LMFDB - Embedded newform 574.2.s.a.387.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [574,2,Mod(37,574)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(574, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 24]))

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

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

chi := DirichletCharacter("574.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 574 = 2 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	574.s (of order $15$, degree $8$, 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:	$4.58341307602$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			387.11
Character	$\chi$	$=$	574.387
Dual form			574.2.s.a.221.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.978148 + 0.207912i) q^{2} +(0.980436 + 1.69816i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-0.0139362 - 0.132594i) q^{5} +(0.605943 + 1.86490i) q^{6} +(-2.51124 + 0.832858i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.422509 + 0.731808i) q^{9} +O(q^{10})$	\(q+(0.978148 + 0.207912i) q^{2} +(0.980436 + 1.69816i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-0.0139362 - 0.132594i) q^{5} +(0.605943 + 1.86490i) q^{6} +(-2.51124 + 0.832858i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.422509 + 0.731808i) q^{9} +(0.0139362 - 0.132594i) q^{10} +(-0.152751 + 1.45333i) q^{11} +(0.204967 + 1.95013i) q^{12} +(1.71263 + 5.27095i) q^{13} +(-2.62953 + 0.292541i) q^{14} +(0.211503 - 0.153666i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-0.124057 + 1.18032i) q^{17} +(-0.565428 + 0.627971i) q^{18} +(-0.609428 - 0.676838i) q^{19} +(0.0411994 - 0.126799i) q^{20} +(-3.87644 - 3.44794i) q^{21} +(-0.451577 + 1.38981i) q^{22} +(0.455593 + 0.0968392i) q^{23} +(-0.204967 + 1.95013i) q^{24} +(4.87335 - 1.03586i) q^{25} +(0.579318 + 5.51184i) q^{26} +4.22564 q^{27} +(-2.63289 - 0.260562i) q^{28} +(-1.39410 + 1.01287i) q^{29} +(0.238830 - 0.106334i) q^{30} +(0.130921 - 1.24563i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.61776 + 1.16550i) q^{33} +(-0.366749 + 1.12874i) q^{34} +(0.145429 + 0.321368i) q^{35} +(-0.683635 + 0.496690i) q^{36} +(-0.859988 - 8.18224i) q^{37} +(-0.455388 - 0.788755i) q^{38} +(-7.27181 + 8.07616i) q^{39} +(0.0666620 - 0.115462i) q^{40} +(4.24491 - 4.79382i) q^{41} +(-3.07487 - 4.17856i) q^{42} +(-3.21803 - 9.90406i) q^{43} +(-0.730667 + 1.26555i) q^{44} +(0.102921 + 0.0458235i) q^{45} +(0.425503 + 0.189446i) q^{46} +(-11.3800 - 2.41890i) q^{47} +(-0.605943 + 1.86490i) q^{48} +(5.61270 - 4.18302i) q^{49} +4.98222 q^{50} +(-2.12601 + 0.946562i) q^{51} +(-0.579318 + 5.51184i) q^{52} +(0.661421 + 0.294484i) q^{53} +(4.13330 + 0.878560i) q^{54} +0.194831 q^{55} +(-2.52118 - 0.802276i) q^{56} +(0.551878 - 1.69851i) q^{57} +(-1.57422 + 0.700889i) q^{58} +(6.02008 - 6.68598i) q^{59} +(0.255719 - 0.0543547i) q^{60} +(8.69556 + 9.65740i) q^{61} +(0.387040 - 1.19119i) q^{62} +(0.451533 - 2.18964i) q^{63} +(0.309017 + 0.951057i) q^{64} +(0.675027 - 0.300541i) q^{65} +(-2.80287 + 0.595769i) q^{66} +(-10.6027 - 4.72064i) q^{67} +(-0.593412 + 1.02782i) q^{68} +(0.282230 + 0.868616i) q^{69} +(0.0754346 + 0.344582i) q^{70} +(6.04582 + 4.39255i) q^{71} +(-0.771963 + 0.343700i) q^{72} +(1.11062 + 1.92366i) q^{73} +(0.859988 - 8.18224i) q^{74} +(6.53707 + 7.26016i) q^{75} +(-0.281445 - 0.866199i) q^{76} +(-0.826821 - 3.77688i) q^{77} +(-8.79203 + 6.38778i) q^{78} +(2.26011 - 3.91463i) q^{79} +(0.0892112 - 0.0990791i) q^{80} +(5.41050 + 9.37126i) q^{81} +(5.14884 - 3.80650i) q^{82} +1.50836 q^{83} +(-2.13890 - 4.72654i) q^{84} +0.158232 q^{85} +(-1.08853 - 10.3567i) q^{86} +(-3.08685 - 1.37435i) q^{87} +(-0.977824 + 1.08598i) q^{88} +(1.57873 + 1.75335i) q^{89} +(0.0911450 + 0.0662207i) q^{90} +(-8.69079 - 11.8103i) q^{91} +(0.376816 + 0.273773i) q^{92} +(2.24364 - 0.998932i) q^{93} +(-10.6284 - 4.73209i) q^{94} +(-0.0812514 + 0.0902389i) q^{95} +(-0.980436 + 1.69816i) q^{96} +(-8.57525 + 6.23028i) q^{97} +(6.35974 - 2.92466i) q^{98} +(-0.999019 - 0.725830i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 14 q^{2} + 2 q^{3} + 14 q^{4} + 4 q^{6} + 2 q^{7} + 28 q^{8} - 58 q^{9}+O(q^{10}) $ 112 * q - 14 * q^2 + 2 * q^3 + 14 * q^4 + 4 * q^6 + 2 * q^7 + 28 * q^8 - 58 * q^9	\( 112 q - 14 q^{2} + 2 q^{3} + 14 q^{4} + 4 q^{6} + 2 q^{7} + 28 q^{8} - 58 q^{9} - 6 q^{11} - 3 q^{12} + 6 q^{13} + 18 q^{14} + 26 q^{15} + 14 q^{16} - 12 q^{17} - 17 q^{18} - 2 q^{19} - 21 q^{21} + 8 q^{22} + 8 q^{23} + 3 q^{24} + 18 q^{25} - 2 q^{26} - 16 q^{27} - 4 q^{28} - 10 q^{29} + 13 q^{30} - 21 q^{31} + 56 q^{32} - 15 q^{33} + 26 q^{34} + 52 q^{35} - 24 q^{36} + 37 q^{37} + 2 q^{38} - 34 q^{39} + 14 q^{41} + 14 q^{42} - 10 q^{43} + 4 q^{44} - 4 q^{45} + 7 q^{46} - 19 q^{47} - 4 q^{48} - 36 q^{49} - 184 q^{50} + 3 q^{51} + 2 q^{52} + 59 q^{53} - 18 q^{54} + 68 q^{55} + 8 q^{56} + 56 q^{57} - 5 q^{58} + 10 q^{59} + 17 q^{60} - 12 q^{61} + 8 q^{62} - q^{63} - 28 q^{64} + 26 q^{65} - 10 q^{66} - 5 q^{67} - 2 q^{68} - 2 q^{69} + 9 q^{70} - 26 q^{71} - 12 q^{72} + 34 q^{73} - 37 q^{74} - 33 q^{75} + 4 q^{76} + 57 q^{77} + 82 q^{78} - 20 q^{79} - 96 q^{81} - 38 q^{82} - 60 q^{83} + 15 q^{84} - 92 q^{85} - 5 q^{86} - 40 q^{87} - 4 q^{88} + 33 q^{89} - 8 q^{90} + 14 q^{92} + 18 q^{93} - 16 q^{94} + 17 q^{95} - 2 q^{96} - 8 q^{97} - 3 q^{98} + 84 q^{99}+O(q^{100}) \) 112 * q - 14 * q^2 + 2 * q^3 + 14 * q^4 + 4 * q^6 + 2 * q^7 + 28 * q^8 - 58 * q^9 - 6 * q^11 - 3 * q^12 + 6 * q^13 + 18 * q^14 + 26 * q^15 + 14 * q^16 - 12 * q^17 - 17 * q^18 - 2 * q^19 - 21 * q^21 + 8 * q^22 + 8 * q^23 + 3 * q^24 + 18 * q^25 - 2 * q^26 - 16 * q^27 - 4 * q^28 - 10 * q^29 + 13 * q^30 - 21 * q^31 + 56 * q^32 - 15 * q^33 + 26 * q^34 + 52 * q^35 - 24 * q^36 + 37 * q^37 + 2 * q^38 - 34 * q^39 + 14 * q^41 + 14 * q^42 - 10 * q^43 + 4 * q^44 - 4 * q^45 + 7 * q^46 - 19 * q^47 - 4 * q^48 - 36 * q^49 - 184 * q^50 + 3 * q^51 + 2 * q^52 + 59 * q^53 - 18 * q^54 + 68 * q^55 + 8 * q^56 + 56 * q^57 - 5 * q^58 + 10 * q^59 + 17 * q^60 - 12 * q^61 + 8 * q^62 - q^63 - 28 * q^64 + 26 * q^65 - 10 * q^66 - 5 * q^67 - 2 * q^68 - 2 * q^69 + 9 * q^70 - 26 * q^71 - 12 * q^72 + 34 * q^73 - 37 * q^74 - 33 * q^75 + 4 * q^76 + 57 * q^77 + 82 * q^78 - 20 * q^79 - 96 * q^81 - 38 * q^82 - 60 * q^83 + 15 * q^84 - 92 * q^85 - 5 * q^86 - 40 * q^87 - 4 * q^88 + 33 * q^89 - 8 * q^90 + 14 * q^92 + 18 * q^93 - 16 * q^94 + 17 * q^95 - 2 * q^96 - 8 * q^97 - 3 * q^98 + 84 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/574\mathbb{Z}\right)^\times$.

$n$	$211$	$493$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.978148	+	0.207912i	0.691655	+	0.147016i
$2$	0.978148	+	0.207912i	0.691655	+	0.147016i
$3$	0.980436	+	1.69816i	0.566055	+	0.980436i	0.996951	+	0.0780342i	$0.0248643\pi$
$3$	0.980436	+	1.69816i	0.566055	+	0.980436i	−0.430896	+	0.902402i	$0.641802\pi$
$4$	0.913545	+	0.406737i	0.456773	+	0.203368i
$5$	−0.0139362	−	0.132594i	−0.00623244	−	0.0592977i	0.990964	−	0.134131i	$-0.0428242\pi$
$5$	−0.0139362	−	0.132594i	−0.00623244	−	0.0592977i	−0.997196	+	0.0748331i	$0.976158\pi$
$6$	0.605943	+	1.86490i	0.247375	+	0.761342i
$7$	−2.51124	+	0.832858i	−0.949161	+	0.314791i
$7$	−2.51124	+	0.832858i	−0.949161	+	0.314791i
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	−0.422509	+	0.731808i	−0.140836	+	0.243936i
$10$	0.0139362	−	0.132594i	0.00440700	−	0.0419298i
$11$	−0.152751	+	1.45333i	−0.0460562	+	0.438195i	0.947060	+	0.321058i	$0.104038\pi$
$11$	−0.152751	+	1.45333i	−0.0460562	+	0.438195i	−0.993116	+	0.117137i	$0.962628\pi$
$12$	0.204967	+	1.95013i	0.0591689	+	0.562954i
$13$	1.71263	+	5.27095i	0.474999	+	1.46190i	0.845959	+	0.533248i	$0.179029\pi$
$13$	1.71263	+	5.27095i	0.474999	+	1.46190i	−0.370959	+	0.928649i	$0.620971\pi$
$14$	−2.62953	+	0.292541i	−0.702771	+	0.0781848i
$15$	0.211503	−	0.153666i	0.0546097	−	0.0396763i
$16$	0.669131	+	0.743145i	0.167283	+	0.185786i
$17$	−0.124057	+	1.18032i	−0.0300882	+	0.286270i	0.969124	+	0.246575i	$0.0793053\pi$
$17$	−0.124057	+	1.18032i	−0.0300882	+	0.286270i	−0.999212	+	0.0396949i	$0.987361\pi$
$18$	−0.565428	+	0.627971i	−0.133273	+	0.148014i
$19$	−0.609428	−	0.676838i	−0.139812	−	0.155277i	0.669172	−	0.743108i	$-0.266649\pi$
$19$	−0.609428	−	0.676838i	−0.139812	−	0.155277i	−0.808984	+	0.587830i	$0.799982\pi$
$20$	0.0411994	−	0.126799i	0.00921247	−	0.0283531i
$21$	−3.87644	−	3.44794i	−0.845909	−	0.752403i
$22$	−0.451577	+	1.38981i	−0.0962766	+	0.296309i
$23$	0.455593	+	0.0968392i	0.0949976	+	0.0201924i	0.255165	−	0.966897i	$-0.417870\pi$
$23$	0.455593	+	0.0968392i	0.0949976	+	0.0201924i	−0.160168	+	0.987090i	$0.551203\pi$
$24$	−0.204967	+	1.95013i	−0.0418387	+	0.398069i
$25$	4.87335	−	1.03586i	0.974670	−	0.207173i
$26$	0.579318	+	5.51184i	0.113614	+	1.08096i
$27$	4.22564			0.813225
$28$	−2.63289	−	0.260562i	−0.497569	−	0.0492415i
$29$	−1.39410	+	1.01287i	−0.258878	+	0.188086i	−0.709652	−	0.704552i	$-0.751148\pi$
$29$	−1.39410	+	1.01287i	−0.258878	+	0.188086i	0.450774	+	0.892638i	$0.351148\pi$
$30$	0.238830	−	0.106334i	0.0436041	−	0.0194138i
$31$	0.130921	−	1.24563i	0.0235140	−	0.223721i	−0.976454	−	0.215726i	$-0.930788\pi$
$31$	0.130921	−	1.24563i	0.0235140	−	0.223721i	0.999968	−	0.00799542i	$-0.00254505\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−2.61776	+	1.16550i	−0.455693	+	0.202887i
$34$	−0.366749	+	1.12874i	−0.0628969	+	0.193577i
$35$	0.145429	+	0.321368i	0.0245820	+	0.0543212i
$36$	−0.683635	+	0.496690i	−0.113939	+	0.0827816i
$37$	−0.859988	−	8.18224i	−0.141381	−	1.34515i	−0.803299	−	0.595576i	$-0.796924\pi$
$37$	−0.859988	−	8.18224i	−0.141381	−	1.34515i	0.661918	−	0.749577i	$-0.269743\pi$
$38$	−0.455388	−	0.788755i	−0.0738737	−	0.127953i
$39$	−7.27181	+	8.07616i	−1.16442	+	1.29322i
$40$	0.0666620	−	0.115462i	0.0105402	−	0.0182562i
$41$	4.24491	−	4.79382i	0.662944	−	0.748669i
$41$	4.24491	−	4.79382i	0.662944	−	0.748669i
$42$	−3.07487	−	4.17856i	−0.474462	−	0.644765i
$43$	−3.21803	−	9.90406i	−0.490744	−	1.51036i	−0.823486	−	0.567337i	$-0.807974\pi$
$43$	−3.21803	−	9.90406i	−0.490744	−	1.51036i	0.332741	−	0.943018i	$-0.392026\pi$
$44$	−0.730667	+	1.26555i	−0.110152	+	0.190789i
$45$	0.102921	+	0.0458235i	0.0153426	+	0.00683096i
$46$	0.425503	+	0.189446i	0.0627370	+	0.0279323i
$47$	−11.3800	−	2.41890i	−1.65995	−	0.352833i	−0.719954	−	0.694022i	$-0.755837\pi$
$47$	−11.3800	−	2.41890i	−1.65995	−	0.352833i	−0.939995	+	0.341188i	$0.889171\pi$
$48$	−0.605943	+	1.86490i	−0.0874603	+	0.269175i
$49$	5.61270	−	4.18302i	0.801814	−	0.597574i
$50$	4.98222			0.704593
$51$	−2.12601	+	0.946562i	−0.297701	+	0.132545i
$52$	−0.579318	+	5.51184i	−0.0803369	+	0.764355i
$53$	0.661421	+	0.294484i	0.0908532	+	0.0404505i	0.451660	−	0.892190i	$-0.350832\pi$
$53$	0.661421	+	0.294484i	0.0908532	+	0.0404505i	−0.360807	+	0.932641i	$0.617499\pi$
$54$	4.13330	+	0.878560i	0.562471	+	0.119557i
$55$	0.194831			0.0262710
$56$	−2.52118	−	0.802276i	−0.336907	−	0.107209i
$57$	0.551878	−	1.69851i	0.0730980	−	0.224973i
$58$	−1.57422	+	0.700889i	−0.206705	+	0.0920312i
$59$	6.02008	−	6.68598i	0.783748	−	0.870440i	−0.210495	−	0.977595i	$-0.567507\pi$
$59$	6.02008	−	6.68598i	0.783748	−	0.870440i	0.994242	+	0.107155i	$0.0341741\pi$
$60$	0.255719	−	0.0543547i	0.0330131	−	0.00701716i
$61$	8.69556	+	9.65740i	1.11335	+	1.23650i	0.969022	+	0.246974i	$0.0794363\pi$
$61$	8.69556	+	9.65740i	1.11335	+	1.23650i	0.144331	+	0.989529i	$0.453897\pi$
$62$	0.387040	−	1.19119i	0.0491541	−	0.151281i
$63$	0.451533	−	2.18964i	0.0568878	−	0.275868i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	0.675027	−	0.300541i	0.0837268	−	0.0372776i
$66$	−2.80287	+	0.595769i	−0.345010	+	0.0733341i
$67$	−10.6027	−	4.72064i	−1.29533	−	0.576718i	−0.360814	−	0.932638i	$-0.617501\pi$
$67$	−10.6027	−	4.72064i	−1.29533	−	0.576718i	−0.934517	+	0.355919i	$0.884168\pi$
$68$	−0.593412	+	1.02782i	−0.0719618	+	0.124641i
$69$	0.282230	+	0.868616i	0.0339766	+	0.104569i
$70$	0.0754346	+	0.344582i	0.00901616	+	0.0411854i
$71$	6.04582	+	4.39255i	0.717507	+	0.521299i	0.885587	−	0.464474i	$-0.153757\pi$
$71$	6.04582	+	4.39255i	0.717507	+	0.521299i	−0.168080	+	0.985773i	$0.553757\pi$
$72$	−0.771963	+	0.343700i	−0.0909767	+	0.0405054i
$73$	1.11062	+	1.92366i	0.129989	+	0.225147i	0.923672	−	0.383184i	$-0.125173\pi$
$73$	1.11062	+	1.92366i	0.129989	+	0.225147i	−0.793683	+	0.608331i	$0.791839\pi$
$74$	0.859988	−	8.18224i	0.0999716	−	0.951167i
$75$	6.53707	+	7.26016i	0.754836	+	0.838331i
$76$	−0.281445	−	0.866199i	−0.0322840	−	0.0993599i
$77$	−0.826821	−	3.77688i	−0.0942250	−	0.430416i
$78$	−8.79203	+	6.38778i	−0.995501	+	0.723274i
$79$	2.26011	−	3.91463i	0.254283	−	0.440430i	−0.710418	−	0.703780i	$-0.751494\pi$
$79$	2.26011	−	3.91463i	0.254283	−	0.440430i	0.964700	+	0.263350i	$0.0848274\pi$
$80$	0.0892112	−	0.0990791i	0.00997412	−	0.0110774i
$81$	5.41050	+	9.37126i	0.601167	+	1.04125i
$82$	5.14884	−	3.80650i	0.568595	−	0.420357i
$83$	1.50836			0.165564			0.0827820	−	0.996568i	$-0.473619\pi$
$83$	1.50836			0.165564			0.0827820	+	0.996568i	$0.473619\pi$
$84$	−2.13890	−	4.72654i	−0.233373	−	0.515708i
$85$	0.158232			0.0171627
$86$	−1.08853	−	10.3567i	−0.117380	−	1.11679i
$87$	−3.08685	−	1.37435i	−0.330945	−	0.147346i
$88$	−0.977824	+	1.08598i	−0.104236	+	0.115766i
$89$	1.57873	+	1.75335i	0.167345	+	0.185855i	0.820984	−	0.570951i	$-0.193425\pi$
$89$	1.57873	+	1.75335i	0.167345	+	0.185855i	−0.653639	+	0.756806i	$0.726759\pi$
$90$	0.0911450	+	0.0662207i	0.00960752	+	0.00698027i
$91$	−8.69079	−	11.8103i	−0.911043	−	1.23805i
$92$	0.376816	+	0.273773i	0.0392858	+	0.0285428i
$93$	2.24364	−	0.998932i	0.232655	−	0.103584i
$94$	−10.6284	−	4.73209i	−1.09624	−	0.488077i
$95$	−0.0812514	+	0.0902389i	−0.00833622	+	0.00925831i
$96$	−0.980436	+	1.69816i	−0.100065	+	0.173318i
$97$	−8.57525	+	6.23028i	−0.870685	+	0.632589i	−0.930771	−	0.365604i	$-0.880863\pi$
$97$	−8.57525	+	6.23028i	−0.870685	+	0.632589i	0.0600860	+	0.998193i	$0.480863\pi$
$98$	6.35974	−	2.92466i	0.642431	−	0.295436i
$99$	−0.999019	−	0.725830i	−0.100405	−	0.0729486i
$100$	4.87335	+	1.03586i	0.487335	+	0.103586i
$101$	8.97402	−	1.90749i	0.892948	−	0.189802i	0.261485	−	0.965208i	$-0.415788\pi$
$101$	8.97402	−	1.90749i	0.892948	−	0.189802i	0.631463	+	0.775406i	$0.282455\pi$
$102$	−2.27636	+	0.483854i	−0.225393	+	0.0479087i
$103$	12.6387	+	14.0367i	1.24533	+	1.38308i	0.894761	+	0.446545i	$0.147346\pi$
$103$	12.6387	+	14.0367i	1.24533	+	1.38308i	0.350571	+	0.936536i	$0.385988\pi$
$104$	−1.71263	+	5.27095i	−0.167938	+	0.516859i
$105$	−0.403153	+	0.562043i	−0.0393437	+	0.0548498i
$106$	0.585741	+	0.425566i	0.0568922	+	0.0413346i
$107$	−6.88341	−	7.64480i	−0.665444	−	0.739051i	0.312038	−	0.950070i	$-0.398988\pi$
$107$	−6.88341	−	7.64480i	−0.665444	−	0.739051i	−0.977482	+	0.211019i	$0.932322\pi$
$108$	3.86032	+	1.71872i	0.371459	+	0.165384i
$109$	0.975807	+	1.69015i	0.0934653	+	0.161887i	0.908967	−	0.416868i	$-0.136872\pi$
$109$	0.975807	+	1.69015i	0.0934653	+	0.161887i	−0.815502	+	0.578755i	$0.803539\pi$
$110$	0.190574	+	0.0405077i	0.0181705	+	0.00386225i
$111$	13.0516	−	9.48257i	1.23881	−	0.900046i
$112$	−2.29928	−	1.30893i	−0.217262	−	0.123682i
$113$	−10.6303	−	7.72334i	−1.00001	−	0.726551i	−0.0379211	−	0.999281i	$-0.512074\pi$
$113$	−10.6303	−	7.72334i	−1.00001	−	0.726551i	−0.962091	+	0.272730i	$0.912074\pi$
$114$	0.892957	−	1.54665i	0.0836331	−	0.144857i
$115$	0.00649106	−	0.0617583i	0.000605294	−	0.00575899i
$116$	−1.68554	+	0.358274i	−0.156499	+	0.0332649i
$117$	−4.58092	−	0.973705i	−0.423507	−	0.0900191i
$118$	7.27862	−	5.28823i	0.670051	−	0.486821i
$119$	−0.671504	−	3.06740i	−0.0615566	−	0.281188i
$120$	0.261431			0.0238653
$121$	8.67079	+	1.84303i	0.788254	+	0.167548i
$122$	6.49766	+	11.2543i	0.588270	+	1.01891i
$123$	12.3026	+	2.50853i	1.10928	+	0.226187i
$124$	0.626244	−	1.08469i	0.0562384	−	0.0974077i
$125$	−0.411262	−	1.26573i	−0.0367844	−	0.113211i
$126$	0.896917	−	2.04791i	0.0799037	−	0.182442i
$127$	−0.528293	+	0.383828i	−0.0468785	+	0.0340592i	−0.610978	−	0.791648i	$-0.709224\pi$
$127$	−0.528293	+	0.383828i	−0.0468785	+	0.0340592i	0.564099	+	0.825707i	$0.309224\pi$
$128$	0.104528	+	0.994522i	0.00923910	+	0.0879041i
$129$	13.6637	−	15.1750i	1.20302	−	1.33609i
$130$	0.722762	−	0.153628i	0.0633904	−	0.0134741i
$131$	−13.3393	+	5.93904i	−1.16546	+	0.518896i	−0.895973	−	0.444108i	$-0.853521\pi$
$131$	−13.3393	+	5.93904i	−1.16546	+	0.518896i	−0.269486	+	0.963004i	$0.586854\pi$
$132$	−2.86549			−0.249409
$133$	2.09413	+	1.19214i	0.181584	+	0.103372i
$134$	−9.38957	−	6.82192i	−0.811135	−	0.589324i
$135$	−0.0588892	−	0.560294i	−0.00506838	−	0.0482224i
$136$	−0.794140	+	0.881982i	−0.0680970	+	0.0756294i
$137$	−3.08907	−	5.35043i	−0.263917	−	0.457118i	0.703362	−	0.710832i	$-0.251681\pi$
$137$	−3.08907	−	5.35043i	−0.263917	−	0.457118i	−0.967279	+	0.253714i	$0.918348\pi$
$138$	0.0954676	+	0.908314i	0.00812674	+	0.0773208i
$139$	3.28113	−	10.0983i	0.278302	−	0.856526i	−0.710025	−	0.704177i	$-0.751316\pi$
$139$	3.28113	−	10.0983i	0.278302	−	0.856526i	0.988327	−	0.152349i	$-0.0486837\pi$
$140$	0.00214354	+	0.352736i	0.000181162	+	0.0298116i
$141$	−7.04970	−	21.6968i	−0.593692	−	1.82720i
$142$	5.00044	+	5.55356i	0.419628	+	0.466044i
$143$	−7.92203	+	1.68388i	−0.662473	+	0.140813i
$144$	−0.826553	+	0.175689i	−0.0688794	+	0.0146408i
$145$	0.153729	+	0.170733i	0.0127665	+	0.0141786i
$146$	0.686403	+	2.11253i	0.0568071	+	0.174834i
$147$	12.6063	+	5.43010i	1.03975	+	0.447867i
$148$	2.54238	−	7.82464i	0.208982	−	0.643181i
$149$	−0.210606	−	2.00378i	−0.0172535	−	0.164156i	0.982502	−	0.186250i	$-0.0596334\pi$
$149$	−0.210606	−	2.00378i	−0.0172535	−	0.164156i	−0.999756	+	0.0220938i	$0.992967\pi$
$150$	4.88475	+	8.46064i	0.398838	+	0.690808i
$151$	−12.5211	+	13.9060i	−1.01895	+	1.13166i	−0.0277055	+	0.999616i	$0.508820\pi$
$151$	−12.5211	+	13.9060i	−1.01895	+	1.13166i	−0.991244	+	0.132042i	$0.957847\pi$
$152$	−0.0952020	−	0.905787i	−0.00772190	−	0.0734690i
$153$	−0.811354	−	0.589483i	−0.0655941	−	0.0476569i
$154$	−0.0234948	−	3.86626i	−0.00189327	−	0.311552i
$155$	−0.166987			−0.0134127
$156$	−9.92800	+	4.42023i	−0.794876	+	0.353902i
$157$	14.5742	−	3.09785i	1.16315	−	0.247235i	0.414404	−	0.910093i	$-0.363990\pi$
$157$	14.5742	−	3.09785i	1.16315	−	0.247235i	0.748745	+	0.662858i	$0.230657\pi$
$158$	3.02462	−	3.35918i	0.240626	−	0.267242i
$159$	0.148399	+	1.41192i	0.0117688	+	0.111973i
$160$	0.107861	−	0.0783659i	0.00852720	−	0.00619537i
$161$	−1.22476	+	0.136257i	−0.0965244	+	0.0107386i
$162$	3.34387	+	10.2914i	0.262719	+	0.808567i
$163$	1.24528	−	2.15689i	0.0975377	−	0.168940i	−0.813127	−	0.582086i	$-0.802237\pi$
$163$	1.24528	−	2.15689i	0.0975377	−	0.168940i	0.910665	+	0.413146i	$0.135570\pi$
$164$	5.82774	−	2.65281i	0.455070	−	0.207150i
$165$	0.191019	+	0.330855i	0.0148708	+	0.0257571i
$166$	1.47540	+	0.313605i	0.114513	+	0.0243405i
$167$	−19.5622			−1.51377			−0.756884	−	0.653550i	$-0.773279\pi$
$167$	−19.5622			−1.51377			−0.756884	+	0.653550i	$0.773279\pi$
$168$	−1.10946	−	5.06796i	−0.0855966	−	0.391002i
$169$	−14.3325	+	10.4132i	−1.10250	+	0.801015i
$170$	0.154775	+	0.0328983i	0.0118707	+	0.00252319i
$171$	0.752805	−	0.160014i	0.0575684	−	0.0122365i
$172$	1.08853	−	10.3567i	0.0829999	−	0.789691i
$173$	−3.59826	+	6.23237i	−0.273571	+	0.473839i	−0.969774	−	0.244007i	$-0.921538\pi$
$173$	−3.59826	+	6.23237i	−0.273571	+	0.473839i	0.696203	+	0.717845i	$0.254871\pi$
$174$	−2.73365	−	1.98611i	−0.207237	−	0.150567i
$175$	−11.3754	+	6.66011i	−0.859903	+	0.503457i
$176$	−1.18224	+	0.858951i	−0.0891150	+	0.0647459i
$177$	17.2562	+	3.66792i	1.29705	+	0.275698i
$178$	1.17968	+	2.04327i	0.0884211	+	0.153150i
$179$	−0.827721	−	0.368525i	−0.0618667	−	0.0275448i	0.375570	−	0.926794i	$-0.377447\pi$
$179$	−0.827721	−	0.368525i	−0.0618667	−	0.0275448i	−0.437437	+	0.899249i	$0.644114\pi$
$180$	0.0753852	+	0.0837237i	0.00561888	+	0.00624040i
$181$	−5.36957	−	3.90122i	−0.399117	−	0.289975i	0.370064	−	0.929006i	$-0.379336\pi$
$181$	−5.36957	−	3.90122i	−0.399117	−	0.289975i	−0.769181	+	0.639031i	$0.779336\pi$
$182$	−6.04539	−	13.3591i	−0.448114	−	0.990241i
$183$	−7.87442	+	24.2350i	−0.582094	+	1.79150i
$184$	0.311661	+	0.346135i	0.0229760	+	0.0255174i
$185$	−1.07293	+	0.228058i	−0.0788833	+	0.0167672i
$186$	2.40230	−	0.510625i	0.176145	−	0.0374408i
$187$	−1.69645	−	0.360591i	−0.124057	−	0.0263690i
$188$	−9.41233	−	6.83846i	−0.686464	−	0.498746i
$189$	−10.6116	+	3.51936i	−0.771882	+	0.255996i
$190$	−0.0982376	+	0.0713738i	−0.00712691	+	0.00517800i
$191$	10.4054	−	18.0227i	0.752911	−	1.30408i	−0.193495	−	0.981101i	$-0.561982\pi$
$191$	10.4054	−	18.0227i	0.752911	−	1.30408i	0.946406	−	0.322979i	$-0.104684\pi$
$192$	−1.31208	+	1.45721i	−0.0946912	+	0.105165i
$193$	3.97166	+	1.76830i	0.285886	+	0.127285i	0.544670	−	0.838651i	$-0.316655\pi$
$193$	3.97166	+	1.76830i	0.285886	+	0.127285i	−0.258784	+	0.965935i	$0.583322\pi$
$194$	−9.68321	+	4.31124i	−0.695214	+	0.309529i
$195$	1.17219	+	0.851645i	0.0839422	+	0.0609876i
$196$	6.82884	−	1.53849i	0.487774	−	0.109892i
$197$	−20.8429	−	15.1433i	−1.48500	−	1.07891i	−0.975903	−	0.218203i	$-0.929980\pi$
$197$	−20.8429	−	15.1433i	−1.48500	−	1.07891i	−0.509095	−	0.860711i	$-0.670020\pi$
$198$	−0.826279	−	0.917676i	−0.0587211	−	0.0652164i
$199$	−5.00732	+	5.56119i	−0.354959	+	0.394222i	−0.894007	−	0.448053i	$-0.852118\pi$
$199$	−5.00732	+	5.56119i	−0.354959	+	0.394222i	0.539048	+	0.842275i	$0.318784\pi$
$200$	4.55149	+	2.02645i	0.321839	+	0.143292i
$201$	−2.37888	−	22.6335i	−0.167793	−	1.59644i
$202$	9.17450			0.645516
$203$	2.65734	−	3.70465i	0.186509	−	0.260016i
$204$	−2.32721			−0.162937
$205$	−0.694788	−	0.496042i	−0.0485261	−	0.0346450i
$206$	9.44415	+	16.3577i	0.658005	+	1.13970i
$207$	−0.263360	+	0.292491i	−0.0183048	+	0.0203295i
$208$	−2.77110	+	4.79969i	−0.192141	+	0.332798i
$209$	1.07676	−	0.782312i	0.0744810	−	0.0541136i
$210$	−0.511198	+	0.465941i	−0.0352760	+	0.0321530i
$211$	0.654182	+	2.01336i	0.0450357	+	0.138606i	0.971046	−	0.238893i	$-0.0767844\pi$
$211$	0.654182	+	2.01336i	0.0450357	+	0.138606i	−0.926010	+	0.377498i	$0.876784\pi$
$212$	0.484461	+	0.538049i	0.0332729	+	0.0369533i
$213$	−1.53173	+	14.5734i	−0.104952	+	0.998554i
$214$	−5.14355	−	8.90888i	−0.351606	−	0.608999i
$215$	−1.26837	+	0.564715i	−0.0865021	+	0.0385132i
$216$	3.41862	+	2.48377i	0.232607	+	0.168999i
$217$	0.708656	+	3.23711i	0.0481067	+	0.219749i
$218$	0.603082	+	1.85609i	0.0408458	+	0.125711i
$219$	−2.17779	+	3.77204i	−0.147161	+	0.254891i
$220$	0.177987	+	0.0792450i	0.0119999	+	0.00534269i
$221$	−6.43388	+	1.36756i	−0.432790	+	0.0919923i
$222$	14.7380	−	6.56176i	0.989147	−	0.440397i
$223$	4.06586	+	12.5134i	0.272270	+	0.837962i	0.989929	+	0.141567i	$0.0452139\pi$
$223$	4.06586	+	12.5134i	0.272270	+	0.837962i	−0.717658	+	0.696395i	$0.754786\pi$
$224$	−1.97690	−	1.75837i	−0.132087	−	0.117486i
$225$	−1.30098	+	4.00402i	−0.0867323	+	0.266935i
$226$	−8.79220	−	9.76473i	−0.584849	−	0.649540i
$227$	14.0033	−	2.97650i	0.929435	−	0.197557i	0.281769	−	0.959482i	$-0.409079\pi$
$227$	14.0033	−	2.97650i	0.929435	−	0.197557i	0.647666	+	0.761925i	$0.275745\pi$
$228$	1.19501	−	1.32719i	0.0791415	−	0.0878955i
$229$	10.9416	−	4.87151i	0.723040	−	0.321918i	−0.0120128	−	0.999928i	$-0.503824\pi$
$229$	10.9416	−	4.87151i	0.723040	−	0.321918i	0.735053	+	0.678010i	$0.237157\pi$
$230$	0.0191895	−	0.0590592i	0.00126532	−	0.00389425i
$231$	5.60313	−	5.10707i	0.368659	−	0.336021i
$232$	−1.72320			−0.113134
$233$	−14.9328	−	3.17407i	−0.978283	−	0.207941i	−0.309093	−	0.951032i	$-0.600026\pi$
$233$	−14.9328	−	3.17407i	−0.978283	−	0.207941i	−0.669190	+	0.743091i	$0.733359\pi$
$234$	−4.27837	−	1.90486i	−0.279686	−	0.124524i
$235$	−0.162137	+	1.54263i	−0.0105767	+	0.100630i
$236$	8.21905	−	3.65936i	0.535015	−	0.238204i
$237$	8.86358			0.575752
$238$	−0.0190813	−	3.13998i	−0.00123686	−	0.203535i
$239$	−8.43840	+	25.9707i	−0.545835	+	1.67991i	0.173161	+	0.984894i	$0.444602\pi$
$239$	−8.43840	+	25.9707i	−0.545835	+	1.67991i	−0.718996	+	0.695014i	$0.755398\pi$
$240$	0.255719	+	0.0543547i	0.0165066	+	0.00350858i
$241$	7.79026	+	3.46845i	0.501815	+	0.223422i	0.642002	−	0.766703i	$-0.278104\pi$
$241$	7.79026	+	3.46845i	0.501815	+	0.223422i	−0.140188	+	0.990125i	$0.544771\pi$
$242$	8.09812	+	3.60552i	0.520567	+	0.231771i
$243$	−4.27083	+	7.39730i	−0.273974	+	0.474537i
$244$	4.01577	+	12.3593i	0.257084	+	0.791222i
$245$	−0.632862	−	0.685913i	−0.0404320	−	0.0438214i
$246$	11.5122	+	5.01156i	0.733989	+	0.319525i
$247$	2.52385	−	4.37144i	0.160589	−	0.278148i
$248$	0.838078	−	0.930780i	0.0532180	−	0.0591046i
$249$	1.47885	+	2.56144i	0.0937183	+	0.162325i
$250$	−0.139114	−	1.32358i	−0.00879834	−	0.0837106i
$251$	−4.77337	+	3.46805i	−0.301292	+	0.218902i	−0.728151	−	0.685417i	$-0.759620\pi$
$251$	−4.77337	+	3.46805i	−0.301292	+	0.218902i	0.426859	+	0.904318i	$0.359620\pi$
$252$	1.30310	−	1.81668i	0.0820877	−	0.114440i
$253$	−0.210331	+	0.647334i	−0.0132234	+	0.0406975i
$254$	−0.596551	+	0.265602i	−0.0374309	+	0.0166653i
$255$	0.155137	+	0.268704i	0.00971503	+	0.0168269i
$256$	−0.104528	+	0.994522i	−0.00653303	+	0.0621576i
$257$	6.55814	−	2.91987i	0.409086	−	0.182137i	−0.191868	−	0.981421i	$-0.561454\pi$
$257$	6.55814	−	2.91987i	0.409086	−	0.182137i	0.600953	+	0.799284i	$0.294788\pi$
$258$	16.5201	−	12.0026i	1.02850	−	0.747249i
$259$	8.97429	+	19.8314i	0.557635	+	1.23226i
$260$	0.738909			0.0458252
$261$	−0.152208	−	1.44816i	−0.00942142	−	0.0896389i
$262$	−14.2826	+	3.03586i	−0.882381	+	0.187556i
$263$	−1.26542	+	12.0397i	−0.0780293	+	0.742399i	0.883636	+	0.468174i	$0.155088\pi$
$263$	−1.26542	+	12.0397i	−0.0780293	+	0.742399i	−0.961666	+	0.274225i	$0.911579\pi$
$264$	−2.80287	−	0.595769i	−0.172505	−	0.0366670i
$265$	0.0298290	−	0.0918043i	0.00183238	−	0.00563949i
$266$	1.80051	+	1.60148i	0.110396	+	0.0981932i
$267$	−1.42964	+	4.39999i	−0.0874927	+	0.269275i
$268$	−7.76603	−	8.62504i	−0.474385	−	0.526858i
$269$	−7.27284	+	8.07731i	−0.443433	+	0.492482i	−0.922880	−	0.385089i	$-0.874171\pi$
$269$	−7.27284	+	8.07731i	−0.443433	+	0.492482i	0.479446	+	0.877571i	$0.340837\pi$
$270$	0.0588892	−	0.560294i	0.00358388	−	0.0340984i
$271$	−11.1852	−	12.4225i	−0.679455	−	0.754611i	0.300511	−	0.953779i	$-0.402843\pi$
$271$	−11.1852	−	12.4225i	−0.679455	−	0.754611i	−0.979966	+	0.199167i	$0.936176\pi$
$272$	−0.960161	+	0.697598i	−0.0582183	+	0.0422981i
$273$	11.5350	−	26.3376i	0.698130	−	1.59402i
$274$	−1.90915	−	5.87577i	−0.115336	−	0.354968i
$275$	0.761040	+	7.24081i	0.0458924	+	0.436637i
$276$	−0.0954676	+	0.908314i	−0.00574647	+	0.0546741i
$277$	−1.47827	+	14.0648i	−0.0888204	+	0.845069i	0.855889	+	0.517160i	$0.173011\pi$
$277$	−1.47827	+	14.0648i	−0.0888204	+	0.845069i	−0.944709	+	0.327910i	$0.893656\pi$
$278$	5.30898	−	9.19543i	0.318412	−	0.551505i
$279$	0.856244	+	0.622098i	0.0512620	+	0.0372440i
$280$	−0.0712412	+	0.345473i	−0.00425748	+	0.0206460i
$281$	−2.99167	−	9.20741i	−0.178468	−	0.549268i	0.821307	−	0.570487i	$-0.193245\pi$
$281$	−2.99167	−	9.20741i	−0.178468	−	0.549268i	−0.999775	+	0.0212185i	$0.993245\pi$
$282$	−2.38464	−	22.6883i	−0.142003	−	1.35107i
$283$	4.19250	+	1.86662i	0.249218	+	0.110959i	0.527544	−	0.849528i	$-0.323113\pi$
$283$	4.19250	+	1.86662i	0.249218	+	0.110959i	−0.278326	+	0.960487i	$0.589780\pi$
$284$	3.73652	+	6.47185i	0.221722	+	0.384034i
$285$	−0.232902	−	0.0495049i	−0.0137959	−	0.00293242i
$286$	−8.09901			−0.478905
$287$	−6.66745	+	15.5739i	−0.393567	+	0.919296i
$288$	−0.845019			−0.0497932
$289$	15.2507	+	3.24164i	0.897102	+	0.190685i
$290$	0.114872	+	0.198964i	0.00674552	+	0.0116836i
$291$	−18.9875	−	8.45379i	−1.11307	−	0.495570i
$292$	0.232183	+	2.20908i	0.0135875	+	0.129277i
$293$	−7.41345	−	22.8163i	−0.433099	−	1.33294i	−0.895023	−	0.446021i	$-0.852841\pi$
$293$	−7.41345	−	22.8163i	−0.433099	−	1.33294i	0.461924	−	0.886920i	$-0.347159\pi$
$294$	11.2019	+	7.93245i	0.653307	+	0.462630i
$295$	−0.970415	−	0.705048i	−0.0564998	−	0.0410495i
$296$	4.11366	−	7.12506i	0.239101	−	0.414136i
$297$	−0.645471	+	6.14125i	−0.0374540	+	0.356351i
$298$	0.210606	−	2.00378i	0.0122001	−	0.116076i
$299$	0.269829	+	2.56725i	0.0156046	+	0.148468i
$300$	3.01894	+	9.29135i	0.174299	+	0.536436i
$301$	16.3299	+	22.1914i	0.941241	+	1.27909i
$302$	−15.1387	+	10.9989i	−0.871133	+	0.632915i
$303$	12.0377	+	13.3692i	0.691546	+	0.768040i
$304$	0.0952020	−	0.905787i	0.00546021	−	0.0519504i
$305$	1.15933	−	1.28756i	0.0663829	−	0.0737257i
$306$	−0.671064	−	0.745292i	−0.0383621	−	0.0426055i
$307$	−7.41728	+	22.8280i	−0.423326	+	1.30286i	0.481261	+	0.876577i	$0.340179\pi$
$307$	−7.41728	+	22.8280i	−0.423326	+	1.30286i	−0.904588	+	0.426287i	$0.859821\pi$
$308$	0.780859	−	3.78665i	0.0444935	−	0.215765i
$309$	−11.4452	+	35.2248i	−0.651096	+	2.00387i
$310$	−0.163338	−	0.0347185i	−0.00927696	−	0.00197188i
$311$	0.275210	−	2.61844i	0.0156057	−	0.148478i	−0.983944	−	0.178476i	$-0.942883\pi$
$311$	0.275210	−	2.61844i	0.0156057	−	0.148478i	0.999550	+	0.0299976i	$0.00954998\pi$
$312$	−10.6301	+	2.25949i	−0.601809	+	0.127918i
$313$	−0.117592	−	1.11882i	−0.00664671	−	0.0632392i	0.990696	−	0.136095i	$-0.0434553\pi$
$313$	−0.117592	−	1.11882i	−0.00664671	−	0.0632392i	−0.997342	+	0.0728560i	$0.976789\pi$
$314$	14.8998			0.840845
$315$	−0.296625	−	0.0293552i	−0.0167129	−	0.00165398i
$316$	3.65694	−	2.65692i	0.205719	−	0.149464i
$317$	3.36077	−	1.49631i	0.188759	−	0.0840411i	−0.310181	−	0.950678i	$-0.600389\pi$
$317$	3.36077	−	1.49631i	0.188759	−	0.0840411i	0.498940	+	0.866637i	$0.333723\pi$
$318$	−0.148399	+	1.41192i	−0.00832182	+	0.0791768i
$319$	−1.25909	−	2.18080i	−0.0704953	−	0.122101i
$320$	0.121798	−	0.0542278i	0.00680869	−	0.00303143i
$321$	6.23339	−	19.1844i	0.347914	−	1.07077i
$322$	−1.22632	−	0.121362i	−0.0683403	−	0.00676324i
$323$	0.874491	−	0.635355i	0.0486580	−	0.0353521i
$324$	1.13110	+	10.7617i	0.0628390	+	0.597873i
$325$	13.8062	+	23.9131i	0.765833	+	1.32646i
$326$	1.66651	−	1.85084i	0.0922993	−	0.102509i
$327$	−1.91343	+	3.31416i	−0.105813	+	0.183274i
$328$	6.25194	−	1.38318i	0.345206	−	0.0763735i
$329$	30.5927	−	3.40350i	1.68663	−	0.187641i
$330$	0.118057	+	0.363341i	0.00649880	+	0.0200012i
$331$	3.78846	−	6.56181i	0.208233	−	0.360669i	−0.742925	−	0.669374i	$-0.766562\pi$
$331$	3.78846	−	6.56181i	0.208233	−	0.360669i	0.951158	+	0.308705i	$0.0998956\pi$
$332$	1.37795	+	0.613505i	0.0756251	+	0.0336705i
$333$	6.35118	+	2.82773i	0.348043	+	0.154959i
$334$	−19.1347	−	4.06721i	−1.04700	−	0.222548i
$335$	−0.478166	+	1.47164i	−0.0261250	+	0.0804045i
$336$	−0.0315262	−	5.18788i	−0.00171989	−	0.283022i
$337$	−8.84882			−0.482026			−0.241013	−	0.970522i	$-0.577480\pi$
$337$	−8.84882			−0.482026			−0.241013	+	0.970522i	$0.577480\pi$
$338$	−16.1844	+	7.20574i	−0.880313	+	0.391941i
$339$	2.69321	−	25.6242i	0.146275	−	1.39172i
$340$	0.144552	+	0.0643589i	0.00783945	+	0.00349035i
$341$	1.79031	+	0.380542i	0.0969506	+	0.0206075i
$342$	0.769623			0.0416164
$343$	−10.6110	+	15.1792i	−0.572940	+	0.819598i
$344$	3.21803	−	9.90406i	0.173504	−	0.533991i
$345$	0.111240	−	0.0495272i	0.00598895	−	0.00266645i
$346$	−4.81542	+	5.34806i	−0.258878	+	0.287514i
$347$	−9.72826	+	2.06780i	−0.522240	+	0.111006i	−0.461487	−	0.887147i	$-0.652684\pi$
$347$	−9.72826	+	2.06780i	−0.522240	+	0.111006i	−0.0607536	+	0.998153i	$0.519350\pi$
$348$	−2.26098	−	2.51107i	−0.121201	−	0.134607i
$349$	1.40330	−	4.31890i	0.0751168	−	0.231186i	−0.906447	−	0.422319i	$-0.861216\pi$
$349$	1.40330	−	4.31890i	0.0751168	−	0.231186i	0.981564	+	0.191133i	$0.0612163\pi$
$350$	−12.5116	+	4.14948i	−0.668772	+	0.221799i
$351$	7.23698	+	22.2731i	0.386281	+	1.18885i
$352$	−1.33500	+	0.594378i	−0.0711555	+	0.0316805i
$353$	4.35755	−	0.926225i	0.231929	−	0.0492980i	−0.0904810	−	0.995898i	$-0.528840\pi$
$353$	4.35755	−	0.926225i	0.231929	−	0.0492980i	0.322410	+	0.946600i	$0.395507\pi$
$354$	16.1165	+	7.17553i	0.856582	+	0.381375i
$355$	0.498169	−	0.862853i	0.0264400	−	0.0457955i
$356$	0.729085	+	2.24389i	0.0386415	+	0.118926i
$357$	4.55059	−	4.14771i	0.240843	−	0.219520i
$358$	−0.733012	−	0.532565i	−0.0387409	−	0.0281469i
$359$	−7.75369	+	3.45216i	−0.409224	+	0.182198i	−0.601015	−	0.799237i	$-0.705237\pi$
$359$	−7.75369	+	3.45216i	−0.409224	+	0.182198i	0.191791	+	0.981436i	$0.438570\pi$
$360$	0.0563307	+	0.0975676i	0.00296889	+	0.00514226i
$361$	1.89933	−	18.0709i	0.0999649	−	0.951103i
$362$	−4.44112	−	4.93236i	−0.233420	−	0.259239i
$363$	5.37138	+	16.5314i	0.281924	+	0.867674i
$364$	−3.13577	−	14.3241i	−0.164359	−	0.750785i
$365$	0.239587	−	0.174070i	0.0125405	−	0.00911124i
$366$	−12.7411	+	22.0682i	−0.665987	+	1.15352i
$367$	−10.0879	+	11.2037i	−0.526582	+	0.584828i	−0.946488	−	0.322739i	$-0.895396\pi$
$367$	−10.0879	+	11.2037i	−0.526582	+	0.584828i	0.419906	+	0.907568i	$0.362063\pi$
$368$	0.232885	+	0.403369i	0.0121400	+	0.0210271i
$369$	1.71464	+	5.13189i	0.0892605	+	0.267156i
$370$	−1.09690			−0.0570251
$371$	−1.90625	−	0.188651i	−0.0989678	−	0.00979426i
$372$	2.45597			0.127336
$373$	0.803442	+	7.64424i	0.0416006	+	0.395804i	0.995433	+	0.0954638i	$0.0304334\pi$
$373$	0.803442	+	7.64424i	0.0416006	+	0.395804i	−0.953832	+	0.300340i	$0.902900\pi$
$374$	−1.58441	−	0.705423i	−0.0819276	−	0.0364765i
$375$	1.74621	−	1.93936i	0.0901738	−	0.100148i
$376$	−7.78485	−	8.64595i	−0.401473	−	0.445881i
$377$	−7.72637	−	5.61354i	−0.397929	−	0.289112i
$378$	−11.1114	+	1.23617i	−0.571511	+	0.0635819i
$379$	−5.08701	−	3.69593i	−0.261302	−	0.189847i	0.449419	−	0.893321i	$-0.351631\pi$
$379$	−5.08701	−	3.69593i	−0.261302	−	0.189847i	−0.710721	+	0.703474i	$0.751631\pi$
$380$	−0.110930	+	0.0493894i	−0.00569061	+	0.00253362i
$381$	−1.16976	−	0.520811i	−0.0599286	−	0.0266820i
$382$	13.9252	−	15.4655i	0.712475	−	0.791283i
$383$	−2.55324	+	4.42234i	−0.130464	+	0.225971i	−0.923856	−	0.382741i	$-0.874980\pi$
$383$	−2.55324	+	4.42234i	−0.130464	+	0.225971i	0.793391	+	0.608712i	$0.208313\pi$
$384$	−1.58638	+	1.15257i	−0.0809546	+	0.0588169i
$385$	−0.489269	+	0.162267i	−0.0249354	+	0.00826987i
$386$	3.51722	+	2.55541i	0.179022	+	0.130067i
$387$	8.60752	+	1.82958i	0.437545	+	0.0930030i
$388$	−10.3680	+	2.20378i	−0.526354	+	0.111880i
$389$	−5.46879	+	1.16243i	−0.277279	+	0.0589374i	−0.344452	−	0.938804i	$-0.611935\pi$
$389$	−5.46879	+	1.16243i	−0.277279	+	0.0589374i	0.0671734	+	0.997741i	$0.478602\pi$
$390$	0.969507	+	1.07675i	0.0490929	+	0.0545232i
$391$	−0.170821	+	0.525733i	−0.00863878	+	0.0265874i
$392$	6.99948	−	0.0850733i	0.353527	−	0.00429685i
$393$	−23.1638	−	16.8295i	−1.16846	−	0.848935i
$394$	−17.2390	−	19.1459i	−0.868489	−	0.964554i
$395$	−0.550553	−	0.245122i	−0.0277013	−	0.0123334i
$396$	−0.617428	−	1.06942i	−0.0310269	−	0.0537402i
$397$	−26.4602	−	5.62429i	−1.32800	−	0.282275i	−0.511331	−	0.859384i	$-0.670847\pi$
$397$	−26.4602	−	5.62429i	−1.32800	−	0.282275i	−0.816667	+	0.577109i	$0.804181\pi$
$398$	−6.05413	+	4.39858i	−0.303466	+	0.220481i
$399$	0.0287133	+	4.72500i	0.00143746	+	0.236546i
$400$	4.03070	+	2.92848i	0.201535	+	0.146424i
$401$	7.84505	−	13.5880i	0.391763	−	0.678553i	−0.600919	−	0.799310i	$-0.705199\pi$
$401$	7.84505	−	13.5880i	0.391763	−	0.678553i	0.992682	+	0.120756i	$0.0385320\pi$
$402$	2.37888	−	22.6335i	0.118648	−	1.12886i
$403$	6.78985	−	1.44323i	0.338227	−	0.0718923i
$404$	8.97402	+	1.90749i	0.446474	+	0.0949010i
$405$	1.16717	−	0.847998i	0.0579971	−	0.0421373i
$406$	3.36952	−	3.07121i	0.167226	−	0.152421i
$407$	12.0229			0.595951
$408$	−2.27636	−	0.483854i	−0.112696	−	0.0239544i
$409$	10.8540	+	18.7997i	0.536695	+	0.929583i	0.999079	+	0.0429035i	$0.0136608\pi$
$409$	10.8540	+	18.7997i	0.536695	+	0.929583i	−0.462384	+	0.886680i	$0.653006\pi$
$410$	−0.576473	−	0.629656i	−0.0284700	−	0.0310965i
$411$	6.05728	−	10.4915i	0.298783	−	0.517508i
$412$	5.83681	+	17.9638i	0.287559	+	0.885015i
$413$	−9.54942	+	21.8040i	−0.469896	+	1.07290i
$414$	−0.318417	+	0.231343i	−0.0156493	+	0.0113699i
$415$	−0.0210207	−	0.199999i	−0.00103187	−	0.00981756i
$416$	−3.70846	+	4.11866i	−0.181822	+	0.201934i
$417$	20.3655	−	4.32882i	0.997303	−	0.211983i
$418$	1.21588	−	0.541345i	0.0594707	−	0.0264781i
$419$	−17.9410			−0.876477			−0.438238	−	0.898859i	$-0.644397\pi$
$419$	−17.9410			−0.876477			−0.438238	+	0.898859i	$0.644397\pi$
$420$	−0.596902	+	0.349475i	−0.0291258	+	0.0170526i
$421$	−19.5157	−	14.1790i	−0.951135	−	0.691040i	−6.02644e−5	−	1.00000i	$-0.500019\pi$
$421$	−19.5157	−	14.1790i	−0.951135	−	0.691040i	−0.951075	+	0.308960i	$0.900019\pi$
$422$	0.221284	+	2.10538i	0.0107720	+	0.102488i
$423$	6.57834	−	7.30599i	0.319850	−	0.355229i
$424$	0.362008	+	0.627016i	0.0175807	+	0.0304506i
$425$	0.618079	+	5.88063i	0.0299813	+	0.285253i
$426$	−4.52824	+	13.9365i	−0.219394	+	0.675225i
$427$	−29.8799	−	17.0099i	−1.44599	−	0.823168i
$428$	−3.17889	−	9.78361i	−0.153657	−	0.472908i
$429$	−10.6265	−	11.8020i	−0.513054	−	0.569805i
$430$	−1.35806	+	0.288665i	−0.0654916	+	0.0139207i
$431$	36.8485	−	7.83239i	1.77493	−	0.377273i	0.800038	−	0.599949i	$-0.204813\pi$
$431$	36.8485	−	7.83239i	1.77493	−	0.377273i	0.974893	+	0.222676i	$0.0714792\pi$
$432$	2.82751	+	3.14026i	0.136038	+	0.151086i
$433$	2.64076	+	8.12742i	0.126907	+	0.390579i	0.994244	−	0.107143i	$-0.0341702\pi$
$433$	2.64076	+	8.12742i	0.126907	+	0.390579i	−0.867337	+	0.497721i	$0.834170\pi$
$434$	0.0201371	+	3.31371i	0.000966609	+	0.159063i
$435$	−0.139212	+	0.428450i	−0.00667470	+	0.0205426i
$436$	0.203999	+	1.94092i	0.00976979	+	0.0929533i
$437$	−0.212106	−	0.367379i	−0.0101464	−	0.0175741i
$438$	−2.91445	+	3.23683i	−0.139258	+	0.154662i
$439$	−0.743826	−	7.07703i	−0.0355009	−	0.337768i	−0.997828	−	0.0658739i	$-0.979016\pi$
$439$	−0.743826	−	7.07703i	−0.0355009	−	0.337768i	0.962327	−	0.271894i	$-0.0876502\pi$
$440$	0.157622	+	0.114519i	0.00751432	+	0.00545947i
$441$	0.689749	+	5.87478i	0.0328452	+	0.279751i
$442$	−6.57762			−0.312865
$443$	−9.33225	+	4.15498i	−0.443388	+	0.197409i	−0.616273	−	0.787533i	$-0.711358\pi$
$443$	−9.33225	+	4.15498i	−0.443388	+	0.197409i	0.172884	+	0.984942i	$0.444691\pi$
$444$	15.7802	−	3.35418i	0.748894	−	0.159182i
$445$	0.210482	−	0.233764i	0.00997782	−	0.0110815i
$446$	1.37532	+	13.0853i	0.0651235	+	0.619608i
$447$	3.19626	−	2.32222i	0.151178	−	0.109837i
$448$	−1.56811	−	2.13097i	−0.0740863	−	0.100679i
$449$	−0.717945	−	2.20961i	−0.0338819	−	0.104278i	0.932685	−	0.360691i	$-0.117459\pi$
$449$	−0.717945	−	2.20961i	−0.0338819	−	0.104278i	−0.966567	+	0.256413i	$0.917459\pi$
$450$	−2.10504	+	3.64603i	−0.0992324	+	0.171876i
$451$	6.31858	+	6.90152i	0.297530	+	0.324980i
$452$	−6.56987	−	11.3793i	−0.309021	−	0.535239i
$453$	−35.8909	−	7.62884i	−1.68630	−	0.358434i
$454$	14.3162			0.671892
$455$	−1.44485	+	1.31693i	−0.0677356	+	0.0617388i
$456$	1.44484	−	1.04973i	0.0676606	−	0.0491583i
$457$	10.7953	+	2.29461i	0.504982	+	0.107337i	0.453357	−	0.891329i	$-0.350226\pi$
$457$	10.7953	+	2.29461i	0.504982	+	0.107337i	0.0516256	+	0.998667i	$0.483560\pi$
$458$	11.7153	−	2.49017i	0.547421	−	0.116358i
$459$	−0.524220	+	4.98762i	−0.0244685	+	0.232802i
$460$	0.0310492	−	0.0537789i	0.00144768	−	0.00250745i
$461$	−21.8427	−	15.8697i	−1.01732	−	0.739125i	−0.0515863	−	0.998669i	$-0.516428\pi$
$461$	−21.8427	−	15.8697i	−1.01732	−	0.739125i	−0.965731	+	0.259544i	$0.916428\pi$
$462$	6.54251	−	3.83052i	0.304385	−	0.178212i
$463$	33.1628	−	24.0942i	1.54121	−	1.11975i	0.591633	−	0.806207i	$-0.298483\pi$
$463$	33.1628	−	24.0942i	1.54121	−	1.11975i	0.949573	−	0.313545i	$-0.101517\pi$
$464$	−1.68554	−	0.358274i	−0.0782494	−	0.0166324i
$465$	−0.163720	−	0.283571i	−0.00759233	−	0.0131503i
$466$	−13.9466	−	6.20943i	−0.646064	−	0.287646i
$467$	−16.1405	−	17.9259i	−0.746894	−	0.829510i	0.243191	−	0.969978i	$-0.421806\pi$
$467$	−16.1405	−	17.9259i	−0.746894	−	0.829510i	−0.990085	+	0.140469i	$0.955139\pi$
$468$	−3.78884	−	2.75275i	−0.175139	−	0.127246i
$469$	30.5577	+	3.02412i	1.41102	+	0.139641i
$470$	−0.479325	+	1.47521i	−0.0221096	+	0.0680464i
$471$	19.5497	+	21.7122i	0.900804	+	1.00044i
$472$	8.80027	−	1.87055i	0.405065	−	0.0860992i
$473$	14.8854	−	3.16399i	0.684432	−	0.145481i
$474$	8.66989	+	1.84284i	0.398221	+	0.0846446i
$475$	−3.67107	−	2.66719i	−0.168440	−	0.122379i
$476$	0.634175	−	3.07533i	0.0290674	−	0.140958i
$477$	−0.494962	+	0.359611i	−0.0226628	+	0.0164655i
$478$	−13.6536	+	23.6488i	−0.624502	+	1.08167i
$479$	−27.3393	+	30.3634i	−1.24916	+	1.38734i	−0.357958	+	0.933738i	$0.616527\pi$
$479$	−27.3393	+	30.3634i	−1.24916	+	1.38734i	−0.891206	+	0.453599i	$0.850140\pi$
$480$	0.238830	+	0.106334i	0.0109010	+	0.00485345i
$481$	41.6553	−	18.5461i	1.89932	−	0.845631i
$482$	6.89889	+	5.01234i	0.314236	+	0.228306i
$483$	−1.43218	−	1.94625i	−0.0651666	−	0.0885574i
$484$	7.17153	+	5.21042i	0.325979	+	0.236837i
$485$	0.945603	+	1.05020i	0.0429376	+	0.0476870i
$486$	−5.71549	+	6.34770i	−0.259260	+	0.287937i
$487$	33.0590	+	14.7188i	1.49805	+	0.666973i	0.981878	−	0.189514i	$-0.0606913\pi$
$487$	33.0590	+	14.7188i	1.49805	+	0.666973i	0.516168	+	0.856487i	$0.327358\pi$
$488$	1.35838	+	12.9241i	0.0614910	+	0.585048i
$489$	4.88366			0.220847
$490$	−0.476423	−	0.802504i	−0.0215226	−	0.0362534i
$491$	26.2486			1.18458			0.592290	−	0.805725i	$-0.298224\pi$
$491$	26.2486			1.18458			0.592290	+	0.805725i	$0.298224\pi$
$492$	10.2186	+	7.29556i	0.460692	+	0.328909i
$493$	−1.02257	−	1.77114i	−0.0460541	−	0.0797681i
$494$	3.37757	−	3.75117i	0.151964	−	0.168773i
$495$	−0.0823180	+	0.142579i	−0.00369992	+	0.00640845i
$496$	1.01328	−	0.736194i	0.0454978	−	0.0330561i
$497$	−18.8409	−	5.99545i	−0.845130	−	0.268933i
$498$	0.913979	+	2.81294i	0.0409564	+	0.126051i
$499$	25.4809	+	28.2994i	1.14068	+	1.26685i	0.958972	+	0.283501i	$0.0914961\pi$
$499$	25.4809	+	28.2994i	1.14068	+	1.26685i	0.181708	+	0.983352i	$0.441837\pi$
$500$	0.139114	−	1.32358i	0.00622136	−	0.0591923i
$501$	−19.1795	−	33.2198i	−0.856876	−	1.48415i
$502$	−5.39010	+	2.39983i	−0.240572	+	0.107110i
$503$	−33.3338	−	24.2184i	−1.48628	−	1.07985i	−0.975465	−	0.220154i	$-0.929344\pi$
$503$	−33.3338	−	24.2184i	−1.48628	−	1.07985i	−0.510815	−	0.859691i	$-0.670656\pi$
$504$	1.65233	−	1.50605i	0.0736008	−	0.0670848i
$505$	−0.377984	−	1.16332i	−0.0168201	−	0.0517669i
$506$	−0.340324	+	0.589458i	−0.0151292	+	0.0262046i
$507$	−31.7355	−	14.1295i	−1.40942	−	0.627515i
$508$	−0.638737	+	0.135768i	−0.0283394	+	0.00602372i
$509$	−8.56050	+	3.81138i	−0.379437	+	0.168936i	−0.587588	−	0.809160i	$-0.699922\pi$
$509$	−8.56050	+	3.81138i	−0.379437	+	0.168936i	0.208150	+	0.978097i	$0.433256\pi$
$510$	0.0958797	+	0.295087i	0.00424562	+	0.0130667i
$511$	−4.39118	−	3.90578i	−0.194254	−	0.172781i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	−2.57522	−	2.86008i	−0.113699	−	0.126275i
$514$	7.02191	−	1.49255i	0.309723	−	0.0658336i
$515$	1.68505	−	1.87144i	0.0742521	−	0.0824653i
$516$	18.6546	−	8.30557i	0.821224	−	0.365632i
$517$	5.25377	−	16.1695i	0.231061	−	0.711132i
$518$	4.65500	+	21.2639i	0.204529	+	0.934280i
$519$	−14.1115			−0.619425
$520$	0.722762	+	0.153628i	0.0316952	+	0.00673703i
$521$	−2.28261	−	1.01628i	−0.100003	−	0.0445241i	0.356126	−	0.934438i	$-0.384098\pi$
$521$	−2.28261	−	1.01628i	−0.100003	−	0.0445241i	−0.456128	+	0.889914i	$0.650764\pi$
$522$	0.152208	−	1.44816i	0.00666195	−	0.0633842i
$523$	−23.1658	+	10.3141i	−1.01297	+	0.451004i	−0.844988	−	0.534786i	$-0.820392\pi$
$523$	−23.1658	+	10.3141i	−1.01297	+	0.451004i	−0.167984	+	0.985790i	$0.553726\pi$
$524$	−14.6017			−0.637877
$525$	−22.4629	−	12.7876i	−0.980360	−	0.558095i
$526$	−3.74096	+	11.5135i	−0.163114	+	0.502012i
$527$	1.45400	+	0.309057i	0.0633372	+	0.0134627i
$528$	−2.61776	−	1.16550i	−0.113923	−	0.0507219i
$529$	−20.8134	−	9.26670i	−0.904929	−	0.402900i
$530$	0.0482644	−	0.0835963i	0.00209647	−	0.00363119i
$531$	2.34931	+	7.23043i	0.101951	+	0.313774i
$532$	1.42820	+	1.94083i	0.0619203	+	0.0841458i
$533$	32.5380	+	14.1647i	1.40938	+	0.613539i
$534$	−2.31321	+	4.00660i	−0.100102	+	0.173383i
$535$	−0.917724	+	1.01924i	−0.0396767	+	0.0440654i
$536$	−5.80307	−	10.0512i	−0.250654	−	0.434146i
$537$	−0.185711	−	1.76692i	−0.00801402	−	0.0762483i
$538$	−8.79328	+	6.38869i	−0.379105	+	0.275436i
$539$	5.22196	+	8.79606i	0.224926	+	0.378873i
$540$	0.174094	−	0.535806i	0.00749181	−	0.0230574i
$541$	−1.96395	+	0.874407i	−0.0844369	+	0.0375937i	−0.448521	−	0.893773i	$-0.648049\pi$
$541$	−1.96395	+	0.874407i	−0.0844369	+	0.0375937i	0.364084	+	0.931366i	$0.381382\pi$
$542$	−8.35804	−	14.4766i	−0.359009	−	0.621821i
$543$	1.36040	−	12.9433i	0.0583802	−	0.555450i
$544$	−1.08422	+	0.482725i	−0.0464855	+	0.0206967i
$545$	0.210504	−	0.152940i	0.00901699	−	0.00655123i
$546$	16.7588	−	23.3638i	0.717211	−	0.999878i
$547$	35.9591			1.53750			0.768749	−	0.639550i	$-0.220879\pi$
$547$	35.9591			1.53750			0.768749	+	0.639550i	$0.220879\pi$
$548$	−0.645792	−	6.14430i	−0.0275869	−	0.262472i
$549$	−10.7413	+	2.28314i	−0.458428	+	0.0974419i
$550$	−0.761040	+	7.24081i	−0.0324509	+	0.308749i
$551$	1.53515	+	0.326307i	0.0653997	+	0.0139011i
$552$	−0.282230	+	0.868616i	−0.0120125	+	0.0369708i
$553$	−2.41536	+	11.7129i	−0.102712	+	0.498085i
$554$	−4.37019	+	13.4501i	−0.185672	+	0.571438i
$555$	−1.43922	−	1.59841i	−0.0610914	−	0.0678489i
$556$	7.10481	−	7.89069i	0.301311	−	0.334640i
$557$	2.47800	−	23.5766i	0.104996	−	0.998972i	−0.807495	−	0.589875i	$-0.799177\pi$
$557$	2.47800	−	23.5766i	0.104996	−	0.998972i	0.912491	−	0.409097i	$-0.134156\pi$
$558$	0.708192	+	0.786527i	0.0299801	+	0.0332963i
$559$	46.6925	−	33.9241i	1.97488	−	1.43484i
$560$	−0.141512	+	0.323112i	−0.00597999	+	0.0136540i
$561$	−1.05092	−	3.23438i	−0.0443697	−	0.136556i
$562$	−1.01197	−	9.62821i	−0.0426872	−	0.406142i
$563$	3.29645	−	31.3637i	0.138929	−	1.32182i	−0.673685	−	0.739018i	$-0.735290\pi$
$563$	3.29645	−	31.3637i	0.138929	−	1.32182i	0.812614	−	0.582802i	$-0.198044\pi$
$564$	2.38464	−	22.6883i	0.100412	−	0.955352i
$565$	−0.875922	+	1.51714i	−0.0368503	+	0.0638266i
$566$	3.71279	+	2.69750i	0.156060	+	0.113384i
$567$	−21.3920	−	19.0273i	−0.898380	−	0.799073i
$568$	2.30930	+	7.10729i	0.0968960	+	0.298215i
$569$	−3.63237	−	34.5597i	−0.152277	−	1.44882i	−0.757537	−	0.652792i	$-0.773598\pi$
$569$	−3.63237	−	34.5597i	−0.152277	−	1.44882i	0.605260	−	0.796027i	$-0.293069\pi$
$570$	−0.217520	−	0.0968462i	−0.00911092	−	0.00405644i
$571$	4.61016	+	7.98503i	0.192929	+	0.334163i	0.946220	−	0.323525i	$-0.104868\pi$
$571$	4.61016	+	7.98503i	0.192929	+	0.334163i	−0.753290	+	0.657688i	$0.771535\pi$
$572$	−7.92203	−	1.68388i	−0.331237	−	0.0704065i
$573$	40.8075			1.70476
$574$	−9.75973	+	13.8473i	−0.407363	+	0.577975i
$575$	2.32057			0.0967747
$576$	−0.826553	−	0.175689i	−0.0344397	−	0.00732039i
$577$	0.957111	+	1.65776i	0.0398450	+	0.0690136i	0.885260	−	0.465096i	$-0.153980\pi$
$577$	0.957111	+	1.65776i	0.0398450	+	0.0690136i	−0.845415	+	0.534110i	$0.820647\pi$
$578$	14.2435	+	6.34161i	0.592451	+	0.263776i
$579$	0.891098	+	8.47823i	0.0370328	+	0.352343i
$580$	0.0709949	+	0.218500i	0.00294790	+	0.00907271i
$581$	−3.78786	+	1.25625i	−0.157147	+	0.0521180i
$582$	−16.8150	−	12.2168i	−0.697003	−	0.506402i
$583$	−0.529015	+	0.916280i	−0.0219095	+	0.0379485i
$584$	−0.232183	+	2.20908i	−0.00960782	+	0.0914123i
$585$	−0.0652667	+	0.620971i	−0.00269845	+	0.0256740i
$586$	−2.50768	−	23.8590i	−0.103591	−	0.985607i
$587$	−5.76607	−	17.7461i	−0.237991	−	0.732462i	−0.996711	−	0.0810439i	$-0.974175\pi$
$587$	−5.76607	−	17.7461i	−0.237991	−	0.732462i	0.758719	−	0.651418i	$-0.225825\pi$
$588$	9.30785	+	10.0881i	0.383849	+	0.416027i
$589$	−0.922875	+	0.670508i	−0.0380264	+	0.0276278i
$590$	−0.802622	−	0.891402i	−0.0330434	−	0.0366984i
$591$	5.28062	−	50.2418i	0.217216	−	2.06667i
$592$	5.50515	−	6.11409i	0.226260	−	0.251287i
$593$	19.9284	+	22.1327i	0.818360	+	0.908881i	0.997184	−	0.0750001i	$-0.0238957\pi$
$593$	19.9284	+	22.1327i	0.818360	+	0.908881i	−0.178823	+	0.983881i	$0.557229\pi$
$594$	−1.90820	+	5.87285i	−0.0782946	+	0.240966i
$595$	−0.397360	+	0.131785i	−0.0162902	+	0.00540266i
$596$	0.622613	−	1.91621i	0.0255032	−	0.0784908i
$597$	−14.3532	−	3.05086i	−0.587436	−	0.124863i
$598$	−0.269829	+	2.56725i	−0.0110341	+	0.104983i
$599$	−37.7383	+	8.02153i	−1.54195	+	0.327751i	−0.898927	−	0.438098i	$-0.855652\pi$
$599$	−37.7383	+	8.02153i	−1.54195	+	0.327751i	−0.643020	+	0.765849i	$0.722319\pi$
$600$	1.02119	+	9.71599i	0.0416900	+	0.396653i
$601$	−26.6810			−1.08834			−0.544171	−	0.838974i	$-0.683156\pi$
$601$	−26.6810			−1.08834			−0.544171	+	0.838974i	$0.683156\pi$
$602$	11.3592	+	25.1016i	0.462968	+	1.02307i
$603$	7.93436	−	5.76465i	0.323112	−	0.234755i
$604$	−17.0947	+	7.61103i	−0.695572	+	0.309689i
$605$	0.123537	−	1.17538i	0.00502250	−	0.0477859i
$606$	8.99501	+	15.5798i	0.365397	+	0.632887i
$607$	23.0623	−	10.2680i	0.936069	−	0.416765i	0.118733	−	0.992926i	$-0.462117\pi$
$607$	23.0623	−	10.2680i	0.936069	−	0.416765i	0.817336	+	0.576161i	$0.195450\pi$
$608$	0.281445	−	0.866199i	0.0114141	−	0.0351290i
$609$	8.89647	+	0.880431i	0.360503	+	0.0356769i
$610$	1.40169	−	1.01839i	0.0567529	−	0.0412334i
$611$	−6.73994	−	64.1263i	−0.272669	−	2.59427i
$612$	−0.501444	−	0.868527i	−0.0202697	−	0.0351081i
$613$	−16.5192	+	18.3464i	−0.667205	+	0.741006i	−0.977801	−	0.209536i	$-0.932805\pi$
$613$	−16.5192	+	18.3464i	−0.667205	+	0.741006i	0.310596	+	0.950542i	$0.399471\pi$
$614$	−12.0014	+	20.7870i	−0.484337	+	0.838897i
$615$	0.161165	−	1.66620i	0.00649880	−	0.0671877i
$616$	1.55108	−	3.54156i	0.0624950	−	0.142693i
$617$	−7.55165	−	23.2416i	−0.304018	−	0.935672i	−0.980042	−	0.198792i	$-0.936298\pi$
$617$	−7.55165	−	23.2416i	−0.304018	−	0.935672i	0.676024	−	0.736880i	$-0.263702\pi$
$618$	−18.5188	+	32.0755i	−0.744934	+	1.29026i
$619$	−8.41254	−	3.74551i	−0.338129	−	0.150545i	0.230647	−	0.973038i	$-0.425916\pi$
$619$	−8.41254	−	3.74551i	−0.338129	−	0.150545i	−0.568775	+	0.822493i	$0.692583\pi$
$620$	−0.152550	−	0.0679197i	−0.00612656	−	0.00272772i
$621$	1.92517	+	0.409208i	0.0772545	+	0.0164209i
$622$	0.813601	−	2.50401i	0.0326224	−	0.100401i
$623$	−5.42486	−	3.08824i	−0.217343	−	0.123728i
$624$	−10.8675			−0.435050
$625$	22.5953	−	10.0601i	0.903814	−	0.402404i
$626$	0.117592	−	1.11882i	0.00469993	−	0.0447169i
$627$	2.38419	+	1.06151i	0.0952153	+	0.0423926i
$628$	14.5742	+	3.09785i	0.581575	+	0.123617i
$629$	9.76438			0.389331
$630$	−0.284040	−	0.0903855i	−0.0113164	−	0.00360105i
$631$	10.2851	−	31.6542i	0.409443	−	1.26014i	−0.507685	−	0.861543i	$-0.669499\pi$
$631$	10.2851	−	31.6542i	0.409443	−	1.26014i	0.917128	−	0.398593i	$-0.130501\pi$
$632$	4.12943	−	1.83854i	0.164260	−	0.0731332i
$633$	−2.77764	+	3.08488i	−0.110401	+	0.122613i
$634$	3.59843	−	0.764869i	0.142912	−	0.0303768i
$635$	0.0582555	+	0.0646993i	0.00231180	+	0.00256751i
$636$	−0.438712	+	1.35022i	−0.0173961	+	0.0535396i
$637$	31.6610	+	22.4202i	1.25445	+	0.888322i
$638$	−0.778158	−	2.39492i	−0.0308076	−	0.0948160i
$639$	−5.76892	+	2.56849i	−0.228215	+	0.101608i
$640$	0.130411	−	0.0277196i	0.00515493	−	0.00109571i
$641$	7.30060	+	3.25044i	0.288356	+	0.128385i	0.545817	−	0.837904i	$-0.316219\pi$
$641$	7.30060	+	3.25044i	0.288356	+	0.128385i	−0.257461	+	0.966289i	$0.582886\pi$
$642$	10.0858	−	17.4692i	0.398056	−	0.689453i
$643$	−10.7689	−	33.1432i	−0.424683	−	1.30704i	−0.903297	−	0.429015i	$-0.858861\pi$
$643$	−10.7689	−	33.1432i	−0.424683	−	1.30704i	0.478614	−	0.878025i	$-0.341139\pi$
$644$	−1.17429	−	0.373677i	−0.0462736	−	0.0147249i
$645$	−2.20253	−	1.60023i	−0.0867247	−	0.0630092i
$646$	0.987479	−	0.439654i	0.0388519	−	0.0172980i
$647$	−16.8122	−	29.1195i	−0.660954	−	1.14481i	−0.980365	−	0.197190i	$-0.936818\pi$
$647$	−16.8122	−	29.1195i	−0.660954	−	1.14481i	0.319411	−	0.947616i	$-0.396515\pi$
$648$	−1.13110	+	10.7617i	−0.0444339	+	0.422760i
$649$	8.79735	+	9.77045i	0.345326	+	0.383524i
$650$	8.53273	+	26.2610i	0.334681	+	1.03004i
$651$	−4.80236	+	4.37720i	−0.188219	+	0.171556i
$652$	2.01490	−	1.46391i	0.0789097	−	0.0573312i
$653$	−13.4137	+	23.2332i	−0.524919	+	0.909187i	0.474660	+	0.880169i	$0.342571\pi$
$653$	−13.4137	+	23.2332i	−0.524919	+	0.909187i	−0.999579	+	0.0290173i	$0.990762\pi$
$654$	−2.56067	+	2.84391i	−0.100130	+	0.111206i
$655$	0.973377	+	1.68594i	0.0380330	+	0.0658751i
$656$	6.40290	−	0.0531055i	0.249991	−	0.00207342i
$657$	−1.87699			−0.0732285
$658$	30.6318	+	3.03145i	1.19415	+	0.118178i
$659$	29.4293			1.14640			0.573202	−	0.819414i	$-0.305701\pi$
$659$	29.4293			1.14640			0.573202	+	0.819414i	$0.305701\pi$
$660$	0.0399339	+	0.379946i	0.00155443	+	0.0147894i
$661$	−20.9186	−	9.31356i	−0.813639	−	0.362256i	−0.0426391	−	0.999091i	$-0.513577\pi$
$661$	−20.9186	−	9.31356i	−0.813639	−	0.362256i	−0.771000	+	0.636835i	$0.780243\pi$
$662$	5.06995	−	5.63075i	0.197049	−	0.218845i
$663$	−8.63036	−	9.58498i	−0.335175	−	0.372250i
$664$	1.22029	+	0.886591i	0.0473564	+	0.0344064i
$665$	0.128886	−	0.294283i	0.00499799	−	0.0114118i
$666$	5.62448	+	4.08642i	0.217944	+	0.158346i
$667$	−0.733227	+	0.326454i	−0.0283907	+	0.0126403i
$668$	−17.8709	−	7.95666i	−0.691448	−	0.307852i
$669$	−17.2636	+	19.1731i	−0.667448	+	0.741276i
$670$	−0.773689	+	1.34007i	−0.0298902	+	0.0517714i
$671$	−15.3636	+	11.1623i	−0.593107	+	0.430917i
$672$	1.04778	−	5.08107i	0.0404192	−	0.196007i
$673$	30.4068	+	22.0918i	1.17210	+	0.851578i	0.991258	−	0.131935i	$-0.0421189\pi$
$673$	30.4068	+	22.0918i	1.17210	+	0.851578i	0.180838	+	0.983513i	$0.442119\pi$
$674$	−8.65545	−	1.83977i	−0.333395	−	0.0708654i
$675$	20.5930	−	4.37719i	0.792626	−	0.168478i
$676$	−17.3289	+	3.68336i	−0.666494	+	0.141668i
$677$	−20.8855	−	23.1956i	−0.802693	−	0.891481i	0.193279	−	0.981144i	$-0.438088\pi$
$677$	−20.8855	−	23.1956i	−0.802693	−	0.891481i	−0.995972	+	0.0896628i	$0.971421\pi$
$678$	7.96193	−	24.5043i	0.305776	−	0.941082i
$679$	16.3456	−	22.7877i	0.627287	−	0.874513i
$680$	0.128013	+	0.0930066i	0.00490906	+	0.00356664i
$681$	18.7840	+	20.8617i	0.719804	+	0.799423i
$682$	1.67207	+	0.744452i	0.0640267	+	0.0285065i
$683$	−7.76217	−	13.4445i	−0.297011	−	0.514438i	0.678440	−	0.734656i	$-0.262657\pi$
$683$	−7.76217	−	13.4445i	−0.297011	−	0.514438i	−0.975451	+	0.220218i	$0.929323\pi$
$684$	0.752805	+	0.160014i	0.0287842	+	0.00611827i
$685$	−0.666384	+	0.484156i	−0.0254612	+	0.0184987i
$686$	−13.5350	+	12.6413i	−0.516770	+	0.482647i
$687$	19.0001	+	13.8044i	0.724901	+	0.526671i
$688$	5.20687	−	9.01857i	0.198510	−	0.343830i
$689$	−0.419435	+	3.99066i	−0.0159792	+	0.152032i
$690$	0.119106	−	0.0253168i	0.00453430	−	0.000963795i
$691$	−16.5041	−	3.50805i	−0.627844	−	0.133452i	−0.117009	−	0.993131i	$-0.537330\pi$
$691$	−16.5041	−	3.50805i	−0.627844	−	0.133452i	−0.510835	+	0.859679i	$0.670664\pi$
$692$	−5.82211	+	4.23001i	−0.221323	+	0.160801i
$693$	3.11329	+	0.990695i	0.118264	+	0.0376334i
$694$	−9.94559			−0.377529
$695$	−1.38470	−	0.294326i	−0.0525245	−	0.0111644i
$696$	−1.68949	−	2.92628i	−0.0640399	−	0.110920i
$697$	5.13164	+	5.60507i	0.194375	+	0.212307i
$698$	2.27058	−	3.93276i	0.0859428	−	0.148857i
$699$	−9.25060	−	28.4704i	−0.349890	−	1.07685i
$700$	−13.1009	+	1.45750i	−0.495168	+	0.0550885i
$701$	−24.4059	+	17.7319i	−0.921799	+	0.669726i	−0.943971	−	0.330028i	$-0.892942\pi$
$701$	−24.4059	+	17.7319i	−0.921799	+	0.669726i	0.0221721	+	0.999754i	$0.492942\pi$
$702$	2.44799	+	23.2911i	0.0923934	+	0.879065i
$703$	−5.01396	+	5.56856i	−0.189105	+	0.210022i
$704$	−1.42940	+	0.303829i	−0.0538726	+	0.0114510i
$705$	−2.77861	+	1.23712i	−0.104648	+	0.0465925i
$706$	4.45490			0.167662
$707$	−20.9473	+	12.2642i	−0.787804	+	0.461244i
$708$	14.2724	+	10.3695i	0.536391	+	0.389711i
$709$	0.403116	+	3.83539i	0.0151393	+	0.144041i	0.999480	−	0.0322334i	$-0.0102620\pi$
$709$	0.403116	+	3.83539i	0.0151393	+	0.144041i	−0.984341	+	0.176275i	$0.943595\pi$
$710$	0.666680	−	0.740423i	0.0250200	−	0.0277876i
$711$	1.90984	+	3.30794i	0.0716245	+	0.124057i
$712$	0.246621	+	2.34645i	0.00924252	+	0.0879367i
$713$	0.180272	−	0.554820i	0.00675124	−	0.0207782i
$714$	5.31350	−	3.11096i	0.198853	−	0.116425i
$715$	0.333674	+	1.02694i	0.0124787	+	0.0384055i
$716$	−0.606268	−	0.673329i	−0.0226573	−	0.0251635i
$717$	−52.3759	+	11.1328i	−1.95601	+	0.415764i
$718$	−8.30200	+	1.76464i	−0.309828	+	0.0658559i
$719$	26.7316	+	29.6885i	0.996921	+	1.10719i	0.994238	+	0.107197i	$0.0341875\pi$
$719$	26.7316	+	29.6885i	0.996921	+	1.10719i	0.00268357	+	0.999996i	$0.499146\pi$
$720$	0.0348143	+	0.107147i	0.00129745	+	0.00399315i
$721$	−43.4296	−	24.7234i	−1.61740	−	0.920748i
$722$	5.61499	−	17.2812i	0.208968	−	0.643138i
$723$	1.74786	+	16.6297i	0.0650035	+	0.618467i
$724$	−3.31857	−	5.74794i	−0.123334	−	0.213620i
$725$	−5.74474	+	6.38018i	−0.213354	+	0.236954i
$726$	1.81693	+	17.2869i	0.0674326	+	0.641578i
$727$	−2.19731	−	1.59644i	−0.0814939	−	0.0592088i	0.546292	−	0.837595i	$-0.316039\pi$
$727$	−2.19731	−	1.59644i	−0.0814939	−	0.0592088i	−0.627786	+	0.778386i	$0.716039\pi$
$728$	−0.0891055	−	14.6630i	−0.00330247	−	0.543447i
$729$	15.7139			0.581996
$730$	0.270543	−	0.120453i	0.0100132	−	0.00445818i
$731$	12.0892	−	2.56964i	0.447135	−	0.0950416i
$732$	−17.0509	+	18.9369i	−0.630219	+	0.699929i
$733$	1.64315	+	15.6335i	0.0606910	+	0.577437i	0.982036	+	0.188692i	$0.0604246\pi$
$733$	1.64315	+	15.6335i	0.0606910	+	0.577437i	−0.921345	+	0.388745i	$0.872909\pi$
$734$	−12.1968	+	8.86149i	−0.450192	+	0.327084i
$735$	0.544313	−	1.74720i	0.0200773	−	0.0644463i
$736$	0.143931	+	0.442974i	0.00530537	+	0.0163283i
$737$	8.48023	−	14.6882i	0.312373	−	0.541046i
$738$	0.610188	+	5.37624i	0.0224613	+	0.197902i
$739$	16.2219	+	28.0971i	0.596731	+	1.03357i	0.993300	+	0.115563i	$0.0368672\pi$
$739$	16.2219	+	28.0971i	0.596731	+	1.03357i	−0.396570	+	0.918005i	$0.629799\pi$
$740$	−1.07293	−	0.228058i	−0.0394417	−	0.00838359i
$741$	9.89790			0.363608
$742$	−1.82537	−	0.580861i	−0.0670116	−	0.0213241i
$743$	11.5098	−	8.36235i	0.422253	−	0.306785i	−0.356291	−	0.934375i	$-0.615959\pi$
$743$	11.5098	−	8.36235i	0.422253	−	0.306785i	0.778544	+	0.627590i	$0.215959\pi$
$744$	2.40230	+	0.510625i	0.0880726	+	0.0187204i
$745$	−0.262754	+	0.0558500i	−0.00962655	+	0.00204619i
$746$	−0.803442	+	7.64424i	−0.0294161	+	0.279875i
$747$	−0.637296	+	1.10383i	−0.0233174	+	0.0403870i
$748$	−1.40312	−	1.01942i	−0.0513030	−	0.0372738i
$749$	23.6529	+	13.4651i	0.864260	+	0.492003i
$750$	2.11127	−	1.53392i	0.0770925	−	0.0560110i
$751$	−3.50424	−	0.744850i	−0.127872	−	0.0271800i	0.143531	−	0.989646i	$-0.454154\pi$
$751$	−3.50424	−	0.744850i	−0.127872	−	0.0271800i	−0.271403	+	0.962466i	$0.587488\pi$
$752$	−5.81714	−	10.0756i	−0.212129	−	0.367419i
$753$	−10.5693	−	4.70576i	−0.385167	−	0.171487i
$754$	−6.39041	−	7.09727i	−0.232725	−	0.258467i
$755$	2.01835	+	1.46642i	0.0734553	+	0.0533684i
$756$	−11.1256	−	1.10104i	−0.404636	−	0.0400444i
$757$	7.35777	−	22.6449i	0.267423	−	0.823042i	−0.723703	−	0.690112i	$-0.757561\pi$
$757$	7.35777	−	22.6449i	0.267423	−	0.823042i	0.991125	−	0.132930i	$-0.0424386\pi$
$758$	−4.20742	−	4.67282i	−0.152820	−	0.169724i
$759$	−1.30550	+	0.277492i	−0.0473865	+	0.0100723i
$760$	−0.118775	+	0.0252464i	−0.00430842	+	0.000915782i
$761$	46.3627	+	9.85469i	1.68064	+	0.357232i	0.946735	−	0.322014i	$-0.104360\pi$
$761$	46.3627	+	9.85469i	1.68064	+	0.357232i	0.733910	+	0.679246i	$0.237693\pi$
$762$	−1.03592	−	0.752637i	−0.0375273	−	0.0272652i
$763$	−3.85814	−	3.43166i	−0.139674	−	0.124235i
$764$	16.8363	−	12.2323i	0.609118	−	0.442550i
$765$	−0.0668546	+	0.115796i	−0.00241713	+	0.00418660i
$766$	−3.41690	+	3.79485i	−0.123458	+	0.137114i
$767$	45.5516	+	20.2809i	1.64477	+	0.732300i
$768$	−1.79135	+	0.797558i	−0.0646396	+	0.0287794i
$769$	−4.42595	−	3.21564i	−0.159604	−	0.115959i	0.505117	−	0.863051i	$-0.331449\pi$
$769$	−4.42595	−	3.21564i	−0.159604	−	0.115959i	−0.664721	+	0.747092i	$0.731449\pi$
$770$	−0.512314	+	0.0569961i	−0.0184625	+	0.00205400i
$771$	11.3883	+	8.27406i	0.410138	+	0.297983i
$772$	2.90906	+	3.23084i	0.104699	+	0.116280i
$773$	−23.6819	+	26.3014i	−0.851780	+	0.945997i	−0.999071	−	0.0430958i	$-0.986278\pi$
$773$	−23.6819	+	26.3014i	−0.851780	+	0.945997i	0.147291	+	0.989093i	$0.452945\pi$
$774$	8.03903	+	3.57921i	0.288957	+	0.128652i
$775$	−0.652276	−	6.20599i	−0.0234304	−	0.222926i
$776$	−10.5996			−0.380503
$777$	−24.8782	+	34.6832i	−0.892501	+	1.24425i
$778$	−5.59097			−0.200446
$779$	−5.83161	+	0.0483672i	−0.208939	+	0.00173294i
$780$	0.724453	+	1.25479i	0.0259396	+	0.0449287i
$781$	−7.30732	+	8.11560i	−0.261477	+	0.290399i
$782$	−0.276394	+	0.478728i	−0.00988383	+	0.0171193i
$783$	−5.89096	+	4.28003i	−0.210526	+	0.152956i
$784$	6.86422	+	1.37206i	0.245151	+	0.0490021i
$785$	−0.613864	−	1.88928i	−0.0219097	−	0.0674312i
$786$	−19.1586	−	21.2777i	−0.683363	−	0.758952i
$787$	−1.30526	+	12.4188i	−0.0465277	+	0.442681i	0.946315	+	0.323247i	$0.104775\pi$
$787$	−1.30526	+	12.4188i	−0.0465277	+	0.442681i	−0.992842	+	0.119434i	$0.961892\pi$
$788$	−12.8816	−	22.3117i	−0.458890	−	0.794820i
$789$	−21.6860	+	9.65525i	−0.772043	+	0.343736i
$790$	−0.487558	−	0.354232i	−0.0173465	−	0.0126030i
$791$	33.1277	+	10.5417i	1.17788	+	0.374820i
$792$	−0.381591	−	1.17442i	−0.0135593	−	0.0417311i
$793$	−36.0113	+	62.3735i	−1.27880	+	2.21495i
$794$	−24.7126	−	11.0028i	−0.877018	−	0.390473i
$795$	0.185144	−	0.0393536i	0.00656639	−	0.00139573i
$796$	−6.83635	+	3.04374i	−0.242308	+	0.107883i
$797$	7.40328	+	22.7849i	0.262238	+	0.807084i	0.992317	+	0.123722i	$0.0394830\pi$
$797$	7.40328	+	22.7849i	0.262238	+	0.807084i	−0.730079	+	0.683362i	$0.760517\pi$
$798$	−0.954297	+	4.62772i	−0.0337817	+	0.163819i
$799$	4.26686	−	13.1320i	0.150951	−	0.464578i
$800$	3.33376	+	3.70251i	0.117866	+	0.130904i
$801$	−1.95014	+	0.414516i	−0.0689050	+	0.0146462i
$802$	10.4987	−	11.6600i	0.370723	−	0.411729i
$803$	−2.96535	+	1.32026i	−0.104645	+	0.0465910i
$804$	7.03266	−	21.6443i	0.248023	−	0.763335i
$805$	0.0351352	+	0.160496i	0.00123835	+	0.00565675i
$806$	6.94154			0.244505
$807$	−20.8472	−	4.43120i	−0.733855	−	0.155986i
$808$	8.38132	+	3.73161i	0.294854	+	0.131277i
$809$	−2.43635	+	23.1803i	−0.0856574	+	0.814976i	0.864380	+	0.502839i	$0.167711\pi$
$809$	−2.43635	+	23.1803i	−0.0856574	+	0.814976i	−0.950037	+	0.312136i	$0.898955\pi$
$810$	1.31797	−	0.586799i	0.0463088	−	0.0206180i
$811$	−46.5324			−1.63397			−0.816986	−	0.576657i	$-0.804357\pi$
$811$	−46.5324			−1.63397			−0.816986	+	0.576657i	$0.804357\pi$
$812$	3.93442	−	2.30353i	0.138071	−	0.0808381i
$813$	10.1290	−	31.1738i	0.355239	−	1.09331i
$814$	11.7601	+	2.49969i	0.412192	+	0.0876142i
$815$	−0.303344	−	0.135057i	−0.0106257	−	0.00473086i
$816$	−2.12601	−	0.946562i	−0.0744253	−	0.0331363i
$817$	−4.74230	+	8.21390i	−0.165912	+	0.287368i
$818$	6.70813	+	20.6455i	0.234544	+	0.721853i
$819$	12.3148	−	1.37005i	0.430313	−	0.0478733i
$820$	−0.432962	−	0.735752i	−0.0151197	−	0.0256936i
$821$	28.5434	−	49.4386i	0.996172	−	1.72542i	0.422379	−	0.906419i	$-0.361195\pi$
$821$	28.5434	−	49.4386i	0.996172	−	1.72542i	0.573793	−	0.819001i	$-0.305472\pi$
$822$	8.10622	−	9.00287i	0.282737	−	0.314011i
$823$	4.06412	+	7.03927i	0.141666	+	0.245373i	0.928124	−	0.372270i	$-0.121421\pi$
$823$	4.06412	+	7.03927i	0.141666	+	0.245373i	−0.786458	+	0.617644i	$0.788087\pi$
$824$	1.97437	+	18.7848i	0.0687803	+	0.654401i
$825$	−11.5499	+	8.39153i	−0.402117	+	0.292155i
$826$	−13.8741	+	19.3421i	−0.482740	+	0.672997i
$827$	−11.6424	+	35.8316i	−0.404846	+	1.24599i	0.516178	+	0.856481i	$0.327354\pi$
$827$	−11.6424	+	35.8316i	−0.404846	+	1.24599i	−0.921024	+	0.389506i	$0.872646\pi$
$828$	−0.359558	+	0.160085i	−0.0124955	+	0.00556335i
$829$	9.23725	+	15.9994i	0.320823	+	0.555682i	0.980658	−	0.195729i	$-0.0627072\pi$
$829$	9.23725	+	15.9994i	0.320823	+	0.555682i	−0.659835	+	0.751410i	$0.729374\pi$
$830$	0.0210207	−	0.199999i	0.000729640	−	0.00694207i
$831$	−25.3336	+	11.2793i	−0.878814	+	0.391273i
$832$	−4.48373	+	3.25762i	−0.155446	+	0.112938i
$833$	4.24102	+	7.14372i	0.146943	+	0.247515i
$834$	20.8205			0.720954
$835$	0.272622	+	2.59382i	0.00943447	+	0.0897630i
$836$	1.30186	−	0.276720i	0.0450259	−	0.00957055i
$837$	0.553224	−	5.26357i	0.0191222	−	0.181936i
$838$	−17.5490	−	3.73015i	−0.606219	−	0.128856i
$839$	2.00377	−	6.16698i	0.0691780	−	0.212908i	−0.910491	−	0.413529i	$-0.864296\pi$
$839$	2.00377	−	6.16698i	0.0691780	−	0.212908i	0.979669	+	0.200621i	$0.0642960\pi$
$840$	−0.656518	+	0.217735i	−0.0226520	+	0.00751258i
$841$	−8.04389	+	24.7566i	−0.277376	+	0.853674i
$842$	−16.1412	−	17.9267i	−0.556264	−	0.617793i
$843$	12.7026	−	14.1076i	0.437500	−	0.485892i
$844$	−0.221284	+	2.10538i	−0.00761692	+	0.0724702i
$845$	1.58047	+	1.75528i	0.0543697	+	0.0603836i
$846$	7.95359	−	5.77862i	0.273450	−	0.198673i
$847$	−23.3095	+	2.59323i	−0.800922	+	0.0891044i
$848$	0.223733	+	0.688580i	0.00768303	+	0.0236459i
$849$	0.940647	+	8.94966i	0.0322829	+	0.307151i
$850$	−0.618079	+	5.88063i	−0.0211999	+	0.201704i
$851$	0.400558	−	3.81105i	0.0137309	−	0.130641i
$852$	−7.32684	+	12.6905i	−0.251014	+	0.434768i
$853$	31.9623	+	23.2220i	1.09437	+	0.795106i	0.980132	−	0.198347i	$-0.0635574\pi$
$853$	31.9623	+	23.2220i	1.09437	+	0.795106i	0.114238	+	0.993453i	$0.463557\pi$
$854$	−25.6904	−	22.8506i	−0.879108	−	0.781932i
$855$	−0.0317080	−	0.0975872i	−0.00108439	−	0.00333741i
$856$	−1.07529	−	10.2307i	−0.0367528	−	0.349679i
$857$	14.5353	+	6.47155i	0.496518	+	0.221064i	0.639689	−	0.768634i	$-0.279063\pi$
$857$	14.5353	+	6.47155i	0.496518	+	0.221064i	−0.143171	+	0.989698i	$0.545730\pi$
$858$	−7.94056	−	13.7535i	−0.271086	−	0.469535i
$859$	10.2215	+	2.17266i	0.348755	+	0.0741301i	0.378958	−	0.925414i	$-0.376282\pi$
$859$	10.2215	+	2.17266i	0.348755	+	0.0741301i	−0.0302039	+	0.999544i	$0.509616\pi$
$860$	−1.38840			−0.0473442
$861$	−32.9840	+	3.94675i	−1.12409	+	0.134505i
$862$	37.6717			1.28310
$863$	6.26305	+	1.33125i	0.213197	+	0.0453164i	0.313272	−	0.949664i	$-0.398575\pi$
$863$	6.26305	+	1.33125i	0.213197	+	0.0453164i	−0.100075	+	0.994980i	$0.531908\pi$
$864$	2.11282	+	3.65951i	0.0718796	+	0.124499i
$865$	0.876520	+	0.390252i	0.0298026	+	0.0132690i
$866$	0.893266	+	8.49886i	0.0303544	+	0.288803i
$867$	9.44753	+	29.0765i	0.320855	+	0.987489i
$868$	−0.669262	+	3.24548i	−0.0227162	+	0.110159i
$869$	5.34401	+	3.88265i	0.181283	+	0.131710i
$870$	−0.225249	+	0.390143i	−0.00763667	+	0.0132271i
$871$	6.72364	−	63.9712i	0.227822	−	2.16758i
$872$	−0.203999	+	1.94092i	−0.00690828	+	0.0657279i
$873$	−0.936246	−	8.90779i	−0.0316871	−	0.301483i
$874$	−0.131089	−	0.403450i	−0.00443415	−	0.0136469i
$875$	2.08695	+	2.83604i	0.0705520	+	0.0958758i
$876$	−3.52374	+	2.56015i	−0.119056	+	0.0864993i
$877$	36.2814	+	40.2946i	1.22514	+	1.36065i	0.911601	+	0.411076i	$0.134847\pi$
$877$	36.2814	+	40.2946i	1.22514	+	1.36065i	0.313536	+	0.949576i	$0.398486\pi$
$878$	0.743826	−	7.07703i	0.0251029	−	0.238838i
$879$	31.4774	−	34.9592i	1.06171	−	1.17914i
$880$	0.130367	+	0.144788i	0.00439469	+	0.00488079i
$881$	−15.2033	+	46.7910i	−0.512213	+	1.57643i	0.276084	+	0.961133i	$0.410963\pi$
$881$	−15.2033	+	46.7910i	−0.512213	+	1.57643i	−0.788297	+	0.615295i	$0.789037\pi$
$882$	−0.546759	+	5.88981i	−0.0184103	+	0.198320i
$883$	12.2891	−	37.8220i	0.413562	−	1.27281i	−0.499969	−	0.866043i	$-0.666655\pi$
$883$	12.2891	−	37.8220i	0.413562	−	1.27281i	0.913531	−	0.406769i	$-0.133345\pi$
$884$	−6.43388	−	1.36756i	−0.216395	−	0.0459961i
$885$	0.245858	−	2.33918i	0.00826442	−	0.0786307i
$886$	−9.99218	+	2.12390i	−0.335694	+	0.0713540i
$887$	−2.11495	−	20.1224i	−0.0710132	−	0.675645i	−0.970894	−	0.239509i	$-0.923013\pi$
$887$	−2.11495	−	20.1224i	−0.0710132	−	0.675645i	0.899881	−	0.436136i	$-0.143653\pi$
$888$	16.1327			0.541378
$889$	1.00700	−	1.40388i	0.0337737	−	0.0470846i
$890$	0.254485	−	0.184894i	0.00853036	−	0.00619767i
$891$	−14.4460	+	6.43177i	−0.483959	+	0.215472i
$892$	−1.37532	+	13.0853i	−0.0460492	+	0.438129i
$893$	5.29811	+	9.17659i	0.177294	+	0.307083i
$894$	3.60923	−	1.60693i	0.120711	−	0.0537439i
$895$	−0.0373289	+	0.114886i	−0.00124777	+	0.00384023i
$896$	−1.09079	−	2.41043i	−0.0364408	−	0.0805268i
$897$	−4.09507	+	2.97524i	−0.136730	+	0.0993405i
$898$	−0.242853	−	2.31059i	−0.00810411	−	0.0771054i
$899$	1.07914	+	1.86913i	0.0359915	+	0.0623391i
$900$	−2.81709	+	3.12869i	−0.0939030	+	0.104290i
$901$	−0.429640	+	0.744158i	−0.0143134	+	0.0247915i
$902$	4.74560	+	8.06441i	0.158011	+	0.268516i
$903$	−21.6742	+	49.4881i	−0.721271	+	1.64686i
$904$	−4.06040	−	12.4966i	−0.135047	−	0.415632i
$905$	−0.442446	+	0.766339i	−0.0147074	+	0.0254740i
$906$	−33.5204	−	14.9243i	−1.11364	−	0.495825i
$907$	−36.7047	−	16.3420i	−1.21876	−	0.542626i	−0.306355	−	0.951917i	$-0.599109\pi$
$907$	−36.7047	−	16.3420i	−1.21876	−	0.542626i	−0.912404	+	0.409291i	$0.865776\pi$
$908$	14.0033	+	2.97650i	0.464717	+	0.0987787i
$909$	−2.39569	+	7.37319i	−0.0794601	+	0.244553i
$910$	−1.68708	+	0.987755i	−0.0559262	+	0.0327438i
$911$	26.7803			0.887270			0.443635	−	0.896208i	$-0.353689\pi$
$911$	26.7803			0.887270			0.443635	+	0.896208i	$0.353689\pi$
$912$	1.63151	−	0.726397i	0.0540248	−	0.0240534i
$913$	−0.230403	+	2.19214i	−0.00762524	+	0.0725493i
$914$	10.0823	+	4.48893i	0.333493	+	0.148481i
$915$	3.32314	+	0.706356i	0.109860	+	0.0233514i
$916$	11.9771			0.395733
$917$	28.5519	−	26.0241i	0.942865	−	0.859392i
$918$	−1.54975	+	4.76964i	−0.0511494	+	0.157422i
$919$	−17.3660	+	7.73186i	−0.572853	+	0.255051i	−0.672654	−	0.739957i	$-0.734846\pi$
$919$	−17.3660	+	7.73186i	−0.572853	+	0.255051i	0.0998013	+	0.995007i	$0.468179\pi$
$920$	0.0415520	−	0.0461482i	0.00136993	−	0.00152146i
$921$	−46.0379	+	9.78566i	−1.51700	+	0.322449i
$922$	−18.0659	−	20.0642i	−0.594970	−	0.660781i
$923$	−12.7986	+	39.3900i	−0.421271	+	1.29654i
$924$	7.19595	−	2.38655i	0.236729	−	0.0785116i
$925$	−12.6667	−	38.9841i	−0.416479	−	1.28179i
$926$	37.4476	−	16.6727i	1.23060	−	0.547900i
$927$	−15.6122	+	3.31847i	−0.512771	+	0.108993i
$928$	−1.57422	−	0.700889i	−0.0516764	−	0.0230078i
$929$	20.1212	−	34.8509i	0.660154	−	1.14342i	−0.320421	−	0.947275i	$-0.603824\pi$
$929$	20.1212	−	34.8509i	0.660154	−	1.14342i	0.980575	−	0.196145i	$-0.0628422\pi$
$930$	−0.101184	−	0.311414i	−0.00331797	−	0.0102117i
$931$	−6.25176	−	1.24964i	−0.204893	−	0.0409553i
$932$	−12.3508	−	8.97340i	−0.404565	−	0.293933i
$933$	4.71638	−	2.09987i	0.154407	−	0.0687465i
$934$	−12.0608	−	20.8899i	−0.394642	−	0.683540i
$935$	−0.0241701	+	0.229964i	−0.000790448	+	0.00752061i
$936$	−3.13372	−	3.48034i	−0.102429	−	0.113759i
$937$	10.8792	+	33.4827i	0.355407	+	1.09383i	0.955773	+	0.294105i	$0.0950216\pi$
$937$	10.8792	+	33.4827i	0.355407	+	1.09383i	−0.600366	+	0.799725i	$0.704978\pi$
$938$	29.2612	+	9.31133i	0.955412	+	0.304026i
$939$	1.78464	−	1.29662i	0.0582396	−	0.0423135i
$940$	−0.775565	+	1.34332i	−0.0252961	+	0.0438142i
$941$	−36.6305	+	40.6823i	−1.19412	+	1.32620i	−0.261560	+	0.965187i	$0.584237\pi$
$941$	−36.6305	+	40.6823i	−1.19412	+	1.32620i	−0.932560	+	0.361016i	$0.882430\pi$
$942$	14.6083	+	25.3023i	0.475965	+	0.824395i
$943$	2.39818	−	1.77295i	0.0780955	−	0.0577353i
$944$	8.99687			0.292823
$945$	0.614530	+	1.35799i	0.0199907	+	0.0441754i
$946$	15.2180			0.494779
$947$	1.24791	+	11.8730i	0.0405515	+	0.385822i	0.995908	+	0.0903679i	$0.0288043\pi$
$947$	1.24791	+	11.8730i	0.0405515	+	0.385822i	−0.955357	+	0.295454i	$0.904529\pi$
$948$	8.09729	+	3.60514i	0.262988	+	0.117090i
$949$	−8.23739	+	9.14855i	−0.267397	+	0.296975i
$950$	−3.03631	−	3.37216i	−0.0985108	−	0.109407i
$951$	5.83600	+	4.24010i	0.189245	+	0.137495i
$952$	1.25971	−	2.87628i	0.0408276	−	0.0932207i
$953$	26.9226	+	19.5604i	0.872108	+	0.633624i	0.931152	−	0.364632i	$-0.118805\pi$
$953$	26.9226	+	19.5604i	0.872108	+	0.633624i	−0.0590437	+	0.998255i	$0.518805\pi$
$954$	−0.558913	+	0.248844i	−0.0180955	+	0.00805663i
$955$	−2.53471	−	1.12853i	−0.0820214	−	0.0365183i
$956$	−18.2721	+	20.2932i	−0.590963	+	0.656330i
$957$	2.46891	−	4.27627i	0.0798084	−	0.138232i
$958$	−33.0548	+	24.0157i	−1.06795	+	0.775912i
$959$	12.2136	+	10.8635i	0.394397	+	0.350800i
$960$	0.211503	+	0.153666i	0.00682621	+	0.00495953i
$961$	28.7881	+	6.11911i	0.928649	+	0.197391i
$962$	44.6010	−	9.48024i	1.43799	−	0.305655i
$963$	8.50283	−	1.80733i	0.274000	−	0.0582405i
$964$	5.70601	+	6.33717i	0.183778	+	0.204106i
$965$	0.179115	−	0.551260i	0.00576593	−	0.0177457i
$966$	−0.996239	−	2.20149i	−0.0320535	−	0.0708317i
$967$	4.79690	+	3.48515i	0.154258	+	0.112075i	0.662237	−	0.749295i	$-0.269607\pi$
$967$	4.79690	+	3.48515i	0.154258	+	0.112075i	−0.507979	+	0.861369i	$0.669607\pi$
$968$	5.93151	+	6.58761i	0.190646	+	0.211734i
$969$	1.93632	+	0.862106i	0.0622036	+	0.0276948i
$970$	0.706590	+	1.22385i	0.0226873	+	0.0392955i
$971$	4.82766	+	1.02615i	0.154927	+	0.0329308i	0.284722	−	0.958610i	$-0.408099\pi$
$971$	4.82766	+	1.02615i	0.154927	+	0.0329308i	−0.129795	+	0.991541i	$0.541432\pi$
$972$	−6.91035	+	5.02067i	−0.221650	+	0.161038i
$973$	0.170712	+	28.0920i	0.00547277	+	0.900588i
$974$	29.2764	+	21.2705i	0.938075	+	0.681552i
$975$	−27.0723	+	46.8906i	−0.867007	+	1.50170i
$976$	−1.35838	+	12.9241i	−0.0434807	+	0.413691i
$977$	57.2057	−	12.1595i	1.83017	−	0.389015i	0.841642	−	0.540035i	$-0.181589\pi$
$977$	57.2057	−	12.1595i	1.83017	−	0.389015i	0.988531	+	0.151020i	$0.0482558\pi$
$978$	4.77694	+	1.01537i	0.152750	+	0.0324680i
$979$	−2.78935	+	2.02658i	−0.0891481	+	0.0647699i
$980$	−0.299162	−	0.884021i	−0.00955637	−	0.0282390i
$981$	−1.64915			−0.0526533
$982$	25.6750	+	5.45738i	0.819321	+	0.174152i
$983$	20.3743	+	35.2893i	0.649840	+	1.12556i	0.983161	+	0.182742i	$0.0584972\pi$
$983$	20.3743	+	35.2893i	0.649840	+	1.12556i	−0.333321	+	0.942813i	$0.608169\pi$
$984$	8.47850	+	9.26071i	0.270285	+	0.295221i
$985$	−1.71743	+	2.97468i	−0.0547220	+	0.0947813i
$986$	−0.631982	−	1.94504i	−0.0201264	−	0.0619427i
$987$	35.7738	+	48.6145i	1.13869	+	1.54742i
$988$	4.08368	−	2.96697i	0.129919	−	0.0943917i
$989$	−0.507007	−	4.82385i	−0.0161219	−	0.153389i
$990$	−0.110163	+	0.122348i	−0.00350121	+	0.00388849i
$991$	−42.3942	+	9.01116i	−1.34670	+	0.286249i	−0.824154	−	0.566365i	$-0.808349\pi$
$991$	−42.3942	+	9.01116i	−1.34670	+	0.286249i	−0.522541	+	0.852614i	$0.675016\pi$
$992$	1.14420	−	0.509433i	0.0363285	−	0.0161745i
$993$	14.8574			0.471484
$994$	−17.1827	−	9.78168i	−0.545001	−	0.310256i
$995$	0.807162	+	0.586437i	0.0255887	+	0.0185913i
$996$	0.309164	+	2.94150i	0.00979623	+	0.0932049i
$997$	21.2840	−	23.6383i	0.674071	−	0.748632i	−0.304955	−	0.952367i	$-0.598641\pi$
$997$	21.2840	−	23.6383i	0.674071	−	0.748632i	0.979026	+	0.203735i	$0.0653080\pi$
$998$	19.0403	+	32.9787i	0.602710	+	1.04392i
$999$	−3.63400	−	34.5752i	−0.114975	−	1.09391i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	574.2.s.a.387.11	yes	112
7.4	even	3	inner	574.2.s.a.305.11	yes	112
41.16	even	5	inner	574.2.s.a.303.11	yes	112
287.221	even	15	inner	574.2.s.a.221.11	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.s.a.221.11	✓	112	287.221	even	15	inner
574.2.s.a.303.11	yes	112	41.16	even	5	inner
574.2.s.a.305.11	yes	112	7.4	even	3	inner
574.2.s.a.387.11	yes	112	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 574 = 2 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	574.s (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.978148 + 0.207912i) q^{2} +(0.980436 + 1.69816i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-0.0139362 - 0.132594i) q^{5} +(0.605943 + 1.86490i) q^{6} +(-2.51124 + 0.832858i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.422509 + 0.731808i) q^{9} +O(q^{10})\)	\(q+(0.978148 + 0.207912i) q^{2} +(0.980436 + 1.69816i) q^{3} +(0.913545 + 0.406737i) q^{4} +(-0.0139362 - 0.132594i) q^{5} +(0.605943 + 1.86490i) q^{6} +(-2.51124 + 0.832858i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.422509 + 0.731808i) q^{9} +(0.0139362 - 0.132594i) q^{10} +(-0.152751 + 1.45333i) q^{11} +(0.204967 + 1.95013i) q^{12} +(1.71263 + 5.27095i) q^{13} +(-2.62953 + 0.292541i) q^{14} +(0.211503 - 0.153666i) q^{15} +(0.669131 + 0.743145i) q^{16} +(-0.124057 + 1.18032i) q^{17} +(-0.565428 + 0.627971i) q^{18} +(-0.609428 - 0.676838i) q^{19} +(0.0411994 - 0.126799i) q^{20} +(-3.87644 - 3.44794i) q^{21} +(-0.451577 + 1.38981i) q^{22} +(0.455593 + 0.0968392i) q^{23} +(-0.204967 + 1.95013i) q^{24} +(4.87335 - 1.03586i) q^{25} +(0.579318 + 5.51184i) q^{26} +4.22564 q^{27} +(-2.63289 - 0.260562i) q^{28} +(-1.39410 + 1.01287i) q^{29} +(0.238830 - 0.106334i) q^{30} +(0.130921 - 1.24563i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.61776 + 1.16550i) q^{33} +(-0.366749 + 1.12874i) q^{34} +(0.145429 + 0.321368i) q^{35} +(-0.683635 + 0.496690i) q^{36} +(-0.859988 - 8.18224i) q^{37} +(-0.455388 - 0.788755i) q^{38} +(-7.27181 + 8.07616i) q^{39} +(0.0666620 - 0.115462i) q^{40} +(4.24491 - 4.79382i) q^{41} +(-3.07487 - 4.17856i) q^{42} +(-3.21803 - 9.90406i) q^{43} +(-0.730667 + 1.26555i) q^{44} +(0.102921 + 0.0458235i) q^{45} +(0.425503 + 0.189446i) q^{46} +(-11.3800 - 2.41890i) q^{47} +(-0.605943 + 1.86490i) q^{48} +(5.61270 - 4.18302i) q^{49} +4.98222 q^{50} +(-2.12601 + 0.946562i) q^{51} +(-0.579318 + 5.51184i) q^{52} +(0.661421 + 0.294484i) q^{53} +(4.13330 + 0.878560i) q^{54} +0.194831 q^{55} +(-2.52118 - 0.802276i) q^{56} +(0.551878 - 1.69851i) q^{57} +(-1.57422 + 0.700889i) q^{58} +(6.02008 - 6.68598i) q^{59} +(0.255719 - 0.0543547i) q^{60} +(8.69556 + 9.65740i) q^{61} +(0.387040 - 1.19119i) q^{62} +(0.451533 - 2.18964i) q^{63} +(0.309017 + 0.951057i) q^{64} +(0.675027 - 0.300541i) q^{65} +(-2.80287 + 0.595769i) q^{66} +(-10.6027 - 4.72064i) q^{67} +(-0.593412 + 1.02782i) q^{68} +(0.282230 + 0.868616i) q^{69} +(0.0754346 + 0.344582i) q^{70} +(6.04582 + 4.39255i) q^{71} +(-0.771963 + 0.343700i) q^{72} +(1.11062 + 1.92366i) q^{73} +(0.859988 - 8.18224i) q^{74} +(6.53707 + 7.26016i) q^{75} +(-0.281445 - 0.866199i) q^{76} +(-0.826821 - 3.77688i) q^{77} +(-8.79203 + 6.38778i) q^{78} +(2.26011 - 3.91463i) q^{79} +(0.0892112 - 0.0990791i) q^{80} +(5.41050 + 9.37126i) q^{81} +(5.14884 - 3.80650i) q^{82} +1.50836 q^{83} +(-2.13890 - 4.72654i) q^{84} +0.158232 q^{85} +(-1.08853 - 10.3567i) q^{86} +(-3.08685 - 1.37435i) q^{87} +(-0.977824 + 1.08598i) q^{88} +(1.57873 + 1.75335i) q^{89} +(0.0911450 + 0.0662207i) q^{90} +(-8.69079 - 11.8103i) q^{91} +(0.376816 + 0.273773i) q^{92} +(2.24364 - 0.998932i) q^{93} +(-10.6284 - 4.73209i) q^{94} +(-0.0812514 + 0.0902389i) q^{95} +(-0.980436 + 1.69816i) q^{96} +(-8.57525 + 6.23028i) q^{97} +(6.35974 - 2.92466i) q^{98} +(-0.999019 - 0.725830i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 14 q^{2} + 2 q^{3} + 14 q^{4} + 4 q^{6} + 2 q^{7} + 28 q^{8} - 58 q^{9}+O(q^{10}) \) 112 * q - 14 * q^2 + 2 * q^3 + 14 * q^4 + 4 * q^6 + 2 * q^7 + 28 * q^8 - 58 * q^9	\( 112 q - 14 q^{2} + 2 q^{3} + 14 q^{4} + 4 q^{6} + 2 q^{7} + 28 q^{8} - 58 q^{9} - 6 q^{11} - 3 q^{12} + 6 q^{13} + 18 q^{14} + 26 q^{15} + 14 q^{16} - 12 q^{17} - 17 q^{18} - 2 q^{19} - 21 q^{21} + 8 q^{22} + 8 q^{23} + 3 q^{24} + 18 q^{25} - 2 q^{26} - 16 q^{27} - 4 q^{28} - 10 q^{29} + 13 q^{30} - 21 q^{31} + 56 q^{32} - 15 q^{33} + 26 q^{34} + 52 q^{35} - 24 q^{36} + 37 q^{37} + 2 q^{38} - 34 q^{39} + 14 q^{41} + 14 q^{42} - 10 q^{43} + 4 q^{44} - 4 q^{45} + 7 q^{46} - 19 q^{47} - 4 q^{48} - 36 q^{49} - 184 q^{50} + 3 q^{51} + 2 q^{52} + 59 q^{53} - 18 q^{54} + 68 q^{55} + 8 q^{56} + 56 q^{57} - 5 q^{58} + 10 q^{59} + 17 q^{60} - 12 q^{61} + 8 q^{62} - q^{63} - 28 q^{64} + 26 q^{65} - 10 q^{66} - 5 q^{67} - 2 q^{68} - 2 q^{69} + 9 q^{70} - 26 q^{71} - 12 q^{72} + 34 q^{73} - 37 q^{74} - 33 q^{75} + 4 q^{76} + 57 q^{77} + 82 q^{78} - 20 q^{79} - 96 q^{81} - 38 q^{82} - 60 q^{83} + 15 q^{84} - 92 q^{85} - 5 q^{86} - 40 q^{87} - 4 q^{88} + 33 q^{89} - 8 q^{90} + 14 q^{92} + 18 q^{93} - 16 q^{94} + 17 q^{95} - 2 q^{96} - 8 q^{97} - 3 q^{98} + 84 q^{99}+O(q^{100}) \) 112 * q - 14 * q^2 + 2 * q^3 + 14 * q^4 + 4 * q^6 + 2 * q^7 + 28 * q^8 - 58 * q^9 - 6 * q^11 - 3 * q^12 + 6 * q^13 + 18 * q^14 + 26 * q^15 + 14 * q^16 - 12 * q^17 - 17 * q^18 - 2 * q^19 - 21 * q^21 + 8 * q^22 + 8 * q^23 + 3 * q^24 + 18 * q^25 - 2 * q^26 - 16 * q^27 - 4 * q^28 - 10 * q^29 + 13 * q^30 - 21 * q^31 + 56 * q^32 - 15 * q^33 + 26 * q^34 + 52 * q^35 - 24 * q^36 + 37 * q^37 + 2 * q^38 - 34 * q^39 + 14 * q^41 + 14 * q^42 - 10 * q^43 + 4 * q^44 - 4 * q^45 + 7 * q^46 - 19 * q^47 - 4 * q^48 - 36 * q^49 - 184 * q^50 + 3 * q^51 + 2 * q^52 + 59 * q^53 - 18 * q^54 + 68 * q^55 + 8 * q^56 + 56 * q^57 - 5 * q^58 + 10 * q^59 + 17 * q^60 - 12 * q^61 + 8 * q^62 - q^63 - 28 * q^64 + 26 * q^65 - 10 * q^66 - 5 * q^67 - 2 * q^68 - 2 * q^69 + 9 * q^70 - 26 * q^71 - 12 * q^72 + 34 * q^73 - 37 * q^74 - 33 * q^75 + 4 * q^76 + 57 * q^77 + 82 * q^78 - 20 * q^79 - 96 * q^81 - 38 * q^82 - 60 * q^83 + 15 * q^84 - 92 * q^85 - 5 * q^86 - 40 * q^87 - 4 * q^88 + 33 * q^89 - 8 * q^90 + 14 * q^92 + 18 * q^93 - 16 * q^94 + 17 * q^95 - 2 * q^96 - 8 * q^97 - 3 * q^98 + 84 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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