LMFDB - Embedded newform 378.2.w.b.121.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(25,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([10, 12]))

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

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

chi := DirichletCharacter("378.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.w (of order $9$, degree $6$, 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:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			121.4
Character	$\chi$	$=$	378.121
Dual form			378.2.w.b.25.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939693 + 0.342020i) q^{2} +(-1.25782 - 1.19075i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-1.38782 + 0.505123i) q^{5} +(-0.774703 - 1.54914i) q^{6} +(0.493387 + 2.59934i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.164223 + 2.99550i) q^{9} +O(q^{10})$	\(q+(0.939693 + 0.342020i) q^{2} +(-1.25782 - 1.19075i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-1.38782 + 0.505123i) q^{5} +(-0.774703 - 1.54914i) q^{6} +(0.493387 + 2.59934i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.164223 + 2.99550i) q^{9} -1.47688 q^{10} +(4.67947 + 1.70319i) q^{11} +(-0.198146 - 1.72068i) q^{12} +(0.0222706 - 0.126303i) q^{13} +(-0.425394 + 2.61133i) q^{14} +(2.34710 + 1.01719i) q^{15} +(0.173648 + 0.984808i) q^{16} +7.18871 q^{17} +(-0.870203 + 2.87102i) q^{18} -3.10211 q^{19} +(-1.38782 - 0.505123i) q^{20} +(2.47458 - 3.85700i) q^{21} +(3.81474 + 3.20095i) q^{22} +(0.366255 - 2.07714i) q^{23} +(0.402311 - 1.68468i) q^{24} +(-2.15934 + 1.81190i) q^{25} +(0.0641255 - 0.111069i) q^{26} +(3.36034 - 3.96335i) q^{27} +(-1.29287 + 2.30835i) q^{28} +(0.951657 + 5.39711i) q^{29} +(1.85765 + 1.75860i) q^{30} +(-3.32374 - 2.78895i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-3.85786 - 7.71439i) q^{33} +(6.75518 + 2.45868i) q^{34} +(-1.99772 - 3.35818i) q^{35} +(-1.79967 + 2.40025i) q^{36} +(-2.06010 - 3.56819i) q^{37} +(-2.91503 - 1.06098i) q^{38} +(-0.178407 + 0.132347i) q^{39} +(-1.13136 - 0.949322i) q^{40} +(-1.38763 + 7.86966i) q^{41} +(3.64451 - 2.77804i) q^{42} +(1.24289 - 1.04291i) q^{43} +(2.48989 + 4.31262i) q^{44} +(-1.74101 - 4.07425i) q^{45} +(1.05459 - 1.82660i) q^{46} +(-5.51169 + 4.62486i) q^{47} +(0.954243 - 1.44548i) q^{48} +(-6.51314 + 2.56496i) q^{49} +(-2.64882 + 0.964093i) q^{50} +(-9.04211 - 8.55997i) q^{51} +(0.0982460 - 0.0824382i) q^{52} +(0.480436 + 0.832140i) q^{53} +(4.51323 - 2.57503i) q^{54} -7.35456 q^{55} +(-2.00440 + 1.72696i) q^{56} +(3.90189 + 3.69384i) q^{57} +(-0.951657 + 5.39711i) q^{58} +(1.72189 - 9.76534i) q^{59} +(1.14415 + 2.28790i) q^{60} +(4.63674 - 3.89069i) q^{61} +(-2.16942 - 3.75754i) q^{62} +(-7.70530 + 1.90481i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.0328910 + 0.186534i) q^{65} +(-0.986724 - 8.56862i) q^{66} +(11.7030 - 4.25956i) q^{67} +(5.50687 + 4.62082i) q^{68} +(-2.93404 + 2.17654i) q^{69} +(-0.728675 - 3.83892i) q^{70} +(6.07951 - 10.5300i) q^{71} +(-2.51207 + 1.63997i) q^{72} +(-2.68503 + 4.65060i) q^{73} +(-0.715464 - 4.05760i) q^{74} +(4.87359 + 0.292191i) q^{75} +(-2.37635 - 1.99400i) q^{76} +(-2.11837 + 13.0039i) q^{77} +(-0.212914 + 0.0633469i) q^{78} +(-12.3212 - 4.48453i) q^{79} +(-0.738441 - 1.27902i) q^{80} +(-8.94606 + 0.983858i) q^{81} +(-3.99553 + 6.92046i) q^{82} +(-1.46630 - 8.31582i) q^{83} +(4.37487 - 1.36401i) q^{84} +(-9.97661 + 3.63119i) q^{85} +(1.52464 - 0.554922i) q^{86} +(5.22961 - 7.92178i) q^{87} +(0.864731 + 4.90413i) q^{88} +6.03880 q^{89} +(-0.242538 - 4.42400i) q^{90} +(0.339292 - 0.00442735i) q^{91} +(1.61573 - 1.35575i) q^{92} +(0.859722 + 7.46574i) q^{93} +(-6.76109 + 2.46084i) q^{94} +(4.30515 - 1.56695i) q^{95} +(1.39108 - 1.03194i) q^{96} +(0.558612 - 0.468731i) q^{97} +(-6.99762 + 0.182652i) q^{98} +(-4.33343 + 14.2971i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8}+O(q^{10}) $ 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8	$ 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8} - 12 q^{10} - 6 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} - 36 q^{19} + 18 q^{21} + 6 q^{22} - 6 q^{23} + 30 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} + 9 q^{35} - 3 q^{36} + 51 q^{39} - 6 q^{41} - 27 q^{42} - 24 q^{43} + 18 q^{45} + 27 q^{47} + 6 q^{48} - 69 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{52} - 15 q^{53} + 45 q^{54} - 72 q^{55} + 6 q^{56} + 57 q^{57} - 3 q^{58} + 15 q^{59} - 33 q^{60} - 18 q^{61} - 24 q^{62} - 12 q^{63} - 36 q^{64} - 90 q^{65} - 36 q^{66} - 66 q^{67} - 18 q^{68} - 39 q^{69} - 12 q^{70} + 12 q^{71} + 30 q^{73} + 9 q^{74} - 21 q^{75} - 87 q^{77} + 6 q^{78} - 45 q^{79} - 6 q^{80} - 24 q^{81} + 33 q^{82} + 18 q^{83} + 6 q^{84} + 51 q^{85} - 12 q^{86} - 18 q^{87} - 12 q^{88} + 72 q^{89} - 69 q^{90} - 30 q^{91} + 12 q^{92} - 48 q^{93} + 21 q^{95} + 48 q^{97} + 6 q^{98} + 90 q^{99}+O(q^{100}) $ 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8 - 12 * q^10 - 6 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 - 36 * q^19 + 18 * q^21 + 6 * q^22 - 6 * q^23 + 30 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 + 9 * q^35 - 3 * q^36 + 51 * q^39 - 6 * q^41 - 27 * q^42 - 24 * q^43 + 18 * q^45 + 27 * q^47 + 6 * q^48 - 69 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^52 - 15 * q^53 + 45 * q^54 - 72 * q^55 + 6 * q^56 + 57 * q^57 - 3 * q^58 + 15 * q^59 - 33 * q^60 - 18 * q^61 - 24 * q^62 - 12 * q^63 - 36 * q^64 - 90 * q^65 - 36 * q^66 - 66 * q^67 - 18 * q^68 - 39 * q^69 - 12 * q^70 + 12 * q^71 + 30 * q^73 + 9 * q^74 - 21 * q^75 - 87 * q^77 + 6 * q^78 - 45 * q^79 - 6 * q^80 - 24 * q^81 + 33 * q^82 + 18 * q^83 + 6 * q^84 + 51 * q^85 - 12 * q^86 - 18 * q^87 - 12 * q^88 + 72 * q^89 - 69 * q^90 - 30 * q^91 + 12 * q^92 - 48 * q^93 + 21 * q^95 + 48 * q^97 + 6 * q^98 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$2$	0.939693	+	0.342020i	0.664463	+	0.241845i
$3$	−1.25782	−	1.19075i	−0.726203	−	0.687481i
$3$	−1.25782	−	1.19075i	−0.726203	−	0.687481i
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	−1.38782	+	0.505123i	−0.620650	+	0.225898i	−0.633157	−	0.774024i	$-0.718241\pi$
$5$	−1.38782	+	0.505123i	−0.620650	+	0.225898i	0.0125067	+	0.999922i	$0.496019\pi$
$6$	−0.774703	−	1.54914i	−0.316271	−	0.632434i
$7$	0.493387	+	2.59934i	0.186483	+	0.982458i
$7$	0.493387	+	2.59934i	0.186483	+	0.982458i
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	0.164223	+	2.99550i	0.0547409	+	0.998501i
$10$	−1.47688			−0.467031
$11$	4.67947	+	1.70319i	1.41091	+	0.513530i	0.931398	−	0.364003i	$-0.118590\pi$
$11$	4.67947	+	1.70319i	1.41091	+	0.513530i	0.479515	+	0.877534i	$0.340813\pi$
$12$	−0.198146	−	1.72068i	−0.0571998	−	0.496717i
$13$	0.0222706	−	0.126303i	0.00617674	−	0.0350301i	−0.981564	−	0.191136i	$-0.938783\pi$
$13$	0.0222706	−	0.126303i	0.00617674	−	0.0350301i	0.987740	+	0.156106i	$0.0498940\pi$
$14$	−0.425394	+	2.61133i	−0.113691	+	0.697907i
$15$	2.34710	+	1.01719i	0.606018	+	0.262637i
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	7.18871			1.74352			0.871760	−	0.489934i	$-0.162979\pi$
$17$	7.18871			1.74352			0.871760	+	0.489934i	$0.162979\pi$
$18$	−0.870203	+	2.87102i	−0.205109	+	0.676706i
$19$	−3.10211			−0.711672			−0.355836	−	0.934548i	$-0.615804\pi$
$19$	−3.10211			−0.711672			−0.355836	+	0.934548i	$0.615804\pi$
$20$	−1.38782	−	0.505123i	−0.310325	−	0.112949i
$21$	2.47458	−	3.85700i	0.539997	−	0.841667i
$22$	3.81474	+	3.20095i	0.813305	+	0.682444i
$23$	0.366255	−	2.07714i	0.0763695	−	0.433113i	−0.922518	−	0.385954i	$-0.873872\pi$
$23$	0.366255	−	2.07714i	0.0763695	−	0.433113i	0.998887	−	0.0471586i	$-0.0150166\pi$
$24$	0.402311	−	1.68468i	0.0821214	−	0.343884i
$25$	−2.15934	+	1.81190i	−0.431868	+	0.362380i
$26$	0.0641255	−	0.111069i	0.0125761	−	0.0217824i
$27$	3.36034	−	3.96335i	0.646697	−	0.762747i
$28$	−1.29287	+	2.30835i	−0.244329	+	0.436238i
$29$	0.951657	+	5.39711i	0.176718	+	1.00222i	0.936142	+	0.351622i	$0.114370\pi$
$29$	0.951657	+	5.39711i	0.176718	+	1.00222i	−0.759424	+	0.650596i	$0.774519\pi$
$30$	1.85765	+	1.75860i	0.339159	+	0.321075i
$31$	−3.32374	−	2.78895i	−0.596961	−	0.500910i	0.293506	−	0.955957i	$-0.405178\pi$
$31$	−3.32374	−	2.78895i	−0.596961	−	0.500910i	−0.890467	+	0.455047i	$0.849622\pi$
$32$	−0.173648	+	0.984808i	−0.0306970	+	0.174091i
$33$	−3.85786	−	7.71439i	−0.671567	−	1.34290i
$34$	6.75518	+	2.45868i	1.15850	+	0.421661i
$35$	−1.99772	−	3.35818i	−0.337676	−	0.567636i
$36$	−1.79967	+	2.40025i	−0.299945	+	0.400041i
$37$	−2.06010	−	3.56819i	−0.338678	−	0.586607i	0.645506	−	0.763755i	$-0.276646\pi$
$37$	−2.06010	−	3.56819i	−0.338678	−	0.586607i	−0.984184	+	0.177148i	$0.943313\pi$
$38$	−2.91503	−	1.06098i	−0.472880	−	0.172114i
$39$	−0.178407	+	0.132347i	−0.0285680	+	0.0211925i
$40$	−1.13136	−	0.949322i	−0.178883	−	0.150101i
$41$	−1.38763	+	7.86966i	−0.216712	+	1.22903i	0.661199	+	0.750210i	$0.270048\pi$
$41$	−1.38763	+	7.86966i	−0.216712	+	1.22903i	−0.877911	+	0.478824i	$0.841063\pi$
$42$	3.64451	−	2.77804i	0.562361	−	0.428661i
$43$	1.24289	−	1.04291i	0.189540	−	0.159043i	−0.543080	−	0.839681i	$-0.682742\pi$
$43$	1.24289	−	1.04291i	0.189540	−	0.159043i	0.732620	+	0.680638i	$0.238297\pi$
$44$	2.48989	+	4.31262i	0.375366	+	0.650152i
$45$	−1.74101	−	4.07425i	−0.259534	−	0.607353i
$46$	1.05459	−	1.82660i	0.155491	−	0.269318i
$47$	−5.51169	+	4.62486i	−0.803963	+	0.674605i	−0.949159	−	0.314798i	$-0.898063\pi$
$47$	−5.51169	+	4.62486i	−0.803963	+	0.674605i	0.145196	+	0.989403i	$0.453619\pi$
$48$	0.954243	−	1.44548i	0.137733	−	0.208637i
$49$	−6.51314	+	2.56496i	−0.930448	+	0.366423i
$50$	−2.64882	+	0.964093i	−0.374600	+	0.136343i
$51$	−9.04211	−	8.55997i	−1.26615	−	1.19864i
$52$	0.0982460	−	0.0824382i	0.0136243	−	0.0114321i
$53$	0.480436	+	0.832140i	0.0659930	+	0.114303i	0.897134	−	0.441758i	$-0.145645\pi$
$53$	0.480436	+	0.832140i	0.0659930	+	0.114303i	−0.831141	+	0.556062i	$0.812312\pi$
$54$	4.51323	−	2.57503i	0.614173	−	0.350417i
$55$	−7.35456			−0.991689
$56$	−2.00440	+	1.72696i	−0.267849	+	0.230774i
$57$	3.90189	+	3.69384i	0.516818	+	0.489261i
$58$	−0.951657	+	5.39711i	−0.124959	+	0.708676i
$59$	1.72189	−	9.76534i	0.224171	−	1.27134i	−0.640091	−	0.768299i	$-0.721104\pi$
$59$	1.72189	−	9.76534i	0.224171	−	1.27134i	0.864263	−	0.503040i	$-0.167785\pi$
$60$	1.14415	+	2.28790i	0.147709	+	0.295366i
$61$	4.63674	−	3.89069i	0.593674	−	0.498152i	−0.295731	−	0.955271i	$-0.595563\pi$
$61$	4.63674	−	3.89069i	0.593674	−	0.498152i	0.889405	+	0.457120i	$0.151119\pi$
$62$	−2.16942	−	3.75754i	−0.275516	−	0.477208i
$63$	−7.70530	+	1.90481i	−0.970777	+	0.239984i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	0.0328910	+	0.186534i	0.00407963	+	0.0231367i
$66$	−0.986724	−	8.56862i	−0.121457	−	1.05472i
$67$	11.7030	−	4.25956i	1.42975	−	0.520388i	0.492892	−	0.870090i	$-0.335940\pi$
$67$	11.7030	−	4.25956i	1.42975	−	0.520388i	0.936861	+	0.349703i	$0.113717\pi$
$68$	5.50687	+	4.62082i	0.667807	+	0.560356i
$69$	−2.93404	+	2.17654i	−0.353216	+	0.262025i
$70$	−0.728675	−	3.83892i	−0.0870933	−	0.458839i
$71$	6.07951	−	10.5300i	0.721505	−	1.24968i	−0.238891	−	0.971046i	$-0.576784\pi$
$71$	6.07951	−	10.5300i	0.721505	−	1.24968i	0.960396	−	0.278637i	$-0.0898826\pi$
$72$	−2.51207	+	1.63997i	−0.296050	+	0.193273i
$73$	−2.68503	+	4.65060i	−0.314259	+	0.544312i	−0.979280	−	0.202513i	$-0.935089\pi$
$73$	−2.68503	+	4.65060i	−0.314259	+	0.544312i	0.665021	+	0.746825i	$0.268423\pi$
$74$	−0.715464	−	4.05760i	−0.0831710	−	0.471686i
$75$	4.87359	+	0.292191i	0.562753	+	0.0337393i
$76$	−2.37635	−	1.99400i	−0.272586	−	0.228727i
$77$	−2.11837	+	13.0039i	−0.241411	+	1.48193i
$78$	−0.212914	+	0.0633469i	−0.0241077	+	0.00717262i
$79$	−12.3212	−	4.48453i	−1.38624	−	0.504550i	−0.462175	−	0.886789i	$-0.652931\pi$
$79$	−12.3212	−	4.48453i	−1.38624	−	0.504550i	−0.924063	+	0.382239i	$0.875153\pi$
$80$	−0.738441	−	1.27902i	−0.0825602	−	0.142999i
$81$	−8.94606	+	0.983858i	−0.994007	+	0.109318i
$82$	−3.99553	+	6.92046i	−0.441232	+	0.764237i
$83$	−1.46630	−	8.31582i	−0.160948	−	0.912780i	−0.953145	−	0.302515i	$-0.902174\pi$
$83$	−1.46630	−	8.31582i	−0.160948	−	0.912780i	0.792197	−	0.610265i	$-0.208937\pi$
$84$	4.37487	−	1.36401i	0.477337	−	0.148826i
$85$	−9.97661	+	3.63119i	−1.08211	+	0.393858i
$86$	1.52464	−	0.554922i	0.164406	−	0.0598388i
$87$	5.22961	−	7.92178i	0.560673	−	0.849304i
$88$	0.864731	+	4.90413i	0.0921806	+	0.522782i
$89$	6.03880			0.640112			0.320056	−	0.947399i	$-0.396298\pi$
$89$	6.03880			0.640112			0.320056	+	0.947399i	$0.396298\pi$
$90$	−0.242538	−	4.42400i	−0.0255657	−	0.466331i
$91$	0.339292	−	0.00442735i	0.0355674	−	0.000464112i
$92$	1.61573	−	1.35575i	0.168451	−	0.141347i
$93$	0.859722	+	7.46574i	0.0891490	+	0.774161i
$94$	−6.76109	+	2.46084i	−0.697354	+	0.253816i
$95$	4.30515	−	1.56695i	0.441699	−	0.160765i
$96$	1.39108	−	1.03194i	0.141976	−	0.105322i
$97$	0.558612	−	0.468731i	0.0567185	−	0.0475925i	−0.613988	−	0.789316i	$-0.710436\pi$
$97$	0.558612	−	0.468731i	0.0567185	−	0.0475925i	0.670706	+	0.741723i	$0.265991\pi$
$98$	−6.99762	+	0.182652i	−0.706866	+	0.0184507i
$99$	−4.33343	+	14.2971i	−0.435526	+	1.43691i
$100$	−2.81882			−0.281882
$101$	−0.524545	−	2.97484i	−0.0521941	−	0.296008i	0.947526	−	0.319680i	$-0.103575\pi$
$101$	−0.524545	−	2.97484i	−0.0521941	−	0.296008i	−0.999720	+	0.0236721i	$0.992464\pi$
$102$	−5.56912	−	11.1363i	−0.551425	−	1.10266i
$103$	8.58581	−	3.12498i	0.845985	−	0.307913i	0.117583	−	0.993063i	$-0.462485\pi$
$103$	8.58581	−	3.12498i	0.845985	−	0.307913i	0.728402	+	0.685150i	$0.240263\pi$
$104$	0.120517	−	0.0438644i	0.0118176	−	0.00430126i
$105$	−1.48599	+	6.60278i	−0.145018	+	0.644365i
$106$	0.166854	+	0.946274i	0.0162063	+	0.0919103i
$107$	9.07986	−	15.7268i	0.877783	−	1.52036i	0.0240141	−	0.999712i	$-0.492355\pi$
$107$	9.07986	−	15.7268i	0.877783	−	1.52036i	0.853769	−	0.520653i	$-0.174311\pi$
$108$	5.12176	−	0.876121i	0.492841	−	0.0843048i
$109$	−7.17154	−	12.4215i	−0.686909	−	1.18976i	−0.972833	−	0.231509i	$-0.925634\pi$
$109$	−7.17154	−	12.4215i	−0.686909	−	1.18976i	0.285923	−	0.958252i	$-0.407700\pi$
$110$	−6.91102	−	2.51541i	−0.658940	−	0.239835i
$111$	−1.65760	+	6.94121i	−0.157332	+	0.658830i
$112$	−2.47417	+	0.937262i	−0.233788	+	0.0885630i
$113$	11.9541	+	10.0307i	1.12455	+	0.943606i	0.998825	−	0.0484600i	$-0.0154313\pi$
$113$	11.9541	+	10.0307i	1.12455	+	0.943606i	0.125720	+	0.992066i	$0.459876\pi$
$114$	2.40321	+	4.80560i	0.225081	+	0.450085i
$115$	0.540916	+	3.06769i	0.0504407	+	0.286063i
$116$	−2.74019	+	4.74614i	−0.254420	+	0.440668i
$117$	0.381997	+	0.0459698i	0.0353156	+	0.00424991i
$118$	4.95799	−	8.58750i	0.456420	−	0.790543i
$119$	3.54682	+	18.6859i	0.325136	+	1.71293i
$120$	0.292638	+	2.54124i	0.0267141	+	0.231983i
$121$	10.5701	+	8.86936i	0.960917	+	0.806306i
$122$	5.68781	−	2.07019i	0.514950	−	0.187426i
$123$	11.1162	−	8.24629i	1.00231	−	0.743543i
$124$	−0.753430	−	4.27292i	−0.0676600	−	0.383719i
$125$	5.77374	−	10.0004i	0.516419	−	0.894464i
$126$	−7.89210	−	0.845430i	−0.703084	−	0.0753169i
$127$	−3.04941	−	5.28174i	−0.270592	−	0.468678i	0.698422	−	0.715686i	$-0.253886\pi$
$127$	−3.04941	−	5.28174i	−0.270592	−	0.468678i	−0.969013	+	0.247008i	$0.920553\pi$
$128$	−0.766044	+	0.642788i	−0.0677094	+	0.0568149i
$129$	−2.80519	−	0.168182i	−0.246983	−	0.0148076i
$130$	−0.0328910	+	0.186534i	−0.00288473	+	0.0163601i
$131$	1.18049	−	6.69490i	0.103140	−	0.584936i	−0.888807	−	0.458282i	$-0.848465\pi$
$131$	1.18049	−	6.69490i	0.103140	−	0.584936i	0.991947	−	0.126654i	$-0.0404238\pi$
$132$	2.00342	−	8.38935i	0.174376	−	0.730199i
$133$	−1.53054	−	8.06343i	−0.132715	−	0.699188i
$134$	12.4541			1.07587
$135$	−2.66154	+	7.19778i	−0.229069	+	0.619487i
$136$	3.59436	+	6.22561i	0.308214	+	0.533842i
$137$	−2.20497	+	1.85019i	−0.188383	+	0.158072i	−0.732102	−	0.681195i	$-0.761460\pi$
$137$	−2.20497	+	1.85019i	−0.188383	+	0.158072i	0.543718	+	0.839268i	$0.317016\pi$
$138$	−3.50151	+	1.04178i	−0.298069	+	0.0886825i
$139$	−17.0287	+	6.19796i	−1.44436	+	0.525704i	−0.941010	−	0.338379i	$-0.890121\pi$
$139$	−17.0287	+	6.19796i	−1.44436	+	0.525704i	−0.503350	+	0.864083i	$0.667899\pi$
$140$	0.628257	−	3.85663i	0.0530974	−	0.325944i
$141$	12.4398	+	0.745815i	1.04762	+	0.0628089i
$142$	9.31435	−	7.81567i	0.781643	−	0.655876i
$143$	0.319331	−	0.553098i	0.0267038	−	0.0462524i
$144$	−2.92148	+	0.681891i	−0.243456	+	0.0568243i
$145$	−4.04693	−	7.00949i	−0.336079	−	0.582107i
$146$	−4.11370	+	3.45181i	−0.340452	+	0.285673i
$147$	11.2466	+	4.52927i	0.927603	+	0.373568i
$148$	0.715464	−	4.05760i	0.0588108	−	0.333533i
$149$	−10.4666	−	8.78253i	−0.857458	−	0.719493i	0.103961	−	0.994581i	$-0.466848\pi$
$149$	−10.4666	−	8.78253i	−0.857458	−	0.719493i	−0.961419	+	0.275089i	$0.911293\pi$
$150$	4.47974	+	1.94143i	0.365769	+	0.158517i
$151$	11.7279	+	4.26860i	0.954401	+	0.347373i	0.771837	−	0.635821i	$-0.219338\pi$
$151$	11.7279	+	4.26860i	0.954401	+	0.347373i	0.182564	+	0.983194i	$0.441560\pi$
$152$	−1.55105	−	2.68650i	−0.125807	−	0.217904i
$153$	1.18055	+	21.5338i	0.0954418	+	1.74090i
$154$	−6.43820	+	11.4951i	−0.518805	+	0.926302i
$155$	6.02150	+	2.19165i	0.483658	+	0.176037i
$156$	−0.221739	−	0.0132942i	−0.0177533	−	0.00106438i
$157$	−0.679350	+	3.85279i	−0.0542181	+	0.307486i	−0.999842	−	0.0177761i	$-0.994341\pi$
$157$	−0.679350	+	3.85279i	−0.0542181	+	0.307486i	0.945624	+	0.325262i	$0.105452\pi$
$158$	−10.0443	−	8.42817i	−0.799082	−	0.670509i
$159$	0.386569	−	1.61876i	0.0306569	−	0.128376i
$160$	−0.256458	−	1.45445i	−0.0202748	−	0.114984i
$161$	5.57989	−	0.0728109i	0.439757	−	0.00573830i
$162$	−8.74305	−	2.13521i	−0.686919	−	0.167758i
$163$	−8.43985	+	14.6183i	−0.661060	+	1.14499i	0.319277	+	0.947661i	$0.396560\pi$
$163$	−8.43985	+	14.6183i	−0.661060	+	1.14499i	−0.980337	+	0.197329i	$0.936773\pi$
$164$	−6.12151	+	5.13655i	−0.478009	+	0.401097i
$165$	9.25071	+	8.75745i	0.720167	+	0.681767i
$166$	1.46630	−	8.31582i	0.113807	−	0.645433i
$167$	11.7113	+	9.82697i	0.906250	+	0.760434i	0.971402	−	0.237442i	$-0.0763088\pi$
$167$	11.7113	+	9.82697i	0.906250	+	0.760434i	−0.0651521	+	0.997875i	$0.520753\pi$
$168$	4.57755	+	0.214543i	0.353166	+	0.0165524i
$169$	12.2005	+	4.44064i	0.938504	+	0.341587i
$170$	−10.6169			−0.814278
$171$	−0.509436	−	9.29236i	−0.0389575	−	0.710605i
$172$	1.62248			0.123713
$173$	1.72669	+	9.79255i	0.131278	+	0.744514i	0.977380	+	0.211492i	$0.0678324\pi$
$173$	1.72669	+	9.79255i	0.131278	+	0.744514i	−0.846102	+	0.533021i	$0.821057\pi$
$174$	7.62363	−	5.65541i	0.577946	−	0.428736i
$175$	−5.77514	−	4.71889i	−0.436560	−	0.356715i
$176$	−0.864731	+	4.90413i	−0.0651815	+	0.369663i
$177$	−13.7939	+	10.2327i	−1.03681	+	0.769137i
$178$	5.67462	+	2.06539i	0.425330	+	0.154808i
$179$	−15.1992			−1.13604			−0.568019	−	0.823015i	$-0.692290\pi$
$179$	−15.1992			−1.13604			−0.568019	+	0.823015i	$0.692290\pi$
$180$	1.28519	−	4.24016i	0.0957922	−	0.316043i
$181$	−5.62905	−	9.74980i	−0.418404	−	0.724697i	0.577375	−	0.816479i	$-0.304077\pi$
$181$	−5.62905	−	9.74980i	−0.418404	−	0.724697i	−0.995779	+	0.0917821i	$0.970744\pi$
$182$	0.320344	+	0.111884i	0.0237455	+	0.00829341i
$183$	−10.4650	−	0.627421i	−0.773597	−	0.0463803i
$184$	1.98198	−	0.721382i	0.146114	−	0.0531810i
$185$	4.66141	+	3.91139i	0.342714	+	0.287571i
$186$	−1.74556	+	7.30954i	−0.127991	+	0.535962i
$187$	33.6394	+	12.2437i	2.45995	+	0.895350i
$188$	−7.19501			−0.524750
$189$	11.9600	+	6.77919i	0.869965	+	0.493113i
$190$	4.58145			0.332373
$191$	−24.2282	−	8.81834i	−1.75309	−	0.638073i	−0.753283	−	0.657696i	$-0.771531\pi$
$191$	−24.2282	−	8.81834i	−1.75309	−	0.638073i	−0.999807	+	0.0196235i	$0.993753\pi$
$192$	1.66013	−	0.493928i	0.119810	−	0.0356462i
$193$	−2.38990	−	2.00536i	−0.172029	−	0.144349i	0.552708	−	0.833375i	$-0.313594\pi$
$193$	−2.38990	−	2.00536i	−0.172029	−	0.144349i	−0.724737	+	0.689026i	$0.758039\pi$
$194$	0.685240	−	0.249407i	0.0491973	−	0.0179064i
$195$	0.180745	−	0.273791i	0.0129434	−	0.0196066i
$196$	−6.63808	−	2.22169i	−0.474149	−	0.158692i
$197$	−3.60060	−	6.23641i	−0.256532	−	0.444326i	0.708779	−	0.705431i	$-0.249247\pi$
$197$	−3.60060	−	6.23641i	−0.256532	−	0.444326i	−0.965310	+	0.261105i	$0.915913\pi$
$198$	−8.96197	+	11.9527i	−0.636900	+	0.849443i
$199$	−15.8574			−1.12410			−0.562049	−	0.827104i	$-0.689987\pi$
$199$	−15.8574			−1.12410			−0.562049	+	0.827104i	$0.689987\pi$
$200$	−2.64882	−	0.964093i	−0.187300	−	0.0681717i
$201$	−19.7924	−	8.57765i	−1.39605	−	0.605021i
$202$	0.524545	−	2.97484i	0.0369068	−	0.209309i
$203$	−13.5594	+	5.13655i	−0.951683	+	0.360515i
$204$	−1.42441	−	12.3695i	−0.0997289	−	0.866036i
$205$	−2.04937	−	11.6226i	−0.143134	−	0.811755i
$206$	9.13683			0.636593
$207$	6.28221	+	0.756005i	0.436644	+	0.0525460i
$208$	0.128251			0.00889261
$209$	−14.5162	−	5.28347i	−1.00411	−	0.365465i
$210$	−3.65466	+	5.69634i	−0.252195	+	0.393085i
$211$	13.5243	+	11.3483i	0.931054	+	0.781247i	0.976006	−	0.217742i	$-0.0698691\pi$
$211$	13.5243	+	11.3483i	0.931054	+	0.781247i	−0.0449521	+	0.998989i	$0.514314\pi$
$212$	−0.166854	+	0.946274i	−0.0114596	+	0.0649904i
$213$	−20.1856	+	6.00569i	−1.38309	+	0.411503i
$214$	13.9111	−	11.6728i	0.950946	−	0.797939i
$215$	−1.19811	+	2.07519i	−0.0817103	+	0.141526i
$216$	5.11253	+	0.928460i	0.347864	+	0.0631737i
$217$	5.60953	−	10.0156i	0.380800	−	0.679900i
$218$	−2.49065	−	14.1252i	−0.168688	−	0.956678i
$219$	8.91500	−	2.65242i	0.602420	−	0.179234i
$220$	−5.63392	−	4.72742i	−0.379839	−	0.318723i
$221$	0.160097	−	0.907954i	0.0107693	−	0.0610756i
$222$	−3.93167	+	5.95567i	−0.263876	+	0.399718i
$223$	−7.32614	−	2.66650i	−0.490594	−	0.178562i	0.0848644	−	0.996393i	$-0.472954\pi$
$223$	−7.32614	−	2.66650i	−0.490594	−	0.178562i	−0.575459	+	0.817831i	$0.695177\pi$
$224$	−2.64553	+	0.0345210i	−0.176762	+	0.00230653i
$225$	−5.78217	−	6.17075i	−0.385478	−	0.411384i
$226$	7.80247	+	13.5143i	0.519013	+	0.898957i
$227$	8.54087	+	3.10862i	0.566878	+	0.206327i	0.609530	−	0.792763i	$-0.291358\pi$
$227$	8.54087	+	3.10862i	0.566878	+	0.206327i	−0.0426518	+	0.999090i	$0.513581\pi$
$228$	0.614670	+	5.33773i	0.0407075	+	0.353500i
$229$	21.8472	+	18.3320i	1.44371	+	1.21141i	0.937017	+	0.349285i	$0.113575\pi$
$229$	21.8472	+	18.3320i	1.44371	+	1.21141i	0.506690	+	0.862129i	$0.330869\pi$
$230$	−0.540916	+	3.06769i	−0.0356669	+	0.202277i
$231$	18.1489	−	13.8341i	1.19411	−	0.910215i
$232$	−4.19821	+	3.52272i	−0.275626	+	0.231278i
$233$	−2.37481	−	4.11329i	−0.155579	−	0.269471i	0.777691	−	0.628647i	$-0.216391\pi$
$233$	−2.37481	−	4.11329i	−0.155579	−	0.269471i	−0.933270	+	0.359176i	$0.883058\pi$
$234$	0.343237	+	0.173848i	0.0224381	+	0.0113648i
$235$	5.31309	−	9.20254i	0.346588	−	0.600307i
$236$	7.59609	−	6.37387i	0.494463	−	0.414904i
$237$	10.1578	+	20.3122i	0.659822	+	1.31942i
$238$	−3.05804	+	18.7721i	−0.198223	+	1.21681i
$239$	8.82413	−	3.21172i	0.570786	−	0.207749i	−0.0404719	−	0.999181i	$-0.512886\pi$
$239$	8.82413	−	3.21172i	0.570786	−	0.207749i	0.611258	+	0.791432i	$0.290664\pi$
$240$	−0.594166	+	2.48807i	−0.0383532	+	0.160604i
$241$	−22.1346	+	18.5731i	−1.42581	+	1.19640i	−0.477679	+	0.878535i	$0.658522\pi$
$241$	−22.1346	+	18.5731i	−1.42581	+	1.19640i	−0.948136	+	0.317866i	$0.897034\pi$
$242$	6.89914	+	11.9497i	0.443493	+	0.768153i
$243$	12.4241	+	9.41502i	0.797004	+	0.603974i
$244$	6.05284			0.387493
$245$	7.74341	−	6.84963i	0.494708	−	0.437607i
$246$	13.2662	−	3.94701i	0.845822	−	0.251652i
$247$	−0.0690856	+	0.391804i	−0.00439581	+	0.0249299i
$248$	0.753430	−	4.27292i	0.0478429	−	0.271330i
$249$	−8.05773	+	12.2058i	−0.510638	+	0.773512i
$250$	8.84588	−	7.42257i	0.559463	−	0.469445i
$251$	8.57593	+	14.8539i	0.541308	+	0.937573i	0.998829	+	0.0483742i	$0.0154040\pi$
$251$	8.57593	+	14.8539i	0.541308	+	0.937573i	−0.457521	+	0.889199i	$0.651263\pi$
$252$	−7.12699	−	3.49370i	−0.448958	−	0.220083i
$253$	5.25163	−	9.09609i	0.330167	−	0.571866i
$254$	−1.05905	−	6.00617i	−0.0664507	−	0.376861i
$255$	16.8726	+	7.31228i	1.05660	+	0.457913i
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	16.4863	+	13.8337i	1.02839	+	0.862920i	0.990658	−	0.136368i	$-0.0435430\pi$
$257$	16.4863	+	13.8337i	1.02839	+	0.862920i	0.0377296	+	0.999288i	$0.487987\pi$
$258$	−2.57849	−	1.11747i	−0.160530	−	0.0695707i
$259$	8.25852	−	7.11539i	0.513159	−	0.442129i
$260$	−0.0947059	+	0.164035i	−0.00587341	+	0.0101730i
$261$	−16.0108	+	3.73702i	−0.991042	+	0.231316i
$262$	3.39909	−	5.88739i	0.209996	−	0.363724i
$263$	−1.81815	−	10.3112i	−0.112112	−	0.635818i	−0.988140	−	0.153558i	$-0.950927\pi$
$263$	−1.81815	−	10.3112i	−0.112112	−	0.635818i	0.876028	−	0.482261i	$-0.160184\pi$
$264$	4.75193	−	7.19820i	0.292461	−	0.443018i
$265$	−1.08709	−	0.912177i	−0.0667794	−	0.0560346i
$266$	1.31962	−	8.10062i	0.0809110	−	0.496681i
$267$	−7.59572	−	7.19071i	−0.464851	−	0.440064i
$268$	11.7030	+	4.25956i	0.714877	+	0.260194i
$269$	−1.08274	−	1.87535i	−0.0660156	−	0.114342i	0.831128	−	0.556080i	$-0.187695\pi$
$269$	−1.08274	−	1.87535i	−0.0660156	−	0.114342i	−0.897144	+	0.441738i	$0.854362\pi$
$270$	−4.96282	+	5.85340i	−0.302028	+	0.356227i
$271$	5.46952	−	9.47348i	0.332249	−	0.575473i	−0.650703	−	0.759332i	$-0.725526\pi$
$271$	5.46952	−	9.47348i	0.332249	−	0.575473i	0.982953	+	0.183859i	$0.0588591\pi$
$272$	1.24831	+	7.07950i	0.0756897	+	0.429258i
$273$	−0.432040	−	0.398443i	−0.0261482	−	0.0241149i
$274$	−2.70480	+	0.984466i	−0.163403	+	0.0594738i
$275$	−13.1906	+	4.80098i	−0.795422	+	0.289510i
$276$	−3.64666	−	0.218632i	−0.219503	−	0.0131601i
$277$	−1.83518	−	10.4078i	−0.110265	−	0.625346i	−0.988986	−	0.148009i	$-0.952713\pi$
$277$	−1.83518	−	10.4078i	−0.110265	−	0.625346i	0.878721	−	0.477336i	$-0.158398\pi$
$278$	−18.1216			−1.08686
$279$	7.80847	−	10.4143i	0.467481	−	0.623486i
$280$	1.90941	−	3.40917i	0.114109	−	0.203737i
$281$	−0.458484	+	0.384713i	−0.0273508	+	0.0229501i	−0.656361	−	0.754447i	$-0.727905\pi$
$281$	−0.458484	+	0.384713i	−0.0273508	+	0.0229501i	0.629010	+	0.777397i	$0.283461\pi$
$282$	11.4345	+	4.95549i	0.680914	+	0.295095i
$283$	22.5248	−	8.19834i	1.33896	−	0.487341i	0.429474	−	0.903079i	$-0.358699\pi$
$283$	22.5248	−	8.19834i	1.33896	−	0.487341i	0.909484	+	0.415738i	$0.136477\pi$
$284$	11.4257	−	4.15863i	0.677993	−	0.246769i
$285$	−7.28095	−	3.15543i	−0.431286	−	0.186911i
$286$	0.489244	−	0.410525i	0.0289296	−	0.0242748i
$287$	−21.1406	+	0.275859i	−1.24789	+	0.0162834i
$288$	−2.97851	−	0.358436i	−0.175510	−	0.0211210i
$289$	34.6776			2.03986
$290$	−1.40548	−	7.97090i	−0.0825329	−	0.468067i
$291$	−1.26078	−	0.0755886i	−0.0739080	−	0.00443108i
$292$	−5.04620	+	1.83667i	−0.295307	+	0.107483i
$293$	−8.68671	+	3.16170i	−0.507483	+	0.184709i	−0.583057	−	0.812432i	$-0.698143\pi$
$293$	−8.68671	+	3.16170i	−0.507483	+	0.184709i	0.0755737	+	0.997140i	$0.475921\pi$
$294$	9.01924	+	8.10268i	0.526013	+	0.472558i
$295$	2.54303	+	14.4223i	0.148061	+	0.839696i
$296$	2.06010	−	3.56819i	0.119741	−	0.207397i
$297$	22.4749	−	12.8231i	1.30413	−	0.744071i
$298$	−6.83159	−	11.8327i	−0.395744	−	0.685448i
$299$	−0.254191	−	0.0925180i	−0.0147002	−	0.00535045i
$300$	3.54557	+	3.35651i	0.204703	+	0.193788i
$301$	3.32411	+	2.71615i	0.191599	+	0.156556i
$302$	9.56065	+	8.02234i	0.550153	+	0.461634i
$303$	−2.88251	+	4.36642i	−0.165596	+	0.250844i
$304$	−0.538675	−	3.05498i	−0.0308951	−	0.175215i
$305$	−4.46966	+	7.74168i	−0.255932	+	0.443288i
$306$	−6.25564	+	20.6389i	−0.357611	+	1.17985i
$307$	11.7241	−	20.3067i	0.669127	−	1.15896i	−0.309022	−	0.951055i	$-0.600002\pi$
$307$	11.7241	−	20.3067i	0.669127	−	1.15896i	0.978149	−	0.207907i	$-0.0666652\pi$
$308$	−9.98149	+	8.59987i	−0.568748	+	0.490023i
$309$	−14.5205	−	6.29291i	−0.826041	−	0.357991i
$310$	4.90877	+	4.11895i	0.278799	+	0.233941i
$311$	−19.4928	+	7.09478i	−1.10533	+	0.402308i	−0.829279	−	0.558834i	$-0.811249\pi$
$311$	−19.4928	+	7.09478i	−1.10533	+	0.402308i	−0.276053	+	0.961142i	$0.589027\pi$
$312$	−0.203820	−	0.0883317i	−0.0115390	−	0.00500080i
$313$	−2.40149	−	13.6195i	−0.135740	−	0.769821i	−0.974341	−	0.225075i	$-0.927737\pi$
$313$	−2.40149	−	13.6195i	−0.135740	−	0.769821i	0.838601	−	0.544746i	$-0.183374\pi$
$314$	−1.95611	+	3.38808i	−0.110390	+	0.191201i
$315$	9.73137	−	6.53566i	0.548301	−	0.368243i
$316$	−6.55595	−	11.3552i	−0.368801	−	0.638782i
$317$	12.9395	−	10.8575i	0.726754	−	0.609819i	−0.202490	−	0.979284i	$-0.564904\pi$
$317$	12.9395	−	10.8575i	0.726754	−	0.609819i	0.929245	+	0.369465i	$0.120459\pi$
$318$	0.916905	−	1.38892i	0.0514175	−	0.0778870i
$319$	−4.73905	+	26.8765i	−0.265336	+	1.50479i
$320$	0.256458	−	1.45445i	0.0143364	−	0.0813060i
$321$	−30.1475	+	8.96960i	−1.68267	+	0.500634i
$322$	5.26828	+	1.84001i	0.293590	+	0.102540i
$323$	−22.3001			−1.24081
$324$	−7.48549	−	4.99674i	−0.415861	−	0.277597i
$325$	0.180758	+	0.313082i	0.0100267	+	0.0173667i
$326$	−12.9306	+	10.8501i	−0.716160	+	0.600930i
$327$	−5.77038	+	24.1635i	−0.319103	+	1.33625i
$328$	−7.50914	+	2.73310i	−0.414623	+	0.150910i
$329$	−14.7410	−	12.0449i	−0.812697	−	0.664058i
$330$	5.69760	+	11.3932i	0.313643	+	0.627177i
$331$	−7.34641	+	6.16437i	−0.403795	+	0.338825i	−0.821958	−	0.569547i	$-0.807118\pi$
$331$	−7.34641	+	6.16437i	−0.403795	+	0.338825i	0.418163	+	0.908372i	$0.362674\pi$
$332$	4.22205	−	7.31281i	0.231715	−	0.401343i
$333$	10.3502	−	6.75700i	0.567188	−	0.370281i
$334$	7.64403	+	13.2398i	0.418263	+	0.724452i
$335$	−14.0900	+	11.8230i	−0.769822	+	0.645957i
$336$	4.22811	+	1.76722i	0.230662	+	0.0964097i
$337$	1.60895	−	9.12481i	0.0876451	−	0.497060i	−0.909109	−	0.416558i	$-0.863236\pi$
$337$	1.60895	−	9.12481i	0.0876451	−	0.497060i	0.996754	−	0.0805024i	$-0.0256525\pi$
$338$	9.94598	+	8.34567i	0.540990	+	0.453944i
$339$	−3.09206	−	26.8511i	−0.167937	−	1.45835i
$340$	−9.97661	−	3.63119i	−0.541057	−	0.196929i
$341$	−10.8032	−	18.7117i	−0.585028	−	1.01330i
$342$	2.69946	−	8.90620i	0.145970	−	0.481592i
$343$	−9.88071	−	15.6643i	−0.533508	−	0.845795i
$344$	1.52464	+	0.554922i	0.0822029	+	0.0299194i
$345$	2.97248	−	4.50269i	0.160033	−	0.242417i
$346$	−1.72669	+	9.79255i	−0.0928275	+	0.526451i
$347$	−17.9880	−	15.0938i	−0.965649	−	0.810276i	0.0162138	−	0.999869i	$-0.494839\pi$
$347$	−17.9880	−	15.0938i	−0.965649	−	0.810276i	−0.981863	+	0.189593i	$0.939283\pi$
$348$	9.09814	−	2.70691i	0.487711	−	0.145106i
$349$	−3.13495	−	17.7792i	−0.167810	−	0.951697i	−0.946120	−	0.323817i	$-0.895034\pi$
$349$	−3.13495	−	17.7792i	−0.167810	−	0.951697i	0.778310	−	0.627880i	$-0.216077\pi$
$350$	−3.81290	−	6.40952i	−0.203808	−	0.342603i
$351$	−0.425745	−	0.512685i	−0.0227246	−	0.0273651i
$352$	−2.48989	+	4.31262i	−0.132712	+	0.229864i
$353$	−1.25490	+	1.05299i	−0.0667917	+	0.0560449i	−0.675572	−	0.737294i	$-0.736103\pi$
$353$	−1.25490	+	1.05299i	−0.0667917	+	0.0560449i	0.608781	+	0.793339i	$0.291659\pi$
$354$	−16.4618	+	4.89779i	−0.874937	+	0.260315i
$355$	−3.11828	+	17.6846i	−0.165501	+	0.938602i
$356$	4.62599	+	3.88167i	0.245177	+	0.205728i
$357$	17.7890	−	27.7269i	0.941494	−	1.46746i
$358$	−14.2825	−	5.19842i	−0.754856	−	0.274745i
$359$	15.4242			0.814058			0.407029	−	0.913415i	$-0.366565\pi$
$359$	15.4242			0.814058			0.407029	+	0.913415i	$0.366565\pi$
$360$	2.65790	−	3.54488i	0.140084	−	0.186832i
$361$	−9.37694			−0.493523
$362$	−1.95495	−	11.0871i	−0.102750	−	0.582723i
$363$	−2.73407	−	23.7424i	−0.143502	−	1.24615i
$364$	0.262758	+	0.214701i	0.0137723	+	0.0112534i
$365$	1.37719	−	7.81045i	0.0720856	−	0.408818i
$366$	−9.61932	−	4.16883i	−0.502810	−	0.217908i
$367$	−3.02098	−	1.09955i	−0.157694	−	0.0573958i	0.261967	−	0.965077i	$-0.415629\pi$
$367$	−3.02098	−	1.09955i	−0.157694	−	0.0573958i	−0.419661	+	0.907681i	$0.637851\pi$
$368$	2.10918			0.109949
$369$	−23.8015	−	2.86428i	−1.23905	−	0.149108i
$370$	3.04252	+	5.26980i	0.158173	+	0.273964i
$371$	−1.92597	+	1.65938i	−0.0999915	+	0.0861509i
$372$	−4.14030	+	6.27171i	−0.214665	+	0.325173i
$373$	27.7582	−	10.1032i	1.43726	−	0.523122i	0.498261	−	0.867027i	$-0.333972\pi$
$373$	27.7582	−	10.1032i	1.43726	−	0.523122i	0.939004	+	0.343906i	$0.111750\pi$
$374$	27.4231	+	23.0107i	1.41801	+	1.18985i
$375$	−19.1703	+	5.70363i	−0.989951	+	0.294534i
$376$	−6.76109	−	2.46084i	−0.348677	−	0.126908i
$377$	0.702864			0.0361993
$378$	8.92015	+	10.4609i	0.458803	+	0.538052i
$379$	−12.2076			−0.627063			−0.313532	−	0.949578i	$-0.601512\pi$
$379$	−12.2076			−0.627063			−0.313532	+	0.949578i	$0.601512\pi$
$380$	4.30515	+	1.56695i	0.220850	+	0.0803827i
$381$	−2.45362	+	10.2746i	−0.125703	+	0.526382i
$382$	−19.7510	−	16.5731i	−1.01055	−	0.847952i
$383$	−22.0326	+	8.01920i	−1.12581	+	0.409762i	−0.836770	−	0.547555i	$-0.815559\pi$
$383$	−22.0326	+	8.01920i	−1.12581	+	0.409762i	−0.289042	+	0.957316i	$0.593337\pi$
$384$	1.72895	+	0.103657i	0.0882299	+	0.00528974i
$385$	−3.62865	−	19.1170i	−0.184933	−	0.974293i
$386$	−1.55990	−	2.70182i	−0.0793966	−	0.137519i
$387$	3.32816	+	3.55182i	0.169180	+	0.180549i
$388$	0.729217			0.0370204
$389$	15.2909	+	5.56545i	0.775282	+	0.282179i	0.699204	−	0.714922i	$-0.253538\pi$
$389$	15.2909	+	5.56545i	0.775282	+	0.282179i	0.0760778	+	0.997102i	$0.475760\pi$
$390$	0.263487	−	0.195461i	0.0133422	−	0.00989757i
$391$	2.63290	−	14.9319i	0.133152	−	0.755140i
$392$	−5.47789	−	4.35806i	−0.276675	−	0.220115i
$393$	−9.45680	+	7.01530i	−0.477032	+	0.353875i
$394$	−1.25047	−	7.09179i	−0.0629980	−	0.357279i
$395$	19.3647			0.974346
$396$	−12.5096	+	8.16671i	−0.628630	+	0.410393i
$397$	−17.4435			−0.875463			−0.437732	−	0.899106i	$-0.644218\pi$
$397$	−17.4435			−0.875463			−0.437732	+	0.899106i	$0.644218\pi$
$398$	−14.9010	−	5.42354i	−0.746922	−	0.271857i
$399$	−7.67639	+	11.9648i	−0.384300	+	0.598991i
$400$	−2.15934	−	1.81190i	−0.107967	−	0.0905951i
$401$	0.667691	−	3.78667i	0.0333429	−	0.189097i	−0.963587	−	0.267395i	$-0.913837\pi$
$401$	0.667691	−	3.78667i	0.0333429	−	0.189097i	0.996930	+	0.0782975i	$0.0249484\pi$
$402$	−15.6650	−	14.8297i	−0.781301	−	0.739641i
$403$	−0.426273	+	0.357686i	−0.0212342	+	0.0178176i
$404$	1.51037	−	2.61603i	0.0751435	−	0.130152i
$405$	11.9185	−	5.88428i	0.592236	−	0.292392i
$406$	−14.4985	+	0.189188i	−0.719547	+	0.00938923i
$407$	−3.56286	−	20.2060i	−0.176604	−	1.00157i
$408$	2.89210	−	12.1107i	0.143180	−	0.599568i
$409$	−25.4160	−	21.3265i	−1.25674	−	1.05453i	−0.996021	−	0.0891150i	$-0.971596\pi$
$409$	−25.4160	−	21.3265i	−1.25674	−	1.05453i	−0.260718	−	0.965415i	$-0.583959\pi$
$410$	2.04937	−	11.6226i	0.101211	−	0.573997i
$411$	4.97657	+	0.298366i	0.245476	+	0.0147173i
$412$	8.58581	+	3.12498i	0.422993	+	0.153957i
$413$	26.2330	−	0.342309i	1.29084	−	0.0168439i
$414$	5.64478	+	2.85906i	0.277426	+	0.140515i
$415$	6.23548	+	10.8002i	0.306087	+	0.530159i
$416$	0.120517	+	0.0438644i	0.00590881	+	0.00215063i
$417$	28.7993	+	12.4811i	1.41031	+	0.611202i
$418$	−11.8337	−	9.92967i	−0.578806	−	0.485676i
$419$	2.08673	−	11.8344i	0.101943	−	0.578150i	−0.890454	−	0.455074i	$-0.849613\pi$
$419$	2.08673	−	11.8344i	0.101943	−	0.578150i	0.992397	−	0.123076i	$-0.0392760\pi$
$420$	−5.38252	+	4.10284i	−0.262640	+	0.200198i
$421$	−25.1466	+	21.1005i	−1.22557	+	1.02838i	−0.227056	+	0.973882i	$0.572910\pi$
$421$	−25.1466	+	21.1005i	−1.22557	+	1.02838i	−0.998514	+	0.0544942i	$0.982645\pi$
$422$	8.82739	+	15.2895i	0.429711	+	0.744281i
$423$	−14.7589	−	15.7508i	−0.717603	−	0.765829i
$424$	−0.480436	+	0.832140i	−0.0233320	+	0.0404123i
$425$	−15.5229	+	13.0252i	−0.752970	+	0.631817i
$426$	−21.0223	−	1.26037i	−1.01853	−	0.0610652i
$427$	12.4009	+	10.1329i	0.600123	+	0.490363i
$428$	17.0645	−	6.21099i	0.824846	−	0.300219i
$429$	−1.06026	+	0.315454i	−0.0511900	+	0.0152303i
$430$	−1.83561	+	1.54026i	−0.0885209	+	0.0742779i
$431$	−5.20063	−	9.00776i	−0.250506	−	0.433889i	0.713159	−	0.701002i	$-0.247264\pi$
$431$	−5.20063	−	9.00776i	−0.250506	−	0.433889i	−0.963665	+	0.267113i	$0.913930\pi$
$432$	4.48665	+	2.62106i	0.215864	+	0.126106i
$433$	28.9506			1.39128			0.695639	−	0.718392i	$-0.255121\pi$
$433$	28.9506			1.39128			0.695639	+	0.718392i	$0.255121\pi$
$434$	8.69676	−	7.49297i	0.417458	−	0.359674i
$435$	−3.25625	+	13.6356i	−0.156125	+	0.653776i
$436$	2.49065	−	14.1252i	0.119281	−	0.676474i
$437$	−1.13616	+	6.44350i	−0.0543500	+	0.308234i
$438$	9.28454	+	0.556645i	0.443632	+	0.0265975i
$439$	−22.6853	+	19.0352i	−1.08271	+	0.908502i	−0.996143	−	0.0877438i	$-0.972034\pi$
$439$	−22.6853	+	19.0352i	−1.08271	+	0.908502i	−0.0865676	+	0.996246i	$0.527590\pi$
$440$	−3.67728	−	6.36923i	−0.175307	−	0.303641i
$441$	−8.75296	−	19.0889i	−0.416807	−	0.908995i
$442$	0.460980	−	0.798441i	0.0219266	−	0.0379780i
$443$	−5.29615	−	30.0359i	−0.251627	−	1.42705i	−0.804583	−	0.593840i	$-0.797611\pi$
$443$	−5.29615	−	30.0359i	−0.251627	−	1.42705i	0.552956	−	0.833211i	$-0.313500\pi$
$444$	−5.73152	+	4.25179i	−0.272006	+	0.201781i
$445$	−8.38074	+	3.05034i	−0.397285	+	0.144600i
$446$	−5.97232	−	5.01137i	−0.282798	−	0.237295i
$447$	2.70730	+	23.5100i	0.128051	+	1.11198i
$448$	−2.49779	−	0.872384i	−0.118009	−	0.0412163i
$449$	3.63600	−	6.29774i	0.171594	−	0.297209i	−0.767384	−	0.641188i	$-0.778442\pi$
$449$	3.63600	−	6.29774i	0.171594	−	0.297209i	0.938977	+	0.343980i	$0.111775\pi$
$450$	−3.32294	−	7.77623i	−0.156645	−	0.366575i
$451$	−19.8969	+	34.4624i	−0.936908	+	1.62277i
$452$	2.70977	+	15.3679i	0.127457	+	0.722844i
$453$	−9.66871	−	19.3341i	−0.454276	−	0.908395i
$454$	6.96258	+	5.84230i	0.326770	+	0.274193i
$455$	−0.468638	+	0.177528i	−0.0219701	+	0.00832266i
$456$	−1.24801	+	5.22606i	−0.0584435	+	0.244732i
$457$	−7.66734	−	2.79068i	−0.358663	−	0.130543i	0.156403	−	0.987693i	$-0.450010\pi$
$457$	−7.66734	−	2.79068i	−0.358663	−	0.130543i	−0.515066	+	0.857151i	$0.672232\pi$
$458$	14.2598	+	24.6987i	0.666315	+	1.15409i
$459$	24.1565	−	28.4914i	1.12753	−	1.32986i
$460$	−1.55750	+	2.69768i	−0.0726190	+	0.125780i
$461$	5.71301	+	32.4001i	0.266082	+	1.50902i	0.765938	+	0.642915i	$0.222275\pi$
$461$	5.71301	+	32.4001i	0.266082	+	1.50902i	−0.499856	+	0.866109i	$0.666614\pi$
$462$	21.7859	−	6.79248i	1.01357	−	0.316015i
$463$	22.4995	−	8.18914i	1.04564	−	0.380581i	0.238624	−	0.971112i	$-0.423304\pi$
$463$	22.4995	−	8.18914i	1.04564	−	0.380581i	0.807015	+	0.590531i	$0.201082\pi$
$464$	−5.14987	+	1.87440i	−0.239077	+	0.0870167i
$465$	−4.96426	−	9.92680i	−0.230212	−	0.460345i
$466$	−0.824763	−	4.67746i	−0.0382064	−	0.216679i
$467$	24.8746			1.15106			0.575530	−	0.817781i	$-0.304796\pi$
$467$	24.8746			1.15106			0.575530	+	0.817781i	$0.304796\pi$
$468$	0.263078	+	0.280758i	0.0121608	+	0.0129780i
$469$	16.8462	+	28.3186i	0.777884	+	1.30763i
$470$	8.14012	−	6.83037i	0.375476	−	0.315062i
$471$	5.44221	−	4.03718i	0.250764	−	0.186023i
$472$	9.31798	−	3.39147i	0.428895	−	0.156105i
$473$	7.59236	−	2.76339i	0.349097	−	0.127061i
$474$	2.59807	+	22.5614i	0.119333	+	1.03628i
$475$	6.69850	−	5.62071i	0.307348	−	0.257896i
$476$	−9.29405	+	16.5941i	−0.425992	+	0.760589i
$477$	−2.41378	+	1.57580i	−0.110519	+	0.0721511i
$478$	9.39045			0.429509
$479$	−0.753313	−	4.27225i	−0.0344197	−	0.195204i	0.962749	−	0.270395i	$-0.0871544\pi$
$479$	−0.753313	−	4.27225i	−0.0344197	−	0.195204i	−0.997169	+	0.0751913i	$0.976043\pi$
$480$	−1.40930	+	2.13481i	−0.0643257	+	0.0974402i
$481$	−0.496552	+	0.180730i	−0.0226408	+	0.00824058i
$482$	−27.1521	+	9.88255i	−1.23674	+	0.450138i
$483$	−7.10520	−	6.55268i	−0.323298	−	0.298157i
$484$	2.39605	+	13.5886i	0.108911	+	0.617666i
$485$	−0.538484	+	0.932681i	−0.0244513	+	0.0423509i
$486$	8.45468	+	13.0965i	0.383512	+	0.594069i
$487$	18.1088	+	31.3654i	0.820589	+	1.42130i	0.905244	+	0.424891i	$0.139688\pi$
$487$	18.1088	+	31.3654i	0.820589	+	1.42130i	−0.0846555	+	0.996410i	$0.526979\pi$
$488$	5.68781	+	2.07019i	0.257475	+	0.0937132i
$489$	28.0225	−	8.33737i	1.26722	−	0.377029i
$490$	9.61914	−	3.78815i	0.434548	−	0.171131i
$491$	12.6889	+	10.6473i	0.572644	+	0.480505i	0.882522	−	0.470271i	$-0.155844\pi$
$491$	12.6889	+	10.6473i	0.572644	+	0.480505i	−0.309878	+	0.950776i	$0.600288\pi$
$492$	13.8161	+	0.828331i	0.622878	+	0.0373441i
$493$	6.84119	+	38.7983i	0.308112	+	1.74739i
$494$	−0.198924	+	0.344547i	−0.00895002	+	0.0155019i
$495$	−1.20779	−	22.0306i	−0.0542859	−	0.990202i
$496$	2.16942	−	3.75754i	0.0974097	−	0.168718i
$497$	30.3707	+	10.6073i	1.36231	+	0.475804i
$498$	−11.7464	+	8.71380i	−0.526370	+	0.390475i
$499$	−12.2740	−	10.2991i	−0.549459	−	0.461051i	0.325299	−	0.945611i	$-0.394535\pi$
$499$	−12.2740	−	10.2991i	−0.549459	−	0.461051i	−0.874758	+	0.484561i	$0.838980\pi$
$500$	10.8511	−	3.94947i	0.485275	−	0.176626i
$501$	−3.02926	−	26.3058i	−0.135338	−	1.17526i
$502$	2.97839	+	16.8913i	0.132932	+	0.753895i
$503$	−5.13150	+	8.88802i	−0.228802	+	0.396297i	−0.957453	−	0.288588i	$-0.906814\pi$
$503$	−5.13150	+	8.88802i	−0.228802	+	0.396297i	0.728651	+	0.684885i	$0.240148\pi$
$504$	−5.50227	−	5.72058i	−0.245090	−	0.254815i
$505$	2.23063	+	3.86357i	0.0992618	+	0.171927i
$506$	8.04597	−	6.75137i	0.357687	−	0.300135i
$507$	−10.0584	−	20.1133i	−0.446709	−	0.893265i
$508$	1.05905	−	6.00617i	0.0469877	−	0.266481i
$509$	0.777950	−	4.41198i	0.0344820	−	0.195557i	−0.962701	−	0.270569i	$-0.912788\pi$
$509$	0.777950	−	4.41198i	0.0344820	−	0.195557i	0.997183	+	0.0750115i	$0.0238993\pi$
$510$	13.3541	+	12.6421i	0.591331	+	0.559800i
$511$	−13.4133	−	4.68475i	−0.593368	−	0.207241i
$512$	−1.00000			−0.0441942
$513$	−10.4241	+	12.2947i	−0.460236	+	0.542826i
$514$	10.7607	+	18.6380i	0.474633	+	0.822089i
$515$	−10.3370	+	8.67379i	−0.455504	+	0.382213i
$516$	−2.04079	−	1.93197i	−0.0898409	−	0.0850504i
$517$	−33.6688	+	12.2544i	−1.48075	+	0.538950i
$518$	10.1941	−	3.86170i	0.447902	−	0.169673i
$519$	9.48863	−	14.3733i	0.416504	−	0.630919i
$520$	−0.145098	+	0.121752i	−0.00636296	+	0.00533916i
$521$	−1.84037	+	3.18761i	−0.0806279	+	0.139652i	−0.903520	−	0.428546i	$-0.859026\pi$
$521$	−1.84037	+	3.18761i	−0.0806279	+	0.139652i	0.822892	+	0.568198i	$0.192359\pi$
$522$	−16.3233	−	1.96436i	−0.714453	−	0.0859777i
$523$	−3.21909	−	5.57564i	−0.140761	−	0.243806i	0.787022	−	0.616925i	$-0.211622\pi$
$523$	−3.21909	−	5.57564i	−0.140761	−	0.243806i	−0.927783	+	0.373119i	$0.878288\pi$
$524$	5.20770	−	4.36978i	0.227500	−	0.190895i
$525$	1.64506	+	12.8123i	0.0717964	+	0.559173i
$526$	1.81815	−	10.3112i	0.0792751	−	0.449591i
$527$	−23.8934	−	20.0489i	−1.04081	−	0.873346i
$528$	6.92728	−	5.13884i	0.301471	−	0.223639i
$529$	17.4326	+	6.34494i	0.757938	+	0.275867i
$530$	−0.709548	−	1.22897i	−0.0308208	−	0.0533831i
$531$	29.5349	+	3.55424i	1.28170	+	0.154241i
$532$	4.01061	−	7.16076i	0.173882	−	0.310458i
$533$	0.963055	+	0.350523i	0.0417145	+	0.0151829i
$534$	−4.67828	−	9.35495i	−0.202449	−	0.404828i
$535$	−4.65720	+	26.4123i	−0.201348	+	1.14190i
$536$	9.54040	+	8.00535i	0.412083	+	0.345778i
$537$	19.1178	+	18.0984i	0.824994	+	0.781004i
$538$	−0.376030	−	2.13257i	−0.0162118	−	0.0919418i
$539$	−34.8466	+	0.909569i	−1.50095	+	0.0391779i
$540$	−6.66551	+	3.80301i	−0.286838	+	0.163656i
$541$	0.412078	−	0.713739i	0.0177166	−	0.0306861i	−0.857031	−	0.515265i	$-0.827694\pi$
$541$	0.412078	−	0.713739i	0.0177166	−	0.0306861i	0.874748	+	0.484578i	$0.161027\pi$
$542$	8.37979	−	7.03147i	0.359943	−	0.302028i
$543$	−4.52926	+	18.9663i	−0.194369	+	0.813921i
$544$	−1.24831	+	7.07950i	−0.0535207	+	0.303531i
$545$	16.2272	+	13.6162i	0.695095	+	0.583254i
$546$	−0.269709	−	0.522180i	−0.0115425	−	0.0223473i
$547$	−1.44375	−	0.525482i	−0.0617303	−	0.0224680i	0.310970	−	0.950420i	$-0.399346\pi$
$547$	−1.44375	−	0.525482i	−0.0617303	−	0.0224680i	−0.372701	+	0.927952i	$0.621568\pi$
$548$	−2.87839			−0.122959
$549$	12.4160	+	13.2504i	0.529903	+	0.565515i
$550$	−14.0371			−0.598545
$551$	−2.95214	−	16.7424i	−0.125765	−	0.713251i
$552$	−3.35196	−	1.45268i	−0.142669	−	0.0618300i
$553$	5.57773	−	34.2395i	0.237189	−	1.45601i
$554$	1.83518	−	10.4078i	0.0779693	−	0.442186i
$555$	−1.20573	−	10.4704i	−0.0511802	−	0.444444i
$556$	−17.0287	−	6.19796i	−0.722180	−	0.262852i
$557$	−5.63545			−0.238782			−0.119391	−	0.992847i	$-0.538094\pi$
$557$	−5.63545			−0.238782			−0.119391	+	0.992847i	$0.538094\pi$
$558$	10.8994	−	7.11556i	0.461410	−	0.301226i
$559$	−0.104043	−	0.180207i	−0.00440053	−	0.00762195i
$560$	2.96026	−	2.55051i	0.125094	−	0.107779i
$561$	−27.7330	−	55.4565i	−1.17089	−	2.34138i
$562$	−0.562413	+	0.204702i	−0.0237240	+	0.00863482i
$563$	28.0751	+	23.5578i	1.18323	+	0.992844i	0.999952	+	0.00978165i	$0.00311365\pi$
$563$	28.0751	+	23.5578i	1.18323	+	0.992844i	0.183273	+	0.983062i	$0.441331\pi$
$564$	9.05002	+	8.56746i	0.381075	+	0.360755i
$565$	−21.6568	−	7.88243i	−0.911108	−	0.331616i
$566$	23.9704			1.00755
$567$	−6.97126	−	22.7684i	−0.292765	−	0.956184i
$568$	12.1590			0.510181
$569$	43.3062	+	15.7622i	1.81549	+	0.660785i	0.996169	+	0.0874520i	$0.0278724\pi$
$569$	43.3062	+	15.7622i	1.81549	+	0.660785i	0.819323	+	0.573333i	$0.194350\pi$
$570$	−5.76263	−	5.45536i	−0.241370	−	0.228500i
$571$	9.16912	+	7.69380i	0.383716	+	0.321976i	0.814159	−	0.580642i	$-0.197198\pi$
$571$	9.16912	+	7.69380i	0.383716	+	0.321976i	−0.430443	+	0.902618i	$0.641643\pi$
$572$	0.600147	−	0.218436i	0.0250934	−	0.00913325i
$573$	19.9743	+	39.9416i	0.834437	+	1.66859i
$574$	−19.9600	−	6.97127i	−0.833113	−	0.290975i
$575$	2.97270	+	5.14886i	0.123970	+	0.214722i
$576$	−2.67629	−	1.35553i	−0.111512	−	0.0564804i
$577$	6.93741			0.288808			0.144404	−	0.989519i	$-0.453873\pi$
$577$	6.93741			0.288808			0.144404	+	0.989519i	$0.453873\pi$
$578$	32.5863	+	11.8604i	1.35541	+	0.493329i
$579$	0.618174	+	5.36816i	0.0256904	+	0.223093i
$580$	1.40548	−	7.97090i	0.0583596	−	0.330974i
$581$	20.8922	−	7.91434i	0.866754	−	0.328342i
$582$	−1.15889	−	0.502241i	−0.0480375	−	0.0208186i
$583$	0.830896	+	4.71224i	0.0344122	+	0.195161i
$584$	−5.37006			−0.222214
$585$	−0.553362	+	0.129158i	−0.0228787	+	0.00534003i
$586$	−9.24420			−0.381874
$587$	6.05588	+	2.20416i	0.249953	+	0.0909754i	0.463958	−	0.885857i	$-0.346429\pi$
$587$	6.05588	+	2.20416i	0.249953	+	0.0909754i	−0.214005	+	0.976832i	$0.568651\pi$
$588$	5.70403	+	10.6988i	0.235230	+	0.441211i
$589$	10.3106	+	8.65161i	0.424840	+	0.356483i
$590$	−2.54303	+	14.4223i	−0.104695	+	0.593755i
$591$	−2.89712	+	12.1317i	−0.119171	+	0.499032i
$592$	3.15625	−	2.64841i	0.129721	−	0.108849i
$593$	−10.6110	+	18.3789i	−0.435743	+	0.754730i	−0.997356	−	0.0726705i	$-0.976848\pi$
$593$	−10.6110	+	18.3789i	−0.435743	+	0.754730i	0.561613	+	0.827400i	$0.310181\pi$
$594$	25.5053	−	4.36290i	1.04649	−	0.179012i
$595$	−14.3610	−	24.1410i	−0.588745	−	0.989685i
$596$	−2.37259	−	13.4556i	−0.0971850	−	0.551163i
$597$	19.9457	+	18.8822i	0.816323	+	0.772796i
$598$	−0.207218	−	0.173877i	−0.00847379	−	0.00711036i
$599$	4.47973	−	25.4058i	0.183037	−	1.03805i	−0.745415	−	0.666601i	$-0.767749\pi$
$599$	4.47973	−	25.4058i	0.183037	−	1.03805i	0.928452	−	0.371453i	$-0.121140\pi$
$600$	2.18375	+	4.36674i	0.0891511	+	0.178272i
$601$	−13.2906	−	4.83740i	−0.542137	−	0.197322i	0.0564126	−	0.998408i	$-0.482034\pi$
$601$	−13.2906	−	4.83740i	−0.542137	−	0.197322i	−0.598549	+	0.801086i	$0.704256\pi$
$602$	2.19467	+	3.68926i	0.0894480	+	0.150363i
$603$	14.6814	+	34.3569i	0.597873	+	1.39912i
$604$	6.24027	+	10.8085i	0.253913	+	0.439790i
$605$	−19.1495	−	6.96983i	−0.778536	−	0.283364i
$606$	−4.20208	+	3.11721i	−0.170698	+	0.126628i
$607$	−12.2475	−	10.2769i	−0.497111	−	0.417126i	0.359455	−	0.933162i	$-0.382963\pi$
$607$	−12.2475	−	10.2769i	−0.497111	−	0.417126i	−0.856567	+	0.516036i	$0.827407\pi$
$608$	0.538675	−	3.05498i	0.0218462	−	0.123896i
$609$	23.1716	+	9.68502i	0.938962	+	0.392457i
$610$	−6.84792	+	5.74609i	−0.277264	+	0.232652i
$611$	0.461384	+	0.799140i	0.0186656	+	0.0323297i
$612$	−12.9373	+	17.2547i	−0.522960	+	0.697480i
$613$	−3.56592	+	6.17635i	−0.144026	+	0.249460i	−0.929009	−	0.370057i	$-0.879338\pi$
$613$	−3.56592	+	6.17635i	−0.144026	+	0.249460i	0.784983	+	0.619517i	$0.212672\pi$
$614$	17.9623	−	15.0722i	0.724899	−	0.608263i
$615$	−11.2618	+	17.0594i	−0.454121	+	0.687900i
$616$	−12.3209	+	4.66737i	−0.496422	+	0.188054i
$617$	−19.5666	+	7.12168i	−0.787724	+	0.286708i	−0.704389	−	0.709814i	$-0.748779\pi$
$617$	−19.5666	+	7.12168i	−0.787724	+	0.286708i	−0.0833342	+	0.996522i	$0.526557\pi$
$618$	−11.4925	−	10.8797i	−0.462296	−	0.437645i
$619$	−1.99718	+	1.67583i	−0.0802734	+	0.0673574i	−0.682041	−	0.731314i	$-0.738908\pi$
$619$	−1.99718	+	1.67583i	−0.0802734	+	0.0673574i	0.601768	+	0.798671i	$0.294463\pi$
$620$	3.20397	+	5.54944i	0.128675	+	0.222871i
$621$	−7.00168	−	8.43147i	−0.280968	−	0.338343i
$622$	−20.7438			−0.831749
$623$	2.97947	+	15.6969i	0.119370	+	0.628883i
$624$	−0.161317	−	0.152715i	−0.00645784	−	0.00611350i
$625$	−0.514028	+	2.91520i	−0.0205611	+	0.116608i
$626$	2.40149	−	13.6195i	0.0959828	−	0.544345i
$627$	11.9675	+	23.9308i	0.477935	+	0.955706i
$628$	−2.99694	+	2.51473i	−0.119591	+	0.100349i
$629$	−14.8094	−	25.6507i	−0.590491	−	1.02276i
$630$	11.3798	−	2.81318i	0.453383	−	0.112080i
$631$	−12.2131	+	21.1537i	−0.486196	+	0.842116i	−0.999874	−	0.0158668i	$-0.994949\pi$
$631$	−12.2131	+	21.1537i	−0.486196	+	0.842116i	0.513678	+	0.857983i	$0.328283\pi$
$632$	−2.27686	−	12.9127i	−0.0905685	−	0.513640i
$633$	−3.49822	−	30.3782i	−0.139042	−	1.20743i
$634$	15.8726	−	5.77717i	0.630383	−	0.229441i
$635$	6.89995	+	5.78975i	0.273816	+	0.229759i
$636$	1.33665	−	0.991562i	0.0530016	−	0.0393180i
$637$	0.178910	+	0.879750i	0.00708869	+	0.0348570i
$638$	−13.6455	+	23.6348i	−0.540232	+	0.935710i
$639$	32.5411	+	16.4819i	1.28731	+	0.652014i
$640$	0.738441	−	1.27902i	0.0291894	−	0.0505576i
$641$	−0.763082	−	4.32766i	−0.0301399	−	0.170932i	0.966022	−	0.258459i	$-0.0832147\pi$
$641$	−0.763082	−	4.32766i	−0.0301399	−	0.170932i	−0.996162	+	0.0875270i	$0.972104\pi$
$642$	−31.3972	−	1.88239i	−1.23915	−	0.0742918i
$643$	−19.6269	−	16.4689i	−0.774008	−	0.649470i	0.167724	−	0.985834i	$-0.446358\pi$
$643$	−19.6269	−	16.4689i	−0.774008	−	0.649470i	−0.941732	+	0.336364i	$0.890803\pi$
$644$	4.32124	+	3.53091i	0.170281	+	0.139137i
$645$	3.97803	−	1.18356i	0.156635	−	0.0466026i
$646$	−20.9553	−	7.62710i	−0.824475	−	0.300084i
$647$	23.6990	+	41.0479i	0.931704	+	1.61376i	0.780409	+	0.625269i	$0.215011\pi$
$647$	23.6990	+	41.0479i	0.931704	+	1.61376i	0.151295	+	0.988489i	$0.451656\pi$
$648$	−5.32508	−	7.25559i	−0.209189	−	0.285026i
$649$	24.6898	−	42.7639i	0.969158	−	1.67863i
$650$	0.0627767	+	0.356024i	0.00246230	+	0.0139644i
$651$	−18.9818	+	5.91821i	−0.743956	+	0.231953i
$652$	−15.8617	+	5.77320i	−0.621194	+	0.226096i
$653$	−46.1484	+	16.7967i	−1.80593	+	0.657304i	−0.808277	+	0.588802i	$0.799600\pi$
$653$	−46.1484	+	16.7967i	−1.80593	+	0.657304i	−0.997651	+	0.0685021i	$0.978178\pi$
$654$	−13.6868	+	20.7327i	−0.535196	+	0.810712i
$655$	1.74345	+	9.88757i	0.0681221	+	0.386339i
$656$	−7.99106			−0.311998
$657$	−14.3718	−	7.27927i	−0.560699	−	0.283991i
$658$	−9.73239	−	16.3602i	−0.379408	−	0.637788i
$659$	−16.9942	+	14.2598i	−0.662000	+	0.555484i	−0.910686	−	0.413100i	$-0.864446\pi$
$659$	−16.9942	+	14.2598i	−0.662000	+	0.555484i	0.248685	+	0.968584i	$0.420001\pi$
$660$	1.45728	+	12.6548i	0.0567244	+	0.492589i
$661$	−3.08453	+	1.12268i	−0.119974	+	0.0436671i	−0.401310	−	0.915942i	$-0.631445\pi$
$661$	−3.08453	+	1.12268i	−0.119974	+	0.0436671i	0.281335	+	0.959610i	$0.409223\pi$
$662$	−9.01171	+	3.27999i	−0.350250	+	0.127481i
$663$	−1.28252	+	0.951407i	−0.0498089	+	0.0369496i
$664$	6.46856	−	5.42777i	0.251029	−	0.210638i
$665$	6.19713	+	10.4174i	0.240315	+	0.403971i
$666$	12.0370	−	2.80952i	0.466426	−	0.108867i
$667$	11.5591			0.447570
$668$	2.65474	+	15.0558i	0.102715	+	0.582526i
$669$	6.03983	+	12.0776i	0.233513	+	0.466946i
$670$	−17.2840	+	6.29086i	−0.667739	+	0.243037i
$671$	28.3241	−	10.3091i	1.09344	−	0.397979i
$672$	3.36870	+	3.10674i	0.129950	+	0.119845i
$673$	−5.14845	−	29.1983i	−0.198458	−	1.12551i	−0.907407	−	0.420253i	$-0.861941\pi$
$673$	−5.14845	−	29.1983i	−0.198458	−	1.12551i	0.708949	−	0.705260i	$-0.249170\pi$
$674$	4.63279	−	8.02422i	0.178448	−	0.309081i
$675$	−0.0749056	+	14.6468i	−0.00288312	+	0.563756i
$676$	6.49178	+	11.2441i	0.249684	+	0.432465i
$677$	10.9023	+	3.96812i	0.419010	+	0.152507i	0.542916	−	0.839787i	$-0.317320\pi$
$677$	10.9023	+	3.96812i	0.419010	+	0.152507i	−0.123906	+	0.992294i	$0.539542\pi$
$678$	6.27804	−	26.2893i	0.241107	−	1.00964i
$679$	1.49400	+	1.22076i	0.0573346	+	0.0468484i
$680$	−8.13300	−	6.82440i	−0.311886	−	0.261704i
$681$	−7.04129	−	14.0801i	−0.269823	−	0.539552i
$682$	−3.75192	−	21.2782i	−0.143669	−	0.814785i
$683$	−10.6622	+	18.4675i	−0.407978	+	0.706638i	−0.994663	−	0.103177i	$-0.967099\pi$
$683$	−10.6622	+	18.4675i	−0.407978	+	0.706638i	0.586685	+	0.809815i	$0.300433\pi$
$684$	5.58277	−	7.44582i	0.213462	−	0.284698i
$685$	2.12552	−	3.68151i	0.0812119	−	0.140663i
$686$	−3.92731	−	18.0991i	−0.149945	−	0.691026i
$687$	−5.65103	−	49.0730i	−0.215600	−	1.87225i
$688$	1.24289	+	1.04291i	0.0473849	+	0.0397607i
$689$	0.115801	−	0.0421481i	0.00441167	−	0.00160572i
$690$	4.33323	−	3.21450i	0.164963	−	0.122374i
$691$	5.02712	+	28.5102i	0.191241	+	1.08458i	0.917672	+	0.397340i	$0.130067\pi$
$691$	5.02712	+	28.5102i	0.191241	+	1.08458i	−0.726431	+	0.687239i	$0.758822\pi$
$692$	−4.97181	+	8.61142i	−0.189000	+	0.327357i
$693$	−39.3010	−	4.21006i	−1.49292	−	0.159927i
$694$	−11.7409	−	20.3358i	−0.445677	−	0.771935i
$695$	20.5020	−	17.2032i	0.777686	−	0.652556i
$696$	9.47527	+	0.568080i	0.359159	+	0.0215330i
$697$	−9.97529	+	56.5727i	−0.377841	+	2.14284i
$698$	3.13495	−	17.7792i	0.118659	−	0.672951i
$699$	−1.91082	+	8.00159i	−0.0722740	+	0.302648i
$700$	−1.39077	−	7.32707i	−0.0525661	−	0.276937i
$701$	−29.1013			−1.09914			−0.549571	−	0.835447i	$-0.685209\pi$
$701$	−29.1013			−1.09914			−0.549571	+	0.835447i	$0.685209\pi$
$702$	−0.224721	−	0.627380i	−0.00848154	−	0.0236789i
$703$	6.39064	+	11.0689i	0.241027	+	0.417472i
$704$	−3.81474	+	3.20095i	−0.143773	+	0.120640i
$705$	−17.6408	+	5.24857i	−0.664393	+	0.197673i
$706$	−1.53937	+	0.560283i	−0.0579348	+	0.0210865i
$707$	7.47382	−	2.83122i	0.281082	−	0.106479i
$708$	−17.1442	−	1.02786i	−0.644319	−	0.0386295i
$709$	−17.1082	+	14.3555i	−0.642512	+	0.539132i	−0.904789	−	0.425861i	$-0.859971\pi$
$709$	−17.1082	+	14.3555i	−0.642512	+	0.539132i	0.262276	+	0.964993i	$0.415527\pi$
$710$	−8.97872	+	15.5516i	−0.336965	+	0.583641i
$711$	11.4100	−	37.6445i	0.427909	−	1.41178i
$712$	3.01940	+	5.22975i	0.113157	+	0.195993i
$713$	−7.01036	+	5.88239i	−0.262540	+	0.220297i
$714$	26.1994	−	19.9706i	0.980486	−	0.747379i
$715$	−0.163790	+	0.928900i	−0.00612541	+	0.0347389i
$716$	−11.6432	−	9.76983i	−0.435128	−	0.365116i
$717$	−14.9235	−	6.46758i	−0.557330	−	0.241536i
$718$	14.4940	+	5.27539i	0.540912	+	0.196876i
$719$	9.25947	+	16.0379i	0.345320	+	0.598112i	0.985412	−	0.170187i	$-0.0544371\pi$
$719$	9.25947	+	16.0379i	0.345320	+	0.598112i	−0.640092	+	0.768298i	$0.721104\pi$
$720$	3.71003	−	2.42205i	0.138265	−	0.0902643i
$721$	12.3590	+	20.7756i	0.460274	+	0.773725i
$722$	−8.81144	−	3.20710i	−0.327928	−	0.119356i
$723$	49.9573	+	2.99514i	1.85793	+	0.111390i
$724$	1.95495	−	11.0871i	0.0726551	−	0.412047i
$725$	−11.8340	−	9.92990i	−0.439503	−	0.368787i
$726$	5.55120	−	23.2457i	0.206024	−	0.862728i
$727$	8.54634	+	48.4687i	0.316966	+	1.79760i	0.560977	+	0.827831i	$0.310426\pi$
$727$	8.54634	+	48.4687i	0.316966	+	1.79760i	−0.244011	+	0.969773i	$0.578463\pi$
$728$	0.173480	+	0.291621i	0.00642960	+	0.0108082i
$729$	−4.41630	−	26.6364i	−0.163567	−	0.986532i
$730$	3.96547	−	6.86840i	0.146769	−	0.254211i
$731$	8.93481	−	7.49720i	0.330466	−	0.277294i
$732$	−7.61338	−	7.20742i	−0.281399	−	0.266394i
$733$	5.85955	−	33.2311i	0.216427	−	1.22742i	−0.661985	−	0.749517i	$-0.730286\pi$
$733$	5.85955	−	33.2311i	0.216427	−	1.22742i	0.878413	−	0.477903i	$-0.158603\pi$
$734$	−2.46272	−	2.06647i	−0.0909008	−	0.0762748i
$735$	−17.8960	−	0.604869i	−0.660105	−	0.0223109i
$736$	1.98198	+	0.721382i	0.0730568	+	0.0265905i
$737$	62.0188			2.28449
$738$	−21.3864	−	10.8321i	−0.787244	−	0.398736i
$739$	−40.5541			−1.49181			−0.745904	−	0.666054i	$-0.767982\pi$
$739$	−40.5541			−1.49181			−0.745904	+	0.666054i	$0.767982\pi$
$740$	1.05666	+	5.99260i	0.0388435	+	0.220292i
$741$	0.553439	−	0.410555i	0.0203311	−	0.0150821i
$742$	−2.37737	+	0.900589i	−0.0872758	+	0.0330617i
$743$	−4.55051	+	25.8072i	−0.166942	+	0.946776i	0.780097	+	0.625658i	$0.215170\pi$
$743$	−4.55051	+	25.8072i	−0.166942	+	0.946776i	−0.947039	+	0.321117i	$0.895942\pi$
$744$	−6.03566	+	4.47741i	−0.221278	+	0.164150i
$745$	18.9620	+	6.90160i	0.694713	+	0.252855i
$746$	29.5397			1.08152
$747$	24.6693	−	5.75796i	0.902601	−	0.210673i
$748$	17.8991	+	31.0022i	0.654457	+	1.13355i
$749$	45.3591	+	15.8422i	1.65739	+	0.578863i
$750$	−19.9650	−	1.19698i	−0.729017	−	0.0437075i
$751$	−5.58754	+	2.03370i	−0.203892	+	0.0742106i	−0.441947	−	0.897041i	$-0.645712\pi$
$751$	−5.58754	+	2.03370i	−0.203892	+	0.0742106i	0.238055	+	0.971252i	$0.423490\pi$
$752$	−5.51169	−	4.62486i	−0.200991	−	0.168651i
$753$	6.90038	−	28.8954i	0.251464	−	1.05301i
$754$	0.660476	+	0.240394i	0.0240531	+	0.00875462i
$755$	−18.4323			−0.670820
$756$	4.80435	+	12.8809i	0.174732	+	0.468475i
$757$	30.3047			1.10144			0.550722	−	0.834689i	$-0.314352\pi$
$757$	30.3047			1.10144			0.550722	+	0.834689i	$0.314352\pi$
$758$	−11.4714	−	4.17525i	−0.416660	−	0.151652i
$759$	−17.4368	+	5.18786i	−0.632915	+	0.188307i
$760$	3.50959	+	2.94490i	0.127306	+	0.106823i
$761$	11.6792	−	4.25089i	0.423372	−	0.154095i	−0.121543	−	0.992586i	$-0.538784\pi$
$761$	11.6792	−	4.25089i	0.423372	−	0.154095i	0.544915	+	0.838492i	$0.316562\pi$
$762$	−5.81976	+	8.81575i	−0.210828	+	0.319361i
$763$	28.7493	−	24.7699i	1.04079	−	0.896730i
$764$	−12.8916	−	22.3288i	−0.466400	−	0.807829i
$765$	−12.5156	−	29.2886i	−0.452503	−	1.05893i
$766$	−23.4466			−0.847159
$767$	−1.19504	−	0.434959i	−0.0431504	−	0.0157055i
$768$	1.58923	+	0.688740i	0.0573462	+	0.0248528i
$769$	8.29013	−	47.0156i	0.298950	−	1.69543i	−0.351752	−	0.936093i	$-0.614414\pi$
$769$	8.29013	−	47.0156i	0.298950	−	1.69543i	0.650701	−	0.759334i	$-0.274475\pi$
$770$	3.12859	−	19.2052i	0.112746	−	0.692106i
$771$	−4.26437	−	37.0313i	−0.153577	−	1.33365i
$772$	−0.541746	−	3.07239i	−0.0194979	−	0.110578i
$773$	14.7989			0.532278			0.266139	−	0.963935i	$-0.414252\pi$
$773$	14.7989			0.532278			0.266139	+	0.963935i	$0.414252\pi$
$774$	1.91265	+	4.47592i	0.0687488	+	0.160884i
$775$	12.2304			0.439328
$776$	0.685240	+	0.249407i	0.0245987	+	0.00895318i
$777$	−18.8604	−	0.883959i	−0.676613	−	0.0317119i
$778$	12.4653	+	10.4596i	0.446902	+	0.374996i
$779$	4.30458	−	24.4125i	0.154228	−	0.874669i
$780$	0.314448	−	0.0935558i	0.0112591	−	0.00334984i
$781$	46.3835	−	38.9204i	1.65973	−	1.39268i
$782$	7.58114	−	13.1309i	0.271101	−	0.469561i
$783$	24.5885	+	14.3644i	0.878723	+	0.513340i
$784$	−3.65699	−	5.96879i	−0.130607	−	0.213171i
$785$	−1.00332	−	5.69011i	−0.0358100	−	0.203089i
$786$	−11.2859	+	3.35781i	−0.402553	+	0.119769i
$787$	−24.0005	−	20.1388i	−0.855525	−	0.717871i	0.105474	−	0.994422i	$-0.466364\pi$
$787$	−24.0005	−	20.1388i	−0.855525	−	0.717871i	−0.960999	+	0.276551i	$0.910809\pi$
$788$	1.25047	−	7.09179i	0.0445463	−	0.252635i
$789$	−9.99121	+	15.1346i	−0.355697	+	0.538808i
$790$	18.1969	+	6.62313i	0.647417	+	0.235640i
$791$	−20.1751	+	36.0217i	−0.717345	+	1.28079i
$792$	−14.5483	+	3.39567i	−0.516952	+	0.120660i
$793$	−0.388141	−	0.672281i	−0.0137833	−	0.0238734i
$794$	−16.3915	−	5.96602i	−0.581713	−	0.211726i
$795$	0.281188	+	2.44181i	0.00997271	+	0.0866020i
$796$	−12.1474	−	10.1929i	−0.430555	−	0.361278i
$797$	4.90675	−	27.8275i	0.173806	−	0.985702i	−0.765707	−	0.643189i	$-0.777611\pi$
$797$	4.90675	−	27.8275i	0.173806	−	0.985702i	0.939513	−	0.342513i	$-0.111278\pi$
$798$	−11.3057	+	8.61778i	−0.400216	+	0.305066i
$799$	−39.6220	+	33.2468i	−1.40173	+	1.17619i
$800$	−1.40941	−	2.44117i	−0.0498301	−	0.0863083i
$801$	0.991708	+	18.0892i	0.0350403	+	0.639152i
$802$	1.92254	−	3.32994i	0.0678873	−	0.117584i
$803$	−20.4854	+	17.1893i	−0.722913	+	0.606596i
$804$	−9.64824	−	19.2932i	−0.340267	−	0.680417i
$805$	−7.70708	+	2.91958i	−0.271639	+	0.102902i
$806$	−0.522901	+	0.190321i	−0.0184184	+	0.00670375i
$807$	−0.871193	+	3.64813i	−0.0306674	+	0.128420i
$808$	2.31401	−	1.94169i	0.0814068	−	0.0683084i
$809$	−16.1538	−	27.9791i	−0.567936	−	0.983693i	−0.996770	−	0.0803102i	$-0.974409\pi$
$809$	−16.1538	−	27.9791i	−0.567936	−	0.983693i	0.428834	−	0.903383i	$-0.358924\pi$
$810$	13.2123	−	1.45304i	0.464232	−	0.0510547i
$811$	−10.0881			−0.354241			−0.177121	−	0.984189i	$-0.556678\pi$
$811$	−10.0881			−0.354241			−0.177121	+	0.984189i	$0.556678\pi$
$812$	−13.6888	−	4.78099i	−0.480383	−	0.167780i
$813$	−18.1602	+	5.40310i	−0.636907	+	0.189495i
$814$	3.56286	−	20.2060i	0.124878	−	0.708219i
$815$	4.32894	−	24.5506i	0.151636	−	0.859970i
$816$	6.85978	−	10.3912i	0.240140	−	0.363763i
$817$	−3.85559	+	3.23522i	−0.134890	+	0.113186i
$818$	−16.5891	−	28.7332i	−0.580025	−	1.00463i
$819$	0.0689815	+	1.01562i	0.00241041	+	0.0354887i
$820$	5.90093	−	10.2207i	0.206069	−	0.356922i
$821$	3.12431	+	17.7188i	0.109039	+	0.618391i	0.989530	+	0.144328i	$0.0461021\pi$
$821$	3.12431	+	17.7188i	0.109039	+	0.618391i	−0.880491	+	0.474063i	$0.842787\pi$
$822$	4.57440	+	1.98246i	0.159551	+	0.0691462i
$823$	27.5583	−	10.0304i	0.960621	−	0.349637i	0.186344	−	0.982485i	$-0.440336\pi$
$823$	27.5583	−	10.0304i	0.960621	−	0.349637i	0.774277	+	0.632847i	$0.218114\pi$
$824$	6.99922	+	5.87304i	0.243829	+	0.204597i
$825$	22.3081	+	9.66793i	0.776670	+	0.336594i
$826$	24.7680	+	8.65055i	0.861790	+	0.300991i
$827$	−9.08092	+	15.7286i	−0.315775	+	0.546938i	−0.979602	−	0.200948i	$-0.935598\pi$
$827$	−9.08092	+	15.7286i	−0.315775	+	0.546938i	0.663827	+	0.747886i	$0.268931\pi$
$828$	4.32650	+	4.61726i	0.150356	+	0.160461i
$829$	−3.68634	+	6.38494i	−0.128032	+	0.221758i	−0.922914	−	0.385006i	$-0.874199\pi$
$829$	−3.68634	+	6.38494i	−0.128032	+	0.221758i	0.794882	+	0.606764i	$0.207533\pi$
$830$	2.16556	+	12.2815i	0.0751676	+	0.426297i
$831$	−10.0848	+	15.2764i	−0.349838	+	0.529933i
$832$	0.0982460	+	0.0824382i	0.00340607	+	0.00285803i
$833$	−46.8211	+	18.4388i	−1.62225	+	0.638866i
$834$	22.7937	+	21.5783i	0.789282	+	0.747197i
$835$	−21.2170	−	7.72235i	−0.734244	−	0.267243i
$836$	−7.72391	−	13.3782i	−0.267137	−	0.462695i
$837$	−22.2225	+	3.80134i	−0.768120	+	0.131394i
$838$	6.00850	−	10.4070i	0.207560	−	0.359505i
$839$	−1.52037	−	8.62246i	−0.0524891	−	0.297681i	0.947251	−	0.320494i	$-0.103849\pi$
$839$	−1.52037	−	8.62246i	−0.0524891	−	0.297681i	−0.999740	+	0.0228132i	$0.992738\pi$
$840$	−6.46117	+	2.01448i	−0.222931	+	0.0695062i
$841$	−0.972095	+	0.353814i	−0.0335205	+	0.0122005i
$842$	−30.8469	+	11.2273i	−1.06305	+	0.386920i
$843$	1.03479	+	0.0620397i	0.0356400	+	0.00213676i
$844$	3.06572	+	17.3866i	0.105526	+	0.598470i
$845$	−19.1752			−0.659646
$846$	−8.48177	−	19.8487i	−0.291609	−	0.682414i
$847$	−17.8393	+	31.8513i	−0.612967	+	1.09442i
$848$	−0.736071	+	0.617637i	−0.0252768	+	0.0212097i
$849$	−38.0943	−	16.5094i	−1.30739	−	0.566599i
$850$	−19.0416	+	6.93059i	−0.653123	+	0.237717i
$851$	−8.16614	+	2.97223i	−0.279932	+	0.101887i
$852$	−19.3234	−	8.37441i	−0.662009	−	0.286902i
$853$	−32.1911	+	27.0116i	−1.10220	+	0.924858i	−0.997571	−	0.0696531i	$-0.977811\pi$
$853$	−32.1911	+	27.0116i	−1.10220	+	0.924858i	−0.104632	+	0.994511i	$0.533366\pi$
$854$	8.18742	+	13.7631i	0.280168	+	0.470965i
$855$	5.40079	+	12.6388i	0.184703	+	0.432236i
$856$	18.1597			0.620686
$857$	4.05641	+	23.0050i	0.138564	+	0.785837i	0.972311	+	0.233690i	$0.0750801\pi$
$857$	4.05641	+	23.0050i	0.138564	+	0.785837i	−0.833747	+	0.552147i	$0.813809\pi$
$858$	−1.10421	−	0.0662021i	−0.0376972	−	0.00226010i
$859$	2.10544	−	0.766317i	0.0718367	−	0.0261464i	−0.305852	−	0.952079i	$-0.598941\pi$
$859$	2.10544	−	0.766317i	0.0718367	−	0.0261464i	0.377689	+	0.925933i	$0.376719\pi$
$860$	−2.25171	+	0.819555i	−0.0767826	+	0.0279466i
$861$	26.9195	+	24.8262i	0.917414	+	0.846073i
$862$	−1.80616	−	10.2432i	−0.0615181	−	0.348886i
$863$	−21.1156	+	36.5733i	−0.718784	+	1.24497i	0.242698	+	0.970102i	$0.421967\pi$
$863$	−21.1156	+	36.5733i	−0.718784	+	1.24497i	−0.961482	+	0.274868i	$0.911366\pi$
$864$	3.31962	+	3.99751i	0.112936	+	0.135998i
$865$	−7.34278	−	12.7181i	−0.249662	−	0.432427i
$866$	27.2047	+	9.90169i	0.924452	+	0.336473i
$867$	−43.6182	−	41.2924i	−1.48135	−	1.40236i
$868$	10.7350	−	4.06662i	0.364371	−	0.138030i
$869$	−50.0185	−	41.9705i	−1.69676	−	1.42375i
$870$	−7.72351	+	11.6995i	−0.261852	+	0.396652i
$871$	−0.277360	−	1.57299i	−0.00939799	−	0.0532986i
$872$	7.17154	−	12.4215i	0.242859	−	0.420644i
$873$	1.49582	+	1.59635i	0.0506259	+	0.0540282i
$874$	−3.27145	+	5.66632i	−0.110658	+	0.191666i
$875$	28.8431	+	10.0738i	0.975076	+	0.340558i
$876$	8.53423	+	3.69857i	0.288345	+	0.124963i
$877$	16.4989	+	13.8442i	0.557129	+	0.467487i	0.877347	−	0.479857i	$-0.159311\pi$
$877$	16.4989	+	13.8442i	0.557129	+	0.467487i	−0.320217	+	0.947344i	$0.603756\pi$
$878$	−27.8277	+	10.1284i	−0.939138	+	0.341818i
$879$	14.6911	+	6.36685i	0.495519	+	0.214749i
$880$	−1.27711	−	7.24283i	−0.0430512	−	0.244156i
$881$	18.0694	−	31.2972i	0.608775	−	1.05443i	−0.382668	−	0.923886i	$-0.624995\pi$
$881$	18.0694	−	31.2972i	0.608775	−	1.05443i	0.991443	−	0.130543i	$-0.0416719\pi$
$882$	−1.69630	−	20.9314i	−0.0571175	−	0.704796i
$883$	13.4012	+	23.2116i	0.450987	+	0.781132i	0.998448	−	0.0556995i	$-0.0177389\pi$
$883$	13.4012	+	23.2116i	0.450987	+	0.781132i	−0.547461	+	0.836831i	$0.684406\pi$
$884$	0.706262	−	0.592625i	0.0237542	−	0.0199321i
$885$	13.9746	−	21.1687i	0.469753	−	0.711579i
$886$	5.29615	−	30.0359i	0.177928	−	1.00908i
$887$	4.39155	−	24.9057i	0.147454	−	0.836253i	−0.817910	−	0.575346i	$-0.804867\pi$
$887$	4.39155	−	24.9057i	0.147454	−	0.836253i	0.965364	−	0.260907i	$-0.0840215\pi$
$888$	−6.84006	+	2.03508i	−0.229537	+	0.0682928i
$889$	12.2245	−	10.5324i	0.409996	−	0.353245i
$890$	−8.91860			−0.298952
$891$	−43.5385	−	10.6329i	−1.45860	−	0.356215i
$892$	−3.89816	−	6.75181i	−0.130520	−	0.226067i
$893$	17.0979	−	14.3468i	0.572158	−	0.480098i
$894$	−5.49685	+	23.0181i	−0.183842	+	0.769840i
$895$	21.0936	−	7.67745i	0.705082	−	0.256629i
$896$	−2.04878	−	1.67407i	−0.0684449	−	0.0559266i
$897$	0.209561	+	0.419049i	0.00699703	+	0.0139916i
$898$	5.57068	−	4.67435i	0.185896	−	0.155985i
$899$	11.8892	−	20.5927i	0.396527	−	0.686806i
$900$	−0.462914	−	8.44378i	−0.0154305	−	0.281459i
$901$	3.45372	+	5.98201i	0.115060	+	0.199290i
$902$	−30.4838	+	25.5789i	−1.01500	+	0.851686i
$903$	−0.946881	−	7.37461i	−0.0315102	−	0.245412i
$904$	−2.70977	+	15.3679i	−0.0901256	+	0.511128i
$905$	12.7369	+	10.6876i	0.423390	+	0.355266i
$906$	−2.47297	−	21.4750i	−0.0821588	−	0.713459i
$907$	−32.6847	−	11.8963i	−1.08528	−	0.395009i	−0.263408	−	0.964685i	$-0.584846\pi$
$907$	−32.6847	−	11.8963i	−1.08528	−	0.395009i	−0.821869	+	0.569676i	$0.807069\pi$
$908$	4.54450	+	7.87131i	0.150815	+	0.261219i
$909$	8.82500	−	2.05981i	0.292707	−	0.0683196i
$910$	−0.501094	+	0.00653868i	−0.0166111	+	0.000216755i
$911$	25.8389	+	9.40459i	0.856081	+	0.311588i	0.732517	−	0.680749i	$-0.238345\pi$
$911$	25.8389	+	9.40459i	0.856081	+	0.311588i	0.123564	+	0.992337i	$0.460568\pi$
$912$	−2.96016	+	4.48404i	−0.0980208	+	0.148481i
$913$	7.30188	−	41.4110i	0.241657	−	1.37050i
$914$	−6.25047	−	5.24477i	−0.206747	−	0.173481i
$915$	14.8405	−	4.41539i	0.490610	−	0.145968i
$916$	4.95237	+	28.0863i	0.163631	+	0.927996i
$917$	17.9847	−	0.234680i	0.593909	−	0.00774980i
$918$	32.4443	−	18.5111i	1.07082	−	0.610959i
$919$	−23.0212	+	39.8739i	−0.759400	+	1.31532i	0.183758	+	0.982972i	$0.441174\pi$
$919$	−23.0212	+	39.8739i	−0.759400	+	1.31532i	−0.943157	+	0.332347i	$0.892160\pi$
$920$	−2.38624	+	2.00229i	−0.0786719	+	0.0660135i
$921$	−38.9269	+	11.5817i	−1.28269	+	0.381630i
$922$	−5.71301	+	32.4001i	−0.188148	+	1.06704i
$923$	−1.19458	−	1.00237i	−0.0393199	−	0.0329933i
$924$	22.7952	+	1.06838i	0.749908	+	0.0351471i
$925$	10.9137	+	3.97225i	0.358839	+	0.130607i
$926$	23.9434			0.786830
$927$	10.7709	+	25.2056i	0.353762	+	0.827861i
$928$	−5.48037			−0.179902
$929$	−5.85730	−	33.2184i	−0.192172	−	1.08986i	−0.916389	−	0.400288i	$-0.868910\pi$
$929$	−5.85730	−	33.2184i	−0.192172	−	1.08986i	0.724218	−	0.689572i	$-0.242201\pi$
$930$	−1.26971	−	11.0260i	−0.0416354	−	0.361557i
$931$	20.2044	−	7.95679i	0.662174	−	0.260773i
$932$	0.824763	−	4.67746i	0.0270160	−	0.153215i
$933$	32.9665	+	14.2871i	1.07927	+	0.467737i
$934$	23.3745	+	8.50762i	0.764837	+	0.278378i
$935$	−52.8698			−1.72903
$936$	0.151188	+	0.353804i	0.00494172	+	0.0115644i
$937$	7.72979	+	13.3884i	0.252521	+	0.437380i	0.964219	−	0.265106i	$-0.0854069\pi$
$937$	7.72979	+	13.3884i	0.252521	+	0.437380i	−0.711698	+	0.702486i	$0.752074\pi$
$938$	6.14470	+	32.3725i	0.200632	+	1.05700i
$939$	−13.1968	+	19.9905i	−0.430662	+	0.652365i
$940$	9.98534	−	3.63437i	0.325686	−	0.118540i
$941$	−13.6075	−	11.4180i	−0.443591	−	0.372217i	0.393460	−	0.919342i	$-0.371278\pi$
$941$	−13.6075	−	11.4180i	−0.443591	−	0.372217i	−0.837051	+	0.547125i	$0.815722\pi$
$942$	6.49480	−	1.93236i	0.211612	−	0.0629596i
$943$	15.8381	+	5.76460i	0.515760	+	0.187721i
$944$	9.91599			0.322738
$945$	−20.0227	−	3.36696i	−0.651337	−	0.109527i
$946$	8.07962			0.262691
$947$	−14.3788	−	5.23344i	−0.467247	−	0.170064i	0.0976580	−	0.995220i	$-0.468865\pi$
$947$	−14.3788	−	5.23344i	−0.467247	−	0.170064i	−0.564905	+	0.825156i	$0.691087\pi$
$948$	−5.27506	+	22.0894i	−0.171326	+	0.717429i
$949$	0.527587	+	0.442698i	0.0171262	+	0.0143706i
$950$	8.21693	−	2.99072i	0.266592	−	0.0970317i
$951$	−29.2042	−	1.75091i	−0.947010	−	0.0567770i
$952$	−14.4091	+	12.4146i	−0.467000	+	0.402359i
$953$	−9.73375	−	16.8594i	−0.315307	−	0.546128i	0.664196	−	0.747559i	$-0.268774\pi$
$953$	−9.73375	−	16.8594i	−0.315307	−	0.546128i	−0.979503	+	0.201431i	$0.935441\pi$
$954$	−2.80717	+	0.655210i	−0.0908853	+	0.0212132i
$955$	38.0786			1.23219
$956$	8.82413	+	3.21172i	0.285393	+	0.103875i
$957$	37.9641	−	28.1627i	1.22720	−	0.910372i
$958$	0.753313	−	4.27225i	0.0243384	−	0.138030i
$959$	−5.89718	−	4.81861i	−0.190430	−	0.155601i
$960$	−2.05446	+	1.52405i	−0.0663074	+	0.0491886i
$961$	−2.11409	−	11.9896i	−0.0681963	−	0.386760i
$962$	−0.528419			−0.0170369
$963$	48.6007	+	24.6160i	1.56614	+	0.793240i
$964$	−28.8947			−0.930634
$965$	4.32969	+	1.57588i	0.139378	+	0.0507294i
$966$	−4.43555	−	8.58762i	−0.142712	−	0.276302i
$967$	−24.2875	−	20.3797i	−0.781034	−	0.655366i	0.162475	−	0.986713i	$-0.448052\pi$
$967$	−24.2875	−	20.3797i	−0.781034	−	0.655366i	−0.943509	+	0.331347i	$0.892497\pi$
$968$	−2.39605	+	13.5886i	−0.0770118	+	0.436756i
$969$	28.0496	+	26.5539i	0.901082	+	0.853035i
$970$	−0.825005	+	0.692261i	−0.0264893	+	0.0222272i
$971$	0.112027	−	0.194036i	0.00359511	−	0.00622692i	−0.864222	−	0.503110i	$-0.832189\pi$
$971$	0.112027	−	0.194036i	0.00359511	−	0.00622692i	0.867817	+	0.496883i	$0.165522\pi$
$972$	3.46553	+	15.1984i	0.111157	+	0.487488i
$973$	−24.5124	−	41.2055i	−0.785830	−	1.32099i
$974$	6.28913	+	35.6674i	0.201517	+	1.14286i
$975$	0.145442	−	0.609040i	0.00465787	−	0.0195049i
$976$	4.63674	+	3.89069i	0.148418	+	0.124538i
$977$	−4.56864	+	25.9100i	−0.146164	+	0.828935i	0.820262	+	0.571988i	$0.193828\pi$
$977$	−4.56864	+	25.9100i	−0.146164	+	0.828935i	−0.966425	+	0.256947i	$0.917283\pi$
$978$	29.1841	+	1.74970i	0.933205	+	0.0559494i
$979$	28.2584	+	10.2852i	0.903142	+	0.328717i
$980$	10.3347	−	0.269756i	0.330128	−	0.00861703i
$981$	36.0308	−	23.5223i	1.15038	−	0.751008i
$982$	8.28211	+	14.3450i	0.264293	+	0.457769i
$983$	−30.6896	−	11.1701i	−0.978847	−	0.356271i	−0.197455	−	0.980312i	$-0.563268\pi$
$983$	−30.6896	−	11.1701i	−0.978847	−	0.356271i	−0.781392	+	0.624041i	$0.785490\pi$
$984$	12.6996	+	5.50376i	0.404848	+	0.175454i
$985$	8.14712	+	6.83625i	0.259589	+	0.217821i
$986$	−6.84119	+	38.7983i	−0.217868	+	1.23559i
$987$	4.19900	+	32.7032i	0.133656	+	1.04095i
$988$	−0.304770	+	0.255732i	−0.00969601	+	0.00813592i
$989$	−1.71105	−	2.96363i	−0.0544084	−	0.0942381i
$990$	6.39996	−	21.1151i	0.203404	−	0.671081i
$991$	22.9028	−	39.6688i	0.727531	−	1.26012i	−0.230392	−	0.973098i	$-0.574001\pi$
$991$	22.9028	−	39.6688i	0.727531	−	1.26012i	0.957924	−	0.287023i	$-0.0926657\pi$
$992$	3.32374	−	2.78895i	0.105529	−	0.0885492i
$993$	16.5807	+	0.994080i	0.526173	+	0.0315462i
$994$	24.9112	+	20.3550i	0.790134	+	0.645622i
$995$	22.0071	−	8.00993i	0.697672	−	0.253932i
$996$	−14.0183	+	4.17078i	−0.444188	+	0.132156i
$997$	−6.36848	+	5.34379i	−0.201692	+	0.169239i	−0.738039	−	0.674758i	$-0.764248\pi$
$997$	−6.36848	+	5.34379i	−0.201692	+	0.169239i	0.536348	+	0.843997i	$0.319804\pi$
$998$	−8.01127	−	13.8759i	−0.253592	−	0.439235i
$999$	−21.0646	−	3.82544i	−0.666455	−	0.121031i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.w.b.121.4	yes	72
7.4	even	3		378.2.v.a.67.6	✓	72
27.25	even	9		378.2.v.a.79.6	yes	72
189.25	even	9	inner	378.2.w.b.25.4	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.v.a.67.6	✓	72	7.4	even	3
378.2.v.a.79.6	yes	72	27.25	even	9
378.2.w.b.25.4	yes	72	189.25	even	9	inner
378.2.w.b.121.4	yes	72	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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939693 + 0.342020i) q^{2} +(-1.25782 - 1.19075i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-1.38782 + 0.505123i) q^{5} +(-0.774703 - 1.54914i) q^{6} +(0.493387 + 2.59934i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.164223 + 2.99550i) q^{9} +O(q^{10})\)	\(q+(0.939693 + 0.342020i) q^{2} +(-1.25782 - 1.19075i) q^{3} +(0.766044 + 0.642788i) q^{4} +(-1.38782 + 0.505123i) q^{5} +(-0.774703 - 1.54914i) q^{6} +(0.493387 + 2.59934i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.164223 + 2.99550i) q^{9} -1.47688 q^{10} +(4.67947 + 1.70319i) q^{11} +(-0.198146 - 1.72068i) q^{12} +(0.0222706 - 0.126303i) q^{13} +(-0.425394 + 2.61133i) q^{14} +(2.34710 + 1.01719i) q^{15} +(0.173648 + 0.984808i) q^{16} +7.18871 q^{17} +(-0.870203 + 2.87102i) q^{18} -3.10211 q^{19} +(-1.38782 - 0.505123i) q^{20} +(2.47458 - 3.85700i) q^{21} +(3.81474 + 3.20095i) q^{22} +(0.366255 - 2.07714i) q^{23} +(0.402311 - 1.68468i) q^{24} +(-2.15934 + 1.81190i) q^{25} +(0.0641255 - 0.111069i) q^{26} +(3.36034 - 3.96335i) q^{27} +(-1.29287 + 2.30835i) q^{28} +(0.951657 + 5.39711i) q^{29} +(1.85765 + 1.75860i) q^{30} +(-3.32374 - 2.78895i) q^{31} +(-0.173648 + 0.984808i) q^{32} +(-3.85786 - 7.71439i) q^{33} +(6.75518 + 2.45868i) q^{34} +(-1.99772 - 3.35818i) q^{35} +(-1.79967 + 2.40025i) q^{36} +(-2.06010 - 3.56819i) q^{37} +(-2.91503 - 1.06098i) q^{38} +(-0.178407 + 0.132347i) q^{39} +(-1.13136 - 0.949322i) q^{40} +(-1.38763 + 7.86966i) q^{41} +(3.64451 - 2.77804i) q^{42} +(1.24289 - 1.04291i) q^{43} +(2.48989 + 4.31262i) q^{44} +(-1.74101 - 4.07425i) q^{45} +(1.05459 - 1.82660i) q^{46} +(-5.51169 + 4.62486i) q^{47} +(0.954243 - 1.44548i) q^{48} +(-6.51314 + 2.56496i) q^{49} +(-2.64882 + 0.964093i) q^{50} +(-9.04211 - 8.55997i) q^{51} +(0.0982460 - 0.0824382i) q^{52} +(0.480436 + 0.832140i) q^{53} +(4.51323 - 2.57503i) q^{54} -7.35456 q^{55} +(-2.00440 + 1.72696i) q^{56} +(3.90189 + 3.69384i) q^{57} +(-0.951657 + 5.39711i) q^{58} +(1.72189 - 9.76534i) q^{59} +(1.14415 + 2.28790i) q^{60} +(4.63674 - 3.89069i) q^{61} +(-2.16942 - 3.75754i) q^{62} +(-7.70530 + 1.90481i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.0328910 + 0.186534i) q^{65} +(-0.986724 - 8.56862i) q^{66} +(11.7030 - 4.25956i) q^{67} +(5.50687 + 4.62082i) q^{68} +(-2.93404 + 2.17654i) q^{69} +(-0.728675 - 3.83892i) q^{70} +(6.07951 - 10.5300i) q^{71} +(-2.51207 + 1.63997i) q^{72} +(-2.68503 + 4.65060i) q^{73} +(-0.715464 - 4.05760i) q^{74} +(4.87359 + 0.292191i) q^{75} +(-2.37635 - 1.99400i) q^{76} +(-2.11837 + 13.0039i) q^{77} +(-0.212914 + 0.0633469i) q^{78} +(-12.3212 - 4.48453i) q^{79} +(-0.738441 - 1.27902i) q^{80} +(-8.94606 + 0.983858i) q^{81} +(-3.99553 + 6.92046i) q^{82} +(-1.46630 - 8.31582i) q^{83} +(4.37487 - 1.36401i) q^{84} +(-9.97661 + 3.63119i) q^{85} +(1.52464 - 0.554922i) q^{86} +(5.22961 - 7.92178i) q^{87} +(0.864731 + 4.90413i) q^{88} +6.03880 q^{89} +(-0.242538 - 4.42400i) q^{90} +(0.339292 - 0.00442735i) q^{91} +(1.61573 - 1.35575i) q^{92} +(0.859722 + 7.46574i) q^{93} +(-6.76109 + 2.46084i) q^{94} +(4.30515 - 1.56695i) q^{95} +(1.39108 - 1.03194i) q^{96} +(0.558612 - 0.468731i) q^{97} +(-6.99762 + 0.182652i) q^{98} +(-4.33343 + 14.2971i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8}+O(q^{10}) \) 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8	\( 72 q + 3 q^{6} + 3 q^{7} + 36 q^{8} - 12 q^{10} - 6 q^{11} + 12 q^{13} - 3 q^{14} - 6 q^{15} + 24 q^{17} - 36 q^{19} + 18 q^{21} + 6 q^{22} - 6 q^{23} + 30 q^{25} - 18 q^{26} + 6 q^{27} + 3 q^{29} + 15 q^{30} - 9 q^{31} - 18 q^{33} - 9 q^{34} + 9 q^{35} - 3 q^{36} + 51 q^{39} - 6 q^{41} - 27 q^{42} - 24 q^{43} + 18 q^{45} + 27 q^{47} + 6 q^{48} - 69 q^{49} + 6 q^{50} + 6 q^{51} - 6 q^{52} - 15 q^{53} + 45 q^{54} - 72 q^{55} + 6 q^{56} + 57 q^{57} - 3 q^{58} + 15 q^{59} - 33 q^{60} - 18 q^{61} - 24 q^{62} - 12 q^{63} - 36 q^{64} - 90 q^{65} - 36 q^{66} - 66 q^{67} - 18 q^{68} - 39 q^{69} - 12 q^{70} + 12 q^{71} + 30 q^{73} + 9 q^{74} - 21 q^{75} - 87 q^{77} + 6 q^{78} - 45 q^{79} - 6 q^{80} - 24 q^{81} + 33 q^{82} + 18 q^{83} + 6 q^{84} + 51 q^{85} - 12 q^{86} - 18 q^{87} - 12 q^{88} + 72 q^{89} - 69 q^{90} - 30 q^{91} + 12 q^{92} - 48 q^{93} + 21 q^{95} + 48 q^{97} + 6 q^{98} + 90 q^{99}+O(q^{100}) \) 72 * q + 3 * q^6 + 3 * q^7 + 36 * q^8 - 12 * q^10 - 6 * q^11 + 12 * q^13 - 3 * q^14 - 6 * q^15 + 24 * q^17 - 36 * q^19 + 18 * q^21 + 6 * q^22 - 6 * q^23 + 30 * q^25 - 18 * q^26 + 6 * q^27 + 3 * q^29 + 15 * q^30 - 9 * q^31 - 18 * q^33 - 9 * q^34 + 9 * q^35 - 3 * q^36 + 51 * q^39 - 6 * q^41 - 27 * q^42 - 24 * q^43 + 18 * q^45 + 27 * q^47 + 6 * q^48 - 69 * q^49 + 6 * q^50 + 6 * q^51 - 6 * q^52 - 15 * q^53 + 45 * q^54 - 72 * q^55 + 6 * q^56 + 57 * q^57 - 3 * q^58 + 15 * q^59 - 33 * q^60 - 18 * q^61 - 24 * q^62 - 12 * q^63 - 36 * q^64 - 90 * q^65 - 36 * q^66 - 66 * q^67 - 18 * q^68 - 39 * q^69 - 12 * q^70 + 12 * q^71 + 30 * q^73 + 9 * q^74 - 21 * q^75 - 87 * q^77 + 6 * q^78 - 45 * q^79 - 6 * q^80 - 24 * q^81 + 33 * q^82 + 18 * q^83 + 6 * q^84 + 51 * q^85 - 12 * q^86 - 18 * q^87 - 12 * q^88 + 72 * q^89 - 69 * q^90 - 30 * q^91 + 12 * q^92 - 48 * q^93 + 21 * q^95 + 48 * q^97 + 6 * q^98 + 90 * q^99

Introduction

L-functions

Modular forms

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