LMFDB - Embedded newform 966.2.be.b.61.3

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			61.3
Character	$\chi$	$=$	966.61
Dual form			966.2.be.b.871.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.786053 - 0.618159i) q^{2} +(-0.814576 - 0.580057i) q^{3} +(0.235759 + 0.971812i) q^{4} +(-2.22749 + 0.429313i) q^{5} +(0.281733 + 0.959493i) q^{6} +(-1.35585 - 2.27193i) q^{7} +(0.415415 - 0.909632i) q^{8} +(0.327068 + 0.945001i) q^{9} +O(q^{10})$	\(q+(-0.786053 - 0.618159i) q^{2} +(-0.814576 - 0.580057i) q^{3} +(0.235759 + 0.971812i) q^{4} +(-2.22749 + 0.429313i) q^{5} +(0.281733 + 0.959493i) q^{6} +(-1.35585 - 2.27193i) q^{7} +(0.415415 - 0.909632i) q^{8} +(0.327068 + 0.945001i) q^{9} +(2.01631 + 1.03948i) q^{10} +(-3.00837 - 3.82546i) q^{11} +(0.371662 - 0.928368i) q^{12} +(-3.53018 - 5.49307i) q^{13} +(-0.338650 + 2.62399i) q^{14} +(2.06348 + 0.942361i) q^{15} +(-0.888835 + 0.458227i) q^{16} +(5.38397 + 5.13361i) q^{17} +(0.327068 - 0.945001i) q^{18} +(4.01901 - 3.83212i) q^{19} +(-0.942361 - 2.06348i) q^{20} +(-0.213412 + 2.63713i) q^{21} +4.86667i q^{22} +(0.568411 + 4.76203i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.135550 - 0.0542660i) q^{25} +(-0.620681 + 6.50006i) q^{26} +(0.281733 - 0.959493i) q^{27} +(1.88824 - 1.85326i) q^{28} +(1.24414 - 0.365313i) q^{29} +(-1.03948 - 2.01631i) q^{30} +(-0.248695 - 2.60445i) q^{31} +(0.981929 + 0.189251i) q^{32} +(0.231565 + 4.86116i) q^{33} +(-1.05870 - 7.36344i) q^{34} +(3.99550 + 4.47862i) q^{35} +(-0.841254 + 0.540641i) q^{36} +(-7.65729 + 2.65021i) q^{37} +(-5.52802 + 0.527862i) q^{38} +(-0.310692 + 6.52223i) q^{39} +(-0.534815 + 2.20454i) q^{40} +(-6.64646 + 5.75919i) q^{41} +(1.79792 - 1.94100i) q^{42} +(-6.18678 + 2.82541i) q^{43} +(3.00837 - 3.82546i) q^{44} +(-1.13424 - 1.96456i) q^{45} +(2.49689 - 4.09458i) q^{46} +(6.48137 + 3.74202i) q^{47} +(0.989821 + 0.142315i) q^{48} +(-3.32337 + 6.16078i) q^{49} +(-0.140094 - 0.0411355i) q^{50} +(-1.40787 - 7.30472i) q^{51} +(4.50596 - 4.72572i) q^{52} +(-6.18563 - 0.294658i) q^{53} +(-0.814576 + 0.580057i) q^{54} +(8.34344 + 7.22963i) q^{55} +(-2.62986 + 0.289525i) q^{56} +(-5.49664 + 0.790297i) q^{57} +(-1.20378 - 0.481921i) q^{58} +(-5.72641 + 11.1077i) q^{59} +(-0.429313 + 2.22749i) q^{60} +(5.19894 + 7.30089i) q^{61} +(-1.41448 + 2.20097i) q^{62} +(1.70353 - 2.02435i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(10.2217 + 10.7202i) q^{65} +(2.82294 - 3.96427i) q^{66} +(-0.557422 - 1.39237i) q^{67} +(-3.71958 + 6.44250i) q^{68} +(2.29923 - 4.20874i) q^{69} +(-0.372175 - 5.99029i) q^{70} +(1.62412 - 11.2960i) q^{71} +(0.995472 + 0.0950560i) q^{72} +(5.99252 - 1.45377i) q^{73} +(7.65729 + 2.65021i) q^{74} +(-0.141893 - 0.0344229i) q^{75} +(4.67162 + 3.00227i) q^{76} +(-4.61230 + 12.0216i) q^{77} +(4.27600 - 4.93476i) q^{78} +(9.94389 - 0.473686i) q^{79} +(1.78315 - 1.40228i) q^{80} +(-0.786053 + 0.618159i) q^{81} +(8.78457 - 0.418460i) q^{82} +(-1.43567 + 1.65686i) q^{83} +(-2.61311 + 0.414331i) q^{84} +(-14.1967 - 9.12364i) q^{85} +(6.60969 + 1.60349i) q^{86} +(-1.22535 - 0.424097i) q^{87} +(-4.72948 + 1.14736i) q^{88} +(11.8805 + 1.13445i) q^{89} +(-0.322839 + 2.24539i) q^{90} +(-7.69351 + 15.4681i) q^{91} +(-4.49379 + 1.67508i) q^{92} +(-1.30815 + 2.26578i) q^{93} +(-2.78154 - 6.94795i) q^{94} +(-7.30712 + 10.2614i) q^{95} +(-0.690079 - 0.723734i) q^{96} +(3.75044 + 4.32824i) q^{97} +(6.42068 - 2.78833i) q^{98} +(2.63112 - 4.09410i) 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} + 36 q^{23} + 24 q^{25} + 12 q^{26} + 44 q^{28} + 8 q^{29} - 48 q^{31} + 16 q^{32} - 46 q^{35} + 32 q^{36} - 22 q^{37} + 66 q^{38} + 8 q^{39} + 176 q^{43} - 8 q^{46} + 120 q^{47} - 24 q^{49} - 48 q^{50} - 22 q^{51} - 12 q^{52} - 44 q^{53} + 44 q^{57} + 18 q^{58} + 12 q^{59} - 32 q^{64} - 108 q^{70} - 48 q^{71} - 16 q^{72} + 252 q^{73} + 22 q^{74} - 36 q^{75} - 42 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 12 q^{82} - 22 q^{84} - 76 q^{85} + 22 q^{86} + 24 q^{87} - 22 q^{88} + 16 q^{92} + 12 q^{94} + 26 q^{95} + 2 q^{98} + 88 q^{99}+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 + 36 * q^23 + 24 * q^25 + 12 * q^26 + 44 * q^28 + 8 * q^29 - 48 * q^31 + 16 * q^32 - 46 * q^35 + 32 * q^36 - 22 * q^37 + 66 * q^38 + 8 * q^39 + 176 * q^43 - 8 * q^46 + 120 * q^47 - 24 * q^49 - 48 * q^50 - 22 * q^51 - 12 * q^52 - 44 * q^53 + 44 * q^57 + 18 * q^58 + 12 * q^59 - 32 * q^64 - 108 * q^70 - 48 * q^71 - 16 * q^72 + 252 * q^73 + 22 * q^74 - 36 * q^75 - 42 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 12 * q^82 - 22 * q^84 - 76 * q^85 + 22 * q^86 + 24 * q^87 - 22 * q^88 + 16 * q^92 + 12 * q^94 + 26 * q^95 + 2 * q^98 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−2.22749	+	0.429313i	−0.996163	+	0.191995i	−0.661178	−	0.750229i	$-0.729943\pi$
$5$	−2.22749	+	0.429313i	−0.996163	+	0.191995i	−0.334985	+	0.942224i	$0.608731\pi$
$6$	0.281733	+	0.959493i	0.115017	+	0.391711i
$7$	−1.35585	−	2.27193i	−0.512461	−	0.858710i
$7$	−1.35585	−	2.27193i	−0.512461	−	0.858710i
$8$	0.415415	−	0.909632i	0.146871	−	0.321603i
$9$	0.327068	+	0.945001i	0.109023	+	0.315000i
$10$	2.01631	+	1.03948i	0.637612	+	0.328712i
$11$	−3.00837	−	3.82546i	−0.907059	−	1.15342i	−0.987651	−	0.156672i	$-0.949923\pi$
$11$	−3.00837	−	3.82546i	−0.907059	−	1.15342i	0.0805915	−	0.996747i	$-0.474319\pi$
$12$	0.371662	−	0.928368i	0.107290	−	0.267997i
$13$	−3.53018	−	5.49307i	−0.979097	−	1.52350i	−0.846537	−	0.532330i	$-0.821317\pi$
$13$	−3.53018	−	5.49307i	−0.979097	−	1.52350i	−0.132560	−	0.991175i	$-0.542320\pi$
$14$	−0.338650	+	2.62399i	−0.0905079	+	0.701290i
$15$	2.06348	+	0.942361i	0.532789	+	0.243317i
$16$	−0.888835	+	0.458227i	−0.222209	+	0.114557i
$17$	5.38397	+	5.13361i	1.30581	+	1.24508i	0.950646	+	0.310277i	$0.100422\pi$
$17$	5.38397	+	5.13361i	1.30581	+	1.24508i	0.355159	+	0.934806i	$0.384427\pi$
$18$	0.327068	−	0.945001i	0.0770907	−	0.222739i
$19$	4.01901	−	3.83212i	0.922025	−	0.879149i	−0.0709496	−	0.997480i	$-0.522603\pi$
$19$	4.01901	−	3.83212i	0.922025	−	0.879149i	0.992974	+	0.118331i	$0.0377545\pi$
$20$	−0.942361	−	2.06348i	−0.210718	−	0.461409i
$21$	−0.213412	+	2.63713i	−0.0465702	+	0.575469i
$22$			4.86667i			1.03758i
$23$	0.568411	+	4.76203i	0.118522	+	0.992951i
$23$	0.568411	+	4.76203i	0.118522	+	0.992951i
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	0.135550	−	0.0542660i	0.0271100	−	0.0108532i
$26$	−0.620681	+	6.50006i	−0.121726	+	1.27477i
$27$	0.281733	−	0.959493i	0.0542195	−	0.184655i
$28$	1.88824	−	1.85326i	0.356844	−	0.350232i
$29$	1.24414	−	0.365313i	0.231031	−	0.0678368i	−0.164168	−	0.986432i	$-0.552494\pi$
$29$	1.24414	−	0.365313i	0.231031	−	0.0678368i	0.395199	+	0.918596i	$0.370676\pi$
$30$	−1.03948	−	2.01631i	−0.189782	−	0.368126i
$31$	−0.248695	−	2.60445i	−0.0446669	−	0.467773i	−0.989939	−	0.141491i	$-0.954810\pi$
$31$	−0.248695	−	2.60445i	−0.0446669	−	0.467773i	0.945273	−	0.326282i	$-0.105796\pi$
$32$	0.981929	+	0.189251i	0.173582	+	0.0334552i
$33$	0.231565	+	4.86116i	0.0403104	+	0.846219i
$34$	−1.05870	−	7.36344i	−0.181566	−	1.26282i
$35$	3.99550	+	4.47862i	0.675363	+	0.757025i
$36$	−0.841254	+	0.540641i	−0.140209	+	0.0901068i
$37$	−7.65729	+	2.65021i	−1.25885	+	0.435692i	−0.873385	−	0.487030i	$-0.838080\pi$
$37$	−7.65729	+	2.65021i	−1.25885	+	0.435692i	−0.385465	+	0.922722i	$0.625959\pi$
$38$	−5.52802	+	0.527862i	−0.896763	+	0.0856305i
$39$	−0.310692	+	6.52223i	−0.0497506	+	1.04439i
$40$	−0.534815	+	2.20454i	−0.0845616	+	0.348568i
$41$	−6.64646	+	5.75919i	−1.03800	+	0.899434i	−0.995023	−	0.0996416i	$-0.968230\pi$
$41$	−6.64646	+	5.75919i	−1.03800	+	0.899434i	−0.0429792	+	0.999076i	$0.513685\pi$
$42$	1.79792	−	1.94100i	0.277425	−	0.299503i
$43$	−6.18678	+	2.82541i	−0.943476	+	0.430871i	−0.826924	−	0.562314i	$-0.809911\pi$
$43$	−6.18678	+	2.82541i	−0.943476	+	0.430871i	−0.116552	+	0.993185i	$0.537184\pi$
$44$	3.00837	−	3.82546i	0.453530	−	0.576710i
$45$	−1.13424	−	1.96456i	−0.169083	−	0.292860i
$46$	2.49689	−	4.09458i	0.368146	−	0.603712i
$47$	6.48137	+	3.74202i	0.945406	+	0.545830i	0.891651	−	0.452724i	$-0.149548\pi$
$47$	6.48137	+	3.74202i	0.945406	+	0.545830i	0.0537549	+	0.998554i	$0.482881\pi$
$48$	0.989821	+	0.142315i	0.142868	+	0.0205414i
$49$	−3.32337	+	6.16078i	−0.474766	+	0.880112i
$50$	−0.140094	−	0.0411355i	−0.0198124	−	0.00581743i
$51$	−1.40787	−	7.30472i	−0.197141	−	1.02287i
$52$	4.50596	−	4.72572i	0.624864	−	0.655339i
$53$	−6.18563	−	0.294658i	−0.849662	−	0.0404744i	−0.381767	−	0.924259i	$-0.624684\pi$
$53$	−6.18563	−	0.294658i	−0.849662	−	0.0404744i	−0.467895	+	0.883784i	$0.654987\pi$
$54$	−0.814576	+	0.580057i	−0.110850	+	0.0789357i
$55$	8.34344	+	7.22963i	1.12503	+	0.974843i
$56$	−2.62986	+	0.289525i	−0.351430	+	0.0386894i
$57$	−5.49664	+	0.790297i	−0.728048	+	0.104677i
$58$	−1.20378	−	0.481921i	−0.158064	−	0.0632794i
$59$	−5.72641	+	11.1077i	−0.745515	+	1.44610i	0.144185	+	0.989551i	$0.453944\pi$
$59$	−5.72641	+	11.1077i	−0.745515	+	1.44610i	−0.889700	+	0.456547i	$0.849086\pi$
$60$	−0.429313	+	2.22749i	−0.0554241	+	0.287567i
$61$	5.19894	+	7.30089i	0.665657	+	0.934784i	0.999971	−	0.00767795i	$-0.00244399\pi$
$61$	5.19894	+	7.30089i	0.665657	+	0.934784i	−0.334314	+	0.942462i	$0.608505\pi$
$62$	−1.41448	+	2.20097i	−0.179639	+	0.279523i
$63$	1.70353	−	2.02435i	0.214624	−	0.255044i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	10.2217	+	10.7202i	1.26784	+	1.32968i
$66$	2.82294	−	3.96427i	0.347480	−	0.487968i
$67$	−0.557422	−	1.39237i	−0.0681000	−	0.170106i	0.890414	−	0.455152i	$-0.150415\pi$
$67$	−0.557422	−	1.39237i	−0.0681000	−	0.170106i	−0.958514	+	0.285047i	$0.907991\pi$
$68$	−3.71958	+	6.44250i	−0.451065	+	0.781268i
$69$	2.29923	−	4.20874i	0.276795	−	0.506673i
$70$	−0.372175	−	5.99029i	−0.0444834	−	0.715976i
$71$	1.62412	−	11.2960i	0.192748	−	1.34059i	−0.631948	−	0.775011i	$-0.717744\pi$
$71$	1.62412	−	11.2960i	0.192748	−	1.34059i	0.824695	−	0.565577i	$-0.191347\pi$
$72$	0.995472	+	0.0950560i	0.117317	+	0.0112025i
$73$	5.99252	−	1.45377i	0.701371	−	0.170151i	0.130812	−	0.991407i	$-0.458242\pi$
$73$	5.99252	−	1.45377i	0.701371	−	0.170151i	0.570559	+	0.821256i	$0.306726\pi$
$74$	7.65729	+	2.65021i	0.890142	+	0.308081i
$75$	−0.141893	−	0.0344229i	−0.0163844	−	0.00397481i
$76$	4.67162	+	3.00227i	0.535871	+	0.344384i
$77$	−4.61230	+	12.0216i	−0.525620	+	1.36998i
$78$	4.27600	−	4.93476i	0.484161	−	0.558752i
$79$	9.94389	−	0.473686i	1.11877	−	0.0532938i	0.519967	−	0.854186i	$-0.325944\pi$
$79$	9.94389	−	0.473686i	1.11877	−	0.0532938i	0.598808	+	0.800893i	$0.295641\pi$
$80$	1.78315	−	1.40228i	0.199362	−	0.156780i
$81$	−0.786053	+	0.618159i	−0.0873392	+	0.0686843i
$82$	8.78457	−	0.418460i	0.970093	−	0.0462112i
$83$	−1.43567	+	1.65686i	−0.157586	+	0.181864i	−0.829052	−	0.559171i	$-0.811119\pi$
$83$	−1.43567	+	1.65686i	−0.157586	+	0.181864i	0.671466	+	0.741035i	$0.265665\pi$
$84$	−2.61311	+	0.414331i	−0.285113	+	0.0452072i
$85$	−14.1967	−	9.12364i	−1.53984	−	0.989597i
$86$	6.60969	+	1.60349i	0.712741	+	0.172909i
$87$	−1.22535	−	0.424097i	−0.131371	−	0.0454680i
$88$	−4.72948	+	1.14736i	−0.504165	+	0.122309i
$89$	11.8805	+	1.13445i	1.25933	+	0.120252i	0.703290	−	0.710903i	$-0.251714\pi$
$89$	11.8805	+	1.13445i	1.25933	+	0.120252i	0.556041	+	0.831155i	$0.312320\pi$
$90$	−0.322839	+	2.24539i	−0.0340302	+	0.236685i
$91$	−7.69351	+	15.4681i	−0.806500	+	1.62150i
$92$	−4.49379	+	1.67508i	−0.468510	+	0.174639i
$93$	−1.30815	+	2.26578i	−0.135649	+	0.234950i
$94$	−2.78154	−	6.94795i	−0.286894	−	0.716626i
$95$	−7.30712	+	10.2614i	−0.749695	+	1.05280i
$96$	−0.690079	−	0.723734i	−0.0704309	−	0.0738658i
$97$	3.75044	+	4.32824i	0.380800	+	0.439466i	0.913501	−	0.406837i	$-0.133368\pi$
$97$	3.75044	+	4.32824i	0.380800	+	0.439466i	−0.532701	+	0.846303i	$0.678823\pi$
$98$	6.42068	−	2.78833i	0.648587	−	0.281664i
$99$	2.63112	−	4.09410i	0.264437	−	0.411473i
$100$	0.0846935	+	0.118935i	0.00846935	+	0.0118935i
$101$	2.09819	−	10.8864i	0.208777	−	1.08324i	−0.714655	−	0.699478i	$-0.753416\pi$
$101$	2.09819	−	10.8864i	0.208777	−	1.08324i	0.923432	−	0.383762i	$-0.125372\pi$
$102$	−3.40882	+	6.61219i	−0.337524	+	0.654704i
$103$	−1.08303	−	0.433580i	−0.106714	−	0.0427219i	0.317691	−	0.948194i	$-0.397093\pi$
$103$	−1.08303	−	0.433580i	−0.106714	−	0.0427219i	−0.424405	+	0.905472i	$0.639517\pi$
$104$	−6.46317	+	0.929263i	−0.633766	+	0.0911218i
$105$	−0.656783	−	5.96579i	−0.0640954	−	0.582202i
$106$	4.68009	+	4.05532i	0.454571	+	0.393888i
$107$	−1.82736	+	1.30126i	−0.176658	+	0.125798i	−0.664966	−	0.746874i	$-0.731554\pi$
$107$	−1.82736	+	1.30126i	−0.176658	+	0.125798i	0.488308	+	0.872672i	$0.337614\pi$
$108$	0.998867	+	0.0475819i	0.0961161	+	0.00457857i
$109$	3.76167	−	3.94512i	0.360303	−	0.377874i	−0.518486	−	0.855086i	$-0.673504\pi$
$109$	3.76167	−	3.94512i	0.360303	−	0.377874i	0.878788	+	0.477212i	$0.158353\pi$
$110$	−2.08932	−	10.8404i	−0.199209	−	1.03360i
$111$	7.77472	+	2.28286i	0.737943	+	0.216680i
$112$	2.24618	+	1.39809i	0.212244	+	0.132107i
$113$	−13.0099	−	1.87055i	−1.22387	−	0.175966i	−0.500077	−	0.865981i	$-0.666695\pi$
$113$	−13.0099	−	1.87055i	−1.22387	−	0.175966i	−0.723796	+	0.690014i	$0.757604\pi$
$114$	4.80918	+	2.77658i	0.450421	+	0.260051i
$115$	−3.31053	−	10.3633i	−0.308708	−	0.966385i
$116$	0.648332	+	1.12294i	0.0601961	+	0.104263i
$117$	4.03635	−	5.13264i	0.373161	−	0.474512i
$118$	11.3676	−	5.19140i	1.04647	−	0.477907i
$119$	4.36338	−	19.1924i	0.399990	−	1.75937i
$120$	1.71440	−	1.48554i	0.156503	−	0.135611i
$121$	−2.99048	+	12.3269i	−0.271861	+	1.12063i
$122$	0.426468	−	8.95266i	0.0386106	−	0.810536i
$123$	8.75470	−	0.835973i	0.789385	−	0.0753771i
$124$	2.47240	−	0.855707i	0.222028	−	0.0768448i
$125$	9.26320	−	5.95310i	0.828526	−	0.532461i
$126$	−2.59043	+	0.538199i	−0.230774	+	0.0479465i
$127$	−2.63520	−	18.3282i	−0.233836	−	1.62637i	−0.681257	−	0.732044i	$-0.738567\pi$
$127$	−2.63520	−	18.3282i	−0.233836	−	1.62637i	0.447421	−	0.894323i	$-0.352343\pi$
$128$	0.0475819	+	0.998867i	0.00420569	+	0.0882882i
$129$	6.67850	+	1.28718i	0.588009	+	0.113330i
$130$	−1.40800	−	14.7453i	−0.123490	−	1.29325i
$131$	6.18889	+	12.0048i	0.540726	+	1.04886i	0.987998	+	0.154464i	$0.0493652\pi$
$131$	6.18889	+	12.0048i	0.540726	+	1.04886i	−0.447272	+	0.894398i	$0.647604\pi$
$132$	−4.66953	+	1.37110i	−0.406431	+	0.119339i
$133$	−14.1555	−	3.93517i	−1.22744	−	0.341222i
$134$	−0.422545	+	1.43906i	−0.0365023	+	0.124315i
$135$	−0.215633	+	2.25821i	−0.0185587	+	0.194356i
$136$	6.90628	−	2.76486i	0.592208	−	0.237084i
$137$	−7.42290	+	4.28561i	−0.634181	+	0.366145i	−0.782369	−	0.622815i	$-0.785989\pi$
$137$	−7.42290	+	4.28561i	−0.634181	+	0.366145i	0.148188	+	0.988959i	$0.452656\pi$
$138$	−4.40899	+	1.88701i	−0.375318	+	0.160633i
$139$			6.56637i			0.556952i	0.960443	+	0.278476i	$0.0898293\pi$
$139$			6.56637i			0.556952i	−0.960443	+	0.278476i	$0.910171\pi$
$140$	−3.41040	+	4.93875i	−0.288232	+	0.417400i
$141$	−3.10899	−	6.80773i	−0.261824	−	0.573314i
$142$	−8.25937	+	7.87529i	−0.693111	+	0.660880i
$143$	−10.3934	+	30.0298i	−0.869141	+	2.51122i
$144$	−0.723734	−	0.690079i	−0.0603112	−	0.0575066i
$145$	−2.61447	+	1.34785i	−0.217120	+	0.111933i
$146$	−5.60910	−	2.56159i	−0.464212	−	0.211999i
$147$	6.28074	−	3.09068i	0.518027	−	0.254915i
$148$	−4.38078	−	6.81663i	−0.360098	−	0.560323i
$149$	−1.23842	+	3.09343i	−0.101456	+	0.253424i	−0.970408	−	0.241472i	$-0.922370\pi$
$149$	−1.23842	+	3.09343i	−0.101456	+	0.253424i	0.868952	+	0.494896i	$0.164794\pi$
$150$	0.0902567	+	0.114771i	0.00736943	+	0.00937099i
$151$	8.07342	+	4.16214i	0.657006	+	0.338710i	0.754285	−	0.656547i	$-0.227984\pi$
$151$	8.07342	+	4.16214i	0.657006	+	0.338710i	−0.0972792	+	0.995257i	$0.531014\pi$
$152$	−1.81626	−	5.24774i	−0.147318	−	0.425648i
$153$	−3.09034	+	6.76690i	−0.249839	+	0.547071i
$154$	11.0567	−	6.59845i	0.890978	−	0.531718i
$155$	1.67209	+	5.69461i	0.134305	+	0.457402i
$156$	−6.41163	+	1.23574i	−0.513341	+	0.0989384i
$157$	1.53005	+	6.30694i	0.122111	+	0.503348i	0.999713	+	0.0239584i	$0.00762692\pi$
$157$	1.53005	+	6.30694i	0.122111	+	0.503348i	−0.877602	+	0.479390i	$0.840858\pi$
$158$	−8.10924	−	5.77456i	−0.645136	−	0.459400i
$159$	4.86775	+	3.82804i	0.386038	+	0.303583i
$160$	−2.26848			−0.179339
$161$	10.0483	−	7.74797i	0.791920	−	0.610625i
$162$	1.00000			0.0785674
$163$	4.52201	+	3.55615i	0.354191	+	0.278539i	0.779362	−	0.626574i	$-0.215544\pi$
$163$	4.52201	+	3.55615i	0.354191	+	0.278539i	−0.425171	+	0.905113i	$0.639786\pi$
$164$	−7.16381	−	5.10133i	−0.559400	−	0.398347i
$165$	−2.60277	−	10.7287i	−0.202625	−	0.835232i
$166$	2.15272	−	0.414902i	0.167083	−	0.0322027i
$167$	−1.49252	−	5.08304i	−0.115494	−	0.393337i	0.881374	−	0.472420i	$-0.156619\pi$
$167$	−1.49252	−	5.08304i	−0.115494	−	0.393337i	−0.996868	+	0.0790821i	$0.974801\pi$
$168$	2.31016	+	1.28963i	0.178233	+	0.0994971i
$169$	−12.3113	+	26.9579i	−0.947020	+	2.07369i
$170$	5.51947	+	15.9475i	0.423324	+	1.22311i
$171$	4.93585	+	2.54461i	0.377454	+	0.194591i
$172$	−4.20435	−	5.34627i	−0.320579	−	0.407649i
$173$	−4.90993	+	12.2644i	−0.373295	+	0.932445i	0.616162	+	0.787619i	$0.288687\pi$
$173$	−4.90993	+	12.2644i	−0.373295	+	0.932445i	−0.989457	+	0.144826i	$0.953738\pi$
$174$	0.701030	+	1.09082i	0.0531449	+	0.0826951i
$175$	−0.307074	−	0.234384i	−0.0232126	−	0.0177178i
$176$	4.42688	+	2.02169i	0.333688	+	0.152390i
$177$	11.1077	−	5.72641i	0.834905	−	0.430423i
$178$	−8.63744	−	8.23578i	−0.647403	−	0.617298i
$179$	−0.730488	+	2.11061i	−0.0545992	+	0.157754i	−0.969003	−	0.247050i	$-0.920539\pi$
$179$	−0.730488	+	2.11061i	−0.0545992	+	0.157754i	0.914404	+	0.404804i	$0.132660\pi$
$180$	1.64178	−	1.56543i	0.122371	−	0.116680i
$181$	−7.77918	−	17.0340i	−0.578222	−	1.26613i	−0.942303	−	0.334762i	$-0.891344\pi$
$181$	−7.77918	−	17.0340i	−0.578222	−	1.26613i	0.364081	−	0.931367i	$-0.381383\pi$
$182$	15.6093	−	7.40294i	1.15704	−	0.548742i
$183$		−	8.96282i		−	0.662550i
$184$	4.56782	+	1.46117i	0.336744	+	0.107719i
$185$	15.9187	−	9.19069i	1.17037	−	0.675713i
$186$	2.42889	−	0.972380i	0.178095	−	0.0712983i
$187$	3.44140	−	36.0400i	0.251660	−	2.63551i
$188$	−2.10850	+	7.18089i	−0.153778	+	0.523720i
$189$	−2.56189	+	0.660847i	−0.186350	+	0.0480695i
$190$	12.0870	−	3.54905i	0.876881	−	0.257475i
$191$	1.52622	+	2.96045i	0.110433	+	0.214211i	0.937575	−	0.347782i	$-0.113065\pi$
$191$	1.52622	+	2.96045i	0.110433	+	0.214211i	−0.827142	+	0.561993i	$0.810035\pi$
$192$	0.0950560	+	0.995472i	0.00686008	+	0.0718420i
$193$	−8.96680	−	1.72821i	−0.645444	−	0.124399i	−0.143984	−	0.989580i	$-0.545991\pi$
$193$	−8.96680	−	1.72821i	−0.645444	−	0.124399i	−0.501460	+	0.865181i	$0.667204\pi$
$194$	−0.272506	−	5.72059i	−0.0195648	−	0.410715i
$195$	−2.10802	−	14.6616i	−0.150958	−	1.04994i
$196$	−6.77063	−	1.77723i	−0.483617	−	0.126945i
$197$	−22.1457	+	14.2322i	−1.57782	+	1.01400i	−0.601179	+	0.799114i	$0.705302\pi$
$197$	−22.1457	+	14.2322i	−1.57782	+	1.01400i	−0.976639	+	0.214888i	$0.931061\pi$
$198$	−4.59901	+	1.59173i	−0.326837	+	0.113119i
$199$	−9.08150	+	0.867178i	−0.643770	+	0.0614726i	−0.411835	−	0.911259i	$-0.635112\pi$
$199$	−9.08150	+	0.867178i	−0.643770	+	0.0614726i	−0.231936	+	0.972731i	$0.574506\pi$
$200$	0.00694738	−	0.145843i	0.000491254	−	0.0103127i
$201$	−0.353593	+	1.45753i	−0.0249405	+	0.102806i
$202$	−8.37883	+	7.26030i	−0.589532	+	0.510833i
$203$	−2.51683	−	2.33130i	−0.176647	−	0.163625i
$204$	6.76690	−	3.09034i	0.473778	−	0.216367i
$205$	12.3324	−	15.6819i	0.861333	−	1.09527i
$206$	0.583298	+	1.01030i	0.0406403	+	0.0703911i
$207$	−4.31421	+	2.09466i	−0.299858	+	0.145589i
$208$	5.65483	+	3.26481i	0.392092	+	0.226374i
$209$	−26.7503	−	3.84611i	−1.85036	−	0.266041i
$210$	−3.17154	+	5.09543i	−0.218857	+	0.351618i
$211$	7.26256	+	2.13248i	0.499975	+	0.146806i	0.521990	−	0.852952i	$-0.325190\pi$
$211$	7.26256	+	2.13248i	0.499975	+	0.146806i	−0.0220147	+	0.999758i	$0.507008\pi$
$212$	−1.17197	−	6.08074i	−0.0804910	−	0.417627i
$213$	−7.87529	+	8.25937i	−0.539606	+	0.565923i
$214$	2.24079	+	0.106742i	0.153177	+	0.00729674i
$215$	12.5680	−	8.94963i	0.857130	−	0.610360i
$216$	−0.755750	−	0.654861i	−0.0514222	−	0.0445576i
$217$	−5.57995	+	4.09625i	−0.378792	+	0.278072i
$218$	−5.39559	+	0.775768i	−0.365435	+	0.0525416i
$219$	−5.72463	−	2.29180i	−0.386835	−	0.154865i
$220$	−5.05880	+	9.81270i	−0.341064	+	0.661572i
$221$	9.19287	−	47.6971i	0.618379	−	3.20846i
$222$	−4.70017	−	6.60046i	−0.315455	−	0.442994i
$223$	−7.86649	+	12.2405i	−0.526779	+	0.819684i	−0.998057	−	0.0623002i	$-0.980156\pi$
$223$	−7.86649	+	12.2405i	−0.526779	+	0.819684i	0.471278	+	0.881985i	$0.343793\pi$
$224$	−0.901377	−	2.48747i	−0.0602258	−	0.166201i
$225$	0.0956155	+	0.110346i	0.00637437	+	0.00735641i
$226$	9.07021	+	9.51257i	0.603342	+	0.632766i
$227$	0.215742	−	0.302967i	0.0143193	−	0.0201086i	−0.807354	−	0.590067i	$-0.799101\pi$
$227$	0.215742	−	0.302967i	0.0143193	−	0.0201086i	0.821674	+	0.569958i	$0.193041\pi$
$228$	−2.06390	−	5.15538i	−0.136685	−	0.341423i
$229$	7.85019	−	13.5969i	0.518755	−	0.898510i	−0.481007	−	0.876717i	$-0.659729\pi$
$229$	7.85019	−	13.5969i	0.518755	−	0.898510i	0.999762	−	0.0217938i	$-0.00693772\pi$
$230$	−3.80393	+	10.1926i	−0.250824	+	0.672078i
$231$	10.7303	−	7.11708i	0.705999	−	0.468269i
$232$	0.184535	−	1.28347i	0.0121153	−	0.0842637i
$233$	−28.5520	−	2.72639i	−1.87051	−	0.178612i	−0.902694	−	0.430283i	$-0.858414\pi$
$233$	−28.5520	−	2.72639i	−1.87051	−	0.178612i	−0.967813	+	0.251672i	$0.919020\pi$
$234$	−6.34557	+	1.53942i	−0.414823	+	0.100635i
$235$	−16.0437	−	5.55277i	−1.04657	−	0.362223i
$236$	−12.1446	−	2.94625i	−0.790548	−	0.191785i
$237$	−8.37482	−	5.38217i	−0.544003	−	0.349609i
$238$	−15.2938	+	12.3890i	−0.991350	+	0.803059i
$239$	−4.05026	+	4.67425i	−0.261989	+	0.302352i	−0.871470	−	0.490449i	$-0.836833\pi$
$239$	−4.05026	+	4.67425i	−0.261989	+	0.302352i	0.609480	+	0.792801i	$0.291378\pi$
$240$	−2.26591	+	0.107939i	−0.146264	+	0.00696741i
$241$	9.66895	−	7.60374i	0.622832	−	0.489800i	−0.256162	−	0.966634i	$-0.582458\pi$
$241$	9.66895	−	7.60374i	0.622832	−	0.489800i	0.878994	+	0.476834i	$0.158216\pi$
$242$	9.97066	−	7.84101i	0.640938	−	0.504039i
$243$	0.998867	−	0.0475819i	0.0640774	−	0.00305238i
$244$	−5.86940	+	6.77364i	−0.375750	+	0.433638i
$245$	4.75785	−	15.1498i	0.303968	−	0.967887i
$246$	−7.39843	−	4.75468i	−0.471706	−	0.303147i
$247$	−35.2380	−	8.54864i	−2.24214	−	0.543937i
$248$	−2.47240	−	0.855707i	−0.156998	−	0.0543375i
$249$	2.13054	−	0.516863i	0.135017	−	0.0327549i
$250$	−10.9613	−	1.04668i	−0.693255	−	0.0661979i
$251$	1.69670	−	11.8008i	0.107095	−	0.744862i	−0.863536	−	0.504288i	$-0.831755\pi$
$251$	1.69670	−	11.8008i	0.107095	−	0.744862i	0.970631	−	0.240574i	$-0.0773358\pi$
$252$	2.36891	+	1.17825i	0.149227	+	0.0742226i
$253$	16.5070	−	16.5004i	1.03778	−	1.03737i
$254$	−9.25835	+	16.0359i	−0.580921	+	1.00618i
$255$	6.27203	+	15.6668i	0.392770	+	0.981091i
$256$	0.580057	−	0.814576i	0.0362536	−	0.0509110i
$257$	−17.2466	−	18.0877i	−1.07582	−	1.12828i	−0.991268	−	0.131863i	$-0.957904\pi$
$257$	−17.2466	−	18.0877i	−1.07582	−	1.12828i	−0.0845472	−	0.996419i	$-0.526944\pi$
$258$	−4.45398	−	5.14017i	−0.277293	−	0.320013i
$259$	16.4032	+	13.8036i	1.01925	+	0.857712i
$260$	−8.00816	+	12.4609i	−0.496645	+	0.772795i
$261$	0.752139	+	1.05623i	0.0465562	+	0.0653791i
$262$	2.55606	−	13.2621i	0.157914	−	0.819336i
$263$	−0.351376	+	0.681575i	−0.0216668	+	0.0420277i	−0.899420	−	0.437085i	$-0.856011\pi$
$263$	−0.351376	+	0.681575i	−0.0216668	+	0.0420277i	0.877754	+	0.479112i	$0.159041\pi$
$264$	4.51806	+	1.80876i	0.278067	+	0.111321i
$265$	13.9049	−	1.99923i	0.854172	−	0.122811i
$266$	8.69440	+	11.8436i	0.533088	+	0.726177i
$267$	−9.01953	−	7.81547i	−0.551986	−	0.478299i
$268$	1.22171	−	0.869974i	0.0746277	−	0.0531421i
$269$	−21.2725	−	1.01334i	−1.29701	−	0.0617842i	−0.612315	−	0.790614i	$-0.709761\pi$
$269$	−21.2725	−	1.01334i	−1.29701	−	0.0617842i	−0.684695	+	0.728830i	$0.740064\pi$
$270$	1.56543	−	1.64178i	0.0952691	−	0.0999154i
$271$	3.41769	+	17.7327i	0.207610	+	1.07718i	0.924843	+	0.380349i	$0.124196\pi$
$271$	3.41769	+	17.7327i	0.207610	+	1.07718i	−0.717233	+	0.696833i	$0.754592\pi$
$272$	−7.13782	−	2.09585i	−0.432794	−	0.127080i
$273$	15.2393	−	8.13727i	0.922326	−	0.492490i
$274$	8.48398	+	1.21981i	0.512536	+	0.0736916i
$275$	−0.615378	−	0.355288i	−0.0371087	−	0.0214247i
$276$	4.63217	+	1.24217i	0.278824	+	0.0747700i
$277$	6.18626	+	10.7149i	0.371696	+	0.643797i	0.989827	−	0.142279i	$-0.0454430\pi$
$277$	6.18626	+	10.7149i	0.371696	+	0.643797i	−0.618130	+	0.786075i	$0.712110\pi$
$278$	4.05906	−	5.16152i	0.243446	−	0.309567i
$279$	2.37987	−	1.08685i	0.142479	−	0.0650680i
$280$	5.73369	−	1.77395i	0.342653	−	0.106014i
$281$	4.58285	−	3.97107i	0.273390	−	0.236894i	−0.507365	−	0.861731i	$-0.669380\pi$
$281$	4.58285	−	3.97107i	0.273390	−	0.236894i	0.780755	+	0.624838i	$0.214835\pi$
$282$	−1.76443	+	7.27308i	−0.105070	+	0.433106i
$283$	−0.00283627	+	0.0595406i	−0.000168599	+	0.00353932i	−0.998950	−	0.0458122i	$-0.985412\pi$
$283$	−0.00283627	+	0.0595406i	−0.000168599	+	0.00353932i	0.998781	+	0.0493515i	$0.0157155\pi$
$284$	11.3605	−	1.08479i	0.674121	−	0.0643707i
$285$	11.9044	−	4.12016i	0.705156	−	0.244057i
$286$	26.7330	−	17.1802i	1.58075	−	1.01589i
$287$	22.0961	+	7.29174i	1.30429	+	0.430418i
$288$	0.142315	+	0.989821i	0.00838598	+	0.0583258i
$289$	1.82434	+	38.2977i	0.107314	+	2.25280i
$290$	2.88830	+	0.556675i	0.169607	+	0.0326891i
$291$	−0.544394	−	5.70115i	−0.0319129	−	0.334207i
$292$	2.82558	+	5.48086i	0.165355	+	0.320743i
$293$	1.50790	−	0.442761i	0.0880927	−	0.0258664i	−0.237389	−	0.971415i	$-0.576292\pi$
$293$	1.50790	−	0.442761i	0.0880927	−	0.0258664i	0.325482	+	0.945548i	$0.394473\pi$
$294$	−6.84753	−	1.45305i	−0.399356	−	0.0847437i
$295$	7.98683	−	27.2006i	0.465011	−	1.58368i
$296$	−0.770234	+	8.06625i	−0.0447689	+	0.468841i
$297$	−4.51806	+	1.80876i	−0.262164	+	0.104955i
$298$	2.88570	−	1.66606i	0.167164	−	0.0965122i
$299$	24.1516	−	19.9332i	1.39672	−	1.15276i
$300$		−	0.146009i		−	0.00842983i
$301$	14.8075	+	10.2251i	0.853488	+	0.589367i
$302$	−3.77328	−	8.26232i	−0.217128	−	0.475443i
$303$	−8.02388	+	7.65075i	−0.460960	+	0.439524i
$304$	−1.81626	+	5.24774i	−0.104170	+	0.300979i
$305$	−14.7149	−	14.0307i	−0.842576	−	0.803394i
$306$	6.61219	−	3.40882i	0.377994	−	0.194869i
$307$	−3.33951	−	1.52510i	−0.190596	−	0.0870423i	0.317831	−	0.948147i	$-0.397046\pi$
$307$	−3.33951	−	1.52510i	−0.190596	−	0.0870423i	−0.508427	+	0.861105i	$0.669773\pi$
$308$	−12.7701	−	1.64810i	−0.727643	−	0.0939089i
$309$	0.630710	+	0.981403i	0.0358798	+	0.0558301i
$310$	2.20583	−	5.50988i	0.125282	−	0.312940i
$311$	9.35626	+	11.8974i	0.530545	+	0.674642i	0.975268	−	0.221026i	$-0.0709404\pi$
$311$	9.35626	+	11.8974i	0.530545	+	0.674642i	−0.444723	+	0.895668i	$0.646698\pi$
$312$	5.80377	+	2.99205i	0.328574	+	0.169391i
$313$	7.98012	+	23.0570i	0.451063	+	1.30326i	0.909932	+	0.414757i	$0.136133\pi$
$313$	7.98012	+	23.0570i	0.451063	+	1.30326i	−0.458869	+	0.888504i	$0.651745\pi$
$314$	2.69599	−	5.90340i	0.152144	−	0.333148i
$315$	−2.92550	+	5.24056i	−0.164833	+	0.295272i
$316$	2.80469	+	9.55191i	0.157776	+	0.537337i
$317$	−7.78588	+	1.50061i	−0.437299	+	0.0842824i	−0.403149	−	0.915134i	$-0.632084\pi$
$317$	−7.78588	+	1.50061i	−0.437299	+	0.0842824i	−0.0341496	+	0.999417i	$0.510872\pi$
$318$	−1.45997	−	6.01809i	−0.0818712	−	0.337478i
$319$	−5.14033	−	3.66041i	−0.287803	−	0.204944i
$320$	1.78315	+	1.40228i	0.0996809	+	0.0783900i
$321$	2.24333			0.125211
$322$	−12.6880	−	0.121154i	−0.707075	−	0.00675162i
$323$	41.3109			2.29860
$324$	−0.786053	−	0.618159i	−0.0436696	−	0.0343422i
$325$	−0.776604	−	0.553017i	−0.0430782	−	0.0306759i
$326$	−1.35627	−	5.59064i	−0.0751171	−	0.309637i
$327$	−5.35256	+	1.03162i	−0.295997	+	0.0570488i
$328$	2.47770	+	8.43829i	0.136808	+	0.465926i
$329$	−0.286114	−	19.7989i	−0.0157740	−	1.09155i
$330$	−4.58616	+	10.0423i	−0.252460	+	0.552810i
$331$	−1.93340	−	5.58618i	−0.106269	−	0.307044i	0.879312	−	0.476245i	$-0.158003\pi$
$331$	−1.93340	−	5.58618i	−0.106269	−	0.307044i	−0.985582	+	0.169201i	$0.945881\pi$
$332$	−1.94863	−	1.00459i	−0.106945	−	0.0551339i
$333$	−5.00891	−	6.36934i	−0.274486	−	0.349038i
$334$	−1.96893	+	4.91815i	−0.107735	+	0.269109i
$335$	1.83942	+	2.86219i	0.100498	+	0.156378i
$336$	−1.01872	−	2.44177i	−0.0555755	−	0.133209i
$337$	1.91013	+	0.872326i	0.104051	+	0.0475186i	0.466761	−	0.884384i	$-0.345421\pi$
$337$	1.91013	+	0.872326i	0.104051	+	0.0475186i	−0.362709	+	0.931902i	$0.618148\pi$
$338$	26.3416	−	13.5800i	1.43279	−	0.738656i
$339$	9.51257	+	9.07021i	0.516652	+	0.492626i
$340$	5.51947	−	15.9475i	0.299335	−	0.864872i
$341$	−9.21505	+	8.78654i	−0.499023	+	0.475818i
$342$	−2.30687	−	5.05133i	−0.124741	−	0.273145i
$343$	18.5029	−	0.802605i	0.999061	−	0.0433366i
$344$			6.80141i			0.366708i
$345$	−3.31464	+	10.3620i	−0.178454	+	0.557872i
$346$	11.4408	−	6.60536i	0.615062	−	0.355106i
$347$	−6.09893	+	2.44164i	−0.327408	+	0.131074i	−0.529542	−	0.848283i	$-0.677636\pi$
$347$	−6.09893	+	2.44164i	−0.327408	+	0.131074i	0.202135	+	0.979358i	$0.435212\pi$
$348$	0.123256	−	1.29079i	0.00660720	−	0.0691938i
$349$	2.14698	−	7.31195i	0.114925	−	0.391400i	−0.881861	−	0.471510i	$-0.843709\pi$
$349$	2.14698	−	7.31195i	0.114925	−	0.391400i	0.996786	+	0.0801102i	$0.0255272\pi$
$350$	0.0964895	+	0.374059i	0.00515758	+	0.0199943i
$351$	−6.26513	+	1.83961i	−0.334408	+	0.0981911i
$352$	−2.23004	−	4.32567i	−0.118861	−	0.230559i
$353$	−0.447227	−	4.68358i	−0.0238035	−	0.249282i	−0.999540	−	0.0303329i	$-0.990343\pi$
$353$	−0.447227	−	4.68358i	−0.0238035	−	0.249282i	0.975736	−	0.218949i	$-0.0702628\pi$
$354$	−12.2711	−	2.36505i	−0.652200	−	0.125701i
$355$	1.23181	+	25.8589i	0.0653779	+	1.37245i
$356$	1.69846	+	11.8131i	0.0900184	+	0.626092i
$357$	−14.6870	+	13.1027i	−0.777318	+	0.693467i
$358$	1.87889	−	1.20749i	0.0993026	−	0.0638179i
$359$	17.7068	−	6.12840i	0.934531	−	0.323444i	0.182978	−	0.983117i	$-0.441426\pi$
$359$	17.7068	−	6.12840i	0.934531	−	0.323444i	0.751553	+	0.659673i	$0.229305\pi$
$360$	−2.25821	+	0.215633i	−0.119018	+	0.0113649i
$361$	0.563256	−	11.8242i	0.0296450	−	0.622326i
$362$	−4.41489	+	18.1984i	−0.232041	+	0.956487i
$363$	9.58628	−	8.30656i	0.503149	−	0.435981i
$364$	−16.8459	−	3.82990i	−0.882965	−	0.200741i
$365$	−12.7241	+	5.81092i	−0.666012	+	0.304157i
$366$	−5.54045	+	7.04525i	−0.289604	+	0.368261i
$367$	−10.6141	−	18.3841i	−0.554050	−	0.959644i	−0.997977	−	0.0635803i	$-0.979748\pi$
$367$	−10.6141	−	18.3841i	−0.554050	−	0.959644i	0.443926	−	0.896063i	$-0.353585\pi$
$368$	−2.68731	−	3.97220i	−0.140086	−	0.207065i
$369$	−7.61628	−	4.39726i	−0.396488	−	0.228912i
$370$	−18.1943	−	2.61594i	−0.945876	−	0.135996i
$371$	7.71732	+	14.4529i	0.400663	+	0.750355i
$372$	−2.51032	−	0.737096i	−0.130154	−	0.0382167i
$373$	0.103006	+	0.534447i	0.00533346	+	0.0276726i	0.984498	−	0.175396i	$-0.0561206\pi$
$373$	0.103006	+	0.534447i	0.00533346	+	0.0276726i	−0.979164	+	0.203069i	$0.934909\pi$
$374$	−24.9836	+	26.2020i	−1.29187	+	1.35487i
$375$	−10.9987	−	0.523934i	−0.567971	−	0.0270558i
$376$	6.09632	−	4.34117i	0.314394	−	0.223879i
$377$	−6.39873	−	5.54453i	−0.329552	−	0.285558i
$378$	2.42229	+	1.06419i	0.124589	+	0.0547363i
$379$	−4.66364	+	0.670530i	−0.239555	+	0.0344428i	−0.261047	−	0.965326i	$-0.584068\pi$
$379$	−4.66364	+	0.670530i	−0.239555	+	0.0344428i	0.0214915	+	0.999769i	$0.493159\pi$
$380$	−11.6949	−	4.68192i	−0.599935	−	0.240178i
$381$	−8.48484	+	16.4583i	−0.434692	+	0.843184i
$382$	0.630340	−	3.27051i	0.0322510	−	0.167334i
$383$	7.15582	+	10.0489i	0.365646	+	0.513477i	0.955881	−	0.293754i	$-0.0949046\pi$
$383$	7.15582	+	10.0489i	0.365646	+	0.513477i	−0.590236	+	0.807231i	$0.700965\pi$
$384$	0.540641	−	0.841254i	0.0275895	−	0.0429300i
$385$	5.11283	−	28.7580i	0.260574	−	1.46564i
$386$	5.98007	+	6.90137i	0.304378	+	0.351271i
$387$	−4.69351	−	4.92241i	−0.238585	−	0.250220i
$388$	−3.32203	+	4.66514i	−0.168651	+	0.236837i
$389$	7.83340	+	19.5669i	0.397169	+	0.992080i	0.983321	+	0.181879i	$0.0582179\pi$
$389$	7.83340	+	19.5669i	0.397169	+	0.992080i	−0.586152	+	0.810201i	$0.699358\pi$
$390$	−7.40617	+	12.8279i	−0.375026	+	0.649564i
$391$	−21.3861	+	28.5566i	−1.08154	+	1.44417i
$392$	4.22347	+	5.58232i	0.213317	+	0.281950i
$393$	1.92213	−	13.3687i	0.0969587	−	0.674362i
$394$	26.2055	+	2.50232i	1.32021	+	0.126065i
$395$	−21.9465	+	5.32417i	−1.10425	+	0.267888i
$396$	4.59901	+	1.59173i	0.231109	+	0.0799875i
$397$	−32.9130	−	7.98461i	−1.65186	−	0.400736i	−0.701691	−	0.712482i	$-0.747571\pi$
$397$	−32.9130	−	7.98461i	−1.65186	−	0.400736i	−0.950166	+	0.311746i	$0.899086\pi$
$398$	7.67459	+	4.93216i	0.384693	+	0.247227i
$399$	9.24810	+	11.4165i	0.462984	+	0.571539i
$400$	−0.0956155	+	0.110346i	−0.00478077	+	0.00551731i
$401$	−27.9540	+	1.33161i	−1.39596	+	0.0664975i	−0.732015	−	0.681288i	$-0.761420\pi$
$401$	−27.9540	+	1.33161i	−1.39596	+	0.0664975i	−0.663940	+	0.747786i	$0.731117\pi$
$402$	1.17893	−	0.927120i	0.0587996	−	0.0462405i
$403$	−13.4285	+	10.5603i	−0.668921	+	0.526046i
$404$	11.0742	−	0.527530i	0.550963	−	0.0262456i
$405$	1.48554	−	1.71440i	0.0738171	−	0.0851894i
$406$	0.537248	+	3.38832i	0.0266632	+	0.168160i
$407$	33.1743	+	21.3198i	1.64439	+	1.05678i
$408$	−7.22946	−	1.75385i	−0.357912	−	0.0868284i
$409$	−19.7831	−	6.84700i	−0.978211	−	0.338562i	−0.209253	−	0.977861i	$-0.567103\pi$
$409$	−19.7831	−	6.84700i	−0.978211	−	0.338562i	−0.768958	+	0.639299i	$0.779225\pi$
$410$	−19.3879	+	4.70344i	−0.957498	+	0.232286i
$411$	8.53241	+	0.814747i	0.420873	+	0.0401885i
$412$	0.166024	−	1.15472i	0.00817941	−	0.0568891i
$413$	33.0000	−	2.05028i	1.62383	−	0.100888i
$414$	4.68603	+	1.02036i	0.230306	+	0.0501478i
$415$	2.48664	−	4.30698i	0.122064	−	0.211421i
$416$	−2.42682	−	6.06190i	−0.118985	−	0.297209i
$417$	3.80887	−	5.34881i	0.186521	−	0.261932i
$418$	18.6497	+	19.5592i	0.912185	+	0.956672i
$419$	12.4256	+	14.3400i	0.607032	+	0.700553i	0.973191	−	0.230000i	$-0.0738726\pi$
$419$	12.4256	+	14.3400i	0.607032	+	0.700553i	−0.366158	+	0.930553i	$0.619327\pi$
$420$	5.64279	−	2.04476i	0.275340	−	0.0997740i
$421$	2.14754	−	3.34163i	0.104665	−	0.162861i	−0.784971	−	0.619533i	$-0.787322\pi$
$421$	2.14754	−	3.34163i	0.104665	−	0.162861i	0.889635	+	0.456671i	$0.150959\pi$
$422$	−4.39054	−	6.16566i	−0.213728	−	0.300140i
$423$	−1.41637	+	7.34880i	−0.0688660	+	0.357311i
$424$	−2.83764	+	5.50424i	−0.137808	+	0.267310i
$425$	1.00838	+	0.403694i	0.0489135	+	0.0195820i
$426$	11.2960	−	1.62412i	0.547293	−	0.0786888i
$427$	9.53818	−	21.7105i	0.461585	−	1.05065i
$428$	−1.69540	−	1.46907i	−0.0819501	−	0.0710102i
$429$	25.8852	−	18.4328i	1.24975	−	0.889943i
$430$	−15.4114	−	0.734136i	−0.743204	−	0.0354032i
$431$	−11.8011	+	12.3766i	−0.568439	+	0.596161i	−0.943718	−	0.330750i	$-0.892698\pi$
$431$	−11.8011	+	12.3766i	−0.568439	+	0.596161i	0.375280	+	0.926912i	$0.377547\pi$
$432$	0.189251	+	0.981929i	0.00910535	+	0.0472431i
$433$	−6.42394	−	1.88624i	−0.308715	−	0.0906468i	0.123706	−	0.992319i	$-0.460522\pi$
$433$	−6.42394	−	1.88624i	−0.308715	−	0.0906468i	−0.432420	+	0.901672i	$0.642340\pi$
$434$	6.91827	+	0.229424i	0.332088	+	0.0110127i
$435$	2.91152	+	0.418613i	0.139597	+	0.0200710i
$436$	4.72077	+	2.72553i	0.226084	+	0.130529i
$437$	20.5331	+	16.9604i	0.982232	+	0.811327i
$438$	3.08317	+	5.34021i	0.147320	+	0.255165i
$439$	−7.09839	+	9.02634i	−0.338788	+	0.430804i	−0.925358	−	0.379095i	$-0.876235\pi$
$439$	−7.09839	+	9.02634i	−0.338788	+	0.430804i	0.586570	+	0.809899i	$0.300478\pi$
$440$	10.0423	−	4.58616i	0.478747	−	0.218637i
$441$	−6.90891	−	1.12559i	−0.328996	−	0.0535994i
$442$	−36.7105	+	31.8098i	−1.74614	+	1.51304i
$443$	1.90540	−	7.85417i	0.0905283	−	0.373163i	−0.908468	−	0.417954i	$-0.862747\pi$
$443$	1.90540	−	7.85417i	0.0905283	−	0.373163i	0.998996	+	0.0447915i	$0.0142624\pi$
$444$	−0.385554	+	8.09376i	−0.0182976	+	0.384113i
$445$	−26.9507	+	2.57348i	−1.27759	+	0.121995i
$446$	13.7501	−	4.75894i	0.651084	−	0.225342i
$447$	2.80315	−	1.80148i	0.132585	−	0.0852070i
$448$	−0.829123	+	2.51248i	−0.0391724	+	0.118704i
$449$	−0.273309	−	1.90091i	−0.0128982	−	0.0897093i	0.982355	−	0.187023i	$-0.0598840\pi$
$449$	−0.273309	−	1.90091i	−0.0128982	−	0.0897093i	−0.995254	+	0.0973140i	$0.968975\pi$
$450$	−0.00694738	−	0.145843i	−0.000327503	−	0.00687513i
$451$	42.0266	+	8.09996i	1.97895	+	0.381412i
$452$	−1.24939	−	13.0842i	−0.0587664	−	0.615430i
$453$	−4.16214	−	8.07342i	−0.195554	−	0.379323i
$454$	−0.356866	+	0.104785i	−0.0167486	+	0.00491782i
$455$	10.4965	−	37.7579i	0.492086	−	1.77012i
$456$	−1.56451	+	5.32822i	−0.0732647	+	0.249517i
$457$	−3.04037	+	31.8402i	−0.142223	+	1.48942i	0.589471	+	0.807789i	$0.299336\pi$
$457$	−3.04037	+	31.8402i	−0.142223	+	1.48942i	−0.731694	+	0.681634i	$0.761270\pi$
$458$	−14.5757	+	5.83524i	−0.681079	+	0.272663i
$459$	6.44250	−	3.71958i	0.300710	−	0.173615i
$460$	9.29072	−	5.66046i	0.433182	−	0.263920i
$461$		−	0.0720510i		−	0.00335575i	−0.999999	−	0.00167788i	$-0.999466\pi$
$461$		−	0.0720510i		−	0.00335575i	0.999999	−	0.00167788i	$-0.000534085\pi$
$462$	−12.8340	−	1.03860i	−0.597093	−	0.0483202i
$463$	−7.54559	−	16.5225i	−0.350673	−	0.767868i	−0.999973	−	0.00733507i	$-0.997665\pi$
$463$	−7.54559	−	16.5225i	−0.350673	−	0.767868i	0.649300	−	0.760533i	$-0.275062\pi$
$464$	−0.938440	+	0.894801i	−0.0435660	+	0.0415401i
$465$	1.94116	−	5.60860i	0.0900189	−	0.260093i
$466$	20.7581	+	19.7928i	0.961600	+	0.916883i
$467$	15.4706	−	7.97567i	0.715896	−	0.369070i	−0.0614781	−	0.998108i	$-0.519581\pi$
$467$	15.4706	−	7.97567i	0.715896	−	0.369070i	0.777374	+	0.629038i	$0.216551\pi$
$468$	5.93956	+	2.71251i	0.274556	+	0.125386i
$469$	−2.40760	+	3.15427i	−0.111173	+	0.145651i
$470$	9.17869	+	14.2823i	0.423381	+	0.658794i
$471$	2.41204	−	6.02499i	0.111141	−	0.277617i
$472$	7.72507	+	9.82322i	0.355575	+	0.452151i
$473$	29.4207	+	15.1674i	1.35276	+	0.697398i
$474$	3.25602	+	9.40764i	0.149554	+	0.432107i
$475$	0.336823	−	0.737540i	0.0154545	−	0.0338406i
$476$	19.6801	−	0.284398i	0.902036	−	0.0130354i
$477$	−1.74467	−	5.94180i	−0.0798830	−	0.272056i
$478$	6.07315	−	1.17050i	0.277779	−	0.0535376i
$479$	−3.71595	−	15.3174i	−0.169786	−	0.699868i	−0.991515	−	0.129990i	$-0.958506\pi$
$479$	−3.71595	−	15.3174i	−0.169786	−	0.699868i	0.821729	−	0.569878i	$-0.193010\pi$
$480$	1.84785	+	1.31585i	0.0843425	+	0.0600600i
$481$	41.5895	+	32.7063i	1.89632	+	1.49128i
$482$	−12.3006			−0.560278
$483$	−12.6794	+	0.482703i	−0.576932	+	0.0219637i
$484$	−12.6845			−0.576566
$485$	−10.2122	−	8.03098i	−0.463713	−	0.364668i
$486$	−0.814576	−	0.580057i	−0.0369499	−	0.0263119i
$487$	−6.53911	−	26.9546i	−0.296315	−	1.22143i	−0.904098	−	0.427325i	$-0.859456\pi$
$487$	−6.53911	−	26.9546i	−0.296315	−	1.22143i	0.607783	−	0.794103i	$-0.292059\pi$
$488$	8.80085	−	1.69622i	0.398396	−	0.0767845i
$489$	−1.62075	−	5.51977i	−0.0732929	−	0.249613i
$490$	−13.1049	+	8.96746i	−0.592020	+	0.405109i
$491$	−10.9482	+	23.9733i	−0.494087	+	1.08190i	0.484259	+	0.874924i	$0.339089\pi$
$491$	−10.9482	+	23.9733i	−0.494087	+	1.08190i	−0.978346	+	0.206975i	$0.933638\pi$
$492$	2.87641	+	8.31083i	0.129678	+	0.374681i
$493$	8.57379	+	4.42010i	0.386144	+	0.199071i
$494$	22.4145	+	28.5024i	1.00848	+	1.28238i
$495$	−4.10313	+	10.2491i	−0.184422	+	0.460664i
$496$	1.41448	+	2.20097i	0.0635119	+	0.0988264i
$497$	−27.8658	+	11.6257i	−1.24995	+	0.521486i
$498$	−1.99422	−	0.910729i	−0.0893631	−	0.0408108i
$499$	−31.5638	+	16.2723i	−1.41299	+	0.728446i	−0.984547	−	0.175123i	$-0.943968\pi$
$499$	−31.5638	+	16.2723i	−1.41299	+	0.728446i	−0.428442	+	0.903569i	$0.640938\pi$
$500$	7.96917	+	7.59859i	0.356392	+	0.339819i
$501$	−1.73269	+	5.00627i	−0.0774107	+	0.223663i
$502$	−8.62849	+	8.22725i	−0.385108	+	0.367200i
$503$	2.24885	+	4.92430i	0.100271	+	0.219564i	0.953119	−	0.302597i	$-0.0978535\pi$
$503$	2.24885	+	4.92430i	0.100271	+	0.219564i	−0.852847	+	0.522160i	$0.825126\pi$
$504$	−1.13375	−	2.39053i	−0.0505010	−	0.106483i
$505$			25.1502i			1.11917i
$506$	−23.1752	+	2.76627i	−1.03026	+	0.122976i
$507$	25.6656	−	14.8180i	1.13985	−	0.658092i
$508$	17.1903	−	6.88196i	0.762697	−	0.305338i
$509$	1.99185	−	20.8596i	0.0882872	−	0.924585i	−0.837474	−	0.546477i	$-0.815969\pi$
$509$	1.99185	−	20.8596i	0.0882872	−	0.924585i	0.925761	−	0.378108i	$-0.123425\pi$
$510$	4.75441	−	16.1920i	0.210529	−	0.716995i
$511$	−11.4278	−	11.6435i	−0.505536	−	0.515079i
$512$	−0.959493	+	0.281733i	−0.0424040	+	0.0124509i
$513$	−2.54461	−	4.93585i	−0.112347	−	0.217923i
$514$	2.37566	+	24.8791i	0.104786	+	1.09737i
$515$	2.59858	+	0.500835i	0.114507	+	0.0220694i
$516$	0.323624	+	6.79371i	0.0142468	+	0.299076i
$517$	−5.18344	−	36.0516i	−0.227968	−	1.58555i
$518$	−4.36099	−	20.9901i	−0.191611	−	0.922253i
$519$	11.1136	−	7.14225i	0.487831	−	0.313510i
$520$	13.9977	−	4.84464i	0.613839	−	0.212452i
$521$	−35.3193	+	3.37259i	−1.54737	+	0.147756i	−0.833498	−	0.552523i	$-0.813665\pi$
$521$	−35.3193	+	3.37259i	−1.54737	+	0.147756i	−0.713870	+	0.700279i	$0.753059\pi$
$522$	0.0616978	−	1.29520i	0.00270044	−	0.0566892i
$523$	−7.77302	+	32.0408i	−0.339890	+	1.40105i	0.503616	+	0.863928i	$0.332003\pi$
$523$	−7.77302	+	32.0408i	−0.339890	+	1.40105i	−0.843506	+	0.537120i	$0.819512\pi$
$524$	−10.2073	+	8.84467i	−0.445908	+	0.386381i
$525$	0.114179	+	0.369044i	0.00498316	+	0.0161064i
$526$	0.697522	−	0.318548i	0.0304134	−	0.0138893i
$527$	12.0313	−	15.2990i	0.524090	−	0.666435i
$528$	−2.43333	−	4.21466i	−0.105897	−	0.183419i
$529$	−22.3538	+	5.41358i	−0.971905	+	0.235373i
$530$	−12.1658	−	7.02395i	−0.528450	−	0.305101i
$531$	−12.3697	−	1.77849i	−0.536799	−	0.0771801i
$532$	0.486958	−	14.6842i	0.0211123	−	0.636641i
$533$	55.0989	+	16.1785i	2.38660	+	0.700768i
$534$	2.25863	+	11.7189i	0.0977404	+	0.507125i
$535$	3.51178	−	3.68305i	0.151828	−	0.159232i
$536$	−1.49811	−	0.0713637i	−0.0647085	−	0.00308244i
$537$	1.81931	−	1.29552i	0.0785090	−	0.0559060i
$538$	16.0949	+	13.9463i	0.693902	+	0.601270i
$539$	33.5658	−	5.82054i	1.44578	−	0.250709i
$540$	−2.24539	+	0.322839i	−0.0966263	+	0.0138928i
$541$	18.2928	+	7.32333i	0.786469	+	0.314855i	0.729909	−	0.683545i	$-0.239563\pi$
$541$	18.2928	+	7.32333i	0.786469	+	0.314855i	0.0565600	+	0.998399i	$0.481987\pi$
$542$	8.27511	−	16.0515i	0.355447	−	0.689470i
$543$	−3.54397	+	18.3879i	−0.152086	+	0.789099i
$544$	4.31514	+	6.05976i	0.185010	+	0.259810i
$545$	−6.68538	+	10.4026i	−0.286370	+	0.445600i
$546$	−17.0091	−	3.02400i	−0.727920	−	0.129415i
$547$	−12.0582	−	13.9160i	−0.515573	−	0.595003i	0.436944	−	0.899489i	$-0.356061\pi$
$547$	−12.0582	−	13.9160i	−0.515573	−	0.595003i	−0.952517	+	0.304486i	$0.901515\pi$
$548$	−5.91482	−	6.20329i	−0.252669	−	0.264991i
$549$	−5.19894	+	7.30089i	−0.221886	+	0.311595i
$550$	0.264095	+	0.659677i	0.0112610	+	0.0281287i
$551$	3.60029	−	6.23589i	0.153378	−	0.265658i
$552$	−2.87327	−	3.83983i	−0.122295	−	0.163434i
$553$	−14.5586	−	21.9496i	−0.619093	−	0.933392i
$554$	1.76079	−	12.2466i	0.0748089	−	0.520307i
$555$	−18.2981	−	1.74726i	−0.776713	−	0.0741671i
$556$	−6.38128	+	1.54808i	−0.270626	+	0.0656533i
$557$	−15.1361	−	5.23865i	−0.641337	−	0.221969i	−0.0130066	−	0.999915i	$-0.504140\pi$
$557$	−15.1361	−	5.23865i	−0.641337	−	0.221969i	−0.628331	+	0.777946i	$0.716261\pi$
$558$	−2.54255	−	0.616815i	−0.107635	−	0.0261119i
$559$	37.3607	+	24.0102i	1.58019	+	1.01553i
$560$	−5.60356	−	2.14991i	−0.236794	−	0.0908504i
$561$	−23.7085	+	27.3611i	−1.00097	+	1.15519i
$562$	−6.05712	+	0.288536i	−0.255504	+	0.0121712i
$563$	20.8113	−	16.3662i	0.877091	−	0.689752i	−0.0744662	−	0.997224i	$-0.523725\pi$
$563$	20.8113	−	16.3662i	0.877091	−	0.689752i	0.951557	+	0.307471i	$0.0994829\pi$
$564$	5.88286	−	4.62633i	0.247713	−	0.194804i
$565$	29.7825	−	1.41872i	1.25296	−	0.0596859i
$566$	0.0390350	−	0.0450488i	0.00164076	−	0.00189354i
$567$	2.47018	+	0.947732i	0.103738	+	0.0398010i
$568$	−9.60052	−	6.16988i	−0.402829	−	0.258882i
$569$	11.2077	+	2.71896i	0.469852	+	0.113985i	0.463693	−	0.885996i	$-0.346524\pi$
$569$	11.2077	+	2.71896i	0.469852	+	0.113985i	0.00615960	+	0.999981i	$0.498039\pi$
$570$	−11.9044	−	4.12016i	−0.498621	−	0.172574i
$571$	14.0036	−	3.39725i	0.586034	−	0.142170i	0.0682303	−	0.997670i	$-0.478265\pi$
$571$	14.0036	−	3.39725i	0.586034	−	0.142170i	0.517804	+	0.855499i	$0.326750\pi$
$572$	−31.6337	−	3.02065i	−1.32267	−	0.126300i
$573$	0.474009	−	3.29680i	0.0198020	−	0.137726i
$574$	−12.8612	−	19.3906i	−0.536817	−	0.809347i
$575$	0.335464	+	0.614647i	0.0139898	+	0.0256326i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	14.3778	+	35.9140i	0.598556	+	1.49512i	0.849752	+	0.527183i	$0.176752\pi$
$577$	14.3778	+	35.9140i	0.598556	+	1.49512i	−0.251196	+	0.967936i	$0.580824\pi$
$578$	22.2400	−	31.2317i	0.925063	−	1.29907i
$579$	6.30168	+	6.60901i	0.261889	+	0.274661i
$580$	−1.92625	−	2.22301i	−0.0799830	−	0.0923053i
$581$	5.71082	+	1.01532i	0.236925	+	0.0421224i
$582$	−3.09629	+	4.81793i	−0.128346	+	0.199710i
$583$	17.4815	+	24.5493i	0.724010	+	1.01673i
$584$	1.16699	−	6.05490i	0.0482903	−	0.250554i
$585$	−6.78741	+	13.1657i	−0.280625	+	0.544336i
$586$	−1.45899	−	0.584091i	−0.0602703	−	0.0241286i
$587$	−18.2538	+	2.62450i	−0.753414	+	0.108325i	−0.508312	−	0.861173i	$-0.669730\pi$
$587$	−18.2538	+	2.62450i	−0.753414	+	0.108325i	−0.245101	+	0.969497i	$0.578821\pi$
$588$	4.48430	+	5.37504i	0.184930	+	0.221663i
$589$	−10.9801	−	9.51429i	−0.452426	−	0.392029i
$590$	−23.0924	+	16.4440i	−0.950699	+	0.676990i
$591$	26.2949	+	1.25258i	1.08163	+	0.0515242i
$592$	5.59167	−	5.86438i	0.229816	−	0.241024i
$593$	−3.79094	−	19.6692i	−0.155675	−	0.807719i	−0.972869	−	0.231356i	$-0.925684\pi$
$593$	−3.79094	−	19.6692i	−0.155675	−	0.807719i	0.817194	−	0.576363i	$-0.195528\pi$
$594$	4.66953	+	1.37110i	0.191593	+	0.0562569i
$595$	−1.47982	+	44.6241i	−0.0606669	+	1.82941i
$596$	−3.29820	−	0.474210i	−0.135100	−	0.0194244i
$597$	7.90058	+	4.56140i	0.323349	+	0.186686i
$598$	−31.3063	+	0.739011i	−1.28021	+	0.0302204i
$599$	−1.91426	−	3.31559i	−0.0782144	−	0.135471i	0.824265	−	0.566204i	$-0.191589\pi$
$599$	−1.91426	−	3.31559i	−0.0782144	−	0.135471i	−0.902480	+	0.430733i	$0.858255\pi$
$600$	−0.0902567	+	0.114771i	−0.00368471	+	0.00468550i
$601$	−40.5904	+	18.5370i	−1.65572	+	0.756141i	−0.655719	+	0.755005i	$0.727634\pi$
$601$	−40.5904	+	18.5370i	−1.65572	+	0.756141i	−0.999999	+	0.00113611i	$0.999638\pi$
$602$	−5.31869	−	17.1909i	−0.216774	−	0.700648i
$603$	1.13348	−	0.982165i	0.0461588	−	0.0399969i
$604$	−2.14143	+	8.82711i	−0.0871337	+	0.359170i
$605$	1.36914	−	28.7419i	0.0556636	−	1.16852i
$606$	11.0366	−	1.05387i	0.448330	−	0.0428103i
$607$	−26.0124	+	9.00297i	−1.05581	+	0.365419i	−0.799181	−	0.601091i	$-0.794733\pi$
$607$	−26.0124	+	9.00297i	−1.05581	+	0.365419i	−0.256629	+	0.966510i	$0.582612\pi$
$608$	4.67162	−	3.00227i	0.189459	−	0.121758i
$609$	0.697863	+	3.35892i	0.0282788	+	0.136110i
$610$	2.89354	+	20.1250i	0.117156	+	0.814839i
$611$	−2.32524	−	48.8127i	−0.0940690	−	1.97475i
$612$	−7.30472	−	1.40787i	−0.295276	−	0.0569098i
$613$	2.48540	+	26.0283i	0.100384	+	1.05127i	0.895575	+	0.444911i	$0.146765\pi$
$613$	2.48540	+	26.0283i	0.100384	+	1.05127i	−0.795190	+	0.606360i	$0.792629\pi$
$614$	1.68228	+	3.26316i	0.0678912	+	0.131691i
$615$	−19.1421	+	5.62063i	−0.771884	+	0.226646i
$616$	9.01918	+	9.18943i	0.363393	+	0.370253i
$617$	9.20720	−	31.3568i	0.370668	−	1.26238i	−0.537319	−	0.843379i	$-0.680563\pi$
$617$	9.20720	−	31.3568i	0.370668	−	1.26238i	0.907986	−	0.419000i	$-0.137619\pi$
$618$	0.110892	−	1.16131i	0.00446073	−	0.0467149i
$619$	9.70283	−	3.88443i	0.389990	−	0.156128i	−0.168377	−	0.985723i	$-0.553853\pi$
$619$	9.70283	−	3.88443i	0.389990	−	0.156128i	0.558367	+	0.829594i	$0.311428\pi$
$620$	−5.13988	+	2.96751i	−0.206423	+	0.119178i
$621$	4.72927	+	0.796232i	0.189779	+	0.0319517i
$622$		−	15.1357i		−	0.606886i
$623$	−13.5307	−	28.5299i	−0.542098	−	1.14303i
$624$	−2.71251	−	5.93956i	−0.108587	−	0.237773i
$625$	−18.6063	+	17.7411i	−0.744251	+	0.709642i
$626$	7.98012	−	23.0570i	0.318950	−	0.921545i
$627$	19.5592	+	18.6497i	0.781119	+	0.744796i
$628$	−5.76843	+	2.97383i	−0.230186	+	0.118669i
$629$	−54.8318	−	25.0408i	−2.18629	−	0.998444i
$630$	5.53910	−	2.31094i	0.220683	−	0.0920699i
$631$	−16.3475	−	25.4373i	−0.650786	−	1.01264i	−0.997216	−	0.0745666i	$-0.976243\pi$
$631$	−16.3475	−	25.4373i	−0.650786	−	1.01264i	0.346430	−	0.938076i	$-0.387394\pi$
$632$	3.69996	−	9.24206i	0.147177	−	0.367629i
$633$	−4.67895	−	5.94976i	−0.185971	−	0.236482i
$634$	7.04773	+	3.63336i	0.279901	+	0.144299i
$635$	13.7384	+	39.6946i	0.545193	+	1.57523i
$636$	−2.57252	+	5.63303i	−0.102007	+	0.223364i
$637$	45.5737	−	3.49321i	1.80570	−	0.138406i
$638$	1.77785	+	6.05482i	0.0703860	+	0.239713i
$639$	11.2059	−	2.15977i	0.443300	−	0.0854390i
$640$	−0.534815	−	2.20454i	−0.0211404	−	0.0871420i
$641$	7.99113	+	5.69046i	0.315631	+	0.224759i	0.726882	−	0.686762i	$-0.240969\pi$
$641$	7.99113	+	5.69046i	0.315631	+	0.224759i	−0.411251	+	0.911522i	$0.634908\pi$
$642$	−1.76338	−	1.38674i	−0.0695950	−	0.0547301i
$643$	30.9734			1.22147			0.610736	−	0.791834i	$-0.290874\pi$
$643$	30.9734			1.22147			0.610736	+	0.791834i	$0.290874\pi$
$644$	9.89855	+	7.93843i	0.390057	+	0.312818i
$645$	−15.4289			−0.607512
$646$	−32.4725	−	25.5367i	−1.27761	−	1.00473i
$647$	−3.30908	−	2.35638i	−0.130093	−	0.0926390i	0.513158	−	0.858294i	$-0.328476\pi$
$647$	−3.30908	−	2.35638i	−0.130093	−	0.0926390i	−0.643251	+	0.765655i	$0.722415\pi$
$648$	0.235759	+	0.971812i	0.00926149	+	0.0381764i
$649$	59.7192	−	11.5099i	2.34418	−	0.451804i
$650$	0.268599	+	0.914765i	0.0105353	+	0.0358800i
$651$	6.92135	−	0.100021i	0.271269	−	0.00392013i
$652$	−2.38980	+	5.23293i	−0.0935918	+	0.204937i
$653$	5.34520	+	15.4439i	0.209174	+	0.604368i	0.999970	−	0.00771143i	$-0.00245465\pi$
$653$	5.34520	+	15.4439i	0.209174	+	0.604368i	−0.790797	+	0.612079i	$0.790333\pi$
$654$	4.84510	+	2.49782i	0.189459	+	0.0976727i
$655$	−18.9395	−	24.0835i	−0.740027	−	0.941021i
$656$	3.26860	−	8.16456i	0.127617	−	0.318772i
$657$	3.33377	+	5.18745i	0.130063	+	0.202382i
$658$	−12.0139	+	15.7398i	−0.468352	+	0.613602i
$659$	−28.0512	−	12.8105i	−1.09272	−	0.499028i	−0.214226	−	0.976784i	$-0.568723\pi$
$659$	−28.0512	−	12.8105i	−1.09272	−	0.499028i	−0.878492	+	0.477757i	$0.841450\pi$
$660$	9.81270	−	5.05880i	0.381959	−	0.196913i
$661$	13.6444	+	13.0099i	0.530705	+	0.506026i	0.907375	−	0.420321i	$-0.138083\pi$
$661$	13.6444	+	13.0099i	0.530705	+	0.506026i	−0.376670	+	0.926347i	$0.622931\pi$
$662$	−1.93340	+	5.58618i	−0.0751436	+	0.217113i
$663$	−35.1554	+	33.5206i	−1.36532	+	1.30183i
$664$	0.910729	+	1.99422i	0.0353432	+	0.0773907i
$665$	33.2206	+	2.68840i	1.28824	+	0.104252i
$666$			8.10294i			0.313983i
$667$	2.44681	+	5.71698i	0.0947409	+	0.221362i
$668$	4.58788	−	2.64882i	0.177511	−	0.102486i
$669$	13.5080	−	5.40780i	0.522251	−	0.209078i
$670$	0.323408	−	3.38688i	0.0124943	−	0.130847i
$671$	12.2889	−	41.8522i	0.474408	−	1.61569i
$672$	−0.708635	+	2.54909i	−0.0273362	+	0.0983331i
$673$	−23.2976	+	6.84080i	−0.898058	+	0.263694i	−0.698006	−	0.716092i	$-0.745929\pi$
$673$	−23.2976	+	6.84080i	−0.898058	+	0.263694i	−0.200052	+	0.979785i	$0.564111\pi$
$674$	−0.962225	−	1.86646i	−0.0370635	−	0.0718932i
$675$	−0.0138790	−	0.145348i	−0.000534204	−	0.00559444i
$676$	−29.1005	−	5.60866i	−1.11925	−	0.215718i
$677$	0.990332	+	20.7896i	0.0380616	+	0.799011i	0.934526	+	0.355895i	$0.115824\pi$
$677$	0.990332	+	20.7896i	0.0380616	+	0.799011i	−0.896464	+	0.443116i	$0.853873\pi$
$678$	−1.87055	−	13.0099i	−0.0718380	−	0.499644i
$679$	4.74845	−	14.3892i	0.182229	−	0.552206i
$680$	−14.1967	+	9.12364i	−0.544417	+	0.349876i
$681$	−0.351476	+	0.121647i	−0.0134686	+	0.00466153i
$682$	12.6750	−	1.21032i	0.485351	−	0.0463454i
$683$	−0.636017	+	13.3516i	−0.0243365	+	0.510886i	0.953484	+	0.301443i	$0.0974682\pi$
$683$	−0.636017	+	13.3516i	−0.0243365	+	0.510886i	−0.977821	+	0.209443i	$0.932835\pi$
$684$	−1.30921	+	5.39663i	−0.0500588	+	0.206345i
$685$	14.6945	−	12.7329i	0.561450	−	0.486499i
$686$	−15.0404	−	10.8068i	−0.574244	−	0.412606i
$687$	−14.2816	+	6.52217i	−0.544876	+	0.248836i
$688$	4.20435	−	5.34627i	0.160290	−	0.203825i
$689$	20.2178	+	35.0183i	0.770239	+	1.33409i
$690$	9.01086	−	6.09612i	0.343037	−	0.232075i
$691$	−20.9107	−	12.0728i	−0.795481	−	0.459271i	0.0464076	−	0.998923i	$-0.485223\pi$
$691$	−20.9107	−	12.0728i	−0.795481	−	0.459271i	−0.841889	+	0.539651i	$0.818556\pi$
$692$	−13.0762	−	1.88008i	−0.497084	−	0.0714699i
$693$	−12.8689	−	0.426759i	−0.488850	−	0.0162112i
$694$	6.30341	+	1.85085i	0.239274	+	0.0702572i
$695$	−2.81903	−	14.6265i	−0.106932	−	0.554815i
$696$	−0.894801	+	0.938440i	−0.0339173	+	0.0355715i
$697$	−65.3498	−	3.11299i	−2.47530	−	0.117913i
$698$	−6.20759	+	4.42041i	−0.234961	+	0.167315i
$699$	21.6763	+	18.7827i	0.819875	+	0.710426i
$700$	0.155382	−	0.353676i	0.00587288	−	0.0133677i
$701$	−0.455142	+	0.0654395i	−0.0171905	+	0.00247161i	−0.150905	−	0.988548i	$-0.548219\pi$
$701$	−0.455142	+	0.0654395i	−0.0171905	+	0.00247161i	0.133714	+	0.991020i	$0.457310\pi$
$702$	6.06190	+	2.42682i	0.228792	+	0.0915944i
$703$	−20.6188	+	39.9949i	−0.777653	+	1.50844i
$704$	−0.921023	+	4.77872i	−0.0347124	+	0.180105i
$705$	9.84787	+	13.8294i	0.370892	+	0.520845i
$706$	−2.54365	+	3.95800i	−0.0957316	+	0.148961i
$707$	−27.5781	+	9.99337i	−1.03718	+	0.375839i
$708$	8.18373	+	9.44452i	0.307563	+	0.354947i
$709$	−9.14847	−	9.59464i	−0.343578	−	0.360334i	0.529161	−	0.848522i	$-0.322507\pi$
$709$	−9.14847	−	9.59464i	−0.343578	−	0.360334i	−0.872739	+	0.488187i	$0.837658\pi$
$710$	15.0167	−	21.0880i	0.563566	−	0.791417i
$711$	3.69996	+	9.24206i	0.138759	+	0.346604i
$712$	5.96727	−	10.3356i	0.223633	−	0.387344i
$713$	12.2611	−	2.66469i	0.459182	−	0.0997935i
$714$	19.6443	−	1.22049i	0.735169	−	0.0456758i
$715$	10.2590	−	71.3530i	0.383665	−	2.66845i
$716$	−2.22333	−	0.212302i	−0.0830898	−	0.00793411i
$717$	6.01057	−	1.45815i	0.224469	−	0.0544556i
$718$	−17.7068	−	6.12840i	−0.660813	−	0.228710i
$719$	−28.0499	−	6.80482i	−1.04608	−	0.253777i	−0.324342	−	0.945940i	$-0.605143\pi$
$719$	−28.0499	−	6.80482i	−1.04608	−	0.253777i	−0.721741	+	0.692163i	$0.756658\pi$
$720$	1.90837	+	1.22643i	0.0711207	+	0.0457065i
$721$	0.483357	+	3.04844i	0.0180012	+	0.113530i
$722$	−7.75198	+	8.94626i	−0.288499	+	0.332945i
$723$	−12.2867	+	0.585288i	−0.456947	+	0.0217671i
$724$	14.7198	−	11.5758i	0.547059	−	0.430212i
$725$	0.148819	−	0.117033i	0.00552700	−	0.00434648i
$726$	−12.6701	+	0.603551i	−0.470231	+	0.0223999i
$727$	30.9756	−	35.7477i	1.14882	−	1.32581i	0.211486	−	0.977381i	$-0.432170\pi$
$727$	30.9756	−	35.7477i	1.14882	−	1.32581i	0.937335	−	0.348429i	$-0.113285\pi$
$728$	10.8743	+	13.4240i	0.403028	+	0.497525i
$729$	−0.841254	−	0.540641i	−0.0311575	−	0.0200237i
$730$	13.5939	+	3.29785i	0.503134	+	0.122059i
$731$	−47.8140	−	16.5486i	−1.76847	−	0.612072i
$732$	8.71017	−	2.11306i	0.321937	−	0.0781011i
$733$	−36.6975	−	3.50418i	−1.35545	−	0.129430i	−0.608101	−	0.793860i	$-0.708068\pi$
$733$	−36.6975	−	3.50418i	−1.35545	−	0.129430i	−0.747351	+	0.664430i	$0.768675\pi$
$734$	−3.02108	+	21.0121i	−0.111510	+	0.775570i
$735$	−12.6634	+	9.58086i	−0.467096	+	0.353395i
$736$	−0.343080	+	4.78354i	−0.0126461	+	0.176324i
$737$	−3.64953	+	6.32118i	−0.134432	+	0.232844i
$738$	3.26860	+	8.16456i	0.120319	+	0.300541i
$739$	−15.0821	+	21.1798i	−0.554802	+	0.779111i	−0.992790	−	0.119870i	$-0.961752\pi$
$739$	−15.0821	+	21.1798i	−0.554802	+	0.779111i	0.437987	+	0.898981i	$0.355692\pi$
$740$	12.6846	+	13.3032i	0.466295	+	0.489036i
$741$	23.7453	+	27.4035i	0.872306	+	1.00669i
$742$	2.86794	−	16.1312i	0.105285	−	0.592197i
$743$	2.50920	−	3.90440i	0.0920538	−	0.143239i	−0.792172	−	0.610297i	$-0.791050\pi$
$743$	2.50920	−	3.90440i	0.0920538	−	0.143239i	0.884226	+	0.467059i	$0.154686\pi$
$744$	1.51760	+	2.13117i	0.0556380	+	0.0781326i
$745$	1.43052	−	7.42225i	0.0524102	−	0.271930i
$746$	0.249405	−	0.483778i	0.00913136	−	0.0177124i
$747$	−2.03529	−	0.814809i	−0.0744675	−	0.0298123i
$748$	35.8354	−	5.15236i	1.31027	−	0.188389i
$749$	5.43400	+	2.38734i	0.198554	+	0.0872316i
$750$	8.32170	+	7.21080i	0.303866	+	0.263301i
$751$	−19.9586	+	14.2124i	−0.728299	+	0.518619i	−0.883018	−	0.469339i	$-0.844492\pi$
$751$	−19.9586	+	14.2124i	−0.728299	+	0.518619i	0.154719	+	0.987959i	$0.450553\pi$
$752$	−7.47557	−	0.356105i	−0.272606	−	0.0129858i
$753$	−8.22725	+	8.62849i	−0.299818	+	0.314440i
$754$	1.60234	+	8.31373i	0.0583538	+	0.302768i
$755$	−19.7703	−	5.80509i	−0.719515	−	0.211269i
$756$	−1.24621	−	2.33387i	−0.0453241	−	0.0848822i
$757$	21.8957	+	3.14813i	0.795814	+	0.114421i	0.528216	−	0.849110i	$-0.322861\pi$
$757$	21.8957	+	3.14813i	0.795814	+	0.114421i	0.267598	+	0.963531i	$0.413770\pi$
$758$	4.08036	+	2.35580i	0.148205	+	0.0855664i
$759$	−23.0173	+	3.86586i	−0.835476	+	0.140322i
$760$	6.29862	+	10.9095i	0.228475	+	0.395730i
$761$	31.3770	−	39.8991i	1.13741	−	1.44634i	0.260640	−	0.965436i	$-0.416066\pi$
$761$	31.3770	−	39.8991i	1.13741	−	1.44634i	0.876774	−	0.480903i	$-0.159691\pi$
$762$	16.8434	−	7.69212i	0.610171	−	0.278656i
$763$	−14.0633	−	3.19728i	−0.509126	−	0.115749i
$764$	−2.51718	+	2.18115i	−0.0910683	+	0.0789112i
$765$	3.97857	−	16.3999i	0.143846	−	0.592940i
$766$	0.586990	−	12.3224i	0.0212088	−	0.445228i
$767$	81.2306	−	7.75658i	2.93307	−	0.280074i
$768$	−0.945001	+	0.327068i	−0.0340998	+	0.0118020i
$769$	40.7002	−	26.1564i	1.46769	−	0.943225i	0.469506	−	0.882929i	$-0.344432\pi$
$769$	40.7002	−	26.1564i	1.46769	−	0.943225i	0.998181	−	0.0602958i	$-0.0192044\pi$
$770$	−21.7960	+	19.4448i	−0.785472	+	0.700741i
$771$	3.55677	+	24.7379i	0.128094	+	0.890913i
$772$	−0.434510	−	9.12148i	−0.0156383	−	0.328289i
$773$	38.8176	+	7.48148i	1.39617	+	0.269090i	0.831179	−	0.556005i	$-0.187667\pi$
$773$	38.8176	+	7.48148i	1.39617	+	0.269090i	0.564993	+	0.825095i	$0.308879\pi$
$774$	0.646515	+	6.77062i	0.0232385	+	0.243365i
$775$	−0.175044	−	0.339537i	−0.00628776	−	0.0121965i
$776$	5.49509	−	1.61351i	0.197262	−	0.0579215i
$777$	−5.35480	−	20.7589i	−0.192102	−	0.744720i
$778$	5.93798	−	20.2229i	0.212887	−	0.725026i
$779$	−4.64229	+	48.6163i	−0.166327	+	1.74186i
$780$	13.7513	−	5.50519i	0.492376	−	0.197118i
$781$	−48.0984	+	27.7696i	−1.72109	+	0.993674i
$782$	34.4631	−	9.22704i	1.23240	−	0.329958i
$783$		−	1.29666i		−	0.0463390i
$784$	0.130891	−	6.99878i	0.00467467	−	0.249956i
$785$	−6.11581	−	13.3918i	−0.218283	−	0.477972i
$786$	−9.77489	+	9.32034i	−0.348659	+	0.332445i
$787$	15.8237	−	45.7196i	0.564054	−	1.62973i	−0.196538	−	0.980496i	$-0.562970\pi$
$787$	15.8237	−	45.7196i	0.564054	−	1.62973i	0.760592	−	0.649231i	$-0.224909\pi$
$788$	−19.0521	−	18.1661i	−0.678702	−	0.647141i
$789$	0.681575	−	0.351376i	0.0242647	−	0.0125093i
$790$	20.5423	+	9.38136i	0.730863	+	0.333774i
$791$	13.3897	+	32.0939i	0.476084	+	1.14113i
$792$	−2.63112	−	4.09410i	−0.0934928	−	0.145478i
$793$	21.7511	−	54.3317i	0.772405	−	1.92937i
$794$	20.9356	+	26.6218i	0.742977	+	0.944772i
$795$	−12.4863	−	6.43712i	−0.442843	−	0.228301i
$796$	−2.98378	−	8.62106i	−0.105757	−	0.305565i
$797$	−5.74306	+	12.5755i	−0.203430	+	0.445449i	−0.983658	−	0.180046i	$-0.942375\pi$
$797$	−5.74306	+	12.5755i	−0.203430	+	0.445449i	0.780229	+	0.625494i	$0.215103\pi$
$798$	−0.212297	−	14.6908i	−0.00751523	−	0.520047i
$799$	15.6855	+	53.4198i	0.554912	+	1.88986i
$800$	0.143370	−	0.0276324i	0.00506891	−	0.000976951i
$801$	2.81368	+	11.5981i	0.0994164	+	0.409800i
$802$	22.7965	+	16.2333i	0.804971	+	0.573217i
$803$	−23.5891	−	18.5507i	−0.832441	−	0.654639i
$804$	−1.49981			−0.0528942
$805$	−19.0562	+	21.5724i	−0.671644	+	0.760326i
$806$	17.0835			0.601739
$807$	16.7403	+	13.1647i	0.589287	+	0.463420i
$808$	−9.03102	−	6.43096i	−0.317710	−	0.226240i
$809$	0.601750	+	2.48045i	0.0211564	+	0.0872079i	0.981411	−	0.191918i	$-0.0614706\pi$
$809$	0.601750	+	2.48045i	0.0211564	+	0.0872079i	−0.960255	+	0.279125i	$0.909955\pi$
$810$	−2.22749	+	0.429313i	−0.0782659	+	0.0150845i
$811$	−5.31157	−	18.0895i	−0.186514	−	0.635210i	−0.998660	−	0.0517546i	$-0.983519\pi$
$811$	−5.31157	−	18.0895i	−0.186514	−	0.635210i	0.812145	−	0.583455i	$-0.198300\pi$
$812$	1.67222	−	2.99551i	0.0586833	−	0.105122i
$813$	7.50198	−	16.4270i	0.263106	−	0.576122i
$814$	−12.8977	−	37.2655i	−0.452064	−	1.30615i
$815$	−11.5994	−	5.97991i	−0.406310	−	0.209467i
$816$	4.59858	+	5.84757i	0.160983	+	0.204706i
$817$	−14.0374	+	35.0638i	−0.491108	+	1.22673i
$818$	11.3180	+	17.6112i	0.395726	+	0.615761i
$819$	−17.1337	−	2.21126i	−0.598699	−	0.0772675i
$820$	18.1474	+	8.28762i	0.633733	+	0.289416i
$821$	3.32189	−	1.71256i	0.115935	−	0.0597686i	−0.399284	−	0.916827i	$-0.630741\pi$
$821$	3.32189	−	1.71256i	0.115935	−	0.0597686i	0.515218	+	0.857059i	$0.327711\pi$
$822$	−6.20329	−	5.91482i	−0.216364	−	0.206303i
$823$	10.6325	−	30.7206i	0.370626	−	1.07085i	−0.593369	−	0.804931i	$-0.702202\pi$
$823$	10.6325	−	30.7206i	0.370626	−	1.07085i	0.963994	−	0.265922i	$-0.0856764\pi$
$824$	−0.844305	+	0.805044i	−0.0294128	+	0.0280450i
$825$	0.295184	+	0.646363i	0.0102770	+	0.0225035i
$826$	−27.2072	−	18.7876i	−0.946659	−	0.653706i
$827$			22.6318i			0.786985i	0.919328	+	0.393492i	$0.128733\pi$
$827$			22.6318i			0.786985i	−0.919328	+	0.393492i	$0.871267\pi$
$828$	−3.05272	−	3.69877i	−0.106090	−	0.128541i
$829$	29.2951	−	16.9135i	1.01746	−	0.587431i	0.104093	−	0.994568i	$-0.466806\pi$
$829$	29.2951	−	16.9135i	1.01746	−	0.587431i	0.913367	+	0.407137i	$0.133473\pi$
$830$	−4.61703	+	1.84838i	−0.160259	+	0.0641582i
$831$	1.17608	−	12.3165i	0.0407978	−	0.427254i
$832$	−1.83961	+	6.26513i	−0.0637770	+	0.217204i
$833$	−49.5200	+	16.1086i	−1.71576	+	0.558131i
$834$	−6.30039	+	1.84996i	−0.218165	+	0.0640589i
$835$	5.50677	+	10.6816i	0.190570	+	0.369654i
$836$	−2.56893	−	26.9030i	−0.0888482	−	0.930461i
$837$	−2.56902	−	0.495138i	−0.0887982	−	0.0171145i
$838$	−0.902842	−	18.9530i	−0.0311882	−	0.654720i
$839$	4.45991	+	31.0194i	0.153973	+	1.07091i	0.909474	+	0.415760i	$0.136484\pi$
$839$	4.45991	+	31.0194i	0.153973	+	1.07091i	−0.755501	+	0.655147i	$0.772607\pi$
$840$	−5.69951	−	1.88085i	−0.196652	−	0.0648955i
$841$	−22.9819	+	14.7696i	−0.792480	+	0.509296i
$842$	−3.75374	+	1.29918i	−0.129362	+	0.0447727i
$843$	−6.03653	+	0.576418i	−0.207909	+	0.0198529i
$844$	−0.360155	+	7.56059i	−0.0123971	+	0.260246i
$845$	15.8498	−	65.3338i	0.545250	−	2.24755i
$846$	5.65606	−	4.90101i	0.194460	−	0.168500i
$847$	32.0605	−	9.91922i	1.10161	−	0.340828i
$848$	5.63303	−	2.57252i	0.193439	−	0.0883406i
$849$	0.0368473	−	0.0468552i	0.00126460	−	0.00160806i
$850$	−0.543092	−	0.940662i	−0.0186279	−	0.0322645i
$851$	−16.9729	−	34.9578i	−0.581823	−	1.19834i
$852$	−9.88322	−	5.70608i	−0.338594	−	0.195487i
$853$	19.1900	+	2.75910i	0.657053	+	0.0944699i	0.462774	−	0.886476i	$-0.346854\pi$
$853$	19.1900	+	2.75910i	0.657053	+	0.0944699i	0.194279	+	0.980946i	$0.437763\pi$
$854$	−20.9181	+	11.1695i	−0.715802	+	0.382213i
$855$	−12.0870	−	3.54905i	−0.413366	−	0.121375i
$856$	0.424553	+	2.20279i	0.0145109	+	0.0752899i
$857$	−2.27728	+	2.38834i	−0.0777903	+	0.0815841i	−0.761479	−	0.648190i	$-0.775526\pi$
$857$	−2.27728	+	2.38834i	−0.0777903	+	0.0815841i	0.683688	+	0.729774i	$0.260375\pi$
$858$	−31.7415	−	1.51204i	−1.08364	−	0.0516201i
$859$	15.6850	−	11.1692i	0.535164	−	0.381088i	−0.280286	−	0.959917i	$-0.590429\pi$
$859$	15.6850	−	11.1692i	0.535164	−	0.381088i	0.815450	+	0.578828i	$0.196490\pi$
$860$	11.6604	+	10.1038i	0.397615	+	0.344536i
$861$	−13.7693	−	18.7567i	−0.469257	−	0.639225i
$862$	16.9270	−	2.43374i	0.576536	−	0.0828934i
$863$	−18.6877	−	7.48144i	−0.636138	−	0.254671i	0.0310995	−	0.999516i	$-0.490099\pi$
$863$	−18.6877	−	7.48144i	−0.636138	−	0.254671i	−0.667237	+	0.744845i	$0.732523\pi$
$864$	0.458227	−	0.888835i	0.0155892	−	0.0302388i
$865$	5.67153	−	29.4267i	0.192838	−	1.00054i
$866$	3.88356	+	5.45370i	0.131969	+	0.185324i
$867$	20.7288	−	32.2546i	0.703986	−	1.09542i
$868$	−5.29631	−	4.45693i	−0.179768	−	0.151278i
$869$	−31.7270	−	36.6149i	−1.07627	−	1.24208i
$870$	−2.02984	−	2.12883i	−0.0688180	−	0.0721742i
$871$	−5.68061	+	7.97730i	−0.192480	+	0.270300i
$872$	−2.02596	−	5.06060i	−0.0686076	−	0.171373i
$873$	−2.86354	+	4.95980i	−0.0969162	+	0.167864i
$874$	−5.65588	−	26.0245i	−0.191313	−	0.880293i
$875$	−26.0845	−	12.9739i	−0.881818	−	0.438598i
$876$	0.877561	−	6.10357i	0.0296501	−	0.206221i
$877$	−43.7883	−	4.18127i	−1.47862	−	0.141192i	−0.675658	−	0.737215i	$-0.736140\pi$
$877$	−43.7883	−	4.18127i	−1.47862	−	0.141192i	−0.802967	+	0.596024i	$0.796746\pi$
$878$	11.1594	−	2.70725i	0.376612	−	0.0913652i
$879$	−1.48513	−	0.514008i	−0.0500922	−	0.0173371i
$880$	−10.7287	−	2.60277i	−0.361666	−	0.0877392i
$881$	7.26607	+	4.66962i	0.244800	+	0.157324i	0.657288	−	0.753640i	$-0.271704\pi$
$881$	7.26607	+	4.66962i	0.244800	+	0.157324i	−0.412488	+	0.910963i	$0.635340\pi$
$882$	4.73498	+	5.15558i	0.159435	+	0.173597i
$883$	−10.8887	+	12.5662i	−0.366434	+	0.422888i	−0.908785	−	0.417264i	$-0.862989\pi$
$883$	−10.8887	+	12.5662i	−0.366434	+	0.422888i	0.542351	+	0.840152i	$0.317534\pi$
$884$	48.5199	−	2.31129i	1.63190	−	0.0777371i
$885$	−22.2838	+	17.5242i	−0.749062	+	0.589069i
$886$	−6.35287	+	4.99595i	−0.213429	+	0.167842i
$887$	−30.8061	+	1.46747i	−1.03437	+	0.0492730i	−0.557891	−	0.829914i	$-0.688389\pi$
$887$	−30.8061	+	1.46747i	−1.03437	+	0.0492730i	−0.476476	+	0.879187i	$0.658086\pi$
$888$	5.30630	−	6.12380i	0.178068	−	0.205501i
$889$	−38.0676	+	30.8373i	−1.27675	+	1.03425i
$890$	22.7755	+	14.6369i	0.763437	+	0.490631i
$891$	4.72948	+	1.14736i	0.158444	+	0.0384380i
$892$	−13.7501	−	4.75894i	−0.460386	−	0.159341i
$893$	40.3886	−	9.79817i	1.35155	−	0.327883i
$894$	−3.31703	−	0.316738i	−0.110938	−	0.0105933i
$895$	0.721042	−	5.01496i	0.0241018	−	0.167632i
$896$	2.20485	−	1.46241i	0.0736588	−	0.0488558i
$897$	−31.2357	+	2.22779i	−1.04293	+	0.0743836i
$898$	−0.960226	+	1.66316i	−0.0320432	+	0.0555004i
$899$	−1.26085	−	3.14945i	−0.0420517	−	0.105040i
$900$	−0.0846935	+	0.118935i	−0.00282312	+	0.00396451i
$901$	−31.7906	−	33.3410i	−1.05910	−	1.11075i
$902$	−28.0281	−	32.3461i	−0.933233	−	1.07701i
$903$	−6.13064	−	16.9183i	−0.204015	−	0.563007i
$904$	−7.10604	+	11.0572i	−0.236343	+	0.367757i
$905$	24.6409	+	34.6034i	0.819093	+	1.15025i
$906$	−1.71900	+	8.91900i	−0.0571098	+	0.296314i
$907$	1.68963	−	3.27743i	0.0561034	−	0.108825i	−0.859117	−	0.511780i	$-0.828986\pi$
$907$	1.68963	−	3.27743i	0.0561034	−	0.108825i	0.915220	+	0.402954i	$0.132017\pi$
$908$	0.345290	+	0.138233i	0.0114588	+	0.00458743i
$909$	10.9739	−	1.57781i	0.363982	−	0.0523328i
$910$	−31.5912	+	23.1912i	−1.04724	+	0.768781i
$911$	22.3526	+	19.3687i	0.740576	+	0.641713i	0.941159	−	0.337964i	$-0.109738\pi$
$911$	22.3526	+	19.3687i	0.740576	+	0.641713i	−0.200583	+	0.979677i	$0.564284\pi$
$912$	4.52347	−	3.22115i	0.149787	−	0.106663i
$913$	10.6573	+	0.507669i	0.352705	+	0.0168014i
$914$	22.0722	−	23.1487i	0.730084	−	0.765690i
$915$	3.84785	+	19.9646i	0.127206	+	0.660008i
$916$	15.0644	+	4.42331i	0.497742	+	0.146150i
$917$	18.8829	−	30.3374i	0.623568	−	1.00183i
$918$	−7.36344	−	1.05870i	−0.243030	−	0.0349424i
$919$	12.8635	+	7.42677i	0.424329	+	0.244986i	0.696928	−	0.717141i	$-0.254550\pi$
$919$	12.8635	+	7.42677i	0.424329	+	0.244986i	−0.272599	+	0.962128i	$0.587883\pi$
$920$	−10.8021	−	1.29372i	−0.356133	−	0.0426527i
$921$	1.83564	+	3.17942i	0.0604864	+	0.104765i
$922$	−0.0445390	+	0.0566359i	−0.00146681	+	0.00186521i
$923$	−67.7832	+	30.9556i	−2.23111	+	1.01891i
$924$	9.44621	+	8.74987i	0.310758	+	0.287850i
$925$	−0.894128	+	0.774767i	−0.0293988	+	0.0254742i
$926$	−4.28232	+	17.6520i	−0.140726	+	0.580080i
$927$	0.0555089	−	1.16527i	0.00182315	−	0.0382726i
$928$	1.29079	−	0.123256i	0.0423724	−	0.00404607i
$929$	53.0058	−	18.3455i	1.73906	−	0.601896i	0.741455	−	0.671002i	$-0.234136\pi$
$929$	53.0058	−	18.3455i	1.73906	−	0.601896i	0.997609	+	0.0691059i	$0.0220146\pi$
$930$	−4.99286	+	3.20872i	−0.163722	+	0.105218i
$931$	10.2522	+	37.4958i	0.336003	+	1.22888i
$932$	−4.08186	−	28.3900i	−0.133706	−	0.929945i
$933$	−0.720185	−	15.1185i	−0.0235778	−	0.494959i
$934$	−17.0910	−	3.29402i	−0.559234	−	0.107784i
$935$	7.80676	+	81.7561i	0.255308	+	2.67371i
$936$	−2.99205	−	5.80377i	−0.0977982	−	0.189702i
$937$	29.1778	−	8.56737i	0.953196	−	0.279884i	0.232079	−	0.972697i	$-0.425447\pi$
$937$	29.1778	−	8.56737i	0.953196	−	0.279884i	0.721117	+	0.692813i	$0.243629\pi$
$938$	3.84234	−	0.991143i	0.125457	−	0.0323620i
$939$	6.87398	−	23.4106i	0.224324	−	0.763977i
$940$	1.61381	−	16.9005i	0.0526366	−	0.551235i
$941$	−25.8977	+	10.3679i	−0.844240	+	0.337983i	−0.753141	−	0.657859i	$-0.771462\pi$
$941$	−25.8977	+	10.3679i	−0.844240	+	0.337983i	−0.0910991	+	0.995842i	$0.529038\pi$
$942$	−5.62040	+	3.24494i	−0.183122	+	0.105726i
$943$	−31.2033	−	28.3770i	−1.01612	−	0.924083i
$944$		−	12.4969i		−	0.406739i
$945$	5.42287	−	2.57188i	0.176406	−	0.0836633i
$946$	−13.7503	−	30.1090i	−0.447062	−	0.978929i
$947$	−33.6708	+	32.1050i	−1.09415	+	1.04327i	−0.0952973	+	0.995449i	$0.530380\pi$
$947$	−33.6708	+	32.1050i	−1.09415	+	1.04327i	−0.998856	+	0.0478240i	$0.984771\pi$
$948$	3.25602	−	9.40764i	0.105750	−	0.305546i
$949$	−29.1404	−	27.7853i	−0.945936	−	0.901948i
$950$	−0.720677	+	0.371535i	−0.0233819	+	0.0120542i
$951$	7.21263	+	3.29390i	0.233886	+	0.106812i
$952$	−15.6454	−	11.9419i	−0.507071	−	0.387039i
$953$	2.86582	+	4.45931i	0.0928331	+	0.144451i	0.884564	−	0.466419i	$-0.154456\pi$
$953$	2.86582	+	4.45931i	0.0928331	+	0.144451i	−0.791731	+	0.610870i	$0.790820\pi$
$954$	−2.30157	+	5.74905i	−0.0745162	+	0.186133i
$955$	−4.67059	−	5.93914i	−0.151137	−	0.192186i
$956$	−5.49737	−	2.83409i	−0.177798	−	0.0916611i
$957$	2.06394	+	5.96337i	0.0667177	+	0.192768i
$958$	−6.54763	+	14.3373i	−0.211544	+	0.463217i
$959$	19.8009	+	11.0537i	0.639405	+	0.356943i
$960$	−0.639105	−	2.17659i	−0.0206270	−	0.0702492i
$961$	23.7185	−	4.57136i	0.765112	−	0.147463i
$962$	−12.4738	−	51.4178i	−0.402172	−	1.65778i
$963$	−1.82736	−	1.30126i	−0.0588860	−	0.0419325i
$964$	9.66895	+	7.60374i	0.311416	+	0.244900i
$965$	20.7154			0.666851
$966$	10.2651	+	7.45845i	0.330273	+	0.239972i
$967$	21.0705			0.677582			0.338791	−	0.940862i	$-0.389982\pi$
$967$	21.0705			0.677582			0.338791	+	0.940862i	$0.389982\pi$
$968$	9.97066	+	7.84101i	0.320469	+	0.252020i
$969$	−33.6508	−	23.9626i	−1.08102	−	0.769791i
$970$	3.06293	+	12.6256i	0.0983447	+	0.405382i
$971$	−25.5312	+	4.92074i	−0.819336	+	0.157914i	−0.581661	−	0.813431i	$-0.697597\pi$
$971$	−25.5312	+	4.92074i	−0.819336	+	0.157914i	−0.237674	+	0.971345i	$0.576385\pi$
$972$	0.281733	+	0.959493i	0.00903658	+	0.0307758i
$973$	14.9184	−	8.90299i	0.478261	−	0.285417i
$974$	−11.5221	+	25.2299i	−0.369193	+	0.808419i
$975$	0.311821	+	0.900949i	0.00998627	+	0.0288534i
$976$	−7.96647	−	4.10700i	−0.255000	−	0.131462i
$977$	−9.17383	−	11.6655i	−0.293497	−	0.373211i	0.616834	−	0.787093i	$-0.288415\pi$
$977$	−9.17383	−	11.6655i	−0.293497	−	0.373211i	−0.910331	+	0.413882i	$0.864173\pi$
$978$	−2.13810	+	5.34072i	−0.0683689	+	0.170777i
$979$	−31.4012	−	48.8613i	−1.00359	−	1.56161i
$980$	15.8445	+	1.05203i	0.506133	+	0.0336057i
$981$	4.95847	+	2.26446i	0.158312	+	0.0722985i
$982$	23.4252	−	12.0765i	0.747528	−	0.385377i
$983$	−37.3755	−	35.6375i	−1.19209	−	1.13666i	−0.987468	−	0.157819i	$-0.949554\pi$
$983$	−37.3755	−	35.6375i	−1.19209	−	1.13666i	−0.204626	−	0.978840i	$-0.565598\pi$
$984$	2.87641	−	8.31083i	0.0916965	−	0.264940i
$985$	43.2193	−	41.2095i	1.37708	−	1.31304i
$986$	−4.00713	−	8.77439i	−0.127613	−	0.279434i
$987$	−11.2514	+	16.2936i	−0.358136	+	0.518632i
$988$		−	36.2601i		−	1.15359i
$989$	−16.9713	−	27.8556i	−0.539656	−	0.885758i
$990$	9.56088	−	5.51997i	0.303865	−	0.175436i
$991$	30.4486	−	12.1898i	0.967232	−	0.387221i	0.166366	−	0.986064i	$-0.446797\pi$
$991$	30.4486	−	12.1898i	0.967232	−	0.387221i	0.800867	+	0.598843i	$0.204373\pi$
$992$	0.248695	−	2.60445i	0.00789607	−	0.0826914i
$993$	−1.66541	+	5.67185i	−0.0528501	+	0.179991i
$994$	29.0906	+	8.08706i	0.922697	+	0.256506i
$995$	19.8566	−	5.83043i	0.629498	−	0.184837i
$996$	1.00459	+	1.94863i	0.0318315	+	0.0617446i
$997$	1.53871	+	16.1140i	0.0487313	+	0.510337i	0.986578	+	0.163288i	$0.0522101\pi$
$997$	1.53871	+	16.1140i	0.0487313	+	0.510337i	−0.937847	+	0.347049i	$0.887184\pi$
$998$	34.8697	+	6.72058i	1.10378	+	0.212736i
$999$	0.385554	+	8.09376i	0.0121984	+	0.256075i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.be.b.61.3	✓	320
7.3	odd	6	inner	966.2.be.b.199.11	yes	320
23.20	odd	22	inner	966.2.be.b.733.11	yes	320
161.66	even	66	inner	966.2.be.b.871.3	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.be.b.61.3	✓	320	1.1	even	1	trivial
966.2.be.b.199.11	yes	320	7.3	odd	6	inner
966.2.be.b.733.11	yes	320	23.20	odd	22	inner
966.2.be.b.871.3	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)

\(f(q)\)	\(=\)	\(q+(-0.786053 - 0.618159i) q^{2} +(-0.814576 - 0.580057i) q^{3} +(0.235759 + 0.971812i) q^{4} +(-2.22749 + 0.429313i) q^{5} +(0.281733 + 0.959493i) q^{6} +(-1.35585 - 2.27193i) q^{7} +(0.415415 - 0.909632i) q^{8} +(0.327068 + 0.945001i) q^{9} +O(q^{10})\)	\(q+(-0.786053 - 0.618159i) q^{2} +(-0.814576 - 0.580057i) q^{3} +(0.235759 + 0.971812i) q^{4} +(-2.22749 + 0.429313i) q^{5} +(0.281733 + 0.959493i) q^{6} +(-1.35585 - 2.27193i) q^{7} +(0.415415 - 0.909632i) q^{8} +(0.327068 + 0.945001i) q^{9} +(2.01631 + 1.03948i) q^{10} +(-3.00837 - 3.82546i) q^{11} +(0.371662 - 0.928368i) q^{12} +(-3.53018 - 5.49307i) q^{13} +(-0.338650 + 2.62399i) q^{14} +(2.06348 + 0.942361i) q^{15} +(-0.888835 + 0.458227i) q^{16} +(5.38397 + 5.13361i) q^{17} +(0.327068 - 0.945001i) q^{18} +(4.01901 - 3.83212i) q^{19} +(-0.942361 - 2.06348i) q^{20} +(-0.213412 + 2.63713i) q^{21} +4.86667i q^{22} +(0.568411 + 4.76203i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.135550 - 0.0542660i) q^{25} +(-0.620681 + 6.50006i) q^{26} +(0.281733 - 0.959493i) q^{27} +(1.88824 - 1.85326i) q^{28} +(1.24414 - 0.365313i) q^{29} +(-1.03948 - 2.01631i) q^{30} +(-0.248695 - 2.60445i) q^{31} +(0.981929 + 0.189251i) q^{32} +(0.231565 + 4.86116i) q^{33} +(-1.05870 - 7.36344i) q^{34} +(3.99550 + 4.47862i) q^{35} +(-0.841254 + 0.540641i) q^{36} +(-7.65729 + 2.65021i) q^{37} +(-5.52802 + 0.527862i) q^{38} +(-0.310692 + 6.52223i) q^{39} +(-0.534815 + 2.20454i) q^{40} +(-6.64646 + 5.75919i) q^{41} +(1.79792 - 1.94100i) q^{42} +(-6.18678 + 2.82541i) q^{43} +(3.00837 - 3.82546i) q^{44} +(-1.13424 - 1.96456i) q^{45} +(2.49689 - 4.09458i) q^{46} +(6.48137 + 3.74202i) q^{47} +(0.989821 + 0.142315i) q^{48} +(-3.32337 + 6.16078i) q^{49} +(-0.140094 - 0.0411355i) q^{50} +(-1.40787 - 7.30472i) q^{51} +(4.50596 - 4.72572i) q^{52} +(-6.18563 - 0.294658i) q^{53} +(-0.814576 + 0.580057i) q^{54} +(8.34344 + 7.22963i) q^{55} +(-2.62986 + 0.289525i) q^{56} +(-5.49664 + 0.790297i) q^{57} +(-1.20378 - 0.481921i) q^{58} +(-5.72641 + 11.1077i) q^{59} +(-0.429313 + 2.22749i) q^{60} +(5.19894 + 7.30089i) q^{61} +(-1.41448 + 2.20097i) q^{62} +(1.70353 - 2.02435i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(10.2217 + 10.7202i) q^{65} +(2.82294 - 3.96427i) q^{66} +(-0.557422 - 1.39237i) q^{67} +(-3.71958 + 6.44250i) q^{68} +(2.29923 - 4.20874i) q^{69} +(-0.372175 - 5.99029i) q^{70} +(1.62412 - 11.2960i) q^{71} +(0.995472 + 0.0950560i) q^{72} +(5.99252 - 1.45377i) q^{73} +(7.65729 + 2.65021i) q^{74} +(-0.141893 - 0.0344229i) q^{75} +(4.67162 + 3.00227i) q^{76} +(-4.61230 + 12.0216i) q^{77} +(4.27600 - 4.93476i) q^{78} +(9.94389 - 0.473686i) q^{79} +(1.78315 - 1.40228i) q^{80} +(-0.786053 + 0.618159i) q^{81} +(8.78457 - 0.418460i) q^{82} +(-1.43567 + 1.65686i) q^{83} +(-2.61311 + 0.414331i) q^{84} +(-14.1967 - 9.12364i) q^{85} +(6.60969 + 1.60349i) q^{86} +(-1.22535 - 0.424097i) q^{87} +(-4.72948 + 1.14736i) q^{88} +(11.8805 + 1.13445i) q^{89} +(-0.322839 + 2.24539i) q^{90} +(-7.69351 + 15.4681i) q^{91} +(-4.49379 + 1.67508i) q^{92} +(-1.30815 + 2.26578i) q^{93} +(-2.78154 - 6.94795i) q^{94} +(-7.30712 + 10.2614i) q^{95} +(-0.690079 - 0.723734i) q^{96} +(3.75044 + 4.32824i) q^{97} +(6.42068 - 2.78833i) q^{98} +(2.63112 - 4.09410i) 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	\( 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9} + 22 q^{14} + 16 q^{16} - 66 q^{17} - 16 q^{18} + 36 q^{23} + 24 q^{25} + 12 q^{26} + 44 q^{28} + 8 q^{29} - 48 q^{31} + 16 q^{32} - 46 q^{35} + 32 q^{36} - 22 q^{37} + 66 q^{38} + 8 q^{39} + 176 q^{43} - 8 q^{46} + 120 q^{47} - 24 q^{49} - 48 q^{50} - 22 q^{51} - 12 q^{52} - 44 q^{53} + 44 q^{57} + 18 q^{58} + 12 q^{59} - 32 q^{64} - 108 q^{70} - 48 q^{71} - 16 q^{72} + 252 q^{73} + 22 q^{74} - 36 q^{75} - 42 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 12 q^{82} - 22 q^{84} - 76 q^{85} + 22 q^{86} + 24 q^{87} - 22 q^{88} + 16 q^{92} + 12 q^{94} + 26 q^{95} + 2 q^{98} + 88 q^{99}+O(q^{100}) \) 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 + 36 * q^23 + 24 * q^25 + 12 * q^26 + 44 * q^28 + 8 * q^29 - 48 * q^31 + 16 * q^32 - 46 * q^35 + 32 * q^36 - 22 * q^37 + 66 * q^38 + 8 * q^39 + 176 * q^43 - 8 * q^46 + 120 * q^47 - 24 * q^49 - 48 * q^50 - 22 * q^51 - 12 * q^52 - 44 * q^53 + 44 * q^57 + 18 * q^58 + 12 * q^59 - 32 * q^64 - 108 * q^70 - 48 * q^71 - 16 * q^72 + 252 * q^73 + 22 * q^74 - 36 * q^75 - 42 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 12 * q^82 - 22 * q^84 - 76 * q^85 + 22 * q^86 + 24 * q^87 - 22 * q^88 + 16 * q^92 + 12 * q^94 + 26 * q^95 + 2 * q^98 + 88 * q^99

Introduction

L-functions

Modular forms

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