LMFDB - Embedded newform 740.2.be.a.51.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [740,2,Mod(51,740)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(740, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 11]))

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

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

chi := DirichletCharacter("740.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.be (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:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$304$
Relative dimension:	$76$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			51.14
Character	$\chi$	$=$	740.51
Dual form			740.2.be.a.711.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.16908 - 0.795771i) q^{2} +(-0.450967 - 0.781098i) q^{3} +(0.733498 + 1.86064i) q^{4} +(0.965926 + 0.258819i) q^{5} +(-0.0943580 + 1.27203i) q^{6} +(2.84609 - 1.64319i) q^{7} +(0.623124 - 2.75893i) q^{8} +(1.09326 - 1.89358i) q^{9} +(-0.923284 - 1.07124i) q^{10} -2.76913 q^{11} +(1.12256 - 1.41202i) q^{12} +(4.40649 + 1.18072i) q^{13} +(-4.63491 - 0.343813i) q^{14} +(-0.233438 - 0.871201i) q^{15} +(-2.92396 + 2.72955i) q^{16} +(0.910419 + 3.39773i) q^{17} +(-2.78496 + 1.34376i) q^{18} +(0.156042 - 0.582356i) q^{19} +(0.226936 + 1.98708i) q^{20} +(-2.56698 - 1.48205i) q^{21} +(3.23734 + 2.20359i) q^{22} +(1.20084 + 1.20084i) q^{23} +(-2.43601 + 0.757467i) q^{24} +(0.866025 + 0.500000i) q^{25} +(-4.21196 - 4.88691i) q^{26} -4.67789 q^{27} +(5.14499 + 4.09027i) q^{28} +(-0.280016 - 0.280016i) q^{29} +(-0.420369 + 1.20427i) q^{30} +(5.98672 - 5.98672i) q^{31} +(5.59044 - 0.864263i) q^{32} +(1.24879 + 2.16296i) q^{33} +(1.63946 - 4.69671i) q^{34} +(3.17440 - 0.850578i) q^{35} +(4.32517 + 0.645223i) q^{36} +(1.50943 + 5.89251i) q^{37} +(-0.645847 + 0.556647i) q^{38} +(-1.06493 - 3.97436i) q^{39} +(1.31596 - 2.50365i) q^{40} +(0.748977 - 0.432422i) q^{41} +(1.82164 + 3.77537i) q^{42} +(-0.482448 - 0.482448i) q^{43} +(-2.03115 - 5.15236i) q^{44} +(1.54610 - 1.54610i) q^{45} +(-0.448287 - 2.35948i) q^{46} -7.27413i q^{47} +(3.45066 + 1.05296i) q^{48} +(1.90015 - 3.29116i) q^{49} +(-0.614568 - 1.27370i) q^{50} +(2.24339 - 2.24339i) q^{51} +(1.03527 + 9.06495i) q^{52} +(-0.837930 + 1.45134i) q^{53} +(5.46883 + 3.72253i) q^{54} +(-2.67478 - 0.716704i) q^{55} +(-2.75999 - 8.87609i) q^{56} +(-0.525246 + 0.140739i) q^{57} +(0.104533 + 0.550190i) q^{58} +(-7.59618 + 2.03539i) q^{59} +(1.44977 - 1.07337i) q^{60} +(3.68670 - 13.7589i) q^{61} +(-11.7630 + 2.23490i) q^{62} -7.18572i q^{63} +(-7.22343 - 3.43832i) q^{64} +(3.95075 + 2.28097i) q^{65} +(0.261290 - 3.52242i) q^{66} +(-4.35361 - 7.54067i) q^{67} +(-5.65416 + 4.18619i) q^{68} +(0.396435 - 1.47952i) q^{69} +(-4.38800 - 1.53170i) q^{70} +(4.03663 - 2.33055i) q^{71} +(-4.54302 - 4.19616i) q^{72} +4.22786i q^{73} +(2.92444 - 8.08997i) q^{74} -0.901934i q^{75} +(1.19801 - 0.136819i) q^{76} +(-7.88120 + 4.55021i) q^{77} +(-1.91770 + 5.49379i) q^{78} +(0.270699 - 1.01026i) q^{79} +(-3.53079 + 1.87977i) q^{80} +(-1.17020 - 2.02684i) q^{81} +(-1.21972 - 0.0904777i) q^{82} +(5.63912 + 3.25575i) q^{83} +(0.874681 - 5.86331i) q^{84} +3.51759i q^{85} +(0.180103 + 0.947939i) q^{86} +(-0.0924420 + 0.344998i) q^{87} +(-1.72551 + 7.63985i) q^{88} +(-15.9878 + 4.28392i) q^{89} +(-3.03786 + 0.577174i) q^{90} +(14.4814 - 3.88028i) q^{91} +(-1.35352 + 3.11515i) q^{92} +(-7.37603 - 1.97640i) q^{93} +(-5.78854 + 8.50405i) q^{94} +(0.301449 - 0.522126i) q^{95} +(-3.19618 - 3.97693i) q^{96} +(11.7848 - 11.7848i) q^{97} +(-4.84044 + 2.33555i) q^{98} +(-3.02737 + 5.24356i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 304 q + 4 q^{2} - 12 q^{4} - 8 q^{8} - 152 q^{9} + 16 q^{13} - 24 q^{14} + 20 q^{16} - 60 q^{18} - 16 q^{22} - 24 q^{24} - 32 q^{29} - 56 q^{32} - 32 q^{37} + 40 q^{38} + 20 q^{42} + 12 q^{44} - 8 q^{46}+ \cdots - 36 q^{98}+O(q^{100}) $ 304 * q + 4 * q^2 - 12 * q^4 - 8 * q^8 - 152 * q^9 + 16 * q^13 - 24 * q^14 + 20 * q^16 - 60 * q^18 - 16 * q^22 - 24 * q^24 - 32 * q^29 - 56 * q^32 - 32 * q^37 + 40 * q^38 + 20 * q^42 + 12 * q^44 - 8 * q^46 + 104 * q^49 + 4 * q^50 - 40 * q^52 + 40 * q^54 + 4 * q^56 - 48 * q^57 - 12 * q^58 - 28 * q^60 - 16 * q^61 - 60 * q^62 + 24 * q^65 - 52 * q^66 - 200 * q^68 - 196 * q^72 + 20 * q^74 - 40 * q^76 + 96 * q^77 - 48 * q^78 - 152 * q^81 + 32 * q^82 - 112 * q^84 + 12 * q^88 - 8 * q^89 + 140 * q^92 - 16 * q^93 - 28 * q^94 - 132 * q^96 + 48 * q^97 - 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{11}{12}\right)$	$1$	$-1$

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 $

$2$	−1.16908	−	0.795771i	−0.826665	−	0.562695i
$2$	−1.16908	−	0.795771i	−0.826665	−	0.562695i
$3$	−0.450967	−	0.781098i	−0.260366	−	0.450967i	0.705973	−	0.708238i	$-0.250510\pi$
$3$	−0.450967	−	0.781098i	−0.260366	−	0.450967i	−0.966339	+	0.257272i	$0.917177\pi$
$4$	0.733498	+	1.86064i	0.366749	+	0.930320i
$5$	0.965926	+	0.258819i	0.431975	+	0.115747i
$5$	0.965926	+	0.258819i	0.431975	+	0.115747i
$6$	−0.0943580	+	1.27203i	−0.0385215	+	0.519305i
$7$	2.84609	−	1.64319i	1.07572	−	0.621068i	0.145982	−	0.989287i	$-0.453366\pi$
$7$	2.84609	−	1.64319i	1.07572	−	0.621068i	0.929739	+	0.368219i	$0.120033\pi$
$8$	0.623124	−	2.75893i	0.220308	−	0.975430i
$9$	1.09326	−	1.89358i	0.364419	−	0.631193i
$10$	−0.923284	−	1.07124i	−0.291968	−	0.338754i
$11$	−2.76913			−0.834924			−0.417462	−	0.908694i	$-0.637080\pi$
$11$	−2.76913			−0.834924			−0.417462	+	0.908694i	$0.637080\pi$
$12$	1.12256	−	1.41202i	0.324055	−	0.407615i
$13$	4.40649	+	1.18072i	1.22214	+	0.327472i	0.811515	−	0.584332i	$-0.198643\pi$
$13$	4.40649	+	1.18072i	1.22214	+	0.327472i	0.410626	+	0.911804i	$0.365310\pi$
$14$	−4.63491	−	0.343813i	−1.23873	−	0.0918878i
$15$	−0.233438	−	0.871201i	−0.0602733	−	0.224943i
$16$	−2.92396	+	2.72955i	−0.730990	+	0.682388i
$17$	0.910419	+	3.39773i	0.220809	+	0.824071i	0.984040	+	0.177945i	$0.0569450\pi$
$17$	0.910419	+	3.39773i	0.220809	+	0.824071i	−0.763231	+	0.646125i	$0.776388\pi$
$18$	−2.78496	+	1.34376i	−0.656421	+	0.316728i
$19$	0.156042	−	0.582356i	0.0357984	−	0.133602i	−0.945714	−	0.325000i	$-0.894636\pi$
$19$	0.156042	−	0.582356i	0.0357984	−	0.133602i	0.981512	+	0.191399i	$0.0613023\pi$
$20$	0.226936	+	1.98708i	0.0507444	+	0.444325i
$21$	−2.56698	−	1.48205i	−0.560162	−	0.323410i
$22$	3.23734	+	2.20359i	0.690203	+	0.469808i
$23$	1.20084	+	1.20084i	0.250393	+	0.250393i	0.821132	−	0.570739i	$-0.193343\pi$
$23$	1.20084	+	1.20084i	0.250393	+	0.250393i	−0.570739	+	0.821132i	$0.693343\pi$
$24$	−2.43601	+	0.757467i	−0.497247	+	0.154617i
$25$	0.866025	+	0.500000i	0.173205	+	0.100000i
$26$	−4.21196	−	4.88691i	−0.826034	−	0.958401i
$27$	−4.67789			−0.900261
$28$	5.14499	+	4.09027i	0.972311	+	0.772989i
$29$	−0.280016	−	0.280016i	−0.0519977	−	0.0519977i	0.680630	−	0.732628i	$-0.261706\pi$
$29$	−0.280016	−	0.280016i	−0.0519977	−	0.0519977i	−0.732628	+	0.680630i	$0.761706\pi$
$30$	−0.420369	+	1.20427i	−0.0767485	+	0.219868i
$31$	5.98672	−	5.98672i	1.07525	−	1.07525i	0.0783182	−	0.996928i	$-0.475045\pi$
$31$	5.98672	−	5.98672i	1.07525	−	1.07525i	0.996928	−	0.0783182i	$-0.0249550\pi$
$32$	5.59044	−	0.864263i	0.988260	−	0.152782i
$33$	1.24879	+	2.16296i	0.217386	+	0.376523i
$34$	1.63946	−	4.69671i	0.281165	−	0.805478i
$35$	3.17440	−	0.850578i	0.536572	−	0.143774i
$36$	4.32517	+	0.645223i	0.720861	+	0.107537i
$37$	1.50943	+	5.89251i	0.248148	+	0.968722i
$37$	1.50943	+	5.89251i	0.248148	+	0.968722i
$38$	−0.645847	+	0.556647i	−0.104770	+	0.0903001i
$39$	−1.06493	−	3.97436i	−0.170525	−	0.636408i
$40$	1.31596	−	2.50365i	0.208071	−	0.395862i
$41$	0.748977	−	0.432422i	0.116971	−	0.0675330i	−0.440373	−	0.897815i	$-0.645154\pi$
$41$	0.748977	−	0.432422i	0.116971	−	0.0675330i	0.557344	+	0.830282i	$0.311821\pi$
$42$	1.82164	+	3.77537i	0.281085	+	0.582552i
$43$	−0.482448	−	0.482448i	−0.0735726	−	0.0735726i	0.669363	−	0.742936i	$-0.266567\pi$
$43$	−0.482448	−	0.482448i	−0.0735726	−	0.0735726i	−0.742936	+	0.669363i	$0.766567\pi$
$44$	−2.03115	−	5.15236i	−0.306208	−	0.776747i
$45$	1.54610	−	1.54610i	0.230479	−	0.230479i
$46$	−0.448287	−	2.35948i	−0.0660962	−	0.347886i
$47$		−	7.27413i		−	1.06104i	−0.847672	−	0.530521i	$-0.821996\pi$
$47$		−	7.27413i		−	1.06104i	0.847672	−	0.530521i	$-0.178004\pi$
$48$	3.45066	+	1.05296i	0.498059	+	0.151982i
$49$	1.90015	−	3.29116i	0.271450	−	0.470166i
$50$	−0.614568	−	1.27370i	−0.0869130	−	0.180128i
$51$	2.24339	−	2.24339i	0.314138	−	0.314138i
$52$	1.03527	+	9.06495i	0.143566	+	1.25708i
$53$	−0.837930	+	1.45134i	−0.115099	+	0.199356i	−0.917819	−	0.396999i	$-0.870052\pi$
$53$	−0.837930	+	1.45134i	−0.115099	+	0.199356i	0.802721	+	0.596355i	$0.203385\pi$
$54$	5.46883	+	3.72253i	0.744214	+	0.506572i
$55$	−2.67478	−	0.716704i	−0.360667	−	0.0966403i
$56$	−2.75999	−	8.87609i	−0.368819	−	1.18612i
$57$	−0.525246	+	0.140739i	−0.0695706	+	0.0186414i
$58$	0.104533	+	0.550190i	0.0137258	+	0.0722435i
$59$	−7.59618	+	2.03539i	−0.988938	+	0.264985i	−0.716805	−	0.697274i	$-0.754396\pi$
$59$	−7.59618	+	2.03539i	−0.988938	+	0.264985i	−0.272134	+	0.962259i	$0.587729\pi$
$60$	1.44977	−	1.07337i	0.187164	−	0.138571i
$61$	3.68670	−	13.7589i	0.472033	−	1.76165i	−0.160415	−	0.987050i	$-0.551283\pi$
$61$	3.68670	−	13.7589i	0.472033	−	1.76165i	0.632448	−	0.774603i	$-0.282050\pi$
$62$	−11.7630	+	2.23490i	−1.49390	+	0.283833i
$63$		−	7.18572i		−	0.905316i
$64$	−7.22343	−	3.43832i	−0.902929	−	0.429790i
$65$	3.95075	+	2.28097i	0.490030	+	0.282919i
$66$	0.261290	−	3.52242i	0.0321625	−	0.433580i
$67$	−4.35361	−	7.54067i	−0.531878	−	0.921239i	−0.999308	−	0.0372090i	$-0.988153\pi$
$67$	−4.35361	−	7.54067i	−0.531878	−	0.921239i	0.467430	−	0.884030i	$-0.345180\pi$
$68$	−5.65416	+	4.18619i	−0.685668	+	0.507650i
$69$	0.396435	−	1.47952i	0.0477252	−	0.178113i
$70$	−4.38800	−	1.53170i	−0.524466	−	0.183073i
$71$	4.03663	−	2.33055i	0.479060	−	0.276585i	−0.240965	−	0.970534i	$-0.577464\pi$
$71$	4.03663	−	2.33055i	0.479060	−	0.276585i	0.720025	+	0.693948i	$0.244130\pi$
$72$	−4.54302	−	4.19616i	−0.535400	−	0.494522i
$73$			4.22786i			0.494833i	0.968909	+	0.247417i	$0.0795816\pi$
$73$			4.22786i			0.494833i	−0.968909	+	0.247417i	$0.920418\pi$
$74$	2.92444	−	8.08997i	0.339959	−	0.940440i
$75$		−	0.901934i		−	0.104146i
$76$	1.19801	−	0.136819i	0.137421	−	0.0156943i
$77$	−7.88120	+	4.55021i	−0.898146	+	0.518545i
$78$	−1.91770	+	5.49379i	−0.217136	+	0.622049i
$79$	0.270699	−	1.01026i	0.0304560	−	0.113663i	−0.949024	−	0.315202i	$-0.897928\pi$
$79$	0.270699	−	1.01026i	0.0304560	−	0.113663i	0.979481	+	0.201539i	$0.0645943\pi$
$80$	−3.53079	+	1.87977i	−0.394754	+	0.210164i
$81$	−1.17020	−	2.02684i	−0.130022	−	0.225205i
$82$	−1.21972	−	0.0904777i	−0.134696	−	0.00999159i
$83$	5.63912	+	3.25575i	0.618974	+	0.357365i	0.776469	−	0.630155i	$-0.217009\pi$
$83$	5.63912	+	3.25575i	0.618974	+	0.357365i	−0.157496	+	0.987520i	$0.550342\pi$
$84$	0.874681	−	5.86331i	0.0954356	−	0.639740i
$85$			3.51759i			0.381536i
$86$	0.180103	+	0.947939i	0.0194210	+	0.102219i
$87$	−0.0924420	+	0.344998i	−0.00991082	+	0.0369877i
$88$	−1.72551	+	7.63985i	−0.183940	+	0.814411i
$89$	−15.9878	+	4.28392i	−1.69470	+	0.454095i	−0.971597	−	0.236641i	$-0.923953\pi$
$89$	−15.9878	+	4.28392i	−1.69470	+	0.454095i	−0.723107	+	0.690736i	$0.757287\pi$
$90$	−3.03786	+	0.577174i	−0.320218	+	0.0608395i
$91$	14.4814	−	3.88028i	1.51806	−	0.406764i
$92$	−1.35352	+	3.11515i	−0.141114	+	0.324777i
$93$	−7.37603	−	1.97640i	−0.764858	−	0.204943i
$94$	−5.78854	+	8.50405i	−0.597043	+	0.877126i
$95$	0.301449	−	0.522126i	0.0309281	−	0.0535690i
$96$	−3.19618	−	3.97693i	−0.326209	−	0.405893i
$97$	11.7848	−	11.7848i	1.19657	−	1.19657i	0.221381	−	0.975187i	$-0.428944\pi$
$97$	11.7848	−	11.7848i	1.19657	−	1.19657i	0.975187	−	0.221381i	$-0.0710564\pi$
$98$	−4.84044	+	2.33555i	−0.488958	+	0.235926i
$99$	−3.02737	+	5.24356i	−0.304262	+	0.526998i
$100$	−0.295092	+	1.97811i	−0.0295092	+	0.197811i
$101$			1.75774i			0.174902i	0.996169	+	0.0874509i	$0.0278721\pi$
$101$			1.75774i			0.174902i	−0.996169	+	0.0874509i	$0.972128\pi$
$102$	−4.40793	+	0.837480i	−0.436450	+	0.0829229i
$103$	−1.82211	+	1.82211i	−0.179537	+	0.179537i	−0.791154	−	0.611617i	$-0.790519\pi$
$103$	−1.82211	+	1.82211i	−0.179537	+	0.179537i	0.611617	+	0.791154i	$0.290519\pi$
$104$	6.00331	−	11.4215i	0.588673	−	1.11997i
$105$	−2.09593	−	2.09593i	−0.204542	−	0.204542i
$106$	2.13454	−	1.02993i	0.207325	−	0.100036i
$107$	−3.23107	+	1.86546i	−0.312360	+	0.180341i	−0.647982	−	0.761656i	$-0.724387\pi$
$107$	−3.23107	+	1.86546i	−0.312360	+	0.180341i	0.335622	+	0.941997i	$0.391053\pi$
$108$	−3.43123	−	8.70388i	−0.330170	−	0.837531i
$109$	0.00991505	+	0.0370035i	0.000949690	+	0.00354429i	0.966399	−	0.257046i	$-0.0827493\pi$
$109$	0.00991505	+	0.0370035i	0.000949690	+	0.00354429i	−0.965449	+	0.260591i	$0.916083\pi$
$110$	2.55670	+	2.96639i	0.243771	+	0.282834i
$111$	3.92192	−	3.83634i	0.372252	−	0.364129i
$112$	−3.83668	+	12.5732i	−0.362532	+	1.18805i
$113$	5.26403	−	1.41049i	0.495198	−	0.132688i	−0.00257224	−	0.999997i	$-0.500819\pi$
$113$	5.26403	−	1.41049i	0.495198	−	0.132688i	0.497771	+	0.867309i	$0.334152\pi$
$114$	0.726051	+	0.253440i	0.0680009	+	0.0237368i
$115$	0.849124	+	1.47073i	0.0791813	+	0.137146i
$116$	0.315618	−	0.726401i	0.0293044	−	0.0674446i
$117$	7.05321	−	7.05321i	0.652069	−	0.652069i
$118$	10.5003	+	3.66528i	0.966626	+	0.337417i
$119$	8.17426	+	8.17426i	0.749333	+	0.749333i
$120$	−2.54905	+	0.101173i	−0.232695	+	0.00923575i
$121$	−3.33191			−0.302901
$122$	−15.2590	+	13.1515i	−1.38149	+	1.19068i
$123$	−0.675528	−	0.390016i	−0.0609103	−	0.0351666i
$124$	15.5304	+	6.74788i	1.39467	+	0.605978i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−5.71819	+	8.40069i	−0.509417	+	0.748393i
$127$	13.3457	+	7.70516i	1.18424	+	0.683722i	0.956992	−	0.290115i	$-0.0936934\pi$
$127$	13.3457	+	7.70516i	1.18424	+	0.683722i	0.227249	+	0.973837i	$0.427027\pi$
$128$	5.70866	+	9.76786i	0.504579	+	0.863365i
$129$	−0.159271	+	0.594407i	−0.0140230	+	0.0523346i
$130$	−2.80362	−	5.81053i	−0.245894	−	0.509617i
$131$	−3.26954	−	12.2021i	−0.285661	−	1.06610i	−0.948355	−	0.317210i	$-0.897254\pi$
$131$	−3.26954	−	12.2021i	−0.285661	−	1.06610i	0.662695	−	0.748890i	$-0.269413\pi$
$132$	−3.10851	+	3.91007i	−0.270561	+	0.340328i
$133$	−0.512813	−	1.91384i	−0.0444665	−	0.165951i
$134$	−0.910926	+	12.2801i	−0.0786920	+	1.06084i
$135$	−4.51850	−	1.21073i	−0.388890	−	0.104203i
$136$	9.94142	−	0.394578i	0.852470	−	0.0338348i
$137$	17.6162			1.50505			0.752526	−	0.658562i	$-0.228835\pi$
$137$	17.6162			1.50505			0.752526	+	0.658562i	$0.228835\pi$
$138$	−1.64082	+	1.41420i	−0.139676	+	0.120385i
$139$	−11.4468	+	19.8264i	−0.970903	+	1.68165i	−0.278062	+	0.960563i	$0.589692\pi$
$139$	−11.4468	+	19.8264i	−0.970903	+	1.68165i	−0.692841	+	0.721090i	$0.743641\pi$
$140$	3.91104	+	5.28252i	0.330543	+	0.446454i
$141$	−5.68181	+	3.28039i	−0.478495	+	0.276259i
$142$	−6.57373	−	0.487632i	−0.551655	−	0.0409212i
$143$	−12.2022	−	3.26956i	−1.02040	−	0.273414i
$144$	1.97198	+	8.52085i	0.164331	+	0.710071i
$145$	−0.198001	−	0.342949i	−0.0164431	−	0.0284803i
$146$	3.36440	−	4.94271i	0.278440	−	0.409061i
$147$	−3.42762			−0.282706
$148$	−9.85667	+	7.13064i	−0.810213	+	0.586135i
$149$	11.8023			0.966879			0.483439	−	0.875378i	$-0.339387\pi$
$149$	11.8023			0.966879			0.483439	+	0.875378i	$0.339387\pi$
$150$	−0.717733	+	1.05443i	−0.0586026	+	0.0860941i
$151$	−1.93634	−	3.35383i	−0.157577	−	0.272931i	0.776417	−	0.630219i	$-0.217035\pi$
$151$	−1.93634	−	3.35383i	−0.157577	−	0.272931i	−0.933994	+	0.357288i	$0.883702\pi$
$152$	−1.50945	−	0.793389i	−0.122432	−	0.0643523i
$153$	7.42919	+	1.99065i	0.600614	+	0.160934i
$154$	12.8347	+	0.952062i	1.03425	+	0.0767194i
$155$	7.33220	−	4.23325i	0.588937	−	0.340023i
$156$	6.61374	−	4.89663i	0.529523	−	0.392045i
$157$	3.74295	−	6.48298i	0.298720	−	0.517398i	−0.677123	−	0.735869i	$-0.736774\pi$
$157$	3.74295	−	6.48298i	0.298720	−	0.517398i	0.975843	+	0.218471i	$0.0701070\pi$
$158$	−1.12041	+	0.965664i	−0.0891348	+	0.0768241i
$159$	1.51151			0.119871
$160$	5.62364	+	0.612099i	0.444588	+	0.0483907i
$161$	5.39092	+	1.44449i	0.424864	+	0.113842i
$162$	−0.244846	+	3.30075i	−0.0192369	+	0.259331i
$163$	2.80498	+	10.4683i	0.219703	+	0.819942i	0.984458	+	0.175621i	$0.0561933\pi$
$163$	2.80498	+	10.4683i	0.219703	+	0.819942i	−0.764755	+	0.644321i	$0.777140\pi$
$164$	1.35396	+	1.07640i	0.105726	+	0.0840524i
$165$	0.646419	+	2.41247i	0.0503237	+	0.187811i
$166$	−4.00176	−	8.29367i	−0.310596	−	0.643714i
$167$	−1.46877	+	5.48153i	−0.113657	+	0.424173i	−0.999183	−	0.0404164i	$-0.987132\pi$
$167$	−1.46877	+	5.48153i	−0.113657	+	0.424173i	0.885526	+	0.464590i	$0.153798\pi$
$168$	−5.68843	+	6.15864i	−0.438872	+	0.475149i
$169$	6.76474	+	3.90563i	0.520365	+	0.300433i
$170$	2.79919	−	4.11235i	0.214688	−	0.315403i
$171$	−0.932142	−	0.932142i	−0.0712827	−	0.0712827i
$172$	0.543787	−	1.25154i	0.0414634	−	0.0954288i
$173$	−11.7214	−	6.76737i	−0.891163	−	0.514513i	−0.0168404	−	0.999858i	$-0.505361\pi$
$173$	−11.7214	−	6.76737i	−0.891163	−	0.514513i	−0.874323	+	0.485345i	$0.838694\pi$
$174$	0.382612	−	0.329768i	0.0290057	−	0.0249996i
$175$	3.28638			0.248427
$176$	8.09683	−	7.55849i	0.610322	−	0.569742i
$177$	5.01547	+	5.01547i	0.376985	+	0.376985i
$178$	22.1000	+	7.71438i	1.65647	+	0.578217i
$179$	−5.78369	+	5.78369i	−0.432294	+	0.432294i	−0.889408	−	0.457114i	$-0.848883\pi$
$179$	−5.78369	+	5.78369i	−0.432294	+	0.432294i	0.457114	+	0.889408i	$0.348883\pi$
$180$	4.01080	+	1.74267i	0.298947	+	0.129891i
$181$	2.93728	+	5.08752i	0.218327	+	0.378153i	0.954296	−	0.298862i	$-0.0966069\pi$
$181$	2.93728	+	5.08752i	0.218327	+	0.378153i	−0.735970	+	0.677014i	$0.763274\pi$
$182$	−20.0177	−	6.98752i	−1.48381	−	0.517949i
$183$	−12.4097	+	3.32516i	−0.917348	+	0.245803i
$184$	4.06132	−	2.56477i	0.299405	−	0.189078i
$185$	−0.0670976	+	6.08239i	−0.00493311	+	0.447186i
$186$	7.05041	+	8.18020i	0.516961	+	0.599801i
$187$	−2.52107	−	9.40876i	−0.184359	−	0.688037i
$188$	13.5345	−	5.33556i	0.987108	−	0.389136i
$189$	−13.3137	+	7.68667i	−0.968430	+	0.559123i
$190$	−0.767911	+	0.370522i	−0.0557101	+	0.0268805i
$191$	−10.4883	−	10.4883i	−0.758903	−	0.758903i	0.217219	−	0.976123i	$-0.430301\pi$
$191$	−10.4883	−	10.4883i	−0.758903	−	0.758903i	−0.976123	+	0.217219i	$0.930301\pi$
$192$	0.571868	+	7.19277i	0.0412710	+	0.519094i
$193$	2.11208	−	2.11208i	0.152031	−	0.152031i	−0.626993	−	0.779025i	$-0.715715\pi$
$193$	2.11208	−	2.11208i	0.152031	−	0.152031i	0.779025	+	0.626993i	$0.215715\pi$
$194$	−23.1554	+	4.39939i	−1.66246	+	0.315858i
$195$		−	4.11456i		−	0.294650i
$196$	7.51742	+	1.12144i	0.536959	+	0.0801028i
$197$	−13.8858	+	24.0509i	−0.989320	+	1.71355i	−0.368431	+	0.929655i	$0.620105\pi$
$197$	−13.8858	+	24.0509i	−0.989320	+	1.71355i	−0.620889	+	0.783898i	$0.713228\pi$
$198$	7.71192	−	3.72105i	0.548062	−	0.264444i
$199$	−19.1849	+	19.1849i	−1.35998	+	1.35998i	−0.486056	+	0.873928i	$0.661565\pi$
$199$	−19.1849	+	19.1849i	−1.35998	+	1.35998i	−0.873928	+	0.486056i	$0.838435\pi$
$200$	1.91911	−	2.07774i	0.135701	−	0.146919i
$201$	−3.92667	+	6.80118i	−0.276966	+	0.479719i
$202$	1.39876	−	2.05494i	0.0984163	−	0.144585i
$203$	−1.25707	−	0.336831i	−0.0882292	−	0.0236409i
$204$	5.81967	+	2.52862i	0.407458	+	0.177039i
$205$	0.835375	−	0.223838i	0.0583451	−	0.0156335i
$206$	3.58017	−	0.680210i	0.249442	−	0.0473925i
$207$	3.58672	−	0.961059i	0.249294	−	0.0667982i
$208$	−16.1072	+	8.57538i	−1.11684	+	0.594596i
$209$	−0.432100	+	1.61262i	−0.0298890	+	0.111547i
$210$	0.782433	+	4.11820i	0.0539930	+	0.284183i
$211$			12.1321i			0.835206i	0.908629	+	0.417603i	$0.137130\pi$
$211$			12.1321i			0.835206i	−0.908629	+	0.417603i	$0.862870\pi$
$212$	−3.31504	−	0.494533i	−0.227678	−	0.0339646i
$213$	−3.64078	−	2.10200i	−0.249462	−	0.144027i
$214$	5.26187	+	0.390319i	0.359694	+	0.0266817i
$215$	−0.341142	−	0.590876i	−0.0232657	−	0.0402974i
$216$	−2.91491	+	12.9060i	−0.198334	+	0.878142i
$217$	7.20142	−	26.8761i	0.488864	−	1.82447i
$218$	0.0178548	−	0.0511502i	0.00120928	−	0.00346433i
$219$	3.30237	−	1.90662i	0.223153	−	0.128838i
$220$	−0.628415	−	5.50249i	−0.0423677	−	0.370978i
$221$			16.0470i			1.07944i
$222$	−7.63788	+	1.36404i	−0.512621	+	0.0915481i
$223$			24.5404i			1.64335i	0.569957	+	0.821674i	$0.306960\pi$
$223$			24.5404i			1.64335i	−0.569957	+	0.821674i	$0.693040\pi$
$224$	14.4908	−	11.6459i	0.968204	−	0.778127i
$225$	1.89358	−	1.09326i	0.126239	−	0.0728838i
$226$	−7.27651	−	2.53998i	−0.484026	−	0.168957i
$227$	−4.56378	+	17.0323i	−0.302909	+	1.13047i	0.631822	+	0.775114i	$0.282307\pi$
$227$	−4.56378	+	17.0323i	−0.302909	+	1.13047i	−0.934731	+	0.355357i	$0.884359\pi$
$228$	−0.647132	−	0.874062i	−0.0428574	−	0.0578862i
$229$	7.07259	+	12.2501i	0.467370	+	0.809508i	0.999305	−	0.0372770i	$-0.0118684\pi$
$229$	7.07259	+	12.2501i	0.467370	+	0.809508i	−0.531935	+	0.846785i	$0.678535\pi$
$230$	0.177666	−	2.39511i	0.0117150	−	0.157929i
$231$	7.10832	+	4.10399i	0.467693	+	0.270023i
$232$	−0.947031	+	0.598062i	−0.0621757	+	0.0392647i
$233$			3.47650i			0.227753i	0.993495	+	0.113876i	$0.0363268\pi$
$233$			3.47650i			0.227753i	−0.993495	+	0.113876i	$0.963673\pi$
$234$	−13.8585	+	2.63303i	−0.905959	+	0.172127i
$235$	1.88268	−	7.02627i	0.122813	−	0.458344i
$236$	−9.35891	−	12.6408i	−0.609213	−	0.822846i
$237$	−0.911191	+	0.244153i	−0.0591882	+	0.0158594i
$238$	−3.05153	−	16.0612i	−0.197801	−	1.04109i
$239$	9.52562	−	2.55238i	0.616161	−	0.165100i	0.0627791	−	0.998027i	$-0.480004\pi$
$239$	9.52562	−	2.55238i	0.616161	−	0.165100i	0.553382	+	0.832928i	$0.313337\pi$
$240$	3.06055	+	1.91018i	0.197558	+	0.123301i
$241$	−28.0062	−	7.50425i	−1.80404	−	0.483391i	−0.809443	−	0.587199i	$-0.800231\pi$
$241$	−28.0062	−	7.50425i	−1.80404	−	0.483391i	−0.994597	+	0.103807i	$0.966897\pi$
$242$	3.89528	+	2.65144i	0.250398	+	0.170441i
$243$	−8.07228	+	13.9816i	−0.517837	+	0.896920i
$244$	28.3046	−	3.23254i	1.81202	−	0.206942i
$245$	2.68722	−	2.68722i	0.171680	−	0.171680i
$246$	0.479383	+	0.993525i	0.0305643	+	0.0633449i
$247$	1.37519	−	2.38190i	0.0875014	−	0.151557i
$248$	−12.7865	−	20.2474i	−0.811943	−	1.28571i
$249$		−	5.87294i		−	0.372182i
$250$	−0.263970	−	1.38936i	−0.0166949	−	0.0878708i
$251$	−0.305893	+	0.305893i	−0.0193078	+	0.0193078i	−0.716695	−	0.697387i	$-0.754346\pi$
$251$	−0.305893	+	0.305893i	−0.0193078	+	0.0193078i	0.697387	+	0.716695i	$0.254346\pi$
$252$	13.3700	−	5.27071i	0.842234	−	0.332024i
$253$	−3.32529	−	3.32529i	−0.209059	−	0.209059i
$254$	−9.47068	−	19.6281i	−0.594244	−	1.23158i
$255$	2.74758	−	1.58632i	0.172060	−	0.0993390i
$256$	1.09910	−	15.9622i	0.0686934	−	0.997638i
$257$	1.30755	+	4.87986i	0.0815629	+	0.304397i	0.994641	−	0.103387i	$-0.0329682\pi$
$257$	1.30755	+	4.87986i	0.0815629	+	0.304397i	−0.913078	+	0.407784i	$0.866301\pi$
$258$	0.659212	−	0.568167i	0.0410408	−	0.0353725i
$259$	13.9785	+	14.2903i	0.868580	+	0.887958i
$260$	−1.34619	+	9.02401i	−0.0834872	+	0.559645i
$261$	−0.836363	+	0.224103i	−0.0517696	+	0.0138716i
$262$	−5.88770	+	16.8670i	−0.363743	+	1.04205i
$263$	−8.19266	−	14.1901i	−0.505181	−	0.874999i	−0.999982	−	0.00599258i	$-0.998092\pi$
$263$	−8.19266	−	14.1901i	−0.505181	−	0.874999i	0.494801	−	0.869006i	$-0.335241\pi$
$264$	6.74562	−	2.09753i	0.415164	−	0.129094i
$265$	−1.18501	+	1.18501i	−0.0727947	+	0.0727947i
$266$	−0.923461	+	2.64552i	−0.0566210	+	0.162207i
$267$	10.5561	+	10.5561i	0.646025	+	0.646025i
$268$	10.8371	−	13.6316i	0.661982	−	0.832680i
$269$	−12.5471			−0.765013			−0.382506	−	0.923953i	$-0.624939\pi$
$269$	−12.5471			−0.765013			−0.382506	+	0.923953i	$0.624939\pi$
$270$	4.31903	+	5.01113i	0.262848	+	0.304967i
$271$	6.97894	+	4.02929i	0.423940	+	0.244762i	0.696762	−	0.717303i	$-0.254624\pi$
$271$	6.97894	+	4.02929i	0.423940	+	0.244762i	−0.272821	+	0.962065i	$0.587957\pi$
$272$	−11.9363	−	7.44980i	−0.723745	−	0.451710i
$273$	−9.56152	−	9.56152i	−0.578689	−	0.578689i
$274$	−20.5947	−	14.0184i	−1.24417	−	0.846885i
$275$	−2.39814	−	1.38457i	−0.144613	−	0.0834924i
$276$	3.04363	−	0.347599i	0.183205	−	0.0209230i
$277$	−6.93088	+	25.8664i	−0.416436	+	1.55416i	0.365506	+	0.930809i	$0.380896\pi$
$277$	−6.93088	+	25.8664i	−0.416436	+	1.55416i	−0.781942	+	0.623351i	$0.785771\pi$
$278$	29.1595	−	14.0696i	1.74887	−	0.843841i
$279$	−4.79129	−	17.8813i	−0.286847	−	1.07053i
$280$	−0.368643	−	9.28798i	−0.0220306	−	0.555063i
$281$	−7.90287	−	29.4939i	−0.471445	−	1.75946i	−0.634583	−	0.772855i	$-0.718828\pi$
$281$	−7.90287	−	29.4939i	−0.471445	−	1.75946i	0.163137	−	0.986603i	$-0.447839\pi$
$282$	9.25293	+	0.686372i	0.551004	+	0.0408729i
$283$	23.2086	+	6.21873i	1.37961	+	0.369665i	0.870979	−	0.491320i	$-0.163485\pi$
$283$	23.2086	+	6.21873i	1.37961	+	0.369665i	0.508630	+	0.860985i	$0.330152\pi$
$284$	7.29718	+	5.80126i	0.433008	+	0.344242i
$285$	−0.543775			−0.0322104
$286$	11.6635	+	13.5325i	0.689676	+	0.800193i
$287$	1.42110	−	2.46142i	0.0838851	−	0.145293i
$288$	4.47524	−	11.5308i	0.263706	−	0.679459i
$289$	4.00672	−	2.31328i	0.235689	−	0.136075i
$290$	−0.0414288	+	0.558498i	−0.00243278	+	0.0327961i
$291$	−14.5197	−	3.89053i	−0.851158	−	0.228067i
$292$	−7.86652	+	3.10113i	−0.460353	+	0.181480i
$293$	−8.90709	−	15.4275i	−0.520358	−	0.901286i	−0.999720	−	0.0236689i	$-0.992465\pi$
$293$	−8.90709	−	15.4275i	−0.520358	−	0.901286i	0.479362	−	0.877617i	$-0.340868\pi$
$294$	4.00717	+	2.72760i	0.233703	+	0.159077i
$295$	−7.86414			−0.457868
$296$	17.1976	−	0.492648i	0.999590	−	0.0286346i
$297$	12.9537			0.751650
$298$	−13.7978	−	9.39189i	−0.799285	−	0.544058i
$299$	3.87365	+	6.70936i	0.224019	+	0.388012i
$300$	1.67817	−	0.661567i	0.0968894	−	0.0381956i
$301$	−2.16584	−	0.580336i	−0.124837	−	0.0334500i
$302$	−0.405149	+	5.46178i	−0.0233137	+	0.314290i
$303$	1.37297	−	0.792683i	0.0788749	−	0.0455384i
$304$	1.13331	+	2.12871i	0.0649998	+	0.122090i
$305$	7.12215	−	12.3359i	0.407813	−	0.706353i
$306$	−7.10122	−	8.23916i	−0.405950	−	0.471001i
$307$	0.521528			0.0297652			0.0148826	−	0.999889i	$-0.495263\pi$
$307$	0.521528			0.0297652			0.0148826	+	0.999889i	$0.495263\pi$
$308$	−14.2471	−	11.3265i	−0.811806	−	0.645387i
$309$	2.24495	+	0.601533i	0.127711	+	0.0342200i
$310$	−11.9406	−	0.885743i	−0.678182	−	0.0503068i
$311$	3.48662	+	13.0122i	0.197708	+	0.737856i	0.991549	+	0.129731i	$0.0414114\pi$
$311$	3.48662	+	13.0122i	0.197708	+	0.737856i	−0.793841	+	0.608125i	$0.791922\pi$
$312$	−11.6286	+	0.461542i	−0.658339	+	0.0261297i
$313$	−4.21541	−	15.7321i	−0.238269	−	0.889233i	−0.976648	−	0.214847i	$-0.931075\pi$
$313$	−4.21541	−	15.7321i	−0.238269	−	0.889233i	0.738379	−	0.674387i	$-0.235592\pi$
$314$	−9.53478	+	4.60060i	−0.538079	+	0.259627i
$315$	1.85980	−	6.94088i	0.104788	−	0.391074i
$316$	2.07829	−	0.237352i	0.116913	−	0.0133521i
$317$	1.07224	+	0.619060i	0.0602232	+	0.0347699i	0.529809	−	0.848117i	$-0.322264\pi$
$317$	1.07224	+	0.619060i	0.0602232	+	0.0347699i	−0.469586	+	0.882887i	$0.655597\pi$
$318$	−1.76708	−	1.20282i	−0.0990930	−	0.0674507i
$319$	0.775402	+	0.775402i	0.0434142	+	0.0434142i
$320$	−6.08740	−	5.19072i	−0.340296	−	0.290170i
$321$	2.91422	+	1.68252i	0.162656	+	0.0939093i
$322$	−5.15294	−	5.97867i	−0.287162	−	0.333178i
$323$	2.12075			0.118002
$324$	2.91288	−	3.66400i	0.161827	−	0.203556i
$325$	3.22578	+	3.22578i	0.178934	+	0.178934i
$326$	5.05114	−	14.4704i	0.279757	−	0.801443i
$327$	0.0244320	−	0.0244320i	0.00135109	−	0.00135109i
$328$	−0.726318	−	2.33583i	−0.0401042	−	0.128975i
$329$	−11.9528	−	20.7028i	−0.658979	−	1.14138i
$330$	1.16406	−	3.33477i	0.0640792	−	0.183573i
$331$	10.0566	−	2.69465i	0.552759	−	0.148111i	0.0283814	−	0.999597i	$-0.490965\pi$
$331$	10.0566	−	2.69465i	0.552759	−	0.148111i	0.524378	+	0.851486i	$0.324298\pi$
$332$	−1.92149	+	12.8805i	−0.105455	+	0.706907i
$333$	12.8081	+	3.58381i	0.701880	+	0.196391i
$334$	6.07915	−	5.23954i	0.332636	−	0.286695i
$335$	−2.25359	−	8.41052i	−0.123127	−	0.459516i
$336$	11.5511	−	2.67326i	0.630164	−	0.145838i
$337$	1.18488	−	0.684093i	0.0645447	−	0.0372649i	−0.467380	−	0.884056i	$-0.654802\pi$
$337$	1.18488	−	0.684093i	0.0645447	−	0.0372649i	0.531925	+	0.846791i	$0.321469\pi$
$338$	−4.80055	−	9.94918i	−0.261115	−	0.541164i
$339$	−3.47564	−	3.47564i	−0.188771	−	0.188771i
$340$	−6.54497	+	2.58015i	−0.354951	+	0.139928i
$341$	−16.5780	+	16.5780i	−0.897750	+	0.897750i
$342$	0.347978	+	1.83152i	0.0188165	+	0.0990373i
$343$			10.5154i			0.567779i
$344$	−1.63167	+	1.03042i	−0.0879736	+	0.0555564i
$345$	0.765854	−	1.32650i	0.0412322	−	0.0714163i
$346$	8.31801	+	17.2392i	0.447179	+	0.926783i
$347$	17.5712	−	17.5712i	0.943270	−	0.943270i	−0.0552054	−	0.998475i	$-0.517581\pi$
$347$	17.5712	−	17.5712i	0.943270	−	0.943270i	0.998475	+	0.0552054i	$0.0175814\pi$
$348$	−0.709723	+	0.0810543i	−0.0380452	+	0.00434497i
$349$	2.85173	−	4.93935i	0.152650	−	0.264397i	−0.779551	−	0.626339i	$-0.784553\pi$
$349$	2.85173	−	4.93935i	0.152650	−	0.264397i	0.932201	+	0.361942i	$0.117886\pi$
$350$	−3.84204	−	2.61521i	−0.205366	−	0.139789i
$351$	−20.6131	−	5.52326i	−1.10025	−	0.294810i
$352$	−15.4807	+	2.39326i	−0.825122	+	0.127561i
$353$	−22.8139	+	6.11298i	−1.21426	+	0.325361i	−0.808433	−	0.588588i	$-0.799684\pi$
$353$	−22.8139	+	6.11298i	−1.21426	+	0.325361i	−0.405830	+	0.913949i	$0.633017\pi$
$354$	−1.87232	−	9.85464i	−0.0995128	−	0.523768i
$355$	4.50228	−	1.20638i	0.238956	−	0.0640281i
$356$	−19.6979	−	26.6053i	−1.04398	−	1.41008i
$357$	2.69857	−	10.0712i	0.142824	−	0.533025i
$358$	11.3641	−	2.15911i	0.600611	−	0.114112i
$359$			31.9778i			1.68772i	0.536560	+	0.843862i	$0.319723\pi$
$359$			31.9778i			1.68772i	−0.536560	+	0.843862i	$0.680277\pi$
$360$	−3.30217	−	5.22900i	−0.174040	−	0.275592i
$361$	16.1397	+	9.31826i	0.849458	+	0.490435i
$362$	0.614582	−	8.28513i	0.0323017	−	0.435457i
$363$	1.50258	+	2.60255i	0.0788652	+	0.136598i
$364$	17.8419	+	24.0985i	0.935169	+	1.26311i
$365$	−1.09425	+	4.08380i	−0.0572757	+	0.213756i
$366$	17.1540	+	5.98786i	0.896651	+	0.312991i
$367$	−12.1558	+	7.01815i	−0.634527	+	0.366344i	−0.782503	−	0.622647i	$-0.786057\pi$
$367$	−12.1558	+	7.01815i	−0.634527	+	0.366344i	0.147976	+	0.988991i	$0.452724\pi$
$368$	−6.78898	−	0.233455i	−0.353900	−	0.0121697i
$369$		−	1.89099i		−	0.0984413i
$370$	4.91863	−	7.05741i	0.255707	−	0.366897i
$371$			5.50751i			0.285936i
$372$	−1.73293	−	15.1738i	−0.0898484	−	0.786726i
$373$	−7.58014	+	4.37639i	−0.392485	+	0.226601i	−0.683236	−	0.730197i	$-0.739428\pi$
$373$	−7.58014	+	4.37639i	−0.392485	+	0.226601i	0.290751	+	0.956799i	$0.406095\pi$
$374$	−4.53988	+	13.0058i	−0.234752	+	0.672514i
$375$	0.233438	−	0.871201i	0.0120547	−	0.0449886i
$376$	−20.0689	−	4.53269i	−1.03497	−	0.233756i
$377$	−0.903270	−	1.56451i	−0.0465208	−	0.0805763i
$378$	21.6816	+	1.60832i	1.11518	+	0.0827230i
$379$	−5.25996	−	3.03684i	−0.270186	−	0.155992i	0.358786	−	0.933420i	$-0.383191\pi$
$379$	−5.25996	−	3.03684i	−0.270186	−	0.155992i	−0.628972	+	0.777428i	$0.716524\pi$
$380$	1.19260	+	0.177911i	0.0611791	+	0.00912662i
$381$		−	13.8991i		−	0.712072i
$382$	3.91537	+	20.6079i	0.200328	+	1.05439i
$383$	2.34709	−	8.75945i	0.119931	−	0.447587i	−0.879678	−	0.475570i	$-0.842242\pi$
$383$	2.34709	−	8.75945i	0.119931	−	0.447587i	0.999608	+	0.0279831i	$0.00890846\pi$
$384$	5.05524	−	8.86401i	0.257974	−	0.452339i
$385$	−8.79033	+	2.35536i	−0.447997	+	0.120040i
$386$	−4.14993	+	0.788462i	−0.211226	+	0.0401316i
$387$	−1.44099	+	0.386113i	−0.0732498	+	0.0196272i
$388$	30.5715	+	13.2832i	1.55203	+	0.674351i
$389$	−33.8403	−	9.06749i	−1.71577	−	0.459740i	−0.738945	−	0.673766i	$-0.764676\pi$
$389$	−33.8403	−	9.06749i	−1.71577	−	0.459740i	−0.976828	+	0.214026i	$0.931342\pi$
$390$	−3.27425	+	4.81026i	−0.165798	+	0.243577i
$391$	−2.98687	+	5.17341i	−0.151053	+	0.261631i
$392$	−7.89606	−	7.29320i	−0.398811	−	0.368362i
$393$	−8.05656	+	8.05656i	−0.406400	+	0.406400i
$394$	35.3726	−	17.0675i	1.78204	−	0.859849i
$395$	0.522951	−	0.905777i	0.0263125	−	0.0455746i
$396$	−11.9770	−	1.78671i	−0.601865	−	0.0897854i
$397$			4.77898i			0.239850i	0.992783	+	0.119925i	$0.0382654\pi$
$397$			4.77898i			0.239850i	−0.992783	+	0.119925i	$0.961735\pi$
$398$	37.6955	−	7.16192i	1.88951	−	0.358995i
$399$	−1.26364	+	1.26364i	−0.0632610	+	0.0632610i
$400$	−3.89700	+	0.901881i	−0.194850	+	0.0450940i
$401$	20.1158	+	20.1158i	1.00454	+	1.00454i	0.999990	+	0.00454755i	$0.00144753\pi$
$401$	20.1158	+	20.1158i	1.00454	+	1.00454i	0.00454755	+	0.999990i	$0.498552\pi$
$402$	10.0028	−	4.82641i	0.498893	−	0.240719i
$403$	33.4490	−	19.3118i	1.66622	−	0.961990i
$404$	−3.27052	+	1.28930i	−0.162715	+	0.0641451i
$405$	−0.605739	−	2.26065i	−0.0300994	−	0.112332i
$406$	1.20158	+	1.39412i	0.0596333	+	0.0691892i
$407$	−4.17980	−	16.3171i	−0.207185	−	0.808810i
$408$	−4.79146	−	7.58728i	−0.237212	−	0.375626i
$409$	−13.3185	+	3.56868i	−0.658558	+	0.176460i	−0.572595	−	0.819838i	$-0.694063\pi$
$409$	−13.3185	+	3.56868i	−0.658558	+	0.176460i	−0.0859628	+	0.996298i	$0.527397\pi$
$410$	−1.15474	−	0.403082i	−0.0570288	−	0.0199068i
$411$	−7.94432	−	13.7600i	−0.391864	−	0.678729i
$412$	−4.72679	−	2.05377i	−0.232872	−	0.101182i
$413$	−18.2749	+	18.2749i	−0.899248	+	0.899248i
$414$	−4.95795	−	1.73065i	−0.243670	−	0.0850569i
$415$	4.60432	+	4.60432i	0.226017	+	0.226017i
$416$	25.6547	+	2.79236i	1.25782	+	0.136906i
$417$	20.6485			1.01116
$418$	1.78843	−	1.54143i	0.0874752	−	0.0753937i
$419$	15.3363	+	8.85440i	0.749226	+	0.432566i	0.825414	−	0.564528i	$-0.190942\pi$
$419$	15.3363	+	8.85440i	0.749226	+	0.432566i	−0.0761882	+	0.997093i	$0.524275\pi$
$420$	2.36242	−	5.43714i	0.115274	−	0.265305i
$421$	4.23180	+	4.23180i	0.206245	+	0.206245i	0.802669	−	0.596424i	$-0.203412\pi$
$421$	4.23180	+	4.23180i	0.206245	+	0.206245i	−0.596424	+	0.802669i	$0.703412\pi$
$422$	9.65435	−	14.1834i	0.469966	−	0.690436i
$423$	−13.7741	−	7.95250i	−0.669722	−	0.386664i
$424$	3.48201	+	3.21616i	0.169101	+	0.156190i
$425$	−0.910419	+	3.39773i	−0.0441618	+	0.164814i
$426$	2.58365	+	5.35463i	0.125178	+	0.259433i
$427$	−12.1159	−	45.2171i	−0.586329	−	2.18821i
$428$	−5.84094	−	4.64355i	−0.282332	−	0.224455i
$429$	2.94892	+	11.0055i	0.142375	+	0.531352i
$430$	−0.0713788	+	0.962252i	−0.00344219	+	0.0464039i
$431$	15.9374	+	4.27040i	0.767675	+	0.205698i	0.621344	−	0.783538i	$-0.286587\pi$
$431$	15.9374	+	4.27040i	0.767675	+	0.205698i	0.146331	+	0.989236i	$0.453254\pi$
$432$	13.6780	−	12.7686i	0.658082	−	0.614327i
$433$	23.0300			1.10675			0.553376	−	0.832932i	$-0.313339\pi$
$433$	23.0300			1.10675			0.553376	+	0.832932i	$0.313339\pi$
$434$	−29.8062	+	25.6896i	−1.43074	+	1.23314i
$435$	−0.178584	+	0.309317i	−0.00856246	+	0.0148306i
$436$	−0.0615775	+	0.0455903i	−0.00294903	+	0.00218338i
$437$	0.886699	−	0.511936i	0.0424166	−	0.0244892i
$438$	−5.37797	−	0.398932i	−0.256969	−	0.0190617i
$439$	−29.7892	−	7.98200i	−1.42176	−	0.380960i	−0.535654	−	0.844438i	$-0.679935\pi$
$439$	−29.7892	−	7.98200i	−1.42176	−	0.380960i	−0.886109	+	0.463478i	$0.846601\pi$
$440$	−3.64406	+	6.93293i	−0.173724	+	0.330515i
$441$	−4.15471	−	7.19617i	−0.197843	−	0.342675i
$442$	12.7697	−	18.7603i	0.607395	−	0.892334i
$443$	9.13729			0.434126			0.217063	−	0.976158i	$-0.430352\pi$
$443$	9.13729			0.434126			0.217063	+	0.976158i	$0.430352\pi$
$444$	10.0148	+	4.48334i	0.475280	+	0.212770i
$445$	−16.5518			−0.784630
$446$	19.5286	−	28.6897i	0.924704	−	1.35850i
$447$	−5.32243	−	9.21872i	−0.251742	−	0.436030i
$448$	−26.2083	+	2.08372i	−1.23823	+	0.0984464i
$449$	−17.6764	−	4.73637i	−0.834200	−	0.223523i	−0.183655	−	0.982991i	$-0.558793\pi$
$449$	−17.6764	−	4.73637i	−0.834200	−	0.223523i	−0.650545	+	0.759468i	$0.725460\pi$
$450$	−3.08373	−	0.228747i	−0.145368	−	0.0107833i
$451$	−2.07402	+	1.19743i	−0.0976616	+	0.0563849i
$452$	6.48558	+	8.75987i	0.305056	+	0.412030i
$453$	−1.74645	+	3.02494i	−0.0820553	+	0.142124i
$454$	18.8892	−	16.2804i	0.886514	−	0.764075i
$455$	14.9923			0.702848
$456$	0.0609968	+	1.53682i	0.00285644	+	0.0719681i
$457$	−7.82346	−	2.09629i	−0.365966	−	0.0980603i	0.0711495	−	0.997466i	$-0.477333\pi$
$457$	−7.82346	−	2.09629i	−0.365966	−	0.0980603i	−0.437116	+	0.899405i	$0.644000\pi$
$458$	1.47983	−	19.9495i	0.0691480	−	0.932178i
$459$	−4.25884	−	15.8942i	−0.198786	−	0.741879i
$460$	−2.11366	+	2.65869i	−0.0985500	+	0.123962i
$461$	0.0198594	+	0.0741162i	0.000924943	+	0.00345194i	0.966387	−	0.257093i	$-0.0827646\pi$
$461$	0.0198594	+	0.0741162i	0.000924943	+	0.00345194i	−0.965462	+	0.260545i	$0.916098\pi$
$462$	−5.04436	−	10.4545i	−0.234685	−	0.486387i
$463$	−0.697388	+	2.60269i	−0.0324104	+	0.120957i	−0.980236	−	0.197833i	$-0.936610\pi$
$463$	−0.697388	+	2.60269i	−0.0324104	+	0.120957i	0.947825	+	0.318790i	$0.103276\pi$
$464$	1.58308	+	0.0544378i	0.0734925	+	0.00252721i
$465$	−6.61316	−	3.81811i	−0.306678	−	0.177061i
$466$	2.76649	−	4.06431i	0.128155	−	0.188275i
$467$	2.76797	+	2.76797i	0.128087	+	0.128087i	0.768244	−	0.640157i	$-0.221131\pi$
$467$	2.76797	+	2.76797i	0.128087	+	0.128087i	−0.640157	+	0.768244i	$0.721131\pi$
$468$	18.2970	+	7.94996i	0.845779	+	0.367487i
$469$	−24.7815	−	14.3076i	−1.14430	−	0.660664i
$470$	−7.79231	+	6.71609i	−0.359433	+	0.309790i
$471$	−6.75179			−0.311106
$472$	0.882144	+	22.2257i	0.0406040	+	1.02302i
$473$	1.33596	+	1.33596i	0.0614276	+	0.0614276i
$474$	1.25954	+	0.439664i	0.0578528	+	0.0201945i
$475$	0.426314	−	0.426314i	0.0195606	−	0.0195606i
$476$	−9.21354	+	21.2051i	−0.422302	+	0.971936i
$477$	1.83215	+	3.17337i	0.0838882	+	0.145299i
$478$	−13.1673	−	4.59627i	−0.602259	−	0.210228i
$479$	34.2631	−	9.18078i	1.56552	−	0.419480i	0.631116	−	0.775689i	$-0.282597\pi$
$479$	34.2631	−	9.18078i	1.56552	−	0.419480i	0.934407	+	0.356208i	$0.115931\pi$
$480$	−2.05797	−	4.66865i	−0.0939329	−	0.213094i
$481$	−0.306095	+	27.7475i	−0.0139567	+	1.26518i
$482$	26.7699	+	31.0596i	1.21933	+	1.41473i
$483$	−1.30284	−	4.86226i	−0.0592812	−	0.221240i
$484$	−2.44395	−	6.19949i	−0.111089	−	0.281795i
$485$	14.4334	−	8.33313i	0.655387	−	0.378388i
$486$	20.5633	−	9.92193i	0.932770	−	0.450068i
$487$	−22.6634	−	22.6634i	−1.02698	−	1.02698i	−0.999626	−	0.0273529i	$-0.991292\pi$
$487$	−22.6634	−	22.6634i	−1.02698	−	1.02698i	−0.0273529	−	0.999626i	$-0.508708\pi$
$488$	−35.6627	−	18.7449i	−1.61438	−	0.848541i
$489$	6.91183	−	6.91183i	0.312564	−	0.312564i
$490$	−5.27999	+	1.00317i	−0.238526	+	0.0453184i
$491$			35.0493i			1.58175i	0.611975	+	0.790877i	$0.290375\pi$
$491$			35.0493i			1.58175i	−0.611975	+	0.790877i	$0.709625\pi$
$492$	0.230181	−	1.54299i	0.0103774	−	0.0695634i
$493$	0.696488	−	1.20635i	0.0313682	−	0.0543314i
$494$	−3.50316	+	1.69030i	−0.157615	+	0.0760502i
$495$	−4.28135	+	4.28135i	−0.192432	+	0.192432i
$496$	−1.16387	+	33.8460i	−0.0522595	+	1.51973i
$497$	7.65908	−	13.2659i	0.343557	−	0.595058i
$498$	−4.67351	+	6.86593i	−0.209425	+	0.307670i
$499$	−4.03021	−	1.07989i	−0.180417	−	0.0483426i	0.167479	−	0.985876i	$-0.446437\pi$
$499$	−4.03021	−	1.07989i	−0.180417	−	0.0483426i	−0.347896	+	0.937533i	$0.613104\pi$
$500$	−0.797010	+	1.83433i	−0.0356433	+	0.0820338i
$501$	4.94398	−	1.32473i	0.220881	−	0.0591848i
$502$	0.601034	−	0.114193i	0.0268254	−	0.00509667i
$503$	28.8191	−	7.72207i	1.28498	−	0.344310i	0.449230	−	0.893416i	$-0.351699\pi$
$503$	28.8191	−	7.72207i	1.28498	−	0.344310i	0.835752	+	0.549106i	$0.185032\pi$
$504$	−19.8249	−	4.47760i	−0.883073	−	0.199448i
$505$	−0.454937	+	1.69785i	−0.0202444	+	0.0755532i
$506$	1.24136	+	6.53370i	0.0551854	+	0.290459i
$507$		−	7.04523i		−	0.312890i
$508$	−4.54746	+	30.4833i	−0.201761	+	1.35248i
$509$	32.2274	+	18.6065i	1.42845	+	0.824718i	0.996999	−	0.0774174i	$-0.0246674\pi$
$509$	32.2274	+	18.6065i	1.42845	+	0.824718i	0.431454	+	0.902135i	$0.358001\pi$
$510$	−4.47449	−	0.331913i	−0.198134	−	0.0146973i
$511$	6.94718	+	12.0329i	0.307325	+	0.532302i
$512$	−13.9872	+	17.7865i	−0.618152	+	0.786059i
$513$	−0.729947	+	2.72420i	−0.0322279	+	0.120276i
$514$	2.35461	−	6.74546i	0.103857	−	0.297529i
$515$	−2.23161	+	1.28842i	−0.0983367	+	0.0567747i
$516$	−1.22280	+	0.139651i	−0.0538309	+	0.00614778i
$517$			20.1430i			0.885889i
$518$	−4.97015	−	27.8302i	−0.218376	−	1.22279i
$519$			12.2074i			0.535847i
$520$	8.75485	−	9.47854i	0.383925	−	0.415661i
$521$	21.3107	−	12.3037i	0.933639	−	0.539037i	0.0456783	−	0.998956i	$-0.485455\pi$
$521$	21.3107	−	12.3037i	0.933639	−	0.539037i	0.887961	+	0.459920i	$0.152122\pi$
$522$	1.15611	+	0.403559i	0.0506015	+	0.0176633i
$523$	−8.89673	+	33.2031i	−0.389027	+	1.45187i	0.442693	+	0.896673i	$0.354023\pi$
$523$	−8.89673	+	33.2031i	−0.389027	+	1.45187i	−0.831720	+	0.555195i	$0.812643\pi$
$524$	20.3055	−	15.0336i	0.887048	−	0.656747i
$525$	−1.48205	−	2.56698i	−0.0646819	−	0.112032i
$526$	−1.71419	+	23.1088i	−0.0747422	+	1.00759i
$527$	25.7917	+	14.8908i	1.12350	+	0.648655i
$528$	−9.55532	−	2.91579i	−0.415842	−	0.126893i
$529$		−	20.1160i		−	0.874607i
$530$	2.32837	−	0.442376i	0.101138	−	0.0192156i
$531$	−4.45041	+	16.6092i	−0.193131	+	0.720776i
$532$	3.18483	−	2.35796i	0.138080	−	0.102231i
$533$	3.81093	−	1.02114i	0.165070	−	0.0442303i
$534$	−3.94071	−	20.7412i	−0.170531	−	0.897561i
$535$	−3.60380	+	0.965634i	−0.155806	+	0.0417480i
$536$	−23.5170	+	7.31254i	−1.01578	+	0.315854i
$537$	7.12588	+	1.90937i	0.307505	+	0.0823956i
$538$	14.6686	+	9.98465i	0.632409	+	0.430469i
$539$	−5.26177	+	9.11365i	−0.226640	+	0.392553i
$540$	−1.06158	−	9.29536i	−0.0456832	−	0.400009i
$541$	16.2421	−	16.2421i	0.698302	−	0.698302i	−0.265742	−	0.964044i	$-0.585617\pi$
$541$	16.2421	−	16.2421i	0.698302	−	0.698302i	0.964044	+	0.265742i	$0.0856169\pi$
$542$	−4.95255	−	10.2642i	−0.212730	−	0.440885i
$543$	2.64924	−	4.58861i	0.113690	−	0.196916i
$544$	8.02618	+	18.2080i	0.344120	+	0.780661i
$545$			0.0383088i			0.00164097i
$546$	3.56941	+	18.7870i	0.152757	+	0.804008i
$547$	−11.8048	+	11.8048i	−0.504739	+	0.504739i	−0.912907	−	0.408168i	$-0.866168\pi$
$547$	−11.8048	+	11.8048i	−0.504739	+	0.504739i	0.408168	+	0.912907i	$0.366168\pi$
$548$	12.9214	+	32.7774i	0.551977	+	1.40018i
$549$	−22.0231	−	22.0231i	−0.939924	−	0.939924i
$550$	1.70182	+	3.52704i	0.0725658	+	0.150393i
$551$	−0.206763	+	0.119375i	−0.00880841	+	0.00508554i
$552$	−3.83486	−	2.01566i	−0.163222	−	0.0857922i
$553$	−0.889621	−	3.32011i	−0.0378305	−	0.141185i
$554$	28.6865	−	24.7245i	1.21877	−	1.05044i
$555$	4.78120	−	2.69055i	0.202951	−	0.114207i
$556$	−45.2860	−	6.75570i	−1.92055	−	0.286506i
$557$	−37.6479	+	10.0877i	−1.59519	+	0.427430i	−0.943586	−	0.331128i	$-0.892571\pi$
$557$	−37.6479	+	10.0877i	−1.59519	+	0.427430i	−0.651605	+	0.758558i	$0.725904\pi$
$558$	−8.62804	+	24.7175i	−0.365254	+	1.04638i
$559$	−1.55627	−	2.69554i	−0.0658232	−	0.114009i
$560$	−6.96013	+	11.1517i	−0.294119	+	0.471247i
$561$	−6.21224	+	6.21224i	−0.262281	+	0.262281i
$562$	−14.2313	+	40.7696i	−0.600311	+	1.71976i
$563$	−27.6303	−	27.6303i	−1.16448	−	1.16448i	−0.983484	−	0.180994i	$-0.942068\pi$
$563$	−27.6303	−	27.6303i	−1.16448	−	1.16448i	−0.180994	−	0.983484i	$-0.557932\pi$
$564$	−10.2712	−	8.16564i	−0.432497	−	0.343835i
$565$	5.44973			0.229272
$566$	−22.1841	−	25.7389i	−0.932466	−	1.08189i
$567$	−6.66097	−	3.84572i	−0.279735	−	0.161505i
$568$	−3.91451	−	12.5890i	−0.164249	−	0.528224i
$569$	−11.3129	−	11.3129i	−0.474261	−	0.474261i	0.429030	−	0.903290i	$-0.358856\pi$
$569$	−11.3129	−	11.3129i	−0.474261	−	0.474261i	−0.903290	+	0.429030i	$0.858856\pi$
$570$	0.635717	+	0.432720i	0.0266272	+	0.0181247i
$571$	−23.0654	−	13.3168i	−0.965256	−	0.557291i	−0.0674692	−	0.997721i	$-0.521492\pi$
$571$	−23.0654	−	13.3168i	−0.965256	−	0.557291i	−0.897787	+	0.440431i	$0.854826\pi$
$572$	−2.86679	−	25.1020i	−0.119866	−	1.04957i
$573$	−3.46249	+	12.9222i	−0.144648	+	0.539833i
$574$	−3.62011	+	1.74673i	−0.151101	+	0.0729071i
$575$	0.439539	+	1.64038i	0.0183300	+	0.0684087i
$576$	−14.4078	+	9.91916i	−0.600325	+	0.413299i
$577$	3.18534	+	11.8879i	0.132607	+	0.494898i	0.999996	−	0.00273331i	$-0.000870042\pi$
$577$	3.18534	+	11.8879i	0.132607	+	0.494898i	−0.867389	+	0.497631i	$0.834203\pi$
$578$	−6.52502	−	0.484019i	−0.271405	−	0.0201325i
$579$	−2.60222	−	0.697264i	−0.108145	−	0.0289773i
$580$	0.492870	−	0.619961i	0.0204653	−	0.0257425i
$581$	21.3992			0.887790
$582$	13.8787	+	16.1027i	0.575290	+	0.667477i
$583$	2.32034	−	4.01894i	0.0960986	−	0.166448i
$584$	11.6644	+	2.63448i	0.482675	+	0.109016i
$585$	8.63838	−	4.98737i	0.357153	−	0.206202i
$586$	−1.86367	+	25.1240i	−0.0769876	+	1.03786i
$587$	8.07569	+	2.16387i	0.333319	+	0.0893126i	0.421597	−	0.906783i	$-0.361470\pi$
$587$	8.07569	+	2.16387i	0.333319	+	0.0893126i	−0.0882778	+	0.996096i	$0.528136\pi$
$588$	−2.51416	−	6.37757i	−0.103682	−	0.263007i
$589$	−2.55222	−	4.42058i	−0.105162	−	0.182147i
$590$	9.19382	+	6.25806i	0.378503	+	0.257640i
$591$	25.0481			1.03034
$592$	−20.4974	−	13.1094i	−0.842438	−	0.538793i
$593$	38.7440			1.59102			0.795512	−	0.605938i	$-0.207202\pi$
$593$	38.7440			1.59102			0.795512	+	0.605938i	$0.207202\pi$
$594$	−15.1439	−	10.3082i	−0.621362	−	0.422950i
$595$	5.78007	+	10.0114i	0.236960	+	0.410426i
$596$	8.65694	+	21.9598i	0.354602	+	0.899507i
$597$	23.6371	+	6.33353i	0.967401	+	0.259214i
$598$	0.810502	−	10.9263i	0.0331439	−	0.446810i
$599$	−24.3550	+	14.0614i	−0.995118	+	0.574531i	−0.906800	−	0.421561i	$-0.861482\pi$
$599$	−24.3550	+	14.0614i	−0.995118	+	0.574531i	−0.0883175	+	0.996092i	$0.528149\pi$
$600$	−2.48838	−	0.562017i	−0.101588	−	0.0229442i
$601$	17.0938	−	29.6074i	0.697272	−	1.20771i	−0.272137	−	0.962258i	$-0.587730\pi$
$601$	17.0938	−	29.6074i	0.697272	−	1.20771i	0.969409	−	0.245451i	$-0.0789362\pi$
$602$	2.07023	+	2.40198i	0.0843764	+	0.0978972i
$603$	−19.0385			−0.775306
$604$	4.81998	−	6.06286i	0.196122	−	0.246694i
$605$	−3.21838	−	0.862363i	−0.130846	−	0.0350600i
$606$	−2.23590	−	0.165857i	−0.0908274	−	0.00673747i
$607$	−4.93722	−	18.4259i	−0.200395	−	0.747886i	−0.990804	−	0.135306i	$-0.956798\pi$
$607$	−4.93722	−	18.4259i	−0.200395	−	0.747886i	0.790409	−	0.612580i	$-0.209868\pi$
$608$	0.369034	−	3.39049i	0.0149663	−	0.137502i
$609$	0.303800	+	1.13380i	0.0123106	+	0.0459437i
$610$	−18.1429	+	8.75410i	−0.734586	+	0.354443i
$611$	8.58869	−	32.0534i	0.347461	−	1.29674i
$612$	1.74542	+	15.2832i	0.0705545	+	0.617786i
$613$	−33.3706	−	19.2665i	−1.34783	−	0.778168i	−0.359885	−	0.932997i	$-0.617184\pi$
$613$	−33.3706	−	19.2665i	−1.34783	−	0.778168i	−0.987941	+	0.154829i	$0.950517\pi$
$614$	−0.609708	−	0.415016i	−0.0246058	−	0.0167487i
$615$	−0.551566	−	0.551566i	−0.0222413	−	0.0222413i
$616$	7.64277	+	24.5790i	0.307936	+	0.990318i
$617$	9.02659	+	5.21150i	0.363397	+	0.209807i	0.670570	−	0.741846i	$-0.266050\pi$
$617$	9.02659	+	5.21150i	0.363397	+	0.209807i	−0.307173	+	0.951654i	$0.599383\pi$
$618$	−2.14585	−	2.48971i	−0.0863186	−	0.100151i
$619$	1.68175			0.0675954			0.0337977	−	0.999429i	$-0.489240\pi$
$619$	1.68175			0.0675954			0.0337977	+	0.999429i	$0.489240\pi$
$620$	13.2547	+	10.5375i	0.532322	+	0.423197i
$621$	−5.61742	−	5.61742i	−0.225419	−	0.225419i
$622$	6.27862	−	17.9869i	0.251750	−	0.721209i
$623$	−38.4634	+	38.4634i	−1.54101	+	1.54101i
$624$	13.9620	+	8.71411i	0.558929	+	0.348844i
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	−7.59102	+	21.7466i	−0.303398	+	0.869171i
$627$	1.45448	−	0.389726i	0.0580862	−	0.0155641i
$628$	14.8079	+	2.20903i	0.590901	+	0.0881498i
$629$	−18.6469	+	10.4933i	−0.743502	+	0.418395i
$630$	−7.69760	+	6.63447i	−0.306680	+	0.264323i
$631$	6.66054	+	24.8575i	0.265152	+	0.989560i	0.962157	+	0.272494i	$0.0878486\pi$
$631$	6.66054	+	24.8575i	0.265152	+	0.989560i	−0.697005	+	0.717066i	$0.745485\pi$
$632$	−2.61857	−	1.37636i	−0.104161	−	0.0547487i
$633$	9.47634	−	5.47116i	0.376651	−	0.217459i
$634$	−0.760909	−	1.57699i	−0.0302196	−	0.0626303i
$635$	10.8967	+	10.8967i	0.432424	+	0.432424i
$636$	1.10869	+	2.81238i	0.0439625	+	0.111518i
$637$	12.2589	−	12.2589i	0.485716	−	0.485716i
$638$	−0.289465	−	1.52355i	−0.0114600	−	0.0603179i
$639$		−	10.1916i		−	0.403172i
$640$	2.98603	+	10.9125i	0.118033	+	0.431356i
$641$	−5.90271	+	10.2238i	−0.233143	+	0.403815i	−0.958731	−	0.284314i	$-0.908234\pi$
$641$	−5.90271	+	10.2238i	−0.233143	+	0.403815i	0.725588	+	0.688129i	$0.241568\pi$
$642$	−2.06805	−	4.28605i	−0.0816194	−	0.169157i
$643$	−9.46191	+	9.46191i	−0.373141	+	0.373141i	−0.868620	−	0.495479i	$-0.834993\pi$
$643$	−9.46191	+	9.46191i	−0.373141	+	0.373141i	0.495479	+	0.868620i	$0.334993\pi$
$644$	1.26655	+	11.0901i	0.0499091	+	0.437011i
$645$	−0.307688	+	0.532931i	−0.0121152	+	0.0209841i
$646$	−2.47933	−	1.68763i	−0.0975479	−	0.0663990i
$647$	44.8687	+	12.0225i	1.76397	+	0.472655i	0.987516	−	0.157517i	$-0.0503490\pi$
$647$	44.8687	+	12.0225i	1.76397	+	0.472655i	0.776455	+	0.630172i	$0.217016\pi$
$648$	−6.32110	+	1.96552i	−0.248316	+	0.0772131i
$649$	21.0348	−	5.63626i	0.825689	−	0.221243i
$650$	−1.20421	−	6.33817i	−0.0472331	−	0.248603i
$651$	−24.2404	+	6.49520i	−0.950058	+	0.254567i
$652$	−17.4203	+	12.8975i	−0.682233	+	0.505107i
$653$	−3.78754	+	14.1353i	−0.148218	+	0.553157i	0.851373	+	0.524561i	$0.175770\pi$
$653$	−3.78754	+	14.1353i	−0.148218	+	0.553157i	−0.999591	+	0.0285965i	$0.990896\pi$
$654$	−0.0480052	+	0.00912069i	−0.00187715	+	0.000356647i
$655$		−	12.6325i		−	0.493593i
$656$	−1.00966	+	3.30876i	−0.0394206	+	0.129185i
$657$	8.00578	+	4.62214i	0.312335	+	0.180327i
$658$	−2.50094	+	33.7150i	−0.0974968	+	1.31435i
$659$	13.9118	+	24.0960i	0.541928	+	0.938647i	0.998793	+	0.0491110i	$0.0156388\pi$
$659$	13.9118	+	24.0960i	0.541928	+	0.938647i	−0.456865	+	0.889536i	$0.651028\pi$
$660$	−4.01459	+	2.97230i	−0.156268	+	0.115696i
$661$	1.63132	−	6.08817i	0.0634510	−	0.236802i	−0.926916	−	0.375268i	$-0.877551\pi$
$661$	1.63132	−	6.08817i	0.0634510	−	0.236802i	0.990367	+	0.138466i	$0.0442172\pi$
$662$	−13.9013	−	4.85246i	−0.540288	−	0.188596i
$663$	12.5343	−	7.23667i	0.486791	−	0.281049i
$664$	12.4963	−	13.5292i	0.484949	−	0.525036i
$665$		−	1.98136i		−	0.0768337i
$666$	−12.1218	−	14.3821i	−0.469711	−	0.557294i
$667$		−	0.672511i		−	0.0260397i
$668$	−11.2765	+	1.28784i	−0.436301	+	0.0498279i
$669$	19.1685	−	11.0669i	0.741096	−	0.427872i
$670$	−4.05822	+	11.6259i	−0.156783	+	0.449148i
$671$	−10.2089	+	38.1003i	−0.394112	+	1.47085i
$672$	−15.6315	−	6.06676i	−0.602997	−	0.234030i
$673$	0.618248	+	1.07084i	0.0238317	+	0.0412777i	0.877695	−	0.479219i	$-0.159080\pi$
$673$	0.618248	+	1.07084i	0.0238317	+	0.0412777i	−0.853864	+	0.520497i	$0.825747\pi$
$674$	−1.92960	−	0.143136i	−0.0743256	−	0.00551339i
$675$	−4.05117	−	2.33895i	−0.155930	−	0.0900261i
$676$	−2.30504	+	15.4515i	−0.0886553	+	0.594289i
$677$			27.5120i			1.05737i	0.848817	+	0.528686i	$0.177315\pi$
$677$			27.5120i			1.05737i	−0.848817	+	0.528686i	$0.822685\pi$
$678$	1.29749	+	6.82911i	0.0498298	+	0.262270i
$679$	14.1760	−	52.9054i	0.544023	−	2.03032i
$680$	9.70480	+	2.19190i	0.372162	+	0.0840554i
$681$	15.3620	−	4.11623i	0.588672	−	0.157734i
$682$	32.5733	−	6.18873i	1.24730	−	0.236979i
$683$	10.8568	−	2.90907i	0.415423	−	0.111312i	−0.0450524	−	0.998985i	$-0.514345\pi$
$683$	10.8568	−	2.90907i	0.415423	−	0.111312i	0.460476	+	0.887672i	$0.347679\pi$
$684$	1.05066	−	2.41810i	0.0401728	−	0.0924585i
$685$	17.0159	+	4.55941i	0.650145	+	0.174206i
$686$	8.36786	−	12.2934i	0.319487	−	0.469363i
$687$	6.37901	−	11.0488i	0.243374	−	0.421537i
$688$	2.72753	+	0.0937924i	0.103986	+	0.00357580i
$689$	−5.40595	+	5.40595i	−0.205950	+	0.205950i
$690$	−1.95093	+	0.941339i	−0.0742708	+	0.0358362i
$691$	−10.6357	+	18.4216i	−0.404601	+	0.700790i	−0.994275	−	0.106852i	$-0.965923\pi$
$691$	−10.6357	+	18.4216i	−0.404601	+	0.700790i	0.589674	+	0.807641i	$0.299256\pi$
$692$	3.99399	−	26.7732i	0.151829	−	1.01776i
$693$			19.8982i			0.755870i
$694$	−34.5247	+	6.55949i	−1.31054	+	0.248995i
$695$	−16.1882	+	16.1882i	−0.614053	+	0.614053i
$696$	0.894224	+	0.470018i	0.0338955	+	0.0178160i
$697$	2.15114	+	2.15114i	0.0814801	+	0.0814801i
$698$	−7.26449	+	3.50517i	−0.274965	+	0.132673i
$699$	2.71548	−	1.56779i	0.102709	−	0.0592991i
$700$	2.41055	+	6.11477i	0.0911104	+	0.231117i
$701$	4.67314	+	17.4404i	0.176502	+	0.658714i	0.996291	+	0.0860484i	$0.0274240\pi$
$701$	4.67314	+	17.4404i	0.176502	+	0.658714i	−0.819789	+	0.572666i	$0.805909\pi$
$702$	19.7031	+	22.8604i	0.743646	+	0.862812i
$703$	3.66707	+	0.0404531i	0.138306	+	0.00152572i
$704$	20.0026	+	9.52115i	0.753877	+	0.358842i
$705$	−6.33723	+	1.69806i	−0.238674	+	0.0639525i
$706$	31.5359	+	11.0081i	1.18687	+	0.414295i
$707$	2.88830	+	5.00269i	0.108626	+	0.188145i
$708$	−5.65314	+	13.0108i	−0.212458	+	0.488976i
$709$	−31.2445	+	31.2445i	−1.17341	+	1.17341i	−0.192023	+	0.981390i	$0.561505\pi$
$709$	−31.2445	+	31.2445i	−1.17341	+	1.17341i	−0.981390	+	0.192023i	$0.938495\pi$
$710$	−6.22353	−	2.17242i	−0.233565	−	0.0815296i
$711$	−1.61707	−	1.61707i	−0.0606448	−	0.0606448i
$712$	1.85666	+	46.7787i	0.0695814	+	1.75311i
$713$	14.3782			0.538469
$714$	−11.1692	+	9.62661i	−0.417998	+	0.360267i
$715$	−10.9401	−	6.31630i	−0.409138	−	0.236216i
$716$	−15.0037	−	6.51904i	−0.560715	−	0.243628i
$717$	−6.28940	−	6.28940i	−0.234882	−	0.234882i
$718$	25.4470	−	37.3846i	0.949674	−	1.39518i
$719$	1.61058	+	0.929866i	0.0600643	+	0.0346782i	0.529731	−	0.848165i	$-0.322293\pi$
$719$	1.61058	+	0.929866i	0.0600643	+	0.0346782i	−0.469667	+	0.882844i	$0.655626\pi$
$720$	−0.300576	+	8.74089i	−0.0112018	+	0.325754i
$721$	−2.19181	+	8.17994i	−0.0816272	+	0.304637i
$722$	−11.4534	−	23.7373i	−0.426252	−	0.883410i
$723$	6.76834	+	25.2598i	0.251717	+	0.939421i
$724$	−7.31156	+	9.19691i	−0.271732	+	0.341801i
$725$	−0.102493	−	0.382509i	−0.00380650	−	0.0142060i
$726$	0.314393	−	4.23830i	0.0116682	−	0.157298i
$727$	50.4341	+	13.5138i	1.87050	+	0.501198i	0.999959	+	0.00909798i	$0.00289602\pi$
$727$	50.4341	+	13.5138i	1.87050	+	0.501198i	0.870539	+	0.492100i	$0.163771\pi$
$728$	−1.68172	−	42.3712i	−0.0623289	−	1.57038i
$729$	7.54014			0.279265
$730$	4.52903	−	3.90351i	0.167627	−	0.144476i
$731$	1.20000	−	2.07846i	0.0443836	−	0.0768746i
$732$	−15.2894	−	20.6509i	−0.565112	−	0.763279i
$733$	−5.01033	+	2.89271i	−0.185061	+	0.106845i	−0.589668	−	0.807646i	$-0.700741\pi$
$733$	−5.01033	+	2.89271i	−0.185061	+	0.106845i	0.404608	+	0.914490i	$0.367408\pi$
$734$	19.7959	+	1.46844i	0.730681	+	0.0542011i
$735$	−3.31083	−	0.887134i	−0.122122	−	0.0327224i
$736$	7.75109	+	5.67540i	0.285709	+	0.209198i
$737$	12.0557	+	20.8811i	0.444078	+	0.769165i
$738$	−1.50480	+	2.21073i	−0.0553924	+	0.0813779i
$739$	−26.1700			−0.962679			−0.481339	−	0.876534i	$-0.659849\pi$
$739$	−26.1700			−0.962679			−0.481339	+	0.876534i	$0.659849\pi$
$740$	−11.3664	+	4.33658i	−0.417836	+	0.159416i
$741$	−2.48067			−0.0911295
$742$	4.38272	−	6.43873i	0.160895	−	0.236373i
$743$	−24.8838	−	43.1001i	−0.912899	−	1.58119i	−0.809948	−	0.586502i	$-0.800505\pi$
$743$	−24.8838	−	43.1001i	−0.912899	−	1.58119i	−0.102952	−	0.994686i	$-0.532829\pi$
$744$	−10.0489	+	19.1184i	−0.368412	+	0.700915i
$745$	11.4001	+	3.05465i	0.417668	+	0.111914i
$746$	12.3444	+	0.915694i	0.451960	+	0.0335259i
$747$	12.3300	−	7.11874i	0.451132	−	0.260461i
$748$	15.6571	−	11.5921i	0.572481	−	0.423850i
$749$	−6.13062	+	10.6185i	−0.224008	+	0.387993i
$750$	−0.966184	+	0.832741i	−0.0352800	+	0.0304074i
$751$	−21.6095			−0.788541			−0.394271	−	0.918994i	$-0.629003\pi$
$751$	−21.6095			−0.788541			−0.394271	+	0.918994i	$0.629003\pi$
$752$	19.8551	+	21.2693i	0.724042	+	0.775611i
$753$	0.376880	+	0.100985i	0.0137343	+	0.00368008i
$754$	−0.188995	+	2.54783i	−0.00688281	+	0.0927866i
$755$	−1.00232	−	3.74072i	−0.0364782	−	0.136139i
$756$	−24.0677	−	19.1339i	−0.875334	−	0.695892i
$757$	−10.9313	−	40.7960i	−0.397303	−	1.48276i	−0.817822	−	0.575471i	$-0.804819\pi$
$757$	−10.9313	−	40.7960i	−0.397303	−	1.48276i	0.420519	−	0.907284i	$-0.361848\pi$
$758$	3.73269	+	7.73603i	0.135577	+	0.280985i
$759$	−1.09778	+	4.09697i	−0.0398469	+	0.148711i
$760$	−1.25267	−	1.15703i	−0.0454391	−	0.0419698i
$761$	1.20559	+	0.696050i	0.0437028	+	0.0252318i	0.521692	−	0.853134i	$-0.325301\pi$
$761$	1.20559	+	0.696050i	0.0437028	+	0.0252318i	−0.477989	+	0.878366i	$0.658634\pi$
$762$	−11.0605	+	16.2491i	−0.400679	+	0.588644i
$763$	0.0890229	+	0.0890229i	0.00322285	+	0.00322285i
$764$	11.8217	−	27.2080i	0.427696	−	0.984350i
$765$	6.66083	+	3.84563i	0.240823	+	0.139039i
$766$	−9.71445	+	8.37276i	−0.350997	+	0.302520i
$767$	−35.8757			−1.29540
$768$	−12.9637	+	6.33993i	−0.467787	+	0.228772i
$769$	32.9246	+	32.9246i	1.18729	+	1.18729i	0.977813	+	0.209480i	$0.0671771\pi$
$769$	32.9246	+	32.9246i	1.18729	+	1.18729i	0.209480	+	0.977813i	$0.432823\pi$
$770$	12.1509	+	4.24148i	0.437889	+	0.152852i
$771$	3.22198	−	3.22198i	0.116037	−	0.116037i
$772$	5.47904	+	2.38062i	0.197195	+	0.0856803i
$773$	11.8502	+	20.5251i	0.426221	+	0.738237i	0.996534	−	0.0831911i	$-0.0265112\pi$
$773$	11.8502	+	20.5251i	0.426221	+	0.738237i	−0.570312	+	0.821428i	$0.693178\pi$
$774$	1.99189	+	0.695303i	0.0715972	+	0.0249921i
$775$	8.17801	−	2.19129i	0.293763	−	0.0787135i
$776$	−25.1702	−	39.8570i	−0.903556	−	1.43078i
$777$	4.85831	−	17.3630i	0.174291	−	0.622895i
$778$	32.3464	+	37.5298i	1.15968	+	1.34551i
$779$	−0.134952	−	0.503647i	−0.00483515	−	0.0180450i
$780$	7.65572	−	3.01803i	0.274119	−	0.108063i
$781$	−11.1780	+	6.45360i	−0.399979	+	0.230928i
$782$	7.60874	−	3.67127i	0.272088	−	0.131284i
$783$	1.30989	+	1.30989i	0.0468115	+	0.0468115i
$784$	3.42742	+	14.8098i	0.122408	+	0.528921i
$785$	5.29333	−	5.29333i	0.188927	−	0.188927i
$786$	15.8299	−	3.00759i	0.564635	−	0.107277i
$787$		−	53.7851i		−	1.91723i	−0.284705	−	0.958615i	$-0.591896\pi$
$787$		−	53.7851i		−	1.91723i	0.284705	−	0.958615i	$-0.408104\pi$
$788$	−54.9352	−	8.19516i	−1.95699	−	0.291940i
$789$	−7.38923	+	12.7985i	−0.263064	+	0.455640i
$790$	−1.33216	+	0.642778i	−0.0473962	+	0.0228690i
$791$	12.6642	−	12.6642i	0.450287	−	0.450287i
$792$	12.5802	+	11.6197i	0.447019	+	0.412889i
$793$	32.4908	−	56.2757i	1.15378	−	1.99841i
$794$	3.80297	−	5.58701i	0.134962	−	0.198276i
$795$	1.46001	+	0.391209i	0.0517813	+	0.0138747i
$796$	−49.7684	−	21.6241i	−1.76399	−	0.766447i
$797$	29.4049	−	7.87902i	1.04158	−	0.279089i	0.302809	−	0.953051i	$-0.402075\pi$
$797$	29.4049	−	7.87902i	1.04158	−	0.279089i	0.738766	+	0.673962i	$0.235409\pi$
$798$	2.48286	−	0.471728i	0.0878922	−	0.0166990i
$799$	24.7156	−	6.62251i	0.874373	−	0.234288i
$800$	5.27360	+	2.04675i	0.186450	+	0.0723634i
$801$	−9.36686	+	34.9576i	−0.330962	+	1.23517i
$802$	−7.50944	−	39.5246i	−0.265168	−	1.39566i
$803$		−	11.7075i		−	0.413148i
$804$	−15.5348	−	2.31745i	−0.547869	−	0.0817303i
$805$	4.83337	+	2.79055i	0.170354	+	0.0983538i
$806$	−54.4724	−	4.04070i	−1.91871	−	0.142328i
$807$	5.65835	+	9.80054i	0.199183	+	0.344995i
$808$	4.84949	+	1.09529i	0.170604	+	0.0385322i
$809$	4.05753	−	15.1429i	0.142655	−	0.532396i	−0.857194	−	0.514994i	$-0.827794\pi$
$809$	4.05753	−	15.1429i	0.142655	−	0.532396i	0.999849	−	0.0174014i	$-0.00553933\pi$
$810$	−1.09080	+	3.12491i	−0.0383268	+	0.109798i
$811$	−19.3187	+	11.1537i	−0.678371	+	0.391658i	−0.799241	−	0.601011i	$-0.794765\pi$
$811$	−19.3187	+	11.1537i	−0.678371	+	0.391658i	0.120870	+	0.992668i	$0.461432\pi$
$812$	−0.295338	−	2.58602i	−0.0103643	−	0.0907516i
$813$		−	7.26831i		−	0.254911i
$814$	−8.09816	+	22.4022i	−0.283840	+	0.785196i
$815$			10.8376i			0.379625i
$816$	−0.436136	+	12.6830i	−0.0152678	+	0.443995i
$817$	−0.356238	+	0.205674i	−0.0124632	+	0.00719563i
$818$	18.4103	+	6.42640i	0.643700	+	0.224694i
$819$	8.48430	−	31.6638i	0.296465	−	1.10642i
$820$	1.02923	+	1.39015i	0.0359422	+	0.0485461i
$821$	−7.30066	−	12.6451i	−0.254795	−	0.441318i	0.710045	−	0.704156i	$-0.248675\pi$
$821$	−7.30066	−	12.6451i	−0.254795	−	0.441318i	−0.964840	+	0.262839i	$0.915341\pi$
$822$	−1.66223	+	22.4084i	−0.0579769	+	0.781581i
$823$	−11.0673	−	6.38973i	−0.385783	−	0.222732i	0.294548	−	0.955637i	$-0.404831\pi$
$823$	−11.0673	−	6.38973i	−0.385783	−	0.222732i	−0.680331	+	0.732905i	$0.738164\pi$
$824$	3.89167	+	6.16247i	0.135573	+	0.214680i
$825$			2.49757i			0.0869543i
$826$	35.9074	−	6.82219i	1.24938	−	0.237374i
$827$	13.0765	−	48.8020i	0.454713	−	1.69701i	−0.234217	−	0.972184i	$-0.575253\pi$
$827$	13.0765	−	48.8020i	0.454713	−	1.69701i	0.688930	−	0.724828i	$-0.258081\pi$
$828$	4.41904	+	5.96866i	0.153572	+	0.207425i
$829$	8.19774	−	2.19658i	0.284719	−	0.0762903i	−0.113633	−	0.993523i	$-0.536249\pi$
$829$	8.19774	−	2.19658i	0.284719	−	0.0762903i	0.398352	+	0.917232i	$0.369582\pi$
$830$	−1.71884	−	9.04680i	−0.0596617	−	0.314019i
$831$	23.3298	−	6.25119i	0.809301	−	0.216851i
$832$	−27.7703	−	23.6797i	−0.962762	−	0.820947i
$833$	12.9124	+	3.45987i	0.447389	+	0.119877i
$834$	−24.1397	−	16.4315i	−0.835890	−	0.568975i
$835$	−2.83745	+	4.91460i	−0.0981939	+	0.170077i
$836$	−3.31745	+	0.378871i	−0.114736	+	0.0131035i
$837$	−28.0052	+	28.0052i	−0.968003	+	0.968003i
$838$	−10.8833	−	22.5557i	−0.375956	−	0.779172i
$839$	6.86045	−	11.8826i	0.236849	−	0.410234i	−0.722959	−	0.690890i	$-0.757219\pi$
$839$	6.86045	−	11.8826i	0.236849	−	0.410234i	0.959808	+	0.280656i	$0.0905520\pi$
$840$	−7.08857	+	4.47652i	−0.244579	+	0.154455i
$841$		−	28.8432i		−	0.994592i
$842$	−1.57977	−	8.31486i	−0.0544425	−	0.286549i
$843$	−19.4737	+	19.4737i	−0.670709	+	0.670709i
$844$	−22.5734	+	8.89885i	−0.777009	+	0.306311i
$845$	5.52339	+	5.52339i	0.190010	+	0.190010i
$846$	9.77471	+	20.2582i	0.336061	+	0.696490i
$847$	−9.48293	+	5.47497i	−0.325837	+	0.188122i
$848$	−1.51143	−	6.53083i	−0.0519026	−	0.224269i
$849$	−5.60889	−	20.9326i	−0.192496	−	0.718407i
$850$	3.76817	−	3.24774i	0.129247	−	0.111396i
$851$	−5.26339	+	8.88856i	−0.180427	+	0.304696i
$852$	1.24057	−	8.31599i	0.0425011	−	0.284901i
$853$	18.5117	−	4.96019i	0.633828	−	0.169834i	0.0724216	−	0.997374i	$-0.476927\pi$
$853$	18.5117	−	4.96019i	0.633828	−	0.169834i	0.561406	+	0.827540i	$0.310261\pi$
$854$	−21.8180	+	62.5039i	−0.746597	+	2.13884i
$855$	−0.659124	−	1.14164i	−0.0225416	−	0.0390431i
$856$	3.13333	+	10.0767i	0.107095	+	0.344416i
$857$	29.0047	−	29.0047i	0.990780	−	0.990780i	−0.00917752	−	0.999958i	$-0.502921\pi$
$857$	29.0047	−	29.0047i	0.990780	−	0.990780i	0.999958	+	0.00917752i	$0.00292134\pi$
$858$	5.31035	−	15.2130i	0.181292	−	0.519364i
$859$	−5.71944	−	5.71944i	−0.195145	−	0.195145i	0.602770	−	0.797915i	$-0.294064\pi$
$859$	−5.71944	−	5.71944i	−0.195145	−	0.195145i	−0.797915	+	0.602770i	$0.794064\pi$
$860$	0.849180	−	1.06815i	0.0289568	−	0.0364236i
$861$	−2.56348			−0.0873633
$862$	−15.2338	−	17.6749i	−0.518865	−	0.602010i
$863$	6.50639	+	3.75646i	0.221480	+	0.127872i	0.606635	−	0.794980i	$-0.292519\pi$
$863$	6.50639	+	3.75646i	0.221480	+	0.127872i	−0.385155	+	0.922852i	$0.625852\pi$
$864$	−26.1515	+	4.04293i	−0.889692	+	0.137543i
$865$	−9.57050	−	9.57050i	−0.325407	−	0.325407i
$866$	−26.9239	−	18.3266i	−0.914912	−	0.622763i
$867$	−3.61380	−	2.08643i	−0.122731	−	0.0708587i
$868$	55.2889	−	6.31430i	1.87663	−	0.214321i
$869$	−0.749601	+	2.79755i	−0.0254285	+	0.0949004i
$870$	0.454925	−	0.219504i	0.0154234	−	0.00744189i
$871$	−10.2807	−	38.3683i	−0.348350	−	1.30006i
$872$	0.108268	−	0.00429721i	0.00366643	−	0.000145522i
$873$	−9.43164	−	35.1993i	−0.319213	−	1.19132i
$874$	−1.44401	−	0.107115i	−0.0488443	−	0.00362321i
$875$	3.17440	+	0.850578i	0.107314	+	0.0287548i
$876$	5.96982	+	4.74601i	0.201702	+	0.160353i
$877$	−33.0892			−1.11734			−0.558672	−	0.829389i	$-0.688689\pi$
$877$	−33.0892			−1.11734			−0.558672	+	0.829389i	$0.688689\pi$
$878$	28.4742	+	33.0370i	0.960957	+	1.11494i
$879$	−8.03361	+	13.9146i	−0.270967	+	0.469328i
$880$	9.77722	−	5.20532i	0.329590	−	0.175471i
$881$	−45.4308	+	26.2295i	−1.53060	+	0.883694i	−0.531268	+	0.847204i	$0.678284\pi$
$881$	−45.4308	+	26.2295i	−1.53060	+	0.883694i	−0.999334	+	0.0364900i	$0.988382\pi$
$882$	−0.869310	+	11.7191i	−0.0292712	+	0.394603i
$883$	10.0426	+	2.69090i	0.337960	+	0.0905560i	0.423808	−	0.905752i	$-0.360693\pi$
$883$	10.0426	+	2.69090i	0.337960	+	0.0905560i	−0.0858480	+	0.996308i	$0.527360\pi$
$884$	−29.8577	+	11.7705i	−1.00422	+	0.395883i
$885$	3.54647	+	6.14267i	0.119213	+	0.206483i
$886$	−10.6822	−	7.27119i	−0.358877	−	0.244280i
$887$	7.86354			0.264032			0.132016	−	0.991248i	$-0.457855\pi$
$887$	7.86354			0.264032			0.132016	+	0.991248i	$0.457855\pi$
$888$	−8.14035	−	13.2108i	−0.273172	−	0.443327i
$889$	50.6442			1.69855
$890$	19.3504	+	13.1714i	0.648626	+	0.441507i
$891$	3.24043	+	5.61259i	0.108558	+	0.188029i
$892$	−45.6609	+	18.0004i	−1.52884	+	0.602697i
$893$	−4.23613	−	1.13507i	−0.141757	−	0.0379836i
$894$	−1.11364	+	15.0129i	−0.0372456	+	0.502105i
$895$	−7.08355	+	4.08969i	−0.236777	+	0.136703i
$896$	32.2978	+	18.4198i	1.07899	+	0.615362i
$897$	3.49378	−	6.05140i	0.116654	−	0.202050i
$898$	16.8960	+	19.6035i	0.563828	+	0.654179i
$899$	−3.35276			−0.111821
$900$	3.42309	+	2.72136i	0.114103	+	0.0907121i
$901$	−5.69412	−	1.52573i	−0.189699	−	0.0508296i
$902$	3.37757	+	0.250545i	0.112461	+	0.00834223i
$903$	0.523425	+	1.95345i	0.0174185	+	0.0650067i
$904$	−0.611312	−	15.4020i	−0.0203319	−	0.512264i
$905$	1.52045	+	5.67440i	0.0505415	+	0.188623i
$906$	4.44889	−	2.14662i	0.147805	−	0.0713167i
$907$	10.6078	−	39.5887i	0.352225	−	1.31452i	−0.531716	−	0.846923i	$-0.678453\pi$
$907$	10.6078	−	39.5887i	0.352225	−	1.31452i	0.883941	−	0.467599i	$-0.154881\pi$
$908$	−35.0384	+	4.00158i	−1.16279	+	0.132797i
$909$	3.32842	+	1.92166i	0.110397	+	0.0637376i
$910$	−17.5272	−	11.9304i	−0.581020	−	0.395489i
$911$	−4.05910	−	4.05910i	−0.134484	−	0.134484i	0.636660	−	0.771144i	$-0.280315\pi$
$911$	−4.05910	−	4.05910i	−0.134484	−	0.134484i	−0.771144	+	0.636660i	$0.780315\pi$
$912$	1.15164	−	1.84520i	0.0381348	−	0.0611008i
$913$	−15.6155	−	9.01559i	−0.516796	−	0.298372i
$914$	7.47809	+	8.67641i	0.247353	+	0.286990i
$915$	−12.8474			−0.424723
$916$	−17.6053	+	22.1449i	−0.581694	+	0.731690i
$917$	−29.3557	−	29.3557i	−0.969412	−	0.969412i
$918$	−7.66923	+	21.9707i	−0.253122	+	0.725141i
$919$	−10.3504	+	10.3504i	−0.341427	+	0.341427i	−0.856904	−	0.515476i	$-0.827615\pi$
$919$	−10.3504	+	10.3504i	−0.341427	+	0.341427i	0.515476	+	0.856904i	$0.327615\pi$
$920$	4.58675	−	1.42623i	0.151221	−	0.0470215i
$921$	−0.235192	−	0.407364i	−0.00774983	−	0.0134231i
$922$	0.0357623	−	0.102451i	0.00117777	−	0.00337405i
$923$	20.5391	−	5.50344i	0.676053	−	0.181148i
$924$	−2.42211	+	16.2363i	−0.0796815	+	0.534135i
$925$	−1.63905	+	5.85777i	−0.0538916	+	0.192602i
$926$	2.88645	−	2.48779i	0.0948545	−	0.0817539i
$927$	1.45827	+	5.44233i	0.0478958	+	0.178750i
$928$	−1.80742	−	1.32341i	−0.0593316	−	0.0434430i
$929$	31.1807	−	18.0022i	1.02301	−	0.590633i	0.108033	−	0.994147i	$-0.465545\pi$
$929$	31.1807	−	18.0022i	1.02301	−	0.590633i	0.914973	+	0.403514i	$0.132211\pi$
$930$	4.69298	+	9.72624i	0.153889	+	0.318936i
$931$	−1.62012	−	1.62012i	−0.0530974	−	0.0530974i
$932$	−6.46851	+	2.55000i	−0.211883	+	0.0835282i
$933$	8.59148	−	8.59148i	0.281272	−	0.281272i
$934$	−1.03331	−	5.43866i	−0.0338110	−	0.177958i
$935$		−	9.74067i		−	0.318554i
$936$	−15.0643	−	23.8544i	−0.492392	−	0.779704i
$937$	−28.1349	+	48.7312i	−0.919129	+	1.59198i	−0.118387	+	0.992967i	$0.537772\pi$
$937$	−28.1349	+	48.7312i	−0.919129	+	1.59198i	−0.800741	+	0.599010i	$0.795561\pi$
$938$	17.5860	+	36.4472i	0.574203	+	1.19004i
$939$	−10.3873	+	10.3873i	−0.338978	+	0.338978i
$940$	14.4543	−	1.65076i	0.471448	−	0.0538419i
$941$	−4.59103	+	7.95190i	−0.149663	+	0.259225i	−0.931103	−	0.364756i	$-0.881152\pi$
$941$	−4.59103	+	7.95190i	−0.149663	+	0.259225i	0.781440	+	0.623981i	$0.214486\pi$
$942$	7.89338	+	5.37287i	0.257180	+	0.175058i
$943$	1.41868	+	0.380133i	0.0461984	+	0.0123788i
$944$	16.6552	−	26.6856i	0.542082	−	0.868541i
$945$	−14.8495	+	3.97891i	−0.483055	+	0.129434i
$946$	−0.498728	−	2.62497i	−0.0162150	−	0.0853450i
$947$	−12.5313	+	3.35774i	−0.407211	+	0.109112i	−0.456609	−	0.889667i	$-0.650936\pi$
$947$	−12.5313	+	3.35774i	−0.407211	+	0.109112i	0.0493983	+	0.998779i	$0.484270\pi$
$948$	−1.12264	−	1.51631i	−0.0364616	−	0.0492475i
$949$	−4.99190	+	18.6300i	−0.162044	+	0.604756i
$950$	−0.837643	+	0.159147i	−0.0271767	+	0.00516342i
$951$		−	1.11670i		−	0.0362116i
$952$	27.6458	−	17.4587i	0.896006	−	0.565838i
$953$	−24.2661	−	14.0100i	−0.786056	−	0.453830i	0.0525160	−	0.998620i	$-0.483276\pi$
$953$	−24.2661	−	14.0100i	−0.786056	−	0.453830i	−0.838572	+	0.544790i	$0.816609\pi$
$954$	0.383349	−	5.16789i	0.0124114	−	0.167317i
$955$	−7.41631	−	12.8454i	−0.239986	−	0.415668i
$956$	11.7361	+	15.8516i	0.379572	+	0.512677i
$957$	0.255984	−	0.955345i	0.00827479	−	0.0308819i
$958$	−47.3621	−	16.5325i	−1.53020	−	0.534142i
$959$	50.1373	−	28.9468i	1.61902	−	0.934740i
$960$	−1.30924	+	7.09570i	−0.0422557	+	0.229013i
$961$		−	40.6816i		−	1.31231i
$962$	22.4385	−	32.1955i	0.723446	−	1.03802i
$963$			8.15772i			0.262879i
$964$	−6.57982	−	57.6139i	−0.211922	−	1.85562i
$965$	2.58676	−	1.49347i	0.0832709	−	0.0480765i
$966$	−2.34612	+	6.72113i	−0.0754851	+	0.216249i
$967$	−6.54936	+	24.4425i	−0.210613	+	0.786019i	0.777052	+	0.629437i	$0.216714\pi$
$967$	−6.54936	+	24.4425i	−0.210613	+	0.786019i	−0.987665	+	0.156582i	$0.949952\pi$
$968$	−2.07620	+	9.19253i	−0.0667315	+	0.295459i
$969$	−0.956389	−	1.65651i	−0.0307236	−	0.0532149i
$970$	−23.5051	−	1.74358i	−0.754703	−	0.0559830i
$971$	19.9647	+	11.5266i	0.640699	+	0.369908i	0.784884	−	0.619643i	$-0.212723\pi$
$971$	19.9647	+	11.5266i	0.640699	+	0.369908i	−0.144185	+	0.989551i	$0.546056\pi$
$972$	−31.9357	−	4.76413i	−1.02434	−	0.152810i
$973$			75.2370i			2.41199i
$974$	8.46049	+	44.5303i	0.271091	+	1.42684i
$975$	1.06493	−	3.97436i	0.0341050	−	0.127282i
$976$	26.7760	+	50.2936i	0.857078	+	1.60986i
$977$	−24.7139	+	6.62207i	−0.790668	+	0.211859i	−0.631483	−	0.775390i	$-0.717553\pi$
$977$	−24.7139	+	6.62207i	−0.790668	+	0.211859i	−0.159185	+	0.987249i	$0.550887\pi$
$978$	−13.5807	+	2.58025i	−0.434263	+	0.0825074i
$979$	44.2723	−	11.8627i	1.41495	−	0.379135i
$980$	6.97102	+	3.02888i	0.222681	+	0.0967540i
$981$	0.0809087	+	0.0216794i	0.00258322	+	0.000692170i
$982$	27.8912	−	40.9755i	0.890045	−	1.30758i
$983$	−24.4688	+	42.3812i	−0.780434	+	1.35175i	0.151256	+	0.988495i	$0.451668\pi$
$983$	−24.4688	+	42.3812i	−0.780434	+	1.35175i	−0.931689	+	0.363256i	$0.881665\pi$
$984$	−1.49697	+	1.62071i	−0.0477215	+	0.0516663i
$985$	−19.6375	+	19.6375i	−0.625701	+	0.625701i
$986$	−1.77423	+	0.856078i	−0.0565030	+	0.0272631i
$987$	−10.7806	+	18.6726i	−0.343151	+	0.594355i
$988$	5.44057	+	0.811616i	0.173087	+	0.0258210i
$989$		−	1.15869i		−	0.0368442i
$990$	8.41222	−	1.59827i	0.267358	−	0.0507964i
$991$	−33.4028	+	33.4028i	−1.06108	+	1.06108i	−0.0630670	+	0.998009i	$0.520088\pi$
$991$	−33.4028	+	33.4028i	−1.06108	+	1.06108i	−0.998009	+	0.0630670i	$0.979912\pi$
$992$	28.2943	−	38.6425i	0.898345	−	1.22690i
$993$	−6.63996	−	6.63996i	−0.210713	−	0.210713i
$994$	−19.5107	+	9.41405i	−0.618842	+	0.298596i
$995$	−23.4966	+	13.5658i	−0.744894	+	0.430065i
$996$	10.9274	−	4.30779i	0.346248	−	0.136497i
$997$	−5.51393	−	20.5783i	−0.174628	−	0.651721i	−0.996615	−	0.0822140i	$-0.973801\pi$
$997$	−5.51393	−	20.5783i	−0.174628	−	0.651721i	0.821987	−	0.569507i	$-0.192866\pi$
$998$	3.85230	+	4.46961i	0.121942	+	0.141483i
$999$	−7.06094	−	27.5645i	−0.223398	−	0.872103i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.be.a.51.14	✓	304
4.3	odd	2	inner	740.2.be.a.51.26	yes	304
37.8	odd	12	inner	740.2.be.a.711.26	yes	304
148.119	even	12	inner	740.2.be.a.711.14	yes	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.be.a.51.14	✓	304	1.1	even	1	trivial
740.2.be.a.51.26	yes	304	4.3	odd	2	inner
740.2.be.a.711.14	yes	304	148.119	even	12	inner
740.2.be.a.711.26	yes	304	37.8	odd	12	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:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.16908 - 0.795771i) q^{2} +(-0.450967 - 0.781098i) q^{3} +(0.733498 + 1.86064i) q^{4} +(0.965926 + 0.258819i) q^{5} +(-0.0943580 + 1.27203i) q^{6} +(2.84609 - 1.64319i) q^{7} +(0.623124 - 2.75893i) q^{8} +(1.09326 - 1.89358i) q^{9} +(-0.923284 - 1.07124i) q^{10} -2.76913 q^{11} +(1.12256 - 1.41202i) q^{12} +(4.40649 + 1.18072i) q^{13} +(-4.63491 - 0.343813i) q^{14} +(-0.233438 - 0.871201i) q^{15} +(-2.92396 + 2.72955i) q^{16} +(0.910419 + 3.39773i) q^{17} +(-2.78496 + 1.34376i) q^{18} +(0.156042 - 0.582356i) q^{19} +(0.226936 + 1.98708i) q^{20} +(-2.56698 - 1.48205i) q^{21} +(3.23734 + 2.20359i) q^{22} +(1.20084 + 1.20084i) q^{23} +(-2.43601 + 0.757467i) q^{24} +(0.866025 + 0.500000i) q^{25} +(-4.21196 - 4.88691i) q^{26} -4.67789 q^{27} +(5.14499 + 4.09027i) q^{28} +(-0.280016 - 0.280016i) q^{29} +(-0.420369 + 1.20427i) q^{30} +(5.98672 - 5.98672i) q^{31} +(5.59044 - 0.864263i) q^{32} +(1.24879 + 2.16296i) q^{33} +(1.63946 - 4.69671i) q^{34} +(3.17440 - 0.850578i) q^{35} +(4.32517 + 0.645223i) q^{36} +(1.50943 + 5.89251i) q^{37} +(-0.645847 + 0.556647i) q^{38} +(-1.06493 - 3.97436i) q^{39} +(1.31596 - 2.50365i) q^{40} +(0.748977 - 0.432422i) q^{41} +(1.82164 + 3.77537i) q^{42} +(-0.482448 - 0.482448i) q^{43} +(-2.03115 - 5.15236i) q^{44} +(1.54610 - 1.54610i) q^{45} +(-0.448287 - 2.35948i) q^{46} -7.27413i q^{47} +(3.45066 + 1.05296i) q^{48} +(1.90015 - 3.29116i) q^{49} +(-0.614568 - 1.27370i) q^{50} +(2.24339 - 2.24339i) q^{51} +(1.03527 + 9.06495i) q^{52} +(-0.837930 + 1.45134i) q^{53} +(5.46883 + 3.72253i) q^{54} +(-2.67478 - 0.716704i) q^{55} +(-2.75999 - 8.87609i) q^{56} +(-0.525246 + 0.140739i) q^{57} +(0.104533 + 0.550190i) q^{58} +(-7.59618 + 2.03539i) q^{59} +(1.44977 - 1.07337i) q^{60} +(3.68670 - 13.7589i) q^{61} +(-11.7630 + 2.23490i) q^{62} -7.18572i q^{63} +(-7.22343 - 3.43832i) q^{64} +(3.95075 + 2.28097i) q^{65} +(0.261290 - 3.52242i) q^{66} +(-4.35361 - 7.54067i) q^{67} +(-5.65416 + 4.18619i) q^{68} +(0.396435 - 1.47952i) q^{69} +(-4.38800 - 1.53170i) q^{70} +(4.03663 - 2.33055i) q^{71} +(-4.54302 - 4.19616i) q^{72} +4.22786i q^{73} +(2.92444 - 8.08997i) q^{74} -0.901934i q^{75} +(1.19801 - 0.136819i) q^{76} +(-7.88120 + 4.55021i) q^{77} +(-1.91770 + 5.49379i) q^{78} +(0.270699 - 1.01026i) q^{79} +(-3.53079 + 1.87977i) q^{80} +(-1.17020 - 2.02684i) q^{81} +(-1.21972 - 0.0904777i) q^{82} +(5.63912 + 3.25575i) q^{83} +(0.874681 - 5.86331i) q^{84} +3.51759i q^{85} +(0.180103 + 0.947939i) q^{86} +(-0.0924420 + 0.344998i) q^{87} +(-1.72551 + 7.63985i) q^{88} +(-15.9878 + 4.28392i) q^{89} +(-3.03786 + 0.577174i) q^{90} +(14.4814 - 3.88028i) q^{91} +(-1.35352 + 3.11515i) q^{92} +(-7.37603 - 1.97640i) q^{93} +(-5.78854 + 8.50405i) q^{94} +(0.301449 - 0.522126i) q^{95} +(-3.19618 - 3.97693i) q^{96} +(11.7848 - 11.7848i) q^{97} +(-4.84044 + 2.33555i) q^{98} +(-3.02737 + 5.24356i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 304 q + 4 q^{2} - 12 q^{4} - 8 q^{8} - 152 q^{9} + 16 q^{13} - 24 q^{14} + 20 q^{16} - 60 q^{18} - 16 q^{22} - 24 q^{24} - 32 q^{29} - 56 q^{32} - 32 q^{37} + 40 q^{38} + 20 q^{42} + 12 q^{44} - 8 q^{46}+ \cdots - 36 q^{98}+O(q^{100}) \) 304 * q + 4 * q^2 - 12 * q^4 - 8 * q^8 - 152 * q^9 + 16 * q^13 - 24 * q^14 + 20 * q^16 - 60 * q^18 - 16 * q^22 - 24 * q^24 - 32 * q^29 - 56 * q^32 - 32 * q^37 + 40 * q^38 + 20 * q^42 + 12 * q^44 - 8 * q^46 + 104 * q^49 + 4 * q^50 - 40 * q^52 + 40 * q^54 + 4 * q^56 - 48 * q^57 - 12 * q^58 - 28 * q^60 - 16 * q^61 - 60 * q^62 + 24 * q^65 - 52 * q^66 - 200 * q^68 - 196 * q^72 + 20 * q^74 - 40 * q^76 + 96 * q^77 - 48 * q^78 - 152 * q^81 + 32 * q^82 - 112 * q^84 + 12 * q^88 - 8 * q^89 + 140 * q^92 - 16 * q^93 - 28 * q^94 - 132 * q^96 + 48 * q^97 - 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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