LMFDB - Embedded newform 360.2.br.e.77.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(77,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 10, 3]))

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

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

chi := DirichletCharacter("360.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.br (of order $12$, degree $4$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			77.10
Character	$\chi$	$=$	360.77
Dual form			360.2.br.e.173.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15671 + 0.813649i) q^{2} +(0.674078 - 1.59550i) q^{3} +(0.675951 - 1.88231i) q^{4} +(0.576180 - 2.16056i) q^{5} +(0.518465 + 2.39399i) q^{6} +(0.331473 - 1.23707i) q^{7} +(0.749662 + 2.72727i) q^{8} +(-2.09124 - 2.15098i) q^{9} +O(q^{10})$	\(q+(-1.15671 + 0.813649i) q^{2} +(0.674078 - 1.59550i) q^{3} +(0.675951 - 1.88231i) q^{4} +(0.576180 - 2.16056i) q^{5} +(0.518465 + 2.39399i) q^{6} +(0.331473 - 1.23707i) q^{7} +(0.749662 + 2.72727i) q^{8} +(-2.09124 - 2.15098i) q^{9} +(1.09146 + 2.96795i) q^{10} +(-0.0407683 - 0.0706128i) q^{11} +(-2.54758 - 2.34730i) q^{12} +(2.59129 - 0.694333i) q^{13} +(0.623127 + 1.70064i) q^{14} +(-3.05878 - 2.37568i) q^{15} +(-3.08618 - 2.54470i) q^{16} +(-2.70590 + 2.70590i) q^{17} +(4.16910 + 0.786527i) q^{18} +1.60200 q^{19} +(-3.67737 - 2.54498i) q^{20} +(-1.75031 - 1.36275i) q^{21} +(0.104611 + 0.0485074i) q^{22} +(-8.79321 + 2.35613i) q^{23} +(4.85669 + 0.642309i) q^{24} +(-4.33603 - 2.48974i) q^{25} +(-2.43242 + 2.91154i) q^{26} +(-4.84155 + 1.88664i) q^{27} +(-2.10450 - 1.46014i) q^{28} +(4.67863 - 2.70121i) q^{29} +(5.47109 + 0.259197i) q^{30} +(4.39731 - 7.61637i) q^{31} +(5.64030 + 0.432405i) q^{32} +(-0.140144 + 0.0174473i) q^{33} +(0.928286 - 5.33160i) q^{34} +(-2.48178 - 1.42895i) q^{35} +(-5.46239 + 2.48240i) q^{36} +(4.67714 - 4.67714i) q^{37} +(-1.85305 + 1.30347i) q^{38} +(0.638921 - 4.60243i) q^{39} +(6.32437 - 0.0482888i) q^{40} +(5.35270 + 3.09038i) q^{41} +(3.13340 + 0.152164i) q^{42} +(-2.59179 + 9.67270i) q^{43} +(-0.160473 + 0.0290079i) q^{44} +(-5.85225 + 3.27889i) q^{45} +(8.25412 - 9.87995i) q^{46} +(-0.249195 - 0.0667716i) q^{47} +(-6.14039 + 3.20868i) q^{48} +(4.64170 + 2.67989i) q^{49} +(7.04130 - 0.648101i) q^{50} +(2.49328 + 6.14125i) q^{51} +(0.444631 - 5.34694i) q^{52} +(5.50554 - 5.50554i) q^{53} +(4.06520 - 6.12161i) q^{54} +(-0.176053 + 0.0473967i) q^{55} +(3.62233 - 0.0233703i) q^{56} +(1.07988 - 2.55600i) q^{57} +(-3.21397 + 6.93127i) q^{58} +(-5.94730 - 3.43368i) q^{59} +(-6.53935 + 4.15173i) q^{60} +(3.97906 - 2.29731i) q^{61} +(1.11064 + 12.3878i) q^{62} +(-3.35411 + 1.87402i) q^{63} +(-6.87601 + 4.08906i) q^{64} +(-0.00709990 - 5.99869i) q^{65} +(0.147910 - 0.134209i) q^{66} +(-1.59401 - 5.94892i) q^{67} +(3.26429 + 6.92240i) q^{68} +(-2.16810 + 15.6178i) q^{69} +(4.03336 - 0.366428i) q^{70} +0.475607i q^{71} +(4.29859 - 7.31588i) q^{72} +(-2.68905 + 2.68905i) q^{73} +(-1.60454 + 9.21563i) q^{74} +(-6.89521 + 5.23986i) q^{75} +(1.08288 - 3.01547i) q^{76} +(-0.100867 + 0.0270272i) q^{77} +(3.00572 + 5.84353i) q^{78} +(-0.618226 + 0.356933i) q^{79} +(-7.27617 + 5.20167i) q^{80} +(-0.253450 + 8.99643i) q^{81} +(-8.70600 + 0.780546i) q^{82} +(5.18428 + 1.38912i) q^{83} +(-3.74824 + 2.37348i) q^{84} +(4.28717 + 7.40535i) q^{85} +(-4.87223 - 13.2973i) q^{86} +(-1.15601 - 9.28557i) q^{87} +(0.162018 - 0.164122i) q^{88} +3.71234 q^{89} +(4.10149 - 8.55440i) q^{90} -3.43577i q^{91} +(-1.50880 + 18.1442i) q^{92} +(-9.18779 - 12.1499i) q^{93} +(0.342575 - 0.125522i) q^{94} +(0.923043 - 3.46123i) q^{95} +(4.49191 - 8.70763i) q^{96} +(-4.49423 + 16.7727i) q^{97} +(-7.54958 + 0.676866i) q^{98} +(-0.0666307 + 0.235360i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 6 q^{2} - 8 q^{6}+O(q^{10}) $ 256 * q + 6 * q^2 - 8 * q^6	$ 256 q + 6 q^{2} - 8 q^{6} - 10 q^{12} + 28 q^{15} + 12 q^{16} - 28 q^{18} - 54 q^{20} + 14 q^{22} - 28 q^{25} - 32 q^{28} + 14 q^{30} - 32 q^{31} - 114 q^{32} + 4 q^{33} - 40 q^{36} - 30 q^{38} + 46 q^{40} + 24 q^{41} - 10 q^{42} - 16 q^{46} + 24 q^{47} - 2 q^{48} + 78 q^{50} + 38 q^{52} - 8 q^{55} - 96 q^{56} - 80 q^{57} - 18 q^{58} - 2 q^{60} - 144 q^{63} - 84 q^{65} - 4 q^{66} - 30 q^{68} - 30 q^{70} - 86 q^{72} + 64 q^{73} + 16 q^{76} - 82 q^{78} + 72 q^{81} - 64 q^{82} + 48 q^{86} - 4 q^{87} + 38 q^{88} + 78 q^{90} - 108 q^{92} - 24 q^{95} - 116 q^{96} + 36 q^{97}+O(q^{100}) $ 256 * q + 6 * q^2 - 8 * q^6 - 10 * q^12 + 28 * q^15 + 12 * q^16 - 28 * q^18 - 54 * q^20 + 14 * q^22 - 28 * q^25 - 32 * q^28 + 14 * q^30 - 32 * q^31 - 114 * q^32 + 4 * q^33 - 40 * q^36 - 30 * q^38 + 46 * q^40 + 24 * q^41 - 10 * q^42 - 16 * q^46 + 24 * q^47 - 2 * q^48 + 78 * q^50 + 38 * q^52 - 8 * q^55 - 96 * q^56 - 80 * q^57 - 18 * q^58 - 2 * q^60 - 144 * q^63 - 84 * q^65 - 4 * q^66 - 30 * q^68 - 30 * q^70 - 86 * q^72 + 64 * q^73 + 16 * q^76 - 82 * q^78 + 72 * q^81 - 64 * q^82 + 48 * q^86 - 4 * q^87 + 38 * q^88 + 78 * q^90 - 108 * q^92 - 24 * q^95 - 116 * q^96 + 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.15671	+	0.813649i	−0.817917	+	0.575337i
$2$	−1.15671	+	0.813649i	−0.817917	+	0.575337i
$3$	0.674078	−	1.59550i	0.389179	−	0.921162i
$3$	0.674078	−	1.59550i	0.389179	−	0.921162i
$4$	0.675951	−	1.88231i	0.337975	−	0.941155i
$5$	0.576180	−	2.16056i	0.257676	−	0.966231i
$5$	0.576180	−	2.16056i	0.257676	−	0.966231i
$6$	0.518465	+	2.39399i	0.211662	+	0.977343i
$7$	0.331473	−	1.23707i	0.125285	−	0.467570i	−0.874565	−	0.484909i	$-0.838853\pi$
$7$	0.331473	−	1.23707i	0.125285	−	0.467570i	0.999850	+	0.0173388i	$0.00551938\pi$
$8$	0.749662	+	2.72727i	0.265045	+	0.964236i
$9$	−2.09124	−	2.15098i	−0.697079	−	0.716994i
$10$	1.09146	+	2.96795i	0.345151	+	0.938547i
$11$	−0.0407683	−	0.0706128i	−0.0122921	−	0.0212906i	0.859814	−	0.510608i	$-0.170579\pi$
$11$	−0.0407683	−	0.0706128i	−0.0122921	−	0.0212906i	−0.872106	+	0.489317i	$0.837246\pi$
$12$	−2.54758	−	2.34730i	−0.735423	−	0.677608i
$13$	2.59129	−	0.694333i	0.718694	−	0.192573i	0.119105	−	0.992882i	$-0.461998\pi$
$13$	2.59129	−	0.694333i	0.718694	−	0.192573i	0.599589	+	0.800308i	$0.295331\pi$
$14$	0.623127	+	1.70064i	0.166538	+	0.454515i
$15$	−3.05878	−	2.37568i	−0.789774	−	0.613398i
$16$	−3.08618	−	2.54470i	−0.771545	−	0.636174i
$17$	−2.70590	+	2.70590i	−0.656278	+	0.656278i	−0.954497	−	0.298220i	$-0.903607\pi$
$17$	−2.70590	+	2.70590i	−0.656278	+	0.656278i	0.298220	+	0.954497i	$0.403607\pi$
$18$	4.16910	+	0.786527i	0.982666	+	0.185386i
$19$	1.60200			0.367525			0.183763	−	0.982971i	$-0.441172\pi$
$19$	1.60200			0.367525			0.183763	+	0.982971i	$0.441172\pi$
$20$	−3.67737	−	2.54498i	−0.822286	−	0.569075i
$21$	−1.75031	−	1.36275i	−0.381950	−	0.297376i
$22$	0.104611	+	0.0485074i	0.0223032	+	0.0103418i
$23$	−8.79321	+	2.35613i	−1.83351	+	0.491288i	−0.998281	−	0.0586117i	$-0.981333\pi$
$23$	−8.79321	+	2.35613i	−1.83351	+	0.491288i	−0.835231	+	0.549900i	$0.814666\pi$
$24$	4.85669	+	0.642309i	0.991368	+	0.131111i
$25$	−4.33603	−	2.48974i	−0.867207	−	0.497949i
$26$	−2.43242	+	2.91154i	−0.477037	+	0.571000i
$27$	−4.84155	+	1.88664i	−0.931756	+	0.363084i
$28$	−2.10450	−	1.46014i	−0.397713	−	0.275940i
$29$	4.67863	−	2.70121i	0.868799	−	0.501601i	0.00185004	−	0.999998i	$-0.499411\pi$
$29$	4.67863	−	2.70121i	0.868799	−	0.501601i	0.866949	+	0.498397i	$0.166078\pi$
$30$	5.47109	+	0.259197i	0.998880	+	0.0473227i
$31$	4.39731	−	7.61637i	0.789781	−	1.36794i	−0.136320	−	0.990665i	$-0.543527\pi$
$31$	4.39731	−	7.61637i	0.789781	−	1.36794i	0.926101	−	0.377276i	$-0.123139\pi$
$32$	5.64030	+	0.432405i	0.997074	+	0.0764391i
$33$	−0.140144	+	0.0174473i	−0.0243959	+	0.00303719i
$34$	0.928286	−	5.33160i	0.159200	−	0.914361i
$35$	−2.48178	−	1.42895i	−0.419498	−	0.241536i
$36$	−5.46239	+	2.48240i	−0.910398	+	0.413733i
$37$	4.67714	−	4.67714i	0.768917	−	0.768917i	−0.208999	−	0.977916i	$-0.567021\pi$
$37$	4.67714	−	4.67714i	0.768917	−	0.768917i	0.977916	+	0.208999i	$0.0670206\pi$
$38$	−1.85305	+	1.30347i	−0.300605	+	0.211451i
$39$	0.638921	−	4.60243i	0.102309	−	0.736979i
$40$	6.32437	−	0.0482888i	0.999971	−	0.00763513i
$41$	5.35270	+	3.09038i	0.835951	+	0.482637i	0.855886	−	0.517165i	$-0.173013\pi$
$41$	5.35270	+	3.09038i	0.835951	+	0.482637i	−0.0199349	+	0.999801i	$0.506346\pi$
$42$	3.13340	+	0.152164i	0.483495	+	0.0234795i
$43$	−2.59179	+	9.67270i	−0.395244	+	1.47507i	0.426119	+	0.904667i	$0.359880\pi$
$43$	−2.59179	+	9.67270i	−0.395244	+	1.47507i	−0.821363	+	0.570405i	$0.806786\pi$
$44$	−0.160473	+	0.0290079i	−0.0241922	+	0.00437310i
$45$	−5.85225	+	3.27889i	−0.872403	+	0.488788i
$46$	8.25412	−	9.87995i	1.21700	−	1.45672i
$47$	−0.249195	−	0.0667716i	−0.0363488	−	0.00973964i	0.240599	−	0.970625i	$-0.422656\pi$
$47$	−0.249195	−	0.0667716i	−0.0363488	−	0.00973964i	−0.276948	+	0.960885i	$0.589323\pi$
$48$	−6.14039	+	3.20868i	−0.886289	+	0.463133i
$49$	4.64170	+	2.67989i	0.663100	+	0.382841i
$50$	7.04130	−	0.648101i	0.995791	−	0.0916553i
$51$	2.49328	+	6.14125i	0.349129	+	0.859948i
$52$	0.444631	−	5.34694i	0.0616593	−	0.741487i
$53$	5.50554	−	5.50554i	0.756244	−	0.756244i	−0.219392	−	0.975637i	$-0.570408\pi$
$53$	5.50554	−	5.50554i	0.756244	−	0.756244i	0.975637	+	0.219392i	$0.0704075\pi$
$54$	4.06520	−	6.12161i	0.553204	−	0.833046i
$55$	−0.176053	+	0.0473967i	−0.0237390	+	0.00639097i
$56$	3.62233	−	0.0233703i	0.484054	−	0.00312298i
$57$	1.07988	−	2.55600i	0.143033	−	0.338550i
$58$	−3.21397	+	6.93127i	−0.422015	+	0.910120i
$59$	−5.94730	−	3.43368i	−0.774273	−	0.447027i	0.0601240	−	0.998191i	$-0.480850\pi$
$59$	−5.94730	−	3.43368i	−0.774273	−	0.447027i	−0.834397	+	0.551164i	$0.814184\pi$
$60$	−6.53935	+	4.15173i	−0.844227	+	0.535986i
$61$	3.97906	−	2.29731i	0.509466	−	0.294140i	−0.223148	−	0.974785i	$-0.571633\pi$
$61$	3.97906	−	2.29731i	0.509466	−	0.294140i	0.732614	+	0.680644i	$0.238300\pi$
$62$	1.11064	+	12.3878i	0.141052	+	1.57325i
$63$	−3.35411	+	1.87402i	−0.422579	+	0.236105i
$64$	−6.87601	+	4.08906i	−0.859502	+	0.511133i
$65$	−0.00709990	−	5.99869i	−0.000880634	−	0.744046i
$66$	0.147910	−	0.134209i	0.0182064	−	0.0165200i
$67$	−1.59401	−	5.94892i	−0.194739	−	0.726776i	−0.992334	−	0.123583i	$-0.960561\pi$
$67$	−1.59401	−	5.94892i	−0.194739	−	0.726776i	0.797595	−	0.603193i	$-0.206105\pi$
$68$	3.26429	+	6.92240i	0.395853	+	0.839465i
$69$	−2.16810	+	15.6178i	−0.261009	+	1.88016i
$70$	4.03336	−	0.366428i	0.482079	−	0.0437965i
$71$			0.475607i			0.0564442i	0.999602	+	0.0282221i	$0.00898457\pi$
$71$			0.475607i			0.0564442i	−0.999602	+	0.0282221i	$0.991015\pi$
$72$	4.29859	−	7.31588i	0.506594	−	0.862185i
$73$	−2.68905	+	2.68905i	−0.314729	+	0.314729i	−0.846739	−	0.532009i	$-0.821437\pi$
$73$	−2.68905	+	2.68905i	−0.314729	+	0.314729i	0.532009	+	0.846739i	$0.321437\pi$
$74$	−1.60454	+	9.21563i	−0.186524	+	1.07130i
$75$	−6.89521	+	5.23986i	−0.796190	+	0.605047i
$76$	1.08288	−	3.01547i	0.124214	−	0.345898i
$77$	−0.100867	+	0.0270272i	−0.0114949	+	0.00308004i
$78$	3.00572	+	5.84353i	0.340331	+	0.661649i
$79$	−0.618226	+	0.356933i	−0.0695558	+	0.0401581i	−0.534375	−	0.845248i	$-0.679453\pi$
$79$	−0.618226	+	0.356933i	−0.0695558	+	0.0401581i	0.464819	+	0.885406i	$0.346119\pi$
$80$	−7.27617	+	5.20167i	−0.813500	+	0.581565i
$81$	−0.253450	+	8.99643i	−0.0281612	+	0.999603i
$82$	−8.70600	+	0.780546i	−0.961417	+	0.0861969i
$83$	5.18428	+	1.38912i	0.569049	+	0.152476i	0.531860	−	0.846832i	$-0.321493\pi$
$83$	5.18428	+	1.38912i	0.569049	+	0.152476i	0.0371885	+	0.999308i	$0.488160\pi$
$84$	−3.74824	+	2.37348i	−0.408967	+	0.258968i
$85$	4.28717	+	7.40535i	0.465009	+	0.803223i
$86$	−4.87223	−	13.2973i	−0.525386	−	1.43388i
$87$	−1.15601	−	9.28557i	−0.123938	−	0.995517i
$88$	0.162018	−	0.164122i	0.0172712	−	0.0174955i
$89$	3.71234			0.393508			0.196754	−	0.980453i	$-0.436960\pi$
$89$	3.71234			0.393508			0.196754	+	0.980453i	$0.436960\pi$
$90$	4.10149	−	8.55440i	0.432335	−	0.901713i
$91$		−	3.43577i		−	0.360166i
$92$	−1.50880	+	18.1442i	−0.157304	+	1.89166i
$93$	−9.18779	−	12.1499i	−0.952729	−	1.25989i
$94$	0.342575	−	0.125522i	0.0353339	−	0.0129466i
$95$	0.923043	−	3.46123i	0.0947023	−	0.355114i
$96$	4.49191	−	8.70763i	0.458453	−	0.888718i
$97$	−4.49423	+	16.7727i	−0.456320	+	1.70301i	0.227860	+	0.973694i	$0.426827\pi$
$97$	−4.49423	+	16.7727i	−0.456320	+	1.70301i	−0.684179	+	0.729314i	$0.739839\pi$
$98$	−7.54958	+	0.676866i	−0.762623	+	0.0683738i
$99$	−0.0666307	+	0.235360i	−0.00669663	+	0.0236546i
$100$	−7.61741	+	6.47881i	−0.761741	+	0.647881i
$101$	4.21474	+	7.30015i	0.419383	+	0.726392i	0.995877	−	0.0907087i	$-0.0289132\pi$
$101$	4.21474	+	7.30015i	0.419383	+	0.726392i	−0.576495	+	0.817101i	$0.695580\pi$
$102$	−7.88082	−	5.07499i	−0.780317	−	0.502499i
$103$	3.54410	+	13.2268i	0.349211	+	1.30327i	0.887615	+	0.460585i	$0.152360\pi$
$103$	3.54410	+	13.2268i	0.349211	+	1.30327i	−0.538405	+	0.842686i	$0.680973\pi$
$104$	3.83622	+	6.54663i	0.376173	+	0.641949i
$105$	−3.95280	+	2.99647i	−0.385754	+	0.292425i
$106$	−1.88873	+	10.8479i	−0.183450	+	1.05364i
$107$	−2.62166	−	2.62166i	−0.253445	−	0.253445i	0.568936	−	0.822381i	$-0.307355\pi$
$107$	−2.62166	−	2.62166i	−0.253445	−	0.253445i	−0.822381	+	0.568936i	$0.807355\pi$
$108$	0.278591	+	10.3886i	0.0268074	+	0.999641i
$109$	2.43745			0.233465			0.116733	−	0.993163i	$-0.462758\pi$
$109$	2.43745			0.233465			0.116733	+	0.993163i	$0.462758\pi$
$110$	0.165078	−	0.198070i	0.0157396	−	0.0188852i
$111$	−4.30961	−	10.6151i	−0.409051	−	1.00754i
$112$	−4.17097	+	2.97434i	−0.394119	+	0.281049i
$113$	11.4795	−	3.07591i	1.07990	−	0.289357i	0.325343	−	0.945596i	$-0.394520\pi$
$113$	11.4795	−	3.07591i	1.07990	−	0.289357i	0.754553	+	0.656239i	$0.227854\pi$
$114$	0.830583	+	3.83519i	0.0777912	+	0.359198i
$115$	0.0240926	+	20.3558i	0.00224665	+	1.89819i
$116$	−1.92199	−	10.6325i	−0.178452	−	0.987203i
$117$	−6.91249	−	4.12180i	−0.639060	−	0.381060i
$118$	9.67310	−	0.867253i	0.890481	−	0.0798371i
$119$	2.45047	+	4.24434i	0.224634	+	0.389078i
$120$	4.18607	−	10.1231i	0.382135	−	0.924107i
$121$	5.49668	−	9.52052i	0.499698	−	0.865502i
$122$	−2.73341	+	5.89488i	−0.247471	+	0.533697i
$123$	8.53884	−	6.45707i	0.769921	−	0.582214i
$124$	−11.3640	−	13.4254i	−1.02052	−	1.20564i
$125$	−7.87757	+	7.93372i	−0.704592	+	0.709613i
$126$	2.35494	−	4.89677i	0.209794	−	0.436239i
$127$	−5.21945	−	5.21945i	−0.463152	−	0.463152i	0.436535	−	0.899687i	$-0.356205\pi$
$127$	−5.21945	−	5.21945i	−0.463152	−	0.463152i	−0.899687	+	0.436535i	$0.856205\pi$
$128$	4.62649	−	10.3245i	0.408928	−	0.912567i
$129$	13.6857	+	10.6554i	1.20496	+	0.938152i
$130$	4.88904	+	6.93296i	0.428797	+	0.608061i
$131$	6.20429	−	10.7461i	0.542071	−	0.938895i	−0.456714	−	0.889614i	$-0.650974\pi$
$131$	6.20429	−	10.7461i	0.542071	−	0.938895i	0.998785	−	0.0492814i	$-0.0156931\pi$
$132$	−0.0618890	+	0.275588i	−0.00538675	+	0.0239868i
$133$	0.531022	−	1.98180i	0.0460454	−	0.171844i
$134$	6.68414	+	5.58421i	0.577421	+	0.482402i
$135$	1.28659	+	11.5475i	0.110732	+	0.993850i
$136$	−9.40824	−	5.35122i	−0.806750	−	0.458863i
$137$	15.3334	+	4.10858i	1.31002	+	0.351020i	0.845231	−	0.534400i	$-0.179463\pi$
$137$	15.3334	+	4.10858i	1.31002	+	0.351020i	0.464792	+	0.885420i	$0.346129\pi$
$138$	−10.1995	−	19.8293i	−0.868242	−	1.68798i
$139$	−1.44584	+	2.50427i	−0.122635	+	0.212409i	−0.920806	−	0.390021i	$-0.872468\pi$
$139$	−1.44584	+	2.50427i	−0.122635	+	0.212409i	0.798171	+	0.602431i	$0.205801\pi$
$140$	−4.36728	+	3.70559i	−0.369103	+	0.313180i
$141$	−0.274511	+	0.352581i	−0.0231180	+	0.0296927i
$142$	−0.386977	−	0.550139i	−0.0324744	−	0.0461667i
$143$	−0.154671	−	0.154671i	−0.0129343	−	0.0129343i
$144$	0.980341	+	11.9599i	0.0816950	+	0.996657i
$145$	−3.14038	−	11.6648i	−0.260795	−	0.968711i
$146$	0.922504	−	5.29839i	0.0763470	−	0.438498i
$147$	7.40462	−	5.59938i	0.610723	−	0.461829i
$148$	−5.64231	−	11.9653i	−0.463795	−	0.983544i
$149$	−0.883832	−	0.510281i	−0.0724063	−	0.0418038i	0.463360	−	0.886170i	$-0.346644\pi$
$149$	−0.883832	−	0.510281i	−0.0724063	−	0.0418038i	−0.535766	+	0.844366i	$0.679977\pi$
$150$	3.71234	−	11.6713i	0.303112	−	0.952955i
$151$	7.47197	+	12.9418i	0.608060	+	1.05319i	0.991560	+	0.129650i	$0.0413853\pi$
$151$	7.47197	+	12.9418i	0.608060	+	1.05319i	−0.383500	+	0.923541i	$0.625281\pi$
$152$	1.20096	+	4.36910i	0.0974108	+	0.354381i
$153$	11.4790	+	0.161663i	0.928025	+	0.0130697i
$154$	0.0946830	−	0.113333i	0.00762977	−	0.00913263i
$155$	−13.9220	−	13.8891i	−1.11824	−	1.11560i
$156$	−8.23132	−	4.31366i	−0.659033	−	0.345369i
$157$	−3.61694	−	13.4986i	−0.288663	−	1.07731i	−0.946121	−	0.323814i	$-0.895035\pi$
$157$	−3.61694	−	13.4986i	−0.288663	−	1.07731i	0.657457	−	0.753492i	$-0.271632\pi$
$158$	0.424689	−	0.915886i	0.0337865	−	0.0728640i
$159$	−5.07292	−	12.4953i	−0.402309	−	0.990938i
$160$	4.18407	−	11.9371i	0.330780	−	0.943708i
$161$			11.6589i			0.918847i
$162$	−7.02677	−	10.6125i	−0.552075	−	0.833794i
$163$	9.18304	+	9.18304i	0.719271	+	0.719271i	0.968456	−	0.249185i	$-0.0801627\pi$
$163$	9.18304	+	9.18304i	0.719271	+	0.719271i	−0.249185	+	0.968456i	$0.580163\pi$
$164$	9.43522	−	7.98649i	0.736767	−	0.623640i
$165$	−0.0430521	+	0.312842i	−0.00335160	+	0.0243547i
$166$	−7.12696	+	2.61137i	−0.553160	+	0.202682i
$167$	−2.07025	−	7.72629i	−0.160201	−	0.597878i	−0.998604	−	0.0528269i	$-0.983177\pi$
$167$	−2.07025	−	7.72629i	−0.160201	−	0.597878i	0.838403	−	0.545051i	$-0.183490\pi$
$168$	2.40445	−	5.79518i	0.185507	−	0.447108i
$169$	−5.02566	+	2.90157i	−0.386589	+	0.223198i
$170$	−10.9844	−	5.07758i	−0.842463	−	0.389432i
$171$	−3.35017	−	3.44588i	−0.256194	−	0.263513i
$172$	16.4551	+	11.4168i	1.25469	+	0.870524i
$173$	23.0932	+	6.18781i	1.75574	+	0.470450i	0.985837	−	0.167706i	$-0.0536360\pi$
$173$	23.0932	+	6.18781i	1.75574	+	0.470450i	0.769907	+	0.638156i	$0.220303\pi$
$174$	8.89237	+	9.80011i	0.674128	+	0.742944i
$175$	−4.51728	+	4.53871i	−0.341474	+	0.343094i
$176$	−0.0538698	+	0.321667i	−0.00406059	+	0.0242466i
$177$	−9.48737	+	7.17435i	−0.713115	+	0.539257i
$178$	−4.29410	+	3.02055i	−0.321857	+	0.226399i
$179$		−	21.1813i		−	1.58317i	−0.611060	−	0.791584i	$-0.709257\pi$
$179$		−	21.1813i		−	1.58317i	0.611060	−	0.791584i	$-0.290743\pi$
$180$	2.21605	+	13.2321i	0.165175	+	0.986264i
$181$		−	0.781333i		−	0.0580760i	−0.999578	−	0.0290380i	$-0.990756\pi$
$181$		−	0.781333i		−	0.0580760i	0.999578	−	0.0290380i	$-0.00924438\pi$
$182$	2.79551	+	3.97418i	0.207217	+	0.294586i
$183$	−0.983162	−	7.89715i	−0.0726774	−	0.583774i
$184$	−13.0178	−	22.2152i	−0.959681	−	1.63772i
$185$	−7.41036	−	12.8001i	−0.544820	−	0.941082i
$186$	20.5134	+	6.57831i	1.50411	+	0.482345i
$187$	0.301386	+	0.0807563i	0.0220396	+	0.00590548i
$188$	−0.294128	+	0.423928i	−0.0214515	+	0.0309181i
$189$	0.729070	+	6.61473i	0.0530320	+	0.481151i
$190$	1.74853	+	4.75466i	0.126852	+	0.344940i
$191$	−4.26521	+	2.46252i	−0.308620	+	0.178182i	−0.646309	−	0.763076i	$-0.723688\pi$
$191$	−4.26521	+	2.46252i	−0.308620	+	0.178182i	0.337689	+	0.941258i	$0.390355\pi$
$192$	1.88912	+	13.7270i	0.136336	+	0.990663i
$193$	2.31764	+	8.64955i	0.166827	+	0.622608i	0.997800	+	0.0662950i	$0.0211178\pi$
$193$	2.31764	+	8.64955i	0.166827	+	0.622608i	−0.830973	+	0.556313i	$0.812215\pi$
$194$	−8.44857	−	23.0578i	−0.606572	−	1.65546i
$195$	−9.57569	−	4.03226i	−0.685729	−	0.288756i
$196$	8.18193	−	6.92565i	0.584424	−	0.494689i
$197$	−16.2824	−	16.2824i	−1.16007	−	1.16007i	−0.984459	−	0.175615i	$-0.943809\pi$
$197$	−16.2824	−	16.2824i	−1.16007	−	1.16007i	−0.175615	−	0.984459i	$-0.556191\pi$
$198$	−0.114428	−	0.326457i	−0.00813206	−	0.0232003i
$199$		−	1.89362i		−	0.134235i	−0.997745	−	0.0671176i	$-0.978620\pi$
$199$		−	1.89362i		−	0.134235i	0.997745	−	0.0671176i	$-0.0213803\pi$
$200$	3.53965	−	13.6920i	0.250291	−	0.968171i
$201$	−10.5660	−	1.46680i	−0.745267	−	0.103460i
$202$	−10.8150	−	5.01483i	−0.760940	−	0.352842i
$203$	−1.79075	−	6.68319i	−0.125686	−	0.469068i
$204$	13.2451	−	0.541934i	0.927341	−	0.0379430i
$205$	9.76107	−	9.78420i	0.681743	−	0.683358i
$206$	−14.8614	−	12.4159i	−1.03545	−	0.865054i
$207$	23.4567	+	13.9868i	1.63035	+	0.972150i
$208$	−9.76405	−	4.45120i	−0.677015	−	0.308635i
$209$	−0.0653111	−	0.113122i	−0.00451766	−	0.00782482i
$210$	2.13417	−	6.68223i	0.147271	−	0.461118i
$211$	16.9304	+	9.77477i	1.16554	+	0.672923i	0.952625	−	0.304148i	$-0.0983719\pi$
$211$	16.9304	+	9.77477i	1.16554	+	0.672923i	0.212912	+	0.977071i	$0.431705\pi$
$212$	−6.64166	−	14.0846i	−0.456151	−	0.967335i
$213$	0.758831	+	0.320596i	0.0519943	+	0.0219669i
$214$	5.16560	+	0.899385i	0.353113	+	0.0614807i
$215$	19.4051	+	11.1729i	1.32342	+	0.761988i
$216$	−8.77490	−	11.7899i	−0.597056	−	0.802199i
$217$	−7.96443	−	7.96443i	−0.540661	−	0.540661i
$218$	−2.81942	+	1.98323i	−0.190955	+	0.134321i
$219$	2.47775	+	6.10300i	0.167431	+	0.412403i
$220$	−0.0297879	+	0.363424i	−0.00200830	+	0.0245021i
$221$	−5.13297	+	8.89056i	−0.345281	+	0.598044i
$222$	13.6220	+	8.77210i	0.914246	+	0.588744i
$223$	20.3672	+	5.45736i	1.36389	+	0.365452i	0.865242	−	0.501355i	$-0.167165\pi$
$223$	20.3672	+	5.45736i	1.36389	+	0.365452i	0.498644	+	0.866807i	$0.333832\pi$
$224$	2.40453	−	6.83415i	0.160659	−	0.456626i
$225$	3.71228	+	14.5334i	0.247485	+	0.968892i
$226$	−10.7757	+	12.8982i	−0.716787	+	0.857974i
$227$	−6.06863	+	22.6484i	−0.402789	+	1.50323i	0.405308	+	0.914180i	$0.367164\pi$
$227$	−6.06863	+	22.6484i	−0.402789	+	1.50323i	−0.808097	+	0.589049i	$0.799502\pi$
$228$	−4.08124	−	3.76039i	−0.270287	−	0.249038i
$229$	−6.98940	+	12.1060i	−0.461873	+	0.799987i	−0.999054	−	0.0434796i	$-0.986156\pi$
$229$	−6.98940	+	12.1060i	−0.461873	+	0.799987i	0.537182	+	0.843467i	$0.319489\pi$
$230$	−16.5904	−	23.5261i	−1.09394	−	1.55127i
$231$	−0.0248703	+	0.179152i	−0.00163634	+	0.0117873i
$232$	10.8743	+	10.7349i	0.713933	+	0.704780i
$233$	−13.3037	−	13.3037i	−0.871557	−	0.871557i	0.121085	−	0.992642i	$-0.461363\pi$
$233$	−13.3037	−	13.3037i	−0.871557	−	0.871557i	−0.992642	+	0.121085i	$0.961363\pi$
$234$	11.3494	−	0.856626i	0.741936	−	0.0559994i
$235$	−0.287845	+	0.499928i	−0.0187770	+	0.0326117i
$236$	−10.4833	+	8.87367i	−0.682406	+	0.577627i
$237$	0.152754	+	1.22698i	0.00992242	+	0.0797009i
$238$	−6.28788	−	2.91564i	−0.407583	−	0.188993i
$239$	−14.1304	+	24.4746i	−0.914021	+	1.58313i	−0.105692	+	0.994399i	$0.533706\pi$
$239$	−14.1304	+	24.4746i	−0.914021	+	1.58313i	−0.808329	+	0.588732i	$0.799627\pi$
$240$	3.39457	+	15.1155i	0.219118	+	0.975698i
$241$	−7.91359	−	13.7067i	−0.509759	−	0.882929i	−0.999936	−	0.0113057i	$-0.996401\pi$
$241$	−7.91359	−	13.7067i	−0.509759	−	0.882929i	0.490177	−	0.871623i	$-0.336932\pi$
$242$	1.38831	+	15.4848i	0.0892439	+	0.995403i
$243$	14.1830	+	6.46868i	0.909837	+	0.414966i
$244$	−1.63460	−	9.04269i	−0.104645	−	0.578899i
$245$	8.46451	−	8.48457i	0.540778	−	0.542059i
$246$	−4.62316	+	14.4166i	−0.294762	+	0.919167i
$247$	4.15125	−	1.11233i	0.264138	−	0.0707755i
$248$	24.0684	+	6.28297i	1.52835	+	0.398969i
$249$	5.71096	−	7.33514i	0.361917	−	0.464846i
$250$	2.65680	−	15.5866i	0.168031	−	0.985782i
$251$	1.23580			0.0780028			0.0390014	−	0.999239i	$-0.487582\pi$
$251$	1.23580			0.0780028			0.0390014	+	0.999239i	$0.487582\pi$
$252$	1.26028	+	7.58023i	0.0793901	+	0.477510i
$253$	0.524858	+	0.524858i	0.0329975	+	0.0329975i
$254$	10.2842	+	1.79058i	0.645288	+	0.112351i
$255$	14.7051	−	1.84840i	0.920870	−	0.115751i
$256$	3.04903	+	15.7068i	0.190565	+	0.981675i
$257$	−6.23962	−	23.2866i	−0.389217	−	1.45258i	−0.831411	−	0.555658i	$-0.812467\pi$
$257$	−6.23962	−	23.2866i	−0.389217	−	1.45258i	0.442194	−	0.896919i	$-0.354200\pi$
$258$	−24.5001	−	1.18977i	−1.52531	−	0.0740721i
$259$	−4.23562	−	7.33631i	−0.263189	−	0.455856i
$260$	−11.2962	−	4.04145i	−0.700560	−	0.250640i
$261$	−15.5944	−	4.41478i	−0.965267	−	0.273268i
$262$	1.56703	+	17.4783i	0.0968117	+	1.07981i
$263$	1.73197	−	6.46379i	0.106798	−	0.398574i	−0.891745	−	0.452538i	$-0.850519\pi$
$263$	1.73197	−	6.46379i	0.106798	−	0.398574i	0.998543	+	0.0539633i	$0.0171854\pi$
$264$	−0.152644	−	0.369130i	−0.00939458	−	0.0227184i
$265$	−8.72286	−	15.0672i	−0.535841	−	0.925573i
$266$	0.998252	+	2.72443i	0.0612068	+	0.167046i
$267$	2.50241	−	5.92304i	0.153145	−	0.362484i
$268$	−12.2752	−	1.02076i	−0.749826	−	0.0623527i
$269$			25.7571i			1.57044i	0.619217	+	0.785220i	$0.287450\pi$
$269$			25.7571i			1.57044i	−0.619217	+	0.785220i	$0.712550\pi$
$270$	−10.8838	−	12.3103i	−0.662368	−	0.749178i
$271$	−7.56744			−0.459689			−0.229845	−	0.973227i	$-0.573822\pi$
$271$	−7.56744			−0.459689			−0.229845	+	0.973227i	$0.573822\pi$
$272$	15.2366	−	1.46520i	0.923855	−	0.0888410i
$273$	−5.48177	−	2.31598i	−0.331772	−	0.140169i
$274$	−21.0793	+	7.72360i	−1.27344	+	0.466600i
$275$	0.000965046		0.407682i	5.81945e−5		0.0245842i
$276$	27.9320	+	14.6379i	1.68131	+	0.881097i
$277$	−7.15052	−	1.91598i	−0.429633	−	0.115120i	0.0375208	−	0.999296i	$-0.488054\pi$
$277$	−7.15052	−	1.91598i	−0.429633	−	0.115120i	−0.467154	+	0.884176i	$0.654721\pi$
$278$	−0.365180	−	4.07312i	−0.0219020	−	0.244289i
$279$	−25.5785	+	6.46910i	−1.53135	+	0.387295i
$280$	2.03662	−	7.83973i	0.121711	−	0.468513i
$281$	−11.3627	+	6.56027i	−0.677843	+	0.391353i	−0.799042	−	0.601275i	$-0.794659\pi$
$281$	−11.3627	+	6.56027i	−0.677843	+	0.391353i	0.121199	+	0.992628i	$0.461326\pi$
$282$	0.0306518	−	0.631190i	0.00182529	−	0.0375868i
$283$	−30.4566	+	8.16082i	−1.81046	+	0.485111i	−0.995529	−	0.0944518i	$-0.969890\pi$
$283$	−30.4566	+	8.16082i	−1.81046	+	0.485111i	−0.814928	+	0.579562i	$0.803223\pi$
$284$	0.895241	+	0.321487i	0.0531228	+	0.0190767i
$285$	−4.90018	−	3.80585i	−0.290262	−	0.225439i
$286$	0.304758	+	0.0530615i	0.0180207	+	0.00313759i
$287$	5.59731	−	5.59731i	0.330399	−	0.330399i
$288$	−10.8651	−	13.0365i	−0.640233	−	0.768180i
$289$			2.35619i			0.138599i
$290$	13.1236	+	10.9376i	0.770644	+	0.642280i
$291$	23.7313	+	18.4766i	1.39116	+	1.08312i
$292$	3.24396	+	6.87929i	0.189838	+	0.402580i
$293$	−0.292386	−	1.09120i	−0.0170814	−	0.0637486i	0.956859	−	0.290552i	$-0.0938391\pi$
$293$	−0.292386	−	1.09120i	−0.0170814	−	0.0637486i	−0.973940	+	0.226804i	$0.927172\pi$
$294$	−4.00907	+	12.5016i	−0.233814	+	0.729109i
$295$	−10.8454	+	10.8711i	−0.631442	+	0.632939i
$296$	16.2621	+	9.24955i	0.945215	+	0.537619i
$297$	0.330603	+	0.264960i	0.0191835	+	0.0153746i
$298$	1.43753	−	0.128883i	0.0832736	−	0.00746599i
$299$	−21.1498	+	12.2108i	−1.22312	+	0.706171i
$300$	5.20222	+	16.5208i	0.300350	+	0.953829i
$301$	11.1067	+	6.41248i	0.640182	+	0.369609i
$302$	−19.1730	−	8.89037i	−1.10328	−	0.511583i
$303$	14.4885	−	1.80375i	0.832340	−	0.103623i
$304$	−4.94408	−	4.07662i	−0.283562	−	0.233810i
$305$	−2.67082	−	9.92066i	−0.152931	−	0.568055i
$306$	−13.4094	+	9.15291i	−0.766566	+	0.523237i
$307$	−2.11831	+	2.11831i	−0.120899	+	0.120899i	−0.764967	−	0.644069i	$-0.777245\pi$
$307$	−2.11831	+	2.11831i	−0.120899	+	0.120899i	0.644069	+	0.764967i	$0.277245\pi$
$308$	−0.0173075	+	0.208132i	−0.000986185	+	0.0118594i
$309$	23.4923	+	3.26126i	1.33643	+	0.185527i
$310$	27.4045	+	4.73800i	1.55647	+	0.269100i
$311$	5.20587	+	3.00561i	0.295198	+	0.170433i	0.640284	−	0.768139i	$-0.278817\pi$
$311$	5.20587	+	3.00561i	0.295198	+	0.170433i	−0.345086	+	0.938571i	$0.612150\pi$
$312$	13.0311	−	1.70775i	0.737738	−	0.0966826i
$313$	−17.8633	−	4.78646i	−1.00969	−	0.270547i	−0.284192	−	0.958767i	$-0.591725\pi$
$313$	−17.8633	−	4.78646i	−1.00969	−	0.270547i	−0.725501	+	0.688221i	$0.758392\pi$
$314$	15.1669	+	12.6710i	0.855916	+	0.715068i
$315$	2.11637	+	8.32654i	0.119244	+	0.469147i
$316$	0.253968	+	1.40496i	0.0142868	+	0.0790353i
$317$	−0.650198	+	2.42657i	−0.0365188	+	0.136290i	−0.981778	−	0.190029i	$-0.939142\pi$
$317$	−0.650198	+	2.42657i	−0.0365188	+	0.136290i	0.945260	+	0.326319i	$0.105808\pi$
$318$	16.0346	+	10.3258i	0.899178	+	0.579041i
$319$	−0.381480	−	0.220247i	−0.0213588	−	0.0123315i
$320$	4.87283	+	17.2121i	0.272400	+	0.962184i
$321$	−5.95005	+	2.41565i	−0.332099	+	0.134828i
$322$	−9.48622	−	13.4859i	−0.528646	−	0.751540i
$323$	−4.33487	+	4.33487i	−0.241199	+	0.241199i
$324$	16.7628	+	6.55821i	0.931264	+	0.364345i
$325$	−12.9646	−	3.44099i	−0.719147	−	0.190872i
$326$	−18.0939	−	3.15033i	−1.00213	−	0.174481i
$327$	1.64303	−	3.88895i	0.0908599	−	0.215059i
$328$	−4.41560	+	16.9150i	−0.243811	+	0.933975i
$329$	−0.165203	+	0.286140i	−0.00910793	+	0.0157754i
$330$	−0.204745	−	0.396896i	−0.0112708	−	0.0218484i
$331$	7.76315	−	4.48206i	0.426701	−	0.246356i	−0.271239	−	0.962512i	$-0.587433\pi$
$331$	7.76315	−	4.48206i	0.426701	−	0.246356i	0.697940	+	0.716156i	$0.254100\pi$
$332$	6.11908	−	8.81944i	0.335828	−	0.484030i
$333$	−19.8414	−	0.279434i	−1.08730	−	0.0153129i
$334$	8.68117	+	7.25261i	0.475012	+	0.396845i
$335$	−13.7714	+	0.0162995i	−0.752414	+	0.000890538i
$336$	1.93400	+	8.65971i	0.105508	+	0.472426i
$337$	13.6917	−	3.66868i	0.745835	−	0.199846i	0.134165	−	0.990959i	$-0.457165\pi$
$337$	13.6917	−	3.66868i	0.745835	−	0.199846i	0.611670	+	0.791113i	$0.290498\pi$
$338$	3.45237	−	7.44540i	0.187784	−	0.404976i
$339$	2.83044	−	20.3889i	0.153728	−	1.10737i
$340$	16.8371	−	3.06414i	0.913119	−	0.166176i
$341$	−0.717085			−0.0388323
$342$	6.67891	+	1.26002i	0.361154	+	0.0681341i
$343$	11.1930	−	11.1930i	0.604367	−	0.604367i
$344$	−28.3230	+	0.182732i	−1.52708	+	0.00985226i
$345$	32.4939	+	13.6830i	1.74941	+	0.736666i
$346$	−31.7468	+	11.6323i	−1.70672	+	0.625355i
$347$	33.5484	−	8.98928i	1.80097	−	0.482570i	0.806844	−	0.590764i	$-0.201174\pi$
$347$	33.5484	−	8.98928i	1.80097	−	0.482570i	0.994130	+	0.108194i	$0.0345069\pi$
$348$	−18.2597	−	4.10061i	−0.978824	−	0.219816i
$349$	−14.0523	−	24.3394i	−0.752205	−	1.30286i	−0.946752	−	0.321964i	$-0.895657\pi$
$349$	−14.0523	−	24.3394i	−0.752205	−	1.30286i	0.194547	−	0.980893i	$-0.437676\pi$
$350$	1.53225	−	8.92545i	0.0819024	−	0.477085i
$351$	−11.2359	+	8.25047i	−0.599727	+	0.440377i
$352$	−0.199412	−	0.415906i	−0.0106287	−	0.0221679i
$353$	1.68642	−	6.29381i	0.0897592	−	0.334986i	−0.906414	−	0.422391i	$-0.861191\pi$
$353$	1.68642	−	6.29381i	0.0897592	−	0.334986i	0.996173	+	0.0874053i	$0.0278575\pi$
$354$	5.13673	−	16.0180i	0.273014	−	0.851349i
$355$	1.02758	+	0.274036i	0.0545382	+	0.0145443i
$356$	2.50936	−	6.98778i	0.132996	−	0.370352i
$357$	8.42364	−	1.04871i	0.445827	−	0.0555035i
$358$	17.2342	+	24.5007i	0.910855	+	1.29490i
$359$	−1.23589			−0.0652279			−0.0326139	−	0.999468i	$-0.510383\pi$
$359$	−1.23589			−0.0652279			−0.0326139	+	0.999468i	$0.510383\pi$
$360$	−13.3296	−	13.5026i	−0.702533	−	0.711651i
$361$	−16.4336			−0.864925
$362$	0.635731	+	0.903774i	0.0334133	+	0.0475013i
$363$	−11.4848	−	15.1875i	−0.602796	−	0.797138i
$364$	−6.46718	−	2.32241i	−0.338972	−	0.121727i
$365$	4.26047	+	7.35922i	0.223003	+	0.385199i
$366$	7.56274	+	8.33476i	0.395311	+	0.435665i
$367$	−1.27568	+	4.76091i	−0.0665901	+	0.248518i	−0.991195	−	0.132410i	$-0.957729\pi$
$367$	−1.27568	+	4.76091i	−0.0665901	+	0.248518i	0.924605	+	0.380927i	$0.124395\pi$
$368$	33.1331	+	15.1046i	1.72718	+	0.787382i
$369$	−4.54641	−	17.9763i	−0.236676	−	0.935808i
$370$	18.9864	+	8.77656i	0.987057	+	0.456272i
$371$	−4.98583	−	8.63570i	−0.258851	−	0.448343i
$372$	−29.0804	+	9.08150i	−1.50775	+	0.470854i
$373$	3.62940	−	0.972495i	0.187923	−	0.0503539i	−0.163630	−	0.986522i	$-0.552320\pi$
$373$	3.62940	−	0.972495i	0.187923	−	0.0503539i	0.351553	+	0.936168i	$0.385654\pi$
$374$	−0.414324	+	0.151811i	−0.0214242	+	0.00784998i
$375$	7.34814	+	17.9166i	0.379456	+	0.925210i
$376$	−0.00470768	−	0.729679i	−0.000242780	−	0.0376303i
$377$	10.2481	−	10.2481i	0.527805	−	0.527805i
$378$	−6.22539	−	7.05811i	−0.320199	−	0.363030i
$379$	4.55780			0.234118			0.117059	−	0.993125i	$-0.462653\pi$
$379$	4.55780			0.234118			0.117059	+	0.993125i	$0.462653\pi$
$380$	−5.89117	−	4.07707i	−0.302211	−	0.209149i
$381$	−11.8460	+	4.80932i	−0.606887	+	0.246389i
$382$	2.92998	−	6.31880i	0.149911	−	0.323298i
$383$	−9.78570	+	2.62207i	−0.500026	+	0.133982i	−0.500012	−	0.866018i	$-0.666671\pi$
$383$	−9.78570	+	2.62207i	−0.500026	+	0.133982i	−1.39781e−5		1.00000i	$0.500004\pi$
$384$	−13.3541	−	14.3411i	−0.681476	−	0.731841i
$385$	0.000276367		0.233502i	1.40849e−5		0.0119003i
$386$	−9.71853	−	8.11926i	−0.494660	−	0.413260i
$387$	26.2258	−	14.6530i	1.33313	−	0.744854i
$388$	28.5335	+	19.7970i	1.44857	+	1.00504i
$389$	−16.0688	+	9.27730i	−0.814719	+	0.470378i	−0.848592	−	0.529048i	$-0.822549\pi$
$389$	−16.0688	+	9.27730i	−0.814719	+	0.470378i	0.0338732	+	0.999426i	$0.489216\pi$
$390$	14.3571	−	3.12711i	0.727001	−	0.158347i
$391$	17.4181	−	30.1690i	0.880871	−	1.52571i
$392$	−3.82907	+	14.6682i	−0.193397	+	0.740855i
$393$	−12.9633	−	17.1427i	−0.653912	−	0.864734i
$394$	32.0822	+	5.58584i	1.61628	+	0.281411i
$395$	0.414965	+	1.54137i	0.0208792	+	0.0775548i
$396$	0.397982	+	0.284511i	0.0199993	+	0.0142972i
$397$	−2.02257	+	2.02257i	−0.101510	+	0.101510i	−0.756038	−	0.654528i	$-0.772867\pi$
$397$	−2.02257	+	2.02257i	−0.101510	+	0.101510i	0.654528	+	0.756038i	$0.272867\pi$
$398$	1.54074	+	2.19037i	0.0772304	+	0.109793i
$399$	−2.80401	−	2.18313i	−0.140376	−	0.109293i
$400$	7.04614	+	18.7177i	0.352307	+	0.935884i
$401$	24.1537	+	13.9451i	1.20618	+	0.696386i	0.961922	−	0.273325i	$-0.0881234\pi$
$401$	24.1537	+	13.9451i	1.20618	+	0.696386i	0.244255	+	0.969711i	$0.421457\pi$
$402$	13.4152	−	6.90035i	0.669091	−	0.344158i
$403$	6.10640	−	22.7894i	0.304182	−	1.13522i
$404$	16.5901	−	2.99891i	0.825389	−	0.149202i
$405$	19.2913	+	5.73116i	0.958592	+	0.284784i
$406$	7.50915	+	6.27346i	0.372673	+	0.311346i
$407$	−0.520945	−	0.139587i	−0.0258223	−	0.00691906i
$408$	−14.8798	+	11.4037i	−0.736657	+	0.564567i
$409$	−0.792371	−	0.457476i	−0.0391802	−	0.0226207i	0.480282	−	0.877114i	$-0.340534\pi$
$409$	−0.792371	−	0.457476i	−0.0391802	−	0.0226207i	−0.519462	+	0.854493i	$0.673868\pi$
$410$	−3.32981	+	19.2596i	−0.164448	+	0.951162i
$411$	16.8912	−	21.6950i	0.833180	−	1.07013i
$412$	27.2925	+	2.26954i	1.34461	+	0.111812i
$413$	−6.21908	+	6.21908i	−0.306021	+	0.306021i
$414$	−38.5129	+	2.90686i	−1.89281	+	0.142864i
$415$	5.98836	−	10.4006i	0.293957	−	0.510543i
$416$	14.9159	−	2.79576i	0.731311	−	0.137074i
$417$	3.02095	+	3.99491i	0.147937	+	0.195632i
$418$	0.167588	+	0.0777090i	0.00819698	+	0.00380087i
$419$	13.0333	+	7.52478i	0.636719	+	0.367610i	0.783349	−	0.621582i	$-0.213510\pi$
$419$	13.0333	+	7.52478i	0.636719	+	0.367610i	−0.146631	+	0.989191i	$0.546843\pi$
$420$	2.96838	+	9.46585i	0.144842	+	0.461886i
$421$	−8.53560	+	4.92803i	−0.415999	+	0.240177i	−0.693364	−	0.720587i	$-0.743872\pi$
$421$	−8.53560	+	4.92803i	−0.415999	+	0.240177i	0.277365	+	0.960765i	$0.410539\pi$
$422$	−27.5368	+	2.46884i	−1.34047	+	0.120181i
$423$	0.377502	+	0.675650i	0.0183548	+	0.0328512i
$424$	19.1424	+	10.8878i	0.929637	+	0.528759i
$425$	18.4699	−	4.99588i	0.895921	−	0.242336i
$426$	−1.13860	+	0.246586i	−0.0551653	+	0.0119471i
$427$	−1.52299	−	5.68389i	−0.0737028	−	0.275063i
$428$	−6.70688	+	3.16266i	−0.324189	+	0.152873i
$429$	−0.351038	+	0.142517i	−0.0169483	+	0.00688081i
$430$	−31.5369	+	2.86510i	−1.52084	+	0.138168i
$431$		−	0.402357i		−	0.0193808i	−0.999953	−	0.00969042i	$-0.996915\pi$
$431$		−	0.402357i		−	0.0193808i	0.999953	−	0.00969042i	$-0.00308460\pi$
$432$	19.7428	+	6.49777i	0.949877	+	0.312624i
$433$	−17.7173	+	17.7173i	−0.851441	+	0.851441i	−0.990311	−	0.138870i	$-0.955653\pi$
$433$	−17.7173	+	17.7173i	−0.851441	+	0.851441i	0.138870	+	0.990311i	$0.455653\pi$
$434$	15.6928	+	2.73228i	0.753277	+	0.131153i
$435$	−20.7281	−	2.85252i	−0.993836	−	0.136768i
$436$	1.64760	−	4.58804i	0.0789055	−	0.219727i
$437$	−14.0868	+	3.77454i	−0.673862	+	0.180561i
$438$	−7.83173	−	5.04338i	−0.374215	−	0.240982i
$439$	−11.3508	+	6.55341i	−0.541746	+	0.312777i	−0.745786	−	0.666185i	$-0.767926\pi$
$439$	−11.3508	+	6.55341i	−0.541746	+	0.312777i	0.204040	+	0.978963i	$0.434593\pi$
$440$	−0.261244	−	0.444613i	−0.0124543	−	0.0211961i
$441$	−3.94251	−	15.5885i	−0.187738	−	0.742309i
$442$	−1.29645	−	14.4602i	−0.0616657	−	0.687803i
$443$	−17.7060	−	4.74431i	−0.841237	−	0.225409i	−0.187627	−	0.982240i	$-0.560080\pi$
$443$	−17.7060	−	4.74431i	−0.841237	−	0.225409i	−0.653610	+	0.756832i	$0.726746\pi$
$444$	−22.8940	+	0.936731i	−1.08650	+	0.0444553i
$445$	2.13898	−	8.02074i	0.101397	−	0.380220i
$446$	−27.9992	+	10.2591i	−1.32580	+	0.485784i
$447$	−1.40992	+	1.06618i	−0.0666871	+	0.0504288i
$448$	2.77926	+	9.86156i	0.131308	+	0.465915i
$449$	−34.6065			−1.63318			−0.816591	−	0.577217i	$-0.804139\pi$
$449$	−34.6065			−1.63318			−0.816591	+	0.577217i	$0.804139\pi$
$450$	−16.1191	−	13.7904i	−0.759861	−	0.650085i
$451$		−	0.503959i		−	0.0237305i
$452$	1.96973	−	23.6871i	0.0926482	−	1.11415i
$453$	25.6854	−	3.19772i	1.20680	−	0.150242i
$454$	−11.4082	−	31.1354i	−0.535415	−	1.46126i
$455$	−7.42318	−	1.97962i	−0.348004	−	0.0928061i
$456$	7.78044	+	1.02898i	0.364353	+	0.0481865i
$457$	−9.38401	+	35.0216i	−0.438965	+	1.63824i	0.292430	+	0.956287i	$0.405536\pi$
$457$	−9.38401	+	35.0216i	−0.438965	+	1.63824i	−0.731395	+	0.681954i	$0.761130\pi$
$458$	−1.76533	−	19.6900i	−0.0824885	−	0.920055i
$459$	7.99570	−	18.2058i	0.373207	−	0.849775i
$460$	38.3322	+	13.7142i	1.78725	+	0.639427i
$461$	−8.16410	−	14.1406i	−0.380240	−	0.658595i	0.610856	−	0.791741i	$-0.290825\pi$
$461$	−8.16410	−	14.1406i	−0.380240	−	0.658595i	−0.991096	+	0.133146i	$0.957492\pi$
$462$	−0.116999	−	0.227462i	−0.00544328	−	0.0105825i
$463$	5.84950	+	21.8306i	0.271849	+	1.01456i	0.957923	+	0.287024i	$0.0926659\pi$
$463$	5.84950	+	21.8306i	0.271849	+	1.01456i	−0.686074	+	0.727532i	$0.740667\pi$
$464$	−21.3128	−	3.56927i	−0.989424	−	0.165699i
$465$	−31.5445	+	12.8502i	−1.46284	+	0.595914i
$466$	26.2131	+	4.56398i	1.21430	+	0.211422i
$467$	12.9000	+	12.9000i	0.596940	+	0.596940i	0.939497	−	0.342557i	$-0.111293\pi$
$467$	12.9000	+	12.9000i	0.596940	+	0.596940i	−0.342557	+	0.939497i	$0.611293\pi$
$468$	−12.4310	+	10.2253i	−0.574623	+	0.472666i
$469$	−7.88763			−0.364217
$470$	−0.0738129	−	0.812476i	−0.00340474	−	0.0374767i
$471$	−23.9751	−	3.32829i	−1.10472	−	0.153359i
$472$	4.90610	−	18.7940i	0.225822	−	0.865064i
$473$	0.788679	−	0.211326i	0.0362635	−	0.00971678i
$474$	−1.17502	−	1.29497i	−0.0539706	−	0.0594800i
$475$	−6.94635	−	3.98858i	−0.318720	−	0.183009i
$476$	9.64555	−	1.74358i	0.442103	−	0.0799169i
$477$	−23.3557	−	0.328927i	−1.06938	−	0.0150605i
$478$	−3.56896	−	39.8072i	−0.163240	−	1.82074i
$479$	−18.1803	−	31.4892i	−0.830678	−	1.43878i	−0.897501	−	0.441012i	$-0.854620\pi$
$479$	−18.1803	−	31.4892i	−0.830678	−	1.43878i	0.0668230	−	0.997765i	$-0.478714\pi$
$480$	−16.2252	−	14.7222i	−0.740576	−	0.671973i
$481$	8.87231	−	15.3673i	0.404543	−	0.700688i
$482$	20.3062	+	9.41582i	0.924922	+	0.428879i
$483$	18.6017	+	7.85898i	0.846407	+	0.357596i
$484$	−14.2051	−	16.7819i	−0.645686	−	0.762811i
$485$	33.6489	+	19.3741i	1.52792	+	0.879734i
$486$	−21.6688	+	4.05757i	−0.982916	+	0.184055i
$487$	−24.5168	−	24.5168i	−1.11096	−	1.11096i	−0.993021	−	0.117941i	$-0.962371\pi$
$487$	−24.5168	−	24.5168i	−1.11096	−	1.11096i	−0.117941	−	0.993021i	$-0.537629\pi$
$488$	9.24833	+	9.12976i	0.418652	+	0.413285i
$489$	20.8416	−	8.46145i	0.942490	−	0.382640i
$490$	−2.88751	+	16.7013i	−0.130444	+	0.754488i
$491$	−13.6928	+	23.7166i	−0.617947	+	1.07032i	0.371913	+	0.928268i	$0.378702\pi$
$491$	−13.6928	+	23.7166i	−0.617947	+	1.07032i	−0.989860	+	0.142048i	$0.954631\pi$
$492$	−6.38237	−	20.4374i	−0.287740	−	0.921389i
$493$	−5.35070	+	19.9691i	−0.240984	+	0.899363i
$494$	−3.89675	+	4.66430i	−0.175323	+	0.209857i
$495$	0.470118	+	0.279569i	0.0211302	+	0.0125657i
$496$	−32.9523	+	12.3157i	−1.47960	+	0.552990i
$497$	0.588362	+	0.157651i	0.0263916	+	0.00707162i
$498$	−0.637684	+	13.1313i	−0.0285753	+	0.588429i
$499$	2.00307	−	3.46942i	0.0896697	−	0.155312i	−0.817702	−	0.575642i	$-0.804752\pi$
$499$	2.00307	−	3.46942i	0.0896697	−	0.155312i	0.907372	+	0.420330i	$0.138086\pi$
$500$	9.60886	+	20.1908i	0.429721	+	0.902962i
$501$	−13.7228	−	1.90503i	−0.613090	−	0.0851107i
$502$	−1.42946	+	1.00550i	−0.0637998	+	0.0448779i
$503$	−22.0280	−	22.0280i	−0.982180	−	0.982180i	0.0176637	−	0.999844i	$-0.494377\pi$
$503$	−22.0280	−	22.0280i	−0.982180	−	0.982180i	−0.999844	+	0.0176637i	$0.994377\pi$
$504$	−7.62542	−	7.74270i	−0.339663	−	0.344887i
$505$	18.2009	−	4.90000i	0.809928	−	0.218047i
$506$	−1.03416	−	0.180058i	−0.0459739	−	0.00800454i
$507$	1.24176	+	9.97433i	0.0551486	+	0.442975i
$508$	−13.3527	+	6.29654i	−0.592431	+	0.279364i
$509$	4.51480	+	2.60662i	0.200115	+	0.115536i	0.596709	−	0.802458i	$-0.296475\pi$
$509$	4.51480	+	2.60662i	0.200115	+	0.115536i	−0.396594	+	0.917994i	$0.629808\pi$
$510$	−15.5056	+	14.1029i	−0.686599	+	0.624486i
$511$	2.43521	+	4.21790i	0.107727	+	0.186589i
$512$	−16.3067	−	15.6873i	−0.720659	−	0.693289i
$513$	−7.75618	+	3.02240i	−0.342444	+	0.133442i
$514$	26.1645	+	21.8589i	1.15407	+	0.964156i
$515$	30.6192	−	0.0362402i	1.34925	−	0.00159693i
$516$	29.3075	−	18.5583i	1.29019	−	0.816982i
$517$	0.00544434	+	0.0203185i	0.000239442	+	0.000893608i
$518$	10.8686	+	5.03967i	0.477537	+	0.221430i
$519$	25.4393	−	32.6741i	1.11666	−	1.43424i
$520$	16.3547	−	4.51635i	0.717202	−	0.198055i
$521$			39.8254i			1.74478i	0.488807	+	0.872392i	$0.337432\pi$
$521$			39.8254i			1.74478i	−0.488807	+	0.872392i	$0.662568\pi$
$522$	21.6302	−	7.58173i	0.946729	−	0.331843i
$523$	−23.7526	−	23.7526i	−1.03863	−	1.03863i	−0.999223	−	0.0394052i	$-0.987454\pi$
$523$	−23.7526	−	23.7526i	−1.03863	−	1.03863i	−0.0394052	−	0.999223i	$-0.512546\pi$
$524$	−16.0338	−	18.9423i	−0.700439	−	0.827497i
$525$	4.19652	+	10.2668i	0.183151	+	0.448078i
$526$	3.25588	+	8.88594i	0.141963	+	0.387445i
$527$	8.71046	+	32.5079i	0.379433	+	1.41606i
$528$	0.476907	+	0.302778i	0.0207547	+	0.0131767i
$529$	51.8506	−	29.9360i	2.25438	−	1.30156i
$530$	22.3493	+	10.3310i	0.970789	+	0.448752i
$531$	5.05144	+	19.9732i	0.219214	+	0.866762i
$532$	−3.37142	−	2.33915i	−0.146169	−	0.101415i
$533$	16.0161	+	4.29151i	0.693735	+	0.185886i
$534$	1.92472	+	8.88732i	0.0832907	+	0.384592i
$535$	−7.17479	+	4.15370i	−0.310193	+	0.179580i
$536$	15.0294	−	8.80697i	0.649169	−	0.380403i
$537$	−33.7948	−	14.2779i	−1.45835	−	0.616136i
$538$	−20.9573	−	29.7935i	−0.903531	−	1.28449i
$539$		−	0.437018i		−	0.0188237i
$540$	22.6056	+	5.38378i	0.972792	+	0.231681i
$541$			32.6429i			1.40343i	0.712458	+	0.701714i	$0.247582\pi$
$541$			32.6429i			1.40343i	−0.712458	+	0.701714i	$0.752418\pi$
$542$	8.75332	−	6.15724i	0.375987	−	0.264476i
$543$	−1.24662	−	0.526679i	−0.0534974	−	0.0226020i
$544$	−16.4322	+	14.0921i	−0.704523	+	0.604192i
$545$	1.40441	−	5.26626i	0.0601583	−	0.225582i
$546$	8.22520	−	1.78132i	0.352006	−	0.0762336i
$547$	−27.9695	−	7.49440i	−1.19589	−	0.320437i	−0.394678	−	0.918820i	$-0.629144\pi$
$547$	−27.9695	−	7.49440i	−1.19589	−	0.320437i	−0.801211	+	0.598382i	$0.795810\pi$
$548$	18.0983	−	26.0851i	0.773119	−	1.11430i
$549$	−13.2626	−	3.75466i	−0.566035	−	0.160245i
$550$	−0.332826	−	0.470784i	−0.0141918	−	0.0200743i
$551$	7.49518	−	4.32734i	0.319305	−	0.184351i
$552$	−44.2193	+	5.79506i	−1.88210	+	0.246654i
$553$	0.236627	+	0.883105i	0.0100624	+	0.0375535i
$554$	9.83000	−	3.60179i	0.417637	−	0.153025i
$555$	−25.4177	+	3.19495i	−1.07892	+	0.135618i
$556$	3.73650	+	4.41429i	0.158463	+	0.187207i
$557$	11.0441	+	11.0441i	0.467955	+	0.467955i	0.901251	−	0.433297i	$-0.142650\pi$
$557$	11.0441	+	11.0441i	0.467955	+	0.467955i	−0.433297	+	0.901251i	$0.642650\pi$
$558$	24.3233	−	28.2948i	1.02969	−	1.19781i
$559$			26.8643i			1.13624i
$560$	4.02301	+	10.7254i	0.170003	+	0.453230i
$561$	0.332005	−	0.426426i	0.0140172	−	0.0180037i
$562$	7.80560	−	16.8336i	0.329259	−	0.710082i
$563$	5.94847	+	22.2000i	0.250698	+	0.935618i	0.970433	+	0.241369i	$0.0775965\pi$
$563$	5.94847	+	22.2000i	0.250698	+	0.935618i	−0.719735	+	0.694249i	$0.755737\pi$
$564$	0.478111	+	0.755042i	0.0201321	+	0.0317930i
$565$	−0.0314527	−	26.5743i	−0.00132323	−	1.11799i
$566$	28.5894	−	34.2207i	1.20170	−	1.43840i
$567$	11.0452	+	3.29561i	0.463857	+	0.138403i
$568$	−1.29711	+	0.356545i	−0.0544255	+	0.0149603i
$569$	11.6829	+	20.2353i	0.489771	+	0.848308i	0.999931	−	0.0117718i	$-0.00374716\pi$
$569$	11.6829	+	20.2353i	0.489771	+	0.848308i	−0.510160	+	0.860080i	$0.670414\pi$
$570$	8.76471	+	0.415235i	0.367113	+	0.0173923i
$571$	−11.8358	−	6.83342i	−0.495314	−	0.285970i	0.231462	−	0.972844i	$-0.425649\pi$
$571$	−11.8358	−	6.83342i	−0.495314	−	0.285970i	−0.726776	+	0.686874i	$0.758982\pi$
$572$	−0.395689	+	0.186589i	−0.0165446	+	0.00780168i
$573$	1.05386	+	8.46506i	0.0440258	+	0.353633i
$574$	−1.92021	+	11.0287i	−0.0801481	+	0.460329i
$575$	43.9938	+	11.6766i	1.83467	+	0.486946i
$576$	23.1749	+	6.23899i	0.965620	+	0.259958i
$577$	−4.09065	−	4.09065i	−0.170296	−	0.170296i	0.616813	−	0.787109i	$-0.288423\pi$
$577$	−4.09065	−	4.09065i	−0.170296	−	0.170296i	−0.787109	+	0.616813i	$0.788423\pi$
$578$	−1.91711	−	2.72542i	−0.0797413	−	0.113363i
$579$	15.3626	+	2.13268i	0.638449	+	0.0886311i
$580$	−24.0796	−	1.97367i	−0.999850	−	0.0819523i
$581$	3.43690	−	5.95289i	0.142587	−	0.246967i
$582$	−42.4838	−	2.06310i	−1.76101	−	0.0855181i
$583$	−0.613214	−	0.164310i	−0.0253967	−	0.00680503i
$584$	−9.34964	−	5.31789i	−0.386891	−	0.220056i
$585$	−12.8882	+	12.5600i	−0.532863	+	0.519290i
$586$	1.22606	+	1.02430i	0.0506481	+	0.0423135i
$587$	−5.73943	+	21.4198i	−0.236892	+	0.884091i	0.740396	+	0.672171i	$0.234638\pi$
$587$	−5.73943	+	21.4198i	−0.236892	+	0.884091i	−0.977287	+	0.211920i	$0.932028\pi$
$588$	−5.53460	−	17.7227i	−0.228243	−	0.730872i
$589$	7.04452	−	12.2015i	0.290264	−	0.502753i
$590$	3.69970	−	21.3990i	0.152314	−	0.880983i
$591$	−36.9542	+	15.0030i	−1.52009	+	0.617140i
$592$	−26.3364	+	2.53260i	−1.08242	+	0.104089i
$593$	−12.0581	−	12.0581i	−0.495166	−	0.495166i	0.414763	−	0.909929i	$-0.363864\pi$
$593$	−12.0581	−	12.0581i	−0.495166	−	0.495166i	−0.909929	+	0.414763i	$0.863864\pi$
$594$	−0.597996	−	0.0374873i	−0.0245361	−	0.00153812i
$595$	10.5821	−	2.84888i	0.433822	−	0.116793i
$596$	−1.55793	+	1.31872i	−0.0638154	+	0.0540169i
$597$	−3.02127	−	1.27645i	−0.123652	−	0.0522415i
$598$	14.5288	−	31.3329i	0.594127	−	1.28130i
$599$	−8.65485	+	14.9906i	−0.353628	+	0.612501i	−0.986882	−	0.161443i	$-0.948385\pi$
$599$	−8.65485	+	14.9906i	−0.353628	+	0.612501i	0.633254	+	0.773944i	$0.281719\pi$
$600$	−19.4596	−	14.8770i	−0.794434	−	0.607350i
$601$	7.87153	+	13.6339i	0.321086	+	0.556138i	0.980712	−	0.195456i	$-0.0626187\pi$
$601$	7.87153	+	13.6339i	0.321086	+	0.556138i	−0.659626	+	0.751594i	$0.729285\pi$
$602$	−18.0648	+	1.61962i	−0.736265	+	0.0660106i
$603$	−9.46257	+	15.8693i	−0.385346	+	0.646247i
$604$	29.4112	−	5.31652i	1.19673	−	0.216326i
$605$	−17.4026	−	17.3614i	−0.707515	−	0.705843i
$606$	−15.2913	+	13.8749i	−0.621167	+	0.563631i
$607$	14.9159	−	3.99670i	0.605417	−	0.162221i	0.0569274	−	0.998378i	$-0.481870\pi$
$607$	14.9159	−	3.99670i	0.605417	−	0.162221i	0.548490	+	0.836157i	$0.315203\pi$
$608$	9.03579	+	0.692715i	0.366450	+	0.0280933i
$609$	−11.8701	−	1.64784i	−0.481002	−	0.0667739i
$610$	11.1613	+	9.30220i	0.451908	+	0.376635i
$611$	−0.692098			−0.0279993
$612$	8.06356	−	21.4978i	0.325950	−	0.868998i
$613$	−18.9496	−	18.9496i	−0.765369	−	0.765369i	0.211918	−	0.977287i	$-0.432029\pi$
$613$	−18.9496	−	18.9496i	−0.765369	−	0.765369i	−0.977287	+	0.211918i	$0.932029\pi$
$614$	0.726708	−	4.17384i	0.0293276	−	0.168442i
$615$	−9.03097	−	22.1691i	−0.364164	−	0.893944i
$616$	−0.149327	−	0.254830i	−0.00601654	−	0.0102674i
$617$	2.43868	+	9.10128i	0.0981776	+	0.366404i	0.997482	−	0.0709193i	$-0.0225933\pi$
$617$	2.43868	+	9.10128i	0.0981776	+	0.366404i	−0.899304	+	0.437323i	$0.855927\pi$
$618$	−29.8273	+	15.3422i	−1.19983	+	0.617152i
$619$	−6.33537	−	10.9732i	−0.254640	−	0.441049i	0.710158	−	0.704043i	$-0.248624\pi$
$619$	−6.33537	−	10.9732i	−0.254640	−	0.441049i	−0.964798	+	0.262993i	$0.915290\pi$
$620$	−35.5541	+	16.8172i	−1.42789	+	0.675393i
$621$	38.1276	−	27.9970i	1.53001	−	1.12348i
$622$	−8.46719	+	0.759135i	−0.339503	+	0.0304385i
$623$	1.23054	−	4.59245i	0.0493006	−	0.183993i
$624$	−13.6836	+	12.5781i	−0.547783	+	0.503526i
$625$	12.6024	+	21.5912i	0.504094	+	0.863649i
$626$	24.5571	−	8.99792i	0.981501	−	0.359629i
$627$	−0.224511	+	0.0279507i	−0.00896611	+	0.00111624i
$628$	−27.8534	−	2.31619i	−1.11147	−	0.0924259i
$629$			25.3117i			1.00925i
$630$	−9.22290	−	7.90940i	−0.367449	−	0.315118i
$631$	24.5179			0.976043			0.488021	−	0.872832i	$-0.337719\pi$
$631$	24.5179			0.976043			0.488021	+	0.872832i	$0.337719\pi$
$632$	−1.43691	−	1.41849i	−0.0571573	−	0.0564245i
$633$	27.0081	−	20.4235i	1.07347	−	0.811761i
$634$	−1.22229	−	3.33587i	−0.0485433	−	0.132484i
$635$	−14.2843	+	8.26959i	−0.566855	+	0.328169i
$636$	−26.9490	+	1.10264i	−1.06860	+	0.0437226i
$637$	13.8887	+	3.72147i	0.550290	+	0.147450i
$638$	0.620465	−	0.0556284i	0.0245644	−	0.00220235i
$639$	1.02302	−	0.994608i	0.0404702	−	0.0393461i
$640$	−19.6410	−	15.9446i	−0.776380	−	0.630265i
$641$	−0.697521	+	0.402714i	−0.0275504	+	0.0159062i	−0.513712	−	0.857963i	$-0.671730\pi$
$641$	−0.697521	+	0.402714i	−0.0275504	+	0.0159062i	0.486162	+	0.873869i	$0.338397\pi$
$642$	4.91699	−	7.63546i	0.194058	−	0.301347i
$643$	15.5853	−	4.17608i	0.614626	−	0.164689i	0.0619425	−	0.998080i	$-0.480270\pi$
$643$	15.5853	−	4.17608i	0.614626	−	0.164689i	0.552684	+	0.833391i	$0.313604\pi$
$644$	21.9456	+	7.88081i	0.864777	+	0.310547i
$645$	30.9070	−	23.4294i	1.21696	−	0.922531i
$646$	1.48712	−	8.54124i	0.0585099	−	0.336051i
$647$	−18.0425	+	18.0425i	−0.709322	+	0.709322i	−0.966393	−	0.257071i	$-0.917243\pi$
$647$	−18.0425	+	18.0425i	−0.709322	+	0.709322i	0.257071	+	0.966393i	$0.417243\pi$
$648$	−24.7257	+	6.05305i	−0.971317	+	0.237786i
$649$			0.559941i			0.0219796i
$650$	17.7960	−	6.56843i	0.698018	−	0.257635i
$651$	−18.0759	+	7.33860i	−0.708450	+	0.287622i
$652$	23.4926	−	11.0780i	0.920041	−	0.433850i
$653$	−9.58873	−	35.7856i	−0.375236	−	1.40040i	−0.853000	−	0.521912i	$-0.825219\pi$
$653$	−9.58873	−	35.7856i	−0.375236	−	1.40040i	0.477763	−	0.878489i	$-0.341448\pi$
$654$	1.26373	+	5.83524i	0.0494158	+	0.228176i
$655$	−19.6429	−	19.5965i	−0.767512	−	0.765697i
$656$	−8.65531	−	23.1585i	−0.337933	−	0.904186i
$657$	11.4075	+	0.160657i	0.445050	+	0.00626781i
$658$	−0.0417257	−	0.465398i	−0.00162664	−	0.0181431i
$659$	0.656471	−	0.379014i	0.0255725	−	0.0147643i	−0.487159	−	0.873313i	$-0.661967\pi$
$659$	0.656471	−	0.379014i	0.0255725	−	0.0147643i	0.512732	+	0.858549i	$0.328634\pi$
$660$	0.559764	+	0.292503i	0.0217888	+	0.0113857i
$661$	−33.1861	−	19.1600i	−1.29079	−	0.745238i	−0.311996	−	0.950083i	$-0.600998\pi$
$661$	−33.1861	−	19.1600i	−1.29079	−	0.745238i	−0.978794	+	0.204845i	$0.934331\pi$
$662$	−5.33288	+	11.5009i	−0.207268	+	0.446996i
$663$	10.7249	+	14.1826i	0.416519	+	0.550806i
$664$	0.0979391	+	15.1803i	0.00380077	+	0.589110i
$665$	−3.97583	−	2.28918i	−0.154176	−	0.0887705i
$666$	23.1781	−	15.8207i	0.898134	−	0.613041i
$667$	−34.7757	+	34.7757i	−1.34652	+	1.34652i
$668$	−15.9427	−	1.32573i	−0.616840	−	0.0512941i
$669$	22.4363	−	28.8171i	0.867436	−	1.11413i
$670$	15.9163	−	11.2240i	0.614899	−	0.433620i
$671$	−0.324439	−	0.187315i	−0.0125248	−	0.00723122i
$672$	−9.28304	−	8.44317i	−0.358101	−	0.325702i
$673$	29.5722	+	7.92384i	1.13992	+	0.305441i	0.778920	−	0.627123i	$-0.215768\pi$
$673$	29.5722	+	7.92384i	1.13992	+	0.305441i	0.361003	+	0.932565i	$0.382434\pi$
$674$	−12.8523	+	15.3838i	−0.495052	+	0.592564i
$675$	25.6904	+	3.87368i	0.988822	+	0.149098i
$676$	2.06455	+	11.4212i	0.0794058	+	0.439276i
$677$	7.74938	−	28.9211i	0.297833	−	1.11153i	−0.641108	−	0.767450i	$-0.721525\pi$
$677$	7.74938	−	28.9211i	0.297833	−	1.11153i	0.938941	−	0.344077i	$-0.111808\pi$
$678$	13.3154	+	25.8870i	0.511375	+	0.994183i
$679$	19.2593	+	11.1194i	0.739106	+	0.426723i
$680$	−16.9825	+	17.2438i	−0.651248	+	0.661269i
$681$	32.0448	+	24.9493i	1.22796	+	0.956060i
$682$	0.829458	−	0.583455i	0.0317616	−	0.0223417i
$683$	−11.0463	+	11.0463i	−0.422677	+	0.422677i	−0.886124	−	0.463448i	$-0.846612\pi$
$683$	−11.0463	+	11.0463i	−0.422677	+	0.422677i	0.463448	+	0.886124i	$0.346612\pi$
$684$	−8.75077	+	3.97682i	−0.334594	+	0.152057i
$685$	17.7116	−	30.7615i	0.676727	−	1.17534i
$686$	−3.83988	+	22.0543i	−0.146607	+	0.842036i
$687$	14.6037	+	19.3120i	0.557167	+	0.736798i
$688$	32.6128	−	23.2564i	1.24335	−	0.886641i
$689$	10.4438	−	18.0891i	0.397875	−	0.689140i
$690$	−48.7192	+	10.6114i	−1.85471	+	0.403971i
$691$	7.57382	−	4.37275i	0.288122	−	0.166347i	−0.348973	−	0.937133i	$-0.613469\pi$
$691$	7.57382	−	4.37275i	0.288122	−	0.166347i	0.637094	+	0.770786i	$0.280136\pi$
$692$	27.2572	−	39.2859i	1.03616	−	1.49343i
$693$	0.269072	+	0.160443i	0.0102212	+	0.00609471i
$694$	−31.4917	+	37.6946i	−1.19541	+	1.43087i
$695$	4.57756	+	4.56674i	0.173637	+	0.173226i
$696$	24.4576	−	10.1138i	0.927065	−	0.383363i
$697$	−22.8461	+	6.12161i	−0.865359	+	0.231872i
$698$	36.0582	+	16.7199i	1.36482	+	0.632857i
$699$	−30.1939	+	12.2584i	−1.14204	+	0.463654i
$700$	5.48981	+	11.5709i	0.207495	+	0.437337i
$701$	15.1262			0.571310			0.285655	−	0.958333i	$-0.407789\pi$
$701$	15.1262			0.571310			0.285655	+	0.958333i	$0.407789\pi$
$702$	6.28366	−	18.6855i	0.237161	−	0.705237i
$703$	7.49280	−	7.49280i	0.282596	−	0.282596i
$704$	0.569064	+	0.318831i	0.0214474	+	0.0120164i
$705$	0.603605	+	0.796248i	0.0227331	+	0.0299884i
$706$	3.17026	+	8.65226i	0.119314	+	0.325632i
$707$	10.4279	−	2.79415i	0.392182	−	0.105085i
$708$	7.09136	+	22.7077i	0.266510	+	0.853407i
$709$	21.8706	+	37.8809i	0.821367	+	1.42265i	0.904665	+	0.426124i	$0.140121\pi$
$709$	21.8706	+	37.8809i	0.821367	+	1.42265i	−0.0832981	+	0.996525i	$0.526545\pi$
$710$	−1.41158	+	0.519108i	−0.0529756	+	0.0194818i
$711$	2.06061	+	0.583362i	0.0772790	+	0.0218778i
$712$	2.78300	+	10.1246i	0.104297	+	0.379434i
$713$	−20.7213	+	77.3331i	−0.776020	+	2.89615i
$714$	−8.89042	+	8.06694i	−0.332716	+	0.301898i
$715$	−0.423295	+	0.245058i	−0.0158303	+	0.00916465i
$716$	−39.8699	−	14.3175i	−1.49001	−	0.535072i
$717$	29.5242	+	39.0429i	1.10260	+	1.45808i
$718$	1.42957	−	1.00558i	0.0533510	−	0.0375280i
$719$	28.9479			1.07958			0.539788	−	0.841801i	$-0.318505\pi$
$719$	28.9479			1.07958			0.539788	+	0.841801i	$0.318505\pi$
$720$	26.4049	+	4.77297i	0.984053	+	0.177878i
$721$	17.5373			0.653122
$722$	19.0089	−	13.3712i	0.707437	−	0.497623i
$723$	−27.2035	+	3.38672i	−1.01171	+	0.125953i
$724$	−1.47071	−	0.528142i	−0.0546585	−	0.0196283i
$725$	−27.0120	+	0.0639415i	−1.00320	+	0.00237473i
$726$	25.6419	+	8.22294i	0.951659	+	0.305182i
$727$	6.19009	−	23.1017i	0.229578	−	0.856796i	−0.750941	−	0.660369i	$-0.770400\pi$
$727$	6.19009	−	23.1017i	0.229578	−	0.856796i	0.980519	−	0.196426i	$-0.0629336\pi$
$728$	9.37027	−	2.57566i	0.347285	−	0.0954604i
$729$	19.8812	−	18.2685i	0.736340	−	0.676611i
$730$	−10.9160	−	5.04595i	−0.404017	−	0.186759i
$731$	−19.1602	−	33.1865i	−0.708667	−	1.22745i
$732$	−15.5295	−	3.48747i	−0.573985	−	0.128901i
$733$	0.499891	−	0.133945i	0.0184639	−	0.00494738i	−0.249575	−	0.968355i	$-0.580291\pi$
$733$	0.499891	−	0.133945i	0.0184639	−	0.00494738i	0.268039	+	0.963408i	$0.413624\pi$
$734$	−2.39812	−	6.54495i	−0.0885162	−	0.241578i
$735$	−7.83139	−	19.2244i	−0.288865	−	0.709102i
$736$	−50.6152	+	9.48708i	−1.86570	+	0.349699i
$737$	−0.355085	+	0.355085i	−0.0130797	+	0.0130797i
$738$	19.8853	+	17.0941i	0.731986	+	0.629244i
$739$	38.8662			1.42972			0.714859	−	0.699269i	$-0.246491\pi$
$739$	38.8662			1.42972			0.714859	+	0.699269i	$0.246491\pi$
$740$	−29.1028	+	5.29635i	−1.06984	+	0.194698i
$741$	1.02355	−	7.37312i	0.0376012	−	0.270858i
$742$	12.7936	+	5.93228i	0.469667	+	0.217781i
$743$	21.6807	−	5.80932i	0.795387	−	0.213123i	0.161829	−	0.986819i	$-0.448261\pi$
$743$	21.6807	−	5.80932i	0.795387	−	0.213123i	0.633558	+	0.773695i	$0.281594\pi$
$744$	26.2485	−	34.1659i	0.962315	−	1.25258i
$745$	−1.61174	+	1.61556i	−0.0590495	+	0.0591895i
$746$	−3.40689	+	4.07795i	−0.124735	+	0.149304i
$747$	−7.85358	−	14.0563i	−0.287348	−	0.514293i
$748$	0.355731	−	0.512716i	0.0130068	−	0.0187467i
$749$	−4.11219	+	2.37418i	−0.150256	+	0.0867505i
$750$	−23.0775	−	14.7455i	−0.842671	−	0.538429i
$751$	10.3025	−	17.8445i	0.375945	−	0.651155i	−0.614523	−	0.788899i	$-0.710652\pi$
$751$	10.3025	−	17.8445i	0.375945	−	0.651155i	0.990468	+	0.137743i	$0.0439850\pi$
$752$	0.599148	+	0.840195i	0.0218487	+	0.0306388i
$753$	0.833024	−	1.97171i	0.0303571	−	0.0718532i
$754$	−3.51572	+	20.1925i	−0.128035	+	0.735366i
$755$	32.2668	−	8.68680i	1.17431	−	0.316145i
$756$	12.9438	+	3.09889i	0.470761	+	0.112706i
$757$	8.54756	−	8.54756i	0.310666	−	0.310666i	−0.534501	−	0.845168i	$-0.679501\pi$
$757$	8.54756	−	8.54756i	0.310666	−	0.310666i	0.845168	+	0.534501i	$0.179501\pi$
$758$	−5.27205	+	3.70845i	−0.191489	+	0.134697i
$759$	1.19121	−	0.483615i	0.0432380	−	0.0175541i
$760$	10.1317	−	0.0773589i	0.367514	−	0.00280610i
$761$	11.9028	+	6.87207i	0.431475	+	0.249112i	0.699975	−	0.714167i	$-0.253194\pi$
$761$	11.9028	+	6.87207i	0.431475	+	0.249112i	−0.268500	+	0.963280i	$0.586528\pi$
$762$	9.78922	−	15.2014i	0.354626	−	0.550690i
$763$	0.807949	−	3.01531i	0.0292497	−	0.109161i
$764$	1.75215	+	9.69298i	0.0633907	+	0.350680i
$765$	6.96327	−	24.7080i	0.251758	−	0.893319i
$766$	9.18576	−	10.9951i	0.331895	−	0.397269i
$767$	−17.7953	−	4.76823i	−0.642550	−	0.172171i
$768$	27.1155	+	5.72287i	0.978445	+	0.206506i
$769$	14.9077	+	8.60697i	0.537586	+	0.310375i	0.744100	−	0.668068i	$-0.232879\pi$
$769$	14.9077	+	8.60697i	0.537586	+	0.310375i	−0.206514	+	0.978444i	$0.566212\pi$
$770$	−0.190308	−	0.269868i	−0.00685822	−	0.00972538i
$771$	−41.3597	−	5.74166i	−1.48953	−	0.206781i
$772$	17.8477	+	1.48415i	0.642354	+	0.0534158i
$773$	−14.8770	+	14.8770i	−0.535089	+	0.535089i	−0.922082	−	0.386993i	$-0.873514\pi$
$773$	−14.8770	+	14.8770i	−0.535089	+	0.535089i	0.386993	+	0.922082i	$0.373514\pi$
$774$	−18.4133	+	38.2879i	−0.661851	+	1.37623i
$775$	−38.0297	+	22.0767i	−1.36607	+	0.793017i
$776$	−49.1128	+	0.316862i	−1.76305	+	0.0113747i
$777$	−14.5602	+	1.81269i	−0.522345	+	0.0650297i
$778$	11.0384	−	23.8055i	0.395746	−	0.853468i
$779$	8.57505	+	4.95081i	0.307233	+	0.177381i
$780$	−14.0627	+	15.2988i	−0.503524	+	0.547785i
$781$	0.0335840	−	0.0193897i	0.00120173	−	0.000693819i
$782$	4.39934	+	49.0690i	0.157320	+	1.75470i
$783$	−17.5556	+	21.9049i	−0.627386	+	0.782817i
$784$	−7.50563	−	20.0823i	−0.268058	−	0.717226i
$785$	−31.2485	+	0.0369850i	−1.11531	+	0.00132005i
$786$	28.9429	+	9.28152i	1.03236	+	0.331061i
$787$	9.62487	+	35.9205i	0.343090	+	1.28043i	0.894828	+	0.446411i	$0.147298\pi$
$787$	9.62487	+	35.9205i	0.343090	+	1.28043i	−0.551738	+	0.834017i	$0.686035\pi$
$788$	−41.6547	+	19.6424i	−1.48389	+	0.699733i
$789$	−9.14550	−	7.12045i	−0.325588	−	0.253495i
$790$	−1.73413	−	1.44528i	−0.0616975	−	0.0514208i
$791$		−	15.2205i		−	0.541180i
$792$	−0.691841	−	0.00527941i	−0.0245835	−	0.000187596i
$793$	8.71578	−	8.71578i	0.309506	−	0.309506i
$794$	0.693862	−	3.98518i	0.0246242	−	0.141429i
$795$	−29.9197	+	3.76084i	−1.06114	+	0.133383i
$796$	−3.56438	−	1.27999i	−0.126336	−	0.0453682i
$797$	−6.78553	+	1.81818i	−0.240356	+	0.0644032i	−0.376986	−	0.926219i	$-0.623039\pi$
$797$	−6.78553	+	1.81818i	−0.240356	+	0.0644032i	0.136630	+	0.990622i	$0.456373\pi$
$798$	5.01973	+	0.243768i	0.177696	+	0.00862930i
$799$	0.854975	−	0.493620i	0.0302468	−	0.0174630i
$800$	−23.3800	−	15.9178i	−0.826607	−	0.562780i
$801$	−7.76339	−	7.98519i	−0.274306	−	0.282143i
$802$	−39.2852	+	3.52216i	−1.38721	+	0.124372i
$803$	0.299509	+	0.0802533i	0.0105695	+	0.00283208i
$804$	−9.90305	+	18.8970i	−0.349254	+	0.666445i
$805$	25.1896	+	6.71760i	0.887818	+	0.236764i
$806$	11.4792	+	31.3292i	0.404339	+	1.10352i
$807$	41.0955	+	17.3623i	1.44663	+	0.611182i
$808$	−16.7499	+	16.9674i	−0.589258	+	0.596911i
$809$	−14.4439			−0.507820			−0.253910	−	0.967228i	$-0.581717\pi$
$809$	−14.4439			−0.507820			−0.253910	+	0.967228i	$0.581717\pi$
$810$	−26.9776	+	9.06705i	−0.947895	+	0.318584i
$811$		−	25.5871i		−	0.898486i	−0.893410	−	0.449243i	$-0.851694\pi$
$811$		−	25.5871i		−	0.898486i	0.893410	−	0.449243i	$-0.148306\pi$
$812$	−13.7903	−	1.14675i	−0.483944	−	0.0402430i
$813$	−5.10104	+	12.0738i	−0.178901	+	0.423448i
$814$	0.716156	−	0.262405i	0.0251013	−	0.00919729i
$815$	25.1316	−	14.5494i	0.880321	−	0.509644i
$816$	7.93293	−	25.2977i	0.277708	−	0.885595i
$817$	−4.15206	+	15.4957i	−0.145262	+	0.542126i
$818$	1.28877	−	0.115546i	0.0450607	−	0.00403996i
$819$	−7.39028	+	7.18501i	−0.258237	+	0.251064i
$820$	−11.8189	−	24.9870i	−0.412734	−	0.872584i
$821$	−10.6850	−	18.5070i	−0.372910	−	0.645900i	0.617102	−	0.786883i	$-0.288307\pi$
$821$	−10.6850	−	18.5070i	−0.372910	−	0.645900i	−0.990012	+	0.140984i	$0.954973\pi$
$822$	−1.88606	+	38.8382i	−0.0657840	+	1.35464i
$823$	1.46604	+	5.47134i	0.0511029	+	0.190719i	0.986759	−	0.162195i	$-0.0518575\pi$
$823$	1.46604	+	5.47134i	0.0511029	+	0.190719i	−0.935656	+	0.352914i	$0.885191\pi$
$824$	−33.4161	+	19.5813i	−1.16410	+	0.682148i
$825$	0.651107	+	0.273270i	0.0226686	+	0.00951404i
$826$	2.13352	−	12.2538i	0.0742346	−	0.426365i
$827$	3.85687	+	3.85687i	0.134117	+	0.134117i	0.770978	−	0.636862i	$-0.219768\pi$
$827$	3.85687	+	3.85687i	0.134117	+	0.134117i	−0.636862	+	0.770978i	$0.719768\pi$
$828$	42.1831	−	34.6984i	1.46596	−	1.20585i
$829$	−13.7695			−0.478234			−0.239117	−	0.970991i	$-0.576858\pi$
$829$	−13.7695			−0.478234			−0.239117	+	0.970991i	$0.576858\pi$
$830$	1.53561	+	16.9028i	0.0533019	+	0.586706i
$831$	−7.87695	+	10.1171i	−0.273248	+	0.350959i
$832$	−14.9786	+	15.3702i	−0.519288	+	0.532865i
$833$	−19.8115	+	5.30847i	−0.686427	+	0.183928i
$834$	−6.74482	−	2.16296i	−0.233554	−	0.0748970i
$835$	−17.8859	+	0.0211694i	−0.618969	+	0.000732596i
$836$	−0.257078	+	0.0464707i	−0.00889122	+	0.00160722i
$837$	−6.92047	+	45.1712i	−0.239206	+	1.56134i
$838$	−21.1983	+	1.90055i	−0.732282	+	0.0656536i
$839$	1.74258	+	3.01824i	0.0601605	+	0.104201i	0.894537	−	0.446994i	$-0.147505\pi$
$839$	1.74258	+	3.01824i	0.0601605	+	0.104201i	−0.834377	+	0.551195i	$0.814172\pi$
$840$	−11.1354	−	8.53402i	−0.384209	−	0.294452i
$841$	0.0930259	−	0.161126i	0.00320779	−	0.00555605i
$842$	5.86351	−	12.6453i	0.202070	−	0.435785i
$843$	2.80755	+	22.5513i	0.0966970	+	0.776709i
$844$	29.8433	−	25.2610i	1.02725	−	0.869519i
$845$	3.37332	+	12.5301i	0.116046	+	0.431048i
$846$	−0.986401	−	0.474376i	−0.0339132	−	0.0163094i
$847$	−9.95560	−	9.95560i	−0.342078	−	0.342078i
$848$	−31.0010	+	2.98117i	−1.06458	+	0.102374i
$849$	−7.50954	+	54.0945i	−0.257727	+	1.85652i
$850$	−17.2994	+	20.8068i	−0.593364	+	0.713667i
$851$	−30.1071	+	52.1470i	−1.03206	+	1.78758i
$852$	1.11639	−	1.21165i	0.0382470	−	0.0415104i
$853$	−12.3076	+	45.9325i	−0.421403	+	1.57270i	0.350251	+	0.936656i	$0.386096\pi$
$853$	−12.3076	+	45.9325i	−0.421403	+	1.57270i	−0.771654	+	0.636042i	$0.780570\pi$
$854$	6.38635	+	5.33542i	0.218536	+	0.182574i
$855$	−9.37534	+	5.25280i	−0.320630	+	0.179642i
$856$	5.18461	−	9.11532i	0.177206	−	0.311555i
$857$	24.0647	+	6.44812i	0.822036	+	0.220264i	0.645236	−	0.763983i	$-0.276759\pi$
$857$	24.0647	+	6.44812i	0.822036	+	0.220264i	0.176799	+	0.984247i	$0.443426\pi$
$858$	0.290090	−	0.450473i	0.00990351	−	0.0153789i
$859$	6.39051	−	11.0687i	0.218041	−	0.377659i	−0.736168	−	0.676799i	$-0.763367\pi$
$859$	6.39051	−	11.0687i	0.218041	−	0.377659i	0.954209	+	0.299140i	$0.0966999\pi$
$860$	34.1478	−	28.9741i	1.16443	−	0.988007i
$861$	−5.15748	−	12.7035i	−0.175766	−	0.432935i
$862$	0.327377	+	0.465409i	0.0111505	+	0.0158519i
$863$	−12.2542	−	12.2542i	−0.417138	−	0.417138i	0.467078	−	0.884216i	$-0.345307\pi$
$863$	−12.2542	−	12.2542i	−0.417138	−	0.417138i	−0.884216	+	0.467078i	$0.845307\pi$
$864$	−28.1236	+	8.54771i	−0.956784	+	0.290799i
$865$	26.6750	−	46.3289i	0.906976	−	1.57523i
$866$	6.07811	−	34.9095i	0.206542	−	1.18627i
$867$	3.75930	+	1.58826i	0.127672	+	0.0539400i
$868$	−20.3751	+	9.60796i	−0.691576	+	0.326116i
$869$	0.0504081	+	0.0291031i	0.00170998	+	0.000987256i
$870$	26.2973	−	13.5659i	0.891563	−	0.459925i
$871$	−8.26106	−	14.3086i	−0.279916	−	0.484828i
$872$	1.82726	+	6.64759i	0.0618789	+	0.225116i
$873$	45.4762	−	25.4087i	1.53914	−	0.859953i
$874$	13.2231	−	15.8277i	0.447279	−	0.535381i
$875$	7.20339	+	12.3750i	0.243519	+	0.418350i
$876$	13.1626	−	0.538559i	0.444722	−	0.0181962i
$877$	12.1090	+	45.1914i	0.408892	+	1.52600i	0.796764	+	0.604291i	$0.206543\pi$
$877$	12.1090	+	45.1914i	0.408892	+	1.52600i	−0.387872	+	0.921713i	$0.626790\pi$
$878$	7.79744	−	16.8160i	0.263151	−	0.567512i
$879$	−1.93810	−	0.269052i	−0.0653705	−	0.00907490i
$880$	0.663942	+	0.301727i	0.0223815	+	0.0101712i
$881$		−	8.42147i		−	0.283727i	−0.989886	−	0.141863i	$-0.954691\pi$
$881$		−	8.42147i		−	0.283727i	0.989886	−	0.141863i	$-0.0453093\pi$
$882$	17.2439	+	14.8235i	0.580632	+	0.499134i
$883$	3.40536	+	3.40536i	0.114600	+	0.114600i	0.762081	−	0.647482i	$-0.224178\pi$
$883$	3.40536	+	3.40536i	0.114600	+	0.114600i	−0.647482	+	0.762081i	$0.724178\pi$
$884$	13.2652	+	15.6714i	0.446156	+	0.527087i
$885$	10.0342	+	24.6318i	0.337295	+	0.827987i
$886$	24.3409	−	8.91868i	0.817748	−	0.299629i
$887$	−9.22633	−	34.4331i	−0.309790	−	1.15615i	−0.928743	−	0.370723i	$-0.879110\pi$
$887$	−9.22633	−	34.4331i	−0.309790	−	1.15615i	0.618954	−	0.785427i	$-0.287557\pi$
$888$	25.7196	−	19.7112i	0.863092	−	0.661466i
$889$	−8.18696	+	4.72675i	−0.274582	+	0.158530i
$890$	4.05189	+	11.0180i	0.135820	+	0.369325i
$891$	0.645596	−	0.348873i	0.0216283	−	0.0116877i
$892$	24.0396	−	34.6484i	0.804907	−	1.16011i
$893$	−0.399212	−	0.106968i	−0.0133591	−	0.00357956i
$894$	0.763372	−	2.38045i	0.0255310	−	0.0796141i
$895$	−45.7636	−	12.2043i	−1.52971	−	0.407944i
$896$	−11.2386	−	9.14561i	−0.375457	−	0.305533i
$897$	5.22578	+	41.9755i	0.174484	+	1.40152i
$898$	40.0296	−	28.1575i	1.33581	−	0.939629i
$899$		−	47.5122i		−	1.58462i
$900$	29.8656	+	2.83618i	0.995521	+	0.0945393i
$901$			29.7949i			0.992612i
$902$	0.410046	+	0.582934i	0.0136530	+	0.0194096i
$903$	17.7179	−	13.3983i	0.589615	−	0.445867i
$904$	16.9946	+	29.0017i	0.565230	+	0.964582i
$905$	−1.68812	−	0.450188i	−0.0561149	−	0.0149648i
$906$	−27.1087	+	24.5977i	−0.900625	+	0.817204i
$907$	47.5009	+	12.7278i	1.57724	+	0.422620i	0.938070	−	0.346445i	$-0.112611\pi$
$907$	47.5009	+	12.7278i	1.57724	+	0.422620i	0.639170	+	0.769065i	$0.279278\pi$
$908$	38.5293	+	26.7323i	1.27864	+	0.887141i
$909$	6.88846	−	24.3322i	0.228476	−	0.807048i
$910$	10.1972	−	3.75002i	0.338033	−	0.124312i
$911$	5.60975	−	3.23879i	0.185859	−	0.107306i	−0.404183	−	0.914678i	$-0.632444\pi$
$911$	5.60975	−	3.23879i	0.185859	−	0.107306i	0.590043	+	0.807372i	$0.299111\pi$
$912$	−9.83693	+	5.14032i	−0.325733	+	0.170213i
$913$	−0.113265	−	0.422709i	−0.00374851	−	0.0139896i
$914$	−17.6407	−	48.1451i	−0.583503	−	1.59250i
$915$	−17.6287	−	2.42600i	−0.582788	−	0.0802012i
$916$	18.0628	+	21.3393i	0.596810	+	0.705070i
$917$	−11.2372	−	11.2372i	−0.371086	−	0.371086i
$918$	5.56445	+	27.5645i	0.183654	+	0.909765i
$919$			31.5470i			1.04064i	0.853972	+	0.520319i	$0.174187\pi$
$919$			31.5470i			1.04064i	−0.853972	+	0.520319i	$0.825813\pi$
$920$	−55.4978	+	15.3257i	−1.82971	+	0.505273i
$921$	1.95186	+	4.80768i	0.0643160	+	0.158418i
$922$	20.9490	+	9.71389i	0.689919	+	0.319910i
$923$	0.330230	+	1.23244i	0.0108697	+	0.0405661i
$924$	0.320408	+	0.167911i	0.0105406	+	0.00552387i
$925$	−31.9251	+	8.63535i	−1.04969	+	0.283929i
$926$	−24.5286	−	20.4922i	−0.806061	−	0.673417i
$927$	21.0390	−	35.2836i	0.691011	−	1.15887i
$928$	27.5569	−	13.2126i	0.904599	−	0.433724i
$929$	−10.4004	−	18.0141i	−0.341227	−	0.591023i	0.643434	−	0.765502i	$-0.277509\pi$
$929$	−10.4004	−	18.0141i	−0.341227	−	0.591023i	−0.984661	+	0.174479i	$0.944176\pi$
$930$	26.0322	−	40.5301i	0.853631	−	1.32903i
$931$	7.43602	+	4.29319i	0.243706	+	0.140704i
$932$	−34.0344	+	16.0491i	−1.11484	+	0.525706i
$933$	8.30462	−	6.27995i	0.271881	−	0.205596i
$934$	−25.4176	−	4.42547i	−0.831689	−	0.144806i
$935$	0.348132	−	0.604633i	0.0113851	−	0.0197736i
$936$	6.05922	−	21.9422i	0.198052	−	0.717203i
$937$	24.4429	+	24.4429i	0.798514	+	0.798514i	0.982861	−	0.184347i	$-0.0590171\pi$
$937$	24.4429	+	24.4429i	0.798514	+	0.798514i	−0.184347	+	0.982861i	$0.559017\pi$
$938$	9.12369	−	6.41776i	0.297899	−	0.209547i
$939$	−19.6781	+	25.2745i	−0.642169	+	0.824801i
$940$	0.746451	+	0.879741i	0.0243465	+	0.0286940i
$941$	3.59109	−	6.21994i	0.117066	−	0.202764i	−0.801538	−	0.597944i	$-0.795984\pi$
$941$	3.59109	−	6.21994i	0.117066	−	0.202764i	0.918604	+	0.395180i	$0.129318\pi$
$942$	30.4403	−	15.6575i	0.991798	−	0.510148i
$943$	−54.3488	−	14.5627i	−1.76984	−	0.474227i
$944$	9.61679	+	25.7310i	0.313000	+	0.837474i
$945$	14.7116	+	2.23608i	0.478568	+	0.0727396i
$946$	−0.740327	+	0.886151i	−0.0240701	+	0.0288112i
$947$	2.44092	−	9.10965i	0.0793194	−	0.296024i	−0.914859	−	0.403774i	$-0.867698\pi$
$947$	2.44092	−	9.10965i	0.0793194	−	0.296024i	0.994178	+	0.107750i	$0.0343647\pi$
$948$	2.41281	+	0.541848i	0.0783644	+	0.0175984i
$949$	−5.10100	+	8.83519i	−0.165585	+	0.286802i
$950$	11.2802	−	1.03826i	0.365978	−	0.0336856i
$951$	3.43331	+	2.67309i	0.111333	+	0.0866809i
$952$	−9.73843	+	9.86491i	−0.315624	+	0.319724i
$953$	20.1838	+	20.1838i	0.653817	+	0.653817i	0.953910	−	0.300093i	$-0.0970176\pi$
$953$	20.1838	+	20.1838i	0.653817	+	0.653817i	−0.300093	+	0.953910i	$0.597018\pi$
$954$	27.2834	−	18.6229i	0.883332	−	0.602938i
$955$	2.86289	+	10.6341i	0.0926409	+	0.344111i
$956$	36.5173	+	43.1415i	1.18105	+	1.39529i
$957$	−0.608551	+	0.460187i	−0.0196717	+	0.0148757i
$958$	46.6504	+	21.6314i	1.50721	+	0.698880i
$959$	10.1652	−	17.6067i	0.328253	−	0.568550i
$960$	30.7465	+	3.82767i	0.992340	+	0.123538i
$961$	−23.1728	−	40.1364i	−0.747508	−	1.29472i
$962$	2.24090	+	24.9944i	0.0722496	+	0.805853i
$963$	−0.156630	+	11.1216i	−0.00504734	+	0.358390i
$964$	−31.1495	+	5.63075i	−1.00326	+	0.181354i
$965$	20.0232	−	0.0236990i	0.644571	−	0.000762898i
$966$	−27.9112	+	6.04470i	−0.898028	+	0.194485i
$967$	−49.6247	+	13.2969i	−1.59582	+	0.427600i	−0.943778	−	0.330580i	$-0.892756\pi$
$967$	−49.6247	+	13.2969i	−1.59582	+	0.427600i	−0.652046	+	0.758179i	$0.726089\pi$
$968$	30.0857	+	7.85376i	0.966991	+	0.252429i
$969$	3.99424	+	9.83832i	0.128313	+	0.316052i
$970$	−54.6857	+	4.96816i	−1.75585	+	0.159518i
$971$	−23.6328			−0.758412			−0.379206	−	0.925312i	$-0.623803\pi$
$971$	−23.6328			−0.758412			−0.379206	+	0.925312i	$0.623803\pi$
$972$	21.7630	−	22.3242i	0.698050	−	0.716049i
$973$	2.61871	+	2.61871i	0.0839521	+	0.0839521i
$974$	48.3068	+	8.41073i	1.54785	+	0.269497i
$975$	−14.2293	+	18.3655i	−0.455701	+	0.588168i
$976$	−18.1261	−	3.03558i	−0.580201	−	0.0971666i
$977$	−13.5422	−	50.5402i	−0.433254	−	1.61692i	−0.745211	−	0.666828i	$-0.767651\pi$
$977$	−13.5422	−	50.5402i	−0.433254	−	1.61692i	0.311958	−	0.950096i	$-0.399015\pi$
$978$	−17.2230	+	26.7452i	−0.550732	+	0.855217i
$979$	−0.151346	−	0.262139i	−0.00483704	−	0.00837800i
$980$	−10.2490	−	21.6680i	−0.327392	−	0.692158i
$981$	−5.09729	−	5.24291i	−0.162744	−	0.167393i
$982$	−3.45842	−	38.5743i	−0.110363	−	1.23096i
$983$	3.49299	−	13.0360i	0.111409	−	0.415785i	−0.887584	−	0.460646i	$-0.847618\pi$
$983$	3.49299	−	13.0360i	0.111409	−	0.415785i	0.998993	+	0.0448611i	$0.0142845\pi$
$984$	24.0114	+	18.4471i	0.765456	+	0.588072i
$985$	−44.5607	+	25.7975i	−1.41982	+	0.821977i
$986$	−10.0586	−	27.4520i	−0.320332	−	0.874251i
$987$	0.345176	+	0.456462i	0.0109871	+	0.0145293i
$988$	0.712302	−	8.56582i	0.0226613	−	0.272515i
$989$		−	91.1607i		−	2.89874i
$990$	−0.771261	+	0.0591309i	−0.0245123	+	0.00187930i
$991$	−11.0800			−0.351967			−0.175983	−	0.984393i	$-0.556311\pi$
$991$	−11.0800			−0.351967			−0.175983	+	0.984393i	$0.556311\pi$
$992$	28.0955	−	41.0572i	0.892035	−	1.30357i
$993$	−1.91815	−	15.4074i	−0.0608707	−	0.488938i
$994$	−0.808836	+	0.296364i	−0.0256547	+	0.00940008i
$995$	−4.09128	−	1.09107i	−0.129702	−	0.0345891i
$996$	−9.94668	−	15.7080i	−0.315173	−	0.497726i
$997$	20.8772	+	5.59402i	0.661186	+	0.177164i	0.573781	−	0.819009i	$-0.305476\pi$
$997$	20.8772	+	5.59402i	0.661186	+	0.177164i	0.0874049	+	0.996173i	$0.472143\pi$
$998$	0.505920	+	5.64290i	0.0160146	+	0.178623i
$999$	−13.8205	+	31.4687i	−0.437262	+	0.995624i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.br.e.77.10	✓	256
5.3	odd	4	inner	360.2.br.e.293.42	yes	256
8.5	even	2	inner	360.2.br.e.77.21	yes	256
9.2	odd	6	inner	360.2.br.e.317.12	yes	256
40.13	odd	4	inner	360.2.br.e.293.12	yes	256
45.38	even	12	inner	360.2.br.e.173.21	yes	256
72.29	odd	6	inner	360.2.br.e.317.42	yes	256
360.173	even	12	inner	360.2.br.e.173.10	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.br.e.77.10	✓	256	1.1	even	1	trivial
360.2.br.e.77.21	yes	256	8.5	even	2	inner
360.2.br.e.173.10	yes	256	360.173	even	12	inner
360.2.br.e.173.21	yes	256	45.38	even	12	inner
360.2.br.e.293.12	yes	256	40.13	odd	4	inner
360.2.br.e.293.42	yes	256	5.3	odd	4	inner
360.2.br.e.317.12	yes	256	9.2	odd	6	inner
360.2.br.e.317.42	yes	256	72.29	odd	6	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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.br (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.15671 + 0.813649i) q^{2} +(0.674078 - 1.59550i) q^{3} +(0.675951 - 1.88231i) q^{4} +(0.576180 - 2.16056i) q^{5} +(0.518465 + 2.39399i) q^{6} +(0.331473 - 1.23707i) q^{7} +(0.749662 + 2.72727i) q^{8} +(-2.09124 - 2.15098i) q^{9} +O(q^{10})\)	\(q+(-1.15671 + 0.813649i) q^{2} +(0.674078 - 1.59550i) q^{3} +(0.675951 - 1.88231i) q^{4} +(0.576180 - 2.16056i) q^{5} +(0.518465 + 2.39399i) q^{6} +(0.331473 - 1.23707i) q^{7} +(0.749662 + 2.72727i) q^{8} +(-2.09124 - 2.15098i) q^{9} +(1.09146 + 2.96795i) q^{10} +(-0.0407683 - 0.0706128i) q^{11} +(-2.54758 - 2.34730i) q^{12} +(2.59129 - 0.694333i) q^{13} +(0.623127 + 1.70064i) q^{14} +(-3.05878 - 2.37568i) q^{15} +(-3.08618 - 2.54470i) q^{16} +(-2.70590 + 2.70590i) q^{17} +(4.16910 + 0.786527i) q^{18} +1.60200 q^{19} +(-3.67737 - 2.54498i) q^{20} +(-1.75031 - 1.36275i) q^{21} +(0.104611 + 0.0485074i) q^{22} +(-8.79321 + 2.35613i) q^{23} +(4.85669 + 0.642309i) q^{24} +(-4.33603 - 2.48974i) q^{25} +(-2.43242 + 2.91154i) q^{26} +(-4.84155 + 1.88664i) q^{27} +(-2.10450 - 1.46014i) q^{28} +(4.67863 - 2.70121i) q^{29} +(5.47109 + 0.259197i) q^{30} +(4.39731 - 7.61637i) q^{31} +(5.64030 + 0.432405i) q^{32} +(-0.140144 + 0.0174473i) q^{33} +(0.928286 - 5.33160i) q^{34} +(-2.48178 - 1.42895i) q^{35} +(-5.46239 + 2.48240i) q^{36} +(4.67714 - 4.67714i) q^{37} +(-1.85305 + 1.30347i) q^{38} +(0.638921 - 4.60243i) q^{39} +(6.32437 - 0.0482888i) q^{40} +(5.35270 + 3.09038i) q^{41} +(3.13340 + 0.152164i) q^{42} +(-2.59179 + 9.67270i) q^{43} +(-0.160473 + 0.0290079i) q^{44} +(-5.85225 + 3.27889i) q^{45} +(8.25412 - 9.87995i) q^{46} +(-0.249195 - 0.0667716i) q^{47} +(-6.14039 + 3.20868i) q^{48} +(4.64170 + 2.67989i) q^{49} +(7.04130 - 0.648101i) q^{50} +(2.49328 + 6.14125i) q^{51} +(0.444631 - 5.34694i) q^{52} +(5.50554 - 5.50554i) q^{53} +(4.06520 - 6.12161i) q^{54} +(-0.176053 + 0.0473967i) q^{55} +(3.62233 - 0.0233703i) q^{56} +(1.07988 - 2.55600i) q^{57} +(-3.21397 + 6.93127i) q^{58} +(-5.94730 - 3.43368i) q^{59} +(-6.53935 + 4.15173i) q^{60} +(3.97906 - 2.29731i) q^{61} +(1.11064 + 12.3878i) q^{62} +(-3.35411 + 1.87402i) q^{63} +(-6.87601 + 4.08906i) q^{64} +(-0.00709990 - 5.99869i) q^{65} +(0.147910 - 0.134209i) q^{66} +(-1.59401 - 5.94892i) q^{67} +(3.26429 + 6.92240i) q^{68} +(-2.16810 + 15.6178i) q^{69} +(4.03336 - 0.366428i) q^{70} +0.475607i q^{71} +(4.29859 - 7.31588i) q^{72} +(-2.68905 + 2.68905i) q^{73} +(-1.60454 + 9.21563i) q^{74} +(-6.89521 + 5.23986i) q^{75} +(1.08288 - 3.01547i) q^{76} +(-0.100867 + 0.0270272i) q^{77} +(3.00572 + 5.84353i) q^{78} +(-0.618226 + 0.356933i) q^{79} +(-7.27617 + 5.20167i) q^{80} +(-0.253450 + 8.99643i) q^{81} +(-8.70600 + 0.780546i) q^{82} +(5.18428 + 1.38912i) q^{83} +(-3.74824 + 2.37348i) q^{84} +(4.28717 + 7.40535i) q^{85} +(-4.87223 - 13.2973i) q^{86} +(-1.15601 - 9.28557i) q^{87} +(0.162018 - 0.164122i) q^{88} +3.71234 q^{89} +(4.10149 - 8.55440i) q^{90} -3.43577i q^{91} +(-1.50880 + 18.1442i) q^{92} +(-9.18779 - 12.1499i) q^{93} +(0.342575 - 0.125522i) q^{94} +(0.923043 - 3.46123i) q^{95} +(4.49191 - 8.70763i) q^{96} +(-4.49423 + 16.7727i) q^{97} +(-7.54958 + 0.676866i) q^{98} +(-0.0666307 + 0.235360i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 6 q^{2} - 8 q^{6}+O(q^{10}) \) 256 * q + 6 * q^2 - 8 * q^6	\( 256 q + 6 q^{2} - 8 q^{6} - 10 q^{12} + 28 q^{15} + 12 q^{16} - 28 q^{18} - 54 q^{20} + 14 q^{22} - 28 q^{25} - 32 q^{28} + 14 q^{30} - 32 q^{31} - 114 q^{32} + 4 q^{33} - 40 q^{36} - 30 q^{38} + 46 q^{40} + 24 q^{41} - 10 q^{42} - 16 q^{46} + 24 q^{47} - 2 q^{48} + 78 q^{50} + 38 q^{52} - 8 q^{55} - 96 q^{56} - 80 q^{57} - 18 q^{58} - 2 q^{60} - 144 q^{63} - 84 q^{65} - 4 q^{66} - 30 q^{68} - 30 q^{70} - 86 q^{72} + 64 q^{73} + 16 q^{76} - 82 q^{78} + 72 q^{81} - 64 q^{82} + 48 q^{86} - 4 q^{87} + 38 q^{88} + 78 q^{90} - 108 q^{92} - 24 q^{95} - 116 q^{96} + 36 q^{97}+O(q^{100}) \) 256 * q + 6 * q^2 - 8 * q^6 - 10 * q^12 + 28 * q^15 + 12 * q^16 - 28 * q^18 - 54 * q^20 + 14 * q^22 - 28 * q^25 - 32 * q^28 + 14 * q^30 - 32 * q^31 - 114 * q^32 + 4 * q^33 - 40 * q^36 - 30 * q^38 + 46 * q^40 + 24 * q^41 - 10 * q^42 - 16 * q^46 + 24 * q^47 - 2 * q^48 + 78 * q^50 + 38 * q^52 - 8 * q^55 - 96 * q^56 - 80 * q^57 - 18 * q^58 - 2 * q^60 - 144 * q^63 - 84 * q^65 - 4 * q^66 - 30 * q^68 - 30 * q^70 - 86 * q^72 + 64 * q^73 + 16 * q^76 - 82 * q^78 + 72 * q^81 - 64 * q^82 + 48 * q^86 - 4 * q^87 + 38 * q^88 + 78 * q^90 - 108 * q^92 - 24 * q^95 - 116 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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