075	+	0.948734i	$0.397635\pi$
$558$	1.99248	+	1.02720i	0.0843486	+	0.0434847i
$559$	−7.06817	−	15.4771i	−0.298952	−	0.654613i
$560$	−0.181559	−	4.55684i	−0.00767225	−	0.192561i
$561$	2.55071	+	17.7406i	0.107691	+	0.749008i
$562$	−10.0044	+	0.955301i	−0.422009	+	0.0402969i
$563$	7.28052	−	30.0107i	0.306837	−	1.26480i	−0.584476	−	0.811411i	$-0.698700\pi$
$563$	7.28052	−	30.0107i	0.306837	−	1.26480i	0.891313	−	0.453389i	$-0.149785\pi$
$564$	2.75479	−	11.3554i	0.115998	−	0.478149i
$565$	3.82261	−	0.365015i	0.160819	−	0.0153563i
$566$	2.38602	+	16.5951i	0.100292	+	0.697546i
$567$	−0.105331	−	2.64365i	−0.00442350	−	0.111023i
$568$	5.52032	+	12.0878i	0.231628	+	0.507194i
$569$	−5.53279	−	2.85235i	−0.231947	−	0.119577i	0.338336	−	0.941025i	$-0.390136\pi$
$569$	−5.53279	−	2.85235i	−0.231947	−	0.119577i	−0.570283	+	0.821449i	$0.693166\pi$
$570$	−7.87512	−	6.19306i	−0.329852	−	0.259399i
$571$	8.65907	−	4.46406i	0.362371	−	0.186815i	−0.267420	−	0.963580i	$-0.586171\pi$
$571$	8.65907	−	4.46406i	0.362371	−	0.186815i	0.629790	+	0.776765i	$0.283141\pi$
$572$	8.20960	+	1.58227i	0.343261	+	0.0661580i
$573$	−14.7904	−	4.34286i	−0.617879	−	0.181426i
$574$	−1.48476	+	0.581049i	−0.0619725	+	0.0242525i
$575$	2.87729	−	9.29510i	0.119991	−	0.387633i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−25.4437	+	24.2605i	−1.05923	+	1.00998i	−0.0593031	+	0.998240i	$0.518888\pi$
$577$	−25.4437	+	24.2605i	−1.05923	+	1.00998i	−0.999931	+	0.0117378i	$0.996264\pi$
$578$	0.525922	+	1.51955i	0.0218755	+	0.0632050i
$579$	0.714053	−	14.9898i	0.0296750	−	0.622955i
$580$	−1.14905	+	7.99182i	−0.0477117	+	0.331842i
$581$	−2.48172	−	5.54800i	−0.102959	−	0.230170i
$582$	−2.13348	−	4.67166i	−0.0884355	−	0.193647i
$583$	−12.4283	+	35.9093i	−0.514728	+	1.48721i
$584$	6.60517	+	2.64431i	0.273324	+	0.109422i
$585$	2.01192	+	2.82534i	0.0831826	+	0.116814i
$586$	1.75581	+	1.67417i	0.0725320	+	0.0691591i
$587$	−39.4120	+	11.5724i	−1.62671	+	0.477645i	−0.962810	−	0.270179i	$-0.912917\pi$
$587$	−39.4120	+	11.5724i	−1.62671	+	0.477645i	−0.663898	+	0.747823i	$0.731099\pi$
$588$	−6.85206	−	1.43152i	−0.282574	−	0.0590347i
$589$	−1.85426	−	12.8966i	−0.0764033	−	0.531397i
$590$	−1.88927	+	5.45870i	−0.0777801	+	0.224731i
$591$	−11.1920	−	1.06870i	−0.460376	−	0.0439605i
$592$	−0.00343928	−	0.0721994i	−0.000141354	−	0.00296738i
$593$	−8.42446	+	3.37265i	−0.345951	+	0.138498i	−0.538130	−	0.842862i	$-0.680869\pi$
$593$	−8.42446	+	3.37265i	−0.345951	+	0.138498i	0.192179	+	0.981360i	$0.438445\pi$
$594$	3.49533	+	2.24631i	0.143415	+	0.0921673i
$595$	12.7667	+	14.9672i	0.523382	+	0.613594i
$596$	20.9032	+	6.13774i	0.856229	+	0.251412i
$597$	−5.69399	−	9.86228i	−0.233039	−	0.403636i
$598$	9.16471	−	3.02290i	0.374773	−	0.123616i
$599$	6.38006	−	11.0506i	0.260682	−	0.451515i	−0.705741	−	0.708470i	$-0.749386\pi$
$599$	6.38006	−	11.0506i	0.260682	−	0.451515i	0.966423	+	0.256955i	$0.0827192\pi$
$600$	−0.478331	−	1.97171i	−0.0195278	−	0.0804945i
$601$	32.0331	−	36.9682i	1.30666	−	1.50796i	0.601674	−	0.798742i	$-0.294501\pi$
$601$	32.0331	−	36.9682i	1.30666	−	1.50796i	0.704985	−	0.709223i	$-0.250954\pi$
$602$	−21.9335	−	4.40454i	−0.893943	−	0.179516i
$603$	1.69624	−	11.7976i	0.0690763	−	0.480436i
$604$	−14.5715	−	7.51211i	−0.592904	−	0.305663i
$605$	−10.7470	−	1.02621i	−0.436928	−	0.0417216i
$606$	−15.0540	+	2.90142i	−0.611526	+	0.117862i
$607$	36.5530	−	28.7456i	1.48364	−	1.16675i	0.537384	−	0.843338i	$-0.319413\pi$
$607$	36.5530	−	28.7456i	1.48364	−	1.16675i	0.946258	−	0.323412i	$-0.104830\pi$
$608$	−2.41451	+	5.28703i	−0.0979212	+	0.214417i
$609$	11.4692	+	4.69539i	0.464754	+	0.190267i
$610$	−7.83287	+	2.29994i	−0.317144	+	0.0931218i
$611$	23.4062	−	2.23502i	0.946912	−	0.0904191i
$612$	4.00470	+	1.60324i	0.161880	+	0.0648071i
$613$	−39.2349	+	7.56191i	−1.58468	+	0.305423i	−0.904124	−	0.427271i	$-0.859475\pi$
$613$	−39.2349	+	7.56191i	−1.58468	+	0.305423i	−0.680559	+	0.732693i	$0.738263\pi$
$614$	−6.44253	+	9.04727i	−0.259999	+	0.365118i
$615$	0.873845	−	0.561586i	0.0352368	−	0.0226453i
$616$	8.01466	−	7.52383i	0.322920	−	0.303144i
$617$	13.1685	+	8.46289i	0.530144	+	0.340703i	0.778173	−	0.628050i	$-0.216147\pi$
$617$	13.1685	+	8.46289i	0.530144	+	0.340703i	−0.248029	+	0.968753i	$0.579783\pi$
$618$	1.92820	+	0.371631i	0.0775637	+	0.0149492i
$619$	21.9193	−	20.9000i	0.881012	−	0.840043i	−0.107026	−	0.994256i	$-0.534133\pi$
$619$	21.9193	−	20.9000i	0.881012	−	0.840043i	0.988038	+	0.154213i	$0.0492843\pi$
$620$	−1.93198	+	3.34629i	−0.0775902	+	0.134390i
$621$	4.78656	+	0.298083i	0.192078	+	0.0119617i
$622$	11.1853			0.448489
$623$	−11.0410	+	0.967696i	−0.442350	+	0.0387699i
$624$	1.31774	−	1.52075i	0.0527518	−	0.0608788i
$625$	−0.510987	+	10.7269i	−0.0204395	+	0.429077i
$626$	24.7957	+	19.4996i	0.991036	+	0.779359i
$627$	−1.14908	−	24.1221i	−0.0458897	−	0.963344i
$628$	5.13682	−	7.21365i	0.204981	−	0.287856i
$629$	0.204185	+	0.235642i	0.00814140	+	0.00939568i
$630$	4.56031	+	0.0354701i	0.181687	+	0.00141316i
$631$	7.21873	−	15.8068i	0.287373	−	0.629260i	−0.709799	−	0.704404i	$-0.751214\pi$
$631$	7.21873	−	15.8068i	0.287373	−	0.629260i	0.997173	+	0.0751443i	$0.0239417\pi$
$632$	7.70895	+	7.35047i	0.306645	+	0.292386i
$633$	−5.04486	+	20.7952i	−0.200515	+	0.826535i
$634$	11.1481	+	15.6553i	0.442746	+	0.621750i
$635$	−2.62632	+	2.06536i	−0.104222	+	0.0819615i
$636$	5.98911	+	6.91180i	0.237483	+	0.274071i
$637$	−1.78749	−	13.9718i	−0.0708229	−	0.553584i
$638$	−16.3726	+	10.5220i	−0.648198	+	0.416572i
$639$	−12.3368	+	4.93891i	−0.488036	+	0.195380i
$640$	1.53208	−	0.789840i	0.0605606	−	0.0312212i
$641$	13.5469	+	39.1412i	0.535070	+	1.54598i	0.811144	+	0.584847i	$0.198845\pi$
$641$	13.5469	+	39.1412i	0.535070	+	1.54598i	−0.276074	+	0.961136i	$0.589033\pi$
$642$	2.03428	+	8.38540i	0.0802865	+	0.330945i
$643$	40.3529			1.59136			0.795681	−	0.605716i	$-0.207113\pi$
$643$	40.3529			1.59136			0.795681	+	0.605716i	$0.207113\pi$
$644$	3.84625	−	12.0916i	0.151563	−	0.476475i
$645$	14.5748			0.573882
$646$	−5.91104	−	24.3656i	−0.232567	−	0.958654i
$647$	−5.73821	−	16.5795i	−0.225592	−	0.651806i	−0.999821	−	0.0189004i	$-0.993983\pi$
$647$	−5.73821	−	16.5795i	−0.225592	−	0.651806i	0.774229	−	0.632905i	$-0.218138\pi$
$648$	0.888835	−	0.458227i	0.0349168	−	0.0180008i
$649$	−12.9264	+	5.17497i	−0.507407	+	0.203135i
$650$	3.43453	−	2.20724i	0.134713	−	0.0865751i
$651$	4.26045	+	4.12607i	0.166980	+	0.161713i
$652$	8.70592	+	10.0472i	0.340950	+	0.393478i
$653$	15.5930	−	12.2625i	0.610202	−	0.479868i	−0.264594	−	0.964360i	$-0.585238\pi$
$653$	15.5930	−	12.2625i	0.610202	−	0.479868i	0.874796	+	0.484492i	$0.160995\pi$
$654$	2.76562	+	3.88377i	0.108144	+	0.151868i
$655$	−1.85377	+	7.64133i	−0.0724327	+	0.298572i
$656$	−0.436142	−	0.415860i	−0.0170285	−	0.0162366i
$657$	−2.95560	+	6.47187i	−0.115309	+	0.252492i
$658$	15.6653	−	26.6522i	0.610696	−	1.03901i
$659$	−16.5650	−	19.1171i	−0.645282	−	0.744696i	0.335017	−	0.942212i	$-0.391258\pi$
$659$	−16.5650	−	19.1171i	−0.645282	−	0.744696i	−0.980300	+	0.197516i	$0.936712\pi$
$660$	−4.15423	+	5.83380i	−0.161703	+	0.227080i
$661$	0.834288	+	17.5139i	0.0324500	+	0.681210i	0.955227	+	0.295875i	$0.0956112\pi$
$661$	0.834288	+	17.5139i	0.0324500	+	0.681210i	−0.922777	+	0.385335i	$0.874086\pi$
$662$	4.98291	+	3.91860i	0.193666	+	0.152301i
$663$	−0.413021	+	8.67038i	−0.0160404	+	0.336730i
$664$	1.50433	−	1.73609i	0.0583794	−	0.0673735i
$665$	−15.2069	−	21.7106i	−0.589700	−	0.841900i
$666$	0.0722813			0.00280084
$667$	−10.5841	+	19.8148i	−0.409817	+	0.767231i
$668$	5.48046	−	9.49243i	0.212045	−	0.367273i
$669$	−4.60573	+	4.39156i	−0.178068	+	0.169787i
$670$	20.1733	+	3.88808i	0.779361	+	0.150210i
$671$	−16.5542	−	10.6387i	−0.639068	−	0.410704i
$672$	−0.603743	−	2.57595i	−0.0232899	−	0.0993693i
$673$	−21.8943	+	14.0706i	−0.843962	+	0.542382i	−0.889686	−	0.456573i	$-0.849077\pi$
$673$	−21.8943	+	14.0706i	−0.843962	+	0.542382i	0.0457240	+	0.998954i	$0.485441\pi$
$674$	−11.3960	+	16.0034i	−0.438957	+	0.616429i
$675$	1.99223	−	0.383971i	0.0766810	−	0.0147791i
$676$	−8.30970	−	3.32670i	−0.319604	−	0.127950i
$677$	23.3744	−	2.23199i	0.898353	−	0.0857823i	0.364347	−	0.931263i	$-0.381292\pi$
$677$	23.3744	−	2.23199i	0.898353	−	0.0857823i	0.534006	+	0.845481i	$0.320686\pi$
$678$	2.13754	−	0.627638i	0.0820917	−	0.0241043i
$679$	−1.82910	−	13.4643i	−0.0701946	−	0.516713i
$680$	−3.08881	+	6.76354i	−0.118450	+	0.259370i
$681$	9.12031	−	7.17229i	0.349491	−	0.274843i
$682$	−9.14566	+	1.76268i	−0.350205	+	0.0674965i
$683$	29.2897	+	2.79683i	1.12074	+	0.107018i	0.638935	−	0.769261i	$-0.279375\pi$
$683$	29.2897	+	2.79683i	1.12074	+	0.107018i	0.481805	+	0.876279i	$0.339981\pi$
$684$	−5.16616	−	2.66334i	−0.197533	−	0.101835i
$685$	−5.46184	+	37.9879i	−0.208686	+	1.45144i
$686$	−16.2590	−	8.86823i	−0.620771	−	0.338591i
$687$	3.38107	−	3.90196i	0.128996	−	0.148869i
$688$	−1.99348	−	8.21724i	−0.0760008	−	0.313279i
$689$	−9.20161	+	15.9377i	−0.350553	+	0.607176i
$690$	−0.905797	+	8.21675i	−0.0344831	+	0.312806i
$691$	21.4815	+	37.2071i	0.817196	+	1.41542i	0.907740	+	0.419532i	$0.137806\pi$
$691$	21.4815	+	37.2071i	0.817196	+	1.41542i	−0.0905448	+	0.995892i	$0.528861\pi$
$692$	2.90927	+	0.854237i	0.110594	+	0.0324732i
$693$	7.13395	+	8.36358i	0.270996	+	0.317706i
$694$	−0.710357	−	0.456519i	−0.0269648	−	0.0173292i
$695$	29.4404	−	11.7862i	1.11674	−	0.447075i
$696$	0.222881	+	4.67884i	0.00844826	+	0.177351i
$697$	2.58778	+	0.247103i	0.0980192	+	0.00935969i
$698$	−7.09733	+	20.5064i	−0.268638	+	0.776178i
$699$	4.26663	+	29.6750i	0.161379	+	1.12241i
$700$	0.297113	−	5.35973i	0.0112298	−	0.202579i
$701$	40.9762	−	12.0317i	1.54765	−	0.454431i	0.607253	−	0.794509i	$-0.292271\pi$
$701$	40.9762	−	12.0317i	1.54765	−	0.454431i	0.940397	+	0.340077i	$0.110453\pi$
$702$	1.45633	+	1.38861i	0.0549656	+	0.0524096i
$703$	−0.243693	−	0.342219i	−0.00919104	−	0.0129070i
$704$	3.85728	+	1.54422i	0.145377	+	0.0582001i
$705$	−6.58745	+	19.0332i	−0.248098	+	0.716831i
$706$	4.54152	+	9.94455i	0.170922	+	0.374268i
$707$	−40.3472	−	4.16961i	−1.51741	−	0.156814i
$708$	−0.476923	+	3.31707i	−0.0179239	+	0.124663i
$709$	0.675972	−	14.1904i	0.0253867	−	0.532932i	−0.949976	−	0.312324i	$-0.898893\pi$
$709$	0.675972	−	14.1904i	0.0253867	−	0.532932i	0.975362	−	0.220608i	$-0.0708043\pi$
$710$	−7.49168	−	21.6458i	−0.281158	−	0.812352i
$711$	−7.70895	+	7.35047i	−0.289108	+	0.275664i
$712$	−2.09456	−	3.62788i	−0.0784969	−	0.135961i
$713$	−8.22673	+	6.92090i	−0.308094	+	0.259190i
$714$	8.91606	+	7.12459i	0.333675	+	0.266631i
$715$	−13.8275	−	4.06011i	−0.517118	−	0.151840i
$716$	−7.25260	−	1.39782i	−0.271042	−	0.0522391i
$717$	13.3626	−	6.88891i	0.499036	−	0.257271i
$718$	4.27912	+	3.36514i	0.159695	+	0.125586i
$719$	40.2895	+	20.7707i	1.50255	+	0.774616i	0.996148	−	0.0876847i	$-0.0279468\pi$
$719$	40.2895	+	20.7707i	1.50255	+	0.774616i	0.506397	+	0.862301i	$0.330977\pi$
$720$	0.716046	+	1.56792i	0.0266855	+	0.0584330i
$721$	4.59923	+	2.41653i	0.171284	+	0.0899963i
$722$	2.10378	+	14.6321i	0.0782944	+	0.544550i
$723$	−25.1926	+	2.40560i	−0.936924	+	0.0894654i
$724$	2.76444	−	11.3952i	0.102740	−	0.423499i
$725$	−2.24057	+	9.23575i	−0.0832126	+	0.343007i
$726$	−6.23489	+	0.595359i	−0.231398	+	0.0220959i
$727$	−2.01366	−	14.0053i	−0.0746824	−	0.519427i	−0.992483	−	0.122385i	$-0.960946\pi$
$727$	−2.01366	−	14.0053i	−0.0746824	−	0.519427i	0.917800	−	0.397042i	$-0.129963\pi$
$728$	4.50100	−	2.84339i	0.166818	−	0.105383i
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$	−10.9004	−	5.61957i	−0.403444	−	0.207990i
$731$	28.6712	+	22.5473i	1.06044	+	0.833941i
$732$	−4.20961	+	2.17020i	−0.155592	+	0.0802131i
$733$	−9.27329	−	1.78728i	−0.342517	−	0.0660147i	0.0150923	−	0.999886i	$-0.495196\pi$
$733$	−9.27329	−	1.78728i	−0.342517	−	0.0660147i	−0.357609	+	0.933871i	$0.616408\pi$
$734$	−26.9193	−	7.90422i	−0.993610	−	0.291750i
$735$	11.5228	+	3.57901i	0.425025	+	0.132014i
$736$	4.75647	−	0.613166i	0.175326	−	0.0226016i
$737$	24.7610	+	42.8873i	0.912084	+	1.57978i
$738$	0.436142	−	0.415860i	0.0160546	−	0.0153080i
$739$	13.1886	+	38.1060i	0.485151	+	1.40175i	0.876452	+	0.481489i	$0.159904\pi$
$739$	13.1886	+	38.1060i	0.485151	+	1.40175i	−0.391301	+	0.920263i	$0.627975\pi$
$740$	−0.00592825	+	0.124449i	−0.000217927	+	0.00457485i
$741$	1.66447	−	11.5767i	0.0611460	−	0.425280i
$742$	9.88031	+	22.0879i	0.362718	+	0.810873i
$743$	19.5030	+	42.7056i	0.715495	+	1.56672i	0.820112	+	0.572203i	$0.193911\pi$
$743$	19.5030	+	42.7056i	0.715495	+	1.56672i	−0.104617	+	0.994513i	$0.533362\pi$
$744$	−0.733182	+	2.11839i	−0.0268797	+	0.0776639i
$745$	−34.8619	−	13.9566i	−1.27724	−	0.511330i
$746$	−2.76019	−	3.87614i	−0.101058	−	0.141915i
$747$	1.66255	+	1.58524i	0.0608294	+	0.0580007i
$748$	−17.1970	+	5.04950i	−0.628785	+	0.184628i
$749$	−1.26358	+	22.7942i	−0.0461703	+	0.832882i
$750$	1.72423	+	11.9923i	0.0629601	+	0.437897i
$751$	−4.17793	+	12.0713i	−0.152455	+	0.440490i	−0.995204	−	0.0978162i	$-0.968814\pi$
$751$	−4.17793	+	12.0713i	−0.152455	+	0.440490i	0.842750	+	0.538306i	$0.180935\pi$
$752$	11.6319	+	1.11071i	0.424171	+	0.0405034i
$753$	−0.913566	−	19.1781i	−0.0332922	−	0.698889i
$754$	−8.75046	+	3.50316i	−0.318673	+	0.127577i
$755$	23.7721	+	15.2774i	0.865155	+	0.556001i
$756$	2.60175	−	0.480490i	0.0946249	−	0.0174753i
$757$	−8.54263	−	2.50834i	−0.310487	−	0.0911672i	0.122777	−	0.992434i	$-0.460820\pi$
$757$	−8.54263	−	2.50834i	−0.310487	−	0.0911672i	−0.433264	+	0.901267i	$0.642638\pi$
$758$	0.376275	+	0.651727i	0.0136669	+	0.0236718i
$759$	−16.3984	+	11.3202i	−0.595224	+	0.410898i
$760$	5.00928	−	8.67632i	0.181706	−	0.314723i
$761$	−2.03111	−	8.37237i	−0.0736279	−	0.303498i	0.923077	−	0.384616i	$-0.125666\pi$
$761$	−2.03111	−	8.37237i	−0.0736279	−	0.303498i	−0.996705	+	0.0811179i	$0.974151\pi$
$762$	−1.26936	+	1.46493i	−0.0459842	+	0.0530686i
$763$	4.03297	+	11.9525i	0.146003	+	0.432709i
$764$	2.19376	−	15.2579i	0.0793675	−	0.552013i
$765$	−6.60891	−	3.40713i	−0.238946	−	0.123185i
$766$	−4.09348	−	0.390880i	−0.147904	−	0.0141231i
$767$	−6.62153	+	1.27620i	−0.239090	+	0.0460808i
$768$	0.786053	−	0.618159i	0.0283642	−	0.0223059i
$769$	14.5994	−	31.9682i	0.526467	−	1.15280i	−0.440465	−	0.897770i	$-0.645187\pi$
$769$	14.5994	−	31.9682i	0.526467	−	1.15280i	0.966932	−	0.255033i	$-0.0820862\pi$
$770$	−14.9850	+	11.5968i	−0.540021	+	0.417921i
$771$	−23.8880	+	7.01414i	−0.860304	+	0.252608i
$772$	14.9389	−	1.42649i	0.537661	−	0.0513404i
$773$	−14.2572	−	5.70774i	−0.512797	−	0.205293i	0.100808	−	0.994906i	$-0.467857\pi$
$773$	−14.2572	−	5.70774i	−0.512797	−	0.205293i	−0.613605	+	0.789613i	$0.710281\pi$
$774$	8.30279	−	1.60023i	0.298438	−	0.0575191i
$775$	−2.63818	+	3.70480i	−0.0947662	+	0.133080i
$776$	4.32049	−	2.77661i	0.155096	−	0.0996745i
$777$	0.183067	+	0.0553036i	0.00656750	+	0.00198400i
$778$	−20.0552	−	12.8887i	−0.719013	−	0.462081i
$779$	−3.43934	−	0.662878i	−0.123227	−	0.0237501i
$780$	−2.51026	+	2.39353i	−0.0898817	+	0.0857020i
$781$	27.6066	−	47.8161i	0.987844	−	1.71100i
$782$	−14.4932	+	14.7625i	−0.518275	+	0.527906i
$783$	−4.68414			−0.167398
$784$	0.441795	−	6.98604i	0.0157784	−	0.249502i
$785$	−9.99612	+	11.5361i	−0.356777	+	0.411742i
$786$	−0.217055	+	4.55655i	−0.00774210	+	0.162527i
$787$	27.9275	+	21.9624i	0.995508	+	0.782876i	0.976186	−	0.216937i	$-0.0696067\pi$
$787$	27.9275	+	21.9624i	0.995508	+	0.782876i	0.0193225	+	0.999813i	$0.493849\pi$
$788$	−0.534957	−	11.2301i	−0.0190571	−	0.400057i
$789$	−14.8711	+	20.8835i	−0.529425	+	0.743473i
$790$	−12.0233	−	13.8756i	−0.427770	−	0.493673i
$791$	5.89398	+	0.0458432i	0.209566	+	0.00163000i
$792$	−1.72601	+	3.77944i	−0.0613311	+	0.134296i
$793$	−6.89732	−	6.57658i	−0.244931	−	0.233541i
$794$	3.83706	−	15.8166i	0.136172	−	0.561310i
$795$	−9.14413	−	12.8411i	−0.324309	−	0.455428i
$796$	8.95156	−	7.03958i	0.317279	−	0.249511i
$797$	11.2796	+	13.0174i	0.399544	+	0.461098i	0.919497	−	0.393096i	$-0.128596\pi$
$797$	11.2796	+	13.0174i	0.399544	+	0.461098i	−0.519953	+	0.854195i	$0.674051\pi$
$798$	−11.0466	−	10.6982i	−0.391045	−	0.378711i
$799$	−42.4031	+	27.2508i	−1.50011	+	0.964064i
$800$	1.88356	−	0.754065i	0.0665940	−	0.0266602i
$801$	3.72344	−	1.91956i	0.131561	−	0.0678245i
$802$	−6.69685	−	19.3493i	−0.236474	−	0.683247i
$803$	−6.96937	−	28.7281i	−0.245944	−	1.01379i
$804$	11.9189			0.420348
$805$	−8.58088	+	20.1176i	−0.302436	+	0.709051i
$806$	−4.51081			−0.158886
$807$	0.468743	+	1.93219i	0.0165005	+	0.0680161i
$808$	−5.01429	−	14.4878i	−0.176402	−	0.509680i
$809$	−43.9633	+	22.6646i	−1.54567	+	0.796846i	−0.999175	−	0.0406189i	$-0.987067\pi$
$809$	−43.9633	+	22.6646i	−1.54567	+	0.796846i	−0.546491	+	0.837465i	$0.684037\pi$
$810$	−1.60022	+	0.640630i	−0.0562259	+	0.0225095i
$811$	−35.4770	+	22.7997i	−1.24577	+	0.800605i	−0.986270	−	0.165139i	$-0.947193\pi$
$811$	−35.4770	+	22.7997i	−1.24577	+	0.800605i	−0.259496	+	0.965744i	$0.583556\pi$
$812$	−3.01536	+	12.0206i	−0.105819	+	0.421842i
$813$	−11.3133	−	13.0563i	−0.396776	−	0.457904i
$814$	−0.236069	+	0.185647i	−0.00827421	+	0.00650691i
$815$	−13.2922	−	18.6662i	−0.465604	−	0.653849i
$816$	−1.01699	+	4.19210i	−0.0356019	+	0.146753i
$817$	−35.5688	−	33.9148i	−1.24439	−	1.18653i
$818$	−10.4176	+	22.8114i	−0.364244	+	0.797583i
$819$	2.62601	+	4.63120i	0.0917601	+	0.161827i
$820$	0.680231	+	0.785028i	0.0237547	+	0.0274144i
$821$	−5.53376	+	7.77108i	−0.193130	+	0.271212i	−0.899774	−	0.436356i	$-0.856269\pi$
$821$	−5.53376	+	7.77108i	−0.193130	+	0.271212i	0.706644	+	0.707569i	$0.250208\pi$
$822$	1.05943	+	22.2402i	0.0369518	+	0.775714i
$823$	21.3200	+	16.7662i	0.743168	+	0.584434i	0.916313	−	0.400463i	$-0.131151\pi$
$823$	21.3200	+	16.7662i	0.743168	+	0.584434i	−0.173145	+	0.984896i	$0.555393\pi$
$824$	−0.0934361	+	1.96147i	−0.00325500	+	0.0683309i
$825$	−5.52039	+	6.37087i	−0.192195	+	0.221805i
$826$	−3.74585	+	8.03626i	−0.130335	+	0.279617i
$827$	−16.9158			−0.588220			−0.294110	−	0.955772i	$-0.595023\pi$
$827$	−16.9158			−0.588220			−0.294110	+	0.955772i	$0.595023\pi$
$828$	0.386149	+	4.78026i	0.0134196	+	0.166126i
$829$	−6.62973	+	11.4830i	−0.230260	+	0.398822i	−0.957885	−	0.287154i	$-0.907291\pi$
$829$	−6.62973	+	11.4830i	−0.230260	+	0.398822i	0.727625	+	0.685976i	$0.240624\pi$
$830$	−2.86571	+	2.73245i	−0.0994704	+	0.0948448i
$831$	19.6466	+	3.78658i	0.681534	+	0.131355i
$832$	1.69281	+	1.08790i	0.0586875	+	0.0377162i
$833$	17.1306	+	24.8663i	0.593540	+	0.861567i
$834$	15.4772	−	9.94659i	0.535931	−	0.344422i
$835$	−10.9591	+	15.3900i	−0.379257	+	0.532591i
$836$	23.7130	−	4.57032i	0.820133	−	0.158068i
$837$	−2.08110	−	0.833148i	−0.0719335	−	0.0287978i
$838$	−5.31371	+	0.507398i	−0.183559	+	0.0175278i
$839$	17.1802	−	5.04455i	0.593125	−	0.174157i	0.0286249	−	0.999590i	$-0.490887\pi$
$839$	17.1802	−	5.04455i	0.593125	−	0.174157i	0.564500	+	0.825433i	$0.309069\pi$
$840$	0.613891	+	4.51894i	0.0211813	+	0.155918i
$841$	−2.93233	+	6.42091i	−0.101115	+	0.221411i
$842$	2.51077	−	1.97449i	0.0865267	−	0.0680453i
$843$	9.86826	−	1.90195i	0.339881	−	0.0655067i
$844$	−21.3015	−	2.03405i	−0.733228	−	0.0700148i
$845$	13.7134	+	7.06976i	0.471756	+	0.243207i
$846$	−1.66292	+	11.5658i	−0.0571723	+	0.397642i
$847$	−16.2466	−	3.26254i	−0.558241	−	0.112102i
$848$	−5.98911	+	6.91180i	−0.205667	+	0.237352i
$849$	−3.95269	−	16.2932i	−0.135656	−	0.559181i
$850$	−4.37602	+	7.57950i	−0.150096	+	0.259975i
$851$	−0.133519	+	0.319903i	−0.00457698	+	0.0109661i
$852$	−6.64435	−	11.5084i	−0.227632	−	0.394270i
$853$	−21.8557	−	6.41741i	−0.748325	−	0.219728i	−0.114734	−	0.993396i	$-0.536602\pi$
$853$	−21.8557	−	6.41741i	−0.748325	−	0.219728i	−0.633591	+	0.773668i	$0.718420\pi$
$854$	−12.3222	+	2.27565i	−0.421656	+	0.0778711i
$855$	8.42814	+	5.41644i	0.288236	+	0.185238i
$856$	−8.01054	+	3.20694i	−0.273795	+	0.109611i
$857$	0.225275	+	4.72911i	0.00769526	+	0.161543i	0.999444	+	0.0333456i	$0.0106162\pi$
$857$	0.225275	+	4.72911i	0.00769526	+	0.161543i	−0.991749	+	0.128198i	$0.959081\pi$
$858$	−8.32283	−	0.794734i	−0.284137	−	0.0271318i
$859$	8.39941	−	24.2685i	0.286584	−	0.828031i	−0.706189	−	0.708024i	$-0.749587\pi$
$859$	8.39941	−	24.2685i	0.286584	−	0.828031i	0.992773	−	0.120007i	$-0.0382918\pi$
$860$	2.07421	+	14.4265i	0.0707300	+	0.491938i
$861$	1.42280	−	0.719553i	0.0484889	−	0.0245223i
$862$	−27.0161	+	7.93264i	−0.920172	+	0.270187i
$863$	12.9334	+	12.3320i	0.440258	+	0.419786i	0.877513	−	0.479552i	$-0.159201\pi$
$863$	12.9334	+	12.3320i	0.440258	+	0.419786i	−0.437255	+	0.899338i	$0.644049\pi$
$864$	0.580057	+	0.814576i	0.0197339	+	0.0277124i
$865$	−4.85200	−	1.94245i	−0.164973	−	0.0660452i
$866$	−7.80543	+	22.5523i	−0.265239	+	0.766359i
$867$	−0.667983	−	1.46268i	−0.0226859	−	0.0496752i
$868$	−3.47775	+	4.80429i	−0.118042	+	0.163068i
$869$	6.29836	−	43.8061i	0.213657	−	1.48602i
$870$	0.384177	−	8.06486i	0.0130248	−	0.273424i
$871$	7.84433	+	22.6647i	0.265795	+	0.767964i
$872$	−3.45065	+	3.29019i	−0.116854	+	0.111420i
$873$	2.56789	+	4.44771i	0.0869098	+	0.150532i
$874$	21.3304	−	17.9447i	0.721513	−	0.606987i
$875$	−4.80853	+	31.6922i	−0.162558	+	1.07139i
$876$	−6.82662	−	2.00448i	−0.230650	−	0.0677250i
$877$	37.7327	+	7.27238i	1.27414	+	0.245571i	0.781084	−	0.624426i	$-0.214667\pi$
$877$	37.7327	+	7.27238i	1.27414	+	0.245571i	0.493058	+	0.869997i	$0.335879\pi$
$878$	6.93023	−	3.57278i	0.233884	−	0.120575i
$879$	−1.90700	−	1.49968i	−0.0643216	−	0.0505831i
$880$	−6.36563	−	3.28171i	−0.214585	−	0.110626i
$881$	−5.51060	−	12.0665i	−0.185657	−	0.406532i	0.793802	−	0.608176i	$-0.208099\pi$
$881$	−5.51060	−	12.0665i	−0.185657	−	0.406532i	−0.979459	+	0.201645i	$0.935371\pi$
$882$	6.95711	+	0.773704i	0.234258	+	0.0260520i
$883$	−2.03341	−	14.1427i	−0.0684296	−	0.475938i	−0.995005	−	0.0998285i	$-0.968171\pi$
$883$	−2.03341	−	14.1427i	−0.0684296	−	0.475938i	0.926575	−	0.376110i	$-0.122738\pi$
$884$	−8.64091	+	0.825107i	−0.290625	+	0.0277513i
$885$	1.36184	−	5.61356i	0.0457776	−	0.188698i
$886$	5.76130	−	23.7484i	0.193555	−	0.797843i
$887$	45.1992	−	4.31600i	1.51764	−	0.144917i	0.697294	−	0.716785i	$-0.254387\pi$
$887$	45.1992	−	4.31600i	1.51764	−	0.144917i	0.820346	+	0.571868i	$0.193781\pi$
$888$	0.0102867	+	0.0715455i	0.000345199	+	0.00240091i
$889$	−4.33577	+	2.73901i	−0.145417	+	0.0918635i
$890$	2.99960	+	6.56821i	0.100547	+	0.220167i
$891$	−3.69303	−	1.90389i	−0.123721	−	0.0637827i
$892$	−5.00232	−	3.93387i	−0.167490	−	0.131716i
$893$	60.3654	−	31.1205i	2.02005	−	1.04141i
$894$	−21.3920	−	4.12297i	−0.715456	−	0.137893i
$895$	12.2156	+	3.58682i	0.408322	+	0.119894i
$896$	2.46380	−	0.964193i	0.0823099	−	0.0322114i
$897$	−8.83587	+	3.88037i	−0.295021	+	0.129562i
$898$	3.77514	+	6.53873i	0.125978	+	0.218200i
$899$	7.59946	−	7.24607i	0.253456	−	0.241670i
$900$	0.663587	+	1.91731i	0.0221196	+	0.0639103i
$901$	1.87717	−	39.4067i	0.0625378	−	1.31283i
$902$	−0.356336	+	2.47837i	−0.0118647	+	0.0825208i
$903$	22.2529	+	2.29968i	0.740529	+	0.0765286i
$904$	0.925453	+	2.02646i	0.0307801	+	0.0673991i
$905$	−6.61053	+	19.0999i	−0.219741	+	0.634901i
$906$	15.2195	+	6.09299i	0.505636	+	0.202426i
$907$	33.1122	+	46.4995i	1.09947	+	1.54399i	0.809652	+	0.586910i	$0.199656\pi$
$907$	33.1122	+	46.4995i	1.09947	+	1.54399i	0.289820	+	0.957081i	$0.406405\pi$
$908$	8.39724	+	8.00676i	0.278672	+	0.265714i
$909$	14.7100	−	4.31925i	0.487900	−	0.143260i
$910$	−8.18907	+	4.14146i	−0.271465	+	0.137288i
$911$	−7.29568	−	50.7426i	−0.241717	−	1.68118i	−0.643503	−	0.765443i	$-0.722520\pi$
$911$	−7.29568	−	50.7426i	−0.241717	−	1.68118i	0.401787	−	0.915733i	$-0.368389\pi$
$912$	1.90101	−	5.49260i	0.0629487	−	0.181878i
$913$	−9.50135	−	0.907269i	−0.314449	−	0.0300262i
$914$	−0.519610	−	10.9080i	−0.0171872	−	0.360803i
$915$	7.57878	−	3.03409i	0.250547	−	0.100304i
$916$	4.34342	+	2.79135i	0.143511	+	0.0922287i
$917$	−4.03603	+	11.3743i	−0.133281	+	0.375613i
$918$	−4.13896	−	1.21531i	−0.136606	−	0.0401112i
$919$	20.1976	+	34.9833i	0.666258	+	1.15399i	0.978943	+	0.204136i	$0.0654384\pi$
$919$	20.1976	+	34.9833i	0.666258	+	1.15399i	−0.312684	+	0.949857i	$0.601228\pi$
$920$	−8.26202	+	0.272788i	−0.272391	+	0.00899355i
$921$	5.55336	−	9.61870i	0.182989	−	0.316947i
$922$	−0.431949	−	1.78052i	−0.0142255	−	0.0586382i
$923$	17.5110	−	20.2088i	0.576383	−	0.665182i
$924$	−7.26318	+	8.25160i	−0.238941	+	0.271458i
$925$	−0.0208706	+	0.145159i	−0.000686223	+	0.00477278i
$926$	−8.02967	−	4.13958i	−0.263871	−	0.136035i
$927$	−1.95480	−	0.186661i	−0.0642040	−	0.00613074i
$928$	−4.59950	+	0.886480i	−0.150986	+	0.0291001i
$929$	−30.0630	+	23.6418i	−0.986334	+	0.775661i	−0.974527	−	0.224269i	$-0.928001\pi$
$929$	−30.0630	+	23.6418i	−0.986334	+	0.775661i	−0.0118065	+	0.999930i	$0.503758\pi$
$930$	1.60515	−	3.51478i	0.0526348	−	0.115254i
$931$	−19.7924	−	35.5472i	−0.648670	−	1.16501i
$932$	−28.7658	+	8.44639i	−0.942254	+	0.276671i
$933$	−11.1346	+	1.06323i	−0.364532	+	0.0348085i
$934$	20.1943	+	8.08458i	0.660778	+	0.264535i
$935$	30.3354	−	5.84667i	0.992074	−	0.191207i
$936$	−1.16722	+	1.63913i	−0.0381517	+	0.0535765i
$937$	25.6076	−	16.4570i	0.836564	−	0.537627i	−0.0507934	−	0.998709i	$-0.516175\pi$
$937$	25.6076	−	16.4570i	0.836564	−	0.537627i	0.887358	+	0.461082i	$0.152539\pi$
$938$	30.1871	+	9.11937i	0.985645	+	0.297758i
$939$	−26.5370	−	17.0543i	−0.866002	−	0.556546i
$940$	−19.7770	−	3.81170i	−0.645053	−	0.124324i
$941$	11.8424	−	11.2917i	0.386050	−	0.368098i	−0.472058	−	0.881568i	$-0.656489\pi$
$941$	11.8424	−	11.2917i	0.386050	−	0.368098i	0.858108	+	0.513470i	$0.171640\pi$
$942$	−4.42786	+	7.66927i	−0.144267	+	0.249878i
$943$	1.03487	+	2.69846i	0.0337000	+	0.0878741i
$944$	−3.35118			−0.109072
$945$	−4.54304	+	0.398176i	−0.147785	+	0.0129527i
$946$	−23.0067	+	26.5511i	−0.748012	+	0.863252i
$947$	0.873463	−	18.3362i	0.0283837	−	0.595848i	−0.939211	−	0.343340i	$-0.888442\pi$
$947$	0.873463	−	18.3362i	0.0283837	−	0.595848i	0.967595	−	0.252508i	$-0.0812553\pi$
$948$	−8.37275	−	6.58440i	−0.271934	−	0.213851i
$949$	−0.681219	−	14.3005i	−0.0221133	−	0.464215i
$950$	6.84032	−	9.60589i	0.221929	−	0.311656i
$951$	−12.5857	−	14.5247i	−0.408120	−	0.470995i
$952$	−5.78319	+	9.83924i	−0.187434	+	0.318892i
$953$	−8.40405	+	18.4023i	−0.272234	+	0.596109i	−0.995532	−	0.0944271i	$-0.969898\pi$
$953$	−8.40405	+	18.4023i	−0.272234	+	0.596109i	0.723298	+	0.690536i	$0.242625\pi$
$954$	−6.61899	−	6.31120i	−0.214298	−	0.204333i
$955$	−6.26421	+	25.8214i	−0.202705	+	0.835561i
$956$	8.72049	+	12.2462i	0.282041	+	0.396071i
$957$	15.2983	−	12.0307i	0.494524	−	0.388898i
$958$	−13.1309	−	15.1539i	−0.424241	−	0.489600i
$959$	−14.3331	+	57.1383i	−0.462839	+	1.84509i
$960$	−1.45006	+	0.931897i	−0.0468005	+	0.0300768i
$961$	−24.1142	+	9.65388i	−0.777879	+	0.311416i
$962$	−0.129279	+	0.0666479i	−0.00416812	+	0.00214882i
$963$	−2.82215	−	8.15406i	−0.0909424	−	0.262761i
$964$	−5.96641	−	24.5939i	−0.192165	−	0.792115i
$965$	−25.8671			−0.832690
$966$	−2.67945	+	12.4024i	−0.0862099	+	0.399042i
$967$	−41.6206			−1.33843			−0.669214	−	0.743070i	$-0.733369\pi$
$967$	−41.6206			−1.33843			−0.669214	+	0.743070i	$0.733369\pi$
$968$	−1.47662	−	6.08670i	−0.0474602	−	0.195634i
$969$	8.20038	+	23.6934i	0.263434	+	0.761143i
$970$	−7.86840	+	4.05644i	−0.252639	+	0.130244i
$971$	−8.87169	+	3.55169i	−0.284706	+	0.113979i	−0.509620	−	0.860400i	$-0.670214\pi$
$971$	−8.87169	+	3.55169i	−0.284706	+	0.113979i	0.224914	+	0.974379i	$0.427790\pi$
$972$	−0.841254	+	0.540641i	−0.0269832	+	0.0173411i
$973$	46.8095	−	13.3499i	1.50064	−	0.427979i
$974$	12.9755	+	14.9745i	0.415761	+	0.479813i
$975$	−3.20917	+	2.52372i	−0.102776	+	0.0808237i
$976$	−2.74721	−	3.85791i	−0.0879359	−	0.123489i
$977$	−0.586980	+	2.41956i	−0.0187791	+	0.0774087i	−0.980430	−	0.196868i	$-0.936923\pi$
$977$	−0.586980	+	2.41956i	−0.0187791	+	0.0774087i	0.961651	+	0.274276i	$0.0884383\pi$
$978$	−9.62155	−	9.17413i	−0.307663	−	0.293356i
$979$	−7.23046	+	15.8325i	−0.231087	+	0.506009i
$980$	−1.90271	+	11.9149i	−0.0607799	+	0.380606i
$981$	−3.12228	−	3.60330i	−0.0996866	−	0.115044i
$982$	5.27275	−	7.40454i	0.168260	−	0.236288i
$983$	−2.30351	−	48.3566i	−0.0734706	−	1.54234i	−0.671585	−	0.740927i	$-0.734386\pi$
$983$	−2.30351	−	48.3566i	−0.0734706	−	1.54234i	0.598115	−	0.801410i	$-0.295917\pi$
$984$	0.473697	+	0.372519i	0.0151009	+	0.0118755i
$985$	−0.922100	+	19.3573i	−0.0293805	+	0.616773i
$986$	13.2321	−	15.2707i	0.421396	−	0.486317i
$987$	−13.0609	+	28.0206i	−0.415733	+	0.891904i
$988$	11.6957			0.372090
$989$	−8.25475	+	39.7025i	−0.262486	+	1.26247i
$990$	3.58088	−	6.20227i	0.113808	−	0.197121i
$991$	7.70332	−	7.34510i	0.244704	−	0.233325i	−0.557794	−	0.829979i	$-0.688352\pi$
$991$	7.70332	−	7.34510i	0.244704	−	0.233325i	0.802498	+	0.596654i	$0.203504\pi$
$992$	−2.20117	−	0.424241i	−0.0698872	−	0.0134697i
$993$	−5.33283	−	3.42720i	−0.169232	−	0.108759i
$994$	−8.02295	−	34.2310i	−0.254473	−	1.08574i
$995$	−16.5132	+	10.6124i	−0.523505	+	0.336436i
$996$	−1.33249	+	1.87123i	−0.0422217	+	0.0592921i
$997$	10.5884	−	2.04075i	0.335339	−	0.0646313i	−0.0188022	−	0.999823i	$-0.505985\pi$
$997$	10.5884	−	2.04075i	0.335339	−	0.0646313i	0.354141	+	0.935192i	$0.384773\pi$
$998$	6.08321	+	2.43535i	0.192561	+	0.0770897i
$999$	−0.0719540	+	0.00687077i	−0.00227652	+	0.000217382i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.a.823.6	yes	160
7.2	even	3	inner	966.2.y.a.961.3	yes	160
23.9	even	11	inner	966.2.y.a.193.3	✓	160
161.9	even	33	inner	966.2.y.a.331.6	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.a.193.3	✓	160	23.9	even	11	inner
966.2.y.a.331.6	yes	160	161.9	even	33	inner
966.2.y.a.823.6	yes	160	1.1	even	1	trivial
966.2.y.a.961.3	yes	160	7.2	even	3	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)

\(f(q)\)	\(=\)	\(q+(-0.235759 - 0.971812i) q^{2} +(0.327068 + 0.945001i) q^{3} +(-0.888835 + 0.458227i) q^{4} +(1.60022 - 0.640630i) q^{5} +(0.841254 - 0.540641i) q^{6} +(2.54430 - 0.725627i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.786053 + 0.618159i) q^{9} +O(q^{10})\)	\(q+(-0.235759 - 0.971812i) q^{2} +(0.327068 + 0.945001i) q^{3} +(-0.888835 + 0.458227i) q^{4} +(1.60022 - 0.640630i) q^{5} +(0.841254 - 0.540641i) q^{6} +(2.54430 - 0.725627i) q^{7} +(0.654861 + 0.755750i) q^{8} +(-0.786053 + 0.618159i) q^{9} +(-0.999838 - 1.40408i) q^{10} +(0.979556 - 4.03779i) q^{11} +(-0.723734 - 0.690079i) q^{12} +(0.835916 - 1.83040i) q^{13} +(-1.30501 - 2.30151i) q^{14} +(1.12878 + 1.30268i) q^{15} +(0.580057 - 0.814576i) q^{16} +(0.205254 + 4.30881i) q^{17} +(0.786053 + 0.618159i) q^{18} +(0.276559 - 5.80569i) q^{19} +(-1.12878 + 1.30268i) q^{20} +(1.51788 + 2.16704i) q^{21} -4.15491 q^{22} +(-4.18787 + 2.33705i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-1.46838 + 1.40010i) q^{25} +(-1.97588 - 0.380820i) q^{26} +(-0.841254 - 0.540641i) q^{27} +(-1.92896 + 1.81083i) q^{28} +(3.94055 - 2.53244i) q^{29} +(0.999838 - 1.40408i) q^{30} +(2.20117 - 0.424241i) q^{31} +(-0.928368 - 0.371662i) q^{32} +(4.13609 - 0.394949i) q^{33} +(4.13896 - 1.21531i) q^{34} +(3.60658 - 2.79112i) q^{35} +(0.415415 - 0.909632i) q^{36} +(0.0568169 - 0.0446813i) q^{37} +(-5.70724 + 1.09998i) q^{38} +(2.00313 + 0.191276i) q^{39} +(1.53208 + 0.789840i) q^{40} +(0.0857628 - 0.596493i) q^{41} +(1.74810 - 1.98599i) q^{42} +(5.53723 - 6.39031i) q^{43} +(0.979556 + 4.03779i) q^{44} +(-0.861844 + 1.49276i) q^{45} +(3.25849 + 3.51884i) q^{46} +(5.84239 + 10.1193i) q^{47} +(0.959493 + 0.281733i) q^{48} +(5.94693 - 3.69243i) q^{49} +(1.70682 + 1.09690i) q^{50} +(-4.00470 + 1.60324i) q^{51} +(0.0957464 + 2.00997i) q^{52} +(-9.10421 - 0.869346i) q^{53} +(-0.327068 + 0.945001i) q^{54} +(-1.01923 - 7.08887i) q^{55} +(2.21456 + 1.44767i) q^{56} +(5.57684 - 1.63751i) q^{57} +(-3.39007 - 3.23243i) q^{58} +(-1.94388 - 2.72979i) q^{59} +(-1.60022 - 0.640630i) q^{60} +(1.54903 - 4.47561i) q^{61} +(-0.931228 - 2.03910i) q^{62} +(-1.55140 + 2.14316i) q^{63} +(-0.142315 + 0.989821i) q^{64} +(0.165037 - 3.46455i) q^{65} +(-1.35894 - 3.92639i) q^{66} +(-8.62614 + 8.22500i) q^{67} +(-2.15685 - 3.73577i) q^{68} +(-3.57823 - 3.19316i) q^{69} +(-3.56272 - 2.84688i) q^{70} +(12.7504 + 3.74386i) q^{71} +(-0.981929 - 0.189251i) q^{72} +(6.32391 - 3.26020i) q^{73} +(-0.0568169 - 0.0446813i) q^{74} +(-1.80336 - 0.929694i) q^{75} +(2.41451 + 5.28703i) q^{76} +(-0.437642 - 10.9841i) q^{77} +(-0.286372 - 1.99176i) q^{78} +(10.6034 - 1.01250i) q^{79} +(0.406375 - 1.67510i) q^{80} +(0.235759 - 0.971812i) q^{81} +(-0.599898 + 0.0572833i) q^{82} +(-0.326923 - 2.27380i) q^{83} +(-2.34214 - 1.23061i) q^{84} +(3.08881 + 6.76354i) q^{85} +(-7.51563 - 3.87458i) q^{86} +(3.68199 + 2.89555i) q^{87} +(3.69303 - 1.90389i) q^{88} +(-4.11341 - 0.792796i) q^{89} +(1.65387 + 0.485619i) q^{90} +(0.798633 - 5.26366i) q^{91} +(2.65143 - 3.99624i) q^{92} +(1.12084 + 1.94135i) q^{93} +(8.45667 - 8.06342i) q^{94} +(-3.27675 - 9.46754i) q^{95} +(0.0475819 - 0.998867i) q^{96} +(0.730897 - 5.08350i) q^{97} +(-4.99039 - 4.90877i) q^{98} +(1.72601 + 3.77944i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} - 16 q^{6} - 2 q^{7} + 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 - 16 * q^6 - 2 * q^7 + 16 * q^8 + 8 * q^9	\( 160 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} - 16 q^{6} - 2 q^{7} + 16 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{12} + 4 q^{13} - 9 q^{14} - 18 q^{15} + 8 q^{16} + 9 q^{17} - 8 q^{18} + 18 q^{20} + 7 q^{21} + 52 q^{22} + 22 q^{23} - 80 q^{24} + 42 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 54 q^{29} + 2 q^{30} - 15 q^{31} - 8 q^{32} + 18 q^{33} + 84 q^{34} + 82 q^{35} - 16 q^{36} + 3 q^{37} + 11 q^{38} + 2 q^{39} - 13 q^{40} + 22 q^{41} - 2 q^{42} - 96 q^{43} + 4 q^{44} - 20 q^{45} - 26 q^{47} + 16 q^{48} - 2 q^{49} - 4 q^{50} + 13 q^{51} - 2 q^{52} + 16 q^{53} + 8 q^{54} - 34 q^{55} + 2 q^{56} - 22 q^{57} - 5 q^{58} - 6 q^{59} - 2 q^{60} + 40 q^{61} - 8 q^{62} - 2 q^{63} - 16 q^{64} - 82 q^{65} + 4 q^{66} + 10 q^{67} - 46 q^{68} - 22 q^{69} + 100 q^{70} + 92 q^{71} - 8 q^{72} + 68 q^{73} - 3 q^{74} + 2 q^{75} - 7 q^{77} - 18 q^{78} - 78 q^{79} + 2 q^{80} + 8 q^{81} + 55 q^{82} - 42 q^{83} - 9 q^{84} + 50 q^{85} + 40 q^{86} + 6 q^{87} + 7 q^{88} - 80 q^{89} + 4 q^{90} - 62 q^{91} + 66 q^{92} + 26 q^{93} + 4 q^{94} - 17 q^{95} + 8 q^{96} - 8 q^{97} - 3 q^{98} + 36 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 - 16 * q^6 - 2 * q^7 + 16 * q^8 + 8 * q^9 - 2 * q^10 + 4 * q^11 - 8 * q^12 + 4 * q^13 - 9 * q^14 - 18 * q^15 + 8 * q^16 + 9 * q^17 - 8 * q^18 + 18 * q^20 + 7 * q^21 + 52 * q^22 + 22 * q^23 - 80 * q^24 + 42 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 54 * q^29 + 2 * q^30 - 15 * q^31 - 8 * q^32 + 18 * q^33 + 84 * q^34 + 82 * q^35 - 16 * q^36 + 3 * q^37 + 11 * q^38 + 2 * q^39 - 13 * q^40 + 22 * q^41 - 2 * q^42 - 96 * q^43 + 4 * q^44 - 20 * q^45 - 26 * q^47 + 16 * q^48 - 2 * q^49 - 4 * q^50 + 13 * q^51 - 2 * q^52 + 16 * q^53 + 8 * q^54 - 34 * q^55 + 2 * q^56 - 22 * q^57 - 5 * q^58 - 6 * q^59 - 2 * q^60 + 40 * q^61 - 8 * q^62 - 2 * q^63 - 16 * q^64 - 82 * q^65 + 4 * q^66 + 10 * q^67 - 46 * q^68 - 22 * q^69 + 100 * q^70 + 92 * q^71 - 8 * q^72 + 68 * q^73 - 3 * q^74 + 2 * q^75 - 7 * q^77 - 18 * q^78 - 78 * q^79 + 2 * q^80 + 8 * q^81 + 55 * q^82 - 42 * q^83 - 9 * q^84 + 50 * q^85 + 40 * q^86 + 6 * q^87 + 7 * q^88 - 80 * q^89 + 4 * q^90 - 62 * q^91 + 66 * q^92 + 26 * q^93 + 4 * q^94 - 17 * q^95 + 8 * q^96 - 8 * q^97 - 3 * q^98 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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