LMFDB - Embedded newform 720.2.cf.a.11.67

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(11,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 2, 0]))

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

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

chi := DirichletCharacter("720.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.cf (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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$96$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.67
Character	$\chi$	$=$	720.11
Dual form			720.2.cf.a.131.67

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.796641 + 1.16849i) q^{2} +(0.727595 + 1.57182i) q^{3} +(-0.730726 + 1.86173i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(-1.25701 + 2.10236i) q^{6} +(-0.518056 + 0.897299i) q^{7} +(-2.75753 + 0.629287i) q^{8} +(-1.94121 + 2.28729i) q^{9} +(-0.467069 - 1.33486i) q^{10} +(-1.55740 + 0.417303i) q^{11} +(-3.45797 + 0.206019i) q^{12} +(1.74243 + 0.466882i) q^{13} +(-1.46119 + 0.109483i) q^{14} +(-0.295987 - 1.70657i) q^{15} +(-2.93208 - 2.72083i) q^{16} -1.18273i q^{17} +(-4.21912 - 0.446130i) q^{18} +(1.51361 + 1.51361i) q^{19} +(1.18768 - 1.60917i) q^{20} +(-1.78732 - 0.161418i) q^{21} +(-1.72830 - 1.48736i) q^{22} +(-3.38170 + 1.95243i) q^{23} +(-2.99549 - 3.87647i) q^{24} +(0.866025 + 0.500000i) q^{25} +(0.842543 + 2.40794i) q^{26} +(-5.00762 - 1.38700i) q^{27} +(-1.29197 - 1.62016i) q^{28} +(1.72168 - 0.461322i) q^{29} +(1.75831 - 1.70538i) q^{30} +(0.697025 - 0.402428i) q^{31} +(0.843441 - 5.59362i) q^{32} +(-1.78908 - 2.14431i) q^{33} +(1.38201 - 0.942214i) q^{34} +(0.732642 - 0.732642i) q^{35} +(-2.83983 - 5.28539i) q^{36} +(-2.03820 - 2.03820i) q^{37} +(-0.562830 + 2.97443i) q^{38} +(0.533929 + 3.07848i) q^{39} +(2.82645 + 0.105858i) q^{40} +(2.35653 + 4.08163i) q^{41} +(-1.23524 - 2.21706i) q^{42} +(2.76608 + 10.3231i) q^{43} +(0.361125 - 3.20439i) q^{44} +(2.46706 - 1.70693i) q^{45} +(-4.97539 - 2.39609i) q^{46} +(-1.26415 + 2.18958i) q^{47} +(2.14328 - 6.58835i) q^{48} +(2.96324 + 5.13248i) q^{49} +(0.105668 + 1.41026i) q^{50} +(1.85904 - 0.860551i) q^{51} +(-2.14245 + 2.90277i) q^{52} +(4.53096 - 4.53096i) q^{53} +(-2.36858 - 6.95628i) q^{54} +1.61234 q^{55} +(0.863899 - 2.80034i) q^{56} +(-1.27782 + 3.48041i) q^{57} +(1.91061 + 1.64425i) q^{58} +(-1.94446 + 7.25683i) q^{59} +(3.39346 + 0.695989i) q^{60} +(-0.829778 - 3.09678i) q^{61} +(1.02551 + 0.493875i) q^{62} +(-1.04673 - 2.92679i) q^{63} +(7.20800 - 3.47056i) q^{64} +(-1.56222 - 0.901947i) q^{65} +(1.08035 - 3.79877i) q^{66} +(0.0601583 - 0.224514i) q^{67} +(2.20193 + 0.864254i) q^{68} +(-5.52937 - 3.89484i) q^{69} +(1.43973 + 0.272430i) q^{70} -6.66133i q^{71} +(3.91359 - 7.52886i) q^{72} +0.623657i q^{73} +(0.757897 - 4.00532i) q^{74} +(-0.155792 + 1.72503i) q^{75} +(-3.92396 + 1.71190i) q^{76} +(0.432373 - 1.61364i) q^{77} +(-3.17181 + 3.07633i) q^{78} +(14.0767 + 8.12717i) q^{79} +(2.12797 + 3.38700i) q^{80} +(-1.46340 - 8.88023i) q^{81} +(-2.89202 + 6.00516i) q^{82} +(1.34707 + 5.02734i) q^{83} +(1.60656 - 3.20956i) q^{84} +(-0.306114 + 1.14243i) q^{85} +(-9.85888 + 11.4560i) q^{86} +(1.97780 + 2.37051i) q^{87} +(4.03197 - 2.13078i) q^{88} +3.14310 q^{89} +(3.95989 + 1.52292i) q^{90} +(-1.32161 + 1.32161i) q^{91} +(-1.16379 - 7.72251i) q^{92} +(1.13969 + 0.802791i) q^{93} +(-3.56557 + 0.267160i) q^{94} +(-1.07028 - 1.85378i) q^{95} +(9.40583 - 2.74416i) q^{96} +(-5.74419 + 9.94922i) q^{97} +(-3.63660 + 7.55125i) q^{98} +(2.06874 - 4.37230i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 12 q^{6} + 24 q^{12} + 20 q^{18} - 24 q^{24} + 24 q^{27} - 12 q^{36} + 48 q^{39} - 80 q^{42} + 24 q^{46} - 40 q^{48} - 192 q^{49} + 40 q^{51} + 12 q^{54} - 36 q^{58} + 72 q^{59} - 28 q^{60} + 72 q^{64}+ \cdots - 32 q^{99}+O(q^{100}) $ 384 * q - 12 * q^6 + 24 * q^12 + 20 * q^18 - 24 * q^24 + 24 * q^27 - 12 * q^36 + 48 * q^39 - 80 * q^42 + 24 * q^46 - 40 * q^48 - 192 * q^49 + 40 * q^51 + 12 * q^54 - 36 * q^58 + 72 * q^59 - 28 * q^60 + 72 * q^64 - 72 * q^66 - 156 * q^68 - 112 * q^72 - 168 * q^74 + 12 * q^76 - 116 * q^78 + 72 * q^82 - 120 * q^83 - 116 * q^84 - 36 * q^90 + 48 * q^93 + 20 * q^96 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.796641	+	1.16849i	0.563310	+	0.826245i
$2$	0.796641	+	1.16849i	0.563310	+	0.826245i
$3$	0.727595	+	1.57182i	0.420077	+	0.907488i
$3$	0.727595	+	1.57182i	0.420077	+	0.907488i
$4$	−0.730726	+	1.86173i	−0.365363	+	0.930865i
$5$	−0.965926	−	0.258819i	−0.431975	−	0.115747i
$5$	−0.965926	−	0.258819i	−0.431975	−	0.115747i
$6$	−1.25701	+	2.10236i	−0.513174	+	0.858284i
$7$	−0.518056	+	0.897299i	−0.195807	+	0.339147i	−0.947165	−	0.320748i	$-0.896066\pi$
$7$	−0.518056	+	0.897299i	−0.195807	+	0.339147i	0.751358	+	0.659895i	$0.229399\pi$
$8$	−2.75753	+	0.629287i	−0.974936	+	0.222486i
$9$	−1.94121	+	2.28729i	−0.647070	+	0.762430i
$10$	−0.467069	−	1.33486i	−0.147700	−	0.422119i
$11$	−1.55740	+	0.417303i	−0.469573	+	0.125822i	−0.485843	−	0.874046i	$-0.661487\pi$
$11$	−1.55740	+	0.417303i	−0.469573	+	0.125822i	0.0162703	+	0.999868i	$0.494821\pi$
$12$	−3.45797	+	0.206019i	−0.998230	+	0.0594726i
$13$	1.74243	+	0.466882i	0.483262	+	0.129490i	0.492221	−	0.870470i	$-0.336185\pi$
$13$	1.74243	+	0.466882i	0.483262	+	0.129490i	−0.00895891	+	0.999960i	$0.502852\pi$
$14$	−1.46119	+	0.109483i	−0.390519	+	0.0292607i
$15$	−0.295987	−	1.70657i	−0.0764235	−	0.440635i
$16$	−2.93208	−	2.72083i	−0.733020	−	0.680207i
$17$		−	1.18273i		−	0.286855i	−0.989661	−	0.143427i	$-0.954188\pi$
$17$		−	1.18273i		−	0.286855i	0.989661	−	0.143427i	$-0.0458124\pi$
$18$	−4.21912	−	0.446130i	−0.994456	−	0.105154i
$19$	1.51361	+	1.51361i	0.347245	+	0.347245i	0.859083	−	0.511837i	$-0.171035\pi$
$19$	1.51361	+	1.51361i	0.347245	+	0.347245i	−0.511837	+	0.859083i	$0.671035\pi$
$20$	1.18768	−	1.60917i	0.265573	−	0.359821i
$21$	−1.78732	−	0.161418i	−0.390026	−	0.0352243i
$22$	−1.72830	−	1.48736i	−0.368475	−	0.317106i
$23$	−3.38170	+	1.95243i	−0.705134	+	0.407109i	−0.809257	−	0.587455i	$-0.800130\pi$
$23$	−3.38170	+	1.95243i	−0.705134	+	0.407109i	0.104123	+	0.994564i	$0.466797\pi$
$24$	−2.99549	−	3.87647i	−0.611452	−	0.791281i
$25$	0.866025	+	0.500000i	0.173205	+	0.100000i
$26$	0.842543	+	2.40794i	0.165236	+	0.472236i
$27$	−5.00762	−	1.38700i	−0.963716	−	0.266929i
$28$	−1.29197	−	1.62016i	−0.244160	−	0.306181i
$29$	1.72168	−	0.461322i	0.319708	−	0.0856654i	−0.0953964	−	0.995439i	$-0.530412\pi$
$29$	1.72168	−	0.461322i	0.319708	−	0.0856654i	0.415104	+	0.909774i	$0.363745\pi$
$30$	1.75831	−	1.70538i	0.321023	−	0.311359i
$31$	0.697025	−	0.402428i	0.125189	−	0.0722781i	−0.436098	−	0.899899i	$-0.643640\pi$
$31$	0.697025	−	0.402428i	0.125189	−	0.0722781i	0.561287	+	0.827621i	$0.310306\pi$
$32$	0.843441	−	5.59362i	0.149101	−	0.988822i
$33$	−1.78908	−	2.14431i	−0.311439	−	0.373277i
$34$	1.38201	−	0.942214i	0.237013	−	0.161588i
$35$	0.732642	−	0.732642i	0.123839	−	0.123839i
$36$	−2.83983	−	5.28539i	−0.473304	−	0.880899i
$37$	−2.03820	−	2.03820i	−0.335078	−	0.335078i	0.519433	−	0.854511i	$-0.326143\pi$
$37$	−2.03820	−	2.03820i	−0.335078	−	0.335078i	−0.854511	+	0.519433i	$0.826143\pi$
$38$	−0.562830	+	2.97443i	−0.0913030	+	0.482517i
$39$	0.533929	+	3.07848i	0.0854971	+	0.492951i
$40$	2.82645	+	0.105858i	0.446900	+	0.0167377i
$41$	2.35653	+	4.08163i	0.368028	+	0.637443i	0.989257	−	0.146186i	$-0.0466998\pi$
$41$	2.35653	+	4.08163i	0.368028	+	0.637443i	−0.621229	+	0.783629i	$0.713366\pi$
$42$	−1.23524	−	2.21706i	−0.190602	−	0.342099i
$43$	2.76608	+	10.3231i	0.421823	+	1.57426i	0.770765	+	0.637119i	$0.219874\pi$
$43$	2.76608	+	10.3231i	0.421823	+	1.57426i	−0.348943	+	0.937144i	$0.613459\pi$
$44$	0.361125	−	3.20439i	0.0544416	−	0.483080i
$45$	2.46706	−	1.70693i	0.367768	−	0.254454i
$46$	−4.97539	−	2.39609i	−0.733581	−	0.353285i
$47$	−1.26415	+	2.18958i	−0.184396	+	0.319383i	−0.943373	−	0.331735i	$-0.892366\pi$
$47$	−1.26415	+	2.18958i	−0.184396	+	0.319383i	0.758977	+	0.651117i	$0.225699\pi$
$48$	2.14328	−	6.58835i	0.309355	−	0.950947i
$49$	2.96324	+	5.13248i	0.423319	+	0.733211i
$50$	0.105668	+	1.41026i	0.0149437	+	0.199441i
$51$	1.85904	−	0.860551i	0.260317	−	0.120501i
$52$	−2.14245	+	2.90277i	−0.297104	+	0.402541i
$53$	4.53096	−	4.53096i	0.622375	−	0.622375i	−0.323763	−	0.946138i	$-0.604948\pi$
$53$	4.53096	−	4.53096i	0.622375	−	0.622375i	0.946138	+	0.323763i	$0.104948\pi$
$54$	−2.36858	−	6.95628i	−0.322323	−	0.946630i
$55$	1.61234			0.217407
$56$	0.863899	−	2.80034i	0.115443	−	0.374211i
$57$	−1.27782	+	3.48041i	−0.169251	+	0.460991i
$58$	1.91061	+	1.64425i	0.250875	+	0.215901i
$59$	−1.94446	+	7.25683i	−0.253147	+	0.944759i	0.715964	+	0.698137i	$0.245987\pi$
$59$	−1.94446	+	7.25683i	−0.253147	+	0.944759i	−0.969112	+	0.246622i	$0.920679\pi$
$60$	3.39346	+	0.695989i	0.438094	+	0.0898518i
$61$	−0.829778	−	3.09678i	−0.106242	−	0.396501i	0.892241	−	0.451560i	$-0.149132\pi$
$61$	−0.829778	−	3.09678i	−0.106242	−	0.396501i	−0.998483	+	0.0550583i	$0.982466\pi$
$62$	1.02551	+	0.493875i	0.130240	+	0.0627221i
$63$	−1.04673	−	2.92679i	−0.131875	−	0.368741i
$64$	7.20800	−	3.47056i	0.901000	−	0.433820i
$65$	−1.56222	−	0.901947i	−0.193769	−	0.111873i
$66$	1.08035	−	3.79877i	0.132982	−	0.467596i
$67$	0.0601583	−	0.224514i	0.00734951	−	0.0274287i	−0.962154	−	0.272507i	$-0.912147\pi$
$67$	0.0601583	−	0.224514i	0.00734951	−	0.0274287i	0.969503	+	0.245079i	$0.0788138\pi$
$68$	2.20193	+	0.864254i	0.267023	+	0.104806i
$69$	−5.52937	−	3.89484i	−0.665658	−	0.468883i
$70$	1.43973	+	0.272430i	0.172081	+	0.0325616i
$71$		−	6.66133i		−	0.790555i	−0.918562	−	0.395277i	$-0.870648\pi$
$71$		−	6.66133i		−	0.790555i	0.918562	−	0.395277i	$-0.129352\pi$
$72$	3.91359	−	7.52886i	0.461221	−	0.887285i
$73$			0.623657i			0.0729935i	0.999334	+	0.0364968i	$0.0116199\pi$
$73$			0.623657i			0.0729935i	−0.999334	+	0.0364968i	$0.988380\pi$
$74$	0.757897	−	4.00532i	0.0881037	−	0.465609i
$75$	−0.155792	+	1.72503i	−0.0179893	+	0.199189i
$76$	−3.92396	+	1.71190i	−0.450109	+	0.196368i
$77$	0.432373	−	1.61364i	0.0492735	−	0.183891i
$78$	−3.17181	+	3.07633i	−0.359137	+	0.348326i
$79$	14.0767	+	8.12717i	1.58375	+	0.914378i	0.994305	+	0.106570i	$0.0339867\pi$
$79$	14.0767	+	8.12717i	1.58375	+	0.914378i	0.589445	+	0.807809i	$0.299347\pi$
$80$	2.12797	+	3.38700i	0.237914	+	0.378678i
$81$	−1.46340	−	8.88023i	−0.162600	−	0.986692i
$82$	−2.89202	+	6.00516i	−0.319370	+	0.663159i
$83$	1.34707	+	5.02734i	0.147860	+	0.551823i	0.999611	+	0.0278758i	$0.00887429\pi$
$83$	1.34707	+	5.02734i	0.147860	+	0.551823i	−0.851751	+	0.523947i	$0.824459\pi$
$84$	1.60656	−	3.20956i	0.175290	−	0.350192i
$85$	−0.306114	+	1.14243i	−0.0332027	+	0.123914i
$86$	−9.85888	+	11.4560i	−1.06311	+	1.23533i
$87$	1.97780	+	2.37051i	0.212042	+	0.254145i
$88$	4.03197	−	2.13078i	0.429810	−	0.227142i
$89$	3.14310			0.333168			0.166584	−	0.986027i	$-0.446726\pi$
$89$	3.14310			0.333168			0.166584	+	0.986027i	$0.446726\pi$
$90$	3.95989	+	1.52292i	0.417409	+	0.160530i
$91$	−1.32161	+	1.32161i	−0.138542	+	0.138542i
$92$	−1.16379	−	7.72251i	−0.121334	−	0.805127i
$93$	1.13969	+	0.802791i	0.118181	+	0.0832455i
$94$	−3.56557	+	0.267160i	−0.367760	+	0.0275555i
$95$	−1.07028	−	1.85378i	−0.109809	−	0.190194i
$96$	9.40583	−	2.74416i	0.959978	−	0.280075i
$97$	−5.74419	+	9.94922i	−0.583234	+	1.01019i	0.411859	+	0.911247i	$0.364880\pi$
$97$	−5.74419	+	9.94922i	−0.583234	+	1.01019i	−0.995093	+	0.0989431i	$0.968454\pi$
$98$	−3.63660	+	7.55125i	−0.367352	+	0.762791i
$99$	2.06874	−	4.37230i	0.207916	−	0.439432i
$100$	−1.56369	+	1.24694i	−0.156369	+	0.124694i
$101$	−1.68243	−	6.27890i	−0.167408	−	0.624774i	−0.997721	−	0.0674767i	$-0.978505\pi$
$101$	−1.68243	−	6.27890i	−0.167408	−	0.624774i	0.830313	−	0.557297i	$-0.188162\pi$
$102$	2.48653	+	1.48671i	0.246203	+	0.147207i
$103$	8.37067	+	14.4984i	0.824786	+	1.42857i	0.902083	+	0.431563i	$0.142038\pi$
$103$	8.37067	+	14.4984i	0.824786	+	1.42857i	−0.0772963	+	0.997008i	$0.524629\pi$
$104$	−5.09861	−	0.190957i	−0.499960	−	0.0187249i
$105$	1.68464	+	0.618511i	0.164404	+	0.0603605i
$106$	8.90391	+	1.68482i	0.864824	+	0.163644i
$107$	−9.77886	−	9.77886i	−0.945358	−	0.945358i	0.0532242	−	0.998583i	$-0.483050\pi$
$107$	−9.77886	−	9.77886i	−0.945358	−	0.945358i	−0.998583	+	0.0532242i	$0.983050\pi$
$108$	6.24142	−	8.30931i	0.600581	−	0.799564i
$109$	13.9094	−	13.9094i	1.33228	−	1.33228i	0.428945	−	0.903330i	$-0.358885\pi$
$109$	13.9094	−	13.9094i	1.33228	−	1.33228i	0.903330	−	0.428945i	$-0.141115\pi$
$110$	1.28445	+	1.88400i	0.122468	+	0.179632i
$111$	1.72069	−	4.68666i	0.163321	−	0.444838i
$112$	3.96038	−	1.22141i	0.374221	−	0.115412i
$113$	−6.92489	+	3.99809i	−0.651439	+	0.376108i	−0.789007	−	0.614384i	$-0.789405\pi$
$113$	−6.92489	+	3.99809i	−0.651439	+	0.376108i	0.137568	+	0.990492i	$0.456071\pi$
$114$	−5.08477	+	1.27952i	−0.476233	+	0.119838i
$115$	3.77180	−	1.01065i	0.351722	−	0.0942437i
$116$	−0.399217	+	3.54240i	−0.0370664	+	0.328904i
$117$	−4.45031	+	3.07912i	−0.411432	+	0.284665i
$118$	−10.0286	+	3.50901i	−0.923204	+	0.323031i
$119$	1.06126	+	0.612722i	0.0972860	+	0.0561681i
$120$	1.89012	+	4.51967i	0.172543	+	0.412588i
$121$	−7.27493	+	4.20019i	−0.661358	+	0.381835i
$122$	2.95751	−	3.43660i	0.267760	−	0.311136i
$123$	−4.70097	+	6.67380i	−0.423872	+	0.601756i
$124$	0.239877	+	1.59174i	0.0215416	+	0.142942i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	2.58605	−	3.55469i	0.230384	−	0.316677i
$127$			8.00350i			0.710196i	0.934829	+	0.355098i	$0.115552\pi$
$127$			8.00350i			0.710196i	−0.934829	+	0.355098i	$0.884448\pi$
$128$	9.79749	+	5.65766i	0.865984	+	0.500072i
$129$	−14.2135	+	11.8588i	−1.25143	+	1.04411i
$130$	−0.190613	−	2.54396i	−0.0167179	−	0.223120i
$131$	4.75537	+	1.27420i	0.415478	+	0.111327i	0.460502	−	0.887659i	$-0.347670\pi$
$131$	4.75537	+	1.27420i	0.415478	+	0.111327i	−0.0450233	+	0.998986i	$0.514336\pi$
$132$	5.29946	−	1.76388i	0.461259	−	0.153526i
$133$	−2.14229	+	0.574025i	−0.185760	+	0.0497743i
$134$	0.310266	−	0.108563i	0.0268029	−	0.00937839i
$135$	4.47800	+	2.63581i	0.385405	+	0.226854i
$136$	0.744278	+	3.26143i	0.0638213	+	0.279665i
$137$	−3.03086	+	5.24961i	−0.258944	+	0.448504i	−0.965959	−	0.258694i	$-0.916708\pi$
$137$	−3.03086	+	5.24961i	−0.258944	+	0.448504i	0.707015	+	0.707198i	$0.250041\pi$
$138$	0.146149	−	9.56379i	0.0124410	−	0.814124i
$139$	13.7012	+	3.67121i	1.16212	+	0.311388i	0.787811	−	0.615917i	$-0.211214\pi$
$139$	13.7012	+	3.67121i	1.16212	+	0.311388i	0.374306	+	0.927305i	$0.377881\pi$
$140$	0.828621	+	1.89934i	0.0700312	+	0.160524i
$141$	−4.36140	−	0.393890i	−0.367296	−	0.0331715i
$142$	7.78368	−	5.30669i	0.653192	−	0.445328i
$143$	−2.90848			−0.243220
$144$	11.9151	−	1.42482i	0.992926	−	0.118735i
$145$	−1.78241			−0.148021
$146$	−0.728735	+	0.496831i	−0.0603106	+	0.0411180i
$147$	−5.91127	+	8.39203i	−0.487553	+	0.692163i
$148$	5.28394	−	2.30521i	0.434337	−	0.189487i
$149$	−20.7227	−	5.55262i	−1.69767	−	0.454888i	−0.725316	−	0.688416i	$-0.758307\pi$
$149$	−20.7227	−	5.55262i	−1.69767	−	0.454888i	−0.972350	+	0.233527i	$0.924973\pi$
$150$	−2.13979	+	1.19219i	−0.174713	+	0.0973418i
$151$	8.34896	−	14.4608i	0.679429	−	1.17681i	−0.295724	−	0.955273i	$-0.595561\pi$
$151$	8.34896	−	14.4608i	0.679429	−	1.17681i	0.975153	−	0.221532i	$-0.0711058\pi$
$152$	−5.12632	−	3.22133i	−0.415799	−	0.261285i
$153$	2.70525	+	2.29593i	0.218707	+	0.185615i
$154$	2.22996	−	0.780268i	0.179695	−	0.0628758i
$155$	−0.777430	+	0.208312i	−0.0624447	+	0.0167320i
$156$	−6.12145	−	1.25549i	−0.490108	−	0.100520i
$157$	6.17591	+	1.65483i	0.492892	+	0.132070i	0.496699	−	0.867923i	$-0.334545\pi$
$157$	6.17591	+	1.65483i	0.492892	+	0.132070i	−0.00380745	+	0.999993i	$0.501212\pi$
$158$	1.71756	+	22.9229i	0.136642	+	1.82364i
$159$	10.4185	+	3.82513i	0.826243	+	0.303352i
$160$	−2.26244	+	5.18473i	−0.178861	+	0.409889i
$161$		−	4.04587i		−	0.318859i
$162$	9.21063	−	8.78432i	0.723655	−	0.690162i
$163$	4.55692	+	4.55692i	0.356925	+	0.356925i	0.862678	−	0.505753i	$-0.168785\pi$
$163$	4.55692	+	4.55692i	0.356925	+	0.356925i	−0.505753	+	0.862678i	$0.668785\pi$
$164$	−9.32086	+	1.40467i	−0.727837	+	0.109686i
$165$	1.17313	+	2.53430i	0.0913279	+	0.197295i
$166$	−4.80125	+	5.57903i	−0.372650	+	0.433016i
$167$	0.641453	−	0.370343i	0.0496371	−	0.0286580i	−0.474976	−	0.879999i	$-0.657543\pi$
$167$	0.641453	−	0.370343i	0.0496371	−	0.0286580i	0.524613	+	0.851341i	$0.324210\pi$
$168$	5.03019	−	0.679623i	0.388087	−	0.0524341i
$169$	−8.44026	−	4.87298i	−0.649250	−	0.374845i
$170$	−1.57878	+	0.552418i	−0.121087	+	0.0423685i
$171$	−6.40029	+	0.523831i	−0.489443	+	0.0400583i
$172$	−21.2401	−	2.39370i	−1.61954	−	0.182518i
$173$	10.5059	−	2.81504i	0.798746	−	0.214023i	0.163713	−	0.986508i	$-0.447653\pi$
$173$	10.5059	−	2.81504i	0.798746	−	0.214023i	0.635034	+	0.772485i	$0.280986\pi$
$174$	−1.19431	+	4.19947i	−0.0905404	+	0.318361i
$175$	−0.897299	+	0.518056i	−0.0678294	+	0.0391613i
$176$	5.70182	+	3.01385i	0.429791	+	0.227177i
$177$	−12.8212	+	2.22370i	−0.963699	+	0.167144i
$178$	2.50392	+	3.67267i	0.187677	+	0.275278i
$179$	9.85890	−	9.85890i	0.736889	−	0.736889i	−0.235086	−	0.971975i	$-0.575537\pi$
$179$	9.85890	−	9.85890i	0.736889	−	0.736889i	0.971975	+	0.235086i	$0.0755372\pi$
$180$	1.37510	+	5.84030i	0.102494	+	0.435310i
$181$	−12.2180	−	12.2180i	−0.908157	−	0.908157i	0.0879662	−	0.996123i	$-0.471963\pi$
$181$	−12.2180	−	12.2180i	−0.908157	−	0.908157i	−0.996123	+	0.0879662i	$0.971963\pi$
$182$	−2.59713	−	0.491435i	−0.192512	−	0.0364276i
$183$	4.26382	−	3.55746i	0.315190	−	0.262975i
$184$	8.09653	−	7.51195i	0.596884	−	0.553788i
$185$	1.44122	+	2.49627i	0.105961	+	0.183530i
$186$	−0.0301237	+	1.97125i	−0.00220877	+	0.144539i
$187$	0.493558	+	1.84199i	0.0360926	+	0.134699i
$188$	−3.15265	−	3.95349i	−0.229931	−	0.288338i
$189$	3.83878	−	3.77478i	0.279230	−	0.274575i
$190$	1.31349	−	2.72741i	0.0952907	−	0.197867i
$191$	−11.3382	+	19.6384i	−0.820407	+	1.42099i	0.0849730	+	0.996383i	$0.472920\pi$
$191$	−11.3382	+	19.6384i	−0.820407	+	1.42099i	−0.905380	+	0.424603i	$0.860414\pi$
$192$	10.6996	+	8.80448i	0.772176	+	0.635409i
$193$	8.64567	+	14.9747i	0.622329	+	1.07790i	0.989051	+	0.147574i	$0.0471466\pi$
$193$	8.64567	+	14.9747i	0.622329	+	1.07790i	−0.366722	+	0.930330i	$0.619520\pi$
$194$	−16.2016	+	1.21395i	−1.16321	+	0.0871565i
$195$	0.281032	−	3.11177i	0.0201251	−	0.222839i
$196$	−11.7206	+	1.76631i	−0.837186	+	0.126165i
$197$	7.92962	−	7.92962i	0.564962	−	0.564962i	−0.365751	−	0.930713i	$-0.619188\pi$
$197$	7.92962	−	7.92962i	0.564962	−	0.564962i	0.930713	+	0.365751i	$0.119188\pi$
$198$	6.75702	−	1.06585i	0.480200	−	0.0757468i
$199$	17.7321			1.25699			0.628497	−	0.777812i	$-0.283670\pi$
$199$	17.7321			1.25699			0.628497	+	0.777812i	$0.283670\pi$
$200$	−2.70274	−	0.833789i	−0.191112	−	0.0589578i
$201$	0.396665	−	0.0687974i	0.0279786	−	0.00485260i
$202$	5.99652	−	6.96792i	0.421914	−	0.490261i
$203$	−0.477981	+	1.78385i	−0.0335477	+	0.125202i
$204$	0.243666	+	4.08985i	0.0170600	+	0.286347i
$205$	−1.21983	−	4.55246i	−0.0851965	−	0.317958i
$206$	−10.2728	+	21.3311i	−0.715740	+	1.48620i
$207$	2.09883	−	11.5250i	0.145879	−	0.801044i
$208$	−3.83863	−	6.10978i	−0.266161	−	0.423637i
$209$	−2.98892	−	1.72566i	−0.206748	−	0.119366i
$210$	0.619334	+	2.46122i	0.0427381	+	0.169840i
$211$	2.15062	−	8.02624i	0.148055	−	0.552549i	−0.851545	−	0.524281i	$-0.824334\pi$
$211$	2.15062	−	8.02624i	0.148055	−	0.552549i	0.999600	−	0.0282679i	$-0.00899916\pi$
$212$	5.12453	+	11.7463i	0.351954	+	0.806740i
$213$	10.4704	−	4.84675i	0.717419	−	0.332094i
$214$	3.63624	−	19.2167i	0.248568	−	1.31363i
$215$		−	10.6873i		−	0.728867i
$216$	14.6815	+	0.673484i	0.998949	+	0.0458248i
$217$			0.833920i			0.0566102i
$218$	27.3337	+	5.17215i	1.85127	+	0.350302i
$219$	−0.980274	+	0.453770i	−0.0662408	+	0.0306629i
$220$	−1.17818	+	3.00174i	−0.0794326	+	0.202377i
$221$	0.552197	−	2.06083i	0.0371448	−	0.138626i
$222$	6.84707	−	1.72298i	0.459545	−	0.115639i
$223$	−12.1243	−	6.99995i	−0.811901	−	0.468751i	0.0357147	−	0.999362i	$-0.488629\pi$
$223$	−12.1243	−	6.99995i	−0.811901	−	0.468751i	−0.847616	+	0.530611i	$0.821963\pi$
$224$	4.58220	+	3.65463i	0.306161	+	0.244185i
$225$	−2.82478	+	1.01025i	−0.188319	+	0.0673498i
$226$	−10.1884	−	4.90661i	−0.677720	−	0.326383i
$227$	−0.120374	−	0.449244i	−0.00798953	−	0.0298173i	0.961816	−	0.273697i	$-0.0882465\pi$
$227$	−0.120374	−	0.449244i	−0.00798953	−	0.0298173i	−0.969806	+	0.243880i	$0.921580\pi$
$228$	−5.54584	−	4.92218i	−0.367282	−	0.325979i
$229$	1.98404	−	7.40455i	0.131109	−	0.489306i	−0.868874	−	0.495033i	$-0.835156\pi$
$229$	1.98404	−	7.40455i	0.131109	−	0.489306i	0.999984	+	0.00572638i	$0.00182277\pi$
$230$	4.18570	+	3.60218i	0.275997	+	0.237520i
$231$	2.85093	−	0.494464i	0.187578	−	0.0325334i
$232$	−4.45728	+	2.35554i	−0.292635	+	0.154649i
$233$	16.7359			1.09641			0.548204	−	0.836345i	$-0.315312\pi$
$233$	16.7359			1.09641			0.548204	+	0.836345i	$0.315312\pi$
$234$	−7.14322	−	2.74718i	−0.466967	−	0.179589i
$235$	1.78778	−	1.78778i	0.116622	−	0.116622i
$236$	−12.0894	−	8.92282i	−0.786953	−	0.580826i
$237$	−2.53230	+	28.0392i	−0.164490	+	1.82134i
$238$	0.129490	+	1.72819i	0.00839357	+	0.112022i
$239$	9.47357	+	16.4087i	0.612794	+	1.06139i	0.990767	+	0.135574i	$0.0432879\pi$
$239$	9.47357	+	16.4087i	0.612794	+	1.06139i	−0.377973	+	0.925817i	$0.623379\pi$
$240$	−3.77544	+	5.80914i	−0.243703	+	0.374978i
$241$	9.12780	−	15.8098i	0.587973	−	1.01840i	−0.406524	−	0.913640i	$-0.633259\pi$
$241$	9.12780	−	15.8098i	0.587973	−	1.01840i	0.994498	−	0.104760i	$-0.0334074\pi$
$242$	−10.7034	−	5.15463i	−0.688039	−	0.331352i
$243$	12.8933	−	8.76141i	0.827107	−	0.562045i
$244$	6.37170	+	0.718071i	0.407906	+	0.0459698i
$245$	−1.53388	−	5.72453i	−0.0979963	−	0.365727i
$246$	−11.5432	−	0.176397i	−0.735970	−	0.0112467i
$247$	1.93068	+	3.34403i	0.122846	+	0.212775i
$248$	−1.66883	+	1.54834i	−0.105971	+	0.0983195i
$249$	−6.92193	+	5.77522i	−0.438660	+	0.365990i
$250$	0.262935	−	1.38956i	0.0166295	−	0.0878832i
$251$	−19.2173	−	19.2173i	−1.21298	−	1.21298i	−0.970040	−	0.242944i	$-0.921887\pi$
$251$	−19.2173	−	19.2173i	−1.21298	−	1.21298i	−0.242944	−	0.970040i	$-0.578113\pi$
$252$	6.21377	+	0.189955i	0.391431	+	0.0119661i
$253$	4.45190	−	4.45190i	0.279889	−	0.279889i
$254$	−9.35199	+	6.37592i	−0.586796	+	0.400061i
$255$	−2.01842	+	0.350074i	−0.126398	+	0.0219225i
$256$	1.19417	+	15.9554i	0.0746359	+	0.997211i
$257$	16.2984	−	9.40986i	1.01666	−	0.586971i	0.103528	−	0.994627i	$-0.466987\pi$
$257$	16.2984	−	9.40986i	1.01666	−	0.586971i	0.913136	+	0.407656i	$0.133654\pi$
$258$	−25.1799	−	7.16105i	−1.56763	−	0.445827i
$259$	2.88477	−	0.772973i	0.179251	−	0.0480302i
$260$	2.82073	−	2.24935i	0.174935	−	0.139499i
$261$	−2.28696	+	4.83350i	−0.141559	+	0.299186i
$262$	2.29944	+	6.57166i	0.142060	+	0.405999i
$263$	2.06273	+	1.19092i	0.127193	+	0.0734350i	0.562247	−	0.826970i	$-0.309937\pi$
$263$	2.06273	+	1.19092i	0.127193	+	0.0734350i	−0.435053	+	0.900405i	$0.643271\pi$
$264$	6.28284	+	4.78718i	0.386682	+	0.294630i
$265$	−5.54927	+	3.20387i	−0.340889	+	0.196812i
$266$	−2.37738	−	2.04595i	−0.145766	−	0.125445i
$267$	2.28690	+	4.94037i	0.139956	+	0.302346i
$268$	0.374025	+	0.276057i	0.0228472	+	0.0168628i
$269$	−8.26651	−	8.26651i	−0.504018	−	0.504018i	0.408666	−	0.912684i	$-0.365994\pi$
$269$	−8.26651	−	8.26651i	−0.504018	−	0.504018i	−0.912684	+	0.408666i	$0.865994\pi$
$270$	0.487452	+	7.33228i	0.0296654	+	0.446229i
$271$			0.259099i			0.0157391i	0.999969	+	0.00786956i	$0.00250499\pi$
$271$			0.259099i			0.0157391i	−0.999969	+	0.00786956i	$0.997495\pi$
$272$	−3.21801	+	3.46787i	−0.195121	+	0.210270i
$273$	−3.03892	−	1.11573i	−0.183924	−	0.0675269i
$274$	−8.54861	+	0.640528i	−0.516440	+	0.0386957i
$275$	−1.55740	−	0.417303i	−0.0939146	−	0.0251643i
$276$	11.2916	−	7.44813i	0.679674	−	0.448325i
$277$	−1.97304	+	0.528673i	−0.118548	+	0.0317649i	−0.317605	−	0.948223i	$-0.602879\pi$
$277$	−1.97304	+	0.528673i	−0.118548	+	0.0317649i	0.199057	+	0.979988i	$0.436212\pi$
$278$	6.62514	+	18.9343i	0.397349	+	1.13560i
$279$	−0.432603	+	2.37550i	−0.0258993	+	0.142217i
$280$	−1.55924	+	2.48133i	−0.0931826	+	0.148288i
$281$	−2.68369	+	4.64828i	−0.160095	+	0.277293i	−0.934903	−	0.354904i	$-0.884514\pi$
$281$	−2.68369	+	4.64828i	−0.160095	+	0.277293i	0.774807	+	0.632197i	$0.217847\pi$
$282$	−3.01422	−	5.41003i	−0.179494	−	0.322163i
$283$	21.3517	+	5.72118i	1.26923	+	0.340089i	0.829735	−	0.558157i	$-0.188491\pi$
$283$	21.3517	+	5.72118i	1.26923	+	0.340089i	0.439493	+	0.898246i	$0.355158\pi$
$284$	12.4016	+	4.86761i	0.735900	+	0.288840i
$285$	2.13507	−	3.03109i	0.126471	−	0.179546i
$286$	−2.31702	−	3.39853i	−0.137008	−	0.200959i
$287$	−4.88325			−0.288249
$288$	11.1569	+	12.7876i	0.657429	+	0.753516i
$289$	15.6011			0.917714
$290$	−1.41994	−	2.08273i	−0.0833819	−	0.122302i
$291$	−19.8178	−	1.78980i	−1.16174	−	0.104920i
$292$	−1.16108	−	0.455722i	−0.0679471	−	0.0266691i
$293$	−21.4536	−	5.74848i	−1.25333	−	0.335830i	−0.429711	−	0.902967i	$-0.641384\pi$
$293$	−21.4536	−	5.74848i	−1.25333	−	0.335830i	−0.823624	+	0.567137i	$0.808051\pi$
$294$	−14.5151	−	0.221813i	−0.846540	−	0.0129364i
$295$	3.75641	−	6.50630i	0.218707	−	0.378811i
$296$	6.90302	+	4.33779i	0.401230	+	0.252129i
$297$	8.37765	+	0.0704198i	0.486121	+	0.00408617i
$298$	−10.0204	−	28.6376i	−0.580464	−	1.65893i
$299$	−6.80393	+	1.82311i	−0.393481	+	0.105433i
$300$	−3.09770	−	1.55057i	−0.178846	−	0.0895220i
$301$	−10.6959	−	2.86596i	−0.616502	−	0.165191i
$302$	23.5484	−	1.76443i	1.35506	−	0.101532i
$303$	8.64515	−	7.21296i	0.496651	−	0.414374i
$304$	−0.319749	−	8.55629i	−0.0183388	−	0.490737i
$305$			3.20602i			0.183576i
$306$	−0.527652	+	4.99009i	−0.0301639	+	0.285265i
$307$	−9.14967	−	9.14967i	−0.522199	−	0.522199i	0.396036	−	0.918235i	$-0.370386\pi$
$307$	−9.14967	−	9.14967i	−0.522199	−	0.522199i	−0.918235	+	0.396036i	$0.870386\pi$
$308$	2.68821	+	1.98409i	0.153175	+	0.113054i
$309$	−16.6984	+	23.7061i	−0.949938	+	1.34859i
$310$	−0.862743	−	0.742468i	−0.0490005	−	0.0421693i
$311$	7.80662	−	4.50716i	0.442673	−	0.255577i	−0.262058	−	0.965052i	$-0.584401\pi$
$311$	7.80662	−	4.50716i	0.442673	−	0.255577i	0.704731	+	0.709475i	$0.251068\pi$
$312$	−3.40957	−	8.15301i	−0.193029	−	0.461573i
$313$	−26.7135	−	15.4230i	−1.50994	−	0.871762i	−0.999933	−	0.0115888i	$-0.996311\pi$
$313$	−26.7135	−	15.4230i	−1.50994	−	0.871762i	−0.510003	−	0.860173i	$-0.670356\pi$
$314$	2.98634	+	8.53478i	0.168529	+	0.481646i
$315$	0.253553	+	3.09798i	0.0142861	+	0.174551i
$316$	−25.4168	+	20.2682i	−1.42981	+	1.14018i
$317$	6.83060	−	1.83025i	0.383645	−	0.102797i	−0.0618416	−	0.998086i	$-0.519697\pi$
$317$	6.83060	−	1.83025i	0.383645	−	0.102797i	0.445487	+	0.895289i	$0.353031\pi$
$318$	3.83022	+	15.2212i	0.214788	+	0.853561i
$319$	−2.48883	+	1.43692i	−0.139347	+	0.0804523i
$320$	−7.86064	+	1.48674i	−0.439423	+	0.0831111i
$321$	8.25552	−	22.4856i	0.460778	−	1.25503i
$322$	4.72754	−	3.22310i	0.263456	−	0.179616i
$323$	1.79019	−	1.79019i	0.0996090	−	0.0996090i
$324$	17.6019	+	3.76455i	0.977885	+	0.209142i
$325$	1.27555	+	1.27555i	0.0707545	+	0.0707545i
$326$	−1.69447	+	8.95493i	−0.0938482	+	0.495968i
$327$	31.9834	+	11.7426i	1.76868	+	0.649366i
$328$	−9.06672	−	9.77229i	−0.500626	−	0.539585i
$329$	−1.30980	−	2.26865i	−0.0722118	−	0.125074i
$330$	−2.02673	+	3.38971i	−0.111568	+	0.186597i
$331$	0.985273	+	3.67709i	0.0541555	+	0.202111i	0.987703	−	0.156343i	$-0.0499706\pi$
$331$	0.985273	+	3.67709i	0.0541555	+	0.202111i	−0.933547	+	0.358454i	$0.883304\pi$
$332$	−10.3439	−	1.16572i	−0.567695	−	0.0639775i
$333$	8.61853	−	0.705382i	0.472292	−	0.0386547i
$334$	0.943749	+	0.454499i	0.0516396	+	0.0248691i
$335$	−0.116217	+	0.201294i	−0.00634961	+	0.0109978i
$336$	4.80138	+	5.33629i	0.261937	+	0.291119i
$337$	−3.92670	−	6.80125i	−0.213901	−	0.370488i	0.739031	−	0.673671i	$-0.235284\pi$
$337$	−3.92670	−	6.80125i	−0.213901	−	0.370488i	−0.952932	+	0.303184i	$0.901950\pi$
$338$	−1.02983	−	13.7444i	−0.0560156	−	0.747594i
$339$	−11.3228	−	7.97566i	−0.614969	−	0.433179i
$340$	−1.90322	−	1.40471i	−0.103216	−	0.0761809i
$341$	−0.917611	+	0.917611i	−0.0496914	+	0.0496914i
$342$	−5.71083	−	7.06136i	−0.308806	−	0.381834i
$343$	−13.3933			−0.723169
$344$	−14.1238	−	26.7257i	−0.761502	−	1.44096i
$345$	4.33290	+	5.19323i	0.233276	+	0.279594i
$346$	11.6587	+	10.0334i	0.626778	+	0.539399i
$347$	1.65248	−	6.16715i	0.0887099	−	0.331070i	−0.907281	−	0.420525i	$-0.861846\pi$
$347$	1.65248	−	6.16715i	0.0887099	−	0.331070i	0.995991	+	0.0894551i	$0.0285126\pi$
$348$	−5.85847	+	1.94994i	−0.314047	+	0.104528i
$349$	−4.82975	−	18.0249i	−0.258531	−	0.964849i	−0.966092	−	0.258197i	$-0.916871\pi$
$349$	−4.82975	−	18.0249i	−0.258531	−	0.964849i	0.707562	−	0.706652i	$-0.249795\pi$
$350$	−1.32017	−	0.635778i	−0.0705659	−	0.0339838i
$351$	−8.07784	−	4.75472i	−0.431163	−	0.253788i
$352$	1.02066	+	9.06346i	0.0544016	+	0.483084i
$353$	13.4016	+	7.73740i	0.713294	+	0.411820i	0.812279	−	0.583269i	$-0.198226\pi$
$353$	13.4016	+	7.73740i	0.713294	+	0.411820i	−0.0989857	+	0.995089i	$0.531560\pi$
$354$	−12.8123	−	13.2099i	−0.680963	−	0.702099i
$355$	−1.72408	+	6.43435i	−0.0915047	+	0.341500i
$356$	−2.29674	+	5.85160i	−0.121727	+	0.310134i
$357$	−0.190914	+	2.11393i	−0.0101043	+	0.111881i
$358$	19.3740	+	3.66600i	1.02395	+	0.193754i
$359$			4.11646i			0.217258i	0.994082	+	0.108629i	$0.0346461\pi$
$359$			4.11646i			0.217258i	−0.994082	+	0.108629i	$0.965354\pi$
$360$	−5.72885	+	6.25941i	−0.301937	+	0.329900i
$361$		−	14.4180i		−	0.758841i
$362$	4.54322	−	24.0100i	0.238786	−	1.26194i
$363$	−11.8951	−	8.37882i	−0.624332	−	0.439774i
$364$	−1.49474	−	3.42621i	−0.0783458	−	0.179582i
$365$	0.161414	−	0.602406i	0.00844881	−	0.0315314i
$366$	7.55358	+	2.14820i	0.394832	+	0.112288i
$367$	−4.03789	−	2.33128i	−0.210776	−	0.121692i	0.390896	−	0.920435i	$-0.372165\pi$
$367$	−4.03789	−	2.33128i	−0.210776	−	0.121692i	−0.601672	+	0.798743i	$0.705499\pi$
$368$	15.2276	+	3.47637i	0.793796	+	0.181218i
$369$	−13.9104	−	2.53323i	−0.724146	−	0.131875i
$370$	−1.76873	+	3.67269i	−0.0919517	+	0.190934i
$371$	1.71833	+	6.41291i	0.0892115	+	0.332942i
$372$	−2.32738	+	1.53518i	−0.120669	+	0.0795955i
$373$	1.74419	−	6.50939i	0.0903105	−	0.337043i	−0.905956	−	0.423371i	$-0.860847\pi$
$373$	1.74419	−	6.50939i	0.0903105	−	0.337043i	0.996267	+	0.0863279i	$0.0275133\pi$
$374$	−1.75915	+	2.04412i	−0.0909634	+	0.105699i
$375$	0.596954	−	1.62593i	0.0308266	−	0.0839626i
$376$	2.10807	−	6.83335i	0.108716	−	0.352403i
$377$	3.21528			0.165595
$378$	7.46892	+	1.47842i	0.384160	+	0.0760417i
$379$	−18.4480	+	18.4480i	−0.947611	+	0.947611i	−0.998694	−	0.0510834i	$-0.983733\pi$
$379$	−18.4480	+	18.4480i	−0.947611	+	0.947611i	0.0510834	+	0.998694i	$0.483733\pi$
$380$	4.23333	−	0.637969i	0.217165	−	0.0327271i
$381$	−12.5800	+	5.82331i	−0.644495	+	0.298337i
$382$	−31.9798	+	2.39617i	−1.63623	+	0.122599i
$383$	−10.8005	−	18.7070i	−0.551880	−	0.955883i	−0.998139	−	0.0609798i	$-0.980577\pi$
$383$	−10.8005	−	18.7070i	−0.551880	−	0.955883i	0.446259	−	0.894904i	$-0.352756\pi$
$384$	−1.76420	+	19.5163i	−0.0900289	+	0.995939i
$385$	−0.835280	+	1.44675i	−0.0425698	+	0.0737331i
$386$	−10.6103	+	22.0318i	−0.540050	+	1.12139i
$387$	−28.9815	−	13.7126i	−1.47321	−	0.697048i
$388$	−14.3253	−	17.9643i	−0.727259	−	0.911998i
$389$	−1.37991	−	5.14991i	−0.0699644	−	0.261111i	0.922080	−	0.386999i	$-0.126488\pi$
$389$	−1.37991	−	5.14991i	−0.0699644	−	0.261111i	−0.992044	+	0.125889i	$0.959822\pi$
$390$	3.85995	−	2.15058i	0.195456	−	0.108899i
$391$	2.30920	+	3.99965i	0.116781	+	0.202271i
$392$	−11.4010	−	12.2883i	−0.575839	−	0.620651i
$393$	1.45718	+	8.40166i	0.0735050	+	0.423808i
$394$	15.5827	+	2.94860i	0.785046	+	0.148548i
$395$	−11.4936	−	11.4936i	−0.578304	−	0.578304i
$396$	6.62835	+	7.04639i	0.333087	+	0.354094i
$397$	1.02090	−	1.02090i	0.0512376	−	0.0512376i	−0.681024	−	0.732261i	$-0.738465\pi$
$397$	1.02090	−	1.02090i	0.0512376	−	0.0512376i	0.732261	+	0.681024i	$0.238465\pi$
$398$	14.1261	+	20.7197i	0.708078	+	1.03859i
$399$	−2.46098	−	2.94963i	−0.123203	−	0.147666i
$400$	−1.17884	−	3.82235i	−0.0589420	−	0.191117i
$401$	33.1456	−	19.1366i	1.65521	−	0.955639i	0.680336	−	0.732900i	$-0.261834\pi$
$401$	33.1456	−	19.1366i	1.65521	−	0.955639i	0.974878	−	0.222739i	$-0.0714997\pi$
$402$	0.396389	+	0.408692i	0.0197701	+	0.0203837i
$403$	1.40240	−	0.375772i	0.0698586	−	0.0187186i
$404$	12.9190	+	1.45593i	0.642745	+	0.0724353i
$405$	−0.884832	+	8.95640i	−0.0439677	+	0.445047i
$406$	−2.46519	+	0.862573i	−0.122345	+	0.0428088i
$407$	4.02483	+	2.32374i	0.199504	+	0.115183i
$408$	−4.58483	+	3.54287i	−0.226983	+	0.175398i
$409$	−32.7034	+	18.8813i	−1.61708	+	0.933622i	−0.629410	+	0.777074i	$0.716703\pi$
$409$	−32.7034	+	18.8813i	−1.61708	+	0.933622i	−0.987670	+	0.156548i	$0.949963\pi$
$410$	4.34773	−	5.05203i	0.214719	−	0.249502i
$411$	−10.4567	−	0.944368i	−0.515789	−	0.0465822i
$412$	−33.1088	+	4.98955i	−1.63115	+	0.245817i
$413$	−5.50421	−	5.50421i	−0.270844	−	0.270844i
$414$	15.1388	−	6.72885i	0.744034	−	0.330705i
$415$		−	5.20469i		−	0.255488i
$416$	4.08120	−	9.35269i	0.200097	−	0.458553i
$417$	4.19842	+	24.2069i	0.205598	+	1.18541i
$418$	−0.364692	−	4.86725i	−0.0178377	−	0.238065i
$419$	−37.7937	−	10.1268i	−1.84634	−	0.494727i	−0.847023	−	0.531556i	$-0.821607\pi$
$419$	−37.7937	−	10.1268i	−1.84634	−	0.494727i	−0.999322	+	0.0368296i	$0.988274\pi$
$420$	−2.38251	+	2.68439i	−0.116255	+	0.130985i
$421$	15.7822	−	4.22883i	0.769178	−	0.206101i	0.147170	−	0.989111i	$-0.452984\pi$
$421$	15.7822	−	4.22883i	0.769178	−	0.206101i	0.622008	+	0.783011i	$0.286317\pi$
$422$	11.0918	−	3.88105i	0.539942	−	0.188927i
$423$	−2.55421	−	7.14191i	−0.124190	−	0.347252i
$424$	−9.64300	+	15.3455i	−0.468305	+	0.745245i
$425$	0.591366	−	1.02428i	0.0286855	−	0.0496847i
$426$	14.0045	+	8.37340i	0.678521	+	0.405692i
$427$	3.20860	+	0.859743i	0.155275	+	0.0416059i
$428$	25.3513	−	11.0599i	1.22540	−	0.534602i
$429$	−2.11620	−	4.57160i	−0.102171	−	0.220719i
$430$	12.4880	−	8.51394i	0.602223	−	0.410578i
$431$	15.9795			0.769704			0.384852	−	0.922978i	$-0.374252\pi$
$431$	15.9795			0.769704			0.384852	+	0.922978i	$0.374252\pi$
$432$	10.9089	+	17.6917i	0.524856	+	0.851191i
$433$	2.66467			0.128056			0.0640279	−	0.997948i	$-0.479605\pi$
$433$	2.66467			0.128056			0.0640279	+	0.997948i	$0.479605\pi$
$434$	−0.974425	+	0.664335i	−0.0467739	+	0.0318891i
$435$	−1.29687	−	2.80162i	−0.0621804	−	0.134328i
$436$	15.7316	+	36.0594i	0.753405	+	1.72693i
$437$	−8.07378	−	2.16336i	−0.386221	−	0.103488i
$438$	−1.31115	−	0.783946i	−0.0626492	−	0.0374584i
$439$	18.9678	−	32.8533i	0.905286	−	1.56800i	0.0847528	−	0.996402i	$-0.472990\pi$
$439$	18.9678	−	32.8533i	0.905286	−	1.56800i	0.820533	−	0.571599i	$-0.193677\pi$
$440$	−4.44607	+	1.01462i	−0.211958	+	0.0483702i
$441$	−17.4917	−	3.18543i	−0.832940	−	0.151687i
$442$	2.84795	−	0.996504i	0.135463	−	0.0473988i
$443$	−1.34150	+	0.359455i	−0.0637367	+	0.0170782i	−0.290547	−	0.956861i	$-0.593837\pi$
$443$	−1.34150	+	0.359455i	−0.0637367	+	0.0170782i	0.226810	+	0.973939i	$0.427170\pi$
$444$	7.46794	+	6.62812i	0.354413	+	0.314557i
$445$	−3.03600	−	0.813493i	−0.143920	−	0.0385633i
$446$	−1.47934	−	19.7435i	−0.0700486	−	0.934882i
$447$	−6.35001	−	36.6123i	−0.300345	−	1.73170i
$448$	−0.620016	+	8.26567i	−0.0292930	+	0.390516i
$449$		−	11.0084i		−	0.519520i	−0.965673	−	0.259760i	$-0.916357\pi$
$449$		−	11.0084i		−	0.519520i	0.965673	−	0.259760i	$-0.0836434\pi$
$450$	−3.43080	−	2.49592i	−0.161729	−	0.117659i
$451$	−5.37333	−	5.37333i	−0.253020	−	0.253020i
$452$	−2.38316	−	15.8138i	−0.112095	−	0.743818i
$453$	28.8044	+	2.60140i	1.35335	+	0.122225i
$454$	0.429040	−	0.498542i	0.0201359	−	0.0233977i
$455$	1.61863	−	0.934517i	0.0758826	−	0.0438109i
$456$	1.33346	−	10.4015i	0.0624449	−	0.487093i
$457$	19.8830	+	11.4794i	0.930086	+	0.536986i	0.886839	−	0.462079i	$-0.152896\pi$
$457$	19.8830	+	11.4794i	0.930086	+	0.536986i	0.0432474	+	0.999064i	$0.486230\pi$
$458$	10.2327	−	3.58044i	0.478142	−	0.167303i
$459$	−1.64045	+	5.92267i	−0.0765698	+	0.276447i
$460$	−0.874593	+	7.76058i	−0.0407781	+	0.361839i
$461$	20.7741	−	5.56641i	0.967548	−	0.259254i	0.259756	−	0.965674i	$-0.416358\pi$
$461$	20.7741	−	5.56641i	0.967548	−	0.259254i	0.707792	+	0.706421i	$0.249691\pi$
$462$	2.84895	+	2.93737i	0.132545	+	0.136659i
$463$	−11.0960	+	6.40627i	−0.515674	+	0.297725i	−0.735163	−	0.677890i	$-0.762894\pi$
$463$	−11.0960	+	6.40627i	−0.515674	+	0.297725i	0.219489	+	0.975615i	$0.429561\pi$
$464$	−6.30328	−	3.33176i	−0.292622	−	0.154673i
$465$	−0.893082	−	1.07041i	−0.0414157	−	0.0496391i
$466$	13.3325	+	19.5557i	0.617618	+	0.905901i
$467$	−19.8483	+	19.8483i	−0.918470	+	0.918470i	−0.996918	−	0.0784478i	$-0.975004\pi$
$467$	−19.8483	+	19.8483i	−0.918470	+	0.918470i	0.0784478	+	0.996918i	$0.475004\pi$
$468$	−2.48054	−	10.5353i	−0.114663	−	0.486993i
$469$	0.170291	+	0.170291i	0.00786329	+	0.00786329i
$470$	3.51322	+	0.664780i	0.162053	+	0.0306640i
$471$	1.89248	+	10.9114i	0.0872007	+	0.502773i
$472$	0.795296	−	21.2346i	0.0366065	−	0.977401i
$473$	−8.61576	−	14.9229i	−0.396153	−	0.686157i
$474$	−34.7808	+	19.3783i	−1.59754	+	0.890073i
$475$	0.554019	+	2.06763i	0.0254201	+	0.0948692i
$476$	−1.91622	+	1.52806i	−0.0878296	+	0.0700384i
$477$	1.56808	+	19.1592i	0.0717974	+	0.877237i
$478$	−11.6263	+	24.1416i	−0.531776	+	1.10421i
$479$	−14.9611	+	25.9133i	−0.683588	+	1.18401i	0.290290	+	0.956939i	$0.406248\pi$
$479$	−14.9611	+	25.9133i	−0.683588	+	1.18401i	−0.973878	+	0.227071i	$0.927085\pi$
$480$	−9.79557	+	0.216247i	−0.447105	+	0.00987027i
$481$	−2.59981	−	4.50301i	−0.118541	−	0.205320i
$482$	25.7452	−	1.92903i	1.17266	−	0.0878648i
$483$	6.35936	−	2.94375i	0.289361	−	0.133945i
$484$	−2.50363	−	16.6132i	−0.113801	−	0.755143i
$485$	8.12351	−	8.12351i	0.368869	−	0.368869i
$486$	20.5089	+	8.08598i	0.930305	+	0.366787i
$487$	−33.0657			−1.49835			−0.749174	−	0.662373i	$-0.769549\pi$
$487$	−33.0657			−1.49835			−0.749174	+	0.662373i	$0.769549\pi$
$488$	4.23690	+	8.01730i	0.191796	+	0.362926i
$489$	−3.84704	+	10.4782i	−0.173969	+	0.473842i
$490$	5.46709	−	6.35272i	0.246978	−	0.286987i
$491$	7.76084	−	28.9639i	0.350242	−	1.30712i	−0.536125	−	0.844138i	$-0.680113\pi$
$491$	7.76084	−	28.9639i	0.350242	−	1.30712i	0.886367	−	0.462983i	$-0.153221\pi$
$492$	−8.98969	−	13.6286i	−0.405287	−	0.614427i
$493$	−0.545621	−	2.03629i	−0.0245735	−	0.0917097i
$494$	−2.36940	+	4.91996i	−0.106604	+	0.221359i
$495$	−3.12988	+	3.68788i	−0.140678	+	0.165758i
$496$	−3.13867	−	0.716537i	−0.140930	−	0.0321734i
$497$	5.97721	+	3.45094i	0.268114	+	0.154796i
$498$	−12.2626	−	3.48742i	−0.549499	−	0.156275i
$499$	0.391748	−	1.46202i	0.0175371	−	0.0654492i	−0.956603	−	0.291395i	$-0.905881\pi$
$499$	0.391748	−	1.46202i	0.0175371	−	0.0654492i	0.974140	+	0.225946i	$0.0725473\pi$
$500$	1.83314	−	0.799741i	0.0819807	−	0.0357655i
$501$	1.04883	+	0.738786i	0.0468582	+	0.0330065i
$502$	7.14588	−	37.7644i	0.318936	−	1.68551i
$503$			15.1895i			0.677268i	0.940918	+	0.338634i	$0.109965\pi$
$503$			15.1895i			0.677268i	−0.940918	+	0.338634i	$0.890035\pi$
$504$	4.72818	+	7.41203i	0.210610	+	0.330158i
$505$			6.50039i			0.289264i
$506$	8.74856	+	1.65542i	0.388921	+	0.0735926i
$507$	1.51834	−	16.8121i	0.0674320	−	0.746651i
$508$	−14.9004	−	5.84837i	−0.661097	−	0.259479i
$509$	1.90517	−	7.11017i	0.0844450	−	0.315153i	−0.910764	−	0.412928i	$-0.864506\pi$
$509$	1.90517	−	7.11017i	0.0844450	−	0.315153i	0.995209	+	0.0977754i	$0.0311727\pi$
$510$	−2.01701	−	2.07962i	−0.0893148	−	0.0920869i
$511$	−0.559607	−	0.323089i	−0.0247555	−	0.0142926i
$512$	−17.6923	+	14.1061i	−0.781898	+	0.623407i
$513$	−5.48019	−	9.67895i	−0.241956	−	0.427336i
$514$	23.9792	+	11.5481i	1.05768	+	0.509367i
$515$	−4.33298	−	16.1709i	−0.190934	−	0.712574i
$516$	−11.6918	−	35.1272i	−0.514701	−	1.54639i
$517$	1.05507	−	3.93758i	0.0464019	−	0.173174i
$518$	3.20134	+	2.75504i	0.140659	+	0.121050i
$519$	12.0687	+	14.4651i	0.529759	+	0.634947i
$520$	4.87545	+	1.50407i	0.213803	+	0.0659577i
$521$	23.6628			1.03669			0.518344	−	0.855172i	$-0.326549\pi$
$521$	23.6628			1.03669			0.518344	+	0.855172i	$0.326549\pi$
$522$	−7.46977	+	1.17828i	−0.326943	+	0.0515720i
$523$	−28.0139	+	28.0139i	−1.22496	+	1.22496i	−0.259118	+	0.965846i	$0.583432\pi$
$523$	−28.0139	+	28.0139i	−1.22496	+	1.22496i	−0.965846	+	0.259118i	$0.916568\pi$
$524$	−5.84708	+	7.92212i	−0.255431	+	0.346080i
$525$	−1.46716	−	1.03345i	−0.0640321	−	0.0451036i
$526$	0.251683	+	3.35900i	0.0109739	+	0.146460i
$527$	−0.475964	−	0.824394i	−0.0207333	−	0.0359112i
$528$	−0.588592	+	11.1551i	−0.0256152	+	0.485462i
$529$	−3.87605	+	6.71352i	−0.168524	+	0.291892i
$530$	−8.16445	−	3.93191i	−0.354641	−	0.170791i
$531$	−12.8239	−	18.5346i	−0.556509	−	0.804333i
$532$	0.496748	−	4.40782i	0.0215368	−	0.191103i
$533$	2.20044	+	8.21216i	0.0953117	+	0.355708i
$534$	−3.95092	+	6.60792i	−0.170973	+	0.285953i
$535$	6.91470	+	11.9766i	0.298949	+	0.517794i
$536$	−0.0246051	+	0.656961i	−0.00106278	+	0.0283764i
$537$	22.6697	+	8.32309i	0.978268	+	0.359168i
$538$	3.07387	−	16.2447i	0.132524	−	0.700361i
$539$	−6.75674	−	6.75674i	−0.291033	−	0.291033i
$540$	−8.17936	+	6.41078i	−0.351984	+	0.275876i
$541$	−23.9401	+	23.9401i	−1.02927	+	1.02927i	−0.0297064	+	0.999559i	$0.509457\pi$
$541$	−23.9401	+	23.9401i	−1.02927	+	1.02927i	−0.999559	+	0.0297064i	$0.990543\pi$
$542$	−0.302754	+	0.206409i	−0.0130044	+	0.00886601i
$543$	10.3147	−	28.0942i	0.442646	−	1.20564i
$544$	−6.61576	−	0.997565i	−0.283648	−	0.0427703i
$545$	−17.0354	+	9.83541i	−0.729718	+	0.421303i
$546$	−1.11721	−	4.43977i	−0.0478123	−	0.190005i
$547$	−5.36858	+	1.43851i	−0.229544	+	0.0615062i	−0.371758	−	0.928330i	$-0.621245\pi$
$547$	−5.36858	+	1.43851i	−0.229544	+	0.0615062i	0.142213	+	0.989836i	$0.454578\pi$
$548$	−7.55862	−	9.47867i	−0.322888	−	0.404909i
$549$	8.69400	+	4.11355i	0.371051	+	0.175562i
$550$	−0.753073	−	2.15224i	−0.0321111	−	0.0917718i
$551$	3.30421	+	1.90768i	0.140764	+	0.0812701i
$552$	17.6984	+	7.26060i	0.753294	+	0.309032i
$553$	−14.5850	+	8.42066i	−0.620218	+	0.358083i
$554$	−2.18955	−	1.88430i	−0.0930250	−	0.0800564i
$555$	−2.87505	+	4.08162i	−0.122039	+	0.173255i
$556$	−16.8466	+	22.8252i	−0.714455	+	0.968004i
$557$	23.1230	+	23.1230i	0.979752	+	0.979752i	0.999799	−	0.0200466i	$-0.00638147\pi$
$557$	23.1230	+	23.1230i	0.979752	+	0.979752i	−0.0200466	+	0.999799i	$0.506381\pi$
$558$	−3.12037	+	1.38693i	−0.132096	+	0.0587133i
$559$			19.2787i			0.815404i
$560$	−4.14156	+	0.154770i	−0.175013	+	0.00654023i
$561$	−2.53615	+	2.11600i	−0.107076	+	0.0893377i
$562$	−7.56940	+	0.567158i	−0.319296	+	0.0239241i
$563$	10.9701	+	2.93942i	0.462334	+	0.123882i	0.482465	−	0.875915i	$-0.339742\pi$
$563$	10.9701	+	2.93942i	0.462334	+	0.123882i	−0.0201309	+	0.999797i	$0.506408\pi$
$564$	3.92031	−	7.83193i	0.165075	−	0.329784i
$565$	7.72371	−	2.06956i	0.324939	−	0.0870671i
$566$	10.3245	+	29.5070i	0.433973	+	1.24027i
$567$	8.72634	+	3.28734i	0.366472	+	0.138055i
$568$	4.19189	+	18.3689i	0.175888	+	0.770740i
$569$	−4.43840	+	7.68753i	−0.186067	+	0.322278i	−0.943936	−	0.330129i	$-0.892908\pi$
$569$	−4.43840	+	7.68753i	−0.186067	+	0.322278i	0.757868	+	0.652408i	$0.226241\pi$
$570$	5.24268	+	0.0801158i	0.219592	+	0.00335568i
$571$	26.7006	+	7.15440i	1.11738	+	0.299402i	0.769825	−	0.638255i	$-0.220344\pi$
$571$	26.7006	+	7.15440i	1.11738	+	0.299402i	0.347560	+	0.937658i	$0.387010\pi$
$572$	2.12530	−	5.41481i	0.0888634	−	0.226405i
$573$	−39.1176	−	3.53282i	−1.63416	−	0.147586i
$574$	−3.89020	−	5.70602i	−0.162374	−	0.238165i
$575$	−3.90486			−0.162844
$576$	−6.05406	+	23.2239i	−0.252252	+	0.967661i
$577$	22.5437			0.938506			0.469253	−	0.883064i	$-0.344523\pi$
$577$	22.5437			0.938506			0.469253	+	0.883064i	$0.344523\pi$
$578$	12.4285	+	18.2297i	0.516958	+	0.758257i
$579$	−17.2470	+	24.4849i	−0.716760	+	1.01756i
$580$	1.30246	−	3.31837i	0.0540815	−	0.137788i
$581$	−5.20889	−	1.39572i	−0.216101	−	0.0579041i
$582$	−13.6963	−	24.5827i	−0.567730	−	1.01898i
$583$	−5.16572	+	8.94728i	−0.213942	+	0.370559i
$584$	−0.392459	−	1.71976i	−0.0162401	−	0.0711640i
$585$	5.09561	−	1.82238i	0.210677	−	0.0753461i
$586$	−10.3738	−	29.6478i	−0.428538	−	1.22474i
$587$	30.7178	−	8.23081i	1.26786	−	0.339722i	0.438649	−	0.898659i	$-0.355457\pi$
$587$	30.7178	−	8.23081i	1.26786	−	0.339722i	0.829210	+	0.558937i	$0.188791\pi$
$588$	−11.3042	−	17.1375i	−0.466176	−	0.706737i
$589$	1.66414	+	0.445905i	0.0685697	+	0.0183732i
$590$	10.5950	−	0.793863i	0.436191	−	0.0326828i
$591$	18.2335	+	6.69435i	0.750024	+	0.275369i
$592$	0.430568	+	11.5218i	0.0176962	+	0.473541i
$593$		−	14.6662i		−	0.602270i	−0.953582	−	0.301135i	$-0.902635\pi$
$593$		−	14.6662i		−	0.602270i	0.953582	−	0.301135i	$-0.0973654\pi$
$594$	6.59170	+	9.84528i	0.270461	+	0.403957i
$595$	−0.866519	−	0.866519i	−0.0355238	−	0.0355238i
$596$	25.4801	−	34.5226i	1.04370	−	1.41410i
$597$	12.9018	+	27.8716i	0.528035	+	1.14071i
$598$	−7.55056	−	6.49794i	−0.308766	−	0.265721i
$599$	−8.46909	+	4.88963i	−0.346038	+	0.199785i	−0.662939	−	0.748674i	$-0.730691\pi$
$599$	−8.46909	+	4.88963i	−0.346038	+	0.199785i	0.316901	+	0.948459i	$0.397358\pi$
$600$	−0.655936	−	4.85487i	−0.0267785	−	0.198199i
$601$	−7.99779	−	4.61753i	−0.326237	−	0.188353i	0.327932	−	0.944701i	$-0.393648\pi$
$601$	−7.99779	−	4.61753i	−0.326237	−	0.188353i	−0.654169	+	0.756348i	$0.726982\pi$
$602$	−5.17197	−	14.7812i	−0.210794	−	0.602436i
$603$	0.396749	+	0.573428i	0.0161569	+	0.0233518i
$604$	20.8214	+	26.1104i	0.847209	+	1.06242i
$605$	8.11414	−	2.17418i	0.329887	−	0.0883928i
$606$	15.3153	+	4.35561i	0.622143	+	0.176934i
$607$	−13.9484	+	8.05309i	−0.566147	+	0.326865i	−0.755609	−	0.655023i	$-0.772659\pi$
$607$	−13.9484	+	8.05309i	−0.566147	+	0.326865i	0.189462	+	0.981888i	$0.439326\pi$
$608$	9.74319	−	7.18991i	0.395138	−	0.291589i
$609$	−3.15166	+	0.546622i	−0.127712	+	0.0221503i
$610$	−3.74619	+	2.55405i	−0.151679	+	0.103410i
$611$	−3.22497	+	3.22497i	−0.130468	+	0.130468i
$612$	−6.25121	+	3.35876i	−0.252690	+	0.135770i
$613$	13.4015	+	13.4015i	0.541283	+	0.541283i	0.923905	−	0.382622i	$-0.124979\pi$
$613$	13.4015	+	13.4015i	0.541283	+	0.541283i	−0.382622	+	0.923905i	$0.624979\pi$
$614$	3.40227	−	17.9803i	0.137304	−	0.725625i
$615$	6.26809	−	5.22969i	0.252754	−	0.210882i
$616$	−0.176843	+	4.72175i	−0.00712520	+	0.190245i
$617$	22.0138	+	38.1290i	0.886243	+	1.53502i	0.844283	+	0.535898i	$0.180027\pi$
$617$	22.0138	+	38.1290i	0.886243	+	1.53502i	0.0419603	+	0.999119i	$0.486640\pi$
$618$	−41.0029	−	0.626585i	−1.64938	−	0.0252049i
$619$	6.06535	+	22.6362i	0.243787	+	0.909826i	0.973989	+	0.226594i	$0.0727592\pi$
$619$	6.06535	+	22.6362i	0.243787	+	0.909826i	−0.730202	+	0.683231i	$0.760574\pi$
$620$	0.180268	−	1.59958i	0.00723974	−	0.0642409i
$621$	19.6423	−	5.08657i	0.788218	−	0.204117i
$622$	11.4856	+	5.53136i	0.460532	+	0.221787i
$623$	−1.62830	+	2.82030i	−0.0652364	+	0.112993i
$624$	6.81049	−	10.4791i	0.272638	−	0.419498i
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	−3.25943	−	43.5010i	−0.130273	−	1.73865i
$627$	0.537687	−	5.95361i	0.0214731	−	0.237764i
$628$	−7.59375	+	10.2887i	−0.303024	+	0.410562i
$629$	−2.41064	+	2.41064i	−0.0961187	+	0.0961187i
$630$	−3.41796	+	2.76425i	−0.136175	+	0.110130i
$631$	−17.0096			−0.677140			−0.338570	−	0.940941i	$-0.609943\pi$
$631$	−17.0096			−0.677140			−0.338570	+	0.940941i	$0.609943\pi$
$632$	−43.9312	−	13.5527i	−1.74749	−	0.539097i
$633$	14.1805	−	2.45947i	0.563626	−	0.0977550i
$634$	7.58017	+	6.52342i	0.301047	+	0.259078i
$635$	2.07146	−	7.73079i	0.0822033	−	0.306787i
$636$	−14.7344	+	16.6014i	−0.584259	+	0.658287i
$637$	2.76696	+	10.3264i	0.109631	+	0.409149i
$638$	−3.66173	−	1.76345i	−0.144969	−	0.0698156i
$639$	15.2364	+	12.9311i	0.602743	+	0.511544i
$640$	−7.99934	−	8.00066i	−0.316202	−	0.316254i
$641$	32.2616	+	18.6263i	1.27426	+	0.735693i	0.975786	−	0.218726i	$-0.0701900\pi$
$641$	32.2616	+	18.6263i	1.27426	+	0.735693i	0.298471	+	0.954419i	$0.403523\pi$
$642$	32.8509	−	8.26650i	1.29652	−	0.326253i
$643$	−2.91924	+	10.8948i	−0.115124	+	0.429648i	−0.999296	−	0.0375131i	$-0.988056\pi$
$643$	−2.91924	+	10.8948i	−0.115124	+	0.429648i	0.884172	+	0.467161i	$0.154723\pi$
$644$	7.53231	+	2.95642i	0.296815	+	0.116499i
$645$	16.7985	−	7.77602i	0.661439	−	0.306181i
$646$	3.51796	+	0.665677i	0.138412	+	0.0261907i
$647$			12.1147i			0.476279i	0.971231	+	0.238140i	$0.0765376\pi$
$647$			12.1147i			0.476279i	−0.971231	+	0.238140i	$0.923462\pi$
$648$	9.62360	+	23.5666i	0.378051	+	0.925785i
$649$		−	12.1132i		−	0.475485i
$650$	−0.474307	+	2.50661i	−0.0186038	+	0.0983174i
$651$	−1.31077	+	0.606756i	−0.0513731	+	0.0237806i
$652$	−11.8136	+	5.15389i	−0.462657	+	0.201842i
$653$	−4.73040	+	17.6541i	−0.185115	+	0.690858i	0.809491	+	0.587132i	$0.199743\pi$
$653$	−4.73040	+	17.6541i	−0.185115	+	0.690858i	−0.994606	+	0.103726i	$0.966924\pi$
$654$	11.7582	+	46.7268i	0.459782	+	1.82716i
$655$	−4.26355	−	2.46156i	−0.166591	−	0.0961811i
$656$	4.19588	−	18.3794i	0.163822	−	0.717593i
$657$	−1.42648	−	1.21065i	−0.0556525	−	0.0472319i
$658$	1.60744	−	3.33778i	0.0626646	−	0.130120i
$659$	−4.20971	−	15.7109i	−0.163987	−	0.612008i	−0.998167	−	0.0605159i	$-0.980725\pi$
$659$	−4.20971	−	15.7109i	−0.163987	−	0.612008i	0.834180	−	0.551492i	$-0.185941\pi$
$660$	−5.57541	+	0.332172i	−0.217023	+	0.0129298i
$661$	11.2194	−	41.8712i	0.436383	−	1.62860i	−0.301353	−	0.953513i	$-0.597438\pi$
$661$	11.2194	−	41.8712i	0.436383	−	1.62860i	0.737736	−	0.675090i	$-0.235895\pi$
$662$	−3.51172	+	4.08060i	−0.136487	+	0.158597i
$663$	3.64101	−	0.631496i	0.141405	−	0.0245253i
$664$	−6.87824	−	13.0154i	−0.266927	−	0.505095i
$665$	2.21786			0.0860051
$666$	7.69010	+	9.50871i	0.297985	+	0.368455i
$667$	−4.92151	+	4.92151i	−0.190562	+	0.190562i
$668$	0.220752	+	1.46483i	0.00854117	+	0.0566760i
$669$	2.18107	−	24.1502i	0.0843251	−	0.933702i
$670$	−0.327792	+	0.0245607i	−0.0126637	+	0.000948864i
$671$	2.58459	+	4.47664i	0.0997770	+	0.172819i
$672$	−2.41041	+	9.86147i	−0.0929837	+	0.380414i
$673$	−20.4753	+	35.4642i	−0.789263	+	1.36704i	0.137155	+	0.990550i	$0.456204\pi$
$673$	−20.4753	+	35.4642i	−0.789263	+	1.36704i	−0.926419	+	0.376495i	$0.877129\pi$
$674$	4.81900	−	10.0065i	0.185621	−	0.385434i
$675$	−3.64322	−	3.70499i	−0.140228	−	0.142605i
$676$	15.2397	−	12.1527i	0.586142	−	0.467410i
$677$	−5.31507	−	19.8361i	−0.204275	−	0.762364i	−0.989669	−	0.143369i	$-0.954207\pi$
$677$	−5.31507	−	19.8361i	−0.204275	−	0.762364i	0.785395	−	0.618995i	$-0.212460\pi$
$678$	0.299276	−	19.5843i	0.0114936	−	0.752129i
$679$	−5.95162	−	10.3085i	−0.228402	−	0.395604i
$680$	0.125202	−	3.34293i	0.00480129	−	0.128196i
$681$	0.618544	−	0.516074i	0.0237027	−	0.0197760i
$682$	−1.80322	−	0.341210i	−0.0690490	−	0.0130656i
$683$	−3.63546	−	3.63546i	−0.139107	−	0.139107i	0.634124	−	0.773231i	$-0.281361\pi$
$683$	−3.63546	−	3.63546i	−0.139107	−	0.139107i	−0.773231	+	0.634124i	$0.781361\pi$
$684$	3.70163	−	12.2984i	0.141535	−	0.470241i
$685$	4.28629	−	4.28629i	0.163771	−	0.163771i
$686$	−10.6696	−	15.6499i	−0.407368	−	0.597515i
$687$	13.0822	−	2.26896i	0.499116	−	0.0865664i
$688$	19.9771	−	37.7943i	0.761621	−	1.44089i
$689$	10.0103	−	5.77944i	0.381361	−	0.220179i
$690$	−2.61646	+	9.20008i	−0.0996069	+	0.350241i
$691$	26.1748	−	7.01352i	0.995737	−	0.266807i	0.276079	−	0.961135i	$-0.410965\pi$
$691$	26.1748	−	7.01352i	0.995737	−	0.266807i	0.719659	+	0.694328i	$0.244298\pi$
$692$	−2.43607	+	21.6161i	−0.0926054	+	0.821721i
$693$	2.85153	+	4.12137i	0.108321	+	0.156558i
$694$	8.52267	−	2.98210i	0.323516	−	0.113199i
$695$	−12.2841	−	7.09224i	−0.465963	−	0.269024i
$696$	−6.94557	−	5.29215i	−0.263271	−	0.200598i
$697$	4.82747	−	2.78714i	0.182854	−	0.105571i
$698$	17.2143	−	20.0029i	0.651569	−	0.757119i
$699$	12.1770	+	26.3058i	0.460576	+	0.994977i
$700$	−0.308800	−	2.04909i	−0.0116716	−	0.0774481i
$701$	22.1708	+	22.1708i	0.837378	+	0.837378i	0.988513	−	0.151135i	$-0.0482928\pi$
$701$	22.1708	+	22.1708i	0.837378	+	0.837378i	−0.151135	+	0.988513i	$0.548293\pi$
$702$	−0.879311	−	13.2267i	−0.0331875	−	0.499208i
$703$		−	6.17007i		−	0.232708i
$704$	−9.77744	+	8.41296i	−0.368501	+	0.317075i
$705$	4.11085	+	1.50928i	0.154823	+	0.0568429i
$706$	1.63519	+	21.8235i	0.0615410	+	0.821338i
$707$	6.50564	+	1.74318i	0.244670	+	0.0655591i
$708$	5.22885	−	25.4945i	0.196512	−	0.958142i
$709$	27.1498	−	7.27476i	1.01963	−	0.273209i	0.289982	−	0.957032i	$-0.406351\pi$
$709$	27.1498	−	7.27476i	1.01963	−	0.273209i	0.729648	+	0.683823i	$0.239684\pi$
$710$	−8.89194	+	3.11130i	−0.333708	+	0.116765i
$711$	−45.9150	+	16.4209i	−1.72195	+	0.615832i
$712$	−8.66720	+	1.97791i	−0.324817	+	0.0741252i
$713$	−1.57142	+	2.72178i	−0.0588502	+	0.101932i
$714$	−2.62219	+	1.46096i	−0.0981329	+	0.0546750i
$715$	2.80938	+	0.752771i	0.105065	+	0.0281520i
$716$	11.1505	+	25.5588i	0.416712	+	0.955176i
$717$	−18.8985	+	26.8296i	−0.705779	+	1.00197i
$718$	−4.81003	+	3.27934i	−0.179509	+	0.122384i
$719$	46.1574			1.72138			0.860691	−	0.509127i	$-0.170032\pi$
$719$	46.1574			1.72138			0.860691	+	0.509127i	$0.170032\pi$
$720$	−11.8779	−	1.70759i	−0.442663	−	0.0636382i
$721$	−17.3459			−0.645995
$722$	16.8472	−	11.4860i	0.626989	−	0.427463i
$723$	31.4915	+	2.84408i	1.17118	+	0.105772i
$724$	31.6746	−	13.8186i	1.17718	−	0.513565i
$725$	1.72168	+	0.461322i	0.0639415	+	0.0171331i
$726$	0.314404	−	20.5742i	0.0116686	−	0.763581i
$727$	1.54673	−	2.67902i	0.0573652	−	0.0993594i	−0.835917	−	0.548856i	$-0.815063\pi$
$727$	1.54673	−	2.67902i	0.0573652	−	0.0993594i	0.893282	+	0.449497i	$0.148397\pi$
$728$	2.81271	−	4.47605i	0.104246	−	0.165893i
$729$	23.1524	+	13.8912i	0.857498	+	0.514487i
$730$	0.832493	−	0.291291i	0.0308120	−	0.0107812i
$731$	12.2095	−	3.27153i	0.451585	−	0.121002i
$732$	3.50734	+	10.5376i	0.129635	+	0.389481i
$733$	−31.7558	−	8.50895i	−1.17293	−	0.314285i	−0.380810	−	0.924653i	$-0.624355\pi$
$733$	−31.7558	−	8.50895i	−1.17293	−	0.314285i	−0.792118	+	0.610368i	$0.791022\pi$
$734$	−0.492681	−	6.57542i	−0.0181852	−	0.242703i
$735$	7.88187	−	6.57613i	0.290727	−	0.242564i
$736$	8.06888	+	20.5627i	0.297423	+	0.757952i
$737$			0.374762i			0.0138045i
$738$	−8.12154	−	18.2722i	−0.298958	−	0.672608i
$739$	−27.1276	−	27.1276i	−0.997906	−	0.997906i	0.00209211	−	0.999998i	$-0.499334\pi$
$739$	−27.1276	−	27.1276i	−0.997906	−	0.997906i	−0.999998	+	0.00209211i	$0.999334\pi$
$740$	−5.70053	+	0.859079i	−0.209556	+	0.0315804i
$741$	−3.85145	+	5.46776i	−0.141486	+	0.200863i
$742$	−6.12451	+	7.11664i	−0.224838	+	0.261260i
$743$	−40.9184	+	23.6242i	−1.50115	+	0.866689i	−0.501151	+	0.865360i	$0.667090\pi$
$743$	−40.9184	+	23.6242i	−1.50115	+	0.866689i	−0.999999	+	0.00132930i	$0.999577\pi$
$744$	−3.64793	−	1.49653i	−0.133740	−	0.0548654i
$745$	18.5794	+	10.7268i	0.680698	+	0.393001i
$746$	8.99563	−	3.14759i	0.329353	−	0.115241i
$747$	−14.1140	−	6.67798i	−0.516402	−	0.244335i
$748$	−3.78994	−	0.427114i	−0.138574	−	0.0156168i
$749$	13.8406	−	3.70857i	0.505723	−	0.135508i
$750$	2.37544	−	0.597748i	0.0867387	−	0.0218267i
$751$	36.1502	−	20.8713i	1.31914	−	0.761605i	0.335548	−	0.942023i	$-0.391078\pi$
$751$	36.1502	−	20.8713i	1.31914	−	0.761605i	0.983590	+	0.180418i	$0.0577451\pi$
$752$	9.66406	−	2.98047i	0.352412	−	0.108686i
$753$	16.2236	−	44.1884i	0.591222	−	1.61032i
$754$	2.56143	+	3.75702i	0.0932816	+	0.136822i
$755$	−11.8072	+	11.8072i	−0.429709	+	0.429709i
$756$	4.22253	+	9.90511i	0.153572	+	0.360245i
$757$	8.29675	+	8.29675i	0.301551	+	0.301551i	0.841620	−	0.540070i	$-0.181602\pi$
$757$	8.29675	+	8.29675i	0.301551	+	0.301551i	−0.540070	+	0.841620i	$0.681602\pi$
$758$	−36.2527	−	6.85983i	−1.31676	−	0.249160i
$759$	10.2368	+	3.75839i	0.371571	+	0.136421i
$760$	4.11790	+	4.43836i	0.149372	+	0.160996i
$761$	0.354254	+	0.613585i	0.0128417	+	0.0222424i	0.872375	−	0.488838i	$-0.162579\pi$
$761$	0.354254	+	0.613585i	0.0128417	+	0.0222424i	−0.859533	+	0.511080i	$0.829246\pi$
$762$	−16.8262	−	10.0605i	−0.609550	−	0.364454i
$763$	5.27503	+	19.6867i	0.190969	+	0.712706i
$764$	−28.2763	−	35.4591i	−1.02300	−	1.28286i
$765$	−2.01884	−	2.91787i	−0.0729915	−	0.105496i
$766$	13.2548	−	27.5230i	0.478915	−	0.994447i
$767$	−6.77617	+	11.7367i	−0.244673	+	0.423787i
$768$	−24.2100	+	13.4861i	−0.873604	+	0.486637i
$769$	−10.1132	−	17.5166i	−0.364691	−	0.631664i	0.624035	−	0.781396i	$-0.285492\pi$
$769$	−10.1132	−	17.5166i	−0.364691	−	0.631664i	−0.988727	+	0.149732i	$0.952159\pi$
$770$	−2.35593	+	0.176524i	−0.0849017	+	0.00636149i
$771$	26.6492	+	18.7714i	0.959747	+	0.676037i
$772$	−34.1965	+	5.15347i	−1.23076	+	0.185477i
$773$	−2.86041	+	2.86041i	−0.102882	+	0.102882i	−0.756674	−	0.653792i	$-0.773177\pi$
$773$	−2.86041	+	2.86041i	−0.102882	+	0.102882i	0.653792	+	0.756674i	$0.273177\pi$
$774$	−7.06494	−	44.7886i	−0.253944	−	1.60989i
$775$	0.804855			0.0289112
$776$	9.57888	−	31.0501i	0.343862	−	1.11463i
$777$	3.31392	+	3.97192i	0.118886	+	0.142492i
$778$	4.91831	−	5.71504i	0.176330	−	0.204894i
$779$	−2.61112	+	9.74484i	−0.0935531	+	0.349145i
$780$	5.58792	+	2.79706i	0.200080	+	0.100151i
$781$	2.77980	+	10.3743i	0.0994690	+	0.371223i
$782$	−2.83394	+	5.88456i	−0.101341	+	0.210431i
$783$	−9.26136	−	0.0778480i	−0.330974	−	0.00278206i
$784$	5.27615	−	23.1113i	0.188434	−	0.825403i
$785$	−5.53717	−	3.19689i	−0.197630	−	0.114102i
$786$	−8.65639	+	8.39580i	−0.308763	+	0.299468i
$787$	10.8436	−	40.4687i	0.386531	−	1.44255i	−0.449208	−	0.893427i	$-0.648294\pi$
$787$	10.8436	−	40.4687i	0.386531	−	1.44255i	0.835739	−	0.549126i	$-0.185039\pi$
$788$	8.96844	+	20.5572i	0.319487	+	0.732320i
$789$	−0.371070	+	4.10873i	−0.0132105	+	0.146275i
$790$	4.27384	−	22.5863i	0.152056	−	0.803585i
$791$		−	8.28493i		−	0.294578i
$792$	−2.95320	+	13.3586i	−0.104937	+	0.474677i
$793$		−	5.78331i		−	0.205372i
$794$	2.00620	+	0.379619i	0.0711975	+	0.0134722i
$795$	−9.07351	−	6.39130i	−0.321804	−	0.226676i
$796$	−12.9573	+	33.0124i	−0.459259	+	1.17009i
$797$	−9.50379	+	35.4686i	−0.336642	+	1.25636i	0.565437	+	0.824792i	$0.308708\pi$
$797$	−9.50379	+	35.4686i	−0.336642	+	1.25636i	−0.902078	+	0.431572i	$0.857959\pi$
$798$	1.48609	−	5.22542i	0.0526069	−	0.184978i
$799$	2.58968	+	1.49515i	0.0916164	+	0.0528948i
$800$	3.52725	−	4.42250i	0.124707	−	0.156359i
$801$	−6.10141	+	7.18918i	−0.215583	+	0.254017i
$802$	48.7661	+	23.4852i	1.72199	+	0.829292i
$803$	−0.260254	−	0.971282i	−0.00918417	−	0.0342758i
$804$	−0.161771	+	0.788756i	−0.00570524	+	0.0278173i
$805$	−1.04715	+	3.90801i	−0.0369071	+	0.137739i
$806$	1.55630	+	1.33933i	0.0548182	+	0.0471760i
$807$	6.97876	−	19.0081i	0.245664	−	0.669117i
$808$	8.59057	+	16.2556i	0.302215	+	0.571868i
$809$	50.7087			1.78282			0.891412	−	0.453193i	$-0.149715\pi$
$809$	50.7087			1.78282			0.891412	+	0.453193i	$0.149715\pi$
$810$	−11.1703	+	6.10112i	−0.392485	+	0.214371i
$811$	3.10372	−	3.10372i	0.108986	−	0.108986i	−0.650511	−	0.759497i	$-0.725445\pi$
$811$	3.10372	−	3.10372i	0.108986	−	0.108986i	0.759497	+	0.650511i	$0.225445\pi$
$812$	−2.97178	−	2.19338i	−0.104289	−	0.0769725i
$813$	−0.407255	+	0.188519i	−0.0142831	+	0.00661165i
$814$	0.491088	+	6.55415i	0.0172126	+	0.229723i
$815$	−3.22223	−	5.58106i	−0.112870	−	0.195496i
$816$	−7.79226	−	2.53492i	−0.272784	−	0.0887401i
$817$	−11.4384	+	19.8119i	−0.400180	+	0.693132i
$818$	−48.1155	−	23.1719i	−1.68232	−	0.810186i
$819$	−0.457383	−	5.58842i	−0.0159823	−	0.195275i
$820$	9.36682	+	1.05561i	0.327103	+	0.0368635i
$821$	10.6491	+	39.7431i	0.371657	+	1.38704i	0.858168	+	0.513369i	$0.171603\pi$
$821$	10.6491	+	39.7431i	0.371657	+	1.38704i	−0.486511	+	0.873674i	$0.661731\pi$
$822$	−7.22672	−	12.9708i	−0.252061	−	0.452408i
$823$	−10.4538	−	18.1065i	−0.364396	−	0.631152i	0.624283	−	0.781198i	$-0.285391\pi$
$823$	−10.4538	−	18.1065i	−0.364396	−	0.631152i	−0.988679	+	0.150046i	$0.952058\pi$
$824$	−32.2061	−	34.7123i	−1.12195	−	1.20926i
$825$	−0.477231	−	2.75157i	−0.0166150	−	0.0957974i
$826$	2.04672	−	10.8165i	0.0712145	−	0.376353i
$827$	28.5675	+	28.5675i	0.993389	+	0.993389i	0.999978	−	0.00658945i	$-0.00209750\pi$
$827$	28.5675	+	28.5675i	0.993389	+	0.993389i	−0.00658945	+	0.999978i	$0.502098\pi$
$828$	19.9228	+	12.3291i	0.692365	+	0.428465i
$829$	27.3058	−	27.3058i	0.948370	−	0.948370i	−0.0503611	−	0.998731i	$-0.516037\pi$
$829$	27.3058	−	27.3058i	0.948370	−	0.948370i	0.998731	+	0.0503611i	$0.0160372\pi$
$830$	6.08161	−	4.14627i	0.211096	−	0.143919i
$831$	−2.26655	−	2.71659i	−0.0786257	−	0.0942374i
$832$	14.1798	−	2.68191i	0.491594	−	0.0929786i
$833$	6.07035	−	3.50472i	0.210325	−	0.121431i
$834$	−24.9408	+	24.1900i	−0.863628	+	0.837630i
$835$	−0.715448	+	0.191704i	−0.0247591	+	0.00663418i
$836$	5.39679	−	4.30359i	0.186652	−	0.148843i
$837$	−4.04860	+	1.04843i	−0.139940	+	0.0362389i
$838$	−18.2750	−	52.2289i	−0.631299	−	1.80422i
$839$	18.3362	+	10.5864i	0.633036	+	0.365484i	0.781927	−	0.623370i	$-0.214237\pi$
$839$	18.3362	+	10.5864i	0.633036	+	0.365484i	−0.148891	+	0.988854i	$0.547570\pi$
$840$	−5.03469	−	0.645442i	−0.173713	−	0.0222699i
$841$	−22.3634	+	12.9115i	−0.771151	+	0.445224i
$842$	17.5141	+	15.0725i	0.603575	+	0.519431i
$843$	−9.25888	−	0.836194i	−0.318893	−	0.0288001i
$844$	13.3712	+	9.86886i	0.460255	+	0.339700i
$845$	6.89144	+	6.89144i	0.237073	+	0.237073i
$846$	6.31045	−	8.67411i	0.216958	−	0.298222i
$847$		−	8.70372i		−	0.299063i
$848$	−25.6131	+	0.957162i	−0.879557	+	0.0328691i
$849$	6.54278	+	37.7237i	0.224548	+	1.29467i
$850$	1.66796	−	0.124977i	0.0572106	−	0.00428666i
$851$	10.8720	+	2.91315i	0.372688	+	0.0998615i
$852$	1.37236	+	23.0347i	0.0470164	+	0.789156i
$853$	−3.20081	+	0.857656i	−0.109594	+	0.0293656i	−0.313199	−	0.949687i	$-0.601401\pi$
$853$	−3.20081	+	0.857656i	−0.109594	+	0.0293656i	0.203605	+	0.979053i	$0.434734\pi$
$854$	1.55151	+	4.43412i	0.0530915	+	0.151732i
$855$	6.31779	+	1.15054i	0.216064	+	0.0393475i
$856$	33.1193	+	20.8118i	1.13199	+	0.711334i
$857$	−9.45403	+	16.3749i	−0.322943	+	0.559355i	−0.981094	−	0.193532i	$-0.938006\pi$
$857$	−9.45403	+	16.3749i	−0.322943	+	0.559355i	0.658151	+	0.752886i	$0.271339\pi$
$858$	3.65601	−	6.11468i	0.124814	−	0.208752i
$859$	20.7295	+	5.55446i	0.707282	+	0.189516i	0.594490	−	0.804103i	$-0.297354\pi$
$859$	20.7295	+	5.55446i	0.707282	+	0.189516i	0.112792	+	0.993619i	$0.464021\pi$
$860$	19.8969	+	7.80948i	0.678477	+	0.266301i
$861$	−3.55303	−	7.67557i	−0.121087	−	0.261583i
$862$	12.7299	+	18.6718i	0.433582	+	0.635964i
$863$	0.524131			0.0178416			0.00892081	−	0.999960i	$-0.497160\pi$
$863$	0.524131			0.0178416			0.00892081	+	0.999960i	$0.497160\pi$
$864$	−11.9820	+	26.8409i	−0.407636	+	0.913145i
$865$	−10.8765			−0.369811
$866$	2.12278	+	3.11363i	0.0721352	+	0.105806i
$867$	11.3513	+	24.5221i	0.385511	+	0.832815i
$868$	−1.55253	−	0.609367i	−0.0526964	−	0.0206833i
$869$	−25.3145	−	6.78299i	−0.858735	−	0.230097i
$870$	2.24052	−	3.74727i	0.0759607	−	0.127044i
$871$	0.209643	−	0.363112i	0.00710348	−	0.0123036i
$872$	−29.6026	+	47.1085i	−1.00247	+	1.59530i
$873$	−11.6061	−	32.4522i	−0.392807	−	1.09834i
$874$	−3.90404	−	11.1575i	−0.132056	−	0.377409i
$875$	1.00081	−	0.268165i	0.0338334	−	0.00906565i
$876$	−0.128485	−	2.15659i	−0.00434112	−	0.0728643i
$877$	2.63366	+	0.705688i	0.0889325	+	0.0238294i	0.303011	−	0.952987i	$-0.402008\pi$
$877$	2.63366	+	0.705688i	0.0889325	+	0.0238294i	−0.214078	+	0.976816i	$0.568675\pi$
$878$	53.4992	−	4.00858i	1.80551	−	0.135283i
$879$	−6.57400	−	37.9037i	−0.221736	−	1.27846i
$880$	−4.72750	−	4.38689i	−0.159364	−	0.147882i
$881$			48.6117i			1.63777i	0.573959	+	0.818884i	$0.305407\pi$
$881$			48.6117i			1.63777i	−0.573959	+	0.818884i	$0.694593\pi$
$882$	−10.2125	−	22.9765i	−0.343873	−	0.773660i
$883$	33.4241	+	33.4241i	1.12481	+	1.12481i	0.991008	+	0.133801i	$0.0427182\pi$
$883$	33.4241	+	33.4241i	1.12481	+	1.12481i	0.133801	+	0.991008i	$0.457282\pi$
$884$	3.43320	+	2.53394i	0.115471	+	0.0852256i
$885$	12.9599	+	1.17044i	0.435641	+	0.0393439i
$886$	−1.48871	−	1.28117i	−0.0500144	−	0.0430419i
$887$	−26.7733	+	15.4576i	−0.898961	+	0.519015i	−0.876863	−	0.480741i	$-0.840368\pi$
$887$	−26.7733	+	15.4576i	−0.898961	+	0.519015i	−0.0220979	+	0.999756i	$0.507035\pi$
$888$	−1.79561	+	14.0064i	−0.0602568	+	0.470025i
$889$	−7.18153	−	4.14626i	−0.240861	−	0.139061i
$890$	−1.46804	−	4.19559i	−0.0492089	−	0.140636i
$891$	5.98485	+	13.2194i	0.200500	+	0.442865i
$892$	21.8915	−	17.4571i	0.732983	−	0.584506i
$893$	−5.22759	+	1.40073i	−0.174935	+	0.0468736i
$894$	37.7223	−	36.5868i	1.26162	−	1.22364i
$895$	−12.0746	+	6.97129i	−0.403611	+	0.233025i
$896$	−10.1523	+	5.86029i	−0.339163	+	0.195779i
$897$	−7.81609	−	9.36804i	−0.260972	−	0.312790i
$898$	12.8632	−	8.76976i	0.429251	−	0.292651i
$899$	1.01440	−	1.01440i	0.0338323	−	0.0338323i
$900$	0.183335	−	5.99720i	0.00611116	−	0.199907i
$901$	−5.35891	−	5.35891i	−0.178531	−	0.178531i
$902$	1.99805	−	10.5593i	0.0665279	−	0.351585i
$903$	−3.27753	−	18.8973i	−0.109069	−	0.628862i
$904$	16.5797	−	15.3826i	0.551432	−	0.511618i
$905$	8.63944	+	14.9639i	0.287185	+	0.497418i
$906$	19.9071	+	35.7300i	0.661368	+	1.18705i
$907$	−8.99169	−	33.5574i	−0.298564	−	1.11426i	−0.938345	−	0.345700i	$-0.887642\pi$
$907$	−8.99169	−	33.5574i	−0.298564	−	1.11426i	0.639781	−	0.768557i	$-0.279025\pi$
$908$	0.924331	+	0.104169i	0.0306750	+	0.00345698i
$909$	17.6276	+	8.34046i	0.584671	+	0.276636i
$910$	2.38144	+	1.14688i	0.0789440	+	0.0380186i
$911$	−13.3228	+	23.0758i	−0.441404	+	0.764534i	−0.997794	−	0.0663873i	$-0.978853\pi$
$911$	−13.3228	+	23.0758i	−0.441404	+	0.764534i	0.556390	+	0.830921i	$0.312186\pi$
$912$	13.2163	−	6.72810i	0.437634	−	0.222790i
$913$	−4.19586	−	7.26743i	−0.138863	−	0.240517i
$914$	2.42601	+	32.3780i	0.0802453	+	1.07097i
$915$	−5.03927	+	2.33268i	−0.166593	+	0.0771161i
$916$	12.3355	+	9.10445i	0.407576	+	0.300819i
$917$	−3.60688	+	3.60688i	−0.119110	+	0.119110i
$918$	−8.22742	+	2.80139i	−0.271545	+	0.0924598i
$919$	−11.6923			−0.385693			−0.192847	−	0.981229i	$-0.561772\pi$
$919$	−11.6923			−0.385693			−0.192847	+	0.981229i	$0.561772\pi$
$920$	−9.76488	+	5.16045i	−0.321939	+	0.170135i
$921$	7.72434	−	21.0388i	0.254526	−	0.693254i
$922$	23.0538	+	19.8399i	0.759237	+	0.653392i
$923$	3.11006	−	11.6069i	0.102369	−	0.382045i
$924$	−1.16269	+	5.66899i	−0.0382498	+	0.186496i
$925$	−0.746033	−	2.78423i	−0.0245294	−	0.0915450i
$926$	−16.3252	−	7.86202i	−0.536478	−	0.258362i
$927$	−49.4113	−	8.99833i	−1.62288	−	0.295544i
$928$	−1.12833	−	10.0195i	−0.0370392	−	0.328907i
$929$	−33.9481	−	19.5999i	−1.11380	−	0.643053i	−0.173989	−	0.984748i	$-0.555666\pi$
$929$	−33.9481	−	19.5999i	−1.11380	−	0.643053i	−0.939811	+	0.341695i	$0.888999\pi$
$930$	0.539295	−	1.89629i	0.0176842	−	0.0621818i
$931$	−3.28338	+	12.2537i	−0.107608	+	0.401600i
$932$	−12.2294	+	31.1578i	−0.400587	+	1.02061i
$933$	12.7645	+	8.99119i	0.417890	+	0.294358i
$934$	−39.0045	−	7.38052i	−1.27627	−	0.241498i
$935$		−	1.90696i		−	0.0623644i
$936$	10.3342	−	11.2913i	0.337785	−	0.369068i
$937$		−	8.79446i		−	0.287303i	−0.989628	−	0.143651i	$-0.954116\pi$
$937$		−	8.79446i		−	0.287303i	0.989628	−	0.143651i	$-0.0458844\pi$
$938$	−0.0633220	+	0.334643i	−0.00206754	+	0.0109265i
$939$	4.80557	−	53.2104i	0.156824	−	1.73646i
$940$	2.02199	+	4.63475i	0.0659500	+	0.151169i
$941$	−9.76036	+	36.4261i	−0.318179	+	1.18746i	0.602815	+	0.797881i	$0.294046\pi$
$941$	−9.76036	+	36.4261i	−0.318179	+	1.18746i	−0.920994	+	0.389578i	$0.872621\pi$
$942$	−11.2423	+	10.9038i	−0.366293	+	0.355266i
$943$	−15.9382	−	9.20190i	−0.519018	−	0.299655i
$944$	25.4459	−	15.9871i	0.828194	−	0.520334i
$945$	−4.68496	+	2.65261i	−0.152402	+	0.0862895i
$946$	10.5736	−	21.9556i	0.343777	−	0.713839i
$947$	7.21943	+	26.9433i	0.234600	+	0.875539i	0.978329	+	0.207058i	$0.0663888\pi$
$947$	7.21943	+	26.9433i	0.234600	+	0.875539i	−0.743729	+	0.668482i	$0.766945\pi$
$948$	−50.3511	−	25.2035i	−1.63533	−	0.818570i
$949$	−0.291174	+	1.08668i	−0.00945191	+	0.0352750i
$950$	−1.97464	+	2.29452i	−0.0640658	+	0.0744441i
$951$	7.84674	+	9.40477i	0.254448	+	0.304970i
$952$	−3.31205	−	1.02176i	−0.107344	−	0.0331155i
$953$	−0.350019			−0.0113382			−0.00566912	−	0.999984i	$-0.501805\pi$
$953$	−0.350019			−0.0113382			−0.00566912	+	0.999984i	$0.501805\pi$
$954$	−21.1380	+	17.0952i	−0.684369	+	0.553479i
$955$	16.0347	−	16.0347i	0.518871	−	0.518871i
$956$	−37.4712	+	5.64696i	−1.21190	+	0.182636i
$957$	−4.06944	−	2.86648i	−0.131546	−	0.0926600i
$958$	−42.1980	+	3.16180i	−1.36335	+	0.102153i
$959$	−3.14031	−	5.43918i	−0.101406	−	0.175640i
$960$	−8.05624	−	11.2737i	−0.260014	−	0.363858i
$961$	−15.1761	+	26.2858i	−0.489552	+	0.847928i
$962$	3.19059	−	6.62514i	0.102869	−	0.213603i
$963$	41.3499	−	3.38428i	1.33248	−	0.109057i
$964$	22.7637	+	28.5462i	0.733169	+	0.919410i
$965$	−4.47533	−	16.7021i	−0.144066	−	0.537661i
$966$	8.50586	+	5.08571i	0.273672	+	0.163630i
$967$	−26.3372	−	45.6174i	−0.846948	−	1.46696i	−0.883919	−	0.467640i	$-0.845104\pi$
$967$	−26.3372	−	45.6174i	−0.846948	−	1.46696i	0.0369713	−	0.999316i	$-0.488229\pi$
$968$	17.4178	−	16.1602i	0.559828	−	0.519408i
$969$	4.11639	+	1.51132i	0.132238	+	0.0485505i
$970$	15.9637	+	3.02070i	0.512565	+	0.0969887i
$971$	−29.6463	−	29.6463i	−0.951395	−	0.951395i	0.0474776	−	0.998872i	$-0.484882\pi$
$971$	−29.6463	−	29.6463i	−0.951395	−	0.951395i	−0.998872	+	0.0474776i	$0.984882\pi$
$972$	6.88991	+	30.4061i	0.220994	+	0.975275i
$973$	−10.3921	+	10.3921i	−0.333157	+	0.333157i
$974$	−26.3415	−	38.6368i	−0.844035	−	1.23800i
$975$	−1.07684	+	2.93300i	−0.0344865	+	0.0939313i
$976$	−5.99282	+	11.3377i	−0.191826	+	0.362910i
$977$	32.9221	−	19.0076i	1.05327	−	0.608107i	0.129708	−	0.991552i	$-0.458596\pi$
$977$	32.9221	−	19.0076i	1.05327	−	0.608107i	0.923564	+	0.383445i	$0.125263\pi$
$978$	−15.3084	+	3.85216i	−0.489508	+	0.123179i
$979$	−4.89505	+	1.31162i	−0.156446	+	0.0419197i
$980$	11.7784	+	1.32739i	0.376247	+	0.0424018i
$981$	4.81377	+	58.8158i	0.153692	+	1.87784i
$982$	40.0265	−	14.0054i	1.27730	−	0.446929i
$983$	−37.3347	−	21.5552i	−1.19079	−	0.687505i	−0.232307	−	0.972643i	$-0.574627\pi$
$983$	−37.3347	−	21.5552i	−1.19079	−	0.687505i	−0.958487	+	0.285138i	$0.907961\pi$
$984$	8.76334	−	21.3615i	0.279365	−	0.680979i
$985$	−9.71176	+	5.60709i	−0.309443	+	0.178657i
$986$	1.94471	−	2.25974i	0.0619322	−	0.0719648i
$987$	2.61289	−	3.70943i	0.0831691	−	0.118072i
$988$	−7.63647	+	1.15083i	−0.242949	+	0.0366127i
$989$	−29.5092	−	29.5092i	−0.938338	−	0.938338i
$990$	−6.80264	−	0.719311i	−0.216202	−	0.0228612i
$991$		−	15.2160i		−	0.483351i	−0.970357	−	0.241676i	$-0.922303\pi$
$991$		−	15.2160i		−	0.483351i	0.970357	−	0.241676i	$-0.0776970\pi$
$992$	−1.66313	−	4.23832i	−0.0528044	−	0.134567i
$993$	−5.06282	+	4.22410i	−0.160664	+	0.134048i
$994$	0.729306	+	9.73345i	0.0231322	+	0.308726i
$995$	−17.1279	−	4.58940i	−0.542990	−	0.145494i
$996$	−5.69387	−	17.1069i	−0.180417	−	0.542052i
$997$	4.81679	−	1.29065i	0.152549	−	0.0408754i	−0.181736	−	0.983347i	$-0.558172\pi$
$997$	4.81679	−	1.29065i	0.152549	−	0.0408754i	0.334285	+	0.942472i	$0.391505\pi$
$998$	2.02044	−	0.706955i	0.0639559	−	0.0223783i
$999$	7.37953	+	13.0335i	0.233478	+	0.412362i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.cf.a.11.67	✓	384
9.5	odd	6	inner	720.2.cf.a.491.93	yes	384
16.3	odd	4	inner	720.2.cf.a.371.93	yes	384
144.131	even	12	inner	720.2.cf.a.131.67	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.cf.a.11.67	✓	384	1.1	even	1	trivial
720.2.cf.a.131.67	yes	384	144.131	even	12	inner
720.2.cf.a.371.93	yes	384	16.3	odd	4	inner
720.2.cf.a.491.93	yes	384	9.5	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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.cf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.796641 + 1.16849i) q^{2} +(0.727595 + 1.57182i) q^{3} +(-0.730726 + 1.86173i) q^{4} +(-0.965926 - 0.258819i) q^{5} +(-1.25701 + 2.10236i) q^{6} +(-0.518056 + 0.897299i) q^{7} +(-2.75753 + 0.629287i) q^{8} +(-1.94121 + 2.28729i) q^{9} +(-0.467069 - 1.33486i) q^{10} +(-1.55740 + 0.417303i) q^{11} +(-3.45797 + 0.206019i) q^{12} +(1.74243 + 0.466882i) q^{13} +(-1.46119 + 0.109483i) q^{14} +(-0.295987 - 1.70657i) q^{15} +(-2.93208 - 2.72083i) q^{16} -1.18273i q^{17} +(-4.21912 - 0.446130i) q^{18} +(1.51361 + 1.51361i) q^{19} +(1.18768 - 1.60917i) q^{20} +(-1.78732 - 0.161418i) q^{21} +(-1.72830 - 1.48736i) q^{22} +(-3.38170 + 1.95243i) q^{23} +(-2.99549 - 3.87647i) q^{24} +(0.866025 + 0.500000i) q^{25} +(0.842543 + 2.40794i) q^{26} +(-5.00762 - 1.38700i) q^{27} +(-1.29197 - 1.62016i) q^{28} +(1.72168 - 0.461322i) q^{29} +(1.75831 - 1.70538i) q^{30} +(0.697025 - 0.402428i) q^{31} +(0.843441 - 5.59362i) q^{32} +(-1.78908 - 2.14431i) q^{33} +(1.38201 - 0.942214i) q^{34} +(0.732642 - 0.732642i) q^{35} +(-2.83983 - 5.28539i) q^{36} +(-2.03820 - 2.03820i) q^{37} +(-0.562830 + 2.97443i) q^{38} +(0.533929 + 3.07848i) q^{39} +(2.82645 + 0.105858i) q^{40} +(2.35653 + 4.08163i) q^{41} +(-1.23524 - 2.21706i) q^{42} +(2.76608 + 10.3231i) q^{43} +(0.361125 - 3.20439i) q^{44} +(2.46706 - 1.70693i) q^{45} +(-4.97539 - 2.39609i) q^{46} +(-1.26415 + 2.18958i) q^{47} +(2.14328 - 6.58835i) q^{48} +(2.96324 + 5.13248i) q^{49} +(0.105668 + 1.41026i) q^{50} +(1.85904 - 0.860551i) q^{51} +(-2.14245 + 2.90277i) q^{52} +(4.53096 - 4.53096i) q^{53} +(-2.36858 - 6.95628i) q^{54} +1.61234 q^{55} +(0.863899 - 2.80034i) q^{56} +(-1.27782 + 3.48041i) q^{57} +(1.91061 + 1.64425i) q^{58} +(-1.94446 + 7.25683i) q^{59} +(3.39346 + 0.695989i) q^{60} +(-0.829778 - 3.09678i) q^{61} +(1.02551 + 0.493875i) q^{62} +(-1.04673 - 2.92679i) q^{63} +(7.20800 - 3.47056i) q^{64} +(-1.56222 - 0.901947i) q^{65} +(1.08035 - 3.79877i) q^{66} +(0.0601583 - 0.224514i) q^{67} +(2.20193 + 0.864254i) q^{68} +(-5.52937 - 3.89484i) q^{69} +(1.43973 + 0.272430i) q^{70} -6.66133i q^{71} +(3.91359 - 7.52886i) q^{72} +0.623657i q^{73} +(0.757897 - 4.00532i) q^{74} +(-0.155792 + 1.72503i) q^{75} +(-3.92396 + 1.71190i) q^{76} +(0.432373 - 1.61364i) q^{77} +(-3.17181 + 3.07633i) q^{78} +(14.0767 + 8.12717i) q^{79} +(2.12797 + 3.38700i) q^{80} +(-1.46340 - 8.88023i) q^{81} +(-2.89202 + 6.00516i) q^{82} +(1.34707 + 5.02734i) q^{83} +(1.60656 - 3.20956i) q^{84} +(-0.306114 + 1.14243i) q^{85} +(-9.85888 + 11.4560i) q^{86} +(1.97780 + 2.37051i) q^{87} +(4.03197 - 2.13078i) q^{88} +3.14310 q^{89} +(3.95989 + 1.52292i) q^{90} +(-1.32161 + 1.32161i) q^{91} +(-1.16379 - 7.72251i) q^{92} +(1.13969 + 0.802791i) q^{93} +(-3.56557 + 0.267160i) q^{94} +(-1.07028 - 1.85378i) q^{95} +(9.40583 - 2.74416i) q^{96} +(-5.74419 + 9.94922i) q^{97} +(-3.63660 + 7.55125i) q^{98} +(2.06874 - 4.37230i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 12 q^{6} + 24 q^{12} + 20 q^{18} - 24 q^{24} + 24 q^{27} - 12 q^{36} + 48 q^{39} - 80 q^{42} + 24 q^{46} - 40 q^{48} - 192 q^{49} + 40 q^{51} + 12 q^{54} - 36 q^{58} + 72 q^{59} - 28 q^{60} + 72 q^{64}+ \cdots - 32 q^{99}+O(q^{100}) \) 384 * q - 12 * q^6 + 24 * q^12 + 20 * q^18 - 24 * q^24 + 24 * q^27 - 12 * q^36 + 48 * q^39 - 80 * q^42 + 24 * q^46 - 40 * q^48 - 192 * q^49 + 40 * q^51 + 12 * q^54 - 36 * q^58 + 72 * q^59 - 28 * q^60 + 72 * q^64 - 72 * q^66 - 156 * q^68 - 112 * q^72 - 168 * q^74 + 12 * q^76 - 116 * q^78 + 72 * q^82 - 120 * q^83 - 116 * q^84 - 36 * q^90 + 48 * q^93 + 20 * q^96 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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