LMFDB - Embedded newform 690.2.w.b.37.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(7,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 38]))

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

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.w (of order $44$, degree $20$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			37.7
Character	$\chi$	$=$	690.37
Dual form			690.2.w.b.373.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.877679 + 0.479249i) q^{2} +(-0.997452 - 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(-2.09572 - 0.779713i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(-0.448960 - 1.20371i) q^{7} +(0.0713392 + 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +O(q^{10})$	\(q+(0.877679 + 0.479249i) q^{2} +(-0.997452 - 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(-2.09572 - 0.779713i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(-0.448960 - 1.20371i) q^{7} +(0.0713392 + 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +(-1.46569 - 1.68871i) q^{10} +(0.00232980 - 0.00793457i) q^{11} +(-0.479249 - 0.877679i) q^{12} +(5.34764 + 1.99457i) q^{13} +(0.182833 - 1.27163i) q^{14} +(2.03476 + 0.927233i) q^{15} +(-0.415415 + 0.909632i) q^{16} +(1.76969 - 0.384973i) q^{17} +(0.800541 + 0.599278i) q^{18} +(5.16179 - 3.31728i) q^{19} +(-0.477097 - 2.18458i) q^{20} +(0.361945 + 1.23267i) q^{21} +(0.00584745 - 0.00584745i) q^{22} +(1.70179 - 4.48374i) q^{23} -1.00000i q^{24} +(3.78410 + 3.26812i) q^{25} +(3.73761 + 4.31344i) q^{26} +(-0.977147 - 0.212565i) q^{27} +(0.769898 - 1.02846i) q^{28} +(3.74079 - 5.82078i) q^{29} +(1.34149 + 1.78897i) q^{30} +(1.20413 - 1.38964i) q^{31} +(-0.800541 + 0.599278i) q^{32} +(-0.00288991 + 0.00774814i) q^{33} +(1.73772 + 0.510241i) q^{34} +(0.00234851 + 2.87270i) q^{35} +(0.415415 + 0.909632i) q^{36} +(-1.50039 - 2.00428i) q^{37} +(6.12020 - 0.437725i) q^{38} +(-5.19172 - 2.37098i) q^{39} +(0.628219 - 2.14601i) q^{40} +(0.636167 + 4.42464i) q^{41} +(-0.273085 + 1.25535i) q^{42} +(-0.451519 + 6.31307i) q^{43} +(0.00793457 - 0.00232980i) q^{44} +(-1.96343 - 1.07003i) q^{45} +(3.64246 - 3.11970i) q^{46} +(0.432950 + 0.432950i) q^{47} +(0.479249 - 0.877679i) q^{48} +(4.04290 - 3.50319i) q^{49} +(1.75498 + 4.68189i) q^{50} +(-1.79265 + 0.257744i) q^{51} +(1.21322 + 5.57706i) q^{52} +(-11.7829 + 4.39479i) q^{53} +(-0.755750 - 0.654861i) q^{54} +(-0.0110693 + 0.0148121i) q^{55} +(1.16861 - 0.533688i) q^{56} +(-5.38529 + 2.94059i) q^{57} +(6.07282 - 3.31601i) q^{58} +(-3.99100 + 1.82263i) q^{59} +(0.320035 + 2.21305i) q^{60} +(1.16714 + 1.01133i) q^{61} +(1.72283 - 0.642582i) q^{62} +(-0.273085 - 1.25535i) q^{63} +(-0.989821 + 0.142315i) q^{64} +(-9.65197 - 8.34967i) q^{65} +(-0.00624970 + 0.00541540i) q^{66} +(2.37799 - 4.35496i) q^{67} +(1.28063 + 1.28063i) q^{68} +(-2.01732 + 4.35091i) q^{69} +(-1.37468 + 2.52243i) q^{70} +(13.8586 - 4.06927i) q^{71} +(-0.0713392 + 0.997452i) q^{72} +(-2.82922 + 13.0057i) q^{73} +(-0.356308 - 2.47817i) q^{74} +(-3.54131 - 3.52975i) q^{75} +(5.58135 + 2.54892i) q^{76} +(-0.0105969 + 0.000757905i) q^{77} +(-3.42037 - 4.56909i) q^{78} +(-5.54935 - 12.1514i) q^{79} +(1.57985 - 1.58243i) q^{80} +(0.959493 + 0.281733i) q^{81} +(-1.56215 + 4.18829i) q^{82} +(-2.53753 + 1.89957i) q^{83} +(-0.841306 + 0.970919i) q^{84} +(-4.00895 - 0.573056i) q^{85} +(-3.42182 + 5.32446i) q^{86} +(-4.14651 + 5.53909i) q^{87} +(0.00808056 + 0.00175782i) q^{88} +(-1.24013 - 1.43119i) q^{89} +(-1.21045 - 1.88011i) q^{90} -7.33247i q^{91} +(4.69202 - 0.992450i) q^{92} +(-1.30020 + 1.30020i) q^{93} +(0.172500 + 0.587482i) q^{94} +(-13.4042 + 2.92738i) q^{95} +(0.841254 - 0.540641i) q^{96} +(-4.18289 - 3.13127i) q^{97} +(5.22727 - 1.13712i) q^{98} +(0.00343529 - 0.00752224i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{6}+O(q^{10}) $ 240 * q + 24 * q^6	$ 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) $ 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{21}{22}\right)$

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 $

$2$	0.877679	+	0.479249i	0.620613	+	0.338880i
$2$	0.877679	+	0.479249i	0.620613	+	0.338880i
$3$	−0.997452	−	0.0713392i	−0.575879	−	0.0411877i
$3$	−0.997452	−	0.0713392i	−0.575879	−	0.0411877i
$4$	0.540641	+	0.841254i	0.270320	+	0.420627i
$5$	−2.09572	−	0.779713i	−0.937235	−	0.348698i
$5$	−2.09572	−	0.779713i	−0.937235	−	0.348698i
$6$	−0.841254	−	0.540641i	−0.343440	−	0.220716i
$7$	−0.448960	−	1.20371i	−0.169691	−	0.454959i	0.824070	−	0.566488i	$-0.191698\pi$
$7$	−0.448960	−	1.20371i	−0.169691	−	0.454959i	−0.993761	+	0.111529i	$0.964425\pi$
$8$	0.0713392	+	0.997452i	0.0252222	+	0.352653i
$9$	0.989821	+	0.142315i	0.329940	+	0.0474383i
$10$	−1.46569	−	1.68871i	−0.463493	−	0.534017i
$11$	0.00232980	−	0.00793457i	0.000702461	−	0.00239236i	−0.959141	−	0.282929i	$-0.908694\pi$
$11$	0.00232980	−	0.00793457i	0.000702461	−	0.00239236i	0.959843	+	0.280536i	$0.0905123\pi$
$12$	−0.479249	−	0.877679i	−0.138347	−	0.253364i
$13$	5.34764	+	1.99457i	1.48317	+	0.553193i	0.955171	−	0.296054i	$-0.0956708\pi$
$13$	5.34764	+	1.99457i	1.48317	+	0.553193i	0.527996	+	0.849247i	$0.322943\pi$
$14$	0.182833	−	1.27163i	0.0488642	−	0.339858i
$15$	2.03476	+	0.927233i	0.525372	+	0.239411i
$16$	−0.415415	+	0.909632i	−0.103854	+	0.227408i
$17$	1.76969	−	0.384973i	0.429214	−	0.0933697i	0.00723156	−	0.999974i	$-0.497698\pi$
$17$	1.76969	−	0.384973i	0.429214	−	0.0933697i	0.421982	+	0.906604i	$0.361334\pi$
$18$	0.800541	+	0.599278i	0.188689	+	0.141251i
$19$	5.16179	−	3.31728i	1.18420	−	0.761037i	0.208043	−	0.978120i	$-0.433291\pi$
$19$	5.16179	−	3.31728i	1.18420	−	0.761037i	0.976153	+	0.217083i	$0.0696543\pi$
$20$	−0.477097	−	2.18458i	−0.106682	−	0.488486i
$21$	0.361945	+	1.23267i	0.0789828	+	0.268991i
$22$	0.00584745	−	0.00584745i	0.00124668	−	0.00124668i
$23$	1.70179	−	4.48374i	0.354849	−	0.934924i
$23$	1.70179	−	4.48374i	0.354849	−	0.934924i
$24$		−	1.00000i		−	0.204124i
$25$	3.78410	+	3.26812i	0.756819	+	0.653624i
$26$	3.73761	+	4.31344i	0.733007	+	0.845935i
$27$	−0.977147	−	0.212565i	−0.188052	−	0.0409082i
$28$	0.769898	−	1.02846i	0.145497	−	0.194361i
$29$	3.74079	−	5.82078i	0.694647	−	1.08089i	−0.297366	−	0.954763i	$-0.596108\pi$
$29$	3.74079	−	5.82078i	0.694647	−	1.08089i	0.992014	−	0.126129i	$-0.0402553\pi$
$30$	1.34149	+	1.78897i	0.244921	+	0.326619i
$31$	1.20413	−	1.38964i	0.216269	−	0.249587i	−0.637241	−	0.770665i	$-0.719924\pi$
$31$	1.20413	−	1.38964i	0.216269	−	0.249587i	0.853509	+	0.521077i	$0.174470\pi$
$32$	−0.800541	+	0.599278i	−0.141517	+	0.105938i
$33$	−0.00288991	+	0.00774814i	−0.000503068	+	0.00134878i
$34$	1.73772	+	0.510241i	0.298017	+	0.0875056i
$35$	0.00234851	+	2.87270i	0.000396971	+	0.485574i
$36$	0.415415	+	0.909632i	0.0692358	+	0.151605i
$37$	−1.50039	−	2.00428i	−0.246662	−	0.329502i	0.660074	−	0.751201i	$-0.270525\pi$
$37$	−1.50039	−	2.00428i	−0.246662	−	0.329502i	−0.906736	+	0.421699i	$0.861434\pi$
$38$	6.12020	−	0.437725i	0.992827	−	0.0710084i
$39$	−5.19172	−	2.37098i	−0.831341	−	0.379661i
$40$	0.628219	−	2.14601i	0.0993301	−	0.339313i
$41$	0.636167	+	4.42464i	0.0993525	+	0.691012i	0.977239	+	0.212143i	$0.0680441\pi$
$41$	0.636167	+	4.42464i	0.0993525	+	0.691012i	−0.877886	+	0.478869i	$0.841047\pi$
$42$	−0.273085	+	1.25535i	−0.0421379	+	0.193705i
$43$	−0.451519	+	6.31307i	−0.0688561	+	0.962734i	0.839183	+	0.543849i	$0.183033\pi$
$43$	−0.451519	+	6.31307i	−0.0688561	+	0.962734i	−0.908039	+	0.418885i	$0.862421\pi$
$44$	0.00793457	−	0.00232980i	0.00119618	−	0.000351230i
$45$	−1.96343	−	1.07003i	−0.292690	−	0.159510i
$46$	3.64246	−	3.11970i	0.537051	−	0.459974i
$47$	0.432950	+	0.432950i	0.0631522	+	0.0631522i	0.737978	−	0.674825i	$-0.235781\pi$
$47$	0.432950	+	0.432950i	0.0631522	+	0.0631522i	−0.674825	+	0.737978i	$0.735781\pi$
$48$	0.479249	−	0.877679i	0.0691736	−	0.126682i
$49$	4.04290	−	3.50319i	0.577557	−	0.500456i
$50$	1.75498	+	4.68189i	0.248191	+	0.662119i
$51$	−1.79265	+	0.257744i	−0.251021	+	0.0360914i
$52$	1.21322	+	5.57706i	0.168243	+	0.773399i
$53$	−11.7829	+	4.39479i	−1.61851	+	0.603671i	−0.985379	−	0.170377i	$-0.945502\pi$
$53$	−11.7829	+	4.39479i	−1.61851	+	0.603671i	−0.633127	+	0.774048i	$0.718229\pi$
$54$	−0.755750	−	0.654861i	−0.102844	−	0.0891153i
$55$	−0.0110693	+	0.0148121i	−0.00149258	+	0.00199726i
$56$	1.16861	−	0.533688i	0.156162	−	0.0713170i
$57$	−5.38529	+	2.94059i	−0.713299	+	0.389491i
$58$	6.07282	−	3.31601i	0.797400	−	0.435413i
$59$	−3.99100	+	1.82263i	−0.519584	+	0.237286i	−0.657905	−	0.753101i	$-0.728557\pi$
$59$	−3.99100	+	1.82263i	−0.519584	+	0.237286i	0.138320	+	0.990388i	$0.455830\pi$
$60$	0.320035	+	2.21305i	0.0413163	+	0.285703i
$61$	1.16714	+	1.01133i	0.149437	+	0.129488i	0.726371	−	0.687303i	$-0.241205\pi$
$61$	1.16714	+	1.01133i	0.149437	+	0.129488i	−0.576934	+	0.816791i	$0.695751\pi$
$62$	1.72283	−	0.642582i	0.218799	−	0.0816080i
$63$	−0.273085	−	1.25535i	−0.0344054	−	0.158159i
$64$	−0.989821	+	0.142315i	−0.123728	+	0.0177894i
$65$	−9.65197	−	8.34967i	−1.19718	−	1.03565i
$66$	−0.00624970	+	0.00541540i	−0.000769285	+	0.000666589i
$67$	2.37799	−	4.35496i	0.290518	−	0.532043i	−0.691134	−	0.722727i	$-0.742889\pi$
$67$	2.37799	−	4.35496i	0.290518	−	0.532043i	0.981652	+	0.190683i	$0.0610703\pi$
$68$	1.28063	+	1.28063i	0.155299	+	0.155299i
$69$	−2.01732	+	4.35091i	−0.242857	+	0.523788i
$70$	−1.37468	+	2.52243i	−0.164305	+	0.301488i
$71$	13.8586	−	4.06927i	1.64472	−	0.482933i	0.677214	−	0.735786i	$-0.263187\pi$
$71$	13.8586	−	4.06927i	1.64472	−	0.482933i	0.967505	+	0.252853i	$0.0813689\pi$
$72$	−0.0713392	+	0.997452i	−0.00840740	+	0.117551i
$73$	−2.82922	+	13.0057i	−0.331135	+	1.52220i	0.447245	+	0.894412i	$0.352405\pi$
$73$	−2.82922	+	13.0057i	−0.331135	+	1.52220i	−0.778380	+	0.627793i	$0.783958\pi$
$74$	−0.356308	−	2.47817i	−0.0414199	−	0.288082i
$75$	−3.54131	−	3.52975i	−0.408915	−	0.407580i
$76$	5.58135	+	2.54892i	0.640225	+	0.292381i
$77$	−0.0105969		0.000757905i	−0.00120763		8.63712e-5i
$78$	−3.42037	−	4.56909i	−0.387281	−	0.517347i
$79$	−5.54935	−	12.1514i	−0.624351	−	1.36714i	−0.912312	−	0.409495i	$-0.865705\pi$
$79$	−5.54935	−	12.1514i	−0.624351	−	1.36714i	0.287962	−	0.957642i	$-0.407022\pi$
$80$	1.57985	−	1.58243i	0.176632	−	0.176921i
$81$	0.959493	+	0.281733i	0.106610	+	0.0313036i
$82$	−1.56215	+	4.18829i	−0.172511	+	0.462519i
$83$	−2.53753	+	1.89957i	−0.278530	+	0.208505i	−0.729405	−	0.684082i	$-0.760203\pi$
$83$	−2.53753	+	1.89957i	−0.278530	+	0.208505i	0.450875	+	0.892587i	$0.351112\pi$
$84$	−0.841306	+	0.970919i	−0.0917940	+	0.105936i
$85$	−4.00895	−	0.573056i	−0.434832	−	0.0621566i
$86$	−3.42182	+	5.32446i	−0.368984	+	0.574151i
$87$	−4.14651	+	5.53909i	−0.444552	+	0.593853i
$88$	0.00808056	+	0.00175782i	0.000861390	+	0.000187384i
$89$	−1.24013	−	1.43119i	−0.131454	−	0.151706i	0.686206	−	0.727407i	$-0.259275\pi$
$89$	−1.24013	−	1.43119i	−0.131454	−	0.151706i	−0.817660	+	0.575701i	$0.804729\pi$
$90$	−1.21045	−	1.88011i	−0.127592	−	0.198181i
$91$		−	7.33247i		−	0.768652i
$92$	4.69202	−	0.992450i	0.489177	−	0.103470i
$93$	−1.30020	+	1.30020i	−0.134825	+	0.134825i
$94$	0.172500	+	0.587482i	0.0177920	+	0.0605941i
$95$	−13.4042	+	2.92738i	−1.37524	+	0.300343i
$96$	0.841254	−	0.540641i	0.0858601	−	0.0551789i
$97$	−4.18289	−	3.13127i	−0.424708	−	0.317933i	0.365455	−	0.930829i	$-0.380913\pi$
$97$	−4.18289	−	3.13127i	−0.424708	−	0.317933i	−0.790163	+	0.612896i	$0.790004\pi$
$98$	5.22727	−	1.13712i	0.528034	−	0.114867i
$99$	0.00343529	−	0.00752224i	0.000345260	−	0.000756014i
$100$	−0.703481	+	4.95026i	−0.0703481	+	0.495026i
$101$	−0.383773	+	2.66920i	−0.0381869	+	0.265596i	−0.999966	−	0.00823041i	$-0.997380\pi$
$101$	−0.383773	+	2.66920i	−0.0381869	+	0.265596i	0.961779	+	0.273826i	$0.0882892\pi$
$102$	−1.69689	−	0.632909i	−0.168017	−	0.0626673i
$103$	3.48788	+	6.38757i	0.343671	+	0.629386i	0.991158	−	0.132691i	$-0.0423616\pi$
$103$	3.48788	+	6.38757i	0.343671	+	0.629386i	−0.647487	+	0.762077i	$0.724180\pi$
$104$	−1.60799	+	5.47630i	−0.157676	+	0.536996i
$105$	0.202593	−	2.86555i	0.0197711	−	0.279649i
$106$	−12.4478	−	1.78972i	−1.20904	−	0.173833i
$107$	−0.964952	−	13.4918i	−0.0932854	−	1.30430i	−0.801368	−	0.598171i	$-0.795894\pi$
$107$	−0.964952	−	13.4918i	−0.0932854	−	1.30430i	0.708083	−	0.706129i	$-0.249560\pi$
$108$	−0.349464	−	0.936950i	−0.0336272	−	0.0901580i
$109$	14.0939	+	9.05757i	1.34995	+	0.867558i	0.997662	−	0.0683348i	$-0.0217686\pi$
$109$	14.0939	+	9.05757i	1.34995	+	0.867558i	0.352284	+	0.935893i	$0.385405\pi$
$110$	−0.0168140	+	0.00769529i	−0.00160315	+	0.000733717i
$111$	1.35358	+	2.10621i	0.128476	+	0.199913i
$112$	1.28144	+	0.0916501i	0.121084	+	0.00866012i
$113$	−12.2649	−	6.69716i	−1.15379	−	0.630016i	−0.215716	−	0.976456i	$-0.569209\pi$
$113$	−12.2649	−	6.69716i	−1.15379	−	0.630016i	−0.938072	+	0.346440i	$0.887390\pi$
$114$	−6.13583			−0.574673
$115$	−7.06251	+	8.06975i	−0.658583	+	0.752508i
$116$	6.91918			0.642430
$117$	5.00935	+	2.73531i	0.463115	+	0.252880i
$118$	−4.37631	−	0.313000i	−0.402872	−	0.0288140i
$119$	−1.25792	−	1.95736i	−0.115313	−	0.179431i
$120$	−0.779713	+	2.09572i	−0.0711777	+	0.191312i
$121$	9.25373	+	5.94701i	0.841248	+	0.540637i
$122$	0.539695	+	1.44698i	0.0488617	+	0.131003i
$123$	−0.318896	−	4.45875i	−0.0287539	−	0.402032i
$124$	1.82005	+	0.261683i	0.163445	+	0.0234998i
$125$	−5.38222	−	9.79958i	−0.481400	−	0.876501i
$126$	0.361945	−	1.23267i	0.0322446	−	0.109815i
$127$	−2.43067	−	4.45144i	−0.215687	−	0.395001i	0.747326	−	0.664458i	$-0.231338\pi$
$127$	−2.43067	−	4.45144i	−0.215687	−	0.395001i	−0.963012	+	0.269457i	$0.913156\pi$
$128$	−0.936950	−	0.349464i	−0.0828154	−	0.0308886i
$129$	0.900738	−	6.26477i	0.0793056	−	0.551582i
$130$	−4.46976	−	11.9540i	−0.392024	−	1.04844i
$131$	−4.78860	+	10.4856i	−0.418382	+	0.916129i	0.576689	+	0.816964i	$0.304345\pi$
$131$	−4.78860	+	10.4856i	−0.418382	+	0.916129i	−0.995071	+	0.0991653i	$0.968383\pi$
$132$	−0.00808056	+	0.00175782i	−0.000703322	+	0.000152998i
$133$	−6.31048	−	4.72396i	−0.547188	−	0.409620i
$134$	4.17422	−	2.68261i	0.360598	−	0.231742i
$135$	1.88209	+	1.20737i	0.161984	+	0.103914i
$136$	0.510241	+	1.73772i	0.0437528	+	0.149008i
$137$	10.5041	−	10.5041i	0.897429	−	0.897429i	−0.0977792	−	0.995208i	$-0.531174\pi$
$137$	10.5041	−	10.5041i	0.897429	−	0.897429i	0.995208	+	0.0977792i	$0.0311739\pi$
$138$	−3.85573	+	2.85190i	−0.328222	+	0.242770i
$139$		−	12.9902i		−	1.10182i	−0.834566	−	0.550909i	$-0.814281\pi$
$139$		−	12.9902i		−	1.10182i	0.834566	−	0.550909i	$-0.185719\pi$
$140$	−2.41540	+	1.55507i	−0.204138	+	0.131428i
$141$	−0.400960	−	0.462733i	−0.0337670	−	0.0389691i
$142$	14.1136	+	3.07023i	1.18439	+	0.257648i
$143$	0.0282849	−	0.0377842i	0.00236530	−	0.00315968i
$144$	−0.540641	+	0.841254i	−0.0450534	+	0.0701045i
$145$	−12.3782	+	9.28200i	−1.02795	+	0.770828i
$146$	−8.71613	+	10.0589i	−0.721352	+	0.832485i
$147$	−4.28251	+	3.20585i	−0.353216	+	0.264414i
$148$	0.874939	−	2.34580i	0.0719195	−	0.192824i
$149$	3.10831	+	0.912683i	0.254643	+	0.0747699i	0.406563	−	0.913623i	$-0.366727\pi$
$149$	3.10831	+	0.912683i	0.254643	+	0.0747699i	−0.151920	+	0.988393i	$0.548545\pi$
$150$	−1.41651	−	4.79516i	−0.115657	−	0.391523i
$151$	−1.81157	−	3.96678i	−0.147423	−	0.322812i	0.821486	−	0.570229i	$-0.193146\pi$
$151$	−1.81157	−	3.96678i	−0.147423	−	0.322812i	−0.968909	+	0.247417i	$0.920418\pi$
$152$	3.67707	+	4.91199i	0.298250	+	0.398415i
$153$	1.80647	−	0.129201i	0.146044	−	0.0104453i
$154$	−0.00966389	−	0.00441335i	−0.000778739	−	0.000355638i
$155$	−3.60705	+	1.97343i	−0.289725	+	0.158510i
$156$	−0.812261	−	5.64940i	−0.0650330	−	0.452314i
$157$	−4.62335	+	21.2532i	−0.368984	+	1.69619i	0.300843	+	0.953674i	$0.402732\pi$
$157$	−4.62335	+	21.2532i	−0.368984	+	1.69619i	−0.669827	+	0.742517i	$0.733632\pi$
$158$	0.952989	−	13.3245i	0.0758158	−	1.06004i
$159$	12.0664	−	3.54301i	0.956928	−	0.280979i
$160$	2.14498	−	0.631727i	0.169575	−	0.0499424i
$161$	−6.16115	−	0.0354462i	−0.485567	−	0.00279356i
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	−1.60656	+	2.94220i	−0.125836	+	0.230451i	−0.933000	−	0.359876i	$-0.882819\pi$
$163$	−1.60656	+	2.94220i	−0.125836	+	0.230451i	0.807165	+	0.590326i	$0.201001\pi$
$164$	−3.37830	+	2.92732i	−0.263801	+	0.228585i
$165$	0.0120978	−	0.0139847i	0.000941810	−	0.00108870i
$166$	−3.13750	+	0.451105i	−0.243517	+	0.0350125i
$167$	0.575368	+	2.64492i	0.0445233	+	0.204670i	0.994035	−	0.109061i	$-0.0347845\pi$
$167$	0.575368	+	2.64492i	0.0445233	+	0.204670i	−0.949512	+	0.313731i	$0.898421\pi$
$168$	−1.20371	+	0.448960i	−0.0928681	+	0.0346380i
$169$	14.7942	+	12.8192i	1.13801	+	0.986095i
$170$	−3.24394	−	2.42425i	−0.248799	−	0.185931i
$171$	5.58135	−	2.54892i	0.426816	−	0.194921i
$172$	−5.55500	+	3.03326i	−0.423565	+	0.231284i
$173$	−12.3561	+	6.74697i	−0.939421	+	0.512962i	−0.874552	−	0.484931i	$-0.838845\pi$
$173$	−12.3561	+	6.74697i	−0.939421	+	0.512962i	−0.0648683	+	0.997894i	$0.520663\pi$
$174$	−6.29391	+	2.87433i	−0.477140	+	0.217902i
$175$	2.23496	−	6.02220i	0.168947	−	0.455236i
$176$	0.00624970	+	0.00541540i	0.000471089	+	0.000408201i
$177$	4.11086	−	1.53327i	0.308991	−	0.115248i
$178$	−0.402543	−	1.85046i	−0.0301719	−	0.138698i
$179$	−25.0923	+	3.60772i	−1.87548	+	0.269654i	−0.983297	−	0.182010i	$-0.941740\pi$
$179$	−25.0923	+	3.60772i	−1.87548	+	0.269654i	−0.892188	+	0.451664i	$0.850830\pi$
$180$	−0.161343	−	2.23024i	−0.0120258	−	0.166232i
$181$	4.62077	−	4.00392i	0.343459	−	0.297609i	−0.466001	−	0.884784i	$-0.654306\pi$
$181$	4.62077	−	4.00392i	0.343459	−	0.297609i	0.809460	+	0.587175i	$0.199760\pi$
$182$	3.51408	−	6.43556i	0.260481	−	0.477035i
$183$	−1.09202	−	1.09202i	−0.0807245	−	0.0807245i
$184$	4.59372	+	1.37759i	0.338653	+	0.101557i
$185$	1.58163	+	5.37029i	0.116284	+	0.394831i
$186$	−1.76428	+	0.518039i	−0.129363	+	0.0379845i
$187$	0.00106843	−	0.0149387i	7.81317e−5	−	0.00109242i
$188$	−0.130150	+	0.598291i	−0.00949218	+	0.0436348i
$189$	0.182833	+	1.27163i	0.0132992	+	0.0924977i
$190$	−13.1675	−	3.85465i	−0.955273	−	0.279645i
$191$	1.87604	+	0.856759i	0.135746	+	0.0619929i	0.482130	−	0.876100i	$-0.339863\pi$
$191$	1.87604	+	0.856759i	0.135746	+	0.0619929i	−0.346384	+	0.938093i	$0.612591\pi$
$192$	0.997452	−	0.0713392i	0.0719849	−	0.00514846i
$193$	3.83572	+	5.12392i	0.276101	+	0.368828i	0.917061	−	0.398746i	$-0.130555\pi$
$193$	3.83572	+	5.12392i	0.276101	+	0.368828i	−0.640960	+	0.767574i	$0.721464\pi$
$194$	−2.17058	−	4.75290i	−0.155838	−	0.341238i
$195$	9.03172	+	9.01696i	0.646775	+	0.645718i
$196$	5.13283	+	1.50713i	0.366631	+	0.107652i
$197$	−5.08046	+	13.6212i	−0.361968	+	0.970473i	0.620528	+	0.784185i	$0.286918\pi$
$197$	−5.08046	+	13.6212i	−0.361968	+	0.970473i	−0.982495	+	0.186288i	$0.940354\pi$
$198$	0.00662011	−	0.00495575i	0.000470471	−	0.000352190i
$199$	7.68702	−	8.87130i	0.544919	−	0.628870i	−0.414773	−	0.909925i	$-0.636139\pi$
$199$	7.68702	−	8.87130i	0.544919	−	0.628870i	0.959692	+	0.281055i	$0.0906845\pi$
$200$	−2.98984	+	4.00760i	−0.211414	+	0.283380i
$201$	−2.68261	+	4.17422i	−0.189217	+	0.294427i
$202$	−1.61604	+	2.15878i	−0.113704	+	0.151891i
$203$	−8.68599	−	1.88952i	−0.609637	−	0.132618i
$204$	−1.18601	−	1.36872i	−0.0830371	−	0.0958299i
$205$	2.11672	−	9.76883i	0.147838	−	0.682285i
$206$			7.27780i			0.507068i
$207$	2.32258	−	4.19591i	0.161430	−	0.291636i
$208$	−4.03581	+	4.03581i	−0.279833	+	0.279833i
$209$	−0.0142953	−	0.0486852i	−0.000988824	−	0.00336762i
$210$	1.55112	−	2.41794i	0.107038	−	0.166853i
$211$	14.3018	−	9.19122i	0.984577	−	0.632749i	0.0538829	−	0.998547i	$-0.482840\pi$
$211$	14.3018	−	9.19122i	0.984577	−	0.632749i	0.930694	+	0.365798i	$0.119204\pi$
$212$	−10.0675	−	7.53640i	−0.691436	−	0.517602i
$213$	−14.1136	+	3.07023i	−0.967050	+	0.210369i
$214$	5.61901	−	12.3039i	0.384108	−	0.841078i
$215$	5.86864	−	12.8784i	0.400238	−	0.878298i
$216$	0.142315	−	0.989821i	0.00968330	−	0.0673488i
$217$	−2.21333	−	0.825531i	−0.150251	−	0.0560407i
$218$	8.02905	+	14.7041i	0.543796	+	0.995888i
$219$	3.74983	−	12.7708i	0.253390	−	0.862967i
$220$	−0.0184452	−	0.00130407i	−0.00124358	−	8.79205e-5i
$221$	10.2315	+	1.47107i	0.688247	+	0.0989550i
$222$	0.178609	+	2.49728i	0.0119874	+	0.167606i
$223$	−4.56170	−	12.2304i	−0.305474	−	0.819008i	−0.995460	−	0.0951847i	$-0.969656\pi$
$223$	−4.56170	−	12.2304i	−0.305474	−	0.819008i	0.689985	−	0.723823i	$-0.257617\pi$
$224$	1.08077	+	0.694566i	0.0722117	+	0.0464077i
$225$	3.28048	+	3.77339i	0.218699	+	0.251559i
$226$	−7.55507	−	11.7559i	−0.502556	−	0.781992i
$227$	−20.7884	−	1.48682i	−1.37978	−	0.0986836i	−0.638365	−	0.769734i	$-0.720389\pi$
$227$	−20.7884	−	1.48682i	−1.37978	−	0.0986836i	−0.741412	+	0.671050i	$0.765843\pi$
$228$	−5.38529	−	2.94059i	−0.356650	−	0.194745i
$229$	1.01627			0.0671572			0.0335786	−	0.999436i	$-0.489310\pi$
$229$	1.01627			0.0671572			0.0335786	+	0.999436i	$0.489310\pi$
$230$	−10.0660	+	3.69795i	−0.663735	+	0.243836i
$231$	0.0106240			0.000699005
$232$	6.07282	+	3.31601i	0.398700	+	0.217707i
$233$	12.2432	+	0.875649i	0.802077	+	0.0573657i	0.466358	−	0.884596i	$-0.345566\pi$
$233$	12.2432	+	0.875649i	0.802077	+	0.0573657i	0.335720	+	0.941962i	$0.391021\pi$
$234$	3.08571	+	4.80145i	0.201719	+	0.313881i
$235$	−0.569766	−	1.24492i	−0.0371674	−	0.0812095i
$236$	−3.69099	−	2.37206i	−0.240263	−	0.154408i
$237$	4.66834	+	12.5163i	0.303241	+	0.813021i
$238$	−0.165986	−	2.32079i	−0.0107593	−	0.150434i
$239$	−4.73601	−	0.680936i	−0.306347	−	0.0440461i	−0.0125730	−	0.999921i	$-0.504002\pi$
$239$	−4.73601	−	0.680936i	−0.306347	−	0.0440461i	−0.293774	+	0.955875i	$0.594911\pi$
$240$	−1.68871	+	1.46569i	−0.109006	+	0.0946102i
$241$	−1.68769	+	5.74774i	−0.108714	+	0.370245i	−0.995822	−	0.0913167i	$-0.970892\pi$
$241$	−1.68769	+	5.74774i	−0.108714	+	0.370245i	0.887108	+	0.461561i	$0.152711\pi$
$242$	5.27171	+	9.65441i	0.338878	+	0.620609i
$243$	−0.936950	−	0.349464i	−0.0601054	−	0.0224181i
$244$	−0.219784	+	1.52863i	−0.0140702	+	0.0978606i
$245$	−11.2043	+	4.18941i	−0.715815	+	0.267652i
$246$	1.85696	−	4.06618i	0.118396	−	0.259250i
$247$	34.2199	−	7.44409i	2.17736	−	0.473656i
$248$	1.47201	+	1.10193i	0.0934724	+	0.0699726i
$249$	2.66658	−	1.71370i	0.168987	−	0.108602i
$250$	−0.0274207	−	11.1803i	−0.00173424	−	0.707105i
$251$	7.41141	+	25.2409i	0.467804	+	1.59319i	0.768748	+	0.639552i	$0.220880\pi$
$251$	7.41141	+	25.2409i	0.467804	+	1.59319i	−0.300944	+	0.953642i	$0.597302\pi$
$252$	0.908427	−	0.908427i	0.0572255	−	0.0572255i
$253$	−0.0316117	−	0.0239492i	−0.00198741	−	0.00150567i
$254$		−	5.07183i		−	0.318235i
$255$	3.95786	+	0.857591i	0.247851	+	0.0537044i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	27.7447	+	6.03549i	1.73067	+	0.376483i	0.964070	−	0.265647i	$-0.0855854\pi$
$257$	27.7447	+	6.03549i	1.73067	+	0.376483i	0.766596	+	0.642130i	$0.221949\pi$
$258$	3.79294	−	5.06678i	0.236138	−	0.315444i
$259$	−1.73896	+	2.70587i	−0.108054	+	0.168135i
$260$	1.80594	−	12.6339i	0.112000	−	0.783523i
$261$	4.53110	−	5.22917i	0.280468	−	0.323677i
$262$	−9.22806	+	6.90804i	−0.570111	+	0.426780i
$263$	6.02473	−	16.1529i	0.371501	−	0.996032i	−0.607884	−	0.794026i	$-0.707981\pi$
$263$	6.02473	−	16.1529i	0.371501	−	0.996032i	0.979384	−	0.202006i	$-0.0647460\pi$
$264$	−0.00793457	−	0.00232980i	−0.000488339	−	0.000143389i
$265$	28.1204	−	0.0229892i	1.72742	−	0.00141221i
$266$	−3.27462	−	7.17041i	−0.200780	−	0.439646i
$267$	1.13487	+	1.51601i	0.0694532	+	0.0927786i
$268$	4.94927	−	0.353979i	0.302325	−	0.0216227i
$269$	0.719166	+	0.328432i	0.0438483	+	0.0200248i	0.437218	−	0.899355i	$-0.355964\pi$
$269$	0.719166	+	0.328432i	0.0438483	+	0.0200248i	−0.393370	+	0.919380i	$0.628691\pi$
$270$	1.07324	+	1.96167i	0.0653151	+	0.119384i
$271$	−2.35649	−	16.3898i	−0.143147	−	0.995608i	−0.927107	−	0.374797i	$-0.877713\pi$
$271$	−2.35649	−	16.3898i	−0.143147	−	0.995608i	0.783960	−	0.620811i	$-0.213197\pi$
$272$	−0.384973	+	1.76969i	−0.0233424	+	0.107303i
$273$	−0.523093	+	7.31379i	−0.0316590	+	0.442651i
$274$	14.2534	−	4.18516i	0.861077	−	0.252835i
$275$	0.0347473	−	0.0224111i	0.00209534	−	0.00135144i
$276$	−4.75086	+	0.655197i	−0.285968	+	0.0394382i
$277$	−8.04938	−	8.04938i	−0.483641	−	0.483641i	0.422652	−	0.906292i	$-0.361099\pi$
$277$	−8.04938	−	8.04938i	−0.483641	−	0.483641i	−0.906292	+	0.422652i	$0.861099\pi$
$278$	6.22556	−	11.4013i	0.373384	−	0.683802i
$279$	1.38964	−	1.20413i	0.0831958	−	0.0720896i
$280$	−2.86521	+	0.207278i	−0.171229	+	0.0123873i
$281$	−25.4979	+	3.66604i	−1.52108	+	0.218698i	−0.851622	−	0.524156i	$-0.824381\pi$
$281$	−25.4979	+	3.66604i	−1.52108	+	0.218698i	−0.669454	+	0.742854i	$0.733472\pi$
$282$	−0.130150	−	0.598291i	−0.00775033	−	0.0356277i
$283$	−4.67868	+	1.74506i	−0.278119	+	0.103733i	−0.484653	−	0.874706i	$-0.661054\pi$
$283$	−4.67868	+	1.74506i	−0.278119	+	0.103733i	0.206534	+	0.978439i	$0.433781\pi$
$284$	10.9158	+	9.45863i	0.647736	+	0.561266i
$285$	13.5789	−	1.96368i	0.804344	−	0.116318i
$286$	0.0429332	−	0.0196069i	0.00253869	−	0.00115938i
$287$	5.04036	−	2.75224i	0.297523	−	0.162460i
$288$	−0.877679	+	0.479249i	−0.0517177	+	0.0282400i
$289$	−12.4801	+	5.69949i	−0.734125	+	0.335264i
$290$	−15.3125	+	2.21438i	−0.899179	+	0.130033i
$291$	3.94885	+	3.42170i	0.231486	+	0.200584i
$292$	−12.4707	+	4.65133i	−0.729793	+	0.272199i
$293$	3.58820	+	16.4947i	0.209625	+	0.963631i	0.954912	+	0.296887i	$0.0959486\pi$
$293$	3.58820	+	16.4947i	0.209625	+	0.963631i	−0.745287	+	0.666743i	$0.767688\pi$
$294$	−5.29507	+	0.761316i	−0.308815	+	0.0444009i
$295$	9.78516	−	0.707889i	0.569714	−	0.0412149i
$296$	1.89214	−	1.63955i	0.109978	−	0.0952967i
$297$	−0.00396317	+	0.00725800i	−0.000229966	+	0.000421152i
$298$	2.29070	+	2.29070i	0.132697	+	0.132697i
$299$	18.0437	−	20.5831i	1.04349	−	1.19035i
$300$	1.05484	−	4.88747i	0.0609010	−	0.282178i
$301$	7.80180	−	2.29082i	0.449689	−	0.132040i
$302$	0.311101	−	4.34976i	0.0179018	−	0.250300i
$303$	0.573214	−	2.63502i	0.0329303	−	0.151378i
$304$	0.873220	+	6.07338i	0.0500826	+	0.348332i
$305$	−1.65745	−	3.02951i	−0.0949056	−	0.173469i
$306$	1.64742	+	0.752351i	0.0941767	+	0.0430090i
$307$	−27.8580	+	1.99244i	−1.58994	+	0.113715i	−0.838056	−	0.545584i	$-0.816308\pi$
$307$	−27.8580	+	1.99244i	−1.58994	+	0.113715i	−0.751881	+	0.659299i	$0.770853\pi$
$308$	−0.00636670	−	0.00850492i	−0.000362776	−	0.000484613i
$309$	−3.02331	−	6.62012i	−0.171990	−	0.376606i
$310$	−4.11160	+	0.00336135i	−0.233523	+	0.000190912i
$311$	8.74213	+	2.56692i	0.495721	+	0.145557i	0.520030	−	0.854148i	$-0.325921\pi$
$311$	8.74213	+	2.56692i	0.495721	+	0.145557i	−0.0243096	+	0.999704i	$0.507739\pi$
$312$	1.99457	−	5.34764i	0.112920	−	0.302750i
$313$	−8.58334	+	6.42540i	−0.485159	+	0.363185i	−0.813682	−	0.581311i	$-0.802540\pi$
$313$	−8.58334	+	6.42540i	−0.485159	+	0.363185i	0.328523	+	0.944496i	$0.393449\pi$
$314$	−14.2434	+	16.4378i	−0.803801	+	0.927636i
$315$	−0.406503	+	2.84379i	−0.0229038	+	0.160229i
$316$	7.22219	−	11.2379i	0.406280	−	0.632184i
$317$	−7.89057	+	10.5406i	−0.443179	+	0.592017i	−0.965394	−	0.260796i	$-0.916015\pi$
$317$	−7.89057	+	10.5406i	−0.443179	+	0.592017i	0.522215	+	0.852814i	$0.325106\pi$
$318$	12.2884	+	2.67318i	0.689100	+	0.149905i
$319$	−0.0374701	−	0.0432428i	−0.00209792	−	0.00242113i
$320$	2.18535	+	0.473524i	0.122165	+	0.0264708i
$321$			13.5263i			0.754962i
$322$	−5.39052	−	2.98383i	−0.300402	−	0.166283i
$323$	7.85772	−	7.85772i	0.437215	−	0.437215i
$324$	0.281733	+	0.959493i	0.0156518	+	0.0533052i
$325$	13.7175	+	25.0244i	0.760910	+	1.38810i
$326$	−2.82009	+	1.81236i	−0.156190	+	0.100377i
$327$	−13.4118	−	10.0399i	−0.741674	−	0.555210i
$328$	−4.36798	+	0.950196i	−0.241181	+	0.0524658i
$329$	0.326768	−	0.715522i	0.0180153	−	0.0394480i
$330$	0.0173201	−	0.00647619i	0.000953440	−	0.000356503i
$331$	−4.89025	+	34.0124i	−0.268792	+	1.86949i	0.191175	+	0.981556i	$0.438770\pi$
$331$	−4.89025	+	34.0124i	−0.268792	+	1.86949i	−0.459968	+	0.887936i	$0.652139\pi$
$332$	−2.96991	−	1.10772i	−0.162995	−	0.0607940i
$333$	−1.19988	−	2.19741i	−0.0657528	−	0.120417i
$334$	−0.762588	+	2.59714i	−0.0417270	+	0.142109i
$335$	−8.37922	+	7.27264i	−0.457806	+	0.397347i
$336$	−1.27163	−	0.182833i	−0.0693733	−	0.00997437i
$337$	1.73694	+	24.2856i	0.0946172	+	1.32292i	0.793888	+	0.608064i	$0.208054\pi$
$337$	1.73694	+	24.2856i	0.0946172	+	1.32292i	−0.699271	+	0.714857i	$0.746492\pi$
$338$	6.84094	+	18.3413i	0.372098	+	0.997634i
$339$	11.7559	+	7.55507i	0.638494	+	0.410335i
$340$	−1.68532	−	3.68236i	−0.0913992	−	0.199704i
$341$	−0.00822084	−	0.0127919i	−0.000445183	−	0.000692719i
$342$	6.12020	+	0.437725i	0.330942	+	0.0236695i
$343$	−13.9249	−	7.60355i	−0.751872	−	0.410553i
$344$	−6.32919			−0.341247
$345$	7.62021	−	7.54536i	0.410258	−	0.406228i
$346$	−14.0782			−0.756849
$347$	10.1267	+	5.52961i	0.543631	+	0.296845i	0.727502	−	0.686106i	$-0.240681\pi$
$347$	10.1267	+	5.52961i	0.543631	+	0.296845i	−0.183871	+	0.982950i	$0.558863\pi$
$348$	−6.90155	−	0.493609i	−0.369962	−	0.0264602i
$349$	−0.331551	−	0.515903i	−0.0177475	−	0.0276157i	0.832266	−	0.554376i	$-0.187043\pi$
$349$	−0.331551	−	0.515903i	−0.0177475	−	0.0276157i	−0.850014	+	0.526760i	$0.823407\pi$
$350$	4.84771	−	4.21446i	0.259121	−	0.225272i
$351$	−4.80145	−	3.08571i	−0.256283	−	0.164703i
$352$	0.00288991	+	0.00774814i	0.000154033	+	0.000412977i
$353$	0.515124	+	7.20238i	0.0274173	+	0.383344i	0.992572	+	0.121662i	$0.0388225\pi$
$353$	0.515124	+	7.20238i	0.0274173	+	0.383344i	−0.965154	+	0.261682i	$0.915723\pi$
$354$	4.34283	+	0.624405i	0.230819	+	0.0331868i
$355$	−32.2167	−	2.27771i	−1.70989	−	0.120889i
$356$	0.533527	−	1.81703i	0.0282769	−	0.0963023i
$357$	1.11508	+	2.04211i	0.0590161	+	0.108080i
$358$	−23.7520	−	8.85902i	−1.25533	−	0.468214i
$359$	4.25547	−	29.5974i	0.224595	−	1.56209i	−0.495744	−	0.868469i	$-0.665104\pi$
$359$	4.25547	−	29.5974i	0.224595	−	1.56209i	0.720338	−	0.693623i	$-0.243987\pi$
$360$	0.927233	−	2.03476i	0.0488695	−	0.107241i
$361$	7.74684	−	16.9632i	0.407729	−	0.892801i
$362$	5.97442	−	1.29966i	0.314009	−	0.0683084i
$363$	−8.80590	−	6.59201i	−0.462190	−	0.345991i
$364$	6.16847	−	3.96424i	0.323316	−	0.207782i
$365$	16.0700	−	25.0504i	0.841142	−	1.31120i
$366$	−0.435094	−	1.48179i	−0.0227427	−	0.0774546i
$367$	−17.5440	+	17.5440i	−0.915792	+	0.915792i	−0.996720	−	0.0809284i	$-0.974211\pi$
$367$	−17.5440	+	17.5440i	−0.915792	+	0.915792i	0.0809284	+	0.996720i	$0.474211\pi$
$368$	3.37160	+	3.41062i	0.175757	+	0.177791i
$369$			4.47013i			0.232706i
$370$	−1.18554	+	5.47138i	−0.0616334	+	0.284444i
$371$	10.5801	+	12.2101i	0.549291	+	0.633916i
$372$	−1.79674	−	0.390857i	−0.0931567	−	0.0202650i
$373$	12.6934	−	16.9564i	0.657239	−	0.877969i	−0.340827	−	0.940126i	$-0.610707\pi$
$373$	12.6934	−	16.9564i	0.657239	−	0.877969i	0.998066	+	0.0621569i	$0.0197979\pi$
$374$	0.00809708	−	0.0125993i	0.000418690	−	0.000651495i
$375$	4.66941	+	10.1586i	0.241127	+	0.524586i
$376$	−0.400960	+	0.462733i	−0.0206780	+	0.0238636i
$377$	31.6143	−	23.6662i	1.62822	−	1.21887i
$378$	−0.448960	+	1.20371i	−0.0230920	+	0.0619121i
$379$	11.4920	+	3.37437i	0.590307	+	0.173330i	0.563225	−	0.826304i	$-0.309560\pi$
$379$	11.4920	+	3.37437i	0.590307	+	0.173330i	0.0270816	+	0.999633i	$0.491379\pi$
$380$	−9.70953	−	9.69367i	−0.498088	−	0.497275i
$381$	2.10691	+	4.61350i	0.107940	+	0.236357i
$382$	1.23596	+	1.65105i	0.0632373	+	0.0844751i
$383$	24.2304	−	1.73300i	1.23812	−	0.0885520i	0.563122	−	0.826374i	$-0.309600\pi$
$383$	24.2304	−	1.73300i	1.23812	−	0.0885520i	0.674996	+	0.737822i	$0.264145\pi$
$384$	0.909632	+	0.415415i	0.0464195	+	0.0211991i
$385$	0.0227991	+	0.00667417i	0.00116195	+	0.000340147i
$386$	0.910897	+	6.33542i	0.0463634	+	0.322465i
$387$	−1.34537	+	6.18455i	−0.0683888	+	0.314378i
$388$	0.372753	−	5.21177i	0.0189237	−	0.264587i
$389$	−1.54275	+	0.452993i	−0.0782206	+	0.0229676i	−0.320609	−	0.947212i	$-0.603887\pi$
$389$	−1.54275	+	0.452993i	−0.0782206	+	0.0229676i	0.242388	+	0.970179i	$0.422069\pi$
$390$	3.60558	+	12.2424i	0.182576	+	0.619920i
$391$	1.28554	−	8.58999i	0.0650124	−	0.434414i
$392$	3.78268	+	3.78268i	0.191054	+	0.191054i
$393$	5.52444	−	10.1172i	0.278671	−	0.510348i
$394$	−10.9870	+	9.52027i	−0.553516	+	0.479624i
$395$	2.15531	+	29.7928i	0.108445	+	1.49904i
$396$	0.00818537	−	0.00117688i	0.000411330	−	5.91404e-5i
$397$	5.84838	+	26.8846i	0.293522	+	1.34930i	0.853631	+	0.520879i	$0.174396\pi$
$397$	5.84838	+	26.8846i	0.293522	+	1.34930i	−0.560109	+	0.828419i	$0.689241\pi$
$398$	10.9983	−	4.10215i	0.551295	−	0.205622i
$399$	5.95739	+	5.16211i	0.298243	+	0.258429i
$400$	−4.54476	+	2.08451i	−0.227238	+	0.104225i
$401$	12.8502	−	5.86850i	0.641709	−	0.293059i	−0.0678596	−	0.997695i	$-0.521617\pi$
$401$	12.8502	−	5.86850i	0.641709	−	0.293059i	0.709569	+	0.704636i	$0.248890\pi$
$402$	−4.35496	+	2.37799i	−0.217206	+	0.118603i
$403$	9.21100	−	5.02959i	0.458833	−	0.250542i
$404$	−2.45296	+	1.12023i	−0.122039	+	0.0557335i
$405$	−1.79116	−	1.33856i	−0.0890034	−	0.0665137i
$406$	−6.71796	−	5.82115i	−0.333407	−	0.288899i
$407$	−0.0193987	+	0.00723534i	−0.000961558	+	0.000358643i
$408$	−0.384973	−	1.76969i	−0.0190590	−	0.0876129i
$409$	−19.6906	+	2.83108i	−0.973636	+	0.139988i	−0.610731	−	0.791838i	$-0.709124\pi$
$409$	−19.6906	+	2.83108i	−0.973636	+	0.139988i	−0.362905	+	0.931826i	$0.618215\pi$
$410$	6.53950	−	7.55946i	0.322963	−	0.373335i
$411$	−11.2267	+	9.72802i	−0.553774	+	0.479848i
$412$	−3.48788	+	6.38757i	−0.171835	+	0.314693i
$413$	3.98572	+	3.98572i	0.196124	+	0.196124i
$414$	4.04936	−	2.56957i	0.199015	−	0.126287i
$415$	6.79907	−	2.00243i	0.333753	−	0.0982952i
$416$	−5.47630	+	1.60799i	−0.268498	+	0.0788381i
$417$	−0.926713	+	12.9571i	−0.0453813	+	0.634514i
$418$	0.0107857	−	0.0495809i	0.000527545	−	0.00242508i
$419$	2.00492	+	13.9445i	0.0979466	+	0.681234i	0.978342	+	0.206994i	$0.0663680\pi$
$419$	2.00492	+	13.9445i	0.0979466	+	0.681234i	−0.880396	+	0.474240i	$0.842723\pi$
$420$	2.52018	−	1.37880i	0.122972	−	0.0672785i
$421$	−32.3308	−	14.7650i	−1.57571	−	0.719600i	−0.580215	−	0.814464i	$-0.697031\pi$
$421$	−32.3308	−	14.7650i	−1.57571	−	0.719600i	−0.995490	+	0.0948631i	$0.969759\pi$
$422$	16.9573	−	1.21281i	0.825467	−	0.0590386i
$423$	0.366928	+	0.490158i	0.0178406	+	0.0238323i
$424$	−5.22418	−	11.4394i	−0.253709	−	0.555544i
$425$	7.95483	+	4.32680i	0.385866	+	0.209880i
$426$	−13.8586	−	4.06927i	−0.671454	−	0.197157i
$427$	0.693351	−	1.85895i	0.0335536	−	0.0899608i
$428$	10.8283	−	8.10598i	0.523407	−	0.391817i
$429$	−0.0309084	+	0.0356702i	−0.00149227	+	0.00172217i
$430$	11.3227	−	8.49054i	0.546030	−	0.409450i
$431$	5.17177	−	8.04744i	0.249116	−	0.387631i	−0.694065	−	0.719913i	$-0.744182\pi$
$431$	5.17177	−	8.04744i	0.249116	−	0.387631i	0.943180	+	0.332281i	$0.107818\pi$
$432$	0.599278	−	0.800541i	0.0288328	−	0.0385161i
$433$	−3.31868	−	0.721934i	−0.159485	−	0.0346939i	0.132114	−	0.991235i	$-0.457824\pi$
$433$	−3.31868	−	0.721934i	−0.159485	−	0.0346939i	−0.291599	+	0.956541i	$0.594187\pi$
$434$	−1.54696	−	1.78529i	−0.0742565	−	0.0856966i
$435$	13.0088	−	8.37530i	0.623725	−	0.401565i
$436$			16.7534i			0.802342i
$437$	−6.08951	−	28.7894i	−0.291301	−	1.37719i
$438$	9.41152	−	9.41152i	0.449700	−	0.449700i
$439$	−3.30043	−	11.2402i	−0.157521	−	0.536466i	0.842477	−	0.538733i	$-0.181097\pi$
$439$	−3.30043	−	11.2402i	−0.157521	−	0.536466i	−0.999997	+	0.00226649i	$0.999279\pi$
$440$	−0.0155640	−	0.00998441i	−0.000741985	−	0.000475988i
$441$	4.50030	−	2.89217i	0.214300	−	0.137722i
$442$	8.27499	+	6.19458i	0.393601	+	0.294646i
$443$	−29.2673	+	6.36671i	−1.39053	+	0.302492i	−0.844627	−	0.535356i	$-0.820178\pi$
$443$	−29.2673	+	6.36671i	−1.39053	+	0.302492i	−0.545905	+	0.837847i	$0.683814\pi$
$444$	−1.04006	+	2.27741i	−0.0493589	+	0.108081i
$445$	1.48306	+	3.96633i	0.0703037	+	0.188022i
$446$	1.85770	−	12.9206i	0.0879644	−	0.611806i
$447$	−3.03528	−	1.13210i	−0.143564	−	0.0535466i
$448$	0.615696	+	1.12756i	0.0290889	+	0.0532723i
$449$	5.73362	−	19.5269i	0.270586	−	0.921532i	−0.706325	−	0.707888i	$-0.749648\pi$
$449$	5.73362	−	19.5269i	0.270586	−	0.921532i	0.976911	−	0.213645i	$-0.0685335\pi$
$450$	1.07081	+	4.88399i	0.0504786	+	0.230233i
$451$	0.0365897	+	0.00526081i	0.00172294	+	0.000247722i
$452$	−0.996914	−	13.9387i	−0.0468909	−	0.655621i
$453$	1.52397	+	4.08591i	0.0716022	+	0.191973i
$454$	−17.5330	−	11.2678i	−0.822865	−	0.528823i
$455$	−5.71722	+	15.3668i	−0.268028	+	0.720408i
$456$	−3.31728	−	5.16179i	−0.155346	−	0.241723i
$457$	−2.46422	−	0.176244i	−0.115271	−	0.00824436i	0.0135844	−	0.999908i	$-0.495676\pi$
$457$	−2.46422	−	0.176244i	−0.115271	−	0.00824436i	−0.128856	+	0.991663i	$0.541130\pi$
$458$	0.891962	+	0.487048i	0.0416786	+	0.0227583i
$459$	−1.81108			−0.0845341
$460$	−10.6070	−	1.57853i	−0.494553	−	0.0735992i
$461$	−7.14319			−0.332692			−0.166346	−	0.986067i	$-0.553197\pi$
$461$	−7.14319			−0.332692			−0.166346	+	0.986067i	$0.553197\pi$
$462$	0.00932443	+	0.00509152i	0.000433812	+	0.000236879i
$463$	31.4308	+	2.24797i	1.46071	+	0.104472i	0.778943	−	0.627095i	$-0.215756\pi$
$463$	31.4308	+	2.24797i	1.46071	+	0.104472i	0.681770	+	0.731567i	$0.261211\pi$
$464$	3.74079	+	5.82078i	0.173662	+	0.270223i
$465$	3.73864	−	1.71108i	0.173375	−	0.0793493i
$466$	10.3259	+	6.63607i	0.478339	+	0.307410i
$467$	6.37265	+	17.0857i	0.294891	+	0.790634i	0.996916	+	0.0784810i	$0.0250070\pi$
$467$	6.37265	+	17.0857i	0.294891	+	0.790634i	−0.702024	+	0.712153i	$0.747720\pi$
$468$	0.407168	+	5.69295i	0.0188214	+	0.263157i
$469$	−6.30973	−	0.907202i	−0.291356	−	0.0418907i
$470$	0.0965545	−	1.36570i	0.00445373	−	0.0629950i
$471$	6.12776	−	20.8692i	0.282352	−	0.961603i
$472$	−2.10270	−	3.85081i	−0.0967847	−	0.177248i
$473$	0.0490395	+	0.0182908i	0.00225484	+	0.000841011i
$474$	−1.90112	+	13.2226i	−0.0873214	+	0.607334i
$475$	30.3740	+	4.31644i	1.39365	+	0.198052i
$476$	0.966552	−	2.11645i	0.0443019	−	0.0970075i
$477$	−12.2884	+	2.67318i	−0.562648	+	0.122397i
$478$	−3.83036	−	2.86737i	−0.175197	−	0.131151i
$479$	6.05871	−	3.89370i	0.276830	−	0.177908i	−0.394858	−	0.918742i	$-0.629206\pi$
$479$	6.05871	−	3.89370i	0.276830	−	0.177908i	0.671687	+	0.740835i	$0.265570\pi$
$480$	−2.18458	+	0.477097i	−0.0997119	+	0.0217764i
$481$	−4.02585	−	13.7108i	−0.183563	−	0.625158i
$482$	−4.23585	+	4.23585i	−0.192938	+	0.192938i
$483$	6.14292	+	0.474887i	0.279513	+	0.0216081i
$484$			10.9999i			0.499997i
$485$	6.32468	+	9.82373i	0.287189	+	0.446073i
$486$	−0.654861	−	0.755750i	−0.0297051	−	0.0342815i
$487$	−19.1047	−	4.15597i	−0.865717	−	0.188325i	−0.242287	−	0.970205i	$-0.577898\pi$
$487$	−19.1047	−	4.15597i	−0.865717	−	0.188325i	−0.623430	+	0.781879i	$0.714261\pi$
$488$	−0.925495	+	1.23632i	−0.0418952	+	0.0559654i
$489$	1.81236	−	2.82009i	0.0819578	−	0.127529i
$490$	−11.8415	−	1.69267i	−0.534946	−	0.0764672i
$491$	−6.12896	+	7.07320i	−0.276596	+	0.319209i	−0.877002	−	0.480486i	$-0.840460\pi$
$491$	−6.12896	+	7.07320i	−0.276596	+	0.319209i	0.600406	+	0.799695i	$0.295006\pi$
$492$	3.57853	−	2.67885i	0.161332	−	0.120772i
$493$	4.37921	−	11.7411i	0.197230	−	0.528793i
$494$	33.6017	+	9.86634i	1.51181	+	0.443908i
$495$	−0.0130646	+	0.0130860i	−0.000587210	+	0.000588171i
$496$	0.763850	+	1.67260i	0.0342979	+	0.0751018i
$497$	−11.1202	−	14.8548i	−0.498809	−	0.666330i
$498$	3.16169	−	0.226128i	0.141679	−	0.0101331i
$499$	−2.42276	−	1.10644i	−0.108457	−	0.0495309i	0.360447	−	0.932780i	$-0.382624\pi$
$499$	−2.42276	−	1.10644i	−0.108457	−	0.0495309i	−0.468905	+	0.883249i	$0.655351\pi$
$500$	5.33408	−	9.82586i	0.238547	−	0.439426i
$501$	−0.385215	−	2.67923i	−0.0172101	−	0.119699i
$502$	−5.59186	+	25.7054i	−0.249577	+	1.14729i
$503$	−1.79423	+	25.0866i	−0.0800006	+	1.11855i	0.785905	+	0.618347i	$0.212197\pi$
$503$	−1.79423	+	25.0866i	−0.0800006	+	1.11855i	−0.865906	+	0.500207i	$0.833257\pi$
$504$	1.23267	−	0.361945i	0.0549075	−	0.0161223i
$505$	2.88549	−	5.29467i	0.128403	−	0.235610i
$506$	−0.0162673	−	0.0361696i	−0.000723168	−	0.00160793i
$507$	−13.8420	−	13.8420i	−0.614744	−	0.614744i
$508$	2.43067	−	4.45144i	0.107843	−	0.197501i
$509$	17.2204	−	14.9215i	0.763280	−	0.661386i	−0.183590	−	0.983003i	$-0.558772\pi$
$509$	17.2204	−	14.9215i	0.763280	−	0.661386i	0.946870	+	0.321617i	$0.104226\pi$
$510$	3.06273	+	2.64949i	0.135620	+	0.117321i
$511$	16.9253	−	2.43349i	0.748731	−	0.107651i
$512$	−0.212565	−	0.977147i	−0.00939415	−	0.0431842i
$513$	−5.74897	+	2.14425i	−0.253823	+	0.0946711i
$514$	21.4584	+	18.5938i	0.946491	+	0.820139i
$515$	−2.32915	−	16.1061i	−0.102635	−	0.709720i
$516$	5.75724	−	2.62924i	0.253448	−	0.115746i
$517$	0.00444396	−	0.00242658i	0.000195445	−	0.000106721i
$518$	−2.82303	+	1.54149i	−0.124037	+	0.0677293i
$519$	12.8060	−	5.84830i	0.562121	−	0.256712i
$520$	7.63984	−	10.2230i	0.335029	−	0.448310i
$521$	23.9723	+	20.7721i	1.05025	+	0.910043i	0.996077	−	0.0884888i	$-0.0282037\pi$
$521$	23.9723	+	20.7721i	1.05025	+	0.910043i	0.0541685	+	0.998532i	$0.482749\pi$
$522$	6.48292	−	2.41801i	0.283750	−	0.105833i
$523$	2.51334	+	11.5536i	0.109900	+	0.505204i	0.998883	+	0.0472622i	$0.0150496\pi$
$523$	2.51334	+	11.5536i	0.109900	+	0.505204i	−0.888982	+	0.457942i	$0.848587\pi$
$524$	−11.4099	+	1.64050i	−0.498446	+	0.0716657i
$525$	−2.65888	+	5.84742i	−0.116043	+	0.255202i
$526$	13.0291	−	11.2897i	0.568094	−	0.492256i
$527$	1.59597	−	2.92280i	0.0695216	−	0.127319i
$528$	−0.00584745	−	0.00584745i	−0.000254478	−	0.000254478i
$529$	−17.2078	−	15.2608i	−0.748165	−	0.663513i
$530$	24.6917	+	13.4565i	1.07254	+	0.584512i
$531$	−4.20977	+	1.23610i	−0.182688	+	0.0536421i
$532$	0.562350	−	7.86268i	0.0243810	−	0.340890i
$533$	−5.42324	+	24.9302i	−0.234906	+	1.07985i
$534$	0.269507	+	1.87446i	0.0116627	+	0.0811159i
$535$	−8.49745	+	29.0274i	−0.367377	+	1.25496i
$536$	4.51351	+	2.06125i	0.194954	+	0.0890325i
$537$	25.2857	−	1.80847i	1.09116	−	0.0780412i
$538$	0.473796	+	0.632917i	0.0204268	+	0.0272870i
$539$	−0.0183772	−	0.0402404i	−0.000791561	−	0.00173328i
$540$	0.00182805	+	2.23607i	7.86667e−5	+	0.0962250i
$541$	−16.6280	−	4.88243i	−0.714894	−	0.209912i	−0.0959945	−	0.995382i	$-0.530603\pi$
$541$	−16.6280	−	4.88243i	−0.714894	−	0.209912i	−0.618900	+	0.785470i	$0.712421\pi$
$542$	5.78654	−	15.5143i	0.248553	−	0.666396i
$543$	−4.89463	+	3.66407i	−0.210049	+	0.157241i
$544$	−1.18601	+	1.36872i	−0.0508496	+	0.0586836i
$545$	−22.4745	−	29.9713i	−0.962702	−	1.28383i
$546$	−3.96424	+	6.16847i	−0.169654	+	0.263986i
$547$	10.3626	−	13.8429i	0.443074	−	0.591878i	−0.522295	−	0.852765i	$-0.674924\pi$
$547$	10.3626	−	13.8429i	0.443074	−	0.591878i	0.965369	+	0.260887i	$0.0840149\pi$
$548$	14.5156	+	3.15768i	0.620076	+	0.134889i
$549$	1.01133	+	1.16714i	0.0431627	+	0.0498124i
$550$	0.0412375	−	0.00301714i	0.00175837	−	0.000128651i
$551$		−	42.4549i		−	1.80864i
$552$	−4.48374	−	1.70179i	−0.190841	−	0.0724332i
$553$	−12.1353	+	12.1353i	−0.516045	+	0.516045i
$554$	−3.20712	−	10.9224i	−0.136257	−	0.464050i
$555$	−1.19449	−	5.46943i	−0.0507031	−	0.232165i
$556$	10.9281	−	7.02305i	0.463454	−	0.297844i
$557$	−6.07087	−	4.54459i	−0.257231	−	0.192561i	0.462877	−	0.886422i	$-0.346817\pi$
$557$	−6.07087	−	4.54459i	−0.257231	−	0.192561i	−0.720108	+	0.693862i	$0.755908\pi$
$558$	1.79674	−	0.390857i	0.0760621	−	0.0165463i
$559$	−15.0064	+	32.8594i	−0.634702	+	1.38980i
$560$	−2.61407	−	1.19123i	−0.110465	−	0.0503385i
$561$	−0.00213142	+	0.0148244i	−8.99888e−5	+	0.000625886i
$562$	−24.1359	−	9.00222i	−1.01811	−	0.379736i
$563$	7.48755	+	13.7124i	0.315563	+	0.577910i	0.986531	−	0.163576i	$-0.0523030\pi$
$563$	7.48755	+	13.7124i	0.315563	+	0.577910i	−0.670968	+	0.741486i	$0.734121\pi$
$564$	0.172500	−	0.587482i	0.00726357	−	0.0247374i
$565$	20.4820	+	23.5985i	0.861686	+	0.992797i
$566$	−4.94270	−	0.710653i	−0.207757	−	0.0298710i
$567$	−0.0916501	−	1.28144i	−0.00384894	−	0.0538153i
$568$	5.04756	+	13.5330i	0.211791	+	0.567834i
$569$	15.8222	+	10.1683i	0.663303	+	0.426279i	0.828506	−	0.559981i	$-0.189191\pi$
$569$	15.8222	+	10.1683i	0.663303	+	0.426279i	−0.165203	+	0.986260i	$0.552828\pi$
$570$	12.8590	+	4.78419i	0.538604	+	0.200388i
$571$	−11.4768	−	17.8583i	−0.480290	−	0.747346i	0.513563	−	0.858052i	$-0.328325\pi$
$571$	−11.4768	−	17.8583i	−0.480290	−	0.747346i	−0.993853	+	0.110706i	$0.964689\pi$
$572$	0.0470781	+	0.00336709i	0.00196843	+	0.000140785i
$573$	−1.81014	−	0.988412i	−0.0756197	−	0.0412915i
$574$	5.74283			0.239701
$575$	21.0931	−	11.4052i	0.879645	−	0.475631i
$576$	−1.00000			−0.0416667
$577$	−33.3676	−	18.2201i	−1.38911	−	0.758512i	−0.401564	−	0.915831i	$-0.631533\pi$
$577$	−33.3676	−	18.2201i	−1.38911	−	0.758512i	−0.987548	+	0.157319i	$0.949715\pi$
$578$	−13.6850	−	0.978772i	−0.569222	−	0.0407116i
$579$	−3.46041	−	5.38450i	−0.143810	−	0.223772i
$580$	−14.5007	−	5.39497i	−0.602108	−	0.224014i
$581$	3.42578	+	2.20161i	0.142125	+	0.0913383i
$582$	1.82598	+	4.89564i	0.0756892	+	0.202931i
$583$	0.00741900	+	0.103731i	0.000307264	+	0.00429611i
$584$	−13.1744	−	1.89420i	−0.545161	−	0.0783824i
$585$	−8.36544	−	9.63830i	−0.345869	−	0.398495i
$586$	−4.75578	+	16.1967i	−0.196459	+	0.669079i
$587$	−13.3592	−	24.4655i	−0.551392	−	1.00980i	−0.993608	−	0.112890i	$-0.963989\pi$
$587$	−13.3592	−	24.4655i	−0.551392	−	1.00980i	0.442216	−	0.896909i	$-0.354193\pi$
$588$	−5.01223	−	1.86947i	−0.206701	−	0.0770955i
$589$	1.60564	−	11.1675i	0.0661594	−	0.460149i
$590$	8.92748	+	4.06823i	0.367539	+	0.167486i
$591$	6.03924	−	13.2241i	0.248421	−	0.543966i
$592$	2.44644	−	0.532191i	0.100548	−	0.0218729i
$593$	−7.55903	−	5.65862i	−0.310412	−	0.232372i	0.432701	−	0.901538i	$-0.357561\pi$
$593$	−7.55903	−	5.65862i	−0.310412	−	0.232372i	−0.743113	+	0.669166i	$0.766652\pi$
$594$	−0.00695678	+	0.00447085i	−0.000285440	+	0.000183441i
$595$	1.11007	+	5.08289i	0.0455083	+	0.208378i
$596$	0.912683	+	3.10831i	0.0373850	+	0.127321i
$597$	−8.30031	+	8.30031i	−0.339709	+	0.339709i
$598$	25.7010	−	9.41790i	1.05099	−	0.385126i
$599$			24.5789i			1.00427i	0.864790	+	0.502134i	$0.167452\pi$
$599$			24.5789i			1.00427i	−0.864790	+	0.502134i	$0.832548\pi$
$600$	3.26812	−	3.78410i	0.133420	−	0.154485i
$601$	−22.7364	−	26.2392i	−0.927437	−	1.07032i	−0.997349	−	0.0727664i	$-0.976817\pi$
$601$	−22.7364	−	26.2392i	−0.927437	−	1.07032i	0.0699119	−	0.997553i	$-0.477728\pi$
$602$	7.94535	+	1.72841i	0.323828	+	0.0704445i
$603$	2.97356	−	3.97221i	0.121093	−	0.161761i
$604$	2.35766	−	3.66859i	0.0959319	−	0.149273i
$605$	−14.7563	−	19.6785i	−0.599928	−	0.800046i
$606$	1.76593	−	2.03799i	0.0717360	−	0.0827878i
$607$	6.48163	−	4.85209i	0.263081	−	0.196940i	−0.459592	−	0.888130i	$-0.652004\pi$
$607$	6.48163	−	4.85209i	0.263081	−	0.196940i	0.722673	+	0.691190i	$0.242913\pi$
$608$	−2.14425	+	5.74897i	−0.0869610	+	0.233151i
$609$	8.52906	+	2.50436i	0.345615	+	0.101482i
$610$	−0.00282315	−	3.45327i	−0.000114306	−	0.139819i
$611$	1.45171	+	3.17881i	0.0587300	+	0.128601i
$612$	1.08534	+	1.44985i	0.0438723	+	0.0586066i
$613$	−44.3781	+	3.17399i	−1.79242	+	0.128196i	−0.927524	−	0.373763i	$-0.878067\pi$
$613$	−44.3781	+	3.17399i	−1.79242	+	0.128196i	−0.864891	+	0.501959i	$0.832613\pi$
$614$	−25.4052	−	11.6022i	−1.02527	−	0.468226i
$615$	−2.80822	+	9.59294i	−0.113238	+	0.386825i
$616$	−0.00151195	−	0.0105158i	−6.09181e−5	−	0.000423695i
$617$	7.42937	−	34.1523i	0.299095	−	1.37492i	−0.544870	−	0.838521i	$-0.683421\pi$
$617$	7.42937	−	34.1523i	0.299095	−	1.37492i	0.843965	−	0.536398i	$-0.180215\pi$
$618$	0.519192	−	7.25926i	0.0208850	−	0.292010i
$619$	−43.4470	+	12.7572i	−1.74628	+	0.512755i	−0.989948	−	0.141429i	$-0.954830\pi$
$619$	−43.4470	+	12.7572i	−1.74628	+	0.512755i	−0.756336	+	0.654184i	$0.773012\pi$
$620$	−3.61027	−	1.96753i	−0.144992	−	0.0790178i
$621$	−2.61599	+	4.01953i	−0.104976	+	0.161298i
$622$	6.44259	+	6.44259i	0.258324	+	0.258324i
$623$	−1.16597	+	2.13531i	−0.0467134	+	0.0855493i
$624$	4.31344	−	3.73761i	0.172676	−	0.149624i
$625$	3.63877	+	24.7338i	0.145551	+	0.989351i
$626$	−10.6128	+	1.52589i	−0.424172	+	0.0609867i
$627$	0.0107857	+	0.0495809i	0.000430738	+	0.00198007i
$628$	−20.3789	+	7.60094i	−0.813207	+	0.303311i
$629$	−3.42682	−	2.96936i	−0.136636	−	0.118396i
$630$	−1.71966	+	2.30112i	−0.0685130	+	0.0916788i
$631$	0.688339	−	0.314354i	0.0274023	−	0.0125142i	−0.401667	−	0.915786i	$-0.631569\pi$
$631$	0.688339	−	0.314354i	0.0274023	−	0.0125142i	0.429069	+	0.903272i	$0.358842\pi$
$632$	11.7245	−	6.40208i	0.466377	−	0.254661i
$633$	−14.9211	+	8.14752i	−0.593059	+	0.323835i
$634$	−11.9769	+	5.46969i	−0.475665	+	0.217229i
$635$	1.62316	+	11.2242i	0.0644132	+	0.445418i
$636$	9.50416	+	8.23540i	0.376865	+	0.326555i
$637$	28.6073	−	10.6700i	1.13346	−	0.422760i
$638$	−0.0121627	−	0.0559108i	−0.000481524	−	0.00221353i
$639$	14.2967	−	2.05556i	0.565569	−	0.0813165i
$640$	1.69110	+	1.46293i	0.0668468	+	0.0578274i
$641$	−22.9960	+	19.9262i	−0.908289	+	0.787037i	−0.977581	−	0.210560i	$-0.932471\pi$
$641$	−22.9960	+	19.9262i	−0.908289	+	0.787037i	0.0692924	+	0.997596i	$0.477926\pi$
$642$	−6.48244	+	11.8717i	−0.255842	+	0.468539i
$643$	−25.9937	−	25.9937i	−1.02509	−	1.02509i	−0.999677	−	0.0254147i	$-0.991909\pi$
$643$	−25.9937	−	25.9937i	−1.02509	−	1.02509i	−0.0254147	−	0.999677i	$-0.508091\pi$
$644$	−3.30115	−	5.20225i	−0.130084	−	0.204997i
$645$	−6.77242	+	12.4269i	−0.266664	+	0.489309i
$646$	10.6624	−	3.13075i	0.419505	−	0.123178i
$647$	0.0758563	−	1.06061i	0.00298222	−	0.0416969i	−0.995743	−	0.0921720i	$-0.970619\pi$
$647$	0.0758563	−	1.06061i	0.00298222	−	0.0416969i	0.998725	+	0.0504752i	$0.0160736\pi$
$648$	−0.212565	+	0.977147i	−0.00835035	+	0.0383860i
$649$	0.00516354	+	0.0359132i	0.000202687	+	0.00140972i
$650$	0.0466604	+	28.5374i	0.00183017	+	1.11933i
$651$	2.14880	+	0.981325i	0.0842182	+	0.0384612i
$652$	−3.34371	+	0.239147i	−0.130950	+	0.00936570i
$653$	12.1079	+	16.1743i	0.473819	+	0.632948i	0.972240	−	0.233988i	$-0.0751775\pi$
$653$	12.1079	+	16.1743i	0.473819	+	0.632948i	−0.498421	+	0.866935i	$0.666087\pi$
$654$	−6.95962	−	15.2394i	−0.272142	−	0.595909i
$655$	18.2113	−	18.2411i	0.711575	−	0.712739i
$656$	−4.28906	−	1.25938i	−0.167460	−	0.0491706i
$657$	−4.65133	+	12.4707i	−0.181466	+	0.486529i
$658$	0.629711	−	0.471396i	0.0245487	−	0.0183769i
$659$	−17.4624	+	20.1527i	−0.680239	+	0.785038i	−0.985942	−	0.167089i	$-0.946563\pi$
$659$	−17.4624	+	20.1527i	−0.680239	+	0.785038i	0.305703	+	0.952127i	$0.401109\pi$
$660$	0.0183052	+	0.00261662i	0.000712528	+	0.000101852i
$661$	−11.2251	+	17.4665i	−0.436604	+	0.679370i	−0.987927	−	0.154923i	$-0.950487\pi$
$661$	−11.2251	+	17.4665i	−0.436604	+	0.679370i	0.551322	+	0.834292i	$0.314123\pi$
$662$	−20.5925	+	27.5083i	−0.800350	+	1.06914i
$663$	−10.1005	−	2.19723i	−0.392272	−	0.0853335i
$664$	−2.07575	−	2.39555i	−0.0805549	−	0.0929653i
$665$	9.54167	+	14.8205i	0.370010	+	0.574713i
$666$		−	2.50366i		−	0.0970148i
$667$	−19.7328	−	26.6785i	−0.764057	−	1.03300i
$668$	−1.91398	+	1.91398i	−0.0740542	+	0.0740542i
$669$	3.67757	+	12.5247i	0.142183	+	0.484231i
$670$	−10.8397	+	2.36731i	−0.418773	+	0.0914572i
$671$	0.0107437	−	0.00690456i	0.000414756	−	0.000266548i
$672$	−1.02846	−	0.769898i	−0.0396738	−	0.0296995i
$673$	−17.9320	+	3.90086i	−0.691227	+	0.150367i	−0.544438	−	0.838801i	$-0.683257\pi$
$673$	−17.9320	+	3.90086i	−0.691227	+	0.150367i	−0.146788	+	0.989168i	$0.546894\pi$
$674$	−10.1144	+	22.1474i	−0.389591	+	0.853086i
$675$	−3.00293	−	3.99780i	−0.115583	−	0.153875i
$676$	−2.78589	+	19.3763i	−0.107149	+	0.745241i
$677$	11.2249	+	4.18668i	0.431409	+	0.160907i	0.555781	−	0.831328i	$-0.312419\pi$
$677$	11.2249	+	4.18668i	0.431409	+	0.160907i	−0.124373	+	0.992236i	$0.539692\pi$
$678$	6.69716	+	12.2649i	0.257203	+	0.471032i
$679$	−1.89119	+	6.44080i	−0.0725772	+	0.247175i
$680$	0.285600	−	4.03962i	0.0109523	−	0.154912i
$681$	20.6294	+	2.96606i	0.790520	+	0.113660i
$682$	−0.00108476	−	0.0151670i	−4.15378e−5	−	0.000580774i
$683$	1.10159	+	2.95349i	0.0421514	+	0.113012i	0.956320	−	0.292322i	$-0.0944279\pi$
$683$	1.10159	+	2.95349i	0.0421514	+	0.113012i	−0.914169	+	0.405334i	$0.867155\pi$
$684$	5.16179	+	3.31728i	0.197366	+	0.126839i
$685$	−30.2039	+	13.8235i	−1.15403	+	0.528170i
$686$	−8.57756	−	13.3469i	−0.327493	−	0.509589i
$687$	−1.01368	−	0.0725001i	−0.0386745	−	0.00276605i
$688$	−5.55500	−	3.03326i	−0.211782	−	0.115642i
$689$	−71.7764			−2.73446
$690$	10.3042	−	2.97042i	0.392274	−	0.113082i
$691$	−44.7995			−1.70425			−0.852126	−	0.523337i	$-0.824687\pi$
$691$	−44.7995			−1.70425			−0.852126	+	0.523337i	$0.824687\pi$
$692$	−12.3561	−	6.74697i	−0.469710	−	0.256481i
$693$	−0.0105969		0.000757905i	−0.000402543		2.87904e-5i
$694$	6.23795	+	9.70644i	0.236789	+	0.368451i
$695$	−10.1286	+	27.2239i	−0.384202	+	1.03266i
$696$	−5.82078	−	3.74079i	−0.220636	−	0.141794i
$697$	2.82919	+	7.58534i	0.107163	+	0.287315i
$698$	−0.0437491	−	0.611693i	−0.00165593	−	0.0231529i
$699$	−12.1495	−	1.74684i	−0.459537	−	0.0660714i
$700$	6.27451	−	1.37568i	0.237154	−	0.0519960i
$701$	2.12892	−	7.25045i	0.0804084	−	0.273846i	−0.909469	−	0.415772i	$-0.863511\pi$
$701$	2.12892	−	7.25045i	0.0804084	−	0.273846i	0.989877	+	0.141926i	$0.0453296\pi$
$702$	−2.73531	−	5.00935i	−0.103238	−	0.189066i
$703$	−14.3934	−	5.36848i	−0.542859	−	0.202476i
$704$	−0.00117688	+	0.00818537i	−4.43553e−5	+	0.000308498i
$705$	0.479503	+	1.28239i	0.0180591	+	0.0482977i
$706$	−2.99962	+	6.56825i	−0.112892	+	0.247199i
$707$	3.38524	−	0.736414i	0.127315	−	0.0276957i
$708$	3.51237	+	2.62933i	0.132003	+	0.0988161i
$709$	18.6039	−	11.9560i	0.698685	−	0.449018i	−0.142479	−	0.989798i	$-0.545507\pi$
$709$	18.6039	−	11.9560i	0.698685	−	0.449018i	0.841164	+	0.540780i	$0.181871\pi$
$710$	−27.1843	−	17.4389i	−1.02021	−	0.654472i
$711$	−3.76354	−	12.8175i	−0.141144	−	0.480692i
$712$	1.33907	−	1.33907i	0.0501839	−	0.0501839i
$713$	−4.18161	−	7.76391i	−0.156603	−	0.290761i
$714$			2.32672i			0.0870751i
$715$	−0.0887382	+	0.0571311i	−0.00331862	+	0.00213658i
$716$	−16.6009	−	19.1585i	−0.620405	−	0.715986i
$717$	4.67537	+	1.01706i	0.174605	+	0.0379829i
$718$	17.9195	−	23.9376i	0.668748	−	0.893343i
$719$	−25.7252	+	40.0292i	−0.959389	+	1.49284i	−0.0916663	+	0.995790i	$0.529219\pi$
$719$	−25.7252	+	40.0292i	−0.959389	+	1.49284i	−0.867723	+	0.497049i	$0.834417\pi$
$720$	1.78897	−	1.34149i	0.0666709	−	0.0499943i
$721$	6.12286	−	7.06615i	0.228027	−	0.263157i
$722$	14.9288	−	11.1756i	0.555594	−	0.415913i
$723$	2.09343	−	5.61270i	0.0778555	−	0.208739i
$724$	5.86649	+	1.72256i	0.218026	+	0.0640183i
$725$	33.1785	−	9.80105i	1.23222	−	0.364002i
$726$	−4.56954	−	10.0059i	−0.169591	−	0.371353i
$727$	0.787438	+	1.05189i	0.0292045	+	0.0390126i	0.814906	−	0.579593i	$-0.196789\pi$
$727$	0.787438	+	1.05189i	0.0292045	+	0.0390126i	−0.785701	+	0.618606i	$0.787698\pi$
$728$	7.31379	−	0.523093i	0.271067	−	0.0193871i
$729$	0.909632	+	0.415415i	0.0336901	+	0.0153857i
$730$	26.1097	−	14.2847i	0.966362	−	0.528700i
$731$	1.63131	+	11.3460i	0.0603362	+	0.419648i
$732$	0.328275	−	1.50906i	0.0121334	−	0.0557764i
$733$	−0.984793	+	13.7692i	−0.0363742	+	0.508577i	0.946307	+	0.323271i	$0.104782\pi$
$733$	−0.984793	+	13.7692i	−0.0363742	+	0.508577i	−0.982681	+	0.185307i	$0.940672\pi$
$734$	−23.8060	+	6.99007i	−0.878696	+	0.258008i
$735$	11.4746	−	3.37944i	0.423247	−	0.124652i
$736$	1.32465	+	4.60926i	0.0488271	+	0.169900i
$737$	−0.0290145	−	0.0290145i	−0.00106876	−	0.00106876i
$738$	−2.14231	+	3.92334i	−0.0788594	+	0.144420i
$739$	−32.4974	+	28.1591i	−1.19543	+	1.03585i	−0.196973	+	0.980409i	$0.563111\pi$
$739$	−32.4974	+	28.1591i	−1.19543	+	1.03585i	−0.998462	+	0.0554410i	$0.982344\pi$
$740$	−3.66268	+	4.23395i	−0.134643	+	0.155643i
$741$	−34.6638	+	4.98390i	−1.27341	+	0.183088i
$742$	3.43426	+	15.7870i	0.126076	+	0.579560i
$743$	1.07146	−	0.399632i	0.0393079	−	0.0146611i	−0.329733	−	0.944074i	$-0.606959\pi$
$743$	1.07146	−	0.399632i	0.0393079	−	0.0146611i	0.369041	+	0.929413i	$0.379686\pi$
$744$	−1.38964	−	1.20413i	−0.0509468	−	0.0441457i
$745$	−5.80253	−	4.33632i	−0.212588	−	0.158870i
$746$	19.2671	−	8.79898i	0.705418	−	0.322153i
$747$	−2.78204	+	1.51911i	−0.101789	+	0.0555812i
$748$	0.0131448	−	0.00717763i	0.000480623	−	0.000262440i
$749$	−15.8070	+	7.21880i	−0.577574	+	0.263769i
$750$	−0.770243	+	11.1538i	−0.0281253	+	0.407278i
$751$	−0.717626	−	0.621827i	−0.0261866	−	0.0226908i	0.641669	−	0.766982i	$-0.278242\pi$
$751$	−0.717626	−	0.621827i	−0.0261866	−	0.0226908i	−0.667856	+	0.744291i	$0.732788\pi$
$752$	−0.573679	+	0.213971i	−0.0209199	+	0.00780273i
$753$	−5.59186	−	25.7054i	−0.203779	−	0.936755i
$754$	39.0892	−	5.62018i	1.42355	−	0.204675i
$755$	0.703594	+	9.72578i	0.0256064	+	0.353957i
$756$	−0.970919	+	0.841306i	−0.0353120	+	0.0305980i
$757$	14.9570	−	27.3916i	0.543620	−	0.995566i	−0.451054	−	0.892497i	$-0.648952\pi$
$757$	14.9570	−	27.3916i	0.543620	−	0.995566i	0.994674	−	0.103069i	$-0.0328663\pi$
$758$	8.46916	+	8.46916i	0.307614	+	0.307614i
$759$	0.0298226	+	0.0261433i	0.00108249	+	0.000948943i
$760$	−3.87617	−	13.1612i	−0.140603	−	0.477407i
$761$	−47.0387	+	13.8118i	−1.70515	+	0.500677i	−0.981818	−	0.189823i	$-0.939209\pi$
$761$	−47.0387	+	13.8118i	−1.70515	+	0.500677i	−0.723332	+	0.690500i	$0.757391\pi$
$762$	−0.361820	+	5.05890i	−0.0131074	+	0.183265i
$763$	4.57510	−	21.0314i	0.165630	−	0.761387i
$764$	0.293513	+	2.04143i	0.0106189	+	0.0738562i
$765$	−3.88659	−	1.13776i	−0.140520	−	0.0411357i
$766$	22.0971	+	10.0914i	0.798400	+	0.364617i
$767$	−24.9778	+	1.78645i	−0.901896	+	0.0645049i
$768$	0.599278	+	0.800541i	0.0216246	+	0.0288870i
$769$	−3.14935	−	6.89613i	−0.113569	−	0.248681i	0.844309	−	0.535856i	$-0.180011\pi$
$769$	−3.14935	−	6.89613i	−0.113569	−	0.248681i	−0.957878	+	0.287175i	$0.907284\pi$
$770$	0.0168117	+	0.0167842i	0.000605851	+	0.000604861i
$771$	−27.2434	−	7.99939i	−0.981148	−	0.288091i
$772$	−2.23677	+	5.99702i	−0.0805032	+	0.215837i
$773$	40.2913	−	30.1617i	1.44918	−	1.08484i	0.469804	−	0.882771i	$-0.344324\pi$
$773$	40.2913	−	30.1617i	1.44918	−	1.08484i	0.979371	−	0.202069i	$-0.0647665\pi$
$774$	−4.14474	+	4.78328i	−0.148980	+	0.171932i
$775$	9.09808	−	1.32329i	0.326813	−	0.0475341i
$776$	2.82489	−	4.39562i	0.101408	−	0.157793i
$777$	1.92756	−	2.57492i	0.0691509	−	0.0923747i
$778$	−1.57114	−	0.341780i	−0.0563280	−	0.0122534i
$779$	17.9615	+	20.7287i	0.643538	+	0.742683i
$780$	−2.70264	+	12.4729i	−0.0967699	+	0.446602i
$781$		−	0.119443i		−	0.00427400i
$782$	5.24503	−	6.92316i	0.187562	−	0.247572i
$783$	−4.89260	+	4.89260i	−0.174847	+	0.174847i
$784$	1.50713	+	5.13283i	0.0538262	+	0.183315i
$785$	26.2607	−	40.9359i	0.937283	−	1.46107i
$786$	9.69736	−	6.23212i	0.345893	−	0.222292i
$787$	4.13747	+	3.09727i	0.147485	+	0.110406i	0.670472	−	0.741935i	$-0.266092\pi$
$787$	4.13747	+	3.09727i	0.147485	+	0.110406i	−0.522987	+	0.852341i	$0.675182\pi$
$788$	−14.2056	+	3.09024i	−0.506054	+	0.110085i
$789$	−7.16172	+	15.6820i	−0.254964	+	0.558293i
$790$	−12.3865	+	27.1814i	−0.440692	+	0.967073i
$791$	−2.55496	+	17.7702i	−0.0908441	+	0.631834i
$792$	0.00774814	+	0.00288991i	0.000275318	+	0.000102688i
$793$	4.22428	+	7.73619i	0.150009	+	0.274720i
$794$	−7.75140	+	26.3988i	−0.275087	+	0.936860i
$795$	−28.0503	−	1.98315i	−0.994843	−	0.0703352i
$796$	11.6189	+	1.67055i	0.411822	+	0.0592111i
$797$	−1.22332	−	17.1043i	−0.0433323	−	0.605864i	−0.972004	−	0.234963i	$-0.924503\pi$
$797$	−1.22332	−	17.1043i	−0.0433323	−	0.605864i	0.928672	−	0.370902i	$-0.120951\pi$
$798$	2.75474	+	7.38575i	0.0975169	+	0.261453i
$799$	0.932863	+	0.599514i	0.0330023	+	0.0212093i
$800$	−4.98784	−	0.348541i	−0.176347	−	0.0123228i
$801$	−1.02383	−	1.59311i	−0.0361753	−	0.0562899i
$802$	14.0908	+	1.00780i	0.497565	+	0.0355865i
$803$	0.0966033	+	0.0527494i	0.00340906	+	0.00186149i
$804$	−4.96191			−0.174993
$805$	12.8844	+	4.87821i	0.454116	+	0.171934i
$806$	10.4947			0.369661
$807$	−0.693903	−	0.378900i	−0.0244265	−	0.0133379i
$808$	−2.68978	−	0.192377i	−0.0946261	−	0.00676779i
$809$	17.8934	+	27.8427i	0.629100	+	0.978898i	0.998763	+	0.0497323i	$0.0158368\pi$
$809$	17.8934	+	27.8427i	0.629100	+	0.978898i	−0.369663	+	0.929166i	$0.620527\pi$
$810$	−0.930559	−	2.03324i	−0.0326965	−	0.0714407i
$811$	34.0505	+	21.8829i	1.19567	+	0.768413i	0.978202	−	0.207653i	$-0.0665826\pi$
$811$	34.0505	+	21.8829i	1.19567	+	0.768413i	0.217472	+	0.976067i	$0.430219\pi$
$812$	−3.10643	−	8.32867i	−0.109014	−	0.292279i
$813$	1.18126	+	16.5161i	0.0414285	+	0.579246i
$814$	−0.0204934	−	0.00294650i	−0.000718292	−	0.000103275i
$815$	5.66097	−	4.91337i	0.198295	−	0.172108i
$816$	0.510241	−	1.73772i	0.0178620	−	0.0608324i
$817$	18.6116	+	34.0845i	0.651136	+	1.19247i
$818$	−18.6388	−	6.95191i	−0.651690	−	0.243068i
$819$	1.04352	−	7.25784i	0.0364635	−	0.253609i
$820$	9.36245	−	3.50073i	0.326951	−	0.122251i
$821$	−11.1789	+	24.4783i	−0.390145	+	0.854299i	0.608030	+	0.793914i	$0.291960\pi$
$821$	−11.1789	+	24.4783i	−0.390145	+	0.854299i	−0.998175	+	0.0603849i	$0.980767\pi$
$822$	−14.5156	+	3.15768i	−0.506290	+	0.110137i
$823$	−7.13753	−	5.34309i	−0.248799	−	0.186248i	0.467599	−	0.883941i	$-0.345119\pi$
$823$	−7.13753	−	5.34309i	−0.248799	−	0.186248i	−0.716397	+	0.697693i	$0.754210\pi$
$824$	−6.12248	+	3.93468i	−0.213287	+	0.137071i
$825$	−0.0362576	+	0.0198752i	−0.00126233	+	0.000691964i
$826$	1.58803	+	5.40833i	0.0552546	+	0.188180i
$827$	15.7862	−	15.7862i	0.548940	−	0.548940i	−0.377194	−	0.926134i	$-0.623111\pi$
$827$	15.7862	−	15.7862i	0.548940	−	0.548940i	0.926134	+	0.377194i	$0.123111\pi$
$828$	4.78550	−	0.314604i	0.166308	−	0.0109333i
$829$		−	44.9834i		−	1.56234i	−0.624319	−	0.781170i	$-0.714623\pi$
$829$		−	44.9834i		−	1.56234i	0.624319	−	0.781170i	$-0.285377\pi$
$830$	6.92706	+	1.50096i	0.240442	+	0.0520991i
$831$	7.45464	+	8.60311i	0.258598	+	0.298439i
$832$	−5.57706	−	1.21322i	−0.193350	−	0.0420607i
$833$	5.80606	−	7.75598i	0.201168	−	0.268729i
$834$	−7.02305	+	10.9281i	−0.243188	+	0.378408i
$835$	0.856469	−	5.99164i	0.0296393	−	0.207349i
$836$	0.0332280	−	0.0383471i	0.00114921	−	0.00132626i
$837$	−1.47201	+	1.10193i	−0.0508799	+	0.0380883i
$838$	−4.92322	+	13.1997i	−0.170070	+	0.455974i
$839$	6.57291	+	1.92998i	0.226922	+	0.0666303i	0.393217	−	0.919446i	$-0.371362\pi$
$839$	6.57291	+	1.92998i	0.226922	+	0.0666303i	−0.166295	+	0.986076i	$0.553180\pi$
$840$	2.87270	−	0.00234851i	0.0991175	−	8.10314e-5i
$841$	−7.84097	−	17.1693i	−0.270378	−	0.592046i
$842$	−21.2999	−	28.4534i	−0.734044	−	0.980568i
$843$	25.6944	−	1.83770i	0.884964	−	0.0632939i
$844$	15.4643	+	7.06230i	0.532303	+	0.243094i
$845$	−21.0092	−	38.4008i	−0.722737	−	1.32103i
$846$	0.0871370	+	0.606051i	0.00299583	+	0.0208365i
$847$	3.00391	−	13.8088i	0.103216	−	0.474475i
$848$	0.897148	−	12.5438i	0.0308082	−	0.430755i
$849$	4.79125	−	1.40684i	0.164435	−	0.0482826i
$850$	4.90818	+	7.60988i	0.168349	+	0.261017i
$851$	−11.5400	+	3.31646i	−0.395587	+	0.113687i
$852$	−10.2133	−	10.2133i	−0.349900	−	0.349900i
$853$	11.4708	−	21.0072i	0.392753	−	0.719273i	−0.604237	−	0.796805i	$-0.706522\pi$
$853$	11.4708	−	21.0072i	0.392753	−	0.719273i	0.996990	+	0.0775315i	$0.0247038\pi$
$854$	1.49944	−	1.29927i	0.0513097	−	0.0444601i
$855$	−13.6844	+	0.989971i	−0.467996	+	0.0338563i
$856$	13.3886	−	1.92499i	0.457612	−	0.0657947i
$857$	−5.52315	−	25.3895i	−0.188667	−	0.867289i	−0.969987	−	0.243158i	$-0.921817\pi$
$857$	−5.52315	−	25.3895i	−0.188667	−	0.867289i	0.781319	−	0.624131i	$-0.214547\pi$
$858$	−0.0442225	+	0.0164941i	−0.00150973	+	0.000563101i
$859$	43.0688	+	37.3194i	1.46949	+	1.27332i	0.888063	+	0.459721i	$0.152051\pi$
$859$	43.0688	+	37.3194i	1.46949	+	1.27332i	0.581427	+	0.813599i	$0.302495\pi$
$860$	14.0068	−	2.02556i	0.477628	−	0.0690711i
$861$	−5.22386	+	2.38566i	−0.178029	+	0.0813029i
$862$	8.39588	−	4.58450i	0.285965	−	0.156149i
$863$	10.5310	−	5.75038i	0.358480	−	0.195745i	−0.289909	−	0.957054i	$-0.593625\pi$
$863$	10.5310	−	5.75038i	0.358480	−	0.195745i	0.648389	+	0.761309i	$0.275443\pi$
$864$	0.909632	−	0.415415i	0.0309463	−	0.0141327i
$865$	31.1557	−	4.50552i	1.05933	−	0.153192i
$866$	−2.56675	−	2.22410i	−0.0872216	−	0.0755779i
$867$	12.8549	−	4.79464i	0.436576	−	0.162835i
$868$	−0.502138	−	2.30829i	−0.0170437	−	0.0783485i
$869$	−0.109345	+	0.0157214i	−0.00370927	+	0.000533312i
$870$	15.4314	−	1.11636i	0.523174	−	0.0378481i
$871$	21.4029	−	18.5457i	0.725209	−	0.628397i
$872$	−8.02905	+	14.7041i	−0.271898	+	0.497944i
$873$	−3.69469	−	3.69469i	−0.125046	−	0.125046i
$874$	8.45268	−	28.1863i	0.285916	−	0.953415i
$875$	−9.37943	+	10.8782i	−0.317083	+	0.367752i
$876$	12.7708	−	3.74983i	0.431484	−	0.126695i
$877$	3.20148	−	44.7625i	0.108106	−	1.51152i	−0.596897	−	0.802318i	$-0.703600\pi$
$877$	3.20148	−	44.7625i	0.108106	−	1.51152i	0.705003	−	0.709204i	$-0.250946\pi$
$878$	2.49015	−	11.4470i	0.0840384	−	0.386318i
$879$	−2.40234	−	16.7087i	−0.0810290	−	0.563569i
$880$	−0.00887518	−	0.0162221i	−0.000299182	−	0.000546848i
$881$	−11.5691	−	5.28341i	−0.389772	−	0.178003i	0.210883	−	0.977511i	$-0.432366\pi$
$881$	−11.5691	−	5.28341i	−0.389772	−	0.178003i	−0.600655	+	0.799509i	$0.705093\pi$
$882$	5.33589	−	0.381630i	0.179669	−	0.0128502i
$883$	18.3202	+	24.4729i	0.616523	+	0.823579i	0.994772	−	0.102126i	$-0.0325644\pi$
$883$	18.3202	+	24.4729i	0.616523	+	0.823579i	−0.378248	+	0.925704i	$0.623473\pi$
$884$	4.29404	+	9.40264i	0.144424	+	0.316245i
$885$	−9.81073	+	0.00802055i	−0.329784	+	0.000269608i
$886$	−28.7385	−	8.43840i	−0.965490	−	0.283493i
$887$	4.52899	−	12.1427i	0.152069	−	0.407712i	−0.838470	−	0.544948i	$-0.816549\pi$
$887$	4.52899	−	12.1427i	0.152069	−	0.407712i	0.990538	+	0.137236i	$0.0438220\pi$
$888$	−2.00428	+	1.50039i	−0.0672593	+	0.0503497i
$889$	−4.26696	+	4.92433i	−0.143109	+	0.165157i
$890$	−0.599209	+	4.19192i	−0.0200855	+	0.140513i
$891$	0.00447085	−	0.00695678i	0.000149779	−	0.000233061i
$892$	7.82262	−	10.4498i	0.261921	−	0.349885i
$893$	3.67101	+	0.798580i	0.122846	+	0.0267235i
$894$	−2.12145	−	2.44828i	−0.0709518	−	0.0818827i
$895$	55.3994	+	12.0040i	1.85180	+	0.401249i
$896$			1.28471i			0.0429191i
$897$	−19.4661	+	19.2434i	−0.649954	+	0.642518i
$898$	14.3905	−	14.3905i	0.480218	−	0.480218i
$899$	−3.58441	−	12.2074i	−0.119547	−	0.407139i
$900$	−1.40082	+	4.79976i	−0.0466939	+	0.159992i
$901$	−19.1602	+	12.3135i	−0.638320	+	0.410224i
$902$	0.0295928	+	0.0221529i	0.000985332	+	0.000737610i
$903$	−7.94535	+	1.72841i	−0.264405	+	0.0575177i
$904$	5.80513	−	12.7115i	0.193076	−	0.422777i
$905$	−12.8057	+	4.78823i	−0.425677	+	0.159166i
$906$	−0.620616	+	4.31648i	−0.0206186	+	0.143405i
$907$	−49.1625	−	18.3367i	−1.63241	−	0.608859i	−0.644603	−	0.764518i	$-0.722977\pi$
$907$	−49.1625	−	18.3367i	−1.63241	−	0.608859i	−0.987811	+	0.155659i	$0.950250\pi$
$908$	−9.98828	−	18.2922i	−0.331473	−	0.607047i
$909$	−0.759734	+	2.58742i	−0.0251988	+	0.0858192i
$910$	−12.3824	+	10.7472i	−0.410473	+	0.356265i
$911$	22.3520	+	3.21374i	0.740556	+	0.106476i	0.502260	−	0.864717i	$-0.332502\pi$
$911$	22.3520	+	3.21374i	0.740556	+	0.106476i	0.238296	+	0.971193i	$0.423411\pi$
$912$	−0.437725	−	6.12020i	−0.0144945	−	0.202660i
$913$	0.00916033	+	0.0245598i	0.000303163	+	0.000812811i
$914$	−2.07833	−	1.33566i	−0.0687450	−	0.0441797i
$915$	1.43711	+	3.14003i	0.0475093	+	0.103806i
$916$	0.549439	+	0.854944i	0.0181540	+	0.0282481i
$917$	14.7715	+	1.05648i	0.487797	+	0.0348879i
$918$	−1.58955	−	0.867960i	−0.0524629	−	0.0286469i
$919$	−39.9355			−1.31735			−0.658676	−	0.752427i	$-0.728883\pi$
$919$	−39.9355			−1.31735			−0.658676	+	0.752427i	$0.728883\pi$
$920$	−8.55303	−	6.46883i	−0.281985	−	0.213271i
$921$	27.9291			0.920296
$922$	−6.26943	−	3.42337i	−0.206473	−	0.112743i
$923$	82.2274	+	5.88102i	2.70655	+	0.193576i
$924$	0.00574375	+	0.00893744i	0.000188955	+	0.000294020i
$925$	0.872627	−	12.4878i	0.0286918	−	0.410598i
$926$	26.5088	+	17.0362i	0.871133	+	0.559843i
$927$	2.54333	+	6.81893i	0.0835339	+	0.223963i
$928$	0.493609	+	6.90155i	0.0162035	+	0.226554i
$929$	35.3977	+	5.08942i	1.16136	+	0.166979i	0.695933	−	0.718107i	$-0.254991\pi$
$929$	35.3977	+	5.08942i	1.16136	+	0.166979i	0.465428	+	0.885086i	$0.345900\pi$
$930$	4.10136	+	0.289965i	0.134489	+	0.00950833i
$931$	9.24752	−	31.4942i	0.303075	−	1.03218i
$932$	5.88252	+	10.7730i	0.192688	+	0.352882i
$933$	−8.53674	−	3.18404i	−0.279480	−	0.104241i
$934$	−2.59518	+	18.0499i	−0.0849169	+	0.590610i
$935$	−0.0138870	+	0.0304742i	−0.000454154	+	0.000996613i
$936$	−2.37098	+	5.19172i	−0.0774979	+	0.169697i
$937$	59.7443	−	12.9966i	1.95176	−	0.424580i	0.965062	−	0.262022i	$-0.0843894\pi$
$937$	59.7443	−	12.9966i	1.95176	−	0.424580i	0.986699	−	0.162557i	$-0.0519743\pi$
$938$	−5.10314	−	3.82016i	−0.166623	−	0.124733i
$939$	9.01985	−	5.79671i	0.294352	−	0.189168i
$940$	0.739254	−	1.15237i	0.0241118	−	0.0375862i
$941$	7.56525	+	25.7649i	0.246620	+	0.839911i	0.986018	+	0.166641i	$0.0532923\pi$
$941$	7.56525	+	25.7649i	0.246620	+	0.839911i	−0.739398	+	0.673269i	$0.764890\pi$
$942$	15.3798	−	15.3798i	0.501100	−	0.501100i
$943$	20.9215	+	4.67742i	0.681299	+	0.152318i
$944$		−	4.38749i		−	0.142801i
$945$	0.608341	−	2.80755i	0.0197893	−	0.0913295i
$946$	0.0342751	+	0.0395556i	0.00111438	+	0.00128606i
$947$	4.99762	+	1.08717i	0.162401	+	0.0353281i	0.293030	−	0.956103i	$-0.405336\pi$
$947$	4.99762	+	1.08717i	0.162401	+	0.0353281i	−0.130630	+	0.991431i	$0.541700\pi$
$948$	−8.00549	+	10.6941i	−0.260006	+	0.347328i
$949$	−41.0704	+	63.9068i	−1.33320	+	2.07450i
$950$	24.5900	+	18.3452i	0.797804	+	0.595195i
$951$	8.62242	−	9.95081i	0.279601	−	0.322677i
$952$	1.86263	−	1.39435i	0.0603682	−	0.0451911i
$953$	−1.72176	+	4.61621i	−0.0557731	+	0.149534i	−0.961848	−	0.273583i	$-0.911791\pi$
$953$	−1.72176	+	4.61621i	−0.0557731	+	0.149534i	0.906075	+	0.423117i	$0.139064\pi$
$954$	−12.0664	−	3.54301i	−0.390664	−	0.114709i
$955$	−3.26363	−	3.25830i	−0.105609	−	0.105436i
$956$	−1.98764	−	4.35233i	−0.0642849	−	0.140764i
$957$	0.0342897	+	0.0458057i	0.00110843	+	0.00148069i
$958$	7.18365	−	0.513785i	0.232093	−	0.0165996i
$959$	−17.3599	−	7.92798i	−0.560579	−	0.256008i
$960$	−2.14601	−	0.628219i	−0.0692620	−	0.0202757i
$961$	3.93059	+	27.3378i	0.126793	+	0.881866i
$962$	3.03748	−	13.9631i	0.0979322	−	0.450187i
$963$	0.964952	−	13.4918i	0.0310951	−	0.434767i
$964$	−5.74774	+	1.68769i	−0.185122	+	0.0543568i
$965$	−4.04341	−	13.7291i	−0.130162	−	0.441955i
$966$	5.16392	+	3.36079i	0.166147	+	0.108132i
$967$	13.9933	+	13.9933i	0.449994	+	0.449994i	0.895352	−	0.445358i	$-0.146924\pi$
$967$	13.9933	+	13.9933i	0.449994	+	0.449994i	−0.445358	+	0.895352i	$0.646924\pi$
$968$	−5.27171	+	9.65441i	−0.169439	+	0.310304i
$969$	−8.39827	+	7.27714i	−0.269791	+	0.233775i
$970$	0.843028	+	11.6532i	0.0270680	+	0.374161i
$971$	40.8211	−	5.86919i	1.31001	−	0.188351i	0.548308	−	0.836277i	$-0.315272\pi$
$971$	40.8211	−	5.86919i	1.31001	−	0.188351i	0.761704	+	0.647925i	$0.224363\pi$
$972$	−0.212565	−	0.977147i	−0.00681803	−	0.0313420i
$973$	−15.6365	+	5.83210i	−0.501282	+	0.186968i
$974$	−14.7761	−	12.8035i	−0.473455	−	0.410251i
$975$	−11.8973	−	25.9392i	−0.381019	−	0.830719i
$976$	−1.40479	+	0.641546i	−0.0449662	+	0.0205354i
$977$	−19.6198	+	10.7132i	−0.627694	+	0.342747i	−0.761408	−	0.648273i	$-0.775492\pi$
$977$	−19.6198	+	10.7132i	−0.627694	+	0.342747i	0.133714	+	0.991020i	$0.457310\pi$
$978$	2.94220	−	1.60656i	0.0940811	−	0.0513721i
$979$	−0.0142451	+	0.00650554i	−0.000455277	+	0.000207918i
$980$	−9.58185	−	7.16066i	−0.306081	−	0.228739i
$981$	12.6614	+	10.9711i	0.404247	+	0.350282i
$982$	−8.76908	+	3.27070i	−0.279833	+	0.104372i
$983$	7.89419	+	36.2890i	0.251786	+	1.15744i	0.913230	+	0.407445i	$0.133580\pi$
$983$	7.89419	+	36.2890i	0.251786	+	1.15744i	−0.661444	+	0.749995i	$0.730056\pi$
$984$	4.42464	−	0.636167i	0.141052	−	0.0202802i
$985$	21.2679	−	24.5850i	0.677651	−	0.783344i
$986$	9.47045	−	8.20619i	0.301601	−	0.261338i
$987$	−0.376980	+	0.690388i	−0.0119994	+	0.0219753i
$988$	24.7630	+	24.7630i	0.787818	+	0.787818i
$989$	27.5377	+	12.7680i	0.875649	+	0.406000i
$990$	−0.0177380	+	0.00522409i	−0.000563750	+	0.000166033i
$991$	−18.8633	+	5.53877i	−0.599213	+	0.175945i	−0.567252	−	0.823544i	$-0.691993\pi$
$991$	−18.8633	+	5.53877i	−0.599213	+	0.175945i	−0.0319612	+	0.999489i	$0.510175\pi$
$992$	−0.131176	+	1.83408i	−0.00416484	+	0.0582320i
$993$	7.30421	−	33.5769i	0.231792	−	1.06553i
$994$	−2.64079	−	18.3671i	−0.0837608	−	0.582569i
$995$	−23.0269	+	12.5981i	−0.730002	+	0.399387i
$996$	2.88332	+	1.31677i	0.0913615	+	0.0417234i
$997$	−5.62920	+	0.402608i	−0.178279	+	0.0127507i	−0.160193	−	0.987086i	$-0.551212\pi$
$997$	−5.62920	+	0.402608i	−0.178279	+	0.0127507i	−0.0180855	+	0.999836i	$0.505757\pi$
$998$	−1.59614	−	2.13220i	−0.0505251	−	0.0674936i
$999$	1.04006	+	2.27741i	0.0329059	+	0.0720540i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.b.37.7	✓	240
5.3	odd	4	inner	690.2.w.b.313.7	yes	240
23.5	odd	22	inner	690.2.w.b.97.7	yes	240
115.28	even	44	inner	690.2.w.b.373.7	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.b.37.7	✓	240	1.1	even	1	trivial
690.2.w.b.97.7	yes	240	23.5	odd	22	inner
690.2.w.b.313.7	yes	240	5.3	odd	4	inner
690.2.w.b.373.7	yes	240	115.28	even	44	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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.877679 + 0.479249i) q^{2} +(-0.997452 - 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(-2.09572 - 0.779713i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(-0.448960 - 1.20371i) q^{7} +(0.0713392 + 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +O(q^{10})\)	\(q+(0.877679 + 0.479249i) q^{2} +(-0.997452 - 0.0713392i) q^{3} +(0.540641 + 0.841254i) q^{4} +(-2.09572 - 0.779713i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(-0.448960 - 1.20371i) q^{7} +(0.0713392 + 0.997452i) q^{8} +(0.989821 + 0.142315i) q^{9} +(-1.46569 - 1.68871i) q^{10} +(0.00232980 - 0.00793457i) q^{11} +(-0.479249 - 0.877679i) q^{12} +(5.34764 + 1.99457i) q^{13} +(0.182833 - 1.27163i) q^{14} +(2.03476 + 0.927233i) q^{15} +(-0.415415 + 0.909632i) q^{16} +(1.76969 - 0.384973i) q^{17} +(0.800541 + 0.599278i) q^{18} +(5.16179 - 3.31728i) q^{19} +(-0.477097 - 2.18458i) q^{20} +(0.361945 + 1.23267i) q^{21} +(0.00584745 - 0.00584745i) q^{22} +(1.70179 - 4.48374i) q^{23} -1.00000i q^{24} +(3.78410 + 3.26812i) q^{25} +(3.73761 + 4.31344i) q^{26} +(-0.977147 - 0.212565i) q^{27} +(0.769898 - 1.02846i) q^{28} +(3.74079 - 5.82078i) q^{29} +(1.34149 + 1.78897i) q^{30} +(1.20413 - 1.38964i) q^{31} +(-0.800541 + 0.599278i) q^{32} +(-0.00288991 + 0.00774814i) q^{33} +(1.73772 + 0.510241i) q^{34} +(0.00234851 + 2.87270i) q^{35} +(0.415415 + 0.909632i) q^{36} +(-1.50039 - 2.00428i) q^{37} +(6.12020 - 0.437725i) q^{38} +(-5.19172 - 2.37098i) q^{39} +(0.628219 - 2.14601i) q^{40} +(0.636167 + 4.42464i) q^{41} +(-0.273085 + 1.25535i) q^{42} +(-0.451519 + 6.31307i) q^{43} +(0.00793457 - 0.00232980i) q^{44} +(-1.96343 - 1.07003i) q^{45} +(3.64246 - 3.11970i) q^{46} +(0.432950 + 0.432950i) q^{47} +(0.479249 - 0.877679i) q^{48} +(4.04290 - 3.50319i) q^{49} +(1.75498 + 4.68189i) q^{50} +(-1.79265 + 0.257744i) q^{51} +(1.21322 + 5.57706i) q^{52} +(-11.7829 + 4.39479i) q^{53} +(-0.755750 - 0.654861i) q^{54} +(-0.0110693 + 0.0148121i) q^{55} +(1.16861 - 0.533688i) q^{56} +(-5.38529 + 2.94059i) q^{57} +(6.07282 - 3.31601i) q^{58} +(-3.99100 + 1.82263i) q^{59} +(0.320035 + 2.21305i) q^{60} +(1.16714 + 1.01133i) q^{61} +(1.72283 - 0.642582i) q^{62} +(-0.273085 - 1.25535i) q^{63} +(-0.989821 + 0.142315i) q^{64} +(-9.65197 - 8.34967i) q^{65} +(-0.00624970 + 0.00541540i) q^{66} +(2.37799 - 4.35496i) q^{67} +(1.28063 + 1.28063i) q^{68} +(-2.01732 + 4.35091i) q^{69} +(-1.37468 + 2.52243i) q^{70} +(13.8586 - 4.06927i) q^{71} +(-0.0713392 + 0.997452i) q^{72} +(-2.82922 + 13.0057i) q^{73} +(-0.356308 - 2.47817i) q^{74} +(-3.54131 - 3.52975i) q^{75} +(5.58135 + 2.54892i) q^{76} +(-0.0105969 + 0.000757905i) q^{77} +(-3.42037 - 4.56909i) q^{78} +(-5.54935 - 12.1514i) q^{79} +(1.57985 - 1.58243i) q^{80} +(0.959493 + 0.281733i) q^{81} +(-1.56215 + 4.18829i) q^{82} +(-2.53753 + 1.89957i) q^{83} +(-0.841306 + 0.970919i) q^{84} +(-4.00895 - 0.573056i) q^{85} +(-3.42182 + 5.32446i) q^{86} +(-4.14651 + 5.53909i) q^{87} +(0.00808056 + 0.00175782i) q^{88} +(-1.24013 - 1.43119i) q^{89} +(-1.21045 - 1.88011i) q^{90} -7.33247i q^{91} +(4.69202 - 0.992450i) q^{92} +(-1.30020 + 1.30020i) q^{93} +(0.172500 + 0.587482i) q^{94} +(-13.4042 + 2.92738i) q^{95} +(0.841254 - 0.540641i) q^{96} +(-4.18289 - 3.13127i) q^{97} +(5.22727 - 1.13712i) q^{98} +(0.00343529 - 0.00752224i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{6}+O(q^{10}) \) 240 * q + 24 * q^6	\( 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) \) 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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