LMFDB - Embedded newform 462.2.y.c.235.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(25,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 24]))

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

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

chi := DirichletCharacter("462.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.y (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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			235.4
Character	$\chi$	$=$	462.235
Dual form			462.2.y.c.289.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.104528 - 0.994522i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(1.47378 + 0.656170i) q^{5} +(0.809017 - 0.587785i) q^{6} +(2.61272 + 0.416765i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(0.104528 - 0.994522i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(1.47378 + 0.656170i) q^{5} +(0.809017 - 0.587785i) q^{6} +(2.61272 + 0.416765i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(0.806628 - 1.39712i) q^{10} +(-1.70000 - 2.84780i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.214810 + 0.156068i) q^{13} +(0.687586 - 2.55484i) q^{14} +(0.498523 + 1.53430i) q^{15} +(0.913545 + 0.406737i) q^{16} +(0.568060 + 5.40473i) q^{17} +(0.978148 + 0.207912i) q^{18} +(4.17281 - 0.886958i) q^{19} +(-1.30515 - 0.948248i) q^{20} +(1.43853 + 2.22050i) q^{21} +(-3.00990 + 1.39302i) q^{22} +(4.45155 + 7.71031i) q^{23} +(-0.913545 + 0.406737i) q^{24} +(-1.60418 - 1.78162i) q^{25} +(0.177667 - 0.197319i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-2.46898 - 0.950873i) q^{28} +(-3.02479 - 9.30934i) q^{29} +(1.57800 - 0.335415i) q^{30} +(3.87054 - 1.72328i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.978806 - 3.16890i) q^{33} +5.43450 q^{34} +(3.57711 + 2.32861i) q^{35} +(0.309017 - 0.951057i) q^{36} +(0.655520 - 0.728029i) q^{37} +(-0.445922 - 4.24266i) q^{38} +(0.0277543 + 0.264065i) q^{39} +(-1.07948 + 1.19888i) q^{40} +(2.45766 - 7.56389i) q^{41} +(2.35870 - 1.19855i) q^{42} -5.30708 q^{43} +(1.07076 + 3.13902i) q^{44} +(-0.806628 + 1.39712i) q^{45} +(8.13339 - 3.62122i) q^{46} +(-7.86620 + 1.67201i) q^{47} +(0.309017 + 0.951057i) q^{48} +(6.65261 + 2.17778i) q^{49} +(-1.93954 + 1.40916i) q^{50} +(-3.63639 + 4.03862i) q^{51} +(-0.177667 - 0.197319i) q^{52} +(-7.30581 + 3.25276i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-0.636793 - 5.31253i) q^{55} +(-1.20374 + 2.35606i) q^{56} +(3.45129 + 2.50751i) q^{57} +(-9.57452 + 2.03513i) q^{58} +(-12.2626 - 2.60650i) q^{59} +(-0.168631 - 1.60442i) q^{60} +(6.63131 + 2.95245i) q^{61} +(-1.30926 - 4.02947i) q^{62} +(-0.687586 + 2.55484i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.214175 + 0.370963i) q^{65} +(-3.04923 - 1.30468i) q^{66} +(3.08352 - 5.34081i) q^{67} +(0.568060 - 5.40473i) q^{68} +(-2.75121 + 8.46735i) q^{69} +(2.68976 - 3.31411i) q^{70} +(-6.52272 + 4.73904i) q^{71} +(-0.913545 - 0.406737i) q^{72} +(8.60251 + 1.82852i) q^{73} +(-0.655520 - 0.728029i) q^{74} +(0.250597 - 2.38427i) q^{75} -4.26603 q^{76} +(-3.25477 - 8.14902i) q^{77} +0.265519 q^{78} +(-1.15608 + 10.9993i) q^{79} +(1.07948 + 1.19888i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-7.26556 - 3.23483i) q^{82} +(-7.60122 + 5.52261i) q^{83} +(-0.945431 - 2.47106i) q^{84} +(-2.70922 + 8.33813i) q^{85} +(-0.554740 + 5.27800i) q^{86} +(4.89421 - 8.47702i) q^{87} +(3.23375 - 0.736781i) q^{88} +(-7.87892 - 13.6467i) q^{89} +(1.30515 + 0.948248i) q^{90} +(0.496194 + 0.497288i) q^{91} +(-2.75121 - 8.46735i) q^{92} +(3.87054 + 1.72328i) q^{93} +(0.840611 + 7.99788i) q^{94} +(6.73181 + 1.43089i) q^{95} +(0.978148 - 0.207912i) q^{96} +(-14.3558 - 10.4301i) q^{97} +(2.86124 - 6.38853i) q^{98} +(3.00990 - 1.39302i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + q^{5} + 10 q^{6} + 9 q^{7} + 10 q^{8} + 5 q^{9}+O(q^{10}) $ 40 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + q^5 + 10 * q^6 + 9 * q^7 + 10 * q^8 + 5 * q^9	\( 40 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + q^{5} + 10 q^{6} + 9 q^{7} + 10 q^{8} + 5 q^{9} + 4 q^{10} + 2 q^{11} - 20 q^{12} - 2 q^{13} - 3 q^{14} - 2 q^{15} + 5 q^{16} + 6 q^{17} - 5 q^{18} - q^{19} - 2 q^{20} - 2 q^{21} + 4 q^{22} - 20 q^{23} - 5 q^{24} + 16 q^{25} + 4 q^{26} - 10 q^{27} + 13 q^{28} + 16 q^{29} - q^{30} + 30 q^{31} + 20 q^{32} + 2 q^{33} + 32 q^{34} + 3 q^{35} - 10 q^{36} + 19 q^{37} + 6 q^{38} + q^{39} - q^{40} - 12 q^{41} + 11 q^{42} - 36 q^{43} - 3 q^{44} - 4 q^{45} + 10 q^{46} + 25 q^{47} - 10 q^{48} + 29 q^{49} + 12 q^{50} - 14 q^{51} - 4 q^{52} - 18 q^{53} + 20 q^{54} + 12 q^{55} - 4 q^{56} + 12 q^{57} + 8 q^{58} - 14 q^{59} + q^{60} + 35 q^{61} - 40 q^{62} + 3 q^{63} - 10 q^{64} - 2 q^{65} + 3 q^{66} - 24 q^{67} + 6 q^{68} - 40 q^{69} - 32 q^{70} - 34 q^{71} - 5 q^{72} - 39 q^{73} - 19 q^{74} + 6 q^{75} - 28 q^{76} - 31 q^{77} + 12 q^{78} - 17 q^{79} + q^{80} + 5 q^{81} + 4 q^{82} - 24 q^{83} + 3 q^{84} - 112 q^{85} + 7 q^{86} + 2 q^{87} - 2 q^{88} - 38 q^{89} + 2 q^{90} - 36 q^{91} - 40 q^{92} + 30 q^{93} - 10 q^{94} - 42 q^{95} - 5 q^{96} + 4 q^{97} - 50 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + q^5 + 10 * q^6 + 9 * q^7 + 10 * q^8 + 5 * q^9 + 4 * q^10 + 2 * q^11 - 20 * q^12 - 2 * q^13 - 3 * q^14 - 2 * q^15 + 5 * q^16 + 6 * q^17 - 5 * q^18 - q^19 - 2 * q^20 - 2 * q^21 + 4 * q^22 - 20 * q^23 - 5 * q^24 + 16 * q^25 + 4 * q^26 - 10 * q^27 + 13 * q^28 + 16 * q^29 - q^30 + 30 * q^31 + 20 * q^32 + 2 * q^33 + 32 * q^34 + 3 * q^35 - 10 * q^36 + 19 * q^37 + 6 * q^38 + q^39 - q^40 - 12 * q^41 + 11 * q^42 - 36 * q^43 - 3 * q^44 - 4 * q^45 + 10 * q^46 + 25 * q^47 - 10 * q^48 + 29 * q^49 + 12 * q^50 - 14 * q^51 - 4 * q^52 - 18 * q^53 + 20 * q^54 + 12 * q^55 - 4 * q^56 + 12 * q^57 + 8 * q^58 - 14 * q^59 + q^60 + 35 * q^61 - 40 * q^62 + 3 * q^63 - 10 * q^64 - 2 * q^65 + 3 * q^66 - 24 * q^67 + 6 * q^68 - 40 * q^69 - 32 * q^70 - 34 * q^71 - 5 * q^72 - 39 * q^73 - 19 * q^74 + 6 * q^75 - 28 * q^76 - 31 * q^77 + 12 * q^78 - 17 * q^79 + q^80 + 5 * q^81 + 4 * q^82 - 24 * q^83 + 3 * q^84 - 112 * q^85 + 7 * q^86 + 2 * q^87 - 2 * q^88 - 38 * q^89 + 2 * q^90 - 36 * q^91 - 40 * q^92 + 30 * q^93 - 10 * q^94 - 42 * q^95 - 5 * q^96 + 4 * q^97 - 50 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	0.104528	−	0.994522i	0.0739128	−	0.703233i
$2$	0.104528	−	0.994522i	0.0739128	−	0.703233i
$3$	0.669131	+	0.743145i	0.386323	+	0.429055i
$3$	0.669131	+	0.743145i	0.386323	+	0.429055i
$4$	−0.978148	−	0.207912i	−0.489074	−	0.103956i
$5$	1.47378	+	0.656170i	0.659095	+	0.293448i	0.708898	−	0.705311i	$-0.249193\pi$
$5$	1.47378	+	0.656170i	0.659095	+	0.293448i	−0.0498027	+	0.998759i	$0.515859\pi$
$6$	0.809017	−	0.587785i	0.330280	−	0.239962i
$7$	2.61272	+	0.416765i	0.987515	+	0.157522i
$7$	2.61272	+	0.416765i	0.987515	+	0.157522i
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−0.104528	+	0.994522i	−0.0348428	+	0.331507i
$10$	0.806628	−	1.39712i	0.255078	−	0.441808i
$11$	−1.70000	−	2.84780i	−0.512571	−	0.858645i
$11$	−1.70000	−	2.84780i	−0.512571	−	0.858645i
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	0.214810	+	0.156068i	0.0595775	+	0.0432856i	0.617175	−	0.786826i	$-0.288277\pi$
$13$	0.214810	+	0.156068i	0.0595775	+	0.0432856i	−0.557598	+	0.830111i	$0.688277\pi$
$14$	0.687586	−	2.55484i	0.183765	−	0.682811i
$15$	0.498523	+	1.53430i	0.128718	+	0.396154i
$16$	0.913545	+	0.406737i	0.228386	+	0.101684i
$17$	0.568060	+	5.40473i	0.137775	+	1.31084i	0.816884	+	0.576802i	$0.195699\pi$
$17$	0.568060	+	5.40473i	0.137775	+	1.31084i	−0.679110	+	0.734037i	$0.737634\pi$
$18$	0.978148	+	0.207912i	0.230552	+	0.0490053i
$19$	4.17281	−	0.886958i	0.957308	−	0.203482i	0.297337	−	0.954773i	$-0.403902\pi$
$19$	4.17281	−	0.886958i	0.957308	−	0.203482i	0.659972	+	0.751291i	$0.270568\pi$
$20$	−1.30515	−	0.948248i	−0.291841	−	0.212035i
$21$	1.43853	+	2.22050i	0.313914	+	0.484553i
$22$	−3.00990	+	1.39302i	−0.641713	+	0.296992i
$23$	4.45155	+	7.71031i	0.928212	+	1.60771i	0.786312	+	0.617830i	$0.211988\pi$
$23$	4.45155	+	7.71031i	0.928212	+	1.60771i	0.141901	+	0.989881i	$0.454679\pi$
$24$	−0.913545	+	0.406737i	−0.186477	+	0.0830248i
$25$	−1.60418	−	1.78162i	−0.320836	−	0.356324i
$26$	0.177667	−	0.197319i	0.0348434	−	0.0386975i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	−2.46898	−	0.950873i	−0.466593	−	0.179698i
$29$	−3.02479	−	9.30934i	−0.561689	−	1.72870i	−0.677589	−	0.735441i	$-0.736975\pi$
$29$	−3.02479	−	9.30934i	−0.561689	−	1.72870i	0.115900	−	0.993261i	$-0.463025\pi$
$30$	1.57800	−	0.335415i	0.288102	−	0.0612381i
$31$	3.87054	−	1.72328i	0.695170	−	0.309510i	−0.0285606	−	0.999592i	$-0.509092\pi$
$31$	3.87054	−	1.72328i	0.695170	−	0.309510i	0.723731	+	0.690082i	$0.242426\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	0.978806	−	3.16890i	0.170388	−	0.551635i
$34$	5.43450			0.932008
$35$	3.57711	+	2.32861i	0.604642	+	0.393607i
$36$	0.309017	−	0.951057i	0.0515028	−	0.158509i
$37$	0.655520	−	0.728029i	0.107767	−	0.119687i	−0.686848	−	0.726801i	$-0.741006\pi$
$37$	0.655520	−	0.728029i	0.107767	−	0.119687i	0.794615	+	0.607114i	$0.207673\pi$
$38$	−0.445922	−	4.24266i	−0.0723381	−	0.688251i
$39$	0.0277543	+	0.264065i	0.00444425	+	0.0422842i
$40$	−1.07948	+	1.19888i	−0.170681	+	0.189560i
$41$	2.45766	−	7.56389i	0.383821	−	1.18128i	−0.553510	−	0.832842i	$-0.686712\pi$
$41$	2.45766	−	7.56389i	0.383821	−	1.18128i	0.937332	−	0.348439i	$-0.113288\pi$
$42$	2.35870	−	1.19855i	0.363956	−	0.184940i
$43$	−5.30708			−0.809321			−0.404661	−	0.914467i	$-0.632610\pi$
$43$	−5.30708			−0.809321			−0.404661	+	0.914467i	$0.632610\pi$
$44$	1.07076	+	3.13902i	0.161424	+	0.473226i
$45$	−0.806628	+	1.39712i	−0.120245	+	0.208270i
$46$	8.13339	−	3.62122i	1.19920	−	0.533919i
$47$	−7.86620	+	1.67201i	−1.14740	+	0.243888i	−0.742097	−	0.670293i	$-0.766169\pi$
$47$	−7.86620	+	1.67201i	−1.14740	+	0.243888i	−0.405307	+	0.914181i	$0.632835\pi$
$48$	0.309017	+	0.951057i	0.0446028	+	0.137273i
$49$	6.65261	+	2.17778i	0.950373	+	0.311112i
$50$	−1.93954	+	1.40916i	−0.274293	+	0.199285i
$51$	−3.63639	+	4.03862i	−0.509196	+	0.565520i
$52$	−0.177667	−	0.197319i	−0.0246380	−	0.0273633i
$53$	−7.30581	+	3.25276i	−1.00353	+	0.446800i	−0.841658	−	0.540011i	$-0.818420\pi$
$53$	−7.30581	+	3.25276i	−1.00353	+	0.446800i	−0.161872	+	0.986812i	$0.551753\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	−0.636793	−	5.31253i	−0.0858651	−	0.716342i
$56$	−1.20374	+	2.35606i	−0.160857	+	0.314841i
$57$	3.45129	+	2.50751i	0.457135	+	0.332128i
$58$	−9.57452	+	2.03513i	−1.25720	+	0.267225i
$59$	−12.2626	−	2.60650i	−1.59646	−	0.339338i	−0.678064	−	0.735003i	$-0.737181\pi$
$59$	−12.2626	−	2.60650i	−1.59646	−	0.339338i	−0.918395	+	0.395666i	$0.870514\pi$
$60$	−0.168631	−	1.60442i	−0.0217702	−	0.207129i
$61$	6.63131	+	2.95245i	0.849052	+	0.378022i	0.784678	−	0.619903i	$-0.212828\pi$
$61$	6.63131	+	2.95245i	0.849052	+	0.378022i	0.0643742	+	0.997926i	$0.479495\pi$
$62$	−1.30926	−	4.02947i	−0.166276	−	0.511744i
$63$	−0.687586	+	2.55484i	−0.0866277	+	0.321880i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	0.214175	+	0.370963i	0.0265652	+	0.0460122i
$66$	−3.04923	−	1.30468i	−0.375334	−	0.160595i
$67$	3.08352	−	5.34081i	0.376712	−	0.652484i	−0.613870	−	0.789407i	$-0.710388\pi$
$67$	3.08352	−	5.34081i	0.376712	−	0.652484i	0.990582	+	0.136923i	$0.0437214\pi$
$68$	0.568060	−	5.40473i	0.0688873	−	0.655419i
$69$	−2.75121	+	8.46735i	−0.331207	+	1.01935i
$70$	2.68976	−	3.31411i	0.321488	−	0.396112i
$71$	−6.52272	+	4.73904i	−0.774105	+	0.562420i	−0.903204	−	0.429212i	$-0.858791\pi$
$71$	−6.52272	+	4.73904i	−0.774105	+	0.562420i	0.129099	+	0.991632i	$0.458791\pi$
$72$	−0.913545	−	0.406737i	−0.107662	−	0.0479344i
$73$	8.60251	+	1.82852i	1.00685	+	0.214012i	0.681685	−	0.731646i	$-0.261248\pi$
$73$	8.60251	+	1.82852i	1.00685	+	0.214012i	0.325163	+	0.945658i	$0.394581\pi$
$74$	−0.655520	−	0.728029i	−0.0762027	−	0.0846317i
$75$	0.250597	−	2.38427i	0.0289365	−	0.275312i
$76$	−4.26603			−0.489348
$77$	−3.25477	−	8.14902i	−0.370915	−	0.928667i
$78$	0.265519			0.0300641
$79$	−1.15608	+	10.9993i	−0.130069	+	1.23752i	0.713560	+	0.700594i	$0.247082\pi$
$79$	−1.15608	+	10.9993i	−0.130069	+	1.23752i	−0.843629	+	0.536927i	$0.819585\pi$
$80$	1.07948	+	1.19888i	0.120689	+	0.134039i
$81$	−0.978148	−	0.207912i	−0.108683	−	0.0231013i
$82$	−7.26556	−	3.23483i	−0.802347	−	0.357228i
$83$	−7.60122	+	5.52261i	−0.834342	+	0.606185i	−0.920784	−	0.390072i	$-0.872450\pi$
$83$	−7.60122	+	5.52261i	−0.834342	+	0.606185i	0.0864423	+	0.996257i	$0.472450\pi$
$84$	−0.945431	−	2.47106i	−0.103155	−	0.269615i
$85$	−2.70922	+	8.33813i	−0.293857	+	0.904397i
$86$	−0.554740	+	5.27800i	−0.0598192	+	0.569142i
$87$	4.89421	−	8.47702i	0.524714	−	0.908832i
$88$	3.23375	−	0.736781i	0.344719	−	0.0785411i
$89$	−7.87892	−	13.6467i	−0.835164	−	1.44655i	−0.893897	−	0.448273i	$-0.852039\pi$
$89$	−7.87892	−	13.6467i	−0.835164	−	1.44655i	0.0587329	−	0.998274i	$-0.481294\pi$
$90$	1.30515	+	0.948248i	0.137575	+	0.0999541i
$91$	0.496194	+	0.497288i	0.0520152	+	0.0521300i
$92$	−2.75121	−	8.46735i	−0.286833	−	0.882782i
$93$	3.87054	+	1.72328i	0.401357	+	0.178696i
$94$	0.840611	+	7.99788i	0.0867025	+	0.824919i
$95$	6.73181	+	1.43089i	0.690669	+	0.146806i
$96$	0.978148	−	0.207912i	0.0998318	−	0.0212199i
$97$	−14.3558	−	10.4301i	−1.45761	−	1.05902i	−0.983977	−	0.178297i	$-0.942941\pi$
$97$	−14.3558	−	10.4301i	−1.45761	−	1.05902i	−0.473636	−	0.880721i	$-0.657059\pi$
$98$	2.86124	−	6.38853i	0.289029	−	0.645339i
$99$	3.00990	−	1.39302i	0.302507	−	0.140003i
$100$	1.19870	+	2.07621i	0.119870	+	0.207621i
$101$	2.81010	−	1.25114i	0.279615	−	0.124493i	−0.262138	−	0.965030i	$-0.584428\pi$
$101$	2.81010	−	1.25114i	0.279615	−	0.124493i	0.541753	+	0.840538i	$0.317761\pi$
$102$	3.63639	+	4.03862i	0.360056	+	0.399883i
$103$	−4.37033	+	4.85375i	−0.430622	+	0.478254i	−0.918932	−	0.394416i	$-0.870947\pi$
$103$	−4.37033	+	4.85375i	−0.430622	+	0.478254i	0.488310	+	0.872670i	$0.337613\pi$
$104$	−0.214810	+	0.156068i	−0.0210638	+	0.0153038i
$105$	0.663060	+	4.21646i	0.0647081	+	0.411484i
$106$	2.47127	+	7.60579i	0.240031	+	0.738740i
$107$	0.606907	−	0.129002i	0.0586719	−	0.0124711i	−0.178482	−	0.983943i	$-0.557119\pi$
$107$	0.606907	−	0.129002i	0.0586719	−	0.0124711i	0.237154	+	0.971472i	$0.423785\pi$
$108$	0.913545	−	0.406737i	0.0879060	−	0.0391383i
$109$	6.62041	−	11.4669i	0.634120	−	1.09833i	−0.352581	−	0.935781i	$-0.614696\pi$
$109$	6.62041	−	11.4669i	0.634120	−	1.09833i	0.986701	−	0.162547i	$-0.0519709\pi$
$110$	−5.35000	+	0.0779932i	−0.510102	+	0.00743636i
$111$	0.979660			0.0929852
$112$	2.21732	+	1.44342i	0.209518	+	0.136391i
$113$	−4.03762	+	12.4265i	−0.379827	+	1.16899i	0.560336	+	0.828265i	$0.310672\pi$
$113$	−4.03762	+	12.4265i	−0.379827	+	1.16899i	−0.940164	+	0.340723i	$0.889328\pi$
$114$	2.85453	−	3.17028i	0.267352	−	0.296924i
$115$	1.50134	+	14.2843i	0.140001	+	1.33202i
$116$	1.02317	+	9.73480i	0.0949988	+	0.903853i
$117$	−0.177667	+	0.197319i	−0.0164253	+	0.0182422i
$118$	−3.87402	+	11.9230i	−0.356632	+	1.09760i
$119$	−0.768321	+	14.3578i	−0.0704319	+	1.31618i
$120$	−1.61326			−0.147269
$121$	−5.21997	+	9.68256i	−0.474543	+	0.880232i
$122$	3.62944	−	6.28637i	0.328594	−	0.569141i
$123$	7.26556	−	3.23483i	0.655113	−	0.291675i
$124$	−4.14425	+	0.880888i	−0.372165	+	0.0791061i
$125$	−3.68778	−	11.3498i	−0.329845	−	1.01516i
$126$	2.46898	+	0.950873i	0.219954	+	0.0847105i
$127$	−5.47550	+	3.97819i	−0.485872	+	0.353007i	−0.803595	−	0.595177i	$-0.797082\pi$
$127$	−5.47550	+	3.97819i	−0.485872	+	0.353007i	0.317722	+	0.948184i	$0.397082\pi$
$128$	−0.669131	+	0.743145i	−0.0591433	+	0.0656853i
$129$	−3.55113	−	3.94393i	−0.312659	−	0.347243i
$130$	0.391318	−	0.174226i	0.0343208	−	0.0152806i
$131$	0.467047	+	0.808948i	0.0408060	+	0.0706781i	0.885707	−	0.464244i	$-0.153674\pi$
$131$	0.467047	+	0.808948i	0.0408060	+	0.0706781i	−0.844901	+	0.534923i	$0.820341\pi$
$132$	−1.61627	+	2.89615i	−0.140678	+	0.252077i
$133$	11.2720	−	0.578291i	0.977410	−	0.0501442i
$134$	−4.98924	−	3.62489i	−0.431004	−	0.313143i
$135$	−1.57800	+	0.335415i	−0.135813	+	0.0288679i
$136$	−5.31574	−	1.12990i	−0.455821	−	0.0968877i
$137$	0.299520	+	2.84974i	0.0255897	+	0.243470i	0.999838	+	0.0179925i	$0.00572751\pi$
$137$	0.299520	+	2.84974i	0.0255897	+	0.243470i	−0.974248	+	0.225477i	$0.927606\pi$
$138$	8.13339	+	3.62122i	0.692360	+	0.308258i
$139$	0.00101062	+	0.00311037i	8.57196e−5	+	0.000263818i	0.951099	−	0.308885i	$-0.0999559\pi$
$139$	0.00101062	+	0.00311037i	8.57196e−5	+	0.000263818i	−0.951014	+	0.309149i	$0.899956\pi$
$140$	−3.01480	−	3.02145i	−0.254797	−	0.255359i
$141$	−6.50606	−	4.72693i	−0.547910	−	0.398080i
$142$	4.03126	+	6.98236i	0.338296	+	0.585946i
$143$	0.0792747	−	0.877053i	0.00662928	−	0.0733428i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	1.65063	−	15.7047i	0.137078	−	1.30421i
$146$	2.71771	−	8.36425i	0.224919	−	0.692230i
$147$	2.83306	+	6.40108i	0.233667	+	0.527952i
$148$	−0.792561	+	0.575830i	−0.0651481	+	0.0473329i
$149$	−0.467169	−	0.207997i	−0.0382720	−	0.0170398i	0.387511	−	0.921865i	$-0.373335\pi$
$149$	−0.467169	−	0.207997i	−0.0382720	−	0.0170398i	−0.425783	+	0.904825i	$0.640001\pi$
$150$	−2.34502	−	0.498449i	−0.191470	−	0.0406982i
$151$	−9.68019	−	10.7509i	−0.787763	−	0.874899i	0.206870	−	0.978368i	$-0.433672\pi$
$151$	−9.68019	−	10.7509i	−0.787763	−	0.874899i	−0.994633	+	0.103470i	$0.967006\pi$
$152$	−0.445922	+	4.24266i	−0.0361690	+	0.344125i
$153$	−5.43450			−0.439353
$154$	−8.44459	+	2.38514i	−0.680485	+	0.192200i
$155$	6.83510			0.549009
$156$	0.0277543	−	0.264065i	0.00222213	−	0.0211421i
$157$	−12.2294	−	13.5822i	−0.976016	−	1.08398i	−0.996450	−	0.0841844i	$-0.973172\pi$
$157$	−12.2294	−	13.5822i	−0.976016	−	1.08398i	0.0204342	−	0.999791i	$-0.493495\pi$
$158$	10.8182	+	2.29949i	0.860652	+	0.182937i
$159$	−7.30581	−	3.25276i	−0.579388	−	0.257960i
$160$	1.30515	−	0.948248i	0.103181	−	0.0749656i
$161$	8.41727	+	22.0001i	0.663373	+	1.73385i
$162$	−0.309017	+	0.951057i	−0.0242787	+	0.0747221i
$163$	−1.08724	+	10.3444i	−0.0851594	+	0.810237i	0.865689	+	0.500581i	$0.166880\pi$
$163$	−1.08724	+	10.3444i	−0.0851594	+	0.810237i	−0.950849	+	0.309656i	$0.899786\pi$
$164$	−3.97657	+	6.88762i	−0.310518	+	0.537833i
$165$	3.52189	−	4.02801i	0.274178	−	0.313580i
$166$	4.69781	+	8.13685i	0.364621	+	0.631542i
$167$	−1.48785	−	1.08099i	−0.115133	−	0.0836492i	0.528729	−	0.848791i	$-0.322669\pi$
$167$	−1.48785	−	1.08099i	−0.115133	−	0.0836492i	−0.643862	+	0.765142i	$0.722669\pi$
$168$	−2.55635	+	0.681955i	−0.197227	+	0.0526140i
$169$	−3.99544	−	12.2967i	−0.307341	−	0.945899i
$170$	8.00926	+	3.56595i	0.614283	+	0.273496i
$171$	0.445922	+	4.24266i	0.0341005	+	0.324445i
$172$	5.19110	+	1.10340i	0.395818	+	0.0841337i
$173$	6.08416	−	1.29323i	0.462570	−	0.0983223i	0.0292690	−	0.999572i	$-0.490682\pi$
$173$	6.08416	−	1.29323i	0.462570	−	0.0983223i	0.433301	+	0.901249i	$0.357349\pi$
$174$	−7.91900	−	5.75349i	−0.600338	−	0.436171i
$175$	−3.44875	−	5.32344i	−0.260701	−	0.402414i
$176$	−0.394725	−	3.29305i	−0.0297535	−	0.248223i
$177$	−6.26829	−	10.8570i	−0.471154	−	0.816062i
$178$	−14.3955	+	6.40929i	−1.07899	+	0.480397i
$179$	6.06109	+	6.73152i	0.453027	+	0.503138i	0.925783	−	0.378056i	$-0.123407\pi$
$179$	6.06109	+	6.73152i	0.453027	+	0.503138i	−0.472756	+	0.881194i	$0.656741\pi$
$180$	1.07948	−	1.19888i	0.0804596	−	0.0893594i
$181$	−0.546797	+	0.397271i	−0.0406431	+	0.0295289i	−0.607921	−	0.793997i	$-0.707996\pi$
$181$	−0.546797	+	0.397271i	−0.0406431	+	0.0295289i	0.567278	+	0.823526i	$0.307996\pi$
$182$	0.546430	−	0.441495i	0.0405041	−	0.0327258i
$183$	2.24312	+	6.90360i	0.165816	+	0.510329i
$184$	−8.70855	+	1.85106i	−0.642003	+	0.136462i
$185$	1.44381	−	0.642823i	0.106151	−	0.0472613i
$186$	2.11842	−	3.66921i	0.155330	−	0.269040i
$187$	14.4259	−	10.8058i	1.05493	−	0.790197i
$188$	8.04194			0.586519
$189$	−2.35870	+	1.19855i	−0.171570	+	0.0871816i
$190$	2.12672	−	6.54536i	0.154288	−	0.474851i
$191$	12.4504	−	13.8276i	0.900879	−	1.00053i	−0.0991063	−	0.995077i	$-0.531598\pi$
$191$	12.4504	−	13.8276i	0.900879	−	1.00053i	0.999985	−	0.00545043i	$-0.00173493\pi$
$192$	−0.104528	−	0.994522i	−0.00754369	−	0.0717734i
$193$	0.784732	+	7.46623i	0.0564863	+	0.537431i	0.985774	+	0.168075i	$0.0537551\pi$
$193$	0.784732	+	7.46623i	0.0564863	+	0.537431i	−0.929288	+	0.369356i	$0.879578\pi$
$194$	−11.8736	+	13.1869i	−0.852472	+	0.946767i
$195$	−0.132368	+	0.407386i	−0.00947904	+	0.0291735i
$196$	−6.05445	−	3.51335i	−0.432461	−	0.250953i
$197$	20.4240			1.45515			0.727576	−	0.686027i	$-0.240647\pi$
$197$	20.4240			1.45515			0.727576	+	0.686027i	$0.240647\pi$
$198$	−1.07076	−	3.13902i	−0.0760959	−	0.223081i
$199$	−4.44212	+	7.69397i	−0.314893	+	0.545411i	−0.979415	−	0.201858i	$-0.935302\pi$
$199$	−4.44212	+	7.69397i	−0.314893	+	0.545411i	0.664522	+	0.747269i	$0.268635\pi$
$200$	2.19014	−	0.975113i	0.154866	−	0.0689509i
$201$	6.03227	−	1.28220i	0.425484	−	0.0904393i
$202$	−0.950547	−	2.92548i	−0.0668802	−	0.205836i
$203$	−4.02312	−	25.5833i	−0.282367	−	1.79560i
$204$	4.39660	−	3.19432i	0.307824	−	0.223647i
$205$	8.58525	−	9.53488i	0.599620	−	0.665945i
$206$	4.37033	+	4.85375i	0.304496	+	0.338177i
$207$	−8.13339	+	3.62122i	−0.565309	+	0.251692i
$208$	0.132760	+	0.229947i	0.00920523	+	0.0159439i
$209$	−9.61968	−	10.3755i	−0.665407	−	0.717689i
$210$	4.26267	−	0.218688i	0.294152	−	0.0150909i
$211$	13.1604	+	9.56156i	0.905997	+	0.658245i	0.939999	−	0.341177i	$-0.110825\pi$
$211$	13.1604	+	9.56156i	0.905997	+	0.658245i	−0.0340025	+	0.999422i	$0.510825\pi$
$212$	7.82245	−	1.66271i	0.537248	−	0.114196i
$213$	−7.88634	−	1.67629i	−0.540363	−	0.114858i
$214$	−0.0648564	−	0.617067i	−0.00443349	−	0.0421818i
$215$	−7.82147	−	3.48234i	−0.533420	−	0.237494i
$216$	−0.309017	−	0.951057i	−0.0210259	−	0.0647112i
$217$	10.8309	−	2.88933i	0.735246	−	0.196141i
$218$	−10.7120	−	7.78276i	−0.725511	−	0.527115i
$219$	4.39735	+	7.61643i	0.297145	+	0.514671i
$220$	−0.481661	+	5.32884i	−0.0324736	+	0.359270i
$221$	−0.721482	+	1.24964i	−0.0485321	+	0.0840601i
$222$	0.102402	−	0.974293i	0.00687279	−	0.0653903i
$223$	−1.52732	+	4.70059i	−0.102277	+	0.314775i	−0.989082	−	0.147369i	$-0.952920\pi$
$223$	−1.52732	+	4.70059i	−0.102277	+	0.314775i	0.886805	+	0.462144i	$0.152920\pi$
$224$	1.66729	−	2.05430i	0.111400	−	0.137259i
$225$	1.93954	−	1.40916i	0.129303	−	0.0939440i
$226$	11.9364	+	5.31443i	0.793997	+	0.353510i
$227$	−7.59165	−	1.61366i	−0.503876	−	0.107102i	−0.0510410	−	0.998697i	$-0.516254\pi$
$227$	−7.59165	−	1.61366i	−0.503876	−	0.107102i	−0.452835	+	0.891594i	$0.649587\pi$
$228$	−2.85453	−	3.17028i	−0.189046	−	0.209957i
$229$	0.109197	−	1.03894i	0.00721596	−	0.0686552i	−0.990321	−	0.138794i	$-0.955677\pi$
$229$	0.109197	−	1.03894i	0.00721596	−	0.0686552i	0.997537	+	0.0701386i	$0.0223441\pi$
$230$	14.3630			0.947067
$231$	3.87803	−	7.87152i	0.255156	−	0.517908i
$232$	9.78842			0.642641
$233$	−0.243802	+	2.31963i	−0.0159720	+	0.151964i	−0.999601	−	0.0282411i	$-0.991009\pi$
$233$	−0.243802	+	2.31963i	−0.0159720	+	0.151964i	0.983629	+	0.180205i	$0.0576761\pi$
$234$	0.177667	+	0.197319i	0.0116145	+	0.0128992i
$235$	−12.6902	−	2.69738i	−0.827817	−	0.175958i
$236$	11.4527	+	5.09909i	0.745510	+	0.331922i
$237$	−8.94766	+	6.50086i	−0.581213	+	0.422276i
$238$	14.1988	+	2.26491i	0.920373	+	0.146812i
$239$	2.84024	−	8.74137i	0.183720	−	0.565432i	−0.816204	−	0.577764i	$-0.803925\pi$
$239$	2.84024	−	8.74137i	0.183720	−	0.565432i	0.999924	+	0.0123318i	$0.00392542\pi$
$240$	−0.168631	+	1.60442i	−0.0108851	+	0.103565i
$241$	11.2395	−	19.4673i	0.723997	−	1.25400i	−0.235388	−	0.971901i	$-0.575636\pi$
$241$	11.2395	−	19.4673i	0.723997	−	1.25400i	0.959385	−	0.282099i	$-0.0910306\pi$
$242$	9.08388	+	6.20348i	0.583934	+	0.398775i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−5.87255	−	4.26666i	−0.375952	−	0.273145i
$245$	8.37551	+	7.57482i	0.535092	+	0.483938i
$246$	−2.45766	−	7.56389i	−0.156694	−	0.482256i
$247$	1.03479	+	0.460716i	0.0658419	+	0.0293147i
$248$	0.442870	+	4.21363i	0.0281223	+	0.267566i
$249$	−9.19031	−	1.95346i	−0.582412	−	0.123795i
$250$	−11.6731	+	2.48120i	−0.738273	+	0.156925i
$251$	21.9965	+	15.9814i	1.38841	+	1.00874i	0.996038	+	0.0889297i	$0.0283446\pi$
$251$	21.9965	+	15.9814i	1.38841	+	1.00874i	0.392370	+	0.919808i	$0.371655\pi$
$252$	1.20374	−	2.35606i	0.0758286	−	0.148418i
$253$	14.3898	−	25.7847i	0.904679	−	1.62107i
$254$	3.38405	+	5.86134i	0.212334	+	0.367773i
$255$	−8.00926	+	3.56595i	−0.501560	+	0.223309i
$256$	0.669131	+	0.743145i	0.0418207	+	0.0464466i
$257$	1.20131	−	1.33419i	0.0749354	−	0.0832242i	−0.704511	−	0.709693i	$-0.748834\pi$
$257$	1.20131	−	1.33419i	0.0749354	−	0.0832242i	0.779447	+	0.626469i	$0.215500\pi$
$258$	−4.29351	+	3.11942i	−0.267303	+	0.194207i
$259$	2.01611	−	1.62894i	0.125275	−	0.101217i
$260$	−0.132368	−	0.407386i	−0.00820909	−	0.0252650i
$261$	9.57452	−	2.03513i	0.592648	−	0.125971i
$262$	0.853337	−	0.379930i	0.0527193	−	0.0234721i
$263$	6.59096	−	11.4159i	0.406416	−	0.703933i	−0.588069	−	0.808811i	$-0.700112\pi$
$263$	6.59096	−	11.4159i	0.406416	−	0.703933i	0.994485	+	0.104878i	$0.0334451\pi$
$264$	2.71134	+	1.91014i	0.166871	+	0.117561i
$265$	−12.9015			−0.792535
$266$	0.603125	−	11.2707i	0.0369800	−	0.691053i
$267$	4.86944	−	14.9866i	0.298005	−	0.917165i
$268$	−4.12655	+	4.58300i	−0.252069	+	0.279951i
$269$	−1.18361	−	11.2613i	−0.0721658	−	0.686611i	−0.969472	−	0.245203i	$-0.921146\pi$
$269$	−1.18361	−	11.2613i	−0.0721658	−	0.686611i	0.897306	−	0.441409i	$-0.145521\pi$
$270$	0.168631	+	1.60442i	0.0102626	+	0.0976418i
$271$	5.25494	−	5.83620i	0.319215	−	0.354524i	−0.562087	−	0.827078i	$-0.690001\pi$
$271$	5.25494	−	5.83620i	0.319215	−	0.354524i	0.881301	+	0.472554i	$0.156668\pi$
$272$	−1.67935	+	5.16851i	−0.101826	+	0.313387i
$273$	−0.0375387	+	0.701495i	−0.00227195	+	0.0424564i
$274$	2.86544			0.173108
$275$	−2.34659	+	7.59715i	−0.141505	+	0.458125i
$276$	4.45155	−	7.71031i	0.267952	−	0.464106i
$277$	3.26613	−	1.45418i	0.196243	−	0.0873730i	−0.306262	−	0.951947i	$-0.599078\pi$
$277$	3.26613	−	1.45418i	0.196243	−	0.0873730i	0.502505	+	0.864574i	$0.332412\pi$
$278$	0.00319897		0.000679961i	0.000191861		4.07814e-5i
$279$	1.30926	+	4.02947i	0.0783830	+	0.241238i
$280$	−3.32003	+	2.68246i	−0.198410	+	0.160307i
$281$	−9.39889	+	6.82869i	−0.560691	+	0.407365i	−0.831712	−	0.555208i	$-0.812639\pi$
$281$	−9.39889	+	6.82869i	−0.560691	+	0.407365i	0.271021	+	0.962573i	$0.412639\pi$
$282$	−5.38111	+	5.97633i	−0.320440	+	0.355885i
$283$	9.26689	+	10.2919i	0.550860	+	0.611791i	0.952698	−	0.303919i	$-0.0982953\pi$
$283$	9.26689	+	10.2919i	0.550860	+	0.611791i	−0.401838	+	0.915711i	$0.631629\pi$
$284$	7.36549	−	3.27933i	0.437061	−	0.194592i
$285$	3.44110	+	5.96016i	0.203833	+	0.353050i
$286$	−0.863962	−	0.170517i	−0.0510871	−	0.0100829i
$287$	9.57353	−	18.7381i	0.565108	−	1.10607i
$288$	0.809017	+	0.587785i	0.0476718	+	0.0346356i
$289$	−12.2599	+	2.60591i	−0.721168	+	0.153289i
$290$	−15.4461	−	3.28318i	−0.907029	−	0.192795i
$291$	−1.85483	−	17.6476i	−0.108732	−	1.03452i
$292$	−8.03435	−	3.57712i	−0.470175	−	0.209335i
$293$	−5.14119	−	15.8230i	−0.300352	−	0.924387i	−0.981371	−	0.192122i	$-0.938463\pi$
$293$	−5.14119	−	15.8230i	−0.300352	−	0.924387i	0.681019	−	0.732265i	$-0.261537\pi$
$294$	6.66215	−	2.14845i	0.388544	−	0.125300i
$295$	−16.3621	−	11.8878i	−0.952640	−	0.692134i
$296$	0.489830	+	0.848410i	0.0284708	+	0.0493128i
$297$	3.04923	+	1.30468i	0.176934	+	0.0757054i
$298$	−0.255690	+	0.442868i	−0.0148117	+	0.0256547i
$299$	−0.247100	+	2.35100i	−0.0142901	+	0.135962i
$300$	−0.740839	+	2.28007i	−0.0427724	+	0.131640i
$301$	−13.8659	−	2.21180i	−0.799217	−	0.127486i
$302$	−11.7039	+	8.50338i	−0.673484	+	0.489315i
$303$	2.81010	+	1.25114i	0.161436	+	0.0718759i
$304$	4.17281	+	0.886958i	0.239327	+	0.0508705i
$305$	7.83580	+	8.70254i	0.448677	+	0.498306i
$306$	−0.568060	+	5.40473i	−0.0324738	+	0.308968i
$307$	8.53238			0.486969			0.243484	−	0.969905i	$-0.421710\pi$
$307$	8.53238			0.486969			0.243484	+	0.969905i	$0.421710\pi$
$308$	1.48937	+	8.64765i	0.0848647	+	0.492745i
$309$	−6.53136			−0.371556
$310$	0.714463	−	6.79766i	0.0405788	−	0.386081i
$311$	18.0891	+	20.0900i	1.02574	+	1.13920i	0.990175	+	0.139834i	$0.0446569\pi$
$311$	18.0891	+	20.0900i	1.02574	+	1.13920i	0.0355665	+	0.999367i	$0.488676\pi$
$312$	−0.259717	−	0.0552046i	−0.0147036	−	0.00312534i
$313$	22.1993	+	9.88375i	1.25478	+	0.558662i	0.923038	−	0.384709i	$-0.125698\pi$
$313$	22.1993	+	9.88375i	1.25478	+	0.558662i	0.331739	+	0.943371i	$0.392365\pi$
$314$	−14.7861	+	10.7427i	−0.834428	+	0.606247i
$315$	−2.68976	+	3.31411i	−0.151551	+	0.186729i
$316$	3.41770	−	10.5186i	0.192261	−	0.591718i
$317$	−2.51007	+	23.8817i	−0.140980	+	1.34133i	0.663868	+	0.747850i	$0.268914\pi$
$317$	−2.51007	+	23.8817i	−0.140980	+	1.34133i	−0.804848	+	0.593481i	$0.797753\pi$
$318$	−3.99860	+	6.92578i	−0.224230	+	0.388379i
$319$	−21.3690	+	24.4399i	−1.19644	+	1.36837i
$320$	−0.806628	−	1.39712i	−0.0450919	−	0.0781014i
$321$	0.501968	+	0.364701i	0.0280171	+	0.0203556i
$322$	22.7595	−	6.07151i	1.26834	−	0.338352i
$323$	7.16417	+	22.0490i	0.398625	+	1.22684i
$324$	0.913545	+	0.406737i	0.0507525	+	0.0225965i
$325$	−0.0665384	−	0.633071i	−0.00369089	−	0.0351164i
$326$	10.1741	+	2.16257i	0.563491	+	0.119774i
$327$	12.9515	−	2.75292i	0.716218	−	0.152237i
$328$	6.43423	+	4.67474i	0.355271	+	0.258119i
$329$	−21.2490	+	1.09014i	−1.17150	+	0.0601015i
$330$	−3.63781	−	3.92363i	−0.200255	−	0.215989i
$331$	−9.02689	−	15.6350i	−0.496163	−	0.859379i	0.503828	−	0.863804i	$-0.331925\pi$
$331$	−9.02689	−	15.6350i	−0.496163	−	0.859379i	−0.999990	+	0.00442542i	$0.998591\pi$
$332$	8.58333	−	3.82154i	0.471071	−	0.209734i
$333$	0.655520	+	0.728029i	0.0359223	+	0.0398957i
$334$	−1.23059	+	1.36670i	−0.0673347	+	0.0747827i
$335$	8.04891	−	5.84788i	0.439759	−	0.319504i
$336$	0.411008	+	2.61363i	0.0224223	+	0.142585i
$337$	10.6818	+	32.8752i	0.581875	+	1.79083i	0.611472	+	0.791266i	$0.290578\pi$
$337$	10.6818	+	32.8752i	0.581875	+	1.79083i	−0.0295969	+	0.999562i	$0.509422\pi$
$338$	−12.6470	+	2.68819i	−0.687904	+	0.146218i
$339$	−11.9364	+	5.31443i	−0.648296	+	0.288640i
$340$	4.38362	−	7.59265i	0.237735	−	0.411769i
$341$	−11.4875	−	8.09297i	−0.622083	−	0.438259i
$342$	4.26603			0.230681
$343$	16.4738	+	8.46251i	0.889501	+	0.456933i
$344$	1.63998	−	5.04733i	0.0884216	−	0.272134i
$345$	−9.61071	+	10.6738i	−0.517423	+	0.574657i
$346$	−0.650175	−	6.18601i	−0.0349536	−	0.332562i
$347$	2.92911	+	27.8686i	0.157243	+	1.49607i	0.733999	+	0.679150i	$0.237651\pi$
$347$	2.92911	+	27.8686i	0.157243	+	1.49607i	−0.576757	+	0.816916i	$0.695682\pi$
$348$	−6.54973	+	7.27421i	−0.351103	+	0.389939i
$349$	9.08138	−	27.9496i	0.486115	−	1.49611i	−0.344244	−	0.938880i	$-0.611865\pi$
$349$	9.08138	−	27.9496i	0.486115	−	1.49611i	0.830359	−	0.557228i	$-0.188135\pi$
$350$	−5.65477	+	2.87341i	−0.302260	+	0.153590i
$351$	−0.265519			−0.0141724
$352$	−3.31627	+	0.0483452i	−0.176758	+	0.00257681i
$353$	−2.43661	+	4.22033i	−0.129688	+	0.224626i	−0.923556	−	0.383465i	$-0.874731\pi$
$353$	−2.43661	+	4.22033i	−0.129688	+	0.224626i	0.793868	+	0.608090i	$0.208064\pi$
$354$	−11.4527	+	5.09909i	−0.608706	+	0.271013i
$355$	−12.7227	+	2.70429i	−0.675250	+	0.143529i
$356$	4.86944	+	14.9866i	0.258080	+	0.794288i
$357$	−11.1840	+	9.03626i	−0.591921	+	0.478250i
$358$	7.32820	−	5.32425i	0.387308	−	0.281395i
$359$	9.12076	−	10.1296i	0.481375	−	0.534622i	−0.452716	−	0.891655i	$-0.649545\pi$
$359$	9.12076	−	10.1296i	0.481375	−	0.534622i	0.934092	+	0.357033i	$0.116212\pi$
$360$	−1.07948	−	1.19888i	−0.0568935	−	0.0631867i
$361$	−0.731714	+	0.325780i	−0.0385113	+	0.0171463i
$362$	0.337939	+	0.585328i	0.0177617	+	0.0307641i
$363$	−10.6884	+	2.59970i	−0.560995	+	0.136449i
$364$	−0.381959	−	0.589586i	−0.0200201	−	0.0309027i
$365$	11.4784	+	8.33955i	0.600807	+	0.436512i
$366$	7.10025	−	1.50920i	0.371136	−	0.0788874i
$367$	4.49132	+	0.954660i	0.234445	+	0.0498328i	0.323636	−	0.946182i	$-0.395095\pi$
$367$	4.49132	+	0.954660i	0.234445	+	0.0498328i	−0.0891908	+	0.996015i	$0.528428\pi$
$368$	0.930627	+	8.85433i	0.0485123	+	0.461564i
$369$	7.26556	+	3.23483i	0.378230	+	0.168399i
$370$	−0.488383	−	1.50309i	−0.0253898	−	0.0781419i
$371$	−20.4437	+	5.45373i	−1.06138	+	0.283144i
$372$	−3.42767	−	2.49035i	−0.177717	−	0.129119i
$373$	−9.29018	−	16.0911i	−0.481027	−	0.833164i	0.518736	−	0.854935i	$-0.326403\pi$
$373$	−9.29018	−	16.0911i	−0.481027	−	0.833164i	−0.999763	+	0.0217710i	$0.993070\pi$
$374$	−9.23867	−	15.4764i	−0.477720	−	0.800264i
$375$	5.96695	−	10.3351i	0.308132	−	0.533701i
$376$	0.840611	−	7.99788i	0.0433512	−	0.412459i
$377$	0.803140	−	2.47181i	0.0413638	−	0.127305i
$378$	0.945431	+	2.47106i	0.0486277	+	0.127098i
$379$	−17.0095	+	12.3581i	−0.873720	+	0.634794i	−0.931582	−	0.363530i	$-0.881571\pi$
$379$	−17.0095	+	12.3581i	−0.873720	+	0.634794i	0.0578629	+	0.998325i	$0.481571\pi$
$380$	−6.28720	−	2.79924i	−0.322527	−	0.143598i
$381$	−6.62020	−	1.40717i	−0.339163	−	0.0720913i
$382$	−12.4504	−	13.8276i	−0.637018	−	0.707480i
$383$	1.53675	−	14.6212i	0.0785244	−	0.747110i	−0.882438	−	0.470429i	$-0.844099\pi$
$383$	1.53675	−	14.6212i	0.0785244	−	0.747110i	0.960962	−	0.276680i	$-0.0892343\pi$
$384$	−1.00000			−0.0510310
$385$	0.550319	−	14.1456i	0.0280468	−	0.720924i
$386$	7.50736			0.382114
$387$	0.554740	−	5.27800i	0.0281990	−	0.268296i
$388$	11.8736	+	13.1869i	0.602789	+	0.669465i
$389$	−11.8457	−	2.51788i	−0.600601	−	0.127662i	−0.102430	−	0.994740i	$-0.532662\pi$
$389$	−11.8457	−	2.51788i	−0.600601	−	0.127662i	−0.498171	+	0.867079i	$0.665995\pi$
$390$	0.391318	+	0.174226i	0.0198151	+	0.00882227i
$391$	−39.1434	+	28.4393i	−1.97957	+	1.43824i
$392$	−4.12696	+	5.65404i	−0.208443	+	0.285572i
$393$	−0.288651	+	0.888375i	−0.0145605	+	0.0448126i
$394$	2.13489	−	20.3121i	0.107554	−	1.02331i
$395$	−8.92124	+	15.4520i	−0.448876	+	0.777476i
$396$	−3.23375	+	0.736781i	−0.162502	+	0.0370246i
$397$	10.9908	+	19.0367i	0.551614	+	0.955424i	0.998158	+	0.0606620i	$0.0193212\pi$
$397$	10.9908	+	19.0367i	0.551614	+	0.955424i	−0.446544	+	0.894762i	$0.647345\pi$
$398$	7.18749	+	5.22202i	0.360277	+	0.261756i
$399$	7.97222	+	7.98980i	0.399110	+	0.399991i
$400$	−0.740839	−	2.28007i	−0.0370420	−	0.114003i
$401$	17.0794	+	7.60426i	0.852906	+	0.379738i	0.786154	−	0.618031i	$-0.212069\pi$
$401$	17.0794	+	7.60426i	0.852906	+	0.379738i	0.0667528	+	0.997770i	$0.478736\pi$
$402$	−0.644631	−	6.13325i	−0.0321513	−	0.305899i
$403$	1.10038	+	0.233893i	0.0548138	+	0.0116510i
$404$	−3.00881	+	0.639543i	−0.149694	+	0.0318185i
$405$	−1.30515	−	0.948248i	−0.0648535	−	0.0471188i
$406$	−25.8637	+	1.32689i	−1.28359	+	0.0658525i
$407$	−3.18767	−	0.629140i	−0.158007	−	0.0311853i
$408$	−2.71725	−	4.70641i	−0.134524	−	0.233002i
$409$	−10.3216	+	4.59549i	−0.510372	+	0.227232i	−0.645732	−	0.763564i	$-0.723448\pi$
$409$	−10.3216	+	4.59549i	−0.510372	+	0.227232i	0.135360	+	0.990797i	$0.456781\pi$
$410$	−8.58525	−	9.53488i	−0.423995	−	0.470894i
$411$	−1.91735	+	2.12944i	−0.0945761	+	0.105037i
$412$	5.28398	−	3.83904i	0.260323	−	0.189136i
$413$	−30.9525	−	11.9207i	−1.52307	−	0.586579i
$414$	2.75121	+	8.46735i	0.135215	+	0.416148i
$415$	−14.8263	+	3.15143i	−0.727795	+	0.154698i
$416$	0.242564	−	0.107996i	0.0118927	−	0.00529496i
$417$	−0.00163522	+	0.00283228i	−8.00769e−5	+	0.000138697i
$418$	−11.3242	+	8.48244i	−0.553885	+	0.414890i
$419$	19.4778			0.951554			0.475777	−	0.879566i	$-0.342167\pi$
$419$	19.4778			0.951554			0.475777	+	0.879566i	$0.342167\pi$
$420$	0.228080	−	4.26217i	0.0111291	−	0.207973i
$421$	−0.901167	+	2.77351i	−0.0439202	+	0.135172i	−0.970612	−	0.240649i	$-0.922640\pi$
$421$	−0.901167	+	2.77351i	−0.0439202	+	0.135172i	0.926692	+	0.375822i	$0.122640\pi$
$422$	10.8848	−	12.0888i	0.529865	−	0.588474i
$423$	−0.840611	−	7.99788i	−0.0408719	−	0.388870i
$424$	−0.835935	−	7.95339i	−0.0405966	−	0.386251i
$425$	8.71790	−	9.68221i	0.422880	−	0.469656i
$426$	−2.49146	+	7.66792i	−0.120712	+	0.371512i
$427$	16.0953	+	10.4776i	0.778905	+	0.507048i
$428$	−0.620466			−0.0299914
$429$	0.704822	−	0.527950i	0.0340291	−	0.0254897i
$430$	−4.28083	+	7.41462i	−0.206440	+	0.357565i
$431$	−12.1978	+	5.43081i	−0.587547	+	0.261593i	−0.678906	−	0.734225i	$-0.737546\pi$
$431$	−12.1978	+	5.43081i	−0.587547	+	0.261593i	0.0913588	+	0.995818i	$0.470879\pi$
$432$	−0.978148	+	0.207912i	−0.0470611	+	0.0100032i
$433$	1.96081	+	6.03476i	0.0942307	+	0.290012i	0.987052	−	0.160398i	$-0.0512778\pi$
$433$	1.96081	+	6.03476i	0.0942307	+	0.290012i	−0.892822	+	0.450410i	$0.851278\pi$
$434$	−1.74137	−	11.0735i	−0.0835886	−	0.531547i
$435$	12.7754	−	9.28185i	0.612532	−	0.445031i
$436$	−8.85984	+	9.83985i	−0.424309	+	0.471243i
$437$	25.4142	+	28.2253i	1.21573	+	1.35020i
$438$	8.03435	−	3.57712i	0.383896	−	0.170922i
$439$	1.69467	+	2.93525i	0.0808820	+	0.140092i	0.903629	−	0.428316i	$-0.140893\pi$
$439$	1.69467	+	2.93525i	0.0808820	+	0.140092i	−0.822747	+	0.568408i	$0.807560\pi$
$440$	5.24930	+	1.03604i	0.250251	+	0.0493912i
$441$	−2.86124	+	6.38853i	−0.136249	+	0.304216i
$442$	1.16738	+	0.848153i	0.0555267	+	0.0403425i
$443$	19.4153	−	4.12684i	0.922447	−	0.196072i	0.277876	−	0.960617i	$-0.410370\pi$
$443$	19.4153	−	4.12684i	0.922447	−	0.196072i	0.644571	+	0.764545i	$0.277036\pi$
$444$	−0.958252	−	0.203683i	−0.0454766	−	0.00966635i
$445$	−2.65726	−	25.2822i	−0.125966	−	1.19849i
$446$	4.51520	+	2.01029i	0.213801	+	0.0951902i
$447$	−0.158025	−	0.486352i	−0.00747434	−	0.0230036i
$448$	−1.86877	−	1.87289i	−0.0882909	−	0.0884857i
$449$	3.21648	+	2.33691i	0.151795	+	0.110286i	0.661091	−	0.750306i	$-0.270094\pi$
$449$	3.21648	+	2.33691i	0.151795	+	0.110286i	−0.509295	+	0.860592i	$0.670094\pi$
$450$	−1.19870	−	2.07621i	−0.0565074	−	0.0978737i
$451$	−25.7185	+	5.85972i	−1.21104	+	0.275923i
$452$	6.53301	−	11.3155i	0.307287	−	0.532236i
$453$	1.51219	−	14.3876i	0.0710491	−	0.675987i
$454$	−2.39836	+	7.38139i	−0.112561	+	0.346426i
$455$	0.404976	+	1.05848i	0.0189856	+	0.0496224i
$456$	−3.45129	+	2.50751i	−0.161622	+	0.117425i
$457$	−34.3806	−	15.3072i	−1.60826	−	0.716042i	−0.611111	−	0.791545i	$-0.709277\pi$
$457$	−34.3806	−	15.3072i	−1.60826	−	0.716042i	−0.997146	+	0.0755027i	$0.975944\pi$
$458$	−1.02184	−	0.217198i	−0.0477473	−	0.0101490i
$459$	−3.63639	−	4.03862i	−0.169732	−	0.188507i
$460$	1.50134	−	14.2843i	0.0700003	−	0.666009i
$461$	23.6276			1.10045			0.550225	−	0.835017i	$-0.314542\pi$
$461$	23.6276			1.10045			0.550225	+	0.835017i	$0.314542\pi$
$462$	−7.42304	−	4.67959i	−0.345351	−	0.217714i
$463$	−18.9562			−0.880970			−0.440485	−	0.897760i	$-0.645194\pi$
$463$	−18.9562			−0.880970			−0.440485	+	0.897760i	$0.645194\pi$
$464$	1.02317	−	9.73480i	0.0474994	−	0.451927i
$465$	4.57358	+	5.07947i	0.212095	+	0.235555i
$466$	2.28143	+	0.484934i	0.105685	+	0.0224641i
$467$	0.759780	+	0.338276i	0.0351584	+	0.0156535i	0.424241	−	0.905550i	$-0.360541\pi$
$467$	0.759780	+	0.338276i	0.0351584	+	0.0156535i	−0.389082	+	0.921203i	$0.627208\pi$
$468$	0.214810	−	0.156068i	0.00992958	−	0.00721426i
$469$	10.2822	−	12.6689i	0.474789	−	0.584997i
$470$	−4.00909	+	12.3387i	−0.184926	+	0.569143i
$471$	1.91043	−	18.1765i	0.0880278	−	0.837529i
$472$	6.26829	−	10.8570i	0.288521	−	0.499734i
$473$	9.02205	+	15.1135i	0.414834	+	0.694920i
$474$	5.52996	+	9.57817i	0.253999	+	0.439940i
$475$	−8.27415	−	6.01152i	−0.379644	−	0.275828i
$476$	3.73668	−	13.8843i	0.171271	−	0.636385i
$477$	−2.47127	−	7.60579i	−0.113152	−	0.348245i
$478$	−8.39660	−	3.73841i	−0.384051	−	0.170991i
$479$	−0.459228	−	4.36926i	−0.0209827	−	0.199637i	0.979009	−	0.203819i	$-0.0653354\pi$
$479$	−0.459228	−	4.36926i	−0.0209827	−	0.199637i	−0.999991	+	0.00418223i	$0.998669\pi$
$480$	1.57800	+	0.335415i	0.0720256	+	0.0153095i
$481$	0.254434	−	0.0540817i	0.0116012	−	0.00246591i
$482$	−18.1858	−	13.2128i	−0.828342	−	0.601826i
$483$	−10.7170	+	20.9762i	−0.487642	+	0.954451i
$484$	7.11902	−	8.38568i	0.323592	−	0.381167i
$485$	−14.3134	−	24.7916i	−0.649939	−	1.12573i
$486$	−0.913545	+	0.406737i	−0.0414393	+	0.0184499i
$487$	−9.88257	−	10.9757i	−0.447822	−	0.497357i	0.476391	−	0.879233i	$-0.341945\pi$
$487$	−9.88257	−	10.9757i	−0.447822	−	0.497357i	−0.924213	+	0.381877i	$0.875278\pi$
$488$	−4.85713	+	5.39439i	−0.219872	+	0.244193i
$489$	−8.41491	+	6.11379i	−0.380535	+	0.276475i
$490$	8.40881	−	7.53784i	0.379871	−	0.340525i
$491$	10.7221	+	32.9993i	0.483882	+	1.48924i	0.833594	+	0.552378i	$0.186280\pi$
$491$	10.7221	+	32.9993i	0.483882	+	1.48924i	−0.349712	+	0.936857i	$0.613720\pi$
$492$	−7.77935	+	1.65355i	−0.350720	+	0.0745479i
$493$	48.5962	−	21.6364i	2.18866	−	0.974455i
$494$	0.566357	−	0.980960i	0.0254816	−	0.0441355i
$495$	5.35000	−	0.0779932i	0.240464	−	0.00350553i
$496$	4.23684			0.190240
$497$	−19.0171	+	9.66333i	−0.853034	+	0.433460i
$498$	−2.90341	+	8.93577i	−0.130105	+	0.400421i
$499$	3.61926	−	4.01959i	0.162020	−	0.179942i	−0.656668	−	0.754180i	$-0.728035\pi$
$499$	3.61926	−	4.01959i	0.162020	−	0.179942i	0.818689	+	0.574238i	$0.194702\pi$
$500$	1.24743	+	11.8685i	0.0557869	+	0.530777i
$501$	−0.192236	−	1.82901i	−0.00858849	−	0.0817140i
$502$	18.1931	−	20.2055i	0.811999	−	0.901816i
$503$	7.93394	−	24.4181i	0.353757	−	1.08875i	−0.602970	−	0.797764i	$-0.706016\pi$
$503$	7.93394	−	24.4181i	0.353757	−	1.08875i	0.956727	−	0.290988i	$-0.0939838\pi$
$504$	−2.21732	−	1.44342i	−0.0987675	−	0.0642952i
$505$	4.96243			0.220825
$506$	−24.1393	−	17.0062i	−1.07312	−	0.756018i
$507$	6.46475	−	11.1973i	0.287110	−	0.497288i
$508$	6.18296	−	2.75283i	0.274325	−	0.122137i
$509$	−24.8202	+	5.27570i	−1.10014	+	0.233841i	−0.721989	−	0.691904i	$-0.756772\pi$
$509$	−24.8202	+	5.27570i	−1.10014	+	0.233841i	−0.378147	+	0.925746i	$0.623439\pi$
$510$	2.70922	+	8.33813i	0.119966	+	0.369219i
$511$	21.7139	+	8.36264i	0.960566	+	0.369941i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−2.85453	+	3.17028i	−0.126031	+	0.139971i
$514$	−1.20131	−	1.33419i	−0.0529873	−	0.0588484i
$515$	−9.62580	+	4.28568i	−0.424164	+	0.188850i
$516$	2.65354	+	4.59606i	0.116815	+	0.202330i
$517$	18.1341	+	19.5590i	0.797539	+	0.860203i
$518$	−1.40927	−	2.17533i	−0.0619199	−	0.0955787i
$519$	5.03215	+	3.65607i	0.220887	+	0.160484i
$520$	−0.418990	+	0.0890591i	−0.0183739	+	0.00390550i
$521$	−18.5941	−	3.95229i	−0.814621	−	0.173153i	−0.218282	−	0.975886i	$-0.570045\pi$
$521$	−18.5941	−	3.95229i	−0.814621	−	0.173153i	−0.596339	+	0.802733i	$0.703379\pi$
$522$	−1.02317	−	9.73480i	−0.0447829	−	0.426081i
$523$	4.57988	+	2.03909i	0.200264	+	0.0891634i	0.504418	−	0.863460i	$-0.331707\pi$
$523$	4.57988	+	2.03909i	0.200264	+	0.0891634i	−0.304154	+	0.952623i	$0.598374\pi$
$524$	−0.288651	−	0.888375i	−0.0126098	−	0.0388089i
$525$	1.64842	−	6.12500i	0.0719431	−	0.267317i
$526$	−10.6644	−	7.74814i	−0.464990	−	0.337835i
$527$	11.5125	+	19.9403i	0.501494	+	0.868613i
$528$	2.18309	−	2.49682i	0.0950069	−	0.108660i
$529$	−28.1326	+	48.7271i	−1.22316	+	2.11857i
$530$	−1.34858	+	12.8309i	−0.0585785	+	0.557337i
$531$	3.87402	−	11.9230i	0.168118	−	0.517414i
$532$	−11.1460	−	1.77793i	−0.483238	−	0.0770832i
$533$	1.70841	−	1.24123i	0.0739995	−	0.0537638i
$534$	−14.3955	−	6.40929i	−0.622954	−	0.277357i
$535$	0.979097	+	0.208113i	0.0423300	+	0.00899753i
$536$	4.12655	+	4.58300i	0.178240	+	0.197955i
$537$	−0.946835	+	9.00853i	−0.0408590	+	0.388747i
$538$	−11.3233			−0.488182
$539$	−5.10758	−	22.6476i	−0.219999	−	0.975500i
$540$	1.61326			0.0694235
$541$	−0.737387	+	7.01577i	−0.0317028	+	0.301632i	0.967169	+	0.254135i	$0.0817909\pi$
$541$	−0.737387	+	7.01577i	−0.0317028	+	0.301632i	−0.998871	+	0.0474962i	$0.984876\pi$
$542$	−5.25494	−	5.83620i	−0.225719	−	0.250686i
$543$	−0.661109	−	0.140523i	−0.0283709	−	0.00603042i
$544$	4.96466	+	2.21041i	0.212858	+	0.0947705i
$545$	17.2813	−	12.5556i	0.740248	−	0.537822i
$546$	0.693728	+	0.110659i	0.0296888	+	0.00473578i
$547$	0.787024	−	2.42221i	0.0336507	−	0.103566i	−0.932820	−	0.360342i	$-0.882660\pi$
$547$	0.787024	−	2.42221i	0.0336507	−	0.103566i	0.966471	+	0.256775i	$0.0826601\pi$
$548$	0.299520	−	2.84974i	0.0127949	−	0.121735i
$549$	−3.62944	+	6.28637i	−0.154901	+	0.268296i
$550$	7.31024	+	3.12786i	0.311710	+	0.133372i
$551$	−20.8789	−	36.1633i	−0.889470	−	1.54061i
$552$	−7.20276	−	5.23311i	−0.306570	−	0.222736i
$553$	−7.60464	+	28.2564i	−0.323382	+	1.20158i
$554$	−1.10481	−	3.40024i	−0.0469387	−	0.144463i
$555$	1.44381	+	0.642823i	0.0612861	+	0.0272863i
$556$	−0.000341853	−	0.00325252i	−1.44978e−5	−	0.000137937i
$557$	−24.2872	−	5.16241i	−1.02908	−	0.218738i	−0.337720	−	0.941247i	$-0.609656\pi$
$557$	−24.2872	−	5.16241i	−1.02908	−	0.218738i	−0.691362	+	0.722508i	$0.742989\pi$
$558$	4.14425	−	0.880888i	0.175440	−	0.0372910i
$559$	−1.14001	−	0.828267i	−0.0482173	−	0.0350319i
$560$	2.32072	+	3.58223i	0.0980685	+	0.151377i
$561$	17.6831	+	3.49005i	0.746580	+	0.147350i
$562$	5.80883	+	10.0612i	0.245031	+	0.424406i
$563$	4.56838	−	2.03397i	0.192534	−	0.0857218i	−0.308205	−	0.951320i	$-0.599728\pi$
$563$	4.56838	−	2.03397i	0.192534	−	0.0857218i	0.500739	+	0.865598i	$0.333062\pi$
$564$	5.38111	+	5.97633i	0.226585	+	0.251649i
$565$	−14.1045	+	15.6646i	−0.593380	+	0.659015i
$566$	11.2042	−	8.14033i	0.470948	−	0.342163i
$567$	−2.46898	−	0.950873i	−0.103687	−	0.0399329i
$568$	−2.49146	−	7.66792i	−0.104539	−	0.321739i
$569$	−1.14374	+	0.243109i	−0.0479480	+	0.0101917i	−0.231823	−	0.972758i	$-0.574469\pi$
$569$	−1.14374	+	0.243109i	−0.0479480	+	0.0101917i	0.183875	+	0.982950i	$0.441136\pi$
$570$	6.28720	−	2.79924i	0.263342	−	0.117247i
$571$	−3.85309	+	6.67374i	−0.161247	+	0.279287i	−0.935316	−	0.353813i	$-0.884885\pi$
$571$	−3.85309	+	6.67374i	−0.161247	+	0.279287i	0.774069	+	0.633101i	$0.218218\pi$
$572$	−0.259892	+	0.841405i	−0.0108666	+	0.0351809i
$573$	18.6068			0.777311
$574$	−17.6347	−	11.4797i	−0.736058	−	0.479155i
$575$	6.59577	−	20.2997i	0.275062	−	0.846555i
$576$	0.669131	−	0.743145i	0.0278804	−	0.0309644i
$577$	0.735979	+	7.00238i	0.0306392	+	0.291513i	0.999103	+	0.0423566i	$0.0134866\pi$
$577$	0.735979	+	7.00238i	0.0306392	+	0.291513i	−0.968463	+	0.249156i	$0.919847\pi$
$578$	1.31013	+	12.4651i	0.0544944	+	0.518479i
$579$	−5.02340	+	5.57905i	−0.208765	+	0.231858i
$580$	−4.87976	+	15.0183i	−0.202621	+	0.623603i
$581$	−22.1615	+	11.2611i	−0.919414	+	0.467189i
$582$	−17.7448			−0.735544
$583$	21.6831	+	15.2758i	0.898023	+	0.632659i
$584$	−4.39735	+	7.61643i	−0.181964	+	0.315170i
$585$	−0.391318	+	0.174226i	−0.0161790	+	0.00720335i
$586$	−16.2737	+	3.45908i	−0.672260	+	0.142893i
$587$	−1.59441	−	4.90709i	−0.0658084	−	0.202537i	0.912745	−	0.408529i	$-0.133958\pi$
$587$	−1.59441	−	4.90709i	−0.0658084	−	0.202537i	−0.978554	+	0.205991i	$0.933958\pi$
$588$	−1.44029	−	6.85022i	−0.0593967	−	0.282498i
$589$	14.6226	−	10.6239i	0.602513	−	0.437751i
$590$	−13.5330	+	15.0299i	−0.557144	+	0.618771i
$591$	13.6663	+	15.1780i	0.562158	+	0.624340i
$592$	0.894964	−	0.398464i	0.0367828	−	0.0163767i
$593$	14.7188	+	25.4938i	0.604430	+	1.04690i	0.992141	+	0.125122i	$0.0399323\pi$
$593$	14.7188	+	25.4938i	0.604430	+	1.04690i	−0.387712	+	0.921781i	$0.626734\pi$
$594$	1.61627	−	2.89615i	0.0663163	−	0.118830i
$595$	−10.5535	+	20.6561i	−0.432651	+	0.846817i
$596$	0.413715	+	0.300582i	0.0169464	+	0.0123123i
$597$	−8.69009	+	1.84714i	−0.355662	+	0.0755982i
$598$	2.31229	+	0.491492i	0.0945565	+	0.0200986i
$599$	−0.290180	−	2.76088i	−0.0118564	−	0.112806i	0.986993	−	0.160763i	$-0.0513956\pi$
$599$	−0.290180	−	2.76088i	−0.0118564	−	0.112806i	−0.998849	+	0.0479571i	$0.984729\pi$
$600$	2.19014	+	0.975113i	0.0894121	+	0.0398088i
$601$	0.894934	+	2.75432i	0.0365051	+	0.112351i	0.967649	−	0.252302i	$-0.0811876\pi$
$601$	0.894934	+	2.75432i	0.0365051	+	0.112351i	−0.931143	+	0.364653i	$0.881188\pi$
$602$	−3.64907	+	13.5587i	−0.148725	+	0.552613i
$603$	4.98924	+	3.62489i	0.203177	+	0.147617i
$604$	7.23341	+	12.5286i	0.294323	+	0.509783i
$605$	−14.0465	+	10.8448i	−0.571072	+	0.440904i
$606$	1.53802	−	2.66392i	0.0624777	−	0.108214i
$607$	−1.95694	+	18.6191i	−0.0794299	+	0.755725i	0.880227	+	0.474552i	$0.157390\pi$
$607$	−1.95694	+	18.6191i	−0.0794299	+	0.755725i	−0.959657	+	0.281173i	$0.909277\pi$
$608$	1.31828	−	4.05724i	0.0534632	−	0.164543i
$609$	16.3201	−	20.1083i	0.661325	−	0.814831i
$610$	9.47393	−	6.88321i	0.383588	−	0.278693i
$611$	−1.95068	−	0.868501i	−0.0789163	−	0.0351358i
$612$	5.31574	+	1.12990i	0.214876	+	0.0456733i
$613$	−14.5767	−	16.1890i	−0.588747	−	0.653869i	0.372993	−	0.927834i	$-0.378332\pi$
$613$	−14.5767	−	16.1890i	−0.588747	−	0.653869i	−0.961740	+	0.273965i	$0.911665\pi$
$614$	0.891877	−	8.48564i	0.0359932	−	0.342453i
$615$	12.8305			0.517374
$616$	8.75595	−	0.577286i	0.352787	−	0.0232595i
$617$	−36.5719			−1.47233			−0.736165	−	0.676802i	$-0.763365\pi$
$617$	−36.5719			−1.47233			−0.736165	+	0.676802i	$0.763365\pi$
$618$	−0.682713	+	6.49558i	−0.0274627	+	0.261291i
$619$	1.41479	+	1.57128i	0.0568651	+	0.0631550i	0.770906	−	0.636949i	$-0.219804\pi$
$619$	1.41479	+	1.57128i	0.0568651	+	0.0631550i	−0.714041	+	0.700104i	$0.753137\pi$
$620$	−6.68574	−	1.42110i	−0.268506	−	0.0570727i
$621$	−8.13339	−	3.62122i	−0.326382	−	0.145314i
$622$	21.8708	−	15.8901i	0.876940	−	0.637134i
$623$	−14.8979	−	38.9386i	−0.596874	−	1.56004i
$624$	−0.0820500	+	0.252524i	−0.00328463	+	0.0101090i
$625$	0.759442	−	7.22561i	0.0303777	−	0.289024i
$626$	12.1501	−	21.0445i	0.485614	−	0.841108i
$627$	1.27369	−	14.0914i	0.0508661	−	0.562756i
$628$	9.13831	+	15.8280i	0.364658	+	0.631607i
$629$	4.30717	+	3.12934i	0.171738	+	0.124775i
$630$	3.01480	+	3.02145i	0.120112	+	0.120377i
$631$	12.7911	+	39.3670i	0.509207	+	1.56718i	0.793582	+	0.608464i	$0.208214\pi$
$631$	12.7911	+	39.3670i	0.509207	+	1.56718i	−0.284375	+	0.958713i	$0.591786\pi$
$632$	−10.1037	−	4.49847i	−0.401905	−	0.178940i
$633$	1.70038	+	16.1780i	0.0675838	+	0.643017i
$634$	23.4885	+	4.99264i	0.932848	+	0.198283i
$635$	−10.6801	+	2.27012i	−0.423826	+	0.0900869i
$636$	6.46987	+	4.70064i	0.256547	+	0.186392i
$637$	1.08916	+	1.50607i	0.0431542	+	0.0596727i
$638$	22.0724	+	23.8066i	0.873854	+	0.942513i
$639$	−4.03126	−	6.98236i	−0.159474	−	0.276218i
$640$	−1.47378	+	0.656170i	−0.0582564	+	0.0259374i
$641$	24.0494	+	26.7096i	0.949894	+	1.05496i	0.998423	+	0.0561420i	$0.0178800\pi$
$641$	24.0494	+	26.7096i	0.949894	+	1.05496i	−0.0485291	+	0.998822i	$0.515453\pi$
$642$	0.415173	−	0.461096i	0.0163856	−	0.0181980i
$643$	−16.4952	+	11.9845i	−0.650508	+	0.472622i	−0.863444	−	0.504444i	$-0.831697\pi$
$643$	−16.4952	+	11.9845i	−0.650508	+	0.472622i	0.212936	+	0.977066i	$0.431697\pi$
$644$	−3.65924	−	23.2694i	−0.144194	−	0.916944i
$645$	−2.64570	−	8.14263i	−0.104174	−	0.320616i
$646$	22.6771	−	4.82017i	0.892219	−	0.189647i
$647$	30.6129	−	13.6297i	1.20352	−	0.535840i	0.295730	−	0.955272i	$-0.404437\pi$
$647$	30.6129	−	13.6297i	1.20352	−	0.535840i	0.907787	+	0.419431i	$0.137770\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	13.4237	+	39.3526i	0.526927	+	1.54473i
$650$	−0.636558			−0.0249679
$651$	9.39445	+	6.11555i	0.368197	+	0.239687i
$652$	3.21421	−	9.89231i	0.125878	−	0.387413i
$653$	14.9222	−	16.5728i	0.583952	−	0.648544i	−0.376688	−	0.926340i	$-0.622937\pi$
$653$	14.9222	−	16.5728i	0.583952	−	0.648544i	0.960640	+	0.277796i	$0.0896039\pi$
$654$	−1.38404	−	13.1683i	−0.0541203	−	0.514921i
$655$	0.157517	+	1.49868i	0.00615471	+	0.0585581i
$656$	5.32169	−	5.91034i	0.207777	−	0.230760i
$657$	−2.71771	+	8.36425i	−0.106028	+	0.326320i
$658$	−1.13696	+	21.2466i	−0.0443232	+	0.828278i
$659$	−41.5684			−1.61928			−0.809638	−	0.586930i	$-0.800336\pi$
$659$	−41.5684			−1.61928			−0.809638	+	0.586930i	$0.800336\pi$
$660$	−4.28239	+	3.20775i	−0.166692	+	0.124861i
$661$	20.1328	−	34.8710i	0.783075	−	1.35633i	−0.147067	−	0.989127i	$-0.546983\pi$
$661$	20.1328	−	34.8710i	0.783075	−	1.35633i	0.930142	−	0.367200i	$-0.119683\pi$
$662$	−16.4929	+	7.34313i	−0.641016	+	0.285399i
$663$	−1.41143	+	0.300009i	−0.0548155	+	0.0116514i
$664$	−2.90341	−	8.93577i	−0.112674	−	0.346775i
$665$	16.9920	+	6.54410i	0.658921	+	0.253769i
$666$	0.792561	−	0.575830i	0.0307111	−	0.0223129i
$667$	58.3129	−	64.7631i	2.25789	−	2.50764i
$668$	1.23059	+	1.36670i	0.0476128	+	0.0528794i
$669$	−4.51520	+	2.01029i	−0.174568	+	0.0777225i
$670$	−4.97450	−	8.61609i	−0.192182	−	0.332869i
$671$	−2.86526	−	23.9038i	−0.110612	−	0.922798i
$672$	2.64228	−	0.135557i	0.101928	−	0.00522923i
$673$	16.7121	+	12.1420i	0.644203	+	0.468041i	0.861292	−	0.508111i	$-0.169656\pi$
$673$	16.7121	+	12.1420i	0.644203	+	0.468041i	−0.217088	+	0.976152i	$0.569656\pi$
$674$	33.8117	−	7.18690i	1.30238	−	0.276829i
$675$	2.34502	+	0.498449i	0.0902598	+	0.0191853i
$676$	1.35150	+	12.8587i	0.0519808	+	0.494564i
$677$	31.4857	+	14.0184i	1.21010	+	0.538769i	0.909788	−	0.415073i	$-0.136244\pi$
$677$	31.4857	+	14.0184i	1.21010	+	0.538769i	0.300307	+	0.953843i	$0.402911\pi$
$678$	4.03762	+	12.4265i	0.155064	+	0.477238i
$679$	−33.1608	−	33.2340i	−1.27260	−	1.27540i
$680$	−7.09284	−	5.15325i	−0.271998	−	0.197618i
$681$	−3.88063	−	6.72145i	−0.148706	−	0.257566i
$682$	−9.24941	+	10.5786i	−0.354178	+	0.405076i
$683$	12.6293	−	21.8746i	0.483247	−	0.837008i	−0.516568	−	0.856246i	$-0.672791\pi$
$683$	12.6293	−	21.8746i	0.483247	−	0.837008i	0.999815	+	0.0192383i	$0.00612412\pi$
$684$	0.445922	−	4.24266i	0.0170502	−	0.162222i
$685$	−1.42849	+	4.39644i	−0.0545797	+	0.167979i
$686$	10.1381	−	15.4990i	0.387076	−	0.591754i
$687$	0.845152	−	0.614039i	0.0322446	−	0.0234270i
$688$	−4.84826	−	2.15858i	−0.184838	−	0.0822952i
$689$	−2.07701	−	0.441482i	−0.0791278	−	0.0168191i
$690$	9.61071	+	10.6738i	0.365873	+	0.406344i
$691$	1.61195	−	15.3367i	0.0613217	−	0.583437i	−0.920115	−	0.391649i	$-0.871905\pi$
$691$	1.61195	−	15.3367i	0.0613217	−	0.583437i	0.981436	−	0.191788i	$-0.0614285\pi$
$692$	−6.22008			−0.236452
$693$	8.44459	−	2.38514i	0.320784	−	0.0906038i
$694$	28.0221			1.06371
$695$	−0.000551497		0.00524714i	−2.09195e−5		0.000199035i
$696$	6.54973	+	7.27421i	0.248267	+	0.275728i
$697$	42.2768	+	8.98622i	1.60135	+	0.340377i
$698$	−26.8472	−	11.9532i	−1.01618	−	0.452434i
$699$	−1.88695	+	1.37095i	−0.0713711	+	0.0518542i
$700$	2.26658	+	5.92415i	0.0856687	+	0.223912i
$701$	2.54263	−	7.82541i	0.0960338	−	0.295562i	−0.891488	−	0.453044i	$-0.850338\pi$
$701$	2.54263	−	7.82541i	0.0960338	−	0.295562i	0.987522	+	0.157483i	$0.0503379\pi$
$702$	−0.0277543	+	0.264065i	−0.00104752	+	0.00996648i
$703$	2.08963	−	3.61935i	0.0788119	−	0.136506i
$704$	−0.298564	+	3.30316i	−0.0112526	+	0.124492i
$705$	−6.48685	−	11.2356i	−0.244309	−	0.423156i
$706$	3.94252	+	2.86441i	0.148379	+	0.107803i
$707$	7.86342	−	2.09772i	0.295735	−	0.0788927i
$708$	3.87402	+	11.9230i	0.145594	+	0.448094i
$709$	7.50275	+	3.34044i	0.281772	+	0.125453i	0.542757	−	0.839890i	$-0.317381\pi$
$709$	7.50275	+	3.34044i	0.281772	+	0.125453i	−0.260985	+	0.965343i	$0.584047\pi$
$710$	1.35959	+	12.9357i	0.0510246	+	0.485467i
$711$	−10.8182	−	2.29949i	−0.405715	−	0.0862375i
$712$	15.4135	−	3.27624i	0.577645	−	0.122782i
$713$	30.5169	+	22.1718i	1.14287	+	0.830342i
$714$	7.81771	+	12.0673i	0.292570	+	0.451607i
$715$	0.692329	−	1.24057i	0.0258917	−	0.0463946i
$716$	−4.52908	−	7.84459i	−0.169260	−	0.293166i
$717$	8.39660	−	3.73841i	0.313577	−	0.139613i
$718$	−9.12076	−	10.1296i	−0.340384	−	0.378035i
$719$	−15.4056	+	17.1097i	−0.574533	+	0.638083i	−0.958442	−	0.285288i	$-0.907911\pi$
$719$	−15.4056	+	17.1097i	−0.574533	+	0.638083i	0.383909	+	0.923371i	$0.374578\pi$
$720$	−1.30515	+	0.948248i	−0.0486401	+	0.0353391i
$721$	−13.4413	+	10.8601i	−0.500581	+	0.404451i
$722$	0.247511	+	0.761759i	0.00921139	+	0.0283497i
$723$	21.9877	−	4.67363i	0.817732	−	0.173814i
$724$	0.617445	−	0.274904i	0.0229472	−	0.0102167i
$725$	−11.7334	+	20.3229i	−0.435768	+	0.754772i
$726$	1.46822	+	10.9016i	0.0544907	+	0.404595i
$727$	9.41403			0.349147			0.174574	−	0.984644i	$-0.444145\pi$
$727$	9.41403			0.349147			0.174574	+	0.984644i	$0.444145\pi$
$728$	−0.626281	+	0.318238i	−0.0232115	+	0.0117947i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	9.49368	−	10.5438i	0.351377	−	0.390244i
$731$	−3.01474	−	28.6833i	−0.111504	−	1.06089i
$732$	−0.758759	−	7.21911i	−0.0280445	−	0.266826i
$733$	−13.7510	+	15.2720i	−0.507905	+	0.564086i	−0.941496	−	0.337024i	$-0.890580\pi$
$733$	−13.7510	+	15.2720i	−0.507905	+	0.564086i	0.433591	+	0.901110i	$0.357246\pi$
$734$	1.41890	−	4.36693i	0.0523726	−	0.161186i
$735$	−0.0248813	+	11.2928i	−0.000917760	+	0.416540i
$736$	8.90310			0.328173
$737$	−20.4516	+	0.298147i	−0.753343	+	0.0109824i
$738$	3.97657	−	6.88762i	0.146380	−	0.253537i
$739$	−12.8752	+	5.73242i	−0.473622	+	0.210870i	−0.629645	−	0.776883i	$-0.716800\pi$
$739$	−12.8752	+	5.73242i	−0.473622	+	0.210870i	0.156022	+	0.987754i	$0.450133\pi$
$740$	−1.54591	+	0.328592i	−0.0568286	+	0.0120793i
$741$	0.350028	+	1.07728i	0.0128586	+	0.0395747i
$742$	3.28691	+	20.9017i	0.120666	+	0.767327i
$743$	33.7920	−	24.5514i	1.23971	−	0.900702i	0.242131	−	0.970244i	$-0.422154\pi$
$743$	33.7920	−	24.5514i	1.23971	−	0.900702i	0.997579	+	0.0695418i	$0.0221537\pi$
$744$	−2.83500	+	3.14858i	−0.103936	+	0.115433i
$745$	−0.552024	−	0.613085i	−0.0202246	−	0.0224617i
$746$	−16.9740	+	7.55731i	−0.621462	+	0.276693i
$747$	−4.69781	−	8.13685i	−0.171884	−	0.297712i
$748$	−16.3573	+	7.57034i	−0.598082	+	0.276799i
$749$	1.63944	−	0.0841086i	0.0599039	−	0.00307326i
$750$	−9.65473	−	7.01457i	−0.352541	−	0.256136i
$751$	−33.0240	+	7.01947i	−1.20506	+	0.256144i	−0.766315	−	0.642465i	$-0.777912\pi$
$751$	−33.0240	+	7.01947i	−1.20506	+	0.256144i	−0.438749	+	0.898610i	$0.644578\pi$
$752$	−7.86620	−	1.67201i	−0.286851	−	0.0609720i
$753$	2.84204	+	27.0402i	0.103570	+	0.985401i
$754$	−2.37432	−	1.05711i	−0.0864676	−	0.0384979i
$755$	−7.21205	−	22.1964i	−0.262473	−	0.807809i
$756$	2.55635	−	0.681955i	0.0929736	−	0.0248025i
$757$	−1.06155	−	0.771263i	−0.0385828	−	0.0280320i	0.568327	−	0.822803i	$-0.307591\pi$
$757$	−1.06155	−	0.771263i	−0.0385828	−	0.0280320i	−0.606910	+	0.794771i	$0.707591\pi$
$758$	10.5125	+	18.2081i	0.381829	+	0.661348i
$759$	28.7904	−	6.55963i	1.04503	−	0.238100i
$760$	−3.44110	+	5.96016i	−0.124822	+	0.216198i
$761$	1.11293	−	10.5888i	0.0403436	−	0.383843i	−0.955656	−	0.294485i	$-0.904852\pi$
$761$	1.11293	−	10.5888i	0.0403436	−	0.383843i	0.996000	−	0.0893580i	$-0.0284815\pi$
$762$	−2.09146	+	6.43684i	−0.0757655	+	0.233182i
$763$	22.0763	−	27.2006i	0.799215	−	0.984728i
$764$	−15.0532	+	10.9368i	−0.544607	+	0.395680i
$765$	−8.00926	−	3.56595i	−0.289576	−	0.128927i
$766$	−14.3805	−	3.05667i	−0.519588	−	0.110442i
$767$	−2.22734	−	2.47371i	−0.0804245	−	0.0893205i
$768$	−0.104528	+	0.994522i	−0.00377185	+	0.0358867i
$769$	32.0528			1.15585			0.577927	−	0.816089i	$-0.303862\pi$
$769$	32.0528			1.15585			0.577927	+	0.816089i	$0.303862\pi$
$770$	−14.0105	−	2.02592i	−0.504905	−	0.0730090i
$771$	1.79532			0.0646570
$772$	0.784732	−	7.46623i	0.0282431	−	0.268715i
$773$	0.708680	+	0.787069i	0.0254895	+	0.0283089i	0.755755	−	0.654855i	$-0.227270\pi$
$773$	0.708680	+	0.787069i	0.0254895	+	0.0283089i	−0.730265	+	0.683164i	$0.760604\pi$
$774$	−5.19110	−	1.10340i	−0.186590	−	0.0396610i
$775$	−9.27927	−	4.13140i	−0.333321	−	0.148404i
$776$	14.3558	−	10.4301i	0.515344	−	0.374419i
$777$	2.55958	+	0.408288i	0.0918243	+	0.0146473i
$778$	−3.74230	+	11.5176i	−0.134168	+	0.412927i
$779$	3.54648	−	33.7425i	0.127066	−	1.20895i
$780$	0.214175	−	0.370963i	0.00766871	−	0.0132826i
$781$	24.5845	+	10.5191i	0.879703	+	0.376401i
$782$	24.1919	+	41.9017i	0.865102	+	1.49840i
$783$	7.91900	+	5.75349i	0.283002	+	0.205613i
$784$	5.19168	+	4.69536i	0.185417	+	0.167692i
$785$	−9.11132	−	28.0418i	−0.325197	−	1.00085i
$786$	0.853337	+	0.379930i	0.0304375	+	0.0135517i
$787$	−3.89885	−	37.0950i	−0.138979	−	1.32230i	−0.812428	−	0.583062i	$-0.801855\pi$
$787$	−3.89885	−	37.0950i	−0.138979	−	1.32230i	0.673449	−	0.739234i	$-0.264812\pi$
$788$	−19.9777	−	4.24639i	−0.711676	−	0.151271i
$789$	12.8939	−	2.74067i	0.459034	−	0.0975706i
$790$	14.4349	+	10.4875i	0.513569	+	0.373130i
$791$	−15.7281	+	30.7843i	−0.559227	+	1.09456i
$792$	0.394725	+	3.29305i	0.0140260	+	0.117014i
$793$	0.963686	+	1.66915i	0.0342215	+	0.0592734i
$794$	20.0812	−	8.94075i	0.712657	−	0.317295i
$795$	−8.63281	−	9.58771i	−0.306174	−	0.340041i
$796$	5.94471	−	6.60227i	0.210705	−	0.234011i
$797$	26.6337	−	19.3505i	0.943416	−	0.685432i	−0.00582478	−	0.999983i	$-0.501854\pi$
$797$	26.6337	−	19.3505i	0.943416	−	0.685432i	0.949240	+	0.314551i	$0.101854\pi$
$798$	8.77936	−	7.09339i	0.310786	−	0.251103i
$799$	−13.5052	−	41.5649i	−0.477781	−	1.47046i
$800$	−2.34502	+	0.498449i	−0.0829089	+	0.0176228i
$801$	14.3955	−	6.40929i	0.508640	−	0.226461i
$802$	9.34789	−	16.1910i	0.330085	−	0.571725i
$803$	−9.41704	−	27.6067i	−0.332320	−	0.974221i
$804$	−6.16703			−0.217495
$805$	−2.03062	+	37.9466i	−0.0715698	+	1.33744i
$806$	0.347633	−	1.06990i	0.0122448	−	0.0376857i
$807$	7.57676	−	8.41485i	0.266715	−	0.296217i
$808$	0.321533	+	3.05918i	0.0113115	+	0.107622i
$809$	−2.95785	−	28.1421i	−0.103993	−	0.989423i	−0.914744	−	0.404033i	$-0.867608\pi$
$809$	−2.95785	−	28.1421i	−0.103993	−	0.989423i	0.810752	−	0.585390i	$-0.199059\pi$
$810$	−1.07948	+	1.19888i	−0.0379290	+	0.0421244i
$811$	−13.1870	+	40.5855i	−0.463059	+	1.42515i	0.398348	+	0.917235i	$0.369584\pi$
$811$	−13.1870	+	40.5855i	−0.463059	+	1.42515i	−0.861407	+	0.507916i	$0.830416\pi$
$812$	−1.38387	+	25.8607i	−0.0485644	+	0.907534i
$813$	7.85338			0.275430
$814$	−0.958896	+	3.10445i	−0.0336093	+	0.108811i
$815$	−8.39005	+	14.5320i	−0.293891	+	0.509034i
$816$	−4.96466	+	2.21041i	−0.173798	+	0.0773798i
$817$	−22.1454	+	4.70715i	−0.774770	+	0.164682i
$818$	3.49141	+	10.7455i	0.122074	+	0.375706i
$819$	−0.546430	+	0.441495i	−0.0190938	+	0.0154271i
$820$	−10.3801	+	7.54155i	−0.362487	+	0.263362i
$821$	−4.76561	+	5.29275i	−0.166321	+	0.184718i	−0.820544	−	0.571584i	$-0.806329\pi$
$821$	−4.76561	+	5.29275i	−0.166321	+	0.184718i	0.654223	+	0.756302i	$0.272996\pi$
$822$	1.91735	+	2.12944i	0.0668754	+	0.0742726i
$823$	−34.3207	+	15.2806i	−1.19635	+	0.532647i	−0.905592	−	0.424150i	$-0.860573\pi$
$823$	−34.3207	+	15.2806i	−1.19635	+	0.532647i	−0.290754	+	0.956798i	$0.593906\pi$
$824$	−3.26568	−	5.65632i	−0.113765	−	0.197047i
$825$	−7.21596	+	3.33962i	−0.251227	+	0.116271i
$826$	−15.0908	+	29.5369i	−0.525077	+	1.02772i
$827$	−32.1345	−	23.3471i	−1.11742	−	0.811857i	−0.133608	−	0.991034i	$-0.542656\pi$
$827$	−32.1345	−	23.3471i	−1.11742	−	0.811857i	−0.983817	+	0.179177i	$0.942656\pi$
$828$	8.70855	−	1.85106i	0.302643	−	0.0643287i
$829$	−17.4865	−	3.71686i	−0.607330	−	0.129092i	−0.106026	−	0.994363i	$-0.533813\pi$
$829$	−17.4865	−	3.71686i	−0.607330	−	0.129092i	−0.501304	+	0.865271i	$0.667146\pi$
$830$	1.58439	+	15.0745i	0.0549951	+	0.523244i
$831$	3.26613	+	1.45418i	0.113301	+	0.0504448i
$832$	−0.0820500	−	0.252524i	−0.00284457	−	0.00875469i
$833$	−7.99123	+	37.1927i	−0.276880	+	1.28865i
$834$	0.00264584	+	0.00192231i	9.16178e−5	+	6.65642e-5i
$835$	−1.48345	−	2.56942i	−0.0513371	−	0.0889184i
$836$	7.25228	+	12.1488i	0.250825	+	0.420176i
$837$	−2.11842	+	3.66921i	−0.0732233	+	0.126826i
$838$	2.03599	−	19.3711i	0.0703320	−	0.669164i
$839$	−1.58343	+	4.87331i	−0.0546662	+	0.168245i	−0.974662	−	0.223683i	$-0.928192\pi$
$839$	−1.58343	+	4.87331i	−0.0546662	+	0.168245i	0.919996	+	0.391928i	$0.128192\pi$
$840$	−4.21499	−	0.672349i	−0.145431	−	0.0231982i
$841$	−54.0530	+	39.2718i	−1.86390	+	1.35420i
$842$	2.66412	+	1.18614i	0.0918115	+	0.0408771i
$843$	−11.3638	−	2.41545i	−0.391390	−	0.0831924i
$844$	−10.8848	−	12.0888i	−0.374671	−	0.416114i
$845$	2.18032	−	20.7443i	0.0750052	−	0.713626i
$846$	−8.04194			−0.276488
$847$	−17.6737	+	23.1223i	−0.607275	+	0.794492i
$848$	−7.99720			−0.274625
$849$	−1.44763	+	13.7733i	−0.0496826	+	0.472698i
$850$	−8.71790	−	9.68221i	−0.299021	−	0.332097i
$851$	8.53141	+	1.81341i	0.292453	+	0.0621628i
$852$	7.36549	+	3.27933i	0.252337	+	0.112348i
$853$	39.3121	−	28.5619i	1.34602	−	0.977942i	0.346823	−	0.937931i	$-0.387261\pi$
$853$	39.3121	−	28.5619i	1.34602	−	0.977942i	0.999199	−	0.0400113i	$-0.0127394\pi$
$854$	12.1026	−	14.9119i	0.414144	−	0.510275i
$855$	−2.12672	+	6.54536i	−0.0727322	+	0.223847i
$856$	−0.0648564	+	0.617067i	−0.00221674	+	0.0210909i
$857$	−1.07354	+	1.85943i	−0.0366714	+	0.0635168i	−0.883779	−	0.467905i	$-0.845009\pi$
$857$	−1.07354	+	1.85943i	−0.0366714	+	0.0635168i	0.847107	+	0.531422i	$0.178342\pi$
$858$	−0.451384	−	0.756147i	−0.0154100	−	0.0258144i
$859$	12.3048	+	21.3126i	0.419835	+	0.727175i	0.995923	−	0.0902126i	$-0.0287546\pi$
$859$	12.3048	+	21.3126i	0.419835	+	0.727175i	−0.576088	+	0.817388i	$0.695421\pi$
$860$	6.92654	+	5.03242i	0.236193	+	0.171604i
$861$	20.3310	−	5.42369i	0.692880	−	0.184839i
$862$	4.12604	+	12.6987i	0.140534	+	0.432518i
$863$	−2.15131	−	0.957827i	−0.0732316	−	0.0326048i	0.369794	−	0.929114i	$-0.379428\pi$
$863$	−2.15131	−	0.957827i	−0.0732316	−	0.0326048i	−0.443026	+	0.896509i	$0.646095\pi$
$864$	0.104528	+	0.994522i	0.00355613	+	0.0338343i
$865$	9.81530	+	2.08631i	0.333730	+	0.0709365i
$866$	6.20667	−	1.31927i	0.210911	−	0.0448305i
$867$	−10.1400	−	7.36715i	−0.344373	−	0.250202i
$868$	−11.1949	+	0.574334i	−0.379980	+	0.0194942i
$869$	33.2893	−	15.4066i	1.12926	−	0.522634i
$870$	−7.89561	−	13.6756i	−0.267686	−	0.463646i
$871$	1.49590	−	0.666018i	0.0506867	−	0.0225672i
$872$	8.85984	+	9.83985i	0.300032	+	0.333219i
$873$	11.8736	−	13.1869i	0.401859	−	0.446310i
$874$	30.7272	−	22.3246i	1.03936	−	0.755142i
$875$	−4.90493	−	31.1908i	−0.165817	−	1.05444i
$876$	−2.71771	−	8.36425i	−0.0918229	−	0.282602i
$877$	−57.0223	+	12.1205i	−1.92551	+	0.409279i	−0.926013	+	0.377493i	$0.876786\pi$
$877$	−57.0223	+	12.1205i	−1.92551	+	0.409279i	−0.999495	+	0.0317865i	$0.989880\pi$
$878$	3.09631	−	1.37857i	0.104495	−	0.0465243i
$879$	8.31862	−	14.4083i	0.280580	−	0.485979i
$880$	1.57906	−	5.11225i	0.0532302	−	0.172334i
$881$	−13.9796			−0.470986			−0.235493	−	0.971876i	$-0.575670\pi$
$881$	−13.9796			−0.470986			−0.235493	+	0.971876i	$0.575670\pi$
$882$	6.05445	+	3.51335i	0.203864	+	0.118301i
$883$	8.09322	−	24.9084i	0.272358	−	0.838233i	−0.717548	−	0.696509i	$-0.754736\pi$
$883$	8.09322	−	24.9084i	0.272358	−	0.838233i	0.989906	−	0.141724i	$-0.0452645\pi$
$884$	0.965531	−	1.07233i	0.0324743	−	0.0360664i
$885$	−2.11406	−	20.1139i	−0.0710633	−	0.676122i
$886$	−2.07479	−	19.7403i	−0.0697038	−	0.663187i
$887$	−18.4138	+	20.4506i	−0.618276	+	0.686665i	−0.968218	−	0.250107i	$-0.919534\pi$
$887$	−18.4138	+	20.4506i	−0.618276	+	0.686665i	0.349943	+	0.936771i	$0.386201\pi$
$888$	−0.302731	+	0.931712i	−0.0101590	+	0.0312662i
$889$	−15.9639	+	8.11189i	−0.535413	+	0.272064i
$890$	−25.4214			−0.852128
$891$	1.07076	+	3.13902i	0.0358719	+	0.105161i
$892$	2.47125	−	4.28033i	0.0827435	−	0.143316i
$893$	−31.3412	+	13.9540i	−1.04879	+	0.466952i
$894$	−0.500205	+	0.106322i	−0.0167294	+	0.00355594i
$895$	4.51570	+	13.8979i	0.150943	+	0.464556i
$896$	−2.05797	+	1.66276i	−0.0687519	+	0.0555489i
$897$	−1.91247	+	1.38949i	−0.0638556	+	0.0463938i
$898$	2.66032	−	2.95459i	0.0887761	−	0.0985959i
$899$	−27.7502	−	30.8197i	−0.925520	−	1.02789i
$900$	−2.19014	+	0.975113i	−0.0730047	+	0.0325038i
$901$	−21.7304	−	37.6381i	−0.723944	−	1.25391i
$902$	3.13931	+	26.1901i	0.104527	+	0.872035i
$903$	−7.63441	−	11.7844i	−0.254057	−	0.392159i
$904$	−10.5706	−	7.68001i	−0.351574	−	0.255433i
$905$	−1.06654	+	0.226699i	−0.0354529	+	0.00753575i
$906$	−14.1507	−	3.00782i	−0.470125	−	0.0999281i
$907$	−3.61349	−	34.3801i	−0.119984	−	1.14157i	−0.874410	−	0.485187i	$-0.838751\pi$
$907$	−3.61349	−	34.3801i	−0.119984	−	1.14157i	0.754426	−	0.656385i	$-0.227915\pi$
$908$	7.09026	+	3.15679i	0.235299	+	0.104762i
$909$	0.950547	+	2.92548i	0.0315276	+	0.0970321i
$910$	1.09502	−	0.292116i	0.0362994	−	0.00968355i
$911$	11.6409	+	8.45763i	0.385681	+	0.280214i	0.763683	−	0.645591i	$-0.223389\pi$
$911$	11.6409	+	8.45763i	0.385681	+	0.280214i	−0.378002	+	0.925805i	$0.623389\pi$
$912$	2.13302	+	3.69449i	0.0706312	+	0.122337i
$913$	28.6494	+	12.2583i	0.948157	+	0.405691i
$914$	−18.8171	+	32.5922i	−0.622415	+	1.07805i
$915$	−1.22407	+	11.6463i	−0.0404666	+	0.385014i
$916$	−0.322819	+	0.993536i	−0.0106662	+	0.0328273i
$917$	0.883120	+	2.30820i	0.0291632	+	0.0762236i
$918$	−4.39660	+	3.19432i	−0.145109	+	0.105428i
$919$	−0.909915	−	0.405120i	−0.0300153	−	0.0133637i	0.391674	−	0.920104i	$-0.371896\pi$
$919$	−0.909915	−	0.405120i	−0.0300153	−	0.0133637i	−0.421689	+	0.906740i	$0.638563\pi$
$920$	−14.0491	−	2.98623i	−0.463185	−	0.0984531i
$921$	5.70928	+	6.34080i	0.188127	+	0.208936i
$922$	2.46976	−	23.4982i	0.0813373	−	0.773872i
$923$	−2.14076			−0.0704639
$924$	−5.42987	+	6.89322i	−0.178630	+	0.226770i
$925$	−2.34864			−0.0772229
$926$	−1.98146	+	18.8524i	−0.0651150	+	0.619527i
$927$	−4.37033	−	4.85375i	−0.143541	−	0.159418i
$928$	−9.57452	−	2.03513i	−0.314299	−	0.0668063i
$929$	−23.1685	−	10.3153i	−0.760134	−	0.338433i	−0.0102016	−	0.999948i	$-0.503247\pi$
$929$	−23.1685	−	10.3153i	−0.760134	−	0.338433i	−0.749932	+	0.661515i	$0.769914\pi$
$930$	5.52971	−	4.01757i	0.181326	−	0.131741i
$931$	29.6917	+	3.18688i	0.973106	+	0.104446i
$932$	0.720752	−	2.21825i	0.0236090	−	0.0726611i
$933$	−2.82580	+	26.8857i	−0.0925126	+	0.880199i
$934$	0.415841	−	0.720258i	0.0136067	−	0.0235676i
$935$	28.3511	−	6.45953i	0.927179	−	0.211249i
$936$	−0.132760	−	0.229947i	−0.00433939	−	0.00751604i
$937$	5.52597	+	4.01485i	0.180525	+	0.131159i	0.674378	−	0.738386i	$-0.264412\pi$
$937$	5.52597	+	4.01485i	0.180525	+	0.131159i	−0.493853	+	0.869546i	$0.664412\pi$
$938$	−11.5247	−	11.5502i	−0.376296	−	0.377126i
$939$	7.50915	+	23.1108i	0.245052	+	0.754192i
$940$	11.8521	+	5.27688i	0.386572	+	0.172113i
$941$	−3.97006	−	37.7726i	−0.129420	−	1.23135i	−0.845746	−	0.533585i	$-0.820844\pi$
$941$	−3.97006	−	37.7726i	−0.129420	−	1.23135i	0.716326	−	0.697766i	$-0.245822\pi$
$942$	−17.8772	−	3.79992i	−0.582472	−	0.123808i
$943$	69.2603	−	14.7217i	2.25543	−	0.479406i
$944$	−10.1423	−	7.36882i	−0.330104	−	0.239835i
$945$	−4.26267	+	0.218688i	−0.138665	+	0.00711393i
$946$	15.9738	−	7.39284i	0.519352	−	0.240362i
$947$	21.4539	+	37.1593i	0.697159	+	1.20752i	0.969447	+	0.245300i	$0.0788863\pi$
$947$	21.4539	+	37.1593i	0.697159	+	1.20752i	−0.272288	+	0.962216i	$0.587780\pi$
$948$	10.1037	−	4.49847i	0.328154	−	0.146104i
$949$	1.56253	+	1.73536i	0.0507218	+	0.0563323i
$950$	−6.84348	+	7.60045i	−0.222032	+	0.246591i
$951$	−19.4271	+	14.1146i	−0.629968	+	0.457699i
$952$	−13.4176	−	5.16752i	−0.434868	−	0.167480i
$953$	8.78126	+	27.0259i	0.284453	+	0.875456i	0.986562	+	0.163387i	$0.0522418\pi$
$953$	8.78126	+	27.0259i	0.284453	+	0.875456i	−0.702109	+	0.712069i	$0.747758\pi$
$954$	−7.82245	+	1.66271i	−0.253261	+	0.0538323i
$955$	27.4224	−	12.2092i	0.887368	−	0.395082i
$956$	−4.59561	+	7.95983i	−0.148633	+	0.257439i
$957$	−32.4611	+	0.473223i	−1.04932	+	0.0152971i
$958$	−4.39333			−0.141942
$959$	−0.405112	+	7.57041i	−0.0130817	+	0.244461i
$960$	0.498523	−	1.53430i	0.0160898	−	0.0495192i
$961$	−8.73162	+	9.69745i	−0.281665	+	0.312821i
$962$	−0.0271898	−	0.258694i	−0.000876634	−	0.00834062i
$963$	0.0648564	+	0.617067i	0.00208997	+	0.0198847i
$964$	−15.0413	+	16.7051i	−0.484449	+	0.538035i
$965$	−3.74259	+	11.5185i	−0.120478	+	0.370794i
$966$	19.7411	+	12.8509i	0.635158	+	0.413472i
$967$	−36.3488			−1.16890			−0.584450	−	0.811430i	$-0.698690\pi$
$967$	−36.3488			−1.16890			−0.584450	+	0.811430i	$0.698690\pi$
$968$	−7.59560	−	7.95656i	−0.244132	−	0.255734i
$969$	−11.5919	+	20.0777i	−0.372385	+	0.644989i
$970$	−26.1519	+	11.6436i	−0.839688	+	0.373853i
$971$	−29.9876	+	6.37407i	−0.962349	+	0.204554i	−0.662190	−	0.749336i	$-0.730373\pi$
$971$	−29.9876	+	6.37407i	−0.962349	+	0.204554i	−0.300159	+	0.953889i	$0.597040\pi$
$972$	0.309017	+	0.951057i	0.00991172	+	0.0305052i
$973$	0.00134417	+	0.00854771i	4.30922e−5	+	0.000274027i
$974$	−11.9486	+	8.68116i	−0.382858	+	0.278162i
$975$	0.425940	−	0.473055i	0.0136410	−	0.0151499i
$976$	4.85713	+	5.39439i	0.155473	+	0.172670i
$977$	−28.6821	+	12.7701i	−0.917621	+	0.408551i	−0.810529	−	0.585698i	$-0.800821\pi$
$977$	−28.6821	+	12.7701i	−0.917621	+	0.408551i	−0.107092	+	0.994249i	$0.534154\pi$
$978$	5.20070	+	9.00787i	0.166300	+	0.288040i
$979$	−25.4689	+	45.6371i	−0.813989	+	1.45857i
$980$	−6.61759	−	9.15066i	−0.211391	−	0.292307i
$981$	10.7120	+	7.78276i	0.342009	+	0.248484i
$982$	33.9393	−	7.21401i	1.08305	−	0.230208i
$983$	58.4456	+	12.4230i	1.86413	+	0.396232i	0.995129	−	0.0985862i	$-0.0314320\pi$
$983$	58.4456	+	12.4230i	1.86413	+	0.396232i	0.868997	+	0.494818i	$0.164765\pi$
$984$	0.831330	+	7.90957i	0.0265018	+	0.252148i
$985$	30.1006	+	13.4016i	0.959084	+	0.427012i
$986$	−16.4382	−	50.5916i	−0.523499	−	1.61116i
$987$	−15.0285	−	15.0617i	−0.478363	−	0.479418i
$988$	−0.916385	−	0.665793i	−0.0291541	−	0.0211817i
$989$	−23.6247	−	40.9192i	−0.751222	−	1.30116i
$990$	0.481661	−	5.32884i	0.0153082	−	0.169362i
$991$	11.2798	−	19.5372i	0.358314	−	0.620619i	−0.629365	−	0.777110i	$-0.716685\pi$
$991$	11.2798	−	19.5372i	0.358314	−	0.620619i	0.987679	+	0.156491i	$0.0500183\pi$
$992$	0.442870	−	4.21363i	0.0140611	−	0.133783i
$993$	5.57892	−	17.1702i	0.177042	−	0.544879i
$994$	7.62256	+	19.9230i	0.241773	+	0.631920i
$995$	−11.5953	+	8.42445i	−0.367595	+	0.267073i
$996$	8.58333	+	3.82154i	0.271973	+	0.121090i
$997$	−39.0593	−	8.30232i	−1.23702	−	0.262937i	−0.457441	−	0.889240i	$-0.651234\pi$
$997$	−39.0593	−	8.30232i	−1.23702	−	0.262937i	−0.779580	+	0.626303i	$0.784567\pi$
$998$	−3.61926	−	4.01959i	−0.114566	−	0.127238i
$999$	−0.102402	+	0.974293i	−0.00323987	+	0.0308253i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.y.c.235.4	yes	40
7.2	even	3	inner	462.2.y.c.37.2	yes	40
11.3	even	5	inner	462.2.y.c.25.2	✓	40
77.58	even	15	inner	462.2.y.c.289.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.y.c.25.2	✓	40	11.3	even	5	inner
462.2.y.c.37.2	yes	40	7.2	even	3	inner
462.2.y.c.235.4	yes	40	1.1	even	1	trivial
462.2.y.c.289.4	yes	40	77.58	even	15	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.104528 - 0.994522i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(1.47378 + 0.656170i) q^{5} +(0.809017 - 0.587785i) q^{6} +(2.61272 + 0.416765i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(0.104528 - 0.994522i) q^{2} +(0.669131 + 0.743145i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(1.47378 + 0.656170i) q^{5} +(0.809017 - 0.587785i) q^{6} +(2.61272 + 0.416765i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(0.806628 - 1.39712i) q^{10} +(-1.70000 - 2.84780i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.214810 + 0.156068i) q^{13} +(0.687586 - 2.55484i) q^{14} +(0.498523 + 1.53430i) q^{15} +(0.913545 + 0.406737i) q^{16} +(0.568060 + 5.40473i) q^{17} +(0.978148 + 0.207912i) q^{18} +(4.17281 - 0.886958i) q^{19} +(-1.30515 - 0.948248i) q^{20} +(1.43853 + 2.22050i) q^{21} +(-3.00990 + 1.39302i) q^{22} +(4.45155 + 7.71031i) q^{23} +(-0.913545 + 0.406737i) q^{24} +(-1.60418 - 1.78162i) q^{25} +(0.177667 - 0.197319i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(-2.46898 - 0.950873i) q^{28} +(-3.02479 - 9.30934i) q^{29} +(1.57800 - 0.335415i) q^{30} +(3.87054 - 1.72328i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.978806 - 3.16890i) q^{33} +5.43450 q^{34} +(3.57711 + 2.32861i) q^{35} +(0.309017 - 0.951057i) q^{36} +(0.655520 - 0.728029i) q^{37} +(-0.445922 - 4.24266i) q^{38} +(0.0277543 + 0.264065i) q^{39} +(-1.07948 + 1.19888i) q^{40} +(2.45766 - 7.56389i) q^{41} +(2.35870 - 1.19855i) q^{42} -5.30708 q^{43} +(1.07076 + 3.13902i) q^{44} +(-0.806628 + 1.39712i) q^{45} +(8.13339 - 3.62122i) q^{46} +(-7.86620 + 1.67201i) q^{47} +(0.309017 + 0.951057i) q^{48} +(6.65261 + 2.17778i) q^{49} +(-1.93954 + 1.40916i) q^{50} +(-3.63639 + 4.03862i) q^{51} +(-0.177667 - 0.197319i) q^{52} +(-7.30581 + 3.25276i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-0.636793 - 5.31253i) q^{55} +(-1.20374 + 2.35606i) q^{56} +(3.45129 + 2.50751i) q^{57} +(-9.57452 + 2.03513i) q^{58} +(-12.2626 - 2.60650i) q^{59} +(-0.168631 - 1.60442i) q^{60} +(6.63131 + 2.95245i) q^{61} +(-1.30926 - 4.02947i) q^{62} +(-0.687586 + 2.55484i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.214175 + 0.370963i) q^{65} +(-3.04923 - 1.30468i) q^{66} +(3.08352 - 5.34081i) q^{67} +(0.568060 - 5.40473i) q^{68} +(-2.75121 + 8.46735i) q^{69} +(2.68976 - 3.31411i) q^{70} +(-6.52272 + 4.73904i) q^{71} +(-0.913545 - 0.406737i) q^{72} +(8.60251 + 1.82852i) q^{73} +(-0.655520 - 0.728029i) q^{74} +(0.250597 - 2.38427i) q^{75} -4.26603 q^{76} +(-3.25477 - 8.14902i) q^{77} +0.265519 q^{78} +(-1.15608 + 10.9993i) q^{79} +(1.07948 + 1.19888i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(-7.26556 - 3.23483i) q^{82} +(-7.60122 + 5.52261i) q^{83} +(-0.945431 - 2.47106i) q^{84} +(-2.70922 + 8.33813i) q^{85} +(-0.554740 + 5.27800i) q^{86} +(4.89421 - 8.47702i) q^{87} +(3.23375 - 0.736781i) q^{88} +(-7.87892 - 13.6467i) q^{89} +(1.30515 + 0.948248i) q^{90} +(0.496194 + 0.497288i) q^{91} +(-2.75121 - 8.46735i) q^{92} +(3.87054 + 1.72328i) q^{93} +(0.840611 + 7.99788i) q^{94} +(6.73181 + 1.43089i) q^{95} +(0.978148 - 0.207912i) q^{96} +(-14.3558 - 10.4301i) q^{97} +(2.86124 - 6.38853i) q^{98} +(3.00990 - 1.39302i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + q^{5} + 10 q^{6} + 9 q^{7} + 10 q^{8} + 5 q^{9}+O(q^{10}) \) 40 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + q^5 + 10 * q^6 + 9 * q^7 + 10 * q^8 + 5 * q^9	\( 40 q - 5 q^{2} + 5 q^{3} + 5 q^{4} + q^{5} + 10 q^{6} + 9 q^{7} + 10 q^{8} + 5 q^{9} + 4 q^{10} + 2 q^{11} - 20 q^{12} - 2 q^{13} - 3 q^{14} - 2 q^{15} + 5 q^{16} + 6 q^{17} - 5 q^{18} - q^{19} - 2 q^{20} - 2 q^{21} + 4 q^{22} - 20 q^{23} - 5 q^{24} + 16 q^{25} + 4 q^{26} - 10 q^{27} + 13 q^{28} + 16 q^{29} - q^{30} + 30 q^{31} + 20 q^{32} + 2 q^{33} + 32 q^{34} + 3 q^{35} - 10 q^{36} + 19 q^{37} + 6 q^{38} + q^{39} - q^{40} - 12 q^{41} + 11 q^{42} - 36 q^{43} - 3 q^{44} - 4 q^{45} + 10 q^{46} + 25 q^{47} - 10 q^{48} + 29 q^{49} + 12 q^{50} - 14 q^{51} - 4 q^{52} - 18 q^{53} + 20 q^{54} + 12 q^{55} - 4 q^{56} + 12 q^{57} + 8 q^{58} - 14 q^{59} + q^{60} + 35 q^{61} - 40 q^{62} + 3 q^{63} - 10 q^{64} - 2 q^{65} + 3 q^{66} - 24 q^{67} + 6 q^{68} - 40 q^{69} - 32 q^{70} - 34 q^{71} - 5 q^{72} - 39 q^{73} - 19 q^{74} + 6 q^{75} - 28 q^{76} - 31 q^{77} + 12 q^{78} - 17 q^{79} + q^{80} + 5 q^{81} + 4 q^{82} - 24 q^{83} + 3 q^{84} - 112 q^{85} + 7 q^{86} + 2 q^{87} - 2 q^{88} - 38 q^{89} + 2 q^{90} - 36 q^{91} - 40 q^{92} + 30 q^{93} - 10 q^{94} - 42 q^{95} - 5 q^{96} + 4 q^{97} - 50 q^{98} - 4 q^{99}+O(q^{100}) \) 40 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 + q^5 + 10 * q^6 + 9 * q^7 + 10 * q^8 + 5 * q^9 + 4 * q^10 + 2 * q^11 - 20 * q^12 - 2 * q^13 - 3 * q^14 - 2 * q^15 + 5 * q^16 + 6 * q^17 - 5 * q^18 - q^19 - 2 * q^20 - 2 * q^21 + 4 * q^22 - 20 * q^23 - 5 * q^24 + 16 * q^25 + 4 * q^26 - 10 * q^27 + 13 * q^28 + 16 * q^29 - q^30 + 30 * q^31 + 20 * q^32 + 2 * q^33 + 32 * q^34 + 3 * q^35 - 10 * q^36 + 19 * q^37 + 6 * q^38 + q^39 - q^40 - 12 * q^41 + 11 * q^42 - 36 * q^43 - 3 * q^44 - 4 * q^45 + 10 * q^46 + 25 * q^47 - 10 * q^48 + 29 * q^49 + 12 * q^50 - 14 * q^51 - 4 * q^52 - 18 * q^53 + 20 * q^54 + 12 * q^55 - 4 * q^56 + 12 * q^57 + 8 * q^58 - 14 * q^59 + q^60 + 35 * q^61 - 40 * q^62 + 3 * q^63 - 10 * q^64 - 2 * q^65 + 3 * q^66 - 24 * q^67 + 6 * q^68 - 40 * q^69 - 32 * q^70 - 34 * q^71 - 5 * q^72 - 39 * q^73 - 19 * q^74 + 6 * q^75 - 28 * q^76 - 31 * q^77 + 12 * q^78 - 17 * q^79 + q^80 + 5 * q^81 + 4 * q^82 - 24 * q^83 + 3 * q^84 - 112 * q^85 + 7 * q^86 + 2 * q^87 - 2 * q^88 - 38 * q^89 + 2 * q^90 - 36 * q^91 - 40 * q^92 + 30 * q^93 - 10 * q^94 - 42 * q^95 - 5 * q^96 + 4 * q^97 - 50 * q^98 - 4 * q^99

Introduction

L-functions

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