LMFDB - Embedded newform 231.2.be.a.200.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(2,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 10, 3]))

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

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

chi := DirichletCharacter("231.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.be (of order $30$, degree $8$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			200.21
Character	$\chi$	$=$	231.200
Dual form			231.2.be.a.149.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50815 - 0.320568i) q^{2} +(-1.65685 + 0.504814i) q^{3} +(0.344674 - 0.153459i) q^{4} +(2.08179 + 1.87445i) q^{5} +(-2.33696 + 1.29247i) q^{6} +(-0.0538576 + 2.64520i) q^{7} +(-2.02413 + 1.47062i) q^{8} +(2.49032 - 1.67281i) q^{9} +O(q^{10})$	\(q+(1.50815 - 0.320568i) q^{2} +(-1.65685 + 0.504814i) q^{3} +(0.344674 - 0.153459i) q^{4} +(2.08179 + 1.87445i) q^{5} +(-2.33696 + 1.29247i) q^{6} +(-0.0538576 + 2.64520i) q^{7} +(-2.02413 + 1.47062i) q^{8} +(2.49032 - 1.67281i) q^{9} +(3.74054 + 2.15960i) q^{10} +(-2.73361 - 1.87813i) q^{11} +(-0.493605 + 0.428254i) q^{12} +(5.92698 + 1.92579i) q^{13} +(0.766742 + 4.00664i) q^{14} +(-4.39546 - 2.05477i) q^{15} +(-3.08619 + 3.42756i) q^{16} +(0.112542 + 0.0239216i) q^{17} +(3.21954 - 3.32117i) q^{18} +(1.49827 - 3.36517i) q^{19} +(1.00519 + 0.326605i) q^{20} +(-1.24610 - 4.40990i) q^{21} +(-4.72477 - 1.95621i) q^{22} +(2.65577 - 1.53331i) q^{23} +(2.61130 - 3.45841i) q^{24} +(0.297634 + 2.83180i) q^{25} +(9.55615 + 1.00439i) q^{26} +(-3.28165 + 4.02875i) q^{27} +(0.387366 + 0.919996i) q^{28} +(-4.30196 - 3.12556i) q^{29} +(-7.28773 - 1.68987i) q^{30} +(-2.41451 - 2.68158i) q^{31} +(-1.05371 + 1.82508i) q^{32} +(5.47730 + 1.73183i) q^{33} +0.177399 q^{34} +(-5.07042 + 5.40580i) q^{35} +(0.601643 - 0.958734i) q^{36} +(-0.258461 + 2.45909i) q^{37} +(1.18086 - 5.55549i) q^{38} +(-10.7923 - 0.198731i) q^{39} +(-6.97042 - 0.732620i) q^{40} +(3.91730 - 2.84608i) q^{41} +(-3.29299 - 6.25135i) q^{42} -7.32577i q^{43} +(-1.23042 - 0.227848i) q^{44} +(8.31992 + 1.18556i) q^{45} +(3.51378 - 3.16382i) q^{46} +(0.274554 - 0.616659i) q^{47} +(3.38308 - 7.23691i) q^{48} +(-6.99420 - 0.284929i) q^{49} +(1.35666 + 4.17538i) q^{50} +(-0.198542 + 0.0171784i) q^{51} +(2.33840 - 0.245776i) q^{52} +(2.76812 - 2.49242i) q^{53} +(-3.65774 + 7.12796i) q^{54} +(-2.17032 - 9.03388i) q^{55} +(-3.78107 - 5.43345i) q^{56} +(-0.783628 + 6.33194i) q^{57} +(-7.48998 - 3.33475i) q^{58} +(4.55396 + 10.2284i) q^{59} +(-1.83032 - 0.0337038i) q^{60} +(0.347132 + 0.312559i) q^{61} +(-4.50108 - 3.27023i) q^{62} +(4.29079 + 6.67751i) q^{63} +(1.84642 - 5.68270i) q^{64} +(8.72891 + 15.1189i) q^{65} +(8.81577 + 0.856018i) q^{66} +(2.95979 - 5.12650i) q^{67} +(0.0424613 - 0.00902543i) q^{68} +(-3.62618 + 3.88114i) q^{69} +(-5.91405 + 9.77819i) q^{70} +(12.8230 - 4.16644i) q^{71} +(-2.58069 + 7.04830i) q^{72} +(2.28108 + 5.12339i) q^{73} +(0.398507 + 3.79154i) q^{74} +(-1.92267 - 4.54162i) q^{75} -1.38981i q^{76} +(5.11527 - 7.12980i) q^{77} +(-16.3402 + 3.15995i) q^{78} +(2.06117 + 9.69704i) q^{79} +(-12.8496 + 1.35054i) q^{80} +(3.40344 - 8.33166i) q^{81} +(4.99552 - 5.54809i) q^{82} +(3.17120 + 9.75996i) q^{83} +(-1.10624 - 1.32875i) q^{84} +(0.189449 + 0.260754i) q^{85} +(-2.34841 - 11.0484i) q^{86} +(8.70555 + 3.00690i) q^{87} +(8.29521 - 0.218501i) q^{88} +(-9.16047 + 5.28880i) q^{89} +(12.9278 - 0.879091i) q^{90} +(-5.41333 + 15.5744i) q^{91} +(0.680074 - 0.936041i) q^{92} +(5.35419 + 3.22411i) q^{93} +(0.216389 - 1.01803i) q^{94} +(9.42692 - 4.19714i) q^{95} +(0.824519 - 3.55583i) q^{96} +(0.935987 - 2.88067i) q^{97} +(-10.6397 + 1.81240i) q^{98} +(-9.94933 - 0.104367i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9}+O(q^{10}) $ 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9	$ 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9} - 16 q^{12} - 40 q^{13} + 12 q^{15} + 34 q^{16} - 5 q^{18} - 10 q^{19} - 76 q^{22} - 25 q^{24} - 18 q^{25} + 6 q^{27} + 10 q^{28} - 35 q^{30} - 8 q^{33} - 96 q^{34} - 48 q^{36} - 10 q^{37} - 45 q^{39} - 120 q^{40} + 34 q^{42} - 24 q^{45} - 50 q^{46} + 14 q^{48} - 56 q^{49} - 45 q^{51} - 10 q^{52} + 48 q^{55} + 60 q^{57} + 44 q^{58} - 47 q^{60} - 50 q^{61} + 60 q^{63} - 72 q^{64} + 77 q^{66} - 80 q^{67} + 78 q^{69} + 36 q^{70} + 55 q^{72} - 70 q^{73} - 11 q^{75} + 36 q^{78} - 90 q^{79} + 23 q^{81} - 6 q^{82} + 125 q^{84} + 160 q^{85} + 86 q^{88} + 30 q^{90} - 128 q^{91} - 38 q^{93} - 210 q^{94} + 135 q^{96} + 40 q^{97} + 80 q^{99}+O(q^{100}) $ 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9 - 16 * q^12 - 40 * q^13 + 12 * q^15 + 34 * q^16 - 5 * q^18 - 10 * q^19 - 76 * q^22 - 25 * q^24 - 18 * q^25 + 6 * q^27 + 10 * q^28 - 35 * q^30 - 8 * q^33 - 96 * q^34 - 48 * q^36 - 10 * q^37 - 45 * q^39 - 120 * q^40 + 34 * q^42 - 24 * q^45 - 50 * q^46 + 14 * q^48 - 56 * q^49 - 45 * q^51 - 10 * q^52 + 48 * q^55 + 60 * q^57 + 44 * q^58 - 47 * q^60 - 50 * q^61 + 60 * q^63 - 72 * q^64 + 77 * q^66 - 80 * q^67 + 78 * q^69 + 36 * q^70 + 55 * q^72 - 70 * q^73 - 11 * q^75 + 36 * q^78 - 90 * q^79 + 23 * q^81 - 6 * q^82 + 125 * q^84 + 160 * q^85 + 86 * q^88 + 30 * q^90 - 128 * q^91 - 38 * q^93 - 210 * q^94 + 135 * q^96 + 40 * q^97 + 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.50815	−	0.320568i	1.06643	−	0.226676i	0.358909	−	0.933372i	$-0.383149\pi$
$2$	1.50815	−	0.320568i	1.06643	−	0.226676i	0.707517	+	0.706697i	$0.249815\pi$
$3$	−1.65685	+	0.504814i	−0.956585	+	0.291455i
$3$	−1.65685	+	0.504814i	−0.956585	+	0.291455i
$4$	0.344674	−	0.153459i	0.172337	−	0.0767293i
$5$	2.08179	+	1.87445i	0.931003	+	0.838279i	0.987093	−	0.160146i	$-0.0511967\pi$
$5$	2.08179	+	1.87445i	0.931003	+	0.838279i	−0.0560899	+	0.998426i	$0.517863\pi$
$6$	−2.33696	+	1.29247i	−0.954061	+	0.527649i
$7$	−0.0538576	+	2.64520i	−0.0203563	+	0.999793i
$7$	−0.0538576	+	2.64520i	−0.0203563	+	0.999793i
$8$	−2.02413	+	1.47062i	−0.715639	+	0.519942i
$9$	2.49032	−	1.67281i	0.830108	−	0.557602i
$10$	3.74054	+	2.15960i	1.18286	+	0.682927i
$11$	−2.73361	−	1.87813i	−0.824214	−	0.566279i
$11$	−2.73361	−	1.87813i	−0.824214	−	0.566279i
$12$	−0.493605	+	0.428254i	−0.142492	+	0.123626i
$13$	5.92698	+	1.92579i	1.64385	+	0.534119i	0.977394	−	0.211426i	$-0.0678107\pi$
$13$	5.92698	+	1.92579i	1.64385	+	0.534119i	0.666455	+	0.745545i	$0.267811\pi$
$14$	0.766742	+	4.00664i	0.204920	+	1.07082i
$15$	−4.39546	−	2.05477i	−1.13490	−	0.530540i
$16$	−3.08619	+	3.42756i	−0.771547	+	0.856890i
$17$	0.112542	+	0.0239216i	0.0272955	+	0.00580184i	0.221539	−	0.975151i	$-0.428892\pi$
$17$	0.112542	+	0.0239216i	0.0272955	+	0.00580184i	−0.194244	+	0.980953i	$0.562225\pi$
$18$	3.21954	−	3.32117i	0.758854	−	0.782807i
$19$	1.49827	−	3.36517i	0.343727	−	0.772023i	−0.656122	−	0.754655i	$-0.727804\pi$
$19$	1.49827	−	3.36517i	0.343727	−	0.772023i	0.999849	−	0.0173686i	$-0.00552886\pi$
$20$	1.00519	+	0.326605i	0.224767	+	0.0730311i
$21$	−1.24610	−	4.40990i	−0.271922	−	0.962319i
$22$	−4.72477	−	1.95621i	−1.00732	−	0.417065i
$23$	2.65577	−	1.53331i	0.553766	−	0.319717i	−0.196874	−	0.980429i	$-0.563079\pi$
$23$	2.65577	−	1.53331i	0.553766	−	0.319717i	0.750639	+	0.660712i	$0.229746\pi$
$24$	2.61130	−	3.45841i	0.533030	−	0.705945i
$25$	0.297634	+	2.83180i	0.0595268	+	0.566360i
$26$	9.55615	+	1.00439i	1.87412	+	0.196977i
$27$	−3.28165	+	4.02875i	−0.631553	+	0.775333i
$28$	0.387366	+	0.919996i	0.0732052	+	0.173863i
$29$	−4.30196	−	3.12556i	−0.798854	−	0.580402i	0.111723	−	0.993739i	$-0.464363\pi$
$29$	−4.30196	−	3.12556i	−0.798854	−	0.580402i	−0.910578	+	0.413338i	$0.864363\pi$
$30$	−7.28773	−	1.68987i	−1.33055	−	0.308526i
$31$	−2.41451	−	2.68158i	−0.433659	−	0.481627i	0.486216	−	0.873838i	$-0.338377\pi$
$31$	−2.41451	−	2.68158i	−0.433659	−	0.481627i	−0.919875	+	0.392212i	$0.871710\pi$
$32$	−1.05371	+	1.82508i	−0.186272	+	0.322632i
$33$	5.47730	+	1.73183i	0.953475	+	0.301473i
$34$	0.177399			0.0304238
$35$	−5.07042	+	5.40580i	−0.857057	+	0.913746i
$36$	0.601643	−	0.958734i	0.100274	−	0.159789i
$37$	−0.258461	+	2.45909i	−0.0424907	+	0.404272i	0.952518	+	0.304483i	$0.0984836\pi$
$37$	−0.258461	+	2.45909i	−0.0424907	+	0.404272i	−0.995009	+	0.0997894i	$0.968183\pi$
$38$	1.18086	−	5.55549i	0.191560	−	0.901220i
$39$	−10.7923	−	0.198731i	−1.72815	−	0.0318224i
$40$	−6.97042	−	0.732620i	−1.10212	−	0.115837i
$41$	3.91730	−	2.84608i	0.611779	−	0.444483i	−0.238261	−	0.971201i	$-0.576578\pi$
$41$	3.91730	−	2.84608i	0.611779	−	0.444483i	0.850040	+	0.526718i	$0.176578\pi$
$42$	−3.29299	−	6.25135i	−0.508119	−	0.964604i
$43$		−	7.32577i		−	1.11717i	−0.829447	−	0.558585i	$-0.811344\pi$
$43$		−	7.32577i		−	1.11717i	0.829447	−	0.558585i	$-0.188656\pi$
$44$	−1.23042	−	0.227848i	−0.185492	−	0.0343493i
$45$	8.31992	+	1.18556i	1.24026	+	0.176733i
$46$	3.51378	−	3.16382i	0.518078	−	0.466480i
$47$	0.274554	−	0.616659i	0.0400478	−	0.0899489i	−0.892414	−	0.451218i	$-0.850990\pi$
$47$	0.274554	−	0.616659i	0.0400478	−	0.0899489i	0.932462	+	0.361269i	$0.117656\pi$
$48$	3.38308	−	7.23691i	0.488305	−	1.04456i
$49$	−6.99420	−	0.284929i	−0.999171	−	0.0407041i
$50$	1.35666	+	4.17538i	0.191861	+	0.590487i
$51$	−0.198542	+	0.0171784i	−0.0278014	+	0.00240545i
$52$	2.33840	−	0.245776i	0.324278	−	0.0340830i
$53$	2.76812	−	2.49242i	0.380230	−	0.342361i	−0.456749	−	0.889596i	$-0.650986\pi$
$53$	2.76812	−	2.49242i	0.380230	−	0.342361i	0.836979	+	0.547235i	$0.184320\pi$
$54$	−3.65774	+	7.12796i	−0.497755	+	0.969993i
$55$	−2.17032	−	9.03388i	−0.292646	−	1.21813i
$56$	−3.78107	−	5.43345i	−0.505267	−	0.726075i
$57$	−0.783628	+	6.33194i	−0.103794	+	0.838686i
$58$	−7.48998	−	3.33475i	−0.983482	−	0.437874i
$59$	4.55396	+	10.2284i	0.592875	+	1.33162i	0.921948	+	0.387314i	$0.126597\pi$
$59$	4.55396	+	10.2284i	0.592875	+	1.33162i	−0.329073	+	0.944304i	$0.606736\pi$
$60$	−1.83032	−	0.0337038i	−0.236294	−	0.00435114i
$61$	0.347132	+	0.312559i	0.0444458	+	0.0400191i	0.691054	−	0.722803i	$-0.257147\pi$
$61$	0.347132	+	0.312559i	0.0444458	+	0.0400191i	−0.646608	+	0.762822i	$0.723813\pi$
$62$	−4.50108	−	3.27023i	−0.571638	−	0.415319i
$63$	4.29079	+	6.67751i	0.540589	+	0.841287i
$64$	1.84642	−	5.68270i	0.230803	−	0.710337i
$65$	8.72891	+	15.1189i	1.08269	+	1.87527i
$66$	8.81577	+	0.856018i	1.08515	+	0.105368i
$67$	2.95979	−	5.12650i	0.361596	−	0.626302i	−0.626628	−	0.779319i	$-0.715565\pi$
$67$	2.95979	−	5.12650i	0.361596	−	0.626302i	0.988224	+	0.153016i	$0.0488987\pi$
$68$	0.0424613	−	0.00902543i	0.00514919	−	0.00109449i
$69$	−3.62618	+	3.88114i	−0.436541	+	0.467234i
$70$	−5.91405	+	9.77819i	−0.706864	+	1.16872i
$71$	12.8230	−	4.16644i	1.52181	−	0.494465i	0.575518	−	0.817789i	$-0.304800\pi$
$71$	12.8230	−	4.16644i	1.52181	−	0.494465i	0.946288	+	0.323324i	$0.104800\pi$
$72$	−2.58069	+	7.04830i	−0.304137	+	0.830651i
$73$	2.28108	+	5.12339i	0.266980	+	0.599648i	0.996433	−	0.0843831i	$-0.0268920\pi$
$73$	2.28108	+	5.12339i	0.266980	+	0.599648i	−0.729453	+	0.684031i	$0.760225\pi$
$74$	0.398507	+	3.79154i	0.0463255	+	0.440758i
$75$	−1.92267	−	4.54162i	−0.222011	−	0.524422i
$76$		−	1.38981i		−	0.159422i
$77$	5.11527	−	7.12980i	0.582939	−	0.812516i
$78$	−16.3402	+	3.15995i	−1.85016	+	0.357794i
$79$	2.06117	+	9.69704i	0.231900	+	1.09100i	0.927862	+	0.372924i	$0.121645\pi$
$79$	2.06117	+	9.69704i	0.231900	+	1.09100i	−0.695962	+	0.718078i	$0.745022\pi$
$80$	−12.8496	+	1.35054i	−1.43663	+	0.150995i
$81$	3.40344	−	8.33166i	0.378160	−	0.925740i
$82$	4.99552	−	5.54809i	0.551663	−	0.612684i
$83$	3.17120	+	9.75996i	0.348085	+	1.07129i	0.959912	+	0.280303i	$0.0904350\pi$
$83$	3.17120	+	9.75996i	0.348085	+	1.07129i	−0.611827	+	0.790992i	$0.709565\pi$
$84$	−1.10624	−	1.32875i	−0.120700	−	0.144979i
$85$	0.189449	+	0.260754i	0.0205486	+	0.0282828i
$86$	−2.34841	−	11.0484i	−0.253235	−	1.19138i
$87$	8.70555	+	3.00690i	0.933333	+	0.322373i
$88$	8.29521	−	0.218501i	0.884272	−	0.0232923i
$89$	−9.16047	+	5.28880i	−0.971008	+	0.560612i	−0.899543	−	0.436832i	$-0.856101\pi$
$89$	−9.16047	+	5.28880i	−0.971008	+	0.560612i	−0.0714645	+	0.997443i	$0.522767\pi$
$90$	12.9278	−	0.879091i	1.36271	−	0.0926643i
$91$	−5.41333	+	15.5744i	−0.567471	+	1.63264i
$92$	0.680074	−	0.936041i	0.0709026	−	0.0975890i
$93$	5.35419	+	3.22411i	0.555204	+	0.334325i
$94$	0.216389	−	1.01803i	0.0223188	−	0.105002i
$95$	9.42692	−	4.19714i	0.967182	−	0.430617i
$96$	0.824519	−	3.55583i	0.0841521	−	0.362915i
$97$	0.935987	−	2.88067i	0.0950351	−	0.292488i	−0.892228	−	0.451586i	$-0.850859\pi$
$97$	0.935987	−	2.88067i	0.0950351	−	0.292488i	0.987263	+	0.159098i	$0.0508585\pi$
$98$	−10.6397	+	1.81240i	−1.07477	+	0.183080i
$99$	−9.94933	−	0.104367i	−0.999945	−	0.0104893i
$100$	0.537150	+	0.930372i	0.0537150	+	0.0930372i
$101$	−4.37455	−	4.85843i	−0.435284	−	0.483432i	0.485094	−	0.874462i	$-0.338785\pi$
$101$	−4.37455	−	4.85843i	−0.435284	−	0.483432i	−0.920378	+	0.391030i	$0.872119\pi$
$102$	−0.293925	+	0.0895538i	−0.0291029	+	0.00886715i
$103$	1.60228	−	15.2447i	0.157878	−	1.50211i	−0.572976	−	0.819572i	$-0.694211\pi$
$103$	1.60228	−	15.2447i	0.157878	−	1.50211i	0.730854	−	0.682534i	$-0.239122\pi$
$104$	−14.8291	+	4.81827i	−1.45411	+	0.472471i
$105$	5.67202	−	11.5162i	0.553532	−	1.12387i
$106$	3.37576	−	4.64633i	0.327882	−	0.451292i
$107$	−8.56899	−	3.81516i	−0.828396	−	0.368825i	−0.0516697	−	0.998664i	$-0.516454\pi$
$107$	−8.56899	−	3.81516i	−0.828396	−	0.368825i	−0.776726	+	0.629839i	$0.783121\pi$
$108$	−0.512851	+	1.89220i	−0.0493491	+	0.182077i
$109$	−16.1551	−	9.32717i	−1.54738	−	0.893381i	−0.998341	−	0.0575849i	$-0.981660\pi$
$109$	−16.1551	−	9.32717i	−1.54738	−	0.893381i	−0.549040	−	0.835796i	$-0.685007\pi$
$110$	−6.16915	−	12.9288i	−0.588206	−	1.23271i
$111$	−0.813153	−	4.20483i	−0.0771810	−	0.399105i
$112$	−8.90037	−	8.34819i	−0.841006	−	0.788830i
$113$	1.43062	+	1.96909i	0.134582	+	0.185236i	0.870989	−	0.491303i	$-0.163479\pi$
$113$	1.43062	+	1.96909i	0.134582	+	0.185236i	−0.736407	+	0.676539i	$0.763479\pi$
$114$	0.847987	+	9.80075i	0.0794213	+	0.917924i
$115$	8.40285	+	1.78608i	0.783570	+	0.166553i
$116$	−1.96242	−	0.417124i	−0.182206	−	0.0387290i
$117$	17.9816	−	5.11885i	1.66240	−	0.473237i
$118$	10.1470	+	13.9661i	0.934103	+	1.28568i
$119$	−0.0693387	+	0.296409i	−0.00635627	+	0.0271717i
$120$	11.9188	−	2.30492i	1.08803	−	0.210410i
$121$	3.94522	+	10.2682i	0.358657	+	0.933470i
$122$	0.623726	+	0.360108i	0.0564695	+	0.0326027i
$123$	−5.05364	+	6.69305i	−0.455671	+	0.603492i
$124$	−1.24373	−	0.553744i	−0.111690	−	0.0497277i
$125$	3.54442	−	4.87848i	0.317023	−	0.436344i
$126$	8.61177	+	8.69522i	0.767197	+	0.774632i
$127$	−11.3486	+	3.68738i	−1.00702	+	0.327202i	−0.765669	−	0.643235i	$-0.777592\pi$
$127$	−11.3486	+	3.68738i	−1.00702	+	0.327202i	−0.241355	+	0.970437i	$0.577592\pi$
$128$	1.40357	−	13.3540i	0.124059	−	1.18034i
$129$	3.69816	+	12.1377i	0.325605	+	1.06867i
$130$	18.0112	+	20.0035i	1.57969	+	1.75442i
$131$	−0.483915	−	0.838165i	−0.0422799	−	0.0732309i	0.844111	−	0.536168i	$-0.180129\pi$
$131$	−0.483915	−	0.838165i	−0.0422799	−	0.0732309i	−0.886391	+	0.462937i	$0.846795\pi$
$132$	2.15364	−	0.243622i	0.187451	−	0.0212046i
$133$	8.82087	+	4.14447i	0.764866	+	0.359371i
$134$	2.82042	−	8.68037i	0.243647	−	0.749870i
$135$	−14.3834	+	2.23571i	−1.23792	+	0.192420i
$136$	−0.262980	+	0.117086i	−0.0225504	+	0.0100401i
$137$	−1.05299	+	4.95392i	−0.0899628	+	0.423242i	0.910000	+	0.414609i	$0.136081\pi$
$137$	−1.05299	+	4.95392i	−0.0899628	+	0.423242i	−0.999963	+	0.00863342i	$0.997252\pi$
$138$	−4.22467	+	7.01579i	−0.359628	+	0.597224i
$139$	−11.5531	+	15.9015i	−0.979923	+	1.34875i	−0.0430518	+	0.999073i	$0.513708\pi$
$139$	−11.5531	+	15.9015i	−0.979923	+	1.34875i	−0.936871	+	0.349675i	$0.886292\pi$
$140$	−0.918074	+	2.64133i	−0.0775914	+	0.223233i
$141$	−0.143598	+	1.16031i	−0.0120931	+	0.0977159i
$142$	18.0034	−	10.3943i	1.51081	−	0.872267i
$143$	−12.5851	−	16.3960i	−1.05242	−	1.37111i
$144$	−1.95197	+	13.6983i	−0.162664	+	1.14153i
$145$	−3.09707	−	14.5706i	−0.257197	−	1.21002i
$146$	5.08262	+	6.99562i	0.420641	+	0.578962i
$147$	11.7322	−	3.05869i	0.967655	−	0.252276i
$148$	0.288284	+	0.887247i	0.0236968	+	0.0729312i
$149$	2.85169	−	3.16712i	0.233619	−	0.259460i	−0.614924	−	0.788586i	$-0.710813\pi$
$149$	2.85169	−	3.16712i	0.233619	−	0.259460i	0.848543	+	0.529126i	$0.177480\pi$
$150$	−4.35558	−	6.23312i	−0.355632	−	0.508932i
$151$	−9.24660	+	0.971857i	−0.752477	+	0.0790886i	−0.472998	−	0.881063i	$-0.656828\pi$
$151$	−9.24660	+	0.971857i	−0.752477	+	0.0790886i	−0.279479	+	0.960152i	$0.590162\pi$
$152$	1.91619	+	9.01494i	0.155423	+	0.731208i
$153$	0.320283	−	0.128689i	0.0258933	−	0.0104039i
$154$	5.42903	−	12.3926i	0.437484	−	0.998626i
$155$		−	10.1084i		−	0.811923i
$156$	−3.75032	+	1.58767i	−0.300266	+	0.127116i
$157$	−1.03977	−	9.89276i	−0.0829827	−	0.789528i	−0.954309	−	0.298823i	$-0.903406\pi$
$157$	−1.03977	−	9.89276i	−0.0829827	−	0.789528i	0.871326	−	0.490705i	$-0.163261\pi$
$158$	6.21712	+	13.9639i	0.494608	+	1.11091i
$159$	−3.32815	+	5.52697i	−0.263940	+	0.438317i
$160$	−5.61463	+	1.82431i	−0.443876	+	0.144224i
$161$	3.91288	+	7.10762i	0.308378	+	0.560159i
$162$	2.46204	−	13.6565i	0.193436	−	1.07295i
$163$	−12.5372	+	2.66487i	−0.981991	+	0.208729i	−0.670816	−	0.741624i	$-0.734056\pi$
$163$	−12.5372	+	2.66487i	−0.981991	+	0.208729i	−0.311175	+	0.950353i	$0.600723\pi$
$164$	0.913433	−	1.58211i	0.0713271	−	0.123542i
$165$	8.15634	+	13.8722i	0.634970	+	1.07995i
$166$	7.91139	+	13.7029i	0.614043	+	1.06355i
$167$	−6.28028	+	19.3287i	−0.485983	+	1.49570i	0.344570	+	0.938761i	$0.388025\pi$
$167$	−6.28028	+	19.3287i	−0.485983	+	1.49570i	−0.830553	+	0.556940i	$0.811975\pi$
$168$	9.00756	+	7.09369i	0.694949	+	0.547290i
$169$	20.9032	+	15.1871i	1.60794	+	1.16824i
$170$	0.369308	+	0.332526i	0.0283246	+	0.0255036i
$171$	−1.89810	−	10.8867i	−0.145151	−	0.832526i
$172$	−1.12420	−	2.52500i	−0.0857197	−	0.192529i
$173$	−17.8415	−	7.94354i	−1.35646	−	0.603936i	−0.405743	−	0.913987i	$-0.632987\pi$
$173$	−17.8415	−	7.94354i	−1.35646	−	0.603936i	−0.950720	+	0.310051i	$0.899654\pi$
$174$	14.0932	+	1.74415i	1.06840	+	0.132223i
$175$	−7.50671	+	0.634789i	−0.567454	+	0.0479855i
$176$	14.8738	−	3.57333i	1.12116	−	0.269350i
$177$	−12.7087	−	14.6480i	−0.955241	−	1.10101i
$178$	−12.1200	+	10.9129i	−0.908431	+	0.817955i
$179$	2.01849	−	0.212152i	0.150869	−	0.0158570i	−0.0287929	−	0.999585i	$-0.509166\pi$
$179$	2.01849	−	0.212152i	0.150869	−	0.0158570i	0.179662	+	0.983728i	$0.442500\pi$
$180$	3.04959	−	0.868131i	0.227303	−	0.0647067i
$181$	2.01671	+	6.20679i	0.149901	+	0.461347i	0.997609	−	0.0691164i	$-0.0220180\pi$
$181$	2.01671	+	6.20679i	0.149901	+	0.461347i	−0.847708	+	0.530463i	$0.822018\pi$
$182$	−3.17149	+	25.2239i	−0.235087	+	1.86972i
$183$	−0.732932	−	0.342628i	−0.0541799	−	0.0253278i
$184$	−3.12072	+	7.00924i	−0.230062	+	0.516728i
$185$	−5.14750	+	4.63483i	−0.378452	+	0.340760i
$186$	9.10849	+	3.14608i	0.667867	+	0.230681i
$187$	−0.262718	−	0.276762i	−0.0192119	−	0.0202388i
$188$		−	0.254679i		−	0.0185743i
$189$	−10.4801	−	8.89760i	−0.762316	−	0.647205i
$190$	12.8718	−	9.35190i	0.933817	−	0.678458i
$191$	21.2854	+	2.23719i	1.54016	+	0.161877i	0.836224	−	0.548388i	$-0.184758\pi$
$191$	21.2854	+	2.23719i	1.54016	+	0.161877i	0.703934	+	0.710265i	$0.251425\pi$
$192$	−0.190540	+	10.3475i	−0.0137510	+	0.746766i
$193$	4.25921	−	20.0380i	0.306585	−	1.44237i	−0.507515	−	0.861643i	$-0.669436\pi$
$193$	4.25921	−	20.0380i	0.306585	−	1.44237i	0.814100	−	0.580725i	$-0.197231\pi$
$194$	0.488161	−	4.64454i	0.0350479	−	0.333459i
$195$	−22.0948	−	20.6434i	−1.58224	−	1.47830i
$196$	−2.45444	+	0.975112i	−0.175317	+	0.0696509i
$197$	−11.1508			−0.794460			−0.397230	−	0.917719i	$-0.630028\pi$
$197$	−11.1508			−0.794460			−0.397230	+	0.917719i	$0.630028\pi$
$198$	−15.0386	+	3.03203i	−1.06874	+	0.215477i
$199$	0.476430	−	0.825201i	0.0337732	−	0.0584969i	−0.848645	−	0.528963i	$-0.822581\pi$
$199$	0.476430	−	0.825201i	0.0337732	−	0.0584969i	0.882418	+	0.470466i	$0.155914\pi$
$200$	−4.76695	−	5.29423i	−0.337074	−	0.374359i
$201$	−2.31600	+	9.98801i	−0.163358	+	0.704500i
$202$	−8.15495	−	5.92492i	−0.573780	−	0.416876i
$203$	8.49943	−	11.2112i	0.596543	−	0.786874i
$204$	−0.0657960	+	0.0363889i	−0.00460664	+	0.00254773i
$205$	13.4898	+	1.41784i	0.942169	+	0.0990260i
$206$	−2.47048	−	23.5050i	−0.172126	−	1.63767i
$207$	4.04880	−	8.26102i	0.281411	−	0.574181i
$208$	−24.8926	+	14.3717i	−1.72599	+	0.996500i
$209$	−10.4159	+	6.38510i	−0.720485	+	0.441667i
$210$	4.86254	−	19.1865i	0.335547	−	1.32400i
$211$	−9.90749	−	3.21914i	−0.682059	−	0.221615i	−0.0525627	−	0.998618i	$-0.516739\pi$
$211$	−9.90749	−	3.21914i	−0.682059	−	0.221615i	−0.629497	+	0.777003i	$0.716739\pi$
$212$	0.571613	−	1.28386i	0.0392586	−	0.0881762i
$213$	−19.1425	+	13.3764i	−1.31162	+	0.916535i
$214$	−14.1464	−	3.00690i	−0.967026	−	0.205548i
$215$	13.7318	−	15.2507i	0.936501	−	1.04009i
$216$	0.717738	−	12.9808i	0.0488359	−	0.883230i
$217$	7.22337	−	6.24244i	0.490355	−	0.423765i
$218$	−27.3544	−	8.88799i	−1.85267	−	0.601971i
$219$	−6.36578	−	7.33719i	−0.430160	−	0.495801i
$220$	−2.13438	−	2.78069i	−0.143900	−	0.187474i
$221$	0.620968	+	0.358516i	0.0417708	+	0.0241164i
$222$	−2.57429	−	6.08086i	−0.172775	−	0.408120i
$223$	21.2304	−	15.4248i	1.42169	−	1.03292i	0.430203	−	0.902732i	$-0.358442\pi$
$223$	21.2304	−	15.4248i	1.42169	−	1.03292i	0.991489	−	0.130188i	$-0.0415581\pi$
$224$	−4.77097	−	2.88558i	−0.318774	−	0.192801i
$225$	5.47826	+	6.55421i	0.365217	+	0.436948i
$226$	2.78883	+	2.51107i	0.185510	+	0.167034i
$227$	−6.05041	+	2.69381i	−0.401580	+	0.178795i	−0.597580	−	0.801809i	$-0.703871\pi$
$227$	−6.05041	+	2.69381i	−0.401580	+	0.178795i	0.196001	+	0.980604i	$0.437204\pi$
$228$	0.701595	+	2.30271i	0.0464643	+	0.152501i
$229$	−8.38617	+	1.78254i	−0.554174	+	0.117793i	−0.476482	−	0.879184i	$-0.658088\pi$
$229$	−8.38617	+	1.78254i	−0.554174	+	0.117793i	−0.0776917	+	0.996977i	$0.524755\pi$
$230$	13.2454			0.873373
$231$	−4.87603	+	14.3953i	−0.320819	+	0.947140i
$232$	13.3043			0.873467
$233$	2.60386	−	0.553468i	0.170585	−	0.0362589i	−0.121827	−	0.992551i	$-0.538875\pi$
$233$	2.60386	−	0.553468i	0.170585	−	0.0362589i	0.292412	+	0.956292i	$0.405542\pi$
$234$	25.4781	−	13.4843i	1.66555	−	0.881498i
$235$	1.72746	−	0.769114i	0.112687	−	0.0501715i
$236$	3.13926	+	2.82660i	0.204348	+	0.183996i
$237$	−8.31026	−	15.0261i	−0.539809	−	0.976048i
$238$	−0.00955431	+	0.469258i	−0.000619314	+	0.0304175i
$239$	2.31308	−	1.68055i	0.149621	−	0.108706i	−0.510456	−	0.859904i	$-0.670524\pi$
$239$	2.31308	−	1.68055i	0.149621	−	0.108706i	0.660077	+	0.751198i	$0.270524\pi$
$240$	20.6081	−	8.72430i	1.33025	−	0.563151i
$241$	12.2080	+	7.04829i	0.786387	+	0.454021i	0.838689	−	0.544611i	$-0.183323\pi$
$241$	12.2080	+	7.04829i	0.786387	+	0.454021i	−0.0523023	+	0.998631i	$0.516656\pi$
$242$	9.24165	+	14.2213i	0.594076	+	0.914177i
$243$	−1.43305	+	15.5224i	−0.0919302	+	0.995765i
$244$	0.167612	+	0.0544605i	0.0107303	+	0.00348648i
$245$	−14.0263	−	13.7034i	−0.896110	−	0.875480i
$246$	−5.47609	+	11.7142i	−0.349143	+	0.746869i
$247$	15.3609	−	17.0600i	0.977387	−	1.08550i
$248$	8.83088	+	1.87706i	0.560761	+	0.119194i
$249$	−10.1812	−	14.5700i	−0.645207	−	0.923333i
$250$	3.78165	−	8.49373i	0.239173	−	0.537190i
$251$	−9.22758	−	2.99822i	−0.582440	−	0.189246i	0.00295363	−	0.999996i	$-0.499060\pi$
$251$	−9.22758	−	2.99822i	−0.582440	−	0.189246i	−0.585393	+	0.810750i	$0.699060\pi$
$252$	2.50364	+	1.64310i	0.157715	+	0.103506i
$253$	−10.1396	−	0.796425i	−0.637470	−	0.0500708i
$254$	−15.9334	+	9.19913i	−0.999748	+	0.577205i
$255$	−0.445522	−	0.336395i	−0.0278997	−	0.0210659i
$256$	−0.914941	−	8.70508i	−0.0571838	−	0.544068i
$257$	−2.47214	−	0.259833i	−0.154208	−	0.0162079i	0.0271098	−	0.999632i	$-0.491370\pi$
$257$	−2.47214	−	0.259833i	−0.154208	−	0.0162079i	−0.181318	+	0.983425i	$0.558036\pi$
$258$	9.46836	+	17.1201i	0.589474	+	1.06585i
$259$	−6.49088	−	0.816122i	−0.403323	−	0.0507114i
$260$	5.32875	+	3.87157i	0.330475	+	0.240104i
$261$	−15.9417	−	0.587305i	−0.986769	−	0.0363533i
$262$	−0.998507	−	1.10895i	−0.0616880	−	0.0685115i
$263$	2.00110	−	3.46600i	0.123393	−	0.213723i	−0.797711	−	0.603040i	$-0.793956\pi$
$263$	2.00110	−	3.46600i	0.123393	−	0.213723i	0.921104	+	0.389318i	$0.127289\pi$
$264$	−13.6336	+	4.54957i	−0.839093	+	0.280006i
$265$	10.4346			0.640990
$266$	14.6318	+	3.42281i	0.897134	+	0.209866i
$267$	12.5077	−	13.3871i	0.765458	−	0.819277i
$268$	0.233455	−	2.22118i	0.0142605	−	0.135680i
$269$	1.57001	−	7.38633i	0.0957254	−	0.450353i	−0.904014	−	0.427504i	$-0.859393\pi$
$269$	1.57001	−	7.38633i	0.0957254	−	0.450353i	0.999739	−	0.0228488i	$-0.00727362\pi$
$270$	−20.9756	+	7.98265i	−1.27654	+	0.485808i
$271$	−11.5905	−	1.21821i	−0.704072	−	0.0740010i	−0.254275	−	0.967132i	$-0.581837\pi$
$271$	−11.5905	−	1.21821i	−0.704072	−	0.0740010i	−0.449797	+	0.893131i	$0.648504\pi$
$272$	−0.429319	+	0.311918i	−0.0260313	+	0.0189128i
$273$	1.10693	−	28.5371i	0.0669945	−	1.72715i
$274$			7.80883i			0.471749i
$275$	4.50488	−	8.30002i	0.271655	−	0.500510i
$276$	−0.654255	+	1.89419i	−0.0393815	+	0.114017i
$277$	−22.5394	+	20.2946i	−1.35426	+	1.21938i	−0.401428	+	0.915891i	$0.631486\pi$
$277$	−22.5394	+	20.2946i	−1.35426	+	1.21938i	−0.952834	+	0.303492i	$0.901847\pi$
$278$	−12.3264	+	27.6855i	−0.739286	+	1.66046i
$279$	−10.4987	−	2.63901i	−0.628540	−	0.157993i
$280$	2.31334	−	18.3987i	0.138248	−	1.09953i
$281$	2.18997	+	6.74004i	0.130643	+	0.402077i	0.994887	−	0.100996i	$-0.0322028\pi$
$281$	2.18997	+	6.74004i	0.130643	+	0.402077i	−0.864244	+	0.503073i	$0.832203\pi$
$282$	0.155391	+	1.79596i	0.00925342	+	0.106948i
$283$	−19.8798	+	2.08946i	−1.18173	+	0.124205i	−0.674947	−	0.737866i	$-0.735834\pi$
$283$	−19.8798	+	2.08946i	−1.18173	+	0.124205i	−0.506787	+	0.862071i	$0.669167\pi$
$284$	3.78036	−	3.40385i	0.224323	−	0.201982i
$285$	−13.5003	+	11.7129i	−0.799686	+	0.693811i
$286$	−24.2364	−	20.6934i	−1.43313	−	1.22362i
$287$	7.31749	+	10.5153i	0.431938	+	0.620700i
$288$	0.428926	+	6.30771i	0.0252747	+	0.371685i
$289$	−15.5182	−	6.90914i	−0.912834	−	0.406420i
$290$	−9.34171	−	20.9818i	−0.548564	−	1.23210i
$291$	−0.0965885	+	5.24535i	−0.00566212	+	0.307488i
$292$	1.57246	+	1.41585i	0.0920211	+	0.0828562i
$293$	14.8923	+	10.8199i	0.870015	+	0.632103i	0.930591	−	0.366061i	$-0.119294\pi$
$293$	14.8923	+	10.8199i	0.870015	+	0.632103i	−0.0605760	+	0.998164i	$0.519294\pi$
$294$	16.7134	−	8.37394i	0.974748	−	0.488378i
$295$	−9.69216	+	29.8294i	−0.564300	+	1.73674i
$296$	−3.09323	−	5.35763i	−0.179790	−	0.311406i
$297$	16.5373	−	4.84964i	0.959589	−	0.281405i
$298$	3.28550	−	5.69066i	0.190324	−	0.329651i
$299$	18.6935	−	3.97343i	1.08107	−	0.229789i
$300$	−1.35964	−	1.27033i	−0.0784991	−	0.0733424i
$301$	19.3782	+	0.394549i	1.11694	+	0.0227414i
$302$	−13.6337	+	4.42987i	−0.784534	+	0.254911i
$303$	9.70059	+	5.84137i	0.557284	+	0.335578i
$304$	6.91038	+	15.5210i	0.396337	+	0.890188i
$305$	0.136779	+	1.30136i	0.00783194	+	0.0745159i
$306$	0.441782	−	0.296755i	0.0252550	−	0.0169644i
$307$			2.68499i			0.153240i	0.997060	+	0.0766201i	$0.0244129\pi$
$307$			2.68499i			0.153240i	−0.997060	+	0.0766201i	$0.975587\pi$
$308$	0.668971	−	3.24243i	0.0381182	−	0.184755i
$309$	5.04100	+	26.0671i	0.286773	+	1.48291i
$310$	−3.24042	−	15.2450i	−0.184043	−	0.865856i
$311$	4.83479	−	0.508157i	0.274156	−	0.0288150i	0.0335472	−	0.999437i	$-0.489320\pi$
$311$	4.83479	−	0.508157i	0.274156	−	0.0288150i	0.240609	+	0.970622i	$0.422653\pi$
$312$	22.1373	−	15.4691i	1.25328	−	0.875767i
$313$	8.79822	−	9.77141i	0.497305	−	0.552313i	−0.441277	−	0.897371i	$-0.645474\pi$
$313$	8.79822	−	9.77141i	0.497305	−	0.552313i	0.938581	+	0.345058i	$0.112141\pi$
$314$	−4.73944	−	14.5865i	−0.267462	−	0.823163i
$315$	−3.58414	+	21.9440i	−0.201943	+	1.23641i
$316$	2.19852	+	3.02601i	0.123677	+	0.170226i
$317$	6.03048	+	28.3712i	0.338705	+	1.59348i	0.736782	+	0.676131i	$0.236345\pi$
$317$	6.03048	+	28.3712i	0.338705	+	1.59348i	−0.398076	+	0.917352i	$0.630322\pi$
$318$	−3.24760	+	9.40242i	−0.182116	+	0.527261i
$319$	5.88966	+	16.6237i	0.329758	+	0.930749i
$320$	14.4958	−	8.36914i	0.810339	−	0.467849i
$321$	16.1235	+	1.99541i	0.899926	+	0.111373i
$322$	8.17970	+	9.46505i	0.455837	+	0.527467i
$323$	0.249119	−	0.342883i	0.0138613	−	0.0190785i
$324$	−0.105491	−	3.39399i	−0.00586060	−	0.188555i
$325$	−3.68939	+	17.3572i	−0.204650	+	0.962805i
$326$	−18.0538	+	8.03806i	−0.999907	+	0.445187i
$327$	31.4752	+	7.29841i	1.74058	+	0.403603i
$328$	−3.74363	+	11.5217i	−0.206707	+	0.636180i
$329$	1.61640	+	0.759463i	0.0891150	+	0.0418706i
$330$	16.7480	+	18.3068i	0.921947	+	1.00775i
$331$	−8.79063	−	15.2258i	−0.483176	−	0.836886i	0.516637	−	0.856205i	$-0.327184\pi$
$331$	−8.79063	−	15.2258i	−0.483176	−	0.836886i	−0.999813	+	0.0193184i	$0.993850\pi$
$332$	2.59078	+	2.87735i	0.142187	+	0.157915i
$333$	3.46993	+	6.55629i	0.190151	+	0.359283i
$334$	−3.27546	+	31.1639i	−0.179225	+	1.70521i
$335$	15.7710	−	5.12432i	0.861663	−	0.279971i
$336$	18.9609	+	9.33869i	1.03440	+	0.509467i
$337$	7.02448	−	9.66836i	0.382648	−	0.526669i	−0.573636	−	0.819110i	$-0.694468\pi$
$337$	7.02448	−	9.66836i	0.382648	−	0.526669i	0.956284	+	0.292441i	$0.0944676\pi$
$338$	36.3938	+	16.2036i	1.97956	+	0.881357i
$339$	−3.36436	−	2.54029i	−0.182727	−	0.137969i
$340$	0.105313	+	0.0608025i	0.00571140	+	0.00329748i
$341$	1.56395	+	11.8652i	0.0846924	+	0.642535i
$342$	−6.35255	−	15.8103i	−0.343507	−	0.854925i
$343$	1.13038	−	18.4857i	0.0610350	−	0.998136i
$344$	10.7734	+	14.8283i	0.580864	+	0.799491i
$345$	−14.8239	+	1.28261i	−0.798093	+	0.0690532i
$346$	−29.4541	−	6.26067i	−1.58346	−	0.336576i
$347$	0.858255	+	0.182428i	0.0460736	+	0.00979324i	0.230891	−	0.972980i	$-0.425836\pi$
$347$	0.858255	+	0.182428i	0.0460736	+	0.00979324i	−0.184817	+	0.982773i	$0.559169\pi$
$348$	3.46201	−	0.299542i	0.185583	−	0.0160571i
$349$	−9.68706	−	13.3331i	−0.518536	−	0.713704i	0.466793	−	0.884366i	$-0.345409\pi$
$349$	−9.68706	−	13.3331i	−0.518536	−	0.713704i	−0.985330	+	0.170663i	$0.945409\pi$
$350$	−11.1178	+	3.36377i	−0.594271	+	0.179801i
$351$	−27.2088	+	17.5585i	−1.45230	+	0.937206i
$352$	6.30819	−	3.01005i	0.336228	−	0.160436i
$353$	11.9580	+	6.90393i	0.636458	+	0.367459i	0.783249	−	0.621708i	$-0.213561\pi$
$353$	11.9580	+	6.90393i	0.636458	+	0.367459i	−0.146791	+	0.989168i	$0.546894\pi$
$354$	−23.8623	−	18.0174i	−1.26827	−	0.957615i
$355$	34.5045	+	15.3624i	1.83131	+	0.815350i
$356$	−2.34576	+	3.22866i	−0.124325	+	0.171119i
$357$	−0.0347473	−	0.526109i	−0.00183902	−	0.0278446i
$358$	2.97618	−	0.967020i	0.157296	−	0.0511086i
$359$	0.198890	−	1.89231i	0.0104970	−	0.0998724i	−0.988019	−	0.154333i	$-0.950677\pi$
$359$	0.198890	−	1.89231i	0.0104970	−	0.0998724i	0.998516	+	0.0544604i	$0.0173439\pi$
$360$	−18.5841	+	9.83570i	−0.979470	+	0.518387i
$361$	3.63392	+	4.03588i	0.191259	+	0.212415i
$362$	5.03120	+	8.71430i	0.264434	+	0.458013i
$363$	−11.7202	−	15.0212i	−0.615150	−	0.788410i
$364$	0.524187	+	6.19879i	0.0274749	+	0.324905i
$365$	−4.85482	+	14.9416i	−0.254113	+	0.782078i
$366$	−1.21521	−	0.281781i	−0.0635200	−	0.0147289i
$367$	3.34096	−	1.48749i	0.174397	−	0.0776465i	−0.317681	−	0.948198i	$-0.602904\pi$
$367$	3.34096	−	1.48749i	0.174397	−	0.0776465i	0.492078	+	0.870551i	$0.336237\pi$
$368$	−2.94069	+	13.8349i	−0.153294	+	0.721193i
$369$	4.99439	−	13.6405i	0.259998	−	0.710098i
$370$	−6.27745	+	8.64016i	−0.326349	+	0.449181i
$371$	6.44389	+	7.45647i	0.334550	+	0.387121i
$372$	2.34021	+	0.289620i	0.121334	+	0.0150161i
$373$	27.4023	−	15.8207i	1.41884	−	0.819167i	0.422641	−	0.906297i	$-0.361103\pi$
$373$	27.4023	−	15.8207i	1.41884	−	0.819167i	0.996197	+	0.0871304i	$0.0277697\pi$
$374$	−0.484941	−	0.333180i	−0.0250757	−	0.0172283i
$375$	−3.40986	+	9.87220i	−0.176084	+	0.509798i
$376$	0.351136	+	1.65196i	0.0181085	+	0.0851936i
$377$	−19.4785	−	26.8098i	−1.00319	−	1.38078i
$378$	−18.6579	−	10.0594i	−0.959659	−	0.517398i
$379$	4.21106	+	12.9603i	0.216308	+	0.665726i	0.999058	+	0.0433906i	$0.0138160\pi$
$379$	4.21106	+	12.9603i	0.216308	+	0.665726i	−0.782751	+	0.622335i	$0.786184\pi$
$380$	2.60512	−	2.89328i	0.133640	−	0.148422i
$381$	16.9415	−	11.8384i	0.867940	−	0.606499i
$382$	32.8189	−	3.44940i	1.67916	−	0.176487i
$383$	5.16686	+	24.3082i	0.264014	+	1.24209i	0.887703	+	0.460416i	$0.152300\pi$
$383$	5.16686	+	24.3082i	0.264014	+	1.24209i	−0.623689	+	0.781673i	$0.714367\pi$
$384$	4.41581	+	22.8342i	0.225343	+	1.16525i
$385$	24.0133	−	5.25440i	1.22383	−	0.267789i
$386$		−	31.5858i		−	1.60767i
$387$	−12.2546	−	18.2436i	−0.622937	−	0.927372i
$388$	−0.119454	−	1.13653i	−0.00606435	−	0.0576984i
$389$	−8.83423	−	19.8420i	−0.447913	−	1.00603i	−0.986545	−	0.163488i	$-0.947725\pi$
$389$	−8.83423	−	19.8420i	−0.447913	−	1.00603i	0.538632	−	0.842541i	$-0.318941\pi$
$390$	−39.9399	−	24.0505i	−2.02244	−	1.21784i
$391$	0.335565	−	0.109032i	0.0169703	−	0.00551397i
$392$	14.5762	−	9.70907i	0.736210	−	0.490382i
$393$	1.22489	+	1.14443i	0.0617877	+	0.0577288i
$394$	−16.8171	+	3.57458i	−0.847232	+	0.180085i
$395$	−13.8857	+	24.0507i	−0.698665	+	1.21012i
$396$	−3.44529	+	1.49084i	−0.173132	+	0.0749174i
$397$	0.109118	+	0.188997i	0.00547646	+	0.00948550i	0.868751	−	0.495250i	$-0.164923\pi$
$397$	0.109118	+	0.188997i	0.00547646	+	0.00948550i	−0.863274	+	0.504735i	$0.831590\pi$
$398$	0.453997	−	1.39726i	0.0227568	−	0.0700382i
$399$	−16.7071	−	2.41388i	−0.836400	−	0.120845i
$400$	−10.6247	−	7.71930i	−0.531235	−	0.385965i
$401$	−8.34354	−	7.51256i	−0.416656	−	0.375159i	0.433972	−	0.900926i	$-0.357112\pi$
$401$	−8.34354	−	7.51256i	−0.416656	−	0.375159i	−0.850629	+	0.525767i	$0.823778\pi$
$402$	−0.291051	+	15.8059i	−0.0145163	+	0.788326i
$403$	−9.14658	−	20.5436i	−0.455623	−	1.02335i
$404$	−2.25336	−	1.00326i	−0.112109	−	0.0499140i
$405$	22.7025	−	10.9652i	1.12810	−	0.544864i
$406$	9.22449	−	19.6329i	0.457804	−	0.974365i
$407$	5.32503	−	6.23677i	0.263952	−	0.309145i
$408$	0.376612	−	0.326751i	0.0186451	−	0.0161766i
$409$	7.25956	−	6.53654i	0.358962	−	0.323211i	−0.469841	−	0.882751i	$-0.655689\pi$
$409$	7.25956	−	6.53654i	0.358962	−	0.323211i	0.828803	+	0.559540i	$0.189022\pi$
$410$	20.7992	−	2.18609i	1.02720	−	0.107963i
$411$	−0.756163	−	8.73948i	−0.0372988	−	0.431087i
$412$	−1.78717	−	5.50033i	−0.0880474	−	0.270982i
$413$	−27.3013	+	11.4953i	−1.34341	+	0.565645i
$414$	3.45799	−	13.7568i	0.169951	−	0.676110i
$415$	−11.6928	+	26.2624i	−0.573976	+	1.28917i
$416$	−9.76008	+	8.78801i	−0.478527	+	0.430868i
$417$	11.1145	−	32.1786i	0.544280	−	1.57579i
$418$	−13.6620	+	12.9687i	−0.668228	+	0.634321i
$419$			30.9478i			1.51190i	0.654629	+	0.755950i	$0.272825\pi$
$419$			30.9478i			1.51190i	−0.654629	+	0.755950i	$0.727175\pi$
$420$	0.187730	−	4.83976i	0.00916029	−	0.236156i
$421$	−16.1660	+	11.7453i	−0.787880	+	0.572429i	−0.907334	−	0.420411i	$-0.861886\pi$
$421$	−16.1660	+	11.7453i	−0.787880	+	0.572429i	0.119453	+	0.992840i	$0.461886\pi$
$422$	−15.9740	−	1.67893i	−0.777601	−	0.0817291i
$423$	−0.347822	−	1.99496i	−0.0169117	−	0.0969981i
$424$	−1.93763	+	9.11585i	−0.0940998	+	0.442705i
$425$	−0.0342447	+	0.325817i	−0.00166111	+	0.0158044i
$426$	−24.5818	+	26.3101i	−1.19099	+	1.27473i
$427$	−0.845479	+	0.901402i	−0.0409156	+	0.0436219i
$428$	−3.53897			−0.171063
$429$	29.1287	+	20.8127i	1.40635	+	1.00484i
$430$	15.8208	−	27.4024i	0.762945	−	1.32146i
$431$	−23.0269	−	25.5740i	−1.10917	−	1.23186i	−0.970393	−	0.241533i	$-0.922350\pi$
$431$	−23.0269	−	25.5740i	−1.10917	−	1.23186i	−0.138776	−	0.990324i	$-0.544317\pi$
$432$	−3.68099	−	23.6815i	−0.177102	−	1.13938i
$433$	0.184946	+	0.134371i	0.00888793	+	0.00645746i	0.592220	−	0.805776i	$-0.298252\pi$
$433$	0.184946	+	0.134371i	0.00888793	+	0.00645746i	−0.583332	+	0.812234i	$0.698252\pi$
$434$	8.89283	−	11.7301i	0.426870	−	0.563065i
$435$	12.4868	+	22.5778i	0.598697	+	1.08252i
$436$	−6.99958	−	0.735685i	−0.335219	−	0.0352329i
$437$	−1.18079	−	11.2344i	−0.0564846	−	0.537415i
$438$	−11.9526	−	9.02494i	−0.571119	−	0.431228i
$439$	17.5858	−	10.1531i	0.839323	−	0.484583i	−0.0177112	−	0.999843i	$-0.505638\pi$
$439$	17.5858	−	10.1531i	0.839323	−	0.484583i	0.857034	+	0.515260i	$0.172305\pi$
$440$	17.6784	+	15.0941i	0.842786	+	0.719582i
$441$	−17.8945	+	10.9904i	−0.852117	+	0.523351i
$442$	1.05144	+	0.341635i	0.0500121	+	0.0162499i
$443$	15.4917	−	34.7949i	0.736032	−	1.65315i	−0.0210032	−	0.999779i	$-0.506686\pi$
$443$	15.4917	−	34.7949i	0.736032	−	1.65315i	0.757035	−	0.653375i	$-0.226647\pi$
$444$	−0.925539	−	1.32451i	−0.0439241	−	0.0628583i
$445$	−28.9837	−	6.16068i	−1.37396	−	0.292044i
$446$	27.0740	−	30.0687i	1.28199	−	1.42380i
$447$	−3.12602	+	6.68702i	−0.147856	+	0.316285i
$448$	14.9324	+	5.19021i	0.705492	+	0.245215i
$449$	3.27958	+	1.06560i	0.154773	+	0.0502888i	0.385379	−	0.922758i	$-0.374071\pi$
$449$	3.27958	+	1.06560i	0.154773	+	0.0502888i	−0.230606	+	0.973047i	$0.574071\pi$
$450$	10.3631	+	8.12861i	0.488522	+	0.383186i
$451$	−16.0537	+	0.422864i	−0.755938	+	0.0199119i
$452$	0.795272	+	0.459150i	0.0374064	+	0.0215966i
$453$	14.8296	−	6.27804i	0.696758	−	0.294968i
$454$	−8.26139	+	6.00225i	−0.387726	+	0.281700i
$455$	−40.4627	+	22.2755i	−1.89692	+	1.04429i
$456$	−7.72571	−	13.9691i	−0.361790	−	0.654164i
$457$	0.986280	+	0.888050i	0.0461362	+	0.0415412i	0.691876	−	0.722016i	$-0.256784\pi$
$457$	0.986280	+	0.888050i	0.0461362	+	0.0415412i	−0.645740	+	0.763557i	$0.723451\pi$
$458$	−12.0762	+	5.37668i	−0.564284	+	0.251236i
$459$	−0.465698	+	0.374902i	−0.0217369	+	0.0174989i
$460$	3.17033	−	0.673874i	0.147817	−	0.0314196i
$461$	−5.03276			−0.234399			−0.117200	−	0.993108i	$-0.537392\pi$
$461$	−5.03276			−0.234399			−0.117200	+	0.993108i	$0.537392\pi$
$462$	−2.73914	+	23.2734i	−0.127436	+	1.08278i
$463$	27.0883			1.25890			0.629449	−	0.777042i	$-0.283281\pi$
$463$	27.0883			1.25890			0.629449	+	0.777042i	$0.283281\pi$
$464$	23.9897	−	5.09917i	1.11369	−	0.236723i
$465$	5.10285	+	16.7481i	0.236639	+	0.776673i
$466$	3.74960	−	1.66943i	0.173697	−	0.0773348i
$467$	−12.8705	−	11.5887i	−0.595578	−	0.536261i	0.315270	−	0.949002i	$-0.397905\pi$
$467$	−12.8705	−	11.5887i	−0.595578	−	0.536261i	−0.910848	+	0.412741i	$0.864571\pi$
$468$	5.41225	−	4.52376i	0.250181	−	0.209111i
$469$	13.4012	+	8.10534i	0.618812	+	0.374270i
$470$	2.35872	−	1.71371i	0.108800	−	0.0790476i
$471$	6.71675	+	15.8660i	0.309492	+	0.731065i
$472$	−24.2598	−	14.0064i	−1.11665	−	0.644698i
$473$	−13.7588	+	20.0258i	−0.632630	+	0.920787i
$474$	−17.3500	−	19.9976i	−0.796913	−	0.918521i
$475$	9.97542	+	3.24121i	0.457704	+	0.148717i
$476$	0.0215872	+	0.112805i	0.000989449	+	0.00517040i
$477$	2.72417	−	10.8375i	0.124731	−	0.496214i
$478$	2.94975	−	3.27603i	0.134919	−	0.149842i
$479$	1.97526	+	0.419854i	0.0902519	+	0.0191836i	0.252816	−	0.967514i	$-0.418643\pi$
$479$	1.97526	+	0.419854i	0.0902519	+	0.0191836i	−0.162564	+	0.986698i	$0.551977\pi$
$480$	8.38169	−	5.85695i	0.382570	−	0.267332i
$481$	−6.26760	+	14.0773i	−0.285778	+	0.641867i
$482$	20.6710	+	6.71642i	0.941538	+	0.305924i
$483$	−10.0711	−	9.80101i	−0.458251	−	0.445962i
$484$	2.93555	+	2.93374i	0.133434	+	0.133352i
$485$	7.34820	−	4.24248i	0.333665	−	0.192641i
$486$	2.81474	+	23.8696i	0.127679	+	1.08275i
$487$	3.05966	+	29.1107i	0.138646	+	1.31913i	0.813667	+	0.581332i	$0.197468\pi$
$487$	3.05966	+	29.1107i	0.138646	+	1.31913i	−0.675020	+	0.737799i	$0.735865\pi$
$488$	−1.16230	−	0.122163i	−0.0526148	−	0.00553004i
$489$	19.4271	−	10.7443i	0.878522	−	0.485872i
$490$	−25.5468	−	16.1705i	−1.15409	−	0.730508i
$491$	5.45828	+	3.96567i	0.246329	+	0.178968i	0.704098	−	0.710103i	$-0.251351\pi$
$491$	5.45828	+	3.96567i	0.246329	+	0.178968i	−0.457769	+	0.889071i	$0.651351\pi$
$492$	−0.714751	+	3.08244i	−0.0322235	+	0.138967i
$493$	−0.409384	−	0.454667i	−0.0184377	−	0.0204772i
$494$	17.6977	−	30.6532i	0.796255	−	1.37915i
$495$	−20.5167	−	18.8668i	−0.922159	−	0.847999i
$496$	16.6429			0.747289
$497$	10.3305	+	34.1438i	0.463384	+	1.53156i
$498$	−20.0255	−	18.7100i	−0.897362	−	0.838414i
$499$	−0.705429	+	6.71170i	−0.0315793	+	0.300457i	0.967320	+	0.253558i	$0.0816007\pi$
$499$	−0.705429	+	6.71170i	−0.0315793	+	0.300457i	−0.998900	+	0.0468996i	$0.985066\pi$
$500$	0.473024	−	2.22540i	0.0211543	−	0.0995231i
$501$	0.648089	−	35.1952i	0.0289545	−	1.57241i
$502$	−14.8777	−	1.56371i	−0.664026	−	0.0697920i
$503$	2.46312	−	1.78957i	0.109825	−	0.0797928i	−0.531517	−	0.847048i	$-0.678378\pi$
$503$	2.46312	−	1.78957i	0.109825	−	0.0797928i	0.641342	+	0.767255i	$0.278378\pi$
$504$	−18.5052	−	7.20605i	−0.824287	−	0.320983i
$505$		−	18.3141i		−	0.814966i
$506$	−15.5474	+	2.04929i	−0.691165	+	0.0911023i
$507$	−42.3002	−	14.6105i	−1.87862	−	0.648876i
$508$	−3.34570	+	3.01248i	−0.148441	+	0.133657i
$509$	3.31827	−	7.45296i	0.147080	−	0.330346i	−0.824949	−	0.565206i	$-0.808797\pi$
$509$	3.31827	−	7.45296i	0.147080	−	0.330346i	0.972029	+	0.234860i	$0.0754632\pi$
$510$	−0.779753	−	0.364515i	−0.0345280	−	0.0161410i
$511$	−13.6753	+	5.75799i	−0.604958	+	0.254719i
$512$	4.12827	+	12.7055i	0.182446	+	0.561510i
$513$	8.64063	+	17.0795i	0.381493	+	0.754076i
$514$	−3.81167	+	0.400622i	−0.168125	+	0.0176707i
$515$	31.9111	−	28.7328i	1.40617	−	1.26612i
$516$	3.13730	+	3.61604i	0.138112	+	0.159187i
$517$	−1.90869	+	1.17005i	−0.0839441	+	0.0514589i
$518$	−10.0509	+	0.849929i	−0.441610	+	0.0373437i
$519$	33.5707	+	4.15464i	1.47359	+	0.182369i
$520$	−39.9027	−	17.7658i	−1.74985	−	0.779083i
$521$	3.57960	+	8.03991i	0.156825	+	0.352235i	0.974821	−	0.222989i	$-0.0715815\pi$
$521$	3.57960	+	8.03991i	0.156825	+	0.352235i	−0.817996	+	0.575224i	$0.804915\pi$
$522$	−24.2309	+	4.22467i	−1.06056	+	0.184909i
$523$	19.2905	+	17.3692i	0.843514	+	0.759503i	0.972687	−	0.232119i	$-0.0745658\pi$
$523$	19.2905	+	17.3692i	0.843514	+	0.759503i	−0.129174	+	0.991622i	$0.541232\pi$
$524$	−0.295416	−	0.214633i	−0.0129053	−	0.00937627i
$525$	12.1171	−	4.84125i	0.528832	−	0.211289i
$526$	1.90687	−	5.86875i	0.0831435	−	0.255890i
$527$	−0.207586	−	0.359550i	−0.00904261	−	0.0156623i
$528$	−22.8399	+	13.4290i	−0.993979	+	0.584422i
$529$	−6.79793	+	11.7744i	−0.295562	+	0.511929i
$530$	15.7369	−	3.34499i	0.683568	−	0.145297i
$531$	28.4509	+	17.8540i	1.23466	+	0.774799i
$532$	3.67632	+	0.0748517i	0.159389	+	0.00324523i
$533$	28.6987	−	9.32478i	1.24308	−	0.403901i
$534$	14.5720	−	24.1994i	0.630594	−	1.04721i
$535$	−10.6875	−	24.0045i	−0.462060	−	1.03780i
$536$	1.54813	+	14.7295i	0.0668689	+	0.636215i
$537$	−3.23724	+	1.37047i	−0.139697	+	0.0591400i
$538$		−	11.6430i		−	0.501966i
$539$	18.5843	+	13.9149i	0.800481	+	0.599358i
$540$	−4.61448	+	2.97784i	−0.198575	+	0.128146i
$541$	−2.37417	−	11.1696i	−0.102073	−	0.480218i	−0.999256	−	0.0385586i	$-0.987723\pi$
$541$	−2.37417	−	11.1696i	−0.102073	−	0.480218i	0.897183	−	0.441659i	$-0.145610\pi$
$542$	−17.8708	+	1.87829i	−0.767615	+	0.0806796i
$543$	−6.47466	−	9.26567i	−0.277854	−	0.397628i
$544$	−0.162246	+	0.180193i	−0.00695624	+	0.00772569i
$545$	−16.1482	−	49.6992i	−0.691714	−	2.12888i
$546$	−7.47867	−	43.3933i	−0.320058	−	1.85706i
$547$	10.5858	+	14.5701i	0.452618	+	0.622975i	0.972957	−	0.230985i	$-0.0741947\pi$
$547$	10.5858	+	14.5701i	0.452618	+	0.622975i	−0.520340	+	0.853959i	$0.674195\pi$
$548$	0.397284	+	1.86908i	0.0169711	+	0.0798429i
$549$	1.38732	+	0.197689i	0.0592096	+	0.00843717i
$550$	4.13334	−	13.9618i	0.176246	−	0.595335i
$551$	−16.9635	+	9.79391i	−0.722671	+	0.417234i
$552$	1.63220	−	13.1887i	0.0694711	−	0.561347i
$553$	−25.7617	+	4.92995i	−1.09550	+	0.209643i
$554$	−27.4871	+	37.8328i	−1.16782	+	1.60736i
$555$	6.18893	−	10.2778i	0.262705	−	0.436267i
$556$	−1.54183	+	7.25375i	−0.0653883	+	0.307628i
$557$	−12.3675	+	5.50636i	−0.524027	+	0.233312i	−0.651662	−	0.758509i	$-0.725928\pi$
$557$	−12.3675	+	5.50636i	−0.524027	+	0.233312i	0.127635	+	0.991821i	$0.459261\pi$
$558$	−16.6796	−	0.614489i	−0.706104	−	0.0260134i
$559$	14.1079	−	43.4197i	0.596702	−	1.83646i
$560$	−2.88042	−	34.0625i	−0.121720	−	1.43940i
$561$	0.574999	+	0.325929i	0.0242765	+	0.0137607i
$562$	5.46346	+	9.46298i	0.230462	+	0.399172i
$563$	7.31401	+	8.12303i	0.308249	+	0.342345i	0.877287	−	0.479966i	$-0.159351\pi$
$563$	7.31401	+	8.12303i	0.308249	+	0.342345i	−0.569038	+	0.822311i	$0.692684\pi$
$564$	0.128565	+	0.421965i	0.00541358	+	0.0177679i
$565$	−0.712696	+	6.78085i	−0.0299834	+	0.285273i
$566$	−29.3120	+	9.52406i	−1.23208	+	0.400326i
$567$	21.8556	+	9.45150i	0.917851	+	0.396926i
$568$	−19.8282	+	27.2911i	−0.831972	+	1.14511i
$569$	3.59273	+	1.59959i	0.150615	+	0.0670582i	0.480660	−	0.876907i	$-0.340397\pi$
$569$	3.59273	+	1.59959i	0.150615	+	0.0670582i	−0.330045	+	0.943965i	$0.607064\pi$
$570$	−16.6057	+	21.9926i	−0.695535	+	0.921168i
$571$	19.8670	+	11.4702i	0.831409	+	0.480014i	0.854335	−	0.519723i	$-0.173965\pi$
$571$	19.8670	+	11.4702i	0.831409	+	0.480014i	−0.0229257	+	0.999737i	$0.507298\pi$
$572$	−6.85388	−	3.71998i	−0.286575	−	0.155540i
$573$	−36.3962	+	7.03849i	−1.52047	+	0.294037i
$574$	14.4068	+	13.5130i	0.601327	+	0.564021i
$575$	5.13247	+	7.06423i	0.214039	+	0.294599i
$576$	−4.90787	−	17.2405i	−0.204494	−	0.718353i
$577$	22.4842	+	4.77917i	0.936031	+	0.198959i	0.650583	−	0.759435i	$-0.274524\pi$
$577$	22.4842	+	4.77917i	0.936031	+	0.198959i	0.285447	+	0.958394i	$0.407858\pi$
$578$	−25.6187	−	5.44541i	−1.06560	−	0.226499i
$579$	3.05859	+	35.3502i	0.127111	+	1.46910i
$580$	−3.30345	−	4.54681i	−0.137168	−	0.188796i
$581$	−25.9879	+	7.86283i	−1.07816	+	0.326205i
$582$	1.53582	+	7.94176i	0.0636618	+	0.329196i
$583$	−12.2481	+	1.61441i	−0.507263	+	0.0668622i
$584$	−12.1518	−	7.01583i	−0.502844	−	0.290317i
$585$	47.0289	+	23.0492i	1.94440	+	0.952969i
$586$	25.9283	+	11.5440i	1.07109	+	0.476879i
$587$	21.1584	−	29.1220i	0.873299	−	1.20199i	−0.104933	−	0.994479i	$-0.533463\pi$
$587$	21.1584	−	29.1220i	0.873299	−	1.20199i	0.978232	−	0.207514i	$-0.0665371\pi$
$588$	3.57440	−	2.85465i	0.147406	−	0.117724i
$589$	−12.6416	+	4.10750i	−0.520887	+	0.169246i
$590$	−5.05492	+	48.0943i	−0.208108	+	1.98001i
$591$	18.4752	−	5.62907i	0.759968	−	0.231549i
$592$	−7.63102	−	8.47511i	−0.313633	−	0.348325i
$593$	−10.5952	−	18.3514i	−0.435093	−	0.753602i	0.562211	−	0.826994i	$-0.309951\pi$
$593$	−10.5952	−	18.3514i	−0.435093	−	0.753602i	−0.997303	+	0.0733917i	$0.976618\pi$
$594$	23.3861	−	12.6153i	0.959543	−	0.517613i
$595$	−0.699951	+	0.487088i	−0.0286952	+	0.0199686i
$596$	0.496879	−	1.52924i	0.0203530	−	0.0626400i
$597$	−0.372801	+	1.60775i	−0.0152577	+	0.0658006i
$598$	26.9190	−	11.9851i	1.10080	−	0.490107i
$599$	−4.83992	+	22.7700i	−0.197754	+	0.930359i	0.761577	+	0.648074i	$0.224425\pi$
$599$	−4.83992	+	22.7700i	−0.197754	+	0.930359i	−0.959331	+	0.282284i	$0.908908\pi$
$600$	10.5707	+	6.36534i	0.431549	+	0.259864i
$601$	−17.3540	+	23.8857i	−0.707884	+	0.974319i	0.291956	+	0.956432i	$0.405694\pi$
$601$	−17.3540	+	23.8857i	−0.707884	+	0.974319i	−0.999840	+	0.0178874i	$0.994306\pi$
$602$	29.3517	−	5.61698i	1.19629	−	0.228931i
$603$	−1.20482	−	17.7178i	−0.0490639	−	0.721525i
$604$	−3.03792	+	1.75394i	−0.123611	+	0.0713669i
$605$	−11.0340	+	28.7713i	−0.448598	+	1.16972i
$606$	16.5025	+	5.69998i	0.670370	+	0.231546i
$607$	6.46935	+	30.4359i	0.262583	+	1.23535i	0.889742	+	0.456463i	$0.150884\pi$
$607$	6.46935	+	30.4359i	0.262583	+	1.23535i	−0.627160	+	0.778891i	$0.715783\pi$
$608$	4.56297	+	6.28040i	0.185053	+	0.254704i
$609$	−8.42272	+	22.8660i	−0.341306	+	0.926577i
$610$	0.623460	+	1.91881i	0.0252431	+	0.0776904i
$611$	2.81484	−	3.12619i	0.113876	−	0.126472i
$612$	0.0906446	−	0.0935058i	0.00366409	−	0.00377975i
$613$	12.2515	−	1.28768i	0.494833	−	0.0520091i	0.146174	−	0.989259i	$-0.453304\pi$
$613$	12.2515	−	1.28768i	0.494833	−	0.0520091i	0.348659	+	0.937250i	$0.386637\pi$
$614$	0.860721	+	4.04937i	0.0347359	+	0.163419i
$615$	−23.0664	+	4.46070i	−0.930126	+	0.179873i
$616$	0.131220	+	21.9543i	0.00528700	+	0.884563i
$617$		−	39.8753i		−	1.60532i	−0.596436	−	0.802660i	$-0.703417\pi$
$617$		−	39.8753i		−	1.60532i	0.596436	−	0.802660i	$-0.296583\pi$
$618$	15.9589	+	37.6972i	0.641961	+	1.51640i
$619$	−3.55354	−	33.8096i	−0.142829	−	1.35892i	−0.797641	−	0.603133i	$-0.793919\pi$
$619$	−3.55354	−	33.8096i	−0.142829	−	1.35892i	0.654812	−	0.755792i	$-0.272748\pi$
$620$	−1.55121	−	3.48408i	−0.0622983	−	0.139924i
$621$	−2.53798	+	15.7312i	−0.101846	+	0.631271i
$622$	7.12871	−	2.31626i	0.285835	−	0.0928735i
$623$	−13.4966	−	24.5161i	−0.540729	−	0.982219i
$624$	33.9883	−	36.3780i	1.36062	−	1.45628i
$625$	30.4491	−	6.47215i	1.21796	−	0.258886i
$626$	10.1367	−	17.5572i	0.405143	−	0.701727i
$627$	14.0344	−	15.8373i	0.560479	−	0.632480i
$628$	−1.87651	−	3.25021i	−0.0748809	−	0.129698i
$629$	−0.0879131	+	0.270569i	−0.00350533	+	0.0107883i
$630$	1.62912	+	34.2439i	0.0649055	+	1.36431i
$631$	−24.6256	−	17.8915i	−0.980328	−	0.712250i	−0.0225460	−	0.999746i	$-0.507177\pi$
$631$	−24.6256	−	17.8915i	−0.980328	−	0.712250i	−0.957782	+	0.287496i	$0.907177\pi$
$632$	−18.4327	−	16.5969i	−0.733215	−	0.660190i
$633$	18.0403	+	0.332196i	0.717038	+	0.0132036i
$634$	18.1898	+	40.8549i	0.722408	+	1.62256i
$635$	−30.5372	−	13.5960i	−1.21183	−	0.539541i
$636$	−0.298966	+	2.41573i	−0.0118548	+	0.0957901i
$637$	−40.9058	−	15.1582i	−1.62075	−	0.600588i
$638$	14.2115	+	23.1831i	0.562640	+	0.917827i
$639$	24.9637	−	31.8261i	0.987550	−	1.25902i
$640$	27.9534	−	25.1694i	1.10496	−	0.994907i
$641$	1.80237	−	0.189437i	0.0711895	−	0.00748232i	−0.0688667	−	0.997626i	$-0.521938\pi$
$641$	1.80237	−	0.189437i	0.0711895	−	0.00748232i	0.140056	+	0.990144i	$0.455272\pi$
$642$	24.9564	−	2.15929i	0.984950	−	0.0852205i
$643$	10.7920	+	33.2143i	0.425594	+	1.30984i	0.902424	+	0.430849i	$0.141786\pi$
$643$	10.7920	+	33.2143i	0.425594	+	1.30984i	−0.476830	+	0.878995i	$0.658214\pi$
$644$	2.43939	+	1.84935i	0.0961255	+	0.0728744i
$645$	−15.0528	+	32.2002i	−0.592703	+	1.26788i
$646$	0.265792	−	0.596979i	0.0104575	−	0.0234878i
$647$	33.7914	−	30.4259i	1.32848	−	1.19617i	0.364186	−	0.931326i	$-0.381347\pi$
$647$	33.7914	−	30.4259i	1.32848	−	1.19617i	0.964292	−	0.264840i	$-0.0853193\pi$
$648$	5.36370	+	21.8696i	0.210706	+	0.859118i
$649$	6.76149	−	36.5132i	0.265412	−	1.43327i
$650$			27.3600i			1.07315i
$651$	−8.81679	+	13.9893i	−0.345557	+	0.548283i
$652$	−3.91230	+	2.84245i	−0.153218	+	0.111319i
$653$	−28.2953	−	2.97395i	−1.10728	−	0.116380i	−0.466806	−	0.884360i	$-0.654595\pi$
$653$	−28.2953	−	2.97395i	−1.10728	−	0.116380i	−0.640474	+	0.767980i	$0.721262\pi$
$654$	49.8090	+	0.917189i	1.94769	+	0.0358649i
$655$	0.563691	−	2.65196i	0.0220252	−	0.103621i
$656$	−2.33440	+	22.2103i	−0.0911429	+	0.867167i
$657$	14.2511	+	8.94311i	0.555988	+	0.348904i
$658$	2.68124	+	0.627221i	0.104526	+	0.0244516i
$659$	−21.3739			−0.832607			−0.416304	−	0.909226i	$-0.636675\pi$
$659$	−21.3739			−0.832607			−0.416304	+	0.909226i	$0.636675\pi$
$660$	4.94008	+	3.52972i	0.192292	+	0.137394i
$661$	−14.1200	+	24.4566i	−0.549204	+	0.951250i	0.449125	+	0.893469i	$0.351736\pi$
$661$	−14.1200	+	24.4566i	−0.549204	+	0.951250i	−0.998329	+	0.0577807i	$0.981598\pi$
$662$	−18.1385	−	20.1449i	−0.704974	−	0.782953i
$663$	−1.20984	−	0.280535i	−0.0469862	−	0.0108951i
$664$	−20.7721	−	15.0918i	−0.806115	−	0.585677i
$665$	10.5946	+	25.1622i	0.410840	+	0.975747i
$666$	7.33493	+	8.77555i	0.284223	+	0.340046i
$667$	−16.2175	−	1.70452i	−0.627942	−	0.0659994i
$668$	0.801510	+	7.62586i	0.0310114	+	0.295053i
$669$	−27.3890	+	36.2740i	−1.05892	+	1.40243i
$670$	22.1424	−	12.7839i	0.855437	−	0.493887i
$671$	−0.361895	−	1.50638i	−0.0139708	−	0.0581530i
$672$	9.36148	+	2.37253i	0.361127	+	0.0915223i
$673$	−30.8697	−	10.0302i	−1.18994	−	0.386635i	−0.353889	−	0.935287i	$-0.615141\pi$
$673$	−30.8697	−	10.0302i	−1.18994	−	0.386635i	−0.836050	+	0.548653i	$0.815141\pi$
$674$	7.49462	−	16.8332i	0.288682	−	0.648391i
$675$	−12.3853	−	8.09387i	−0.476712	−	0.311533i
$676$	9.53538	+	2.02681i	0.366745	+	0.0779541i
$677$	5.44548	−	6.04782i	0.209287	−	0.232437i	−0.629358	−	0.777116i	$-0.716682\pi$
$677$	5.44548	−	6.04782i	0.209287	−	0.232437i	0.838644	+	0.544679i	$0.183349\pi$
$678$	−5.88831	−	2.75264i	−0.226139	−	0.105714i
$679$	7.56955	+	2.63102i	0.290493	+	0.100969i
$680$	−0.766941	−	0.249194i	−0.0294108	−	0.00955616i
$681$	8.66476	−	7.51759i	0.332034	−	0.288075i
$682$	6.16227	+	17.3932i	0.235965	+	0.666018i
$683$	33.9081	+	19.5769i	1.29746	+	0.749088i	0.979965	−	0.199172i	$-0.0638251\pi$
$683$	33.9081	+	19.5769i	1.29746	+	0.749088i	0.317495	+	0.948260i	$0.397158\pi$
$684$	−2.32488	−	3.46107i	−0.0888940	−	0.132337i
$685$	−11.4780	+	8.33923i	−0.438551	+	0.318626i
$686$	−4.22114	−	28.2417i	−0.161164	−	1.07827i
$687$	12.9948	−	7.18686i	0.495783	−	0.274196i
$688$	25.1095	+	22.6087i	0.957291	+	0.861949i
$689$	21.2065	−	9.44174i	0.807903	−	0.359702i
$690$	−21.9456	+	6.68644i	−0.835455	+	0.254549i
$691$	−10.2193	+	2.17218i	−0.388761	+	0.0826338i	−0.398146	−	0.917322i	$-0.630346\pi$
$691$	−10.2193	+	2.17218i	−0.388761	+	0.0826338i	0.00938441	+	0.999956i	$0.497013\pi$
$692$	−7.36849			−0.280108
$693$	0.811920	−	26.3124i	0.0308423	−	0.999524i
$694$	1.35286			0.0513539
$695$	−53.8577	+	11.4478i	−2.04294	+	0.434240i
$696$	−22.0432	+	6.71618i	−0.835545	+	0.254576i
$697$	0.508944	−	0.226596i	0.0192776	−	0.00858295i
$698$	−18.8837	−	17.0030i	−0.714760	−	0.643573i
$699$	−4.03482	+	2.23148i	−0.152611	+	0.0844024i
$700$	−2.48995	+	1.37076i	−0.0941113	+	0.0518100i
$701$	−28.0546	+	20.3829i	−1.05961	+	0.769851i	−0.974016	−	0.226479i	$-0.927279\pi$
$701$	−28.0546	+	20.3829i	−1.05961	+	0.769851i	−0.0855933	+	0.996330i	$0.527279\pi$
$702$	−35.4063	+	35.2033i	−1.33633	+	1.32866i
$703$	7.88802	+	4.55415i	0.297502	+	0.171763i
$704$	−15.7203	+	12.0664i	−0.592479	+	0.454771i
$705$	−2.47389	+	2.14636i	−0.0931719	+	0.0808364i
$706$	20.2476	+	6.57885i	0.762029	+	0.247598i
$707$	13.0871	−	11.3099i	0.492192	−	0.425353i
$708$	−6.62820	−	3.09852i	−0.249103	−	0.116449i
$709$	4.59343	−	5.10152i	0.172510	−	0.191592i	−0.650690	−	0.759344i	$-0.725520\pi$
$709$	4.59343	−	5.10152i	0.172510	−	0.191592i	0.823200	+	0.567752i	$0.192187\pi$
$710$	56.9627	+	12.1078i	2.13777	+	0.454398i
$711$	21.3543	+	20.7008i	0.800847	+	0.776342i
$712$	10.7642	−	24.1768i	0.403406	−	0.906064i
$713$	−10.5241	−	3.41948i	−0.394129	−	0.128060i
$714$	−0.221058	−	0.782314i	−0.00827288	−	0.0292774i
$715$	4.53394	−	57.7233i	0.169560	−	2.15873i
$716$	0.663163	−	0.382877i	0.0247836	−	0.0143088i
$717$	−2.98407	+	3.95211i	−0.111442	+	0.147594i
$718$	−0.306658	−	2.91766i	−0.0114444	−	0.108886i
$719$	−33.8186	−	3.55448i	−1.26122	−	0.132560i	−0.549782	−	0.835308i	$-0.685289\pi$
$719$	−33.8186	−	3.55448i	−1.26122	−	0.132560i	−0.711439	+	0.702748i	$0.751956\pi$
$720$	−29.7404	+	24.8581i	−1.10836	+	0.926408i
$721$	40.2391	+	5.05941i	1.49858	+	0.188422i
$722$	6.77429	+	4.92181i	0.252113	+	0.183171i
$723$	−23.7849	−	5.51521i	−0.884572	−	0.205113i
$724$	1.64759	+	1.82983i	0.0612322	+	0.0680053i
$725$	7.57054	−	13.1126i	0.281163	−	0.486988i
$726$	−22.4912	−	18.8972i	−0.834725	−	0.701342i
$727$	21.9188			0.812923			0.406461	−	0.913668i	$-0.366763\pi$
$727$	21.9188			0.812923			0.406461	+	0.913668i	$0.366763\pi$
$728$	−11.9466	−	39.4855i	−0.442772	−	1.46343i
$729$	−5.46160	−	26.4418i	−0.202282	−	0.979327i
$730$	−2.53201	+	24.0905i	−0.0937141	+	0.891630i
$731$	0.175244	−	0.824459i	0.00648164	−	0.0304937i
$732$	−0.305201	−	0.00562001i	−0.0112806	−	0.000207722i
$733$	−13.6068	−	1.43013i	−0.502578	−	0.0528231i	−0.150152	−	0.988663i	$-0.547976\pi$
$733$	−13.6068	−	1.43013i	−0.502578	−	0.0528231i	−0.352426	+	0.935840i	$0.614643\pi$
$734$	4.56185	−	3.31437i	0.168381	−	0.122336i
$735$	30.1573	+	15.6239i	1.11237	+	0.576295i
$736$			6.46267i			0.238217i
$737$	−17.7192	+	8.45497i	−0.652694	+	0.311443i
$738$	3.15959	−	22.1731i	0.116306	−	0.816203i
$739$	−9.82988	+	8.85087i	−0.361598	+	0.325584i	−0.829825	−	0.558024i	$-0.811560\pi$
$739$	−9.82988	+	8.85087i	−0.361598	+	0.325584i	0.468227	+	0.883608i	$0.344893\pi$
$740$	−1.06295	+	2.38743i	−0.0390749	+	0.0877637i
$741$	−16.8386	+	36.0202i	−0.618580	+	1.32324i
$742$	12.1087	+	9.17980i	0.444524	+	0.337001i
$743$	−4.73025	−	14.5582i	−0.173536	−	0.534089i	0.826028	−	0.563630i	$-0.190595\pi$
$743$	−4.73025	−	14.5582i	−0.173536	−	0.534089i	−0.999564	+	0.0295409i	$0.990595\pi$
$744$	−15.5790	+	1.34794i	−0.571155	+	0.0494179i
$745$	11.8732	−	1.24792i	0.435000	−	0.0457204i
$746$	36.2553	−	32.6444i	1.32740	−	1.19520i
$747$	24.2239	+	19.0007i	0.886305	+	0.695198i
$748$	−0.133023	−	0.0550760i	−0.00486382	−	0.00201378i
$749$	10.5534	−	22.4612i	0.385612	−	0.820716i
$750$	−1.97788	+	15.9819i	−0.0722221	+	0.583576i
$751$	12.4059	+	5.52345i	0.452697	+	0.201554i	0.620403	−	0.784284i	$-0.286969\pi$
$751$	12.4059	+	5.52345i	0.452697	+	0.201554i	−0.167706	+	0.985837i	$0.553636\pi$
$752$	1.26631	+	2.84417i	0.0461775	+	0.103716i
$753$	16.8023	+	0.309399i	0.612309	+	0.0112751i
$754$	−37.9709	−	34.1892i	−1.38282	−	1.24510i
$755$	−21.0711	−	15.3091i	−0.766857	−	0.557154i
$756$	−4.97763	−	1.45850i	−0.181035	−	0.0530453i
$757$	0.354900	−	1.09227i	0.0128991	−	0.0396992i	−0.944400	−	0.328799i	$-0.893356\pi$
$757$	0.354900	−	1.09227i	0.0128991	−	0.0396992i	0.957299	+	0.289100i	$0.0933560\pi$
$758$	10.5056	+	18.1962i	0.381580	+	0.660916i
$759$	17.2019	−	3.79905i	0.624388	−	0.137897i
$760$	−12.9090	+	22.3590i	−0.468257	+	0.811045i
$761$	−11.8009	+	2.50835i	−0.427781	+	0.0909277i	−0.416771	−	0.909012i	$-0.636838\pi$
$761$	−11.8009	+	2.50835i	−0.427781	+	0.0909277i	−0.0110106	+	0.999939i	$0.503505\pi$
$762$	21.7554	−	23.2850i	0.788115	−	0.843527i
$763$	25.5423	−	42.2313i	0.924695	−	1.52887i
$764$	7.67984	−	2.49533i	0.277847	−	0.0902779i
$765$	0.907981	+	0.332451i	0.0328281	+	0.0120198i
$766$	15.5848	+	35.0041i	0.563103	+	1.26475i
$767$	7.29353	+	69.3933i	0.263354	+	2.50565i
$768$	5.91037	+	13.9612i	0.213272	+	0.503780i
$769$			33.3396i			1.20226i	0.799153	+	0.601128i	$0.205282\pi$
$769$			33.3396i			1.20226i	−0.799153	+	0.601128i	$0.794718\pi$
$770$	34.5314	−	15.6224i	1.24443	−	0.562990i
$771$	4.22715	−	0.817469i	0.152237	−	0.0294404i
$772$	−1.60697	−	7.56019i	−0.0578360	−	0.272097i
$773$	7.77183	−	0.816852i	0.279533	−	0.0293801i	0.0362755	−	0.999342i	$-0.488451\pi$
$773$	7.77183	−	0.816852i	0.279533	−	0.0293801i	0.243258	+	0.969962i	$0.421784\pi$
$774$	−24.3301	−	23.5857i	−0.874528	−	0.847769i
$775$	6.87507	−	7.63553i	0.246960	−	0.274276i
$776$	2.34181	+	7.20735i	0.0840660	+	0.258729i
$777$	11.1664	−	1.92449i	0.400593	−	0.0690408i
$778$	−19.6841	−	27.0928i	−0.705709	−	0.971325i
$779$	−3.70838	−	17.4466i	−0.132867	−	0.625088i
$780$	−10.7834	−	3.72459i	−0.386107	−	0.133362i
$781$	−42.8781	−	12.6939i	−1.53430	−	0.454222i
$782$	0.471132	−	0.272008i	0.0168476	−	0.00972699i
$783$	26.7096	−	7.07454i	0.954523	−	0.252823i
$784$	22.5620	−	23.0937i	0.805786	−	0.824774i
$785$	16.3789	−	22.5436i	0.584588	−	0.804616i
$786$	2.21420	+	1.33331i	0.0789778	+	0.0475578i
$787$	−3.76046	+	17.6916i	−0.134046	+	0.630636i	0.858908	+	0.512131i	$0.171144\pi$
$787$	−3.76046	+	17.6916i	−0.134046	+	0.630636i	−0.992953	+	0.118505i	$0.962190\pi$
$788$	−3.84338	+	1.71118i	−0.136915	+	0.0609583i
$789$	−1.56584	+	6.75283i	−0.0557452	+	0.240407i
$790$	−13.2319	+	40.7235i	−0.470769	+	1.44888i
$791$	−5.28568	+	3.67824i	−0.187937	+	0.130783i
$792$	20.2923	−	14.4204i	0.721054	−	0.512407i
$793$	1.45552	+	2.52104i	0.0516872	+	0.0895248i
$794$	0.225153	+	0.250057i	0.00799037	+	0.00887421i
$795$	−17.2885	+	5.26751i	−0.613161	+	0.186819i
$796$	0.0375787	−	0.357537i	0.00133194	−	0.0126726i
$797$	−34.0865	+	11.0754i	−1.20741	+	0.392310i	−0.842481	−	0.538726i	$-0.818906\pi$
$797$	−34.0865	+	11.0754i	−1.20741	+	0.392310i	−0.364926	+	0.931037i	$0.618906\pi$
$798$	−25.9706	+	1.71525i	−0.919351	+	0.0607193i
$799$	0.0456504	−	0.0628324i	0.00161499	−	0.00222285i
$800$	−5.48189	−	2.44070i	−0.193814	−	0.0862916i
$801$	−13.9654	+	28.4945i	−0.493443	+	1.00680i
$802$	−14.9916	−	8.65542i	−0.529373	−	0.305633i
$803$	3.38684	−	18.2895i	0.119519	−	0.645423i
$804$	0.734481	+	3.79801i	0.0259031	+	0.133946i
$805$	−5.17710	+	22.1311i	−0.182469	+	0.780017i
$806$	−20.3801	−	28.0507i	−0.717857	−	0.988045i
$807$	1.12745	+	13.0306i	0.0396879	+	0.458700i
$808$	15.9996	+	3.40081i	0.562863	+	0.119640i
$809$	−29.1324	−	6.19228i	−1.02424	−	0.217709i	−0.334982	−	0.942225i	$-0.608730\pi$
$809$	−29.1324	−	6.19228i	−1.02424	−	0.217709i	−0.689259	+	0.724515i	$0.742064\pi$
$810$	30.7238	−	23.8149i	1.07952	−	0.836770i
$811$	−18.8564	−	25.9536i	−0.662139	−	0.911356i	0.337411	−	0.941357i	$-0.390449\pi$
$811$	−18.8564	−	25.9536i	−0.662139	−	0.911356i	−0.999550	+	0.0300017i	$0.990449\pi$
$812$	1.20907	−	5.16852i	0.0424300	−	0.181380i
$813$	19.8187	−	3.83265i	0.695072	−	0.134417i
$814$	6.03166	−	11.1130i	0.211410	−	0.389512i
$815$	−31.0950	−	17.9527i	−1.08921	−	0.628855i
$816$	0.553858	−	0.733530i	0.0193889	−	0.0256787i
$817$	−24.6525	−	10.9760i	−0.862481	−	0.384001i
$818$	8.85313	−	12.1853i	0.309542	−	0.426049i
$819$	12.5719	+	47.8407i	0.439299	+	1.67169i
$820$	4.86716	−	1.58144i	0.169969	−	0.0552261i
$821$	1.68986	−	16.0779i	0.0589765	−	0.561124i	−0.924639	−	0.380845i	$-0.875633\pi$
$821$	1.68986	−	16.0779i	0.0589765	−	0.561124i	0.983616	−	0.180279i	$-0.0577001\pi$
$822$	−3.94201	−	12.9381i	−0.137493	−	0.451267i
$823$	−15.1629	−	16.8401i	−0.528546	−	0.587010i	0.418456	−	0.908237i	$-0.362571\pi$
$823$	−15.1629	−	16.8401i	−0.528546	−	0.587010i	−0.947002	+	0.321227i	$0.895905\pi$
$824$	19.1759	+	33.2137i	0.668025	+	1.15705i
$825$	−3.27396	+	16.0261i	−0.113985	+	0.557955i
$826$	−37.4896	+	26.0886i	−1.30443	+	0.907737i
$827$	4.72504	−	14.5422i	0.164306	−	0.505681i	−0.834679	−	0.550737i	$-0.814347\pi$
$827$	4.72504	−	14.5422i	0.164306	−	0.505681i	0.998984	+	0.0450561i	$0.0143467\pi$
$828$	0.127789	−	3.46868i	0.00444096	−	0.120545i
$829$	−8.54585	+	3.80486i	−0.296809	+	0.132148i	−0.549739	−	0.835337i	$-0.685273\pi$
$829$	−8.54585	+	3.80486i	−0.296809	+	0.132148i	0.252929	+	0.967485i	$0.418606\pi$
$830$	−9.21562	+	43.3561i	−0.319879	+	1.50491i
$831$	27.0995	−	45.0033i	0.940071	−	1.56115i
$832$	21.8874	−	30.1254i	0.758809	−	1.04441i
$833$	−0.780327	−	0.199379i	−0.0270367	−	0.00690807i
$834$	6.44696	−	52.0933i	0.223240	−	1.80384i
$835$	−49.3049	+	28.4662i	−1.70627	+	0.985114i
$836$	−2.61025	+	3.79919i	−0.0902772	+	0.131398i
$837$	18.7270	−	0.927437i	0.647299	−	0.0320569i
$838$	9.92088	+	46.6741i	0.342711	+	1.61233i
$839$	22.4050	+	30.8378i	0.773505	+	1.06464i	0.995969	+	0.0896978i	$0.0285901\pi$
$839$	22.4050	+	30.8378i	0.773505	+	1.06464i	−0.222464	+	0.974941i	$0.571410\pi$
$840$	5.45507	+	31.6518i	0.188218	+	1.09209i
$841$	−0.223729	−	0.688567i	−0.00771479	−	0.0237437i
$842$	−20.6156	+	22.8959i	−0.710460	+	0.789046i
$843$	−7.03093	−	10.0617i	−0.242158	−	0.346544i
$844$	−3.90885	+	0.410837i	−0.134548	+	0.0141416i
$845$	15.0487	+	70.7983i	0.517689	+	2.43554i
$846$	−1.16409	−	2.89720i	−0.0400222	−	0.0996078i
$847$	−27.3739	+	9.88290i	−0.940577	+	0.339580i
$848$			17.1800i			0.589963i
$849$	31.8832	−	13.4975i	1.09423	−	0.463235i
$850$	0.0528001	+	0.502360i	0.00181103	+	0.0172308i
$851$	3.08413	+	6.92707i	0.105723	+	0.237457i
$852$	−4.54519	+	7.54807i	−0.155716	+	0.258593i
$853$	−9.14993	+	2.97299i	−0.313288	+	0.101793i	−0.461440	−	0.887171i	$-0.652667\pi$
$853$	−9.14993	+	2.97299i	−0.313288	+	0.101793i	0.148153	+	0.988964i	$0.452667\pi$
$854$	−0.986152	+	1.63049i	−0.0337454	+	0.0557941i
$855$	16.4551	−	26.2217i	0.562753	−	0.896762i
$856$	22.9554	−	4.87933i	0.784601	−	0.166772i
$857$	−0.0352022	+	0.0609721i	−0.00120249	+	0.00208277i	−0.866626	−	0.498958i	$-0.833716\pi$
$857$	−0.0352022	+	0.0609721i	−0.00120249	+	0.00208277i	0.865424	+	0.501041i	$0.167049\pi$
$858$	50.6024	+	22.0510i	1.72754	+	0.752808i
$859$	−19.2494	−	33.3409i	−0.656780	−	1.13758i	−0.981444	−	0.191748i	$-0.938584\pi$
$859$	−19.2494	−	33.3409i	−0.656780	−	1.13758i	0.324664	−	0.945829i	$-0.394749\pi$
$860$	2.39264	−	7.36377i	0.0815882	−	0.251103i
$861$	−17.4323	−	13.7284i	−0.594091	−	0.467862i
$862$	−42.9264	−	31.1878i	−1.46208	−	1.06226i
$863$	0.682715	+	0.614719i	0.0232399	+	0.0209253i	0.680669	−	0.732591i	$-0.261689\pi$
$863$	0.682715	+	0.614719i	0.0232399	+	0.0209253i	−0.657429	+	0.753517i	$0.728356\pi$
$864$	−3.89489	−	10.2344i	−0.132507	−	0.348182i
$865$	−22.2524	−	49.9797i	−0.756604	−	1.69936i
$866$	0.322002	+	0.143364i	0.0109421	+	0.00487172i
$867$	29.1992	+	3.61363i	0.991656	+	0.122725i
$868$	1.53175	−	3.26009i	0.0519910	−	0.110655i
$869$	12.5779	−	30.3791i	0.426677	−	1.03054i
$870$	26.0698	+	30.0480i	0.883848	+	1.01872i
$871$	27.4152	−	24.6848i	0.928929	−	0.836411i
$872$	46.4169	−	4.87861i	1.57187	−	0.165211i
$873$	−2.48790	−	8.73953i	−0.0842025	−	0.295788i
$874$	−5.38220	−	16.5647i	−0.182056	−	0.560310i
$875$	12.7137	+	9.63846i	0.429801	+	0.325839i
$876$	−3.32007	−	1.55205i	−0.112175	−	0.0524389i
$877$	−11.7201	+	26.3238i	−0.395760	+	0.888893i	0.600263	+	0.799803i	$0.295063\pi$
$877$	−11.7201	+	26.3238i	−0.395760	+	0.888893i	−0.996024	+	0.0890900i	$0.971604\pi$
$878$	23.2673	−	20.9499i	0.785232	−	0.707026i
$879$	−30.1363	−	10.4091i	−1.01647	−	0.351090i
$880$	37.6622	+	20.4414i	1.26959	+	0.689078i
$881$			20.6052i			0.694208i	0.937827	+	0.347104i	$0.112835\pi$
$881$			20.6052i			0.694208i	−0.937827	+	0.347104i	$0.887165\pi$
$882$	−23.4644	+	22.3116i	−0.790089	+	0.751270i
$883$	7.32741	−	5.32367i	0.246587	−	0.179156i	−0.457626	−	0.889145i	$-0.651300\pi$
$883$	7.32741	−	5.32367i	0.246587	−	0.179156i	0.704213	+	0.709989i	$0.251300\pi$
$884$	0.269048	+	0.0282781i	0.00904908	+	0.000951097i
$885$	1.00018	−	54.3157i	0.0336205	−	1.82580i
$886$	12.2097	−	57.4421i	0.410193	−	1.92981i
$887$	−2.42842	+	23.1049i	−0.0815383	+	0.775785i	0.874989	+	0.484143i	$0.160868\pi$
$887$	−2.42842	+	23.1049i	−0.0815383	+	0.775785i	−0.956527	+	0.291642i	$0.905798\pi$
$888$	7.82963	+	7.31530i	0.262745	+	0.245485i
$889$	−9.14266	−	30.2179i	−0.306635	−	1.01348i
$890$	−45.6868			−1.53143
$891$	−24.9516	+	16.3834i	−0.835911	+	0.548864i
$892$	4.95049	−	8.57450i	0.165755	−	0.287096i
$893$	−1.66381	−	1.84784i	−0.0556771	−	0.0618357i
$894$	−2.57087	+	11.0872i	−0.0859828	+	0.370810i
$895$	4.59973	+	3.34190i	0.153752	+	0.111707i
$896$	35.2486	+	4.43194i	1.17757	+	0.148061i
$897$	−28.9666	+	16.0202i	−0.967166	+	0.534897i
$898$	5.28772	+	0.555761i	0.176453	+	0.0185460i
$899$	2.00568	+	19.0828i	0.0668931	+	0.636446i
$900$	2.89401	+	1.41838i	0.0964670	+	0.0472793i
$901$	0.371153	−	0.214285i	0.0123649	−	0.00713888i
$902$	−24.0759	+	5.78404i	−0.801638	+	0.192587i
$903$	−32.3059	+	9.12867i	−1.07507	+	0.303783i
$904$	−5.79155	−	1.88179i	−0.192624	−	0.0625874i
$905$	−7.43595	+	16.7014i	−0.247179	+	0.555174i
$906$	20.3529	−	14.2222i	0.676178	−	0.472500i
$907$	34.1636	+	7.26169i	1.13438	+	0.241121i	0.736580	−	0.676350i	$-0.236439\pi$
$907$	34.1636	+	7.26169i	1.13438	+	0.241121i	0.397803	+	0.917471i	$0.369773\pi$
$908$	−1.67203	+	1.85697i	−0.0554881	+	0.0616258i
$909$	−19.0213	−	4.78129i	−0.630895	−	0.158585i
$910$	−53.8832	+	46.5659i	−1.78621	+	1.54365i
$911$	6.00834	+	1.95223i	0.199065	+	0.0646802i	0.406853	−	0.913494i	$-0.366626\pi$
$911$	6.00834	+	1.95223i	0.199065	+	0.0646802i	−0.207787	+	0.978174i	$0.566626\pi$
$912$	−19.2847	−	22.2275i	−0.638580	−	0.736026i
$913$	9.66169	−	32.6359i	0.319755	−	1.08009i
$914$	1.77214	+	1.02315i	0.0586173	+	0.0338427i
$915$	−0.883570	−	2.08712i	−0.0292099	−	0.0689981i
$916$	−2.61695	+	1.90132i	−0.0864663	+	0.0628215i
$917$	2.24318	−	1.23491i	0.0740763	−	0.0407804i
$918$	−0.582162	+	0.714697i	−0.0192142	+	0.0235885i
$919$	−3.73482	−	3.36285i	−0.123200	−	0.110930i	0.605228	−	0.796052i	$-0.293082\pi$
$919$	−3.73482	−	3.36285i	−0.123200	−	0.110930i	−0.728428	+	0.685122i	$0.759749\pi$
$920$	−19.6351	+	8.74213i	−0.647351	+	0.288219i
$921$	−1.35542	−	4.44863i	−0.0446626	−	0.146587i
$922$	−7.59018	+	1.61334i	−0.249969	+	0.0531326i
$923$	84.0252			2.76572
$924$	0.528441	+	5.70994i	0.0173844	+	0.187843i
$925$	−7.04058			−0.231493
$926$	40.8533	−	8.68363i	1.34252	−	0.285362i
$927$	−21.5113	−	40.6446i	−0.706522	−	1.33494i
$928$	10.2374	−	4.55800i	0.336061	−	0.149624i
$929$	−6.65609	−	5.99317i	−0.218379	−	0.196630i	0.552679	−	0.833394i	$-0.313606\pi$
$929$	−6.65609	−	5.99317i	−0.218379	−	0.196630i	−0.771058	+	0.636765i	$0.780272\pi$
$930$	13.0648	+	23.6229i	0.428411	+	0.774624i
$931$	−11.4380	+	23.1098i	−0.374866	+	0.757392i
$932$	0.812548	−	0.590350i	0.0266159	−	0.0193376i
$933$	−7.75402	+	3.28261i	−0.253855	+	0.107468i
$934$	−23.1257	−	13.3516i	−0.756697	−	0.436879i
$935$	−0.0281479	−	1.06861i	−0.000920535	−	0.0349473i
$936$	−28.8693	+	36.8053i	−0.943622	+	1.20302i
$937$	−24.6571	−	8.01159i	−0.805514	−	0.261727i	−0.122817	−	0.992429i	$-0.539193\pi$
$937$	−24.6571	−	8.01159i	−0.805514	−	0.261727i	−0.682697	+	0.730702i	$0.739193\pi$
$938$	22.8094	+	7.92810i	0.744755	+	0.258862i
$939$	−9.64460	+	20.6313i	−0.314740	+	0.673276i
$940$	0.477382	−	0.530187i	0.0155705	−	0.0172928i
$941$	−26.0562	−	5.53841i	−0.849408	−	0.180547i	−0.237413	−	0.971409i	$-0.576299\pi$
$941$	−26.0562	−	5.53841i	−0.849408	−	0.180547i	−0.611995	+	0.790862i	$0.709633\pi$
$942$	15.2160	+	21.7751i	0.495765	+	0.709472i
$943$	6.03951	−	13.5650i	0.196673	−	0.441736i
$944$	−49.1126	−	15.9577i	−1.59848	−	0.519378i
$945$	−5.13926	−	38.1673i	−0.167180	−	1.24158i
$946$	−14.3307	+	34.6126i	−0.465933	+	1.12535i
$947$	−12.5640	+	7.25385i	−0.408276	+	0.235718i	−0.690049	−	0.723763i	$-0.742411\pi$
$947$	−12.5640	+	7.25385i	−0.408276	+	0.235718i	0.281773	+	0.959481i	$0.409078\pi$
$948$	−5.17021	−	3.90381i	−0.167920	−	0.126790i
$949$	3.65334	+	34.7592i	0.118592	+	1.12833i
$950$	16.0835	+	1.69044i	0.521818	+	0.0548452i
$951$	−24.3138	−	43.9626i	−0.788428	−	1.42558i
$952$	−0.295553	−	0.701942i	−0.00957894	−	0.0227501i
$953$	11.0045	+	7.99527i	0.356472	+	0.258992i	0.751579	−	0.659643i	$-0.229292\pi$
$953$	11.0045	+	7.99527i	0.356472	+	0.258992i	−0.395107	+	0.918635i	$0.629292\pi$
$954$	0.634318	−	17.2179i	0.0205368	−	0.557449i
$955$	40.1182	+	44.5558i	1.29819	+	1.44179i
$956$	0.539363	−	0.934205i	0.0174443	−	0.0302143i
$957$	−18.1502	−	24.5699i	−0.586712	−	0.794231i
$958$	3.11359			0.100595
$959$	−13.0474	−	3.05217i	−0.421323	−	0.0985598i
$960$	−19.7925	+	21.1841i	−0.638801	+	0.683715i
$961$	1.87934	−	17.8808i	0.0606240	−	0.576799i
$962$	−4.93978	+	23.2399i	−0.159265	+	0.749283i
$963$	−27.7216	+	4.83328i	−0.893316	+	0.155750i
$964$	5.28940	+	0.555938i	0.170360	+	0.0179056i
$965$	46.4270	−	33.7312i	1.49454	−	1.08585i
$966$	−18.3307	−	11.5530i	−0.589779	−	0.371711i
$967$			3.44228i			0.110696i	0.998467	+	0.0553482i	$0.0176269\pi$
$967$			3.44228i			0.110696i	−0.998467	+	0.0553482i	$0.982373\pi$
$968$	−23.0862	−	14.9822i	−0.742019	−	0.481547i
$969$	−0.239661	+	0.693865i	−0.00769903	+	0.0222902i
$970$	9.72221	−	8.75392i	0.312161	−	0.281071i
$971$	3.82178	−	8.58385i	0.122647	−	0.275469i	−0.841779	−	0.539822i	$-0.818492\pi$
$971$	3.82178	−	8.58385i	0.122647	−	0.275469i	0.964426	+	0.264353i	$0.0851583\pi$
$972$	1.88812	+	5.57009i	0.0605614	+	0.178661i
$973$	−41.4405	−	31.4168i	−1.32852	−	1.00718i
$974$	13.9464	+	42.9226i	0.446871	+	1.37533i
$975$	−2.64939	−	30.6208i	−0.0848485	−	0.980650i
$976$	−2.14263	+	0.225200i	−0.0685840	+	0.00720847i
$977$	28.3387	−	25.5163i	0.906634	−	0.816337i	−0.0769037	−	0.997039i	$-0.524503\pi$
$977$	28.3387	−	25.5163i	0.906634	−	0.816337i	0.983538	+	0.180701i	$0.0578367\pi$
$978$	25.8547	−	22.4317i	0.826743	−	0.717287i
$979$	34.9742	+	2.74709i	1.11778	+	0.0877973i
$980$	−6.93742	−	2.57075i	−0.221608	−	0.0821195i
$981$	−55.8341	+	3.79673i	−1.78264	+	0.121220i
$982$	9.50320	+	4.23110i	0.303259	+	0.135020i
$983$	19.1849	+	43.0900i	0.611903	+	1.37436i	0.907908	+	0.419170i	$0.137679\pi$
$983$	19.1849	+	43.0900i	0.611903	+	1.37436i	−0.296005	+	0.955186i	$0.595655\pi$
$984$	0.386321	−	20.9796i	0.0123155	−	0.668805i
$985$	−23.2135	−	20.9016i	−0.739645	−	0.665979i
$986$	−0.763166	−	0.554472i	−0.0243042	−	0.0176580i
$987$	−3.06153	−	0.442337i	−0.0974495	−	0.0140797i
$988$	2.67648	−	8.23737i	0.0851503	−	0.262066i
$989$	−11.2327	−	19.4556i	−0.357178	−	0.618651i
$990$	−36.9905	−	21.8770i	−1.17564	−	0.695297i
$991$	12.9287	−	22.3932i	0.410694	−	0.711343i	−0.584272	−	0.811558i	$-0.698620\pi$
$991$	12.9287	−	22.3932i	0.410694	−	0.711343i	0.994966	+	0.100215i	$0.0319531\pi$
$992$	7.43832	−	1.58106i	0.236167	−	0.0501988i
$993$	22.2510	+	20.7893i	0.706114	+	0.659728i
$994$	26.5253	+	48.1824i	0.841332	+	1.52825i
$995$	2.53862	−	0.824849i	0.0804798	−	0.0261495i
$996$	−5.74507	−	3.45949i	−0.182040	−	0.109618i
$997$	8.41936	+	18.9102i	0.266644	+	0.598892i	0.996396	−	0.0848196i	$-0.0270314\pi$
$997$	8.41936	+	18.9102i	0.266644	+	0.598892i	−0.729753	+	0.683711i	$0.760365\pi$
$998$	1.08766	+	10.3484i	0.0344294	+	0.327574i
$999$	−9.05888	−	9.11114i	−0.286610	−	0.288264i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.be.a.200.21	yes	224
3.2	odd	2	inner	231.2.be.a.200.8	yes	224
7.2	even	3	inner	231.2.be.a.2.8	✓	224
11.6	odd	10	inner	231.2.be.a.116.21	yes	224
21.2	odd	6	inner	231.2.be.a.2.21	yes	224
33.17	even	10	inner	231.2.be.a.116.8	yes	224
77.72	odd	30	inner	231.2.be.a.149.8	yes	224
231.149	even	30	inner	231.2.be.a.149.21	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.be.a.2.8	✓	224	7.2	even	3	inner
231.2.be.a.2.21	yes	224	21.2	odd	6	inner
231.2.be.a.116.8	yes	224	33.17	even	10	inner
231.2.be.a.116.21	yes	224	11.6	odd	10	inner
231.2.be.a.149.8	yes	224	77.72	odd	30	inner
231.2.be.a.149.21	yes	224	231.149	even	30	inner
231.2.be.a.200.8	yes	224	3.2	odd	2	inner
231.2.be.a.200.21	yes	224	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.be (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50815 - 0.320568i) q^{2} +(-1.65685 + 0.504814i) q^{3} +(0.344674 - 0.153459i) q^{4} +(2.08179 + 1.87445i) q^{5} +(-2.33696 + 1.29247i) q^{6} +(-0.0538576 + 2.64520i) q^{7} +(-2.02413 + 1.47062i) q^{8} +(2.49032 - 1.67281i) q^{9} +O(q^{10})\)	\(q+(1.50815 - 0.320568i) q^{2} +(-1.65685 + 0.504814i) q^{3} +(0.344674 - 0.153459i) q^{4} +(2.08179 + 1.87445i) q^{5} +(-2.33696 + 1.29247i) q^{6} +(-0.0538576 + 2.64520i) q^{7} +(-2.02413 + 1.47062i) q^{8} +(2.49032 - 1.67281i) q^{9} +(3.74054 + 2.15960i) q^{10} +(-2.73361 - 1.87813i) q^{11} +(-0.493605 + 0.428254i) q^{12} +(5.92698 + 1.92579i) q^{13} +(0.766742 + 4.00664i) q^{14} +(-4.39546 - 2.05477i) q^{15} +(-3.08619 + 3.42756i) q^{16} +(0.112542 + 0.0239216i) q^{17} +(3.21954 - 3.32117i) q^{18} +(1.49827 - 3.36517i) q^{19} +(1.00519 + 0.326605i) q^{20} +(-1.24610 - 4.40990i) q^{21} +(-4.72477 - 1.95621i) q^{22} +(2.65577 - 1.53331i) q^{23} +(2.61130 - 3.45841i) q^{24} +(0.297634 + 2.83180i) q^{25} +(9.55615 + 1.00439i) q^{26} +(-3.28165 + 4.02875i) q^{27} +(0.387366 + 0.919996i) q^{28} +(-4.30196 - 3.12556i) q^{29} +(-7.28773 - 1.68987i) q^{30} +(-2.41451 - 2.68158i) q^{31} +(-1.05371 + 1.82508i) q^{32} +(5.47730 + 1.73183i) q^{33} +0.177399 q^{34} +(-5.07042 + 5.40580i) q^{35} +(0.601643 - 0.958734i) q^{36} +(-0.258461 + 2.45909i) q^{37} +(1.18086 - 5.55549i) q^{38} +(-10.7923 - 0.198731i) q^{39} +(-6.97042 - 0.732620i) q^{40} +(3.91730 - 2.84608i) q^{41} +(-3.29299 - 6.25135i) q^{42} -7.32577i q^{43} +(-1.23042 - 0.227848i) q^{44} +(8.31992 + 1.18556i) q^{45} +(3.51378 - 3.16382i) q^{46} +(0.274554 - 0.616659i) q^{47} +(3.38308 - 7.23691i) q^{48} +(-6.99420 - 0.284929i) q^{49} +(1.35666 + 4.17538i) q^{50} +(-0.198542 + 0.0171784i) q^{51} +(2.33840 - 0.245776i) q^{52} +(2.76812 - 2.49242i) q^{53} +(-3.65774 + 7.12796i) q^{54} +(-2.17032 - 9.03388i) q^{55} +(-3.78107 - 5.43345i) q^{56} +(-0.783628 + 6.33194i) q^{57} +(-7.48998 - 3.33475i) q^{58} +(4.55396 + 10.2284i) q^{59} +(-1.83032 - 0.0337038i) q^{60} +(0.347132 + 0.312559i) q^{61} +(-4.50108 - 3.27023i) q^{62} +(4.29079 + 6.67751i) q^{63} +(1.84642 - 5.68270i) q^{64} +(8.72891 + 15.1189i) q^{65} +(8.81577 + 0.856018i) q^{66} +(2.95979 - 5.12650i) q^{67} +(0.0424613 - 0.00902543i) q^{68} +(-3.62618 + 3.88114i) q^{69} +(-5.91405 + 9.77819i) q^{70} +(12.8230 - 4.16644i) q^{71} +(-2.58069 + 7.04830i) q^{72} +(2.28108 + 5.12339i) q^{73} +(0.398507 + 3.79154i) q^{74} +(-1.92267 - 4.54162i) q^{75} -1.38981i q^{76} +(5.11527 - 7.12980i) q^{77} +(-16.3402 + 3.15995i) q^{78} +(2.06117 + 9.69704i) q^{79} +(-12.8496 + 1.35054i) q^{80} +(3.40344 - 8.33166i) q^{81} +(4.99552 - 5.54809i) q^{82} +(3.17120 + 9.75996i) q^{83} +(-1.10624 - 1.32875i) q^{84} +(0.189449 + 0.260754i) q^{85} +(-2.34841 - 11.0484i) q^{86} +(8.70555 + 3.00690i) q^{87} +(8.29521 - 0.218501i) q^{88} +(-9.16047 + 5.28880i) q^{89} +(12.9278 - 0.879091i) q^{90} +(-5.41333 + 15.5744i) q^{91} +(0.680074 - 0.936041i) q^{92} +(5.35419 + 3.22411i) q^{93} +(0.216389 - 1.01803i) q^{94} +(9.42692 - 4.19714i) q^{95} +(0.824519 - 3.55583i) q^{96} +(0.935987 - 2.88067i) q^{97} +(-10.6397 + 1.81240i) q^{98} +(-9.94933 - 0.104367i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9}+O(q^{10}) \) 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9	\( 224 q - 3 q^{3} + 18 q^{4} - 20 q^{6} - 20 q^{7} - 9 q^{9} - 16 q^{12} - 40 q^{13} + 12 q^{15} + 34 q^{16} - 5 q^{18} - 10 q^{19} - 76 q^{22} - 25 q^{24} - 18 q^{25} + 6 q^{27} + 10 q^{28} - 35 q^{30} - 8 q^{33} - 96 q^{34} - 48 q^{36} - 10 q^{37} - 45 q^{39} - 120 q^{40} + 34 q^{42} - 24 q^{45} - 50 q^{46} + 14 q^{48} - 56 q^{49} - 45 q^{51} - 10 q^{52} + 48 q^{55} + 60 q^{57} + 44 q^{58} - 47 q^{60} - 50 q^{61} + 60 q^{63} - 72 q^{64} + 77 q^{66} - 80 q^{67} + 78 q^{69} + 36 q^{70} + 55 q^{72} - 70 q^{73} - 11 q^{75} + 36 q^{78} - 90 q^{79} + 23 q^{81} - 6 q^{82} + 125 q^{84} + 160 q^{85} + 86 q^{88} + 30 q^{90} - 128 q^{91} - 38 q^{93} - 210 q^{94} + 135 q^{96} + 40 q^{97} + 80 q^{99}+O(q^{100}) \) 224 * q - 3 * q^3 + 18 * q^4 - 20 * q^6 - 20 * q^7 - 9 * q^9 - 16 * q^12 - 40 * q^13 + 12 * q^15 + 34 * q^16 - 5 * q^18 - 10 * q^19 - 76 * q^22 - 25 * q^24 - 18 * q^25 + 6 * q^27 + 10 * q^28 - 35 * q^30 - 8 * q^33 - 96 * q^34 - 48 * q^36 - 10 * q^37 - 45 * q^39 - 120 * q^40 + 34 * q^42 - 24 * q^45 - 50 * q^46 + 14 * q^48 - 56 * q^49 - 45 * q^51 - 10 * q^52 + 48 * q^55 + 60 * q^57 + 44 * q^58 - 47 * q^60 - 50 * q^61 + 60 * q^63 - 72 * q^64 + 77 * q^66 - 80 * q^67 + 78 * q^69 + 36 * q^70 + 55 * q^72 - 70 * q^73 - 11 * q^75 + 36 * q^78 - 90 * q^79 + 23 * q^81 - 6 * q^82 + 125 * q^84 + 160 * q^85 + 86 * q^88 + 30 * q^90 - 128 * q^91 - 38 * q^93 - 210 * q^94 + 135 * q^96 + 40 * q^97 + 80 * q^99

Introduction

L-functions

Modular forms

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