LMFDB - Embedded newform 966.2.be.a.61.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(19,966)]

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, 55, 45]))

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

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

chi := DirichletCharacter("966.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.be (of order $66$, 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:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			61.2
Character	$\chi$	$=$	966.61
Dual form			966.2.be.a.871.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.786053 + 0.618159i) q^{2} +(-0.814576 - 0.580057i) q^{3} +(0.235759 + 0.971812i) q^{4} +(-2.19052 + 0.422188i) q^{5} +(-0.281733 - 0.959493i) q^{6} +(1.40168 + 2.24395i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(0.327068 + 0.945001i) q^{9} +O(q^{10})$	\(q+(0.786053 + 0.618159i) q^{2} +(-0.814576 - 0.580057i) q^{3} +(0.235759 + 0.971812i) q^{4} +(-2.19052 + 0.422188i) q^{5} +(-0.281733 - 0.959493i) q^{6} +(1.40168 + 2.24395i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(0.327068 + 0.945001i) q^{9} +(-1.98285 - 1.02223i) q^{10} +(2.09716 + 2.66676i) q^{11} +(0.371662 - 0.928368i) q^{12} +(-1.83259 - 2.85157i) q^{13} +(-0.285326 + 2.63032i) q^{14} +(2.02924 + 0.926723i) q^{15} +(-0.888835 + 0.458227i) q^{16} +(-5.82052 - 5.54986i) q^{17} +(-0.327068 + 0.945001i) q^{18} +(-4.08774 + 3.89765i) q^{19} +(-0.926723 - 2.02924i) q^{20} +(0.159847 - 2.64092i) q^{21} +3.39259i q^{22} +(4.71187 - 0.893486i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-0.0216971 + 0.00868622i) q^{25} +(0.322208 - 3.37432i) q^{26} +(0.281733 - 0.959493i) q^{27} +(-1.85024 + 1.89120i) q^{28} +(-7.73374 + 2.27083i) q^{29} +(1.02223 + 1.98285i) q^{30} +(0.682765 + 7.15024i) q^{31} +(-0.981929 - 0.189251i) q^{32} +(-0.161426 - 3.38875i) q^{33} +(-1.14455 - 7.96049i) q^{34} +(-4.01777 - 4.32365i) q^{35} +(-0.841254 + 0.540641i) q^{36} +(5.57619 - 1.92994i) q^{37} +(-5.62255 + 0.536888i) q^{38} +(-0.161287 + 3.38583i) q^{39} +(0.525939 - 2.16795i) q^{40} +(-1.41638 + 1.22730i) q^{41} +(1.75816 - 1.97709i) q^{42} +(-7.08671 + 3.23639i) q^{43} +(-2.09716 + 2.66676i) q^{44} +(-1.11542 - 1.93196i) q^{45} +(4.25609 + 2.21036i) q^{46} +(-6.47092 - 3.73599i) q^{47} +(0.989821 + 0.142315i) q^{48} +(-3.07061 + 6.29058i) q^{49} +(-0.0224246 - 0.00658445i) q^{50} +(1.52202 + 7.89701i) q^{51} +(2.33914 - 2.45322i) q^{52} +(-10.0495 - 0.478718i) q^{53} +(0.814576 - 0.580057i) q^{54} +(-5.71975 - 4.95619i) q^{55} +(-2.62344 + 0.342839i) q^{56} +(5.59063 - 0.803812i) q^{57} +(-7.48286 - 2.99569i) q^{58} +(-3.19024 + 6.18821i) q^{59} +(-0.422188 + 2.19052i) q^{60} +(6.86349 + 9.63842i) q^{61} +(-3.88330 + 6.04253i) q^{62} +(-1.66209 + 2.05851i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(5.21823 + 5.47272i) q^{65} +(1.96790 - 2.76352i) q^{66} +(-3.78462 - 9.45352i) q^{67} +(4.02117 - 6.96488i) q^{68} +(-4.35645 - 2.00534i) q^{69} +(-0.485479 - 5.88224i) q^{70} +(0.515171 - 3.58310i) q^{71} +(-0.995472 - 0.0950560i) q^{72} +(-3.09323 + 0.750410i) q^{73} +(5.57619 + 1.92994i) q^{74} +(0.0227125 + 0.00550999i) q^{75} +(-4.75150 - 3.05361i) q^{76} +(-3.04453 + 8.44385i) q^{77} +(-2.21976 + 2.56174i) q^{78} +(6.56269 - 0.312619i) q^{79} +(1.75356 - 1.37901i) q^{80} +(-0.786053 + 0.618159i) q^{81} +(-1.87201 + 0.0891750i) q^{82} +(6.46283 - 7.45850i) q^{83} +(2.60416 - 0.467279i) q^{84} +(15.0931 + 9.69972i) q^{85} +(-7.57113 - 1.83674i) q^{86} +(7.61693 + 2.63624i) q^{87} +(-3.29696 + 0.799834i) q^{88} +(-0.248840 - 0.0237613i) q^{89} +(0.317481 - 2.20813i) q^{90} +(3.83007 - 8.10921i) q^{91} +(1.97916 + 4.36840i) q^{92} +(3.59138 - 6.22046i) q^{93} +(-2.77705 - 6.93675i) q^{94} +(7.30874 - 10.2637i) q^{95} +(0.690079 + 0.723734i) q^{96} +(8.10119 + 9.34927i) q^{97} +(-6.30224 + 3.04660i) q^{98} +(-1.83417 + 2.85403i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9}+O(q^{10}) $ 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9	$ 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9} - 22 q^{14} + 16 q^{16} + 66 q^{17} + 16 q^{18} + 40 q^{23} - 48 q^{25} + 12 q^{26} + 44 q^{28} - 24 q^{29} + 24 q^{31} - 16 q^{32} + 98 q^{35} + 32 q^{36} - 22 q^{37} - 66 q^{38} - 8 q^{39} - 88 q^{43} + 4 q^{46} - 144 q^{47} - 24 q^{49} + 80 q^{50} - 22 q^{51} + 12 q^{52} + 44 q^{53} + 44 q^{57} + 10 q^{58} + 12 q^{59} - 32 q^{64} + 108 q^{70} - 16 q^{71} + 16 q^{72} - 180 q^{73} - 22 q^{74} - 12 q^{75} + 18 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 36 q^{82} + 22 q^{84} + 68 q^{85} - 22 q^{86} + 48 q^{87} + 22 q^{88} + 8 q^{92} + 8 q^{93} - 12 q^{94} + 66 q^{95} - 90 q^{98}+O(q^{100}) $ 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9 - 22 * q^14 + 16 * q^16 + 66 * q^17 + 16 * q^18 + 40 * q^23 - 48 * q^25 + 12 * q^26 + 44 * q^28 - 24 * q^29 + 24 * q^31 - 16 * q^32 + 98 * q^35 + 32 * q^36 - 22 * q^37 - 66 * q^38 - 8 * q^39 - 88 * q^43 + 4 * q^46 - 144 * q^47 - 24 * q^49 + 80 * q^50 - 22 * q^51 + 12 * q^52 + 44 * q^53 + 44 * q^57 + 10 * q^58 + 12 * q^59 - 32 * q^64 + 108 * q^70 - 16 * q^71 + 16 * q^72 - 180 * q^73 - 22 * q^74 - 12 * q^75 + 18 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 36 * q^82 + 22 * q^84 + 68 * q^85 - 22 * q^86 + 48 * q^87 + 22 * q^88 + 8 * q^92 + 8 * q^93 - 12 * q^94 + 66 * q^95 - 90 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{22}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.786053	+	0.618159i	0.555823	+	0.437104i
$2$	0.786053	+	0.618159i	0.555823	+	0.437104i
$3$	−0.814576	−	0.580057i	−0.470296	−	0.334896i
$3$	−0.814576	−	0.580057i	−0.470296	−	0.334896i
$4$	0.235759	+	0.971812i	0.117879	+	0.485906i
$5$	−2.19052	+	0.422188i	−0.979631	+	0.188808i	−0.653840	−	0.756633i	$-0.726843\pi$
$5$	−2.19052	+	0.422188i	−0.979631	+	0.188808i	−0.325792	+	0.945442i	$0.605631\pi$
$6$	−0.281733	−	0.959493i	−0.115017	−	0.391711i
$7$	1.40168	+	2.24395i	0.529783	+	0.848133i
$7$	1.40168	+	2.24395i	0.529783	+	0.848133i
$8$	−0.415415	+	0.909632i	−0.146871	+	0.321603i
$9$	0.327068	+	0.945001i	0.109023	+	0.315000i
$10$	−1.98285	−	1.02223i	−0.627031	−	0.323257i
$11$	2.09716	+	2.66676i	0.632318	+	0.804057i	0.991623	−	0.129162i	$-0.0412289\pi$
$11$	2.09716	+	2.66676i	0.632318	+	0.804057i	−0.359306	+	0.933220i	$0.616986\pi$
$12$	0.371662	−	0.928368i	0.107290	−	0.267997i
$13$	−1.83259	−	2.85157i	−0.508269	−	0.790882i	0.488384	−	0.872629i	$-0.337587\pi$
$13$	−1.83259	−	2.85157i	−0.508269	−	0.790882i	−0.996653	+	0.0817465i	$0.973950\pi$
$14$	−0.285326	+	2.63032i	−0.0762565	+	0.702983i
$15$	2.02924	+	0.926723i	0.523947	+	0.239279i
$16$	−0.888835	+	0.458227i	−0.222209	+	0.114557i
$17$	−5.82052	−	5.54986i	−1.41168	−	1.34604i	−0.858337	−	0.513087i	$-0.828502\pi$
$17$	−5.82052	−	5.54986i	−1.41168	−	1.34604i	−0.553347	−	0.832951i	$-0.686650\pi$
$18$	−0.327068	+	0.945001i	−0.0770907	+	0.222739i
$19$	−4.08774	+	3.89765i	−0.937791	+	0.894182i	−0.994556	−	0.104205i	$-0.966770\pi$
$19$	−4.08774	+	3.89765i	−0.937791	+	0.894182i	0.0567643	+	0.998388i	$0.481922\pi$
$20$	−0.926723	−	2.02924i	−0.207221	−	0.453752i
$21$	0.159847	−	2.64092i	0.0348815	−	0.576296i
$22$			3.39259i			0.723303i
$23$	4.71187	−	0.893486i	0.982492	−	0.186305i
$23$	4.71187	−	0.893486i	0.982492	−	0.186305i
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	−0.0216971	+	0.00868622i	−0.00433943	+	0.00173724i
$26$	0.322208	−	3.37432i	0.0631902	−	0.661758i
$27$	0.281733	−	0.959493i	0.0542195	−	0.184655i
$28$	−1.85024	+	1.89120i	−0.349662	+	0.357402i
$29$	−7.73374	+	2.27083i	−1.43612	+	0.421683i	−0.904926	−	0.425568i	$-0.860074\pi$
$29$	−7.73374	+	2.27083i	−1.43612	+	0.421683i	−0.531193	+	0.847251i	$0.678256\pi$
$30$	1.02223	+	1.98285i	0.186632	+	0.362016i
$31$	0.682765	+	7.15024i	0.122628	+	1.28422i	0.822010	+	0.569473i	$0.192853\pi$
$31$	0.682765	+	7.15024i	0.122628	+	1.28422i	−0.699382	+	0.714748i	$0.746541\pi$
$32$	−0.981929	−	0.189251i	−0.173582	−	0.0334552i
$33$	−0.161426	−	3.38875i	−0.0281007	−	0.589905i
$34$	−1.14455	−	7.96049i	−0.196288	−	1.36521i
$35$	−4.01777	−	4.32365i	−0.679127	−	0.730830i
$36$	−0.841254	+	0.540641i	−0.140209	+	0.0901068i
$37$	5.57619	−	1.92994i	0.916719	−	0.317280i	0.172341	−	0.985037i	$-0.444867\pi$
$37$	5.57619	−	1.92994i	0.916719	−	0.317280i	0.744379	+	0.667758i	$0.232746\pi$
$38$	−5.62255	+	0.536888i	−0.912098	+	0.0870948i
$39$	−0.161287	+	3.38583i	−0.0258265	+	0.542166i
$40$	0.525939	−	2.16795i	0.0831583	−	0.342783i
$41$	−1.41638	+	1.22730i	−0.221201	+	0.191672i	−0.758411	−	0.651777i	$-0.774024\pi$
$41$	−1.41638	+	1.22730i	−0.221201	+	0.191672i	0.537210	+	0.843449i	$0.319478\pi$
$42$	1.75816	−	1.97709i	0.271289	−	0.305072i
$43$	−7.08671	+	3.23639i	−1.08071	+	0.493545i	−0.874531	−	0.484969i	$-0.838831\pi$
$43$	−7.08671	+	3.23639i	−1.08071	+	0.493545i	−0.206181	+	0.978514i	$0.566104\pi$
$44$	−2.09716	+	2.66676i	−0.316159	+	0.402029i
$45$	−1.11542	−	1.93196i	−0.166277	−	0.288000i
$46$	4.25609	+	2.21036i	0.627527	+	0.325899i
$47$	−6.47092	−	3.73599i	−0.943881	−	0.544950i	−0.0527064	−	0.998610i	$-0.516785\pi$
$47$	−6.47092	−	3.73599i	−0.943881	−	0.544950i	−0.891175	+	0.453660i	$0.850118\pi$
$48$	0.989821	+	0.142315i	0.142868	+	0.0205414i
$49$	−3.07061	+	6.29058i	−0.438659	+	0.898654i
$50$	−0.0224246	−	0.00658445i	−0.00317131	−	0.000931182i
$51$	1.52202	+	7.89701i	0.213126	+	1.10580i
$52$	2.33914	−	2.45322i	0.324380	−	0.340200i
$53$	−10.0495	−	0.478718i	−1.38041	−	0.0657569i	−0.655808	−	0.754927i	$-0.727672\pi$
$53$	−10.0495	−	0.478718i	−1.38041	−	0.0657569i	−0.724599	+	0.689170i	$0.757975\pi$
$54$	0.814576	−	0.580057i	0.110850	−	0.0789357i
$55$	−5.71975	−	4.95619i	−0.771251	−	0.668293i
$56$	−2.62344	+	0.342839i	−0.350573	+	0.0458138i
$57$	5.59063	−	0.803812i	0.740497	−	0.106467i
$58$	−7.48286	−	2.99569i	−0.982548	−	0.393353i
$59$	−3.19024	+	6.18821i	−0.415334	+	0.805636i	−0.999984	−	0.00564945i	$-0.998202\pi$
$59$	−3.19024	+	6.18821i	−0.415334	+	0.805636i	0.584650	+	0.811286i	$0.301232\pi$
$60$	−0.422188	+	2.19052i	−0.0545043	+	0.282795i
$61$	6.86349	+	9.63842i	0.878779	+	1.23407i	0.971179	+	0.238351i	$0.0766069\pi$
$61$	6.86349	+	9.63842i	0.878779	+	1.23407i	−0.0923996	+	0.995722i	$0.529454\pi$
$62$	−3.88330	+	6.04253i	−0.493179	+	0.767401i
$63$	−1.66209	+	2.05851i	−0.209404	+	0.259348i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	5.21823	+	5.47272i	0.647242	+	0.678808i
$66$	1.96790	−	2.76352i	0.242231	−	0.340166i
$67$	−3.78462	−	9.45352i	−0.462365	−	1.15493i	−0.958094	−	0.286454i	$-0.907524\pi$
$67$	−3.78462	−	9.45352i	−0.462365	−	1.15493i	0.495730	−	0.868477i	$-0.334901\pi$
$68$	4.02117	−	6.96488i	0.487639	−	0.844616i
$69$	−4.35645	−	2.00534i	−0.524454	−	0.241414i
$70$	−0.485479	−	5.88224i	−0.0580258	−	0.703062i
$71$	0.515171	−	3.58310i	0.0611396	−	0.425235i	−0.936146	−	0.351610i	$-0.885634\pi$
$71$	0.515171	−	3.58310i	0.0611396	−	0.425235i	0.997286	−	0.0736248i	$-0.0234567\pi$
$72$	−0.995472	−	0.0950560i	−0.117317	−	0.0112025i
$73$	−3.09323	+	0.750410i	−0.362035	+	0.0878288i	−0.412651	−	0.910889i	$-0.635397\pi$
$73$	−3.09323	+	0.750410i	−0.362035	+	0.0878288i	0.0506152	+	0.998718i	$0.483882\pi$
$74$	5.57619	+	1.92994i	0.648219	+	0.224351i
$75$	0.0227125	+	0.00550999i	0.00262261	+	0.000636238i
$76$	−4.75150	−	3.05361i	−0.545035	−	0.350273i
$77$	−3.04453	+	8.44385i	−0.346956	+	0.962266i
$78$	−2.21976	+	2.56174i	−0.251338	+	0.290060i
$79$	6.56269	−	0.312619i	0.738360	−	0.0351724i	0.324967	−	0.945725i	$-0.394647\pi$
$79$	6.56269	−	0.312619i	0.738360	−	0.0351724i	0.413393	+	0.910553i	$0.364344\pi$
$80$	1.75356	−	1.37901i	0.196053	−	0.154178i
$81$	−0.786053	+	0.618159i	−0.0873392	+	0.0686843i
$82$	−1.87201	+	0.0891750i	−0.206729	+	0.00984773i
$83$	6.46283	−	7.45850i	0.709388	−	0.818677i	−0.280601	−	0.959825i	$-0.590534\pi$
$83$	6.46283	−	7.45850i	0.709388	−	0.818677i	0.989989	+	0.141147i	$0.0450791\pi$
$84$	2.60416	−	0.467279i	0.284137	−	0.0509843i
$85$	15.0931	+	9.69972i	1.63707	+	1.05208i
$86$	−7.57113	−	1.83674i	−0.816416	−	0.198060i
$87$	7.61693	+	2.63624i	0.816620	+	0.282635i
$88$	−3.29696	+	0.799834i	−0.351457	+	0.0852626i
$89$	−0.248840	−	0.0237613i	−0.0263769	−	0.00251869i	0.0818592	−	0.996644i	$-0.473914\pi$
$89$	−0.248840	−	0.0237613i	−0.0263769	−	0.00251869i	−0.108236	+	0.994125i	$0.534520\pi$
$90$	0.317481	−	2.20813i	0.0334654	−	0.232757i
$91$	3.83007	−	8.10921i	0.401501	−	0.850076i
$92$	1.97916	+	4.36840i	0.206342	+	0.455437i
$93$	3.59138	−	6.22046i	0.372409	−	0.645031i
$94$	−2.77705	−	6.93675i	−0.286431	−	0.715471i
$95$	7.30874	−	10.2637i	0.749861	−	1.05303i
$96$	0.690079	+	0.723734i	0.0704309	+	0.0738658i
$97$	8.10119	+	9.34927i	0.822551	+	0.949275i	0.999389	−	0.0349655i	$-0.0111321\pi$
$97$	8.10119	+	9.34927i	0.822551	+	0.949275i	−0.176837	+	0.984240i	$0.556587\pi$
$98$	−6.30224	+	3.04660i	−0.636622	+	0.307753i
$99$	−1.83417	+	2.85403i	−0.184341	+	0.286841i
$100$	−0.0135567	−	0.0190377i	−0.00135567	−	0.00190377i
$101$	0.817912	−	4.24373i	0.0813853	−	0.422267i	−0.918269	−	0.395958i	$-0.870413\pi$
$101$	0.817912	−	4.24373i	0.0813853	−	0.422267i	0.999654	−	0.0263090i	$-0.00837537\pi$
$102$	−3.68522	+	7.14832i	−0.364891	+	0.707790i
$103$	10.3043	+	4.12523i	1.01531	+	0.406471i	0.818830	−	0.574036i	$-0.194623\pi$
$103$	10.3043	+	4.12523i	1.01531	+	0.406471i	0.196485	+	0.980507i	$0.437047\pi$
$104$	3.35516	−	0.482400i	0.329001	−	0.0473032i
$105$	0.764817	+	5.85247i	0.0746385	+	0.571143i
$106$	−7.60353	−	6.58850i	−0.738520	−	0.639932i
$107$	0.0830566	−	0.0591444i	0.00802939	−	0.00571770i	−0.576035	−	0.817425i	$-0.695401\pi$
$107$	0.0830566	−	0.0591444i	0.00802939	−	0.00571770i	0.584065	+	0.811707i	$0.301461\pi$
$108$	0.998867	+	0.0475819i	0.0961161	+	0.00457857i
$109$	−3.05043	+	3.19920i	−0.292179	+	0.306428i	−0.853420	−	0.521224i	$-0.825476\pi$
$109$	−3.05043	+	3.19920i	−0.292179	+	0.306428i	0.561241	+	0.827652i	$0.310324\pi$
$110$	−1.43231	−	7.43155i	−0.136566	−	0.708570i
$111$	−5.66170	−	1.66243i	−0.537385	−	0.157790i
$112$	−2.27410	−	1.35222i	−0.214882	−	0.127772i
$113$	12.6638	+	1.82078i	1.19131	+	0.171285i	0.709318	−	0.704889i	$-0.249003\pi$
$113$	12.6638	+	1.82078i	1.19131	+	0.171285i	0.481996	+	0.876174i	$0.339912\pi$
$114$	4.89142	+	2.82406i	0.458123	+	0.264498i
$115$	−9.94423	+	3.94650i	−0.927304	+	0.368013i
$116$	−4.03012	−	6.98037i	−0.374187	−	0.648111i
$117$	2.09535	−	2.66446i	0.193715	−	0.246329i
$118$	−6.33300	+	2.89218i	−0.583000	+	0.266247i
$119$	4.29511	−	20.8400i	0.393732	−	1.91040i
$120$	−1.68595	+	1.46089i	−0.153906	+	0.133360i
$121$	−0.120161	+	0.495309i	−0.0109237	+	0.0450281i
$122$	−0.563010	+	11.8190i	−0.0509725	+	1.07005i
$123$	1.86565	−	0.178148i	0.168220	−	0.0160631i
$124$	−6.78772	+	2.34925i	−0.609555	+	0.210969i
$125$	9.42735	−	6.05859i	0.843208	−	0.541897i
$126$	−2.57898	+	0.590661i	−0.229753	+	0.0526202i
$127$	0.775779	+	5.39566i	0.0688392	+	0.478787i	0.994856	+	0.101304i	$0.0323014\pi$
$127$	0.775779	+	5.39566i	0.0688392	+	0.478787i	−0.926016	+	0.377484i	$0.876789\pi$
$128$	−0.0475819	−	0.998867i	−0.00420569	−	0.0882882i
$129$	7.64995	+	1.47441i	0.673541	+	0.129814i
$130$	0.718793	+	7.52754i	0.0630423	+	0.660209i
$131$	1.11360	+	2.16009i	0.0972960	+	0.188728i	0.932460	−	0.361273i	$-0.117658\pi$
$131$	1.11360	+	2.16009i	0.0972960	+	0.188728i	−0.835164	+	0.550001i	$0.814627\pi$
$132$	3.25517	−	0.955803i	0.283326	−	0.0831920i
$133$	−14.4758	−	3.70943i	−1.25521	−	0.321649i
$134$	2.86887	−	9.77046i	0.247832	−	0.844039i
$135$	−0.212054	+	2.22073i	−0.0182507	+	0.191130i
$136$	7.46626	−	2.98904i	0.640226	−	0.256308i
$137$	2.10569	−	1.21572i	0.179901	−	0.103866i	−0.407345	−	0.913274i	$-0.633545\pi$
$137$	2.10569	−	1.21572i	0.179901	−	0.103866i	0.587246	+	0.809408i	$0.300212\pi$
$138$	−2.18478	−	4.26928i	−0.185981	−	0.363425i
$139$		−	4.29606i		−	0.364387i	−0.983263	−	0.182193i	$-0.941680\pi$
$139$		−	4.29606i		−	0.364387i	0.983263	−	0.182193i	$-0.0583197\pi$
$140$	3.25455	−	4.92385i	0.275059	−	0.416142i
$141$	3.10397	+	6.79675i	0.261402	+	0.572390i
$142$	2.61987	−	2.49805i	0.219855	−	0.209631i
$143$	3.76120	−	10.8673i	0.314527	−	0.908767i
$144$	−0.723734	−	0.690079i	−0.0603112	−	0.0575066i
$145$	15.9822	−	8.23940i	1.32725	−	0.684245i
$146$	−2.89532	−	1.32225i	−0.239618	−	0.109430i
$147$	6.15014	−	3.34302i	0.507255	−	0.275728i
$148$	3.19017	+	4.96400i	0.262230	+	0.408039i
$149$	−4.00430	+	10.0023i	−0.328045	+	0.819417i	0.669048	+	0.743219i	$0.266702\pi$
$149$	−4.00430	+	10.0023i	−0.328045	+	0.819417i	−0.997093	+	0.0761974i	$0.975722\pi$
$150$	0.0144472	+	0.0183711i	0.00117961	+	0.00149999i
$151$	−1.79908	−	0.927488i	−0.146407	−	0.0754779i	0.383466	−	0.923555i	$-0.374730\pi$
$151$	−1.79908	−	0.927488i	−0.146407	−	0.0754779i	−0.529873	+	0.848077i	$0.677760\pi$
$152$	−1.84732	−	5.33748i	−0.149837	−	0.432927i
$153$	3.34091	−	7.31558i	0.270097	−	0.591429i
$154$	−7.61280	+	4.75531i	−0.613457	+	0.383194i
$155$	−4.51436	−	15.3745i	−0.362602	−	1.23491i
$156$	−3.32841	+	0.641498i	−0.266486	+	0.0513610i
$157$	5.63536	+	23.2293i	0.449750	+	1.85390i	0.516739	+	0.856143i	$0.327146\pi$
$157$	5.63536	+	23.2293i	0.449750	+	1.85390i	−0.0669889	+	0.997754i	$0.521339\pi$
$158$	5.35187	+	3.81105i	0.425772	+	0.303191i
$159$	7.90841	+	6.21925i	0.627178	+	0.493218i
$160$	2.23084			0.176363
$161$	8.60944	+	9.32081i	0.678519	+	0.734583i
$162$	−1.00000			−0.0785674
$163$	9.85930	+	7.75344i	0.772240	+	0.607296i	0.924561	−	0.381035i	$-0.124432\pi$
$163$	9.85930	+	7.75344i	0.772240	+	0.607296i	−0.152321	+	0.988331i	$0.548675\pi$
$164$	−1.52663	−	1.08711i	−0.119210	−	0.0848887i
$165$	1.78430	+	7.35498i	0.138907	+	0.572584i
$166$	9.69067	−	1.86772i	0.752142	−	0.144963i
$167$	4.43758	+	15.1130i	0.343390	+	1.16948i	0.932422	+	0.361370i	$0.117691\pi$
$167$	4.43758	+	15.1130i	0.343390	+	1.16948i	−0.589032	+	0.808110i	$0.700491\pi$
$168$	2.33586	+	1.24248i	0.180216	+	0.0958593i
$169$	0.627349	−	1.37370i	0.0482576	−	0.105670i
$170$	5.86798	+	16.9544i	0.450053	+	1.30034i
$171$	−5.02025	−	2.58812i	−0.383908	−	0.197918i
$172$	−4.81592	−	6.12393i	−0.367210	−	0.466946i
$173$	6.68324	−	16.6939i	0.508118	−	1.26922i	−0.423539	−	0.905878i	$-0.639212\pi$
$173$	6.68324	−	16.6939i	0.508118	−	1.26922i	0.931657	−	0.363339i	$-0.118363\pi$
$174$	4.35769	+	6.78070i	0.330356	+	0.514044i
$175$	−0.0499038	−	0.0365120i	−0.00377237	−	0.00276005i
$176$	−3.08601	−	1.40933i	−0.232617	−	0.106232i
$177$	6.18821	−	3.19024i	0.465134	−	0.239793i
$178$	−0.180913	−	0.172500i	−0.0135600	−	0.0129294i
$179$	−8.42428	+	24.3404i	−0.629660	+	1.81928i	−0.0587486	+	0.998273i	$0.518711\pi$
$179$	−8.42428	+	24.3404i	−0.629660	+	1.81928i	−0.570912	+	0.821011i	$0.693410\pi$
$180$	1.61453	−	1.53945i	0.120340	−	0.114744i
$181$	−7.62656	−	16.6998i	−0.566878	−	1.24129i	−0.948443	−	0.316947i	$-0.897342\pi$
$181$	−7.62656	−	16.6998i	−0.566878	−	1.24129i	0.381566	−	0.924342i	$-0.375385\pi$
$182$	8.02342	−	4.00668i	0.594736	−	0.296995i
$183$		−	11.8324i		−	0.874679i
$184$	−1.14464	+	4.65723i	−0.0843837	+	0.343336i
$185$	−11.4000	+	6.58177i	−0.838142	+	0.483901i
$186$	6.66825	−	2.66956i	0.488940	−	0.195742i
$187$	2.59355	−	27.1609i	0.189659	−	1.98620i
$188$	2.10510	−	7.16931i	0.153530	−	0.522876i
$189$	2.54795	−	0.712704i	0.185336	−	0.0518416i
$190$	12.0896	−	3.54984i	0.877075	−	0.257532i
$191$	−8.02906	−	15.5742i	−0.580963	−	1.12691i	−0.977902	−	0.209065i	$-0.932958\pi$
$191$	−8.02906	−	15.5742i	−0.580963	−	1.12691i	0.396939	−	0.917845i	$-0.370072\pi$
$192$	0.0950560	+	0.995472i	0.00686008	+	0.0718420i
$193$	−3.04826	−	0.587504i	−0.219419	−	0.0422895i	0.0783570	−	0.996925i	$-0.475033\pi$
$193$	−3.04826	−	0.587504i	−0.219419	−	0.0422895i	−0.297776	+	0.954636i	$0.596245\pi$
$194$	0.588629	+	12.3568i	0.0422611	+	0.887170i
$195$	−1.07615	−	7.48482i	−0.0770650	−	0.535999i
$196$	−6.83718	−	1.50100i	−0.488370	−	0.107214i
$197$	−15.2520	+	9.80184i	−1.08666	+	0.698352i	−0.956086	−	0.293087i	$-0.905317\pi$
$197$	−15.2520	+	9.80184i	−1.08666	+	0.698352i	−0.130571	+	0.991439i	$0.541681\pi$
$198$	−3.20600	+	1.10961i	−0.227841	+	0.0788564i
$199$	−14.8305	+	1.41615i	−1.05131	+	0.100388i	−0.606378	−	0.795177i	$-0.707378\pi$
$199$	−14.8305	+	1.41615i	−1.05131	+	0.100388i	−0.444931	+	0.895565i	$0.646772\pi$
$200$	0.00111205	−	0.0233448i	7.86338e−5	−	0.00165073i
$201$	−2.40072	+	9.89590i	−0.169334	+	0.698003i
$202$	3.26622	−	2.83020i	0.229811	−	0.199132i
$203$	−15.9358	−	14.1711i	−1.11848	−	0.994619i
$204$	−7.31558	+	3.34091i	−0.512193	+	0.233911i
$205$	2.58446	−	3.28640i	0.180506	−	0.229532i
$206$	5.54970	+	9.61236i	0.386666	+	0.669725i
$207$	2.38545	+	4.16049i	0.165800	+	0.289174i
$208$	2.93554	+	1.69483i	0.203543	+	0.117515i
$209$	−18.9667	−	2.72700i	−1.31196	−	0.188631i
$210$	−3.01657	+	5.07313i	−0.208163	+	0.350080i
$211$	23.8014	+	6.98871i	1.63855	+	0.481123i	0.965917	−	0.258851i	$-0.0833439\pi$
$211$	23.8014	+	6.98871i	1.63855	+	0.481123i	0.672636	+	0.739974i	$0.265162\pi$
$212$	−1.90404	−	9.87910i	−0.130770	−	0.678499i
$213$	−2.49805	+	2.61987i	−0.171163	+	0.179511i
$214$	0.101848	+	0.00485160i	0.00696215	+	0.000331648i
$215$	14.1572	−	10.0813i	0.965514	−	0.687540i
$216$	0.755750	+	0.654861i	0.0514222	+	0.0445576i
$217$	−15.0878	+	11.5544i	−1.02422	+	0.784364i
$218$	−4.37542	+	0.629090i	−0.296341	+	0.0426074i
$219$	2.95495	+	1.18298i	0.199677	+	0.0799387i
$220$	3.46800	−	6.72699i	0.233813	−	0.453533i
$221$	−5.15915	+	26.7682i	−0.347042	+	1.80063i
$222$	−3.42275	−	4.80659i	−0.229720	−	0.322597i
$223$	−5.58740	+	8.69416i	−0.374160	+	0.582204i	−0.976363	−	0.216139i	$-0.930654\pi$
$223$	−5.58740	+	8.69416i	−0.374160	+	0.582204i	0.602203	+	0.798343i	$0.294290\pi$
$224$	−0.951675	−	2.46867i	−0.0635865	−	0.164945i
$225$	−0.0153049	−	0.0176628i	−0.00102033	−	0.00117752i
$226$	8.82891	+	9.25950i	0.587291	+	0.615933i
$227$	−0.510251	+	0.716547i	−0.0338665	+	0.0475589i	−0.831162	−	0.556030i	$-0.812324\pi$
$227$	−0.510251	+	0.716547i	−0.0338665	+	0.0475589i	0.797296	+	0.603589i	$0.206263\pi$
$228$	2.09919	+	5.24354i	0.139023	+	0.347262i
$229$	−2.06575	+	3.57799i	−0.136509	+	0.236440i	−0.926173	−	0.377099i	$-0.876922\pi$
$229$	−2.06575	+	3.57799i	−0.136509	+	0.236440i	0.789664	+	0.613540i	$0.210255\pi$
$230$	−10.2563	−	3.04496i	−0.676277	−	0.200779i
$231$	7.37791	−	5.11216i	0.485431	−	0.336355i
$232$	1.14709	−	7.97819i	0.0753102	−	0.523794i
$233$	12.0796	+	1.15346i	0.791359	+	0.0755656i	0.482904	−	0.875673i	$-0.339582\pi$
$233$	12.0796	+	1.15346i	0.791359	+	0.0755656i	0.308455	+	0.951239i	$0.400188\pi$
$234$	3.29412	−	0.799144i	0.215343	−	0.0522417i
$235$	15.7520	+	5.45182i	1.02755	+	0.355637i
$236$	−6.76590	−	1.64139i	−0.440423	−	0.106845i
$237$	−5.52714	−	3.55208i	−0.359027	−	0.230732i
$238$	16.2586	−	13.7263i	1.05389	−	0.889745i
$239$	−0.608750	+	0.702534i	−0.0393767	+	0.0454432i	−0.775096	−	0.631843i	$-0.782299\pi$
$239$	−0.608750	+	0.702534i	−0.0393767	+	0.0454432i	0.735720	+	0.677286i	$0.236844\pi$
$240$	−2.22831	+	0.106147i	−0.143837	+	0.00685179i
$241$	16.7815	−	13.1971i	1.08099	−	0.850103i	0.0916629	−	0.995790i	$-0.470782\pi$
$241$	16.7815	−	13.1971i	1.08099	−	0.850103i	0.989331	+	0.145687i	$0.0465394\pi$
$242$	−0.400632	+	0.315061i	−0.0257536	+	0.0202529i
$243$	0.998867	−	0.0475819i	0.0640774	−	0.00305238i
$244$	−7.74860	+	8.94236i	−0.496053	+	0.572476i
$245$	4.07043	−	15.0760i	0.260051	−	0.963172i
$246$	1.57662	+	1.01323i	0.100522	+	0.0646015i
$247$	18.6056	+	4.51366i	1.18384	+	0.287197i
$248$	−6.78772	−	2.34925i	−0.431020	−	0.149178i
$249$	−9.59082	+	2.32671i	−0.607794	+	0.147449i
$250$	11.1556	+	1.06523i	0.705540	+	0.0673709i
$251$	−1.12792	+	7.84487i	−0.0711938	+	0.495164i	0.922761	+	0.385373i	$0.125927\pi$
$251$	−1.12792	+	7.84487i	−0.0711938	+	0.495164i	−0.993955	+	0.109791i	$0.964982\pi$
$252$	−2.39233	−	1.12993i	−0.150703	−	0.0711787i
$253$	12.2643	+	10.6916i	0.771047	+	0.672176i
$254$	−2.72557	+	4.72083i	−0.171018	+	0.296211i
$255$	−6.66806	−	16.6560i	−0.417570	−	1.04304i
$256$	0.580057	−	0.814576i	0.0362536	−	0.0509110i
$257$	3.44127	+	3.60910i	0.214661	+	0.225130i	0.822257	−	0.569116i	$-0.192715\pi$
$257$	3.44127	+	3.60910i	0.214661	+	0.225130i	−0.607596	+	0.794246i	$0.707866\pi$
$258$	5.10185	+	5.88785i	0.317627	+	0.366561i
$259$	12.1467	+	9.80753i	0.754758	+	0.609410i
$260$	−4.08821	+	6.36138i	−0.253540	+	0.394516i
$261$	−4.67539	−	6.56567i	−0.289400	−	0.406405i
$262$	−0.459927	+	2.38633i	−0.0284144	+	0.147428i
$263$	−4.00477	+	7.76818i	−0.246945	+	0.479006i	−0.979432	−	0.201775i	$-0.935329\pi$
$263$	−4.00477	+	7.76818i	−0.246945	+	0.479006i	0.732487	+	0.680781i	$0.238359\pi$
$264$	3.14957	+	1.26090i	0.193843	+	0.0776030i
$265$	22.2158	−	3.19415i	1.36471	−	0.196215i
$266$	−9.08574	−	11.8642i	−0.557082	−	0.727439i
$267$	0.188916	+	0.163696i	0.0115615	+	0.0100181i
$268$	8.29478	−	5.90669i	0.506684	−	0.360808i
$269$	−28.4930	−	1.35729i	−1.73725	−	0.0827553i	−0.845131	−	0.534559i	$-0.820478\pi$
$269$	−28.4930	−	1.35729i	−1.73725	−	0.0827553i	−0.892117	+	0.451804i	$0.850781\pi$
$270$	−1.53945	+	1.61453i	−0.0936881	+	0.0982573i
$271$	−3.80640	−	19.7495i	−0.231222	−	1.19970i	−0.893021	−	0.450014i	$-0.851419\pi$
$271$	−3.80640	−	19.7495i	−0.231222	−	1.19970i	0.661799	−	0.749681i	$-0.269793\pi$
$272$	7.71658	+	2.26579i	0.467886	+	0.137384i
$273$	−7.82369	+	4.38391i	−0.473511	+	0.265326i
$274$	2.40669	+	0.346030i	0.145393	+	0.0209044i
$275$	−0.0686664	−	0.0396446i	−0.00414074	−	0.00239066i
$276$	0.921740	−	4.70642i	0.0554822	−	0.283293i
$277$	1.15156	+	1.99457i	0.0691907	+	0.119842i	0.898545	−	0.438881i	$-0.144625\pi$
$277$	1.15156	+	1.99457i	0.0691907	+	0.119842i	−0.829355	+	0.558723i	$0.811292\pi$
$278$	2.65565	−	3.37693i	0.159275	−	0.202535i
$279$	−6.53367	+	2.98383i	−0.391161	+	0.178637i
$280$	5.60197	−	1.85858i	0.334782	−	0.111072i
$281$	17.8724	−	15.4865i	1.06618	−	0.923850i	0.0689043	−	0.997623i	$-0.478050\pi$
$281$	17.8724	−	15.4865i	1.06618	−	0.923850i	0.997275	+	0.0737737i	$0.0235042\pi$
$282$	−1.76159	+	7.26136i	−0.104901	+	0.432407i
$283$	0.0382398	−	0.802753i	0.00227312	−	0.0477187i	−0.997446	−	0.0714277i	$-0.977244\pi$
$283$	0.0382398	−	0.802753i	0.00227312	−	0.0477187i	0.999719	+	0.0237090i	$0.00754751\pi$
$284$	3.60355	−	0.344097i	0.213831	−	0.0204184i
$285$	−11.9070	+	4.12107i	−0.705312	+	0.244111i
$286$	9.67420	−	6.21723i	0.572048	−	0.367633i
$287$	−4.73930	−	1.45801i	−0.279752	−	0.0860633i
$288$	−0.142315	−	0.989821i	−0.00838598	−	0.0583258i
$289$	2.26868	+	47.6254i	0.133452	+	2.80149i
$290$	17.6561	+	3.40294i	1.03680	+	0.199827i
$291$	−1.17592	−	12.3148i	−0.0689339	−	0.721909i
$292$	−1.45851	−	2.82912i	−0.0853531	−	0.165562i
$293$	9.86902	−	2.89780i	0.576554	−	0.169292i	0.0195610	−	0.999809i	$-0.493773\pi$
$293$	9.86902	−	2.89780i	0.576554	−	0.169292i	0.556993	+	0.830517i	$0.311955\pi$
$294$	6.90085	+	1.17397i	0.402466	+	0.0684674i
$295$	4.37571	−	14.9023i	0.254764	−	0.867645i
$296$	−0.560899	+	5.87400i	−0.0326016	+	0.341419i
$297$	3.14957	−	1.26090i	0.182757	−	0.0731648i
$298$	−9.33058	+	5.38701i	−0.540506	+	0.312061i
$299$	−11.1828	−	11.7988i	−0.646716	−	0.682343i
$300$			0.0233713i			0.00134934i
$301$	−17.1956	−	11.3658i	−0.991135	−	0.655116i
$302$	−0.840834	−	1.84117i	−0.0483846	−	0.105947i
$303$	−3.12786	+	2.98241i	−0.179691	+	0.171335i
$304$	1.84732	−	5.33748i	0.105951	−	0.306125i
$305$	−19.1038	−	18.2155i	−1.09388	−	1.04302i
$306$	7.14832	−	3.68522i	0.408643	−	0.210670i
$307$	0.626064	+	0.285914i	0.0357314	+	0.0163180i	0.433201	−	0.901298i	$-0.357384\pi$
$307$	0.626064	+	0.285914i	0.0357314	+	0.0163180i	−0.397469	+	0.917616i	$0.630111\pi$
$308$	−8.92360	−	0.967994i	−0.508470	−	0.0551566i
$309$	−6.00078	−	9.33740i	−0.341373	−	0.531186i
$310$	5.95536	−	14.8758i	0.338242	−	0.844887i
$311$	8.85927	+	11.2655i	0.502363	+	0.638806i	0.969416	−	0.245423i	$-0.0789268\pi$
$311$	8.85927	+	11.2655i	0.502363	+	0.638806i	−0.467053	+	0.884229i	$0.654684\pi$
$312$	−3.01285	−	1.55323i	−0.170569	−	0.0879346i
$313$	6.42696	+	18.5695i	0.363273	+	1.04961i	0.967516	+	0.252809i	$0.0813544\pi$
$313$	6.42696	+	18.5695i	0.363273	+	1.04961i	−0.604243	+	0.796800i	$0.706524\pi$
$314$	−9.92968	+	21.7430i	−0.560364	+	1.22703i
$315$	2.77177	−	5.21092i	0.156171	−	0.293602i
$316$	1.85102	+	6.30399i	0.104128	+	0.354627i
$317$	−31.7941	+	6.12782i	−1.78574	+	0.344173i	−0.971623	−	0.236533i	$-0.923989\pi$
$317$	−31.7941	+	6.12782i	−1.78574	+	0.344173i	−0.814113	+	0.580706i	$0.802777\pi$
$318$	2.37195	+	9.77731i	0.133012	+	0.548285i
$319$	−22.2746	−	15.8617i	−1.24714	−	0.888085i
$320$	1.75356	+	1.37901i	0.0980267	+	0.0770891i
$321$	−0.101963			−0.00569102
$322$	1.00574	+	12.6487i	0.0560476	+	0.704882i
$323$	45.4242			2.52747
$324$	−0.786053	−	0.618159i	−0.0436696	−	0.0343422i
$325$	0.0645313	+	0.0459526i	0.00357955	+	0.00254899i
$326$	2.95707	+	12.1892i	0.163777	+	0.675099i
$327$	4.34053	−	0.836569i	0.240032	−	0.0462624i
$328$	−0.528005	−	1.79822i	−0.0291542	−	0.0992901i
$329$	−0.686765	−	19.7571i	−0.0378626	−	1.08924i
$330$	−3.14399	+	6.88438i	−0.173071	+	0.378973i
$331$	3.13963	+	9.07138i	0.172570	+	0.498608i	0.997808	−	0.0661772i	$-0.0210802\pi$
$331$	3.13963	+	9.07138i	0.172570	+	0.498608i	−0.825238	+	0.564785i	$0.808959\pi$
$332$	8.77193	+	4.52224i	0.481422	+	0.248190i
$333$	3.64758	+	4.63828i	0.199886	+	0.254176i
$334$	−5.85407	+	14.6228i	−0.320320	+	0.800122i
$335$	12.2815	+	19.1103i	0.671007	+	1.04411i
$336$	1.06806	+	2.42059i	0.0582675	+	0.132054i
$337$	−4.12547	−	1.88404i	−0.224729	−	0.102630i	0.299869	−	0.953980i	$-0.403057\pi$
$337$	−4.12547	−	1.88404i	−0.224729	−	0.102630i	−0.524598	+	0.851350i	$0.675784\pi$
$338$	1.34230	−	0.692002i	0.0730113	−	0.0376400i
$339$	−9.25950	−	8.82891i	−0.502907	−	0.479521i
$340$	−5.86798	+	16.9544i	−0.318236	+	0.919482i
$341$	−17.6361	+	16.8160i	−0.955047	+	0.910636i
$342$	−2.34631	−	5.13771i	−0.126874	−	0.277816i
$343$	−18.4197	+	1.92705i	−0.994572	+	0.104051i
$344$		−	7.79074i		−	0.420049i
$345$	10.3895	+	2.55350i	0.559353	+	0.137476i
$346$	15.5729	−	8.99101i	0.837204	−	0.483360i
$347$	−12.5971	+	5.04313i	−0.676249	+	0.270729i	−0.684259	−	0.729239i	$-0.739874\pi$
$347$	−12.5971	+	5.04313i	−0.676249	+	0.270729i	0.00801037	+	0.999968i	$0.497450\pi$
$348$	−0.766174	+	8.02374i	−0.0410712	+	0.430117i
$349$	−8.34094	+	28.4066i	−0.446480	+	1.52057i	0.362073	+	0.932150i	$0.382069\pi$
$349$	−8.34094	+	28.4066i	−0.446480	+	1.52057i	−0.808554	+	0.588423i	$0.799749\pi$
$350$	−0.0166568	−	0.0595488i	−0.000890344	−	0.00318302i
$351$	−3.25236	+	0.954979i	−0.173598	+	0.0509730i
$352$	−1.55458	−	3.01546i	−0.0828591	−	0.160724i
$353$	3.14562	+	32.9424i	0.167425	+	1.75335i	0.555312	+	0.831642i	$0.312599\pi$
$353$	3.14562	+	32.9424i	0.167425	+	1.75335i	−0.387887	+	0.921707i	$0.626795\pi$
$354$	6.83634	+	1.31760i	0.363347	+	0.0700295i
$355$	0.384247	+	8.06635i	0.0203937	+	0.428117i
$356$	−0.0355746	−	0.247427i	−0.00188545	−	0.0131136i
$357$	−15.5871	+	14.4844i	−0.824957	+	0.766595i
$358$	−21.6681	+	13.9253i	−1.14520	+	0.735974i
$359$	24.9763	−	8.64438i	1.31820	−	0.456233i	0.424714	−	0.905328i	$-0.360375\pi$
$359$	24.9763	−	8.64438i	1.31820	−	0.456233i	0.893484	+	0.449095i	$0.148253\pi$
$360$	2.22073	−	0.212054i	0.117043	−	0.0111762i
$361$	0.613868	−	12.8867i	0.0323088	−	0.678246i
$362$	4.32827	−	17.8414i	0.227489	−	0.937722i
$363$	0.385187	−	0.333767i	0.0202171	−	0.0175182i
$364$	8.78360	+	1.81029i	0.460386	+	0.0948850i
$365$	6.45898	−	2.94972i	0.338078	−	0.154395i
$366$	7.31433	−	9.30092i	0.382326	−	0.486167i
$367$	9.56374	+	16.5649i	0.499223	+	0.864680i	1.00000		0.000896989i	$-0.000285520\pi$
$367$	9.56374	+	16.5649i	0.499223	+	0.864680i	−0.500777	+	0.865577i	$0.666952\pi$
$368$	−3.77865	+	2.95326i	−0.196976	+	0.153950i
$369$	−1.62305	−	0.937068i	−0.0844926	−	0.0487818i
$370$	−13.0296	−	1.87337i	−0.677374	−	0.0973917i
$371$	−13.0119	−	23.2216i	−0.675547	−	1.20561i
$372$	6.89181	+	2.02362i	0.357324	+	0.104920i
$373$	−1.75234	−	9.09200i	−0.0907327	−	0.470766i	−0.998665	−	0.0516497i	$-0.983552\pi$
$373$	−1.75234	−	9.09200i	−0.0907327	−	0.470766i	0.907933	−	0.419116i	$-0.137660\pi$
$374$	18.8284	−	19.7466i	0.973593	−	1.02107i
$375$	−11.1936	−	0.533218i	−0.578036	−	0.0275353i
$376$	6.08650	−	4.33417i	0.313887	−	0.223518i
$377$	20.6482	+	17.8918i	1.06344	+	0.921473i
$378$	2.44339	+	1.01482i	0.125674	+	0.0521965i
$379$	−15.7420	+	2.26335i	−0.808610	+	0.116261i	−0.534206	−	0.845354i	$-0.679389\pi$
$379$	−15.7420	+	2.26335i	−0.808610	+	0.116261i	−0.274404	+	0.961615i	$0.588480\pi$
$380$	11.6975	+	4.68296i	0.600067	+	0.240231i
$381$	2.49786	−	4.84517i	0.127969	−	0.248226i
$382$	3.31607	−	17.2054i	0.169665	−	0.880305i
$383$	−16.1996	−	22.7492i	−0.827763	−	1.16243i	−0.984603	−	0.174806i	$-0.944070\pi$
$383$	−16.1996	−	22.7492i	−0.827763	−	1.16243i	0.156840	−	0.987624i	$-0.449869\pi$
$384$	−0.540641	+	0.841254i	−0.0275895	+	0.0429300i
$385$	3.10421	−	19.7818i	0.158205	−	1.00817i
$386$	−2.03292	−	2.34612i	−0.103473	−	0.119414i
$387$	−5.37623	−	5.63842i	−0.273289	−	0.286617i
$388$	−7.17580	+	10.0770i	−0.364296	+	0.511582i
$389$	−5.99097	−	14.9647i	−0.303754	−	0.758742i	−0.999193	−	0.0401567i	$-0.987214\pi$
$389$	−5.99097	−	14.9647i	−0.303754	−	0.758742i	0.695439	−	0.718585i	$-0.255210\pi$
$390$	3.78089	−	6.54870i	0.191453	−	0.331606i
$391$	−32.3842	−	20.9496i	−1.63774	−	1.05947i
$392$	−4.44653	−	5.40633i	−0.224584	−	0.273061i
$393$	0.345860	−	2.40551i	0.0174463	−	0.121342i
$394$	−18.0479	−	1.72337i	−0.909242	−	0.0868221i
$395$	−14.2437	+	3.45549i	−0.716679	+	0.173865i
$396$	−3.20600	−	1.10961i	−0.161108	−	0.0557599i
$397$	3.93376	+	0.954320i	0.197430	+	0.0478960i	0.333254	−	0.942837i	$-0.391853\pi$
$397$	3.93376	+	0.954320i	0.197430	+	0.0478960i	−0.135825	+	0.990733i	$0.543368\pi$
$398$	−12.5330	−	8.05447i	−0.628222	−	0.403734i
$399$	9.63996	+	11.4184i	0.482602	+	0.571636i
$400$	0.0153049	−	0.0176628i	0.000765246	−	0.000883141i
$401$	17.0359	−	0.811521i	0.850733	−	0.0405254i	0.382315	−	0.924032i	$-0.375127\pi$
$401$	17.0359	−	0.811521i	0.850733	−	0.0405254i	0.468418	+	0.883507i	$0.344824\pi$
$402$	−8.00433	+	6.29468i	−0.399220	+	0.313950i
$403$	19.1382	−	15.0504i	0.953340	−	0.749715i
$404$	4.31694	−	0.205641i	0.214776	−	0.0102310i
$405$	1.46089	−	1.68595i	0.0725920	−	0.0837757i
$406$	−3.76638	−	20.9901i	−0.186922	−	1.04172i
$407$	16.8408	+	10.8229i	0.834769	+	0.536474i
$408$	−7.81565	−	1.89606i	−0.386932	−	0.0938687i
$409$	−2.58733	−	0.895485i	−0.127935	−	0.0442789i	0.262350	−	0.964973i	$-0.415502\pi$
$409$	−2.58733	−	0.895485i	−0.127935	−	0.0442789i	−0.390286	+	0.920694i	$0.627624\pi$
$410$	4.06304	−	0.985682i	0.200659	−	0.0486794i
$411$	−2.42043	−	0.231123i	−0.119391	−	0.0114005i
$412$	−1.57961	+	10.9864i	−0.0778217	+	0.541262i
$413$	−18.3577	+	1.51512i	−0.903324	+	0.0745541i
$414$	−0.696756	+	4.74495i	−0.0342437	+	0.233201i
$415$	−11.0081	+	19.0665i	−0.540365	+	0.935940i
$416$	1.25981	+	3.14686i	0.0617673	+	0.154287i
$417$	−2.49196	+	3.49946i	−0.122032	+	0.171369i
$418$	−13.2231	−	13.8680i	−0.646765	−	0.678307i
$419$	9.39348	+	10.8407i	0.458902	+	0.529601i	0.937291	−	0.348547i	$-0.113325\pi$
$419$	9.39348	+	10.8407i	0.458902	+	0.529601i	−0.478390	+	0.878148i	$0.658779\pi$
$420$	−5.50719	+	2.12303i	−0.268723	+	0.103593i
$421$	−4.46240	+	6.94363i	−0.217484	+	0.338412i	−0.932803	−	0.360386i	$-0.882645\pi$
$421$	−4.46240	+	6.94363i	−0.217484	+	0.338412i	0.715319	+	0.698798i	$0.246281\pi$
$422$	14.3890	+	20.2065i	0.700445	+	0.983638i
$423$	1.41408	−	7.33695i	0.0687550	−	0.356735i
$424$	4.61018	−	8.94250i	0.223890	−	0.434286i
$425$	0.174496	+	0.0698576i	0.00846430	+	0.00338859i
$426$	−3.58310	+	0.515171i	−0.173602	+	0.0249601i
$427$	−12.0077	+	28.9112i	−0.581095	+	1.39911i
$428$	0.0770585	+	0.0667716i	0.00372476	+	0.00322753i
$429$	−9.36742	+	6.67051i	−0.452263	+	0.322055i
$430$	17.3602	+	0.826967i	0.837182	+	0.0398799i
$431$	6.54051	−	6.85949i	0.315045	−	0.330410i	−0.547104	−	0.837065i	$-0.684270\pi$
$431$	6.54051	−	6.85949i	0.315045	−	0.330410i	0.862149	+	0.506655i	$0.169118\pi$
$432$	0.189251	+	0.981929i	0.00910535	+	0.0472431i
$433$	−3.83868	−	1.12714i	−0.184475	−	0.0541668i	0.188190	−	0.982133i	$-0.439738\pi$
$433$	−3.83868	−	1.12714i	−0.184475	−	0.0541668i	−0.372665	+	0.927966i	$0.621556\pi$
$434$	−19.0022	−	0.244257i	−0.912137	−	0.0117247i
$435$	−17.7980	−	2.55897i	−0.853351	−	0.122693i
$436$	−3.82819	−	2.21021i	−0.183337	−	0.105850i
$437$	−15.7784	+	22.0175i	−0.754782	+	1.05324i
$438$	1.59148	+	2.75652i	0.0760437	+	0.131712i
$439$	13.1515	−	16.7234i	0.627685	−	0.798167i	−0.363366	−	0.931646i	$-0.618373\pi$
$439$	13.1515	−	16.7234i	0.627685	−	0.798167i	0.991052	+	0.133480i	$0.0426151\pi$
$440$	6.88438	−	3.14399i	0.328200	−	0.149884i
$441$	−6.94890	−	0.844286i	−0.330900	−	0.0402041i
$442$	−20.6024	+	17.8521i	−0.979956	+	0.849136i
$443$	−5.36173	+	22.1014i	−0.254744	+	1.05007i	0.690404	+	0.723424i	$0.257433\pi$
$443$	−5.36173	+	22.1014i	−0.254744	+	1.05007i	−0.945148	+	0.326643i	$0.894082\pi$
$444$	0.280768	−	5.89404i	0.0133246	−	0.279719i
$445$	0.555120	−	0.0530075i	0.0263152	−	0.00251280i
$446$	−9.76637	+	3.38017i	−0.462451	+	0.160056i
$447$	9.06368	−	5.82488i	0.428698	−	0.275507i
$448$	0.777961	−	2.52879i	0.0367552	−	0.119474i
$449$	−0.00462327	−	0.0321556i	−0.000218186	−	0.00151752i	0.989712	−	0.143074i	$-0.0456985\pi$
$449$	−0.00462327	−	0.0321556i	−0.000218186	−	0.00151752i	−0.989930	+	0.141556i	$0.954789\pi$
$450$	−0.00111205	−	0.0233448i	−5.24225e−5	−	0.00110048i
$451$	−6.24328	−	1.20329i	−0.293985	−	0.0566609i
$452$	1.21615	+	12.7361i	0.0572030	+	0.599057i
$453$	0.927488	+	1.79908i	0.0435772	+	0.0845279i
$454$	−0.844024	+	0.247828i	−0.0396120	+	0.0116311i
$455$	−4.96624	+	19.3804i	−0.232821	+	0.908568i
$456$	−1.59126	+	5.41933i	−0.0745176	+	0.253784i
$457$	2.82466	−	29.5812i	0.132132	−	1.38375i	−0.649667	−	0.760219i	$-0.725091\pi$
$457$	2.82466	−	29.5812i	0.132132	−	1.38375i	0.781799	−	0.623531i	$-0.214302\pi$
$458$	−3.83556	+	1.53553i	−0.179224	+	0.0717504i
$459$	−6.96488	+	4.02117i	−0.325093	+	0.187692i
$460$	−6.17969	−	8.73349i	−0.288130	−	0.407201i
$461$		−	16.4521i		−	0.766251i	−0.923696	−	0.383126i	$-0.874848\pi$
$461$		−	16.4521i		−	0.766251i	0.923696	−	0.383126i	$-0.125152\pi$
$462$	8.95956	+	0.542295i	0.416836	+	0.0252299i
$463$	−14.7075	−	32.2050i	−0.683518	−	1.49669i	−0.858872	−	0.512189i	$-0.828835\pi$
$463$	−14.7075	−	32.2050i	−0.683518	−	1.49669i	0.175355	−	0.984505i	$-0.443893\pi$
$464$	5.83347	−	5.56220i	0.270812	−	0.258219i
$465$	−5.24080	+	15.1423i	−0.243036	+	0.702207i
$466$	8.78216	+	8.37378i	0.406826	+	0.387908i
$467$	4.27336	−	2.20307i	0.197747	−	0.101946i	−0.356509	−	0.934292i	$-0.616033\pi$
$467$	4.27336	−	2.20307i	0.197747	−	0.101946i	0.554256	+	0.832346i	$0.313003\pi$
$468$	3.08335	+	1.40812i	0.142528	+	0.0650903i
$469$	15.9084	−	21.7432i	0.734582	−	1.00401i
$470$	9.01181	+	14.0227i	0.415684	+	0.646817i
$471$	8.88386	−	22.1908i	0.409347	−	1.02250i
$472$	−4.30372	−	5.47262i	−0.198095	−	0.251898i
$473$	−23.4926	−	12.1113i	−1.08019	−	0.556878i
$474$	−2.14888	−	6.20878i	−0.0987012	−	0.285179i
$475$	0.0548364	−	0.120075i	0.00251606	−	0.00550941i
$476$	21.2652	−	0.739189i	0.974689	−	0.0338807i
$477$	−2.83449	−	9.65338i	−0.129782	−	0.441998i
$478$	−0.912787	+	0.175925i	−0.0417499	+	0.00804664i
$479$	−7.16013	−	29.5144i	−0.327155	−	1.34855i	−0.863414	−	0.504496i	$-0.831678\pi$
$479$	−7.16013	−	29.5144i	−0.327155	−	1.34855i	0.536259	−	0.844053i	$-0.319837\pi$
$480$	−1.81719	−	1.29401i	−0.0829428	−	0.0590633i
$481$	−15.7222	−	12.3641i	−0.716871	−	0.563754i
$482$	21.3491			0.972425
$483$	−1.60645	−	12.5865i	−0.0730958	−	0.572704i
$484$	−0.509676			−0.0231671
$485$	−21.6930	−	17.0596i	−0.985028	−	0.774634i
$486$	0.814576	+	0.580057i	0.0369499	+	0.0263119i
$487$	0.756713	+	3.11921i	0.0342899	+	0.141345i	0.986383	−	0.164462i	$-0.0525889\pi$
$487$	0.756713	+	3.11921i	0.0342899	+	0.141345i	−0.952093	+	0.305807i	$0.901074\pi$
$488$	−11.6186	+	2.23930i	−0.525950	+	0.101369i
$489$	−3.53371	−	12.0347i	−0.159800	−	0.544229i
$490$	12.5190	−	9.33438i	0.565549	−	0.421684i
$491$	−5.24340	+	11.4814i	−0.236631	+	0.518150i	−0.990273	−	0.139135i	$-0.955568\pi$
$491$	−5.24340	+	11.4814i	−0.236631	+	0.518150i	0.753642	+	0.657285i	$0.228295\pi$
$492$	0.612970	+	1.77106i	0.0276348	+	0.0798456i
$493$	57.6172	+	29.7037i	2.59495	+	1.33779i
$494$	11.8348	+	15.0492i	0.532473	+	0.677094i
$495$	2.81286	−	7.02618i	0.126429	−	0.315803i
$496$	−3.88330	−	6.04253i	−0.174365	−	0.271317i
$497$	8.76239	−	3.86632i	0.393047	−	0.173428i
$498$	−8.97717	−	4.09974i	−0.402277	−	0.183714i
$499$	1.45318	−	0.749168i	0.0650534	−	0.0335374i	−0.425393	−	0.905009i	$-0.639864\pi$
$499$	1.45318	−	0.749168i	0.0650534	−	0.0335374i	0.490446	+	0.871471i	$0.336834\pi$
$500$	8.11039	+	7.73324i	0.362708	+	0.345841i
$501$	5.15166	−	14.8847i	0.230159	−	0.665001i
$502$	−5.73598	+	5.46925i	−0.256009	+	0.244104i
$503$	0.965364	+	2.11385i	0.0430435	+	0.0942521i	0.929932	−	0.367731i	$-0.119865\pi$
$503$	0.965364	+	2.11385i	0.0430435	+	0.0942521i	−0.886889	+	0.461983i	$0.847138\pi$
$504$	−1.18203	−	2.36703i	−0.0526517	−	0.105436i
$505$			9.64130i			0.429032i
$506$	3.03123	+	15.9854i	0.134755	+	0.710639i
$507$	−1.30785	+	0.755088i	−0.0580837	+	0.0335346i
$508$	−5.06067	+	2.02599i	−0.224531	+	0.0898886i
$509$	−2.29011	+	23.9831i	−0.101507	+	1.06303i	0.790943	+	0.611889i	$0.209590\pi$
$509$	−2.29011	+	23.9831i	−0.101507	+	1.06303i	−0.892451	+	0.451145i	$0.851016\pi$
$510$	5.05461	−	17.2144i	0.223822	−	0.762267i
$511$	−6.01959	−	5.88922i	−0.266291	−	0.260524i
$512$	0.959493	−	0.281733i	0.0424040	−	0.0124509i
$513$	2.58812	+	5.02025i	0.114268	+	0.221650i
$514$	0.474024	+	4.96420i	0.0209083	+	0.218962i
$515$	−24.3135	−	4.68604i	−1.07138	−	0.206491i
$516$	0.370698	+	7.78191i	0.0163191	+	0.342580i
$517$	−3.60759	−	25.0914i	−0.158662	−	1.10352i
$518$	3.48532	+	15.2178i	0.153136	+	0.668633i
$519$	−15.1274	+	9.72182i	−0.664021	+	0.426740i
$520$	−7.14589	+	2.47322i	−0.313368	+	0.108458i
$521$	−17.5163	+	1.67260i	−0.767403	+	0.0732781i	−0.471413	−	0.881913i	$-0.656256\pi$
$521$	−17.5163	+	1.67260i	−0.767403	+	0.0732781i	−0.295991	+	0.955191i	$0.595650\pi$
$522$	0.383521	−	8.05110i	0.0167863	−	0.352387i
$523$	1.34548	−	5.54614i	0.0588337	−	0.242516i	−0.934800	−	0.355174i	$-0.884421\pi$
$523$	1.34548	−	5.54614i	0.0588337	−	0.242516i	0.993634	+	0.112659i	$0.0359366\pi$
$524$	−1.83666	+	1.59147i	−0.0802347	+	0.0695238i
$525$	0.0194714	+	0.0586888i	0.000849801	+	0.00256139i
$526$	−7.94993	+	3.63061i	−0.346634	+	0.158302i
$527$	35.7087	−	45.4074i	1.55550	−	1.97798i
$528$	1.69630	+	2.93807i	0.0738218	+	0.127863i
$529$	21.4034	−	8.41997i	0.930581	−	0.366086i
$530$	19.4373	+	11.2221i	0.844302	+	0.487458i
$531$	−6.89129	−	0.990818i	−0.299057	−	0.0429978i
$532$	0.192070	−	14.9423i	0.00832728	−	0.647831i
$533$	6.09537	+	1.78976i	0.264020	+	0.0775231i
$534$	0.0473074	+	0.245454i	0.00204719	+	0.0106218i
$535$	−0.156967	+	0.164623i	−0.00678629	+	0.00711725i
$536$	10.1714	+	0.484524i	0.439338	+	0.0209282i
$537$	20.9810	−	14.9405i	0.905398	−	0.644731i
$538$	−21.5580	−	18.6801i	−0.929431	−	0.805356i
$539$	−23.2150	+	5.00377i	−0.999941	+	0.215528i
$540$	−2.20813	+	0.317481i	−0.0950228	+	0.0136622i
$541$	−18.8959	−	7.56477i	−0.812398	−	0.325235i	−0.0720006	−	0.997405i	$-0.522938\pi$
$541$	−18.8959	−	7.56477i	−0.812398	−	0.325235i	−0.740397	+	0.672170i	$0.765363\pi$
$542$	9.21629	−	17.8771i	0.395873	−	0.767887i
$543$	−3.47444	+	18.0271i	−0.149103	+	0.773618i
$544$	4.66502	+	6.55110i	0.200011	+	0.280876i
$545$	5.33138	−	8.29578i	0.228371	−	0.355352i
$546$	−8.85979	−	1.39030i	−0.379164	−	0.0594993i
$547$	1.87619	+	2.16524i	0.0802201	+	0.0925790i	0.794441	−	0.607342i	$-0.207764\pi$
$547$	1.87619	+	2.16524i	0.0802201	+	0.0925790i	−0.714221	+	0.699921i	$0.753219\pi$
$548$	1.67788	+	1.75971i	0.0716757	+	0.0751713i
$549$	−6.86349	+	9.63842i	−0.292926	+	0.411358i
$550$	−0.0294688	−	0.0736095i	−0.00125655	−	0.00313872i
$551$	22.7626	−	39.4260i	0.969719	−	1.67960i
$552$	3.63385	−	3.12971i	0.154667	−	0.133209i
$553$	9.90026	+	14.2881i	0.421002	+	0.607593i
$554$	−0.327769	+	2.27968i	−0.0139256	+	0.0968544i
$555$	13.1039	+	1.25127i	0.556231	+	0.0531136i
$556$	4.17496	−	1.01283i	0.177058	−	0.0429537i
$557$	−39.6629	−	13.7275i	−1.68057	−	0.581651i	−0.690639	−	0.723200i	$-0.742670\pi$
$557$	−39.6629	−	13.7275i	−1.68057	−	0.581651i	−0.989931	+	0.141549i	$0.954792\pi$
$558$	−6.98029	−	1.69340i	−0.295499	−	0.0716874i
$559$	22.2158	+	14.2772i	0.939629	+	0.603863i
$560$	5.55235	+	2.00196i	0.234629	+	0.0845984i
$561$	−17.8675	+	20.6202i	−0.754366	+	0.870584i
$562$	23.6218	−	1.12525i	0.996426	−	0.0474656i
$563$	25.4440	−	20.0094i	1.07234	−	0.843294i	0.0841341	−	0.996454i	$-0.473188\pi$
$563$	25.4440	−	20.0094i	1.07234	−	0.843294i	0.988201	+	0.153161i	$0.0489452\pi$
$564$	−5.87337	+	4.61887i	−0.247314	+	0.194490i
$565$	−28.5091	+	1.35806i	−1.19939	+	0.0571339i
$566$	0.526287	−	0.607368i	0.0221215	−	0.0255296i
$567$	−2.48891	−	0.897405i	−0.104524	−	0.0376875i
$568$	3.04529	+	1.95709i	0.127777	+	0.0821176i
$569$	32.7612	+	7.94778i	1.37342	+	0.333188i	0.853530	−	0.521044i	$-0.174457\pi$
$569$	32.7612	+	7.94778i	1.37342	+	0.333188i	0.519891	+	0.854232i	$0.325972\pi$
$570$	−11.9070	−	4.12107i	−0.498731	−	0.172613i
$571$	−25.9984	+	6.30714i	−1.08800	+	0.263946i	−0.739359	−	0.673311i	$-0.764871\pi$
$571$	−25.9984	+	6.30714i	−1.08800	+	0.263946i	−0.348640	+	0.937257i	$0.613356\pi$
$572$	11.4477	+	1.09312i	0.478651	+	0.0457057i
$573$	−2.49365	+	17.3437i	−0.104174	+	0.724543i
$574$	−2.82406	−	4.07571i	−0.117874	−	0.170117i
$575$	−0.0944730	+	0.0603144i	−0.00393980	+	0.00251528i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	1.39515	+	3.48491i	0.0580808	+	0.145079i	0.954570	−	0.297987i	$-0.0963151\pi$
$577$	1.39515	+	3.48491i	0.0580808	+	0.145079i	−0.896489	+	0.443066i	$0.853891\pi$
$578$	−27.6567	+	38.8385i	−1.15037	+	1.61547i
$579$	2.14225	+	2.24673i	0.0890290	+	0.0933709i
$580$	11.7751	+	13.5892i	0.488934	+	0.564260i
$581$	25.7953	+	4.04786i	1.07017	+	0.167934i
$582$	6.68819	−	10.4070i	0.277234	−	0.431385i
$583$	−19.7988	−	27.8036i	−0.819984	−	1.15151i
$584$	0.602378	−	3.12543i	0.0249266	−	0.129331i
$585$	−3.46501	+	6.72118i	−0.143261	+	0.277887i
$586$	9.54887	+	3.82279i	0.394460	+	0.157918i
$587$	−5.79706	+	0.833491i	−0.239270	+	0.0344019i	−0.260907	−	0.965364i	$-0.584021\pi$
$587$	−5.79706	+	0.833491i	−0.239270	+	0.0344019i	0.0216364	+	0.999766i	$0.493112\pi$
$588$	4.69874	+	5.18863i	0.193773	+	0.213975i
$589$	−30.6601	−	26.5671i	−1.26333	−	1.09468i
$590$	12.6515	−	9.00911i	0.520855	−	0.370899i
$591$	18.1095	+	0.862662i	0.744925	+	0.0354852i
$592$	−4.07196	+	4.27055i	−0.167357	+	0.175519i
$593$	5.24706	+	27.2243i	0.215471	+	1.11797i	0.915027	+	0.403392i	$0.132169\pi$
$593$	5.24706	+	27.2243i	0.215471	+	1.11797i	−0.699557	+	0.714577i	$0.746619\pi$
$594$	3.25517	+	0.955803i	0.133561	+	0.0392171i
$595$	−0.610106	+	47.4639i	−0.0250119	+	1.94583i
$596$	−10.6644	−	1.53330i	−0.436829	−	0.0628065i
$597$	12.9020	+	7.44900i	0.528046	+	0.304867i
$598$	−1.49670	−	16.1872i	−0.0612047	−	0.661944i
$599$	−8.48898	−	14.7033i	−0.346850	−	0.600762i	0.638838	−	0.769341i	$-0.279415\pi$
$599$	−8.48898	−	14.7033i	−0.346850	−	0.600762i	−0.985688	+	0.168579i	$0.946082\pi$
$600$	−0.0144472	+	0.0183711i	−0.000589803	+	0.000749995i
$601$	−24.9326	+	11.3863i	−1.01702	+	0.464458i	−0.852951	−	0.521990i	$-0.825190\pi$
$601$	−24.9326	+	11.3863i	−1.01702	+	0.464458i	−0.164070	+	0.986449i	$0.552462\pi$
$602$	−6.49072	−	19.5637i	−0.264542	−	0.797358i
$603$	7.69575	−	6.66841i	0.313395	−	0.271559i
$604$	0.477195	−	1.96703i	0.0194168	−	0.0800371i
$605$	0.0541008	−	1.13572i	0.00219951	−	0.0461734i
$606$	−4.30226	+	0.410816i	−0.174768	+	0.0166883i
$607$	26.6011	−	9.20673i	1.07970	−	0.373689i	0.271408	−	0.962464i	$-0.412511\pi$
$607$	26.6011	−	9.20673i	1.07970	−	0.373689i	0.808297	+	0.588775i	$0.200390\pi$
$608$	4.75150	−	3.05361i	0.192699	−	0.123840i
$609$	4.76086	+	20.7872i	0.192920	+	0.842338i
$610$	−3.75657	−	26.1275i	−0.152099	−	1.05787i
$611$	1.20513	+	25.2988i	0.0487544	+	1.02348i
$612$	7.89701	+	1.52202i	0.319218	+	0.0615242i
$613$	−3.14603	−	32.9467i	−0.127067	−	1.33071i	−0.803986	−	0.594648i	$-0.797291\pi$
$613$	−3.14603	−	32.9467i	−0.127067	−	1.33071i	0.676919	−	0.736058i	$-0.263315\pi$
$614$	0.315380	+	0.611751i	0.0127277	+	0.0246883i
$615$	−4.01154	+	1.17789i	−0.161761	+	0.0474972i
$616$	−6.41605	−	6.27710i	−0.258510	−	0.252912i
$617$	−8.56560	+	29.1718i	−0.344838	+	1.17441i	0.586407	+	0.810017i	$0.300542\pi$
$617$	−8.56560	+	29.1718i	−0.344838	+	1.17441i	−0.931245	+	0.364394i	$0.881276\pi$
$618$	1.05506	−	11.0491i	0.0424409	−	0.444461i
$619$	7.12206	−	2.85124i	0.286260	−	0.114601i	−0.224089	−	0.974569i	$-0.571941\pi$
$619$	7.12206	−	2.85124i	0.286260	−	0.114601i	0.510349	+	0.859968i	$0.329516\pi$
$620$	13.8768	−	8.01178i	0.557306	−	0.321761i
$621$	0.470193	−	4.77273i	0.0188682	−	0.191523i
$622$			14.3317i			0.574649i
$623$	−0.295473	−	0.591689i	−0.0118379	−	0.0237055i
$624$	−1.40812	−	3.08335i	−0.0563698	−	0.123433i
$625$	−18.0084	+	17.1710i	−0.720335	+	0.686838i
$626$	−6.42696	+	18.5695i	−0.256873	+	0.742186i
$627$	13.8680	+	13.2231i	0.553836	+	0.528081i
$628$	−21.2459	+	10.9530i	−0.847803	+	0.437073i
$629$	−43.1672	−	19.7138i	−1.72119	−	0.786040i
$630$	5.39993	−	2.38267i	0.215139	−	0.0949278i
$631$	17.7558	+	27.6286i	0.706847	+	1.09988i	0.990036	+	0.140811i	$0.0449711\pi$
$631$	17.7558	+	27.6286i	0.706847	+	1.09988i	−0.283189	+	0.959064i	$0.591392\pi$
$632$	−2.44187	+	6.09950i	−0.0971324	+	0.242625i
$633$	−15.3342	−	19.4990i	−0.609478	−	0.775015i
$634$	−28.7798	−	14.8370i	−1.14299	−	0.589254i
$635$	−3.97735	−	11.4918i	−0.157836	−	0.456038i
$636$	−4.17946	+	9.15173i	−0.165726	+	0.362890i
$637$	23.5652	−	2.77199i	0.933686	−	0.109830i
$638$	−7.70400	−	26.2374i	−0.305004	−	1.03875i
$639$	3.55452	−	0.685078i	0.140615	−	0.0271013i
$640$	0.525939	+	2.16795i	0.0207896	+	0.0856958i
$641$	8.59762	+	6.12234i	0.339586	+	0.241818i	0.737108	−	0.675774i	$-0.236191\pi$
$641$	8.59762	+	6.12234i	0.339586	+	0.241818i	−0.397523	+	0.917592i	$0.630130\pi$
$642$	−0.0801484	−	0.0630294i	−0.00316320	−	0.00248757i
$643$	−45.7022			−1.80232			−0.901160	−	0.433487i	$-0.857283\pi$
$643$	−45.7022			−1.80232			−0.901160	+	0.433487i	$0.857283\pi$
$644$	−7.02832	+	10.5642i	−0.276954	+	0.416289i
$645$	−17.3799			−0.684331
$646$	35.7058	+	28.0794i	1.40483	+	1.10477i
$647$	−11.2765	−	8.02994i	−0.443324	−	0.315690i	0.336506	−	0.941681i	$-0.390755\pi$
$647$	−11.2765	−	8.02994i	−0.443324	−	0.315690i	−0.779830	+	0.625992i	$0.784694\pi$
$648$	−0.235759	−	0.971812i	−0.00926149	−	0.0381764i
$649$	−23.1929	+	4.47007i	−0.910401	+	0.175465i
$650$	0.0223191	+	0.0760118i	0.000875426	+	0.00298143i
$651$	18.9923	−	0.660183i	0.744368	−	0.0258746i
$652$	−5.21046	+	11.4093i	−0.204057	+	0.446824i
$653$	1.19527	+	3.45351i	0.0467746	+	0.135146i	0.965969	−	0.258658i	$-0.0832801\pi$
$653$	1.19527	+	3.45351i	0.0467746	+	0.135146i	−0.919194	+	0.393804i	$0.871159\pi$
$654$	3.92902	+	2.02555i	0.153637	+	0.0792053i
$655$	−3.35134	−	4.26157i	−0.130948	−	0.166513i
$656$	0.696546	−	1.73989i	0.0271956	−	0.0679312i
$657$	−1.72083	−	2.67767i	−0.0671362	−	0.104466i
$658$	11.6732	−	15.9546i	0.455068	−	0.621976i
$659$	28.2129	+	12.8844i	1.09902	+	0.501905i	0.880557	−	0.473940i	$-0.157169\pi$
$659$	28.2129	+	12.8844i	1.09902	+	0.501905i	0.218462	+	0.975845i	$0.429896\pi$
$660$	−6.72699	+	3.46800i	−0.261848	+	0.134992i
$661$	−27.5814	−	26.2988i	−1.07279	−	1.02290i	−0.999673	−	0.0255807i	$-0.991857\pi$
$661$	−27.5814	−	26.2988i	−1.07279	−	1.02290i	−0.0731181	−	0.997323i	$-0.523295\pi$
$662$	−3.13963	+	9.07138i	−0.122025	+	0.352569i
$663$	19.7296	−	18.8121i	0.766235	−	0.730603i
$664$	4.09974	+	8.97717i	0.159101	+	0.348382i
$665$	33.2757	+	2.01408i	1.29037	+	0.0781026i
$666$			5.90072i			0.228648i
$667$	−34.4114	+	17.6098i	−1.33241	+	0.681856i
$668$	−13.6408	+	7.87552i	−0.527778	+	0.304713i
$669$	9.59447	−	3.84105i	0.370944	−	0.148503i
$670$	−2.15934	+	22.6136i	−0.0834225	+	0.873640i
$671$	−11.3095	+	38.5166i	−0.436598	+	1.48692i
$672$	−0.656755	+	2.56294i	−0.0253349	+	0.0988676i
$673$	−37.3197	+	10.9581i	−1.43857	+	0.422402i	−0.905745	−	0.423824i	$-0.860687\pi$
$673$	−37.3197	+	10.9581i	−1.43857	+	0.422402i	−0.532824	+	0.846226i	$0.678869\pi$
$674$	−2.07820	−	4.03115i	−0.0800494	−	0.155274i
$675$	0.00222158	+	0.0232654i	8.55087e−5	+	0.000895487i
$676$	1.48288	+	0.285803i	0.0570340	+	0.0109924i
$677$	2.38798	+	50.1299i	0.0917775	+	1.92665i	0.309978	+	0.950744i	$0.399678\pi$
$677$	2.38798	+	50.1299i	0.0917775	+	1.92665i	−0.218200	+	0.975904i	$0.570019\pi$
$678$	−1.82078	−	12.6638i	−0.0699268	−	0.486352i
$679$	−9.62405	+	31.2833i	−0.369337	+	1.20054i
$680$	−15.0931	+	9.69972i	−0.578793	+	0.371967i
$681$	0.831276	−	0.287707i	0.0318546	−	0.0110250i
$682$	−24.2578	+	2.31634i	−0.928881	+	0.0886974i
$683$	1.24787	−	26.1960i	0.0477483	−	1.00236i	−0.840160	−	0.542339i	$-0.817539\pi$
$683$	1.24787	−	26.1960i	0.0477483	−	1.00236i	0.887908	−	0.460021i	$-0.152158\pi$
$684$	1.33160	−	5.48891i	0.0509148	−	0.209874i
$685$	−4.09929	+	3.55206i	−0.156626	+	0.135717i
$686$	−15.6701	−	9.87156i	−0.598288	−	0.376898i
$687$	3.75815	−	1.71629i	0.143382	−	0.0654806i
$688$	4.81592	−	6.12393i	0.183605	−	0.233473i
$689$	17.0516	+	29.5342i	0.649613	+	1.12516i
$690$	6.58825	+	8.42956i	0.250810	+	0.320908i
$691$	−14.6081	−	8.43401i	−0.555720	−	0.320845i	0.195706	−	0.980663i	$-0.437300\pi$
$691$	−14.6081	−	8.43401i	−0.555720	−	0.320845i	−0.751426	+	0.659818i	$0.770633\pi$
$692$	17.7990	+	2.55911i	0.676616	+	0.0972827i
$693$	−8.97521	−	0.115368i	−0.340940	−	0.00438248i
$694$	−13.0195	−	3.82286i	−0.494212	−	0.145114i
$695$	1.81374	+	9.41060i	0.0687993	+	0.356964i
$696$	−5.56220	+	5.83347i	−0.210835	+	0.221117i
$697$	15.0554	+	0.717176i	0.570263	+	0.0271650i
$698$	−24.1162	+	17.1731i	−0.912813	+	0.650011i
$699$	−9.17066	−	7.94642i	−0.346866	−	0.300561i
$700$	0.0237175	−	0.0571051i	0.000896438	−	0.00215837i
$701$	43.1238	−	6.20027i	1.62876	−	0.234181i	0.733491	−	0.679699i	$-0.237890\pi$
$701$	43.1238	−	6.20027i	1.62876	−	0.234181i	0.895273	+	0.445518i	$0.146980\pi$
$702$	−3.14686	−	1.25981i	−0.118770	−	0.0475485i
$703$	−15.2718	+	29.6231i	−0.575986	+	1.11726i
$704$	0.642052	−	3.33128i	0.0241983	−	0.125552i
$705$	−9.66883	−	13.5780i	−0.364149	−	0.511376i
$706$	−17.8910	+	27.8390i	−0.673338	+	1.04773i
$707$	10.6692	−	4.11298i	0.401255	−	0.154685i
$708$	4.55924	+	5.26165i	0.171347	+	0.197745i
$709$	−32.8204	−	34.4210i	−1.23260	−	1.29271i	−0.941900	−	0.335893i	$-0.890962\pi$
$709$	−32.8204	−	34.4210i	−1.23260	−	1.29271i	−0.290695	−	0.956816i	$-0.593887\pi$
$710$	−4.68425	+	6.57810i	−0.175797	+	0.246872i
$711$	2.44187	+	6.09950i	0.0915773	+	0.228749i
$712$	0.124986	−	0.216482i	0.00468404	−	0.00811299i
$713$	9.60574	+	33.0809i	0.359738	+	1.23889i
$714$	−21.2060	+	1.75019i	−0.793613	+	0.0654993i
$715$	−3.65095	+	25.3929i	−0.136538	+	0.949642i
$716$	−25.6403	−	2.44836i	−0.958225	−	0.0914994i
$717$	0.903383	−	0.219158i	0.0337374	−	0.00818462i
$718$	24.9763	+	8.64438i	0.932107	+	0.322605i
$719$	11.7797	+	2.85772i	0.439307	+	0.106575i	0.449312	−	0.893375i	$-0.351669\pi$
$719$	11.7797	+	2.85772i	0.439307	+	0.106575i	−0.0100041	+	0.999950i	$0.503184\pi$
$720$	1.87670	+	1.20608i	0.0699404	+	0.0449480i
$721$	5.18651	+	28.9046i	0.193156	+	1.07646i
$722$	8.44855	−	9.75014i	0.314422	−	0.362863i
$723$	−21.3249	+	1.01583i	−0.793083	+	0.0377792i
$724$	14.4311	−	11.3487i	0.536326	−	0.421772i
$725$	0.148075	−	0.116447i	0.00549937	−	0.00432475i
$726$	0.509099	−	0.0242514i	0.0188944	−	0.000900052i
$727$	−12.1165	+	13.9832i	−0.449378	+	0.518609i	−0.934561	−	0.355803i	$-0.884207\pi$
$727$	−12.1165	+	13.9832i	−0.449378	+	0.518609i	0.485183	+	0.874412i	$0.338753\pi$
$728$	5.78533	+	6.85265i	0.214419	+	0.253976i
$729$	−0.841254	−	0.540641i	−0.0311575	−	0.0200237i
$730$	6.90049	+	1.67404i	0.255399	+	0.0619590i
$731$	59.2098	+	20.4927i	2.18995	+	0.757951i
$732$	11.4989	−	2.78960i	0.425012	−	0.103107i
$733$	36.8071	+	3.51465i	1.35950	+	0.129817i	0.749196	−	0.662349i	$-0.230440\pi$
$733$	36.8071	+	3.51465i	1.35950	+	0.129817i	0.610306	+	0.792165i	$0.291046\pi$
$734$	−2.72212	+	18.9328i	−0.100475	+	0.698822i
$735$	−12.0606	+	9.91948i	−0.444863	+	0.365885i
$736$	−4.79581	−	0.0143872i	−0.176776	−	0.000530318i
$737$	17.2733	−	29.9182i	0.636269	−	1.10205i
$738$	−0.696546	−	1.73989i	−0.0256402	−	0.0640462i
$739$	−8.48677	+	11.9180i	−0.312191	+	0.438411i	−0.940623	−	0.339454i	$-0.889758\pi$
$739$	−8.48677	+	11.9180i	−0.312191	+	0.438411i	0.628432	+	0.777865i	$0.283697\pi$
$740$	−9.08388	−	9.52690i	−0.333930	−	0.350216i
$741$	−12.5375	−	14.4690i	−0.460575	−	0.531532i
$742$	4.12657	−	26.2969i	0.151491	−	0.965389i
$743$	−14.3417	+	22.3161i	−0.526146	+	0.818699i	−0.998015	−	0.0629692i	$-0.979943\pi$
$743$	−14.3417	+	22.3161i	−0.526146	+	0.818699i	0.471869	+	0.881668i	$0.343579\pi$
$744$	4.16641	+	5.85091i	0.152748	+	0.214505i
$745$	4.54867	−	23.6007i	0.166650	−	0.864664i
$746$	4.24287	−	8.23002i	0.155343	−	0.301323i
$747$	9.16208	+	3.66794i	0.335223	+	0.134203i
$748$	27.0067	−	3.88298i	0.987462	−	0.141976i
$749$	0.249135	+	0.103474i	0.00910321	+	0.00378084i
$750$	−8.46917	−	7.33858i	−0.309250	−	0.267967i
$751$	−20.1517	+	14.3500i	−0.735346	+	0.523637i	−0.885280	−	0.465059i	$-0.846033\pi$
$751$	−20.1517	+	14.3500i	−0.735346	+	0.523637i	0.149934	+	0.988696i	$0.452094\pi$
$752$	7.46352	+	0.355531i	0.272166	+	0.0129649i
$753$	5.46925	−	5.73598i	0.199310	−	0.209031i
$754$	5.17063	+	26.8278i	0.188303	+	0.977009i
$755$	4.33249	+	1.27213i	0.157675	+	0.0462977i
$756$	1.29332	+	2.30810i	0.0470375	+	0.0839448i
$757$	−37.1077	−	5.33528i	−1.34870	−	0.193914i	−0.570174	−	0.821524i	$-0.693124\pi$
$757$	−37.1077	−	5.33528i	−1.34870	−	0.193914i	−0.778528	+	0.627610i	$0.784033\pi$
$758$	−13.7731	−	7.95192i	−0.500262	−	0.288827i
$759$	−3.78842	−	15.8231i	−0.137511	−	0.574342i
$760$	6.30002	+	10.9119i	0.228526	+	0.395818i
$761$	−3.40913	+	4.33506i	−0.123581	+	0.157146i	−0.843907	−	0.536490i	$-0.819750\pi$
$761$	−3.40913	+	4.33506i	−0.123581	+	0.157146i	0.720326	+	0.693636i	$0.243992\pi$
$762$	4.95854	−	2.26449i	0.179629	−	0.0820337i
$763$	−11.4546	−	2.36077i	−0.414683	−	0.0854658i
$764$	13.2423	−	11.4745i	0.479089	−	0.415133i
$765$	−4.22979	+	17.4354i	−0.152928	+	0.630379i
$766$	1.32885	−	27.8960i	0.0480134	−	1.00792i
$767$	23.4925	−	2.24326i	0.848266	−	0.0809995i
$768$	−0.945001	+	0.327068i	−0.0340998	+	0.0118020i
$769$	30.1611	−	19.3834i	1.08764	−	0.698982i	0.131328	−	0.991339i	$-0.458076\pi$
$769$	30.1611	−	19.3834i	1.08764	−	0.698982i	0.956309	+	0.292357i	$0.0944396\pi$
$770$	14.6684	−	13.6307i	0.528611	−	0.491215i
$771$	−0.709693	−	4.93602i	−0.0255590	−	0.177767i
$772$	−0.147711	−	3.10084i	−0.00531625	−	0.111602i
$773$	−11.5080	−	2.21798i	−0.413913	−	0.0797751i	−0.0219563	−	0.999759i	$-0.506989\pi$
$773$	−11.5080	−	2.21798i	−0.413913	−	0.0797751i	−0.391956	+	0.919984i	$0.628202\pi$
$774$	−0.740557	−	7.75546i	−0.0266188	−	0.278764i
$775$	−0.0769226	−	0.149209i	−0.00276314	−	0.00535975i
$776$	−11.8698	+	3.48527i	−0.426099	+	0.125114i
$777$	−4.20547	−	15.0347i	−0.150870	−	0.539369i
$778$	4.54136	−	15.4664i	0.162816	−	0.554499i
$779$	1.00620	−	10.5374i	0.0360509	−	0.377542i
$780$	7.02012	−	2.81043i	0.251361	−	0.100630i
$781$	10.6356	−	6.14049i	0.380573	−	0.219724i
$782$	−12.5055	−	36.4861i	−0.447197	−	1.30474i
$783$			8.06023i			0.288049i
$784$	−0.153239	−	6.99832i	−0.00547283	−	0.249940i
$785$	−22.1515	−	48.5050i	−0.790621	−	1.73122i
$786$	1.75885	−	1.67706i	0.0627362	−	0.0598188i
$787$	16.2104	−	46.8367i	0.577837	−	1.66955i	−0.154002	−	0.988071i	$-0.549216\pi$
$787$	16.2104	−	46.8367i	0.577837	−	1.66955i	0.731838	−	0.681479i	$-0.238663\pi$
$788$	−13.1213	−	12.5112i	−0.467428	−	0.445691i
$789$	7.76818	−	4.00477i	0.276554	−	0.142574i
$790$	−13.3324	−	6.08869i	−0.474344	−	0.216626i
$791$	13.6648	+	30.9692i	0.485866	+	1.10114i
$792$	−1.83417	−	2.85403i	−0.0651745	−	0.101414i
$793$	14.9066	−	37.2350i	0.529350	−	1.32225i
$794$	2.50222	+	3.18184i	0.0888006	+	0.112919i
$795$	−19.9492	−	10.2846i	−0.707527	−	0.364755i
$796$	−4.87266	−	14.0786i	−0.172707	−	0.499004i
$797$	4.33851	−	9.50002i	0.153678	−	0.336508i	−0.817097	−	0.576501i	$-0.804418\pi$
$797$	4.33851	−	9.50002i	0.153678	−	0.336508i	0.970775	+	0.239993i	$0.0771451\pi$
$798$	0.519131	+	14.9345i	0.0183770	+	0.528676i
$799$	16.9299	+	57.6581i	0.598938	+	2.03980i
$800$	0.0229489	−	0.00442304i	0.000811367	−	0.000156378i
$801$	−0.0589330	−	0.242925i	−0.00208230	−	0.00858334i
$802$	13.8928	+	9.89301i	0.490571	+	0.349334i
$803$	−8.48816	−	6.67517i	−0.299541	−	0.235561i
$804$	−10.1829			−0.359125
$805$	−22.7943	−	16.7826i	−0.803394	−	0.591510i
$806$	24.3472			0.857592
$807$	22.4224	+	17.6332i	0.789306	+	0.620717i
$808$	3.52046	+	2.50691i	0.123849	+	0.0881928i
$809$	−5.29055	−	21.8080i	−0.186006	−	0.766727i	−0.986004	−	0.166724i	$-0.946681\pi$
$809$	−5.29055	−	21.8080i	−0.186006	−	0.766727i	0.799998	−	0.600003i	$-0.204834\pi$
$810$	2.19052	−	0.422188i	0.0769671	−	0.0148342i
$811$	10.4870	+	35.7156i	0.368250	+	1.25414i	0.910353	+	0.413832i	$0.135810\pi$
$811$	10.4870	+	35.7156i	0.368250	+	1.25414i	−0.542103	+	0.840312i	$0.682372\pi$
$812$	10.0147	−	18.8276i	0.351446	−	0.660719i
$813$	−8.35522	+	18.2954i	−0.293030	+	0.641647i
$814$	6.54749	+	18.9177i	0.229489	+	0.663066i
$815$	−24.8704	−	12.8216i	−0.871173	−	0.449121i
$816$	−4.97145	−	6.32171i	−0.174036	−	0.221304i
$817$	16.3543	−	40.8510i	0.572164	−	1.42920i
$818$	−1.48023	−	2.30328i	−0.0517550	−	0.0805324i
$819$	8.91591	+	0.967159i	0.311547	+	0.0337953i
$820$	3.80307	+	1.73680i	0.132809	+	0.0606519i
$821$	8.68019	−	4.47495i	0.302941	−	0.156177i	−0.300053	−	0.953922i	$-0.597005\pi$
$821$	8.68019	−	4.47495i	0.302941	−	0.156177i	0.602994	+	0.797746i	$0.293974\pi$
$822$	−1.75971	−	1.67788i	−0.0613771	−	0.0585229i
$823$	10.8582	−	31.3726i	0.378492	−	1.09358i	−0.581498	−	0.813548i	$-0.697533\pi$
$823$	10.8582	−	31.3726i	0.378492	−	1.09358i	0.959990	−	0.280034i	$-0.0903456\pi$
$824$	−8.03301	+	7.65946i	−0.279843	+	0.266830i
$825$	0.0329379	+	0.0721240i	0.00114675	+	0.00251103i
$826$	−15.3667	−	10.1570i	−0.534677	−	0.353408i
$827$			13.4353i			0.467190i	0.972334	+	0.233595i	$0.0750490\pi$
$827$			13.4353i			0.467190i	−0.972334	+	0.233595i	$0.924951\pi$
$828$	−3.48082	+	3.29908i	−0.120967	+	0.114651i
$829$	6.04841	−	3.49205i	0.210070	−	0.121284i	−0.391274	−	0.920274i	$-0.627965\pi$
$829$	6.04841	−	3.49205i	0.210070	−	0.121284i	0.601344	+	0.798990i	$0.294632\pi$
$830$	−20.4391	+	8.18258i	−0.709451	+	0.284021i
$831$	0.218926	−	2.29270i	0.00759446	−	0.0795328i
$832$	−0.954979	+	3.25236i	−0.0331079	+	0.112755i
$833$	52.7844	−	19.5730i	1.82887	−	0.678163i
$834$	−4.12203	+	1.21034i	−0.142734	+	0.0419106i
$835$	−16.1012	−	31.2319i	−0.557204	−	1.08082i
$836$	−1.82144	−	19.0750i	−0.0629959	−	0.659723i
$837$	7.05296	+	1.35935i	0.243786	+	0.0469859i
$838$	0.682527	+	14.3280i	0.0235775	+	0.494953i
$839$	7.11607	+	49.4934i	0.245674	+	1.70870i	0.622669	+	0.782486i	$0.286048\pi$
$839$	7.11607	+	49.4934i	0.245674	+	1.70870i	−0.376995	+	0.926215i	$0.623042\pi$
$840$	−5.64131	−	1.73550i	−0.194644	−	0.0598806i
$841$	30.2577	−	19.4454i	1.04337	−	0.670532i
$842$	−7.79995	+	2.69959i	−0.268804	+	0.0930339i
$843$	−23.5415	+	2.24794i	−0.810813	+	0.0774233i
$844$	−1.18033	+	24.7781i	−0.0406285	+	0.852897i
$845$	−0.794261	+	3.27399i	−0.0273234	+	0.112629i
$846$	5.64695	−	4.89311i	0.194146	−	0.168228i
$847$	−1.27987	+	0.424628i	−0.0439770	+	0.0145904i
$848$	9.15173	−	4.17946i	0.314272	−	0.143523i
$849$	−0.496792	+	0.631722i	−0.0170498	+	0.0216806i
$850$	0.0939799	+	0.162778i	0.00322349	+	0.00558324i
$851$	24.5499	−	14.0758i	0.841559	−	0.482514i
$852$	−3.13496	−	1.80997i	−0.107402	−	0.0620086i
$853$	34.3209	+	4.93459i	1.17512	+	0.168957i	0.702091	−	0.712088i	$-0.252250\pi$
$853$	34.3209	+	4.93459i	1.17512	+	0.168957i	0.473033	+	0.881045i	$0.343159\pi$
$854$	−27.3105	+	15.3031i	−0.934545	+	0.523661i
$855$	12.0896	+	3.54984i	0.413457	+	0.121402i
$856$	0.0192966	+	0.100120i	0.000659545	+	0.00342205i
$857$	1.08477	−	1.13768i	0.0370552	−	0.0388623i	−0.704946	−	0.709261i	$-0.749029\pi$
$857$	1.08477	−	1.13768i	0.0370552	−	0.0388623i	0.742001	+	0.670399i	$0.233877\pi$
$858$	−11.4867	−	0.547180i	−0.392150	−	0.0186804i
$859$	−16.6812	+	11.8786i	−0.569155	+	0.405294i	−0.828085	−	0.560603i	$-0.810570\pi$
$859$	−16.6812	+	11.8786i	−0.569155	+	0.405294i	0.258930	+	0.965896i	$0.416630\pi$
$860$	13.1348	+	11.3814i	0.447894	+	0.388102i
$861$	3.01479	+	3.93672i	0.102744	+	0.134163i
$862$	9.38144	−	1.34885i	0.319533	−	0.0459419i
$863$	20.7784	+	8.31841i	0.707305	+	0.283162i	0.697291	−	0.716788i	$-0.254388\pi$
$863$	20.7784	+	8.31841i	0.707305	+	0.283162i	0.0100133	+	0.999950i	$0.496813\pi$
$864$	−0.458227	+	0.888835i	−0.0155892	+	0.0302388i
$865$	−7.59180	+	39.3900i	−0.258129	+	1.33930i
$866$	−2.32066	−	3.25891i	−0.0788591	−	0.110742i
$867$	25.7774	−	40.1104i	0.875447	−	1.36222i
$868$	−14.7858	−	11.9384i	−0.501862	−	0.405216i
$869$	14.5967	+	16.8455i	0.495159	+	0.571444i
$870$	−12.4084	−	13.0135i	−0.420683	−	0.441199i
$871$	−20.0217	+	28.1165i	−0.678409	+	0.952692i
$872$	−1.64290	−	4.10377i	−0.0556357	−	0.138971i
$873$	−6.18543	+	10.7135i	−0.209345	+	0.362596i
$874$	−26.0130	+	7.55341i	−0.879902	+	0.255498i
$875$	26.8093	+	12.6623i	0.906318	+	0.428065i
$876$	−0.452982	+	3.15056i	−0.0153048	+	0.106447i
$877$	7.08696	+	0.676723i	0.239310	+	0.0228513i	0.214022	−	0.976829i	$-0.431344\pi$
$877$	7.08696	+	0.676723i	0.239310	+	0.0228513i	0.0252880	+	0.999680i	$0.491950\pi$
$878$	20.6755	−	5.01582i	0.697764	−	0.169276i
$879$	−9.71995	−	3.36411i	−0.327846	−	0.113469i
$880$	7.35498	+	1.78430i	0.247936	+	0.0601487i
$881$	13.0104	+	8.36129i	0.438332	+	0.281699i	0.741137	−	0.671353i	$-0.234287\pi$
$881$	13.0104	+	8.36129i	0.438332	+	0.281699i	−0.302805	+	0.953053i	$0.597923\pi$
$882$	−4.94030	−	4.95918i	−0.166349	−	0.166984i
$883$	5.72065	−	6.60198i	0.192515	−	0.222174i	−0.651283	−	0.758835i	$-0.725769\pi$
$883$	5.72065	−	6.60198i	0.192515	−	0.222174i	0.843798	+	0.536661i	$0.180314\pi$
$884$	−27.2300	+	1.29712i	−0.915843	+	0.0436270i
$885$	−12.2085	+	9.60089i	−0.410385	+	0.322730i
$886$	−17.8768	+	14.0584i	−0.600581	+	0.472302i
$887$	−23.9522	+	1.14099i	−0.804237	+	0.0383106i	−0.445675	−	0.895195i	$-0.647036\pi$
$887$	−23.9522	+	1.14099i	−0.804237	+	0.0383106i	−0.358563	+	0.933506i	$0.616733\pi$
$888$	3.86415	−	4.45947i	0.129672	−	0.149650i
$889$	−11.0202	+	9.30377i	−0.369605	+	0.312038i
$890$	0.469121	+	0.301486i	0.0157250	+	0.0101058i
$891$	−3.29696	−	0.799834i	−0.110452	−	0.0267954i
$892$	−9.76637	−	3.38017i	−0.327002	−	0.113177i
$893$	41.0130	−	9.94965i	1.37245	−	0.332952i
$894$	10.7252	+	1.02414i	0.358706	+	0.0342522i
$895$	8.17735	−	56.8747i	0.273339	−	1.90111i
$896$	2.17471	−	1.50686i	0.0726521	−	0.0503406i
$897$	2.26523	+	16.0977i	0.0756337	+	0.537485i
$898$	0.0162431	−	0.0281339i	0.000542040	−	0.000938841i
$899$	−21.5173	−	53.7476i	−0.717642	−	1.79258i
$900$	0.0135567	−	0.0190377i	0.000451889	−	0.000634589i
$901$	55.8366	+	58.5598i	1.86019	+	1.95091i
$902$	−4.16372	−	4.80519i	−0.138637	−	0.159995i
$903$	7.41425	+	19.2327i	0.246731	+	0.640025i
$904$	−6.91699	+	10.7631i	−0.230056	+	0.357974i
$905$	23.7566	+	33.3615i	0.789697	+	1.10897i
$906$	−0.383060	+	1.98750i	−0.0127263	+	0.0660304i
$907$	19.7978	−	38.4024i	0.657375	−	1.27513i	−0.290618	−	0.956839i	$-0.593861\pi$
$907$	19.7978	−	38.4024i	0.657375	−	1.27513i	0.947993	−	0.318290i	$-0.103109\pi$
$908$	−0.816645	−	0.326935i	−0.0271013	−	0.0108497i
$909$	4.27784	−	0.615061i	0.141887	−	0.0204003i
$910$	−15.8839	+	12.1641i	−0.526546	+	0.403236i
$911$	7.45999	+	6.46412i	0.247161	+	0.214166i	0.769627	−	0.638494i	$-0.220442\pi$
$911$	7.45999	+	6.46412i	0.247161	+	0.214166i	−0.522466	+	0.852660i	$0.674988\pi$
$912$	−4.60082	+	3.27623i	−0.152349	+	0.108487i
$913$	33.4436	+	1.59312i	1.10682	+	0.0527244i
$914$	20.5062	−	21.5063i	0.678285	−	0.711365i
$915$	4.99552	+	25.9192i	0.165147	+	0.856863i
$916$	−3.96415	−	1.16398i	−0.130979	−	0.0384590i
$917$	−3.28622	+	5.52661i	−0.108520	+	0.182505i
$918$	−7.96049	−	1.14455i	−0.262735	−	0.0377756i
$919$	22.8613	+	13.1990i	0.754126	+	0.435395i	0.827183	−	0.561933i	$-0.189942\pi$
$919$	22.8613	+	13.1990i	0.754126	+	0.435395i	−0.0730568	+	0.997328i	$0.523275\pi$
$920$	0.541122	−	10.6850i	0.0178403	−	0.352275i
$921$	−0.344131	−	0.596052i	−0.0113395	−	0.0196406i
$922$	10.1700	−	12.9322i	0.334932	−	0.425900i
$923$	−11.1615	+	5.09730i	−0.367386	+	0.167780i
$924$	6.70746	+	5.96470i	0.220659	+	0.196224i
$925$	−0.104223	+	0.0903101i	−0.00342685	+	0.00296938i
$926$	8.34692	−	34.4065i	0.274297	−	1.13067i
$927$	−0.528130	+	11.0868i	−0.0173461	+	0.364139i
$928$	8.02374	−	0.766174i	0.263392	−	0.0251509i
$929$	3.04653	−	1.05441i	0.0999533	−	0.0345942i	−0.276634	−	0.960975i	$-0.589219\pi$
$929$	3.04653	−	1.05441i	0.0999533	−	0.0345942i	0.376587	+	0.926381i	$0.377098\pi$
$930$	−13.4799	+	8.66299i	−0.442023	+	0.284071i
$931$	−11.9666	−	37.6824i	−0.392190	−	1.23499i
$932$	1.72692	+	12.0110i	0.0565672	+	0.393434i
$933$	−0.681929	−	14.3155i	−0.0223254	−	0.468667i
$934$	4.72093	+	0.909885i	0.154474	+	0.0297724i
$935$	5.78578	+	60.5914i	0.189215	+	1.98155i
$936$	1.55323	+	3.01285i	0.0507690	+	0.0984782i
$937$	14.6514	−	4.30204i	0.478641	−	0.140542i	−0.0335078	−	0.999438i	$-0.510668\pi$
$937$	14.6514	−	4.30204i	0.478641	−	0.140542i	0.512149	+	0.858897i	$0.328850\pi$
$938$	25.9456	−	7.25743i	0.847155	−	0.236963i
$939$	5.53611	−	18.8543i	0.180664	−	0.615285i
$940$	−1.58447	+	16.5933i	−0.0516796	+	0.541213i
$941$	23.0280	−	9.21902i	0.750692	−	0.300532i	0.0354146	−	0.999373i	$-0.488725\pi$
$941$	23.0280	−	9.21902i	0.750692	−	0.300532i	0.715277	+	0.698841i	$0.246301\pi$
$942$	20.7006	−	11.9515i	0.674463	−	0.389402i
$943$	−5.57721	+	7.04838i	−0.181619	+	0.229527i
$944$		−	6.96216i		−	0.226599i
$945$	−5.28045	+	2.63691i	−0.171773	+	0.0857787i
$946$	−10.9797	−	24.0423i	−0.356982	−	0.781682i
$947$	8.89712	−	8.48339i	0.289118	−	0.275673i	−0.531614	−	0.846987i	$-0.678414\pi$
$947$	8.89712	−	8.48339i	0.289118	−	0.275673i	0.820732	+	0.571313i	$0.193566\pi$
$948$	2.14888	−	6.20878i	0.0697923	−	0.201652i
$949$	7.80847	+	7.44536i	0.253474	+	0.241687i
$950$	0.117330	−	0.0604876i	0.00380668	−	0.00196248i
$951$	29.4532	+	13.4508i	0.955086	+	0.436173i
$952$	17.1725	+	12.5642i	0.556565	+	0.407209i
$953$	9.00470	+	14.0116i	0.291691	+	0.453880i	0.955911	−	0.293657i	$-0.0948725\pi$
$953$	9.00470	+	14.0116i	0.291691	+	0.453880i	−0.664220	+	0.747537i	$0.731236\pi$
$954$	3.73926	−	9.34023i	0.121063	−	0.302401i
$955$	24.1631	+	30.7259i	0.781899	+	0.994266i
$956$	−0.826249	−	0.425961i	−0.0267228	−	0.0137766i
$957$	8.94370	+	25.8411i	0.289109	+	0.835325i
$958$	12.6164	−	27.6260i	0.407617	−	0.892556i
$959$	5.67950	+	3.02101i	0.183401	+	0.0975535i
$960$	−0.628499	−	2.14047i	−0.0202847	−	0.0690834i
$961$	−20.2200	+	3.89708i	−0.652257	+	0.125712i
$962$	−4.71552	−	19.4377i	−0.152035	−	0.626695i
$963$	0.0830566	+	0.0591444i	0.00267646	+	0.00190590i
$964$	16.7815	+	13.1971i	0.540497	+	0.425051i
$965$	6.92532			0.222934
$966$	6.51769	−	10.8867i	0.209703	−	0.350273i
$967$	−33.0147			−1.06168			−0.530841	−	0.847472i	$-0.678124\pi$
$967$	−33.0147			−1.06168			−0.530841	+	0.847472i	$0.678124\pi$
$968$	−0.400632	−	0.315061i	−0.0128768	−	0.0101264i
$969$	−37.0014	−	26.3486i	−1.18866	−	0.846439i
$970$	−6.50632	−	26.8194i	−0.208905	−	0.861120i
$971$	−25.0546	+	4.82888i	−0.804040	+	0.154966i	−0.574683	−	0.818376i	$-0.694875\pi$
$971$	−25.0546	+	4.82888i	−0.804040	+	0.154966i	−0.229357	+	0.973342i	$0.573662\pi$
$972$	0.281733	+	0.959493i	0.00903658	+	0.0307758i
$973$	9.64013	−	6.02167i	0.309048	−	0.193046i
$974$	−1.33335	+	2.91964i	−0.0427234	+	0.0935512i
$975$	−0.0259106	−	0.0748637i	−0.000829802	−	0.00239756i
$976$	−10.5171	−	5.42194i	−0.336644	−	0.173552i
$977$	3.99906	+	5.08522i	0.127941	+	0.162691i	0.845803	−	0.533495i	$-0.179122\pi$
$977$	3.99906	+	5.08522i	0.127941	+	0.162691i	−0.717862	+	0.696185i	$0.754879\pi$
$978$	4.66168	−	11.6443i	0.149064	−	0.372344i
$979$	−0.458491	−	0.713426i	−0.0146534	−	0.0228012i
$980$	15.6107	+	0.401389i	0.498665	+	0.0128219i
$981$	−4.02095	−	1.83631i	−0.128379	−	0.0586287i
$982$	−11.2190	+	5.78377i	−0.358011	+	0.184568i
$983$	−37.5308	−	35.7856i	−1.19705	−	1.14138i	−0.986494	−	0.163800i	$-0.947625\pi$
$983$	−37.5308	−	35.7856i	−1.19705	−	1.14138i	−0.210554	−	0.977582i	$-0.567527\pi$
$984$	−0.612970	+	1.77106i	−0.0195408	+	0.0564593i
$985$	29.2715	−	27.9103i	0.932668	−	0.889297i
$986$	26.9285	+	58.9653i	0.857579	+	1.87784i
$987$	−10.9008	+	16.4920i	−0.346976	+	0.524946i
$988$			19.1452i			0.609091i
$989$	−30.4999	+	21.5813i	−0.969842	+	0.686246i
$990$	6.55435	−	3.78416i	0.208311	−	0.120268i
$991$	−1.23477	+	0.494329i	−0.0392239	+	0.0157029i	−0.391191	−	0.920309i	$-0.627937\pi$
$991$	−1.23477	+	0.494329i	−0.0392239	+	0.0157029i	0.351968	+	0.936012i	$0.385513\pi$
$992$	0.682765	−	7.15024i	0.0216778	−	0.227020i
$993$	2.70444	−	9.21049i	0.0858230	−	0.292286i
$994$	9.27770	+	2.37742i	0.294271	+	0.0754071i
$995$	31.8887	−	9.36338i	1.01094	−	0.296839i
$996$	−4.52224	−	8.77193i	−0.143293	−	0.277949i
$997$	−0.943631	−	9.88215i	−0.0298851	−	0.312971i	−0.998038	−	0.0626111i	$-0.980057\pi$
$997$	−0.943631	−	9.88215i	−0.0298851	−	0.312971i	0.968153	−	0.250360i	$-0.0805488\pi$
$998$	1.60538	+	0.309412i	0.0508175	+	0.00979428i
$999$	−0.280768	−	5.89404i	−0.00888310	−	0.186479i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.be.a.61.2	✓	320
7.3	odd	6	inner	966.2.be.a.199.10	yes	320
23.20	odd	22	inner	966.2.be.a.733.10	yes	320
161.66	even	66	inner	966.2.be.a.871.2	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.be.a.61.2	✓	320	1.1	even	1	trivial
966.2.be.a.199.10	yes	320	7.3	odd	6	inner
966.2.be.a.733.10	yes	320	23.20	odd	22	inner
966.2.be.a.871.2	yes	320	161.66	even	66	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.be (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.786053 + 0.618159i) q^{2} +(-0.814576 - 0.580057i) q^{3} +(0.235759 + 0.971812i) q^{4} +(-2.19052 + 0.422188i) q^{5} +(-0.281733 - 0.959493i) q^{6} +(1.40168 + 2.24395i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(0.327068 + 0.945001i) q^{9} +O(q^{10})\)	\(q+(0.786053 + 0.618159i) q^{2} +(-0.814576 - 0.580057i) q^{3} +(0.235759 + 0.971812i) q^{4} +(-2.19052 + 0.422188i) q^{5} +(-0.281733 - 0.959493i) q^{6} +(1.40168 + 2.24395i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(0.327068 + 0.945001i) q^{9} +(-1.98285 - 1.02223i) q^{10} +(2.09716 + 2.66676i) q^{11} +(0.371662 - 0.928368i) q^{12} +(-1.83259 - 2.85157i) q^{13} +(-0.285326 + 2.63032i) q^{14} +(2.02924 + 0.926723i) q^{15} +(-0.888835 + 0.458227i) q^{16} +(-5.82052 - 5.54986i) q^{17} +(-0.327068 + 0.945001i) q^{18} +(-4.08774 + 3.89765i) q^{19} +(-0.926723 - 2.02924i) q^{20} +(0.159847 - 2.64092i) q^{21} +3.39259i q^{22} +(4.71187 - 0.893486i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-0.0216971 + 0.00868622i) q^{25} +(0.322208 - 3.37432i) q^{26} +(0.281733 - 0.959493i) q^{27} +(-1.85024 + 1.89120i) q^{28} +(-7.73374 + 2.27083i) q^{29} +(1.02223 + 1.98285i) q^{30} +(0.682765 + 7.15024i) q^{31} +(-0.981929 - 0.189251i) q^{32} +(-0.161426 - 3.38875i) q^{33} +(-1.14455 - 7.96049i) q^{34} +(-4.01777 - 4.32365i) q^{35} +(-0.841254 + 0.540641i) q^{36} +(5.57619 - 1.92994i) q^{37} +(-5.62255 + 0.536888i) q^{38} +(-0.161287 + 3.38583i) q^{39} +(0.525939 - 2.16795i) q^{40} +(-1.41638 + 1.22730i) q^{41} +(1.75816 - 1.97709i) q^{42} +(-7.08671 + 3.23639i) q^{43} +(-2.09716 + 2.66676i) q^{44} +(-1.11542 - 1.93196i) q^{45} +(4.25609 + 2.21036i) q^{46} +(-6.47092 - 3.73599i) q^{47} +(0.989821 + 0.142315i) q^{48} +(-3.07061 + 6.29058i) q^{49} +(-0.0224246 - 0.00658445i) q^{50} +(1.52202 + 7.89701i) q^{51} +(2.33914 - 2.45322i) q^{52} +(-10.0495 - 0.478718i) q^{53} +(0.814576 - 0.580057i) q^{54} +(-5.71975 - 4.95619i) q^{55} +(-2.62344 + 0.342839i) q^{56} +(5.59063 - 0.803812i) q^{57} +(-7.48286 - 2.99569i) q^{58} +(-3.19024 + 6.18821i) q^{59} +(-0.422188 + 2.19052i) q^{60} +(6.86349 + 9.63842i) q^{61} +(-3.88330 + 6.04253i) q^{62} +(-1.66209 + 2.05851i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(5.21823 + 5.47272i) q^{65} +(1.96790 - 2.76352i) q^{66} +(-3.78462 - 9.45352i) q^{67} +(4.02117 - 6.96488i) q^{68} +(-4.35645 - 2.00534i) q^{69} +(-0.485479 - 5.88224i) q^{70} +(0.515171 - 3.58310i) q^{71} +(-0.995472 - 0.0950560i) q^{72} +(-3.09323 + 0.750410i) q^{73} +(5.57619 + 1.92994i) q^{74} +(0.0227125 + 0.00550999i) q^{75} +(-4.75150 - 3.05361i) q^{76} +(-3.04453 + 8.44385i) q^{77} +(-2.21976 + 2.56174i) q^{78} +(6.56269 - 0.312619i) q^{79} +(1.75356 - 1.37901i) q^{80} +(-0.786053 + 0.618159i) q^{81} +(-1.87201 + 0.0891750i) q^{82} +(6.46283 - 7.45850i) q^{83} +(2.60416 - 0.467279i) q^{84} +(15.0931 + 9.69972i) q^{85} +(-7.57113 - 1.83674i) q^{86} +(7.61693 + 2.63624i) q^{87} +(-3.29696 + 0.799834i) q^{88} +(-0.248840 - 0.0237613i) q^{89} +(0.317481 - 2.20813i) q^{90} +(3.83007 - 8.10921i) q^{91} +(1.97916 + 4.36840i) q^{92} +(3.59138 - 6.22046i) q^{93} +(-2.77705 - 6.93675i) q^{94} +(7.30874 - 10.2637i) q^{95} +(0.690079 + 0.723734i) q^{96} +(8.10119 + 9.34927i) q^{97} +(-6.30224 + 3.04660i) q^{98} +(-1.83417 + 2.85403i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9}+O(q^{10}) \) 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9	\( 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9} - 22 q^{14} + 16 q^{16} + 66 q^{17} + 16 q^{18} + 40 q^{23} - 48 q^{25} + 12 q^{26} + 44 q^{28} - 24 q^{29} + 24 q^{31} - 16 q^{32} + 98 q^{35} + 32 q^{36} - 22 q^{37} - 66 q^{38} - 8 q^{39} - 88 q^{43} + 4 q^{46} - 144 q^{47} - 24 q^{49} + 80 q^{50} - 22 q^{51} + 12 q^{52} + 44 q^{53} + 44 q^{57} + 10 q^{58} + 12 q^{59} - 32 q^{64} + 108 q^{70} - 16 q^{71} + 16 q^{72} - 180 q^{73} - 22 q^{74} - 12 q^{75} + 18 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 36 q^{82} + 22 q^{84} + 68 q^{85} - 22 q^{86} + 48 q^{87} + 22 q^{88} + 8 q^{92} + 8 q^{93} - 12 q^{94} + 66 q^{95} - 90 q^{98}+O(q^{100}) \) 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9 - 22 * q^14 + 16 * q^16 + 66 * q^17 + 16 * q^18 + 40 * q^23 - 48 * q^25 + 12 * q^26 + 44 * q^28 - 24 * q^29 + 24 * q^31 - 16 * q^32 + 98 * q^35 + 32 * q^36 - 22 * q^37 - 66 * q^38 - 8 * q^39 - 88 * q^43 + 4 * q^46 - 144 * q^47 - 24 * q^49 + 80 * q^50 - 22 * q^51 + 12 * q^52 + 44 * q^53 + 44 * q^57 + 10 * q^58 + 12 * q^59 - 32 * q^64 + 108 * q^70 - 16 * q^71 + 16 * q^72 - 180 * q^73 - 22 * q^74 - 12 * q^75 + 18 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 36 * q^82 + 22 * q^84 + 68 * q^85 - 22 * q^86 + 48 * q^87 + 22 * q^88 + 8 * q^92 + 8 * q^93 - 12 * q^94 + 66 * q^95 - 90 * q^98

Introduction

L-functions

Modular forms

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