LMFDB - Embedded newform 138.2.f.a.113.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,2,Mod(5,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 1]))

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

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

chi := DirichletCharacter("138.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	138.f (of order $22$, degree $10$, 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:	$1.10193554789$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			113.4
Character	$\chi$	$=$	138.113
Dual form			138.2.f.a.11.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.540641 + 0.841254i) q^{2} +(1.70890 - 0.282234i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(2.84902 + 0.836549i) q^{5} +(-0.686471 + 1.59021i) q^{6} +(-3.02354 - 2.61991i) q^{7} +(0.989821 + 0.142315i) q^{8} +(2.84069 - 0.964621i) q^{9} +O(q^{10})$	\(q+(-0.540641 + 0.841254i) q^{2} +(1.70890 - 0.282234i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(2.84902 + 0.836549i) q^{5} +(-0.686471 + 1.59021i) q^{6} +(-3.02354 - 2.61991i) q^{7} +(0.989821 + 0.142315i) q^{8} +(2.84069 - 0.964621i) q^{9} +(-2.24405 + 1.94448i) q^{10} +(-2.79349 + 1.79527i) q^{11} +(-0.966633 - 1.43723i) q^{12} +(1.31691 + 1.51980i) q^{13} +(3.83866 - 1.12713i) q^{14} +(5.10480 + 0.625487i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-0.139786 + 0.306088i) q^{17} +(-0.724301 + 2.91125i) q^{18} +(-4.42768 + 2.02205i) q^{19} +(-0.422576 - 2.93908i) q^{20} +(-5.90636 - 3.62383i) q^{21} -3.32063i q^{22} +(0.384545 + 4.78039i) q^{23} +(1.73167 - 0.0361594i) q^{24} +(3.21085 + 2.06349i) q^{25} +(-1.99051 + 0.286192i) q^{26} +(4.58221 - 2.45018i) q^{27} +(-1.12713 + 3.83866i) q^{28} +(-6.14380 - 2.80578i) q^{29} +(-3.28606 + 3.95627i) q^{30} +(1.10880 - 7.71186i) q^{31} +(-0.281733 - 0.959493i) q^{32} +(-4.26712 + 3.85635i) q^{33} +(-0.181924 - 0.283079i) q^{34} +(-6.42246 - 9.99354i) q^{35} +(-2.05751 - 2.18326i) q^{36} +(-2.31258 - 7.87592i) q^{37} +(0.692724 - 4.81800i) q^{38} +(2.67941 + 2.22551i) q^{39} +(2.70097 + 1.23349i) q^{40} +(-0.321149 + 1.09373i) q^{41} +(6.24178 - 3.00956i) q^{42} +(-0.439950 + 0.0632552i) q^{43} +(2.79349 + 1.79527i) q^{44} +(8.90014 - 0.371853i) q^{45} +(-4.22942 - 2.26097i) q^{46} +8.33095i q^{47} +(-0.905794 + 1.47633i) q^{48} +(1.28165 + 8.91409i) q^{49} +(-3.47183 + 1.58553i) q^{50} +(-0.152491 + 0.562526i) q^{51} +(0.835391 - 1.82925i) q^{52} +(0.581719 - 0.671339i) q^{53} +(-0.416105 + 5.17946i) q^{54} +(-9.46055 + 2.77787i) q^{55} +(-2.61991 - 3.02354i) q^{56} +(-6.99577 + 4.70513i) q^{57} +(5.68196 - 3.65157i) q^{58} +(3.38202 - 2.93054i) q^{59} +(-1.55165 - 4.90333i) q^{60} +(7.37119 + 1.05982i) q^{61} +(5.88816 + 5.10212i) q^{62} +(-11.1162 - 4.52579i) q^{63} +(0.959493 + 0.281733i) q^{64} +(2.48053 + 5.43160i) q^{65} +(-0.937195 - 5.67463i) q^{66} +(-6.97092 + 10.8470i) q^{67} +0.336496 q^{68} +(2.00634 + 8.06068i) q^{69} +11.8793 q^{70} +(6.79016 - 10.5657i) q^{71} +(2.94905 - 0.550530i) q^{72} +(4.56063 + 9.98639i) q^{73} +(7.87592 + 2.31258i) q^{74} +(6.06941 + 2.62009i) q^{75} +(3.67865 + 3.18756i) q^{76} +(13.1497 + 1.89064i) q^{77} +(-3.32081 + 1.05086i) q^{78} +(11.8282 - 10.2492i) q^{79} +(-2.49793 + 1.60533i) q^{80} +(7.13901 - 5.48037i) q^{81} +(-0.746481 - 0.861485i) q^{82} +(-5.91068 + 1.73553i) q^{83} +(-0.842757 + 6.87801i) q^{84} +(-0.654309 + 0.755113i) q^{85} +(0.184641 - 0.404308i) q^{86} +(-11.2910 - 3.06081i) q^{87} +(-3.02055 + 1.37944i) q^{88} +(1.63266 + 11.3554i) q^{89} +(-4.49895 + 7.68831i) q^{90} -8.04537i q^{91} +(4.18865 - 2.33564i) q^{92} +(-0.281724 - 13.4917i) q^{93} +(-7.00844 - 4.50405i) q^{94} +(-14.3061 + 2.05691i) q^{95} +(-0.752255 - 1.56016i) q^{96} +(1.88225 - 6.41036i) q^{97} +(-8.19193 - 3.74113i) q^{98} +(-6.20368 + 7.79446i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6}+O(q^{10}) $ 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6	$ 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6} - 4 q^{12} + 8 q^{13} - 22 q^{15} - 8 q^{16} - 28 q^{18} - 66 q^{21} - 4 q^{24} - 48 q^{25} - 38 q^{27} - 44 q^{30} - 16 q^{31} - 22 q^{33} - 44 q^{37} - 24 q^{39} - 44 q^{43} - 16 q^{46} + 4 q^{48} - 76 q^{49} - 8 q^{52} - 6 q^{54} + 64 q^{55} + 66 q^{57} + 36 q^{58} + 22 q^{60} + 88 q^{61} + 110 q^{63} + 8 q^{64} + 88 q^{66} + 44 q^{67} + 82 q^{69} + 112 q^{70} + 28 q^{72} + 52 q^{73} + 136 q^{75} + 82 q^{78} + 88 q^{79} + 36 q^{81} + 44 q^{82} + 22 q^{84} + 20 q^{85} - 10 q^{87} + 8 q^{93} - 56 q^{94} + 4 q^{96} - 132 q^{97} - 66 q^{99}+O(q^{100}) $ 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6 - 4 * q^12 + 8 * q^13 - 22 * q^15 - 8 * q^16 - 28 * q^18 - 66 * q^21 - 4 * q^24 - 48 * q^25 - 38 * q^27 - 44 * q^30 - 16 * q^31 - 22 * q^33 - 44 * q^37 - 24 * q^39 - 44 * q^43 - 16 * q^46 + 4 * q^48 - 76 * q^49 - 8 * q^52 - 6 * q^54 + 64 * q^55 + 66 * q^57 + 36 * q^58 + 22 * q^60 + 88 * q^61 + 110 * q^63 + 8 * q^64 + 88 * q^66 + 44 * q^67 + 82 * q^69 + 112 * q^70 + 28 * q^72 + 52 * q^73 + 136 * q^75 + 82 * q^78 + 88 * q^79 + 36 * q^81 + 44 * q^82 + 22 * q^84 + 20 * q^85 - 10 * q^87 + 8 * q^93 - 56 * q^94 + 4 * q^96 - 132 * q^97 - 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$-1$	$e\left(\frac{13}{22}\right)$

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 $

$2$	−0.540641	+	0.841254i	−0.382291	+	0.594856i
$2$	−0.540641	+	0.841254i	−0.382291	+	0.594856i
$3$	1.70890	−	0.282234i	0.986635	−	0.162948i
$3$	1.70890	−	0.282234i	0.986635	−	0.162948i
$4$	−0.415415	−	0.909632i	−0.207708	−	0.454816i
$5$	2.84902	+	0.836549i	1.27412	+	0.374116i	0.847733	−	0.530424i	$-0.177967\pi$
$5$	2.84902	+	0.836549i	1.27412	+	0.374116i	0.426389	+	0.904540i	$0.359785\pi$
$6$	−0.686471	+	1.59021i	−0.280251	+	0.649199i
$7$	−3.02354	−	2.61991i	−1.14279	−	0.990235i	−1.00000		0.000481787i	$-0.999847\pi$
$7$	−3.02354	−	2.61991i	−1.14279	−	0.990235i	−0.142792	−	0.989753i	$-0.545608\pi$
$8$	0.989821	+	0.142315i	0.349955	+	0.0503159i
$9$	2.84069	−	0.964621i	0.946896	−	0.321540i
$10$	−2.24405	+	1.94448i	−0.709630	+	0.614898i
$11$	−2.79349	+	1.79527i	−0.842269	+	0.541294i	−0.889155	−	0.457607i	$-0.848707\pi$
$11$	−2.79349	+	1.79527i	−0.842269	+	0.541294i	0.0468854	+	0.998900i	$0.485070\pi$
$12$	−0.966633	−	1.43723i	−0.279043	−	0.414892i
$13$	1.31691	+	1.51980i	0.365246	+	0.421516i	0.908390	−	0.418123i	$-0.137312\pi$
$13$	1.31691	+	1.51980i	0.365246	+	0.421516i	−0.543145	+	0.839639i	$0.682767\pi$
$14$	3.83866	−	1.12713i	1.02593	−	0.301239i
$15$	5.10480	+	0.625487i	1.31805	+	0.161500i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	−0.139786	+	0.306088i	−0.0339030	+	0.0742371i	−0.925826	−	0.377950i	$-0.876629\pi$
$17$	−0.139786	+	0.306088i	−0.0339030	+	0.0742371i	0.891923	+	0.452188i	$0.149356\pi$
$18$	−0.724301	+	2.91125i	−0.170719	+	0.686189i
$19$	−4.42768	+	2.02205i	−1.01578	+	0.463890i	−0.852521	−	0.522693i	$-0.824927\pi$
$19$	−4.42768	+	2.02205i	−1.01578	+	0.463890i	−0.163257	+	0.986584i	$0.552200\pi$
$20$	−0.422576	−	2.93908i	−0.0944908	−	0.657198i
$21$	−5.90636	−	3.62383i	−1.28887	−	0.790784i
$22$		−	3.32063i		−	0.707961i
$23$	0.384545	+	4.78039i	0.0801833	+	0.996780i
$23$	0.384545	+	4.78039i	0.0801833	+	0.996780i
$24$	1.73167	−	0.0361594i	0.353476	−	0.00738101i
$25$	3.21085	+	2.06349i	0.642170	+	0.412698i
$26$	−1.99051	+	0.286192i	−0.390371	+	0.0561269i
$27$	4.58221	−	2.45018i	0.881846	−	0.471538i
$28$	−1.12713	+	3.83866i	−0.213008	+	0.725439i
$29$	−6.14380	−	2.80578i	−1.14087	−	0.521020i	−0.246857	−	0.969052i	$-0.579398\pi$
$29$	−6.14380	−	2.80578i	−1.14087	−	0.521020i	−0.894017	+	0.448032i	$0.852125\pi$
$30$	−3.28606	+	3.95627i	−0.599949	+	0.722313i
$31$	1.10880	−	7.71186i	0.199146	−	1.38509i	−0.607624	−	0.794225i	$-0.707877\pi$
$31$	1.10880	−	7.71186i	0.199146	−	1.38509i	0.806770	−	0.590865i	$-0.201214\pi$
$32$	−0.281733	−	0.959493i	−0.0498038	−	0.169616i
$33$	−4.26712	+	3.85635i	−0.742809	+	0.671305i
$34$	−0.181924	−	0.283079i	−0.0311996	−	0.0485476i
$35$	−6.42246	−	9.99354i	−1.08559	−	1.68922i
$36$	−2.05751	−	2.18326i	−0.342919	−	0.363877i
$37$	−2.31258	−	7.87592i	−0.380186	−	1.29479i	−0.898263	−	0.439459i	$-0.855170\pi$
$37$	−2.31258	−	7.87592i	−0.380186	−	1.29479i	0.518077	−	0.855334i	$-0.326648\pi$
$38$	0.692724	−	4.81800i	0.112375	−	0.781583i
$39$	2.67941	+	2.22551i	0.429049	+	0.356366i
$40$	2.70097	+	1.23349i	0.427061	+	0.195032i
$41$	−0.321149	+	1.09373i	−0.0501551	+	0.170813i	−0.980762	−	0.195208i	$-0.937462\pi$
$41$	−0.321149	+	1.09373i	−0.0501551	+	0.170813i	0.930607	+	0.366021i	$0.119280\pi$
$42$	6.24178	−	3.00956i	0.963128	−	0.464385i
$43$	−0.439950	+	0.0632552i	−0.0670917	+	0.00964633i	−0.175779	−	0.984430i	$-0.556244\pi$
$43$	−0.439950	+	0.0632552i	−0.0670917	+	0.00964633i	0.108687	+	0.994076i	$0.465335\pi$
$44$	2.79349	+	1.79527i	0.421135	+	0.270647i
$45$	8.90014	−	0.371853i	1.32675	−	0.0554326i
$46$	−4.22942	−	2.26097i	−0.623594	−	0.333362i
$47$			8.33095i			1.21519i	0.794245	+	0.607597i	$0.207866\pi$
$47$			8.33095i			1.21519i	−0.794245	+	0.607597i	$0.792134\pi$
$48$	−0.905794	+	1.47633i	−0.130740	+	0.213089i
$49$	1.28165	+	8.91409i	0.183093	+	1.27344i
$50$	−3.47183	+	1.58553i	−0.490991	+	0.224228i
$51$	−0.152491	+	0.562526i	−0.0213531	+	0.0787694i
$52$	0.835391	−	1.82925i	0.115848	−	0.253671i
$53$	0.581719	−	0.671339i	0.0799052	−	0.0922155i	−0.714389	−	0.699749i	$-0.753295\pi$
$53$	0.581719	−	0.671339i	0.0799052	−	0.0922155i	0.794294	+	0.607533i	$0.207841\pi$
$54$	−0.416105	+	5.17946i	−0.0566247	+	0.704836i
$55$	−9.46055	+	2.77787i	−1.27566	+	0.374568i
$56$	−2.61991	−	3.02354i	−0.350101	−	0.404038i
$57$	−6.99577	+	4.70513i	−0.926612	+	0.623209i
$58$	5.68196	−	3.65157i	0.746077	−	0.479475i
$59$	3.38202	−	2.93054i	0.440302	−	0.381524i	−0.406309	−	0.913736i	$-0.633185\pi$
$59$	3.38202	−	2.93054i	0.440302	−	0.381524i	0.846611	+	0.532212i	$0.178639\pi$
$60$	−1.55165	−	4.90333i	−0.200317	−	0.633017i
$61$	7.37119	+	1.05982i	0.943784	+	0.135696i	0.596993	−	0.802247i	$-0.296362\pi$
$61$	7.37119	+	1.05982i	0.943784	+	0.135696i	0.346791	+	0.937942i	$0.387271\pi$
$62$	5.88816	+	5.10212i	0.747798	+	0.647970i
$63$	−11.1162	−	4.52579i	−1.40050	−	0.570196i
$64$	0.959493	+	0.281733i	0.119937	+	0.0352166i
$65$	2.48053	+	5.43160i	0.307672	+	0.673707i
$66$	−0.937195	−	5.67463i	−0.115361	−	0.698499i
$67$	−6.97092	+	10.8470i	−0.851634	+	1.32517i	0.0925361	+	0.995709i	$0.470503\pi$
$67$	−6.97092	+	10.8470i	−0.851634	+	1.32517i	−0.944170	+	0.329459i	$0.893134\pi$
$68$	0.336496			0.0408061
$69$	2.00634	+	8.06068i	0.241535	+	0.970392i
$70$	11.8793			1.41985
$71$	6.79016	−	10.5657i	0.805843	−	1.25392i	−0.157998	−	0.987439i	$-0.550504\pi$
$71$	6.79016	−	10.5657i	0.805843	−	1.25392i	0.963841	−	0.266477i	$-0.0858597\pi$
$72$	2.94905	−	0.550530i	0.347549	−	0.0648806i
$73$	4.56063	+	9.98639i	0.533782	+	1.16882i	0.963953	+	0.266072i	$0.0857257\pi$
$73$	4.56063	+	9.98639i	0.533782	+	1.16882i	−0.430172	+	0.902747i	$0.641547\pi$
$74$	7.87592	+	2.31258i	0.915557	+	0.268832i
$75$	6.06941	+	2.62009i	0.700836	+	0.302542i
$76$	3.67865	+	3.18756i	0.421970	+	0.365639i
$77$	13.1497	+	1.89064i	1.49855	+	0.215458i
$78$	−3.32081	+	1.05086i	−0.376008	+	0.118987i
$79$	11.8282	−	10.2492i	1.33078	−	1.15313i	0.354877	−	0.934913i	$-0.384523\pi$
$79$	11.8282	−	10.2492i	1.33078	−	1.15313i	0.975901	−	0.218213i	$-0.0700227\pi$
$80$	−2.49793	+	1.60533i	−0.279278	+	0.179481i
$81$	7.13901	−	5.48037i	0.793224	−	0.608930i
$82$	−0.746481	−	0.861485i	−0.0824351	−	0.0951351i
$83$	−5.91068	+	1.73553i	−0.648781	+	0.190499i	−0.589533	−	0.807744i	$-0.700688\pi$
$83$	−5.91068	+	1.73553i	−0.648781	+	0.190499i	−0.0592477	+	0.998243i	$0.518870\pi$
$84$	−0.842757	+	6.87801i	−0.0919524	+	0.750453i
$85$	−0.654309	+	0.755113i	−0.0709698	+	0.0819035i
$86$	0.184641	−	0.404308i	0.0199104	−	0.0435976i
$87$	−11.2910	−	3.06081i	−1.21053	−	0.328153i
$88$	−3.02055	+	1.37944i	−0.321992	+	0.147049i
$89$	1.63266	+	11.3554i	0.173061	+	1.20367i	0.872370	+	0.488847i	$0.162582\pi$
$89$	1.63266	+	11.3554i	0.173061	+	1.20367i	−0.699309	+	0.714820i	$0.746509\pi$
$90$	−4.49895	+	7.68831i	−0.474231	+	0.810419i
$91$		−	8.04537i		−	0.843383i
$92$	4.18865	−	2.33564i	0.436697	−	0.243507i
$93$	−0.281724	−	13.4917i	−0.0292134	−	1.39903i
$94$	−7.00844	−	4.50405i	−0.722866	−	0.464558i
$95$	−14.3061	+	2.05691i	−1.46777	+	0.211034i
$96$	−0.752255	−	1.56016i	−0.0767767	−	0.159234i
$97$	1.88225	−	6.41036i	0.191114	−	0.650874i	−0.807060	−	0.590469i	$-0.798943\pi$
$97$	1.88225	−	6.41036i	0.191114	−	0.650874i	0.998174	−	0.0604046i	$-0.0192391\pi$
$98$	−8.19193	−	3.74113i	−0.827510	−	0.377911i
$99$	−6.20368	+	7.79446i	−0.623494	+	0.783372i
$100$	0.543180	−	3.77790i	0.0543180	−	0.377790i
$101$	0.162410	+	0.553117i	0.0161604	+	0.0550372i	0.967178	−	0.254098i	$-0.0817786\pi$
$101$	0.162410	+	0.553117i	0.0161604	+	0.0550372i	−0.951018	+	0.309135i	$0.899960\pi$
$102$	−0.390784	−	0.432408i	−0.0386934	−	0.0428148i
$103$	3.74407	+	5.82588i	0.368914	+	0.574041i	0.975233	−	0.221180i	$-0.0709910\pi$
$103$	3.74407	+	5.82588i	0.368914	+	0.574041i	−0.606319	+	0.795221i	$0.707355\pi$
$104$	1.08722	+	1.69174i	0.106610	+	0.165889i
$105$	−13.7959	−	15.2653i	−1.34634	−	1.48974i
$106$	0.250266	+	0.852326i	0.0243079	+	0.0827852i
$107$	−0.163240	+	1.13536i	−0.0157810	+	0.109759i	−0.996189	−	0.0872163i	$-0.972203\pi$
$107$	−0.163240	+	1.13536i	−0.0157810	+	0.109759i	0.980408	+	0.196976i	$0.0631120\pi$
$108$	−4.13228	−	3.15028i	−0.397629	−	0.303136i
$109$	−9.88716	−	4.51532i	−0.947019	−	0.432489i	−0.118815	−	0.992916i	$-0.537910\pi$
$109$	−9.88716	−	4.51532i	−0.947019	−	0.432489i	−0.828203	+	0.560427i	$0.810637\pi$
$110$	2.77787	−	9.46055i	0.264859	−	0.902028i
$111$	−6.17482	−	12.8065i	−0.586088	−	1.21554i
$112$	3.96000	−	0.569362i	0.374185	−	0.0537996i
$113$	3.76459	+	2.41935i	0.354142	+	0.227594i	0.705600	−	0.708610i	$-0.250678\pi$
$113$	3.76459	+	2.41935i	0.354142	+	0.227594i	−0.351458	+	0.936204i	$0.614314\pi$
$114$	−0.176008	−	8.42900i	−0.0164846	−	0.789448i
$115$	−2.90345	+	13.9411i	−0.270748	+	1.30002i
$116$			6.75416i			0.627108i
$117$	5.20696	+	3.04695i	0.481384	+	0.281690i
$118$	0.636867	+	4.42951i	0.0586283	+	0.407769i
$119$	1.22457	−	0.559243i	0.112256	−	0.0512657i
$120$	4.96383	+	1.34561i	0.453133	+	0.122837i
$121$	0.0110428	−	0.0241804i	0.00100389	−	0.00219822i
$122$	−4.87674	+	5.62806i	−0.441519	+	0.509540i
$123$	−0.240123	+	1.95972i	−0.0216512	+	0.176702i
$124$	−7.47556	+	2.19502i	−0.671325	+	0.197119i
$125$	−2.30081	−	2.65528i	−0.205791	−	0.237495i
$126$	9.81719	−	6.90469i	0.874584	−	0.615118i
$127$	8.81530	−	5.66525i	0.782232	−	0.502710i	−0.0875418	−	0.996161i	$-0.527901\pi$
$127$	8.81530	−	5.66525i	0.782232	−	0.502710i	0.869774	+	0.493451i	$0.164265\pi$
$128$	−0.755750	+	0.654861i	−0.0667995	+	0.0578821i
$129$	−0.733978	+	0.232266i	−0.0646232	+	0.0204499i
$130$	−5.91042	−	0.849791i	−0.518378	−	0.0745316i
$131$	−7.37999	−	6.39480i	−0.644793	−	0.558716i	0.269889	−	0.962892i	$-0.413013\pi$
$131$	−7.37999	−	6.39480i	−0.644793	−	0.558716i	−0.914682	+	0.404175i	$0.867559\pi$
$132$	5.28049	+	2.27952i	0.459607	+	0.198407i
$133$	18.6849	+	5.48637i	1.62018	+	0.475729i
$134$	−5.35628	−	11.7286i	−0.462713	−	1.01320i
$135$	15.1045	−	3.14738i	1.29999	−	0.270884i
$136$	−0.181924	+	0.283079i	−0.0155998	+	0.0242738i
$137$	−9.33315			−0.797385			−0.398692	−	0.917085i	$-0.630536\pi$
$137$	−9.33315			−0.797385			−0.398692	+	0.917085i	$0.630536\pi$
$138$	−7.86579	−	2.67009i	−0.669580	−	0.227293i
$139$	20.0639			1.70180			0.850900	−	0.525328i	$-0.176057\pi$
$139$	20.0639			1.70180			0.850900	+	0.525328i	$0.176057\pi$
$140$	−6.42246	+	9.99354i	−0.542797	+	0.844608i
$141$	2.35128	+	14.2368i	0.198013	+	1.19895i
$142$	5.21739	+	11.4245i	0.437834	+	0.958722i
$143$	−6.40722	−	1.88133i	−0.535799	−	0.157325i
$144$	−1.13124	+	2.77854i	−0.0942703	+	0.231545i
$145$	−15.1566	−	13.1333i	−1.25869	−	1.09066i
$146$	−10.8668	−	1.56240i	−0.899339	−	0.129305i
$147$	4.70608	+	14.8716i	0.388151	+	1.22659i
$148$	−6.20351	+	5.37537i	−0.509925	+	0.441853i
$149$	1.22356	−	0.786335i	0.100238	−	0.0644191i	−0.489561	−	0.871969i	$-0.662843\pi$
$149$	1.22356	−	0.786335i	0.100238	−	0.0644191i	0.589800	+	0.807550i	$0.299207\pi$
$150$	−5.48553	+	3.68939i	−0.447892	+	0.301237i
$151$	−1.87590	−	2.16490i	−0.152658	−	0.176177i	0.674269	−	0.738486i	$-0.264459\pi$
$151$	−1.87590	−	2.16490i	−0.152658	−	0.176177i	−0.826927	+	0.562309i	$0.809913\pi$
$152$	−4.67038	+	1.37135i	−0.378817	+	0.111231i
$153$	−0.101829	+	1.00434i	−0.00823235	+	0.0811960i
$154$	−8.69977	+	10.0401i	−0.701047	+	0.809051i
$155$	9.61033	−	21.0437i	0.771920	−	1.69027i
$156$	0.911324	−	3.36179i	0.0729643	−	0.269158i
$157$	−4.03655	+	1.84343i	−0.322152	+	0.147122i	−0.569926	−	0.821696i	$-0.693028\pi$
$157$	−4.03655	+	1.84343i	−0.322152	+	0.147122i	0.247774	+	0.968818i	$0.420301\pi$
$158$	2.22737	+	15.4917i	0.177200	+	1.23245i
$159$	0.804625	−	1.31143i	0.0638109	−	0.104003i
$160$		−	2.96930i		−	0.234744i
$161$	11.3615	−	15.4612i	0.895413	−	1.21851i
$162$	0.750740	+	8.96863i	0.0589837	+	0.704642i
$163$	1.84628	+	1.18653i	0.144612	+	0.0929363i	0.610946	−	0.791672i	$-0.290789\pi$
$163$	1.84628	+	1.18653i	0.144612	+	0.0929363i	−0.466334	+	0.884609i	$0.654426\pi$
$164$	1.12831	−	0.162226i	0.0881059	−	0.0126677i
$165$	−15.3831	+	7.41719i	−1.19758	+	0.577428i
$166$	1.73553	−	5.91068i	0.134703	−	0.458758i
$167$	11.6185	+	5.30598i	0.899065	+	0.410589i	0.810675	−	0.585497i	$-0.199100\pi$
$167$	11.6185	+	5.30598i	0.899065	+	0.410589i	0.0883904	+	0.996086i	$0.471828\pi$
$168$	−5.33052	−	4.42751i	−0.411259	−	0.341590i
$169$	1.27457	−	8.86480i	0.0980436	−	0.681908i
$170$	−0.281495	−	0.958685i	−0.0215897	−	0.0735278i
$171$	−10.6271	+	10.0150i	−0.812677	+	0.765870i
$172$	0.240301	+	0.373915i	0.0183228	+	0.0285108i
$173$	9.24628	+	14.3875i	0.702982	+	1.09386i	0.990689	+	0.136142i	$0.0434705\pi$
$173$	9.24628	+	14.3875i	0.702982	+	1.09386i	−0.287708	+	0.957718i	$0.592893\pi$
$174$	8.67931	−	7.84382i	0.657976	−	0.594638i
$175$	−4.30198	−	14.6512i	−0.325199	−	1.10753i
$176$	0.472575	−	3.28683i	0.0356217	−	0.247754i
$177$	4.95244	−	5.96252i	0.372248	−	0.448171i
$178$	−10.4354	−	4.76570i	−0.782168	−	0.357204i
$179$	−4.74950	+	16.1753i	−0.354994	+	1.20900i	0.567625	+	0.823287i	$0.307862\pi$
$179$	−4.74950	+	16.1753i	−0.354994	+	1.20900i	−0.922619	+	0.385712i	$0.873956\pi$
$180$	−4.03550	−	7.94138i	−0.300788	−	0.591915i
$181$	−22.3862	+	3.21865i	−1.66395	+	0.239240i	−0.909077	−	0.416629i	$-0.863211\pi$
$181$	−22.3862	+	3.21865i	−1.66395	+	0.239240i	−0.754875	+	0.655869i	$0.772302\pi$
$182$	6.76819	+	4.34965i	0.501692	+	0.322418i
$183$	12.8957	−	0.269279i	0.953281	−	0.0199056i
$184$	−0.299689	+	4.78646i	−0.0220934	+	0.352862i
$185$		−	24.3733i		−	1.79196i
$186$	11.5023	+	7.05718i	0.843389	+	0.517458i
$187$	−0.159020	−	1.10601i	−0.0116287	−	0.0808791i
$188$	7.57810	−	3.46080i	0.552690	−	0.252405i
$189$	−20.2738	−	4.59676i	−1.47470	−	0.334365i
$190$	6.00408	−	13.1471i	0.435582	−	0.953791i
$191$	5.13683	−	5.92822i	0.371688	−	0.428951i	−0.538834	−	0.842412i	$-0.681135\pi$
$191$	5.13683	−	5.92822i	0.371688	−	0.428951i	0.910522	+	0.413461i	$0.135680\pi$
$192$	1.71919	+	0.210651i	0.124072	+	0.0152025i
$193$	4.35595	−	1.27902i	0.313548	−	0.0920661i	−0.121172	−	0.992632i	$-0.538665\pi$
$193$	4.35595	−	1.27902i	0.313548	−	0.0920661i	0.434721	+	0.900565i	$0.356847\pi$
$194$	4.37512	+	5.04916i	0.314115	+	0.362508i
$195$	5.77196	+	8.58197i	0.413339	+	0.614568i
$196$	7.57613	−	4.86888i	0.541152	−	0.347777i
$197$	−4.14385	+	3.59067i	−0.295237	+	0.255825i	−0.789865	−	0.613280i	$-0.789850\pi$
$197$	−4.14385	+	3.59067i	−0.295237	+	0.255825i	0.494628	+	0.869105i	$0.335304\pi$
$198$	−3.20315	−	9.43287i	−0.227638	−	0.670365i
$199$	9.25058	+	1.33003i	0.655756	+	0.0942835i	0.462158	−	0.886797i	$-0.347075\pi$
$199$	9.25058	+	1.33003i	0.655756	+	0.0942835i	0.193598	+	0.981081i	$0.437984\pi$
$200$	2.88450	+	2.49944i	0.203965	+	0.176737i
$201$	−8.85124	+	20.5038i	−0.624318	+	1.44623i
$202$	−0.553117	−	0.162410i	−0.0389172	−	0.0114271i
$203$	11.2251	+	24.5796i	0.787850	+	1.72515i
$204$	0.575039	−	0.0949707i	0.0402608	−	0.00664928i
$205$	−1.82992	+	2.84742i	−0.127807	+	0.198872i
$206$	−6.92524			−0.482504
$207$	5.70364	+	13.2087i	0.396430	+	0.918065i
$208$	−2.01098			−0.139436
$209$	8.73855	−	13.5974i	0.604458	−	0.940555i
$210$	20.3006	−	3.35276i	1.40088	−	0.231362i
$211$	−0.549711	−	1.20370i	−0.0378437	−	0.0828661i	0.889766	−	0.456417i	$-0.150867\pi$
$211$	−0.549711	−	1.20370i	−0.0378437	−	0.0828661i	−0.927610	+	0.373551i	$0.878140\pi$
$212$	−0.852326	−	0.250266i	−0.0585380	−	0.0171883i
$213$	8.62171	−	19.9721i	0.590750	−	1.36847i
$214$	−0.866870	−	0.751148i	−0.0592580	−	0.0513474i
$215$	−1.30634	−	0.187824i	−0.0890919	−	0.0128095i
$216$	4.88426	−	1.77313i	0.332332	−	0.120646i
$217$	−23.5569	+	20.4122i	−1.59915	+	1.38567i
$218$	9.14393	−	5.87645i	0.619305	−	0.398003i
$219$	10.6122	+	15.7786i	0.717104	+	1.06622i
$220$	6.45689	+	7.45165i	0.435324	+	0.502390i
$221$	−0.649276	+	0.190645i	−0.0436750	+	0.0128241i
$222$	14.1119	+	1.72912i	0.947126	+	0.116051i
$223$	−3.43565	+	3.96496i	−0.230068	+	0.265513i	−0.859032	−	0.511921i	$-0.828934\pi$
$223$	−3.43565	+	3.96496i	−0.230068	+	0.265513i	0.628964	+	0.777435i	$0.283479\pi$
$224$	−1.66196	+	3.63918i	−0.111044	+	0.243153i
$225$	11.1115	+	2.76447i	0.740767	+	0.184298i
$226$	−4.07058	+	1.85897i	−0.270771	+	0.123657i
$227$	0.0525893	+	0.365766i	0.00349047	+	0.0242768i	0.991492	−	0.130166i	$-0.0415509\pi$
$227$	0.0525893	+	0.365766i	0.00349047	+	0.0242768i	−0.988002	+	0.154443i	$0.950642\pi$
$228$	7.18608	+	4.40899i	0.475910	+	0.291993i
$229$		−	24.3543i		−	1.60938i	−0.593698	−	0.804688i	$-0.702332\pi$
$229$		−	24.3543i		−	1.60938i	0.593698	−	0.804688i	$-0.297668\pi$
$230$	−10.1583	−	9.97968i	−0.669819	−	0.658041i
$231$	23.0051	−	0.480374i	1.51363	−	0.0316063i
$232$	−5.68196	−	3.65157i	−0.373039	−	0.239737i
$233$	−1.72714	+	0.248325i	−0.113149	+	0.0162683i	−0.198656	−	0.980069i	$-0.563658\pi$
$233$	−1.72714	+	0.248325i	−0.113149	+	0.0162683i	0.0855079	+	0.996337i	$0.472749\pi$
$234$	−5.37835	+	2.73307i	−0.351594	+	0.178666i
$235$	−6.96925	+	23.7351i	−0.454624	+	1.54831i
$236$	−4.07065	−	1.85901i	−0.264977	−	0.121011i
$237$	17.3206	−	20.8532i	1.12509	−	1.35456i
$238$	−0.191588	+	1.33252i	−0.0124188	+	0.0863747i
$239$	−6.95175	−	23.6755i	−0.449672	−	1.53144i	−0.803022	−	0.595950i	$-0.796776\pi$
$239$	−6.95175	−	23.6755i	−0.449672	−	1.53144i	0.353350	−	0.935491i	$-0.385042\pi$
$240$	−3.81565	+	3.44834i	−0.246299	+	0.222590i
$241$	−1.26781	−	1.97275i	−0.0816666	−	0.127076i	0.798017	−	0.602634i	$-0.205882\pi$
$241$	−1.26781	−	1.97275i	−0.0816666	−	0.127076i	−0.879684	+	0.475559i	$0.842246\pi$
$242$	0.0143716	+	0.0223627i	0.000923843	+	0.00143753i
$243$	10.6531	−	11.3803i	0.683398	−	0.730046i
$244$	−2.09806	−	7.14533i	−0.134314	−	0.457433i
$245$	−3.80561	+	26.4686i	−0.243132	+	1.69102i
$246$	−1.51880	−	1.26151i	−0.0968354	−	0.0804310i
$247$	−8.90396	−	4.06630i	−0.566546	−	0.258733i
$248$	2.19502	−	7.47556i	0.139384	−	0.474699i
$249$	−9.61094	+	4.63405i	−0.609068	+	0.293671i
$250$	3.47768	−	0.500014i	0.219948	−	0.0316237i
$251$	−8.50239	−	5.46416i	−0.536666	−	0.344894i	0.244068	−	0.969758i	$-0.421518\pi$
$251$	−8.50239	−	5.46416i	−0.536666	−	0.344894i	−0.780734	+	0.624864i	$0.785155\pi$
$252$	0.501020	+	11.9917i	0.0315613	+	0.755406i
$253$	−9.65630	−	12.6636i	−0.607087	−	0.796155i
$254$			10.4788i			0.657497i
$255$	−0.905031	+	1.47508i	−0.0566753	+	0.0923732i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	−1.49729	+	0.683789i	−0.0933983	+	0.0426536i	−0.461566	−	0.887106i	$-0.652712\pi$
$257$	−1.49729	+	0.683789i	−0.0933983	+	0.0426536i	0.368168	+	0.929759i	$0.379985\pi$
$258$	0.201424	−	0.743034i	0.0125401	−	0.0462593i
$259$	−13.6421	+	29.8719i	−0.847676	+	1.85615i
$260$	3.91031	−	4.51273i	0.242507	−	0.279868i
$261$	−20.1591	−	2.04391i	−1.24782	−	0.126515i
$262$	9.36957	−	2.75116i	0.578854	−	0.169967i
$263$	3.18074	+	3.67076i	0.196133	+	0.226349i	0.845294	−	0.534302i	$-0.179425\pi$
$263$	3.18074	+	3.67076i	0.196133	+	0.226349i	−0.649161	+	0.760651i	$0.724880\pi$
$264$	−4.77250	+	3.20983i	−0.293727	+	0.197551i
$265$	2.21894	−	1.42602i	0.136308	−	0.0876000i
$266$	−14.7172	+	12.7526i	−0.902371	+	0.781909i
$267$	5.99492	+	18.9444i	0.366883	+	1.15938i
$268$	12.7626	+	1.83498i	0.779598	+	0.112089i
$269$	7.36354	+	6.38054i	0.448963	+	0.389028i	0.849787	−	0.527127i	$-0.176731\pi$
$269$	7.36354	+	6.38054i	0.448963	+	0.389028i	−0.400824	+	0.916155i	$0.631276\pi$
$270$	−5.51837	+	14.4083i	−0.335837	+	0.876863i
$271$	−14.8160	−	4.35037i	−0.900007	−	0.264266i	−0.201178	−	0.979555i	$-0.564477\pi$
$271$	−14.8160	−	4.35037i	−0.900007	−	0.264266i	−0.698829	+	0.715289i	$0.746295\pi$
$272$	−0.139786	−	0.306088i	−0.00847574	−	0.0185593i
$273$	−2.27068	−	13.7487i	−0.137428	−	0.832111i
$274$	5.04588	−	7.85154i	0.304833	−	0.474329i
$275$	−12.6740			−0.764271
$276$	6.49879	−	5.17356i	0.391181	−	0.311412i
$277$	1.96700			0.118185			0.0590927	−	0.998252i	$-0.481179\pi$
$277$	1.96700			0.118185			0.0590927	+	0.998252i	$0.481179\pi$
$278$	−10.8474	+	16.8788i	−0.650582	+	1.01233i
$279$	−4.28927	−	22.9765i	−0.256792	−	1.37557i
$280$	−4.93486	−	10.8058i	−0.294914	−	0.645772i
$281$	−6.61909	−	1.94354i	−0.394862	−	0.115942i	0.0782730	−	0.996932i	$-0.475059\pi$
$281$	−6.61909	−	1.94354i	−0.394862	−	0.115942i	−0.473135	+	0.880990i	$0.656878\pi$
$282$	−13.2479	−	5.71896i	−0.788903	−	0.340559i
$283$	8.48295	+	7.35052i	0.504259	+	0.436943i	0.869473	−	0.493981i	$-0.164459\pi$
$283$	8.48295	+	7.35052i	0.504259	+	0.436943i	−0.365214	+	0.930924i	$0.619004\pi$
$284$	−12.4316	−	1.78740i	−0.737681	−	0.106063i
$285$	−23.8672	+	7.55272i	−1.41377	+	0.447384i
$286$	5.04668	−	4.37298i	0.298417	−	0.258579i
$287$	3.83650	−	2.46557i	0.226461	−	0.145538i
$288$	−1.72586	−	2.45385i	−0.101697	−	0.144595i
$289$	11.0585	+	12.7622i	0.650499	+	0.750716i
$290$	19.2427	−	5.65018i	1.12997	−	0.331790i
$291$	1.40736	−	11.4859i	0.0825009	−	0.673316i
$292$	7.18939	−	8.29699i	0.420727	−	0.485545i
$293$	4.76749	−	10.4393i	0.278520	−	0.609873i	−0.717737	−	0.696314i	$-0.754822\pi$
$293$	4.76749	−	10.4393i	0.278520	−	0.609873i	0.996257	+	0.0864410i	$0.0275494\pi$
$294$	−15.0551	−	4.08118i	−0.878029	−	0.238019i
$295$	12.0870	−	5.51995i	0.703732	−	0.321384i
$296$	−1.16818	−	8.12487i	−0.0678991	−	0.472248i
$297$	−8.40162	+	15.0708i	−0.487512	+	0.874499i
$298$			1.45445i			0.0842541i
$299$	−6.75881	+	6.87978i	−0.390872	+	0.397868i
$300$	−0.138011	−	6.60936i	−0.00796808	−	0.381591i
$301$	1.49593	+	0.961376i	0.0862240	+	0.0554128i
$302$	2.83542	−	0.407671i	0.163160	−	0.0234589i
$303$	0.433651	+	0.899385i	0.0249126	+	0.0516683i
$304$	1.37135	−	4.67038i	0.0786521	−	0.267864i
$305$	20.1141	+	9.18580i	1.15173	+	0.525977i
$306$	−0.789851	−	0.628650i	−0.0451528	−	0.0359376i
$307$	1.11094	−	7.72674i	0.0634046	−	0.440989i	−0.933248	−	0.359233i	$-0.883038\pi$
$307$	1.11094	−	7.72674i	0.0634046	−	0.440989i	0.996652	−	0.0817554i	$-0.0260526\pi$
$308$	−3.74279	−	12.7468i	−0.213265	−	0.726315i
$309$	8.04250	+	8.89915i	0.457522	+	0.506255i
$310$	12.5073	+	19.4618i	0.710369	+	1.10536i
$311$	−15.3196	−	23.8377i	−0.868694	−	1.35171i	−0.935271	−	0.353933i	$-0.884844\pi$
$311$	−15.3196	−	23.8377i	−0.868694	−	1.35171i	0.0665772	−	0.997781i	$-0.478792\pi$
$312$	2.33542	+	2.58417i	0.132217	+	0.146300i
$313$	−3.74744	−	12.7626i	−0.211818	−	0.721385i	−0.995025	−	0.0996245i	$-0.968236\pi$
$313$	−3.74744	−	12.7626i	−0.211818	−	0.721385i	0.783207	−	0.621761i	$-0.213582\pi$
$314$	0.631532	−	4.39240i	0.0356394	−	0.247878i
$315$	−27.8842	−	22.1933i	−1.57109	−	1.25045i
$316$	−14.2366	−	6.50165i	−0.800873	−	0.365746i
$317$	−1.67282	+	5.69709i	−0.0939547	+	0.319980i	−0.993038	−	0.117798i	$-0.962416\pi$
$317$	−1.67282	+	5.69709i	−0.0939547	+	0.319980i	0.899083	+	0.437779i	$0.144235\pi$
$318$	0.668235	+	1.38591i	0.0374727	+	0.0777179i
$319$	22.1998	−	3.19184i	1.24295	−	0.178709i
$320$	2.49793	+	1.60533i	0.139639	+	0.0897404i
$321$	0.0414761	+	1.98629i	0.00231497	+	0.110864i
$322$	6.86427	+	17.9169i	0.382531	+	0.998468i
$323$		−	1.63791i		−	0.0911357i
$324$	−7.95078	−	4.21725i	−0.441710	−	0.234291i
$325$	1.09232	+	7.59727i	0.0605912	+	0.421421i
$326$	−1.99635	+	0.911701i	−0.110567	+	0.0504944i
$327$	−18.1706	−	4.92574i	−1.00483	−	0.272394i
$328$	−0.473535	+	1.03690i	−0.0261466	+	0.0572531i
$329$	21.8264	−	25.1890i	1.20333	−	1.38871i
$330$	2.07701	−	16.9512i	0.114336	−	0.933131i
$331$	−6.96421	+	2.04488i	−0.382788	+	0.112397i	−0.467464	−	0.884012i	$-0.654832\pi$
$331$	−6.96421	+	2.04488i	−0.382788	+	0.112397i	0.0846768	+	0.996408i	$0.473014\pi$
$332$	4.03408	+	4.65558i	0.221399	+	0.255508i
$333$	−14.1666	−	20.1423i	−0.776324	−	1.10379i
$334$	−10.7451	+	6.90546i	−0.587946	+	0.377850i
$335$	−28.9343	+	25.0717i	−1.58085	+	1.36982i
$336$	6.60655	−	2.09063i	0.360417	−	0.114053i
$337$	−3.18413	−	0.457809i	−0.173451	−	0.0249385i	0.0550421	−	0.998484i	$-0.482471\pi$
$337$	−3.18413	−	0.457809i	−0.173451	−	0.0249385i	−0.228493	+	0.973546i	$0.573380\pi$
$338$	6.76846	+	5.86491i	0.368156	+	0.319009i
$339$	7.11613	+	3.07194i	0.386495	+	0.166845i
$340$	0.958685	+	0.281495i	0.0519920	+	0.0152662i
$341$	10.7474	+	23.5336i	0.582006	+	1.27442i
$342$	−2.67973	−	14.3547i	−0.144903	−	0.776211i
$343$	4.33836	−	6.75062i	0.234250	−	0.364499i
$344$	−0.444474			−0.0239644
$345$	−1.02705	+	24.6435i	−0.0552943	+	1.32676i
$346$	−17.1024			−0.919433
$347$	−6.87059	+	10.6908i	−0.368833	+	0.573915i	−0.975215	−	0.221258i	$-0.928984\pi$
$347$	−6.87059	+	10.6908i	−0.368833	+	0.573915i	0.606383	+	0.795173i	$0.292620\pi$
$348$	1.90625	+	11.5422i	0.102186	+	0.618726i
$349$	−8.25417	−	18.0741i	−0.441836	−	0.967486i	−0.991258	−	0.131940i	$-0.957879\pi$
$349$	−8.25417	−	18.0741i	−0.441836	−	0.967486i	0.549422	−	0.835545i	$-0.314848\pi$
$350$	14.6512	+	4.30198i	0.783140	+	0.229951i
$351$	9.75814	+	3.73735i	0.520851	+	0.199485i
$352$	2.50956	+	2.17455i	0.133760	+	0.115904i
$353$	−26.6533	−	3.83217i	−1.41861	−	0.203966i	−0.610044	−	0.792368i	$-0.708848\pi$
$353$	−26.6533	−	3.83217i	−1.41861	−	0.203966i	−0.808568	+	0.588402i	$0.799757\pi$
$354$	2.33850	+	7.38984i	0.124290	+	0.392766i
$355$	28.1840	−	24.4216i	1.49585	−	1.29616i
$356$	9.65098	−	6.20231i	0.511501	−	0.328722i
$357$	1.93483	−	1.30131i	0.102402	−	0.0688724i
$358$	−11.0398	−	12.7406i	−0.583469	−	0.673359i
$359$	−2.98130	+	0.875389i	−0.157347	+	0.0462013i	−0.359457	−	0.933161i	$-0.617038\pi$
$359$	−2.98130	+	0.875389i	−0.157347	+	0.0462013i	0.202110	+	0.979363i	$0.435220\pi$
$360$	8.86247	+	0.898553i	0.467093	+	0.0473579i
$361$	3.07326	−	3.54673i	0.161751	−	0.186670i
$362$	9.39518	−	20.5726i	0.493800	−	1.08127i
$363$	0.0120465	−	0.0444385i	0.000632279	−	0.00233242i
$364$	−7.31832	+	3.34217i	−0.383584	+	0.175177i
$365$	4.63924	+	32.2666i	0.242829	+	1.68891i
$366$	−6.74544	+	10.9942i	−0.352590	+	0.574675i
$367$			17.1813i			0.896858i	0.893818	+	0.448429i	$0.148016\pi$
$367$			17.1813i			0.896858i	−0.893818	+	0.448429i	$0.851984\pi$
$368$	−3.86460	−	2.83987i	−0.201456	−	0.148038i
$369$	0.142754	+	3.41674i	0.00743146	+	0.177869i
$370$	20.5041	+	13.1772i	1.06596	+	0.685049i
$371$	−3.51770	+	0.505769i	−0.182630	+	0.0262582i
$372$	−12.1555	+	5.86094i	−0.630233	+	0.303875i
$373$	−3.31040	+	11.2742i	−0.171406	+	0.583756i	0.828318	+	0.560259i	$0.189298\pi$
$373$	−3.31040	+	11.2742i	−0.171406	+	0.583756i	−0.999724	+	0.0234971i	$0.992520\pi$
$374$	1.01640	+	0.464176i	0.0525570	+	0.0240020i
$375$	−4.68127	−	3.88824i	−0.241740	−	0.200788i
$376$	−1.18562	+	8.24616i	−0.0611436	+	0.425263i
$377$	−3.82662	−	13.0323i	−0.197081	−	0.671197i
$378$	14.8279	−	14.5702i	0.762663	−	0.749409i
$379$	4.97611	+	7.74298i	0.255606	+	0.397730i	0.945214	−	0.326453i	$-0.105853\pi$
$379$	4.97611	+	7.74298i	0.255606	+	0.397730i	−0.689608	+	0.724183i	$0.742217\pi$
$380$	7.81399	+	12.1588i	0.400849	+	0.623734i
$381$	13.4656	−	12.1693i	0.689861	−	0.623454i
$382$	2.20996	+	7.52642i	0.113071	+	0.385085i
$383$	2.55660	−	17.7815i	0.130636	−	0.908594i	−0.814091	−	0.580737i	$-0.802764\pi$
$383$	2.55660	−	17.7815i	0.130636	−	0.908594i	0.944727	−	0.327857i	$-0.106326\pi$
$384$	−1.10668	+	1.33239i	−0.0564749	+	0.0679933i
$385$	35.8822	+	16.3868i	1.82872	+	0.835150i
$386$	−1.27902	+	4.35595i	−0.0651006	+	0.221712i
$387$	−1.18874	+	0.604073i	−0.0604272	+	0.0307068i
$388$	−6.61299	+	0.950804i	−0.335724	+	0.0482698i
$389$	−13.0570	−	8.39122i	−0.662016	−	0.425452i	0.166023	−	0.986122i	$-0.446907\pi$
$389$	−13.0570	−	8.39122i	−0.662016	−	0.425452i	−0.828039	+	0.560670i	$0.810544\pi$
$390$	−10.3402	+	0.215915i	−0.523595	+	0.0109333i
$391$	−1.51697	−	0.550525i	−0.0767166	−	0.0278412i
$392$			9.00576i			0.454860i
$393$	−14.4165	−	8.84520i	−0.727217	−	0.446181i
$394$	−0.780327	−	5.42729i	−0.0393123	−	0.273423i
$395$	42.2728	−	19.3053i	2.12698	−	0.971357i
$396$	9.66719	+	2.40514i	0.485795	+	0.120863i
$397$	2.27392	−	4.97920i	0.114125	−	0.249899i	−0.843947	−	0.536427i	$-0.819774\pi$
$397$	2.27392	−	4.97920i	0.114125	−	0.249899i	0.958072	+	0.286528i	$0.0925011\pi$
$398$	−6.12014	+	7.06301i	−0.306775	+	0.354037i
$399$	33.4790	+	4.10216i	1.67605	+	0.205365i
$400$	−3.66214	+	1.07530i	−0.183107	+	0.0537651i
$401$	1.43577	+	1.65697i	0.0716992	+	0.0827452i	0.790466	−	0.612506i	$-0.209839\pi$
$401$	1.43577	+	1.65697i	0.0716992	+	0.0827452i	−0.718767	+	0.695251i	$0.755293\pi$
$402$	−12.4636	−	18.5313i	−0.621627	−	0.924259i
$403$	13.1806	−	8.47068i	0.656575	−	0.421955i
$404$	0.435665	−	0.377506i	0.0216752	−	0.0187816i
$405$	24.9238	−	9.64157i	1.23847	−	0.479094i
$406$	−26.7464	−	3.84556i	−1.32740	−	0.190852i
$407$	20.5996	+	17.8496i	1.02108	+	0.884773i
$408$	−0.230995	+	0.535098i	−0.0114360	+	0.0264913i
$409$	−3.48616	−	1.02363i	−0.172380	−	0.0506152i	0.194404	−	0.980922i	$-0.437723\pi$
$409$	−3.48616	−	1.02363i	−0.172380	−	0.0506152i	−0.366783	+	0.930306i	$0.619541\pi$
$410$	−1.40607	−	3.07886i	−0.0694407	−	0.152054i
$411$	−15.9494	+	2.63413i	−0.786727	+	0.129932i
$412$	3.74407	−	5.82588i	0.184457	−	0.287020i
$413$	−17.9034			−0.880971
$414$	−14.1954	−	2.34293i	−0.697668	−	0.115149i
$415$	−18.2915			−0.897895
$416$	1.08722	−	1.69174i	0.0533052	−	0.0829446i
$417$	34.2873	−	5.66272i	1.67905	−	0.277305i
$418$	6.71448	+	14.7027i	0.328416	+	0.719131i
$419$	20.3765	+	5.98307i	0.995456	+	0.292292i	0.738590	−	0.674155i	$-0.235492\pi$
$419$	20.3765	+	5.98307i	0.995456	+	0.292292i	0.256866	+	0.966447i	$0.417310\pi$
$420$	−8.15483	+	18.8906i	−0.397915	+	0.921767i
$421$	28.7303	+	24.8950i	1.40023	+	1.21331i	0.946721	+	0.322054i	$0.104373\pi$
$421$	28.7303	+	24.8950i	1.40023	+	1.21331i	0.453508	+	0.891252i	$0.350172\pi$
$422$	1.30981	+	0.188323i	0.0637607	+	0.00916741i
$423$	8.03621	+	23.6656i	0.390734	+	1.15066i
$424$	0.671339	−	0.581719i	0.0326031	−	0.0282508i
$425$	−1.08044	+	0.694356i	−0.0524090	+	0.0336812i
$426$	12.1404	+	18.0508i	0.588203	+	0.874564i
$427$	−19.5105	−	22.5163i	−0.944178	−	1.08964i
$428$	1.10057	−	0.323157i	0.0531981	−	0.0156204i
$429$	−11.4803	−	1.40667i	−0.554274	−	0.0679147i
$430$	0.864270	−	0.997421i	0.0416788	−	0.0480999i
$431$	−13.9684	+	30.5865i	−0.672833	+	1.47330i	0.197230	+	0.980357i	$0.436805\pi$
$431$	−13.9684	+	30.5865i	−0.672833	+	1.47330i	−0.870063	+	0.492941i	$0.835922\pi$
$432$	−1.14898	+	5.06753i	−0.0552805	+	0.243812i
$433$	28.2901	−	12.9196i	1.35953	−	0.620878i	0.403729	−	0.914879i	$-0.367714\pi$
$433$	28.2901	−	12.9196i	1.35953	−	0.620878i	0.955805	+	0.294000i	$0.0949867\pi$
$434$	−4.43599	−	30.8530i	−0.212934	−	1.48099i
$435$	−29.6079	−	18.1658i	−1.41959	−	0.870984i
$436$			10.8694i			0.520550i
$437$	−11.3688	−	20.3884i	−0.543845	−	0.975311i
$438$	−19.0112	+	0.396976i	−0.908389	+	0.0189682i
$439$	−18.2095	−	11.7025i	−0.869093	−	0.558532i	0.0283821	−	0.999597i	$-0.490964\pi$
$439$	−18.2095	−	11.7025i	−0.869093	−	0.558532i	−0.897475	+	0.441065i	$0.854601\pi$
$440$	−9.75959	+	1.40322i	−0.465270	+	0.0668957i
$441$	12.2395	+	24.0858i	0.582833	+	1.14695i
$442$	0.190645	−	0.649276i	0.00906804	−	0.0308829i
$443$	−23.3040	−	10.6426i	−1.10721	−	0.505645i	−0.223982	−	0.974593i	$-0.571906\pi$
$443$	−23.3040	−	10.6426i	−1.10721	−	0.505645i	−0.883225	+	0.468949i	$0.844633\pi$
$444$	−9.08407	+	10.9368i	−0.431111	+	0.519039i
$445$	−4.84785	+	33.7175i	−0.229810	+	1.59836i
$446$	−1.47808	−	5.03387i	−0.0699891	−	0.238361i
$447$	1.86902	−	1.68910i	0.0884014	−	0.0798917i
$448$	−2.16295	−	3.36562i	−0.102190	−	0.159011i
$449$	6.30751	+	9.81467i	0.297670	+	0.463183i	0.957583	−	0.288159i	$-0.0930432\pi$
$449$	6.30751	+	9.81467i	0.297670	+	0.463183i	−0.659913	+	0.751342i	$0.729407\pi$
$450$	−8.33296	+	7.85301i	−0.392819	+	0.370194i
$451$	−1.06642	−	3.63189i	−0.0502157	−	0.171019i
$452$	0.636855	−	4.42942i	0.0299551	−	0.208343i
$453$	−3.81673	−	3.17016i	−0.179326	−	0.148947i
$454$	−0.336134	−	0.153507i	−0.0157756	−	0.00720446i
$455$	6.73034	−	22.9214i	0.315523	−	1.07457i
$456$	−7.59417	+	3.66163i	−0.355630	+	0.171472i
$457$	−10.3483	+	1.48786i	−0.484074	+	0.0695993i	−0.380031	−	0.924974i	$-0.624087\pi$
$457$	−10.3483	+	1.48786i	−0.484074	+	0.0695993i	−0.104042	+	0.994573i	$0.533178\pi$
$458$	20.4881	+	13.1669i	0.957347	+	0.615250i
$459$	0.109444	+	1.74506i	0.00510840	+	0.0814523i
$460$	13.8874	−	3.15028i	0.647505	−	0.146883i
$461$			22.6459i			1.05472i	0.849641	+	0.527362i	$0.176819\pi$
$461$			22.6459i			1.05472i	−0.849641	+	0.527362i	$0.823181\pi$
$462$	−12.0334	+	19.6129i	−0.559844	+	0.912472i
$463$	5.52918	+	38.4563i	0.256963	+	1.78721i	0.554173	+	0.832402i	$0.313035\pi$
$463$	5.52918	+	38.4563i	0.256963	+	1.78721i	−0.297210	+	0.954812i	$0.596056\pi$
$464$	6.14380	−	2.80578i	0.285219	−	0.130255i
$465$	10.4839	−	38.6740i	0.486177	−	1.79346i
$466$	0.724857	−	1.58721i	0.0335783	−	0.0735263i
$467$	2.32240	−	2.68019i	0.107468	−	0.124025i	−0.699467	−	0.714665i	$-0.746579\pi$
$467$	2.32240	−	2.68019i	0.107468	−	0.124025i	0.806935	+	0.590640i	$0.201125\pi$
$468$	0.608551	−	6.00217i	0.0281303	−	0.277450i
$469$	49.4950	−	14.5330i	2.28547	−	0.671074i
$470$	−16.1994	−	18.6951i	−0.747221	−	0.862339i
$471$	−6.37779	+	4.28950i	−0.293873	+	0.197650i
$472$	3.76466	−	2.41940i	0.173282	−	0.111362i
$473$	1.11544	−	0.966531i	0.0512878	−	0.0444411i
$474$	8.17863	+	25.8451i	0.375657	+	1.18710i
$475$	−18.3891	−	2.64395i	−0.843749	−	0.121313i
$476$	−1.01741	−	0.881591i	−0.0466329	−	0.0404077i
$477$	1.00489	−	2.46820i	0.0460109	−	0.113011i
$478$	23.6755	+	6.95175i	1.08289	+	0.317966i
$479$	11.7548	+	25.7394i	0.537090	+	1.17606i	0.962555	+	0.271088i	$0.0873833\pi$
$479$	11.7548	+	25.7394i	0.537090	+	1.17606i	−0.425465	+	0.904975i	$0.639889\pi$
$480$	−0.838038	−	5.07424i	−0.0382510	−	0.231606i
$481$	8.92434	−	13.8865i	0.406915	−	0.633172i
$482$	2.34501			0.106812
$483$	15.0520	−	29.6283i	0.684892	−	1.34813i
$484$	−0.0265826			−0.00120830
$485$	10.7252	−	16.6887i	0.487005	−	0.757794i
$486$	3.81420	+	15.1146i	0.173015	+	0.685613i
$487$	−1.56441	−	3.42558i	−0.0708903	−	0.155228i	0.870870	−	0.491514i	$-0.163556\pi$
$487$	−1.56441	−	3.42558i	−0.0708903	−	0.155228i	−0.941760	+	0.336286i	$0.890829\pi$
$488$	7.14533	+	2.09806i	0.323454	+	0.0949746i
$489$	3.48999	+	1.50658i	0.157823	+	0.0681300i
$490$	−20.2094	−	17.5115i	−0.912966	−	0.791089i
$491$	37.1255	+	5.33784i	1.67545	+	0.240893i	0.913528	−	0.406775i	$-0.133347\pi$
$491$	37.1255	+	5.33784i	1.67545	+	0.240893i	0.761922	+	0.647668i	$0.224256\pi$
$492$	1.88238	−	0.595674i	0.0848641	−	0.0268551i
$493$	1.71763	−	1.48833i	0.0773580	−	0.0670311i
$494$	8.23464	−	5.29208i	0.370494	−	0.238102i
$495$	−24.1949	+	17.0169i	−1.08748	+	0.764853i
$496$	5.10212	+	5.88816i	0.229092	+	0.264386i
$497$	−48.2115	+	14.1562i	−2.16258	+	0.634992i
$498$	1.29766	−	10.5906i	0.0581494	−	0.474576i
$499$	−16.0723	+	18.5485i	−0.719496	+	0.830343i	−0.991246	−	0.132025i	$-0.957852\pi$
$499$	−16.0723	+	18.5485i	−0.719496	+	0.830343i	0.271750	+	0.962368i	$0.412398\pi$
$500$	−1.45953	+	3.19593i	−0.0652724	+	0.142927i
$501$	21.3524	+	5.78827i	0.953954	+	0.258601i
$502$	9.19348	−	4.19852i	0.410325	−	0.187389i
$503$	−3.03450	−	21.1054i	−0.135302	−	0.941045i	−0.938487	−	0.345315i	$-0.887772\pi$
$503$	−3.03450	−	21.1054i	−0.135302	−	0.941045i	0.803185	−	0.595730i	$-0.203137\pi$
$504$	−10.3589	−	6.06172i	−0.461423	−	0.270010i
$505$			1.71171i			0.0761699i
$506$	15.8739	−	1.27693i	0.705681	−	0.0567666i
$507$	−0.323842	−	15.5088i	−0.0143823	−	0.688770i
$508$	−8.81530	−	5.66525i	−0.391116	−	0.251355i
$509$	−42.4766	+	6.10722i	−1.88274	+	0.270698i	−0.985352	−	0.170535i	$-0.945450\pi$
$509$	−42.4766	+	6.10722i	−1.88274	+	0.270698i	−0.897393	+	0.441233i	$0.854541\pi$
$510$	−0.751621	−	1.55885i	−0.0332824	−	0.0690271i
$511$	12.3742	−	42.1427i	0.547403	−	1.86429i
$512$	0.909632	+	0.415415i	0.0402004	+	0.0183589i
$513$	−15.3341	+	20.1141i	−0.677018	+	0.888058i
$514$	0.234256	−	1.62928i	0.0103326	−	0.0718646i
$515$	5.79330	+	19.7302i	0.255283	+	0.869415i
$516$	0.516182	+	0.571163i	0.0227236	+	0.0251441i
$517$	−14.9563	−	23.2724i	−0.657777	−	1.02352i
$518$	−17.7544	−	27.6264i	−0.780084	−	1.21383i
$519$	19.8616	+	21.9772i	0.871828	+	0.964691i
$520$	1.68228	+	5.72933i	0.0737729	+	0.251248i
$521$	2.73795	−	19.0428i	0.119952	−	0.834282i	−0.837654	−	0.546201i	$-0.816074\pi$
$521$	2.73795	−	19.0428i	0.119952	−	0.834282i	0.957606	−	0.288081i	$-0.0930173\pi$
$522$	12.6183	−	15.8539i	0.552287	−	0.693907i
$523$	16.0627	+	7.33557i	0.702371	+	0.320762i	0.734392	−	0.678725i	$-0.237467\pi$
$523$	16.0627	+	7.33557i	0.702371	+	0.320762i	−0.0320215	+	0.999487i	$0.510194\pi$
$524$	−2.75116	+	9.36957i	−0.120185	+	0.409312i
$525$	−11.4867	−	23.8233i	−0.501322	−	1.03973i
$526$	−4.80768	+	0.691240i	−0.209625	+	0.0301395i
$527$	2.20551	+	1.41739i	0.0960735	+	0.0617427i
$528$	−0.120072	−	5.75025i	−0.00522546	−	0.250247i
$529$	−22.7042	+	3.67655i	−0.987141	+	0.159850i
$530$			2.63766i			0.114572i
$531$	6.78041	−	11.5871i	0.294245	−	0.502838i
$532$	−2.77139	−	19.2755i	−0.120155	−	0.835698i
$533$	−2.08518	+	0.952269i	−0.0903191	+	0.0412474i
$534$	−19.1782	−	5.19888i	−0.829920	−	0.224977i
$535$	−1.41486	+	3.09811i	−0.0611696	+	0.133943i
$536$	−8.44365	+	9.74450i	−0.364710	+	0.420898i
$537$	−3.55120	+	28.9825i	−0.153246	+	1.25069i
$538$	−9.34868	+	2.74502i	−0.403050	+	0.118346i
$539$	−19.5835	−	22.6005i	−0.843520	−	0.973474i
$540$	−9.13760	−	12.4321i	−0.393220	−	0.534991i
$541$	−36.5312	+	23.4772i	−1.57060	+	1.00936i	−0.591420	+	0.806363i	$0.701433\pi$
$541$	−36.5312	+	23.4772i	−1.57060	+	1.00936i	−0.979179	+	0.202999i	$0.934931\pi$
$542$	11.6699	−	10.1120i	0.501265	−	0.434348i
$543$	−37.3474	+	11.8185i	−1.60273	+	0.507180i
$544$	0.333071	+	0.0478884i	0.0142803	+	0.00205320i
$545$	−24.3915	−	21.1353i	−1.04482	−	0.905338i
$546$	12.7938	+	5.52291i	0.547524	+	0.236359i
$547$	−35.4346	−	10.4045i	−1.51507	−	0.444866i	−0.584630	−	0.811300i	$-0.698760\pi$
$547$	−35.4346	−	10.4045i	−1.51507	−	0.444866i	−0.930444	+	0.366434i	$0.880578\pi$
$548$	3.87713	+	8.48973i	0.165623	+	0.362663i
$549$	21.9616	−	4.09979i	0.937296	−	0.174975i
$550$	6.85208	−	10.6620i	0.292174	−	0.454631i
$551$	32.8762			1.40057
$552$	0.838763	+	8.26417i	0.0357001	+	0.351746i
$553$	−62.6151			−2.66267
$554$	−1.06344	+	1.65474i	−0.0451812	+	0.0703033i
$555$	−6.87897	−	41.6515i	−0.291996	−	1.76801i
$556$	−8.33485	−	18.2508i	−0.353477	−	0.774006i
$557$	−18.1238	−	5.32163i	−0.767931	−	0.225485i	−0.125775	−	0.992059i	$-0.540142\pi$
$557$	−18.1238	−	5.32163i	−0.767931	−	0.225485i	−0.642156	+	0.766574i	$0.721960\pi$
$558$	21.6481	+	8.81369i	0.916435	+	0.373113i
$559$	−0.675510	−	0.585333i	−0.0285710	−	0.0247569i
$560$	11.7584	+	1.69061i	0.496884	+	0.0714412i
$561$	−0.583901	−	1.84517i	−0.0246523	−	0.0779033i
$562$	5.21356	−	4.51758i	0.219921	−	0.190562i
$563$	−23.9202	+	15.3726i	−1.00812	+	0.647878i	−0.936905	−	0.349583i	$-0.886323\pi$
$563$	−23.9202	+	15.3726i	−1.00812	+	0.647878i	−0.0712125	+	0.997461i	$0.522687\pi$
$564$	11.9735	−	8.05297i	0.504174	−	0.339091i
$565$	8.70148	+	10.0420i	0.366074	+	0.422472i
$566$	−10.7699	+	3.16232i	−0.452692	+	0.132922i
$567$	−35.9432	−	2.13347i	−1.50947	−	0.0895972i
$568$	8.22470	−	9.49181i	0.345101	−	0.398267i
$569$	13.9582	−	30.5643i	0.585160	−	1.28132i	−0.353163	−	0.935562i	$-0.614894\pi$
$569$	13.9582	−	30.5643i	0.585160	−	1.28132i	0.938323	−	0.345760i	$-0.112379\pi$
$570$	6.54982	−	24.1617i	0.274342	−	1.01202i
$571$	4.45035	−	2.03241i	0.186241	−	0.0850536i	−0.320112	−	0.947380i	$-0.603720\pi$
$571$	4.45035	−	2.03241i	0.186241	−	0.0850536i	0.506353	+	0.862326i	$0.330993\pi$
$572$	0.950338	+	6.60975i	0.0397356	+	0.276367i
$573$	7.10519	−	11.5805i	0.296824	−	0.483784i
$574$			4.56045i			0.190350i
$575$	−8.62956	+	16.1426i	−0.359878	+	0.673194i
$576$	2.99738	−	0.125233i	0.124891	−	0.00521802i
$577$	23.8380	+	15.3197i	0.992387	+	0.637769i	0.932777	−	0.360453i	$-0.117378\pi$
$577$	23.8380	+	15.3197i	0.992387	+	0.637769i	0.0596101	+	0.998222i	$0.481014\pi$
$578$	−16.7149	+	2.40324i	−0.695248	+	0.0999615i
$579$	7.08291	−	3.41512i	0.294356	−	0.141928i
$580$	−5.65018	+	19.2427i	−0.234611	+	0.799011i
$581$	22.4181	+	10.2380i	0.930061	+	0.424744i
$582$	8.90169	+	7.39370i	0.368987	+	0.306479i
$583$	−0.419793	+	2.91972i	−0.0173860	+	0.120922i
$584$	3.09300	+	10.5338i	0.127989	+	0.435891i
$585$	12.2858	+	13.0367i	0.507957	+	0.539001i
$586$	6.20464	+	9.65460i	0.256311	+	0.398828i
$587$	3.26296	+	5.07727i	0.134677	+	0.209561i	0.902041	−	0.431650i	$-0.142068\pi$
$587$	3.26296	+	5.07727i	0.134677	+	0.209561i	−0.767364	+	0.641211i	$0.778432\pi$
$588$	11.5727	−	10.4587i	0.477250	−	0.431309i
$589$	10.6844	+	36.3876i	0.440242	+	1.49933i
$590$	−1.89105	+	13.1525i	−0.0778533	+	0.541481i
$591$	−6.06803	+	7.30563i	−0.249605	+	0.300514i
$592$	7.46664	+	3.40990i	0.306877	+	0.140146i
$593$	−0.946543	+	3.22363i	−0.0388699	+	0.132379i	−0.976642	−	0.214872i	$-0.931067\pi$
$593$	−0.946543	+	3.22363i	−0.0388699	+	0.132379i	0.937772	+	0.347251i	$0.112885\pi$
$594$	−8.13614	−	15.2158i	−0.333830	−	0.624312i
$595$	3.95666	−	0.568882i	0.162207	−	0.0233219i
$596$	−1.22356	−	0.786335i	−0.0501190	−	0.0322095i
$597$	16.1837	−	0.337935i	0.662355	−	0.0138308i
$598$	−2.13355	−	9.40536i	−0.0872474	−	0.384614i
$599$			25.0545i			1.02370i	0.859075	+	0.511849i	$0.171039\pi$
$599$			25.0545i			1.02370i	−0.859075	+	0.511849i	$0.828961\pi$
$600$	5.63476	+	3.45719i	0.230038	+	0.141139i
$601$	−5.44515	−	37.8719i	−0.222112	−	1.54483i	−0.730027	−	0.683418i	$-0.760493\pi$
$601$	−5.44515	−	37.8719i	−0.222112	−	1.54483i	0.507915	−	0.861407i	$-0.330417\pi$
$602$	−1.61752	+	0.738698i	−0.0659253	+	0.0301071i
$603$	−9.33901	+	37.5371i	−0.380314	+	1.52863i
$604$	−1.18999	+	2.60571i	−0.0484199	+	0.106025i
$605$	0.0516893	−	0.0596526i	0.00210147	−	0.00242522i
$606$	−0.991060	−	0.121434i	−0.0402591	−	0.00493291i
$607$	1.78539	−	0.524237i	0.0724666	−	0.0212781i	−0.245298	−	0.969448i	$-0.578886\pi$
$607$	1.78539	−	0.524237i	0.0724666	−	0.0212781i	0.317765	+	0.948170i	$0.397068\pi$
$608$	3.18756	+	3.67865i	0.129273	+	0.149189i
$609$	26.1198	+	38.8360i	1.05843	+	1.57371i
$610$	−18.6021	+	11.9548i	−0.753176	+	0.484037i
$611$	−12.6614	+	10.9711i	−0.512224	+	0.443844i
$612$	0.955880	−	0.324591i	0.0386392	−	0.0131208i
$613$	28.6602	+	4.12071i	1.15757	+	0.166434i	0.694236	−	0.719748i	$-0.255742\pi$
$613$	28.6602	+	4.12071i	1.15757	+	0.166434i	0.463338	+	0.886182i	$0.346652\pi$
$614$	5.89953	+	5.11197i	0.238086	+	0.206302i
$615$	−2.32352	+	5.38242i	−0.0936934	+	0.217040i
$616$	12.7468	+	3.74279i	0.513582	+	0.150801i
$617$	−14.9187	−	32.6675i	−0.600606	−	1.31514i	−0.928817	−	0.370538i	$-0.879173\pi$
$617$	−14.9187	−	32.6675i	−0.600606	−	1.31514i	0.328212	−	0.944604i	$-0.393554\pi$
$618$	−11.8345	+	1.95454i	−0.476055	+	0.0786231i
$619$	4.15672	−	6.46799i	0.167073	−	0.259970i	−0.747614	−	0.664133i	$-0.768801\pi$
$619$	4.15672	−	6.46799i	0.167073	−	0.259970i	0.914687	+	0.404163i	$0.132437\pi$
$620$	−23.1343			−0.929095
$621$	13.4749	+	20.9625i	0.540729	+	0.841197i
$622$	28.3360			1.13617
$623$	24.8137	−	38.6109i	0.994140	−	1.54691i
$624$	−3.43657	+	0.567567i	−0.137573	+	0.0227209i
$625$	−12.2615	−	26.8489i	−0.490459	−	1.07395i
$626$	12.7626	+	3.74744i	0.510096	+	0.149778i
$627$	11.0957	−	25.7030i	0.443118	−	1.02648i
$628$	3.35369	+	2.90599i	0.133827	+	0.115962i
$629$	2.73399	+	0.393088i	0.109011	+	0.0156734i
$630$	33.7455	−	11.4591i	1.34445	−	0.456540i
$631$	−15.4012	+	13.3452i	−0.613113	+	0.531266i	−0.905123	−	0.425150i	$-0.860221\pi$
$631$	−15.4012	+	13.3452i	−0.613113	+	0.531266i	0.292010	+	0.956415i	$0.405676\pi$
$632$	13.1664	−	8.46155i	0.523733	−	0.336583i
$633$	−1.27913	−	1.90186i	−0.0508408	−	0.0755920i
$634$	−3.88830	−	4.48734i	−0.154424	−	0.178215i
$635$	29.8543	−	8.76600i	1.18473	−	0.347868i
$636$	−1.52717	−	0.187124i	−0.0605564	−	0.00741993i
$637$	−11.8598	+	13.6869i	−0.469902	+	0.542296i
$638$	−9.31695	+	20.4013i	−0.368862	+	0.807694i
$639$	9.09683	−	36.5638i	0.359865	−	1.44644i
$640$	−2.70097	+	1.23349i	−0.106765	+	0.0487581i
$641$	4.08684	+	28.4246i	0.161421	+	1.12270i	0.895959	+	0.444137i	$0.146490\pi$
$641$	4.08684	+	28.4246i	0.161421	+	1.12270i	−0.734538	+	0.678567i	$0.762601\pi$
$642$	−1.69340	−	1.03898i	−0.0668330	−	0.0410051i
$643$			12.9601i			0.511097i	0.966796	+	0.255548i	$0.0822560\pi$
$643$			12.9601i			0.511097i	−0.966796	+	0.255548i	$0.917744\pi$
$644$	−18.7837	−	3.91200i	−0.740183	−	0.154154i
$645$	−2.28542	+	0.0477223i	−0.0899884	+	0.00187907i
$646$	1.37790	+	0.885521i	0.0542127	+	0.0348404i
$647$	−41.5048	+	5.96749i	−1.63172	+	0.234606i	−0.896443	−	0.443158i	$-0.853858\pi$
$647$	−41.5048	+	5.96749i	−1.63172	+	0.234606i	−0.735279	+	0.677764i	$0.762949\pi$
$648$	7.84629	−	4.40860i	0.308231	−	0.173186i
$649$	−4.18655	+	14.2581i	−0.164336	+	0.559678i
$650$	−6.98179	−	3.18848i	−0.273848	−	0.125062i
$651$	−34.4954	+	41.5309i	−1.35198	+	1.62773i
$652$	0.312335	−	2.17234i	0.0122320	−	0.0850752i
$653$	8.75808	+	29.8273i	0.342730	+	1.16723i	0.932955	+	0.359993i	$0.117221\pi$
$653$	8.75808	+	29.8273i	0.342730	+	1.16723i	−0.590225	+	0.807239i	$0.700961\pi$
$654$	13.9675	−	12.6230i	0.546174	−	0.493598i
$655$	−15.6762	−	24.3927i	−0.612520	−	0.953100i
$656$	−0.616281	−	0.958952i	−0.0240617	−	0.0374408i
$657$	22.5884	+	23.9689i	0.881258	+	0.935117i
$658$	9.39009	+	31.9797i	0.366064	+	1.24670i
$659$	1.41394	−	9.83414i	0.0550791	−	0.383084i	−0.943572	−	0.331167i	$-0.892558\pi$
$659$	1.41394	−	9.83414i	0.0550791	−	0.383084i	0.998651	−	0.0519171i	$-0.0165332\pi$
$660$	13.1373	+	10.9118i	0.511369	+	0.424741i
$661$	3.03210	+	1.38472i	0.117935	+	0.0538592i	0.473509	−	0.880789i	$-0.342987\pi$
$661$	3.03210	+	1.38472i	0.117935	+	0.0538592i	−0.355574	+	0.934648i	$0.615714\pi$
$662$	2.04488	−	6.96421i	0.0794764	−	0.270672i
$663$	−1.05574	+	0.509041i	−0.0410016	+	0.0197695i
$664$	−6.09751	+	0.876689i	−0.236629	+	0.0340221i
$665$	48.6440	+	31.2616i	1.88633	+	1.21227i
$666$	24.6038	−	1.02796i	0.953377	−	0.0398327i
$667$	11.0501	−	30.4487i	0.427863	−	1.17898i
$668$		−	12.7727i		−	0.494192i
$669$	−4.75215	+	7.74538i	−0.183729	+	0.299454i
$670$	−5.44861	−	37.8959i	−0.210498	−	1.46405i
$671$	−22.4940	+	10.2727i	−0.868371	+	0.396572i
$672$	−1.81302	+	6.68807i	−0.0699389	+	0.257998i
$673$	1.47408	−	3.22779i	0.0568217	−	0.124422i	−0.879091	−	0.476653i	$-0.841850\pi$
$673$	1.47408	−	3.22779i	0.0568217	−	0.124422i	0.935913	+	0.352231i	$0.114577\pi$
$674$	2.10661	−	2.43115i	0.0811434	−	0.0936445i
$675$	19.7687	+	1.58817i	0.760898	+	0.0611285i
$676$	−8.59318	+	2.52319i	−0.330507	+	0.0970456i
$677$	−6.25498	−	7.21864i	−0.240399	−	0.277435i	0.622710	−	0.782452i	$-0.286031\pi$
$677$	−6.25498	−	7.21864i	−0.240399	−	0.277435i	−0.863109	+	0.505018i	$0.831486\pi$
$678$	−6.43155	+	4.32565i	−0.247002	+	0.166126i
$679$	−22.4857	+	14.4507i	−0.862921	+	0.554566i
$680$	−0.755113	+	0.654309i	−0.0289573	+	0.0250916i
$681$	0.193102	+	0.610216i	0.00739967	+	0.0233835i
$682$	−25.6082	−	3.68191i	−0.980589	−	0.140987i
$683$	26.7419	+	23.1720i	1.02325	+	0.886651i	0.993605	−	0.112909i	$-0.0360169\pi$
$683$	26.7419	+	23.1720i	1.02325	+	0.886651i	0.0296448	+	0.999560i	$0.490562\pi$
$684$	13.5247	+	5.50638i	0.517129	+	0.210542i
$685$	−26.5904	−	7.80763i	−1.01597	−	0.298314i
$686$	3.33349	+	7.29933i	0.127273	+	0.278690i
$687$	−6.87361	−	41.6191i	−0.262245	−	1.58787i
$688$	0.240301	−	0.373915i	0.00916138	−	0.0142554i
$689$	1.78637			0.0680553
$690$	−20.1761	−	14.1873i	−0.768093	−	0.540100i
$691$	−16.2491			−0.618147			−0.309073	−	0.951038i	$-0.600019\pi$
$691$	−16.2491			−0.618147			−0.309073	+	0.951038i	$0.600019\pi$
$692$	9.24628	−	14.3875i	0.351491	−	0.546930i
$693$	39.1779	−	7.31374i	1.48825	−	0.277826i
$694$	−5.27919	−	11.5598i	−0.200395	−	0.438805i
$695$	57.1626	+	16.7844i	2.16830	+	0.636670i
$696$	−10.7405	−	4.63653i	−0.407118	−	0.175747i
$697$	−0.289886	−	0.251188i	−0.0109802	−	0.00951442i
$698$	19.6675	+	2.82775i	0.744424	+	0.107032i
$699$	−2.88142	+	0.911820i	−0.108985	+	0.0344882i
$700$	−11.5401	+	9.99955i	−0.436175	+	0.377947i
$701$	25.1960	−	16.1925i	0.951641	−	0.611583i	0.0299686	−	0.999551i	$-0.490459\pi$
$701$	25.1960	−	16.1925i	0.951641	−	0.611583i	0.921673	+	0.387968i	$0.126823\pi$
$702$	−8.41971	+	6.18850i	−0.317781	+	0.233570i
$703$	26.1649	+	30.1959i	0.986826	+	1.13886i
$704$	−3.18612	+	0.935530i	−0.120081	+	0.0352591i
$705$	−5.21091	+	42.5279i	−0.196254	+	1.60169i
$706$	17.6337	−	20.3504i	0.663652	−	0.765896i
$707$	0.958066	−	2.09787i	0.0360318	−	0.0788986i
$708$	−7.48102	−	2.02798i	−0.281154	−	0.0762161i
$709$	−23.8693	+	10.9007i	−0.896429	+	0.409385i	−0.809698	−	0.586846i	$-0.800369\pi$
$709$	−23.8693	+	10.9007i	−0.896429	+	0.409385i	−0.0867306	+	0.996232i	$0.527642\pi$
$710$	5.30732	+	36.9132i	0.199180	+	1.38533i
$711$	23.7137	−	40.5245i	0.889332	−	1.51979i
$712$			11.4721i			0.429937i
$713$	37.2921	+	2.33493i	1.39660	+	0.0874436i
$714$	0.0486788	+	2.33122i	0.00182176	+	0.0872439i
$715$	−16.6805	−	10.7199i	−0.623815	−	0.400902i
$716$	16.6866	−	2.39917i	0.623607	−	0.0896611i
$717$	−18.5619	−	38.4971i	−0.693207	−	1.43770i
$718$	0.875389	−	2.98130i	0.0326692	−	0.111261i
$719$	−22.9762	−	10.4929i	−0.856868	−	0.391319i	−0.0619820	−	0.998077i	$-0.519742\pi$
$719$	−22.9762	−	10.4929i	−0.856868	−	0.391319i	−0.794886	+	0.606759i	$0.792469\pi$
$720$	−5.54732	+	6.96979i	−0.206736	+	0.259749i
$721$	3.94297	−	27.4239i	0.146844	−	1.02132i
$722$	1.32217	+	4.50290i	0.0492061	+	0.167581i
$723$	−2.72333	−	3.01341i	−0.101282	−	0.112070i
$724$	12.2273	+	19.0261i	0.454425	+	0.707100i
$725$	−13.9371	−	21.6866i	−0.517612	−	0.805420i
$726$	0.0308712	+	0.0341595i	0.00114574	+	0.00126778i
$727$	3.47428	+	11.8323i	0.128854	+	0.438836i	0.998495	−	0.0548492i	$-0.0174678\pi$
$727$	3.47428	+	11.8323i	0.128854	+	0.438836i	−0.869641	+	0.493685i	$0.835650\pi$
$728$	1.14497	−	7.96348i	0.0424356	−	0.295146i
$729$	14.9932	−	22.4545i	0.555305	−	0.831647i
$730$	−29.6526	−	13.5419i	−1.09749	−	0.501208i
$731$	0.0421370	−	0.143505i	0.00155849	−	0.00530774i
$732$	−5.60203	−	11.6185i	−0.207057	−	0.429433i
$733$	5.86820	−	0.843720i	0.216747	−	0.0311635i	−0.0330858	−	0.999453i	$-0.510533\pi$
$733$	5.86820	−	0.843720i	0.216747	−	0.0311635i	0.249833	+	0.968289i	$0.419624\pi$
$734$	−14.4539	−	9.28893i	−0.533502	−	0.342861i
$735$	0.966932	+	46.3063i	0.0356658	+	1.70804i
$736$	4.47841	−	1.71576i	0.165076	−	0.0632438i
$737$		−	42.8156i		−	1.57713i
$738$	−2.95153	−	1.72714i	−0.108647	−	0.0635769i
$739$	−5.65645	−	39.3415i	−0.208076	−	1.44720i	−0.779427	−	0.626494i	$-0.784489\pi$
$739$	−5.65645	−	39.3415i	−0.208076	−	1.44720i	0.571351	−	0.820706i	$-0.306420\pi$
$740$	−22.1707	+	10.1250i	−0.815011	+	0.372203i
$741$	−16.3636	−	4.43591i	−0.601134	−	0.162957i
$742$	1.47633	−	3.23272i	0.0541979	−	0.118677i
$743$	3.48982	−	4.02746i	0.128029	−	0.147753i	−0.688116	−	0.725601i	$-0.741562\pi$
$743$	3.48982	−	4.02746i	0.128029	−	0.147753i	0.816145	+	0.577848i	$0.196107\pi$
$744$	1.64122	−	13.3945i	0.0601700	−	0.491066i
$745$	4.14376	−	1.21672i	0.151816	−	0.0445771i
$746$	−7.69472	−	8.88018i	−0.281724	−	0.325126i
$747$	−15.1163	+	10.6317i	−0.553075	+	0.388992i
$748$	−0.939999	+	0.604101i	−0.0343698	+	0.0220881i
$749$	3.46811	−	3.00513i	0.126722	−	0.109805i
$750$	5.80188	−	1.83599i	0.211855	−	0.0670410i
$751$	8.36986	+	1.20340i	0.305421	+	0.0439128i	0.293321	−	0.956014i	$-0.405239\pi$
$751$	8.36986	+	1.20340i	0.305421	+	0.0439128i	0.0120994	+	0.999927i	$0.496149\pi$
$752$	−6.29611	−	5.45561i	−0.229596	−	0.198946i
$753$	−16.0719	−	6.93804i	−0.585693	−	0.252836i
$754$	13.0323	+	3.82662i	0.474608	+	0.139357i
$755$	−3.53343	−	7.73713i	−0.128595	−	0.281583i
$756$	4.24066	+	20.3512i	0.154231	+	0.740167i
$757$	13.9286	−	21.6733i	0.506242	−	0.787729i	−0.490235	−	0.871590i	$-0.663089\pi$
$757$	13.9286	−	21.6733i	0.506242	−	0.787729i	0.996477	+	0.0838617i	$0.0267254\pi$
$758$	−9.20410			−0.334308
$759$	−20.0758	−	18.9155i	−0.728705	−	0.686590i
$760$	−14.4532			−0.524273
$761$	−22.6031	+	35.1712i	−0.819363	+	1.27495i	0.139255	+	0.990257i	$0.455529\pi$
$761$	−22.6031	+	35.1712i	−0.819363	+	1.27495i	−0.958618	+	0.284697i	$0.908107\pi$
$762$	2.95747	+	17.9072i	0.107138	+	0.648709i
$763$	18.0645	+	39.5558i	0.653979	+	1.43202i
$764$	−7.52642	−	2.20996i	−0.272296	−	0.0799534i
$765$	−1.13029	+	2.77620i	−0.0408657	+	0.100374i
$766$	13.5766	+	11.7642i	0.490542	+	0.425057i
$767$	8.90765	+	1.28073i	0.321636	+	0.0462443i
$768$	−0.522563	−	1.65134i	−0.0188564	−	0.0595876i
$769$	16.0631	−	13.9187i	0.579249	−	0.501922i	−0.315240	−	0.949012i	$-0.602085\pi$
$769$	16.0631	−	13.9187i	0.579249	−	0.501922i	0.894489	+	0.447090i	$0.147540\pi$
$770$	−33.1848	+	21.3266i	−1.19590	+	0.768557i
$771$	−2.36573	+	1.59111i	−0.0851997	+	0.0573026i
$772$	−2.97297	−	3.43099i	−0.106999	−	0.123484i
$773$	19.9728	−	5.86455i	0.718372	−	0.210933i	0.0979390	−	0.995192i	$-0.468775\pi$
$773$	19.9728	−	5.86455i	0.718372	−	0.210933i	0.620433	+	0.784259i	$0.286957\pi$
$774$	0.134504	−	1.32662i	0.00483466	−	0.0476844i
$775$	19.4735	−	22.4736i	0.699509	−	0.807277i
$776$	2.77538	−	6.07724i	0.0996305	−	0.218160i
$777$	−14.8820	+	54.8984i	−0.533890	+	1.96947i
$778$	14.1183	−	6.44761i	0.506165	−	0.231158i
$779$	−0.789642	−	5.49208i	−0.0282919	−	0.196774i
$780$	5.40868	−	8.81544i	0.193662	−	0.315643i
$781$			41.7053i			1.49233i
$782$	1.28327	−	0.978522i	0.0458896	−	0.0349919i
$783$	−35.0268	+	2.19676i	−1.25176	+	0.0785058i
$784$	−7.57613	−	4.86888i	−0.270576	−	0.173889i
$785$	−13.0424	+	1.87521i	−0.465502	+	0.0669290i
$786$	15.2352	−	7.34587i	0.543422	−	0.262018i
$787$	1.92259	−	6.54775i	0.0685330	−	0.233402i	−0.918103	−	0.396342i	$-0.870279\pi$
$787$	1.92259	−	6.54775i	0.0685330	−	0.233402i	0.986636	+	0.162940i	$0.0520977\pi$
$788$	4.98761	+	2.27776i	0.177676	+	0.0811419i
$789$	6.47158	+	5.37526i	0.230394	+	0.191364i
$790$	−6.61372	+	45.9994i	−0.235305	+	1.63659i
$791$	−5.04389	−	17.1779i	−0.179340	−	0.610776i
$792$	−7.24981	+	6.83224i	−0.257611	+	0.242773i
$793$	8.09649	+	12.5984i	0.287515	+	0.447382i
$794$	2.95939	+	4.60490i	0.105025	+	0.163422i
$795$	3.38947	−	3.06320i	0.120212	−	0.108640i
$796$	−2.63299	−	8.96714i	−0.0933239	−	0.317832i
$797$	1.65794	−	11.5313i	0.0587274	−	0.408458i	−0.939159	−	0.343482i	$-0.888394\pi$
$797$	1.65794	−	11.5313i	0.0587274	−	0.408458i	0.997887	−	0.0649764i	$-0.0206972\pi$
$798$	−21.5511	+	25.9466i	−0.762900	+	0.918498i
$799$	−2.55000	−	1.16455i	−0.0902126	−	0.0411987i
$800$	1.07530	−	3.66214i	0.0380177	−	0.129476i
$801$	15.5915	+	30.6822i	0.550898	+	1.08410i
$802$	−2.17017	+	0.312024i	−0.0766314	+	0.0110179i
$803$	−30.6683	−	19.7093i	−1.08226	−	0.695528i
$804$	22.3279	−	0.466233i	0.787444	−	0.0164428i
$805$	45.3033	−	34.5448i	1.59673	−	1.21754i
$806$			15.6679i			0.551877i
$807$	14.3844	+	8.82547i	0.506354	+	0.310671i
$808$	0.0820399	+	0.570600i	0.00288615	+	0.0200736i
$809$	4.55250	−	2.07906i	0.160057	−	0.0730957i	−0.333775	−	0.942653i	$-0.608323\pi$
$809$	4.55250	−	2.07906i	0.160057	−	0.0730957i	0.493833	+	0.869557i	$0.335595\pi$
$810$	−5.36382	+	26.1799i	−0.188465	+	0.919867i
$811$	3.68193	−	8.06230i	0.129290	−	0.283106i	−0.833906	−	0.551907i	$-0.813900\pi$
$811$	3.68193	−	8.06230i	0.129290	−	0.283106i	0.963196	+	0.268802i	$0.0866276\pi$
$812$	17.6953	−	20.4215i	0.620984	−	0.716653i
$813$	−26.5469	−	3.25277i	−0.931040	−	0.114080i
$814$	−26.1530	+	7.67922i	−0.916663	+	0.269156i
$815$	4.26750	+	4.92495i	0.149484	+	0.172514i
$816$	−0.325268	−	0.483621i	−0.0113867	−	0.0169301i
$817$	1.82005	−	1.16967i	0.0636755	−	0.0409217i
$818$	2.74589	−	2.37933i	0.0960079	−	0.0831913i
$819$	−7.76073	−	22.8544i	−0.271182	−	0.798596i
$820$	3.35028	+	0.481697i	0.116997	+	0.0168216i
$821$	−16.8253	−	14.5792i	−0.587206	−	0.508817i	0.309820	−	0.950795i	$-0.399731\pi$
$821$	−16.8253	−	14.5792i	−0.587206	−	0.508817i	−0.897026	+	0.441979i	$0.854277\pi$
$822$	6.40694	−	14.8416i	0.223468	−	0.517662i
$823$	27.4492	+	8.05981i	0.956819	+	0.280947i	0.722623	−	0.691242i	$-0.242936\pi$
$823$	27.4492	+	8.05981i	0.956819	+	0.280947i	0.234196	+	0.972189i	$0.424754\pi$
$824$	2.87685	+	6.29942i	0.100220	+	0.219451i
$825$	−21.6586	+	3.57704i	−0.754056	+	0.124536i
$826$	9.67933	−	15.0613i	0.336787	−	0.524051i
$827$	−30.2864			−1.05316			−0.526581	−	0.850125i	$-0.676526\pi$
$827$	−30.2864			−1.05316			−0.526581	+	0.850125i	$0.676526\pi$
$828$	9.64564	−	10.6753i	0.335209	−	0.370992i
$829$	9.73151			0.337989			0.168995	−	0.985617i	$-0.445948\pi$
$829$	9.73151			0.337989			0.168995	+	0.985617i	$0.445948\pi$
$830$	9.88914	−	15.3878i	0.343257	−	0.534118i
$831$	3.36141	−	0.555154i	0.116606	−	0.0192581i
$832$	0.835391	+	1.82925i	0.0289620	+	0.0634179i
$833$	−2.90765	−	0.853763i	−0.100744	−	0.0295811i
$834$	−13.7733	+	31.9058i	−0.476931	+	1.10481i
$835$	28.6626	+	24.8363i	0.991911	+	0.859496i
$836$	−15.9988	−	2.30028i	−0.553330	−	0.0795568i
$837$	−13.8147	−	38.0541i	−0.477506	−	1.31534i
$838$	−16.0496	+	13.9071i	−0.554425	+	0.480412i
$839$	−25.1182	+	16.1425i	−0.867175	+	0.557300i	−0.896888	−	0.442259i	$-0.854177\pi$
$839$	−25.1182	+	16.1425i	−0.867175	+	0.557300i	0.0297121	+	0.999558i	$0.490541\pi$
$840$	−11.4830	−	17.0733i	−0.396200	−	0.589085i
$841$	10.8829	+	12.5595i	0.375272	+	0.433086i
$842$	−36.4758	+	10.7102i	−1.25704	+	0.369099i
$843$	−11.8599	−	1.45318i	−0.408477	−	0.0500503i
$844$	−0.866566	+	1.00007i	−0.0298284	+	0.0344238i
$845$	11.0471	−	24.1898i	0.380032	−	0.832154i
$846$	−24.2535	−	6.03412i	−0.833853	−	0.207457i
$847$	−0.0967389	+	0.0441792i	−0.00332399	+	0.00151801i
$848$	0.126420	+	0.879267i	0.00434127	+	0.0301942i
$849$	16.5711	+	10.1671i	0.568718	+	0.348935i
$850$		−	1.28432i		−	0.0440518i
$851$	36.7607	−	14.0837i	1.26014	−	0.482782i
$852$	−21.7489	+	0.454143i	−0.745104	+	0.0155587i
$853$	−13.4788	−	8.66233i	−0.461507	−	0.296592i	0.289151	−	0.957283i	$-0.406627\pi$
$853$	−13.4788	−	8.66233i	−0.461507	−	0.296592i	−0.750658	+	0.660691i	$0.770263\pi$
$854$	29.4901	−	4.24003i	1.00913	−	0.145091i
$855$	−38.6550	+	19.6430i	−1.32197	+	0.671776i
$856$	−0.323157	+	1.10057i	−0.0110453	+	0.0376167i
$857$	−43.5545	−	19.8907i	−1.48779	−	0.679452i	−0.504823	−	0.863223i	$-0.668442\pi$
$857$	−43.5545	−	19.8907i	−1.48779	−	0.679452i	−0.982969	+	0.183771i	$0.941170\pi$
$858$	7.39008	−	8.89733i	0.252293	−	0.303750i
$859$	−0.0392731	+	0.273151i	−0.00133998	+	0.00931978i	−0.990480	−	0.137653i	$-0.956044\pi$
$859$	−0.0392731	+	0.273151i	−0.00133998	+	0.00931978i	0.989140	+	0.146973i	$0.0469531\pi$
$860$	0.371824	+	1.26632i	0.0126791	+	0.0431810i
$861$	5.86033	−	5.29620i	0.199720	−	0.180494i
$862$	−18.1791	−	28.2872i	−0.619182	−	0.963467i
$863$	−15.6209	−	24.3066i	−0.531741	−	0.827405i	0.466631	−	0.884452i	$-0.345468\pi$
$863$	−15.6209	−	24.3066i	−0.531741	−	0.827405i	−0.998371	+	0.0570475i	$0.981831\pi$
$864$	−3.64189	−	3.70630i	−0.123900	−	0.126091i
$865$	14.3070	+	48.7253i	0.486453	+	1.65671i
$866$	−4.42607	+	30.7840i	−0.150404	+	1.04608i
$867$	22.4998	+	18.6882i	0.764132	+	0.634685i
$868$	28.3534	+	12.9486i	0.962379	+	0.439504i
$869$	−14.6419	+	49.8659i	−0.496694	+	1.69158i
$870$	31.2893	−	15.0866i	1.06081	−	0.511482i
$871$	−25.6653	+	3.69011i	−0.869635	+	0.125035i
$872$	−9.14393	−	5.87645i	−0.309653	−	0.199002i
$873$	−0.836678	−	20.0255i	−0.0283172	−	0.677761i
$874$	23.2983	+	1.45875i	0.788077	+	0.0493430i
$875$			14.0563i			0.475189i
$876$	9.94426	−	16.2078i	0.335985	−	0.547612i
$877$	0.931736	+	6.48037i	0.0314625	+	0.218826i	0.999487	−	0.0320295i	$-0.0101970\pi$
$877$	0.931736	+	6.48037i	0.0314625	+	0.218826i	−0.968024	+	0.250856i	$0.919288\pi$
$878$	19.6896	−	8.99195i	0.664493	−	0.303464i
$879$	5.20083	−	19.1854i	0.175420	−	0.647106i
$880$	4.09597	−	8.96892i	0.138075	−	0.302342i
$881$	−10.8764	+	12.5521i	−0.366437	+	0.422891i	−0.908786	−	0.417263i	$-0.862990\pi$
$881$	−10.8764	+	12.5521i	−0.366437	+	0.422891i	0.542349	+	0.840153i	$0.317535\pi$
$882$	−26.8795	−	2.72527i	−0.905079	−	0.0917647i
$883$	15.5044	−	4.55251i	0.521765	−	0.153204i	−0.0102361	−	0.999948i	$-0.503258\pi$
$883$	15.5044	−	4.55251i	0.521765	−	0.153204i	0.532001	+	0.846744i	$0.321440\pi$
$884$	0.443136	+	0.511406i	0.0149043	+	0.0172004i
$885$	19.0976	−	12.8444i	0.641958	−	0.431760i
$886$	21.5522	−	13.8508i	0.724061	−	0.465326i
$887$	43.3698	−	37.5802i	1.45622	−	1.26182i	0.552619	−	0.833434i	$-0.313629\pi$
$887$	43.3698	−	37.5802i	1.45622	−	1.26182i	0.903597	−	0.428384i	$-0.140917\pi$
$888$	−4.28942	−	13.5549i	−0.143943	−	0.454873i
$889$	−41.4959	−	5.96621i	−1.39173	−	0.200100i
$890$	−25.7440	−	22.3073i	−0.862942	−	0.747743i
$891$	−10.1040	+	28.1258i	−0.338498	+	0.942250i
$892$	5.03387	+	1.47808i	0.168547	+	0.0494897i
$893$	−16.8456	−	36.8867i	−0.563717	−	1.23437i
$894$	0.410496	+	2.48551i	0.0137290	+	0.0831280i
$895$	−27.0629	+	42.1106i	−0.904611	+	1.40760i
$896$	4.00072			0.133655
$897$	−9.60843	+	13.6644i	−0.320816	+	0.456242i
$898$	−11.6667			−0.389324
$899$	−28.4500	+	44.2690i	−0.948860	+	1.47645i
$900$	−2.10123	−	11.2558i	−0.0700411	−	0.375193i
$901$	0.124173	+	0.271900i	0.00413679	+	0.00905831i
$902$	3.63189	+	1.06642i	0.120929	+	0.0355078i
$903$	2.82773	+	1.22069i	0.0941010	+	0.0406222i
$904$	3.38196	+	2.93048i	0.112482	+	0.0974664i
$905$	−66.4713	−	9.55713i	−2.20958	−	0.317690i
$906$	4.73039	−	1.49692i	0.157157	−	0.0497319i
$907$	19.7733	−	17.1337i	0.656561	−	0.568914i	−0.261573	−	0.965184i	$-0.584241\pi$
$907$	19.7733	−	17.1337i	0.656561	−	0.568914i	0.918134	+	0.396270i	$0.129696\pi$
$908$	0.310866	−	0.199782i	0.0103165	−	0.00662999i
$909$	0.994904	+	1.41457i	0.0329989	+	0.0469183i
$910$	15.6440	+	18.0542i	0.518595	+	0.598490i
$911$	38.0462	−	11.1714i	1.26053	−	0.370125i	0.417837	−	0.908522i	$-0.362788\pi$
$911$	38.0462	−	11.1714i	1.26053	−	0.370125i	0.842691	+	0.538397i	$0.180970\pi$
$912$	1.02536	−	8.36825i	0.0339529	−	0.277101i
$913$	13.3957	−	15.4594i	0.443332	−	0.511633i
$914$	4.34305	−	9.50995i	0.143655	−	0.314561i
$915$	36.9655	+	10.0207i	1.22204	+	0.331275i
$916$	−22.1534	+	10.1171i	−0.731970	+	0.334280i
$917$	5.55989	+	38.6699i	0.183604	+	1.27699i
$918$	−1.52720	−	0.851379i	−0.0504053	−	0.0280997i
$919$			10.6628i			0.351732i	0.984414	+	0.175866i	$0.0562725\pi$
$919$			10.6628i			0.351732i	−0.984414	+	0.175866i	$0.943727\pi$
$920$	−4.85793	+	13.3860i	−0.160161	+	0.441324i
$921$	−0.282268	−	13.5178i	−0.00930103	−	0.445426i
$922$	−19.0509	−	12.2433i	−0.627408	−	0.403211i
$923$	24.9997	−	3.59442i	0.822876	−	0.118312i
$924$	−9.99364	−	20.7266i	−0.328767	−	0.681856i
$925$	8.82653	−	30.0604i	0.290214	−	0.988379i
$926$	−35.3408	−	16.1396i	−1.16137	−	0.530380i
$927$	16.2555	+	12.9379i	0.533900	+	0.424936i
$928$	−0.961216	+	6.68541i	−0.0315535	+	0.219459i
$929$	−15.6787	−	53.3969i	−0.514403	−	1.75190i	−0.648791	−	0.760966i	$-0.724725\pi$
$929$	−15.6787	−	53.3969i	−0.514403	−	1.75190i	0.134388	−	0.990929i	$-0.457093\pi$
$930$	26.8666	+	29.7283i	0.880991	+	0.974829i
$931$	−23.6995	−	36.8771i	−0.776720	−	1.20860i
$932$	0.943363	+	1.46790i	0.0309009	+	0.0480827i
$933$	−32.9075	−	36.4126i	−1.07734	−	1.19210i
$934$	0.999138	+	3.40275i	0.0326928	+	0.111341i
$935$	0.472177	−	3.28406i	0.0154418	−	0.107400i
$936$	4.72034	+	3.75696i	0.154289	+	0.122800i
$937$	51.2203	+	23.3915i	1.67329	+	0.764168i	0.999685	+	0.0250802i	$0.00798412\pi$
$937$	51.2203	+	23.3915i	1.67329	+	0.764168i	0.673609	+	0.739088i	$0.264743\pi$
$938$	−14.5330	+	49.4950i	−0.474521	+	1.61607i
$939$	−10.0060	−	20.7524i	−0.326535	−	0.677228i
$940$	24.4853	−	3.52046i	0.798623	−	0.114825i
$941$	34.9124	+	22.4369i	1.13811	+	0.731421i	0.967238	−	0.253872i	$-0.0817042\pi$
$941$	34.9124	+	22.4369i	1.13811	+	0.731421i	0.170875	+	0.985293i	$0.445341\pi$
$942$	−0.160460	−	7.68442i	−0.00522806	−	0.250372i
$943$	−5.35197	−	1.11463i	−0.174284	−	0.0362973i
$944$			4.47506i			0.145651i
$945$	−53.9150	−	30.0563i	−1.75385	−	0.977730i
$946$	0.210047	+	1.46091i	0.00682922	+	0.0474983i
$947$	26.7684	−	12.2247i	0.869855	−	0.397249i	0.0700742	−	0.997542i	$-0.477676\pi$
$947$	26.7684	−	12.2247i	0.869855	−	0.397249i	0.799781	+	0.600292i	$0.204949\pi$
$948$	−26.1640	−	7.09261i	−0.849766	−	0.230357i
$949$	−9.17134	+	20.0824i	−0.297714	+	0.651903i
$950$	12.1661	−	14.0405i	0.394721	−	0.455533i
$951$	−1.25077	+	10.2079i	−0.0405588	+	0.331014i
$952$	1.29169	−	0.379276i	0.0418641	−	0.0122924i
$953$	18.2066	+	21.0115i	0.589770	+	0.680631i	0.969676	−	0.244394i	$-0.0785891\pi$
$953$	18.2066	+	21.0115i	0.589770	+	0.680631i	−0.379906	+	0.925025i	$0.624044\pi$
$954$	1.53310	+	2.17978i	0.0496359	+	0.0705730i
$955$	19.5942	−	12.5924i	0.634053	−	0.407481i
$956$	−18.6481	+	16.1587i	−0.603124	+	0.522610i
$957$	37.0364	−	11.7201i	1.19722	−	0.378856i
$958$	−28.0085	−	4.02701i	−0.904912	−	0.130107i
$959$	28.2192	+	24.4521i	0.911245	+	0.789598i
$960$	4.72180	+	2.03834i	0.152395	+	0.0657871i
$961$	−28.4990	−	8.36806i	−0.919323	−	0.269937i
$962$	6.85724	+	15.0153i	0.221086	+	0.484111i
$963$	0.631477	+	3.38266i	0.0203491	+	0.109005i
$964$	−1.26781	+	1.97275i	−0.0408333	+	0.0635378i
$965$	13.4802			0.433942
$966$	16.7871	+	28.6808i	0.540117	+	0.922791i
$967$	13.5242			0.434908			0.217454	−	0.976071i	$-0.430225\pi$
$967$	13.5242			0.434908			0.217454	+	0.976071i	$0.430225\pi$
$968$	0.0143716	−	0.0223627i	0.000461922	−	0.000718764i
$969$	−0.462274	−	2.79903i	−0.0148504	−	0.0899177i
$970$	8.24095	+	18.0452i	0.264601	+	0.579395i
$971$	0.222806	+	0.0654217i	0.00715018	+	0.00209948i	0.285306	−	0.958437i	$-0.407905\pi$
$971$	0.222806	+	0.0654217i	0.00715018	+	0.00209948i	−0.278156	+	0.960536i	$0.589723\pi$
$972$	−14.7773	−	4.96288i	−0.473983	−	0.159184i
$973$	−60.6641	−	52.5658i	−1.94480	−	1.68518i
$974$	3.72757	+	0.535943i	0.119439	+	0.0171727i
$975$	4.01088	+	12.6747i	0.128451	+	0.405915i
$976$	−5.62806	+	4.87674i	−0.180150	+	0.156101i
$977$	28.0911	−	18.0530i	0.898713	−	0.577568i	−0.00769511	−	0.999970i	$-0.502449\pi$
$977$	28.0911	−	18.0530i	0.898713	−	0.577568i	0.906408	+	0.422402i	$0.138813\pi$
$978$	−3.15425	+	2.12144i	−0.100862	+	0.0678363i
$979$	−24.9467	−	28.7901i	−0.797301	−	0.920135i
$980$	25.6576	−	7.53376i	0.819602	−	0.240657i
$981$	−32.4419	−	3.28924i	−1.03579	−	0.105017i
$982$	−24.5620	+	28.3461i	−0.783806	+	0.904561i
$983$	−3.75446	+	8.22112i	−0.119749	+	0.262213i	−0.960008	−	0.279971i	$-0.909675\pi$
$983$	−3.75446	+	8.22112i	−0.119749	+	0.262213i	0.840260	+	0.542184i	$0.182402\pi$
$984$	−0.516577	+	1.90560i	−0.0164679	+	0.0607484i
$985$	−14.8097	+	6.76336i	−0.471876	+	0.215499i
$986$	0.323446	+	2.24961i	0.0103006	+	0.0716423i
$987$	30.1899	−	49.2056i	0.960956	−	1.56623i
$988$			9.78853i			0.311415i
$989$	−0.471565	−	2.07881i	−0.0149949	−	0.0661022i
$990$	−1.23479	−	29.5541i	−0.0392441	−	0.939290i
$991$	29.7144	+	19.0963i	0.943908	+	0.606613i	0.919500	−	0.393089i	$-0.128594\pi$
$991$	29.7144	+	19.0963i	0.943908	+	0.606613i	0.0244077	+	0.999702i	$0.492230\pi$
$992$	−7.71186	+	1.10880i	−0.244852	+	0.0352044i
$993$	−11.3240	+	5.46003i	−0.359357	+	0.173269i
$994$	14.1562	−	48.2115i	0.449007	−	1.52918i
$995$	25.2425	+	11.5279i	0.800240	+	0.365458i
$996$	8.20781	+	6.81736i	0.260074	+	0.216016i
$997$	−1.36746	+	9.51092i	−0.0433080	+	0.301214i	0.956643	+	0.291265i	$0.0940760\pi$
$997$	−1.36746	+	9.51092i	−0.0433080	+	0.301214i	−0.999951	+	0.00994905i	$0.996833\pi$
$998$	−6.91460	−	23.5490i	−0.218878	−	0.745429i
$999$	−29.8941	−	30.4229i	−0.945809	−	0.962536i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.2.f.a.113.4	yes	80
3.2	odd	2	inner	138.2.f.a.113.5	yes	80
23.11	odd	22	inner	138.2.f.a.11.5	yes	80
69.11	even	22	inner	138.2.f.a.11.4	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.f.a.11.4	✓	80	69.11	even	22	inner
138.2.f.a.11.5	yes	80	23.11	odd	22	inner
138.2.f.a.113.4	yes	80	1.1	even	1	trivial
138.2.f.a.113.5	yes	80	3.2	odd	2	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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	138.f (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.540641 + 0.841254i) q^{2} +(1.70890 - 0.282234i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(2.84902 + 0.836549i) q^{5} +(-0.686471 + 1.59021i) q^{6} +(-3.02354 - 2.61991i) q^{7} +(0.989821 + 0.142315i) q^{8} +(2.84069 - 0.964621i) q^{9} +O(q^{10})\)	\(q+(-0.540641 + 0.841254i) q^{2} +(1.70890 - 0.282234i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(2.84902 + 0.836549i) q^{5} +(-0.686471 + 1.59021i) q^{6} +(-3.02354 - 2.61991i) q^{7} +(0.989821 + 0.142315i) q^{8} +(2.84069 - 0.964621i) q^{9} +(-2.24405 + 1.94448i) q^{10} +(-2.79349 + 1.79527i) q^{11} +(-0.966633 - 1.43723i) q^{12} +(1.31691 + 1.51980i) q^{13} +(3.83866 - 1.12713i) q^{14} +(5.10480 + 0.625487i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-0.139786 + 0.306088i) q^{17} +(-0.724301 + 2.91125i) q^{18} +(-4.42768 + 2.02205i) q^{19} +(-0.422576 - 2.93908i) q^{20} +(-5.90636 - 3.62383i) q^{21} -3.32063i q^{22} +(0.384545 + 4.78039i) q^{23} +(1.73167 - 0.0361594i) q^{24} +(3.21085 + 2.06349i) q^{25} +(-1.99051 + 0.286192i) q^{26} +(4.58221 - 2.45018i) q^{27} +(-1.12713 + 3.83866i) q^{28} +(-6.14380 - 2.80578i) q^{29} +(-3.28606 + 3.95627i) q^{30} +(1.10880 - 7.71186i) q^{31} +(-0.281733 - 0.959493i) q^{32} +(-4.26712 + 3.85635i) q^{33} +(-0.181924 - 0.283079i) q^{34} +(-6.42246 - 9.99354i) q^{35} +(-2.05751 - 2.18326i) q^{36} +(-2.31258 - 7.87592i) q^{37} +(0.692724 - 4.81800i) q^{38} +(2.67941 + 2.22551i) q^{39} +(2.70097 + 1.23349i) q^{40} +(-0.321149 + 1.09373i) q^{41} +(6.24178 - 3.00956i) q^{42} +(-0.439950 + 0.0632552i) q^{43} +(2.79349 + 1.79527i) q^{44} +(8.90014 - 0.371853i) q^{45} +(-4.22942 - 2.26097i) q^{46} +8.33095i q^{47} +(-0.905794 + 1.47633i) q^{48} +(1.28165 + 8.91409i) q^{49} +(-3.47183 + 1.58553i) q^{50} +(-0.152491 + 0.562526i) q^{51} +(0.835391 - 1.82925i) q^{52} +(0.581719 - 0.671339i) q^{53} +(-0.416105 + 5.17946i) q^{54} +(-9.46055 + 2.77787i) q^{55} +(-2.61991 - 3.02354i) q^{56} +(-6.99577 + 4.70513i) q^{57} +(5.68196 - 3.65157i) q^{58} +(3.38202 - 2.93054i) q^{59} +(-1.55165 - 4.90333i) q^{60} +(7.37119 + 1.05982i) q^{61} +(5.88816 + 5.10212i) q^{62} +(-11.1162 - 4.52579i) q^{63} +(0.959493 + 0.281733i) q^{64} +(2.48053 + 5.43160i) q^{65} +(-0.937195 - 5.67463i) q^{66} +(-6.97092 + 10.8470i) q^{67} +0.336496 q^{68} +(2.00634 + 8.06068i) q^{69} +11.8793 q^{70} +(6.79016 - 10.5657i) q^{71} +(2.94905 - 0.550530i) q^{72} +(4.56063 + 9.98639i) q^{73} +(7.87592 + 2.31258i) q^{74} +(6.06941 + 2.62009i) q^{75} +(3.67865 + 3.18756i) q^{76} +(13.1497 + 1.89064i) q^{77} +(-3.32081 + 1.05086i) q^{78} +(11.8282 - 10.2492i) q^{79} +(-2.49793 + 1.60533i) q^{80} +(7.13901 - 5.48037i) q^{81} +(-0.746481 - 0.861485i) q^{82} +(-5.91068 + 1.73553i) q^{83} +(-0.842757 + 6.87801i) q^{84} +(-0.654309 + 0.755113i) q^{85} +(0.184641 - 0.404308i) q^{86} +(-11.2910 - 3.06081i) q^{87} +(-3.02055 + 1.37944i) q^{88} +(1.63266 + 11.3554i) q^{89} +(-4.49895 + 7.68831i) q^{90} -8.04537i q^{91} +(4.18865 - 2.33564i) q^{92} +(-0.281724 - 13.4917i) q^{93} +(-7.00844 - 4.50405i) q^{94} +(-14.3061 + 2.05691i) q^{95} +(-0.752255 - 1.56016i) q^{96} +(1.88225 - 6.41036i) q^{97} +(-8.19193 - 3.74113i) q^{98} +(-6.20368 + 7.79446i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6}+O(q^{10}) \) 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6	\( 80 q + 4 q^{3} + 8 q^{4} + 4 q^{6} - 4 q^{12} + 8 q^{13} - 22 q^{15} - 8 q^{16} - 28 q^{18} - 66 q^{21} - 4 q^{24} - 48 q^{25} - 38 q^{27} - 44 q^{30} - 16 q^{31} - 22 q^{33} - 44 q^{37} - 24 q^{39} - 44 q^{43} - 16 q^{46} + 4 q^{48} - 76 q^{49} - 8 q^{52} - 6 q^{54} + 64 q^{55} + 66 q^{57} + 36 q^{58} + 22 q^{60} + 88 q^{61} + 110 q^{63} + 8 q^{64} + 88 q^{66} + 44 q^{67} + 82 q^{69} + 112 q^{70} + 28 q^{72} + 52 q^{73} + 136 q^{75} + 82 q^{78} + 88 q^{79} + 36 q^{81} + 44 q^{82} + 22 q^{84} + 20 q^{85} - 10 q^{87} + 8 q^{93} - 56 q^{94} + 4 q^{96} - 132 q^{97} - 66 q^{99}+O(q^{100}) \) 80 * q + 4 * q^3 + 8 * q^4 + 4 * q^6 - 4 * q^12 + 8 * q^13 - 22 * q^15 - 8 * q^16 - 28 * q^18 - 66 * q^21 - 4 * q^24 - 48 * q^25 - 38 * q^27 - 44 * q^30 - 16 * q^31 - 22 * q^33 - 44 * q^37 - 24 * q^39 - 44 * q^43 - 16 * q^46 + 4 * q^48 - 76 * q^49 - 8 * q^52 - 6 * q^54 + 64 * q^55 + 66 * q^57 + 36 * q^58 + 22 * q^60 + 88 * q^61 + 110 * q^63 + 8 * q^64 + 88 * q^66 + 44 * q^67 + 82 * q^69 + 112 * q^70 + 28 * q^72 + 52 * q^73 + 136 * q^75 + 82 * q^78 + 88 * q^79 + 36 * q^81 + 44 * q^82 + 22 * q^84 + 20 * q^85 - 10 * q^87 + 8 * q^93 - 56 * q^94 + 4 * q^96 - 132 * q^97 - 66 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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