LMFDB - Embedded newform 966.2.be.b.19.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(19,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 55, 45]))

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

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

chi := DirichletCharacter("966.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.be (of order $66$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			19.16
Character	$\chi$	$=$	966.19
Dual form			966.2.be.b.661.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.995472 - 0.0950560i) q^{2} +(0.690079 - 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(3.91984 - 2.02082i) q^{5} +(-0.755750 + 0.654861i) q^{6} +(-0.423103 + 2.61170i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +O(q^{10})$	\(q+(-0.995472 - 0.0950560i) q^{2} +(0.690079 - 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(3.91984 - 2.02082i) q^{5} +(-0.755750 + 0.654861i) q^{6} +(-0.423103 + 2.61170i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +(-4.09418 + 1.63906i) q^{10} +(-0.326534 - 3.41962i) q^{11} +(0.814576 - 0.580057i) q^{12} +(-3.96910 - 0.570670i) q^{13} +(0.669445 - 2.55966i) q^{14} +(1.24246 - 4.23144i) q^{15} +(0.928368 + 0.371662i) q^{16} +(0.545432 - 1.57592i) q^{17} +(-0.0475819 + 0.998867i) q^{18} +(-0.748112 - 2.16153i) q^{19} +(4.23144 - 1.24246i) q^{20} +(1.59820 + 2.10849i) q^{21} +3.43518i q^{22} +(-1.18504 - 4.64711i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(8.38114 - 11.7697i) q^{25} +(3.89688 + 0.945373i) q^{26} +(-0.755750 - 0.654861i) q^{27} +(-0.909725 + 2.48443i) q^{28} +(-1.26614 - 1.46121i) q^{29} +(-1.63906 + 4.09418i) q^{30} +(-1.05243 + 0.255318i) q^{31} +(-0.888835 - 0.458227i) q^{32} +(-2.70023 - 2.12349i) q^{33} +(-0.692763 + 1.51694i) q^{34} +(3.61928 + 11.0925i) q^{35} +(0.142315 - 0.989821i) q^{36} +(4.64698 - 0.221363i) q^{37} +(0.539259 + 2.22285i) q^{38} +(-3.15200 + 2.47876i) q^{39} +(-4.33039 + 0.834614i) q^{40} +(-0.125153 + 0.194742i) q^{41} +(-1.39054 - 2.25087i) q^{42} +(1.46062 + 4.97441i) q^{43} +(0.326534 - 3.41962i) q^{44} +(-2.20504 - 3.81924i) q^{45} +(0.737943 + 4.73872i) q^{46} +(10.0857 + 5.82299i) q^{47} +(0.909632 - 0.415415i) q^{48} +(-6.64197 - 2.21004i) q^{49} +(-9.46197 + 10.9197i) q^{50} +(-0.764157 - 1.48226i) q^{51} +(-3.78937 - 1.31151i) q^{52} +(7.68164 + 9.76800i) q^{53} +(0.690079 + 0.723734i) q^{54} +(-8.19039 - 12.7445i) q^{55} +(1.14177 - 2.38671i) q^{56} +(-2.08063 - 0.950191i) q^{57} +(1.12151 + 1.57495i) q^{58} +(2.01698 + 5.03818i) q^{59} +(2.02082 - 3.91984i) q^{60} +(5.04310 - 4.80859i) q^{61} +(1.07194 - 0.154121i) q^{62} +(2.62888 + 0.298354i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-16.7114 + 5.78389i) q^{65} +(2.48615 + 2.37054i) q^{66} +(-4.90798 - 3.49496i) q^{67} +(0.833820 - 1.44422i) q^{68} +(-4.18105 - 2.34922i) q^{69} +(-2.54848 - 11.3863i) q^{70} +(0.135164 + 0.295967i) q^{71} +(-0.235759 + 0.971812i) q^{72} +(0.840575 - 4.36131i) q^{73} +(-4.64698 - 0.221363i) q^{74} +(-2.73446 - 14.1877i) q^{75} +(-0.325521 - 2.26405i) q^{76} +(9.06919 + 0.594042i) q^{77} +(3.37335 - 2.16792i) q^{78} +(-5.27795 + 6.71146i) q^{79} +(4.39011 - 0.419205i) q^{80} +(-0.995472 + 0.0950560i) q^{81} +(0.143097 - 0.181963i) q^{82} +(-9.97824 + 6.41263i) q^{83} +(1.17029 + 2.37285i) q^{84} +(-1.04664 - 7.27957i) q^{85} +(-0.981157 - 5.09073i) q^{86} +(-1.93127 - 0.0919975i) q^{87} +(-0.650111 + 3.37310i) q^{88} +(1.38050 - 5.69050i) q^{89} +(1.83201 + 4.01155i) q^{90} +(3.16976 - 10.1246i) q^{91} +(-0.284158 - 4.78741i) q^{92} +(-0.541481 + 0.937872i) q^{93} +(-9.48653 - 6.75533i) q^{94} +(-7.30053 - 6.96104i) q^{95} +(-0.945001 + 0.327068i) q^{96} +(7.46673 + 4.79858i) q^{97} +(6.40182 + 2.83139i) q^{98} +(-3.40021 + 0.488877i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9}+O(q^{10}) $ 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9	$ 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9} + 22 q^{14} + 16 q^{16} - 66 q^{17} - 16 q^{18} + 36 q^{23} + 24 q^{25} + 12 q^{26} + 44 q^{28} + 8 q^{29} - 48 q^{31} + 16 q^{32} - 46 q^{35} + 32 q^{36} - 22 q^{37} + 66 q^{38} + 8 q^{39} + 176 q^{43} - 8 q^{46} + 120 q^{47} - 24 q^{49} - 48 q^{50} - 22 q^{51} - 12 q^{52} - 44 q^{53} + 44 q^{57} + 18 q^{58} + 12 q^{59} - 32 q^{64} - 108 q^{70} - 48 q^{71} - 16 q^{72} + 252 q^{73} + 22 q^{74} - 36 q^{75} - 42 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 12 q^{82} - 22 q^{84} - 76 q^{85} + 22 q^{86} + 24 q^{87} - 22 q^{88} + 16 q^{92} + 12 q^{94} + 26 q^{95} + 2 q^{98} + 88 q^{99}+O(q^{100}) $ 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9 + 22 * q^14 + 16 * q^16 - 66 * q^17 - 16 * q^18 + 36 * q^23 + 24 * q^25 + 12 * q^26 + 44 * q^28 + 8 * q^29 - 48 * q^31 + 16 * q^32 - 46 * q^35 + 32 * q^36 - 22 * q^37 + 66 * q^38 + 8 * q^39 + 176 * q^43 - 8 * q^46 + 120 * q^47 - 24 * q^49 - 48 * q^50 - 22 * q^51 - 12 * q^52 - 44 * q^53 + 44 * q^57 + 18 * q^58 + 12 * q^59 - 32 * q^64 - 108 * q^70 - 48 * q^71 - 16 * q^72 + 252 * q^73 + 22 * q^74 - 36 * q^75 - 42 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 12 * q^82 - 22 * q^84 - 76 * q^85 + 22 * q^86 + 24 * q^87 - 22 * q^88 + 16 * q^92 + 12 * q^94 + 26 * q^95 + 2 * q^98 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{15}{22}\right)$

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 $

$2$	−0.995472	−	0.0950560i	−0.703905	−	0.0672148i
$2$	−0.995472	−	0.0950560i	−0.703905	−	0.0672148i
$3$	0.690079	−	0.723734i	0.398417	−	0.417848i
$3$	0.690079	−	0.723734i	0.398417	−	0.417848i
$4$	0.981929	+	0.189251i	0.490964	+	0.0946256i
$5$	3.91984	−	2.02082i	1.75300	−	0.903737i	0.800433	−	0.599422i	$-0.204603\pi$
$5$	3.91984	−	2.02082i	1.75300	−	0.903737i	0.952571	−	0.304315i	$-0.0984276\pi$
$6$	−0.755750	+	0.654861i	−0.308533	+	0.267346i
$7$	−0.423103	+	2.61170i	−0.159918	+	0.987130i
$7$	−0.423103	+	2.61170i	−0.159918	+	0.987130i
$8$	−0.959493	−	0.281733i	−0.339232	−	0.0996075i
$9$	−0.0475819	−	0.998867i	−0.0158606	−	0.332956i
$10$	−4.09418	+	1.63906i	−1.29469	+	0.518317i
$11$	−0.326534	−	3.41962i	−0.0984538	−	1.03105i	−0.900811	−	0.434211i	$-0.857027\pi$
$11$	−0.326534	−	3.41962i	−0.0984538	−	1.03105i	0.802357	−	0.596844i	$-0.203579\pi$
$12$	0.814576	−	0.580057i	0.235148	−	0.167448i
$13$	−3.96910	−	0.570670i	−1.10083	−	0.158275i	−0.432132	−	0.901810i	$-0.642239\pi$
$13$	−3.96910	−	0.570670i	−1.10083	−	0.158275i	−0.668697	+	0.743535i	$0.733148\pi$
$14$	0.669445	−	2.55966i	0.178917	−	0.684097i
$15$	1.24246	−	4.23144i	0.320803	−	1.09255i
$16$	0.928368	+	0.371662i	0.232092	+	0.0929156i
$17$	0.545432	−	1.57592i	0.132287	−	0.382217i	−0.859332	−	0.511419i	$-0.829120\pi$
$17$	0.545432	−	1.57592i	0.132287	−	0.382217i	0.991618	+	0.129202i	$0.0412414\pi$
$18$	−0.0475819	+	0.998867i	−0.0112152	+	0.235435i
$19$	−0.748112	−	2.16153i	−0.171629	−	0.495889i	0.826079	−	0.563554i	$-0.190566\pi$
$19$	−0.748112	−	2.16153i	−0.171629	−	0.495889i	−0.997708	+	0.0676651i	$0.978445\pi$
$20$	4.23144	−	1.24246i	0.946180	−	0.277823i
$21$	1.59820	+	2.10849i	0.348756	+	0.460111i
$22$			3.43518i			0.732382i
$23$	−1.18504	−	4.64711i	−0.247099	−	0.968990i
$23$	−1.18504	−	4.64711i	−0.247099	−	0.968990i
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	8.38114	−	11.7697i	1.67623	−	2.35393i
$26$	3.89688	+	0.945373i	0.764241	+	0.185403i
$27$	−0.755750	−	0.654861i	−0.145444	−	0.126028i
$28$	−0.909725	+	2.48443i	−0.171922	+	0.469513i
$29$	−1.26614	−	1.46121i	−0.235117	−	0.271340i	0.625914	−	0.779892i	$-0.284726\pi$
$29$	−1.26614	−	1.46121i	−0.235117	−	0.271340i	−0.861031	+	0.508553i	$0.830181\pi$
$30$	−1.63906	+	4.09418i	−0.299250	+	0.747491i
$31$	−1.05243	+	0.255318i	−0.189023	+	0.0458564i	−0.329153	−	0.944277i	$-0.606763\pi$
$31$	−1.05243	+	0.255318i	−0.189023	+	0.0458564i	0.140130	+	0.990133i	$0.455248\pi$
$32$	−0.888835	−	0.458227i	−0.157125	−	0.0810038i
$33$	−2.70023	−	2.12349i	−0.470050	−	0.369651i
$34$	−0.692763	+	1.51694i	−0.118808	+	0.260153i
$35$	3.61928	+	11.0925i	0.611769	+	1.87497i
$36$	0.142315	−	0.989821i	0.0237191	−	0.164970i
$37$	4.64698	−	0.221363i	0.763958	−	0.0363918i	0.338014	−	0.941141i	$-0.390245\pi$
$37$	4.64698	−	0.221363i	0.763958	−	0.0363918i	0.425944	+	0.904749i	$0.359942\pi$
$38$	0.539259	+	2.22285i	0.0874793	+	0.360595i
$39$	−3.15200	+	2.47876i	−0.504725	+	0.396920i
$40$	−4.33039	+	0.834614i	−0.684694	+	0.131964i
$41$	−0.125153	+	0.194742i	−0.0195456	+	0.0304135i	−0.850889	−	0.525346i	$-0.823936\pi$
$41$	−0.125153	+	0.194742i	−0.0195456	+	0.0304135i	0.831343	+	0.555759i	$0.187572\pi$
$42$	−1.39054	−	2.25087i	−0.214565	−	0.347316i
$43$	1.46062	+	4.97441i	0.222742	+	0.758591i	0.992712	+	0.120510i	$0.0384531\pi$
$43$	1.46062	+	4.97441i	0.222742	+	0.758591i	−0.769970	+	0.638080i	$0.779729\pi$
$44$	0.326534	−	3.41962i	0.0492269	−	0.515527i
$45$	−2.20504	−	3.81924i	−0.328708	−	0.569339i
$46$	0.737943	+	4.73872i	0.108804	+	0.698686i
$47$	10.0857	+	5.82299i	1.47115	+	0.849370i	0.999475	−	0.0324017i	$-0.0103156\pi$
$47$	10.0857	+	5.82299i	1.47115	+	0.849370i	0.471677	+	0.881772i	$0.343649\pi$
$48$	0.909632	−	0.415415i	0.131294	−	0.0599600i
$49$	−6.64197	−	2.21004i	−0.948853	−	0.315720i
$50$	−9.46197	+	10.9197i	−1.33812	+	1.54428i
$51$	−0.764157	−	1.48226i	−0.107003	−	0.207558i
$52$	−3.78937	−	1.31151i	−0.525491	−	0.181874i
$53$	7.68164	+	9.76800i	1.05515	+	1.34174i	0.937229	+	0.348715i	$0.113382\pi$
$53$	7.68164	+	9.76800i	1.05515	+	1.34174i	0.117925	+	0.993022i	$0.462376\pi$
$54$	0.690079	+	0.723734i	0.0939079	+	0.0984877i
$55$	−8.19039	−	12.7445i	−1.10439	−	1.71847i
$56$	1.14177	−	2.38671i	0.152575	−	0.318937i
$57$	−2.08063	−	0.950191i	−0.275586	−	0.125856i
$58$	1.12151	+	1.57495i	0.147262	+	0.206801i
$59$	2.01698	+	5.03818i	0.262589	+	0.655915i	0.999805	−	0.0197416i	$-0.00628436\pi$
$59$	2.01698	+	5.03818i	0.262589	+	0.655915i	−0.737216	+	0.675657i	$0.763860\pi$
$60$	2.02082	−	3.91984i	0.260886	−	0.506049i
$61$	5.04310	−	4.80859i	0.645703	−	0.615676i	−0.294761	−	0.955571i	$-0.595240\pi$
$61$	5.04310	−	4.80859i	0.645703	−	0.615676i	0.940463	+	0.339895i	$0.110391\pi$
$62$	1.07194	−	0.154121i	0.136136	−	0.0195734i
$63$	2.62888	+	0.298354i	0.331207	+	0.0375891i
$64$	0.841254	+	0.540641i	0.105157	+	0.0675801i
$65$	−16.7114	+	5.78389i	−2.07280	+	0.717403i
$66$	2.48615	+	2.37054i	0.306024	+	0.291794i
$67$	−4.90798	−	3.49496i	−0.599606	−	0.426977i	0.239538	−	0.970887i	$-0.423004\pi$
$67$	−4.90798	−	3.49496i	−0.599606	−	0.426977i	−0.839144	+	0.543910i	$0.816943\pi$
$68$	0.833820	−	1.44422i	0.101116	−	0.175137i
$69$	−4.18105	−	2.34922i	−0.503339	−	0.282813i
$70$	−2.54848	−	11.3863i	−0.304602	−	1.36092i
$71$	0.135164	+	0.295967i	0.0160410	+	0.0351249i	0.917483	−	0.397775i	$-0.130218\pi$
$71$	0.135164	+	0.295967i	0.0160410	+	0.0351249i	−0.901442	+	0.432900i	$0.857490\pi$
$72$	−0.235759	+	0.971812i	−0.0277845	+	0.114529i
$73$	0.840575	−	4.36131i	0.0983818	−	0.510453i	−0.898988	−	0.437973i	$-0.855696\pi$
$73$	0.840575	−	4.36131i	0.0983818	−	0.510453i	0.997370	−	0.0724801i	$-0.0230914\pi$
$74$	−4.64698	−	0.221363i	−0.540200	−	0.0257329i
$75$	−2.73446	−	14.1877i	−0.315748	−	1.63826i
$76$	−0.325521	−	2.26405i	−0.0373398	−	0.259704i
$77$	9.06919	+	0.594042i	1.03353	+	0.0676974i
$78$	3.37335	−	2.16792i	0.381957	−	0.245469i
$79$	−5.27795	+	6.71146i	−0.593816	+	0.755098i	−0.986354	−	0.164637i	$-0.947355\pi$
$79$	−5.27795	+	6.71146i	−0.593816	+	0.755098i	0.392538	+	0.919736i	$0.371597\pi$
$80$	4.39011	−	0.419205i	0.490830	−	0.0468685i
$81$	−0.995472	+	0.0950560i	−0.110608	+	0.0105618i
$82$	0.143097	−	0.181963i	0.0158025	−	0.0200945i
$83$	−9.97824	+	6.41263i	−1.09525	+	0.703877i	−0.958032	−	0.286663i	$-0.907454\pi$
$83$	−9.97824	+	6.41263i	−1.09525	+	0.703877i	−0.137223	+	0.990540i	$0.543818\pi$
$84$	1.17029	+	2.37285i	0.127689	+	0.258899i
$85$	−1.04664	−	7.27957i	−0.113525	−	0.789581i
$86$	−0.981157	−	5.09073i	−0.105801	−	0.548947i
$87$	−1.93127	−	0.0919975i	−0.207053	−	0.00986317i
$88$	−0.650111	+	3.37310i	−0.0693021	+	0.359573i
$89$	1.38050	−	5.69050i	0.146333	−	0.603191i	−0.850661	−	0.525714i	$-0.823798\pi$
$89$	1.38050	−	5.69050i	0.146333	−	0.603191i	0.996994	−	0.0774775i	$-0.0246866\pi$
$90$	1.83201	+	4.01155i	0.193111	+	0.422855i
$91$	3.16976	−	10.1246i	0.332281	−	1.06135i
$92$	−0.284158	−	4.78741i	−0.0296255	−	0.499122i
$93$	−0.541481	+	0.937872i	−0.0561489	+	0.0972528i
$94$	−9.48653	−	6.75533i	−0.978461	−	0.696759i
$95$	−7.30053	−	6.96104i	−0.749019	−	0.714188i
$96$	−0.945001	+	0.327068i	−0.0964487	+	0.0333812i
$97$	7.46673	+	4.79858i	0.758132	+	0.487222i	0.861711	−	0.507399i	$-0.169393\pi$
$97$	7.46673	+	4.79858i	0.758132	+	0.487222i	−0.103579	+	0.994621i	$0.533030\pi$
$98$	6.40182	+	2.83139i	0.646681	+	0.286013i
$99$	−3.40021	+	0.488877i	−0.341734	+	0.0491339i
$100$	10.4571	−	9.97083i	1.04571	−	0.997083i
$101$	5.22045	−	10.1263i	0.519454	−	1.00760i	−0.472539	−	0.881310i	$-0.656662\pi$
$101$	5.22045	−	10.1263i	0.519454	−	1.00760i	0.991993	−	0.126291i	$-0.0403072\pi$
$102$	0.619799	+	1.54818i	0.0613693	+	0.153293i
$103$	3.72396	+	5.22956i	0.366932	+	0.515284i	0.956224	−	0.292636i	$-0.0945325\pi$
$103$	3.72396	+	5.22956i	0.366932	+	0.515284i	−0.589292	+	0.807920i	$0.700593\pi$
$104$	3.64755	+	1.66578i	0.357671	+	0.163343i
$105$	10.5256	+	5.03528i	1.02719	+	0.491393i
$106$	−6.71835	−	10.4540i	−0.652544	−	1.01538i
$107$	5.61341	+	5.88718i	0.542669	+	0.569135i	0.936776	−	0.349930i	$-0.113795\pi$
$107$	5.61341	+	5.88718i	0.542669	+	0.569135i	−0.394107	+	0.919065i	$0.628946\pi$
$108$	−0.618159	−	0.786053i	−0.0594824	−	0.0756380i
$109$	9.48893	+	3.28415i	0.908875	+	0.314565i	0.741205	−	0.671278i	$-0.234255\pi$
$109$	9.48893	+	3.28415i	0.908875	+	0.314565i	0.167670	+	0.985843i	$0.446376\pi$
$110$	6.94186	+	13.4653i	0.661881	+	1.28387i
$111$	3.04657	−	3.51593i	0.289168	−	0.333717i
$112$	−1.36347	+	2.26737i	−0.128835	+	0.214246i
$113$	19.1050	−	8.72497i	1.79725	−	0.820777i	0.834196	−	0.551468i	$-0.185932\pi$
$113$	19.1050	−	8.72497i	1.79725	−	0.820777i	0.963054	−	0.269308i	$-0.0867951\pi$
$114$	1.98089	+	1.14367i	0.185527	+	0.107114i
$115$	−14.0362	−	15.8212i	−1.30888	−	1.47533i
$116$	−0.966728	−	1.67442i	−0.0897584	−	0.155466i
$117$	−0.381167	+	3.99176i	−0.0352389	+	0.369038i
$118$	−1.52894	−	5.20709i	−0.140750	−	0.479352i
$119$	3.88506	+	2.09128i	0.356143	+	0.191707i
$120$	−2.38427	+	3.71000i	−0.217653	+	0.338675i
$121$	−0.785971	+	0.151484i	−0.0714519	+	0.0137712i
$122$	−5.47735	+	4.30743i	−0.495896	+	0.389977i
$123$	0.0545758	+	0.224964i	0.00492093	+	0.0202844i
$124$	−1.08173	+	0.0515294i	−0.0971426	+	0.00462747i
$125$	5.93028	−	41.2460i	0.530420	−	3.68915i
$126$	−2.58861	−	0.546893i	−0.230612	−	0.0487211i
$127$	−3.98215	+	8.71970i	−0.353359	+	0.773748i	0.646582	+	0.762845i	$0.276198\pi$
$127$	−3.98215	+	8.71970i	−0.353359	+	0.773748i	−0.999941	+	0.0109033i	$0.996529\pi$
$128$	−0.786053	−	0.618159i	−0.0694779	−	0.0546381i
$129$	4.60809	+	2.37564i	0.405720	+	0.209163i
$130$	17.1856	−	4.16917i	1.50727	−	0.365661i
$131$	−5.24874	+	13.1107i	−0.458585	+	1.14549i	0.501344	+	0.865248i	$0.332839\pi$
$131$	−5.24874	+	13.1107i	−0.458585	+	1.14549i	−0.959929	+	0.280242i	$0.909585\pi$
$132$	−2.24956	−	2.59613i	−0.195799	−	0.225964i
$133$	5.96180	−	1.03930i	0.516953	−	0.0901185i
$134$	4.55354	+	3.94567i	0.393366	+	0.340854i
$135$	−4.28577	−	1.03972i	−0.368860	−	0.0894845i
$136$	−0.967326	+	1.35842i	−0.0829475	+	0.116484i
$137$	−16.4537	+	9.49952i	−1.40573	+	0.811599i	−0.994973	−	0.100146i	$-0.968069\pi$
$137$	−16.4537	+	9.49952i	−1.40573	+	0.811599i	−0.410757	+	0.911745i	$0.634736\pi$
$138$	3.93881	+	2.73602i	0.335294	+	0.232905i
$139$		−	8.79251i		−	0.745771i	−0.927877	−	0.372886i	$-0.878368\pi$
$139$		−	8.79251i		−	0.745771i	0.927877	−	0.372886i	$-0.121632\pi$
$140$	1.45461	+	11.5770i	0.122937	+	0.978431i
$141$	11.1742	−	3.28105i	0.941040	−	0.276314i
$142$	−0.106418	−	0.307475i	−0.00893042	−	0.0258028i
$143$	−0.655429	+	13.7592i	−0.0548098	+	1.15060i
$144$	0.327068	−	0.945001i	0.0272557	−	0.0787501i
$145$	−7.91591	−	3.16905i	−0.657381	−	0.263176i
$146$	−1.25134	+	4.26166i	−0.103561	+	0.352698i
$147$	−6.18296	+	3.28192i	−0.509962	+	0.270688i
$148$	4.60489	+	0.662083i	0.378520	+	0.0544229i
$149$	−15.3691	+	10.9443i	−1.25909	+	0.896594i	−0.997643	−	0.0686243i	$-0.978139\pi$
$149$	−15.3691	+	10.9443i	−1.25909	+	0.896594i	−0.261447	+	0.965218i	$0.584200\pi$
$150$	1.37345	+	14.3834i	0.112142	+	1.17440i
$151$	−12.5948	+	5.04221i	−1.02495	+	0.410329i	−0.822380	−	0.568938i	$-0.807354\pi$
$151$	−12.5948	+	5.04221i	−1.02495	+	0.410329i	−0.202572	+	0.979267i	$0.564930\pi$
$152$	0.108836	+	2.28474i	0.00882773	+	0.185317i
$153$	−1.60009	−	0.469828i	−0.129360	−	0.0379834i
$154$	−8.97165	−	1.45343i	−0.722957	−	0.117121i
$155$	−3.60942	+	3.12758i	−0.289916	+	0.251213i
$156$	−3.56415	+	1.83745i	−0.285361	+	0.147114i
$157$	−7.24766	−	1.39687i	−0.578426	−	0.111482i	−0.108357	−	0.994112i	$-0.534559\pi$
$157$	−7.24766	−	1.39687i	−0.578426	−	0.111482i	−0.470069	+	0.882630i	$0.655771\pi$
$158$	5.89202	−	6.17937i	0.468744	−	0.491604i
$159$	12.3704	+	1.18123i	0.981034	+	0.0936774i
$160$	−4.41008			−0.348648
$161$	12.6383	−	1.12878i	0.996035	−	0.0889600i
$162$	1.00000			0.0785674
$163$	−18.1820	−	1.73617i	−1.42413	−	0.135988i	−0.645637	−	0.763644i	$-0.723408\pi$
$163$	−18.1820	−	1.73617i	−1.42413	−	0.135988i	−0.778490	+	0.627656i	$0.784014\pi$
$164$	−0.159746	+	0.167537i	−0.0124741	+	0.0130824i
$165$	−14.8756	−	2.86705i	−1.15807	−	0.223199i
$166$	10.5426	−	5.43510i	0.818266	−	0.421845i
$167$	17.1783	−	14.8851i	1.32930	−	1.15184i	0.352948	−	0.935643i	$-0.385179\pi$
$167$	17.1783	−	14.8851i	1.32930	−	1.15184i	0.976349	−	0.216200i	$-0.0693663\pi$
$168$	−0.939433	−	2.47335i	−0.0724788	−	0.190823i
$169$	2.95467	+	0.867569i	0.227282	+	0.0667361i
$170$	0.349938	+	7.34610i	0.0268390	+	0.563420i
$171$	−2.12348	+	0.850115i	−0.162387	+	0.0650099i
$172$	0.492810	+	5.16094i	0.0375764	+	0.393518i
$173$	−20.6611	+	14.7127i	−1.57083	+	1.11859i	−0.631606	+	0.775289i	$0.717604\pi$
$173$	−20.6611	+	14.7127i	−1.57083	+	1.11859i	−0.939227	+	0.343296i	$0.888457\pi$
$174$	1.91378	+	0.275159i	0.145083	+	0.0208598i
$175$	27.1928	+	26.8688i	2.05558	+	2.03109i
$176$	0.967801	−	3.29603i	0.0729507	−	0.248447i
$177$	5.03818	+	2.01698i	0.378693	+	0.151606i
$178$	−1.91516	+	5.53351i	−0.143548	+	0.414754i
$179$	−0.147036	+	3.08668i	−0.0109900	+	0.230709i	0.986689	+	0.162618i	$0.0519938\pi$
$179$	−0.147036	+	3.08668i	−0.0109900	+	0.230709i	−0.997679	+	0.0680909i	$0.978309\pi$
$180$	−1.44240	−	4.16753i	−0.107510	−	0.310629i
$181$	−1.80134	+	0.528921i	−0.133893	+	0.0393144i	−0.347992	−	0.937497i	$-0.613136\pi$
$181$	−1.80134	+	0.528921i	−0.133893	+	0.0393144i	0.214100	+	0.976812i	$0.431318\pi$
$182$	−4.11781	+	9.77750i	−0.305233	+	0.724756i
$183$		−	6.96817i		−	0.515102i
$184$	−0.172201	+	4.79274i	−0.0126948	+	0.353325i
$185$	17.7681	−	10.2584i	1.30633	−	0.754212i
$186$	0.628179	−	0.882154i	0.0460603	−	0.0646827i
$187$	−5.56716	−	1.35058i	−0.407111	−	0.0987640i
$188$	8.80144	+	7.62649i	0.641911	+	0.556219i
$189$	2.03006	−	1.69672i	0.147665	−	0.123418i
$190$	6.60579	+	7.62348i	0.479234	+	0.553066i
$191$	−4.82403	+	12.0498i	−0.349054	+	0.871896i	0.645117	+	0.764084i	$0.276809\pi$
$191$	−4.82403	+	12.0498i	−0.349054	+	0.871896i	−0.994171	+	0.107812i	$0.965616\pi$
$192$	0.971812	−	0.235759i	0.0701345	−	0.0170144i
$193$	0.0720661	+	0.0371527i	0.00518743	+	0.00267431i	0.460818	−	0.887495i	$-0.347556\pi$
$193$	0.0720661	+	0.0371527i	0.00518743	+	0.00267431i	−0.455631	+	0.890169i	$0.650586\pi$
$194$	−6.97679	−	5.48661i	−0.500904	−	0.393915i
$195$	−7.34622	+	16.0860i	−0.526074	+	1.15194i
$196$	−6.10369	−	3.42710i	−0.435978	−	0.244793i
$197$	1.99650	−	13.8860i	0.142245	−	0.989333i	−0.786229	−	0.617935i	$-0.787969\pi$
$197$	1.99650	−	13.8860i	0.142245	−	0.989333i	0.928474	−	0.371398i	$-0.121121\pi$
$198$	3.43129	−	0.163452i	0.243851	−	0.0116160i
$199$	3.00007	+	12.3665i	0.212670	+	0.876636i	0.973684	+	0.227901i	$0.0731863\pi$
$199$	3.00007	+	12.3665i	0.212670	+	0.876636i	−0.761015	+	0.648735i	$0.775299\pi$
$200$	−11.3575	+	8.93167i	−0.803100	+	0.631565i
$201$	−5.91632	+	1.14028i	−0.417305	+	0.0804289i
$202$	−6.15937	+	9.58417i	−0.433372	+	0.674340i
$203$	4.35195	−	2.68855i	0.305447	−	0.188699i
$204$	−0.469828	−	1.60009i	−0.0328946	−	0.112029i
$205$	−0.0970416	+	1.01627i	−0.00677768	+	0.0709791i
$206$	−3.20999	−	5.55987i	−0.223651	−	0.387374i
$207$	−4.58546	+	1.40482i	−0.318712	+	0.0976418i
$208$	−3.47269	−	2.00496i	−0.240788	−	0.139019i
$209$	−7.14733	+	3.26407i	−0.494391	+	0.225781i
$210$	−9.99928	−	6.01300i	−0.690016	−	0.414936i
$211$	−7.34930	+	8.48154i	−0.505946	+	0.583893i	−0.950056	−	0.312079i	$-0.898975\pi$
$211$	−7.34930	+	8.48154i	−0.505946	+	0.583893i	0.444110	+	0.895972i	$0.353520\pi$
$212$	5.69421	+	11.0452i	0.391080	+	0.758590i
$213$	0.307475	+	0.106418i	0.0210679	+	0.00729166i
$214$	−5.02838	−	6.39411i	−0.343733	−	0.437092i
$215$	15.7778	+	16.5472i	1.07603	+	1.12851i
$216$	0.540641	+	0.841254i	0.0367859	+	0.0572401i
$217$	−0.221526	−	2.85667i	−0.0150381	−	0.193923i
$218$	−9.13379	−	4.17126i	−0.618618	−	0.282514i
$219$	−2.57637	−	3.61800i	−0.174095	−	0.244482i
$220$	−5.63047	−	14.0642i	−0.379606	−	0.948210i
$221$	−3.06420	+	5.94372i	−0.206121	+	0.399818i
$222$	−3.36699	+	3.21042i	−0.225977	+	0.215469i
$223$	6.88967	−	0.990585i	0.461366	−	0.0663345i	0.0922872	−	0.995732i	$-0.470582\pi$
$223$	6.88967	−	0.990585i	0.461366	−	0.0663345i	0.369079	+	0.929398i	$0.379673\pi$
$224$	1.57282	−	2.12750i	0.105088	−	0.142149i
$225$	−12.1551	−	7.81163i	−0.810342	−	0.520775i
$226$	−19.8479	+	6.86942i	−1.32026	+	0.456947i
$227$	18.7366	+	17.8653i	1.24359	+	1.18576i	0.974926	+	0.222531i	$0.0714319\pi$
$227$	18.7366	+	17.8653i	1.24359	+	1.18576i	0.268668	+	0.963233i	$0.413417\pi$
$228$	−1.86320	−	1.32678i	−0.123394	−	0.0878683i
$229$	−10.9971	+	19.0475i	−0.726707	+	1.25869i	0.231561	+	0.972820i	$0.425617\pi$
$229$	−10.9971	+	19.0475i	−0.726707	+	1.25869i	−0.958268	+	0.285872i	$0.907717\pi$
$230$	12.4687	+	17.0838i	0.822161	+	1.12647i
$231$	6.68838	−	6.15374i	0.440063	−	0.404887i
$232$	0.803187	+	1.75873i	0.0527318	+	0.115466i
$233$	−0.536807	+	2.21275i	−0.0351674	+	0.144962i	−0.986689	−	0.162621i	$-0.948005\pi$
$233$	−0.536807	+	2.21275i	−0.0351674	+	0.144962i	0.951521	+	0.307583i	$0.0995203\pi$
$234$	0.758881	−	3.93745i	0.0496096	−	0.257399i
$235$	51.3015	+	2.44379i	3.34654	+	0.159415i
$236$	1.02705	+	5.32885i	0.0668554	+	0.346879i
$237$	1.21511	+	8.45127i	0.0789298	+	0.548969i
$238$	−3.66868	−	2.45111i	−0.237805	−	0.158882i
$239$	9.00150	−	5.78492i	0.582259	−	0.374195i	−0.216105	−	0.976370i	$-0.569335\pi$
$239$	9.00150	−	5.78492i	0.582259	−	0.374195i	0.798364	+	0.602175i	$0.205699\pi$
$240$	2.72613	−	3.46656i	0.175971	−	0.223765i
$241$	−22.7195	+	2.16945i	−1.46349	+	0.139746i	−0.796192	−	0.605044i	$-0.793156\pi$
$241$	−22.7195	+	2.16945i	−1.46349	+	0.139746i	−0.667299	+	0.744790i	$0.732550\pi$
$242$	0.796812	−	0.0760863i	0.0512210	−	0.00489101i
$243$	−0.618159	+	0.786053i	−0.0396549	+	0.0504253i
$244$	5.86199	−	3.76728i	0.375276	−	0.241175i
$245$	−30.5015	+	4.75921i	−1.94867	+	0.304055i
$246$	−0.0329444	−	0.229133i	−0.00210046	−	0.0146090i
$247$	1.73581	+	9.00625i	0.110447	+	0.573054i
$248$	1.08173	+	0.0515294i	0.0686902	+	0.00327212i
$249$	−2.24474	+	11.6468i	−0.142255	+	0.738087i
$250$	−9.82410	+	40.4955i	−0.621331	+	2.56116i
$251$	−10.6317	−	23.2802i	−0.671067	−	1.46943i	−0.871838	−	0.489794i	$-0.837072\pi$
$251$	−10.6317	−	23.2802i	−0.671067	−	1.46943i	0.200771	−	0.979638i	$-0.435655\pi$
$252$	2.52490	+	0.790480i	0.159054	+	0.0497956i
$253$	−15.5044	+	5.56985i	−0.974754	+	0.350173i
$254$	4.79298	−	8.30169i	0.300738	−	0.520894i
$255$	−5.99074	−	4.26599i	−0.375155	−	0.267147i
$256$	0.723734	+	0.690079i	0.0452334	+	0.0431299i
$257$	5.79431	−	2.00543i	0.361439	−	0.125095i	−0.140312	−	0.990107i	$-0.544811\pi$
$257$	5.79431	−	2.00543i	0.361439	−	0.125095i	0.501751	+	0.865012i	$0.332689\pi$
$258$	−4.36141	−	2.80291i	−0.271529	−	0.174501i
$259$	−1.38802	+	12.2302i	−0.0862471	+	0.759946i
$260$	−17.5041	+	2.51670i	−1.08556	+	0.156079i
$261$	−1.39931	+	1.33424i	−0.0866150	+	0.0825872i
$262$	6.47123	−	12.5524i	0.399794	−	0.775492i
$263$	3.09838	+	7.73939i	0.191054	+	0.477231i	0.992706	−	0.120561i	$-0.0384692\pi$
$263$	3.09838	+	7.73939i	0.191054	+	0.477231i	−0.801651	+	0.597792i	$0.796045\pi$
$264$	1.99260	+	2.79821i	0.122636	+	0.172218i
$265$	49.8501	+	22.7658i	3.06227	+	1.39849i
$266$	−6.03359	+	0.467886i	−0.369943	+	0.0286879i
$267$	−3.16575	−	4.92601i	−0.193741	−	0.301467i
$268$	−4.15786	−	4.36064i	−0.253982	−	0.266369i
$269$	7.95233	+	10.1122i	0.484862	+	0.616552i	0.965511	−	0.260361i	$-0.0838414\pi$
$269$	7.95233	+	10.1122i	0.484862	+	0.616552i	−0.480649	+	0.876913i	$0.659599\pi$
$270$	4.16753	+	1.44240i	0.253628	+	0.0877815i
$271$	4.30477	+	8.35008i	0.261496	+	0.507231i	0.982633	−	0.185561i	$-0.0594104\pi$
$271$	4.30477	+	8.35008i	0.261496	+	0.507231i	−0.721137	+	0.692793i	$0.756380\pi$
$272$	1.09207	−	1.26032i	0.0662166	−	0.0764180i
$273$	−5.14017	−	9.28087i	−0.311097	−	0.561704i
$274$	17.2821	−	7.89249i	1.04405	−	0.476803i
$275$	−42.9845	−	24.8171i	−2.59207	−	1.49653i
$276$	−3.66090	−	3.09803i	−0.220360	−	0.186480i
$277$	−8.58441	−	14.8686i	−0.515787	−	0.893370i	−0.999832	−	0.0183265i	$-0.994166\pi$
$277$	−8.58441	−	14.8686i	−0.515787	−	0.893370i	0.484045	−	0.875043i	$-0.339167\pi$
$278$	−0.835782	+	8.75270i	−0.0501269	+	0.524952i
$279$	0.305105	+	1.03909i	0.0182662	+	0.0622089i
$280$	−0.347562	−	11.6628i	−0.0207708	−	0.696986i
$281$	17.2797	−	26.8877i	1.03082	−	1.60398i	0.261409	−	0.965228i	$-0.415813\pi$
$281$	17.2797	−	26.8877i	1.03082	−	1.60398i	0.769409	−	0.638756i	$-0.220551\pi$
$282$	−11.4355	+	2.20401i	−0.680975	+	0.131247i
$283$	18.7283	−	14.7281i	1.11328	−	0.875494i	0.120179	−	0.992752i	$-0.461653\pi$
$283$	18.7283	−	14.7281i	1.11328	−	0.875494i	0.993101	+	0.117258i	$0.0374106\pi$
$284$	0.0767090	+	0.316199i	0.00455184	+	0.0187629i
$285$	−10.0759	+	0.479974i	−0.596844	+	0.0284312i
$286$	1.96035	−	13.6346i	0.115918	−	0.806228i
$287$	−0.455654	−	0.409257i	−0.0268964	−	0.0241577i
$288$	−0.415415	+	0.909632i	−0.0244786	+	0.0536006i
$289$	11.1769	+	8.78959i	0.657463	+	0.517035i
$290$	7.57883	+	3.90716i	0.445044	+	0.229436i
$291$	8.62553	−	2.09253i	0.505637	−	0.122666i
$292$	1.65077	−	4.12342i	0.0966039	−	0.241305i
$293$	14.9346	+	17.2354i	0.872486	+	1.00690i	0.999887	+	0.0150513i	$0.00479114\pi$
$293$	14.9346	+	17.2354i	0.872486	+	1.00690i	−0.127401	+	0.991851i	$0.540663\pi$
$294$	6.46693	−	2.67933i	0.377159	−	0.156262i
$295$	18.0875	+	15.6729i	1.05309	+	0.912511i
$296$	−4.52111	−	1.09681i	−0.262784	−	0.0637507i
$297$	−1.99260	+	2.79821i	−0.115622	+	0.162369i
$298$	16.3399	−	9.43383i	0.946544	−	0.546487i
$299$	2.05159	+	19.1211i	0.118647	+	1.10580i
$300$		−	14.4488i		−	0.834204i
$301$	−13.6097	+	1.71001i	−0.784448	+	0.0985635i
$302$	13.0171	−	3.82216i	0.749050	−	0.219941i
$303$	−3.72620	−	10.7661i	−0.214064	−	0.618498i
$304$	0.108836	−	2.28474i	0.00624215	−	0.131039i
$305$	10.0509	−	29.0401i	0.575511	−	1.66283i
$306$	1.54818	+	0.619799i	0.0885038	+	0.0354316i
$307$	−5.95749	+	20.2893i	−0.340012	+	1.15797i	0.595109	+	0.803645i	$0.297109\pi$
$307$	−5.95749	+	20.2893i	−0.340012	+	1.15797i	−0.935121	+	0.354329i	$0.884709\pi$
$308$	8.79287	+	2.29966i	0.501020	+	0.131035i
$309$	6.35464	+	0.913659i	0.361503	+	0.0519762i
$310$	3.89037	−	2.77032i	0.220958	−	0.157344i
$311$	−0.756086	−	7.91809i	−0.0428737	−	0.448994i	−0.991264	−	0.131890i	$-0.957896\pi$
$311$	−0.756086	−	7.91809i	−0.0428737	−	0.448994i	0.948391	−	0.317104i	$-0.102711\pi$
$312$	3.72268	−	1.49033i	0.210755	−	0.0843736i
$313$	0.572504	+	12.0183i	0.0323598	+	0.679317i	0.955524	+	0.294912i	$0.0952903\pi$
$313$	0.572504	+	12.0183i	0.0323598	+	0.679317i	−0.923165	+	0.384405i	$0.874407\pi$
$314$	7.08206	+	2.07948i	0.399664	+	0.117352i
$315$	10.9077	−	4.14298i	0.614578	−	0.233430i
$316$	−6.45273	+	5.59132i	−0.362994	+	0.314536i
$317$	9.79867	−	5.05157i	0.550348	−	0.283724i	−0.160540	−	0.987029i	$-0.551324\pi$
$317$	9.79867	−	5.05157i	0.550348	−	0.283724i	0.710888	+	0.703305i	$0.248293\pi$
$318$	−12.2021	−	2.35176i	−0.684258	−	0.131880i
$319$	−4.58334	+	4.80687i	−0.256618	+	0.269133i
$320$	4.39011	+	0.419205i	0.245415	+	0.0234343i
$321$	8.13445			0.454021
$322$	−12.6883	−	0.0776792i	−0.707094	−	0.00432889i
$323$	−3.81444			−0.212241
$324$	−0.995472	−	0.0950560i	−0.0553040	−	0.00528089i
$325$	−39.9822	+	41.9321i	−2.21781	+	2.32597i
$326$	17.9347	+	3.45663i	0.993310	+	0.191445i
$327$	8.92497	−	4.60114i	0.493552	−	0.254444i
$328$	0.174948	−	0.151593i	0.00965990	−	0.00837035i
$329$	−19.4752	+	23.8771i	−1.07370	+	1.31639i
$330$	14.5358	+	4.26808i	0.800167	+	0.234950i
$331$	−0.0865726	−	1.81738i	−0.00475846	−	0.0998924i	−0.999997	−	0.00242379i	$-0.999228\pi$
$331$	−0.0865726	−	1.81738i	−0.00475846	−	0.0998924i	0.995239	−	0.0974686i	$-0.0310745\pi$
$332$	−11.0115	+	4.40835i	−0.604336	+	0.241940i
$333$	−0.442224	−	4.63118i	−0.0242337	−	0.253787i
$334$	−18.5154	+	13.1848i	−1.01312	+	0.721439i
$335$	−26.3012	−	3.78154i	−1.43699	−	0.206608i
$336$	0.700072	+	2.55145i	0.0381921	+	0.139193i
$337$	−0.999887	+	3.40530i	−0.0544673	+	0.185499i	−0.982233	−	0.187664i	$-0.939908\pi$
$337$	−0.999887	+	3.40530i	−0.0544673	+	0.185499i	0.927766	+	0.373163i	$0.121727\pi$
$338$	−2.85882	−	1.14450i	−0.155499	−	0.0622526i
$339$	6.86942	−	19.8479i	0.373096	−	1.07799i
$340$	0.349938	−	7.34610i	0.0189780	−	0.398398i
$341$	1.21675	+	3.51556i	0.0658905	+	0.190378i
$342$	2.19468	−	0.644415i	0.118675	−	0.0348460i
$343$	8.58219	−	16.4118i	0.463395	−	0.886152i
$344$		−	5.18442i		−	0.279525i
$345$	−21.1364	−	0.759421i	−1.13794	−	0.0408858i
$346$	21.9661	−	12.6821i	1.18090	−	0.681795i
$347$	0.820158	−	1.15175i	0.0440284	−	0.0618292i	−0.791975	−	0.610554i	$-0.790947\pi$
$347$	0.820158	−	1.15175i	0.0440284	−	0.0618292i	0.836003	+	0.548724i	$0.184886\pi$
$348$	−1.87895	−	0.455829i	−0.100723	−	0.0244350i
$349$	−1.17905	−	1.02166i	−0.0631133	−	0.0546880i	0.622733	−	0.782434i	$-0.286022\pi$
$349$	−1.17905	−	1.02166i	−0.0631133	−	0.0546880i	−0.685846	+	0.727746i	$0.740568\pi$
$350$	−24.5156	−	29.3320i	−1.31041	−	1.56786i
$351$	2.62593	+	3.03049i	0.140162	+	0.161756i
$352$	−1.27673	+	3.18911i	−0.0680497	+	0.169980i
$353$	−11.8623	+	2.87776i	−0.631366	+	0.153168i	−0.538657	−	0.842525i	$-0.681068\pi$
$353$	−11.8623	+	2.87776i	−0.631366	+	0.153168i	−0.0927097	+	0.995693i	$0.529553\pi$
$354$	−4.82364	−	2.48676i	−0.256374	−	0.132170i
$355$	1.12792	+	0.887003i	0.0598636	+	0.0470772i
$356$	2.43249	−	5.32640i	0.128921	−	0.282299i
$357$	4.19453	−	1.36860i	0.221998	−	0.0724341i
$358$	0.439778	−	3.05872i	0.0232430	−	0.161658i
$359$	33.6465	−	1.60278i	1.77580	−	0.0845916i	0.866101	−	0.499869i	$-0.166618\pi$
$359$	33.6465	−	1.60278i	1.77580	−	0.0845916i	0.909695	+	0.415277i	$0.136315\pi$
$360$	1.03972	+	4.28577i	0.0547979	+	0.225880i
$361$	10.8225	−	8.51089i	0.569604	−	0.447941i
$362$	1.84346	−	0.355298i	0.0968901	−	0.0186740i
$363$	−0.432748	+	0.673370i	−0.0227134	+	0.0353427i
$364$	5.02858	−	9.34180i	0.263569	−	0.489643i
$365$	−5.51850	−	18.7943i	−0.288852	−	0.983738i
$366$	−0.662366	+	6.93661i	−0.0346224	+	0.362583i
$367$	13.4584	+	23.3106i	0.702521	+	1.21680i	0.967579	+	0.252570i	$0.0812756\pi$
$367$	13.4584	+	23.3106i	0.702521	+	1.21680i	−0.265058	+	0.964233i	$0.585391\pi$
$368$	0.627000	−	4.75467i	0.0326846	−	0.247854i
$369$	0.200476	+	0.115745i	0.0104364	+	0.00602544i
$370$	−18.6627	+	8.52298i	−0.970229	+	0.443089i
$371$	−28.7612	+	15.9293i	−1.49321	+	0.827007i
$372$	−0.709189	+	0.818447i	−0.0367697	+	0.0424345i
$373$	−8.93598	−	17.3334i	−0.462688	−	0.897489i	−0.998584	−	0.0532047i	$-0.983056\pi$
$373$	−8.93598	−	17.3334i	−0.462688	−	0.897489i	0.535896	−	0.844284i	$-0.319974\pi$
$374$	5.41357	+	1.87365i	0.279929	+	0.0968843i
$375$	−25.7588	−	32.7549i	−1.33018	−	1.69146i
$376$	−8.03664	−	8.42859i	−0.414458	−	0.434671i
$377$	4.19158	+	6.52223i	0.215878	+	0.335912i
$378$	−2.18215	+	1.49607i	−0.112238	+	0.0769493i
$379$	−2.37142	−	1.08299i	−0.121812	−	0.0556295i	0.353577	−	0.935405i	$-0.384965\pi$
$379$	−2.37142	−	1.08299i	−0.121812	−	0.0556295i	−0.475389	+	0.879776i	$0.657693\pi$
$380$	−5.85122	−	8.21688i	−0.300161	−	0.421517i
$381$	3.56274	+	8.89930i	0.182525	+	0.455925i
$382$	5.94759	−	11.5367i	0.304305	−	0.590270i
$383$	14.2273	−	13.5657i	0.726983	−	0.693177i	−0.233238	−	0.972420i	$-0.574932\pi$
$383$	14.2273	−	13.5657i	0.726983	−	0.693177i	0.960220	+	0.279243i	$0.0900835\pi$
$384$	−0.989821	+	0.142315i	−0.0505116	+	0.00726247i
$385$	36.7502	−	15.9986i	1.87296	−	0.815365i
$386$	−0.0682082	−	0.0438347i	−0.00347171	−	0.00223113i
$387$	4.89928	−	1.69566i	0.249044	−	0.0861951i
$388$	6.42366	+	6.12495i	0.326112	+	0.310947i
$389$	−30.0318	−	21.3855i	−1.52267	−	1.08429i	−0.967600	−	0.252488i	$-0.918751\pi$
$389$	−30.0318	−	21.3855i	−1.52267	−	1.08429i	−0.555072	−	0.831802i	$-0.687309\pi$
$390$	8.84203	−	15.3148i	0.447733	−	0.775497i
$391$	−7.96985	−	0.667146i	−0.403052	−	0.0337390i
$392$	5.75028	+	3.99177i	0.290433	+	0.201615i
$393$	5.86663	+	12.8461i	0.295933	+	0.648002i
$394$	−3.30740	+	13.6333i	−0.166624	+	0.686835i
$395$	−7.12608	+	36.9736i	−0.358552	+	1.86034i
$396$	−3.43129	−	0.163452i	−0.172429	−	0.00821379i
$397$	0.368626	+	1.91261i	0.0185008	+	0.0959913i	0.990005	−	0.141029i	$-0.0450412\pi$
$397$	0.368626	+	1.91261i	0.0185008	+	0.0959913i	−0.971505	+	0.237021i	$0.923829\pi$
$398$	−1.81098	−	12.5957i	−0.0907763	−	0.631363i
$399$	3.36194	−	5.03195i	0.168307	−	0.251913i
$400$	12.1551	−	7.81163i	0.607756	−	0.390581i
$401$	4.85894	−	6.17865i	0.242644	−	0.308547i	−0.649443	−	0.760410i	$-0.724998\pi$
$401$	4.85894	−	6.17865i	0.242644	−	0.308547i	0.892087	+	0.451863i	$0.149240\pi$
$402$	5.99792	−	0.572732i	0.299149	−	0.0285653i
$403$	4.32292	−	0.412789i	0.215340	−	0.0205625i
$404$	7.04252	−	8.95529i	0.350378	−	0.445542i
$405$	−3.71000	+	2.38427i	−0.184351	+	0.118475i
$406$	−4.58781	+	2.26270i	−0.227689	+	0.112296i
$407$	−2.27437	−	15.8186i	−0.112736	−	0.784100i
$408$	0.315603	+	1.63750i	0.0156247	+	0.0810685i
$409$	5.48784	+	0.261418i	0.271356	+	0.0129263i	0.182819	−	0.983147i	$-0.441478\pi$
$409$	5.48784	+	0.261418i	0.271356	+	0.0129263i	0.0885373	+	0.996073i	$0.471781\pi$
$410$	0.193204	−	1.00244i	0.00954169	−	0.0495070i
$411$	−4.47919	+	18.4635i	−0.220942	+	0.910737i
$412$	2.66696	+	5.83982i	0.131392	+	0.287707i
$413$	−14.0116	+	3.13609i	−0.689466	+	0.154317i
$414$	4.69824	−	0.962584i	0.230906	−	0.0473084i
$415$	−26.1544	+	45.3007i	−1.28387	+	2.22372i
$416$	3.26638	+	2.32598i	0.160147	+	0.114040i
$417$	−6.36344	−	6.06753i	−0.311619	−	0.297128i
$418$	7.42523	−	2.56990i	0.363180	−	0.125698i
$419$	−18.9580	−	12.1835i	−0.926157	−	0.595205i	−0.0117190	−	0.999931i	$-0.503730\pi$
$419$	−18.9580	−	12.1835i	−0.926157	−	0.595205i	−0.914438	+	0.404726i	$0.867367\pi$
$420$	9.38243	+	6.93627i	0.457816	+	0.338455i
$421$	5.64579	−	0.811742i	0.275159	−	0.0395619i	−0.00335402	−	0.999994i	$-0.501068\pi$
$421$	5.64579	−	0.811742i	0.275159	−	0.0395619i	0.278513	+	0.960433i	$0.410159\pi$
$422$	8.12224	−	7.74454i	0.395384	−	0.376998i
$423$	5.33649	−	10.3514i	0.259469	−	0.503300i
$424$	−4.61851	−	11.5365i	−0.224295	−	0.560261i
$425$	−13.9767	−	19.6276i	−0.677971	−	0.952077i
$426$	−0.295967	−	0.135164i	−0.0143397	−	0.00654871i
$427$	10.4248	+	15.2056i	0.504493	+	0.735850i
$428$	4.39781	+	6.84313i	0.212576	+	0.330775i
$429$	9.50567	+	9.96926i	0.458938	+	0.481321i
$430$	−14.1334	−	17.9721i	−0.681573	−	0.866691i
$431$	−19.1094	−	6.61383i	−0.920468	−	0.318577i	−0.174576	−	0.984644i	$-0.555855\pi$
$431$	−19.1094	−	6.61383i	−0.920468	−	0.318577i	−0.745892	+	0.666067i	$0.767977\pi$
$432$	−0.458227	−	0.888835i	−0.0220464	−	0.0427641i
$433$	10.6501	−	12.2909i	0.511811	−	0.590661i	−0.439751	−	0.898120i	$-0.644933\pi$
$433$	10.6501	−	12.2909i	0.511811	−	0.590661i	0.951561	+	0.307459i	$0.0994786\pi$
$434$	−0.0510210	+	2.86479i	−0.00244909	+	0.137514i
$435$	−7.75616	+	3.54212i	−0.371879	+	0.169832i
$436$	8.69593	+	5.02060i	0.416459	+	0.240443i
$437$	−9.15832	+	6.03807i	−0.438102	+	0.288840i
$438$	2.22079	+	3.84652i	0.106113	+	0.183794i
$439$	−0.803784	+	8.41761i	−0.0383625	+	0.401751i	0.955813	+	0.293976i	$0.0949786\pi$
$439$	−0.803784	+	8.41761i	−0.0383625	+	0.401751i	−0.994175	+	0.107775i	$0.965627\pi$
$440$	4.26808	+	14.5358i	0.203473	+	0.692965i
$441$	−1.89150	+	6.73960i	−0.0900712	+	0.320933i
$442$	3.61532	−	5.62554i	0.171963	−	0.267580i
$443$	−10.9487	+	2.11019i	−0.520188	+	0.100258i	−0.442586	−	0.896726i	$-0.645939\pi$
$443$	−10.9487	+	2.11019i	−0.520188	+	0.100258i	−0.0776028	+	0.996984i	$0.524727\pi$
$444$	3.65691	−	2.87583i	0.173549	−	0.136481i
$445$	−6.08812	−	25.0956i	−0.288604	−	1.18964i
$446$	−6.95263	+	0.331195i	−0.329217	+	0.0156825i
$447$	−2.68515	+	18.6756i	−0.127003	+	0.883326i
$448$	−1.76793	+	1.96836i	−0.0835268	+	0.0929961i
$449$	−11.4784	+	25.1342i	−0.541699	+	1.18615i	0.418853	+	0.908054i	$0.362432\pi$
$449$	−11.4784	+	25.1342i	−0.541699	+	1.18615i	−0.960552	+	0.278100i	$0.910295\pi$
$450$	11.3575	+	8.93167i	0.535400	+	0.421043i
$451$	0.706809	+	0.364385i	0.0332823	+	0.0171582i
$452$	20.4110	−	4.95165i	0.960052	−	0.232906i
$453$	−5.04221	+	12.5948i	−0.236904	+	0.591757i
$454$	−16.9536	−	19.5655i	−0.795671	−	0.918253i
$455$	−8.03512	−	46.0925i	−0.376692	−	2.16085i
$456$	1.72865	+	1.49788i	0.0809514	+	0.0701448i
$457$	8.41780	+	2.04214i	0.393768	+	0.0955271i	0.427754	−	0.903895i	$-0.359305\pi$
$457$	8.41780	+	2.04214i	0.393768	+	0.0955271i	−0.0339859	+	0.999422i	$0.510820\pi$
$458$	12.7578	−	17.9159i	0.596135	−	0.837155i
$459$	−1.44422	+	0.833820i	−0.0674104	+	0.0389194i
$460$	−10.7883	−	18.1916i	−0.503008	−	0.848189i
$461$		−	3.43295i		−	0.159888i	−0.996799	−	0.0799442i	$-0.974526\pi$
$461$		−	3.43295i		−	0.159888i	0.996799	−	0.0799442i	$-0.0254742\pi$
$462$	−7.24305	+	5.49011i	−0.336977	+	0.255423i
$463$	−4.92419	+	1.44587i	−0.228847	+	0.0671954i	−0.394145	−	0.919048i	$-0.628959\pi$
$463$	−4.92419	+	1.44587i	−0.228847	+	0.0671954i	0.165299	+	0.986244i	$0.447141\pi$
$464$	−0.632371	−	1.82712i	−0.0293571	−	0.0848218i
$465$	−0.227249	+	4.77054i	−0.0105384	+	0.221228i
$466$	0.744712	−	2.15170i	0.0344981	−	0.0996757i
$467$	30.7022	+	12.2913i	1.42073	+	0.568774i	0.949649	−	0.313316i	$-0.101440\pi$
$467$	30.7022	+	12.2913i	1.42073	+	0.568774i	0.471080	+	0.882090i	$0.343864\pi$
$468$	−1.12972	+	3.84748i	−0.0522215	+	0.177850i
$469$	11.2044	−	11.3395i	0.517370	−	0.523608i
$470$	−50.8369	−	7.30925i	−2.34493	−	0.337150i
$471$	−6.01242	+	4.28142i	−0.277038	+	0.197278i
$472$	−0.515862	−	5.40235i	−0.0237445	−	0.248663i
$473$	16.5337	−	6.61908i	0.760219	−	0.304346i
$474$	−0.406263	−	8.52851i	−0.0186603	−	0.391727i
$475$	−31.7105	−	9.31105i	−1.45498	−	0.427220i
$476$	3.41908	+	2.78874i	0.156713	+	0.127822i
$477$	9.39142	−	8.13772i	0.430004	−	0.372600i
$478$	−9.51064	+	4.90307i	−0.435006	+	0.224261i
$479$	−27.9872	−	5.39409i	−1.27877	−	0.246462i	−0.495753	−	0.868464i	$-0.665108\pi$
$479$	−27.9872	−	5.39409i	−1.27877	−	0.246462i	−0.783016	+	0.622001i	$0.786320\pi$
$480$	−3.04331	+	3.19173i	−0.138907	+	0.145682i
$481$	−18.5706	−	1.77328i	−0.846748	−	0.0808546i
$482$	22.8228			1.03955
$483$	7.90447	−	9.92569i	0.359666	−	0.451635i
$484$	−0.800436			−0.0363835
$485$	38.9654	+	3.72075i	1.76933	+	0.168950i
$486$	0.690079	−	0.723734i	0.0313026	−	0.0328292i
$487$	16.3288	+	3.14712i	0.739929	+	0.142610i	0.545269	−	0.838261i	$-0.316427\pi$
$487$	16.3288	+	3.14712i	0.739929	+	0.142610i	0.194660	+	0.980871i	$0.437640\pi$
$488$	−6.19355	+	3.19300i	−0.280369	+	0.144540i
$489$	−13.8036	+	11.9609i	−0.624219	+	0.540889i
$490$	30.8158	−	1.83831i	1.39212	−	0.0830464i
$491$	−25.3786	−	7.45182i	−1.14532	−	0.336296i	−0.346608	−	0.938010i	$-0.612666\pi$
$491$	−25.3786	−	7.45182i	−1.14532	−	0.336296i	−0.798712	+	0.601714i	$0.794485\pi$
$492$	0.0110147	+	0.231227i	0.000496582	+	0.0104245i
$493$	−2.99334	+	1.19835i	−0.134813	+	0.0539712i
$494$	−0.871854	−	9.13046i	−0.0392266	−	0.410799i
$495$	−12.3403	+	8.78752i	−0.554657	+	0.394970i
$496$	−1.07194	−	0.154121i	−0.0481314	−	0.00692026i
$497$	−0.830167	+	0.227783i	−0.0372381	+	0.0102175i
$498$	3.34168	−	11.3807i	0.149744	−	0.509981i
$499$	−14.4155	−	5.77108i	−0.645325	−	0.258349i	0.0258298	−	0.999666i	$-0.491777\pi$
$499$	−14.4155	−	5.77108i	−0.645325	−	0.258349i	−0.671155	+	0.741317i	$0.734201\pi$
$500$	13.6290	−	39.3783i	0.609506	−	1.76105i
$501$	1.08154	−	22.7044i	0.0483198	−	1.01436i
$502$	8.37064	+	24.1854i	0.373600	+	1.07945i
$503$	26.3232	−	7.72919i	1.17369	−	0.344628i	0.363954	−	0.931417i	$-0.381426\pi$
$503$	26.3232	−	7.72919i	1.17369	−	0.344628i	0.809740	+	0.586789i	$0.199608\pi$
$504$	−2.43833	−	1.02691i	−0.108612	−	0.0457421i
$505$		−	50.2429i		−	2.23578i
$506$	15.9637	−	4.07084i	0.709671	−	0.180971i
$507$	2.66684	−	1.53970i	0.118439	−	0.0683806i
$508$	−5.56040	+	7.80849i	−0.246703	+	0.346446i
$509$	33.0504	+	8.01794i	1.46493	+	0.355389i	0.887409	−	0.460984i	$-0.152503\pi$
$509$	33.0504	+	8.01794i	1.46493	+	0.355389i	0.577525	+	0.816373i	$0.304019\pi$
$510$	5.55811	+	4.81613i	0.246117	+	0.213262i
$511$	11.0348	+	4.04061i	0.488151	+	0.178746i
$512$	−0.654861	−	0.755750i	−0.0289410	−	0.0333997i
$513$	−0.850115	+	2.12348i	−0.0375335	+	0.0937541i
$514$	−5.95870	+	1.44557i	−0.262827	+	0.0637612i
$515$	25.1653	+	12.9736i	1.10892	+	0.571686i
$516$	4.07523	+	3.20479i	0.179402	+	0.141083i
$517$	16.6191	−	36.3907i	0.730906	−	1.60046i
$518$	2.54428	−	12.0429i	0.111789	−	0.529133i
$519$	−3.60971	+	25.1061i	−0.158449	+	1.10203i
$520$	17.6640	−	0.841441i	0.774619	−	0.0368996i
$521$	−1.61675	−	6.66434i	−0.0708312	−	0.291970i	0.925369	−	0.379069i	$-0.123756\pi$
$521$	−1.61675	−	6.66434i	−0.0708312	−	0.291970i	−0.996200	+	0.0870986i	$0.972240\pi$
$522$	1.51980	−	1.19518i	0.0665198	−	0.0523117i
$523$	−23.8106	+	4.58912i	−1.04117	+	0.200668i	−0.681048	−	0.732239i	$-0.738475\pi$
$523$	−23.8106	+	4.58912i	−1.04117	+	0.200668i	−0.360117	+	0.932907i	$0.617263\pi$
$524$	−7.63512	+	11.8805i	−0.333542	+	0.519001i
$525$	38.2110	−	1.13872i	1.66767	−	0.0496980i
$526$	−2.34868	−	7.99886i	−0.102407	−	0.348767i
$527$	−0.171670	+	1.79781i	−0.00747807	+	0.0783139i
$528$	−1.71759	−	2.97495i	−0.0747484	−	0.129468i
$529$	−20.1913	+	11.0141i	−0.877884	+	0.478873i
$530$	−47.4604	−	27.4012i	−2.06155	−	1.19023i
$531$	4.93650	−	2.25442i	0.214226	−	0.0978337i
$532$	6.05075	+	0.107762i	0.262333	+	0.00467207i
$533$	0.607877	−	0.701527i	0.0263301	−	0.0303865i
$534$	2.68317	+	5.20463i	0.116112	+	0.225226i
$535$	33.9006	+	11.7331i	1.46565	+	0.507266i
$536$	3.72453	+	4.73613i	0.160875	+	0.204570i
$537$	2.13247	+	2.23647i	0.0920227	+	0.0965106i
$538$	−6.95509	−	10.8223i	−0.299855	−	0.466584i
$539$	−5.38866	+	23.4347i	−0.232106	+	1.00940i
$540$	−4.01155	−	1.83201i	−0.172630	−	0.0788374i
$541$	−8.54555	−	12.0005i	−0.367402	−	0.515944i	0.588947	−	0.808172i	$-0.299543\pi$
$541$	−8.54555	−	12.0005i	−0.367402	−	0.515944i	−0.956349	+	0.292228i	$0.905603\pi$
$542$	−3.49155	−	8.72146i	−0.149975	−	0.374619i
$543$	−0.860269	+	1.66869i	−0.0369177	+	0.0716103i
$544$	−1.20693	+	1.15080i	−0.0517466	+	0.0493403i
$545$	43.8318	−	6.30206i	1.87755	−	0.269950i
$546$	4.23469	+	9.72745i	0.181228	+	0.416296i
$547$	2.54654	+	1.63656i	0.108882	+	0.0699742i	0.593949	−	0.804503i	$-0.297568\pi$
$547$	2.54654	+	1.63656i	0.108882	+	0.0699742i	−0.485067	+	0.874477i	$0.661205\pi$
$548$	−17.9541	+	6.21398i	−0.766961	+	0.265448i
$549$	−5.04310	−	4.80859i	−0.215234	−	0.205225i
$550$	40.4309	+	28.7907i	1.72398	+	1.22764i
$551$	−2.21123	+	3.82996i	−0.0942014	+	0.163162i
$552$	3.34984	+	3.43200i	0.142578	+	0.146075i
$553$	−15.2952	−	16.6241i	−0.650419	−	0.706928i
$554$	7.13219	+	15.6173i	0.303018	+	0.663516i
$555$	4.83702	−	19.9384i	0.205320	−	0.846340i
$556$	1.66399	−	8.63362i	0.0705691	−	0.366147i
$557$	33.6476	+	1.60283i	1.42569	+	0.0679141i	0.746178	−	0.665747i	$-0.231887\pi$
$557$	33.6476	+	1.60283i	1.42569	+	0.0679141i	0.679516	+	0.733661i	$0.262190\pi$
$558$	−0.204952	−	1.06339i	−0.00867630	−	0.0450169i
$559$	−2.95859	−	20.5775i	−0.125135	−	0.870334i
$560$	−0.762632	+	11.6430i	−0.0322271	+	0.492008i
$561$	−4.81924	+	3.09714i	−0.203468	+	0.130761i
$562$	−19.7573	+	25.1234i	−0.833409	+	1.05977i
$563$	18.7020	−	1.78582i	0.788194	−	0.0752634i	0.306807	−	0.951772i	$-0.400739\pi$
$563$	18.7020	−	1.78582i	0.788194	−	0.0752634i	0.481387	+	0.876508i	$0.340133\pi$
$564$	11.5932	−	1.10702i	0.488163	−	0.0466140i
$565$	57.2570	−	72.8083i	2.40882	−	3.06307i
$566$	−20.0435	+	12.8812i	−0.842490	+	0.541435i
$567$	0.172929	−	2.64009i	0.00726234	−	0.110874i
$568$	−0.0463050	−	0.322059i	−0.00194292	−	0.0135133i
$569$	7.07521	+	36.7097i	0.296608	+	1.53895i	0.758298	+	0.651908i	$0.226031\pi$
$569$	7.07521	+	36.7097i	0.296608	+	1.53895i	−0.461690	+	0.887041i	$0.652757\pi$
$570$	10.0759	+	0.479974i	0.422033	+	0.0201039i
$571$	8.60926	−	44.6691i	0.360286	−	1.86934i	−0.120809	−	0.992676i	$-0.538549\pi$
$571$	8.60926	−	44.6691i	0.360286	−	1.86934i	0.481096	−	0.876668i	$-0.340239\pi$
$572$	−3.24752	+	13.3865i	−0.135786	+	0.559716i
$573$	5.39192	+	11.8067i	0.225251	+	0.493230i
$574$	0.414689	+	0.450717i	0.0173088	+	0.0188126i
$575$	−64.6270	−	25.0005i	−2.69513	−	1.04259i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	10.3212	+	7.34967i	0.429676	+	0.305971i	0.774357	−	0.632749i	$-0.218073\pi$
$577$	10.3212	+	7.34967i	0.429676	+	0.305971i	−0.344681	+	0.938720i	$0.612013\pi$
$578$	−10.2908	−	9.81222i	−0.428039	−	0.408134i
$579$	0.0766199	−	0.0265184i	0.00318422	−	0.00110207i
$580$	−7.17312	−	4.60988i	−0.297847	−	0.191415i
$581$	−12.5260	−	28.7734i	−0.519668	−	1.19372i
$582$	−8.78538	+	1.26315i	−0.364166	+	0.0523591i
$583$	30.8945	−	29.4579i	1.27952	−	1.22002i
$584$	−2.03525	+	3.94783i	−0.0842192	+	0.163363i
$585$	6.57250	+	16.4173i	0.271739	+	0.678772i
$586$	−13.2286	−	18.5770i	−0.546469	−	0.767408i
$587$	14.8983	+	6.80385i	0.614921	+	0.280825i	0.698426	−	0.715683i	$-0.253884\pi$
$587$	14.8983	+	6.80385i	0.614921	+	0.280825i	−0.0835052	+	0.996507i	$0.526612\pi$
$588$	−6.69233	+	2.05248i	−0.275987	+	0.0846427i
$589$	1.33922	+	2.08386i	0.0551814	+	0.0858640i
$590$	−16.5158	−	17.3213i	−0.679944	−	0.713105i
$591$	−8.67199	−	11.0273i	−0.356718	−	0.453604i
$592$	4.39637	+	1.52160i	0.180690	+	0.0625374i
$593$	−1.31281	−	2.54650i	−0.0539107	−	0.104572i	0.860341	−	0.509719i	$-0.170251\pi$
$593$	−1.31281	−	2.54650i	−0.0539107	−	0.104572i	−0.914252	+	0.405147i	$0.867220\pi$
$594$	2.24956	−	2.59613i	0.0923006	−	0.106521i
$595$	19.4549	+	0.346486i	0.797574	+	0.0142045i
$596$	−17.1626	+	7.83791i	−0.703009	+	0.321053i
$597$	11.0203	+	6.36259i	0.451032	+	0.260403i
$598$	−0.224722	−	19.2296i	−0.00918959	−	0.786355i
$599$	9.40153	+	16.2839i	0.384136	+	0.665343i	0.991649	−	0.128967i	$-0.0411660\pi$
$599$	9.40153	+	16.2839i	0.384136	+	0.665343i	−0.607513	+	0.794310i	$0.707833\pi$
$600$	−1.37345	+	14.3834i	−0.0560708	+	0.587200i
$601$	10.0307	+	34.1615i	0.409161	+	1.39348i	0.864265	+	0.503037i	$0.167784\pi$
$601$	10.0307	+	34.1615i	0.409161	+	1.39348i	−0.455103	+	0.890439i	$0.650398\pi$
$602$	13.7106	−	0.408588i	0.558802	−	0.0166528i
$603$	−3.25747	+	5.06872i	−0.132654	+	0.206414i
$604$	−13.3215	+	2.56750i	−0.542043	+	0.104470i
$605$	−2.77476	+	2.18209i	−0.112810	+	0.0887148i
$606$	2.68594	+	11.0716i	0.109109	+	0.449752i
$607$	3.87197	−	0.184445i	0.157159	−	0.00748639i	0.0311448	−	0.999515i	$-0.490085\pi$
$607$	3.87197	−	0.184445i	0.157159	−	0.00748639i	0.126014	+	0.992028i	$0.459782\pi$
$608$	−0.325521	+	2.26405i	−0.0132016	+	0.0918193i
$609$	1.05739	−	5.00496i	0.0428478	−	0.202811i
$610$	−12.7658	+	27.9532i	−0.516871	+	1.13179i
$611$	−36.7082	−	28.8676i	−1.48505	−	1.16786i
$612$	−1.48226	−	0.764157i	−0.0599167	−	0.0308892i
$613$	−20.3185	+	4.92921i	−0.820656	+	0.199089i	−0.624041	−	0.781392i	$-0.714510\pi$
$613$	−20.3185	+	4.92921i	−0.820656	+	0.199089i	−0.196615	+	0.980481i	$0.562995\pi$
$614$	7.85913	−	19.6312i	0.317169	−	0.792249i
$615$	0.668540	+	0.771536i	0.0269581	+	0.0311113i
$616$	−8.53446	−	3.12506i	−0.343863	−	0.125912i
$617$	3.69515	+	3.20187i	0.148761	+	0.128902i	0.726062	−	0.687629i	$-0.241349\pi$
$617$	3.69515	+	3.20187i	0.148761	+	0.128902i	−0.577301	+	0.816532i	$0.695894\pi$
$618$	−6.23901	−	1.51357i	−0.250970	−	0.0608847i
$619$	−1.82725	+	2.56602i	−0.0734435	+	0.103137i	−0.849664	−	0.527325i	$-0.823195\pi$
$619$	−1.82725	+	2.56602i	−0.0734435	+	0.103137i	0.776220	+	0.630462i	$0.217134\pi$
$620$	−4.13609	+	2.38797i	−0.166109	+	0.0959033i
$621$	−2.14762	+	4.28809i	−0.0861808	+	0.172075i
$622$			7.95411i			0.318931i
$623$	14.2778	+	6.01312i	0.572027	+	0.240911i
$624$	−3.84748	+	1.12972i	−0.154023	+	0.0452251i
$625$	−36.4761	−	105.391i	−1.45904	−	4.21563i
$626$	0.572504	−	12.0183i	0.0228819	−	0.480350i
$627$	−2.56990	+	7.42523i	−0.102632	+	0.296535i
$628$	−6.85232	−	2.74326i	−0.273437	−	0.109468i
$629$	2.18576	−	7.44400i	0.0871518	−	0.296812i
$630$	−11.2521	+	3.08738i	−0.448295	+	0.123004i
$631$	−29.8869	−	4.29709i	−1.18978	−	0.171064i	−0.481146	−	0.876641i	$-0.659779\pi$
$631$	−29.8869	−	4.29709i	−1.18978	−	0.171064i	−0.708634	+	0.705576i	$0.750688\pi$
$632$	6.95500	−	4.95263i	0.276655	−	0.197005i
$633$	1.06678	+	11.1719i	0.0424009	+	0.444042i
$634$	−10.2345	+	4.09727i	−0.406463	+	0.162723i
$635$	2.01152	+	42.2270i	0.0798247	+	1.67573i
$636$	11.9233	+	3.50099i	0.472788	+	0.138823i
$637$	25.1014	+	12.5622i	0.994555	+	0.497734i
$638$	5.01951	−	4.34943i	0.198724	−	0.172196i
$639$	0.289201	−	0.149093i	0.0114406	−	0.00589804i
$640$	−4.33039	−	0.834614i	−0.171174	−	0.0329910i
$641$	−13.8588	+	14.5347i	−0.547391	+	0.574087i	−0.938073	−	0.346439i	$-0.887391\pi$
$641$	−13.8588	+	14.5347i	−0.547391	+	0.574087i	0.390682	+	0.920526i	$0.372239\pi$
$642$	−8.09761	−	0.773228i	−0.319587	−	0.0305169i
$643$	−36.6531			−1.44546			−0.722729	−	0.691132i	$-0.757112\pi$
$643$	−36.6531			−1.44546			−0.722729	+	0.691132i	$0.757112\pi$
$644$	12.6235	+	1.28343i	0.497436	+	0.0505743i
$645$	22.8637			0.900258
$646$	3.79717	+	0.362586i	0.149398	+	0.0142658i
$647$	17.9207	−	18.7947i	0.704536	−	0.738896i	−0.270065	−	0.962842i	$-0.587045\pi$
$647$	17.9207	−	18.7947i	0.704536	−	0.738896i	0.974602	+	0.223946i	$0.0718938\pi$
$648$	0.981929	+	0.189251i	0.0385738	+	0.00743449i
$649$	16.5701	−	8.54246i	0.650432	−	0.335321i
$650$	43.7870	−	37.9417i	1.71747	−	1.48820i
$651$	−2.22034	−	1.81100i	−0.0870219	−	0.0709788i
$652$	−17.5249	−	5.14578i	−0.686328	−	0.201524i
$653$	0.572828	+	12.0251i	0.0224165	+	0.470580i	0.981968	+	0.189047i	$0.0605399\pi$
$653$	0.572828	+	12.0251i	0.0224165	+	0.470580i	−0.959552	+	0.281533i	$0.909157\pi$
$654$	−9.32192	+	3.73193i	−0.364516	+	0.145930i
$655$	5.92016	+	61.9987i	0.231320	+	2.42249i
$656$	−0.188566	+	0.134277i	−0.00736226	+	0.00524264i
$657$	−4.39637	−	0.632103i	−0.171519	−	0.0246607i
$658$	21.6567	−	21.9178i	0.844265	−	0.854444i
$659$	3.42844	−	11.6762i	0.133553	−	0.454840i	−0.865375	−	0.501125i	$-0.832920\pi$
$659$	3.42844	−	11.6762i	0.133553	−	0.454840i	0.998928	+	0.0462844i	$0.0147380\pi$
$660$	−14.0642	−	5.63047i	−0.547449	−	0.219166i
$661$	−4.31880	+	12.4783i	−0.167982	+	0.485351i	−0.997301	−	0.0734239i	$-0.976607\pi$
$661$	−4.31880	+	12.4783i	−0.167982	+	0.485351i	0.829319	+	0.558775i	$0.188729\pi$
$662$	−0.0865726	+	1.81738i	−0.00336474	+	0.0706346i
$663$	2.18713	+	6.31931i	0.0849412	+	0.245422i
$664$	11.3807	−	3.34168i	0.441657	−	0.129682i
$665$	21.2690	−	16.1216i	0.824778	−	0.625168i
$666$			4.65224i			0.180271i
$667$	−5.28996	+	7.61551i	−0.204828	+	0.294874i
$668$	19.6849	−	11.3651i	0.761631	−	0.439728i
$669$	4.03750	−	5.66987i	0.156099	−	0.219210i
$670$	25.8226	+	6.26450i	0.997615	+	0.242019i
$671$	−18.0903	−	15.6753i	−0.698368	−	0.605139i
$672$	−0.454371	−	2.60644i	−0.0175278	−	0.100546i
$673$	10.3201	+	11.9100i	0.397811	+	0.459098i	0.918950	−	0.394373i	$-0.129038\pi$
$673$	10.3201	+	11.9100i	0.397811	+	0.459098i	−0.521140	+	0.853471i	$0.674493\pi$
$674$	1.31905	−	3.29484i	0.0508081	−	0.126912i
$675$	−14.0415	+	3.40644i	−0.540459	+	0.131114i
$676$	2.73709	+	1.41107i	0.105273	+	0.0542718i
$677$	−19.2799	−	15.1619i	−0.740986	−	0.582718i	0.174695	−	0.984623i	$-0.444106\pi$
$677$	−19.2799	−	15.1619i	−0.740986	−	0.582718i	−0.915682	+	0.401905i	$0.868348\pi$
$678$	−8.72497	+	19.1050i	−0.335081	+	0.733724i
$679$	−15.6916	+	17.4706i	−0.602190	+	0.670459i
$680$	−1.04664	+	7.27957i	−0.0401370	+	0.279159i
$681$	25.8595	−	1.23184i	0.990938	−	0.0472042i
$682$	−0.877061	−	3.61530i	−0.0335844	−	0.138437i
$683$	−22.7720	+	17.9081i	−0.871347	+	0.685235i	−0.950196	−	0.311652i	$-0.899118\pi$
$683$	−22.7720	+	17.9081i	−0.871347	+	0.685235i	0.0788497	+	0.996887i	$0.474875\pi$
$684$	−2.24600	+	0.432880i	−0.0858778	+	0.0165516i
$685$	−45.2989	+	70.4864i	−1.73078	+	2.69315i
$686$	−10.1034	+	15.5217i	−0.385748	+	0.592620i
$687$	6.19646	+	21.1032i	0.236410	+	0.805138i
$688$	−0.492810	+	5.16094i	−0.0187882	+	0.196759i
$689$	−24.9149	−	43.1538i	−0.949181	−	1.64403i
$690$	20.9685	+	2.76512i	0.798256	+	0.105266i
$691$	2.62135	+	1.51344i	0.0997210	+	0.0575740i	0.549031	−	0.835802i	$-0.314997\pi$
$691$	2.62135	+	1.51344i	0.0997210	+	0.0575740i	−0.449310	+	0.893376i	$0.648330\pi$
$692$	−23.0721	+	10.5367i	−0.877070	+	0.400545i
$693$	0.161840	−	9.08718i	0.00614778	−	0.345193i
$694$	−0.925925	+	1.06857i	−0.0351476	+	0.0405625i
$695$	−17.7681	−	34.4652i	−0.673981	−	1.30734i
$696$	1.82712	+	0.632371i	0.0692567	+	0.0239700i
$697$	0.238635	+	0.303449i	0.00903894	+	0.0114940i
$698$	1.07660	+	1.12911i	0.0407499	+	0.0427373i
$699$	1.23100	+	1.91548i	0.0465608	+	0.0724500i
$700$	21.6164	+	31.5295i	0.817023	+	1.19170i
$701$	12.4068	+	5.66597i	0.468596	+	0.214001i	0.635696	−	0.771939i	$-0.280713\pi$
$701$	12.4068	+	5.66597i	0.468596	+	0.214001i	−0.167100	+	0.985940i	$0.553440\pi$
$702$	−2.32598	−	3.26638i	−0.0877884	−	0.123282i
$703$	−3.95494	−	9.87897i	−0.149163	−	0.372592i
$704$	1.57409	−	3.05331i	0.0593257	−	0.115076i
$705$	37.1708	−	35.4423i	1.39993	−	1.33483i
$706$	12.0821	−	1.73715i	0.454717	−	0.0653784i
$707$	24.2380	+	17.9187i	0.911563	+	0.673902i
$708$	4.56542	+	2.93402i	0.171579	+	0.110267i
$709$	26.7432	−	9.25590i	1.00436	−	0.347613i	0.225116	−	0.974332i	$-0.427724\pi$
$709$	26.7432	−	9.25590i	1.00436	−	0.347613i	0.779245	+	0.626720i	$0.215603\pi$
$710$	−1.03849	−	0.990202i	−0.0389740	−	0.0371616i
$711$	6.95500	+	4.95263i	0.260833	+	0.185738i
$712$	−2.92778	+	5.07106i	−0.109723	+	0.190046i
$713$	2.43367	+	4.58822i	0.0911417	+	0.171830i
$714$	−4.30563	+	0.963689i	−0.161134	+	0.0360652i
$715$	25.2356	+	55.2582i	0.943756	+	2.06654i
$716$	−0.728537	+	3.00307i	−0.0272267	+	0.112230i
$717$	2.02501	−	10.5067i	0.0756253	−	0.392382i
$718$	−33.6465	−	1.60278i	−1.25568	−	0.0598153i
$719$	−6.01544	−	31.2111i	−0.224338	−	1.16398i	−0.903038	−	0.429560i	$-0.858669\pi$
$719$	−6.01544	−	31.2111i	−0.224338	−	1.16398i	0.678700	−	0.734415i	$-0.262544\pi$
$720$	−0.627620	−	4.36519i	−0.0233900	−	0.162681i
$721$	−15.2337	+	7.51322i	−0.567332	+	0.279807i
$722$	−11.5825	+	7.44361i	−0.431055	+	0.277022i
$723$	−14.1081	+	17.9400i	−0.524687	+	0.667194i
$724$	−1.86889	+	0.178457i	−0.0694566	+	0.00663230i
$725$	−27.8097	+	2.65550i	−1.03283	+	0.0986229i
$726$	0.494797	−	0.629185i	0.0183636	−	0.0233513i
$727$	−21.4527	+	13.7868i	−0.795636	+	0.511324i	−0.874189	−	0.485586i	$-0.838606\pi$
$727$	−21.4527	+	13.7868i	−0.795636	+	0.511324i	0.0785530	+	0.996910i	$0.474970\pi$
$728$	−5.89380	+	8.82150i	−0.218439	+	0.326947i
$729$	0.142315	+	0.989821i	0.00527092	+	0.0366601i
$730$	3.70700	+	19.2338i	0.137202	+	0.711873i
$731$	8.63595	+	0.411381i	0.319412	+	0.0152155i
$732$	1.31873	−	6.84224i	0.0487418	−	0.252897i
$733$	−2.55159	+	10.5178i	−0.0942450	+	0.388483i	−0.999324	−	0.0367601i	$-0.988296\pi$
$733$	−2.55159	+	10.5178i	−0.0942450	+	0.388483i	0.905079	+	0.425243i	$0.139811\pi$
$734$	−11.1816	−	24.4843i	−0.412721	−	0.903733i
$735$	−17.6041	+	25.3592i	−0.649335	+	0.935389i
$736$	−1.07612	+	4.67354i	−0.0396663	+	0.172269i
$737$	−10.3488	+	17.9247i	−0.381203	+	0.660264i
$738$	−0.188566	−	0.134277i	−0.00694121	−	0.00494281i
$739$	−31.4567	−	29.9939i	−1.15715	−	1.10334i	−0.993146	−	0.116883i	$-0.962710\pi$
$739$	−31.4567	−	29.9939i	−1.15715	−	1.10334i	−0.164007	−	0.986459i	$-0.552442\pi$
$740$	19.3884	−	6.71038i	0.712731	−	0.246679i
$741$	7.71597	+	4.95876i	0.283453	+	0.182164i
$742$	30.1452	−	13.1232i	1.10666	−	0.481768i
$743$	−9.56096	+	1.37466i	−0.350757	+	0.0504313i	−0.315442	−	0.948945i	$-0.602153\pi$
$743$	−9.56096	+	1.37466i	−0.350757	+	0.0504313i	−0.0353156	+	0.999376i	$0.511244\pi$
$744$	0.783776	−	0.747329i	0.0287346	−	0.0273984i
$745$	−38.1281	+	73.9582i	−1.39691	+	2.70962i
$746$	7.24788	+	18.1043i	0.265364	+	0.662846i
$747$	6.88015	+	9.66182i	0.251731	+	0.353507i
$748$	−5.21095	−	2.37976i	−0.190531	−	0.0870127i
$749$	−17.7506	+	12.1697i	−0.648593	+	0.444670i
$750$	22.5286	+	35.0551i	0.822627	+	1.28003i
$751$	−9.37782	−	9.83517i	−0.342201	−	0.358891i	0.530034	−	0.847976i	$-0.322179\pi$
$751$	−9.37782	−	9.83517i	−0.342201	−	0.358891i	−0.872236	+	0.489086i	$0.837331\pi$
$752$	7.19906	+	9.15435i	0.262523	+	0.333825i
$753$	−24.1854	−	8.37064i	−0.881364	−	0.305043i
$754$	−3.55263	−	6.89113i	−0.129379	−	0.250960i
$755$	−39.1803	+	45.2165i	−1.42592	+	1.64560i
$756$	2.31448	−	1.28187i	0.0841769	−	0.0466210i
$757$	−40.7050	+	18.5893i	−1.47945	+	0.675641i	−0.981482	−	0.191556i	$-0.938647\pi$
$757$	−40.7050	+	18.5893i	−1.47945	+	0.675641i	−0.497965	+	0.867197i	$0.665919\pi$
$758$	2.25774	+	1.30350i	0.0820046	+	0.0473454i
$759$	−6.66818	+	15.0647i	−0.242040	+	0.546814i
$760$	5.04366	+	8.73587i	0.182953	+	0.316883i
$761$	−3.55345	+	37.2134i	−0.128812	+	1.34898i	0.667731	+	0.744403i	$0.267266\pi$
$761$	−3.55345	+	37.2134i	−0.128812	+	1.34898i	−0.796543	+	0.604582i	$0.793340\pi$
$762$	−2.70068	−	9.19766i	−0.0978352	−	0.333196i
$763$	−12.5920	+	23.3927i	−0.455862	+	0.846874i
$764$	−7.01730	+	10.9191i	−0.253877	+	0.395040i
$765$	−7.22153	+	1.39184i	−0.261095	+	0.0503219i
$766$	−15.4524	+	12.1519i	−0.558318	+	0.439066i
$767$	−5.13047	−	21.1481i	−0.185250	−	0.763612i
$768$	0.998867	−	0.0475819i	0.0360435	−	0.00171696i
$769$	−1.11078	+	7.72566i	−0.0400558	+	0.278594i	−0.999999	−	0.00160139i	$-0.999490\pi$
$769$	−1.11078	+	7.72566i	−0.0400558	+	0.278594i	0.959943	+	0.280196i	$0.0903994\pi$
$770$	−38.1046	+	12.4328i	−1.37319	+	0.448049i
$771$	2.54713	−	5.57745i	0.0917328	−	0.200867i
$772$	0.0637326	+	0.0501199i	0.00229379	+	0.00180385i
$773$	−37.4759	−	19.3202i	−1.34791	−	0.694898i	−0.375209	−	0.926940i	$-0.622429\pi$
$773$	−37.4759	−	19.3202i	−1.34791	−	0.694898i	−0.972706	+	0.232042i	$0.925459\pi$
$774$	−5.03828	+	1.22227i	−0.181097	+	0.0439337i
$775$	−5.81560	+	14.5267i	−0.208902	+	0.521813i
$776$	−5.81236	−	6.70782i	−0.208652	−	0.240797i
$777$	7.89355	+	9.44434i	0.283180	+	0.338814i
$778$	27.8630	+	24.1434i	0.998936	+	0.865583i
$779$	0.514568	+	0.124833i	0.0184363	+	0.00447260i
$780$	−10.2578	+	14.4050i	−0.367287	+	0.515782i
$781$	0.967961	−	0.558852i	0.0346364	−	0.0199973i
$782$	7.87034	+	1.42171i	0.281443	+	0.0508401i
$783$			1.93346i			0.0690961i
$784$	−5.34480	−	4.52030i	−0.190886	−	0.161439i
$785$	−31.2325	+	9.17068i	−1.11473	+	0.327316i
$786$	−4.61897	−	13.3456i	−0.164753	−	0.476023i
$787$	−2.59483	+	54.4723i	−0.0924959	+	1.94173i	0.188613	+	0.982051i	$0.439601\pi$
$787$	−2.59483	+	54.4723i	−0.0924959	+	1.94173i	−0.281109	+	0.959676i	$0.590702\pi$
$788$	4.58835	−	13.2572i	0.163453	−	0.472267i
$789$	7.73939	+	3.09838i	0.275529	+	0.110305i
$790$	10.6084	−	36.1288i	0.377429	−	1.28541i
$791$	14.7036	+	53.5882i	0.522801	+	1.90538i
$792$	3.40021	+	0.488877i	0.120821	+	0.0173715i
$793$	−22.7607	+	16.2078i	−0.808255	+	0.575556i
$794$	−0.185151	−	1.93899i	−0.00657078	−	0.0688123i
$795$	50.8769	−	20.3680i	1.80442	−	0.722380i
$796$	0.605488	+	12.7108i	0.0214610	+	0.450521i
$797$	16.3832	+	4.81055i	0.580324	+	0.170399i	0.558703	−	0.829368i	$-0.311299\pi$
$797$	16.3832	+	4.81055i	0.580324	+	0.170399i	0.0216210	+	0.999766i	$0.493117\pi$
$798$	−3.82503	+	4.68959i	−0.135405	+	0.166010i
$799$	14.6776	−	12.7182i	0.519257	−	0.449939i
$800$	−12.8426	+	6.62084i	−0.454056	+	0.234082i
$801$	−5.74974	−	1.10817i	−0.203157	−	0.0391553i
$802$	−5.42426	+	5.68880i	−0.191537	+	0.200879i
$803$	−15.1885	−	1.45033i	−0.535991	−	0.0511810i
$804$	−6.02520			−0.212492
$805$	47.2589	−	29.9642i	1.66566	−	1.05610i
$806$	−4.34258			−0.152961
$807$	12.8063	+	1.22285i	0.450803	+	0.0430464i
$808$	−7.86188	+	8.24530i	−0.276580	+	0.290069i
$809$	10.4794	+	2.01974i	0.368436	+	0.0710102i	0.370109	−	0.928988i	$-0.379320\pi$
$809$	10.4794	+	2.01974i	0.368436	+	0.0710102i	−0.00167289	+	0.999999i	$0.500532\pi$
$810$	3.91984	−	2.02082i	0.137729	−	0.0710043i
$811$	3.72355	−	3.22648i	0.130752	−	0.113297i	−0.587030	−	0.809565i	$-0.699703\pi$
$811$	3.72355	−	3.22648i	0.130752	−	0.113297i	0.717782	+	0.696268i	$0.245158\pi$
$812$	4.78211	−	1.81635i	0.167819	−	0.0637414i
$813$	9.01386	+	2.64671i	0.316130	+	0.0928242i
$814$	0.760420	+	15.9632i	0.0266527	+	0.559509i
$815$	−74.7792	+	29.9371i	−2.61940	+	1.04865i
$816$	−0.158519	−	1.66009i	−0.00554928	−	0.0581147i
$817$	9.65963	−	6.87859i	0.337948	−	0.240651i
$818$	−5.43815	−	0.781887i	−0.190140	−	0.0273381i
$819$	−10.2640	−	2.68442i	−0.358653	−	0.0938011i
$820$	−0.287618	+	0.979535i	−0.0100440	+	0.0342069i
$821$	44.4281	+	17.7863i	1.55055	+	0.620747i	0.979729	−	0.200328i	$-0.0642007\pi$
$821$	44.4281	+	17.7863i	1.55055	+	0.620747i	0.570821	+	0.821074i	$0.306625\pi$
$822$	6.21398	−	17.9541i	0.216737	−	0.626221i
$823$	0.925137	−	19.4210i	0.0322483	−	0.676974i	−0.923643	−	0.383254i	$-0.874803\pi$
$823$	0.925137	−	19.4210i	0.0322483	−	0.676974i	0.955891	−	0.293721i	$-0.0948935\pi$
$824$	−2.09977	−	6.06689i	−0.0731490	−	0.211350i
$825$	−47.6237	+	13.9836i	−1.65805	+	0.486846i
$826$	14.2463	−	1.79000i	0.495691	−	0.0622821i
$827$		−	48.9562i		−	1.70237i	−0.524864	−	0.851186i	$-0.675884\pi$
$827$		−	48.9562i		−	1.70237i	0.524864	−	0.851186i	$-0.324116\pi$
$828$	−4.76846	+	0.511630i	−0.165716	+	0.0177804i
$829$	39.8309	−	22.9964i	1.38338	−	0.798697i	0.390825	−	0.920465i	$-0.372190\pi$
$829$	39.8309	−	22.9964i	1.38338	−	0.798697i	0.992559	+	0.121768i	$0.0388565\pi$
$830$	30.3420	−	42.6094i	1.05319	−	1.47899i
$831$	−16.6849	−	4.04770i	−0.578791	−	0.140413i
$832$	−3.03049	−	2.62593i	−0.105063	−	0.0910379i
$833$	−7.10558	+	9.26179i	−0.246194	+	0.320902i
$834$	5.75787	+	6.64494i	0.199379	+	0.230095i
$835$	37.2561	−	93.0613i	1.28930	−	3.22052i
$836$	−7.63590	+	1.85245i	−0.264093	+	0.0640683i
$837$	0.962574	+	0.496241i	0.0332714	+	0.0171526i
$838$	17.7140	+	13.9304i	0.611920	+	0.481219i
$839$	6.60313	−	14.4588i	0.227965	−	0.499174i	−0.760738	−	0.649059i	$-0.775163\pi$
$839$	6.60313	−	14.4588i	0.227965	−	0.499174i	0.988704	+	0.149885i	$0.0478902\pi$
$840$	−8.68061	−	7.79671i	−0.299510	−	0.269012i
$841$	3.59512	−	25.0046i	0.123970	−	0.862228i
$842$	−5.69738	+	0.271400i	−0.196345	+	0.00935305i
$843$	−7.53520	−	31.0605i	−0.259526	−	1.06978i
$844$	−8.82163	+	6.93740i	−0.303653	+	0.238795i
$845$	13.3350	−	2.57011i	0.458739	−	0.0884146i
$846$	−6.29629	+	9.79722i	−0.216471	+	0.336835i
$847$	−0.0630830	−	2.11681i	−0.00216756	−	0.0727346i
$848$	3.50099	+	11.9233i	0.120224	+	0.409447i
$849$	2.26478	−	23.7178i	0.0777270	−	0.813994i
$850$	12.0477	+	20.8673i	0.413234	+	0.715741i
$851$	−6.53557	−	21.3327i	−0.224037	−	0.731275i
$852$	0.281779	+	0.162685i	0.00965359	+	0.00557350i
$853$	4.43313	−	2.02454i	0.151787	−	0.0693190i	−0.338073	−	0.941120i	$-0.609775\pi$
$853$	4.43313	−	2.02454i	0.151787	−	0.0693190i	0.489860	+	0.871801i	$0.337048\pi$
$854$	−8.93225	−	16.1277i	−0.305655	−	0.551878i
$855$	−6.60579	+	7.62348i	−0.225913	+	0.260718i
$856$	−3.72742	−	7.23018i	−0.127401	−	0.247123i
$857$	50.1909	+	17.3712i	1.71449	+	0.593390i	0.994887	−	0.100998i	$-0.0322034\pi$
$857$	50.1909	+	17.3712i	1.71449	+	0.593390i	0.719601	+	0.694388i	$0.244325\pi$
$858$	−8.51499	−	10.8277i	−0.290697	−	0.369651i
$859$	13.1862	+	13.8293i	0.449906	+	0.471848i	0.909154	−	0.416460i	$-0.136729\pi$
$859$	13.1862	+	13.8293i	0.449906	+	0.471848i	−0.459248	+	0.888308i	$0.651881\pi$
$860$	12.3611	+	19.2342i	0.421508	+	0.655880i
$861$	−0.610631	+	0.0473525i	−0.0208102	+	0.00161377i
$862$	18.3942	+	8.40035i	0.626509	+	0.286117i
$863$	−8.29194	−	11.6444i	−0.282261	−	0.396380i	0.648967	−	0.760816i	$-0.275201\pi$
$863$	−8.29194	−	11.6444i	−0.282261	−	0.396380i	−0.931228	+	0.364436i	$0.881262\pi$
$864$	0.371662	+	0.928368i	0.0126442	+	0.0315837i
$865$	−51.2565	+	99.4237i	−1.74277	+	3.38051i
$866$	−11.7702	+	11.2229i	−0.399967	+	0.381368i
$867$	14.0742	−	2.02357i	0.477987	−	0.0687241i
$868$	0.323106	−	2.84697i	0.0109669	−	0.0966324i
$869$	24.6741	+	15.8571i	0.837011	+	0.537914i
$870$	8.05774	−	2.78881i	0.273183	−	0.0945495i
$871$	17.4858	+	16.6727i	0.592484	+	0.564932i
$872$	−8.17931	−	5.82446i	−0.276987	−	0.197241i
$873$	4.43786	−	7.68660i	0.150199	−	0.260152i
$874$	9.69081	−	5.14018i	0.327797	−	0.173869i
$875$	105.213	+	32.9394i	3.55685	+	1.11356i
$876$	−1.84510	−	4.04020i	−0.0623401	−	0.136506i
$877$	2.81054	−	11.5852i	0.0949052	−	0.391204i	−0.904470	−	0.426536i	$-0.859734\pi$
$877$	2.81054	−	11.5852i	0.0949052	−	0.391204i	0.999376	+	0.0353318i	$0.0112488\pi$
$878$	1.60029	−	8.30309i	0.0540072	−	0.280216i
$879$	22.7799	+	1.08514i	0.768346	+	0.0366008i
$880$	−2.86705	−	14.8756i	−0.0966481	−	0.501458i
$881$	0.156840	+	1.09085i	0.00528408	+	0.0367516i	0.992293	−	0.123915i	$-0.0395449\pi$
$881$	0.156840	+	1.09085i	0.00528408	+	0.0367516i	−0.987009	+	0.160666i	$0.948636\pi$
$882$	2.52357	−	6.52929i	0.0849731	−	0.219853i
$883$	−10.9606	+	7.04397i	−0.368855	+	0.237049i	−0.711916	−	0.702264i	$-0.752172\pi$
$883$	−10.9606	+	7.04397i	−0.368855	+	0.237049i	0.343061	+	0.939313i	$0.388536\pi$
$884$	−4.13369	+	5.25641i	−0.139031	+	0.176792i
$885$	23.8248	−	2.27499i	0.800862	−	0.0764731i
$886$	11.0997	−	1.05989i	0.372902	−	0.0356078i
$887$	5.06877	−	6.44547i	0.170193	−	0.216418i	−0.693473	−	0.720483i	$-0.743920\pi$
$887$	5.06877	−	6.44547i	0.170193	−	0.216418i	0.863666	+	0.504065i	$0.168163\pi$
$888$	−3.91372	+	2.51519i	−0.131336	+	0.0844044i
$889$	−21.0884	−	14.0895i	−0.707282	−	0.472547i
$890$	3.67507	+	25.5606i	0.123188	+	0.856795i
$891$	0.650111	+	3.37310i	0.0217796	+	0.113003i
$892$	6.95263	+	0.331195i	0.232791	+	0.0110892i
$893$	5.04131	−	26.1568i	0.168701	−	0.875304i
$894$	4.44822	−	18.3358i	0.148771	−	0.613241i
$895$	5.66125	+	12.3964i	0.189235	+	0.414366i
$896$	1.94703	−	1.79139i	0.0650456	−	0.0598462i
$897$	15.2544	+	11.7103i	0.509328	+	0.390995i
$898$	13.8156	−	23.9293i	0.461031	−	0.798530i
$899$	1.70561	+	1.21456i	0.0568851	+	0.0405077i
$900$	−10.4571	−	9.97083i	−0.348570	−	0.332361i
$901$	19.5834	−	6.77788i	0.652418	−	0.225804i
$902$	−0.668971	−	0.429922i	−0.0222743	−	0.0143148i
$903$	−8.15415	+	11.0298i	−0.271353	+	0.367050i
$904$	−20.7893	+	2.98904i	−0.691440	+	0.0994141i
$905$	−5.99211	+	5.71346i	−0.199184	+	0.189922i
$906$	6.21659	−	12.0585i	0.206532	−	0.400617i
$907$	−12.2439	−	30.5838i	−0.406552	−	1.01552i	−0.980481	−	0.196614i	$-0.937006\pi$
$907$	−12.2439	−	30.5838i	−0.406552	−	1.01552i	0.573929	−	0.818905i	$-0.305419\pi$
$908$	15.0170	+	21.0884i	0.498356	+	0.699844i
$909$	−10.3632	−	4.73271i	−0.343725	−	0.156974i
$910$	3.61737	+	46.6476i	0.119915	+	1.54635i
$911$	−20.7179	−	32.2377i	−0.686416	−	1.06808i	−0.993213	−	0.116309i	$-0.962894\pi$
$911$	−20.7179	−	32.2377i	−0.686416	−	1.06808i	0.306797	−	0.951775i	$-0.400743\pi$
$912$	−1.57844	−	1.65542i	−0.0522673	−	0.0548164i
$913$	25.1870	+	32.0279i	0.833568	+	1.05997i
$914$	−8.18556	−	2.83305i	−0.270754	−	0.0937090i
$915$	−14.0814	−	27.3141i	−0.465516	−	0.902976i
$916$	−14.4031	+	16.6221i	−0.475892	+	0.549208i
$917$	−32.0206	−	19.2553i	−1.05741	−	0.635867i
$918$	1.51694	−	0.692763i	0.0500664	−	0.0228646i
$919$	12.9391	+	7.47038i	0.426821	+	0.246425i	0.697991	−	0.716106i	$-0.254077\pi$
$919$	12.9391	+	7.47038i	0.426821	+	0.246425i	−0.271170	+	0.962531i	$0.587411\pi$
$920$	9.01025	+	19.1347i	0.297059	+	0.630854i
$921$	10.5729	+	18.3129i	0.348390	+	0.603430i
$922$	−0.326323	+	3.41741i	−0.0107469	+	0.112546i
$923$	−0.367579	−	1.25186i	−0.0120990	−	0.0412054i
$924$	7.73212	−	4.77675i	0.254368	−	0.157144i
$925$	36.3416	−	56.5486i	1.19490	−	1.85931i
$926$	5.03933	−	0.971252i	0.165603	−	0.0319173i
$927$	5.04645	−	3.96857i	0.165747	−	0.130345i
$928$	0.455829	+	1.87895i	0.0149633	+	0.0616797i
$929$	25.5382	−	1.21653i	0.837880	−	0.0399132i	0.375746	−	0.926723i	$-0.377387\pi$
$929$	25.5382	−	1.21653i	0.837880	−	0.0399132i	0.462135	+	0.886810i	$0.347084\pi$
$930$	0.679688	−	4.72734i	0.0222879	−	0.155015i
$931$	0.191880	+	16.0102i	0.00628861	+	0.524712i
$932$	−0.945872	+	2.07117i	−0.0309831	+	0.0678435i
$933$	−6.25235	−	4.91690i	−0.204693	−	0.160972i
$934$	−29.3948	−	15.1541i	−0.961828	−	0.495857i
$935$	−24.5516	+	5.95616i	−0.802924	+	0.194787i
$936$	1.49033	−	3.72268i	0.0487131	−	0.121679i
$937$	−27.8158	−	32.1012i	−0.908704	−	1.04870i	−0.998608	−	0.0527496i	$-0.983201\pi$
$937$	−27.8158	−	32.1012i	−0.908704	−	1.04870i	0.0899040	−	0.995950i	$-0.471344\pi$
$938$	−12.2315	+	10.2231i	−0.399373	+	0.333795i
$939$	9.09316	+	7.87926i	0.296744	+	0.257130i
$940$	49.9120	+	12.1085i	1.62795	+	0.394936i
$941$	33.9940	−	47.7379i	1.10817	−	1.55621i	0.313077	−	0.949728i	$-0.398640\pi$
$941$	33.9940	−	47.7379i	1.10817	−	1.55621i	0.795096	−	0.606484i	$-0.207421\pi$
$942$	6.39217	−	3.69052i	0.208268	−	0.120244i
$943$	1.05330	+	0.350822i	0.0343001	+	0.0114243i
$944$			5.42692i			0.176631i
$945$	4.52875	−	10.7532i	0.147320	−	0.349803i
$946$	−17.0880	+	5.01748i	−0.555578	+	0.163132i
$947$	11.0264	+	31.8586i	0.358308	+	1.03526i	0.969777	+	0.243995i	$0.0784580\pi$
$947$	11.0264	+	31.8586i	0.358308	+	1.03526i	−0.611468	+	0.791269i	$0.709421\pi$
$948$	−0.406263	+	8.52851i	−0.0131948	+	0.276993i
$949$	−5.82520	+	16.8308i	−0.189094	+	0.546351i
$950$	30.6819	+	12.2832i	0.995451	+	0.398518i
$951$	3.10587	−	10.5776i	0.100715	−	0.343003i
$952$	−3.13851	−	3.10112i	−0.101720	−	0.100508i
$953$	−24.8530	−	3.57332i	−0.805066	−	0.115751i	−0.272518	−	0.962151i	$-0.587856\pi$
$953$	−24.8530	−	3.57332i	−0.805066	−	0.115751i	−0.532548	+	0.846400i	$0.678766\pi$
$954$	−10.1224	+	7.20816i	−0.327726	+	0.233373i
$955$	5.44111	+	56.9819i	0.176070	+	1.84389i
$956$	9.93364	−	3.97683i	0.321277	−	0.128620i
$957$	0.316028	+	6.63424i	0.0102157	+	0.214454i
$958$	27.3477	+	8.03002i	0.883566	+	0.259438i
$959$	−17.8483	−	46.9913i	−0.576352	−	1.51743i
$960$	3.33292	−	2.88799i	0.107569	−	0.0932095i
$961$	−26.5115	+	13.6676i	−0.855209	+	0.440891i
$962$	18.3180	+	3.53050i	0.590595	+	0.113828i
$963$	5.61341	−	5.88718i	0.180890	−	0.189712i
$964$	−22.7195	−	2.16945i	−0.731746	−	0.0698732i
$965$	0.357566			0.0115105
$966$	−8.81218	+	9.12938i	−0.283527	+	0.293733i
$967$	−8.94976			−0.287805			−0.143902	−	0.989592i	$-0.545965\pi$
$967$	−8.94976			−0.287805			−0.143902	+	0.989592i	$0.545965\pi$
$968$	0.796812	+	0.0760863i	0.0256105	+	0.00244551i
$969$	−2.63227	+	2.76064i	−0.0845606	+	0.0886846i
$970$	−38.4353	−	7.40780i	−1.23408	−	0.237850i
$971$	−23.3374	+	12.0312i	−0.748931	+	0.386101i	−0.790041	−	0.613054i	$-0.789941\pi$
$971$	−23.3374	+	12.0312i	−0.748931	+	0.386101i	0.0411099	+	0.999155i	$0.486911\pi$
$972$	−0.755750	+	0.654861i	−0.0242407	+	0.0210047i
$973$	22.9634	+	3.72014i	0.736174	+	0.119262i
$974$	−15.9557	−	4.68502i	−0.511254	−	0.150118i
$975$	2.75683	+	57.8729i	0.0882891	+	1.85342i
$976$	6.46902	−	2.58981i	0.207068	−	0.0828977i
$977$	4.66132	+	48.8155i	0.149129	+	1.56175i	0.691979	+	0.721918i	$0.256739\pi$
$977$	4.66132	+	48.8155i	0.149129	+	1.56175i	−0.542850	+	0.839829i	$0.682655\pi$
$978$	14.8780	−	10.5946i	0.475747	−	0.338778i
$979$	−19.9101	−	2.86264i	−0.636330	−	0.0914905i
$980$	−30.8510	−	1.09924i	−0.985499	−	0.0351140i
$981$	2.82893	−	9.63445i	0.0903208	−	0.307604i
$982$	24.5553	+	9.83047i	0.783592	+	0.313703i
$983$	15.0911	−	43.6029i	0.481332	−	1.39072i	−0.399258	−	0.916838i	$-0.630732\pi$
$983$	15.0911	−	43.6029i	0.481332	−	1.39072i	0.880590	−	0.473879i	$-0.157146\pi$
$984$	0.0110147	−	0.231227i	0.000351137	−	0.00737126i
$985$	−20.2350	−	58.4652i	−0.644741	−	1.86286i
$986$	3.09370	−	0.908393i	0.0985235	−	0.0289291i
$987$	3.84127	+	30.5720i	0.122269	+	0.973117i
$988$			9.17200i			0.291800i
$989$	21.3858	−	12.6826i	0.680028	−	0.403282i
$990$	13.1198	−	7.57471i	0.416974	−	0.240740i
$991$	−17.4839	+	24.5527i	−0.555394	+	0.779942i	−0.992859	−	0.119294i	$-0.961937\pi$
$991$	−17.4839	+	24.5527i	−0.555394	+	0.779942i	0.437465	+	0.899235i	$0.355876\pi$
$992$	1.05243	+	0.255318i	0.0334148	+	0.00810635i
$993$	−1.37504	−	1.19148i	−0.0436357	−	0.0378105i
$994$	0.848060	−	0.147839i	0.0268988	−	0.00468917i
$995$	36.7502	+	42.4120i	1.16506	+	1.34455i
$996$	−4.40835	+	11.0115i	−0.139684	+	0.348913i
$997$	14.5655	−	3.53356i	0.461295	−	0.111909i	0.00162483	−	0.999999i	$-0.499483\pi$
$997$	14.5655	−	3.53356i	0.461295	−	0.111909i	0.459670	+	0.888090i	$0.347968\pi$
$998$	13.8016	+	7.11523i	0.436883	+	0.225229i
$999$	−3.65691	−	2.87583i	−0.115700	−	0.0909871i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.be.b.19.16	✓	320
7.3	odd	6	inner	966.2.be.b.157.16	yes	320
23.17	odd	22	inner	966.2.be.b.523.16	yes	320
161.17	even	66	inner	966.2.be.b.661.16	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.be.b.19.16	✓	320	1.1	even	1	trivial
966.2.be.b.157.16	yes	320	7.3	odd	6	inner
966.2.be.b.523.16	yes	320	23.17	odd	22	inner
966.2.be.b.661.16	yes	320	161.17	even	66	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.be (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.995472 - 0.0950560i) q^{2} +(0.690079 - 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(3.91984 - 2.02082i) q^{5} +(-0.755750 + 0.654861i) q^{6} +(-0.423103 + 2.61170i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +O(q^{10})\)	\(q+(-0.995472 - 0.0950560i) q^{2} +(0.690079 - 0.723734i) q^{3} +(0.981929 + 0.189251i) q^{4} +(3.91984 - 2.02082i) q^{5} +(-0.755750 + 0.654861i) q^{6} +(-0.423103 + 2.61170i) q^{7} +(-0.959493 - 0.281733i) q^{8} +(-0.0475819 - 0.998867i) q^{9} +(-4.09418 + 1.63906i) q^{10} +(-0.326534 - 3.41962i) q^{11} +(0.814576 - 0.580057i) q^{12} +(-3.96910 - 0.570670i) q^{13} +(0.669445 - 2.55966i) q^{14} +(1.24246 - 4.23144i) q^{15} +(0.928368 + 0.371662i) q^{16} +(0.545432 - 1.57592i) q^{17} +(-0.0475819 + 0.998867i) q^{18} +(-0.748112 - 2.16153i) q^{19} +(4.23144 - 1.24246i) q^{20} +(1.59820 + 2.10849i) q^{21} +3.43518i q^{22} +(-1.18504 - 4.64711i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(8.38114 - 11.7697i) q^{25} +(3.89688 + 0.945373i) q^{26} +(-0.755750 - 0.654861i) q^{27} +(-0.909725 + 2.48443i) q^{28} +(-1.26614 - 1.46121i) q^{29} +(-1.63906 + 4.09418i) q^{30} +(-1.05243 + 0.255318i) q^{31} +(-0.888835 - 0.458227i) q^{32} +(-2.70023 - 2.12349i) q^{33} +(-0.692763 + 1.51694i) q^{34} +(3.61928 + 11.0925i) q^{35} +(0.142315 - 0.989821i) q^{36} +(4.64698 - 0.221363i) q^{37} +(0.539259 + 2.22285i) q^{38} +(-3.15200 + 2.47876i) q^{39} +(-4.33039 + 0.834614i) q^{40} +(-0.125153 + 0.194742i) q^{41} +(-1.39054 - 2.25087i) q^{42} +(1.46062 + 4.97441i) q^{43} +(0.326534 - 3.41962i) q^{44} +(-2.20504 - 3.81924i) q^{45} +(0.737943 + 4.73872i) q^{46} +(10.0857 + 5.82299i) q^{47} +(0.909632 - 0.415415i) q^{48} +(-6.64197 - 2.21004i) q^{49} +(-9.46197 + 10.9197i) q^{50} +(-0.764157 - 1.48226i) q^{51} +(-3.78937 - 1.31151i) q^{52} +(7.68164 + 9.76800i) q^{53} +(0.690079 + 0.723734i) q^{54} +(-8.19039 - 12.7445i) q^{55} +(1.14177 - 2.38671i) q^{56} +(-2.08063 - 0.950191i) q^{57} +(1.12151 + 1.57495i) q^{58} +(2.01698 + 5.03818i) q^{59} +(2.02082 - 3.91984i) q^{60} +(5.04310 - 4.80859i) q^{61} +(1.07194 - 0.154121i) q^{62} +(2.62888 + 0.298354i) q^{63} +(0.841254 + 0.540641i) q^{64} +(-16.7114 + 5.78389i) q^{65} +(2.48615 + 2.37054i) q^{66} +(-4.90798 - 3.49496i) q^{67} +(0.833820 - 1.44422i) q^{68} +(-4.18105 - 2.34922i) q^{69} +(-2.54848 - 11.3863i) q^{70} +(0.135164 + 0.295967i) q^{71} +(-0.235759 + 0.971812i) q^{72} +(0.840575 - 4.36131i) q^{73} +(-4.64698 - 0.221363i) q^{74} +(-2.73446 - 14.1877i) q^{75} +(-0.325521 - 2.26405i) q^{76} +(9.06919 + 0.594042i) q^{77} +(3.37335 - 2.16792i) q^{78} +(-5.27795 + 6.71146i) q^{79} +(4.39011 - 0.419205i) q^{80} +(-0.995472 + 0.0950560i) q^{81} +(0.143097 - 0.181963i) q^{82} +(-9.97824 + 6.41263i) q^{83} +(1.17029 + 2.37285i) q^{84} +(-1.04664 - 7.27957i) q^{85} +(-0.981157 - 5.09073i) q^{86} +(-1.93127 - 0.0919975i) q^{87} +(-0.650111 + 3.37310i) q^{88} +(1.38050 - 5.69050i) q^{89} +(1.83201 + 4.01155i) q^{90} +(3.16976 - 10.1246i) q^{91} +(-0.284158 - 4.78741i) q^{92} +(-0.541481 + 0.937872i) q^{93} +(-9.48653 - 6.75533i) q^{94} +(-7.30053 - 6.96104i) q^{95} +(-0.945001 + 0.327068i) q^{96} +(7.46673 + 4.79858i) q^{97} +(6.40182 + 2.83139i) q^{98} +(-3.40021 + 0.488877i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9}+O(q^{10}) \) 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9	\( 320 q + 16 q^{2} + 16 q^{4} - 32 q^{8} - 16 q^{9} + 22 q^{14} + 16 q^{16} - 66 q^{17} - 16 q^{18} + 36 q^{23} + 24 q^{25} + 12 q^{26} + 44 q^{28} + 8 q^{29} - 48 q^{31} + 16 q^{32} - 46 q^{35} + 32 q^{36} - 22 q^{37} + 66 q^{38} + 8 q^{39} + 176 q^{43} - 8 q^{46} + 120 q^{47} - 24 q^{49} - 48 q^{50} - 22 q^{51} - 12 q^{52} - 44 q^{53} + 44 q^{57} + 18 q^{58} + 12 q^{59} - 32 q^{64} - 108 q^{70} - 48 q^{71} - 16 q^{72} + 252 q^{73} + 22 q^{74} - 36 q^{75} - 42 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 12 q^{82} - 22 q^{84} - 76 q^{85} + 22 q^{86} + 24 q^{87} - 22 q^{88} + 16 q^{92} + 12 q^{94} + 26 q^{95} + 2 q^{98} + 88 q^{99}+O(q^{100}) \) 320 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 - 16 * q^9 + 22 * q^14 + 16 * q^16 - 66 * q^17 - 16 * q^18 + 36 * q^23 + 24 * q^25 + 12 * q^26 + 44 * q^28 + 8 * q^29 - 48 * q^31 + 16 * q^32 - 46 * q^35 + 32 * q^36 - 22 * q^37 + 66 * q^38 + 8 * q^39 + 176 * q^43 - 8 * q^46 + 120 * q^47 - 24 * q^49 - 48 * q^50 - 22 * q^51 - 12 * q^52 - 44 * q^53 + 44 * q^57 + 18 * q^58 + 12 * q^59 - 32 * q^64 - 108 * q^70 - 48 * q^71 - 16 * q^72 + 252 * q^73 + 22 * q^74 - 36 * q^75 - 42 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 12 * q^82 - 22 * q^84 - 76 * q^85 + 22 * q^86 + 24 * q^87 - 22 * q^88 + 16 * q^92 + 12 * q^94 + 26 * q^95 + 2 * q^98 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more