LMFDB - Embedded newform 336.2.bq.b.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(37,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 0, 4]))

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

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

chi := DirichletCharacter("336.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bq (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$30$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			109.2
Character	$\chi$	$=$	336.109
Dual form			336.2.bq.b.37.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37310 - 0.338535i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.77079 + 0.929682i) q^{4} +(0.552230 + 0.147970i) q^{5} +(1.41393 - 0.0283840i) q^{6} +(-2.64020 - 0.171366i) q^{7} +(-2.11673 - 1.87602i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-1.37310 - 0.338535i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.77079 + 0.929682i) q^{4} +(0.552230 + 0.147970i) q^{5} +(1.41393 - 0.0283840i) q^{6} +(-2.64020 - 0.171366i) q^{7} +(-2.11673 - 1.87602i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-0.708172 - 0.390126i) q^{10} +(-1.26103 - 4.70621i) q^{11} +(-1.95107 - 0.439690i) q^{12} +(3.13926 + 3.13926i) q^{13} +(3.56723 + 1.12910i) q^{14} -0.571711 q^{15} +(2.27138 + 3.29254i) q^{16} +(1.06055 - 1.83693i) q^{17} +(-1.35840 + 0.393369i) q^{18} +(0.705751 - 2.63390i) q^{19} +(0.840318 + 0.775421i) q^{20} +(2.59459 - 0.517806i) q^{21} +(0.138293 + 6.88898i) q^{22} +(3.94016 - 2.27485i) q^{23} +(2.53016 + 1.26424i) q^{24} +(-4.04706 - 2.33657i) q^{25} +(-3.24776 - 5.37326i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-4.51591 - 2.75800i) q^{28} +(-6.07512 - 6.07512i) q^{29} +(0.785014 + 0.193544i) q^{30} +(5.31847 - 9.21186i) q^{31} +(-2.00419 - 5.28992i) q^{32} +(2.43611 + 4.21947i) q^{33} +(-2.07811 + 2.16325i) q^{34} +(-1.43264 - 0.485302i) q^{35} +(1.99839 - 0.0802659i) q^{36} +(6.78498 + 1.81803i) q^{37} +(-1.86073 + 3.37768i) q^{38} +(-3.84480 - 2.21979i) q^{39} +(-0.891331 - 1.34921i) q^{40} -6.70476i q^{41} +(-3.73791 - 0.167360i) q^{42} +(-4.07045 + 4.07045i) q^{43} +(2.14227 - 9.50606i) q^{44} +(0.552230 - 0.147970i) q^{45} +(-6.18033 + 1.78971i) q^{46} +(-3.63560 - 6.29704i) q^{47} +(-3.04616 - 2.59247i) q^{48} +(6.94127 + 0.904880i) q^{49} +(4.76600 + 4.57841i) q^{50} +(-0.548983 + 2.04883i) q^{51} +(2.64045 + 8.47749i) q^{52} +(2.10160 + 7.84326i) q^{53} +(1.21031 - 0.731546i) q^{54} -2.78551i q^{55} +(5.26711 + 5.31579i) q^{56} +2.72681i q^{57} +(6.28509 + 10.3984i) q^{58} +(2.33926 + 8.73023i) q^{59} +(-1.01238 - 0.531509i) q^{60} +(2.16126 - 8.06594i) q^{61} +(-10.4213 + 10.8483i) q^{62} +(-2.37216 + 1.17169i) q^{63} +(0.961123 + 7.94206i) q^{64} +(1.26908 + 2.19811i) q^{65} +(-1.91658 - 6.61845i) q^{66} +(-10.8258 + 2.90076i) q^{67} +(3.58578 - 2.26684i) q^{68} +(-3.21712 + 3.21712i) q^{69} +(1.80286 + 1.15136i) q^{70} +6.12421i q^{71} +(-2.77115 - 0.566311i) q^{72} +(-6.80779 - 3.93048i) q^{73} +(-8.70097 - 4.79329i) q^{74} +(4.51391 + 1.20950i) q^{75} +(3.69842 - 4.00795i) q^{76} +(2.52287 + 12.6414i) q^{77} +(4.52780 + 4.34959i) q^{78} +(-0.530647 - 0.919108i) q^{79} +(0.767130 + 2.15434i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-2.26979 + 9.20628i) q^{82} +(4.20420 + 4.20420i) q^{83} +(5.07586 + 1.49522i) q^{84} +(0.857480 - 0.857480i) q^{85} +(6.96711 - 4.21113i) q^{86} +(7.44047 + 4.29576i) q^{87} +(-6.15968 + 12.3275i) q^{88} +(3.57428 - 2.06361i) q^{89} +(-0.808358 + 0.0162274i) q^{90} +(-7.75031 - 8.82623i) q^{91} +(9.09207 - 0.365186i) q^{92} +(-2.75304 + 10.2745i) q^{93} +(2.86026 + 9.87721i) q^{94} +(0.779474 - 1.35009i) q^{95} +(3.30503 + 4.59095i) q^{96} +4.40749 q^{97} +(-9.22470 - 3.59235i) q^{98} +(-3.44519 - 3.44519i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8}+O(q^{10}) $ 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8	$ 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8} - 8 q^{10} + 4 q^{11} + 8 q^{13} + 32 q^{14} + 8 q^{15} + 12 q^{16} - 16 q^{17} - 4 q^{18} - 8 q^{19} - 64 q^{20} + 12 q^{21} + 24 q^{22} - 8 q^{24} - 8 q^{26} - 8 q^{28} - 64 q^{29} - 52 q^{31} - 4 q^{33} + 32 q^{34} - 8 q^{35} + 24 q^{37} - 40 q^{38} - 60 q^{40} + 24 q^{42} - 32 q^{43} - 12 q^{44} - 8 q^{45} + 4 q^{46} - 8 q^{47} + 32 q^{48} + 20 q^{49} - 16 q^{50} - 8 q^{51} - 16 q^{52} + 4 q^{54} - 104 q^{56} + 4 q^{58} + 52 q^{59} - 16 q^{60} + 4 q^{61} - 144 q^{62} + 8 q^{63} - 64 q^{64} + 24 q^{65} + 24 q^{66} + 12 q^{68} + 24 q^{69} - 48 q^{70} + 4 q^{72} + 16 q^{74} + 16 q^{75} - 8 q^{76} + 8 q^{77} - 56 q^{78} + 28 q^{79} + 68 q^{80} + 60 q^{81} + 28 q^{82} + 8 q^{83} + 24 q^{84} - 80 q^{85} + 36 q^{86} + 40 q^{88} + 8 q^{90} + 36 q^{91} - 184 q^{92} + 4 q^{93} + 60 q^{94} - 16 q^{95} + 36 q^{96} + 24 q^{97} + 124 q^{98} - 8 q^{99}+O(q^{100}) $ 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8 - 8 * q^10 + 4 * q^11 + 8 * q^13 + 32 * q^14 + 8 * q^15 + 12 * q^16 - 16 * q^17 - 4 * q^18 - 8 * q^19 - 64 * q^20 + 12 * q^21 + 24 * q^22 - 8 * q^24 - 8 * q^26 - 8 * q^28 - 64 * q^29 - 52 * q^31 - 4 * q^33 + 32 * q^34 - 8 * q^35 + 24 * q^37 - 40 * q^38 - 60 * q^40 + 24 * q^42 - 32 * q^43 - 12 * q^44 - 8 * q^45 + 4 * q^46 - 8 * q^47 + 32 * q^48 + 20 * q^49 - 16 * q^50 - 8 * q^51 - 16 * q^52 + 4 * q^54 - 104 * q^56 + 4 * q^58 + 52 * q^59 - 16 * q^60 + 4 * q^61 - 144 * q^62 + 8 * q^63 - 64 * q^64 + 24 * q^65 + 24 * q^66 + 12 * q^68 + 24 * q^69 - 48 * q^70 + 4 * q^72 + 16 * q^74 + 16 * q^75 - 8 * q^76 + 8 * q^77 - 56 * q^78 + 28 * q^79 + 68 * q^80 + 60 * q^81 + 28 * q^82 + 8 * q^83 + 24 * q^84 - 80 * q^85 + 36 * q^86 + 40 * q^88 + 8 * q^90 + 36 * q^91 - 184 * q^92 + 4 * q^93 + 60 * q^94 - 16 * q^95 + 36 * q^96 + 24 * q^97 + 124 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.37310	−	0.338535i	−0.970926	−	0.239380i
$2$	−1.37310	−	0.338535i	−0.970926	−	0.239380i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$4$	1.77079	+	0.929682i	0.885394	+	0.464841i
$5$	0.552230	+	0.147970i	0.246965	+	0.0661740i	0.380178	−	0.924913i	$-0.375863\pi$
$5$	0.552230	+	0.147970i	0.246965	+	0.0661740i	−0.133213	+	0.991087i	$0.542529\pi$
$6$	1.41393	−	0.0283840i	0.577234	−	0.0115877i
$7$	−2.64020	−	0.171366i	−0.997900	−	0.0647703i
$7$	−2.64020	−	0.171366i	−0.997900	−	0.0647703i
$8$	−2.11673	−	1.87602i	−0.748378	−	0.663272i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	−0.708172	−	0.390126i	−0.223944	−	0.123369i
$11$	−1.26103	−	4.70621i	−0.380214	−	1.41898i	−0.845576	−	0.533856i	$-0.820743\pi$
$11$	−1.26103	−	4.70621i	−0.380214	−	1.41898i	0.465362	−	0.885120i	$-0.345924\pi$
$12$	−1.95107	−	0.439690i	−0.563225	−	0.126928i
$13$	3.13926	+	3.13926i	0.870675	+	0.870675i	0.992546	−	0.121871i	$-0.0388894\pi$
$13$	3.13926	+	3.13926i	0.870675	+	0.870675i	−0.121871	+	0.992546i	$0.538889\pi$
$14$	3.56723	+	1.12910i	0.953382	+	0.301765i
$15$	−0.571711			−0.147615
$16$	2.27138	+	3.29254i	0.567846	+	0.823135i
$17$	1.06055	−	1.83693i	0.257222	−	0.445522i	−0.708275	−	0.705937i	$-0.750526\pi$
$17$	1.06055	−	1.83693i	0.257222	−	0.445522i	0.965497	+	0.260415i	$0.0838594\pi$
$18$	−1.35840	+	0.393369i	−0.320179	+	0.0927179i
$19$	0.705751	−	2.63390i	0.161910	−	0.604258i	−0.836504	−	0.547961i	$-0.815404\pi$
$19$	0.705751	−	2.63390i	0.161910	−	0.604258i	0.998414	−	0.0562965i	$-0.0179292\pi$
$20$	0.840318	+	0.775421i	0.187901	+	0.173389i
$21$	2.59459	−	0.517806i	0.566185	−	0.112995i
$22$	0.138293	+	6.88898i	0.0294843	+	1.46874i
$23$	3.94016	−	2.27485i	0.821580	−	0.474339i	−0.0293813	−	0.999568i	$-0.509354\pi$
$23$	3.94016	−	2.27485i	0.821580	−	0.474339i	0.850961	+	0.525229i	$0.176020\pi$
$24$	2.53016	+	1.26424i	0.516466	+	0.258062i
$25$	−4.04706	−	2.33657i	−0.809413	−	0.467315i
$26$	−3.24776	−	5.37326i	−0.636939	−	1.05378i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−4.51591	−	2.75800i	−0.853427	−	0.521212i
$29$	−6.07512	−	6.07512i	−1.12812	−	1.12812i	−0.990482	−	0.137639i	$-0.956049\pi$
$29$	−6.07512	−	6.07512i	−1.12812	−	1.12812i	−0.137639	−	0.990482i	$-0.543951\pi$
$30$	0.785014	+	0.193544i	0.143323	+	0.0353361i
$31$	5.31847	−	9.21186i	0.955226	−	1.65450i	0.221375	−	0.975189i	$-0.428945\pi$
$31$	5.31847	−	9.21186i	0.955226	−	1.65450i	0.733850	−	0.679311i	$-0.237721\pi$
$32$	−2.00419	−	5.28992i	−0.354294	−	0.935134i
$33$	2.43611	+	4.21947i	0.424073	+	0.734516i
$34$	−2.07811	+	2.16325i	−0.356393	+	0.370995i
$35$	−1.43264	−	0.485302i	−0.242160	−	0.0820310i
$36$	1.99839	−	0.0802659i	0.333065	−	0.0133777i
$37$	6.78498	+	1.81803i	1.11544	+	0.298882i	0.769039	−	0.639202i	$-0.220735\pi$
$37$	6.78498	+	1.81803i	1.11544	+	0.298882i	0.346406	+	0.938085i	$0.387402\pi$
$38$	−1.86073	+	3.37768i	−0.301850	+	0.547931i
$39$	−3.84480	−	2.21979i	−0.615660	−	0.355452i
$40$	−0.891331	−	1.34921i	−0.140932	−	0.213328i
$41$		−	6.70476i		−	1.04711i	−0.851993	−	0.523554i	$-0.824606\pi$
$41$		−	6.70476i		−	1.04711i	0.851993	−	0.523554i	$-0.175394\pi$
$42$	−3.73791	−	0.167360i	−0.576772	−	0.0258242i
$43$	−4.07045	+	4.07045i	−0.620737	+	0.620737i	−0.945720	−	0.324983i	$-0.894642\pi$
$43$	−4.07045	+	4.07045i	−0.620737	+	0.620737i	0.324983	+	0.945720i	$0.394642\pi$
$44$	2.14227	−	9.50606i	0.322959	−	1.43309i
$45$	0.552230	−	0.147970i	0.0823216	−	0.0220580i
$46$	−6.18033	+	1.78971i	−0.911240	+	0.263878i
$47$	−3.63560	−	6.29704i	−0.530306	−	0.918517i	−0.999375	−	0.0353555i	$-0.988744\pi$
$47$	−3.63560	−	6.29704i	−0.530306	−	0.918517i	0.469069	−	0.883162i	$-0.344590\pi$
$48$	−3.04616	−	2.59247i	−0.439675	−	0.374191i
$49$	6.94127	+	0.904880i	0.991610	+	0.129269i
$50$	4.76600	+	4.57841i	0.674014	+	0.647485i
$51$	−0.548983	+	2.04883i	−0.0768730	+	0.286894i
$52$	2.64045	+	8.47749i	0.366165	+	1.17562i
$53$	2.10160	+	7.84326i	0.288676	+	1.07735i	0.946111	+	0.323843i	$0.104975\pi$
$53$	2.10160	+	7.84326i	0.288676	+	1.07735i	−0.657434	+	0.753512i	$0.728358\pi$
$54$	1.21031	−	0.731546i	0.164702	−	0.0995507i
$55$		−	2.78551i		−	0.375597i
$56$	5.26711	+	5.31579i	0.703847	+	0.710352i
$57$			2.72681i			0.361175i
$58$	6.28509	+	10.3984i	0.825272	+	1.36537i
$59$	2.33926	+	8.73023i	0.304545	+	1.13658i	0.933336	+	0.359004i	$0.116884\pi$
$59$	2.33926	+	8.73023i	0.304545	+	1.13658i	−0.628790	+	0.777575i	$0.716450\pi$
$60$	−1.01238	−	0.531509i	−0.130698	−	0.0686175i
$61$	2.16126	−	8.06594i	0.276721	−	1.03274i	−0.677958	−	0.735101i	$-0.737135\pi$
$61$	2.16126	−	8.06594i	0.276721	−	1.03274i	0.954679	−	0.297637i	$-0.0961985\pi$
$62$	−10.4213	+	10.8483i	−1.32351	+	1.37773i
$63$	−2.37216	+	1.17169i	−0.298864	+	0.147619i
$64$	0.961123	+	7.94206i	0.120140	+	0.992757i
$65$	1.26908	+	2.19811i	0.157410	+	0.272642i
$66$	−1.91658	−	6.61845i	−0.235915	−	0.814675i
$67$	−10.8258	+	2.90076i	−1.32258	+	0.354385i	−0.849945	−	0.526872i	$-0.823365\pi$
$67$	−10.8258	+	2.90076i	−1.32258	+	0.354385i	−0.472638	+	0.881257i	$0.656698\pi$
$68$	3.58578	−	2.26684i	0.434840	−	0.274895i
$69$	−3.21712	+	3.21712i	−0.387296	+	0.387296i
$70$	1.80286	+	1.15136i	0.215483	+	0.137614i
$71$			6.12421i			0.726810i	0.931631	+	0.363405i	$0.118386\pi$
$71$			6.12421i			0.726810i	−0.931631	+	0.363405i	$0.881614\pi$
$72$	−2.77115	−	0.566311i	−0.326584	−	0.0667404i
$73$	−6.80779	−	3.93048i	−0.796792	−	0.460028i	0.0455564	−	0.998962i	$-0.485494\pi$
$73$	−6.80779	−	3.93048i	−0.796792	−	0.460028i	−0.842348	+	0.538934i	$0.818827\pi$
$74$	−8.70097	−	4.79329i	−1.01147	−	0.557208i
$75$	4.51391	+	1.20950i	0.521222	+	0.139661i
$76$	3.69842	−	4.00795i	0.424238	−	0.459744i
$77$	2.52287	+	12.6414i	0.287508	+	1.44062i
$78$	4.52780	+	4.34959i	0.512672	+	0.492494i
$79$	−0.530647	−	0.919108i	−0.0597025	−	0.103408i	0.834629	−	0.550812i	$-0.185682\pi$
$79$	−0.530647	−	0.919108i	−0.0597025	−	0.103408i	−0.894332	+	0.447404i	$0.852349\pi$
$80$	0.767130	+	2.15434i	0.0857677	+	0.240862i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−2.26979	+	9.20628i	−0.250657	+	1.01666i
$83$	4.20420	+	4.20420i	0.461471	+	0.461471i	0.899137	−	0.437666i	$-0.144195\pi$
$83$	4.20420	+	4.20420i	0.461471	+	0.461471i	−0.437666	+	0.899137i	$0.644195\pi$
$84$	5.07586	+	1.49522i	0.553821	+	0.163141i
$85$	0.857480	−	0.857480i	0.0930068	−	0.0930068i
$86$	6.96711	−	4.21113i	0.751282	−	0.454098i
$87$	7.44047	+	4.29576i	0.797702	+	0.460554i
$88$	−6.15968	+	12.3275i	−0.656624	+	1.31412i
$89$	3.57428	−	2.06361i	0.378872	−	0.218742i	−0.298455	−	0.954424i	$-0.596471\pi$
$89$	3.57428	−	2.06361i	0.378872	−	0.218742i	0.677328	+	0.735682i	$0.263138\pi$
$90$	−0.808358	+	0.0162274i	−0.0852084	+	0.00171052i
$91$	−7.75031	−	8.82623i	−0.812453	−	0.925241i
$92$	9.09207	−	0.365186i	0.947914	−	0.0380733i
$93$	−2.75304	+	10.2745i	−0.285477	+	1.06542i
$94$	2.86026	+	9.87721i	0.295013	+	1.01876i
$95$	0.779474	−	1.35009i	0.0799723	−	0.138516i
$96$	3.30503	+	4.59095i	0.337318	+	0.468561i
$97$	4.40749			0.447513			0.223756	−	0.974645i	$-0.428168\pi$
$97$	4.40749			0.447513			0.223756	+	0.974645i	$0.428168\pi$
$98$	−9.22470	−	3.59235i	−0.931835	−	0.362882i
$99$	−3.44519	−	3.44519i	−0.346254	−	0.346254i
$100$	−4.99422	−	7.90006i	−0.499422	−	0.790006i
$101$	3.03230	+	11.3167i	0.301725	+	1.12605i	0.935728	+	0.352723i	$0.114744\pi$
$101$	3.03230	+	11.3167i	0.301725	+	1.12605i	−0.634002	+	0.773331i	$0.718589\pi$
$102$	1.44741	−	2.62740i	0.143315	−	0.260151i
$103$	5.32720	−	3.07566i	0.524905	−	0.303054i	−0.214034	−	0.976826i	$-0.568660\pi$
$103$	5.32720	−	3.07566i	0.524905	−	0.303054i	0.738939	+	0.673772i	$0.235327\pi$
$104$	−0.755674	−	12.5343i	−0.0740999	−	1.22909i
$105$	1.50943	+	0.0979718i	0.147305	+	0.00956107i
$106$	−0.230477	−	11.4810i	−0.0223859	−	1.11514i
$107$	0.0190179	+	0.00509583i	0.00183853	+	0.000492633i	0.259738	−	0.965679i	$-0.416364\pi$
$107$	0.0190179	+	0.00509583i	0.00183853	+	0.000492633i	−0.257900	+	0.966172i	$0.583030\pi$
$108$	−1.90952	+	0.594752i	−0.183744	+	0.0572300i
$109$	6.90763	−	1.85089i	0.661631	−	0.177283i	0.0876488	−	0.996151i	$-0.472065\pi$
$109$	6.90763	−	1.85089i	0.661631	−	0.177283i	0.573982	+	0.818868i	$0.305398\pi$
$110$	−0.942991	+	3.82477i	−0.0899106	+	0.364677i
$111$	−7.02433			−0.666720
$112$	−5.43267	−	9.08219i	−0.513339	−	0.858186i
$113$	−8.24638			−0.775754			−0.387877	−	0.921711i	$-0.626791\pi$
$113$	−8.24638			−0.775754			−0.387877	+	0.921711i	$0.626791\pi$
$114$	0.923121	−	3.74418i	0.0864582	−	0.350674i
$115$	2.51248	−	0.673218i	0.234290	−	0.0627779i
$116$	−5.10982	−	16.4057i	−0.474435	−	1.52323i
$117$	4.28831	+	1.14905i	0.396455	+	0.106230i
$118$	−0.256540	−	12.7794i	−0.0236165	−	1.17644i
$119$	−3.11486	+	4.66812i	−0.285539	+	0.427926i
$120$	1.21016	+	1.07254i	0.110472	+	0.0979089i
$121$	−11.0320	+	6.36931i	−1.00291	+	0.579028i
$122$	−5.69822	+	10.3437i	−0.515893	+	0.936470i
$123$	1.73532	+	6.47630i	0.156468	+	0.583948i
$124$	17.9820	−	11.3678i	1.61483	−	1.02086i
$125$	−3.91047	−	3.91047i	−0.349763	−	0.349763i
$126$	3.65386	−	0.805786i	0.325512	−	0.0717851i
$127$	−8.18132			−0.725975			−0.362988	−	0.931794i	$-0.618243\pi$
$127$	−8.18132			−0.725975			−0.362988	+	0.931794i	$0.618243\pi$
$128$	1.36895	−	11.2306i	0.120999	−	0.992653i
$129$	2.87824	−	4.98526i	0.253415	−	0.438928i
$130$	−0.998433	−	3.44785i	−0.0875683	−	0.302396i
$131$	−3.96705	+	14.8052i	−0.346603	+	1.29354i	0.544125	+	0.839004i	$0.316862\pi$
$131$	−3.96705	+	14.8052i	−0.346603	+	1.29354i	−0.890728	+	0.454536i	$0.849805\pi$
$132$	0.391074	+	9.73661i	0.0340386	+	0.847463i
$133$	−2.31468	+	6.83307i	−0.200708	+	0.592502i
$134$	15.8469	−	0.318119i	1.36896	−	0.0274813i
$135$	−0.495116	+	0.285855i	−0.0426128	+	0.0246025i
$136$	−5.69103	+	1.89868i	−0.488002	+	0.162811i
$137$	−10.5390	−	6.08472i	−0.900411	−	0.519852i	−0.0230772	−	0.999734i	$-0.507346\pi$
$137$	−10.5390	−	6.08472i	−0.900411	−	0.519852i	−0.877333	+	0.479881i	$0.840680\pi$
$138$	5.50653	−	3.32831i	0.468747	−	0.283325i
$139$	−7.34267	+	7.34267i	−0.622797	+	0.622797i	−0.946246	−	0.323449i	$-0.895158\pi$
$139$	−7.34267	+	7.34267i	−0.622797	+	0.622797i	0.323449	+	0.946246i	$0.395158\pi$
$140$	−2.08572	−	2.19127i	−0.176276	−	0.185196i
$141$	5.14151	+	5.14151i	0.432993	+	0.432993i
$142$	2.07326	−	8.40913i	0.173984	−	0.705679i
$143$	10.8153	−	18.7327i	0.904425	−	1.56651i
$144$	3.61335	+	1.71573i	0.301112	+	0.142978i
$145$	−2.45593	−	4.25380i	−0.203954	−	0.353259i
$146$	8.01715	+	7.70160i	0.663504	+	0.637389i
$147$	−6.93895	+	0.922485i	−0.572315	+	0.0760853i
$148$	10.3246	+	9.52722i	0.848675	+	0.783133i
$149$	−5.22226	−	1.39930i	−0.427824	−	0.114635i	0.0384805	−	0.999259i	$-0.487748\pi$
$149$	−5.22226	−	1.39930i	−0.427824	−	0.114635i	−0.466305	+	0.884624i	$0.654415\pi$
$150$	−5.78858	−	3.18888i	−0.472636	−	0.260371i
$151$	8.36655	+	4.83043i	0.680861	+	0.393095i	0.800179	−	0.599761i	$-0.204738\pi$
$151$	8.36655	+	4.83043i	0.680861	+	0.393095i	−0.119319	+	0.992856i	$0.538071\pi$
$152$	−6.43513	+	4.25126i	−0.521958	+	0.344823i
$153$		−	2.12111i		−	0.171481i
$154$	0.815416	−	18.2120i	0.0657081	−	1.46756i
$155$	4.30010	−	4.30010i	0.345392	−	0.345392i
$156$	−4.74462	−	7.50523i	−0.379874	−	0.600899i
$157$	6.73732	−	1.80526i	0.537697	−	0.144075i	0.0202565	−	0.999795i	$-0.493552\pi$
$157$	6.73732	−	1.80526i	0.537697	−	0.144075i	0.517440	+	0.855719i	$0.326885\pi$
$158$	0.417480	+	1.44167i	0.0332129	+	0.114693i
$159$	−4.05997	−	7.03208i	−0.321977	−	0.557680i
$160$	−0.324026	−	3.21781i	−0.0256165	−	0.254390i
$161$	−10.7926	+	5.33084i	−0.850577	+	0.420129i
$162$	−0.979728	+	1.01987i	−0.0769747	+	0.0801285i
$163$	1.85117	−	6.90867i	0.144995	−	0.541128i	−0.854761	−	0.519022i	$-0.826296\pi$
$163$	1.85117	−	6.90867i	0.144995	−	0.541128i	0.999756	−	0.0221062i	$-0.00703718\pi$
$164$	6.23329	−	11.8727i	0.486738	−	0.927103i
$165$	0.720942	+	2.69059i	0.0561252	+	0.209462i
$166$	−4.34951	−	7.19605i	−0.337587	−	0.558521i
$167$			10.0759i			0.779696i	0.920879	+	0.389848i	$0.127472\pi$
$167$			10.0759i			0.779696i	−0.920879	+	0.389848i	$0.872528\pi$
$168$	−6.46346	−	3.77143i	−0.498667	−	0.290972i
$169$			6.70996i			0.516150i
$170$	−1.46769	+	0.887116i	−0.112567	+	0.0680387i
$171$	−0.705751	−	2.63390i	−0.0539701	−	0.201419i
$172$	−10.9921	+	3.42368i	−0.838141	+	0.261053i
$173$	2.38820	−	8.91288i	0.181571	−	0.677634i	−0.813767	−	0.581191i	$-0.802587\pi$
$173$	2.38820	−	8.91288i	0.181571	−	0.677634i	0.995339	−	0.0964427i	$-0.0307465\pi$
$174$	−8.76222	−	8.41735i	−0.664262	−	0.638118i
$175$	10.2846	+	6.86254i	0.777445	+	0.518759i
$176$	12.6311	−	14.8416i	0.952106	−	1.11873i
$177$	−4.51910	−	7.82731i	−0.339676	−	0.588337i
$178$	−5.60643	+	1.62352i	−0.420220	+	0.121688i
$179$	−5.91044	+	1.58370i	−0.441767	+	0.118371i	−0.472845	−	0.881146i	$-0.656773\pi$
$179$	−5.91044	+	1.58370i	−0.441767	+	0.118371i	0.0310776	+	0.999517i	$0.490106\pi$
$180$	1.11545	+	0.251376i	0.0831405	+	0.0187364i
$181$	9.20598	−	9.20598i	0.684275	−	0.684275i	−0.276685	−	0.960961i	$-0.589236\pi$
$181$	9.20598	−	9.20598i	0.684275	−	0.684275i	0.960961	+	0.276685i	$0.0892360\pi$
$182$	7.65393	+	14.7430i	0.567347	+	1.09283i
$183$			8.35048i			0.617285i
$184$	−12.6079	−	2.57655i	−0.929468	−	0.189946i
$185$	3.47786	+	2.00794i	0.255697	+	0.147627i
$186$	7.25847	−	13.1759i	0.532217	−	0.966102i
$187$	−9.98238	−	2.67477i	−0.729984	−	0.195599i
$188$	−0.583629	−	14.5307i	−0.0425655	−	1.05976i
$189$	1.98807	−	1.74573i	0.144611	−	0.126983i
$190$	−1.52734	+	1.58992i	−0.110805	+	0.115345i
$191$	2.45010	+	4.24369i	0.177283	+	0.307063i	0.940949	−	0.338549i	$-0.109936\pi$
$191$	2.45010	+	4.24369i	0.177283	+	0.307063i	−0.763666	+	0.645611i	$0.776603\pi$
$192$	−2.98393	−	7.42268i	−0.215346	−	0.535686i
$193$	11.2536	−	19.4918i	0.810054	−	1.40305i	−0.102772	−	0.994705i	$-0.532771\pi$
$193$	11.2536	−	19.4918i	0.810054	−	1.40305i	0.912826	−	0.408349i	$-0.133895\pi$
$194$	−6.05191	−	1.49209i	−0.434502	−	0.107126i
$195$	−1.79475	−	1.79475i	−0.128525	−	0.128525i
$196$	11.4503	+	8.05552i	0.817876	+	0.575394i
$197$	−2.64335	+	2.64335i	−0.188331	+	0.188331i	−0.794974	−	0.606643i	$-0.792516\pi$
$197$	−2.64335	+	2.64335i	−0.188331	+	0.188331i	0.606643	+	0.794974i	$0.292516\pi$
$198$	3.56426	+	5.89689i	0.253301	+	0.419074i
$199$	0.834899	+	0.482029i	0.0591844	+	0.0341701i	0.529300	−	0.848435i	$-0.322455\pi$
$199$	0.834899	+	0.482029i	0.0591844	+	0.0341701i	−0.470116	+	0.882605i	$0.655788\pi$
$200$	4.18311	+	12.5383i	0.295790	+	0.886589i
$201$	9.70615	−	5.60385i	0.684619	−	0.395265i
$202$	−0.332545	−	16.5655i	−0.0233978	−	1.16554i
$203$	14.9984	+	17.0806i	1.05268	+	1.19882i
$204$	−2.87690	+	3.11767i	−0.201423	+	0.218281i
$205$	0.992100	−	3.70257i	0.0692913	−	0.258599i
$206$	−8.35598	+	2.41974i	−0.582189	+	0.168591i
$207$	2.27485	−	3.94016i	0.158113	−	0.273860i
$208$	−3.20568	+	17.4666i	−0.222274	+	1.21109i
$209$	−13.2857			−0.918988
$210$	−2.03942	−	0.645519i	−0.140734	−	0.0445450i
$211$	−15.4192	−	15.4192i	−1.06150	−	1.06150i	−0.997981	−	0.0635205i	$-0.979767\pi$
$211$	−15.4192	−	15.4192i	−1.06150	−	1.06150i	−0.0635205	−	0.997981i	$-0.520233\pi$
$212$	−3.57026	+	15.8426i	−0.245206	+	1.08807i
$213$	−1.58506	−	5.91553i	−0.108607	−	0.405326i
$214$	−0.0243883	−	0.0134353i	−0.00166715	−	0.000918418i
$215$	−2.85013	+	1.64552i	−0.194377	+	0.112224i
$216$	2.82330	−	0.170213i	0.192101	−	0.0115815i
$217$	−15.6204	+	23.4097i	−1.06038	+	1.58916i
$218$	−10.1114	+	0.202983i	−0.684832	+	0.0137477i
$219$	7.59310	+	2.03457i	0.513094	+	0.137483i
$220$	2.58963	−	4.93254i	0.174593	−	0.332552i
$221$	9.09598	−	2.43726i	0.611862	−	0.163948i
$222$	9.64509	+	2.37798i	0.647336	+	0.159600i
$223$	18.0653			1.20974			0.604872	−	0.796323i	$-0.293224\pi$
$223$	18.0653			1.20974			0.604872	+	0.796323i	$0.293224\pi$
$224$	4.38494	+	14.3099i	0.292981	+	0.956118i
$225$	−4.67315			−0.311543
$226$	11.3231	+	2.79169i	0.753200	+	0.185700i
$227$	13.8548	−	3.71238i	0.919574	−	0.246399i	0.232171	−	0.972675i	$-0.425417\pi$
$227$	13.8548	−	3.71238i	0.919574	−	0.246399i	0.687403	+	0.726276i	$0.258751\pi$
$228$	−2.53507	+	4.82861i	−0.167889	+	0.319782i
$229$	−3.11190	−	0.833831i	−0.205640	−	0.0551011i	0.154528	−	0.987988i	$-0.450614\pi$
$229$	−3.11190	−	0.833831i	−0.205640	−	0.0551011i	−0.360169	+	0.932887i	$0.617281\pi$
$230$	−3.67779	+	0.0738300i	−0.242506	+	0.00486821i
$231$	−5.70874	−	11.5577i	−0.375608	−	0.760441i
$232$	1.46238	+	24.2564i	0.0960102	+	1.59251i
$233$	−7.61482	+	4.39642i	−0.498864	+	0.288019i	−0.728244	−	0.685318i	$-0.759663\pi$
$233$	−7.61482	+	4.39642i	−0.498864	+	0.288019i	0.229381	+	0.973337i	$0.426330\pi$
$234$	−5.49928	−	3.02950i	−0.359499	−	0.198045i
$235$	−1.07592	−	4.01537i	−0.0701850	−	0.261934i
$236$	−3.97401	+	17.6342i	−0.258686	+	1.14789i
$237$	0.750448	+	0.750448i	0.0487469	+	0.0487469i
$238$	5.85732	−	5.35529i	0.379674	−	0.347132i
$239$	24.1656			1.56315			0.781573	−	0.623814i	$-0.214418\pi$
$239$	24.1656			1.56315			0.781573	+	0.623814i	$0.214418\pi$
$240$	−1.29857	−	1.88238i	−0.0838226	−	0.121507i
$241$	−5.81111	+	10.0651i	−0.374326	+	0.648352i	−0.990226	−	0.139472i	$-0.955459\pi$
$241$	−5.81111	+	10.0651i	−0.374326	+	0.648352i	0.615900	+	0.787825i	$0.288793\pi$
$242$	17.3042	−	5.01097i	1.11235	−	0.322117i
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$	11.3259	−	12.2738i	0.725066	−	0.785749i
$245$	3.69928	+	1.52680i	0.236338	+	0.0975436i
$246$	−0.190308	−	9.48005i	−0.0121336	−	0.604426i
$247$	10.4840	−	6.05296i	0.667084	−	0.385141i
$248$	−28.5394	+	9.52152i	−1.81225	+	0.604617i
$249$	−5.14908	−	2.97282i	−0.326309	−	0.188395i
$250$	4.04562	+	6.69329i	0.255868	+	0.423321i
$251$	5.65201	−	5.65201i	0.356752	−	0.356752i	−0.505862	−	0.862614i	$-0.668826\pi$
$251$	5.65201	−	5.65201i	0.356752	−	0.356752i	0.862614	+	0.505862i	$0.168826\pi$
$252$	−5.28989	−	0.130538i	−0.333232	−	0.00822313i
$253$	−15.6746	−	15.6746i	−0.985452	−	0.985452i
$254$	11.2337	+	2.76966i	0.704868	+	0.173784i
$255$	−0.606330	+	1.05019i	−0.0379699	+	0.0657657i
$256$	−5.68164	+	14.9572i	−0.355103	+	0.934827i
$257$	−2.40546	−	4.16638i	−0.150048	−	0.259891i	0.781197	−	0.624285i	$-0.214610\pi$
$257$	−2.40546	−	4.16638i	−0.150048	−	0.259891i	−0.931245	+	0.364394i	$0.881276\pi$
$258$	−5.63979	+	5.87086i	−0.351118	+	0.365504i
$259$	−17.6021	−	5.96267i	−1.09374	−	0.370502i
$260$	0.203728	+	5.07223i	0.0126347	+	0.314566i
$261$	−8.29877	−	2.22365i	−0.513681	−	0.137640i
$262$	10.4592	−	18.9860i	0.646174	−	1.17296i
$263$	−15.0660	−	8.69835i	−0.929008	−	0.536363i	−0.0425103	−	0.999096i	$-0.513536\pi$
$263$	−15.0660	−	8.69835i	−0.929008	−	0.536363i	−0.886498	+	0.462733i	$0.846869\pi$
$264$	2.75920	−	13.5017i	0.169817	−	0.830972i
$265$			4.64226i			0.285172i
$266$	5.49151	−	8.59886i	0.336706	−	0.527230i
$267$	−2.91838	+	2.91838i	−0.178602	+	0.178602i
$268$	−21.8670	−	4.92791i	−1.33574	−	0.301020i
$269$	−14.0792	+	3.77250i	−0.858422	+	0.230014i	−0.661075	−	0.750320i	$-0.729899\pi$
$269$	−14.0792	+	3.77250i	−0.858422	+	0.230014i	−0.197348	+	0.980334i	$0.563233\pi$
$270$	0.776614	−	0.224893i	0.0472632	−	0.0136866i
$271$	2.17009	+	3.75871i	0.131824	+	0.228325i	0.924380	−	0.381474i	$-0.124583\pi$
$271$	2.17009	+	3.75871i	0.131824	+	0.228325i	−0.792556	+	0.609799i	$0.791250\pi$
$272$	8.45710	−	0.680462i	0.512787	−	0.0412591i
$273$	9.77062	+	6.51956i	0.591345	+	0.394582i
$274$	12.4112	+	11.9227i	0.749790	+	0.720279i
$275$	−5.89296	+	21.9928i	−0.355359	+	1.32622i
$276$	−8.68775	+	2.70594i	−0.522941	+	0.162879i
$277$	7.30490	+	27.2623i	0.438909	+	1.63803i	0.731535	+	0.681804i	$0.238804\pi$
$277$	7.30490	+	27.2623i	0.438909	+	1.63803i	−0.292625	+	0.956227i	$0.594529\pi$
$278$	12.5679	−	7.59644i	0.753775	−	0.455604i
$279$		−	10.6369i		−	0.636817i
$280$	2.12208	+	3.71491i	0.126818	+	0.222008i
$281$		−	18.0495i		−	1.07674i	−0.842708	−	0.538370i	$-0.819040\pi$
$281$		−	18.0495i		−	1.07674i	0.842708	−	0.538370i	$-0.180960\pi$
$282$	−5.31921	−	8.80037i	−0.316754	−	0.524054i
$283$	−3.49129	−	13.0297i	−0.207535	−	0.774533i	−0.988662	−	0.150160i	$-0.952021\pi$
$283$	−3.49129	−	13.0297i	−0.207535	−	0.774533i	0.781126	−	0.624373i	$-0.214645\pi$
$284$	−5.69357	+	10.8447i	−0.337851	+	0.643514i
$285$	−0.403485	+	1.50583i	−0.0239004	+	0.0891976i
$286$	−21.1922	+	22.0605i	−1.25312	+	1.30446i
$287$	−1.14897	+	17.7019i	−0.0678214	+	1.04491i
$288$	−4.38064	−	3.57911i	−0.258132	−	0.210901i
$289$	6.25045	+	10.8261i	0.367674	+	0.636829i
$290$	1.93217	+	6.67229i	0.113461	+	0.391810i
$291$	−4.25731	+	1.14074i	−0.249568	+	0.0668715i
$292$	−8.40106	−	13.2891i	−0.491635	−	0.777687i
$293$	10.6795	−	10.6795i	0.623905	−	0.623905i	−0.322623	−	0.946528i	$-0.604565\pi$
$293$	10.6795	−	10.6795i	0.623905	−	0.623905i	0.946528	+	0.322623i	$0.104565\pi$
$294$	9.84014	+	1.08241i	0.573889	+	0.0631277i
$295$			5.16723i			0.300848i
$296$	−10.9513	−	16.5770i	−0.636534	−	0.963520i
$297$	4.21947	+	2.43611i	0.244839	+	0.141358i
$298$	6.69695	+	3.68929i	0.387944	+	0.213715i
$299$	19.5105	+	5.22784i	1.12832	+	0.302334i
$300$	6.86874	+	6.33827i	0.396567	+	0.365940i
$301$	11.4443	−	10.0492i	0.659639	−	0.579229i
$302$	−9.85282	−	9.46502i	−0.566966	−	0.544651i
$303$	−5.85796	−	10.1463i	−0.336531	−	0.582889i
$304$	10.2752	−	3.65888i	0.589326	−	0.209851i
$305$	2.38703	−	4.13445i	0.136681	−	0.236738i
$306$	−0.718069	+	2.91249i	−0.0410493	+	0.166496i
$307$	22.4784	+	22.4784i	1.28291	+	1.28291i	0.939003	+	0.343909i	$0.111751\pi$
$307$	22.4784	+	22.4784i	1.28291	+	1.28291i	0.343909	+	0.939003i	$0.388249\pi$
$308$	−7.28503	+	24.7307i	−0.415103	+	1.40916i
$309$	−4.34964	+	4.34964i	−0.247442	+	0.247442i
$310$	−7.36018	+	4.44872i	−0.418030	+	0.252670i
$311$	22.7952	+	13.1608i	1.29260	+	0.746282i	0.979114	−	0.203311i	$-0.0651704\pi$
$311$	22.7952	+	13.1608i	1.29260	+	0.746282i	0.313484	+	0.949593i	$0.398504\pi$
$312$	3.97404	+	11.9116i	0.224986	+	0.674363i
$313$	23.1822	−	13.3843i	1.31034	−	0.756524i	0.328186	−	0.944613i	$-0.393563\pi$
$313$	23.1822	−	13.3843i	1.31034	−	0.756524i	0.982152	+	0.188089i	$0.0602294\pi$
$314$	−9.86213	+	0.197978i	−0.556552	+	0.0111725i
$315$	−1.48335	+	0.296035i	−0.0835774	+	0.0166797i
$316$	−0.0851858	−	2.12088i	−0.00479207	−	0.119309i
$317$	−7.11830	+	26.5659i	−0.399804	+	1.49209i	0.413638	+	0.910441i	$0.364258\pi$
$317$	−7.11830	+	26.5659i	−0.399804	+	1.49209i	−0.813442	+	0.581646i	$0.802409\pi$
$318$	3.19413	+	11.0302i	0.179118	+	0.618541i
$319$	−20.9299	+	36.2517i	−1.17185	+	2.02970i
$320$	−0.644422	+	4.52806i	−0.0360243	+	0.253126i
$321$	−0.0196888			−0.00109892
$322$	16.6240	−	3.66608i	0.926418	−	0.204303i
$323$	−4.08981	−	4.08981i	−0.227563	−	0.227563i
$324$	1.69052	−	1.06871i	0.0939179	−	0.0593726i
$325$	−5.36968	−	20.0399i	−0.297856	−	1.11161i
$326$	−4.88066	+	8.85958i	−0.270315	+	0.490687i
$327$	−6.19321	+	3.57565i	−0.342485	+	0.197734i
$328$	−12.5782	+	14.1922i	−0.694517	+	0.783632i
$329$	8.51959	+	17.2484i	0.469700	+	0.950937i
$330$	−0.0790638	−	3.93851i	−0.00435232	−	0.216808i
$331$	27.8935	+	7.47403i	1.53316	+	0.410810i	0.924050	−	0.382272i	$-0.124858\pi$
$331$	27.8935	+	7.47403i	1.53316	+	0.410810i	0.609114	+	0.793082i	$0.291525\pi$
$332$	3.53618	+	11.3533i	0.194073	+	0.623095i
$333$	6.78498	−	1.81803i	0.371815	−	0.0996275i
$334$	3.41104	−	13.8352i	0.186644	−	0.757027i
$335$	−6.40756			−0.350082
$336$	7.59820	+	7.36664i	0.414516	+	0.401883i
$337$	−17.1492			−0.934177			−0.467088	−	0.884211i	$-0.654697\pi$
$337$	−17.1492			−0.934177			−0.467088	+	0.884211i	$0.654697\pi$
$338$	2.27155	−	9.21342i	0.123556	−	0.501144i
$339$	7.96539	−	2.13432i	0.432621	−	0.115920i
$340$	2.31560	−	0.721232i	0.125581	−	0.0391143i
$341$	−50.0597	−	13.4135i	−2.71089	−	0.726380i
$342$	0.0773979	+	3.85552i	0.00418520	+	0.208483i
$343$	−18.1712	−	3.57856i	−0.981155	−	0.193224i
$344$	16.2523	−	0.979826i	0.876264	−	0.0528287i
$345$	−2.25263	+	1.30056i	−0.121278	+	0.0700196i
$346$	−6.29655	+	11.4298i	−0.338505	+	0.614468i
$347$	−8.01901	−	29.9273i	−0.430483	−	1.60658i	−0.751651	−	0.659562i	$-0.770742\pi$
$347$	−8.01901	−	29.9273i	−0.430483	−	1.60658i	0.321168	−	0.947022i	$-0.395925\pi$
$348$	9.18181	+	14.5242i	0.492197	+	0.778576i
$349$	−3.44356	−	3.44356i	−0.184330	−	0.184330i	0.608910	−	0.793240i	$-0.291607\pi$
$349$	−3.44356	−	3.44356i	−0.184330	−	0.184330i	−0.793240	+	0.608910i	$0.791607\pi$
$350$	−11.7986	−	12.9046i	−0.630661	−	0.689782i
$351$	−4.43959			−0.236968
$352$	−22.3681	+	16.1029i	−1.19223	+	0.858285i
$353$	10.7408	−	18.6035i	0.571673	−	0.990166i	−0.424722	−	0.905324i	$-0.639628\pi$
$353$	10.7408	−	18.6035i	0.571673	−	0.990166i	0.996394	−	0.0848423i	$-0.0270387\pi$
$354$	3.55534	+	12.2775i	0.188964	+	0.652543i
$355$	−0.906197	+	3.38197i	−0.0480960	+	0.179497i
$356$	8.24779	−	0.331275i	0.437132	−	0.0175575i
$357$	1.80052	−	5.31524i	0.0952938	−	0.281313i
$358$	8.65174	−	0.173680i	0.457259	−	0.00917927i
$359$	8.64538	−	4.99141i	0.456286	−	0.263437i	−0.254195	−	0.967153i	$-0.581811\pi$
$359$	8.64538	−	4.99141i	0.456286	−	0.263437i	0.710481	+	0.703716i	$0.248477\pi$
$360$	−1.44652	−	0.722781i	−0.0762382	−	0.0380939i
$361$	10.0151	+	5.78225i	0.527113	+	0.304329i
$362$	−15.7572	+	9.52416i	−0.828183	+	0.500579i
$363$	9.00756	−	9.00756i	0.472774	−	0.472774i
$364$	−5.51856	−	22.8347i	−0.289251	−	1.19686i
$365$	−3.17788	−	3.17788i	−0.166338	−	0.166338i
$366$	2.82693	−	11.4660i	0.147766	−	0.599338i
$367$	−12.1116	+	20.9779i	−0.632221	+	1.09504i	0.354876	+	0.934913i	$0.384523\pi$
$367$	−12.1116	+	20.9779i	−0.632221	+	1.09504i	−0.987097	+	0.160125i	$0.948810\pi$
$368$	16.4396	+	7.80607i	0.856976	+	0.406919i
$369$	−3.35238	−	5.80649i	−0.174518	−	0.302274i
$370$	−4.09568	−	3.93448i	−0.212924	−	0.204544i
$371$	−4.20456	−	21.0679i	−0.218290	−	1.09379i
$372$	−14.4271	+	15.6345i	−0.748009	+	0.810612i
$373$	−10.1318	−	2.71481i	−0.524606	−	0.140568i	−0.0132098	−	0.999913i	$-0.504205\pi$
$373$	−10.1318	−	2.71481i	−0.524606	−	0.140568i	−0.511396	+	0.859345i	$0.670872\pi$
$374$	12.8013	+	7.05211i	0.661938	+	0.364656i
$375$	4.78933	+	2.76512i	0.247320	+	0.142790i
$376$	−4.11776	+	20.1496i	−0.212357	+	1.03914i
$377$		−	38.1428i		−	1.96445i
$378$	−3.32081	+	1.72402i	−0.170804	+	0.0886739i
$379$	−2.59204	+	2.59204i	−0.133144	+	0.133144i	−0.770538	−	0.637394i	$-0.780012\pi$
$379$	−2.59204	+	2.59204i	−0.133144	+	0.133144i	0.637394	+	0.770538i	$0.280012\pi$
$380$	2.63544	−	1.66606i	0.135195	−	0.0854670i
$381$	7.90255	−	2.11748i	0.404860	−	0.108482i
$382$	−1.92758	−	6.65644i	−0.0986236	−	0.340573i
$383$	−7.22773	−	12.5188i	−0.369320	−	0.639681i	0.620139	−	0.784492i	$-0.287076\pi$
$383$	−7.22773	−	12.5188i	−0.369320	−	0.639681i	−0.989459	+	0.144811i	$0.953743\pi$
$384$	1.58439	+	11.2022i	0.0808529	+	0.571661i
$385$	−0.477341	+	7.35428i	−0.0243275	+	0.374809i
$386$	−22.0510	+	22.9544i	−1.12237	+	1.16835i
$387$	−1.48989	+	5.56033i	−0.0757352	+	0.282648i
$388$	7.80473	+	4.09756i	0.396225	+	0.208022i
$389$	3.16708	+	11.8197i	0.160577	+	0.599283i	0.998563	+	0.0535908i	$0.0170666\pi$
$389$	3.16708	+	11.8197i	0.160577	+	0.599283i	−0.837986	+	0.545692i	$0.816267\pi$
$390$	1.85678	+	3.07195i	0.0940217	+	0.155554i
$391$		−	9.65041i		−	0.488042i
$392$	−12.9952	−	14.9373i	−0.656359	−	0.754449i
$393$		−	15.3275i		−	0.773171i
$394$	4.52443	−	2.73470i	0.227938	−	0.137772i
$395$	−0.157039	−	0.586079i	−0.00790150	−	0.0294888i
$396$	−2.89777	−	9.30362i	−0.145618	−	0.467525i
$397$	−1.00705	+	3.75837i	−0.0505424	+	0.188627i	−0.986582	−	0.163269i	$-0.947796\pi$
$397$	−1.00705	+	3.75837i	−0.0505424	+	0.188627i	0.936039	+	0.351896i	$0.114463\pi$
$398$	−0.983213	−	0.944515i	−0.0492840	−	0.0473443i
$399$	0.467283	−	7.19932i	0.0233934	−	0.360417i
$400$	−1.49917	−	18.6324i	−0.0749585	−	0.931619i
$401$	0.695858	+	1.20526i	0.0347495	+	0.0601879i	0.882877	−	0.469604i	$-0.155603\pi$
$401$	0.695858	+	1.20526i	0.0347495	+	0.0601879i	−0.848128	+	0.529792i	$0.822270\pi$
$402$	−15.2246	+	4.40875i	−0.759333	+	0.219889i
$403$	45.6146	−	12.2224i	2.27222	−	0.608840i
$404$	−5.15137	+	22.8586i	−0.256290	+	1.13726i
$405$	0.404260	−	0.404260i	0.0200879	−	0.0200879i
$406$	−14.8119	−	28.5308i	−0.735104	−	1.41596i
$407$		−	34.2242i		−	1.69643i
$408$	5.00570	−	3.30693i	0.247819	−	0.163718i
$409$	−25.3454	−	14.6332i	−1.25325	−	0.723563i	−0.281495	−	0.959563i	$-0.590830\pi$
$409$	−25.3454	−	14.6332i	−1.25325	−	0.723563i	−0.971753	+	0.235999i	$0.924164\pi$
$410$	−2.61570	+	4.74812i	−0.129180	+	0.234493i
$411$	11.7548	+	3.14968i	0.579820	+	0.155362i
$412$	12.2927	−	0.493742i	0.605619	−	0.0243249i
$413$	−4.68003	−	23.4504i	−0.230289	−	1.15392i
$414$	−4.45747	+	4.64010i	−0.219073	+	0.228048i
$415$	1.69959	+	2.94378i	0.0834297	+	0.144505i
$416$	10.3148	−	22.8981i	0.505723	−	1.12267i
$417$	5.19205	−	8.99289i	0.254256	−	0.440384i
$418$	18.2425	+	4.49766i	0.892269	+	0.219988i
$419$	21.4455	+	21.4455i	1.04768	+	1.04768i	0.998805	+	0.0488783i	$0.0155646\pi$
$419$	21.4455	+	21.4455i	1.04768	+	1.04768i	0.0488783	+	0.998805i	$0.484435\pi$
$420$	2.58180	+	1.57678i	0.125979	+	0.0769388i
$421$	12.2573	−	12.2573i	0.597386	−	0.597386i	−0.342230	−	0.939616i	$-0.611182\pi$
$421$	12.2573	−	12.2573i	0.597386	−	0.597386i	0.939616	+	0.342230i	$0.111182\pi$
$422$	15.9521	+	26.3920i	0.776536	+	1.28474i
$423$	−6.29704	−	3.63560i	−0.306172	−	0.176769i
$424$	10.2656	−	20.5447i	0.498540	−	0.997740i
$425$	−8.58426	+	4.95613i	−0.416398	+	0.240407i
$426$	0.173830	+	8.65920i	0.00842208	+	0.419540i
$427$	−7.08838	+	20.9253i	−0.343031	+	1.01265i
$428$	0.0289392	+	0.0267043i	0.00139883	+	0.00129080i
$429$	−5.59844	+	20.8936i	−0.270295	+	1.00875i
$430$	4.47056	−	1.29459i	0.215590	−	0.0624308i
$431$	2.92714	−	5.06996i	0.140995	−	0.244211i	−0.786876	−	0.617111i	$-0.788303\pi$
$431$	2.92714	−	5.06996i	0.140995	−	0.244211i	0.927872	+	0.372899i	$0.121636\pi$
$432$	−3.93429	−	0.722067i	−0.189288	−	0.0347405i
$433$	2.55989			0.123021			0.0615103	−	0.998106i	$-0.480408\pi$
$433$	2.55989			0.123021			0.0615103	+	0.998106i	$0.480408\pi$
$434$	29.3733	−	26.8558i	1.40997	−	1.28912i
$435$	3.47321	+	3.47321i	0.166528	+	0.166528i
$436$	13.9527	+	3.14436i	0.668213	+	0.150587i
$437$	−3.21096	−	11.9835i	−0.153601	−	0.573246i
$438$	−9.73729	−	5.36419i	−0.465266	−	0.256311i
$439$	16.1972	−	9.35148i	0.773052	−	0.446322i	−0.0609104	−	0.998143i	$-0.519400\pi$
$439$	16.1972	−	9.35148i	0.773052	−	0.446322i	0.833962	+	0.551822i	$0.186067\pi$
$440$	−5.22565	+	5.89617i	−0.249123	+	0.281089i
$441$	6.46375	−	2.68698i	0.307798	−	0.127952i
$442$	−13.3148	+	0.267288i	−0.633318	+	0.0127136i
$443$	0.382603	+	0.102518i	0.0181780	+	0.00487078i	0.267897	−	0.963448i	$-0.413671\pi$
$443$	0.382603	+	0.102518i	0.0181780	+	0.00487078i	−0.249719	+	0.968318i	$0.580338\pi$
$444$	−12.4386	−	6.53039i	−0.590310	−	0.309919i
$445$	2.27917	−	0.610703i	0.108043	−	0.0289501i
$446$	−24.8054	−	6.11574i	−1.17457	−	0.289589i
$447$	5.40648			0.255718
$448$	−1.17655	−	21.1333i	−0.0555869	−	0.998454i
$449$	−2.89756			−0.136744			−0.0683722	−	0.997660i	$-0.521781\pi$
$449$	−2.89756			−0.136744			−0.0683722	+	0.997660i	$0.521781\pi$
$450$	6.41668	+	1.58202i	0.302485	+	0.0745773i
$451$	−31.5540	+	8.45487i	−1.48582	+	0.398124i
$452$	−14.6026	−	7.66651i	−0.686848	−	0.360602i
$453$	−9.33168	−	2.50042i	−0.438441	−	0.117480i
$454$	−20.2807	+	0.407127i	−0.951821	+	0.0191074i
$455$	−2.97394	−	6.02092i	−0.139420	−	0.282265i
$456$	5.11555	−	5.77194i	0.239557	−	0.270296i
$457$	−24.7385	+	14.2828i	−1.15722	+	0.668119i	−0.950635	−	0.310310i	$-0.899567\pi$
$457$	−24.7385	+	14.2828i	−1.15722	+	0.668119i	−0.206581	+	0.978429i	$0.566234\pi$
$458$	3.99066	+	2.19842i	0.186471	+	0.102725i
$459$	0.548983	+	2.04883i	0.0256243	+	0.0956314i
$460$	5.07495	+	1.14368i	0.236621	+	0.0533245i
$461$	−4.97846	−	4.97846i	−0.231870	−	0.231870i	0.581603	−	0.813473i	$-0.302426\pi$
$461$	−4.97846	−	4.97846i	−0.231870	−	0.231870i	−0.813473	+	0.581603i	$0.802426\pi$
$462$	3.92597	+	17.8025i	0.182653	+	0.828245i
$463$	28.9381			1.34487			0.672434	−	0.740157i	$-0.265249\pi$
$463$	28.9381			1.34487			0.672434	+	0.740157i	$0.265249\pi$
$464$	6.20365	−	33.8015i	0.287997	−	1.56920i
$465$	−3.04063	+	5.26652i	−0.141006	+	0.244229i
$466$	11.9442	−	3.45883i	0.553306	−	0.160227i
$467$	1.23861	−	4.62255i	0.0573160	−	0.213906i	−0.931328	−	0.364181i	$-0.881349\pi$
$467$	1.23861	−	4.62255i	0.0573160	−	0.213906i	0.988644	+	0.150274i	$0.0480157\pi$
$468$	6.52545	+	6.02149i	0.301639	+	0.278344i
$469$	29.0793	−	5.80341i	1.34276	−	0.267977i
$470$	0.117993	+	5.87773i	0.00544260	+	0.271119i
$471$	−6.04051	+	3.48749i	−0.278332	+	0.160695i
$472$	11.4265	−	22.8681i	0.525946	−	1.05259i
$473$	24.2893	+	14.0234i	1.11682	+	0.644799i
$474$	−0.776385	−	1.28449i	−0.0356606	−	0.0589986i
$475$	−9.01052	+	9.01052i	−0.413431	+	0.413431i
$476$	−9.85562	+	5.37043i	−0.451732	+	0.246153i
$477$	5.74167	+	5.74167i	0.262893	+	0.262893i
$478$	−33.1818	−	8.18091i	−1.51770	−	0.374186i
$479$	−7.07946	+	12.2620i	−0.323469	+	0.560265i	−0.981201	−	0.192987i	$-0.938182\pi$
$479$	−7.07946	+	12.2620i	−0.323469	+	0.560265i	0.657732	+	0.753252i	$0.271516\pi$
$480$	1.14582	+	3.02430i	0.0522991	+	0.138040i
$481$	15.5926	+	27.0071i	0.710960	+	1.23142i
$482$	11.3866	−	11.8531i	0.518646	−	0.539896i
$483$	9.04514	−	7.94253i	0.411568	−	0.361398i
$484$	−25.4567	+	1.02248i	−1.15712	+	0.0464762i
$485$	2.43395	+	0.652174i	0.110520	+	0.0296137i
$486$	0.682383	−	1.23869i	0.0309535	−	0.0561881i
$487$	−14.0333	−	8.10210i	−0.635907	−	0.367141i	0.147129	−	0.989117i	$-0.452997\pi$
$487$	−14.0333	−	8.10210i	−0.635907	−	0.367141i	−0.783036	+	0.621976i	$0.786330\pi$
$488$	−19.7067	+	13.0189i	−0.892078	+	0.589337i
$489$			7.15238i			0.323442i
$490$	−4.56260	−	3.34878i	−0.206117	−	0.151282i
$491$	−9.60833	+	9.60833i	−0.433618	+	0.433618i	−0.889857	−	0.456239i	$-0.849196\pi$
$491$	−9.60833	+	9.60833i	−0.433618	+	0.433618i	0.456239	+	0.889857i	$0.349196\pi$
$492$	−2.94802	+	13.0814i	−0.132907	+	0.589757i
$493$	−17.6026	+	4.71660i	−0.792781	+	0.212425i
$494$	−16.4447	+	4.76209i	−0.739884	+	0.214257i
$495$	−1.39275	−	2.41232i	−0.0625996	−	0.108426i
$496$	42.4107	−	3.41239i	1.90430	−	0.153221i
$497$	1.04948	−	16.1691i	0.0470757	−	0.725284i
$498$	6.06378	+	5.82511i	0.271724	+	0.261029i
$499$	8.78548	−	32.7878i	0.393292	−	1.46779i	−0.431378	−	0.902171i	$-0.641973\pi$
$499$	8.78548	−	32.7878i	0.393292	−	1.46779i	0.824670	−	0.565614i	$-0.191361\pi$
$500$	−3.28912	−	10.5601i	−0.147094	−	0.472263i
$501$	−2.60783	−	9.73256i	−0.116509	−	0.434819i
$502$	−9.67417	+	5.84736i	−0.431779	+	0.260980i
$503$			35.7944i			1.59599i	0.602663	+	0.797996i	$0.294106\pi$
$503$			35.7944i			1.59599i	−0.602663	+	0.797996i	$0.705894\pi$
$504$	7.21934	+	1.97005i	0.321575	+	0.0877532i
$505$			6.69812i			0.298062i
$506$	16.2163	+	26.8291i	0.720903	+	1.19270i
$507$	−1.73666	−	6.48132i	−0.0771280	−	0.287846i
$508$	−14.4874	−	7.60603i	−0.642774	−	0.337463i
$509$	−6.46629	+	24.1325i	−0.286613	+	1.06966i	0.661039	+	0.750352i	$0.270116\pi$
$509$	−6.46629	+	24.1325i	−0.286613	+	1.06966i	−0.947652	+	0.319304i	$0.896551\pi$
$510$	1.18808	−	1.23675i	0.0526089	−	0.0547644i
$511$	17.3003	+	11.5439i	0.765322	+	0.510670i
$512$	12.8650	−	18.6143i	0.568557	−	0.822644i
$513$	1.36341	+	2.36149i	0.0601959	+	0.104262i
$514$	1.89246	+	6.53517i	0.0834730	+	0.288254i
$515$	3.39695	−	0.910209i	0.149687	−	0.0401086i
$516$	9.73146	−	6.15199i	0.428404	−	0.270826i
$517$	−25.0506	+	25.0506i	−1.10172	+	1.10172i
$518$	22.1509	+	14.1463i	0.973253	+	0.621551i
$519$			9.22729i			0.405033i
$520$	1.43739	−	7.03363i	0.0630337	−	0.308445i
$521$	38.6860	+	22.3354i	1.69487	+	0.978531i	0.950482	+	0.310779i	$0.100590\pi$
$521$	38.6860	+	22.3354i	1.69487	+	0.978531i	0.744384	+	0.667752i	$0.232743\pi$
$522$	10.6422	+	5.86271i	0.465798	+	0.256604i
$523$	−38.5208	−	10.3216i	−1.68440	−	0.451333i	−0.715462	−	0.698651i	$-0.753784\pi$
$523$	−38.5208	−	10.3216i	−1.68440	−	0.451333i	−0.968934	+	0.247318i	$0.920451\pi$
$524$	−20.7890	+	22.5289i	−0.908171	+	0.984178i
$525$	−11.7103	−	3.96685i	−0.511081	−	0.173127i
$526$	17.7424	+	17.0440i	0.773603	+	0.743155i
$527$	−11.2811	−	19.5394i	−0.491411	−	0.851148i
$528$	−8.35944	+	17.6050i	−0.363798	+	0.766161i
$529$	−1.15011	+	1.99205i	−0.0500047	+	0.0866108i
$530$	1.57157	−	6.37427i	0.0682645	−	0.276880i
$531$	6.39097	+	6.39097i	0.277345	+	0.277345i
$532$	−10.4514	+	9.94800i	−0.453125	+	0.431300i
$533$	21.0480	−	21.0480i	0.911690	−	0.911690i
$534$	4.99520	−	3.01925i	0.216163	−	0.130656i
$535$	0.00974824	+	0.00562815i	0.000421453	+	0.000243326i
$536$	28.3572	+	14.1692i	1.22485	+	0.612018i
$537$	5.29915	−	3.05947i	0.228675	−	0.132026i
$538$	20.6092	−	0.413721i	0.888525	−	0.0178368i
$539$	−4.49456	−	33.8081i	−0.193594	−	1.45622i
$540$	−1.14250	+	0.0458889i	−0.0491654	+	0.00197474i
$541$	4.79724	−	17.9035i	0.206249	−	0.769733i	−0.782816	−	0.622254i	$-0.786217\pi$
$541$	4.79724	−	17.9035i	0.206249	−	0.769733i	0.989065	−	0.147480i	$-0.0471161\pi$
$542$	−1.70729	−	5.89572i	−0.0733344	−	0.253243i
$543$	−6.50961	+	11.2750i	−0.279354	+	0.483856i
$544$	−11.8428	−	1.92868i	−0.507755	−	0.0826916i
$545$	4.08848			0.175131
$546$	−11.2089	−	12.2597i	−0.479697	−	0.524666i
$547$	−3.03460	−	3.03460i	−0.129750	−	0.129750i	0.639249	−	0.769000i	$-0.279245\pi$
$547$	−3.03460	−	3.03460i	−0.129750	−	0.129750i	−0.769000	+	0.639249i	$0.779245\pi$
$548$	−13.0056	−	20.5727i	−0.555570	−	0.878822i
$549$	−2.16126	−	8.06594i	−0.0922404	−	0.344246i
$550$	15.5369	−	28.2033i	0.662497	−	1.20259i
$551$	−20.2888	+	11.7137i	−0.864331	+	0.499022i
$552$	12.8452	−	0.774416i	0.546727	−	0.0329614i
$553$	1.24351	+	2.51756i	0.0528794	+	0.107058i
$554$	−0.801110	−	39.9067i	−0.0340359	−	1.69547i
$555$	−3.87905	−	1.03939i	−0.164656	−	0.0441195i
$556$	−19.8287	+	6.17596i	−0.840922	+	0.261919i
$557$	22.7883	−	6.10612i	0.965573	−	0.258724i	0.258615	−	0.965980i	$-0.416734\pi$
$557$	22.7883	−	6.10612i	0.965573	−	0.258724i	0.706958	+	0.707256i	$0.250067\pi$
$558$	−3.60098	+	14.6056i	−0.152441	+	0.618302i
$559$	−25.5564			−1.08092
$560$	−1.65619	−	5.81933i	−0.0699870	−	0.245911i
$561$	10.3345			0.436324
$562$	−6.11037	+	24.7837i	−0.257751	+	1.04544i
$563$	23.4245	−	6.27657i	0.987224	−	0.264526i	0.271140	−	0.962540i	$-0.412599\pi$
$563$	23.4245	−	6.27657i	0.987224	−	0.264526i	0.716084	+	0.698014i	$0.245933\pi$
$564$	4.32456	+	13.8845i	0.182097	+	0.584643i
$565$	−4.55390	−	1.22021i	−0.191584	−	0.0513348i
$566$	0.382880	+	19.0729i	0.0160937	+	0.801694i
$567$	−1.46851	+	2.20079i	−0.0616714	+	0.0924246i
$568$	11.4891	−	12.9633i	0.482073	−	0.543929i
$569$	23.2308	−	13.4123i	0.973885	−	0.562273i	0.0734668	−	0.997298i	$-0.476594\pi$
$569$	23.2308	−	13.4123i	0.973885	−	0.562273i	0.900419	+	0.435025i	$0.143260\pi$
$570$	1.06380	−	1.93105i	0.0445577	−	0.0808829i
$571$	−2.98438	−	11.1379i	−0.124892	−	0.466105i	0.874943	−	0.484225i	$-0.160898\pi$
$571$	−2.98438	−	11.1379i	−0.124892	−	0.466105i	−0.999836	+	0.0181203i	$0.994232\pi$
$572$	36.5672	−	23.1169i	1.52895	−	0.966565i
$573$	−3.46496	−	3.46496i	−0.144751	−	0.144751i
$574$	7.57034	−	23.9174i	0.315980	−	0.998293i
$575$	−21.2614			−0.886663
$576$	4.80338	+	6.39746i	0.200141	+	0.266561i
$577$	−8.16185	+	14.1367i	−0.339782	+	0.588520i	−0.984392	−	0.175992i	$-0.943687\pi$
$577$	−8.16185	+	14.1367i	−0.339782	+	0.588520i	0.644609	+	0.764512i	$0.277020\pi$
$578$	−4.91746	−	16.9813i	−0.204539	−	0.706328i
$579$	−5.82530	+	21.7403i	−0.242091	+	0.903497i
$580$	−0.394255	−	9.81581i	−0.0163706	−	0.407579i
$581$	−10.3795	−	11.8204i	−0.430613	−	0.490392i
$582$	6.23187	−	0.125102i	0.258319	−	0.00518565i
$583$	34.2619	−	19.7811i	1.41898	−	0.819250i
$584$	7.03663	+	21.0913i	0.291178	+	0.872765i
$585$	2.19811	+	1.26908i	0.0908807	+	0.0524700i
$586$	−18.2794	+	11.0486i	−0.755116	+	0.456415i
$587$	−17.4634	+	17.4634i	−0.720793	+	0.720793i	−0.968767	−	0.247974i	$-0.920235\pi$
$587$	−17.4634	+	17.4634i	−0.720793	+	0.720793i	0.247974	+	0.968767i	$0.420235\pi$
$588$	−13.1450	−	4.81749i	−0.542092	−	0.198670i
$589$	−20.5096	−	20.5096i	−0.845083	−	0.845083i
$590$	1.74929	−	7.09511i	0.0720171	−	0.292101i
$591$	1.86913	−	3.23742i	0.0768856	−	0.133170i
$592$	9.42535	+	26.4693i	0.387380	+	1.08788i
$593$	1.85289	+	3.20929i	0.0760889	+	0.131790i	0.901559	−	0.432656i	$-0.142423\pi$
$593$	1.85289	+	3.20929i	0.0760889	+	0.131790i	−0.825470	+	0.564445i	$0.809090\pi$
$594$	−4.96904	−	4.77346i	−0.203882	−	0.195857i
$595$	−2.41086	+	2.11697i	−0.0988356	+	0.0867874i
$596$	−7.94661	−	7.33290i	−0.325506	−	0.300367i
$597$	−0.931209	−	0.249517i	−0.0381118	−	0.0102120i
$598$	−25.0201	−	13.7833i	−1.02315	−	0.563642i
$599$	−31.3617	−	18.1067i	−1.28140	−	0.739819i	−0.304300	−	0.952576i	$-0.598422\pi$
$599$	−31.3617	−	18.1067i	−1.28140	−	0.739819i	−0.977105	+	0.212757i	$0.931756\pi$
$600$	−7.28571	−	11.0284i	−0.297438	−	0.450231i
$601$			39.8369i			1.62498i	0.582974	+	0.812490i	$0.301889\pi$
$601$			39.8369i			1.62498i	−0.582974	+	0.812490i	$0.698111\pi$
$602$	−19.1162	+	9.92428i	−0.779117	+	0.404483i
$603$	−7.92504	+	7.92504i	−0.322732	+	0.322732i
$604$	10.3246	+	16.3319i	0.420103	+	0.664536i
$605$	−7.03465	+	1.88493i	−0.285999	+	0.0766332i
$606$	4.60867	+	15.9150i	0.187215	+	0.646501i
$607$	15.2433	+	26.4021i	0.618705	+	1.07163i	0.989722	+	0.143003i	$0.0456757\pi$
$607$	15.2433	+	26.4021i	0.618705	+	1.07163i	−0.371017	+	0.928626i	$0.620991\pi$
$608$	−15.3476	+	1.54546i	−0.622426	+	0.0626769i
$609$	−18.9082	−	12.6167i	−0.766197	−	0.511254i
$610$	−4.67728	+	4.86891i	−0.189377	+	0.197136i
$611$	8.35496	−	31.1812i	0.338006	−	1.26145i
$612$	1.97196	−	3.75603i	0.0797116	−	0.151829i
$613$	1.92528	+	7.18524i	0.0777613	+	0.290209i	0.993845	−	0.110777i	$-0.0353341\pi$
$613$	1.92528	+	7.18524i	0.0777613	+	0.290209i	−0.916084	+	0.400987i	$0.868667\pi$
$614$	−23.2553	−	38.4748i	−0.938509	−	1.55272i
$615$			3.83318i			0.154569i
$616$	18.3753	−	31.4915i	0.740361	−	1.26883i
$617$			47.7120i			1.92081i	0.278600	+	0.960407i	$0.410130\pi$
$617$			47.7120i			1.92081i	−0.278600	+	0.960407i	$0.589870\pi$
$618$	7.44498	−	4.49997i	0.299481	−	0.181015i
$619$	5.51286	+	20.5743i	0.221580	+	0.826949i	0.983746	+	0.179567i	$0.0574696\pi$
$619$	5.51286	+	20.5743i	0.221580	+	0.826949i	−0.762165	+	0.647382i	$0.775864\pi$
$620$	11.6123	−	3.61684i	0.466361	−	0.145256i
$621$	−1.17755	+	4.39467i	−0.0472534	+	0.176352i
$622$	−26.8446	−	25.7881i	−1.07637	−	1.03401i
$623$	−9.79042	+	4.83582i	−0.392245	+	0.193743i
$624$	−1.42424	−	17.7012i	−0.0570153	−	0.708613i
$625$	10.1020	+	17.4972i	0.404081	+	0.699888i
$626$	−36.3625	+	10.5299i	−1.45334	+	0.420860i
$627$	12.8330	−	3.43858i	0.512499	−	0.137324i
$628$	13.6087	+	3.06683i	0.543045	+	0.122380i
$629$	10.5354	−	10.5354i	0.420076	−	0.420076i
$630$	2.13700	+	0.0956815i	0.0851403	+	0.00381204i
$631$			16.5547i			0.659034i	0.944150	+	0.329517i	$0.106886\pi$
$631$			16.5547i			0.659034i	−0.944150	+	0.329517i	$0.893114\pi$
$632$	−0.601023	+	2.94101i	−0.0239074	+	0.116987i
$633$	18.8846	+	10.9030i	0.750595	+	0.433356i
$634$	18.7676	−	34.0677i	0.745356	−	1.35300i
$635$	−4.51797	−	1.21059i	−0.179290	−	0.0480407i
$636$	−0.651755	−	16.2268i	−0.0258438	−	0.643434i
$637$	18.9498	+	24.6311i	0.750819	+	0.975921i
$638$	41.0113	−	42.6915i	1.62365	−	1.69017i
$639$	3.06211	+	5.30372i	0.121135	+	0.209812i
$640$	2.41776	−	5.99930i	0.0955703	−	0.237143i
$641$	0.929330	−	1.60965i	0.0367063	−	0.0635772i	−0.847089	−	0.531452i	$-0.821647\pi$
$641$	0.929330	−	1.60965i	0.0367063	−	0.0635772i	0.883795	+	0.467874i	$0.154980\pi$
$642$	0.0270346	+	0.00666534i	0.00106697	+	0.000263060i
$643$	14.7438	+	14.7438i	0.581437	+	0.581437i	0.935298	−	0.353861i	$-0.115131\pi$
$643$	14.7438	+	14.7438i	0.581437	+	0.581437i	−0.353861	+	0.935298i	$0.615131\pi$
$644$	−24.0674	−	0.593910i	−0.948390	−	0.0234033i
$645$	2.32712	−	2.32712i	0.0916302	−	0.0916302i
$646$	4.23116	+	7.00025i	0.166473	+	0.275421i
$647$	−14.4712	−	8.35498i	−0.568923	−	0.328468i	0.187796	−	0.982208i	$-0.439866\pi$
$647$	−14.4712	−	8.35498i	−0.568923	−	0.328468i	−0.756719	+	0.653740i	$0.773199\pi$
$648$	−2.68304	+	0.895137i	−0.105400	+	0.0351643i
$649$	38.1364	−	22.0181i	1.49699	−	0.864285i
$650$	0.588879	+	29.3346i	0.0230977	+	1.15060i
$651$	9.02928	−	26.6549i	0.353885	−	1.04469i
$652$	9.70090	−	10.5128i	0.379916	−	0.411712i
$653$	−1.63544	+	6.10355i	−0.0639997	+	0.238850i	−0.990515	−	0.137408i	$-0.956123\pi$
$653$	−1.63544	+	6.10355i	−0.0639997	+	0.238850i	0.926515	+	0.376258i	$0.122789\pi$
$654$	9.71436	−	2.81310i	0.379861	−	0.110001i
$655$	−4.38145	+	7.58890i	−0.171198	+	0.296523i
$656$	22.0757	−	15.2291i	0.861911	−	0.594595i
$657$	−7.86096			−0.306685
$658$	−5.85902	−	26.5679i	−0.228408	−	1.03573i
$659$	−14.1458	−	14.1458i	−0.551044	−	0.551044i	0.375698	−	0.926742i	$-0.377403\pi$
$659$	−14.1458	−	14.1458i	−0.551044	−	0.551044i	−0.926742	+	0.375698i	$0.877403\pi$
$660$	−1.22476	+	5.43471i	−0.0476737	+	0.211546i
$661$	0.588385	+	2.19588i	0.0228855	+	0.0854100i	0.976424	−	0.215861i	$-0.0692558\pi$
$661$	0.588385	+	2.19588i	0.0228855	+	0.0854100i	−0.953539	+	0.301271i	$0.902589\pi$
$662$	−35.7702	−	19.7055i	−1.39025	−	0.765875i
$663$	−8.15523	+	4.70843i	−0.316723	+	0.182860i
$664$	−1.01202	−	16.7863i	−0.0392741	−	0.651436i
$665$	−2.28932	+	3.43092i	−0.0887761	+	0.133045i
$666$	−9.93190	+	0.199379i	−0.384853	+	0.00772577i
$667$	−37.7569	−	10.1169i	−1.46195	−	0.391729i
$668$	−9.36737	+	17.8423i	−0.362435	+	0.690338i
$669$	−17.4498	+	4.67565i	−0.674647	+	0.180771i
$670$	8.79820	+	2.16918i	0.339904	+	0.0838028i
$671$	−40.6854			−1.57064
$672$	−7.93919	−	12.6874i	−0.306261	−	0.489426i
$673$	4.05920			0.156471			0.0782354	−	0.996935i	$-0.475071\pi$
$673$	4.05920			0.156471			0.0782354	+	0.996935i	$0.475071\pi$
$674$	23.5475	+	5.80560i	0.907016	+	0.223623i
$675$	4.51391	−	1.20950i	0.173741	−	0.0465537i
$676$	−6.23813	+	11.8819i	−0.239928	+	0.456997i
$677$	0.812688	+	0.217759i	0.0312341	+	0.00836916i	0.274402	−	0.961615i	$-0.411520\pi$
$677$	0.812688	+	0.217759i	0.0312341	+	0.00836916i	−0.243168	+	0.969984i	$0.578187\pi$
$678$	−11.6598	+	0.234065i	−0.447792	+	0.00898922i
$679$	−11.6366	−	0.755294i	−0.446573	−	0.0289855i
$680$	−3.42370	+	0.206410i	−0.131293	+	0.00791546i
$681$	−12.4219	+	7.17176i	−0.476006	+	0.274822i
$682$	64.1959	+	35.3649i	2.45819	+	1.35419i
$683$	4.77821	+	17.8325i	0.182833	+	0.682342i	0.995084	+	0.0990342i	$0.0315753\pi$
$683$	4.77821	+	17.8325i	0.182833	+	0.682342i	−0.812251	+	0.583308i	$0.801758\pi$
$684$	1.19895	−	5.32020i	0.0458431	−	0.203423i
$685$	−4.91962	−	4.91962i	−0.187969	−	0.187969i
$686$	23.7394	+	11.0653i	0.906374	+	0.422475i
$687$	3.22168			0.122915
$688$	−22.6477	−	4.15657i	−0.863434	−	0.158468i
$689$	−18.0246	+	31.2195i	−0.686683	+	1.18937i
$690$	3.53336	−	1.02320i	0.134513	−	0.0389524i
$691$	−0.486415	+	1.81532i	−0.0185041	+	0.0690582i	−0.974561	−	0.224125i	$-0.928048\pi$
$691$	−0.486415	+	1.81532i	−0.0185041	+	0.0690582i	0.956056	+	0.293183i	$0.0947144\pi$
$692$	12.5151	−	13.5626i	0.475754	−	0.515571i
$693$	8.50558	+	9.68635i	0.323100	+	0.367954i
$694$	0.879424	+	43.8078i	0.0333825	+	1.66292i
$695$	−5.14133	+	2.96835i	−0.195022	+	0.112596i
$696$	−7.69058	−	23.0514i	−0.291511	−	0.873762i
$697$	−12.3162	−	7.11076i	−0.466509	−	0.269339i
$698$	3.56258	+	5.89411i	0.134846	+	0.223095i
$699$	6.21748	−	6.21748i	0.235167	−	0.235167i
$700$	11.8319	+	21.7135i	0.447205	+	0.820695i
$701$	31.7249	+	31.7249i	1.19823	+	1.19823i	0.974695	+	0.223540i	$0.0717613\pi$
$701$	31.7249	+	31.7249i	1.19823	+	1.19823i	0.223540	+	0.974695i	$0.428239\pi$
$702$	6.09599	+	1.50296i	0.230078	+	0.0567254i
$703$	9.57702	−	16.5879i	0.361204	−	0.625624i
$704$	36.1650	−	14.5384i	1.36302	−	0.547936i
$705$	2.07851	+	3.60008i	0.0782812	+	0.135587i
$706$	−21.0460	+	21.9083i	−0.792078	+	0.824531i
$707$	−6.06657	−	30.3980i	−0.228157	−	1.14323i
$708$	−0.725459	−	18.0618i	−0.0272644	−	0.678805i
$709$	0.243920	+	0.0653581i	0.00916060	+	0.00245458i	0.263396	−	0.964688i	$-0.415157\pi$
$709$	0.243920	+	0.0653581i	0.00916060	+	0.00245458i	−0.254236	+	0.967142i	$0.581824\pi$
$710$	2.38921	−	4.33700i	0.0896655	−	0.162765i
$711$	−0.919108	−	0.530647i	−0.0344692	−	0.0199008i
$712$	−11.4372	−	2.33729i	−0.428625	−	0.0875936i
$713$		−	48.3949i		−	1.81240i
$714$	−4.27169	+	6.68880i	−0.159864	+	0.250322i
$715$	8.74444	−	8.74444i	0.327023	−	0.327023i
$716$	−11.9385	−	2.69044i	−0.446162	−	0.100546i
$717$	−23.3422	+	6.25453i	−0.871731	+	0.233580i
$718$	−13.5607	+	3.92693i	−0.506081	+	0.146552i
$719$	−7.74196	−	13.4095i	−0.288727	−	0.500089i	0.684780	−	0.728750i	$-0.259898\pi$
$719$	−7.74196	−	13.4095i	−0.288727	−	0.500089i	−0.973506	+	0.228661i	$0.926565\pi$
$720$	1.74152	+	1.48214i	0.0649027	+	0.0552363i
$721$	−14.5919	+	7.20745i	−0.543431	+	0.268419i
$722$	−11.7943	−	11.3301i	−0.438937	−	0.421661i
$723$	3.00805	−	11.2262i	0.111871	−	0.417507i
$724$	24.8605	−	7.74321i	0.923933	−	0.287774i
$725$	10.3914	+	38.7814i	0.385928	+	1.44030i
$726$	−15.4176	+	9.31888i	−0.572202	+	0.345856i
$727$			39.5787i			1.46789i	0.679207	+	0.733946i	$0.262324\pi$
$727$			39.5787i			1.46789i	−0.679207	+	0.733946i	$0.737676\pi$
$728$	−0.152825	+	33.2225i	−0.00566408	+	1.23131i
$729$		−	1.00000i		−	0.0370370i
$730$	3.28771	+	5.43935i	0.121684	+	0.201319i
$731$	3.16021	+	11.7941i	0.116885	+	0.436220i
$732$	−7.76329	+	14.7869i	−0.286939	+	0.546540i
$733$	−1.99659	+	7.45138i	−0.0737458	+	0.275223i	−0.992946	−	0.118568i	$-0.962170\pi$
$733$	−1.99659	+	7.45138i	−0.0737458	+	0.275223i	0.919200	+	0.393791i	$0.128836\pi$
$734$	23.7322	−	24.7045i	0.875970	−	0.911860i
$735$	−3.96840	−	0.517329i	−0.146377	−	0.0190820i
$736$	−19.9306	−	16.2839i	−0.734651	−	0.600232i
$737$	27.3032	+	47.2906i	1.00573	+	1.74197i
$738$	2.63744	+	9.10777i	0.0970855	+	0.335262i
$739$	14.4458	−	3.87074i	0.531398	−	0.142388i	0.0168641	−	0.999858i	$-0.494632\pi$
$739$	14.4458	−	3.87074i	0.531398	−	0.142388i	0.514534	+	0.857470i	$0.327965\pi$
$740$	4.29180	+	6.78894i	0.157770	+	0.249567i
$741$	−8.56018	+	8.56018i	−0.314466	+	0.314466i
$742$	−1.35895	+	30.3516i	−0.0498887	+	1.11424i
$743$			26.9107i			0.987258i	0.869673	+	0.493629i	$0.164330\pi$
$743$			26.9107i			0.987258i	−0.869673	+	0.493629i	$0.835670\pi$
$744$	25.1026	−	16.5836i	0.920306	−	0.607985i
$745$	−2.67683	−	1.54547i	−0.0980716	−	0.0566217i
$746$	12.9929	+	7.15768i	0.475705	+	0.262061i
$747$	5.74305	+	1.53885i	0.210127	+	0.0563034i
$748$	−15.1900	−	14.0169i	−0.555402	−	0.512509i
$749$	−0.0493378	−	0.0167130i	−0.00180276	−	0.000610681i
$750$	−5.64012	−	5.41813i	−0.205948	−	0.197842i
$751$	−8.68564	−	15.0440i	−0.316944	−	0.548962i	0.662905	−	0.748703i	$-0.269323\pi$
$751$	−8.68564	−	15.0440i	−0.316944	−	0.548962i	−0.979849	+	0.199741i	$0.935990\pi$
$752$	12.4754	−	26.2733i	0.454932	−	0.958090i
$753$	−3.99658	+	6.92228i	−0.145643	+	0.252262i
$754$	−12.9127	+	52.3738i	−0.470252	+	1.90734i
$755$	3.90551	+	3.90551i	0.142136	+	0.142136i
$756$	5.14343	−	1.24303i	0.187065	−	0.0452087i
$757$	17.3384	−	17.3384i	0.630174	−	0.630174i	−0.317938	−	0.948112i	$-0.602990\pi$
$757$	17.3384	−	17.3384i	0.630174	−	0.630174i	0.948112	+	0.317938i	$0.102990\pi$
$758$	4.43662	−	2.68163i	0.161145	−	0.0974012i
$759$	19.1973	+	11.0836i	0.696820	+	0.402309i
$760$	−4.18273	+	1.39547i	−0.151723	+	0.0506191i
$761$	−11.7387	+	6.77734i	−0.425528	+	0.245678i	−0.697439	−	0.716644i	$-0.745677\pi$
$761$	−11.7387	+	6.77734i	−0.425528	+	0.245678i	0.271912	+	0.962322i	$0.412344\pi$
$762$	−11.5678	+	0.232219i	−0.419057	+	0.00841240i
$763$	−18.5547	+	3.70299i	−0.671724	+	0.134057i
$764$	0.393319	+	9.79249i	0.0142298	+	0.354280i
$765$	0.313860	−	1.17134i	0.0113476	−	0.0423499i
$766$	5.68633	+	19.6364i	0.205455	+	0.709491i
$767$	−20.0629	+	34.7500i	−0.724431	+	1.25475i
$768$	1.61683	−	15.9181i	0.0583422	−	0.574395i
$769$	−31.4444			−1.13392			−0.566958	−	0.823747i	$-0.691880\pi$
$769$	−31.4444			−1.13392			−0.566958	+	0.823747i	$0.691880\pi$
$770$	3.14511	−	9.93654i	0.113342	−	0.358088i
$771$	3.40183	+	3.40183i	0.122514	+	0.122514i
$772$	38.0490	−	24.0536i	1.36941	−	0.865710i
$773$	−5.75933	−	21.4941i	−0.207149	−	0.773090i	−0.988784	−	0.149354i	$-0.952281\pi$
$773$	−5.75933	−	21.4941i	−0.207149	−	0.773090i	0.781635	−	0.623736i	$-0.214386\pi$
$774$	3.92813	−	7.13050i	0.141194	−	0.256300i
$775$	−43.0484	+	24.8540i	−1.54634	+	0.892782i
$776$	−9.32948	−	8.26852i	−0.334909	−	0.296823i
$777$	18.5456	+	1.20373i	0.665320	+	0.0431836i
$778$	−0.347326	−	17.3018i	−0.0124522	−	0.620299i
$779$	−17.6597	−	4.73189i	−0.632723	−	0.169538i
$780$	−1.50958	−	4.84667i	−0.0540515	−	0.173539i
$781$	28.8218	−	7.72279i	1.03133	−	0.276343i
$782$	−3.26700	+	13.2509i	−0.116828	+	0.473853i
$783$	8.59152			0.307036
$784$	12.7869	+	24.9097i	0.456676	+	0.889633i
$785$	3.98767			0.142326
$786$	−5.18890	+	21.0462i	−0.185082	+	0.750692i
$787$	9.93205	−	2.66129i	0.354039	−	0.0948646i	−0.0774159	−	0.996999i	$-0.524667\pi$
$787$	9.93205	−	2.66129i	0.354039	−	0.0948646i	0.431455	+	0.902134i	$0.358000\pi$
$788$	−7.13828	+	2.22334i	−0.254291	+	0.0792030i
$789$	16.8039	+	4.50260i	0.598235	+	0.160297i
$790$	0.0172221	+	0.857906i	0.000612734	+	0.0305229i
$791$	21.7721	+	1.41315i	0.774125	+	0.0502458i
$792$	0.829315	+	13.7558i	0.0294684	+	0.488790i
$793$	32.1059	−	18.5363i	1.14011	−	0.658245i
$794$	2.65512	−	4.81968i	0.0942266	−	0.171044i
$795$	−1.20150	−	4.48408i	−0.0426130	−	0.159034i
$796$	1.03030	+	1.62976i	0.0365179	+	0.0577654i
$797$	14.1208	+	14.1208i	0.500183	+	0.500183i	0.911495	−	0.411312i	$-0.134929\pi$
$797$	14.1208	+	14.1208i	0.500183	+	0.500183i	−0.411312	+	0.911495i	$0.634929\pi$
$798$	−3.07885	+	9.72717i	−0.108990	+	0.344338i
$799$	−15.4230			−0.545626
$800$	−4.24920	+	26.0916i	−0.150232	+	0.922476i
$801$	2.06361	−	3.57428i	0.0729140	−	0.126291i
$802$	−0.547457	−	1.89051i	−0.0193314	−	0.0667563i
$803$	−9.91287	+	36.9953i	−0.349818	+	1.30554i
$804$	22.3973	−	0.899596i	0.789893	−	0.0317263i
$805$	−6.74881	+	1.34687i	−0.237864	+	0.0474710i
$806$	−66.7709	+	1.34040i	−2.35190	+	0.0472135i
$807$	12.6230	−	7.28792i	0.444352	−	0.256547i
$808$	14.8118	−	29.6431i	0.521076	−	1.04284i
$809$	−26.8829	−	15.5208i	−0.945151	−	0.545683i	−0.0535799	−	0.998564i	$-0.517063\pi$
$809$	−26.8829	−	15.5208i	−0.945151	−	0.545683i	−0.891571	+	0.452880i	$0.850397\pi$
$810$	−0.691945	+	0.418232i	−0.0243125	+	0.0146952i
$811$	18.8182	−	18.8182i	0.660798	−	0.660798i	−0.294770	−	0.955568i	$-0.595243\pi$
$811$	18.8182	−	18.8182i	0.660798	−	0.660798i	0.955568	+	0.294770i	$0.0952431\pi$
$812$	10.6796	+	44.1899i	0.374779	+	1.55076i
$813$	−3.06897	−	3.06897i	−0.107633	−	0.107633i
$814$	−11.5861	+	46.9931i	−0.406091	+	1.64711i
$815$	2.04455	−	3.54126i	0.0716173	−	0.124045i
$816$	−7.99282	+	2.84614i	−0.279805	+	0.0996347i
$817$	7.84842	+	13.5939i	0.274582	+	0.475589i
$818$	29.8478	+	28.6730i	1.04360	+	1.00253i
$819$	−11.1251	−	3.76859i	−0.388742	−	0.131685i
$820$	5.19901	−	5.63413i	0.181557	−	0.196752i
$821$	−16.2758	−	4.36108i	−0.568029	−	0.152203i	−0.0366363	−	0.999329i	$-0.511664\pi$
$821$	−16.2758	−	4.36108i	−0.568029	−	0.152203i	−0.531392	+	0.847126i	$0.678331\pi$
$822$	−15.0742	−	8.30421i	−0.525771	−	0.289643i
$823$	19.8233	+	11.4450i	0.690997	+	0.398947i	0.803985	−	0.594649i	$-0.202709\pi$
$823$	19.8233	+	11.4450i	0.690997	+	0.398947i	−0.112989	+	0.993596i	$0.536042\pi$
$824$	−17.0463	−	3.48356i	−0.593835	−	0.121356i
$825$		−	22.7686i		−	0.792702i
$826$	−1.51263	+	33.7840i	−0.0526312	+	1.17550i
$827$	11.0427	−	11.0427i	0.383991	−	0.383991i	−0.488547	−	0.872538i	$-0.662473\pi$
$827$	11.0427	−	11.0427i	0.383991	−	0.383991i	0.872538	+	0.488547i	$0.162473\pi$
$828$	7.69137	−	4.86230i	0.267294	−	0.168976i
$829$	−13.5111	+	3.62028i	−0.469258	+	0.125737i	−0.485696	−	0.874128i	$-0.661434\pi$
$829$	−13.5111	+	3.62028i	−0.469258	+	0.125737i	0.0164383	+	0.999865i	$0.494767\pi$
$830$	−1.33713	−	4.61747i	−0.0464126	−	0.160275i
$831$	−14.1120	−	24.4427i	−0.489540	−	0.847907i
$832$	−21.9150	+	27.9494i	−0.759766	+	0.968972i
$833$	9.02379	−	11.7910i	0.312656	−	0.408533i
$834$	−10.1736	+	10.5904i	−0.352283	+	0.366716i
$835$	−1.49093	+	5.56421i	−0.0515956	+	0.192557i
$836$	−23.5261	−	12.3514i	−0.813667	−	0.427183i
$837$	2.75304	+	10.2745i	0.0951591	+	0.355139i
$838$	−22.1867	−	36.7069i	−0.766428	−	1.26802i
$839$		−	53.1523i		−	1.83502i	−0.397711	−	0.917511i	$-0.630195\pi$
$839$		−	53.1523i		−	1.83502i	0.397711	−	0.917511i	$-0.369805\pi$
$840$	−3.01126	−	3.03909i	−0.103898	−	0.104859i
$841$			44.8142i			1.54532i
$842$	−20.9800	+	12.6810i	−0.723020	+	0.437015i
$843$	4.67155	+	17.4344i	0.160897	+	0.600474i
$844$	−12.9692	−	41.6391i	−0.446418	−	1.43328i
$845$	−0.992870	+	3.70544i	−0.0341558	+	0.127471i
$846$	7.41566	+	7.12379i	0.254956	+	0.244921i
$847$	30.2180	−	14.9257i	1.03830	−	0.512854i
$848$	−21.0507	+	24.7346i	−0.722885	+	0.849391i
$849$	6.74465	+	11.6821i	0.231476	+	0.400928i
$850$	13.4648	−	3.89917i	0.461840	−	0.133740i
$851$	30.8696	−	8.27150i	1.05820	−	0.283543i
$852$	2.69276	−	11.9488i	0.0922523	−	0.409358i
$853$	1.06999	−	1.06999i	0.0366359	−	0.0366359i	−0.688552	−	0.725187i	$-0.741753\pi$
$853$	1.06999	−	1.06999i	0.0366359	−	0.0366359i	0.725187	+	0.688552i	$0.241753\pi$
$854$	16.8170	−	26.3328i	0.575465	−	0.901089i
$855$		−	1.55895i		−	0.0533149i
$856$	−0.0306960	−	0.0464644i	−0.00104917	−	0.00158812i
$857$	8.63353	+	4.98457i	0.294916	+	0.170270i	0.640157	−	0.768244i	$-0.278869\pi$
$857$	8.63353	+	4.98457i	0.294916	+	0.170270i	−0.345241	+	0.938514i	$0.612203\pi$
$858$	14.7604	−	26.7937i	0.503912	−	0.914723i
$859$	19.4777	+	5.21904i	0.664572	+	0.178071i	0.575308	−	0.817937i	$-0.304882\pi$
$859$	19.4777	+	5.21904i	0.664572	+	0.178071i	0.0892633	+	0.996008i	$0.471549\pi$
$860$	−6.57678	+	0.264159i	−0.224266	+	0.00900773i
$861$	−3.47176	−	17.3961i	−0.118317	−	0.592856i
$862$	−5.73560	+	5.97060i	−0.195355	+	0.203360i
$863$	3.83756	+	6.64685i	0.130632	+	0.226261i	0.923920	−	0.382585i	$-0.124966\pi$
$863$	3.83756	+	6.64685i	0.130632	+	0.226261i	−0.793288	+	0.608846i	$0.791633\pi$
$864$	5.15771	+	2.32336i	0.175469	+	0.0790424i
$865$	2.63767	−	4.56858i	0.0896835	−	0.155336i
$866$	−3.51498	−	0.866613i	−0.119444	−	0.0294487i
$867$	−8.83947	−	8.83947i	−0.300204	−	0.300204i
$868$	−49.4240	+	26.9316i	−1.67756	+	0.914120i
$869$	−3.65636	+	3.65636i	−0.124033	+	0.124033i
$870$	−3.59325	−	5.94486i	−0.121823	−	0.201550i
$871$	−43.0913	−	24.8788i	−1.46009	−	0.842985i
$872$	−18.0939	−	9.04098i	−0.612737	−	0.306166i
$873$	3.81700	−	2.20374i	0.129186	−	0.0745854i
$874$	0.352137	+	17.5415i	0.0119112	+	0.593349i
$875$	9.65429	+	10.9945i	0.326374	+	0.371683i
$876$	11.5543	+	10.6620i	0.390383	+	0.360234i
$877$	−6.09125	+	22.7329i	−0.205687	+	0.767635i	0.783552	+	0.621326i	$0.213406\pi$
$877$	−6.09125	+	22.7329i	−0.205687	+	0.767635i	−0.989239	+	0.146308i	$0.953261\pi$
$878$	−25.4062	+	7.35715i	−0.857417	+	0.248292i
$879$	−7.55157	+	13.0797i	−0.254708	+	0.441167i
$880$	9.17139	−	6.32695i	0.309167	−	0.213281i
$881$	39.8610			1.34295			0.671476	−	0.741026i	$-0.265660\pi$
$881$	39.8610			1.34295			0.671476	+	0.741026i	$0.265660\pi$
$882$	−9.78500	+	1.50128i	−0.329478	+	0.0505509i
$883$	8.10085	+	8.10085i	0.272615	+	0.272615i	0.830152	−	0.557537i	$-0.188253\pi$
$883$	8.10085	+	8.10085i	0.272615	+	0.272615i	−0.557537	+	0.830152i	$0.688253\pi$
$884$	18.3729	+	4.14050i	0.617949	+	0.139260i
$885$	−1.33738	−	4.99117i	−0.0449555	−	0.167776i
$886$	−0.490644	−	0.270291i	−0.0164835	−	0.00908062i
$887$	42.9162	−	24.7777i	1.44098	−	0.831953i	0.443069	−	0.896487i	$-0.353890\pi$
$887$	42.9162	−	24.7777i	1.44098	−	0.831953i	0.997915	+	0.0645342i	$0.0205562\pi$
$888$	14.8686	+	13.1778i	0.498959	+	0.442217i
$889$	21.6003	+	1.40200i	0.724451	+	0.0470216i
$890$	−3.33627	+	0.0669742i	−0.111832	+	0.00224498i
$891$	−4.70621	−	1.26103i	−0.157664	−	0.0422459i
$892$	31.9899	+	16.7950i	1.07110	+	0.562338i
$893$	−19.1516	+	5.13165i	−0.640883	+	0.171724i
$894$	−7.42362	−	1.83028i	−0.248283	−	0.0612138i
$895$	−3.49826			−0.116934
$896$	−5.53883	+	29.4163i	−0.185039	+	0.982731i
$897$	−20.1988			−0.674419
$898$	3.97863	+	0.980925i	0.132769	+	0.0327339i
$899$	−88.2735	+	23.6528i	−2.94409	+	0.788866i
$900$	−8.27515	−	4.34454i	−0.275838	−	0.144818i
$901$	16.6364	+	4.45771i	0.554239	+	0.148508i
$902$	46.1890	−	0.927224i	1.53792	−	0.0308732i
$903$	−8.45342	+	12.6688i	−0.281312	+	0.421592i
$904$	17.4554	+	15.4703i	0.580557	+	0.514536i
$905$	6.44603	−	3.72162i	0.214273	−	0.123711i
$906$	11.9668	+	6.59241i	0.397571	+	0.219018i
$907$	−9.59965	−	35.8264i	−0.318751	−	1.18960i	−0.920446	−	0.390870i	$-0.872174\pi$
$907$	−9.59965	−	35.8264i	−0.318751	−	1.18960i	0.601695	−	0.798726i	$-0.294492\pi$
$908$	27.9852	+	6.30670i	0.928722	+	0.209295i
$909$	8.28441	+	8.28441i	0.274776	+	0.274776i
$910$	2.04521	+	9.27409i	0.0677982	+	0.307433i
$911$	10.9952			0.364287			0.182144	−	0.983272i	$-0.441696\pi$
$911$	10.9952			0.364287			0.182144	+	0.983272i	$0.441696\pi$
$912$	−8.97814	+	6.19364i	−0.297296	+	0.205092i
$913$	14.4843	−	25.0875i	0.479359	−	0.830274i
$914$	38.8035	−	11.2368i	1.28351	−	0.371680i
$915$	−1.23562	+	4.61138i	−0.0408482	+	0.152448i
$916$	−4.73532	−	4.36962i	−0.156459	−	0.144376i
$917$	13.0109	−	38.4089i	0.429658	−	1.26837i
$918$	−0.0602056	−	2.99910i	−0.00198708	−	0.0989849i
$919$	14.1746	−	8.18373i	0.467578	−	0.269956i	−0.247647	−	0.968850i	$-0.579657\pi$
$919$	14.1746	−	8.18373i	0.467578	−	0.269956i	0.715225	+	0.698894i	$0.246324\pi$
$920$	−6.58122	−	3.28844i	−0.216976	−	0.108417i
$921$	−27.5303	−	15.8947i	−0.907156	−	0.523747i
$922$	5.15052	+	8.52128i	0.169623	+	0.280634i
$923$	−19.2255	+	19.2255i	−0.632816	+	0.632816i
$924$	0.636012	−	25.7736i	0.0209232	−	0.847888i
$925$	−23.2113	−	23.2113i	−0.763183	−	0.763183i
$926$	−39.7348	−	9.79656i	−1.30577	−	0.321935i
$927$	3.07566	−	5.32720i	0.101018	−	0.174968i
$928$	−19.9612	+	44.3126i	−0.655258	+	1.45463i
$929$	6.15373	+	10.6586i	0.201897	+	0.349696i	0.949140	−	0.314855i	$-0.101956\pi$
$929$	6.15373	+	10.6586i	0.201897	+	0.349696i	−0.747242	+	0.664552i	$0.768623\pi$
$930$	5.95798	−	6.20208i	0.195370	−	0.203374i
$931$	7.28217	−	17.6440i	0.238663	−	0.578258i
$932$	−17.5715	+	0.705766i	−0.575574	+	0.0231181i
$933$	−25.4248	−	6.81254i	−0.832369	−	0.223033i
$934$	−3.26562	+	5.92790i	−0.106855	+	0.193967i
$935$	−5.11679	−	2.95418i	−0.167337	−	0.0966120i
$936$	−6.92158	−	10.4772i	−0.226239	−	0.342457i
$937$		−	45.7825i		−	1.49565i	−0.663897	−	0.747824i	$-0.731099\pi$
$937$		−	45.7825i		−	1.49565i	0.663897	−	0.747824i	$-0.268901\pi$
$938$	−41.8934	−	1.87572i	−1.36787	−	0.0612444i
$939$	−18.9282	+	18.9282i	−0.617699	+	0.617699i
$940$	1.82780	−	8.11063i	0.0596162	−	0.264540i
$941$	35.4942	−	9.51065i	1.15708	−	0.310038i	0.371280	−	0.928521i	$-0.378919\pi$
$941$	35.4942	−	9.51065i	1.15708	−	0.310038i	0.785798	+	0.618483i	$0.212252\pi$
$942$	9.47485	−	2.74374i	0.308707	−	0.0893959i
$943$	−15.2523	−	26.4178i	−0.496684	−	0.860282i
$944$	−23.4313	+	27.5318i	−0.762623	+	0.896083i
$945$	1.35619	−	0.669868i	0.0441168	−	0.0217908i
$946$	−28.6042	−	27.4783i	−0.930002	−	0.893398i
$947$	9.29271	−	34.6809i	0.301973	−	1.12698i	−0.633548	−	0.773704i	$-0.718402\pi$
$947$	9.29271	−	34.6809i	0.301973	−	1.12698i	0.935520	−	0.353273i	$-0.114931\pi$
$948$	0.631207	+	2.02656i	0.0205006	+	0.0658197i
$949$	−9.03264	−	33.7103i	−0.293212	−	1.09428i
$950$	15.4227	−	9.32194i	0.500378	−	0.302444i
$951$		−	27.5030i		−	0.891846i
$952$	15.3508	−	4.03764i	0.497522	−	0.130861i
$953$			21.2952i			0.689818i	0.938636	+	0.344909i	$0.112090\pi$
$953$			21.2952i			0.689818i	−0.938636	+	0.344909i	$0.887910\pi$
$954$	−5.94011	−	9.82762i	−0.192318	−	0.318181i
$955$	0.725080	+	2.70603i	0.0234630	+	0.0875652i
$956$	42.7922	+	22.4664i	1.38400	+	0.726614i
$957$	10.8341	−	40.4335i	0.350217	−	1.30703i
$958$	13.8719	−	14.4403i	0.448181	−	0.466543i
$959$	26.7824	+	17.8709i	0.864849	+	0.577081i
$960$	−0.549484	−	4.54056i	−0.0177345	−	0.146546i
$961$	−41.0723	−	71.1393i	−1.32491	−	2.29482i
$962$	−12.2673	−	42.3620i	−0.395512	−	1.36581i
$963$	0.0190179	−	0.00509583i	0.000612844	−	0.000164211i
$964$	−19.6476	+	12.4207i	−0.632807	+	0.400045i
$965$	9.09879	−	9.09879i	0.292900	−	0.292900i
$966$	−15.1087	+	7.84377i	−0.486114	+	0.252369i
$967$		−	9.65502i		−	0.310484i	−0.987876	−	0.155242i	$-0.950384\pi$
$967$		−	9.65502i		−	0.310484i	0.987876	−	0.155242i	$-0.0496158\pi$
$968$	35.3007	+	7.21402i	1.13461	+	0.231867i
$969$	5.00897	+	2.89193i	0.160911	+	0.0929023i
$970$	−3.12126	−	1.71947i	−0.100218	−	0.0552090i
$971$	40.1495	+	10.7580i	1.28846	+	0.345242i	0.837075	−	0.547088i	$-0.184264\pi$
$971$	40.1495	+	10.7580i	1.28846	+	0.345242i	0.451385	+	0.892329i	$0.350930\pi$
$972$	−1.35632	+	1.46983i	−0.0435039	+	0.0471448i
$973$	20.6444	−	18.1278i	0.661828	−	0.581150i
$974$	16.5262	+	15.8757i	0.529533	+	0.508691i
$975$	10.3734	+	17.9673i	0.332216	+	0.575414i
$976$	31.4665	−	11.2048i	1.00722	−	0.358657i
$977$	11.8041	−	20.4454i	0.377648	−	0.654105i	−0.613072	−	0.790027i	$-0.710066\pi$
$977$	11.8041	−	20.4454i	0.377648	−	0.654105i	0.990720	+	0.135922i	$0.0433997\pi$
$978$	2.42133	−	9.82090i	0.0774256	−	0.314038i
$979$	−14.2190	−	14.2190i	−0.454442	−	0.454442i
$980$	5.13121	+	6.14279i	0.163910	+	0.196224i
$981$	5.05673	−	5.05673i	0.161449	−	0.161449i
$982$	16.4459	−	9.94041i	0.524810	−	0.317211i
$983$	12.5286	+	7.23338i	0.399600	+	0.230709i	0.686311	−	0.727308i	$-0.259229\pi$
$983$	12.5286	+	7.23338i	0.399600	+	0.230709i	−0.286712	+	0.958017i	$0.592562\pi$
$984$	8.47644	−	16.9641i	0.270219	−	0.540795i
$985$	−1.85087	+	1.06860i	−0.0589736	+	0.0340484i
$986$	25.7668	−	0.517257i	0.820582	−	0.0164728i
$987$	−12.6935	−	14.4557i	−0.404039	−	0.460129i
$988$	24.1924	−	0.971694i	0.769661	−	0.0309137i
$989$	−6.77854	+	25.2979i	−0.215545	+	0.804425i
$990$	1.09573	+	3.78384i	0.0348246	+	0.120258i
$991$	−5.59446	+	9.68989i	−0.177714	+	0.307810i	−0.941097	−	0.338136i	$-0.890204\pi$
$991$	−5.59446	+	9.68989i	−0.177714	+	0.307810i	0.763383	+	0.645946i	$0.223537\pi$
$992$	−59.3892	−	9.67197i	−1.88561	−	0.307085i
$993$	−28.8775			−0.916398
$994$	−6.91485	+	21.8465i	−0.219326	+	0.692928i
$995$	0.389731	+	0.389731i	0.0123553	+	0.0123553i
$996$	−6.35415	−	10.0512i	−0.201339	−	0.318486i
$997$	−8.86235	−	33.0747i	−0.280673	−	1.04749i	−0.951943	−	0.306274i	$-0.900918\pi$
$997$	−8.86235	−	33.0747i	−0.280673	−	1.04749i	0.671270	−	0.741213i	$-0.265749\pi$
$998$	−23.1631	+	42.0467i	−0.733216	+	1.33096i
$999$	−6.08325	+	3.51217i	−0.192466	+	0.111120i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bq.b.109.2	yes	120
7.2	even	3	inner	336.2.bq.b.205.19	yes	120
16.5	even	4	inner	336.2.bq.b.277.19	yes	120
112.37	even	12	inner	336.2.bq.b.37.2	✓	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bq.b.37.2	✓	120	112.37	even	12	inner
336.2.bq.b.109.2	yes	120	1.1	even	1	trivial
336.2.bq.b.205.19	yes	120	7.2	even	3	inner
336.2.bq.b.277.19	yes	120	16.5	even	4	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bq (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37310 - 0.338535i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.77079 + 0.929682i) q^{4} +(0.552230 + 0.147970i) q^{5} +(1.41393 - 0.0283840i) q^{6} +(-2.64020 - 0.171366i) q^{7} +(-2.11673 - 1.87602i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-1.37310 - 0.338535i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(1.77079 + 0.929682i) q^{4} +(0.552230 + 0.147970i) q^{5} +(1.41393 - 0.0283840i) q^{6} +(-2.64020 - 0.171366i) q^{7} +(-2.11673 - 1.87602i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-0.708172 - 0.390126i) q^{10} +(-1.26103 - 4.70621i) q^{11} +(-1.95107 - 0.439690i) q^{12} +(3.13926 + 3.13926i) q^{13} +(3.56723 + 1.12910i) q^{14} -0.571711 q^{15} +(2.27138 + 3.29254i) q^{16} +(1.06055 - 1.83693i) q^{17} +(-1.35840 + 0.393369i) q^{18} +(0.705751 - 2.63390i) q^{19} +(0.840318 + 0.775421i) q^{20} +(2.59459 - 0.517806i) q^{21} +(0.138293 + 6.88898i) q^{22} +(3.94016 - 2.27485i) q^{23} +(2.53016 + 1.26424i) q^{24} +(-4.04706 - 2.33657i) q^{25} +(-3.24776 - 5.37326i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-4.51591 - 2.75800i) q^{28} +(-6.07512 - 6.07512i) q^{29} +(0.785014 + 0.193544i) q^{30} +(5.31847 - 9.21186i) q^{31} +(-2.00419 - 5.28992i) q^{32} +(2.43611 + 4.21947i) q^{33} +(-2.07811 + 2.16325i) q^{34} +(-1.43264 - 0.485302i) q^{35} +(1.99839 - 0.0802659i) q^{36} +(6.78498 + 1.81803i) q^{37} +(-1.86073 + 3.37768i) q^{38} +(-3.84480 - 2.21979i) q^{39} +(-0.891331 - 1.34921i) q^{40} -6.70476i q^{41} +(-3.73791 - 0.167360i) q^{42} +(-4.07045 + 4.07045i) q^{43} +(2.14227 - 9.50606i) q^{44} +(0.552230 - 0.147970i) q^{45} +(-6.18033 + 1.78971i) q^{46} +(-3.63560 - 6.29704i) q^{47} +(-3.04616 - 2.59247i) q^{48} +(6.94127 + 0.904880i) q^{49} +(4.76600 + 4.57841i) q^{50} +(-0.548983 + 2.04883i) q^{51} +(2.64045 + 8.47749i) q^{52} +(2.10160 + 7.84326i) q^{53} +(1.21031 - 0.731546i) q^{54} -2.78551i q^{55} +(5.26711 + 5.31579i) q^{56} +2.72681i q^{57} +(6.28509 + 10.3984i) q^{58} +(2.33926 + 8.73023i) q^{59} +(-1.01238 - 0.531509i) q^{60} +(2.16126 - 8.06594i) q^{61} +(-10.4213 + 10.8483i) q^{62} +(-2.37216 + 1.17169i) q^{63} +(0.961123 + 7.94206i) q^{64} +(1.26908 + 2.19811i) q^{65} +(-1.91658 - 6.61845i) q^{66} +(-10.8258 + 2.90076i) q^{67} +(3.58578 - 2.26684i) q^{68} +(-3.21712 + 3.21712i) q^{69} +(1.80286 + 1.15136i) q^{70} +6.12421i q^{71} +(-2.77115 - 0.566311i) q^{72} +(-6.80779 - 3.93048i) q^{73} +(-8.70097 - 4.79329i) q^{74} +(4.51391 + 1.20950i) q^{75} +(3.69842 - 4.00795i) q^{76} +(2.52287 + 12.6414i) q^{77} +(4.52780 + 4.34959i) q^{78} +(-0.530647 - 0.919108i) q^{79} +(0.767130 + 2.15434i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-2.26979 + 9.20628i) q^{82} +(4.20420 + 4.20420i) q^{83} +(5.07586 + 1.49522i) q^{84} +(0.857480 - 0.857480i) q^{85} +(6.96711 - 4.21113i) q^{86} +(7.44047 + 4.29576i) q^{87} +(-6.15968 + 12.3275i) q^{88} +(3.57428 - 2.06361i) q^{89} +(-0.808358 + 0.0162274i) q^{90} +(-7.75031 - 8.82623i) q^{91} +(9.09207 - 0.365186i) q^{92} +(-2.75304 + 10.2745i) q^{93} +(2.86026 + 9.87721i) q^{94} +(0.779474 - 1.35009i) q^{95} +(3.30503 + 4.59095i) q^{96} +4.40749 q^{97} +(-9.22470 - 3.59235i) q^{98} +(-3.44519 - 3.44519i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8}+O(q^{10}) \) 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8	\( 120 q - 4 q^{4} - 8 q^{5} - 8 q^{6} + 24 q^{8} - 8 q^{10} + 4 q^{11} + 8 q^{13} + 32 q^{14} + 8 q^{15} + 12 q^{16} - 16 q^{17} - 4 q^{18} - 8 q^{19} - 64 q^{20} + 12 q^{21} + 24 q^{22} - 8 q^{24} - 8 q^{26} - 8 q^{28} - 64 q^{29} - 52 q^{31} - 4 q^{33} + 32 q^{34} - 8 q^{35} + 24 q^{37} - 40 q^{38} - 60 q^{40} + 24 q^{42} - 32 q^{43} - 12 q^{44} - 8 q^{45} + 4 q^{46} - 8 q^{47} + 32 q^{48} + 20 q^{49} - 16 q^{50} - 8 q^{51} - 16 q^{52} + 4 q^{54} - 104 q^{56} + 4 q^{58} + 52 q^{59} - 16 q^{60} + 4 q^{61} - 144 q^{62} + 8 q^{63} - 64 q^{64} + 24 q^{65} + 24 q^{66} + 12 q^{68} + 24 q^{69} - 48 q^{70} + 4 q^{72} + 16 q^{74} + 16 q^{75} - 8 q^{76} + 8 q^{77} - 56 q^{78} + 28 q^{79} + 68 q^{80} + 60 q^{81} + 28 q^{82} + 8 q^{83} + 24 q^{84} - 80 q^{85} + 36 q^{86} + 40 q^{88} + 8 q^{90} + 36 q^{91} - 184 q^{92} + 4 q^{93} + 60 q^{94} - 16 q^{95} + 36 q^{96} + 24 q^{97} + 124 q^{98} - 8 q^{99}+O(q^{100}) \) 120 * q - 4 * q^4 - 8 * q^5 - 8 * q^6 + 24 * q^8 - 8 * q^10 + 4 * q^11 + 8 * q^13 + 32 * q^14 + 8 * q^15 + 12 * q^16 - 16 * q^17 - 4 * q^18 - 8 * q^19 - 64 * q^20 + 12 * q^21 + 24 * q^22 - 8 * q^24 - 8 * q^26 - 8 * q^28 - 64 * q^29 - 52 * q^31 - 4 * q^33 + 32 * q^34 - 8 * q^35 + 24 * q^37 - 40 * q^38 - 60 * q^40 + 24 * q^42 - 32 * q^43 - 12 * q^44 - 8 * q^45 + 4 * q^46 - 8 * q^47 + 32 * q^48 + 20 * q^49 - 16 * q^50 - 8 * q^51 - 16 * q^52 + 4 * q^54 - 104 * q^56 + 4 * q^58 + 52 * q^59 - 16 * q^60 + 4 * q^61 - 144 * q^62 + 8 * q^63 - 64 * q^64 + 24 * q^65 + 24 * q^66 + 12 * q^68 + 24 * q^69 - 48 * q^70 + 4 * q^72 + 16 * q^74 + 16 * q^75 - 8 * q^76 + 8 * q^77 - 56 * q^78 + 28 * q^79 + 68 * q^80 + 60 * q^81 + 28 * q^82 + 8 * q^83 + 24 * q^84 - 80 * q^85 + 36 * q^86 + 40 * q^88 + 8 * q^90 + 36 * q^91 - 184 * q^92 + 4 * q^93 + 60 * q^94 - 16 * q^95 + 36 * q^96 + 24 * q^97 + 124 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more