LMFDB - Embedded newform 966.2.be.a.61.1

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			61.1
Character	$\chi$	$=$	966.61
Dual form			966.2.be.a.871.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.786053 + 0.618159i) q^{2} +(-0.814576 - 0.580057i) q^{3} +(0.235759 + 0.971812i) q^{4} +(-2.60993 + 0.503023i) q^{5} +(-0.281733 - 0.959493i) q^{6} +(-0.258273 - 2.63312i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(0.327068 + 0.945001i) q^{9} +O(q^{10})$	\(q+(0.786053 + 0.618159i) q^{2} +(-0.814576 - 0.580057i) q^{3} +(0.235759 + 0.971812i) q^{4} +(-2.60993 + 0.503023i) q^{5} +(-0.281733 - 0.959493i) q^{6} +(-0.258273 - 2.63312i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(0.327068 + 0.945001i) q^{9} +(-2.36249 - 1.21795i) q^{10} +(2.04183 + 2.59640i) q^{11} +(0.371662 - 0.928368i) q^{12} +(-0.193322 - 0.300814i) q^{13} +(1.42467 - 2.22942i) q^{14} +(2.41777 + 1.10416i) q^{15} +(-0.888835 + 0.458227i) q^{16} +(-0.0559081 - 0.0533083i) q^{17} +(-0.327068 + 0.945001i) q^{18} +(4.27696 - 4.07808i) q^{19} +(-1.10416 - 2.41777i) q^{20} +(-1.31697 + 2.29469i) q^{21} +3.30308i q^{22} +(4.27374 - 2.17603i) q^{23} +(0.866025 - 0.500000i) q^{24} +(1.91687 - 0.767401i) q^{25} +(0.0339900 - 0.355959i) q^{26} +(0.281733 - 0.959493i) q^{27} +(2.49800 - 0.871773i) q^{28} +(3.39515 - 0.996905i) q^{29} +(1.21795 + 2.36249i) q^{30} +(-0.943540 - 9.88120i) q^{31} +(-0.981929 - 0.189251i) q^{32} +(-0.157167 - 3.29934i) q^{33} +(-0.0109938 - 0.0764632i) q^{34} +(1.99859 + 6.74233i) q^{35} +(-0.841254 + 0.540641i) q^{36} +(5.77857 - 1.99998i) q^{37} +(5.88282 - 0.561741i) q^{38} +(-0.0170143 + 0.357173i) q^{39} +(0.626639 - 2.58304i) q^{40} +(5.64615 - 4.89242i) q^{41} +(-2.45369 + 0.989645i) q^{42} +(1.67143 - 0.763316i) q^{43} +(-2.04183 + 2.59640i) q^{44} +(-1.32898 - 2.30187i) q^{45} +(4.70452 + 0.931379i) q^{46} +(8.61380 + 4.97318i) q^{47} +(0.989821 + 0.142315i) q^{48} +(-6.86659 + 1.36013i) q^{49} +(1.98114 + 0.581716i) q^{50} +(0.0146196 + 0.0758535i) q^{51} +(0.246757 - 0.258792i) q^{52} +(-1.66313 - 0.0792245i) q^{53} +(0.814576 - 0.580057i) q^{54} +(-6.63508 - 5.74933i) q^{55} +(2.50246 + 0.858902i) q^{56} +(-5.84943 + 0.841021i) q^{57} +(3.28501 + 1.31512i) q^{58} +(1.80727 - 3.50561i) q^{59} +(-0.503023 + 2.60993i) q^{60} +(5.11984 + 7.18981i) q^{61} +(5.36648 - 8.35040i) q^{62} +(2.40382 - 1.10528i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(0.655873 + 0.687859i) q^{65} +(1.91597 - 2.69061i) q^{66} +(2.15582 + 5.38498i) q^{67} +(0.0386248 - 0.0669000i) q^{68} +(-4.74351 - 0.706474i) q^{69} +(-2.59683 + 6.53528i) q^{70} +(0.201782 - 1.40343i) q^{71} +(-0.995472 - 0.0950560i) q^{72} +(-13.9323 + 3.37993i) q^{73} +(5.77857 + 1.99998i) q^{74} +(-2.00658 - 0.486790i) q^{75} +(4.97145 + 3.19496i) q^{76} +(6.30926 - 6.04695i) q^{77} +(-0.234164 + 0.270240i) q^{78} +(-2.89129 + 0.137729i) q^{79} +(2.08930 - 1.64305i) q^{80} +(-0.786053 + 0.618159i) q^{81} +(7.46247 - 0.355481i) q^{82} +(-6.95058 + 8.02139i) q^{83} +(-2.54049 - 0.738858i) q^{84} +(0.172732 + 0.111008i) q^{85} +(1.78568 + 0.433202i) q^{86} +(-3.34387 - 1.15732i) q^{87} +(-3.20997 + 0.778731i) q^{88} +(2.35481 + 0.224857i) q^{89} +(0.378268 - 2.63091i) q^{90} +(-0.742149 + 0.586730i) q^{91} +(3.12226 + 3.64026i) q^{92} +(-4.96307 + 8.59629i) q^{93} +(3.69669 + 9.23388i) q^{94} +(-9.11122 + 12.7949i) q^{95} +(0.690079 + 0.723734i) q^{96} +(-9.95130 - 11.4844i) q^{97} +(-6.23828 - 3.17551i) q^{98} +(-1.78578 + 2.77873i) 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
$5$	−2.60993	+	0.503023i	−1.16720	+	0.224959i	−0.735797	−	0.677202i	$-0.763192\pi$
$5$	−2.60993	+	0.503023i	−1.16720	+	0.224959i	−0.431400	+	0.902161i	$0.641980\pi$
$6$	−0.281733	−	0.959493i	−0.115017	−	0.391711i
$7$	−0.258273	−	2.63312i	−0.0976180	−	0.995224i
$7$	−0.258273	−	2.63312i	−0.0976180	−	0.995224i
$8$	−0.415415	+	0.909632i	−0.146871	+	0.321603i
$9$	0.327068	+	0.945001i	0.109023	+	0.315000i
$10$	−2.36249	−	1.21795i	−0.747086	−	0.385150i
$11$	2.04183	+	2.59640i	0.615635	+	0.782843i	0.989483	−	0.144647i	$-0.0462045\pi$
$11$	2.04183	+	2.59640i	0.615635	+	0.782843i	−0.373849	+	0.927490i	$0.621962\pi$
$12$	0.371662	−	0.928368i	0.107290	−	0.267997i
$13$	−0.193322	−	0.300814i	−0.0536177	−	0.0834308i	0.813410	−	0.581691i	$-0.197609\pi$
$13$	−0.193322	−	0.300814i	−0.0536177	−	0.0834308i	−0.867027	+	0.498260i	$0.833972\pi$
$14$	1.42467	−	2.22942i	0.380758	−	0.595838i
$15$	2.41777	+	1.10416i	0.624266	+	0.285093i
$16$	−0.888835	+	0.458227i	−0.222209	+	0.114557i
$17$	−0.0559081	−	0.0533083i	−0.0135597	−	0.0129292i	0.683269	−	0.730167i	$-0.260558\pi$
$17$	−0.0559081	−	0.0533083i	−0.0135597	−	0.0129292i	−0.696829	+	0.717238i	$0.745406\pi$
$18$	−0.327068	+	0.945001i	−0.0770907	+	0.222739i
$19$	4.27696	−	4.07808i	0.981203	−	0.935575i	−0.0167288	−	0.999860i	$-0.505325\pi$
$19$	4.27696	−	4.07808i	0.981203	−	0.935575i	0.997932	+	0.0642851i	$0.0204767\pi$
$20$	−1.10416	−	2.41777i	−0.246897	−	0.540630i
$21$	−1.31697	+	2.29469i	−0.287387	+	0.500741i
$22$			3.30308i			0.704219i
$23$	4.27374	−	2.17603i	0.891137	−	0.453734i
$23$	4.27374	−	2.17603i	0.891137	−	0.453734i
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	1.91687	−	0.767401i	0.383375	−	0.153480i
$26$	0.0339900	−	0.355959i	0.00666599	−	0.0698094i
$27$	0.281733	−	0.959493i	0.0542195	−	0.184655i
$28$	2.49800	−	0.871773i	0.472078	−	0.164750i
$29$	3.39515	−	0.996905i	0.630463	−	0.185121i	0.0491380	−	0.998792i	$-0.484353\pi$
$29$	3.39515	−	0.996905i	0.630463	−	0.185121i	0.581325	+	0.813671i	$0.302534\pi$
$30$	1.21795	+	2.36249i	0.222366	+	0.431330i
$31$	−0.943540	−	9.88120i	−0.169465	−	1.77472i	−0.535909	−	0.844276i	$-0.680031\pi$
$31$	−0.943540	−	9.88120i	−0.169465	−	1.77472i	0.366444	−	0.930440i	$-0.380575\pi$
$32$	−0.981929	−	0.189251i	−0.173582	−	0.0334552i
$33$	−0.157167	−	3.29934i	−0.0273592	−	0.574341i
$34$	−0.0109938	−	0.0764632i	−0.00188541	−	0.0131133i
$35$	1.99859	+	6.74233i	0.337824	+	1.13966i
$36$	−0.841254	+	0.540641i	−0.140209	+	0.0901068i
$37$	5.77857	−	1.99998i	0.949991	−	0.328795i	0.192247	−	0.981347i	$-0.438423\pi$
$37$	5.77857	−	1.99998i	0.949991	−	0.328795i	0.757744	+	0.652552i	$0.226301\pi$
$38$	5.88282	−	0.561741i	0.954319	−	0.0911265i
$39$	−0.0170143	+	0.357173i	−0.00272446	+	0.0571935i
$40$	0.626639	−	2.58304i	0.0990803	−	0.408415i
$41$	5.64615	−	4.89242i	0.881781	−	0.764067i	−0.0909864	−	0.995852i	$-0.529002\pi$
$41$	5.64615	−	4.89242i	0.881781	−	0.764067i	0.972767	+	0.231785i	$0.0744565\pi$
$42$	−2.45369	+	0.989645i	−0.378613	+	0.152706i
$43$	1.67143	−	0.763316i	0.254890	−	0.116405i	−0.283872	−	0.958862i	$-0.591619\pi$
$43$	1.67143	−	0.763316i	0.254890	−	0.116405i	0.538763	+	0.842458i	$0.318892\pi$
$44$	−2.04183	+	2.59640i	−0.307817	+	0.391422i
$45$	−1.32898	−	2.30187i	−0.198113	−	0.343142i
$46$	4.70452	+	0.931379i	0.693644	+	0.137324i
$47$	8.61380	+	4.97318i	1.25645	+	0.725413i	0.972383	−	0.233391i	$-0.0749822\pi$
$47$	8.61380	+	4.97318i	1.25645	+	0.725413i	0.284069	+	0.958804i	$0.408316\pi$
$48$	0.989821	+	0.142315i	0.142868	+	0.0205414i
$49$	−6.86659	+	1.36013i	−0.980941	+	0.194304i
$50$	1.98114	+	0.581716i	0.280176	+	0.0822670i
$51$	0.0146196	+	0.0758535i	0.00204715	+	0.0106216i
$52$	0.246757	−	0.258792i	0.0342191	−	0.0358880i
$53$	−1.66313	−	0.0792245i	−0.228448	−	0.0108823i	−0.0669542	−	0.997756i	$-0.521328\pi$
$53$	−1.66313	−	0.0792245i	−0.228448	−	0.0108823i	−0.161494	+	0.986874i	$0.551631\pi$
$54$	0.814576	−	0.580057i	0.110850	−	0.0789357i
$55$	−6.63508	−	5.74933i	−0.894675	−	0.775240i
$56$	2.50246	+	0.858902i	0.334405	+	0.114776i
$57$	−5.84943	+	0.841021i	−0.774776	+	0.111396i
$58$	3.28501	+	1.31512i	0.431343	+	0.172684i
$59$	1.80727	−	3.50561i	0.235286	−	0.456391i	−0.741400	−	0.671063i	$-0.765838\pi$
$59$	1.80727	−	3.50561i	0.235286	−	0.456391i	0.976686	+	0.214672i	$0.0688682\pi$
$60$	−0.503023	+	2.60993i	−0.0649400	+	0.336941i
$61$	5.11984	+	7.18981i	0.655529	+	0.920561i	0.999833	−	0.0182970i	$-0.00582443\pi$
$61$	5.11984	+	7.18981i	0.655529	+	0.920561i	−0.344304	+	0.938858i	$0.611885\pi$
$62$	5.36648	−	8.35040i	0.681544	−	1.06050i
$63$	2.40382	−	1.10528i	0.302853	−	0.139252i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	0.655873	+	0.687859i	0.0813510	+	0.0853185i
$66$	1.91597	−	2.69061i	0.235840	−	0.331191i
$67$	2.15582	+	5.38498i	0.263376	+	0.657881i	0.999827	−	0.0186102i	$-0.00592414\pi$
$67$	2.15582	+	5.38498i	0.263376	+	0.657881i	−0.736451	+	0.676491i	$0.763500\pi$
$68$	0.0386248	−	0.0669000i	0.00468394	−	0.00811282i
$69$	−4.74351	−	0.706474i	−0.571052	−	0.0850495i
$70$	−2.59683	+	6.53528i	−0.310381	+	0.781116i
$71$	0.201782	−	1.40343i	0.0239472	−	0.166556i	−0.974338	−	0.225088i	$-0.927733\pi$
$71$	0.201782	−	1.40343i	0.0239472	−	0.166556i	0.998286	+	0.0585321i	$0.0186420\pi$
$72$	−0.995472	−	0.0950560i	−0.117317	−	0.0112025i
$73$	−13.9323	+	3.37993i	−1.63065	+	0.395591i	−0.943618	−	0.331036i	$-0.892602\pi$
$73$	−13.9323	+	3.37993i	−1.63065	+	0.395591i	−0.687032	+	0.726627i	$0.741087\pi$
$74$	5.77857	+	1.99998i	0.671745	+	0.232493i
$75$	−2.00658	−	0.486790i	−0.231699	−	0.0562097i
$76$	4.97145	+	3.19496i	0.570265	+	0.366487i
$77$	6.30926	−	6.04695i	0.719007	−	0.689114i
$78$	−0.234164	+	0.270240i	−0.0265139	+	0.0305986i
$79$	−2.89129	+	0.137729i	−0.325296	+	0.0154957i	−0.209595	−	0.977788i	$-0.567214\pi$
$79$	−2.89129	+	0.137729i	−0.325296	+	0.0154957i	−0.115701	+	0.993284i	$0.536911\pi$
$80$	2.08930	−	1.64305i	0.233591	−	0.183698i
$81$	−0.786053	+	0.618159i	−0.0873392	+	0.0686843i
$82$	7.46247	−	0.355481i	0.824092	−	0.0392563i
$83$	−6.95058	+	8.02139i	−0.762925	+	0.880462i	−0.995754	−	0.0920553i	$-0.970656\pi$
$83$	−6.95058	+	8.02139i	−0.762925	+	0.880462i	0.232829	+	0.972518i	$0.425202\pi$
$84$	−2.54049	−	0.738858i	−0.277190	−	0.0806160i
$85$	0.172732	+	0.111008i	0.0187354	+	0.0120405i
$86$	1.78568	+	0.433202i	0.192555	+	0.0467134i
$87$	−3.34387	−	1.15732i	−0.358500	−	0.124078i
$88$	−3.20997	+	0.778731i	−0.342184	+	0.0830130i
$89$	2.35481	+	0.224857i	0.249609	+	0.0238348i	0.219111	−	0.975700i	$-0.429684\pi$
$89$	2.35481	+	0.224857i	0.249609	+	0.0238348i	0.0304987	+	0.999535i	$0.490290\pi$
$90$	0.378268	−	2.63091i	0.0398729	−	0.277322i
$91$	−0.742149	+	0.586730i	−0.0777983	+	0.0615060i
$92$	3.12226	+	3.64026i	0.325519	+	0.379523i
$93$	−4.96307	+	8.59629i	−0.514647	+	0.891394i
$94$	3.69669	+	9.23388i	0.381284	+	0.952402i
$95$	−9.11122	+	12.7949i	−0.934791	+	1.31273i
$96$	0.690079	+	0.723734i	0.0704309	+	0.0738658i
$97$	−9.95130	−	11.4844i	−1.01040	−	1.16607i	−0.986065	−	0.166362i	$-0.946798\pi$
$97$	−9.95130	−	11.4844i	−1.01040	−	1.16607i	−0.0243367	−	0.999704i	$-0.507747\pi$
$98$	−6.23828	−	3.17551i	−0.630161	−	0.320775i
$99$	−1.78578	+	2.77873i	−0.179478	+	0.279273i
$100$	1.19769	+	1.68192i	0.119769	+	0.168192i
$101$	1.01806	−	5.28219i	0.101301	−	0.525598i	−0.895458	−	0.445146i	$-0.853152\pi$
$101$	1.01806	−	5.28219i	0.101301	−	0.525598i	0.996759	−	0.0804515i	$-0.0256362\pi$
$102$	−0.0353978	+	0.0686621i	−0.00350490	+	0.00679856i
$103$	8.28820	+	3.31810i	0.816661	+	0.326942i	0.742112	−	0.670276i	$-0.233824\pi$
$103$	8.28820	+	3.31810i	0.816661	+	0.326942i	0.0745487	+	0.997217i	$0.476248\pi$
$104$	0.353939	−	0.0508887i	0.0347066	−	0.00499005i
$105$	2.28293	−	6.65144i	0.222791	−	0.649114i
$106$	−1.25833	−	1.09035i	−0.122220	−	0.105904i
$107$	−2.58747	+	1.84253i	−0.250140	+	0.178124i	−0.698249	−	0.715855i	$-0.746037\pi$
$107$	−2.58747	+	1.84253i	−0.250140	+	0.178124i	0.448109	+	0.893979i	$0.352098\pi$
$108$	0.998867	+	0.0475819i	0.0961161	+	0.00457857i
$109$	11.1670	−	11.7116i	1.06961	−	1.12177i	0.0774206	−	0.996999i	$-0.475332\pi$
$109$	11.1670	−	11.7116i	1.06961	−	1.12177i	0.992185	−	0.124772i	$-0.0398199\pi$
$110$	−1.66153	−	8.62082i	−0.158420	−	0.821963i
$111$	−5.86719	−	1.72276i	−0.556889	−	0.163517i
$112$	1.43613	+	2.22206i	0.135701	+	0.209965i
$113$	−0.311909	−	0.0448458i	−0.0293420	−	0.00421874i	0.127628	−	0.991822i	$-0.459264\pi$
$113$	−0.311909	−	0.0448458i	−0.0293420	−	0.00421874i	−0.156970	+	0.987603i	$0.550173\pi$
$114$	−5.11785	−	2.95479i	−0.479330	−	0.276741i
$115$	−10.0596	+	7.82908i	−0.938062	+	0.730066i
$116$	1.76924	+	3.06441i	0.164270	+	0.284524i
$117$	0.221040	−	0.281076i	0.0204352	−	0.0259855i
$118$	3.58763	−	1.63842i	0.330268	−	0.150828i
$119$	−0.125927	+	0.160981i	−0.0115437	+	0.0147571i
$120$	−2.00876	+	1.74060i	−0.183374	+	0.158894i
$121$	0.0211372	−	0.0871287i	0.00192156	−	0.00792079i
$122$	−0.419979	+	8.81645i	−0.0380231	+	0.798204i
$123$	−7.43710	+	0.710157i	−0.670581	+	0.0640327i
$124$	9.38021	−	3.24652i	0.842368	−	0.291546i
$125$	6.56322	−	4.21793i	0.587032	−	0.377263i
$126$	2.57277	+	0.617139i	0.229200	+	0.0549791i
$127$	1.35630	+	9.43327i	0.120352	+	0.837067i	0.957158	+	0.289567i	$0.0935113\pi$
$127$	1.35630	+	9.43327i	0.120352	+	0.837067i	−0.836806	+	0.547500i	$0.815580\pi$
$128$	−0.0475819	−	0.998867i	−0.00420569	−	0.0882882i
$129$	−1.80427	−	0.347745i	−0.158857	−	0.0306172i
$130$	0.0903442	+	0.946128i	0.00792371	+	0.0829809i
$131$	−5.79159	−	11.2341i	−0.506013	−	0.981529i	−0.994073	−	0.108718i	$-0.965325\pi$
$131$	−5.79159	−	11.2341i	−0.506013	−	0.981529i	0.488059	−	0.872810i	$-0.337705\pi$
$132$	3.16928	−	0.930585i	0.275851	−	0.0809971i
$133$	−11.8427	−	10.2085i	−1.02689	−	0.885188i
$134$	−1.63419	+	5.56552i	−0.141172	+	0.480788i
$135$	−0.252656	+	2.64593i	−0.0217451	+	0.227725i
$136$	0.0717160	−	0.0287107i	0.00614959	−	0.00246193i
$137$	−17.2800	+	9.97662i	−1.47633	+	0.852360i	−0.999643	−	0.0267120i	$-0.991496\pi$
$137$	−17.2800	+	9.97662i	−1.47633	+	0.852360i	−0.476688	+	0.879072i	$0.658163\pi$
$138$	−3.29194	−	3.48757i	−0.280228	−	0.296882i
$139$		−	12.2569i		−	1.03962i	−0.854283	−	0.519809i	$-0.826003\pi$
$139$		−	12.2569i		−	1.03962i	0.854283	−	0.519809i	$-0.173997\pi$
$140$	−6.08109	+	3.53182i	−0.513946	+	0.298493i
$141$	−4.13187	−	9.04753i	−0.347966	−	0.761939i
$142$	1.02615	−	0.978435i	0.0861129	−	0.0821085i
$143$	0.386303	−	1.11615i	0.0323043	−	0.0933372i
$144$	−0.723734	−	0.690079i	−0.0603112	−	0.0575066i
$145$	−8.35964	+	4.30969i	−0.694230	+	0.357901i
$146$	−13.0409	−	5.95556i	−1.07927	−	0.492885i
$147$	6.38231	+	2.87509i	0.526404	+	0.237133i
$148$	3.30596	+	5.14417i	0.271748	+	0.422848i
$149$	1.98398	−	4.95573i	0.162534	−	0.405990i	−0.824636	−	0.565664i	$-0.808620\pi$
$149$	1.98398	−	4.95573i	0.162534	−	0.405990i	0.987170	+	0.159674i	$0.0510443\pi$
$150$	−1.27636	−	1.62303i	−0.104215	−	0.132520i
$151$	−19.1710	−	9.88332i	−1.56011	−	0.804293i	−0.560398	−	0.828224i	$-0.689352\pi$
$151$	−19.1710	−	9.88332i	−1.56011	−	0.804293i	−0.999714	+	0.0239304i	$0.992382\pi$
$152$	1.93283	+	5.58456i	0.156774	+	0.452967i
$153$	0.0320906	−	0.0702686i	0.00259437	−	0.00568088i
$154$	8.69739	−	0.853097i	0.700856	−	0.0687445i
$155$	7.43305	+	25.3146i	0.597037	+	2.03332i
$156$	−0.351117	+	0.0676722i	−0.0281118	+	0.00541811i
$157$	−0.872809	−	3.59777i	−0.0696578	−	0.287133i	0.926320	−	0.376739i	$-0.122955\pi$
$157$	−0.872809	−	3.59777i	−0.0696578	−	0.287133i	−0.995977	+	0.0896055i	$0.971439\pi$
$158$	−2.35785	−	1.67902i	−0.187580	−	0.133575i
$159$	1.30879	+	1.02924i	0.103794	+	0.0816242i
$160$	2.65797			0.210131
$161$	−6.83353	−	10.6913i	−0.538558	−	0.842589i
$162$	−1.00000			−0.0785674
$163$	13.5141	+	10.6276i	1.05850	+	0.832416i	0.986298	−	0.164974i	$-0.0527540\pi$
$163$	13.5141	+	10.6276i	1.05850	+	0.832416i	0.0722050	+	0.997390i	$0.476996\pi$
$164$	6.08564	+	4.33356i	0.475209	+	0.338395i
$165$	2.06984	+	8.53199i	0.161137	+	0.664215i
$166$	−10.4220	+	2.00868i	−0.808906	+	0.155904i
$167$	3.48898	+	11.8824i	0.269985	+	0.919484i	0.977171	+	0.212456i	$0.0681464\pi$
$167$	3.48898	+	11.8824i	0.269985	+	0.919484i	−0.707186	+	0.707028i	$0.750035\pi$
$168$	−1.54023	−	2.15121i	−0.118831	−	0.165969i
$169$	5.34728	−	11.7089i	0.411329	−	0.900685i
$170$	0.0671557	+	0.194034i	0.00515061	+	0.0148817i
$171$	5.25264	+	2.70793i	0.401680	+	0.207080i
$172$	1.13585	+	1.44436i	0.0866080	+	0.110131i
$173$	−1.44548	+	3.61063i	−0.109898	+	0.274511i	−0.973114	−	0.230322i	$-0.926022\pi$
$173$	−1.44548	+	3.61063i	−0.109898	+	0.274511i	0.863217	+	0.504834i	$0.168446\pi$
$174$	−1.91305	−	2.97676i	−0.145028	−	0.225668i
$175$	−2.51573	−	4.84915i	−0.190171	−	0.366562i
$176$	−3.00459	−	1.37215i	−0.226479	−	0.103430i
$177$	−3.50561	+	1.80727i	−0.263498	+	0.135842i
$178$	1.71201	+	1.63240i	0.128320	+	0.122353i
$179$	5.16086	−	14.9113i	0.385741	−	1.11453i	−0.570336	−	0.821411i	$-0.693187\pi$
$179$	5.16086	−	14.9113i	0.385741	−	1.11453i	0.956077	−	0.293114i	$-0.0946916\pi$
$180$	1.92366	−	1.83421i	0.143381	−	0.136714i
$181$	4.23432	+	9.27187i	0.314735	+	0.689172i	0.999205	−	0.0398681i	$-0.0126938\pi$
$181$	4.23432	+	9.27187i	0.314735	+	0.689172i	−0.684470	+	0.729041i	$0.739967\pi$
$182$	−0.946061	+	0.00243513i	−0.0701267	+	0.000180504i
$183$		−	8.82645i		−	0.652470i
$184$	0.204008	+	4.79149i	0.0150397	+	0.353233i
$185$	−14.0756	+	8.12657i	−1.03486	+	0.597477i
$186$	−9.21511	+	3.68918i	−0.675685	+	0.270503i
$187$	0.0242546	−	0.254006i	0.00177367	−	0.0185748i
$188$	−2.80221	+	9.54346i	−0.204372	+	0.696029i
$189$	−2.59922	−	0.494023i	−0.189065	−	0.0359349i
$190$	−15.0712	+	4.42530i	−1.09338	+	0.321045i
$191$	8.52591	+	16.5380i	0.616913	+	1.19665i	0.965753	+	0.259463i	$0.0835455\pi$
$191$	8.52591	+	16.5380i	0.616913	+	1.19665i	−0.348840	+	0.937182i	$0.613424\pi$
$192$	0.0950560	+	0.995472i	0.00686008	+	0.0718420i
$193$	−4.16443	−	0.802629i	−0.299763	−	0.0577745i	0.0371523	−	0.999310i	$-0.488171\pi$
$193$	−4.16443	−	0.802629i	−0.299763	−	0.0577745i	−0.336915	+	0.941535i	$0.609383\pi$
$194$	−0.723058	−	15.1788i	−0.0519125	−	1.08978i
$195$	−0.135260	−	0.940757i	−0.00968620	−	0.0673690i
$196$	−2.94065	−	6.35237i	−0.210046	−	0.453741i
$197$	15.4113	−	9.90425i	1.09801	−	0.705648i	0.139362	−	0.990241i	$-0.455495\pi$
$197$	15.4113	−	9.90425i	1.09801	−	0.705648i	0.958648	+	0.284593i	$0.0918585\pi$
$198$	−3.12141	+	1.08033i	−0.221829	+	0.0767759i
$199$	14.1357	−	1.34979i	1.00205	−	0.0956843i	0.418887	−	0.908038i	$-0.362420\pi$
$199$	14.1357	−	1.34979i	1.00205	−	0.0956843i	0.583165	+	0.812354i	$0.301814\pi$
$200$	−0.0982461	+	2.06244i	−0.00694705	+	0.145837i
$201$	1.36752	−	5.63698i	0.0964572	−	0.397602i
$202$	4.06548	−	3.52276i	0.286046	−	0.247861i
$203$	−3.50184	−	8.68234i	−0.245781	−	0.609381i
$204$	−0.0702686	+	0.0320906i	−0.00491979	+	0.00224679i
$205$	−12.2751	+	15.6090i	−0.857328	+	1.09018i
$206$	4.46386	+	7.73163i	0.311012	+	0.538688i
$207$	3.45415	+	3.32698i	0.240080	+	0.231241i
$208$	0.309672	+	0.178789i	0.0214719	+	0.0123968i
$209$	19.3211	+	2.77796i	1.33647	+	0.192156i
$210$	5.90615	−	3.81717i	0.407563	−	0.263410i
$211$	0.486755	+	0.142924i	0.0335096	+	0.00983930i	0.298444	−	0.954427i	$-0.403532\pi$
$211$	0.486755	+	0.142924i	0.0335096	+	0.00983930i	−0.264935	+	0.964266i	$0.585350\pi$
$212$	−0.315106	−	1.63492i	−0.0216415	−	0.112287i
$213$	−0.978435	+	1.02615i	−0.0670413	+	0.0703109i
$214$	−3.17286	−	0.151142i	−0.216892	−	0.0103319i
$215$	−3.97835	+	2.83297i	−0.271321	+	0.193207i
$216$	0.755750	+	0.654861i	0.0514222	+	0.0445576i
$217$	−25.7746	+	5.03650i	−1.74970	+	0.341900i
$218$	16.0175	−	2.30297i	1.08484	−	0.155977i
$219$	13.3095	+	5.32830i	0.899370	+	0.360053i
$220$	4.02299	−	7.80351i	0.271230	−	0.526112i
$221$	−0.00522764	+	0.0271236i	−0.000351649	+	0.00182453i
$222$	−3.54698	−	4.98104i	−0.238058	−	0.334305i
$223$	−2.94273	+	4.57898i	−0.197060	+	0.306631i	−0.925695	−	0.378271i	$-0.876519\pi$
$223$	−2.94273	+	4.57898i	−0.197060	+	0.306631i	0.728635	+	0.684902i	$0.240155\pi$
$224$	−0.244715	+	2.63441i	−0.0163507	+	0.176019i
$225$	1.35214	+	1.56046i	0.0901429	+	0.104030i
$226$	−0.217455	−	0.228061i	−0.0144649	−	0.0151704i
$227$	−14.8981	+	20.9214i	−0.988820	+	1.38860i	−0.0684069	+	0.997658i	$0.521792\pi$
$227$	−14.8981	+	20.9214i	−0.988820	+	1.38860i	−0.920413	+	0.390946i	$0.872148\pi$
$228$	−2.19637	−	5.48626i	−0.145458	−	0.363337i
$229$	4.72694	−	8.18731i	0.312365	−	0.541033i	−0.666509	−	0.745497i	$-0.732212\pi$
$229$	4.72694	−	8.18731i	0.312365	−	0.541033i	0.978874	+	0.204465i	$0.0655454\pi$
$230$	−12.7470	−	0.0643522i	−0.840512	−	0.00424326i
$231$	−8.64695	+	1.26597i	−0.568927	+	0.0832946i
$232$	−0.503578	+	3.50246i	−0.0330615	+	0.229948i
$233$	27.8747	+	2.66171i	1.82613	+	0.174375i	0.950935	−	0.309391i	$-0.100125\pi$
$233$	27.8747	+	2.66171i	1.82613	+	0.174375i	0.875198	+	0.483765i	$0.160731\pi$
$234$	0.347499	−	0.0843023i	0.0227167	−	0.00551101i
$235$	−24.9831	−	8.64672i	−1.62972	−	0.564050i
$236$	3.83287	+	0.929844i	0.249499	+	0.0605277i
$237$	2.43507	+	1.56492i	0.158175	+	0.101653i
$238$	−0.198497	+	0.0486962i	−0.0128667	+	0.00315651i
$239$	−12.0166	+	13.8679i	−0.777289	+	0.897039i	−0.996911	−	0.0785457i	$-0.974972\pi$
$239$	−12.0166	+	13.8679i	−0.777289	+	0.897039i	0.219621	+	0.975585i	$0.429518\pi$
$240$	−2.65495	+	0.126471i	−0.171377	+	0.00816367i
$241$	−22.4270	+	17.6368i	−1.44465	+	1.13608i	−0.478505	+	0.878085i	$0.658821\pi$
$241$	−22.4270	+	17.6368i	−1.44465	+	1.13608i	−0.966145	+	0.258000i	$0.916937\pi$
$242$	0.0704744	−	0.0554216i	0.00453026	−	0.00356264i
$243$	0.998867	−	0.0475819i	0.0640774	−	0.00305238i
$244$	−5.78010	+	6.67059i	−0.370033	+	0.427040i
$245$	17.2372	−	7.00389i	1.10124	−	0.447462i
$246$	−6.28495	−	4.03909i	−0.400713	−	0.257523i
$247$	−2.05357	−	0.498191i	−0.130666	−	0.0316991i
$248$	9.38021	+	3.24652i	0.595644	+	0.206154i
$249$	10.3146	−	2.50230i	0.653664	−	0.158577i
$250$	7.76639	+	0.741600i	0.491190	+	0.0469029i
$251$	−1.98592	+	13.8124i	−0.125350	+	0.871829i	0.825990	+	0.563685i	$0.190617\pi$
$251$	−1.98592	+	13.8124i	−0.125350	+	0.871829i	−0.951340	+	0.308144i	$0.900292\pi$
$252$	1.64084	+	2.07548i	0.103363	+	0.130743i
$253$	14.3761	+	6.65326i	0.903817	+	0.418287i
$254$	−4.76513	+	8.25346i	−0.298991	+	0.517868i
$255$	−0.0763122	−	0.190619i	−0.00477885	−	0.0119370i
$256$	0.580057	−	0.814576i	0.0362536	−	0.0509110i
$257$	−2.42051	−	2.53856i	−0.150987	−	0.158351i	0.643896	−	0.765113i	$-0.277317\pi$
$257$	−2.42051	−	2.53856i	−0.150987	−	0.158351i	−0.794884	+	0.606762i	$0.792468\pi$
$258$	−1.20329	−	1.38867i	−0.0749137	−	0.0864550i
$259$	−6.75863	−	14.6991i	−0.419961	−	0.913357i
$260$	−0.513842	+	0.799554i	−0.0318671	+	0.0495862i
$261$	2.05252	+	2.88236i	0.127048	+	0.178414i
$262$	2.39197	−	12.4107i	0.147777	−	0.766737i
$263$	0.503794	−	0.977224i	0.0310653	−	0.0602582i	−0.872792	−	0.488092i	$-0.837693\pi$
$263$	0.503794	−	0.977224i	0.0310653	−	0.0602582i	0.903857	+	0.427834i	$0.140723\pi$
$264$	3.06647	+	1.22763i	0.188728	+	0.0755555i
$265$	4.38050	−	0.629821i	0.269092	−	0.0386896i
$266$	−2.99850	−	15.3451i	−0.183850	−	0.940866i
$267$	−1.78774	−	1.54909i	−0.109408	−	0.0948026i
$268$	−4.72494	+	3.36461i	−0.288621	+	0.205526i
$269$	−11.3516	−	0.540745i	−0.692122	−	0.0329698i	−0.301426	−	0.953490i	$-0.597463\pi$
$269$	−11.3516	−	0.540745i	−0.692122	−	0.0329698i	−0.390696	+	0.920520i	$0.627766\pi$
$270$	−1.83421	+	1.92366i	−0.111626	+	0.117070i
$271$	−3.51269	−	18.2256i	−0.213381	−	1.10713i	−0.917710	−	0.397252i	$-0.869964\pi$
$271$	−3.51269	−	18.2256i	−0.213381	−	1.10713i	0.704329	−	0.709874i	$-0.251248\pi$
$272$	0.0741204	+	0.0217637i	0.00449421	+	0.00131962i
$273$	0.944873	−	0.0474477i	0.0571863	−	0.00287167i
$274$	−19.7501	−	2.83964i	−1.19315	−	0.171549i
$275$	5.90641	+	3.41007i	0.356170	+	0.205635i
$276$	−0.431766	−	4.77636i	−0.0259892	−	0.287503i
$277$	−2.62175	−	4.54100i	−0.157526	−	0.272842i	0.776450	−	0.630179i	$-0.217018\pi$
$277$	−2.62175	−	4.54100i	−0.157526	−	0.272842i	−0.933976	+	0.357336i	$0.883685\pi$
$278$	7.57672	−	9.63458i	0.454421	−	0.577844i
$279$	9.02914	−	4.12347i	0.540560	−	0.246866i
$280$	−6.96329	−	0.982883i	−0.416136	−	0.0587385i
$281$	−0.566093	+	0.490522i	−0.0337703	+	0.0292621i	−0.671582	−	0.740930i	$-0.734385\pi$
$281$	−0.566093	+	0.490522i	−0.0337703	+	0.0292621i	0.637812	+	0.770192i	$0.279840\pi$
$282$	2.34494	−	9.66599i	0.139639	−	0.575601i
$283$	−0.422980	+	8.87945i	−0.0251436	+	0.527829i	0.950800	+	0.309805i	$0.100264\pi$
$283$	−0.422980	+	8.87945i	−0.0251436	+	0.527829i	−0.975944	+	0.218023i	$0.930039\pi$
$284$	1.41144	−	0.134776i	0.0837535	−	0.00799749i
$285$	14.8436	−	5.13741i	0.879257	−	0.304314i
$286$	0.993613	−	0.638557i	0.0587536	−	0.0377586i
$287$	−14.3405	−	13.6034i	−0.846496	−	0.802983i
$288$	−0.142315	−	0.989821i	−0.00838598	−	0.0583258i
$289$	−0.808609	−	16.9748i	−0.0475652	−	0.998517i
$290$	−9.23520	−	1.77994i	−0.542309	−	0.104522i
$291$	1.44448	+	15.1272i	0.0846767	+	0.886775i
$292$	−6.56932	−	12.7427i	−0.384440	−	0.745710i
$293$	17.7820	−	5.22126i	1.03883	−	0.305029i	0.282536	−	0.959257i	$-0.408824\pi$
$293$	17.7820	−	5.22126i	1.03883	−	0.305029i	0.756298	+	0.654227i	$0.227006\pi$
$294$	3.23957	+	6.20525i	0.188936	+	0.361898i
$295$	−2.95344	+	10.0585i	−0.171956	+	0.585628i
$296$	−0.581257	+	6.08719i	−0.0337849	+	0.353811i
$297$	3.06647	−	1.22763i	0.177935	−	0.0712344i
$298$	4.62294	−	2.66906i	0.267800	−	0.154614i
$299$	−1.48079	−	0.864930i	−0.0856361	−	0.0500202i
$300$		−	2.06478i		−	0.119210i
$301$	−2.44158	−	4.20392i	−0.140731	−	0.242310i
$302$	−8.95994	−	19.6195i	−0.515586	−	1.12898i
$303$	−3.89326	+	3.71222i	−0.223662	+	0.213261i
$304$	−1.93283	+	5.58456i	−0.110856	+	0.320296i
$305$	−16.9791	−	16.1895i	−0.972220	−	0.927010i
$306$	0.0686621	−	0.0353978i	0.00392515	−	0.00202356i
$307$	−26.2055	−	11.9677i	−1.49563	−	0.683031i	−0.511304	−	0.859400i	$-0.670838\pi$
$307$	−26.2055	−	11.9677i	−1.49563	−	0.683031i	−0.984324	+	0.176369i	$0.943565\pi$
$308$	7.36396	+	4.70579i	0.419601	+	0.268137i
$309$	−4.82669	−	7.51047i	−0.274581	−	0.427256i
$310$	−9.80570	+	24.4935i	−0.556926	+	1.39113i
$311$	−0.879159	−	1.11794i	−0.0498525	−	0.0633927i	0.760488	−	0.649353i	$-0.224960\pi$
$311$	−0.879159	−	1.11794i	−0.0498525	−	0.0633927i	−0.810340	+	0.585960i	$0.800718\pi$
$312$	−0.317828	−	0.163852i	−0.0179935	−	0.00927629i
$313$	−1.24727	−	3.60375i	−0.0705000	−	0.203696i	0.904246	−	0.427011i	$-0.140433\pi$
$313$	−1.24727	−	3.60375i	−0.0705000	−	0.203696i	−0.974746	+	0.223315i	$0.928312\pi$
$314$	1.53792	−	3.36757i	0.0867898	−	0.190043i
$315$	−5.71784	+	4.09387i	−0.322164	+	0.230664i
$316$	−0.815495	−	2.77732i	−0.0458752	−	0.156236i
$317$	−6.66010	+	1.28363i	−0.374068	+	0.0720957i	−0.372821	−	0.927903i	$-0.621609\pi$
$317$	−6.66010	+	1.28363i	−0.374068	+	0.0720957i	−0.00124773	+	0.999999i	$0.500397\pi$
$318$	0.392541	+	1.61808i	0.0220126	+	0.0907373i
$319$	9.52067	+	6.77964i	0.533055	+	0.379587i
$320$	2.08930	+	1.64305i	0.116796	+	0.0918490i
$321$	3.17646			0.177293
$322$	1.23738	−	12.6281i	0.0689563	−	0.703736i
$323$	−0.456512			−0.0254010
$324$	−0.786053	−	0.618159i	−0.0436696	−	0.0343422i
$325$	−0.601418	−	0.428268i	−0.0333607	−	0.0237560i
$326$	4.05324	+	16.7077i	0.224488	+	0.925353i
$327$	−15.8898	+	3.06251i	−0.878708	+	0.169357i
$328$	2.10480	+	7.16830i	0.116218	+	0.395803i
$329$	10.8702	−	23.9656i	0.599296	−	1.32126i
$330$	−3.64713	+	7.98609i	−0.200768	+	0.439620i
$331$	4.79019	+	13.8403i	0.263293	+	0.760734i	0.996717	+	0.0809633i	$0.0257997\pi$
$331$	4.79019	+	13.8403i	0.263293	+	0.760734i	−0.733424	+	0.679771i	$0.762079\pi$
$332$	−9.43394	−	4.86354i	−0.517755	−	0.266921i
$333$	3.77997	+	4.80662i	0.207141	+	0.263401i
$334$	−4.60267	+	11.4969i	−0.251847	+	0.629083i
$335$	−8.33532	−	12.9700i	−0.455407	−	0.708628i
$336$	0.119087	−	2.64307i	0.00649674	−	0.144191i
$337$	11.2891	+	5.15556i	0.614957	+	0.280841i	0.698441	−	0.715668i	$-0.253877\pi$
$337$	11.2891	+	5.15556i	0.614957	+	0.280841i	−0.0834841	+	0.996509i	$0.526605\pi$
$338$	11.4412	−	5.89835i	0.622320	−	0.320828i
$339$	0.228061	+	0.217455i	0.0123866	+	0.0118106i
$340$	−0.0671557	+	0.194034i	−0.00364203	+	0.0105230i
$341$	23.7290	−	22.6255i	1.28500	−	1.22524i
$342$	2.45493	+	5.37554i	0.132747	+	0.290676i
$343$	5.35482	+	17.7292i	0.289133	+	0.957289i
$344$			1.83748i			0.0990702i
$345$	12.7356	−	0.542247i	0.685662	−	0.0291936i
$346$	−3.36817	+	1.94461i	−0.181074	+	0.104543i
$347$	12.3057	−	4.92644i	0.660602	−	0.264465i	−0.0170424	−	0.999855i	$-0.505425\pi$
$347$	12.3057	−	4.92644i	0.660602	−	0.264465i	0.677645	+	0.735390i	$0.263001\pi$
$348$	0.336354	−	3.52246i	0.0180305	−	0.188824i
$349$	6.92239	−	23.5755i	0.370547	−	1.26197i	−0.537558	−	0.843227i	$-0.680653\pi$
$349$	6.92239	−	23.5755i	0.370547	−	1.26197i	0.908105	−	0.418742i	$-0.137529\pi$
$350$	1.02005	−	5.36681i	0.0545239	−	0.286868i
$351$	−0.343094	+	0.100741i	−0.0183130	+	0.00537718i
$352$	−1.51356	−	2.93590i	−0.0806730	−	0.156484i
$353$	0.445528	+	4.66578i	0.0237131	+	0.248335i	0.999554	+	0.0298536i	$0.00950410\pi$
$353$	0.445528	+	4.66578i	0.0237131	+	0.248335i	−0.975841	+	0.218481i	$0.929890\pi$
$354$	−3.87277	−	0.746416i	−0.205835	−	0.0396715i
$355$	0.179318	+	3.76435i	0.00951722	+	0.199791i
$356$	0.336649	+	2.34144i	0.0178424	+	0.124096i
$357$	0.195955	−	0.0580859i	0.0103710	−	0.00307423i
$358$	13.2743	−	8.53087i	0.701568	−	0.450870i
$359$	4.24469	−	1.46910i	0.224026	−	0.0775362i	−0.212749	−	0.977107i	$-0.568242\pi$
$359$	4.24469	−	1.46910i	0.224026	−	0.0775362i	0.436775	+	0.899571i	$0.356120\pi$
$360$	2.64593	−	0.252656i	0.139453	−	0.0133161i
$361$	0.757653	−	15.9051i	0.0398765	−	0.837110i
$362$	−2.40309	+	9.90566i	−0.126303	+	0.520630i
$363$	−0.0677575	+	0.0587122i	−0.00355634	+	0.00308159i
$364$	−0.745159	−	0.582902i	−0.0390570	−	0.0305524i
$365$	34.6621	−	15.8297i	1.81430	−	0.828562i
$366$	5.45615	−	6.93806i	0.285197	−	0.362658i
$367$	8.31399	+	14.4002i	0.433987	+	0.751687i	0.997212	−	0.0746163i	$-0.0237732\pi$
$367$	8.31399	+	14.4002i	0.433987	+	0.751687i	−0.563226	+	0.826303i	$0.690440\pi$
$368$	−2.80154	+	3.89248i	−0.146040	+	0.202909i
$369$	6.47001	+	3.73546i	0.336816	+	0.194461i
$370$	−16.0877	−	2.31306i	−0.836360	−	0.120250i
$371$	0.220933	+	4.39966i	0.0114703	+	0.228419i
$372$	−9.52407	−	2.79652i	−0.493800	−	0.144993i
$373$	1.61751	+	8.39243i	0.0837514	+	0.434544i	0.999465	+	0.0327116i	$0.0104143\pi$
$373$	1.61751	+	8.39243i	0.0837514	+	0.434544i	−0.915713	+	0.401832i	$0.868374\pi$
$374$	0.176082	−	0.184669i	0.00910496	−	0.00954901i
$375$	−7.79288	−	0.371221i	−0.402423	−	0.0191697i
$376$	−8.10207	+	5.76946i	−0.417832	+	0.297537i
$377$	−0.956238	−	0.828585i	−0.0492488	−	0.0426743i
$378$	−1.73774	−	1.99506i	−0.0893797	−	0.102615i
$379$	4.90063	−	0.704604i	0.251729	−	0.0361931i	−0.0152953	−	0.999883i	$-0.504869\pi$
$379$	4.90063	−	0.704604i	0.251729	−	0.0361931i	0.267024	+	0.963690i	$0.413960\pi$
$380$	−14.5823	−	5.83787i	−0.748056	−	0.299477i
$381$	4.36702	−	8.47084i	0.223729	−	0.433974i
$382$	−3.52127	+	18.2701i	−0.180164	+	0.934779i
$383$	−7.00015	−	9.83034i	−0.357691	−	0.502307i	0.596045	−	0.802951i	$-0.296738\pi$
$383$	−7.00015	−	9.83034i	−0.357691	−	0.502307i	−0.953736	+	0.300644i	$0.902798\pi$
$384$	−0.540641	+	0.841254i	−0.0275895	+	0.0429300i
$385$	−13.4250	+	18.9558i	−0.684201	+	0.966079i
$386$	−2.77731	−	3.20519i	−0.141362	−	0.163140i
$387$	1.26800	+	1.32985i	0.0644563	+	0.0675998i
$388$	8.81458	−	12.3783i	0.447492	−	0.628415i
$389$	−0.369551	−	0.923094i	−0.0187370	−	0.0468027i	0.918704	−	0.394946i	$-0.129237\pi$
$389$	−0.369551	−	0.923094i	−0.0187370	−	0.0468027i	−0.937441	+	0.348143i	$0.886812\pi$
$390$	0.475216	−	0.823098i	0.0240635	−	0.0416792i
$391$	−0.354937	−	0.106168i	−0.0179500	−	0.00536916i
$392$	1.61527	−	6.81109i	0.0815835	−	0.344012i
$393$	−1.79874	+	12.5105i	−0.0907342	+	0.631070i
$394$	18.2365	+	1.74138i	0.918742	+	0.0877292i
$395$	7.47679	−	1.81385i	0.376198	−	0.0912647i
$396$	−3.12141	−	1.08033i	−0.156857	−	0.0542887i
$397$	5.83428	+	1.41538i	0.292814	+	0.0710359i	0.379475	−	0.925202i	$-0.376105\pi$
$397$	5.83428	+	1.41538i	0.292814	+	0.0710359i	−0.0866611	+	0.996238i	$0.527620\pi$
$398$	11.9458	+	7.67709i	0.598788	+	0.384818i
$399$	3.72525	+	15.1850i	0.186496	+	0.760201i
$400$	−1.35214	+	1.56046i	−0.0676071	+	0.0780228i
$401$	−32.4880	+	1.54759i	−1.62237	+	0.0772832i	−0.838951	−	0.544207i	$-0.816831\pi$
$401$	−32.4880	+	1.54759i	−1.62237	+	0.0772832i	−0.783422	+	0.621490i	$0.786528\pi$
$402$	4.55949	−	3.58562i	0.227407	−	0.178835i
$403$	−2.79000	+	2.19408i	−0.138980	+	0.109295i
$404$	5.37331	−	0.255962i	0.267332	−	0.0127346i
$405$	1.74060	−	2.00876i	0.0864910	−	0.0998159i
$406$	2.61443	−	8.98948i	0.129752	−	0.446140i
$407$	16.9916	+	10.9198i	0.842242	+	0.541276i
$408$	−0.0750720	−	0.0182123i	−0.00371662	−	0.000901641i
$409$	32.0654	+	11.0980i	1.58553	+	0.548759i	0.970782	−	0.239962i	$-0.0771351\pi$
$409$	32.0654	+	11.0980i	1.58553	+	0.548759i	0.614752	+	0.788721i	$0.289256\pi$
$410$	−19.2977	+	4.68158i	−0.953046	+	0.231207i
$411$	19.8629	+	1.89668i	0.979764	+	0.0935562i
$412$	−1.27055	+	8.83684i	−0.0625953	+	0.435360i
$413$	−9.69744	−	3.85334i	−0.477180	−	0.189610i
$414$	0.658545	+	4.75040i	0.0323657	+	0.233470i
$415$	14.1056	−	24.4316i	0.692416	−	1.19930i
$416$	0.132898	+	0.331964i	0.00651588	+	0.0162759i
$417$	−7.10970	+	9.98418i	−0.348164	+	0.488927i
$418$	13.4702	+	14.1272i	0.658850	+	0.690982i
$419$	25.1484	+	29.0228i	1.22858	+	1.41786i	0.876163	+	0.482015i	$0.160095\pi$
$419$	25.1484	+	29.0228i	1.22858	+	1.41786i	0.352418	+	0.935843i	$0.385359\pi$
$420$	7.00217	+	0.650443i	0.341671	+	0.0317384i
$421$	−3.92064	+	6.10064i	−0.191080	+	0.297327i	−0.923554	−	0.383469i	$-0.874729\pi$
$421$	−3.92064	+	6.10064i	−0.191080	+	0.297327i	0.732474	+	0.680796i	$0.238366\pi$
$422$	0.294265	+	0.413238i	0.0143246	+	0.0201161i
$423$	−1.88236	+	9.76662i	−0.0915235	+	0.474869i
$424$	0.762953	−	1.47992i	0.0370523	−	0.0718713i
$425$	−0.148078	−	0.0592813i	−0.00718282	−	0.00287557i
$426$	−1.40343	+	0.201782i	−0.0679963	+	0.00977639i
$427$	17.6093	−	15.3381i	0.852173	−	0.742261i
$428$	−2.40061	−	2.08014i	−0.116038	−	0.100547i
$429$	−0.962104	+	0.685111i	−0.0464508	+	0.0330775i
$430$	−4.87842	−	0.232388i	−0.235258	−	0.0112067i
$431$	−26.0134	+	27.2820i	−1.25302	+	1.31413i	−0.323100	+	0.946365i	$0.604725\pi$
$431$	−26.0134	+	27.2820i	−1.25302	+	1.31413i	−0.929919	+	0.367764i	$0.880123\pi$
$432$	0.189251	+	0.981929i	0.00910535	+	0.0472431i
$433$	−18.0289	−	5.29375i	−0.866412	−	0.254401i	−0.181823	−	0.983331i	$-0.558200\pi$
$433$	−18.0289	−	5.29375i	−0.866412	−	0.254401i	−0.684588	+	0.728930i	$0.740018\pi$
$434$	−23.3736	−	11.9739i	−1.12197	−	0.574764i
$435$	9.30943	+	1.33849i	0.446353	+	0.0641759i
$436$	14.0142	+	8.09111i	0.671159	+	0.387494i
$437$	9.40464	−	26.7355i	0.449885	−	1.27893i
$438$	7.16820	+	12.4157i	0.342510	+	0.593245i
$439$	1.83817	−	2.33743i	0.0877313	−	0.111559i	−0.740206	−	0.672380i	$-0.765272\pi$
$439$	1.83817	−	2.33743i	0.0877313	−	0.111559i	0.827937	+	0.560821i	$0.189514\pi$
$440$	7.98609	−	3.64713i	0.380722	−	0.173870i
$441$	−3.53116	−	6.04408i	−0.168151	−	0.287813i
$442$	−0.0208759	+	0.0180891i	−0.000992965	+	0.000860409i
$443$	1.56801	−	6.46342i	0.0744984	−	0.307087i	−0.922356	−	0.386341i	$-0.873739\pi$
$443$	1.56801	−	6.46342i	0.0744984	−	0.307087i	0.996854	+	0.0792544i	$0.0252540\pi$
$444$	0.290958	−	6.10796i	0.0138082	−	0.289871i
$445$	−6.25900	+	0.597662i	−0.296705	+	0.0283319i
$446$	−5.14368	+	1.78025i	−0.243560	+	0.0842970i
$447$	−4.49071	+	2.88600i	−0.212403	+	0.136503i
$448$	−1.82084	+	1.91951i	−0.0860267	+	0.0906885i
$449$	−0.277893	−	1.93279i	−0.0131146	−	0.0912138i	0.982213	−	0.187771i	$-0.0601262\pi$
$449$	−0.277893	−	1.93279i	−0.0131146	−	0.0912138i	−0.995327	+	0.0965568i	$0.969217\pi$
$450$	0.0982461	+	2.06244i	0.00463137	+	0.0972244i
$451$	24.2311	+	4.67017i	1.14100	+	0.219910i
$452$	−0.0299538	−	0.313690i	−0.00140891	−	0.0147547i
$453$	9.88332	+	19.1710i	0.464359	+	0.900731i
$454$	−24.6435	+	7.23597i	−1.15657	+	0.339601i
$455$	1.64182	−	1.90464i	0.0769696	−	0.0892911i
$456$	1.66492	−	5.67020i	0.0779671	−	0.265531i
$457$	3.50397	−	36.6952i	0.163909	−	1.71653i	−0.422371	−	0.906423i	$-0.638802\pi$
$457$	3.50397	−	36.6952i	0.163909	−	1.71653i	0.586280	−	0.810108i	$-0.300592\pi$
$458$	8.77669	−	3.51366i	0.410108	−	0.164182i
$459$	−0.0669000	+	0.0386248i	−0.00312263	+	0.00180285i
$460$	−9.98003	−	7.93025i	−0.465321	−	0.369750i
$461$			31.3468i			1.45997i	0.683464	+	0.729984i	$0.260473\pi$
$461$			31.3468i			1.45997i	−0.683464	+	0.729984i	$0.739527\pi$
$462$	−7.57953	−	4.35007i	−0.352632	−	0.202384i
$463$	6.17984	+	13.5320i	0.287202	+	0.628884i	0.997156	−	0.0753637i	$-0.0240118\pi$
$463$	6.17984	+	13.5320i	0.287202	+	0.628884i	−0.709954	+	0.704248i	$0.751284\pi$
$464$	−2.56092	+	2.44183i	−0.118888	+	0.113359i
$465$	8.62915	−	24.9323i	0.400167	−	1.15621i
$466$	20.2656	+	19.3232i	0.938788	+	0.895132i
$467$	11.3631	−	5.85809i	0.525822	−	0.271080i	−0.174811	−	0.984602i	$-0.555931\pi$
$467$	11.3631	−	5.85809i	0.525822	−	0.271080i	0.700633	+	0.713522i	$0.252901\pi$
$468$	0.325265	+	0.148543i	0.0150354	+	0.00686642i
$469$	13.6225	−	7.06732i	0.629028	−	0.326339i
$470$	−14.2930	−	22.2403i	−0.659285	−	1.02587i
$471$	−1.37594	+	3.43694i	−0.0634000	+	0.158366i
$472$	2.43805	+	3.10023i	0.112220	+	0.142700i
$473$	5.39464	+	2.78113i	0.248046	+	0.127877i
$474$	0.946721	+	2.73537i	0.0434843	+	0.125640i
$475$	5.06888	−	11.0993i	0.232576	−	0.509271i
$476$	−0.186131	−	0.0844249i	−0.00853131	−	0.00386961i
$477$	−0.469088	−	1.59757i	−0.0214781	−	0.0731476i
$478$	−18.0182	+	3.47273i	−0.824135	+	0.158839i
$479$	2.61791	+	10.7912i	0.119615	+	0.493061i	0.999829	+	0.0184838i	$0.00588392\pi$
$479$	2.61791	+	10.7912i	0.119615	+	0.493061i	−0.880214	+	0.474577i	$0.842601\pi$
$480$	−2.16511	−	1.54177i	−0.0988235	−	0.0703719i
$481$	−1.71874	−	1.35164i	−0.0783680	−	0.0616293i
$482$	−28.5311			−1.29956
$483$	−0.635106	+	12.6727i	−0.0288983	+	0.576627i
$484$	0.0896560			0.00407527
$485$	31.7491	+	24.9678i	1.44165	+	1.13373i
$486$	0.814576	+	0.580057i	0.0369499	+	0.0263119i
$487$	−8.44489	−	34.8103i	−0.382674	−	1.57741i	−0.759110	−	0.650963i	$-0.774365\pi$
$487$	−8.44489	−	34.8103i	−0.382674	−	1.57741i	0.376435	−	0.926443i	$-0.377150\pi$
$488$	−8.66694	+	1.67042i	−0.392334	+	0.0756162i
$489$	−4.84363	−	16.4959i	−0.219037	−	0.745970i
$490$	17.8788	+	5.14988i	0.807684	+	0.232648i
$491$	0.709166	−	1.55286i	0.0320042	−	0.0700795i	−0.892955	−	0.450146i	$-0.851372\pi$
$491$	0.709166	−	1.55286i	0.0320042	−	0.0700795i	0.924959	+	0.380067i	$0.124099\pi$
$492$	−2.44350	−	7.06003i	−0.110162	−	0.318291i
$493$	−0.242960	−	0.125254i	−0.0109423	−	0.00564117i
$494$	−1.30626	−	1.66104i	−0.0587712	−	0.0747337i
$495$	3.26300	−	8.15058i	0.146661	−	0.366341i
$496$	5.36648	+	8.35040i	0.240962	+	0.374944i
$497$	−3.74750	−	0.168849i	−0.168098	−	0.00757391i
$498$	9.65468	+	4.40914i	0.432636	+	0.197578i
$499$	−19.3562	+	9.97883i	−0.866504	+	0.446714i	−0.833356	−	0.552737i	$-0.813584\pi$
$499$	−19.3562	+	9.97883i	−0.866504	+	0.446714i	−0.0331480	+	0.999450i	$0.510553\pi$
$500$	5.64637	+	5.38380i	0.252513	+	0.240771i
$501$	4.05041	−	11.7029i	0.180959	−	0.522846i
$502$	−10.0993	+	9.62965i	−0.450753	+	0.429792i
$503$	1.11208	+	2.43513i	0.0495854	+	0.108577i	0.932803	−	0.360386i	$-0.117355\pi$
$503$	1.11208	+	2.43513i	0.0495854	+	0.108577i	−0.883218	+	0.468963i	$0.844628\pi$
$504$	0.00681005	+	2.64574i	0.000303344	+	0.117851i
$505$			14.2983i			0.636265i
$506$	7.18760	+	14.1165i	0.319528	+	0.627556i
$507$	−11.1476	+	6.43607i	−0.495082	+	0.285836i
$508$	−8.84760	+	3.54204i	−0.392549	+	0.157153i
$509$	−2.71969	+	28.4819i	−0.120548	+	1.26244i	0.709484	+	0.704722i	$0.248928\pi$
$509$	−2.71969	+	28.4819i	−0.120548	+	1.26244i	−0.830032	+	0.557716i	$0.811678\pi$
$510$	0.0578472	−	0.197009i	0.00256152	−	0.00872372i
$511$	12.4981	+	35.8124i	0.552883	+	1.58425i
$512$	0.959493	−	0.281733i	0.0424040	−	0.0124509i
$513$	−2.70793	−	5.25264i	−0.119558	−	0.231910i
$514$	−0.333417	−	3.49170i	−0.0147064	−	0.154012i
$515$	−23.3007	−	4.49085i	−1.02675	−	0.197890i
$516$	−0.0874307	−	1.83540i	−0.00384892	−	0.0807988i
$517$	4.67556	+	32.5192i	0.205631	+	1.43019i
$518$	3.77373	−	15.7322i	0.165808	−	0.691232i
$519$	3.27182	−	2.10267i	0.143617	−	0.0922971i
$520$	−0.898158	+	0.310856i	−0.0393868	+	0.0136319i
$521$	−27.4911	+	2.62508i	−1.20441	+	0.115007i	−0.677894	−	0.735160i	$-0.737107\pi$
$521$	−27.4911	+	2.62508i	−1.20441	+	0.115007i	−0.526513	+	0.850167i	$0.676501\pi$
$522$	−0.168368	+	3.53447i	−0.00736926	+	0.154700i
$523$	−2.67906	+	11.0432i	−0.117147	+	0.482886i	0.882768	+	0.469810i	$0.155678\pi$
$523$	−2.67906	+	11.0432i	−0.117147	+	0.482886i	−0.999915	+	0.0130762i	$0.995838\pi$
$524$	9.55202	−	8.27687i	0.417282	−	0.361577i
$525$	−0.763530	+	5.40927i	−0.0333232	+	0.236080i
$526$	1.00009	−	0.456725i	0.0436059	−	0.0199142i
$527$	−0.473998	+	0.602737i	−0.0206477	+	0.0262557i
$528$	1.65154	+	2.86055i	0.0718741	+	0.124490i
$529$	13.5298	−	18.5996i	0.588252	−	0.808678i
$530$	3.83263	+	2.21277i	0.166479	+	0.0961167i
$531$	3.90390	+	0.561296i	0.169415	+	0.0243582i
$532$	7.12870	−	13.9156i	0.309069	−	0.603317i
$533$	−2.56323	−	0.752633i	−0.111026	−	0.0326001i
$534$	−0.447678	−	2.32277i	−0.0193729	−	0.100516i
$535$	5.82628	−	6.11043i	0.251892	−	0.264177i
$536$	−5.79391	−	0.275998i	−0.250259	−	0.0119213i
$537$	−12.8533	+	9.15282i	−0.554662	+	0.394973i
$538$	−8.58872	−	7.44217i	−0.370286	−	0.320855i
$539$	−17.5518	−	15.0513i	−0.756011	−	0.648303i
$540$	−2.63091	+	0.378268i	−0.113216	+	0.0162781i
$541$	14.8032	+	5.92631i	0.636439	+	0.254792i	0.667366	−	0.744730i	$-0.267422\pi$
$541$	14.8032	+	5.92631i	0.636439	+	0.254792i	−0.0309268	+	0.999522i	$0.509846\pi$
$542$	8.50515	−	16.4977i	0.365327	−	0.708636i
$543$	1.92904	−	10.0088i	0.0827828	−	0.429518i
$544$	0.0448091	+	0.0629256i	0.00192117	+	0.00269791i
$545$	−23.2539	+	36.1838i	−0.996089	+	1.54994i
$546$	0.772051	+	0.546785i	0.0330407	+	0.0234003i
$547$	27.8930	+	32.1903i	1.19262	+	1.37636i	0.908669	+	0.417518i	$0.137100\pi$
$547$	27.8930	+	32.1903i	1.19262	+	1.37636i	0.283951	+	0.958839i	$0.408355\pi$
$548$	−13.7693	−	14.4408i	−0.588196	−	0.616882i
$549$	−5.11984	+	7.18981i	−0.218510	+	0.306854i
$550$	2.53479	+	6.33159i	0.108084	+	0.269980i
$551$	10.4555	−	18.1094i	0.445418	−	0.771486i
$552$	2.61316	−	4.02137i	0.111223	−	0.171161i
$553$	1.10940	+	7.57753i	0.0471765	+	0.322229i
$554$	0.746227	−	5.19013i	0.0317042	−	0.220507i
$555$	16.1795	+	1.54496i	0.686784	+	0.0655799i
$556$	11.9114	−	2.88968i	0.505156	−	0.122550i
$557$	−3.32072	−	1.14931i	−0.140703	−	0.0486979i	0.255809	−	0.966727i	$-0.417658\pi$
$557$	−3.32072	−	1.14931i	−0.140703	−	0.0486979i	−0.396512	+	0.918030i	$0.629779\pi$
$558$	9.64634	+	2.34018i	0.408362	+	0.0990676i
$559$	−0.552739	−	0.355224i	−0.0233784	−	0.0150244i
$560$	−4.86594	−	5.07702i	−0.205623	−	0.214543i
$561$	−0.167095	+	0.192838i	−0.00705476	+	0.00814163i
$562$	−0.748200	+	0.0356412i	−0.0315609	+	0.00150343i
$563$	−27.3910	+	21.5405i	−1.15439	+	0.907825i	−0.996820	−	0.0796819i	$-0.974610\pi$
$563$	−27.3910	+	21.5405i	−1.15439	+	0.907825i	−0.157574	+	0.987507i	$0.550367\pi$
$564$	7.81837	−	6.14843i	0.329213	−	0.258896i
$565$	0.836621	−	0.0398532i	0.0351969	−	0.00167663i
$566$	−5.82140	+	6.71825i	−0.244692	+	0.282389i
$567$	1.83070	+	1.91011i	0.0768822	+	0.0802173i
$568$	1.19278	+	0.766553i	0.0500479	+	0.0321638i
$569$	16.4548	+	3.99189i	0.689821	+	0.167349i	0.565321	−	0.824871i	$-0.308752\pi$
$569$	16.4548	+	3.99189i	0.689821	+	0.167349i	0.124500	+	0.992220i	$0.460267\pi$
$570$	14.8436	+	5.13741i	0.621728	+	0.215182i
$571$	43.9564	−	10.6637i	1.83952	−	0.446263i	0.843637	−	0.536915i	$-0.180410\pi$
$571$	43.9564	−	10.6637i	1.83952	−	0.446263i	0.995883	+	0.0906522i	$0.0288952\pi$
$572$	1.17576	+	0.112272i	0.0491611	+	0.00469432i
$573$	2.64796	−	18.4169i	0.110620	−	0.769379i
$574$	−2.86338	−	19.5577i	−0.119515	−	0.816324i
$575$	6.52235	−	7.45085i	0.272001	−	0.310722i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	9.52884	+	23.8019i	0.396691	+	0.990886i	0.983459	+	0.181131i	$0.0579758\pi$
$577$	9.52884	+	23.8019i	0.396691	+	0.990886i	−0.586768	+	0.809755i	$0.699600\pi$
$578$	9.85751	−	13.8429i	0.410018	−	0.575790i
$579$	2.92668	+	3.06941i	0.121629	+	0.127560i
$580$	−6.15907	−	7.10795i	−0.255741	−	0.295141i
$581$	22.9164	+	16.2300i	0.950732	+	0.673332i
$582$	−8.21561	+	12.7837i	−0.340548	+	0.529903i
$583$	−3.19012	−	4.47990i	−0.132121	−	0.185538i
$584$	2.71318	−	14.0773i	0.112272	−	0.582524i
$585$	−0.435513	+	0.844777i	−0.0180062	+	0.0349272i
$586$	17.2051	+	6.88790i	0.710738	+	0.284537i
$587$	−37.9409	+	5.45508i	−1.56599	+	0.225155i	−0.870057	−	0.492952i	$-0.835918\pi$
$587$	−37.9409	+	5.45508i	−1.56599	+	0.225155i	−0.695933	+	0.718107i	$0.745009\pi$
$588$	−1.28936	+	6.88023i	−0.0531722	+	0.283736i
$589$	−44.3318	−	38.4137i	−1.82666	−	1.58281i
$590$	−8.53931	+	6.08082i	−0.351558	+	0.250343i
$591$	−18.2987	−	0.871675i	−0.752708	−	0.0358559i
$592$	−4.21975	+	4.42555i	−0.173431	+	0.181889i
$593$	−7.41411	−	38.4680i	−0.304461	−	1.57969i	−0.735605	−	0.677410i	$-0.763102\pi$
$593$	−7.41411	−	38.4680i	−0.304461	−	1.57969i	0.431144	−	0.902283i	$-0.358110\pi$
$594$	3.16928	+	0.930585i	0.130037	+	0.0381824i
$595$	0.247685	−	0.483493i	0.0101541	−	0.0198213i
$596$	5.28378	+	0.759693i	0.216432	+	0.0311182i
$597$	−12.2975	−	7.09999i	−0.503305	−	0.290583i
$598$	−0.629313	−	1.59524i	−0.0257345	−	0.0652343i
$599$	−10.8708	−	18.8287i	−0.444168	−	0.769322i	0.553826	−	0.832633i	$-0.313167\pi$
$599$	−10.8708	−	18.8287i	−0.444168	−	0.769322i	−0.997994	+	0.0633110i	$0.979834\pi$
$600$	1.27636	−	1.62303i	0.0521073	−	0.0662598i
$601$	0.110111	−	0.0502861i	0.00449153	−	0.00205121i	−0.413168	−	0.910655i	$-0.635578\pi$
$601$	0.110111	−	0.0502861i	0.00449153	−	0.00205121i	0.417660	+	0.908604i	$0.362850\pi$
$602$	0.679477	−	4.81379i	0.0276934	−	0.196195i
$603$	−4.38371	+	3.79851i	−0.178519	+	0.154687i
$604$	5.08500	−	20.9607i	0.206906	−	0.852877i
$605$	−0.0113389	+	0.238033i	−0.000460991	+	0.00967740i
$606$	−5.35505	+	0.511345i	−0.217534	+	0.0207720i
$607$	21.6525	−	7.49399i	0.878846	−	0.304172i	0.149866	−	0.988706i	$-0.452116\pi$
$607$	21.6525	−	7.49399i	0.878846	−	0.304172i	0.728980	+	0.684535i	$0.239995\pi$
$608$	−4.97145	+	3.19496i	−0.201619	+	0.129573i
$609$	−2.18374	+	9.10369i	−0.0884895	+	0.368900i
$610$	−3.33876	−	23.2216i	−0.135183	−	0.940215i
$611$	−0.169230	−	3.55258i	−0.00684632	−	0.143722i
$612$	0.0758535	+	0.0146196i	0.00306620	+	0.000590961i
$613$	−0.195631	−	2.04874i	−0.00790147	−	0.0827480i	0.990661	−	0.136348i	$-0.0435365\pi$
$613$	−0.195631	−	2.04874i	−0.00790147	−	0.0827480i	−0.998562	+	0.0535999i	$0.982930\pi$
$614$	−13.2010	−	25.6064i	−0.532750	−	1.03339i
$615$	19.0531	−	5.59450i	0.768295	−	0.225592i
$616$	2.87954	+	8.25110i	0.116020	+	0.332446i
$617$	5.24788	−	17.8727i	0.211272	−	0.719526i	−0.783857	−	0.620942i	$-0.786750\pi$
$617$	5.24788	−	17.8727i	0.211272	−	0.719526i	0.995129	−	0.0985843i	$-0.0314314\pi$
$618$	0.848633	−	8.88729i	0.0341370	−	0.357499i
$619$	35.9285	−	14.3836i	1.44409	−	0.578127i	0.488431	−	0.872602i	$-0.337569\pi$
$619$	35.9285	−	14.3836i	1.44409	−	0.578127i	0.955659	+	0.294476i	$0.0951450\pi$
$620$	−22.8486	+	13.1917i	−0.917624	+	0.529790i
$621$	−0.883832	−	4.71369i	−0.0354670	−	0.189154i
$622$		−	1.42222i		−	0.0570259i
$623$	−0.0161093	−	6.25856i	−0.000645406	−	0.250744i
$624$	−0.148543	−	0.325265i	−0.00594650	−	0.0130210i
$625$	−22.4796	+	21.4343i	−0.899184	+	0.857370i
$626$	1.24727	−	3.60375i	0.0498510	−	0.144035i
$627$	−14.1272	−	13.4702i	−0.564184	−	0.537949i
$628$	3.29058	−	1.69641i	0.131309	−	0.0676942i
$629$	−0.429684	−	0.196230i	−0.0171326	−	0.00782421i
$630$	−7.02519	−	0.316530i	−0.279890	−	0.0126108i
$631$	−7.49325	−	11.6597i	−0.298302	−	0.464166i	0.659456	−	0.751743i	$-0.270787\pi$
$631$	−7.49325	−	11.6597i	−0.298302	−	0.464166i	−0.957758	+	0.287577i	$0.907150\pi$
$632$	1.07580	−	2.68723i	0.0427931	−	0.106892i
$633$	−0.313594	−	0.398768i	−0.0124643	−	0.0158496i
$634$	−6.02868	−	3.10800i	−0.239429	−	0.123434i
$635$	−8.28500	−	23.9379i	−0.328780	−	0.949948i
$636$	−0.691671	+	1.51455i	−0.0274265	+	0.0600557i
$637$	1.73660	+	1.80263i	0.0688068	+	0.0714226i
$638$	3.29286	+	11.2144i	0.130366	+	0.443984i
$639$	1.39224	−	0.268332i	0.0550760	−	0.0106150i
$640$	0.626639	+	2.58304i	0.0247701	+	0.102104i
$641$	−16.3854	−	11.6680i	−0.647184	−	0.460858i	0.208732	−	0.977973i	$-0.433067\pi$
$641$	−16.3854	−	11.6680i	−0.647184	−	0.460858i	−0.855916	+	0.517115i	$0.827006\pi$
$642$	2.49686	+	1.96356i	0.0985434	+	0.0774954i
$643$	−1.56375			−0.0616683			−0.0308342	−	0.999525i	$-0.509816\pi$
$643$	−1.56375			−0.0616683			−0.0308342	+	0.999525i	$0.509816\pi$
$644$	8.77882	−	9.16146i	0.345934	−	0.361012i
$645$	4.88395			0.192305
$646$	−0.358843	−	0.282197i	−0.0141185	−	0.0111029i
$647$	15.6586	+	11.1504i	0.615603	+	0.438369i	0.844853	−	0.534999i	$-0.179688\pi$
$647$	15.6586	+	11.1504i	0.615603	+	0.438369i	−0.229250	+	0.973368i	$0.573627\pi$
$648$	−0.235759	−	0.971812i	−0.00926149	−	0.0381764i
$649$	12.7921	−	2.46547i	0.502133	−	0.0967782i
$650$	−0.208009	−	0.708413i	−0.00815878	−	0.0277863i
$651$	23.9169	+	10.8482i	0.937376	+	0.425173i
$652$	−7.14194	+	15.6387i	−0.279700	+	0.612457i
$653$	−10.7386	−	31.0272i	−0.420235	−	1.21419i	−0.934315	−	0.356448i	$-0.883988\pi$
$653$	−10.7386	−	31.0272i	−0.420235	−	1.21419i	0.514080	−	0.857742i	$-0.328133\pi$
$654$	−14.3833	−	7.41513i	−0.562433	−	0.289954i
$655$	20.7667	+	26.4070i	0.811421	+	1.03181i
$656$	−2.77666	+	6.93577i	−0.108411	+	0.270796i
$657$	−7.75084	−	12.0605i	−0.302389	−	0.470527i
$658$	23.3591	−	12.1187i	0.910633	−	0.472435i
$659$	4.77427	+	2.18034i	0.185979	+	0.0849339i	0.506228	−	0.862400i	$-0.331039\pi$
$659$	4.77427	+	2.18034i	0.185979	+	0.0849339i	−0.320249	+	0.947333i	$0.603767\pi$
$660$	−7.80351	+	4.02299i	−0.303751	+	0.156595i
$661$	1.17769	+	1.12292i	0.0458068	+	0.0436767i	0.712637	−	0.701533i	$-0.247501\pi$
$661$	1.17769	+	1.12292i	0.0458068	+	0.0436767i	−0.666830	+	0.745210i	$0.732349\pi$
$662$	−4.79019	+	13.8403i	−0.186176	+	0.537920i
$663$	0.0199915	−	0.0190619i	0.000776407	−	0.000740302i
$664$	−4.40914	−	9.65468i	−0.171108	−	0.374674i
$665$	36.0437	+	20.6863i	1.39771	+	0.802181i
$666$			6.11488i			0.236947i
$667$	12.3407	−	11.6485i	0.477834	−	0.451030i
$668$	−10.7249	+	6.19200i	−0.414957	+	0.239576i
$669$	5.05315	−	2.02297i	0.195366	−	0.0782127i
$670$	1.46553	−	15.3477i	0.0566182	−	0.592932i
$671$	−8.21377	+	27.9735i	−0.317089	+	1.07991i
$672$	1.72745	−	2.00398i	0.0666377	−	0.0773051i
$673$	−49.4125	+	14.5088i	−1.90471	+	0.559274i	−0.918057	+	0.396448i	$0.870243\pi$
$673$	−49.4125	+	14.5088i	−1.90471	+	0.559274i	−0.986655	+	0.162826i	$0.947939\pi$
$674$	5.68688	+	11.0310i	0.219050	+	0.424899i
$675$	−0.196270	−	2.05543i	−0.00755443	−	0.0791135i
$676$	12.6395	+	2.43607i	0.486135	+	0.0936949i
$677$	0.922254	+	19.3605i	0.0354451	+	0.744084i	0.944718	+	0.327884i	$0.106336\pi$
$677$	0.922254	+	19.3605i	0.0354451	+	0.744084i	−0.909273	+	0.416200i	$0.863361\pi$
$678$	0.0448458	+	0.311909i	0.00172229	+	0.0119788i
$679$	−27.6696	+	29.1690i	−1.06186	+	1.11940i
$680$	−0.172732	+	0.111008i	−0.00662396	+	0.00425696i
$681$	24.2712	−	8.40036i	0.930076	−	0.321902i
$682$	32.6384	−	3.11659i	1.24979	−	0.119340i
$683$	0.986106	−	20.7009i	0.0377323	−	0.792098i	−0.898130	−	0.439731i	$-0.855074\pi$
$683$	0.986106	−	20.7009i	0.0377323	−	0.792098i	0.935862	−	0.352367i	$-0.114623\pi$
$684$	−1.39324	+	5.74300i	−0.0532717	+	0.219589i
$685$	40.0812	−	34.7306i	1.53142	−	1.32699i
$686$	−6.75031	+	17.2463i	−0.257728	+	0.658465i
$687$	−8.59956	+	3.92729i	−0.328094	+	0.149835i
$688$	−1.13585	+	1.44436i	−0.0433040	+	0.0550655i
$689$	0.297686	+	0.515608i	0.0113409	+	0.0196431i
$690$	10.3461	+	7.44640i	0.393868	+	0.283480i
$691$	21.6551	+	12.5026i	0.823799	+	0.475620i	0.851725	−	0.523990i	$-0.175557\pi$
$691$	21.6551	+	12.5026i	0.823799	+	0.475620i	−0.0279260	+	0.999610i	$0.508890\pi$
$692$	−3.84964	−	0.553494i	−0.146341	−	0.0210407i
$693$	7.77793	+	3.98449i	0.295459	+	0.151358i
$694$	12.7182	+	3.73441i	0.482777	+	0.141756i
$695$	6.16551	+	31.9897i	0.233871	+	1.21344i
$696$	2.44183	−	2.56092i	0.0925574	−	0.0970714i
$697$	−0.576472	−	0.0274607i	−0.0218354	−	0.00104015i
$698$	20.0148	−	14.2525i	0.757571	−	0.539464i
$699$	−21.1621	−	18.3371i	−0.800425	−	0.693572i
$700$	4.11936	−	3.58805i	0.155697	−	0.135615i
$701$	−31.9539	+	4.59427i	−1.20688	+	0.173523i	−0.716250	−	0.697844i	$-0.754143\pi$
$701$	−31.9539	+	4.59427i	−1.20688	+	0.173523i	−0.490631	+	0.871367i	$0.663234\pi$
$702$	−0.331964	−	0.132898i	−0.0125292	−	0.00501593i
$703$	16.5586	−	32.1193i	0.624521	−	1.21140i
$704$	0.625112	−	3.24339i	0.0235598	−	0.122240i
$705$	15.3350	+	21.5350i	0.577550	+	0.811055i
$706$	−2.53399	+	3.94296i	−0.0953678	+	0.148395i
$707$	−14.1716	−	1.31642i	−0.532976	−	0.0495090i
$708$	−2.58280	−	2.98071i	−0.0970676	−	0.112022i
$709$	2.66133	+	2.79112i	0.0999482	+	0.104823i	0.771808	−	0.635856i	$-0.219353\pi$
$709$	2.66133	+	2.79112i	0.0999482	+	0.104823i	−0.671860	+	0.740678i	$0.734504\pi$
$710$	−2.18601	+	3.06983i	−0.0820397	+	0.115209i
$711$	−1.07580	−	2.68723i	−0.0403458	−	0.100779i
$712$	−1.18276	+	2.04860i	−0.0443258	+	0.0767746i
$713$	−25.5342	−	40.1766i	−0.956264	−	1.50462i
$714$	0.189937	+	0.0754728i	0.00710823	+	0.00282450i
$715$	−0.446776	+	3.10740i	−0.0167085	+	0.116210i
$716$	15.7077	+	1.49991i	0.587025	+	0.0560541i
$717$	17.8326	−	4.32614i	0.665971	−	0.161563i
$718$	4.24469	+	1.46910i	0.158410	+	0.0548264i
$719$	20.9724	+	5.08784i	0.782137	+	0.189744i	0.606896	−	0.794781i	$-0.292414\pi$
$719$	20.9724	+	5.08784i	0.782137	+	0.189744i	0.175241	+	0.984526i	$0.443930\pi$
$720$	2.23602	+	1.43700i	0.0833316	+	0.0535540i
$721$	6.59631	−	22.6808i	0.245659	−	0.844676i
$722$	10.4274	−	12.0339i	0.388069	−	0.447855i
$723$	28.4988	−	1.35757i	1.05988	−	0.0504884i
$724$	−8.01223	+	6.30089i	−0.297772	+	0.234171i
$725$	5.74305	−	4.51638i	0.213291	−	0.167734i
$726$	−0.0895544	+	0.00426600i	−0.00332368	+	0.000158326i
$727$	−30.1070	+	34.7453i	−1.11661	+	1.28863i	−0.163318	+	0.986573i	$0.552220\pi$
$727$	−30.1070	+	34.7453i	−1.11661	+	1.28863i	−0.953289	+	0.302060i	$0.902326\pi$
$728$	−0.225409	−	0.918818i	−0.00835420	−	0.0340537i
$729$	−0.841254	−	0.540641i	−0.0311575	−	0.0200237i
$730$	37.0315	+	8.98375i	1.37060	+	0.332503i
$731$	−0.134137	−	0.0464254i	−0.00496125	−	0.00171711i
$732$	8.57765	−	2.08091i	0.317039	−	0.0769128i
$733$	37.0480	+	3.53766i	1.36840	+	0.130666i	0.753245	−	0.657740i	$-0.228487\pi$
$733$	37.0480	+	3.53766i	1.36840	+	0.130666i	0.615155	+	0.788406i	$0.289094\pi$
$734$	−2.36641	+	16.4587i	−0.0873457	+	0.607503i
$735$	−18.1036	−	4.29333i	−0.667762	−	0.158362i
$736$	−4.60833	+	1.32789i	−0.169865	+	0.0489468i
$737$	−9.57974	+	16.5926i	−0.352874	+	0.611196i
$738$	2.77666	+	6.93577i	0.102210	+	0.255309i
$739$	15.3228	−	21.5179i	0.563660	−	0.791550i	−0.430137	−	0.902764i	$-0.641535\pi$
$739$	15.3228	−	21.5179i	0.563660	−	0.791550i	0.993796	+	0.111214i	$0.0354740\pi$
$740$	−11.2160	−	11.7630i	−0.412307	−	0.432415i
$741$	1.38381	+	1.59700i	0.0508356	+	0.0586674i
$742$	−2.54603	+	3.59494i	−0.0934676	+	0.131974i
$743$	−1.59838	+	2.48714i	−0.0586390	+	0.0912441i	−0.869335	−	0.494223i	$-0.835453\pi$
$743$	−1.59838	+	2.48714i	−0.0586390	+	0.0912441i	0.810696	+	0.585467i	$0.199089\pi$
$744$	−5.75773	−	8.08560i	−0.211089	−	0.296432i
$745$	−2.68520	+	13.9321i	−0.0983779	+	0.510433i
$746$	−3.91641	+	7.59677i	−0.143390	+	0.278138i
$747$	−9.85354	−	3.94476i	−0.360522	−	0.144331i
$748$	0.252564	−	0.0363132i	0.00923466	−	0.00132774i
$749$	5.51986	+	6.33722i	0.201691	+	0.231557i
$750$	−5.89614	−	5.10904i	−0.215297	−	0.186556i
$751$	19.4892	−	13.8782i	0.711170	−	0.506422i	−0.166287	−	0.986077i	$-0.553178\pi$
$751$	19.4892	−	13.8782i	0.711170	−	0.506422i	0.877457	+	0.479655i	$0.159238\pi$
$752$	−9.93510	−	0.473267i	−0.362296	−	0.0172583i
$753$	9.62965	−	10.0993i	0.350924	−	0.368038i
$754$	−0.239457	−	1.24242i	−0.00872050	−	0.0452462i
$755$	55.0065	+	16.1514i	2.00189	+	0.587808i
$756$	−0.132692	−	2.64242i	−0.00482596	−	0.0961040i
$757$	−35.1849	−	5.05882i	−1.27882	−	0.183866i	−0.530772	−	0.847515i	$-0.678098\pi$
$757$	−35.1849	−	5.05882i	−1.27882	−	0.183866i	−0.748044	+	0.663649i	$0.769007\pi$
$758$	4.28771	+	2.47551i	0.155737	+	0.0899147i
$759$	−7.85115	−	13.7585i	−0.284979	−	0.499403i
$760$	−7.85373	−	13.6031i	−0.284885	−	0.493435i
$761$	−20.9235	+	26.6064i	−0.758478	+	0.964483i	−0.999982	−	0.00591684i	$-0.998117\pi$
$761$	−20.9235	+	26.6064i	−0.758478	+	0.964483i	0.241505	+	0.970400i	$0.422359\pi$
$762$	8.66904	−	3.95902i	0.314046	−	0.143420i
$763$	−33.7222	−	26.3792i	−1.22083	−	0.954993i
$764$	−14.0617	+	12.1846i	−0.508735	+	0.440822i
$765$	−0.0484076	+	0.199539i	−0.00175018	+	0.00721434i
$766$	0.574221	−	12.0544i	0.0207474	−	0.435542i
$767$	−1.40392	+	0.134058i	−0.0506926	+	0.00484056i
$768$	−0.945001	+	0.327068i	−0.0340998	+	0.0118020i
$769$	−18.2270	+	11.7138i	−0.657282	+	0.422409i	−0.826321	−	0.563200i	$-0.809570\pi$
$769$	−18.2270	+	11.7138i	−0.657282	+	0.422409i	0.169039	+	0.985609i	$0.445934\pi$
$770$	−22.2705	+	6.60152i	−0.802572	+	0.237902i
$771$	0.499182	+	3.47188i	0.0179776	+	0.125037i
$772$	−0.201799	−	4.23627i	−0.00726289	−	0.152467i
$773$	−27.0807	−	5.21938i	−0.974026	−	0.187728i	−0.322679	−	0.946508i	$-0.604583\pi$
$773$	−27.0807	−	5.21938i	−0.974026	−	0.187728i	−0.651347	+	0.758780i	$0.725796\pi$
$774$	0.174663	+	1.82916i	0.00627815	+	0.0657477i
$775$	−9.39149	−	18.2169i	−0.337352	−	0.654372i
$776$	14.5805	−	4.28122i	0.523410	−	0.153687i
$777$	−3.02089	+	15.8939i	−0.108374	+	0.570191i
$778$	0.280132	−	0.954042i	0.0100432	−	0.0342041i
$779$	4.19673	−	43.9501i	0.150363	−	1.57468i
$780$	0.882350	−	0.353240i	0.0315932	−	0.0126480i
$781$	4.05586	−	2.34165i	0.145130	−	0.0837909i
$782$	−0.213371	−	0.302862i	−0.00763012	−	0.0108303i
$783$		−	3.53848i		−	0.126455i
$784$	5.48002	−	4.35538i	0.195715	−	0.155549i
$785$	4.08774	+	8.95089i	0.145898	+	0.319471i
$786$	−9.14737	+	8.72200i	−0.326276	+	0.311103i
$787$	7.18588	−	20.7622i	0.256149	−	0.740094i	−0.741461	−	0.670996i	$-0.765867\pi$
$787$	7.18588	−	20.7622i	0.256149	−	0.740094i	0.997610	−	0.0690979i	$-0.0220121\pi$
$788$	13.2584	+	12.6419i	0.472312	+	0.450348i
$789$	−0.977224	+	0.503794i	−0.0347901	+	0.0179355i
$790$	6.99840	+	3.19606i	0.248992	+	0.113711i
$791$	−0.0375264	+	0.832876i	−0.00133428	+	0.0296136i
$792$	−1.78578	−	2.77873i	−0.0634549	−	0.0987378i
$793$	1.17302	−	2.93007i	0.0416552	−	0.104050i
$794$	3.71112	+	4.71908i	0.131703	+	0.167474i
$795$	−3.93358	−	2.02790i	−0.139510	−	0.0719223i
$796$	4.64436	+	13.4190i	0.164615	+	0.475623i
$797$	4.03002	−	8.82452i	0.142751	−	0.312580i	−0.824729	−	0.565528i	$-0.808673\pi$
$797$	4.03002	−	8.82452i	0.142751	−	0.312580i	0.967480	+	0.252947i	$0.0813999\pi$
$798$	−6.45850	+	14.2390i	−0.228628	+	0.504056i
$799$	−0.216470	−	0.737228i	−0.00765814	−	0.0260812i
$800$	−2.02747	+	0.390762i	−0.0716817	+	0.0138155i
$801$	0.557693	+	2.29884i	0.0197051	+	0.0812256i
$802$	−26.4939	−	18.8663i	−0.935534	−	0.666191i
$803$	−37.2230	−	29.2725i	−1.31357	−	1.03300i
$804$	5.80048			0.204567
$805$	23.2130	+	24.4660i	0.818151	+	0.862314i
$806$	−3.54938			−0.125021
$807$	8.93311	+	7.02507i	0.314460	+	0.247294i
$808$	4.38194	+	3.12036i	0.154156	+	0.109774i
$809$	−4.16246	−	17.1579i	−0.146344	−	0.603240i	−0.996992	−	0.0775036i	$-0.975305\pi$
$809$	−4.16246	−	17.1579i	−0.146344	−	0.603240i	0.850648	−	0.525736i	$-0.176210\pi$
$810$	2.60993	−	0.503023i	0.0917037	−	0.0176744i
$811$	−14.0522	−	47.8575i	−0.493441	−	1.68051i	−0.709972	−	0.704230i	$-0.751293\pi$
$811$	−14.0522	−	47.8575i	−0.493441	−	1.68051i	0.216531	−	0.976276i	$-0.430526\pi$
$812$	7.61201	−	5.45007i	0.267129	−	0.191260i
$813$	−7.71052	+	16.8837i	−0.270420	+	0.592137i
$814$	6.60610	+	19.0871i	0.231544	+	0.669002i
$815$	−40.6167	−	20.9394i	−1.42274	−	0.733474i
$816$	−0.0477525	−	0.0607222i	−0.00167167	−	0.00212570i
$817$	4.03578	−	10.0809i	0.141194	−	0.352686i
$818$	18.3448	+	28.5451i	0.641412	+	0.998057i
$819$	−0.797193	−	0.509430i	−0.0278562	−	0.0178009i
$820$	−18.0630	−	8.24909i	−0.630787	−	0.288071i
$821$	−40.3411	+	20.7973i	−1.40791	+	0.725830i	−0.983714	−	0.179739i	$-0.942475\pi$
$821$	−40.3411	+	20.7973i	−1.40791	+	0.725830i	−0.424199	+	0.905569i	$0.639444\pi$
$822$	14.4408	+	13.7693i	0.503682	+	0.480260i
$823$	−12.6014	+	36.4094i	−0.439257	+	1.26915i	0.480615	+	0.876932i	$0.340413\pi$
$823$	−12.6014	+	36.4094i	−0.439257	+	1.26915i	−0.919872	+	0.392218i	$0.871708\pi$
$824$	−6.46129	+	6.16083i	−0.225090	+	0.214623i
$825$	−2.83319	−	6.20381i	−0.0986389	−	0.215989i
$826$	−5.24073	−	9.02348i	−0.182348	−	0.313967i
$827$		−	3.81889i		−	0.132796i	−0.997793	−	0.0663978i	$-0.978849\pi$
$827$		−	3.81889i		−	0.132796i	0.997793	−	0.0663978i	$-0.0211506\pi$
$828$	−2.41885	+	4.14115i	−0.0840609	+	0.143915i
$829$	12.9860	−	7.49747i	0.451022	−	0.260398i	−0.257240	−	0.966348i	$-0.582813\pi$
$829$	12.9860	−	7.49747i	0.451022	−	0.260398i	0.708262	+	0.705950i	$0.249480\pi$
$830$	26.1904	−	10.4850i	0.909080	−	0.363941i
$831$	−0.498426	+	5.21975i	−0.0172902	+	0.181071i
$832$	−0.100741	+	0.343094i	−0.00349258	+	0.0118946i
$833$	0.456404	+	0.290004i	0.0158135	+	0.0100480i
$834$	−11.7604	+	3.45317i	−0.407230	+	0.119573i
$835$	−15.0831	−	29.2571i	−0.521972	−	1.01248i
$836$	1.85548	+	19.4314i	0.0641730	+	0.672050i
$837$	−9.74677	−	1.87854i	−0.336898	−	0.0649317i
$838$	1.82727	+	38.3592i	0.0631221	+	1.32510i
$839$	0.495056	+	3.44319i	0.0170912	+	0.118872i	0.996581	−	0.0826219i	$-0.0263294\pi$
$839$	0.495056	+	3.44319i	0.0170912	+	0.118872i	−0.979490	+	0.201494i	$0.935420\pi$
$840$	5.10200	+	4.83974i	0.176036	+	0.166987i
$841$	−13.8631	+	8.90930i	−0.478039	+	0.307217i
$842$	−6.85300	+	2.37184i	−0.236170	+	0.0817392i
$843$	0.745657	−	0.0712016i	0.0256818	−	0.00245231i
$844$	−0.0241385	+	0.506729i	−0.000830881	+	0.0174423i
$845$	−8.06618	+	33.2493i	−0.277485	+	1.14381i
$846$	−7.51696	+	6.51348i	−0.258438	+	0.223938i
$847$	−0.234879	−	0.0331537i	−0.00807054	−	0.00113917i
$848$	1.51455	−	0.691671i	0.0520098	−	0.0237521i
$849$	5.49514	−	6.98763i	0.188593	−	0.239815i
$850$	−0.0797516	−	0.138134i	−0.00273546	−	0.00473795i
$851$	20.3441	−	21.1218i	0.697387	−	0.724044i
$852$	−1.22790	−	0.708930i	−0.0420672	−	0.0242875i
$853$	17.0891	+	2.45704i	0.585119	+	0.0841275i	0.428516	−	0.903534i	$-0.359037\pi$
$853$	17.0891	+	2.45704i	0.585119	+	0.0841275i	0.156603	+	0.987662i	$0.449946\pi$
$854$	23.3232	−	1.17120i	0.798104	−	0.0400776i
$855$	−15.0712	−	4.42530i	−0.515424	−	0.151342i
$856$	−0.601149	−	3.11906i	−0.0205468	−	0.106607i
$857$	5.95404	−	6.24442i	0.203386	−	0.213305i	−0.614139	−	0.789198i	$-0.710497\pi$
$857$	5.95404	−	6.24442i	0.203386	−	0.213305i	0.817526	+	0.575892i	$0.195345\pi$
$858$	−1.17977	−	0.0561995i	−0.0402768	−	0.00191862i
$859$	12.3932	−	8.82513i	0.422849	−	0.301109i	−0.348753	−	0.937215i	$-0.613395\pi$
$859$	12.3932	−	8.82513i	0.422849	−	0.301109i	0.771602	+	0.636105i	$0.219456\pi$
$860$	−3.69104	−	3.19831i	−0.125864	−	0.109061i
$861$	3.79073	+	19.3993i	0.129188	+	0.661127i
$862$	−37.3125	+	5.36473i	−1.27087	+	0.182723i
$863$	−37.4979	−	15.0119i	−1.27644	−	0.511011i	−0.368314	−	0.929702i	$-0.620065\pi$
$863$	−37.4979	−	15.0119i	−1.27644	−	0.511011i	−0.908129	+	0.418691i	$0.862489\pi$
$864$	−0.458227	+	0.888835i	−0.0155892	+	0.0302388i
$865$	1.95637	−	10.1506i	0.0665186	−	0.345131i
$866$	−10.8993	−	15.3059i	−0.370372	−	0.520115i
$867$	−9.18767	+	14.2963i	−0.312030	+	0.485527i
$868$	−10.9711	−	23.8607i	−0.372384	−	0.809885i
$869$	−6.26112	−	7.22572i	−0.212394	−	0.245116i
$870$	6.49030	+	6.80683i	0.220042	+	0.230773i
$871$	1.20311	−	1.68954i	0.0407659	−	0.0572477i
$872$	6.01433	+	15.0231i	0.203671	+	0.508745i
$873$	7.59803	−	13.1602i	0.257154	−	0.445404i
$874$	23.9193	−	15.2019i	0.809083	−	0.514213i
$875$	−12.8014	−	16.1923i	−0.432766	−	0.547401i
$876$	−2.04028	+	14.1905i	−0.0689348	+	0.479452i
$877$	−12.5845	−	1.20167i	−0.424948	−	0.0405776i	−0.119608	−	0.992821i	$-0.538164\pi$
$877$	−12.5845	−	1.20167i	−0.424948	−	0.0405776i	−0.305340	+	0.952244i	$0.598770\pi$
$878$	2.88981	−	0.701059i	0.0975262	−	0.0236596i
$879$	−17.5134	−	6.06145i	−0.590712	−	0.204448i
$880$	8.53199	+	2.06984i	0.287613	+	0.0697743i
$881$	−26.6435	−	17.1228i	−0.897643	−	0.576880i	0.00844710	−	0.999964i	$-0.497311\pi$
$881$	−26.6435	−	17.1228i	−0.897643	−	0.576880i	−0.906090	+	0.423084i	$0.860948\pi$
$882$	0.960522	−	6.93379i	0.0323425	−	0.233473i
$883$	−21.5691	+	24.8921i	−0.725859	+	0.837686i	−0.991999	−	0.126248i	$-0.959706\pi$
$883$	−21.5691	+	24.8921i	−0.725859	+	0.837686i	0.266140	+	0.963935i	$0.414252\pi$
$884$	−0.0275915	+	0.00131434i	−0.000928002	+	4.42062e-5i
$885$	8.24030	−	6.48024i	0.276995	−	0.217831i
$886$	5.22796	−	4.11131i	0.175637	−	0.138122i
$887$	−55.6720	+	2.65198i	−1.86928	+	0.0890449i	−0.951428	−	0.307871i	$-0.900383\pi$
$887$	−55.6720	+	2.65198i	−1.86928	+	0.0890449i	−0.917855	+	0.396916i	$0.870080\pi$
$888$	4.00440	−	4.62132i	0.134379	−	0.155081i
$889$	24.4886	−	6.00765i	0.821321	−	0.201490i
$890$	−5.28936	−	3.39927i	−0.177300	−	0.113944i
$891$	−3.20997	−	0.778731i	−0.107538	−	0.0260885i
$892$	−5.14368	−	1.78025i	−0.172223	−	0.0596070i
$893$	57.1219	−	13.8576i	1.91151	−	0.463728i
$894$	−5.31394	−	0.507420i	−0.177725	−	0.0169707i
$895$	−5.96876	+	41.5136i	−0.199513	+	1.38765i
$896$	−2.61784	+	0.383269i	−0.0874560	+	0.0128041i
$897$	0.704505	+	1.56349i	0.0235227	+	0.0522035i
$898$	0.976331	−	1.69105i	0.0325806	−	0.0564312i
$899$	−13.0541	−	32.6075i	−0.435378	−	1.08752i
$900$	−1.19769	+	1.68192i	−0.0399230	+	0.0560640i
$901$	0.0887589	+	0.0930876i	0.00295699	+	0.00310120i
$902$	16.1601	+	18.6497i	0.538071	+	0.620967i
$903$	−0.449658	+	4.84067i	−0.0149637	+	0.161087i
$904$	0.170365	−	0.265093i	0.00566625	−	0.00881686i
$905$	−15.7153	−	22.0690i	−0.522393	−	0.733598i
$906$	−4.08189	+	21.1789i	−0.135612	+	0.703621i
$907$	−7.88222	+	15.2894i	−0.261725	+	0.507675i	−0.982681	−	0.185305i	$-0.940673\pi$
$907$	−7.88222	+	15.2894i	−0.261725	+	0.507675i	0.720956	+	0.692981i	$0.243703\pi$
$908$	−23.8440	−	9.54571i	−0.791292	−	0.316786i
$909$	5.32465	−	0.765569i	0.176608	−	0.0253923i
$910$	2.46793	−	0.482246i	0.0818111	−	0.0159863i
$911$	33.6289	+	29.1396i	1.11417	+	0.965438i	0.999609	−	0.0279780i	$-0.00890682\pi$
$911$	33.6289	+	29.1396i	1.11417	+	0.965438i	0.114566	+	0.993416i	$0.463452\pi$
$912$	4.81380	−	3.42789i	0.159401	−	0.113509i
$913$	−35.0186	−	1.66814i	−1.15895	−	0.0552075i
$914$	25.4378	−	26.6784i	0.841408	−	0.882443i
$915$	4.43991	+	23.0364i	0.146779	+	0.761561i
$916$	9.07094	+	2.66347i	0.299712	+	0.0880035i
$917$	−28.0849	+	18.1514i	−0.927445	+	0.599411i
$918$	−0.0764632	−	0.0109938i	−0.00252366	−	0.000362848i
$919$	13.9176	+	8.03535i	0.459100	+	0.265062i	0.711666	−	0.702518i	$-0.247941\pi$
$919$	13.9176	+	8.03535i	0.459100	+	0.265062i	−0.252565	+	0.967580i	$0.581274\pi$
$920$	−2.94268	−	12.4028i	−0.0970172	−	0.408910i
$921$	14.4045	+	24.9493i	0.474643	+	0.822106i
$922$	−19.3773	+	24.6403i	−0.638159	+	0.811485i
$923$	−0.461180	+	0.210614i	−0.0151799	+	0.00693244i
$924$	−3.26888	−	8.10474i	−0.107538	−	0.266626i
$925$	9.54200	−	8.26819i	0.313739	−	0.271857i
$926$	−3.50722	+	14.4570i	−0.115255	+	0.475086i
$927$	−0.424798	+	8.91760i	−0.0139522	+	0.292892i
$928$	−3.52246	+	0.336354i	−0.115630	+	0.0110414i
$929$	−8.24641	+	2.85411i	−0.270556	+	0.0936403i	−0.458977	−	0.888448i	$-0.651784\pi$
$929$	−8.24641	+	2.85411i	−0.270556	+	0.0936403i	0.188421	+	0.982088i	$0.439663\pi$
$930$	22.1951	−	14.2639i	0.727805	−	0.467732i
$931$	−23.8215	+	33.8197i	−0.780717	+	1.10840i
$932$	3.98503	+	27.7165i	0.130534	+	0.907884i
$933$	0.0676720	+	1.42061i	0.00221548	+	0.0465087i
$934$	12.5532	+	2.41944i	0.410755	+	0.0791664i
$935$	0.0644680	+	0.675139i	0.00210833	+	0.0220794i
$936$	0.163852	+	0.317828i	0.00535567	+	0.0103885i
$937$	−4.82645	+	1.41717i	−0.157673	+	0.0462970i	−0.359617	−	0.933100i	$-0.617092\pi$
$937$	−4.82645	+	1.41717i	−0.157673	+	0.0462970i	0.201943	+	0.979397i	$0.435274\pi$
$938$	15.0767	+	2.86557i	0.492273	+	0.0935643i
$939$	−1.07439	+	3.65902i	−0.0350612	+	0.119408i
$940$	2.51300	−	26.3174i	0.0819652	−	0.858378i
$941$	−39.0396	+	15.6291i	−1.27265	+	0.509494i	−0.906950	−	0.421238i	$-0.861596\pi$
$941$	−39.0396	+	15.6291i	−1.27265	+	0.509494i	−0.365703	+	0.930731i	$0.619172\pi$
$942$	−3.20614	+	1.85106i	−0.104462	+	0.0603109i
$943$	13.4842	−	33.1951i	0.439105	−	1.08098i
$944$			3.94405i			0.128368i
$945$	7.03229	−	0.0181009i	0.228760	−	0.000588821i
$946$	2.52129	+	5.52086i	0.0819743	+	0.179499i
$947$	4.83927	−	4.61424i	0.157255	−	0.149943i	−0.607367	−	0.794422i	$-0.707774\pi$
$947$	4.83927	−	4.61424i	0.157255	−	0.149943i	0.764622	+	0.644479i	$0.222926\pi$
$948$	−0.946721	+	2.73537i	−0.0307481	+	0.0888407i
$949$	3.71014	+	3.53761i	0.120436	+	0.114836i
$950$	10.8455	−	5.59127i	0.351876	−	0.181405i
$951$	6.16973	+	2.81762i	0.200067	+	0.0913677i
$952$	−0.0941210	−	0.181421i	−0.00305048	−	0.00587989i
$953$	14.3200	+	22.2824i	0.463871	+	0.721798i	0.991843	−	0.127464i	$-0.0406838\pi$
$953$	14.3200	+	22.2824i	0.463871	+	0.721798i	−0.527972	+	0.849262i	$0.677047\pi$
$954$	0.618822	−	1.54574i	0.0200351	−	0.0500453i
$955$	−30.5710	−	38.8742i	−0.989256	−	1.25794i
$956$	−16.3100	−	8.40839i	−0.527503	−	0.271947i
$957$	−3.82273	−	11.0451i	−0.123571	−	0.357036i
$958$	−4.61284	+	10.1007i	−0.149034	+	0.326339i
$959$	30.7326	+	42.9236i	0.992406	+	1.38607i
$960$	−0.748835	−	2.55030i	−0.0241686	−	0.0823105i
$961$	−66.3080	+	12.7798i	−2.13897	+	0.412252i
$962$	−0.515499	−	2.12491i	−0.0166203	−	0.0685100i
$963$	−2.58747	−	1.84253i	−0.0833799	−	0.0593746i
$964$	−22.4270	−	17.6368i	−0.722325	−	0.568042i
$965$	11.2726			0.362879
$966$	−8.33295	+	9.56880i	−0.268108	+	0.307871i
$967$	29.1270			0.936661			0.468330	−	0.883553i	$-0.344856\pi$
$967$	29.1270			0.936661			0.468330	+	0.883553i	$0.344856\pi$
$968$	0.0704744	+	0.0554216i	0.00226513	+	0.00178132i
$969$	0.371864	+	0.264803i	0.0119460	+	0.00850670i
$970$	9.52244	+	39.2520i	0.305747	+	1.26031i
$971$	−54.5835	+	10.5201i	−1.75167	+	0.337607i	−0.961400	−	0.275154i	$-0.911271\pi$
$971$	−54.5835	+	10.5201i	−1.75167	+	0.337607i	−0.790269	+	0.612760i	$0.790059\pi$
$972$	0.281733	+	0.959493i	0.00903658	+	0.0307758i
$973$	−32.2738	+	3.16563i	−1.03465	+	0.101485i
$974$	14.8802	−	32.5830i	0.476792	−	1.04403i
$975$	0.241481	+	0.697714i	0.00773358	+	0.0223447i
$976$	−7.84526	−	4.04451i	−0.251121	−	0.129462i
$977$	−25.5862	−	32.5355i	−0.818575	−	1.04090i	−0.998363	−	0.0571974i	$-0.981784\pi$
$977$	−25.5862	−	32.5355i	−0.818575	−	1.04090i	0.179788	−	0.983705i	$-0.442459\pi$
$978$	6.38973	−	15.9608i	0.204321	−	0.510369i
$979$	4.22430	+	6.57314i	0.135009	+	0.210079i
$980$	10.8703	+	15.1000i	0.347238	+	0.482353i
$981$	14.7199	+	6.72234i	0.469969	+	0.214628i
$982$	1.51735	−	0.782251i	0.0484207	−	0.0249626i
$983$	−8.68048	−	8.27682i	−0.276864	−	0.263989i	0.538906	−	0.842366i	$-0.318838\pi$
$983$	−8.68048	−	8.27682i	−0.276864	−	0.263989i	−0.815770	+	0.578377i	$0.803686\pi$
$984$	2.44350	−	7.06003i	0.0778960	−	0.225066i
$985$	−35.2404	+	33.6017i	−1.12285	+	1.07064i
$986$	−0.113552	−	0.248644i	−0.00361623	−	0.00791844i
$987$	−22.7560	+	13.2164i	−0.724333	+	0.420683i
$988$		−	2.11314i		−	0.0672279i
$989$	5.48226	−	6.89930i	0.174326	−	0.219385i
$990$	7.60325	−	4.38974i	0.241647	−	0.139515i
$991$	−47.1990	+	18.8956i	−1.49932	+	0.600239i	−0.968891	−	0.247487i	$-0.920395\pi$
$991$	−47.1990	+	18.8956i	−1.49932	+	0.600239i	−0.530434	+	0.847726i	$0.677971\pi$
$992$	−0.943540	+	9.88120i	−0.0299574	+	0.313728i
$993$	4.12622	−	14.0526i	0.130941	−	0.445946i
$994$	−2.84136	−	2.44928i	−0.0901225	−	0.0776863i
$995$	−36.2142	+	10.6334i	−1.14807	+	0.337103i
$996$	4.86354	+	9.43394i	0.154107	+	0.298926i
$997$	5.34037	+	55.9269i	0.169131	+	1.77122i	0.539162	+	0.842202i	$0.318741\pi$
$997$	5.34037	+	55.9269i	0.169131	+	1.77122i	−0.370031	+	0.929020i	$0.620653\pi$
$998$	−21.3835	−	4.12134i	−0.676884	−	0.130459i
$999$	−0.290958	−	6.10796i	−0.00920550	−	0.193247i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.be.a.61.1	✓	320
7.3	odd	6	inner	966.2.be.a.199.9	yes	320
23.20	odd	22	inner	966.2.be.a.733.9	yes	320
161.66	even	66	inner	966.2.be.a.871.1	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.be.a.61.1	✓	320	1.1	even	1	trivial
966.2.be.a.199.9	yes	320	7.3	odd	6	inner
966.2.be.a.733.9	yes	320	23.20	odd	22	inner
966.2.be.a.871.1	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)

\(f(q)\)	\(=\)	\(q+(0.786053 + 0.618159i) q^{2} +(-0.814576 - 0.580057i) q^{3} +(0.235759 + 0.971812i) q^{4} +(-2.60993 + 0.503023i) q^{5} +(-0.281733 - 0.959493i) q^{6} +(-0.258273 - 2.63312i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(0.327068 + 0.945001i) q^{9} +O(q^{10})\)	\(q+(0.786053 + 0.618159i) q^{2} +(-0.814576 - 0.580057i) q^{3} +(0.235759 + 0.971812i) q^{4} +(-2.60993 + 0.503023i) q^{5} +(-0.281733 - 0.959493i) q^{6} +(-0.258273 - 2.63312i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(0.327068 + 0.945001i) q^{9} +(-2.36249 - 1.21795i) q^{10} +(2.04183 + 2.59640i) q^{11} +(0.371662 - 0.928368i) q^{12} +(-0.193322 - 0.300814i) q^{13} +(1.42467 - 2.22942i) q^{14} +(2.41777 + 1.10416i) q^{15} +(-0.888835 + 0.458227i) q^{16} +(-0.0559081 - 0.0533083i) q^{17} +(-0.327068 + 0.945001i) q^{18} +(4.27696 - 4.07808i) q^{19} +(-1.10416 - 2.41777i) q^{20} +(-1.31697 + 2.29469i) q^{21} +3.30308i q^{22} +(4.27374 - 2.17603i) q^{23} +(0.866025 - 0.500000i) q^{24} +(1.91687 - 0.767401i) q^{25} +(0.0339900 - 0.355959i) q^{26} +(0.281733 - 0.959493i) q^{27} +(2.49800 - 0.871773i) q^{28} +(3.39515 - 0.996905i) q^{29} +(1.21795 + 2.36249i) q^{30} +(-0.943540 - 9.88120i) q^{31} +(-0.981929 - 0.189251i) q^{32} +(-0.157167 - 3.29934i) q^{33} +(-0.0109938 - 0.0764632i) q^{34} +(1.99859 + 6.74233i) q^{35} +(-0.841254 + 0.540641i) q^{36} +(5.77857 - 1.99998i) q^{37} +(5.88282 - 0.561741i) q^{38} +(-0.0170143 + 0.357173i) q^{39} +(0.626639 - 2.58304i) q^{40} +(5.64615 - 4.89242i) q^{41} +(-2.45369 + 0.989645i) q^{42} +(1.67143 - 0.763316i) q^{43} +(-2.04183 + 2.59640i) q^{44} +(-1.32898 - 2.30187i) q^{45} +(4.70452 + 0.931379i) q^{46} +(8.61380 + 4.97318i) q^{47} +(0.989821 + 0.142315i) q^{48} +(-6.86659 + 1.36013i) q^{49} +(1.98114 + 0.581716i) q^{50} +(0.0146196 + 0.0758535i) q^{51} +(0.246757 - 0.258792i) q^{52} +(-1.66313 - 0.0792245i) q^{53} +(0.814576 - 0.580057i) q^{54} +(-6.63508 - 5.74933i) q^{55} +(2.50246 + 0.858902i) q^{56} +(-5.84943 + 0.841021i) q^{57} +(3.28501 + 1.31512i) q^{58} +(1.80727 - 3.50561i) q^{59} +(-0.503023 + 2.60993i) q^{60} +(5.11984 + 7.18981i) q^{61} +(5.36648 - 8.35040i) q^{62} +(2.40382 - 1.10528i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(0.655873 + 0.687859i) q^{65} +(1.91597 - 2.69061i) q^{66} +(2.15582 + 5.38498i) q^{67} +(0.0386248 - 0.0669000i) q^{68} +(-4.74351 - 0.706474i) q^{69} +(-2.59683 + 6.53528i) q^{70} +(0.201782 - 1.40343i) q^{71} +(-0.995472 - 0.0950560i) q^{72} +(-13.9323 + 3.37993i) q^{73} +(5.77857 + 1.99998i) q^{74} +(-2.00658 - 0.486790i) q^{75} +(4.97145 + 3.19496i) q^{76} +(6.30926 - 6.04695i) q^{77} +(-0.234164 + 0.270240i) q^{78} +(-2.89129 + 0.137729i) q^{79} +(2.08930 - 1.64305i) q^{80} +(-0.786053 + 0.618159i) q^{81} +(7.46247 - 0.355481i) q^{82} +(-6.95058 + 8.02139i) q^{83} +(-2.54049 - 0.738858i) q^{84} +(0.172732 + 0.111008i) q^{85} +(1.78568 + 0.433202i) q^{86} +(-3.34387 - 1.15732i) q^{87} +(-3.20997 + 0.778731i) q^{88} +(2.35481 + 0.224857i) q^{89} +(0.378268 - 2.63091i) q^{90} +(-0.742149 + 0.586730i) q^{91} +(3.12226 + 3.64026i) q^{92} +(-4.96307 + 8.59629i) q^{93} +(3.69669 + 9.23388i) q^{94} +(-9.11122 + 12.7949i) q^{95} +(0.690079 + 0.723734i) q^{96} +(-9.95130 - 11.4844i) q^{97} +(-6.23828 - 3.17551i) q^{98} +(-1.78578 + 2.77873i) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more