LMFDB - Embedded newform 360.2.bo.a.43.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(43,360)]

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([6, 6, 8, 9]))

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

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

chi := DirichletCharacter("360.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bo (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:	$272$
Relative dimension:	$68$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			43.6
Character	$\chi$	$=$	360.43
Dual form			360.2.bo.a.67.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36313 - 0.376650i) q^{2} +(-0.727225 + 1.57199i) q^{3} +(1.71627 + 1.02685i) q^{4} +(2.06459 + 0.858752i) q^{5} +(1.58339 - 1.86892i) q^{6} +(2.73850 - 0.733779i) q^{7} +(-1.95274 - 2.04617i) q^{8} +(-1.94229 - 2.28638i) q^{9} +O(q^{10})$	\(q+(-1.36313 - 0.376650i) q^{2} +(-0.727225 + 1.57199i) q^{3} +(1.71627 + 1.02685i) q^{4} +(2.06459 + 0.858752i) q^{5} +(1.58339 - 1.86892i) q^{6} +(2.73850 - 0.733779i) q^{7} +(-1.95274 - 2.04617i) q^{8} +(-1.94229 - 2.28638i) q^{9} +(-2.49087 - 1.94822i) q^{10} +(3.11812 - 5.40074i) q^{11} +(-2.86231 + 1.95120i) q^{12} +(3.49373 + 0.936143i) q^{13} +(-4.00932 - 0.0312183i) q^{14} +(-2.85137 + 2.62101i) q^{15} +(1.89116 + 3.52470i) q^{16} +(-2.72591 + 2.72591i) q^{17} +(1.78644 + 3.84820i) q^{18} -3.02550i q^{19} +(2.66159 + 3.59388i) q^{20} +(-0.838014 + 4.83851i) q^{21} +(-6.28461 + 6.18749i) q^{22} +(-3.65415 - 0.979127i) q^{23} +(4.63663 - 1.58166i) q^{24} +(3.52509 + 3.54595i) q^{25} +(-4.40983 - 2.59200i) q^{26} +(5.00663 - 1.39054i) q^{27} +(5.45349 + 1.55267i) q^{28} +(1.53565 - 2.65982i) q^{29} +(4.87400 - 2.49882i) q^{30} +(0.328863 - 0.189869i) q^{31} +(-1.25032 - 5.51695i) q^{32} +(6.22232 + 8.82919i) q^{33} +(4.74250 - 2.68907i) q^{34} +(6.28403 + 0.836738i) q^{35} +(-0.985724 - 5.91848i) q^{36} +(6.40883 + 6.40883i) q^{37} +(-1.13956 + 4.12416i) q^{38} +(-4.01233 + 4.81132i) q^{39} +(-2.27447 - 5.90142i) q^{40} +(2.03343 + 3.52201i) q^{41} +(2.96475 - 6.27990i) q^{42} +(-3.77169 + 1.01062i) q^{43} +(10.8973 - 6.06728i) q^{44} +(-2.04661 - 6.38838i) q^{45} +(4.61231 + 2.71102i) q^{46} +(-4.33973 + 1.16283i) q^{47} +(-6.91608 + 0.409626i) q^{48} +(0.898784 - 0.518913i) q^{49} +(-3.46959 - 6.16133i) q^{50} +(-2.30275 - 6.26744i) q^{51} +(5.03491 + 5.19421i) q^{52} +(-7.68791 + 7.68791i) q^{53} +(-7.34846 + 0.00974690i) q^{54} +(11.0755 - 8.47264i) q^{55} +(-6.84902 - 4.17055i) q^{56} +(4.75604 + 2.20022i) q^{57} +(-3.09512 + 3.04729i) q^{58} +(-0.770452 + 0.444821i) q^{59} +(-7.58510 + 1.57043i) q^{60} +(-4.37174 - 2.52402i) q^{61} +(-0.519799 + 0.134951i) q^{62} +(-6.99666 - 4.83603i) q^{63} +(-0.373605 + 7.99127i) q^{64} +(6.40922 + 4.93300i) q^{65} +(-5.15634 - 14.3790i) q^{66} +(-1.50718 - 0.403848i) q^{67} +(-7.47749 + 1.87929i) q^{68} +(4.19656 - 5.03223i) q^{69} +(-8.25081 - 3.50747i) q^{70} +7.23594i q^{71} +(-0.885522 + 8.43895i) q^{72} +(-11.0030 - 11.0030i) q^{73} +(-6.32221 - 11.1500i) q^{74} +(-8.13772 + 2.96270i) q^{75} +(3.10673 - 5.19257i) q^{76} +(4.57602 - 17.0780i) q^{77} +(7.28153 - 5.04722i) q^{78} +(-4.90963 + 8.50373i) q^{79} +(0.877627 + 8.90111i) q^{80} +(-1.45503 + 8.88160i) q^{81} +(-1.44528 - 5.56687i) q^{82} +(7.55982 - 2.02565i) q^{83} +(-6.40669 + 7.44367i) q^{84} +(-7.96877 + 3.28701i) q^{85} +(5.52197 + 0.0429965i) q^{86} +(3.06444 + 4.34831i) q^{87} +(-17.1397 + 4.16605i) q^{88} -1.52070i q^{89} +(0.383613 + 9.47907i) q^{90} +10.2545 q^{91} +(-5.26609 - 5.43271i) q^{92} +(0.0593146 + 0.655046i) q^{93} +(6.35362 + 0.0494720i) q^{94} +(2.59815 - 6.24642i) q^{95} +(9.58183 + 2.04657i) q^{96} +(0.361190 + 1.34798i) q^{97} +(-1.42061 + 0.368821i) q^{98} +(-18.4044 + 3.36060i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8}+O(q^{10}) $ 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8	$ 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8} - 8 q^{10} - 8 q^{11} - 10 q^{12} - 4 q^{16} - 16 q^{17} + 20 q^{18} + 14 q^{20} + 6 q^{22} - 4 q^{25} - 48 q^{26} - 8 q^{27} + 8 q^{28} - 34 q^{30} - 22 q^{32} + 4 q^{33} - 16 q^{35} - 8 q^{36} - 26 q^{38} - 2 q^{40} - 8 q^{41} - 66 q^{42} - 4 q^{43} - 40 q^{46} - 38 q^{48} - 42 q^{50} - 16 q^{51} + 14 q^{52} + 24 q^{56} + 16 q^{57} + 6 q^{58} + 14 q^{60} - 76 q^{62} - 4 q^{65} - 44 q^{66} - 4 q^{67} - 46 q^{68} + 18 q^{70} + 38 q^{72} - 16 q^{73} - 120 q^{75} - 38 q^{78} + 92 q^{80} - 32 q^{81} - 4 q^{83} - 40 q^{86} - 42 q^{88} - 14 q^{90} - 32 q^{91} + 52 q^{92} + 108 q^{96} - 4 q^{97} - 140 q^{98}+O(q^{100}) $ 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8 - 8 * q^10 - 8 * q^11 - 10 * q^12 - 4 * q^16 - 16 * q^17 + 20 * q^18 + 14 * q^20 + 6 * q^22 - 4 * q^25 - 48 * q^26 - 8 * q^27 + 8 * q^28 - 34 * q^30 - 22 * q^32 + 4 * q^33 - 16 * q^35 - 8 * q^36 - 26 * q^38 - 2 * q^40 - 8 * q^41 - 66 * q^42 - 4 * q^43 - 40 * q^46 - 38 * q^48 - 42 * q^50 - 16 * q^51 + 14 * q^52 + 24 * q^56 + 16 * q^57 + 6 * q^58 + 14 * q^60 - 76 * q^62 - 4 * q^65 - 44 * q^66 - 4 * q^67 - 46 * q^68 + 18 * q^70 + 38 * q^72 - 16 * q^73 - 120 * q^75 - 38 * q^78 + 92 * q^80 - 32 * q^81 - 4 * q^83 - 40 * q^86 - 42 * q^88 - 14 * q^90 - 32 * q^91 + 52 * q^92 + 108 * q^96 - 4 * q^97 - 140 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.36313	−	0.376650i	−0.963881	−	0.266332i
$2$	−1.36313	−	0.376650i	−0.963881	−	0.266332i
$3$	−0.727225	+	1.57199i	−0.419863	+	0.907587i
$3$	−0.727225	+	1.57199i	−0.419863	+	0.907587i
$4$	1.71627	+	1.02685i	0.858134	+	0.513425i
$5$	2.06459	+	0.858752i	0.923314	+	0.384045i
$5$	2.06459	+	0.858752i	0.923314	+	0.384045i
$6$	1.58339	−	1.86892i	0.646418	−	0.762983i
$7$	2.73850	−	0.733779i	1.03506	−	0.277343i	0.298993	−	0.954255i	$-0.403349\pi$
$7$	2.73850	−	0.733779i	1.03506	−	0.277343i	0.736063	+	0.676913i	$0.236683\pi$
$8$	−1.95274	−	2.04617i	−0.690398	−	0.723430i
$9$	−1.94229	−	2.28638i	−0.647430	−	0.762125i
$10$	−2.49087	−	1.94822i	−0.787682	−	0.616082i
$11$	3.11812	−	5.40074i	0.940148	−	1.62838i	0.174962	−	0.984575i	$-0.444020\pi$
$11$	3.11812	−	5.40074i	0.940148	−	1.62838i	0.765186	−	0.643809i	$-0.222647\pi$
$12$	−2.86231	+	1.95120i	−0.826277	+	0.563264i
$13$	3.49373	+	0.936143i	0.968987	+	0.259639i	0.708400	−	0.705811i	$-0.249417\pi$
$13$	3.49373	+	0.936143i	0.968987	+	0.259639i	0.260587	+	0.965450i	$0.416084\pi$
$14$	−4.00932	−	0.0312183i	−1.07154	−	0.00834345i
$15$	−2.85137	+	2.62101i	−0.736221	+	0.676742i
$16$	1.89116	+	3.52470i	0.472789	+	0.881175i
$17$	−2.72591	+	2.72591i	−0.661130	+	0.661130i	−0.955646	−	0.294516i	$-0.904841\pi$
$17$	−2.72591	+	2.72591i	−0.661130	+	0.661130i	0.294516	+	0.955646i	$0.404841\pi$
$18$	1.78644	+	3.84820i	0.421067	+	0.907030i
$19$		−	3.02550i		−	0.694097i	−0.937847	−	0.347048i	$-0.887184\pi$
$19$		−	3.02550i		−	0.694097i	0.937847	−	0.347048i	$-0.112816\pi$
$20$	2.66159	+	3.59388i	0.595149	+	0.803615i
$21$	−0.838014	+	4.83851i	−0.182870	+	1.05585i
$22$	−6.28461	+	6.18749i	−1.33988	+	1.31918i
$23$	−3.65415	−	0.979127i	−0.761943	−	0.204162i	−0.143134	−	0.989703i	$-0.545718\pi$
$23$	−3.65415	−	0.979127i	−0.761943	−	0.204162i	−0.618809	+	0.785541i	$0.712385\pi$
$24$	4.63663	−	1.58166i	0.946448	−	0.322855i
$25$	3.52509	+	3.54595i	0.705018	+	0.709189i
$26$	−4.40983	−	2.59200i	−0.864838	−	0.508334i
$27$	5.00663	−	1.39054i	0.963527	−	0.267610i
$28$	5.45349	+	1.55267i	1.03061	+	0.293427i
$29$	1.53565	−	2.65982i	0.285163	−	0.493917i	−0.687486	−	0.726198i	$-0.741286\pi$
$29$	1.53565	−	2.65982i	0.285163	−	0.493917i	0.972649	+	0.232281i	$0.0746190\pi$
$30$	4.87400	−	2.49882i	0.889867	−	0.456219i
$31$	0.328863	−	0.189869i	0.0590656	−	0.0341015i	−0.470176	−	0.882572i	$-0.655810\pi$
$31$	0.328863	−	0.189869i	0.0590656	−	0.0341015i	0.529242	+	0.848471i	$0.322476\pi$
$32$	−1.25032	−	5.51695i	−0.221028	−	0.975268i
$33$	6.22232	+	8.82919i	1.08317	+	1.53697i
$34$	4.74250	−	2.68907i	0.813331	−	0.461171i
$35$	6.28403	+	0.836738i	1.06219	+	0.141434i
$36$	−0.985724	−	5.91848i	−0.164287	−	0.986413i
$37$	6.40883	+	6.40883i	1.05361	+	1.05361i	0.998479	+	0.0551263i	$0.0175562\pi$
$37$	6.40883	+	6.40883i	1.05361	+	1.05361i	0.0551263	+	0.998479i	$0.482444\pi$
$38$	−1.13956	+	4.12416i	−0.184860	+	0.669027i
$39$	−4.01233	+	4.81132i	−0.642487	+	0.770427i
$40$	−2.27447	−	5.90142i	−0.359625	−	0.933097i
$41$	2.03343	+	3.52201i	0.317569	+	0.550046i	0.979980	−	0.199095i	$-0.0638001\pi$
$41$	2.03343	+	3.52201i	0.317569	+	0.550046i	−0.662411	+	0.749140i	$0.730467\pi$
$42$	2.96475	−	6.27990i	0.457471	−	0.969010i
$43$	−3.77169	+	1.01062i	−0.575178	+	0.154118i	−0.534670	−	0.845061i	$-0.679564\pi$
$43$	−3.77169	+	1.01062i	−0.575178	+	0.154118i	−0.0405075	+	0.999179i	$0.512897\pi$
$44$	10.8973	−	6.06728i	1.64283	−	0.914677i
$45$	−2.04661	−	6.38838i	−0.305090	−	0.952323i
$46$	4.61231	+	2.71102i	0.680048	+	0.399718i
$47$	−4.33973	+	1.16283i	−0.633015	+	0.169616i	−0.561038	−	0.827790i	$-0.689598\pi$
$47$	−4.33973	+	1.16283i	−0.633015	+	0.169616i	−0.0719777	+	0.997406i	$0.522931\pi$
$48$	−6.91608	+	0.409626i	−0.998251	+	0.0591244i
$49$	0.898784	−	0.518913i	0.128398	−	0.0741305i
$50$	−3.46959	−	6.16133i	−0.490674	−	0.871343i
$51$	−2.30275	−	6.26744i	−0.322449	−	0.877618i
$52$	5.03491	+	5.19421i	0.698216	+	0.720308i
$53$	−7.68791	+	7.68791i	−1.05602	+	1.05602i	−0.0576805	+	0.998335i	$0.518370\pi$
$53$	−7.68791	+	7.68791i	−1.05602	+	1.05602i	−0.998335	+	0.0576805i	$0.981630\pi$
$54$	−7.34846	+	0.00974690i	−0.999999	+	0.00132639i
$55$	11.0755	−	8.47264i	1.49343	−	1.14245i
$56$	−6.84902	−	4.17055i	−0.915239	−	0.557314i
$57$	4.75604	+	2.20022i	0.629954	+	0.291426i
$58$	−3.09512	+	3.04729i	−0.406409	+	0.400129i
$59$	−0.770452	+	0.444821i	−0.100304	+	0.0579107i	−0.549313	−	0.835617i	$-0.685111\pi$
$59$	−0.770452	+	0.444821i	−0.100304	+	0.0579107i	0.449009	+	0.893527i	$0.351777\pi$
$60$	−7.58510	+	1.57043i	−0.979232	+	0.202741i
$61$	−4.37174	−	2.52402i	−0.559744	−	0.323168i	0.193299	−	0.981140i	$-0.438081\pi$
$61$	−4.37174	−	2.52402i	−0.559744	−	0.323168i	−0.753043	+	0.657972i	$0.771415\pi$
$62$	−0.519799	+	0.134951i	−0.0660145	+	0.0171388i
$63$	−6.99666	−	4.83603i	−0.881496	−	0.609283i
$64$	−0.373605	+	7.99127i	−0.0467007	+	0.998909i
$65$	6.40922	+	4.93300i	0.794966	+	0.611864i
$66$	−5.15634	−	14.3790i	−0.634702	−	1.76993i
$67$	−1.50718	−	0.403848i	−0.184131	−	0.0493379i	0.165575	−	0.986197i	$-0.447052\pi$
$67$	−1.50718	−	0.403848i	−0.184131	−	0.0493379i	−0.349706	+	0.936859i	$0.613719\pi$
$68$	−7.47749	+	1.87929i	−0.906779	+	0.227898i
$69$	4.19656	−	5.03223i	0.505207	−	0.605810i
$70$	−8.25081	−	3.50747i	−0.986161	−	0.419223i
$71$			7.23594i			0.858748i	0.903127	+	0.429374i	$0.141266\pi$
$71$			7.23594i			0.858748i	−0.903127	+	0.429374i	$0.858734\pi$
$72$	−0.885522	+	8.43895i	−0.104360	+	0.994540i
$73$	−11.0030	−	11.0030i	−1.28780	−	1.28780i	−0.936120	−	0.351681i	$-0.885610\pi$
$73$	−11.0030	−	11.0030i	−1.28780	−	1.28780i	−0.351681	−	0.936120i	$-0.614390\pi$
$74$	−6.32221	−	11.1500i	−0.734942	−	1.29616i
$75$	−8.13772	+	2.96270i	−0.939662	+	0.342103i
$76$	3.10673	−	5.19257i	0.356367	−	0.595628i
$77$	4.57602	−	17.0780i	0.521486	−	1.94621i
$78$	7.28153	−	5.04722i	0.824471	−	0.571485i
$79$	−4.90963	+	8.50373i	−0.552376	+	0.956744i	0.445726	+	0.895169i	$0.352946\pi$
$79$	−4.90963	+	8.50373i	−0.552376	+	0.956744i	−0.998102	+	0.0615746i	$0.980388\pi$
$80$	0.877627	+	8.90111i	0.0981217	+	0.995174i
$81$	−1.45503	+	8.88160i	−0.161670	+	0.986845i
$82$	−1.44528	−	5.56687i	−0.159604	−	0.614758i
$83$	7.55982	−	2.02565i	0.829798	−	0.222344i	0.181172	−	0.983451i	$-0.442011\pi$
$83$	7.55982	−	2.02565i	0.829798	−	0.222344i	0.648625	+	0.761108i	$0.275344\pi$
$84$	−6.40669	+	7.44367i	−0.699027	+	0.812172i
$85$	−7.96877	+	3.28701i	−0.864335	+	0.356527i
$86$	5.52197	+	0.0429965i	0.595450	+	0.00463643i
$87$	3.06444	+	4.34831i	0.328543	+	0.466188i
$88$	−17.1397	+	4.16605i	−1.82710	+	0.444103i
$89$		−	1.52070i		−	0.161194i	−0.996747	−	0.0805970i	$-0.974317\pi$
$89$		−	1.52070i		−	0.161194i	0.996747	−	0.0805970i	$-0.0256827\pi$
$90$	0.383613	+	9.47907i	0.0404363	+	0.999182i
$91$	10.2545			1.07497
$92$	−5.26609	−	5.43271i	−0.549028	−	0.566399i
$93$	0.0593146	+	0.655046i	0.00615064	+	0.0679252i
$94$	6.35362	+	0.0494720i	0.655326	+	0.00510265i
$95$	2.59815	−	6.24642i	0.266565	−	0.640869i
$96$	9.58183	+	2.04657i	0.977942	+	0.208877i
$97$	0.361190	+	1.34798i	0.0366733	+	0.136867i	0.981835	−	0.189735i	$-0.0607630\pi$
$97$	0.361190	+	1.34798i	0.0366733	+	0.136867i	−0.945162	+	0.326602i	$0.894096\pi$
$98$	−1.42061	+	0.368821i	−0.143504	+	0.0372565i
$99$	−18.4044	+	3.36060i	−1.84971	+	0.337753i
$100$	2.40885	+	9.70554i	0.240885	+	0.970554i
$101$	1.57653	+	0.910213i	0.156871	+	0.0905695i	0.576381	−	0.817181i	$-0.304465\pi$
$101$	1.57653	+	0.910213i	0.156871	+	0.0905695i	−0.419510	+	0.907751i	$0.637798\pi$
$102$	0.778317	+	9.41070i	0.0770648	+	0.931798i
$103$	−4.34114	−	1.16320i	−0.427745	−	0.114614i	0.0385226	−	0.999258i	$-0.487735\pi$
$103$	−4.34114	−	1.16320i	−0.427745	−	0.114614i	−0.466267	+	0.884644i	$0.654402\pi$
$104$	−4.90685	−	8.97681i	−0.481156	−	0.880248i
$105$	−5.88524	+	9.26992i	−0.574341	+	0.904651i
$106$	13.3753	−	7.58400i	1.29912	−	0.736623i
$107$	6.14874	−	6.14874i	0.594421	−	0.594421i	−0.344401	−	0.938823i	$-0.611918\pi$
$107$	6.14874	−	6.14874i	0.594421	−	0.594421i	0.938823	+	0.344401i	$0.111918\pi$
$108$	10.0206	+	2.75452i	0.964234	+	0.265053i
$109$	2.31606			0.221839			0.110919	−	0.993829i	$-0.464620\pi$
$109$	2.31606			0.221839			0.110919	+	0.993829i	$0.464620\pi$
$110$	−18.2887	+	7.37774i	−1.74376	+	0.703440i
$111$	−14.7353	+	5.41394i	−1.39861	+	0.513869i
$112$	7.76529	+	8.26471i	0.733751	+	0.780942i
$113$	1.24820	−	4.65836i	0.117421	−	0.438221i	−0.882036	−	0.471183i	$-0.843827\pi$
$113$	1.24820	−	4.65836i	0.117421	−	0.438221i	0.999457	+	0.0329616i	$0.0104939\pi$
$114$	−5.65441	−	4.79056i	−0.529584	−	0.448677i
$115$	−6.70351	−	5.15951i	−0.625105	−	0.481126i
$116$	5.36682	−	2.98809i	0.498297	−	0.277437i
$117$	−4.64546	−	9.80624i	−0.429473	−	0.906588i
$118$	1.21777	−	0.316159i	0.112105	−	0.0291048i
$119$	−5.46469	+	9.46513i	−0.500948	+	0.867667i
$120$	10.9310	+	0.716230i	0.997860	+	0.0653825i
$121$	−13.9453	−	24.1540i	−1.26776	−	2.19582i
$122$	5.00859	+	5.08720i	0.453457	+	0.460574i
$123$	−7.01532	+	0.635239i	−0.632550	+	0.0572776i
$124$	0.759385	+	0.0118265i	0.0681948	+	0.00106205i
$125$	4.23279	+	10.3481i	0.378592	+	0.925564i
$126$	7.71589	+	9.22746i	0.687386	+	0.822047i
$127$	−4.97299	−	4.97299i	−0.441282	−	0.441282i	0.451161	−	0.892443i	$-0.351010\pi$
$127$	−4.97299	−	4.97299i	−0.441282	−	0.441282i	−0.892443	+	0.451161i	$0.851010\pi$
$128$	3.51919	−	10.7525i	0.311055	−	0.950392i
$129$	1.15418	−	6.66400i	0.101620	−	0.586733i
$130$	−6.87861	−	9.13838i	−0.603294	−	0.801489i
$131$	−8.27979	−	14.3410i	−0.723409	−	1.25298i	−0.959626	−	0.281280i	$-0.909241\pi$
$131$	−8.27979	−	14.3410i	−0.723409	−	1.25298i	0.236217	−	0.971700i	$-0.424092\pi$
$132$	1.61292	+	21.5427i	0.140387	+	1.87505i
$133$	−2.22005	−	8.28533i	−0.192503	−	0.718429i
$134$	1.90238	+	1.11818i	0.164341	+	0.0965960i
$135$	11.5308	+	1.42855i	0.992413	+	0.122950i
$136$	10.9007	+	0.254673i	0.934724	+	0.0218380i
$137$	4.28012	+	15.9736i	0.365675	+	1.36472i	0.866503	+	0.499171i	$0.166362\pi$
$137$	4.28012	+	15.9736i	0.365675	+	1.36472i	−0.500828	+	0.865547i	$0.666971\pi$
$138$	−7.61587	+	5.27897i	−0.648306	+	0.449376i
$139$	0.154325	−	0.0890995i	0.0130897	−	0.00755732i	−0.493441	−	0.869779i	$-0.664261\pi$
$139$	0.154325	−	0.0890995i	0.0130897	−	0.00755732i	0.506531	+	0.862222i	$0.330928\pi$
$140$	9.92588	+	7.88882i	0.838890	+	0.666727i
$141$	1.32801	−	7.66765i	0.111839	−	0.645732i
$142$	2.72542	−	9.86356i	0.228712	−	0.827731i
$143$	15.9497	−	15.9497i	1.33378	−	1.33378i
$144$	4.38562	−	11.1699i	0.365468	−	0.930824i
$145$	5.45462	−	4.17271i	0.452981	−	0.346525i
$146$	10.8543	+	19.1428i	0.898305	+	1.58427i
$147$	0.162107	+	1.79024i	0.0133704	+	0.147657i
$148$	4.41837	+	17.5802i	0.363188	+	1.44508i
$149$	10.9591	+	18.9817i	0.897804	+	1.55504i	0.830295	+	0.557324i	$0.188172\pi$
$149$	10.9591	+	18.9817i	0.897804	+	1.55504i	0.0675095	+	0.997719i	$0.478495\pi$
$150$	12.2087	−	0.973481i	0.996836	−	0.0794844i
$151$	10.6039	+	6.12219i	0.862937	+	0.498217i	0.864995	−	0.501781i	$-0.167322\pi$
$151$	10.6039	+	6.12219i	0.862937	+	0.498217i	−0.00205779	+	0.999998i	$0.500655\pi$
$152$	−6.19068	+	5.90801i	−0.502130	+	0.479203i
$153$	11.5270	+	0.937951i	0.931899	+	0.0758289i
$154$	−12.6702	+	21.5560i	−1.02099	+	1.73703i
$155$	0.842019	−	0.109591i	0.0676326	−	0.00880256i
$156$	−11.8267	+	4.13745i	−0.946897	+	0.331261i
$157$	3.36840	−	12.5710i	0.268827	−	1.00328i	−0.691038	−	0.722818i	$-0.742846\pi$
$157$	3.36840	−	12.5710i	0.268827	−	1.00328i	0.959866	−	0.280460i	$-0.0904869\pi$
$158$	9.89542	−	9.74251i	0.787237	−	0.775072i
$159$	−6.49446	−	17.6761i	−0.515044	−	1.40181i
$160$	2.15628	−	12.4640i	0.170469	−	0.985363i
$161$	−10.7254			−0.845277
$162$	5.32866	−	11.5588i	0.418659	−	0.908143i
$163$	−14.0489	−	14.0489i	−1.10039	−	1.10039i	−0.994363	−	0.106029i	$-0.966186\pi$
$163$	−14.0489	−	14.0489i	−1.10039	−	1.10039i	−0.106029	−	0.994363i	$-0.533814\pi$
$164$	−0.126658	+	8.13275i	−0.00989032	+	0.635061i
$165$	5.26448	+	23.5721i	0.409839	+	1.83509i
$166$	−11.0680	−	0.0861803i	−0.859044	−	0.00668889i
$167$	2.61588	−	9.76261i	0.202423	−	0.755453i	−0.787797	−	0.615936i	$-0.788778\pi$
$167$	2.61588	−	9.76261i	0.202423	−	0.755453i	0.990220	−	0.139518i	$-0.0445552\pi$
$168$	11.5368	−	7.73365i	0.890086	−	0.596664i
$169$	0.0714698	+	0.0412631i	0.00549768	+	0.00317409i
$170$	12.1006	−	1.47920i	0.928071	−	0.113449i
$171$	−6.91743	+	5.87639i	−0.528989	+	0.449379i
$172$	−7.51099	−	2.13846i	−0.572708	−	0.163056i
$173$	2.88168	+	10.7546i	0.219090	+	0.817655i	0.984687	+	0.174334i	$0.0557773\pi$
$173$	2.88168	+	10.7546i	0.219090	+	0.817655i	−0.765597	+	0.643321i	$0.777556\pi$
$174$	−2.53946	−	7.08155i	−0.192516	−	0.536851i
$175$	12.2554	+	7.12394i	0.926422	+	0.538519i
$176$	24.9329	+	0.776788i	1.87938	+	0.0585526i
$177$	−0.138961	−	1.53463i	−0.0104449	−	0.115349i
$178$	−0.572773	+	2.07292i	−0.0429311	+	0.155372i
$179$			23.1890i			1.73322i	0.498982	+	0.866612i	$0.333707\pi$
$179$			23.1890i			1.73322i	−0.498982	+	0.866612i	$0.666293\pi$
$180$	3.04738	−	13.0657i	0.227138	−	0.973862i
$181$		−	21.2209i		−	1.57734i	−0.614819	−	0.788668i	$-0.710771\pi$
$181$		−	21.2209i		−	1.57734i	0.614819	−	0.788668i	$-0.289229\pi$
$182$	−13.9783	−	3.86237i	−1.03614	−	0.286298i
$183$	7.14697	−	5.03679i	0.528319	−	0.372330i
$184$	5.13215	+	9.38899i	0.378347	+	0.692165i
$185$	7.72804	+	18.7352i	0.568177	+	1.37744i
$186$	0.165870	−	0.915257i	0.0121622	−	0.0671099i
$187$	6.22222	+	23.2216i	0.455014	+	1.69813i
$188$	−8.64220	−	2.46053i	−0.630297	−	0.179453i
$189$	12.6903	−	7.48177i	0.923085	−	0.544219i
$190$	−5.89435	+	7.53612i	−0.427621	+	0.546727i
$191$	−21.4998	−	12.4129i	−1.55567	−	0.898168i	−0.997662	−	0.0683347i	$-0.978231\pi$
$191$	−21.4998	−	12.4129i	−1.55567	−	0.898168i	−0.558011	−	0.829834i	$-0.688435\pi$
$192$	−12.2905	−	6.39875i	−0.886989	−	0.461790i
$193$	0.316329	−	1.18056i	0.0227699	−	0.0849783i	−0.953606	−	0.301058i	$-0.902660\pi$
$193$	0.316329	−	1.18056i	0.0227699	−	0.0849783i	0.976376	+	0.216079i	$0.0693270\pi$
$194$	0.0153667	−	1.97352i	0.00110326	−	0.141690i
$195$	−12.4156	+	6.48781i	−0.889097	+	0.464602i
$196$	2.07540	+	0.0323219i	0.148243	+	0.00230871i
$197$	−0.197150	−	0.197150i	−0.0140464	−	0.0140464i	0.700049	−	0.714095i	$-0.253162\pi$
$197$	−0.197150	−	0.197150i	−0.0140464	−	0.0140464i	−0.714095	+	0.700049i	$0.753162\pi$
$198$	26.3534	+	2.35108i	1.87286	+	0.167084i
$199$	−3.23091			−0.229033			−0.114517	−	0.993421i	$-0.536532\pi$
$199$	−3.23091			−0.229033			−0.114517	+	0.993421i	$0.536532\pi$
$200$	0.372012	−	14.1372i	0.0263052	−	0.999654i
$201$	1.73090	−	2.07558i	0.122088	−	0.146400i
$202$	−1.80620	−	1.83454i	−0.127084	−	0.129078i
$203$	2.25366	−	8.41076i	0.158176	−	0.590319i
$204$	2.48359	−	13.1212i	0.173886	−	0.918667i
$205$	1.17368	+	9.01774i	0.0819734	+	0.629826i
$206$	5.47943	+	3.22069i	0.381770	+	0.224396i
$207$	4.85876	+	10.2565i	0.337707	+	0.712877i
$208$	3.30757	+	14.0848i	0.229339	+	0.976602i
$209$	−16.3399	−	9.43386i	−1.13026	−	0.652554i
$210$	11.5139	−	10.4195i	0.794534	−	0.719011i
$211$	11.1101	+	19.2432i	0.764850	+	1.32476i	0.940326	+	0.340275i	$0.110520\pi$
$211$	11.1101	+	19.2432i	0.764850	+	1.32476i	−0.175476	+	0.984484i	$0.556147\pi$
$212$	−21.0889	+	5.30019i	−1.44839	+	0.364018i
$213$	−11.3748	−	5.26215i	−0.779389	−	0.360557i
$214$	−10.6975	+	6.06563i	−0.731265	+	0.414638i
$215$	−8.65488	−	1.15242i	−0.590258	−	0.0785947i
$216$	−12.6219	−	7.52904i	−0.858815	−	0.512286i
$217$	0.761270	−	0.761270i	0.0516784	−	0.0516784i
$218$	−3.15711	−	0.872347i	−0.213826	−	0.0590828i
$219$	25.2982	−	9.29491i	1.70949	−	0.628092i
$220$	27.7087	−	3.16841i	1.86812	−	0.213614i
$221$	−12.0754	+	6.97176i	−0.812282	+	0.468971i
$222$	22.1253	−	1.82989i	1.48495	−	0.122814i
$223$	−1.32068	−	4.92885i	−0.0884394	−	0.330060i	0.907504	−	0.420044i	$-0.137985\pi$
$223$	−1.32068	−	4.92885i	−0.0884394	−	0.330060i	−0.995943	+	0.0899834i	$0.971319\pi$
$224$	−7.47223	−	14.1907i	−0.499259	−	0.948157i
$225$	1.26062	−	14.9469i	0.0840415	−	0.996462i
$226$	−3.45604	+	5.87983i	−0.229892	+	0.391120i
$227$	−2.58485	−	9.64678i	−0.171562	−	0.640279i	−0.997112	−	0.0759495i	$-0.975801\pi$
$227$	−2.58485	−	9.64678i	−0.171562	−	0.640279i	0.825549	−	0.564330i	$-0.190865\pi$
$228$	5.90336	+	8.65991i	0.390959	+	0.573516i
$229$	−1.07834	−	1.86775i	−0.0712590	−	0.123424i	0.828194	−	0.560441i	$-0.189368\pi$
$229$	−1.07834	−	1.86775i	−0.0712590	−	0.123424i	−0.899453	+	0.437017i	$0.856035\pi$
$230$	7.19445	+	9.55798i	0.474388	+	0.630234i
$231$	23.5185	+	19.6130i	1.54741	+	1.29044i
$232$	−8.44117	+	2.05175i	−0.554190	+	0.134704i
$233$	−7.23514	−	7.23514i	−0.473990	−	0.473990i	0.429214	−	0.903203i	$-0.358791\pi$
$233$	−7.23514	−	7.23514i	−0.473990	−	0.473990i	−0.903203	+	0.429214i	$0.858791\pi$
$234$	2.63886	+	15.1169i	0.172508	+	0.988225i
$235$	−9.95837	−	1.32599i	−0.649612	−	0.0864979i
$236$	−1.77907	−	0.0277068i	−0.115807	−	0.00180356i
$237$	−9.79735	−	13.9020i	−0.636406	−	0.903032i
$238$	11.0142	−	10.8440i	0.713941	−	0.702909i
$239$	4.89795	+	8.48350i	0.316822	+	0.548752i	0.979823	−	0.199866i	$-0.0640508\pi$
$239$	4.89795	+	8.48350i	0.316822	+	0.548752i	−0.663001	+	0.748619i	$0.730717\pi$
$240$	−14.6307	−	5.09349i	−0.944405	−	0.328783i
$241$	1.96422	−	3.40213i	0.126527	−	0.219151i	−0.795802	−	0.605557i	$-0.792950\pi$
$241$	1.96422	−	3.40213i	0.126527	−	0.219151i	0.922329	+	0.386406i	$0.126284\pi$
$242$	9.91173	+	38.1777i	0.637150	+	2.45415i
$243$	−12.9036	−	8.74621i	−0.827769	−	0.561070i
$244$	−4.91128	−	8.82103i	−0.314413	−	0.564708i
$245$	2.30124	−	0.299512i	0.147021	−	0.0191351i
$246$	9.80209	+	1.77641i	0.624958	+	0.113260i
$247$	2.83230	−	10.5703i	0.180215	−	0.672571i
$248$	−1.03069	−	0.302144i	−0.0654488	−	0.0191862i
$249$	−2.31339	+	13.3570i	−0.146605	+	0.846468i
$250$	−1.87224	−	15.7002i	−0.118411	−	0.992965i
$251$	16.3537			1.03223			0.516117	−	0.856518i	$-0.327377\pi$
$251$	16.3537			1.03223			0.516117	+	0.856518i	$0.327377\pi$
$252$	−7.04226	−	15.4845i	−0.443621	−	0.975429i
$253$	−16.6821	+	16.6821i	−1.04879	+	1.04879i
$254$	4.90577	+	8.65193i	0.307816	+	0.542871i
$255$	0.627943	−	14.9172i	0.0393233	−	0.934152i
$256$	−8.84705	+	13.3315i	−0.552940	+	0.833221i
$257$	−15.9841	−	4.28293i	−0.997062	−	0.267162i	−0.276848	−	0.960914i	$-0.589290\pi$
$257$	−15.9841	−	4.28293i	−0.997062	−	0.267162i	−0.720214	+	0.693752i	$0.755956\pi$
$258$	−4.08330	+	8.64920i	−0.254215	+	0.538476i
$259$	22.2533	+	12.8479i	1.38275	+	0.798332i
$260$	5.93449	+	15.0477i	0.368042	+	0.933217i
$261$	−9.06403	+	1.65507i	−0.561049	+	0.102446i
$262$	5.88491	+	22.6673i	0.363571	+	1.40039i
$263$	4.44188	+	16.5773i	0.273898	+	1.02220i	0.956576	+	0.291483i	$0.0941486\pi$
$263$	4.44188	+	16.5773i	0.273898	+	1.02220i	−0.682678	+	0.730720i	$0.739185\pi$
$264$	5.91543	−	29.9730i	0.364070	−	1.84471i
$265$	−22.4744	+	9.27040i	−1.38059	+	0.569476i
$266$	−0.0944510	+	12.1302i	−0.00579116	+	0.743750i
$267$	2.39052	+	1.10589i	0.146298	+	0.0676794i
$268$	−2.17204	−	2.24076i	−0.132678	−	0.136876i
$269$	9.29592			0.566782			0.283391	−	0.959004i	$-0.408541\pi$
$269$	9.29592			0.566782			0.283391	+	0.959004i	$0.408541\pi$
$270$	−15.1800	−	6.29038i	−0.923823	−	0.382820i
$271$			2.99104i			0.181693i	0.995865	+	0.0908464i	$0.0289572\pi$
$271$			2.99104i			0.181693i	−0.995865	+	0.0908464i	$0.971043\pi$
$272$	−14.7631	−	4.45289i	−0.895147	−	0.269996i
$273$	−7.45734	+	16.1200i	−0.451339	+	0.975625i
$274$	0.182096	−	23.3863i	0.0110008	−	1.41282i
$275$	30.1424	−	7.98142i	1.81765	−	0.481298i
$276$	12.3698	−	4.32742i	0.744573	−	0.260480i
$277$	−13.0249	+	3.49000i	−0.782588	+	0.209694i	−0.627925	−	0.778274i	$-0.716096\pi$
$277$	−13.0249	+	3.49000i	−0.782588	+	0.209694i	−0.154663	+	0.987967i	$0.549429\pi$
$278$	−0.243925	+	0.0633280i	−0.0146296	+	0.00379816i
$279$	−1.07286	−	0.383124i	−0.0642304	−	0.0229370i
$280$	−10.5590	−	14.4921i	−0.631019	−	0.866069i
$281$	5.17075	−	8.95600i	0.308461	−	0.534270i	−0.669565	−	0.742754i	$-0.733519\pi$
$281$	5.17075	−	8.95600i	0.308461	−	0.534270i	0.978026	+	0.208483i	$0.0668527\pi$
$282$	−4.69828	+	9.95183i	−0.279778	+	0.592623i
$283$	−6.73976	+	25.1531i	−0.400637	+	1.49520i	0.411326	+	0.911488i	$0.365066\pi$
$283$	−6.73976	+	25.1531i	−0.400637	+	1.49520i	−0.811963	+	0.583709i	$0.801601\pi$
$284$	−7.43023	+	12.4188i	−0.440903	+	0.736921i
$285$	7.92986	+	8.62681i	0.469724	+	0.511008i
$286$	−27.7491	+	15.7342i	−1.64084	+	0.930380i
$287$	8.15294	+	8.15294i	0.481253	+	0.481253i
$288$	−10.1853	+	13.5742i	−0.600176	+	0.799868i
$289$			2.13883i			0.125814i
$290$	−9.00703	+	3.63348i	−0.528911	+	0.213365i
$291$	−2.38167	−	0.412498i	−0.139616	−	0.0241811i
$292$	−7.58566	−	30.1825i	−0.443917	−	1.76630i
$293$	18.8164	+	5.04183i	1.09926	+	0.294547i	0.762465	−	0.647029i	$-0.223989\pi$
$293$	18.8164	+	5.04183i	1.09926	+	0.294547i	0.336800	+	0.941576i	$0.390656\pi$
$294$	0.453322	−	2.50140i	0.0264383	−	0.145885i
$295$	−1.97266	+	0.256747i	−0.114853	+	0.0149484i
$296$	0.598757	−	25.6283i	0.0348020	−	1.48962i
$297$	8.10131	−	31.3754i	0.470086	−	1.82059i
$298$	−7.78925	−	30.0024i	−0.451219	−	1.73799i
$299$	−11.8500	−	6.84161i	−0.685304	−	0.395661i
$300$	−17.0088	−	3.27143i	−0.982001	−	0.188876i
$301$	−9.58721	+	5.53518i	−0.552598	+	0.319042i
$302$	−12.1487	−	12.3393i	−0.699078	−	0.710050i
$303$	−2.57734	+	1.81636i	−0.148064	+	0.104347i
$304$	10.6640	−	5.72169i	0.611621	−	0.328162i
$305$	−6.85835	−	8.96532i	−0.392708	−	0.513353i
$306$	−15.3595	−	5.62019i	−0.878045	−	0.321285i
$307$	11.3101	−	11.3101i	0.645503	−	0.645503i	−0.306400	−	0.951903i	$-0.599125\pi$
$307$	11.3101	−	11.3101i	0.645503	−	0.645503i	0.951903	+	0.306400i	$0.0991245\pi$
$308$	25.3902	−	24.6115i	1.44674	−	1.40237i
$309$	4.98552	−	5.97830i	0.283616	−	0.340094i
$310$	−1.18906	−	0.167760i	−0.0675342	−	0.00952812i
$311$	−16.8226	+	9.71252i	−0.953921	+	0.550746i	−0.894297	−	0.447474i	$-0.852324\pi$
$311$	−16.8226	+	9.71252i	−0.953921	+	0.550746i	−0.0596242	+	0.998221i	$0.518990\pi$
$312$	17.6798	−	1.18535i	1.00092	−	0.0671072i
$313$	8.75151	−	2.34496i	0.494664	−	0.132545i	−0.00285821	−	0.999996i	$-0.500910\pi$
$313$	8.75151	−	2.34496i	0.494664	−	0.132545i	0.497523	+	0.867451i	$0.334243\pi$
$314$	−9.32646	+	15.8673i	−0.526323	+	0.895443i
$315$	−10.2923	−	15.9928i	−0.579905	−	0.901094i
$316$	−17.1583	+	9.55323i	−0.965230	+	0.537411i
$317$	−29.1013	+	7.79767i	−1.63449	+	0.437961i	−0.955213	−	0.295920i	$-0.904374\pi$
$317$	−29.1013	+	7.79767i	−1.63449	+	0.437961i	−0.679279	+	0.733880i	$0.737707\pi$
$318$	2.19509	+	26.5411i	0.123095	+	1.48835i
$319$	−9.57667	−	16.5873i	−0.536191	−	0.928709i
$320$	−7.63386	+	16.1779i	−0.426746	+	0.904372i
$321$	5.19423	+	14.1373i	0.289914	+	0.789065i
$322$	14.6201	+	4.03971i	0.814747	+	0.225124i
$323$	8.24723	+	8.24723i	0.458888	+	0.458888i
$324$	−11.6173	+	13.7491i	−0.645406	+	0.763840i
$325$	8.99621	+	15.6886i	0.499020	+	0.870245i
$326$	13.8590	+	24.4420i	0.767578	+	1.35372i
$327$	−1.68430	+	3.64082i	−0.0931419	+	0.201338i
$328$	3.23586	−	11.0383i	0.178670	−	0.609489i
$329$	−11.0311	+	6.36882i	−0.608165	+	0.351124i
$330$	1.70226	−	34.1148i	0.0937065	−	1.87796i
$331$	1.06195	−	1.83934i	0.0583698	−	0.101099i	−0.835364	−	0.549697i	$-0.814743\pi$
$331$	1.06195	−	1.83934i	0.0583698	−	0.101099i	0.893734	+	0.448598i	$0.148076\pi$
$332$	15.0547	+	4.28624i	0.826235	+	0.235238i
$333$	2.20520	−	27.1008i	0.120844	−	1.48512i
$334$	−7.24289	+	12.3225i	−0.396313	+	0.674255i
$335$	−2.76491	−	2.12808i	−0.151063	−	0.116269i
$336$	−18.6391	+	6.19664i	−1.01685	+	0.338054i
$337$	−6.26468	−	1.67861i	−0.341259	−	0.0914400i	0.0841195	−	0.996456i	$-0.473192\pi$
$337$	−6.26468	−	1.67861i	−0.341259	−	0.0914400i	−0.425378	+	0.905016i	$0.639859\pi$
$338$	−0.0818812	−	0.0831663i	−0.00445375	−	0.00452365i
$339$	6.41515	+	5.34983i	0.348423	+	0.290563i
$340$	−17.0518	−	2.54134i	−0.924765	−	0.137823i
$341$		−	2.36814i		−	0.128242i
$342$	11.6427	−	5.40486i	0.629566	−	0.292261i
$343$	−11.9525	+	11.9525i	−0.645375	+	0.645375i
$344$	9.43304	+	5.74403i	0.508595	+	0.309697i
$345$	12.9856	−	6.78571i	0.699123	−	0.365330i
$346$	0.122600	−	15.7453i	0.00659101	−	0.846473i
$347$	−13.0253	−	3.49013i	−0.699236	−	0.187360i	−0.108348	−	0.994113i	$-0.534556\pi$
$347$	−13.0253	−	3.49013i	−0.699236	−	0.187360i	−0.590888	+	0.806753i	$0.701223\pi$
$348$	0.794350	+	10.6096i	0.0425816	+	0.568734i
$349$	−7.02132	+	12.1613i	−0.375843	+	0.650979i	−0.990453	−	0.137852i	$-0.955980\pi$
$349$	−7.02132	+	12.1613i	−0.375843	+	0.650979i	0.614610	+	0.788831i	$0.289313\pi$
$350$	−14.0225	−	14.3269i	−0.749536	−	0.765805i
$351$	18.7936	−	0.171264i	1.00313	−	0.00914142i
$352$	−33.6942	−	10.4498i	−1.79591	−	0.556978i
$353$	15.4571	−	4.14172i	0.822700	−	0.220442i	0.177173	−	0.984180i	$-0.443305\pi$
$353$	15.4571	−	4.14172i	0.822700	−	0.220442i	0.645526	+	0.763738i	$0.276638\pi$
$354$	−0.388595	+	2.14424i	−0.0206536	+	0.113965i
$355$	−6.21388	+	14.9393i	−0.329798	+	0.792894i
$356$	1.56153	−	2.60993i	0.0827610	−	0.138326i
$357$	−10.9050	−	15.4737i	−0.577154	−	0.818955i
$358$	8.73413	−	31.6097i	0.461613	−	1.67062i
$359$	−5.37051			−0.283445			−0.141722	−	0.989906i	$-0.545264\pi$
$359$	−5.37051			−0.283445			−0.141722	+	0.989906i	$0.545264\pi$
$360$	−9.07521	+	16.6626i	−0.478305	+	0.878194i
$361$	9.84636			0.518230
$362$	−7.99286	+	28.9269i	−0.420095	+	1.52036i
$363$	48.1112	−	4.35648i	2.52518	−	0.228656i
$364$	17.5995	+	10.5298i	0.922465	+	0.551914i
$365$	−13.2678	−	32.1655i	−0.694471	−	1.68362i
$366$	−11.6394	+	4.17390i	−0.608401	+	0.218173i
$367$	8.37787	−	2.24484i	0.437321	−	0.117180i	−0.0334396	−	0.999441i	$-0.510646\pi$
$367$	8.37787	−	2.24484i	0.437321	−	0.117180i	0.470761	+	0.882261i	$0.343979\pi$
$368$	−3.45945	−	14.7315i	−0.180336	−	0.767931i
$369$	4.10313	−	11.4900i	0.213600	−	0.598143i
$370$	−3.47772	−	28.4494i	−0.180798	−	1.47901i
$371$	−15.4121	+	26.6946i	−0.800158	+	1.38591i
$372$	−0.570835	+	1.18514i	−0.0295964	+	0.0614468i
$373$	−19.9114	−	5.33524i	−1.03097	−	0.276248i	−0.296605	−	0.955000i	$-0.595855\pi$
$373$	−19.9114	−	5.33524i	−1.03097	−	0.276248i	−0.734368	+	0.678752i	$0.762521\pi$
$374$	0.264722	−	33.9978i	0.0136884	−	1.75798i
$375$	−19.3453	−	0.871511i	−0.998987	−	0.0450046i
$376$	10.8537	+	6.60912i	0.559738	+	0.340839i
$377$	7.85512	−	7.85512i	0.404559	−	0.404559i
$378$	−20.1166	+	5.41884i	−1.03469	+	0.278715i
$379$			11.3848i			0.584798i	0.956296	+	0.292399i	$0.0944536\pi$
$379$			11.3848i			0.584798i	−0.956296	+	0.292399i	$0.905546\pi$
$380$	10.8733	−	8.05263i	0.557787	−	0.413091i
$381$	11.4340	−	4.20100i	0.585780	−	0.215224i
$382$	24.6318	+	25.0184i	1.26027	+	1.28005i
$383$	−30.3767	−	8.13942i	−1.55218	−	0.415905i	−0.622001	−	0.783017i	$-0.713680\pi$
$383$	−30.3767	−	8.13942i	−1.55218	−	0.415905i	−0.930177	+	0.367112i	$0.880347\pi$
$384$	14.3435	+	13.3516i	0.731963	+	0.681345i
$385$	24.1133	−	31.3294i	1.22893	−	1.59669i
$386$	−0.875856	+	1.49011i	−0.0445799	+	0.0758447i
$387$	9.63638	+	6.66059i	0.489845	+	0.338577i
$388$	−0.764274	+	2.68438i	−0.0388001	+	0.136279i
$389$	13.7505	−	23.8166i	0.697178	−	1.20755i	−0.272263	−	0.962223i	$-0.587772\pi$
$389$	13.7505	−	23.8166i	0.697178	−	1.20755i	0.969441	−	0.245325i	$-0.0788945\pi$
$390$	19.3677	−	4.16743i	0.980722	−	0.211026i
$391$	12.6299	−	7.29187i	0.638721	−	0.368766i
$392$	−2.81688	−	0.825760i	−0.142274	−	0.0417072i
$393$	28.5652	−	2.58658i	1.44092	−	0.130476i
$394$	0.194485	+	0.342999i	0.00979804	+	0.0172800i
$395$	−17.4390	+	13.3406i	−0.877450	+	0.671238i
$396$	−35.0378	−	13.1309i	−1.76071	−	0.659851i
$397$	10.8035	+	10.8035i	0.542214	+	0.542214i	0.924177	−	0.381964i	$-0.124752\pi$
$397$	10.8035	+	10.8035i	0.542214	+	0.542214i	−0.381964	+	0.924177i	$0.624752\pi$
$398$	4.40417	+	1.21692i	0.220761	+	0.0609989i
$399$	14.6389	+	2.53541i	0.732862	+	0.126929i
$400$	−5.83190	+	19.1308i	−0.291595	+	0.956542i
$401$	4.31629	+	7.47604i	0.215545	+	0.373335i	0.953441	−	0.301579i	$-0.0975138\pi$
$401$	4.31629	+	7.47604i	0.215545	+	0.373335i	−0.737896	+	0.674915i	$0.764180\pi$
$402$	−3.14122	+	2.17735i	−0.156670	+	0.108596i
$403$	1.32670	−	0.355489i	0.0660879	−	0.0177082i
$404$	1.77111	+	3.18103i	0.0881158	+	0.158262i
$405$	−10.6311	+	17.0874i	−0.528266	+	0.849079i
$406$	−6.23995	+	10.6161i	−0.309683	+	0.526871i
$407$	54.5959	−	14.6289i	2.70622	−	0.725130i
$408$	−8.32757	+	16.9505i	−0.412276	+	0.839175i
$409$	15.0891	−	8.71172i	0.746110	−	0.430767i	−0.0781764	−	0.996940i	$-0.524910\pi$
$409$	15.0891	−	8.71172i	0.746110	−	0.430767i	0.824287	+	0.566173i	$0.191576\pi$
$410$	1.79665	−	12.7345i	0.0887302	−	0.628910i
$411$	−28.2229	−	4.88812i	−1.39213	−	0.241113i
$412$	−6.25612	−	6.45407i	−0.308217	−	0.317969i
$413$	−1.78348	+	1.78348i	−0.0877595	+	0.0877595i
$414$	−2.76003	−	15.8111i	−0.135648	−	0.777071i
$415$	17.3475	+	2.30987i	0.851554	+	0.113387i
$416$	0.796363	−	20.4452i	0.0390449	−	1.00241i
$417$	0.0278344	+	0.307392i	0.00136306	+	0.0150530i
$418$	18.7202	+	19.0141i	0.915637	+	0.930008i
$419$	−7.08459	+	4.09029i	−0.346105	+	0.199824i	−0.662968	−	0.748647i	$-0.730704\pi$
$419$	−7.08459	+	4.09029i	−0.346105	+	0.199824i	0.316864	+	0.948471i	$0.397370\pi$
$420$	−19.6195	+	9.86641i	−0.957332	+	0.481431i
$421$	−3.46391	−	1.99989i	−0.168821	−	0.0974686i	0.413209	−	0.910636i	$-0.364408\pi$
$421$	−3.46391	−	1.99989i	−0.168821	−	0.0974686i	−0.582030	+	0.813168i	$0.697741\pi$
$422$	−7.89656	−	30.4157i	−0.384399	−	1.48061i
$423$	11.0877	+	7.66372i	0.539101	+	0.372623i
$424$	30.7432	+	0.718257i	1.49302	+	0.0348816i
$425$	−19.2750	−	0.0568504i	−0.934975	−	0.00275765i
$426$	13.5234	+	11.4573i	0.655211	+	0.555110i
$427$	−13.8241	−	3.70415i	−0.668995	−	0.179257i
$428$	16.8667	−	4.23906i	0.815284	−	0.204903i
$429$	13.4737	+	36.6718i	0.650518	+	1.77053i
$430$	11.3637	+	4.83077i	0.548007	+	0.232961i
$431$		−	0.429434i		−	0.0206851i	−0.999947	−	0.0103426i	$-0.996708\pi$
$431$		−	0.429434i		−	0.0206851i	0.999947	−	0.0103426i	$-0.00329220\pi$
$432$	14.3696	+	15.0172i	0.691357	+	0.722513i
$433$	−4.82086	−	4.82086i	−0.231676	−	0.231676i	0.581716	−	0.813392i	$-0.302381\pi$
$433$	−4.82086	−	4.82086i	−0.231676	−	0.231676i	−0.813392	+	0.581716i	$0.802381\pi$
$434$	−1.32445	+	0.750981i	−0.0635755	+	0.0360482i
$435$	2.59271	+	11.6091i	0.124311	+	0.556613i
$436$	3.97499	+	2.37825i	0.190367	+	0.113898i
$437$	−2.96235	+	11.0556i	−0.141708	+	0.528862i
$438$	−37.9857	+	3.14163i	−1.81503	+	0.150113i
$439$	−0.728026	+	1.26098i	−0.0347468	+	0.0601832i	−0.882876	−	0.469606i	$-0.844396\pi$
$439$	−0.728026	+	1.26098i	−0.0347468	+	0.0601832i	0.848129	+	0.529790i	$0.177729\pi$
$440$	−38.9641	−	6.11754i	−1.85754	−	0.291642i
$441$	−2.93213	−	1.04708i	−0.139625	−	0.0498609i
$442$	19.0864	−	4.95522i	0.907845	−	0.235696i
$443$	−18.6199	+	4.98920i	−0.884660	+	0.237044i	−0.672417	−	0.740173i	$-0.734744\pi$
$443$	−18.6199	+	4.98920i	−0.884660	+	0.237044i	−0.212243	+	0.977217i	$0.568077\pi$
$444$	−30.8490	−	5.83913i	−1.46403	−	0.277113i
$445$	1.30590	−	3.13963i	0.0619058	−	0.148833i
$446$	−0.0561878	+	7.21612i	−0.00266057	+	0.341693i
$447$	−37.8087	+	3.42359i	−1.78829	+	0.161930i
$448$	4.84071	+	22.1583i	0.228702	+	1.04688i
$449$		−	23.8578i		−	1.12592i	−0.826485	−	0.562959i	$-0.809663\pi$
$449$		−	23.8578i		−	1.12592i	0.826485	−	0.562959i	$-0.190337\pi$
$450$	−7.34817	+	19.8999i	−0.346396	+	0.938088i
$451$	25.3620			1.19425
$452$	6.92568	−	6.71327i	0.325757	−	0.315766i
$453$	−17.3355	+	12.2171i	−0.814491	+	0.574008i
$454$	−0.109971	+	14.1234i	−0.00516121	+	0.662846i
$455$	21.1714	+	8.80608i	0.992531	+	0.412836i
$456$	−4.78531	−	14.0281i	−0.224093	−	0.656927i
$457$	4.20125	+	15.6793i	0.196526	+	0.733445i	0.991867	+	0.127282i	$0.0406254\pi$
$457$	4.20125	+	15.6793i	0.196526	+	0.733445i	−0.795340	+	0.606163i	$0.792708\pi$
$458$	0.766440	+	2.95215i	0.0358134	+	0.137945i
$459$	−9.85713	+	17.4381i	−0.460092	+	0.813942i
$460$	−6.20698	−	15.7386i	−0.289402	−	0.733816i
$461$	4.54416	+	2.62357i	0.211643	+	0.122192i	0.602075	−	0.798440i	$-0.294341\pi$
$461$	4.54416	+	2.62357i	0.211643	+	0.122192i	−0.390432	+	0.920632i	$0.627674\pi$
$462$	−24.6717	−	35.5934i	−1.14783	−	1.65595i
$463$	−13.1142	−	3.51393i	−0.609467	−	0.163306i	−0.0591323	−	0.998250i	$-0.518833\pi$
$463$	−13.1142	−	3.51393i	−0.609467	−	0.163306i	−0.550335	+	0.834944i	$0.685500\pi$
$464$	12.2792	+	0.382562i	0.570049	+	0.0177600i
$465$	−0.440062	+	1.40334i	−0.0204074	+	0.0650784i
$466$	7.13734	+	12.5876i	0.330631	+	0.583108i
$467$	17.8082	−	17.8082i	0.824065	−	0.824065i	−0.162623	−	0.986688i	$-0.551995\pi$
$467$	17.8082	−	17.8082i	0.824065	−	0.824065i	0.986688	+	0.162623i	$0.0519955\pi$
$468$	2.09668	−	21.6003i	0.0969191	−	0.998476i
$469$	−4.42375			−0.204270
$470$	13.0752	+	5.55832i	0.603112	+	0.256386i
$471$	17.3119	+	14.4370i	0.797691	+	0.665224i
$472$	2.41467	+	0.707854i	0.111144	+	0.0325816i
$473$	−6.30248	+	23.5212i	−0.289788	+	1.08150i
$474$	8.11891	+	22.6405i	0.372914	+	1.03991i
$475$	10.7283	−	10.6652i	0.492246	−	0.489351i
$476$	−19.0981	+	10.6333i	−0.875362	+	0.487376i
$477$	32.5096	+	2.64531i	1.48851	+	0.121121i
$478$	−3.48125	−	13.4090i	−0.159229	−	0.613312i
$479$	−3.54423	+	6.13879i	−0.161940	+	0.280488i	−0.935564	−	0.353156i	$-0.885108\pi$
$479$	−3.54423	+	6.13879i	−0.161940	+	0.280488i	0.773624	+	0.633644i	$0.218442\pi$
$480$	18.0251	+	12.4538i	0.822729	+	0.568433i
$481$	16.3912	+	28.3903i	0.747373	+	1.29449i
$482$	−3.95891	+	3.89774i	−0.180323	+	0.177537i
$483$	7.79975	−	16.8601i	0.354901	−	0.767163i
$484$	0.868622	−	55.7746i	0.0394828	−	2.53521i
$485$	−0.411869	+	3.09320i	−0.0187020	+	0.140455i
$486$	14.2951	+	16.7824i	0.648440	+	0.761266i
$487$	17.7665	+	17.7665i	0.805075	+	0.805075i	0.983884	−	0.178809i	$-0.0572243\pi$
$487$	17.7665	+	17.7665i	0.805075	+	0.805075i	−0.178809	+	0.983884i	$0.557224\pi$
$488$	3.37230	+	13.8741i	0.152657	+	0.628050i
$489$	32.3013	−	11.8680i	1.46072	−	0.536688i
$490$	−3.24971	−	0.458488i	−0.146807	−	0.0207124i
$491$	12.0897	+	20.9400i	0.545600	+	0.945008i	0.998569	+	0.0534811i	$0.0170317\pi$
$491$	12.0897	+	20.9400i	0.545600	+	0.945008i	−0.452968	+	0.891527i	$0.649635\pi$
$492$	−12.6925	−	6.11344i	−0.572221	−	0.275615i
$493$	3.06439	+	11.4365i	0.138013	+	0.515073i
$494$	−7.84210	+	13.3419i	−0.352833	+	0.600281i
$495$	−40.8835	−	8.86654i	−1.83758	−	0.398521i
$496$	1.29116	+	0.800072i	0.0579750	+	0.0359243i
$497$	5.30958	+	19.8156i	0.238167	+	0.888853i
$498$	8.18440	−	17.3361i	0.366752	−	0.776849i
$499$	−3.71718	+	2.14612i	−0.166404	+	0.0960733i	−0.580889	−	0.813983i	$-0.697295\pi$
$499$	−3.71718	+	2.14612i	−0.166404	+	0.0960733i	0.414485	+	0.910056i	$0.363962\pi$
$500$	−3.36136	+	22.1066i	−0.150324	+	0.988637i
$501$	13.4444	+	11.2117i	0.600650	+	0.500904i
$502$	−22.2922	−	6.15962i	−0.994952	−	0.274917i
$503$	27.4702	−	27.4702i	1.22484	−	1.22484i	0.258946	−	0.965892i	$-0.416625\pi$
$503$	27.4702	−	27.4702i	1.22484	−	1.22484i	0.965892	−	0.258946i	$-0.0833752\pi$
$504$	3.76732	+	23.7599i	0.167810	+	1.05835i
$505$	2.47326	+	3.23307i	0.110058	+	0.143870i
$506$	29.0232	−	16.4566i	1.29024	−	0.731585i
$507$	−0.116840	+	0.0823421i	−0.00518903	+	0.00365694i
$508$	−3.42847	−	13.6415i	−0.152114	−	0.605244i
$509$	0.0689067	+	0.119350i	0.00305424	+	0.00529009i	0.867548	−	0.497353i	$-0.165694\pi$
$509$	0.0689067	+	0.119350i	0.00305424	+	0.00529009i	−0.864494	+	0.502643i	$0.832361\pi$
$510$	−6.47455	+	20.0976i	−0.286698	+	0.889939i
$511$	−38.2054	−	22.0579i	−1.69011	−	0.975785i
$512$	17.0810	−	14.8404i	0.754882	−	0.655860i
$513$	−4.20709	−	15.1476i	−0.185747	−	0.668781i
$514$	20.1753	+	11.8586i	0.889895	+	0.523062i
$515$	−7.96378	−	6.12950i	−0.350926	−	0.270098i
$516$	8.82382	−	10.2520i	0.388447	−	0.451321i
$517$	−7.25167	+	27.0636i	−0.318928	+	1.19026i
$518$	−25.4950	−	25.8952i	−1.12019	−	1.13777i
$519$	−19.0017	−	3.29103i	−0.834081	−	0.144460i
$520$	−2.42180	−	22.7472i	−0.106203	−	0.997532i
$521$	−31.4306			−1.37700			−0.688500	−	0.725237i	$-0.741730\pi$
$521$	−31.4306			−1.37700			−0.688500	+	0.725237i	$0.741730\pi$
$522$	12.9789	+	1.15789i	0.568069	+	0.0506793i
$523$	14.3377	+	14.3377i	0.626944	+	0.626944i	0.947298	−	0.320354i	$-0.103802\pi$
$523$	14.3377	+	14.3377i	0.626944	+	0.626944i	−0.320354	+	0.947298i	$0.603802\pi$
$524$	0.515729	−	33.1151i	0.0225297	−	1.44664i
$525$	−20.1112	+	14.0846i	−0.877724	+	0.614704i
$526$	0.188978	−	24.2702i	0.00823984	−	1.05823i
$527$	−0.378885	+	1.41402i	−0.0165045	+	0.0615956i
$528$	−19.3529	+	38.6292i	−0.842226	+	1.68112i
$529$	−7.52446	−	4.34425i	−0.327150	−	0.188880i
$530$	34.1273	−	4.17180i	1.48240	−	0.181211i
$531$	2.51347	+	0.897573i	0.109075	+	0.0389513i
$532$	4.69760	−	16.4995i	0.203667	−	0.715345i
$533$	3.80717	+	14.2085i	0.164907	+	0.615441i
$534$	−2.84207	−	2.40787i	−0.122988	−	0.104199i
$535$	17.9749	−	7.41441i	0.777122	−	0.320553i
$536$	2.11679	+	3.87256i	0.0914316	+	0.167269i
$537$	−36.4528	−	16.8636i	−1.57305	−	0.727718i
$538$	−12.6716	−	3.50131i	−0.546311	−	0.150952i
$539$		−	6.47213i		−	0.278775i
$540$	18.3230	+	14.2922i	0.788498	+	0.615037i
$541$		−	39.8569i		−	1.71358i	−0.515663	−	0.856791i	$-0.672455\pi$
$541$		−	39.8569i		−	1.71358i	0.515663	−	0.856791i	$-0.327545\pi$
$542$	1.12658	−	4.07719i	0.0483906	−	0.175130i
$543$	33.3590	+	15.4324i	1.43157	+	0.662266i
$544$	18.4470	+	11.6304i	0.790907	+	0.498651i
$545$	4.78173	+	1.98892i	0.204827	+	0.0851961i
$546$	16.2369	−	19.1649i	0.694877	−	0.820181i
$547$	1.62589	+	6.06789i	0.0695178	+	0.259444i	0.991934	−	0.126752i	$-0.0404553\pi$
$547$	1.62589	+	6.06789i	0.0695178	+	0.259444i	−0.922417	+	0.386196i	$0.873789\pi$
$548$	−9.05667	+	31.8100i	−0.386882	+	1.35886i
$549$	2.72031	+	14.8978i	0.116100	+	0.635824i
$550$	−44.0943	−	0.473402i	−1.88019	−	0.0201859i
$551$	−8.04729	−	4.64610i	−0.342826	−	0.197931i
$552$	−18.4916	+	1.23978i	−0.787055	+	0.0527684i
$553$	−7.20517	+	26.8901i	−0.306395	+	1.14348i
$554$	19.0691	+	0.148481i	0.810170	+	0.00630834i
$555$	−35.0716	−	1.47635i	−1.48871	−	0.0626674i
$556$	0.356355	+	0.00554980i	0.0151128	+	0.000235364i
$557$	−18.0803	−	18.0803i	−0.766089	−	0.766089i	0.211327	−	0.977415i	$-0.432222\pi$
$557$	−18.0803	−	18.0803i	−0.766089	−	0.766089i	−0.977415	+	0.211327i	$0.932222\pi$
$558$	1.31815	+	0.926343i	0.0558017	+	0.0392152i
$559$	−14.1234			−0.597355
$560$	8.93484	+	23.7317i	0.377566	+	1.00285i
$561$	−41.0291	−	7.10610i	−1.73225	−	0.300020i
$562$	−10.4217	+	10.2607i	−0.439613	+	0.432820i
$563$	5.08003	−	18.9589i	0.214098	−	0.799024i	−0.772384	−	0.635155i	$-0.780936\pi$
$563$	5.08003	−	18.9589i	0.214098	−	0.799024i	0.986482	−	0.163868i	$-0.0523973\pi$
$564$	10.1527	−	11.7961i	0.427508	−	0.496704i
$565$	6.57740	−	8.54571i	0.276713	−	0.359521i
$566$	18.6611	−	31.7485i	0.784385	−	1.33449i
$567$	2.53253	+	25.3900i	0.106356	+	1.06628i
$568$	14.8059	−	14.1299i	0.621244	−	0.592878i
$569$	25.1017	+	14.4925i	1.05232	+	0.607557i	0.923298	−	0.384085i	$-0.125483\pi$
$569$	25.1017	+	14.4925i	1.05232	+	0.607557i	0.129022	+	0.991642i	$0.458816\pi$
$570$	−7.56017	−	14.7463i	−0.316660	−	0.617654i
$571$	−16.8497	−	29.1846i	−0.705139	−	1.22134i	−0.966641	−	0.256134i	$-0.917551\pi$
$571$	−16.8497	−	29.1846i	−0.705139	−	1.22134i	0.261502	−	0.965203i	$-0.415782\pi$
$572$	43.7520	−	10.9960i	1.82936	−	0.459768i
$573$	35.1482	−	24.7705i	1.46834	−	1.03480i
$574$	−8.04275	−	14.1844i	−0.335698	−	0.592044i
$575$	−9.40928	−	16.4089i	−0.392394	−	0.684300i
$576$	18.9967	−	14.6672i	0.791529	−	0.611131i
$577$	−1.34067	+	1.34067i	−0.0558127	+	0.0558127i	−0.734462	−	0.678650i	$-0.762566\pi$
$577$	−1.34067	+	1.34067i	−0.0558127	+	0.0558127i	0.678650	+	0.734462i	$0.262566\pi$
$578$	0.805593	−	2.91552i	0.0335083	−	0.121270i
$579$	1.62578	+	1.35580i	0.0675650	+	0.0563449i
$580$	13.6463	−	1.56042i	0.566633	−	0.0647928i
$581$	19.2162	−	11.0945i	0.797222	−	0.460276i
$582$	3.09117	+	1.45935i	0.128133	+	0.0604919i
$583$	17.5486	+	65.4922i	0.726788	+	2.71241i
$584$	−1.02797	+	43.9999i	−0.0425378	+	1.82073i
$585$	−1.16986	−	24.2352i	−0.0483677	−	1.00200i
$586$	−23.7502	−	13.9599i	−0.981113	−	0.576678i
$587$	−2.49988	−	9.32969i	−0.103181	−	0.385077i	0.894951	−	0.446164i	$-0.147210\pi$
$587$	−2.49988	−	9.32969i	−0.103181	−	0.385077i	−0.998132	+	0.0610864i	$0.980543\pi$
$588$	−1.56009	+	3.23900i	−0.0643371	+	0.133574i
$589$	−0.574449	−	0.994975i	−0.0236698	−	0.0409972i
$590$	2.78570	+	0.393023i	0.114686	+	0.0161805i
$591$	0.453290	−	0.166545i	0.0186459	−	0.00685075i
$592$	−10.4691	+	34.7093i	−0.430278	+	1.42655i
$593$	3.37141	+	3.37141i	0.138447	+	0.138447i	0.772934	−	0.634487i	$-0.218788\pi$
$593$	3.37141	+	3.37141i	0.138447	+	0.138447i	−0.634487	+	0.772934i	$0.718788\pi$
$594$	−22.8607	+	39.7175i	−0.937988	+	1.62963i
$595$	−19.4106	+	14.8488i	−0.795755	+	0.608742i
$596$	−0.682617	+	43.8311i	−0.0279611	+	1.79539i
$597$	2.34960	−	5.07895i	0.0961627	−	0.207868i
$598$	13.5763	+	13.7894i	0.555175	+	0.563888i
$599$	−8.57792	−	14.8574i	−0.350484	−	0.607056i	0.635850	−	0.771812i	$-0.280650\pi$
$599$	−8.57792	−	14.8574i	−0.350484	−	0.607056i	−0.986334	+	0.164756i	$0.947316\pi$
$600$	21.9530	+	10.8657i	0.896229	+	0.443592i
$601$	−6.36560	+	11.0256i	−0.259658	+	0.449742i	−0.966150	−	0.257979i	$-0.916943\pi$
$601$	−6.36560	+	11.0256i	−0.259658	+	0.449742i	0.706492	+	0.707721i	$0.250277\pi$
$602$	15.1535	−	3.93416i	0.617610	−	0.160345i
$603$	2.00403	+	4.23037i	0.0816105	+	0.172274i
$604$	11.9126	+	21.3960i	0.484719	+	0.870590i
$605$	−8.04913	−	61.8438i	−0.327244	−	2.51431i
$606$	4.19739	−	1.50519i	0.170507	−	0.0611442i
$607$	−5.98710	+	22.3442i	−0.243009	+	0.906921i	0.731365	+	0.681986i	$0.238884\pi$
$607$	−5.98710	+	22.3442i	−0.243009	+	0.906921i	−0.974374	+	0.224935i	$0.927783\pi$
$608$	−16.6915	+	3.78284i	−0.676930	+	0.153415i
$609$	11.5827	+	9.65923i	0.469354	+	0.391412i
$610$	5.97206	+	14.8041i	0.241802	+	0.599402i
$611$	−16.2504			−0.657423
$612$	18.8202	+	13.4462i	0.760762	+	0.543532i
$613$	19.5127	−	19.5127i	0.788110	−	0.788110i	−0.193074	−	0.981184i	$-0.561846\pi$
$613$	19.5127	−	19.5127i	0.788110	−	0.788110i	0.981184	+	0.193074i	$0.0618457\pi$
$614$	−19.6772	+	11.1573i	−0.794106	+	0.450270i
$615$	−15.0293	−	4.71291i	−0.606040	−	0.190043i
$616$	−43.8801	+	23.9855i	−1.76798	+	0.966403i
$617$	7.11853	+	1.90740i	0.286581	+	0.0767892i	0.399246	−	0.916844i	$-0.369272\pi$
$617$	7.11853	+	1.90740i	0.286581	+	0.0767892i	−0.112665	+	0.993633i	$0.535939\pi$
$618$	−9.04766	+	6.27142i	−0.363950	+	0.252274i
$619$	−36.6839	−	21.1795i	−1.47445	−	0.851274i	−0.474864	−	0.880059i	$-0.657503\pi$
$619$	−36.6839	−	21.1795i	−1.47445	−	0.851274i	−0.999586	+	0.0287851i	$0.990836\pi$
$620$	1.55767	+	0.676540i	0.0625573	+	0.0271705i
$621$	−19.6565	+	0.179128i	−0.788789	+	0.00718817i
$622$	26.5897	−	6.90324i	1.06615	−	0.276795i
$623$	−1.11586	−	4.16444i	−0.0447059	−	0.166845i
$624$	−24.5464	−	5.04332i	−0.982643	−	0.201894i
$625$	−0.147470	+	24.9996i	−0.00589882	+	0.999983i
$626$	−12.8127	−	0.0997653i	−0.512099	−	0.00398742i
$627$	26.7127	−	18.8256i	1.06680	−	0.751823i
$628$	18.6896	−	18.1164i	0.745798	−	0.722924i
$629$	−34.9398			−1.39314
$630$	8.00607	+	25.6770i	0.318970	+	1.02300i
$631$			20.0513i			0.798231i	0.916901	+	0.399116i	$0.130683\pi$
$631$			20.0513i			0.798231i	−0.916901	+	0.399116i	$0.869317\pi$
$632$	26.9873	−	6.55965i	1.07350	−	0.260929i
$633$	−38.3296	+	3.47076i	−1.52347	+	0.137950i
$634$	42.6060	+	0.331749i	1.69210	+	0.0131754i
$635$	−5.99664	−	14.5378i	−0.237969	−	0.576914i
$636$	7.00450	−	37.0058i	0.277747	−	1.46738i
$637$	3.62589	−	0.971554i	0.143663	−	0.0384944i
$638$	6.80668	+	26.2177i	0.269479	+	1.03797i
$639$	16.5441	−	14.0543i	0.654474	−	0.555979i
$640$	16.4994	−	19.1773i	0.652196	−	0.758051i
$641$	11.9678	−	20.7288i	0.472698	−	0.818737i	−0.526814	−	0.849981i	$-0.676614\pi$
$641$	11.9678	−	20.7288i	0.472698	−	0.818737i	0.999512	+	0.0312439i	$0.00994686\pi$
$642$	−1.75562	−	21.2274i	−0.0692889	−	0.837778i
$643$	8.50291	−	31.7333i	0.335322	−	1.25144i	−0.568197	−	0.822892i	$-0.692359\pi$
$643$	8.50291	−	31.7333i	0.335322	−	1.25144i	0.903519	−	0.428547i	$-0.140974\pi$
$644$	−18.4076	−	11.0133i	−0.725361	−	0.433986i
$645$	8.10564	−	12.7673i	0.319159	−	0.502712i
$646$	−8.13576	−	14.3484i	−0.320097	−	0.564531i
$647$	4.24769	+	4.24769i	0.166994	+	0.166994i	0.785657	−	0.618663i	$-0.212325\pi$
$647$	4.24769	+	4.24769i	0.166994	+	0.166994i	−0.618663	+	0.785657i	$0.712325\pi$
$648$	21.0145	−	14.3662i	0.825529	−	0.564359i
$649$			5.54801i			0.217779i
$650$	−6.35393	−	24.7741i	−0.249222	−	0.971718i
$651$	0.643093	+	1.75032i	0.0252048	+	0.0686005i
$652$	−9.68555	−	38.5377i	−0.379316	−	1.50925i
$653$	−15.4651	−	4.14385i	−0.605195	−	0.162162i	−0.0568066	−	0.998385i	$-0.518092\pi$
$653$	−15.4651	−	4.14385i	−0.605195	−	0.162162i	−0.548389	+	0.836224i	$0.684758\pi$
$654$	3.66724	−	4.32854i	0.143401	−	0.169259i
$655$	−4.77903	−	36.7187i	−0.186732	−	1.43472i
$656$	−8.56850	+	13.8279i	−0.334544	+	0.539890i
$657$	−3.78599	+	46.5279i	−0.147705	+	1.81523i
$658$	17.4357	−	4.52668i	0.679714	−	0.176468i
$659$	0.441064	+	0.254648i	0.0171814	+	0.00991968i	0.508566	−	0.861023i	$-0.330176\pi$
$659$	0.441064	+	0.254648i	0.0171814	+	0.00991968i	−0.491385	+	0.870943i	$0.663509\pi$
$660$	−15.1698	+	45.8619i	−0.590483	+	1.78517i
$661$	43.5267	−	25.1301i	1.69299	−	0.977449i	0.740910	−	0.671604i	$-0.234394\pi$
$661$	43.5267	−	25.1301i	1.69299	−	0.977449i	0.952081	−	0.305845i	$-0.0989391\pi$
$662$	−2.14036	+	2.10729i	−0.0831876	+	0.0819021i
$663$	−2.17796	−	24.0525i	−0.0845849	−	0.934120i
$664$	−18.9072	−	11.5131i	−0.733741	−	0.446795i
$665$	2.53155	−	19.0123i	0.0981692	−	0.737266i
$666$	−13.2135	+	36.1114i	−0.512013	+	1.39929i
$667$	−8.21579	+	8.21579i	−0.318117	+	0.318117i
$668$	14.5143	−	14.0691i	0.561575	−	0.544351i
$669$	8.70852	+	1.50829i	0.336691	+	0.0583138i
$670$	2.96740	+	3.94226i	0.114641	+	0.152303i
$671$	−27.2632	+	15.7404i	−1.05248	+	0.607652i
$672$	27.7416	−	1.42641i	1.07016	−	0.0550251i
$673$	0.469409	−	0.125778i	0.0180944	−	0.00484838i	−0.249760	−	0.968308i	$-0.580352\pi$
$673$	0.469409	−	0.125778i	0.0180944	−	0.00484838i	0.267855	+	0.963459i	$0.413685\pi$
$674$	7.90734	+	4.64777i	0.304579	+	0.179025i
$675$	22.5796	+	12.8515i	0.869091	+	0.494653i
$676$	0.0802904	+	0.144207i	0.00308809	+	0.00554644i
$677$	8.89178	−	2.38255i	0.341739	−	0.0915686i	−0.0838679	−	0.996477i	$-0.526727\pi$
$677$	8.89178	−	2.38255i	0.341739	−	0.0915686i	0.425607	+	0.904908i	$0.360061\pi$
$678$	−6.72970	−	9.70880i	−0.258452	−	0.372864i
$679$	1.97824	+	3.42641i	0.0759179	+	0.131494i
$680$	22.2867	+	9.88676i	0.854657	+	0.379140i
$681$	17.0444	+	2.95203i	0.653142	+	0.113122i
$682$	−0.891961	+	3.22809i	−0.0341549	+	0.123610i
$683$	−15.3076	−	15.3076i	−0.585730	−	0.585730i	0.350742	−	0.936472i	$-0.385929\pi$
$683$	−15.3076	−	15.3076i	−0.585730	−	0.585730i	−0.936472	+	0.350742i	$0.885929\pi$
$684$	−17.9063	+	2.98231i	−0.684666	+	0.114031i
$685$	−4.88067	+	36.6546i	−0.186481	+	1.40050i
$686$	20.7948	−	11.7909i	0.793948	−	0.450181i
$687$	3.72027	−	0.336872i	0.141937	−	0.0128525i
$688$	−10.6950	−	11.3828i	−0.407743	−	0.433967i
$689$	−34.0565	+	19.6625i	−1.29745	+	0.749082i
$690$	−20.2570	+	4.35879i	−0.771171	+	0.165936i
$691$	−7.02677	+	12.1707i	−0.267311	+	0.462996i	−0.968166	−	0.250307i	$-0.919468\pi$
$691$	−7.02677	+	12.1707i	−0.267311	+	0.462996i	0.700856	+	0.713303i	$0.252802\pi$
$692$	−6.09760	+	21.4168i	−0.231796	+	0.814144i
$693$	−47.9346	+	22.7078i	−1.82088	+	0.862598i
$694$	16.4407	+	9.66350i	0.624081	+	0.366822i
$695$	0.395132	−	0.0514275i	0.0149882	−	0.00195075i
$696$	2.91330	−	14.7615i	0.110428	−	0.559533i
$697$	−15.1436	−	4.05773i	−0.573606	−	0.153697i
$698$	14.1516	−	13.9329i	0.535644	−	0.527367i
$699$	16.6351	−	6.11197i	0.629198	−	0.231176i
$700$	13.7184	+	24.8111i	0.518505	+	0.937770i
$701$			38.6931i			1.46142i	0.682688	+	0.730710i	$0.260811\pi$
$701$			38.6931i			1.46142i	−0.682688	+	0.730710i	$0.739189\pi$
$702$	−25.6827	−	6.84516i	−0.969330	−	0.258354i
$703$	19.3899	−	19.3899i	0.731304	−	0.731304i
$704$	41.9938	+	26.9355i	1.58270	+	1.01517i
$705$	9.32641	−	14.6901i	0.351253	−	0.553263i
$706$	−22.6301	−	0.176208i	−0.851696	−	0.00663167i
$707$	4.98524	+	1.33579i	0.187489	+	0.0502376i
$708$	1.33734	−	2.77652i	0.0502602	−	0.104348i
$709$	22.4096	−	38.8145i	0.841609	−	1.45771i	−0.0469252	−	0.998898i	$-0.514942\pi$
$709$	22.4096	−	38.8145i	0.841609	−	1.45771i	0.888534	−	0.458811i	$-0.151724\pi$
$710$	14.0972	−	18.0238i	0.529060	−	0.676420i
$711$	28.9786	−	5.29143i	1.08678	−	0.198444i
$712$	−3.11161	+	2.96953i	−0.116612	+	0.111288i
$713$	−1.38762	+	0.371812i	−0.0519668	+	0.0139245i
$714$	9.03680	+	25.2001i	0.338194	+	0.943090i
$715$	46.6266	−	19.2329i	1.74374	−	0.719268i
$716$	−23.8116	+	39.7985i	−0.889881	+	1.48734i
$717$	−16.8979	+	1.53011i	−0.631062	+	0.0571429i
$718$	7.32073	+	2.02281i	0.273207	+	0.0754905i
$719$	−41.6319			−1.55261			−0.776305	−	0.630358i	$-0.782908\pi$
$719$	−41.6319			−1.55261			−0.776305	+	0.630358i	$0.782908\pi$
$720$	18.6467	−	19.2951i	0.694921	−	0.719086i
$721$	−12.7417			−0.474527
$722$	−13.4219	−	3.70864i	−0.499512	−	0.138021i
$723$	3.91968	+	5.56184i	0.145774	+	0.206847i
$724$	21.7907	−	36.4207i	0.809844	−	1.35357i
$725$	14.8449	−	3.93078i	0.551325	−	0.145986i
$726$	−67.2229	−	12.1826i	−2.49488	−	0.452140i
$727$	−21.4550	+	5.74886i	−0.795723	+	0.213213i	−0.633705	−	0.773575i	$-0.718467\pi$
$727$	−21.4550	+	5.74886i	−0.795723	+	0.213213i	−0.162018	+	0.986788i	$0.551800\pi$
$728$	−20.0244	−	20.9825i	−0.742154	−	0.777662i
$729$	23.1328	−	13.9239i	0.856769	−	0.515700i
$730$	5.97070	+	48.8432i	0.220986	+	1.80777i
$731$	7.52643	−	13.0362i	0.278375	−	0.482160i
$732$	17.4381	−	1.30561i	0.644533	−	0.0482567i
$733$	25.8817	+	6.93497i	0.955962	+	0.256149i	0.702890	−	0.711298i	$-0.251893\pi$
$733$	25.8817	+	6.93497i	0.955962	+	0.256149i	0.253071	+	0.967448i	$0.418559\pi$
$734$	−12.2657	−	0.0955059i	−0.452734	−	0.00352519i
$735$	−1.20269	+	3.83534i	−0.0443619	+	0.141468i
$736$	−0.832929	+	21.3840i	−0.0307022	+	0.788224i
$737$	−6.88065	+	6.88065i	−0.253452	+	0.253452i
$738$	−9.92081	+	14.1169i	−0.365190	+	0.519651i
$739$		−	24.0594i		−	0.885041i	−0.896758	−	0.442520i	$-0.854084\pi$
$739$		−	24.0594i		−	0.885041i	0.896758	−	0.442520i	$-0.145916\pi$
$740$	−5.97488	+	40.0902i	−0.219641	+	1.47375i
$741$	14.5566	+	12.1393i	0.534751	+	0.445948i
$742$	31.0633	−	30.5833i	1.14037	−	1.12275i
$743$	33.1149	+	8.87311i	1.21487	+	0.325523i	0.808670	−	0.588263i	$-0.200188\pi$
$743$	33.1149	+	8.87311i	1.21487	+	0.325523i	0.406197	+	0.913785i	$0.366855\pi$
$744$	1.22451	−	1.40050i	0.0448927	−	0.0513450i
$745$	6.32550	+	48.6007i	0.231748	+	1.78059i
$746$	25.1324	+	14.7723i	0.920162	+	0.540852i
$747$	−19.3147	−	13.3502i	−0.706689	−	0.488458i
$748$	−13.1661	+	46.2439i	−0.481402	+	1.69084i
$749$	12.3265	−	21.3502i	0.450401	−	0.780118i
$750$	26.0420	+	8.47440i	0.950919	+	0.309441i
$751$	−2.80759	+	1.62096i	−0.102450	+	0.0591498i	−0.550350	−	0.834934i	$-0.685506\pi$
$751$	−2.80759	+	1.62096i	−0.102450	+	0.0591498i	0.447899	+	0.894084i	$0.352172\pi$
$752$	−12.3057	−	13.0972i	−0.448744	−	0.477605i
$753$	−11.8928	+	25.7078i	−0.433398	+	0.936843i
$754$	−13.6662	+	7.74895i	−0.497694	+	0.282200i
$755$	16.6354	+	21.7460i	0.605424	+	0.791418i
$756$	29.4627	+	0.190328i	1.07155	+	0.00692217i
$757$	10.4540	+	10.4540i	0.379956	+	0.379956i	0.871086	−	0.491130i	$-0.163416\pi$
$757$	10.4540	+	10.4540i	0.379956	+	0.379956i	−0.491130	+	0.871086i	$0.663416\pi$
$758$	4.28809	−	15.5190i	0.155751	−	0.563676i
$759$	−14.0924	−	38.3557i	−0.511522	−	1.39222i
$760$	−17.8547	+	6.88139i	−0.647660	+	0.249614i
$761$	−8.14265	−	14.1035i	−0.295171	−	0.511251i	0.679854	−	0.733348i	$-0.262043\pi$
$761$	−8.14265	−	14.1035i	−0.295171	−	0.511251i	−0.975025	+	0.222097i	$0.928710\pi$
$762$	−17.1683	+	1.41992i	−0.621943	+	0.0514381i
$763$	6.34255	−	1.69948i	0.229616	−	0.0615253i
$764$	−24.1533	−	43.3810i	−0.873835	−	1.56947i
$765$	22.9930	+	11.8353i	0.831314	+	0.427906i
$766$	38.3418	+	22.5365i	1.38535	+	0.814278i
$767$	−3.10817	+	0.832831i	−0.112229	+	0.0300718i
$768$	−14.5232	−	23.6025i	−0.524061	−	0.851681i
$769$	3.98850	−	2.30276i	0.143829	−	0.0830396i	−0.426359	−	0.904554i	$-0.640204\pi$
$769$	3.98850	−	2.30276i	0.143829	−	0.0830396i	0.570188	+	0.821515i	$0.306871\pi$
$770$	−44.6699	+	33.6238i	−1.60979	+	1.21172i
$771$	18.3568	−	22.0122i	0.661102	−	0.792749i
$772$	1.75516	−	1.70133i	0.0631696	−	0.0612322i
$773$	30.2562	−	30.2562i	1.08824	−	1.08824i	0.0925288	−	0.995710i	$-0.470505\pi$
$773$	30.2562	−	30.2562i	1.08824	−	1.08824i	0.995710	−	0.0925288i	$-0.0294950\pi$
$774$	−10.6270	−	12.7088i	−0.381978	−	0.456809i
$775$	1.83254	+	0.496825i	0.0658267	+	0.0178465i
$776$	2.05288	−	3.37131i	0.0736942	−	0.121023i
$777$	−36.3799	+	25.6385i	−1.30512	+	0.919777i
$778$	−27.7143	+	27.2860i	−0.993605	+	0.978251i
$779$	10.6558	−	6.15215i	0.381785	−	0.220424i
$780$	−27.9705	−	1.61409i	−1.00150	−	0.0577936i
$781$	39.0794	+	22.5625i	1.39837	+	0.807351i
$782$	−19.9627	+	5.18275i	−0.713866	+	0.185335i
$783$	3.98983	−	15.4521i	0.142585	−	0.552215i
$784$	3.52876	+	2.18660i	0.126027	+	0.0780928i
$785$	17.7498	−	23.0615i	0.633516	−	0.823099i
$786$	−39.9124	−	7.23322i	−1.42363	−	0.258000i
$787$	−52.9760	−	14.1949i	−1.88839	−	0.505992i	−0.998786	−	0.0492590i	$-0.984314\pi$
$787$	−52.9760	−	14.1949i	−1.88839	−	0.505992i	−0.889604	−	0.456733i	$-0.849019\pi$
$788$	−0.135919	−	0.540807i	−0.00484192	−	0.0192654i
$789$	−29.2896	−	5.07286i	−1.04274	−	0.180599i
$790$	28.7964	−	11.6166i	1.02453	−	0.413300i
$791$		−	13.6728i		−	0.486150i
$792$	42.8154	+	31.0961i	1.52138	+	1.10495i
$793$	−12.9108	−	12.9108i	−0.458477	−	0.458477i
$794$	−10.6575	−	18.7958i	−0.378221	−	0.667039i
$795$	1.77099	−	42.0712i	0.0628107	−	1.49211i
$796$	−5.54511	−	3.31766i	−0.196541	−	0.117591i
$797$	−12.7429	+	47.5573i	−0.451378	+	1.68457i	0.247146	+	0.968978i	$0.420507\pi$
$797$	−12.7429	+	47.5573i	−0.451378	+	1.68457i	−0.698524	+	0.715587i	$0.746159\pi$
$798$	−18.9998	−	8.96986i	−0.672587	−	0.317530i
$799$	8.65996	−	14.9995i	0.306367	−	0.530644i
$800$	15.1553	−	23.8813i	0.535821	−	0.844332i
$801$	−3.47689	+	2.95364i	−0.122850	+	0.104362i
$802$	−3.06783	−	11.8166i	−0.108329	−	0.417258i
$803$	−93.7328	+	25.1156i	−3.30776	+	0.886311i
$804$	5.10201	−	1.78488i	0.179934	−	0.0629478i
$805$	−22.1435	−	9.21042i	−0.780456	−	0.324625i
$806$	−1.94237	−	0.0151241i	−0.0684171	−	0.000532725i
$807$	−6.76022	+	14.6131i	−0.237971	+	0.514404i
$808$	−1.21612	−	5.00326i	−0.0427828	−	0.176014i
$809$			5.34945i			0.188077i	0.995569	+	0.0940383i	$0.0299776\pi$
$809$			5.34945i			0.188077i	−0.995569	+	0.0940383i	$0.970022\pi$
$810$	20.9276	−	19.2882i	0.735322	−	0.677718i
$811$	28.6897			1.00743			0.503716	−	0.863869i	$-0.331966\pi$
$811$	28.6897			1.00743			0.503716	+	0.863869i	$0.331966\pi$
$812$	12.5045	−	12.1210i	0.438821	−	0.425362i
$813$	−4.70188	−	2.17516i	−0.164902	−	0.0762861i
$814$	−79.9316	−	0.622382i	−2.80160	−	0.0218145i
$815$	−16.9407	−	41.0697i	−0.593407	−	1.43861i
$816$	17.7360	−	19.9692i	0.620885	−	0.699063i
$817$	3.05763	+	11.4112i	0.106973	+	0.399229i
$818$	−23.8498	+	6.19191i	−0.833889	+	0.216495i
$819$	−19.9172	−	23.4457i	−0.695964	−	0.819258i
$820$	−7.24551	+	16.6821i	−0.253024	+	0.582563i
$821$	−3.41807	−	1.97342i	−0.119291	−	0.0688729i	0.439167	−	0.898405i	$-0.355274\pi$
$821$	−3.41807	−	1.97342i	−0.119291	−	0.0688729i	−0.558458	+	0.829533i	$0.688607\pi$
$822$	36.6305	+	17.2933i	1.27764	+	0.603174i
$823$	−45.9267	−	12.3060i	−1.60090	−	0.428961i	−0.655589	−	0.755118i	$-0.727579\pi$
$823$	−45.9267	−	12.3060i	−1.60090	−	0.428961i	−0.945316	+	0.326157i	$0.894246\pi$
$824$	6.09700	+	11.1541i	0.212399	+	0.388572i
$825$	−9.37360	+	53.1877i	−0.326347	+	1.85176i
$826$	3.10288	−	1.75938i	0.107963	−	0.0612166i
$827$	−31.2909	+	31.2909i	−1.08809	+	1.08809i	−0.0923660	+	0.995725i	$0.529443\pi$
$827$	−31.2909	+	31.2909i	−1.08809	+	1.08809i	−0.995725	+	0.0923660i	$0.970557\pi$
$828$	−2.19295	+	22.5921i	−0.0762104	+	0.785131i
$829$	−44.7080			−1.55277			−0.776386	−	0.630257i	$-0.782949\pi$
$829$	−44.7080			−1.55277			−0.776386	+	0.630257i	$0.782949\pi$
$830$	−22.7769	−	9.68259i	−0.790598	−	0.336088i
$831$	3.98576	−	23.0129i	0.138265	−	0.798310i
$832$	−8.78625	+	27.5696i	−0.304608	+	0.955804i
$833$	−1.03549	+	3.86451i	−0.0358777	+	0.133898i
$834$	0.0778372	−	0.429500i	0.00269528	−	0.0148724i
$835$	13.7844	−	17.9094i	0.477028	−	0.619781i
$836$	−18.3565	−	32.9697i	−0.634875	−	1.14028i
$837$	1.38248	−	1.40790i	0.0477854	−	0.0486643i
$838$	11.1979	−	2.90720i	0.386823	−	0.100427i
$839$	−8.10455	+	14.0375i	−0.279800	+	0.484628i	−0.971335	−	0.237715i	$-0.923602\pi$
$839$	−8.10455	+	14.0375i	−0.279800	+	0.484628i	0.691535	+	0.722343i	$0.256935\pi$
$840$	30.4602	−	6.05955i	1.05098	−	0.209074i
$841$	9.78357	+	16.9456i	0.337364	+	0.584332i
$842$	3.96851	+	4.03080i	0.136764	+	0.138910i
$843$	10.3184	+	14.6414i	0.355385	+	0.504276i
$844$	−0.692022	+	44.4349i	−0.0238204	+	1.52951i
$845$	0.112121	+	0.146566i	0.00385709	+	0.00504204i
$846$	−12.2275	−	14.6229i	−0.420388	−	0.502744i
$847$	−55.9130	−	55.9130i	−1.92119	−	1.92119i
$848$	−41.6366	−	12.5585i	−1.42981	−	0.431262i
$849$	−34.6391	−	28.8868i	−1.18881	−	0.991392i
$850$	26.2530	+	7.33743i	0.900471	+	0.251672i
$851$	−17.1438	−	29.6939i	−0.587681	−	1.01789i
$852$	−14.1188	−	20.7115i	−0.483702	−	0.709564i
$853$	−1.90020	−	7.09165i	−0.0650617	−	0.242813i	0.925735	−	0.378173i	$-0.123448\pi$
$853$	−1.90020	−	7.09165i	−0.0650617	−	0.242813i	−0.990797	+	0.135360i	$0.956781\pi$
$854$	17.4489	+	10.2561i	0.597090	+	0.350957i
$855$	−19.3280	+	6.19200i	−0.661005	+	0.211762i
$856$	−24.5883	−	0.574457i	−0.840409	−	0.0196346i
$857$	−1.96234	−	7.32354i	−0.0670322	−	0.250168i	0.924277	−	0.381724i	$-0.124669\pi$
$857$	−1.96234	−	7.32354i	−0.0670322	−	0.250168i	−0.991309	+	0.131556i	$0.958003\pi$
$858$	−4.55406	−	55.0635i	−0.155473	−	1.87984i
$859$	2.78755	−	1.60939i	0.0951099	−	0.0549117i	−0.451691	−	0.892175i	$-0.649179\pi$
$859$	2.78755	−	1.60939i	0.0951099	−	0.0549117i	0.546801	+	0.837263i	$0.315846\pi$
$860$	−13.6707	−	10.8651i	−0.466168	−	0.370498i
$861$	−18.7453	+	6.88730i	−0.638840	+	0.234719i
$862$	−0.161747	+	0.585376i	−0.00550911	+	0.0199380i
$863$	−2.29117	+	2.29117i	−0.0779923	+	0.0779923i	−0.745027	−	0.667035i	$-0.767563\pi$
$863$	−2.29117	+	2.29117i	−0.0779923	+	0.0779923i	0.667035	+	0.745027i	$0.267563\pi$
$864$	−13.9315	−	25.8827i	−0.473958	−	0.880548i
$865$	−3.28601	+	24.6785i	−0.111728	+	0.839093i
$866$	4.75570	+	8.38726i	0.161605	+	0.285011i
$867$	−3.36222	−	1.55541i	−0.114187	−	0.0528246i
$868$	2.08826	−	0.524834i	0.0708800	−	0.0178140i
$869$	30.6176	+	53.0313i	1.03863	+	1.79896i
$870$	0.838351	−	16.8013i	0.0284228	−	0.569617i
$871$	−4.88763	−	2.82187i	−0.165611	−	0.0956155i
$872$	−4.52267	−	4.73906i	−0.153157	−	0.160485i
$873$	2.38045	−	3.44398i	0.0805661	−	0.116561i
$874$	8.20218	−	13.9545i	0.277443	−	0.472019i
$875$	19.1847	+	25.2324i	0.648563	+	0.853011i
$876$	52.9630	+	10.0249i	1.78945	+	0.338709i
$877$	−9.91150	+	36.9902i	−0.334688	+	1.24907i	0.569520	+	0.821978i	$0.307129\pi$
$877$	−9.91150	+	36.9902i	−0.334688	+	1.24907i	−0.904207	+	0.427094i	$0.859537\pi$
$878$	1.46735	−	1.44467i	0.0495205	−	0.0487553i
$879$	−21.6094	+	25.9126i	−0.728868	+	0.874009i
$880$	50.8091	+	23.0149i	1.71278	+	0.775832i
$881$	26.5596			0.894815			0.447407	−	0.894330i	$-0.352347\pi$
$881$	26.5596			0.894815			0.447407	+	0.894330i	$0.352347\pi$
$882$	3.60250	+	2.53170i	0.121303	+	0.0852467i
$883$	14.0808	+	14.0808i	0.473857	+	0.473857i	0.903160	−	0.429304i	$-0.141241\pi$
$883$	14.0808	+	14.0808i	0.473857	+	0.473857i	−0.429304	+	0.903160i	$0.641241\pi$
$884$	−27.8836	−	0.434255i	−0.937829	−	0.0146056i
$885$	1.03096	−	3.28771i	0.0346555	−	0.110515i
$886$	27.2607	+	0.212263i	0.915839	+	0.00713112i
$887$	−2.80277	+	10.4601i	−0.0941079	+	0.351215i	−0.996883	−	0.0788981i	$-0.974860\pi$
$887$	−2.80277	+	10.4601i	−0.0941079	+	0.351215i	0.902775	+	0.430114i	$0.141526\pi$
$888$	39.8520	+	19.5788i	1.33735	+	0.657021i
$889$	−17.2676	−	9.96947i	−0.579138	−	0.334365i
$890$	−2.96267	+	3.78787i	−0.0993088	+	0.126970i
$891$	43.4303	+	35.5521i	1.45497	+	1.19104i
$892$	2.79455	−	9.81538i	0.0935683	−	0.328643i
$893$	3.51813	+	13.1299i	0.117730	+	0.439374i
$894$	52.8279	+	9.57387i	1.76683	+	0.320198i
$895$	−19.9136	+	47.8758i	−0.665637	+	1.60031i
$896$	1.74738	−	32.0279i	0.0583758	−	1.06998i
$897$	19.3726	−	13.6527i	0.646831	−	0.455850i
$898$	−8.98604	+	32.5213i	−0.299868	+	1.08525i
$899$		−	1.16629i		−	0.0388980i
$900$	17.5118	−	24.3585i	0.583728	−	0.811950i
$901$		−	41.9131i		−	1.39633i
$902$	−34.5717	−	9.55259i	−1.15111	−	0.318067i
$903$	−1.72918	−	19.0963i	−0.0575434	−	0.635485i
$904$	−11.9692	+	6.54253i	−0.398089	+	0.217601i
$905$	18.2235	−	43.8125i	0.605769	−	1.45638i
$906$	28.2321	−	10.1241i	0.937949	−	0.336350i
$907$	0.371774	+	1.38748i	0.0123445	+	0.0460705i	0.971823	−	0.235710i	$-0.0757416\pi$
$907$	0.371774	+	1.38748i	0.0123445	+	0.0460705i	−0.959479	+	0.281781i	$0.909075\pi$
$908$	5.46951	−	19.2107i	0.181512	−	0.637530i
$909$	−0.980997	−	5.37245i	−0.0325376	−	0.178193i
$910$	−25.5426	−	19.9781i	−0.846730	−	0.662267i
$911$	22.4953	+	12.9877i	0.745302	+	0.430300i	0.823994	−	0.566599i	$-0.191741\pi$
$911$	22.4953	+	12.9877i	0.745302	+	0.430300i	−0.0786919	+	0.996899i	$0.525074\pi$
$912$	1.23932	+	20.9246i	0.0410381	+	0.692883i
$913$	12.6324	−	47.1448i	0.418072	−	1.56027i
$914$	0.178740	−	22.9553i	0.00591220	−	0.759295i
$915$	19.0809	−	4.26144i	0.630796	−	0.140879i
$916$	0.0671676	−	4.31285i	0.00221928	−	0.142501i
$917$	−33.1974	−	33.1974i	−1.09627	−	1.09627i
$918$	20.0047	−	20.0578i	0.660253	−	0.662006i
$919$	31.5142			1.03956			0.519778	−	0.854301i	$-0.326015\pi$
$919$	31.5142			1.03956			0.519778	+	0.854301i	$0.326015\pi$
$920$	2.53300	+	23.7917i	0.0835105	+	0.784389i
$921$	9.55437	+	26.0044i	0.314827	+	0.856873i
$922$	−5.20613	−	5.28784i	−0.171455	−	0.174146i
$923$	−6.77387	+	25.2804i	−0.222965	+	0.832116i
$924$	20.2245	+	57.8111i	0.665339	+	1.90185i
$925$	−0.133660	+	45.3171i	−0.00439471	+	1.49002i
$926$	16.5529	+	9.72942i	0.543961	+	0.319729i
$927$	5.77222	+	12.1847i	0.189584	+	0.400200i
$928$	−16.5941	−	5.14646i	−0.544730	−	0.168941i
$929$	13.7084	+	7.91453i	0.449757	+	0.259667i	0.707728	−	0.706485i	$-0.249720\pi$
$929$	13.7084	+	7.91453i	0.449757	+	0.259667i	−0.257971	+	0.966153i	$0.583054\pi$
$930$	1.12843	−	1.74719i	0.0370027	−	0.0572927i
$931$	−1.56997	−	2.71927i	−0.0514537	−	0.0891205i
$932$	−4.98804	−	19.8468i	−0.163389	−	0.650105i
$933$	−3.03416	−	33.5081i	−0.0993341	−	1.09700i
$934$	−30.9824	+	17.5675i	−1.01378	+	0.574826i
$935$	−7.09527	+	53.2866i	−0.232040	+	1.74266i
$936$	−10.9938	+	28.6544i	−0.359345	+	0.936600i
$937$	34.5526	−	34.5526i	1.12878	−	1.12878i	0.138410	−	0.990375i	$-0.455801\pi$
$937$	34.5526	−	34.5526i	1.12878	−	1.12878i	0.990375	−	0.138410i	$-0.0441991\pi$
$938$	6.03017	+	1.66621i	0.196892	+	0.0544037i
$939$	−2.67807	+	15.4626i	−0.0873954	+	0.504602i
$940$	−15.7296	−	12.5015i	−0.513045	−	0.407754i
$941$	−26.1263	+	15.0840i	−0.851693	+	0.491725i	−0.861222	−	0.508229i	$-0.830300\pi$
$941$	−26.1263	+	15.0840i	−0.851693	+	0.491725i	0.00952879	+	0.999955i	$0.496967\pi$
$942$	−18.1608	−	26.2002i	−0.591709	−	0.853648i
$943$	−3.98198	−	14.8610i	−0.129671	−	0.483939i
$944$	−3.02491	−	1.87439i	−0.0984523	−	0.0610061i
$945$	32.6253	−	4.54898i	1.06130	−	0.147978i
$946$	17.4504	−	29.6887i	0.567361	−	0.965262i
$947$	0.629095	+	2.34781i	0.0204428	+	0.0762937i	0.975394	−	0.220470i	$-0.0707592\pi$
$947$	0.629095	+	2.34781i	0.0204428	+	0.0762937i	−0.954951	+	0.296764i	$0.904093\pi$
$948$	−2.53962	−	33.9200i	−0.0824830	−	1.10167i
$949$	−28.1411	−	48.7418i	−0.913499	−	1.58223i
$950$	−18.6411	+	10.4972i	−0.604797	+	0.340575i
$951$	8.90534	−	51.4175i	0.288776	−	1.66733i
$952$	30.0384	−	7.30126i	0.973549	−	0.236635i
$953$	18.8838	+	18.8838i	0.611705	+	0.611705i	0.943390	−	0.331685i	$-0.107617\pi$
$953$	18.8838	+	18.8838i	0.611705	+	0.611705i	−0.331685	+	0.943390i	$0.607617\pi$
$954$	−43.3186	−	15.8507i	−1.40249	−	0.513184i
$955$	−33.7288	−	44.0907i	−1.09144	−	1.42674i
$956$	−0.305082	+	19.5894i	−0.00986706	+	0.633567i
$957$	33.0394	−	2.99173i	1.06801	−	0.0967088i
$958$	7.14344	−	7.03305i	0.230794	−	0.227228i
$959$	23.4422	+	40.6031i	0.756989	+	1.31114i
$960$	−19.8799	−	23.7653i	−0.641621	−	0.767022i
$961$	−15.4279	+	26.7219i	−0.497674	+	0.861997i
$962$	−11.6501	−	44.8736i	−0.375615	−	1.44678i
$963$	−26.0010	−	2.11570i	−0.837869	−	0.0681776i
$964$	6.86461	−	3.82201i	0.221094	−	0.123099i
$965$	1.66690	−	2.16572i	0.0536593	−	0.0697170i
$966$	−16.9825	+	20.0448i	−0.546402	+	0.644932i
$967$	1.23005	−	4.59062i	0.0395559	−	0.147624i	−0.943324	−	0.331875i	$-0.892319\pi$
$967$	1.23005	−	4.59062i	0.0395559	−	0.147624i	0.982879	+	0.184250i	$0.0589856\pi$
$968$	−22.1916	+	75.7010i	−0.713264	+	2.43312i
$969$	−18.9621	+	6.96696i	−0.609152	+	0.223811i
$970$	1.72649	−	4.06132i	0.0554342	−	0.130401i
$971$	14.7042			0.471881			0.235941	−	0.971767i	$-0.424183\pi$
$971$	14.7042			0.471881			0.235941	+	0.971767i	$0.424183\pi$
$972$	−13.1651	−	28.2609i	−0.422269	−	0.906470i
$973$	0.357239	−	0.357239i	0.0114526	−	0.0114526i
$974$	−17.5263	−	30.9098i	−0.561580	−	0.990414i
$975$	−31.2045	+	2.73281i	−0.999344	+	0.0875200i
$976$	0.628786	−	20.1824i	0.0201270	−	0.646023i
$977$	52.7128	+	14.1243i	1.68643	+	0.451878i	0.969465	−	0.245230i	$-0.0788636\pi$
$977$	52.7128	+	14.1243i	1.68643	+	0.451878i	0.716966	+	0.697108i	$0.245530\pi$
$978$	−48.5011	+	4.01131i	−1.55089	+	0.128268i
$979$	−8.21291	−	4.74173i	−0.262486	−	0.151546i
$980$	4.25710	+	1.84899i	0.135988	+	0.0590637i
$981$	−4.49846	−	5.29539i	−0.143625	−	0.169069i
$982$	−8.59283	−	33.0976i	−0.274208	−	1.05619i
$983$	12.5498	+	46.8366i	0.400278	+	1.49386i	0.812602	+	0.582819i	$0.198050\pi$
$983$	12.5498	+	46.8366i	0.400278	+	1.49386i	−0.412324	+	0.911037i	$0.635283\pi$
$984$	14.9989	+	13.1141i	0.478148	+	0.418061i
$985$	−0.237732	−	0.576338i	−0.00757477	−	0.0183637i
$986$	0.130373	−	16.7437i	0.00415193	−	0.533226i
$987$	−1.98960	−	21.9723i	−0.0633297	−	0.699387i
$988$	15.7151	−	15.2331i	0.499963	−	0.484629i
$989$	14.7719			0.469718
$990$	52.3902	+	27.4851i	1.66507	+	0.873533i
$991$			44.9681i			1.42846i	0.699911	+	0.714230i	$0.253223\pi$
$991$			44.9681i			1.42846i	−0.699911	+	0.714230i	$0.746777\pi$
$992$	−1.45868	−	1.57692i	−0.0463132	−	0.0500674i
$993$	2.11915	+	3.00698i	0.0672492	+	0.0954236i
$994$	0.225894	−	29.0112i	0.00716492	−	0.920180i
$995$	−6.67052	−	2.77455i	−0.211470	−	0.0879592i
$996$	−17.6861	+	20.5488i	−0.560405	+	0.651112i
$997$	39.0518	−	10.4639i	1.23678	−	0.331395i	0.419566	−	0.907725i	$-0.362182\pi$
$997$	39.0518	−	10.4639i	1.23678	−	0.331395i	0.817217	+	0.576330i	$0.195516\pi$
$998$	5.87535	−	1.52536i	0.185981	−	0.0482846i
$999$	40.9985	+	23.1749i	1.29713	+	0.733222i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bo.a.43.6	✓	272
5.2	odd	4	inner	360.2.bo.a.187.40	yes	272
8.3	odd	2	inner	360.2.bo.a.43.51	yes	272
9.4	even	3	inner	360.2.bo.a.283.51	yes	272
40.27	even	4	inner	360.2.bo.a.187.51	yes	272
45.22	odd	12	inner	360.2.bo.a.67.51	yes	272
72.67	odd	6	inner	360.2.bo.a.283.40	yes	272
360.67	even	12	inner	360.2.bo.a.67.6	yes	272

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bo.a.43.6	✓	272	1.1	even	1	trivial
360.2.bo.a.43.51	yes	272	8.3	odd	2	inner
360.2.bo.a.67.6	yes	272	360.67	even	12	inner
360.2.bo.a.67.51	yes	272	45.22	odd	12	inner
360.2.bo.a.187.40	yes	272	5.2	odd	4	inner
360.2.bo.a.187.51	yes	272	40.27	even	4	inner
360.2.bo.a.283.40	yes	272	72.67	odd	6	inner
360.2.bo.a.283.51	yes	272	9.4	even	3	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.bo (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36313 - 0.376650i) q^{2} +(-0.727225 + 1.57199i) q^{3} +(1.71627 + 1.02685i) q^{4} +(2.06459 + 0.858752i) q^{5} +(1.58339 - 1.86892i) q^{6} +(2.73850 - 0.733779i) q^{7} +(-1.95274 - 2.04617i) q^{8} +(-1.94229 - 2.28638i) q^{9} +O(q^{10})\)	\(q+(-1.36313 - 0.376650i) q^{2} +(-0.727225 + 1.57199i) q^{3} +(1.71627 + 1.02685i) q^{4} +(2.06459 + 0.858752i) q^{5} +(1.58339 - 1.86892i) q^{6} +(2.73850 - 0.733779i) q^{7} +(-1.95274 - 2.04617i) q^{8} +(-1.94229 - 2.28638i) q^{9} +(-2.49087 - 1.94822i) q^{10} +(3.11812 - 5.40074i) q^{11} +(-2.86231 + 1.95120i) q^{12} +(3.49373 + 0.936143i) q^{13} +(-4.00932 - 0.0312183i) q^{14} +(-2.85137 + 2.62101i) q^{15} +(1.89116 + 3.52470i) q^{16} +(-2.72591 + 2.72591i) q^{17} +(1.78644 + 3.84820i) q^{18} -3.02550i q^{19} +(2.66159 + 3.59388i) q^{20} +(-0.838014 + 4.83851i) q^{21} +(-6.28461 + 6.18749i) q^{22} +(-3.65415 - 0.979127i) q^{23} +(4.63663 - 1.58166i) q^{24} +(3.52509 + 3.54595i) q^{25} +(-4.40983 - 2.59200i) q^{26} +(5.00663 - 1.39054i) q^{27} +(5.45349 + 1.55267i) q^{28} +(1.53565 - 2.65982i) q^{29} +(4.87400 - 2.49882i) q^{30} +(0.328863 - 0.189869i) q^{31} +(-1.25032 - 5.51695i) q^{32} +(6.22232 + 8.82919i) q^{33} +(4.74250 - 2.68907i) q^{34} +(6.28403 + 0.836738i) q^{35} +(-0.985724 - 5.91848i) q^{36} +(6.40883 + 6.40883i) q^{37} +(-1.13956 + 4.12416i) q^{38} +(-4.01233 + 4.81132i) q^{39} +(-2.27447 - 5.90142i) q^{40} +(2.03343 + 3.52201i) q^{41} +(2.96475 - 6.27990i) q^{42} +(-3.77169 + 1.01062i) q^{43} +(10.8973 - 6.06728i) q^{44} +(-2.04661 - 6.38838i) q^{45} +(4.61231 + 2.71102i) q^{46} +(-4.33973 + 1.16283i) q^{47} +(-6.91608 + 0.409626i) q^{48} +(0.898784 - 0.518913i) q^{49} +(-3.46959 - 6.16133i) q^{50} +(-2.30275 - 6.26744i) q^{51} +(5.03491 + 5.19421i) q^{52} +(-7.68791 + 7.68791i) q^{53} +(-7.34846 + 0.00974690i) q^{54} +(11.0755 - 8.47264i) q^{55} +(-6.84902 - 4.17055i) q^{56} +(4.75604 + 2.20022i) q^{57} +(-3.09512 + 3.04729i) q^{58} +(-0.770452 + 0.444821i) q^{59} +(-7.58510 + 1.57043i) q^{60} +(-4.37174 - 2.52402i) q^{61} +(-0.519799 + 0.134951i) q^{62} +(-6.99666 - 4.83603i) q^{63} +(-0.373605 + 7.99127i) q^{64} +(6.40922 + 4.93300i) q^{65} +(-5.15634 - 14.3790i) q^{66} +(-1.50718 - 0.403848i) q^{67} +(-7.47749 + 1.87929i) q^{68} +(4.19656 - 5.03223i) q^{69} +(-8.25081 - 3.50747i) q^{70} +7.23594i q^{71} +(-0.885522 + 8.43895i) q^{72} +(-11.0030 - 11.0030i) q^{73} +(-6.32221 - 11.1500i) q^{74} +(-8.13772 + 2.96270i) q^{75} +(3.10673 - 5.19257i) q^{76} +(4.57602 - 17.0780i) q^{77} +(7.28153 - 5.04722i) q^{78} +(-4.90963 + 8.50373i) q^{79} +(0.877627 + 8.90111i) q^{80} +(-1.45503 + 8.88160i) q^{81} +(-1.44528 - 5.56687i) q^{82} +(7.55982 - 2.02565i) q^{83} +(-6.40669 + 7.44367i) q^{84} +(-7.96877 + 3.28701i) q^{85} +(5.52197 + 0.0429965i) q^{86} +(3.06444 + 4.34831i) q^{87} +(-17.1397 + 4.16605i) q^{88} -1.52070i q^{89} +(0.383613 + 9.47907i) q^{90} +10.2545 q^{91} +(-5.26609 - 5.43271i) q^{92} +(0.0593146 + 0.655046i) q^{93} +(6.35362 + 0.0494720i) q^{94} +(2.59815 - 6.24642i) q^{95} +(9.58183 + 2.04657i) q^{96} +(0.361190 + 1.34798i) q^{97} +(-1.42061 + 0.368821i) q^{98} +(-18.4044 + 3.36060i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8}+O(q^{10}) \) 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8	\( 272 q - 2 q^{2} - 8 q^{3} - 8 q^{6} - 8 q^{8} - 8 q^{10} - 8 q^{11} - 10 q^{12} - 4 q^{16} - 16 q^{17} + 20 q^{18} + 14 q^{20} + 6 q^{22} - 4 q^{25} - 48 q^{26} - 8 q^{27} + 8 q^{28} - 34 q^{30} - 22 q^{32} + 4 q^{33} - 16 q^{35} - 8 q^{36} - 26 q^{38} - 2 q^{40} - 8 q^{41} - 66 q^{42} - 4 q^{43} - 40 q^{46} - 38 q^{48} - 42 q^{50} - 16 q^{51} + 14 q^{52} + 24 q^{56} + 16 q^{57} + 6 q^{58} + 14 q^{60} - 76 q^{62} - 4 q^{65} - 44 q^{66} - 4 q^{67} - 46 q^{68} + 18 q^{70} + 38 q^{72} - 16 q^{73} - 120 q^{75} - 38 q^{78} + 92 q^{80} - 32 q^{81} - 4 q^{83} - 40 q^{86} - 42 q^{88} - 14 q^{90} - 32 q^{91} + 52 q^{92} + 108 q^{96} - 4 q^{97} - 140 q^{98}+O(q^{100}) \) 272 * q - 2 * q^2 - 8 * q^3 - 8 * q^6 - 8 * q^8 - 8 * q^10 - 8 * q^11 - 10 * q^12 - 4 * q^16 - 16 * q^17 + 20 * q^18 + 14 * q^20 + 6 * q^22 - 4 * q^25 - 48 * q^26 - 8 * q^27 + 8 * q^28 - 34 * q^30 - 22 * q^32 + 4 * q^33 - 16 * q^35 - 8 * q^36 - 26 * q^38 - 2 * q^40 - 8 * q^41 - 66 * q^42 - 4 * q^43 - 40 * q^46 - 38 * q^48 - 42 * q^50 - 16 * q^51 + 14 * q^52 + 24 * q^56 + 16 * q^57 + 6 * q^58 + 14 * q^60 - 76 * q^62 - 4 * q^65 - 44 * q^66 - 4 * q^67 - 46 * q^68 + 18 * q^70 + 38 * q^72 - 16 * q^73 - 120 * q^75 - 38 * q^78 + 92 * q^80 - 32 * q^81 - 4 * q^83 - 40 * q^86 - 42 * q^88 - 14 * q^90 - 32 * q^91 + 52 * q^92 + 108 * q^96 - 4 * q^97 - 140 * q^98

Introduction

L-functions

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